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 = 200 + 10;
const long long MAXL = 20;
const long long INF = 1e18 + 200;
char s[MAXN];
long long dp[MAXN][MAXN];
long long mul(long long a, long long b) {
  if (a == 0 || b == 0) return 0;
  if (a < INF / b)
    return min(INF, a * b);
  else
    return INF;
}
long long add(long long a, long long b) { return min(a + b, INF); }
long long calc(long long n) {
  for (long long i = n; i >= 0; i--)
    for (long long j = i; j <= n; j++) {
      long long &res = dp[i][j];
      res = 0;
      if ((j - i) % 2) continue;
      if (i == j) {
        res = 1;
        continue;
      }
      if (s[i] == ')' || s[j - 1] == '(') continue;
      for (long long k = i + 1; k < j; k += 2) {
        if (s[k] == '(') continue;
        res = add(res, mul(dp[i + 1][k], dp[k + 1][j]));
      }
    }
  return dp[0][n];
}
long long mn[MAXN];
vector<pair<long long, long long>> res;
int32_t main() {
  memset(mn, 63, sizeof mn);
  long long n, m;
  cin >> n >> m;
  long long k;
  cin >> k;
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < m; j++) {
      long long x;
      cin >> x;
      mn[i + j] = min(mn[i + j], x);
    }
  for (long long i = 0; i < n + m - 1; i++) res.push_back({mn[i], i});
  sort(res.begin(), res.end());
  for (auto v : res) {
    long long cur = v.second;
    s[cur] = '(';
    long long t = calc(m + n - 1);
    if (t < k) s[cur] = ')', k -= t;
  }
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < m; j++) cout << s[i + j];
    cout << '\n';
  }
}
