Three Substrings

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.

Examples

Input

a?c der cod

Output

7

Input

atcoder atcoder ???????

Output

7

inputFormat

Input

Input is given from Standard Input in the following format:

a b c

outputFormat

Output

Print the minimum possible length of s.

Examples

Input

a?c der cod

Output

7

Input

atcoder atcoder ???????

Output

7

样例

a?c
der
cod

7