How Many Different XORs

Choose any subset of the list nums and combine its numbers with XOR (^); the empty subset gives 0. Many different subsets give the same result. Write xor_values(nums) that returns a tuple (count, largest): how many different values these XORs can take, and the largest of them.

Examples

xor_values([1, 2, 3])     # returns (4, 3)
xor_values([6, 10, 12])   # returns (4, 12)
xor_values([5, 5])        # returns (2, 5)
xor_values([])            # returns (1, 0)

In the first example the eight subsets give 0, 1, 2, 3, 1 ^ 2 = 3, 1 ^ 3 = 2, 2 ^ 3 = 1 and 1 ^ 2 ^ 3 = 0: only four different values. In the second, 6 ^ 10 is already 12, so 12 adds nothing new.

Constraints

• 0 <= len(nums) <= 20,000
• 0 <= nums[i] < 2**60
• The count can be as large as 2^60, so the values cannot be listed one by one.