From 4a2d92951d2c68240f02d7b21ab187a5b38271d3 Mon Sep 17 00:00:00 2001
From: J08nY
Date: Thu, 27 Mar 2025 17:03:30 +0100
Subject: More details on ctr and non-uniqueness.

---
 epare/countermeasures.ipynb | 669 ++++++++++++++++++++++++++++++++++----------
 1 file changed, 528 insertions(+), 141 deletions(-)

diff --git a/epare/countermeasures.ipynb b/epare/countermeasures.ipynb
index 3d931d2..f695521 100644
--- a/epare/countermeasures.ipynb
+++ b/epare/countermeasures.ipynb
@@ -10,7 +10,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 204,
+   "execution_count": 2,
    "id": "33ee6084-2ac3-4f95-9610-0fbc06026538",
    "metadata": {},
    "outputs": [],
@@ -38,7 +38,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 205,
+   "execution_count": 3,
    "id": "b1b9596c-1eba-4ace-af84-8cb279d84cc2",
    "metadata": {},
    "outputs": [],
@@ -49,7 +49,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 206,
+   "execution_count": 4,
    "id": "b0afb195-8390-44c5-931e-75a70ccd4e9e",
    "metadata": {},
    "outputs": [],
@@ -61,7 +61,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 207,
+   "execution_count": 5,
    "id": "52c877e1-5021-4ec2-9daa-dd20bec6bcb2",
    "metadata": {},
    "outputs": [],
@@ -1116,7 +1116,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 226,
+   "execution_count": 6,
    "id": "20a26f27-620d-4d7f-92bd-b949482b5c9a",
    "metadata": {},
    "outputs": [],
@@ -1126,7 +1126,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 227,
+   "execution_count": 7,
    "id": "144340bd-5372-4beb-a46e-fd60c596b254",
    "metadata": {},
    "outputs": [],
@@ -1141,7 +1141,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 228,
+   "execution_count": 8,
    "id": "f103129c-17d3-4217-999b-94ecb4ec523d",
    "metadata": {},
    "outputs": [
@@ -1185,7 +1185,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 229,
+   "execution_count": 9,
    "id": "08d99bd5-2b87-4a04-995d-7a87f9b67102",
    "metadata": {},
    "outputs": [],
@@ -1197,7 +1197,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 230,
+   "execution_count": 10,
    "id": "2a869bed-8e21-46af-8f70-065f4afd6a82",
    "metadata": {},
    "outputs": [],
@@ -1208,7 +1208,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 231,
+   "execution_count": 11,
    "id": "e440399a-bc01-488b-8822-08cc0bf1672d",
    "metadata": {},
    "outputs": [],
@@ -1221,7 +1221,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 232,
+   "execution_count": 12,
    "id": "7ea6d6ae-a6f5-4b53-8c40-787d79970cb6",
    "metadata": {},
    "outputs": [
@@ -1229,7 +1229,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "3752128619\n",
+      "3188254931\n",
       "32\n"
      ]
     }
@@ -1270,7 +1270,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 233,
+   "execution_count": 13,
    "id": "b5f398fc-90d7-455e-97bd-62b682d55961",
    "metadata": {},
    "outputs": [],
@@ -1300,19 +1300,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 234,
+   "execution_count": 17,
    "id": "5f03e586-33df-4525-a722-f5f63d6ca28d",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "e4879058a89a44af9abf2e7a58b1022f",
+       "model_id": "f6984b3117d940a98a6a79a427492f2d",
        "version_major": 2,
        "version_minor": 0
       },
       "text/plain": [
-       "Collecting scalarmults:   0%|          | 0/1000 [00:00<?, ?it/s]"
+       "Collecting scalarmults:   0%|          | 0/100 [00:00<?, ?it/s]"
       ]
      },
      "metadata": {},
@@ -1321,12 +1321,12 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "69ff8872b4454bacb5f1c4a7503e6d3b",
+       "model_id": "d646ad0b77344351a0cf9acbbbaac484",
        "version_major": 2,
        "version_minor": 0
       },
       "text/plain": [
-       "Computing dlogs:   0%|          | 0/1000 [00:00<?, ?it/s]"
+       "Computing dlogs:   0%|          | 0/100 [00:00<?, ?it/s]"
       ]
      },
      "metadata": {},
@@ -1343,7 +1343,8 @@
    "source": [
     "key = 0x20959f2b437de1e522baf6d814911938157390d3ea5118660b852ab0d5387006  # any key works\n",
     "msplit = MultiplicativeSplitting(mult, rand_bits=32)  # change the mask size here to your liking\n",
-    "tries = 1000\n",
+    "tries = 100\n",
+    "num_workers = 20\n",
     "\n",
     "blens = [None for _ in range(tries)]\n",
     "ts = [None for _ in range(tries)]\n",
@@ -1374,7 +1375,7 @@
     "        dlog = future.result()\n",
     "        t = int((dlog - key) / 92)\n",
     "        ts[i] = t\n",
-    "        blens[i] = s.bit_length()\n",
+    "        blens[i] = t.bit_length()\n",
     "\n",
     "mask_len = max(blens)\n",
     "print(mask_len)"
@@ -1382,19 +1383,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 235,
+   "execution_count": 20,
    "id": "5fbf8a38-983d-49a6-9cac-5350f960dc3e",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "89d1369c99644e88bd73b6230963716a",
+       "model_id": "4a1915bb130e4c68bd8c450c37f9fd25",
        "version_major": 2,
        "version_minor": 0
       },
       "text/plain": [
-       "Factoring:   0%|          | 0/1000 [00:00<?, ?it/s]"
+       "Factoring:   0%|          | 0/100 [00:00<?, ?it/s]"
       ]
      },
      "metadata": {},
@@ -1402,15 +1403,15 @@
     }
    ],
    "source": [
-    "num_workers = 25\n",
-    "\n",
     "with TaskExecutor(max_workers=num_workers) as pool:\n",
+    "    fulls = []\n",
     "    for t in ts:\n",
     "        full = t * (real_n + 92) + key\n",
+    "        fulls.append(full)\n",
     "        pool.submit_task(t,\n",
     "                         pari_factor,\n",
     "                         full)\n",
-    "    facts = [None for _ in ss]\n",
+    "    facts = [None for _ in ts]\n",
     "    for t, future in tqdm(pool.as_completed(), desc=\"Factoring\", total=len(ts)):\n",
     "        result = future.result()\n",
     "        facts[ts.index(t)] = result"
@@ -1418,7 +1419,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 236,
+   "execution_count": 38,
    "id": "0973fe4b-cdf5-4e91-850b-25375eeabb7e",
    "metadata": {
     "scrolled": true
@@ -1428,117 +1429,477 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Only one candidate, we got the mask: 3223834487 True\n",
-      "Only one candidate, we got the mask: 2377873873 True\n",
-      "Only one candidate, we got the mask: 2549271668 True\n",
-      "Only one candidate, we got the mask: 2536406777 True\n",
-      "Only one candidate, we got the mask: 3474268328 True\n",
-      "Only one candidate, we got the mask: 3550639425 True\n",
-      "Only one candidate, we got the mask: 3814005975 True\n",
-      "Only one candidate, we got the mask: 4238733795 True\n",
