Problem2396--Savior

2396: Savior

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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: x2+y2=z2.

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≤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.

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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