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 int a[21][11], fg[21];
int main() {
  long long int n, i, j, k, l, x0, x1, x2, x3, x4, y0, y1, y2, y3, y4, tmp, ans,
      ct;
  scanf("%I64d", &n);
  if (n > 11) {
    for (i = 0; i < n; i++) {
      scanf("%I64d %I64d %I64d %I64d %I64d", &x0, &x1, &x2, &x3, &x4);
    }
    printf("0");
  } else {
    for (i = 0; i < n; i++) {
      scanf("%I64d %I64d %I64d %I64d %I64d", &a[i][0], &a[i][1], &a[i][2],
            &a[i][3], &a[i][4]);
    }
    for (i = 0; i < n; i++) {
      tmp = 1;
      for (j = 0; j < n; j++) {
        if (j != i) {
          for (k = 0; k < n; k++) {
            if ((k != i) && (k != j)) {
              x0 = a[i][0] - a[j][0];
              x1 = a[i][1] - a[j][1];
              x2 = a[i][2] - a[j][2];
              x3 = a[i][3] - a[j][3];
              x4 = a[i][4] - a[j][4];
              y0 = a[i][0] - a[k][0];
              y1 = a[i][1] - a[k][1];
              y2 = a[i][2] - a[k][2];
              y3 = a[i][3] - a[k][3];
              y4 = a[i][4] - a[k][4];
              ans = (x0 * y0) + (x1 * y1) + (x2 * y2) + (x3 * y3) + (x4 * y4);
              if (ans > 0) {
                tmp = 0;
              }
            }
          }
        }
      }
      if (tmp) {
        fg[i] = 1;
      }
    }
    ct = 0;
    for (i = 0; i < 12; i++) {
      if (fg[i]) {
        ct++;
      }
    }
    if (!ct) {
      printf("0");
    } else {
      printf("%I64d\n", ct);
      for (i = 0; i < 12; i++) {
        if (fg[i]) {
          printf("%I64d\n", i + 1);
        }
      }
    }
  }
  return 0;
}
