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;
long long f[202][202];
int main() {
  int n, m;
  long long k;
  while (cin >> n >> m >> k) {
    int l = n + m - 1;
    vector<int> a(202), d(202);
    for (int i = 0; i < l; i++) {
      a[i] = n * m;
      d[i] = i;
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        int x;
        cin >> x;
        if (a[i + j] > x) {
          a[i + j] = x;
        }
      }
    }
    sort(begin(d), begin(d) + l,
         [&a](const int& i, const int& j) { return a[i] < a[j]; });
    string s = string(202, '\0');
    memset(f, 0, sizeof f);
    for (int I = 0; I < l; I++) {
      s[d[I]] = '(';
      f[0][0] = 1;
      for (int i = 0; i < l; i++) {
        for (int j = i & 1; j <= i && j <= l - i; j += 2) {
          if (f[i][j]) {
            if (f[i][j] > k) {
              f[i][j] = k;
            }
            if (s[i] != ')') {
              f[i + 1][j + 1] += f[i][j];
            }
            if (s[i] != '(' && j) {
              f[i + 1][j - 1] += f[i][j];
            }
            f[i][j] = 0;
          }
        }
      }
      if (k > f[l][0]) {
        k -= f[l][0];
        s[d[I]] = ')';
      }
      f[l][0] = 0;
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        cout << s[i + j];
      }
      cout << "\n";
    }
  }
}
