X₂₃₀

X₂-CEVA CONJUGATE OF X₁₁₄

X₂₃₀ is the midpoint of the centers of the (equilateral) pedal triangles of X₁₅ and X₁₆.

5, 6, 7 3, 4, 5 Kepler Kimberling

X₂₃₀ (X₂-CEVA CONJUGATE OF X₁₁₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 6}, {5, 32}

• Related Centers: X₂ (CENTROID), X₁₁₄ (KIEPERT ANTIPODE), X₆ (SYMMEDIAN POINT), X₅ (NINE-POINT CENTER), X₃₂ (3rd POWER POINT)

Trilinears: \(bc[a^{2}(2a^{2} - b^{2} - c^{2}) + (b^{2} - c^{2})^{2}] : :\)

Barycentrics: \(2 a^{4} - a^{2} b^{2} + b^{4} - a^{2} c^{2} - 2 b^{2} c^{2} + c^{4} : :\)

Search Value (6, 9, 13): \(0.191902362158\)

▸ Linear Combinations2 combinations

• X₂₃₀ = X₁₃ + X₁₄ + X₁₅ + X₁₆

• X₂₃₀ = \(3\) X₂ + X₃₈₅, \(9\) X₂ - X₇₇₇₉, \(5\) X₂ - X₇₈₄₀, \(9\) X₂ - \(5\) X₇₉₂₅, X₂ + \(3\) X₈₈₅₉, \(6\) X₂ + X₁₅₄₈₀, \(5\) X₂ - \(3\) X₄₁₁₃₃, \(11\) X₂ - \(3\) X₄₁₁₃₆, \(2\) X₂ - \(3\) X₄₁₁₃₉, \(7\) X₂ + X₄₄₃₆₇, \(3\) X₂ - \(4\) X₄₄₃₈₁, X₄ + \(3\) X₂₁₄₄₅, X₄ - \(3\) X₃₉₆₆₃, X₁₅ + \(3\) X₂₂₅₁₁, X₁₆ + \(3\) X₂₂₅₁₀, X₉₈ + \(3\) X₃₈₂₂₇, \(3\) X₉₈ + X₄₃₄₆₀, X₉₉ + \(3\) X₁₄₅₆₈, X₉₉ - \(3\) X₃₅₂₉₇, \(3\) X₁₁₅ + X₆₇₈₁, \(5\) X₁₁₅ - \(3\) X₃₉₅₆₃, \(4\) X₁₄₀ - \(3\) X₁₀₂₅₆, X₁₄₈ + \(3\) X₁₃₅₈₆, \(3\) X₁₈₇ - X₆₇₈₁, \(5\) X₁₈₇ + \(3\) X₃₉₅₆₃, X₁₈₇ + \(2\) X₄₃₂₉₁, X₃₁₆ - \(5\) X₁₄₀₆₁, X₃₁₆ - \(3\) X₃₃₂₂₈, \(3\) X₃₂₅ - X₇₇₇₉, \(5\) X₃₂₅ - \(3\) X₇₈₄₀, \(3\) X₃₂₅ - \(5\) X₇₉₂₅, X₃₂₅ + \(9\) X₈₈₅₉, \(2\) X₃₂₅ + X₁₅₄₈₀, \(2\) X₃₂₅ - \(3\) X₂₂₁₁₀, X₃₂₅ + \(3\) X₂₂₃₂₉, \(5\) X₃₂₅ - \(9\) X₄₁₁₃₃, \(11\) X₃₂₅ - \(9\) X₄₁₁₃₆, \(2\) X₃₂₅ - \(9\) X₄₁₁₃₉, \(7\) X₃₂₅ + \(3\) X₄₄₃₆₇, X₃₂₅ - \(4\) X₄₄₃₈₁, X₃₂₅ - \(6\) X₄₄₄₀₁, \(3\) X₃₈₅ + X₇₇₇₉, \(5\) X₃₈₅ + \(3\) X₇₈₄₀, \(3\) X₃₈₅ + \(5\) X₇₉₂₅, X₃₈₅ - \(9\) X₈₈₅₉, \(2\) X₃₈₅ + \(3\) X₂₂₁₁₀, X₃₈₅ - \(3\) X₂₂₃₂₉, \(5\) X₃₈₅ + \(9\) X₄₁₁₃₃, \(11\) X₃₈₅ + \(9\) X₄₁₁₃₆, \(2\) X₃₈₅ + \(9\) X₄₁₁₃₉, \(7\) X₃₈₅ - \(3\) X₄₄₃₆₇, X₃₈₅ + \(2\) X₄₄₃₇₇, X₃₈₅ + \(4\) X₄₄₃₈₁, X₃₈₅ + \(6\) X₄₄₄₀₁, \(3\) X₄₆₈ - X₁₆₃₁₆

