confused! frankfurt to budapest

I am planning to visit munich, vienna, salzburg, prague and budapest. However I am not sure which route to take.

1) I can fly into frankurt and go to budapest via a plane. Is there any cheap route? Will train be cheaper? How long does it take?

From budapest i will go back to vienna, salzburg and munich ( i really wanted to visit the beautiful castle)

Finally from munich i will take a train to prague.

Any suggestions to make this trip better, more cost efficient? Or should i start from munich --%26gt; salzburg--%26gt; vienna---%26gt; budapest---%26gt; prague?

Please help!

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A logical round trip by train would be:

Frankfurt - Munich - Salzburg - Vienna - Budapest - Prague - Frankfurt

one way routes

Frankfurt - Munich - Salzburg - Prague - Vienna - Budapest

And if you%26#39;re happy with a day trip to Salzburg from Munich

Frankfurt - Munich - Salzburg - Munich - Prague - Vienna - Budapest

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