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.

Constraints

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

Examples

Input:
dimensions = [10, 30, 5, 60]

Expected output:
expected = 4500

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

Expected output:
long long expected = 4500;

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

Expected output:
long expected = 4500;

Input:
dimensions = [5, 10]

Expected output:
expected = 0

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

Expected output:
long long expected = 0;

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

Expected output:
long expected = 0;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Wikipedia: Matrix chain multiplication