Write the following code in MIPS:

There are several ways to find prime numbers. A standard one is to divide the number x by the numbers $2...$sqrt$($x$)$ and if it divides evenly by any of them, it is not prime. However, you are to write rather different algorithm, discovered by the ancient Greek polymath Eratosthenes of Cyrene. There are several variants on this algorithm, and you are to implement the following one. Note that each bit represents a number, such that the first bit is $0,$ the second bit is $1,$ etc.

$1.$ Request an integer from the user. If it is less than $3$ or greater than $160,000,$ show an error message and go back to $1.$

$2.$ Allocate ceiling$($n$/8)$ bytes of memory and fill it with all one bits. That is$,$ put hex FF in each byte, meaning that initially we assume all numbers are prime. If n is not an even multiple of $8,$ round up$.$ Use the SBRK $($SysAlloc in my SysCalls.asm file$)$ system call to allocate memory. Do not allocate it using the $.$space directive in your program.

$3.$ Starting with bit $2,$ representing the number $2,$ set each bit to zero that is a multiple of $2,$ but do not set bit $2$ to zero, since $2$ is prime. See example below. $($The bit may already be zero, but that doesn$$t matter.$)$

$4.$ Find the next non$-$zero bit in the array, compute its position as a number $($this will be $3)$ and set every third bit to zero. The $$array$$ is zero origin, so as shown, the first bit is numbered zero, then $1,$ etc. Whether you consider the high bit or the low bit in the byte to be the $$zeroth$$ bit in that byte is up to you as long as you are consistent. I$$m showing it with the high bit as zero for convenience because that is also the byte order.

$5.$ The algorithm terminates when you have used bits up to n$/2.6.$ Go through the array and compute the bit position of every $1$ bit, and print the position. Those will be your primes. Print one prime number per line, or if you$$re ambitious, print $10$ per line separated by spaces.

$7.$ Stop

$($SAMPLE OUTPUT Example, where the user entered $16$:$)$

Bit position:

$04812$

Initial array: $1111111111111111$

First pass: $1111010101010101$ # This uses $2$

Second pass: $1111010100010100$ # This uses $3($what will the third pass use?$)$

Prints starting with bit $2$: $2,3,5,7,11,13$