Knight Moves Queries

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.

Input

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.

Output

For each query, print the minimum number of moves.

Constraints

$1 \le n \le 10^5$

$1 \le x, y \le 10^9$

Example

Input

4
1 1
2 3
4 1
42 1337

Output

0
1
3
669