Matrix Multiplications

Given n matrices with sizes , respectively. The matrices are ordered from left to right from 1 to n. You are allowed to place brackets to prioritize some multiplications.

What is the minimum number of operations to multiply all the matrices?

Input

The first line contains a single integer n ().

The next n lines contain the dimensions of each of the matrices (1 ≤ ≤ 1000).

It’s guaranteed that for .

Output

The program should print the minimum number of operations required to multiply all the matrices.

Examples