Ganja Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣼⣷
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠈⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢻⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⢻⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡿⣿⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣿⢻⣿⣧⣦⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣴⣷⣿⣿⣛⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⢿⣿⣿⣷⣀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⢠⣴⣿⣿⣿⣫⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⢲⣿⣿⣿⣾⣿⣿⠖⠀⠀⣤⣿⣿⣿⣯⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣟⣿⣿⣿⣶⠀⠐⢿⣿⣷⣼⣿⡿⠂⢰⣾⣿⣿⣯⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣯⣿⣿⣷⠀⠘⣿⣯⣿⡿⠃⢀⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠹⠿⢿⣿⣽⣿⣶⠀⠙⣯⣿⠃⢀⡾⣿⣾⣿⠟⠛⠃
⠀⠀⠀⠠⠤⢤⣤⣦⣶⣾⡿⣿⣿⣿⣿⣿⣷⣷⣶⣦⣌⡙⠻⢿⣧⡀⢙⡏⢀⣾⠿⠛⠁⣀⣠⣤⣶⣶⣷⣾⣿⣿⣷⣶⣦⣤⣤⣤⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡦⠬⢁⠘⠁⠉⣤⣴⣾⣿⣛⣛⢛⣻⢻⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠙⣉⣩⣥⣶⣶⠖⠋⢱⠈⠳⣶⣤⣌⣉⠉⠙⠋⠙⠋⠙⠋⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⡿⠟⠉⠀⠀⠀⢸⠀⠀⠀⠙⠻⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠻⠻⠿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⡀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⢀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣄⢰⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢤⣴⣶⣶⣿⣾⣷⣿⣶⣶⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣵⣴⣾⣾⣿⣿⣿⣿⣿⣿⣶⠆
⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣭⣿⣿⡿⠋⣿⠛⢿⣿⣷⣭⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠟⠉⠀⠀⣿⠀⠀⠉⠛⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠃⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢿⠀⢈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⢀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠺⠀⢀⣿⠄⠀⠀⠀⠀⠀⠀⢀⣤⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⢬⡆⠀⠀⠀⠀⠀⢿⡝⣆⠀⢠⣿⠄⠀⠀⠀⣀⣴⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡹⢄⡀⠀⠀⠀⢿⡝⣌⠀⢀⡟⠀⢀⣰⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⢷⣄⠀⠀⣸⣿⣿⠀⢈⡁⣤⣾⣿⢟⣡⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⡀⠘⣿⡝⠀⢠⡞⢃⣟⣁⣼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣰⠀⠀⠀⢄⡸⣿⣿⡄⢸⣿⢠⣿⣼⡿⣷⠛⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠶⣶⣦⣷⣿⣿⣿⣶⣿⣼⣿⢋⣠⣥⡴⠖⠾⣿⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠾⠿⠿⠿⣿⣿⣿⣿⣿⠿⠟⠓⠙⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⡿⢻⠛⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠀⠘⠇⠀⠀⠈⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣇⠠⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣟⣾⣿⡗⠂⣴⡞⠁⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣐⣿⣿⣿⣿⣊⣐