Multiplication Puzzle，划分区间DP。无条件划分区间。详见本文具体内容

# 题目

Multiplication Puzzle

# 限制

Time Limit: 1000MS
Memory Limit: 65536K

# 描述

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
$$10 \times 15 \times 0 + 50 \times 20 \times 5 + 10 \times 50 \times 5 = 500+5000+2500 = 8000$$
If he would take the cards in the opposite order, i.e. 50, then 20, then 1, the score would be
$$1 \times 50 \times 20 + 1 \times 20 \times 5 + 10 \times 1 \times 5 = 1000+100+50 = 1150$$

# 输入格式

The first line of the input contains the number of cards $N$ $(3 \le N \le 100)$. The second line contains $N$ integers in the range from $1$ to $100$, separated by spaces.

# 输出格式

Output must contain a single integer - the minimal score.

# 思路

• $2,3,4: \quad 1 \times 2 \times 3+1 \times 3 \times 4+1 \times 4 \times 5$
• $2,4,3: \quad 1 \times 2 \times 3+3 \times 4 \times 5+1 \times 3 \times 5$
• $3,2,4: \quad 2 \times 3 \times 4+1 \times 2 \times 4+1 \times 4 \times 5$
• $3,4,2: \quad 2 \times 3 \times 4+2 \times 4 \times 5+1 \times 2 \times 5$
• $4,2,3: \quad 3 \times 4 \times 5+1 \times 2 \times 3+1 \times 3 \times 5$
• $4,3,2: \quad 3 \times 4 \times 5+2 \times 3 \times 5+1 \times 2 \times 5$

$3,4: \quad 2 \times 3 \times 4+2 \times 4 \times 5$
$4,3: \quad 3 \times 4 \times 5+2 \times 3 \times 5$

$3,4,2: \quad 2 \times 3 \times 4+2 \times 4 \times 5+1 \times 2 \times 5$
$4,3,2: \quad 3 \times 4 \times 5+2 \times 3 \times 5+1 \times 2 \times 5$

$2,4: \quad 1 \times 2 \times 3+3 \times 4 \times 5$
$4,2: \quad 3 \times 4 \times 5+1 \times 2 \times 3$

$2,4,3: \quad 1 \times 2 \times 3+3 \times 4 \times 5+1 \times 3 \times 5$
$4,2,3: \quad 3 \times 4 \times 5+1 \times 2 \times 3+1 \times 3 \times 5$

$2,3: \quad 1 \times 2 \times 3+1 \times 3 \times 4$
$3,2: \quad 2 \times 3 \times 4+1 \times 2 \times 4$

$2,3,4: \quad 1 \times 2 \times 3+1 \times 3 \times 4+1 \times 4 \times 5$
$3,2,4: \quad 2 \times 3 \times 4+1 \times 2 \times 4+1 \times 4 \times 5$