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 oo = 0x3f3f3f3f;
const double eps = 1e-9;
long long MA = 2000000000000000000LL;
int mini[210], N;
char seted[210];
long long dp[210][210];
long long calc(int f, int t) {
  if (f == t) return 1;
  long long &res = dp[f][t];
  if (res == -1) {
    res = 0;
    if (seted[f] == ')') return 0;
    if (seted[t - 1] == '(') return 0;
    res = calc(f + 1, t - 1);
    for (int j = f + 2; j < t; j += 2) {
      if (seted[j - 1] == '(') continue;
      long long r1 = calc(f + 1, j - 1);
      if (r1 == 0) continue;
      long long r2 = calc(j, t);
      if (r2 == 0) continue;
      if (r1 == MA || r2 == MA) {
        res = MA;
        break;
      }
      long long mul = r1 * r2;
      if (mul / r1 != r2) {
        res = MA;
        break;
      }
      if (mul >= MA) {
        res = MA;
        break;
      }
      res += mul;
      if (res >= MA) {
        res = MA;
        break;
      }
    }
  }
  return res;
}
long long calc() {
  memset(dp, -1, sizeof(dp));
  return calc(0, N);
}
int main() {
  int R, C;
  long long K;
  cin >> R >> C >> K;
  memset(mini, oo, sizeof(mini));
  for (int r = (0); r < (R); r++)
    for (int c = (0); c < (C); c++) {
      int tmp;
      cin >> tmp;
      mini[r + c] = min(mini[r + c], tmp);
    }
  N = R + C - 1;
  for (int i = (0); i < (N); i++) seted[i] = 0;
  for (int i = (0); i < (N); i++) {
    int next = 0;
    for (int j = (1); j < (N); j++)
      if (mini[j] < mini[next]) next = j;
    mini[next] = oo;
    seted[next] = '(';
    long long r = calc();
    if (r < K) {
      K -= r;
      seted[next] = ')';
    }
  }
  for (int r = (0); r < (R); r++) {
    for (int c = (0); c < (C); c++) printf("%c", seted[r + c]);
    printf("\n");
  }
  return 0;
}
