Connect dots on a grid with one continuous line 2.0

Question

This is the same question posted by webadventurer with one extra condition (number 5) that disallows the previous solution posted here.

(All credits go to webadventurer, including all images.)

Rules:

1. Line must be straight.
2. Line must be continuous.
3. Line must not intersect itself.
4. Line is allowed to take 45 degree turns to itself, for example:

5. Line must not leave the square.

The dots:

Answer 1

I mean, as long as the number of segments doesn't matter..

Answer 2

This might be the intended answer. Only slightly out of the box.

Then of course, people want to know what is the minmum.

OK, I tried. I managed to go down to ...

21 lines instead of 25.



But somehow the apparent waste at the ends is not very satisfactory.