CXX11/TensorSymmetry: add symmetry support for Tensor class

Add a symCoeff() method to the Tensor class template that allows the
user of the class to set multiple elements of a tensor at once if they
are connected by a symmetry operation with respect to the tensor's
indices (symmetry/antisymmetry/hermiticity/antihermiticity under
echange of two indices and combination thereof for different pairs of
indices).

A compile-time resolution of the required symmetry groups via meta
templates is also implemented. For small enough groups this is used to
unroll the loop that goes through all the elements of the Tensor that
are connected by this group. For larger groups or groups where the
symmetries are defined at run time, a standard run-time implementation
of the same algorithm is provided.

For example, the following code completely initializes all elements of
the totally antisymmetric tensor in three dimensions ('epsilon
tensor'):

SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym;
Eigen::Tensor<double, 3> epsilon(3,3,3);
epsilon.setZero();
epsilon.symCoeff(sym, 0, 1, 2) =  1;

8 files changed, 2336 insertions, 0 deletions

diff --git a/unsupported/Eigen/CXX11/TensorSymmetry b/unsupported/Eigen/CXX11/TensorSymmetry
new file mode 100644
index 000000000..5bbab0a80
--- /dev/null
+++ b/unsupported/Eigen/CXX11/TensorSymmetry
@@ -0,0 +1,41 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_MODULE
+#define EIGEN_CXX11_TENSORSYMMETRY_MODULE
+
+#include <Eigen/CXX11/Tensor>
+
+#include <Eigen/src/Core/util/DisableStupidWarnings.h>
+
+/** \defgroup CXX11_TensorSymmetry_Module Tensor Symmetry Module
+  *
+  * This module provides a classes that allow for the definition of
+  * symmetries w.r.t. tensor indices.
+  *
+  * Including this module will implicitly include the Tensor module.
+  *
+  * \code
+  * #include <Eigen/TensorSymmetry>
+  * \endcode
+  */
+
+#include "src/TensorSymmetry/util/TemplateGroupTheory.h"
+#include "src/TensorSymmetry/Symmetry.h"
+#include "src/TensorSymmetry/StaticSymmetry.h"
+#include "src/TensorSymmetry/DynamicSymmetry.h"
+
+#include <Eigen/src/Core/util/ReenableStupidWarnings.h>
+
+#endif // EIGEN_CXX11_TENSORSYMMETRY_MODULE
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/Eigen/CXX11/src/Tensor/Tensor.h b/unsupported/Eigen/CXX11/src/Tensor/Tensor.h
index c40905af4..ff3d6513e 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/Tensor.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/Tensor.h
@@ -92,6 +92,9 @@ struct tensor_index_linearization_helper<Index, NumIndices, 0, RowMajor>
     return std_array_get<RowMajor ? 0 : NumIndices - 1>(indices);
   }
 };
+
+/* Forward-declaration required for the symmetry support. */
+template<typename Tensor_, typename Symmetry_, int Flags = 0> class tensor_symmetry_value_setter;
 } // end namespace internal
 
 template<typename Scalar_, std::size_t NumIndices_, int Options_>
@@ -283,6 +286,18 @@ class Tensor
       #endif
     }
 
+    template<typename Symmetry_, typename... IndexTypes>
+    internal::tensor_symmetry_value_setter<Self, Symmetry_> symCoeff(const Symmetry_& symmetry, Index firstIndex, IndexTypes... otherIndices)
+    {
+      return symCoeff(symmetry, std::array<Index, NumIndices>{{firstIndex, otherIndices...}});
+    }
+
+    template<typename Symmetry_, typename... IndexTypes>
+    internal::tensor_symmetry_value_setter<Self, Symmetry_> symCoeff(const Symmetry_& symmetry, std::array<Index, NumIndices> const& indices)
+    {
+      return internal::tensor_symmetry_value_setter<Self, Symmetry_>(*this, symmetry, indices);
+    }
+
   protected:
     bool checkIndexRange(const std::array<Index, NumIndices>& indices) const
     {
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/DynamicSymmetry.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/DynamicSymmetry.h
new file mode 100644
index 000000000..87332610d
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/DynamicSymmetry.h
@@ -0,0 +1,265 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H
+#define EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H
+
+namespace Eigen {
+
+class DynamicSGroup
+{
+  public:
+    inline explicit DynamicSGroup(std::size_t numIndices) : m_numIndices(numIndices), m_elements(), m_generators(), m_globalFlags(0) { m_elements.push_back(ge(Generator(0, 0, 0))); }
+    inline DynamicSGroup(const DynamicSGroup& o) : m_numIndices(o.m_numIndices), m_elements(o.m_elements), m_generators(o.m_generators), m_globalFlags(o.m_globalFlags) { }
+    inline DynamicSGroup(DynamicSGroup&& o) : m_numIndices(o.m_numIndices), m_elements(), m_generators(o.m_generators), m_globalFlags(o.m_globalFlags) { std::swap(m_elements, o.m_elements); }
+    inline DynamicSGroup& operator=(const DynamicSGroup& o) { m_numIndices = o.m_numIndices; m_elements = o.m_elements; m_generators = o.m_generators; m_globalFlags = o.m_globalFlags; return *this; }
+    inline DynamicSGroup& operator=(DynamicSGroup&& o) { m_numIndices = o.m_numIndices; std::swap(m_elements, o.m_elements); m_generators = o.m_generators; m_globalFlags = o.m_globalFlags; return *this; }
+
+    void add(int one, int two, int flags = 0);
+
+    template<typename Gen_>
+    inline void add(Gen_) { add(Gen_::One, Gen_::Two, Gen_::Flags); }
+    inline void addSymmetry(int one, int two) { add(one, two, 0); }
+    inline void addAntiSymmetry(int one, int two) { add(one, two, NegationFlag); }
+    inline void addHermiticity(int one, int two) { add(one, two, ConjugationFlag); }
+    inline void addAntiHermiticity(int one, int two) { add(one, two, NegationFlag | ConjugationFlag); }
+
+    template<typename Op, typename RV, typename Index, std::size_t N, typename... Args>
+    inline RV apply(const std::array<Index, N>& idx, RV initial, Args&&... args) const
+    {
+      eigen_assert(N == m_numIndices);
+      for (std::size_t i = 0; i < size(); i++)
+        initial = Op::run(h_permute(i, idx, typename internal::gen_numeric_list<int, N>::type()), m_elements[i].flags, initial, std::forward<Args>(args)...);
+      return initial;
+    }
+
+    template<typename Op, typename RV, typename Index, typename... Args>
+    inline RV apply(const std::vector<Index>& idx, RV initial, Args&&... args) const
+    {
+      eigen_assert(idx.size() == m_numIndices);
+      for (std::size_t i = 0; i < size(); i++)
+        initial = Op::run(h_permute(i, idx), m_elements[i].flags, initial, std::forward<Args>(args)...);
+      return initial;
+    }
+
+    inline int globalFlags() const { return m_globalFlags; }
+    inline std::size_t size() const { return m_elements.size(); }
+  private:
+    struct GroupElement {
+      std::vector<int> representation;
+      int flags;
+      bool isId() const
+      {
+        for (std::size_t i = 0; i < representation.size(); i++)
+          if (i != (size_t)representation[i])
+            return false;
+        return true;
+      }
+    };
+    struct Generator {
+      int one;
+      int two;
+      int flags;
+      constexpr inline Generator(int one_, int two_, int flags_) : one(one_), two(two_), flags(flags_) {}
+    };
+
+    std::size_t m_numIndices;
+    std::vector<GroupElement> m_elements;
+    std::vector<Generator> m_generators;
+    int m_globalFlags;
+
+    template<typename Index, std::size_t N, int... n>
+    inline std::array<Index, N> h_permute(std::size_t which, const std::array<Index, N>& idx, internal::numeric_list<int, n...>) const
+    {
+      return std::array<Index, N>{{ idx[m_elements[which].representation[n]]... }};
+    }
+
+    template<typename Index>
+    inline std::vector<Index> h_permute(std::size_t which, std::vector<Index> idx) const
+    {
+      std::vector<Index> result;
+      result.reserve(idx.size());
+      for (auto k : m_elements[which].representation)
+        result.push_back(idx[k]);
+      return result;
+    }
+
+    inline GroupElement ge(Generator const& g) const
+    {
+      GroupElement result;
+      result.representation.reserve(m_numIndices);
+      result.flags = g.flags;
+      for (std::size_t k = 0; k < m_numIndices; k++) {
+        if (k == (std::size_t)g.one)
+          result.representation.push_back(g.two);
+        else if (k == (std::size_t)g.two)
+          result.representation.push_back(g.one);
+        else
+          result.representation.push_back(int(k));
+      }
+      return result;
+    }
+
+    GroupElement mul(GroupElement, GroupElement) const;
+    inline GroupElement mul(Generator g1, GroupElement g2) const
+    {
+      return mul(ge(g1), g2);
+    }
+
+    inline GroupElement mul(GroupElement g1, Generator g2) const
+    {
+      return mul(g1, ge(g2));
+    }
+
+    inline GroupElement mul(Generator g1, Generator g2) const
+    {
+      return mul(ge(g1), ge(g2));
+    }
+
+    inline int findElement(GroupElement e) const
+    {
+      for (auto ee : m_elements) {
+        if (ee.representation == e.representation)
+          return ee.flags ^ e.flags;
+      }
+      return -1;
+    }
+
+    void updateGlobalFlags(int flagDiffOfSameGenerator);
+};
+
+// dynamic symmetry group that auto-adds the template parameters in the constructor
+template<std::size_t NumIndices, typename... Gen>
+class DynamicSGroupFromTemplateArgs : public DynamicSGroup
+{
+  public:
+    inline DynamicSGroupFromTemplateArgs() : DynamicSGroup(NumIndices)
+    {
+      add_all(internal::type_list<Gen...>());
+    }
+    inline DynamicSGroupFromTemplateArgs(DynamicSGroupFromTemplateArgs const& other) : DynamicSGroup(other) { }
+    inline DynamicSGroupFromTemplateArgs(DynamicSGroupFromTemplateArgs&& other) : DynamicSGroup(other) { }
+    inline DynamicSGroupFromTemplateArgs<NumIndices, Gen...>& operator=(const DynamicSGroupFromTemplateArgs<NumIndices, Gen...>& o) { DynamicSGroup::operator=(o); return *this; }
+    inline DynamicSGroupFromTemplateArgs<NumIndices, Gen...>& operator=(DynamicSGroupFromTemplateArgs<NumIndices, Gen...>&& o) { DynamicSGroup::operator=(o); return *this; }
+  
+  private:
+    template<typename Gen1, typename... GenNext>
+    inline void add_all(internal::type_list<Gen1, GenNext...>)
+    {
+      add(Gen1());
+      add_all(internal::type_list<GenNext...>());
+    }
+
+    inline void add_all(internal::type_list<>)
+    {
+    }
+};
+
+inline DynamicSGroup::GroupElement DynamicSGroup::mul(GroupElement g1, GroupElement g2) const
+{
+  eigen_internal_assert(g1.representation.size() == m_numIndices);
+  eigen_internal_assert(g2.representation.size() == m_numIndices);
+
+  GroupElement result;
+  result.representation.reserve(m_numIndices);
+  for (std::size_t i = 0; i < m_numIndices; i++)
+    result.representation.push_back(g2.representation[g1.representation[i]]);
+  result.flags = g1.flags ^ g2.flags;
+  return result;
+}
+
+inline void DynamicSGroup::add(int one, int two, int flags)
+{
+  eigen_assert(one >= 0 && (std::size_t)one < m_numIndices);
+  eigen_assert(two >= 0 && (std::size_t)two < m_numIndices);
+  eigen_assert(one != two);
+  Generator g{one, two ,flags};
+  GroupElement e = ge(g);
+
+  /* special case for first generator */
+  if (m_elements.size() == 1) {
+    while (!e.isId()) {
+      m_elements.push_back(e);
+      e = mul(e, g);
+    }
+
+    if (e.flags > 0)
+      updateGlobalFlags(e.flags);
+
+    // only add in case we didn't have identity
+    if (m_elements.size() > 1)
+      m_generators.push_back(g);
+    return;
+  }
+
+  int p = findElement(e);
+  if (p >= 0) {
+    updateGlobalFlags(p);
+    return;
+  }
+
+  std::size_t coset_order = m_elements.size();
+  m_elements.push_back(e);
+  for (std::size_t i = 1; i < coset_order; i++)
+    m_elements.push_back(mul(m_elements[i], e));
+  m_generators.push_back(g);
+
+  std::size_t coset_rep = coset_order;
+  do {
+    for (auto g : m_generators) {
+      e = mul(m_elements[coset_rep], g);
+      p = findElement(e);
+      if (p < 0) {
+        // element not yet in group
+        m_elements.push_back(e);
+        for (std::size_t i = 1; i < coset_order; i++)
+          m_elements.push_back(mul(m_elements[i], e));
+      } else if (p > 0) {
+        updateGlobalFlags(p);
+      }
+    }
+    coset_rep += coset_order;
+  } while (coset_rep < m_elements.size());
+}
+
+inline void DynamicSGroup::updateGlobalFlags(int flagDiffOfSameGenerator)
+{
+    switch (flagDiffOfSameGenerator) {
+      case 0:
+      default:
+        // nothing happened
+        break;
+      case NegationFlag:
+        // every element is it's own negative => whole tensor is zero
+        m_globalFlags |= GlobalZeroFlag;
+        break;
+      case ConjugationFlag:
+        // every element is it's own conjugate => whole tensor is real
+        m_globalFlags |= GlobalRealFlag;
+        break;
+      case (NegationFlag | ConjugationFlag):
+        // every element is it's own negative conjugate => whole tensor is imaginary
+        m_globalFlags |= GlobalImagFlag;
+        break;
+      /* NOTE:
+       *   since GlobalZeroFlag == GlobalRealFlag | GlobalImagFlag, if one generator
+       *   causes the tensor to be real and the next one to be imaginary, this will
+       *   trivially give the correct result
+       */
+    }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/StaticSymmetry.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/StaticSymmetry.h
new file mode 100644
index 000000000..048e753fc
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/StaticSymmetry.h
@@ -0,0 +1,216 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H
+#define EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename list> struct tensor_static_symgroup_permutate;
+
+template<int... nn>
+struct tensor_static_symgroup_permutate<numeric_list<int, nn...>>
+{
+  constexpr static std::size_t N = sizeof...(nn);
+
+  template<typename T>
+  constexpr static inline std::array<T, N> run(const std::array<T, N>& indices)
+  {
+    return {{indices[nn]...}};
+  }
+};
+
+template<typename indices_, int flags_>
+struct tensor_static_symgroup_element
+{
+  typedef indices_ indices;
+  constexpr static int flags = flags_;
+};
+
+template<typename Gen, int N>
+struct tensor_static_symgroup_element_ctor
+{
+  typedef tensor_static_symgroup_element<
+    typename gen_numeric_list_swapped_pair<int, N, Gen::One, Gen::Two>::type,
+    Gen::Flags
+  > type;
+};
+
+template<int N>
+struct tensor_static_symgroup_identity_ctor
+{
+  typedef tensor_static_symgroup_element<
+    typename gen_numeric_list<int, N>::type,
+    0
+  > type;
+};
+
+template<typename iib>
+struct tensor_static_symgroup_multiply_helper
+{
+  template<int... iia>
+  constexpr static inline numeric_list<int, get<iia, iib>::value...> helper(numeric_list<int, iia...>) {
+    return numeric_list<int, get<iia, iib>::value...>();
+  }
+};
+
+template<typename A, typename B>
+struct tensor_static_symgroup_multiply
+{
+  private:
+    typedef typename A::indices iia;
+    typedef typename B::indices iib;
+    constexpr static int ffa = A::flags;
+    constexpr static int ffb = B::flags;
+  
+  public:
+    static_assert(iia::count == iib::count, "Cannot multiply symmetry elements with different number of indices.");
+
+    typedef tensor_static_symgroup_element<
+      decltype(tensor_static_symgroup_multiply_helper<iib>::helper(iia())),
+      ffa ^ ffb
+    > type;
+};
+
+template<typename A, typename B>
+struct tensor_static_symgroup_equality
+{
+    typedef typename A::indices iia;
+    typedef typename B::indices iib;
+    constexpr static int ffa = A::flags;
+    constexpr static int ffb = B::flags;
+    static_assert(iia::count == iib::count, "Cannot compare symmetry elements with different number of indices.");
+
+    constexpr static bool value = is_same<iia, iib>::value;
+
+  private:
+    /* this should be zero if they are identical, or else the tensor
+     * will be forced to be pure real, pure imaginary or even pure zero
+     */
+    constexpr static int flags_cmp_ = ffa ^ ffb;
+
+    /* either they are not equal, then we don't care whether the flags
+     * match, or they are equal, and then we have to check
+     */
+    constexpr static bool is_zero      = value && flags_cmp_ == NegationFlag;
+    constexpr static bool is_real      = value && flags_cmp_ == ConjugationFlag;
+    constexpr static bool is_imag      = value && flags_cmp_ == (NegationFlag | ConjugationFlag);
+
+  public:
+    constexpr static int global_flags = 
+      (is_real ? GlobalRealFlag : 0) |
+      (is_imag ? GlobalImagFlag : 0) |
+      (is_zero ? GlobalZeroFlag : 0);
+};
+
+template<std::size_t NumIndices, typename... Gen>
+struct tensor_static_symgroup
+{
+  typedef StaticSGroup<NumIndices, Gen...> type;
+  constexpr static std::size_t size = type::static_size;
+};
+
+template<typename Index, std::size_t N, int... ii>
+constexpr static inline std::array<Index, N> tensor_static_symgroup_index_permute(std::array<Index, N> idx, internal::numeric_list<int, ii...>)
+{
+  return {{ idx[ii]... }};
+}
+
+template<typename Index, int... ii>
+static inline std::vector<Index> tensor_static_symgroup_index_permute(std::vector<Index> idx, internal::numeric_list<int, ii...>)
+{
+  return {{ idx[ii]... }};
+}
+
+template<typename T> struct tensor_static_symgroup_do_apply;
+
+template<typename first, typename... next>
+struct tensor_static_symgroup_do_apply<internal::type_list<first, next...>>
+{
+  template<typename Op, typename RV, typename Index, std::size_t N, typename... Args>
+  static inline RV run(const std::array<Index, N>& idx, RV initial, Args&&... args)
+  {
+    initial = Op::run(tensor_static_symgroup_index_permute(idx, typename first::indices()), first::flags, initial, std::forward<Args>(args)...);
+    return tensor_static_symgroup_do_apply<internal::type_list<next...>>::template run<Op>(idx, initial, args...);
+  }
+
+  template<typename Op, typename RV, typename Index, typename... Args>
+  static inline RV run(const std::vector<Index>& idx, RV initial, Args&&... args)
+  {
+    initial = Op::run(tensor_static_symgroup_index_permute(idx, typename first::indices()), first::flags, initial, std::forward<Args>(args)...);
+    return tensor_static_symgroup_do_apply<internal::type_list<next...>>::template run<Op>(idx, initial, args...);
+  }
+};
+
+template<EIGEN_TPL_PP_SPEC_HACK_DEF(typename, empty)>
+struct tensor_static_symgroup_do_apply<internal::type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>>
+{
+  template<typename Op, typename RV, typename Index, std::size_t N, typename... Args>
+  static inline RV run(const std::array<Index, N>&, RV initial, Args&&...)
