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 maxn = 2e2 + 10;
long long a[maxn][maxn];
long long l[maxn];
vector<pair<long long, long long> > vc;
char ans[maxn];
long long dp[maxn][maxn];
int main() {
  long long n, m, k;
  cin >> n >> m >> k;
  fill(l, l + maxn, -1);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cin >> a[i][j];
      l[i + j] = (l[i + j] == -1) ? (a[i][j]) : (min(l[i + j], a[i][j]));
    }
  }
  for (int i = 0; i <= n + m - 2; i++) {
    vc.push_back({l[i], i});
  }
  sort(vc.begin(), vc.end());
  for (int x = 0; x != vc.size(); x++) {
    ans[vc[x].second] = '(';
    memset(dp, 0, sizeof(dp));
    dp[0][0] = 1;
    dp[0][1] = 1;
    for (int i = 0; i != n + m - 1; i++) {
      for (int j = 0; j != n + m - 1; j++) {
        if (ans[i] != ')' && ans[i] != '(') {
          if (j > 0 && i > 0) dp[i][j] += dp[i - 1][j - 1];
          if (dp[i][j] > k) dp[i][j] = k;
          if (i > 0 && j < n + m - 2) dp[i][j] += dp[i - 1][j + 1];
        } else if (ans[i] == ')') {
          if (i > 0 && j < n + m - 2) dp[i][j] += dp[i - 1][j + 1];
        } else {
          if (i > 0 && j > 0) dp[i][j] += dp[i - 1][j - 1];
        }
        if (dp[i][j] > k) dp[i][j] = k;
      }
    }
    if (k > dp[n + m - 2][0]) {
      k -= dp[n + m - 2][0];
      ans[vc[x].second] = ')';
    }
  }
  for (int i = 0; i != n; i++) {
    for (int j = 0; j != m; j++) {
      cout << ans[i + j];
    }
    cout << endl;
  }
}
