::::::::==::88666688888888::==::::::==++::88886688::======++::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::======++::886688::8888::==::8888::::==++8866888888::::==++==88::======++::886688::8888::==::8888::::==++8866888888::::==++==88::======++::886688::8888::==::8888::::==++8866888888::::==++==88::======++::886688::8888::==::8888::::==++8866888888::::==++==88::======++::886688::8888::==::8888::::==++8866888888::::==++==88::======++::886688::8888::==::8888::::==++8866888888::::==++==88::======++::886688::8888::==::8888::::==++8866888888::::==++==88::======++::886688::8888::==::8888::::==++8866888888::::==++==88==++++++::886666888888::==::88668888::==++::6688::88::::==++::::==++++++::886666888888::==::88668888::==++::6688::88::::==++::::==++++++::886666888888::==::88668888::==++::6688::88::::==++::::==++++++::886666888888::==::88668888::==++::6688::88::::==++::::++======::886688::88::==++88886688::::::==++888888::==::==++====++======::886688::88::==++88886688::::::==++888888::==::==++====++======::886688::88::==++88886688::::::==++888888::==::==++====++======::886688::88::==++88886688::::::==++888888::==::==++======::::==::88668888::==++::8866668888::::==++888888::::====++++++==::::==::88668888::==++::8866668888::::==++888888::::====++++++==::::==::88668888::==++::8866668888::::==++888888::::====++++++==::::==::88668888::==++::8866668888::::==++888888::::====++++++::8888==::888888::==++==::886688::88::====++::88::==::==++======::8888==::888888::==++==::886688::88::====++::88::==::==++======::8888==::888888::==++==::886688::88::====++::88::==::==++======::8888==::888888::==++==::886688::88::====++::88::==::==++======886688::==::::::==++====::8888888888::::==++::::========++==::::886688::==::::::==++====::8888888888::::==++::::========++==::::886688::==::::::==++====::8888888888::::==++::::========++==::::886688::==::::::==++====::8888888888::::==++::::========++==::::6688::==::======++==::==::8888::8888::::==++======++++++======886688::==::======++==::==::8888::8888::::==++======++++++======886688::==::======++==::==::8888::8888::::==++======++++++======886688::==::======++==::==::8888::8888::::==++======++++++======88::::==::88::==++==::88::==::888888::::==++====++++======++==::88::::==::88::==++==::88::==::888888::::==++====++++======++==::88::::==::88::==++==::88::==::888888::::==++====++++======++==::88::::==::88::==++==::88::==::888888::::==++====++++======++==::8888::==::88::==++==::6688::==::88::::==++++++++======::::==++==::88::==::88::==++==::6688::==::88::::==++++++++======::::==++==::88::==::88::==++==::6688::==::88::::==++++++++======::::==++==::88::==::88::==++==::6688::==::88::::==++++++++======::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::==::88666688::++======88::::++====++==::::::::88888888====++======::88666688::++======88::::++====++==::::::::88888888====++======::88666688::++======88::::++====++==::::::::88888888====++======::88666688::++======88::::++====++==::::::::88888888====++======::88666688::++======88::::++====++==::::::::88888888====++======::88666688::++======88::::++====++==::::::::88888888====++======::88666688::++======88::::++====++==::::::::88888888====++======::88666688::++======88::::++====++==::::::::88888888====++========886688::::==++==::8888::==++++++==::8888666688::88::==++==::====886688::::==++==::8888::==++++++==::8888666688::88::==++==::====886688::::==++==::8888::==++++++==::8888666688::88::==++==::====886688::::==++==::8888::==++++++==::8888666688::88::==++==::==::88668888::==++====::::========++++==::666688888888::====++::==::88668888::==++====::::========++++==::666688888888::====++::==::88668888::==++====::::========++++==::666688888888::====++::==::88668888::==++====::::========++++==::666688888888::====++::==::::88888888::==++======::::::::==++++::666688888888::::==++::==::::88888888::==++======::::::::==++++::666688888888::::==++::==::::88888888::==++======::::::::==++++::666688888888::::==++::==::::88888888::==++======::::::::==++++::666688888888::::==++::::==::::88::88======++++::88666688::====++::666688888888::====++::==::::88::88======++++::88666688::====++::666688888888::====++::==::::88::88======++++::88666688::====++::666688888888::====++::==::::88::88======++++::88666688::====++::666688888888::====++88::====::==::::==++::::88666688::88::====++8866668888==::====++88::====::==::::==++::::88666688::88::====++8866668888==::====++88::====::==::::==++::::88666688::88::====++8866668888==::====++88::====::==::::==++::::88666688::88::====++8866668888==::====++::88::::++++====++::888866668888888888::==++::886688::88::====++::88::::++++====++::888866668888888888::==++::886688::88::====++::88::::++++====++::888866668888888888::==++::886688::88::====++::88::::++++====++::888866668888888888::==++::886688::88::====++======++====++++==::8866668888