F - Coprime Solitaire

Score : $600$ points

Problem Statement

We have $N$ cards arranged in a row on a table. For each $i = 1, 2, \ldots, N$, the $i$-th card has an integer $A_i$ written on the front and an integer $B_i$ written on the back. Initially, every card is placed face up.

Takahashi will choose any number of cards he likes (possibly zero) and flip them. Then, he will be happy if the following condition is satisfied:

• for every pair of integers $(i, j)$ such that $1 \leq i \lt j \leq N$, the integers visible on the $i$-th and $j$-th cards are coprime.

Determine whether it is possible for Takahashi to be happy.

Constraints

• $1 \leq N \leq 3 \times 10^4$
• $1 \leq A_i, B_i \leq 2 \times 10^6$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $B_1$

$A_2$ $B_2$

$\vdots$

$A_N$ $B_N$

Output

If it is possible for Takahashi to be happy, print Yes; otherwise, print No.

3
2 5
10 9
4 8

Yes

Initially, we see integers $2$, $10$, and $4$. If we flip the first and second cards, we will see $5$, $9$, and $4$, which will make Takahashi happy. Thus, we should print Yes.

2
10 100
1000 10000

No

There is no way to flip cards to make Takahashi happy, so we should print No.