Matrix Chain Multiplication

Matrix i has size dimensions[i] × dimensions[i+1]. Multiplying a p×q matrix by a q×r matrix costs p·q·r scalar multiplications. Choose where to put parentheses so multiplying the whole chain costs the least.

Implement min_multiplications(dimensions).

Input

dimensions: n + 1 sizes describing n matrices.

Output

Return the minimum total cost.

Contraintes

2 ≤ length of dimensions ≤ 200; 1 ≤ each size ≤ 500

Exemples

Entrée :
dimensions = [10, 30, 5, 60]

Sortie attendue :
expected = 4500

Entrée :
std::vector<long long> dimensions = {10, 30, 5, 60};

Sortie attendue :
long long expected = 4500;

Entrée :
long[] dimensions = new long[] {10, 30, 5, 60};

Sortie attendue :
long expected = 4500;

Entrée :
dimensions = [5, 10]

Sortie attendue :
expected = 0

Entrée :
std::vector<long long> dimensions = {5, 10};

Sortie attendue :
long long expected = 0;

Entrée :
long[] dimensions = new long[] {5, 10};

Sortie attendue :
long expected = 0;

Références

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

• Wikipedia: Matrix chain multiplication