/* From Dan Barbasch and Dan Ciubotaru */ max:= {0,0,1,1,2,2,-4,4}, {0,1,1,2,3,4,-13/2,13/2}, {0,1,2,3,4,5,-17/2,17/2}, {0,0,1/4,1/4,1,1,-2,2}, {0,1/4,1/4,3/4,1,5/4,-5/2,5/2}, {0,1/6,5/12,7/12,5/6,1,-23/12,23/12}, {0,1/6,5/12,7/12,1,17/12,-53/24,53/24}, {0,1/6,2/3,5/6,1,11/6,-29/12,29/12}, {0,1/4,3/4,3/4,1,7/4,-5/2,5/2}, {0,1/4,3/4,1,5/4,2,-27/8,27/8}, {0,1/4,3/4,1,7/4,2,-25/8,25/8}, {0,1/8,1/4,3/4,7/8,1,-13/8,13/8}, {0,7/24,5/12,7/12,17/24,1,-43/24,43/24}, {0,1/6,2/3,5/6,1,7/6,-25/12,25/12}, {0,1/6,5/12,7/12,1,19/12,-55/24,55/24}, {0,1/4,3/4,1,2,3,-9/2,9/2}, {-1/4,3/4,5/4,7/4,9/4,11/4,-11/2,11/2}, {-1/12,1/4,5/12,7/12,17/12,19/12,-5/2,5/2}, {-1/12,1/4,7/12,3/4,5/4,7/4,-5/2,5/2}, {0,1/9,5/18,7/18,1,2,-5/2,5/2}, {0,5/18,11/18,8/9,1,2,-5/2,5/2}, {1/12,1/4,7/12,11/12,13/12,23/12,-5/2,5/2}, {-1/6,1/3,2/3,5/6,7/6,11/6,-7/2,7/2}, {-1/6,1/3,2/3,5/6,4/3,5/3,-7/2,7/2}, {-3/32,5/32,11/32,19/32,25/32,27/32,-47/32,47/32}, {-1/32,7/32,9/32,17/32,23/32,25/32,-47/32,47/32}, {-1/12,1/6,1/4,11/24,13/24,5/8,-65/48,65/48}, {-1/48,11/48,17/48,7/16,9/16,31/48,-35/24,35/24}, {-3/32,9/32,11/32,19/32,21/32,27/32,-47/32,47/32}, {-5/96,31/96,37/96,15/32,17/32,77/96,-137/96,137/96}, {1/48,5/48,1/6,7/24,7/16,9/16,-59/48,59/48}, {0,1/12,5/24,1/3,5/12,1,-67/48,67/48}, {0,1/12,1/6,7/24,11/24,1,-35/24,35/24}, {0,1/16,3/16,1/4,1/2,1,-5/4,5/4}, {0,7/48,13/48,1/3,5/12,1,-4/3,4/3}, {-1/48,5/48,3/16,19/48,29/48,11/16,-31/24,31/24}, {0,1/8,5/24,1/3,13/24,2/3,-61/48,61/48}, {-1/48,5/48,3/16,13/48,35/48,13/16,-59/48,59/48}, {-1/12,1/6,3/8,11/24,13/24,5/8,-17/12,17/12}, {1/24,5/48,11/48,3/8,5/8,23/24,-29/24,29/24}, {0,1/12,7/24,13/24,5/6,1,-35/24,35/24}, {-1/8,1/4,3/8,5/8,3/4,7/8,-5/2,5/2}, {1/32,11/96,29/96,53/96,79/96,31/32,-137/96,137/96}, {-1/48,5/48,1/6,5/16,11/16,5/6,-29/24,29/24}, {-1/16,7/48,5/24,7/16,9/16,19/24,-5/4,5/4}, {-1/16,7/48,13/48,7/16,9/16,41/48,-5/4,5/4}, {0,1/12,7/48,3/8,5/8,41/48,-19/16,19/16}, {0,1/12,5/24,3/8,5/8,11/12,-19/16,19/16}, {-1/48,5/48,11/48,5/16,11/16,43/48,-29/24,29/24}, {-1/48,5/48,1/6,7/16,9/16,17/24,-61/48,61/48}, {1/24,3/16,5/16,11/24,13/24,23/24,-31/24,31/24}, {-1/16,3/16,1/4,3/8,7/16,9/16,-21/16,21/16}, {-1/16,3/16,13/48,19/48,23/48,29/48,-4/3,4/3}, {-1/48,11/48,5/16,19/48,23/48,11/16,-65/48,65/48}, {1/96,25/96,31/96,13/32,15/32,71/96,-131/96,131/96}, {-1/24,1/6,7/24,3/8,1/2,5/6,-59/48,59/48}, {-1/24,1/6,1/4,1/3,11/24,3/4,-29/24,29