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>
using namespace std;
bool sortbydesc(long long int a, long long int b) { return a > b; }
bool sortbydesc1(pair<long long int, long long int> a,
                 pair<long long int, long long int> b) {
  return a.first > b.first;
}
struct triple {
  long long int n1;
  long long int n2;
  long long int n3;
};
class Graph {
  long long int V;
  list<long long int> *adj;

 public:
  Graph(long long int V);
  void addEdge(long long int v, long long int w);
  void DFSUtil(long long int v, bool *visited, std::vector<long long int> &v1);
};
Graph::Graph(long long int V) {
  this->V = V;
  adj = new list<long long int>[V];
}
void Graph::addEdge(long long int v, long long int w) { adj[v].push_back(w); }
void Graph::DFSUtil(long long int v, bool *visited, vector<long long int> &v1) {
  visited[v] = true;
  v1.push_back(v);
  list<long long int>::iterator i;
  for (i = adj[v].begin(); i != adj[v].end(); ++i)
    if (!visited[*i]) DFSUtil(*i, visited, v1);
}
bool print1(long long int a[], long long int n, long long int ind) {
  long long int k = 1;
  for (long long int i = ind; i < n + ind; i++) {
    if (a[i % n] == k) {
      k++;
    } else {
      return 0;
    }
  }
  return 1;
}
bool print2(long long int *a, long long int n, long long int ind) {
  long long int k = 1;
  for (long long int i = ind; i < n + ind; i++) {
    if (a[i % n] == k) {
      k++;
    } else {
      return 0;
    }
  }
  return 1;
}
int32_t main() {
  long long int q;
  cin >> q;
  while (q--) {
    long long int n;
    cin >> n;
    long long int *a = new long long int[n];
    for (long long int i = 0; i < n; i++) cin >> a[i];
    long long int k = 0;
    for (long long int i = 0; i < n; i++) {
      if (a[i] == 1) {
        k = i;
        break;
      }
    }
    long long int *b = new long long int[n];
    for (long long int i = 0; i < n; i++) {
      b[i] = a[n - i - 1];
    }
    if (print1(a, n, k) == 1 || print2(b, n, n - k - 1) == 1) {
      cout << "YES" << endl;
    } else {
      cout << "NO" << endl;
    }
  }
  return 0;
}
