Number of triangles

You are given a polygon of $N$ sides with vertices numbered from $1,2,...,N$. Now, exactly $2$ vertices of the polygons are colored black and remaining are colored white. You are required to find the number of triangles denoted by $A$ such that:

1. The triangle is formed by joining only the white-colored vertices of the polygon.
2. The triangle shares at least one side with the polygon.

Input format

• The first line contains $t$ denoting the number of test cases.
• Next $t$ lines contain three space-separated integers $N$, $B1$, and $B2$ where $N$ is the number of sides in the polygon and $B1,B2$denote the vertices that are colored black.

Output format
For each test case, print the answer $A$ representing the number of triangles that can be formed with the given conditions in the problem statement. 
Constraints
$1\le t\le 100$
$5\le N\le {10}^5$
$1\le B1,B2\le N$

SAMPLE INPUT

1
6 2 5

SAMPLE OUTPUT

4

Explanation

The number of triangles which satisfy the property are 4  - $\mathrm{△}$136 , $\mathrm{△}$146 , $\mathrm{△}$346 and $\mathrm{△}$134 

Note:- I personally solving this problem scored only 85/100