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 = 101;
int n, m;
long long K;
char c[M * 2];
struct Prior {
  int i, minval;
} p[M * 2];
void inc(long long& x, long long y) {
  x += y;
  if (x > K) x = K;
}
long long cal() {
  long long dp[2][M] = {0};
  dp[0][0] = 1;
  for (int i = 1; i <= n + m - 1; i++) {
    int now = i & 1, pre = 1 - now;
    memset(dp[now], 0, sizeof dp[now]);
    for (int j = 0; j <= (n + m - 1) / 2; j++) {
      if (c[i] != ')' && j > 0) inc(dp[now][j], dp[pre][j - 1]);
      if (c[i] != '(' && j + 1 <= (n + m - 1) / 2)
        inc(dp[now][j], dp[pre][j + 1]);
    }
  }
  return dp[(n + m - 1) & 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++) {
      int x;
      scanf("%d", &x);
      if (p[i + j - 1].minval == 0 || p[i + j - 1].minval > x) {
        p[i + j - 1].minval = x;
      }
      p[i + j - 1].i = i + j - 1;
    }
  }
  sort(p + 1, p + n + m, [&](Prior a, Prior b) { return a.minval < b.minval; });
  for (int i = 1; i <= n + m - 1; i++) {
    int pos = p[i].i;
    c[pos] = '(';
    long long num = cal();
    if (num < K) {
      c[pos] = ')';
      K -= num;
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      printf("%c", c[i + j - 1]);
    }
    puts("");
  }
}
