#include <bits/stdc++.h>
using namespace std;
template <class T>
void debug(T a, T b) {
  ;
}
template <class T>
void chmin(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
void chmax(T& a, const T& b) {
  if (a < b) a = b;
}
namespace std {
template <class S, class T>
ostream& operator<<(ostream& out, const pair<S, T>& a) {
  out << '(' << a.first << ',' << a.second << ')';
  return out;
}
}  // namespace std
long long int readL() {
  long long int res;
  scanf("%I64d", &res);
  return res;
}
void printL(long long int res) { printf("%I64d", res); }
template <long long int mod>
struct Int_ {
  unsigned x;
  unsigned mpow(Int_ a, unsigned k) {
    Int_ res = 1;
    while (k) {
      if (k & 1) res = res * a;
      a = a * a;
      k >>= 1;
    }
    return res.x;
  }
  unsigned inverse(Int_ a) { return mpow(a, mod - 2); }
  Int_() : x(0) {}
  Int_(long long sig) {
    if (sig < 0)
      x = sig % mod + mod;
    else
      x = sig % mod;
  }
  unsigned get() const { return (unsigned)x; }
  Int_& operator+=(Int_ that) {
    if ((x += that.x) >= mod) x -= mod;
    return *this;
  }
  Int_& operator-=(Int_ that) {
    if ((x += mod - that.x) >= mod) x -= mod;
    return *this;
  }
  Int_& operator*=(Int_ that) {
    x = (unsigned long long)x * that.x % mod;
    return *this;
  }
  Int_& operator=(Int_ that) {
    x = that.x;
    return *this;
  }
  Int_& operator/=(Int_ that) {
    x = (unsigned long long)x * inverse(that.x) % mod;
    return *this;
  }
  bool operator==(Int_ that) const { return x == that.x; }
  bool operator!=(Int_ that) const { return x != that.x; }
  Int_ operator-() const { return Int_(0) - Int_(*this); }
  Int_ operator+(Int_ that) const { return Int_(*this) += that; }
  Int_ operator-(Int_ that) const { return Int_(*this) -= that; }
  Int_ operator*(Int_ that) const { return Int_(*this) *= that; }
  Int_ operator/(Int_ that) const { return Int_(*this) /= that; }
};
namespace std {
template <long long int mod>
ostream& operator<<(ostream& out, const Int_<mod>& a) {
  out << a.get();
  return out;
}
template <long long int mod>
istream& operator>>(istream& in, Int_<mod>& a) {
  in >> a.x;
  return in;
}
};  // namespace std
vector<vector<Int_<1000000007> > > matpow(
    const vector<vector<Int_<1000000007> > >& a,
    const vector<vector<Int_<1000000007> > >& b) {
  int n = a.size();
  vector<vector<Int_<1000000007> > > res(n, vector<Int_<1000000007> >(n));
  for (int i = 0; i < (n); ++i)
    for (int j = 0; j < (n); ++j)
      for (int k = 0; k < (n); ++k) {
        res[i][j] += a[i][k] * b[k][j];
      }
  return res;
}
vector<vector<Int_<1000000007> > > mpow(vector<vector<Int_<1000000007> > > a,
                                        long long int k) {
  int n = a.size();
  vector<vector<Int_<1000000007> > > res(n, vector<Int_<1000000007> >(n));
  for (int i = 0; i < (n); ++i) res[i][i] = 1;
  while (k) {
    if (k & 1) res = matpow(res, a);
    a = matpow(a, a);
    k >>= 1;
  }
  return res;
}
int w[10];
int main() {
  for (int i = 0; i < (7); ++i) cin >> w[i + 1];
  vector<Int_<1000000007> > ever(2);
  ever[1] = 1;
  for (int i = 1; i <= 7; ++i) {
    int n = (1 << i);
    vector<vector<Int_<1000000007> > > M(n, vector<Int_<1000000007> >(n));
    for (int j = 0; j < (n); ++j)
      for (int k = 0; k < (n); ++k)
        for (int l = 0; l < (n / 2); ++l) {
          int l2 = (l << 1) | 1 | (1 << i);
          int fail = 0;
          for (int i2 = 0; i2 < (i); ++i2)
            if (j >> i2 & 1 && k >> i2 & 1 && l2 >> i2 & 1 &&
                l2 >> (i2 + 1) & 1) {
              fail = 1;
              break;
            }
          if (!fail) M[j][k] += 1;
        }
    vector<vector<Int_<1000000007> > > M2 = mpow(M, w[i]);
    vector<Int_<1000000007> > nxt(n);
    for (int i = 0; i < (n); ++i)
      for (int j = 0; j < (n); ++j) {
        nxt[j] += ever[i] * M2[i][j];
      }
    ever.clear();
    if (i == 7)
      ever = nxt;
    else {
      ever.resize(2 * n);
      for (int j = 0; j < (n); ++j) ever[j | n] = nxt[j];
    }
  }
  Int_<1000000007> res = ever[(1 << 7) - 1];
  cout << res << endl;
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

You are given a figure on a grid representing stairs consisting of 7 steps. The width of the stair on height i is wi squares. Formally, the figure is created by consecutively joining rectangles of size wi × i so that the wi sides lie on one straight line. Thus, for example, if all wi = 1, the figure will look like that (different colors represent different rectangles):

<image>

And if w = {5, 1, 0, 3, 0, 0, 1}, then it looks like that:

<image>

Find the number of ways to color some borders of the figure's inner squares so that no square had all four borders colored. The borders of the squares lying on the border of the figure should be considered painted. The ways that differ with the figure's rotation should be considered distinct. 

