⠀⠀⠀⠀⠀⠀⠀⠀ † 𝔒𝔫 𝔶𝔬𝔲𝔯 𝔨𝔫𝔢𝔢𝔰, 𝔪𝔬𝔯𝔱𝔞𝔩. 𝔚𝔬𝔯𝔰𝔥𝔦𝔭 𝔦𝔰 𝔣𝔦𝔩𝔱𝔥𝔶, 𝔞𝔫𝔡 𝔐 𝔠𝔯𝔞𝔳𝔢 𝔢𝔳𝔢𝔯𝔶 𝔰𝔢𝔠𝔬𝔫𝔡 𝔬𝔣 𝔦𝔱.
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀𝔎𝔫𝔢𝔢𝔩𝔦𝔫𝔤 𝔦𝔰 𝔬𝔫𝔩𝔶 𝔱𝔥𝔢 𝔟𝔢𝔤𝔦𝔫𝔫𝔦𝔫𝔤 𝔬𝔣 𝔶𝔬𝔲𝔯 𝔴𝔬𝔯𝔰𝔥𝔦𝔭.
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀𝔑𝔬𝔴 𝔭𝔯𝔬𝔳𝔢 𝔶𝔬𝔲𝔯 𝔣𝔞𝔦𝔱𝔥 𝔦𝔫 𝔴𝔞𝔶𝔰 𝔬𝔫𝔩𝔶 𝔰𝔦𝔫 𝔞𝔩𝔩𝔬𝔴𝔰. †

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡁⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣉⣉⡉⠉⠉⠉⠉⣻⢷⣄⢀⣬⣉⢻⡶⣄⡀⠀⠀⣴⡵⠊⠁⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣯⣛⡛⠻⢶⣤⠈⠀⢸⡿⣌⣻⡧⢷⣾⢿⣄⡼⠃⣀⣄⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣈⢙⢲⡾⠥⠀⠀⠀⠀⠐⣌⠻⣧⠞⠁⢸⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⣿⠋⠈⠁⠀⠀⠀⠀⠀⠈⣿⣆⠹⡆⢀⠏⠀⠀⢸⠡⣤⡀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣷⡞⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⢆⣹⡏⠀⠀⠀⠈⠳⠞⢳⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢸⡷⣿⡀⠀⠀⠀⠀⢠⠏⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣀⣼⣿⣵⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⣿⣧⠀⠀⢀⡤⠋⠀⠀⢸⡭⢯⡙⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⣰⡾⢛⣞⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾⡇⣿⡤⠔⠋⠀⠀⠀⠀⠈⠁⠈⡇⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⣠⢄⣴⢾⣿⣿⣾⠟⠛⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⣯⠀⢛⠻⡶⠛⠳⢦⡀⠀⠀⠀⢀⡇⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡴⠋⢀⡾⣣⠋⠟⡽⠃⠀⢸⣧⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢰⠏⠸⠈⡞⡆⢷⡀⠀⠀⢿⡀⠀⠀⡼⣸⠃⠀⢀⣴⠞⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⢠⠎⠀⠀⡾⠁⠀⠀⣼⠃⣜⣄⠀⡏⣯⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠟⠀⠀⢻⠃⠈⠻⣿⡆⠀⢸⣧⠀⡴⣿⣧⣤⡾⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣸⠃⠀⢰⢠⠇⠀⣼⡏⠀⠁⢻⡆⠀⠀⣀⣀⣀⡀⠀⢠⠏⠀⡆⢠⠘⠐⡄⠀⠈⡇⠀⠈⣻⡟⣡⡿