Sorting with Swap Threshold

You are given an array of distinct integers and a threshold d. You are allowed to swap two elements only if the absolute difference between them is at most d (i.e. \(|a_i - a_j| \le d\)). Your task is to determine whether it is possible to sort the array in non-decreasing order using only these allowed swaps.

Input Format: The input consists of three lines. The first line contains an integer n, representing the number of elements in the array. The second line contains n space-separated integers, representing the array. The third line contains a single integer d, the swap threshold.

Output Format: Output a single line containing "YES" if the array can be sorted using allowed swaps, or "NO" otherwise.

Note: The solution should use an algorithm based on union-find (disjoint set) to group indices that can be mutually swapped if they satisfy the condition \(|a_i - a_j| \le d\), then verify if the sorted order can be obtained by rearranging values within each group.

inputFormat

The first line contains an integer n (\(1 \le n \le 10^5\)), the number of elements in the array.

The second line contains n space-separated integers \(a_1, a_2, \ldots, a_n\) representing the array. All elements are distinct.

The third line contains an integer d (\(0 \le d \le 10^9\)), the maximum allowed absolute difference for a swap.

outputFormat

Output a single line: "YES" if the array can be sorted into non-decreasing order using the allowed swaps; otherwise, output "NO".

## sample

5
4 2 3 1 5
3

YES

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