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
/******************************\
*  Everyone has a different way of thinking, so God Created us
   Hope You Respect My Way..,Thank You ):  *
*                            *
*   Created by : Murad   *
\******************************/
#include<bits\stdc++.h>
using namespace std;
#include<unordered_map>
#define pi 3.1415926536
#define forn(i,a,b)for(int i=a;i<b;i++)
#define LL long long
#define MP make_pair
#define ff first
#define ss second
#define INF INT32_MAX
#define _INF INT32_MIN
#define pq priority_queue
#define MM multimap
#define PB push_back
#define vii vector<int>
#define ipair pair<int,int>
#define lpair pair<LL,LL>
#define MAXN 100004
#define El3zba ios::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define modd 1000000007
#define sfll1(v) scanf("%I64d",&v);
#define sfll2(v1,v2) scanf("%I64d %I64d",&v1,&v2)
#define sfll3(v1,v2,v3) scanf("%I64d %I64d %I64d",&v1,&v2,&v3)
#define endl '\n'
//std::transform(s1.begin(), s1.end(), s1.begin(),::tolower);
char alphz[27] = { 'a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z' };
LL MMIN(LL a, LL b)
{
	if (a <= b)
		return a;
	else
		return b;
}
LL MMAX(LL a, LL b) {
	if (a >= b)
		return a;
	else
		return b;
}
float Euclidean(LL x1, LL x2, LL y1, LL y2) {
	return sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2));
}
int gcd(int a, int b) {
	if (a == 0)return b;
	return gcd(b%a, a);
}
int LCM(int a, int b) {
	return (a*b) / gcd(a, b);
}
void PrimeFactor(LL n)
{
	while (n % 2 == 0) {
		printf("%d ", 2);
		n /= 2;
	}
	for (int i = 3; i <= sqrt(n); i += 2)
	{
		if (n%i == 0) {
			printf("%d ", i);
			n /= i;
		}
	}
	if (n > 2)printf("%d ", n);
}
bool is_square(LL x) {
	LL l = 0, r = x;
	while (l <= r) {
		LL mid = l + (r - l) / 2;
		if (mid*mid == x)return true;
		if (mid*mid > x)r = mid - 1;
		else l = mid + 1;
	}
	return false;
}
bool is_Prime(int x) {
	if (x == 2)return 1;
	else if (x % 2 == 0 || x < 2)return 0;
	for (int i = 3; i*i <= x; i += 2)
		if (x%i == 0)return 0;
	return 1;
}
int main()
{
	El3zba;
	/***  بسم الله الرحمن الرحيم   ***/
	int q;
	cin >> q;
	while (q--)
	{
		int n;
		cin >> n;
		bool ok = 1,ok1=1;
		vii a(n);
		vii temp(n);
		for (int i = 0; i < n; i++)
			cin >> a[i];
		if (n < 4) {
			cout << "YES\n";
			continue;
		}
		if (a[0] == 1)
		{
			for (int i = 0; i < n; i++)
			{
				if (a[i] != i + 1) {
					ok = 0;
					break;
				}
			}
			for (int i = 0; i < n; i++)
			{
				if (i == 0) {
					temp[i] = 1;
				}
				else {
					temp[i] = n - (i-1);
				}

			}
			for (int i = 0; i < n; i++)
			{
				if (a[i] != i + 1 && a[i] != temp[i]) {
					cout << "NO\n";
					ok = 0;
					ok1 = 0;
					break;
				}
			}
			if (ok1 || ok)
			{
				cout << "YES\n";
				continue;
			}
		}
		else {
			if (a[1] > a[0]) {
				int j = 0;
				for (int i = a[0]; i <= n; i++)
					temp[j] = i,j++;
				for (int i = 1; i < a[0]; i++)
					temp[j] = i,j++;
				for (int i = 0; i < n; i++)
				{
					if (a[i] != temp[i])
					{
						cout << "NO\n";
						ok = 0;
						break;
					}
				}
			}
			else {
				int j = 0;
				for (int i = a[0]; i >= 1; i--)
					temp[j] = i,j++;
				for (int i = n; i > a[0]; i--)
					temp[j] = i,j++;
				for(int i=0;i<n;i++)
					if (a[i] != temp[i])
					{
						cout << "NO\n";
						ok = 0;
						break;
					}
			}
		}
		if (ok)
			cout << "YES\n";
	}
	return 0;
}