#include <bits/stdc++.h>
using namespace std;
int i, j, m, n, p, k, l, ans[300005];
struct Node {
  int a[5];
  void read() {
    int i;
    for (i = 0; i < 5; ++i) scanf("%d", &a[i]);
  }
} A[300005];
int main() {
  scanf("%d", &n);
  for (i = 1; i <= n; ++i) A[i].read();
  if (n >= 100)
    printf("%d\n", 0);
  else {
    for (i = 1; i <= n; ++i) {
      int flag = 0;
      for (j = 1; j <= n; ++j)
        for (k = 1; k <= n; ++k)
          if (i != j && i != k && j != k) {
            int s = 0;
            for (l = 0; l < 5; ++l)
              s += (A[j].a[l] - A[i].a[l]) * (A[k].a[l] - A[i].a[l]);
            if (s > 0) flag = 1;
          }
      if (!flag) ans[++ans[0]] = i;
    }
    printf("%d\n", ans[0]);
    for (i = 1; i <= ans[0]; ++i) printf("%d\n", ans[i]);
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 i, j, m, n, p, k, l, ans[300005];
struct Node {
  int a[5];
  void read() {
    int i;
    for (i = 0; i < 5; ++i) scanf("%d", &a[i]);
  }
} A[300005];
int main() {
  scanf("%d", &n);
  for (i = 1; i <= n; ++i) A[i].read();
  if (n >= 100)
    printf("%d\n", 0);
  else {
    for (i = 1; i <= n; ++i) {
      int flag = 0;
      for (j = 1; j <= n; ++j)
        for (k = 1; k <= n; ++k)
          if (i != j && i != k && j != k) {
            int s = 0;
            for (l = 0; l < 5; ++l)
              s += (A[j].a[l] - A[i].a[l]) * (A[k].a[l] - A[i].a[l]);
            if (s > 0) flag = 1;
          }
      if (!flag) ans[++ans[0]] = i;
    }
    printf("%d\n", ans[0]);
    for (i = 1; i <= ans[0]; ++i) printf("%d\n", ans[i]);
  }
}

```