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 (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
	"bufio"
	"os"
	"strings"
	"strconv"
	"math"
)

func max(a, b int) int {
    if a < b {
        return b
    }
    return a
}

func min(a, b int) int {
    if a < b {
        return a
    }
    return b
}

/*
	定义:
		dp[i][j]: A[i:j]合并产生的开销
	初始值:
		dp[i][i]=0
	转移方程:
		dp[i][j]=min(dp[i][k]+dp[k+1][j])+sums[j]-sums[i]+A[i]
*/
func solve(A []int, N int) int {
	dp := make([][]int, N)
	for i := range dp {
		dp[i] = make([]int, N)
	}

	sums := make([]int, N)
	sums[0] = A[0]
	for i:=1; i<N; i++ {
		sums[i] = sums[i-1]+A[i]
	}

	for l:=2; l<=N; l++ {
		for i:=0; i<=N-l; i++ {
			j := i+l-1
			dp[i][j] = math.MaxInt32
			for k:=i; k<j; k++ {
				dp[i][j] = min(dp[i][j], dp[i][k]+dp[k+1][j])
			}
			dp[i][j] += sums[j]-sums[i]+A[i]
		}
	}
	return dp[0][N-1]
}

func readLineNum(bf *bufio.Reader) int {
	line, _ := bf.ReadString('\n')
	line = strings.Trim(line, "\n")
	N, _ := strconv.Atoi(line)
	return N
}

func readLineNums(bf *bufio.Reader) []int {
	line, _ := bf.ReadString('\n')
	line = strings.Trim(line, "\n")
	fields := strings.Split(line, " ")
	nums := []int{}
	for _, field := range fields {
		num, _ := strconv.Atoi(field)
		nums = append(nums, num)
	}
	return nums
}

func readLineFloats(bf *bufio.Reader) []float64 {
	line, _ := bf.ReadString('\n')
	line = strings.Trim(line, "\n")
	fields := strings.Split(line, " ")
	fs := []float64{}
	for _, field := range fields {
		f , _ := strconv.ParseFloat(field, 64)
		fs = append(fs, f)
	}
	return fs
}

func readLineStrs(bf *bufio.Reader) []string {
	line, _ := bf.ReadString('\n')
	line = strings.Trim(line, "\n")
	return strings.Split(line, " ")
}

func main() {
	bf := bufio.NewReader(os.Stdin)
    N := readLineNum(bf)
    A := readLineNums(bf)
    fmt.Println(solve(A, N))
}