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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <complex>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <numeric>
#include <cstring>
#include <ctime>
#include <cstdlib>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <cmath>
#include <bitset>
#include <cassert>
#include <queue>
#include <stack>
#include <deque>
#include <random>
#include <iomanip>
typedef long long int ll;
typedef long double ld;
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
const ll MOD=1000000007;
const ll MAX_N=500010;
const ll INF=9223372036854775807;
ll dp[410][410];
ll b[410][410];

int main(){
    int n;
    cin>>n;
    vector<ll> a(n);
    for(int i=0;i<n;i++) cin>>a[i];
    for(int i=0;i<n;i++){
        dp[i][i+1]=0; 
        b[i][i+1]=a[i];
    }
    for(int w=2;w<=n;w++){
        for(int i=0;i<=n-w;i++){
            b[i][i+w]=b[i][i+w-1]+a[i+w-1];
        }
    }
    for(int wide=2;wide<=n;wide++){
        for(int i=0;i<=n-wide;i++){
            int j=i+wide;
            dp[i][j]=INF;
            for(int k=i+1;k<=j-1;k++){
                dp[i][j]=min(dp[i][j],dp[i][k]+dp[k][j]+b[i][j]);
            }
            //cout<<"i="<<i<<" "<<"j="<<j<<" "<<dp[i][j]<<endl;
        }
    }
    cout<<dp[0][n]<<endl;
    return 0;
}