CF1750C.Complementary XOR

You have two binary strings $a$ and $b$ of length $n$ . You would like to make all the elements of both strings equal to $0$ . Unfortunately, you can modify the contents of these strings using only the following operation:

• You choose two indices $l$ and $r$ ( $1 \le l \le r \le n$ );
• For every $i$ that respects $l \le i \le r$ , change $a_i$ to the opposite. That is, $a_i := 1 - a_i$ ;
• For every $i$ that respects either $1 \le i < l$ or $r < i \le n$ , change $b_i$ to the opposite. That is, $b_i := 1 - b_i$ .

Your task is to determine if this is possible, and if it is, to find such an appropriate chain of operations. The number of operations should not exceed $n + 5$ . It can be proven that if such chain of operations exists, one exists with at most $n + 5$ operations.

Each test consists of multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 10^5$ ) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) — the length of the strings.

The second line of each test case contains a binary string $a$ , consisting only of characters 0 and 1, of length $n$ .

The third line of each test case contains a binary string $b$ , consisting only of characters 0 and 1, of length $n$ .

It is guaranteed that sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$ .

For each testcase, print first "YES" if it's possible to make all the elements of both strings equal to $0$ . Otherwise, print "NO". If the answer is "YES", on the next line print a single integer $k$ ( $0 \le k \le n + 5$ ) — the number of operations. Then $k$ lines follows, each contains two integers $l$ and $r$ ( $1 \le l \le r \le n$ ) — the description of the operation.

If there are several correct answers, print any of them.

In the first test case, we can perform one operation with $l = 2$ and $r = 2$ . So $a_2 := 1 - 1 = 0$ and string $a$ became equal to 000. $b_1 := 1 - 1 = 0$ , $b_3 := 1 - 1 = 0$ and string $b$ became equal to 000.

In the second and in the third test cases, it can be proven that it's impossible to make all elements of both strings equal to $0$ .

In the fourth test case, we can perform an operation with $l = 1$ and $r = 2$ , then string $a$ became equal to 01, and string $b$ doesn't change. Then we perform an operation with $l = 2$ and $r = 2$ , then $a_2 := 1 - 1 = 0$ and $b_1 = 1 - 1 = 0$ . So both of string $a$ and $b$ became equal to 00.

In the fifth test case, we can perform an operation with $l = 1$ and $r = 1$ . Then string $a$ became equal to 011 and string $b$ became equal to 100. Then we can perform an operation with $l = 2$ and $r = 3$ , so both of string $a$ and $b$ became equal to 000.