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 INF = 2147483647;
const long long LLINF = 9223372036854775807LL;
const int maxn = 210;
pair<int, int> p[maxn];
int a[maxn] = {};
long long dp[maxn][maxn] = {};
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  long long k;
  cin >> k;
  k--;
  long long cinf = 1000000000000000009;
  int len = n + m - 1;
  for (int i = 0; i < len; ++i) p[i] = make_pair(10000000, i);
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < m; ++j) {
      int cur;
      scanf("%d", &cur);
      p[i + j].first = min(p[i + j].first, cur);
    }
  sort(p, p + len);
  memset(a, -1, sizeof(a));
  for (int i = 0; i < len; ++i) {
    dp[0][0] = 1;
    a[p[i].second] = 1;
    for (int proc = 1; proc <= len; ++proc) {
      for (int bal = 0; bal <= proc; ++bal) {
        dp[proc][bal] = 0;
        if (a[proc - 1] != 2 && bal != 0) {
          dp[proc][bal] += dp[proc - 1][bal - 1];
        }
        if (a[proc - 1] != 1) dp[proc][bal] += dp[proc - 1][bal + 1];
        dp[proc][bal] = min(dp[proc][bal], cinf);
      }
    }
    if (dp[len][0] <= k) {
      k -= dp[len][0];
      a[p[i].second] = 2;
    }
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      putchar(a[i + j] == 1 ? '(' : ')');
    }
    printf("\n");
  }
  return 0;
}
