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 Mod = 1000000000000000000LL;
int ans[300];
int so[300], num[300];
long long dp[210][210];
int len;
bool cmp(const int &u, const int &v) { return num[u] < num[v]; }
bool ck(long long &x, long long y) {
  x += y;
  if (x > Mod) x = Mod;
}
long long sovle() {
  memset(dp, 0, sizeof(dp));
  if (ans[0] == 0 || ans[0] == 1)
    dp[0][1] = 1;
  else
    return 0;
  for (int i = 0; i < len - 1; i++)
    for (int j = 0; j <= i + 1; j++)
      if (dp[i][j]) {
        if (ans[i + 1] == 0 || ans[i + 1] == 1) ck(dp[i + 1][j + 1], dp[i][j]);
        if ((ans[i + 1] == 0 || ans[i + 1] == 2) && j)
          ck(dp[i + 1][j - 1], dp[i][j]);
      }
  return dp[len - 1][0];
}
int main() {
  int n, m;
  long long k;
  while (scanf("%d %d %I64d", &n, &m, &k) == 3) {
    for (int i = 0; i < 300; i++) num[i] = 1000000;
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) {
        int x;
        scanf("%d", &x);
        if (x < num[i + j]) num[i + j] = x;
      }
    len = n + m - 1;
    for (int i = 0; i < len; i++) so[i] = i;
    memset(ans, 0, sizeof(ans));
    sort(so, so + len, cmp);
    long long now = 0;
    for (int i = 0; i < len; i++) {
      int id = so[i];
      ans[id] = 1;
      long long num = sovle();
      if (now + num < k) {
        ans[id] = 2;
        now += num;
      }
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++)
        if (ans[i + j] == 1)
          putchar('(');
        else
          putchar(')');
      puts("");
    }
  }
  return 0;
}
