10 Year Old Genius Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡿⢿⣿⣛⣟⣿⡿⢿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣯⣷⣿⣿⣿⢟⠃⢿⣟⣿⣿⣾⣷⣽⣺⢆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⢿⣾⢧⣏⡴⠀⠈⢿⣘⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣿⢠⡶⠒⢶⠀⠀⣠⠒⠒⠢⡀⢿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠸⣄⣠⡾⠀⠀⠻⣀⣀⡼⠁⢸⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⡔⠢⠤⠔⠒⢄⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠸⡀⠀⠀⠀⠀⢀⡇⠠⣸⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣮⣉⢉⠉⠩⠄⢴⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣟⢟⡁⠀⠀⠀⠀⢇⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠿⣿⡈⠋⠀⠀⡇⠀⠀⠀⢰⠃⢠⣿⡟⣿⣿⢻⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡆⠛⠇⢀⡀⠀⡇⠀⠀⡞⠀⠀⣸⠟⡊⠁⠚⠌⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡍⠨⠊⣒⠴⠀⡇⡴⠋⡋⢐⠐⠅⡀⠐⢠⠕⠂⢂⠀⠀⠀

new osaka azumanga daioh Osaka Oh my Gah! dot art text art ascii art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⢿⡿⣿⡿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣟⣯⣿⣿⣽⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⢺⡆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣻⣯⣿⣷⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⡿⢋⠞⠃⠀⣷⠀⠈⠻⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣿⣿⡿⠧⠤⣾⡿⢋⠤⠊⠀⠀⠀⢸⡄⠀⠀⠈⠻⣿⣿⡦⠬⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣸⣿⣯⣤⣤⣼⣏⡠⠎⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⣈⣻⣷⣤⣤⣬⣻⣧⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⢾⢏⣿⣿⣿⣿⣿⣮⣅⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⣩⣵⣿⣿⣿⣷⣮⡙⢳⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃⢠⣿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⣧⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠁⠀⠈⢷⣤⣼⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢤⣾⣿⣿⣿⣿⠟⠀⠘⠉⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⠀⣁⢐⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠟⠉⠋⠉⠋⠙⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡆⠈⡄⠀⣘⣠⡞⠁⠀⠀⢀⡀⣄⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⣰⣀⢈⠙⠛⠛⠛⠛⠋⠉⣀⣶⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣧⠉⠉⠙⠒⠛⠛⠛⠚⠛⠉⠉⢰⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠋⠁⠰⣯⠟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⢺⣡⡆⠀⠈⠻⢿⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠊⠉⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⠑⠲⢤⣄⣂⣈⣐⣀⣀⣠⣟⣀⠤⠔⠒⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡒⣒⠲⣒⢒⢲⣶⡒⠖⡲⢶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢠⣣⠔⡊⠖⢫⠘⡴⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣇⢻⣿⣿⣿⣿⡢⣀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⠈⣧⠳⡘⠴⡉⢆⠽⣿⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢛⣿⠿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢄⡾⣣⢁⡛⢣⢉⡻⡿⢿⣷⢦⣉⠓⢒⣊⣭⡭⢀⡏⠀⠀⠀⠈⢳⣱⡢⠑⡌⡿⠁⠀⠀⠀⠀⢀⡇⠨⣭⣖⠢⣼⣿⣿⠿⠋⣄⣾⠏⡒⣽⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡟⢚⢄⡒⢌⢂⠣⡑⠤⡃⢍⠣⡌⢍⣃⢲⣏⡀⠸⠤⣀⣀⠀⠀⠀⠹⣦⠣⣼⠃⠀⢀⣀⡤⠤⠚⢁⣀⣷⠄⢿⡟⢫⢁⠎⡱⢌⠡⢃⠜⣘⡹⣇⠀⠀⠀
⠀⠀⠀⠀⣰⠏⣷⡃⢆⡘⠤⢃⣌⡇⠖⡩⢌⠢⣑⠊⡔⢢⢒⠩⣉⠓⡒⠦⠭⠭⢥⣒⣚⣻⣗⣈⠭⠥⢖⢒⡚⠩⡍⡒⢤⡉⠆⡍⢒⠌⡒⣡⢊⡴⢃⠜⣠⢑⡼⠀⠀⠀
⠀⠀⠀⣰⢫⢰⣉⣿⡌⣴⣁⢣⣼⡏⡜⢰⣈⢱⢠⢩⣐⢡⢊⢱⢠⡍⣰⢉⡜⣤⢓⢸⣏⣀⣀⣿⡘⢢⢡⡒⣌⡑⣆⡑⢢⣌⢱⣈⣬⡘⣤⡁⣎⡟⡌⢢⢡⣾⢃⠀⠀⠀
⠀⠀⢰⡟⡏⠷⡙⢎⣿⡶⡉⢇⣿⡷⢙⠳⡉⠇⡎⢳⠉⢇⢋⠞⢳⢁⠳⠞⡁⢇⠞⡸⢹⡟⣿⡏⢇⡎⠷⡙⢎⡹⢈⡹⢃⠞⡰⣉⠆⢳⠆⢳⡘⣿⡁⡏⣾⠇⢏⠀⠀⠀
⠀⢀⡾⣥⢋⠴⡁⠆⣿⣷⣱⣿⣻⡇⢎⠰⡁⢎⠰⡁⢎⠢⢌⡘⠄⡎⠱⡨⢑⠌⡢⠅⣿⡇⣻⣏⠦⡘⠰⡉⠆⡔⢣⢐⡡⢊⠔⡰⢨⡁⢎⡡⢘⣿⣷⣼⡟⣌⠢⠀⠀⠀
⠀⢸⢇⠹⢌⠢⢅⠓⢾⣟⡿⣷⣿⠇⡊⢔⠡⡊⢔⠡⡊⠔⢢⠘⡰⢈⡱⢐⡉⢆⠡⢍⣿⢦⢙⣿⢂⡍⠱⡘⠌⡔⢡⢂⠒⡡⢊⠔⡡⡘⢄⡒⡡⣿⣿⣿⠒⡄⢣⠀⠀⠀
⠀⣿⢂⠣⢌⠣⡘⢌⠺⣿⣽⢻⣿⢀⠓⡌⢒⠡⢊⠒⡡⡉⢆⡑⢢⢁⠦⢡⠘⠤⣉⢺⣟⢸⡌⣿⡆⡌⢱⠈⡜⢠⠃⡌⢒⠡⢊⠔⡡⡘⢄⠆⡱⣿⢯⡽⢃⠜⡠⠀⠀⠀
⢠⡇⢎⢂⠧⢌⠱⡈⠜⣿⣞⣯⡗⢨⡘⠤⢃⠥⢃⡱⠤⡑⢢⠘⡄⡊⠔⡡⢊⠔⡤⢻⡏⡤⡇⢿⡧⡘⢄⠣⡘⢄⠣⡘⠤⡉⢆⠚⠤⡑⢊⡔⢡⣿⣻⡏⠴⡘⠰⠀⠀⠀
⣼⠓⡌⡒⢌⣂⠣⡉⢆⡹⢯⣷⡏⠔⡨⢒⡉⠆⠥⢂⡱⢈⠆⡱⠠⢅⠓⡄⢣⠘⠤⣿⡇⢇⡹⢸⣷⢁⠎⡰⢁⠎⡰⢁⡒⢡⠊⡜⢠⠃⡥⠘⠤⣿⣳⡟⠤⡑⢃⠀⠀⠀

new osaka azumanga daioh dot art text art ascii art

