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G - Sqrt

Score : $600$ points

Problem Statement

We have a sequence of length $1$: $A=(X)$. Let us perform the following operation on this sequence $10^{100}$ times.

Operation: Let $Y$ be the element at the end of $A$. Choose an integer between $1$ and $\sqrt{Y}$ (inclusive), and append it to the end of $A$.

How many sequences are there that can result from $10^{100}$ operations?

You will be given $T$ test cases to solve.

It can be proved that the answer is less than $2^{63}$ under the Constraints.

Constraints

• $1 \leq T \leq 20$
• $1 \leq X \leq 9\times 10^{18}$
• All values in input are integers.

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Input

Input is given from Standard Input in the following format:

$T$

$\rm case_1$

$\vdots$

$\rm case_T$

Each case is in the following format:

``` $X$ ```

Output

Print $T$ lines. The $i$-th line should contain the answer for $\rm case_i$.

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4
16
1
123456789012
1000000000000000000

5
1
4555793983
23561347048791096

In the first case, the following five sequences can result from the operations.

• $(16,4,2,1,1,1,\ldots)$
• $(16,4,1,1,1,1,\ldots)$
• $(16,3,1,1,1,1,\ldots)$
• $(16,2,1,1,1,1,\ldots)$
• $(16,1,1,1,1,1,\ldots)$