Dice Roller

Rolling 21 6-sided dice:
3, 2, 3, 3, 1, 5, 1, 1, 2, 6, 1, 5, 2, 1, 4, 1, 6, 4, 5, 2, 4

Rolling 11 6-sided dice:
6, 3, 1, 5, 1, 2, 1, 3, 1, 3, 6

Rolling 6 6-sided dice:
3, 5, 5, 4, 3, 4

That’s really cool!!

:dice4d6:

Rolling 4 6-sided dice:
6, 4, 2, 4

Rolling 4 6-sided dice:
3, 5, 5, 6

<:>6d6<:>

Anyone else having problems receiving e-mail results from DAAK?

I have not received battle results for the past several battles.

I think we need to switch to Frood for the remainder of the Tournament…

:8d6:

Doh - RTFM, eh?

Rolling 8 6-sided dice:
1, 6, 4, 3, 6, 4, 4, 3

just trying it out, neat concept…

:dice10d6:
:-)

Rolling 10 6-sided dice:
5, 5, 3, 3, 1, 2, 5, 5, 3, 5

Testing….

Rolling 100 6-sided dice:
1, 6, 5, 4, 5, 1, 3, 5, 3, 6, 5, 3, 6, 1, 2, 6, 1, 6, 4, 3, 2, 2, 4, 1, 5, 5, 4, 1, 1, 6, 6, 2, 5, 5, 5, 3, 5, 1, 2, 1, 1, 6, 3, 1, 1, 5, 1, 2, 5, 4, 5, 6, 5, 2, 1, 4, 6, 5, 4, 1, 4, 3, 2, 3, 1, 1, 5, 6, 2, 1, 1, 3, 1, 3, 3, 1, 2, 3, 3, 6, 6, 1, 6, 5, 2, 1, 2, 2, 5, 5, 2, 3, 2, 4, 6, 3, 4, 5, 2, 6

Okay, that resulted in:
23 1’s (23%)
16 2’s
15 3’s
10 4’s
20 5’s
16 6’s

Not too bad…. Let’s try it with a lot of dice this time and see if it comes closer to statistical norms.

