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>
#pragma GCC target("sse4.2")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
using namespace std;
const long long MAXN = 200 + 7, MOD = 1000 * 1000 * 1000 + 7;
long long n, m, k, a[MAXN][MAXN], d[MAXN];
string s;
long long dp[MAXN][MAXN];
long long ways() {
  long long n = s.size();
  for (long long i = 0; i < MAXN; i++)
    for (long long j = 0; j < MAXN; j++) dp[i][j] = 0;
  dp[0][0] = 1;
  for (long long i = 0; i < n; i++) {
    for (long long j = i % 2; j <= i && j <= n - i; j += 2) {
      if (dp[i][j] > k) dp[i][j] = k;
      if (s[i] != ')') dp[i + 1][j + 1] += dp[i][j];
      if (s[i] != '(' && j) dp[i + 1][j - 1] += dp[i][j];
    }
  }
  return dp[n][0];
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(nullptr);
  cout.tie(nullptr);
  ;
  fill(d, d + MAXN, INT_MAX / 2);
  cin >> n >> m >> k;
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < m; j++) {
      cin >> a[i][j];
      d[i + j] = min(d[i + j], a[i][j]);
    }
  }
  long long N = n + m - 1;
  pair<long long, long long> p[MAXN];
  for (long long i = 0; i < N; i++) {
    p[i] = make_pair(d[i], i);
  }
  sort(p, p + N);
  for (long long i = 0; i < N; i++) s += '?';
  for (long long i = 0; i < N; i++) {
    long long ind = p[i].second;
    s[ind] = '(';
    long long w = ways();
    if (w < k) {
      k -= w;
      s[ind] = ')';
    }
  }
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < m; j++) {
      cout << s[i + j];
    }
    cout << endl;
  }
  return 0;
}
