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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
 
public class CodeForces {
	static char[] s, t;
 
	static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}
 
	static long no(int n) {
		long sum = 0;
		for (int i = 1; i * i <= n; i++) {
			if (n % i == 0)
				sum++;
		}
		return sum;
	}
 
	static long divCount(long n) {
		long sum = 0;
		for (int i = 1; i * i <= n; i++) {
			if (n % i == 0) {
				if (n / i == i) {
					sum++;
				} else {
					sum += 2;
				}
			}
		}
		return sum;
	}
 
	static int[] asc, des, arr;
 
	static boolean isequal(int i) {
		int a = 0;
		for (; a < arr.length && i < asc.length; a++, i++) {
			if (arr[a] != asc[i])
				return false;
		}
		if (a == arr.length)
			return true;
		else
			return false;
	}
 
	static boolean isequal2(int i) {
		int a = 0;
		for (; a < arr.length && i < des.length; a++) {
			if (arr[a] != des[i])
				return false;
			i++;
		}
		if (a == arr.length)
			return true;
		else
			return false;		
	}
 
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int q = sc.nextInt();
		O: while (q-- > 0) {
			int n = sc.nextInt();
			asc = new int[n*2];
			des = new int[2*n];
			arr = new int[n];
			int c = 0;
			if (n == 1) {
				System.out.println("YES");
				continue O;
			}
			for (int i = 0; i < 2*n; i++) {
				if (c == n) {
					c = 0;
				}
				asc[i] = c;
				c++;
			}
 
			c = n - 1;
			for (int i = 0; i < n *2; i++) {
				if (c == -1) {
					c = n - 1;
				}
				des[i] = c;
				c--;
			}
			for (int i = 0; i < n; i++)
				arr[i] = sc.nextInt() - 1;
		//	System.out.println(Arrays.toString(des));
			//System.out.println(Arrays.toString(arr));
			for (int i = 0; i < n * 2 ; i++) {
				if (isequal(i)) {
					System.out.println("YES");
					continue O;
				}
			}
			for (int i = 0; i < n * 2 ; i++) {
				if (isequal2(i)) {
					System.out.println("YES");
					continue O;
				}
			}
			System.out.println("NO");
		}
 
	}
 
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
	}
}