Solution for M24 (Puzzle to the sporadic group Mathieu24, see http://www.sciam.com/article.cfm?id=puzzles-simple-groups-at-play or http://www.math.lsa.umich.edu/~ikriz/) My solution found in summer 2008 follows at the end. ***Sam Coffland*** proposes now, January 2010, a much more manageable solution: ==================================================================================== Sam Cofflands solution is based on the use of trapping tools. These tools trap numbers in there home position while allowing the rest of the board to be moved. The trapping tools start form the most basic T2's which trap 23, and 22. The trapping tools become progressively more complex to trap more numbers. To begin this solution 23 is switched into the 0 position and 22 is moved to the 2 position, then the switch function is applied bringing 23 and 22 to their home positions. Now you can begin to use the trapping tools starting with the T2's To use the tools identify the position of the next lowest number to be trapped (ie.T2's move 21into it's home position) The number is moved using the cycles of one or more of the traps. For example if 21 is in the 10 position it can be brought home by applying T2-1. If it is in the 3 position by applying T2-2. If it is in the 9 position by applying the T2-2 then the T2-1 in reverse (T2-1rev). Once the next lowest number is in it's home position go to the the next set of trapping tools (ie. T3's) T2-1 (23,22) L7SR8S T2-1rev SL8SR7 (10,21,12,8,1,0) (3,4,2) (15,20,5) (14,17,16,19,11,6) (9,7) (18,13) T2-2 (23,22) L3SR10S T2-2rev -- SL10SR3 (6,13,18,8,10,19,3,21,11,16,0) (5,9,12,15,7,14,17,2,20,4,1) T3-1 (23,22,21) R2SL4SL3SL11SR2SR4S T3-1rev - SL4SL2SR11SR3SR4SL2 (1,2,11,8,14,17,16) (3,19,10,20,12,15,13)(4,6,7,18,5,0,9) T3-2 (23,22,21) L2SL6SR5SR8S T3-2rev SL8SL5SR6SR2 (20,4,15,11)(0,1,16,5) (2,9,8,6)(3,18,13,17)(7,14)(10)(12,19) T4-1(23,22,21,20) R6SL9SRSR6SL9SR9SL9SRSR6SL9SRSL6SR5SR8SL2SL6SR5SR8S T4-1rev SL8SL5SR6SR2SL8SL5SR6SLSR9SL6SLSR9SL9SR9SL6SLSR9SL6 (19,5,7,18,2)(0,6,13,4,15) (1,10,14,3,16)(8,12,9,17,11) T4-2 (23,22,21,20) SL10SR3SL10SRSR3SR9SL9SRSR6SL9SR3 T4-2rev L3SR9SL6SLSR9SL9SL3SLSR10SL3SR10S (19,4,14,13,18)(0,16,17,8,1)(2,12,10,3,9)(5,11,7,615) T5-1 (23,22,21,20,19) After T5 there is a 1/3 chance of the puzzle being solved if not use T6 SL4SL10SL2SL4SL7SL2SL10SR3SL10SRSR3SR9SL9SRSR6SL9 SR9SL9SRSR6SL9SRSL6SR5SR8SL2SL6SR5SR8S (18,0,9) (1,17,2)(3,8,6) (4,15,11)(5,13,16)(7,10,14) T5-2 (23,22,21,20,19) 18 will never fall into 3,6 or 8 R6SL9SRSR6SL9SR9SL9SRSR6SL9SRSL6SR5SR8SL2SL6SR5S R8SL2SR3SRSL6SL13SL6SL13SL6SL18SR8SL2SL6SL18SR8S (18,9)(0,12)(1,15)(2,16)(3)(4,10)(5,14)(6)(7,17)(8)(11,13) T6 (23,22,21,20,19,18) one or two rotations will complete the puzzle R11SR9SR3 ===================================my solution from summer 2008 - Bring home 0 - Bring home 15 - The operator h has two cycles of length 11 c1=(1 21 5 9 17 22 4 10 20 2 19) and c2=(3 11 16 6 8 13 12 14 7 18 23) If the actual place of 16 is in c1 apply h immediately to bring 16 home else use operator a to get 16 in c1 for element 17: - R (to get place 17 out of the fixed places of w) - The operator a has 4 cycles of length 5 d1=(1 23 6 14 11) d2=(2 3 18 8 13) d3=(4 20 5 21 7) and d4=(9 19 22 12 10) If the actual place of 17 is in d2 apply a immediately to bring 17 at 18 else use operator w to get 17 in d2 - L (invers of R) - Now we are left with some permutation - Find this permutation in the ordered table of 957 aw-combinations - Apply the found aw-combination Tools h is L8SL5SL5SR10SL5 and yields (0) (15) (1 21 5 9 17 22 4 10 20 2 19) (3 11 16 6 8 13 12 14 7 18 23) a is SR2SR12SR2SR9SL2S and yields (0) (15) (16) (17) (1 23 6 14 11) (2 3 18 8 13) (4 20 5 21 7) (9 19 22 12 10) w is SR5SR12SR3SR7SR13SR2 and yields (0) (15) (16) (17) (1 22 19 3 6) (2 13 5 4 9) (7 11 8 23 18) (10 20 12 21 14) w was constructed so that it has the same fixed elements as a An aw-table has been constructed by a programm using only the cycles of a and w. Here is this table. ( 1 ) ( 2 ) ( 3 10 ) ( 4 23 ) ( 5 8 ) ( 6 9 ) ( 7 ) ( 11 21 ) ( 12 ) ( 13 22 ) ( 14 19 ) ( 18 20 ) wwaawwaa ( 1 ) ( 2 ) ( 3 11 ) ( 4 22 ) ( 5 6 ) ( 7 ) ( 8 9 ) ( 10 21 ) ( 12 ) ( 13 23 ) ( 14 20 ) ( 18 19 ) aaawwaaawa ( 1 ) ( 2 ) ( 3 13 ) ( 4 21 ) ( 5 20 ) ( 6 14 ) ( 7 ) ( 8 18 ) ( 9 19 ) ( 10 22 ) ( 11 23 ) ( 12 ) wwawwwwaaw ( 1 ) ( 2 ) ( 3 14 ) ( 4 8 ) ( 5 23 ) ( 6 13 ) ( 7 ) ( 9 22 ) ( 10 19 ) ( 11 20 ) ( 12 ) ( 18 21 ) waaawaww ( 1 ) ( 2 ) ( 3 18 ) ( 4 6 ) ( 5 22 ) ( 7 ) ( 8 13 ) ( 9 23 ) ( 10 20 ) ( 11 19 ) ( 12 ) ( 14 21 ) aawwaawwwwaa ( 1 ) ( 2 ) ( 3 19 ) ( 4 5 ) ( 6 22 ) ( 7 ) ( 8 23 ) ( 9 13 ) ( 10 14 ) ( 11 18 ) ( 12 ) ( 20 21 ) awwaaaawaa ( 1 ) ( 2 ) ( 3 20 ) ( 4 9 ) ( 5 13 ) ( 6 23 ) ( 7 ) ( 8 22 ) ( 10 18 ) ( 11 14 ) ( 12 ) ( 19 21 ) wwaaaawwaaww ( 1 ) ( 2 ) ( 3 21 ) ( 4 13 ) ( 5 9 ) ( 6 8 ) ( 7 ) ( 10 11 ) ( 12 ) ( 14 18 ) ( 19 20 ) ( 22 23 ) wwaaaawaawwa ( 1 ) ( 2 ) ( 3 22 ) ( 4 11 ) ( 5 18 ) ( 6 19 ) ( 7 ) ( 8 20 ) ( 9 14 ) ( 10 13 ) ( 12 ) ( 21 23 ) aawawwwa ( 1 ) ( 2 ) ( 3 23 ) ( 4 10 ) ( 5 14 ) ( 6 20 ) ( 7 ) ( 8 19 ) ( 9 18 ) ( 11 13 ) ( 12 ) ( 21 22 ) awaaaawaaa ( 1 ) ( 2 ) ( 3 4 ) ( 5 19 ) ( 6 18 ) ( 7 ) ( 8 14 ) ( 9 20 ) ( 10 23 ) ( 11 22 ) ( 12 ) ( 13 21 ) wwwawwwwaw ( 1 ) ( 2 ) ( 3 5 ) ( 4 19 ) ( 6 11 ) ( 7 ) ( 8 10 ) ( 9 21 ) ( 12 ) ( 13 20 ) ( 14 23 ) ( 18 22 ) wawwwaawww ( 1 ) ( 2 ) ( 3 6 ) ( 4 18 ) ( 5 11 ) ( 7 ) ( 8 21 ) ( 9 10 ) ( 12 ) ( 13 14 ) ( 19 22 ) ( 20 23 ) awwwaaaw ( 1 ) ( 2 ) ( 3 8 ) ( 4 14 ) ( 5 10 ) ( 6 21 ) ( 7 ) ( 9 11 ) ( 12 ) ( 13 18 ) ( 19 23 ) ( 20 22 ) waawwawwwwaa ( 1 ) ( 2 12 7 ) ( 3 ) ( 4 23 10 ) ( 5 20 13 ) ( 6 22 19 ) ( 8 9 11 ) ( 14 18 21 ) awaaaawwaaw ( 1 ) ( 2 12 7 ) ( 3 10 23 ) ( 4 ) ( 5 18 11 ) ( 6 13 8 ) ( 9 21 19 ) ( 14 20 22 ) aawaaw ( 1 ) ( 2 12 7 ) ( 3 11 9 ) ( 4 13 6 ) ( 5 14 19 ) ( 8 ) ( 10 22 18 ) ( 20 23 21 ) wwwaawwawwwwa ( 1 ) ( 2 12 7 ) ( 3 13 20 ) ( 4 11 18 ) ( 5 ) ( 6 10 21 ) ( 8 19 14 ) ( 9 23 22 ) awwwa ( 1 ) ( 2 12 7 ) ( 3 14 21 ) ( 4 5 11 ) ( 6 9 20 ) ( 8 22 10 ) ( 13 23 19 ) ( 18 ) aaaawwaw ( 1 ) ( 2 12 7 ) ( 3 18 14 ) ( 4 9 19 ) ( 5 10 6 ) ( 8 23 20 ) ( 11 13 22 ) ( 21 ) wwwawwaaaw ( 1 ) ( 2 12 7 ) ( 3 19 22 ) ( 4 8 13 ) ( 5 21 10 ) ( 6 ) ( 9 18 20 ) ( 11 23 14 ) aawaaawaaawwww ( 1 ) ( 2 12 7 ) ( 3 20 5 ) ( 4 6 8 ) ( 9 14 10 ) ( 11 22 21 ) ( 13 ) ( 18 19 23 ) waawwwwaa ( 1 ) ( 2 12 7 ) ( 3 21 18 ) ( 4 22 20 ) ( 5 19 8 ) ( 6 23 11 ) ( 9 10 13 ) ( 14 ) wwwwaawaaaww ( 1 ) ( 2 12 7 ) ( 3 22 6 ) ( 4 21 9 ) ( 5 8 14 ) ( 10 11 20 ) ( 13 18 23 ) ( 19 ) aawwwwawwa ( 1 ) ( 2 12 7 ) ( 3 23 4 ) ( 5 6 21 ) ( 8 18 22 ) ( 9 13 14 ) ( 10 ) ( 11 19 20 ) aaawaawww ( 1 ) ( 2 12 7 ) ( 3 4 10 ) ( 5 9 22 ) ( 6 11 14 ) ( 8 20 21 ) ( 13 19 18 ) ( 23 ) wwwaawaw ( 1 ) ( 2 12 7 ) ( 3 5 13 ) ( 4 14 22 ) ( 6 18 9 ) ( 8 21 23 ) ( 10 19 11 ) ( 20 ) wwawaawwaa ( 1 ) ( 2 12 7 ) ( 3 6 19 ) ( 4 20 14 ) ( 5 23 9 ) ( 8 10 18 ) ( 11 21 13 ) ( 22 ) aaawawwaaww ( 1 ) ( 2 12 7 ) ( 3 8 11 ) ( 4 19 21 ) ( 5 22 23 ) ( 6 20 18 ) ( 9 ) ( 10 14 13 ) wwawwww ( 1 ) ( 2 12 7 ) ( 3 9 8 ) ( 4 18 5 ) ( 6 14 23 ) ( 10 20 19 ) ( 11 ) ( 13 21 22 ) wawwaaaaw ( 1 ) ( 2 7 12 ) ( 3 ) ( 4 10 23 ) ( 5 13 20 ) ( 6 19 22 ) ( 8 11 9 ) ( 14 21 18 ) wwaawwaaaaw ( 1 ) ( 2 7 12 ) ( 3 10 4 ) ( 5 22 9 ) ( 6 14 11 ) ( 8 21 20 ) ( 13 18 19 ) ( 23 ) awaaaaww ( 1 ) ( 2 7 12 ) ( 3 11 8 ) ( 4 21 19 ) ( 5 23 22 ) ( 6 18 20 ) ( 9 ) ( 10 13 14 ) wwwawwa ( 1 ) ( 2 7 12 ) ( 3 13 5 ) ( 4 22 14 ) ( 6 9 18 ) ( 8 23 21 ) ( 10 11 19 ) ( 20 ) aawwwwaawwwwa ( 1 ) ( 2 7 12 ) ( 3 14 18 ) ( 4 19 9 ) ( 5 6 10 ) ( 8 20 23 ) ( 11 22 13 ) ( 21 ) waaawwaaww ( 1 ) ( 2 7 12 ) ( 3 18 21 ) ( 4 20 22 ) ( 5 8 19 ) ( 6 11 23 ) ( 9 13 10 ) ( 14 ) awaawwwawww ( 1 ) ( 2 7 12 ) ( 3 19 6 ) ( 4 14 20 ) ( 5 9 23 ) ( 8 18 10 ) ( 11 13 21 ) ( 22 ) wwawwwwawwwa ( 1 ) ( 2 7 12 ) ( 3 20 13 ) ( 4 18 11 ) ( 5 ) ( 6 21 10 ) ( 8 14 19 ) ( 9 22 23 ) aaaawwaaaa ( 1 ) ( 2 7 12 ) ( 3 21 14 ) ( 4 11 5 ) ( 6 20 9 ) ( 8 10 22 ) ( 13 19 23 ) ( 18 ) wawwaa ( 1 ) ( 2 7 12 ) ( 3 22 19 ) ( 4 13 8 ) ( 5 10 21 ) ( 6 ) ( 9 20 18 ) ( 11 14 23 ) wwaaawaaawa ( 1 ) ( 2 7 12 ) ( 3 23 10 ) ( 4 ) ( 5 11 18 ) ( 6 8 13 ) ( 9 19 21 ) ( 14 22 20 ) aaw ( 1 ) ( 2 7 12 ) ( 3 4 23 ) ( 5 21 6 ) ( 8 22 18 ) ( 9 14 13 ) ( 10 ) ( 11 20 19 ) wwwaawaaaa ( 1 ) ( 2 7 12 ) ( 3 5 20 ) ( 4 8 6 ) ( 9 10 14 ) ( 11 21 22 ) ( 13 ) ( 18 23 19 ) aaawwaawaa ( 1 ) ( 2 7 12 ) ( 3 6 22 ) ( 4 9 21 ) ( 5 14 8 ) ( 10 20 11 ) ( 13 23 18 ) ( 19 ) wwawwwaaa ( 1 ) ( 2 7 12 ) ( 3 8 9 ) ( 4 5 18 ) ( 6 23 14 ) ( 10 19 20 ) ( 11 ) ( 13 22 21 ) wwwwaawwaw ( 1 ) ( 2 7 12 ) ( 3 9 11 ) ( 4 6 13 ) ( 5 19 14 ) ( 8 ) ( 10 18 22 ) ( 20 21 23 ) wwwwaaawaawwwwaa ( 1 10 ) ( 2 23 ) ( 3 12 ) ( 4 7 ) ( 5 21 ) ( 6 ) ( 8 22 ) ( 9 ) ( 11 19 ) ( 13 14 ) ( 18 ) ( 20 ) wwaaawaawwwwa ( 1 10 ) ( 2 3 ) ( 4 12 ) ( 5 6 ) ( 7 23 ) ( 8 18 ) ( 9 14 ) ( 11 ) ( 13 ) ( 19 20 ) ( 21 ) ( 22 ) wawwwwaaww ( 1 10 ) ( 2 4 ) ( 3 7 ) ( 5 ) ( 6 21 ) ( 8 ) ( 9 13 ) ( 11 20 ) ( 12 23 ) ( 14 ) ( 18 22 ) ( 19 ) awwwawaa ( 1 10 11 ) ( 2 3 21 ) ( 4 13 12 ) ( 5 14 8 ) ( 6 18 9 ) ( 7 23 22 ) ( 19 ) ( 20 ) wwaawwaawaa ( 1 10 11 19 20 ) ( 2 4 21 14 6 ) ( 3 22 5 18 7 ) ( 8 9 12 23 13 ) wwawwwaw ( 1 10 11 20 19 ) ( 2 23 21 18 5 ) ( 3 13 6 14 12 ) ( 4 22 9 8 7 ) aawwaa ( 1 10 12 23 ) ( 2 4 7 3 ) ( 5 19 ) ( 6 22 20 13 ) ( 8 14 ) ( 9 11 18 21 ) waaaawwawwwa ( 1 10 12 3 ) ( 2 23 7 4 ) ( 5 22 14 11 ) ( 6 9 ) ( 8 21 19 13 ) ( 18 20 ) wawwaawaa ( 1 10 12 4 ) ( 2 3 7 23 ) ( 5 9 8 20 ) ( 6 19 18 14 ) ( 11 13 ) ( 21 22 ) aawwawww ( 1 10 13 ) ( 2 3 22 ) ( 4 11 12 ) ( 5 8 19 ) ( 6 20 18 ) ( 7 23 21 ) ( 9 ) ( 14 ) wawwaawwaaa ( 1 10 13 14 9 ) ( 2 4 22 19 18 ) ( 3 21 8 6 7 ) ( 5 20 12 23 11 ) aawaawwaa ( 1 10 13 9 14 ) ( 2 23 22 6 8 ) ( 3 11 18 19 12 ) ( 4 21 20 5 7 ) wwaawwaaaawwaa ( 1 10 14 ) ( 2 4 5 ) ( 3 19 7 ) ( 6 18 20 ) ( 8 12 23 ) ( 9 ) ( 11 22 21 ) ( 13 ) aaawwwa ( 1 10 14 13 9 ) ( 2 3 5 11 6 ) ( 4 8 21 18 12 ) ( 7 23 19 22 20 ) aawwwaaa ( 1 10 14 9 13 ) ( 2 23 5 18 21 ) ( 3 8 20 22 12 ) ( 4 19 6 11 7 ) awwaawa ( 1 10 18 ) ( 2 23 6 ) ( 3 20 12 ) ( 4 9 7 ) ( 5 14 19 ) ( 8 ) ( 11 13 21 ) ( 22 ) awwaaaaww ( 1 10 18 22 8 ) ( 2 3 6 11 5 ) ( 4 20 13 19 12 ) ( 7 23 9 21 14 ) wwaaawaaww ( 1 10 18 8 22 ) ( 2 4 6 14 21 ) ( 3 9 19 13 7 ) ( 5 11 12 23 20 ) aaawwaaww ( 1 10 19 ) ( 2 4 8 ) ( 3 14 7 ) ( 5 12 23 ) ( 6 9 18 ) ( 11 ) ( 13 21 22 ) ( 20 ) wwaaa ( 1 10 19 11 20 ) ( 2 3 8 13 18 ) ( 4 5 22 6 12 ) ( 7 23 14 21 9 ) awwaawwww ( 1 10 19 20 11 ) ( 2 23 8 6 22 ) ( 3 5 9 21 12 ) ( 4 14 18 13 7 ) aaaw ( 1 10 2 23 ) ( 3 7 4 12 ) ( 5 11 8 13 ) ( 6 18 ) ( 9 20 ) ( 14 22 19 21 ) aaaawwawwwaaa ( 1 10 2 3 ) ( 4 7 23 12 ) ( 5 18 19 9 ) ( 6 14 20 8 ) ( 11 21 ) ( 13 22 ) wwaawwwwaawwwwa ( 1 10 2 4 ) ( 3 12 23 7 ) ( 5 14 ) ( 6 11 9 22 ) ( 8 19 ) ( 13 20 21 18 ) wawww ( 1 10 20 ) ( 2 23 9 ) ( 3 18 12 ) ( 4 6 7 ) ( 5 8 14 ) ( 11 ) ( 13 22 21 ) ( 19 ) wwwwawwaaww ( 1 10 20 11 19 ) ( 2 3 9 22 14 ) ( 4 18 21 8 12 ) ( 5 7 23 6 13 ) wwawaawww ( 1 10 20 19 11 ) ( 2 4 9 5 13 ) ( 3 6 8 21 7 ) ( 12 23 18 14 22 ) awwwawwwwaw ( 1 10 21 ) ( 2 3 11 ) ( 4 22 12 ) ( 5 ) ( 6 ) ( 7 23 13 ) ( 8 14 19 ) ( 9 18 20 ) waa ( 1 10 21 5 6 ) ( 2 4 11 8 20 ) ( 3 13 19 9 7 ) ( 12 23 22 14 18 ) aaawaawwwwaa ( 1 10 21 6 5 ) ( 2 23 11 9 19 ) ( 3 22 20 8 12 ) ( 4 13 18 14 7 ) wwwwaawwaaw ( 1 10 22 ) ( 2 3 13 ) ( 4 21 12 ) ( 5 19 14 ) ( 6 9 20 ) ( 7 23 11 ) ( 8 ) ( 18 ) aawwwawwwaw ( 1 10 22 18 8 ) ( 2 23 13 20 14 ) ( 3 21 9 5 12 ) ( 4 11 6 19 7 ) awwwawwaaa ( 1 10 22 8 18 ) ( 2 4 13 5 9 ) ( 3 11 14 20 7 ) ( 6 12 23 21 19 ) aaaawwaaw ( 1 10 5 ) ( 2 4 14 ) ( 3 8 7 ) ( 6 ) ( 9 20 18 ) ( 11 13 22 ) ( 12 23 19 ) ( 21 ) aawaaaw ( 1 10 5 21 6 ) ( 2 3 14 22 9 ) ( 4 19 13 20 12 ) ( 7 23 8 11 18 ) aaawwwawwa ( 1 10 5 6 21 ) ( 2 23 14 20 13 ) ( 3 19 