Sword Text Art

Copy & Paste Sword Text Art Emojis & Symbols

⣴⣶⢶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡄ ⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇ ⠙⠋⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠙⠁ ⠀⠀⠀⠈⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡟⠛⠀⠛⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⣰⣿⡿⠿⠟⠀⠀⠀⠛⠻⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣄⣤⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠻⣷⡀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⡾⠛⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣶⣦⣠⣴⣾⣿⠟⠉⠙⢆⠈⠻⡦⡈⠳⡄⠀⠀⠀⠀⠀⣠⠊⢠⣾⠟⢀⠜⠉⠉⢻⣿⣶⣤⢤⣶⣦⠀⠀⠀ ⠀⠀⠈⢿⣿⣬⣿⠋⠋⠀⠀⠀⠀⠑⢄⠙⢾⢦⠈⢢⡀⠀⢠⠞⢁⣴⠟⢁⡴⠋⠀⠀⠀⠈⠛⢻⣿⣽⣿⠛⠀⠀⠀ ⠀⠀⠀⠸⠏⠉⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠑⢕⢄⢙⡖⠁⣰⡟⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠻⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡵⠋⡠⡾⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢠⠾⠋⢀⠞⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠔⠃⢀⣴⠉⢢⣀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⡰⠋⢀⡴⠋⠀⠑⢄⠙⢥⣄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡠⠎⠁⡠⠋⠀⠀⠀⠀⠀⠳⣄⠙⢧⡈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠐⠆⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠑⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠜⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣏⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣣⡀⠀⠀⠀ ⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀
⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣟⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣌⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⢮⡙⢿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⡙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⠻⢽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣍⠪⣕⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡙⢺⣗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣙⠯⣗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣙⠫⣗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣑⠪⣗⢤⡀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣑⠮⣳⢬⣛⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣑⣾⣷⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⣕⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠉⠻⢿⣿⣯⡳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⡄⠀⠀⠀⠉⠻⣿⡜⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣘⠦⣀⠀⠀⢀⣸⣿⣋⣧⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠻⠟⠛⢋⠁⢉⡀⡈
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆ ⠉⠹⣿⣷⣀⠀⠀⠀⠀⢰⣶⡤⠀⢤⣴⡶⠀⠀⠀⠀⢀⣼⣿⠟⠉⠁ ⠀⠀⠈⠻⣿⣦⣄⠀⢀⣼⡟⠓⠀⠘⠛⣷⣄⠀⢀⣴⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣶⣿⠉⠀⠀⠀⠀⠀⠈⢻⣷⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⢀⡀⢀⣠⡾⠿⡹⢆⠠⡀⠀⠀⠀⢀⠔⣡⠞⡹⢷⡄⡀⢀⡀⠀⠀ ⠀⠸⡯⣿⠛⠁⠀⠀⢈⠲⣌⠢⡀⡠⣡⠞⡡⠊⠀⠀⠛⣿⢿⡛⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢌⡱⢊⡴⢃⠌⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠔⢋⢔⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡐⡡⢂⠔⠉⠢⡙⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠈⡠⠀⠀⠀⠀⠈⠢⡁⠌⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠑⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡈⢢⠀⠀⠀⠀ ⠀⠀⣔⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡡⡀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀
Free AI Art Generator, no sign-up, no login, unlimited
⠀⠀⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢇⢃⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⠂⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡌⠌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡌⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⡰⡹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠡⠱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢇⢣⢱⡤⣤⣴⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠧⢶⣢⣧⠶⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣞⣯⡽⢷⣒⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠱⣪⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⠤⠠⠤⠀⠤⠤⠠⠤⠄⠀⠴⠴⠶⠂⠶⠄
⣠⣤⣞⢯⣟⡲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢼⣳⣄⠀⠹⡇⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠾⣳⢦⢇⡾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⢟⣼⠕⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⡜⠈⠛⢿⡿⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠳⠄⠀⠀⠈⠢⢀⠉⠫⢖⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠈⠪⢕⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠉⠻⢕⡤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⢌⠓⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠐⢱⣕⠹⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠻⢍⡐⠬⣗⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠨⣻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠛⢳⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡋⢺⡏⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⡀⢹⡀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣧⠀⠻⡄⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⠀⢱⡄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⢱⡀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⢳⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢧⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠘⢧⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣆⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠘⡄⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠹⡄⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢹⡀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢳⡀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠀⢣⡀⠻⣶⣶⣦⣤⣤⣴⣾⡻⣧⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠈⢷⠀⠙⢛⡆⢸⡶⠾⠋⣳⠙⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢻⣇⣼⣿⡛⠋⣀⡾⢴⣾⣿⠿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣀⣁⣀⣹⢷⡎⢻⡷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣞⠿⠚⣉⣁⣽⣿⣿⡴⠖⠋⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣴⣪⣿⠟⠋⠉⠉⢻⣦⠴⠎⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⢹⣶⠒⠙⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣻⡟⣿⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⡀⢀⣠⣠⢀⣀⣀⡀⢀⢀⡀⢀⣄⠀⠀⢀⡀⣀⣀⠀⠀⢀⠄⡤⠠⣄⡤⣠⣤⣤⡀⣄⣤⠀ ⠚⡟⠀⠛⢛⠚⡛⣛⣓⠂⢀⠓⠛⡚⣙⠀⠃⠚⡚⡛⠙⠀⠀⠐⠃⠚⠚⠚⢓⠃⡋⡚⠉⣛⠚⠃
⠀⠀⠀⢀⣠⣶⣿⡿⠿⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⡿⣿⣿⣽⣴⡶⢿⣶⣶⣤⣭⡛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⡌⢻⣿⣦⠀⠀⠀⠀⠉⠻⣿⣇⠈⠝⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⢿⣤⣿⣿⣦⡀⠀⠀⠀⠹⣧⡇⠀⣶⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣯⣹⣿⣶⣄⡀⠀⣿⡁⢰⣿⡇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣷⣞⡻⣿⣶⡿⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡿⠁⣼⡿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢁⣾⣿⠧⠈⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢀⣿⠹⠷⣴⣶⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⠇⠀⠀⠀⠙⠻⣿⣿⢿⠛⠻⢽⣿⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠙⢧⣀⠀⠀⠉⠛⠾⣿⡷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣤⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠈⠙⠳⣽⡋⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠉⠓⢦⣉⢻⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠈⠳⢦⣈⠻⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠈⠓⢶⣭⡭⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠈⠻⢿⣤⠝⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠈⠳⢷⣌⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠙⢷⣔⠈⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠙⠻⣄⠀⣉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠦⢌⣳⣌⡓⢦⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣠⠀⠀⠀⢀⣬⣿⣷⡄⠙⢶⣟⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠿⣿⣿⡏⡍⠛⠲⢤⣍⣳⡽⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠤⣄⡀⠙⠻⣿⣮⣳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣈⣳⡽⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣼⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣾⡍⣇⣧⣥⣉⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠿⣼⣷⣿⣿⠟⠻⣹⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⢿⣿⣿⠟⠛⠁⠀⠀⢷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣎⡿⢯⡷⣄⠀⠀⠀⠀⠈⢧⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠉⠙⠻⢯⢳⡀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣝⢄⠀⠘⣦⡀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣣⠀⠹⡙⢆⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠻⡌⢣⡘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠱⡄⠑⣞⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠹⡄⠈⢮⢯⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡜⢆⠈⢳⡳⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢮⢦⡀⠻⡽⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⢧⡳⡀⠙⣌⢎⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡵⡙⢦⠙⣆⠻⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡱⡌⠳⣜⣦⠙⢮⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡜⣄⠙⢮⣦⠈⠣⡝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢆⠀⠹⠧⠀⠙⢎⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢦⠀⠀⡦⢄⠀⠑⣝⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢧⠀⠰⣴⣷⡄⠈⣽⣽⣟⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢇⠀⢉⠛⣇⣾⣿⣯⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣴⣾⣿⣿⣿⡶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣷⠶⠛⢯⣹⣏⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⢿⣟⣫⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣙⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⡟⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣭⢾⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡦⠽⣻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡙⢷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠝⠋⣳⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣷⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⡍⠠
⠀⢀⣤⣐⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡿⠋⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠷⡄⠀⡑⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢆⢳⢜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢣⡣⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⣥⡹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣖⠜⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡮⠺⡔⢥⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡥⠈⡌⠪⣆⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⠘⣣⣼⡟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠻⢟⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣟⠃
⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢝⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠫⡚⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢝⡳⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢝⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⢙⢖⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⣊⢖⢄⡠⣤⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⢊⣾⢇⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠿⣾⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢣⠀⠈⠙⢯⣢⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠱⠶⠶⠚⠓⠑
⢸⢓⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣏⡷⢄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣷⡊⠳⣄⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢷⣨⠈⢷⣄⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⡾⢿⣧⡄⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢎⣧⠛⢧⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠛⣧⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣽⢿⢦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠙⢦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡄⢹⢦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣈⠻⣦⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡈⢿⣆⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡽⢷⣄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣮⡻⣷⣄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣷⣄⠀⠉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡄⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⣙⢦⡀⠀⠀⠀⢰⣿⢻⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣁⠂⣙⣤⣀⣠⣾⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣛⣹⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡟⠙⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡹⠿⢛⣻⡿⠋⠉⢿⣷⣄⠀⠈⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣉⡥⠟⠋⠀⠀⠀⠀⠙⢿⣷⡀⠀⠈⠧⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⣀⡤⢻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣿⢟
⣴⢖⡶⣲⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⢾⣒⣦⠀ ⣿⣿⡾⣫⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣌⠳⣝⣿⡄ ⣿⡿⣿⣿⣿⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣿⣿⣿⢾⣿⠆ ⠀⠀⠈⠹⣿⣿⣟⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢷⣀⣀⣀⠀⢀⣀⣀⣶⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣻⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠉⠿⣿⣿⣖⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣸⣿⡋⠉⠀⠈⠙⣯⣏⣏⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⢿⣿⡿⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⢿⣿⠶⢚⣻⣦⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡷⠂⠀⠀⠰⣿⣿⣾⣮⢧⡀⠀⠀⠀⠀⠀⠀⣰⣟⡛⠻⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣭⣭⣿⣿⣦⡀⠀⠀⣠⣾⣿⣿⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣧⣙⣦⡀⠀⢀⣴⣿⣿⣿⢭⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⣯⣭⣽⣽⣶⣾⡟⡿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡷⣿⣶⣮⣽⣯⣟⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣿⣿⡿⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢿⣿⢿⣿⣷⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⢿⣧⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⣴⣿⠿⢷⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⠀⠀⣀⣠⣞⣷⡿⠿⠟⢦⠈⠳⣜⣢⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⣞⠞⠁⣠⠾⠿⢿⣮⣳⢤⣀⠀⠀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⢹⡿⣿⢖⣻⣽⣾⣿⡏⠀⠀⠀⠈⠳⣄⠈⠳⣝⢄⠈⠳⣄⠀⠀⠀⠀⠀⢀⡼⠃⢀⣞⠷⠉⢀⡞⠁⠀⠀⠀⠸⣿⣷⣾⢭⣓⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠘⢓⣿⣶⣾⣿⠁⠈⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⠶⡳⡄⠈⢳⡄⠀⠀⣴⠋⢀⣴⡿⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠉⠘⢻⣷⣮⣿⣟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡿⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢮⠣⡄⠙⣦⠚⠀⣴⣿⠋⠀⣠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠘⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠑⣬⠞⠁⣠⣞⠟⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡶⠋⢀⢴⠵⠁⣠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⡴⡛⠉⢀⡴⠋⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⡰⠋⠂⢀⣴⣏⠈⢢⣣⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⡞⠂⠀⣠⠞⠀⠙⢦⡀⠙⢭⣂⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⢀⢔⠗⠁⣠⠞⠁⠀⠀⠀⠀⠙⢦⡀⠑⣗⣄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⣴⠛⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠛⠳⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⡀⠂⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠺⣂⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠣⣀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠠⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⡀⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣯⣉⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⠈⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠈⢆⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣦⠈⢆⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣦⠈⣆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⠘⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢱⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢧⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⢇⠘⣧⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⢆⠘⠿⡟⢳⣿⠿⢿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣷⣸⣖⠒⢁⡾⣴⣶⠿⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⢬⣤⡽⠟⣹⣟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣛⣥⣴⡾⠿⠿⣏⣁⡽⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⠀⠀⠀⠹⣧⠔⢻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢻⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⢀⠀⠀⠀ ⡟⠀⠞⠘⠛⡛⡋⠘⠒⠒⠛⠀⠀⡟⠛⠓⠀⠈⠃⠃⠞⠛⠛⠛⠙⡻⠗
Your votes help make this page better.
With great power comes great responsibility!

Related Text & Emojis

