Vanya plays a game of balloons on the field of size n × n, where each cell contains a balloon with one of the values 0, 1, 2 or 3. The goal is to destroy a cross, such that the product of all values of balloons in the cross is maximum possible. There are two types of crosses: normal and rotated. For example:
    
    
      
    **o**  
    **o**  
    ooooo  
    **o**  
    **o**  
    

or
    
    
      
    o***o  
    *o*o*  
    **o**  
    *o*o*  
    o***o  
    

Formally, the cross is given by three integers r, c and d, such that d ≤ r, c ≤ n - d + 1. The normal cross consists of balloons located in cells (x, y) (where x stay for the number of the row and y for the number of the column), such that |x - r|·|y - c| = 0 and |x - r| + |y - c| < d. Rotated cross consists of balloons located in cells (x, y), such that |x - r| = |y - c| and |x - r| < d.

Vanya wants to know the maximum possible product of the values of balls forming one cross. As this value can be large, output it modulo 109 + 7.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 1000) — the number of rows and columns in the table with balloons.

The each of the following n lines contains n characters '0', '1', '2' or '3' — the description of the values in balloons.

Output

Print the maximum possible product modulo 109 + 7. Note, that you are not asked to maximize the remainder modulo 109 + 7, but to find the maximum value and print it this modulo.

Examples

Input

4
1233
0213
2020
0303


Output

108


Input

5
00300
00300
33333
00300
00300


Output

19683


Input

5
00003
02030
00300
03020
30000


Output

108


Input

5
21312
10003
10002
10003
23231


Output

3


Input

5
12131
12111
12112
21311
21212


Output

24

Note

In the first sample, the maximum product is achieved for a rotated cross with a center in the cell (3, 3) and radius 1: 2·2·3·3·3 = 108.
#include <bits/stdc++.h>
using namespace std;
struct Number {
  array<int, 4> powers = {{0, 0, 0, 0}};
  Number() {}
  Number(int a) {
    if (a != -1) powers[a]++;
  }
  long double log_value() const {
    if (powers[0] > 0) return -INFINITY;
    return powers[2] * log(2L) + powers[3] * log(3L);
  }
  int mod() {
    long long result = 1;
    for (int i = 0; i < 4; i++)
      for (int j = 0; j < powers[i]; j++)
        result = (result * i) % (int)(1e9 + 7);
    return result;
  }
  bool is_zero() { return powers[0] > 0; }
};
bool operator<(const Number& a, const Number& b) {
  return a.log_value() < b.log_value();
}
Number operator*(const Number& a, const Number& b) {
  Number result;
  for (int i = 0; i < 4; i++) result.powers[i] = a.powers[i] + b.powers[i];
  return result;
}
Number operator/(const Number& a, const Number& b) {
  Number result;
  for (int i = 0; i < 4; i++) result.powers[i] = a.powers[i] - b.powers[i];
  return result;
}
template <typename T>
using Matrix = vector<vector<T>>;
template <typename T>
Matrix<T> matrix(int R, int C, T x = T()) {
  return Matrix<T>(R, vector<T>(C, x));
}
struct RangeProduct {
  int N;
  Matrix<int>& grid;
  Matrix<Number> hprod;
  Matrix<Number> vprod;
  RangeProduct(int N, Matrix<int>& grid) : N(N), grid(grid) {
    hprod = matrix<Number>(N + 1, N + 1);
    vprod = matrix<Number>(N + 1, N + 1);
    for (int r = 0; r < N; r++)
      for (int c = 0; c < N; c++) {
        hprod[r][c + 1] = hprod[r][c] * grid[r][c];
        vprod[r + 1][c] = vprod[r][c] * grid[r][c];
      }
  }
  bool valid(int r, int c) { return 0 <= r && r < N && 0 <= c && c < N; }
  Number hquery(int r, int c, int radius) {
    int c1 = c - radius, c2 = c + radius;
    if (!valid(r, c1) || !valid(r, c2)) return 0;
    return hprod[r][c2 + 1] / hprod[r][c1];
  }
  Number vquery(int r, int c, int radius) {
    int r1 = r - radius, r2 = r + radius;
    if (!valid(r1, c) || !valid(r2, c)) return 0;
    return vprod[r2 + 1][c] / vprod[r1][c];
  }
  Number cross(int r, int c, int radius) {
    return hquery(r, c, radius) * vquery(r, c, radius) / grid[r][c];
  }
  Number max_cross(int r, int c) {
    int a = 0, b = N;
    while (a < b) {
      int mid = (a + b + 1) / 2;
      if (cross(r, c, mid).is_zero())
        b = mid - 1;
      else
        a = mid;
    }
    return cross(r, c, a);
  }
};
Number solve(int N, Matrix<int>& grid) {
  RangeProduct rp(N, grid);
  Number result(0);
  for (int r = 0; r < N; r++)
    for (int c = 0; c < N; c++) result = max(result, rp.max_cross(r, c));
  return result;
}
Matrix<int> rotate(int N, Matrix<int>& grid, int shift) {
  auto ngrid = matrix<int>(N, N);
  for (int r = 0; r < N; r++)
    for (int c = 0; c < N; c++)
      if ((r + c) % 2 == shift)
        ngrid[(r + c) / 2][(r - c + N) / 2] = grid[r][c];
  return ngrid;
}
int main() {
  ios::sync_with_stdio(false);
  int N;
  cin >> N;
  auto grid = matrix<int>(N, N);
  for (int i = 0; i < N; i++) {
    string s;
    cin >> s;
    for (int j = 0; j < N; j++) grid[i][j] = s[j] - '0';
  }
  auto rgrid0 = rotate(N, grid, 0);
  auto rgrid1 = rotate(N, grid, 1);
  Number answer = max({solve(N, grid), solve(N, rgrid0), solve(N, rgrid1)});
  cout << answer.mod() << endl;
}
