Description:
The sequence of $$$m$$$ integers is called the permutation if it contains all integers from $$$1$$$ to $$$m$$$ exactly once. The number $$$m$$$ is called the length of the permutation.
Dreamoon has two permutations $$$p_1$$$ and $$$p_2$$$ of non-zero lengths $$$l_1$$$ and $$$l_2$$$.
Now Dreamoon concatenates these two permutations into another sequence $$$a$$$ of length $$$l_1 + l_2$$$. First $$$l_1$$$ elements of $$$a$$$ is the permutation $$$p_1$$$ and next $$$l_2$$$ elements of $$$a$$$ is the permutation $$$p_2$$$.
You are given the sequence $$$a$$$, and you need to find two permutations $$$p_1$$$ and $$$p_2$$$. If there are several possible ways to restore them, you should find all of them. (Note that it is also possible that there will be no ways.)
Input Format:
The first line contains an integer $$$t$$$ ($$$1 \le t \le 10\,000$$$) denoting the number of test cases in the input.
Each test case contains two lines. The first line contains one integer $$$n$$$ ($$$2 \leq n \leq 200\,000$$$): the length of $$$a$$$. The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq n-1$$$).
The total sum of $$$n$$$ is less than $$$200\,000$$$.
Output Format:
For each test case, the first line of output should contain one integer $$$k$$$: the number of ways to divide $$$a$$$ into permutations $$$p_1$$$ and $$$p_2$$$.
Each of the next $$$k$$$ lines should contain two integers $$$l_1$$$ and $$$l_2$$$ ($$$1 \leq l_1, l_2 \leq n, l_1 + l_2 = n$$$), denoting, that it is possible to divide $$$a$$$ into two permutations of length $$$l_1$$$ and $$$l_2$$$ ($$$p_1$$$ is the first $$$l_1$$$ elements of $$$a$$$, and $$$p_2$$$ is the last $$$l_2$$$ elements of $$$a$$$). You can print solutions in any order.
Note:
In the first example, two possible ways to divide $$$a$$$ into permutations are $$$\{1\} + \{4, 3, 2, 1\}$$$ and $$$\{1,4,3,2\} + \{1\}$$$.
In the second example, the only way to divide $$$a$$$ into permutations is $$$\{2,4,1,3\} + \{2,1\}$$$.
In the third example, there are no possible ways.