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 p[1010][5];
set<int> st;
int check(int a, int b, int c) {
  int ab[5], ac[5], bc[5];
  for (int i = 0; i < 5; i++) {
    ab[i] = p[b][i] - p[a][i];
    ac[i] = p[c][i] - p[a][i];
    bc[i] = p[c][i] - p[b][i];
  }
  int ans1 = 0, ans2 = 0, ans3 = 0;
  for (int i = 0; i < 5; i++) {
    ans1 += ab[i] * ac[i];
    ans2 += (-ab[i]) * bc[i];
    ans3 += ac[i] * bc[i];
  }
  if (ans1 <= 0) return a;
  if (ans2 <= 0) return b;
  if (ans3 <= 0) return c;
  return -1;
}
int main(void) {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < 5; j++) scanf("%d", &p[i][j]);
  if (n <= 2) {
    printf("%d\n", n);
    for (int i = 0; i < n; i++) printf("%d\n", i + 1);
    return 0;
  }
  for (int i = 0; i < n; i++) st.insert(i);
  while (st.size() > 2) {
    set<int>::iterator it = st.begin();
    int a = *(it++);
    int b = *(it++);
    int c = *(it++);
    int res = check(a, b, c);
    if (res != a) st.erase(a);
    if (res != b) st.erase(b);
    if (res != c) st.erase(c);
  }
  if (st.size() == 2) {
    set<int>::iterator it = st.begin();
    int a = *(it++);
    int b = *(it++);
    int c = 0;
    while (c == a || c == b) c++;
    int res = check(a, b, c);
    if (res != a) st.erase(a);
    if (res != b) st.erase(b);
    if (res != c) st.erase(c);
  }
  if (st.size() == 1) {
    int a = *st.begin();
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (i == a || j == a || i == j) continue;
        if (check(a, i, j) != a) {
          printf("0\n");
          return 0;
        }
      }
    }
    printf("1\n%d\n", a + 1);
    return 0;
  }
  printf("0\n");
  return 0;
}
