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
/*  MOHD SADIQ  */

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

public class Main {

    private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    private static long parseLong() throws IOException{
        String s  = br.readLine().trim();
        return Long.parseLong(s);
    }
    private static int parseInt() throws IOException{
        String s  = br.readLine().trim();
        return Integer.parseInt(s);
    }
    private static int[] intArray() throws IOException{
        String[] s = br.readLine().trim().split(" ");
        int n = s.length;
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(s[i]);
        }
        return a;
    }
    private static long[] longArray() throws IOException {
        String[] s = br.readLine().trim().split(" ");
        int n = s.length;
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = Long.parseLong(s[i]);
        }
        return a;
    }

    private static String[] stringArray() throws IOException{
        String[] s = br.readLine().trim().split(" ");
        return s;
    }

    private static char[] charArray() throws IOException{
        return br.readLine().trim().toCharArray();
    }

    private static long mod = (long)Math.pow(10,9)+7;

    private static String solve() throws IOException {

        int n = parseInt();
        int[] a = intArray();
        if(n==1)
            return "YES";
        int ind = 0;
        for(int i=0;i<n;i++){
            if(a[i] == 1)
                ind = i;
        }

        int c = 0;
        int i = ind;
        int j = (i+1)%n;
        int k = 0;
        boolean ch = false;
        while (c++<n){
//            c++;
            if(a[j] > a[i]){
                k++;
            }
            i = (i+1)%n;
            j = (j+1)%n;
        }
//        System.out.println(k);
        if(k==n-1){
            return "YES";
        }
        i = ind;
        j = (ind-1);
        if(j<0)
            j = n-1;
        c = 0;k = 0;
        while (c++<n){
            if(a[j] > a[i]){
                k++;
            }
            i = (i-1)%n;
            j = (j-1)%n;
            if(i<0)
                i = n-1;
            if(j<0)
                j = n-1;
        }
//        System.out.println(k);
        if(k==n-1)
            return "YES";
//        System.out.println(-1%);
        return "NO";
    }


    public static void main(String[] args) throws IOException {
        int total_test_case = parseInt();
        StringBuffer ans = new StringBuffer();
//        int total_test_case = 1;
        for(int test_case =0;test_case<total_test_case;test_case++){
            ans.append(solve()+"\n");
//            System.out.println(solve());
        }
        System.out.print(ans);
    }
}