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 MAX = 1e9;
void out(vector<int> v) {
  for (int i = 0; i < v.size(); ++i) cout << v[i] << " ";
  cout << endl;
}
long long f(const vector<int>& res) {
  vector<vector<long long> > dyn(res.size(), vector<long long>(res.size()));
  if (res[0] != 1) dyn[0][1] = 1;
  for (int i = 0; i + 1 < res.size(); ++i) {
    for (int j = 0; j < res.size(); ++j) dyn[i][j] = min(dyn[i][j], MAX);
    if (res[i + 1] != 1) dyn[i + 1][1] += dyn[i][0];
    for (int j = 1; j < res.size(); ++j) {
      if (res[i + 1] != 1 && j + 1 < res.size()) dyn[i + 1][j + 1] += dyn[i][j];
      if (res[i + 1] != 0) dyn[i + 1][j - 1] += dyn[i][j];
    }
  }
  return dyn.back()[0];
}
int main() {
  MAX *= MAX + 1;
  long long n, m, k;
  cin >> n >> m >> k;
  vector<int> p(n + m - 1, 1e8);
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < m; ++j) {
      int t;
      cin >> t;
      p[i + j] = min(t, p[i + j]);
    }
  vector<pair<int, int> > ord(p.size());
  for (int i = 0; i < ord.size(); ++i) ord[i] = pair<int, int>(p[i], i);
  sort(ord.begin(), ord.end());
  vector<int> res(n + m - 1, -1);
  --k;
  for (int it = 0; it < ord.size(); ++it) {
    res[ord[it].second] = 0;
    long long cnt = f(res);
    if (cnt == 0) {
      res[ord[it].second] = 1;
    } else {
      if (cnt <= k) {
        k -= cnt;
        res[ord[it].second] = 1;
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      if (res[i + j])
        printf(")");
      else
        printf("(");
    }
    cout << endl;
  }
  return 0;
}
