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 double EPS = 1e-8;
double a[1005], b[1005], c[1005], d[1005], e[1005];
int n;
bool ha[1005];
struct vec {
  double aa, bb, cc, dd, ee;
} t1, t2;
double dmult(vec p, vec q) {
  return p.aa * q.aa + p.bb * q.bb + p.cc * q.cc + p.dd * q.dd + p.ee * q.ee;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++)
    scanf("%lf%lf%lf%lf%lf", &a[i], &b[i], &c[i], &d[i], &e[i]);
  for (int i = 1; i <= n; i++) {
    bool flag = true;
    for (int j = 1; j <= n; j++) {
      if (j == i) continue;
      for (int k = 1; k <= n; k++) {
        if (k == i || k == j) continue;
        t1 = vec{a[j] - a[i], b[j] - b[i], c[j] - c[i], d[j] - d[i],
                 e[j] - e[i]};
        t2 = vec{a[k] - a[i], b[k] - b[i], c[k] - c[i], d[k] - d[i],
                 e[k] - e[i]};
        if (dmult(t1, t2) > EPS) {
          flag = false;
          break;
        }
      }
      if (!flag) break;
    }
    if (flag) ha[i] = 1;
  }
  int cnt = 0, js = 0;
  for (int i = 1; i <= 1000; i++)
    if (ha[i]) cnt++;
  printf("%d\n", cnt);
  for (int i = 1; i <= 1000; i++, js++) {
    if (ha[i]) printf("%d%c", i, js == cnt - 1 ? '\n' : ' ');
  }
  return 0;
}
