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.
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  vector<vector<int>> pts(n, vector<int>(5, 0));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < 5; ++j) {
      cin >> pts[i][j];
    }
  }
  vector<int> cnt;
  vector<vector<vector<int>>> sum(n, vector<vector<int>>(n, vector<int>(5)));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      for (int k = 0; k < 5; ++k) {
        sum[i][j][k] = pts[i][k] + pts[j][k];
      }
    }
  }
  vector<vector<int>> scalar(n, vector<int>(n, 0));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      for (int k = 0; k < 5; ++k) {
        scalar[i][j] += pts[i][k] * pts[j][k];
      }
    }
  }
  vector<bool> used(n, 0);
  for (int i = 0; i < n; ++i) {
    for (int j = i + 1; j < n; ++j) {
      for (int k = j + 1; k < n; ++k) {
        if (!used[i]) {
          if (scalar[i][i] + scalar[j][k] - scalar[i][j] - scalar[i][k] > 0) {
            used[i] = 1;
          }
        }
        if (!used[j]) {
          if (scalar[j][j] + scalar[i][k] - scalar[j][i] - scalar[j][k] > 0) {
            used[j] = 1;
          }
        }
        if (!used[k]) {
          if (scalar[k][k] + scalar[j][i] - scalar[k][i] - scalar[j][k] > 0) {
            used[k] = 1;
          }
        }
      }
    }
  }
  vector<int> ans;
  for (int i = 0; i < n; ++i) {
    if (!used[i]) {
      ans.push_back(i + 1);
    }
  }
  cout << ans.size() << "\n";
  for (int an : ans) {
    cout << an << "\n";
  }
}
