⠀⠀⠀⠀⠀⠀⡤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠒⠀⠴⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠒⢠⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢆⠄⠀⢀⠬⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠰⠁⠈⠳⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢋⡆⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢜⡄⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⢀⢎⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢄⡱⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⢐⠴⠊⢠⠃⠀⡀⠀⠀⠀⠀⠀⠀⡠⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠏⠢⡀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢆⠉⠢⢄⠄⡀⠀⠀⠀
⠀⠀⢀⠬⠊⠁⠀⠀⠆⠀⢠⠃⠀⠀⠀⣀⣀⠜⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠑⡄⠀⣀⡀⠀⠘⡄⠀⠀⠈⡆⠀⠀⠉⠪⢄⠄⠀
⢠⠊⠁⠀⠀⠀⠀⢸⠀⠀⡌⠀⠀⠀⠀⠀⡜⠉⠉⠒⠒⢧⠀⠀⠀⠀⠀⠀⡇⠒⠒⠊⠙⡅⠀⠀⠀⠀⢱⠀⠀⠀⢱⠀⠀⠀⠀⠀⠁⢠
⠁⠉⢒⢄⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⢀⣸⣀⠀⠠⠤⠤⠬⠆⠀⠀⠀⠀⢸⠠⠤⠤⠤⠀⢘⣀⣀⠀⠀⠈⡄⠀⠀⠸⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠈⠊⠢⡀⡇⠀⠀⡀⠀⠀⠀⠀⣏⣈⠉⠉⠉⠉⠉⡍⢆⠀⠀⠀⡌⡏⢙⠉⠉⠉⠁⠈⠀⠀⠀⠀⡇⠀⠀⠀⢀⢤⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⡇⠀⠀⠀⢠⢇⠀⠀⠀⠀⠀⢠⠀⠀⠑⢄⠀⠇⢇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡁⠀⠀⠀⡧⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡼⡀⠀⠀⢸⠘⣄⠀⠀⠀⢀⠞⠀⠀⠀⠀⠉⠀⠘⡄⠀⠀⠀⢀⠎⡇⠀⠀⡜⢣⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠀⠱⡀⠀⠘⠀⠈⠑⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠁⠀⡇⠀⡰⠁⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣇⡞⠀⠀⠀⠈⠢⡀⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⢃⠜⠁⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢈⡳⠁⠀⠀⢀⡀⠀⠈⠃⠑⠦⣀⠀⠀⠀⠀⠉⠐⠒⠈⠁⠀⠀⠀⢀⠤⠊⠀⠁⠀⠀⡀⠀⠀⠀⢷⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣢⠁⣀⠠⢔⠭⡣⡀⠀⢘⢤⡀⠀⢩⢒⣂⡤⠤⢤⡤⠤⢤⣔⣒⡭⠁⢀⡠⠚⠀⢀⡜⠭⢢⠄⣀⢈⣟⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⡢⢼⡀⠈⢹⠊⠁⠀⡏⢒⡞⢹⣶⢺⠀⠈⠉⡎⠁⠀⣦⢔⡪⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠓⠀⠮⢶⣺⢶⠀⢘⡷⠁⡼⢿⠈⢂⡎⠀⡰⣗⡶⠽⠎⠒⠒⠪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡊⠀⠀⠀⠀⠀⢀⠾⠤⡋⡞⡲⠤⡇⠸⠤⢰⠳⠙⡠⠕⡄⠀⠀⠀⠀⠀⠈⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡢⣀⣀⡤⡴⠁⠀⡰⢁⠜⠀⢠⠀⠀⠇⠀⠑⣍⢢⠀⠈⠢⡤⣀⣀⡠⡪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⠕⠉⠀⢀⠞⠀⠈⠉⠢⡌⠀⠀⠰⡔⠉⠉⠀⠑⡄⠀⠈⠢⡑⠪⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⢠⠢⠊⠁⠤⠬⢦⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡤⠧⠤⠄⠑⠵⣠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣪⢍⠑⠤⡀⠀⠀⠈⡆⠀⠀⠀⣀⠤⢄⠀⠀⠀⠀⠀⠀⣠⠤⣀⠀⠀⠀⢀⠃⠀⠀⢀⡠⠒⣉⠕⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠕⡢⣈⠢⠤⣀⣱⢠⣶⣭⠤⣀⠀⠳⢄⠀⠀⢀⠜⠁⣀⠤⣭⣶⡤⣘⣀⡠⠔⣋⠤⠪⠁⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠁⠒⡟⠥⠀⠤⡙⡦⡑⢄⡀⠑⠔⢁⡠⢞⣕⢋⡤⠄⠬⠹⢒⠀⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠑⡸⡊⠒⠀⠉⠉⠁⠲⠝⣻⠈⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠣⢄⣀⣀⢔⠑⠀⠀⠀⠀⠀⠀⠀⠀⠱⢳⢄⠀⠀⢔⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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