Rearrange to Form a Consecutive Sequence

Given an array of integers, determine if it is possible to rearrange the array so that the resulting sequence satisfies the following condition: For every pair of adjacent elements, the difference is either 0 or exactly 1. In other words, if the unique elements (when sorted) are denoted by \(u_1, u_2, \ldots, u_k\), then for every \(i\) from 2 to \(k\) the condition

[ u_i - u_{i-1} \leq 1 ]

must hold true. If this condition holds, output YES, otherwise output NO.

Example:

• For the array [1, 2, 2, 3, 4], the unique sorted array is [1, 2, 3, 4] with consecutive differences of 1, so the answer is YES.
• For the array [1, 3, 3, 4, 5, 7], the unique sorted array is [1, 3, 4, 5, 7] and there is at least one gap greater than 1 (between 1 and 3, and 5 and 7), so the answer is NO.

inputFormat

The input is given via standard input (stdin). The first line contains an integer (n) (the number of elements in the array). The next line contains (n) space-separated integers representing the elements of the array.

outputFormat

Print a single line to standard output (stdout) with the string YES if the array can be rearranged to form a sequence where for every adjacent pair ( (a, b) ), the condition (b - a \in {0, 1}) holds. Otherwise, print NO.## sample

5
1 2 2 3 4

YES