#include <bits/stdc++.h>
using namespace std;
const int Maxn = 1010;
struct node {
  int a, b, c, d, e;
} Q[Maxn], x, y;
int N;
vector<int> V;
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; i++)
    scanf("%d%d%d%d%d", &Q[i].a, &Q[i].b, &Q[i].c, &Q[i].d, &Q[i].e);
  if (N > 11) {
    printf("0\n");
    return 0;
  }
  for (int i = 1; i <= N; i++) {
    bool bk = 1;
    for (int j = 1; j <= N; j++)
      for (int k = 1; k <= N; k++)
        if (i != j && j != k && i != k) {
          int tmp = (Q[j].a - Q[i].a) * (Q[k].a - Q[i].a) +
                    (Q[j].b - Q[i].b) * (Q[k].b - Q[i].b) +
                    (Q[j].c - Q[i].c) * (Q[k].c - Q[i].c) +
                    (Q[j].d - Q[i].d) * (Q[k].d - Q[i].d) +
                    (Q[j].e - Q[i].e) * (Q[k].e - Q[i].e);
          if (tmp > 0) bk = 0;
        }
    if (bk) V.push_back(i);
  }
  cout << V.size() << endl;
  for (auto i : V) cout << i << endl;
  return 0;
}

### Prompt

Your task is to create a CPP solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int Maxn = 1010;
struct node {
  int a, b, c, d, e;
} Q[Maxn], x, y;
int N;
vector<int> V;
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; i++)
    scanf("%d%d%d%d%d", &Q[i].a, &Q[i].b, &Q[i].c, &Q[i].d, &Q[i].e);
  if (N > 11) {
    printf("0\n");
    return 0;
  }
  for (int i = 1; i <= N; i++) {
    bool bk = 1;
    for (int j = 1; j <= N; j++)
      for (int k = 1; k <= N; k++)
        if (i != j && j != k && i != k) {
          int tmp = (Q[j].a - Q[i].a) * (Q[k].a - Q[i].a) +
                    (Q[j].b - Q[i].b) * (Q[k].b - Q[i].b) +
                    (Q[j].c - Q[i].c) * (Q[k].c - Q[i].c) +
                    (Q[j].d - Q[i].d) * (Q[k].d - Q[i].d) +
                    (Q[j].e - Q[i].e) * (Q[k].e - Q[i].e);
          if (tmp > 0) bk = 0;
        }
    if (bk) V.push_back(i);
  }
  cout << V.size() << endl;
  for (auto i : V) cout << i << endl;
  return 0;
}

```