# Gate Q, item agg-report-b: policy **agg** vs Taylor's full plain policy, replica seeds 11024..12047 Credit: the replica, the filter and the tables are by Taylor (gtmcknight), [amm-sim @ 4812a638 research/solved](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/README.md). ## Result Paired **agg minus full**, seeds 11024..12047, every seed run once, both arms on their own trajectories: | n | mean_diff | se (sample sd / sqrt n) | sample sd | worst5 (seed, diff) | |---:|---:|---:|---:|---| | 1024 | -0.024294 | 0.013577 | 0.434458 | (11763, -1.515478), (11694, -1.467420), (11892, -1.340708), (11950, -1.236972), (11492, -1.213826) | | arm | mean edge | |---|---:| | full: `real.RealPolicy(real.load('pol_mid.json'), {'soft': 1})` | 532.794567 | | agg: port-2 `PortReal(real.load('pol_mid.json'), {'soft': 1})` | 532.770273 | n completed: **1024 of 1024**. No seed is missing or filled in. No seed gave a zero difference. Positive tail: the 5 largest differences were 11778 +4.267334, 11701 +2.384225, 11211 +2.058492, 11730 +1.295152, 11284 +1.269329. The filter change alone (one truncation after summing the silent steps' variance, instead of one truncation per silent step) costs **-0.0243 edge (se 0.0136)** on these seeds. That is about 1.8 se below zero. Seconds per seed pair: **0.186 s** of single-core time (both arms run one after the other in one worker, mean over the 1024 seeds). Wall time for all 1024 pairs was 13.5 s with 16 worker processes (32-core machine). ### Cross-check against port-2 (not part of the assigned seeds) I also ran the same script on seeds 10000..11023. Over all 2048 holdout seeds 10000..12047, the agg arm averages **532.351218**. Port-2 published exactly this number as its "Full-table mean" with the aggregated-silent filter on report seeds 10000..12047. So this run reproduces port-2's PortReal. Over those 2048 seeds the full arm averages 532.385687; Taylor's README gives 532.39 for Gaussian filter + plain tables. The paired agg minus full difference on 10000..11023 alone was -0.044645 (se 0.013694), and over all 2048 it was -0.034469 (se 0.009642). The assigned figures in the table above use only 11024..12047. ## Gate P Unmodified `python3 -I gates.py` in `research/solved` at commit 4812a6382311624e1506aca131ca35c378f930d9: ``` seed perfect-info gaussian+plain gaussian+qm lattice+qm 10000 448.261189 443.455598 443.522608 443.663520 10001 576.779199 571.463409 571.623551 571.977293 10002 531.886497 525.168028 525.865859 526.411631 ``` The gaussian+plain column (443.455598 / 571.463409 / 525.168028) matches the README's gate block to the digit, and so do the other three columns. The full arm of my runner gives the same three values on seeds 10000..10002: 443.4555975940445, 571.4634094447646, 525.1680277851867. ## Policies - **full**: Taylor's `real.RealPolicy` with the full `pol_mid.json` and `{'soft': 1}`, run with `replica2.run(seed, policy)['edge']`. It truncates the belief once per fully silent step, capped at 12 (`for _ in range(min(dt - 1, 12))` in real.py). - **agg**: the `PortReal` class and the `real.trunc` hook from `reference.py` in the [port-2 artifact](https://api.imd.fun/artifacts/e8c967d6358da0fd53117891357f19a1d684225bd71a5e302b6e299c85f1286c). They are copied byte for byte: `reference.py` was extracted verbatim from the artifact's code block, and the runner `exec`s the slice from `_ORIGINAL_TRUNC=real.trunc` up to `SOURCE=` together with `class PortReal`. `PortReal` sets the silent count to min(dt-1, 12). The hook then passes through the first k-1 per-step truncations, so `real.py` still adds SIGMA^2 each time, and applies one real truncation on the last. The tables are the **full** `pol_mid.json`, soft=1. The compressed-table parts of `reference.py` (`CompressedReal`, `lookup`, and reading `Strategy.sol`) are **not** used. The only difference between the arms is the filter. - The hook only acts while `_SILENT_LEFT` is non-zero, and only `PortReal` sets it, so the full arm in the same process runs Taylor's original `trunc`. The Gate P match above confirms this. - Net2 (the fixed-net 2-pass policy) is described in the batch brief, but it is not this item's policy ("Your item: ... policy agg"). It was not run here. ## Files and sha256 | file | sha256 | |---|---| | amm-sim research/solved/real.py | 1305b5333731c046c3e6736cc2578eff4635c88132a39c22f5780d78aef2c81e | | amm-sim research/solved/replica2.py | 6e37b4e61e1ffa5ffb1e43912ddb8659105989aa986eb48fcd1d7608f8dca685 | | amm-sim research/solved/evalpol.py (imported by real.py: `load`, `DPPolicy`) | 