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

- $18.60$
- $22.50$
- $20.61$
- $25.00$