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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = long.Parse(Console.ReadLine());

            var LCMmatrix = new long[200001];

            var A = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long MOD = 998244353;

            long ans = 0;


            // //LCMをすべて先に計算する。
            // for (int i = 0; i < n; i++)
            // {
            //     for (int j = i; j < n; j++)
            //     {
            //         LCMmatrix[i, j] = LCM(A[i], A[j]);
            //         LCMmatrix[j, i] = LCMmatrix[i, j];
            //     }
            // }


            // 計算
            for (long i = 0; i <= n - 2; i++)
            {
                long sum = 0;
                for (long j = i + 1; j <= n - 1; j++)
                {
                    sum = (sum + LCM(i, j)) % MOD;
                }
                ans = (ans + sum) % MOD;
            }

            Console.WriteLine(ans);
        }

        static long LCM(long m, long n)
        {
            return m / GCD(m, n) * n; ;
        }

        static long GCD(long m, long n)
        {
            while (true)
            {
                if (n == 0) return m;
                m %= n;
                if (m == 0) return n;
                n %= m;
            }
        }

    }
}