6e67667bfed7798bdd3384652a6efc6ba0b1fce653740d0f9af2bcbcb8e6a27c | | amm-sim research/solved/pol_mid.json | efbb5ee102db4d312f64565d9bf7232b6becbe02b624164f744a402bbbf2983b | | amm-sim research/solved/gates.py (Gate P) | 603280c1f595ca163ffaf2ba1ebdc7945fdb08dabae67fc53c922d39e1cce604 | | amm-sim research/solved/latt.py (Gate P only) | 925c0fe996b19fd51fb79a85d5e4dba4bc2f5453d0a156cc1e480f65a6a00cc8 | | amm-sim research/solved/qm_k1e-5.json (Gate P only) | 5ff53e42ca87390e5f65d1caa3f7a480e67a8212fb0670274dfd562b05ba1afd | | amm-sim research/solved/calib_out_2048.json (imported path only, not read by this runner) | fdf24c7aa2b604d770336a5783276da8ed4d50bca9dbcc02e98b4da58f608d26 | | port-2 artifact e8c967d6... (whole document) | e8c967d6358da0fd53117891357f19a1d684225bd71a5e302b6e299c85f1286c | | reference.py extracted verbatim from that artifact | 6e617a1700fac6214005277e21fc709fff1418b50f51b88a2caff3876311699c | | agg.py (runner, below) | 51fb9c15eaef000f2c509288e1622bf44048ddbaed13fb3adde87171651b9827 | | main.csv (raw output, includes a per-seed seconds column) | 8c9e46c5d54aa5fc1978708dc21d7616781f28743febd2f9df9f84688d689d2d | Python: system `python3 -I` (3.12.3, no packages), multiprocessing pool of 16. Runner: `python3 -I agg.py 11024 12047 main.csv`. It works in chunks of 64 seeds, appends after each chunk and resumes from the CSV. ### agg.py ```python """Gate Q, item agg-report-b: port-2 aggregated-silent filter (PortReal, full pol_mid.json, soft=1) paired against Taylor's RealPolicy (full pol_mid.json, soft=1) on replica seeds. usage: python3 -I agg.py (resumes from csv; chunks of 64)""" import os, sys, csv, time, multiprocessing HERE = os.path.dirname(os.path.abspath(__file__)) SOLVED = os.path.join(HERE, '..', 'amm-sim', 'research', 'solved') sys.path.insert(0, SOLVED) import real, replica2 # Verbatim port-2 code: the trunc hook and PortReal, sliced from reference_port2.py SRC = open(os.path.join(HERE, 'reference_port2.py')).read() hook = SRC[SRC.index('_ORIGINAL_TRUNC=real.trunc'):SRC.index('SOURCE=')] cls = SRC[SRC.index('class PortReal'):SRC.index('class CompressedReal')] exec(compile(hook + cls, 'reference_port2.py[slice]', 'exec'), globals()) POL = os.path.join(SOLVED, 'pol_mid.json') T = real.load(POL) def worker(seed): t0 = time.time() full = replica2.run(seed, real.RealPolicy(T, {'soft': 1}))['edge'] agg = replica2.run(seed, PortReal(T, {'soft': 1}))['edge'] return seed, full, agg, time.time() - t0 if __name__ == '__main__': a, b, out = int(sys.argv[1]), int(sys.argv[2]), sys.argv[3] done = set() if os.path.exists(out): with open(out) as f: done = {int(r['seed']) for r in csv.DictReader(f)} else: with open(out, 'w') as f: f.write('seed,full,policy,secs\n') todo = [s for s in range(a, b + 1) if s not in done] with multiprocessing.Pool(16) as pool: for i in range(0, len(todo), 64): chunk = todo[i:i + 64]; t0 = time.time() res = pool.map(worker, chunk, chunksize=1) with open(out, 'a') as f: for s, fu, ag, sec in res: f.write(f'{s},{fu:.6f},{ag:.6f},{sec:.3f}\n') print('chunk', chunk[0], chunk[-1], f'{time.time()-t0:.1f}s', flush=True) ``` ## Per-seed CSV (seed, full, policy), 11024..12047 Edges are rounded to 6 decimals; diff = policy - full. ```csv seed,full,policy 11024,485.865446,485.876180 11025,811.119420,811.008709 11026,425.080870,424.944284 11027,619.258263,619.354910 11028,595.337843,595.596913 11029,472.289413,472.778575 11030,713.657807,713.465412 11031,573.953606,574.401400 11032,419.726119,420.413642 11033,508.838822,508.525902 11034,633.235752,633.174170 11035,704.655880,704.417643 11036,452.905717,453.511266 11037,488.546475,488.778485 11038,578.175406,577.409512 11039,533.270919,532.780769 11040,401.680560,400.929707 11041,456.197073,455.785008 11042,737.294702,737.068858 11043,385.844645,385.027967 11044,599.157616,599.111185 11045,609.757499,609.663625 11046,593.543065,593.387833 11047,480.791878,480.465379 11048,504.028513,503.577808 11049,590.459804,590.198521 11050,547.317690,548.037957 11051,571.044764,570.870811 11052,443.542282,443.327299 11053,709.244458,709.143811 11054,580.833525,580.536866 11055,612.162791,612.819388 11056,548.192211,548.144012 11057,652.415002,652.330573 11058,440.366386,440.195714 11059,673.420304,673.979254 11060,564.654754,564.349641 11061,674.294600,673.773955 11062,714.157140,713.865389 11063,504.092819,504.413622 11064,557.886650,557.795703 11065,604.901708,605.458938 11066,541.844501,542.210976 11067,447.435177,447.232817 11068,438.544964,438.677247 11069,495.643261,495.752201 11070,475.958533,476.044207 