In python, Implement an algorithm to explore and analyze the Collatz $3$n $+1$ Conjecture, a mathematical hypothesis that has not been proven or disproven.

The conjecture applies the following rules to any positive integer:

If the number is even, divide it by $2.$

If the number is odd, multiply it by $3$ and add $1.$

Repeat the process with the new value until the new value becomes $1.$

The conjecture states that no matter what value you start with, you will always eventually reach $1.$

$3.$ Assignment Details:

Implement the Collatz Sequence Generator:

Analyze Sequence Lengths: For each number in the range $1$ to $10,000,000,$ calculate the length of its Collatz sequence then store the lengths in a suitable data structure. It may take $3-8$ minutes in a normal computing environment.

Identify Top $10$ Sequences: Display the top $10$ starting numbers whose Collatz sequences are the longest within the given range.

Reflection and Theory: Watch the video referenced above and write a brief reflection on why the Collatz Conjecture is hard for both humans and computers to prove.

Expected Output:

For $[1..1,000,000],837799$ has the highest data elements in the sequence. It has $525$ elements and its largest element is $2974984576.$ The list below shows the top $3$ numbers $[833799,626331,939497,...]$

$1.$ Collatz sequence for $837799$ : $5252974984576$

$2.$ Collatz sequence for $626331$ : $5097222283188$

$3.$ Collatz sequence for $939497$ : $5077222283188$ in