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>
#pragma comment(linker, "/STACK:32000000")
using namespace std;
const double PI = acos(-1.0);
template <class T>
inline T SQR(T a) {
  return a * a;
}
char Res[200] = {0};
long long getCnt(int s, long long k) {
  long long D[200], P[200] = {0};
  P[1] = 1;
  for (int i = (1), ei = (s); i < ei; i++) {
    memset(D, 0, sizeof(D));
    if (Res[i] == ')') {
      for (int i = (0), ei = (s - 1); i < ei; i++) D[i] = P[i + 1];
    } else if (Res[i] == '(') {
      for (int i = (1), ei = (s); i < ei; i++) D[i] = P[i - 1];
    } else {
      for (int i = (0), ei = (s); i < ei; i++) {
        if (i > 0) D[i] = P[i - 1];
        if (i < s - 1) D[i] += P[i + 1];
        if (D[i] > k) D[i] = k + 1;
      }
    }
    memcpy(P, D, sizeof(P));
  }
  return D[0];
}
int main() {
  long long k;
  int n, m;
  cin >> n >> m >> k;
  int P[100][100];
  for (int i = (0), ei = (n); i < ei; i++)
    for (int j = (0), ej = (m); j < ej; j++) scanf("%d", &P[i][j]);
  pair<int, int> pr[200];
  for (int i = (0), ei = (n + m - 1); i < ei; i++) {
    pr[i].first = 1e9;
    pr[i].second = i;
  }
  for (int i = (0), ei = (n); i < ei; i++)
    for (int j = (0), ej = (m); j < ej; j++)
      if (pr[i + j].first > P[i][j]) pr[i + j].first = P[i][j];
  sort(pr, pr + n + m - 1);
  k--;
  for (int i = (0), ei = (n + m - 1); i < ei; i++) {
    Res[pr[i].second] = '(';
    long long cnt = getCnt(n + m - 1, k);
    if (k >= cnt) {
      Res[pr[i].second] = ')';
      k -= cnt;
    }
  }
  for (int i = (0), ei = (n); i < ei; i++) {
    for (int j = (0), ej = (m); j < ej; j++) printf("%c", Res[i + j]);
    printf("\n");
  }
  return 0;
}
