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 double PI = acos(-1.0);
const double eps = 1e-8;
long long dp[205][205];
int arr[105][105];
char ans[105][105];
char str[205];
int n, m;
int len;
long long doCount(char* curstr, int curlen) {
  long long ret = 0;
  memset(dp, (0), sizeof(dp));
  dp[0][1] = 1;
  for (int i = 1; i < len; ++i) {
    for (int j = 0; j <= i + 1; ++j) {
      if (curstr[i] != ')' && j) dp[i][j] += dp[i - 1][j - 1];
      if (curstr[i] != '(') dp[i][j] += dp[i - 1][j + 1];
      if (dp[i][j] >= (1000000000000000005LL))
        dp[i][j] = (1000000000000000005LL);
    }
  }
  return dp[len - 1][0];
}
void fix(int pos, char c) {
  for (int i = 0; i < n; ++i) {
    if (pos - i >= 0 && pos - i < m) ans[i][pos - i] = c;
  }
  str[pos] = c;
}
struct node {
  int x, y, p;
  bool operator<(const node& next) const { return p < next.p; }
};
int getPos(int x, int y) { return x + y; }
vector<node> v;
bool flag[205];
int main(int argc, char* argv[]) {
  long long k;
  cin >> n >> m >> k;
  node cur;
  v.clear();
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      scanf("%d", &cur.p);
      cur.x = i;
      cur.y = j;
      v.push_back(cur);
    }
  }
  len = n + m - 1;
  memset(flag, (0), sizeof(flag));
  sort((v).begin(), (v).end());
  for (int i = 0; i < v.size(); ++i) {
    int pos = getPos(v[i].x, v[i].y);
    if (!flag[pos]) {
      flag[pos] = 1;
      fix(pos, '(');
      long long cur = doCount(str, len);
      if (cur < k) {
        fix(pos, ')');
        k -= cur;
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      printf("%c", ans[i][j]);
    }
    puts("");
  }
  return 0;
}
