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 N = 200 + 77;
const long long inf = 1e18 + 1;
int n, m, p[N][N], t[N];
pair<int, int> a[N];
long long k, dp[N][N];
inline long long Get() {
  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (int i = 1; i <= n + m - 1; i++) {
    for (int j = 0; j <= n + m - 1; j++) {
      if (t[i] == 0) {
        dp[i][j] = dp[i - 1][j + 1];
        if (j > 0) {
          dp[i][j] += dp[i - 1][j - 1];
        }
        dp[i][j] = min(dp[i][j], inf);
        continue;
      }
      if (t[i] == 1) {
        if (j > 0) {
          dp[i][j] += dp[i - 1][j - 1];
        }
        dp[i][j] = min(dp[i][j], inf);
        continue;
      }
      dp[i][j] = dp[i - 1][j + 1];
    }
  }
  return dp[n + m - 1][0];
}
int main() {
  scanf("%d %d %I64d", &n, &m, &k);
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      scanf("%d", &p[i][j]);
    }
  }
  for (int i = 1; i <= n + m - 1; i++) {
    a[i].first = n * m;
    a[i].second = i;
    for (int j = 1; j <= n + m - 1; j++) {
      if (j > i || j > n || i - j + 1 > m) {
        continue;
      }
      a[i].first = min(a[i].first, p[j][i - j + 1]);
    }
  }
  sort(a + 1, a + n + m);
  for (int i = 1; i <= n + m - 1; i++) {
    t[a[i].second] = 1;
    long long g = Get();
    if (g < k) {
      t[a[i].second] = 2;
      k -= g;
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      if (t[i + j - 1] == 1) {
        printf("(");
      } else {
        printf(")");
      }
    }
    printf("\n");
  }
  return 0;
}
