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 prioridade[220 * 2];
int resp[220 * 2];
int fixo[220 * 2];
unsigned long long dp[220 * 2][220 * 2];
int M[110 * 2][110 * 2];
int v[220 * 2];
int n, m;
bool comp(int a, int b) { return prioridade[a] < prioridade[b]; }
unsigned long long get(int x, int qnt) {
  ("x=%d qnt=%d fixo[%d]=%d\n", x, qnt, x, fixo[x]);
  if (qnt == -1) return 0;
  if (dp[x][qnt] + 1) return dp[x][qnt];
  if (x == n + m - 1) return (qnt == 0) ? 1 : 0;
  if (fixo[x])
    return dp[x][qnt] = ((2500000000000000000LL < get(x + 1, qnt + resp[x]))
                             ? 2500000000000000000LL
                             : get(x + 1, qnt + resp[x]));
  return dp[x][qnt] = ((2500000000000000000LL <
                        get(x + 1, qnt - 1) + get(x + 1, qnt + 1))
                           ? 2500000000000000000LL
                           : get(x + 1, qnt - 1) + get(x + 1, qnt + 1));
}
int main() {
  long long k;
  scanf("%d%d", &n, &m);
  cin >> k;
  for (int i = 0; i < 220; i++) prioridade[i] = 999999999;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      scanf("%d", &M[i][j]);
      prioridade[i + j] = min(prioridade[i + j], M[i][j]);
    }
  }
  for (int i = 0; i < n + m - 1; i++) v[i] = i;
  sort(v, v + n + m - 1, comp);
  for (int i = 0; i < n + m - 1; i++) {
    ("fixa %d\n", v[i]);
    assert(!fixo[v[i]]);
    fixo[v[i]] = 1;
    resp[v[i]] = 1;
    memset(dp, -1, sizeof(dp));
    if (get(0, 0) < k) {
      k -= get(0, 0);
      resp[v[i]] = -1;
    }
  }
  assert(k == 1);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      printf("%c", (resp[i + j] == 1) ? '(' : ')');
      if (resp[i + j] == 0) printf("?");
    }
    printf("\n");
  }
}
