There are n students standing in a circle in some order. The index of the i-th student is p_i. It is guaranteed that all indices of students are distinct integers from 1 to n (i. e. they form a permutation).

Students want to start a round dance. A clockwise round dance can be started if the student 2 comes right after the student 1 in clockwise order (there are no students between them), the student 3 comes right after the student 2 in clockwise order, and so on, and the student n comes right after the student n - 1 in clockwise order. A counterclockwise round dance is almost the same thing — the only difference is that the student i should be right after the student i - 1 in counterclockwise order (this condition should be met for every i from 2 to n). 

For example, if the indices of students listed in clockwise order are [2, 3, 4, 5, 1], then they can start a clockwise round dance. If the students have indices [3, 2, 1, 4] in clockwise order, then they can start a counterclockwise round dance.

Your task is to determine whether it is possible to start a round dance. Note that the students cannot change their positions before starting the dance; they cannot swap or leave the circle, and no other student can enter the circle. 

You have to answer q independent queries.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 200) — the number of queries. Then q queries follow.

The first line of the query contains one integer n (1 ≤ n ≤ 200) — the number of students.

The second line of the query contains a permutation of indices p_1, p_2, ..., p_n (1 ≤ p_i ≤ n), where p_i is the index of the i-th student (in clockwise order). It is guaranteed that all p_i are distinct integers from 1 to n (i. e. they form a permutation).

Output

For each query, print the answer on it. If a round dance can be started with the given order of students, print "YES". Otherwise print "NO".

Example

Input


5
4
1 2 3 4
3
1 3 2
5
1 2 3 5 4
1
1
5
3 2 1 5 4


Output


YES
YES
NO
YES
YES
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.BigInteger; 

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
	    FastReader fr = new FastReader();
	    int q = fr.nextInt();
	    while(q-->0){
	        int n = fr.nextInt();
	        int[] arr = new int[n];
	        int index = -1;
	        for(int i=0;i<n;i++){
	            arr[i] = fr.nextInt();
	            if(arr[i]==1){
	                index = i;
	            }
	        }
	       int[] a1 = new int[n];
	       int[] a2 = new int[n];
	       int count = 0;
	       
	       boolean flag1=true;
	       boolean flag2 = true;
	        
	        for(int i=index;i<n;i++){
	            a1[count] =arr[i];
	            count++;
	        }
	        for(int i=0;i<index;i++){
	            a1[count] =arr[i];
	            count++;
	        }
	        
	        count=0;
	        for(int i=index;i>=0;i--){
	            a2[count] = arr[i];
	            count++;
	        }
	        for(int i=n-1;i>index;i--){
	            a2[count] = arr[i];
	            count++;
	        }
	        
	        for(int i=0;i<n;i++){
	            if(a1[i]!=i+1){
	                flag1 = false;
	                break;
	            }
	        }
	        for(int i=0;i<n;i++){
	            if(a2[i]!=i+1){
	                flag2 = false;
	                break;
	            }
	        }
	        
	        if(flag1||flag2){
	            System.out.println("YES");
	        }else{
	            System.out.println("NO");
	        }
	       
	    }
	}
}
class FastReader {
 
    BufferedReader bf;
    StringTokenizer st;
 
    public FastReader() {
        bf = new BufferedReader(new InputStreamReader(System.in));
    }
 
    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(bf.readLine());
            } catch (Exception e) {
                System.out.println(e);
            }
        }
        return st.nextToken();
    }
 
    int nextInt() {
        return Integer.parseInt(next());
    }
 
    long nextLong() {
        return Long.parseLong(next());
    }
 
    double nextDouble() {
        return Double.parseDouble(next());
    }
 
    String nextLine() {
        String str = "";
        try {
            str = bf.readLine();
        } catch (Exception e) {
            System.out.println(e);
        }
        return str;
    }
}
