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;
using ll = long long;
using uint = unsigned int;
using rl = double;
using pii = pair<int, int>;
const ll INF = 1000 * 1000 * 1000LL * 1000 * 1000 * 1000LL;
const int MAXN = 209;
int n, m;
ll k;
int sidx[MAXN];
char fseq[MAXN];
int sperm[MAXN];
void addMaxK(ll& a, ll b) {
  a += b;
  if (a > k) a = k + 1;
}
ll dp[MAXN][MAXN];
ll Count() {
  dp[1][0] = 1;
  for (int i = 2; i <= n + m; i++) {
    for (int j = 0; j <= i - 1 && j <= n + m - i; j++) {
      dp[i][j] = 0;
      if (fseq[i] == 0) {
        addMaxK(dp[i][j], dp[i - 1][j + 1]);
        if (j) {
          addMaxK(dp[i][j], dp[i - 1][j - 1]);
        }
        continue;
      } else if (fseq[i] == '(') {
        if (j) {
          addMaxK(dp[i][j], dp[i - 1][j - 1]);
        }
      } else {
        addMaxK(dp[i][j], dp[i - 1][j + 1]);
      }
    }
  }
  return dp[n + m][0];
}
int main() {
  scanf("%d %d %lld", &n, &m, &k);
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      int idx;
      scanf("%d", &idx);
      int ds = j + i;
      if (sidx[ds] == 0 || sidx[ds] > idx) sidx[ds] = idx;
    }
  }
  for (int i = 2; i <= n + m; i++) {
    sperm[i] = i;
  }
  sort(sperm + 2, sperm + n + m + 1,
       [](int a, int b) { return sidx[a] < sidx[b]; });
  for (int i = 2; i <= n + m; i++) {
    int fds = sperm[i];
    fseq[fds] = '(';
    ll zk = Count();
    if (zk >= k) {
      continue;
    }
    k -= zk;
    fseq[fds] = ')';
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      int ds = i + j;
      printf("%c", fseq[ds]);
    }
    printf("\n");
  }
}
