X(16) = 2nd ISODYNAMIC POINT

Trilinears

\(sin(A- π/3) : sin(B - π/3) : sin(C - π/3)\)

\(cos(A + π/6) : cos(B + π/6) : cos(C + π/6)\)

\(3 cos A - sqrt(3) sin A : :\)

Barycentrics

\(a sin(A - π/3) : b sin(B - π/3) : c sin(C- π/3)\)

\((SB + SC)/((SA - Sqrt[3] S) (SB + SC) + 4 SB SC) : :\)

\((S - Sqrt[3] SA) (SB + SC) : :\)

\(a^2*(Sqrt[3]*(a^2 - b^2 - c^2) + 2*S) : :\)

Notes

Let U and V be the points on sideline BC met by the interior and exterior bisectors of angle A. The circle having diameter UV is the A-Apollonian circle. The B- and C- Apollonian circles are similarly constructed. Each circle passes through a vertex and both isodynamic points. The pedal triangle of X(16) is equilateral. If you have The Geometer’s Sketchpad, you can view 2nd isodynamic point. If you have GeoGebra, you can view 2nd isodynamic point.

Let A’B’C’ be the 4th Brocard triangle and A″B″C″ be the 4th anti-Brocard triangle. The circumcircles of AA’A″, BB’B″, CC’C″ concur in two points, X(15) and X(16). (Randy Hutson, July 20, 2016)

The line X(14)X(16) is parallel to the Euler line, and the distance between the two lines is (SB - SC)(SC - SA)(SA - SB)/|(cot(ω) - 31/2)|((E - 8F)S2)1/2. (Kiminari Shinagawa, February 20, 2018)

Consider this picture, –> picture, in which (purple) hexagons are erected on the sides of ABC, with (green) flank-triangles: (1) X(16) of the 3 flank-triangles coincide with X(16) of ABC. (2) the (red) triangle of the centroids of the hexagons is perspective to ABC, and the perspector is X(13). (3) the circumcircle of the centroids (apices of equilaterals erect4d on the sides of ABC) has center X(627). (4) the (green) triangle with vertices on X(15)-of-flank-triangles is perspective to ABC, and the perspector is X(6). (Dan Reznick, October 18, 2021)

