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;
int n;
struct Point {
  double a, b, c, d, e;
  Point() {}
  Point(double a, double b, double c, double d, double e) {
    this->a = a;
    this->b = b;
    this->c = c;
    this->d = d;
    this->e = e;
  }
  int length_square() { return a * a + b * b + c * c + d * d + e * e; }
  double length() { return sqrt(length_square()); }
} points[1000 + 1];
int vec_dot(Point p1, Point p2) {
  return p1.a * p2.a + p1.b * p2.b + p1.c * p2.c + p1.d * p2.d + p1.e * p2.e;
}
Point calc_vec(Point p1, Point p2) {
  return Point(p2.a - p1.a, p2.b - p1.b, p2.c - p1.c, p2.d - p1.d, p2.e - p1.e);
}
Point calc_vec(int p1, int p2) { return calc_vec(points[p1], points[p2]); }
double angle_vect(Point p1, Point p2) {
  return acos(vec_dot(p1, p2) / (p1.length() * p2.length()));
}
void read() {
  cin >> n;
  for (int i = 0; i < n; ++i) {
    int a, b, c, d, e;
    cin >> a >> b >> c >> d >> e;
    points[i] = Point(a, b, c, d, e);
  }
}
bool is_point_good(int p) {
  vector<Point> vect;
  for (int i = 0; i < n; ++i) {
    if (i == p) continue;
    Point ab = calc_vec(points[p], points[i]);
    vect.push_back(ab);
  }
  for (int i = 0; i < vect.size(); ++i) {
    for (int j = i + 1; j < vect.size(); ++j) {
      Point p1 = vect[i];
      Point p2 = vect[j];
      if (angle_vect(p1, p2) * 180.0 / 3.14159265 < 90) return false;
    }
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  read();
  if (n == 1) {
    cout << 1 << endl << 1 << endl;
  } else {
    int first = 0;
    int second = 1;
    for (int i = 0; i < n; ++i) {
      for (int j = i + 1; j < n; ++j) {
        if (calc_vec(i, j).length_square() <
            calc_vec(first, second).length_square()) {
          first = i;
          second = j;
        }
      }
    }
    vector<int> good_points;
    if (is_point_good(first)) good_points.push_back(first + 1);
    if (is_point_good(second)) good_points.push_back(second + 1);
    cout << good_points.size() << endl;
    for (int p : good_points) {
      cout << p << endl;
    }
  }
  return 0;
}
