Minimum Insertions SOLUTIONS MININS

Minimum Insertions SOLUTIONS MININS

You are given a succession of whole numbers $A_1, A_2, ldots, A_N$. This grouping is round ― for each legitimate $i$, the component $A_{i+1}$ trails $A_i$, and the component $A_1$ trails $A_N$. 
 
You may embed any sure whole numbers at any positions you pick in this grouping; how about we mean the subsequent succession by $B$. This grouping is likewise round. For each pair of its components $B_s$ and $B_f$, we should mean the (non-roundabout) arrangement made by beginning at $B_s$ and moving from every component to the one that trails it, until we reach $B_f$, by $B(s, f)$. This arrangement incorporates the components $B_s$ and $B_f$. 
 
For each $K$ from $2$ to $N$ comprehensive, locate the littlest conceivable number of components that should be embedded into $A$ to frame an arrangement $B$ for which there is no aftereffect $B(p, q)$ with the end goal that: 
 
The size of $B(p, q)$ is at any rate $K$. 
 
There is no pair of back to back components in $B(p, q)$ with the end goal that their GCD is equivalent to $1$. 
 
Info 
 
The main line of the information contains a solitary number $T$ indicating the quantity of experiments. The depiction of $T$ experiments follows. 
 
The primary line of each experiment contains a solitary whole number $N$. 
 
The subsequent line contains $N$ space-isolated whole numbers $A_1, A_2, ldots, A_N$. 
 
Yield 
 
For each experiment, print a solitary line containing $N-1$ space-isolated whole numbers. For each $i$ ($1 le I le N-1$), the $i$-th of these whole numbers ought to be the most modest number of embedded components in a substantial arrangement $B$ for $K = i+1$. 
 
Limitations 
 
$1 le T le 2,000$ 
 
$2 le N le 10^5$ 
 
$1 le A_i le 10^9$ for each legitimate $i$ 
 
the total of $N$ over all experiments doesn’t surpass $2 cdot 10^6$ 
 
Model Input 
 
 
 
3 6 4 5 9 
 
Model Output 
 
3 1 0

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