X(16) lies on the Evans conic, Parry circle, Moses Radical circle, Schoutte circle, Parry isodynamic circle, the cubics K001, K018, K048, K050, K073, K114, K129a, K148, K193, K206, K261a, K261b, K262a, K262b, K263, K290, K291, K292, K303b, K304, K341b, K390, K435, K438a, K438b, K439, K440, K441, K458, K463, K468, K469, K471, K505, K508, K513, K514, K523, K524, K639, K640, K641, K730, K802, K803, K881, K882, K883, K884, K885, K894, K900, K909, K912, K940, K942, K944, K946, K1052, K1064, K1099, K1105, K1132a, K1133b, and the curves on Q002, Q016, Q037, Q039, Q043, Q049, Q054, Q067, Q075, Q076, Q090, Q092, Q097, Q123, Q136, Q137, Q138, Q139, Q140, Q142, Q143, as well as these lines: {1, 1250}, {2, 13}, {3, 6}, {4, 18}, {5, 2912}, {11, 11773}, {14, 30}, {17, 140}, {20, 3411}, {21, 5367}, {23, 11630}, {24, 10641}, {35, 5357}, {36, 203}, {40, 10637}, {44, 11791}, {45, 11790}, {51, 3131}, {54, 10677}, {55, 202}, {56, 7006}, {57, 11778}, {74, 5669}, {86, 21869}, {98, 33389}, {99, 22689}, {110, 2379}, {111, 9203}, {115, 6774}, {128, 11601}, {183, 25157}, {184, 2902}, {185, 21648}, {186, 3166}, {214, 5239}, {230, 21157}, {237, 14188}, {298, 3642}, {299, 532}, {302, 316}, {303, 34509}, {323, 3171}, {351, 9163}, {358, 1135}, {376, 10654}, {378, 8739}, {381, 16645}, {383, 6114}, {385, 5981}, {396, 549}, {398, 550}, {399, 5616}, {404, 5362}, {465, 23292}, {466, 13567}, {471, 6111}, {484, 7052}, {485, 2042}, {486, 2041}, {512, 9162}, {523, 16182}, {524, 5464}, {531, 22496}, {533, 617}, {542, 9115}, {559, 16577}, {590, 15765}, {597, 35304}, {615, 18585}, {621, 9988}, {625, 11305}, {627, 635}, {628, 22855}, {629, 31705}, {631, 11488}, {634, 7836}, {636, 7832}, {691, 2378}, {740, 5700}, {842, 5995}, {843, 9202}, {846, 2945}, {940, 21475}, {1080, 9993}, {1138, 5623}, {1147, 3206}, {1154, 2903}, {1157, 8457}, {1181, 19364}, {1263, 8172}, {1276, 8481}, {1337, 2380}, {1338, 3458}, {1495, 3130}, {1498, 17827}, {1511, 6104}, {1513, 9750}, {1593, 11409}, {1656, 5340}, {1657, 5339}, {1658, 11267}, {1682, 11776}, {1724, 11097}, {2043, 6561}, {2044, 6560}, {2045, 5418}, {2046, 5420}, {2059, 13391}, {2070, 2924}, {2132, 8455}, {2133, 8458}, {2307, 7280}, {2381, 10410}, {2549, 5473}, {2777, 10682}, {2854, 13858}, {2925, 10329}, {2928, 2937}, {2953, 2959}, {2981, 21461}, {3065, 5672}, {3070, 14813}, {3071, 14814}, {3096, 11289}, {3124, 14704}, {3129, 34417}, {3201, 11134}, {3231, 14182}, {3412, 3530}, {3440, 8470}, {3464, 7325}, {3465, 7060}, {3479, 8174}, {3480, 8461}, {3483, 16882}, {3484, 8471}, {3515, 11408}, {3524, 16962}, {3631, 22844}, {3734, 25167}, {3849, 9761}, {3850, 5350}, {3923, 5699}, {3972, 35917}, {4383, 21476}, {5054, 16267}, {5056, 5344}, {5059, 5343}, {5066, 12816}, {5068, 5366}, {5365, 22237}, {5460, 31709}, {5469, 31710}, {5470, 25156}, {5471, 6781}, {5472, 6771}, {5474, 9113}, {5529, 11752}, {5610, 17402}, {5613, 6778}, {5617, 9982}, {5624, 8492}, {5663, 10658}, {5667, 6110}, {5673, 8502}, {5674, 8446}, {5678, 8445}, {5682, 8452}, {5872, 22745}, {5917, 23896}, {5999, 22692}, {6000, 10676}, {6137, 9138}, {6138, 9213}, {6241, 11467}, {6294, 8177}, {6296, 23001}, {6297, 23025}, {6300, 22609}, {6301, 22612}, {6304, 22638}, {6305, 22641}, {6564, 18586}, {6565, 18587}, {6581, 23000}, {6642, 10643}, {6694, 10583}, {6695, 7859}, {6759, 10675}, {6773, 6777}, {7059, 7088}, {7164, 8459}, {7326, 8509}, {7327, 8468}, {7329, 8464}, {7426, 34316}, {7488, 11420}, {7502, 11136}, {7622, 9763}, {7709, 32465}, {7751, 33467}, {7790, 11304}, {7844, 11306}, {7846, 11307}, {7865, 11298}, {7877, 35688}, {7880, 11302}, {7914, 11311}, {8173, 8496}, {8292, 9865}, {8431, 8463}, {8433, 8444}, {8437, 8447}, {8442, 8479}, {8448, 8536}, {8453, 8489}, {8465, 8486}, {8466, 8487}, {8467, 8494}, {8469, 8495}, {8484, 16883}, {8598, 12154}, {8837, 13367}, {8884, 19191}, {8918, 23722}, {9112, 21156}, {9147, 14446}, {9744, 9749}, {9754, 16653}, {9885, 22580}, {9932, 10659}, {10187, 35018}, {10188, 22235}, {10282, 30402}, {10546, 16260}, {10636, 10902}, {10662, 13754}, {10663, 12893}, {10664, 17702}, {10681, 13289}, {10788, 22695}, {11003, 14170}, {11004, 11127}, {11008, 22845}, {11146, 15018}, {11202, 11243}, {11449, 11452}, {11453, 12111}, {11464, 11466}, {11540, 33607}, {11586, 18777}, {11676, 22702}, {11779, 11788}, {12367, 14179}, {12584, 32301}, {12817, 15682}, {12972, 12980}, {12973, 12982}, {12981, 13060}, {12983, 13059}, {13049, 13057}, {13050, 13058}, {13103, 22846}, {13704, 23026}, {13706, 23002}, {13824, 23027}, {13826, 23003}, {13860, 22694}, {13881, 16631}, {14136, 16941}, {14178, 23023}, {14186, 23028}, {14368, 14972}, {14705, 20998}, {15080, 34008}, {15412, 23873}, {15640, 33606}, {15764, 32787}, {16319, 32461}, {16459, 16638}, {16806, 32627}, {17277, 21898}, {17821, 17826}, {18400, 32398}, {18538, 35738}, {18909, 18930}, {18925, 18929}, {18980, 19452}, {18981, 19453}, {19185, 19190}, {19357, 19363}, {19440, 19450}, {19441, 19451}, {22114, 22849}, {22490, 31694}, {22572, 31696}, {22604, 31698}, {22633, 31700}, {22690, 31702}, {22701, 22715}, {22708, 22714}, {22797, 22848}, {22890, 22906}, {22962, 22974}, {23008, 25219}, {23014, 25173}, {23249, 35732}, {23267, 35733}, {23358, 32397}, {25161, 31708}, {25168, 31714}, {25169, 31718}, {25170, 31716}, {25214, 31720}, {30464, 30470}, {30465, 36186}, {31378, 36211}, {31693, 33474}, {31695, 33476}, {31697, 33445}, {31699, 33444}, {31701, 33478}, {31707, 33481}, {31711, 33482}, {31713, 33484}, {31715, 33486}, {31717, 33488}, {31719, 33491}, {32171, 32207}, {32466, 32515}, {32785, 35730}, {35726, 35727}

