Double Up

문제

A Double Up game consists of a sequence of $nn$ numbers $a_1,\dots ,a_{n}a\_1,\; \backslash ldots,\; a\_n$, where each $a_{i}a\_i$ 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 $4,2,2,1,84,2,2,1,8$, we can merge the $22$s and obtain $4,4,1,84,4,1,8$, then merge the $44$s and obtain $8,1,88,1,8$, then remove the $11$, and, finally, merge the $88$s, obtaining a single final number, $1616$. We play the game until a single number remains. What is the largest number we can obtain?

입력

The input consists of two lines. The first line contains $nn$ ($1\le n\le 10001\; \backslash leq\; n\; \backslash leq\; 1000$). The second line contains numbers $a_1,\dots ,a_{n}a\_1,\; \backslash ldots,\; a\_n$, where $1\le a_i\le 2^{100}1\backslash leq\; a\_i\backslash leq\; 2^\{100\}$ for each $ii$.

출력

The ouput consists of a single line containing the largest number that can be obtained from the input sequence $a_1,\dots ,a_{n}a\_1,\; \backslash ldots,\; a\_n$.