Answer $Q$ ($1\le Q\le 10^5$) independent queries each of the following form: You are given four integers $a,b,c,d$ ($-10^{18}\le a,b,c,d\le 10^{18}$). In one operation you can either do $a\mathrel{+}=b$, or $b\mathrel{+}=a$. Determine the minimum number of operations to transform $(a,b)$ into $(c,d)$, or if it is impossible to do so, output $-1$.
Input Format
The next $Q$ lines each contain four integers $a,b,c,d$.
Output Format
The answer for each query on a separate line.
Sample Data
Sample Input
4 5 -3 -1 -3 5 3 5 2 5 3 8 19 5 3 5 3
Sample Output
2 -1 3 0
Sample Explanation
First query: $(5,-3)\to (2,-3)\to (-1,-3)$ Second query: Impossible. Third query: $(5,3) \to (8, 3) \to (8, 11) \to (8, 19)$ Fourth query: No operations necessary.
Constraints
- Input 2: $|a|, |b|, |c|,|d|\le 10$
- Input 3: $a,b\ge 0$
- Input 4: $a \geq 0 \geq b$
- Input 5: $a \leq 0 \leq b$
- Input 6: $a,b\le 0$
- Input 7: $c,d\ge 0$
- Input 8: $c \geq 0 \geq d$
- Input 9: $c \leq 0 \leq d$
- Input 10: $c,d\le 0$
- Inputs 11-14: $Q \leq 10^3$
- Inputs 15-19: No additional constraints.