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 LINF = ~(((long long)0x1) << 63) / 2;
const int INF = 0X3F3F3F3F;
const double eps = 1e-7;
pair<int, int> p[210];
long long dp[210][210];
int ok[210];
int main() {
  int n, m, i, j, k, s;
  long long lim;
  cin >> n >> m >> lim;
  s = n + m - 1;
  for (i = 0; i <= s; i++) p[i].first = INF;
  for (i = 0; i < n; i++)
    for (j = 0; j < m; j++) {
      scanf("%d", &k);
      p[i + j + 1].first = min(p[i + j + 1].first, k);
      p[i + j + 1].second = i + j + 1;
    }
  sort(p + 1, p + s + 1);
  for (i = 1; i <= s; i++) {
    ok[p[i].second] = 1;
    memset(dp, 0, sizeof(dp));
    dp[0][0] = 1;
    for (j = 1; j <= s; j++)
      for (k = 0; k <= s; k++) {
        if (ok[j] != 1) dp[j][k] += dp[j - 1][k + 1];
        if (ok[j] != 2 && k) dp[j][k] += dp[j - 1][k - 1];
        if (dp[j][k] > lim) dp[j][k] = lim + 1;
      }
    if (dp[s][0] < lim) lim -= dp[s][0], ok[p[i].second] = 2;
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < m; j++) {
      if (ok[i + j + 1] == 1)
        cout << "(";
      else
        cout << ")";
    }
    cout << endl;
  }
  return 0;
}