X₂₃₀ lies on the cubics K492, K518, K780, K1166.

▸ Incident Central Lines573 lines

{1, 21965}, {2, 6}, {3, 2549}, {4, 3053}, {5, 32}, {10, 4544}, {11, 1914}, {12, 172}, {13, 41406}, {14, 41407}, {15, 21156}, {16, 21157}, {20, 5023}, {21, 44517}, {22, 8553}, {23, 11063}, {24, 27376}, {25, 53}, {26, 44527}, {30, 115}, {37, 6690}, {39, 140}, {50, 858}, {67, 9769}, {76, 7789}, {83, 32992}, {98, 1503}, {99, 14568}, {100, 17737}, {101, 17734}, {105, 9090}, {111, 476}, {112, 403}, {114, 1692}, {125, 8779}, {132, 38970}, {147, 35006}, {148, 13586}, {160, 20885}, {182, 37451}, {185, 15575}, {186, 2079}, {194, 7907}, {216, 1196}, {231, 232}, {233, 11548}, {235, 1968}, {248, 2450}, {251, 2963}, {262, 7607}, {263, 13240}, {274, 17694}, {297, 2966}, {315, 7887}, {316, 14061}, {338, 30737}, {350, 26629}, {376, 5210}, {381, 1384}, {383, 5321}, {384, 44530}, {387, 7410}, {393, 6353}, {397, 37463}, {398, 37464}, {404, 44542}, {427, 571}, {428, 1879}, {439, 2996}, {442, 5277}, {444, 2178}, {460, 39072}, {485, 6423}, {486, 6424}, {495, 2242}, {496, 2241}, {499, 16502}, {511, 2023}, {538, 620}, {542, 2030}, {543, 27088}, {546, 7747}, {547, 5008}, {548, 7756}, {549, 574}, {550, 5206}, {566, 7495}, {570, 1194}, {577, 1368}, {594, 7081}, {609, 7951}, {625, 754}, {626, 7767}, {631, 5013}, {632, 5346}, {641, 45576}, {642, 45577}, {671, 8598}, {691, 15546}, {694, 36897}, {698, 5976}, {732, 2024}, {736, 3934}, {800, 6375}, {868, 35906}, {1003, 11185}, {1015, 15325}, {1030, 4220}, {1040, 9594}, {1078, 6656}, {1080, 5318}, {1086, 1447}, {1100, 24239}, {1107, 4999}, {1108, 36227}, {1146, 35081}, {1151, 26516}, {1152, 26521}, {1180, 13351}, {1249, 38282}, {1281, 28530}, {1285, 3545}, {1312, 46629}, {1313, 46628}, {1329, 4426}, {1333, 37360}, {1352, 37071}, {1353, 39764}, {1379, 31862}, {1380, 31863}, {1504, 8981}, {1505, 13966}, {1506, 3628}, {1560, 16221}, {1562, 21663}, {1570, 34380}, {1572, 5886}, {1575, 3035}, {1576, 44089}, {1594, 10312}, {1625, 45938}, {1627, 2965}, {1656, 2548}, {1799, 16890}, {1834, 6998}, {1865, 4231}, {1901, 2305}, {1909, 26686}, {1970, 12241}, {1975, 16925}, {2021, 2782}, {2071, 34866}, {2072, 10317}, {2076, 5999}, {2080, 15980}, {2207, 3542}, {2243, 37691}, {2271, 5292}, {2275, 5433}, {2276, 5432}, {2280, 29662}, {2459, 13873}, {2460, 13926}, {2482, 5215}, {2502, 35266}, {2886, 4386}, {2896, 7901}, {3016, 46817}, {3058, 10987}, {3070, 6811}, {3071, 6813}, {3086, 16781}, {3087, 8889}, {3091, 22331}, {3094, 22712}, {3096, 7942}, {3124, 32269}, {3147, 41361}, {3162, 8746}, {3163, 23992}, {3172, 11404}, {3199, 21841}, {3229, 11672}, {3266, 36953}, {3269, 15341}, {3284, 5159}, {3285, 8229}, {3363, 7617}, {3424, 43537}, {3509, 17719}, {3522, 44519}, {3523, 7738}, {3525, 31400}, {3526, 5319}, {3530, 7765}, {3534, 15655}, {3548, 23115}, {3552, 32819}, {3553, 5268}, {3554, 5272}, {3582, 16784}, {3584, 