#include <bits/stdc++.h>
using namespace std;
const int N = 1001;
int P[N][5];
int calc(int i, int j) {
  int k, ans = 0;
  for (k = 0; k < 5; k++) ans += P[i][k] * P[j][k];
  return ans;
}
vector<int> sol;
int main() {
  int n, i, j, k;
  scanf("%i", &n);
  for (i = 0; i < n; i++)
    for (j = 0; j < 5; j++) scanf("%i", &P[i][j]);
  bool ok;
  for (i = 0; i < n; i++) {
    ok = false;
    for (j = 0; j < n; j++)
      if (j != i && !ok)
        for (k = 0; k < n; k++)
          if (k != i && k != j)
            if (calc(i, i) - calc(i, j) - calc(i, k) + calc(j, k) > 0) {
              ok = true;
              break;
            }
    if (!ok) sol.push_back(i + 1);
  }
  printf("%i\n", sol.size());
  for (i = 0; i < sol.size(); i++) printf("%i ", sol[i]);
  return 0;
}

### Prompt

Create a solution in cpp for 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 = 1001;
int P[N][5];
int calc(int i, int j) {
  int k, ans = 0;
  for (k = 0; k < 5; k++) ans += P[i][k] * P[j][k];
  return ans;
}
vector<int> sol;
int main() {
  int n, i, j, k;
  scanf("%i", &n);
  for (i = 0; i < n; i++)
    for (j = 0; j < 5; j++) scanf("%i", &P[i][j]);
  bool ok;
  for (i = 0; i < n; i++) {
    ok = false;
    for (j = 0; j < n; j++)
      if (j != i && !ok)
        for (k = 0; k < n; k++)
          if (k != i && k != j)
            if (calc(i, i) - calc(i, j) - calc(i, k) + calc(j, k) > 0) {
              ok = true;
              break;
            }
    if (!ok) sol.push_back(i + 1);
  }
  printf("%i\n", sol.size());
  for (i = 0; i < sol.size(); i++) printf("%i ", sol[i]);
  return 0;
}

```