Super sum#2249

Super sum

5 seconds
64 megabytes
Easy

Given natural numbers. For each number, find how many ways it can be represented as the sum of two other numbers from the given set.

Input

The first line contains the number (1 \leq N \leq 10000). The next line contains natural numbers, each not exceeding . For each number, the number of representations is less than 2^{31}.

Output

Print numbers (one per line) – the number of representations for each number in the same order as given.

Examples

Example 1

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