Problem Statement

For a positive integer $x$, let $\\mathrm{ctz}(x)$ be the number of trailing zeros in the binary representation of $x$.
For example, we have $\\mathrm{ctz}(8)=3$ because the binary representation of $8$ is 1000, and $\\mathrm{ctz}(5)=0$ because the binary representation of $5$ is 101.

You are given a sequence of non-negative integers $T = (T_1,T_2,\\dots,T_N)$.
Consider making a sequence of positive integers $A = (A_1, A_2, \\dots, A_N)$ of your choice so that it satisfies the following conditions.

• $A_1 \\lt A_2 \\lt \\cdots \\lt A_{N-1} \\lt A_N$ holds. In other words, $A$ is strictly increasing.
• $\\mathrm{ctz}(A_i) = T_i$ holds for every integer $i$ such that $1 \\leq i \\leq N$.

What is the minimum possible value of $A_N$ here?

Constraints

• $1 \\leq N \\leq 10^5$
• $0 \\leq T_i \\leq 40$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $T_1$ $T_2$ $\\dots$ $T_N$

Output

Print the answer.

Sample Input 1

4
0 1 3 2

Sample Output 1

12

For example, $A_1=3,A_2=6,A_3=8,A_4=12$ satisfy the conditions.
$A_4$ cannot be $11$ or less, so the answer is $12$.

Sample Input 2

5
4 3 2 1 0

Sample Output 2

31

Sample Input 3

1
40

Sample Output 3

1099511627776

Note that the answer may not fit into a $32$-bit integer.

Sample Input 4

8
2 0 2 2 0 4 2 4

Sample Output 4

80