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>
#pragma comment(linker, "/STACK:65777216")
using namespace std;
int n, m;
long long k;
int d[222];
bool b[222];
bool u[222];
long long r[202][202];
long long calc(int n) {
  memset(r, 0, sizeof(r));
  r[0][0] = 1;
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j <= n; j++) {
      if (u[i - 1]) {
        if (j == 0 && b[i - 1]) continue;
        r[i][j] = r[i - 1][j - (b[i - 1] ? 1 : -1)];
      } else {
        if (j) r[i][j] = r[i - 1][j - 1];
        r[i][j] += r[i - 1][j + 1];
        if (r[i][j] >= k) r[i][j] = k;
      }
    }
  }
  return r[n][0];
}
int main() {
  cin >> n >> m >> k;
  for (int i(0); i < (n + m); i++) d[i] = 1000000;
  for (int i(0); i < (n); i++)
    for (int j(0); j < (m); j++) {
      int x;
      scanf("%d", &x);
      d[i + j] = min(d[i + j], x);
    }
  for (int i(0); i < (n + m - 1); i++) {
    int mn = 1000000, pos = -1;
    for (int j(0); j < (n + m - 1); j++)
      if (!u[j] && d[j] < mn) mn = d[j], pos = j;
    u[pos] = true;
    b[pos] = true;
    long long q = calc(n + m - 1);
    if (q >= k) continue;
    b[pos] = false;
    k -= q;
  }
  for (int i(0); i < (n); i++) {
    for (int j(0); j < (m); j++) printf("%c", b[i + j] ? '(' : ')');
    puts("");
  }
  return 0;
}
