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 long long inf = 2000000000000000000LL;
int A[200];
long long Calc(long long A, long long B) {
  return (A > inf - B) ? inf : (A + B);
}
long long Count(int N) {
  long long F[200][200];
  memset(F, 0, sizeof(F));
  F[0][0] = 1;
  for (int i = 0; i < N; i++)
    for (int j = 0; j <= N; j++) {
      if (A[i] != -1 && j) F[i + 1][j] = Calc(F[i + 1][j], F[i][j - 1]);
      if (A[i] != 1) F[i + 1][j] = Calc(F[i + 1][j], F[i][j + 1]);
    }
  return F[N][0];
}
int main() {
  int M, N, P[100][100];
  long long K;
  cin >> M >> N >> K;
  for (int i = 0; i < M; i++)
    for (int j = 0; j < N; j++) cin >> P[i][j];
  int Len = M + N - 1, Q[200];
  for (int i = 0; i < Len; i++) Q[i] = M * N;
  for (int i = 0; i < M; i++)
    for (int j = 0; j < N; j++) Q[i + j] = min(Q[i + j], P[i][j]);
  int Data[200];
  for (int i = 0; i < Len; i++) Data[i] = i;
  for (int i = 0; i < Len; i++)
    for (int j = i + 1; j < Len; j++)
      if (Q[Data[i]] > Q[Data[j]]) {
        int Tmp = Data[i];
        Data[i] = Data[j];
        Data[j] = Tmp;
      }
  memset(A, 0, sizeof(A));
  for (int i = 0; i < Len; i++) {
    A[Data[i]] = 1;
    long long Tmp = Count(Len);
    if (K > Tmp) {
      A[Data[i]] = -1;
      K -= Tmp;
    }
  }
  for (int i = 0; i < M; i++) {
    for (int j = 0; j < N; j++) putchar((A[i + j] == 1) ? '(' : ')');
    putchar('\n');
  }
  return 0;
}