Rolling 10000 6-sided dice:
2, 2, 2, 6, 6, 1, 5, 5, 3, 3, 2, 3, 2, 6, 4, 6, 2, 5, 1, 5, 5, 1, 5, 1, 6, 6, 4, 4, 3, 6, 5, 4, 2, 1, 4, 2, 1, 3, 6, 3, 5, 2, 6, 1, 1, 3, 6, 2, 2, 6, 1, 1, 6, 5, 1, 6, 5, 5, 4, 1, 4, 3, 5, 6, 3, 2, 1, 3, 4, 1, 6, 3, 2, 5, 3, 2, 2, 2, 4, 3, 2, 5, 3, 2, 3, 4, 1, 2, 2, 5, 3, 6, 1, 1, 5, 4, 3, 5, 6, 6, 5, 6, 2, 1, 5, 4, 3, 6, 6, 6, 3, 2, 4, 6, 3, 1, 3, 4, 3, 4, 2, 5, 3, 3, 6, 1, 6, 2, 6, 6, 1, 5, 6, 3, 6, 5, 1, 2, 5, 1, 1, 1, 2, 5, 6, 4, 6, 2, 2, 3, 6, 4, 1, 2, 6, 6, 3, 6, 1, 3, 5, 2, 2, 4, 5, 1, 2, 5, 2, 6, 5, 3, 1, 1, 2, 6, 5, 2, 2, 6, 4, 1, 3, 5, 2, 2, 4, 5, 2, 5, 2, 6, 1, 3, 4, 5, 3, 6, 4, 5, 5, 3, 2, 6, 3, 3, 5, 1, 5, 1, 1, 2, 1, 3, 6, 3, 5, 4, 1, 6, 3, 2, 6, 3, 5, 3, 2, 2, 2, 5, 6, 1, 2, 2, 6, 5, 4, 5, 5, 3, 5, 6, 4, 5, 3, 4, 1, 1, 1, 2, 1, 4, 4, 6, 6, 3, 3, 2, 4, 4, 6, 4, 5, 2, 5, 4, 6, 3, 2, 5, 5, 1, 4, 3, 5, 6, 6, 6, 1, 1, 2, 1, 4, 6, 1, 4, 2, 4, 5, 6, 2, 5, 3, 6, 6, 2, 4, 5, 4, 6, 3, 3, 6, 6, 5, 5, 5, 5, 5, 6, 5, 6, 1, 3, 6, 1, 6, 2, 5, 4, 1, 6, 2, 4, 5, 2, 5, 2, 6, 3, 2, 2, 5, 1, 2, 4, 6, 1, 2, 4, 6, 1, 4, 6, 4, 3, 1, 3, 5, 5, 1, 5, 4, 3, 3, 3, 4, 1, 5, 3, 4, 6, 5, 3, 6, 6, 6, 5, 6, 2, 3, 6, 3, 6, 5, 6, 3, 5, 3, 1, 3, 3, 6, 1, 6, 2, 3, 3, 3, 1, 6, 6, 6, 5, 3, 6, 4, 3, 5, 4, 4, 1, 3, 1, 6, 2, 6, 2, 6, 3, 3, 3, 5, 2, 3, 4, 4, 6, 1, 6, 6, 1, 6, 6, 5, 3, 5, 3, 5, 3, 1, 3, 4, 4, 3, 3, 5, 3, 5, 4, 5, 2, 1, 4, 4, 3, 2, 1, 2, 3, 1, 2, 3, 1, 1, 2, 3, 6, 5, 1, 3, 5, 4, 6, 2, 6, 3, 1, 3, 1, 4, 2, 3, 4, 5, 6, 1, 6, 6, 3, 3, 6, 5, 5, 1, 5, 1, 3, 5, 5, 4, 1, 4, 1, 6, 6, 1, 2, 6, 3, 3, 4, 4, 5, 2, 3, 4, 3, 3, 4, 5, 5, 4, 3, 3, 4, 2, 4, 6, 1, 3, 4, 1, 6, 4, 1, 6, 4, 3, 6, 6, 5, 3, 4, 4, 5, 6, 2, 1, 2, 5, 5, 6, 3, 2, 3, 6, 4, 1, 6, 4, 3, 3, 5, 3, 6, 5, 2, 3, 1, 2, 3, 6, 4, 1, 3, 2, 6, 5, 3, 2, 3, 1, 2, 5, 3, 5, 5, 1, 6, 4, 4, 2, 6, 3, 4, 6, 1, 6, 3, 2, 1, 5, 1, 5, 6, 4, 1, 6, 2, 3, 1, 5, 4, 3, 4, 1, 2, 2, 1, 1, 6, 4, 2, 6, 6, 6, 5, 1, 6, 1, 3, 1, 6, 3, 6, 5, 1, 6, 5, 3, 3, 6, 2, 1, 2, 6, 1, 3, 1, 1, 4, 1, 5, 6, 6, 5, 6, 5, 5, 5, 6, 2, 6, 5, 4, 6, 4, 5, 6, 3, 2, 2, 2, 3, 2, 3, 2, 2, 6, 3, 3, 3, 4, 1, 3, 3, 5, 2, 2, 4, 1, 1, 5, 6, 6, 3, 6, 4, 2, 5, 6, 3, 6, 1, 6, 2, 4, 1, 4, 4, 4, 6, 6, 1, 1, 3, 4, 5, 4, 5, 3, 4, 5, 2, 4, 5, 5, 3, 2, 6, 1, 1, 3, 1, 2, 2, 3, 5, 3, 6, 2, 6, 6, 2, 1, 6, 4, 4, 5, 2, 2, 1, 6, 1, 3, 4, 5, 1, 6, 1, 1, 1, 2, 4, 2, 3, 5, 4, 2, 2, 4, 4, 2, 3, 5, 2, 2, 3, 5, 6, 5, 1, 1, 4, 2, 4, 1, 1, 4, 1, 1, 5, 2, 2, 2, 4, 5, 1, 1, 6, 2, 5, 3, 3, 1, 2, 5, 3, 4, 3, 2, 2, 4, 3, 6, 6, 6, 6, 1, 4, 1, 1, 2, 2, 3, 4, 5, 1, 5, 6, 1, 6, 4, 3, 3, 5, 4, 1, 1, 2, 4, 3, 4, 2, 6, 3, 2, 5, 3, 2, 2, 3, 2, 4, 5, 5, 2, 4, 5, 6, 4, 5, 6, 2, 2, 3, 6, 6, 3, 1, 1, 1, 4, 5, 3, 3, 1, 4, 1, 4, 5, 3, 1, 1, 1, 6, 5, 2, 3, 4, 2, 6, 3, 1, 1, 4, 3, 1, 4, 6, 2, 4, 1, 5, 2, 3, 2, 3, 6, 3, 1, 4, 5, 1, 5, 6, 6, 3, 1, 3, 1, 2, 3, 3, 3, 4, 1, 6, 5, 4, 5, 6, 2, 6, 5, 4, 2, 6, 1, 1, 2, 1, 5, 1, 2, 3, 6, 1, 6, 1, 4, 6, 3, 6, 3, 5, 4, 4, 5, 2, 2, 4, 1, 3, 3, 5, 6, 4, 5, 6, 4, 6, 1, 3, 1, 2, 5, 6, 3, 5, 1, 6, 4, 3, 6, 1, 2, 3, 4, 6, 4, 5, 3, 5, 2, 5, 3, 1, 3, 2, 1, 1, 2, 1, 3, 2, 3, 2, 2, 5, 6, 2, 4, 4, 4, 4, 4, 5, 6, 2, 5, 4, 6, 1, 2, 1, 6, 5, 2, 2, 6, 3, 2, 1, 4, 5, 2, 6, 6, 4, 5, 6, 5, 3, 3, 3, 6, 1, 1, 6, 2, 5, 3, 2, 6, 5, 3, 5, 3, 5, 1, 3, 2, 2, 4, 5, 1, 5, 5, 6, 3, 3, 5, 1, 5, 2, 3, 4, 3, 4, 4, 4, 3, 1, 6, 3, 5, 2, 1, 2, 1, 2, 5, 2, 4, 2, 1, 4, 1, 5, 3, 3, 1, 2, 4, 6, 4, 6, 4, 6, 4, 1, 3, 1, 1, 3, 3, 6, 5, 3, 2, 5, 5, 6, 1, 2, 1, 1, 5, 2, 5, 1, 4, 6, 3, 2, 5, 6, 1, 3, 5, 5, 3, 2, 5, 4, 4, 1, 3, 2, 4, 4, 1, 2, 4, 1, 3, 5, 1, 1, 6, 6, 2, 4, 5, 4, 5, 4, 4, 6, 6, 2, 5, 3, 4, 3, 6, 1, 4, 2, 3, 1, 6, 3, 2, 4, 4, 5, 2, 4, 5, 2, 3, 1, 6, 2, 5, 5, 6, 2, 4, 5, 4, 3, 1, 1, 5, 6, 2, 2, 2, 5, 3, 2, 2, 5, 5, 5, 3, 1, 2, 2, 2, 5, 2, 2, 1, 1, 6, 6, 3, 4, 5, 1, 6, 6, 2, 5, 6, 3, 1, 1, 1, 3, 3, 3, 1, 2, 1, 4, 2, 3, 5, 4, 2, 1, 5, 2, 1, 4, 2, 4, 1, 6, 4, 1, 5, 5, 5, 4, 2, 5, 5, 3, 2, 1, 5, 2, 2, 5, 5, 4, 1, 4, 1, 2, 4, 5, 3, 5, 3, 4, 2, 4, 4, 6, 4, 2, 4, 2, 6, 5, 1, 4, 1, 2, 5, 5, 4, 6, 4, 2, 4, 4, 5, 4, 6, 3, 2, 3, 2, 4, 1, 3, 1, 4, 2, 5, 6, 6, 1, 5, 4, 1, 2, 5, 3, 1, 3, 6, 1, 6, 2, 4, 4, 1, 1, 3, 3, 3, 5, 4, 1, 6, 1, 2, 3, 3, 6, 2, 2, 6, 1, 5, 1, 3, 4, 3, 3, 1, 3, 3, 6, 4, 6, 4, 4, 1, 1, 1, 3, 6, 5, 3, 5, 5, 4, 1, 2, 4, 3, 3, 4, 3, 2, 4, 5, 5, 1, 1, 5, 3, 4, 5, 6, 3, 3, 4, 3, 3, 4, 6, 2, 3, 2, 6, 2, 6, 1, 3, 4, 3, 5, 1, 6, 1, 5, 4, 5, 5, 5, 4, 1, 2, 3, 1, 5, 5, 4, 1, 1, 2, 1, 3, 4, 3, 3, 5, 3, 4, 2, 6, 6, 6, 6, 6, 1, 4, 3, 6, 2, 2, 3, 3, 3, 6, 3, 1, 4, 1, 2, 5, 3, 2, 1, 6, 4, 4, 5, 6, 1, 6, 6, 1, 6, 5, 6, 6, 3, 3, 6, 5, 4, 3, 2, 6, 2, 4, 1, 5, 5, 2, 4, 1, 4, 4, 1, 2, 2, 6, 2, 2, 5, 1, 2, 5, 6, 2, 5, 3, 4, 4, 1, 2, 6, 2, 1, 1, 6, 1, 6, 4, 3, 3, 5, 6, 1, 6, 2, 2, 5, 3, 4, 4, 4, 6, 3, 3, 1, 1, 5, 5, 5, 6, 6, 5, 1, 1, 6, 1, 2, 5, 5, 4, 2, 3, 4, 2, 3, 5, 4, 1, 2, 2, 4, 5, 1, 6, 2, 2, 1, 1, 6, 5, 6, 5, 4, 6, 5, 3, 1, 1, 2, 5, 4, 3, 2, 2, 5, 4, 1, 2, 4, 2, 4, 2, 1, 4, 2, 3, 5, 3, 3, 4, 2, 2, 3, 5, 2, 2, 1, 2, 2, 2, 1, 6, 5, 2, 1, 3, 6, 2, 5, 3, 4, 2, 5, 4, 5, 1, 6, 4, 3, 3, 2, 4, 4, 4, 2, 5, 6, 3, 1, 2, 4, 1, 1, 3, 2, 2, 5, 1, 3, 4, 4, 6, 6, 3, 