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;
bool nonzero = false;
char a[2003][2003], b[2003][2003];
double take_max = 0, tmp;
int n;
int row[2003][2003][4], col[2003][2003][4], low[2003], high[2003];
int rowcol[2003][2003], cross[2003][2003];
int highest[4], data[4];
long long ans = 1;
int main() {
  scanf("%d\n", &n);
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      scanf("%c", &a[i][j]);
      if (a[i][j] != '0') nonzero = true;
    }
    scanf("\n");
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < 4; j++) row[i][0][j] = 0;
    for (int j = 1; j <= n; j++) {
      for (int k = 0; k < 4; k++) row[i][j][k] = row[i][j - 1][k];
      row[i][j][a[i][j] - '0']++;
    }
    low[0] = -1;
    for (int j = 1; j <= n; j++) {
      if (a[i][j] == '0')
        low[j] = -1;
      else
        low[j] = low[j - 1] + 1;
    }
    high[n + 1] = -1;
    for (int j = n; j >= 1; j--) {
      if (a[i][j] == '0')
        high[j] = -1;
      else
        high[j] = high[j + 1] + 1;
    }
    for (int j = 1; j <= n; j++) rowcol[i][j] = min(low[j], high[j]);
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < 4; j++) col[0][i][j] = 0;
    for (int j = 1; j <= n; j++) {
      for (int k = 0; k < 4; k++) col[j][i][k] = col[j - 1][i][k];
      col[j][i][a[j][i] - '0']++;
    }
    low[0] = -1;
    for (int j = 1; j <= n; j++) {
      if (a[j][i] == '0')
        low[j] = -1;
      else
        low[j] = low[j - 1] + 1;
    }
    high[n + 1] = -1;
    for (int j = n; j >= 1; j--) {
      if (a[j][i] == '0')
        high[j] = -1;
      else
        high[j] = high[j + 1] + 1;
    }
    for (int j = 1; j <= n; j++)
      rowcol[j][i] = min(rowcol[j][i], min(low[j], high[j]));
  }
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) {
      if (rowcol[i][j] >= 0) {
        for (int k = 0; k < 4; k++) data[k] = 0;
        for (int k = 0; k < 4; k++) {
          data[k] +=
              row[i][j + rowcol[i][j]][k] - row[i][j - rowcol[i][j] - 1][k];
          data[k] +=
              col[i + rowcol[i][j]][j][k] - col[i - rowcol[i][j] - 1][j][k];
        }
        data[a[i][j] - '0']--;
        if (data[0] == 0) {
          tmp = log(2.0) * data[2] + log(3.0) * data[3];
          if (tmp > take_max) {
            take_max = tmp;
            for (int k = 0; k < 4; k++) highest[k] = data[k];
          }
        }
      }
    }
  for (int i = 1; i <= 2 * n; i++)
    for (int j = 1; j <= 2 * n; j++) b[i][j] = '0';
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) b[i + j][i - j + n + 1] = a[i][j];
  n *= 2;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) a[i][j] = b[i][j];
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < 4; j++) {
      row[i][0][j] = 0;
      row[i][1][j] = 0;
    }
    for (int j = 2; j <= n; j++) {
      for (int k = 0; k < 4; k++) row[i][j][k] = row[i][j - 2][k];
      row[i][j][a[i][j] - '0']++;
    }
    low[0] = -2;
    low[1] = -2;
    for (int j = 2; j <= n; j++) {
      if (a[i][j] == '0')
        low[j] = -2;
      else
        low[j] = low[j - 2] + 2;
    }
    high[n + 2] = -2;
    high[n + 1] = -2;
    for (int j = n; j >= 2; j--) {
      if (a[i][j] == '0')
        high[j] = -2;
      else
        high[j] = high[j + 2] + 2;
    }
    for (int j = 2; j <= n; j++) cross[i][j] = min(low[j], high[j]);
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < 4; j++) {
      col[0][i][j] = 0;
      col[1][i][j] = 0;
    }
    for (int j = 2; j <= n; j++) {
      for (int k = 0; k < 4; k++) col[j][i][k] = col[j - 2][i][k];
      col[j][i][a[j][i] - '0']++;
    }
    low[0] = -2;
    low[1] = -2;
    for (int j = 2; j <= n; j++) {
      if (a[j][i] == '0')
        low[j] = -2;
      else
        low[j] = low[j - 2] + 2;
    }
    high[n + 2] = -2;
    high[n + 1] = -2;
    for (int j = n; j >= 2; j--) {
      if (a[j][i] == '0')
        high[j] = -2;
      else
        high[j] = high[j + 2] + 2;
    }
    for (int j = 2; j <= n; j++)
      cross[j][i] = min(cross[j][i], min(low[j], high[j]));
  }
  for (int i = 1; i <= n; i++)
    for (int j = 2; j <= n; j++) {
      if (cross[i][j] >= 0) {
        for (int k = 0; k < 4; k++) data[k] = 0;
        for (int k = 0; k < 4; k++) {
          data[k] +=
              row[i][j + cross[i][j]][k] - row[i][j - cross[i][j] - 2][k];
          data[k] +=
              col[i + cross[i][j]][j][k] - col[i - cross[i][j] - 2][j][k];
        }
        data[a[i][j] - '0']--;
        if (data[0] == 0) {
          tmp = log(2.0) * data[2] + log(3.0) * data[3];
          if (tmp > take_max) {
            take_max = tmp;
            for (int k = 0; k < 4; k++) highest[k] = data[k];
          }
        }
      }
    }
  if (take_max == 0)
    printf("%d\n", nonzero);
  else {
    for (int i = 2; i <= 3; i++)
      for (int j = 1; j <= highest[i]; j++) {
        ans *= i;
        ans %= 1000000007;
      }
    printf("%I64d\n", ans);
  }
  return 0;
}
