CF2199B Two Towers

You have two towers made of blocks, standing next to each other. Initially, the height of the first tower is $ a $ , and the height of the second tower is $ b $ . In one action, you can: - take one block and place it on one of the towers, increasing its height by $ 1 $ ; - or take two blocks and place one on each tower, increasing both heights by $ 1 $ . However, this can only be done if their heights are equal. Your goal is to make the height of the first tower equal to $ c $ , and the height of the second tower equal to $ d $ . What is the minimum number of actions you need to perform?

The first line contains one integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Each test case consists of one line containing $ 4 $ integers $ a, b, c, d $ ( $ 1 \le a \le c \le 10^8 $ ; $ 1 \le b \le d \le 10^8 $ ).

For each test case, output one integer — the minimum number of actions that you have to perform.

In the first example, you can first place a block on the first tower, making the heights of both towers equal to $ 2 $ . Then, you can place one block on each tower, raising their heights to $ 3 $ . After that, you can place two blocks on the second tower, increasing its height to $ 5 $ . Thus, in $ 4 $ moves, you can make the height of the first tower equal to $ 3 $ and the second tower equal to $ 5 $ .