#include <bits/stdc++.h>
using namespace std;
int a[1005][6], i, j, k, l, s, n, m, ans, da[1005];
inline bool check(int x, int y, int z) {
  int s = 0;
  for (int i = 1; i <= 5; i++) s += (a[x][i] - a[y][i]) * (a[x][i] - a[z][i]);
  return s > 0;
}
int main() {
  scanf("%d", &n);
  if (n >= 200) return puts("0"), 0;
  for (i = 1; i <= n; i++)
    for (j = 1; j <= 5; j++) scanf("%d", &a[i][j]);
  for (i = 1; i <= n; i++) {
    int bb = 0;
    for (j = 1; j <= n; j++)
      if (i != j) {
        for (k = 1; k <= n; k++)
          if (j != k && i != k)
            if (check(i, j, k)) bb = 1;
      }
    if (!bb) da[++ans] = i;
  }
  printf("%d\n", ans);
  for (i = 1; i <= ans; i++) printf("%d ", da[i]);
}

### Prompt

Please create a solution in cpp 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;
int a[1005][6], i, j, k, l, s, n, m, ans, da[1005];
inline bool check(int x, int y, int z) {
  int s = 0;
  for (int i = 1; i <= 5; i++) s += (a[x][i] - a[y][i]) * (a[x][i] - a[z][i]);
  return s > 0;
}
int main() {
  scanf("%d", &n);
  if (n >= 200) return puts("0"), 0;
  for (i = 1; i <= n; i++)
    for (j = 1; j <= 5; j++) scanf("%d", &a[i][j]);
  for (i = 1; i <= n; i++) {
    int bb = 0;
    for (j = 1; j <= n; j++)
      if (i != j) {
        for (k = 1; k <= n; k++)
          if (j != k && i != k)
            if (check(i, j, k)) bb = 1;
      }
    if (!bb) da[++ans] = i;
  }
  printf("%d\n", ans);
  for (i = 1; i <= ans; i++) printf("%d ", da[i]);
}

```