
Score : 1500 points
Problem Statement
Shik's job is very boring. At day 0, his boss gives him a string S_0 of length N which consists of only lowercase English letters. In the i-th day after day 0, Shik's job is to copy the string S_{i-1} to a string S_i. We denote the j-th letter of S_i as S_i[j].
Shik is inexperienced in this job. In each day, when he is copying letters one by one from the first letter to the last letter, he would make mistakes. That is, he sometimes accidentally writes down the same letter that he wrote previously instead of the correct one. More specifically, S_i[j] is equal to either S_{i-1}[j] or S_{i}[j-1]. (Note that S_i[1] always equals to S_{i-1}[1].)
You are given the string S_0 and another string T.
Please determine the smallest integer i such that S_i could be equal to T. If no such i exists, please print -1.
Constraints
1 \leq N \leq 1,000,000
The lengths of S_0 and T are both N.
Both S_0 and T consist of lowercase English letters.
InputThe input is given from Standard Input in the following format:
N
S_0
T
OutputPrint the smallest integer i such that S_i could be equal to T. If no such i exists, print -1 instead.
Sample Input 15
abcde
aaacc
Sample Output 12
S_0 = abcde, S_1 = aaccc and S_2 = aaacc is a possible sequence such that S_2 = T.
Sample Input 25
abcde
abcde
Sample Output 20
Sample Input 34
acaa
aaca
Sample Output 32
Sample Input 45
abcde
bbbbb
Sample Output 4-1
