Lata has been tasked with a problem by her teacher, if she can solve it, she will pass the teacher's course.

The problem goes as follows: The teacher will randomly pick a set S of x distinct integers from 0 to $2^N -1$ where N=1234567891.

In order to pass the class, Lata has to pick a subset of elements from set S known as set Y, such that the number found by taking the xor of all the elements in the set Y is present in the set S-Y. Note that Y can be an empty set and xor of elements in an empty set is 0.

The teacher is lenient so he will give Lata the chance to choose x i.e. the size of set S.

Lata must pass the class or her parents will be disappointed in her, she asks for your help to find the minimum x that will ensure that she will pass the class regardless of the set S chosen by the teacher.