A7993 | Savior

Misha 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.

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.

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