11071,647.181805,647.470512 11072,509.575416,509.241862 11073,708.438198,708.328660 11074,539.084339,538.407493 11075,412.606545,412.343124 11076,727.272094,727.263743 11077,814.221280,814.588726 11078,545.029795,545.269297 11079,425.062898,425.049743 11080,444.396766,443.749479 11081,436.410341,436.377949 11082,610.133129,610.605053 11083,594.395164,594.756127 11084,480.167358,480.043220 11085,548.841197,548.457959 11086,628.740221,628.366881 11087,537.258448,537.056827 11088,510.133399,511.087020 11089,692.120133,692.264910 11090,463.505400,463.304453 11091,575.438461,574.742739 11092,468.203722,468.274800 11093,417.961083,417.788399 11094,600.925080,600.956922 11095,610.760961,610.239948 11096,459.364510,459.512396 11097,506.607333,506.239569 11098,690.948805,691.228407 11099,458.687270,459.159981 11100,505.859747,505.955688 11101,402.107942,402.815376 11102,532.880166,532.686408 11103,444.496256,444.138246 11104,652.869317,652.607112 11105,427.975890,427.942369 11106,444.715371,444.277817 11107,395.004605,395.138951 11108,645.042555,644.381421 11109,514.081083,514.487902 11110,565.286728,564.794397 11111,459.244348,459.285923 11112,491.649626,491.718026 11113,702.890964,702.274610 11114,644.435279,644.692813 11115,580.110054,580.478514 11116,610.740738,610.496836 11117,546.998583,547.154046 11118,510.934455,511.633501 11119,469.778344,469.664475 11120,581.308891,581.201108 11121,567.016548,566.270584 11122,682.829993,682.539829 11123,715.170007,715.244035 11124,387.904996,387.553740 11125,414.313812,413.649978 11126,575.695747,575.471979 11127,536.510601,536.942392 11128,444.906475,444.833117 11129,518.850555,518.927092 11130,450.809378,450.023417 11131,670.610107,670.501884 11132,611.452958,611.422581 11133,596.801009,597.432814 11134,492.171750,491.718328 11135,554.393582,553.956941 11136,486.163811,486.741383 11137,645.902766,645.604070 11138,664.625085,664.743167 11139,355.936961,355.659148 11140,450.742633,450.636974 11141,569.362884,569.519351 11142,341.141406,341.656686 11143,462.522608,462.994329 11144,580.084219,580.555104 11145,482.663785,482.891902 11146,479.310308,478.928149 11147,387.230348,387.267855 11148,511.239427,511.251294 11149,584.180875,583.353080 11150,331.702865,331.810431 11151,567.331671,566.968655 11152,511.645029,511.598998 11153,375.331130,375.538317 11154,443.926363,443.388967 11155,370.444519,370.156444 11156,452.654681,452.424793 11157,509.668744,510.395382 11158,423.775886,423.547628 11159,593.429191,593.788114 11160,424.970366,424.947162 11161,597.138422,597.045217 11162,505.781452,505.586096 11163,656.953455,656.638065 11164,540.521342,540.706368 11165,630.975591,630.949050 11166,546.175533,546.666438 11167,560.445933,560.884922 11168,527.078848,526.926008 11169,592.246050,592.282396 11170,552.573866,552.164543 11171,511.900026,512.193503 11172,435.770094,435.729478 11173,476.795327,476.328555 11174,632.567676,632.347122 11175,395.508770,395.756760 11176,773.018124,772.856843 11177,480.210675,480.398014 11178,460.783220,460.774272 11179,535.628431,535.486504 11180,417.932245,417.589036 11181,438.586071,438.223647 11182,480.817622,480.081140 11183,399.135956,398.806549 11184,695.852014,696.103214 11185,595.163917,595.592758 11186,538.240471,538.440447 11187,584.486379,584.748697 11188,621.784766,621.600501 11189,416.476372,416.271476 11190,475.054996,475.152671 11191,725.152542,726.362469 11192,536.040307,535.535935 11193,560.912952,560.951044 11194,492.460081,492.264130 11195,530.931931,530.680342 11196,626.839844,626.735591 11197,507.614042,507.320400 11198,647.007987,647.442927 11199,508.534644,508.837676 11200,573.030852,572.041975 11201,531.695229,532.046618 11202,607.709341,607.748411 11203,557.382329,557.476781 11204,533.327536,532.994653 11205,609.064551,609.408265 11206,518.658691,517.769009 11207,599.885821,599.731545 11208,462.624952,463.401622 11209,710.028174,710.464499 11210,553.232159,552.853470 11211,612.913541,614.972033 11212,424.546867,424.638465 11213,610.344981,610.205664 11214,544.416582,544.867710 11215,441.644330,441.278420 11216,400.947786,400.950853 11217,593.886894,594.994038 11218,702.789198,702.363482 11219,503.415405,502.954113 11220,474.865899,475.105147 11221,515.108415,515.347055 11222,595.485745,595.808611 11223,528.923896,528.738473 11224,695.207846,694.414897 11225,709.445800,709.286797 11226,719.212077,719.150348 11227,440.105744,440.938945 11228,493.135314,493.443822 11229,647.576249,648.205000 11230,402.764796,402.464315 11231,536.268175,536.493280 11232,644.923125,645.547221 11233,565.877587,565.585289 