{"problem":{"name":"Products of Min-Max","description":{"content":"Given is a sequence $A$ of $N$ integers. There are $2^N - 1$ non-empty subsequences $B$ of $A$. Find the sum of $\\max\\left(B\\right) \\times \\min\\left(B\\right)$ over all of them. Since the answer can be","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc116_b"},"statements":[{"statement_type":"Markdown","content":"Given is a sequence $A$ of $N$ integers. There are $2^N - 1$ non-empty subsequences $B$ of $A$. Find the sum of $\\max\\left(B\\right) \\times \\min\\left(B\\right)$ over all of them.\nSince the answer can be enormous, report it modulo $998244353$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $0 \\leq A_i \\leq 998244352$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\cdots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc116_b","tags":[],"sample_group":[["3\n2 4 3","63\n\nThere are $7$ subsequences $B$, as follows:\n\n*   $B = \\left(2\\right)$ : $\\max\\left(B\\right) \\times \\min\\left(B\\right) = 4$\n*   $B = \\left(4\\right)$ : $\\max\\left(B\\right) \\times \\min\\left(B\\right) = 16$\n*   $B = \\left(3\\right)$ : $\\max\\left(B\\right) \\times \\min\\left(B\\right) = 9$\n*   $B = \\left(2, 4\\right)$ : $\\max\\left(B\\right) \\times \\min\\left(B\\right) = 8$\n*   $B = \\left(2, 3\\right)$ : $\\max\\left(B\\right) \\times \\min\\left(B\\right) = 6$\n*   $B = \\left(4, 3\\right)$ : $\\max\\left(B\\right) \\times \\min\\left(B\\right) = 12$\n*   $B = \\left(2, 4, 3\\right)$ : $\\max\\left(B\\right) \\times \\min\\left(B\\right) = 8$\n\nThe answer is the sum of them: $63$."],["1\n10","100"],["7\n853983 14095 543053 143209 4324 524361 45154","206521341"]],"created_at":"2026-03-03 11:01:14"}}