From d46258c9cd7cc67960b073ef95178f5aeec4a7d3 Mon Sep 17 00:00:00 2001
From: Dazbo <darren_lester@epam.com>
Date: Fri, 3 Jan 2025 21:44:46 +0000
Subject: [PATCH] Label gates

---
 docs/assets/images/2024d24_circuit_vis.png    |  Bin 43023 -> 141894 bytes
 .../Dazbo's_Advent_of_Code_2024.ipynb         | 1819 ++++++++++++++++-
 2 files changed, 1790 insertions(+), 29 deletions(-)

diff --git a/docs/assets/images/2024d24_circuit_vis.png b/docs/assets/images/2024d24_circuit_vis.png
index db6d5ad0b48a9b11a0e96afb847c8dcd6c1d830f..ba5614cc66cd9582b30c6279e996141cee7ab8a3 100644
GIT binary patch
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diff --git a/src/AoC_2024/Dazbo's_Advent_of_Code_2024.ipynb b/src/AoC_2024/Dazbo's_Advent_of_Code_2024.ipynb
index 44f56a1..5d92049 100644
--- a/src/AoC_2024/Dazbo's_Advent_of_Code_2024.ipynb
+++ b/src/AoC_2024/Dazbo's_Advent_of_Code_2024.ipynb
@@ -46,7 +46,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 85,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -100,7 +100,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 86,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -246,7 +246,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 89,
+   "execution_count": 5,
    "metadata": {
     "id": "p5Ki_HvOJUWk",
     "tags": []
@@ -353,7 +353,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 91,
+   "execution_count": 7,
    "metadata": {
     "id": "lwP0r3BAaxjt",
     "tags": []
@@ -426,7 +426,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 92,
+   "execution_count": 8,
    "metadata": {
     "id": "Y6nbd6WMryWi",
     "tags": []
@@ -454,7 +454,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 93,
+   "execution_count": 9,
    "metadata": {
     "id": "A8sU4Ez_bBKl",
     "tags": []
@@ -624,7 +624,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 94,
+   "execution_count": 10,
    "metadata": {
     "id": "DT5FSYliC9wp",
     "tags": []
@@ -9057,7 +9057,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -9319,13 +9319,22 @@
     "\n",
     "We can observe that we have:\n",
     "\n",
-    "- A value `x`, represented as many `x` wires.\n",
-    "- A value `y`, represented as many `y` wires.\n",
-    "- A value `z`, represented as many `z` wires.\n",
+    "- A value `x`, represented as n `x` wires.\n",
+    "- A value `y`, represented as n `y` wires.\n",
+    "- A value `z`, represented as n+1 `z` wires.\n",
     "- For any combination of bits on wires starting with x and wires starting with y, the sum of the two numbers those bits represent should be produced as a binary number on the wires starting with z.\n",
     "- A series of functions applied between `x` and `y` wires, using only `AND / OR / XOR` to output to `z` wires. These functions are simulating binary addition.\n",
     "\n",
-    "We could just try all combinations of four swaps, and then test that the outputs add the inputs, as required. Our input data has about 200 rows of gate operations. So, to choose any 8 wires from 200 operations is a \"200 Choose 8\" problem:\n",
+    "A quick reminder of what these gates do:\n",
+    "\n",
+    "| x | y | AND | OR | XOR |\n",
+    "|---|---|-----|----|-----|\n",
+    "| 0 | 0 | 0   | 0  | 0   |\n",
+    "| 0 | 1 | 0   | 1  | 1   |\n",
+    "| 1 | 0 | 0   | 1  | 1   |\n",
+    "| 1 | 1 | 1   | 1  | 0   |\n",
+    "\n",
+    "We could just try all combinations of four swaps, and then test that the outputs correctly add the inputs, as required. Our input data has about 200 rows of gate operations. So, to choose any 8 wires from 200 operations is a \"200 Choose 8\" problem:\n",
     "\n",
     "```text\n",
     "200C8 = 200! / (8! * 192!)\n",
@@ -9373,9 +9382,1759 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\u001b[34m20:01:35.981:aoc2024 - DBG: wires={'x00': 1, 'x01': 0, 'x02': 0, 'x03': 1, 'x04': 1, 'x05': 0, 'x06': 0, 'x07': 0, 'x08': 0, 'x09': 0, 'x10': 0, 'x11': 1, 'x12': 0, 'x13': 1, 'x14': 1, 'x15': 1, 'x16': 1, 'x17': 0, 'x18': 0, 'x19': 1, 'x20': 0, 'x21': 0, 'x22': 1, 'x23': 1, 'x24': 1, 'x25': 0, 'x26': 1, 'x27': 1, 'x28': 0, 'x29': 1, 'x30': 0, 'x31': 1, 'x32': 0, 'x33': 1, 'x34': 0, 'x35': 1, 'x36': 1, 'x37': 0, 'x38': 1, 'x39': 1, 'x40': 1, 'x41': 1, 'x42': 0, 'x43': 1, 'x44': 1, 'y00': 1, 'y01': 0, 'y02': 0, 'y03': 1, 'y04': 1, 'y05': 1, 'y06': 0, 'y07': 0, 'y08': 0, 'y09': 1, 'y10': 0, 'y11': 0, 'y12': 0, 'y13': 1, 'y14': 1, 'y15': 0, 'y16': 1, 'y17': 0, 'y18': 1, 'y19': 1, 'y20': 1, 'y21': 0, 'y22': 0, 'y23': 1, 'y24': 1, 'y25': 1, 'y26': 0, 'y27': 1, 'y28': 0, 'y29': 1, 'y30': 0, 'y31': 0, 'y32': 0, 'y33': 1, 'y34': 1, 'y35': 1, 'y36': 1, 'y37': 0, 'y38': 0, 'y39': 0, 'y40': 0, 'y41': 1, 'y42': 0, 'y43': 1, 'y44': 1}\u001b[39m\n",
+      "\u001b[34m20:01:35.983:aoc2024 - DBG: connections_lines=['x36 AND y36 -> rpc', 'swn OR jrk -> kfm', 'x36 XOR y36 -> mvv', 'y28 XOR x28 -> rnh', 'bfp OR wqc -> rgb', 'tkc OR mfm -> brs', 'kmb XOR gfj -> z16', 'x25 AND y25 -> mdt', 'mpp AND hfd -> gjp', 'dhd AND mvb -> vrf', 'y14 XOR x14 -> qvt', 'shc OR bkk -> wvr', 'x29 AND y29 -> gdn', 'x11 XOR y11 -> jpp', 'rws OR fts -> mpp', 'wmq OR ngr -> knj', 'x24 XOR y24 -> gfg', 'tpf AND mgq -> tkc', 'wvr XOR jgw -> fkp', 'brs AND nmr -> qpb', 'x18 AND y18 -> qsw', 'pnb OR vjh -> sfh', 'x44 XOR y44 -> gcd', 'x22 AND y22 -> mhd', 'x37 XOR y37 -> dgg', 'vfj XOR dmh -> z15', 'x30 XOR y30 -> qgd', 'rpw OR gdn -> wrv', 'ptj OR vqm -> vjn', 'gfg AND pqf -> pnb', 'x17 XOR y17 -> rtv', 'y19 AND x19 -> wpt', 'sfp AND sbq -> tcv', 'hvv OR vmr -> kpq', 'pgc XOR fvj -> z02', 'knj AND ctw -> vqm', 'y42 XOR x42 -> vfb', 'y13 XOR x13 -> vdk', 'x43 AND y43 -> nhd', 'krg XOR dkw -> z43', 'y32 AND x32 -> vdm', 'hfd XOR mpp -> z08', 'nfq OR qgm -> cqq', 'x02 AND y02 -> nss', 'rvw XOR dtb -> z10', 'qvt AND qqv -> rgj', 'mvv XOR sgr -> z36', 'y11 AND x11 -> wmq', 'cnd XOR jqv -> z29', 'vdk XOR vjn -> z13', 'x34 AND y34 -> kjj', 'qvt XOR qqv -> z14', 'y18 XOR x18 -> mkt', 'bwk OR krn -> pqf', 'nhs XOR cqq -> z41', 'y31 AND x31 -> z31', 'y23 AND x23 -> bwk', 'sfh AND pmf -> ctp', 'rvw AND dtb -> sgv', 'tns AND chq -> dwv', 'rqt XOR snv -> z22', 'jqv AND cnd -> rpw', 'x33 AND y33 -> vtd', 'ctw XOR knj -> z12', 'bpp OR ghf -> z06', 'ffn AND rdj -> shc', 'cfw OR tnc -> sgr', 'wdm AND psv -> fwc', 'vwn OR wpt -> bvc', 'jkn OR gvk -> z45', 'x00 XOR y00 -> z00', 'qpf XOR mkt -> z18', 'y12 AND x12 -> ptj', 'dvq XOR rkm -> z04', 'x15 XOR y15 -> dmh', 'qrm OR nss -> wdm', 'mhv OR mnv -> rcs', 'qtq OR cqn -> nwk', 'x20 XOR y20 -> tpw', 'x04 AND y04 -> ptd', 'nhd OR pnk -> mdn', 'hjc OR hth -> pgc', 'x20 AND y20 -> qtq', 'gcd XOR mdn -> z44', 'mgq XOR tpf -> mfm', 'x30 AND y30 -> bbk', 'dmh AND vfj -> cpc', 'x44 AND y44 -> gvk', 'dwv OR jvf -> jjj', 'pkh AND fkp -> rws', 'x39 AND y39 -> wqc', 'fwc OR nbc -> rkm', 'bdc AND bbd -> dnc', 'x26 XOR y26 -> tns', 'csh AND mst -> vwn', 'x43 XOR y43 -> dkw', 'bvc XOR tpw -> z20', 'nwk XOR ngm -> z21', 'rtv XOR kfm -> z17', 'x06 AND y06 -> bpp', 'x10 XOR y10 -> dtb', 'y29 XOR x29 -> cnd', 'y08 XOR x08 -> hfd', 'y03 XOR x03 -> psv', 'rgj OR bph -> vfj', 'psv XOR wdm -> z03', 'dnc OR vtd -> mvb', 'gcn AND tqf -> krn', 'y38 XOR x38 -> krj', 'x24 AND y24 -> vjh', 'y41 AND x41 -> vmr', 'jgw AND wvr -> ghf', 'x09 XOR y09 -> sfp', 'y28 AND x28 -> wpw', 'x40 XOR y40 -> mkc', 'hsn AND dgg -> snc', 'jpp XOR stv -> ngr', 'mjb OR cpc -> gfj', 'rcs XOR rnh -> z28', 'sfp XOR sbq -> z09', 'rtv AND kfm -> jfr', 'tjh OR wpw -> jqv', 'x16 XOR y16 -> kmb', 'bgn OR wnm -> snv', 'nmr XOR brs -> z32', 'rpc OR dvm -> hsn', 'gfg XOR pqf -> z24', 'dkw AND krg -> pnk', 'kmb AND gfj -> jrk', 'skt XOR kjn -> z01', 'gcn XOR tqf -> z23', 'jjj XOR rhc -> z27', 'y07 AND x07 -> fts', 'y21 AND x21 -> wnm', 'kvd OR snc -> ntr', 'nht XOR hsp -> z39', 'wrv XOR qgd -> z30', 'y07 XOR x07 -> pkh', 'tdv OR krj -> hsp', 'stv AND jpp -> z11', 'x27 AND y27 -> mhv', 'bdc XOR bbd -> z33', 'x12 XOR y12 -> ctw', 'mvv AND sgr -> dvm', 'x27 XOR y27 -> rhc', 'x21 XOR y21 -> ngm', 'mhn XOR mdg -> z35', 'x19 XOR y19 -> csh', 'y35 XOR x35 -> mhn', 'snv AND rqt -> tfs', 'rkm AND dvq -> cjp', 'pgc AND fvj -> qrm', 'kpq XOR vfb -> z42', 'qgd AND wrv -> gqt', 'y26 AND x26 -> jvf', 'x39 XOR y39 -> nht', 'vdk AND vjn -> jqm', 'bvc AND tpw -> cqn', 'y32 XOR x32 -> nmr', 'x25 XOR y25 -> pmf', 'y09 AND x09 -> prs', 'y14 AND x14 -> bph', 'qpb OR vdm -> bdc', 'gqt OR bbk -> tpf', 'x40 AND y40 -> qgm', 'sfh XOR pmf -> z25', 'x22 XOR y22 -> rqt', 'rhc AND jjj -> mnv', 'csh XOR mst -> z19', 'x42 AND y42 -> krw', 'x34 XOR y34 -> dhd', 'x35 AND y35 -> tnc', 'ngm AND nwk -> bgn', 'tdh OR jqm -> qqv', 'y00 AND x00 -> skt', 'y41 XOR x41 -> nhs', 'ntr XOR bpt -> z38', 'vrf OR kjj -> mdg', 'kvf OR krw -> krg', 'x03 AND y03 -> nbc', 'dhd XOR mvb -> z34', 'qpf AND mkt -> rsd', 'y01 XOR x01 -> kjn', 'x17 AND y17 -> bvg', 'jfr OR bvg -> qpf', 'y13 AND x13 -> tdh', 'bpb OR gjp -> sbq', 'x16 AND y16 -> swn', 'x02 XOR y02 -> fvj', 'y15 AND x15 -> mjb', 'x23 XOR y23 -> tqf', 'rnh AND rcs -> tjh', 'x05 AND y05 -> bkk', 'hsn XOR dgg -> z37', 'qsw OR rsd -> mst', 'sgv OR qnf -> stv', 'y01 AND x01 -> hth', 'y38 AND x38 -> bpt', 'rgb AND mkc -> nfq', 'y33 XOR x33 -> bbd', 'tns XOR chq -> z26', 'ctp OR mdt -> chq', 'nhs AND cqq -> hvv', 'pkh XOR fkp -> z07', 'rdj XOR ffn -> z05', 'mhd OR tfs -> gcn', 'y10 AND x10 -> qnf', 'hsp AND nht -> bfp', 'gcd AND mdn -> jkn', 'ntr AND bpt -> tdv', 'prs OR tcv -> rvw', 'x05 XOR y05 -> ffn', 'y04 XOR x04 -> dvq', 'x31 XOR y31 -> mgq', 'y08 AND x08 -> bpb', 'mhn AND mdg -> cfw', 'y37 AND x37 -> kvd', 'rgb XOR mkc -> z40', 'cjp OR ptd -> rdj', 'x06 XOR y06 -> jgw', 'skt AND kjn -> hjc', 'vfb AND kpq -> kvf']\u001b[39m\n"
+     ]
+    },
+    {
+     "data": {
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AAEBz2rp16+LFi1esWPHuu+/GYrFYLJZOp4/rhIZFm3g8Pnjw4LKysvHjx/fo0aOFajmCSRoAAAAAAAAAAAAAAAAAAAAAoEXs3r179erVq1at2rhx444dO1KpVCQSicVi8Xg8Fos1vBMEQRAEDV9FIpFu3br1799/6NChw4YNu+SSS/Ly8kKrP1GZpAEAAAAAAAAAAAAAAAAAAAAAWlw2m925c+ebb7754Ycf1tXV7du3r7a2tkOHDvn5+V27du3WrdsZZ5xRXFzcs2fPsEtPdCZpAAAAAAAAAAAAAAAAAAAAAABoFAs7AAAAAAAAAAAAAAAAAAAAAACAtsIkDQAAAAAAAAAAAAAAAAAAAAAAjUzSAAAAAAAAAAAAAAAAAAAAAADQ6P8DqCvomHwdMMYAAAAASUVORK5CYII=",
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\u001b[32m20:01:40.401:aoc2024 - INF: Outputs with depth of 3:\u001b[39m\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "bbd = x33 ^ y33\n",
+      "  x33 = 1\n",
+      "  y33 = 1\n",
+      "bbk = x30 & y30\n",
+      "  x30 = 0\n",
+      "  y30 = 0\n",
+      "bdc = qpb | vdm\n",
+      "  qpb = brs & nmr\n",
+      "    brs = mfm | tkc\n",
+      "      mfm = mgq ^ tpf\n",
+      "      tkc = mgq & tpf\n",
+      "    nmr = x32 ^ y32\n",
+      "      x32 = 0\n",
+      "      y32 = 0\n",
+      "  vdm = x32 & y32\n",
+      "    x32 = 0\n",
+      "    y32 = 0\n",
+      "bfp = hsp & nht\n",
+      "  hsp = krj | tdv\n",
+      "    krj = x38 ^ y38\n",
+      "      x38 = 1\n",
+      "      y38 = 0\n",
+      "    tdv = bpt & ntr\n",
+      "      bpt = x38 & y38\n",
+      "      ntr = kvd | snc\n",
+      "  nht = x39 ^ y39\n",
+      "    x39 = 1\n",
+      "    y39 = 0\n",
+      "bgn = ngm & nwk\n",
+      "  ngm = x21 ^ y21\n",
+      "    x21 = 0\n",
+      "    y21 = 0\n",
+      "  nwk = cqn | qtq\n",
+      "    cqn = bvc & tpw\n",
+      "      bvc = vwn | wpt\n",
+      "      tpw = x20 ^ y20\n",
+      "    qtq = x20 & y20\n",
+      "      x20 = 0\n",
+      "      y20 = 1\n",
+      "bkk = x05 & y05\n",
+      "  x05 = 0\n",
+      "  y05 = 1\n",
+      "bpb = x08 & y08\n",
+      "  x08 = 0\n",
+      "  y08 = 0\n",
+      "bph = x14 & y14\n",
+      "  x14 = 1\n",
+      "  y14 = 1\n",
+      "bpp = x06 & y06\n",
+      "  x06 = 0\n",
+      "  y06 = 0\n",
+      "bpt = x38 & y38\n",
+      "  x38 = 1\n",
+      "  y38 = 0\n",
+      "brs = mfm | tkc\n",
+      "  mfm = mgq ^ tpf\n",
+      "    mgq = x31 ^ y31\n",
+      "      x31 = 1\n",
+      "      y31 = 0\n",
+      "    tpf = bbk | gqt\n",
+      "      bbk = x30 & y30\n",
+      "      gqt = qgd & wrv\n",
+      "  tkc = mgq & tpf\n",
+      "    mgq = x31 ^ y31\n",
+      "      x31 = 1\n",
+      "      y31 = 0\n",
+      "    tpf = bbk | gqt\n",
+      "      bbk = x30 & y30\n",
+      "      gqt = qgd & wrv\n",
+      "bvc = vwn | wpt\n",
+      "  vwn = csh & mst\n",
+      "    csh = x19 ^ y19\n",
+      "      x19 = 1\n",
+      "      y19 = 1\n",
+      "    mst = qsw | rsd\n",
+      "      qsw = x18 & y18\n",
+      "      rsd = mkt & qpf\n",
+      "  wpt = x19 & y19\n",
+      "    x19 = 1\n",
+      "    y19 = 1\n",
+      "bvg = x17 & y17\n",
+      "  x17 = 0\n",
+      "  y17 = 0\n",
+      "bwk = x23 & y23\n",
+      "  x23 = 1\n",
+      "  y23 = 1\n",
+      "cfw = mdg & mhn\n",
+      "  mdg = kjj | vrf\n",
+      "    kjj = x34 & y34\n",
+      "      x34 = 0\n",
+      "      y34 = 1\n",
+      "    vrf = dhd & mvb\n",
+      "      dhd = x34 ^ y34\n",
+      "      mvb = dnc | vtd\n",
+      "  mhn = x35 ^ y35\n",
+      "    x35 = 1\n",
+      "    y35 = 1\n",
+      "chq = ctp | mdt\n",
+      "  ctp = pmf & sfh\n",
+      "    pmf = x25 ^ y25\n",
+      "      x25 = 0\n",
+      "      y25 = 1\n",
+      "    sfh = pnb | vjh\n",
+      "      pnb = gfg & pqf\n",
+      "      vjh = x24 & y24\n",
+      "  mdt = x25 & y25\n",
+      "    x25 = 0\n",
+      "    y25 = 1\n",
+      "cjp = dvq & rkm\n",
+      "  dvq = x04 ^ y04\n",
+      "    x04 = 1\n",
+      "    y04 = 1\n",
+      "  rkm = fwc | nbc\n",
+      "    fwc = psv & wdm\n",
+      "      psv = x03 ^ y03\n",
+      "      wdm = nss | qrm\n",
+      "    nbc = x03 & y03\n",
+      "      x03 = 1\n",
+      "      y03 = 1\n",
+      "cnd = x29 ^ y29\n",
+      "  x29 = 1\n",
+      "  y29 = 1\n",
+      "cpc = dmh & vfj\n",
+      "  dmh = x15 ^ y15\n",
+      "    x15 = 1\n",
+      "    y15 = 0\n",
+      "  vfj = bph | rgj\n",
+      "    bph = x14 & y14\n",
+      "      x14 = 1\n",
+      "      y14 = 1\n",
+      "    rgj = qqv & qvt\n",
+      "      qqv = jqm | tdh\n",
+      "      qvt = x14 ^ y14\n",
+      "cqn = bvc & tpw\n",
+      "  bvc = vwn | wpt\n",
+      "    vwn = csh & mst\n",
+      "      csh = x19 ^ y19\n",
+      "      mst = qsw | rsd\n",
+      "    wpt = x19 & y19\n",
+      "      x19 = 1\n",
+      "      y19 = 1\n",
+      "  tpw = x20 ^ y20\n",
+      "    x20 = 0\n",
+      "    y20 = 1\n",
+      "cqq = nfq | qgm\n",
+      "  nfq = mkc & rgb\n",
+      "    mkc = x40 ^ y40\n",
+      "      x40 = 1\n",
+      "      y40 = 0\n",
+      "    rgb = bfp | wqc\n",
+      "      bfp = hsp & nht\n",
+      "      wqc = x39 & y39\n",
+      "  qgm = x40 & y40\n",
+      "    x40 = 1\n",
+      "    y40 = 0\n",
+      "csh = x19 ^ y19\n",
+      "  x19 = 1\n",
+      "  y19 = 1\n",
+      "ctp = pmf & sfh\n",
+      "  pmf = x25 ^ y25\n",
+      "    x25 = 0\n",
+      "    y25 = 1\n",
+      "  sfh = pnb | vjh\n",
+      "    pnb = gfg & pqf\n",
+      "      gfg = x24 ^ y24\n",
+      "      pqf = bwk | krn\n",
+      "    vjh = x24 & y24\n",
+      "      x24 = 1\n",
+      "      y24 = 1\n",
+      "ctw = x12 ^ y12\n",
+      "  x12 = 0\n",
+      "  y12 = 0\n",
+      "dgg = x37 ^ y37\n",
+      "  x37 = 0\n",
+      "  y37 = 0\n",
+      "dhd = x34 ^ y34\n",
+      "  x34 = 0\n",
+      "  y34 = 1\n",
+      "dkw = x43 ^ y43\n",
+      "  x43 = 1\n",
+      "  y43 = 1\n",
+      "dmh = x15 ^ y15\n",
+      "  x15 = 1\n",
+      "  y15 = 0\n",
+      "dnc = bbd & bdc\n",
+      "  bbd = x33 ^ y33\n",
+      "    x33 = 1\n",
+      "    y33 = 1\n",
+      "  bdc = qpb | vdm\n",
