Problem Statement

We call an infinite sequence of positive integers $(a_1,a_2,\cdots)$ good if and only if it satisfies both of the following conditions:

• There exists a finite constant $C$ such that $a_n \le C \cdot n$ for all $1 \le n$;
• For all pairs of positive integers $(n,m)$, $a_n \mid a_m$ if and only if $n\mid m$. Here, $x \mid y$ means $x$ divides $y$.

You are given a positive integer sequence $A=(A_1,A_2,\cdots,A_N)$ of length $N$. Check if there exists a good infinite sequence starting with $(A_1,A_2,\cdots,A_N)$.

You have $T$ testcases to solve.

Constraints

• $1\le T \le 5000$
• $1 \leq N \leq 5000$
• $1 \leq A_i \leq 10^{18}$
• The sum of $N$ across the test cases in a single input is at most $5000$.
• All input values are integers.

Input

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, if there exists a good infinite sequence starting with $(A_1,A_2,\cdots,A_N)$, print Yes, and otherwise print No. In printing Yes or No, you can output each letter in any case (upper or lower).