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;
int n, m;
long long k;
struct p {
  int x, y;
};
int c[100][100], f[200];
long long g[300][300];
p a[200];
int min(int o, int p) {
  if (o < p) return o;
  return p;
}
bool cmp(p a, p b) {
  if (a.x < b.x) {
    return true;
  }
  return false;
}
long long work(int o) {
  f[o] = 0;
  memset(g, 0, sizeof(g));
  g[0][1] = 1;
  bool u = true;
  for (int i = 1; i <= n + m - 2; i++)
    if (f[i] < 0) {
      for (int j = 0; j <= n + m - 2; j++) {
        if (j > 0) g[i][j] += g[i - 1][j - 1];
        if (g[i][j] >= k) g[i][j] = k;
        if (j < n + m - 2) g[i][j] += g[i - 1][j + 1];
        if (g[i][j] >= k) g[i][j] = k;
      }
    } else {
      if (f[i] == 0) {
        for (int j = 1; j <= n + m - 2; j++) g[i][j] = g[i - 1][j - 1];
      } else {
        for (int j = 0; j < n + m - 2; j++) g[i][j] = g[i - 1][j + 1];
      }
    }
  f[o] = -1;
  return g[n + m - 2][0];
}
int main() {
  cin >> n >> m >> k;
  for (int i = 0; i <= n + m - 2; i++) {
    a[i].x = n * m + 100;
    a[i].y = i;
    f[i] = -1;
  }
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      scanf("%d", &c[i][j]);
      a[i + j].x = min(a[i + j].x, c[i][j]);
    }
  sort(a, a + n + m - 1, cmp);
  f[0] = 0;
  f[n + m - 2] = 1;
  for (int i = 0; i <= n + m - 2; i++)
    if (f[a[i].y] < 0) {
      long long tmp = work(a[i].y);
      if (tmp < k) {
        k -= tmp;
        f[a[i].y] = 1;
      } else {
        f[a[i].y] = 0;
      }
    }
  char ch[200][200];
  memset(ch, 0, sizeof(ch));
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++)
      if (f[i + j] == 0) {
        ch[i][j] = '(';
      } else {
        ch[i][j] = ')';
      }
  for (int i = 0; i < n; i++) printf("%s\n", ch[i]);
  return 0;
}
