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 = 2e3;
const int MV = 1e5;
const int MOD = 1e9 + 7;
const long long INF = 4e18;
int MA = -INF, MI = INF, ANS;
long long n, m, k;
long long arr[MAX + 10][MAX + 10], ans[MAX + 10];
long long lab[MAX + 10], dp[MAX + 10][MAX + 10];
pair<long long, long long> tmp[MAX + 10];
void fil() {
  dp[m + n - 1][0] = 1;
  for (int i = m + n - 2; i >= 1; i--) {
    for (int j = 0; j <= i; j++) {
      if (ans[i + 1] == 0)
        dp[i][j] = dp[i + 1][j - 1] + dp[i + 1][j + 1];
      else if (ans[i + 1] == 1)
        dp[i][j] = dp[i + 1][j + 1];
      else
        dp[i][j] = dp[i + 1][j - 1];
      dp[i][j] = min(dp[i][j], INF);
    }
  }
}
int32_t main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  for (int i = 0; i <= MAX; i++) lab[i] = INF;
  cin >> n >> m >> k;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      cin >> arr[i][j];
      lab[i + j - 1] = min(lab[i + j - 1], arr[i][j]);
    }
  }
  for (int i = 1; i <= n + m - 1; i++) tmp[i] = {lab[i], i};
  sort(tmp + 1, tmp + n + m);
  for (int i = 1; i <= n + m - 1; i++) {
    ans[tmp[i].second] = 1, fil();
    if (dp[1][1] >= k)
      continue;
    else
      ans[tmp[i].second] = 2, k -= dp[1][1];
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      if (ans[i + j - 1] == 1)
        cout << "(";
      else
        cout << ")";
    }
    cout << "\n";
  }
  return 0;
}
