D. An abstract painting
time limit per test
0.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

A modern art gallery commissioned artist Malyavich to paint another masterpiece called «Complex Square». According to the terms of the order, the canvas must:

  1. be a square that entirely consists of other squares $$$n$$$;
  2. have size $$$k \times k$$$, and the artist can choose any size as long as it follows the rule $$$1 \leq k \leq n$$$;
  3. the sides of all the squares should be strictly vertical or strictly horizontal;
  4. the lengths of the squares' sides – integer numbers;
  5. two squares with touching sides (not vertexes) should be different colors.

Malyavich wanted to use all shades of black to create this painting, but to his horror, he discovered that he had used all black paint to make the last masterpiece. There were only four paints left: (Yellow), orange (Orange), pink (Pink), and bright (Lime). Fearing to get something very psychedelic Malyavich decided not to mix paints and work only with these four colors.

Help Malyavich to create a masterpiece – write a program that, with given $$$n$$$, selects the appropriate $$$k$$$ and builds the map of colored squares that does not break the terms stated above or informs that a solution does not exist.

Input

One integer number $$$n$$$ $$$( 1 \leq n \leq 1000 )$$$.

Output

In the first line output the selected number $$$k$$$ $$$(1 \leq k \leq n)$$$ – length of the panting's side.

In the next $$$k$$$ lines output $$$k$$$ symbols. The lines should consist of Latin symbols «Y», «O», «P» or «L» indicating the color of the corresponding «pixel» of the painting. The colored squares can consist of one or several adjoining «pixels».

If there are multiple solutions, print any of them.

If a solution does not exist, output the number «$$$-1$$$» (without quotation marks).

Examples
Input
1
Output
1
Y
Input
2
Output
-1
Input
3
Output
-1
Input
4
Output
2
YO
OP