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.

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 $\\rm case_i$.

Sample Input 1

4
16
1
123456789012
1000000000000000000

Sample Output 1

5
1
4555793983
23561347048791096

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

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