Divisibility Homomorphism

AtCoder

IDagc067_c

Time2000ms

Memory256MB

Difficulty—

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: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

5
5
1 2 3 4 5
5
1 4 9 16 25
5
1 4 6 8 10
5
1 2 4 4 5
5
1 2 3 5 4

Output #1

Yes
Yes
Yes
No
No

For the $1$\-st test case, we can let $a_n=n$ and that satisfies the condition.

API Response (JSON)

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