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;
int c[110][110];
char ans[2 * 110];
long long d[2 * 110][110];
long long k;
long long get_count() {
  memset(d, 0, sizeof(d));
  d[1][0] = 1;
  for (int i = 2; i <= n + m - 1; i++)
    for (int j = 0; j <= i / 2; j++) {
      if (ans[i] == 0)
        d[i][j] = min(1000000000000000000LL, d[i - 1][j - 1] + d[i - 1][j]);
      else {
        if (ans[i] == '(')
          d[i][j] = d[i - 1][j];
        else
          d[i][j] = d[i - 1][j - 1];
      }
    }
  return d[n + m - 1][(n + m) / 2];
}
void solve() {
  for (int i = 1; i <= n * m; i++) {
    int pos = 0;
    for (int p = 1; p <= n; p++) {
      for (int q = 1; q <= m; q++)
        if (c[p][q] == i) {
          pos = p + q - 1;
          break;
        }
      if (pos) break;
    }
    if (ans[pos] == 0) {
      ans[pos] = '(';
      long long aux = get_count();
      if (aux < k) {
        k -= aux;
        ans[pos] = ')';
      }
    }
  }
}
int main() {
  cin >> n >> m >> k;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= m; j++) cin >> c[i][j];
  solve();
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) cout << ans[i + j - 1];
    cout << "\n";
  }
  return 0;
}
