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 MAX_N = 100 + 5;
const long long MAX = 1e18;
int n, m;
long long k;
int priorities[MAX_N][MAX_N];
pair<int, int> location[MAX_N * MAX_N];
long long dp[2 * MAX_N][2 * MAX_N];
char res[2 * MAX_N];
long long rec(int pos, int open) {
  if (open < 0) {
    return 0;
  }
  long long& ret = dp[pos][open];
  if (ret != -1) {
    return ret;
  }
  if (pos == m + n - 1) {
    return ret = (open == 0 ? 1 : 0);
  }
  if (res[pos] != -1) {
    ret = rec(pos + 1, open + (res[pos] == '(' ? 1 : -1));
  } else {
    ret = rec(pos + 1, open - 1) + rec(pos + 1, open + 1);
  }
  if (ret > MAX) {
    ret = MAX;
  }
  return ret;
}
int main(int argc, char** argv) {
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cin >> priorities[i][j];
      location[priorities[i][j]] = make_pair(i, j);
    }
  }
  memset(res, -1, sizeof(res));
  res[m + n - 1] = 0;
  for (int i = 1; i <= m * n; i++) {
    pair<int, int> p = location[i];
    int idx = p.first + p.second;
    if (res[idx] != -1) {
      continue;
    }
    res[idx] = '(';
    memset(dp, -1, sizeof(dp));
    long long cnt = rec(0, 0);
    if (k > cnt) {
      res[idx] = ')';
      k -= cnt;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      printf("%c", res[i + j]);
    }
    printf("\n");
  }
  return 0;
}
