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;
int long long bs(vector<int long long> &arr, int long long num,
                 int long long key) {
  if (arr[0] == 1) return 0;
  if (arr[1] == 1) return 1;
  if (arr[0] < arr[1]) {
    int long long lo, hi, mid;
    lo = 0;
    hi = num - 1;
    while (lo < hi) {
      mid = (lo) + ((hi - lo) / 2);
      if (arr[mid] == 1) {
        return mid;
      } else if (arr[mid] <= arr[0]) {
        hi = mid - 1;
      } else if (arr[mid] >= arr[0]) {
        lo = mid + 1;
      }
    }
  } else {
    int long long lo, hi, mid;
    lo = 0;
    hi = num - 1;
    while (lo < hi) {
      mid = (lo) + ((hi - lo) / 2);
      if (arr[mid] == 1) {
        return mid;
      } else if (arr[mid] <= arr[num - 1]) {
        hi = mid - 1;
      } else if (arr[mid] >= arr[num - 1]) {
        lo = mid + 1;
      }
    }
  }
}
int main() {
  int long long t, ic;
  cin >> t;
  for (ic = 1; ic <= t; ic++) {
    int long long i, num;
    cin >> num;
    vector<int long long> arr(num);
    for (i = 0; i < num; i++) {
      cin >> arr[i];
    }
    if (num == 1) {
      if (arr[0] == 1)
        cout << "YES" << endl;
      else
        cout << "NO" << endl;
      continue;
    } else if (num == 2) {
      if (arr[0] == 1 && arr[1] == 2) {
        cout << "YES" << endl;
      } else if (arr[0] == 2 && arr[1] == 1) {
        cout << "YES" << endl;
      } else {
        cout << "NO" << endl;
      }
      continue;
    }
    int long long index;
    index = bs(arr, num, 1);
    int long long check = -1;
    if (index == 0) {
      if (arr[1] == 2) {
        check = 1;
      } else if (arr[num - 1] == 2) {
        check = 2;
      }
    } else if (index == (num - 1)) {
      if (arr[0] == 2) {
        check = 1;
      } else if (arr[num - 2] == 2) {
        check = 2;
      }
    } else {
      if (arr[index + 1] == 2) {
        check = 1;
      } else if (arr[index - 1] == 2) {
        check = 2;
      }
    }
    if (check == -1) {
      cout << "NO" << endl;
      continue;
    }
    int long long k = 1;
    int long long checker = 1;
    if (check == 1) {
      for (i = index; i <= (num - 1); i++) {
        if (arr[i] == k) {
          k++;
        } else {
          checker = 0;
          break;
        }
      }
      if (checker == 1) {
        for (i = 0; i <= (index - 1); i++) {
          if (arr[i] == k) {
            k++;
          } else {
            checker = 0;
            break;
          }
        }
      }
    } else if (check == 2) {
      k = 1;
      for (i = index; i >= 0; i--) {
        if (arr[i] == k) {
          k++;
        } else {
          checker = 0;
          break;
        }
      }
      if (checker == 1) {
        for (i = num - 1; i >= (index + 1); i--) {
          if (arr[i] == k) {
            k++;
          } else {
            checker = 0;
            break;
          }
        }
      }
    }
    if (checker == 1) {
      cout << "YES" << endl;
    } else {
      cout << "NO" << endl;
    }
  }
  return 0;
}
