Merge sort with inversion counting

PHP Hard sorting

Task «Merge sort with inversion counting»

Given an array of integers, it is necessary to implement a merge sort algorithm that also counts the number of inversions in the array. An inversion is a pair of indices (i, j) such that i < j and arr[i] > arr[j]. Output the sorted array and the number of inversions.

Input Format

In the first line, an integer N (1 ≤ N ≤ 10^5) — the number of elements. In the second line, N integers separated by spaces.

Output Format

In the first line, N numbers separated by spaces — an array sorted in ascending order. In the second line, a single integer — the number of inversions.

Examples

Example 1

INPUT

Война и мир
Лев Толстой
1869

OUTPUT

Название: Война и мир, Автор: Лев Толстой, Год: 1869

Example 2

INPUT

3
1 2 3

OUTPUT

1 2 3
0

Example 3

INPUT

1984
Джордж Оруэлл
1949

OUTPUT

Название: 1984, Автор: Джордж Оруэлл, Год: 1949

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