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠛⠉⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠛⠲⢦⣤⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠹⣧⡀⠀⠀⠀ ⢀⣼⠟⠅⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠑⠿⠃⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠹⣧⠀⠀⠀ ⣾⠏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢽⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣿⣆⠀ ⣿⣆⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠐⠂⠄⢀⠀⠀⠀⠀ ⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀ ⠀⢠⠃⠀⠀⠀⣀⣀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠆⠀ ⠀⡞⠀⠀⠠⢴⣤⣾⣦⣽⠇⠀⢦⣶⡶⣤⠀⠘⡀ ⢠⠃⠀⠀⠀⣾⣿⣀⣈⡧⠀⣇⠸⣧⣀⡾⠄⠀⠁ ⢸⠀⢀⠀⠀⠈⢻⣿⣫⣵⣴⣿⢶⣼⡛⠋⠤⢸⠀ ⠀⢳⠃⢰⠞⠛⠛⠛⠿⢯⣿⣿⡥⠽⠛⠛⣷⠎⠀ ⠀⠀⠱⢄⠁⠀⠀⠀⠀⠘⠙⢿⠀⠀⠀⢀⠔⠀⠀ ⠀⠀⠀⠀⠉⠀⠠⢄⣀⡀⠀⢈⣀⠤⠖⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⣀⣤⣤⣶⡶⠾⠛⠛⠛⠛⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣴⣶⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡥⢀⣠⣴⣾⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⡀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣚⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⣿⣿⣷⣦⣬⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⡅⠏⠉⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⡙⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡧⠽⠤⠔⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⣿⣿⣿⣿⠛⢹⣿⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢸⣇⣿⣿⣿⣿⡆⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣴⣶⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣳⢿⡟⢹⣿⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⢿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣛⠉⠁⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⣎⣤⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡀⠀⠘⣿⡿⡟⠋⠉⠀⣠⠭⢭⢮⣍⠛⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣷⣿⣿⡻⣿⣿⣿⣿⡼⠿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⢹⡇⡇⠀⢠⡟⠁⣠⡞⠛⢮⠃⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⢀⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣸⡟⣿⣿⠿⠟⠃⠉⠉⠀⣀⡤⠶⠒⠋⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⢻⣿⠀⠘⢧⠀⣯⠜⠃⢸⡆⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⢸⢻⣿⣿⣿⣿⣿⣿⣇⣿⣿⠇⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣠⣴⡶⠶⣶⢦⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⡼⣻⡄⠀⠀⠙⠚⠛⠛⢉⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⢇⡞⣿⣿⣿⣿⣿⣿⡿⠟⣉⡤⠤⠶⠒⠢⠀⠀⠀⠀⠀⠀⠀⢨⣿⡁⠀⠀⠈⠷⠻⣿⣿⣿⣿⣿⣿⣿⣧⠈⣇⠹⣇⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣟⣿⢡⣿⣿⣿⣿⣿⣿⠖⠋⠁⣀⣠⣄⣀⡀⠀⠐⣄⠀⠀⠀⠀⠺⢳⡏⠀⠀⠀⣰⡄⢻⣿⣿⣿⣿⣿⣿⣿⡆⠈⢧⢿⡄⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⢠⢿⣿⣾⣿⣿⣿⣿⣿⣿⠀⢠⣼⢿⡍⠀⠉⠹⡷⡄⠈⠀⠀⠀⠀⠀⠈⠷⠒⠒⠊⠉⠀⠸⣿⣿⣿⣿⣿⣿⠛⣷⠀⠀⢻⣷⠀⢀⡤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠺⣿⡈⡃⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⢻⣇⠀⠀⠙⣇⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠴ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠙⠿⠦⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠸⣿⡀⠀⠀⣘⣦⠀⠴⠋⠀⢀⣠⠴⠚⠉⠀⠀⠄ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣿⣿⣏⠉⠉⠉⠙⣧⡀⠀⠀⠈⠻⠤⠤⠔⠒⠒⠂ ⠀⠀⢀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢹⣿⣾⣿⡆⠀⠀⡀⣾⣷⣦⡀⠀⠀⠀⠀⠀⠈⠉⠋ ⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⠀⠀⢷⣿⠛⣇⠙⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠐⠒⠒⣺⣽⠒⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣆⢹⡄⠘⢎⠓⢦⣄⡀⠀⠀ ⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣯⣷⠀⠈⡀⠀⠙⠿⣿⣛ ⠀⣸⢻⢹⣿⢸⣿⣬⣏⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠇⣠⣿⣿⣿⡷⢦⣤⣀⡀⠀⠘⠀ ⢀⡏⠘⢾⣿⣾⣿⣿⣿⣿⣇⢸⢿⠿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡍⠉⠚⠫⢽⣗⣲⢶⣶⣾⣿⡴⣫⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠞⠁⢻⣿⣿⣷⢲⣿⣿⢿⣷⣦⣼ ⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⣆⡸⣿⢿⣿⣿⣿⣿⣿⣿⣿⡋⠑⠲⠶⡤⣌⣉⠙⣿⣅⡉⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⠾⠃⣠⣾⡈⣿⣿⣿⡾⣿⣿⣄⣽⣿⢹ ⢸⠇⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣷⣿⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠠⡇⠀⠈⢳⣻⠀⡇⠀⠀⠸⣿⣿⣿⡿⣿⣟⡿⠿⠚⢉⣴⣠⣾⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⡈ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠉⠙⠛⠻⢟⠏⠹⡄⠀⢠⡄⠀⠀⠸⢿⠀⢇⣀⣠⣴⠿⠒⠛⠋⠁⠀⠀⠀⠺⠿⢿⣿⣿⣿⣿⣿⣿⣯⠿⣿⣿⣿⣿⣿⣿⣿ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⡄⠀⠀⡿⣄⠀⠙⢦⣸⠃⠀⢀⣤⣴⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣯⣄⣈⢿⣿⣿⣿⣿⣿ ⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⠀⠀⠈⢧⡀⠀⡽⠀⣠⣿⣿⠏⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿ ⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠁⢰⢁⣾⣿⣿⠋⠀⣀⠀⢀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣇⣨ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⣼⣿⣿⠟⠁⠀⣼⣿⢠⣼⣿⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣄⢀⣾⣟⣿⢏⡀⠀⣼⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣥⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠙⢆⠉⠀⠀⠈⠳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⠀⠒⠉⠁⠀⣈⣉⣺⣖⠒⠒⠒⢒⣓⡤⢄⠀ ⠀⠀⠀⡠⢲⠁⠀⠀⠀⣠⠖⠁⢀⣀⣨⣝⣗⢈⣉⣠⣤⣸⣝⣇ ⠀⢀⠎⠀⠈⠀⠀⢠⢾⣗⣂⣩⣿⣿⣻⣆⣼⣁⡀⣼⣿⣯⢮⠏ ⢀⠎⠀⠀⠀⠀⠀⣸⡾⠀⠈⠉⠉⢚⡿⠉⠁⠤⣀⣀⡀⡴⠋⠀ ⢸⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠐⠉⠁⠀⠀⠀⠀⠈⠀⠀⠈⢆⠀ ⠸⡀⠀⠀⠀⠀⠀⢠⠚⣗⡢⢄⠤⠤⡔⠤⡀⠀⢀⣀⣀⡠⢚⠆ ⠀⠱⣄⠀⠀⠀⠀⠈⠒⠒⠒⠋⠤⠒⠛⠥⢈⣉⠠⣤⠬⠝⠁⠀ ⠀⠀⠈⠑⠢⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⡄⢷⡀⢣⠀⢌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢧⠈⡆⠈⢳⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢸⡀⠀⠹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡎⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢹⡀⣷⡤⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡎⢸⠁⠀⠀⠰⡼⡧⠀⠀⠀⠀⠀⠀⢼⢻⡄⠀⠀⠀⠀⢀⣸⢏⣴⣷⣄⠀⠀⠡⢄⡀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡄⠐⡇⠘⠁⠀⢀⡼⠁⢣⠀⠀⠀⠀⠀⢀⡏⠀⢻⡄⠀⠐⡴⠛⢻⡏⣿⢤⣘⢯⠶⠶⠶⠋⠂⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⡼⠀⢰⡄⢆⣀⣠⣞⣀⡀⠘⣇⠀⢀⣀⣀⣞⣀⣀⡀⠹⣄⡇⠀⠀⣼⣯⠇⠙⡟⢟⠳⣄⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠫⢖⢓⣣⡴⠯⣇⣸⣼⣁⣀⣤⠎⠉⢻⠀⠀⢀⡽⢁⣠⣤⣶⣶⣼⡷⠀⣰⠻⡿⣄⠀⠸⡄⠱⠈⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⠛⠧⠤⠴⢲⡏⠁⣠⣤⡾⣿⡿⢭⣽⡉⠻⠂⢸⠀⣠⠞⠉⠙⣟⣻⣀⣠⢾⠁⣰⠃⣀⣧⡟⢱⢦⣳⡀⠀⡀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⣡⠮⢵⣏⢳⠱⣧⡀⠈⠉⠀⣠⠼⠞⠁⠀⠀⠀⠀⠉⠁⢀⣿⡞⠁⢠⣻⡻⡿⡙⡏⢙⢿⡄⢣⣌⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠟⠋⢹⡆⡞⡏⠸⡄⠈⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣍⣧⠀⣿⡏⡇⡇⠀⢷⠈⢎⢿⣸⡑⠍⠳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡇⣿⠐⣣⠀⢿⠳⣄⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⣠⣾⣿⣟⣻⣿⣺⠟⠁⠀⠸⡄⠈⢾⡏⠿⣶⣤⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡧⣿⣀⣻⣧⣸⣤⣵⡿⣦⣄⠉⠋⠛⠉⢀⡤⡺⣵⡿⢿⣫⣾⡿⣅⣀⠀⠄⠀⢳⠰⡌⢧⢠⠈⢻⣽⡢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡿⣿⢿⡿⠻⣿⡿⠟⠉⠀⢻⣦⣤⣾⣿⣿⠿⠋⠁⠈⠋⠻⡄⢀⣿⣿⣿⣶⣌⣧⠹⡼⣏⡄⠈⣇⢱⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⣿⣿⣿⣿⣶⣿⠙⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⢢⣟⢫⣙⣧⢹⢸⣧⠀⠈⣳⣵ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢹⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢰⠋⠀⢞⡿⠋⣿⣿⡎⣿⠀⣿⣿⡏⣇⢻⣧⠀⢛⠉ ⠀⠀⠀⠀⠀⠀⠀⢠⢿⡿⣿⠋⠻⣿⣿⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⡇⠀⢠⣿⠁⢸⡿⣿⣇⣿⣴⣶⣶⣶⣿⡄⢻⠇⠈⡀ ⠀⠀⠀⠀⠀⠀⢀⠏⢠⣧⠍⠀⠀⣸⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣿⣿⢀⣿⠀⢹⣿⠬⠭⠿⢶⡿⠀⡇⠀⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⢠⠿⠏⢻⣧⣼⢤⣿⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⢸⡏⣿⣿⠀⠀⣿⡀⠀⠀⣾⠁⠀⣧⠀⢸⡄⠀ ⠀⠀⠀⠀⠀⢰⣰⡟⠀⢸⣿⢃⣿⢸⣿⠀⠈⣿⠶⣦⣄⣀⠀⠀⠀⠀⢀⣴⠿⠛⣇⣸⡼⣿⣿⢻⡵⠀⠸⣇⠀⢰⠇⠀⠀⡏⠀⠈⠃⠀ ⠀⠀⠀⠀⢰⣷⡟⣵⠃⢸⣏⠼⡇⣿⠋⠀⠀⠘⢧⡀⠉⠉⠛⣓⡶⠞⠋⠀⠀⠀⠈⠙⢷⣿⡏⠀⣿⠀⠀⢻⣤⣾⠀⠀⣠⡇⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⠟⡸⠁⢀⡿⠛⣾⣿⡟⠀⠀⠀⠀⠈⠳⣤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⠿⠿⣿⢷⣀⢸⣿⡿⠶⠖⠋⡇⠀⠀⠀⠀ ⠀⢀⣾⠿⠒⠒⠷⣤⣾⣷⢻⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡴⡟⠀⠀⣿⡆⡝⣶⣿⣇⠀⠀⠀⡇⠀⠀⠀⠀ ⢀⣾⠃⠀⠀⠀⢰⠙⣿⡿⠾⢇⣸⡇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠋⣼⠁⠀⠀⣿⣿⣷⣌⠻⣿⣷⣄⡔⣧⠀⠀⠀⠀ ⣼⢇⠀⠀⠀⠀⣞⠀⠀⣿⡄⠀⠈⣿⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠹⣄⠀⢠⢻⣿⣿⣿⣷⣾⣿⣿⣯⣼⣆⠀⠀⠀ ⡏⢸⢦⡀⠀⠀⢧⣄⠀⣽⣷⠀⢀⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣹⣶⡾⠚⠉⠉⠉⠛⠳⢄⠀⠙⢿⣿⠆⠀⠀ ⠃⢸⠀⠙⢄⠀⠈⢾⣿⣿⣇⣴⡿⢻⠃⣹⠳⣤⡀⠀⠀⠐⣦⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢿⣦⢀⠀ ⠀⠛⡆⠀⠘⣆⠀⠀⠙⢯⠯⣉⡴⠋⢀⡜⠀⠈⣿⣶⢤⣄⣘⣇⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡀⣰⡶⠂⠀⠀⠀⠉⡇⠀⠘⣿⢧⠀ ⠈⠀⠸⣄⠀⠈⢙⣢⣀⠀⢧⡀⠉⠉⠉⠀⠀⠀⣿⡎⠀⠀⠉⢻⣧⡄⠀⠀⠀⠀⢀⣿⠃⠀⢠⣮⠟⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⢸⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠈⢻⡾⢎⠒⠚⢙⣲⠄⠀⣻⣷⡀⠀⠀⠀⢹⣶⣶⣶⠶⢦⣾⠏⠀⢠⠞⠁⠀⠀⠀⣀⠀⣀⢠⡾⠁⠀⢸⣿⣾⠀ ⠀⠀⠀⠀⠉⠉⠙⢏⣒⠢⢄⡡⠴⠶⠯⡁⠀⡼⢰⡟⡳⢤⣀⠦⢄⣻⣙⠳⠆⠀⢎⣠⠔⠁⠀⠀⡠⡖⠻⢽⣋⠥⠞⠁⠀⣠⣿⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⠶⠒⠒⠊⠉⠁⢠⠃⠸⣧⢳⡀⠀⠶⡀⠈⣀⣈⠉⠓⠲⠏⠀⠠⢶⠋⠀⠙⢦⣀⣀⣀⣀⡤⣞⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⡥⢤⠴⣪⠝⠀⢤⡉⠓⠚⠥⣄⣤⣯⣄⣀⣀⣀⣀⣠⠭⢗⡿⠋⣴⡟⠒⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⠑⠉⠁⠀⠀⠀⠙⠦⢤⣀⡀⠉⠉⠛⠒⠒⠒⠒⡒⠺⠍⠁⡰⠁⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠙⠲⠦⠀⠀⠂⠀⠀⢱⡌⠉⠑⠒⠒⠊⠉⠁⠀⠀⣠⠞⠁⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠀⣀⡤⠔⠊⠁⠈⠟⠒⠂⠤⠤⠤⠤⠒⠊⠁⠀⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣠⠴⠒⣚⣻⣟⣛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣭⠴⠾⠛⠋⠁⠀⠙⣷⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠛⢦⣌⠙⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⠀⠀⠀⠈⠙⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣈⣛⠛⠶⢾⣿⣿⣿⣿⣿⣷⣄⣀⣠⣼⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠾⢛⣩⣷⣿⡯⠥⣭⣥⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠞⣿⣛⣩⣴⣿⠄⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠉⠙⠛⡙⣇⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠻⢶⡄⠀⠀⠀⠀⢳⣹⡆⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠈⠻⣆⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠹⣧⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⢹⡇⠀⠀⠀⠀⢫⡃⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣧⣄⣿⠀⠀⠀⣀⣴⣷⣶⣦⣜⣧⣴⣶⡶⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⡀⠀⠀⢻⡇⣹⠛⣻⣿⡿⣿⣿⣿⡿⠿⠋⣿⣛⡛⢉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢹⣽⡟⠀⠀⣬⣿⡿⣿⣿⣟⣛⣯⠁⠀⠀⠀⠛⢿⣿⣭⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠛⠃⠀⢰⡏⠻⠶⠿⠓⠻⣿⡍⠀⠀⢀⣀⣤⣬⡿⠶⠶⠶⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⠛⠒⢶⣢⣤⢴⠛⠁⠀⢚⣋⠉⠉⣁⣤⣤⣶⣶⣆⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢸⡞⣿⡿⠿⣿⡀⠀⡰⠟⠁⠀⠀⠀⠀⠙⠋⠉⠳⠶⠿⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⣧⢿⡄⠀⠸⡿⢿⢣⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡀⢹⡏⠹⠛⢹⣿⣿⡞⡾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣧⣼⣽⣿⣿⣿⡞⠃⣾⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣻⣿⡷⣻⣻⣿⣷⢠⡇⢰⡿⣆⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣈⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣧⣾⣿⠟⣁⣹⣽⣿⣿⣼⡇⣿⡇⢹⣄⣀⣤⣶⣿⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⣿⣿⣟⣿⡉⠀⠰⣿⣿⣻⣿⣿⣿⡇⣿⡇⢸⠻⡏⠉⢁⡾⠀⠙⢻⣿⣿⣻⣿⣷⣄⣤⣦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡟⢷⡄⣼⣿⣿⣿⠿⣿⠟⢷⣿⡇⢸⠏⣿⢠⡞⢠⡆⠀⠀⡉⠻⣯⢿⣿⡭⢹⣿⣿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⣿⣿⡿⠃⠀⣿⡀⢸⣿⣿⠈⣼⢻⡟⢀⡿⢀⠀⠀⠻⣆⠈⠉⣿⡷⠶⢿⣇⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⣿⠀⠀⠀⣰⣿⢇⣀⣿⣿⣦⣧⡜⣇⢸⠁⣿⠃⠀⢀⠈⠳⣄⣹⣷⠒⠛⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⠾⢿⣶⣿⣿⡉⠹⣵⠶⣶⣿⡈⣼⠁⢀⡄⠘⣧⠀⠈⠙⣿⣠⣄⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⣿⡀⣼⡆⢷⢹⡟⠃⠀⣸⠃⠀⣌⢷⣄⠀⢻⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢿⣷⠈⢹⡇⠀⣰⠏⠀⠀⠘⢷⣝⢷⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢸⣧⣰⠋⠀⢀⡀⠀⣀⠙⢮⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢿⣿⣿⠀⠀⣿⠁⠀⠙⣷⠿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⣿⣇⡟⠀⠐⠃⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣽⠟⣇⣀⠀⣀⣀⣠⣶⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⡟⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⠿⠛⡛⢩⢉⡉⢌⠡⣈⢉⡉⠍⠛⢛⠻⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠩⠡⢄⠢⡑⢌⠂⢆⡘⠄⢣⠐⢢⠘⡌⡑⢂⠆⡡⢂⢉⡛⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢩⠐⡨⢁⠣⠌⢂⠡⢂⡉⢄⢂⡉⢂⡉⠂⡅⢂⠱⡈⠆⠱⡈⢂⠰⢀⠌⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⡌⢢⠑⡄⠣⢌⠢⡁⢎⡐⢌⡐⢂⠘⡠⠡⡁⢦⡌⢄⠡⢌⡑⢌⠢⡑⢌⠠⢃⠤⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡿⠁⡌⠒⢌⠰⢈⠄⡃⡐⢂⢁⠢⢐⠠⢂⣼⣧⠄⡑⠈⣿⣯⣮⣾⣿⣷⣄⠢⢑⡈⢆⠡⡂⢅⠂⡹⢿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠟⢠⠑⠤⣉⠂⢅⠊⣰⣤⣷⣾⣾⣿⣿⣾⡿⠟⠡⠒⣈⠡⠉⡄⠩⢁⠌⠻⢿⣷⣦⡐⡈⠆⡱⢈⠆⢄⡉⢿⣷⡀⠀⠀⠀ ⠀⠀⣼⣿⠏⠰⡁⠎⡐⢠⢁⣶⣾⠿⠛⡉⠤⢀⠤⠀⠤⡐⣉⠰⣁⠂⠅⡃⠄⢃⠂⡌⠒⠠⠙⠻⣿⣶⣬⢀⠣⠘⡄⠢⠌⢿⣿⡀⠀⠀ ⠀⣸⣿⠏⣈⠣⢘⠠⢑⣶⠿⠋⣁⢢⣵⣶⣷⣿⣶⣯⣔⠐⡠⢃⠤⢉⠰⣨⣾⣶⣷⣶⣯⣴⣡⠡⡀⠛⠻⣷⣦⠡⠌⠱⡈⠜⣿⣷⠀⠀ ⢀⣿⡿⠐⡠⢃⠂⣽⠟⢁⠢⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡐⠌⠢⢌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⡑⡈⢙⠻⠾⣄⠰⠡⢸⣿⡇⠀ ⢸⣿⠇⠡⢂⠅⡊⠅⢢⢌⣾⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣷⠈⢡⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠂⠤⠡⢄⠢⡑⠢⣿⣿⠀ ⣾⣿⢈⠱⢈⠢⠑⡌⢆⣿⡟⢿⣿⣿⣿⣯⢿⣽⣫⣿⣿⣿⣿⡇⢂⣿⣿⣿⣿⣯⢷⣻⢾⣿⣿⣿⣿⣿⠻⣿⣎⠐⡡⢊⠔⡁⠆⢻⣿⡀ ⣿⣿⠀⢎⠠⢃⠡⣜⣾⣿⠀⢹⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⢈⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠠⠹⣿⣇⠐⢌⠢⡑⡈⢹⣿⡄ ⢹⣿⡌⠰⢈⠆⣁⣯⣿⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡀⢿⣿⡈⢄⠣⡐⠡⣹⣿⠀ ⢸⣿⡇⢦⣙⡚⢬⣿⣿⡇⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠄⢸⣿⡅⠢⠑⡄⢃⣿⡿⠀ ⠈⣿⣿⢢⢜⡱⣮⡷⣿⣧⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⣿⣿⠏⣶⣿⣿⠛⠿⠻⠟⠛⠋⠁⠀⠀⠀⠀⠀⣼⣿⣍⠳⣩⢄⢩⣿⠇⠀ ⠀⠹⣿⣇⠎⣶⡻⡕⣻⣿⣄⣀⣴⣶⣶⣆⠀⠀⠀⠀⢀⣼⣿⢯⣻⢧⣻⢿⣷⡀⠀⠀⠀⠀⢠⣶⣶⣦⣀⢠⣿⡿⣞⠧⣑⣮⣿⡟⠀⠀ ⠀⠀⢻⣿⣎⡷⢻⡵⢯⣹⣿⡿⠛⡉⣿⣿⠀⠀⣀⣴⣿⠿⡙⣏⢣⠖⡩⢏⢻⣿⣦⣄⠀⠀⢺⣿⡉⠛⣿⣿⣟⡼⣝⡞⣫⣽⡿⠁⠀⠀ ⠀⠀⠀⠻⣿⡖⣍⢛⣴⣿⡏⢥⣵⣶⣿⣿⣾⡿⠿⠿⠿⢿⣿⣷⣎⣱⣽⣾⡿⠿⠿⢿⣿⣶⣿⣿⣧⣶⣌⡹⣿⣯⡒⣼⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣧⣻⣿⡟⠠⡉⠍⣉⠉⠤⢐⡈⠆⢡⠒⢠⢀⣻⣿⣿⣟⡡⠐⠌⠒⠤⢀⠌⠡⡉⢩⠙⡉⢒⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⢣⢉⠒⠤⡉⢆⠡⡐⣬⣴⣾⣾⣿⡿⢋⠙⠿⣿⣿⣶⣭⣔⡈⠌⠱⣀⠃⢆⡑⢂⢉⢹⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⣿⡇⡘⢄⢊⠰⢁⠒⡠⠒⡈⠍⠹⣿⣧⠠⢐⠢⣁⠒⢠⢸⣿⡏⠩⠑⣈⠱⠀⢎⠰⣀⠃⢌⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣷⡈⢄⠊⡰⠁⢎⡐⢡⠒⠌⠡⢹⣿⡇⠌⠒⡠⠉⡄⣿⡿⢀⠡⢃⠔⡨⠑⠌⢂⠄⡉⠄⣾⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣦⣼⣀⣅⠂⠌⡐⠌⡨⠁⣾⣿⣟⣀⣣⣄⣱⣸⣿⣷⡈⠄⠃⠌⡐⢩⣐⣬⣴⣵⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣶⣷⡿⢿⣛⡿⠿⠿⢿⠿⠛⢛⠻⠿⢿⠿⡿⠿⠿⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⢛⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⣡⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠋⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣦⡀⠀⠀⠀⠈⢿⣧⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠘⣿⣇⠀ ⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⢻⣿⡄ ⠀⠀⣠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⣿⡇ ⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⡇ ⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀ ⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀ ⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀ ⠀⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⢿⣿⣷⡆⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⢿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠋⠁⠀⠀⠀⣀⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⢹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣏⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢸⣿⡇⣀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⡿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢸⣿⡏⠻⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⡏⠁⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠀⠀⠀⠈⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡋⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⠄⠀⠀⠀⠀⢠⣾⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⠢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣯⣛⠚⣃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣫⣿⣹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⣿⣿⣿⠿⠿⣿⠂⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠈⠿⢿⣿⣿⣿⠏⠀⡀⠱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⢡⣤⣶⣄⡀⠀⣸⣂⣀⡰⣧⣴⡻⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⣰⠧⢴⣿⢻⣿⣿⣯⠉⠉⣹⢷⠾⣿⣟⣼⡷⠀ ⠀⠀⠀⠀⠀⠀⢻⠿⢿⣿⣿⠿⢯⡉⣩⢋⣔⣹⣇⣻⠿⠋⠁⠀ ⠀⠀⣀⡤⠤⣤⣸⢷⣾⣿⣷⣶⠾⢋⡱⠗⠈⠭⠉⠋⣨⠁⠀⠀ ⢠⣾⣏⣁⣄⠀⠨⡟⢹⣭⣽⡆⠀⠀⣿⣶⠆⠀⠀⠀⢣⠀⠀⠀ ⠈⣿⣿⣿⣿⡀⠀⢇⢸⠛⣻⠀⠀⢰⢸⢀⠿⠖⡀⠀⠀⢧⠀⡀ ⠀⢸⣿⣾⣿⣷⠆⢸⢸⢠⠿⠾⡄⢸⣼⣦⡛⠣⣸⣾⣶⣷⣧⡅ ⠀⠀⢿⣿⣿⣿⡯⠋⣸⣾⣆⣀⣸⢹⡸⣎⣽⡶⢿⣿⠟⠋⠉⠀ ⠀⠀⠀⠀⠀⠂⠀⠙⠋⠉⠁⠀⢹⡽⠏⠋⠉⠀⠀⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣷⣆⡄⣠⣤⣠⣤⣤⣄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣟⠁⠁⠈⣨⣿⣿⡝⢿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣷⡾⢾⡿⠿⠉⠀⠈⢻⡟⠈⠻⣗⠲⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⢶⡞⠉⢛⡀⠂⠀⢸⠆⠀⠀⠈⠶⠀⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣼⢻⢸⣿⠿⠿⢿⡷⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁⢠⣘⠃⠀⢷⡋⠉⠉⠁⢀⡼⠋⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠉⠙⠲⢬⣉⠉⠉⠉⢉⣀⡠⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢀⣀⠤⠶⠂⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⡵⠞⠉⠀⠀⠀⠀⢁⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢰⡏⠙⠒⠒⢴⣤⣀⠀⠀⠀⠀⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣵⠋⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⢀⣠⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢾⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⢠⠟⢳⡀ ⠀⠀⠀⠀⠀⠀⢠⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⣀⣀⡤⠤⠒⠛⢹⠀⠉⠉⠙⠒⢒⠲⠤⠤⠴⠒⠚⠁⠀⠀⢽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣟⢉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢀⣴⢧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣏⠸⣄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⣠⠏⠉⠈⠉⡳⣴⢤⡀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠘⣆⢸⡿⠶⠶⠶⡟⠓⠒⠒⠒⠒⠲⠖⠉⡟⠀⠀⠀⢀⣶⡼⠙⣦⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠇ ⠀⠀⣰⠇⠀⠀⠀⠀⠈⠸⠷⢬⣦⣤⣴⠋⠀⠀⠀⠀⠀⠀⠈⢿⢧⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣾⢿⡁⠀⠙⢿⣄⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠳⢤⣀⡈⢧⠀⣀⡀⠤⠤⠔⢋⠀⠀⠀⣰⠃⢸⡇⠀⠀⡽⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢿⡆⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠋⡇⠀⠀⠀⠀⠀⠀⠀⡼⠁⡹⠀⠀⠈⠉⢸⠀⠀⠀⠀⠀⠀⠈⢧⠀⣰⠃⠀⢸⡇⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠁ ⠀⠀⢧⡤⠟⢁⣀⡈⠙⢧⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣰⡇⠐⢇⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠰⠚⠁⠁⠀⠀⢀⣇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢀⣔⢋⣠⠶⠋⠀⠈⢣⡀⠳⣄⣠⠞⠀⠀⠀⠀⠀⠀⢘⣿⠶⢤⣈⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⡶⡛⢉⣯⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀ ⠸⠘⠋⠁⠀⠀⠀⠀⡾⠉⠳⡾⣅⠀⠀⠀⠀⠀⠀⠈⢻⡯⣧⣄⣰⡽⠉⣻⣟⣩⠛⠉⠉⠙⢻⢯⠁⣀⣀⠤⢷⠿⠉⢧⢸⠇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⢷⠀⠀⠀⠀⠀⠀⣼⠆⠈⠁⠙⠓⠂⡿⠿⢿⣠⡤⠤⠔⠺⠿⠉⠁⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⣻⠀⠀⠀⠀⠀⠀⡗⠒⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⡀⠀⠀⠀⠀⢀⣠⣾⠁⠀⠀⠀⠀⠀
⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢸⣿⣿⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⢀⡀⠀ ⡇⠀⢸⣿⣿⣿⡿⢃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣀⣤⡖⠉⢢ ⡇⠀⢸⣿⠋⠀⢀⡜⠀⠙⢆⠀⢀⡀⠀⠄⠀⣀⠀⠀⡎⠀⠀⢠⣾⣿⣿⣿⣿⣿ ⡇⠀⢸⣿⣿⣿⣿⣿⣠⡤⠼⣮⣄⡀⠀⠀⠀⠀⠈⠑⠳⢄⠀⠈⠻⣿⣿⣿⣿⡟ ⡇⠀⢸⣿⣿⡿⠟⢁⡈⢹⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠈⠁⠀⠀⠀⠈ ⡇⠀⢸⣿⣯⠉⢈⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠶⠂⠤⠄⣀ ⡇⠀⠸⠿⢿⠀⠈⠓⢤⣀⠀⠓⢄⡀⠀⠀⠀⠀⠀⡀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⢸⠀⠀⢠⡇⠀⠘⢄⡀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊ ⡇⠀⠀⠀⢸⠀⠀⣾⣿⠀⠀⠀⢉⠢⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀ ⡇⠀⠀⠀⠈⡄⢸⣿⣿⡆⠀⠀⢸⣷⣄⡀⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣠ ⡇⠀⠀⠀⠀⢣⡞⣿⡇⢱⡀⠀⢸⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠹⠁⠀⠱⡀⠸⣿⣿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⣇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠿⣿⢀⢄⠀⢀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠁ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠊⢁⠤⠂⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⢤⣖⣾⣭⣯⣿⣿⣿⣓⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢤⢶⣖⣶⣻⡿⣯⢻⣭⢻⡽⣯⢷⣻⣞⡿⣿⣿⣮⣕⡦⣄⡀⠀⠀⠀⠀ ⠀⠸⣯⣾⣹⣯⢟⡵⣏⡞⡧⣝⡞⣯⢷⣯⢿⣽⣿⣿⣿⣿⣶⣯⣳⡀⠀⠀ ⠀⠀⠘⣿⡿⣞⢯⣝⢾⡹⣜⠶⣩⢏⡿⣿⡻⡼⣿⣷⣿⣻⣿⣿⠏⣷⡀⠀ ⠀⢀⡶⢩⠿⣎⣷⢪⢇⡻⣌⢏⣗⣫⠽⣾⠳⣍⣿⣿⣽⣿⡟⣭⢻⡍⣧⠀ ⠀⠈⣷⢳⡙⡞⣯⡟⣛⠳⣛⡟⣣⢞⣽⣏⠳⣼⣿⣿⣿⡇⠞⡴⣋⣿⢸⠀ ⠀⠰⣏⣣⢚⣹⣿⣷⣧⣷⣱⣮⣽⡾⣛⣬⣷⣿⣿⣿⡿⡜⣏⠴⣃⢾⢸⠀ ⠀⢸⣇⣧⠌⡼⢻⢿⣿⣿⣷⣾⠧⣽⣿⣿⣿⣿⣿⣿⣜⠳⡜⢦⡹⡜⣼⡄ ⠀⢺⣸⣏⣻⣧⠃⡌⢈⠙⡐⠨⠑⠈⠿⠛⠿⢛⢛⠫⣭⢓⡜⢦⡱⣝⣎⣿ ⠠⡟⡞⢲⢹⣷⡣⠔⡈⠄⡀⠄⡀⠁⠠⢈⠐⡈⠢⣁⠿⡷⢮⠷⡽⢺⡹⡍ ⢐⣧⡟⢂⠣⣹⣿⣷⣌⠰⣈⠐⠠⣈⢁⠢⡐⢌⡱⣤⢿⣛⡞⣣⢝⡣⢟⡅ ⣾⣉⡆⢉⠆⣿⢻⣿⣿⣿⣶⣯⣷⣦⣏⣶⣽⣞⣶⣿⣏⠮⡙⠥⢎⡱⢫⣇ ⣿⣨⠃⢆⢨⡗⢦⢈⠛⠻⣿⢿⣿⣿⣿⣿⣿⡿⠿⠿⣏⠞⡩⡝⢬⠓⣇⡯ ⢻⡽⡿⣶⣿⣿⣷⣬⣂⡡⠀⠄⠠⡀⠄⠐⡀⠐⡁⠂⣿⠈⡕⠸⠦⡙⢆⣧ ⢸⣿⣳⢳⡼⣿⣿⣿⣿⠿⣟⡶⣥⣴⣀⣀⣀⣀⣄⣡⣛⡜⢌⠓⡌⠱⢊⡿ ⠸⡗⣧⡟⡼⣿⣿⣿⣿⣿⠀⠈⠉⠙⠛⠾⣽⣿⣿⣿⣷⣼⣦⣶⡾⣷⢯⣞ ⠀⠘⢮⣛⣱⣿⣿⣿⡏⣿⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣟⢦⡓⣜⡲⣭⣟⣮ ⠀⠀⠀⠀⣹⣻⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠸⡿⣿⣟⠾⣼⣟⡲⣝⣳⣞⣳ ⠀⠀⠀⡴⣻⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠹⣽⣿⡿⣟⢶⣯⢽⣛⡵⠛ ⠀⠀⣾⣻⣿⣿⣿⡿⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢿⠞⠋⠉⠀⠀ ⠀⠀⠹⡽⣿⣿⣿⢏⡟⠀⠀⠀⠀⠀⠀⣠⢾⣵⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⡿⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⡿⠻⠽⠽⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠈⠀⠀⠀⡀⠀⠀⠀⠈⠙⠿⣶⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀ ⡀⠐⠀⠁⠂⠈⠄⠐⠈⠈⠐⠀⠀⠀⠈⠛⣿⣯⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⡜⢤⠐⠈⠀⠁⠈⢀⠐⢀⠁⠂⠐⠀⠛⠛⠛⠛⠛⠛⠛⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠻⣷⣮⣱⡄⣌⡤⠒⠈⠀⠠⠐⢀⠂⠄⠀⠠⠀⡀⠀⠄⡀⢀⡀⠉⠙⠿⣷⣤⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣠⣔⣿⠿⠛⠁⠀⠀⢀⠂⠡⢀⠀⠄⠠⠈⠄⠠⠀⡐⠀⢀⠀⠈⠁⠒⣆⠀⠙⠿⣮⣻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣿⠟⠁⠀⡀⠄⠡⠈⡀⠐⠀⢂⠐⠈⢀⠂⠌⠀⢁⠠⠈⡀⠐⠠⢐⣿⣿⣿⣶⣄⠈⠙⠿⣯⣟⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠄⠂⢀⠐⠀⡁⠀⠠⠈⡀⠄⠐⠀⠀⠂⠈⠄⠀⠂⢀⠂⠁⠀⣿⣿⣿⣿⣿⣦⠀⣀⣀⣉⡛⢷⣯⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠂⢈⠀⠠⠁⡀⢀⠁⠐⠀⠐⠀⡈⠐⠠⠁⠂⢈⠐⠀⡀⠂⠀⢻⣿⣿⣿⣿⣿⣧⡯⡜⣭⢛⣦⡘⢿⣞⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠐⠠⠀⠁⠄⠐⡀⠠⢈⠐⠈⢀⠀⠈⠄⠂⠐⠀⠀⠒⠀⢂⠀⡀⣌⠛⠿⠿⠛⠸⣷⡙⢦⣋⡖⣿⣬⣿⣾⣧⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠌⣀⢠⣀⣆⡀⢀⠂⡀⢂⠈⢀⠠⠁⠀⣐⣬⣶⣷⠀⠀⢂⠀⠀⢻⣷⠂⢀⠠⠀⠹⣿⣲⣝⣾⣿⠿⣛⢛⡛⣛⠻⣷⣤⣤⣀⠀⠀ ⠀⠀⢾⣽⣿⣿⣿⣿⣦⡐⠀⠄⢈⠀⡀⠀⠐⠛⠿⢿⠇⠀⢀⠀⢀⣤⡿⠏⠀⠀⠐⣀⣢⣽⣷⣿⣿⢇⣳⣼⡶⣷⣮⣵⣉⠏⣿⣯⠀⠀ ⠀⢨⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠀⠀⠄⡁⢂⠀⠀⣠⣴⡶⡶⠾⠟⠋⠁⠀⢀⣤⣷⣿⠿⢛⣿⣿⣟⣾⣻⢾⣽⣷⣯⣿⡽⣿⡸⣿⡆⠀ ⠀⠒⣿⣿⣿⣿⣿⣿⣿⡿⠀⢻⣧⣄⠀⢀⢀⣠⣾⠛⠀⠀⡀⠀⢀⢠⣠⣾⡿⢛⠍⣰⣬⣶⢻⣿⣞⣷⣻⣿⣿⣿⣿⣿⣿⣟⡗⣿⣇⠀ ⠀⠈⠻⢿⣿⣿⣿⣿⠟⠁⢀⠀⠘⠻⠿⡿⠛⠋⠀⠀⠀⠁⣠⣴⣾⠿⣛⣵⣬⣷⣿⡿⣯⢿⡘⣿⣟⡾⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⣿⡀ ⢀⣠⣤⣤⣬⣉⡍⠀⠀⠂⠜⢀⣾⣾⣄⠀⠀⠠⠐⣈⣴⣿⢿⣯⣷⣿⣿⡿⣟⣯⣷⣟⣯⣿⣵⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣟⢾⣿⡇ ⣎⡓⠀⠈⢩⡛⠿⣷⣄⠀⠈⢰⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢿⣿⢻⣟⡟⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣻⣞⣿⠃ ⣜⡹⣒⢖⡫⣜⡳⣜⢻⣆⡈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣟⣿⡿⣽⣾⢿⣞⣿⣾⡇⣿⣯⣟⡿⣿⣿⣿⣿⣿⢯⣷⢯⣿⣷ ⣮⠱⡭⣎⠵⣪⠕⣮⡙⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣯⣿⢿⣽⣯⢿⣞⣿⣣⣿⣿⢾⣽⢯⡿⣽⣻⣞⡿⣽⢯⣿⡿ ⣷⢋⢶⡩⢞⡥⣛⠴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣾⡿⣷⣿⣯⣿⣷⣿⣿⣿⡿⣿⢿⣿⣻⢾⣻⣽⣿⣿⣿⡽⣯⣿⣿⠀ ⣟⢯⣶⣙⣎⠶⣩⣞⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣽⣳⣯⢿⣽⣯⣿⣿⣯⣷⣻⣿⣿⣾⣟⣿⡇⠀⠀ ⣿⢞⡶⣏⠾⡿⢟⠫⡔⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣻⢾⣽⣻⣞⣿⠂⠀⠀ ⣿⣿⣶⣮⣷⣼⠾⡱⢌⠳⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣯⣉⠉⢻⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⣷⣿⠏⠀⠀⠀ ⠉⠙⣿⣿⡿⢃⢎⡱⢊⡕⢢⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢙⣿⣿⣿⣿⣧⢃⡄⠘⣿⣽⡄⠀⠉⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀ ⢠⣾⣿⡟⠁⣘⢎⡱⠣⡜⣡⠚⣼⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠠⠀⣿⣿⣿⢾⣿⠰⡘⡄⠘⢷⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⠏⠀⣌⢣⠒⣌⠳⡘⢤⠓⣬⣿⣿⣿⣿⡿⠁⠀⡀⠀⠐⠈⠀⠠⢽⣿⣿⡿⢣⠱⡱⣘⢃⠈⣿⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⢴⡆⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣀⠀⢻⡆⢀⣀⣤⠤⠤⠴⢶⣦⡤⠤⣿ ⢾⣷⡴⠶⠛⠋⢩⣭⣽⣿⣧⣀⣀⣉⣉⡙⣿⣿⣏⣉⣀⣠⣤⣮⣷⣿⣧⣤⣿ ⢸⣿⡤⠶⠞⠛⠉⠉⠁⠁⠀⠀⠀⠈⠉⠙⢻⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⣹ ⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⢠⣿ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠙⠛⠒⠲⠶⠶⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣤⣤⣴⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠹
⣾⣧⡾⢩⣽⡆⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣮⣥⣓⢦⣤⡀⠀⣶⡏⠑⣴⣦⠀⠀ ⣿⣡⡈⢀⣺⣽⡴⢒⣤⡶⠟⠛⠉⠉⡔⠀⠈⠈⠙⠻⣶⣙⢧⣿⣵⣤⢾⣿⠀⠀ ⡟⣼⣧⣾⣿⣧⣿⣋⠅⢢⢉⠒⡌⡡⢌⠡⢍⡘⠤⢀⢈⣽⡿⠋⠹⣿⣏⠉⠆⢠ ⠘⣼⢿⣟⠀⣹⣯⠹⣿⠷⣾⣤⣆⣡⠌⢒⠢⡘⢄⣷⡟⢻⣇⠀⠀⢻⣿⣾⢠⠊ ⠀⠹⡞⣿⣿⣿⣿⣇⢹⣧⠀⠀⢻⣿⣿⣷⣶⣽⣿⣿⣿⡌⣿⣆⠀⠀⢿⣿⡏⠀ ⠀⢠⢻⡿⢛⣿⣿⣿⡆⢿⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⡄⠀⣾⡟⡇⠀ ⠀⠄⣿⠗⣠⠘⣿⣿⣿⡌⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣼⡟⢷⣹⣄ ⣧⣾⠋⠴⣀⠣⣽⣿⣿⣿⡘⣿⡄⠀⠈⣿⣿⣿⠿⠿⢿⠿⣿⣷⣿⠟⣀⢺⣷⣟ ⢹⡃⡘⠔⣠⢻⣿⢡⢞⣻⣷⣽⣿⣤⡾⠟⡍⠎⡌⠓⣌⠆⡡⢂⣤⣦⣴⡿⣣⠞ ⠉⡇⡘⠌⡴⢣⣿⠐⣾⣟⠠⠛⡍⠓⡌⣱⣈⣆⣙⡣⣌⣵⡾⢟⠫⣹⡟⡼⠁⠀ ⠀⠡⢌⠣⣜⢣⣿⠂⡜⠻⠿⠷⠾⠿⠟⡛⢛⠛⡛⠛⠟⡩⢐⣬⣾⣿⣍⡁⢄⠀ ⠀⠈⢆⠳⣌⠧⣿⣶⣈⡱⣈⢌⡱⢈⡒⣡⢊⣔⣡⣭⣶⠾⢟⡋⠘⣷⡍⠻⣦⢽ ⠀⢈⢦⢛⡬⢚⣿⣈⢛⡛⠟⠿⠻⢟⠻⣛⢛⡋⢿⣿⡀⠋⠄⠠⠁⢸⣿⡄⢹⣿ ⠀⢘⡎⢧⢚⣹⡟⡠⢎⡌⡹⢌⠓⡌⠣⠆⢃⠘⡀⢿⡇⢈⣠⣥⣾⠟⢿⡆⢹⣞ ⠀⠘⣘⣣⣍⠾⠃⠁⠂⢀⡁⠂⠔⠠⠁⠄⣢⠴⣴⣾⣿⣟⣛⣉⣀⣤⣻⠇⣸⠝
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡠⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠀⠀⢈⠻⣿⣿⣻⣿⣿ ⠀⠀⠀⠀⠀⠰⠔⠀⠀⢠⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⠀⢧⠀⢠⠡⢹⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⠄⢸⡆⠀⠄⢀⠀⠀⠀⡄⠀⠘⡄⠘⠀⠀⣦⢣⣻⣿⣿⣿ ⢀⢰⡄⠀⠀⠀⣇⡜⠀⢾⡇⠀⡇⠸⡆⡄⠀⣇⠀⠀⡇⢼⡇⡄⠁⡼⣿⣶⣿⣿ ⢸⣸⣧⠀⠀⠰⢸⠁⡌⢸⣇⠀⢿⠘⣷⡗⠀⣿⢸⢧⣧⣼⡇⡇⣄⣧⣼⣷⡻⣿ ⣜⣯⢟⡀⠀⠀⢃⣾⢤⡴⠟⢺⢿⠿⠛⠷⠘⠃⢸⠊⣿⠟⣽⠗⠻⣿⣿⣿⣧⠹ ⣿⣷⣿⣥⠀⠀⠈⢜⡀⠙⠢⠬⠬⠟⠀⠀⠀⠀⠈⠈⠉⢸⣿⡀⠀⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣧⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡝⣧⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⡗⡣⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣿⣷⠈⢧⠀⠹⢿⣿⣿ ⣿⣿⣿⣿⣷⠘⣷⡀⠀⢊⢆⠀⠀⠀⠀⠂⢉⡠⢉⠝⢿⣿⣿⣧⡀⠣⠀⠡⡻⣿ ⣿⣿⣿⣿⣿⡀⣿⣿⡄⠀⠣⠳⣤⣀⠀⠀⠀⡰⠓⢢⡄⢻⣿⣿⣷⣄⠑⠄⠑⡈ ⣿⣿⣿⣿⣿⡇⢹⣯⢮⣆⢡⠑⡙⣻⣭⢩⠉⢀⣶⣿⣷⡀⢻⣿⣿⡿⣿⣦⡀⠈ ⣟⣿⣿⣿⣿⡇⢸⣿⡜⣿⣆⠆⠐⡌⢺⣥⢶⢻⣿⣿⣿⣷⡄⢻⣿⢁⡿⡷⡀⠑ ⣿⣽⣿⣿⣿⡇⢏⠻⡇⢻⣿⣾⠀⠈⠄⠡⠙⠊⠘⣿⣿⣿⣿⡮⡇⣾⠓⡈⠪⡢ ⢻⣧⢿⣿⣿⢰⣷⡑⢼⢸⢋⢿⡆⠀⠈⢆⢩⠂⢄⡈⣟⡛⠿⠃⢻⣿⡑⢔⢄⠈
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⡙⢷⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡪⢫⠇⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⠙⠦⣙⠲⡤⠔⠂⠉⠉⠁⠀⠀⠉⠓⠎⡡⠎⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢆⠀⠀⡸⠋⠀⠤⠠⠤⠤⠠⠄⠀⠀⠀⠀⠈⢦⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⡼⠁⠀⢀⡤⠐⠒⠈⠐⠂⠤⠤⠤⠤⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡅⠀⠒⠉⠀⠉⣄⠀⠀⠀⡔⠈⠉⠐⠄⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⠁⢀⠝⣛⡯⣍⡗⠛⢺⢉⢭⡥⢄⠈⠉⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⣀⣈⣑⣛⣓⣨⠇⠀⠸⣌⣚⣉⠉⢀⣀⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡁⠀⡇⠉⠉⠀⠀⠠⣤⠤⠤⠤⠴⡤⠀⠐⢊⣉⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢁⠠⠀⠈⠒⠤⠔⠋⠀⠀⠄⢀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠥⠀⠀⠀⡠⢂⡴⢲⢲⣄⣠⡐⠄⣀⠀⠈⢙⡯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠼⣿⢥⡀⢰⠁⣰⣯⣧⣼⣼⣀⣇⣿⡆⢸⢀⣠⣼⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣶⡎⠂⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⡎⢼⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⢴⠿⡯⢼⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⢩⣿⣿⡀⠀⠀⠀⠀⠀ ⠄⠒⠉⠉⠁⠀⠈⣤⡻⡫⡇⢹⣿⣿⣿⣿⣿⣿⣿⡇⢸⣼⡇⣸⠉⠒⠢⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣷⡇⠀⠻⣿⣿⣿⣿⣿⠟⠀⢸⠷⡮⠎⠀⠀⠀⠀⠉⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡦⠄⣈⣿⣛⡯⡁⣀⣠⣯⠆⠐⠒⠒⠠⠤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣴⠿⡷⣧⣗⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⢤⡤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡤⠖⠲⡍⣇⠀⠳⠀⠀⠀⠈⠀⠀⠀⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⢦⣀⠀⠈⢻⡆⠀⢃⠀⠀⠠⠀⠀⠀⠰⠀⠀⢠⢿⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⢤⡀⠹⠀⠘⡄⠀⠀⠀⠀⠀⡘⠀⢀⣾⠎⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢣⠀⣀⣀⡀⢀⠃⠠⠾⠋⡀⠀⡰⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⢳⡖⠟⠉⠁⠀⢉⠟⠒⢦⣤⠞⢻⠊⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡯⡀⠀⠱⡆⠀⠀⣠⠎⠀⠀⣰⠃⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠀⠈⢢⣀⣁⡠⠴⣷⣶⣾⡿⠇⠀⢸⠀⢷⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡖⠋⠀⢠⠒⢉⣿⣩⣧⠀⠀⠀⡿⠀⠀⢀⡞⠀⡿⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡇⠀⢀⣼⡄⠘⢿⣿⣿⣀⣀⡾⠁⠀⢀⡀⠀⣴⠃⠠⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣶⡿⠛⠃⠀⠀⣇⣾⣹⣇⠀⢀⣴⣻⣷⣾⢷⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠓⠒⠦⢤⣠⣻⣿⣧⣿⣴⣿⡟⣿⣿⣿⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⣠⠤⣿⡄⠹⠿⠋⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠧⠤⠔⠻⣷⠄⣀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠈⣯⣉⠁⠲⣌⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠒⠒⣊⣉⡩⠽⢿⡉⠀⢀⣠⠤⡖⠚⢻⡟⠒⣦⣞⢣⡴⠚⠳⣌⠱⣄⠈⢢⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣿⣉⣀⣀⡤⠔⠚⠋⢉⠉⢉⡄⠀⡟⠲⠁⠈⠉⢠⢿⢿⠀⠀⠀⢹⣆⠸⡀⠈⢇⠸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡀⠀⠀⢠⡇⠀⠀⠀⠀⢀⣴⠦⠒⠋⠠⠊⠁⣰⠁⠀⠀⣸⢧⣾⣿⣿⣧⠀⠀⢸⣿⠀⡇⠀⠘⡀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣎⠉⢓⠒⢺⠀⠀⠀⠀⠀⠈⠀⢠⡾⠋⠀⢠⡵⠃⢰⠀⠐⠿⣼⣿⣿⣿⣿⠀⠀⣸⢸⠀⡇⠀⢠⠱⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⢱⣀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠟⠁⠀⢺⠀⠀⢾⢻⣿⣿⣿⣿⠀⠀⡏⢸⠀⣇⠀⠈⣧⠳⡈⠳⣀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⡀⠻⣆⢰⡈⢳⣄⠀⠀⣆⠀⠀⣆⠀⠀⠀⠀⢀⣸⡆⠀⠀⠤⠙⡟⠻⡟⠀⠀⣇⢸⠀⠸⡄⠀⠸⣷⡘⢦⡈⠑⠲⣶ ⠀⠀⠀⢸⠀⠀⠀⠉⡏⠙⠛⠉⠈⠙⠒⣇⡈⠑⢾⡶⠒⠒⠋⠙⣲⠿⡖⠒⠒⠀⠀⢴⠃⠀⠀⢹⢸⠀⠀⠹⡄⠀⠹⡌⠢⣌⠓⣴⠏ ⠀⠀⠀⢸⠀⠀⣠⣴⡇⠀⠀⠀⠀⠀⠀⡇⠀⠉⢹⣿⡂⠉⠉⠿⣅⠀⠙⣖⠂⠈⠉⣏⡀⠀⠀⠘⣎⣇⠀⠀⠘⢆⠀⠘⣦⡈⠛⠁⠀ ⠀⠀⠀⠀⢷⣾⣿⡿⠀⠀⠀⠀⠀⠀⡾⢽⠭⣭⠿⣿⡗⠒⡈⠉⢸⠀⠀⠈⢦⠄⠀⠀⢛⡄⠀⠀⠹⣼⣄⣀⣀⣠⠷⠒⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡿⠁⠀⠀⠀⠀⠀⠠⣟⣿⣒⣚⣹⣿⡟⠉⠀⠀⢸⠀⠀⠀⠈⣖⠂⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⡿⠠⠄⢺⣿⡟⠁⠐⠐⡾⠀⠀⠀⠀⠸⡆⠀⠄⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠂⠈⢸⡟⠀⠀⠐⢶⠇⠀⠀⠀⠀⠀⡗⠀⠤⢀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣷⣦⣀⣸⣿⣶⣄⢀⠎⠀⠀⠀⠀⠀⣸⣤⣀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠙⢻⡟⠛⠛⠛⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣯⠴⠦⢤⣬⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣺⣷⣦⣀⣶⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠉⢩⣯⡉⠁⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣏⠻⠿⢃⣠⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠑⠒⠋⢉⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⢼⡿⢆⢀⡾⣍⣴⠈⠑⠢⢄⣀⠀⠀⠀⠀ ⠀⠀⢀⠞⠁⠀⠘⠋⡼⡏⢀⠏⠀⠀⠀⠀⡼⢀⡱⡄⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⣗⣢⠋⠀⠀⠀⠀⠼⢁⡞⠁⣱⠀⠀ ⠀⢸⡇⢰⣀⠤⠂⢰⡏⡏⠀⠐⠒⠚⠻⡷⢀⡠⠞⣿⡀⠀ ⠀⣸⠀⠀⢹⠀⡠⠈⡗⡇⠀⠀⠀⠀⠀⢱⣈⠔⠋⠀⣧⠀ ⢠⣇⣐⡒⣾⠘⠁⢠⣿⣇⡀⠀⠀⠀⢀⡿⣟⡾⢗⡋⠙⡆ ⠸⡉⠀⠈⠙⠒⣶⣿⡟⠟⠉⠓⢶⣶⠟⠉⠀⠀⠀⠈⣵⠇ ⠀⠙⠦⣀⣀⣸⢷⣿⡃⣀⣀⣀⣿⡿⠦⠤⣤⠤⠒⠉⠀⠀ ⠀⠀⠀⠀⠈⣧⠼⢻⢻⠁⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠷⣦⢼⣤⣧⣤⣶⠴⠒⣲⠞⠳⡀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⠀⠙⠿⠧⠼⠗⢛⡯⠟⠀⢇⣰⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⡇⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠚⢿⣿⣗⢖⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⡿⢋⣀⣀⡤⠴⠻⢿⣮⢀⡐⠒⠤⣑⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠁⠀⠀⣴⠏⠀⠙⣮⣵⣦⡈⠳⣕⡄⣠⣷⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣤⣤⣄⠸⣯⢎⢟⢆⢘⣟⢿⣿⠇⠀⠀ ⠀⠀⠀⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠈⡌⡎⠘⣎⡟⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣷⣿⡀⣷⢁⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣾⣷⣧⣿⣿⣿⡏⢿⣧⣿⡜⡀⠀⠀ ⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠻⢿⣿⣿⣿⣿⡿⠕⠂⢻⣿⣧⢁⠀⠀ ⠀⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠉⣿⣿⣿⡿⠁⣠⣶⢷⢿⣿⡌⢆⠀ ⠁⠀⡿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣴⣾⣶⠬⠘⣹⠟⠀⢰⢿⡗⠈⣸⡟⡏⣆⠂ ⢀⡼⢁⢧⡟⣿⣾⣿⡏⢻⡍⠣⠝⢟⡿⠀⠚⠁⠀⠀⠀⠉⠁⢀⣿⢠⢿⢿⠄ ⣿⣹⢼⣼⢹⡿⣿⣯⣧⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠇⣸⡟⣾⠀ ⠻⣿⣾⣿⣿⡃⢹⣿⣿⣶⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣯⣼⣿⠟⠋⠀ ⠀⠙⠿⣽⣿⣻⣺⣿⣿⣿⣿⡐⠗⣄⡀⠀⠀⠀⠀⠀⠀⣠⡞⠩⠊⠣⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠛⠑⠸⠙⣿⡷⠦⠊⠘⠢⠤⣀⣀⠰⠁⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢤⡤⠒⠁⠀⠀⠠⡀⠐⠊⠁⡦⠒⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⡄⠀⠒⠢⠄⢈⠀⠄⠀⢃⠠⠊⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⢠⣷⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣷⠄⠀⢀⡀⠀⠀ ⠀⠀⠀⣼⠃⠹⣦⡀⠀⢠⣿⣿⣿⣤⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠙⣿⣿⣿⡿⠋⣄⠀⡼⣧⠀⠀ ⠀⢠⣾⡃⠀⠀⢨⠟⠻⣿⠛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣾⣿⣿⡆⠻⠁⠀⠐⢾⣄⣨⡷⠀ ⠀⠀⠈⠻⣄⢠⡏⠀⠀⠃⠀⢹⣿⣿⠀⠻⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⠏⠀⠀ ⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⠀⠀⠻⣿⣤⢿⣾⡝⠻⠿⣿⡀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⢀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⡄⢹⣷⠀⠀⠈⠁⢠⣄⣲⣶⣤⣦⣀⠀⠉⠛⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢴⣿⠀ ⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠈⠛⠀⠀⠀⠀⠛⠉⠉⢹⣿⣿⡽⠛⠂⠀⠀⠘⣡⠾⣽⡟⠀⠀⠀⠀⢀⣀⠀⠀⠉⠀ ⠀⠀⠀⠀⠘⠁⣿⡦⠀⠀⠀⠀⠀⡇⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡰⢳⢠⡿⠀⠀⠀⠀⠂⠘⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠉⠁⠊⠉⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠤⣾⡇⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣴⡿⠷⠒⠒⠀⠊⠉⢁⡇⠀⠀⠀⠀⠀⠈⣉⣲⣾⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⢉⡠⠤⠒⢐⣒⣊⣩⣽⣧⣀⣠⣤⣤⣶⣿⣿⡿⢿⡄⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣏⣥⣶⡿⠿⠟⠛⢛⣛⣉⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⡇⣤⠤⠒⠊⢉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣋⡥⠖⠚⣿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⠀⢀⣾⣷⣿⡆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢶⣤⣀⠀⠀ ⠀⠀⠛⠁⠀⠀⢰⣿⣿⣿⣭⣽⣿⣀⣿⣿⣿⣿⢿⢀⡾⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⠋⠁⠈⠙⣿⣠⠀⠙⡟⢻⣧⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠈⠙⠿⣿⡀⣿⣴⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣧⡉⣑⢲⣴⡿⡿⠀⠁⠀⢹⣿⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⢻⢿⣿⡙⠷⠗⠀⠀⠀⢻⣿⡇ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠉⠉⠉⠉⠀⠈⠀⢰⣶⣾⣿⡇ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀ ⠀⢿⣇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣸⡿⠀ ⠀⢈⣿⣷⣄⠈⠛⠿⣿⣿⣿⣿⣿⣿⠿⠋⠉⣠⣾⣿⡁⠀ ⢀⣼⣿⡏⠙⠻⣷⣦⣄⡉⠛⠛⢉⣠⣴⣾⠟⠋⢹⣿⣧⡀ ⢸⣿⣿⡇⠀⠀⠛⠋⠉⠛⢷⣾⠛⠋⠙⠛⠀⠀⢸⣿⣿⡇ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⠀⢻⣿⣧⣄⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣠⣼⣿⡟⠀ ⠀⢸⣿⣿⣿⣷⡀⠀⢠⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⡇⠀ ⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠉⠉⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀ ⠀⠀⠈⠻⣿⣿⣿⡄⠰⠾⠿⠿⠷⠆⠀⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⡆⣿⢀⣀⣿⣤⣯⣟⣍⣁⣿⣻⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⢿⣿⣿⣿⣿⣿⣿⡟⠟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠃⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣡⣿⡀⣹⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡿⡗⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣾⣿⡿⠉⣿⠉⢻⣿⣿⣿⣿⠋⠉⠸⣿⣿⣿⣿⣿⣿⣿⢸⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⡇⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⣟⣿⡇⠀⡇⠀⠸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⠇⠈⣿⣿⡇⣿⣿⣿⢹⣿⡞⠀⡇⠈⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠸⣿⣷⣀⣧⣀⠀⣿⣿⣿⣿⠦⡀⠀⢸⣿⣿⣿⣿⣿⡿⢸⢠⠞⣿⣿⡇⢸⣿⣿⣿⣿⣷⣾⣁⣸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣦⣾⣿⠿⠟⠛⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⡿⠿⠿⠇⠚⠀⠀⢈⣭⣾⠿⠛⠛⠋⠉⠉⢻⠙⣿⣆⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣟⠁⢿⡀⠀⠠⠰⣖⠠⠈⢹⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢻⡄⡀⠒⠶⠀⠐⣦⡇⠀⠞⠉⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠳⠈⠓⢤⡀⠀⠀⢀⣠⠞⢀⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠙⠧⠤⠤⢴⣞⡭⠄⠀⠀⢠⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠐⠾⠶⠾⠿⠿⠟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢰⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⣯⣼⣿⣿⣿ ⣼⡽⠉⠉⠙⠲⢤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢧⠁⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣼⠁⣿⣿⣿⣿ ⠘⢧⡀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡇⠈⢧⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣰⠃⢰⣿⣿⣿⣿ ⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠙⣿⡏⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢧⡀⠀⠙⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠀⠀⠀⠀⠀⢀⡼⠃⠀⣸⣿⣿⣿⣿ ⠀⠀⠀⠈⠑⢆⠀⠀⠀⠀⠀⠘⢷⡀⠘⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⢶⡒⠒⠒⠒⠒⠊⠉⣉⡿⠋⠉⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣾⣷⣄⠀⠀⠀⠀⠀⠹⣶⣻⣿⣿⣿⣿⣿⣿⣇⠀⠀⢤⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣥⡄⠀⢰⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣚⢒⣿⣿⣵⣿⣷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠒⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⡈⢩⡤⠧⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣯⣾⢿⣿⣿⣿⠋⣎⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠏⡸⢻⣿⣸⣿⣗⣼⣿⣿⣿⣿⣿ ⠀⢀⣾⣿⣿⣿⣿⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣟⣿⣿⣿⠋⠀⠈⠑⢿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣯⠞⠁⠀⢻⣿⣯⣿⣿⣿⣿⣿⣟⣿ ⣠⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣤⣄⣠⣤⣾⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠈⣿⣿⣾⣽⣿⣿⣿⣿⣹ ⠉⠉⠉⠉⠉⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠿⣧ ⠀⠀⠀⠀⣸⠁⠉⠉⠲⢦⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠖⠚⠉⠉⠉⠉⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⡀ ⠀⠀⠀⠀⡇⠀⠀⢀⣀⠴⢚⠝⠲⢤⣀⣳⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠤⠤⠖⠚⠉⠁⠀⣀⣀⡤⠀⠈⠉⢲⣤⠴⣒⡭⢛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⠿⠿⢛⡛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣿⢻⣿⣿⣶⣶⣢⣆⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⣛⣛⣭⣵⣶⠾⢟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣾⣿⡟⣻⣿⣿⣿⣿⣿⣿⣭⣭⢠⣾⣿⣯⣭⣤⡬⣩⣭⣽⡶⠿⢟⣛⣯⣭⡶⣶⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁⠿⣿⡿⣿⣿⣿⣿⣿⣯⡄⣿⣿⣿⣿⡟⠃⠈⠱⠶⠾⠛⢋⣭⣿⠶⣟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣾⣿⣿⣿⣿⣟⡓⢠⣾⣿⠿⣛⣛⡛⣟⣛⣛⡛⢶⣶⣶⣶⣶⣶⣥⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⣴⣿⣿⣿⣿⣿⡿⠯⢁⣿⢟⣴⣿⣿⡿⢳⣿⣿⣿⠏⠰⠶⠶⢾⣽⣭⣭⣭⣙⣛⣛⣛⣛⡛⠿⠿⠿⠿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢀⣾⣿⣿⣿⣿⣿⣿⣿⠋⣾⡟⣼⣿⣿⢟⣴⣿⡿⢏⣀⣙⣛⣛⣛⡳⠶⠶⠶⣶⣭⣭⣭⣭⣭⣝⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣼⣿⣿⣿⣿⣿⣿⠟⣂⣼⡟⣱⣿⣿⢏⣼⣿⣿⠁⠬⣭⣙⣛⣛⣛⣛⠛⠿⠿⠿⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢁⣤⣾⣿⣿⣿⣷⣶⣶⣾⣟⣫⣾⣿⣿⡏⣾⣿⣿⡅⢶⣶⣦⣤⣤⣬⣭⣭⣉⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠱⣿⣛⣋⣤⣴⣶⣶⣦⣭⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⡿⠶⠜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⠿⢿⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣶⣿⣷⣶⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠀⠉⢿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠟⠉⠀⢸⣿⠛⠛⠛⠿⠿⢿⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⢻⣿⣿⣿⣿⣿⣿⡎⣿⡇⠀⠀⠀⠙⠉⠻⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⣠⣿⠏⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠛⠛⠛⠉⠉⠉⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡷⠀⠀ ⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠈⠻⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣼⣶⠀⠀⠀⠀⠀⠀⠛⠿⠿⠟⠁⠀⠀ ⣰⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⣭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢿⣶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠿⠿⠿⠿⢿⣿⡿⠿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⡠⠄⠒⠊⠉⠀⠀⠀⢀⣀⠤⠄⠀⣼⣇⠀⣠⡈⣿⣧⣼⣿⡷⢿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠒⠈⠁⠀⠀⠀⣀⡠⠔⠒⢈⣁⠠⠀⠀⠀⣿⣿⣻⣏⣀⣿⣿⡹⣿⣿⣾⣿⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣄⣀⣤⣶⣿⣿⣿⣶⣾⣉⣀⣀⣀⣀⣼⣿⣿⡇⠀⢹⣿⣿⣁⣿⣿⢟⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠼⠿⠟⠻⠿⠿⡿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⢿⡛⢤⣼⣿⣿⣶⢿⣿⣿⣿⣿⣟⣛⣻⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⡤⢿⣿⠚⠃⠘⠛⡻⠉⠀⡿⢹⣯⣿ ⠀⠀⠀⠀⢀⣠⣴⣿⢿⡒⢒⣒⣶⣶⣶⣶⣶⣤⣤⡤⠤⠤⢤⣄⠀⢰⣷⣄⣀⣠⣤⣖⣊⣉⣁⠀⠐⢛⡟⠀⠀⠀⠀⡇⠀⢀⠃⣼⣧⣿ ⠀⠀⢠⠞⠋⡽⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠋⠉⣿⠚⣿⠿⠛⠋⠉⠀⢀⡠⠔⠛⢳⣼⡇⠀⠀⠀⢠⣿⠀⡼⢠⣿⣶⣿ ⠀⠀⣜⠀⣸⣩⣟⣿⠾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣹⡀⢀⣿⡿⠁⠀⠀⠀⢠⠎⣡⠔⠚⠉⢹⣿⣻⠀⠀⢀⡾⠓⣾⣷⣿⣿⣿⣿ ⠀⢀⣀⣨⣽⡟⣿⣿⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⣿⢯⣼⠁⠀⠀⠀⢀⡇⡼⢓⠶⠲⣄⠀⣿⡤⠔⣊⡵⢞⣯⡿⠟⢻⣿⣿⢿ ⡖⠋⠀⢈⡿⢿⣿⣿⡿⠿⠿⠶⢿⣷⣿⣾⣿⣿⣿⣟⣀⣀⣻⣾⣿⠋⢉⣹⠋⠙⠉⢡⠏⣀⣀⠈⣧⣸⡗⣊⣵⠾⠛⠉⢧⡀⢸⣟⡽⠰ ⠁⠧⣄⣼⠀⢸⣿⣿⢳⠀⠀⠀⠀⠀⣠⣭⣽⠟⠛⣿⣾⠟⠋⠉⠉⠉⠉⠉⠉⠙⢲⡟⣸⣏⣟⣇⢻⡾⠟⠋⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀ ⠀⠀⠀⣿⠛⢾⣾⣿⠿⠀⣀⣀⣀⣸⣿⣴⡇⠀⠀⠗⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⣿⣛⣟⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣄⠈⢏⠉⠻⠿⡿⠧⣬⣿⣿⣿⣷⣶⣴⡾⠧⠤⣤⣤⣤⣤⣤⠤⠴⠛⣽⢸⣿⣿⣉⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠳⢌⣣⣀⣀⣀⡴⠟⠁⠀⠀⠉⠉⠉⠉⠛⠒⠛⠋⠉⠀⡏⠀⠀⠀⡇⠸⣿⣿⣽⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢧⠀⠙⠿⠋⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠘⣄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⡛⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠋⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⢸⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠷⠛⠋⠉⠉⠛⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢀⣀⣀⣀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⠉⠉⠉⠙⠒⠦⣬⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡟⠋⣁⣀⡀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⠀⢹⠆⠀⢀⠤⣄⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠈⠉⠋⠀⢰⣇⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⡿⠋⠠⡀⠀⠀⠀⠠⣄⡰⠃⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠃⠀⠀⠙⢦⣀⠀⠻⢂⣠⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣭⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣻⠆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⢀⣴⣿⣿⣿⣿⡏⣿⣿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⢹⣿⣶⣄⠀⠀⢀⣸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣷⣤⣾⣿⣿⣿⣿⣿⣿⠁⢿⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣼⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣷⣀⣿⣿⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣋⣉⠉⠛⠿⣿⣿⣿⡄⣹⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢰⠒⠤⣀⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣙⣉⣀⣀⣈⣽⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣑⣦⣤⡉⠓⠂⠠⣴⣿⣿⣿⡇⠀⠉⠛⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠛⠋⠉⠉⣟⢻⡯⣭⢍⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣳⠤⠤⠤⠀⠀⠀⠀⢿⣿⣿⣿⠇⣠⡇⠀⣀⠈⡙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣤⡤⠤⣀⡿⢸⠃⡸⢘⣧⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣜⣯⣭⠭⠤⠀⠀⣀⣼⣿⣿⡟⣰⣿⡇⢠⣿⣆⣿⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣦⡈⠁⠀⠀⠑⢋⣴⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠈⠑⠿⠖⠚⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⣧⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣛⡛⠛⠲⠶⠛⢉⣼⣿⣿⣿⣿⣿⡿⢹⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠿⣿⡷⠦⠴⣾⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠁⢀⡆⢸⣿⡇⢠⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⢀⣴⡟⠀⢸⣿⡇⢸⡆⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⣠⣾⠏⠀⠀⠈⣿⣇⠘⣿⡈⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⣰⣿⡟⠀⣠⡆⠀⣿⣿⠀⢻⣧⠘⣿⣿⣿⣿⣿⡿⢀⣿⣿⡏⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣴⣿⡿⠀⢰⣿⠃⠀⢺⣿⡆⠈⢿⣷⡘⢿⣿⣿⠟⢁⣾⣿⡿⠀⣸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⠇⢀⣿⣿⠀⠀⠸⣿⣿⡀⠘⣿⣿⣦⣤⣤⣴⣿⣿⡿⠁⢀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⣼⣿⡇⠀⠀⠀⣿⣿⣷⡄⠈⠻⠿⣿⣿⡿⠿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⣸⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢠⣿⣿⣿⠀⢠⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⣿⠀⢸⣧⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣧⡀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣷⣄⠀⠀⠉⠛⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⡿⢶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⣤⣀⡀⠀⣀⣀⣠⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠹⣿⣷⣦⣌⡙⠿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢰⡄⠘⢿⣿⣿⣿⣦⣌⠙⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣦⣬⣭⣽⣿⡍⣿⡇⢸⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣴⢸⣿⣿⣿⣿⣿⡟⣼⣿⣿⠀⠙⢿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⢼⣿⣿⣿⣿⡟⢰⣿⣿⣿⣆⠀⠈⠙⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⢸⣿⣿⣿⣿⡄⢹⣿⣿⣿⠿⢧⡀⠀⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡻⢿⣦⣄⣈⣙⣛⣛⣛⣛⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⡏⣼⣿⣿⣿⣿⣿⣄⠋⣩⣶⡇⠈⣷⠀⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣮⣿⡿⣿⣿⣿⣿⣿⣿⣶⣄⠙⢿⣿⣿⣏⡻⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣦⣌⠙⠻⠿⢿⢁⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣷⣦⣄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣾⢸⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣶⣤⣄⣉⠙⠛⠿⣿⣿⣿⣿⣿⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⡟⢸⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣌⣙⠻⢿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⢸⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣾⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣌⠛⢿⣿⣿⣿⣿⣿⣿⣧⠙⢿⣿⣿⣿⡟⢉⣉⣉⣉⣩⣵⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣡⣾⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣈⠛⠿⣿⣿⣿⣿⣷⡀⠻⣿⡟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⠙⠻⣿⣿⣿⣄⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⡈⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣶⣌⡙⠛⠛⠛⠛⣋⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⡶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⡿⠿⠿⠿⠷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⡿⣿⡛⠹⣇⣀⠀⡀⠀⠀⠀⠀⠀⠉⠛⢿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠟⣁⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀ ⠀⠀⣴⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣝⣿⣿⣟⠃⠀⠀⠀⠀⠈⢿⣦⠀⠀ ⠀⣼⡟⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢿⣿⣷⣶⣤⣀⣄⠀⠀⢻⣧⠀ ⢰⣿⠀⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⠿⠟⠛⠶⣄⡀⠙⠿⣾⣿⣿⣿⠁⠀⠀⣿⡆ ⣾⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣤⣀⣟⣯⡋⠀⠀⠀⢸⣷ ⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠉⠉⠈⣧⠀⠀⠠⣸⣿ ⢿⡇⠾⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠹⣦⣀⡠⢻⡿ ⠸⣿⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠒⠒⣿⠇ ⠀⢻⣧⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⡟⠀ ⠀⠀⠻⣷⡐⠴⠏⠀⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⠟⠀⠀ ⠀⠀⠀⠙⢿⣦⣄⣀⠁⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢠⡴⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠈⢷⡾⠛⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠈⢹⡏⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⠃⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⠤⢤⣄⣀⡀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⠴⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⢤⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠘⣧⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠘⣇⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠈⠙⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⢀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢠⣿⣰⣆⡶⠘⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠁⠾⠰⢿⠇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⠁⠈⠈⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢏⣿⣿⣿⣿⣿⠟⣿⣿⡿⢩⣿⣿⢹⣿⣿⣿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⣤⠀⣰⡿⣡⣾⣿⣿⣿⣿⣿⣴⣿⢿⣧⣿⣿⣿⡄⣿⣿⣿⣧⡻⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⠀⠀⠀⠀⣠⣴⡄⣀⣠⣈⠀⠀⢀⣴⣿⣾⣿⣿⠟⠸⣫⣿⣿⣿⡏⣴⣿⣿⣿⣿⣿⡈⢿⣿⡿⢿⣦⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀ ⠀⠀⠀⠀⢀⣤⠶⠋⠁⡀⢻⣿⣿⡿⠀⠀⠈⣼⣿⣿⣿⠏⣠⣾⣿⠿⣿⠟⣸⣛⢿⣿⣿⣿⠟⣛⡚⢿⣿⣎⠻⣿⣿⠷⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⢻⣔⣦⡈⣷⣝⣾⣿⠉⠁⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣡⣿⠓⣿⣿⣿⠘⣿⣿⣃⣾⣿⣿⡞⣿⣿⣷⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠋⠘⠿⠿⠋⠀⠀⠀⠈⠻⠿⠟⠁⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠶⠶⠶⠤⠤⠄ ⠘⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣀⣀⣀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠶⠶⠶⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠶⣄⠀⠀⣰⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡀⠀⢠⠞⠀⠀⠟⣛⣻⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡇⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣨⣇⣀⣧⠀⠀⠀⣿⣿⡶⠞⣿⣿⣦⣴⣦⣖⠲⣦⣄⣀⣀⣠⣴⣿⠿⣿⣽⠃⡇⠀⠀⢈⠀⢩⠄⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⢈⡇⠀⠀⠸⣯⣶⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣷⣄⡏⠀⡇⠀⠀⠸⣻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣠⣾⣿⣷⣿⠟⡫⢂⣴⣿⠿⡽⠁⣿⣿⣿⣿⣿⣎⢿⠏⠀⠀⡃⠀⠀⠀⠛⢗⠀⠀ ⠃⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⣿⣿⡟⣱⠏⣴⣾⣿⠏⢀⢀⣼⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡇⠀⠀⠀⠀⠈⠢⡀ ⠄⠀⠠⠀⢦⠀⢲⢠⣦⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⣾⣿⣫⣾⣷⢿⠿⣿⡯⠟⠋⣽⣯⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡉ ⠀⠀⠀⠀⠉⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⢠⠎⠴⢻⣿⡟⡽⣟⠈⠚⠊⠁⠀⠀⠀⠈⠿⠿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢦⣀⡀⠙⢶⢾⡞⠀⠀⠀⠀⠀⡄⠀⡰⠁⠀⣠⣿⡿⣹⠁⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣿⢻⣿⣿⣿⡙⢿⣷⣀⣧⠖⠉⠀⠀⠀⠀⠰ ⠀⠀⠁⢠⡤⡀⠀⣀⢤⠀⠀⢠⠁⡰⠁⢀⣴⣿⣿⢣⡿⢸⣿⣆⠀⠀⠀⠉⠀⠀⠀⢀⣾⣿⢘⣿⣿⣻⣧⠀⠙⢻⡇⠀⡀⠀⠀⠀⠀⠀ ⠈⠀⠀⠘⠀⠏⠻⠯⠭⠀⠀⡜⠀⠀⣠⡾⣿⣷⣿⣿⣧⣾⣿⣿⡷⣄⠀⠀⢀⣠⣶⣿⣿⣿⠸⣿⣿⣿⣿⡆⢢⢸⡇⠀⣹⠀⠀⠀⠀⢰ ⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣐⣠⡴⠟⢉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠛⠿⠟⣩⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⡄⢹⣧⣄⣿⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣴⣿⣿⣿⣿⡿⣿⣇⣿⣿⣿⣧⣤⣤⣴⣿⣿⡿⠉⠀⠀⠈⠻⣿⣿⣿⡜⢿⣾⠀⠉⢿⡀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢿⣿⣿⣿⡟⣿⣿⣿⣹⣿⠋⠉⢹⣿⡿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠈⢻⠀⢀⠀⡇⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣥⣶⣿⣿⣿⠉⣿⣽⣿⣷⣿⠻⢉⣽⢿⣿⣿⣿⠃⢀⡠⠒⠁⠀⠀⠀⣼⣿⣿⣿⣇⠘⠓⠶⣤⡦⠼⠦⠤⠼ ⠀⠀⠀⠀⠀⠀⠀⢀⠞⢉⣤⠞⣻⣿⠃⠀⣼⣿⣿⣿⡇⣴⢏⣼⡿⣿⣿⠟⠒⠁⠀⠀⠀⡀⠤⠚⣿⣿⣿⣿⣷⣡⠀⠀⠀⠙⠳⠦⣄⣀ ⠀⠀⠀⠀⠀⠀⢠⠊⣰⡟⢁⣾⣿⠇⠀⣰⣿⣟⣿⣿⣷⣶⠿⣿⣷⣿⠟⠁⠀⣠⡤⠒⠁⠀⠀⣰⡿⣿⣿⣿⣿⣷⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠐⠃⣰⢋⣴⣿⣿⡿⠀⣸⣿⡟⢘⣿⣿⣋⣠⣴⣿⢟⣿⣴⣶⣾⣧⣤⡀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⣾⣿⢯⣾⠀⡴⣿⡟⣠⣾⣿⣾⢧⠋⢰⠇⣿⣿⣿⣿⣯⣿⣿⣿⣷⣄⣾⣿⣿⢿⣿⣿⠻⣿⣿⣟⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠋⣸⣿⣣⣾⣿⣿⣿⣿⠟⣵⣿⠁⣿⡆⢳⡎⠀⢹⠛⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣆⠙⠿⣿⣷⣬⣁⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣴⣿⡿⣿⣿⣿⣿⣿⣿⠀⡟⢸⠀⢻⡱⣸⡁⢀⠇⠀⠀⠀⢀⡟⠛⠛⠛⣡⣿⣿⣿⣿⡙⣿⣿⡄⠀⠀⠉⠙⠛⠛⠛⠉ ⠀⠤⠶⠾⠟⠛⡿⢁⡴⠋⡹⠏⠁⠉⠛⣿⠀⣾⣆⠈⠃⣿⢹⣾⣶⣦⣤⣠⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠛⠋⢠⠊⠀⠀⠀⠀⣰⣯⡴⠋⢹⣇⣰⣻⣿⠿⢿⣭⣿⣧⡤⠊⠀⢠⣿⡿⢸⣿⣿⣿⣿⡄⠀⠛⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⢀⣼⡟⠻⠀⠀⢸⣿⣿⡟⠙⠿⣿⣿⡏⠀⠀⡀⢀⣿⣿⠇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⡧⠀⠀⠀⠀⢻⡏⠀⢠⣷⣾⡿⠁⠀⠔⠁⠋⣽⡟⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⢤⣼⠏⠉⠙⠶⠦⣿⠳⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣯⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⠷⠶⣬⣭⡇⠀⠀⠀⠀⠀⣠⣶⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠉⠁⠀⠀⠀⣠⠶⠚⠉⠙⠛⠋⢁⣀⣄⡀⠙⢿⡄⠀⠀⠀⠀⢸⣧⡾⠋⠉⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⢿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⡷⠄⠀⣠⠟⠁⠀⢀⣀⣀⠀⠀⡞⠉⠈⢳⠀⠘⣿⠀⠀⠀⠀⠈⢿⣿⠋⠉⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠷⣆⠻⡍⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⡀⢰⣿⠀⠀⣰⠞⠉⠉⠳⣦⣇⡀⢀⣾⠀⠀⣿⡄⠀⠀⠀⠀⣨⡿⠛⠓⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣇⠀⠘⣦⡙⢷⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣀⣸⣷⠀⠀⢿⣆⡀⠀⢀⣻⠿⠷⠟⠁⠀⠀⠘⢷⡄⠀⣶⣟⣏⣟⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣦⡀⢈⣷⣄⠙⣷⣜⢧⣄⠀⠀⠀⠀⠀⠀⣿⠟⡙⢻⣿⠀⠀⠀⠉⠛⠚⠛⠳⢤⣀⣀⣧⣀⡀⠀⢘⣿⣄⠉⠉⠀⢹⣦⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢙⣿⢋⣽⠟⠉⣻⣿⠳⣮⣙⠶⣦⣀⠀⠀⢿⣄⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣌⡉⠙⠻⠿⣿⣿⠿⠻⢶⠀⠀⢹⡇⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡇⠾⠁⠀⡴⠿⠻⣷⣤⣉⠛⠓⠿⢷⣄⠀⠙⢷⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠉⠛⠛⠛⠛⠛⢦⣀⣼⡷⠷⢾⣿⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⢠⠾⠿⢶⣯⡉⠲⣦⣤⣼⡇⠀⢀⣠⡾⠿⢷⣤⣀⠀⠰⠴⠾⠛⢦⣄⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⢰⡇⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⣀⠀⠀⠀⠀⠐⢾⣿⣭⣤⡾⢋⣤⡷⠟⠛⠛⠻⣦⠀⠀⠉⠻⣿⣟⣛⠛⠛⠛⣛⣿⠷⠶⠤⠤⠤⠤⠾⠃⡄⠀⣾⠁⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⢷⣤⡀⠀⠀⡼⢿⣍⣡⡴⠛⠉⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⡇⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠹⣿⣦⣀⡀⠀⢀⣰⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⡙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠈⠙⠛⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⡶⠶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⣤⣀⡔⢀⣼⠏⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣮⣥⣶⣿⣷⠶⠚⠛⣹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣌⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢀⣀⣠⣴⡶⠶⠞⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣤⣴⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡶⠿⠋⠉⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠉⠉⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⣀⣠⣴⠶⠞⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠈⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣾⣿⣁⠀⠀⢀⣤⠾⠛⠛⠉⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⣤⣴⣾⠿⠟⠛⠛⠛⠉⠉⠉⠀⠈⠉⠙⠻⢷⣾⣿⣟⠋⠁⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣦⣴⣾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠿⠷⣦⣤⡤⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠈⠻⣶⣤⣀⠀⢀⣠⣶⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⢰⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⣉⣻⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠙⠻⠶⠶⣶⣶⡶⠿⢿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣴⣟⠉⠀⠀⠀⣠⣶⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠷⣦⣤⣄⣀⡀⠀⠀⠀⠈⢉⣿⠆⠀⠀⠀⠀ ⢠⣾⡋⠉⠙⠻⢿⣶⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠶⠶⠞⠋⠉⠀⠀⠀⠀⠀ ⠈⠛⠻⠷⠶⠤⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⠤⢴⡒⠶⠲⠲⠲⠆⠂⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠙⢿⣿⣷⣦⣤⣄⣀⣀⣰⣿⠏⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠙⢛⣿⢻⡿⢻⣿⡋⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⡇⠀⠈⠙⠷⣄⣀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⣰⡇⠀⢀⣄⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠷⠀⢸⣿⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠟⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡶⠶⣶⣶⡖⠀⠀⠀⣀⣶⡏⢰⡿⠀⠀⠈⣿⡀⢙⣿⣦⣀⣀⠀⠻⢧⣄⣀⡀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠗⠛⠉⠁⠀⢀⣠⡶⠛⢿⣷⣿⠃⠀⠀⠀⠙⢿⣾⣟⣁⣉⣹⡿⠂⠀⠈⠉⠉⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⠛⠛⢻⣿⡿⠃⢠⣴⡶⢶⣧⠀⠉⠙⣛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⢀⣠⠾⣿⡿⠀⠀⠀⠘⢻⣿⠃⠀⠀⠀⢹⢿⣛⡷⠶⠤⢤⣀⣀⣀⣿⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣷⣄⣀⡴⠞⠋⣡⢾⡿⠁⠀⠀⠀⢀⡾⢻⣆⠀⠀⠀⠸⣆⠀⠉⠓⠶⣄⣀⠈⣹⣿⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣿⣿⣇⢀⡴⠚⢁⡾⠁⠀⠀⠀⣴⠟⠁⠀⠙⠳⠦⠄⠀⠈⠳⣄⠀⠀⠀⢉⣿⡿⠷⠤⢤⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠶⠚⠛⠁⠀⠀⣹⣿⣿⣄⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡶⠋⠁⠀⢙⡿⢿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⡾⠿⣿⣷⣶⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠒⠋⠁⠀⠀⣀⡴⠋⠁⠀⠈⠉⢹⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠈⠙⢿⣷⣌⠉⠓⠲⠶⢶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠛⠛⢿⣷⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⠏⠙⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄ ⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠻⠿⢿⣷⣶⣶⣦⡄⠀⠀⠀⠀⠈⣿⠛⠛⠿⢿⣿⣿⣿⡿⠿⠛⠛⠛⠛⢉⣼⡟⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢹⣧ ⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⢀⣿⣀⣀⣴⡿⠇⣾⣏⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⢸⣿⣄⡀⠀⠀⢠⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⠛⠛⠛⠁⠀⠻⣿⣦⣤⣤⣠⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣤⣀⣀⣀⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⢰⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠁⠀⠀⠀⠀⢀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⡀⢀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣇⢸⣠⡖⢰⠂⢂⡀⡀⡀⣦⣖⣸⣤⡀⢰⣒⣤⡃⠀⡄⢲⠀⠐⠀⣀⡜⣏⣿⢙⡇⠾⣥⣀⣻⣞⣶⣇⣹⣠⠟⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⡁⠀⠀⣶⣲⠄⠀⠀⣉⠓⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡔⠉⠀⠸⣇⡽⠀⠀⠛⠁⠀⠀⢾⣻⠃⠀⠈⠢⣀⣀⣀⠀⠀ ⠀⠀⠀⢠⠋⣐⣲⣄⠀⣠⢔⡚⡝⣹⣩⢫⣕⣢⣤⣴⣶⣾⣿⢿⣿⣿⡇⠀ ⠀⠀⢠⠇⠀⠙⠳⢀⣜⣕⣾⣼⣷⣿⣿⡿⠿⠿⠿⣿⡉⠀⣤⣤⣿⣿⣿⡀ ⠀⣀⣼⣤⣴⣶⣾⣿⣿⡿⠛⠋⠛⢿⣷⠀⠰⣦⠀⢸⣇⠀⢠⣤⡿⣿⣿⣇ ⢨⣿⣿⠛⠻⣿⡅⠸⣿⠀⠰⣿⡄⠀⢻⡆⠀⢠⣴⣿⣿⡄⣀⣀⣤⣿⣿⣿ ⠰⣿⣿⡄⢀⠀⠑⠀⢿⡄⠀⠻⠇⢀⣼⣷⣠⣼⣿⣿⣿⡿⠿⠟⠛⡻⠉⠀ ⠀⢿⣿⣧⠀⢷⣦⣀⣸⣟⣷⣶⣶⣿⣿⣿⢿⣟⣟⡽⢁⣄⡀⠀⢠⠃⠀⠀ ⠀⠸⣿⣿⣶⣾⡿⠿⠟⠛⠫⢽⣙⣳⣳⣋⡫⠔⢋⠀⠉⠻⠞⢠⠋⠀⠀⠀ ⠀⠀⠉⠉⠉⠣⣀⠀⢀⡾⣆⡆⠀⢀⠤⣄⠀⠸⣯⠇⠀⢀⡴⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠙⠀⠀⠘⠶⠏⠀⠀⣈⠤⠒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠄⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⢀⣠⠖⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠙⢮⣷⢄⠤⣤⣤⢤⣀⣰⢎⣁⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢀⣴⣶⠛⠁⠀⠀⠈⠙⠻⣟⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⣽⣿⠀⠀⠀⠀⠀⠀⠙⡎⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣸⣿⣧⠄⢰⣤⣾⣴⣤⠀⢻⣄⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢧⣿⣟⣷⣐⣾⣿⠿⣿⣷⣼⢻⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣿⣿⠿⣿⡟⠟⠀⣿⣿⣿⣯⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠻⢟⣿⡆⠉⠀⠀⠀⠛⢻⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⡿⢛⡅⠀⢹⣿⢟⣿⣦⡀⠀⣠⣿⣾⣿⢻⡇⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣶⣿⠴⠚⠉⠀⠀⠀⣰⡞⢿⣄⠹⣯⢽⣿⢿⡏⣄⣽⡄⠈⠻⣟⡦⣤⡀⠀⠀⠀⠀ ⠀⣠⣾⠛⠁⠀⡄⢰⣆⣤⡴⣿⡟⠁⠈⠛⠙⠻⣿⡟⣿⡄⠈⣷⢼⣷⣤⡈⠛⢿⡻⣷⡀⠀⠀ ⠀⠙⢧⣄⣀⣤⣴⢿⣻⣦⣾⠿⠃⠀⠀⠀⠀⢀⣿⡆⣿⠃⠀⠘⢾⣽⡞⠻⣷⣄⢿⣿⠃⠀⠀ ⠀⣀⣠⣿⣛⣿⢷⣾⣟⣿⠇⡅⠀⠀⠀⠀⠒⠋⠙⣷⣿⠀⠀⠀⠘⢣⡿⣞⢮⡙⢷⣿⠀⠀⠀ ⢸⠏⠉⢹⣿⣿⣿⣡⣿⡟⠚⠁⠀⠀⠀⠑⠀⠀⢀⣿⣿⠀⠀⠀⢺⣟⢷⣻⡀⣷⣘⡿⠀⠀⠀ ⠀⠀⠀⠈⣻⣿⣿⡿⣿⡷⠇⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⠳⡄⠀⠈⢿⣿⣿⣇⣿⡟⠁⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⢿⣿⣿⣿⣠⣟⡀⢀⡾⣋⣹⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⣹⢿⣿⣿⣿⢿⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣉⣾⣿⣿⠟⠊⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⡿⠿⢿⣷⢤⣤⣴⣄⣤⣶⣿⡿⣿⠹⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠊⠁⠀⠘⢿⡄⠈⣹⣿⣿⠏⠈⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⢿⣿⠻⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡄⠀⠀⠀⣾⡇⠀⢸⣿⠀⡅⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣏⠀⠀⠈⣿⠀⠀⢸⣿⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⢸⡟⠀⠀⠀⢻⡆⠀⠀⢘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡆⠀⢸⡇⠀⠀⠀⢸⣧⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣷⠀⣼⡇⠀⠀⠀⠈⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡀⣹⡇⠀⠀⠀⠀⢻⣧⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⠹⣿⡿⠀⠀⠀⠀⠀⠘⣿⣆⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠘⣿⠃⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠘⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣇⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⣭⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣧⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠜⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⡛⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠨⣵⣤⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡻⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣇⣈⠻⣿⣿⣿⣿⠋⠙⠲⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣾⠟⠿⠿⠟⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⣄⠈⠻⣿⡇⠀⠀⠀⠀⠉⠳⢦⣀⣠⣴⡾⢿⣋⠯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣿⡇⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣤⣾⣿⣟⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠟⠛⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢰⡟⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠛⠃⠀⠉⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⢶⣤⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⣿⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⠛⣶⣤⣰⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢻⡀⠀⠀ ⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠘⣿⡝⢷⡀⣀⣤⠟⠁⠀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⢸⡟⠂⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠙⣭⡏⠀⠀⣀⠘⡄⠀⠀⠀⠀⢠⣿⣿⣿⠋⠓⢶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀ ⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠏⠀⠀⠀⠀⡄⠻⡄⠀⠀⠀⢸⣿⣿⣿⣷⣤⣾⡇⠀⠀⠀⠀⠀⠀⢀⣧⡄⠀⠀⠀⠀⠀⠀⠸⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠘⣄⠻⣄⠀⠀⠈⠻⠛⠻⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠰⣶⣄⣀⣄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠘⢀⠈⣧⠀⠀⠀⠀⠀⢀⣀⠈⠁⠉⠉⠉⠉⡉⠓⠶⣤⠀⠀⢠⡏⢀⣿⣿⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠚⢿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣭⠀⠼⣿⣿⣿⣿⠇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠄⠀⠈⠛⢿⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⢶⣶⣶⣶⣶⣿⣦⡀⠀⠀⢠⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠙⠿⣿⣷⣿⠏⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⢙⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⢠⡄⠀⠀⠀⢠⡇⠀ ⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣴⣤⠶⠂⠀⠀⠉⡃⠀⠀⡞⠀⠀ ⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡼⠋⠀⠀⠀⠀⠈⠛⠃⠀⣼⠃⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⡀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠐⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣉⠉⠉⠉⠛⠛⠛⠲⠶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡴⡀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣇⣀⣀⣀⣀⣠⣟⣁⣀⣀⣀⣤⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣍⡉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠶⠦⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠚⠉⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠁⠀⠀⣠⠎⠀⠀⠀⢠⠃⢠⠋⢠⠇⠀⠀⠀⠀⠀⠂⠀⠀⣴⣿⣷⠀⠀⢻⡞⣆⠀⠀⠀⡀⠀⠀⠈⠱⣄⠀⠀⠀⠉⠳⣝⢾⢦⡀⠀⠈⠹⣦⠈⠻⣷⡝⠲⣄⡀⠀⠀⠀⠀⠀ ⠌⠀⢀⠞⠁⠀⠀⠀⣰⠏⢠⠏⠀⠸⠀⠀⠀⠀⠀⠀⢀⣆⣾⣹⡿⠿⡄⠀⠀⢹⣜⣆⠀⠀⠙⣆⠀⠀⠀⠙⣦⠀⠀⠀⠀⠈⠳⡵⡽⣗⣤⡀⠈⢣⡀⠈⠻⣦⠀⠉⠓⠲⢤⣀⠀ ⠀⡰⠁⠀⠀⠀⣠⢞⠏⢠⠋⠀⠀⡆⠀⠀⠀⠀⠀⢀⡞⡾⠿⣞⣩⠭⢷⡀⠀⠀⠙⣞⣆⠀⠀⠘⢇⠀⠀⠳⡘⣷⡀⠀⠀⠀⠀⠘⣿⡼⡝⢿⣦⡀⠱⠀⠀⠉⢳⡀⠀⠀⠀⠀⠉ ⠞⠀⠀⠀⢀⡴⢁⡞⣰⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⡞⣼⠷⣺⠟⠋⣁⢈⣣⡀⢠⣠⡈⢿⣧⠀⠀⠈⢧⡀⠀⠱⡜⣟⣦⡀⠀⠀⠀⠈⢿⡻⡀⠈⠳⣄⠀⠀⠀⠀⠱⡄⠀⢄⣀⣀ ⠀⠀⠀⢀⠞⢀⢞⡼⠁⠀⠀⠀⢰⠀⡆⠀⠀⠀⢸⣻⠃⠀⢠⡄⣤⠶⠦⣈⣷⡌⢷⠱⣄⠙⢷⡀⠀⠀⠳⡀⠀⠻⡼⣏⠹⢦⡀⠀⠀⠀⢻⣣⠀⠀⠘⢦⠀⠀⠀⠀⠘⢦⡀⠉⠫ ⠀⠀⢣⠟⢀⠔⠋⠀⠀⠀⠀⠀⣾⡀⡇⠀⠀⠀⣎⣧⣤⣤⣬⣧⡘⣷⣦⣖⢤⣝⣾⣧⠈⢦⡀⠙⢦⠀⠀⠹⣄⠀⢹⡻⣶⣲⣽⣦⡀⠀⠀⢻⡆⠀⠀⠈⢷⣄⠀⠀⠀⠀⠉⠂⡄ ⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢀⡼⣻⡇⡇⠀⠀⠀⣿⠋⠉⠉⠙⠛⠃⠻⣿⣿⡭⡿⣍⠙⢷⡠⠙⣦⡀⠑⢦⡀⠈⠳⡄⢻⣷⡶⢶⣶⣿⣦⡀⠺⣷⠀⠀⠀⠈⣯⣷⣄⠀⠀⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⣿⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣹⣘⠃⠀⠙⢶⣮⡙⣦⡀⠀⠀⠀⠈⠲⣿⡄⠀⠀⠙⢿⣿⣦⡙⢧⡀⠀⠀⢱⠈⠙⢦⡀⡏⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣾⣿⡇⢹⡀⠀⢸⡇⠀⠀⣀⡀⠀⠀⠀⠀⠘⣿⣿⣿⣴⣿⣞⠞⠉⠀⢸⣿⣦⣀⠀⢦⡀⠘⢧⠀⠀⠀⠘⣿⣿⣿⣦⡙⢆⠀⠈⢧⠀⠀⠙⠱⡄⡇ ⠀⠀⠀⠀⠀⠀⠀⢠⠿⡧⣿⣿⡟⢇⠀⣇⠀⠸⡇⠀⠀⠛⠁⠀⠀⠀⠀⢀⣿⣟⣯⠽⢛⣿⡷⠂⠀⠸⠛⠿⣿⣷⡀⠙⢦⠈⢣⡀⠀⠀⢿⣿⣿⣿⣿⣎⢣⠀⠈⠳⣤⡤⠴⠓⠻ ⠀⠀⠀⠀⠀⡀⢀⡟⠀⢧⢸⣾⠀⠸⡄⠘⣄⠀⢧⠀⠀⠀⠀⢀⣀⣤⢶⣿⣿⣭⠖⠚⠛⠁⠀⠀⠀⠀⢠⡴⠚⠉⣹⣄⣌⢱⡄⢳⣶⣦⣾⢿⣿⣿⡜⣯⠈⣇⢀⣴⠏⠀⠀⢠⠞ ⠀⠀⢰⡟⢹⠃⢸⣷⠀⠘⣆⣽⣷⣦⣿⡄⠘⡆⠸⡶⠶⢟⣛⠿⣿⣟⣿⠴⣒⣾⠥⠐⣀⡠⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⣼⢿⣮⣿⠋⠛⠺⣿⣿⡇⣟⣧⠟⢻⠏⠀⠀⣰⠏⠀ ⠀⡀⡸⣇⠘⡆⢸⢷⢇⠀⠹⣿⠷⠶⣒⠿⢦⠈⠢⠹⣇⠠⠶⠗⢒⣀⡏⠸⠛⠑⠚⠀⠀⠀⠀⠀⢀⠴⠚⠉⠀⣼⣿⠀⢹⣿⠈⠉⡇⠀⠀⠰⢾⣿⡇⣿⡟⢰⡟⠀⠀⣴⠇⠀⠀ ⠀⢇⢹⢻⠀⢷⣸⠈⢿⣣⠀⠘⣦⣀⠀⠐⠂⠑⢦⡀⣜⢦⡐⠚⠩⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⡈⢀⠾⠏⠀⠀⠀⠀⠀⠀⢸⡟⢠⡿⢁⡟⢀⣠⠄⣏⠔⠀⠀ ⠀⠸⡞⣇⢧⠈⣿⠀⠀⠳⣷⡄⠈⢣⡁⠀⠀⠀⠀⠙⢮⣳⣵⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⣿⣷⡟⠁⢸⢻⡟⠈⠂⡧⠀⠀⢰ ⡇⠀⠘⣽⡌⢧⡸⣇⠀⠀⠙⢯⣦⣀⠉⢢⣀⠀⠀⠀⠀⠹⣇⠈⠉⠉⡭⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⠀⢨⣶⣦⠀⠈⢹⣿⣥⢴⣿⠨⠟⠀⠀⡇⠀⠀⣿ ⠷⡄⠀⠘⠻⡄⠙⠿⣦⡀⠀⠀⠙⠦⣍⡢⢌⠑⠶⣄⣀⠀⠸⠀⢀⣠⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡼⡗⢛⣉⠁⠀⠩⠟⠀⠀⣿⣿⡅⢸⣿⠀⠀⠀⠀⣷⠞⣿⡇ ⡀⢧⢠⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⢷⡦⠴⠒⠚⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣻⠛⡛⣿⠷⣶⡀⠀⠉⠁⠀⠀⢀⣴⣿⢿⡇⠘⢸⣤⡶⠷⣶⠃⣸⣿⠃ ⣧⠘⡞⣆⠀⠈⠣⣴⢄⡀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐⣁⣠⣀⣀⣇⣀⣀⣛⣐⣼⣷⠀⠀⠀⠀⣠⣾⣿⡟⢸⠀⠀⣸⠏⠀⠀⣿⣠⣿⣿⠀ ⡏⢧⢹⠘⡄⠀⡀⠈⠦⣍⠒⠢⢤⣄⣀⠀⠀⠈⠛⢷⣄⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠈⠉⠁⠠⠀⠀⠀⠓⠳⣼⡟⠇⠀⠀⠀⣴⣿⣿⣿⡇⢸⡖⠋⢹⠀⠀⣰⢻⣿⣿⡿⢀ ⢹⠀⢳⣧⢱⠀⠸⡄⠘⡎⠙⠶⠤⣤⣈⠙⢯⡓⠶⢤⣌⠳⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⢀⣾⣿⣿⡿⢿⡃⣸⠁⠀⢸⣶⣊⣥⣾⡿⣿⡇⣼ ⡜⣇⠀⠙⣆⣧⠀⡿⡄⢸⡀⠀⣀⠀⠀⢲⡄⠙⠶⡀⠀⠙⠺⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠐⣼⠋⢹⣆⡠⠏⢀⣾⣿⣿⣿⣿⣿⣿ ⣿⠻⣆⠀⠸⡾⡄⢱⢳⡀⢇⠀⡸⣄⠀⠀⠻⡀⠐⢾⡣⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⡿⠁⠀⣴⣿⠀⡼⠯⣴⣾⣿⣿⣿⣿⣿⡟⣾⣿ ⣿⠀⢹⡀⠀⢻⣃⠸⠘⡇⢸⡄⣷⡹⣧⡀⠀⠱⡄⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣾⣿⠀⣠⣾⣿⣿⣞⣥⣾⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿ ⡇⠀⡼⢻⡀⠀⢻⡄⡆⢸⢸⡇⣸⣿⣌⢳⣦⡀⠙⣶⣦⣤⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰⣿⡏⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿ ⠀⢸⠃⢀⣧⠀⠈⡿⡇⢸⢸⡇⣿⣿⣿⣷⣮⡹⣦⣈⠻⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢁⠏⠀⣼⣿⣆⠀⠀⡇⢸⢸⣻⣿⡿⠉⠇⠙⢿⣿⣾⣗⠌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿ ⡞⠀⣼⣿⡇⠘⡄⢰⠃⡞⣿⢿⡿⢷⠀⠀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⢀⣾⣿⣿⡇⠀⢣⣸⢸⢳⠓⠛⠛⢽⣷⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣲⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⡇⠀⢨⡿⢳⣿⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢍⣳⠴⢺⣿⣿⣿⣿⣿⣿⣿⡟⡰⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⢀⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠤⣀⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣁⣴⣿⣿⣿⠛⣼⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⠀⠁⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣿⣻⣿⢻⢻⡿⣿⣿⣿⠿⡟⡿⢻⠉⡇⣾⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠄⣸⣿⣿⣿⣗⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢿⢻⠸⢰⣧⡽⣿⣻⣖⡛⣿⣾⠀⡇⠇⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⠧⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠊⠀⠀⠀⠀⠂⠨⠉⠓⡶⡂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠲⢏⠂⠀⠀⠀⠀⠀⢸⡄⣀⡔⠚⣷⠀⠀⠀ ⠀⠀⠀⠀⠤⠀⠲⡀⠀⠀⠀⠀⢀⠋⢘⠀⠀⠀⠀⠀⠀⡄⠌⠢⣄⡵⣿⣇⠀⠀ ⠰⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⠀⠸⠀⠀⡄⣄⠘⢸⠹⣷⡶⣼⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠇⣇⢾⠷⠛⠘⠛⠀⠙⠃⠿⣇⣹⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠛⢾⣾⣼⣂⠀⠀⣠⣤⣤⡀⠀⣰⣿⠿⠛⡀⠀ ⠀⠀⠀⠻⡾⠿⠃⠀⠁⠄⠀⠀⠐⠈⠟⡻⡿⣷⣤⣈⢀⠀⢰⣾⠟⠉⠀⠠⠡⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⠁⣾⠚⠇⠙⠏⠁⠇⠰⡆⠛⠁⢀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠸⡆⠈⡆⢥⣀⠤⣴⣖⠠⡄⣰⠇⠰⠳⡇⠀ ⠀⠀⠀⢀⣀⠀⢀⡠⠀⠀⠀⠀⢠⣆⡈⢄⡟⠢⠙⢛⠷⠞⡞⠛⡁⢴⣥⠁⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡁⡟⠤⢄⠀⠙⠉⠈⠋⠁⡀⡠⢧⡁⢩⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⠉⢐⡂⠈⠉⠀⠀⢸⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣞⣛⣉⣉⡁⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠛⢶⣄⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠙⣦⡀⢻⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣠⢤⣤⣤⣌⣹⣄⠻⣿⡀⠀⠀⠀⠀ ⠀⠀⣸⡟⠀⠀⠀⢀⣠⠶⠒⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣾⣧⣠⣿⣿⣿⣿⣽⡆⠘⣧⡀⠀⠀⠀ ⢠⣴⣿⠀⠀⠀⣴⠛⠁⢀⠠⣤⣤⣄⡙⣿⢶⡄⠀⠀⠀⠀⠻⣦⠀⢸⣅⣹⣿⣿⣿⣿⣿⡏⢹⡄⢹⣷⡄⠀⠀ ⢾⢙⡟⠀⠀⢠⡟⠁⢰⣷⣤⣿⣿⣿⣿⡏⢹⠇⠀⠀⠀⠀⠀⠘⢧⡀⢻⣿⣿⣿⣿⣿⡿⠁⣸⠇⠀⢿⣿⡀⠀ ⢸⡾⠁⠀⠀⠸⣷⠀⢠⣼⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⢿⣿⣿⣭⡴⠞⠁⠀⠀⠘⣿⣷⠀ ⢸⡇⠀⠀⠀⠀⢹⡀⠈⠛⠿⣿⣿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⢸⡇⠀⠀⠀⠀⠘⢷⣄⣀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠚⣟⣏⠉⠉⣹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆ ⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⣻⣯⣠⣷⣴⠞⠛⠛⠷⠚⠋⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠶⠶⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⢀⣠⣤⣤⣤⠶⠒⠶⢤⡄⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⢧⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⢞⡿⠃⠀⠀⠙⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇ ⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣁⢀⣀⠀⠀⠀⠀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣭⣷⠖⢶⣿⣽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃ ⠀⠀⠀⢸⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀ ⠀⠀⠀⠘⣧⠘⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀ ⠀⠀⠀⠀⠹⡆⠀⠀⠉⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠲⡶⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠕⢭⢿⡟⠁⠀⢀⢆⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡎⡹⣾⠉⡻⠐⠀⠉⠐⠎⠀ ⠀⠀⠀⠀⠀⠀⡖⠢⣴⣉⠩⣾⠙⡳⠟⠁⠀⠀⠀⠠⠀⡸⠀ ⠀⢐⠦⣿⣻⣯⡵⠺⣏⠙⣻⠟⠉⠀⠀⠀⠀⢀⣰⠗⢠⠃⠀ ⣼⡟⠻⠛⠛⣁⣹⣾⡿⠟⠁⠀⠀⠀⠤⣦⡴⠂⢁⠔⠁⠀⠀ ⡿⡖⢠⠞⠋⠉⠀⠀⠀⠀⠀⠀⣀⠴⠚⢉⠠⠊⠁⠀⠀⠀⠀ ⠘⠚⠞⠢⢀⣀⣀⣀⣀⡐⠉⠭⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠉⠓⠒⠒⠤⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⣠⣋⠿⢋⡡⠶⠒⠒⠒⠤⠤⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⡠⣺⡾⠗⠋⠁⠀⠀⠀⠀⠀⣀⣠⠜⠃⠀⠀⠈⠉⠉⠑⠒⢲⡦⣤⣤⣤⣄⣀⣀⣀⠀⠀⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⣠⡾⠛⠉⠀⣠⣤⣤⣦⣤⡴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣿⡆⠀⡶⡎⠛⣏⠉⢻⣿⣿⡇⣤⣤⢠ ⠀⠀⠀⠀⠀⢸⡠⠚⠁⢀⣀⣴⣿⣿⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣻⣧⠀⢳⣇⠀⠸⡄⢸⣿⣿⡇⣿⡇⣸ ⠀⠀⠀⠀⣠⠏⢀⣠⠶⠛⢁⣤⣴⡾⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢼⣼⣿⠇⢇⠘⣿⠀⠀⠘⠈⣿⣿⡇⢻⡃⢿ ⠀⠀⢀⡔⢡⡶⠋⠁⢠⡾⢫⡟⠙⢿⣿⣿⠀⠀⠀⠀⣼⣧⣄⣀⣠⣤⣶⣿⠿⠛⠋⠉⠉⢻⣿⣿⠀⠈⣧⠸⣇⠀⠀⠈⣿⣿⣇⠈⢿⣾ ⡆⢀⠞⣴⡟⠁⢀⢴⡿⣰⡟⣰⣤⣾⣿⣉⡆⠀⠀⣤⣽⠿⢿⣿⣿⣯⣥⣀⣀⡀⠀⠀⠀⢸⣿⡇⠀⢀⣧⠱⣝⣶⡀⠀⢻⣿⣿⣿⣿⣿ ⢇⣼⣾⡟⢀⡴⠋⣾⢳⣿⠁⡭⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢹⣿⣿⢷⣭⣿⣿⠿⣷⡶⢿⣿⠇⠀⣸⠇⡇⠈⣿⣷⣄⣸⣿⣿⡿⠿⢿ ⣾⠏⡞⣴⣟⠀⢰⢧⣿⢹⡀⢣⢸⢙⣞⡁⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣾⠁⠈⠛⠳⠀⡀⢸⡿⠀⢀⡿⢰⢇⣼⣿⣿⣿⣿⣿⣿⡇⣤⣼ ⡣⣼⣿⠁⡇⠀⣼⡟⣿⠈⣧⠘⡷⠟⠻⣿⣦⠀⠀⠀⠀⠀⠀⠿⣿⣿⣷⣶⣶⣿⠿⠋⢁⣿⠃⠀⣼⠇⡼⣼⣿⣿⣿⣿⠋⠻⠿⠿⣻⣿ ⠉⡟⠉⠉⡇⢠⣿⠃⣿⠀⡹⠏⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠛⠶⣶⣿⠏⢀⣼⣿⣠⣷⣿⣿⣿⠿⠁⠀⠀⣠⣾⠅⠹ ⠔⠁⠀⠀⢳⢸⡿⡇⢻⢷⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢀⡞⣿⡇⢸⣿⣿⣿⠏⠀⠀⠀⠀⠹⡟⠀⢠ ⠄⠀⠀⠀⠘⣾⡇⠘⣬⡆⠙⢦⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣰⣿⣿⣿⠀⣿⣿⣿⠋⠀⠀⠀⠀⣀⣴⣏⣠⣾ ⠀⠀⠀⠀⠀⡿⢷⠀⠈⠻⡄⠀⣽⣷⣄⣀⠽⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⡾⠋⣿⡿⡏⢰⣿⡿⠃⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠇⠈⠁⠀⠀⠀⠈⡿⢄⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠋⠀⣰⠏⢸⣇⣾⠟⠁⠀⠀⢀⣾⣿⣥⣶⣽⣿⣿⣿ ⡄⢴⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⣀⣀⣀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢸⡿⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠛⠋⠉⠉ ⡇⢸⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠙⠒⠬⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠈⠁⠀⠀⠀⠀⣸⣿⣿⠟⠉⠀⠀⠀⠀⢭ ⠁⢸⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⢩ ⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡶⠾⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣨ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣧⣀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⣿⣿⢿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽ ⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⢿⣯⣤⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣵⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⣤⡐⠆⢿⡷⡟⣧⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠈⠃⠀⠀⣲⡟⠉⢝⠿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣹⣿⣤⣀⠀⠄⠈⣿⣿⡿⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣺⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀ ⠀⠘⢿⣿⣿⣿⣿⣿⡿⠻⠁⠀⠀⠀⠀⢀⣀⣠⣠⣶⡾⣿⡟⠁ ⠀⣀⣀⢀⡉⣉⣁⣈⣠⣤⡆⢰⡶⠃⢸⡏⣹⣿⣿⡁⠁⣿⣷⡀ ⠀⣿⣹⢿⣿⡏⠋⣿⣯⣸⣧⣼⣯⡄⠀⡏⠻⠸⠘⠛⠋⠃⠀⠀ ⠀⠉⠀⠈⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⣼⡸⣾⢻⣠⣄⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⡏⠁⠉⠘⠿⢻⠘⣎⣇⣿⡆⠰⣟⢦⣤⢦⣰⣿⣠⢻⠇⣤⠀⢀⡀⢀⠀ ⠀⠀⢻⡀⠀⠀⡀⠸⣼⠟⠈⠁⣇⡼⡎⣇⠉⠘⠁⠙⢡⡯⣴⢽⣰⢏⣿⣻⠃ ⠀⠀⠈⠑⠶⠶⠿⣆⠀⠀⠀⠀⠉⠁⣇⣈⣳⠴⣒⣆⣈⠇⣉⠈⣡⠾⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣉⣑⡖⠟⠈⠉⠻⣯⡥⠞⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⡅⠀⠀⠛⠃⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠦⣴⡞⠀⠈⢢⣀⠀⠀⢠⠀⣄⢙⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⡤⢾⠇⠀⠀⠈⠧⠀⠀⠀⠀⠉⣻⡗⢽⡶⠞⠁⠀⠀⠀⠀⠀ ⠀⡴⠊⠁⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠁⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⢀⣷⢚⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡧⡞⠀⠀⢡⠀⠀⠀⢰⠀⠀⠀⠀⠀⣘⠀⢸⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣸⠀⠀⣸⠀⠀⠀⠘⣇⠀⠀⠀⡠⠻⣧⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡇⢠⠟⢻⠛⢻⠋⠙⣦⠀⣰⡇⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⢸⡀⢸⡀⢸⠀⠀⡿⠒⡏⢸⡄⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡆⢸⠃⠀⣿⠌⡆⠀⢣⡰⡟⠘⣇⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⠈⢧⠀⢸⠀⠘⡄⢸⡇⡇⠀⢹⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢧⣀⣸⡆⠈⢳⣶⣷⢼⠀⢳⡀⣿⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠿⠇⠀⠀⠀⠀⠸⣦⣠⡇⢸⣦⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠙⠻⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠐⠚⠛⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠹⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠈⠙⢻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢹⣿⣿⣮⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢧⠚⠋⠀⠈⠛⠛⠛⠿⢿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠱⣄⠀⠀⠀⠈⠉⠙⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⢿⢿⣿⣿⣷⣶⣤⣈⠳⣄⠀⠀⠀⠀⢤⣽⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⢿⣦⡀⠀⠀⢈⠏⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢹⣿⣦⡀⠀⠀⠀⠘⠛⣿⣿⣿⠷⢄⠀⠀⠀ ⠀⢀⣴⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣆⠀⠀⠀⠀⣿⣿⣁⣀⣼⣷⡄⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣤⣤⣤⣤⣄⣀⣀⣀⣘⣻⣿⣷⣆⣠⡾⣫⣿⣿⣿⣿⣿⣷⡄ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⣯⣿⣿⣿⣿⣿⣿⣟⠛⠻⣽⣟⣿⣿⣿⣶⣶⣿⣿⡟⠋⠉⠻⡇ ⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣶⠿⣿⣿⡆⠸⣿⣾⣿⣟⣿⣿⣷⣼⡇⣀⣀⣠⡇ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠉⣻⠿⣾⡟⣊⣹⣿⣿⣿⣿⣿⣿⣿⡟⣟⣻⣿⣷ ⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠏⠉⠉⠛⠋ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Warning: This item may contain sensitive themes such as nudity.