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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

//package april2020;

import java.util.*;
import java.lang.*;
import java.math.*;
import java.io.*;

public class Main {
	static long[] dp;
	static int n,k, a[];
	static long MOD = (long)1e9+7;
	public static void main(String[] args) throws IOException {
		FastReader scn = new FastReader();
		OutputStream out = new BufferedOutputStream ( System.out );
		n = scn.nextInt();
		a = new int[n];
		long[] ps = new long[n];
		for(int i =0;i<n;i++) {
			a[i] = scn.nextInt();
			if(i>0)
				ps[i]=ps[i-1]+a[i];
			else
				ps[i]=a[i];
		}
		long[][] dp = new long[n][n];
		
//		for(int i=1;i<n;i++) {
//			dp[i][i]=0;
//		}
		for(int l=n-1;l>=0;l--) {
			for(int r=l;r<n;r++) {
				if(l==r) {
					dp[l][r]=0;
				}else {
					dp[l][r] = Long.MAX_VALUE;
					for(int i=l;i<=r-1;i++) {
						dp[l][r] = Math.min(dp[l][r], dp[l][i]+dp[i+1][r]+ps[r]-((l==0)?0:ps[l-1]));
					}
				}
			}
		}
		out.write((dp[0][n-1]+"\n").getBytes());
		out.close();
	}
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
}