+  {
+    // do nothing
+    return initial;
+  }
+
+  template<typename Op, typename RV, typename Index, typename... Args>
+  static inline RV run(const std::vector<Index>&, RV initial, Args&&...)
+  {
+    // do nothing
+    return initial;
+  }
+};
+
+} // end namespace internal
+
+template<std::size_t NumIndices, typename... Gen>
+class StaticSGroup
+{
+    typedef internal::group_theory::enumerate_group_elements<
+      internal::tensor_static_symgroup_multiply,
+      internal::tensor_static_symgroup_equality,
+      typename internal::tensor_static_symgroup_identity_ctor<NumIndices>::type,
+      internal::type_list<typename internal::tensor_static_symgroup_element_ctor<Gen, NumIndices>::type...>
+    > group_elements;
+    typedef typename group_elements::type ge;
+  public:
+    constexpr inline StaticSGroup() {}
+    constexpr inline StaticSGroup(const StaticSGroup<NumIndices, Gen...>&) {}
+    constexpr inline StaticSGroup(StaticSGroup<NumIndices, Gen...>&&) {}
+
+    template<typename Op, typename RV, typename Index, typename... Args>
+    static inline RV apply(const std::array<Index, NumIndices>& idx, RV initial, Args&&... args)
+    {
+      return internal::tensor_static_symgroup_do_apply<ge>::template run<Op, RV>(idx, initial, args...);
+    }
+
+    template<typename Op, typename RV, typename Index, typename... Args>
+    static inline RV apply(const std::vector<Index>& idx, RV initial, Args&&... args)
+    {
+      eigen_assert(idx.size() == NumIndices);
+      return internal::tensor_static_symgroup_do_apply<ge>::template run<Op, RV>(idx, initial, args...);
+    }
+
+    constexpr static std::size_t static_size = ge::count;
+
+    constexpr static inline std::size_t size() {
+      return ge::count;
+    }
+    constexpr static inline int globalFlags() { return group_elements::global_flags; }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/Symmetry.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/Symmetry.h
new file mode 100644
index 000000000..40ad8d7ff
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/Symmetry.h
@@ -0,0 +1,312 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H
+#define EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H
+
+namespace Eigen {
+
+enum {
+  NegationFlag           = 0x01,
+  ConjugationFlag        = 0x02
+};
+
+enum {
+  GlobalRealFlag         = 0x01,
+  GlobalImagFlag         = 0x02,
+  GlobalZeroFlag         = 0x03
+};
+
+namespace internal {
+
+template<std::size_t NumIndices, typename... Sym>                   struct tensor_symmetry_pre_analysis;
+template<std::size_t NumIndices, typename... Sym>                   struct tensor_static_symgroup;
+template<bool instantiate, std::size_t NumIndices, typename... Sym> struct tensor_static_symgroup_if;
+template<typename Tensor_> struct tensor_symmetry_calculate_flags;
+template<typename Tensor_> struct tensor_symmetry_assign_value;
+
+} // end namespace internal
+
+template<int One_, int Two_>
+struct Symmetry
+{
+  static_assert(One_ != Two_, "Symmetries must cover distinct indices.");
+  constexpr static int One = One_;
+  constexpr static int Two = Two_;
+  constexpr static int Flags = 0;
+};
+
+template<int One_, int Two_>
+struct AntiSymmetry
+{
+  static_assert(One_ != Two_, "Symmetries must cover distinct indices.");
+  constexpr static int One = One_;
+  constexpr static int Two = Two_;
+  constexpr static int Flags = NegationFlag;
+};
+
+template<int One_, int Two_>
+struct Hermiticity
+{
+  static_assert(One_ != Two_, "Symmetries must cover distinct indices.");
+  constexpr static int One = One_;
+  constexpr static int Two = Two_;
+  constexpr static int Flags = ConjugationFlag;
+};
+
+template<int One_, int Two_>
+struct AntiHermiticity
+{
+  static_assert(One_ != Two_, "Symmetries must cover distinct indices.");
+  constexpr static int One = One_;
+  constexpr static int Two = Two_;
+  constexpr static int Flags = ConjugationFlag | NegationFlag;
+};
+
+/** \class DynamicSGroup
+  * \ingroup TensorSymmetry_Module
+  *
+  * \brief Dynamic symmetry group
+  *
+  * The %DynamicSGroup class represents a symmetry group that need not be known at
+  * compile time. It is useful if one wants to support arbitrary run-time defineable
+  * symmetries for tensors, but it is also instantiated if a symmetry group is defined
+  * at compile time that would be either too large for the compiler to reasonably
+  * generate (using templates to calculate this at compile time is very inefficient)
+  * or that the compiler could generate the group but that it wouldn't make sense to
+  * unroll the loop for setting coefficients anymore.
+  */
+class DynamicSGroup;
+
+/** \internal
+  *
+  * \class DynamicSGroupFromTemplateArgs
+  * \ingroup TensorSymmetry_Module
+  *
+  * \brief Dynamic symmetry group, initialized from template arguments
+  *
+  * This class is a child class of DynamicSGroup. It uses the template arguments
+  * specified to initialize itself.
+  */
+template<std::size_t NumIndices, typename... Gen>
+class DynamicSGroupFromTemplateArgs;
+
+/** \class StaticSGroup
+  * \ingroup TensorSymmetry_Module
+  *
+  * \brief Static symmetry group
+  *
+  * This class represents a symmetry group that is known and resolved completely
+  * at compile time. Ideally, no run-time penalty is incurred compared to the
+  * manual unrolling of the symmetry.
+  *
+  * <b><i>CAUTION:</i></b>
+  *
+  * Do not use this class directly for large symmetry groups. The compiler
+  * may run into a limit, or segfault or in the very least will take a very,
+  * very, very long time to compile the code. Use the SGroup class instead
+  * if you want a static group. That class contains logic that will
+  * automatically select the DynamicSGroup class instead if the symmetry
+  * group becomes too large. (In that case, unrolling may not even be
+  * beneficial.)
+  */
+template<std::size_t NumIndices, typename... Gen>
+class StaticSGroup;
+
+/** \class SGroup
+  * \ingroup TensorSymmetry_Module
+  *
+  * \brief Symmetry group, initialized from template arguments
+  *
+  * This class represents a symmetry group whose generators are already
+  * known at compile time. It may or may not be resolved at compile time,
+  * depending on the estimated size of the group.
+  *
+  * \sa StaticSGroup
+  * \sa DynamicSGroup
+  */
+template<std::size_t NumIndices, typename... Gen>
+class SGroup : public internal::tensor_symmetry_pre_analysis<NumIndices, Gen...>::root_type
+{
+  public:
+    typedef typename internal::tensor_symmetry_pre_analysis<NumIndices, Gen...>::root_type Base;
+
+    // make standard constructors + assignment operators public
+    inline SGroup() : Base() { }
+    inline SGroup(const SGroup<NumIndices, Gen...>& other) : Base(other) { }
+    inline SGroup(SGroup<NumIndices, Gen...>&& other) : Base(other) { }
+    inline SGroup<NumIndices, Gen...>& operator=(const SGroup<NumIndices, Gen...>& other) { Base::operator=(other); return *this; }
+    inline SGroup<NumIndices, Gen...>& operator=(SGroup<NumIndices, Gen...>&& other) { Base::operator=(other); return *this; }
+
+    // all else is defined in the base class
+};
+
+namespace internal {
+
+/** \internal
+  *
+  * \class tensor_symmetry_pre_analysis
+  * \ingroup TensorSymmetry_Module
+  *
+  * \brief Pre-select whether to use a static or dynamic symmetry group
+  *
+  * When a symmetry group could in principle be determined at compile time,
+  * this template implements the logic whether to actually do that or whether
+  * to rather defer that to runtime.
+  *
+  * The logic is as follows:
+  * <dl>
+  * <dt><b>No generators (trivial symmetry):</b></dt>
+  * <dd>Use a trivial static group. Ideally, this has no performance impact
+  *     compared to not using symmetry at all. In practice, this might not
+  *     be the case.</dd>
+  * <dt><b>More than 4 generators:</b></dt>
+  * <dd>Calculate the group at run time, it is likely far too large for the
+  *     compiler to be able to properly generate it in a realistic time.</dd>
+  * <dt><b>Up to and including 4 generators:</b></dt>
+  * <dd>Actually enumerate all group elements, but then check how many there
+  *     are. If there are more than 16, it is unlikely that unrolling the
+  *     loop (as is done in the static compile-time case) is sensible, so
+  *     use a dynamic group instead. If there are at most 16 elements, actually
+  *     use that static group. Note that the largest group with 4 generators
+  *     still compiles with reasonable resources.</dd>
+  * </dl>
+  *
+  * Note: Example compile time performance with g++-4.6 on an Intenl Core i5-3470
+  *       with 16 GiB RAM (all generators non-redundant and the subgroups don't
+  *       factorize):
+  *
+  *          # Generators          -O0 -ggdb               -O2
+  *          -------------------------------------------------------------------
+  *          1                 0.5 s  /   250 MiB     0.45s /   230 MiB
+  *          2                 0.5 s  /   260 MiB     0.5 s /   250 MiB
+  *          3                 0.65s  /   310 MiB     0.62s /   310 MiB
+  *          4                 2.2 s  /   860 MiB     1.7 s /   770 MiB
+  *          5               130   s  / 13000 MiB   120   s / 11000 MiB
+  *
+  * It is clear that everything is still very efficient up to 4 generators, then
+  * the memory and CPU requirements become unreasonable. Thus we only instantiate
+  * the template group theory logic if the number of generators supplied is 4 or
+  * lower, otherwise this will be forced to be done during runtime, where the
+  * algorithm is reasonably fast.
+  */
+template<std::size_t NumIndices>
+struct tensor_symmetry_pre_analysis<NumIndices>
+{
+  typedef StaticSGroup<NumIndices> root_type;
+};
+
+template<std::size_t NumIndices, typename Gen_, typename... Gens_>
+struct tensor_symmetry_pre_analysis<NumIndices, Gen_, Gens_...>
+{
+  constexpr static std::size_t max_static_generators = 4;
+  constexpr static std::size_t max_static_elements = 16;
+  typedef tensor_static_symgroup_if<(sizeof...(Gens_) + 1 <= max_static_generators), NumIndices, Gen_, Gens_...> helper;
+  constexpr static std::size_t possible_size = helper::size;
+
+  typedef typename conditional<
+    possible_size == 0 || possible_size >= max_static_elements,
+    DynamicSGroupFromTemplateArgs<NumIndices, Gen_, Gens_...>,
+    typename helper::type
+  >::type root_type;
+};
+
+template<bool instantiate, std::size_t NumIndices, typename... Gens>
+struct tensor_static_symgroup_if
+{
+  constexpr static std::size_t size = 0;
+  typedef void type;
+};
+
+template<std::size_t NumIndices, typename... Gens>
+struct tensor_static_symgroup_if<true, NumIndices, Gens...> : tensor_static_symgroup<NumIndices, Gens...> {};
+
+template<typename Tensor_>
+struct tensor_symmetry_assign_value
+{
+  typedef typename Tensor_::Index Index;
+  typedef typename Tensor_::Scalar Scalar;
+  constexpr static std::size_t NumIndices = Tensor_::NumIndices;
+
+  static inline int run(const std::array<Index, NumIndices>& transformed_indices, int transformation_flags, int dummy, Tensor_& tensor, const Scalar& value_)
+  {
+    Scalar value(value_);
+    if (transformation_flags & ConjugationFlag)
+      value = numext::conj(value);
+    if (transformation_flags & NegationFlag)
+      value = -value;
+    tensor.coeffRef(transformed_indices) = value;
+    return dummy;
+  }
+};
+
+template<typename Tensor_>
+struct tensor_symmetry_calculate_flags
+{
+  typedef typename Tensor_::Index Index;
+  constexpr static std::size_t NumIndices = Tensor_::NumIndices;
+
+  static inline int run(const std::array<Index, NumIndices>& transformed_indices, int transform_flags, int current_flags, const std::array<Index, NumIndices>& orig_indices)
+  {
+    if (transformed_indices == orig_indices) {
+      if (transform_flags & (ConjugationFlag | NegationFlag))
+        return current_flags | GlobalImagFlag; // anti-hermitian diagonal
+      else if (transform_flags & ConjugationFlag)
+        return current_flags | GlobalRealFlag; // hermitian diagonal
+      else if (transform_flags & NegationFlag)
+        return current_flags | GlobalZeroFlag; // anti-symmetric diagonal
+    }
+    return current_flags;
+  }
+};
+
+template<typename Tensor_, typename Symmetry_, int Flags>
+class tensor_symmetry_value_setter
+{
+  public:
+    typedef typename Tensor_::Index Index;
+    typedef typename Tensor_::Scalar Scalar;
+    constexpr static std::size_t NumIndices = Tensor_::NumIndices;
+
+    inline tensor_symmetry_value_setter(Tensor_& tensor, Symmetry_ const& symmetry, std::array<Index, NumIndices> const& indices)
+      : m_tensor(tensor), m_symmetry(symmetry), m_indices(indices) { }
+
+    inline tensor_symmetry_value_setter<Tensor_, Symmetry_, Flags>& operator=(Scalar const& value)
+    {
+      doAssign(value);
+      return *this;
+    }
+  private:
+    Tensor_& m_tensor;
+    Symmetry_ m_symmetry;
+    std::array<Index, NumIndices> m_indices;
+
+    inline void doAssign(Scalar const& value)
+    {
+      #ifdef EIGEN_TENSOR_SYMMETRY_CHECK_VALUES
+        int value_flags = m_symmetry.template apply<internal::tensor_symmetry_calculate_flags<Tensor_>, int>(m_indices, m_symmetry.globalFlags(), m_indices);
+        if (value_flags & GlobalRealFlag)
+          eigen_assert(numext::imag(value) == 0);
+        if (value_flags & GlobalImagFlag)
+          eigen_assert(numext::real(value) == 0);
+      #endif
+      m_symmetry.template apply<internal::tensor_symmetry_assign_value<Tensor_>, int>(m_indices, 0, m_tensor, value);
+    }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h
new file mode 100644
index 000000000..716d7d2e5
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h
@@ -0,0 +1,667 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H
+#define EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H
+
+namespace Eigen {
+
+namespace internal {
+
+namespace group_theory {
+
+/** \internal
+  * \file CXX11/Tensor/util/TemplateGroupTheory.h
+  * This file contains C++ templates that implement group theory algorithms.
