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>
inline int in();
inline void wr(int);
const int N = (int)4e2 + 5;
int n, a[N];
inline bool check(int, int);
int main(int argc, char** argv) {
  register int T = in();
  while (T--) {
    n = in();
    for (register int i = 1; i <= n; ++i) a[i + n] = a[i] = in();
    register bool tp = 0;
    for (register int p = 1; p + n - 1 <= (n << 1) && !tp; ++p) {
      if (a[p] != 1 && a[p] != n) continue;
      tp = check(p, a[p]);
    }
    puts(tp ? "YES" : "NO");
  }
}
inline bool check(int p, int x) {
  if (x == 1)
    for (register int i = p; i <= p + n - 1; ++i)
      if (a[i] != i - p + 1) return 0;
  if (x == n)
    for (register int i = p; i <= p + n - 1; ++i)
      if (a[i] != p + n - i) return 0;
  return 1;
}
inline int in() {
  register char c = getchar();
  register int x = 0, f = 1;
  for (; c < '0' || c > '9'; c = getchar())
    if (c == '-') f = -1;
  for (; c >= '0' && c <= '9'; c = getchar())
    x = (x << 1) + (x << 3) + (c & 15);
  return x * f;
}
inline void wr(int x) {
  if (x < 0) putchar('-'), x = -x;
  if (x / 10) wr(x / 10);
  putchar(x % 10 + '0');
}
