#include <bits/stdc++.h>
using namespace std;
const int N = 500000;
const int M = 70;
const int C = 300;
const int MOD = 1e9 + 7;
struct Point {
  int x[5];
  Point() {
    for (int i = 0; i < 5; i++) x[i] = 0;
  }
};
int n;
Point a[N];
vector<int> res;
Point diff(const Point &a, const Point &b) {
  Point res = Point();
  for (int i = 0; i < 5; i++) res.x[i] = a.x[i] - b.x[i];
  return res;
}
bool check(const Point &a, const Point &b) {
  int val = 0;
  for (int i = 0; i < 5; i++) val += a.x[i] * b.x[i];
  return (val > 0);
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 5; j++) scanf("%d", &a[i].x[j]);
  }
  int ans = 0;
  if (n <= C) {
    for (int i = 0; i < n; i++) {
      bool flag = true;
      for (int j = 0; j < n; j++) {
        for (int k = j + 1; k < n; k++) {
          if (j == i || k == i) continue;
          if (check(diff(a[j], a[i]), diff(a[k], a[i]))) {
            flag = false;
            break;
          }
        }
      }
      if (flag) {
        ans++;
        res.push_back(i + 1);
      }
    }
  }
  cout << ans << endl;
  for (int i = 0; i < res.size(); i++) cout << res[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 N = 500000;
const int M = 70;
const int C = 300;
const int MOD = 1e9 + 7;
struct Point {
  int x[5];
  Point() {
    for (int i = 0; i < 5; i++) x[i] = 0;
  }
};
int n;
Point a[N];
vector<int> res;
Point diff(const Point &a, const Point &b) {
  Point res = Point();
  for (int i = 0; i < 5; i++) res.x[i] = a.x[i] - b.x[i];
  return res;
}
bool check(const Point &a, const Point &b) {
  int val = 0;
  for (int i = 0; i < 5; i++) val += a.x[i] * b.x[i];
  return (val > 0);
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 5; j++) scanf("%d", &a[i].x[j]);
  }
  int ans = 0;
  if (n <= C) {
    for (int i = 0; i < n; i++) {
      bool flag = true;
      for (int j = 0; j < n; j++) {
        for (int k = j + 1; k < n; k++) {
          if (j == i || k == i) continue;
          if (check(diff(a[j], a[i]), diff(a[k], a[i]))) {
            flag = false;
            break;
          }
        }
      }
      if (flag) {
        ans++;
        res.push_back(i + 1);
      }
    }
  }
  cout << ans << endl;
  for (int i = 0; i < res.size(); i++) cout << res[i] << " ";
  return 0;
}

```