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⡟⢀⡟⠀⠀⡿⢸⡟⠀⡇⠀⠀⠀⢈⡷⠞⠉⠀⠀⠀⠈⠙⠻⣄⡾⠀⠸⠀⠀⣧⢀⠀⢹⠀⠀⡟⢤⡟⠁⠀⠀⠀⠀⠀⣰⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢸⠃⠀⢸⡏⣼⠁⠀⠀⠀⠀⢀⡞⠀⠀⢀⣠⠤⢤⣀⠀⠀⠈⢦⠀⠀⢀⠀⠃⠘⡄⢸⢀⡼⣱⣾⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣾⠀⠀⢨⢇⣿⣦⠀⠀⡆⠀⡞⠀⢀⠞⠁⠀⠀⠀⠀⠙⢦⠀⠈⡆⠀⡿⠀⠀⠀⡇⠈⣿⡴⣿⠿⠶⣄⡀⠀⠀⢠⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⡟⠀⠀⠸⣈⠈⠈⣆⠀⢣⠀⣇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⡇⠜⠁⠀⠀⢸⠁⡀⠈⠿⢦⣠⡀⢿⣷⢀⣴⣿⠗⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢿⠀⠀⣇⡏⠰⡄⢫⠀⠈⠦⠘⣆⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⡼⠀⠀⠀⠀⠀⡜⠀⡇⠀⠀⣸⣿⡇⢸⣿⢏⡞⢁⡇⡠⠀⠀
⠀⠀⠀⠀⠀⢸⠁⠀⢀⡴⠋⠀⠀⢸⡴⡄⢻⣿⡀⠈⠀⠳⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣠⣾⠟⠁⠀⡀⠀⠀⢠⠇⢠⠃⠀⢀⡟⣼⠁⠉⣡⣏⣠⣮⠜⠁⠀⠀
⠀⠀⠀⠀⠀⢸⢀⡴⠋⠀⠀⠀⠀⠀⣷⢳⡘⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠐⠋⠉⣀⡠⠀⠼⠁⠀⠀⡿⠀⡜⠀⠀⢸⣷⢏⡄⠀⣿⡿⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠟⠀⡀⠀⠀⠀⣀⡤⣿⡆⢣⡇⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠼⣫⡖⢀⡄⠀⠀⣰⠇⣰⠃⠀⣠⣿⠟⢉⣠⡾⠋⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠏⣠⠞⠁⠀⣠⠞⣡⠞⢹⣇⠀⡇⠀⢣⠀⠀⠠⡀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡽⣋⠀⢀⣴⣿⣰⣃⡴⠞⢁⣠⣾⣿⠏⠀⠀⠀⡴⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠞⠁⠀⢀⡼⠁⡰⠁⠀⢸⣿⡀⢧⠀⡈⣇⠈⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢈⣵⣤⣽⣥⣿⡿⠟⣀⣴⣿⠟⢩⠋⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠏⠀⠀⠀⡜⠀⢠⡇⠀⠀⠈⣧⢣⣸⣸⣷⡘⢦⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⡿⣿⣽⣟⠻⣶⣾⣿⣿⠏⢠⠇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠏⠀⠀⠀⠸⡇⠀⣀⡭⠭⣝⣦⠸⡆⢻⣿⡻⠁⣠⣼⡿⣟⢦⡀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣧⣿⣧⢹⢻⣿⣿⡿⢻⠀⡎⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⠀⠀⠀⠀⠀⠈⠉⢁⣠⠖⠚⠻⠶⠿⣾⣿⣧⣴⣯⢻⣿⢹⣶⡜⣿⡛⠛⠛⠉⠉⠉⠀⢁⣿⢹⣿⢹⡟⣸⡿⠁⠸⡴⠃⠀⠀⢀⣴⡟⠁⠀⠀⢀⣠⠶⠁