-      "Only one candidate, we got the mask: 4168083955 True\n",
-      "Only one candidate, we got the mask: 2761553491 True\n",
-      "Only one candidate, we got the mask: 3411331906 True\n",
-      "Only one candidate, we got the mask: 789326198 True\n",
-      "Only one candidate, we got the mask: 2285458765 True\n",
-      "Only one candidate, we got the mask: 774733453 True\n",
-      "Only one candidate, we got the mask: 3283055299 True\n",
-      "Only one candidate, we got the mask: 2838749009 True\n",
-      "Only one candidate, we got the mask: 3276117366 True\n",
-      "Only one candidate, we got the mask: 860570263 True\n",
-      "Only one candidate, we got the mask: 981664829 True\n",
-      "Only one candidate, we got the mask: 4134679928 True\n",
-      "Only one candidate, we got the mask: 3988645114 True\n",
-      "Only one candidate, we got the mask: 2280222647 True\n",
-      "Only one candidate, we got the mask: 3577824626 True\n",
-      "Only one candidate, we got the mask: 3679892960 True\n",
-      "Only one candidate, we got the mask: 1774221601 True\n",
-      "Only one candidate, we got the mask: 2623580147 True\n",
-      "Only one candidate, we got the mask: 1702008059 True\n",
-      "Only one candidate, we got the mask: 3933544069 True\n",
-      "Only one candidate, we got the mask: 3999529804 True\n",
-      "Only one candidate, we got the mask: 3480801033 True\n",
-      "Only one candidate, we got the mask: 3813421579 True\n",
-      "Only one candidate, we got the mask: 3417626666 True\n",
-      "Only one candidate, we got the mask: 4170438661 True\n",
-      "Only one candidate, we got the mask: 3502288943 True\n",
-      "Only one candidate, we got the mask: 2786122643 True\n",
-      "Only one candidate, we got the mask: 2127512283 True\n",
-      "Only one candidate, we got the mask: 2531786983 True\n",
-      "Only one candidate, we got the mask: 3983366093 True\n",
-      "Only one candidate, we got the mask: 2379294079 True\n",
-      "Only one candidate, we got the mask: 2930272946 True\n",
-      "Only one candidate, we got the mask: 2500319501 True\n",
-      "Only one candidate, we got the mask: 2947684105 True\n",
-      "Only one candidate, we got the mask: 3995028346 True\n",
-      "Only one candidate, we got the mask: 3421022802 True\n",
-      "Only one candidate, we got the mask: 3953171129 True\n",
-      "Only one candidate, we got the mask: 2982511438 True\n",
-      "Only one candidate, we got the mask: 2830285508 True\n",
-      "Only one candidate, we got the mask: 277646521 True\n",
-      "Only one candidate, we got the mask: 3775642326 True\n",
-      "Only one candidate, we got the mask: 3528903061 True\n",
-      "Only one candidate, we got the mask: 2433595133 True\n",
-      "Only one candidate, we got the mask: 2809043104 True\n",
-      "Only one candidate, we got the mask: 3918854258 True\n",
-      "Only one candidate, we got the mask: 2172498737 True\n",
-      "Only one candidate, we got the mask: 2614989645 True\n",
-      "Only one candidate, we got the mask: 3881796054 True\n",
-      "Only one candidate, we got the mask: 3763131597 True\n",
-      "Only one candidate, we got the mask: 3333059164 True\n",
-      "Only one candidate, we got the mask: 781918702 True\n",
-      "Only one candidate, we got the mask: 3898624034 True\n",
-      "Only one candidate, we got the mask: 2695908441 True\n",
-      "Only one candidate, we got the mask: 2428288661 True\n",
-      "Only one candidate, we got the mask: 380310234 True\n",
-      "Only one candidate, we got the mask: 3806008683 True\n",
-      "Only one candidate, we got the mask: 1583055543 True\n",
-      "Only one candidate, we got the mask: 3071695987 True\n",
-      "Only one candidate, we got the mask: 2466420323 True\n",
-      "Only one candidate, we got the mask: 3668827111 True\n",
-      "Only one candidate, we got the mask: 3030308051 True\n",
-      "Only one candidate, we got the mask: 4178268350 True\n",
-      "Only one candidate, we got the mask: 601467334 True\n",
-      "Only one candidate, we got the mask: 1756886305 True\n",
-      "Only one candidate, we got the mask: 3789366239 True\n",
-      "Only one candidate, we got the mask: 1709528826 True\n",
-      "Only one candidate, we got the mask: 4179236943 True\n",
-      "Only one candidate, we got the mask: 3246542896 True\n",
-      "Only one candidate, we got the mask: 1036989838 True\n",
-      "Only one candidate, we got the mask: 2843879303 True\n",
-      "Only one candidate, we got the mask: 2943368159 True\n",
-      "Only one candidate, we got the mask: 3694910341 True\n",
-      "Only one candidate, we got the mask: 3509390042 True\n",
-      "Only one candidate, we got the mask: 3797507269 True\n",
-      "Only one candidate, we got the mask: 3948777957 True\n",
-      "Only one candidate, we got the mask: 3649873740 True\n",
-      "Only one candidate, we got the mask: 2612080546 True\n",
-      "Only one candidate, we got the mask: 3671883118 True\n",
-      "Only one candidate, we got the mask: 2973101524 True\n",
-      "Only one candidate, we got the mask: 3724708289 True\n",
-      "Only one candidate, we got the mask: 4134344947 True\n",
-      "Only one candidate, we got the mask: 3489598522 True\n",
-      "Only one candidate, we got the mask: 3984902078 True\n",
-      "Only one candidate, we got the mask: 4259116327 True\n",
-      "Only one candidate, we got the mask: 3389988907 True\n",
-      "Only one candidate, we got the mask: 868217594 True\n",
-      "Only one candidate, we got the mask: 3729431567 True\n",
-      "Only one candidate, we got the mask: 3542657779 True\n",
-      "Only one candidate, we got the mask: 2695799377 True\n",
-      "Only one candidate, we got the mask: 3972219937 True\n",
-      "Only one candidate, we got the mask: 2701111433 True\n",
-      "Only one candidate, we got the mask: 3806713198 True\n",
-      "Only one candidate, we got the mask: 3503145915 True\n",
-      "Only one candidate, we got the mask: 2397268241 True\n",
-      "Only one candidate, we got the mask: 2919558765 True\n",
-      "Only one candidate, we got the mask: 543703399 True\n",
-      "Total recovered masks: 104 out of 1000\n"
+      "Only one candidate, we got the mask: 2921741201 True\n",
+      "Only one candidate, we got the mask: 2072087159 True\n",
+      "Several candidates for r\n",
+      "true r = 4039527236\n",
+      "t = 713461330\n",
+      "full = k + t (n + 92) = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "-----\n",
