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 long long MARSHAL = 1000000000000000000LL;
int N, M, X;
long long K;
int prio[300];
pair<int, int> irvan[300];
char res[300];
long long dp[300][300];
long long solve() {
  memset(dp, 0, sizeof(dp));
  dp[X][0] = 1;
  for (int i = X - 1; i >= 0; i--)
    for (int j = 0; j <= X; j++) {
      if ((!res[i] || res[i] == '(') && j < X) dp[i][j] += dp[i + 1][j + 1];
      if ((!res[i] || res[i] == ')') && j > 0) dp[i][j] += dp[i + 1][j - 1];
      if (dp[i][j] >= MARSHAL) dp[i][j] = MARSHAL;
    }
  return dp[0][0];
}
int main() {
  cin >> N >> M >> K;
  X = N + M - 1;
  for (int i = 0; i < (int)X; i++) prio[i] = N * M;
  for (int i = 0; i < (int)N; i++)
    for (int j = 0; j < (int)M; j++) {
      int x;
      cin >> x;
      prio[i + j] = min(prio[i + j], x);
    }
  for (int i = 0; i < (int)X; i++) irvan[i] = make_pair(prio[i], i);
  sort(irvan, irvan + X);
  K--;
  for (int i = 0; i < (int)X; i++) {
    int pos = irvan[i].second;
    res[pos] = '(';
    long long jahja = solve();
    if (K >= jahja) {
      K -= jahja;
      res[pos] = ')';
    }
  }
  for (int i = 0; i < (int)N; i++) {
    for (int j = 0; j < (int)M; j++) printf("%c", res[i + j]);
    printf("\n");
  }
}
