Problem 2527: Gioconda

While searching in the garbage cans, Jean found a sequence of $N$ positive integers. Because he has no use for this, he gifted it to Nicusor Gioconda, and gave him a challenge too.

Nicusor has to chose pairwise distinct substrings of length $2$ such that every index is taken at least once. If he will give a correct partitioning, he will get the ultimate prize: the magical chicken wing!

In this problem, we consider that a substring is a contiguous subset of indices $[i,i+1,\cdots j-1, j]$ .

Because he is far better at singing than he is at solving problems, he asks for your help.

Input data

First line will contain a single number $N$ ( $1 \leq N \leq 10^5$ ) - the length of the sequence.
The next line contains a sequence $A$ of $N$ positive values ( $1 \leq A_i \leq 500$ ).

Output data

The first line will contain a string that is either YES or NO, that represents the existence of a correct partitioning.

Constraints and clarifications

For $20$ point it is guaranteed that $N \leq 20$ ;
For the other $80$ points we have $N \leq 10^5$ .

Example 1

stdin

5
1 2 1 2 3

stdout

YES

Explanation

For the first example, a valid partitioning is $[1,2], [2,1], [2,3]$ corresponding to the indices $[1,2], [2,3], [4,5]$ .

Example 2