+      "candidate = 3539175297\n",
+      "candidate^-1 = 26490707025138842871232299283028891918970647143044648555061130998090929713163\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1010980488\n",
+      "candidate^-1 = 65382395850142385046254203937937214383274413673251102786718616383197090673492\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1131335308\n",
+      "candidate^-1 = 68241665580096390720464305945366132997268084763730630597092100846220368619186\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1468796812\n",
+      "candidate^-1 = 42974788306596910581678149765329273626138664755529162589164596291869762059227\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2262670616\n",
+      "candidate^-1 = 34120832790048195360232152972683066498634042381865315298546050423110184309593\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2937593624\n",
+      "candidate^-1 = 59928865533177637950767892719235074044242216512664024713011202452441507430870\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1123577112\n",
+      "candidate^-1 = 28797267645146503647782014101216400393084893568537834892905377895952751088363\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2019763618\n",
+      "candidate^-1 = 14492196383530008016252425678693741785643004999654181923797869651794644589503\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3394005924\n",
+      "candidate^-1 = 22747221860032130240154768648455377665756028254576876865697366948740122873062\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1101597609\n",
+      "candidate^-1 = 57299717742129214108904199687105698168184886340705550118886128389159682745636\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1179725099\n",
+      "candidate^-1 = 2589178315658163293839262175945801294566173159335058828325584381259536336976\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3634715564\n",
+      "candidate^-1 = 63500943916056123744437126756972853187061581127739385731937263938095743759671\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1804895148\n",
+      "candidate^-1 = 32692374163422277729585303046592231763960313081236584094052860741701608831649\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 4044771768\n",
+      "candidate^-1 = 52010472181905874507274875250078108352478979351338650049500167853209533299960\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2726036673\n",
+      "candidate^-1 = 33412630048235921446011078560536554607851595990453256418011146175452156477886\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 4039527236\n",
+      "candidate^-1 = 45687569571644186668055030675917308123994386634726534380327839132403948696008\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 734398406\n",
+      "candidate^-1 = 9066633853435455843498663857517672789931561241259438341471383970726271315941\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1203263432\n",
+      "candidate^-1 = 10597089865254233934449136733317910414767585486955432722650386806045786846217\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1009881809\n",
+      "candidate^-1 = 28984392767060016032504851357387483571286009999308363847595739303589289179006\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1697002962\n",
+      "candidate^-1 = 45494443720064260480309537296910755331512056509153753731394733897480245746124\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2203195218\n",
+      "candidate^-1 = 28649858871064607054452099843552849084092443170352775059443064194579841372818\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1817357782\n",
+      "candidate^-1 = 50118945072353882169016617840804831911777393985679884627016719263178234716829\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2359450198\n",
+      "candidate^-1 = 1294589157829081646919631087972900647283086579667529414162792190629768168488\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 902447574\n",
+      "candidate^-1 = 65384748326844555459170606093184463527920626162473168188105721483403217663298\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3609790296\n",
+      "candidate^-1 = 54787658461590321524721469359866553113153040675517735465455334677357430817081\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2022385884\n",
+      "candidate^-1 = 27138001604053383694692114827015342242612190432878413262142527093405813797407\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1348257256\n",
+      "candidate^-1 = 2265531026200892882109354403952576132745401514418176474784886333602094294854\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 848501481\n",
+      "candidate^-1 = 14105944680370155640761438920680636200678344748508620625931659181947238689735\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3959673578\n",
+      "candidate^-1 = 8514341200062059445867282316798770218884343036808910622475199011346783490837\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 908678891\n",
+      "candidate^-1 = 23354947384949399018175600008468789361209019701560882417175629913343216631145\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1011192942\n",
+      "candidate^-1 = 54276003208106767389384229654030684485224380865756826524285054186811627594814\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3029645427\n",
+      "candidate^-1 = 9661464255686672010834950452462494523762003333102787949198579767863096393002\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1979836789\n",
+      "candidate^-1 = 17028682400124118891734564633597540437768686073617821244950398022693566981674\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1258968696\n",
+      "candidate^-1 = 11695781644483879685362356889647048665988891413217912935596458034008096001175\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 54853006610429443711102562796765991385990914712382307462633349524199986834658739412728\n",
+      "above == full? True\n",
+      "-----\n",
+      "---------------------\n",
+      "Several candidates for r\n",
+      "true r = 2546266567\n",
+      "t = 1548864186\n",
+      "full = k + t (n + 92) = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "-----\n",
+      "candidate = 3968039777\n",
+      "candidate^-1 = 47199999723628001336554368590553381329909688423987679279501585692741942222130\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2546266567\n",
+      "candidate^-1 = 53261354779930768597409107118256662925077636528602413316194826191853234093722\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2441870632\n",
+      "candidate^-1 = 57479263860955910841936440041364026045516801621530257119975624597452342910333\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2857178584\n",
