Solomon Golomb’s self–describing sequence ⟨f(1),f(2),f(3),...⟩ is the only nondecreasing sequence of positive integers with the property that it contains exactly f(k) occurrences of k for each k. A few moments thought reveals that the sequence must begin as follows: n 1 2 3 4 5 6 7 8 9 10 11 12 f(n) 1 2 2 3 3 4 4 4 5 5 5 6 In this problem you are expected to write a program that calculates the value of f(n) given the value of n. Input The input may contain multiple test cases. Each test case occupies a separate line and contains an integer n (1 ≤ n ≤ 2, 000, 000, 000). The input terminates with a test case containing a value 0 for n and this case must not be processed. Output For each test case in the input output the value of f(n) on a separate line. Sample Input 100 9999 123456 1000000000 0 Sample Output 21 356 1684 438744