You are given a list of ~N~ integers ~a_1, a_2, \dots, a_N~. 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 ~1~ 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, ~2, 5, 8, 11~ is an arithmetic sequence with a common difference of ~3~.

Constraints

For all subtasks:

• ~1 \le a_i \le 10^9~

Points Awarded	~N~
6 points	~2 \le N \le 400~
5 points	~2 \le N \le 4\,000~
4 points	~2 \le N \le 2 \times 10^5~

Input Specification

The first line contains one integer ~N~.

The second line contains ~N~ integers ~a_i~.

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 ~4^{\text{th}}~ number in the list to be ~7~. The list of numbers becomes ~3, 1, 5, 7~, which can be rearranged to form the arithmetic sequence ~1, 3, 5, 7~.

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.