Problem:
Score : 100 points

Problem Statement

There are N slimes lining up in a row.
Initially, the i-th slime from the left has a size of a_i.

Taro is trying to combine all the slimes into a larger slime.
He will perform the following operation repeatedly until there is only one slime:

Choose two adjacent slimes, and combine them into a new slime. The new slime has a size of x + y, where x and y are the sizes of the slimes before combining them. Here, a cost of x + y is incurred. The positional relationship of the slimes does not change while combining slimes.

Find the minimum possible total cost incurred.

Constraints

All values in input are integers.

2 \leq N \leq 400

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_N

Output

Print the minimum possible total cost incurred.

Sample Input 1

4
10 20 30 40

Sample Output 1

190

Taro should do as follows (slimes being combined are shown in bold):

(10, 20, 30, 40) → (30, 30, 40)

(30, 30, 40) → (60, 40)

(60, 40) → (100)

Sample Input 2

5
10 10 10 10 10

Sample Output 2

120

Taro should do, for example, as follows:

(10, 10, 10, 10, 10) → (20, 10, 10, 10)

(20, 10, 10, 10) → (20, 20, 10)

(20, 20, 10) → (20, 30)

(20, 30) → (50)

Sample Input 3

3
1000000000 1000000000 1000000000

Sample Output 3

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 4

6
7 6 8 6 1 1

Sample Output 4

68

Taro should do, for example, as follows:

(7, 6, 8, 6, 1, 1) → (7, 6, 8, 6, 2)

(7, 6, 8, 6, 2) → (7, 6, 8, 8)

(7, 6, 8, 8) → (13, 8, 8)

(13, 8, 8) → (13, 16)

(13, 16) → (29)

Solution in Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
)

var N int
var a, s []int

func main() {
	N = ReadInt()
	a = ReadInts(N)
	s = make([]int, N+1)
	for i := 0; i < N; i++ {
		s[i+1] = s[i] + a[i]
	}
	memo = make([][]int, N)
	for i := 0; i < N; i++ {
		memo[i] = make([]int, N)
	}
	fmt.Println(f(0, N-1))
}

var memo [][]int

func f(i, j int) int {
	if i == j {
		return a[i]
	}
	if j-1 == i {
		return a[i] + a[j]
	}
	if memo[i][j] > 0 {
		return memo[i][j]
	}
	v := Min(
		f(i, j-1)+s[j+1]-s[i],
		f(i, j-2)+a[j-1]+a[j]+s[j+1]-s[i],
		f(i+1, j)+s[j+1]-s[i],
		f(i+2, j)+a[i]+a[i+1]+s[j+1]-s[i],
	)
	memo[i][j] = v
	return v
}

func Min(xs ...int) int {
	min := xs[0]
	for _, x := range xs[1:] {
		if min > x {
			min = x
		}
	}
	return min
}

var reader = bufio.NewReader(os.Stdin)

func Scan(a ...interface{}) {
	if _, err := fmt.Fscan(reader, a...); err != nil {
		panic(err)
	}
}
func ReadInt() (i int) { Scan(&i); return }
func ReadInts(n int) []int {
	v := make([]int, n)
	for i := 0; i < n; i++ {
		Scan(&v[i])
	}
	return v
}