The multiplication puzzle is played with a row of cards, each containing a
single positive integer. During the move player takes one card out of the row and
scores the number of points equal to the product of the number on the card taken and
the numbers on the cards on the left and on the right of it. It is not allowed to take out
the first and the last card in the row. After the final move, only two cards are left in
the row.

The goal is to take cards in such order as to minimize the total number of
scored points.

For example, if cards in the row contain numbers 10 1 50 20 5, player might
take a card with 1, then 20 and 50, scoring
10*1*50 + 50*20*5 + 10*50*5 = 500+5000+2500 = 8000

If he would take the cards in the opposite order, i.e. 50, then 20, then 1, the
score would be
1*50*20 + 1*20*5 + 10*1*5 = 1000+100+50 = 1150.

Input file format

The first line of the input file contains the number of cards N.
The second line contains N integers a_{i}, separated by spaces.

Output file format

Output file must contain a single integer - the minimal score.