An evil professor has just assigned you the following problem.

A sequence is defined by the following recurrence:

Determine

.

Input consists of a number of lines, each containing one integer, a value of i, no less than zero and no greater than one million. Input is followed by a single line containing the integer -1. This last line is not a value of i and should not be processed.

For each value of i in the input (but not the final -1), output the corresponding value of x_i modulo 1000000.