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 = 100 + 10;
const long long inf = 1e18 + 1;
int ar[MAXn][MAXn], n, m, hp[MAXn * 2], sz;
long long k, dp[MAXn * 2][MAXn * 2];
char ans[2 * MAXn];
pair<int, int> p[2 * MAXn];
long long count() {
  for (int i = 0; i < 2 * MAXn; i++)
    for (int j = 0; j < 2 * MAXn; j++) dp[i][j] = 0;
  if (ans[0] == 0) {
    dp[0][1] = 1;
  } else if (ans[0] == '(') {
    dp[0][1] = 1;
  } else {
    return 0;
  }
  for (int i = 1; i < sz; i++) {
    if (ans[i] == 0) {
      dp[i][0] = dp[i - 1][1];
      for (int j = 1; j <= i + 3; j++)
        dp[i][j] = min(inf, dp[i - 1][j - 1] + dp[i - 1][j + 1]);
    } else if (ans[i] == '(') {
      for (int j = 1; j <= i + 3; j++) dp[i][j] = dp[i - 1][j - 1];
    } else {
      for (int j = 0; j <= i + 3; j++) dp[i][j] = dp[i - 1][j + 1];
    }
  }
  return dp[sz - 1][0];
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) cin >> ar[i][j];
  sz = n + m - 1;
  for (int i = 0; i < sz; i++) hp[i] = MAXn * MAXn;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) hp[i + j] = min(hp[i + j], ar[i][j]);
  for (int i = 0; i < sz; i++) p[i] = pair<int, int>(hp[i], i);
  sort(p, p + sz);
  for (int i = 0; i < sz; i++) ans[i] = 0;
  for (int i = 0; i < sz; i++) {
    ans[p[i].second] = '(';
    long long sal = count();
    if (sal < k) {
      k -= sal;
      ans[p[i].second] = ')';
    }
  }
  for (int i = 0; i < n; i++, cout << '\n')
    for (int j = 0; j < m; j++) cout << ans[i + j];
}
