Menorah

Description:

Input:

The first line contains an integer $$$t$$$ ($$$1\le t\le 10^4$$$) — the number of test cases. Then $$$t$$$ cases follow.

The first line of each test case contains a single integer $$$n$$$ ($$$1\le n\le 10^5$$$) — the number of candles.

The second line contains a string $$$a$$$ of length $$$n$$$ consisting of symbols 0 and 1 — the initial pattern of lights.

The third line contains a string $$$b$$$ of length $$$n$$$ consisting of symbols 0 and 1 — the desired pattern of lights.

It is guaranteed that the sum of $$$n$$$ does not exceed $$$10^5$$$.

Output:

For each test case, output the minimum number of operations required to transform $$$a$$$ to $$$b$$$, or $$$-1$$$ if it's impossible.

Sample Input:

5
5
11010
11010
2
01
11
3
000
101
9
100010111
101101100
9
001011011
011010101

Sample Output:

0
1
-1
3
4

Note:

In the first test case, the two strings are already equal, so we don't have to perform any operations.

In the second test case, we can perform a single operation selecting the second candle to transform $$$01$$$ into $$$11$$$.

In the third test case, it's impossible to perform any operations because there are no lit candles to select.

In the fourth test case, we can perform the following operations to transform $$$a$$$ into $$$b$$$:

1. Select the $$$7$$$-th candle: $$$100010{\color{red}1}11\to 011101{\color{red} 1}00$$$.
2. Select the $$$2$$$-nd candle: $$$0{\color{red} 1}1101100\to 1{\color{red} 1}0010011$$$.
3. Select the $$$1$$$-st candle: $$${\color{red}1}10010011\to {\color{red}1}01101100$$$.

In the fifth test case, we can perform the following operations to transform $$$a$$$ into $$$b$$$:

1. Select the $$$6$$$-th candle: $$$00101{\color{red}1}011\to 11010{\color{red}1}100$$$
2. Select the $$$2$$$-nd candle: $$$1{\color{red}1}0101100\to 0{\color{red}1}1010011$$$
3. Select the $$$8$$$-th candle: $$$0110100{\color{red}1}1\to 1001011{\color{red}1}0$$$
4. Select the $$$7$$$-th candle: $$$100101{\color{red}1}10\to 011010{\color{red}1}01$$$