#include <bits/stdc++.h>
int pn[1000][5], qq[1000];
int main() {
  int n, i, ans = 0, j, k, dst, l;
  scanf("%d", &n);
  for (i = 0; i < n; i++)
    scanf("%d %d %d %d %d", &pn[i][0], &pn[i][1], &pn[i][2], &pn[i][3],
          &pn[i][4]);
  if (n < 15) {
    for (i = 0; i < n; i++) qq[i] = 1;
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        if (j == i) continue;
        for (k = 0; k < n; k++) {
          if (k == i || k == j) continue;
          dst = 0;
          for (l = 0; l < 5; l++)
            dst += (pn[k][l] - pn[i][l]) * (pn[j][l] - pn[i][l]);
          if (dst > 0) {
            qq[i] = 0;
            break;
          }
        }
        if (qq[i] == 0) break;
      }
      if (qq[i] == 1) ans++;
    }
  }
  printf("%d\n", ans);
  for (i = 0; i < n; i++) {
    if (qq[i] == 1) printf("%d\n", i + 1);
  }
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

You are given set of n points in 5-dimensional space. The points are labeled from 1 to n. No two points coincide.

We will call point a bad if there are different points b and c, not equal to a, from the given set such that angle between vectors <image> and <image> is acute (i.e. strictly less than <image>). Otherwise, the point is called good.

The angle between vectors <image> and <image> in 5-dimensional space is defined as <image>, where <image> is the scalar product and <image> is length of <image>.

Given the list of points, print the indices of the good points in ascending order.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 103) — the number of points.

The next n lines of input contain five integers ai, bi, ci, di, ei (|ai|, |bi|, |ci|, |di|, |ei| ≤ 103) — the coordinates of the i-th point. All points are distinct.

Output

First, print a single integer k — the number of good points.

Then, print k integers, each on their own line — the indices of the good points in ascending order.

Examples

Input

6
0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1


Output

1
1


Input

3
0 0 1 2 0
0 0 9 2 0
0 0 5 9 0


Output

0

Note

In the first sample, the first point forms exactly a <image> angle with all other pairs of points, so it is good.

In the second sample, along the cd plane, we can see the points look as follows:

<image>

We can see that all angles here are acute, so no points are good.

### Response

```cpp
#include <bits/stdc++.h>
int pn[1000][5], qq[1000];
int main() {
  int n, i, ans = 0, j, k, dst, l;
  scanf("%d", &n);
  for (i = 0; i < n; i++)
    scanf("%d %d %d %d %d", &pn[i][0], &pn[i][1], &pn[i][2], &pn[i][3],
          &pn[i][4]);
  if (n < 15) {
    for (i = 0; i < n; i++) qq[i] = 1;
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        if (j == i) continue;
        for (k = 0; k < n; k++) {
          if (k == i || k == j) continue;
          dst = 0;
          for (l = 0; l < 5; l++)
            dst += (pn[k][l] - pn[i][l]) * (pn[j][l] - pn[i][l]);
          if (dst > 0) {
            qq[i] = 0;
            break;
          }
        }
        if (qq[i] == 0) break;
      }
      if (qq[i] == 1) ans++;
    }
  }
  printf("%d\n", ans);
  for (i = 0; i < n; i++) {
    if (qq[i] == 1) printf("%d\n", i + 1);
  }
}

```