Problem C: Self­describing Sequence 

Solomon Golomb's self­describing sequence $\langle f(1), f(2), f(3), \dots \rangle$ 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:


\begin{displaymath}\begin{array}{c\vert cccccccccccc}
\mbox{\boldmath $n$} & 1 &...
...)$} & 1 & 2 & 2 & 3 & 3 & 4 & 4 & 4 & 5 & 5 & 5 & 6
\end{array}\end{displaymath}

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 ( $1 \le n \le 2,000,000,000$). 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



Miguel Revilla
2000-12-26