Strange Currency System

Time Limit : 8 sec, Memory Limit : 131072 KB

Problem I: Strange Currency System

The currency system in the Kingdom of Yoax-Musty is strange and fairly inefficient. Like other countries, the kingdom has its own currencty unit denoted by K$ (kingdom dollar). However, the Ministry of Finance issues bills for every value between 1 K$ and (231 - 1) K$ worth.

On the other hand, this system often enables people to make many di erent values just with a small number of bills. For example, if you have four bills of 1 K$, 2 K$, 4 K$, and 8 K$ worth respectively, you can make any values from 1 K$ to 15 K$.

In this problem, you are requested to write a program that finds the minimum value that cannot be made with a given set (multiset in a mathematical sense) of bills. For the case with the four bills (1 K$, 2 K$, 4 K$, and 8 K$), since you can make any values up to 15 K$, your program should report 16 K$.


The input consists of two lines. The first line contains an integer N (1 ≤ N ≤ 10000), the number of bills. The second line contains N integers, each of which represents the value of a bill in K$. There may be multiple bills of the same value.


Print the minimum value unable to be made on a line. The value should be given in K$ and without any currency sign or name.

Sample Input and Output

Input #1

1 2 4 8

Output #1


Input #2

1 1 3 11 2

Output #2


Source: ACM-ICPC Japan Alumni Group Winter Camp , Day 3, Tokyo, Japan, 2009-02-23