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⠻⢿⣏⡉⠙⠛⠛⣹⡿⠟⠛⠉⠉⠉⠉⠉⠛⠛⠿⢿⣛⣛⠛⠛⠛⢛⣿⡿⠿⠿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⢀⠉⢹⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣾⠋⠁⠀⢀⣾⡷⠀⠀⠤⠤⠤⠤⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢀⠕⠁⠀⠀⠀⠀⢠⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⣀⣴⣏⣿⣥⣤⣤⣤⣴⣿⣿⣿ ⣿⣶⣷⣾⣿⣾⣷⣶⣶⣶⣶⣿⣿⣴⠋⠀⠀⠀⠀⠀⠀⠸⡄⡎⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢤⣄⠀⠀⠀⡇⢀⠋⡗⠀⠀⢸⠁⣠⣆⣀⠤⠖⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⡟⠲⣜⣷⠀⠀⣇⢰⠀⢀⠏⠀⢰⡿⢛⡭⠖⠒⢶⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⠅⠀⠈⣿⣧⠁⠈⡍⠐⣾⠆⢰⡿⣰⠋⠀⢈⡍⢻⣷⣀⠀⠀⠀⠀⠀⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⡷⠀⠀⢀⣿⢻⠀⡖⢻⠀⡸⠀⣿⠁⡿⣆⠐⠲⠖⢋⣿⡿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⣿⡶⣶⣿⣿⡿⠀⠀⠘⠀⠁⠀⡇⠀⣧⣼⣟⣶⢶⡿⢋⣼⡟⠐⠂⠀⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠓⠾⠗⣾⣭⡀⠀⣀⣠⣀⣀⣄⠀⠀⠋⠉⠹⠦⠾⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⠄⠀⠀⠀⠀⡴⠁⠀⠈⠳⡝⠛⢿⠟⡽⠀⢸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣜⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡀⠀⢸⡇⡆⠈⢦⡀⠈⢦⡀⠀⠁⠀⢸⠀⢳⣤⠀⠀⠀⠀⠀⠀⠉⠒⠦⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡤⢈⠄⣠⣿⠀⣿⡀⠈⡿⣆⠀⢻⣆⠀⢀⡞⠜⡾⠛⠲⢄⠀⣄⠈⠒⢤⡀⠀⠀⠘⢦⡀⢀⣩⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⠎⠘⣙⡇⢸⣿⣇⠀⢿⡈⠳⡄⠙⢦⡞⠉⠉⠁⠀⠀⠀⠙⠺⣷⣄⠢⡌⠁⢄⡱⣄⠙⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠆⢀⣾⠛⢆⡈⠉⠁⠀⠀⠉⠛⠁⠀⣸⠀⡄⠐⢆⠀⠈⠢⣄⣄⠀⠙⣲⠈⠓⠀⠉⢤⣕⣈⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠉⠁⠀⣀⠉⢹⣯⠏⡉⢉⡓⠒⢚⠁⠀⣸⠀⢈⠳⠀⠠⣈⠛⠁⠀⠈⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡇⣨⣷⠀⠋⠃⢀⠇⠈⠇⡀⠈⡆⢄⠛⠃⢨⣧⠀⠀⠎⠃⠀⠀⢀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠛⡆⠀⢀⣀⠀⠘⠀⠃⢀⠉⠘⠀⠀⡀⠉⢠⢤⣸⡓⠲⠤⣸⠉⠂⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠹⠖⠉⠿⠛⢇⢀⡴⢿⣇⡴⠛⠟⠙⣤⠎⢀⡼⠛⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠓⢄⠀⢨⠋⠀⡜⠋⠀⠀⢀⣀⠼⠛⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡄⠀⠀⢣⡀⠀⠉⢾⠄⢀⣤⠤⠐⠊⠁⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⡇⠀⠀⠀⢳⡄⠀⠘⠀⠀⠁⠀⠀⢀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⠁⠀⠀⠀⠀⢯⠢⢀⣤⣤⡀⠀⢒⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⢦⣀⡀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣿⣿⣿⣶⣿⣶⣤⣄⣠⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡖⠛⠛⠛⠋⠉⠉⣿⣹⣿⣿⣿⣿⣟⣿⣿⣷⣶⡈⡀⡈⠉⠛⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠋⠐⠀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠚⣉⠿⢿⣿⣭⣭⣭⣽⣿⣯⣯⣭⣽⣭⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣛⣿⣽⡿⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡞⢿⣿⣿⣿⡭⢽⣿⠋⠛⢿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠛⣽⡾⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⠹⣿⣯⣳⣤⠃⠀⠀⢸⡇⠀⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⡽⣵⣿⢿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣏⢻⣿⣿⣿⣧⡹⣿⣿⣾⣧⣄⣀⣼⡇⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⡇⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⢠⣄⣆⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⡇⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠛⠟⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣦⣀⣇⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠛⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣽⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⠿⢿⣿⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⠸⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣯⣿⣿⡿⠿⠋⠀⠀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣻⡄⠀⠀⠀⠀ ⠀⠠⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⣠⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⡀⣼⣿⣿⣿⢻⣿⣛⣿⣷⡀⢤⢸⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣧⣋⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣇⡄⠀⣤⣭⣿⣿⣿⣿⣿⡟⣿⣿⣿⢻⣿⣿⡿⣿⣟⢇⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⠛⣿⠦⠀⠀ ⠀⠀⢀⣀⣤⣴⠏⢹⣿⣿⣿⣿⣶⣿⣿⣿⡿⢡⣾⣿⣿⣿⡿⣿⣿⣇⡂⢀⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣧⣼⣿⣿⣧⣿⣿⡿⢳⣿⢯⣿⣿⢸⣿⣿⣿⣿⣾⣿⣿⠀⡇⠀⠀⠀ ⠯⢉⣽⣿⡿⠛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⡇⡇⣿⡇⢹⠇⢸⣿⣾⣿⣿⢟⡽⢋⣿⣿⡿⢧⣸⣿⣿⣿⣿⣿⡀⣸⡏⠸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠇⠀⠀⠀ ⠀⠀⠿⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⡿⠂⠀⣾⣿⣿⣿⣿⠏⢀⣾⣿⣟⣀⡀⢹⣿⣿⣿⣿⣿⣇⣿⣇⣴⣿⣿⠻⣿⣿⣿⣿⣿⣏⣸⠀⠀⠀⠀⠀ ⠛⠃⠀⠀⠀⠈⠁⠘⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⢸⣿⣿⣿⣿⠿⣿⢿⣿⣿⠏⠉⠉⣹⣿⢿⣿⣿⣿⣿⣿⡿⠿⠏⠈⠇⢻⣿⣿⣿⣃⣉⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣸⣿⣿⣿⣿⡆⢸⣿⣿⣿⠏⠀⠙⠫⣕⣳⠤⠀⢠⣿⠏⠀⠻⣿⣿⣿⣿⣷⡀⠀⠀⢀⡞⣿⡏⢹⡏⠀⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢿⣿⣿⣿⣿⣿⡇⠋⢠⣿⣿⣿⣿⣿⣼⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠛⠎⠛⠛⠛⠂⠀⠉⢠⣿⡄⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⣀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠻⣿⣿⣿⡀⠀⢸⣿⢳⡙⣿⡿⣿⣿⡇⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀ ⠿⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⣄⠈⠟⣿⣿⣷⡀⠈⠻⢿⣷⠀⠁⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠹⣿⣿⣿⣶⣤⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⣾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠥⠤⣤⣽⡥⢤⣯⣿⣿⣿⣿⡯⠿⣟⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⢛⣿⣿⣿⠀⠀⠘⢧⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⣰⣶⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠿⠿⠿⠿⠿⠿⠿⠿⣻⣿⣿⣮⣙⢿⠋⠀⠀⠀⠈⢷⡀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣤⣤⣀⣀⣀⣀⣤⣾⣿⣟⣻⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣤⡢⣄⡀⠀⠀⠻⡄⠀⠈⠙⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣒⠄⠀⠹⣆⠀⠀⠀⠀⠈⠛⠲⣤⣀⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠘⢧⣄⠀⠀⠀⠀⢀⡟⠙⠻⣷⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⡇ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⠲⣤⣴⠟⠻⣄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠀ ⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣓⠆⠘⣆⠀⠀⢹⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣧⢀⣿⣿⣿⣷⣦⣄⠀⢀⣀⡉⠉⣩⣭⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠋⡟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠻⣦⡀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠙⣟⢦⠀⠀⠀⢀⡼⠁⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⢠⡘⣎⠳⣤⡤⠾⠷⠶⢿⣇⣀⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢆⣄⣀⣷⠓⠀⡴⢓⡦⡀⠀⠀⠙⢦⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣆⡀⠁⠉⠻⣿⣦⡀⣄⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠗⠯⠽⡟⡭⡖⢛⣷⣽⠟⡻⢲⣼⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⠸⣿⣿⠿⢧⡀⠀⣀⣹⣗⣴⣖⡵⠮⣵⠷⣿⡇⠀⠀⠀⢀⡤⠀⠀ ⠀⠀⠀⠀⠀⡴⠋⠀⠀⠁⠨⠽⣄⢤⣀⡬⠏⠁⠙⠛⢁⣿⣓⣦⡴⠚⠉⢳⡀⠀ ⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⣀⣠⣾⣾⣷⣦⣀⢀⣠⠬⠞⠁⠀⠀⠙⢀⡴⠛⠉⠈ ⠀⢀⡴⠋⠁⢙⣦⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⢀⣀⠤⠖⠉⠀⠀⠀⢀ ⡜⠋⣠⠴⠚⠉⠀⠀⡩⠛⠉⠙⠿⢿⣿⣿⠯⠒⠒⠉⠉⠁⠀⣄⣀⣀⣀⣀⣰⠿ ⠀⠀⠀⠀⠀⢀⡤⡞⠁⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠠⣾⣿⣷⣾⣦⣤⣤⣤ ⣷⣦⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⡰⢹⠁⠀⠀⠀⠀⠀⠀⠈⣿⡏⣿⣿⣛⣛⣛ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢉⡥⠞⠉⠉⢀⣀⡀⠈⠉⠑⠒⣀⠤⢤⡤⠖⠒⣪⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢋⠆⠀⢀⣤⡤⠓⠊⣉⣤⡚⠉⠀⠀⠀⠀⣀⠜⠓⠶⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⣿⢃⡎⠀⢠⠟⠁⣠⠔⠋⠁⠀⠀⠠⠤⡴⠶⠭⠥⠄⠀⠀⡰⠊⠑⠶⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⡹⣿⠖⠛⡉⠉⠁⠀⠎⠀⠼⠥⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⢉⡠⠤⢄⣈⣵⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡵⠋⠀⠁⢠⡞⠁⢰⡄⢠⠀⠀⠀⠀⠀⣄⡈⠙⠲⢤⣤⠤⠶⠯⢥⣤⡔⠚⠉⠁⠒⠦⡙⠦⣄⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣿⡟⠀⠀⣠⣾⡟⠀⠀⡼⡇⢸⢣⠈⡇⢄⠀⠀⠙⠿⣶⠦⣌⡓⠶⠶⣒⡒⠤⣉⠑⠢⣄⢲⣤⣀⣀⡉⣉⡒⠒⠂ ⠀⠀⠀⠀⠀⠀⢀⠞⣿⣠⡴⠿⢋⡼⠃⢀⠞⠀⢳⠘⣼⣆⢻⠈⡣⡀⠀⠀⠘⢷⣌⠙⠢⣄⠠⠄⣀⣉⠒⠢⠬⣳⡌⠙⠻⡓⢦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⢃⣾⣾⠏⡠⠊⣾⠇⢀⠎⠀⡜⠀⢡⣿⣿⣌⡆⢹⣮⠲⣄⠀⠀⠻⣦⡀⠸⣦⢄⠈⠉⠙⠷⠶⣶⣬⢷⣦⡌⢳⡎⠳⡄ ⠀⠀⠀⠀⠀⢀⣨⣟⡵⠊⡀⣸⢛⠀⣼⠀⡼⢀⠆⣸⣿⡏⢩⠹⣼⡆⠱⣌⠑⠤⡀⠈⢻⣦⡈⢦⡙⠢⣄⡀⠀⠈⠻⡕⢤⡙⠲⢷⡀⠈ ⠀⠀⠀⠀⠀⠈⢩⢞⡵⠚⢣⠇⠸⣤⡏⢀⡇⡎⢰⣯⣿⡀⣾⡄⡟⣷⠀⣿⡑⢦⠀⠁⠀⡕⠘⣦⠻⢶⡤⣁⠉⠄⡀⠈⢢⠙⢧⡀⢧⠀ ⠀⠀⠀⠀⢠⣴⣷⢯⡾⢸⡞⣴⢰⠃⢰⢘⢿⠀⣼⡿⠹⡇⢸⣷⣸⣻⡆⢹⣷⣌⢳⡀⢀⢻⣶⡝⢣⡈⢷⠈⢣⡀⠈⠢⡀⢱⡀⠙⢆⠀ ⠀⠀⠀⠀⠀⢰⣿⣾⢇⡞⢰⣧⢸⠀⣼⢸⡼⢠⡿⢿⣤⣿⣸⣿⣷⣿⣷⡈⣿⣿⣿⣿⣼⡌⢿⣿⡄⠱⡈⠇⢠⢻⣦⡀⠈⢢⣣⠹⣮⣃ ⠀⠀⠀⠀⢀⣾⡿⢹⣼⡃⣾⣿⡘⡄⣼⣼⣇⢸⣟⠲⢽⣿⣷⣿⣌⣿⣿⣷⡘⣿⣼⣿⣿⣷⡼⣿⣿⡄⠸⡌⠈⣧⣿⣟⠢⣀⠉⢣⢸⠀ ⠀⠀⠀⠀⣼⡋⠀⠘⡟⣧⡇⠘⣧⢻⣿⣿⣜⢿⡈⠲⠬⠭⣭⣿⣿⣿⣿⣿⣷⣜⣟⡛⠛⣁⡽⣿⣿⡸⣴⢻⡄⢹⣿⡘⣆⢹⡷⠚⢻⡦ ⠀⠀⢀⣾⣯⣤⣦⣄⣡⠸⢧⡀⠈⠻⠛⢿⣿⡆⢷⠀⠀⠀⢹⣿⡟⠙⡓⠻⡿⠛⣾⡟⠉⠀⢠⣿⣿⡇⣿⡼⣷⠀⣿⠷⣞⠛⠼⣷⣄⠁ ⠀⠀⣼⣿⣿⣿⡿⠿⢿⣿⣷⣿⣶⣤⣄⡘⠻⣿⣼⡇⠀⠀⠀⠈⣧⠀⢀⡀⢠⠀⠀⠘⠀⣠⢋⣿⣿⣿⣿⣷⣿⠞⢷⣄⠈⠃⠀⠈⠻⠀ ⣠⠞⠿⠛⢋⣭⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣷⣤⠀⠀⠀⢻⣦⡈⣁⠜⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⠋⠁⠀⠈⠛⠃⠀⠀⢠⠀⠀ ⡁⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣙⣻⣧⣤⣤⣾⣿⣿⣿⣿⣿⡏⠁⣧⣀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣻⣿⣿⣿⡿⠛⠉⢋⣋⣉⡉⣉⣽⡿⢿⠿⠿⠿⣷⣴⡟⠉⢉⣼⣿⣿⣿⣿⣿⢿⡥⠔⠒⠛⠻⣆⠀⠀⠈⢆⠀⠀⠀⠀⠈ ⢀⣼⣿⣻⣿⣿⣿⠟⢉⣤⣾⣿⠿⣛⣿⣿⢛⣵⣀⣭⣴⣶⡾⢋⣼⣷⣾⣿⣿⣿⣿⣿⣿⢏⣿⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀ ⣾⡿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣵⣾⣿⡟⣡⣿⣿⣿⣿⠋⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⠶⠿⣶⣦⡀⠀⠀⠀⣡⠀⠀⠀ ⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢯⡁⠈⠹⡦⢄⠀⢀⣿⣧⠀⣶⡿⢿⠀⠀⣀ ⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠙⠓⣽⣦⣠⣷⣬⣿⣿⣿⣿⣧⣬⣥⣾⡿⠋⠡ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⢀⣀⣤⠜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢋⠀⠀⠀⣀⣠⣴⣶⣾⣿⣍⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⢋⡥⠖⠉⢀⡀
⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠿⠋⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟ ⣿⣿⠟⣁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀ ⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀ ⠀⠉⠻⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⡈⠉⠉⠉⠉⠉⠛⣻⣿⠀⠀⠙⣆⠹⣽⠀⠀⠀⠀⠀⣿⠋⣿⣿⡇⠀⠀⠀⣠⡾⣻⣤⣶⠾⢛⣻⣿⡿⠟⠓⠒⠀⢀⣤⣴⠞⠋⠉⠀⠀⡼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠸⡄⠙⡆⠀⠀⠀⠀⠿⠀⣿⠏⠁⠀⢠⣾⣿⠟⠋⣉⣴⣾⣯⣭⣤⣤⣤⠶⠖⠛⠉⠁⠀⠀⠀⠀⣰⡿⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠞⠁⠀⠀⣴⣿⣿⣅⣴⣾⣯⣑⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣰⡟⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠶⢦⣄⣀⠀⠀⠀⢀⣴⠟⠁⠄⣰⠏⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⣋⣩⣿⣟⠟⣿⠶⣤⣄⠘⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣷⣰⡛⠁⠀⢀⣴⠋⠀⣠⣴⢿⣿⣿⣿⣿⣛⣟⠛⡉ ⠻⣿⠟⠋⠉⠙⠿⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣿⣥⡶⠛⣫⣴⣿⠿⠉⠉⠛⠛⠻⠿⠿ ⠈⠁⠀⠀⠀⠀⠀⠈⣹⠃⢀⡄⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⡀⠀⠈⢿⣿⠅⠀⢀⣰⡿⠋⠁⠀⠀⠀⠀⠀⢀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⠃⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠙⣆⠀⠀⠙⠦⡀⠀⠙⢷⣄⠈⠉⠙⠛⠛⠛⠛⠋⠉⠉⠀⢀⡆ ⣶⣦⣤⣤⠤⣤⣾⠃⠀⠀⡏⠀⠀⠀⠀⣼⡿⡇⠀⠐⡇⠀⠀⠀⠀⠀⣷⠀⠀⠹⡄⠀⠀⠀⠠⡄⠀⠀⠀⠀⠹⣦⣜⢧⡀⠀⠀⠈⠳⣄⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠟⠀ ⢿⣽⣛⠓⢠⣾⠇⠀⠀⢰⠃⠀⠀⠀⢰⣿⣧⡇⠀⠸⢳⠀⠀⠀⠀⠀⣿⡆⠀⠀⢿⣦⠀⠀⠀⠹⣄⠀⠀⠀⠀⠙⣿⣷⣿⣦⡀⠀⠀⠈⠳⢤⡈⠻⣦⣀⠀⠀⣠⠄⠈⣰⠏⠀⠀ ⠀⠈⠉⢻⠟⣿⠀⠀⠀⣼⠀⠀⠀⢀⣿⣿⣻⣧⠀⣆⠘⡆⠀⠀⠀⠀⣿⣿⡄⠀⠈⡿⣷⣄⠀⠐⣞⢧⡀⠀⠀⠀⠈⢿⣿⣿⡻⢶⣤⡀⠀⠀⠙⠲⣬⡛⢷⣟⡁⣠⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠀⠀⠀⢹⠀⠀⠀⣸⣿⣿⣿⣿⡆⢸⡆⢿⡀⠀⠀⠀⣿⠸⣿⣆⠀⢹⡈⠙⢶⡀⠈⢷⣝⢦⡀⠀⢀⣠⢻⣿⣧⣂⠈⠙⠻⠶⣦⣄⣀⣉⣛⣻⣿⣏⣀⡀⠀⠀⠀ ⠀⣀⠀⠀⠄⣿⠀⠀⠀⢸⠀⠀⠀⢻⣿⣿⣿⡀⢳⠀⣿⣌⢇⠀⠀⠀⣿⠀⣿⡹⣧⡀⢳⡀⠀⠉⠳⢤⡙⣿⡿⣾⡁⠀⠀⠻⣿⣟⠻⠿⠿⠶⠾⡿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀ ⠛⠛⠂⠀⠂⢻⡇⠀⠀⢸⡇⠀⢠⣿⣿⣿⣟⢷⣜⣆⢸⡏⢿⣦⠀⠀⣿⡇⣿⡇⠈⢙⢦⣧⡀⠀⢀⣤⡿⠿⢷⣶⡿⠷⢶⣶⠻⣿⠷⢾⡿⣶⣿⠻⣿⡟⠋⠙⠛⠛⠛⠓⢒⡒⠂ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣿⡀⠀⢻⣿⡏⠉⠙⠛⣿⣮⣧⠈⠻⣆⠀⢸⣧⣿⣧⠀⠀⠀⣙⣷⣞⢩⣷⣦⠄⠀⠈⠑⠦⢸⠟⠶⣜⣷⡼⠀⢘⡏⢠⡿⠀⠀⠀⠀⠀⣤⡶⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⣿⣷⠀⠘⣿⡇⠀⠀⠀⣿⣿⣿⣷⣄⠘⢧⡘⣿⣿⣿⣤⣴⣺⡟⠉⠀⢸⣿⣿⡇⠀⠀⠀⢀⠏⠀⠀⢸⠉⣿⣆⣼⠀⣼⡇⠢⠂⣠⣴⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⣿⣿⣷⡀⢹⡇⠀⠀⠀⢿⣿⡿⠉⣿⣇⠀⠙⢾⣿⣿⡙⠻⣏⠀⠀⠀⠀⠙⠛⠀⠀⠀⢀⣟⠀⠀⠀⠘⠀⣿⣿⠃⣴⣿⣠⣶⢟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢸⣿⣿⣷⡈⡇⠠⣀⡀⠀⣀⣠⠴⠻⣿⠀⠀⠀⠻⣿⣧⠀⢘⠦⣄⣀⣀⣀⣀⣀⡠⠶⠻⠅⠀⠀⠀⠀⣸⠟⢁⣼⠛⢿⣿⡾⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠸⣿⣿⣿⣿⣇⠀⠀⠉⠉⠀⢀⠀⠀⡿⠀⠀⠀⠀⠈⠻⠄⠈⠃⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⢾⣷⣾⣟⣁⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢿⣿⡿⣿⡌⠀⠀⠀⢀⣴⠋⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⣠⣿⣏⡿⠋⢨⢹⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⣿⡇⢻⣷⡀⢠⡶⡿⣵⠀⠀⠀⠘⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⢸⣿⠏⢰⡞⠁⢦⡎⢸⣿⠙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠘⣿⢷⡏⠀⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⣼⠃⢠⠏⠀⠀⢸⣧⠈⣿⠀⠈⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠇⠀⢻⣾⡿⠇⠀⠀⠀⠀⠀⢀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠉⠀⠀⠠⣿⡴⠋⢦⠀⠀⣾⢫⣴⠏⠀⠀⠀⠏⠀⠀⠀⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⠀⢀⣟⡿⣷⣄⡀⠀⠀⠀⠀⠁⢀⡈⠉⠉⠓⢶⣀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⣀⡤⠶⠋⠀⠀⠈⣦⠞⣸⣿⠇⠀⠀⠀⢚⣤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣀⡽⢯⡝⢲⣄⠀⠀⠀⠈⠻⠛⠀⠀⠀⠙⠓⢀⣤⡾⠛⢁⣠⡤⠖⠛⠉⠀⠀⠀⠀⠀⣠⡏⣠⡟⡁⡆⠀⢠⡾⠋⠁⠁⠀⢀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠿⡄⠀⠙⠳⣌⣿⣦⡀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠷⠞⢫⠉⠀⠀⢧⠀⠀⠀⠀⠀⢀⡴⠃⡵⠋⠀⣼⠀⣰⠋⠠⠀⠀⠀⣴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⣹⠁⠀⣻⣦⡀⡞⠀⠉⣻⠿⢷⣶⣶⠾⢿⠋⠉⠁⠀⠀⠀⠘⣆⠀⠀⠈⣦⠀⢀⡤⠞⠉⢀⣼⡁⠀⣰⠇⣾⠟⠡⣀⠀⣠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢾⣯⠴⠋⢹⡀⡼⠉⠻⣿⣧⡀⠀⣿⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠘⡄⠀⣀⡼⠚⠁⠀⢀⡤⠊⠀⢣⢀⣿⡞⠁⠀⠀⣸⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢺⡇⠀⠀⢀⡽⢧⡀⠀⢨⠟⢿⣦⢹⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⣀⡤⠟⣋⣡⣦⡤⠖⠊⠉⠀⠀⠀⠀⣿⠏⠀⢀⣠⠚⠋⠁⠊⠙⡿⠿⠿ ⠀⠀⠀⠀⠀⠀⣰⡯⠀⠀⠀⠀⢀⡷⣄⡴⠋⠀⠀⠙⠦⣏⠀⠀⢩⠛⠧⣄⣀⠀⠀⠀⣀⣳⣤⠴⠒⢉⣡⣶⠿⠛⠉⡇⠀⠀⠀⠀⠀⠀⣀⡼⠟⠚⠋⠉⠀⠀⠀⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢞⡵⢊⡽⠁⠀⠀⣾⠀⠙⣆⠀⠀⠀⠀⡰⠋⠙⠦⢇⡀⠀⠀⠀⢉⢉⡟⠁⠀⠀⣠⠶⠛⠉⣸⠀⠀⢸⠀⠀⠀⠀⠀⣴⣾⡥⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠊⠀⣸⠇⠀⠀⢀⡏⠀⠀⢸⣷⣄⠀⡜⠁⠀⠀⢀⡞⠉⠉⠛⠛⢛⣟⣾⣽⢾⡻⠶⠆⠀⠀⣿⠀⠀⠈⣆⠀⠀⣀⣼⣧⡀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠋⠀⣠⡾⠃⠀⠀⣠⢸⡇⠀⠀⣼⣿⣿⣷⣦⣀⡀⢀⠞⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠒⠒⠒⠃⠀⠇⠀⠀⣀⣼⣴⣿⣿⣿⣿⣷⣦⣤⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣴⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣾⣿⣿⡁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠻⣿⣿⣿⣿⣿⣿⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣤⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣤⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣧⡀⠈⢻⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠉⠉⠉⠓⠶⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣶⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡶⡿⠿⣿⣷⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠉⠀⠈⠉⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⢤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⣋⠙⢓⣶⣶⣶⡶⠿⠿⣶⠆⠀⠉⠉⠁⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠠⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⠀⠀⠀⠀⣿⣶⣶⣿⣿⣷⣶⣦⣤⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣯⣧⡀⠀⠀⠈⢽⡇⠀⠀⢀⡇⠀⠀⣿⡏⠁⠀⠀⣀⣹⡆⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠤⣬⣿⣿⣏⢻⡃⢀⠀⢀⣼⡇⠀⠀⢸⣇⠀⠀⣿⣷⡀⡀⠀⣟⣻⣇⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣾⣾⣿⠃⠀⠀⠀⢀⣿⡀⠀⠈⢿⣿⣶⣿⣿⡏⠈⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣀⡀⢉⣿⠙⢿⣿⣿⠟⠛⢀⣠⣾⢣⣤⣾⣿⣿⣆⣤⣼⡟⠛⠛⠛⠁⢀⣤⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠠⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⢿⡄⠀⣤⠛⠉⠀⠀⠉⢿⣟⣀⣠⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⢸⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⠿⡧ ⠀⠀⠀⠀⠀⠀⠀⢷⣴⡇⠀⢀⣤⣶⣿⢿⡿⠷⢶⣾⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣷⣄⣙⠿⣿⣯⣽⣶⣖⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⡷⢶⣧⡇ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡁⠀⠀⢿⣍⡁⢸⡇⠀⠀⠙⠻⠿⠟⠛⠉⠛⣻⣿⠿⣿⣿⠟⠋⠉⠛⠻⠿⠛⢋⣴⡷⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡁⢹⡟⣾⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⠿⢻⣧⠈⠀⠀⠀⠀⠀⠀⠰⠋⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⡿⠿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⢻⡿⠗⠴⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢷⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⣿⡝⠛⠿⠿⣷⠶⠶⣶⠶⠶⢶⡿⠛⢯⣉⠀⡏⠙⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠐⠒⠛⠛⠶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠈⢻⣆⠀⠀⢹⡆⠀⠈⣷⢀⣾⣧⠀⠀⢹⠿⣷⢰⣟⢿⡍⠛⢿⣿⣄⡀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⢿⣧⣤⣼⣷⣲⡶⢿⠋⠈⢿⣧⡀⣿⠀⠹⣆⠙⢿⣿⡄⠀⠈⠙⠻⣷⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠸⣏⠀⢸⠀⠀⠀⣿⡇⠘⢧⠀⠹⣇⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⢸⣧⠀⠀⠙⢦⡈⣇⠀⢀⡏⡇⠀⠈⣧⠀⢹⡏⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⢸⣿⠀⠀⠀⠀⠹⣿⡀⢸⣿⠀⠀⠀⢹⠀⢸⡇⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⢸⣏⠀⠀⠀⠀⠀⠈⣷⠀⣿⡄⠀⠀⣼⠀⣸⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣀⣤⣿⣿⣿⣿⣶⣤⣤⣤⡌⣷⠬⣿⣦⣴⡧⠚⡿⠁⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⢹⣿⣿⡿⠿⠟⠛⠉⠁⠀⠈⠳⢤⣀⢻⠀⡼⠁⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣾⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡁⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣤⢀⡄⣀⣠⡀⢠⡄⠀⠀⣀⣀⡀⣄⠀⠀⣀⣀⢀⣀⣀⠀⢀⡄⠀⣄⡀⣤⣤⣦⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⢸⡟⢸⡇⢸⠈⣧⢸⠇⠀⠀⢻⠉⠀⣿⠀⠀⡏⠁⢸⠉⣿⠀⢸⣇⠀⣿⡇⡇⠈⢻⠉⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣿⡇⢸⡇⢸⠀⢸⡏⠀⠀⠀⣸⡦⠀⣿⠀⠀⣷⠄⢸⡀⣀⠀⡾⢸⠀⡏⣧⡇⠀⢸⠀⢸⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣧⢸⡇⢸⠀⢸⡇⠀⠀⠀⣿⠀⠀⣿⠀⠀⣧⠀⢸⠀⣿⢀⣧⣼⡆⡇⢸⣿⠀⣸⠀⢸⡄⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠘⠓⠛⠀⠸⠃⠀⠀⠀⠛⠓⠓⠛⠒⠒⠛⠚⠘⠓⠛⠺⠃⠘⠃⠛⠈⠛⠀⠛⠀⠘⠓⠓⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣿⣷⣾⡿⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⣶⣾⣟⢹⢿⣏⣿⣾⡟⢙⠛⣒⣤⡤⢄⡀⠀⠀ ⢀⣿⣿⠋⠉⠛⣇⠈⠛⢁⠁⠁⠀⠀⠀⠀⢹⠻⣷⠀⠀ ⠈⢻⣿⠒⣶⢿⠟⣀⠀⠈⣄⠀⠈⠀⣤⠀⣸⣿⠟⠀⠀ ⠀⠀⠉⠛⠿⣭⣴⣿⣾⣛⣿⡿⠟⢉⡽⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⡿⣟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⣖⣿⣷⣾⣯⣭⣿⡟⠁⠀ ⠀⠀⠀⢀⣰⡴⣦⡄⢻⣼⣿⣿⣿⠙⡄⠀⢸⣏⡀⣀⡀ ⠀⠀⢠⡿⢿⣿⣿⡙⠷⣶⣿⡿⣋⣁⣈⡆⠀⠻⢿⣿⠛ ⠀⠀⢀⣧⣼⡆⢿⣿⣶⣾⣵⠟⠋⠀⣀⣸⠀⠀⠈⠀⠀ ⠀⠀⠉⠉⠀⠀⠈⠿⢿⣷⠹⡷⠖⢚⢉⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⣻⠿⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣁⣾⣏⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠒⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠶⣄⡀⢀⡠⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠛⢋⡾⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣍⠉⠉⠁⠐⠆⢦⠛⠁⠋⠁⠘⠣⢤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣦⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠳⣄⠀⠀⠀ ⠰⠶⢖⣋⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⢲⡂⢷⡪⠧⠀⠀ ⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⠀⠴⣄⣿⡄⡟⠈⢷⡈⡇⠀⠀⠀ ⠀⠠⠿⣲⠄⠀⠀⠀⠀⡄⢸⡏⠀⠈⠉⠙⠃⠀⠾⣿⠧⠤⢄⡀ ⠀⠀⢠⠏⣤⠀⠀⠀⢸⣷⢸⠌⠛⠁⠀⠐⠀⠀⣀⣻⣤⠖⠋⠀ ⠀⠀⠈⠳⢿⡶⠶⣀⡼⠈⠿⠀⠀⠀⠀⠀⠐⠉⢀⣼⠃⠀⠀⠀ ⠀⠀⢀⣶⣋⣐⣂⣉⣡⣄⣴⣄⣀⣀⣀⣀⣠⣔⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠁⢀⣩⠷⣮⠟⠋⠉⢹⣷⣿⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠴⣶⠚⣤⡶⠋⢁⡾⠁⠀⢀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⣼⠏⠀⠀⢸⠃⠀⠀⠸⡦⠏⣼⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⢳⣿⠀⠀⠀⣼⣀⠀⠀⠀⢷⠀⢹⡆⢷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡖⠒⠒⠉⠉⠁⠀⠀⠀⠀⢀⣀⠤⠤⣲⠶⠚⠉⠀⠀⠉⠢⣄⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⣀⠀⠀⢀⡤⠚⠉⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠟⠁⠀⡠⠚⠁⠀⡠⠖⠉⠁⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⡇⣀⣀⡠⠶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⢀⠞⠁⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠦⢌⣉⠀⠀⢰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢋⣀⣀⣀⣴⠃⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⣙⠲⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡿⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢄⠙⢮⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢀⠞⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣁⣄⠀⠀⠀⢧⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠎⠀⠀⠀⠀⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⠝⠋⠀⠘⣆⠀⠀⠈⣇⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎⠀⠀⣀⠶⠋⠁⠀⠀⠀⠀⣀⣀⡤⠶⣚⠩⠗⠋⠀⢀⣠⠶⢤⡾⡄⠀⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣀⣴⡺⢥⠤⣤⣶⣶⣾⣿⢿⣦⣤⣀⣀⣀⠤⢴⣲⣯⣷⢿⣤⣸⠀⡇⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢏⣿⡆⢀⠀⠻⣾⣯⡴⡿⢷⠄⠀⠀⠀⠙⠛⣻⠿⣿⣷⣄⠀⢹⢠⡇⣠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣎⣷⠀⡆⠀⠀⠈⠉⢉⣩⡴⠶⠶⢦⡄⠸⠿⣿⣿⣿⠿⠁⡇⣼⣷⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡷⣌⣢⣤⡴⠒⠋⣁⡠⠤⠤⣀⠈⢳⣄⠀⠀⠀⠀⣸⢡⣿⡝⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣧⡀⠉⠀⣀⠴⠊⣡⠀⠀⠀⠨⡕⢄⠙⠷⣒⣤⣞⡵⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠷⡱⡘⢯⠉⠁⠀⠀⠙⠋⠶⠗⠲⠃⠀⠳⣄⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⢀⡔⣒⣖⣶⠶⠶⣒⡒⢶⣒⣒⣠⣾⡀⠙⣷⡀⠱⡀⠀⢤⣤⣄⣤⣤⣤⣀⠤⠀⠀⠉⣹⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠖⡾⢛⣿⡭⠟⠒⠊⠙⡏⢱⠘⡯⢭⣹⠃⠑⣄⢸⢧⠀⢳⠀⠀⠑⢦⣭⣭⠖⠃⠀⠀⣠⠜⠉⠲⢄⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⡆⢣⢸⣾⠀⠤⠶⠒⠒⠻⠿⡲⣇⡰⠃⠀⠀⠈⢿⣼⡀⠈⣷⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⢆⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⢳⢼⠈⣯⣖⢄⡀⠀⠀⠀⠀⠈⢻⣣⠐⢄⠀⠀⠈⣿⣧⠀⢸⡙⠲⢄⣀⣀⠤⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢦⡀⠀⠀⠀⠀ ⣦⠼⢾⣧⣿⠈⠳⡽⣄⠀⢀⣀⡠⠤⠿⣧⡈⠳⡀⠀⠀⠇⠳⡀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠱⡄⠀⠀⠀ ⡇⠀⠀⠀⠀⠱⢄⢨⣿⣿⡇⠀⠀⠀⠀⢹⣷⠀⠘⢦⠀⢸⠀⢱⢸⡀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⢦⡀⠀ ⡇⢄⠀⠀⠀⠀⠀⠻⣿⣿⣿⣠⠤⠔⠒⠫⣅⠀⠀⠈⠳⡀⢣⡸⣟⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠒⠒⠒⠛⠀⠱⣄ ⠀⠈⢆⠀⠀⠀⠀⠀⠈⠉⠁⠘⠦⡄⠀⠀⠈⠳⣄⠀⠀⠙⢆⠱⣿⣷⠀⠀⠀⠀⠀⢇⠀⠀⠀⣠⠴⠚⠉⣀⣀⡤⠤⠔⡖⠒⠒⠒⠉ ⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡠⠤⠬⢷⣄⠀⠈⢣⠀⢻⠀⠀⠀⠀⠀⢸⢀⡴⠊⢀⡠⠶⠯⣙⡆⠈⣢⡠⠾⠚⢆⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠓⠤⡀⡼⠀⠓⣄⠀⠳⡘⡆⠀⠀⣠⠖⢻⠋⠀⡴⢯⠙⠲⣄⠈⢋⠁⡀⠒⠲⡀⠘⡄⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀⡠⣴⠯⠿⣢⣄⠀⠈⠓⢄⡙⣇⢰⠒⠉⠙⠣⣄⠎⠀⡼⠀⠀⢸⠯⠽⡄⠸⣦⡤⡟⠀⣳⠀ ⠀⠀⠀⠀⠀⢡⠀⠀⡠⠊⠀⠀⢀⣴⡻⠚⠁⠀⠀⠈⠙⠿⣦⣀⠀⠉⠺⡿⠀⠀⠀⠀⠈⠣⡄⠇⠀⠀⢸⠀⠀⠙⡤⠵⡿⡏⠉⠀⠀ ⠀⠀⠀⠀⠀⠈⣠⠎⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⡇⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡾⣆⠀⠀⠀⢰⠃⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠁⠀⢀⣼⠟⠁⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠱⡘⡄⠀⢀⠏⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⣀⣴⠟⠁⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣱⢱⢀⠎⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⣼⠊⠐⡜⡄⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡾⠁⠀⠀⢀⣀⣤⣤⣤⣤⢤⣱⡘⣄⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⡸⢹⠀⠀⠹⡝⡄⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⡠⢴⣺⠭⠓⠋⠉⠉⠉⠑⢍⢳⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⢸⠀⠀⠀⠙⣾⡄⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡴⠃⢈⡸⠟⠊⠁⠀⢀⣀⠤⠶⠒⠒⠲⢬⣆⠃⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⣻⡛⠈⠀⠀⠀⠀⠈⠮⠢⠄⠀⣀⠜⡀⠀⠀⠀⠀⢀⣠⢊⣀⣔⣁⡀⣀⣀⡠⣊⣁⣀⡀⠀⠀⡀⠀⠀⢉⡄⢀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣾⣿⣷⣿⣶⣯⣿⣷⣄⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣻⣿⣶⣿⡿⠻⠻⠹⠙⠟⡟⡿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⣾⣿⣿⣿⣿⢟⣷⣿⣿⠿⡛⡜⠀⠀⢂⠇⠱⡘⣴⠐⠈⠎⢻⣿⣿⣿⣿⣷⡀⠀ ⢿⣿⣿⡟⣵⣿⣿⠛⠃⣆⡱⠀⠀⠀⠈⠺⡀⠐⢜⣧⡡⠸⡆⢿⣿⣿⣿⣿⣿⡄ ⢸⣿⣿⣿⣿⡿⡏⠀⢠⢺⢁⣀⣀⡀⠀⠀⠉⠀⢀⠻⣧⣡⣧⢰⢻⣿⣿⣿⣿⡇ ⢘⣿⣿⣿⣿⡳⢠⣿⣸⠏⠀⣀⣀⠀⠀⠀⠀⡔⠁⣀⣈⣗⣿⠘⣼⣿⣿⣿⡟⠀ ⣼⣿⣿⣿⡿⣴⠯⣿⣿⡰⣮⠿⠿⠅⠀⠀⠀⠀⠿⠛⠻⠏⢸⢰⣿⣿⣿⠏⠀⠀ ⣿⣿⣿⣿⢰⠸⣳⣿⠈⠘⠁⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⡏⣸⡿⠋⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⡌⡶⣻⡇⠀⠀⠀⠀⣀⣀⠀⠨⠤⡄⠀⠀⢸⢣⡏⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⣿⣎⠭⣚⣆⠀⠀⠀⠑⢶⣒⢛⡟⠁⠀⣠⣇⡟⢦⡀⠀⠀⠀⠀⠀ ⠀⠈⠉⠛⠛⠛⠛⠚⠥⢣⣵⣦⣄⣀⡀⠐⠒⢁⣠⣾⢿⡾⠢⡑⢌⠓⠤⣀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⡠⠄⡪⢽⣿⡙⢿⣹⣿⣿⣿⣿⢋⠟⢔⡧⠬⢆⢢⠀⠈⠣⡋ ⠀⠀⠀⠀⠀⢠⠊⡠⠞⠀⣎⣻⢣⠀⠀⠉⢙⣧⢣⡃⠀⠀⠀⢠⠚⣏⢧⠀⠀⢡ ⠀⠀⠀⠀⢠⠃⠰⠜⢀⡼⡿⠞⢸⠀⠀⡔⠁⠀⠉⣀⠴⠶⠺⠯⣄⣷⢸⠃⠀⠜ ⠀⠀⠀⠀⡇⠀⣿⠀⠎⠀⣱⣾⡇⠀⢀⡜⢀⢴⡞⠁⠀⠀⠀⠀⠈⢿⡽⡆⠄⠄ ⠀⠀⠀⣜⢧⠀⢸⢳⡎⠉⣿⡟⠀⢀⠔⣡⣹⡝⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠂⠐⠒⢤⡀⠀⠀⠀⠀⠀⢿⠂⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠈⠳⢄⠀⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⠤⠀⠀⠀⠑⣄⠀⠀⣯⠉⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡾⠐⠦⣀⣠⠏⠀⠀⠀⠀⠀ ⠀⢀⡤⠒⠒⢤⡀⠀⠀⠈⠳⣤⠤⠄⠀⠈⢷⣄⣹⠧⠤⠀⠀⠹⣦⡀⠀⣠⡴⠞⠁⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀ ⠀⠈⠧⡀⠀⠀⠙⠢⢄⣀⠀⠙⢶⣄⠀⣀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠛⠚⠉⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠲⣤⠔⠂⠀⠈⡙⠲⢤⣽⠏⠁⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠲⣤⣴⣃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⠒⠒⣚⣉⣉⠙⢲⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⠏⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⢀⣠⠴⢋⡠⣿⡇⠉⠁⠀⠀⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠖⣻⠁⠀⠀⠀⠚⠁⠀⢀⣀⠤⠔⣒⣉⠥⠔⠒⠉⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⣤⠤⠖⢲⠚⢉⠁⠀⠀⢀⣰⣇⡀⠀⣀⡤⠔⣒⣉⠥⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⢀⡠⠞⠀ ⠻⠤⠤⠼⠦⠾⢷⣶⣾⣿⣿⣿⡿⠭⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⣀⣘⣿⣆⡠⠔⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⢿⠙⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢯⣈⡦⠤⠤⠔⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⢄⣤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⣶⠬⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣧⣧⣤⣿⣿⣿⡿⠓⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡿⡟⠙⠧⣻⡇⢼⠇⣀⣤⣤⢤⡀ ⠀⠀⠀⠀⠺⠧⣄⣒⣶⡿⢍⣁⣼⣿⣻⣽⣷⡇ ⠀⠀⢀⣠⣤⣤⢺⠘⠓⢱⣄⣿⢿⣾⣿⣿⡿⠁ ⢀⣾⠿⣯⣿⣿⣿⡀⣠⣎⣇⠙⢿⠿⠟⠋⠀⠀ ⠺⣯⣟⣽⢿⣟⡹⢻⡿⢿⠻⣄⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠟⣫⣿⣷⣿⡀⠀⣷⣿⣷⢤⡀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⡇⢠⣟⡿⣿⣿⣷⡄⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣻⡇⢘⣿⣛⣽⣿⣿⣿⡀⠀ ⠀⠸⠿⣿⣿⣿⣾⠿⠁⠀⠻⣿⣿⣿⣿⣿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠲⣶⠤⣄⣀⣀⣀⣤⣦⠀⠀⠀⠀⢰⣄⣼⣤⣤⣦⣰⣼⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⣻⣿⠁⠀⠀⡀⠀⢀⣈⣀⣀⣀⣠⡟⠀⣀⣤⣤⠴⠟⠉⠀⠀⠀⠸⡾⢿⣷⣿⣿⡿⢿⠏⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⣠⡞⠁⠈⢦⣀⣿⣿⠿⠛⠉⠉⠙⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⣿⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁⠀⢀⣠⣴⠾⠟⠻⢤⣤⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁⢀⡴⠃⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡾⢿⠁⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠁⠀⠀⠀⠀⣴⡞⠁⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠈⣇⣴⢯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣤⣶⡖⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⣼⣯⡀⠀⠀⠀⣀⣘⣷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡞⢻⡁⠀⠀⠤⠿⣤⠿⣅⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠤⠴⠚⣻⣿⣛⣽⣿⣿⣿⣿⡿⠒⠒⠒⠒⠋⠉⠉⣿⣬⣿⣿⣏⠉⠩⢍⣻⣿⣿⠁⠉⢉⣿⣿⣿⡆⠀ ⠀⠀⣤⠾⢿⠟⢧⣼⣧⡀⠀⣀⡤⣿⠂⠀⠀⠉⣀⣉⣉⣋⣉⣉⣡⣤⣤⣴⣖⣋⠻⢿⣿⠀⣰⣿⠛⠁⣀⣤⣴⣶⣤⣄⣤⣤⣼⣋⣿⣿⣯⠤⠖⠚⠛⠛⠛⠓⠒⠋⠉⠉⠉⠀⠀ ⢀⡼⠁⠀⣼⣶⣾⣟⠙⢻⠋⠁⠀⢘⡆⠀⠀⠀⣠⣴⡾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⡿⠿⣧⣴⠿⠛⠋⠉⠉⠉⠉⠁⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⣠⣾⠟⢛⢧⠈⠉⠙⠓⠲⠞⠻⣄⣠⠴⣾⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡁⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣶⠏⠙⠇⠈⢸⡄⣦⡀⠀⠀⠀⠀⢼⠀⠀⠉⠓⠯⠭⠭⣖⣒⣒⣲⣶⡾⠿⠿⣿⡤⠭⠙⣧⣀⣽⠓⠶⣤⣤⣤⣤⣤⣤⣀⣀⣠⣠⣤⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⣷⣶⣾⡗⠚⠛⠛⠿⠿⣿⣯⣤⣀⣀⣀⣤⣴⣤⣿⣿⣛⣿⣿⣷⣦⣤⣨⣟⣤⣾⡏⢿⣏⠀⠀⠀⠀⠈⠉⠁⠀⢽⣿⣾⣿⣿⡉⢉⣩⣭⣿⡟⠻⣿⣿⠉⠉⠛⣿⣿⣿ ⠀⢸⡀⠀⣿⣫⠿⢧⣄⠀⠀⠀⠀⠸⣍⠀⠻⠉⠳⢤⣄⣀⣀⡀⠀⠀⠀⠈⠉⢽⣿⠛⠛⠻⠷⠾⠛⠛⠉⠉⠛⠛⠻⠷⠶⠾⢿⣽⣿⣻⣿⠿⠛⠛⠛⠛⠚⠓⠛⠦⠚⠉⠉⠉⠉ ⠀⠀⠳⣄⣿⡏⠀⠐⠺⢿⠶⣦⣄⣀⣼⣷⣶⣤⣤⣤⣬⣉⣙⣛⠯⠭⠉⠉⠛⢻⠛⢦⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠿⢶⣄⠀⠀⠀⢻⣿⣋⠀⠀⠀⠿⣄⠀⠈⠉⠛⠻⠿⣷⣦⣄⣀⣸⠃⣠⣿⣿⣿⣿⠓⠲⢤⣤⣤⣄⣀⣀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⠾⠛⠿⣿⣤⣄⡀⠈⠛⠦⢤⣀⡀⠀⠀⠀⠉⠻⠿⠟⢿⡃⢻⣿⣀⣀⣀⠀⠈⠉⠛⠛⢩⣿⢿⣿⣍⠙⠲⠤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠦⣤⣀⡈⠉⠛⠿⠟⢻⡿⢳⣶⣌⡉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠾⣇⣸⣿⣿⣿⣀⣠⣴⣿⣽⣿⡏⠀⠙⢶⡖⣶⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣶⣿⣯⣄⣼⣿⡿⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠈⠉⠉⠓⠋⠉⠉⠛⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⢿⣿⣷⣤⣀⠈⠛⠷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⣿⣿⣿⣿⣿⡏⠁⡤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠚⠿⠟⠛⠉⠛⠷⣤⣼⣿⣿⣿⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠙⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣙⣧⣄⠀⠉⠿⣶⣶⣶⣶⠦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⢾⣿⣧⡤⠤⢤⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠿⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣋⣀⣀⣀⣤⠞⠛⢻⡟⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠛⠳⢤⣷⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠳⣄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠨⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠶⠛⠉⠀⠰⢦⡀⣀⡴⠶⠖⠙⠂⢠⣄⡀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣤⣤⣤⣄⣀⢠⣟⣃⣀⣀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠠⣾⣆⠀⠉⣿⠉⠉⠀⠉⠉⣛⡛⠲⠤⣀⣿⠀⢠⡄⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣠⣴⣽⣥⣀⣀⣿⡀⠀⠀⠀⠀⠛⠃⢰⡄⢈⣟⣠⠟⡇⠀⣼⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠉⠀⠀⠀⠈⠉⠙⢷⣀⠀⠀⠀⠀⠀⠞⣠⡿⣩⠟⢰⣇⣼⠏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⠤⠴⠟⠃⠀⠉⢀⣘⣻⡏⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠉⠛⠛⠛⠛⠛⠛⠛⠶⠦⣤⣀⠀⠀⠀⠀⠀⠛⢋⣯⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣾⡞⣻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⣄⡀⠀⠀⠸⠏⣿⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⡯⠻⣷⡷⣿⡾⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⠶⢦⣤⡽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣿⣷⡻⢤⣭⣿⡄⣷⡘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠟⠋⠙⢻⣏⡼⢻⣿⡧⣚⡛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⠀⠀⠀⠀⠀⢀⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣏⠀⣶⣼⣿⡅⣷⠾⠋⣁⣩⣧⡇⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣉⠉⠉⠉⠉⠁⠀⠉⠁⠀⠀⠀⣠⡾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣤⡿⠛⠛⠷⣖⠁⢐⣋⣡⡿⢠⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠠⠀⠀⠀⠈⣷⡞⣏⣡⣤⠞⣫⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠳⠦⣤⣤⣤⡤⠶⠋⠁⠀⠀⠀⠀⢹⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⡿⠛⠛⠛⠳⣿⡛⠉⠉⠁⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡛⠋⣿⠀⠀⢀⣀⣀⣀⣠⡤⠤⠤⠤⠤⠖⠒⠛⠋⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠀⢤⣀⠀⠀⣸⠟⣦⠀⠀⠠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡀⢷⣰⠏⠀⣰⠏⢹⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣄⠀⠉⠙⠋⠉⠀⣸⡇⠀⠰⣏⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠴⢾⠋⢠⠟⠉⢿⣤⡾⠁⠀⠘⣧⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣦⠀⠀⠀⠀⠀⠋⠁⠀⠀⠘⣧⠀⢀⣴⣿⡟⠉⠀⠀⠀⠀⠛⣻⠟⠀⠀⠈⠋⠀⠀⠀⠀⢻⣦⣀⣀⣠⣤⣤⠤⠴⠒⣟⣯⣽⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠞⠛⠉⠻⣆⠀⠀⢀⠤⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣄⠀⠀⠀⠀⣴⠞⠉⢳⡀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⠀⠀⠀⠘⣧⠐⠋⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⡾⠁⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠁⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠘⢧⠀⠀ ⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡟⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣇⠀⠀⠀⠀⠀⠀⢀⣘⣇⣀⣤⣤⣤⣄⣀⣹⡆ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡆⣿⠀⣀⣠⠶⠖⠊⠉⠉⠁⠀⠀⠀⠀⠀⢹⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⣄⣀⣠⣤⣤⡴⢖⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠘⢯⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆
⠀⠀⠀⠀⠀⠀⢤⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠀⢻⣦⡸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⡇⠀⠀⢰⡏⠀⠈⣿⢿⣿⣆⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⣤⡤⣄⣀⠀⠀⠀⣀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⣿⣇⠀⠀⢰⠀⣿⢹⠀⣀⣤⠶⢋⠽⠋⠁⠀⠀⠀⢹⡇⠀⢹⣟⠓⢼⡇⠀⣆⣸⡿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢻⣦⡀⢿⣿⡀⠀⢸⣴⢹⢸⡾⢋⣤⠖⠁⡰⠁⠀⠀⢀⠀⠈⡆⠀⠀⢿⡄⠀⢻⣄⣿⡏⢰⣿⣃⣠⡴⠒⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠈⣏⣿⢿⣾⣞⣷⡀⢸⡿⢸⣿⡴⠋⡀⠀⢠⣧⠃⠀⠀⡇⠀⠀⢹⡀⠀⠸⣿⠀⠀⢹⣿⢠⡿⢋⣽⣵⣶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⣀⣸⣿⣧⣹⣿⣿⣿⣿⡇⣴⠃⠀⢠⠃⢀⡏⣿⠀⠀⢠⠁⠀⠀⠈⡇⠀⠀⢏⢃⠀⠀⢻⣿⢡⣿⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⢠⣾⣏⣠⣼⣇⢹⠈⣿⣏⡠⣶⡏⠀⣸⢰⣿⣀⡀⢸⠀⠀⠒⠀⡃⠀⠛⢻⡊⠲⠤⣬⡏⣿⢿⣧⣀⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣏⣼⠟⢁⣤⣿⢦⡀⡇⢸⡟⣹⠁⢀⡿⢸⠉⠉⠀⢸⠀⠀⠀⠀⢱⠀⠀⠈⡇⠀⠀⡆⢡⢸⣿⣿⣿⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⢁⣴⣿⡉⣿⣷⣽⣳⣤⣷⡏⠀⣼⡇⢸⠇⠀⠀⢸⡀⣀⣀⡤⠼⢤⣤⣤⣿⠤⠤⣸⡈⠀⡟⠏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣤⡟⢻⣌⠿⡾⠀⣹⣿⢋⣿⡇⢀⣿⡇⢸⣦⣤⣶⣿⣿⣿⣷⣤⣴⠛⠁⣉⣤⣶⣆⣠⣽⣷⣿⣷⣿⣭⣭⠭⠶⣶⣄⡀⠀⠀⠀⠀⠀ ⠀⠻⡿⡄⠙⢶⡿⢠⣟⣁⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⠻⣿⣿⣏⣡⣿⣿⣿⣿⣿⣍⠙⠳⢄⠀⠈⠙⠆⠀⠀⠀⠀ ⠀⢀⣸⠶⢤⣾⣇⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⢳⠾⣿⣛⢛⣀⣿⣿⡍⢻⡘⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⢴⣫⠖⣠⠖⣿⣿⢿⠟⢿⣿⢹⡇⣿⠉⠘⣿⣿⣿⣿⣿⣿⠿⢛⠁⠀⠀⠀⠈⠀⠀⠘⠻⡿⣿⣿⡇⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⡰⠊⠀⣼⣿⢻⣾⠀⠈⢻⣸⡇⣿⡷⡄⣸⢏⡽⠋⠀⠈⠳⡏⠀⠀⠀⠀⣀⠀⠀⠀⠀⣤⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠀⠀⢀⣿⠇⠸⣿⠀⠀⠀⠙⡇⢻⡀⣽⣿⡎⠀⠀⠀⠀⠀⢈⡇⠀⠀⣼⣿⠀⠀⠀⣨⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⠀⠀⠙⢦⠀⠀⠀⢡⢸⠉⠻⢿⡻⣦⡀⠀⠀⢀⠎⠀⠀⠀⠙⠁⠀⢀⣜⣿⠟⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢸⣼⡄⠀⠀⢣⠈⠙⠳⢶⣯⣄⣀⣀⣀⣀⣠⣴⣿⣿⡿⢻⣿⣿⣿⡬⢧⣤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣤⣶⠿⡗⠒⠒⠒⠚⠛⠿⠿⢛⣿⡿⢶⣾⡟⠿⣾⣿⣿⠇⠀⠀⠹⣧⠀⠙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣿⣿⣯⠷⢿⣿⠶⠶⠖⠒⠓⠛⠉⠉⣻⣇⢀⣿⣶⠾⠛⡟⠙⠀⠀⠀⠀⠘⣧⠀⢸⣇⣀⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠐⡿⡍⣿⡍⢻⡍⠉⣿⣄⣴⡏⠻⠶⠤⠤⠴⠶⠖⠚⠉⢀⡴⠋⣿⡇⠰⡘⠁⠀⠀⠀⠀⠀⠀⠹⣇⢸⡿⣷⡿⢻⣿⣿ ⣀⣀⡀⠀⣀⣀⣀⣼⣿⡌⣀⠀⢿⡄⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣽⣿⣄⢳⠀⠀⠀⠀⠀⠀⠰⣦⣿⢸⡇⠸⣆⠈⢙⣻ ⡿⣿⠿⢿⣿⣿⣿⣿⣟⣛⡿⣧⡤⣽⣾⣿⣿⣷⡤⠤⠴⠒⠊⠉⢉⣁⣠⣤⡶⢿⣿⣿⣿⣾⡄⠀⣠⣤⣶⡾⠿⠿⣿⣿⠀⢀⡾⠶⣾⢻ ⠀⢭⡭⠯⠿⣿⣿⡿⠿⠿⠟⠛⠛⣟⣛⣿⣿⣿⣷⣦⣴⡶⣾⣿⣿⣍⣙⣒⣻⣿⣿⣿⣿⡿⣷⣟⣫⣿⣿⣿⠀⠀⠈⠻⣦⣾⡇⠀⣸⣾ ⣀⣠⡿⠋⠉⠉⠀⠀⠀⢀⣠⠤⠒⠛⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠉⢿⣿⣿⡿⢲⣿⣿⣿⣿⡛⠛⠀⠀⠀⠀⠙⣿⠀⣰⡋⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⠀⠀⣀⣤⣤⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡟⠁⠈⠉⢿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡏⠀⠀⠀⠀⠉⠙⢻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⡿⠛⠛⠛⠛⠛⠉⠀⠈⠉⠻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⣻⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀ ⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⢸⣦⣤⣤⣤⣤⣤⡴⠖⠋⠉⠀⠙⢦⣀⡤⠔⠊⠁⠉⢷⣦⣤⣤⠤⠖⠒⠋⠉⠹⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⣀⡴⠺⠋⠁⠀⠀⢻⡋⣀⣀⣀⣀⡠⠀⠺⠛⠶⣤⡀⠀⣠⠏⣡⠏⠀⠀⠀⠀⠀⠀⠀⢻⡄⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⠛⠛⠉⠉⠉⠉⠛⢂⠀⠀⠀⢸⡿⠋⢹⠋⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡤⢇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠦⠿⠶⠤⠤⠤⠤⣤⣤⣤⠤⠤⠶⣿⠀⠀⠀ ⠀⠀⠀⢸⣣⠏⠀⠀⠀⠀⠀⠀⢀⣸⣤⠤⠖⢿⡇⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⠷⢤⣀⡀⢀⣤⠚⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠘⣿⡶⠒⠒⠒⠒⢶⠆⠈⡏⠀⠀⠀⠀⢧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠁⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢹⣆⣰⣧⠀⢀⣀⣠⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣿⠀⠀⠀⠀⠀⠀⠀⡿⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣾⣃⠀⠀⠀ ⠀⠀⣴⢟⡧⠀⠀⠀⠀⠀⢸⣯⢟⡥⠒⠚⠒⠒⠂⠉⠻⣷⠖⣻⠛⠁⠀⠲⣾⡷⣦⠼⠿⠶⠶⠶⠶⣶⡛⢧⡀⢷⣄⣤⣤⣤⡴⠒⠋⠀⢠⣶⠖⠛⠉⠁⠀⠙⢧⡀⠀ ⠀⣼⠏⡾⠁⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠁⠀⠀⠀⠀⢹⢀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣴⠇⠘⠁⠀⠀⠈⠻⣤⣠⢴⡟⠁⠀⠀⠀⠀⠀⠀⠈⢻⡄ ⠀⢿⣸⡅⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠦⣄⣀⣀⣴⠃⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢢⠀⠀⠀⠀⠀⠈⢇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇ ⠀⠘⣿⣧⡀⠀⠀⠀⠀⣠⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠈⠉⠙⢷⡄⠂⣤⡀⠀⠀⠀⠀⠀⢀⣿⣀⡞⠀⠀⠀⣀⣠⡴⣿⣄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢠⣾⠿⠧⠀⢠⣤⣶⡟⠋⠉⠉⠛⠛⠲⣤⠤⢴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠁⠺⠛⠋⠉⠉⠁⠀⠀⠙⢶⣴⡾⠛⠋⠒⠀⠙⠓⠻⠷⠦⠤⢤⣤⣤⣤⣾⡇ ⢀⡏⠀⢸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢿ ⢸⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠘⣷⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏ ⠀⠈⠙⠷⠶⠤⠴⠶⠤⠤⠤⠤⠤⠤⠤⠴⠛⠛⠛⠦⠤⠴⠶⠶⠶⠶⠶⠶⠒⠛⠉⠓⠺⠷⠶⠶⠦⠤⠤⠤⠖⠚⠛⠛⠦⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢊⣴⠛⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀ ⠐⠲⢖⠒⠲⠶⢒⡒⠒⠠⠤⣀⢠⣺⣗⣱⣁⠀⢀⣀⠤⠄⢒⠮⠛⣩⠟⠉⠀ ⠀⠀⠀⠈⢢⠀⠀⠀⠉⢢⡤⣿⣿⠷⠀⠸⠿⣿⣯⠲⣤⠞⢁⠀⢰⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⡈⠐⢤⠃⡾⡩⢶⡀⠀⠀⡦⢄⠹⡆⠸⣄⠜⣠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢤⠾⠐⠊⠐⠺⢥⣤⣧⠀⢰⣥⡤⢵⠤⠒⠓⣚⡶⡤⠄⠀⠀⠀ ⠀⠀⠀⠀⡔⣉⣱⢶⡠⠄⣀⡀⠱⣸⠴⠼⢄⣞⣥⣒⠮⠭⣒⡶⡾⣳⡀⠀⠀ ⠀⠀⠀⠸⢻⠱⣁⠋⠩⡛⠐⠾⢻⠃⢹⠁⠘⠭⠅⠐⠂⠙⠄⢱⠀⡗⠇⠀⠀ ⠀⠀⠀⠀⠈⠈⢏⠒⠒⢋⣀⠀⠘⡀⡈⠄⢸⣀⠀⠀⡖⠊⠉⡖⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⡼⠘⡎⢶⢳⡤⢤⡾⠘⠾⡴⡇⠀⢰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⢀⠇⠀⠁⠀⠀⢋⠁⡇⠀⠀⠐⢧⡀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⠀⠈⡼⠀⠀⠀⠀⠈⢻⢦⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⢐⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠒⠑⠒⠀⠀⠀⠒⠒⠉⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠤⠤⠤⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠻⠇⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠻⣆⠀⠀⠀⠀⠀⠀⠀⠛⠛⠶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢠⠀⠀⠀⢀⣴⠟⠛⠛⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠙⢷⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣦⠀⠠⣾⠁⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⡄⠀⠈⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠹⣄⠀⠀⠀⢰⣿⡦⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢠⣿⣷⢀⣴⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠈⠳⢦⣄⣸⣿⣇⣂⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣶⠼⣿⣟⠛⠁⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣶⣶⠶⠶⠒⠚⢿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣶⣶⣤⣀⠀⠀⠀⢀⣠⣶⣶⣶⣦⡀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⠞⠉⠀⢀⡴⠞⠋⠁⠀⠀⠈⠉⠉⠷⢦⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣄⣤⠖⠀⠀⠠⠶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣠⡴⠚⠛⠛⠛⠛⠛⠿⢦⣀⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠛⠋⠉⠉⠛⠶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⡿⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⠁⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⠁⠀⠀⠈⠉⠉⠉⠀⣀⣀⣀⣀⣀⣀⣉⣉⡿⠿⢯⣍⣁⣀⡀⠙⠶⠴⠾⠋⠁⣼⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠹⣧⠀⠀⠀⠀⢀⡾⠋⢉⣁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣦⠀⠀⠀⣼⠇⠀⠀⠙⡇⠀⠀⠀⠀ ⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣘⣷⠴⠶⠶⣾⣷⣤⣼⣿⣦⣤⣤⣴⣿⣧⣤⣤⣤⣿⣦⣀⣀⣤⣾⣀⣀⣾⠋⠀⠀⠀⢀⣻⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠀⠀⣹⡎⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠉⠉⠙⠲⠦⢤⣤⡾⠟⠀⠀⠀⠀ ⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠒⠶⠦⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠛⠛⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠐⠢⢄⡀⠀⣠⠖⠉⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠴⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠠⢄⡀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀ ⠀⢀⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀ ⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇ ⠳⣄⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⣄⠀⣄⠀⢸⣰⠀⠀⣠⠀⣠⠀⢸⣀⡴⠋⠀ ⠀⠈⢳⠄⠀⠀⠀⠀⠲⢧⡽⠒⠛⠓⠛⢒⡞⠘⠷⠾⣋⠙⠋⠉⡿⠛⢻⠀⠀ ⠀⢀⠎⠀⠀⠀⠀⢀⣀⡀⠙⠲⠖⠒⠈⠛⠀⠀⠀⠀⢈⡗⠒⢿⡤⠔⠋⠀⠀ ⠀⠸⡀⠀⠀⠀⠀⣞⡿⡏⠀⠀⠀⠀⠀⠀⢀⣠⠷⠶⡉⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠈⠑⠒⡆⠀⠈⠓⡏⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠘⢄⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⠤⠤⠔⣷⠀⠀⠀⣴⣯⡀⠀⠀⠀⠀⠀⠈⢷⠂⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣖⠉⡷⠤⣼⠟⣿⣷⡀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠓⠣⢴⠃⠀⠁⠞⢿⡄⠀⠀⣀⠤⠖⢚⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡜⠀⠀⠀⢰⣟⣓⡀⠞⠁⢀⡠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡜⠁⠀⠀⣠⠞⠋⠉⠙⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⠀⠉⠀⠀⠀⢀⠇⠀⠀⠀⠀⢯⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢻⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣿⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠀⢣⣀⠀⣀⡠⠞⠀⠀⠀⠀⠀⠀⢹⡄⠸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⢄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⢶⡄⢠⣄⠀⣤⡄⢀⢀⣀⠀⢸⠟⡆⢀⠀⡄⣠⣤⢀⣤⣄⢠⣤⠀⣤⡀⣠⡄ ⣷⢾⡁⡇⢸⡆⣧⡟⠈⠸⢌⠀⢸⡿⣇⢸⠀⡇⡷⡾⢸⡇⢤⢸⠷⢠⣧⠇⠻⢄ ⣿⣾⠇⠣⡼⠁⣧⡿⠀⠰⡼⠁⠸⠿⠏⠘⠤⠃⠇⠛⠘⠧⠊⠸⠶⠘⠉⠇⠳⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠁⡼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⣄⣠⣴⡄⡄⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣡⠙⢋⣰⢠⣿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢇⡀⢠⣠⠟⠀⠢⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣤⣤⠤⠤⢴⠀⠐⠝⠗⢜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⡿⣿⢷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⡶⠎⠶⣔⠻⣛⡳⣂⡄⠀⢈⣀⣀⣀⣀⣀⡇⠙⣧⠙⠻⣿⣿⣿⣷⣶⡄⢀⠀⠀ ⢀⢾⠃⠱⡏⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⠛⢿⣿⣿⠐⠡⠉⡂ ⠘⠂⠀⠸⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠻⠧⣆⠬⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡄⣾⠻⢃⣾⣿⣿⣷⡀⡶⣶⡄⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣹⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⣿⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⠟⢻⣦⢰⡖⢲⡜⣿⡁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣦⡼⠟⠘⠳⠚⢃⠙⠥⠀⠂⠀⠀⠀⠀⠀⠁⢂⠀⠀⣴⢲⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠷⠞⣽⣹⢲⠟ ⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⠁⠋⠀ ⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡄⠸⠇⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⣤⡀⠀ ⠀⠀⣀⡀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣁⡀⡴⢮⠳⠄ ⠀⠀⢙⣟⡳⠀⢻⢦⣄⡀⠀⣀⣴⠟⠁⠀⢄⣀⡠⠄⢸⣏⣹⡝⠋⠀⠀ ⠀⠀⢾⣍⡗⠀⠈⢆⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⣀⠔⠁⠈⠉⠀⠀⠀⠀ ⠀⡴⠶⣦⠀⠀⠀⠀⠑⠠⠄⠀⠀⠀⠤⠀⠒⠉⣠⠶⣄⠀⠀⠀⠀⠀⠀ ⠀⠷⠶⠞⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠿⣴⢏⡴⣄⣀⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⢤⡻⡅⠀⠀⠀⠀⠀⠀⠀⠘⠒⢣⡟⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣄⡿⠙⠚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠙⠳⢶⣀⣤⠶⠛⢛⡹⢉⣩⠟⢉⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣤⡙⣟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢸⣇⠀⠐⢄⠀⠻⣠⠄⣼⠟⡼⠋⢀⠀⢨⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣷⡟⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣈⢿⣆⢰⣈⣆⣸⠡⠊⢡⡞⠀⣤⡆⠀⣸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡿⠗⢉⠙⣦⣤⣀⣤⣀⣀⣠⣤⣤⠖⢫⣿⣿⢯⣿⣼⣿⣿⠿⠀⣠⠿⠁⣾⡿⠁⠀⣿⡇⠀⠀⠀ ⠒⠒⠲⠶⢶⠒⠒⠒⢲⠒⠤⠶⠚⠻⠿⠿⠏⣼⡏⠀⠀⠀⠈⢁⣶⣍⣀⣴⣿⣿⣿⣼⣿⡟⣿⡏⢠⢰⠏⠁⠘⡇⡀⠀⣼⣿⠃⠀⠀⠀ ⢶⣶⣶⣶⣶⣿⣶⣤⣤⣽⣷⣤⣀⣠⣤⠀⢈⣿⡅⠀⢀⣴⣶⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇⠈⠐⣁⣤⢞⣿⣡⣾⣿⠃⠀⠀⠀⠀ ⠀⠈⠙⠛⠛⠛⠉⠉⠉⢉⡟⠛⠻⡋⠁⣠⣿⣿⡇⣼⣿⣿⡏⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣽⣿⣴⣿⣿⡿⠃⣸⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⢩⠀⣰⠎⢀⣾⡟⠋⢻⣷⠿⡋⠁⣇⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⣿⣿⣿⣿⣿⣏⡤⢾⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠶⣾⣯⡀⣴⣾⣶⠟⢠⣘⡟⢀⣰⣿⣿⠀⢣⠀⢻⢷⡒⠒⠒⠒⠢⢤⡀⢻⣷⣦⣽⣿⣿⣿⣵⣶⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀ ⢴⣯⣷⣿⣿⣿⣿⠟⠋⢠⠋⣰⣿⣿⣷⣿⣿⡇⢻⣇⠀⢳⡄⣇⢹⡓⡢⢄⡀⢀⣹⣶⣿⣿⣿⣿⣿⣿⣿⡿⣡⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠀⠀⢀⣎⣀⣿⡏⢛⣿⣿⣿⣧⠈⠻⡇⠀⠀⠘⣷⡇⢹⡀⣻⣿⣟⡃⡈⠻⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⣻⣿⠏⠀⢸⣿⣿⣿⣿⣷⣄⡀⣴⡗⢀⣹⣃⣾⣿⡿⣟⣿⡁⠉⠒⠦⡈⠻⢿⠟⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣏⣼⣿⠏⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣹⣽⣿⣧⡀⠀⠀⠈⠢⡀⢳⠞⠿⠶⠦⠤⡤⠤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠄⠀⠀⠈⠈⢆⠀⠀⠀⠀⠙⢄⠈⠙⡷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⢷⣄⠈⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡓⠀⠀⠀⢄⣠⠞⣿⠀⠀⠀⠀⢀⣾⣀⣱⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢧⡀⠟⠢⣄⡀⣀⣥⣾⣿⢄⣀⣠⠴⢿⣿⡿⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠙⣳⠌⠻⢗⠴⠒⠋⢉⣉⣩⣽⠷⣾⡗⠻⢻⣿⣿⣶⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣆⠈⢿⡉⢈⠣⣈⣴⠿⠋⠁⢰⡆⠈⠳⣄⢱⣿⣷⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⠻⢷⣄⣉⣻⠖⣿⡇⠀⠀⠀⢨⣧⠀⠀⠸⣏⣿⣿⢿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣤⣀⠙⠿⠋⠉⠁⠀⣤⣴⣿⣿⠀⠀⣼⣿⣿⠛⢴⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠾⠻⣿⣿⣿⣶⣄⣀⡀⠀⠀⠀⢀⣽⠀⠾⡿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢹⡇⠀⠀⠀⠘⠳⣦⣤⡴⣾⣿⡇⠀⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⢣⠀⠀⠀⠀⠈⠋⠁⠚⠛⠉⠃⢀⣿⣧⡇⠀⠀⠀
⠀⠀⢀⡶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢷⠀⠀⠀⠀ ⠀⠀⢸⠌⠢⣙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠎⠀⢸⠀⠀⠀⠀ ⠀⠀⠸⡖⠀⠈⠻⡳⣄⣀⣀⣤⢶⣴⠤⠴⠶⠶⢶⠤⡴⣣⢎⡀⠤⡝⠀⠀⠀⠀ ⠀⠀⠀⢩⠄⠀⠀⠑⡌⠢⣀⣁⣀⣀⣀⡠⠤⠤⢰⣾⠞⢁⡀⠫⡽⠁⠀⠀⠀⠀ ⠀⠀⠀⠘⡦⠂⣤⣤⣼⣦⣤⣁⣀⡀⠀⢰⡤⡴⠟⣿⣿⡟⢷⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⢶⡇⢸⣶⣷⣦⡉⢸⡗⠚⠋⢷⣡⣾⣿⣿⣿⣸⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⣧⣘⣿⣿⣿⣻⣾⡷⠀⠀⠾⠗⠒⠛⠋⠉⠁⣆⡠⠔⠚⠀⠀⠀ ⠀⠀⠀⠦⢰⣄⡀⣀⡀⠀⠀⢀⠰⣦⡤⢤⣾⠃⠠⣀⣠⠖⠉⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣰⣛⣆⣀⣉⣽⠶⣾⠀⠈⢻⢩⠇⠀⠀⡞⣭⡭⢭⣽⣁⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⠁⠀⣿⡤⠔⢺⣯⣤⣷⣶⣾⣾⣿⣿⣿⣿⡟⠀⣤⣿⡄⠈⠙⠀⠀⠀ ⠠⠞⠁⡇⠀⠘⢩⣷⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⣴⣿⠮⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⠀⠘⢿⣿⣵⠀⠘⢿⣿⣿⣿⣿⣿⡿⠁⠀⣿⡘⠂⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⡀⠈⣿⣿⠀⠀⢻⡿⣿⣿⣿⠃⠀⢶⣿⠃⠀⠀⣀⠈⢂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢆⢿⢻⣿⣆⢠⢙⠛⠛⢣⣀⣿⣟⠙⠀⡠⠊⠁⠀⠈⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⡙⠻⡿⠿⠷⢖⢾⡟⠇⢁⠴⠋⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠚⠛⠛⠛⠛⠛⠛⠛⠶⠶⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣤⣶⣷⣾⣿⣿⣗⡒⠒⠤⠤⠀⠀⠈⠙⠛⢿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡿⣿⣿⣿⠏⠉⠉⠉⠉⠙⠛⠿⠿⣿⣷⣄⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠙⠻⣷⣤⡀⠀⠀⠀⣿⣠⣾⣿⣃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠙⢿⣦⡀⢀⡿⠿⣛⣛⣛⣉⡉⠛⠛⠲⠶⢦⣄⣀⠀⣴⠟⢽⣭⣭⣉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠀⠉⠻⢾⣀⣀⣿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⣻⡏⢰⡟⠉⣿⠿⢶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⡳⢤⣄⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⡶⢶⣤⣤⣀⠀⠀⠀⡟⠀⣿⡁⢀⡏⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡿⠷⢬⣿⣦⣄⠀⠀⠀⠀⠈⠙⠛⠿⢷⣦⣤⣉⡛⠓⢴⡇⢲⡙⠿⠚⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⢁⣀⣤⢶⣿⣿⠿⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠷⠶⠶⠶⠿⠿⠿⠿⠿⠿⠶⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡟⠁⠀⠀⠀⠀⠀⠀⢀⣾⠏⠡⠖⠋⢉⣴⠟⠋⠁⠀⠀⠀⠉⠻⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢻⡅⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠈⢿⣤⡀⠀⠀⠀⣠⣾⡟⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⢠⡄⢀⡾⠀⠀⠀⠀⠀⣠⡾⠁⠈⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣟⠛⠛⣫⣵⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠉⠛⠒⠒⠚⠛⢿⠃⠀⢠⡿⠁⠀⢀⣤⣤⣄⣀⣿⣠⡿⠁⠀⠀⣰⠃⢰⡟⠁⠀⢀⣠⣤⣤⣄⣻⣦⠀⠀⠀⠀⠀⠈⢻⡟⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠃⠀⢀⡾⠁⢠⣾⠟⠉⠉⠉⢿⣷⣿⠁⠀⠀⣴⠃⣰⡏⠀⣠⣶⣿⠏⠉⠉⠀⠙⢿⣷⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⣠⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡼⠁⢀⣾⠁⠀⣀⣀⠀⠀⣿⡇⠀⠀⣰⠏⢠⡏⠀⢘⣿⣿⡶⣶⣆⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⣿⣆⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⡇⢀⣼⠟⢻⣧⠀⣹⣿⠀⠀⣿⣾⣿⠀⠀⠛⠉⠀⣠⣼⡿⣷⣄⠀⠀⠀⣿⠀⢀⡶⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣧⠀⠀⢸⣿⣷⣄⣀⠀⠛⢦⣤⣄⣀⣀⣀⠀⢸⡇⠀⠀⢸⡇⠈⠁⢰⣿⣿⡀⣿⣿⡄⢸⡿⣿⠃⠀⠀⠀⢠⢞⣻⡥⠶⣿⢿⣷⣄⣠⡇⣠⡾⠃⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣧⡀⠘⢿⡀⠈⠉⠛⠻⠿⠿⠿⠟⠋⠁⡀⣼⠀⠀⢀⣾⣿⡀⠀⠘⣿⣿⡇⠋⠙⣷⣿⣿⢻⡇⠀⠀⣠⡿⠟⢻⣀⣼⢧⣾⣿⡿⠿⠿⠋⢈⣧⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡇⠘⢿⣤⡘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⣸⡇⣸⣿⣄⡀⠹⣿⣿⣤⡀⠉⢿⣿⠈⠃⠀⠈⠁⠀⠀⠈⢿⣯⣽⣿⡿⠇⠀⠀⠀⠀⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⠀⠀⠈⠙⠺⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣾⠏⠈⢻⣿⣶⣽⣿⡿⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡆⠀⢠⣄⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⢀⣼⠋⠀⠀⣸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⣠⠖⠦⡄⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀ ⠀⠘⣷⡀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⡁⠀⠀⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⣠⣿⢺⠃⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀ ⠀⠀⠘⢧⡀⢻⡻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠶⠋⠉⢀⡼⠃⢀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⠻⣯⣙⠻⠿⢶⣶⠶⠞⠛⠁⠘⢦⣶⡶⠿⠿⣷⠶⠶⠦⣤⣄⣀⣀⣠⡼⠃⠀ ⠀⠀⠀⠈⢻⣦⡻⢦⡍⠉⠛⠒⠂⠀⠀⠀⠀⠀⣠⣿⠃⣰⢞⣿⢿⣿⣿⣿⣧⠀⠀⠀⢀⡾⢹⡇⠀⠈⢻⠳⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⢀⣠⡾⢻⠇⠈⠡⠟⣡⣼⣿⣿⣿⣿⣦⣤⣄⣼⠀⠘⣧⠀⠀⢸⡇⠀⠀⢟⠛⠳⣦⣤⣀⡀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠟⠛⠛⠁⣰⠏⠀⣠⣶⡾⠋⣈⠻⣿⣿⣿⠋⣤⠈⠻⣷⡄⢻⣿⠿⠿⣿⡟⠛⠻⡟⠛⢛⣿⣿⠿⠟⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡷⠾⣻⠟⣸⡇⢸⠋⠀⢸⣿⠋⢸⠏⠀⠀⣿⣿⠀⢻⣄⠀⠘⢷⡀⢀⡽⠛⠉⠀⠀⠀⣠⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠰⠾⠿⠟⢹⣷⣸⡀⠀⠀⢿⠀⢸⠀⠀⠀⢸⣿⡇⠀⠻⣇⠀⢈⣽⠏⠀⠀⠀⣠⣴⣾⠏⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⠁⠀⠀⢸⡄⠈⠀⠀⠀⣼⣿⠃⠀⠀⠈⠻⠟⠃⠀⠀⠀⠸⠟⣁⣿⡆⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣘⣿⣧⠀⠀⠀⠃⠀⠀⠀⣠⣿⣿⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⣛⣭⣭⡙⠻⢷⡄⠀⠀⠀⢀⣴⠟⠁⠛⠻⠏⣿⡦⣤⣄⣀⣤⣐⣿⡶⣤⣜⣿⡜⢿⣄⠀⠀⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠉⠉⠈⠀⠀⠀⠙⢦⣀⣠⡾⠁⠀⠀⠀⠀⣠⡿⢣⡄⠈⠉⠙⠛⠻⢷⡀⠙⠿⣿⣄⠉⠁⠀⠛⢮⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⣀⡄⠀⠀⠀⠈⣹⣯⣄⠀⠀⠴⠛⠉⠙⢾⡿⣄⠀⢠⣄⠀⠈⢳⡀⠀⠈⠛⢦⡀⠀⠀⠀⠙⢷⡑⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⢋⣡⡖⠀⠀⢀⣴⢿⢿⠛⢷⣄⡀⠀⠀⠀⢸⡇⠈⢧⡘⣿⣧⡀⠀⠀⢀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⠃⠀⢀⣴⡿⠁⢸⣾⡆⠀⠙⠻⠶⣶⠶⠛⠁⠀⠀⠙⠿⣧⡙⠳⣄⠈⢳⣄⡀⠀⠀⠉⠳⣤⡀⠀⠘⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣴⣶⠿⠏⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠈⠙⠶⢌⣿⣷⡶⢤⣀⣈⠻⣶⣄⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠦⠈⠙⠻⠿⣿⣷⣌⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡙⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠳
⣤⣤⠀⠀⠀⢀⠀⠀⠠⠀⠰⣿⣇⣸⡿⣿⡿⣟⢀⣤⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿ ⣿⣿⣀⣀⣀⣿⣦⣀⣀⣶⠡⠄⢸⡿⣶⣍⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿ ⣿⡿⣿⣿⣿⣿⣿⣏⠙⣷⡀⠀⢸⣿⣄⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡄⠘⣻⣿⣿⣿⣿ ⣿⣷⣿⣿⣿⠟⠛⣿⣛⣯⡁⠠⢸⣟⣿⣿⣤⡴⠛⠛⢿⣿⣿⠿⢛⣀⣠⣭⣥⣖⣒⣉⣐⣒⣶⣦⣄⣀⣠⣴⣷⣯⣽⣦⣼⠿⢭⠿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣇⣤⣴⠞⢋⡽⠿⣯⡥⠤⠤⠖⠲⢦⣭⣤⡤⣴⣦⣭⢿⣯⣄⠈⠻⢿⣿⡟⠓⠒⠀⠘⠻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣡⣤⠞⠋⣠⣴⢺⠿⠛⠉⠉⠻⣶⣄⠈⠓⢤⡉⢻⣿⣦⣰⣿⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣶⣨⡟⢁⣠⣞⣿⣿⡟⠀⠀⣾⡄⢰⠘⢯⡳⣄⠀⠙⣯⣹⡟⠹⣆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⢏⣴⢾⣿⣿⡿⠋⠀⡄⢠⡟⡇⠈⡇⠀⢳⡘⣦⠀⠈⢿⡇⡀⢻⡄⠀⠀⠒⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢰⢿⣿⠟⣵⡿⠿⠏⠀⢀⡸⠃⣺⠆⡇⠀⢻⡄⢾⣷⡈⠃⠀⢸⡇⢱⠈⡇⠀⠀⠈⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢤⣿⡾⢁⣼⣿⣤⣤⡿⣿⣿⡇⠀⡇⢤⡇⠀⢸⣇⠸⠻⣧⠀⠀⣹⢧⠀⡇⢻⠀⠀⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣰⠏⢀⣾⣽⡇⠙⢡⣾⣿⣿⣤⣾⣷⣿⠀⠀⣹⣯⣽⣿⣿⣦⡄⣧⢸⡄⢛⢸⡄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⢿⣤⣾⣽⠟⢰⢶⡋⢹⣿⣿⠙⠉⢹⣿⣶⠾⣿⣿⡿⢿⣾⣿⣿⣿⠀⣇⠸⡼⡗⠀⠀⠀⠀⢈ ⣿⣿⣿⣿⣿⡿⠿⢿⡿⠛⠁⢸⡇⠀⠀⢠⣿⣿⣿⣿⣿⡀⠈⠙⠛⠋⠀⠀⠀⢠⡀⠀⠛⠻⠧⠞⢻⣿⣿⣿⡆⢻⡀⢧⣷⠀⠂⠀⠀⠸ ⣿⣿⠿⡿⠋⠀⠀⢢⠀⠀⠀⢸⣿⣶⣶⣿⣿⣿⣯⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⣿⣿⣿⡿⣧⠸⡇⠘⣿⣇⠄⠀⠀⠀ ⠉⢀⠜⠁⠀⠀⠀⢸⣄⣀⣀⡘⣟⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⢹⡆⢿⡀⢻⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠔⠋⠉⣤⣤⣼⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠻⣿⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⠸⣧⠘⣧⠘⣿⣆⠀⠀⠀ ⠛⠙⢻⣿⣭⡤⠤⠖⠚⠛⠛⠛⡿⠿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⠛⣿⠦⣄⠀⣀⣤⢶⡟⢿⣿⣿⣿⣿⣿⣿⠀⣿⡆⢹⡄⠹⣿⡴⠀⠀ ⠀⣀⣠⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠈⡆⠈⣽⣿⣿⡟⠃⢧⣻⣀⡈⠉⠉⢠⣾⣥⢸⣿⣿⢻⣿⣿⣿⡀⣿⣿⡜⣿⡄⠹⣷⡀⠀ ⣼⣧⣤⣍⡉⠓⠿⣳⣦⡀⠹⣦⣀⠘⣷⡀⠀⢇⣰⡿⣿⠁⡇⡀⠈⣹⣯⠁⠀⠀⢰⣏⠀⠈⢹⡟⣿⣿⣿⣿⣇⣻⣿⣷⣹⣿⡄⠘⣷⣄ ⠉⣻⠁⣸⠛⢳⡶⣤⣍⣛⣦⣀⠈⠓⠺⡷⣄⣸⡿⢷⣟⡀⣇⠙⣶⡋⢸⣷⣶⣶⣿⢸⡀⠀⢸⣷⣼⡆⠈⠉⠉⠙⠛⢿⣧⢻⣿⣆⠘⢷ ⢠⡇⢸⠇⢠⡟⣰⣿⣿⡟⠁⢩⣷⢦⡀⢀⣿⠋⡀⣾⠋⠀⢸⡴⣿⠻⣾⣟⠉⣿⣿⣿⣧⢀⣿⣟⣿⣷⣄⣀⣀⣀⣄⠀⢻⣧⣻⣿⣷⠀ ⣿⠀⣾⣷⣾⢁⣿⣿⣿⣧⣤⣼⠃⣼⣿⡟⠁⠀⢢⠏⠀⠀⠀⣧⡈⢳⣹⣷⣷⣿⣿⣿⣿⡿⠋⠉⠰⠗⢻⡿⣏⡿⠛⡿⠛⠛⢻⣿⣿⣶ ⡇⢠⣿⣿⡇⣾⣿⣿⡏⢠⣿⡟⣸⣿⣿⣀⣆⣴⡟⠀⠀⠀⠀⠸⡝⢦⣏⠉⠉⡿⣡⣿⣿⠀⠀⠀⣴⣆⣾⣏⣵⣙⣿⠁⠀⢀⢹⣿⣿⠿ ⡇⢸⣿⣿⢰⣿⣿⣿⠁⣶⣿⣵⣟⣿⣷⣿⣿⣾⠃⠀⠀⠀⠀⠀⠹⣮⣷⣶⣾⣇⣾⣿⣿⡆⠀⠀⠈⣛⣿⣿⣿⣿⣿⣷⣢⣶⣾⡿⢣⣮ ⣧⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠁⣿⣿⡇⠀⢸⣿⣿⣿⣿⣤⣌⣉⠛⠿⢿⣿⣛⣫⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣒⣢⢄⣀⣀⠀⡠⠒⠋⠙⠳⣆⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⢯⡾⢿⢙⠋⡷⡕⠒⠋⠐⣒⡠⠃⠀⢸⡇ ⠀⠀⠀⠀⠀⢛⢞⠉⠙⠢⣤⠤⣯⡿⠾⢦⢄⣨⢼⠁⢳⢛⣯⡏⣡⠼⠖⠦⢾⡁ ⠀⠀⣀⣤⣾⣛⣿⣿⣶⣤⠖⠎⠉⠁⠘⠛⡿⠒⣏⠤⢬⡇⡤⢋⡵⠊⠉⠀⠀⢿ ⢀⣼⠯⠠⢄⡈⠉⠻⢭⣭⡇⠘⠲⣞⡻⠶⡄⠋⠹⣦⠼⢋⡴⠋⠀⠀⠀⠀⠂⣾ ⣾⠃⢼⠀⠀⠉⢳⠦⢄⣠⠔⢲⠚⢛⣧⣴⡦⠟⢊⣡⠔⠉⠀⠀⠀⠀⠀⠀⣰⠇ ⢻⡆⠀⠀⠀⢀⣼⠦⣼⡷⠛⠉⣁⣤⠶⠒⠒⠉⠁⠠⠀⠀⠀⢀⠀⠀⠈⣰⠏⠀ ⠈⠻⣦⣀⠀⣸⠓⣀⡿⠁⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡼⠁⠀⠀ ⠀⠀⠈⢻⡟⠲⣶⠈⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠉⠀⣐⡵⢋⡵⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣦⡉⠃⠷⠀⠠⠃⠀⠀⠠⠀⠠⢈⣀⡤⢟⣩⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠳⠶⢶⣤⣐⠷⠶⠾⠶⣖⣻⡭⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠉⠉⠉⠉⠉⠉⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⠀⢸⡟⢰⠞⢁⡴⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⣀⣔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠐⠦⡀⠀⠀⠀⠀⢹⣧⢸⣧⡏⣠⣮⠤⠤⣄⡀⠀⠀⠀ ⠀⠹⡉⠉⠛⢷⣶⣤⣌⠑⣄⣼⠟⣡⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠈⢢⡀⠀⠀⠀⢻⣿⣿⠛⣥⠺⡆⠀⠀⡿⠳⡄⠀ ⠑⢄⡉⠒⠠⣼⣯⣯⠛⣻⠟⢁⠜⠁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠹⡁⠲⠶⠤⠿⣿⡆⣻⠀⣿⠀⢰⠃⠀⠘⡆ ⠀⠀⠈⠁⣸⢫⣿⠏⢡⠏⡰⠃⠀⡰⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠑⡀⠀⠀⠀⢹⣿⣷⠀⢻⡇⡸⠀⠀⠀⠈ ⠀⠀⠀⠀⣿⣻⢿⣴⡟⡐⠁⠀⡴⠁⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢱⡀⠤⣴⣿⠈⣿⢄⠘⢿⣇⡀⠀⠀⢀ ⠀⠀⠀⣠⠗⢋⣩⣾⡜⠀⠀⡼⠁⠀⠸⠀⠀⠀⢸⠇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⣧⠀⠀⡧⠖⠉⣸⣶⡇⠀⠙⢣⣿⣆⠀⠀⣸ ⠀⠀⢉⣠⣾⣿⣿⡿⠀⠀⣸⠃⠀⢠⠇⠀⠀⠀⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡄⠀⢱⠀⡴⡏⢿⣬⡓⠤⣈⡆⠻⣧⣴⣿ ⢀⡴⠋⢁⡟⠛⣾⠃⠀⢠⡏⠀⠀⣼⠀⠀⠀⢸⣿⣾⡇⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘⡆⡇⢸⡇⠀⠘⣇⣴⡇⢸⠹⣿⣢⣄⠉⠓⠛⠛⠿ ⠊⠀⢠⠏⠀⠀⡏⠀⠀⣾⠁⠀⢠⣧⣀⣀⣀⣾⠿⡎⢧⠄⠀⠀⣀⣿⡀⠀⠀⠀⠀⡇⠁⠈⣷⠀⠀⣿⡿⢻⠸⡀⢸⣟⢿⣿⣷⡲⢶⠢ ⠀⠠⠃⠀⠀⢸⣷⣒⠙⡿⢿⡟⠛⠿⠿⠿⣾⡏⠉⠉⠉⠉⢛⣓⡶⠤⠖⠯⠭⠽⢿⣷⣀⢀⣿⠀⠀⡏⣠⣞⡆⡇⢘⣿⣆⠹⣿⣿⣦⡀ ⠀⡄⠀⢀⡠⢾⠀⢸⣀⣷⢼⢷⣶⡶⠦⣄⣈⠇⠀⠀⠀⠀⠘⠇⣠⣤⣶⡶⠶⠖⠒⠚⣿⣿⣿⠀⢀⠏⢁⣀⠘⣿⣾⣿⣿⡄⢻⣿⣿⣿ ⢠⠗⠊⠁⠀⣻⠀⢸⣿⣿⠘⢧⣽⣿⣤⣈⣳⠀⠀⠀⠀⠀⠀⢴⣛⣿⣿⣠⣠⣤⣀⣰⠟⢁⣿⠀⢸⡶⠛⠀⣷⣿⣿⣿⣿⡇⣸⣿⣿⣿ ⠘⠀⠀⠀⠀⣽⠀⢸⡿⢸⡄⠀⠀⠙⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⡼⠁⣼⣿⣿⣿⣧⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⠀⢸⡯⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣸⠧⠚⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⠀⢸⣯⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣇⣤⡾⠭⠍⠙⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢘⡆⢸⣿⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⢸⠋⠀⠀⠀⠀⠀⠈⣯⡭⠭⠭⣝⣛⣛ ⠀⠀⢀⣤⣶⣿⡇⢸⣿⣀⡴⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⢚⣿⣿⠀⡘⠀⠀⠀⠀⠀⠀⠀⣹⣦⣀⠤⢶⣞⠋ ⠀⠀⢸⢻⡟⠀⣇⢸⣿⡿⣇⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⢀⣼⣿⡏⢀⣇⣀⣠⣤⣶⣶⠾⢛⣫⠭⠒⠉⠁⠀⠀ ⠀⠀⡿⣞⣧⠀⣿⢈⡿⣇⠈⠓⠦⣄⣀⠈⠑⣦⣄⣀⣀⡠⠔⠊⠉⠀⠀⠀⠀⣀⣼⣿⣿⠀⣼⡯⢷⣿⣿⡩⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠘⣞⣷⡿⣟⣇⠹⡄⠀⠀⠀⠨⠿⠿⠛⠛⠉⠀⠀⠀⠀⢀⣠⡴⠖⠛⣿⣿⣿⠃⣼⣡⢶⢏⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠈⢿⣧⠸⣿⣷⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁⢀⣠⡼⠛⣹⢏⡾⠛⠁⡜⡸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡛ ⠀⠀⣳⡀⠀⢘⣟⣧⡹⣏⢿⡟⠶⣤⣀⣀⣠⣤⣶⣛⠉⢀⣀⣤⠴⠚⠉⠈⢀⣴⡿⠋⠀⠀⢀⡇⡇⠀⠀⠀⠀⠀⣀⣴⡾⣛⣩⡴⠶⠿ ⡤⠀⢸⢀⣠⡾⠋⠀⢳⡘⠦⠙⢦⡴⠛⠉⠀⠀⠀⠙⢿⡋⠉⠀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⢸⡿⡇⠀⠀⢀⣤⣾⣿⣿⣿⠿⠛⠉⠀⠀ ⠀⣀⣸⣟⠋⠀⠀⠀⠀⣳⡀⣤⣞⠕⠈⠑⠒⠢⠤⣄⡀⠙⢦⣄⣀⣘⣿⡟⠁⠀⠀⠀⠀⠀⠈⣿⡇⣠⣶⣿⣿⡿⣿⠋⠀⠀⠀⠀⠀⠀