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: Runtime Error)

from itertools import permutations

ABC = [input().rstrip(), input().rstrip(), input().rstrip()]

cache = [-1] * (3 * 3)


def canMatchShifted(index1, index2, shift):
    # Whether ABC[index1] can match with ABC[index2] shifted to the right by `shift`
    k = 3 * index1 + index2
    if cache[k] == -1:
        S1 = ABC[index1]
        S2 = ABC[index2]
        temp = [True] * (4001)
        for s in range(len(S1)):
            temp[s] = all(x == y or x == "?" or y == "?" for x, y in zip(S1[s:], S2))
        cache[k] = temp

    return cache[k][shift]


# Try all permutation orders of ABC
best = float("inf")
for a, b, c in permutations(range(3)):
    A = ABC[a]
    B = ABC[b]
    C = ABC[c]
    # Match A with `('?' * i) + B`
    for i in range(len(A) + 2):
        if not canMatchShifted(a, b, i):
            continue
        # Match B with `('?' * j) + C`
        # Match A with `('?' * (i + j)) + C`
        for j in range(len(B) + 2):
            if canMatchShifted(b, c, j) and canMatchShifted(a, c, i + j):
                l = max(len(A), i + len(B), i + j + len(C))
                best = min(best, l)
print(best)