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>
int points[1001][5];
bool isBad(int a, int b, int c) {
  return ((points[b][0] - points[a][0]) * (points[c][0] - points[a][0]) +
          (points[b][1] - points[a][1]) * (points[c][1] - points[a][1]) +
          (points[b][2] - points[a][2]) * (points[c][2] - points[a][2]) +
          (points[b][3] - points[a][3]) * (points[c][3] - points[a][3]) +
          (points[b][4] - points[a][4]) * (points[c][4] - points[a][4])) > 0;
}
int DEBUGisBad(int a, int b, int c) {
  return ((points[b][0] - points[a][0]) * (points[c][0] - points[a][0]) +
          (points[b][1] - points[a][1]) * (points[c][1] - points[a][1]) +
          (points[b][2] - points[a][2]) * (points[c][2] - points[a][2]) +
          (points[b][3] - points[a][3]) * (points[c][3] - points[a][3]) +
          (points[b][4] - points[a][4]) * (points[c][4] - points[a][4]));
}
int main(int argc, char const *argv[]) {
  bool good[1001];
  for (int i = 0; i < 1001; ++i) {
    good[i] = true;
  }
  int n;
  scanf("%d", &n);
  int count = n;
  for (int i = 1; i <= n; ++i) {
    scanf("%d %d %d %d %d", &points[i][0], &points[i][1], &points[i][2],
          &points[i][3], &points[i][4]);
  }
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j < n; ++j) {
      if (j == i) continue;
      bool should_break = false;
      for (int k = j + 1; k <= n; ++k) {
        if (k == i) continue;
        if (isBad(i, j, k)) {
          good[i] = false;
          count--;
          should_break = true;
          break;
        }
      }
      if (should_break) break;
    }
  }
  printf("%d\n", count);
  for (int i = 1; i <= n; ++i) {
    if (good[i]) {
      printf("%d\n", i);
    }
  }
  return 0;
}
