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 MX = 202;
const long long INF = 1000000000LL * 1000000000LL;
char s[MX];
long long dp[MX][MX];
long long calc(int len) {
  memset(dp, 0, sizeof dp);
  if (s[0] == ')') return 0;
  dp[0][1] = 1;
  for (int i = 1; i < len; i++) {
    for (int x = 0; x < len; x++) {
      if (s[i] != '(') {
        dp[i][x] += dp[i - 1][x + 1];
      }
      if (s[i] != ')' && x) {
        dp[i][x] += dp[i - 1][x - 1];
      }
      dp[i][x] = min(dp[i][x], INF);
    }
  }
  return dp[len - 1][0];
}
int mn[MX];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  long long k;
  cin >> n >> m >> k;
  for (int i = 0; i < n + m - 1; i++) {
    mn[i] = 10000000;
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      int p;
      cin >> p;
      mn[i + j] = min(mn[i + j], p);
    }
  }
  for (int i = 0; i < n + m - 1; i++) {
    int x = -1;
    for (int j = 0; j < n + m - 1; j++) {
      if (!s[j] && (x == -1 || mn[j] < mn[x])) {
        x = j;
      }
    }
    s[x] = '(';
    long long tmp = calc(n + m - 1);
    if (tmp < k) {
      s[x] = ')';
      k -= tmp;
    }
  }
  for (int i = 0; i < n; i++, printf("\n")) {
    for (int j = 0; j < m; j++) {
      printf("%c", s[i + j]);
    }
  }
}
