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 long long maxn = 1e4 + 10;
const long long ZERO = 0;
const long long SADAT = 7.84e-17;
const long long INF = 1e9;
const long long mod = 1e9 + 7;
int q[300];
char r[300];
long double dp[300][300];
int main() {
  int n, m;
  long long t;
  cin >> n >> m >> t;
  memset(q, 63, sizeof(q));
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      int p;
      cin >> p;
      q[i + j] = min(q[i + j], p);
    }
  int l = n + m - 1;
  vector<pair<int, int> > v;
  for (int i = 0; i < l; i++) {
    v.push_back(make_pair(q[i], i));
  }
  sort(v.begin(), v.end());
  --t;
  for (int i = 0; i < l; i++) {
    r[v[i].second] = '(';
    for (int j = 0; j <= l; j++)
      for (int k = 0; k <= l; k++) dp[j][k] = 0;
    dp[0][0] = 1;
    for (int j = 0; j < l; j++) {
      for (int k = 0; k < l; k++) {
        if (r[j] != ')') dp[j + 1][k + 1] += dp[j][k];
        if (r[j] != '(' && k > 0) dp[j + 1][k - 1] += dp[j][k];
      }
    }
    if (dp[l][0] <= t) {
      t -= (long long)dp[l][0];
      r[v[i].second] = ')';
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) cout << r[i + j];
    cout << '\n';
  }
  return (0);
}
