You are given an array A of N integers . You want to convert the array A into a permutation of N integers. To do this, you can apply the following operation on array A exactly once .

Pick an integer X, where 1 ≤ X ≤ $2\cdot 10^{7}$. For each i , 1 ≤ i ≤ N , replace A_{i} by A_{i} \% X.

Find out whether it is possible to convert A into a permutation of N integers. If it is possible, print YES (all uppercase alphabets) and any possible value of X for which it is possible. Otherwise, print NO (all uppercase alphabets).

Note - An array of N integers is called a permutation if it contains all integers from 1 to N exactly once.

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

• The first line contains an integer T denoting the number of test cases. The T test cases then follow.
• The first line of each test case contains an integer N.
• The second line of each test case contains $N space-separated integers A_{1}, A_{2}, \dots, A_{N}$.

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

For each testcase, output the required answer in a single line. If an answer exists, print YES and an integer X (1 ≤ X ≤ $2 \cdot 10^{7})$ separated by a single space. Otherwise, print NO.

Note that the strings are case-sensitive and must be in uppercase alphabets.

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

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 10^{5}$
$1 ≤ A_{i} ≤ 10^{7}$
- Sum of $N$ over all cases won't exceed $10^{5}$

------ subtasks ------

Subtask #1 (100 points): original constraints

----- Sample Input 1 ------
2
3
2 7 1
2
2 2
----- Sample Output 1 ------
YES 4
NO
----- explanation 1 ------
- In the first case, choosing $X=4$ yields $A$ as $[ 2\% 4, 7\% 4 , 1\% 4] = [2,3,1]$ which is a permutation of $N=3$.
- In the second case, we can't make $A_{i}$ = $1$ for any $i$ and for any value of $X$.

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