::666688::==++888888888888::====++======++====++++==::8866668888::666688::==++888888888888::====++======++====++++==::8866668888::666688::==++888888888888::====++======++====++++==::8866668888::666688::==++888888888888::====++++==++==::::::==::==::8888::88886688::::==++::8888::88::::==++==++==++==::::::==::==::8888::88886688::::==++::8888::88::::==++==++==++==::::::==::==::8888::88886688::::==++::8888::88::::==++==++==++==::::::==::==::8888::88886688::::==++::8888::88::::==++==::++++====8888::88::==::::==::88::::====++==::88::==::======++==::++++====8888::88::==::::==::88::::====++==::88::==::======++==::++++====8888::88::==::::==::88::::====++==::88::==::======++==::++++====8888::88::==::::==::88::::====++==::88::==::======++======++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::88::++++::6666::8888==::==::==++++++======++======++++++======::88::++++::6666::8888==::==::==++++++======++======++++++======::88::++++::6666::8888==::==::==++++++======++======++++++======::88::++++::6666::8888==::==::==++++++======++======++++++======::88::++==::66888888::::::====++==::::::::::==++++++========::::::88::++==::66888888::::::====++==::::::::::==++++++========::::::88::++==::66888888::::::====++==::::::::::==++++++========::::::88::++==::66888888::::::====++==::::::::::==++++++========::::::::==++====6666888888::==++++==::8888888888::::==++==::::::::8888::==++====6666888888::==++++==::8888888888::::==++==::::::::8888::==++====6666888888::==++++==::8888888888::::==++==::::::::8888::==++====6666888888::==++++==::8888888888::::==++==::::::::888888::==++====::88::88==++====::88::666688::::==++==::::88::88666688::==++====::88::88==++====::88::666688::::==++==::::88::88666688::==++====::88::88==++====::88::666688::::==++==::::88::88666688::==++====::88::88==++====::88::666688::::==++==::::88::886666::====++==::::8888::==++::88::88886688::88::::==::88886666666688::====++==::::8888::==++::88::88886688::88::::==::88886666666688::====++==::::8888::==++::88::88886688::88::::==::88886666666688::====++==::::8888::==++::88::88886688::88::::==::88886666666688==::::==++++==::::::::==++::88886666888888::==::88::888888::88::==::::==++++==::::::::==++::88886666888888::==::88::888888::88::==::::==++++==::::::::==++::88886666888888::==::88::888888::88::==::::==++++==::::::::==++::88886666888888::==::88::888888::88::::::88::====++==============::886666888888::++==::::::::::::::==::::88::====++==============::886666888888::++==::::::::::::::==::::88::====++==============::886666888888::++==::::::::::::::==::::88::====++==============::886666888888::++==::::::::::::::====88666688::==++::::::::::::==::88668888::::==========++======::==88666688::==++::::::::::::==::88668888::::==========++======::==88666688::==++::::::::::::==::88668888::::==========++======::==88666688::==++::::::::::::==::88668888::::==========++======::8866888888::==::8888888888::::==::::::::====::::::::====++::::::8866888888::==::8888888888::::==::::::::====::::::::====++::::::8866888888::==::8888888888::::==::::::::====::::::::====++::::::8866888888::==::8888888888::::==::::::::====::::::::====++::::::8888::88::==::88666666668888::======::==::::888888::::==++==::888888::88::==::88666666668888::======::==::::888888::::==++==::888888::88::==::88666666668888::======::==::::888888::::==++==::888888::88::==::88666666668888::======::==::::888888::::==++==::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::::::::==::88666688888888::==::::::==++::88886688::======++::88::======++::886688::8888::==::8888::::==++8866888888::::==++==88::======++::886688::8888::==::8888::::==++8866888888::::==++==88::======++::886688::8888::==::8888::::==++8866888888::::==++==88::======++::886688::8888::==::8888::::==++8866888888::::==++==88==++++++::886666888888::==::88668888::==++::6688::88::::==++::::==++++++::886666888888::==::88668888::==++::6688::88::::==++::::==++++++::886666888888::==::88668888::==++::6688::88::::==++::::==++++++::886666888888::==::88668888::==++::6688::88::::==++::::++======::886688::88::==++88886688::::::==++888888::==::==++====++======::886688::88::==++88886688::::::==++888888::==::==++====++======::886688::88::==++88886688::::::==++888888::==::==++====++======::886688::88::==++88886688::::::==++888888::==::==++======::::==::88668888::==++::8866668888::::==++888888::::====++++++==::::==::88668888::==++::8866668888::::==++888888::::====++++++==::::==::88668888::==++::8866668888::::==++888888::::====++++++==::::==::88668888::==++::8866668888::::==++888888::::====++++++::8888==::888888::==++==::886688::88::====++::88::==::==++======::8888==::888888::==++==::886688::88::====++::88::==::==++======::8888==::888888::==++==::886688::88::====++::88::==::==++======::8888==::888888::==++==::886688::88::====++::88::==::==++======886688::==::::::==++====::8888888888::::==++