E. Binary Subsequence Rotationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputNaman has two binary strings s and t of length n (a binary string is a string which only consists of the characters "0" and "1"). He wants to convert s into t using the following operation as few times as possible.In one operation, he can choose any subsequence of s and rotate it clockwise once.For example, if s = 1\textbf{1}101\textbf{00}, he can choose a subsequence corresponding to indices (1-based) \{2, 6, 7 \} and rotate them clockwise. The resulting string would then be s = 1\textbf{0}101\textbf{10}.A string a is said to be a subsequence of string b if a can be obtained from b by deleting some characters without changing the ordering of the remaining characters.To perform a clockwise rotation on a sequence c of size k is to perform an operation which sets c_1:=c_k, c_2:=c_1, c_3:=c_2, \ldots, c_k:=c_{k-1} simultaneously.Determine the minimum number of operations Naman has to perform to convert s into t or say that it is impossible. InputThe first line contains a single integer n (1 \le n \le 10^6) — the length of the strings.The second line contains the binary string s of length n.The third line contains the binary string t of length n.OutputIf it is impossible to convert s to t after any number of operations, print -1.Otherwise, print the minimum number of operations required.ExamplesInput
6
010000
000001
Output
1Input
10
1111100000
0000011111
Output
5Input
8
10101010
01010101
Output
1Input
10
1111100000
1111100001
Output
-1NoteIn the first test, Naman can choose the subsequence corresponding to indices \{2, 6\} and rotate it once to convert s into t.In the second test, he can rotate the subsequence corresponding to all indices 5 times. It can be proved, that it is the minimum required number of operations.In the last test, it is impossible to convert s into t.
6
010000
000001

1
['binary search', 'constructive algorithms', 'data structures', 'greedy', '*2100']