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;
void rz(vector<vector<int> >& matrix, int rows, int columns) {
  matrix.resize(rows);
  for (int i = 0; i < rows; i++) matrix[i].resize(columns);
}
void cle(vector<vector<int> >& matrix, int rows, int columns) {
  for (int i = 0; i < rows; i++) matrix[i].clear();
  matrix.clear();
}
void printVector(vector<int>& x) {
  int size = x.size();
  for (int i = 0; i < size; i++) {
    cout << x[i] << ' ';
  }
  cout << endl;
}
void printNestedVector(vector<vector<int> >& x) {
  int size = x.size();
  for (int i = 0; i < size; i++) {
    printVector(x[i]);
  }
  cout << endl;
}
void inputVector(vector<int>& x) {
  int size = x.size();
  for (int i = 0; i < size; i++) cin >> x[i];
}
void inputNestedVector(vector<vector<int> >& x) {
  int size = x.size();
  for (int i = 0; i < size; i++) inputVector(x[i]);
}
void uEdge(vector<vector<int> >& graph, int x, int y) {
  graph[x].push_back(y);
  graph[y].push_back(x);
}
void dEdge(vector<vector<int> >& graph, int x, int y) { graph[x].push_back(y); }
void makeGraph(vector<vector<int> >& graph, int edges) {
  for (int i = 0; i < edges; i++) {
    int x, y;
    cin >> x >> y;
    uEdge(graph, x - 1, y - 1);
  }
}
void insertIntoMap(unordered_map<int, int>& myMap, int x) {
  if (myMap.find(x) != myMap.end())
    myMap[x]++;
  else
    myMap.insert(make_pair(x, 1));
}
unordered_map<int, int> getFrequency(vector<int>& x) {
  unordered_map<int, int> myMap;
  int n = x.size();
  for (int i = 0; i < n; i++) {
    insertIntoMap(myMap, x[i]);
  }
  return myMap;
}
int getMaxFrequency(unordered_map<int, int>& x) {
  int max = INT16_MIN;
  for (auto it = x.begin(); it != x.end(); it++) {
    if (max < it->second) max = it->second;
  }
  return max;
}
string toString(vector<int> kids) {
  stringstream ss;
  copy(kids.begin(), kids.end(), ostream_iterator<int>(ss, ""));
  string s = ss.str();
  s = s.substr(0, s.length());
  return s;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    vector<int> kids(2 * n);
    for (int i = 0; i < n; i++) {
      int x;
      cin >> x;
      kids[i] = x;
      kids[i + n] = x;
    }
    vector<int> toFind(n);
    vector<int> toFindReverse(n);
    for (int i = 0; i < n; i++) {
      toFind[i] = i + 1;
      toFindReverse[n - i - 1] = i + 1;
    }
    string s = toString(kids);
    string stf = toString(toFind);
    string stfr = toString(toFindReverse);
    auto ff = s.find(stfr);
    auto fr = s.find(stf);
    if (ff == string::npos && fr == string::npos) {
      cout << "NO" << endl;
    } else {
      cout << "YES" << endl;
    }
  }
  return 0;
}
