F. Relatively Prime Powerstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputConsider some positive integer x. Its prime factorization will be of form x = 2^{k_1} \cdot 3^{k_2} \cdot 5^{k_3} \cdot \dotsLet's call x elegant if the greatest common divisor of the sequence k_1, k_2, \dots is equal to 1. For example, numbers 5 = 5^1, 12 = 2^2 \cdot 3, 72 = 2^3 \cdot 3^2 are elegant and numbers 8 = 2^3 (GCD = 3), 2500 = 2^2 \cdot 5^4 (GCD = 2) are not.Count the number of elegant integers from 2 to n.Each testcase contains several values of n, for each of them you are required to solve the problem separately.InputThe first line contains a single integer T (1 \le T \le 10^5) — the number of values of n in the testcase.Each of the next T lines contains a single integer n_i (2 \le n_i \le 10^{18}).OutputPrint T lines — the i-th line should contain the number of elegant numbers from 2 to n_i.ExampleInput4427210Output21616NoteHere is the list of non-elegant numbers up to 10:  4 = 2^2, GCD = 2;  8 = 2^3, GCD = 3;  9 = 3^2, GCD = 2. The rest have GCD = 1.
Input4427210
Output21616
['combinatorics', 'math', 'number theory', '*2400']