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;
const double hu = 180 / 3.1415926;
int n;
struct Point {
  double a1, a2, a3, a4, a5;
  Point() {}
  Point(double a1, double a2, double a3, double a4, double a5)
      : a1(a1), a2(a2), a3(a3), a4(a4), a5(a5) {}
} point[3007];
double mul(Point p1, Point p2) {
  double ret = p1.a1 * p2.a1 + p1.a2 * p2.a2 + p1.a3 * p2.a3 + p1.a4 * p2.a4 +
               p1.a5 * p2.a5;
  return ret;
}
double modo(Point p) {
  double t = mul(p, p);
  return sqrt(t);
}
Point minuss(Point p1, Point p2) {
  Point ret = Point(p2.a1 - p1.a1, p2.a2 - p1.a2, p2.a3 - p1.a3, p2.a4 - p1.a4,
                    p2.a5 - p1.a5);
  return ret;
}
vector<int> v;
int main() {
  while (~scanf("%d", &n)) {
    for (int i = 0; i < n; i++) {
      scanf("%lf%lf%lf%lf%lf", &point[i].a1, &point[i].a2, &point[i].a3,
            &point[i].a4, &point[i].a5);
    }
    v.clear();
    int ans = 0;
    bool flag = false;
    for (int i = 0; i < n; i++) {
      flag = false;
      for (int j = 0; j < n; j++) {
        if (j == i) continue;
        for (int k = 0; k < n; k++) {
          if (k == j || k == i) continue;
          Point x = minuss(point[i], point[j]);
          Point y = minuss(point[i], point[k]);
          double angle = mul(x, y) / (modo(x) * modo(y));
          angle = hu * acos(angle);
          if (angle < 90) flag = true;
          if (flag) break;
        }
        if (flag) break;
      }
      if (!flag) {
        v.push_back(i + 1);
      }
    }
    printf("%d\n", v.size());
    for (int i = 0; i < v.size(); i++) printf("%d\n", v[i]);
  }
}
