Duizi and Shunzi

Time Limit: 6000/3000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Description

Nike likes playing cards and makes a problem of it.

Now give you n integers, $a_i (1 \le i \le n) $

We define two identical numbers (eg: $ 2,2 $) a Duizi,
and three consecutive positive integers (eg: $ 2,3,4 $) a Shunzi.

Now you want to use these integers to form Shunzi and Duizi as many as possible.

Let s be the total number of the Shunzi and the Duizi you formed.

Try to calculate $max(s)$.

Each number can be used only once.

Input

The input contains several test cases.

For each test case, the first line contains one integer n($ 1 \le n \le 10^6$).
Then the next line contains n space-separated integers $a_i$ ($1 \le a_i \le n$)

Output

For each test case, output the answer in a line.

Sample Input

7 1 2 3 4 5 6 7 9 1 1 1 2 2 2 3 3 3 6 2 2 3 3 3 3 6 1 2 3 3 4 5

Sample Output

2 4 3 2
Hint
Case 1(1,2,3)(4,5,6) Case 2(1,2,3)(1,1)(2,2)(3,3) Case 3(2,2)(3,3)(3,3) Case 4(1,2,3)(3,4,5)

Hint

liuyiding

Source

2017ACM/ICPC广西邀请赛-重现赛(感谢广西大学)

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