Donald loves nature. Being a programmer, Donald writes programs to simulate the growth of trees or to build realistic 3D landscapes. For this purpose, Donald needs a good pseudo-random number generator. He devises the following method to produce an infinite sequence of 40-bit unsigned integers (the lines in green are comments).
On the last line, x >> 20 denotes the quotient of the Euclidean division of x by 2^20
and x % m denotes the remainder of the Euclidean division of x by m.
As a very first test to decide if this is indeed a good pseudo-random number generator, Donald wishes to count the number of even values produced by this sequence, in order to check whether this is close enough to 50%. Your help will be welcome.
One integer n (0 ≤ n < 2^63
).
The output should contain a single line with a single integer corresponding to the number of even values in the sequence S(0), S(1), ..., S(n - 1).