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 Point {
  int idx;
  array<int, 5> d;
};
int product(const Point& p1, const Point& p2, const Point& p3) {
  int s = 0;
  for (int i = 0; i < 5; ++i) {
    s += (p2.d[i] - p1.d[i]) * (p3.d[i] - p1.d[i]);
  }
  return s;
}
bool is_good(const vector<Point>& all, const Point& p) {
  int n = all.size();
  for (int j = 0; j < n - 1; ++j) {
    for (int k = j + 1; k < n; ++k) {
      if (p.idx - 1 == j || p.idx - 1 == k) {
        continue;
      }
      if (product(p, all[j], all[k]) > 0) {
        return false;
      }
    }
  }
  return true;
}
int main() {
  int n;
  scanf("%d", &n);
  vector<Point> points(n);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < 5; ++j) {
      points[i].idx = i + 1;
      scanf("%d", &points[i].d[j]);
    }
  }
  vector<Point> raw(points.begin(), points.end());
  while (points.size() >= 3) {
    auto p1 = points[points.size() - 1];
    auto p2 = points[points.size() - 2];
    auto p3 = points[points.size() - 3];
    points.pop_back();
    points.pop_back();
    points.pop_back();
    bool g1 = true;
    bool g2 = true;
    bool g3 = true;
    if (product(p1, p2, p3) > 0) {
      g1 = false;
    }
    if (product(p2, p1, p3) > 0) {
      g2 = false;
    }
    if (product(p3, p1, p2) > 0) {
      g3 = false;
    }
    if (g1) {
      points.push_back(p1);
    }
    if (g2) {
      points.push_back(p2);
    }
    if (g3) {
      points.push_back(p3);
    }
  }
  vector<Point> ans;
  for (auto p : points) {
    if (is_good(raw, p)) {
      ans.push_back(p);
    }
  }
  printf("%lu\n", ans.size());
  for (int i = 0; i < ans.size(); ++i) {
    printf("%d\n", ans[i].idx);
  }
}
