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;
inline int read() {
  int ans = 0;
  bool f = 1;
  char ch = getchar();
  while (!isdigit(ch)) f ^= ch == '-', ch = getchar();
  while (isdigit(ch)) ans = ((ans << 2) + ans << 1) + (ch ^ 48), ch = getchar();
  return f ? ans : -ans;
}
const int mod = 998244353;
inline int add(int a, int b) { return (a += b) >= mod ? a - mod : a; }
inline int dec(int a, int b) { return (a -= b) < 0 ? a + mod : a; }
inline int mul(int a, int b) { return (long long)a * b % mod; }
inline void Add(int& a, int b) { (a += b) >= mod ? a -= mod : a; }
inline void Dec(int& a, int b) { (a -= b) < 0 ? a += mod : a; }
inline void Mul(int& a, int b) { a = (long long)a * b % mod; }
inline int ksm(int a, int p) {
  int ret = 1;
  for (; p; p >>= 1, a = mul(a, a))
    if (p & 1) Mul(ret, a);
  return ret;
}
const int N = 2e6 + 5;
int n, m;
char s[N], t[N];
int a[N];
int main() {
  for (register int tt = read(); tt; --tt) {
    scanf("%s", s + 1), n = strlen(s + 1);
    scanf("%s", t + 1), m = strlen(t + 1);
    reverse(s + 1, s + n + 1), reverse(t + 1, t + m + 1);
    int pos = 0;
    for (register int i = 1; i <= m; ++i)
      if (t[i] == '1') {
        pos = i;
        break;
      }
    bool f = 1;
    if (!pos) {
      cout << "0\n";
      continue;
    }
    for (register int i = pos; i <= n; ++i) {
      if (s[i] == '1') {
        cout << i - pos << '\n';
        f = 0;
        break;
      }
    }
    if (f) cout << "0\n";
  }
  return 0;
}
