Link with Limit

Link has a function $f(x)$, where $x$ and $f(x)$ are both integers in $[1,n]$.

Let $f_n(x)=f(f_{n-1}(x))$ and $f_1(x) = f(x)$, he define the power of a number $x$ as:
$$g(x) = \lim \limits_{n \to + \infty} \frac{1}{n} \sum_{i=1}^{n} f_i(x)$$

He wants to know whether $x$ has the same power for all $x \in [1,n]$.

The input consists of multiple test cases.

The first line contains an integer $T$ ($1 \leq T \leq 100$) -- the number of test cases.

For each test case:

In the first line, there is an integer $n$ ($1 \leq n \leq 10^5$).

In the second line, there are $n$ integers, the $i$-th integer shows the value of $f(i)$ ($1 \leq f(i) \leq n$).

It is guaranteed that the sum of $n$ over all test cases will not exceed $10^6$.

For each test case, output 'YES' if all $x$ have the same power. Otherwise, output 'NO'.

2
2
1 2
2
1 1

NO
YES

2021“MINIEYE杯”中国大学生算法设计超级联赛（7）