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 Python (3.4.3) (judge verdict: Runtime Error)

import math 
import sys
sys.setrecursionlimit(2000000000000000000000000000000000000000000)
def lcm(x, y):
    ans = int((x * y) / math.gcd(x, y))
    return ans


N = int(input())
A = input().split()
S = 0
for i in range(len(A)):
    A[i] = int(A[i])

for i in range(N-1):
    for j in range(i+1,N):
        
        S += lcm(A[i],A[j])
        S = S % 998244353
        

print(S)