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 N = 201;
const int MOD = 998244353;
const int LOGN = 30;
const long long oo = 2e18;
int n, m, p[N][N], f[N], len;
char s[N];
vector<pair<int, int> > v;
long long dp[N][N];
long long k;
long long add(long long a, long long b) { return min((1ll * a + b), oo); }
long long calc(int idx, int op) {
  if (op < 0) return 0;
  if (idx == len) return (op == 0);
  long long &ret = dp[idx][op];
  if (ret != -1) return ret;
  ret = 0;
  if (s[idx] != ')') ret = add(ret, calc(idx + 1, op + 1));
  if (s[idx] != '(') ret = add(ret, calc(idx + 1, op - 1));
  return ret;
}
int main() {
  cin >> n >> m >> k;
  len = n + m - 1;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < m; ++j) {
      scanf("%d", &p[i][j]);
      if (!f[i + j]) f[i + j] = p[i][j];
      f[i + j] = min(f[i + j], p[i][j]);
    }
  for (int i = 0; i < len; ++i) v.push_back(make_pair(f[i], i));
  sort(v.begin(), v.end());
  for (int i = 0; i < v.size(); ++i) {
    memset(dp, -1, sizeof dp);
    s[v[i].second] = '(';
    long long ways = calc(0, 0);
    if (k > ways) {
      s[v[i].second] = ')';
      k -= ways;
    }
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      printf("%c", s[i + j]);
    }
    puts("");
  }
  return 0;
}
