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 = 1000000000000000001LL;
int g[105][105], ax[210], n, m, N, r[210], ans[210];
long long K, dp[205][205];
bool cmp(int p1, int p2) { return ax[p1] < ax[p2]; }
void Add(long long &a, long long b) {
  if (a == Inf || b == Inf) {
    a = Inf;
    return;
  }
  if (a >= Inf - b) {
    a = Inf;
    return;
  }
  a += b;
}
long long sol() {
  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (int i = 0; i < N; i++) {
    int f1 = 1, f2 = 1;
    if (ans[i] == 1) f1 = 1, f2 = 0;
    if (ans[i] == -1) f1 = 0, f2 = 1;
    for (int j = 0; j <= N; j++)
      if (dp[i][j]) {
        if (f1) Add(dp[i + 1][j + 1], dp[i][j]);
        if (f2 && j) Add(dp[i + 1][j - 1], dp[i][j]);
      }
  }
  return dp[N][0];
}
int main() {
  scanf("%d%d%I64d", &n, &m, &K);
  Inf = K + 1;
  for (int i = 0; i < n + m; i++) ax[i] = 5000000;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      scanf("%d", &g[i][j]);
      ax[i + j] = min(ax[i + j], g[i][j]);
    }
  N = n + m - 1;
  for (int i = 0; i < N; i++) r[i] = i;
  sort(r, r + N, cmp);
  memset(ans, 0, sizeof(ans));
  for (int i = 0; i < N; i++) {
    ans[r[i]] = 1;
    long long ret = sol();
    if (ret >= K)
      continue;
    else {
      K -= ret;
      ans[r[i]] = -1;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) printf("%c", ans[i + j] == 1 ? '(' : ')');
    puts("");
  }
  return 0;
}
