Help me in solving ALBOFACE problem

help
,
1

My issue

i am getting correct ans for
if((n%2==0) && ((n>>1)%2 ==0)) CodeChef: Practical coding for everyone
if(n%4==0) CodeChef: Practical coding for everyone
but not for
if((n&1==0) && ((n>>1)&1 ==0)) CodeChef: Practical coding for everyone
why as they are simply same condition

My code

#include <iostream>
#include<bits/stdc++.h>
#define ll long long int
#define mod 1000000007
using namespace std;
int main() {
    cin.tie(0)->sync_with_stdio(false);
	int t;cin>>t;
	while(t--){
	    ll n;cin>>n;
	    int cnt=0;
	    if(n==1){
	        cout<<"Alice\n";
	    }
	    if(n==2){
	        cout<<"Bob\n";
	    }
	    if(n>2){
	        int cnt=0;
	        while(n){
	            if((n%2==0) && ((n>>1)%2 ==0)){
	                if(cnt%2)cout<<"Bob\n";
	                else cout<<"Alice\n";
	                break;
	            }
	            if(n==2){
	                if(cnt%2==0)cout<<"Bob\n";
	                else cout<<"Alice\n";
	                break;
	            }
	            if(n%2==1)n--;
	            else n>>=1;
	            cnt++;
	        }
	    }
	   
	}
	cerr << "Time : " << 1000 * ((double)clock()) / CLOCKS_PER_SEC << "ms" << endl;
	return 0;
}

Problem Link: Alice vs Bob Faceoff Practice Coding Problem