4, 5, 3, 4, 2, 5, 6, 3, 3, 3, 1, 4, 2, 6, 1, 2, 1, 4, 2, 1, 1, 4, 3, 6, 5, 5, 3, 3, 5, 2, 5, 3, 6, 2, 6, 1, 1, 6, 4, 3, 3, 4, 1, 4, 3, 1, 6, 4, 5, 2, 5, 5, 5, 1, 4, 4, 6, 6, 6, 4, 2, 5, 1, 1, 6, 6, 2, 6, 6, 6, 2, 2, 3, 2, 6, 6, 2, 5, 3, 6, 6, 1, 5, 5, 2, 2, 2, 1, 2, 1, 5, 3, 5, 5, 4, 5, 5, 6, 4, 5, 5, 5, 6, 1, 1, 5, 6, 2, 3, 3, 2, 3, 4, 6, 1, 5, 2, 2, 6, 3, 3, 5, 5, 2, 4, 3, 6, 3, 2, 3, 1, 6, 2, 6, 6, 2, 5, 6, 4, 2, 3, 5, 4, 6, 5, 4, 5, 6, 5, 5, 3, 2, 3, 2, 3, 6, 4, 2, 3, 5, 4, 3, 4, 5, 3, 4, 1, 1, 4, 4, 2, 1, 3, 5, 1, 2, 3, 5, 2, 1, 4, 4, 3, 6, 5, 5, 6, 2, 6, 2, 1, 4, 5, 5, 3, 1, 3, 3, 2, 6, 1, 3, 1, 3, 2, 1, 4, 4, 6, 5, 5, 3, 3, 1, 2, 1, 5, 2, 3, 5, 4, 3, 3, 2, 1, 5, 3, 3, 2, 4, 3, 2, 1, 3, 5, 2, 3, 3, 6, 2, 2, 4, 4, 4, 5, 6, 5, 3, 2, 1, 2, 6, 3, 4, 1, 3, 3, 4, 5, 5, 1, 1, 1, 1, 4, 5, 3, 6, 2, 2, 2, 3, 6, 6, 1, 4, 5, 5, 1, 1, 5, 2, 6, 1, 6, 1, 4, 2, 4, 2, 6, 5, 3, 6, 6, 1, 5, 2, 6, 1, 4, 2, 3, 3, 1, 4, 1, 6, 2, 1, 6, 1, 2, 6, 1, 1, 6, 5, 3, 4, 1, 2, 2, 4, 2, 1, 4, 1, 3, 4, 1, 1, 5, 4, 4, 5, 1, 4, 5, 3, 4, 5, 3, 6, 4, 4, 6, 3, 3, 2, 6, 3, 4, 2, 6, 6, 3, 3, 6, 5, 6, 1, 6, 4, 4, 3, 3, 5, 6, 1, 1, 4, 5, 4, 3, 3, 2, 2, 5, 4, 4, 5, 6, 2, 6, 6, 1, 3, 2, 1, 2, 2, 1, 1, 5, 4, 3, 2, 3, 3, 3, 4, 6, 2, 2, 2, 4, 3, 4, 3, 1, 1, 1, 1, 3, 1, 6, 3, 3, 2, 3, 4, 3, 4, 5, 2, 2, 1, 3, 4, 4, 5, 1, 3, 1, 2, 5, 4, 5, 2, 6, 5, 3, 1, 6, 5, 1, 5, 2, 4, 6, 5, 2, 3, 2, 6, 4, 3, 1, 6, 6, 5, 5, 6, 1, 5, 2, 6, 3, 6, 1, 2, 5, 4, 3, 4, 2, 3, 3, 4, 1, 3, 2, 2, 5, 3, 2, 2, 5, 3, 2, 5, 1, 1, 5, 2, 6, 6, 1, 2, 6, 2, 4, 4, 5, 6, 2, 1, 3, 4, 4, 3, 6, 6, 5, 4, 2, 1, 6, 1, 3, 1, 5, 4, 2, 4, 5, 1, 3, 6, 3, 3, 1, 6, 6, 6, 6, 1, 6, 2, 5, 4, 5, 4, 3, 4, 2, 5, 5, 1, 6, 2, 2, 5, 5, 3, 2, 4, 3, 5, 3, 5, 1, 4, 5, 1, 3, 4, 1, 3, 6, 5, 6, 5, 3, 3, 2, 4, 2, 1, 4, 1, 2, 5, 5, 1, 2, 6, 4, 4, 4, 1, 3, 5, 4, 1, 5, 6, 5, 6, 3, 5, 5, 3, 3, 1, 5, 5, 4, 1, 5, 2, 1, 6, 1, 5, 6, 2, 5, 4, 6, 3, 4, 2, 1, 1, 3, 6, 1, 2, 5, 4, 6, 3, 6, 2, 4, 5, 6, 2, 5, 5, 3, 5, 4, 4, 4, 4, 5, 3, 2, 4, 6, 5, 6, 6, 6, 2, 6, 1, 4, 4, 4, 3, 1, 3, 5, 5, 1, 5, 6, 5, 3, 3, 4, 1, 6, 2, 5, 4, 5, 6, 2, 4, 4, 1, 4, 3, 3, 3, 3, 6, 1, 1, 3, 2, 3, 1, 6, 4, 5, 6, 3, 1, 2, 6, 2, 2, 2, 6, 6, 6, 5, 1, 3, 3, 2, 6, 6, 4, 2, 3, 4, 3, 3, 6, 4, 5, 6, 3, 2, 5, 3, 4, 6, 5, 4, 1, 6, 6, 6, 5, 5, 5, 5, 2, 1, 6, 1, 6, 4, 3, 2, 1, 6, 5, 6, 3, 3, 6, 6, 5, 4, 2, 3, 3, 6, 1, 4, 5, 6, 3, 4, 5, 2, 2, 6, 3, 2, 1, 3, 6, 4, 5, 6, 3, 3, 6, 6, 6, 5, 5, 4, 2, 1, 1, 5, 6, 2, 2, 5, 1, 5, 2, 6, 6, 4, 6, 3, 6, 1, 5, 5, 5, 3, 5, 1, 5, 4, 1, 4, 3, 5, 2, 4, 5, 3, 3, 5, 4, 4, 4, 4, 3, 6, 4, 3, 3, 3, 5, 3, 4, 3, 2, 2, 5, 6, 3, 4, 4, 3, 2, 6, 2, 3, 4, 6, 5, 6, 5, 2, 4, 2, 6, 6, 1, 4, 2, 4, 6, 6, 1, 4, 3, 2, 5, 2, 2, 1, 5, 5, 4, 1, 5, 5, 4, 2, 4, 3, 2, 3, 4, 5, 4, 4, 5, 5, 1, 6, 2, 1, 6, 2, 4, 3, 4, 3, 4, 5, 3, 3, 4, 1, 3, 2, 5, 6, 4, 3, 2, 5, 5, 6, 3, 3, 4, 1, 1, 5, 1, 3, 6, 1, 5, 3, 3, 2, 5, 1, 1, 2, 3, 4, 2, 6, 6, 1, 5, 3, 3, 1, 1, 1, 1, 4, 3, 5, 5, 4, 3, 6, 6, 2, 6, 4, 5, 3, 5, 4, 3, 6, 6, 5, 3, 2, 4, 3, 2, 3, 5, 4, 4, 6, 5, 5, 3, 2, 3, 2, 5, 6, 1, 4, 1, 1, 2, 5, 3, 1, 3, 5, 6, 2, 4, 3, 3, 2, 5, 4, 5, 4, 1, 3, 4, 6, 1, 1, 1, 4, 2, 5, 3, 2, 3, 3, 3, 4, 2, 5, 5, 4, 4, 4, 6, 2, 1, 2, 4, 6, 6, 2, 3, 1, 4, 6, 6, 5, 6, 6, 2, 2, 4, 4, 4, 1, 1, 6, 4, 2, 5, 2, 6, 2, 6, 5, 4, 1, 1, 1, 6, 6, 3, 2, 6, 6, 2, 5, 5, 2, 5, 6, 4, 2, 4, 1, 2, 4, 6, 6, 6, 5, 2, 6, 6, 2, 5, 4, 2, 6, 4, 1, 5, 6, 3, 5, 6, 5, 4, 5, 1, 2, 5, 4, 4, 2, 4, 6, 6, 4, 6, 6, 2, 2, 5, 2, 3, 4, 5, 5, 3, 3, 6, 2, 2, 2, 1, 2, 1, 5, 6, 1, 1, 4, 4, 4, 6, 1, 4, 6, 5, 4, 5, 6, 5, 4, 1, 2, 1, 5, 6, 4, 2, 5, 5, 4, 1, 6, 5, 1, 4, 5, 1, 4, 3, 4, 2, 3, 5, 5, 2, 3, 3, 6, 2, 1, 4, 3, 3, 4, 2, 2, 2, 3, 1, 1, 6, 1, 6, 5, 2, 3, 3, 2, 1, 6, 6, 2, 2, 5, 1, 3, 1, 3, 3, 3, 4, 6, 6, 6, 4, 1, 2, 6, 3, 2, 6, 3, 3, 5, 1, 4, 2, 4, 6, 2, 3, 5, 4, 5, 4, 4, 2, 4, 1, 4, 1, 4, 4, 1, 3, 2, 1, 4, 1, 4, 6, 6, 1, 2, 5, 1, 5, 1, 5, 5, 3, 2, 3, 6, 6, 6, 4, 1, 4, 4, 5, 5, 1, 3, 5, 4, 5, 6, 1, 5, 4, 1, 5, 4, 2, 4, 5, 1, 4, 3, 5, 1, 4, 2, 1, 3, 2, 4, 4, 6, 1, 3, 5, 2, 5, 3, 5, 3, 3, 6, 2, 1, 6, 1, 4, 1, 4, 3, 2, 2, 5, 6, 2, 2, 2, 3, 5, 3, 6, 3, 2, 1, 5, 6, 2, 4, 3, 6, 1, 6, 5, 3, 6, 5, 3, 4, 5, 6, 6, 1, 2, 5, 1, 4, 6, 2, 6, 5, 5, 5, 2, 6, 5, 6, 6, 1, 4, 3, 6, 5, 3, 5, 1, 3, 4, 3, 6, 3, 3, 6, 3, 5, 4, 3, 2, 4, 4, 2, 2, 2, 1, 3, 2, 6, 3, 2, 6, 1, 5, 6, 5, 1, 5, 6, 3, 2, 2, 3, 4, 5, 2, 1, 3, 5, 3, 5, 2, 1, 1, 4, 3, 1, 1, 5, 6, 3, 6, 6, 4, 4, 5, 2, 5, 4, 2, 1, 6, 3, 3, 3, 2, 4, 4, 5, 3, 6, 4, 4, 1, 4, 2, 3, 5, 2, 1, 5, 5, 1, 4, 2, 5, 3, 4, 3, 6, 5, 3, 6, 2, 6, 2, 4, 4, 6, 2, 6, 5, 6, 4, 6, 3, 5, 3, 2, 6, 3, 6, 4, 4, 4, 5, 2, 6, 3, 5, 6, 1, 2, 5, 3, 1, 1, 6, 4, 6, 1, 3, 5, 6, 6, 4, 3, 4, 6, 4, 4, 3, 4, 1, 1, 1, 6, 3, 1, 2, 1, 6, 3, 2, 5, 5, 2, 6, 4, 6, 6, 5, 3, 4, 5, 2, 2, 2, 6, 2, 5, 4, 5, 3, 4, 5, 3, 4, 1, 4, 6, 1, 3, 2, 3, 2, 1, 5, 1, 5, 4, 6, 3, 6, 4, 1, 2, 6, 3, 2, 1, 2, 5, 6, 4, 3, 4, 1, 1, 5, 4, 6, 6, 1, 2, 2, 2, 2, 6, 3, 1, 4, 3, 3, 3, 1, 4, 5, 6, 6, 6, 1, 1, 5, 6, 5, 1, 4, 5, 1, 2, 2, 1, 1, 2, 2, 3, 4, 4, 2, 1, 4, 5, 3, 1, 2, 4, 5, 6, 3, 5, 5, 3, 5, 3, 3, 3, 4, 6, 2, 5, 1, 3, 5, 2, 5, 1, 4, 3, 5, 6, 3, 2, 5, 6, 3, 1, 3, 