+  *
+  * The algorithms allow for a compile-time analysis of finite groups.
+  *
+  * Currently only Dimino's algorithm is implemented, which returns a list
+  * of all elements in a group given a set of (possibly redundant) generators.
+  * (One could also do that with the so-called orbital algorithm, but that
+  * is much more expensive and usually has no advantages.)
+  */
+
+/**********************************************************************
+ *                "Ok kid, here is where it gets complicated."
+ *                         - Amelia Pond in the "Doctor Who" episode
+ *                           "The Big Bang"
+ *
+ * Dimino's algorithm
+ * ==================
+ *
+ * The following is Dimino's algorithm in sequential form:
+ *
+ * Input: identity element, list of generators, equality check,
+ *        multiplication operation
+ * Output: list of group elements
+ *
+ * 1. add identity element
+ * 2. remove identities from list of generators
+ * 3. add all powers of first generator that aren't the
+ *    identity element
+ * 4. go through all remaining generators:
+ *        a. if generator is already in the list of elements
+ *                -> do nothing
+ *        b. otherwise
+ *                i.   remember current # of elements
+ *                     (i.e. the size of the current subgroup)
+ *                ii.  add all current elements (which includes
+ *                     the identity) each multiplied from right
+ *                     with the current generator to the group
+ *                iii. add all remaining cosets that are generated
+ *                     by products of the new generator with itself
+ *                     and all other generators seen so far
+ *
+ * In functional form, this is implemented as a long set of recursive
+ * templates that have a complicated relationship.
+ *
+ * The main interface for Dimino's algorithm is the template
+ * enumerate_group_elements. All lists are implemented as variadic
+ * type_list<typename...> and numeric_list<typename = int, int...>
+ * templates.
+ *
+ * 'Calling' templates is usually done via typedefs.
+ *
+ * This algorithm is an extended version of the basic version. The
+ * extension consists in the fact that each group element has a set
+ * of flags associated with it. Multiplication of two group elements
+ * with each other results in a group element whose flags are the
+ * XOR of the flags of the previous elements. Each time the algorithm
+ * notices that a group element it just calculated is already in the
+ * list of current elements, the flags of both will be compared and
+ * added to the so-called 'global flags' of the group.
+ *
+ * The rationale behind this extension is that this allows not only
+ * for the description of symmetries between tensor indices, but
+ * also allows for the description of hermiticity, antisymmetry and
+ * antihermiticity. Negation and conjugation each are specific bit
+ * in the flags value and if two different ways to reach a group
+ * element lead to two different flags, this poses a constraint on
+ * the allowed values of the resulting tensor. For example, if a
+ * group element is reach both with and without the conjugation
+ * flags, it is clear that the resulting tensor has to be real.
+ *
+ * Note that this flag mechanism is quite generic and may have other
+ * uses beyond tensor properties.
+ *
+ * IMPORTANT: 
+ *     This algorithm assumes the group to be finite. If you try to
+ *     run it with a group that's infinite, the algorithm will only
+ *     terminate once you hit a compiler limit (max template depth).
+ *     Also note that trying to use this implementation to create a
+ *     very large group will probably either make you hit the same
+ *     limit, cause the compiler to segfault or at the very least
+ *     take a *really* long time (hours, days, weeks - sic!) to
+ *     compile. It is not recommended to plug in more than 4
+ *     generators, unless they are independent of each other.
+ */
+
+/** \internal
+  *
+  * \class strip_identities
+  * \ingroup CXX11_TensorSymmetry_Module
+  *
+  * \brief Cleanse a list of group elements of the identity element
+  *
+  * This template is used to make a first pass through all initial
+  * generators of Dimino's algorithm and remove the identity
+  * elements.
+  *
+  * \sa enumerate_group_elements
+  */
+template<template<typename, typename> class Equality, typename id, typename L> struct strip_identities;
+
+template<
+  template<typename, typename> class Equality,
+  typename id,
+  typename t,
+  typename... ts
+>
+struct strip_identities<Equality, id, type_list<t, ts...>>
+{
+  typedef typename conditional<
+    Equality<id, t>::value,
+    typename strip_identities<Equality, id, type_list<ts...>>::type,
+    typename concat<type_list<t>, typename strip_identities<Equality, id, type_list<ts...>>::type>::type
+  >::type type;
+  constexpr static int global_flags = Equality<id, t>::global_flags | strip_identities<Equality, id, type_list<ts...>>::global_flags;
+};
+
+template<
+  template<typename, typename> class Equality,
+  typename id
+  EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, ts)
+>
+struct strip_identities<Equality, id, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(ts)>>
+{
+  typedef type_list<> type;
+  constexpr static int global_flags = 0;
+};
+
+/** \internal
+  *
+  * \class dimino_first_step_elements_helper 
+  * \ingroup CXX11_TensorSymmetry_Module
+  *
+  * \brief Recursive template that adds powers of the first generator to the list of group elements
+  *
+  * This template calls itself recursively to add powers of the first
+  * generator to the list of group elements. It stops if it reaches
+  * the identity element again.
+  *
+  * \sa enumerate_group_elements, dimino_first_step_elements
+  */
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename g,
+  typename current_element,
+  typename elements,
+  bool dont_add_current_element   // = false
+>
+struct dimino_first_step_elements_helper :
+  public dimino_first_step_elements_helper<
+    Multiply,
+    Equality,
+    id,
+    g,
+    typename Multiply<current_element, g>::type,
+    typename concat<elements, type_list<current_element>>::type,
+    Equality<typename Multiply<current_element, g>::type, id>::value
+  > {};
+
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename g,
+  typename current_element,
+  typename elements
+>
+struct dimino_first_step_elements_helper<Multiply, Equality, id, g, current_element, elements, true>
+{
+  typedef elements type;
+  constexpr static int global_flags = Equality<current_element, id>::global_flags;
+};
+
+/** \internal
+  *
+  * \class dimino_first_step_elements
+  * \ingroup CXX11_TensorSymmetry_Module
+  *
+  * \brief Add all powers of the first generator to the list of group elements
+  *
+  * This template takes the first non-identity generator and generates the initial
+  * list of elements which consists of all powers of that generator. For a group
+  * with just one generated, it would be enumerated after this.
+  *
+  * \sa enumerate_group_elements
+  */
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename generators
+>
+struct dimino_first_step_elements
+{
+  typedef typename get<0, generators>::type first_generator;
+  typedef typename skip<1, generators>::type next_generators;
+  typedef type_list<first_generator> generators_done;
+
+  typedef dimino_first_step_elements_helper<
+    Multiply,
+    Equality,
+    id,
+    first_generator,
+    first_generator,
+    type_list<id>,
+    false
+  > helper;
+  typedef typename helper::type type;
+  constexpr static int global_flags = helper::global_flags;
+};
+
+/** \internal
+  *
+  * \class dimino_get_coset_elements
+  * \ingroup CXX11_TensorSymmetry_Module
+  *
+  * \brief Generate all elements of a specific coset
+  *
+  * This template generates all the elements of a specific coset by
+  * multiplying all elements in the given subgroup with the new
+  * coset representative. Note that the first element of the
+  * subgroup is always the identity element, so the first element of
+  * ther result of this template is going to be the coset
+  * representative itself.
+  *
+  * Note that this template accepts an additional boolean parameter
+  * that specifies whether to actually generate the coset (true) or
+  * just return an empty list (false).
+  *
+  * \sa enumerate_group_elements, dimino_add_cosets_for_rep
+  */
+template<
+  template<typename, typename> class Multiply,
+  typename sub_group_elements,
+  typename new_coset_rep,
+  bool generate_coset      // = true
+>
+struct dimino_get_coset_elements
+{
+  typedef typename apply_op_from_right<Multiply, new_coset_rep, sub_group_elements>::type type;
+};
+
+template<
+  template<typename, typename> class Multiply,
+  typename sub_group_elements,
+  typename new_coset_rep
+>
+struct dimino_get_coset_elements<Multiply, sub_group_elements, new_coset_rep, false>
+{
+  typedef type_list<> type;
+};
+
+/** \internal
+  *
+  * \class dimino_add_cosets_for_rep
+  * \ingroup CXX11_TensorSymmetry_Module
+  *
+  * \brief Recursive template for adding coset spaces
+  *
+  * This template multiplies the coset representative with a generator
+  * from the list of previous generators. If the new element is not in
+  * the group already, it adds the corresponding coset. Finally it
+  * proceeds to call itself with the next generator from the list.
+  *
+  * \sa enumerate_group_elements, dimino_add_all_coset_spaces
+  */
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename sub_group_elements,
+  typename elements,
+  typename generators,
+  typename rep_element,
+  int sub_group_size
+>
+struct dimino_add_cosets_for_rep;
+
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename sub_group_elements,
+  typename elements,
+  typename g,
+  typename... gs,
+  typename rep_element,
+  int sub_group_size
+>
+struct dimino_add_cosets_for_rep<Multiply, Equality, id, sub_group_elements, elements, type_list<g, gs...>, rep_element, sub_group_size>
+{
+  typedef typename Multiply<rep_element, g>::type new_coset_rep;
+  typedef contained_in_list_gf<Equality, new_coset_rep, elements> _cil;
+  constexpr static bool add_coset = !_cil::value;
+
+  typedef typename dimino_get_coset_elements<
+    Multiply,
+    sub_group_elements,
+    new_coset_rep,
+    add_coset
+  >::type coset_elements;
+
+  typedef dimino_add_cosets_for_rep<
+    Multiply,
+    Equality,
+    id,
+    sub_group_elements,
+    typename concat<elements, coset_elements>::type,
+    type_list<gs...>,
+    rep_element,
+    sub_group_size
+  > _helper;
+
+  typedef typename _helper::type type;
+  constexpr static int global_flags = _cil::global_flags | _helper::global_flags;
+
+  /* Note that we don't have to update global flags here, since
+   * we will only add these elements if they are not part of
+   * the group already. But that only happens if the coset rep
+   * is not already in the group, so the check for the coset rep
+   * will catch this.
+   */
+};
+
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename sub_group_elements,
+  typename elements
+  EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, empty),
+  typename rep_element,
+  int sub_group_size
+>
+struct dimino_add_cosets_for_rep<Multiply, Equality, id, sub_group_elements, elements, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>, rep_element, sub_group_size>
+{
+  typedef elements type;
+  constexpr static int global_flags = 0;
+};
+
+/** \internal
+  *
+  * \class dimino_add_all_coset_spaces
+  * \ingroup CXX11_TensorSymmetry_Module
+  *
+  * \brief Recursive template for adding all coset spaces for a new generator
+  *
+  * This template tries to go through the list of generators (with
+  * the help of the dimino_add_cosets_for_rep template) as long as
+  * it still finds elements that are not part of the group and add
+  * the corresponding cosets.
+  *
+  * \sa enumerate_group_elements, dimino_add_cosets_for_rep
+  */
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename sub_group_elements,
+  typename elements,
+  typename generators,
+  int sub_group_size,
+  int rep_pos,
+  bool stop_condition        // = false
+>
+struct dimino_add_all_coset_spaces
+{
+  typedef typename get<rep_pos, elements>::type rep_element;
+  typedef dimino_add_cosets_for_rep<
+    Multiply,
+    Equality,
+    id,
+    sub_group_elements,
+    elements,
+    generators,
+    rep_element,
+    sub_group_elements::count
+  > _ac4r;
+  typedef typename _ac4r::type new_elements;
+  
+  constexpr static int new_rep_pos = rep_pos + sub_group_elements::count;
+  constexpr static bool new_stop_condition = new_rep_pos >= new_elements::count;
+
+  typedef dimino_add_all_coset_spaces<
+    Multiply,
+    Equality,
+    id,
+    sub_group_elements,
+    new_elements,
+    generators,
+    sub_group_size,
+    new_rep_pos,
+    new_stop_condition
+  > _helper;
+
+  typedef typename _helper::type type;
+  constexpr static int global_flags = _helper::global_flags | _ac4r::global_flags;
+};
+
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename sub_group_elements,
+  typename elements,
+  typename generators,
+  int sub_group_size,
+  int rep_pos
+>
+struct dimino_add_all_coset_spaces<Multiply, Equality, id, sub_group_elements, elements, generators, sub_group_size, rep_pos, true>
+{
+  typedef elements type;
+  constexpr static int global_flags = 0;
+};
+
+/** \internal
+  *
+  * \class dimino_add_generator
+  * \ingroup CXX11_TensorSymmetry_Module
+  *
+  * \brief Enlarge the group by adding a new generator.
+  *
+  * It accepts a boolean parameter that determines if the generator is redundant,
+  * i.e. was already seen in the group. In that case, it reduces to a no-op.
+  *
+  * \sa enumerate_group_elements, dimino_add_all_coset_spaces
+  */
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename elements,
+  typename generators_done,
+  typename current_generator,
+  bool redundant          // = false
+>
+struct dimino_add_generator
+{
+  /* this template is only called if the generator is not redundant
+   * => all elements of the group multiplied with the new generator
+   *    are going to be new elements of the most trivial coset space
+   */
+  typedef typename apply_op_from_right<Multiply, current_generator, elements>::type multiplied_elements;
+  typedef typename concat<elements, multiplied_elements>::type new_elements;
+
+  constexpr static int rep_pos = elements::count;
+
+  typedef dimino_add_all_coset_spaces<
+    Multiply,
+    Equality,
+    id,
+    elements, // elements of previous subgroup
+    new_elements,
+    typename concat<generators_done, type_list<current_generator>>::type,
+    elements::count, // size of previous subgroup
+    rep_pos,
+    false // don't stop (because rep_pos >= new_elements::count is always false at this point)
+  > _helper;
+  typedef typename _helper::type type;
+  constexpr static int global_flags = _helper::global_flags;
+};
+
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename elements,
+  typename generators_done,
+  typename current_generator
+>
+struct dimino_add_generator<Multiply, Equality, id, elements, generators_done, current_generator, true>
+{
+  // redundant case
+  typedef elements type;
+  constexpr static int global_flags = 0;
+};
+
+/** \internal
+  *
+  * \class dimino_add_remaining_generators
+  * \ingroup CXX11_TensorSymmetry_Module
+  *
+  * \brief Recursive template that adds all remaining generators to a group
+  *
+  * Loop through the list of generators that remain and successively
+  * add them to the group.
