Chessboard Distance

 The Chessboard Distance for any two points 

(X1,Y1)$(X_1,Y_1)$ and (X2,Y2)$(X_2,Y_2)$ on a Cartesian plane is defined as max(|X1−X2|,|Y1−Y2|)$max(|X_1-X_2|,|Y_1-Y_2|)$.

You are given two points (X1,Y1)$(X_1,Y_1)$ and (X2,Y2)$(X_2,Y_2)$. Output their Chessboard Distance.

Note that, |P|$|P|$ denotes the absolute value of integer P$P$. For example, |−4|=4$|-4|=4$ and |7|=7$|7|=7$.

Input Format

• First line will contain T$T$, the number of test cases. Then the test cases follow.
• Each test case consists of a single line of input containing 4$4$ space separated integers - X1,Y1,X2,Y2$X_1,Y_1,X_2,Y_2$ - as defined in the problem statement.

Output Format

For each test case, output in a single line the chessboard distance between (X1,Y1)$(X_1,Y_1)$ and (X2,Y2)$(X_2,Y_2)$

Constraints

• 1≤T≤1000$1\le T\le 1000$
• 1≤X1,Y1,X2,Y2≤105$1\le X_1,Y_1,X_2,Y_2\le {10}^5$

Subtasks

Subtask #1 (100 points): original constraints

Sample Input 1 

3
2 4 5 1
5 5 5 3
1 4 3 3

Sample Output 1 

3
2
2

Explanation

• In the first case, the distance between (2,4)$(2,4)$ and (5,1)$(5,1)$ is max(|2−5|,|4−1|)=max(|−3|,|3|)=3$max(|2-5|,|4-1|)=max(|-3|,|3|)=3$.

• In the second case, the distance between (5,5)$(5,5)$ and (5,3)$(5,3)$ is max(|5−5|,|5−3|)=max(|0|,|2|)=2$max(|5-5|,|5-3|)=max(|0|,|2|)=2$.

• In the third case, the distance between (1,4)$(1,4)$ and (3,3)$(3,3)$ is max(|1−3|,|4−3|)=max(|−2|,|1|)=2$max(|1-3|,|4-3|)=max(|-2|,|1|)=2$.