Confusion in problem Codeforces Round #443 (Div. 1) problem

Problem
In this problem is it necessary to apply all given operations type? because we can simply find the result of given input and output the XOR of (result,n) .
For example:
3
| 3
^ 2
| 1
result of operations is 1 ,so to get 1 we can have 3^2, so output :
1
^ 2
am I missing something?

1 Like

3 is no of line not the first no.
Resultant operations should be such that they give correct output for all values.

e.g. - Explanation given in question -
((x&1)&3)&5 = x&(1&3&5) = x&1.
And this statement in true for all x.

And your e.g. -
(((x|3)^2)|1) = ((x|3)^2) != (x^2)

e.g. x = 1. Output after all operations (((1|3)^2)|1) but your output 1^2=3