+  *
+  * \sa enumerate_group_elements, dimino_add_generator
+  */
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename generators_done,
+  typename remaining_generators,
+  typename elements
+>
+struct dimino_add_remaining_generators
+{
+  typedef typename get<0, remaining_generators>::type first_generator;
+  typedef typename skip<1, remaining_generators>::type next_generators;
+
+  typedef contained_in_list_gf<Equality, first_generator, elements> _cil;
+
+  typedef dimino_add_generator<
+    Multiply,
+    Equality,
+    id,
+    elements,
+    generators_done,
+    first_generator,
+    _cil::value
+  > _helper;
+
+  typedef typename _helper::type new_elements;
+
+  typedef dimino_add_remaining_generators<
+    Multiply,
+    Equality,
+    id,
+    typename concat<generators_done, type_list<first_generator>>::type,
+    next_generators,
+    new_elements
+  > _next_iter;
+
+  typedef typename _next_iter::type type;
+  constexpr static int global_flags =
+    _cil::global_flags |
+    _helper::global_flags |
+    _next_iter::global_flags;
+};
+
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename generators_done,
+  typename elements
+>
+struct dimino_add_remaining_generators<Multiply, Equality, id, generators_done, type_list<>, elements>
+{
+  typedef elements type;
+  constexpr static int global_flags = 0;
+};
+
+/** \internal
+  *
+  * \class enumerate_group_elements_noid
+  * \ingroup CXX11_TensorSymmetry_Module
+  *
+  * \brief Helper template that implements group element enumeration
+  *
+  * This is a helper template that implements the actual enumeration
+  * of group elements. This has been split so that the list of
+  * generators can be cleansed of the identity element before
+  * performing the actual operation.
+  *
+  * \sa enumerate_group_elements
+  */
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename generators,
+  int initial_global_flags = 0
+>
+struct enumerate_group_elements_noid
+{
+  typedef dimino_first_step_elements<Multiply, Equality, id, generators> first_step;
+  typedef typename first_step::type first_step_elements;
+
+  typedef dimino_add_remaining_generators<
+    Multiply,
+    Equality,
+    id,
+    typename first_step::generators_done,
+    typename first_step::next_generators, // remaining_generators
+    typename first_step::type // first_step elements
+  > _helper;
+
+  typedef typename _helper::type type;
+  constexpr static int global_flags =
+    initial_global_flags |
+    first_step::global_flags |
+    _helper::global_flags;
+};
+
+// in case when no generators are specified
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  int initial_global_flags
+>
+struct enumerate_group_elements_noid<Multiply, Equality, id, type_list<>, initial_global_flags>
+{
+  typedef type_list<id> type;
+  constexpr static int global_flags = initial_global_flags;
+};
+
+/** \internal
+  *
+  * \class enumerate_group_elements
+  * \ingroup CXX11_TensorSymmetry_Module
+  *
+  * \brief Enumerate all elements in a finite group
+  *
+  * This template enumerates all elements in a finite group. It accepts
+  * the following template parameters:
+  *
+  * \tparam Multiply      The multiplication operation that multiplies two group elements
+  *                       with each other.
+  * \tparam Equality      The equality check operation that checks if two group elements
+  *                       are equal to another.
+  * \tparam id            The identity element
+  * \tparam _generators   A list of (possibly redundant) generators of the group
+  */
+template<
+  template<typename, typename> class Multiply,
+  template<typename, typename> class Equality,
+  typename id,
+  typename _generators
+>
+struct enumerate_group_elements
+  : public enumerate_group_elements_noid<
+      Multiply,
+      Equality,
+      id,
+      typename strip_identities<Equality, id, _generators>::type,
+      strip_identities<Equality, id, _generators>::global_flags
+    >
+{
+};
+
+} // end namespace group_theory
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/test/CMakeLists.txt b/unsupported/test/CMakeLists.txt
index 61e8f56fd..0a6c56c19 100644
--- a/unsupported/test/CMakeLists.txt
+++ b/unsupported/test/CMakeLists.txt
@@ -100,4 +100,5 @@ if(EIGEN_TEST_CXX11)
   #        clash there)
   ei_add_test(cxx11_meta "-std=c++0x")
   ei_add_test(cxx11_tensor_simple "-std=c++0x")
+  ei_add_test(cxx11_tensor_symmetry "-std=c++0x")
 endif()
diff --git a/unsupported/test/cxx11_tensor_symmetry.cpp b/unsupported/test/cxx11_tensor_symmetry.cpp
new file mode 100644
index 000000000..ebbc8a68d
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_symmetry.cpp
@@ -0,0 +1,819 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+#include <Eigen/CXX11/TensorSymmetry>
+
+#include <map>
+#include <set>
+
+using Eigen::Tensor;
+using Eigen::SGroup;
+using Eigen::DynamicSGroup;
+using Eigen::StaticSGroup;
+using Eigen::Symmetry;
+using Eigen::AntiSymmetry;
+using Eigen::Hermiticity;
+using Eigen::AntiHermiticity;
+
+using Eigen::NegationFlag;
+using Eigen::ConjugationFlag;
+using Eigen::GlobalZeroFlag;
+using Eigen::GlobalRealFlag;
+using Eigen::GlobalImagFlag;
+
+// helper function to determine if the compiler intantiated a static
+// or dynamic symmetry group
+template<std::size_t NumIndices, typename... Sym>
+bool isDynGroup(StaticSGroup<NumIndices, Sym...> const& dummy)
+{
+  (void)dummy;
+  return false;
+}
+
+bool isDynGroup(DynamicSGroup const& dummy)
+{
+  (void)dummy;
+  return true;
+}
+
+// helper class for checking that the symmetry groups are correct
+struct checkIdx {
+  template<typename ArrType>
+  static inline int doCheck_(ArrType e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)
+  {
+    // use decimal representation of value
+    uint64_t value = e[0];
+    for (std::size_t i = 1; i < e.size(); i++)
+      value = value * 10 + e[i];
+
+    // we want to make sure that we find each element
+    auto it = expected.find(value);
+    VERIFY((it != expected.end()));
+    VERIFY_IS_EQUAL(it->second, flags);
+
+    // we want to make sure we only have each element once;
+    // set::insert returns true for the second part of the pair
+    // if the element was really inserted and not already there
+    auto p = found.insert(value);
+    VERIFY((p.second));
+
+    return dummy;
+  }
+
+  static inline int run(std::vector<int> e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)
+  {
+    return doCheck_(e, flags, dummy, found, expected);
+  }
+
+  template<std::size_t N>
+  static inline int run(std::array<int, N> e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)
+  {
+    return doCheck_(e, flags, dummy, found, expected);
+  }
+};
+
+static void test_symgroups_static()
+{
+  std::array<int, 7> identity{{0,1,2,3,4,5,6}};
+
+  // Simple static symmetry group
+  StaticSGroup<7,
+    AntiSymmetry<0,1>,
+    Hermiticity<0,2>
+  > group;
+
+  std::set<uint64_t> found;
+  std::map<uint64_t, int> expected;
+  expected[ 123456] = 0;
+  expected[1023456] = NegationFlag;
+  expected[2103456] = ConjugationFlag;
+  expected[1203456] = ConjugationFlag | NegationFlag;
+  expected[2013456] = ConjugationFlag | NegationFlag;
+  expected[ 213456] = ConjugationFlag;
+
+  VERIFY_IS_EQUAL(group.size(), 6u);
+  VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
+  group.apply<checkIdx, int>(identity, 0, found, expected);
+  VERIFY_IS_EQUAL(found.size(), 6u);
+}
+
+static void test_symgroups_dynamic()
+{
+  std::vector<int> identity;
+  for (int i = 0; i <= 6; i++)
+    identity.push_back(i);
+
+  // Simple dynamic symmetry group
+  DynamicSGroup group(7);
+  group.add(0,1,NegationFlag);
+  group.add(0,2,ConjugationFlag);
+
+  VERIFY_IS_EQUAL(group.size(), 6u);
+  VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
+
+  std::set<uint64_t> found;
+  std::map<uint64_t, int> expected;
+  expected[ 123456] = 0;
+  expected[1023456] = NegationFlag;
+  expected[2103456] = ConjugationFlag;
+  expected[1203456] = ConjugationFlag | NegationFlag;
+  expected[2013456] = ConjugationFlag | NegationFlag;
+  expected[ 213456] = ConjugationFlag;
+
+  VERIFY_IS_EQUAL(group.size(), 6u);
+  VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
+  group.apply<checkIdx, int>(identity, 0, found, expected);
+  VERIFY_IS_EQUAL(found.size(), 6u);
+}
+
+static void test_symgroups_selection()
+{
+  std::array<int, 7> identity7{{0,1,2,3,4,5,6}};
+  std::array<int, 10> identity10{{0,1,2,3,4,5,6,7,8,9}};
+
+  {
+    // Do the same test as in test_symgroups_static but
+    // require selection via SGroup
+    SGroup<7,
+      AntiSymmetry<0,1>,
+      Hermiticity<0,2>
+    > group;
+
+    std::set<uint64_t> found;
+    std::map<uint64_t, int> expected;
+    expected[ 123456] = 0;
+    expected[1023456] = NegationFlag;
+    expected[2103456] = ConjugationFlag;
+    expected[1203456] = ConjugationFlag | NegationFlag;
+    expected[2013456] = ConjugationFlag | NegationFlag;
+    expected[ 213456] = ConjugationFlag;
+
+    VERIFY(!isDynGroup(group));
+    VERIFY_IS_EQUAL(group.size(), 6u);
+    VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
+    group.apply<checkIdx, int>(identity7, 0, found, expected);
+    VERIFY_IS_EQUAL(found.size(), 6u);
+  }
+
+  {
+    // simple factorizing group: 5 generators, 2^5 = 32 elements
+    // selection should make this dynamic, although static group
+    // can still be reasonably generated
+    SGroup<10,
+      Symmetry<0,1>,
+      Symmetry<2,3>,
+      Symmetry<4,5>,
+      Symmetry<6,7>,
+      Symmetry<8,9>
+    > group;
+
+    std::set<uint64_t> found;
+    std::map<uint64_t, int> expected;
+    expected[ 123456789] = 0; expected[ 123456798] = 0; expected[ 123457689] = 0; expected[ 123457698] = 0;
+    expected[ 123546789] = 0; expected[ 123546798] = 0; expected[ 123547689] = 0; expected[ 123547698] = 0;
+    expected[ 132456789] = 0; expected[ 132456798] = 0; expected[ 132457689] = 0; expected[ 132457698] = 0;
+    expected[ 132546789] = 0; expected[ 132546798] = 0; expected[ 132547689] = 0; expected[ 132547698] = 0;
+    expected[1023456789] = 0; expected[1023456798] = 0; expected[1023457689] = 0; expected[1023457698] = 0;
+    expected[1023546789] = 0; expected[1023546798] = 0; expected[1023547689] = 0; expected[1023547698] = 0;
+    expected[1032456789] = 0; expected[1032456798] = 0; expected[1032457689] = 0; expected[1032457698] = 0;
+    expected[1032546789] = 0; expected[1032546798] = 0; expected[1032547689] = 0; expected[1032547698] = 0;
+
+    VERIFY(isDynGroup(group));
+    VERIFY_IS_EQUAL(group.size(), 32u);
+    VERIFY_IS_EQUAL(group.globalFlags(), 0);
+    group.apply<checkIdx, int>(identity10, 0, found, expected);
+    VERIFY_IS_EQUAL(found.size(), 32u);
+
+    // no verify that we could also generate a static group
+    // with these generators
+    found.clear();
+    StaticSGroup<10,
+      Symmetry<0,1>,
+      Symmetry<2,3>,
+      Symmetry<4,5>,
+      Symmetry<6,7>,
+      Symmetry<8,9>
+    > group_static;
+    VERIFY_IS_EQUAL(group_static.size(), 32u);
+    VERIFY_IS_EQUAL(group_static.globalFlags(), 0);
+    group_static.apply<checkIdx, int>(identity10, 0, found, expected);
+    VERIFY_IS_EQUAL(found.size(), 32u);
+  }
+
+  {
+    // try to create a HUGE group
+    SGroup<7,
+      Symmetry<0,1>,
+      Symmetry<1,2>,
+      Symmetry<2,3>,
+      Symmetry<3,4>,
+      Symmetry<4,5>,
+      Symmetry<5,6>
+    > group;
+
+    std::set<uint64_t> found;
+    uint64_t pre_expected[5040] = {
+       123456, 1023456,  213456, 2013456, 1203456, 2103456,  132456, 1032456,  312456, 3012456, 1302456, 3102456,
+       231456, 2031456,  321456, 3021456, 2301456, 3201456, 1230456, 2130456, 1320456, 3120456, 2310456, 3210456,
+       124356, 1024356,  214356, 2014356, 1204356, 2104356,  142356, 1042356,  412356, 4012356, 1402356, 4102356,
+       241356, 2041356,  421356, 4021356, 2401356, 4201356, 1240356, 2140356, 1420356, 4120356, 2410356, 4210356,
+       134256, 1034256,  314256, 3014256, 1304256, 3104256,  143256, 1043256,  413256, 4013256, 1403256, 4103256,
+       341256, 3041256,  431256, 4031256, 3401256, 4301256, 1340256, 3140256, 1430256, 4130256, 3410256, 4310256,
+       234156, 2034156,  324156, 3024156, 2304156, 3204156,  243156, 2043156,  423156, 4023156, 2403156, 4203156,
+       342156, 3042156,  432156, 4032156, 3402156, 4302156, 2340156, 3240156, 2430156, 4230156, 3420156, 4320156,
+      1234056, 2134056, 1324056, 3124056, 2314056, 3214056, 1243056, 2143056, 1423056, 4123056, 2413056, 4213056,
+      1342056, 3142056, 1432056, 4132056, 3412056, 4312056, 2341056, 3241056, 2431056, 4231056, 3421056, 4321056,
+       123546, 1023546,  213546, 2013546, 1203546, 2103546,  132546, 1032546,  312546, 3012546, 1302546, 3102546,
+       231546, 2031546,  321546, 3021546, 2301546, 3201546, 1230546, 2130546, 1320546, 3120546, 2310546, 3210546,
