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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Stack;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * Author - Patwari26
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        task solver = new task();
        solver.solve(1, in, out);
        out.close();
    }

    static class task {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int q=in.ni();
            for(int i=0;i<q;i++){
                int n=in.ni();
                int[] arr=new int[n];
                int ind=0;
                for(int j=0;j<n;j++){
                    arr[j]=in.ni();
                    if(arr[j]==1) ind=j;
                }
                boolean poss=true;
                int curr=1;
                for(int j=ind;j<n;j++){
                    if(arr[j]!=curr){
                        poss=false;
                    }
                    curr++;
                }
                for(int j=0;j<ind;j++){
                    if(arr[j]!=curr){
                        poss=false;
                    }
                    curr++;
                }
                if(poss==true){
                    out.println("YES");
                }
                else{
                    poss=true;
                    curr=1;
                    for(int j=ind;j>=0;j--){
                        if(arr[j]!=curr){
                            poss=false;
                        }
                        curr++;
                    }
                    for(int j=n-1;j>ind;j--){
                        if(arr[j]!=curr){
                            poss=false;
                        }
                        curr++;
                    }
                    if(poss==true){
                        out.println("YES");
                    }
                    else{
                        out.println("NO");
                    }
                }
            }
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ni() {
            return Integer.parseInt(next());
        }
        public long nll() {
            return Long.parseLong(next());
        }
        public double nd() {
            return Double.parseDouble(next());
        }
        public String nl(){
            String str = "";
            try {
                str = reader.readLine();
            }   catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}