⠀⠀⠁⢄⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠉⠓⠚⠉⠉⣽⠟⠋⢉⡿⠋⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠐⠷⣿⡄⠀⠀⣠⣾⠟⢩⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⡿⠁⠀⠀⣸⠁⠀⠀⠀⠀⣼⠉⠉⢻⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠓⣦⡀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⡟⠀⠀⠀⠀⠀⠀⣿⢸⡀⠀⠀⠀⠀⠀⠿⠇⢠⢾⣿⠋⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⣼⡿⠀⠀⢀⡴⠃⠀⠀⠀⠀⢀⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣦⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠛⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣇⣴⠞⠉⣻⠀⠀⠸⣞⡇⠀⠀⠀⠀⠀⢀⡴⢋⡾⠁⢀⡞⠀⠀⠀⢀⣠⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣿⠀⣼⡟⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⣸⠁⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠙⣷⡀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠛⠁⠀⢠⡏⠀⠀⢀⣿⠃⠀⠀⠀⠀⢠⠟⢀⡞⠁⠀⢸⠃⢀⣴⠞⠋⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⡤⢏⣾⠏⣼⡟⠀⢀⡼⠃⠀⣀⠀⠀⠀⠀⢀⡏⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠸⠿⠀⠀⠀⠀⣴⠋⢀⡾⠀⠀⠀⢸⣴⠟⠁⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⠾⠋⢀⣾⠃⢰⡿⠀⠀⡾⢀⡴⠛⠉⠇⠀⠀⠀⣼⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠹⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⢀⣤⡄⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⡾⠁⠀⠀⢀⣠⡴⠖⠶⣄⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⡔⠁⠀⢀⣾⠃⠀⠙⢿⣆⠀⠓⠋⠁⠀⠀⢶⠀⠀⢀⡏⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢻⣧⡏⢠⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢸⠃⠀⢀⡴⠛⠁⠀⠀⠀⣾⠀⠀⣠⡞⠁⠀⠀⢀⡴⠋⠀⠀⠀⣼⠏⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⣀⣼⠀⠀⣸⠁⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⢀⣤⣾⠟⠛⠋⠸⣿⢀⡾⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⠀⣴⠋⠀⠀⠀⠀⢀⡼⠃⢀⣴⠋⠀⠀⠀⣴⠋⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⣸⣿⠁⠀⢠⡏⠀⠀⣼⢿⠀⠀⢀⣀⣤⠤⠶⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡿⣧⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⣸⠃⡾⠀⠀⣤⡄⠀⠀⠀⠀⢐⠃⠀⠀⠀⣿⣸⠃⠀⠀⠀⠀⢀⡾⠁⣠⠞⠁⣀⠀⢠⡞⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢠⣾⠋⠀⠀⠀⣰⢿⣿⠀⠀⣼⠁⠀⣰⡏⠈⠛⢛⣉⡁⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡗⢿⣦⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⢠⡏⣸⠃⠀⠸⠿⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡾⠀⣴⠋⡠⡾⠁⢠⠏⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣰⡿⠁⠀⠀⢀⡼⠃⠈⠉⠀⢠⡇⠀⢰⣿⣤⠶⠚⠋⠉⢹⡇⠀⠀⠀⢀⡼⠁⢰⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⣷⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⡌⠻⣷⣾⡏⠀⠀⠀⠀⠀⠀⠀⣾⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣼⠁⣸⢣⡖⢱⠇⢠⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⡿⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⣇⣀⡴⠟⠚⠛⢲⡄⠀⣼⠃⠀⠀⢀⡾⠀⠀⢸⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣿⣠⣶⠟⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⣿⠁⢀⣤⠖⠋⠻⣦⢠⡇⣸⠁⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⣆⠀⠀⢰⠏⣰⣷⠏⠀⢸⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠟⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⡇⢠⡏⠀⠀⠀⡼⠀⠀⠀⠘⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡿⣰⣏⣤⣤⣤⡀⠘⣾⠀⡟⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⣾⢠⣿⠃⠀⠀⠘⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣼⡟⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣄⠀⠀⢀⡾⢀⡾⠁⠀⠀⢰⠇⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣿⣿⣇⣿⡏⠀⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠘⣷⠟⠋⠁⠀⠈⠻⣦⣸⢰⡇⠀⠀⣇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⢀⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⡤⠖⠋⠁⠀⢰⠃⠀⢠⡟⠀⣼⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⢀⣼⡟⢹⡏⣟⠀⠀⠀⠀⠀⢀⣾⣹⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠸⡷⡆⠀⠉⠁⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⡿⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⡟⠀⢠⡟⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⢀⣤⢾⣿⣏