+       125346, 1025346,  215346, 2015346, 1205346, 2105346,  152346, 1052346,  512346, 5012346, 1502346, 5102346,
+       251346, 2051346,  521346, 5021346, 2501346, 5201346, 1250346, 2150346, 1520346, 5120346, 2510346, 5210346,
+       135246, 1035246,  315246, 3015246, 1305246, 3105246,  153246, 1053246,  513246, 5013246, 1503246, 5103246,
+       351246, 3051246,  531246, 5031246, 3501246, 5301246, 1350246, 3150246, 1530246, 5130246, 3510246, 5310246,
+       235146, 2035146,  325146, 3025146, 2305146, 3205146,  253146, 2053146,  523146, 5023146, 2503146, 5203146,
+       352146, 3052146,  532146, 5032146, 3502146, 5302146, 2350146, 3250146, 2530146, 5230146, 3520146, 5320146,
+      1235046, 2135046, 1325046, 3125046, 2315046, 3215046, 1253046, 2153046, 1523046, 5123046, 2513046, 5213046,
+      1352046, 3152046, 1532046, 5132046, 3512046, 5312046, 2351046, 3251046, 2531046, 5231046, 3521046, 5321046,
+       124536, 1024536,  214536, 2014536, 1204536, 2104536,  142536, 1042536,  412536, 4012536, 1402536, 4102536,
+       241536, 2041536,  421536, 4021536, 2401536, 4201536, 1240536, 2140536, 1420536, 4120536, 2410536, 4210536,
+       125436, 1025436,  215436, 2015436, 1205436, 2105436,  152436, 1052436,  512436, 5012436, 1502436, 5102436,
+       251436, 2051436,  521436, 5021436, 2501436, 5201436, 1250436, 2150436, 1520436, 5120436, 2510436, 5210436,
+       145236, 1045236,  415236, 4015236, 1405236, 4105236,  154236, 1054236,  514236, 5014236, 1504236, 5104236,
+       451236, 4051236,  541236, 5041236, 4501236, 5401236, 1450236, 4150236, 1540236, 5140236, 4510236, 5410236,
+       245136, 2045136,  425136, 4025136, 2405136, 4205136,  254136, 2054136,  524136, 5024136, 2504136, 5204136,
+       452136, 4052136,  542136, 5042136, 4502136, 5402136, 2450136, 4250136, 2540136, 5240136, 4520136, 5420136,
+      1245036, 2145036, 1425036, 4125036, 2415036, 4215036, 1254036, 2154036, 1524036, 5124036, 2514036, 5214036,
+      1452036, 4152036, 1542036, 5142036, 4512036, 5412036, 2451036, 4251036, 2541036, 5241036, 4521036, 5421036,
+       134526, 1034526,  314526, 3014526, 1304526, 3104526,  143526, 1043526,  413526, 4013526, 1403526, 4103526,
+       341526, 3041526,  431526, 4031526, 3401526, 4301526, 1340526, 3140526, 1430526, 4130526, 3410526, 4310526,
+       135426, 1035426,  315426, 3015426, 1305426, 3105426,  153426, 1053426,  513426, 5013426, 1503426, 5103426,
+       351426, 3051426,  531426, 5031426, 3501426, 5301426, 1350426, 3150426, 1530426, 5130426, 3510426, 5310426,
+       145326, 1045326,  415326, 4015326, 1405326, 4105326,  154326, 1054326,  514326, 5014326, 1504326, 5104326,
+       451326, 4051326,  541326, 5041326, 4501326, 5401326, 1450326, 4150326, 1540326, 5140326, 4510326, 5410326,
+       345126, 3045126,  435126, 4035126, 3405126, 4305126,  354126, 3054126,  534126, 5034126, 3504126, 5304126,
+       453126, 4053126,  543126, 5043126, 4503126, 5403126, 3450126, 4350126, 3540126, 5340126, 4530126, 5430126,
+      1345026, 3145026, 1435026, 4135026, 3415026, 4315026, 1354026, 3154026, 1534026, 5134026, 3514026, 5314026,
+      1453026, 4153026, 1543026, 5143026, 4513026, 5413026, 3451026, 4351026, 3541026, 5341026, 4531026, 5431026,
+       234516, 2034516,  324516, 3024516, 2304516, 3204516,  243516, 2043516,  423516, 4023516, 2403516, 4203516,
+       342516, 3042516,  432516, 4032516, 3402516, 4302516, 2340516, 3240516, 2430516, 4230516, 3420516, 4320516,
+       235416, 2035416,  325416, 3025416, 2305416, 3205416,  253416, 2053416,  523416, 5023416, 2503416, 5203416,
+       352416, 3052416,  532416, 5032416, 3502416, 5302416, 2350416, 3250416, 2530416, 5230416, 3520416, 5320416,
+       245316, 2045316,  425316, 4025316, 2405316, 4205316,  254316, 2054316,  524316, 5024316, 2504316, 5204316,
+       452316, 4052316,  542316, 5042316, 4502316, 5402316, 2450316, 4250316, 2540316, 5240316, 4520316, 5420316,
+       345216, 3045216,  435216, 4035216, 3405216, 4305216,  354216, 3054216,  534216, 5034216, 3504216, 5304216,
+       453216, 4053216,  543216, 5043216, 4503216, 5403216, 3450216, 4350216, 3540216, 5340216, 4530216, 5430216,
+      2345016, 3245016, 2435016, 4235016, 3425016, 4325016, 2354016, 3254016, 2534016, 5234016, 3524016, 5324016,
+      2453016, 4253016, 2543016, 5243016, 4523016, 5423016, 3452016, 4352016, 3542016, 5342016, 4532016, 5432016,
+      1234506, 2134506, 1324506, 3124506, 2314506, 3214506, 1243506, 2143506, 1423506, 4123506, 2413506, 4213506,
+      1342506, 3142506, 1432506, 4132506, 3412506, 4312506, 2341506, 3241506, 2431506, 4231506, 3421506, 4321506,
+      1235406, 2135406, 1325406, 3125406, 2315406, 3215406, 1253406, 2153406, 1523406, 5123406, 2513406, 5213406,
+      1352406, 3152406, 1532406, 5132406, 3512406, 5312406, 2351406, 3251406, 2531406, 5231406, 3521406, 5321406,
+      1245306, 2145306, 1425306, 4125306, 2415306, 4215306, 1254306, 2154306, 1524306, 5124306, 2514306, 5214306,
+      1452306, 4152306, 1542306, 5142306, 4512306, 5412306, 2451306, 4251306, 2541306, 5241306, 4521306, 5421306,
+      1345206, 3145206, 1435206, 4135206, 3415206, 4315206, 1354206, 3154206, 1534206, 5134206, 3514206, 5314206,
+      1453206, 4153206, 1543206, 5143206, 4513206, 5413206, 3451206, 4351206, 3541206, 5341206, 4531206, 5431206,
+      2345106, 3245106, 2435106, 4235106, 3425106, 4325106, 2354106, 3254106, 2534106, 5234106, 3524106, 5324106,
+      2453106, 4253106, 2543106, 5243106, 4523106, 5423106, 3452106, 4352106, 3542106, 5342106, 4532106, 5432106,
+       123465, 1023465,  213465, 2013465, 1203465, 2103465,  132465, 1032465,  312465, 3012465, 1302465, 3102465,
+       231465, 2031465,  321465, 3021465, 2301465, 3201465, 1230465, 2130465, 1320465, 3120465, 2310465, 3210465,
+       124365, 1024365,  214365, 2014365, 1204365, 2104365,  142365, 1042365,  412365, 4012365, 1402365, 4102365,
+       241365, 2041365,  421365, 4021365, 2401365, 4201365, 1240365, 2140365, 1420365, 4120365, 2410365, 4210365,
+       134265, 1034265,  314265, 3014265, 1304265, 3104265,  143265, 1043265,  413265, 4013265, 1403265, 4103265,
+       341265, 3041265,  431265, 4031265, 3401265, 4301265, 1340265, 3140265, 1430265, 4130265, 3410265, 4310265,
+       234165, 2034165,  324165, 3024165, 2304165, 3204165,  243165, 2043165,  423165, 4023165, 2403165, 4203165,
+       342165, 3042165,  432165, 4032165, 3402165, 4302165, 2340165, 3240165, 2430165, 4230165, 3420165, 4320165,
+      1234065, 2134065, 1324065, 3124065, 2314065, 3214065, 1243065, 2143065, 1423065, 4123065, 2413065, 4213065,
+      1342065, 3142065, 1432065, 4132065, 3412065, 4312065, 2341065, 3241065, 2431065, 4231065, 3421065, 4321065,
+       123645, 1023645,  213645, 2013645, 1203645, 2103645,  132645, 1032645,  312645, 3012645, 1302645, 3102645,
+       231645, 2031645,  321645, 3021645, 2301645, 3201645, 1230645, 2130645, 1320645, 3120645, 2310645, 3210645,
+       126345, 1026345,  216345, 2016345, 1206345, 2106345,  162345, 1062345,  612345, 6012345, 1602345, 6102345,
+       261345, 2061345,  621345, 6021345, 2601345, 6201345, 1260345, 2160345, 1620345, 6120345, 2610345, 6210345,
+       136245, 1036245,  316245, 3016245, 1306245, 3106245,  163245, 1063245,  613245, 6013245, 1603245, 6103245,
+       361245, 3061245,  631245, 6031245, 3601245, 6301245, 1360245, 3160245, 1630245, 6130245, 3610245, 6310245,
+       236145, 2036145,  326145, 3026145, 2306145, 3206145,  263145, 2063145,  623145, 6023145, 2603145, 6203145,
+       362145, 3062145,  632145, 6032145, 3602145, 6302145, 2360145, 3260145, 2630145, 6230145, 3620145, 6320145,
+      1236045, 2136045, 1326045, 3126045, 2316045, 3216045, 1263045, 2163045, 1623045, 6123045, 2613045, 6213045,
+      1362045, 3162045, 1632045, 6132045, 3612045, 6312045, 2361045, 3261045, 2631045, 6231045, 3621045, 6321045,
+       124635, 1024635,  214635, 2014635, 1204635, 2104635,  142635, 1042635,  412635, 4012635, 1402635, 4102635,
+       241635, 2041635,  421635, 4021635, 2401635, 4201635, 1240635, 2140635, 1420635, 4120635, 2410635, 4210635,
+       126435, 1026435,  216435, 2016435, 1206435, 2106435,  162435, 1062435,  612435, 6012435, 1602435, 6102435,
+       261435, 2061435,  621435, 6021435, 2601435, 6201435, 1260435, 2160435, 1620435, 6120435, 2610435, 6210435,
+       146235, 1046235,  416235, 4016235, 1406235, 4106235,  164235, 1064235,  614235, 6014235, 1604235, 6104235,
+       461235, 4061235,  641235, 6041235, 4601235, 6401235, 1460235, 4160235, 1640235, 6140235, 4610235, 6410235,
+       246135, 2046135,  426135, 4026135, 2406135, 4206135,  264135, 2064135,  624135, 6024135, 2604135, 6204135,
+       462135, 4062135,  642135, 6042135, 4602135, 6402135, 2460135, 4260135, 2640135, 6240135, 4620135, 6420135,
+      1246035, 2146035, 1426035, 4126035, 2416035, 4216035, 1264035, 2164035, 1624035, 6124035, 2614035, 6214035,
+      1462035, 4162035, 1642035, 6142035, 4612035, 6412035, 2461035, 4261035, 2641035, 6241035, 4621035, 6421035,
+       134625, 1034625,  314625, 3014625, 1304625, 3104625,  143625, 1043625,  413625, 4013625, 1403625, 4103625,
+       341625, 3041625,  431625, 4031625, 3401625, 4301625, 1340625, 3140625, 1430625, 4130625, 3410625, 4310625,
+       136425, 1036425,  316425, 3016425, 1306425, 3106425,  163425, 1063425,  613425, 6013425, 1603425, 6103425,
+       361425, 3061425,  631425, 6031425, 3601425, 6301425, 1360425, 3160425, 1630425, 6130425, 3610425, 6310425,
+       146325, 1046325,  416325, 4016325, 1406325, 4106325,  164325, 1064325,  614325, 6014325, 1604325, 6104325,
+       461325, 4061325,  641325, 6041325, 4601325, 6401325, 1460325, 4160325, 1640325, 6140325, 4610325, 6410325,
+       346125, 3046125,  436125, 4036125, 3406125, 4306125,  364125, 3064125,  634125, 6034125, 3604125, 6304125,
+       463125, 4063125,  643125, 6043125, 4603125, 6403125, 3460125, 4360125, 3640125, 6340125, 4630125, 6430125,
+      1346025, 3146025, 1436025, 4136025, 3416025, 4316025, 1364025, 3164025, 1634025, 6134025, 3614025, 6314025,
+      1463025, 4163025, 1643025, 6143025, 4613025, 6413025, 3461025, 4361025, 3641025, 6341025, 4631025, 6431025,
+       234615, 2034615,  324615, 3024615, 2304615, 3204615,  243615, 2043615,  423615, 4023615, 2403615, 4203615,
+       342615, 3042615,  432615, 4032615, 3402615, 4302615, 2340615, 3240615, 2430615, 4230615, 3420615, 4320615,
+       236415, 2036415,  326415, 3026415, 2306415, 3206415,  263415, 2063415,  623415, 6023415, 2603415, 6203415,
+       362415, 3062415,  632415, 6032415, 3602415, 6302415, 2360415, 3260415, 2630415, 6230415, 3620415, 6320415,
+       246315, 2046315,  426315, 4026315, 2406315, 4206315,  264315, 2064315,  624315, 6024315, 2604315, 6204315,
+       462315, 4062315,  642315, 6042315, 4602315, 6402315, 2460315, 4260315, 2640315, 6240315, 4620315, 6420315,
+       346215, 3046215,  436215, 4036215, 3406215, 4306215,  364215, 3064215,  634215, 6034215, 3604215, 6304215,
+       463215, 4063215,  643215, 6043215, 4603215, 6403215, 3460215, 4360215, 3640215, 6340215, 4630215, 6430215,
+      2346015, 3246015, 2436015, 4236015, 3426015, 4326015, 2364015, 3264015, 2634015, 6234015, 3624015, 6324015,
+      2463015, 4263015, 2643015, 6243015, 4623015, 6423015, 3462015, 4362015, 3642015, 6342015, 4632015, 6432015,
+      1234605, 2134605, 1324605, 3124605, 2314605, 3214605, 1243605, 2143605, 1423605, 4123605, 2413605, 4213605,
+      1342605, 3142605, 1432605, 4132605, 3412605, 4312605, 2341605, 3241605, 2431605, 4231605, 3421605, 4321605,
+      1236405, 2136405, 1326405, 3126405, 2316405, 3216405, 1263405, 2163405, 1623405, 6123405, 2613405, 6213405,
+      1362405, 3162405, 1632405, 6132405, 3612405, 6312405, 2361405, 3261405, 2631405, 6231405, 3621405, 6321405,
+      1246305, 2146305, 1426305, 4126305, 2416305, 4216305, 1264305, 2164305, 1624305, 6124305, 2614305, 6214305,
+      1462305, 4162305, 1642305, 6142305, 4612305, 6412305, 2461305, 4261305, 2641305, 6241305, 4621305, 6421305,
+      1346205, 3146205, 1436205, 4136205, 3416205, 4316205, 1364205, 3164205, 1634205, 6134205, 3614205, 6314205,
+      1463205, 4163205, 1643205, 6143205, 4613205, 6413205, 3461205, 4361205, 3641205, 6341205, 4631205, 6431205,
+      2346105, 3246105, 2436105, 4236105, 3426105, 4326105, 2364105, 3264105, 2634105, 6234105, 3624105, 6324105,
+      2463105, 4263105, 2643105, 6243105, 4623105, 6423105, 3462105, 4362105, 3642105, 6342105, 4632105, 6432105,
+       123564, 1023564,  213564, 2013564, 1203564, 2103564,  132564, 1032564,  312564, 3012564, 1302564, 3102564,
+       231564, 2031564,  321564, 3021564, 2301564, 3201564, 1230564, 2130564, 1320564, 3120564, 2310564, 3210564,
+       125364, 1025364,  215364, 2015364, 1205364, 2105364,  152364, 1052364,  512364, 5012364, 1502364, 5102364,
+       251364, 2051364,  521364, 5021364, 2501364, 5201364, 1250364, 2150364, 1520364, 5120364, 2510364, 5210364,