X(16) = midpoint of X(i) and X(j) for these {i,j}: {3, 5615}, {13, 6779}, {617, 3181}, {621, 14712}, {2379, 5614}, {6778, 25235}

X(16) = reflection of X(i) in X(j) for these (i,j): (14,395), (15,187), (299,619), (316,623), (622,624)

X(16) = isogonal conjugate of X(14)

X(16) = isotomic conjugate of X(301)

X(16) = complement of X(622)

X(16) = anticomplement of X(624)

X(16) = circumcircle-inverse of X(15)

X(16) = nine-point-circle-inverse of X(6113)

X(16) = Brocard-circle-inverse of X(15)

X(16) = polar-circle-inverse of X(6117)

X(16) = orthoptic-circle-of-Steiner-inellipse-inverse of X(6115)

X(16) = 2nd-Brocard-circle-inverse of X(3104)

X(16) = circumcircle-of-outer-Napoleon-triangle-inverse of X(13)

X(16) = Lucas-inner-circle-inverse of X(15)

X(16) = Lucas-circles-radical-circle-inverse of X(15)

X(16) = outer-Montesdeoca-Lemoine-circle-inverse of X(15)

X(16) = inner-Montesdeoca-Lemoine-circle-inverse of X(15)

X(16) = antigonal image of X(11601)

X(16) = symgonal image of X(33527)

X(16) = complement of the isogonal conjugate of X(3439)

X(16) = complement of the isotomic conjugate of X(2993)

X(16) = isogonal conjugate of the anticomplement of X(619)

X(16) = isogonal conjugate of the complement of X(617)

X(16) = isotomic conjugate of the isogonal conjugate of X(34395)

X(16) = isogonal conjugate of the isotomic conjugate of X(299)

X(16) = isotomic conjugate of the polar conjugate of X(8740)

X(16) = isogonal conjugate of the polar conjugate of X(471)

X(16) = Thomson-isogonal conjugate of X(5464)

X(16) = excentral-isogonal conjugate of X(2946)

X(16) = tangential-isogonal conjugate of X(2926)

X(16) = orthic-isogonal conjugate of X(2903)

X(16) = psi-transform of X(15)

X(16) = X(i)-complementary conjugate of X(j) for these (i,j): {2993, 2887}, {3439, 10}

X(16) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 203}, {3, 3166}, {4, 2903}, {6, 3171}, {13, 5612}, {14, 61}, {30, 5669}, {54, 3201}, {74, 15}, {471, 8740}, {6151, 6}, {7150, 7005}, {11118, 11127}, {17403, 6138}, {32037, 35444}

