You are given a list of integers . Determine whether or not you can modify the list into an arithmetic sequence by rearranging the list and/or changing the value of **at most** number.

An arithmetic sequence is a sequence in which each term is obtained by adding the previous term by a constant number, called the common difference. For example, is an arithmetic sequence with a common difference of .

#### Constraints

For all subtasks:

Points Awarded | |
---|---|

6 points | |

5 points | |

4 points |

#### Input Specification

The first line contains one integer .

The second line contains integers .

#### Output Specification

Output `YES`

if the list can be modified to become an arithmetic sequence and `NO`

otherwise.

#### Sample Input 1

```
4
3 1 5 10
```

#### Sample Output 1

`YES`

#### Explanation for Sample Output 1

We can change the number in the list to be . The list of numbers becomes , which can be rearranged to form the arithmetic sequence .

#### Sample Input 2

```
5
3 6 9 12 15
```

#### Sample Output 2

`YES`

#### Explanation for Sample Output 2

The list is already an arithmetic sequence, so no changes are necessary.

## Comments

Can change element in array to negative number?