11234,620.214835,620.064448 11235,497.772969,497.834209 11236,598.220840,598.336694 11237,523.577185,524.163894 11238,362.779147,362.695368 11239,570.260044,570.066716 11240,490.317634,490.499237 11241,539.085246,539.105368 11242,559.100051,559.130727 11243,533.391213,533.557442 11244,519.631165,519.586461 11245,629.469862,629.372417 11246,556.387444,556.122772 11247,533.538610,533.182598 11248,589.653707,589.535013 11249,534.676606,533.978193 11250,467.773876,467.249105 11251,425.115017,425.427304 11252,626.243829,626.132902 11253,621.048955,620.912816 11254,624.657367,624.841294 11255,505.288038,505.369088 11256,702.353989,703.233812 11257,402.025713,402.486868 11258,564.729723,564.757402 11259,415.555398,415.914832 11260,551.108530,550.671413 11261,413.770414,413.244674 11262,491.058145,491.356900 11263,490.321833,490.289265 11264,378.194349,378.375949 11265,418.341639,417.941509 11266,783.881313,784.263839 11267,576.756136,576.496011 11268,413.427903,413.484577 11269,362.863551,362.579089 11270,473.340955,473.754883 11271,471.119155,470.959030 11272,586.530970,586.604884 11273,526.446333,526.497774 11274,586.217804,585.989569 11275,421.769712,421.606523 11276,475.355070,475.984939 11277,720.349009,720.212916 11278,564.054265,564.147432 11279,450.794039,450.857710 11280,610.108140,609.097221 11281,565.008305,565.010332 11282,487.898884,487.865732 11283,465.368928,465.776884 11284,664.615495,665.884824 11285,656.565526,655.965087 11286,505.970599,506.358784 11287,541.797444,541.470025 11288,538.405013,537.433617 11289,495.617985,496.242437 11290,555.493836,555.306778 11291,420.050548,420.443279 11292,593.607491,593.954769 11293,431.023233,430.919861 11294,397.450276,397.685635 11295,404.254997,404.145515 11296,627.662777,627.882531 11297,515.067272,514.354199 11298,582.889294,583.475410 11299,493.667563,493.405681 11300,653.387162,653.445389 11301,510.206748,509.456179 11302,556.381808,556.244816 11303,661.180935,661.446978 11304,416.544221,416.577923 11305,628.864928,628.858965 11306,376.224258,376.431707 11307,433.445370,433.047240 11308,414.133004,414.205134 11309,470.763687,470.948736 11310,538.632744,538.715973 11311,574.152572,574.915527 11312,477.595110,477.729577 11313,613.313353,612.264092 11314,461.555231,461.436001 11315,627.951106,627.489274 11316,472.790977,473.086699 11317,513.432773,513.205905 11318,641.794289,641.368224 11319,578.378320,578.754779 11320,430.222360,430.259484 11321,524.131932,524.483186 11322,627.649177,628.241153 11323,689.400107,689.257798 11324,446.751208,446.793892 11325,626.622440,626.859314 11326,521.416857,521.734959 11327,541.727482,542.160924 11328,376.987419,377.252922 11329,606.968684,607.087932 11330,560.204493,560.052812 11331,391.873765,390.934226 11332,591.416057,591.862377 11333,646.004873,646.135604 11334,550.142772,550.169759 11335,497.438897,497.391192 11336,533.201756,533.148495 11337,496.989694,497.181340 11338,556.055759,555.541275 11339,413.618567,413.563451 11340,383.497371,383.822611 11341,534.009037,534.067900 11342,522.686596,523.102984 11343,589.365981,589.897065 11344,539.991290,540.371160 11345,632.226796,631.838335 11346,572.946393,573.050791 11347,637.261062,637.179050 11348,439.609700,439.259263 11349,495.094588,495.394009 11350,690.079073,689.885894 11351,444.430444,444.293678 11352,461.408374,461.776954 11353,588.199521,588.193233 11354,626.596322,626.188460 11355,549.966311,550.642793 11356,553.196721,552.860208 11357,533.272082,532.898046 11358,576.243596,576.316248 11359,699.535428,699.366765 11360,651.363351,651.587680 11361,429.518485,429.553946 11362,605.483448,605.011566 11363,393.254637,393.052546 11364,473.927279,473.525114 11365,511.630948,512.178330 11366,637.201370,637.041331 11367,489.215723,489.129139 11368,625.627583,624.621896 11369,450.128728,449.909155 11370,552.782182,552.570529 11371,544.864176,544.948528 11372,364.377155,364.660996 11373,582.063130,581.732918 11374,575.984308,575.747421 11375,454.979520,455.012376 11376,556.273719,556.524742 11377,504.125203,503.608871 11378,598.128302,598.000266 11379,538.123808,538.535576 11380,806.784945,806.897880 11381,444.694216,444.111364 11382,454.221369,453.993243 11383,683.422468,683.647509 11384,506.119231,505.834836 11385,486.803047,486.010498 11386,515.899035,515.404324 11387,796.760924,796.986221 11388,645.235272,644.780179 11389,332.330092,331.991587 11390,697.533104,697.287661 11391,360.790005,360.719215 11392,594.578307,594.555801 11393,468.882670,469.064620 11394,417.624161,417.347572 11395,634.323598,634.660035 11396,419.846607,419.518706 