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;
int N, M, i, j;
unsigned long long K, f;
int id[5000];
int a[1208][1208];
int det[5000];
int tot_a[5000];
char ans[1208][1208];
pair<unsigned long long, bool> dp[1208][1208];
inline bool cmp(const int &x, const int &y) { return (tot_a[x] < tot_a[y]); }
int func(int x, int y) {
  if (x > N || y < 1) return (int)2e9;
  return min(func(x + 1, y - 1), a[x][y]);
}
void make_ans(int x, int y, char c) {
  if (x > N || y < 1) return;
  ans[x][y] = c;
  make_ans(x + 1, y - 1, c);
}
const unsigned long long inf = (unsigned long long)4e18;
unsigned long long calc_ways() {
  unsigned long long nval;
  bool ofl;
  for (int i = 0; i <= N + M - 1; i++)
    for (int j = -N - M + 1; j <= N + M - 1; j++)
      dp[i][N + M - 1 + j] = make_pair(0, false);
  dp[0][N + M - 1] = make_pair(1, false);
  for (int i = 0; i < N + M - 1; i++)
    for (int j = 0; j <= N + M - 1; j++) {
      if (dp[i][N + M - 1 + j].first == 0) continue;
      if (det[i + 1] != 0) {
        nval = dp[i][N + M - 1 + j].first +
               dp[i + 1][N + M - 1 + j + det[i + 1]].first;
        dp[i + 1][N + M - 1 + j + det[i + 1]].first = min(nval, inf);
      } else {
        nval = dp[i][N + M - 1 + j].first + dp[i + 1][N + M - 1 + j - 1].first;
        dp[i + 1][N + M - 1 + j - 1].first = min(nval, inf);
        nval = dp[i][N + M - 1 + j].first + dp[i + 1][N + M - 1 + j + 1].first;
        dp[i + 1][N + M - 1 + j + 1].first = min(nval, inf);
      }
    }
  return (dp[N + M - 1][N + M - 1].second ? 2 * inf
                                          : dp[N + M - 1][N + M - 1].first);
}
int main() {
  scanf("%d%d%lld", &N, &M, &K);
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= M; j++) scanf("%d", &a[i][j]);
  for (int i = 1; i <= M; i++) tot_a[i] = func(1, i);
  for (int i = 2; i <= N; i++) tot_a[M + i - 1] = func(i, M);
  for (int i = 1; i <= N + M - 1; i++) id[i] = i;
  sort(id + 1, id + N + M, cmp);
  for (int i = 1; i <= N + M - 1; i++) {
    det[id[i]] = 1;
    f = calc_ways();
    if (f < K) {
      det[id[i]] = -1;
      K -= f;
    }
  }
  for (int i = 1; i <= M; i++)
    if (det[i] == 1)
      make_ans(1, i, '(');
    else
      make_ans(1, i, ')');
  for (int i = 2; i <= N; i++)
    if (det[M + i - 1] == 1)
      make_ans(i, M, '(');
    else
      make_ans(i, M, ')');
  for (int i = 1; i <= N; i++) {
    for (int j = 1; j <= M; j++) putchar(ans[i][j]);
    puts("");
  }
  return 0;
}