⠀⠀⡇⠀⠀⠀⣀⡀⢀⡴⠛⠒⢤⣤⣀⣀⠀⠀⠻⣟⠛⢻⣿⣿⣿⣯⣟⣻⣆⣀⣒⡦⣄⣀⣾⠟⠿⠿⢻⣿⣰⣟⠳⣦⠀⢁⣠⢤⣾⠛⣱⣅⣤⣴⠾⠛⠁⠀⠀
⠀⠀⢻⡀⢠⠋⠀⣱⠏⠁⠀⢠⠎⠀⠀⠀⢹⠀⠀⠹⡿⢿⣿⢿⣿⣯⣽⠉⠁⠈⠉⠉⠛⠋⠁⠀⠀⢀⠘⢁⣿⣽⠏⣩⣉⣥⠴⠶⢿⣩⡽⠟⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠳⠾⣠⣞⣇⠀⠀⠀⠈⠀⠀⠀⠀⠸⣦⠀⠀⣷⠘⢿⡀⠟⠛⠁⠀⠀⠀⢸⠀⠀⠀⢀⣼⣵⠋⢀⣾⠛⠛⠛⣉⡁⡇⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⡿⠴⣿⠀⠀⠀⠀⠀⣠⢴⣶⠦⢽⣶⣠⣏⠀⠈⢳⣠⠀⠀⠐⣰⢃⣏⡔⢀⠆⢁⣴⠟⢁⡾⢹⠀⣰⠋⢀⠇⣇⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡜⢸⡇⣠⡾⠀⣰⡅⡠⢊⣴⡯⢀⠰⣷⣍⢉⠛⢧⠀⢆⠹⣇⠀⠀⡿⠞⠋⢀⠞⠀⠋⢁⢮⡞⠁⢸⠀⣿⢠⡞⣠⡟⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣤⣇⠈⠻⣵⠃⣴⢏⡽⠃⣾⠏⣰⣿⠟⣩⣿⣿⣷⡿⢇⠈⣆⠘⢆⠀⡇⢀⣴⢿⠏⡰⢠⣿⡟⠀⠀⢸⣼⣁⡈⢹⠃⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣻⣿⣿⣶⠋⡰⠿⠀⠀⠀⢸⡔⢷⣿⡾⣿⣸⣿⠟⡄⢿⡄⠘⣧⠈⠳⠃⠀⣠⢋⠞⠀⣻⡏⠀⠀⢀⣼⠁⢻⢃⠾⡄⢶⠅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡉⠻⣿⣿⡏⡜⢡⠇⢰⡀⠀⠀⢱⣤⣤⣽⣿⢿⡿⡄⢱⠈⢷⡄⠋⢧⠀⠠⠾⣿⠋⠀⣴⡏⠀⢀⡰⠊⢸⠀⢼⢼⡓⣻⣏⢰⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣈⣿⢤⡼⣿⣧⣟⠛⢲⣾⠁⠀⢀⣠⣿⣿⡟⠀⣸⢷⠸⡀⢇⠈⡿⡆⠀⢳⣄⡴⠃⠀⣴⣻⣧⠔⠋⠀⢀⠸⠀⢸⠘⢿⣯⢹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⣿⣿⣈⣻⣿⣿⣄⣴⣫⣄⣰⡯⡽⢷⣿⡇⠀⣿⢿⡆⠱⡘⡄⢇⢸⡄⢸⣿⠃⢀⡞⢹⣿⡧⠄⠀⠀⣠⠟⣳⣾⡀⠈⠻⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⡻⢿⣿⡟⠚⢻⣷⣿⣷⢣⣻⣿⡇⢀⠟⣌⣷⡀⢻⣷⢸⢸⠃⢸⠇⣰⡏⠇⢸⣿⠁⠀⠀⠀⢻⣿⣿⠟⢉⡙⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣹⣿⣮⣣⡱⣤⣾⣿⢿⣿⣶⣿⢿⣧⢮⠀⢹⠃⢧⠈⣿⣯⡿⠀⣼⢟⣽⠀⡀⣸⡏⠀⠀⠀⠀⣼⣉⡠⠤⠤⢽⠙⣎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠫⠭⣬⣿⣟⣿⢋⡜⢻⡿⢡⡿⠀⠀⣏⣼⠀⣼⠀⠈⣧⢸⢿⣿⡘⠹⣽⣿⠀⣷⡿⠀⠀⠀⠀⠀⣟⠒⠤⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠉⣹⢟⡞⢱⡼⣱⣿⣿⡄⠀⣿⣽⢠⣿⠀⠀⣏⣾⣦⢹⣧⠀⢘⣿⢰⣿⠁⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡇⡸⠀⡼⢻⠏⡟⢿⣟⠃⠸⣿⡿⢻⠀⢸⣿⣮⡈⣿⠻⣦⣼⢿⣸⡏⠀⠀⠀⠀⠀⠀⠀⢨⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⡿⠇⢰⠃⢸⠀⡇⠈⡏⠀⠀⠙⠁⢸⡆⢸⣯⣿⣇⡼⠀⣿⡟⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⠀⢀⡇⠀⣿⢀⣇⡀⡇⠀⠀⠀⠀⢸⡇⢸⣧⢿⣷⡇⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣾⡼⠀⠀⢿⡞⡷⠽⣿⠀⠀⠀⠀⠈⣇⢸⣿⡎⡏⣧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