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.

见题面

见题面