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 Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {n:usize,
    a:[i64;n],}

    let mut ds = vec![0; n + 1];
    let mut dp = vec![vec![-INF; n + 1]; n + 1];
    for i in 0..n {
        ds[i + 1] = ds[i] + a[i];
    }
    let mut g = G {
        n: n,
        a: a,
        ds: ds,
        dp: dp,
    };
    println!("{}", g.f(1, n));
}
struct G {
    n: usize,
    a: Vec<i64>,
    ds: Vec<i64>,
    dp: Vec<Vec<i64>>,
}

impl G {
    fn f(&mut self, l: usize, r: usize) -> i64 {
        if self.dp[l][r] != -INF {
            return self.dp[l][r];
        }
        if l == r {
            self.dp[l][r] = 0;
            return 0;
        }
        // dbg!(l, r);
        let mut ret = INF;
        for m in l..r {
            ret = min(ret, self.f(l, m) + self.f(m + 1, r));
        }
        self.dp[l][r] = ret + self.ds[r] - self.ds[l - 1];
        return self.dp[l][r];
    }
}

const INF: i64 = 1 << 60;