Dual lattice#1085

Dual lattice

1 second
64 megabytes
Easy

Two infinite uniform rectangular lattices are given with cell sizes x_1 \times y_1 and x_2 \times y_2. The lattices are located on planes parallel to each other and to the coordinate axes so that one node of the second lattice is displaced by D_x horizontally and D_y vertically relative to a node of the first lattice. As a result of overlaying, a new "composite" lattice with smaller cells of various sizes is formed. You are required to output, in ascending order, all the distinct areas of the cells of the composite lattice.

Input

The first line contains the integers x_1, y_1, x_2, y_2, D_x, D_y separated by spaces.

1 \leq x_1, y_1, x_2, y_2 \leq 100. 0 \leq D_x < x_1, 0 \leq D_y < y_1. All numbers are integers.

Output

The first line should contain — the number of distinct areas obtained. Each of the next lines should contain one area.

Examples

Example 1

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