+      "    qpb = brs & nmr\n",
+      "      brs = mfm | tkc\n",
+      "      nmr = x32 ^ y32\n",
+      "    vdm = x32 & y32\n",
+      "      x32 = 0\n",
+      "      y32 = 0\n",
+      "dtb = x10 ^ y10\n",
+      "  x10 = 0\n",
+      "  y10 = 0\n",
+      "dvm = mvv & sgr\n",
+      "  mvv = x36 ^ y36\n",
+      "    x36 = 1\n",
+      "    y36 = 1\n",
+      "  sgr = cfw | tnc\n",
+      "    cfw = mdg & mhn\n",
+      "      mdg = kjj | vrf\n",
+      "      mhn = x35 ^ y35\n",
+      "    tnc = x35 & y35\n",
+      "      x35 = 1\n",
+      "      y35 = 1\n",
+      "dvq = x04 ^ y04\n",
+      "  x04 = 1\n",
+      "  y04 = 1\n",
+      "dwv = chq & tns\n",
+      "  chq = ctp | mdt\n",
+      "    ctp = pmf & sfh\n",
+      "      pmf = x25 ^ y25\n",
+      "      sfh = pnb | vjh\n",
+      "    mdt = x25 & y25\n",
+      "      x25 = 0\n",
+      "      y25 = 1\n",
+      "  tns = x26 ^ y26\n",
+      "    x26 = 1\n",
+      "    y26 = 0\n",
+      "ffn = x05 ^ y05\n",
+      "  x05 = 0\n",
+      "  y05 = 1\n",
+      "fkp = jgw ^ wvr\n",
+      "  jgw = x06 ^ y06\n",
+      "    x06 = 0\n",
+      "    y06 = 0\n",
+      "  wvr = bkk | shc\n",
+      "    bkk = x05 & y05\n",
+      "      x05 = 0\n",
+      "      y05 = 1\n",
+      "    shc = ffn & rdj\n",
+      "      ffn = x05 ^ y05\n",
+      "      rdj = cjp | ptd\n",
+      "fts = x07 & y07\n",
+      "  x07 = 0\n",
+      "  y07 = 0\n",
+      "fvj = x02 ^ y02\n",
+      "  x02 = 0\n",
+      "  y02 = 0\n",
+      "fwc = psv & wdm\n",
+      "  psv = x03 ^ y03\n",
+      "    x03 = 1\n",
+      "    y03 = 1\n",
+      "  wdm = nss | qrm\n",
+      "    nss = x02 & y02\n",
+      "      x02 = 0\n",
+      "      y02 = 0\n",
+      "    qrm = fvj & pgc\n",
+      "      fvj = x02 ^ y02\n",
+      "      pgc = hjc | hth\n",
+      "gcd = x44 ^ y44\n",
+      "  x44 = 1\n",
+      "  y44 = 1\n",
+      "gcn = mhd | tfs\n",
+      "  mhd = x22 & y22\n",
+      "    x22 = 1\n",
+      "    y22 = 0\n",
+      "  tfs = rqt & snv\n",
+      "    rqt = x22 ^ y22\n",
+      "      x22 = 1\n",
+      "      y22 = 0\n",
+      "    snv = bgn | wnm\n",
+      "      bgn = ngm & nwk\n",
+      "      wnm = x21 & y21\n",
+      "gdn = x29 & y29\n",
+      "  x29 = 1\n",
+      "  y29 = 1\n",
+      "gfg = x24 ^ y24\n",
+      "  x24 = 1\n",
+      "  y24 = 1\n",
+      "gfj = cpc | mjb\n",
+      "  cpc = dmh & vfj\n",
+      "    dmh = x15 ^ y15\n",
+      "      x15 = 1\n",
+      "      y15 = 0\n",
+      "    vfj = bph | rgj\n",
+      "      bph = x14 & y14\n",
+      "      rgj = qqv & qvt\n",
+      "  mjb = x15 & y15\n",
+      "    x15 = 1\n",
+      "    y15 = 0\n",
+      "ghf = jgw & wvr\n",
+      "  jgw = x06 ^ y06\n",
+      "    x06 = 0\n",
+      "    y06 = 0\n",
+      "  wvr = bkk | shc\n",
+      "    bkk = x05 & y05\n",
+      "      x05 = 0\n",
+      "      y05 = 1\n",
+      "    shc = ffn & rdj\n",
+      "      ffn = x05 ^ y05\n",
+      "      rdj = cjp | ptd\n",
+      "gjp = hfd & mpp\n",
+      "  hfd = x08 ^ y08\n",
+      "    x08 = 0\n",
+      "    y08 = 0\n",
+      "  mpp = fts | rws\n",
+      "    fts = x07 & y07\n",
+      "      x07 = 0\n",
+      "      y07 = 0\n",
+      "    rws = fkp & pkh\n",
+      "      fkp = jgw ^ wvr\n",
+      "      pkh = x07 ^ y07\n",
+      "gqt = qgd & wrv\n",
+      "  qgd = x30 ^ y30\n",
+      "    x30 = 0\n",
+      "    y30 = 0\n",
+      "  wrv = gdn | rpw\n",
+      "    gdn = x29 & y29\n",
+      "      x29 = 1\n",
+      "      y29 = 1\n",
+      "    rpw = cnd & jqv\n",
+      "      cnd = x29 ^ y29\n",
+      "      jqv = tjh | wpw\n",
+      "gvk = x44 & y44\n",
+      "  x44 = 1\n",
+      "  y44 = 1\n",
+      "hfd = x08 ^ y08\n",
+      "  x08 = 0\n",
+      "  y08 = 0\n",
+      "hjc = kjn & skt\n",
+      "  kjn = x01 ^ y01\n",
+      "    x01 = 0\n",
+      "    y01 = 0\n",
+      "  skt = x00 & y00\n",
+      "    x00 = 1\n",
+      "    y00 = 1\n",
+      "hsn = dvm | rpc\n",
+      "  dvm = mvv & sgr\n",
+      "    mvv = x36 ^ y36\n",
+      "      x36 = 1\n",
+      "      y36 = 1\n",
+      "    sgr = cfw | tnc\n",
+      "      cfw = mdg & mhn\n",
+      "      tnc = x35 & y35\n",
+      "  rpc = x36 & y36\n",
+      "    x36 = 1\n",
+      "    y36 = 1\n",
+      "hsp = krj | tdv\n",
+      "  krj = x38 ^ y38\n",
+      "    x38 = 1\n",
+      "    y38 = 0\n",
+      "  tdv = bpt & ntr\n",
+      "    bpt = x38 & y38\n",
+      "      x38 = 1\n",
+      "      y38 = 0\n",
+      "    ntr = kvd | snc\n",
+      "      kvd = x37 & y37\n",
+      "      snc = dgg & hsn\n",
+      "hth = x01 & y01\n",
+      "  x01 = 0\n",
+      "  y01 = 0\n",
+      "hvv = cqq & nhs\n",
+      "  cqq = nfq | qgm\n",
+      "    nfq = mkc & rgb\n",
+      "      mkc = x40 ^ y40\n",
+      "      rgb = bfp | wqc\n",
+      "    qgm = x40 & y40\n",
+      "      x40 = 1\n",
+      "      y40 = 0\n",
+      "  nhs = x41 ^ y41\n",
+      "    x41 = 1\n",
+      "    y41 = 1\n",
+      "jfr = kfm & rtv\n",
+      "  kfm = jrk | swn\n",
+      "    jrk = gfj & kmb\n",
+      "      gfj = cpc | mjb\n",
+      "      kmb = x16 ^ y16\n",
+      "    swn = x16 & y16\n",
+      "      x16 = 1\n",
+      "      y16 = 1\n",
+      "  rtv = x17 ^ y17\n",
+      "    x17 = 0\n",
+      "    y17 = 0\n",
+      "jgw = x06 ^ y06\n",
+      "  x06 = 0\n",
+      "  y06 = 0\n",
+      "jjj = dwv | jvf\n",
+      "  dwv = chq & tns\n",
+      "    chq = ctp | mdt\n",
+      "      ctp = pmf & sfh\n",
+      "      mdt = x25 & y25\n",
+      "    tns = x26 ^ y26\n",
+      "      x26 = 1\n",
+      "      y26 = 0\n",
+      "  jvf = x26 & y26\n",
+      "    x26 = 1\n",
+      "    y26 = 0\n",
+      "jkn = gcd & mdn\n",
+      "  gcd = x44 ^ y44\n",
+      "    x44 = 1\n",
+      "    y44 = 1\n",
+      "  mdn = nhd | pnk\n",
+      "    nhd = x43 & y43\n",
+      "      x43 = 1\n",
+      "      y43 = 1\n",
+      "    pnk = dkw & krg\n",
+      "      dkw = x43 ^ y43\n",
+      "      krg = krw | kvf\n",
+      "jpp = x11 ^ y11\n",
+      "  x11 = 1\n",
+      "  y11 = 0\n",
+      "jqm = vdk & vjn\n",
+      "  vdk = x13 ^ y13\n",
+      "    x13 = 1\n",
+      "    y13 = 1\n",
+      "  vjn = ptj | vqm\n",
+      "    ptj = x12 & y12\n",
+      "      x12 = 0\n",
+      "      y12 = 0\n",
+      "    vqm = ctw & knj\n",
+      "      ctw = x12 ^ y12\n",
+      "      knj = ngr | wmq\n",
+      "jqv = tjh | wpw\n",
+      "  tjh = rcs & rnh\n",
+      "    rcs = mhv | mnv\n",
+      "      mhv = x27 & y27\n",
+      "      mnv = jjj & rhc\n",
+      "    rnh = x28 ^ y28\n",
+      "      x28 = 0\n",
+      "      y28 = 0\n",
+      "  wpw = x28 & y28\n",
+      "    x28 = 0\n",
+      "    y28 = 0\n",
+      "jrk = gfj & kmb\n",
+      "  gfj = cpc | mjb\n",
+      "    cpc = dmh & vfj\n",
+      "      dmh = x15 ^ y15\n",
+      "      vfj = bph | rgj\n",
+      "    mjb = x15 & y15\n",
+      "      x15 = 1\n",
+      "      y15 = 0\n",
+      "  kmb = x16 ^ y16\n",
+      "    x16 = 1\n",
+      "    y16 = 1\n",
+      "jvf = x26 & y26\n",
+      "  x26 = 1\n",
+      "  y26 = 0\n",
+      "kfm = jrk | swn\n",
+      "  jrk = gfj & kmb\n",
+      "    gfj = cpc | mjb\n",
+      "      cpc = dmh & vfj\n",
+      "      mjb = x15 & y15\n",
+      "    kmb = x16 ^ y16\n",
+      "      x16 = 1\n",
+      "      y16 = 1\n",
+      "  swn = x16 & y16\n",
+      "    x16 = 1\n",
+      "    y16 = 1\n",
+      "kjj = x34 & y34\n",
+      "  x34 = 0\n",
+      "  y34 = 1\n",
+      "kjn = x01 ^ y01\n",
+      "  x01 = 0\n",
+      "  y01 = 0\n",
+      "kmb = x16 ^ y16\n",
+      "  x16 = 1\n",
+      "  y16 = 1\n",
+      "knj = ngr | wmq\n",
+      "  ngr = jpp ^ stv\n",
+      "    jpp = x11 ^ y11\n",
+      "      x11 = 1\n",