+       135264, 1035264,  315264, 3015264, 1305264, 3105264,  153264, 1053264,  513264, 5013264, 1503264, 5103264,
+       351264, 3051264,  531264, 5031264, 3501264, 5301264, 1350264, 3150264, 1530264, 5130264, 3510264, 5310264,
+       235164, 2035164,  325164, 3025164, 2305164, 3205164,  253164, 2053164,  523164, 5023164, 2503164, 5203164,
+       352164, 3052164,  532164, 5032164, 3502164, 5302164, 2350164, 3250164, 2530164, 5230164, 3520164, 5320164,
+      1235064, 2135064, 1325064, 3125064, 2315064, 3215064, 1253064, 2153064, 1523064, 5123064, 2513064, 5213064,
+      1352064, 3152064, 1532064, 5132064, 3512064, 5312064, 2351064, 3251064, 2531064, 5231064, 3521064, 5321064,
+       123654, 1023654,  213654, 2013654, 1203654, 2103654,  132654, 1032654,  312654, 3012654, 1302654, 3102654,
+       231654, 2031654,  321654, 3021654, 2301654, 3201654, 1230654, 2130654, 1320654, 3120654, 2310654, 3210654,
+       126354, 1026354,  216354, 2016354, 1206354, 2106354,  162354, 1062354,  612354, 6012354, 1602354, 6102354,
+       261354, 2061354,  621354, 6021354, 2601354, 6201354, 1260354, 2160354, 1620354, 6120354, 2610354, 6210354,
+       136254, 1036254,  316254, 3016254, 1306254, 3106254,  163254, 1063254,  613254, 6013254, 1603254, 6103254,
+       361254, 3061254,  631254, 6031254, 3601254, 6301254, 1360254, 3160254, 1630254, 6130254, 3610254, 6310254,
+       236154, 2036154,  326154, 3026154, 2306154, 3206154,  263154, 2063154,  623154, 6023154, 2603154, 6203154,
+       362154, 3062154,  632154, 6032154, 3602154, 6302154, 2360154, 3260154, 2630154, 6230154, 3620154, 6320154,
+      1236054, 2136054, 1326054, 3126054, 2316054, 3216054, 1263054, 2163054, 1623054, 6123054, 2613054, 6213054,
+      1362054, 3162054, 1632054, 6132054, 3612054, 6312054, 2361054, 3261054, 2631054, 6231054, 3621054, 6321054,
+       125634, 1025634,  215634, 2015634, 1205634, 2105634,  152634, 1052634,  512634, 5012634, 1502634, 5102634,
+       251634, 2051634,  521634, 5021634, 2501634, 5201634, 1250634, 2150634, 1520634, 5120634, 2510634, 5210634,
+       126534, 1026534,  216534, 2016534, 1206534, 2106534,  162534, 1062534,  612534, 6012534, 1602534, 6102534,
+       261534, 2061534,  621534, 6021534, 2601534, 6201534, 1260534, 2160534, 1620534, 6120534, 2610534, 6210534,
+       156234, 1056234,  516234, 5016234, 1506234, 5106234,  165234, 1065234,  615234, 6015234, 1605234, 6105234,
+       561234, 5061234,  651234, 6051234, 5601234, 6501234, 1560234, 5160234, 1650234, 6150234, 5610234, 6510234,
+       256134, 2056134,  526134, 5026134, 2506134, 5206134,  265134, 2065134,  625134, 6025134, 2605134, 6205134,
+       562134, 5062134,  652134, 6052134, 5602134, 6502134, 2560134, 5260134, 2650134, 6250134, 5620134, 6520134,
+      1256034, 2156034, 1526034, 5126034, 2516034, 5216034, 1265034, 2165034, 1625034, 6125034, 2615034, 6215034,
+      1562034, 5162034, 1652034, 6152034, 5612034, 6512034, 2561034, 5261034, 2651034, 6251034, 5621034, 6521034,
+       135624, 1035624,  315624, 3015624, 1305624, 3105624,  153624, 1053624,  513624, 5013624, 1503624, 5103624,
+       351624, 3051624,  531624, 5031624, 3501624, 5301624, 1350624, 3150624, 1530624, 5130624, 3510624, 5310624,
+       136524, 1036524,  316524, 3016524, 1306524, 3106524,  163524, 1063524,  613524, 6013524, 1603524, 6103524,
+       361524, 3061524,  631524, 6031524, 3601524, 6301524, 1360524, 3160524, 1630524, 6130524, 3610524, 6310524,
+       156324, 1056324,  516324, 5016324, 1506324, 5106324,  165324, 1065324,  615324, 6015324, 1605324, 6105324,
+       561324, 5061324,  651324, 6051324, 5601324, 6501324, 1560324, 5160324, 1650324, 6150324, 5610324, 6510324,
+       356124, 3056124,  536124, 5036124, 3506124, 5306124,  365124, 3065124,  635124, 6035124, 3605124, 6305124,
+       563124, 5063124,  653124, 6053124, 5603124, 6503124, 3560124, 5360124, 3650124, 6350124, 5630124, 6530124,
+      1356024, 3156024, 1536024, 5136024, 3516024, 5316024, 1365024, 3165024, 1635024, 6135024, 3615024, 6315024,
+      1563024, 5163024, 1653024, 6153024, 5613024, 6513024, 3561024, 5361024, 3651024, 6351024, 5631024, 6531024,
+       235614, 2035614,  325614, 3025614, 2305614, 3205614,  253614, 2053614,  523614, 5023614, 2503614, 5203614,
+       352614, 3052614,  532614, 5032614, 3502614, 5302614, 2350614, 3250614, 2530614, 5230614, 3520614, 5320614,
+       236514, 2036514,  326514, 3026514, 2306514, 3206514,  263514, 2063514,  623514, 6023514, 2603514, 6203514,
+       362514, 3062514,  632514, 6032514, 3602514, 6302514, 2360514, 3260514, 2630514, 6230514, 3620514, 6320514,
+       256314, 2056314,  526314, 5026314, 2506314, 5206314,  265314, 2065314,  625314, 6025314, 2605314, 6205314,
+       562314, 5062314,  652314, 6052314, 5602314, 6502314, 2560314, 5260314, 2650314, 6250314, 5620314, 6520314,
+       356214, 3056214,  536214, 5036214, 3506214, 5306214,  365214, 3065214,  635214, 6035214, 3605214, 6305214,
+       563214, 5063214,  653214, 6053214, 5603214, 6503214, 3560214, 5360214, 3650214, 6350214, 5630214, 6530214,
+      2356014, 3256014, 2536014, 5236014, 3526014, 5326014, 2365014, 3265014, 2635014, 6235014, 3625014, 6325014,
+      2563014, 5263014, 2653014, 6253014, 5623014, 6523014, 3562014, 5362014, 3652014, 6352014, 5632014, 6532014,
+      1235604, 2135604, 1325604, 3125604, 2315604, 3215604, 1253604, 2153604, 1523604, 5123604, 2513604, 5213604,
+      1352604, 3152604, 1532604, 5132604, 3512604, 5312604, 2351604, 3251604, 2531604, 5231604, 3521604, 5321604,
+      1236504, 2136504, 1326504, 3126504, 2316504, 3216504, 1263504, 2163504, 1623504, 6123504, 2613504, 6213504,
+      1362504, 3162504, 1632504, 6132504, 3612504, 6312504, 2361504, 3261504, 2631504, 6231504, 3621504, 6321504,
+      1256304, 2156304, 1526304, 5126304, 2516304, 5216304, 1265304, 2165304, 1625304, 6125304, 2615304, 6215304,
+      1562304, 5162304, 1652304, 6152304, 5612304, 6512304, 2561304, 5261304, 2651304, 6251304, 5621304, 6521304,
+      1356204, 3156204, 1536204, 5136204, 3516204, 5316204, 1365204, 3165204, 1635204, 6135204, 3615204, 6315204,
+      1563204, 5163204, 1653204, 6153204, 5613204, 6513204, 3561204, 5361204, 3651204, 6351204, 5631204, 6531204,
+      2356104, 3256104, 2536104, 5236104, 3526104, 5326104, 2365104, 3265104, 2635104, 6235104, 3625104, 6325104,
+      2563104, 5263104, 2653104, 6253104, 5623104, 6523104, 3562104, 5362104, 3652104, 6352104, 5632104, 6532104,
+       124563, 1024563,  214563, 2014563, 1204563, 2104563,  142563, 1042563,  412563, 4012563, 1402563, 4102563,
+       241563, 2041563,  421563, 4021563, 2401563, 4201563, 1240563, 2140563, 1420563, 4120563, 2410563, 4210563,
+       125463, 1025463,  215463, 2015463, 1205463, 2105463,  152463, 1052463,  512463, 5012463, 1502463, 5102463,
+       251463, 2051463,  521463, 5021463, 2501463, 5201463, 1250463, 2150463, 1520463, 5120463, 2510463, 5210463,
+       145263, 1045263,  415263, 4015263, 1405263, 4105263,  154263, 1054263,  514263, 5014263, 1504263, 5104263,
+       451263, 4051263,  541263, 5041263, 4501263, 5401263, 1450263, 4150263, 1540263, 5140263, 4510263, 5410263,
+       245163, 2045163,  425163, 4025163, 2405163, 4205163,  254163, 2054163,  524163, 5024163, 2504163, 5204163,
+       452163, 4052163,  542163, 5042163, 4502163, 5402163, 2450163, 4250163, 2540163, 5240163, 4520163, 5420163,
+      1245063, 2145063, 1425063, 4125063, 2415063, 4215063, 1254063, 2154063, 1524063, 5124063, 2514063, 5214063,
+      1452063, 4152063, 1542063, 5142063, 4512063, 5412063, 2451063, 4251063, 2541063, 5241063, 4521063, 5421063,
+       124653, 1024653,  214653, 2014653, 1204653, 2104653,  142653, 1042653,  412653, 4012653, 1402653, 4102653,
+       241653, 2041653,  421653, 4021653, 2401653, 4201653, 1240653, 2140653, 1420653, 4120653, 2410653, 4210653,
+       126453, 1026453,  216453, 2016453, 1206453, 2106453,  162453, 1062453,  612453, 6012453, 1602453, 6102453,
+       261453, 2061453,  621453, 6021453, 2601453, 6201453, 1260453, 2160453, 1620453, 6120453, 2610453, 6210453,
+       146253, 1046253,  416253, 4016253, 1406253, 4106253,  164253, 1064253,  614253, 6014253, 1604253, 6104253,
+       461253, 4061253,  641253, 6041253, 4601253, 6401253, 1460253, 4160253, 1640253, 6140253, 4610253, 6410253,
+       246153, 2046153,  426153, 4026153, 2406153, 4206153,  264153, 2064153,  624153, 6024153, 2604153, 6204153,
+       462153, 4062153,  642153, 6042153, 4602153, 6402153, 2460153, 4260153, 2640153, 6240153, 4620153, 6420153,
+      1246053, 2146053, 1426053, 4126053, 2416053, 4216053, 1264053, 2164053, 1624053, 6124053, 2614053, 6214053,
+      1462053, 4162053, 1642053, 6142053, 4612053, 6412053, 2461053, 4261053, 2641053, 6241053, 4621053, 6421053,
+       125643, 1025643,  215643, 2015643, 1205643, 2105643,  152643, 1052643,  512643, 5012643, 1502643, 5102643,
+       251643, 2051643,  521643, 5021643, 2501643, 5201643, 1250643, 2150643, 1520643, 5120643, 2510643, 5210643,
+       126543, 1026543,  216543, 2016543, 1206543, 2106543,  162543, 1062543,  612543, 6012543, 1602543, 6102543,
+       261543, 2061543,  621543, 6021543, 2601543, 6201543, 1260543, 2160543, 1620543, 6120543, 2610543, 6210543,
+       156243, 1056243,  516243, 5016243, 1506243, 5106243,  165243, 1065243,  615243, 6015243, 1605243, 6105243,
+       561243, 5061243,  651243, 6051243, 5601243, 6501243, 1560243, 5160243, 1650243, 6150243, 5610243, 6510243,
+       256143, 2056143,  526143, 5026143, 2506143, 5206143,  265143, 2065143,  625143, 6025143, 2605143, 6205143,
+       562143, 5062143,  652143, 6052143, 5602143, 6502143, 2560143, 5260143, 2650143, 6250143, 5620143, 6520143,
+      1256043, 2156043, 1526043, 5126043, 2516043, 5216043, 1265043, 2165043, 1625043, 6125043, 2615043, 6215043,
+      1562043, 5162043, 1652043, 6152043, 5612043, 6512043, 2561043, 5261043, 2651043, 6251043, 5621043, 6521043,
+       145623, 1045623,  415623, 4015623, 1405623, 4105623,  154623, 1054623,  514623, 5014623, 1504623, 5104623,
+       451623, 4051623,  541623, 5041623, 4501623, 5401623, 1450623, 4150623, 1540623, 5140623, 4510623, 5410623,
+       146523, 1046523,  416523, 4016523, 1406523, 4106523,  164523, 1064523,  614523, 6014523, 1604523, 6104523,
+       461523, 4061523,  641523, 6041523, 4601523, 6401523, 1460523, 4160523, 1640523, 6140523, 4610523, 6410523,
+       156423, 1056423,  516423, 5016423, 1506423, 5106423,  165423, 1065423,  615423, 6015423, 1605423, 6105423,
+       561423, 5061423,  651423, 6051423, 5601423, 6501423, 1560423, 5160423, 1650423, 6150423, 5610423, 6510423,
+       456123, 4056123,  546123, 5046123, 4506123, 5406123,  465123, 4065123,  645123, 6045123, 4605123, 6405123,
+       564123, 5064123,  654123, 6054123, 5604123, 6504123, 4560123, 5460123, 4650123, 6450123, 5640123, 6540123,
+      1456023, 4156023, 1546023, 5146023, 4516023, 5416023, 1465023, 4165023, 1645023, 6145023, 4615023, 6415023,
+      1564023, 5164023, 1654023, 6154023, 5614023, 6514023, 4561023, 5461023, 4651023, 6451023, 5641023, 6541023,
+       245613, 2045613,  425613, 4025613, 2405613, 4205613,  254613, 2054613,  524613, 5024613, 2504613, 5204613,
+       452613, 4052613,  542613, 5042613, 4502613, 5402613, 2450613, 4250613, 2540613, 5240613, 4520613, 5420613,
+       246513, 2046513,  426513, 4026513, 2406513, 4206513,  264513, 2064513,  624513, 6024513, 2604513, 6204513,
+       462513, 4062513,  642513, 6042513, 4602513, 6402513, 2460513, 4260513, 2640513, 6240513, 4620513, 6420513,
+       256413, 2056413,  526413, 5026413, 2506413, 5206413,  265413, 2065413,  625413, 6025413, 2605413, 6205413,
+       562413, 5062413,  652413, 6052413, 5602413, 6502413, 2560413, 5260413, 2650413, 6250413, 5620413, 6520413,
+       456213, 4056213,  546213, 5046213, 4506213, 5406213,  465213, 4065213,  645213, 6045213, 4605213, 6405213,
+       564213, 5064213,  654213, 6054213, 5604213, 6504213, 4560213, 5460213, 4650213, 6450213, 5640213, 6540213,
+      2456013, 4256013, 2546013, 5246013, 4526013, 5426013, 2465013, 4265013, 2645013, 6245013, 4625013, 6425013,
+      2564013, 5264013, 2654013, 6254013, 5624013, 6524013, 4562013, 5462013, 4652013, 6452013, 5642013, 6542013,
+      1245603, 2145603, 1425603, 4125603, 2415603, 4215603, 1254603, 2154603, 1524603, 5124603, 2514603, 5214603,
+      1452603, 4152603, 1542603, 5142603, 4512603, 5412603, 2451603, 4251603, 2541603, 5241603, 4521603, 5421603,
+      1246503, 2146503, 1426503, 4126503, 2416503, 4216503, 1264503, 2164503, 1624503, 6124503, 2614503, 6214503,
+      1462503, 4162503, 1642503, 6142503, 4612503, 6412503, 2461503, 4261503, 2641503, 6241503, 4621503, 6421503,
+      1256403, 2156403, 1526403, 5126403, 2516403, 5216403, 1265403, 2165403, 1625403, 6125403, 2615403, 6215403,
