Solomon Golomb's selfdescribing 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:
In this problem you are expected to write a program that calculates the value of f(n) given the value of n.
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.
For each test case in the input output the value of f(n) on a separate line.
100 9999 123456 1000000000 0
21 356 1684 438744
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