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
//package com.company.p1203.a;

import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.util.LinkedList;
import java.util.Scanner;

public class p1203a {
    public static void main(String[] args) {
        Boolean debug = false;
        Scanner sc = getScanner(debug);

        int n_problem = sc.nextInt();

        for (int i = 0; i < n_problem; i++) {
            int n = sc.nextInt(); //number of problems



            LinkedList<Integer> l = new LinkedList<Integer>();

            for (int i1 = 0; i1 < n; i1++) {
                int k = sc.nextInt();
                l.add(k);
            }

            if (n==1 || n==2) {
                System.out.println("YES");
                continue;
            }

            while (l.getFirst() != 1) {
                Integer f = l.getFirst();
                l.addLast(f);
                l.removeFirst();
            }

            if (l.get(1)==n) {
                Integer f = l.getFirst();
                l.addLast(f);
                l.removeFirst();
            }

            int diff = l.get(1) - l.get(0);
            boolean ok = true;
            for (int i1 = 1; i1 < l.size(); i1++) {
                if (!((l.get(i1) - l.get(i1-1)) == diff)) {
                    ok = false;
                }
            }

//            System.out.println("===========");
//            l.forEach(System.out::println);
            if (ok) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }


        }
    }

    private static Scanner getScanner(Boolean debug) {
        Scanner sc;
        if (debug) {
            sc = new Scanner("5\n" +
                    "4\n" +
                    "1 2 3 4\n" +
                    "3\n" +
                    "1 3 2\n" +
                    "5\n" +
                    "1 2 3 5 4\n" +
                    "1\n" +
                    "1\n" +
                    "5\n" +
                    "3 2 1 5 4");
        } else {
            sc = new Scanner(System.in);
        }
        return sc;
    }
}
