单点时限: 2.0 sec
内存限制: 1024 MB
Cuber QQ’s research interests lie in number theory, especially for greatest common divisor (GCD) and least common multiple (LCM).
He is also an artist, the creator of beautiful things. On his birthday, his friends will send him some positive integer sets as gifts.
Assume Cuber QQ receive a non-empty positive integer set $S={p_1,p_2,\cdots ,p_k}$, if $\gcd(p_1,p_2,\cdots ,p_k)=1$ and $\operatorname{lcm}(p_1,p_2,\cdots ,p_k)=n$, Cuber QQ think it is a beautiful set.
Cuber QQ will give his friends $n$, his friends now want to know the number of non-empty positive integer sets which is beautiful.
The only line contains one integer $n$ ($1\le n\le 10^{12}$).
The output contains one integer indicating the answer.
Print the answer modulo $998~244~353$.
4
2
100
322
For the first example, all beautiful sets are ${1,4},{1,2,4}$.