#include <bits/stdc++.h>
using namespace std;
int n, a[12][6], ans[12], cnt;
bool check(int x, int p, int q) {
  int tot = 0;
  for (int i = 1; i <= 5; i++)
    tot = tot + (a[p][i] - a[x][i]) * (a[q][i] - a[x][i]);
  if (tot <= 0)
    return 1;
  else
    return 0;
}
int main() {
  cin >> n;
  if (n > 32) {
    cout << 0;
    return 0;
  };
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= 5; j++) cin >> a[i][j];
  for (int k = 1; k <= n; k++) {
    bool flag = 0;
    for (int i = 1; i <= n; i++)
      for (int j = 1; j <= n; j++) {
        if (i == j || j == k || i == k || flag) continue;
        if (!check(k, i, j)) flag = 1;
      }
    if (!flag) {
      cnt++;
      ans[cnt] = k;
    }
  }
  cout << cnt << endl;
  for (int i = 1; i <= cnt; i++) cout << ans[i] << endl;
}

### Prompt

Please create a solution in CPP 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>
using namespace std;
int n, a[12][6], ans[12], cnt;
bool check(int x, int p, int q) {
  int tot = 0;
  for (int i = 1; i <= 5; i++)
    tot = tot + (a[p][i] - a[x][i]) * (a[q][i] - a[x][i]);
  if (tot <= 0)
    return 1;
  else
    return 0;
}
int main() {
  cin >> n;
  if (n > 32) {
    cout << 0;
    return 0;
  };
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= 5; j++) cin >> a[i][j];
  for (int k = 1; k <= n; k++) {
    bool flag = 0;
    for (int i = 1; i <= n; i++)
      for (int j = 1; j <= n; j++) {
        if (i == j || j == k || i == k || flag) continue;
        if (!check(k, i, j)) flag = 1;
      }
    if (!flag) {
      cnt++;
      ans[cnt] = k;
    }
  }
  cout << cnt << endl;
  for (int i = 1; i <= cnt; i++) cout << ans[i] << endl;
}

```