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 pt[5][1005];
bool ar[10005];
inline long long sq(long long x) { return x * x; }
inline long long dis(int i, int j) {
  return sq(pt[0][i] - pt[0][j]) + sq(pt[1][i] - pt[1][j]) +
         sq(pt[2][i] - pt[2][j]) + sq(pt[3][i] - pt[3][j]) +
         sq(pt[4][i] - pt[4][j]);
}
inline bool func(int i, int j, int k) {
  while (i == j || j == k || i == k)
    ;
  long long l2 = (pt[0][i] - pt[0][k]) * (pt[0][i] - pt[0][j]) +
                 (pt[1][i] - pt[1][k]) * (pt[1][i] - pt[1][j]) +
                 (pt[2][i] - pt[2][k]) * (pt[2][i] - pt[2][j]) +
                 (pt[3][i] - pt[3][k]) * (pt[3][i] - pt[3][j]) +
                 (pt[4][i] - pt[4][k]) * (pt[4][i] - pt[4][j]);
  ;
  return (l2 <= 0);
}
int main() {
  int n, c;
  cin >> n;
  memset(ar, 0, sizeof(ar));
  for (int i = 0; i < n; i++) {
    scanf("%lld %lld %lld", &pt[0][i], &pt[1][i], &pt[2][i]);
    scanf("%lld", &pt[3][i]);
    scanf("%lld", &pt[4][i]);
  }
  c = n;
  for (int i = 0; i < n; i++)
    if (!ar[i])
      for (int j = 0; j < n; j++)
        if (j != i)
          for (int k = j + 1; k < n; k++)
            if (k != i && func(i, j, k)) {
              ar[j] = 1;
              ar[k] = 1;
            } else if (k != i) {
              ar[i] = 1;
              j = n;
              break;
            }
  for (int i = 0; i < n; i++) c -= ar[i];
  cout << c << endl;
  for (int i = 0; i < n; i++)
    if (!ar[i]) cout << i + 1 << endl;
}
