#include <bits/stdc++.h>
using namespace std;
vector<vector<int> > mults;
vector<array<int, 5> > points;
inline bool check(int a, int b, int c) {
  int angle = (mults[b][c] + mults[a][a] - mults[a][b] - mults[a][c]);
  return angle <= 0;
}
int main() {
  int n = 1;
  cin >> n;
  points.resize(n);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < points[i].size(); ++j) {
      cin >> points[i][j];
    }
  }
  mults.resize(n);
  for (int i = 0; i < n; ++i) {
    mults[i].assign(n, 0);
  }
  for (int i = 0; i < n; ++i) {
    for (int j = i; j < n; ++j) {
      for (int h = 0; h < points[i].size(); ++h) {
        mults[i][j] += points[i][h] * points[j][h];
      }
      mults[j][i] = mults[i][j];
    }
  }
  vector<int> result;
  for (int i = 0; i < n; ++i) {
    bool flag = true;
    for (int j = 0; j < n && flag; ++j) {
      if (j == i) {
        continue;
      }
      for (int h = j + 1; h < n && flag; ++h) {
        if (h == i) {
          continue;
        }
        flag = check(i, j, h);
      }
    }
    if (flag) {
      result.push_back(i + 1);
    }
  }
  cout << result.size() << endl;
  for (int i = 0; i < result.size(); ++i) {
    cout << result[i] << endl;
  }
}

### 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;
vector<vector<int> > mults;
vector<array<int, 5> > points;
inline bool check(int a, int b, int c) {
  int angle = (mults[b][c] + mults[a][a] - mults[a][b] - mults[a][c]);
  return angle <= 0;
}
int main() {
  int n = 1;
  cin >> n;
  points.resize(n);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < points[i].size(); ++j) {
      cin >> points[i][j];
    }
  }
  mults.resize(n);
  for (int i = 0; i < n; ++i) {
    mults[i].assign(n, 0);
  }
  for (int i = 0; i < n; ++i) {
    for (int j = i; j < n; ++j) {
      for (int h = 0; h < points[i].size(); ++h) {
        mults[i][j] += points[i][h] * points[j][h];
      }
      mults[j][i] = mults[i][j];
    }
  }
  vector<int> result;
  for (int i = 0; i < n; ++i) {
    bool flag = true;
    for (int j = 0; j < n && flag; ++j) {
      if (j == i) {
        continue;
      }
      for (int h = j + 1; h < n && flag; ++h) {
        if (h == i) {
          continue;
        }
        flag = check(i, j, h);
      }
    }
    if (flag) {
      result.push_back(i + 1);
    }
  }
  cout << result.size() << endl;
  for (int i = 0; i < result.size(); ++i) {
    cout << result[i] << endl;
  }
}

```