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 int INF = 2147483647;
const long long INFF = 1000000000000000001LL;
const double PI = 3.141592653589793;
long long wyn[205][205], k, f;
int n, m, res[205], i, j, P[105][105], k1, k2, d, l;
pair<int, int> poz[10005];
long long szukaj(int k, int a) {
  int i, j;
  res[k] = a;
  wyn[0][1] = 1;
  for (i = 1; i < l; i++) {
    for (j = 0; j <= i + 1; j++) wyn[i][j] = 0;
    if (res[i] == 0 || res[i] == -1) {
      for (j = 1; j <= i + 1; j++) wyn[i][j] += wyn[i - 1][j - 1];
    }
    if (res[i] == 1 || res[i] == -1) {
      for (j = 0; j < i; j++)
        wyn[i][j] = min(wyn[i][j] + wyn[i - 1][j + 1], INFF);
    }
  }
  res[k] = -1;
  return wyn[l - 1][0];
}
int main() {
  cin >> n >> m >> k;
  for (i = 0; i < n; i++)
    for (j = 0; j < m; j++) {
      scanf("%d", &P[i][j]);
      poz[P[i][j]] = pair<int, int>(i, j);
    }
  l = n + m - 1;
  for (i = 0; i < l; i++) res[i] = -1;
  res[0] = 0;
  res[l - 1] = 1;
  for (i = 1; i <= n * m; i++) {
    k1 = poz[i].first;
    k2 = poz[i].second;
    d = k1 + k2;
    if (res[d] != -1) continue;
    f = szukaj(d, 0);
    if (f >= k)
      res[d] = 0;
    else {
      res[d] = 1;
      k -= f;
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < m; j++)
      if (res[i + j] == 0)
        printf("(");
      else
        printf(")");
    printf("\n");
  }
  return 0;
}