18 11 12 ) ( 4 8 9 22 7 ) wwaawww ( 1 10 6 ) ( 2 23 18 ) ( 3 9 12 ) ( 4 20 7 ) ( 5 ) ( 8 19 14 ) ( 11 22 13 ) ( 21 ) waaaawwaw ( 1 10 6 21 5 ) ( 2 3 18 13 8 ) ( 4 9 11 14 12 ) ( 7 23 20 22 19 ) wwawwwawwwa ( 1 10 6 5 21 ) ( 2 4 18 19 22 ) ( 3 20 14 11 7 ) ( 8 13 12 23 9 ) aawwaawwa ( 1 10 7 23 ) ( 2 3 12 4 ) ( 5 20 14 18 ) ( 6 8 9 19 ) ( 11 22 ) ( 13 21 ) aaawaaawaaa ( 1 10 7 3 ) ( 2 4 12 23 ) ( 5 8 ) ( 6 13 18 11 ) ( 9 21 20 22 ) ( 14 19 ) wwwawwaaaaw ( 1 10 7 4 ) ( 2 23 12 3 ) ( 5 13 19 22 ) ( 6 20 ) ( 8 11 14 21 ) ( 9 18 ) wwawaaa ( 1 10 8 ) ( 2 4 19 ) ( 3 5 7 ) ( 6 20 9 ) ( 11 21 13 ) ( 12 23 14 ) ( 18 ) ( 22 ) aaawaawwaw ( 1 10 8 18 22 ) ( 2 23 19 9 11 ) ( 3 14 6 13 12 ) ( 4 5 20 21 7 ) wwwwawwwa ( 1 10 8 22 18 ) ( 2 3 19 21 20 ) ( 4 14 11 9 12 ) ( 5 13 6 7 23 ) wwwwaw ( 1 10 9 ) ( 2 23 20 ) ( 3 6 12 ) ( 4 18 7 ) ( 5 19 8 ) ( 11 21 22 ) ( 13 ) ( 14 ) waawwa ( 1 10 9 13 14 ) ( 2 3 20 21 19 ) ( 4 6 22 5 12 ) ( 7 23 18 11 8 ) awwaaawaaaww ( 1 10 9 14 13 ) ( 2 4 20 8 11 ) ( 3 18 5 22 7 ) ( 6 19 21 12 23 ) wwaawwwwaaww ( 1 11 ) ( 2 13 ) ( 3 8 ) ( 4 5 ) ( 6 ) ( 7 21 ) ( 9 ) ( 10 19 ) ( 12 22 ) ( 14 23 ) ( 18 ) ( 20 ) awwawwwwaaw ( 1 11 ) ( 2 21 ) ( 3 ) ( 4 ) ( 5 18 ) ( 6 14 ) ( 7 22 ) ( 8 9 ) ( 10 ) ( 12 13 ) ( 19 20 ) ( 23 ) awwwwaawaaaww ( 1 11 10 ) ( 2 21 3 ) ( 4 12 13 ) ( 5 8 14 ) ( 6 9 18 ) ( 7 22 23 ) ( 19 ) ( 20 ) aaawaawwaa ( 1 11 10 19 20 ) ( 2 22 3 14 9 ) ( 4 8 18 12 21 ) ( 5 6 7 13 23 ) wwwaawwawwww ( 1 11 10 20 19 ) ( 2 13 3 18 8 ) ( 4 6 5 12 22 ) ( 7 21 23 9 14 ) waawwawwwwa ( 1 11 12 13 ) ( 2 21 7 22 ) ( 3 23 ) ( 4 10 ) ( 5 6 19 9 ) ( 8 20 14 18 ) waawwwaw ( 1 11 12 21 ) ( 2 22 7 13 ) ( 3 20 4 6 ) ( 5 8 ) ( 9 23 18 10 ) ( 14 19 ) wwawaawwa ( 1 11 12 22 ) ( 2 13 7 21 ) ( 3 5 10 14 ) ( 4 8 23 19 ) ( 6 18 ) ( 9 20 ) wwaaaawaaww ( 1 11 14 ) ( 2 22 8 ) ( 3 10 4 ) ( 5 7 13 ) ( 6 ) ( 9 18 20 ) ( 12 21 19 ) ( 23 ) wwawwaawwww ( 1 11 14 23 6 ) ( 2 21 8 10 9 ) ( 3 18 7 22 5 ) ( 4 20 12 13 19 ) wwwwawwwwaw ( 1 11 14 6 23 ) ( 2 13 8 18 3 ) ( 4 7 21 5 20 ) ( 9 10 12 22 19 ) wawaw ( 1 11 18 ) ( 2 13 9 ) ( 3 10 23 ) ( 4 ) ( 5 ) ( 6 12 22 ) ( 7 21 20 ) ( 8 14 19 ) awaaawaaaww ( 1 11 18 4 5 ) ( 2 21 9 10 8 ) ( 3 14 12 13 6 ) ( 7 22 20 23 19 ) wwwaww ( 1 11 18 5 4 ) ( 2 22 9 14 3 ) ( 6 19 23 12 21 ) ( 7 13 20 8 10 ) aawwwwaawaaa ( 1 11 19 ) ( 2 22 5 ) ( 3 4 23 ) ( 6 18 9 ) ( 7 13 8 ) ( 10 ) ( 12 21 14 ) ( 20 ) waawwwwa ( 1 11 19 10 20 ) ( 2 21 5 23 18 ) ( 3 6 12 13 14 ) ( 4 9 7 22 8 ) aawwaaaawwaa ( 1 11 19 20 10 ) ( 2 13 5 9 4 ) ( 3 7 21 8 6 ) ( 12 22 14 18 23 ) wwwaawwawaaa ( 1 11 2 13 ) ( 3 14 4 19 ) ( 5 23 8 10 ) ( 6 20 ) ( 7 21 12 22 ) ( 9 18 ) wwwaawwww ( 1 11 2 21 ) ( 3 10 ) ( 4 23 ) ( 5 9 14 20 ) ( 6 8 18 19 ) ( 7 22 12 13 ) aawwwwawwaawww ( 1 11 2 22 ) ( 3 18 23 20 ) ( 4 9 10 6 ) ( 5 19 ) ( 7 13 12 21 ) ( 8 14 ) wwaawaw ( 1 11 20 ) ( 2 13 6 ) ( 3 23 4 ) ( 5 14 8 ) ( 7 21 18 ) ( 9 12 22 ) ( 10 ) ( 19 ) wawwaaawww ( 1 11 20 10 19 ) ( 2 21 6 4 14 ) ( 3 5 7 22 18 ) ( 8 12 13 9 23 ) wawwa ( 1 11 20 19 10 ) ( 2 22 6 8 23 ) ( 3 12 21 9 5 ) ( 4 7 13 18 14 ) wwwwaa ( 1 11 23 ) ( 2 21 4 ) ( 3 12 13 ) ( 5 19 8 ) ( 6 ) ( 7 22 10 ) ( 9 20 18 ) ( 14 ) waaawaaww ( 1 11 23 14 6 ) ( 2 22 4 19 18 ) ( 3 5 9 12 21 ) ( 7 13 10 8 20 ) wwwwawwaaaw ( 1 11 23 6 14 ) ( 2 13 4 9 5 ) ( 3 20 8 12 22 ) ( 7 21 10 18 19 ) waaaawwaa ( 1 11 3 ) ( 2 21 10 ) ( 4 7 22 ) ( 5 14 19 ) ( 6 18 20 ) ( 8 ) ( 9 ) ( 12 13 23 ) aawaaaa ( 1 11 3 8 9 ) ( 2 22 10 5 20 ) ( 4 14 18 7 13 ) ( 6 12 21 23 19 ) awww ( 1 11 3 9 8 ) ( 2 13 10 6 19 ) ( 4 20 5 7 21 ) ( 12 22 23 18 14 ) awwaaaawa ( 1 11 4 ) ( 2 21 23 ) ( 3 7 22 ) ( 5 ) ( 6 20 9 ) ( 8 19 14 ) ( 10 12 13 ) ( 18 ) wwwaawaaa ( 1 11 4 18 5 ) ( 2 13 23 20 14 ) ( 3 6 8 7 21 ) ( 9 19 12 22 10 ) wwwwawwaawa ( 1 11 4 5 18 ) ( 2 22 23 8 6 ) ( 3 19 9 7 13 ) ( 10 14 20 12 21 ) aawwwwaww ( 1 11 5 ) ( 2 22 19 ) ( 3 23 10 ) ( 4 ) ( 6 9 20 ) ( 7 13 14 ) ( 8 12 21 ) ( 18 ) waaawaawwwwaaa ( 1 11 5 18 4 ) ( 2 13 19 6 10 ) ( 3 12 22 8 20 ) ( 7 21 14 9 23 ) wwaawwa ( 1 11 5 4 18 ) ( 2 21 19 3 20 ) ( 6 7 22 14 10 ) ( 8 23 9 12 13 ) aaawwaawa ( 1 11 6 ) ( 2 13 20 ) ( 3 4 10 ) ( 5 8 19 ) ( 7 21 9 ) ( 12 22 18 ) ( 14 ) ( 23 ) waaawwaawaa ( 1 11 6 14 23 ) ( 2 22 20 5 10 ) ( 3 7 13 9 19 ) ( 4 12 21 18 8 ) wwwaaawaaw ( 1 11 6 23 14 ) ( 2 21 20 3 19 ) ( 4 8 7 22 9 ) ( 5 12 13 18 10 ) wwaaawaaaw ( 1 11 7 13 ) ( 2 22 12 21 ) ( 3 6 10 18 ) ( 4 20 23 9 ) ( 5 14 ) ( 8 19 ) waawaaaw ( 1 11 7 21 ) ( 2 13 12 22 ) ( 3 19 23 5 ) ( 4 14 10 8 ) ( 6 9 ) ( 18 20 ) aawawww ( 1 11 7 22 ) ( 2 21 12 13 ) ( 3 4 ) ( 5 20 8 6 ) ( 9 19 18 14 ) ( 10 23 ) aaaawwaaa ( 1 11 8 ) ( 2 22 14 ) ( 3 ) ( 4 10 23 ) ( 5 12 21 ) ( 6 20 18 ) ( 7 13 19 ) ( 9 ) aawwwawwwaa ( 1 11 8 3 9 ) ( 2 21 14 4 6 ) ( 5 10 18 12 13 ) ( 7 22 19 23 20 ) awwaawwaw ( 1 11 8 9 3 ) ( 2 13 14 20 23 ) ( 4 12 22 5 6 ) ( 7 21 19 18 10 ) awaaaawaa ( 1 11 9 ) ( 2 13 18 ) ( 3 ) ( 4 23 10 ) ( 5 19 14 ) ( 6 7 21 ) ( 8 ) ( 12 22 20 ) wwwawwaawww ( 1 11 9 3 8 ) ( 2 21 18 23 5 ) ( 4 19 12 13 20 ) ( 6 10 14 7 22 ) aawwwwaawwww ( 1 11 9 8 3 ) ( 2 22 18 19 4 ) ( 5 23 7 13 6 ) ( 10 12 21 20 14 ) awwaawwwa ( 1 12 ) ( 2 7 ) ( 3 ) ( 4 ) ( 5 19 ) ( 6 9 ) ( 8 14 ) ( 10 ) ( 11 13 ) ( 18 20 ) ( 21 22 ) ( 23 ) wawwaaaawwa ( 1 12 ) ( 2 7 ) ( 3 10 ) ( 4 23 ) ( 5 14 ) ( 6 ) ( 8 19 ) ( 9 ) ( 11 22 ) ( 13 21 ) ( 18 ) ( 20 ) waawwwwaawa ( 1 12 ) ( 2 7 ) ( 3 11 23 13 ) ( 4 22 10 21 ) ( 5 18 14 9 ) ( 6 8 20 19 ) wwwwawwaawwww ( 1 12 ) ( 2 7 ) ( 3 13 23 11 ) ( 4 21 10 22 ) ( 5 9 14 18 ) ( 6 19 20 8 ) waaaawwawww ( 1 12 ) ( 2 7 ) ( 3 14 4 8 ) ( 5 10 19 23 ) ( 6 22 18 11 ) ( 9 13 20 21 ) aaaawwaawaaaa ( 1 12 ) ( 2 7 ) ( 3 18 10 20 ) ( 4 6 23 9 ) ( 5 11 8 21 ) ( 13 19 22 14 ) awwaawaww ( 1 12 ) ( 2 7 ) ( 3 19 4 5 ) ( 6 13 18 21 ) ( 8 10 14 23 ) ( 9 22 20 11 ) wawaaaw ( 1 12 ) ( 2 7 ) ( 3 20 10 18 ) ( 4 9 23 6 ) ( 5 21 8 11 ) ( 13 14 22 19 ) aawawwaaw ( 1 12 ) ( 2 7 ) ( 3 21 23 22 ) ( 4 13 10 