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 inv = 1000000000;
const int minv = -inv;
const long long llinv = numeric_limits<long long>::max() - 10ll;
const int max_m = 110;
const int max_n = 110;
const int max_l = max_m + max_n - 1;
int m, n;
long long k;
int p[max_m][max_n];
int dstp[max_m + max_n - 1];
int atp[max_m + max_n - 1];
pair<int, int> Q[max_m + max_n - 1];
char f[max_m + max_n - 1];
long long dp[max_l + 1][max_l + 1];
int l;
bool valid(int i, int j) {
  int ub = min(i, l - i);
  return (j % 2 == i % 2 and 0 <= j and j <= ub);
}
long long currct;
bool enough() {
  l = m + n - 1;
  dp[0][0] = 1ll;
  for (int i = 1; i <= l; ++i)
    for (int j = i % 2; j <= min(i, l - i); j += 2) {
      long long s1 =
          ((f[i - 1] != ')' and valid(i - 1, j - 1)) ? dp[i - 1][j - 1] : 0ll);
      long long s2 =
          ((f[i - 1] != '(' and valid(i - 1, j + 1)) ? dp[i - 1][j + 1] : 0ll);
      if (llinv - s1 < s2)
        dp[i][j] = llinv;
      else
        dp[i][j] = s1 + s2;
    }
  currct = dp[l][0];
  return (currct >= k);
}
int main() {
  scanf("%d", &m);
  scanf("%d", &n);
  cin >> k;
  for (int d = 0; d < m + n - 1; ++d) dstp[d] = inv;
  for (int i = 0; i < m; ++i)
    for (int j = 0; j < n; ++j) {
      scanf("%d", &p[i][j]);
      --p[i][j];
      dstp[i + j] = min(dstp[i + j], p[i][j]);
    }
  for (int d = 0; d < m + n - 1; ++d) Q[d] = pair<int, int>(dstp[d], d);
  sort(Q, Q + m + n - 1);
  for (int d = 0; d < m + n - 1; ++d) {
    atp[d] = Q[d].second;
  }
  fill(f, f + m + n - 1, '-');
  for (int i = 0; i < m + n - 1; ++i) {
    f[atp[i]] = '(';
    if (not enough()) {
      f[atp[i]] = ')';
      k -= currct;
    }
  }
  for (int i = 0; i < m; ++i) {
    for (int j = 0; j < n; ++j) printf("%c", f[i + j]);
    printf("\n");
  }
  return 0;
}
