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;
int n, m, i, j, k, f[100010], a[500][500], b[100010], ans[100010];
long long K, g[500][500];
bool cmp(int a, int b) { return f[a] < f[b]; }
int main() {
  scanf("%d%d%I64d", &n, &m, &K);
  for (i = 1; i <= n + m - 1; i++) f[i] = 0x37373737;
  for (i = 1; i <= n; i++)
    for (j = 1; j <= m; j++) scanf("%d", &a[i][j]);
  for (i = 1; i <= n; i++)
    for (j = 1; j <= m; j++) f[i + j - 1] = min(f[i + j - 1], a[i][j]);
  for (i = 1; i <= n + m - 1; i++) b[i] = i;
  sort(b + 1, b + n + m, cmp);
  ans[1] = 1;
  ans[n + m - 1] = 2;
  for (i = 1; i <= n + m - 1; i++)
    if ((b[i] == 1) || (b[i] == n + m - 1))
      continue;
    else {
      ans[b[i]] = 1;
      memset(g, 0, sizeof(g));
      g[0][0] = 1;
      for (j = 1; j <= n + m - 1; j++)
        for (k = 0; k <= j; k++) {
          if (ans[j] == 1) {
            if (k > 0) g[j][k] = g[j - 1][k - 1];
          } else if (ans[j] == 2)
            g[j][k] = g[j - 1][k + 1];
          else {
            if (k > 0) g[j][k] = g[j - 1][k - 1];
            g[j][k] = g[j][k] + g[j - 1][k + 1];
          }
          if (g[j][k] > K) g[j][k] = K + 1;
        }
      if (g[n + m - 1][0] < K) {
        ans[b[i]] = 2;
        K = K - g[n + m - 1][0];
      }
    }
  for (i = 1; i <= n; i++) {
    for (j = 1; j <= m; j++)
      if (ans[i + j - 1] == 1)
        cout << "(";
      else
        cout << ")";
    cout << endl;
  }
}
