# Minimum Insertions SOLUTIONS MININS

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### 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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