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.

输入描述:

The first line contains one integer n (1 ≤ n ≤ 106) which is the number of lawns. The next line contains n integers ai which are the number of mushrooms on the i-lawn (1 ≤ ai ≤ 107). All the numbers are different.

输出描述:

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