{"raw_statement":[{"iden":"problem statement","content":"You have an integer sequence of length $N$: $a_1, a_2, ..., a_N$.\nYou repeatedly perform the following operation until the length of the sequence becomes $1$:\n\n*   First, choose an element of the sequence.\n*   If that element is at either end of the sequence, delete the element.\n*   If that element is not at either end of the sequence, replace the element with the sum of the two elements that are adjacent to it. Then, delete those two elements.\n\nYou would like to maximize the final element that remains in the sequence.\nFind the maximum possible value of the final element, and the way to achieve it."},{"iden":"constraints","content":"*   All input values are integers.\n*   $2 \\leq N \\leq 1000$\n*   $|a_i| \\leq 10^9$"},{"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":"5\n1 4 3 7 5"},{"iden":"sample output 1","content":"11\n3\n1\n4\n2\n\nThe sequence would change as follows:\n\n*   After the first operation: $4, 3, 7, 5$\n*   After the second operation: $4, 3, 7$\n*   After the third operation: $11(4+7)$"},{"iden":"sample input 2","content":"4\n100 100 -1 100"},{"iden":"sample output 2","content":"200\n2\n3\n1\n\n*   After the first operation: $100, 200(100+100)$\n*   After the second operation: $200$"},{"iden":"sample input 3","content":"6\n-1 -2 -3 1 2 3"},{"iden":"sample output 3","content":"4\n3\n2\n1\n2\n\n*   After the first operation: $-4, 1, 2, 3$\n*   After the second operation: $1, 2, 3$\n*   After the third operation: $4$"},{"iden":"sample input 4","content":"9\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000"},{"iden":"sample output 4","content":"5000000000\n4\n2\n2\n2\n2"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}