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, cur, ii, a[102][102], b[222], c[222];
long long f[222][222], k, cz;
char d[222], r[102][102];
bool cmp(int i, int j) { return b[i] < b[j]; }
inline long long go(int n) {
  f[0][0] = 1;
  for (i = 1; i <= n; i++)
    for (j = 0; j <= i; j++) {
      f[i][j] = 0;
      if (j > 0 && d[i - 1] != ')') f[i][j] += f[i - 1][j - 1];
      if (d[i - 1] != '(') f[i][j] += f[i - 1][j + 1];
      if (f[i][j] > k + 5) f[i][j] = k + 5;
    }
  return f[n][0];
}
int main() {
  scanf("%d%d%I64d", &n, &m, &k);
  for (i = 0; i < n; i++)
    for (j = 0; j < m; j++) {
      scanf("%d", &a[i][j]);
      if (b[i + j] == 0 || a[i][j] < b[i + j]) b[i + j] = a[i][j];
    }
  for (i = 0; i < n + m - 1; i++) c[i] = i;
  sort(c, c + n + m - 1, cmp);
  for (ii = 0; ii < n + m - 1; ii++) {
    cur = c[ii];
    d[cur] = '(';
    cz = go(n + m - 1);
    if (k > cz) {
      d[cur] = ')';
      k -= cz;
    }
  }
  for (i = 0; i < n; i++)
    for (j = 0; j < m; j++) r[i][j] = d[i + j];
  for (i = 0; i < n; i++) puts(r[i]);
  return 0;
}
