H. Defense Deployment
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

In an infinite plane, there are $$$n$$$ launch towers with distinct coordinates, where the coordinates of the $$$i$$$-th launch tower are $$$(a_i,b_i)$$$. The launch towers can fire light arrows.

If a launch tower is located at $$$(x,y)$$$, it will fire one light arrow in the positive direction and one in the negative direction parallel to each of the coordinate axes, with $$$(x,y)$$$ as the center. The light arrows move along the rays in the direction of firing and do not stop. The area covered by the light arrows is considered the attack range of the arrows.

Each launch tower continuously fires light arrows in the four directions around it. The light arrows are penetrating and will not stop upon encountering other light arrows or launch towers. When two launch towers are within each other's attack range, we consider them to be attacking each other.

You are asked to find the number of pairs $$$(i,j)$$$ such that the $$$i$$$-th launch tower and the $$$j$$$-th launch tower will attack each other. Where $$$1 \leq i \lt j \leq n$$$.

Input

The input consists of multiple data sets.

First, there is a line with an integer $$$T(1 \le T \le 50)$$$, indicating the number of data sets.

For each data set, first, there is a line with an integer $$$n(1 \le n \le 10^5)$$$, indicating the number of launch towers.

Next, there is a line with $$$n$$$ integers $$$a_1, a_2, \dots, a_n(1 \leq a_i \leq 10^5)$$$.

Then, there is a line with $$$n$$$ integers $$$b_1, b_2, \dots, b_n(1 \leq b_i \leq 10^5)$$$.

It is guaranteed that for all data in a test case, the sum of $$$n$$$ does not exceed $$$10^5$$$.

Output

Output a total of $$$T$$$ lines.

For each data set, output an integer representing the number of pairs that satisfy the problem's conditions.

Example
Input
2
4
1 2 3 1
2 3 1 3
4
1 1 1 1
2 3 4 5
Output
2
6
Note

In the first data set, the following pairs satisfy the conditions: $$$(1,4),(2,4)$$$.

In the second data set, the following pairs satisfy the conditions: $$$(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)$$$.