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 $f(l,r) = x$.

Input

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 $2 \cdot 10^5$.

Output

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.

Note

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.