X(16) = X(i)-cross conjugate of X(j) for these (i,j): {74, 8455}, {1095, 7005}, {1154, 11601}, {1511, 15}, {3201, 61}, {6138, 17403}, {14817, 14}, {19294, 323}, {34328, 11145}, {34395, 8740}

X(16) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14}, {2, 2154}, {15, 2166}, {17, 3376}, {31, 301}, {63, 8738}, {75, 3458}, {94, 2151}, {554, 7126}, {661, 23896}, {662, 20579}, {1577, 5994}, {2153, 11092}, {6137, 32680}, {7043, 33654}, {23870, 32678}, {24041, 30453}

X(16) = crosspoint of X(i) and X(j) for these (i,j): {1, 7150}, {2, 2993}, {14, 17}, {249, 10410}, {299, 471}, {2381, 16459}, {11601, 36211}

X(16) = crosssum of X(i) and X(j) for these (i,j): {2, 3181}, {3, 10662}, {6, 3130}, {15, 5616}, {16, 61}, {395, 8015}, {396, 30462}, {523, 30468}, {533, 618}, {6105, 36209}, {6110, 6117}, {9201, 30470}, {11543, 11556}, {18776, 30469}, {20579, 30453}, {23284, 30463}

X(16) = X(i)-line conjugate of X(j) for these (i,j): {14, 11549}, {549, 396}, {9138, 6137}, {16182, 523}

X(16) = X(i)-vertex conjugate of X(j) for these (i,j): {4, 16258}, {14, 3458}, {15, 512}, {3457, 32908}

X(16) = trilinear pole of line {526, 6138}

X(16) = crossdifference of every pair of points on line {396, 523}

X(16) = X(6)-Hirst inverse of X(15)

X(16) = X(16)-of-2nd-Brocard triangle

X(16) = X(16)-of-circumsymmedial-triangle

X(16) = {X(371),:ref:X(372) <X(372)>}-harmonic conjugate of X(62)

X(16) = X(75)-isoconjugate of X(3458)

X(16) = X(1577)-isoconjugate of X(5994)

X(16) = inner-Napoleon-to-outer-Napoleon similarity image of X(14)

X(16) = orthocentroidal-to-ABC similarity image of X(14)

X(16) = 4th-Brocard-to-circumsymmedial similarity image of X(14)

X(16) = X(2379)-of-2nd-Parry-triangle

X(16) = homothetic center of (equilateral) 1st isogonal triangle of X(14) and pedal triangle of X(16)

X(16) = homothetic center of (equilateral) 1st isogonal triangle of X(13) and triangle formed by circumcenters of BC:ref:X(13) <X(13)>, CA:ref:X(13) <X(13)>, AB:ref:X(13) <X(13)>

X(16) = radical center of Lucas(-2/sqrt(3)) circles

X(16) = eigencenter of outer Napoleon triangle

X(16) = X(14) of 4th anti-Brocard triangle

X(16) = X(16)-of-:ref:`X(3) <X(3)>`PU(1)

X(16) = Thomson-isogonal conjugate of X(5464)

X(16) = X(10658)-of-orthocentroidal-triangle

X(16) = {X(15),:ref:X(62) <X(62)>}-harmonic conjugate of X(6)

X(16) = Cundy-Parry Phi transform of X(62)

X(16) = Cundy-Parry Psi transform of X(18)

X(16) = X(1276)-of-orthic-triangle if ABC is acute

X(16) = barycentric product X(i)*X(j) for these {i,j}: {3, 471}, {6, 299}, {13, 323}, {14, 11130}, {15, 11078}, {17, 11126}, {18, 11145}, {50, 300}, {54, 33530}, {61, 19779}, {69, 8740}, {75, 2152}, {76, 34395}, {97, 6116}, {99, 6138}, {110, 23871}, {249, 30468}, {298, 11081}, {303, 8604}, {523, 17403}, {526, 23895}, {532, 2981}, {559, 5239}, {619, 6151}, {691, 9205}, {2987, 6783}, {3166, 19775}, {3171, 11122}, {3268, 5995}, {3457, 7799}, {3458, 11128}, {5612, 13582}, {6111, 14919}, {10409, 14446}, {10410, 35444}, {10411, 20578}, {10678, 11144}, {11092, 36208}, {11118, 19295}, {11119, 19294}, {11127, 11601}, {11131, 36211}, {11132, 21461}, {11134, 34390}, {11135, 34389}, {14922, 16459}, {17402, 23283}