+      "      y11 = 0\n",
+      "    stv = qnf | sgv\n",
+      "      qnf = x10 & y10\n",
+      "      sgv = dtb & rvw\n",
+      "  wmq = x11 & y11\n",
+      "    x11 = 1\n",
+      "    y11 = 0\n",
+      "kpq = hvv | vmr\n",
+      "  hvv = cqq & nhs\n",
+      "    cqq = nfq | qgm\n",
+      "      nfq = mkc & rgb\n",
+      "      qgm = x40 & y40\n",
+      "    nhs = x41 ^ y41\n",
+      "      x41 = 1\n",
+      "      y41 = 1\n",
+      "  vmr = x41 & y41\n",
+      "    x41 = 1\n",
+      "    y41 = 1\n",
+      "krg = krw | kvf\n",
+      "  krw = x42 & y42\n",
+      "    x42 = 0\n",
+      "    y42 = 0\n",
+      "  kvf = kpq & vfb\n",
+      "    kpq = hvv | vmr\n",
+      "      hvv = cqq & nhs\n",
+      "      vmr = x41 & y41\n",
+      "    vfb = x42 ^ y42\n",
+      "      x42 = 0\n",
+      "      y42 = 0\n",
+      "krj = x38 ^ y38\n",
+      "  x38 = 1\n",
+      "  y38 = 0\n",
+      "krn = gcn & tqf\n",
+      "  gcn = mhd | tfs\n",
+      "    mhd = x22 & y22\n",
+      "      x22 = 1\n",
+      "      y22 = 0\n",
+      "    tfs = rqt & snv\n",
+      "      rqt = x22 ^ y22\n",
+      "      snv = bgn | wnm\n",
+      "  tqf = x23 ^ y23\n",
+      "    x23 = 1\n",
+      "    y23 = 1\n",
+      "krw = x42 & y42\n",
+      "  x42 = 0\n",
+      "  y42 = 0\n",
+      "kvd = x37 & y37\n",
+      "  x37 = 0\n",
+      "  y37 = 0\n",
+      "kvf = kpq & vfb\n",
+      "  kpq = hvv | vmr\n",
+      "    hvv = cqq & nhs\n",
+      "      cqq = nfq | qgm\n",
+      "      nhs = x41 ^ y41\n",
+      "    vmr = x41 & y41\n",
+      "      x41 = 1\n",
+      "      y41 = 1\n",
+      "  vfb = x42 ^ y42\n",
+      "    x42 = 0\n",
+      "    y42 = 0\n",
+      "mdg = kjj | vrf\n",
+      "  kjj = x34 & y34\n",
+      "    x34 = 0\n",
+      "    y34 = 1\n",
+      "  vrf = dhd & mvb\n",
+      "    dhd = x34 ^ y34\n",
+      "      x34 = 0\n",
+      "      y34 = 1\n",
+      "    mvb = dnc | vtd\n",
+      "      dnc = bbd & bdc\n",
+      "      vtd = x33 & y33\n",
+      "mdn = nhd | pnk\n",
+      "  nhd = x43 & y43\n",
+      "    x43 = 1\n",
+      "    y43 = 1\n",
+      "  pnk = dkw & krg\n",
+      "    dkw = x43 ^ y43\n",
+      "      x43 = 1\n",
+      "      y43 = 1\n",
+      "    krg = krw | kvf\n",
+      "      krw = x42 & y42\n",
+      "      kvf = kpq & vfb\n",
+      "mdt = x25 & y25\n",
+      "  x25 = 0\n",
+      "  y25 = 1\n",
+      "mfm = mgq ^ tpf\n",
+      "  mgq = x31 ^ y31\n",
+      "    x31 = 1\n",
+      "    y31 = 0\n",
+      "  tpf = bbk | gqt\n",
+      "    bbk = x30 & y30\n",
+      "      x30 = 0\n",
+      "      y30 = 0\n",
+      "    gqt = qgd & wrv\n",
+      "      qgd = x30 ^ y30\n",
+      "      wrv = gdn | rpw\n",
+      "mgq = x31 ^ y31\n",
+      "  x31 = 1\n",
+      "  y31 = 0\n",
+      "mhd = x22 & y22\n",
+      "  x22 = 1\n",
+      "  y22 = 0\n",
+      "mhn = x35 ^ y35\n",
+      "  x35 = 1\n",
+      "  y35 = 1\n",
+      "mhv = x27 & y27\n",
+      "  x27 = 1\n",
+      "  y27 = 1\n",
+      "mjb = x15 & y15\n",
+      "  x15 = 1\n",
+      "  y15 = 0\n",
+      "mkc = x40 ^ y40\n",
+      "  x40 = 1\n",
+      "  y40 = 0\n",
+      "mkt = x18 ^ y18\n",
+      "  x18 = 0\n",
+      "  y18 = 1\n",
+      "mnv = jjj & rhc\n",
+      "  jjj = dwv | jvf\n",
+      "    dwv = chq & tns\n",
+      "      chq = ctp | mdt\n",
+      "      tns = x26 ^ y26\n",
+      "    jvf = x26 & y26\n",
+      "      x26 = 1\n",
+      "      y26 = 0\n",
+      "  rhc = x27 ^ y27\n",
+      "    x27 = 1\n",
+      "    y27 = 1\n",
+      "mpp = fts | rws\n",
+      "  fts = x07 & y07\n",
+      "    x07 = 0\n",
+      "    y07 = 0\n",
+      "  rws = fkp & pkh\n",
+      "    fkp = jgw ^ wvr\n",
+      "      jgw = x06 ^ y06\n",
+      "      wvr = bkk | shc\n",
+      "    pkh = x07 ^ y07\n",
+      "      x07 = 0\n",
+      "      y07 = 0\n",
+      "mst = qsw | rsd\n",
+      "  qsw = x18 & y18\n",
+      "    x18 = 0\n",
+      "    y18 = 1\n",
+      "  rsd = mkt & qpf\n",
+      "    mkt = x18 ^ y18\n",
+      "      x18 = 0\n",
+      "      y18 = 1\n",
+      "    qpf = bvg | jfr\n",
+      "      bvg = x17 & y17\n",
+      "      jfr = kfm & rtv\n",
+      "mvb = dnc | vtd\n",
+      "  dnc = bbd & bdc\n",
+      "    bbd = x33 ^ y33\n",
+      "      x33 = 1\n",
+      "      y33 = 1\n",
+      "    bdc = qpb | vdm\n",
+      "      qpb = brs & nmr\n",
+      "      vdm = x32 & y32\n",
+      "  vtd = x33 & y33\n",
+      "    x33 = 1\n",
+      "    y33 = 1\n",
+      "mvv = x36 ^ y36\n",
+      "  x36 = 1\n",
+      "  y36 = 1\n",
+      "nbc = x03 & y03\n",
+      "  x03 = 1\n",
+      "  y03 = 1\n",
+      "nfq = mkc & rgb\n",
+      "  mkc = x40 ^ y40\n",
+      "    x40 = 1\n",
+      "    y40 = 0\n",
+      "  rgb = bfp | wqc\n",
+      "    bfp = hsp & nht\n",
+      "      hsp = krj | tdv\n",
+      "      nht = x39 ^ y39\n",
+      "    wqc = x39 & y39\n",
+      "      x39 = 1\n",
+      "      y39 = 0\n",
+      "ngm = x21 ^ y21\n",
+      "  x21 = 0\n",
+      "  y21 = 0\n",
+      "ngr = jpp ^ stv\n",
+      "  jpp = x11 ^ y11\n",
+      "    x11 = 1\n",
+      "    y11 = 0\n",
+      "  stv = qnf | sgv\n",
+      "    qnf = x10 & y10\n",
+      "      x10 = 0\n",
+      "      y10 = 0\n",
+      "    sgv = dtb & rvw\n",
+      "      dtb = x10 ^ y10\n",
+      "      rvw = prs | tcv\n",
+      "nhd = x43 & y43\n",
+      "  x43 = 1\n",
+      "  y43 = 1\n",
+      "nhs = x41 ^ y41\n",
+      "  x41 = 1\n",
+      "  y41 = 1\n",
+      "nht = x39 ^ y39\n",
+      "  x39 = 1\n",
+      "  y39 = 0\n",
+      "nmr = x32 ^ y32\n",
+      "  x32 = 0\n",
+      "  y32 = 0\n",
+      "nss = x02 & y02\n",
+      "  x02 = 0\n",
+      "  y02 = 0\n",
+      "ntr = kvd | snc\n",
+      "  kvd = x37 & y37\n",
+      "    x37 = 0\n",
+      "    y37 = 0\n",
+      "  snc = dgg & hsn\n",
+      "    dgg = x37 ^ y37\n",
+      "      x37 = 0\n",
+      "      y37 = 0\n",
+      "    hsn = dvm | rpc\n",
+      "      dvm = mvv & sgr\n",
+      "      rpc = x36 & y36\n",
+      "nwk = cqn | qtq\n",
+      "  cqn = bvc & tpw\n",
+      "    bvc = vwn | wpt\n",
+      "      vwn = csh & mst\n",
+      "      wpt = x19 & y19\n",
+      "    tpw = x20 ^ y20\n",
+      "      x20 = 0\n",
+      "      y20 = 1\n",
+      "  qtq = x20 & y20\n",
+      "    x20 = 0\n",
+      "    y20 = 1\n",
+      "pgc = hjc | hth\n",
+      "  hjc = kjn & skt\n",
+      "    kjn = x01 ^ y01\n",
+      "      x01 = 0\n",
+      "      y01 = 0\n",
+      "    skt = x00 & y00\n",
+      "      x00 = 1\n",
+      "      y00 = 1\n",
+      "  hth = x01 & y01\n",
+      "    x01 = 0\n",
+      "    y01 = 0\n",
+      "pkh = x07 ^ y07\n",
+      "  x07 = 0\n",
+      "  y07 = 0\n",
+      "pmf = x25 ^ y25\n",
+      "  x25 = 0\n",
+      "  y25 = 1\n",
+      "pnb = gfg & pqf\n",
+      "  gfg = x24 ^ y24\n",
+      "    x24 = 1\n",
+      "    y24 = 1\n",
+      "  pqf = bwk | krn\n",
+      "    bwk = x23 & y23\n",
+      "      x23 = 1\n",
+      "      y23 = 1\n",
+      "    krn = gcn & tqf\n",
+      "      gcn = mhd | tfs\n",
+      "      tqf = x23 ^ y23\n",
+      "pnk = dkw & krg\n",
+      "  dkw = x43 ^ y43\n",
+      "    x43 = 1\n",
+      "    y43 = 1\n",
+      "  krg = krw | kvf\n",
+      "    krw = x42 & y42\n",
+      "      x42 = 0\n",
+      "      y42 = 0\n",
+      "    kvf = kpq & vfb\n",
+      "      kpq = hvv | vmr\n",
+      "      vfb = x42 ^ y42\n",
+      "pqf = bwk | krn\n",
+      "  bwk = x23 & y23\n",
+      "    x23 = 1\n",
+      "    y23 = 1\n",
+      "  krn = gcn & tqf\n",
+      "    gcn = mhd | tfs\n",
+      "      mhd = x22 & y22\n",
+      "      tfs = rqt & snv\n",
+      "    tqf = x23 ^ y23\n",
+      "      x23 = 1\n",
+      "      y23 = 1\n",
+      "prs = x09 & y09\n",