11 ) ( 5 20 14 6 ) ( 8 18 19 9 ) awwwawa ( 1 12 ) ( 2 7 ) ( 3 22 23 21 ) ( 4 11 10 13 ) ( 5 6 14 20 ) ( 8 9 19 18 ) waawwaww ( 1 12 ) ( 2 7 ) ( 3 4 ) ( 5 ) ( 6 20 ) ( 8 ) ( 9 18 ) ( 10 23 ) ( 11 21 ) ( 13 22 ) ( 14 ) ( 19 ) aawwaaww ( 1 12 ) ( 2 7 ) ( 3 5 4 19 ) ( 6 21 18 13 ) ( 8 23 14 10 ) ( 9 11 20 22 ) aawaawwa ( 1 12 ) ( 2 7 ) ( 3 6 10 9 ) ( 4 18 23 20 ) ( 5 22 8 13 ) ( 11 14 21 19 ) wwaa ( 1 12 ) ( 2 7 ) ( 3 8 4 14 ) ( 5 23 19 10 ) ( 6 11 18 22 ) ( 9 21 20 13 ) aaawaawwwwa ( 1 12 ) ( 2 7 ) ( 3 9 10 6 ) ( 4 20 23 18 ) ( 5 13 8 22 ) ( 11 19 21 14 ) aaawww ( 1 12 2 ) ( 3 ) ( 4 23 10 ) ( 5 18 22 ) ( 6 21 8 ) ( 7 ) ( 9 13 19 ) ( 11 14 20 ) wawwwwawwaaa ( 1 12 2 ) ( 3 10 23 ) ( 4 ) ( 5 20 21 ) ( 6 11 19 ) ( 7 ) ( 8 9 22 ) ( 13 14 18 ) wwaawaaaw ( 1 12 2 ) ( 3 11 20 ) ( 4 13 18 ) ( 5 19 8 ) ( 6 10 22 ) ( 7 ) ( 9 23 21 ) ( 14 ) wawwaawa ( 1 12 2 ) ( 3 13 9 ) ( 4 11 6 ) ( 5 8 14 ) ( 7 ) ( 10 21 18 ) ( 19 ) ( 20 23 22 ) wwawaa ( 1 12 2 ) ( 3 14 11 ) ( 4 5 21 ) ( 6 18 9 ) ( 7 ) ( 8 13 10 ) ( 19 22 23 ) ( 20 ) wwwwaawwwwaaw ( 1 12 2 ) ( 3 18 5 ) ( 4 9 8 ) ( 6 14 10 ) ( 7 ) ( 11 21 13 ) ( 19 23 20 ) ( 22 ) awwaaw ( 1 12 2 ) ( 3 19 13 ) ( 4 8 22 ) ( 5 11 10 ) ( 6 20 18 ) ( 7 ) ( 9 ) ( 14 21 23 ) wwwaawaaaawa ( 1 12 2 ) ( 3 20 14 ) ( 4 6 19 ) ( 5 10 9 ) ( 7 ) ( 8 23 18 ) ( 11 ) ( 13 21 22 ) aaawaaaa ( 1 12 2 ) ( 3 21 6 ) ( 4 22 9 ) ( 5 14 19 ) ( 7 ) ( 8 ) ( 10 13 20 ) ( 11 18 23 ) aaaawwawwwaa ( 1 12 2 ) ( 3 22 18 ) ( 4 21 20 ) ( 5 ) ( 6 23 13 ) ( 7 ) ( 8 19 14 ) ( 9 10 11 ) wwaaawaawwww ( 1 12 2 ) ( 3 23 4 ) ( 5 9 11 ) ( 6 22 14 ) ( 7 ) ( 8 20 13 ) ( 10 ) ( 18 21 19 ) waaww ( 1 12 2 ) ( 3 4 10 ) ( 5 6 13 ) ( 7 ) ( 8 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10 11 ) ( 2 8 18 3 13 ) ( 4 22 12 5 6 ) ( 7 14 9 23 21 ) wwawwwawwwaaa ( 1 19 20 11 10 ) ( 2 5 18 21 23 ) ( 3 12 14 6 13 ) ( 4 7 8 9 22 ) aaawwwaaa ( 1 19 21 ) ( 2 5 13 ) ( 3 10 23 ) ( 4 ) ( 6 18 20 ) ( 7 8 22 ) ( 9 ) ( 11 12 14 ) wawaaawaaa ( 1 19 21 4 9 ) ( 2 8 13 3 18 ) ( 5 11 23 20 12 ) ( 6 7 14 22 10 ) wwwwaawwawww ( 1 19 21 9 4 ) ( 2 14 13 20 23 ) ( 3 7 5 22 18 ) ( 6 10 12 8 11 ) aaawaa ( 1 19 22 ) ( 2 5 11 ) ( 3 ) ( 4 23 10 ) ( 6 ) ( 7 8 21 ) ( 9 20 18 ) ( 12 14 13 ) aawawwwaww ( 1 19 22 3 6 ) ( 2 8 11 4 20 ) ( 5 13 10 18 12 ) ( 7 14 21 23 9 ) awwaawaaaaw ( 1 19 22 6 3 ) ( 2 14 11 18 10 ) ( 4 7 5 21 20 ) ( 8 13 9 23 12 ) aaawwaaaawa ( 1 19 23 ) ( 2 8 3 ) ( 4 7 14 ) ( 5 10 12 ) ( 6 9 20 ) ( 11 21 22 ) ( 13 ) ( 18 ) awwaawwwwaa ( 1 19 23 13 18 ) ( 2 5 3 11 6 ) ( 4 22 9 7 8 ) ( 10 21 20 12 14 ) aawwaawwwwaaww ( 1 19 23 18 13 ) ( 2 14 3 9 22 ) ( 4 20 21 7 5 ) ( 6 11 12 8 10 ) awwwwaawwwwaaw ( 1 19 3 ) ( 2 8 23 ) ( 4 12 5 ) ( 6 ) ( 7 14 10 ) ( 9 18 20 ) ( 11 13 21 ) ( 22 ) aaawwwawwaaa ( 1 19 3 22 6 ) ( 2 5 23 21 18 ) ( 4 11 9 12 14 ) ( 7 8 10 13 20 ) awwwaaawww ( 1 19 3 6 22 ) ( 2 14 23 20 13 ) ( 4 18 21 12 8 ) ( 5 10 9 11 7 ) wawwaawaaaa ( 1 19 4 ) ( 2 8 10 ) ( 3 12 5 ) ( 6 20 18 ) ( 7 14 23 ) ( 9 ) ( 11 22 13 ) ( 21 ) awwawa ( 1 19 4 21 9 ) ( 2 5 10 22 20 ) ( 3 13 6 12 14 ) ( 7 8 23 11 18 ) wawwaaaawwaaaa ( 1 19 4 9 21 ) ( 2 14 10 18 11 ) ( 3 20 22 12 8 ) ( 5 23 6 13 7 ) aaaawwawww ( 1 19 6 ) ( 2 14 9 ) ( 3 ) ( 4 10 23 ) ( 5 18 7 ) ( 8 20 12 ) ( 11 21 13 ) ( 22 ) aawwaaaa ( 1 19 6 22 3 ) ( 2 5 9 13 4 ) ( 7 8 18 11 23 ) ( 10 12 14 20 21 ) wwwawawa ( 1 19 6 3 22 ) ( 2 8 9 10 21 ) ( 4 13 7 14 18 ) ( 5 20 23 11 12 ) waawwaaaaw ( 1 19 7 14 ) ( 2 8 12 5 ) ( 3 10 ) ( 4 23 ) ( 6 21 20 13 ) ( 9 22 18 11 ) wawwaaww ( 1 19 7 5 ) ( 2 14 12 8 ) ( 3 21 23 11 ) ( 4 22 10 13 ) ( 6 18 ) ( 9 20 ) waawwwwaaww ( 1 19 7 8 ) ( 2 5 12 14 ) ( 3 18 4 20 ) ( 6 10 9 23 ) ( 11 13 ) ( 21 22 ) waaaawwawwwaaa ( 1 19 9 ) ( 2 14 6 ) ( 3 23 10 ) ( 4 ) ( 5 20 7 ) ( 8 18 12 ) ( 11 13 22 ) ( 21 ) waaawwawwwwa ( 1 19 9 21 4 ) ( 2 5 6 11 3 ) ( 7 8 20 13 10 ) ( 12 14 18 22 23 ) aawaaawaa ( 1 19 9 4 21 ) ( 2 8 6 23 22 ) ( 3 11 7 14 20 ) ( 5 18 10 13 12 ) awaawwwa ( 1 2 ) ( 3 ) ( 4 ) ( 5 14 ) ( 6 18 ) ( 7 12 ) ( 8 19 ) ( 9 20 ) ( 10 ) ( 11 21 ) ( 13 22 ) ( 23 ) waaaawaaaa ( 1 2 ) ( 3 10 ) ( 4 23 ) ( 5 19 ) ( 6 20 ) ( 7 12 ) ( 8 14 ) ( 9 18 ) ( 11 ) ( 13 ) ( 21 ) ( 22 ) waawwaaw ( 1 2 ) ( 3 11 10 21 ) ( 4 22 23 13 ) ( 5 20 8 18 ) ( 6 19 9 14 ) ( 7 12 ) awwwawwaaaaw ( 1 2 ) ( 3 13 10 22 ) ( 4 21 23 11 ) ( 5 6 8 9 ) ( 7 12 ) ( 14 20 19 18 ) aawwaaaw ( 1 2 ) ( 3 14 23 5 ) ( 4 8 10 19 ) ( 6 21 20 22 ) ( 7 12 ) ( 9 11 18 13 ) aaawaw ( 1 2 ) ( 3 18 4 6 ) ( 5 21 19 13 ) ( 7 12 ) ( 8 11 14 22 ) ( 9 10 20 23 ) awwawwwa ( 1 2 ) ( 3 19 23 8 ) ( 4 5 10 14 ) ( 6 11 20 13 ) ( 7 12 ) ( 9 21 18 22 ) wwaawwwaw ( 1 2 ) ( 3 20 4 9 ) ( 5 11 19 22 ) ( 6 10 18 23 ) ( 7 12 ) ( 8 21 14 13 ) wwawwaawwaaa ( 1 2 ) ( 3 21 10 11 ) ( 4 13 23 22 ) ( 5 18 8 20 ) ( 6 14 9 19 ) ( 7 12 ) aawwaawaaaaww ( 1 2 ) ( 3 22 10 13 ) ( 4 11 23 21 ) ( 5 9 8 6 ) ( 7 12 ) ( 14 18 19 20 ) waaawwa ( 1 2 ) ( 3 23 ) ( 4 10 ) ( 5 ) ( 6 9 ) ( 7 12 ) ( 8 ) ( 11 22 ) ( 13 21 ) ( 14 ) ( 18 20 ) ( 19 ) wawwwwawww ( 1 2 ) ( 3 4 ) ( 5 8 ) ( 6 ) ( 7 12 ) ( 9 ) ( 10 23 ) ( 11 13 ) ( 14 19 ) ( 18 ) ( 20 ) ( 21 22 ) awwaaaawwaw ( 1 2 ) ( 3 5 23 14 ) ( 4 19 10 8 ) ( 6 22 20 21 ) ( 7 12 ) ( 9 13 18 11 ) awaaa ( 1 2 ) ( 3 6 4 18 ) ( 5 13 19 21 ) ( 7 12 ) ( 8 22 14 11 ) ( 9 23 20 10 ) wawaaww ( 1 2 ) ( 3 8 23 19 ) ( 4 14 10 5 ) ( 6 13 20 11 ) ( 7 12 ) ( 9 22 18 21 ) wwwaawwwaww ( 1 2 ) ( 3 9 4 20 ) ( 5 22 19 11 ) ( 6 23 18 10 ) ( 7 12 ) ( 8 13 14 21 ) aaawwawwwwa ( 1 2 12 ) ( 3 ) ( 4 10 23 ) ( 5 22 18 ) ( 6 8 21 ) ( 7 ) ( 9 19 13 ) ( 11 20 14 ) aaawwaawwaw ( 1 2 12 ) ( 3 10 4 ) ( 5 13 6 ) ( 7 ) ( 8 11 18 ) ( 9 14 21 ) ( 19 22 20 ) ( 23 ) awwwaawwaww ( 1 2 12 ) ( 3 11 14 ) ( 4 21 5 ) ( 6 9 18 ) ( 7 ) ( 8 10 13 ) ( 19 23 22 ) ( 20 ) aawaawwaaaw ( 1 2 12 ) ( 3 13 19 ) ( 4 22 8 ) ( 5 10 11 ) ( 6 18 20 ) ( 7 ) ( 9 ) ( 14 23 21 ) awaawwaawww ( 1 2 12 ) ( 3 14 20 ) ( 4 19 6 ) ( 5 9 10 ) ( 7 ) ( 8 18 23 ) ( 11 ) ( 13 22 21 ) awwwwaa ( 1 