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;
const int maxn = 1100;
const long long mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;
long long a[maxn][6];
bool mark[maxn];
long long get(long long x1, long long y1, long long x2, long long y2) {
  return (y2 - y1) * (y2 - y1) + (x2 - x1) * (x2 - x1);
}
bool isgood(int i, int j, int k) {
  long long res = 0;
  for (int u = 0; u < 5; u++) {
    res += (a[j][u] - a[i][u]) * (a[k][u] - a[i][u]);
  }
  return res <= 0;
}
int main() {
  if (fopen("/home/lianyi/123.txt", "r") != NULL) {
    freopen("/home/lianyi/123.txt", "r", stdin);
  } else {
    std::ios::sync_with_stdio(false);
    cin.tie(0);
  }
  int n;
  while (cin >> n) {
    for (int i = 1; i <= n; i++) {
      for (int j = 0; j < 5; j++) {
        cin >> a[i][j];
      }
      mark[i] = false;
    }
    if (n >= 50) {
      cout << 0 << '\n';
      continue;
    }
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= n; j++) {
        for (int k = 1; k <= n; k++) {
          if (i != j && i != k && j != k && isgood(i, j, k) == false) {
            mark[i] = true;
            goto loop1;
          }
        }
      }
    loop1:;
    }
    int cnt = 0;
    for (int i = 1; i <= n; i++) {
      if (mark[i] == false) {
        cnt++;
      }
    }
    cout << cnt << '\n';
    for (int i = 1; i <= n; i++) {
      if (mark[i] == false) {
        cout << i << '\n';
      }
    }
  }
  return 0;
}
