Problem: 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 different 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 #36; 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 $.



Input

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.

Output

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.

Example

Input




Output

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main(){
	int n;
	cin >> n;

	vector<long long> k(n + 1);
	for(int i = 0; i < n; ++i){
		cin >> k[i];
	}
	k[n] = 1LL << 62;

	sort(k.begin(), k.end());
	long long s = 0;
	for(int i = 0; ; ++i){
		if(k[i] > s + 1) break;
		s += k[i];
	}
	
	cout << s + 1 << endl;
}