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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

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