Why does my code not match the output?

#include

#include

#include

using namespace std;

$//$ Converts a single digit to its Roman numeral representation

string roman$\_$digit$($int digit, string one, string five, string ten$)\{$

if $($digit $==1)$ return one;

if $($digit $==2)$ return one $+$ one;

if $($digit $==3)$ return one $+$ one $+$ one;

if $($digit $==4)$ return one $+$ five;

if $($digit $==5)$ return five;

if $($digit $==6)$ return five $+$ one;

if $($digit $==7)$ return five $+$ one $+$ one;

if $($digit $==8)$ return five $+$ one $+$ one $+$ one;

if $($digit $==9)$ return one $+$ ten;

return $""$;

$\}$

$//$ Converts an integer to its Roman numeral representation

string roman$\_$numeral$($int n$)\{$

string result $=""$;

$//$ Process the thousands place

result $+=$ roman$\_$digit$($n $/1000,"$M$","","")$;

n $\%=1000$;

$//$ Process the hundreds place

result $+=$ roman$\_$digit$($n $/100,"$C$","$D$","$M$")$;

n $\%=100$;

$//$ Process the tens place

result $+=$ roman$\_$digit$($n $/10,"$X$","$L$","$C$")$;

n $\%=10$;

$//$ Process the ones place

result $+=$ roman$\_$digit$($n$,$ "I", $"$V$","$X$")$;

return result;

$\}$

int main$()\{$

$//$ Constants defining the range and start year of the Super Bowl

const int START$\_$SUPERBOWL $=1967$;

const int MIN$\_$ROMAN $=1$;

const int MAX$\_$ROMAN $=3999$;

const int MAX$\_$YEAR $=$ START$\_$SUPERBOWL $+$ MAX$\_$ROMAN $-1$;

$//$ Display the welcome message

cout endl;

cout The Super Bowl is the annual final playoff game $*"$ endl;

cout of the NFL to determine the league champion. $*"$ endl;

cout The first Super Bowl took place on January $15,1967.*"$ endl;

cout Super Bowl I $($Los Angeles Memorial Coliseum$)--->1967*"$ endl;

cout This Roman Numerals Convertor is written by Yi Pike. $*"$ endl;

cout If you had a time machine, which year of Super Bowl $*"$ endl;

cout would you want to attend $(1967-5965)?*"$ endl;

cout endl;

string input;

while $($true$)\{$

cout $$ "Please enter the year you want to attend $($click Q or q to quit$)$: $"$;

cin $>>$ input;

$//$ Check if user wants to quit

if $($input $=="$Q$"||$ input $=="$q$")\{$

cout $$ "Back to $2023,$ and have a great day!" $$ endl;

break;

$\}$

int year;

try $\{$

$//$ Convert input to integer

year $=$ stoi$($input$)$;

$\}$

catch $(...)\{$

$//$ Handle non$-$numeric input

cout $$ "Please use a four$-$digit number to represent a year $(1967-5965)!"$ endl;

cin.clear$()$; $//$ Clear the error flag on cin

cin.ignore$($numeric$\_$limits::max$(),\text{'}$

$\text{'})$; $//$ Ignore the rest of the invalid input

continue;

$\}$

$//$ Check if the year is within the valid range

if $($year $$ START$\_$SUPERBOWL$)\{$

cout $$ "The time machine will bring you to the year of $"$ year : Wait!!! The year you entered is TOO EARLY for the first Super Bowl!" $$ endl;

$\}$

else if $($year $>$ MAX$\_$YEAR$)\{$

cout $$ "The time machine will bring you to the year of $"$ year : Hold on$!!!$ The year you entered is TOO BIG for Roman numerals!" $$ endl;

$\}$

else $\{$

$//$ Calculate the Super Bowl number and display the result

int super$\_$bowl$\_$number $=$ year $-$ START$\_$SUPERBOWL $+1$;

cout $$ "The time machine will bring you to the year of $"$ year : It is Super Bowl $"$ roman$\_$numeral$($super$\_$bowl$\_$number$)$ endl;

$\}$

cout We will help you find out the result and other interesting information...next time:$)"$ endl;

$\}$

return $0$;

$\}$