A two dimensional array is called a bracket array if each grid contains one of the two possible brackets — "(" or ")". A path through the two dimensional array cells is called monotonous if any two consecutive cells in the path are side-adjacent and each cell of the path is located below or to the right from the previous one. 

A two dimensional array whose size equals n × m is called a correct bracket array, if any string formed by writing out the brackets on some monotonous way from cell (1, 1) to cell (n, m) forms a correct bracket sequence. 

Let's define the operation of comparing two correct bracket arrays of equal size (a and b) like that. Let's consider a given two dimensional array of priorities (c) — a two dimensional array of same size, containing different integers from 1 to nm. Let's find such position (i, j) in the two dimensional array, that ai, j ≠ bi, j. If there are several such positions, let's choose the one where number ci, j is minimum. If ai, j = "(", then a < b, otherwise a > b. If the position (i, j) is not found, then the arrays are considered equal.

Your task is to find a k-th two dimensional correct bracket array. It is guaranteed that for the given sizes of n and m there will be no less than k two dimensional correct bracket arrays.

Input

The first line contains integers n, m and k — the sizes of the array and the number of the sought correct bracket array (1 ≤ n, m ≤ 100, 1 ≤ k ≤ 1018). Then an array of priorities is given, n lines each containing m numbers, number pi, j shows the priority of character j in line i (1 ≤ pi, j ≤ nm, all pi, j are different).

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.

Output

Print the k-th two dimensional correct bracket array.

Examples

Input

1 2 1
1 2


Output

()


Input

2 3 1
1 2 3
4 5 6


Output

(()
())


Input

3 2 2
3 6
1 4
2 5


Output

()
)(
()

Note

In the first sample exists only one correct two-dimensional bracket array.

In the second and in the third samples two arrays exist.

A bracket sequence is called regular if it is possible to obtain correct arithmetic expression by inserting characters «+» and «1» into this sequence. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
#include <bits/stdc++.h>
int main() {
  int N, M;
  long long int what;
  scanf("%d %d %I64i", &N, &M, &what);
  static int data[205][205];
  static int p[205 * 205];
  int i, j;
  for (i = 0; i < N; i++) {
    for (j = 0; j < M; j++) {
      scanf("%d", &(data[i][j]));
      (data[i][j])--;
      p[data[i][j]] = i + j;
    }
  }
  static char res[205];
  memset(res, '.', sizeof(res));
  static long long int a[205][205];
  int x, y;
  int K = N + M - 1;
  for (i = 0; i < (N * M); i++) {
    if (res[p[i]] == '.') {
      res[p[i]] = '(';
      memset(a, 0, sizeof(a));
      a[0][0] = 1LL;
      for (x = 1; x <= K; x++) {
        for (y = 0; y <= K; y++) {
          if ((y > 0) && (res[x - 1] != ')')) a[x][y] += a[x - 1][y - 1];
          if (res[x - 1] != '(') a[x][y] += a[x - 1][y + 1];
          if (a[x][y] > 2000000000000000000LL) a[x][y] = 2000000000000000000LL;
        }
      }
      if (a[K][0] < what) {
        res[p[i]] = ')';
        what -= a[K][0];
      }
    }
  }
  for (i = 0; i < N; i++) {
    for (j = 0; j < M; j++) {
      printf("%c", res[i + j]);
    }
    printf("\n");
  }
  return 0;
}
