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Description

The Recaman's sequence is defined by a0 = 0 ; for m > 0, a

_m

= a

_m−1

− m if the rsulting a

_m

is positive and not already in the sequence, otherwise a

_m

= a

_m−1

+ m.

The first few numbers in the Recaman's Sequence is 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9 ... Given k, your task is to calculate a_k

.

Input

The input consists of several test cases. Each line of the input contains an integer k where 0 <= k <= 500000.

The last line contains an integer −1, which should not be processed.

Output

For each k given in the input, print one line containing a

_k

to the output.

7
10000
-1

20
18658

Source

Shanghai 2004 Preliminary