⣿⣀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣯⢿⢿⣻⣯⣡⣤⣄⡤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⣶⡿⢿⣷⣿⣿⢿⣻⣾⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣼⣿⢿⣿⣿⡿⣿⣿⣿⣿⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⣫⣿⡇⣬⡐⣶⢹⣯⠻⣿⡿⣿⣦⡙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢸⡿⢋⣼⣟⡃⣿⣆⣿⡜⣽⣷⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣽⣷⠧⣠⡾⣿⣯⠁⣿⣿⣿⣧⠐⣿⡇⠀⠈⢿⡄
⠀⠀⠀⠀⠐⠊⠉⠉⠈⠁⣉⡽⣿⣾⣿⣿⣿⣷⠀⣿⣿⣿⡟⠁⠘⣿⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⠿⠛⣻⣿⠟⣼⡿⠿⢅⣿⡿⠛⡛⣃⣀⣹⣧⣤⣤⣀⣁⡀
⠀⠀⠀⠀⠀⠀⣾⠋⠁⢀⣀⣼⣟⣥⣤⡿⢿⣤⡼⣿⣿⡴⠛⣩⣿⣟⣿⣟⢿⣿⣿⣿⣛⠲⠶⢤⣀
⠀⠀⠀⠀⠀⠜⣡⡴⠾⠛⣻⣿⣷⣾⣿⡏⣞⠀⠙⢿⡿⠀⣸⡿⣿⣏⠃⢻⣷⡱⠝⠻⣿⣷⣄⠀⠈⠓
⠀⠀⠀⠀⠀⠋⠁⠀⠀⣠⣿⣿⣿⣿⢻⣿⢿⣧⠀⣿⡇⣼⡟⢠⣿⣉⠀⠀⠹⣿⣖⠆⠀⠙⠻⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⢁⡿⡇⢘⡏⣿⢶⣶⣿⣶⣏⡀⢸⣿⡃⠀⠀⠀⠙⢿⣟⡃⠀⠀⠈⠛⢧⡀
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⣼⡇⢀⣼⢿⣿⣼⣾⣿⡿⣯⡉⢺⣿⣄⡀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣼⠛⠀⠀⢰⣿⣹⣿⠛⣡⡗⡾⢻⣿⡃⠸⣿⣾⡟⠙⢿⣦⡀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⡧⠋⠀⣴⣿⣟⠁⣼⣟⠊⠀⠘⣿⣿⠀⠀⠙⠻⣄⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡇⠀⢰⣿⡟⠁⠀⣽⣿⠄⠀⠀⠘⣿⣷⠀⠀⠀⠈⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠁⢀⣿⡏⠀⠀⠀⣾⣷⠂⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢼⡟⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠇

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⡄⣽⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢡⣿⡂⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣧⣝⠋⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⢸⣷⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⠈⠰⢿⣿⣷⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣭⣿⣿⣶⠶⣿⣿⡀⠉⣀⡴⠞⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠛⠃⣿⣿⡷⠤⠿⣿⣿⣶⣫⣴⠴⠶⣶⢶⡶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢶⣦⣄⠀⠀⣾⠟⢣⠀⣄⣀⣹⣿⣿⡿⣟⣉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⠙⢮⡓⢤⡁⠀⣽⡤⣼⣿⣷⠀⠹⢿⠙⠚⠻⢷⣄⠀⢀⣠⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣷⣼⣦⡻⣄⣿⣧⣄⣘⣾⡟⢠⣀⠅⢀⣰⠂⣠⢾⡟⢉⣀⣀⣀⣄⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⢦⣤⣤⣽⣻⣿⣿⣿⣿⡿⡟⠛⠛⣧⡾⠇⢠⣾⣣⣾⣿⡿⠏⣫⠥⠴⠒⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠛⠿⣿⣿⣿⣤⡀⣀⠀⣠⡆⠀⣿⣷⣿⣁⣑⡈⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣋⣹⣿⣷⠾⣿⣯⠀⠀⢾⣿⣿⣙⠛⠛⠉⠛⠛⠛⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠚⠉⠠⠶⣿⣿⣁⠀⠀⢶⣿⡁⢀⣀⠠⢀⣹⣽⠿⠶⠤⠄
⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣦⣿⣿⣶⣤⡞⠋⠿⠋⠀⠛⢻⣿⠄⠀⠾⢀⣿⣿⣷⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠉⠁⠉⢀⣀⣤⡵⠿⠿⢿⣿⣿⣿⣿⡦⠐⠂⢦⡾⣼⠛⠲⠆⠀⢠⣿⣿⣯⣥⣄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣠⣴⠞⠭⠅⠒⠊⢉⣽⡿⠿⣿⡿⡇⠠⢀⠀⠀⠀⣿⣤⠀⠀⣠⣾⣽⣿⡿⠾⠿⠶⠦
⠀⠀⢠⠾⠙⠀⠀⠀⠀⢀⣴⠿⠍⠉⣠⣿⠟⢁⣠⣷⣦⣤⡦⢻⣵⣦⣼⣿⣿⣿⣷⣶⣂⣄
