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

public class CodeChef_Long_F {
    static 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;
        }
    }

    public static void main(String[] args) {
        FastReader fs = new FastReader();
        int t = fs.nextInt();
        while (t-->0){
            int n = fs.nextInt();
            int inp[] = new int[n];
            int f =0;
            int l =0 ;
            for(int i=0 ; i<n ; i++){
                inp[i]=fs.nextInt();
                if(inp[i]==1){
                    f=i;
                }else if(inp[i]==n){
                    l=i;
                }

            }
            boolean flag1 = true;
            int prev= f ;
            prev = (prev+1)%(n);
            int prev2 = 1;
            while (prev!=f){
                if(inp[prev]-prev2==1){
                    prev2 = inp[prev];
                    prev = (prev+1)%(n);
                    continue;
                }else{
                    flag1 = false;
                    break;
                }
            }
            boolean flag2 = true;
            prev = l ;
            prev = (prev+1)%(n);
             prev2 = n;
            while (prev!=l){
                if(inp[prev]-prev2==-1){
                    prev2 = inp[prev];
                    prev = (prev+1)%(n);
                    continue;
                }else{
                    flag2 = false;
                    break;
                }
            }
            if(flag1 || flag2){
                System.out.println("YES");
            }else{
                System.out.println("NO");
            }


        }

    }
}
