⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⠉⢹⣿⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣿⡿⠟⢻⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⣓⡦⣤⡀⠀⢨⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⡎⠀⣴⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⣾⣩⣿⡆⢻⠳⣾⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡜⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠁⠈⡇⠈⡿⣷⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡼⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢈⢀⡀⠀⠀⠀⢸⠋⢻⠀⢰⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡜⡇⠀⢀⡟⠁⠉⣷⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠸⠦⣼⠀⢸⣾⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠞⣄⡀⠀⠈⠷⣄⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⣠⣾⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠉⠁⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣥⣾⣿⣿⣿⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠹⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⣀⡤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠏⠀⠀⠀⠀⠀
⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢾⠀⠀⣾⠃⣄⠄⠀⠀⠀⠀⠀⢡⠀⠀⢀⠀⠀⠀⠀⠀⠀⡘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢦⠀⠀⠀⢀⡠⠖⠋⠁⠀⡇⠀⢸⢺⠀⠘⣆⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⠀⠀⠀⠀⢰⠃⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢣⡤⠚⠁⠀⠀⠀⠀⠀⡇⠀⠘⡞⠀⠀⠈⢣⡀⠀⠀⠀⠀⢱⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⠖⡇⠀⠀⠀⠀⠙⢄⠀⠀⣀⡎⠀⠈⡄⠀⠀⡰⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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🖤⛓🐼⛓🖤
🖤✝🥀⛓️(your name here)⛓️🥀✝🖤 May death never stop you.
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀
⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀
⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⣠⠔⠚⠉⠉⠲⢦⣤⡴⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢾⣯⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⡞⠁⠀⠀⠀⠀⠀⠀⢹⣧⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠤⣤⠆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⢀⣤⣖⣿⠏⠉⠿⣷⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢶⣶⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠉⠀⠀⠀⢀⣘⠿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠈⠂⡄⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⢀⣠⡴⠞⠉⠉⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠢⠀⠁⠀⠀⠀⠀⣼⣿⡏⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣄⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡞⠀⠀⢀⣠⢤⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠟⠀⠀⣾⣭⣿⣿⣿⣿⣶⣦⣝⡓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⢟⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⢀⣤⠀⠀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠑⠫⢝⡛⠿⡿⢿⣿⡡⠖⠁⠀⠀⣈⠛⠶⢤⣀⡀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠁⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⣿⡿⠀⠀⠀⣠⡾⠋⠀⠀⠀⠛⠹⠯⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⡟⠅⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢈⡦⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡞⠁⠈⠳⣤⣄⡀⠀⠀⠀⣿⣟⠀⠀⣾⠃⠀⠀⠀⢀⡔⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡔⡼⠁⠀⠀⠀⠈⠒⠢