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;
struct node {
  int data;
  node* next;
};
void insert(node*& head, int data) {
  node* temp = new node();
  temp->data = data;
  if (head == NULL) {
    temp->next = NULL;
    head = temp;
  } else {
    node* p = head;
    if (p->data <= data) {
      while (p->next != NULL) {
        if (p->data <= data && p->next->data >= data) break;
        p = p->next;
      }
      node* t = new node();
      t = p->next;
      p->next = temp;
      temp->next = t;
    } else {
      temp->next = p;
      head = temp;
    }
  }
}
void show(node* head) {
  if (head == NULL) return;
  if (head->next == NULL)
    cout << head->data << "\n";
  else
    cout << head->data << "-->";
  show(head->next);
}
void merge(node* h1, node* h2, node*& h3) {
  if (!h1 && !h2) return;
  if (h1->data < h2->data) {
    insert(h3, h1->data);
    merge(h1->next, h2, h3);
  } else {
    insert(h3, h2->data);
    merge(h1, h2->next, h3);
  }
  if (h1 == NULL && h2 != NULL) {
    merge(h1, h2->next, h3);
  } else if (h1 != NULL && h2 == NULL)
    merge(h1->next, h2, h3);
}
bool fin(int* a, int low, int high, int k) {
  if (low < high) {
    if (a[low] + a[high] == k)
      return true;
    else if (a[low] + a[high] > k)
      fin(a, low, --high, k);
    else
      fin(a, ++low, high, k);
  }
  return false;
}
bool prime(int n) {
  int c = 0;
  for (int i = 1; i <= n; i++) {
    if (n % i == 0) ++c;
  }
  if (c == 2)
    return true;
  else
    return false;
}
int search(long long* a, long long n, long long v) {
  int low = 0;
  int high = n;
  while (low < high) {
    int mid = low + (high - low) / 2;
    if (a[mid] < v)
      low = mid + 1;
    else
      high = mid;
  }
  return low;
}
bool check(long long* a, long long n, long long v) {
  int low = 0;
  int high = n - 1;
  while (low <= high) {
    int mid = low + (high - low) / 2;
    if (a[mid] == v)
      return true;
    else if (a[mid] > v)
      high = mid - 1;
    else if (a[mid] < v)
      low = mid + 1;
  }
  return false;
}
bool is_sorted(long long* a, int s, int n) {
  if (n - s == 0 || n - s == 1)
    return true;
  else {
    for (int i = s + 1; i < n; i++) {
      if (a[i - 1] > a[i]) return false;
    }
    return true;
  }
}
bool is_rev(long long* a, long long s, long long n) {
  if (n - s == 0 || n - s == 1)
    return true;
  else {
    for (int i = s + 1; i < n; i++) {
      if (a[i - 1] < a[i]) return false;
    }
    return true;
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    long long int a[n];
    unordered_map<long long, int> M;
    for (int i = 0; i < n; i++) {
      cin >> a[i];
      M[a[i]] = i;
    }
    if (is_sorted(a, 0ll, n) || is_rev(a, 0ll, n))
      cout << "YES"
           << "\n";
    else {
      long long y = M[1];
      if (y == 0) {
        if (is_sorted(a, 1ll, n) || is_rev(a, 1ll, n))
          cout << "YES"
               << "\n";
        else
          cout << "NO"
               << "\n";
      } else if (y == n - 1) {
        if (is_sorted(a, 0ll, n - 1) || is_rev(a, 0ll, n - 1))
          cout << "YES"
               << "\n";
        else
          cout << "NO"
               << "\n";
      } else {
        if (a[y - 1] == 2) {
          if (is_rev(a, 0ll, y) && is_rev(a, y + 1, n) && a[n - 1] > a[0])
            cout << "YES"
                 << "\n";
          else
            cout << "NO"
                 << "\n";
        } else if (a[y + 1] == 2) {
          if (is_sorted(a, 0ll, y) && is_sorted(a, y + 1, n) && a[0] > a[n - 1])
            cout << "YES"
                 << "\n";
          else
            cout << "NO"
                 << "\n";
        } else
          cout << "NO"
               << "\n";
      }
    }
  }
}
