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;
long long k;
int pri[210];
int inf[210];
int A[210];
bool cmp(int a, int b) { return pri[a] < pri[b]; }
long long have[210][210];
long long hm() {
  for (int c = 0; c < 210; c++)
    for (int d = 0; d < 210; d++) have[c][d] = 0ll;
  have[1][0] = 1ll;
  for (int c = 1; c < n + m; c++) {
    for (int d = 0; d < 210; d++)
      if (have[c][d] != 0ll) {
        have[c][d] = min(have[c][d], k + 2ll);
        if (A[c + 1] != -1) {
          have[c + 1][d + 1] += have[c][d];
        }
        if (A[c + 1] != 1 and d > 0) {
          have[c + 1][d - 1] += have[c][d];
        }
      }
  }
  return have[n + m][0];
}
int main() {
  scanf("%d%d", &n, &m);
  cin >> k;
  k--;
  for (int c = 0; c < 210; c++) pri[c] = 1000000000;
  for (int c = 1; c <= n; c++)
    for (int d = 1; d <= m; d++) {
      int x;
      scanf("%d", &x);
      pri[c + d] = min(pri[c + d], x);
    }
  for (int c = 2; c <= n + m; c++) inf[c] = c;
  sort(inf + 2, inf + n + m + 1, cmp);
  for (int c = 2; c <= n + m; c++) {
    int p = inf[c];
    A[p] = 1;
    long long r = hm();
    if (k >= r) {
      k -= r;
      A[p] = -1;
    }
  }
  for (int c = 1; c <= n; c++) {
    for (int d = 1; d <= m; d++) {
      if (A[c + d] == 1) printf("(");
      if (A[c + d] == -1) printf(")");
    }
    printf("\n");
  }
  return 0;
}
