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)

fn main() {
    proconio::input! {
        n: usize,
        a: [u64; n],
    }

    println!("{}", DP::new(n, a).calc(0, n - 1));
}

struct DP {
    dp: Vec<Vec<Option<u64>>>,
    cum: Vec<u64>,
}

impl DP {
    fn new(n: usize, a: Vec<u64>) -> DP {
        let mut cum = vec![0; n + 1];
        for i in 1..=n {
            cum[i] = cum[i - 1] + a[i - 1];
        }
        DP {
            dp: vec![vec![None; n]; n],
            cum: cum,
        }
    }

    fn calc(&mut self, l: usize, r: usize) -> u64 {
        if let Some(v) = self.dp[l][r] {
            v
        } else {
            let v = if l == r {
                0
            } else {
                let mut v = std::u64::MAX;
                for m in l..r {
                    v = std::cmp::min(v, self.calc(l, m) + self.calc(m + 1, r))
                }
                v + self.cum[r + 1] - self.cum[l]
            };
            self.dp[l][r] = Some(v);
            v
        }
    }
}