human
PYTHON3 solution for "Polycarp likes squares and cubes of positive integers. Here is the beginning of the sequence of numbers he likes: 1, 4, 8, 9, ....

For a given number n, count the number of integers from 1 to n that Polycarp likes. In other words, find the number of such x that x is a square of a positive integer number or a cube of a positive integer number (or both a square and a cube simultaneously).

Input

The first line contains an integer t (1 ≤ t ≤ 20) — the number of test cases.

Then t lines contain the test cases, one per line. Each of the lines contains one integer n (1 ≤ n ≤ 10^9).

Output

For each test case, print the answer you are looking for — the number of integers from 1 to n that Polycarp likes.

Example

Input

6
10
1
25
1000000000
999999999
500000000

Output

4
1
6
32591
32590
23125":



Can you provide a Python code to find the number of such x that x is a square of a positive integer number or a cube of a positive integer number (or both a square and a cube simultaneously)?
assistant
#Here is Python code to find the number of such x that x is a square of a positive integer number or a cube of a positive integer number (or both a square and a cube simultaneously).
 def root(n,k):
    lo = 0
    hi = n + 1
    while hi - lo > 1:
        mid = (lo+hi)//2
        if mid**k > n:
            hi = mid
        else:
            lo = mid
    return lo

for _ in range(int(input())):
    n = int(input())
    ans = root(n,2)
    ans += root(n,3)
    ans -= root(n,6)
    print(ans)