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 MAX = 110;
const int INF = 1000000001;
int tab[MAX + 1][MAX + 1];
pair<int, int> per[MAX * MAX];
unsigned long long dp[MAX + MAX][MAX + MAX];
int out[MAX + MAX];
int n, m;
unsigned long long k;
bool cmp(const pair<int, int> &lhs, const pair<int, int> &rhs) {
  return tab[lhs.first][lhs.second] < tab[rhs.first][rhs.second];
}
unsigned long long solve(int x, int y, int c) {
  --x, --y;
  out[x + y] = c;
  for (int i = 0; i <= n + m - 2; ++i)
    for (int t = 0; t < i + 2; ++t) {
      dp[i][t] = 0;
      if (out[i] == 1)
        dp[i][t] = (t && i ? dp[i - 1][t - 1] : 0);
      else if (out[i] == -1)
        dp[i][t] = dp[i - 1][t + 1];
      else
        dp[i][t] = (t && i ? dp[i - 1][t - 1] : 0) + (dp[i - 1][t + 1]);
      if (i == 0 && t == 1) dp[i][t] = 1;
      if (dp[i][t] > k) dp[i][t] = k + 1;
    }
  return dp[n + m - 2][0];
}
int main(int argc, char *argv[]) {
  ios_base::sync_with_stdio(0);
  cin >> n >> m >> k;
  --k;
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= m; ++j) {
      per[(i - 1) * m + j - 1] = make_pair(i, j);
      cin >> tab[i][j];
    }
  sort(per, per + n * m, cmp);
  solve(1, 1, 1);
  for (int i = 0; i < n * m; ++i)
    if (out[per[i].first + per[i].second - 2] == 0) {
      unsigned long long t = solve(per[i].first, per[i].second, 1);
      if (t <= k) {
        k -= t;
        solve(per[i].first, per[i].second, -1);
      }
    }
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= m; ++j) cout << (out[i + j - 2] == 1 ? '(' : ')');
    cout << endl;
  }
  return 0;
}
