Problem:
Score : 700 points

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

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main {
	
	public static void main(String[] args) {
		Scanner read = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		int n,datos[], suma=0,temp=0, mod=998244353;
		n = read.nextInt();
		datos = new int[n];
		
		
		for(int i=0; i<n;i++)
			datos[i] = read.nextInt();
		for(int i=0;i<n-1;i++) {
			for(int j=i+1;j<n;j++) {
				temp = mcm(datos[i],datos[j],mod);
				suma=(suma+temp)%mod;
				//suma=suma%mod;
				//System.out.println(datos[i]+" "+datos[j]);
			}
		}
		System.out.println(suma);
	}
	public static int mcm(int a, int b,int mod) {
		int result=((a*b)%mod)/mcd(a,b);
		return result;
	}
	public static int mcd(int a, int b) {
		return b == 0 ? a:mcd(b,a%b);
	}

}