#include <bits/stdc++.h>
int read() {
  int x = 0, flag = 1;
  char c;
  while ((c = getchar()) < '0' || c > '9')
    if (c == '-') flag = -1;
  while (c >= '0' && c <= '9')
    x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
  return x * flag;
}
int n, m, a[1005][6], b[1005];
int main() {
  n = read();
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= 5; j++) a[i][j] = read();
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++)
      for (int k = 1; k <= n; k++) {
        if (i == j || i == k || j == k) continue;
        int s = 0;
        for (int l = 1; l <= 5; l++)
          s += (a[j][l] - a[i][l]) * (a[k][l] - a[i][l]);
        if (s > 0) goto In;
      }
    b[++m] = i;
  In:;
  }
  printf("%d\n", m);
  for (int i = 1; i <= m; i++) printf("%d\n", b[i]);
}

### Prompt

Generate 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 read() {
  int x = 0, flag = 1;
  char c;
  while ((c = getchar()) < '0' || c > '9')
    if (c == '-') flag = -1;
  while (c >= '0' && c <= '9')
    x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
  return x * flag;
}
int n, m, a[1005][6], b[1005];
int main() {
  n = read();
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= 5; j++) a[i][j] = read();
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++)
      for (int k = 1; k <= n; k++) {
        if (i == j || i == k || j == k) continue;
        int s = 0;
        for (int l = 1; l <= 5; l++)
          s += (a[j][l] - a[i][l]) * (a[k][l] - a[i][l]);
        if (s > 0) goto In;
      }
    b[++m] = i;
  In:;
  }
  printf("%d\n", m);
  for (int i = 1; i <= m; i++) printf("%d\n", b[i]);
}

```