+      1562403, 5162403, 1652403, 6152403, 5612403, 6512403, 2561403, 5261403, 2651403, 6251403, 5621403, 6521403,
+      1456203, 4156203, 1546203, 5146203, 4516203, 5416203, 1465203, 4165203, 1645203, 6145203, 4615203, 6415203,
+      1564203, 5164203, 1654203, 6154203, 5614203, 6514203, 4561203, 5461203, 4651203, 6451203, 5641203, 6541203,
+      2456103, 4256103, 2546103, 5246103, 4526103, 5426103, 2465103, 4265103, 2645103, 6245103, 4625103, 6425103,
+      2564103, 5264103, 2654103, 6254103, 5624103, 6524103, 4562103, 5462103, 4652103, 6452103, 5642103, 6542103,
+       134562, 1034562,  314562, 3014562, 1304562, 3104562,  143562, 1043562,  413562, 4013562, 1403562, 4103562,
+       341562, 3041562,  431562, 4031562, 3401562, 4301562, 1340562, 3140562, 1430562, 4130562, 3410562, 4310562,
+       135462, 1035462,  315462, 3015462, 1305462, 3105462,  153462, 1053462,  513462, 5013462, 1503462, 5103462,
+       351462, 3051462,  531462, 5031462, 3501462, 5301462, 1350462, 3150462, 1530462, 5130462, 3510462, 5310462,
+       145362, 1045362,  415362, 4015362, 1405362, 4105362,  154362, 1054362,  514362, 5014362, 1504362, 5104362,
+       451362, 4051362,  541362, 5041362, 4501362, 5401362, 1450362, 4150362, 1540362, 5140362, 4510362, 5410362,
+       345162, 3045162,  435162, 4035162, 3405162, 4305162,  354162, 3054162,  534162, 5034162, 3504162, 5304162,
+       453162, 4053162,  543162, 5043162, 4503162, 5403162, 3450162, 4350162, 3540162, 5340162, 4530162, 5430162,
+      1345062, 3145062, 1435062, 4135062, 3415062, 4315062, 1354062, 3154062, 1534062, 5134062, 3514062, 5314062,
+      1453062, 4153062, 1543062, 5143062, 4513062, 5413062, 3451062, 4351062, 3541062, 5341062, 4531062, 5431062,
+       134652, 1034652,  314652, 3014652, 1304652, 3104652,  143652, 1043652,  413652, 4013652, 1403652, 4103652,
+       341652, 3041652,  431652, 4031652, 3401652, 4301652, 1340652, 3140652, 1430652, 4130652, 3410652, 4310652,
+       136452, 1036452,  316452, 3016452, 1306452, 3106452,  163452, 1063452,  613452, 6013452, 1603452, 6103452,
+       361452, 3061452,  631452, 6031452, 3601452, 6301452, 1360452, 3160452, 1630452, 6130452, 3610452, 6310452,
+       146352, 1046352,  416352, 4016352, 1406352, 4106352,  164352, 1064352,  614352, 6014352, 1604352, 6104352,
+       461352, 4061352,  641352, 6041352, 4601352, 6401352, 1460352, 4160352, 1640352, 6140352, 4610352, 6410352,
+       346152, 3046152,  436152, 4036152, 3406152, 4306152,  364152, 3064152,  634152, 6034152, 3604152, 6304152,
+       463152, 4063152,  643152, 6043152, 4603152, 6403152, 3460152, 4360152, 3640152, 6340152, 4630152, 6430152,
+      1346052, 3146052, 1436052, 4136052, 3416052, 4316052, 1364052, 3164052, 1634052, 6134052, 3614052, 6314052,
+      1463052, 4163052, 1643052, 6143052, 4613052, 6413052, 3461052, 4361052, 3641052, 6341052, 4631052, 6431052,
+       135642, 1035642,  315642, 3015642, 1305642, 3105642,  153642, 1053642,  513642, 5013642, 1503642, 5103642,
+       351642, 3051642,  531642, 5031642, 3501642, 5301642, 1350642, 3150642, 1530642, 5130642, 3510642, 5310642,
+       136542, 1036542,  316542, 3016542, 1306542, 3106542,  163542, 1063542,  613542, 6013542, 1603542, 6103542,
+       361542, 3061542,  631542, 6031542, 3601542, 6301542, 1360542, 3160542, 1630542, 6130542, 3610542, 6310542,
+       156342, 1056342,  516342, 5016342, 1506342, 5106342,  165342, 1065342,  615342, 6015342, 1605342, 6105342,
+       561342, 5061342,  651342, 6051342, 5601342, 6501342, 1560342, 5160342, 1650342, 6150342, 5610342, 6510342,
+       356142, 3056142,  536142, 5036142, 3506142, 5306142,  365142, 3065142,  635142, 6035142, 3605142, 6305142,
+       563142, 5063142,  653142, 6053142, 5603142, 6503142, 3560142, 5360142, 3650142, 6350142, 5630142, 6530142,
+      1356042, 3156042, 1536042, 5136042, 3516042, 5316042, 1365042, 3165042, 1635042, 6135042, 3615042, 6315042,
+      1563042, 5163042, 1653042, 6153042, 5613042, 6513042, 3561042, 5361042, 3651042, 6351042, 5631042, 6531042,
+       145632, 1045632,  415632, 4015632, 1405632, 4105632,  154632, 1054632,  514632, 5014632, 1504632, 5104632,
+       451632, 4051632,  541632, 5041632, 4501632, 5401632, 1450632, 4150632, 1540632, 5140632, 4510632, 5410632,
+       146532, 1046532,  416532, 4016532, 1406532, 4106532,  164532, 1064532,  614532, 6014532, 1604532, 6104532,
+       461532, 4061532,  641532, 6041532, 4601532, 6401532, 1460532, 4160532, 1640532, 6140532, 4610532, 6410532,
+       156432, 1056432,  516432, 5016432, 1506432, 5106432,  165432, 1065432,  615432, 6015432, 1605432, 6105432,
+       561432, 5061432,  651432, 6051432, 5601432, 6501432, 1560432, 5160432, 1650432, 6150432, 5610432, 6510432,
+       456132, 4056132,  546132, 5046132, 4506132, 5406132,  465132, 4065132,  645132, 6045132, 4605132, 6405132,
+       564132, 5064132,  654132, 6054132, 5604132, 6504132, 4560132, 5460132, 4650132, 6450132, 5640132, 6540132,
+      1456032, 4156032, 1546032, 5146032, 4516032, 5416032, 1465032, 4165032, 1645032, 6145032, 4615032, 6415032,
+      1564032, 5164032, 1654032, 6154032, 5614032, 6514032, 4561032, 5461032, 4651032, 6451032, 5641032, 6541032,
+       345612, 3045612,  435612, 4035612, 3405612, 4305612,  354612, 3054612,  534612, 5034612, 3504612, 5304612,
+       453612, 4053612,  543612, 5043612, 4503612, 5403612, 3450612, 4350612, 3540612, 5340612, 4530612, 5430612,
+       346512, 3046512,  436512, 4036512, 3406512, 4306512,  364512, 3064512,  634512, 6034512, 3604512, 6304512,
+       463512, 4063512,  643512, 6043512, 4603512, 6403512, 3460512, 4360512, 3640512, 6340512, 4630512, 6430512,
+       356412, 3056412,  536412, 5036412, 3506412, 5306412,  365412, 3065412,  635412, 6035412, 3605412, 6305412,
+       563412, 5063412,  653412, 6053412, 5603412, 6503412, 3560412, 5360412, 3650412, 6350412, 5630412, 6530412,
+       456312, 4056312,  546312, 5046312, 4506312, 5406312,  465312, 4065312,  645312, 6045312, 4605312, 6405312,
+       564312, 5064312,  654312, 6054312, 5604312, 6504312, 4560312, 5460312, 4650312, 6450312, 5640312, 6540312,
+      3456012, 4356012, 3546012, 5346012, 4536012, 5436012, 3465012, 4365012, 3645012, 6345012, 4635012, 6435012,
+      3564012, 5364012, 3654012, 6354012, 5634012, 6534012, 4563012, 5463012, 4653012, 6453012, 5643012, 6543012,
+      1345602, 3145602, 1435602, 4135602, 3415602, 4315602, 1354602, 3154602, 1534602, 5134602, 3514602, 5314602,
+      1453602, 4153602, 1543602, 5143602, 4513602, 5413602, 3451602, 4351602, 3541602, 5341602, 4531602, 5431602,
+      1346502, 3146502, 1436502, 4136502, 3416502, 4316502, 1364502, 3164502, 1634502, 6134502, 3614502, 6314502,
+      1463502, 4163502, 1643502, 6143502, 4613502, 6413502, 3461502, 4361502, 3641502, 6341502, 4631502, 6431502,
+      1356402, 3156402, 1536402, 5136402, 3516402, 5316402, 1365402, 3165402, 1635402, 6135402, 3615402, 6315402,
+      1563402, 5163402, 1653402, 6153402, 5613402, 6513402, 3561402, 5361402, 3651402, 6351402, 5631402, 6531402,
+      1456302, 4156302, 1546302, 5146302, 4516302, 5416302, 1465302, 4165302, 1645302, 6145302, 4615302, 6415302,
+      1564302, 5164302, 1654302, 6154302, 5614302, 6514302, 4561302, 5461302, 4651302, 6451302, 5641302, 6541302,
+      3456102, 4356102, 3546102, 5346102, 4536102, 5436102, 3465102, 4365102, 3645102, 6345102, 4635102, 6435102,
+      3564102, 5364102, 3654102, 6354102, 5634102, 6534102, 4563102, 5463102, 4653102, 6453102, 5643102, 6543102,
+       234561, 2034561,  324561, 3024561, 2304561, 3204561,  243561, 2043561,  423561, 4023561, 2403561, 4203561,
+       342561, 3042561,  432561, 4032561, 3402561, 4302561, 2340561, 3240561, 2430561, 4230561, 3420561, 4320561,
+       235461, 2035461,  325461, 3025461, 2305461, 3205461,  253461, 2053461,  523461, 5023461, 2503461, 5203461,
+       352461, 3052461,  532461, 5032461, 3502461, 5302461, 2350461, 3250461, 2530461, 5230461, 3520461, 5320461,
+       245361, 2045361,  425361, 4025361, 2405361, 4205361,  254361, 2054361,  524361, 5024361, 2504361, 5204361,
+       452361, 4052361,  542361, 5042361, 4502361, 5402361, 2450361, 4250361, 2540361, 5240361, 4520361, 5420361,
+       345261, 3045261,  435261, 4035261, 3405261, 4305261,  354261, 3054261,  534261, 5034261, 3504261, 5304261,
+       453261, 4053261,  543261, 5043261, 4503261, 5403261, 3450261, 4350261, 3540261, 5340261, 4530261, 5430261,
+      2345061, 3245061, 2435061, 4235061, 3425061, 4325061, 2354061, 3254061, 2534061, 5234061, 3524061, 5324061,
+      2453061, 4253061, 2543061, 5243061, 4523061, 5423061, 3452061, 4352061, 3542061, 5342061, 4532061, 5432061,
+       234651, 2034651,  324651, 3024651, 2304651, 3204651,  243651, 2043651,  423651, 4023651, 2403651, 4203651,
+       342651, 3042651,  432651, 4032651, 3402651, 4302651, 2340651, 3240651, 2430651, 4230651, 3420651, 4320651,
+       236451, 2036451,  326451, 3026451, 2306451, 3206451,  263451, 2063451,  623451, 6023451, 2603451, 6203451,
+       362451, 3062451,  632451, 6032451, 3602451, 6302451, 2360451, 3260451, 2630451, 6230451, 3620451, 6320451,
+       246351, 2046351,  426351, 4026351, 2406351, 4206351,  264351, 2064351,  624351, 6024351, 2604351, 6204351,
+       462351, 4062351,  642351, 6042351, 4602351, 6402351, 2460351, 4260351, 2640351, 6240351, 4620351, 6420351,
+       346251, 3046251,  436251, 4036251, 3406251, 4306251,  364251, 3064251,  634251, 6034251, 3604251, 6304251,
+       463251, 4063251,  643251, 6043251, 4603251, 6403251, 3460251, 4360251, 3640251, 6340251, 4630251, 6430251,
+      2346051, 3246051, 2436051, 4236051, 3426051, 4326051, 2364051, 3264051, 2634051, 6234051, 3624051, 6324051,
+      2463051, 4263051, 2643051, 6243051, 4623051, 6423051, 3462051, 4362051, 3642051, 6342051, 4632051, 6432051,
+       235641, 2035641,  325641, 3025641, 2305641, 3205641,  253641, 2053641,  523641, 5023641, 2503641, 5203641,
+       352641, 3052641,  532641, 5032641, 3502641, 5302641, 2350641, 3250641, 2530641, 5230641, 3520641, 5320641,
+       236541, 2036541,  326541, 3026541, 2306541, 3206541,  263541, 2063541,  623541, 6023541, 2603541, 6203541,
+       362541, 3062541,  632541, 6032541, 3602541, 6302541, 2360541, 3260541, 2630541, 6230541, 3620541, 6320541,
+       256341, 2056341,  526341, 5026341, 2506341, 5206341,  265341, 2065341,  625341, 6025341, 2605341, 6205341,
+       562341, 5062341,  652341, 6052341, 5602341, 6502341, 2560341, 5260341, 2650341, 6250341, 5620341, 6520341,
+       356241, 3056241,  536241, 5036241, 3506241, 5306241,  365241, 3065241,  635241, 6035241, 3605241, 6305241,
+       563241, 5063241,  653241, 6053241, 5603241, 6503241, 3560241, 5360241, 3650241, 6350241, 5630241, 6530241,
+      2356041, 3256041, 2536041, 5236041, 3526041, 5326041, 2365041, 3265041, 2635041, 6235041, 3625041, 6325041,
+      2563041, 5263041, 2653041, 6253041, 5623041, 6523041, 3562041, 5362041, 3652041, 6352041, 5632041, 6532041,
+       245631, 2045631,  425631, 4025631, 2405631, 4205631,  254631, 2054631,  524631, 5024631, 2504631, 5204631,
+       452631, 4052631,  542631, 5042631, 4502631, 5402631, 2450631, 4250631, 2540631, 5240631, 4520631, 5420631,
+       246531, 2046531,  426531, 4026531, 2406531, 4206531,  264531, 2064531,  624531, 6024531, 2604531, 6204531,
+       462531, 4062531,  642531, 6042531, 4602531, 6402531, 2460531, 4260531, 2640531, 6240531, 4620531, 6420531,
+       256431, 2056431,  526431, 5026431, 2506431, 5206431,  265431, 2065431,  625431, 6025431, 2605431, 6205431,
+       562431, 5062431,  652431, 6052431, 5602431, 6502431, 2560431, 5260431, 2650431, 6250431, 5620431, 6520431,
+       456231, 4056231,  546231, 5046231, 4506231, 5406231,  465231, 4065231,  645231, 6045231, 4605231, 6405231,
+       564231, 5064231,  654231, 6054231, 5604231, 6504231, 4560231, 5460231, 4650231, 6450231, 5640231, 6540231,
+      2456031, 4256031, 2546031, 5246031, 4526031, 5426031, 2465031, 4265031, 2645031, 6245031, 4625031, 6425031,
+      2564031, 5264031, 2654031, 6254031, 5624031, 6524031, 4562031, 5462031, 4652031, 6452031, 5642031, 6542031,
+       345621, 3045621,  435621, 4035621, 3405621, 4305621,  354621, 3054621,  534621, 5034621, 3504621, 5304621,
+       453621, 4053621,  543621, 5043621, 4503621, 5403621, 3450621, 4350621, 3540621, 5340621, 4530621, 5430621,
+       346521, 3046521,  436521, 4036521, 3406521, 4306521,  364521, 3064521,  634521, 6034521, 3604521, 6304521,
+       463521, 4063521,  643521, 6043521, 4603521, 6403521, 3460521, 4360521, 3640521, 6340521, 4630521, 6430521,
+       356421, 3056421,  536421, 5036421, 3506421, 5306421,  365421, 3065421,  635421, 6035421, 3605421, 6305421,
+       563421, 5063421,  653421, 6053421, 5603421, 6503421, 3560421, 5360421, 3650421, 6350421, 5630421, 6530421,
+       456321, 4056321,  546321, 5046321, 4506321, 5406321,  465321, 4065321,  645321, 6045321, 4605321, 6405321,
