#include <bits/stdc++.h>
using namespace std;
int n, ans[1010];
struct point {
  int x[5];
  void Read() {
    for (int i = 0; i < 5; ++i) scanf("%d", x + i);
  }
} p[1010];
void Init() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) p[i].Read();
}
void Work() {
  int i, j, k, t, res, flag;
  for (i = 1; i <= n; ++i) {
    flag = true;
    for (j = 1; j <= n && flag; ++j) {
      if (i == j) continue;
      for (k = j + 1; k <= n && flag; ++k) {
        if (i == k) continue;
        for (t = 0, res = 0; t < 5; ++t)
          res += (p[j].x[t] - p[i].x[t]) * (p[k].x[t] - p[i].x[t]);
        if (res > 0) flag = false;
      }
    }
    if (flag) ans[++ans[0]] = i;
  }
  printf("%d\n", ans[0]);
  for (i = 1; i <= ans[0]; ++i) printf("%d\n", ans[i]);
}
int main() {
  Init();
  Work();
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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, ans[1010];
struct point {
  int x[5];
  void Read() {
    for (int i = 0; i < 5; ++i) scanf("%d", x + i);
  }
} p[1010];
void Init() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) p[i].Read();
}
void Work() {
  int i, j, k, t, res, flag;
  for (i = 1; i <= n; ++i) {
    flag = true;
    for (j = 1; j <= n && flag; ++j) {
      if (i == j) continue;
      for (k = j + 1; k <= n && flag; ++k) {
        if (i == k) continue;
        for (t = 0, res = 0; t < 5; ++t)
          res += (p[j].x[t] - p[i].x[t]) * (p[k].x[t] - p[i].x[t]);
        if (res > 0) flag = false;
      }
    }
    if (flag) ans[++ans[0]] = i;
  }
  printf("%d\n", ans[0]);
  for (i = 1; i <= ans[0]; ++i) printf("%d\n", ans[i]);
}
int main() {
  Init();
  Work();
  return 0;
}

```