⣀⣸⣧⣿⡆⠀⠀⠀⠀⣼⡟⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⢀⣤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠠⠇⣠⠞⠁⠀⠀⠀⣀⣀⣀⣘⡃⠀⡾⠀⢰⡏⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⣴⢏⡁⠈⠛⠛⠛⠛⠻⣿⡇⠀⣀⣠⣾⠟⢠⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣇⣤⡴⢶⣾⠟⠛⠛⠉⠛⠿⣶⣄⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⣰⡟⠉⠈⠉⠛⢿⣝⠳⠦⣿⣀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣰⠋⠀⣠⡞⠁⠈⢧⣀⣀⡤⠶⡄⣰⣿⣷⡿⠟⠋⠁⠀⢸⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣧⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢹⡀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠉⠛⢦⡀⠀⠀⠀⠻⡄⠀⠀⠀⢰⠃⠀⢸⡏⠀⣀⣠⣤⣤⣄⣀⡼⣵⡿⠛⠁⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡾⣧⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⠀⠀⠸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢀⣴⠞⠁⠀⠀⠀⠀⣀⣤⢠⡀⠀⠀⢻⡀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢀⡖⠦⣄⠀⠀⠀⠈⠳⣄⠀⠀⠙⢦⡀⠀⠀⠘⣦⠀⠀⢸⡄⠀⠘⠛⠋⠉⠀⠀⠀⠈⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡀⢹⣦⠹⣧⣤⣤⣤⣤⡀⠀⣼⠃⢸⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢀⡴⠛⠁⠀⠀⢀⣠⠖⠋⠉⠀⠀⠹⡄⠀⢸⡇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⡞⠀⠀⠈⠳⣄⠀⠀⠀⠙⢦⡀⠀⠈⢳⡄⠀⠀⠀⠲⣤⡀⠙⠳⠤⠖⣻⠀⠀⠀⢀⡾⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣏⣷⠈⣿⡄⠀⠀⠀⠀⠘⣿⡀⣿⠀⢸⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣰⠟⠁⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⣷⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢀⡞⠁⠀⠀⠀⠀⠙⢦⠀⠀⠀⠈⢳⡄⠀⠀⢻⡄⠀⠀⠀⠈⠻⡄⠀⠀⠀⡟⠀⢀⣴⠟⣴⡟⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀
⣃⠀⠀⠀⠀⠛⠟⠁⠘⣿⣄⠀⠀⠀⠀⢸⣧⣿⠀⢸⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠃⢠⡞⠁⠀⠀⣠⡾⠉⠀⠀⠀⠀⠀⣠⣴⡾⢻⡾⡆⠀⢿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢀⡾⣰⡾⠻⣧⡄⠀⠀⠈⢳⡀⠀⠀⠀⢻⡄⠀⠀⠻⣄⣀⣀⣀⣀⡇⠀⠀⢸⠇⣠⡟⠁⢰⣿⠁⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠸⠆⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠷⢶⣦⣄⢿⣿⠀⠈⡇⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⡿⢛⡿⠃⣰⠏⠀⠀⢀⣼⠋⠀⠀⠀⠀⢀⣴⣿⠛⠹⣷⡘⣿⢳⡀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⡞⣽⠟⠁⠀⢈⣿⣦⠀⠀⠀⠳⡀⠀⠀⠀⠹⡄⠀⠀⠹⣆⠉⠉⠛⣷⡄⢀⡟⣴⠋⢠⣤⣿⡏⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀
⠀⠃⠀⠀⠀⠀⠀⠀⣿⣼⣇⠀⠀⠀⠸⣿⣾⣿⠀⠀⢻⠀⠀⠀⠀⢿⠀⣀⣴⠟⠉⠀⣾⠁⣼⠃⠀⠀⢠⡾⠁⠀⠀⠀⢀⣤⣿⠉⠘⢷⡄⠹⣷⡹⣷⣧⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣾⣿⠏⠀⠀⢀⡾⠁⠈⣿⣦⠀⠀⢻⡄⠀⠀⠀⢻⡄⠀⠀⠸⣆⠀⠀⠈⣿⣼⡿⠁⠀⣾⡿⣼⠁⠀⠀⠀⢠⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡿⣦⡀⠀⠀⢻⡅⣿⠀⠀⠘⣇⠀⠀⠀⢘⣿⠟⠁⠀⠀⣾⠁⣼⠃⠀⠀⣰⡟⠀⠀⠀⠀⣠⢾⣷⣌⠳⣄⠀⠙⢦⡘⢿⣽⣷⣆⠘⣿⠀⠀⠀⠀⠀⠀⢀⣾⠁⣼⣿⠏⠀⠀⣰⠟⠀⣠⢾⣽⠛⣷⡄⠀⢻⡄⠀⠀⠀⢻⡀⠀⠀⠹⣆⠀⠀⢸⣿⠁⠀⠀⣾⠁⡇⠀⠀⠀⣰⡿⢁⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢻⡟⣻⣦⡀⠈⣧⣿⠀⠀⠀⠹⣆⠀⣠⡞⠁⠀⠀⠀⣼⠃⣰⠃⠀⠀⣰⠏⠀⠀⠀⢠⣾⣋⠀⠙⢿⣷⣌⠳⣄⠈⠙⣮⣻⣿⣿⡆⢹⣇⠀⠀⠀⠀⠀⣼⠏⣼⣿⠋⠀⢀⡾⠃⣠⠞⣡⠞⢁⡼⠋⢿⣦⠀⢳⡀⠀⠀⠈⢷⠀⠀⠀⢻⡀⠀⠈⢿⡆⠀⣸⠇⠀⠁⠀⠀⣴⡟⠁⢸⣿⠃⢀⣶⡗⠀⠀⠀⣼⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡌⠻⣷⣄⣿⢸⡄⠀⠀⠀⢙⣶⠏⠀⠀⠀⠀⢰⡏⢀⡏⠀⠀⣰⡏⠀⠀⢀⣴⠟⠀⠉⠳⣦⡀⠈⠻⢷⣌⠳⢦⡈⠛⢿⣿⣿⡆⢿⡆⠀⠀⠀⣼⠏⣼⡿⠁⢀⡴⢋⡴⠟⣡⡾⢁⣠⣞⠁⠀⠀⠻⣷⡀⢳⡀⠀⠀⠘⣇⠀⠀⠈⣷⠀⠀⠘⣧⢀⡟⠀⠀⢦⠀⣼⡟⠀⠀⢸⡟⢀⣾⡿⠁⠀⠀⣼⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠈⠛⢿⡏⣿⡀⠀⠀⣾⠃⠀⠀⠀⠀⠀⡾⠀⣼⠁⠀⢰⡟⠀⠀⢠⡾⠃⠀⠀⠀⠀⠙⢯⠓⢦⣤⡍⠳⠄⠙⠶⣄⡙⢿⣿⣎⣿⡀⠀⣰⡟⣼⡟⢀⡴⣫⡶⠋⢠⣼⠋⢠⡞⠙⠁⠀⠀⠀⠀⠙⣷⡈⢧⠀⠀⠀⠹⡄⠀⠀⢸⡄⠀⠀⢻⣿⠇⠀⠀⠀⣿⡟⠀⠀⠀⣿⣇⣾⣿⠃⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠈⣧⠘⢷⣄⠀⢿⡆⠀⠀⠀⠀⢸⠃⢀⡏⠀⢀⣿⠁⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠁⠳⠌⡙⠀⠙⣿⣿⡷⣰⣿⣾⠏⠀⣋⡼⠟⢠⠖⠋⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⡸⡇⠀⠀⣠⠇⠀⠀⢘⡇⠀⠀⠘⣿⡀⠀⠀⢠⡿⠀⠀⠀⢸⣿⣿⣻⠇⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⣿⠀⠀⠻⣦⡘⣿⡄⠀⠀⠀⣿⠀⢸⡇⠀⣸⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⣤⣶⣦⡀⢹⠀⠀⠈⠻⢷⣿⣿⠇⠀⢂⠉⣼⠃⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⡇⠀⣴⠋⠀⠀⢠⣾⠃⠀⠀⠀⠸⣧⠀⢠⣿⠃⠀⠀⢀⣿⣿⣷⡏⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⢻⡆⠀⠀⠘⢿⣾⣿⣆⠀⠀⢹⡀⢸⡄⠀⠙⠷⣦⣌⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣿⠃⣾⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⡄⣿⠀⣶⠚⠻⣦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢤⣰⠃⠀⠀⢠⡿⠁⠀⠀⠀⠀⢀⣿⢀⣾⠏⠀⠀⠀⣼⣿⡿⣿⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠈⢿⣦⡀⠀⠀⠙⣿⣿⠀⠀⠘⣧⠈⠓⢦⣄⠀⠈⠉⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣼⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⠀⠘⣧⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣀⡟⣿⠀⠀⠀⣿⡁⠀⠀⠀⠀⣠⣾⢃⣾⠏⠀⠀⢀⣾⠟⢹⡇⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠘⠿⣷⣦⣄⠀⠙⢷⣤⣠⣿⠏⠁⠀⠀⣸⠛⣦⠀⠀⠘⡇⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣰⠇⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠀⠀⠘⣧⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣿⠀⣞⠁⠀⠈⠳⠤⣤⣈⠻⢦⡀⠀⠀⣿⣁⣾⠏⠀⠀⣴⣿⠋⠀⣿⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠈⣿⠃⠀⢀⣠⡼⠟⠀⣸⠇⠀⣰⢧⣾⣿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢰⡟⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⠀⠀⠀⡼⣇⠀⠀⢳⡄⠀⠀⠀⠀⠀⠙⢷⣌⡙⠲⣄⡀⠀⠀⠈⠙⠶⣿⣆⡀⠘⢿⣧⠀⢠⣾⠟⠁⠀⢸⡟⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⢻⣆⣴⢿⣏⠀⢠⡞⢁⣴⠞⣡⣿⠃⡷⠈⢧⠀⠀⢀⣀⣀⣤⣤⣄⣼⣇⣀⣀⡟⡇⠀⠀⣧⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣇⠀⠀⢸⡇⠸⣆⣀⣀⣻⣀⣀⣀⣀⣀⡀⠀⠉⠛⢷⣶⣵⣦⡀⠀⠀⠀⣹⡿⢻⡇⣠⣟⣴⡿⠁⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠈⢻⣿⠀⠙⠻⠿⣆⣾⠁⢠⣿⠃⠀⡇⢀⣸⡶⠟⠋⠉⠁⠀⠀⢠⠏⠉⠙⣿⢷⣧⡀⠀⠹⣆⠹⣆⠀⠀⠀⠀⠀⠀⠀⣾⠁⡿⠀⠀⢈⣧⡶⢿⡏⠉⠉⢿⠀⠀⠉⠉⠛⠷⣦⣄⡚⢰⢿⣿⣷⡄⠀⣴⡟⢠⣿⡿⣯⣿⠏⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢀⣶⣶⡆⠀⠈⢿⣄⠀⠹⠇⠀⠀⠀⠙⣿⣇⢸⣇⠀⢀⣷⡟⢿⣷⣤⠀⠀⠀⠀⢀⡟⠀⠀⢠⡏⣸⠀⠙⢶⡀⠹⣆⠹⣆⠀⠀⠀⠀⠀⣸⠃⣼⠃⣠⣶⠟⢹⡄⠀⢷⠀⠀⠘⣧⠀⠀⠀⠀⣤⣤⣽⣿⣦⣿⢨⣿⣿⣾⠋⠀⠀⢉⣼⡟⠁⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⢆⣤⣸⡟⣿⡇⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣤⡞⣿⠘⡋⢿⣽⣗⢦⣄⠀⣼⠁⠀⠀⣼⠀⡏⠀⠀⠀⠙⣦⠹⣆⠹⡆⠀⠀⠀⢰⠏⣼⢋⣴⠟⠀⠀⠀⣇⠀⠘⡇⠀⠀⢹⡄⣀⣤⣶⣯⡽⢃⣤⢿⣿⣿⣿⣿⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⣿⠆⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢹⡌⣿⣷⣯⣘⠳⣟⣻⣷⣄⡀⢠⡇⢸⠇⠀⠀⠀⠀⢹⣷⣿⡄⢹⡄⠀⢠⡟⣰⢏⣾⠃⠀⠀⠀⠀⢸⡄⠀⢻⣠⣴⣾⣟⣛⣶⢿⣯⣶⣿⠁⣾⣫⣿⡏⣿⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣁⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⣿⣧⣿⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⢸⡟⠀⠀⠈⣧⢿⡉⢿⢯⣟⡊⠛⠷⣟⣛⣿⡦⣼⣀⣀⡀⠀⠀⢸⡟⣧⢿⡀⢷⠀⡾⢠⡟⣾⡏⠀⠀⠀⢀⣀⣬⣷⠾⠿⢯⣤⣴⢿⣋⡤⢞⣿⢡⡏⣼⠿⠋⠘⣷⡿⠀⠀⣼⡟⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣖⣒⣶⣺⣿⠀⠀⠀⠸⣏⢷⡸⣇⠾⣝⣷⠶⣬⣙⠿⢶⣿⣿⣟⣿⣷⣶⣿⣤⣿⡜⣷⡸⠿⠃⣼⢳⣿⣷⣶⣾⣿⣿⣿⣻⣿⣷⣾⣿⣽⠟⣿⠿⠚⣹⢧⡟⣸⠏⠀⠀⠀⣿⣿⣛⣳⣿⡁⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠉⠁⢹⣿⣇⠀⠀⠀⠹⣯⢳⣝⣦⡈⢻⣄⠘⠿⠟⢶⣦⣍⡙⠻⡿⢿⣯⣿⢻⢇⣾⡛⠒⢚⣿⣸⣿⣿⣿⣿⡿⠿⢛⣿⢿⣿⣯⠍⢉⣤⡿⣠⣾⣿⢟⣼⠏⠀⠀⠀⣠⣿⠁⠀⠀⣿⠃⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⣶⢾⣿⣿⣆⠀⠀⠀⠈⢷⡙⢿⣿⣶⣽⣷⠤⠴⠟⠁⠈⠻⣦⡹⣆⠿⣧⣼⣿⣩⣭⣹⣍⣙⣿⣧⣶⠟⠋⢀⣴⡋⠀⠀⠉⢛⣛⣻⣿⣞⣿⠿⣧⡾⠁⠀⠀⠀⣰⢿⡟⣻⣿⠿⠟⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣿⣦⠀⠀⠀⠀⠛⢿⣌⠙⠛⠿⢿⡟⠛⠛⠛⠛⠉⣛⣟⣶⢟⣿⣿⢵⣖⠒⠾⣿⣷⣿⢻⣆⠴⢋⣉⣩⡍⠉⠉⠉⠉⣷⠛⣋⣴⠞⠋⠀⠀⠀⢀⣴⢿⣿⣷⡿⠁⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠻⢦⣤⣸⡇⠀⠰⠦⣶⣶⣶⣶⣟⣿⠟⢹⡼⣿⣷⣾⠇⣾⠻⣿⢏⣭⠿⠛⠛⠛⠋⢀⣰⣿⠿⠟⠉⠀⠀⠀⠀⠀⣠⣾⣡⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣏⠳⣦⡀⠀⠀⠀⠀⠈⠉⢻⣶⣦⣤⣄⠀⠀⠀⣽⣏⣀⠙⣧⠉⠉⠉⢰⣟⣤⣝⣿⣡⣤⣤⣶⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⡾⣫⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⢳⣌⣻⣦⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣶⣾⣫⣟⠙⣧⠹⠀⠀⢀⣾⡾⢡⠽⣮⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⡾⢋⣰⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣇⡿⣿⣿⣷⣯⣻⣦⡙⢶⣄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣤⠜⣷⠀⠀⢸⡿⠷⢋⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣴⠞⣉⣼⣿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢻⣞⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⢿⡿⡟⣇⢻⢹⡛⣿⢶⣍⠻⣶⣖⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠀⠀⠀⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣳⡾⠟⢻⣷⡟⢻⡇⣿⣸⣿⣿⣿⣿⣿⣿⡀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⣿⣟⡿⣸⢹⠟⣿⢸⡞⡇⢹⡀⢹⠶⣄⠉⠻⢦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠛⢉⣤⢶⡟⢸⡇⢸⠁⣿⣿⣿⣿⣿⣿⣿⣿⠃⠠⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⣿⣿⡇⡿⣼⣸⢻⣧⣯⢿⠸⡇⢸⡆⢻⡟⢳⣄⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣤⡾⣷⢸⣄⢸⠇⣼⢠⣿⣿⣿⢿⣿⢻⣿⣿⣅⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⣿⢿⣸⡇⡿⡏⣸⢻⣿⣸⡆⣷⠘⣧⡌⣷⠼⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