Careless Chef solution codechef – Chef has a sequence of integers $A$ of length $N$ . He creates another sequence $B$ of length $2 \cdot N$ using sequence $A$ . Initially, $B$ is empty. Chef performs the following process.

For each element $A_{i}$ $(1 \leq i \leq N)$ of $A$ :

Choose any arbitrary integer $k$ (Note that the value of $k$ can be different for different elements).
Add $A_{i} - k$ and $A_{i} + k$ to $B$ .

Chef then shuffles the sequence $B$ randomly after this process.

Since Chef is careless, he lost both $A$ and $B$ and now only vaguely remembers the elements of $B$ . Chef would like to know if the sequence $B$ (which he vaguely remembers) can be correct or not. Can you help him?

Formally, you are provided with a sequence $B$ of size $2 \cdot N$ . You are required to tell if the provided sequence can be achieved from any sequence $A$ of size $N$ using the given process or not.

Careless Chef solution codechef

The first line of the input contains a single integer $T$ – the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$ .
The second line of each test case contains $2 \cdot N$ space-separated integers $B_{1}, B_{2}, \dots, B_{2 \cdot N} .$

Output Format

For each test case, print YES if the provided sequence $B$ can be achieved from any sequence $A$ of size $N$ using the given process. Otherwise, print NO.

You may print each character of YES and NO in uppercase or lowercase (for example, the strings yEs, yes, Yes and YES will be treated identical).

Constraints

$1 \leq T \leq 10^{4}$
$1 \leq N \leq 10^{5}$
$| B | = 2 \cdot N$
$- 10^{5} \leq B_{i} \leq 10^{5}$
It is guaranteed that the sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$