K. Da Capo
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
May you, the beauty of this world, always shine.

Before Kiana travels to the moon, she must take a subway to bid farewell to her friends. However, an unexpected challenge arises: she must construct the subway herself.

Kiana's task is to build a cuboid subway with dimensions $$$w \times h \times l$$$. Prior to building the subway, she must create a time-stasis field of the same size. In her form as the Herrscher of Finality, Kiana can generate non-intersecting cuboid spaces, which can then be assembled to create the required field.

However, there are constraints on the small spaces: each cuboid space must have at least one face that is a square. In other words, if the dimensions of the cuboid space are $$$a \times b \times c$$$, then at least one of the following conditions must hold: $$$a=b, b=c$$$, or $$$a=c$$$.

Since Kiana's power is limited, she seeks your assistance as captain to develop a plan to accomplish the task.

Input

A single line containing three integers $$$w, h, l$$$ ($$$1\le w,h,l \le 10^9$$$), representing the dimensions of the required field. You can envision this field as a cuboid with the lower left corner at $$$(0,0,0)$$$ and the upper right corner at $$$(w,h,l)$$$.

Output

The first line contains an integer $$$n$$$ ($$$1\le n \le 10^5$$$), representing the number of spaces generated.

Each of the next $$$n$$$ lines contains $$$6$$$ integers $$$x_l, y_l, z_l, x_r, y_r, z_r$$$ ($$$0 \leq x_l \lt x_r \leq w$$$, $$$0 \leq y_l \lt y_r \leq h$$$, $$$0 \leq z_l \lt z_r \leq l$$$), representing a cuboid space with its lower left corner at $$$(x_l,y_l,z_l)$$$ and upper right corner at $$$(x_r,y_r,z_r)$$$.

Your solution must ensure that no two spaces intersect and that all spaces fit together to form the required field precisely.

Example
Input
3 5 7
Output
4
0 0 0 3 3 7 
0 3 0 2 5 7 
2 3 0 3 4 7 
2 4 0 3 5 7