+      "candidate^-1 = 75748083438556289408418666080557136798495350712469032724680328085740307176009\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1757828696\n",
+      "candidate^-1 = 17227168816999813895475622948114925759056198231882304548407742991291781760271\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3736310456\n",
+      "candidate^-1 = 48879952893042060686454552217703589967985177807205861867478155758152793393123\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3133866544\n",
+      "candidate^-1 = 33664482913723953820412695074440929318832358645764599964801070204254096100835\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3515657392\n",
+      "candidate^-1 = 47055055788379089607666629310627900110700983250840595692632775802152517281392\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3329733203\n",
+      "candidate^-1 = 63341901525758342256800386523708293549278712718872106311460104915244606307703\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1566933272\n",
+      "candidate^-1 = 67328965827447907640825390148881858637664717291529199929602140408508192201670\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1868155228\n",
+      "candidate^-1 = 20876963026325756053051468762266305473624587344612836898098502903292333983733\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 119081236569616103969202985151515360402172033984486476071765168905412656991728103589856\n",
+      "above == full? True\n",
+      "-----\n",
+      "---------------------\n",
+      "Several candidates for r\n",
+      "true r = 586356740\n",
+      "t = 404263194\n",
+      "full = k + t (n + 92) = 31080944018917461343795538061263727736823600975872546557801979004011543724824943696960\n",
+      "-----\n",
+      "candidate = 938170784\n",
+      "candidate^-1 = 52975562029403857607630522378170505964905977660731390116544502276802695405629\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 31080944018917461343795538061263727736823600975872546557801979004011543724824943696960\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1876341568\n",
+      "candidate^-1 = 64929252394581111463744079025655690213625872965265138476701155444907974104071\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 31080944018917461343795538061263727736823600975872546557801979004011543724824943696960\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 437122240\n",
+      "candidate^-1 = 34960422445902541801696735185321223222583924317096364308996315884209127750875\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 31080944018917461343795538061263727736823600975872546557801979004011543724824943696960\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1222440419\n",
+      "candidate^-1 = 68600022163021642948955277628963692751947775934147947283493669830758786832741\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 31080944018917461343795538061263727736823600975872546557801979004011543724824943696960\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 586356740\n",
+      "candidate^-1 = 23254545039239479916322727266560109973972949641331114716984956752473710406996\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 31080944018917461343795538061263727736823600975872546557801979004011543724824943696960\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2444880838\n",
+      "candidate^-1 = 72741482461390004134406456651052283607146772101973417060175739221886019817627\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 31080944018917461343795538061263727736823600975872546557801979004011543724824943696960\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1172713480\n",
+      "candidate^-1 = 11627272519619739958161363633280054986986474820665557358492478376236855203498\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 31080944018917461343795538061263727736823600975872546557801979004011543724824943696960\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 469085392\n",
+      "candidate^-1 = 29068181299049349895403409083200137467466187051663893396231195940592138008745\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 31080944018917461343795538061263727736823600975872546557801979004011543724824943696960\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2345426960\n",
+      "candidate^-1 = 5813636259809869979080681816640027493493237410332778679246239188118427601749\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 31080944018917461343795538061263727736823600975872546557801979004011543724824943696960\n",
+      "above == full? True\n",
+      "-----\n",
+      "---------------------\n",
+      "Several candidates for r\n",
+      "true r = 4099981182\n",
+      "t = 2642778076\n",
+      "full = k + t (n + 92) = 203184555558590712836289545636923662903278351877540745889142089702149488986478501195426\n",
+      "-----\n",
+      "candidate = 3228686923\n",
+      "candidate^-1 = 67416396472256627079998760927485239166988608007947808690086396876984288458738\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 203184555558590712836289545636923662903278351877540745889142089702149488986478501195426\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3923474478\n",
+      "candidate^-1 = 53037483928698273854873915437268008099102139343418152750051187589693742832853\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 203184555558590712836289545636923662903278351877540745889142089702149488986478501195426\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2767445934\n",
+      "candidate^-1 = 27397167377793821380093463966638862719922863829406518913862257281139501333519\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 203184555558590712836289545636923662903278351877540745889142089702149488986478501195426\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3082729947\n",
+      "candidate^-1 = 67502252272888712178930437829250192126129995527986739863701511477792036332722\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 203184555558590712836289545636923662903278351877540745889142089702149488986478501195426\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 4099981182\n",
+      "candidate^-1 = 53728758251263460792603093081868749337569947904541549081333778030796416192083\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 203184555558590712836289545636923662903278351877540745889142089702149488986478501195426\n",
+      "above == full? True\n",
+      "-----\n",
+      "---------------------\n",
+      "Only one candidate, we got the mask: 4240436952 True\n",
+      "Several candidates for r\n",
