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

D. Savior

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMisha decided to help Pasha and Akim be friends again. He had a cunning plan — to destroy all the laughy mushrooms. He knows that the laughy mushrooms can easily burst when they laugh. Mushrooms grow on the lawns. There are *a*[*t*] mushrooms on the *t*-th lawn.

Misha knows that the lawns where the mushrooms grow have a unique ability. A lawn (say, *i*) can transfer laugh to other lawn (say, *j*) if there exists an integer (say, *b*) such, that some permutation of numbers *a*[*i*], *a*[*j*] and *b* is a beautiful triple (*i* ≠ *j*). A beautiful triple is such three pairwise coprime numbers *x*, *y*, *z*, which satisfy the following condition: *x*^{2} + *y*^{2} = *z*^{2}.

Misha wants to know on which minimal number of lawns he should laugh for all the laughy mushrooms to burst.

Input

The first line contains one integer *n* (1 ≤ *n* ≤ 10^{6}) which is the number of lawns. The next line contains *n* integers *a*_{i} which are the number of mushrooms on the *i*-lawn (1 ≤ *a*_{i} ≤ 10^{7}). All the numbers are different.

Output

Print a single number — the minimal number of lawns on which Misha should laugh for all the mushrooms to burst.

Examples

Input

1

2

Output

1

Input

2

1 2

Output

2

Input

2

3 5

Output

1

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/24/2018 07:20:36 (d1).

Desktop version, switch to mobile version.

User lists

Name |
---|