{"problem":{"name":"Add and Remove","description":{"content":"There is a stack of $N$ cards, each of which has a non-negative integer written on it. The integer written on the $i$\\-th card from the top is $A_i$. Snuke will repeat the following operation until tw","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc035_d"},"statements":[{"statement_type":"Markdown","content":"There is a stack of $N$ cards, each of which has a non-negative integer written on it. The integer written on the $i$\\-th card from the top is $A_i$.\nSnuke will repeat the following operation until two cards remain:\n\n*   Choose three consecutive cards from the stack.\n*   Eat the middle card of the three.\n*   For each of the other two cards, replace the integer written on it by the sum of that integer and the integer written on the card eaten.\n*   Return the two cards to the original position in the stack, without swapping them.\n\nFind the minimum possible sum of the integers written on the last two cards remaining.\n\n## Constraints\n\n*   $2 \\leq N \\leq 18$\n*   $0 \\leq A_i \\leq 10^9 (1\\leq i\\leq N)$\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":"agc035_d","tags":[],"sample_group":[["4\n3 1 4 2","16\n\nWe can minimize the sum of the integers written on the last two cards remaining by doing as follows:\n\n*   Initially, the integers written on the cards are $3$, $1$, $4$, and $2$ from top to bottom.\n*   Choose the first, second, and third card from the top. Eat the second card with $1$ written on it, add $1$ to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now $4$, $5$, and $2$ from top to bottom.\n*   Choose the first, second, and third card from the top. Eat the second card with $5$ written on it, add $5$ to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now $9$ and $7$ from top to bottom.\n*   The sum of the integers written on the last two cards remaining is $16$."],["6\n5 2 4 1 6 9","51"],["10\n3 1 4 1 5 9 2 6 5 3","115"]],"created_at":"2026-03-03 11:01:14"}}