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;
int row, col;
int val[300];
long long batas = 2000000000000000000LL;
long long dp[210][210];
long long Solve(string str) {
  for (int(i) = 0; (i) < (210); ++(i))
    for (int(j) = 0; (j) < (210); ++(j)) dp[i][j] = 0;
  dp[0][0] = 1LL;
  for (int i = 0; i < ((int)str.size()); ++i) {
    for (int(j) = 0; (j) < (205); ++(j)) {
      if (!dp[i][j]) continue;
      if (str[i] != ')') {
        dp[i + 1][j + 1] = min(dp[i + 1][j + 1] + dp[i][j], batas);
      }
      if (str[i] != '(' && j) {
        dp[i + 1][j - 1] = min(dp[i + 1][j - 1] + dp[i][j], batas);
      }
    }
  }
  return dp[((int)str.size())][0];
}
int main() {
  long long k;
  cin >> row >> col >> k;
  --k;
  for (int(i) = 0; (i) < (300); ++(i)) val[i] = -1;
  vector<pair<int, pair<int, int> > > pri;
  for (int(i) = 0; (i) < (row); ++(i))
    for (int(j) = 0; (j) < (col); ++(j)) {
      int p;
      cin >> p;
      pri.push_back(make_pair(p, make_pair(i, j)));
    }
  sort(pri.begin(), pri.end());
  for (int(i) = 0; (i) < (((int)pri.size())); ++(i)) {
    int x = pri[i].second.first + pri[i].second.second;
    if (val[x] != -1) continue;
    val[x] = 0;
    string str;
    for (int(j) = 0; (j) < (row + col - 1); ++(j)) {
      if (val[j] == -1) {
        str += "?";
      } else if (val[j] == 0) {
        str += "(";
      } else {
        str += ")";
      }
    }
    long long itu = Solve(str);
    if (itu <= k) {
      k -= itu;
      val[x] = 1;
    }
  }
  for (int(r) = 0; (r) < (row); ++(r)) {
    for (int(c) = 0; (c) < (col); ++(c)) {
      if (val[r + c] == 0) {
        cout << "(";
      } else {
        cout << ")";
      }
    }
    cout << endl;
  }
  return 0;
}
