LowerImageLimit = {
0, 4359, 4070, 4113, 3996, 4017, 4342, 4307, 4180, 4162, 4270, 4261, 4312, 4258, 4304, 4294, 4184, 0,
4064, 4391, 4417, 4011, 4375, 4387, 4360, 4185, 4205, 4309, 4275, 3994, 3992, 4410, 4060, 4053, 4038, 4221,
4351, 4236, 4249, 4278, 4221, 4235, 4226, 4210, 4201, 4118, 4094, 4079, 4077, 4046, 4245, 4236, 4232, 4384,
4102, 4401, 4001, 4030, 4244, 4249, 4238, 4231, 4229, 4026, 3991, 4427, 3975, 4375, 4136, 4121, 4110, 4267,
4126, 3995, 4006, 4036, 4115, 4131, 4132, 4125, 4146, 4202, 4156, 4139, 4131, 4094, 4251, 4235, 4224, 4403,
4128, 4009, 4018, 4054, 4047, 4052, 4055, 4057, 4069, 4010, 4407, 4387, 4378, 4331, 4034, 4015, 4006, 4168,
4034, 4346, 4363, 4409, 4394, 4397, 4395, 4399, 4421, 4193, 4146, 4140, 4121, 4092, 4025, 3998, 4404, 4149,
4054, 4396, 3995, 4049, 3998, 3997, 3993, 4008, 4038, 4348, 4308, 4291, 4281, 4261, 4385, 4334, 4319, 4320,
4122, 4041, 4052, 4116, 4027, 4029, 4021, 4035, 4078, 4311, 4254, 4240, 4256, 4207, 4261, 4210, 4200, 4192,
4249, 4178, 4191, 4248, 4228, 4230, 4240, 4240, 4294, 4409, 4350, 4343, 4341, 4320, 4091, 4047, 4019, 4424,
4100, 4025, 4027, 4131, 4355, 4371, 4357, 4383, 4431, 4042, 3993, 4416, 3997, 4396, 4405, 4312, 4300, 4297,
4130, 4060, 4075, 4137, 4238, 4234, 4255, 4273, 4322, 4411, 4354, 4345, 4334, 4315, 4327, 4264, 4239, 4234,
4156, 4011, 4030, 4099, 4086, 4092, 4110, 4128, 4160, 4395, 4372, 4367, 4355, 4314, 4074, 4018, 4405, 4138,
4368, 4237, 4254, 4295, 4178, 4202, 4228, 4248, 4278, 4328, 4306, 4300, 4272, 4244, 4247, 4204, 4178, 4322,
3989, 4278, 4305, 4362, 4081, 4075, 4116, 4133, 4167, 4038, 4004, 4006, 3982, 4357, 4351, 4294, 4250, 4406,
4108, 4399, 3986, 4037, 4061, 4064, 4095, 4118, 4151, 4193, 4170, 4169, 4152, 4106, 4108, 4057, 4021, 4169,
4299, 4163, 4190, 4252, 4224, 4215, 4261, 4270, 4306, 4298, 4279, 4264, 4266, 4207, 4335, 4273, 4233, 4381,
4145, 4013, 4041, 4084, 4294, 4283, 3943, 4335, 3991, 4244, 4212, 4215, 4209, 4150, 4064, 4011, 4409, 4127,
4279, 4135, 4176, 4227, 4314, 4306, 3958, 3968, 4005, 4292, 4263, 4259, 4244, 4211, 4295, 4234, 4189, 4345,
4133, 4002, 4035, 4103, 4276, 4271, 4296, 4301, 4369, 4011, 4383, 4372, 4369, 4328, 4328, 4255, 4201, 4355,
4204, 4089, 4129, 4197, 4150, 4150, 4174, 4192, 4242, 4327, 4280, 4276, 4274, 4218, 4424, 4352, 4304, 4005,
4072, 4394, 3986, 4069, 4310, 4304, 4332, 4348, 4402, 4422, 4360, 4347, 4332, 4287, 4326, 4247, 4208, 4350,
4105, 3974, 4022, 4090, 4307, 4303, 4340, 4361, 4416, 4026, 4419, 4406, 4383, 4331, 4080, 4017, 4389, 4110,
4343, 4222, 4257, 4335, 4007, 3994, 4028, 4041, 4093, 4030, 3987, 4423, 4409, 4359, 4061, 3981, 4358, 4089,
