Dreamoon Likes Permutations

2000ms

262144K

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:

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:

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.

Sample Input:

6
5
1 4 3 2 1
6
2 4 1 3 2 1
4
2 1 1 3
4
1 3 3 1
12
2 1 3 4 5 6 7 8 9 1 10 2
3
1 1 1

Sample Output:

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.

Informação

Provedor Codeforces

Código CF1330B