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 main;

import java.io.*;
import java.util.*;
import java.math.BigInteger;

public final class Main {
    BufferedReader br;
    StringTokenizer stk;
    
    public static void main(String[] args) throws Exception {
        new Main().run();
    }
    
    {
        stk = null;
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    
    long mod = 998244353;
    StringBuilder res = new StringBuilder(1000005);
    void run() throws Exception {
        int t = ni();
        while(t-- > 0) {
            int n = ni();
            int[] a = new int[n];
            int[] b = new int[n << 1];
            for(int i = 0; i < n; i++) {
                a[i] = ni();
            }
            for(int i = 0; i < b.length; i++) {
                b[i] = a[i % n];
            }
            Arrays.sort(a);
            boolean ok = false;
            for(int i = 0; i < n; i++) {
                if(check(a, b, i)) {
                    ok = true;
                    break;
                }
            }
            reverse(a);
            for(int i = 0; i < n; i++) {
                if(check(a, b, i)) {
                    ok = true;
                    break;
                }
            }
            System.out.println(ok ? "YES" : "NO");
        }
    }
    
    boolean check(int[] a, int[] b, int sb) {
        for(int i = 0, j = sb; i < a.length; i++, j++) {
            if(a[i] != b[j]) {
                return false;
            }
        }
        return true;
    }
    
    //Reader & Writer
    String nextToken() throws Exception {
        if (stk == null || !stk.hasMoreTokens())
            stk = new StringTokenizer(br.readLine(), " ");
        return stk.nextToken();
    }

    String nt() throws Exception {
        return nextToken();
    }

    int ni() throws Exception {
        return Integer.parseInt(nextToken());
    }

    long nl() throws Exception {
        return Long.parseLong(nextToken());
    }
    
    double nd() throws Exception {
        return Double.parseDouble(nextToken());
    }
    
    //Some Misc methods
    int get(int l, int r, int[] a) {
        return l == 0 ? a[r] : a[r] - a[l - 1];
    }
    
    void shuffle(int[] a) {
        Random r = new Random();
        for(int i = 0; i < a.length; i++) {
            int idx = r.nextInt(a.length);
            int temp = a[i];
            a[i] = a[idx];
            a[idx] = temp;
        }
    }
    
    void reverse(int[] a) {
        for(int i = 0, j = a.length - 1; i < j; i++, j--) {
            int temp = a[i];
            a[i] = a[j];
            a[j] = temp;
        }
    }
}