# Mark and Lightbulbs solution codeforces

## Mark and Lightbulbs solution codeforces

Mark has just purchased a rack of n lightbulbs. The state of the lightbulbs can be described with binary string =12s=s1s2…sn, where =si=1 means that the i-th lightbulb is turned on, while =si=0 means that the i-th lightbulb is turned off.

Unfortunately, the lightbulbs are broken, and the only operation he can perform to change the state of the lightbulbs is the following:

• Select an index i from 2,3,,12,3,…,n−1 such that 1+1si−1≠si+1.
• Toggle si. Namely, if si is 0, set si to 1 or vice versa.

Mark wants the state of the lightbulbs to be another binary string t. Help Mark determine the minimum number of operations to do so.

Input

The first line of the input contains a single integer q (11041≤q≤104) — the number of test cases.

The first line of each test case contains a single integer n (321053≤n≤2⋅105) — the number of lightbulbs.

The second line of each test case contains a binary string s of length n — the initial state of the lightbulbs.

The third line of each test case contains a binary string t of length n — the final state of the lightbulbs.

It is guaranteed that the sum of n across all test cases does not exceed 21052⋅105.

Output

For each test case, print a line containing the minimum number of operations Mark needs to perform to transform s to t. If there is no such sequence of operations, print 1−1.

Example
input

Copy
4
4
0100
0010
4
1010
0100
5
01001
00011
6
000101
010011

output

Copy
2
-1
-1
5

Note

In the first test case, one sequence of operations that achieves the minimum number of operations is the following.

• Select =3i=3, changing 0100 to 0110.
• Select =2i=2, changing 0110 to 0010.

In the second test case, there is no sequence of operations because one cannot change the first digit or the last digit of s.In the third test case, even though the first digits of s and t are the same and the last digits of s and t are the same, it can be shown that there is no sequence of operations that satisfies the condition.

In the fourth test case, one sequence that achieves the minimum number of operations is the following:

• Select =3i=3, changing 000101 to 001101.
• Select =2i=2, changing 001101 to 011101.
• Select =4i=4, changing 011101 to 011001.
• Select =5i=5, changing 011001 to 011011.
• Select =3i=3, changing 011011 to 010011.