+      "  x09 = 0\n",
+      "  y09 = 1\n",
+      "psv = x03 ^ y03\n",
+      "  x03 = 1\n",
+      "  y03 = 1\n",
+      "ptd = x04 & y04\n",
+      "  x04 = 1\n",
+      "  y04 = 1\n",
+      "ptj = x12 & y12\n",
+      "  x12 = 0\n",
+      "  y12 = 0\n",
+      "qgd = x30 ^ y30\n",
+      "  x30 = 0\n",
+      "  y30 = 0\n",
+      "qgm = x40 & y40\n",
+      "  x40 = 1\n",
+      "  y40 = 0\n",
+      "qnf = x10 & y10\n",
+      "  x10 = 0\n",
+      "  y10 = 0\n",
+      "qpb = brs & nmr\n",
+      "  brs = mfm | tkc\n",
+      "    mfm = mgq ^ tpf\n",
+      "      mgq = x31 ^ y31\n",
+      "      tpf = bbk | gqt\n",
+      "    tkc = mgq & tpf\n",
+      "      mgq = x31 ^ y31\n",
+      "      tpf = bbk | gqt\n",
+      "  nmr = x32 ^ y32\n",
+      "    x32 = 0\n",
+      "    y32 = 0\n",
+      "qpf = bvg | jfr\n",
+      "  bvg = x17 & y17\n",
+      "    x17 = 0\n",
+      "    y17 = 0\n",
+      "  jfr = kfm & rtv\n",
+      "    kfm = jrk | swn\n",
+      "      jrk = gfj & kmb\n",
+      "      swn = x16 & y16\n",
+      "    rtv = x17 ^ y17\n",
+      "      x17 = 0\n",
+      "      y17 = 0\n",
+      "qqv = jqm | tdh\n",
+      "  jqm = vdk & vjn\n",
+      "    vdk = x13 ^ y13\n",
+      "      x13 = 1\n",
+      "      y13 = 1\n",
+      "    vjn = ptj | vqm\n",
+      "      ptj = x12 & y12\n",
+      "      vqm = ctw & knj\n",
+      "  tdh = x13 & y13\n",
+      "    x13 = 1\n",
+      "    y13 = 1\n",
+      "qrm = fvj & pgc\n",
+      "  fvj = x02 ^ y02\n",
+      "    x02 = 0\n",
+      "    y02 = 0\n",
+      "  pgc = hjc | hth\n",
+      "    hjc = kjn & skt\n",
+      "      kjn = x01 ^ y01\n",
+      "      skt = x00 & y00\n",
+      "    hth = x01 & y01\n",
+      "      x01 = 0\n",
+      "      y01 = 0\n",
+      "qsw = x18 & y18\n",
+      "  x18 = 0\n",
+      "  y18 = 1\n",
+      "qtq = x20 & y20\n",
+      "  x20 = 0\n",
+      "  y20 = 1\n",
+      "qvt = x14 ^ y14\n",
+      "  x14 = 1\n",
+      "  y14 = 1\n",
+      "rcs = mhv | mnv\n",
+      "  mhv = x27 & y27\n",
+      "    x27 = 1\n",
+      "    y27 = 1\n",
+      "  mnv = jjj & rhc\n",
+      "    jjj = dwv | jvf\n",
+      "      dwv = chq & tns\n",
+      "      jvf = x26 & y26\n",
+      "    rhc = x27 ^ y27\n",
+      "      x27 = 1\n",
+      "      y27 = 1\n",
+      "rdj = cjp | ptd\n",
+      "  cjp = dvq & rkm\n",
+      "    dvq = x04 ^ y04\n",
+      "      x04 = 1\n",
+      "      y04 = 1\n",
+      "    rkm = fwc | nbc\n",
+      "      fwc = psv & wdm\n",
+      "      nbc = x03 & y03\n",
+      "  ptd = x04 & y04\n",
+      "    x04 = 1\n",
+      "    y04 = 1\n",
+      "rgb = bfp | wqc\n",
+      "  bfp = hsp & nht\n",
+      "    hsp = krj | tdv\n",
+      "      krj = x38 ^ y38\n",
+      "      tdv = bpt & ntr\n",
+      "    nht = x39 ^ y39\n",
+      "      x39 = 1\n",
+      "      y39 = 0\n",
+      "  wqc = x39 & y39\n",
+      "    x39 = 1\n",
+      "    y39 = 0\n",
+      "rgj = qqv & qvt\n",
+      "  qqv = jqm | tdh\n",
+      "    jqm = vdk & vjn\n",
+      "      vdk = x13 ^ y13\n",
+      "      vjn = ptj | vqm\n",
+      "    tdh = x13 & y13\n",
+      "      x13 = 1\n",
+      "      y13 = 1\n",
+      "  qvt = x14 ^ y14\n",
+      "    x14 = 1\n",
+      "    y14 = 1\n",
+      "rhc = x27 ^ y27\n",
+      "  x27 = 1\n",
+      "  y27 = 1\n",
+      "rkm = fwc | nbc\n",
+      "  fwc = psv & wdm\n",
+      "    psv = x03 ^ y03\n",
+      "      x03 = 1\n",
+      "      y03 = 1\n",
+      "    wdm = nss | qrm\n",
+      "      nss = x02 & y02\n",
+      "      qrm = fvj & pgc\n",
+      "  nbc = x03 & y03\n",
+      "    x03 = 1\n",
+      "    y03 = 1\n",
+      "rnh = x28 ^ y28\n",
+      "  x28 = 0\n",
+      "  y28 = 0\n",
+      "rpc = x36 & y36\n",
+      "  x36 = 1\n",
+      "  y36 = 1\n",
+      "rpw = cnd & jqv\n",
+      "  cnd = x29 ^ y29\n",
+      "    x29 = 1\n",
+      "    y29 = 1\n",
+      "  jqv = tjh | wpw\n",
+      "    tjh = rcs & rnh\n",
+      "      rcs = mhv | mnv\n",
+      "      rnh = x28 ^ y28\n",
+      "    wpw = x28 & y28\n",
+      "      x28 = 0\n",
+      "      y28 = 0\n",
+      "rqt = x22 ^ y22\n",
+      "  x22 = 1\n",
+      "  y22 = 0\n",
+      "rsd = mkt & qpf\n",
+      "  mkt = x18 ^ y18\n",
+      "    x18 = 0\n",
+      "    y18 = 1\n",
+      "  qpf = bvg | jfr\n",
+      "    bvg = x17 & y17\n",
+      "      x17 = 0\n",
+      "      y17 = 0\n",
+      "    jfr = kfm & rtv\n",
+      "      kfm = jrk | swn\n",
+      "      rtv = x17 ^ y17\n",
+      "rtv = x17 ^ y17\n",
+      "  x17 = 0\n",
+      "  y17 = 0\n",
+      "rvw = prs | tcv\n",
+      "  prs = x09 & y09\n",
+      "    x09 = 0\n",
+      "    y09 = 1\n",
+      "  tcv = sbq & sfp\n",
+      "    sbq = bpb | gjp\n",
+      "      bpb = x08 & y08\n",
+      "      gjp = hfd & mpp\n",
+      "    sfp = x09 ^ y09\n",
+      "      x09 = 0\n",
+      "      y09 = 1\n",
+      "rws = fkp & pkh\n",
+      "  fkp = jgw ^ wvr\n",
+      "    jgw = x06 ^ y06\n",
+      "      x06 = 0\n",
+      "      y06 = 0\n",
+      "    wvr = bkk | shc\n",
+      "      bkk = x05 & y05\n",
+      "      shc = ffn & rdj\n",
+      "  pkh = x07 ^ y07\n",
+      "    x07 = 0\n",
+      "    y07 = 0\n",
+      "sbq = bpb | gjp\n",
+      "  bpb = x08 & y08\n",
+      "    x08 = 0\n",
+      "    y08 = 0\n",
+      "  gjp = hfd & mpp\n",
+      "    hfd = x08 ^ y08\n",
+      "      x08 = 0\n",
+      "      y08 = 0\n",
+      "    mpp = fts | rws\n",
+      "      fts = x07 & y07\n",
+      "      rws = fkp & pkh\n",
+      "sfh = pnb | vjh\n",
+      "  pnb = gfg & pqf\n",
+      "    gfg = x24 ^ y24\n",
+      "      x24 = 1\n",
+      "      y24 = 1\n",
+      "    pqf = bwk | krn\n",
+      "      bwk = x23 & y23\n",
+      "      krn = gcn & tqf\n",
+      "  vjh = x24 & y24\n",
+      "    x24 = 1\n",
+      "    y24 = 1\n",
+      "sfp = x09 ^ y09\n",
+      "  x09 = 0\n",
+      "  y09 = 1\n",
+      "sgr = cfw | tnc\n",
+      "  cfw = mdg & mhn\n",
+      "    mdg = kjj | vrf\n",
+      "      kjj = x34 & y34\n",
+      "      vrf = dhd & mvb\n",
+      "    mhn = x35 ^ y35\n",
+      "      x35 = 1\n",
+      "      y35 = 1\n",
+      "  tnc = x35 & y35\n",
+      "    x35 = 1\n",
+      "    y35 = 1\n",
+      "sgv = dtb & rvw\n",
+      "  dtb = x10 ^ y10\n",
+      "    x10 = 0\n",
+      "    y10 = 0\n",
+      "  rvw = prs | tcv\n",
+      "    prs = x09 & y09\n",
+      "      x09 = 0\n",
+      "      y09 = 1\n",
+      "    tcv = sbq & sfp\n",
+      "      sbq = bpb | gjp\n",
+      "      sfp = x09 ^ y09\n",
+      "shc = ffn & rdj\n",
+      "  ffn = x05 ^ y05\n",
+      "    x05 = 0\n",
+      "    y05 = 1\n",
+      "  rdj = cjp | ptd\n",
+      "    cjp = dvq & rkm\n",
+      "      dvq = x04 ^ y04\n",
+      "      rkm = fwc | nbc\n",
+      "    ptd = x04 & y04\n",
+      "      x04 = 1\n",
+      "      y04 = 1\n",
+      "skt = x00 & y00\n",
+      "  x00 = 1\n",
+      "  y00 = 1\n",
+      "snc = dgg & hsn\n",
+      "  dgg = x37 ^ y37\n",
+      "    x37 = 0\n",
+      "    y37 = 0\n",
+      "  hsn = dvm | rpc\n",
+      "    dvm = mvv & sgr\n",
+      "      mvv = x36 ^ y36\n",
+      "      sgr = cfw | tnc\n",
+      "    rpc = x36 & y36\n",
+      "      x36 = 1\n",
+      "      y36 = 1\n",
+      "snv = bgn | wnm\n",
+      "  bgn = ngm & nwk\n",
+      "    ngm = x21 ^ y21\n",
+      "      x21 = 0\n",
+      "      y21 = 0\n",
+      "    nwk = cqn | qtq\n",
+      "      cqn = bvc & tpw\n",
+      "      qtq = x20 & y20\n",
+      "  wnm = x21 & y21\n",
+      "    x21 = 0\n",
+      "    y21 = 0\n",
+      "stv = qnf | sgv\n",
+      "  qnf = x10 & y10\n",
+      "    x10 = 0\n",
+      "    y10 = 0\n",
+      "  sgv = dtb & rvw\n",
+      "    dtb = x10 ^ y10\n",
+      "      x10 = 0\n",
