{"problem":{"name":"LCMs","description":{"content":"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}","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc038_c"},"statements":[{"statement_type":"Markdown","content":"We have an integer sequence of length $N$: $A_0,A_1,\\cdots,A_{N-1}$.\nFind the following sum ($\\mathrm{lcm}(a, b)$ denotes the least common multiple of $a$ and $b$):\n\n*   $\\sum_{i=0}^{N-2} \\sum_{j=i+1}^{N-1} \\mathrm{lcm}(A_i,A_j)$\n\nSince the answer may be enormous, compute it modulo $998244353$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 200000$\n*   $1 \\leq A_i \\leq 1000000$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_0\\ A_1\\ \\cdots\\ A_{N-1}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc038_c","tags":[],"sample_group":[["3\n2 4 6","22\n\n$\\mathrm{lcm}(2,4)+\\mathrm{lcm}(2,6)+\\mathrm{lcm}(4,6)=4+6+12=22$."],["8\n1 2 3 4 6 8 12 12","313"],["10\n356822 296174 484500 710640 518322 888250 259161 609120 592348 713644","353891724"]],"created_at":"2026-03-03 11:01:14"}}