#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e3 + 5;
int N, x[MAXN][10], ans[MAXN];
bool ok(int a, int o, int b) {
  int sum = 0;
  for (int i = 0; i <= 4; i++) sum += (x[a][i] - x[o][i]) * (x[b][i] - x[o][i]);
  return sum <= 0;
}
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; i++)
    for (int j = 0; j <= 4; j++) scanf("%d", &x[i][j]);
  for (int i = 1; i <= N; i++)
    if (ans[i] == 0) {
      for (int j = 1; j <= N; j++)
        for (int k = 1; k <= N; k++)
          if (i != j && j != k && i != k) {
            if (!ok(j, i, k))
              ans[i] = -1;
            else
              ans[j] = ans[k] = -1;
          }
      if (!ans[i]) ans[i] = 1;
    }
  int tol = 0;
  for (int i = 1; i <= N; i++) tol += (ans[i] == 1);
  printf("%d\n", tol);
  for (int i = 1; i <= N; i++)
    if (ans[i] == 1) printf("%d\n", i);
  return 0;
}

### Prompt

Please formulate 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 MAXN = 1e3 + 5;
int N, x[MAXN][10], ans[MAXN];
bool ok(int a, int o, int b) {
  int sum = 0;
  for (int i = 0; i <= 4; i++) sum += (x[a][i] - x[o][i]) * (x[b][i] - x[o][i]);
  return sum <= 0;
}
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; i++)
    for (int j = 0; j <= 4; j++) scanf("%d", &x[i][j]);
  for (int i = 1; i <= N; i++)
    if (ans[i] == 0) {
      for (int j = 1; j <= N; j++)
        for (int k = 1; k <= N; k++)
          if (i != j && j != k && i != k) {
            if (!ok(j, i, k))
              ans[i] = -1;
            else
              ans[j] = ans[k] = -1;
          }
      if (!ans[i]) ans[i] = 1;
    }
  int tol = 0;
  for (int i = 1; i <= N; i++) tol += (ans[i] == 1);
  printf("%d\n", tol);
  for (int i = 1; i <= N; i++)
    if (ans[i] == 1) printf("%d\n", i);
  return 0;
}

```