Maximum degree of a prime#1904

Maximum degree of a prime

4 seconds
64 megabytes
Hard

You are given a natural number n > 1. For each distinct prime divisor of , it appears in the prime factorization of raised to a certain power. Your task is to determine the highest of these exponents.

Input

The first line of the input contains a natural number T \leq 500, representing the number of natural numbers provided. The following lines contain these numbers. It is guaranteed that each number does not exceed 10^{18}.

Output

For each natural number from the input, output the maximum power of a prime number in its prime factorization on a separate line.

Examples

Example 1

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