1, 6, 5, 5, 5, 2, 4, 2, 4, 1, 6, 4, 2, 4, 5, 5, 3, 6, 4, 3, 4, 6, 1, 4, 2, 3, 3, 1, 6, 3, 3, 1, 3, 2, 5, 1, 4, 3, 3, 2, 3, 3, 5, 5, 6, 3, 3, 3, 2, 1, 6, 6, 6, 1, 3, 2, 4, 5, 3, 3, 2, 6, 3, 4, 1, 2, 5, 5, 4, 1, 6, 1, 3, 4, 5, 3, 6, 2, 5, 2, 2, 5, 1, 2, 5, 4, 3, 2, 3, 5, 4, 4, 5, 1, 1, 5, 2, 5, 3, 5, 6, 3, 5, 3, 6, 4, 5, 5, 5, 4, 1, 1, 3, 2, 2, 1, 5, 5, 2, 2, 4, 6, 5, 2, 6, 5, 1, 2, 4, 4, 6, 4, 6, 5, 6, 5, 3, 5, 4, 2, 3, 5, 2, 5, 6, 4, 5, 5, 3, 1, 6, 6, 1, 4, 2, 1, 3, 2, 2, 1, 6, 2, 4, 5, 1, 3, 4, 3, 1, 2, 4, 3, 6, 6, 2, 5, 3, 6, 3, 5, 1, 2, 5, 1, 6, 6, 2, 2, 2, 3, 3, 1, 5, 6, 5, 5, 2, 2, 1, 3, 3, 5, 6, 3, 4, 1, 1, 1, 1, 4, 5, 1, 5, 4, 2, 5, 3, 3, 6, 5, 6, 2, 5, 4, 2, 4, 3, 3, 6, 3, 6, 3, 2, 5, 5, 5, 6, 5, 5, 6, 2, 4, 1, 1, 1, 3, 5, 4, 5, 5, 2, 5, 1, 1, 2, 2, 4, 4, 5, 3, 1, 5, 5, 2, 3, 3, 1, 3, 2, 5, 2, 3, 2, 3, 4, 3, 5, 2, 1, 3, 1, 3, 2, 1, 3, 4, 3, 6, 2, 2, 2, 2, 6, 1, 4, 3, 3, 4, 5, 4, 3, 1, 1, 5, 3, 4, 2, 1, 6, 2, 4, 1, 4, 5, 1, 6, 2, 4, 6, 3, 6, 2, 5, 5, 2, 3, 1, 5, 1, 6, 2, 4, 6, 3, 2, 2, 6, 3, 2, 6, 4, 5, 6, 2, 4, 1, 2, 6, 5, 2, 3, 4, 3, 2, 2, 5, 4, 3, 3, 5, 2, 5, 2, 2, 1, 3, 3, 1, 6, 5, 1, 4, 3, 6, 6, 1, 1, 1, 6, 5, 2, 2, 2, 5, 3, 4, 3, 1, 6, 5, 6, 2, 3, 1, 3, 4, 4, 6, 4, 4, 4, 4, 1, 6, 4, 6, 1, 4, 1, 6, 2, 2, 2, 4, 6, 5, 1, 3, 6, 1, 1, 5, 2, 4, 5, 5, 2, 3, 4, 6, 6, 1, 3, 6, 1, 1, 6, 1, 4, 6, 1, 6, 2, 3, 3, 2, 2, 4, 4, 1, 4, 5, 6, 6, 2, 5, 5, 3, 1, 2, 3, 1, 3, 6, 1, 4, 6, 6, 5, 4, 6, 5, 4, 2, 2, 6, 3, 4, 4, 1, 4, 1, 5, 4, 1, 1, 2, 5, 4, 3, 1, 6, 3, 4, 5, 3, 1, 4, 3, 5, 2, 2, 4, 5, 3, 5, 5, 6, 2, 2, 6, 6, 3, 5, 4, 3, 5, 5, 2, 2, 2, 3, 2, 4, 6, 6, 1, 6, 4, 3, 4, 5, 5, 1, 4, 2, 6, 2, 1, 2, 3, 1, 2, 6, 5, 5, 3, 4, 4, 4, 6, 5, 6, 1, 3, 6, 1, 3, 5, 4, 5, 3, 3, 4, 4, 6, 5, 4, 1, 5, 5, 4, 6, 1, 3, 4, 6, 5, 2, 3, 3, 1, 2, 3, 1, 5, 2, 2, 1, 1, 5, 6, 3, 2, 3, 6, 1, 1, 3, 2, 6, 2, 5, 5, 3, 2, 3, 2, 6, 4, 4, 3, 4, 6, 5, 5, 4, 6, 6, 5, 6, 5, 4, 3, 6, 1, 2, 6, 2, 5, 1, 1, 1, 6, 6, 3, 1, 2, 5, 1, 6, 2, 3, 3, 2, 1, 2, 6, 1, 1, 4, 1, 5, 1, 3, 5, 2, 5, 5, 3, 4, 6, 4, 4, 5, 4, 1, 6, 6, 5, 6, 5, 1, 3, 1, 2, 4, 3, 1, 4, 3, 5, 5, 2, 6, 1, 1, 1, 5, 5, 4, 2, 4, 2, 6, 3, 5, 1, 2, 4, 5, 2, 2, 6, 4, 3, 2, 2, 5, 3, 5, 2, 1, 4, 4, 6, 4, 4, 6, 3, 2, 4, 5, 5, 5, 4, 1, 3, 4, 3, 1, 3, 4, 2, 2, 2, 5, 3, 3, 3, 5, 2, 5, 5, 5, 2, 4, 3, 5, 4, 5, 6, 1, 3, 5, 6, 1, 6, 3, 5, 2, 3, 1, 5, 5, 3, 6, 3, 5, 3, 6, 4, 4, 4, 2, 3, 5, 6, 5, 4, 4, 3, 4, 5, 5, 2, 4, 6, 1, 1, 4, 2, 3, 5, 1, 2, 1, 1, 4, 5, 3, 4, 3, 1, 1, 4, 3, 6, 4, 1, 4, 2, 4, 1, 6, 3, 2, 4, 2, 3, 5, 6, 4, 1, 4, 5, 3, 4, 5, 6, 3, 2, 4, 5, 3, 5, 3, 6, 4, 6, 6, 2, 2, 4, 2, 2, 6, 3, 5, 2, 5, 4, 1, 3, 4, 4, 2, 1, 1, 6, 1, 3, 2, 4, 1, 5, 2, 3, 4, 6, 3, 4, 1, 4, 1, 2, 6, 1, 5, 4, 2, 4, 1, 3, 6, 5, 6, 1, 5, 1, 1, 5, 4, 3, 3, 5, 1, 4, 2, 4, 4, 5, 1, 4, 3, 2, 6, 2, 2, 4, 5, 4, 2, 6, 6, 1, 5, 6, 2, 4, 1, 3, 3, 4, 5, 5, 2, 6, 3, 4, 4, 1, 2, 5, 5, 4, 6, 4, 5, 2, 2, 4, 5, 3, 4, 5, 4, 2, 4, 6, 6, 4, 2, 3, 2, 1, 2, 4, 6, 5, 1, 4, 5, 2, 2, 3, 5, 1, 1, 4, 2, 3, 1, 1, 5, 4, 5, 3, 6, 3, 2, 6, 1, 4, 2, 2, 4, 3, 5, 4, 1, 5, 1, 6, 1, 2, 2, 5, 3, 3, 3, 5, 5, 3, 5, 4, 1, 4, 6, 6, 6, 2, 6, 6, 5, 1, 1, 2, 4, 6, 6, 5, 5, 6, 4, 5, 2, 6, 4, 5, 2, 6, 3, 1, 2, 2, 4, 2, 5, 4, 2, 4, 5, 1, 4, 3, 2, 5, 5, 5, 4, 4, 3, 2, 4, 1, 6, 6, 6, 3, 4, 2, 3, 6, 2, 4, 2, 5, 6, 6, 2, 2, 4, 1, 3, 1, 4, 4, 5, 2, 3, 2, 6, 5, 4, 3, 5, 3, 2, 5, 6, 6, 6, 2, 5, 1, 6, 6, 6, 6, 6, 2, 2, 3, 2, 4, 4, 5, 2, 2, 1, 4, 4, 6, 3, 1, 3, 2, 3, 5, 6, 3, 4, 6, 5, 3, 6, 4, 3, 6, 4, 2, 1, 5, 4, 3, 3, 1, 2, 4, 3, 2, 2, 6, 2, 5, 6, 4, 6, 3, 2, 6, 6, 6, 5, 4, 2, 5, 2, 4, 4, 5, 5, 5, 4, 3, 1, 6, 4, 2, 4, 1, 4, 5, 6, 5, 4, 6, 3, 3, 3, 5, 3, 2, 4, 1, 6, 5, 6, 1, 3, 4, 6, 1, 3, 3, 4, 3, 3, 1, 5, 6, 1, 3, 5, 1, 2, 2, 1, 4, 5, 3, 3, 1, 5, 6, 2, 5, 5, 1, 6, 1, 5, 5, 2, 1, 2, 5, 4, 4, 6, 3, 3, 1, 5, 2, 2, 6, 3, 2, 4, 1, 5, 6, 2, 4, 6, 3, 3, 5, 4, 2, 6, 2, 6, 1, 2, 2, 6, 6, 5, 6, 2, 2, 1, 1, 3, 2, 6, 6, 4, 4, 1, 3, 3, 2, 6, 3, 4, 2, 1, 1, 4, 1, 2, 4, 1, 4, 5, 1, 3, 3, 6, 5, 4, 1, 5, 1, 2, 4, 6, 6, 2, 6, 2, 5, 1, 2, 1, 4, 4, 2, 5, 1, 2, 6, 4, 3, 4, 2, 3, 6, 5, 3, 5, 2, 3, 3, 3, 5, 1, 2, 4, 2, 2, 6, 6, 3, 1, 6, 6, 4, 2, 5, 5, 3, 4, 2, 6, 2, 4, 3, 2, 2, 6, 6, 4, 3, 2, 6, 1, 2, 2, 5, 3, 3, 4, 2, 5, 5, 2, 5, 3, 3, 3, 1, 6, 1, 3, 6, 2, 6, 2, 3, 1, 1, 2, 4, 3, 4, 4, 4, 5, 5, 2, 2, 2, 6, 3, 6, 4, 5, 5, 6, 2, 2, 1, 1, 2, 3, 6, 4, 2, 2, 1, 3, 2, 2, 1, 5, 6, 4, 2, 4, 3, 3, 5, 4, 3, 2, 4, 1, 1, 2, 6, 2, 3, 1, 3, 5, 3, 3, 2, 5, 4, 2, 2, 6, 4, 2, 4, 4, 6, 6, 1, 3, 2, 6, 6, 5, 2, 4, 5, 3, 6, 5, 4, 2, 5, 1, 1, 2, 4, 3, 6, 1, 4, 2, 1, 2, 3, 5, 5, 3, 4, 6, 5, 6, 6, 5, 4, 2, 2, 3, 4, 1, 1, 2, 3, 5, 2, 3, 1, 5, 6, 1, 6, 3, 2, 1, 5, 4, 5, 4, 1, 2, 4, 6, 2, 3, 4, 5, 4, 6, 1, 2, 6, 2, 3, 3, 1, 4, 6, 1, 3, 5, 1, 2, 2, 2, 2, 1, 6, 1, 4, 6, 2, 1, 5, 3, 4, 3, 2, 2, 2, 3, 3, 2, 4, 5, 4, 4, 3, 4, 4, 5, 2, 5, 1, 3, 6, 3, 3, 6, 3, 1, 5, 5, 2, 4, 2, 6, 1, 3, 1, 2, 6, 4, 4, 3, 3, 1, 1, 6, 5, 4, 4, 6, 3, 5, 3, 2, 2, 5, 1, 4, 6, 6, 3, 1, 4, 4, 1, 4, 1, 1, 6, 6, 5, 3, 2, 1, 4, 2, 6, 2, 6, 4, 1, 2, 3, 4, 4, 4, 2, 5, 2, 2, 5, 4, 3, 3, 2, 3, 6, 2, 4, 6, 1, 2, 2, 3, 2, 6, 5, 2, 1, 5, 5, 2, 6, 1, 5, 4, 5, 1, 3, 6, 