In a multidimensional space consisting of many different planes, the planes are not gender defined, planes are called love triangles if plane A loves plane B, plane B loves plane C and plane C loves plane A. Then, the relationship between the three planes A, B, C is called a love triangle. There are n planes numbered 1, 2, ..., n. The ~i^{th}~ plane is called the ~j^{th}~ plane if f[i] = j and i ≠ j. Your task is to check whether a love triangle exists in the given n planes?

Input:

Each test contains multiple test cases.

• The first line contains a single integer t (1 ≤ t ≤ ~10^3~) — the number of test cases. Each test case consists of two lines.
• For each testcase consisting of two lines:
  • The first line contains an integer n (2 ≤ n ≤ ~10^9~) – the number of planes;
  • The second line contains n integers ~f_1, f_2, ..., f_n~ (1 ≤ ~f_i~ ≤ n, ~f_i~ ≠ i), that is, the ith member loves the fith member.

Output:

Each testcase prints on 1 line, each line prints YES if a love triangle exists, otherwise prints NO

Example

Input

2
5 
2 4 5 1 3
5 
5 5 5 5 1

Output

YES
NO