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;
long long dotProduct(vector<long long> a, vector<long long> b,
                     vector<long long> c) {
  long long ans = 0;
  for (int i = 0; i < 5; i++) ans += (b[i] - a[i]) * (c[i] - a[i]);
  return ans;
}
int main() {
  long long n, i, j, k;
  scanf("%lld", &n);
  if (n == 1) {
    printf("1\n1");
    return 0;
  }
  if (n == 2) {
    printf("2\n1\n2");
    return 0;
  }
  vector<long long> point[n];
  for (i = 0; i < n; i++) {
    long long temp;
    for (j = 0; j < 5; j++) {
      scanf("%lld", &temp);
      point[i].push_back(temp);
    }
  }
  bool foundGood = false;
  for (i = 0; i < n; i++) {
    bool isGood = true;
    for (j = 0; j < n; j++) {
      for (k = 0; k < n; k++) {
        if (i != j && j != k && k != i &&
            dotProduct(point[i], point[j], point[k]) > 0) {
          isGood = false;
          break;
        }
      }
      if (!isGood) break;
    }
    if (isGood) {
      foundGood = true;
      break;
    }
  }
  if (foundGood)
    printf("1\n%d", i + 1);
  else
    printf("0");
}