3, 1, 4, 5, 3, 5, 2, 3, 1, 5, 2, 2, 6, 4, 4, 2, 3, 3, 4, 4, 1, 3, 6, 1, 4, 5, 4, 2, 5, 6, 2, 1, 1, 5, 6, 4, 4, 1, 6, 5, 5, 2, 6, 5, 6, 4, 1, 3, 6, 4, 1, 6, 1, 6, 6, 4, 4, 4, 5, 3, 4, 1, 4, 4, 5, 3, 2, 3, 3, 2, 1, 2, 3, 6, 1, 3, 4, 1, 6, 3, 5, 6, 3, 5, 5, 3, 3, 3, 6, 1, 5, 3, 1, 3, 1, 6, 5, 2, 3, 1, 4, 4, 3, 6, 4, 3, 3, 1, 4, 2, 3, 3, 1, 5, 2, 6, 1, 4, 3, 1, 4, 2, 4, 5, 4, 4, 5, 2, 6, 2, 3, 3, 5, 6, 3, 2, 2, 6, 2, 5, 1, 5, 2, 2, 3, 3, 2, 4, 6, 4, 4, 4, 6, 1, 3, 3, 5, 1, 5, 5, 2, 2, 2, 1, 1, 4, 2, 3, 4, 4, 2, 5, 2, 3, 6, 5, 5, 2, 2, 4, 5, 6, 1, 5, 6, 3, 2, 5, 4, 1, 3, 6, 2, 5, 6, 3, 2, 2, 5, 6, 6, 6, 4, 1, 2, 3, 5, 1, 4, 1, 5, 3, 6, 6, 2, 6, 3, 3, 4, 6, 3, 1, 6, 5, 5, 6, 1, 1, 2, 6, 6, 1, 5, 4, 1, 1, 1, 6, 2, 5, 6, 6, 1, 6, 5, 3, 5, 1, 5, 3, 1, 2, 4, 6, 1, 2, 5, 1, 3, 1, 1, 3, 1, 6, 6, 1, 1, 6, 1, 2, 4, 1, 1, 5, 6, 6, 1, 5, 1, 6, 1, 1, 2, 4, 1, 2, 6, 6, 3, 2, 6, 3, 5, 6, 2, 4, 1, 2, 4, 1, 3, 2, 2, 4, 6, 1, 4, 1, 5, 4, 1, 6, 4, 2, 3, 5, 3, 3, 4, 5, 5, 3, 1, 3, 2, 2, 1, 2, 3, 4, 3, 6, 6, 4, 4, 5, 5, 1, 6, 3, 4, 6, 2, 2, 1, 5, 6, 3, 2, 4, 2, 6, 6, 3, 2, 2, 4, 3, 4, 1, 1, 6, 1, 6, 4, 4, 5, 2, 4, 4, 5, 2, 3, 1, 4, 4, 6, 3, 1, 1, 6, 2, 6, 6, 4, 2, 1, 2, 5, 4, 3, 5, 3, 3, 5, 1, 1, 3, 3, 4, 1, 1, 6, 3, 2, 3, 1, 1, 6, 1, 2, 5, 3, 1, 5, 1, 3, 5, 2, 1, 2, 5, 6, 5, 2, 4, 5, 2, 6, 1, 6, 1, 2, 5, 3, 4, 2, 4, 5, 1, 4, 6, 6, 6, 6, 4, 6, 3, 2, 2, 3, 3, 6, 2, 2, 2, 6, 6, 3, 6, 1, 3, 6, 3, 1, 3, 6, 3, 6, 4, 3, 3, 4, 2, 3, 3, 6, 3, 6, 1, 5, 2, 4, 4, 4, 5, 5, 4, 5, 2, 3, 5, 4, 2, 2, 5, 4, 2, 1, 3, 6, 4, 6, 3, 5, 3, 6, 5, 5, 5, 5, 4, 1, 2, 1, 5, 1, 6, 2, 5, 2, 4, 4, 5, 6, 5, 4, 3, 1, 5, 6, 6, 2, 6, 3, 1, 3, 3, 5, 2, 1, 3, 5, 2, 5, 6, 6, 6, 5, 2, 4, 1, 6, 2, 6, 5, 1, 3, 2, 1, 1, 2, 1, 3, 2, 4, 3, 4, 6, 1, 5, 1, 4, 3, 2, 3, 2, 2, 2, 1, 3, 6, 1, 3, 1, 1, 1, 1, 3, 3, 2, 4, 5, 2, 1, 6, 6, 3, 4, 5, 4, 2, 5, 2, 5, 6, 4, 6, 2, 6, 1, 4, 5, 2, 1, 5, 2, 2, 6, 4, 4, 1, 2, 3, 3, 2, 2, 2, 5, 5, 6, 3, 1, 5, 4, 5, 5, 1, 5, 6, 1, 5, 4, 5, 6, 4, 4, 1, 5, 3, 5, 3, 4, 1, 5, 1, 3, 1, 2, 2, 6, 2, 4, 6, 6, 1, 5, 4, 2, 3, 3, 2, 2, 1, 1, 2, 4, 4, 3, 2, 1, 2, 5, 5, 2, 3, 5, 5, 4, 1, 6, 3, 2, 4, 3, 2, 4, 1, 5, 6, 4, 2, 2, 5, 2, 2, 1, 6, 6, 3, 2, 1, 4, 6, 6, 6, 3, 4, 4, 6, 5, 4, 2, 6, 1, 4, 1, 5, 5, 6, 5, 2, 2, 6, 1, 4, 2, 1, 4, 2, 3, 5, 3, 1, 4, 2, 6, 1, 6, 4, 6, 4, 1, 2, 3, 2, 6, 4, 1, 4, 4, 6, 6, 6, 6, 6, 4, 1, 6, 1, 3, 3, 5, 5, 3, 3, 6, 2, 4, 5, 5, 3, 3, 6, 4, 5, 2, 4, 3, 2, 1, 1, 2, 6, 1, 1, 6, 4, 1, 5, 4, 4, 2, 3, 2, 4, 6, 2, 6, 3, 1, 5, 6, 3, 4, 4, 2, 6, 1, 5, 2, 2, 5, 3, 1, 6, 3, 1, 3, 4, 5, 1, 1, 1, 4, 3, 4, 3, 4, 3, 6, 4, 2, 5, 6, 5, 3, 1, 5, 3, 5, 6, 4, 4, 2, 5, 3, 5, 5, 6, 2, 4, 6, 3, 4, 4, 5, 2, 6, 3, 5, 6, 6, 6, 5, 6, 5, 1, 1, 3, 3, 6, 3, 1, 3, 4, 6, 6, 2, 4, 5, 4, 2, 5, 6, 6, 2, 5, 1, 2, 1, 6, 1, 6, 5, 5, 6, 4, 5, 6, 1, 2, 5, 3, 3, 2, 1, 2, 1, 2, 6, 5, 6, 1, 4, 6, 6, 5, 4, 1, 6, 4, 1, 6, 4, 6, 5, 3, 3, 4, 3, 3, 6, 1, 6, 2, 2, 6, 3, 3, 2, 2, 2, 1, 3, 5, 6, 3, 3, 3, 3, 2, 1, 3, 2, 4, 3, 6, 1, 5, 4, 3, 2, 3, 4, 1, 4, 6, 6, 1, 2, 1, 2, 4, 2, 4, 2, 1, 1, 5, 4, 3, 1, 4, 6, 2, 2, 2, 2, 2, 1, 6, 5, 3, 2, 2, 3, 6, 2, 3, 6, 3, 3, 1, 6, 4, 5, 2, 5, 5, 6, 2, 2, 1, 6, 2, 3, 2, 4, 4, 4, 5, 4, 2, 1, 5, 4, 3, 4, 5, 6, 3, 2, 3, 4, 2, 6, 3, 3, 5, 2, 3, 1, 4, 3, 1, 6, 5, 2, 4, 3, 5, 2, 1, 6, 3, 5, 4, 5, 3, 2, 5, 6, 3, 1, 3, 4, 1, 6, 1, 5, 1, 3, 6, 5, 6, 6, 4, 5, 2, 1, 2, 6, 3, 2, 6, 5, 1, 3, 4, 4, 5, 2, 3, 1, 2, 6, 5, 2, 5, 5, 1, 6, 2, 1, 4, 2, 6, 2, 6, 1, 3, 2, 1, 5, 4, 6, 4, 5, 3, 1, 2, 1, 3, 4, 1, 4, 3, 6, 6, 1, 4, 1, 1, 5, 1, 5, 6, 1, 6, 6, 2, 2, 1, 2, 1, 5, 2, 4, 3, 4, 5, 4, 5, 1, 2, 6, 5, 4, 5, 5, 5, 2, 6, 5, 1, 1, 3, 6, 1, 3, 6, 2, 5, 1, 4, 6, 5, 5, 4, 2, 3, 2, 5, 2, 3, 6, 1, 2, 4, 5, 6, 2, 1, 6, 1, 1, 6, 4, 1, 1, 6, 6, 3, 5, 6, 6, 4, 4, 5, 1, 5, 2, 3, 4, 3, 5, 4, 3, 1, 1, 2, 1, 3, 2, 6, 3, 2, 6, 1, 2, 6, 6, 1, 2, 5, 6, 1, 2, 4, 6, 3, 3, 1, 5, 6, 3, 4, 3, 5, 4, 4, 6, 4, 6, 2, 4, 3, 3, 3, 3, 5, 2, 3, 6, 4, 1, 6, 5, 3, 3, 4, 5, 5, 4, 4, 5, 1, 1, 2, 6, 5, 6, 6, 3, 6, 1, 6, 2, 4, 2, 5, 2, 4, 2, 1, 1, 2, 1, 5, 5, 3, 3, 3, 2, 6, 1, 1, 1, 1, 2, 6, 6, 1, 5, 2, 6, 5, 2, 2, 3, 4, 6, 4, 1, 1, 5, 2, 3, 6, 1, 1, 2, 3, 4, 4, 3, 4, 4, 4, 5, 6, 3, 5, 6, 2, 6, 6, 1, 2, 2, 3, 5, 2, 1, 6, 3, 6, 2, 5, 5, 2, 6, 6, 5, 4, 4, 2, 2, 1, 5, 6, 6, 1, 5, 6, 2, 5, 6, 2, 6, 1, 5, 4, 3, 5, 4, 5, 4, 5, 3, 2, 1, 3, 2, 5, 6, 6, 6, 1, 6, 5, 1, 6, 5, 5, 6, 1, 3, 6, 3, 3, 1, 2, 6, 3, 6, 4, 1, 3, 2, 4, 5, 2, 6, 1, 6, 6, 6, 6, 1, 6, 4, 1, 6, 3, 6, 5, 4, 3, 5, 1, 5, 5, 2, 5, 1, 2, 3, 2, 4, 4, 5, 3, 5, 5, 3, 5, 5, 3, 5, 5, 2, 3, 6, 1, 6, 6, 6, 4, 2, 4, 4, 1, 3, 6, 6, 4, 1, 2, 5, 5, 6, 4, 1, 5, 3, 4, 4, 1, 1, 2, 5, 2, 5, 4, 3, 4, 4, 2, 2, 5, 6, 6, 6, 2, 5, 6, 6, 5, 2, 4, 4, 1, 2, 5, 6, 4, 3, 3, 4, 3, 5, 3, 5, 3, 1, 1, 1, 4, 3, 2, 3, 2, 1, 2, 4, 6, 2, 3, 5, 3, 1, 2, 4, 2, 1, 3, 6, 3, 5, 4, 5, 4, 6, 4, 6, 6, 4, 1, 4, 6, 3, 6, 2, 4, 2, 6, 3, 3, 2, 2, 6, 3, 4, 3, 4, 4, 6, 4, 6, 5, 1, 5, 2, 6, 2, 2, 6, 6, 2, 3, 6, 5, 3, 2, 2, 4, 1, 5, 6, 3, 6, 6, 5, 3, 3, 2, 1, 2, 6, 6, 1, 6, 5, 2, 6, 1, 3, 5, 1, 5, 2, 6, 4, 4, 1, 5, 2, 2, 3, 2, 4, 3, 1, 2, 6, 3, 4, 6, 5, 3, 6, 5, 3, 5, 1, 2, 5, 4, 1, 6, 2, 2, 5, 6, 6, 6, 4, 