Bowing to Parents

Wookje bowed deeply to his parents before leaving for military training. When he was young, his parents used to tell him:

"Wookje, remember this. Agent's bow must be artistic."

Today, however, his parents were very disappointed in him, because they did not think his bow was artistic. A bow is artistic when the following conditions hold.

1. The bow is represented by a sequence of integers $a_1, \ldots, a_N$ of length $N$.
2. The sequence must first decrease by a constant amount and then increase by a constant amount. That is, there is an index $i$ with $2 \le i \le N-1$ such that $a_1, \ldots, a_i$ is an arithmetic sequence with common difference $x < 0$, and $a_i, \ldots, a_N$ is an arithmetic sequence with common difference $y > 0$.

You must judge whether the sequence representing Wookje's bow is artistic.

Alas! The soccer player Messi shuffled the sequence. Given the shuffled sequence in no particular order, determine whether the original bow could have been artistic.

The first line contains the length $N$ of the sequence.

The second line contains the sequence $a_1, \ldots, a_N$ representing Wookje's bow, shuffled into arbitrary order, with the numbers separated by spaces.

If the sequence can be rearranged into a sequence representing an artistic bow, print Yes. Otherwise, print No.

• $3 \le N \le 402,000$
• $1 \le a_i \le 10^9$