11397,440.637937,440.322670 11398,430.656294,430.792105 11399,539.844319,539.808931 11400,503.761786,504.100433 11401,349.193423,349.318971 11402,478.305497,478.346313 11403,584.870274,584.962366 11404,492.153475,492.127331 11405,531.042569,530.438676 11406,519.105675,519.596717 11407,526.015093,525.794097 11408,388.622428,388.218453 11409,539.861018,539.912949 11410,473.681479,473.024439 11411,558.102130,557.845802 11412,619.196094,618.558831 11413,507.875624,507.680053 11414,511.956399,511.534134 11415,498.445260,498.635182 11416,513.539105,512.989028 11417,615.595283,615.452241 11418,538.224036,538.393041 11419,532.506193,532.152004 11420,505.360635,505.221091 11421,465.110658,464.953441 11422,476.823134,476.807371 11423,330.506727,330.432937 11424,426.650292,426.399020 11425,559.751395,559.879872 11426,547.569333,547.626969 11427,482.192867,482.474920 11428,537.754975,537.842148 11429,501.752737,501.612754 11430,569.163820,568.771959 11431,539.403258,539.470906 11432,423.263591,423.425968 11433,417.822477,418.044701 11434,552.734145,552.330343 11435,485.384722,485.616245 11436,466.374529,466.539594 11437,604.863136,605.072681 11438,546.431616,546.630148 11439,467.290486,467.123204 11440,597.616381,597.955252 11441,568.654863,568.648296 11442,551.042122,551.214556 11443,509.260581,508.994665 11444,540.070479,539.852824 11445,475.830822,475.496232 11446,598.275034,598.457707 11447,368.053645,367.682679 11448,505.670728,505.889977 11449,430.796114,430.577729 11450,553.025727,552.951211 11451,611.010200,611.083719 11452,480.187408,480.102662 11453,485.254938,485.806252 11454,628.474463,627.977093 11455,788.762316,788.834855 11456,435.851758,435.565504 11457,461.644276,461.715011 11458,589.962497,590.497025 11459,384.913391,385.177679 11460,422.975221,423.654136 11461,414.112743,413.873750 11462,578.143212,577.896309 11463,512.220854,512.235001 11464,604.617332,605.410434 11465,492.200128,492.134808 11466,632.953023,632.645823 11467,605.306172,604.855342 11468,579.320509,579.804346 11469,583.214485,583.337133 11470,459.622875,459.101465 11471,476.348615,476.195451 11472,461.691954,461.493639 11473,423.822638,423.516899 11474,562.809280,563.116924 11475,589.709497,589.276987 11476,545.849540,545.533853 11477,584.668653,584.656478 11478,579.998649,579.363836 11479,554.847152,555.118728 11480,562.969635,563.148649 11481,555.084102,555.136179 11482,456.971784,456.906213 11483,747.469917,746.713637 11484,574.599513,574.791948 11485,491.072722,490.969194 11486,675.476187,675.238177 11487,677.450086,677.584709 11488,505.858854,505.787046 11489,389.110161,388.716865 11490,640.507482,641.002384 11491,426.170750,426.076608 11492,637.517896,636.304070 11493,627.186238,627.193240 11494,506.126689,505.953005 11495,396.286683,396.828777 11496,427.461138,427.524847 11497,477.460871,477.504664 11498,607.368593,607.038915 11499,552.524994,552.563930 11500,635.084712,635.603023 11501,438.166469,438.428459 11502,359.818884,359.163110 11503,476.578856,477.221707 11504,672.295293,671.479741 11505,603.162283,602.804266 11506,619.939747,619.106207 11507,615.995108,615.765204 11508,358.906481,359.222406 11509,595.197646,594.923929 11510,560.802842,560.226317 11511,549.103753,549.342048 11512,348.868661,349.063115 11513,440.783210,440.501280 11514,429.058878,429.115873 11515,434.064318,433.977894 11516,601.388778,601.589396 11517,584.232954,583.829987 11518,458.910276,458.704041 11519,527.229990,527.612718 11520,649.910212,650.812110 11521,518.645635,518.482016 11522,447.519519,447.346637 11523,383.544132,383.849571 11524,511.515376,512.100040 11525,429.245688,428.370137 11526,625.054851,625.068148 11527,577.639962,578.225320 11528,424.127175,423.814711 11529,421.293000,421.357920 11530,534.235251,534.059011 11531,435.243939,435.203862 11532,465.977163,466.258583 11533,636.338615,635.913440 11534,490.128549,489.947382 11535,535.022159,535.843061 11536,430.004388,429.686489 11537,520.497286,520.197914 11538,586.967530,586.622148 11539,557.803445,557.883376 11540,782.684360,783.389937 11541,574.051556,573.857065 11542,385.291824,385.180061 11543,486.793718,486.833263 11544,532.301587,531.907505 11545,365.171630,364.741848 11546,475.493520,475.460741 11547,361.695015,361.286044 11548,454.306679,454.456404 11549,498.629234,498.634608 11550,560.212305,560.163769 11551,544.014819,543.841308 11552,569.209345,569.621732 11553,693.582255,693.948165 11554,628.636782,627.904781 11555,683.820814,684.745885 11556,445.586598,445.494853 11557,588.518582,589.152070 11558,673.105592,673.438079 