Problem S1: Hat Circle

Problem DescriptionCopy Anchor Link

At a recent social gathering, $N$ people sit around a circular table, where $N$ is even. The seats are numbered clockwise from $1$ to $N$. Each person is wearing a hat with a number on it. Specifically, the person at seat $i$ is wearing a hat with the number $H_i$ on it.

Each person looks at the person who is directly across (diametrically opposite) them in the circle.

Determine the number of people who see someone with a hat with the same number as their own.

Input SpecificationCopy Anchor Link

The first line of input will consist of one even positive integer $N$, representing the number of people at the social gathering.

The next $N$ lines each contain a single non-negative integer $H_i$, representing the hat number of person $i$.

The following table shows how the available $15$ marks are distributed:

Output SpecificationCopy Anchor Link

Output a single integer representing the number of people who see their hat number on the person directly across from them.

Sample Input 1Copy Anchor Link

4
0
1
0
1 

Output for Sample Input 1Copy Anchor Link

4

Explanation of Output for Sample Input 1Copy Anchor Link

The four seats around the table are shown below. Hat numbers are shown inside each seat and seat numbers are shown beside each seat.

Notice that every person sees their hat number. The people in seats $1$ and $3$ both see hat number $0$, and the people in seats $2$ and $4$ both see hat number $1$.

Sample Input 2Copy Anchor Link

4
1
0
0
1 

Output for Sample Input 2Copy Anchor Link

0

Explanation of Output for Sample Input 2Copy Anchor Link

The four seats around the table are shown below. Hat numbers are shown inside each seat and seat numbers are shown beside each seat.

Notice that no person sees their hat number. The people in seats $1$ and $4$ both see hat number $0$, and the people in seats $2$ and $3$ both see hat number $1$.