CF1720A.Burenka Plays with Fractions

Burenka came to kindergarden. This kindergarten is quite strange, so each kid there receives two fractions ($\frac{a}{b}$ and $\frac{c}{d}$) with integer numerators and denominators. Then children are commanded to play with their fractions.

Burenka is a clever kid, so she noticed that when she claps once, she can multiply numerator or denominator of one of her two fractions by any integer of her choice (but she can't multiply denominators by $0$). Now she wants know the minimal number of claps to make her fractions equal (by value). Please help her and find the required number of claps!

布伦卡来到了幼儿园。这所幼儿园非常特别，每个孩子都会收到两个分数（$\frac{a}{b}$ 和 $\frac{c}{d}$），其中分子和分母均为整数。然后孩子们被要求用他们的分数进行游戏。

布伦卡是个聪明的孩子，她注意到：每次她拍一次手，就可以任选自己两个分数中的一个，将其分子或分母乘以任意整数（但不允许将分母乘以 $0$）。现在她想知道：使自己的两个分数（数值上）相等所需的最少拍手次数是多少？请帮帮她，找出所需的最少拍手次数！

The first line contains one integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. Then follow the descriptions of each test case.

The only line of each test case contains four integers $a$, $b$, $c$ and $d$ ($0 \leq a, c \leq 10^9$, $1 \leq b, d \leq 10^9$) — numerators and denominators of the fractions given to Burenka initially.

第一行包含一个整数 $t$（$1 \leq t \leq 10^4$），表示测试用例的数量。随后是每个测试用例的描述。

每个测试用例仅有一行，包含四个整数 $a$、$b$、$c$ 和 $d$（$0 \leq a, c \leq 10^9$，$1 \leq b, d \leq 10^9$），分别表示初始时给 Burenka 的两个分数的分子与分母。

For each test case print a single integer — the minimal number of claps Burenka needs to make her fractions equal.

对于每个测试用例，输出一个整数——Burenka 使她的分数相等所需的最少拍手次数。

In the first case, Burenka can multiply $c$ by $2$, then the fractions will be equal.

In the second case, fractions are already equal.

In the third case, Burenka can multiply $a$ by $4$, then $b$ by $3$. Then the fractions will be equal ($\frac{1 \cdot 4}{2 \cdot 3} = \frac{2}{3}$).

在第一种情况下，Burenka 可以将 $c$ 乘以 $2$，此时两个分数将相等。

在第二种情况下，两个分数已经相等。

在第三种情况下，Burenka 可以先将 $a$ 乘以 $4$，再将 $b$ 乘以 $3$，此时两个分数将相等（$\frac{1 \cdot 4}{2 \cdot 3} = \frac{2}{3}$）。