⡏⢸⣿⣸⠀⡿⣸⣿⡿⣷⡜⣿⣿⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⣿⠸⣿⢹⣿⣇⣯⣿⣿⢛⣧⢹⡆⣿⡇⢹⠇⣿⣶⣿⡅⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⡏⢸⣿⡇⠃⣾⠇⣿⢰⢧⣿⡏⣧⢻⣇⣿⣿⢻⡿⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠻⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢽⡇⢻⣾⡿⣸⢻⣧⡏⢸⠛⣷⣧⢸⣿⣸⣄⣿⢿⢹⣿⠀⢹⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⣧⢸⢹⡿⡇⡟⢠⡏⣼⢿⡇⣿⢸⡼⣿⣿⡏⣼⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠘⣿⡄⠻⣇⡟⣼⢹⠁⡟⢸⡇⣹⣮⣟⢻⡟⣿⠚⢸⣿⠀⢸⡇⠀⢻⡿⠛⢿⣿⣿⣿⠟⣿⡿⠀⡏⡿⠀⡀⡛⢸⢸⣿⢠⣇⣾⡟⢻⡆⣷⠸⡎⣷⣿⠋⢠⣿⠃⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠸⣷⡀⢻⣇⡏⣾⢸⠇⣾⠀⡿⢠⣿⣄⡇⢸⣾⡜⠻⡇⢸⡇⠀⠈⡇⠀⠈⢿⣿⠃⠀⢸⡇⢠⣅⡇⠀⡁⡇⡾⢸⡟⣼⣿⠉⣿⠀⣷⢸⡆⣧⡿⠃⢀⣿⠏⠂⢘⠏⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠹⣧⠈⠹⣧⡿⣼⢀⡏⢸⡇⣿⠀⢘⣷⣈⣿⣇⣀⡇⠈⡇⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⠘⢻⡇⠀⣇⣧⣇⣼⢿⠋⢹⡆⢸⡆⢸⡎⢁⡿⠁⢀⣾⠏⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢹⣧⠀⠈⢷⣿⠘⠃⣸⠀⠿⠀⢸⡇⢉⣿⣽⡻⣿⠀⣷⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠇⠀⢸⡇⢠⣿⡇⣿⡇⠸⣇⠀⣿⠀⣷⠀⣷⠾⠁⢀⣾⠏⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢹⣧⠀⠀⠷⢾⠀⣿⢠⡆⢀⣿⠀⣸⢳⠏⢻⣿⣀⣿⠀⠀⠁⠀⠀⢸⡇⠀⠀⢸⠀⠀⢸⣇⢾⣿⠀⡿⣧⠀⢿⣆⢸⡄⢸⣤⠟⠀⢠⣾⠏⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠹⣧⡀⠀⠘⢦⡇⢸⠁⣼⡇⣼⡏⣾⠀⣼⣿⠉⣿⣧⣤⡆⠀⠀⢸⡇⠀⠀⢸⣠⡴⣿⠁⢸⣿⠀⣇⣿⡆⢸⣿⠘⣇⣼⠁⠀⢠⣿⠃⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠹⣷⡀⠀⠀⣷⣸⣼⣿⣷⢿⣧⡇⢀⣿⡇⠀⣿⡆⠈⣷⠶⠄⢸⡧⠤⠶⣿⠀⠀⣿⠀⢸⣿⡆⢹⢸⣿⡀⣿⣧⡿⠉⠀⣰⣿⠇⠀⠀⠀⠀⡿⣠⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣦⣤⠻⣷⡀⠀⠈⠻⣿⣽⠻⢸⣿⠁⢸⢻⠁⢸⣿⠇⢰⡇⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡆⠀⣿⡇⢸⡄⣿⠇⣿⡿⠁⠀⣼⡿⠁⠀⠀⠀⠀⢸⡿⠋⢸⡇⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⠤⣄⠘⠃⠹⣿⣦⣼⣿⣄⠀⠀⠙⢿⣧⣸⠛⢀⡟⣿⠀⣼⡿⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⢸⡇⠀⣧⣧⠀⡄⣻⣿⡿⠁⢀⣾⡏⠀⠀⠀⢀⣠⣴⠿⠁⠀⠘⣧⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢰⡄⠀⠀⢸⡏⠀⠀⠀⠙⠃⠀⠈⠻⣷⣯⣿⣄⠀⠀⠈⢿⣿⣆⣸⣇⡇⢀⡏⠁⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠈⣿⠀⢉⣿⣦⣷⣿⡿⠁⣰⣿⠏⣀⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠙⣆⠰⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢦⡀⠀⠀⠀⢿⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⣇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⠀⠀⠈⢿⣿⣿⣼⠃⢸⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠘⠀⠀⠀⢿⡀⢈⣿⣿⣿⡟⠁⣴⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠈⢷⡄⠀⠀⠘⣧⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⠀⠈⢿⣿⣿⣶⣾⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⣷⣿⣿⣿⡿⢀⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠈⢿⣿⣿⣿⣷⣤⣤⣾⡇⠀⠀⢸⡇⠀⠀⢸⣷⣄⣴⣿⣿⣿⣿⡿⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⢷⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⢿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿⣤⣀⣼⣿⣿⣿⣿⣿⣿⡿⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⢿⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠒⠒⠒⠒⠲⠶⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠉⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣠⡾⠋⠁⠀⣀⡀⠀⠀⢀⣴⡶⠀⡀⣠⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⣰⡾⢋⡀⠀⠀⣰⡟⠀⠀⣤⣿⡿⠁⢈⣶⠏⢻⡌⠐⠁⢸⣆⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣼⠟⢠⡿⠇⠂⣴⡟⣀⣀⡾⢋⣾⠁⣠⡿⠁⠀⠈⢷⡐⢂⢸⡿⣆⠀⠀⢿⡄⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡞⠃⠀⠀⠀⠀⠀⣼⠏⢠⡿⢁⣤⣶⣿⢟⣻⠟⠙⣻⣿⣾⠏⠀⠀⠀⠀⠈⣷⣘⣘⣧⠹⣖⠀⠸⣷⠀⠀⠀⠀⠸⣆⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⣼⠏⢀⣿⡃⠛⣽⢿⣯⣿⣿⣶⣦⣿⣾⠋⠀⠀⠀⠀⠀⠀⠘⢿⡻⣿⠛⠻⣷⣤⣿⡄⠀⢀⡀⠀⢹⡇⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⣸⡿⣸⣿⡿⠂⣾⣯⣾⣿⡷⠋⠙⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⣀⣼⣷⣿⣦⣤⣹⣏⢻⣷⣤⢈⣿⠀⠈⣿⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀
⠀⠀⢠⡟⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⡿⢻⣇⣾⢳⡟⠀⣾⣿⣦⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣻⠟⠉⢻⣿⣿⣿⢿⣾⡿⣿⢿⣿⡆⠄⣿⡂⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀
⠀⢀⡿⠀⠀⡀⠀⠀⠀⠀⠀⢈⣿⣿⣵⢻⣿⠇⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣧⣤⣼⣿⣿⣿⡇⠿⣧⢻⣄⣿⡇⠀⣿⠇⢈⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀
