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;
class point {
 public:
  int id, val, st;
};
bool operator<(const point &a, const point &b) {
  if (a.val < b.val) return true;
  return false;
}
const int maxn = 1000 * 1000 * 1000;
int n, m, i, j, col, x, y;
int pp[101][101];
int a[500];
unsigned long long k, p;
point b[501];
string ans;
char s[101][101];
unsigned long long dp[221][221];
bool mark[221][221];
unsigned long long rec(int i, int j) {
  if (i == col) {
    if (j == 0) return 1;
    return 0;
  }
  if (mark[i][j] == 1) return dp[i][j];
  dp[i][j] = 0;
  if (ans[i] == '(')
    dp[i][j] = rec(i + 1, j + 1);
  else if (ans[i] == ')') {
    if (j > 0) dp[i][j] = rec(i + 1, j - 1);
  } else {
    dp[i][j] = rec(i + 1, j + 1);
    if (j > 0) dp[i][j] += rec(i + 1, j - 1);
  }
  dp[i][j] = min(dp[i][j], k + 1);
  mark[i][j] = 1;
  return dp[i][j];
}
int main() {
  cin >> n >> m >> k;
  for (i = 1; i <= n; i++)
    for (j = 1; j <= m; j++) cin >> pp[i][j];
  for (i = 1; i <= n; i++)
    for (j = 1; j <= m; j++) a[i + j] = maxn;
  for (i = 1; i <= n; i++)
    for (j = 1; j <= m; j++) a[i + j] = min(a[i + j], pp[i][j]);
  for (j = 1; j <= m; j++) {
    b[j].val = a[j + 1];
    b[j].id = j;
    b[j].st = 1 + j;
  }
  for (i = 2; i <= n; i++) {
    b[m + i - 1].val = a[m + i];
    b[m + i - 1].id = m + i - 1;
    b[m + i - 1].st = m + i;
  }
  col = m + n - 1;
  sort(b + 1, b + col + 1);
  ans = "";
  for (i = 1; i <= col; i++) ans += " ";
  for (i = 1; i <= col; i++) {
    ans[b[i].id - 1] = '(';
    memset(mark, 0, sizeof(mark));
    p = rec(0, 0);
    if (p < k) {
      ans[b[i].id - 1] = ')';
      for (x = 1; x <= n; x++)
        for (y = 1; y <= m; y++)
          if (x + y == b[i].st) s[x][y] = ')';
      k -= p;
    } else {
      for (x = 1; x <= n; x++)
        for (y = 1; y <= m; y++)
          if (x + y == b[i].st) s[x][y] = '(';
    }
  }
  for (i = 1; i <= n; i++) {
    for (j = 1; j <= m; j++) cout << s[i][j];
    cout << endl;
  }
  return 0;
}
