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;
int L;
int priority[2 * 105];
char answer[2 * 105];
bool compare_by_priority(int a, int b) { return priority[a] < priority[b]; }
long long count() {
  long long save[2 * 105][2 * 105];
  memset(save, 0, sizeof(save));
  save[0][0] = 1;
  for (int size = 1; size <= L; size++) {
    for (int diff = 0; diff <= size; diff++) {
      if (answer[size - 1] != ')' && diff != 0)
        save[size][diff] += save[size - 1][diff - 1];
      if (answer[size - 1] != '(' && diff != size)
        save[size][diff] += save[size - 1][diff + 1];
      save[size][diff] = min(save[size][diff], 1000000000000000000LL);
    }
  }
  return save[L][0];
}
int main() {
  int N, M;
  long long K;
  scanf("%d %d %I64d\n", &N, &M, &K);
  L = N + M - 1;
  for (int i = 0; i < L; i++) priority[i] = INT_MAX;
  for (int i = 0; i < N; i++)
    for (int j = 0; j < M; j++) {
      int p;
      scanf("%d", &p);
      priority[i + j] = min(priority[i + j], p);
    }
  vector<int> order;
  for (int i = 0; i < L; i++) order.push_back(i);
  sort(order.begin(), order.end(), compare_by_priority);
  long long total = 0;
  for (int i = 0; i < L; i++) {
    answer[order[i]] = '(';
    long long c = count();
    if (K <= total + c)
      continue;
    else {
      answer[order[i]] = ')';
      total += c;
    }
  }
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < M; j++) printf("%c", answer[i + j]);
    printf("\n");
  }
  return 0;
}
