{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 18$\n*   $0 \\leq A_i \\leq 10^9 (1\\leq i\\leq N)$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $...$ $A_N$"},{"iden":"sample input 1","content":"4\n3 1 4 2"},{"iden":"sample output 1","content":"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 $16$."},{"iden":"sample input 2","content":"6\n5 2 4 1 6 9"},{"iden":"sample output 2","content":"51"},{"iden":"sample input 3","content":"10\n3 1 4 1 5 9 2 6 5 3"},{"iden":"sample output 3","content":"115"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}