A Double Up game consists of a sequence of $$$n$$$ numbers $$$a_1, \ldots, a_n$$$, where each $$$a_i$$$ is a power of two. In one move one can either remove one of the numbers, or merge two identical adjacent numbers into a single number of twice the value. For example, for sequence $$$4,2,2,1,8$$$, we can merge the $$$2$$$s and obtain $$$4,4,1,8$$$, then merge the $$$4$$$s and obtain $$$8,1,8$$$, then remove the $$$1$$$, and, finally, merge the $$$8$$$s, obtaining a single final number, $$$16$$$. We play the game until a single number remains. What is the largest number we can obtain?
The input consists of two lines. The first line contains $$$n$$$ ($$$1 \leq n \leq 1000$$$). The second line contains numbers $$$a_1, \ldots, a_n$$$, where $$$1\leq a_i\leq 2^{100}$$$ for each $$$i$$$.
The ouput consists of a single line containing the largest number that can be obtained from the input sequence $$$a_1, \ldots, a_n$$$.
5 4 2 2 1 8
16
