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 maxn = 100 + 9;
const long long M = 1e9 + 7;
const long long I = 1e9, II = 1e18 + 1;
pair<int, int> mn[maxn * 2];
long long dp[maxn * 2][maxn * 2];
int c[maxn][maxn], cur[maxn * 2];
long long k;
int n, m;
int f(int x, int y) {
  if (y == -1) return 1;
  if (y == 1 && x == 1) return 1;
  if (y == 0 && x == 0) return 1;
  return 0;
}
void cal() {
  memset(dp, 0, sizeof dp);
  dp[0][0] = 1;
  for (int i = 1; i < n + m; i++) {
    dp[i][0] = dp[i - 1][1] * f(0, cur[i - 1]);
    for (int t = 1; t <= i; t++) {
      dp[i][t] = dp[i - 1][t - 1] * f(1, cur[i - 1]) +
                 dp[i - 1][t + 1] * f(0, cur[i - 1]);
      if (dp[i][t] >= II) dp[i][t] = II;
    }
  }
  return;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  for (int i = 0; i < maxn * 2; i++) {
    mn[i].first = I;
    mn[i].second = i;
    cur[i] = -1;
  }
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++)
    for (int t = 0; t < m; t++) {
      cin >> c[i][t];
      mn[i + t].first = min(mn[i + t].first, c[i][t]);
    }
  sort(mn, mn + n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    cur[mn[i].second] = 1;
    cal();
    if (dp[n + m - 1][0] >= k) continue;
    k -= dp[n + m - 1][0];
    cur[mn[i].second] = 0;
  }
  for (int i = 0; i < n; i++) {
    for (int t = 0; t < m; t++) cout << ((cur[i + t]) ? "(" : ")");
    cout << "\n";
  }
}