4290, 4171, 4202, 4249, 4312, 4300, 4337, 4344, 4386, 4221, 4199, 4185, 4171, 4119, 4352, 4316, 4275, 4422,
4322, 4195, 4207, 4262, 4103, 4081, 4116, 4137, 4184, 4398, 4365, 4362, 4344, 4307, 4031, 3982, 4372, 4099,
4317, 4205, 4221, 4275, 4326, 4317, 4355, 4374, 4413, 4175, 4144, 4142, 4131, 4075, 4400, 4361, 4328, 4042,
4211, 4085, 4101, 4149, 4023, 3998, 4027, 4047, 4091, 4281, 4260, 4251, 4237, 4193, 4102, 4055, 4029, 4173,
4194, 4073, 4096, 4123, 4213, 4179, 4215, 4229, 4278, 4345, 4323, 4330, 4311, 4255, 4284, 4255, 4223, 4361,
4155, 4025, 4053, 4085, 4370, 4332, 4359, 4367, 4415, 4177, 4150, 4154, 4145, 4099, 4318, 4273, 4249, 4400,
4116, 4004, 4018, 4056, 4156, 4117, 4133, 4138, 4179, 4374, 4336, 4332, 4329, 4299, 4377, 4340, 4316, 4035,
4081, 4398, 4392, 3979, 4196, 4118, 4139, 4149, 4203, 4382, 4322, 4311, 4310, 4304, 4377, 4311, 4289, 4015,
4178, 4015, 3993, 4011, 4164, 4074, 4112, 4118, 4175, 4074, 4015, 3996, 3990, 3996, 4042, 3992, 3978, 4150,
4060, 4337, 4332, 4354, 4263, 4172, 4205, 4205, 4266, 4387, 4312, 4299, 4290, 4296, 4293, 4236, 4220, 4405,
4424, 4102, 4093, 4125, 4153, 4083, 4099, 4118, 4171, 4023, 4411, 4397, 4391, 4394, 4222, 4188, 4187, 4082,
4235, 4107, 4114, 4160, 4116, 4009, 4041, 4067, 4195, 4100, 4401, 4373, 4360, 4361, 4094, 4044, 4046, 4420,
}

UpperImageLimit = {
0, 8359, 8070, 8113, 7996, 8017, 8342, 8307, 8180, 8162, 8270, 8261, 8312, 8258, 8304, 8294, 8184, 0,
8064, 8391, 8417, 8011, 8375, 8387, 8360, 8185, 8205, 8309, 8275, 7994, 7992, 8410, 8060, 8053, 8038, 8221,
8351, 8236, 8249, 8278, 8221, 8235, 8226, 8210, 8201, 8118, 8094, 8079, 8077, 8046, 8245, 8236, 8232, 8384,
8102, 8401, 8001, 8030, 8244, 8249, 8238, 8231, 8229, 8026, 7991, 8427, 7975, 8375, 8136, 8121, 8110, 8267,
8126, 7995, 8006, 8036, 8115, 8131, 8132, 8125, 8146, 8202, 8156, 8139, 8131, 8094, 8251, 8235, 8224, 8403,
8128, 8009, 8018, 8054, 8047, 8052, 8055, 8057, 8069, 8010, 8407, 8387, 8378, 8331, 8034, 8015, 8006, 8168,
8034, 8346, 8363, 8409, 8394, 8397, 8395, 8399, 8421, 8193, 8146, 8140, 8121, 8092, 8025, 7998, 8404, 8149,
8054, 8396, 7995, 8049, 7998, 7997, 7993, 8008, 8038, 8348, 8308, 8291, 8281, 8261, 8385, 8334, 8319, 8320,
8122, 8041, 8052, 8116, 8027, 8029, 8021, 8035, 8078, 8311, 8254, 8240, 8256, 8207, 8261, 8210, 8200, 8192,
8249, 8178, 8191, 8248, 8228, 8230, 8240, 8240, 8294, 8409, 8350, 8343, 8341, 8320, 8091, 8047, 8019, 8424,
8100, 8025, 8027, 8131, 8355, 8371, 8357, 8383, 8431, 8042, 7993, 8416, 7997, 8396, 8405, 8312, 8300, 8297,
8130, 8060, 8075, 8137, 8238, 8234, 8255, 8273, 8322, 8411, 8354, 8345, 8334, 8315, 8327, 8264, 8239, 8234,
