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;
struct unit {
  int x, y, w;
};
struct unit a[10010];
int n, m, n1;
int c[210];
long long f[210][210];
long long k, inf = 1e18;
bool cmp(struct unit aa, struct unit bb) { return aa.w < bb.w; }
long long calc() {
  int i, j;
  long long ret;
  f[1][0] = 1;
  for (i = 2; i <= n + m; i++)
    for (j = 0; j <= min(i - 2 + 1, n + m - i); j++) {
      f[i][j] = 0;
      if (c[i] == -1) {
        if (j > 0) f[i][j] += f[i - 1][j - 1];
        f[i][j] += f[i - 1][j + 1];
      } else if (c[i] == 0) {
        if (j > 0) f[i][j] += f[i - 1][j - 1];
      } else if (c[i] == 1)
        f[i][j] += f[i - 1][j + 1];
      if (f[i][j] > inf) f[i][j] = inf;
    }
  ret = f[n + m][0];
  return ret;
}
int main() {
  int i, j;
  long long s;
  cin >> n >> m >> k;
  for (i = 1; i <= n; i++)
    for (j = 1; j <= m; j++) {
      a[(i - 1) * m + j].x = i;
      a[(i - 1) * m + j].y = j;
      cin >> a[(i - 1) * m + j].w;
    }
  sort(a + 1, a + n * m + 1, cmp);
  memset(c, -1, sizeof(c));
  for (i = 1; i <= n * m; i++)
    if (c[a[i].x + a[i].y] != -1)
      continue;
    else {
      c[a[i].x + a[i].y] = 0;
      s = calc();
      if (s < k) {
        c[a[i].x + a[i].y] = 1;
        k -= s;
      }
    }
  for (i = 1; i <= n; i++) {
    for (j = 1; j <= m; j++)
      if (c[i + j] == 0)
        printf("(");
      else
        printf(")");
    printf("\n");
  }
  return 0;
}