2 12 ) ( 3 18 22 ) ( 4 20 21 ) ( 5 ) ( 6 13 23 ) ( 7 ) ( 8 14 19 ) ( 9 11 10 ) wwaawwwawwa ( 1 2 12 ) ( 3 19 9 ) ( 4 14 18 ) ( 5 6 23 ) ( 7 ) ( 8 20 10 ) ( 11 21 22 ) ( 13 ) awwaaawww ( 1 2 12 ) ( 3 20 11 ) ( 4 18 13 ) ( 5 8 19 ) ( 6 22 10 ) ( 7 ) ( 9 21 23 ) ( 14 ) wawwwaw ( 1 2 12 ) ( 3 21 8 ) ( 4 11 19 ) ( 5 23 13 ) ( 6 ) ( 7 ) ( 9 20 18 ) ( 10 22 14 ) wwawwaaaa ( 1 2 12 ) ( 3 22 5 ) ( 4 13 14 ) ( 6 20 9 ) ( 7 ) ( 8 23 11 ) ( 10 21 19 ) ( 18 ) waaawwawa ( 1 2 12 ) ( 3 23 10 ) ( 4 ) ( 5 21 20 ) ( 6 19 11 ) ( 7 ) ( 8 22 9 ) ( 13 18 14 ) wawaawwwa ( 1 2 12 ) ( 3 4 23 ) ( 5 11 9 ) ( 6 14 22 ) ( 7 ) ( 8 13 20 ) ( 10 ) ( 18 19 21 ) wwwwaawaa ( 1 2 12 ) ( 3 5 18 ) ( 4 8 9 ) ( 6 10 14 ) ( 7 ) ( 11 13 21 ) ( 19 20 23 ) ( 22 ) awawwwaww ( 1 2 12 ) ( 3 6 21 ) ( 4 9 22 ) ( 5 19 14 ) ( 7 ) ( 8 ) ( 10 20 13 ) ( 11 23 18 ) wawwaaawaaa ( 1 2 12 ) ( 3 8 6 ) ( 4 5 20 ) ( 7 ) ( 9 23 14 ) ( 10 19 18 ) ( 11 22 13 ) ( 21 ) wwaaaaw ( 1 2 12 ) ( 3 9 13 ) ( 4 6 11 ) ( 5 14 8 ) ( 7 ) ( 10 18 21 ) ( 19 ) ( 20 22 23 ) waawawww ( 1 2 7 ) ( 3 ) ( 4 23 10 ) ( 5 9 21 ) ( 6 13 14 ) ( 8 20 22 ) ( 11 19 18 ) ( 12 ) aaaawaa ( 1 2 7 ) ( 3 10 23 ) ( 4 ) ( 5 6 22 ) ( 8 18 21 ) ( 9 11 14 ) ( 12 ) ( 13 19 20 ) awaawwww ( 1 2 7 ) ( 3 11 18 ) ( 4 13 20 ) ( 5 8 14 ) ( 6 23 21 ) ( 9 10 22 ) ( 12 ) ( 19 ) waawaaaaww ( 1 2 7 ) ( 3 13 6 ) ( 4 11 9 ) ( 5 19 8 ) ( 10 21 20 ) ( 12 ) ( 14 ) ( 18 23 22 ) aawwwawwaaaa ( 1 2 7 ) ( 3 14 13 ) ( 4 5 22 ) ( 6 ) ( 8 11 10 ) ( 9 18 20 ) ( 12 ) ( 19 21 23 ) aaawwawww ( 1 2 7 ) ( 3 18 19 ) ( 4 9 14 ) ( 5 23 20 ) ( 6 8 10 ) ( 11 ) ( 12 ) ( 13 21 22 ) awwwaawaaa ( 1 2 7 ) ( 3 19 11 ) ( 4 8 21 ) ( 5 13 10 ) ( 6 9 20 ) ( 12 ) ( 14 22 23 ) ( 18 ) awwaww ( 1 2 7 ) ( 3 20 8 ) ( 4 6 5 ) ( 9 19 10 ) ( 11 21 13 ) ( 12 ) ( 14 23 18 ) ( 22 ) aawwaawawww ( 1 2 7 ) ( 3 21 9 ) ( 4 22 6 ) ( 5 ) ( 8 19 14 ) ( 10 13 18 ) ( 11 20 23 ) ( 12 ) waaaawaawwaaa ( 1 2 7 ) ( 3 22 20 ) ( 4 21 18 ) ( 5 14 19 ) ( 6 10 11 ) ( 8 ) ( 9 23 13 ) ( 12 ) waaaw ( 1 2 7 ) ( 3 23 4 ) ( 5 18 13 ) ( 6 11 8 ) ( 9 22 19 ) ( 10 ) ( 12 ) ( 14 20 21 ) aaaawwwawwwaww ( 1 2 7 ) ( 3 4 10 ) ( 5 20 11 ) ( 6 21 19 ) ( 8 9 13 ) ( 12 ) ( 14 18 22 ) ( 23 ) wwaawwawaa ( 1 2 7 ) ( 3 5 21 ) ( 4 14 11 ) ( 6 20 18 ) ( 8 13 23 ) ( 9 ) ( 10 19 22 ) ( 12 ) awwaawwwwaw ( 1 2 7 ) ( 3 6 14 ) ( 4 20 19 ) ( 5 10 18 ) ( 8 23 9 ) ( 11 22 21 ) ( 12 ) ( 13 ) wwaaaawwa ( 1 2 7 ) ( 3 8 22 ) ( 4 19 13 ) ( 5 11 23 ) ( 6 18 9 ) ( 10 14 21 ) ( 12 ) ( 20 ) awawwaaa ( 1 2 7 ) ( 3 9 5 ) ( 4 18 8 ) ( 6 19 23 ) ( 10 20 14 ) ( 11 13 22 ) ( 12 ) ( 21 ) awwwwaawa ( 1 20 ) ( 2 18 ) ( 3 13 ) ( 4 22 ) ( 5 ) ( 6 12 ) ( 7 9 ) ( 8 ) ( 10 11 ) ( 14 ) ( 19 ) ( 21 23 ) wwawaaaw ( 1 20 ) ( 2 6 ) ( 3 5 ) ( 4 14 ) ( 7 18 ) ( 8 23 ) ( 9 12 ) ( 10 19 ) ( 11 ) ( 13 ) ( 21 ) ( 22 ) aawwwawwwaww ( 1 20 ) ( 2 9 ) ( 3 ) ( 4 ) ( 5 13 ) ( 6 7 ) ( 8 21 ) ( 10 ) ( 11 19 ) ( 12 18 ) ( 14 22 ) ( 23 ) awawwwaa ( 1 20 10 ) ( 2 9 23 ) ( 3 12 18 ) ( 4 7 6 ) ( 5 14 8 ) ( 11 ) ( 13 21 22 ) ( 19 ) aawwaawwaw ( 1 20 10 11 19 ) ( 2 6 23 22 8 ) ( 3 21 5 12 9 ) ( 4 13 14 7 18 ) wwwwaawwwwaa ( 1 20 10 19 11 ) ( 2 18 23 5 21 ) ( 3 14 13 12 6 ) ( 4 8 22 7 9 ) waaawwawwwa ( 1 20 11 ) ( 2 6 13 ) ( 3 4 23 ) ( 5 8 14 ) ( 7 18 21 ) ( 9 22 12 ) ( 10 ) ( 19 ) wwaaawwaw ( 1 20 11 10 19 ) ( 2 9 13 4 5 ) ( 3 8 7 6 21 ) ( 12 18 22 23 14 ) aaaawwaaww ( 1 20 11 19 10 ) ( 2 18 13 8 3 ) ( 4 12 6 22 5 ) ( 7 9 21 14 23 ) waaaawwaww ( 1 20 12 18 ) ( 2 9 7 6 ) ( 3 10 ) ( 4 23 ) ( 5 21 19 22 ) ( 8 13 14 11 ) wwaaaw ( 1 20 12 6 ) ( 2 18 7 9 ) ( 3 21 4 11 ) ( 5 14 ) ( 8 19 ) ( 10 22 23 13 ) wwaawwawwwwaa ( 1 20 12 9 ) ( 2 6 7 18 ) ( 3 14 23 19 ) ( 4 5 10 8 ) ( 11 22 ) ( 13 21 ) wwaawaaa ( 1 20 13 ) ( 2 6 11 ) ( 3 ) ( 4 10 23 ) ( 5 ) ( 7 18 22 ) ( 8 19 14 ) ( 9 21 12 ) wwwwaww ( 1 20 13 3 5 ) ( 2 9 11 23 19 ) ( 4 8 12 18 21 ) ( 6 22 10 14 7 ) awwaawwaaa ( 1 20 13 5 3 ) ( 2 18 11 14 10 ) ( 4 7 9 22 8 ) ( 6 21 19 23 12 ) waawwaw ( 1 20 14 ) ( 2 18 19 ) ( 3 10 23 ) ( 4 ) ( 5 12 6 ) ( 7 9 8 ) ( 11 13 21 ) ( 22 ) aawawwaa ( 1 20 14 22 4 ) ( 2 6 19 13 10 ) ( 3 12 9 5 21 ) ( 7 18 8 11 23 ) aaaawaawwwa ( 1 20 14 4 22 ) ( 2 9 19 23 11 ) ( 3 21 7 6 8 ) ( 5 10 13 12 18 ) wawwww ( 1 20 19 ) ( 2 18 14 ) ( 3 23 4 ) ( 5 7 9 ) ( 6 8 12 ) ( 10 ) ( 11 ) ( 13 22 21 ) awwaawaw ( 1 20 19 10 11 ) ( 2 9 14 3 22 ) ( 4 21 12 18 8 ) ( 5 23 13 7 6 ) wwwawwaaaaww ( 1 20 19 11 10 ) ( 2 6 14 21 4 ) ( 3 7 18 5 22 ) ( 8 13 23 12 9 ) awaawwa ( 1 20 2 18 ) ( 3 11 23 22 ) ( 4 21 10 13 ) ( 5 8 ) ( 6 7 9 12 ) ( 14 19 ) aaaawaawwaaaa ( 1 20 2 6 ) ( 3 8 10 14 ) ( 4 19 23 5 ) ( 7 18 12 9 ) ( 11 13 ) ( 21 22 ) waaw ( 1 20 2 9 ) ( 3 4 ) ( 5 11 14 21 ) ( 6 12 18 7 ) ( 8 22 19 13 ) ( 10 23 ) wwwawaa ( 1 20 21 ) ( 2 6 22 ) ( 3 10 4 ) ( 5 14 19 ) ( 7 18 11 ) ( 8 ) ( 9 13 12 ) ( 23 ) aaawwawa ( 1 20 21 23 8 ) ( 2 9 22 3 14 ) ( 4 19 7 6 11 ) ( 5 12 18 13 10 ) aawaawwaaw ( 1 20 21 8 23 ) ( 2 18 22 19 4 ) ( 3 12 6 13 14 ) ( 5 10 7 9 11 ) awwwwawwa ( 1 20 22 ) ( 2 6 21 ) ( 3 23 10 ) ( 4 ) ( 5 19 8 ) ( 7 18 13 ) ( 9 11 12 ) ( 14 ) awwaa ( 1 20 22 14 4 ) ( 2 18 21 5 23 ) ( 3 7 9 13 19 ) ( 6 11 8 10 12 ) wwwwawwaawww ( 1 20 22 4 14 ) ( 2 9 21 10 8 ) ( 3 19 12 18 11 ) ( 5 7 6 13 23 ) wwawwwaww ( 1 20 23 ) ( 2 9 10 ) ( 3 7 6 ) ( 4 12 18 ) ( 5 19 14 ) ( 8 ) ( 11 13 22 ) ( 21 ) awwwaawwaa ( 1 20 23 21 8 ) ( 2 6 10 13 19 ) ( 3 22 5 7 18 ) ( 4 11 14 12 9 ) wwaaaawwawwwa ( 1 20 23 8 21 ) ( 2 18 10 14 11 ) ( 3 19 13 7 9 ) ( 4 5 22 12 6 ) aawwwaawaaa ( 1 20 3 ) ( 2 9 4 ) ( 5 ) ( 6 23 7 ) ( 8 14 19 ) ( 10 12 18 ) ( 11 22 21 ) ( 13 ) awwwawwwwaww ( 1 20 3 13 5 ) ( 2 6 4 21 14 ) ( 7 18 23 11 8 ) ( 9 10 22 19 12 ) wawwwwaawww ( 1 20 3 5 13 ) ( 2 18 4 19 22 ) ( 6 10 8 11 12 ) ( 7 9 23 14 21 ) aawwaaw ( 1 20 4 ) ( 2 9 3 ) ( 5 8 19 ) ( 6 10 7 ) ( 11 21 13 ) ( 12 18 23 ) ( 14 ) ( 22 ) waawwwaaa ( 1 20 4 14 22 ) ( 2 18 3 8 13 ) ( 5 11 7 9 10 ) ( 6 23 19 21 12 ) wwwawaawwaaa ( 1 20 4 22 14 ) ( 2 6 3 11 5 ) ( 7 18 10 21 19 ) ( 8 12 9 23 13 ) aawwawwww ( 1 20 5 ) ( 2 18 8 ) ( 3 ) ( 4 23 10 ) ( 6 14 12 ) ( 7 9 19 ) ( 11 21 22 ) ( 13 ) wwaawwww ( 1 20 5 13 3 ) ( 2 6 8 22 23 ) ( 4 12 9 14 11 ) ( 7 18 19 21 10 ) wwaaawaawww ( 1 20 5 3 13 ) ( 2 9 8 10 21 ) ( 4 11 7 6 19 ) ( 12 18 14 23 22 ) wwaawaaaawa ( 1 20 7 18 ) ( 2 6 12 9 ) ( 3 19 4 8 ) ( 5 23 14 10 ) ( 11 21 ) ( 13 22 ) waaaawwaaaawwaa ( 1 20 7 6 ) ( 2 9 12 18 ) ( 3 23 ) ( 4 10 ) ( 5 22 8 11 ) ( 13 19 21 14 ) awwaaawa ( 1 20 7 9 ) ( 2 18 12 6 ) ( 3 22 10 21 ) ( 4 13 23 11 ) ( 5 19 ) ( 8 14 ) wawaaa ( 1 20 8 ) ( 2 18 5 ) ( 3 4 10 ) ( 6 19 12 ) ( 7 9 14 ) ( 11 22 13 ) ( 21 ) ( 23 ) aaaww ( 1 20 8 21 23 ) ( 2 6 5 11 3 ) ( 4 7 18 14 13 ) ( 9 19 22 10 12 ) wwawaawwww ( 1 20 8 23 21 ) ( 2 9 5 4 13 ) ( 3 11 12 18 19 ) ( 6 14 10 22 7 ) aawwawaaa ( 1 21 ) ( 2 11 ) ( 3 ) ( 4 ) ( 5 6 ) ( 7 13 ) ( 8 20 ) ( 9 19 ) ( 10 ) ( 12 22 ) ( 14 18 ) ( 23 ) wawaaaww ( 1 21 ) ( 2 13 ) ( 3 18 ) ( 4 9 ) ( 5 ) ( 6 10 ) ( 7 22 ) ( 8 ) ( 11 12 ) ( 14 ) ( 19 ) ( 20 23 ) waaawwwa ( 1 21 ) ( 2 22 ) ( 3 14 ) ( 4 19 ) ( 5 10 ) ( 6 ) ( 7 11 ) ( 8 23 ) ( 9 ) ( 12 13 ) ( 18 ) ( 20 ) awwaaawaaa ( 1 21 10 ) ( 2 11 3 ) ( 4 12 22 ) ( 5 ) ( 6 ) ( 7 13 23 ) ( 8 19 14 ) ( 9 20 18 ) waawaa ( 1 21 10 5 6 ) ( 2 13 3 8 18 ) ( 4 14 9 12 11 ) ( 7 22 23 19 20 ) wwaawwwwaa ( 1 21 10 6 5 ) ( 2 22 3 9 14 ) ( 4 20 19 12 13 ) ( 7 11 23 18 8 ) awwaaaawwaaaaw ( 1 21 12 11 ) ( 2 13 7 22 ) ( 3 6 4 20 ) ( 5 8 ) ( 9 10 18 23 ) ( 14 19 ) waawwawaa ( 1 21 12 13 ) ( 2 22 7 11 ) ( 3 19 10 8 ) ( 4 14 23 5 ) ( 6 18 ) ( 9 20 ) awaaawwa ( 1 21 12 22 ) ( 2 11 7 13 ) ( 3 23 ) ( 4 10 ) ( 5 18 19 20 ) ( 6 8 9 14 ) aawwawwwwaa ( 1 21 14 ) ( 2 13 8 ) ( 3 ) ( 4 10 23 ) ( 5 7 22 ) ( 6 9 20 ) ( 11 19 12 ) ( 18 ) wwawaaawaa ( 1 21 14 18 3 ) ( 2 22 8 6 23 ) ( 4 12 13 19 20 ) ( 5 9 10 7 11 ) wwwwawwww ( 1 21 14 3 18 ) ( 2 11 8 4 20 ) ( 5 23 6 7 13 ) ( 9 12 22 19 10 ) waaawaaaawa ( 1 21 18 ) ( 2 22 9 ) ( 3 ) ( 4 23 10 ) ( 5 8 19 ) ( 6 12 13 ) ( 7 11 20 ) ( 14 ) wwwaawwaawa ( 1 21 18 14 3 ) ( 2 13 9 5 4 ) ( 6 8 10 12 11 ) ( 7 22 20 19 23 ) aaawwwawww ( 1 21 18 3 14 ) ( 2 11 9 23 19 ) ( 4 5 12 22 6 ) ( 7 13 20 10 8 ) awwaaaa ( 1 21 19 ) ( 2 13 5 ) ( 3 23 10 ) ( 4 ) ( 6 20 18 ) ( 7 22 8 ) ( 9 ) ( 11 14 12 ) aaaawaawwa ( 1 21 19 4 9 ) ( 2 11 5 3 6 ) ( 7 13 8 10 20 ) ( 12 22 14 23 18 ) wwaaawwwaaaww ( 1 21 19 9 4 ) ( 2 22 5 20 10 ) ( 3 12 13 14 6 ) ( 7 11 8 18 23 ) aaawaaaaw ( 1 21 2 11 ) ( 3 10 ) ( 4 23 ) ( 5 20 14 9 ) ( 6 19 18 8 ) ( 7 13 12 22 ) aaaawwaawaaaaw ( 1 21 2 13 ) ( 3 9 23 6 ) ( 4 18 10 20 ) ( 5 19 ) ( 7 22 12 11 ) ( 8 14 ) awwwwawwaaa ( 1 21 2 22 ) ( 3 8 4 5 ) ( 6 20 ) ( 7 11 12 13 ) ( 9 18 ) ( 10 19 23 14 ) awaawwaww ( 1 21 20 ) ( 2 22 6 ) ( 3 4 10 ) ( 5 19 14 ) ( 7 11 18 ) ( 8 ) ( 9 12 13 ) ( 23 ) wawwwwaa ( 1 21 20 23 8 ) ( 2 11 6 3 5 ) ( 4 14 7 13 18 ) ( 9 10 19 12 22 ) awwwwaawwa ( 1 21 20 8 23 ) ( 2 13 6 19 10 ) ( 3 7 22 18 5 ) ( 4 12 11 9 14 ) aawwaawaa ( 1 21 23 ) ( 2 11 4 ) ( 3 12 22 ) ( 5 14 19 ) ( 6 9 18 ) ( 7 13 10 ) ( 8 ) ( 20 ) aawawwaaww ( 1 21 23 20 8 ) ( 2 22 4 18 19 ) ( 3 6 14 12 13 ) ( 5 7 11 10 9 ) wwwwaaaawaawwaaa ( 1 21 23 8 20 ) ( 2 13 4 5 9 ) ( 3 19 18 12 11 ) ( 6 7 22 10 14 ) aawawwaaaa ( 1 21 3 ) ( 2 11 10 ) ( 4 7 13 ) ( 5 19 8 ) ( 6 20 9 ) ( 12 22 23 ) ( 14 ) ( 18 ) wwaaw ( 1 21 3 14 18 ) ( 2 13 10 19 6 ) ( 4 8 9 7 22 ) ( 5 20 12 11 23 ) awwawwwwa ( 1 21 3 18 14 ) ( 2 22 10 20 5 ) ( 4 6 19 7 11 ) ( 8 12 13 23 9 ) waawww ( 1 21 4 ) ( 2 11 23 ) ( 3 7 13 ) ( 5 8 14 ) ( 6 18 20 ) ( 9 ) ( 10 12 22 ) ( 19 ) wawwwawwwa ( 1 21 4 19 9 ) ( 2 13 23 14 20 ) ( 3 5 18 7 22 ) ( 6 12 11 10 8 ) aaawwaa ( 1 21 4 9 19 ) ( 2 22 23 6 8 ) ( 3 20 14 7 11 ) ( 5 12 13 10 18 ) wwaawaaaww ( 1 21 5 ) ( 2 13 19 ) ( 3 4 23 ) ( 6 ) ( 7 22 14 ) ( 8 12 11 ) ( 9 18 20 ) ( 10 ) aaawwwwaawaaaw ( 1 21 5 10 6 ) ( 2 11 19 23 9 ) ( 3 20 12 22 8 ) ( 4 18 7 13 14 ) awaawwaaa ( 1 21 5 6 10 ) ( 2 22 19 18 4 ) ( 3 7 11 14 20 ) ( 8 9 23 12 13 ) awwaaww ( 1 21 6 ) ( 2 22 20 ) ( 3 23 4 ) ( 5 ) ( 7 11 9 ) ( 8 14 19 ) ( 10 ) ( 12 13 18 ) aawwaw ( 1 21 6 10 5 ) ( 2 11 20 4 8 ) ( 3 19 7 13 9 ) ( 12 22 18 23 14 ) waawwawww ( 1 21 6 5 10 ) ( 2 13 20 14 23 ) ( 3 12 11 18 19 ) ( 4 7 22 9 8 ) wwaaawww ( 1 21 7 11 ) ( 2 22 12 13 ) ( 3 5 23 19 ) ( 4 8 10 14 ) ( 6 9 ) ( 18 20 ) wwawaaw ( 1 21 7 13 ) ( 2 11 12 22 ) ( 3 4 ) ( 5 9 8 18 ) ( 6 14 20 19 ) ( 10 23 ) aawaawwaw ( 1 21 7 22 ) ( 2 13 12 11 ) ( 3 20 10 9 ) ( 4 6 23 18 ) ( 5 14 ) ( 8 19 ) aawaawwaawww ( 1 21 8 ) ( 2 13 14 ) ( 3 10 4 ) ( 5 12 11 ) ( 6 18 9 ) ( 7 22 19 ) ( 20 ) ( 23 ) waw ( 1 21 8 20 23 ) ( 2 22 14 9 3 ) ( 4 7 11 19 6 ) ( 5 18 10 12 13 ) wwaaawwawww ( 1 21 8 23 20 ) ( 2 11 14 10 18 ) ( 3 9 7 13 19 ) ( 4 6 12 22 5 ) aawwaawww ( 1 21 9 ) ( 2 22 18 ) ( 3 10 23 ) ( 4 ) ( 5 14 8 ) ( 6 7 11 ) ( 12 13 20 ) ( 19 ) waawwaawwwa ( 1 21 9 19 4 ) ( 2 13 18 8 3 ) ( 5 23 12 11 20 ) ( 6 14 10 7 22 ) wwwawaaww ( 1 21 9 4 19 ) ( 2 11 18 10 14 ) ( 3 8 12 22 20 ) ( 5 7 13 6 23 ) wwwwawwaa ( 1 22 ) ( 2 11 ) ( 3 6 ) ( 4 20 ) ( 5 ) ( 7 21 ) ( 8 ) ( 9 23 ) ( 10 18 ) ( 12 13 ) ( 14 ) ( 19 ) wwaawwaaaaww ( 1 22 ) ( 2 13 ) ( 3 ) ( 4 ) ( 5 9 ) ( 6 19 ) ( 7 11 ) ( 8 18 ) ( 10 ) ( 12 21 ) ( 14 20 ) ( 23 ) awwaaaawaaw ( 1 22 ) ( 2 21 ) ( 3 19 ) ( 4 14 ) ( 5 23 ) ( 6 ) ( 7 13 ) ( 8 10 ) ( 9 ) ( 11 12 ) ( 18 ) ( 20 ) aawwwawa ( 1 22 10 ) ( 2 13 3 ) ( 4 12 21 ) ( 5 14 19 ) ( 6 20 9 ) ( 7 11 23 ) ( 8 ) ( 18 ) wwawwwawwwaaaa ( 1 22 10 18 8 ) ( 2 21 3 20 19 ) ( 4 9 14 12 11 ) ( 5 7 13 23 6 ) aawaaww ( 1 22 10 8 18 ) ( 2 11 3 5 6 ) ( 4 19 20 12 13 ) ( 7 21 23 14 9 ) aaaawwawwwa ( 1 22 12 11 ) ( 2 21 7 13 ) ( 3 14 10 5 ) ( 4 19 23 8 ) ( 6 18 ) ( 9 20 ) wwwwaawaaawww ( 1 22 12 13 ) ( 2 11 7 21 ) ( 3 18 4 9 ) ( 5 8 ) ( 6 23 20 10 ) ( 14 19 ) aaww ( 1 22 12 21 ) ( 2 13 7 11 ) ( 3 23 ) ( 4 10 ) ( 5 20 19 18 ) ( 6 14 9 8 ) aaawwwawwaaaa ( 1 22 14 ) ( 2 11 8 ) ( 3 23 10 ) ( 4 ) ( 5 7 21 ) ( 6 18 9 ) ( 12 13 19 ) ( 