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
////////////////////////////////////////////////////
//                                                //
//  For her who keeps the fire kindling in me...  //
//                                                //
////////////////////////////////////////////////////


import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileOutputStream;
import java.io.IOException; 
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
// import java.util.Scanner;
// import java.util.Arrays;
// import java.util.ArrayList;
// import java.util.Collections; 
// import java.util.StringTokenizer;
import java.util.*;
import java.lang.Math;
import java.awt.Point;
import java.awt.geom.*;

public class Main{

    static long gcd(long a, long b){
        if(a==0)    
            return b;
        return gcd(b%a, a);
    }

    void solve(){
        try{
            FastReader s = new FastReader();
            BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out));
            int  q, i, j, x, n, dis1, dis2;
            //long hcf, n, m, pn, pm, val, a1, a2;
            q = s.nextInt();
            for(; q>0; q--){
                n = s.nextInt();
                int arr[] = new int[n];
                for(i=0; i<n; i++)
                    arr[i] = s.nextInt();
                
                dis1 = 0;
                for(i=1; i<n; i++)
                    if(arr[i-1] - arr[i] != 1)
                        dis1++;
                dis2 = 0;
                for(i=1; i<n; i++)
                    if(arr[i]-arr[i-1] != 1)
                        dis2++;

                if(dis1<=1 || dis2<=1)
                    w.write("YES\n");
                else
                    w.write("NO\n");
            }
            w.close();
        }catch(Exception e){
            e.printStackTrace();
        }
    }

    public static void main(String args[]){
        (new Main()).solve();
    }
}
                
                
//========================================### FAST IO ###=========================================//
class FastReader 
{ 
    BufferedReader br; 
    StringTokenizer st; 

    public FastReader() 
    { 
        br = new BufferedReader(new
                    InputStreamReader(System.in)); 
    } 

    String next() 
    { 
        while (st == null || !st.hasMoreElements()) 
        { 
            try
            { 
                st = new StringTokenizer(br.readLine()); 
            } 
            catch (IOException  e) 
            { 
                e.printStackTrace(); 
            } 
        } 
        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 = br.readLine(); 
        } 
        catch (IOException e) 
        { 
            e.printStackTrace(); 
        } 
        return str;
    } 
}
    //====================================================================================================//