+      "      y10 = 0\n",
+      "    rvw = prs | tcv\n",
+      "      prs = x09 & y09\n",
+      "      tcv = sbq & sfp\n",
+      "swn = x16 & y16\n",
+      "  x16 = 1\n",
+      "  y16 = 1\n",
+      "tcv = sbq & sfp\n",
+      "  sbq = bpb | gjp\n",
+      "    bpb = x08 & y08\n",
+      "      x08 = 0\n",
+      "      y08 = 0\n",
+      "    gjp = hfd & mpp\n",
+      "      hfd = x08 ^ y08\n",
+      "      mpp = fts | rws\n",
+      "  sfp = x09 ^ y09\n",
+      "    x09 = 0\n",
+      "    y09 = 1\n",
+      "tdh = x13 & y13\n",
+      "  x13 = 1\n",
+      "  y13 = 1\n",
+      "tdv = bpt & ntr\n",
+      "  bpt = x38 & y38\n",
+      "    x38 = 1\n",
+      "    y38 = 0\n",
+      "  ntr = kvd | snc\n",
+      "    kvd = x37 & y37\n",
+      "      x37 = 0\n",
+      "      y37 = 0\n",
+      "    snc = dgg & hsn\n",
+      "      dgg = x37 ^ y37\n",
+      "      hsn = dvm | rpc\n",
+      "tfs = rqt & snv\n",
+      "  rqt = x22 ^ y22\n",
+      "    x22 = 1\n",
+      "    y22 = 0\n",
+      "  snv = bgn | wnm\n",
+      "    bgn = ngm & nwk\n",
+      "      ngm = x21 ^ y21\n",
+      "      nwk = cqn | qtq\n",
+      "    wnm = x21 & y21\n",
+      "      x21 = 0\n",
+      "      y21 = 0\n",
+      "tjh = rcs & rnh\n",
+      "  rcs = mhv | mnv\n",
+      "    mhv = x27 & y27\n",
+      "      x27 = 1\n",
+      "      y27 = 1\n",
+      "    mnv = jjj & rhc\n",
+      "      jjj = dwv | jvf\n",
+      "      rhc = x27 ^ y27\n",
+      "  rnh = x28 ^ y28\n",
+      "    x28 = 0\n",
+      "    y28 = 0\n",
+      "tkc = mgq & tpf\n",
+      "  mgq = x31 ^ y31\n",
+      "    x31 = 1\n",
+      "    y31 = 0\n",
+      "  tpf = bbk | gqt\n",
+      "    bbk = x30 & y30\n",
+      "      x30 = 0\n",
+      "      y30 = 0\n",
+      "    gqt = qgd & wrv\n",
+      "      qgd = x30 ^ y30\n",
+      "      wrv = gdn | rpw\n",
+      "tnc = x35 & y35\n",
+      "  x35 = 1\n",
+      "  y35 = 1\n",
+      "tns = x26 ^ y26\n",
+      "  x26 = 1\n",
+      "  y26 = 0\n",
+      "tpf = bbk | gqt\n",
+      "  bbk = x30 & y30\n",
+      "    x30 = 0\n",
+      "    y30 = 0\n",
+      "  gqt = qgd & wrv\n",
+      "    qgd = x30 ^ y30\n",
+      "      x30 = 0\n",
+      "      y30 = 0\n",
+      "    wrv = gdn | rpw\n",
+      "      gdn = x29 & y29\n",
+      "      rpw = cnd & jqv\n",
+      "tpw = x20 ^ y20\n",
+      "  x20 = 0\n",
+      "  y20 = 1\n",
+      "tqf = x23 ^ y23\n",
+      "  x23 = 1\n",
+      "  y23 = 1\n",
+      "vdk = x13 ^ y13\n",
+      "  x13 = 1\n",
+      "  y13 = 1\n",
+      "vdm = x32 & y32\n",
+      "  x32 = 0\n",
+      "  y32 = 0\n",
+      "vfb = x42 ^ y42\n",
+      "  x42 = 0\n",
+      "  y42 = 0\n",
+      "vfj = bph | rgj\n",
+      "  bph = x14 & y14\n",
+      "    x14 = 1\n",
+      "    y14 = 1\n",
+      "  rgj = qqv & qvt\n",
+      "    qqv = jqm | tdh\n",
+      "      jqm = vdk & vjn\n",
+      "      tdh = x13 & y13\n",
+      "    qvt = x14 ^ y14\n",
+      "      x14 = 1\n",
+      "      y14 = 1\n",
+      "vjh = x24 & y24\n",
+      "  x24 = 1\n",
+      "  y24 = 1\n",
+      "vjn = ptj | vqm\n",
+      "  ptj = x12 & y12\n",
+      "    x12 = 0\n",
+      "    y12 = 0\n",
+      "  vqm = ctw & knj\n",
+      "    ctw = x12 ^ y12\n",
+      "      x12 = 0\n",
+      "      y12 = 0\n",
+      "    knj = ngr | wmq\n",
+      "      ngr = jpp ^ stv\n",
+      "      wmq = x11 & y11\n",
+      "vmr = x41 & y41\n",
+      "  x41 = 1\n",
+      "  y41 = 1\n",
+      "vqm = ctw & knj\n",
+      "  ctw = x12 ^ y12\n",
+      "    x12 = 0\n",
+      "    y12 = 0\n",
+      "  knj = ngr | wmq\n",
+      "    ngr = jpp ^ stv\n",
+      "      jpp = x11 ^ y11\n",
+      "      stv = qnf | sgv\n",
+      "    wmq = x11 & y11\n",
+      "      x11 = 1\n",
+      "      y11 = 0\n",
+      "vrf = dhd & mvb\n",
+      "  dhd = x34 ^ y34\n",
+      "    x34 = 0\n",
+      "    y34 = 1\n",
+      "  mvb = dnc | vtd\n",
+      "    dnc = bbd & bdc\n",
+      "      bbd = x33 ^ y33\n",
+      "      bdc = qpb | vdm\n",
+      "    vtd = x33 & y33\n",
+      "      x33 = 1\n",
+      "      y33 = 1\n",
+      "vtd = x33 & y33\n",
+      "  x33 = 1\n",
+      "  y33 = 1\n",
+      "vwn = csh & mst\n",
+      "  csh = x19 ^ y19\n",
+      "    x19 = 1\n",
+      "    y19 = 1\n",
+      "  mst = qsw | rsd\n",
+      "    qsw = x18 & y18\n",
+      "      x18 = 0\n",
+      "      y18 = 1\n",
+      "    rsd = mkt & qpf\n",
+      "      mkt = x18 ^ y18\n",
+      "      qpf = bvg | jfr\n",
+      "wdm = nss | qrm\n",
+      "  nss = x02 & y02\n",
+      "    x02 = 0\n",
+      "    y02 = 0\n",
+      "  qrm = fvj & pgc\n",
+      "    fvj = x02 ^ y02\n",
+      "      x02 = 0\n",
+      "      y02 = 0\n",
+      "    pgc = hjc | hth\n",
+      "      hjc = kjn & skt\n",
+      "      hth = x01 & y01\n",
+      "wmq = x11 & y11\n",
+      "  x11 = 1\n",
+      "  y11 = 0\n",
+      "wnm = x21 & y21\n",
+      "  x21 = 0\n",
+      "  y21 = 0\n",
+      "wpt = x19 & y19\n",
+      "  x19 = 1\n",
+      "  y19 = 1\n",
+      "wpw = x28 & y28\n",
+      "  x28 = 0\n",
+      "  y28 = 0\n",
+      "wqc = x39 & y39\n",
+      "  x39 = 1\n",
+      "  y39 = 0\n",
+      "wrv = gdn | rpw\n",
+      "  gdn = x29 & y29\n",
+      "    x29 = 1\n",
+      "    y29 = 1\n",
+      "  rpw = cnd & jqv\n",
+      "    cnd = x29 ^ y29\n",
+      "      x29 = 1\n",
+      "      y29 = 1\n",
+      "    jqv = tjh | wpw\n",
+      "      tjh = rcs & rnh\n",
+      "      wpw = x28 & y28\n",
+      "wvr = bkk | shc\n",
+      "  bkk = x05 & y05\n",
+      "    x05 = 0\n",
+      "    y05 = 1\n",
+      "  shc = ffn & rdj\n",
+      "    ffn = x05 ^ y05\n",
+      "      x05 = 0\n",
+      "      y05 = 1\n",
+      "    rdj = cjp | ptd\n",
+      "      cjp = dvq & rkm\n",
+      "      ptd = x04 & y04\n",
+      "z00 = x00 ^ y00\n",
+      "  x00 = 1\n",
+      "  y00 = 1\n",
+      "z01 = kjn ^ skt\n",
+      "  kjn = x01 ^ y01\n",
+      "    x01 = 0\n",
+      "    y01 = 0\n",
+      "  skt = x00 & y00\n",
+      "    x00 = 1\n",
+      "    y00 = 1\n",
+      "z02 = fvj ^ pgc\n",
+      "  fvj = x02 ^ y02\n",
+      "    x02 = 0\n",
+      "    y02 = 0\n",
+      "  pgc = hjc | hth\n",
+      "    hjc = kjn & skt\n",
+      "      kjn = x01 ^ y01\n",
+      "      skt = x00 & y00\n",
+      "    hth = x01 & y01\n",
+      "      x01 = 0\n",
+      "      y01 = 0\n",
+      "z03 = psv ^ wdm\n",
+      "  psv = x03 ^ y03\n",
+      "    x03 = 1\n",
+      "    y03 = 1\n",
+      "  wdm = nss | qrm\n",
+      "    nss = x02 & y02\n",
+      "      x02 = 0\n",
+      "      y02 = 0\n",
+      "    qrm = fvj & pgc\n",
+      "      fvj = x02 ^ y02\n",
+      "      pgc = hjc | hth\n",
+      "z04 = dvq ^ rkm\n",
+      "  dvq = x04 ^ y04\n",
+      "    x04 = 1\n",
+      "    y04 = 1\n",
+      "  rkm = fwc | nbc\n",
+      "    fwc = psv & wdm\n",
+      "      psv = x03 ^ y03\n",
+      "      wdm = nss | qrm\n",
+      "    nbc = x03 & y03\n",
+      "      x03 = 1\n",
+      "      y03 = 1\n",
+      "z05 = ffn ^ rdj\n",
+      "  ffn = x05 ^ y05\n",
+      "    x05 = 0\n",
+      "    y05 = 1\n",
+      "  rdj = cjp | ptd\n",
+      "    cjp = dvq & rkm\n",
+      "      dvq = x04 ^ y04\n",
+      "      rkm = fwc | nbc\n",
+      "    ptd = x04 & y04\n",
+      "      x04 = 1\n",
+      "      y04 = 1\n",
+      "z06 = bpp | ghf\n",
+      "  bpp = x06 & y06\n",
+      "    x06 = 0\n",
+      "    y06 = 0\n",
+      "  ghf = jgw & wvr\n",
+      "    jgw = x06 ^ y06\n",
+      "      x06 = 0\n",
+      "      y06 = 0\n",
+      "    wvr = bkk | shc\n",
+      "      bkk = x05 & y05\n",
+      "      shc = ffn & rdj\n",
+      "z07 = fkp ^ pkh\n",
+      "  fkp = jgw ^ wvr\n",
+      "    jgw = x06 ^ y06\n",
