#include <bits/stdc++.h>
using namespace std;
const int N = 1e6;
int d() {
  int ret;
  scanf("%d", &ret);
  return ret;
}
long long lld() {
  long long ret;
  scanf("%lld", &ret);
  return ret;
}
int cnt = 0;
vector<int> v;
int n = 10;
void solve(int i) {
  if (cnt == n) {
    for (int i = 0; i < v.size(); i++) cout << v[i] << " ";
    cout << endl;
    v.pop_back();
    cnt--;
  }
  v.push_back(i);
  cnt++;
  solve(i + 1);
  v.pop_back();
  v.push_back(i + 1);
  cnt++;
  solve(i + 1);
  v.pop_back();
}
int arr[500];
int main() {
  int t = d();
  while (t--) {
    int n = d();
    for (int i = 0; i < n; i++) scanf("%d", arr + i);
    bool flag = true;
    if (n == 1) {
      puts("YES");
      continue;
    }
    for (int i = 0; i < n; i++) {
      if (i == 0) {
        if (arr[0] - 1 == arr[n - 1] || arr[0] - 1 == arr[1] || arr[0] == 1) {
        } else
          flag = false;
      } else if (i == n - 1) {
        if (arr[n - 1] - 1 == arr[0] || arr[n - 1] - 1 == arr[n - 2] ||
            arr[n - 1] == 1) {
        } else
          flag = false;
      } else {
        if (arr[i] - 1 == arr[i - 1] || arr[i] - 1 == arr[i + 1] ||
            arr[i] == 1) {
        } else
          flag = false;
      }
    }
    if (flag)
      puts("YES");
    else
      puts("NO");
  }
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 1e6;
int d() {
  int ret;
  scanf("%d", &ret);
  return ret;
}
long long lld() {
  long long ret;
  scanf("%lld", &ret);
  return ret;
}
int cnt = 0;
vector<int> v;
int n = 10;
void solve(int i) {
  if (cnt == n) {
    for (int i = 0; i < v.size(); i++) cout << v[i] << " ";
    cout << endl;
    v.pop_back();
    cnt--;
  }
  v.push_back(i);
  cnt++;
  solve(i + 1);
  v.pop_back();
  v.push_back(i + 1);
  cnt++;
  solve(i + 1);
  v.pop_back();
}
int arr[500];
int main() {
  int t = d();
  while (t--) {
    int n = d();
    for (int i = 0; i < n; i++) scanf("%d", arr + i);
    bool flag = true;
    if (n == 1) {
      puts("YES");
      continue;
    }
    for (int i = 0; i < n; i++) {
      if (i == 0) {
        if (arr[0] - 1 == arr[n - 1] || arr[0] - 1 == arr[1] || arr[0] == 1) {
        } else
          flag = false;
      } else if (i == n - 1) {
        if (arr[n - 1] - 1 == arr[0] || arr[n - 1] - 1 == arr[n - 2] ||
            arr[n - 1] == 1) {
        } else
          flag = false;
      } else {
        if (arr[i] - 1 == arr[i - 1] || arr[i] - 1 == arr[i + 1] ||
            arr[i] == 1) {
        } else
          flag = false;
      }
    }
    if (flag)
      puts("YES");
    else
      puts("NO");
  }
}

```