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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

fun main(args: Array<String>) {
    val MOD = 998244353L
    val N = nextInt()
    val A = listOfLong()
    var ans = 0L
    for (i in 0 until N-1) {
        for (j in i+1 until N) {
            ans += lcm(A[i], A[j])
            ans %= MOD
        }
    }
    println(ans)
}
fun next() = readLine()!!
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun listOfString() = next().split(" ")
fun listOfLong(delta: Long = 0L) = listOfString().map { java.lang.Long.parseLong(it) + delta }
tailrec fun gcd(a: Long, b: Long): Long = if (a % b == 0L) b else gcd(b, a % b)
tailrec fun lcm(a: Long, b: Long): Long = a / gcd(a, b) * b