URI Online Judge | 2159

Approximate Number of Primes

By M.C. Pinto, UNILA BR Brazil

Timelimit: 1

Schoenfeld and Rosser published a paper in 1962 describing a minimum and a maximum value to the quantity of prime numbers up to n, for n ≥ 17. This quantity is represented by the function (n) and the inequality is shown below.

Your task is, given a natural number n, to compute the interval's minimum and maximum values to the approximate number of primes up to n.


The input is a natural number n (17 ≤ n ≤ 109).


The output is given as two values P and M with 1 decimal place each, such that P < (n) < M according to the given inequality above. These two values have one blank space between them.

Input Samples Output Samples


6.0 7.5


12.8 16.0


21.7 27.3