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;
int c[110][110], a[11100], n, m;
long long p;
char s[210];
long long f[210][210];
inline void upd(long long &a, long long b) {
  if (b == 1000000000000000001LL) {
    a = 1000000000000000001LL;
    return;
  }
  if (a >= 1000000000000000001LL - b) {
    a = 1000000000000000001LL;
    return;
  }
  a += b;
}
long long ff() {
  memset(f, 0, sizeof f);
  f[0][0] = 1;
  for (int i = 0; i < n + m - 1; i++) {
    bool f0, f1;
    if (!s[i]) f0 = f1 = 1;
    if (s[i] == '(') f0 = 1, f1 = 0;
    if (s[i] == ')') f0 = 0, f1 = 1;
    for (int j = 0; j < n + m; j++)
      if (f[i][j]) {
        if (f0) upd(f[i + 1][j + 1], f[i][j]);
        if (f1 && j) upd(f[i + 1][j - 1], f[i][j]);
      }
  }
  return f[n + m - 1][0];
}
int main() {
  scanf("%d%d", &n, &m);
  cin >> p;
  p--;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) scanf("%d", &c[i][j]);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) a[c[i][j] - 1] = i + j;
  memset(s, 0, sizeof s);
  for (int i = 0; i < n * m; i++)
    if (!s[a[i]]) {
      s[a[i]] = '(';
      long long T = ff();
      if (T > p) continue;
      p -= T, s[a[i]] = ')';
    }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) putchar(s[i + j]);
    puts("");
  }
  return 0;
}
