Binary Subsequence Rotation

2000ms

262144K

Description:

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 $$$s = 1\textbf{1}101\textbf{00}$$$, 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.

Input:

The 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 $$$n$$$.

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.

Sample Input:

6
010000
000001

Sample Output:

Sample Input:

10
1111100000
0000011111

Sample Output:

Sample Input:

8
10101010
01010101

Sample Output:

Sample Input:

10
1111100000
1111100001

Sample 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 $$$t$$$.

Informação

Provedor Codeforces

Código CF1370E