Solve the programming task below in a Python markdown code block.
Tracy gives Charlie a [Directed Acyclic Graph] with N vertices. Among these N vertices, K vertices are *sources*, and L vertices are *sinks*. 

Find out the maximum number of edges this graph can have.

Note:
A *source* is a vertex with no incoming edge.
A *sink* is a vertex with no outgoing edge.
A vertex can be both, a source, and a sink.

------ Input Format ------ 

- First line will contain T, number of test cases. Then the test cases follow. 
- Each test case contains of a single line of input, three space-separated integers N, K, and L - the number of vertices, the number of sources and the number of sinks respectively.

------ Output Format ------ 

- For each test case, output in a single line, the maximum number of edges this graph can have.

------ Constraints ------ 

$1 ≤ T ≤ 10^{5}$
$2 ≤ N ≤ 10^{9}$
$1 ≤ K < N$
$1 ≤ L < N$

----- Sample Input 1 ------ 
2
3 1 1
5 3 3

----- Sample Output 1 ------ 
3
4

----- explanation 1 ------ 
Test case $1$: Assume that the vertices are numbered $1,2,$ and $3$. Let $1$ be a source and $3$ be a sink. The edges of a possible DAG are $1\rightarrow 2, 2\rightarrow 3,$ and $1\rightarrow 3$.

The number of edges in this graph are $3$. It can be shown that this is the maximum number of edges possible under given constraints.

Test case $2$: Assume that the vertices are numbered $1,2,3,4,$ and $5$. Let $1,2,$ and $3$ be sources and $3, 4, $ and $5$ be  sinks. The edges of a possible DAG are $1\rightarrow 4, 2\rightarrow 4, 1\rightarrow 5$ and $2\rightarrow 5$.

The number of edges in this graph are $4$. It can be shown that this is the maximum number of edges possible under given constraints.