You are given an array $$$a_1, a_2, \\ldots, a_n$$$ of positive integers.
Let $$$f(l,r)$$$ for $$$1 \\leq l \\leq r \\leq n$$$ be the smallest positive integer that doesn't divide $$$\\operatorname{lcm}(a_l, a_{l+1}, \\ldots, a_r)$$$. Here, $$$\\operatorname{lcm}$$$ of an array of integers denotes the least common multiple (LCM) of these integers.
Determine every positive integer $$$x$$$ such that there exists a pair of integers $$$(l,r)$$$ such that $$$1 \\leq l \\leq r \\leq n$$$ and $$$f(l,r) = x$$$.
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \\le t \\le 10^4$$$). The description of the test cases follows.
The first line of each test case contains $$$n$$$ ($$$1 \\le n \\le 2 \\cdot 10^5$$$), denoting the size of the array.
The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$1 \\le a_i \\le n$$$).
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \\cdot 10^5$$$.
For each test case, output two lines.
The first line should contain a single integer $$$k$$$ — the number of suitable integers $$$x$$$.
The second line should contain $$$k$$$ integers $$$x_1 \\lt x_2 \\lt \\ldots \\lt x_k$$$, the suitable integers in increasing order.
31132 3 154 3 1 3 4
1232 3 432 3 5
In the first test case, the only $$$(l,r)$$$ pair is $$$(1,1)$$$, and $$$f(1,1) = 2$$$.
In the second test case, $$$(l,r)=(1,1)$$$ yields the set of divisors $$$\\{ 1,2 \\}$$$, $$$(l,r)=(1,2)$$$ yields the set of divisors $$$\\{ 1, 2, 3, 6\\}$$$, and $$$(l,r)=(2,2)$$$ yields the set of divisors $$$\\{ 1, 3 \\}$$$. This means $$$f(1,1)=3$$$, $$$f(1,2)=4$$$, and $$$f(2,2)=2$$$. Since no other $$$(l,r)$$$ pair produces a different $$$f$$$ value, the answer is $$$[2,3,4]$$$.
For the last test case, $$$f(2,2)=2$$$, $$$f(1,1)=3$$$, and $$$f(1,5)=5$$$. It can be seen that no other values can be obtained.