16785}, {3624, 9575}, {3684, 33140}, {3705, 17362}, {3712, 4037}, {3726, 17724}, {3734, 8369}, {3785, 7784}, {3788, 3933}, {3818, 41412}, {3830, 43618}, {3845, 18362}, {3849, 5461}, {3850, 39590}, {3925, 10315}, {3926, 32970}, {3943, 37764}, {3972, 8370}, {4045, 7817}, {4071, 4434}, {4136, 8669}, {4189, 44520}, {4251, 45939}, {4395, 33891}, {4478, 30179}, {4590, 37803}, {4892, 4987}, {5000, 41200}, {5001, 41201}, {5012, 9604}, {5017, 5480}, {5020, 8573}, {5024, 5054}, {5025, 7750}, {5034, 38110}, {5039, 38317}, {5041, 5368}, {5052, 18583}, {5055, 15484}, {5058, 7584}, {5062, 7583}, {5063, 30739}, {5066, 14537}, {5067, 31404}, {5070, 43136}, {5071, 18584}, {5077, 8182}, {5094, 6749}, {5104, 6034}, {5106, 44215}, {5111, 40336}, {5116, 37455}, {5124, 19649}, {5184, 38220}, {5204, 9597}, {5217, 9598}, {5218, 31477}, {5280, 31460}, {5283, 7483}, {5291, 17757}, {5418, 6422}, {5420, 6421}, {5471, 6114}, {5472, 6115}, {5503, 10153}, {5585, 10304}, {5641, 44576}, {5965, 6721}, {5977, 35101}, {5980, 10617}, {5981, 10616}, {5988, 17768}, {6128, 39602}, {6146, 14585}, {6179, 7752}, {6194, 44453}, {6292, 7852}, {6321, 38225}, {6337, 6392}, {6409, 26295}, {6410, 26294}, {6560, 13711}, {6561, 13834}, {6564, 26438}, {6565, 18539}, {6636, 44521}, {6640, 22120}, {6642, 9608}, {6675, 16589}, {6683, 7829}, {6691, 16604}, {6719, 40553}, {6720, 44340}, {6756, 27371}, {6772, 35304}, {6775, 35303}, {6791, 32225}, {7000, 23261}, {7031, 7741}, {7179, 17365}, {7181, 7200}, {7374, 23251}, {7386, 36748}, {7467, 8266}, {7488, 44523}, {7492, 44522}, {7494, 36751}, {7505, 8743}, {7512, 44525}, {7525, 9700}, {7576, 10986}, {7615, 11159}, {7616, 10336}, {7754, 7763}, {7759, 7862}, {7760, 7769}, {7761, 7844}, {7764, 7805}, {7768, 7899}, {7770, 32832}, {7771, 7790}, {7773, 20065}, {7776, 14023}, {7783, 33259}, {7785, 32967}, {7786, 7856}, {7787, 16921}, {7791, 7851}, {7794, 7874}, {7795, 32954}, {7796, 7940}, {7797, 7824}, {7800, 7866}, {7801, 17131}, {7802, 33229}, {7803, 11285}, {7810, 7853}, {7811, 7934}, {7813, 31274}, {7814, 7877}, {7815, 7834}, {7818, 14929}, {7820, 8368}, {7821, 7826}, {7822, 33185}, {7823, 32966}, {7830, 7861}, {7836, 17129}, {7839, 16923}, {7841, 14907}, {7845, 31275}, {7847, 43459}, {7854, 7867}, {7855, 7888}, {7864, 33004}, {7876, 7932}, {7879, 33218}, {7889, 31239}, {7891, 20081}, {7892, 31276}, {7893, 7912}, {7904, 7933}, {7920, 33015}, {7923, 33021}, {7938, 14065}, {7968, 26300}, {7969, 26301}, {8352, 9166}, {8354, 46893}, {8355, 14971}, {8550, 9744}, {8557, 24345}, {8587, 43535}, {8588, 8703}, {8589, 12100}, {8623, 21531}, {8716, 33216}, {8744, 37943}, {8749, 40347}, {8778, 37197}, {8791, 14910}, {8854, 10962}, {8855, 10960}, {8882, 23295}, {8901, 41270}, {8960, 44647}, {8976, 31411}, {9112, 16267}, {9113, 16268}, {9164, 17968}, {9167, 39785}, {9475, 44887}, {9593, 31423}, {9595, 