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 size = 250;
const long long inf = 1000ll * 1000 * 1000 * 1000 * 1000 * 1000 + 1;
vector<pair<int, int> > h;
int pr[size], p[size][size], len;
long long could[size][size];
char buf[size];
long long calc_cnt() {
  int i, j;
  if (buf[0] == ')') return 0;
  for (i = 0; i < len; i++)
    for (j = 0; j < len; j++) could[i][j] = 0;
  could[0][1] = 1;
  for (i = 1; i < len; i++) {
    if (buf[i] == ')') {
      for (j = 0; j <= i; j++) could[i][j] = could[i - 1][j + 1];
      continue;
    }
    if (buf[i] == '(') {
      for (j = 1; j <= i + 1; j++) could[i][j] = could[i - 1][j - 1];
      continue;
    }
    if (buf[i] == 0) {
      could[i][0] = could[i - 1][1];
      could[i][i + 1] = could[i - 1][i];
      for (j = 1; j <= i; j++) {
        could[i][j] = could[i - 1][j - 1] + could[i - 1][j + 1];
        if (could[i][j] > inf) could[i][j] = inf;
      }
    }
  }
  return could[len - 1][0];
}
int main() {
  int n, m, i, j;
  long long k, d;
  cin >> n >> m >> k;
  for (i = 0; i < n; i++)
    for (j = 0; j < m; j++) cin >> p[i][j];
  len = n + m - 1;
  for (i = 0; i < len; i++) pr[i] = n * m + 1;
  for (i = 0; i < n; i++)
    for (j = 0; j < m; j++) pr[i + j] = min(pr[i + j], p[i][j]);
  for (i = 0; i < len; i++) h.push_back(make_pair(pr[i], i));
  sort(h.begin(), h.end());
  for (i = 0; i < len; i++) buf[i] = 0;
  for (i = 0; i < len; i++) {
    buf[h[i].second] = '(';
    d = calc_cnt();
    if (d < k) {
      k -= d;
      buf[h[i].second] = ')';
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < m; j++) cout << buf[i + j];
    cout << endl;
  }
  return 0;
}
