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>
using namespace std;
struct node {
  int x, y;
};
int n, m, e, c[105][105], ans[2 * 105];
node a[105 * 105];
long long kk, f[2 * 105][2 * 105];
bool cmp(node a, node b) { return c[a.x][a.y] < c[b.x][b.y]; }
int main() {
  scanf("%d%d%I64d", &n, &m, &kk);
  for (int i = (1); i <= (n); i++)
    for (int j = (1); j <= (m); j++) {
      scanf("%d", &c[i][j]);
      a[++e].x = i;
      a[e].y = j;
    }
  sort(a + 1, a + n * m + 1, cmp);
  for (int k = (1); k <= (n * m); k++)
    if (!ans[a[k].x + a[k].y]) {
      int t = a[k].x + a[k].y;
      ans[t] = 1;
      f[1][1] = 1;
      for (int i = (2); i <= (n + m); i++)
        for (int j = (1); j <= (i); j++) {
          if (ans[i] == 1)
            f[i][j] = f[i - 1][j - 1];
          else if (ans[i] == 2)
            f[i][j] = f[i - 1][j + 1];
          else
            f[i][j] = f[i - 1][j - 1] + f[i - 1][j + 1];
          if (f[i][j] > kk) f[i][j] = kk;
        }
      if (kk > f[n + m][1]) {
        kk -= f[n + m][1];
        ans[t] = 2;
      } else
        ans[t] = 1;
    }
  for (int i = (1); i <= (n); i++) {
    for (int j = (1); j <= (m); j++)
      if (ans[i + j] == 1)
        printf("(");
      else
        printf(")");
    printf("\n");
  }
  return 0;
}
