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;
long long inf = 1100000000000000000LL;
long long dp[210][210];
string s = "(";
int ma[210][210];
int n, m;
long long cal(void) {
  int i, j;
  for (i = 0; i < 210; i++)
    for (j = 0; j < 210; j++) dp[i][j] = 0;
  dp[0][0] = 1;
  for (i = 0; i < n + m - 1; i++)
    for (j = 0; j < i + 1; j++) {
      if (s[i] != '(' && j > 0)
        dp[i + 1][j - 1] = min(inf, dp[i + 1][j - 1] + dp[i][j]);
      if (s[i] != ')') dp[i + 1][j + 1] = min(inf, dp[i + 1][j + 1] + dp[i][j]);
    }
  return dp[n + m - 1][0];
}
int main() {
  int i, j;
  long long k;
  cin >> n >> m >> k;
  char out[210][210];
  vector<pair<int, int> > pri;
  if ((n + m) % 2 < 1) return 0;
  for (i = 0; i < n; i++)
    for (j = 0; j < m; j++) scanf("%d", &ma[i][j]);
  for (i = 1; i < n + m - 2; i++) {
    int mi = 11000;
    for (j = 0; j < n; j++) {
      if (i - j < 0 || i - j >= m) continue;
      mi = min(mi, (ma[j][i - j]));
    }
    pri.push_back(make_pair(mi, i));
  }
  sort(pri.begin(), pri.end());
  for (i = 0; i < n + m - 3; i++) s += " ";
  s += ")";
  if (cal() < k) return 0;
  for (i = 0; i < n + m - 3; i++) {
    int t = pri[i].second;
    s[t] = '(';
    long long ka = cal();
    if (ka < k) {
      k -= ka;
      s[t] = ')';
    }
  }
  for (i = 0; i < m + n - 1; i++)
    for (j = 0; j < n; j++) {
      if (i - j < 0 || i - j >= m) continue;
      out[j][i - j] = s[i];
    }
  for (i = 0; i < n; i++) {
    for (j = 0; j < m; j++) cout << out[i][j];
    cout << endl;
  }
  return 0;
}
