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.
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}.
For each natural number from the input, output the maximum power of a prime number in its prime factorization on a separate line.
Example 1