CONCATENATE #'s with a twist: #~#~# /or/ #~# /or/ #

CONCATENATE #'s with a twist

I'm doing a database import of a CSV file, but before I do, I need to re-translate three columns of data into one in the following format;

1~2~3

I can't just simply Concatenate with "~" because some concatenations will have 1, 2 or all 3 fields to concatenate. Which means, if I only have a number in the first column; I get 1~~. other combos give me ~~3, 2~, so on. I need a formula that will only give me an output like this.

1
1~2
1~2~3
2~3
2
3

Here's my very bad attempt;
=IF(ISBLANK(D10:F10),"",CONCATENATE(D10&"~"&E10&"~"&F10))

Excel Snap shot of desired output enclosed (output.gif) anyone got any ideas?

With
A2:C2 containing a value or blank

Try this...

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Is that something you can work with?