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: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main {
	
	public static void main(String[] args) throws IOException {
		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		
		int N = Integer.parseInt(br.readLine());
		
		st = new StringTokenizer(br.readLine());
		int[] psa = new int[N+1];
		psa[0] = 0;
		for(int i=1; i<=N; i++) {
			psa[i] = Integer.parseInt(st.nextToken()) + psa[i-1];
		}

		long[][] dp = new long[N][N];
		for(int i=N-1; i>=0; i--) {
			for(int j=i+1; j<N; j++) {
				dp[i][j] = Long.MAX_VALUE;
				for(int k=i; k<j; k++) {
					dp[i][j] = Math.min(dp[i][j], dp[i][k]+dp[k+1][j]);
				}
				dp[i][j] += psa[j+1]-psa[i];
			}
		}
		System.out.println(dp[0][N-1]);
	}
}