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 = 205, inf = 2e18;
long long dp[maxn][maxn], priority[maxn];
bool cmp(long long i, long long j) { return priority[i] < priority[j]; }
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long a, b, k;
  cin >> a >> b >> k;
  long long n = a + b - 1;
  string s = "";
  vector<long long> P;
  for (long long i = 0; i < n; i++) {
    s += ' ';
    P.push_back(i);
  }
  fill(priority, priority + n, a * b + 1);
  for (long long i = 0; i < a; i++) {
    for (long long j = 0; j < b; j++) {
      long long c;
      cin >> c;
      priority[i + j] = min(priority[i + j], c);
    }
  }
  sort(P.begin(), P.end(), cmp);
  dp[0][0] = 1;
  for (long long i = 1; i <= n; i++) {
    dp[i][0] = dp[i - 1][1];
    for (long long j = 1; j <= i; j++) {
      dp[i][j] = min(inf, dp[i - 1][j - 1] + dp[i - 1][j + 1]);
    }
  }
  for (auto id : P) {
    dp[id + 1][0] = 0;
    for (long long j = 1; j <= id + 1; j++) dp[id + 1][j] = dp[id][j - 1];
    for (long long i = id + 2; i <= n; i++) {
      if (s[i - 1] == ' ') {
        dp[i][0] = dp[i - 1][1];
        for (long long j = 1; j <= i; j++) {
          dp[i][j] = min(inf, dp[i - 1][j - 1] + dp[i - 1][j + 1]);
        }
      } else if (s[i - 1] == '(') {
        dp[i][0] = 0;
        for (long long j = 1; j <= i; j++) {
          dp[i][j] = dp[i - 1][j - 1];
        }
      } else {
        for (long long j = 0; j <= i; j++) {
          dp[i][j] = dp[i - 1][j + 1];
        }
      }
    }
    if (dp[n][0] >= k) {
      s[id] = '(';
      continue;
    }
    k -= dp[n][0];
    for (long long j = 0; j <= id + 1; j++) dp[id + 1][j] = dp[id][j + 1];
    for (long long i = id + 2; i <= n; i++) {
      if (s[i - 1] == ' ') {
        dp[i][0] = dp[i - 1][1];
        for (long long j = 1; j <= i; j++) {
          dp[i][j] = min(inf, dp[i - 1][j - 1] + dp[i - 1][j + 1]);
        }
      } else if (s[i - 1] == '(') {
        dp[i][0] = 0;
        for (long long j = 1; j <= i; j++) {
          dp[i][j] = dp[i - 1][j - 1];
        }
      } else {
        for (long long j = 0; j <= i; j++) {
          dp[i][j] = dp[i - 1][j + 1];
        }
      }
    }
    s[id] = ')';
  }
  for (long long i = 0; i < a; i++) {
    for (long long j = 0; j < b; j++) {
      cout << s[i + j];
    }
    cout << '\n';
  }
}
