Burenka came to kindergarden. This kindergarten is quite strange, so each kid there receives two fractions (abab and cdcd) 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 00). 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!
The first line contains one integer tt (1≤t≤1041≤t≤104) — the number of test cases. Then follow the desc
The only line of each test case contains four integers aa, bb, cc and dd (0≤a,c≤1090≤a,c≤109, 1≤b,d≤1091≤b,d≤109) — numerators and denominators of the fractions given to Burenka initially.
For each test case print a single integer — the minimal number of claps Burenka needs to make her fractions equal.
8
2 1 1 1
6 3 2 1
1 2 2 3
0 1 0 100
0 1 228 179
100 3 25 6
999999999 300000000 666666666 100000000
33 15 0 84
1
0
2
0
1
1
1
1
In the first case, Burenka can multiply cc by 22, then the fractions will be equal.
In the second case, fractions are already equal.
In the third case, Burenka can multiply aa by 44, then bb by 33. Then the fractions will be equal (1⋅42⋅3=231⋅42⋅3=23).