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 Ruby (2.3.3) (judge verdict: Wrong Answer)

a = gets.chomp
b = gets.chomp
c = gets.chomp

def overlap(a, b, index)
	s = a.clone
	eindex = [s.size - 1, index + b.size - 1].min
	i = index
	while i <= eindex
		if s[i] != "?" && b[i - index] != "?" && s[i] != b[i - index]
			return
		end
		if s[i] == "?"
			s[i] = b[i - index]
		end
		i += 1
	end
	s << b[i - index, b.size]
	return s
end

def f(a, b)
	a.size.times{|i|
		o = overlap(a, b, i)
		if o
			return o
		end
	}
	a + b
end

min = a.size + b.size + c.size
s = f(a, f(b, c))
if s.size < min
	min = s.size
end
s = f(a, f(c, b))
if s.size < min
	min = s.size
end
s = f(b, f(a, c))
if s.size < min
	min = s.size
end
s = f(b, f(c, a))
if s.size < min
	min = s.size
end
s = f(c, f(a, b))
if s.size < min
	min = s.size
end
s = f(c, f(b, a))
if s.size < min
	min = s.size
end

puts min