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;
long long inf = 1000000000000000000LL;
long long f[205][205], k;
int n, m, e, b[205], bo[205][205], sa[205];
char c[205];
bool cmp(int i, int j) { return b[i] < b[j]; }
void ud(int i, int j, long long x) {
  if (bo[i][j] != e) bo[i][j] = e, f[i][j] = 0;
  f[i][j] += x;
  if (f[i][j] > inf) f[i][j] = inf;
}
void dp() {
  ++e;
  bo[0][0] = e;
  f[0][0] = 1;
  for (int i = 0; i <= n - 1; ++i)
    for (int j = 0; j <= i; ++j)
      if (bo[i][j] == e) {
        if (c[i + 1] != '(' && j) ud(i + 1, j - 1, f[i][j]);
        if (c[i + 1] != ')') ud(i + 1, j + 1, f[i][j]);
      }
  if (bo[n][0] != e) f[n][0] = 0;
}
int main() {
  scanf("%d%d%I64d", &n, &m, &k);
  memset(b, 50, sizeof(b));
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= m; ++j) {
      int x;
      scanf("%d", &x);
      b[i + j - 1] = ((b[i + j - 1]) < (x) ? (b[i + j - 1]) : (x));
    }
  n += m - 1;
  for (int i = 1; i <= n; ++i) sa[i] = i;
  sort(sa + 1, sa + 1 + n, cmp);
  for (int i = 1; i <= n; ++i) {
    c[sa[i]] = '(';
    dp();
    if (f[n][0] < k) c[sa[i]] = ')', k -= f[n][0];
  }
  n -= m - 1;
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= m; ++j) printf("%c", c[i + j - 1]);
    puts("");
  }
  return 0;
}
