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 MAXN = 210;
int mi[MAXN];
int idx[MAXN];
int n, m;
long long k;
char s[MAXN];
bool cmp(int x, int y) { return mi[x] < mi[y]; }
void init() {
  scanf("%d%d%lld", &n, &m, &k);
  for (int i = 0; i < n; ++i)
    for (int x, j = 0; j < m; ++j) {
      scanf("%d", &x);
      if (mi[i + j] == 0 || x < mi[i + j]) mi[i + j] = x;
    }
  for (int i = 0; i < n + m - 1; ++i) idx[i] = i;
  sort(idx, idx + n + m - 1, cmp);
}
long long cal() {
  static long long f[2][MAXN];
  int w = 0;
  memset(f[w], 0, sizeof(f[w]));
  f[w][0] = 1;
  for (int i = 0; i < n + m - 1; ++i) {
    memset(f[w ^ 1], 0, sizeof(f[w ^ 1]));
    for (int j = 0; j <= i + 1; ++j) {
      if (j > 0 && s[i] != ')') f[w ^ 1][j] += f[w][j - 1];
      if (s[i] != '(') f[w ^ 1][j] += f[w][j + 1];
      if (f[w ^ 1][j] > k) f[w ^ 1][j] = k + 1;
    }
    w ^= 1;
  }
  return f[w][0];
}
void solve() {
  long long tot;
  for (int i = 0; i < n + m - 1; ++i) {
    s[idx[i]] = '(';
    if ((tot = cal()) < k) {
      k -= tot;
      s[idx[i]] = ')';
    }
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) printf("%c", s[i + j]);
    puts("");
  }
}
int main() {
  init();
  solve();
  return 0;
}