+      "true r = 1054759622\n",
+      "t = 694271292\n",
+      "full = k + t (n + 92) = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "-----\n",
+      "candidate = 2082978083\n",
+      "candidate^-1 = 70926800923833726814245799453581520027922406161928168992184434104522114548589\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1465316453\n",
+      "candidate^-1 = 60239579291535863658082545576886406273278056948782152971212929977157790371263\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 4165956166\n",
+      "candidate^-1 = 73904871841796046067051717563361197245134087215863527914521121358767683675551\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1054759622\n",
+      "candidate^-1 = 32916166462770436865868266168928274812999826737500918380668592970627433533542\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1150690474\n",
+      "candidate^-1 = 71499038532384546579941614468655340824282611408865892492623092957903951282093\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2930632906\n",
+      "candidate^-1 = 68561261025647114488970090625013640367811912609290519904035369295085521586888\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 891931754\n",
+      "candidate^-1 = 71506829279038074109757883564477355140976176319499648868114881886397351037606\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1582042478\n",
+      "candidate^-1 = 3588093433295855163732315625904528984462656656446659629430225432413461610135\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2863810801\n",
+      "candidate^-1 = 68817051866482904589958336845935410415616665963668120410224486154991202020843\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 4027416659\n",
+      "candidate^-1 = 9445019186430103977146513323452829598031350649704699735484053900399235680239\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 791021239\n",
+      "candidate^-1 = 7176186866591710327464631251809057968925313312893319258860450864826923220270\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1328364218\n",
+      "candidate^-1 = 61241335234879901001880976060972940299803372432205022907074540241147849493070\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2538649658\n",
+      "candidate^-1 = 40460798138314952610978306328523747705796793263233053748780937033651947724626\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1269324829\n",
+      "candidate^-1 = 4038653516871539902098976983906620949247818256667220660704065454290642646739\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2131580798\n",
+      "candidate^-1 = 13269399537091224226648020073813398658821185281376945290634379651910514289428\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 1065790399\n",
+      "candidate^-1 = 26538799074182448453296040147626797317642370562753890581268759303821028578856\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 53377620017317855809796612613608262425705269850145672571876348376319535218874908447234\n",
+      "above == full? True\n",
+      "-----\n",
+      "---------------------\n",
+      "Several candidates for r\n",
+      "true r = 3634113672\n",
+      "t = 2680190962\n",
+      "full = k + t (n + 92) = 206060968331406077945547732896592415701478405398401148885296351493997971930068100577944\n",
+      "-----\n",
+      "candidate = 3634113672\n",
+      "candidate^-1 = 37634033022565823810085029464398851788513344511265489647294862481459002347491\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 206060968331406077945547732896592415701478405398401148885296351493997971930068100577944\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 4048089192\n",
+      "candidate^-1 = 71468722554076888672183327062398623529815128497721212450005095375489413086598\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 206060968331406077945547732896592415701478405398401148885296351493997971930068100577944\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3735061274\n",
+      "candidate^-1 = 44928566482470354552499773065160058438807120959047383098649899561745326911344\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 206060968331406077945547732896592415701478405398401148885296351493997971930068100577944\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 3201481092\n",
+      "candidate^-1 = 1161365723043170098011311460592818537044462272356022390519677080027379528226\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 206060968331406077945547732896592415701478405398401148885296351493997971930068100577944\n",
+      "above == full? True\n",
+      "-----\n",
+      "---------------------\n",
+      "Several candidates for r\n",
+      "true r = 2376091517\n",
+      "t = 1953095034\n",
+      "full = k + t (n + 92) = 150159693718128688257542828458944146909547607961398772887284238536472708007326310110880\n",
+      "-----\n",
+      "candidate = 3246914120\n",
+      "candidate^-1 = 44590844092197648231531019613425704807242597656472481439265521332832917097606\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 150159693718128688257542828458944146909547607961398772887284238536472708007326310110880\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2376091517\n",
+      "candidate^-1 = 19772973002144164969938083673165593098966704920762394800382781683851452496636\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 150159693718128688257542828458944146909547607961398772887284238536472708007326310110880\n",
+      "above == full? True\n",
+      "-----\n",
+      "candidate = 2597531296\n",
+      "candidate^-1 = 17297083735367877629484956680211693777880362935691158380652997359534519970751\n",
+      "(key * candidate^-1)_mod(n+92) * candidate = 150159693718128688257542828458944146909547607961398772887284238536472708007326310110880\n",
+      "above == full? True\n",
+      "-----\n",
+      "---------------------\n",
+      "Only one candidate, we got the mask: 3341139537 True\n",
+      "Only one candidate, we got the mask: 3722808561 True\n",
+      "Only one candidate, we got the mask: 2045751181 True\n",
+      "Only one candidate, we got the mask: 2166075112 True\n",
+      "Only one candidate, we got the mask: 1985265929 True\n",
+      "Only one candidate, we got the mask: 4284624218 True\n",
+      "Only one candidate, we got the mask: 3985300601 True\n",
+      "Only one candidate, we got the mask: 3864453118 True\n",
+      "Only one candidate, we got the mask: 2479654721 True\n",
+      "Total recovered masks: 12 out of 100\n"
      ]
     }
    ],
    "source": [
     "candidate_amounts = []\n",
-    "for t, blen, r, (primes, powers), result in zip(ts, blens, rs, facts, results):\n",