+      "      x06 = 0\n",
+      "      y06 = 0\n",
+      "    wvr = bkk | shc\n",
+      "      bkk = x05 & y05\n",
+      "      shc = ffn & rdj\n",
+      "  pkh = x07 ^ y07\n",
+      "    x07 = 0\n",
+      "    y07 = 0\n",
+      "z08 = hfd ^ mpp\n",
+      "  hfd = x08 ^ y08\n",
+      "    x08 = 0\n",
+      "    y08 = 0\n",
+      "  mpp = fts | rws\n",
+      "    fts = x07 & y07\n",
+      "      x07 = 0\n",
+      "      y07 = 0\n",
+      "    rws = fkp & pkh\n",
+      "      fkp = jgw ^ wvr\n",
+      "      pkh = x07 ^ y07\n",
+      "z09 = sbq ^ sfp\n",
+      "  sbq = bpb | gjp\n",
+      "    bpb = x08 & y08\n",
+      "      x08 = 0\n",
+      "      y08 = 0\n",
+      "    gjp = hfd & mpp\n",
+      "      hfd = x08 ^ y08\n",
+      "      mpp = fts | rws\n",
+      "  sfp = x09 ^ y09\n",
+      "    x09 = 0\n",
+      "    y09 = 1\n",
+      "z10 = dtb ^ rvw\n",
+      "  dtb = x10 ^ y10\n",
+      "    x10 = 0\n",
+      "    y10 = 0\n",
+      "  rvw = prs | tcv\n",
+      "    prs = x09 & y09\n",
+      "      x09 = 0\n",
+      "      y09 = 1\n",
+      "    tcv = sbq & sfp\n",
+      "      sbq = bpb | gjp\n",
+      "      sfp = x09 ^ y09\n",
+      "z11 = jpp & stv\n",
+      "  jpp = x11 ^ y11\n",
+      "    x11 = 1\n",
+      "    y11 = 0\n",
+      "  stv = qnf | sgv\n",
+      "    qnf = x10 & y10\n",
+      "      x10 = 0\n",
+      "      y10 = 0\n",
+      "    sgv = dtb & rvw\n",
+      "      dtb = x10 ^ y10\n",
+      "      rvw = prs | tcv\n",
+      "z12 = ctw ^ knj\n",
+      "  ctw = x12 ^ y12\n",
+      "    x12 = 0\n",
+      "    y12 = 0\n",
+      "  knj = ngr | wmq\n",
+      "    ngr = jpp ^ stv\n",
+      "      jpp = x11 ^ y11\n",
+      "      stv = qnf | sgv\n",
+      "    wmq = x11 & y11\n",
+      "      x11 = 1\n",
+      "      y11 = 0\n",
+      "z13 = vdk ^ vjn\n",
+      "  vdk = x13 ^ y13\n",
+      "    x13 = 1\n",
+      "    y13 = 1\n",
+      "  vjn = ptj | vqm\n",
+      "    ptj = x12 & y12\n",
+      "      x12 = 0\n",
+      "      y12 = 0\n",
+      "    vqm = ctw & knj\n",
+      "      ctw = x12 ^ y12\n",
+      "      knj = ngr | wmq\n",
+      "z14 = qqv ^ qvt\n",
+      "  qqv = jqm | tdh\n",
+      "    jqm = vdk & vjn\n",
+      "      vdk = x13 ^ y13\n",
+      "      vjn = ptj | vqm\n",
+      "    tdh = x13 & y13\n",
+      "      x13 = 1\n",
+      "      y13 = 1\n",
+      "  qvt = x14 ^ y14\n",
+      "    x14 = 1\n",
+      "    y14 = 1\n",
+      "z15 = dmh ^ vfj\n",
+      "  dmh = x15 ^ y15\n",
+      "    x15 = 1\n",
+      "    y15 = 0\n",
+      "  vfj = bph | rgj\n",
+      "    bph = x14 & y14\n",
+      "      x14 = 1\n",
+      "      y14 = 1\n",
+      "    rgj = qqv & qvt\n",
+      "      qqv = jqm | tdh\n",
+      "      qvt = x14 ^ y14\n",
+      "z16 = gfj ^ kmb\n",
+      "  gfj = cpc | mjb\n",
+      "    cpc = dmh & vfj\n",
+      "      dmh = x15 ^ y15\n",
+      "      vfj = bph | rgj\n",
+      "    mjb = x15 & y15\n",
+      "      x15 = 1\n",
+      "      y15 = 0\n",
+      "  kmb = x16 ^ y16\n",
+      "    x16 = 1\n",
+      "    y16 = 1\n",
+      "z17 = kfm ^ rtv\n",
+      "  kfm = jrk | swn\n",
+      "    jrk = gfj & kmb\n",
+      "      gfj = cpc | mjb\n",
+      "      kmb = x16 ^ y16\n",
+      "    swn = x16 & y16\n",
+      "      x16 = 1\n",
+      "      y16 = 1\n",
+      "  rtv = x17 ^ y17\n",
+      "    x17 = 0\n",
+      "    y17 = 0\n",
+      "z18 = mkt ^ qpf\n",
+      "  mkt = x18 ^ y18\n",
+      "    x18 = 0\n",
+      "    y18 = 1\n",
+      "  qpf = bvg | jfr\n",
+      "    bvg = x17 & y17\n",
+      "      x17 = 0\n",
+      "      y17 = 0\n",
+      "    jfr = kfm & rtv\n",
+      "      kfm = jrk | swn\n",
+      "      rtv = x17 ^ y17\n",
+      "z19 = csh ^ mst\n",
+      "  csh = x19 ^ y19\n",
+      "    x19 = 1\n",
+      "    y19 = 1\n",
+      "  mst = qsw | rsd\n",
+      "    qsw = x18 & y18\n",
+      "      x18 = 0\n",
+      "      y18 = 1\n",
+      "    rsd = mkt & qpf\n",
+      "      mkt = x18 ^ y18\n",
+      "      qpf = bvg | jfr\n",
+      "z20 = bvc ^ tpw\n",
+      "  bvc = vwn | wpt\n",
+      "    vwn = csh & mst\n",
+      "      csh = x19 ^ y19\n",
+      "      mst = qsw | rsd\n",
+      "    wpt = x19 & y19\n",
+      "      x19 = 1\n",
+      "      y19 = 1\n",
+      "  tpw = x20 ^ y20\n",
+      "    x20 = 0\n",
+      "    y20 = 1\n",
+      "z21 = ngm ^ nwk\n",
+      "  ngm = x21 ^ y21\n",
+      "    x21 = 0\n",
+      "    y21 = 0\n",
+      "  nwk = cqn | qtq\n",
+      "    cqn = bvc & tpw\n",
+      "      bvc = vwn | wpt\n",
+      "      tpw = x20 ^ y20\n",
+      "    qtq = x20 & y20\n",
+      "      x20 = 0\n",
+      "      y20 = 1\n",
+      "z22 = rqt ^ snv\n",
+      "  rqt = x22 ^ y22\n",
+      "    x22 = 1\n",
+      "    y22 = 0\n",
+      "  snv = bgn | wnm\n",
+      "    bgn = ngm & nwk\n",
+      "      ngm = x21 ^ y21\n",
+      "      nwk = cqn | qtq\n",
+      "    wnm = x21 & y21\n",
+      "      x21 = 0\n",
+      "      y21 = 0\n",
+      "z23 = gcn ^ tqf\n",
+      "  gcn = mhd | tfs\n",
+      "    mhd = x22 & y22\n",
+      "      x22 = 1\n",
+      "      y22 = 0\n",
+      "    tfs = rqt & snv\n",
+      "      rqt = x22 ^ y22\n",
+      "      snv = bgn | wnm\n",
+      "  tqf = x23 ^ y23\n",
+      "    x23 = 1\n",
+      "    y23 = 1\n",
+      "z24 = gfg ^ pqf\n",
+      "  gfg = x24 ^ y24\n",
+      "    x24 = 1\n",
+      "    y24 = 1\n",
+      "  pqf = bwk | krn\n",
+      "    bwk = x23 & y23\n",
+      "      x23 = 1\n",
+      "      y23 = 1\n",
+      "    krn = gcn & tqf\n",
+      "      gcn = mhd | tfs\n",
+      "      tqf = x23 ^ y23\n",
+      "z25 = pmf ^ sfh\n",
+      "  pmf = x25 ^ y25\n",
+      "    x25 = 0\n",
+      "    y25 = 1\n",
+      "  sfh = pnb | vjh\n",
+      "    pnb = gfg & pqf\n",
+      "      gfg = x24 ^ y24\n",
+      "      pqf = bwk | krn\n",
+      "    vjh = x24 & y24\n",
+      "      x24 = 1\n",
+      "      y24 = 1\n",
+      "z26 = chq ^ tns\n",
+      "  chq = ctp | mdt\n",
+      "    ctp = pmf & sfh\n",
+      "      pmf = x25 ^ y25\n",
+      "      sfh = pnb | vjh\n",
+      "    mdt = x25 & y25\n",
+      "      x25 = 0\n",
+      "      y25 = 1\n",
+      "  tns = x26 ^ y26\n",
+      "    x26 = 1\n",
+      "    y26 = 0\n",
+      "z27 = jjj ^ rhc\n",
+      "  jjj = dwv | jvf\n",
+      "    dwv = chq & tns\n",
+      "      chq = ctp | mdt\n",
+      "      tns = x26 ^ y26\n",
+      "    jvf = x26 & y26\n",
+      "      x26 = 1\n",
+      "      y26 = 0\n",
+      "  rhc = x27 ^ y27\n",
+      "    x27 = 1\n",
+      "    y27 = 1\n",
+      "z28 = rcs ^ rnh\n",
+      "  rcs = mhv | mnv\n",
+      "    mhv = x27 & y27\n",
+      "      x27 = 1\n",
+      "      y27 = 1\n",
+      "    mnv = jjj & rhc\n",
+      "      jjj = dwv | jvf\n",
+      "      rhc = x27 ^ y27\n",
+      "  rnh = x28 ^ y28\n",
+      "    x28 = 0\n",
+      "    y28 = 0\n",
+      "z29 = cnd ^ jqv\n",
+      "  cnd = x29 ^ y29\n",
+      "    x29 = 1\n",
+      "    y29 = 1\n",
+      "  jqv = tjh | wpw\n",
+      "    tjh = rcs & rnh\n",
+      "      rcs = mhv | mnv\n",
+      "      rnh = x28 ^ y28\n",
+      "    wpw = x28 & y28\n",
+      "      x28 = 0\n",
+      "      y28 = 0\n",
+      "z30 = qgd ^ wrv\n",
+      "  qgd = x30 ^ y30\n",
+      "    x30 = 0\n",
+      "    y30 = 0\n",
+      "  wrv = gdn | rpw\n",
+      "    gdn = x29 & y29\n",
+      "      x29 = 1\n",
+      "      y29 = 1\n",
+      "    rpw = cnd & jqv\n",
+      "      cnd = x29 ^ y29\n",
+      "      jqv = tjh | wpw\n",
+      "z31 = x31 & y31\n",
+      "  x31 = 1\n",
+      "  y31 = 0\n",
+      "z32 = brs ^ nmr\n",
+      "  brs = mfm | tkc\n",
+      "    mfm = mgq ^ tpf\n",
+      "      mgq = x31 ^ y31\n",