37696}, {9620, 26446}, {9650, 10592}, {9665, 10593}, {9675, 42215}, {9696, 40111}, {9699, 12106}, {9759, 34319}, {9760, 41746}, {9762, 41745}, {9764, 41747}, {9765, 41749}, {9855, 41135}, {10018, 39575}, {10154, 34481}, {10164, 31443}, {10257, 14961}, {10264, 14901}, {10272, 46301}, {10298, 44538}, {10303, 22332}, {10316, 11585}, {10352, 13196}, {10691, 22052}, {10988, 34612}, {11054, 41134}, {11173, 20423}, {11179, 40248}, {11231, 31398}, {11272, 46305}, {11317, 20112}, {11360, 23208}, {11413, 44528}, {11485, 20426}, {11486, 20425}, {11632, 37461}, {11645, 38010}, {11668, 11669}, {11676, 14651}, {11799, 46633}, {11812, 39593}, {12007, 43461}, {12088, 44537}, {12108, 31652}, {12359, 23128}, {12815, 35018}, {12962, 31454}, {13178, 38221}, {13337, 15302}, {13345, 37439}, {13449, 23514}, {14001, 32828}, {14041, 14712}, {14043, 46226}, {14482, 15709}, {14581, 37942}, {14586, 40631}, {14588, 19577}, {14694, 14995}, {14881, 46321}, {15109, 15246}, {15122, 44468}, {15301, 35022}, {15355, 22353}, {15448, 20998}, {15515, 15712}, {15602, 41983}, {15603, 15689}, {15905, 30771}, {16081, 16089}, {16196, 22401}, {16252, 32445}, {16434, 36743}, {16529, 16961}, {16530, 16960}, {16808, 41408}, {16809, 41409}, {16968, 46835}, {16976, 40349}, {17128, 33225}, {17602, 41269}, {17735, 17747}, {18253, 21879}, {18353, 34603}, {18365, 30745}, {18806, 32189}, {18840, 32952}, {18860, 38737}, {19103, 43430}, {19104, 43431}, {19130, 41413}, {19312, 23905}, {19544, 36744}, {21158, 36772}, {21397, 44269}, {21448, 34288}, {21554, 33863}, {21840, 29683}, {22253, 34511}, {22512, 41017}, {22513, 41016}, {22682, 40927}, {23004, 39555}, {23005, 39554}, {23972, 35080}, {23976, 35088}, {23980, 35079}, {23986, 35086}, {24243, 45595}, {24244, 45596}, {25488, 30489}, {25555, 44500}, {25681, 39248}, {26242, 29665}, {26369, 44635}, {26370, 44636}, {26468, 42262}, {26469, 42265}, {26517, 44646}, {26518, 44644}, {26522, 44645}, {26523, 44643}, {28697, 41009}, {29012, 35021}, {30478, 31490}, {30516, 40130}, {30537, 39389}, {30677, 44095}, {31409, 31479}, {31416, 31493}, {31467, 46219}, {32006, 32972}, {32431, 33628}, {32452, 32521}, {32479, 36523}, {32494, 39388}, {32497, 39387}, {32518, 45900}, {32640, 34150}, {32661, 44665}, {32762, 39828}, {32815, 32985}, {32816, 32969}, {32818, 32959}, {32823, 32958}, {32826, 33239}, {32827, 32984}, {32829, 32977}, {32830, 33203}, {32834, 33181}, {32838, 32968}, {32867, 32975}, {32980, 39143}, {33758, 39087}, {33900, 35298}, {34254, 42406}, {34828, 41760}, {35002, 38739}, {35085, 40621}, {35087, 35133}, {35606, 45662}, {36759, 46054}, {36760, 46053}, {37182, 44882}, {37362, 41332}, {37453, 45141}, {37897, 40350}, {37910, 46216}, {37911, 40135}, {40107, 44499}, {40236, 44536}, {40323, 41489}, {40884, 41254}, {40938, 40939}, {42006, 43528}, {44214, 46634}, {44648, 45514}, {45524, 45868}, {45525, 45869}