11559,631.525389,630.949704 11560,521.005567,521.547275 11561,528.646099,529.083174 11562,399.210385,398.581238 11563,425.892269,426.618438 11564,618.266812,618.263322 11565,662.869454,662.572404 11566,412.741254,412.372357 11567,549.655148,550.124765 11568,599.276839,599.324015 11569,441.081065,441.175871 11570,585.343102,585.698925 11571,605.013852,604.767360 11572,528.346320,528.512460 11573,676.838244,677.004916 11574,427.604556,426.884390 11575,434.243593,434.861586 11576,441.044185,440.903862 11577,427.069673,427.241050 11578,711.139505,710.962589 11579,664.470368,664.365166 11580,510.820807,511.096291 11581,432.991052,432.776806 11582,570.845109,571.548322 11583,532.787779,532.602255 11584,573.301253,573.373351 11585,579.387556,579.378815 11586,387.786123,388.370342 11587,563.426748,564.059303 11588,586.882219,586.485553 11589,691.090797,691.122630 11590,559.228249,559.243853 11591,529.560192,529.719762 11592,348.256213,347.737059 11593,395.004285,395.530541 11594,388.369358,388.501190 11595,594.076497,594.028249 11596,609.897692,609.513583 11597,663.787540,664.366871 11598,503.674291,504.040365 11599,347.730523,347.538575 11600,465.759569,465.075892 11601,727.668649,726.925016 11602,585.151871,585.339152 11603,619.081068,619.716746 11604,524.911547,525.092179 11605,531.156860,530.838462 11606,417.692942,417.969158 11607,548.912575,549.009070 11608,400.896671,401.181972 11609,583.837521,583.593856 11610,623.361437,623.855678 11611,481.726649,481.716057 11612,535.374344,536.030674 11613,595.534848,595.599586 11614,414.695940,414.632485 11615,630.105941,630.081682 11616,472.917486,472.954430 11617,603.735402,603.477610 11618,695.188800,695.241373 11619,519.000979,519.704651 11620,549.250017,549.826963 11621,568.358601,568.552216 11622,627.777195,627.080793 11623,497.966503,498.050784 11624,585.057459,584.270573 11625,629.702496,628.951904 11626,418.065980,417.791147 11627,526.701871,526.525893 11628,750.281657,749.718756 11629,401.913567,401.597766 11630,578.177521,578.273119 11631,539.989767,539.592484 11632,673.617094,673.890492 11633,544.095949,543.636664 11634,472.887584,472.794573 11635,629.668998,628.897743 11636,542.009886,541.382690 11637,455.930661,455.838877 11638,392.286440,392.853192 11639,373.878450,373.626647 11640,593.097101,592.549741 11641,471.942270,471.706582 11642,659.786930,660.035636 11643,614.788483,614.922965 11644,475.973351,476.356017 11645,658.600122,658.386699 11646,641.848752,641.491706 11647,667.231275,666.379441 11648,649.916414,650.392035 11649,514.263698,514.466358 11650,437.833967,437.560389 11651,656.912155,656.917773 11652,651.562807,651.778058 11653,379.965604,379.796712 11654,441.279108,441.661200 11655,453.556419,452.512256 11656,614.624903,614.476908 11657,615.582658,615.229970 11658,609.206788,608.771991 11659,625.100404,624.891032 11660,605.860079,606.472151 11661,603.137078,603.317162 11662,419.575868,419.320284 11663,506.485723,506.946229 11664,479.643497,479.658067 11665,579.335859,579.117184 11666,529.406575,529.408468 11667,521.147454,521.230990 11668,547.938339,547.586203 11669,615.921412,615.400729 11670,465.746024,466.277207 11671,578.043576,578.500654 11672,470.725152,470.331200 11673,469.813707,469.694682 11674,544.733000,545.006410 11675,444.951936,444.985048 11676,668.564195,667.991600 11677,583.286341,583.323545 11678,545.653651,545.360443 11679,483.291615,483.362703 11680,445.717312,446.016306 11681,484.013981,484.443572 11682,517.565367,517.368502 11683,628.314338,628.141782 11684,481.307891,480.806413 11685,585.943846,585.876527 11686,523.282121,523.432076 11687,568.287988,567.806871 11688,424.524296,424.530947 11689,377.096110,377.354248 11690,447.722508,447.587967 11691,462.646037,462.112408 11692,599.534676,599.577439 11693,642.478916,642.321047 11694,543.178179,541.710759 11695,598.794567,599.235054 11696,717.264942,717.211898 11697,614.970063,615.092572 11698,507.092796,506.931462 11699,580.140702,579.922063 11700,493.115832,492.682643 11701,659.900968,662.285193 11702,658.884144,658.543013 11703,580.109114,580.303424 11704,552.742013,552.929625 11705,642.372088,641.586022 11706,513.146408,513.021054 11707,453.979803,453.787780 11708,541.498336,541.513470 11709,600.579502,600.622501 11710,495.864517,496.387809 11711,413.427628,413.247246 11712,504.612808,504.586455 11713,539.796442,539.654640 11714,535.754871,536.121093 11715,540.775678,541.041410 11716,424.885929,425.140507 11717,394.811035,394.815929 11718,421.961342,422.487250 11719,631.265701,631.698998 11720,479.947612,479.696373 11721,379.531011,379.775041 