Given a number N calculate the number R of different presentations of N in the form A*A+B*B with A and B being positive integers including zero. 1*1+2*2 and 2*2+1*1 are not different presentations. So for input 5 the output is 1.

Input

Fifty tests with one positive integer < 10^9.

Output

Print the illustrated above number R for each test.

Example

Input:
5
7
986244509
Output:
1
0
2