▸ Functional Relations39 relations

• X₂₃₀ = QA-P₆ (Parabola Axes Crosspoint) of quadrangle ABCX₂; see http://www.chrisvantienhoven.nl/quadrangle-objects/15-mathematics/quadrangle-objects/artikelen-qa/27-qa-p6.html

• X₂₃₀ = midpoint of X_i and X_j for these {i,j}: {2, 22329}, {6, 15993}, {98, 1513}, {115, 187}, {193, 44369}, {297, 2966}, {325, 385}, {395, 396}, {468, 16315}, {671, 8598}, {2080, 15980}, {3229, 35078}, {3580, 14999}, {5912, 5913}, {6108, 6109}, {6782, 6783}, {7426, 16092}, {9127, 16341}, {11537, 11549}, {11632, 37461}, {11799, 46633}, {14568, 35297}, {21445, 39663}, {32456, 32457}, {44376, 44388}, {44392, 44394}

• X₂₃₀ = reflection of X_i in X_j for these {i,j}: {2, 44401}, {69, 44395}, {99, 32459}, {114, 10011}, {115, 43291}, {325, 44377}, {625, 6722}, {6390, 620}, {15301, 35022}, {15480, 385}, {16320, 468}, {22110, 2}, {31173, 8355}, {35088, 44334}, {37350, 5461}, {37459, 14693}, {44377, 44381}, {44380, 3589}

• X₂₃₀ = complement of X₃₂₅

• X₂₃₀ = anticomplement of X₄₄₃₇₇

• X₂₃₀ = circumcircle-inverse of X₅₉₄₁

• X₂₃₀ = orthoptic-circle-of-Steiner-inellipse-inverse of X₆₇₉₂

• X₂₃₀ = Moses-Parry-circle-inverse of X₂₄₉₃

• X₂₃₀ = isogonal conjugate of X₂₉₈₇

• X₂₃₀ = isotomic conjugate of X₈₇₈₁

• X₂₃₀ = polar conjugate of X₃₅₁₄₂

• X₂₃₀ = complement of the isogonal conjugate of X₁₉₇₆

• X₂₃₀ = complement of the isotomic conjugate of X₉₈

• X₂₃₀ = isotomic conjugate of the isogonal conjugate of X₁₆₉₂

• X₂₃₀ = isotomic conjugate of the polar conjugate of X₄₆₀

• X₂₃₀ = isogonal conjugate of the polar conjugate of X₄₄₁₄₅

• X₂₃₀ = polar conjugate of the isotomic conjugate of X₃₅₆₄

• X₂₃₀ = X_i-complementary conjugate of X_j for these (i,j): {31, 114}, {32, 16591}, {98, 2887}, {248, 18589}, {290, 21235}, {293, 1368}, {560, 11672}, {661, 36471}, {685, 21259}, {798, 35088}, {878, 34846}, {1821, 626}, {1910, 141}, {1933, 46840}, {1973, 15595}, {1976, 10}, {2395, 21253}, {2422, 8287}, {2715, 4369}, {2966, 42327}, {3404, 21248}, {6531, 20305}, {9154, 21256}, {11610, 21247}, {14600, 1214}, {14601, 37}, {15628, 21244}, {15630, 24040}, {32676, 41167}, {32696, 8062}, {36036, 23301}, {36084, 512}, {36104, 30476}, {36120, 21243}, {43187, 21263}, {46273, 40379}, {46289, 36213}

