Consider some positive integer $$$x$$$. Its prime factorization will be of form $$$x = 2^{k_1} \cdot 3^{k_2} \cdot 5^{k_3} \cdot \dots$$$
Let'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.
The 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 $$$n_i$$$ ($$$2 \le n_i \le 10^{18}$$$).
Print $$$T$$$ lines — the $$$i$$$-th line should contain the number of elegant numbers from $$$2$$$ to $$$n_i$$$.
4
4
2
72
10
2
1
61
6
Here is the list of non-elegant numbers up to $$$10$$$:
The rest have $$$GCD = 1$$$.
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