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 OCaml (4.02.3) (judge verdict: Accepted)

let eqs a b o =
  let a, b, o = if o < 0 then b, a, -o else a, b, o in
  let rec f i =
    if i+o >= String.length a || i >= String.length b then true
    else (a.[i+o] = '?' || b.[i] = '?' || a.[i+o] = b.[i]) && f (i+1)
  in f 0

let max3 a b = max (max a b)
let min3 a b = min (min a b)

let () =
  Scanf.scanf "%s %s %s" @@ fun a b c ->
  let la, lb, lc = String.(length a, length b, length c) in
  let ab = Array.init 4001 (fun i -> eqs a b (i-2000)) in
  let bc = Array.init 4001 (fun i -> eqs b c (i-2000)) in
  let ac = Array.init 4001 (fun i -> eqs a c (i-2000)) in

  let ans = ref 6000 in
  for i = -4000 to 4000 do
    if la - i < !ans && i < (!ans - lb) && (abs i > 2000 || ab.(i+2000)) then
      for j = -4000 to 4000 do
        if (la - j < !ans) && j < (!ans - lc) &&
           (abs j > 2000 || ac.(j+2000)) &&
           (abs (j-i) > 2000 || bc.(j-i+2000))
        then
          ans := min !ans (max3 la (i+lb) (j+lc) - min3 0 i j)
      done;
  done;
  Printf.printf "%d\n" !ans