following operations on a triple of integers. In one operation, you should:
Choose an integer d and an arithmetic operation ― either addition or multiplication.
Choose a subset of elements of the triple.
Apply the arithmetic operation to each of the chosen elements, i.e. either add d to each of them or multiply each of them by d.
For example, if we have a triple (3,5,7), we may choose to add 3 to the first and third element, and we get (6,5,10) using one operation.
You are given an initial triple (p,q,r) and a target triple (a,b,c). Find the minimum number of operations needed to transform (p,q,r) into (a,b,c).
Input
The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains three space-separated integers p, q and r.
The second line contains three space-separated integers a, b and c.
Output
For each test case, print a single line containing one integer ― the minimum required number of operations.
Constraints
1≤T≤1,000
|p|,|q|,|r|,|a|,|b|,|c|≤109
Subtasks
Subtask #1 (10 points): |p|,|q|,|r|,|a|,|b|,|c|≤10
Subtask #2 (90 points): original constraints
Example Input
2
3 5 7
6 5 10
8 6 3
9 7 8
Example Output
1
2
Explanation
Example case 1: We add 3 to the first and third element of (3,5,7) to form (6,5,10).
Example case 2: We can add 1 to each element to form (9,7,4) and then multiply the third element by 2.