#include <bits/stdc++.h>
using namespace std;
int n;
vector<int> a[1024];
bool asd(int i, int j, int k) {
  int r = 0;
  for (int _ = 0, ThxDem = 5; _ < ThxDem; ++_)
    r += (a[j][_] - a[i][_]) * (a[k][_] - a[i][_]);
  return r > 0;
}
int main() {
  scanf("%d", &n);
  for (int i = 0, ThxDem = n; i < ThxDem; ++i) {
    for (int _ = 0, ThxDem = 5; _ < ThxDem; ++_) {
      int k;
      scanf("%d", &k);
      a[i].push_back(k);
    }
  }
  vector<int> r;
  for (int i = 0, ThxDem = n; i < ThxDem; ++i) {
    bool g = true;
    for (int j = 0, ThxDem = n; j < ThxDem; ++j) {
      if (j == i) continue;
      for (int k = j + 1, ThxDem = n; k < ThxDem; ++k) {
        if (k == i) continue;
        if (asd(i, j, k)) {
          g = false;
          break;
        }
      }
      if (!g) break;
    }
    if (g) r.push_back(i);
  }
  printf("%d\n", ((int)r.size()));
  for (int x : r) printf("%d\n", x + 1);
  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;
vector<int> a[1024];
bool asd(int i, int j, int k) {
  int r = 0;
  for (int _ = 0, ThxDem = 5; _ < ThxDem; ++_)
    r += (a[j][_] - a[i][_]) * (a[k][_] - a[i][_]);
  return r > 0;
}
int main() {
  scanf("%d", &n);
  for (int i = 0, ThxDem = n; i < ThxDem; ++i) {
    for (int _ = 0, ThxDem = 5; _ < ThxDem; ++_) {
      int k;
      scanf("%d", &k);
      a[i].push_back(k);
    }
  }
  vector<int> r;
  for (int i = 0, ThxDem = n; i < ThxDem; ++i) {
    bool g = true;
    for (int j = 0, ThxDem = n; j < ThxDem; ++j) {
      if (j == i) continue;
      for (int k = j + 1, ThxDem = n; k < ThxDem; ++k) {
        if (k == i) continue;
        if (asd(i, j, k)) {
          g = false;
          break;
        }
      }
      if (!g) break;
    }
    if (g) r.push_back(i);
  }
  printf("%d\n", ((int)r.size()));
  for (int x : r) printf("%d\n", x + 1);
  return 0;
}

```