X(16) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 301}, {6, 14}, {13, 94}, {15, 11092}, {25, 8738}, {31, 2154}, {32, 3458}, {50, 15}, {61, 16771}, {62, 8836}, {110, 23896}, {186, 470}, {299, 76}, {300, 20573}, {323, 298}, {471, 264}, {512, 20579}, {526, 23870}, {1154, 33529}, {1576, 5994}, {2088, 30465}, {2152, 1}, {2153, 2166}, {2981, 11117}, {3124, 30453}, {3166, 19773}, {3171, 3181}, {3201, 11126}, {3457, 1989}, {3458, 11085}, {5995, 476}, {6104, 8838}, {6116, 324}, {6137, 23284}, {6138, 523}, {6151, 11120}, {7051, 554}, {8603, 11600}, {8604, 18}, {8737, 6344}, {8740, 4}, {9205, 35522}, {10632, 473}, {10638, 7043}, {10678, 11143}, {11062, 6117}, {11078, 300}, {11081, 13}, {11086, 36210}, {11088, 11582}, {11126, 302}, {11130, 299}, {11134, 62}, {11135, 61}, {11136, 6105}, {11145, 303}, {11244, 8918}, {14270, 6137}, {17403, 99}, {19294, 618}, {19295, 533}, {19627, 34394}, {19779, 34389}, {20578, 10412}, {21461, 11087}, {21462, 11138}, {23871, 850}, {23895, 35139}, {30468, 338}, {32729, 9207}, {33530, 311}, {34328, 630}, {34394, 11086}, {34395, 6}, {34397, 8739}, {36208, 11078}