• X₂₃₀ = X_i-Ceva conjugate of X_j for these (i,j): {2, 114}, {297, 1503}, {648, 38359}, {2396, 804}, {2966, 523}, {6531, 6}, {31635, 157}, {39645, 5254}, {40120, 25}, {44145, 460}, {44767, 525}

• X₂₃₀ = X_i-cross conjugate of X_j for these (i,j): {1692, 460}, {36472, 2501}

• X₂₃₀ = X_i-isoconjugate of X_j for these (i,j): {1, 2987}, {2, 36051}, {6, 8773}, {19, 43705}, {31, 8781}, {48, 35142}, {63, 3563}, {75, 32654}, {92, 42065}, {647, 36105}, {656, 32697}, {661, 10425}, {662, 35364}, {1755, 40428}, {1821, 34157}, {1959, 2065}, {2159, 36891}

• X₂₃₀ = crosspoint of X_i and X_j for these (i,j): {2, 98}, {22456, 34537}

• X₂₃₀ = crosssum of X_i and X_j for these (i,j): {6, 511}, {520, 41172}, {1084, 39469}, {32654, 42065}

• X₂₃₀ = trilinear pole of line {5477, 42663}

• X₂₃₀ = crossdifference of every pair of points on line {3, 512}

• X₂₃₀ = X₂-Hirst inverse of X₁₉₃

• X₂₃₀ = X_i-beth conjugate of X_j for these (i,j): (281, 230), (645, 230)

• X₂₃₀ = centroid of quadrangle X₁₃X₁₄X₁₅X₁₆

• X₂₃₀ = radical center of cirumcircle, nine-point circle and Lester circle

• X₂₃₀ = perspector of circumconic centered at X₁₁₄

• X₂₃₀ = center of circumconic that is locus of trilinear poles of lines passing through X₁₁₄

• X₂₃₀ = inverse-in-Steiner-inellipse of X₆

• X₂₃₀ = X₉₁₀-of-orthic-triangle if ABC is acute

• X₂₃₀ = PU(4)-harmonic conjugate of X₂₅₀₁

• X₂₃₀ = X₁₃-antipedal-to-X₁₆-pedal similarity image of X₁₄

• X₂₃₀ = X₁₄-antipedal-to-X₁₅-pedal similarity image of X₁₃

• X₂₃₀ = barycentric product X_i*X_j for these {i,j}: {1, 1733}, {3, 44145}, {4, 3564}, {13, 6782}, {14, 6783}, {30, 36875}, {69, 460}, {75, 8772}, {76, 1692}, {98, 114}, {305, 44099}, {511, 14265}, {523, 4226}, {542, 34174}, {670, 42663}, {671, 5477}, {1821, 17462}, {1916, 12829}, {2782, 46039}, {2974, 3563}, {7612, 10011}, {11606, 12830}, {31842, 40120}, {38359, 44768}

• X₂₃₀ = barycentric quotient X_i/X_j for these {i,j}: {1, 8773}, {2, 8781}, {3, 43705}, {4, 35142}, {6, 2987}, {25, 3563}, {30, 36891}, {31, 36051}, {32, 32654}, {98, 40428}, {110, 10425}, {112, 32697}, {114, 325}, {162, 36105}, {184, 42065}, {237, 34157}, {460, 4}, {512, 35364}, {1692, 6}, {1733, 75}, {1976, 2065}, {3564, 69}, {4226, 99}, {5477, 524}, {6782, 298}, {6783, 299}, {8772, 1}, {10011, 1007}, {12829, 385}, {12830, 7779}, {14265, 290}, {17462, 1959}, {34174, 5641}, {35296, 14253}, {36875, 1494}, {39072, 37183}, {42663, 512}, {44099, 25}, {44145, 264}, {46039, 46142}

