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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll MOD = 998244353;

ll pow(ll n, ll k, ll m) {
	ll r = 1;
	for (; k > 0; k >>= 1) {
		if (k & 1) r = (r*n) % m;
		n = (n*n) % m; 
	}
	return r;
}

ll mo(ll a) {
	if (a >= 0) return a % MOD;
	else if (abs(a) % MOD == 0) return 0;
	else return MOD - abs(a) / MOD;
}

int main() {
	ll n; cin >> n;
	ll ans = 0;
	vector<ll> res(1000001, 0);
	vector<ll> c(1000001, 0);
	for (ll i = 0; i < n; ++i) {
		ll a; cin >> a;
		c[a]++;
	}
	for (ll i = 1000000; i > 0; --i) {
		ll sum_of_sq = 0; ll sq_of_sum = 0;
		for (ll j = 1; j*i < 1000001; ++j) {
			sum_of_sq += pow(j*i, 2, MOD) * c[j*i];
			sum_of_sq %= MOD;
			sq_of_sum += j*i * c[j*i];
			sq_of_sum %= MOD;
		}
		sq_of_sum = pow(sq_of_sum, 2, MOD);
		res[i] = (sq_of_sum - sum_of_sq) * pow(2*i, MOD-2, MOD);
		res[i] = mo(res[i]);
		for (ll j = 2; j*i < 1000001; ++j) {
			res[i] -= res[j*i] * j;
			res[i] = mo(res[i]);
		}
		ans += res[i];
		ans %= MOD;

		//if (i%100000 == 0) cout << "hoge" << endl;
	}
	cout << ans << endl;

	return 0;
}