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
#include<bits/stdc++.h>

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define ll long long
#define mp make_pair
#define pb push_back
#define ff first
#define ss second
#define pii pair<int, int>
#define pll pair<ll, ll>

#define show(x) cout<<#x<<" "<<x<<'\n'
#define iosbase ios_base::sync_with_stdio(false); cin.tie(NULL);
#define oset tree<int , null_type, less_equal<int> , rb_tree_tag, tree_order_statistics_node_update>

using namespace std;
using namespace __gnu_pbds;

const ll N = 200005;
const ll mm = 1e9 + 7;
const ll inf = 1e7;

int a[2];
int main()
{
	iosbase;
	int test;
	cin>>test;
	while(test--)
	{
		int n;
		cin>>n;
		int a[n];
		
		int pos1=-1,posn=-1;
		for(int i=0;i<n;i++)
		{
			cin>>a[i];
			if(a[i]==1) pos1=i;
			if(a[i]==n) posn=i;
		}
		if(n<=3)
		{
			cout<<"YES\n";
			continue;
		}
		vector<int> ref1,ref2;
		for(int i=0;i<n;i++)
		{
			ref1.pb(i+1);
			ref2.pb(n-i);
		}
		//show(pos1);show(posn);
		vector<int> sahi;
		if(pos1>posn)
		{
			if(pos1!=n-1 ||(pos1==n-1 && a[n-2]==5))
			{
				for(int i=pos1;i<n;i++)
				{
					//cout<<"here2";
					sahi.pb(a[i]);
					//cout<<a[i]<<" ";
				}
				for(int i=0;i<pos1;i++)
				{
					sahi.pb(a[i]);
					//cout<<a[i]<<" ";
				}
				//cout<<'\n';
				if(sahi==ref1)
				{
					cout<<"YES\n";
					continue;
				}
				else
				{
					cout<<"NO\n";
					continue;
				}
			}
			else
			{
				for(int i=0;i<n;i++) sahi.pb(a[i]);
				if(sahi==ref2)
				{
					cout<<"YES\n";
					continue;
				}
				else
				{
					cout<<"NO\n";
					continue;
				}
			}
		}
		if(pos1<posn)
		{
			if(posn!=n-1||(posn==n-1 && a[n-2]==1))
			{
				for(int i=posn;i<n;i++)
				{
					//cout<<"here2";
					sahi.pb(a[i]);
					//cout<<a[i]<<" ";
				}
				for(int i=0;i<posn;i++)
				{
					sahi.pb(a[i]);
					//cout<<a[i]<<" ";
				}
				//cout<<'\n';
				if(sahi==ref2)
				{
					cout<<"YES\n";
					continue;
				}
				else
				{
					cout<<"NO\n";
					continue;
				}
			}
			else
			{
				for(int i=0;i<n;i++) sahi.pb(a[i]);
				if(sahi==ref1)
				{
					cout<<"YES\n";
					continue;
				}
				else
				{
					cout<<"NO\n";
					continue;
				}
			}
		}

	}
}