⠀⠀⠁⠀⠀⠀⠀⠀⣰⡿⠋⠀⢀⣴⠟⢡⠴⣻⡿⣿⣿⡝⡇⢺⡿⢹⠏⣿⣿⣿⣧⣍⠙⠿⣿⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠠⠞⠁⠀⢀⣴⣿⠟⢸⡿⠡⠀⠈⠙⣿⠂⢿⣿⢿⠿⣿⣧⡄⠀⠈⠛⠿⣤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣰⣾⠟⠀⠀⢸⠇⠀⠖⠶⠶⢽⠀⠊⢿⣿⢧⠙⣿⣷⣆⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⢠⠟⠠⠀⠀⠀⣿⢿⣿⠁⠀⢻⣿⣇⠀⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⢸⡟⠀⠀⠈⢻⡿⡄⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⢻⣿⡀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣦⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣴⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣰⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⣀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣀⣀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⣄⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⣠⣴⣾⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠿⠟⠋⠁⠀⢸⡇⠀⠈⠙⠻⠿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢡⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⣸⡌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⡝⢸⡧⠈⡇
⠀⠀⠀⠀⠀⠀⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡱⣌⢸⣷⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢊⡟
⠀⠀⠀⠀⠀⠀⢹⡔⢯⡓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⢮⢸⣗⠅⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡚⢁⠞⡼
⠀⠀⠀⠀⠀⠀⠀⢳⡠⣝⢶⣀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⣼⣽⢮⡳⢸⣿⡣⠀⣳⠀⠀⠀⠀⠀⠀⣠⢖⡁⡆⣣⠏⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢒⡂⠙⣾⡤⠈⠳⣄⠀⠀⠀⠀⠀⡏⣿⠣⡑⢸⣿⣪⠀⢸⠀⠀⠀⠀⣠⢾⡵⡏⢇⡵⠍⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡯⢭⣌⠳⣇⡆⡈⠳⣄⠀⠀⠀⣇⣿⡑⢌⢸⣿⣗⠅⢸⡇⠀⢀⣔⣵⡟⡇⢣⡾⠍⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣒⡢⠙⢿⣴⢀⠈⢳⡀⠀⡧⡷⣝⠂⢸⣿⣵⡃⠸⡇⢠⢯⡞⡇⡇⣰⡿⠍⢀⡾
⠀⢰⠤⣄⡀⠀⠀⠀⠀⠀⠀⠳⡷⣬⢥⡀⠻⣧⣆⠀⠹⣴⡗⣟⢮⠃⢸⣿⡯⡂⠨⣷⣣⡏⠇⠃⣼⠿⠉⢀⡞
⠀⠈⢧⡙⠮⣉⠒⠦⢄⡀⠀⠀⠙⢞⢿⣒⡀⠙⢿⣼⡀⠘⡟⢯⠣⡑⢸⣿⣿⠅⢰⣷⢻⠓⢀⣾⡿⠁⢀⡞⠀⠀⠀⢀⣀⠤⡀⡂⠒⣒⣒⠖⠂
⠀⠀⠀⠳⡹⠬⠙⢶⣄⡉⠓⠦⣄⡈⠳⡻⣯⢅⡈⢻⣷⣹⣧⢳⡑⢌⢸⣿⣟⠅⢸⡿⠘⢀⣾⣿⠁⢠⢏⡠⣔⣾⣿⡳⠲⣑⣥⠷⢩⠟⠁
⠀⠀⠀⠀⠑⢮⢯⣄⣈⠛⢷⣆⢀⠉⠲⢽⣾⣷⣂⠀⠹⣿⣿⡰⣝⠂⢸⣿⡕⠀⣺⡇⢠⣿⡟⠃⣰⣻⢵⢟⠣⢃⣡⡴⠟⠋⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠑⢽⢿⣒⣀⠈⠛⠷⣤⣄⠈⠛⢷⣯⢄⠙⣿⣔⢮⡓⢸⣿⡫⢠⣿⣷⣿⡟⢂⡼⡛⠉⢈⣠⡶⠟⠉⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⢛⠯⣥⣀⠈⠙⠻⣷⣤⡉⠳⣄⠘⣿⡰⡕⢸⡯⠂⣼⣿⣿⠏⣰⠟⢁⣤⡶⠟⠁⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢿⣷⣤⣀⠀⠉⠛⢷⣌⠻⣌⢷⣌⢸⣏⣰⣿⣿⡵⢛⣡⣾⠿⢉⣡⠴⠊⠁
⠀⠀⠀⠀⠀⢀⡠⠤⠶⠒⠒⠒⠒⠒⠚⠛⠻⠿⠶⢦⣤⣌⣙⠿⣷⣷⣸⣿⣿⣿⣿⣖⣛⣣⡤⠶⠟⠒⠒⣒⣚⣋⣛⣉⠩⢁⡠⠃
⠀⠀⠀⠀⠀⠀⠉⠓⠦⢬⣈⣩⢩⣍⡋⢛⡛⣛⢛⡓⠒⢒⠌⣽⣿⣿⣟⡿⣿⣿⠿⣿⣟⣓⢛⣛⣛⣋⣉⣭⣭⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⢚⡷⢿⣿⠿⠟⢛⣩⣠⠞⣿⡟⢶⣬⣉⠒⠬⢭⡛⠿⣛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠖⢋⣥⢶⡺⠟⠉⠀⠀⣿⠇⠀⠉⠚⢝⣲⣆⣍⠓⢬⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⣋⠤⠴⠚⠋⠉⠀⠀⠀⠀⠀⣟⡰⠀⠀⠀⠀⠈⠉⠛⠢⠤⢍⡊⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡓⢖⣂⢀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⡎⠡⠛⣽⠿⠿⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣶⣶⡞⣷⠀⣿⢊⡷⢞⣽⣶⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣁⣤⠘⢻⠠⣟⣛⣽⣰⠿⣿⣷⠯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠅⢉⣉⠛⣛⡾⢋⣣⣴⠁⢠⡟⢻⣇⠨⡛⠒⠿⣷⢶⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣼⣿⣾⣿⠟⡇⢠⠟⠁⢀⣿⢇⢻⣿⠷⣾⣶⣤⠶⠌⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢳⣯⢿⡿⠹⣦⢡⡞⣴⣇⣿⣿⣎⣿⣿⠛⠦⣌⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠍⢀⠤⢋⡠⠏⠀⣾⡿⡀⠉⣆⡿⢧⠈⢻⡝⣿⣷⣷⢮⣳⠜⢯⣷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠊⣠⡾⠋⠀⠀⣴⡿⠀⣱⡜⣏⣿⡈⢧⠈⠇⡼⣿⠛⢷⠈⠳⣌⠻⡤⠈⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠋⢀⠀⢀⣼⣏⡴⠞⢹⣿⠏⢘⡃⠈⠑⡞⣱⣿⡏⠀⠀⠀⠘⠱⣶⡀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠉⡐⢁⡄⠘⠀⢉⡚⠀⣼⠧⠂⠀⣅⢀⢀⠀⠻⠑⠷⠀⡀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢉⠄⠉⠀⠀⠉⡉⠁⣤⠃⢸⡇⠀⢄⠀⠃⠀⠀⠀⠀⠣⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠸⠁⠀⠀⠇⢠⢦⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⡇⢸⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⡀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⡀⠀⠀⢈⣿⣿⣿⡏⠀⠀⠀⣠⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣄⠀⠀⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⠟
⠀⠀⠐⠶⣤⣤⣄⣀⢀⠀⠀⠈⠙⣿⣿⣿⣿⣦⠀⣽⣿⣿⡅⢠⣾⣿⣿⣿⡟⠁⠀⠀⢀⣀⣀⣤⣤⡤⠖
⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣶⣤⡀⠀⠙⢿⣿⣿⣇⢸⣿⣿⢀⣿⣿⣿⠟⠁⠀⣠⣴⣾⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣷⣦⣌⡛⢿⣿⣌⣿⣏⣼⣿⠟⢉⣠⣶⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠿⢿⣿⣿⣿⣦⣝⢿⣿⣿⢟⣥⣾⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣬⣿⣿⡿⢿⢿⣿⣿⣯⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠿⠿⠿⠛⠋⠀⡏⠀⠉⠛⠿⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠐⠀⠂⠐⠂⠀⠐⠀⠀⠂⠐⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢤⣀⣿⣿⠀⣀⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠹⠇⣹⢚⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣾⠾⣿⣿⡿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣾⡿⣢⣤⣀⡙⠧⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣤⣿⣿⣿⣍⠙⢿⣅⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⣤⡶⠾⠿⠋⠁⢠⠾⣋⣴⣿⣿⣷⣄⠈⠙⠶⠖⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣯⣼⣿⣬⠻⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⣶⣿⣿⣯⡤⣀⣤⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⣿⣿⢻⣿⣿⣾⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣶⣶⣶⣾⣷⣶⣿⣷⣿⣿⣿⣿⣿⠿⠷⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠾⠋⠉⠁⣠⡿⠋⠉⢈⣿⡿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⠈⠙⠛⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣰⠏⠀⢀⣴⡿⠛⢾⣿⣯⡿⣿⣿⣿⢿⣿⣩⣿⣿⡿⠿⠲⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠋⠀⠠⠾⠋⠁⢠⡾⢻⣿⡇⢻⣿⢿⣿⣿⣿⡏⣁⣀⣀⣀⠀⠘⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣤⣠⣐⡿⢃⣾⣏⠴⣿⣿⣜⣿⣿⣿⣿⣿⡉⠉⠉⠛⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣉⣹⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⣷⣦⣝⣿⢷⣶⣶⠶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠉⢉⣹⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣟⣉⣀⣀⡀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠋⠀⠀⢠⣾⡿⠋⣹⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣻⡟⠁⣸⣛⣿⣿⠙⣿⣿⣷⣾⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣯⡀⢠⡟⡟⢣⣿⣶⣿⣿⣿⡿⣿⣿⠿⠟⣉⡽⢋⢻⡿⢿⣴⠶⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣤⣤⣤⣤⣤⣤⣤⣴⣋⡀⠈⠻⣷⣾⣿⡛⢻⣍⠻⣿⠁⠛⣹⣦⣻⣤⣧⣈⡉⠁⠀⠀⠘⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣙⣻⣿⣿⣶⣤⣽⣿⣿⣷⣽⣿⠇⡘⢿⣿⢿⣿⡿⣿⣿⣿⡿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣻⣿⣰⣤⣄⡈⠃⠀⠁⠙⠓⠶⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⣋⠤⠜⠃⣠⠟⣻⣿⣿⣿⣿⣿⣉⣿⣿⣿⠋⣻⣿⣿⣴⡈⠻⣿⣿⣿⣟⣠⣄⠐⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡃⠼⠂⠁⠀⣠⣎⣥⠞⣣⣾⣿⣿⣻⢼⣿⢟⣿⣿⠀⢸⣿⣿⣿⣧⡲⣉⡻⣿⣿⣿⣿⠋⠸⠛⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠙⠉⠁⠀⠀⣴⢮⡽⢫⡥⢾⣿⣿⣿⣿⢃⣼⣿⢘⣿⣿⣤⣿⣿⣿⣿⣿⣷⣯⣿⣇⢛⡇⠉⠁⠀⠀⠀⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣵⣯⣶⣶⣤⣼⣿⣿⣽⢋⣼⢿⡇⢸⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣯⣷⣓⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠟⠁⣀⣀⣉⣙⣿⡿⢣⣾⣿⡆⣀⣼⣿⡿⢋⣬⣾⢿⣿⣿⠆⠙⢿⣿⣟⠛⠉⠻⡟⠿⠿⢿⣿⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⣠⠶⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⡏⡊⣿⣿⢶⠁⢢⡝⠻⣷⣄⠀⠀⠀⠀⠀⠈⠉⠛⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠀⠀⠁⠀⠀⠀⢰⣟⢹⣿⣷⣿⣿⣿⣿⣿⡿⠃⣴⣿⣿⡰⡃⢻⣿⡆⡄⠀⠁⠦⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⠇⣤⣿⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣏⡴⢙⠀⣿⡇⠀⠀⠀⠀⠙⢬⡻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠿⠿⠛⠛⠟⢚⣻⣿⣿⣿⣿⣿⣿⣿⣏⡙⢻⣿⡀⣿⠎⠀⢸⣿⠀⠄⠀⠀⠀⠈⠁⢾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⢟⠛⢩⠁⠤⠄⠐⠋⠉⢀⣴⡿⣍⣽⠿⣿⣿⣿⣿⣿⣻⣿⣤⢬⡿⣿⠃⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡀
⠀⠀⠀⠀⠀⢠⠾⠯⠙⠃⠀⠀⠀⠀⠀⠀⢀⣠⡾⢛⣶⣿⣿⢇⣸⣿⠟⣧⣿⣧⡀⢻⣿⣇⢻⣛⠁⠀⠀⢻⣏⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣥⣤⣿⣿⡿⢃⣼⣿⡇⠀⡿⢛⣿⣧⠀⠹⣿⣧⡛⢂⠀⠀⠸⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣽⣿⠿⠟⢉⡴⢀⣼⢿⡏⠁⠀⢒⣻⣽⣷⠀⠀⠻⣿⣿⣄⢀⡀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⠟⠉⠀⢀⡙⢠⣼⠿⡌⠁⠀⠀⠸⣧⣿⣿⠂⠀⠀⠈⢿⣿⣄⠃⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⠟⠉⠀⠀⠀⠀⣈⠁⢶⣿⡷⠀⠀⠀⠀⠠⠎⣿⣿⡇⠀⠀⠀⠀⠛⢿⣼⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠏⠁⠀⠀⠀⠀⠀⣴⢃⣿⣼⠷⠀⠀⠀⠀⠀⠀⡶⢿⣿⡆⠀⠀⠀⠀⠀⠀⠙⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⢠⡜⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠦⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⠛⠻⢻⣿⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⢿⡝⣏⠹⠿⣞⣿⣿⣿⣿⡿⣿⣿⡯⢿⡿⣽⣿⡟⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣻⡝⠿⣿⣿⡋⣄⠿⡄⠀⡁⢈⣽⣿⣿⣏⠉⣈⠔⡿⠷⠛⠋⠵⣯⡿⣯⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⠿⣋⠛⠃⠠⠚⣛⠿⠙⢥⠠⠀⣸⣿⣿⣿⣿⣧⠊⡷⠆⠀⠁⠀⠷⢽⡂⠈⠛⠵⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣧⣟⣉⠐⠀⠀⠀⠀⠂⠀⠠⠀⢀⣿⣿⣿⣿⣿⣿⡃⠃⣤⠀⠀⠀⠘⠀⠚⠀⠠⠀⢠⡿⢣⣽⣦⡀
⠀⠀⠀⠀⣠⣾⣤⣿⡛⣿⣏⠸⠃⣀⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⢘⠁⢻⡾⠿⢷⣄
⠀⠀⠀⣰⠿⡟⠿⠿⢻⡅⠈⢀⡀⡄⠀⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢤⡃⠿⠃⣷⡰⠻⣆
⠀⠀⣸⣿⣶⣿⠶⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⠈⠉⠀⠀⠙⣛⢶⣽⣆
