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>
const int MAXN = 110;
const long long MAX = 1e18 + 10;
using namespace std;
int n, m;
int c[MAXN][MAXN], vet[MAXN * 2], idx[MAXN * MAXN], calculado[MAXN * 2],
    resp[MAXN][MAXN];
long long k, dp[MAXN * 2][MAXN * 2];
long long findDp(int ind, int soma) {
  if (soma < 0) return 0LL;
  if (ind == n + m) return (soma == 0) ? 1LL : 0LL;
  if (dp[ind][soma] != -1) return dp[ind][soma];
  if (calculado[ind])
    return dp[ind][soma] = findDp(ind + 1, soma + calculado[ind]);
  return dp[ind][soma] =
             min(1LL * (findDp(ind + 1, soma + 1) + findDp(ind + 1, soma - 1)),
                 MAX);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> m >> k;
  for (int i = 1; i < n + 1; i++)
    for (int j = 1; j < m + 1; j++) cin >> c[i][j];
  for (int i = 1; i < n + m; i++) {
    int x = min(i, n), y = 1;
    if (i > n) y = i - n + 1;
    vet[i] = MAXN * MAXN;
    for (int nx = x, ny = y; ny <= m; nx--, ny++) {
      if (nx <= 0) break;
      vet[i] = min(vet[i], c[nx][ny]);
    }
    idx[vet[i]] = i;
  }
  long long tot = 0;
  for (int i = 1; i < n * m + 1; i++) {
    if (idx[i] == 0) continue;
    memset(dp, -1, sizeof dp);
    calculado[idx[i]] = 1;
    long long temp = findDp(1, 0);
    if (tot + temp < k) {
      calculado[idx[i]] = -1;
      tot += temp;
    }
  }
  for (int i = 1; i < n + m; i++) {
    int x = min(i, n), y = 1;
    if (i > n) y = i - n + 1;
    for (int nx = x, ny = y; ny <= m; nx--, ny++) {
      if (nx <= 0) break;
      resp[nx][ny] = calculado[i];
    }
  }
  for (int i = 1; i < n + 1; i++) {
    for (int j = 1; j < m + 1; j++) printf("%c", (resp[i][j] == 1) ? '(' : ')');
    printf("\n");
  }
}
