Description

Input

The first line of input contains an integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

Then follows the description of each test case.

The only line of each test case description contains $3$ integers $n$, $x$, $y$ ($1 \le n \le 10^9$, $1 \le x, y \le n$).

Output

For each test case, output a single integer — the maximum score among all permutations of length $n$.

8
7 2 3
12 6 3
9 1 9
2 2 2
100 20 50
24 4 6
1000000000 5575 25450
4 4 1
 
 
 
 

12
-3
44
0
393
87
179179179436104
-6

Note

The first test case is explained in the problem statement above.

In the second test case, one of the optimal permutations will be $[12,11,\color{blue}{\underline{\color{black}{2}}},4,8,\color{blue}{\underline{\color{red}{\underline{\color{black}{9}}}}},10,6,\color{blue}{\underline{\color{black}{1}}},5,3,\color{blue}{\underline{\color{red}{\underline{\color{black}{7}}}}}]$. The score of this permutation is $(9 + 7) - (2 + 9 + 1 + 7) = -3$. It can be shown that a score greater than $-3$ can not be achieved. Note that the answer to the problem can be negative.

In the third test case, the score of the permutation will be $(p_1 + p_2 + \ldots + p_9) - p_9$. One of the optimal permutations for this case is $[9, 8, 7, 6, 5, 4, 3, 2, 1]$, and its score is $44$. It can be shown that a score greater than $44$ can not be achieved.

In the fourth test case, $x = y$, so the score of any permutation will be $0$.