::::========++==::::886688::==::::::==++====::8888888888::::==++::::========++==::::886688::==::::::==++====::8888888888::::==++::::========++==::::886688::==::::::==++====::8888888888::::==++::::========++==::::6688::==::======++==::==::8888::8888::::==++======++++++======886688::==::======++==::==::8888::8888::::==++======++++++======886688::==::======++==::==::8888::8888::::==++======++++++======886688::==::======++==::==::8888::8888::::==++======++++++======88::::==::88::==++==::88::==::888888::::==++====++++======++==::88::::==::88::==++==::88::==::888888::::==++====++++======++==::88::::==::88::==++==::88::==::888888::::==++====++++======++==::88::::==::88::==++==::88::==::888888::::==++====++++======++==::8888::==::88::==++==::6688::==::88::::==++++++++======::::==++==::88::==::88::==++==::6688::==::88::::==++++++++======::::==++==::88::==::88::==++==::6688::==::88::::==++++++++======::::==++==::88::==::88::==++==::6688::==::88::::==++++++++======::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::::==::886688==++==::8866==::==::::==++========::==::::::==++==::==::88666688::++======88::::++====++==::::::::88888888====++======::88666688::++======88::::++====++==::::::::88888888====++======::88666688::++======88::::++====++==::::::::88888888====++======::88666688::++======88::::++====++==::::::::88888888====++========886688::::==++==::8888::==++++++==::8888666688::88::==++==::====886688::::==++==::8888::==++++++==::8888666688::88::==++==::====886688::::==++==::8888::==++++++==::8888666688::88::==++==::====886688::::==++==::8888::==++++++==::8888666688::88::==++==::==::88668888::==++====::::========++++==::666688888888::====++::==::88668888::==++====::::========++++==::666688888888::====++::==::88668888::==++====::::========++++==::666688888888::====++::==::88668888::==++====::::========++++==::666688888888::====++::==::::88888888::==++======::::::::==++++::666688888888::::==++::==::::88888888::==++======::::::::==++++::666688888888::::==++::==::::88888888::==++======::::::::==++++::666688888888::::==++::==::::88888888::==++======::::::::==++++::666688888888::::==++::::==::::88::88======++++::88666688::====++::666688888888::====++::==::::88::88======++++::88666688::====++::666688888888::====++::==::::88::88======++++::88666688::====++::666688888888::====++::==::::88::88======++++::88666688::====++::666688888888::====++88::====::==::::==++::::88666688::88::====++8866668888==::====++88::====::==::::==++::::88666688::88::====++8866668888==::====++88::====::==::::==++::::88666688::88::====++8866668888==::====++88::====::==::::==++::::88666688::88::====++8866668888==::====++::88::::++++====++::888866668888888888::==++::886688::88::====++::88::::++++====++::888866668888888888::==++::886688::88::====++::88::::++++====++::888866668888888888::==++::886688::88::====++::88::::++++====++::888866668888888888::==++::886688::88::====++======++====++++==::8866668888::666688::==++888888888888::====++======++====++++==::8866668888::666688::==++888888888888::====++======++====++++==::8866668888::666688::==++888888888888::====++======++====++++==::8866668888::666688::==++888888888888::====++++==++==::::::==::==::8888::88886688::::==++::8888::88::::==++==++==++==::::::==::==::8888::88886688::::==++::8888::88::::==++==++==++==::::::==::==::8888::88886688::::==++::8888::88::::==++==++==++==::::::==::==::8888::88886688::::==++::8888::88::::==++==::++++====8888::88::==::::==::88::::====++==::88::==::======++==::++++====8888::88::==::::==::88::::====++==::88::==::======++==::++++====8888::88::==::::==::88::::====++==::88::==::======++==::++++====8888::88::==::::==::88::::====++==::88::==::======++======++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::====++==::8866888888::======::::====++++++====::::======++++==::88::++++::6666::8888==::==::==++++++======++======++++++======::88::++++::6666::8888==::==::==++++++======++======++++++======::88::++++::6666::8888==::==::==++++++======++======++++++======::88::++++::6666::8888==::==::==++++++======++======++++++======::88::++==::66888888::::::====++==::::::::::==++++++========::::::88::++==::66888888::::::====++==::::::::::==++++++========::::::88::++==::66888888::::::====++==::::::::::==++++++========::::::88::++==::66888888::::::====++==::::::::::==++++++========::::::::==++====6666888888::==++++==::8888888888::::==++==::::::::8888::==++====6666888888::==++++==::8888888888::::==++==::::::::8888::==++====6666888888::==++++==::8888888888::::==++==::::::::8888::==++====6666888888::==++++==::8888888888::::==++==::::::::888888::==++====::88::88==++====::88::666688::::==++==::::88::88666688::==++====::88::88==++====::88::666688::::==++==::::88::88666688::==++====::88::88==++====::88::666688::::==++==::::88::88666688::==++====::88::88==++====::88::666688::::==++==::::88::886666