# Recovering BST

## 题意翻译

\$\$
仓鼠 $\textsf{Dima}$ 把一颗**二叉排序树**的所有边都吃掉了！！不仅如此，这棵树的所有顶点都被这只珂爱的仓鼠搞乱了。
不过他还是知道这棵树的一些性质……那就是任意两个直接相连的点之间的权值最大公约数不是 $1$ 。为了不让打造这棵树的 $\textsf{Andrew}$ 生气，还请你帮帮 $\textsf{Dima}$ ：若可以**按上述性质**修复这颗二叉排序树，输出`Yes`；否则输出`No`。
树上点数 $2 \leq n \leq 700$ ；点权 $2 \leq a_i \leq 10^9$

## 题目描述

Dima the hamster enjoys nibbling different things: cages, sticks, bad problemsetters and even trees!
Recently he found a binary search tree and instinctively nibbled all of its edges, hence messing up the vertices. Dima knows that if Andrew, who has been thoroughly assembling the tree for a long time, comes home and sees his creation demolished, he'll get extremely upset.
To not let that happen, Dima has to recover the binary search tree. Luckily, he noticed that any two vertices connected by a direct edge had their greatest common divisor value exceed $ 1 $ .
Help Dima construct such a binary search tree or determine that it's impossible. The definition and properties of a binary search tree can be found [here.](https://en.wikipedia.org/wiki/Binary_search_tree)

## 输入输出格式

### 输入格式

The first line contains the number of vertices $ n $ ( $ 2 \le n \le 700 $ ).
The second line features $ n $ distinct integers $ a_i $ ( $ 2 \le a_i \le 10^9 $ ) — the values of vertices in ascending order.

### 输出格式

If it is possible to reassemble the binary search tree, such that the greatest common divisor of any two vertices connected by the edge is greater than $ 1 $ , print "Yes" (quotes for clarity).
Otherwise, print "No" (quotes for clarity).

## 输入输出样例

### 输入样例 #1

```
6
3 6 9 18 36 108
```

### 输出样例 #1

```
Yes
```

### 输入样例 #2

```
2
7 17
```

### 输出样例 #2

```
No
```

### 输入样例 #3

```
9
4 8 10 12 15 18 33 44 81
```

### 输出样例 #3

```
Yes
```

## 说明

The picture below illustrates one of the possible trees for the first example.
![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1025D/a6281ebfc3addc046e3a216e978640a7d00d938f.png)The picture below illustrates one of the possible trees for the third example.
![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1025D/422d22e6560dde35033dafdd73125c60e4d294d8.png)