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 p[111][111], a[222];
long long dp[222][222];
long long k;
long long q(long long x) {
  if (x > k) {
    return k + 1;
  } else
    return x;
}
long long f(int n, int cur) {
  if (cur < 0) return 0;
  if (n == 0) {
    if (!a[0]) return cur == 1 || cur == -1;
    return cur == a[0];
  }
  if (dp[n][cur + 111] != -1) return dp[n][cur + 111];
  if (!a[n])
    return dp[n][cur + 111] = q(f(n - 1, cur - 1) + f(n - 1, cur + 1));
  else
    return dp[n][cur + 111] = f(n - 1, cur - a[n]);
}
int main() {
  int n, m;
  cin >> n >> m >> k;
  k--;
  vector<pair<int, int> > q;
  for (int i = (0); i <= ((n)-1); i++)
    for (int j = (0); j <= ((m)-1); j++) {
      cin >> p[i][j];
      q.push_back(make_pair(p[i][j], i + j));
    }
  sort((q).begin(), (q).end());
  memset((a), 0, sizeof(a));
  for (int i = (0); i <= (((int)((q).end() - (q).begin())) - 1); i++)
    if (!a[q[i].second]) {
      memset(dp, -1, sizeof(dp));
      a[q[i].second] = 1;
      long long cnt = f(n + m - 2, 0);
      if (cnt <= k) {
        k -= cnt;
        a[q[i].second] = -1;
      } else {
        continue;
      }
    }
  for (int i = (0); i <= ((n)-1); i++) {
    for (int j = (0); j <= ((m)-1); j++)
      if (a[i + j] < 0)
        printf(")");
      else
        printf("(");
    puts("");
  }
  return 0;
}
