Statement

Baby Bob is learning about mathematical expressions. He despises operands and operators, and only likes round brackets. He's got a sequence A of positive integers A_1, A_2, …, A_N. He wants to bracketize the sequence. A bracketized sequence created from A is a sequence of strings B_1, B_2, …, B_N such that each B_i has length A_i, and B_i consists only of either opening brackets "(", or closing brackets ")", but not both. For example let A=(1,3,4). (1) A possible bracketized sequence created from A is ")", ")))", "((((". (2) The sequence ")", ")()", "((((" is not a bracketized sequence created from A, because the second element consists of both opening and closing brackets. (3) The sequence "(", "))))", "((((" is not a bracketized sequence created from A, because the length of the second element is not 3. (4) The sequence "(", ")" is not a bracketized sequence created from A, because it consists of only 2 strings. Take the string B_1 + B_2 + … + B_N (i.e...