For given numbers $n$, $a$ and a set $S$, define the set $a^S$ = {${{a^t~mod~n:t~is~in~S}}$}.

For $n = 998244353$ and $S$ = Set of natural numbers, find

$$\sum_{i=1}^{n}{|i^S|}$$

Give $ans$ modulo $10^9+7$ .

Note: $|X|$ denote the size of set $X$.