Sum of Unique Prime Factors

You are given a positive integer n. Your task is to compute the sum of its unique prime factors. In other words, if the set of prime factors of n is \(\{p_1, p_2, \ldots, p_k\}\), you must calculate:

\(S(n)=\sum_{i=1}^{k} p_i\)

Note that if n does not have any prime factors (for example, when n = 1), the answer is 0.

The input format is standardized for competitive programming: you will read the input from stdin and write the output to stdout.

inputFormat

The first line contains a single integer T, the number of test cases. Each of the following T lines contains a single integer n for which you need to compute the sum of unique prime factors.

Constraints:

• 1 \(\leq T \leq 10^4\)
• 1 \(\leq n \leq 10^9\)

outputFormat

For each test case, output a single line containing the sum of the unique prime factors of n.

## sample

5
12
30
1
10
7

5
10
0
7
7

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