⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⡰⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⣿⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⠁⠀⠀⠀⣿⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⡧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠤⠖⠒⠒⠚⠛⠉⠉⠉⠓⠲⠤⢄⡀⠀⣀⣰⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡿⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠛⠁⠀⠈⠋⠭⠛⣒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠲⡻⣿⡇⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⣨⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣇⠸⣄⡇⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀
⠀⠀⢱⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣉⣁⣠⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣆⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠘⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣦⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣻⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡜⠀⢞⡞⢹⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠉⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡾⣿⠀⠀⠀⠀⢀⢾⠀⠀⠀⠀⢀⠇⣼⠏⠉⠙⣧⠀⠀⠀⠀⠀⠀⢀⣿⠉⠉⣷⡄⠀⠀⠀⠀⠀⠀⢻⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⣾⠋⠀⣿⠀⠀⠀⠀⠎⢸⠀⠀⠀⠀⢸⣼⠏⠀⠀⠠⡹⣵⡀⠀⠀⣰⠠⡿⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡞⡟⠁⠀⠀⡇⠀⠀⡴⡜⣀⢸⠀⠀⠀⠀⣾⠏⠀⠀⠉⠁⠀⠘⠿⡤⠚⠿⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠛⢧⣀⠀⢸⠀⠀⠀⣷⠋⡠⢽⠀⠀⠀⠀⡿⢠⣶⣿⠿⠿⢿⠆⠀⠀⠀⠀⠀⢶⣶⣶⣦⣄⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢙⡏⠀⠀⠀⡿⡄⢇⠈⡀⠀⠀⠘⡇⢈⢫⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡌⡇⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠁⢀⡇⠀⡇⠘⢢⣉⡇⠀⠀⠀⢷⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢱⣁⣀⣀⠴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡄⠸⡇⠀⠇⠀⣾⡀⢹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠐⠀⠀⠀⠀⢀⡴⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢧⠀⣷⡀⢰⠀⡟⡇⠀⢣⠀⠀⠀⡗⣲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⣰⠀⢀⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢷⣟⢷⡈⣆⡇⠹⡄⠈⢳⡀⠀⢹⡟⠀⢧⠉⠁⠀⠒⠒⢲⠲⣾⣉⡝⠁⡰⠃⡴⢺⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠉⠃⠻⣾⣷⡀⢙⡿⠿⣟⣦⡀⢣⡀⠀⠙⠢⣄⠀⢀⡏⠀⠘⡄⠙⣾⣒⠉⢀⣾⡴⠋⠀⠀⢀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢦⡉⢉⡙⠒⣒⢄⠀⠉⣳⠟⠀⠀⢳⠀⠈⡏⠛⣓⣒⡦⢬⣦⣎⣤⣒⠒⠛⡍⠙⡌⠙⠯⣉⠀⢠⢔⣊⡁⢜⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢦⡈⢉⠦⠤⣑⡞⠁⠀⠀⠀⢸⠀⠀⠛⡏⠀⠉⢉⠝⣹⡏⢳⡙⠛⢳⠺⠀⢡⠀⠀⠈⠳⢧⡔⠛⢦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠒⠒⡲⠋⠀⠀⠀⠀⠀⠈⡇⠀⠀⢳⠀⠀⠧⠔⡟⡟⠜⠁⠀⠈⡇⠀⠘⡆⠀⠀⠀⠈⠻⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣞⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠸⠄⠀⠠⢰⣧⡧⠤⠤⠤⠤⠇⠀⠀⢳⠀⠀⠀⠀⢀⠜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⢻⡠⠤⠤⠤⢤⡀⠘⠙⠃⠀⢠⠖⢒⣀⠉⠑⢾⡀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⡀⠀⠀⠀⠀⠀⡼⠀⠀⡀⠉⣈⣹⡄⠀⠀⢀⣜⢋⣡⠤⠄⠀⠀⢧⣀⡠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠀⡏⠀⠈⠉⠑⠒⢲⠁⠀⠠⠤⠀⣀⠘⡇⠀⠀⠀⢹⢀⡠⠤⠚⠀⠀⠘⡆⠀⠸⣄⡠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠤⠚⡁⠆⡤⢲⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⢄⣀⡀⢳⣧⠀⠀⠀⠘⣼⠀⢄⣀⠀⠀⠀⢧⠀⠀⢿⣱⢙⣚⣑⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠑⠒⠛⠒⠒⠁⢸⠁⠀⠀⠀⠀⠀⠃⠀⠀⠠⠶⣉⣁⡞⠉⠀⠀⠀⠀⢸⣄⣬⢵⠆⠀⠀⣸⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀
⠀⠀⡜⠁⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠷⠶⠱⡄
⠀⢸⣸⣿⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠫⢀⣖⡃⢀⣸⢹
⠀⡇⣿⣿⣶⣤⡀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣠⡪⢀⣤⣾⣿⣿⣿⣿⣸
⠀⡇⠛⠛⠛⢿⣿⣷⣦⣀⠀⣳⣄⠀⢠⣾⠇⣠⣾⣿⣿⣿⣿⣿⣿⣽
⠀⠯⣠⣠⣤⣤⣤⣭⣭⡽⠿⠾⠞⠛⠷⠧⣾⣿⣿⣯⣿⡛⣽⣿⡿⡼
⠀⡇⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣮⡛⢿⠃
⠀⣧⣛⣭⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣎⡇
⠀⡸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣟⡇
⣜⣿⣿⡧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣸⣿⡜⡄
⠉⠉⢹⡇⠀⠀⠀⢀⣞⠡⠀⠀⠀⠀⠀⠀⡝⣦⠀⠀⠀⠀⢿⣿⣿⣹
⠀⠀⢸⠁⠀⠀⢠⣏⣨⣉⡃⠀⠀⠀⢀⣜⡉⢉⣇⠀⠀⠀⢹⡄⠀⠀
⠀⠀⡾⠄⠀⠀⢸⣾⢏⡍⡏⠑⠆⠀⢿⣻⣿⣿⣿⠀⠀⢰⠈⡇⠀⠀
⠀⢰⢇⢀⣆⠀⢸⠙⠾⠽⠃⠀⠀⠀⠘⠿⡿⠟⢹⠀⢀⡎⠀⡇⠀⠀
⠀⠘⢺⣻⡺⣦⣫⡀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⢜⣠⣾⡙⣆⡇⠀⠀ɪɴꜱᴄʀɪʙᴇ ʏᴏᴜʀ ꜰᴜᴍᴏ ɪɴ ꜰᴜᴍᴏ ᴀᴄᴀᴅᴇᴍʏ
⠀⠀⠀⠙⢿⡿⡝⠿⢧⡢⣠⣤⣍⣀⣤⡄⢀⣞⣿⡿⣻⣿⠞⠀⠀ ᴊᴏɪɴ ᴛᴏ ᴢᴜɴᴘᴇᴛ ɢʀᴏᴜᴘ
⠀⠀⠀⢠⠏⠄⠐⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠳⢤⣉⢳⠀⠀⠀ ᗜ‿ᗜ
⢀⡠⠖⠉⠀⠀⣠⠇⣿⡿⣿⡿⢹⣿⣿⣿⣿⣧⣠⡀⠀⠈⠉⢢⡀⠀
⢿⠀⠀⣠⠴⣋⡤⠚⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⢿⣦⣄⠀⢈⡇⠀
⠈⢓⣤⣵⣾⠁⣀⣀⠤⣤⣀⠀⠀⠀⠀⢀⡤⠶⠤⢌⡹⠿⠷⠻⢤⡀
⢰⠋⠈⠉⠘⠋⠁⠀⠀⠈⠙⠳⢄⣀⡴⠉⠀⠀⠀⠀⠙⠂⠀⠀⢀⡇
⢸⡠⡀⠀⠒⠂⠐⠢⠀⣀⠀⠀⠀⠀⠀⢀⠤⠚⠀⠀⢸⣔⢄⠀⢾⠀
⠀⠑⠸⢿⠀⠀⠀⠀⢈⡗⠭⣖⡒⠒⢊⣱⠀⠀⠀⠀⢨⠟⠂⠚⠋⠀
⠀⠀⠀⠘⠦⣄⣀⣠⠞⠀⠀⠀⠈⠉⠉⠀⠳⠤⠤⡤⠞⠀⠀⠀⠀⠀