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
//Created by Aminul on 8/13/2019.

import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class A {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int test = in.nextInt();
        for (int t = 1; t <= test; t++) {
            int n = in.nextInt();
            //int a[] = new int[n];
            ArrayDeque<Integer> d = new ArrayDeque<>();
            for (int i = 0; i < n; i++) {
                d.addLast(in.nextInt());
            }
            if (solve(n, d)) pw.println("YES");
            else pw.println("NO");
        }

        pw.close();
    }

    static boolean solve(int n, ArrayDeque<Integer> d) {

        for (int i = 0; i < n + 1; i++) {
            int x = d.pollLast();
            d.addFirst(x);
            
            if(isSorted(d)) return true;
        }
        return false;
    }

    static int[] toArray(ArrayDeque<Integer> d) {
        int n = d.size();
        int a[] = new int[n], i = 0;
        for (int  k : d) {
            a[i++] = k;
        }
        return a;
    }


    static boolean isSorted(ArrayDeque<Integer> d) {
        int a[] = toArray(d), n = a.length;
        for (int i = 0; i < n-1; i++) {
            if(a[i] > a[i+1]) return false;
        }
        return true;
    }

    static boolean x(int i, int n, int a[]) {
        for (int j = i; j > 0; j--) {
            if (a[j] + 1 != a[j - 1]) return false;
        }
        for (int j = i; j < n - 1; j++) {
            if (a[j] + 1 != a[j + 1]) return false;
        }
        return true;
    }

    static boolean y(int i, int n, int a[]) {
        for (int j = i; j > 0; j--) {
            if (a[j] - 1 != a[j - 1]) return false;
        }
        for (int j = i; j < n - 1; j++) {
            if (a[j] - 1 != a[j + 1]) return false;
        }
        return true;
    }


    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}