+    "for t, blen, r, (primes, powers), full, result in zip(ts, blens, rs, facts, fulls, results):\n",
     "    #print(primes, powers)\n",
     "    #print(s, blen, r, r.bit_length())\n",
     "    candidates = set()\n",
@@ -1550,31 +1911,49 @@
     "    if len(candidates) == 1:\n",
     "        candidate = candidates.pop()\n",
     "        print(\"Only one candidate, we got the mask:\", candidate, candidate == r)\n",
+    "    else:\n",
+    "        if len(candidate_amounts) > 10:\n",
+    "            # Do not print everything\n",
+    "            continue\n",
+    "        print(\"Several candidates for r\")\n",
+    "        print(f\"true r = {r}\")\n",
+    "        print(f\"t = {t}\")\n",
+    "        print(f\"full = k + t (n + 92) = {full}\")\n",
+    "        print(\"-----\")\n",
+    "        for candidate in candidates:\n",
+    "            print(f\"candidate = {candidate}\")            \n",
+    "            candidate_inverse = mod(candidate, real_n + 92).inverse() \n",
+    "            print(f\"candidate^-1 = {candidate_inverse}\")\n",
+    "            multiplied = candidate * int(candidate_inverse * key)\n",
+    "            print(f\"(key * candidate^-1)_mod(n+92) * candidate = {multiplied}\")\n",
+    "            print(f\"above == full? {multiplied == full}\")\n",
+    "            print(\"-----\")\n",
+    "        print(\"---------------------\")\n",
     "    #print(\"--\")\n",
     "print(f\"Total recovered masks: {len(list(filter(lambda a: a == 1, candidate_amounts)))} out of {tries}\")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 237,
+   "execution_count": 36,
    "id": "6274ff91-325f-4c6b-a4d7-d66b994d730f",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "d557894c3fbd4543b9fd6c240b676212",
+       "model_id": "aba07231a8d44a2f92c75ef741f73f50",
        "version_major": 2,
        "version_minor": 0
       },
-      "image/png": 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",
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",
       "text/html": [
        "\n",
        "            <div style=\"display: inline-block;\">\n",
        "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
        "                    Figure\n",
        "                </div>\n",
-       "                <img 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0fr5ZdflpeXlyPKAAAAoA4cdg3ghQsXtHLlSh09etRRJQAAAFAHDguArq6uCgoK4mHPAAAAjYxD7wJ+8sknNX36dH3//ffXPNbixYsVEhIiDw8PRUdHa9euXVfsv27dOnXt2lUeHh4KCwvT+++/f1mf/fv3a+jQofLx8VHz5s3Vu3dv5efnX/NcAQAAGjOHBsBFixbp448/VkBAgLp06aJevXpVetXU2rVrlZycrFmzZik3N1fh4eGKj49XcXFxlf23b9+uESNGaMyYMdqzZ48SEhKUkJCgffv22focPnxY/fr1U9euXbV161Z9+eWXSk1N5fE0AADgumcxDMNw1OCzZ8++4vuzZs2q0TjR0dHq3bu3Fi1aJEmyWq0KDAzU+PHjNXXq1Mv6JyYmqqysTBs3brS13XrrrYqIiNDSpUslScOHD5erq6tWrlxZ0925TGlpqXx8fFRSUiJvb+8abRMydVOd68H+vp0zpKGnAACoZ3X5/L7eOOQu4ItqGvCu5Pz588rJydG0adNsbU5OToqLi1N2dnaV22RnZ9ueRXhRfHy80tPTJf0cIDdt2qQnnnhC8fHx2rNnjzp06KBp06YpISGh2rmUl5ervLzc9nNpaWnddwwAAKCBOPQU8EU5OTlatWqVVq1aZXtGYE2dOnVKFRUV8vPzq9Tu5+enwsLCKrcpLCy8Yv/i4mKdPXtWc+bM0aBBg/TRRx9p2LBhuvfee7Vt27Zq55KWliYfHx/bKzAwsFb7AgAA0Bg4dAWwuLhYw4cP19atW9WiRQtJ0unTp3XHHXdozZo1at26tSPLV8tqtUqS7rnnHk2ePFmSFBERoe3bt2vp0qXq379/ldtNmzat0spiaWkpIRAAADQ5Dl0BHD9+vM6cOaOvvvpK33//vb7//nvt27dPpaWlmjBhQo3G8PX1lbOzs4qKiiq1FxUVyd/fv8pt/P39r9jf19dXLi4u6tatW6U+N9988xXvAnZ3d5e3t3elFwAAQFPj0ACYkZGhP//5z7r55pttbd26ddPixYv1wQcf1GgMNzc3RUZGKisry9ZmtVqVlZWlmJiYKreJiYmp1F+SMjMzbf3d3NzUu3dvHThwoFKfgwcPKjg4uEbzAgAAaKocegrYarXK1dX1snZXV1fbadiaSE5OVlJSkqKiotSnTx8tWLBAZWVlGj16tCRp1KhRateundLS0iRJEydOVP/+/TVv3jwNGTJEa9as0e7du7Vs2TLbmCkpKUpMTNTtt9+uO+64QxkZGXrvvfe0devWa9tpAACARs6hK4B33nmnJk6cqBMnTtjajh8/rsmTJ2vAgAE1HicxMVEvvPCCZs6cqYiICOXl5SkjI8N2o0d+fr4KCgps/WNjY7V69WotW7ZM4eHh+tvf/qb09HT16NHD1mfYsGFaunSp5s6dq7CwML366qv6+9//rn79+tlhzwEAABovhz4H8NixYxo6dKi++uor280Sx44dU48ePbRhwwa1b9/eUaXrBc8BbPp4DiAAmA/PAXTwKeDAwEDl5uZq8+bN+uabbyT9fKNFXFycI8sCAADgChwaACXJYrHo17/+tX796187uhQAAABqwOEBMCsrSy+++KL2798v6ecVwEmTJrEKCFOoj1P+nMYGANSWQ28C+fOf/6xBgwbJy8tLEydO1MSJE+Xt7a277rpLixcvdmRpAAAAVMOhK4DPPvusXnzxRY0bN87WNmHCBPXt21fPPvusxo4d68jyAAAAqIJDVwBPnz6tQYMGXdY+cOBAlZSUOLI0AAAAquHQADh06FCtX7/+svZ3331X//Vf/+XI0gAAAKiGQ08Bd+vWTc8884y2bt1q+xq2HTt26LPPPtPjjz+ul19+2da3pt8NDAAAgGvj0AC4YsUK3Xjjjfr666/19ddf29pbtGihFStW2H62WCwEQAAAgHri0AB45MgRRw4PAACAOnDoNYC/ZBiGHPitcwAAAKghhwfAN998U2FhYfL09JSnp6d69uyplStXOrosAAAAquHQU8Dz589Xamqqxo0bp759+0qSPv30Uz322GM6deqUJk+e7MjyAAAAqIJDA+DChQu1ZMkSjRo1ytY2dOhQde/eXU899RQBEAAAoAE49BRwQUGBYmNjL2uPjY1VQUGBI0sDAACgGg4NgJ06ddLbb799WfvatWsVGhrqyNIAAACohkNPAc+ePVuJiYn6+OOPbdcAfvbZZ8rKyqoyGAIAAMDxHLoCeN9992nXrl3y9fVVenq60tPT5evrq127dmnYsGGOLA0AAIBqOGwF8MKFC/rf//1fpaamatWqVY4qAwAAgFpy2Aqgq6ur/v73vztqeAAAANSRQ08BJyQkKD093ZElAAAAUEsOvQkkNDRUf/zjH/XZZ58pMjJSzZs3r/T+hAkTHFkeAAAAVXBoAFyxYoVatGihnJwc5eTkVHrPYrEQAAEAABqAQwPgkSNHbH82DEPSz8EPAAAADceh1wBKP68C9ujRQx4eHvLw8FCPHj306quvOrosAAAAquHQFcCZM2dq/vz5Gj9+vGJiYiRJ2dnZmjx5svLz8/XHP/7RkeUBAABQBYcGwCVLlmj58uUaMWKErW3o0KHq2bOnxo8fTwAEAABoAA4NgBcuXFBUVNRl7ZGRkfrPf/7jyNJAjYRM3dTQUwAAoN459BrABx98UEuWLLmsfdmyZRo5cqQjSwMAAKAaDl0BlH6+CeSjjz7SrbfeKknauXOn8vPzNWrUKCUnJ9v6zZ8/39FTAQAAgBwcAPft26devXpJkg4fPixJ8vX1la+vr/bt22frx6NhAAAA6o9DA+CWLVscOTwAAADqwOHPAQQAAEDjQgAEAAAwGQIgAACAyRAAAQAATIYACAAAYDIEQAAAAJMhAAIAAJgMARAAAMBkCIAAAAAmQwAEAAAwGQIgAACAyRAAAQAATIYACAAAYDIEQAAAAJMhAAIAAJgMARAAAMBkCIAAAAAmQwAEAAAwmSYVABcvXqyQkBB5eHgoOjpau3btumL/devWqWvXrvLw8FBYWJjef//9avs+9thjslgsWrBggZ1nDQAA0Lg0mQC4du1aJScna9asWcrNzVV4eLji4+NVXFxcZf/t27drxIgRGjNmjPbs2aOEhAQlJCRo3759l/Vdv369duzYoYCAAEfvBgAAQINrMgFw/vz5evTRRzV69Gh169ZNS5cuVbNmzfTaa69V2f+ll17SoEGDlJKSoptvvll/+tOf1KtXLy1atKhSv+PHj2v8+PH661//KldX1/rYFQAAgAbVJALg+fPnlZOTo7i4OFubk5OT4uLilJ2dXeU22dnZlfpLUnx8fKX+VqtVDz74oFJSUtS9e3fHTB4AAKCRcWnoCdTEqVOnVFFRIT8/v0rtfn5++uabb6rcprCwsMr+hYWFtp+fe+45ubi4aMKECTWaR3l5ucrLy20/l5aW1nQXAAAAGo0msQLoCDk5OXrppZf0xhtvyGKx1GibtLQ0+fj42F6BgYEOniUAAID9NYkA6OvrK2dnZxUVFVVqLyoqkr+/f5Xb+Pv7X7H/J598ouLiYgUFBcnFxUUuLi46evSoHn/8cYWEhFQ55rRp01RSUmJ7HTt27Np3DgAAoJ41iQDo5uamyMhIZWVl2dqsVquysrIUExNT5TYxMTGV+ktSZmamrf+DDz6oL7/8Unl5ebZXQECAUlJS9OGHH1Y5pru7u7y9vSu9AAAAmpomcQ2gJCUnJyspKUlRUVHq06ePFixYoLKyMo0ePVqSNGrUKLVr105paWmSpIkTJ6p///6aN2+ehgwZojVr1mj37t1atmyZJKlVq1Zq1apVpRqurq7y9/dXly5d6nfnAAAA6lGTCYCJiYk6efKkZs6cqcLCQkVERCgjI8N2o0d+fr6cnP5/QTM2NlarV6/WjBkzNH36dIWGhio9PV09evRoqF0AAABoFCyGYRgNPYmmqrS0VD4+PiopKanx6eCQqZscPCuYzbdzhjT0FACgSanL5/f1psmsAAKoWn38o4KQCQDXlyZxEwgAAADshwAIAABgMgRAAAAAkyEAAgAAmAwBEAAAwGQIgAAAACZDAAQAADAZAiAAAIDJEAABAABMhgAIAABgMgRAAAAAkyEAAgAAmAwBEAAAwGQIgAAAACZDAAQAADAZAiAAAIDJEAABAABMhgAIAABgMgRAAAAAkyEAAgAAmIxLQ08AQOMXMnWTw2t8O2eIw2sAAH7GCiAAAIDJEAABAABMhgAIAABgMgRAAAAAkyEAAgAAmAwBEAAAwGQIgAAAACZDAAQAADAZAiAAAIDJ8E0gABoFvm0EAOoPK4AAAAAmQwAEAAAwGQIgAACAyRAAAQAATIYACAAAYDIEQAAAAJMhAAIAAJgMARAAAMBkCIAAAAAmQwAEAAAwGQIgAACAyRAAAQAATIYACAAAYDIEQAAAAJMhAAIAAJgMARAAAMBkCIAAAAAm49LQEwCA+hIydVNDT+GafTtnSENPAcB1gBVAAAAAk2lSAXDx4sUKCQmRh4eHoqOjtWvXriv2X7dunbp27SoPDw+FhYXp/ffft7134cIFTZkyRWFhYWrevLkCAgI0atQonThxwtG7AQAA0KCaTABcu3atkpOTNWvWLOXm5io8PFzx8fEqLi6usv/27ds1YsQIjRkzRnv27FFCQoISEhK0b98+SdK5c+eUm5ur1NRU5ebm6p133tGBAwc0dOjQ+twtAACAemcxDMNo6EnURHR0tHr37q1FixZJkqxWqwIDAzV+/HhNnTr1sv6JiYkqKyvTxo0bbW233nqrIiIitHTp0iprfP755+rTp4+OHj2qoKCgq86ptLRUPj4+Kikpkbe3d43243q4BglAw+EaQODa1eXz+3rTJFYAz58/r5ycHMXFxdnanJycFBcXp+zs7Cq3yc7OrtRfkuLj46vtL0klJSWyWCxq0aKFXeYNAADQGDWJu4BPnTqliooK+fn5VWr38/PTN998U+U2hYWFVfYvLCyssv9PP/2kKVOmaMSIEdX+a6C8vFzl5eW2n0tLS2uzGwCAeuToMy6sxqIpaxIrgI524cIFPfDAAzIMQ0uWLKm2X1pamnx8fGyvwMDAepwlAACAfTSJAOjr6ytnZ2cVFRVVai8qKpK/v3+V2/j7+9eo/8Xwd/ToUWVmZl7xWoBp06appKTE9jp27Fgd9wgAAKDhNIkA6ObmpsjISGVlZdnarFarsrKyFBMTU+U2MTExlfpLUmZmZqX+F8PfoUOHtHnzZrVq1eqK83B3d5e3t3elFwAAQFPTJK4BlKTk5GQlJSUpKipKffr00YIFC1RWVqbRo0dLkkaNGqV27dopLS1NkjRx4kT1799f8+bN05AhQ7RmzRrt3r1by5Ytk/Rz+PvNb36j3Nxcbdy4URUVFbbrA1u2bCk3N7eG2VEAAAAHazIBMDExUSdPntTMmTNVWFioiIgIZWRk2G70yM/Pl5PT/y9oxsbGavXq1ZoxY4amT5+u0NBQpaenq0ePHpKk48ePa8OGDZKkiIiISrW2bNmiX/3qV/WyXwAAAPWtyTwHsDHiOYAA6ht3ntYcdwGjOjwHsIlcAwgAAAD7IQACAACYDAEQAADAZAiAAAAAJkMABAAAMBkCIAAAgMk0mecAAgAAVKc2j/2xlp9z4EyaBlYAAQAATIYACAAAYDKcAgYAwMTq4xuq+NaUxocVQAAAAJMhAAIAAJgMp4ABAJVwShC4/rECCAAAYDIEQAAAAJPhFDAANCH1cXoWwPWPFUAAAACTIQACAACYDKeAAQCoA+6WrjkuXWh8WAEEAAAwGQIgAACAyRAAAQAATIYACAAAYDIEQAAAAJMhAAIAAJgMARAAAMBkCIAAAAAmQwAEAAAwGQIgAACAyRAAAQAATIbvAgYA1Du+G7Zm+D3BUVgBBAAAMBkCIAAAgMkQAAEAAEyGAAgAAGAyBEAAAACTIQACAACYDAEQAADAZAiAAAAAJkMABAAAMBkCIAAAgMkQAAEAAEyGAAgAAGAyBEAAAACTIQACAACYDAEQAADAZAiAAAAAJkMABAAAMBkCIAAAgMkQAAEAAEyGAAgAAGAyTSoALl68WCEhIfLw8FB0dLR27dp1xf7r1q1T165d5eHhobCwML3//vuV3jcMQzNnzlTbtm3l6empuLg4HTp0yJG7AAAA0OCaTABcu3atkpOTNWvWLOXm5io8PFzx8fEqLi6usv/27ds1YsQIjRkzRnv27FFCQoISEhK0b98+W5+5c+fq5Zdf1tKlS7Vz5041b95c8fHx+umnn+prtwAAAOqdxTAMo6EnURPR0dHq3bu3Fi1aJEmyWq0KDAzU+PHjNXXq1Mv6JyYmqqysTBs3brS13XrrrYqIiNDSpUtlGIYCAgL0+OOP6w9/+IMkqaSkRH5+fnrjjTc0fPjwq86ptLRUPj4+Kikpkbe3d432I2Tqphr1AwAAjmEtP6djCx6o1ef39caloSdQE+fPn1dOTo6mTZtma3NyclJcXJyys7Or3CY7O1vJycmV2uLj45Weni5JOnLkiAoLCxUXF2d738fHR9HR0crOzq4yAJaXl6u8vNz2c0lJiaSfg2BNWcvP1bgvAACwv4ufxU1kDcwhmkQAPHXqlCoqKuTn51ep3c/PT998802V2xQWFlbZv7Cw0Pb+xbbq+lwqLS1Ns2fPvqw9MDCwZjsCAAAaje+++04+Pj4NPY0G0SQCYGMxbdq0SquKp0+fVnBwsPLz8x32H1BpaakCAwN17Ngxhy1TO7rG9bAP1Gg841OjcdW4HvaBGo1n/PqqUVJSoqCgILVs2dIh4zcFTSIA+vr6ytnZWUVFRZXai4qK5O/vX+U2/v7+V+x/8X+LiorUtm3bSn0iIiKqHNPd3V3u7u6Xtfv4+Dj8GgJvb+8mX+N62AdqNJ7xqdG4alwP+0CNxjN+fdVwcmoy98LaXZPYczc3N0VGRiorK8vWZrValZWVpZiYmCq3iYmJqdRfkjIzM239O3ToIH9//0p9SktLtXPnzmrHBAAAuB40iRVASUpOTlZSUpKioqLUp08fLViwQGVlZRo9erQkadSoUWrXrp3S0tIkSRMnTlT//v01b948DRkyRGvWrNHu3bu1bNkySZLFYtGkSZP09NNPKzQ0VB06dFBqaqoCAgKUkJDQULsJAADgcE0mACYmJurkyZOaOXOmCgsLFRERoYyMDNtNHPn5+ZWWcmNjY7V69WrNmDFD06dPV2hoqNLT09WjRw9bnyeeeEJlZWX6n//5H50+fVr9+vVTRkaGPDw8ajQnd3d3zZo1q8rTwvZyPdS4HvaBGo1nfGo0rhrXwz5Qo/GMfz3VaOyazHMAAQAAYB9N4hpAAAAA2A8BEAAAwGQIgAAAACZDAAQAADAZAmAdLV68WCEhIfLw8FB0dLR27dpl1/E//vhj3X333QoICJDFYrF9h7G9pKWlqXfv3vLy8lKbNm2UkJCgAwcO2LXGkiVL1LNnT9vDPGNiYvTBBx/Ytcal5syZY3vEj7089dRTslgslV5du3a12/iSdPz4cf32t79Vq1at5OnpqbCwMO3evdtu44eEhFy2DxaLRWPHjrVbjYqKCqWmpqpDhw7y9PTUTTfdpD/96U92/67NM2fOaNKkSQoODpanp6diY2P1+eef13m8qx1rhmFo5syZatu2rTw9PRUXF6dDhw7Zbfx33nlHAwcOVKtWrWSxWJSXl2fXfbhw4YKmTJmisLAwNW/eXAEBARo1apROnDhhtxrSz8dJ165d1bx5c914442Ki4vTzp077Vrjlx577DFZLBYtWLDArjUeeuihy46TQYMG2XUf9u/fr6FDh8rHx0fNmzdX7969lZ+fb7caVR3rFotFzz//vN1qnD17VuPGjVP79u3l6empbt26aenSpTUevyY1ioqK9NBDDykgIEDNmjXToEGDanXs1eRz7qefftLYsWPVqlUr3XDDDbrvvvsu+xKJ6xUBsA7Wrl2r5ORkzZo1S7m5uQoPD1d8fLyKi4vtVqOsrEzh4eFavHix3cb8pW3btmns2LHasWOHMjMzdeHCBQ0cOFBlZWV2q9G+fXvNmTNHOTk52r17t+68807dc889+uqrr+xW45c+//xzvfLKK+rZs6fdx+7evbsKCgpsr08//dRuY//www/q27evXF1d9cEHH+jrr7/WvHnzdOONN9qtxueff15p/pmZmZKk+++/3241nnvuOS1ZskSLFi3S/v379dxzz2nu3LlauHCh3WpI0iOPPKLMzEytXLlSe/fu1cCBAxUXF6fjx4/XabyrHWtz587Vyy+/rKVLl2rnzp1q3ry54uPj9dNPP9ll/LKyMvXr10/PPfdcneZ/tRrnzp1Tbm6uUlNTlZubq3feeUcHDhzQ0KFD7VZDkjp37qxFixZp7969+vTTTxUSEqKBAwfq5MmTdqtx0fr167Vjxw4FBATUah9qWmPQoEGVjpe33nrLbuMfPnxY/fr1U9euXbV161Z9+eWXSk1NrfHjx2pS45dzLygo0GuvvSaLxaL77rvPbjWSk5OVkZGhVatWaf/+/Zo0aZLGjRunDRs22KWGYRhKSEjQv/71L7377rvas2ePgoODFRcXV+PPqZp8zk2ePFnvvfee1q1bp23btunEiRO69957a7wPTZqBWuvTp48xduxY288VFRVGQECAkZaW5pB6koz169c7ZOyLiouLDUnGtm3bHFrnxhtvNF599VW7j3vmzBkjNDTUyMzMNPr3729MnDjRbmPPmjXLCA8Pt9t4l5oyZYrRr18/h41flYkTJxo33XSTYbVa7TbmkCFDjIcffrhS27333muMHDnSbjXOnTtnODs7Gxs3bqzU3qtXL+PJJ5+85vEvPdasVqvh7+9vPP/887a206dPG+7u7sZbb711zeP/0pEjRwxJxp49e2o9bk1rXLRr1y5DknH06FGH1SgpKTEkGZs3b7ZrjX//+99Gu3btjH379hnBwcHGiy++WKfxq6uRlJRk3HPPPXUe82rjJyYmGr/97W/tMn51NS51zz33GHfeeadda3Tv3t344x//WKntWo7DS2scOHDAkGTs27fP1lZRUWG0bt3aWL58eZ1qXPo5d/r0acPV1dVYt26drc/+/fsNSUZ2dnadajQlrADW0vnz55WTk6O4uDhbm5OTk+Li4pSdnd2AM7s2JSUlkuSwL8auqKjQmjVrVFZW5pCv2hs7dqyGDBlS6f8Xezp06JACAgLUsWNHjRw5slana65mw4YNioqK0v333682bdrolltu0fLly+02/qXOnz+vVatW6eGHH5bFYrHbuLGxscrKytLBgwclSV988YU+/fRTDR482G41/vOf/6iiouKy1RJPT0+7rspedOTIERUWFlb678rHx0fR0dFN/ni3WCxq0aKFQ8Y/f/68li1bJh8fH4WHh9ttXKvVqgcffFApKSnq3r273ca91NatW9WmTRt16dJFv/vd7/Tdd9/ZZVyr1apNmzapc+fOio+PV5s2bRQdHW33S3x+qaioSJs2bdKYMWPsOm5sbKw2bNig48ePyzAMbdmyRQcPHtTAgQPtMn55ebkkVTrWnZyc5O7uXudj/dLPuZycHF24cKHS8d21a1cFBQU16eO7pgiAtXTq1ClVVFTYvoHkIj8/PxUWFjbQrK6N1WrVpEmT1Ldv30rflGIPe/fu1Q033CB3d3c99thjWr9+vbp162bXGmvWrFFubq7tawDtLTo6Wm+88YYyMjK0ZMkSHTlyRLfddpvOnDljl/H/9a9/acmSJQoNDdWHH36o3/3ud5owYYL+8pe/2GX8S6Wnp+v06dN66KGH7Dru1KlTNXz4cHXt2lWurq665ZZbNGnSJI0cOdJuNby8vBQTE6M//elPOnHihCoqKrRq1SplZ2eroKDAbnUuunhMX0/H+08//aQpU6ZoxIgR8vb2tuvYGzdu1A033CAPDw+9+OKLyszMlK+vr93Gf+655+Ti4qIJEybYbcxLDRo0SG+++aaysrL03HPPadu2bRo8eLAqKiqueezi4mKdPXtWc+bM0aBBg/TRRx9p2LBhuvfee7Vt2zY7zP5yf/nLX+Tl5WX305oLFy5Ut27d1L59e7m5uWnQoEFavHixbr/9druMfzGITZs2TT/88IPOnz+v5557Tv/+97/rdKxX9TlXWFgoNze3y/4h1JSP79poMl8FB8cZO3as9u3b55AVlC5duigvL08lJSX629/+pqSkJG3bts1uIfDYsWOaOHGiMjMza3UNTW38cgWrZ8+eio6OVnBwsN5++227/KvaarUqKipKzz77rCTplltu0b59+7R06VIlJSVd8/iXWrFihQYPHlyn66eu5O2339Zf//pXrV69Wt27d1deXp4mTZqkgIAAu+7HypUr9fDDD6tdu3ZydnZWr169NGLECOXk5NitxvXqwoULeuCBB2QYhpYsWWL38e+44w7l5eXp1KlTWr58uR544AHt3LlTbdq0ueaxc3Jy9NJLLyk3N9euK9eXGj58uO3PYWFh6tmzp2666SZt3bpVAwYMuKaxrVarJOmee+7R5MmTJUkRERHavn27li5dqv79+1/T+FV57bXXNHLkSLv//bhw4ULt2LFDGzZsUHBwsD7++GONHTtWAQEBdjkT4+rqqnfeeUdjxoxRy5Yt5ezsrLi4OA0ePLhON5Y58nOuqWIFsJZ8fX3l7Ox82V1CRUVF8vf3b6BZ1d24ceO0ceNGbdmyRe3bt7f7+G5uburUqZMiIyOVlpam8PBwvfTSS3YbPycnR8XFxerVq5dcXFzk4uKibdu26eWXX5aLi4td/tV+qRYtWqhz58765z//aZfx2rZte1kgvvnmm+16mvmio0ePavPmzXrkkUfsPnZKSoptFTAsLEwPPvigJk+ebPeV2Ztuuknbtm3T2bNndezYMe3atUsXLlxQx44d7VpHku2Yvh6O94vh7+jRo8rMzLT76p8kNW/eXJ06ddKtt96qFStWyMXFRStWrLDL2J988omKi4sVFBRkO9aPHj2qxx9/XCEhIXapUZWOHTvK19fXLse7r6+vXFxc6u14/+STT3TgwAG7H+8//vijpk+frvnz5+vuu+9Wz549NW7cOCUmJuqFF16wW53IyEjl5eXp9OnTKigoUEZGhr777rtaH+vVfc75+/vr/PnzOn36dKX+TfH4rgsCYC25ubkpMjJSWVlZtjar1aqsrCyHXNvmKIZhaNy4cVq/fr3+8Y9/qEOHDvVS12q12q7tsIcBAwZo7969ysvLs72ioqI0cuRI5eXlydnZ2W61Ljp79qwOHz6stm3b2mW8vn37XvZogoMHDyo4ONgu4//S66+/rjZt2mjIkCF2H/vcuXNycqr8V4qzs7Nt1cPemjdvrrZt2+qHH37Qhx9+qHvuucfuNTp06CB/f/9Kx3tpaal27tzZpI73i+Hv0KFD2rx5s1q1alUvde15vD/44IP68ssvKx3rAQEBSklJ0YcffmiXGlX597//re+++84ux7ubm5t69+5db8f7ihUrFBkZadfrMKWf/3u6cOFCvR3vPj4+at26tQ4dOqTdu3fX+Fi/2udcZGSkXF1dKx3fBw4cUH5+fpM6vuuKU8B1kJycrKSkJEVFRalPnz5asGCBysrKNHr0aLvVOHv2bKV/cR45ckR5eXlq2bKlgoKCrnn8sWPHavXq1Xr33Xfl5eVlu97Bx8dHnp6e1zy+JE2bNk2DBw9WUFCQzpw5o9WrV2vr1q12/cvay8vrsusWmzdvrlatWtntesY//OEPuvvuuxUcHKwTJ05o1qxZcnZ21ogRI+wy/uTJkxUbG6tnn31WDzzwgHbt2qVly5Zp2bJldhn/IqvVqtdff11JSUlycbH/oX/33XfrmWeeUVBQkLp37649e/Zo/vz5evjhh+1a58MPP5RhGOrSpYv++c9/KiUlRV27dq3z8Xe1Y23SpEl6+umnFRoaqg4dOig1NVUBAQFKSEiwy/jff/+98vPzbc/luxgO/P39a7wKcaUabdu21W9+8xvl5uZq48aNqqiosB3vLVu2lJub2zXXaNWqlZ555hkNHTpUbdu21alTp7R48WIdP368Vo8autrv6tLg6urqKn9/f3Xp0sUuNVq2bKnZs2frvvvuk7+/vw4fPqwnnnhCnTp1Unx8vF32ISUlRYmJibr99tt1xx13KCMjQ++99562bt1ql324+PlQWlqqdevWad68eTUetzY1+vfvr5SUFHl6eio4OFjbtm3Tm2++qfnz59utxrp169S6dWsFBQVp7969mjhxohISEmp8o8nVPud8fHw0ZswYJScnq2XLlvL29tb48eMVExOjW2+9tcb70WQ15C3ITdnChQuNoKAgw83NzejTp4+xY8cOu46/ZcsWQ9Jlr6SkJLuMX9XYkozXX3/dLuMbhmE8/PDDRnBwsOHm5ma0bt3aGDBggPHRRx/Zbfzq2PsxMImJiUbbtm0NNzc3o127dkZiYqLxz3/+027jG4ZhvPfee0aPHj0Md3d3o2vXrsayZcvsOr5hGMaHH35oSDIOHDhg97ENwzBKS0uNiRMnGkFBQYaHh4fRsWNH48knnzTKy8vtWmft2rVGx44dDTc3N8Pf398YO3ascfr06TqPd7VjzWq1GqmpqYafn5/h7u5uDBgwoFa/w6uN//rrr1f5/qxZs+xS4+LjZap6bdmyxS41fvzxR2PYsGFGQECA4ebmZrRt29YYOnSosWvXrhqPX5Pf1aXq8hiYK9U4d+6cMXDgQKN169aGq6urERwcbDz66KNGYWGhXfdhxYoVRqdOnQwPDw8jPDzcSE9Pt9s+XPTKK68Ynp6edT42rlajoKDAeOihh4yAgADDw8PD6NKlizFv3rxaPVrqajVeeuklo3379oarq6sRFBRkzJgxo1Z/n9Tkc+7HH380fv/73xs33nij0axZM2PYsGFGQUFBjWs0ZRbDsPNj+gEAANCocQ0gAACAyRAAAQAATIYACAAAYDIEQAAAAJMhAAIAAJgMARAAAMBkCIAAAAAmQwAE0GT86le/0qRJk2w/h4SEaMGCBVfcxmKxKD093aHzakxq8jsBAL4KDkCT9fnnn6t58+Z2HfOpp55Senq68vLy7DouADQmBEAATVbr1q0begoA0CRxChhArVmtVs2dO1edOnWSu7u7goKC9Mwzz9jenzJlijp37qxmzZqpY8eOSk1N1YULF2zvP/XUU4qIiNDKlSsVEhIiHx8fDR8+XGfOnLH1KSsr06hRo3TDDTeobdu2VX6p/aWnOw8dOqTbb79dHh4e6tatmzIzMy/b5kpze+ONNzR79mx98cUXslgsslgseuONNyRJp0+f1iOPPKLWrVvL29tbd955p7744otqf0fffvutLBaL3n77bd12223y9PRU7969dfDgQX3++eeKiorSDTfcoMGDB+vkyZO27T7//HP9+te/lq+vr3x8fNS/f3/l5uba3jcMQ0899ZSCgoLk7u6ugIAATZgwodp5vPrqq2rRooWysrIkSX/7298UFhYmT09PtWrVSnFxcSorK6t2ewDXJ1YAAdTatGnTtHz5cr344ovq16+fCgoK9M0339je9/Ly0htvvKGAgADt3btXjz76qLy8vPTEE0/Y+hw+fFjp6enauHGjfvjhBz3wwAOaM2eOLUimpKRo27Ztevfdd9WmTRtNnz5dubm5ioiIqHJOVqtV9957r/z8/LRz506VlJRUul6wJnNLTEzUvn37lJGRoc2bN0uSfHx8JEn333+/PD099cEHH8jHx0evvPKKBgwYoIMHD6ply5bV/q5mzZqlBQsWKCgoSA8//LD++7//W15eXnrppZfUrFkzPfDAA5o5c6aWLFkiSTpz5oySkpK0cOFCGYahefPm6a677tKhQ4fk5eWlv//973rxxRe1Zs0ade/eXYWFhdUG0blz52ru3Ln66KOP1KdPHxUUFGjEiBGaO3euhg0bpjNnzuiTTz4RXwkPmJABALVQWlpquLu7G8uXL6/xNs8//7wRGRlp+3nWrFlGs2bNjNLSUltbSkqKER0dbRiGYZw5c8Zwc3Mz3n77bdv73333neHp6WlMnDjR1hYcHGy8+OKLhmEYxocffmi4uLgYx48ft73/wQcfGJKM9evX12pu4eHhlfp88sknhre3t/HTTz9Var/pppuMV155pcpxjxw5YkgyXn31VVvbW2+9ZUgysrKybG1paWlGly5dqp1fRUWF4eXlZbz33nuGYRjGvHnzjM6dOxvnz5+vsv/F38kTTzxhtG3b1ti3b5/tvZycHEOS8e2331ZbD4A5sAIIoFb279+v8vJyDRgwoNo+a9eu1csvv6zDhw/r7Nmz+s9//iNvb+9KfUJCQuTl5WX7uW3btiouLpb08+rg+fPnFR0dbXu/ZcuW6tKlyxXnFRgYqICAAFtbTExMneZ2qS+++EJnz55Vq1atKrX/+OOPOnz48BW37dmzp+3Pfn5+kqSwsLBKbRf3W5KKioo0Y8YMbd26VcXFxaqoqNC5c+eUn58v6eeVyAULFqhjx44aNGiQ7rrrLt19991ycfn/v87nzZunsrIy7d69Wx07drS1h4eHa8CAAQoLC1N8fLwGDhyo3/zmN7rxxhuvuA8Arj9cAwigVjw9Pa/4fnZ2tkaOHKm77rpLGzdu1J49e/Tkk0/q/Pnzlfq5urpW+tlischqtdp9vnWZ26XOnj2rtm3bKi8vr9LrwIEDSklJueK2v9xPi8VSZdsv9zspKUl5eXl66aWXtH37duXl5alVq1a2OQYGBurAgQP685//LE9PT/3+97/X7bffXukay9tuu00VFRV6++23K83F2dlZmZmZ+uCDD9StWzctXLhQXbp00ZEjR67ymwNwvSEAAqiV0NBQeXp62m4quNT27dsVHBysJ598UlFRUQoNDdXRo0drVeOmm26Sq6urdu7caWv74YcfdPDgwWq3ufnmm3Xs2DEVFBTY2nbs2FHrubm5uamioqJSW69evVRYWCgXFxd16tSp0svX17dW+3Y1n332mSZMmKC77rpL3bt3l7u7u06dOlWpj6enp+6++269/PLL2rp1q7Kzs7V3717b+3369NEHH3ygZ599Vi+88EKlbS0Wi/r27avZs2drz549cnNz0/r16+26DwAaP04BA6gVDw8PTZkyRU888YTc3NzUt29fnTx5Ul999ZXGjBmj0NBQ5efna82aNerdu7c2bdpU64Bxww03aMyYMUpJSVGrVq3Upk0bPfnkk3Jyqv7frHFxcercubOSkpL0/PPPq7S0VE8++WSlPjWZW0hIiI4cOaK8vDy1b99eXl5eiouLU0xMjBISEjR37lx17txZJ06c0KZNmzRs2DBFRUXVav+uJDQ0VCtXrlRUVJRKS0uVkpJSadX1jTfeUEVFhaKjo9WsWTOtWrVKnp6eCg4OrjRObGys3n//fQ0ePFguLi6aNGmSdu7cqaysLA0cOFBt2rTRzp07dfLkSd188812mz+ApoEVQAC1lpqaqscff1wzZ87UzTffrMTERNt1bEOHDtXkyZM1btw4RUREaPv27UpNTa11jeeff1633Xab7r77bsXFxalfv36KjIystr+Tk5PWr1+vH3/8UX369NEjjzxS6dE0NZ3bfffdp0GDBumOO+5Q69at9dZbb8lisej999/X7bffrtGjR6tz584aPny4jh49aruuz15WrFihH374Qb169dKDDz6oCRMmqE2bNrb3W7RooeXLl6tv377q2bOnNm/erPfee++y6xMlqV+/ftq0aZNmzJihhQsXytvbWx9//LHuuusude7cWTNmzNC8efM0ePBgu+4DgMbPYhjc/w8AAGAmrAACAACYDAEQAADAZAiAAAAAJkMABAAAMBkCIAAAgMkQAAEAAEyGAAgAAGAyBEAAAACTIQACAACYDAEQAADAZAiAAAAAJkMABAAAMJn/A1cXgnhL9+q3AAAAAElFTkSuQmCC' 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+       "                <img 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' width=640.0/>\n",
        "            </div>\n",
        "        "
       ],
@@ -1599,25 +1978,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 238,
+   "execution_count": 37,
    "id": "9f22ca9d-bdc2-4ea5-b2bc-249a256bb8ad",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "c64139ea7ed94a1ea0e153e7728d34eb",
+       "model_id": "7aebc586f3684a8dbc8977aa2bcb8c38",
        "version_major": 2,
        "version_minor": 0
       },
-      "image/png": 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",
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",
       "text/html": [
        "\n",
        "            <div style=\"display: inline-block;\">\n",
        "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
        "                    Figure\n",
        "                </div>\n",
-       "                <img 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' 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+       "                <img 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' width=640.0/>\n",
        "            </div>\n",
        "        "
       ],
@@ -1637,6 +2016,14 @@
     "plt.ylabel(\"proportion\")\n",
     "plt.show()"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1009372d-08af-4dbd-9382-be1f02b4ad42",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
-- 
cgit v1.2.3-70-g09d2