# Symmetric and Transitive

## 输入输出格式

### 输入格式

A single line contains a single integer \$ n \$ \$ (1<=n<=4000) \$ .

### 输出格式

In a single line print the answer to the problem modulo \$ 10^{9}+7 \$ .

## 输入输出样例

### 输入样例 #1

``````1
``````

### 输出样例 #1

``````1
``````

### 输入样例 #2

``````2
``````

### 输出样例 #2

``````3
``````

### 输入样例 #3

``````3
``````

### 输出样例 #3

``````10
``````

## 说明

If \$ n=1 \$ there is only one such relation — an empty one, i.e. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF568B/519c456ed02b51bdfd523585bf0281cdbd8600fd.png). In other words, for a single element \$ x \$ of set \$ A \$ the following is hold: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF568B/3abfc110a65cf385b201a329b8a306e1eb23baef.png). If \$ n=2 \$ there are three such relations. Let's assume that set \$ A \$ consists of two elements, \$ x \$ and \$ y \$ . Then the valid relations are ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF568B/519c456ed02b51bdfd523585bf0281cdbd8600fd.png), \$ ρ={(x,x)} \$ , \$ ρ={(y,y)} \$ . It is easy to see that the three listed binary relations are symmetric and transitive relations, but they are not equivalence relations.