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.util.*;


import java.awt.Point;
import java.io.*;
import java.math.BigInteger;
public class Solutions {
	 
static int MAX=Integer.MAX_VALUE;
		static int MIN=Integer.MIN_VALUE;
//static ArrayList<ArrayList<Integer>>list=new ArrayList<ArrayList<Integer>>();
	static FastScanner scr=new FastScanner();
	static PrintStream out=new PrintStream(System.out);
//	static ArrayList<Integer>list[];
	static StringBuilder sb=new StringBuilder();
	public static void main(String []args) {
		int t=scr.nextInt();
		while(t-->0) {
			solve();
		}
//		out.println(sb);
	}
	static HashMap<Integer,Integer>hm;
	static void solve() {
		int n=scr.nextInt();
		int []a=scr.readArray(n);
		if(n==1 || n==2) {
			out.println("YES");
			return;
		}
		int pos=-1;
		for(int i=0;i<n;i++) {
			if(a[i]==1) {
				pos=i;
			}
			a[i]--;
		}
		boolean okL=true;
		boolean okR=true;
		for(int i=1;i<n;i++) {
			okL&=(a[(pos-i+n)%n]==i);
			okR&=(a[(pos+i+n)%n]==i);
		}
		if(okL || okR) {
			out.println("YES");
		}else {
			out.println("NO");
		}
	}
	static class pair{
		int x;
		int y;
		pair(int x,int y){
			this.x=x;
			this.y=y;
		}
	}
	static boolean isVowel(char c) {
		return c=='a' || c=='e'||c=='i'|| c=='o' || c=='u';
	}
	static int gcd(int a,int b){
		if(b==0) {
			return a;
		}
		
		return gcd(b,a%b);
	}
	static long modPow(long base,long exp,long mod) {
		if(exp==0) {
			return 1;
		}
		if(exp%2==0) {
			long res=(modPow(base,exp/2,mod));
			return (res*res)%mod;
		}
		return (base*modPow(base,exp-1,mod))%mod;
	}
	static long gcd(long a,long b) {
		if(b==0) {
			return a;
		}
		return gcd(b,a%b);
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
	 	String next() {
	 		while (!st.hasMoreTokens())
	 			try {
	 				st=new StringTokenizer(br.readLine());
	 			} catch (IOException e) {
	 				e.printStackTrace();
	 			}
	 			return st.nextToken();
		}
		int[] sort(int a[]) {
			Arrays.sort(a);
			return a;
		}
		int []reverse(int a[]){
			int b[]=new int[a.length];
			int index=0;
			for(int i=a.length-1;i>=0;i--) {
				b[index]=a[i];
			}
			return b;
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long[] readLongArray(int n) {
			long  [] a=new long  [n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}

}
