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
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class a{ 
     static int[] count,count1;
     static long[] arr;
     static char[] ch,ch1;
     static long[] darr;
     static long[][] mat,mat1;
     static long x;
     static long maxl;
     static double dec;
     static String s;
     // static long minl;
     static int mx = (int)1e6;
     static long mod = 998244353l;
     // static int minl = -1;
     // static long n;
     static int n,n1,n2;
     static long a,g;
     static long b;
     static long c;
     static long d;
     static long y;
     static int m;
     static long k;
     static int q;
     static String[] str,str1;
     static Set<Character> set,set1;
     static List<Long> list;
     static Map<Long,Integer> map;
     static StringBuilder sb;

     public static boolean solve(){

        long k = arr[0];
        for(int i = 0 ; i < n ; i++){
            if(k != arr[i])
                break;
            k += 1;
            if(k > n)
                k = 1;
            if(i == n-1)
                return true;    
        }

        k = arr[0];
        for(int i = 0 ; i < n ; i++){
            if(k != arr[i])
                return false;
            k -= 1;
            if(k < 1)
                k = n;
        }

        return true;

     }

     public static void main(String[] args) {

            FastScanner sc = new FastScanner();
            // Scanner sc = new Scanner(System.in);
            int t = sc.nextInt();
            // int t = 1;
            while(t > 0){
                
                // x = sc.nextLong();
                // y = sc.nextLong();
                
                // a = sc.nextLong();
                // b = sc.nextLong();
                // c = sc.nextLong();
                // d = sc.nextLong();

                n = sc.nextInt();
                // n1 = sc.nextInt();
                // n = sc.nextLong();

                // k = sc.nextLong();
                
                // ch = sc.next().toCharArray();
                // ch1 = sc.next().toCharArray();

                // m = sc.nextInt();
                 
                arr = new long[n];
                for(int i = 0; i < n ; i++){
                    arr[i] = sc.nextLong();
                }

                // n1 = sc.nextInt();
                //  darr = new long[n1];
                //  for(int i = 0; i < n1 ; i++){
                //      darr[i] = sc.nextLong();
                //  }

                // mat = new long[n][m];

                // for(int i = 0 ; i < n ; i++){
                //     for(int j = 0 ; j < m ; j++){
                //         mat[i][j] = sc.nextLong();
                //     }
                // }


                System.out.println(solve()?"YES":"NO");
                 // solve();
                 // System.out.println(solve());
                 // sb = new StringBuilder();
                 // sb.append(str);

                 t -= 1;
            }

     }

    public static int log(long n){

         if(n == 0 || n == 1)
             return 0;

         if(n == 2)
             return 1;

         double num = Math.log(n);
         double den = Math.log(2);

         if(den == 0)
             return 0;

         return (int)(num/den);
     }

     public static long gcd(long a,long b){

        if(b%a == 0)
            return a;

        return gcd(b%a,a);

     }

     // public static void swap(int i,int j){
     //     long temp = arr[j];
     //     arr[j] = arr[i];
     //     arr[i] = temp;
     // } 

    static final Random random=new Random();
    
    static void ruffleSort(long[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static class Node{
        int first;
        int second;
        Node(int f,int s){
            this.first = f;
            this.second = s;
        }
    }

     static class FastScanner {

                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer st=new StringTokenizer("");
                String next() {
                        while (!st.hasMoreTokens())
                                try {
                                        st=new StringTokenizer(br.readLine());
                                } catch (IOException e) {
                                        e.printStackTrace();
                                }
                        return st.nextToken();
                }
                
                int nextInt() {
                        return Integer.parseInt(next());
                }
                int[] readArray(int n) {
                        int[] a=new int[n];
                        for (int i=0; i<n; i++) a[i]=nextInt();
                        return a;
                }
                long nextLong() {
                        return Long.parseLong(next());
                }
        }

}