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 int N = 222;
const int INF = 1e6;
const long long INFLL = 1e18;
int n, m, a[N][N], priority[2 * N];
long long k, dp[2 * N][2 * N];
char fix[2 * N];
long long getCnt();
int main() {
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) cin >> a[i][j];
  fill(priority, priority + n + m - 1, INF);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) priority[i + j] = min(priority[i + j], a[i][j]);
  vector<int> fill_order(n + m - 1);
  iota(fill_order.begin(), fill_order.end(), 0);
  sort(fill_order.begin(), fill_order.end(),
       [&](int i, int j) { return priority[i] < priority[j]; });
  fill(fix, fix + n + m - 1, '?');
  for (int diag : fill_order) {
    fix[diag] = '(';
    long long cnt = getCnt();
    if (k > cnt) {
      k -= cnt;
      fix[diag] = ')';
    }
  }
  for (int i = 0; i < n; i++, cout << endl)
    for (int j = 0; j < m; j++) cout << fix[i + j];
}
long long getCnt() {
  memset(dp, 0, sizeof dp);
  if (fix[0] != ')') dp[0][1] = 1;
  for (int ind = 1; ind < n + m - 1; ind++)
    for (int open = 0; open <= ind + 1; open++) {
      switch (fix[ind]) {
        case ')':
          dp[ind][open] = dp[ind - 1][open + 1];
          break;
        case '(':
          if (open > 0) dp[ind][open] = dp[ind - 1][open - 1];
          break;
        case '?':
          dp[ind][open] =
              dp[ind - 1][open + 1] + (open > 0 ? dp[ind - 1][open - 1] : 0);
          break;
      }
      dp[ind][open] = min(dp[ind][open], INFLL);
    }
  return dp[n + m - 2][0];
}
