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;
char res[110][110];
vector<pair<int, pair<int, int> > > a;
long long n, m, k;
long long INF = 3000000000000000000ll;
long long dp[210][210];
long long r(int num, int cnt) {
  if (num == n + m - 1) return (cnt == 0);
  if (cnt < 0) return 0;
  if (dp[num][cnt] != -1) return dp[num][cnt];
  int x, y;
  if (num < m) {
    x = 0;
    y = num;
  } else {
    x = num - m + 1;
    y = m - 1;
  }
  if (res[x][y] == '(') return dp[num][cnt] = r(num + 1, cnt + 1);
  if (res[x][y] == ')') return dp[num][cnt] = r(num + 1, cnt - 1);
  long long v = r(num + 1, cnt + 1) + r(num + 1, cnt - 1);
  if (v > INF) v = INF;
  return dp[num][cnt] = v;
}
int main() {
  cin >> n >> m >> k;
  for (int i = (0); i < (n); ++i)
    for (int j = (0); j < (m); ++j) {
      res[i][j] = '.';
      int c;
      scanf("%d", &c);
      a.push_back(make_pair(c, make_pair(i, j)));
    }
  sort(a.begin(), a.end());
  for (int i = (0); i < (a.size()); ++i) {
    int x = a[i].second.first;
    int y = a[i].second.second;
    if (res[x][y] == '.') {
      int x1 = x, y1 = y;
      while ((x1 < n) && (y1 >= 0)) {
        res[x1][y1] = '(';
        x1++;
        y1--;
      }
      x1 = x, y1 = y;
      while ((x1 >= 0) && (y1 < m)) {
        res[x1][y1] = '(';
        x1--;
        y1++;
      }
      memset(dp, -1, sizeof(dp));
      long long c = r(0, 0);
      if (c < k) {
        k -= c;
        int x1 = x, y1 = y;
        while ((x1 < n) && (y1 >= 0)) {
          res[x1][y1] = ')';
          x1++;
          y1--;
        }
        x1 = x, y1 = y;
        while ((x1 >= 0) && (y1 < m)) {
          res[x1][y1] = ')';
          x1--;
          y1++;
        }
      }
    }
  }
  for (int i = (0); i < (n); ++i) {
    for (int j = (0); j < (m); ++j) printf("%c", res[i][j]);
    printf("\n");
  }
  return 0;
}
