An XOR operation on a list is defined here as the xor () of all its elements (e.g.: ).

The of set is defined here as the sum of the s of all non-empty subsets of known as . The set can be expressed as:

For example: Given set

• The set of possible non-empty subsets is:

• The of these non-empty subsets is then calculated as follows:
  =

Given a list of space-separated integers, determine and print .

For example, . There are three possible subsets, . The XOR of , of and of . The XorSum is the sum of these: and .

Note: The cardinality of powerset is , so the set of non-empty subsets of set of size contains subsets.

Function Description

Complete the xoringNinja function in the editor below. It should return an integer that represents the XorSum of the input array, modulo .

xoringNinja has the following parameter(s):

• arr: an integer array