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;
inline long long read() {
  long long S = 0;
  char ch = ' ';
  bool f = 0;
  while (!isdigit(ch)) {
    f |= (ch == '-');
    ch = getchar();
  }
  while (isdigit(ch)) {
    S = (S << 3) + (S << 1) + (ch - '0');
    ch = getchar();
  }
  return (f) ? (-S) : (S);
}
inline void write(long long x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  if (x < 10) {
    putchar(x + '0');
    return;
  }
  write(x / 10);
  putchar(x % 10 + '0');
}
const int N = 105;
int n, m, nn, cnt = 0, jyl[N << 1];
long long up, dp[N << 1][N << 1];
struct node {
  int num, x, y, id;
} wwx[N * N];
inline bool cmpnum(node a, node b) { return a.num < b.num; }
inline void Ad(long long &x, long long y) { x += y; }
int main() {
  int i, j, k, now = 1;
  n = read();
  m = read();
  up = read();
  nn = n + m - 1;
  for (i = 1; i <= n; i++)
    for (j = 1; j <= m; j++) {
      wwx[++cnt].num = read();
      wwx[cnt].x = i;
      wwx[cnt].y = j;
      wwx[cnt].id = i + j - 1;
    }
  sort(wwx + 1, wwx + cnt + 1, cmpnum);
  memset(jyl, 0, sizeof jyl);
  for (i = 1; i <= nn; i++) {
    while ((now <= cnt) && (jyl[wwx[now].id] != 0)) now++;
    jyl[wwx[now].id] = -1;
    memset(dp, 0, sizeof dp);
    dp[0][0] = 1;
    for (j = 0; j < nn; j++)
      for (k = 0; k <= j; k++)
        if (dp[j][k]) {
          dp[j][k] = min(dp[j][k], up);
          if ((jyl[j + 1] != -1) && (k > 0)) Ad(dp[j + 1][k - 1], dp[j][k]);
          if (jyl[j + 1] != 1) Ad(dp[j + 1][k + 1], dp[j][k]);
        }
    if (up > dp[nn][0]) {
      up -= dp[nn][0];
      jyl[wwx[now].id] = 1;
    }
  }
  for (i = 1; i <= n; i++, putchar('\n'))
    for (j = 1; j <= m; j++) {
      (jyl[i + j - 1] == -1) ? putchar('(') : putchar(')');
    }
  return 0;
}