• X₂₃₀ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {2, 6, 3815}, {2, 69, 7778}, {2, 183, 141}, {2, 193, 1007}, {2, 325, 44377}, {2, 385, 325}, {2, 1611, 40326}, {2, 1654, 30761}, {2, 1992, 11184}, {2, 2895, 30760}, {2, 3815, 3055}, {2, 5276, 37661}, {2, 5304, 7736}, {2, 5306, 9300}, {2, 5912, 44398}, {2, 5913, 24855}, {2, 7610, 11168}, {2, 7735, 6}, {2, 7736, 31489}, {2, 7766, 7777}, {2, 7777, 37647}, {2, 7779, 7925}, {2, 7792, 3589}, {2, 7806, 7792}, {2, 7840, 41133}, {2, 8859, 22329}, {2, 8860, 15597}, {2, 11163, 9771}, {2, 11174, 15491}, {2, 11580, 5913}, {2, 13638, 590}, {2, 13758, 615}, {2, 16989, 11174}, {2, 16990, 7868}, {2, 16997, 37664}, {2, 17004, 37688}, {2, 17008, 183}, {2, 23055, 7610}, {2, 26243, 1211}, {2, 26244, 1213}, {2, 26282, 5718}, {2, 34229, 15271}, {2, 37637, 3054}, {2, 37667, 69}, {2, 37668, 37690}, {2, 37689, 7735}, {2, 42850, 21358}, {2, 44401, 41139}, {3, 3767, 5254}, {5, 32, 7745}, {5, 18907, 5475}, {6, 3054, 3055}, {6, 3815, 9300}, {6, 7735, 5306}, {6, 8253, 31463}, {6, 21001, 40805}, {6, 31489, 7736}, {6, 37637, 2}, {32, 5475, 18907}, {32, 7746, 5}, {39, 7749, 140}, {39, 7755, 5305}, {50, 44529, 858}, {69, 37667, 8667}, {76, 7807, 7789}, {76, 7857, 7807}, {98, 36899, 41932}, {98, 38227, 1513}, {99, 35297, 32459}, {100, 17737, 21956}, {114, 12829, 12830}, {140, 5305, 39}, {141, 13468, 183}, {141, 15598, 16990}, {183, 7868, 16990}, {183, 16990, 15598}, {183, 17008, 13468}, {193, 1007, 9766}, {231, 3003, 16310}, {232, 6103, 16318}, {232, 16318, 1990}, {316, 14061, 33228}, {325, 22329, 385}, {325, 44377, 22110}, {376, 43448, 44526}, {381, 1384, 7737}, {385, 3329, 39097}, {385, 7925, 7779}, {385, 39095, 6}, {385, 39101, 39093}, {385, 44381, 22110}, {427, 10311, 6748}, {468, 6103, 1990}, {468, 16306, 16308}, {468, 16310, 2493}, {468, 16313, 16335}, {468, 16317, 10418}, {468, 16318, 232}, {468, 16325, 16321}, {549, 15048, 574}, {571, 9722, 6748}, {574, 5309, 15048}, {590, 615, 141}, {597, 15491, 11174}, {597, 15597, 2}, {626, 7780, 7767}, {626, 7886, 8361}, {631, 5286, 5013}, {632, 31406, 31455}, {671, 26613, 8598}, {1078, 7828, 6656}, {1078, 7919, 7831}, {1609, 2165, 53}, {1656, 30435, 2548}, {1691, 44534, 1513}, {2076, 44531, 5999}, {2080, 38224, 15980}, {2493, 3003, 16308}, {2493, 16306, 1990}, {2549, 21843, 3}, {3003, 3018, 16303}, {3003, 3291, 2493}, {3003, 6103, 16306}, {3003, 16310, 1990}, {3018, 10418, 2493}, {3018, 16303, 1990}, {3053, 13881, 4}, {3054, 3815, 2}, {3054, 5306, 3815}, {3054, 7735, 9300}, {3055, 9300, 3815}, {3068, 3069, 193}, {3068, 