2, 2, 1, 3, 5, 4, 4, 1, 3, 6, 5, 3, 5, 2, 3, 3, 4, 1, 4, 5, 6, 1, 5, 5, 3, 1, 4, 2, 1, 3, 5, 2, 5, 6, 5, 4, 3, 2, 4, 6, 2, 3, 3, 6, 4, 5, 3, 1, 5, 6, 6, 5, 1, 4, 3, 3, 5, 1, 4, 5, 4, 3, 1, 2, 2, 5, 5, 5, 6, 3, 4, 1, 5, 6, 1, 2, 5, 4, 3, 4, 3, 2, 2, 3, 6, 5, 6, 4, 5, 3, 2, 2, 6, 2, 4, 1, 1, 2, 6, 6, 4, 3, 1, 3, 3, 1, 4, 1, 4, 6, 5, 1, 2, 6, 4, 1, 4, 3, 4, 3, 6, 6, 5, 5, 2, 2, 6, 2, 4, 5, 1, 2, 2, 1, 4, 5, 2, 1, 6, 5, 1, 4, 6, 2, 3, 4, 2, 1, 6, 5, 4, 6, 4, 2, 4, 6, 4, 4, 1, 1, 2, 1, 2, 3, 2, 5, 2, 3, 6, 1, 2, 6, 4, 2, 1, 1, 5, 3, 1, 4, 2, 5, 4, 6, 6, 2, 5, 3, 5, 5, 4, 1, 5, 5, 4, 1, 4, 5, 3, 3, 5, 5, 2, 3, 6, 3, 3, 4, 5, 4, 2, 6, 2, 5, 5, 1, 1, 3, 4, 5, 1, 1, 6, 6, 6, 3, 6, 3, 2, 3, 5, 6, 1, 1, 2, 1, 3, 4, 4, 2, 1, 6, 2, 3, 5, 6, 3, 5, 3, 1, 4, 4, 2, 3, 4, 1, 6, 4, 4, 1, 1, 3, 1, 2, 3, 2, 2, 6, 6, 6, 2, 1, 5, 3, 3, 3, 3, 6, 1, 6, 6, 5, 3, 2, 1, 1, 2, 1, 4, 6, 1, 4, 2, 1, 5, 5, 3, 1, 4, 3, 6, 5, 4, 4, 2, 1, 1, 4, 6, 2, 3, 6, 6, 6, 1, 1, 6, 3, 1, 4, 2, 2, 2, 3, 2, 1, 2, 5, 1, 5, 1, 1, 4, 5, 5, 6, 5, 5, 3, 4, 1, 6, 4, 6, 5, 5, 1, 5, 1, 2, 3, 3, 3, 5, 6, 5, 5, 1, 3, 6, 6, 4, 6, 4, 2, 4, 3, 6, 3, 5, 4, 4, 5, 1, 4, 4, 6, 4, 3, 6, 5, 5, 3, 2, 3, 2, 6, 2, 2, 3, 1, 2, 1, 1, 5, 2, 5, 1, 2, 2, 6, 5, 5, 4, 6, 2, 2, 5, 6, 4, 5, 5, 2, 1, 6, 5, 3, 6, 6, 5, 2, 1, 6, 2, 1, 4, 4, 5, 4, 5, 6, 4, 4, 4, 2, 3, 6, 3, 2, 5, 6, 1, 3, 2, 1, 2, 6, 4, 1, 6, 2, 3, 6, 1, 5, 1, 4, 2, 5, 2, 1, 5, 5, 4, 2, 6, 6, 1, 3, 2, 6, 2, 2, 2, 3, 3, 4, 3, 6, 4, 2, 1, 1, 2, 1, 5, 2, 5, 1, 6, 6, 1, 5, 5, 4, 6, 5, 4, 1, 1, 5, 6, 2, 1, 2, 5, 3, 5, 1, 3, 3, 3, 3, 3, 4, 4, 2, 6, 2, 2, 6, 2, 3, 4, 1, 6, 4, 6, 4, 4, 6, 3, 4, 2, 3, 5, 6, 6, 3, 1, 2, 6, 3, 5, 2, 1, 3, 4, 6, 4, 6, 6, 6, 2, 3, 1, 2, 6, 6, 5, 3, 5, 1, 1, 1, 4, 6, 1, 3, 2, 1, 4, 2, 4, 3, 3, 4, 5, 1, 4, 3, 6, 3, 3, 1, 6, 3, 2, 5, 2, 1, 2, 1, 1, 2, 1, 4, 1, 1, 6, 3, 2, 4, 4, 5, 1, 1, 3, 5, 1, 1, 1, 6, 4, 4, 1, 3, 6, 3, 1, 1, 3, 2, 2, 3, 4, 2, 1, 5, 3, 1, 2, 4, 4, 6, 2, 5, 1, 5, 3, 1, 5, 4, 1, 2, 1, 2, 4, 6, 4, 5, 1, 6, 1, 3, 3, 4, 4, 3, 3, 1, 3, 4, 4, 1, 4, 6, 5, 4, 5, 2, 5, 3, 6, 5, 5, 6, 1, 3, 6, 4, 1, 1, 4, 2, 3, 6, 5, 1, 3, 2, 1, 5, 6, 5, 6, 3, 5, 4, 6, 3, 6, 4, 5, 5, 3, 4, 5, 3, 6, 4, 1, 1, 5, 4, 2, 2, 4, 1, 2, 6, 2, 3, 5, 1, 2, 4, 4, 6, 2, 3, 2, 1, 1, 1, 5, 3, 4, 3, 6, 3, 1, 1, 3, 5, 5, 5, 1, 2, 5, 3, 2, 1, 5, 6, 1, 6, 4, 5, 5, 5, 1, 1, 5, 2, 1, 3, 5, 4, 6, 5, 1, 6, 5, 4, 5, 3, 2, 5, 5, 1, 1, 1, 1, 6, 1, 2, 6, 4, 6, 5, 2, 1, 5, 6, 2, 5, 3, 6, 3, 2, 4, 3, 2, 3, 6, 1, 6, 2, 6, 5, 2, 1, 5, 2, 6, 5, 3, 5, 3, 3, 4, 4, 3, 2, 4, 5, 6, 6, 4, 2, 1, 2, 5, 3, 4, 4, 3, 4, 6, 2, 2, 1, 2, 1, 2, 2, 6, 5, 1, 2, 1, 4, 5, 4, 5, 2, 2, 5, 2, 6, 1, 3, 1, 5, 5, 5, 3, 1, 2, 2, 3, 4, 3, 5, 4, 5, 6, 3, 3, 6, 4, 4, 3, 3, 2, 1, 5, 3, 6, 6, 2, 6, 2, 3, 4, 1, 2, 1, 2, 4, 3, 4, 1, 5, 3, 4, 3, 2, 1, 6, 1, 4, 4, 4, 1, 5, 5, 5, 1, 4, 5, 3, 3, 1, 6, 1, 1, 2, 2, 2, 5, 4, 6, 6, 2, 2, 4, 4, 4, 4, 4, 4, 2, 1, 1, 2, 5, 6, 6, 6, 3, 4, 3, 5, 5, 2, 6, 5, 3, 1, 1, 2, 4, 1, 1, 6, 3, 5, 4, 6, 2, 1, 4, 3, 1, 5, 4, 5, 4, 4, 4, 6, 2, 6, 5, 6, 2, 4, 5, 5, 5, 5, 6, 3, 5, 1, 2, 1, 5, 5, 1, 1, 5, 4, 4, 5, 2, 1, 3, 5, 5, 1, 4, 1, 6, 2, 6, 1, 6, 4, 6, 4, 3, 5, 6, 2, 6, 1, 2, 5, 6, 2, 6, 4, 6, 3, 2, 1, 3, 5, 5, 2, 5, 2, 2, 5, 4, 2, 6, 3, 6, 5, 1, 2, 4, 1, 3, 4, 1, 5, 3, 6, 1, 2, 4, 6, 4, 6, 6, 1, 5, 4, 2, 4, 6, 4, 2, 4, 5, 2, 1, 4, 1, 1, 5, 4, 1, 2, 2, 2, 6, 4, 2, 6, 5, 5, 5, 2, 5, 4, 2, 3, 2, 4, 6, 2, 1, 2, 5, 6, 3, 6, 3, 3, 6, 2, 1, 1, 3, 2, 2, 3, 5, 3, 2, 4, 2, 1, 5, 1, 4, 1, 3, 6, 5, 2, 2, 5, 4, 1, 4, 6, 6, 1, 2, 5, 2, 3, 5, 5, 4, 1, 1, 3, 4, 3, 6, 6, 3, 5, 6, 1, 6, 2, 6, 4, 4, 2, 3, 1, 2, 1, 1, 1, 1, 3, 6, 3, 5, 5, 1, 3, 6, 2, 5, 3, 4, 5, 2, 6, 4, 1, 6, 3, 3, 6, 1, 1, 2, 3, 2, 3, 3, 2, 4, 4, 4, 4, 6, 2, 2, 1, 4, 1, 3, 3, 4, 6, 1, 5, 6, 5, 6, 6, 2, 3, 6, 2, 3, 1, 5, 4, 4, 2, 5, 1, 5, 3, 4, 5, 4, 6, 5, 1, 6, 1, 4, 3, 1, 4, 2, 1, 2, 1, 1, 4, 4, 6, 5, 6, 6, 4, 4, 3, 5, 3, 4, 4, 5, 1, 2, 2, 6, 6, 3, 6, 1, 6, 3, 2, 4, 4, 3, 6, 5, 3, 3, 2, 2, 2, 2, 2, 5, 5, 5, 4, 1, 2, 1, 5, 3, 2, 1, 3, 2, 3, 2, 2, 3, 5, 4, 6, 2, 6, 6, 1, 2, 2, 3, 3, 3, 4, 5, 2, 3, 3, 5, 4, 5, 6, 3, 1, 1, 3, 4, 2, 6, 5, 4, 2, 4, 1, 2, 6, 6, 1, 6, 1, 3, 3, 4, 6, 1, 3, 1, 3, 5, 6, 1, 4, 5, 3, 5, 6, 6, 2, 1, 5, 1, 4, 1, 4, 4, 2, 3, 4, 3, 2, 4, 5, 5, 2, 4, 5, 4, 5, 2, 3, 5, 2, 6, 4, 5, 4, 3, 4, 5, 3, 3, 5, 1, 3, 2, 4, 5, 5, 1, 1, 6, 5, 6, 5, 6, 4, 3, 4, 3, 4, 6, 1, 6, 6, 4, 5, 3, 6, 2, 2, 3, 4, 1, 3, 1, 2, 1, 5, 6, 1, 6, 6, 6, 6, 5, 6, 3, 1, 3, 5, 5, 2, 6, 5, 1, 4, 3, 4, 4, 4, 5, 6, 2, 5, 2, 2, 1, 3, 1, 1, 3, 1, 1, 3, 6, 5, 2, 2, 6, 4, 1, 4, 6, 6, 3, 1, 4, 5, 5, 1, 3, 4, 6, 5, 2, 2, 1, 3, 4, 1, 4, 1, 1, 5, 3, 6, 3, 5, 2, 2, 2, 3, 6, 2, 2, 3, 2, 5, 1, 1, 6, 4, 4, 5, 2, 6, 1, 2, 2, 4, 2, 6, 5, 3, 4, 1, 3, 1, 5, 4, 2, 1, 6, 2, 3, 2, 4, 5, 1, 5, 5, 6, 2, 2, 5, 3, 1, 5, 4, 3, 3, 6, 2, 1, 2, 6, 1, 5, 6, 6, 2, 2, 1, 2, 3, 3, 4, 1, 1, 5, 5, 5, 5, 1, 6, 3, 3, 1, 1, 1, 3, 3, 1, 5, 4, 3, 4, 4, 1, 3, 4, 3, 4, 4, 5, 6, 1, 2, 1, 1, 6, 6, 6, 4, 6, 6, 1, 3, 6, 2, 4, 2, 5, 4, 6, 2, 6, 3, 5, 1, 5, 3, 3, 3, 1, 1, 3, 1, 3, 3, 2, 3, 3, 1, 1, 3, 6, 1, 5, 5, 2, 3, 1, 6, 1, 1, 2, 6, 4, 1, 1, 2, 3, 4, 5, 4, 4, 1, 4, 