Score : $600$ points
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.
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:
$X$
Print $T$ lines. The $i$-th line should contain the answer for $\rm case_i$.
4 16 1 123456789012 1000000000000000000
5 1 4555793983 23561347048791096
In the first case, the following five sequences can result from the operations.