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() {
  int t;
  cin >> t;
  for (int k = 0; k < t; k++) {
    int m, flag = 0, pos, i, b = 0;
    int a[300] = {0};
    cin >> m;
    for (int j = 0; j < m; j++) {
      cin >> a[j];
      if (a[j] == 1) {
        pos = j;
      }
    }
    if (m > 1) {
      int count = 2, b = 0;
      if (pos == m - 1) {
        i = pos - 1;
        if (a[i] == count) {
          b = 1;
          while (i > 0) {
            i--;
            count++;
            if (a[i] != count) {
              flag = 1;
              break;
            }
          }
        }
        if ((flag == 1 && b == 1) || b == 0) {
          i = 0;
          count = 2;
          flag = 0;
          if (a[i] == count) {
            while (i < m - 2) {
              i++;
              count++;
              if (a[i] != count) {
                flag = 1;
                break;
              }
            }
          } else {
            flag = 1;
          }
        }
      } else if (pos == 0) {
        i = pos + 1;
        if (a[i] == count) {
          b = 1;
          while (i < m - 1) {
            i++;
            count++;
            if (a[i] != count) {
              flag = 1;
              break;
            }
          }
        }
        if ((flag == 1 && b == 1) || b == 0) {
          i = m - 1;
          count = 2;
          flag = 0;
          if (a[i] == count) {
            while (i > 1) {
              i--;
              count++;
              if (a[i] != count) {
                flag = 1;
                break;
              }
            }
          } else {
            flag = 1;
          }
        }
      } else {
        i = pos + 1;
        if (a[i] == count) {
          b = 1;
          while (a[i] != m) {
            i++;
            count++;
            if (a[i] != count) {
              flag = 1;
              break;
            }
            if (i == m - 1) {
              i = -1;
            }
          }
        }
        if ((flag == 1 && b == 1) || b == 0) {
          i = pos - 1;
          count = 2;
          flag = 0;
          if (a[i] == count) {
            while (a[i] != m) {
              i--;
              count++;
              if (a[i] != count) {
                flag = 1;
                break;
              }
              if (i == 0) {
                i = m;
              }
            }
          } else {
            flag = 1;
          }
        }
      }
    }
    if (flag == 1) {
      cout << "NO"
           << "\n";
    } else {
      cout << "YES"
           << "\n";
    }
  }
  return 0;
}
