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Let $\sigma_0(n)$ be the number of positive divisors of $n$.

For example, $\sigma_0(1) = 1$, $\sigma_0(2) = 2$ and $\sigma_0(6) = 4$.

Let $$S_3(n) = \sum _{i=1}^n \sigma_0(i^3).$$

Given $N$, find $S_3(N)$.

Input

First line contains $T$ ($1 \le T \le 10000$), the number of test cases.

Each of the next $T$ lines contains a single integer $N$. ($1 \le N \le 10^{11}$)

Output

For each number $N$, output a single line containing $S_3(N)$.

Example

Input

5
1
2
3
10
100

Output

1
5
9
73
2302

Explanation for Input

- $S_3(3) = \sigma_0(1^3) + \sigma_0(2^3) + \sigma_0(3^3) = 1 + 4 + 4 = 9$

Information

There are 5 Input files.

- Input #1: $1 \le N \le 10000$, TL = 1s.

- Input #2: $1 \le T \le 300,\ 1 \le N \le 10^{8}$, TL = 20s.

- Input #3: $1 \le T \le 75,\ 1 \le N \le 10^{9}$, TL = 20s.

- Input #4: $1 \le T \le 15,\ 1 \le N \le 10^{10}$, TL = 20s.

- Input #5: $1 \le T \le 2,\ 1 \le N \le 10^{11}$, TL = 20s.

My C++ solution runs in 7.1 sec. (total time)

Source Limit is 12 KB.