#D11904. Relatively Prime Powers
Relatively Prime Powers
Relatively Prime Powers
Consider some positive integer x. Its prime factorization will be of form x = 2^{k_1} ⋅ 3^{k_2} ⋅ 5^{k_3} ⋅ ...
Let's call x elegant if the greatest common divisor of the sequence k_1, k_2, ... is equal to 1. For example, numbers 5 = 5^1, 12 = 2^2 ⋅ 3, 72 = 2^3 ⋅ 3^2 are elegant and numbers 8 = 2^3 (GCD = 3), 2500 = 2^2 ⋅ 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.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) — the number of values of n in the testcase.
Each of the next T lines contains a single integer n_i (2 ≤ n_i ≤ 10^{18}).
Output
Print T lines — the i-th line should contain the number of elegant numbers from 2 to n_i.
Example
Input
4 4 2 72 10
Output
2 1 61 6
Note
Here 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.
inputFormat
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) — the number of values of n in the testcase.
Each of the next T lines contains a single integer n_i (2 ≤ n_i ≤ 10^{18}).
outputFormat
Output
Print T lines — the i-th line should contain the number of elegant numbers from 2 to n_i.
Example
Input
4 4 2 72 10
Output
2 1 61 6
Note
Here 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.
样例
4
4
2
72
10
2
1
61
6