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 <bits/stdc++.h>
using namespace std;

typedef long long lli;

const lli INF = 1LL<<60;

int main() {
  int N;
  cin >> N;
  vector<lli> a(N);
  for(int i = 0; i < N; ++i) {
    cin >> a[i];
  }
  a.push_back(INF);
  sort(a.begin(), a.end());
  lli sum = 0;
  for(int i = 0; i < a.size(); ++i) {
    if(sum+1 < a[i]) {
      cout << sum+1 << endl;
      break;
    }
    sum += a[i];
  }
  return 0;
}