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;
char forma[210];
unsigned long long int ways(int n) {
  map<int, unsigned long long int> now, later;
  now[0] = 1;
  for (int i = 0; i < n; i++) {
    later.clear();
    switch (forma[i]) {
      case '*':
        for (map<int, unsigned long long int>::iterator it = now.begin();
             it != now.end(); it++) {
          if (it->first > 0) {
            later[it->first - 1] += it->second;
            if (later[it->first - 1] > (1LL << 60))
              later[it->first - 1] = (1LL << 60);
          }
          later[it->first + 1] += it->second;
          if (later[it->first + 1] > (1LL << 60))
            later[it->first + 1] = (1LL << 60);
        }
        break;
      case '(':
        for (map<int, unsigned long long int>::iterator it = now.begin();
             it != now.end(); it++) {
          later[it->first + 1] += it->second;
          if (later[it->first + 1] > (1LL << 60))
            later[it->first + 1] = (1LL << 60);
        }
        break;
      case ')':
        for (map<int, unsigned long long int>::iterator it = now.begin();
             it != now.end(); it++) {
          if (it->first > 0) {
            later[it->first - 1] += it->second;
            if (later[it->first - 1] > (1LL << 60))
              later[it->first - 1] = (1LL << 60);
          }
        }
        break;
    }
    now = later;
  }
  return now[0];
}
int main() {
  memset(forma, '*', sizeof(forma));
  unsigned long long int n, m, k;
  cin >> n >> m >> k;
  int len = n + m - 2;
  forma[0] = '(';
  forma[len] = ')';
  forma[len + 1] = 0;
  map<int, int> best;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) best[i + j] = n * m + 1000;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      int a;
      cin >> a;
      best[i + j] = min(best[i + j], a);
    }
  vector<pair<int, int> > ord;
  for (int i = 1; i < n + m - 2; i++) ord.push_back(pair<int, int>(best[i], i));
  sort(ord.begin(), ord.end());
  for (int i = 1; i < n + m - 2; i++) {
    forma[ord[i - 1].second] = '(';
    unsigned long long int w = ways(n + m - 1);
    if (w < k) forma[ord[i - 1].second] = ')', k -= w;
  }
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      cout << forma[i + j];
      if (j == m - 1) cout << endl;
    }
  return 0;
}
