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 _10p18 = 1000000000;
long long n, m, p[110][110], P[2 * 110];
long long k;
vector<pair<long long, long long> > vp;
long long res[2 * 110];
long long f[2 * 110][110];
long long ololo() {
  memset(f, 0, sizeof(long long) * 2 * 110 * 110);
  f[0][1] = 1;
  for (int j = 0; j < n + m - 2; j++) {
    for (int i = 0; i < 110 - 1; i++) {
      if (f[j][i] == 0) continue;
      if (res[j + 1] == 1 || res[j + 1] == 0)
        f[j + 1][i + 1] = min(f[j + 1][i + 1] + f[j][i], _10p18);
      if ((res[j + 1] == 2 || res[j + 1] == 0) && i - 1 >= 0)
        f[j + 1][i - 1] = min(f[j + 1][i - 1] + f[j][i], _10p18);
    }
  }
  return f[n + m - 2][0];
}
int main() {
  _10p18 *= _10p18;
  _10p18 += 20;
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cin >> p[i][j];
      if (P[i + j] == 0)
        P[i + j] = p[i][j];
      else
        P[i + j] = min(P[i + j], p[i][j]);
    }
  }
  for (int i = 0; i < n + m - 1; i++) vp.push_back(make_pair(P[i], i));
  sort(vp.begin(), vp.end());
  for (int i = 0; i < vp.size(); i++) {
    res[vp[i].second] = 1;
    long long x;
    if (k > (x = ololo())) {
      k -= x;
      res[vp[i].second] = 2;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      if (res[i + j] == 1)
        cout << '(';
      else
        cout << ')';
    }
    cout << endl;
  }
  return 0;
}
