p02745 Panasonic Programming Contest 2020 - 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
```python
R=range
def F(a,b):A=len(a);r=[all([len(set([a[i+j],b[j],'?']))<3for j in R(min(A-i,len(b)))])for i in R(A)];return r+[1]
def Z(X):
 i,j,k=X;U,V,W=M[i][j],M[j][k],M[i][k];A,B,C=map(len,[S[i]for i in X]);q=A+B+C
 for l in R(A+1):
  if U[l]:
   for r in R(l,A+B+1):
    if(B<r-l or V[r-l])*W[min(A,r)]:q=min(q,max(A,l+B,r+C))
 return q
S=[input()for i in'abc']
T=R(3)
M=[[F(S[i],S[j])for j in T]for i in T]
from itertools import *;print(min([Z(i)for i in permutations(T)]))
```