X(16) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11772, 11771}, {1, 11781, 11780}, {2, 616, 3643}, {2, 622, 624}, {2, 5335, 18582}, {2, 10653, 13}, {2, 18582, 16966}, {3, 6, 15}, {3, 15, 10645}, {3, 61, 5238}, {3, 62, 61}, {3, 371, 3389}, {3, 372, 3390}, {3, 1152, 35739}, {3, 5237, 5351}, {3, 5611, 9735}, {3, 5864, 14541}, {3, 10635, 11516}, {3, 11481, 10646}, {3, 11485, 11480}, {3, 11486, 6}, {3, 13349, 21159}, {3, 15794, 15785}, {3, 18470, 10635}, {3, 22236, 5352}, {3, 22238, 62}, {4, 10633, 10642}, {4, 11489, 18581}, {4, 18581, 16809}, {5, 5318, 16808}, {5, 23303, 16967}, {6, 15, 61}, {6, 10645, 34754}, {6, 10646, 10645}, {6, 11480, 11485}, {6, 11481, 3}, {6, 11486, 62}, {6, 19780, 32}, {6, 22238, 11486}, {13, 16242, 2}, {13, 16966, 18582}, {13, 33416, 16966}, {14, 395, 16268}, {14, 15442, 11582}, {14, 16961, 11543}, {14, 16963, 395}, {14, 19107, 5321}, {15, 61, 34754}, {15, 62, 6}, {15, 5237, 10646}, {15, 10645, 5238}, {15, 10646, 3}, {15, 34755, 62}, {15, 35739, 6396}, {17, 33417, 23302}, {18, 16809, 18581}, {18, 19106, 16809}, {18, 22862, 31703}, {32, 3098, 15}, {32, 3104, 61}, {35, 5357, 10638}, {36, 5353, 7051}, {36, 7127, 203}, {39, 5092, 15}, {50, 3581, 15}, {61, 5351, 3}, {61, 10645, 15}, {62, 3364, 3390}, {62, 3365, 3389}, {62, 5237, 3}, {62, 5351, 5238}, {62, 10646, 15}, {62, 11481, 10645}, {62, 14538, 3106}, {62, 34755, 11486}, {62, 35739, 3365}, {140, 397, 17}, {140, 11542, 23302}, {140, 23302, 33417}, {182, 574, 15}, {182, 3107, 61}, {182, 9736, 3}, {187, 11481, 21159}, {216, 11430, 15}, {298, 11300, 3642}, {299, 30472, 7799}, {302, 11303, 623}, {323, 11145, 11130}, {323, 34395, 3171}, {371, 372, 62}, {371, 3364, 61}, {371, 6200, 15}, {372, 3365, 61}, {372, 6396, 15}, {389, 22052, 15}, {395, 5321, 11543}, {395, 11543, 16961}, {396, 549, 16241}, {397, 23302, 11542}, {485, 2042, 3366}, {486, 2041, 3367}, {500, 17454, 15}, {566, 14805, 15}, {569, 14806, 15}, {572, 4256, 15}, {573, 4257, 15}, {575, 8589, 15}, {576, 8588, 15}, {576, 9735, 5611}, {577, 11438, 15}, {578, 10979, 15}, {622, 5335, 33517}, {624, 6672, 2}, {627, 22907, 22894}, {991, 4262, 15}, {1151, 6221, 15}, {1152, 6398, 15}, {1250, 19373, 1}, {1340, 1341, 15}, {1350, 1384, 15}, {1351, 5210, 15}, {1379, 1380, 15}, {1620, 33636, 15}, {1670, 1671, 3104}, {1689, 1690, 3107}, {1691, 35002, 15}, {2030, 18860, 15}, {2076, 5615, 3104}, {2076, 9301, 15}, {2076, 19780, 187}, {2080, 5104, 15}, {2902, 3165, 3200}, {3003, 10564, 15}, {3053, 33878, 15}, {3094, 26316, 15}, {3104, 3107, 3094}, {3311, 6411, 15}, {3312, 6412, 15}, {3364, 3365, 3}, {3371, 3372, 3365}, {3385, 3386, 3364}, {3389, 3390, 61}, {3391, 3392, 5}, {3430, 33628, 15}, {3592, 6451, 15}, {3594, 6452, 15}, {5008, 14810, 15}, {5013, 12017, 15}, {5024, 5085, 15}, {5030, 13329, 15}, {5033, 9737, 15}, {5093, 5585, 15}, {5237, 10646, 11481}, {5237, 11486, 10645}, {5237, 22238, 61}, {5237, 34755, 15}, {5238, 34754, 15}, {5318, 16773, 23303}, {5318, 23303, 5}, {5321, 11543, 14}, {5335, 18582, 13}, {5351, 11486, 34754}, {5351, 30559, 21159}, {5353, 7051, 203}, {5357, 10638, 7005}, {5474, 9113, 23013}, {5615, 13349, 14539}, {5615, 21402, 21159}, {6104, 36208, 11081}, {6199, 6409, 15}, {6200, 6396, 10646}, {6200, 11486, 3390}, {6302, 6306, 14904}, {6395, 6410, 15}, {6396, 11486, 3389}, {6407, 6468, 15}, {6408, 6469, 15}, {6425, 6445, 15}, {6426, 6446, 15}, {6429, 9690, 15}, {6437, 6449, 15}, {6438, 6450, 15}, {6439, 9691, 15}, {6453, 6480, 15}, {6454, 6481, 15}, {6582, 22687, 5980}, {6672, 33517, 16966}, {6777, 16530, 6782}, {7051, 7127, 5353}, {9675, 9738, 15}, {10633, 32586, 8839}, {10642, 11476, 4}, {10646, 11481, 5351}, {10646, 11486, 61}, {10646, 34755, 6}, {10653, 18582, 5335}, {10668, 10672, 6}, {10675, 30403, 6759}, {11126, 11130, 323}, {11134, 22115, 3201}, {11477, 15655, 15}, {11480, 11485, 15}, {11481, 11486, 15}, {11481, 22238, 6}, {11481, 34755, 61}, {11486, 22238, 34755}, {11489, 18581, 18}, {11542, 23302, 17}, {11543, 16961, 16268}, {11582, 15743, 15442}, {11771, 11780, 1}, {11772, 11781, 1}, {11773, 11782, 11}, {11774, 11783, 55}, {11775, 11784, 1}, {11776, 11785, 1682}, {11777, 11786, 56}, {11778, 11787, 57}, {11779, 11788, 11993}, {12054, 12055, 15}, {14539, 21159, 3}, {15037, 15109, 15}, {16242, 16966, 33416}, {16808, 16965, 5318}, {16808, 16967, 5}, {16809, 19106, 4}, {16961, 19107, 14}, {16963, 19107, 16961}, {16965, 16967, 16808}, {16966, 33416, 2}, {17851, 17852, 15}, {21309, 31884, 15}, {22511, 23005, 115}, {33440, 33441, 6298}, {35209, 35210, 36}