CF682B.Alyona and Mex

普及/提高-

通过率:0%

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题目描述

Someone gave Alyona an array containing nn positive integers a1,a2,...,ana_{1},a_{2},...,a_{n} . In one operation, Alyona can choose any element of the array and decrease it, i.e. replace with any positive integer that is smaller than the current one. Alyona can repeat this operation as many times as she wants. In particular, she may not apply any operation to the array at all.

Formally, after applying some operations Alyona will get an array of nn positive integers b1,b2,...,bnb_{1},b_{2},...,b_{n} such that 1<=bi<=ai1<=b_{i}<=a_{i} for every 1<=i<=n1<=i<=n . Your task is to determine the maximum possible value of mex of this array.

Mex of an array in this problem is the minimum positive integer that doesn't appear in this array. For example, mex of the array containing 11 , 33 and 44 is equal to 22 , while mex of the array containing 22 , 33 and 22 is equal to 11 .

输入格式

The first line of the input contains a single integer nn ( 1<=n<=1000001<=n<=100000 ) — the number of elements in the Alyona's array.

The second line of the input contains nn integers a1,a2,...,ana_{1},a_{2},...,a_{n} ( 1<=ai<=1091<=a_{i}<=10^{9} ) — the elements of the array.

输出格式

Print one positive integer — the maximum possible value of mex of the array after Alyona applies some (possibly none) operations.

输入输出样例

  • 输入#1

    5
    1 3 3 3 6
    

    输出#1

    5
    
  • 输入#2

    2
    2 1
    

    输出#2

    3
    

说明/提示

In the first sample case if one will decrease the second element value to 22 and the fifth element value to 44 then the mex value of resulting array 11 22 33 33 44 will be equal to 55 .

To reach the answer to the second sample case one must not decrease any of the array elements.

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