CF850A.Five Dimensional Points

普及/提高-

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题目描述

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 and is acute (i.e. strictly less than ). Otherwise, the point is called good.

The angle between vectors and in 5-dimensional space is defined as , where is the scalar product and is length of .

Given the list of points, print the indices of the good points in ascending order.

输入格式

The first line of input contains a single integer $n$ ( $1<=n<=10^{3}$ ) — the number of points.

The next $n$ lines of input contain five integers $a_{i},b_{i},c_{i},d_{i},e_{i}$ ( $|a_{i}|,|b_{i}|,|c_{i}|,|d_{i}|,|e_{i}|<=10^{3}$ ) — the coordinates of the i-th point. All points are distinct.

输出格式

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.

输入输出样例

输入#1

输出#1

1
1

输入#2
```
3
0 0 1 2 0
0 0 9 2 0
0 0 5 9 0
```
输出#2
```
0
```

说明/提示

In the first sample, the first point forms exactly a 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:

We can see that all angles here are acute, so no points are good.

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