OK, I've done some really interesting investigation the runflags issue. Chris Foster was very inspiring with his test program and span idea (which we've been debating versus Chris Kulla's similar "index" idea). But I felt there were two problems with Chris F's program in terms of making a final decision: (1) his test loops did not actually resemble the inside of our shadeops, particularly in our use of VaryingRef and the integer ops it uses to control the stepping, which also can't be known at compile time; (2) he tested a few different runflag scenarios (all-on, every-other-on, and random), but I didn't feel like we really knew what would be typical runflags "in the wild".

So, the first step was that I modified the shading system to check after every instruction, and dump the runflags once every <very large prime> instructions (not perfect, but supposed to make it so it's not likely to keep sampling in the same shader or at the same instruction). I did this for a production test frame that we are using as a benchmark, so it's "real" full production shaders on show assets.

I ended up sampling 4508 run states, which I then collated, sorted, and counted, and ended up with 198 unique run states (remember, to keep the data sets reasonable, these are *sampled*, not a comprehensive set of all run states it ever saw).

Below is the list, one runflag per "line", sorted from most-frequently-seen to least-frequently-seen. The first column is the number of times that run state was found. I'm putting it inline below as well as attaching it (to preserve the original line breaks that separate run states).

The "all on" sets are generally from batches of primary rays that coherently hit objects. The few "big spans of 1" ones are primaries from pixels that were split between more than one object, and conditional states from primaries. The vast number of very sparse 1's in seas of 0's are from secondary rays, which our renderer creates batches from, though it can only shade hits together if they hit objects with the same shaders. The most common run state is a single "1", which is a from a secondary ray batch of which only one ray hit a particular object. Our renderer adjusts the offsets so that sparse secondary batches always begin and end with a point "on".

Enjoy. In follow-up emails, I'll discuss what I did with those runflags next.

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count run state
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4285 rf 1
9 rf 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
5 rf 1 0 0 1
4 rf 1 1
3 rf 1 0 0 0 1
3 rf 1 0 0 0 0 0 0 0 1
2 rf 1 0 1
2 rf 1 0 0 1 0 0 0 0 0 1
2 rf 1 0 0 0 0 1
2 rf 1 0 0 0 0 0 1
2 rf 1 0 0 0 0 0 0 0 0 0 0 1
2 rf 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
2 rf 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 rf 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 rf 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 rf 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 rf 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 rf 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1
1 rf 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 rf 1 1 1 1 1 1 1 1
1 rf 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1
1 rf 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1
1 rf 1 1 1 0 1
1 rf 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1
1 rf 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1
1 rf 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1
1 rf 1 1 1
1 rf 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 rf 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1
1 rf 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 1
1 rf 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1
1 rf 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1
1 rf 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 1
1 rf 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1
1 rf 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1
1 rf 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 1 0 0 1 0 0 0 0 1
1 rf 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1
1 rf 1 1 0 0 1
1 rf 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1
1 rf 1 1 0 0 0 1
1 rf 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1
1 rf 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1
1 rf 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1
1 rf 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1
1 rf 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1
1 rf 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1
1 rf 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1
1 rf 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1
1 rf 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1
1 rf 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1
1 rf 1 0 1 1 0 0 0 0 0 0 1
1 rf 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
1 rf 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1
1 rf 1 0 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1
1 rf 1 0 1 0 1 0 0 1
1 rf 1 0 1 0 1 0 0 0 0 0 1 0 1 1
1 rf 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1
1 rf 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 1 0 0 0 0 1
1 rf 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1
1 rf 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
1 rf 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1
1 rf 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1
1 rf 1 0 0 1 1 0 0 0 0 0 0 0 1
1 rf 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1
1 rf 1 0 0 1 1
1 rf 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1
1 rf 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1
1 rf 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1
1 rf 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1
1 rf 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
1 rf 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1
1 rf 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1
1 rf 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 1
1 rf 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1
1 rf 1 0 0 0 1 1
1 rf 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1
1 rf 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1
1 rf 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0
1 rf 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 1 1 1
1 rf 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1
1 rf 1 0 0 0 0 1 0 1 0 0 1
1 rf 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1
1 rf 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1
1 rf 1 0 0 0 0 1 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1
1 rf 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1
1 rf 1 0 0 0 0 0 1 0 1
1 rf 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1
1 rf 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1
1 rf 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1
1 rf 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 1 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
1 rf 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1
1 rf 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
1 rf 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1
1 rf 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
1 rf 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
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Larry Gritz
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