Problem:
Score : 500 points

Problem Statement

Snuke has a string s.
From this string, Anuke, Bnuke, and Cnuke obtained strings a, b, and c, respectively, as follows:

Choose a non-empty (contiguous) substring of s (possibly s itself). Then, replace some characters (possibly all or none) in it with ?s.

For example, if s is mississippi, we can choose the substring ssissip and replace its 1-st and 3-rd characters with ? to obtain ?s?ssip.

You are given the strings a, b, and c.
Find the minimum possible length of s.

Constraints

1 \leq |a|, |b|, |c| \leq 2000

a, b, and c consists of lowercase English letters and ?s.

Input

Input is given from Standard Input in the following format:

a
b
c

Output

Print the minimum possible length of s.

Sample Input 1

a?c
der
cod

Sample Output 1

7

For example, s could be atcoder.

Sample Input 2

atcoder
atcoder
???????

Sample Output 2

7

a, b, and c may not be distinct.

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::marker::Bytes;
fn main() {
    proconio::input! {
        a: Bytes,
        b: Bytes,
        c: Bytes,
    }
    let an=a.len();
    let bn=b.len();
    let cn=c.len();
    let k=an.max(bn).max(cn)*2;
    let m=k*2+1;
    let f=|c1: u8, c2: u8| c1!=c2 && c1!=b'?' && c2!=b'?';
    let g=|a: &Vec<u8>, b: &Vec<u8>| {
        let mut ab=vec![true;m*2+1];
        for (i,&a) in a.iter().enumerate() {
            for (j,&b) in b.iter().enumerate() {
                if f(a,b) {
                    ab[m+i-j]=false;
                }
            }
        }
        ab
    };
    let ab=g(&a,&b);
    let ac=g(&a,&c);
    let bc=g(&b,&c);
    let mut t=k*3;
    for (i,&ab) in ab[m-k..=m+k].iter().enumerate() {
        for (j,&ac) in ac[m-k..=m+k].iter().enumerate() {
            if ab && ac && bc[m+j-i] {
                let l=i.min(j).min(k);
                let r=an.max((bn+i).max(cn+j).max(k)-k);
                t=t.min(r+k-l);
            }
    }}
    println!("{}",t);
}