On his quest to solve Terminus Est, Max finds an ancient scroll that claims to be the key to solving the problem.

The scroll proclaims:

The one to solve Terminus Est shall be able to recognize patterns.

Max interprets this as the ability to recognize arithmetic patterns.

Max defines an arithmetic pattern as a list () of integers where the difference between any adjacent pair is the same.

The difference of an adjacent pair of integers is defined as for all , .

Can you determine if a list of numbers is an arithmetic pattern?

#### Input Specification

The first line contains a single integer, . .

The next line describes the list of numbers by providing space separated integers where the th integer describes .

#### Output Specification

`YES`

if the input list is an arithmetic pattern.
`NO`

if the input list is not an arithmetic pattern.

#### Sample Input

```
5
2 4 6 8 10
```

#### Sample Output

`YES`

## Comments