1, 3, 6, 3, 5, 6, 4, 1, 6, 5, 6, 5, 6, 2, 6, 6, 3, 6, 1, 3, 3, 1, 3, 5, 4, 6, 3, 1, 4, 3, 5, 4, 6, 4, 1, 5, 4, 5, 5, 3, 3, 5, 2, 3, 1, 1, 3, 3, 1, 4, 5, 3, 5, 1, 2, 2, 1, 4, 3, 4, 1, 1, 2, 6, 5, 2, 4, 2, 6, 3, 5, 3, 2, 1, 5, 2, 1, 1, 5, 1, 4, 3, 4, 2, 4, 5, 4, 4, 3, 6, 2, 3, 1, 3, 3, 5, 5, 6, 1, 5, 3, 5, 1, 4, 6, 5, 6, 6, 6, 4, 1, 4, 1, 4, 5, 5, 3, 3, 3, 5, 3, 4, 1, 3, 1, 4, 1, 5, 3, 2, 3, 6, 1, 4, 4, 6, 3, 3, 6, 2, 1, 6, 5, 1, 4, 4, 5, 1, 6, 2, 5, 2, 5, 6, 5, 5, 3, 6, 3, 6, 1, 6, 6, 1, 3, 3, 1, 6, 5, 6, 1, 5, 6, 6, 6, 4, 3, 5, 4, 3, 6, 3, 5, 4, 3, 3, 3, 6, 3, 6, 5, 3, 6, 5, 4, 2, 1, 4, 1, 5, 4, 2, 4, 3, 1, 4, 1, 4, 2, 5, 1, 1, 1, 5, 5, 4, 2, 2, 3, 4, 1, 2, 1, 6, 6, 4, 2, 6, 2, 3, 5, 5, 5, 3, 2, 5, 6, 3, 3, 2, 1, 3, 2, 1, 2, 1, 4, 3, 2, 1, 1, 3, 2, 2, 2, 1, 6, 4, 6, 2, 6, 4, 6, 4, 6, 2, 3, 6, 4, 6, 1, 4, 2, 3, 5, 3, 4, 3, 6, 5, 3, 1, 2, 4, 2, 4, 4, 2, 1, 4, 3, 1, 2, 3, 5, 1, 5, 1, 1, 2, 1, 1, 6, 2, 3, 5, 5, 6, 2, 5, 5, 5, 5, 6, 3, 1, 3, 1, 2, 4, 4, 5, 4, 5, 1, 3, 6, 5, 4, 6, 1, 4, 1, 1, 5, 4, 5, 3, 4, 1, 2, 2, 5, 6, 2, 1, 1, 5, 1, 3, 2, 5, 1, 6, 3, 2, 2, 3, 6, 5, 2, 1, 2, 2, 1, 1, 6, 6, 4, 3, 6, 5, 4, 5, 5, 6, 6, 5, 5, 1, 1, 1, 5, 2, 6, 2, 3, 2, 4, 3, 1, 6, 3, 3, 2, 4, 3, 1, 3, 6, 3, 3, 5, 1, 1, 3, 6, 1, 1, 4, 1, 2, 4, 6, 4, 4, 1, 1, 5, 5, 3, 5, 4, 6, 1, 5, 3, 4, 6, 5, 4, 2, 1, 2, 2, 2, 4, 1, 2, 4, 5, 3, 6, 2, 2, 3, 5, 2, 3, 4, 6, 6, 3, 4, 5, 4, 3, 1, 2, 2, 6, 5, 3, 1, 6, 5, 2, 3, 5, 4, 1, 4, 6, 6, 5, 2, 3, 4, 3, 6, 2, 3, 5, 5, 1, 4, 2, 3, 5, 3, 5, 4, 2, 1, 4, 1, 5, 6, 3, 4, 4, 3, 2, 4, 3, 1, 5, 5, 5, 1, 4, 6, 4, 3, 5, 5, 6, 1, 1, 4, 3, 5, 2, 5, 6, 6, 5, 5, 5, 1, 3, 3, 4, 4, 6, 6, 4, 4, 5, 2, 5, 3, 2, 3, 5, 6, 1, 5, 6, 1, 3, 3, 6, 4, 1, 6, 3, 5, 5, 2, 6, 1, 4, 3, 5, 3, 3, 3, 1, 1, 5, 5, 3, 1, 1, 2, 1, 1, 6, 6, 2, 3, 3, 2, 6, 4, 2, 3, 3, 6, 4, 2, 1, 2, 5, 6, 5, 1, 2, 5, 2, 1, 4, 4, 1, 4, 6, 1, 5, 6, 1, 1, 2, 3, 2, 2, 1, 3, 4, 3, 3, 2, 5, 3, 3, 3, 3, 2, 4, 4, 6, 5, 5, 3, 2, 5, 1, 1, 6, 6, 1, 6, 6, 2, 3, 1, 3, 3, 4, 6, 6, 1, 2, 4, 4, 5, 6, 6, 6, 3, 4, 6, 1, 2, 3, 3, 1, 3, 4, 6, 2, 4, 6, 1, 5, 3, 2, 2, 5, 6, 2, 4, 6, 3, 1, 4, 1, 1, 3, 1, 3, 1, 6, 4, 2, 2, 6, 3, 4, 4, 2, 6, 1, 2, 1, 6, 4, 3, 2, 3, 2, 3, 1, 2, 5, 2, 5, 6, 2, 2, 6, 5, 2, 5, 2, 4, 1, 2, 6, 5, 6, 2, 4, 6, 3, 5, 6, 1, 1, 1, 3, 3, 4, 4, 4, 2, 5, 3, 2, 6, 5, 2, 5, 6, 1, 6, 3, 1, 2, 3, 5, 1, 4, 3, 1, 1, 2, 1, 1, 2, 1, 4, 5, 4, 1, 2, 6, 5, 5, 2, 5, 3, 3, 3, 2, 3, 3, 5, 4, 4, 1, 3, 5, 5, 6, 5, 5, 1, 5, 6, 3, 6, 4, 1, 4, 5, 3, 3, 4, 1, 4, 2, 4, 1, 5, 6, 4, 1, 4, 1, 5, 5, 3, 4, 4, 2, 2, 3, 3, 1, 3, 5, 1, 6, 5, 4, 5, 2, 6, 2, 2, 4, 4, 5, 5, 2, 4, 2, 3, 2, 2, 2, 1, 5, 5, 4, 6, 1, 1, 2, 2, 3, 1, 2, 3, 6, 5, 1, 1, 5, 2, 2, 3, 5, 1, 1, 1, 5, 3, 3, 1, 4, 5, 1, 3, 4, 5, 2, 4, 5, 4, 6, 2, 5, 1, 4, 4, 6, 4, 4, 4, 5, 6, 1, 4, 6, 1, 4, 5, 4, 1, 5, 1, 5, 6, 3, 3, 5, 5, 1, 4, 3, 6, 5, 1, 6, 2, 4, 5, 6, 2, 3, 5, 1, 3, 2, 1, 4, 6, 5, 1, 6, 4, 2, 5, 3, 5, 1, 1, 3, 1, 5, 6, 6, 3, 1, 6, 5, 4, 5, 5, 6, 2, 3, 6, 4, 4, 6, 1, 4, 5, 2, 3, 2, 3, 2, 4, 1, 2, 5, 4, 3, 4, 4, 3, 6, 4, 3, 5, 2, 1, 3, 1, 2, 6, 6, 6, 3, 6, 1, 1, 4, 2, 3, 5, 5, 4, 3, 6, 6, 2, 4, 3, 5, 1, 5, 5, 4, 2, 3, 6, 3, 6, 6, 4, 5, 6, 4, 2, 5, 4, 2, 2, 6, 5, 1, 5, 3, 3, 4, 2, 5, 2, 5, 3, 2, 4, 1, 6, 5, 4, 5, 1, 4, 5, 5, 2, 4, 2, 3, 2, 6, 5, 4, 5, 3, 4, 3, 5, 1, 1, 1, 5, 2, 5, 2, 4, 2, 3, 3, 6, 6, 2, 6, 4, 6, 5, 5, 4, 6, 2, 6, 5, 6, 3, 4, 3, 1, 6, 1, 1, 1, 1, 6, 2, 6, 2, 6, 1, 4, 2, 1, 4, 4, 1, 1, 4, 5, 5, 2, 5, 1, 1, 3, 1, 3, 6, 3, 4, 6, 3, 5, 1, 4, 4, 3, 3, 6, 2, 4, 3, 3, 5, 6, 1, 5, 1, 5, 4, 6, 6, 2, 6, 6, 4, 6, 3, 4, 2, 6, 4, 5, 4, 5, 3, 2, 1, 6, 1, 2, 3, 4, 5, 1, 4, 5, 6, 4, 4, 3, 4, 3, 4, 3, 2, 2, 3, 5, 6, 5, 4, 4, 3, 2, 2, 6, 4, 2, 5, 5, 3, 2, 3, 1, 3, 6, 6, 2, 4, 3, 5, 1, 6, 3, 3, 1, 5, 6, 6, 4, 4, 4, 2, 1, 6, 4, 6, 3, 5, 5, 2, 2, 6, 4, 3, 3, 4, 3, 4, 1, 5, 3, 1, 5, 5, 4, 5, 3, 3, 5, 1, 1, 2, 3, 1, 1, 6, 1, 4, 5, 5, 5, 6, 5, 3, 3, 1, 6, 5, 5, 6, 4, 1, 1, 2, 6, 4, 1, 3, 1, 5, 3, 1, 1, 5, 2, 1, 5, 2, 4, 3, 1, 3, 3, 6, 5, 5, 6, 5, 4, 5, 4, 2, 6, 4, 4, 5, 2, 5, 1, 2, 3, 4, 3, 4, 3, 4, 4, 1, 5, 2, 3, 6, 5, 5, 5, 4, 4, 5, 2, 1, 3, 6, 2, 2, 4, 6, 1, 5, 4, 1, 1, 1, 5, 3, 4, 1, 6, 2, 1, 5, 4, 4, 4, 2, 2, 3, 5, 6, 1, 6, 6, 4, 5, 2, 5, 2, 1, 5, 1, 5, 6, 1, 5, 5, 3, 2, 5, 2, 4, 6, 1, 1, 4, 4, 2, 6, 6, 6, 5, 1, 6, 5, 4, 5, 6, 3, 6, 1, 2, 6, 5, 2, 1, 4, 6, 3, 5, 5, 5, 2, 5, 5, 3, 2, 2, 4, 1, 2, 4, 5, 3, 4, 3, 6, 2, 3, 2, 1, 4, 3, 1, 3, 4, 1, 6, 4, 4, 4, 2, 2, 6, 6, 6, 3, 1, 2, 6, 2, 4, 4, 1, 6, 1, 4, 6, 3, 6, 2, 3, 4, 4, 4, 6, 2, 5, 5, 6, 2, 3, 1, 4, 3, 1, 4, 5, 1, 6, 5, 3, 4, 2, 3, 3, 3, 1, 3, 5, 1, 4, 2, 4, 2, 5, 3, 4, 4, 2, 3, 6, 4, 3, 3, 6, 3, 1, 4, 4, 6, 2, 6, 3, 4, 3, 6, 6, 3, 2, 4, 4, 6, 6, 1, 1, 5, 4, 4, 2, 5, 6, 1, 2, 2, 4, 2, 5, 4, 6, 2, 3, 1, 2, 6, 5, 5, 5, 4, 2, 1, 2, 5, 6, 1, 6, 6, 5, 3, 3, 1, 1, 3, 1, 3, 5, 5, 4, 3, 2, 4, 5, 5, 4, 1, 4, 3, 6, 2, 6, 1, 2, 2, 6, 1, 3, 6, 1, 2, 2, 3, 2, 3, 5, 3, 6, 4, 1, 4, 6, 2, 1, 5, 6, 5, 5, 3, 1, 4, 5, 1, 5, 6, 2, 5, 1, 5, 4, 1, 6, 6, 4, 1, 3, 3, 3, 3, 6, 3, 6, 6, 5, 1, 4, 5, 5, 2, 1, 6, 6, 5, 6, 4, 5, 2, 3, 6, 6, 1, 6, 6, 1, 4, 6, 4, 1, 3, 6, 6, 5, 6, 5, 4, 6, 2, 2, 5, 4, 3, 5