26456, 44594}, {3068, 44365, 44394}, {3068, 44595, 6}, {3069, 26463, 44597}, {3069, 44364, 44392}, {3069, 44596, 6}, {3096, 7942, 8363}, {3291, 6103, 16310}, {3291, 10418, 16317}, {3314, 37671, 3631}, {3329, 17006, 2}, {3523, 7738, 15815}, {3526, 5319, 9606}, {3526, 9605, 31401}, {3767, 21843, 2549}, {3785, 14064, 7784}, {3788, 7751, 3933}, {3815, 5306, 6}, {3934, 6680, 7819}, {5008, 7603, 7753}, {5013, 5286, 9607}, {5013, 44535, 631}, {5023, 44518, 20}, {5025, 7793, 7750}, {5055, 15484, 31415}, {5055, 21309, 15484}, {5206, 7748, 550}, {5210, 44526, 376}, {5304, 7736, 6}, {5306, 37637, 3055}, {5319, 31401, 9605}, {5346, 31455, 7772}, {5368, 9698, 5041}, {5475, 18907, 7745}, {5585, 44541, 10304}, {6103, 10418, 3018}, {6179, 7752, 7762}, {6189, 6190, 193}, {6292, 7852, 8364}, {6392, 32989, 6337}, {7610, 15271, 34229}, {7612, 9752, 9756}, {7615, 37809, 11159}, {7735, 7736, 5304}, {7735, 37637, 3815}, {7736, 31489, 3815}, {7737, 43620, 381}, {7747, 39565, 546}, {7749, 7755, 39}, {7754, 33233, 7763}, {7756, 15513, 548}, {7761, 7844, 33184}, {7762, 33249, 7752}, {7766, 7777, 41624}, {7766, 41624, 32455}, {7767, 8361, 626}, {7771, 7790, 8356}, {7772, 31455, 31406}, {7774, 14614, 3629}, {7778, 8667, 69}, {7779, 7925, 325}, {7780, 7886, 626}, {7792, 37688, 2}, {7806, 17004, 2}, {7806, 37688, 3589}, {7815, 7834, 8362}, {7817, 34506, 8359}, {7828, 7831, 7919}, {7830, 7861, 8357}, {7831, 7919, 6656}, {7868, 16990, 141}, {7891, 20081, 32820}, {8105, 8106, 2493}, {8553, 44524, 22}, {8584, 9771, 11163}, {8960, 45515, 44647}, {8974, 13950, 9740}, {9605, 31401, 9606}, {9744, 9755, 8550}, {9753, 13860, 5480}, {11063, 44533, 23}, {11174, 16989, 597}, {11174, 39093, 39101}, {11488, 11489, 3620}, {13638, 13758, 183}, {13846, 13847, 15533}, {13910, 13972, 8177}, {13910, 45871, 590}, {13972, 45872, 615}, {14537, 39601, 43457}, {14971, 31173, 8355}, {15271, 34229, 11168}, {15480, 41139, 44377}, {16303, 16310, 3018}, {16303, 16317, 2493}, {16644, 16645, 21358}, {17129, 33245, 7836}, {20065, 32961, 7773}, {22110, 41139, 2}, {22329, 44377, 15480}, {22329, 44401, 22110}, {23302, 23303, 34573}, {24855, 44398, 22110}, {26456, 44594, 6}, {26463, 44597, 6}, {32787, 32788, 8584}, {35007, 39565, 7747}, {36899, 41932, 34369}, {37637, 37689, 5306}, {37640, 37641, 5032}, {37647, 41624, 7777}, {39022, 39023, 6}, {39107, 39108, 1992}, {39601, 43457, 5066}, {43622, 43623, 3763}, {44192, 44193, 157}, {44364, 44365, 44369}, {44377, 44381, 2}, {44377, 44401, 44381}, {44390, 44391, 141}, {44594, 44595, 26456}, {44596, 44597, 26463}