/24}, {0,1/8,5/24,1/3,11/24,2/3,-59/48,59/48}, {1/24,1/6,7/24,3/8,1/2,5/6,-61/48,61/48}, {1/48,5/48,11/48,5/16,9/16,43/48,-7/6,7/6}, {1/32,3/32,17/96,23/96,47/96,73/96,-109/96,109/96}, {1/48,5/48,3/16,13/48,25/48,13/16,-55/48,55/48}, {1/16,1/8,1/4,5/16,9/16,15/16,-19/16,19/16}, {-1/96,13/96,7/32,9/32,35/96,61/96,-113/96,113/96}, {1/48,5/48,3/16,5/16,19/48,29/48,-29/24,29/24}, {1/24,1/6,1/4,1/3,13/24,3/4,-31/24,31/24}, {5/48,3/16,5/16,19/48,23/48,43/48,-31/24,31/24}, {1/16,5/24,1/3,19/48,23/48,15/16,-61/48,61/48}, {13/96,7/32,9/32,35/96,49/96,83/96,-127/96,127/96}, {1/96,25/96,31/96,13/32,19/32,71/96,-137/96,137/96}, {1/16,7/48,13/48,25/48,41/48,15/16,-35/24,35/24}, {3/32,17/96,23/96,47/96,73/96,29/32,-137/96,137/96}, {13/96,7/32,9/32,35/96,61/96,83/96,-133/96,133/96}, {5/96,19/96,9/32,11/32,41/96,55/96,-107/96,107/96}, {5/96,19/96,31/96,37/96,15/32,17/32,-103/96,103/96}, {3/32,5/32,9/32,11/32,19/32,21/32,-33/32,33/32}, {1/16,3/16,1/4,5/16,11/16,3/4,-9/8,9/8}, {1/12,1/6,1/4,1/3,7/12,3/4,-13/12,13/12}, {1/16,3/16,1/4,7/16,9/16,5/8,-19/16,19/16}, {1/48,11/48,7/24,7/16,9/16,17/24,-7/6,7/6}, {1/12,1/6,11/48,3/8,5/8,37/48,-53/48,53/48}, {1/16,3/16,13/48,19/48,25/48,29/48,-7/6,7/6}, {1/48,11/48,5/16,19/48,25/48,11/16,-55/48,55/48}, {3/32,5/32,23/96,29/96,53/96,67/96,-103/96,103/96}, {1/12,1/6,1/4,3/8,11/24,13/24,-55/48,55/48}, {-1/60,17/60,7/20,11/20,13/20,49/60,-3/2,3/2}, {-1/15,7/30,2/5,3/5,7/10,13/15,-3/2,3/2}, {-1/20,1/4,7/20,11/20,3/4,17/20,-3/2,3/2}, {1/30,1/3,2/5,9/20,11/20,23/30,-3/2,3/2}, {-1/20,3/20,1/4,7/20,9/20,3/4,-3/2,3/2}, {-1/10,1/5,4/15,11/30,13/30,9/10,-3/2,3/2}, {-1/20,3/20,13/60,19/60,29/60,17/20,-3/2,3/2}, {-1/60,11/60,17/60,7/20,9/20,13/20,-3/2,3/2}, {1/20,1/10,1/6,4/15,8/15,19/20,-3/2,3/2}, {-1/15,2/15,7/30,3/10,2/5,3/5,-3/2,3/2}, {1/20,1/10,4/15,7/15,5/6,19/20,-3/2,3/2}, {-1/10,1/5,11/30,17/30,11/15,9/10,-3/2,3/2}, {1/30,7/30,1/3,9/20,11/20,3/5,-3/2,3/2}, {-1/20,3/20,19/60,31/60,47/60,17/20,-3/2,3/2}, {1/96,5/96,1/12,1/8,3/16,5/16,-7/16,7/16}, {-1/48,1/12,11/96,5/32,7/32,11/32,-19/32,19/32}, {-1/192,13/192,7/64,13/64,59/192,109/192,-157/192,157/192}, {1/48,1/12,5/32,7/32,7/24,23/48,-35/48,35/48}, {13/192,25/192,11/64,13/64,47/192,83/192,-131/192,131/192}, {1/32,7/96,5/48,1/6,11/32,17/32,-25/32,25/32}, {5/192,19/192,13/64,19/64,77/192,91/192,-175/192,175/192}, {1/64,5/64,23/192,37/192,49/192,73/192,-121/192,121/192}}