⠀⢰⣿⣿⣿⣿⣶⣶⣭⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⡆
⢀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⠛⣽⣿⣿
⢸⣿⣿⡿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠷⠘⢋⣛⣿
⣿⣽⡿⣿⠙⠃⠍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠕⠺⢿⣿
⣿⣻⣶⡃⠠⠈⣀⠂⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣻⣿⣿⣿⣿⣿⣿⣟⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠄⠀⠀⠄⠀⢾⣿
⣯⠩⠱⣶⣴⣤⠶⡤⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⢠⠤⠀⣾⣥
⣿⢻⣴⡶⣞⠷⠠⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠂⠐⠀⣤⢴⣿
⢸⣿⣿⡳⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠐⡆⢀⡤⠰⡶⠲⣾⣴
⠈⣷⣯⣿⣿⡛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⠀⠀⠀⠀⠀⠀⠐⠀⢡⠈⣃⢰⡇⣀⣾⣿
⠀⠸⣿⣿⠃⡀⠀⡐⡂⠀⠰⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠉⡈⠋⣡⣾⠇
⠀⠀⠹⣧⣄⠛⢠⠇⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⠻⡟⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡐⣂⢻⣈⣶⣵⡏
⠀⠀⠀⠹⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠋⣠⣾⣿⣿⠃⠀⠂⠘⣿⣿⣷⣄⠛⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⠏
⠀⠀⠀⠀⠙⢿⣿⣿⣿⡛⡿⠿⢛⠙⣋⠉⠄⡀⠁⣼⣿⣿⡿⠃⠀⠠⠀⠀⠙⣿⣿⣿⣶⠁⠀⢀⠉⠋⠉⠛⠛⠛⠻⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⣷⢦⢶⠆⣀⣾⡄⢀⢸⣿⣿⠟⠁⠀⢀⢠⣄⠠⠀⠘⠻⣿⣿⡏⠀⠀⢀⡘⠀⠴⠔⢥⣤⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣯⠷⣿⣶⣾⣳⣜⢡⠿⠿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠲⠀⠀⠙⠻⣠⡔⢉⣇⣈⠀⣤⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣍⣯⡙⣿⣯⡑⠰⠰⢇⠀⠐⠆⠀⣹⣇⡿⣠⢀⢛⣤⡷⢾⣁⣾⣦⡥⣽⣧⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣿⣡⡹⢷⣿⢆⣾⣧⣟⣯⣙⢱⡛⣈⣠⡟⣳⣶⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠾⣿⣿⣿⣿⣿⣿⣿⣯⠽⠾⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠐⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠀⠀⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠀⠀⠀⢸⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢟⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠔⢆⢱⠀⡀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⣾⠻⠋⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⠹⣧⠀⡀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⢸⣿⣴⠃⠀⠀⠀⠀⠀⢀⡠⠞⠉⠁⡸⠁⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠆⠈⠻⣷⢠⡀⠀⠀⠀⠀⢰⡌⠀⠀⠀⢸⡿⢃⠀⠀⠀⠀⢠⠖⠞⠀⠀⣠⡾⠀⢚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠄⠀⠈⠻⣇⢆⠀⠀⠀⠀⡉⠂⠀⠀⢸⣷⢋⣀⡄⢀⡄⡟⠀⠀⣠⣾⠟⠀⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡖⠤⢄⡘⢿⣀⡄⠀⠀⠰⡄⠀⠀⢸⣷⣏⠀⣠⡜⠀⠃⢀⣴⠿⠃⢒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠀⠀⠙⣇⣤⠀⢀⠁⠀⠀⢸⣿⣯⣼⡇⠀⠀⣴⠿⠇⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡄⠀⠈⢻⣾⠘⢷⣁⠀⢸⣿⣿⠋⠁⢠⣾⠗⢀⡐⠈
⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⡒⠶⠑⠶⡒⠢⢤⢤⣙⣲⡂⠀⠙⣿⣬⢿⡀⢸⣿⡟⠀⣰⣿⣿⡵⠋⣀⣀⡤⢤⠴⣶⠶⠒⠠⠶⠰⠶⠢
