Retro Palette Color Snap

A retro game console's video chip cannot display arbitrary 24-bit colors: each of its red, green, and blue channels can only be set to one of sixteen brightness levels, and internally every channel is stored as a single hexadecimal digit repeated twice -- so any color the console can actually render has a six-digit hex code whose digits come in three equal pairs. An art tool needs to convert an artist's freely-chosen source color into the closest color the console can render.

Given a source color as a 6-digit hexadecimal RGB string, output the console-representable color (also a 6-digit hexadecimal RGB string, with each channel's two digits equal) that minimizes the sum, over the three channels, of the squared difference between the source channel value and the chosen channel value. Each channel can be optimized independently of the other two. No channel value in the test data is ever exactly equidistant between two supported levels, so the closest level for each channel is always unique.

Input format

A single line containing a string of the form "#RRGGBB": a '#' character followed by exactly 6 lowercase hexadecimal digits (0-9, a-f).

Output format

A single line containing the nearest console-representable color in the same "#RRGGBB" format, using lowercase hexadecimal digits, where digits 1-2 are equal, digits 3-4 are equal, and digits 5-6 are equal.

Constraints

• The input always has exactly 7 characters: '#' followed by 6 lowercase hex digits.
• The sixteen supported levels per channel are 0x00, 0x11, 0x22, ..., 0xff (every multiple of 17 from 0 to 255).

#09f166

#11ee66

#4e3fe1

#5544dd