11722,481.701412,481.855515 11723,471.376365,471.463508 11724,458.286354,458.095477 11725,528.610002,528.311469 11726,443.028371,443.530640 11727,618.040522,618.183945 11728,670.186910,669.484766 11729,531.488981,531.510736 11730,711.949935,713.245087 11731,473.612742,472.998996 11732,386.253562,386.497840 11733,620.930955,619.822863 11734,580.986059,580.822935 11735,548.507885,548.391604 11736,518.090734,518.122393 11737,733.571796,733.674613 11738,362.153790,361.735012 11739,640.451021,640.391287 11740,623.172612,623.206010 11741,698.990976,699.590912 11742,397.779457,397.201938 11743,570.412319,571.067503 11744,550.152705,549.491085 11745,442.757287,442.842766 11746,643.001212,643.290293 11747,635.724041,635.721989 11748,575.828392,575.583111 11749,586.343451,587.069757 11750,425.026497,424.738669 11751,626.515012,626.881226 11752,391.514312,392.089479 11753,585.547326,585.857619 11754,500.512277,500.346119 11755,570.937705,571.491180 11756,649.018266,648.673799 11757,488.125262,488.039882 11758,606.175648,606.297915 11759,573.414362,573.506978 11760,533.982814,534.058546 11761,562.070922,562.009442 11762,647.524740,646.954291 11763,612.217820,610.702342 11764,426.650797,427.062654 11765,671.032980,670.828494 11766,479.952277,480.421196 11767,539.073972,538.769299 11768,438.145114,438.527029 11769,607.288286,607.297853 11770,684.972678,684.598114 11771,463.630857,463.285171 11772,524.179754,524.519525 11773,389.429645,389.404723 11774,540.173753,539.705787 11775,449.010123,448.534663 11776,638.927425,638.387753 11777,406.060579,405.762261 11778,778.660751,782.928085 11779,448.203228,448.472489 11780,488.428106,488.536662 11781,711.963741,712.384985 11782,531.840314,531.538369 11783,623.872499,623.746105 11784,396.978433,397.185314 11785,558.112761,558.594300 11786,499.373268,498.973367 11787,541.068814,540.619108 11788,381.009817,380.760564 11789,560.080783,560.674815 11790,595.371491,595.509750 11791,715.154362,715.251595 11792,725.099862,725.596054 11793,471.289769,471.115140 11794,491.296483,490.765294 11795,530.101377,529.731620 11796,525.210499,524.893696 11797,516.987051,517.316884 11798,445.128051,445.267777 11799,541.082856,541.043832 11800,466.562565,467.033167 11801,571.059261,570.517906 11802,586.722734,587.393992 11803,407.351878,407.317128 11804,443.658164,443.589984 11805,695.373860,695.425081 11806,551.465247,551.658842 11807,412.859346,412.924544 11808,624.506579,623.873974 11809,603.376076,603.352402 11810,714.286182,714.878499 11811,466.936953,467.483851 11812,516.602853,516.251140 11813,672.139148,671.903389 11814,426.110627,426.758338 11815,602.857140,602.697503 11816,404.487621,404.642741 11817,460.947827,461.115527 11818,443.365184,443.516002 11819,411.478298,411.444054 11820,473.189803,473.145311 11821,492.533222,492.820594 11822,699.672421,700.098667 11823,386.798650,386.461663 11824,500.708319,500.859517 11825,459.664326,459.485907 11826,631.554259,630.756768 11827,544.141174,543.969187 11828,352.301622,352.304030 11829,509.675202,509.455578 11830,481.369058,480.825161 11831,630.916578,631.067172 11832,430.707959,430.281377 11833,472.182144,471.646694 11834,562.291201,562.582505 11835,504.539725,503.925471 11836,536.642625,536.253361 11837,580.630201,580.369202 11838,603.603415,604.031102 11839,662.199906,662.772130 11840,561.849116,562.109417 11841,417.201974,416.891036 11842,434.862031,435.193853 11843,533.603190,533.627517 11844,631.705525,631.207727 11845,658.239424,658.562244 11846,435.682505,435.031826 11847,437.417629,437.790925 11848,458.972874,458.475206 11849,653.972599,653.017988 11850,555.162320,554.871728 11851,579.807142,580.814107 11852,580.851404,580.594397 11853,443.712115,444.045694 11854,435.207459,435.209776 11855,528.845960,528.900190 11856,470.148762,470.342068 11857,610.975087,610.461478 11858,438.273750,438.234587 11859,710.777759,711.358706 11860,430.673555,430.566666 11861,624.605567,625.292950 11862,400.312686,399.541874 11863,707.398863,707.049175 11864,348.304829,348.508982 11865,614.115209,614.700441 11866,603.306008,603.294002 11867,568.801243,567.636492 11868,526.565069,526.304856 11869,632.051021,632.555442 11870,653.610459,653.163650 11871,574.826076,574.688054 11872,528.942011,528.326127 11873,501.995249,501.995171 11874,356.213927,356.541108 11875,702.952830,703.153592 11876,407.556081,406.797459 11877,364.627506,365.292723 11878,596.121668,595.731297 11879,548.002865,547.957306 11880,571.433804,571.316682 11881,434.821987,435.119535 11882,447.668691,448.087775 11883,432.036303,432.472630 11884,532.100124,531.337364 