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 N = 101;
int n, m;
long long k;
int c[N][N];
long long F[2 * N][2 * N];
int res[2 * N];
pair<int, int> prio[2 * N];
long long cnt() {
  for (int i = 0; i < (n + m); ++i)
    for (int j = 0; j < (n + m); ++j) F[i][j] = 0;
  F[0][1] = 1;
  for (int i = 1; i <= (n + m - 2); ++i) {
    for (int j = 0; j <= i + 1; j++) {
      if (res[i] == 1)
        F[i][j] = (j > 0) ? F[i - 1][j - 1] : 0;
      else if (res[i] == 2)
        F[i][j] = F[i - 1][j + 1];
      else
        F[i][j] = min(((j > 0) ? F[i - 1][j - 1] : 0) + F[i - 1][j + 1],
                      1000000000000000001LL);
    }
  }
  return F[n + m - 2][0];
}
int main() {
  cin >> n >> m >> k;
  for (int i = 1; i <= (m + n - 1); ++i) {
    prio[i].first = n * m + 1;
    prio[i].second = i;
  }
  res[0] = 1;
  for (int i = 1; i <= (n + m - 3); ++i) res[i] = 0;
  res[n + m - 2] = 2;
  for (int i = 0; i < (n); ++i)
    for (int j = 0; j < (m); ++j) {
      cin >> c[i][j];
      prio[i + j].first = min(prio[i + j].first, c[i][j]);
    }
  sort(prio + 1, prio + n + m - 2);
  for (int i = 1; i <= (n + m - 3); ++i) {
    res[prio[i].second] = 1;
    long long c = cnt();
    if (k <= c) continue;
    k -= c;
    res[prio[i].second] = 2;
  }
  for (int i = 0; i < (n); ++i) {
    for (int j = 0; j < (m); ++j) printf("%c", (res[i + j] == 1) ? '(' : ')');
    printf("\n");
  }
}
