#D4850. Binary Subsequence Rotation
Binary Subsequence Rotation
Binary Subsequence Rotation
Naman 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 = 1110100, he can choose a subsequence corresponding to indices (1-based) {2, 6, 7 } and rotate them clockwise. The resulting string would then be s = 1010110.
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, …, 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.
Input
The first line contains a single integer n (1 ≤ n ≤ 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.
Output
If it is impossible to convert s to t after any number of operations, print -1.
Otherwise, print the minimum number of operations required.
Examples
Input
6 010000 000001
Output
1
Input
10 1111100000 0000011111
Output
5
Input
8 10101010 01010101
Output
1
Input
10 1111100000 1111100001
Output
-1
Note
In 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.
inputFormat
Input
The first line contains a single integer n (1 ≤ n ≤ 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.
outputFormat
Output
If it is impossible to convert s to t after any number of operations, print -1.
Otherwise, print the minimum number of operations required.
Examples
Input
6 010000 000001
Output
1
Input
10 1111100000 0000011111
Output
5
Input
8 10101010 01010101
Output
1
Input
10 1111100000 1111100001
Output
-1
Note
In 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.
样例
10
1111100000
1111100001
-1