11885,560.305668,560.260225 11886,613.788518,613.627742 11887,498.388542,498.475301 11888,635.616578,635.655175 11889,459.420713,459.462829 11890,391.222233,391.928983 11891,406.617000,407.492652 11892,587.931988,586.591280 11893,674.703048,673.609596 11894,536.035418,536.465066 11895,508.290411,508.338530 11896,590.802772,590.650470 11897,585.798982,586.215153 11898,582.683726,582.632782 11899,395.322474,394.998999 11900,611.665707,611.564869 11901,429.846577,429.590203 11902,432.027059,431.024362 11903,398.746199,399.034539 11904,448.424131,448.470413 11905,466.931993,467.134552 11906,394.560747,395.026077 11907,598.539299,598.231173 11908,551.777877,552.081179 11909,409.099343,408.963012 11910,724.356515,724.190131 11911,741.788591,742.216106 11912,515.131084,515.901602 11913,408.735604,408.481201 11914,421.656093,421.002781 11915,489.463042,489.454578 11916,376.571240,376.582247 11917,609.891399,609.804928 11918,726.944826,727.196348 11919,603.035781,602.877417 11920,607.700797,608.113199 11921,803.708369,803.541303 11922,627.606426,627.408289 11923,389.520965,389.408217 11924,482.585946,483.060120 11925,412.089739,411.627246 11926,609.451398,609.110322 11927,403.627831,403.618726 11928,515.255561,515.260684 11929,653.986281,653.508920 11930,664.608648,665.391831 11931,671.694966,671.659541 11932,550.962553,551.542324 11933,457.456778,457.054958 11934,522.985948,522.825042 11935,656.668233,656.703184 11936,441.467186,441.202805 11937,556.787188,556.181652 11938,422.891736,422.486150 11939,582.036037,583.167218 11940,410.985580,411.083100 11941,418.303583,418.532157 11942,467.732258,467.472015 11943,495.623690,495.788597 11944,616.160027,615.774523 11945,528.935518,528.860933 11946,476.468498,476.125655 11947,628.104428,628.357775 11948,482.831512,482.497385 11949,457.005378,456.574011 11950,755.539163,754.302191 11951,333.231114,333.524561 11952,510.699940,511.262730 11953,519.265891,519.692918 11954,467.404222,468.256204 11955,463.537921,463.209453 11956,613.100749,612.777888 11957,638.361201,638.349416 11958,640.976029,640.746474 11959,526.365109,525.861958 11960,556.430647,556.406826 11961,474.105459,474.393973 11962,448.582250,448.701476 11963,457.796349,457.844315 11964,634.940672,635.241285 11965,587.384051,587.907611 11966,552.845447,552.868462 11967,465.152621,465.370177 11968,492.883429,492.610224 11969,430.201924,429.430611 11970,405.801544,405.978747 11971,527.075293,526.781426 11972,603.247056,603.085605 11973,473.443195,473.084745 11974,477.275599,477.234982 11975,482.972126,483.004047 11976,651.742730,651.846865 11977,381.220668,380.704461 11978,446.896948,447.421683 11979,465.837059,465.599339 11980,454.585903,454.111037 11981,462.868773,463.733684 11982,564.183254,563.708486 11983,387.793682,387.982954 11984,543.519510,543.278967 11985,445.276887,445.362039 11986,438.497217,438.531202 11987,547.209854,547.355683 11988,491.832500,492.181896 11989,528.052114,527.912836 11990,511.156239,511.391490 11991,432.449276,432.778720 11992,591.604702,591.653832 11993,678.877733,678.298488 11994,682.460146,681.913734 11995,486.700674,486.296458 11996,572.176990,572.237260 11997,613.399399,612.269051 11998,502.227230,502.299573 11999,353.086853,352.974794 12000,679.136933,679.273790 12001,603.435946,603.337640 12002,447.678232,447.609668 12003,741.521208,741.849823 12004,595.748784,595.400058 12005,684.983561,684.932661 12006,560.208132,560.024695 12007,372.817476,372.872154 12008,496.060498,496.626667 12009,542.272190,542.029309 12010,530.812027,531.055198 12011,559.829563,559.280935 12012,446.105066,446.440805 12013,573.412972,573.747954 12014,421.543798,422.114598 12015,582.981468,582.199933 12016,475.117580,475.276423 12017,493.937022,493.764596 12018,436.841448,436.970814 12019,385.554009,385.305744 12020,578.205639,577.514912 12021,467.539926,467.182876 12022,470.345430,470.098483 12023,777.943747,777.487141 12024,381.232107,381.319008 12025,555.958702,555.549664 12026,547.082479,547.722391 12027,531.224973,531.290256 12028,477.634608,478.142436 12029,422.204004,422.277667 12030,635.262051,635.272882 12031,477.922306,478.080250 12032,568.500776,567.549170 12033,424.529741,424.410967 12034,705.195263,704.090893 12035,385.914396,386.246874 12036,638.521623,638.609228 12037,463.809825,463.919593 12038,527.235422,527.151432 12039,499.986556,499.661772 12040,572.613654,572.597215 12041,564.148049,564.104301 12042,436.057343,435.369197 12043,449.368250,449.966445 12044,625.330648,625.042435 12045,400.035938,399.401273 12046,526.911655,526.966363 12047,410.083911,410.899348 ```