Migrated from Lutece 1985 方程的解

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Description

给定一个四元二次方程：

$AX_1^2+BX_2^2+CX_3^2+DX_4^2=0$

试求$-1000 \le X_1,X_2,X_3,X_4 \le 1000$非零整数解的个数。

Input

第一行四个整数$A,B,C,D$

$-10000 \le A,B,C,D \le 10000$

Output

第一行一个整数$x$，表示方程整数解的个数。

Samples

-5891 4371 -5007 4394

3536

2996 4828 2392 -3903

3328

1 -10 -100 1000

567888

Resources

2018 UESTC ACM Training for Search Algorithm and String