There is a knight on an infinite chessboard. The rows and columns are $1$ -indexed.
Your task is to efficiently process queries of the form: when the knight starts at position $(x,y)$ , what is the minimum number of moves the knight needs to do to reach the top-left corner.
The first line has an integer $n$ : the number of queries.
After this, there are $n$ lines. Each line has two integers $x$ and $y$ : the knight position.
For each query, print the minimum number of moves.
4 1 1 2 3 4 1 42 1337\n · \n · \n · \n · \n
0 1 3 669\n \n \n \n