20 ) wwwwaawwaww ( 1 22 14 20 4 ) ( 2 21 8 9 10 ) ( 3 12 11 19 18 ) ( 5 6 23 7 13 ) waawwwwaaw ( 1 22 14 4 20 ) ( 2 13 8 3 18 ) ( 5 10 9 7 11 ) ( 6 12 21 19 23 ) awaaaawaaaw ( 1 22 18 ) ( 2 21 9 ) ( 3 23 4 ) ( 5 19 14 ) ( 6 12 11 ) ( 7 13 20 ) ( 8 ) ( 10 ) wwa ( 1 22 18 10 8 ) ( 2 13 9 4 5 ) ( 3 14 7 11 20 ) ( 6 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1 5 3 ) ( 2 14 23 ) ( 4 12 19 ) ( 6 18 9 ) ( 7 8 10 ) ( 11 21 22 ) ( 13 ) ( 20 ) aawwawwwwa ( 1 5 3 13 20 ) ( 2 19 23 11 9 ) ( 4 21 18 12 8 ) ( 6 7 14 10 22 ) aaaawwaawwa ( 1 5 3 20 13 ) ( 2 8 23 6 22 ) ( 4 9 11 12 14 ) ( 7 19 10 18 21 ) aaawwa ( 1 5 4 ) ( 2 14 10 ) ( 3 12 19 ) ( 6 9 20 ) ( 7 8 23 ) ( 11 ) ( 13 22 21 ) ( 18 ) awwwaawwawwww ( 1 5 4 11 18 ) ( 2 19 10 13 6 ) ( 3 22 20 12 8 ) ( 7 14 23 21 9 ) wawaawwww ( 1 5 4 18 11 ) ( 2 8 10 9 21 ) ( 3 6 13 12 14 ) ( 7 19 23 20 22 ) awwawwww ( 1 5 6 ) ( 2 8 9 ) ( 3 4 23 ) ( 7 19 18 ) ( 10 ) ( 11 13 22 ) ( 12 14 20 ) ( 21 ) waawwaawwwwaa ( 1 5 6 10 21 ) ( 2 14 9 3 22 ) ( 4 13 12 19 20 ) ( 7 8 18 23 11 ) aaawwwwawwaaww ( 1 5 6 21 10 ) ( 2 19 9 11 23 ) ( 3 12 8 20 22 ) ( 4 7 14 18 13 ) waawwaawww ( 1 5 7 14 ) ( 2 19 12 8 ) ( 3 9 4 6 ) ( 10 18 23 20 ) ( 11 13 ) ( 21 22 ) wwaaawa ( 1 5 7 19 ) ( 2 8 12 14 ) ( 3 11 23 21 ) ( 4 13 10 22 ) ( 6 18 ) ( 9 20 ) waaawwawwwaa ( 1 5 7 8 ) ( 2 14 12 19 ) ( 3 10 ) ( 4 23 ) ( 6 22 20 11 ) ( 9 21 18 13 ) wwawwaaaaww ( 1 5 9 ) ( 2 8 6 ) ( 3 10 4 ) ( 7 19 20 ) ( 11 21 13 ) ( 12 14 18 ) ( 22 ) ( 23 ) awwwwawwaa ( 1 5 9 22 23 ) ( 2 19 6 13 10 ) ( 3 7 14 20 11 ) ( 4 12 8 18 21 ) wawwwwa ( 1 5 9 23 22 ) ( 2 14 6 4 21 ) ( 3 11 12 19 18 ) ( 7 8 20 10 13 ) wwaawaaaa ( 1 6 ) ( 2 18 ) ( 3 ) ( 4 ) ( 5 21 ) ( 7 20 ) ( 8 13 ) ( 9 12 ) ( 10 ) ( 11 14 ) ( 19 22 ) ( 23 ) waawwwwawwa ( 1 6 ) ( 2 20 ) ( 3 19 ) ( 4 8 ) ( 5 10 ) ( 7 9 ) ( 11 ) ( 12 18 ) ( 13 ) ( 14 23 ) ( 21 ) ( 22 ) awaaaawwaa ( 1 6 ) ( 2 9 ) ( 3 22 ) ( 4 13 ) ( 5 ) ( 7 18 ) ( 8 ) ( 10 21 ) ( 11 23 ) ( 12 20 ) ( 14 ) ( 19 ) aawaaaawwa ( 1 6 10 ) ( 2 18 23 ) ( 3 12 9 ) ( 4 7 20 ) ( 5 ) ( 8 14 19 ) ( 11 13 22 ) ( 21 ) wawwaawwww ( 1 6 10 21 5 ) ( 2 20 23 13 14 ) ( 3 11 19 12 18 ) ( 4 22 8 7 9 ) wwawww ( 1 6 10 5 21 ) ( 2 9 23 19 11 ) ( 3 8 22 12 20 ) ( 4 14 13 7 18 ) aawwwwaawa ( 1 6 11 ) ( 2 20 13 ) ( 3 10 4 ) ( 5 19 8 ) ( 7 9 21 ) ( 12 18 22 ) ( 14 ) ( 23 ) waawwwwaawwww ( 1 6 11 14 23 ) ( 2 9 13 5 4 ) ( 3 12 20 22 8 ) ( 7 18 21 19 10 ) 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9 ) aawwaaaaww ( 1 6 19 3 22 ) ( 2 18 14 10 11 ) ( 4 21 7 20 5 ) ( 8 23 13 12 9 ) awwaawaaaawww ( 1 6 2 18 ) ( 3 4 ) ( 5 22 14 13 ) ( 7 20 12 9 ) ( 8 11 19 21 ) ( 10 23 ) wwaaaawaawwaaa ( 1 6 2 20 ) ( 3 14 10 8 ) ( 4 5 23 19 ) ( 7 9 12 18 ) ( 11 13 ) ( 21 22 ) aawaa ( 1 6 2 9 ) ( 3 21 23 13 ) ( 4 11 10 22 ) ( 5 8 ) ( 7 18 12 20 ) ( 14 19 ) waaawaw ( 1 6 21 ) ( 2 20 22 ) ( 3 4 23 ) ( 5 ) ( 7 9 11 ) ( 8 19 14 ) ( 10 ) ( 12 18 13 ) wawwaaaa ( 1 6 21 10 5 ) ( 2 18 22 4 19 ) ( 3 14 7 20 11 ) ( 8 12 9 13 23 ) awaaaaw ( 1 6 21 5 10 ) ( 2 9 22 14 3 ) ( 4 12 20 13 19 ) ( 7 18 11 8 23 ) wwawwwwaa ( 1 6 22 ) ( 2 20 21 ) ( 3 ) ( 4 10 23 ) ( 5 8 14 ) ( 7 9 13 ) ( 11 12 18 ) ( 19 ) waaawaaawa ( 1 6 22 19 3 ) ( 2 9 21 8 10 ) ( 4 7 18 13 14 ) ( 5 23 12 20 11 ) aaaawwawaa ( 1 6 22 3 19 ) ( 2 18 21 23 5 ) ( 4 14 12 9 11 ) ( 7 20 13 10 8 ) wwaawwaaaa ( 1 6 23 ) ( 2 18 10 ) ( 3 7 20 ) ( 4 12 9 ) ( 5 8 19 ) ( 11 ) ( 13 21 22 ) ( 14 ) waaaaww ( 1 6 23 11 14 ) ( 2 20 10 22 5 ) ( 3 13 19 7 9 ) ( 4 21 8 12 18 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19 ) awaawwwaww ( 1 6 7 9 ) ( 2 20 12 18 ) ( 3 5 4 14 ) ( 8 10 19 23 ) ( 11 21 ) ( 13 22 ) wwwaawa ( 1 6 8 ) ( 2 9 5 ) ( 3 10 23 ) ( 4 ) ( 7 18 14 ) ( 11 21 22 ) ( 12 20 19 ) ( 13 ) wwaaaawwaaw ( 1 6 8 13 4 ) ( 2 20 5 22 10 ) ( 3 12 18 19 11 ) ( 7 9 14 21 23 ) wwwwaawaaaw ( 1 6 8 4 13 ) ( 2 18 5 23 21 ) ( 3 11 7 20 14 ) ( 9 19 10 22 12 ) wwwwaawwa ( 1 7 ) ( 2 12 ) ( 3 ) ( 4 ) ( 5 8 ) ( 6 20 ) ( 9 18 ) ( 10 ) ( 11 22 ) ( 13 21 ) ( 14 19 ) ( 23 ) awaawwwwaaw ( 1 7 ) ( 2 12 ) ( 3 10 ) ( 4 23 ) ( 5 ) ( 6 18 ) ( 8 ) ( 9 20 ) ( 11 13 ) ( 14 ) ( 19 ) ( 21 22 ) aaawaaaawa ( 1 7 ) ( 2 12 ) ( 3 11 4 22 ) ( 5 9 19 20 ) ( 6 14 18 8 ) ( 10 21 23 13 ) awwaaawaaaa ( 1 7 ) ( 2 12 ) ( 3 13 4 21 ) ( 5 18 19 6 ) ( 8 20 14 9 ) ( 10 22 23 11 ) awawww ( 1 7 ) ( 2 12 ) ( 3 14 10 19 ) ( 4 8 23 5 ) ( 6 11 9 21 ) ( 13 18 22 20 ) aawwwwawwaaww ( 1 7 ) ( 2 12 ) ( 3 18 23 9 ) ( 4 6 10 20 ) ( 5 13 14 11 ) ( 8 22 19 21 ) wwwaawwaawaa ( 1 7 ) ( 2 12 ) ( 3 19 10 14 ) ( 4 5 23 8 ) ( 6 21 9 11 ) ( 13 20 22 18 ) awwwwaawaaaw ( 1 7 ) ( 2 12 ) ( 3 20 23 6 ) ( 4 9 10 18 ) ( 5 22 14 21 ) ( 8 13 19 11 ) waaawaaw ( 1 7 ) ( 2 12 ) ( 3 21 4 13 ) ( 5 6 19 18 ) ( 8 9 14 20 ) ( 10 11 23 22 ) wwwaw ( 1 7 ) ( 2 12 ) ( 3 22 4 11 ) ( 5 20 19 9 ) ( 6 8 18 14 ) ( 10 13 23 21 ) awaaawwaa ( 1 7 ) ( 2 12 ) ( 3 23 ) ( 4 10 ) ( 5 19 ) ( 6 ) ( 8 14 ) ( 9 ) ( 11 21 ) ( 13 22 ) ( 18 ) ( 20 ) wwwwawwwwa ( 1 7 ) ( 2 12 ) ( 3 4 ) ( 5 14 ) ( 6 9 ) ( 8 19 ) ( 10 23 ) ( 11 ) ( 13 ) ( 18 20 ) ( 21 ) ( 22 ) awwaawwa ( 1 7 ) ( 2 12 ) ( 3 5 10 8 ) ( 4 19 23 14 ) ( 6 13 9 22 ) ( 11 18 21 20 ) awwwaaww ( 1 7 ) ( 2 12 ) ( 3 6 23 20 ) ( 4 18 10 9 ) ( 5 21 14 22 ) ( 8 11 19 13 ) aawwawa ( 1 7 ) ( 2 12 ) ( 3 8 10 5 ) ( 4 14 23 19 ) ( 6 22 9 13 ) ( 11 20 21 18 ) waawwwa ( 1 7 ) ( 2 12 ) ( 3 9 23 18 ) ( 4 20 10 6 ) ( 5 11 14 13 ) ( 8 21 19 22 ) waaaawaawww ( 1 7 12 ) ( 2 ) ( 3 ) ( 4 23 10 ) ( 5 6 11 ) ( 8 18 13 ) ( 9 22 14 ) ( 19 20 21 ) wwwawaawwa ( 1 7 12 ) ( 2 ) ( 3 10 23 ) ( 4 ) ( 5 9 13 ) ( 6 21 14 ) ( 8 20 11 ) ( 18 22 19 ) aawwwaawa ( 1 7 12 ) ( 2 ) ( 3 11 6 ) ( 4 13 9 ) ( 5 ) ( 8 19 14 ) ( 10 22 20 ) ( 18 23 21 ) awwawwwwaa ( 1 7 12 ) ( 2 ) ( 3 13 18 ) ( 4 11 20 ) ( 5 14 19 ) ( 6 23 22 ) ( 8 ) ( 9 10 21 ) wwaaaawaaw ( 1 7 12 ) ( 2 ) ( 3 14 22 ) ( 4 5 13 ) ( 6 20 18 ) ( 8 21 10 ) ( 9 ) ( 11 23 19 ) waawwawaaa ( 1 7 12 ) ( 2 ) ( 3 18 8 ) ( 4 9 5 ) ( 