CCC '24 S1 - Hat Circle

Canadian Computing Competition: 2024 Stage 1, Senior #1

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 Specification

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 Specification

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

Sample Input 1

Sample Output 1

Explanation

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 $1$.

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Sample Input 2

Sample Output 2

Explanation

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 $1$.