int gdCosT[] = {
  1024,
  1023,
  1023,
  1022,
  1021,
  1020,
  1018,
  1016,
  1014,
  1011,
  1008,
  1005,
  1001,
  997,
  993,
  989,
  984,
  979,
  973,
  968,
  962,
  955,
  949,
  942,
  935,
  928,
  920,
  912,
  904,
  895,
  886,
  877,
  868,
  858,
  848,
  838,
  828,
  817,
  806,
  795,
  784,
  772,
  760,
  748,
  736,
  724,
  711,
  698,
  685,
  671,
  658,
  644,
  630,
  616,
  601,
  587,
  572,
  557,
  542,
  527,
  512,
  496,
  480,
  464,
  448,
  432,
  416,
  400,
  383,
  366,
  350,
  333,
  316,
  299,
  282,
  265,
  247,
  230,
  212,
  195,
  177,
  160,
  142,
  124,
  107,
  89,
  71,
  53,
  35,
  17,
  0,
  -17,
  -35,
  -53,
  -71,
  -89,
  -107,
  -124,
  -142,
  -160,
  -177,
  -195,
  -212,
  -230,
  -247,
  -265,
  -282,
  -299,
  -316,
  -333,
  -350,
  -366,
  -383,
  -400,
  -416,
  -432,
  -448,
  -464,
  -480,
  -496,
  -512,
  -527,
  -542,
  -557,
  -572,
  -587,
  -601,
  -616,
  -630,
  -644,
  -658,
  -671,
  -685,
  -698,
  -711,
  -724,
  -736,
  -748,
  -760,
  -772,
  -784,
  -795,
  -806,
  -817,
  -828,
  -838,
  -848,
  -858,
  -868,
  -877,
  -886,
  -895,
  -904,
  -912,
  -920,
  -928,
  -935,
  -942,
  -949,
  -955,
  -962,
  -968,
  -973,
  -979,
  -984,
  -989,
  -993,
  -997,
  -1001,
  -1005,
  -1008,
  -1011,
  -1014,
  -1016,
  -1018,
  -1020,
  -1021,
  -1022,
  -1023,
  -1023,
  -1024,
  -1023,
  -1023,
  -1022,
  -1021,
  -1020,
  -1018,
  -1016,
  -1014,
  -1011,
  -1008,
  -1005,
  -1001,
  -997,
  -993,
  -989,
  -984,
  -979,
  -973,
  -968,
  -962,
  -955,
  -949,
  -942,
  -935,
  -928,
  -920,
  -912,
  -904,
  -895,
  -886,
  -877,
  -868,
  -858,
  -848,
  -838,
  -828,
  -817,
  -806,
  -795,
  -784,
  -772,
  -760,
  -748,
  -736,
  -724,
  -711,
  -698,
  -685,
  -671,
  -658,
  -644,
  -630,
  -616,
  -601,
  -587,
  -572,
  -557,
  -542,
  -527,
  -512,
  -496,
  -480,
  -464,
  -448,
  -432,
  -416,
  -400,
  -383,
  -366,
  -350,
  -333,
  -316,
  -299,
  -282,
  -265,
  -247,
  -230,
  -212,
  -195,
  -177,
  -160,
  -142,
  -124,
  -107,
  -89,
  -71,
  -53,
  -35,
  -17,
  0,
  17,
  35,
  53,
  71,
  89,
  107,
  124,
  142,
  160,
  177,
  195,
  212,
  230,
  247,
  265,
  282,
  299,
  316,
  333,
  350,
  366,
  383,
  400,
  416,
  432,
  448,
  464,
  480,
  496,
  512,
  527,
  542,
  557,
  572,
  587,
  601,
  616,
  630,
  644,
  658,
  671,
  685,
  698,
  711,
  724,
  736,
  748,
  760,
  772,
  784,
  795,
  806,
  817,
  828,
  838,
  848,
  858,
  868,
  877,
  886,
  895,
  904,
  912,
  920,
  928,
  935,
  942,
  949,
  955,
  962,
  968,
  973,
  979,
  984,
  989,
  993,
  997,
  1001,
  1005,
  1008,
  1011,
  1014,
  1016,
  1018,
  1020,
  1021,
  1022,
  1023,
  1023
};

