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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import itertools
word = []
for _ in range(3):
    word.append(input())


def Z(S):
    A = [0]*len(S)
    i = 1
    j = 0
    A[0] = len(S)
    while i < len(S):
        while i+j < len(S) and (S[j] == S[i+j] or S[i+j] == '?'):
            j += 1
        A[i] = j
        if not j:
            i += 1
            continue
        k = 1
        while len(S)-i > k < j - A[k]:
            A[i+k] = A[k]
            k += 1
        i += k
        j -= k
    return A


ans = 10000

for w in itertools.permutations(word, 3):
    f = Z(w[0] + '0' + w[1])
    s = Z(w[1] + '0' + w[2])

    dup = 0
    for i in range(len(w[1])):
        if f[len(w[0])+1+i] == len(w[1]) - i:
            dup += len(w[1]) - i

    for i in range(len(w[2])):
        if s[len(w[1])+1+i] == len(w[2]) - i:
            dup += len(w[2]) - i

    ans = min(ans, len(w[2]) + len(w[1]) + len(w[1]) - dup)

print(ans)