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.io.*;
import java.util.*;
public class studcircle {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner inputs = new Scanner(System.in);
		int q = inputs.nextInt();
		for(int k=0;k<q;k++) {
			boolean prin = false;
			int n = inputs.nextInt();
			if(n==1) {
				System.out.println("YES");
				prin = true;
				inputs.nextInt();
			}
			if(n==2) {
				int t1 = inputs.nextInt();
				int t2 = inputs.nextInt();
				if(Math.abs(t2-t1)==1) {
					System.out.println("YES");
				}
				else {
					System.out.println("NO");
				}
				prin = true;
			}
			if(n>2) {
				int prev = inputs.nextInt();
				int nex = inputs.nextInt();
				boolean up = false;
				//checks if you used the big jump once
				boolean used = false;
				//if it is a step
				if(Math.abs(prev-nex)==1) {
					if(prev<nex) {
						up = true;
					}
				}
				else {
					if(nex<prev) {
						up = true;
					}
					used = true;
					if(Math.abs(nex-prev)!=n-1) {
						System.out.println("NO");
						prin = true;
						continue;
					}
				}
				prev = nex;
				int i;
				for(i = 2;i<n;i++) {
					nex = inputs.nextInt();
					if(up) {
						if(nex-prev==1) {
							
						}
						else if(prev-nex == n-1) {
							if(used) {
								System.out.println("NO");
								prin = true;
								break;
							}
							else
								used = true;
						}
						else {
							System.out.println("NO");
							prin = true;
							break;
						}
					}
					else {
						if(prev-nex==1) {
							
						}
						else if(nex-prev==n-1) {
							if(used) {
								System.out.println("NO");
								prin = true;
								break;
							}
							else
								used = true;
						}
						else {
							System.out.println("NO");
							prin = true;
							break;
						}
					}
					prev = nex;
					//end of loop
				}
				//clears out all input
				for(int p=i+1;p<n;p++) {
					inputs.nextInt();
				}
			}
			if(!prin) {
				System.out.println("YES");
			}
			//end of for loop
		}
	}

}
