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;
const int MAXN = 4e2 + 10;
const int DELTA = 26003;
long long n, m, k, dp[MAXN][MAXN], prio[MAXN], local[MAXN], inp;
char answer[MAXN];
bool cmp(int i, int j) { return local[i] < local[j]; }
int main() {
  ios::sync_with_stdio(0);
  cin >> n >> m >> k;
  const int w = n + m - 1;
  for (int i = 0; i != w; ++i) {
    prio[i] = i;
    local[i] = 1e9;
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cin >> inp;
      local[i + j] = min(local[i + j], inp);
    }
  }
  sort(prio, prio + w, cmp);
  for (int q = 0; q != w; ++q) {
    answer[prio[q]] = '(';
    dp[0][0] = 1;
    for (int i = 1; i <= w; i++) {
      for (int j = 0; j <= w; j++) {
        dp[i][j] = 0;
        if (answer[i - 1] != ')' && j) dp[i][j] += dp[i - 1][j - 1];
        if (answer[i - 1] != '(' && j != w) dp[i][j] += dp[i - 1][j + 1];
        dp[i][j] = min(dp[i][j], (long long)1e18);
      }
    }
    if (dp[w][0] < k) {
      answer[prio[q]] = ')';
      k -= dp[w][0];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cout << answer[i + j];
    }
    cout << endl;
  }
}
