Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Lucky Tickets

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya thinks that lucky tickets are the tickets whose numbers are divisible by 3. He gathered quite a large collection of such tickets but one day his younger brother Leonid was having a sulk and decided to destroy the collection. First he tore every ticket exactly in two, but he didn’t think it was enough and Leonid also threw part of the pieces away. Having seen this, Vasya got terrified but still tried to restore the collection. He chose several piece pairs and glued each pair together so that each pair formed a lucky ticket. The rest of the pieces Vasya threw away reluctantly. Thus, after the gluing of the 2*t* pieces he ended up with *t* tickets, each of which was lucky.

When Leonid tore the tickets in two pieces, one piece contained the first several letters of his number and the second piece contained the rest.

Vasya can glue every pair of pieces in any way he likes, but it is important that he gets a lucky ticket in the end. For example, pieces 123 and 99 can be glued in two ways: 12399 and 99123.

What maximum number of tickets could Vasya get after that?

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{4}) — the number of pieces. The second line contains *n* space-separated numbers *a*_{i} (1 ≤ *a*_{i} ≤ 10^{8}) — the numbers on the pieces. Vasya can only glue the pieces in pairs. Even if the number of a piece is already lucky, Vasya should glue the piece with some other one for it to count as lucky. Vasya does not have to use all the pieces. The numbers on the pieces an on the resulting tickets may coincide.

Output

Print the single number — the maximum number of lucky tickets that will be able to be restored. Don't forget that every lucky ticket is made of exactly two pieces glued together.

Examples

Input

3

123 123 99

Output

1

Input

6

1 1 1 23 10 3

Output

1

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/26/2017 12:01:20 (c4).

Desktop version, switch to mobile version.

User lists

Name |
---|