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?

Input

Input is given from Standard Input in the following format:
N
$T_1 T_2 \dots T_N$

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分