Description
Dr. Xenovian has developed a fantastic new computer game, but it requires a new type of multi-core computer that she designed. The cores in this computer must come in multiples of 12 AND they must be arranged on the motherboard in a perfect square.
Atfter talking to each customer, Dr. Xenovian determines the minimum number of cores they need ( x ) and the maximum number of cores they can afford ( y ). Given this range in the number of cores possible, she then needs to calculate how many of these values are divisible by 12 (d ), how many are perfect squares ( s ), and how many values have both qualities ( b ).
Write a program to perform these calculations.
Input Format
The first line contains C, the number of customers she needs to perform calculations for. C ranges then follow, each on a new line.
Each test contains two space-separated integers denoting the MIN( x ) and the MAX( y ) number of cores, inclusive.
Constraints
1 ≤ C ≤ 100
1 ≤ x ≤ y ≤ 109
Output Format
With each customer result on a new line, print out d, s, and b (where d is the number of values divisible by 12, s is the number of perfect squares, and b is the number of values that meet both criteria).
Example 0
Sample Input
2
6 12
25 37
Sample Output
1 1 0
1 2 1
Explanation
Two customer orders are put in.
The first can afford a computer with 6 to 12 cores in it. Of those, only one possibility is a multiple of 12 (12 itself), one is a perfect square (9), and none meet both criteria.
The second customer can afford a computer with 25 to 37 cores. Of those, one is a multiple of 12 (36 cores), two are perfect squares (25 and 36) and one meet both criteria (36).