+       564321, 5064321,  654321, 6054321, 5604321, 6504321, 4560321, 5460321, 4650321, 6450321, 5640321, 6540321,
+      3456021, 4356021, 3546021, 5346021, 4536021, 5436021, 3465021, 4365021, 3645021, 6345021, 4635021, 6435021,
+      3564021, 5364021, 3654021, 6354021, 5634021, 6534021, 4563021, 5463021, 4653021, 6453021, 5643021, 6543021,
+      2345601, 3245601, 2435601, 4235601, 3425601, 4325601, 2354601, 3254601, 2534601, 5234601, 3524601, 5324601,
+      2453601, 4253601, 2543601, 5243601, 4523601, 5423601, 3452601, 4352601, 3542601, 5342601, 4532601, 5432601,
+      2346501, 3246501, 2436501, 4236501, 3426501, 4326501, 2364501, 3264501, 2634501, 6234501, 3624501, 6324501,
+      2463501, 4263501, 2643501, 6243501, 4623501, 6423501, 3462501, 4362501, 3642501, 6342501, 4632501, 6432501,
+      2356401, 3256401, 2536401, 5236401, 3526401, 5326401, 2365401, 3265401, 2635401, 6235401, 3625401, 6325401,
+      2563401, 5263401, 2653401, 6253401, 5623401, 6523401, 3562401, 5362401, 3652401, 6352401, 5632401, 6532401,
+      2456301, 4256301, 2546301, 5246301, 4526301, 5426301, 2465301, 4265301, 2645301, 6245301, 4625301, 6425301,
+      2564301, 5264301, 2654301, 6254301, 5624301, 6524301, 4562301, 5462301, 4652301, 6452301, 5642301, 6542301,
+      3456201, 4356201, 3546201, 5346201, 4536201, 5436201, 3465201, 4365201, 3645201, 6345201, 4635201, 6435201,
+      3564201, 5364201, 3654201, 6354201, 5634201, 6534201, 4563201, 5463201, 4653201, 6453201, 5643201, 6543201,
+      1234560, 2134560, 1324560, 3124560, 2314560, 3214560, 1243560, 2143560, 1423560, 4123560, 2413560, 4213560,
+      1342560, 3142560, 1432560, 4132560, 3412560, 4312560, 2341560, 3241560, 2431560, 4231560, 3421560, 4321560,
+      1235460, 2135460, 1325460, 3125460, 2315460, 3215460, 1253460, 2153460, 1523460, 5123460, 2513460, 5213460,
+      1352460, 3152460, 1532460, 5132460, 3512460, 5312460, 2351460, 3251460, 2531460, 5231460, 3521460, 5321460,
+      1245360, 2145360, 1425360, 4125360, 2415360, 4215360, 1254360, 2154360, 1524360, 5124360, 2514360, 5214360,
+      1452360, 4152360, 1542360, 5142360, 4512360, 5412360, 2451360, 4251360, 2541360, 5241360, 4521360, 5421360,
+      1345260, 3145260, 1435260, 4135260, 3415260, 4315260, 1354260, 3154260, 1534260, 5134260, 3514260, 5314260,
+      1453260, 4153260, 1543260, 5143260, 4513260, 5413260, 3451260, 4351260, 3541260, 5341260, 4531260, 5431260,
+      2345160, 3245160, 2435160, 4235160, 3425160, 4325160, 2354160, 3254160, 2534160, 5234160, 3524160, 5324160,
+      2453160, 4253160, 2543160, 5243160, 4523160, 5423160, 3452160, 4352160, 3542160, 5342160, 4532160, 5432160,
+      1234650, 2134650, 1324650, 3124650, 2314650, 3214650, 1243650, 2143650, 1423650, 4123650, 2413650, 4213650,
+      1342650, 3142650, 1432650, 4132650, 3412650, 4312650, 2341650, 3241650, 2431650, 4231650, 3421650, 4321650,
+      1236450, 2136450, 1326450, 3126450, 2316450, 3216450, 1263450, 2163450, 1623450, 6123450, 2613450, 6213450,
+      1362450, 3162450, 1632450, 6132450, 3612450, 6312450, 2361450, 3261450, 2631450, 6231450, 3621450, 6321450,
+      1246350, 2146350, 1426350, 4126350, 2416350, 4216350, 1264350, 2164350, 1624350, 6124350, 2614350, 6214350,
+      1462350, 4162350, 1642350, 6142350, 4612350, 6412350, 2461350, 4261350, 2641350, 6241350, 4621350, 6421350,
+      1346250, 3146250, 1436250, 4136250, 3416250, 4316250, 1364250, 3164250, 1634250, 6134250, 3614250, 6314250,
+      1463250, 4163250, 1643250, 6143250, 4613250, 6413250, 3461250, 4361250, 3641250, 6341250, 4631250, 6431250,
+      2346150, 3246150, 2436150, 4236150, 3426150, 4326150, 2364150, 3264150, 2634150, 6234150, 3624150, 6324150,
+      2463150, 4263150, 2643150, 6243150, 4623150, 6423150, 3462150, 4362150, 3642150, 6342150, 4632150, 6432150,
+      1235640, 2135640, 1325640, 3125640, 2315640, 3215640, 1253640, 2153640, 1523640, 5123640, 2513640, 5213640,
+      1352640, 3152640, 1532640, 5132640, 3512640, 5312640, 2351640, 3251640, 2531640, 5231640, 3521640, 5321640,
+      1236540, 2136540, 1326540, 3126540, 2316540, 3216540, 1263540, 2163540, 1623540, 6123540, 2613540, 6213540,
+      1362540, 3162540, 1632540, 6132540, 3612540, 6312540, 2361540, 3261540, 2631540, 6231540, 3621540, 6321540,
+      1256340, 2156340, 1526340, 5126340, 2516340, 5216340, 1265340, 2165340, 1625340, 6125340, 2615340, 6215340,
+      1562340, 5162340, 1652340, 6152340, 5612340, 6512340, 2561340, 5261340, 2651340, 6251340, 5621340, 6521340,
+      1356240, 3156240, 1536240, 5136240, 3516240, 5316240, 1365240, 3165240, 1635240, 6135240, 3615240, 6315240,
+      1563240, 5163240, 1653240, 6153240, 5613240, 6513240, 3561240, 5361240, 3651240, 6351240, 5631240, 6531240,
+      2356140, 3256140, 2536140, 5236140, 3526140, 5326140, 2365140, 3265140, 2635140, 6235140, 3625140, 6325140,
+      2563140, 5263140, 2653140, 6253140, 5623140, 6523140, 3562140, 5362140, 3652140, 6352140, 5632140, 6532140,
+      1245630, 2145630, 1425630, 4125630, 2415630, 4215630, 1254630, 2154630, 1524630, 5124630, 2514630, 5214630,
+      1452630, 4152630, 1542630, 5142630, 4512630, 5412630, 2451630, 4251630, 2541630, 5241630, 4521630, 5421630,
+      1246530, 2146530, 1426530, 4126530, 2416530, 4216530, 1264530, 2164530, 1624530, 6124530, 2614530, 6214530,
+      1462530, 4162530, 1642530, 6142530, 4612530, 6412530, 2461530, 4261530, 2641530, 6241530, 4621530, 6421530,
+      1256430, 2156430, 1526430, 5126430, 2516430, 5216430, 1265430, 2165430, 1625430, 6125430, 2615430, 6215430,
+      1562430, 5162430, 1652430, 6152430, 5612430, 6512430, 2561430, 5261430, 2651430, 6251430, 5621430, 6521430,
+      1456230, 4156230, 1546230, 5146230, 4516230, 5416230, 1465230, 4165230, 1645230, 6145230, 4615230, 6415230,
+      1564230, 5164230, 1654230, 6154230, 5614230, 6514230, 4561230, 5461230, 4651230, 6451230, 5641230, 6541230,
+      2456130, 4256130, 2546130, 5246130, 4526130, 5426130, 2465130, 4265130, 2645130, 6245130, 4625130, 6425130,
+      2564130, 5264130, 2654130, 6254130, 5624130, 6524130, 4562130, 5462130, 4652130, 6452130, 5642130, 6542130,
+      1345620, 3145620, 1435620, 4135620, 3415620, 4315620, 1354620, 3154620, 1534620, 5134620, 3514620, 5314620,
+      1453620, 4153620, 1543620, 5143620, 4513620, 5413620, 3451620, 4351620, 3541620, 5341620, 4531620, 5431620,
+      1346520, 3146520, 1436520, 4136520, 3416520, 4316520, 1364520, 3164520, 1634520, 6134520, 3614520, 6314520,
+      1463520, 4163520, 1643520, 6143520, 4613520, 6413520, 3461520, 4361520, 3641520, 6341520, 4631520, 6431520,
+      1356420, 3156420, 1536420, 5136420, 3516420, 5316420, 1365420, 3165420, 1635420, 6135420, 3615420, 6315420,
+      1563420, 5163420, 1653420, 6153420, 5613420, 6513420, 3561420, 5361420, 3651420, 6351420, 5631420, 6531420,
+      1456320, 4156320, 1546320, 5146320, 4516320, 5416320, 1465320, 4165320, 1645320, 6145320, 4615320, 6415320,
+      1564320, 5164320, 1654320, 6154320, 5614320, 6514320, 4561320, 5461320, 4651320, 6451320, 5641320, 6541320,
+      3456120, 4356120, 3546120, 5346120, 4536120, 5436120, 3465120, 4365120, 3645120, 6345120, 4635120, 6435120,
+      3564120, 5364120, 3654120, 6354120, 5634120, 6534120, 4563120, 5463120, 4653120, 6453120, 5643120, 6543120,
+      2345610, 3245610, 2435610, 4235610, 3425610, 4325610, 2354610, 3254610, 2534610, 5234610, 3524610, 5324610,
+      2453610, 4253610, 2543610, 5243610, 4523610, 5423610, 3452610, 4352610, 3542610, 5342610, 4532610, 5432610,
+      2346510, 3246510, 2436510, 4236510, 3426510, 4326510, 2364510, 3264510, 2634510, 6234510, 3624510, 6324510,
+      2463510, 4263510, 2643510, 6243510, 4623510, 6423510, 3462510, 4362510, 3642510, 6342510, 4632510, 6432510,
+      2356410, 3256410, 2536410, 5236410, 3526410, 5326410, 2365410, 3265410, 2635410, 6235410, 3625410, 6325410,
+      2563410, 5263410, 2653410, 6253410, 5623410, 6523410, 3562410, 5362410, 3652410, 6352410, 5632410, 6532410,
+      2456310, 4256310, 2546310, 5246310, 4526310, 5426310, 2465310, 4265310, 2645310, 6245310, 4625310, 6425310,
+      2564310, 5264310, 2654310, 6254310, 5624310, 6524310, 4562310, 5462310, 4652310, 6452310, 5642310, 6542310,
+      3456210, 4356210, 3546210, 5346210, 4536210, 5436210, 3465210, 4365210, 3645210, 6345210, 4635210, 6435210,
+      3564210, 5364210, 3654210, 6354210, 5634210, 6534210, 4563210, 5463210, 4653210, 6453210, 5643210, 6543210
+    };
+    std::map<uint64_t, int> expected;
+    for (std::size_t i = 0; i < 5040; i++)
+      expected[pre_expected[i]] = 0; // flags are 0, everything is symmetric here
+
+    VERIFY(isDynGroup(group));
+    VERIFY_IS_EQUAL(group.size(), 5040u);
+    VERIFY_IS_EQUAL(group.globalFlags(), 0);
+    group.apply<checkIdx, int>(identity7, 0, found, expected);
+    VERIFY_IS_EQUAL(found.size(), 5040u);
+  }
+}
+
+static void test_tensor_epsilon()
+{
+  SGroup<3, AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym;
+  Tensor<int, 3> epsilon(3,3,3);
+
+  epsilon.setZero();
+  epsilon.symCoeff(sym, 0, 1, 2) =  1;
+
+  for (int i = 0; i < 3; i++) {
+    for (int j = 0; j < 3; j++) {
+      for (int k = 0; k < 3; k++) {
+        VERIFY_IS_EQUAL((epsilon(i,j,k)), (- (j - i) * (k - j) * (i - k) / 2) );
+      }
+    }
+  }
+}
+
+static void test_tensor_sym()
+{
+  SGroup<4, Symmetry<0,1>, Symmetry<2,3>> sym;
+  Tensor<int, 4> t(10,10,10,10);
+
+  t.setZero();
+
+  for (int l = 0; l < 10; l++) {
+    for (int k = l; k < 10; k++) {
+      for (int j = 0; j < 10; j++) {
+        for (int i = j; i < 10; i++) {
+          t.symCoeff(sym, i, j, k, l) = (i + j) * (k + l);
+        }
+      }
+    }
+  }
+
+  for (int l = 0; l < 10; l++) {
+    for (int k = 0; k < 10; k++) {
+      for (int j = 0; j < 10; j++) {
+        for (int i = 0; i < 10; i++) {
+          VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
+        }
+      }
+    }
+  }
+
+}
+
+static void test_tensor_asym()
+{
+  SGroup<4, AntiSymmetry<0,1>, AntiSymmetry<2,3>> sym;
+  Tensor<int, 4> t(10,10,10,10);
+
+  t.setZero();
+
+  for (int l = 0; l < 10; l++) {
+    for (int k = l + 1; k < 10; k++) {
+      for (int j = 0; j < 10; j++) {
+        for (int i = j + 1; i < 10; i++) {
+          t.symCoeff(sym, i, j, k, l) = ((i * j) + (k * l));
+        }
+      }
+    }
+  }
+
+  for (int l = 0; l < 10; l++) {
+    for (int k = 0; k < 10; k++) {
+      for (int j = 0; j < 10; j++) {
+        for (int i = 0; i < 10; i++) {
+          if (i < j && k < l)
+            VERIFY_IS_EQUAL((t(i, j, k, l)), (((i * j) + (k * l))));
+          else if (i > j && k > l)
+            VERIFY_IS_EQUAL((t(i, j, k, l)), (((i * j) + (k * l))));
+          else if (i < j && k > l)
+            VERIFY_IS_EQUAL((t(i, j, k, l)), (- ((i * j) + (k * l))));
+          else if (i > j && k < l)
+            VERIFY_IS_EQUAL((t(i, j, k, l)), (- ((i * j) + (k * l))));
+          else
+            VERIFY_IS_EQUAL((t(i, j, k, l)), 0);
+        }
+      }
+    }
+  }
+}
+
+static void test_tensor_dynsym()
+{
+  DynamicSGroup sym(4);
+  sym.addSymmetry(0,1);
+  sym.addSymmetry(2,3);
+  Tensor<int, 4> t(10,10,10,10);
+
+  t.setZero();
+
+  for (int l = 0; l < 10; l++) {
+    for (int k = l; k < 10; k++) {
+      for (int j = 0; j < 10; j++) {
+        for (int i = j; i < 10; i++) {
+          t.symCoeff(sym, i, j, k, l) = (i + j) * (k + l);
+        }
+      }
+    }
+  }
+
+  for (int l = 0; l < 10; l++) {
+    for (int k = 0; k < 10; k++) {
+      for (int j = 0; j < 10; j++) {
+        for (int i = 0; i < 10; i++) {
+          VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
+        }
+      }
+    }
+  }
+}
+
+static void test_tensor_randacc()
+{
+  SGroup<4, Symmetry<0,1>, Symmetry<2,3>> sym;
+  Tensor<int, 4> t(10,10,10,10);
+
+  t.setZero();
+
+  // set elements 1 million times, that way we access the
+  // entire matrix
+  for (int n = 0; n < 1000000; n++) {
+    int i = rand() % 10;
+    int j = rand() % 10;
+    int k = rand() % 10;
+    int l = rand() % 10;
+    // only access those indices in a given order
+    if (i < j)
+      std::swap(i, j);
+    if (k < l)
+      std::swap(k, l);
+    t.symCoeff(sym, i, j, k, l) = (i + j) * (k + l);
+  }
+
+  for (int l = 0; l < 10; l++) {
+    for (int k = 0; k < 10; k++) {
+      for (int j = 0; j < 10; j++) {
+        for (int i = 0; i < 10; i++) {
+          VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
+        }
+      }
+    }
+  }
+}
+
+void test_cxx11_tensor_symmetry()
+{
+  CALL_SUBTEST(test_symgroups_static());
+  CALL_SUBTEST(test_symgroups_dynamic());
+  CALL_SUBTEST(test_symgroups_selection());
+  CALL_SUBTEST(test_tensor_epsilon());
+  CALL_SUBTEST(test_tensor_sym());
+  CALL_SUBTEST(test_tensor_asym());
+  CALL_SUBTEST(test_tensor_dynsym());
+  CALL_SUBTEST(test_tensor_randacc());
+}
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */