Score : 700 points
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):
Since the answer may be enormous, compute it modulo 998244353.
Input is given from Standard Input in the following format:
N A_0\ A_1\ \cdots\ A_{N-1}
Print the sum modulo 998244353.
3 2 4 6
22
\mathrm{lcm}(2,4)+\mathrm{lcm}(2,6)+\mathrm{lcm}(4,6)=4+6+12=22.
8 1 2 3 4 6 8 12 12
313
10 356822 296174 484500 710640 518322 888250 259161 609120 592348 713644
353891724