The goal of the matrix-chain multiplication problem is to find the most efficient way to multiply given $n$ matrices $M_1,M_2,M_3,...,M_n$.

Write a program which reads dimensions of $M_i$, and finds the minimum number of scalar multiplications to compute the maxrix-chain multiplication $M_1M_2...M_n$.

In the first line, an integer $n$ is given. 

In the following $n$ lines, the dimension of matrix $M_i\ (i=1...n)$ is given by two integers $r$ and $c$ which respectively represents the number of rows and columns of $M_i$.