A. Moon Spotting
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Sophie is trying to determine when the new moon is so that she can figure out the exact date of Lunar New Year. She looks at the moon and determines how much is lit up, but she doesn't know what state this corresponds to. Can you help her?

She has written down the shape of the lit portion of the moon as follows:

  • If none of the moon is lit up, she writes down "0".
  • If all of the moon is lit up, she writes down "100".
  • Otherwise, she writes down the integer percentage of the moon that is lit up, along with 'L' if the left side of the moon is lit or 'R' if the right side of the moon is lit. For example, if 37% of the right side of the moon is lit, then she writes down "37R".

The possible lunar phases, in order, are:

  • New moon – the moon is unlit
  • Waxing crescent – the lit portion of the moon is growing in size, but it is less than half of the moon
  • First quarter – the lit portion of the moon is growing in size, and it is exactly half of the moon
  • Waxing gibbous – the lit portion of the moon is growing in size, and it is greater than half of the moon
  • Full moon – the moon is fully lit
  • Waning gibbous – the lit portion of the moon is shrinking in size, and it is greater than half of the moon
  • Third quarter – the lit portion of the moon is shrinking in size, and it is exactly half of the moon
  • Waning crescent – the lit portion of the moon is shrinking in size, but it is less than half of the moon

She lives in Austin, TX (in the Northern hemisphere), so the light moves from right to left on the moon. For some images, please view Wikipedia.

Input

The first line contains the description of the Moon. If the moon is completely dim, it contains "0" without quotes. If the moon is completely lit, it contains "100", completely lit. Otherwise, it contains some integer $$$p$$$ following directly by a character $$$s$$$ ($$$1 \leq p \leq 99$$$, $$$s \in \{\mathtt{'L', 'R'}\}$$$) — the portion of the moon lit up and the side of the moon that is lit up, respectively. $$$p$$$ and $$$s$$$ are not separated by a space.

Output

Output the string corresponding to the lunar phase of the moon according to the table above.

Examples
Input
0
Output
New moon
Input
100
Output
Full moon
Input
37R
Output
Waxing crescent