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;
char s[2 * 110], m[110][110];
long long d[2 * 110][2 * 110];
int a[110 * 110], u[2 * 110], n;
long long get() {
  int i, j;
  for (i = 0; i <= n; i++)
    for (j = 0; j <= n; d[i][j] = 0, j++)
      ;
  d[0][0] = 1;
  for (i = 0; i < n; i++)
    for (j = 0; j <= i; j++) {
      if (d[i][j] > 2000000000000000000ll) d[i][j] = 2000000000000000000ll;
      if (s[i] == '(')
        d[i + 1][j + 1] += d[i][j];
      else if (s[i] == ')') {
        if (j > 0) d[i + 1][j - 1] += d[i][j];
      } else {
        d[i + 1][j + 1] += d[i][j];
        if (j > 0) d[i + 1][j - 1] += d[i][j];
      }
    }
  return d[n][0];
}
int main() {
  int i, j, r, c, p, l;
  long long k;
  scanf("%d%d%lld", &r, &c, &k);
  k--;
  for (i = 0; i < r; i++)
    for (j = 0; j < c; scanf("%d", &p), a[p - 1] = i * c + j, j++)
      ;
  n = r + c - 1;
  for (l = 0; l < r * c; l++) {
    i = a[l] / c;
    j = a[l] % c;
    if (u[i + j]) continue;
    u[i + j] = 1;
    s[i + j] = '(';
    long long t = get();
    if (k >= t) {
      k -= t;
      s[i + j] = ')';
    }
  }
  for (i = 0; i < r; printf("%s\n", m[i]), i++)
    for (j = 0; j < c; m[i][j] = s[i + j], j++)
      ;
  return 0;
}
