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 EPS = 1e-9;
struct Point {
  double a, b, c, d, e;
};
Point makePoint(double a, double b, double c, double d, double e) {
  Point ret;
  ret.a = a;
  ret.b = b;
  ret.c = c;
  ret.d = d;
  ret.e = e;
  return ret;
}
Point makeVector(Point B, Point A) {
  return makePoint(A.a - B.a, A.b - B.b, A.c - B.c, A.d - B.d, A.e - B.e);
}
double sprod(Point A, Point B) {
  return A.a * B.a + A.b * B.b + A.c * B.c + A.d * B.d + A.e * B.e;
}
double sprod(Point A, Point B, Point C) {
  return sprod(makeVector(B, A), makeVector(B, C));
}
double angle(Point A, Point B) {
  double up = sprod(A, B);
  double down = sqrt(sprod(A, A)) * sqrt(sprod(B, B));
  return acos(up / down);
}
double angle(Point A, Point B, Point C) {
  Point D = makeVector(B, A);
  Point E = makeVector(B, C);
  return angle(D, E);
}
vector<Point> points;
double degn = 3.14159265358979323846 / 2;
int n;
bool check(int idx) {
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      if (i != idx && j != idx) {
        if (sprod(points[i], points[idx], points[j]) > EPS) {
          return false;
        }
      }
    }
  }
  return true;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int a, b, c, d, e;
    scanf("%d%d%d%d%d", &a, &b, &c, &d, &e);
    points.push_back(makePoint(a, b, c, d, e));
  }
  if (n < 3) {
    printf("%d\n", n);
    for (int i = 0; i < n; i++) {
      printf("%d\n", i + 1);
    }
    return 0;
  }
  int ans = -1;
  for (int i = 0; i < n; i++) {
    Point A = points[i];
    Point B = points[(i + 1) % n];
    Point C = points[(i + 2) % n];
    if (sprod(B, A, C) <= EPS && check(i)) {
      ans = i;
      break;
    }
  }
  if (ans == -1) {
    printf("0\n");
  } else {
    printf("1\n");
    printf("%d\n", ans + 1);
  }
}
