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;
vector<int> points[1005];
int badx[1005];
void bad(int a, int b, int c) {
  long long int sca = 0;
  long long int scb = 0;
  long long int scc = 0;
  for (int i = 0; i < 5; i++) {
    sca += (points[b][i] - points[a][i]) * (points[c][i] - points[a][i]);
    scb += (points[a][i] - points[b][i]) * (points[c][i] - points[b][i]);
    scc += (points[b][i] - points[c][i]) * (points[a][i] - points[c][i]);
  }
  if (sca > 0) {
    badx[a] = 1;
  }
  if (scb > 0) {
    badx[b] = 1;
  }
  if (scc > 0) {
    badx[c] = 1;
  }
}
vector<int> w;
int main() {
  int n;
  cin >> n;
  if (n == 1) {
    cout << 1 << endl << 1;
    return 0;
  }
  if (n == 2) {
    cout << 2 << endl << "1 2";
    return 0;
  }
  for (int i = 0; i < n; i++) {
    points[i].resize(6);
    for (int j = 0; j < 5; j++) {
      scanf("%d", &points[i][j]);
    }
    points[i][5] = i + 1;
  }
  random_shuffle(points, points + n);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i == j) {
        continue;
      }
      for (int k = 0; k < n; k++) {
        if (i == k) {
          continue;
        }
        if (j == k) {
          continue;
        }
        if (badx[i]) {
          goto z;
        }
        bad(i, j, k);
      }
      if (badx[i]) {
        goto z;
      }
    }
  z:
    if (badx[i] == 0) {
      cout << 1 << endl << points[i][5];
      return 0;
    }
  }
  cout << 0;
  return 0;
}
