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;
const int INF = 1 << 29;
const double EPS = 1e-10;
const unsigned long long limit = 1000000000000000010LL;
unsigned long long dp[500][500];
unsigned long long get_num(string &s) {
  int sz = s.size();
  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (int i = 0; i < sz; i++) {
    for (int j = 0; j < sz; j++) {
      if (dp[i][j] == 0) continue;
      if (s[i] == '(') {
        dp[i + 1][j + 1] = min(dp[i + 1][j + 1] + dp[i][j], limit);
      } else if (s[i] == ')') {
        if (j > 0) dp[i + 1][j - 1] = min(dp[i + 1][j - 1] + dp[i][j], limit);
      } else {
        dp[i + 1][j + 1] = min(dp[i + 1][j + 1] + dp[i][j], limit);
        if (j > 0) dp[i + 1][j - 1] = min(dp[i + 1][j - 1] + dp[i][j], limit);
      }
    }
  }
  return dp[sz][0];
}
int main() {
  int n, m, c;
  unsigned long long k;
  int pri[400];
  while (cin >> n >> m >> k) {
    k--;
    int sz = n + m - 1;
    string s(sz, '?');
    vector<pair<int, int> > vp;
    s[0] = '(';
    s[sz - 1] = ')';
    fill(pri, pri + 400, 50000);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) {
        cin >> c;
        pri[i + j] = min(pri[i + j], c);
      }
    for (int i = 0; i < sz; i++) {
      if (i == 0 || i == sz - 1) continue;
      vp.push_back(pair<int, int>(pri[i], i));
    }
    sort(vp.begin(), vp.end());
    for (int turn = 0; turn < sz - 2; turn++) {
      int pos = vp[turn].second;
      s[pos] = '(';
      unsigned long long cnt = get_num(s);
      if (cnt <= k) {
        s[pos] = ')';
        k -= cnt;
      }
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        cout << s[i + j];
      }
      cout << endl;
    }
  }
  return 0;
}
