Dark Rock Pro 3 Will it fit? Ram, case, mb!?

[adaver]

Planning on building a new PC and with that being said I wanted to cool my i7 6700k with the Dark Rock Pro 3 by be quiet! As for the case I'll be going with the Phanteks p400s. The clearance for the CPU fan on the Phanteks case is 160mm where as the Dark Rock Pro 3 is 163mm. Will it realistically fit I've seen people fit in noctua DH-14's in the p400 cases where I think there was s tiny bit of clearance https://youtu.be/wu9b0E7PfAA?t=3m6s (https://youtu.be/XQvWeqo7XBw?t=6m48s) <- see the side view on that youtube link . As for ram I was going with Kingston HyperX Fury 2666mhz 2x8gb. These Ram sticks are according to my research 32,4mm tall, but I couldn't really verify that. Would they fit under the massive Dark Rock Pro 3? Last but not least the motherboard I was going with is the Asus Z170 PRO GAMING AURA. I would really appreciate all the help because this would be my second PC build in question.

 

[Isokolon]

Ram should fit. But install it first.
As for the case, usually there's some headroom. However it can create a certain noise when the cooler is too close or even touching the side panel

 

[synphul]

Here's someone's build that used a dark rock 3 (not the pro 3) which is 160mm tall in their p400s.
https://pcpartpicker.com/b/tX4CmG

The dark rock pro 3 is a great cooler but it's pushing awfully close for the case tolerances where it might cause problems. The dark rock 3 performs similarly. Here's some cooling comparisons for the dark rock 3.
https://www.techpowerup.com/reviews/beQuiet/Dark_Rock_3/6.html

 

[adaver]

Ram should fit. But install it first.
As for the case, usually there's some headroom. However it can create a certain noise when the cooler is too close or even touching the side panel

the phanteks p400 is wider in width 210mm where as the nzxt s340 is 203mm wide in width. However, I saw a s340 with the Dark Rock Pro 3 inside of it -> here https://pcpartpicker.com/b/6KFdnQ. I don't know if I should take the risk since I couldn't find any p400 that used the Pro version of the Dark Rock cooler and the regular non-pro version is out of stock. Otherwise, I could go with the nzxt s340 since I think that's also a great case in my mind and by that I know it's been done and is possible