Team · Interview Problem

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Codeforces

Medium

Combinatorics

Bit Manipulation

Math

Team

Count how many teams of 3 students can be formed such that the total skill level is even.

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CF 401C

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Problem Statement

You are given the skill levels of $n$ students. Count the number of different teams of exactly 3 students whose combined skill is even.

A team is identified only by the chosen 3 students, so the order does not matter.

The task is to determine how many such teams can be formed.

Input Format

The first line contains an integer $n$ .
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ representing the skill values.

Output Format

Print a single integer — the number of 3-person teams with even total skill.

Constraints

$3 \le n$
Skill values fit in standard 32-bit signed integers.
The answer may be large; use 64-bit integer arithmetic.

Examples

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Example 1

Input

5
1 2 3 4 5

Output

Explanation

The valid teams are {1,2,3}, {1,4,5}, and {2,3,5}. Each has an even sum.

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