\(6^{th}\) round, April \(14^{th}\), 2012

Let‟s say that there exists a huge cake made from blueberries, strawberries and chocolate. It‟s shaped
like a square, and has area of 100 square meters. Proffesionals strongly advise that cake is being cut
with wet knife and eaten with dry spoon. Also:

Every cut begins and ends on the cake‟s perimeter

A cut cannot lie completely on one of the sides

No two cuts have the same starting and ending points, i.e. all cuts are different
Parts obtained by these cuts are separated and counted only after last cut has been made. During
cutting, the cake keeps its square form.
At least how many cuts need to be made in order to obtain at least K parts? Exactly what cuts to
make?

If only the number of cuts N is correct, you will get 50% of the points for that test case.

The first and only line of input contains an integer K (\(1 \le K \le 1\,000\,000\)), minimum number of parts
that we must have after cutting is done.

The first line of output should contain the requested number of cuts, N.
The following N lines should have four integers each, coordinates of starting and ending point for each
cut made. Coordinates are represented in millimeters, and opposing corners of the cake have
coordinates (-5000, -5000) and (5000, 5000). So for each point (x, y) lying on the side of the square, the
following will hold:
max( |x|, |y| ) = 5000.

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출처 COCI 2011/2012 Contest 6