⠀⣾⠁⠀⠁⠀⠀⠀⢀⣠⠾⠋⠀⣿⠿⠸⣿⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⡈⣿⣿⠷⣤⣿⠁⠀⠀⠀⠁⠂⠀⠀⠀⢿⠀⠀
⢠⡇⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⢹⡀⢀⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⠇⢸⣿⣤⠘⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀
⠈⠛⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⠀⠰⠟⠀⣠⢻⢼⢡⠇⠘⢧⡀⠀⠀⠀⠂⠀⠀⠀⢿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⢠⣏⡟⠀⡾⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠲⠶⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣠⡾⠁⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠓⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠙⠳⠦⡤⠶⠋⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⠄⢠⣤⣀⣤⣤⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⢻⡇⠀⣼⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡛⣿⣿⣟⣿⣷⣾⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡇⠈⢻⣿⣟⠉⠁⣲⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⣿⠀⠀⢸⣿⠃⠀⠀⢺⠶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡏⠀⠀⢸⢿⡆⠐⠀⢸⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣾⠃⠀⠀⠻⠘⠇⠀⠀⢸⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⣿⣿⣶⣤⣶⣶⣶⣶⣶⡞⢸⡞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⡇⠀⢸⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⠁⠀⠈⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣾⠀⠀⠀⣷⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠋⠀⠀⠀⠻⢤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣾⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠛⠛⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⣹⣿⡿⣿⣷⡀⣶⡀⠀⠸⡝⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠋⣀⣠⣤⣤⣶⣶⡿⣿⢿⣟⡿⣿⢿⣿⣿⢿⣹⣏⡷⣿⣿⡤⣷⠀⠀⢻⠀⠉⠙⠲⣄⠀⠀⠀⠀⢀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⣻⢯⣿⣽⣳⣯⠿⠽⠿⠾⠟⣿⣿⡻⣮⢯⣗⡾⣝⡾⣽⣷⡸⡆⠀⠈⠳⣄⣀⠀⠈⠳⣄⠀⠀⡼⠁⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠷⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣾⣟⡾⣝⣳⢯⣾⡵⣿⣻⠾⣿⡇⠙⠾⢦⡀⠈⣉⠳⡄⠀⠈⠳⣄⣇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣾⣹⡽⣞⣳⡿⣿⣳⡻⣿⢿⡷⣄⠀⠀⠙⢷⣦⣼⡇⠀⠀⠀⠈⠻⣦⠀⠹⡤⣄⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣹⢾⣿⣟⡛⠻⢧⣸⣷⠿⠷⣿⡃⠘⢢⣄⠀⠀⠉⠻⡝⢳⣄⠀⠀⠀⠙⣆⠀⢧⡽⢧⠀⢀⣴⡿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠹⣿⡽⣞⢿⡾⣯⣷⢦⣄⠉⠛⠛⠛⠳⢤⡀⠈⠻⣦⡀⠀⠘⣦⠙⠳⣤⡀⠀⠘⣧⠀⠀⠸⣇⣯⠀⢰⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃⠀⣀⡤⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣞⣳⣯⢟⣷⣿⡿⣶⣤⣀⠀⠀⠉⢢⡀⠈⠱⡄⠀⠘⣧⠀⠀⠻⡄⠀⢻⡆⠀⠀⠹⣿⡆⢸⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡿⠉⠕⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣭⣙⣿⠺⢿⡟⠻⣯⣻⣶⣄⠀⠀⠙⢆⠀⠹⡄⠀⠸⡷⣄⠀⠙⣄⠈⣿⡄⠀⠀⢻⣿⡀⠳⣄⠈⢷⡄⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠁⢠⣶⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣽⣿⢱⡄⠹⣧⠀⠙⣏⢿⣿⣷⡀⠀⠈⢧⡸⡇⠀⢠⣿⠘⣷⡀⠸⡆⠘⣿⡄⠀⠈⣿⡇⠀⢻⠀⣸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠳⠿⠂⠙⢶⡝⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣾⣿⠈⣿⣆⡻⣧⣦⡈⢳⣿⡿⠁⠀⣾⡟⠀⣧⠀⠈⣿⡀⠘⢷⠀⢹⠀⢸⡇⠀⠀⣿⣧⢀⡏⠰⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢀⠈⠻⢄⣻⣿⢧⠘⣿⣷⡄⠀⠈⠻⣦⣸⣧⠀⣸⡷⠖⠚⠉⢹⡆⠀⣇⠀⢀⣿⣿⣼⣧⣾⣿⣿⡜⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠿⢺⠀⠉⠙⠻⢧⣿⡿⠿⠷⠤⢤⣉⣻⣿⠏⠁⠀⠀⠀⠀⣼⣇⠀⢻⠀⢸⣿⣿⣯⠉⢿⣿⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢰⣧⣀⡀⣉⣷⣾⠇⠀⣀⣀⣤⣤⣈⣹⠁⠀⠀⠀⠀⢰⣿⢻⠀⢼⠀⣼⢣⣾⠙⣧⠈⢿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⣉⣩⣤⣤⡄⠀⣈⣭⣽⣿⣭⡏⠀⠀⠀⠀⠀⢸⣿⣸⠀⣼⣰⣯⣾⠿⣧⠘⣆⠘⢷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡇⣰⣿⣿⣿⣿⣿⡿⣿⣟⣯⣿⣟⠳⣤⠀⠀⠀⢠⣿⣿⣿⣦⣿⣿⣿⣿⣶⣿⣷⣹⠀⢘⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠐⢿⣆⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣟⠃⠉⠀⠀⢠⡟⠀⠀⠀⠸⣿⠉⠛⠻⠿⢻⡿⣿⣿⣿⡿⣿⠀⣿⣑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠐⠀⠻⢷⡀⠀⣠⣾⣿⡿⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⣾⣁⣤⡀⠀⠀⣸⠀⠀⠀⠀⠘⣷⡿⠙⣇⣀⣧⠀⢻⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠇⠀⠀⠀⠰⡀⢨⠙⢶⣿⣻⠃⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡷⠀⣀⣄⣀⢰⣿⠛⣿⠀⠀⡞⠁⠀⠀⠀⠀⢀⣿⣃⡀⠀⠈⣿⢀⡟⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣴⠃⠀⠀⠀⠀⠀⢹⡀⠱⣎⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣧⣽⡄⠀⠁⠀⠀⠀⠀⣀⣴⠟⠁⠉⠀⠀⣾⡾⠁⠈⠀
