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>
char s[200];
long long c[200][400];
long long count(int n, int d) {
  if (n == 0) return d == 0;
  if (c[n][d] == -1) {
    long long cc = 0;
    if (s[n - 1] != ')' && d > 0) cc += count(n - 1, d - 1);
    if (s[n - 1] != '(') cc += count(n - 1, d + 1);
    const long long inf = 1000000000000000000;
    if (cc > inf) cc = inf;
    c[n][d] = cc;
  }
  return c[n][d];
}
int main() {
  int n, m;
  long long k;
  scanf("%d%d%I64d", &n, &m, &k);
  int i, j, p[200];
  memset(p, -1, sizeof(p));
  for (i = 0; i < n; i++)
    for (j = 0; j < m; j++) {
      int pp;
      scanf("%d", &pp);
      pp--;
      if (p[i + j] == -1 || pp < p[i + j]) p[i + j] = pp;
    }
  memset(s, '?', sizeof(s));
  s[m + n - 1] = '\0';
  for (i = 0; i < m + n - 1; i++) {
    int mi = -1;
    for (j = 0; j < m + n - 1; j++)
      if (p[j] != -1)
        if (mi == -1 || p[j] < p[mi]) mi = j;
    p[mi] = -1;
    s[mi] = '(';
    memset(c, -1, sizeof(c));
    long long c = count(m + n - 1, 0);
    if (k > c) {
      k -= c;
      s[mi] = ')';
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < m; j++) putchar(s[i + j]);
    putchar('\n');
  }
  return 0;
}