8156, 8011, 8030, 8099, 8086, 8092, 8110, 8128, 8160, 8395, 8372, 8367, 8355, 8314, 8074, 8018, 8405, 8138,
8368, 8237, 8254, 8295, 8178, 8202, 8228, 8248, 8278, 8328, 8306, 8300, 8272, 8244, 8247, 8204, 8178, 8322,
7989, 8278, 8305, 8362, 8081, 8075, 8116, 8133, 8167, 8038, 8004, 8006, 7982, 8357, 8351, 8294, 8250, 8406,
8108, 8399, 7986, 8037, 8061, 8064, 8095, 8118, 8151, 8193, 8170, 8169, 8152, 8106, 8108, 8057, 8021, 8169,
8299, 8163, 8190, 8252, 8224, 8215, 8261, 8270, 8306, 8298, 8279, 8264, 8266, 8207, 8335, 8273, 8233, 8381,
8145, 8013, 8041, 8084, 8294, 8283, 7943, 8335, 7991, 8244, 8212, 8215, 8209, 8150, 8064, 8011, 8409, 8127,
8279, 8135, 8176, 8227, 8314, 8306, 7958, 7968, 8005, 8292, 8263, 8259, 8244, 8211, 8295, 8234, 8189, 8345,
8133, 8002, 8035, 8103, 8276, 8271, 8296, 8301, 8369, 8011, 8383, 8372, 8369, 8328, 8328, 8255, 8201, 8355,
8204, 8089, 8129, 8197, 8150, 8150, 8174, 8192, 8242, 8327, 8280, 8276, 8274, 8218, 8424, 8352, 8304, 8005,
8072, 8394, 7986, 8069, 8310, 8304, 8332, 8348, 8402, 8422, 8360, 8347, 8332, 8287, 8326, 8247, 8208, 8350,
8105, 7974, 8022, 8090, 8307, 8303, 8340, 8361, 8416, 8026, 8419, 8406, 8383, 8331, 8080, 8017, 8389, 8110,
8343, 8222, 8257, 8335, 8007, 7994, 8028, 8041, 8093, 8030, 7987, 8423, 8409, 8359, 8061, 7981, 8358, 8089,
8290, 8171, 8202, 8249, 8312, 8300, 8337, 8344, 8386, 8221, 8199, 8185, 8171, 8119, 8352, 8316, 8275, 8422,
8322, 8195, 8207, 8262, 8103, 8081, 8116, 8137, 8184, 8398, 8365, 8362, 8344, 8307, 8031, 7982, 8372, 8099,
8317, 8205, 8221, 8275, 8326, 8317, 8355, 8374, 8413, 8175, 8144, 8142, 8131, 8075, 8400, 8361, 8328, 8042,
8211, 8085, 8101, 8149, 8023, 7998, 8027, 8047, 8091, 8281, 8260, 8251, 8237, 8193, 8102, 8055, 8029, 8173,
8194, 8073, 8096, 8123, 8213, 8179, 8215, 8229, 8278, 8345, 8323, 8330, 8311, 8255, 8284, 8255, 8223, 8361,
8155, 8025, 8053, 8085, 8370, 8332, 8359, 8367, 8415, 8177, 8150, 8154, 8145, 8099, 8318, 8273, 8249, 8400,
8116, 8004, 8018, 8056, 8156, 8117, 8133, 8138, 8179, 8374, 8336, 8332, 8329, 8299, 8377, 8340, 8316, 8035,
8081, 8398, 8392, 7979, 8196, 8118, 8139, 8149, 8203, 8382, 8322, 8311, 8310, 8304, 8377, 8311, 8289, 8015,
8178, 8015, 7993, 8011, 8164, 8074, 8112, 8118, 8175, 8074, 8015, 7996, 7990, 7996, 8042, 7992, 7978, 8150,
8060, 8337, 8332, 8354, 8263, 8172, 8205, 8205, 8266, 8387, 8312, 8299, 8290, 8296, 8293, 8236, 8220, 8405,
8424, 8102, 8093, 8125, 8153, 8083, 8099, 8118, 8171, 8023, 8411, 8397, 8391, 8394, 8222, 8188, 8187, 8082,
8235, 8107, 8114, 8160, 8116, 8009, 8041, 8067, 8195, 8100, 8401, 8373, 8360, 8361, 8094, 8044, 8046, 8420,
}
