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 $998244353$.

Sample Input 1

3
2 4 6

Sample Output 1

22

$\\mathrm{lcm}(2,4)+\\mathrm{lcm}(2,6)+\\mathrm{lcm}(4,6)=4+6+12=22$.

Sample Input 2

8
1 2 3 4 6 8 12 12

Sample Output 2

313

Sample Input 3

10
356822 296174 484500 710640 518322 888250 259161 609120 592348 713644

Sample Output 3

353891724