You are standing at point on an infinite plane. In one step, you can move from some point to any point as long as the Euclidean distance, , between the two points is either or . In other words, each step you take must be exactly or in length.
You are given queries in the form of , , and . For each query, print the minimum number of steps it takes to get from point to point on a new line.
The first line contains an integer, , denoting the number of queries you must process.
Each of the subsequent lines contains three space-separated integers describing the respective values of , , and for a query.
For each query, print the minimum number of steps necessary to get to point on a new line.
Sample Input 0
32 3 11 2 03 4 11
Sample Output 0
We perform the following queries:
One optimal possible path requires two steps of length : . Thus, we print the number of steps, , on a new line.
The starting and destination points are both , so we needn't take any steps. Thus, we print on a new line.
One optimal possible path requires two steps of length and one step of length : . Thus, we print on a new line.