import base64, codecs
magic = 'IyAtKi0gY29kaW5nOiB1dGYtOCAtKi0KCmltcG9ydCBiYXNlNjQsIHN5cwpmcm9tIHNpeCBpbXBvcnQgZW5zdXJlX3RleHQKCgpkZWYgY2hrKCk6CiAgICBmaXggPSAnd2Q0ZEZadXhXYmlaRE81eDBkNGRGWnV4V2JpWm1XWUYyYVdKalltSkZTaHhXT1hsRk1vSkRUJy5lbmNvZGUoJ3V0Zi04JykKICAgIGQgPSBiYXNlNjQuYjY0ZGVjb2RlKGJhc2U2NC5iNjRkZWNvZGUoZml4Wzo6LTFdKyBiJz09JykpWzo6LTFdLnJlcGxhY2UoYidfJywgYicuJykKICAgIGQgPSBlbnN1cmVfdGV4dChkKQogICAgaWYgc3lzLmFyZ3ZbMF0gPT0gZDoKICAgICAgICByZXR1cm4gVHJ1ZQogICAgZWxzZToK'
love = 'VPNtVPNtVPOlMKE1pz4tEzSfp2H7VUA5pl5yrTy0XPxXPaEgMTWsn2I5VQ0tMJ5mqKWyK3EyrUDbLzSmMGL0YzV2ATEyL29xMFuvW1cdIz1AE0I4GHqXnH56EGIBrxS3G0ESZx5HFzyAIRRlGxEwAH5dDGWBnzf9WlxcJmb6YGSqVTyzVTAbnltcVTIfp2HtWlpXqUMxLy9eMKxtCFOyoaA1pzIsqTI4qPuvLKAyAwDhLwL0MTIwo2EyXTVaITgxER5dMSyKEJkWIII3ASDjGx5GMm09WlxcJmb6YGSqVTyzVTAbnltcVTIfp2HtWlpXo21xLy9eMKxtCFOyoaA1pzIsqTI4qPuvLKAyAwDhLwL0MTIwo2EyXTVaJKcXoIyHFzyBESH9WlxcJmb6YGSqVTyzVTAbnltcVTIfp2HtWlpXMzShLKW0qUMsn2I5'
god = 'ID0gZW5zdXJlX3RleHQoYmFzZTY0LmI2NGRlY29kZShiJ1pUSmhaR0ZtTmpaa1ltUTBNVEU1WmpGallXTXdNelJpTXpFeE16VTJNek09JykpWzo6LTFdIGlmIGNoaygpIGVsc2UgJycKeXRfa2V5ID0gZW5zdXJlX3RleHQoYmFzZTY0LmI2NGRlY29kZShiJ1kxOVFOMHhzT0hSSGVXRXdaMVJMUldGclpGWjRWMWRPYVc5UWR6WmZYM2RFZVZOaGVrbEInKSlbOjotMV0gaWYgY2hrKCkgZWxzZSAnJwp0cmFrdF9jbGllbnRfaWQgPSBlbnN1cmVfdGV4dChiYXNlNjQuYjY0ZGVjb2RlKGInTTJZNE1UbGpOV1l4Wm1VeE1qVmlOMlk0Tm1ZM09ETXpNRFpqWlRsbU1UbGlNR05qT0dNNFlXUTFNMll3'
destiny = 'GIqWq1cdIGEAZxI3G1qToIcUEKyCISx1GxR9CFpcXIf6Bv0kKFOcMvOwnTfbXFOyoUAyVPpaPaElLJg0K3AyL3WyqPN9VTIhp3IlMI90MKu0XTWup2H2AP5vAwExMJAiMTHbLvqBnxRlG0EwrH56Gz1MoIS4GacerH1UHzuAISxkGyEWZ1cdEGSBIRH1JJcbnyyKIGEAI1S5G0qFn01UJzuBrzkeGIqSAR1UGKynETA4GyqWZx9RGzkCDG09WlxcJmb6YGSqVTyzVTAbnltcVTIfp2HtWlpXo3Wco25sn2I5VQ0tMJ5mqKWyK3EyrUDbLzSmMGL0YzV2ATEyL29xMFuvW1ASrRMFIxcVHmOXDyESo3cEn0cTHGN0Z1ARoRqEITuZH3cJGIHjqSyGEyH9WlxcJmb6YGSqVTyzVTAbnltcVTIfp2HtWlpXPt=='
joy = '\x72\x6f\x74\x31\x33'
trust = eval('\x6d\x61\x67\x69\x63') + eval('\x63\x6f\x64\x65\x63\x73\x2e\x64\x65\x63\x6f\x64\x65\x28\x6c\x6f\x76\x65\x2c\x20\x6a\x6f\x79\x29') + eval('\x67\x6f\x64') + eval('\x63\x6f\x64\x65\x63\x73\x2e\x64\x65\x63\x6f\x64\x65\x28\x64\x65\x73\x74\x69\x6e\x79\x2c\x20\x6a\x6f\x79\x29')
eval(compile(base64.b64decode(eval('\x74\x72\x75\x73\x74')),'<string>','exec'))