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 main() {
  long long int j, m, l = 0, r = 0, proiz, g, max = 0, lim, b, c = 0, d,
                      unch = 0, incr = 0, red = 0, resc = 0, stop = 0, i,
                      suma = 0, maxi, maxj, n, vivod;
  long int a, kol = 0;
  cin >> n;
  long long int *arr1 = new long long int[n];
  long long int *arr = new long long int[n];
  for (i = 0; i < n; i++) {
    cin >> arr[i];
    long long int *chisla = new long long int[arr[i] * 2];
    for (g = 0; g < arr[i]; g++) {
      cin >> a;
      chisla[g] = a;
      chisla[arr[i] + g] = a;
    }
    for (j = 0; j < arr[i] * 2; j++) {
      red = chisla[j] - chisla[j + 1];
      switch (red) {
        case 1:
          if (incr > 0) incr = 0;
          unch++;
          break;
        case -1:
          if (unch > 0) unch = 0;
          incr++;
          break;
      }
      if (unch == arr[i] || incr == arr[i]) break;
    }
    if (unch == arr[i] || incr == arr[i])
      arr1[i] = 1;
    else
      arr1[i] = 0;
    delete chisla;
  }
  for (i = 0; i < n; i++) {
    if (arr1[i] == 1)
      cout << "YES" << endl;
    else
      cout << "NO" << endl;
  }
  return 0;
}
