Broken

In a rectangular coordinate system, a point M(x, y) is given. Connect point M to the origin using a broken line such that each adjacent segment of the line is perpendicular to the next, and each segment has a length of 1. Determine the shortest possible length of this broken line.

Input Data

The input consists of a single line containing two numbers, which are the coordinates of point M (x, y); where ( |x| , |y| < 100).

Output Data

The first line should contain the number n, which represents the number of segments. This is followed by n+1 pairs of numbers, which are the vertices of the broken line.

Examples