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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

# coding: utf-8
# Your code here!
def Eratosthenes(N): #N以下の素数のリストを返す
    #iが素数のときis_prime_list[i]=1，それ以外は0
    N+=1
    is_prime_list = [True]*N
    m = int(N**0.5)+1
    for i in range(3,m,2):
        if is_prime_list[i]:
            is_prime_list[i*i::2*i]=[False]*((N-i*i-1)//(2*i)+1)
    return [2] + [i for i in range(3,N,2) if is_prime_list[i]]

#aを破壊的にgcd-zetaする
def zeta_gcd(a):
    n = len(a)-1
    seive = [True]*(n+1)
    for p in range(1,n):
        if seive[p]:
            for i in range(n//p,0,-1):
                a[i] += a[p*i]
                a[i] %= MOD
#    return a

#aを破壊的にgcd-mobiusする
def mobius_gcd(a,primes):
    n = len(a)
    seive = [True]*(n+1)
    for p in range(1,n):
        if seive[p]:
            for i in range(1,n):
                if i*p >= n: break
                a[i] -= a[p*i] 
                a[i] %= MOD
#    return a

################################################

#################################################

SIZE=1000001; MOD=998244353 #ここを変更する

SIZE += 1
inv = [0]*SIZE  # inv[j] = j^{-1} mod MOD
inv[1] = 1
for i in range(2,SIZE):
    inv[i] = MOD - (MOD//i)*inv[MOD%i]%MOD

################################################
#################################################
import sys
#sys.setrecursionlimit(10**6)
readline = sys.stdin.readline 

n = int(input())
a = [int(i) for i in readline().split()]

num = [0]*SIZE
for i in a: num[i] += i

assert n != 3

zeta_gcd(num)
ans = [i*i for i in num]
mobius_gcd(ans)

res = 0
for i,c in enumerate(ans):
    res = (res + c*inv[i])%MOD
for i in a:
    res = (res-i)%MOD
        
print(res*inv[2]%MOD)