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;
const long long inf = (long long)(1e18) + 1;
int p[100][100], ans[100 + 100], x[100 * 100], y[100 * 100], n, m;
long long res[200][100];
void sum(long long& a, long long b) { a = min(inf, a + b); }
long long calc() {
  int maxb = (n + m - 1) / 2;
  for (int i = 0; i < n + m; ++i)
    for (int b = 0; b <= min(i, maxb); ++b) res[i][b] = 0;
  res[0][0] = 1;
  for (int i = 0; i < n + m - 1; ++i)
    for (int b = 0; b <= min(i, maxb); ++b)
      if (res[i][b] > 0) {
        if (ans[i] >= 0) sum(res[i + 1][b + 1], res[i][b]);
        if ((ans[i] <= 0) && (b > 0)) sum(res[i + 1][b - 1], res[i][b]);
      }
  return res[n + m - 1][0];
}
int main() {
  long long k;
  cin >> n >> m >> k;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < m; ++j) {
      cin >> p[i][j];
      p[i][j]--;
      x[p[i][j]] = i, y[p[i][j]] = j;
    }
  for (int i = 0; i < n * m; ++i) {
    if (ans[x[i] + y[i]] != 0) continue;
    ans[x[i] + y[i]] = 1;
    long long tmp = calc();
    if (tmp >= k) continue;
    ans[x[i] + y[i]] = -1;
    k -= tmp;
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j)
      if (ans[i + j] == 1)
        printf("%c", '(');
      else
        printf("%c", ')');
    printf("\n");
  }
  return 0;
}