⠀⠀⠀⠀⠀⠉⠉⠙⠒⠳⣦⣭⣄⠀⠂⠈⠂⠀⠀⠈⠙⠿⣧⣄⠈⠻⣼⡧⢸⡿⢃⣾⣿⣟⡿⡾⠋⠉⢁⣀⣠⡌⠀⠒⠒⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠣⠤⣄⣀⣀⠀⠀⠀⠀⠙⠳⣦⣹⣇⣾⣡⣾⠿⡛⣉⣠⢤⣞⠚⠃⠀⠤⠄⠭⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⠒⠢⠤⠐⠚⠂⠟⠉⣿⣷⡿⠿⠿⠯⢄⡲⠤⠼⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠁⠀⠀⢀⡀⠘⠗⠄⠙⠿⣅⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢋⣤⡠⡤⠐⠛⠉⠀⠀⠇⠀⠺⡄⢢⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠙⢧⣀⠈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠳⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀
⢦⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠
⠀⢿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⡿
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠸⣿⣿⣿⣿⣿⣿⠇⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠉⠍⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⣠⣾⣿⡿⠁⠀⠀⠈⢿⣿⣷⣄⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠈⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠋⠀⠀⠀⢀⡀⠀⠀⠀⠙⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠠⠄⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠤⠈⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠒⠀⠀⠀⠐⠂⠀⡀⠃⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠉⢄⢀⡀⠀⠀⡀⢀⠈⠁⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⢀⡀⠈⠀⡀⠀⢀⡀⠉⠀⣀⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠤⠀⡤⠀⡅⠰⣤⡀⢴⠀⣡⠴⠀⡁⠠⠄⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠁⢶⠆⠙⢢⣈⡀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠰⠀⠀⠁⠠⠈⠀⠰⠀⢸⠀⠠⠀⠈⢠⠘⠁⠀⠰⠀⠆⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⠀⢸⠀⠀⠐⠆⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠜⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢸⣿⡏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡃⢸⣿⢟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⠇⢘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢧⣸⣧⣿⣿⣯⠀⠀⠀⠀⠀⠀⣀⣠⢶⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⣻⣟⠂⠘⠟⠻⢿⣧⠀⠀⠀⣠⠐⣿⢠⡿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣦⡀⠀⢸⣿⡄⢀⣶⣧⣿⡏⢀⡰⠊⠀⣰⣿⣛⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣶⡀⢿⣙⢶⣿⣿⣿⣧⠌⢡⣀⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣿⣟⣿⣿⣿⣾⣿⡺⣿⣿⣿⠁⢠⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⣀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣗⣿⣿⢃⣷⣿⣿⣿⠟⣁⣀⡀⠤⠄⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠻⠿⣿⣿⣿⣿⣶⣦⣭⣬⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣥⣶⣤⡤⠾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡴⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣖⣿⣿⣿⣿⣿⣿⣿⣯⣭⡉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠿⠛⠉⢠⡇⠘⢿⣿⣿⣟⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠉⠛⢿⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠑



