Problem Statement

We have an integer sequence of length $N$: $A_0,A_1,\cdots,A_{N-1}$.

Find the following sum ($\mathrm{lcm}(a, b)$ denotes the least common multiple of $a$ and $b$):

• $\sum_{i=0}^{N-2} \sum_{j=i+1}^{N-1} \mathrm{lcm}(A_i,A_j)$

Since the answer may be enormous, compute it modulo $998244353$.

Constraints

• $1 \leq N \leq 200000$
• $1 \leq A_i \leq 1000000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_0\ A_1\ \cdots\ A_{N-1}

Output

Print the sum modulo $998244353$.