#include <bits/stdc++.h>
using namespace std;
const int maxn = 1005;
struct Point {
  int a[5];
  void read() {
    for (int i = 0; i < 5; i++) {
      cin >> a[i];
    }
  }
  Point() {}
} p[maxn];
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    p[i].read();
  }
  if (n > 100) {
    printf("0\n");
  } else {
    vector<int> ans;
    for (int i = 1; i <= n; i++) {
      bool flag = true;
      for (int j = 1; j <= n; j++) {
        for (int k = 1; k <= n; k++) {
          if (j == i) continue;
          if (k == i || k == j) continue;
          int b[5], c[5];
          int ret = 0;
          for (int l = 0; l < 5; l++) {
            b[l] = p[j].a[l] - p[i].a[l];
            c[l] = p[k].a[l] - p[i].a[l];
            ret += b[l] * c[l];
          }
          if (ret > 0) flag = false;
        }
      }
      if (flag) {
        ans.push_back(i);
      }
    }
    cout << ans.size() << endl;
    for (int i = 0; i < ans.size(); i++) {
      cout << ans[i] << " ";
    }
  }
  return 0;
}

### Prompt

Your task is to create 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>
using namespace std;
const int maxn = 1005;
struct Point {
  int a[5];
  void read() {
    for (int i = 0; i < 5; i++) {
      cin >> a[i];
    }
  }
  Point() {}
} p[maxn];
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    p[i].read();
  }
  if (n > 100) {
    printf("0\n");
  } else {
    vector<int> ans;
    for (int i = 1; i <= n; i++) {
      bool flag = true;
      for (int j = 1; j <= n; j++) {
        for (int k = 1; k <= n; k++) {
          if (j == i) continue;
          if (k == i || k == j) continue;
          int b[5], c[5];
          int ret = 0;
          for (int l = 0; l < 5; l++) {
            b[l] = p[j].a[l] - p[i].a[l];
            c[l] = p[k].a[l] - p[i].a[l];
            ret += b[l] * c[l];
          }
          if (ret > 0) flag = false;
        }
      }
      if (flag) {
        ans.push_back(i);
      }
    }
    cout << ans.size() << endl;
    for (int i = 0; i < ans.size(); i++) {
      cout << ans[i] << " ";
    }
  }
  return 0;
}

```