Count Inversions

An inversion is a pair of positions i < j with numbers[i] > numbers[j]. Count all inversions. Lists can be long, so a merge-sort based O(n log n) count is needed.

Implement count_inversions(numbers).

Input

numbers: The list of integers.

Output

Return the number of inversions.

Contraintes

0 ≤ length ≤ 200,000

Exemples

Entrée :
numbers = [2, 4, 1, 3, 5]

Sortie attendue :
expected = 3

Entrée :
std::vector<long long> numbers = {2, 4, 1, 3, 5};

Sortie attendue :
long long expected = 3;

Entrée :
long[] numbers = new long[] {2, 4, 1, 3, 5};

Sortie attendue :
long expected = 3;

Entrée :
numbers = [1, 2, 3]

Sortie attendue :
expected = 0

Entrée :
std::vector<long long> numbers = {1, 2, 3};

Sortie attendue :
long long expected = 0;

Entrée :
long[] numbers = new long[] {1, 2, 3};

Sortie attendue :
long expected = 0;

Références

Ce défi a été adapté pour CodeUtility. Suivez l'énoncé et les contraintes ci-dessus.

• Wikipedia: Inversion (discrete mathematics)