Problem Statement

There are $N$ boxes numbered from $1$ to $N$, and $N$ balls numbered from $1$ to $N$.

You have assigned Snuke the following procedure as homework.

• Put each ball into any box he likes. Multiple balls can be placed in the same box, and there can be boxes without balls.
• For $i = 1, 2, \cdots, N$ in this order, perform the following operations.
• If box $i$ contains no balls, do nothing.
  • If box $i$ contains balls, take all of them out and arrange them in a line in any order he likes. Let $k$ be the number of balls taken out, and $(x_1, x_2, \cdots, x_k)$ be the ball numbers in the line. For each $1 \leq j \leq k$, put ball $x_j$ into box $x_{j+1}$. Here, $x_{k+1}$ means $x_1$. All these operations of putting balls into boxes happen simultaneously.

He claims that he has completed the homework and reports the final state to you. Specifically, he says that ball $i$ is in box $A_i$ after the procedure.

You doubt whether he has correctly performed the procedure. Determine whether the state he reported is a possible result of the procedure.

There are $T$ test cases for each input.

Constraints

• $1 \leq T \leq 250000$
• $1 \leq N \leq 250000$
• $1 \leq A_i \leq N$
• The sum of $N$ over all test cases in each input is at most $250000$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
case_1
case_2
\vdots
case_T

Each test case is given in the following format:

N
A_1 A_2 \cdots A_N

Output

For each test case, print Yes if the state Snuke reported is a possible result of the procedure, and No otherwise.