Hello, I am having a problem with my c$++$ assignment and wondering what I can do to fix it

Instructions are:

Write a version of the binary search algorithm that can be used to search a list of strings. $($Use the selection sort that you designed in Exercise $8$ to sort the list.$)$ Write a program to test the function and prompt the user to enter $10$ strings. The program should output the position of the string if found in the list and the following message if not:

x is not in the list

What I got so far:

#include

#include

#include

$//$ Binary search function for integers

int binarySearch$($const std::vector& arr, int key$)\{$

int left $=0$;

int right $=$ arr.size$()-1$;

while $($left $<=$ right$)\{$

int mid $=$ left $+($right $-$ left$)/2$;

if $($arr$[$mid$]==$ key$)\{$

return mid; $//$ Key found, return its position

$\}$

if $($arr$[$mid$]<$ key$)\{$

left $=$ mid $+1$;

$\}$ else $\{$

right $=$ mid $-1$;

$\}$

$\}$

return $-1$; $//$ Key not found

$\}$

int main$()\{$

std::vector intList;

int key;

$//$ Input $10$ integers from the user

for $($int i $=0$; i $<10$; i$++)\{$

std::cout $<<$ "Enter integer $"<<($i $+1)<<"$: $"$;

std::cin $>>$ key;

intList.push$\_$back$($key$)$;

$\}$

$//$ Sort the list of integers

std::sort$($intList$.$begin$(),$ intList.end$())$;

$//$ Prompt the user to enter an integer to search for

std::cout $<<$ "Enter an integer to search for: $"$;

std::cin $>>$ key;

$//$ Perform binary search

int result $=$ binarySearch$($intList$,$ key$)$;

if $($result $!=-1)\{$

std::cout $<<$ key $<<"$ is found at position $"<<$ result $<<$ std::endl;

$\}$ else $\{$

std::cout $<<$ key $<<"$ is not in the list." $<<$ std::endl;

$\}$

return $0$;

$\}$

My output$($the problem$)$

Enter integer $1$: $2$

Enter integer $2$: $4$

Enter integer $3$: $5$

Enter integer $4$: $6$

Enter integer $5$: $23$

Enter integer $6$: $24$

Enter integer $7$: $28$

Enter integer $8$: $64$

Enter integer $9$: $3$

Enter integer $10$: $10$

Enter an integer to search for: $10$

$10$ is found at position $5$

My problem is that $10$ should be on position $10$ but says its position $5.$ Its late at night so I am tired atm. Please make sure yours is runnable. ty