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 MAXN = 210;
const long long INF = 1000000000000000000LL;
int n, m;
long long dp[2][MAXN * 2][2];
int ch[MAXN * 2];
int r[MAXN * MAXN], c[MAXN * MAXN];
inline long long add(int s, int sum) { return dp[s][sum][0] + dp[s][sum][1]; }
long long get() {
  memset(dp, 0, sizeof(dp));
  dp[1][1][1] = 1;
  int now(0);
  for (int i = m + n - 1; i >= 2; --i, now = !now) {
    for (int j = 0; j <= m + n; ++j) dp[now][j][0] = dp[now][j][1] = 0;
    for (int j = 0; j <= m + n - i + 1; ++j) {
      if (ch[i] == ')') {
        if (j > 0) dp[now][j][1] += add(!now, j - 1);
      } else if (ch[i] == '(') {
        dp[now][j][0] += add(!now, j + 1);
      } else if (ch[i] == -1) {
        dp[now][j][0] += add(!now, j + 1);
        if (j > 0) dp[now][j][1] += add(!now, j - 1);
      }
      dp[now][j][0] = dp[now][j][0] > INF ? INF : dp[now][j][0];
      dp[now][j][1] = dp[now][j][1] > INF ? INF : dp[now][j][1];
    }
  }
  return dp[!now][0][0];
}
int main() {
  long long th;
  while (scanf("%d%d%I64d", &n, &m, &th) != EOF) {
    for (int i = 1; i <= n; ++i)
      for (int j = 1; j <= m; ++j) {
        int ta;
        scanf("%d", &ta);
        r[ta] = i;
        c[ta] = j;
      }
    memset(ch, -1, sizeof(ch));
    ch[2] = '(';
    ch[n + m] = ')';
    for (int i = 1; i <= n * m; ++i) {
      if (ch[r[i] + c[i]] != -1) continue;
      ch[r[i] + c[i]] = '(';
      long long nn = get();
      if (th > nn) {
        th -= nn;
        ch[r[i] + c[i]] = ')';
      }
    }
    for (int i = 1; i <= n; ++i, puts(""))
      for (int j = 1; j <= m; ++j) printf("%c", ch[i + j]);
  }
  return 0;
}
