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;
struct node {
  double a;
  double b;
  double c;
  double d;
  double e;
} x[1010];
int rui(node x, node y, node z) {
  double p = (y.a - x.a) * (z.a - x.a) + (y.b - x.b) * (z.b - x.b) +
             (y.c - x.c) * (z.c - x.c) + (y.d - x.d) * (z.d - x.d) +
             (y.e - x.e) * (z.e - x.e);
  p = p / ((y.a - x.a) * (y.a - x.a) + (y.b - x.b) * (y.b - x.b) +
           (y.c - x.c) * (y.c - x.c) + (y.d - x.d) * (y.d - x.d) +
           (y.e - x.e) * (y.e - x.e));
  p = p / ((z.a - x.a) * (z.a - x.a) + (z.b - x.b) * (z.b - x.b) +
           (z.c - x.c) * (z.c - x.c) + (z.d - x.d) * (z.d - x.d) +
           (z.e - x.e) * (z.e - x.e));
  if (p == 1)
    return 2;
  else if (p > 0)
    return 1;
  else if (p <= 0)
    return 0;
}
bool use[1010];
vector<int> ans;
int main() {
  int n;
  scanf("%d", &n);
  ans.clear();
  memset(use, 0, sizeof(use));
  for (int i = 1; i <= n; i++)
    scanf("%lf%lf%lf%lf%lf", &x[i].a, &x[i].b, &x[i].c, &x[i].d, &x[i].e);
  for (int i = 1; i <= n; i++) {
    if (use[i] == 0) {
      int flag = 1;
      for (int j = 1; j <= n; j++) {
        if (j == i) continue;
        for (int k = 1; k <= n; k++) {
          if (k == i || k == j) continue;
          int q = rui(x[i], x[j], x[k]);
          if (q == 0) {
            use[j] = 1;
            use[k] = 1;
          } else if (q == 1) {
            use[i] = 1;
            flag = 0;
            goto L;
          }
        }
      }
    L:
      if (flag == 1) ans.push_back(i);
    }
  }
  printf("%d\n", ans.size());
  for (int i = 0; i < ans.size(); i++) printf("%d\n", ans[i]);
  return 0;
}
