Solve the programming task below in a Python markdown code block.
Chef is given two binary strings A and B, each having length N.

Chef wants to find the number of binary strings C, of length N, such that H(A, C) = H(B, C), where H(X, Y) denotes the *hamming distance* between the strings X and Y.

Since the answer can be large, output it modulo 10^{9}+7.

Note: [Hamming distance] between two strings of equal length is the number of positions at which the corresponding characters are different.

------ Input Format ------ 

- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of multiple lines of input.
- The first line of each test case contains a single integer N, the length of the strings.
- The second line contains the binary string A.
- The third line contains the binary string B.

------ Output Format ------ 

For each test case, output in a new line, the number of binary strings C which satisfy the given conditions modulo 10^{9} + 7.

------ Constraints ------ 

$1 ≤ T ≤ 1000$
$1 ≤ N ≤ 2 \cdot 10^{5}$
$A$ and $B$ consist of $0$ and $1$ only.
- Sum of $N$ over all test cases do not exceed $2 \cdot 10^{5}$.

----- Sample Input 1 ------ 
3
2
11
00
5
10101
10101
3
101
011

----- Sample Output 1 ------ 
2
32
4

----- explanation 1 ------ 
Test case $1$: The number of strings $C$, of length $2$, such that $H(A, C) = H(B, C)$ is $2$. The strings are:
- $C = 10$: Here, $H(11, 10) = H(00, 10) = 1$, as there is only one position where the corresponding characters are different.
- $C = 01$: Here, $H(11, 01) = H(00, 01) = 1$.

Test case $3$: The number of strings $C$, of length $3$, such that $H(A, C) = H(B, C)$ is $4$. The strings are:
- $C = 000$: Here, $H(101, 000) = H(011, 000) = 2$, as there are two positions where the corresponding characters are different.
- $C = 111$: Here, $H(101, 111) = H(011, 111) = 1$, as there is only one position where the corresponding characters are different.
- $C = 001$: Here, $H(101, 001) = H(011, 001) = 1$, as there is only one position where the corresponding characters are different.
- $C = 110$: Here, $H(101, 110) = H(011, 110) = 2$, as there are two positions where the corresponding characters are different.