Initially, you have an array of length $2$, which is $a = [a_1, a_2]$. Here $a_1 \geq a_2 \geq 0$.

In each step, you must choose the two largest integers $a_i$ and $a_j$ in the array, where $a_i \geq a_j$, and insert two integers $a_i + a_j$ and $a_i - a_j$ to the array (in any positions).

Thus, you can construct an array of any even length $\geq 4$.

Now you are given an array of even length $N$.

Please determine whether you can form this array by the steps. If so, then find out which is the initial array.

Constraints

• $1 \leq T \leq 1000$
• $4 \leq N \leq 10^7$
• $0 \leq a_i \leq 10^9$

•  The sum of $N$ across all test cases does not exceed $10^7$.

Input Format

• The first line contains a single integer $T$ —- the number of test cases.
• For each testcase:
  • The first line contains one odd integer $N$ —- the length of the arrays.
  • The second line contains $N$ positive integers $a_1, a_2, ... , a_N$.
• The sum of $N$ over all test cases does not exceed $10^7$.

Output Format

• For each testcase, output "$YES$" if you can construct the given array by the steps. Otherwise, output "$NO$".
• If you can construct such an array, then print two integers $a_1, a_2$. Note that $a_1 \geq a_2$.