#include <bits/stdc++.h>
using namespace std;
const int MAX = 1005;
int p[MAX][5];
inline int check(int a, int b, int c) {
  int sum = 0;
  for (int i = 0; i < 5; i++) sum += (p[a][i] - p[b][i]) * (p[a][i] - p[c][i]);
  return sum > 0;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < 5; j++) scanf("%d", &p[i][j]);
  vector<int> T;
  int per[n];
  for (int i = 0; i < n; i++) per[i] = i;
  random_shuffle(per, per + n);
  for (int i = 0; i < n; i++) {
    int da = 0;
    for (int j = 0; j < n; j++) {
      for (int k = (j + 1); k < (n); k++) {
        if (j != i && k != i && check(per[i], per[j], per[k])) {
          da = 1;
          break;
        }
      }
      if (da) break;
    }
    if (!da) T.push_back(per[i]);
  }
  sort(T.begin(), T.end());
  printf("%d\n", (int)T.size());
  for (auto it : T) printf("%d ", it + 1);
  printf("\n");
  return 0;
}

### 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>
using namespace std;
const int MAX = 1005;
int p[MAX][5];
inline int check(int a, int b, int c) {
  int sum = 0;
  for (int i = 0; i < 5; i++) sum += (p[a][i] - p[b][i]) * (p[a][i] - p[c][i]);
  return sum > 0;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < 5; j++) scanf("%d", &p[i][j]);
  vector<int> T;
  int per[n];
  for (int i = 0; i < n; i++) per[i] = i;
  random_shuffle(per, per + n);
  for (int i = 0; i < n; i++) {
    int da = 0;
    for (int j = 0; j < n; j++) {
      for (int k = (j + 1); k < (n); k++) {
        if (j != i && k != i && check(per[i], per[j], per[k])) {
          da = 1;
          break;
        }
      }
      if (da) break;
    }
    if (!da) T.push_back(per[i]);
  }
  sort(T.begin(), T.end());
  printf("%d\n", (int)T.size());
  for (auto it : T) printf("%d ", it + 1);
  printf("\n");
  return 0;
}

```