Input

The single line of the input contains 7 numbers w1, w2, ..., w7 (0 ≤ wi ≤ 105). It is guaranteed that at least one of the wi's isn't equal to zero.

Output

In the single line of the output display a single number — the answer to the problem modulo 109 + 7.

Examples

Input

0 1 0 0 0 0 0


Output

1


Input

0 2 0 0 0 0 0


Output

7


Input

1 1 1 0 0 0 0


Output

9


Input

5 1 0 3 0 0 1


Output

411199181

Note

All the possible ways of painting the third sample are given below:

<image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
void debug(T a, T b) {
  ;
}
template <class T>
void chmin(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
void chmax(T& a, const T& b) {
  if (a < b) a = b;
}
namespace std {
template <class S, class T>
ostream& operator<<(ostream& out, const pair<S, T>& a) {
  out << '(' << a.first << ',' << a.second << ')';
  return out;
}
}  // namespace std
long long int readL() {
  long long int res;
  scanf("%I64d", &res);
  return res;
}
void printL(long long int res) { printf("%I64d", res); }
template <long long int mod>
struct Int_ {
  unsigned x;
  unsigned mpow(Int_ a, unsigned k) {
    Int_ res = 1;
    while (k) {
      if (k & 1) res = res * a;
      a = a * a;
      k >>= 1;
    }
    return res.x;
  }
  unsigned inverse(Int_ a) { return mpow(a, mod - 2); }
  Int_() : x(0) {}
  Int_(long long sig) {
    if (sig < 0)
      x = sig % mod + mod;
    else
      x = sig % mod;
  }
  unsigned get() const { return (unsigned)x; }
  Int_& operator+=(Int_ that) {
    if ((x += that.x) >= mod) x -= mod;
    return *this;
  }
  Int_& operator-=(Int_ that) {
    if ((x += mod - that.x) >= mod) x -= mod;
    return *this;
  }
  Int_& operator*=(Int_ that) {
    x = (unsigned long long)x * that.x % mod;
    return *this;
  }
  Int_& operator=(Int_ that) {
    x = that.x;
    return *this;
  }
  Int_& operator/=(Int_ that) {
    x = (unsigned long long)x * inverse(that.x) % mod;
    return *this;
  }
  bool operator==(Int_ that) const { return x == that.x; }
  bool operator!=(Int_ that) const { return x != that.x; }
  Int_ operator-() const { return Int_(0) - Int_(*this); }
  Int_ operator+(Int_ that) const { return Int_(*this) += that; }
  Int_ operator-(Int_ that) const { return Int_(*this) -= that; }
  Int_ operator*(Int_ that) const { return Int_(*this) *= that; }
  Int_ operator/(Int_ that) const { return Int_(*this) /= that; }
};
namespace std {
template <long long int mod>
ostream& operator<<(ostream& out, const Int_<mod>& a) {
  out << a.get();
  return out;
}
template <long long int mod>
istream& operator>>(istream& in, Int_<mod>& a) {
  in >> a.x;
  return in;
}
};  // namespace std
vector<vector<Int_<1000000007> > > matpow(
    const vector<vector<Int_<1000000007> > >& a,
    const vector<vector<Int_<1000000007> > >& b) {
  int n = a.size();
  vector<vector<Int_<1000000007> > > res(n, vector<Int_<1000000007> >(n));
  for (int i = 0; i < (n); ++i)
    for (int j = 0; j < (n); ++j)
      for (int k = 0; k < (n); ++k) {
        res[i][j] += a[i][k] * b[k][j];
      }
  return res;
}
vector<vector<Int_<1000000007> > > mpow(vector<vector<Int_<1000000007> > > a,
                                        long long int k) {
  int n = a.size();
  vector<vector<Int_<1000000007> > > res(n, vector<Int_<1000000007> >(n));
  for (int i = 0; i < (n); ++i) res[i][i] = 1;
  while (k) {
    if (k & 1) res = matpow(res, a);
    a = matpow(a, a);
    k >>= 1;
  }
  return res;
}
int w[10];
int main() {
  for (int i = 0; i < (7); ++i) cin >> w[i + 1];
  vector<Int_<1000000007> > ever(2);
  ever[1] = 1;
  for (int i = 1; i <= 7; ++i) {
    int n = (1 << i);
    vector<vector<Int_<1000000007> > > M(n, vector<Int_<1000000007> >(n));
    for (int j = 0; j < (n); ++j)
      for (int k = 0; k < (n); ++k)
        for (int l = 0; l < (n / 2); ++l) {
          int l2 = (l << 1) | 1 | (1 << i);
          int fail = 0;
          for (int i2 = 0; i2 < (i); ++i2)
            if (j >> i2 & 1 && k >> i2 & 1 && l2 >> i2 & 1 &&
                l2 >> (i2 + 1) & 1) {
              fail = 1;
              break;
            }
          if (!fail) M[j][k] += 1;
        }
    vector<vector<Int_<1000000007> > > M2 = mpow(M, w[i]);
    vector<Int_<1000000007> > nxt(n);
    for (int i = 0; i < (n); ++i)
      for (int j = 0; j < (n); ++j) {
        nxt[j] += ever[i] * M2[i][j];
      }
    ever.clear();
    if (i == 7)
      ever = nxt;
    else {
      ever.resize(2 * n);
      for (int j = 0; j < (n); ++j) ever[j | n] = nxt[j];
    }
  }
  Int_<1000000007> res = ever[(1 << 7) - 1];
  cout << res << endl;
  return 0;
}

```