Gimme a sec…. counting…

Phew!

Ones:  1652 or 16.52%
Twos:  1674 or 16.74%
Threes:  1687 or 16.87%
Fours:  1623 or 16.23%
Fives:    1693 or 16.93%
Sixes:    1671 or 16.71%

Since “perfect” would be 16.6666667% each, the “worst” result was the fours and that only delivered 44 “too few” fours than it should have - and that is out of ten thousand rolls.

Good enough for me!  8-)

This method starting sorting in my game.  Testing out if it sorts here…
Rolling 30d6:
(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6)

Yeah so the dice roller sorts now.  Can anyone explain how I use it now with the rolls sorted?

The new dice roller should be much eacsier for your games. Now you can specify multiple “groups” of dice to roll at the same time.

For instance…

dice 3d6 1d6 1d6 2d6 3d6
Rolling 3d6 1d6 1d6 2d6 3d6:
(2, 4, 5)  (5)  (4)  (2, 5)  (3, 4, 6)

Why is this easier? You can do a battle like so…

Attackers: 5 inf, 3 arm
5d6 @ 1, 3d6 @ 3
dice 5d6 3d6
Rolling 5d6 3d6:
(2, 3, 3, 4, 4)  (3, 3, 6)

Defenders: 4 inf, 1 ftr
4d6 @ 2, 1d6 @ 4
dice 4d6 1d6
Rolling 4d6 1d6:
(2, 4, 5, 5)  (2)

Since they are sorted it’s easy to find the hits.