int gdSinT[] = {
  0,
  17,
  35,
  53,
  71,
  89,
  107,
  124,
  142,
  160,
  177,
  195,
  212,
  230,
  247,
  265,
  282,
  299,
  316,
  333,
  350,
  366,
  383,
  400,
  416,
  432,
  448,
  464,
  480,
  496,
  512,
  527,
  542,
  557,
  572,
  587,
  601,
  616,
  630,
  644,
  658,
  671,
  685,
  698,
  711,
  724,
  736,
  748,
  760,
  772,
  784,
  795,
  806,
  817,
  828,
  838,
  848,
  858,
  868,
  877,
  886,
  895,
  904,
  912,
  920,
  928,
  935,
  942,
  949,
  955,
  962,
  968,
  973,
  979,
  984,
  989,
  993,
  997,
  1001,
  1005,
  1008,
  1011,
  1014,
  1016,
  1018,
  1020,
  1021,
  1022,
  1023,
  1023,
  1024,
  1023,
  1023,
  1022,
  1021,
  1020,
  1018,
  1016,
  1014,
  1011,
  1008,
  1005,
  1001,
  997,
  993,
  989,
  984,
  979,
  973,
  968,
  962,
  955,
  949,
  942,
  935,
  928,
  920,
  912,
  904,
  895,
  886,
  877,
  868,
  858,
  848,
  838,
  828,
  817,
  806,
  795,
  784,
  772,
  760,
  748,
  736,
  724,
  711,
  698,
  685,
  671,
  658,
  644,
  630,
  616,
  601,
  587,
  572,
  557,
  542,
  527,
  512,
  496,
  480,
  464,
  448,
  432,
  416,
  400,
  383,
  366,
  350,
  333,
  316,
  299,
  282,
  265,
  247,
  230,
  212,
  195,
  177,
  160,
  142,
  124,
  107,
  89,
  71,
  53,
  35,
  17,
  0,
  -17,
  -35,
  -53,
  -71,
  -89,
  -107,
  -124,
  -142,
  -160,
  -177,
  -195,
  -212,
  -230,
  -247,
  -265,
  -282,
  -299,
  -316,
  -333,
  -350,
  -366,
  -383,
  -400,
  -416,
  -432,
  -448,
  -464,
  -480,
  -496,
  -512,
  -527,
  -542,
  -557,
  -572,
  -587,
  -601,
  -616,
  -630,
  -644,
  -658,
  -671,
  -685,
  -698,
  -711,
  -724,
  -736,
  -748,
  -760,
  -772,
  -784,
  -795,
  -806,
  -817,
  -828,
  -838,
  -848,
  -858,
  -868,
  -877,
  -886,
  -895,
  -904,
  -912,
  -920,
  -928,
  -935,
  -942,
  -949,
  -955,
  -962,
  -968,
  -973,
  -979,
  -984,
  -989,
  -993,
  -997,
  -1001,
  -1005,
  -1008,
  -1011,
  -1014,
  -1016,
  -1018,
  -1020,
  -1021,
  -1022,
  -1023,
  -1023,
  -1024,
  -1023,
  -1023,
  -1022,
  -1021,
  -1020,
  -1018,
  -1016,
  -1014,
  -1011,
  -1008,
  -1005,
  -1001,
  -997,
  -993,
  -989,
  -984,
  -979,
  -973,
  -968,
  -962,
  -955,
  -949,
  -942,
  -935,
  -928,
  -920,
  -912,
  -904,
  -895,
  -886,
  -877,
  -868,
  -858,
  -848,
  -838,
  -828,
  -817,
  -806,
  -795,
  -784,
  -772,
  -760,
  -748,
  -736,
  -724,
  -711,
  -698,
  -685,
  -671,
  -658,
  -644,
  -630,
  -616,
  -601,
  -587,
  -572,
  -557,
  -542,
  -527,
  -512,
  -496,
  -480,
  -464,
  -448,
  -432,
  -416,
  -400,
  -383,
  -366,
  -350,
  -333,
  -316,
  -299,
  -282,
  -265,
  -247,
  -230,
  -212,
  -195,
  -177,
  -160,
  -142,
  -124,
  -107,
  -89,
  -71,
  -53,
  -35,
  -17
};