⢤⣦⣴⣿⣿⣄⣸⣟⠀⠀⢀⣤⢾⡄⠀⠘⠛⢷⠀⠀⠀⣀⣠⡤⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠊⣼⠁⠀⠀⣀⣤⣤⣤⣴⣿⠋⠀⠀⠙⠿⢧⣉⣙⣛⣻⣄⠀⠉⠀⠀⢰⠟⠒⠛⠩⠰⠂⠀⢻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⣸⡃⠀⣰⡾⠋⠁⠀⢠⡟⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢦⡀⠈⣷⡀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠖⠒⠛⠟⠛⣿⢿⡄⠀⠀⠀⠘⠿⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠘⢧⡀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣿⣷⠀⢐⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠛⠹⢿⣼⣟⣿⣏⡟⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢻⡇⠀⠀⠀⠘⣿⣶⠟⣟⣷⣉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢼⢀⠺⣷⠀⠈⠀⠀⠈⠿⣯⣻⢅⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣥⡶⣶⠶⣶⣦⡀⠀⠀⠊⢂⠀⠙⢿⣅⡀⠄⠀⢀⠈⠉⠛⢻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⢠⠂⠠⣴⡿⢋⢁⠀⠄⡀⢠⠀⠌⠻⠶⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠶⠶⢦⣴⣾⣃⣀⠂⠀⣄⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠂⠀⣼⠟⢂⢨⣶⣿⣿⣿⣶⣜⠀⠂⠙⠒⡀⠒⢀⠡⠈⠁⠌⠁⠌⡀⠂⠄⠠⢀⠉⠙⢛⠾⡏⠑⠀⠠⠈⠉⡙⠿⣦⣠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⢰⡿⠀⠈⣾⣿⣿⣿⣿⣿⡯⠀⠂⠄⠂⡁⠠⠌⢀⠂⡐⢀⠐⡀⢁⠂⠄⠂⡈⠐⡀⢈⠰⠁⡐⣤⣤⣦⣀⡁⠄⠻⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⠀⢸⣧⢁⠂⢻⣿⣿⣿⣿⡟⠁⠠⠁⡈⠐⢀⢠⣴⣀⠠⣀⣂⠠⠐⠀⡈⠐⠄⠠⢁⠠⠠⠀⠂⣿⣿⣿⣿⣿⣿⡤⡅⠘⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⡿⢽⠂⢌⠠⣬⠉⡉⢁⠠⠈⠄⠐⡀⠡⠠⠀⠉⠛⠛⠉⠛⠳⠶⠿⠗⠀⡈⠄⠠⠀⢂⠁⡀⢿⣿⣿⣿⣿⣿⠏⠀⠄⣿⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣾⠏⠔⠢⡘⠄⡒⠠⢁⠰⠀⠁⠠⠈⠐⠀⡐⠀⡁⠃⠄⠡⢈⠐⠁⠂⠠⠀⠌⠀⠂⠄⡁⠂⠄⠠⢀⠙⠛⠟⠛⠋⠄⠡⢲⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⡿⠡⠌⡈⠳⢀⠃⠌⡡⠈⠄⡈⠄⠁⡐⠈⡀⠄⠑⠀⠒⠈⠀⠀⠂⠈⠂⠡⠈⡀⠌⠐⠠⢀⠡⢈⠐⡀⠆⠡⠌⡑⠌⡌⠡⢻⣷⡀⠀⠀⠀⠀
⠀⠀⠀⣸⡟⢁⠂⠌⠄⡁⠂⠌⡐⠠⠁⠂⠄⠰⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠄⠡⢀⠂⠄⢂⠐⡈⠡⠊⠔⡡⢌⢁⠣⣼⣷⡀⠀⠀⠀
⠀⠀⣰⡟⠀⠌⢈⠰⠐⠀⡁⠂⠠⠁⢠⠁⠈⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⢀⠠⠐⠀⠀⠠⠀⠀⠂⠰⠈⠄⠂⡀⠑⢈⠒⠠⠂⠆⠡⠄⢹⣷⠀⠀⠀
⠀⢠⡟⢀⠂⠌⠠⠀⢂⠁⠠⠀⠡⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⢡⠈⠐⠠⢁⠂⡈⠤⠑⡈⠐⠠⢀⢻⣇⠀⠀
⠀⣿⠁⡄⢂⠈⠠⢁⠀⢂⠠⢁⠠⠁⠀⠀⠀⠁⠀⠀⠐⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠄⠀⠢⠁⠂⠄⢂⠐⠠⠐⠀⠡⠀⠂⢸⣿⠀⠀
⢰⡇⠂⡔⠠⢈⠐⠠⠈⡀⠐⡀⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⡀⠠⠀⠀⢃⠈⡐⠠⢈⠐⡈⠄⠂⠡⠈⢀⢻⡇⢀
⢸⡇⠒⡠⢁⠂⠌⠐⡀⢀⠡⠀⠂⠀⠀⡀⠀⠀⠂⠀⠀⠀⡀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⡀⢀⠂⡐⢀⠂⠄⠠⠐⢈⠀⠌⠠⢘⣿⡀
⢸⡇⢂⡑⢂⠌⢠⠁⡐⠀⡐⠠⠁⠀⢀⠀⠀⠂⠀⠀⡀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠐⠀⢀⠐⠀⠀⠀⠁⠀⠀⠀⢀⠂⠄⢂⠈⠄⢡⡀⠂⠄⡘⠀⡉⢹⣧
⠸⣇⢂⠣⢌⡐⢢⠐⡀⢂⠐⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⡀⠐⠈⠄⠂⠌⡐⠘⢿⣤⠂⠠⢁⠐⠨⣿
⠀⢿⡆⡑⢢⠐⡡⢂⠑⠢⡐⠠⢈⠀⠀⢂⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠄⠂⠀⠀⢈⠐⡈⠰⢀⠐⡈⢈⠻⢶⣅⣢⣬⡷⡏
⠀⠈⢿⣴⠁⡊⠴⢁⠎⡁⢆⡁⢂⢉⡀⠄⠠⠀⠀⠀⠈⠀⠐⠈⠀⠠⠀⠈⠀⠀⠀⠀⠠⠀⠠⠀⠀⡁⠀⠀⠀⡁⠊⠐⠠⢁⢂⠐⣀⢂⠡⠂⢍⢹⡿⠠⠀
⠀⠀⠈⢻⣾⡤⢉⠦⡘⡐⠢⠘⡄⢢⢁⠂⠄⠡⠈⢀⠁⠌⠀⠄⠁⠀⠄⠀⠀⠀⠀⠀⠀⠄⠠⠀⢁⠀⠌⠀⡈⠡⢈⠔⡁⠢⠈⡔⣀⠢⢁⡉⢢⡿⠁⠠⠀
⠀⠀⠀⠸⠟⢷⣌⡄⢃⡑⢂⠆⡱⢈⠜⡒⢄⠂⡐⡈⢄⠀⡐⢀⠂⡐⠀⠄⡐⠀⠐⠠⠀⠄⡀⢄⢈⠀⡀⡄⠣⢀⠌⡄⢡⠂⢆⠡⡉⠔⡊⢡⣾⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠹⢷⣦⡌⢂⠩⢄⠣⢌⠰⠉⠴⣀⠐⢂⢂⡐⢂⡐⠠⢁⠂⡐⢈⠐⣀⠂⠄⡠⠀⢄⠢⡐⢄⠣⢌⠢⠌⣂⡩⢀⠣⢘⣠⣵⣟⣁⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣮⣄⡊⢄⠣⢉⠒⡌⢊⠔⡠⢐⠠⠄⡁⠂⠔⡀⢂⠡⠀⢌⡐⢄⠣⢌⠢⡑⢌⠢⢌⠢⡑⣌⣻⣦⣵⣾⣿⣿⣿⣿⣿⣶⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠧⣬⣔⠉⡜⢠⢃⠒⠤⢁⠑⢂⠐⠡⢠⠉⡤⠘⡄⢃⠆⡱⢈⠢⡑⣨⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣎⠄⢃⡌⠬⡑⡈⢶⣾⣦⠃⡅⢊⠔⡡⡘⢄⢊⣴⠿⠛⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠻⣧⣊⢄⠣⣐⣡⣿⡙⣿⡌⡐⢡⠊⠔⣡⣮⡿⠋⠀⠀⠂⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢙⠛⠛⠛⠋⠁⠀⢘⠛⠷⢶⠾⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⣾⡯⠉⠉⠉⠉⣹⣿⠄⠀⠿⡀⠁⠀
⠐⠀⠂⠔⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