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 n, m;
long long k;
int ar[205];
long long dp[205][205];
long long stt(int idx, int op) {
  if (op == -1) return 0;
  if (idx == n + m - 1) {
    if (op == 0) return 1;
    return 0;
  }
  if (dp[idx][op] != -1) return dp[idx][op];
  long long sm = 0;
  if (ar[idx] != 0)
    sm = stt(idx + 1, op + ar[idx]);
  else {
    sm += stt(idx + 1, op + 1);
    if (sm > k)
      sm = k + 1;
    else
      sm += stt(idx + 1, op - 1);
  }
  if (sm > k) sm = k + 1;
  dp[idx][op] = sm;
  return sm;
}
struct port {
  int idx, c;
};
port cst[205];
bool cmp(port a, port b) { return a.c < b.c; }
int main() {
  scanf("%d%d%I64d", &n, &m, &k);
  int i, j, x;
  for (i = 0; i < n; i++) {
    for (j = 0; j < m; j++) {
      cst[i + j].idx = i + j;
      ar[i + j] = 0;
      scanf("%d", &x);
      if (i == 0 || j == m - 1)
        cst[i + j].c = x;
      else
        cst[i + j].c = min(cst[i + j].c, x);
    }
  }
  sort(cst, cst + n + m - 1, cmp);
  int p = 0;
  long long v;
  for (p = 0; p < n + m - 1; p++) {
    memset(dp, -1, sizeof dp);
    ar[cst[p].idx] = 1;
    v = stt(0, 0);
    if (v < k) {
      ar[cst[p].idx] = -1;
      k -= v;
    } else
      ar[cst[p].idx] = 1;
  }
  int c = 9;
  for (i = 0; i < n; i++) {
    for (j = 0; j < m; j++)
      if (ar[i + j] == 1)
        printf("(");
      else
        printf(")");
    printf("\n");
  }
}
