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 unsigned long long int M = 3e2 + 5, LG = 26, inf = 1e18 + 1,
                             mod = 95542721;
unsigned long long int x, y, k, n;
unsigned long long int dp[M][M];
unsigned long long int vaz[M];
unsigned long long int oly[M];
unsigned long long int c[M];
unsigned long long int calc() {
  for (int i = 0; i < n + 1; i++)
    for (int k = 0; k < M; k++) {
      dp[i][k] = 0;
    }
  dp[0][0] = 1;
  for (int i = 0; i < n; i++)
    for (int k = 1; k < M; k++) {
      if (vaz[i] == 0 || vaz[i] == 1) dp[i + 1][k] += dp[i][k - 1];
      if (vaz[i] == 0 || vaz[i] == 2) dp[i + 1][k - 1] += dp[i][k];
      dp[i + 1][k] = min(dp[i + 1][k], inf);
      dp[i + 1][k] = min(dp[i + 1][k], inf);
    }
  return dp[n][0];
}
int main() {
  ios::sync_with_stdio(0);
  cin >> x >> y >> k;
  n = x + y - 1;
  fill(c, c + n, inf);
  for (int i = 0; i < x; i++)
    for (int j = 0; j < y; j++) {
      unsigned long long int f;
      cin >> f;
      c[i + j] = min(c[i + j], f);
    }
  iota(oly, oly + n, 0);
  sort(oly, oly + n, [](unsigned long long int a, unsigned long long int b) {
    return c[a] < c[b];
  });
  unsigned long long int res = 0;
  for (int ii = 0; ii < n; ii++) {
    unsigned long long int i = oly[ii];
    vaz[i] = 1;
    unsigned long long int f = calc();
    if (res + f < k) {
      res += f;
      vaz[i] = 2;
    }
  }
  for (int i = 0; i < x; i++) {
    for (int j = 0; j < y; j++) {
      cout << (vaz[i + j] == 1 ? '(' : ')');
    }
    cout << '\n';
  }
}
