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 node {
  int v, fr;
  node(){};
  node(int a, int b) { v = a, fr = b; }
} C[115 + 115];
long long f[115 + 115][115], K;
int ar[115 + 115], n, m, P[115][115];
inline bool cmp(node a, node b) { return a.v < b.v; }
inline void pluss(long long &p, long long p1) {
  p += p1;
  if (p > 2000000000000000011LL) p = 2000000000000000011LL;
}
int main() {
  int i, j, e, t, k;
  cin >> n >> m >> K;
  for (i = 1; i <= n; ++i)
    for (j = 1; j <= m; ++j) scanf("%d", &P[i][j]);
  for (i = 1; i < n + m; ++i) C[i] = node((~0U >> 1), i);
  for (i = 1; i <= n; ++i)
    for (j = 1; j <= m; ++j) C[i + j - 1].v = min(C[i + j - 1].v, P[i][j]);
  sort(C + 1, C + n + m, cmp);
  for (e = ((n + m) >> 1) + 1, t = 1; t < n + m; ++t) {
    ar[C[t].fr] = 1;
    memset(f, 0, sizeof(f));
    for (f[0][0] = i = 1; i < n + m; ++i) {
      if (ar[i]) {
        k = (ar[i] == 1 ? -1 : 1);
        for (j = 0; j <= e; ++j)
          if (j + k > -1) pluss(f[i][j], f[i - 1][j + k]);
      } else
        for (j = 0; j <= e; ++j) {
          if (j > 0) pluss(f[i][j], f[i - 1][j - 1]);
          pluss(f[i][j], f[i - 1][j + 1]);
        }
    }
    if (f[n + m - 1][0] < K) {
      ar[C[t].fr] = 2;
      K -= f[n + m - 1][0];
    }
  }
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= m; ++j) {
      if (ar[i + j - 1] == 1)
        printf("(");
      else
        printf(")");
    }
    printf("\n");
  }
  return 0;
}
