{"problem":{"name":"Active Infants","description":{"content":"There are $N$ children standing in a line from left to right. The activeness of the $i$\\-th child from the left is $A_i$. You can rearrange these children just one time in any order you like. When a c","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc163_e"},"statements":[{"statement_type":"Markdown","content":"There are $N$ children standing in a line from left to right. The activeness of the $i$\\-th child from the left is $A_i$.\nYou can rearrange these children just one time in any order you like.\nWhen a child who originally occupies the $x$\\-th position from the left in the line moves to the $y$\\-th position from the left, that child earns $A_x \\times |x-y|$ happiness points.\nFind the maximum total happiness points the children can earn.\n\n## Constraints\n\n*   $2 \\leq N \\leq 2000$\n*   $1 \\leq A_i \\leq 10^9$\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$A_1$ $A_2$ $...$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc163_e","tags":[],"sample_group":[["4\n1 3 4 2","20\n\nIf we move the $1$\\-st child from the left to the $3$\\-rd position from the left, the $2$\\-nd child to the $4$\\-th position, the $3$\\-rd child to the $1$\\-st position, and the $4$\\-th child to the $2$\\-nd position, the children earns $1 \\times |1-3|+3 \\times |2-4|+4 \\times |3-1|+2 \\times |4-2|=20$ happiness points in total."],["6\n5 5 6 1 1 1","58"],["6\n8 6 9 1 2 1","85"]],"created_at":"2026-03-03 11:01:13"}}