**Question -You are given a primitive calculator that can perform the following three operations with the current number 𝑥: multiply 𝑥 by 2, multiply 𝑥 by 3, or add 1 to 𝑥. Your goal is given apositive integer 𝑛, find the minimum number of operations needed to obtain the number 𝑛
starting from the number 1.**

```
ll n;
cin>>n;
vector<ll>vec;
vec.pb(n);
if(n==1)
{
cout<<0<<endl<<1;
}
else
{
while(n!=1)
{
if(n%3==0)
n=n/3;
else if(n%2==0)
n=n/2;
else
n=n-1;
vec.pb(n);
}
cout<<vec.size()-1<<endl;
for(int i=(vec.size()-1);i>=0;i--)
cout<<vec(i)<<" ";
}
return 0;
```

}

for input 96234 iam getting

15

1 2 4 5 10 11 22 66 198 594 1782 5346 16038 16039 32078 96234

but the optimal soln is

14

1 3 9 10 11 22 66 198 594 1782 5346 16038 16039 32078 96234

i know i am going wrong at the step when 10 is converted into 5 in my code but it should convert it in to 9, Please help me,