⠀⠀⠀⠀⠀⠀⣤⣄⣤⣤⠀⠀⠈⣿⡄⠩⠁⠀⠀⠀⠀⡀⠁⠈⠹⡀⠀⣿⣿⡷⡀⠀⠀⠀⠀⠀⢠⣿⣴⣸⢩⡿⣿⣿⣧⡘⢿⣷⣽⣿⠿⣿⣿⣆⡀⠀⠀⣀⣴⠏⠁⠀⠀⣷⠂⠼⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠏⠸⣿⣧⡀⣀⣼⣿⡇⠀⠀⠀⠀⠀⠹⣧⡀⢆⠀⠱⣴⣿⣿⠃⠙⣦⠀⠀⠀⠀⣸⣿⢿⣾⣰⢀⠋⡿⣿⣿⣾⣻⠻⢶⣶⡾⠟⠋⠁⢀⣼⣿⠋⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣇⣀⡀⢿⣇⣹⡷⠻⣿⣿⠀⠀⠀⠀⠀⠀⠉⣳⡀⠡⣠⣿⣿⠋⠀⢦⡀⠳⡄⠀⠀⣼⣿⢏⠼⣿⣼⢀⠀⡞⢻⣿⣿⣷⣶⣦⣤⡀⣠⠶⢾⣽⡇⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡟⠋⣹⣿⠉⢀⡼⠛⣿⣷⠀⠀⠀⠀⠀⠀⢀⣹⣄⢸⣿⣿⢤⡀⠀⠑⣄⠘⢦⠀⢿⣇⠀⠜⠙⢻⣼⣰⡇⡄⠘⠛⣿⣿⣯⣽⣿⣷⣄⡀⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⠀⠀⠈⢿⣧⡟⠁⣰⣿⠋⠀⠀⠀⠀⠀⢠⠎⠉⠉⢻⣿⣿⣄⡙⢄⠀⠈⢳⣄⠀⢸⣯⡶⡀⢠⠎⡜⢻⣧⡇⡏⢠⠇⣹⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⢿⣧⠀⠀⠉⢿⣷⣤⣿⠃⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣻⣿⡇⠀⠙⠲⣕⢀⠀⠹⡔⠨⣿⣿⣷⢃⡜⢠⠃⡐⢋⣧⣼⢠⠇⠠⠋⢹⠿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⠈⢻⣧⡀⠀⠀⠉⣿⡏⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣿⣿⡇⠓⠀⠀⠈⠳⣄⠀⠈⢆⢻⣿⣿⣿⣶⡁⠀⠠⠂⣠⠋⡿⢤⡀⢠⠃⠠⠋⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⠶⣜⠻⣷⣄⠀⠀⣿⠃⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢠⣿⣿⠃⢀⠀⠀⠀⠀⠈⠳⣄⠈⢿⡻⢿⣿⣿⣿⣤⡀⠘⠁⡴⠁⡜⢙⠷⣤⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⠀⠈⡻⣷⣾⣿⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠳⡄⠀⠀⢰⡆⠈⠳⡌⢻⣽⣹⢿⣿⣿⣿⣦⡞⢀⡞⢀⡞⣰⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠉⠙⣻⡟⠀⢠⢦⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠉⢦⡀⢸⠃⠀⠀⠙⢦⠙⣷⣎⡝⢿⣿⣿⣿⣿⣄⡈⠀⠇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⢀⣿⡇⠀⣼⡞⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠈⠳⣬⣿⣷⣌⡙⣿⣿⣿⣿⣿⣾⣀⣩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠋⢿⣿⣆⣸⣿⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⢿⣿⣇⢶⣿⣏⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠀⠢⠽⣿⣿⡿⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠢⠀⠀⠀⠀⠀⠈⣿⣿⠛⣾⣿⣡⣿⡏⠛⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠉⣿⡇⠀⢼⡇⠀⠀⠀⣀⣠⠤⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⡅⠀⠀⠀⢠⣿⠇⠀⣼⠀⢀⡖⠋⠁⠀⠀⣿⣿⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣿⣿⣧⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⡄⠀⠀⢸⣿⠀⠀⣿⢀⡏⠀⠀⠀⠀⢰⣿⣿⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣴⣿⣿⢿⣽⣧⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⢿⣄⠀⣽⡏⠀⠐⣿⡞⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠘⢦⠀⠀⠀⡀⠀⡇⠀⠀⣠⣾⣿⡟⠁⠸⣿⣿⡆⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⢩⡏⠸⢿⣷⣿⡇⠀⠀⣿⣷⣄⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⡇⠀⡇⠀⠀⢿⣿⣿⠀⡈⠀⠙⣿⣷⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⢧⡟⠀⣶⠀⢈⣿⠀⠀⢸⣿⣯⢻⣆⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⡄⠀⡇⠀⣇⠀⠀⠈⢻⣿⣷⡀⠀⠀⠹⣿⡇⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣗⡾⢿⣾⠟⠀⣸⡏⠀⠀⣼⣿⡿⣶⢻⣆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣠⣤⣷⢀⡇⠀⢻⠀⠀⠀⠀⢻⣿⣿⣶⠀⠀⠻⣿⡄⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡿⢻⣇⠀⠛⠀⢠⣿⠁⡀⠀⣿⣹⣿⣿⣶⢿⣦⣤⣽⣛⡀⠀⠀⠀⣠⣾⡋⢸⡏⢿⡇⠀⢸⡆⠀⠀⠀⠀⡙⠻⣿⣧⠀⠀⣻⣿⡀⠺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠁⠀⢻⣦⠀⢀⣾⠏⠀⢣⠀⣿⡟⡇⠀⠀⠀⠙⠻⠿⠿⣿⣷⣦⡾⣡⠞⢻⢸⡇⢸⡇⠀⠀⢷⠀⠀⠀⢠⠇⢰⢻⣿⡄⠀⠀⢿⣧⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⡆⠀⠀⠹⢿⣾⠃⠀⠀⢸⣴⣏⠀⢹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⢺⡇⠀⡷⢤⣀⢸⠀⠀⠀⡞⢀⣾⢺⣿⣷⠀⠀⠈⢻⡆⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣷⠀⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣶⣛⣝⣿⡳⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢸⡇⠈⣷⠀⠈⢳⡀⠀⢠⠇⣸⡏⠀⣿⣿⡄⠀⠀⠘⣿⣄⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣶⠀⠈⠀⠀⠀⠁⠂⠀⣿⡏⣿⡿⣿⡟⡷⠀⠀⠀⣴⡟⣿⠻⡗⠀⠀⠀⠀⣧⠀⣿⠀⠀⠀⢻⠀⡾⢠⡏⠀⠀⠸⣿⣷⠀⠀⣤⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣆⠀⠀⠐⠀⠀⠘⢒⣿⡇⢿⣷⠤⡿⠃⣴⠆⠀⣿⢿⣿⣷⠸⣆⠀⠀⢀⡿⠀⣻⠀⠀⠀⢸⣦⡇⡾⠀⠀⠀⠀⢻⣿⣶⣿⣿⠟⠇⢿⡿⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣽⡯⢹⡏⣿⣆⠈⠙⠛⠷⠤⠟⠶⠭⣭⣤⡼⠆⢀⣼⠇⠀⣻⠀⠀⢐⠁⣿⣼⠃⠀⠀⣶⣶⣿⡿⠟⠋⠀⠀⢀⣸⣷⣿⡿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢧⠊⠈⠁⣈⣿⢡⢃⢣⢹⣿⣶⣄⣀⠀⠀⠀⢿⣭⣶⣶⣤⣴⠟⠋⠀⠀⢸⡀⠀⠁⣸⣿⠃⠀⠀⠀⢸⣿⡇⠀⠀⠀⣠⣴⣿⡟⣻⡛⣿⣻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣆⠈⡁⣹⢇⠢⣍⠆⢾⠋⣷⡈⠙⠛⠛⠛⠛⢟⠋⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣿⠃⠀⠀⠀⠀⠀⢿⣿⣤⣴⣿⠟⣿⡉⣧⣿⣷⣿⣧⣿⣿⡿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣆⢠⠏⡆⡓⢬⡘⣿⠀⠘⣧⣴⣶⡆⠀⡀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣾⡗⠀⠀⠀⠀⠀⠀⠘⠟⠛⢹⣇⠀⢹⣇⠻⢻⡿⠁⢿⣿⣸⡧⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⡎⡜⢲⡍⢢⢼⡏⣠⠀⠘⣿⣿⡇⠀⠈⢄⠀⢣⡀⠀⠀⠀⠀⠀⠀⣿⣾⣿⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠸⣿⠀⠈⣿⠀⠘⣷⢀⣾⣿⣿⡇⠸⣆⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⢤⢩⢆⣼⡧⠇⠀⠀⠹⣿⣷⠀⠀⠀⠠⠀⠱⢄⠀⠀⠀⠀⠀⢸⣏⡟⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢿⡇⠀⢸⡇⠀⣿⣿⠋⠸⣿⣿⣆⠘⢦⠀⠀⠀⠹⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⡍⢆⣿⠁⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠠⠀⠈⠳⣄⠀⠀⠀⠈⣿⣇⡀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠸⣷⡀⣀⣷⣾⡿⠁⠀⠀⠿⢿⣟⣇⠘⠀⠀⠀⠀⢹⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡜⢢⣿⡄⡀⠀⠀⢰⣿⣿⣿⣷⣄⠀⠀⠉⢆⠀⠈⢧⡀⠀⠀⠸⡇⠈⠙⠒⠦⣄⣀⠀⠀⠀⠙⠢⡀⠿⠛⠛⠉⠀⠀⡀⠀⠀⠀⠀⠈⢻⠆⠀⠀⠀⢠⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⠬⢷⣝⠆⠀⣼⣿⡿⠀⠙⠻⢿⣦⡀⠀⠑⣆⠀⠙⠳⣀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⡑⠆⡀⠀⠀⠀⠀⠙⠂⠀⣀⣠⡴⠟⠀⠀⠀⢀⣯⣿⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣽⣿⣶⣿⣿⡇⠀⠀⠀⠀⠈⠛⢦⣀⠈⠳⣄⠀⢀⣿⡇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⣸⣿⠏⢹⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⠀⠻⢿⣯⡒⢤⣄⡀⠀⠀⠀⠉⠓⢦⣈⣴⡟⣡⣧⠀⠀⠈⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⢰⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇⠨⡄⢸⣿⡿⣟⣣⣈⠉⠛⠶⣄⡀⠀⠀⠈⠉⢻⡦⢿⡀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡼⠋⠀⣐⣾⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡻⢷⣝⣿⣿⡇⠀⠉⠉⠙⠲⠤⠈⠙⡛⠖⠛⣱⣾⣿⣽⣧⣀⣀⣀⣀⡀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⢰⡾⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⢦⡈⠛⢿⣿⣄⠀⠠⠀⢠⢶⣞⡭⠷⠂⢈⣽⣧⢌⣹⡟⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠶⠒⠶⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢬⣾⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠈⠷⢄⣾⣿⡟⠛⠲⠒⠛⠛⠓⠚⠛⠛⠋⢩⣟⠖⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠙⢦⣐⢸⣿⣿⠇⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣍⣚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣶⣶⣿⡷⠾⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⢶⣄⡉⢸⣿⣿⡀⠀⠀⠀⠀⣠⠔⣁⣠⠶⢈⣯⣻⣝⢻⡛⡶⢶⣳⠷⡷⠿⠿⠿⠞⠛⠛⠛⠛⠋⠉⠉⢉⣁⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠠⠈⠙⠛⣿⣿⡿⠶⠶⠶⠿⠓⠛⠛⠀⠀⣸⠁⣿⣿⣿⣿⣷⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⡘⣿⣿⣷⠀⠤⠄⠒⠀⠂⠈⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣶⡟⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⡄⢰⢾⡆⠀⠀⣸⠇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⣟⠐⣿⣀⡼⠋⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣽⣿⠏⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠚⣏⣸⣿⠏⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡱⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡔⠛⠿⣿⠀⠀⠀⠀⢀⣄⡶⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠲⣡⢋⣷⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⠋⠀⠀⢀⣠⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣎⠳⣄⣿⠃⠀⠀⠀⠀⠉⣙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣞⣤⡓⢼⣇⠀⠀⠀⠀⠐⡒⠤⢕⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠉⠉⠛⠓⢤⡀⠀⠀⠙⠒⠦⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣾⣿⣞⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⢇⣿⣿⣿⣁⡽⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⣿⢁⡿⣼⣿⢧⣼⠛⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣿⣧⣿⣀⡿⢁⣿⣏⣲⣏⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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