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

$1 \le t \le 100$

$5\le N \le10^5$

$1\le B1, B2 \le N$