$\textbf{M}$ and $\textbf{N}$ starts from same location.$\textbf{M}$ travels $10$ $km$ East then $10$ $km$ North-East. $\textbf{N}$ travels $5$ $km$ South then $4$ $km$ South-East.What is the shortest distance (in $km$) between $\textbf{M}$ and $\textbf{N}$ at the end of their travel?

1. $18.60$
2. $22.50$
3. $20.61$
4. $25.00$