LCC '18 Contest 4 J1 - Terminus Quest

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Points: 3 (partial)
Time limit: 2.0s
Memory limit: 64M

Problem type

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 (a) of N integers where the difference between any adjacent pair is the same.

The difference of an adjacent pair of integers is defined as a_i - a_{i - 1} for all i, 2 \le i \le N.

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

Input Specification

The first line contains a single integer, N. 2 \leq N \leq 1000.

The next line describes the list of numbers by providing N space separated integers where the ith integer describes a_i. 0 \leq a_i \leq 10^6

Output Specification

YES if the input list is an arithmetic pattern. NO if the input list is not an arithmetic pattern.

Sample Input

2 4 6 8 10

Sample Output



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