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 oo = 2000000009;
const double eps = 1e-9;
const int mx = 202;
int pr[mx], n, m;
int ans[mx], tot;
long long dp[mx][mx];
long long k;
long long solve(int sum, int i) {
  if (sum < 0) return 0;
  if (i == tot) return (sum == 0);
  long long &ret = dp[sum][i];
  if (ret != -1) return ret;
  ret = 0;
  if (ans[i]) return ret = solve(sum + ans[i], i + 1);
  unsigned long long tmp = solve(sum - 1, i + 1) + solve(sum + 1, i + 1);
  if (tmp > k)
    ret = k;
  else
    ret = tmp;
  return ret;
}
int main() {
  cin >> n >> m >> k;
  tot = n + m - 1;
  for (int i = 0; i < (tot); ++i) pr[i] = oo;
  for (int i = 0; i < (n); ++i) {
    int x;
    for (int j = 0; j < (m); ++j) {
      scanf("%d", &x);
      pr[i + j] = min(pr[i + j], x);
    }
  }
  vector<pair<int, int> > v;
  for (int i = 0; i < (tot); ++i) v.push_back(make_pair(pr[i], i));
  sort((v).begin(), (v).end());
  for (int i = 0; i < (tot); ++i) {
    for (int j = 0; j < (2); ++j) {
      ans[v[i].second] = j ? -1 : 1;
      memset(dp, -1, sizeof(dp));
      long long tmp = solve(0, 0);
      ;
      if (tmp >= k) break;
      k -= tmp;
    }
  }
  for (int i = 0; i < (n); ++i) {
    for (int j = 0; j < (m); ++j) printf("%c", ans[i + j] == -1 ? ')' : '(');
    printf("\n");
  }
  return 0;
}