+      "      tpf = bbk | gqt\n",
+      "    tkc = mgq & tpf\n",
+      "      mgq = x31 ^ y31\n",
+      "      tpf = bbk | gqt\n",
+      "  nmr = x32 ^ y32\n",
+      "    x32 = 0\n",
+      "    y32 = 0\n",
+      "z33 = bbd ^ bdc\n",
+      "  bbd = x33 ^ y33\n",
+      "    x33 = 1\n",
+      "    y33 = 1\n",
+      "  bdc = qpb | vdm\n",
+      "    qpb = brs & nmr\n",
+      "      brs = mfm | tkc\n",
+      "      nmr = x32 ^ y32\n",
+      "    vdm = x32 & y32\n",
+      "      x32 = 0\n",
+      "      y32 = 0\n",
+      "z34 = dhd ^ mvb\n",
+      "  dhd = x34 ^ y34\n",
+      "    x34 = 0\n",
+      "    y34 = 1\n",
+      "  mvb = dnc | vtd\n",
+      "    dnc = bbd & bdc\n",
+      "      bbd = x33 ^ y33\n",
+      "      bdc = qpb | vdm\n",
+      "    vtd = x33 & y33\n",
+      "      x33 = 1\n",
+      "      y33 = 1\n",
+      "z35 = mdg ^ mhn\n",
+      "  mdg = kjj | vrf\n",
+      "    kjj = x34 & y34\n",
+      "      x34 = 0\n",
+      "      y34 = 1\n",
+      "    vrf = dhd & mvb\n",
+      "      dhd = x34 ^ y34\n",
+      "      mvb = dnc | vtd\n",
+      "  mhn = x35 ^ y35\n",
+      "    x35 = 1\n",
+      "    y35 = 1\n",
+      "z36 = mvv ^ sgr\n",
+      "  mvv = x36 ^ y36\n",
+      "    x36 = 1\n",
+      "    y36 = 1\n",
+      "  sgr = cfw | tnc\n",
+      "    cfw = mdg & mhn\n",
+      "      mdg = kjj | vrf\n",
+      "      mhn = x35 ^ y35\n",
+      "    tnc = x35 & y35\n",
+      "      x35 = 1\n",
+      "      y35 = 1\n",
+      "z37 = dgg ^ hsn\n",
+      "  dgg = x37 ^ y37\n",
+      "    x37 = 0\n",
+      "    y37 = 0\n",
+      "  hsn = dvm | rpc\n",
+      "    dvm = mvv & sgr\n",
+      "      mvv = x36 ^ y36\n",
+      "      sgr = cfw | tnc\n",
+      "    rpc = x36 & y36\n",
+      "      x36 = 1\n",
+      "      y36 = 1\n",
+      "z38 = bpt ^ ntr\n",
+      "  bpt = x38 & y38\n",
+      "    x38 = 1\n",
+      "    y38 = 0\n",
+      "  ntr = kvd | snc\n",
+      "    kvd = x37 & y37\n",
+      "      x37 = 0\n",
+      "      y37 = 0\n",
+      "    snc = dgg & hsn\n",
+      "      dgg = x37 ^ y37\n",
+      "      hsn = dvm | rpc\n",
+      "z39 = hsp ^ nht\n",
+      "  hsp = krj | tdv\n",
+      "    krj = x38 ^ y38\n",
+      "      x38 = 1\n",
+      "      y38 = 0\n",
+      "    tdv = bpt & ntr\n",
+      "      bpt = x38 & y38\n",
+      "      ntr = kvd | snc\n",
+      "  nht = x39 ^ y39\n",
+      "    x39 = 1\n",
+      "    y39 = 0\n",
+      "z40 = mkc ^ rgb\n",
+      "  mkc = x40 ^ y40\n",
+      "    x40 = 1\n",
+      "    y40 = 0\n",
+      "  rgb = bfp | wqc\n",
+      "    bfp = hsp & nht\n",
+      "      hsp = krj | tdv\n",
+      "      nht = x39 ^ y39\n",
+      "    wqc = x39 & y39\n",
+      "      x39 = 1\n",
+      "      y39 = 0\n",
+      "z41 = cqq ^ nhs\n",
+      "  cqq = nfq | qgm\n",
+      "    nfq = mkc & rgb\n",
+      "      mkc = x40 ^ y40\n",
+      "      rgb = bfp | wqc\n",
+      "    qgm = x40 & y40\n",
+      "      x40 = 1\n",
+      "      y40 = 0\n",
+      "  nhs = x41 ^ y41\n",
+      "    x41 = 1\n",
+      "    y41 = 1\n",
+      "z42 = kpq ^ vfb\n",
+      "  kpq = hvv | vmr\n",
+      "    hvv = cqq & nhs\n",
+      "      cqq = nfq | qgm\n",
+      "      nhs = x41 ^ y41\n",
+      "    vmr = x41 & y41\n",
+      "      x41 = 1\n",
+      "      y41 = 1\n",
+      "  vfb = x42 ^ y42\n",
+      "    x42 = 0\n",
+      "    y42 = 0\n",
+      "z43 = dkw ^ krg\n",
+      "  dkw = x43 ^ y43\n",
+      "    x43 = 1\n",
+      "    y43 = 1\n",
+      "  krg = krw | kvf\n",
+      "    krw = x42 & y42\n",
+      "      x42 = 0\n",
+      "      y42 = 0\n",
+      "    kvf = kpq & vfb\n",
+      "      kpq = hvv | vmr\n",
+      "      vfb = x42 ^ y42\n",
+      "z44 = gcd ^ mdn\n",
+      "  gcd = x44 ^ y44\n",
+      "    x44 = 1\n",
+      "    y44 = 1\n",
+      "  mdn = nhd | pnk\n",
+      "    nhd = x43 & y43\n",
+      "      x43 = 1\n",
+      "      y43 = 1\n",
+      "    pnk = dkw & krg\n",
+      "      dkw = x43 ^ y43\n",
+      "      krg = krw | kvf\n",
+      "z45 = gvk | jkn\n",
+      "  gvk = x44 & y44\n",
+      "    x44 = 1\n",
+      "    y44 = 1\n",
+      "  jkn = gcd & mdn\n",
+      "    gcd = x44 ^ y44\n",
+      "      x44 = 1\n",
+      "      y44 = 1\n",
+      "    mdn = nhd | pnk\n",
+      "      nhd = x43 & y43\n",
+      "      pnk = dkw & krg\n"
+     ]
+    }
+   ],
    "source": [
     "def pprint_output(output, wires, ops: dict[str, Operation], maxdepth, depth=0):\n",
     "    \"\"\" Print the operations that result in an output, recursively. \"\"\"\n",
@@ -9453,8 +11212,10 @@
     "    create_vis(wires, operations) # Create a graphical representation\n",
     "    \n",
     "    # View text-based representation of all wires\n",
+    "    MAXDEPTH=3\n",
+    "    logger.info(f\"Outputs with depth of {MAXDEPTH}:\")\n",
     "    for output in sorted(operations.keys()):\n",
-    "        pprint_output(output, wires, operations, maxdepth=3)\n",
+    "        pprint_output(output, wires, operations, maxdepth=MAXDEPTH)\n",
     "    \n",
     "soln = visualise_operations(input_data)"
    ]
@@ -9489,7 +11250,7 @@
     "\n",
     "But again, we need a carry bit. Unlike the previous case, the new carry bit is created by combining the previous carry bit (`c00`) with our two bits, `x01` and `y01`. So we have three inputs, rather than two. Here, we can set the new carry bit `c01` in one of two ways:\n",
     "\n",
-    "- `(x01 ^ y01) & c01` - two values are true including carry bit - carry over required\n",
+    "- `(x01 ^ y01) & c00` - two values are true including carry bit - carry over required\n",
     "- `x01 & y01` - two values are true excluding carry bit - carry over required\n",
     "\n",
     "So we need an `OR` operation for these two cases, i.e.\n",
@@ -9501,23 +11262,23 @@
     "So we can conclude that the general pattern we should see is:\n",
     "\n",
     "```python\n",
-    "zn = a ^ b     # An XOR of two inputs, where one is an OR and one is an XOR \n",
-    "  a = c | d      # An OR of two intermediate inputs, where both are AND\n",
-    "    c = e & f\n",
-    "    d = x(n-1) & y(n-1)\n",
-    "  b = xn ^ yn    # An XOR of the input values themselves\n",
+    "zn = cn ^ sn     # XOR of carry and sum\n",
+    "  cn = ic(n-1) | c(n-1) # OR of two carries\n",
+    "    ic(n-1) = e & f          # Intermediate carry\n",
+    "    c(n-1) = x(n-1) & y(n-1) # Carry from x(n-1) and y(n-1)\n",
+    "  sn = xn ^ yn          # An XOR of the input values themselves\n",
     "```\n",
     "\n",
     "If we look at the printed output, we can see that `z05` follows the pattern:\n",
     "\n",
     "```python\n",
-    "z05 = ffn ^ rdj    # An XOR of two inputs, where one is an OR and one is an XOR\n",
-    "  ffn = x05 ^ y05    # The XOR of the input values themselves\n",
+    "z05 = ffn ^ rdj    # XOR of carry and sum\n",
+    "  ffn = x05 ^ y05      # The XOR of the input values themselves\n",
     "    x05 = 0\n",
     "    y05 = 1\n",
-    "  rdj = cjp | ptd    # An OR of two intermediate inputs, where both are AND\n",
-    "    cjp = dvq & rkm\n",
-    "    ptd = x04 & y04\n",
+    "  rdj = cjp | ptd      # OR of two carries\n",
+    "    cjp = dvq & rkm        # Intermediate carry\n",
+    "    ptd = x04 & y04        # Carry from x04 and y04\n",
     "```\n",
     "\n",
     "But there are some obvious issues. In my data, I can immediately see issues with `z06`, `z11` and `z31`. So these are going to be part of the answer.  But what else?\n",
@@ -9597,7 +11358,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 134,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -9852,7 +11613,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 167,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [],
    "source": [