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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
import java.lang.*;
import java.io.*;
public class Main
{
    static FastScanner sc = new FastScanner(System.in);
    static PrintWriter out = new PrintWriter(System.out);
    static long arr[] = new long[401];
    static long pre[] = new long[401];
    static long dp[][]=new long[401][401];
    static long res=Long.MAX_VALUE;
    public static long ok(int l,int r) throws Exception{
        if(l==r) return 0;
        if(dp[l][r]!=-1) return dp[l][r];
        long min=Long.MAX_VALUE;
        for(int k=l;k<r;k++){
            long temp=ok(l,k)+ok(k+1,r)+pre[r];
            if(l>0){
                temp-=pre[l-1];
            }
            min=Math.min(min,temp);
        }

        return dp[l][r]=min;

    }
    public static void main(String args[]) throws Exception
    {
        
        int n=sc.nextInt();
        for(int i=0;i<n;i++) arr[i]=sc.nextLong();
        pre[0]=arr[0];
        for(int i=0;i<n;i++){
            Arrays.fill(dp[i],-1);
        }
        
        for(int i=1;i<n;i++) pre[i]=pre[i-1]+arr[i];
        out.println(ok(0,n-1));


        out.close();
    }


}
class FastScanner
{

    final private int BUFFER_SIZE = 1 << 17;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public FastScanner(InputStream in)
    {
        din = new DataInputStream(in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }
    public String nextLine() throws Exception
    {
        StringBuffer sb = new StringBuffer("");
        byte c = read();
        while (c <= ' ') c = read();
        do
        {
            sb.append((char)c);
            c = read();
        }
        while(c > ' ');
        return sb.toString();
    }

    public char nextChar() throws Exception
    {
        byte c = read();
        while(c <= ' ') c = read();
        return (char)c;
    }

    public int nextInt() throws Exception
    {
        int ret = 0;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = c == '-';
        if (neg) c = read();
        do
        {
            ret = ret * 10 + c - '0';
            c = read();
        }
        while (c > ' ');
        if (neg) return -ret;
        return ret;
    }

    public long nextLong() throws Exception
    {
        long ret = 0;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = c == '-';
        if (neg) c = read();
        do
        {
            ret = ret * 10 + c - '0';
            c = read();
        }
        while (c > ' ');
        if (neg) return -ret;
        return ret;
    }

    private void fillBuffer() throws Exception
    {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1) buffer[0] = -1;
    }

    private byte read() throws Exception
    {
        if (bufferPointer == bytesRead) fillBuffer();
        return buffer[bufferPointer++];
    }
    public double nextDouble() throws Exception
    {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do
        {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');

        if (c == '.')
        {
            while ((c = read()) >= '0' && c <= '9')
            {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }


}