6 19 10 ) ( 11 22 21 ) ( 13 ) ( 14 23 20 ) wwawaaawaaa ( 1 7 12 ) ( 2 ) ( 3 19 21 ) ( 4 8 11 ) ( 5 22 10 ) ( 6 18 9 ) ( 13 23 14 ) ( 20 ) wwwawwaaww ( 1 7 12 ) ( 2 ) ( 3 20 19 ) ( 4 6 14 ) ( 5 23 18 ) ( 8 10 9 ) ( 11 13 22 ) ( 21 ) wwaawwawwww ( 1 7 12 ) ( 2 ) ( 3 21 20 ) ( 4 22 18 ) ( 5 8 14 ) ( 6 10 13 ) ( 9 23 11 ) ( 19 ) wwwaawww ( 1 7 12 ) ( 2 ) ( 3 22 9 ) ( 4 21 6 ) ( 5 19 8 ) ( 10 11 18 ) ( 13 20 23 ) ( 14 ) aawaww ( 1 7 12 ) ( 2 ) ( 3 23 4 ) ( 5 20 22 ) ( 6 13 19 ) ( 8 9 21 ) ( 10 ) ( 11 14 18 ) aaawwwawwwa ( 1 7 12 ) ( 2 ) ( 3 4 10 ) ( 5 18 21 ) ( 6 22 8 ) ( 9 11 19 ) ( 13 14 20 ) ( 23 ) aawwaawaaa ( 1 7 12 ) ( 2 ) ( 3 5 11 ) ( 4 14 21 ) ( 6 ) ( 8 22 23 ) ( 9 18 20 ) ( 10 19 13 ) waaawaaawww ( 1 7 12 ) ( 2 ) ( 3 6 5 ) ( 4 20 8 ) ( 9 19 23 ) ( 10 18 14 ) ( 11 ) ( 13 21 22 ) aaaawaawwaa ( 1 7 12 ) ( 2 ) ( 3 8 13 ) ( 4 19 22 ) ( 5 21 23 ) ( 6 9 20 ) ( 10 14 11 ) ( 18 ) wawwaaaww ( 1 7 12 ) ( 2 ) ( 3 9 14 ) ( 4 18 19 ) ( 5 10 20 ) ( 6 8 23 ) ( 11 21 13 ) ( 22 ) wawa ( 1 7 2 ) ( 3 ) ( 4 10 23 ) ( 5 21 9 ) ( 6 14 13 ) ( 8 22 20 ) ( 11 18 19 ) ( 12 ) waawaaa ( 1 7 2 ) ( 3 10 4 ) ( 5 11 20 ) ( 6 19 21 ) ( 8 13 9 ) ( 12 ) ( 14 22 18 ) ( 23 ) waaaawwaaaaww ( 1 7 2 ) ( 3 11 19 ) ( 4 21 8 ) ( 5 10 13 ) ( 6 20 9 ) ( 12 ) ( 14 23 22 ) ( 18 ) aww ( 1 7 2 ) ( 3 13 14 ) ( 4 22 5 ) ( 6 ) ( 8 10 11 ) ( 9 20 18 ) ( 12 ) ( 19 23 21 ) wwwwawwaaa ( 1 7 2 ) ( 3 14 6 ) ( 4 19 20 ) ( 5 18 10 ) ( 8 9 23 ) ( 11 21 22 ) ( 12 ) ( 13 ) wwawwaawww ( 1 7 2 ) ( 3 18 11 ) ( 4 20 13 ) ( 5 14 8 ) ( 6 21 23 ) ( 9 22 10 ) ( 12 ) ( 19 ) wwwaaawaa ( 1 7 2 ) ( 3 19 18 ) ( 4 14 9 ) ( 5 20 23 ) ( 6 10 8 ) ( 11 ) ( 12 ) ( 13 22 21 ) aawwaawwwa ( 1 7 2 ) ( 3 20 22 ) ( 4 18 21 ) ( 5 19 14 ) ( 6 11 10 ) ( 8 ) ( 9 13 23 ) ( 12 ) wwwwaawwww ( 1 7 2 ) ( 3 21 5 ) ( 4 11 14 ) ( 6 18 20 ) ( 8 23 13 ) ( 9 ) ( 10 22 19 ) ( 12 ) wwwaawwawww ( 1 7 2 ) ( 3 22 8 ) ( 4 13 19 ) ( 5 23 11 ) ( 6 9 18 ) ( 10 21 14 ) ( 12 ) ( 20 ) aawwwwaw ( 1 7 2 ) ( 3 23 10 ) ( 4 ) ( 5 22 6 ) ( 8 21 18 ) ( 9 14 11 ) ( 12 ) ( 13 20 19 ) wwaawa ( 1 7 2 ) ( 3 4 23 ) ( 5 13 18 ) ( 6 8 11 ) ( 9 19 22 ) ( 10 ) ( 12 ) ( 14 21 20 ) wawwwawwwaa ( 1 7 2 ) ( 3 5 9 ) ( 4 8 18 ) ( 6 23 19 ) ( 10 14 20 ) ( 11 22 13 ) ( 12 ) ( 21 ) awaawwaaaa ( 1 7 2 ) ( 3 6 13 ) ( 4 9 11 ) ( 5 8 19 ) ( 10 20 21 ) ( 12 ) ( 14 ) ( 18 22 23 ) aawwaaawaaw ( 1 7 2 ) ( 3 8 20 ) ( 4 5 6 ) ( 9 10 19 ) ( 11 13 21 ) ( 12 ) ( 14 18 23 ) ( 22 ) waaawaaaawaa ( 1 7 2 ) ( 3 9 21 ) ( 4 6 22 ) ( 5 ) ( 8 14 19 ) ( 10 18 13 ) ( 11 23 20 ) ( 12 ) wwaaaawwawwwaaaa ( 1 8 ) ( 2 14 ) ( 3 9 ) ( 4 6 ) ( 5 12 ) ( 7 19 ) ( 10 18 ) ( 11 ) ( 13 ) ( 20 23 ) ( 21 ) ( 22 ) waaawwaaaa ( 1 8 ) ( 2 19 ) ( 3 ) ( 4 ) ( 5 7 ) ( 6 13 ) ( 9 11 ) ( 10 ) ( 12 14 ) ( 18 22 ) ( 20 21 ) ( 23 ) wwaaaawaaa ( 1 8 10 ) ( 2 19 4 ) ( 3 7 5 ) ( 6 9 20 ) ( 11 13 21 ) ( 12 14 23 ) ( 18 ) ( 22 ) wwaawaww ( 1 8 10 18 22 ) ( 2 5 4 9 13 ) ( 3 20 11 7 14 ) ( 6 21 12 19 23 ) waaaawaawwa ( 1 8 10 22 18 ) ( 2 14 4 21 6 ) ( 3 13 9 7 19 ) ( 5 23 11 20 12 ) waaaawaa ( 1 8 11 ) ( 2 14 22 ) ( 3 ) ( 4 23 10 ) ( 5 21 12 ) ( 6 18 20 ) ( 7 19 13 ) ( 9 ) wwaaawaaaww ( 1 8 11 3 9 ) ( 2 19 22 4 18 ) ( 5 13 23 6 7 ) ( 10 20 12 14 21 ) waawwwwaw ( 1 8 11 9 3 ) ( 2 5 22 20 10 ) ( 4 7 14 13 18 ) ( 6 23 12 19 21 ) wwaaaawwaaaa ( 1 8 12 14 ) ( 2 19 7 5 ) ( 3 4 ) ( 6 22 9 21 ) ( 10 23 ) ( 11 18 13 20 ) aawaawwwwaa ( 1 8 12 19 ) ( 2 5 7 14 ) ( 3 21 10 13 ) ( 4 22 23 11 ) ( 6 20 ) ( 9 18 ) wwaawwaw ( 1 8 12 5 ) ( 2 14 7 19 ) ( 3 18 23 6 ) ( 4 20 10 9 ) ( 11 21 ) ( 13 22 ) waawwwaww ( 1 8 13 ) ( 2 14 21 ) ( 3 10 23 ) ( 4 ) ( 5 22 12 ) ( 6 ) ( 7 19 11 ) ( 9 20 18 ) wwwawww ( 1 8 13 4 6 ) ( 2 19 21 3 20 ) ( 5 11 10 9 7 ) ( 12 14 22 23 18 ) wwawwaa ( 1 8 13 6 4 ) ( 2 5 21 18 23 ) ( 3 7 14 11 20 ) ( 9 10 12 19 22 ) aaawwwawwwaww ( 1 8 18 ) ( 2 5 20 ) ( 3 4 23 ) ( 6 7 14 ) ( 9 12 19 ) ( 10 ) ( 11 21 13 ) ( 22 ) aawwwwaawwa ( 1 8 18 10 22 ) ( 2 19 20 3 21 ) ( 4 11 12 14 9 ) ( 5 6 23 13 7 ) wwwwaaw ( 1 8 18 22 10 ) ( 2 14 20 13 23 ) ( 3 12 5 9 21 ) ( 4 7 19 6 11 ) aaawwaawaw ( 1 8 2 14 ) ( 3 6 10 20 ) ( 4 9 23 18 ) ( 5 7 19 12 ) ( 11 22 ) ( 13 21 ) wwwaaawaawwwwa ( 1 8 2 19 ) ( 3 23 ) ( 4 10 ) ( 5 12 14 7 ) ( 6 21 18 11 ) ( 9 22 20 13 ) awwww ( 1 8 2 5 ) ( 3 22 4 21 ) ( 6 9 ) ( 7 14 12 19 ) ( 10 11 23 13 ) ( 18 20 ) awaaaawaaw ( 1 8 20 ) ( 2 5 18 ) ( 3 10 4 ) ( 6 12 19 ) ( 7 14 9 ) ( 11 13 22 ) ( 21 ) ( 23 ) wwwaa ( 1 8 20 21 23 ) ( 2 14 18 11 10 ) ( 3 7 19 9 13 ) ( 4 12 5 6 22 ) wwawwaawwa ( 1 8 20 23 21 ) ( 2 19 18 4 22 ) ( 3 13 12 14 6 ) ( 5 9 10 11 7 ) aawwwwaawaaaw ( 1 8 21 ) ( 2 14 13 ) ( 3 4 10 ) ( 5 11 12 ) ( 6 9 18 ) ( 7 19 22 ) ( 20 ) ( 23 ) awa ( 1 8 21 20 23 ) ( 2 5 13 9 4 ) ( 3 12 19 11 18 ) ( 6 10 7 14 22 ) waaaawwaaw ( 1 8 21 23 20 ) ( 2 19 13 10 6 ) ( 3 18 7 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12 19 ) ( 7 14 23 9 21 ) aawwwawwaa ( 1 8 6 ) ( 2 5 9 ) ( 3 23 10 ) ( 4 ) ( 7 14 18 ) ( 11 22 21 ) ( 12 19 20 ) ( 13 ) aaawwawwwaaa ( 1 8 6 13 4 ) ( 2 14 9 22 3 ) ( 5 20 11 23 12 ) ( 7 19 18 21 10 ) awwaawwaww ( 1 8 6 4 13 ) ( 2 19 9 23 11 ) ( 3 22 7 5 18 ) ( 10 21 12 14 20 ) awwwawwwaa ( 1 8 7 14 ) ( 2 5 12 19 ) ( 3 13 23 22 ) ( 4 11 10 21 ) ( 6 18 ) ( 9 20 ) aaaaw ( 1 8 7 19 ) ( 2 14 12 5 ) ( 3 20 4 18 ) ( 6 23 9 10 ) ( 11 13 ) ( 21 22 ) wwwwaawwawwwwaa ( 1 8 7 5 ) ( 2 19 12 14 ) ( 3 10 ) ( 4 23 ) ( 6 11 20 22 ) ( 9 13 18 21 ) wwwaawwa ( 1 8 9 ) ( 2 5 6 ) ( 3 ) ( 4 10 23 ) ( 7 14 20 ) ( 11 ) ( 12 19 18 ) ( 13 21 22 ) awawwa ( 1 8 9 11 3 ) ( 2 14 6 21 4 ) ( 5 18 13 10 12 ) ( 7 19 20 22 23 ) wawaawwaaa ( 1 8 9 3 11 ) ( 2 19 6 10 13 ) ( 4 21 7 5 20 ) ( 12 14 18 23 22 ) wwwaaawaaww ( 1 9 ) ( 2 18 ) ( 3 8 ) ( 4 19 ) ( 5 23 ) ( 6 7 ) ( 10 14 ) ( 11 ) ( 12 20 ) ( 13 ) ( 21 ) ( 22 ) wwawwwawwwaa ( 1 9 ) ( 2 20 ) ( 3 ) ( 4 ) ( 5 22 ) ( 6 12 ) ( 7 18 ) ( 8 11 ) ( 10 ) ( 13 14 ) ( 19 21 ) ( 23 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12 ) wwaaaa