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.io.*;
import java.text.*;
import java.math.*;
import static java.lang.Integer.*;
import static java.lang.Double.*;
import java.lang.Math.*;

public class A {

	public static void main(String[] args) throws Exception {
		new A().run();
	}

	public void run() throws Exception {
		FastIO file = new FastIO();
		int q = file.nextInt();
		while (q-->0) {
			int n = file.nextInt();
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = file.nextInt();
			boolean aa = false;
			boolean bb = false;
			for (int i = 0; i < n; i++) {
				boolean aaa = true;
				boolean bbb = true;
				for (int j = 0, k = i; j < n; j++, k++) {
					k %= n;
					if (k == 0) {
						if (a[k] == 1) {
							if (a[n-1] != n) aaa = false;
						}
						else {
							if (a[k] != a[n-1] + 1) aaa = false;
						}
					}
					else {
						if (a[k] == 1) {
							if (a[k-1] != n) {
								aaa = false;
							}
						}
						else {
							if (a[k] != a[k-1] + 1) aaa = false;
						}
					}
				}
				for (int j = 0, k = i; j < n; j++, k--) {
					if (k < 0) k = n - 1;
					if (k == n - 1) {
						if (a[k] == 1) {
							if (a[0] != n) bbb= false;
						}
						else {
							if (a[k] != a[0] + 1) {
								bbb = false;
							}
						}
						
					}
					else {
						if (a[k] == 1) {
							if (a[k+1] != n) bbb= false;
						}
						else {
							if (a[k] != a[k+1] + 1) bbb = false;
						}
						
					}
				}
				if (aaa) aa = true;
				if (bbb) bb = true;
			}
			if (aa || bb) {
				System.out.println("YES");
			}
			else {
				System.out.println("NO");
			}
		}
	}

	public static class FastIO {
		BufferedReader br;
		StringTokenizer st;

		public FastIO() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	public static long pow(long n, long p, long mod) {
		if (p == 0)
			return 1;
		if (p == 1)
			return n % mod;
		if (p % 2 == 0) {
			long temp = pow(n, p / 2, mod);
			return (temp * temp) % mod;
		} else {
			long temp = pow(n, (p - 1) / 2, mod);
			temp = (temp * temp) % mod;
			return (temp * n) % mod;

		}
	}

	public static long pow(long n, long p) {
		if (p == 0)
			return 1;
		if (p == 1)
			return n;
		if (p % 2 == 0) {
			long temp = pow(n, p / 2);
			return (temp * temp);
		} else {
			long temp = pow(n, (p - 1) / 2);
			temp = (temp * temp);
			return (temp * n);

		}
	}

	public static long gcd(long x, long y) {
		if (x == 0)
			return y;
		else
			return gcd(y % x, x);
	}

	public static boolean isPrime(int n) {
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;

		if (n % 2 == 0 || n % 3 == 0)
			return false;

		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;

		return true;
	}
}
