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 $1 \le i \lt l$ or $r \lt i \le n$, 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.

你有两个长度为 $n$ 的二进制字符串 $a$ 和 $b$。你的目标是使这两个字符串的所有元素都变为 $0$。不幸的是，你只能使用以下操作来修改这两个字符串的内容：

• 选择两个下标 $l$ 和 $r$（满足 $1 \le l \le r \le n$）；
• 对每个满足 $l \le i \le r$ 的 $i$，将 $a_i$ 翻转（即 $a_i := 1 - a_i$）；
• 对每个满足 $1 \le i < l$ 或 $r < i \le n$ 的 $i$，将 $b_i$ 翻转（即 $b_i := 1 - b_i$）。

你的任务是判断该目标是否可达；若可达，则需找出一串满足要求的操作序列。操作次数不得超过 $n + 5$。可以证明：若存在可行的操作序列，则必存在一个操作次数不超过 $n + 5$ 的可行序列。

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 $2 \cdot 10^5$.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 10^5$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$2 \le n \le 2 \cdot 10^5$），表示字符串的长度。

每个测试用例的第二行包含一个长度为 $n$ 的二进制字符串 $a$，仅由字符 0 和 1 组成。

每个测试用例的第三行包含一个长度为 $n$ 的二进制字符串 $b$，仅由字符 0 和 1 组成。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$。

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.

对于每个测试用例，如果可以将两个字符串的所有元素都变为 $0$，则首先输出 "YES"；否则输出 "NO"。如果答案为 "YES"，则在下一行输出一个整数 $k$（$0 \le k \le n + 5$），表示操作次数；随后输出 $k$ 行，每行包含两个整数 $l$ 和 $r$（$1 \le l \le r \le n$），表示一次操作的区间。

若存在多个正确答案，输出任意一个即可。

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.

在第一个测试用例中，我们可以执行一次操作，其中 $l = 2$ 且 $r = 2$。于是 $a_2 := 1 - 1 = 0$，字符串 $a$ 变为 000；$b_1 := 1 - 1 = 0$，$b_3 := 1 - 1 = 0$，字符串 $b$ 也变为 000。

在第二个和第三个测试用例中，可以证明无法使两个字符串的所有元素均变为 $0$。

在第四个测试用例中，我们首先执行一次操作，其中 $l = 1$ 且 $r = 2$，此时字符串 $a$ 变为 01，而字符串 $b$ 保持不变；接着再执行一次操作，其中 $l = 2$ 且 $r = 2$，于是 $a_2 := 1 - 1 = 0$ 且 $b_1 := 1 - 1 = 0$。最终，字符串 $a$ 和 $b$ 均变为 00。

在第五个测试用例中，我们首先执行一次操作，其中 $l = 1$ 且 $r = 1$，此时字符串 $a$ 变为 011，字符串 $b$ 变为 100；然后执行一次操作，其中 $l = 2$ 且 $r = 3$，于是字符串 $a$ 和 $b$ 均变为 000。