Magical Modulo

 You are given an array 

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

• Pick an integer X$X$, where 1≤X≤2⋅107$1\le X\le 2\cdot {10}^7$. For each i$i$ , 1≤i≤N$1\le i\le N$ , replace Ai$A_i$ by Ai%X$A_i\mathrm{\%}X$.

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

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

Input Format

• The first line contains an integer T$T$ denoting the number of test cases. The T$T$ test cases then follow.
• The first line of each test case contains an integer N$N$.
• The second line of each test case contains N$N$ space-separated integers A1,A2,…,AN$A_1,A_2,\dots ,A_N$.

Output Format

For each testcase, output the required answer in a single line. If an answer exists, print YES and an integer X$X$ (1≤X≤2⋅107)$(1\le X\le 2\cdot {10}^7)$ 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$1\le T\le 100$
• 1≤N≤105$1\le N\le {10}^5$
• 1≤Ai≤107$1\le A_i\le {10}^7$
• Sum of N$N$ over all cases won't exceed 105${10}^5$

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

• In the first case, choosing X=4$X=4$ yields A$A$ as [2%4,7%4,1%4]=[2,3,1]$[2\mathrm{\%}4,7\mathrm{\%}4,1\mathrm{\%}4]=[2,3,1]$ which is a permutation of N=3$N=3$.
• In the second case, we can't make Ai$A_i$ = 1$1$ for any i$i$ and for any value of X$X$.