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 M = 100 + 10;
long long int MAX = 1e+18;
int a[M][M];
struct NODE {
  int index;
  int value;
  bool operator<(const NODE& x) const { return value < x.value; }
} b[2 * M];
char s[2 * M];
long long int dp[2 * M][2 * M];
long long int cal(string s, int len) {
  dp[0][0] = 1;
  for (int i = 0; i < len; i++) {
    for (int j = 0; j <= i; j++) {
      if (dp[i][j] > 0) {
        if (s[i] == '?') {
          dp[i + 1][j + 1] = dp[i][j] + dp[i + 1][j + 1];
          if (j - 1 >= 0) {
            dp[i + 1][j - 1] += dp[i][j];
          }
        }
        if (s[i] == '(') {
          dp[i + 1][j + 1] = dp[i][j] + dp[i + 1][j + 1];
        }
        if (s[i] == ')') {
          if (j - 1 >= 0) {
            dp[i + 1][j - 1] += dp[i][j];
          }
        }
        if (dp[i + 1][j + 1] > MAX) {
          dp[i + 1][j + 1] = MAX;
        }
        if (j - 1 >= 0) {
          if (dp[i + 1][j - 1] > MAX) {
            dp[i + 1][j - 1] = MAX;
          }
        }
      }
    }
  }
  return dp[len][0];
}
int main() {
  int n, m;
  long long int k;
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cin >> a[i][j];
    }
  }
  int len = n + m - 1;
  for (int i = 0; i < len; i++) {
    int min_v = n * m + 100;
    for (int r = 0; r <= i; r++) {
      if (r < n && i - r < m && a[r][i - r] < min_v) {
        min_v = a[r][i - r];
      }
    }
    b[i].value = min_v;
    b[i].index = i;
  }
  sort(b, b + len);
  for (int i = 0; i < len; i++) {
    s[i] = '?';
  }
  for (int i = 0; i < len; i++) {
    for (int r = 0; r < 2 * M; r++) {
      for (int rr = 0; rr < 2 * M; rr++) {
        dp[r][rr] = 0;
      }
    }
    s[b[i].index] = '(';
    long long int num = cal(s, len);
    if (num < k) {
      k -= num;
      s[b[i].index] = ')';
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cout << s[i + j];
    }
    cout << endl;
  }
  return 0;
}
