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 Max_NM(105);
struct node {
  int x, y, v;
  inline bool operator<(const node &b) const { return v < b.v; }
};
node A[Max_NM * Max_NM];
int N, M, V[Max_NM + Max_NM];
long long int K, F[Max_NM + Max_NM][Max_NM];
inline void upd(long long int &a, long long int b) { a = min(a + b, K); }
long long int dp() {
  F[0][0] = 1LL;
  for (int i = 1; i <= N + M - 1; ++i) {
    memset(F[i], 0, sizeof(F[i]));
    for (int j = 0; j <= i - 1; ++j) {
      if (V[i] != 0) upd(F[i][j + 1], F[i - 1][j]);
      if (V[i] != 1) upd(F[i][j], F[i - 1][j]);
    }
    for (int j = 0; j <= i; ++j)
      if (j - (i - j) < 0) F[i][j] = 0LL;
  }
  return F[N + M - 1][(N + M - 1) / 2];
}
int main() {
  scanf("%d%d%lld", &N, &M, &K);
  for (int i = 1, tot = 0; i <= N; ++i)
    for (int j = 1; j <= M; ++j)
      ++tot, A[tot].x = i, A[tot].y = j, scanf("%d", &A[tot].v);
  sort(A + 1, A + 1 + N * M);
  memset(V, -1, sizeof(V));
  for (int i = 1, p; i <= N * M; ++i) {
    p = A[i].x + A[i].y - 1;
    if (V[p] == -1) {
      V[p] = 1;
      long long int tmp;
      if (K > (tmp = dp())) V[p] = 0, K -= tmp;
    }
  }
  for (int i = 1; i <= N; ++i) {
    for (int j = 1; j <= M; ++j)
      if (V[i + j - 1] == 1)
        putchar('(');
      else
        putchar(')');
    putchar('\n');
  }
  return 0;
}
