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 main() {
  int n, m, a[200], idx[200];
  long long s, dp[200][200];
  scanf("%d%d%I64d", &n, &m, &s);
  memset(a, 63, sizeof(a));
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      scanf("%d", a + n + m);
      a[i + j] = min(a[i + j], a[n + m]);
    }
  for (int i = 0; i < n + m - 1; i++) idx[i] = i;
  sort(idx, idx + n + m - 1, [&](int x, int y) { return a[x] < a[y]; });
  char ans[200] = {};
  for (int t = 0; t < n + m - 1; t++) {
    ans[idx[t]] = '(';
    memset(dp, 0, sizeof(dp));
    dp[0][0] = 1;
    for (int i = 0; i < n + m - 1; i++)
      for (int c = i & 1; c <= i && c <= n + m - 1 - i; c += 2) {
        if (c && ans[i] != '(') dp[i + 1][c - 1] += min(dp[i][c], s);
        if (ans[i] != ')') dp[i + 1][c + 1] += min(dp[i][c], s);
      }
    if (s > dp[n + m - 1][0]) {
      s -= dp[n + m - 1][0];
      ans[idx[t]] = ')';
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) putchar(ans[i + j]);
    puts("");
  }
}
