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# [Solution] Complementary XOR Codeforces Solution

C. Complementary XOR
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 or $r, 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.

Input

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1\le t\le {10}^{5}$) — 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 $2\cdot {10}^{5}$.

Output

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.

Note

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.