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 MAXN = 100 + 4;
const long long INF = 1000 * 1000 * 1000 + 10;
long long nmat, mmat, n;
long long k;
long long arr[2 * MAXN];
long long blar[2 * MAXN];
set<pair<long long, int> > s;
long long dp[2 * MAXN][2 * MAXN];
long long mat[MAXN][MAXN];
long long foo() {
  for (long long i = 0; i < n; i++) memset(dp[i], 0, sizeof dp[i]);
  dp[0][0] = 0;
  dp[0][1] = 1;
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < n; j++) {
      if (i == 0 && (j == 0 || j == 1)) continue;
      if (blar[i] == 0) {
        if (i && j) dp[i][j] = dp[i - 1][j - 1];
        if (i) dp[i][j] += dp[i - 1][j + 1];
      }
      if (blar[i] == 1)
        if (i && j) dp[i][j] = dp[i - 1][j - 1];
      if (blar[i] == 2)
        if (i) dp[i][j] = dp[i - 1][j + 1];
      if (dp[i][j] >= (long long)1e18 + 30) dp[i][j] = (long long)1e18 + 30;
    }
  return dp[n - 1][0];
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> nmat >> mmat >> k;
  n = nmat + mmat - 1;
  fill(arr, arr + nmat + mmat - 1, INF);
  for (long long i = 0; i < nmat; i++)
    for (long long u, j = 0; j < mmat; j++) {
      cin >> u;
      arr[i + j] = min(arr[i + j], u);
    }
  for (long long i = 0; i < n; i++) s.insert({arr[i], i});
  for (auto it = s.begin(); it != s.end(); it++) {
    long long u = it->second;
    blar[u] = 1;
    long long cnt = foo();
    if (cnt >= k) continue;
    k -= cnt;
    blar[u] = 2;
  }
  for (long long i = 0; i < nmat; i++) {
    for (long long j = 0; j < mmat; j++) cout << (blar[i + j] == 1 ? '(' : ')');
    cout << '\n';
  }
}
