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 i, j, m, n, p[305][305], id[305][305], tot, vis[305], ans[305][305];
long long k, f[305][305];
struct Node {
  int x, y;
} A[305 * 305];
void jia(long long &x, long long y) {
  x += y;
  if (x >= k) x = k;
}
long long work() {
  memset(f, 0, sizeof(f));
  f[0][0] = 1;
  int i, j;
  for (i = 0; i < tot; ++i)
    for (j = 0; j <= i; ++j)
      if (vis[i + 1] == 1)
        jia(f[i + 1][j + 1], f[i][j]);
      else if (vis[i + 1] == 2) {
        if (j) jia(f[i + 1][j - 1], f[i][j]);
      } else {
        jia(f[i + 1][j + 1], f[i][j]);
        if (j) jia(f[i + 1][j - 1], f[i][j]);
      }
  return f[tot][0];
}
int main() {
  scanf("%d%d%I64d", &n, &m, &k);
  for (i = 1; i <= n; ++i)
    for (j = 1; j <= m; ++j) {
      scanf("%d", &p[i][j]);
      A[p[i][j]].x = i;
      A[p[i][j]].y = j;
    }
  for (i = 1; i <= n; ++i) id[i][1] = ++tot;
  for (j = 2; j <= m; ++j) id[n][j] = ++tot;
  for (i = 1; i < n; ++i)
    for (j = 2; j <= m; ++j) {
      int x = i, y = j;
      while (x != n && y != 1) ++x, --y;
      id[i][j] = id[x][y];
    }
  for (i = 1; i <= n * m; ++i)
    if (vis[id[A[i].x][A[i].y]])
      ans[A[i].x][A[i].y] = vis[id[A[i].x][A[i].y]];
    else {
      vis[id[A[i].x][A[i].y]] = 1;
      ans[A[i].x][A[i].y] = 1;
      long long r = work();
      if (r < k) k -= r, vis[id[A[i].x][A[i].y]] = 2, ans[A[i].x][A[i].y] = 2;
    }
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= m; ++j)
      if (ans[i][j] == 1)
        printf("(");
      else
        printf(")");
    puts("");
  }
}
