Boxers

TimeLimit:2000MS  MemoryLimit:256MB
64-bit integer IO format:%I64d
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Problem Description

There are n boxers, the weight of the -th boxer is . Each of them can change the weight by no more than  before the competition (the weight cannot become equal to zero, that is, it must remain positive). Weight is always an integer number.

It is necessary to choose the largest boxing team in terms of the number of people, that all the boxers' weights in the team are different (i.e. unique).

Write a program that for given current values ai will find the maximum possible number of boxers in a team.

It is possible that after some change the weight of some boxer is  (but no more).


Input

The first line contains an integer  (  ) — the number of boxers. The next line contains n integers , where (   ) is the weight of the -th boxer.

Output

Print a single integer — the maximum possible number of people in a team.

SampleInput 1
4
3 2 4 1
SampleOutput 1
4
SampleInput 2
6
1 1 1 4 4 4
SampleOutput 2
5
Note

In the first example, boxers should not change their weights — you can just make a team out of all of them. In the second example, one boxer with a weight of 1 can be increased by one (get the weight of 2), one boxer with a weight of 4 can be reduced by one, and the other can be increased by one (resulting the boxers with a weight of 3 and 5, respectively). Thus, you can get a team consisting of boxers with weights of 5,4,3,2,1.

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题目统计信息详细
总AC数11
通过人数11
尝试人数14
总提交量72
AC率15.28%
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