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣓⣳⣬⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠽⢟⣳⣦⣳⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⣶⠓⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠾⣿⣸⣿⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣇⡇⣇⣿⡛⠿⠭⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣂⣸⣿⡸⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡆⢸⣿⣷⣋⣴⡶⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣐⠘⣿⡇⣾⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠸⠳⣠⠼⣋⣹⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⢇⣿⢴⢰⣷⠀⠀⠀⠀⠀⠀⠀⢸⢸⢿⢠⡟⣩⣛⠭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⢯⡿⣾⣼⣿⣬⣳⣄⢀⢀⢸⡄⢻⢨⣾⢟⣛⣋⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠺⣞⢻⣿⢿⣝⢿⣦⡇⢦⣧⢠⠞⠋⠉⠑⠒⠒⠀⠀⢀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡤⣀⠉⣿⣲⣷⣭⣳⣝⢿⣼⣿⡿⠴⠥⠭⠉⣉⣴⣤⣴⣿⣿⠟⠁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠶⣍⣾⠀⣿⣾⡆⠹⣷⣦⣹⣿⡿⣿⣿⣧⣙⡿⠀⠀⠀⣀⣾⠛⢻⣿⣯⣤⣶⡶⢴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢩⣿⡆⣁⣽⣿⣆⣿⣿⡇⠈⣿⣿⡇⠙⢣⠘⣿⣿⡿⣧⣴⣴⣾⣿⠻⠿⢿⣫⡉⠻⣿⣤⡀⣹⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠉⣿⣿⣿⣧⢻⣿⠏⣰⣿⣿⣿⣄⢻⣿⡇⢰⣿⣇⣿⣬⡵⠿⠿⣉⠙⣿⣶⣷⡈⣿⣿⣾⣿⣿⠷⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢈⠿⡟⢉⠍⣛⡿⢿⢀⣻⣿⠟⠁⣬⣿⣿⣷⡌⣿⣿⣿⣿⣿⣷⣶⣿⣷⣦⣦⡙⢿⣿⣶⣆⠈⢷⣿⣆⣽⡛
⠀⠀⠀⠀⠀⠀⠀⠳⣄⣹⣦⡹⠿⠛⠿⣦⣽⣿⠀⠘⣦⣿⣿⣿⣿⣾⣿⠟⠹⣿⣦⣸⡯⢄⡀⠙⣿⣆⠈⢻⣿⣧⣾⣛⡻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠖⢀⣀⣨⣿⣿⣄⠐⣿⣿⡿⠛⢛⣻⡏⢀⣾⣿⣉⡉⢿⣦⣷⣼⣿⡋⡉⠈⣿⣅⣙⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⣿⣶⣬⡽⠛⣙⠛⠿⢷⣿⠿⠀⠸⣿⣿⡇⣼⣿⣿⣉⠛⠻⣶⣤⡹⣿⣏⠛⣾⣿⣿⣍⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣇⡀⠀⣹⣿⣿⣷⡇⢀⢸⣿⣿⣧⣿⣿⣽⢏⡿⢧⣁⡀⠀⠨⣿⣥⠬⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠾⣿⡿⠷⠿⢛⣿⣿⣷⣶⣾⣿⣿⣿⣿⢟⡵⠫⣼⣶⠿⢿⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢉⣠⣤⣴⠾⠋⣁⣴⣶⠿⠛⣉⡾⠟⢁⣾⠀⠀⠀⠈⠙⠲⠮⠉⠛⠻⢦⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠴⠾⠛⠉⠁⠀⣨⣼⠕⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⢋⠥⣾⠟⠁⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠁

⠀⢠⠤⡀⢠⠈⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⣼⡀⠀⣼⠀⢰⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢹⠀⡠⠚⣆
⡇⠸⠇⠀⢿⡄⠘⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⡘⠆⠁⣠⠋
⠃⠀⠈⠀⢀⣀⣀⣀⠛⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣴⠀⠘⠛⠀⣼⠁⠀⢀
⠀⢃⠀⠀⠀⠀⠀⠈⠛⢀⣤⢠⡇⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠉⠘⠂⠀⠀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠘⠧⣄⠀⠹⠀⠀⠀⠀⠀⠠⠄
⠀⠈⢦⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠐⠶⠀⠀⠛⠀⠉⢈⡵⠈⠹⡆⠀⠀⠀⠀⠀⠀⠈⡇⠀⠳⣤⡀⠀⢀⡤⣤⠁
⠀⠀⠀⠉⠲⣄⠀⢾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣀⣀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡼⠃⠀⠈
⠀⠀⠀⠀⠀⠈⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠉⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠛⠀⠀⠀⢀⡛⠀⢠⡤⠚⠁
⠀⠀⠀⠀⠀⠀⣗⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣹⠶⠒⠋⠉⠉⠉⠉⠁⠒⠲⣤⡀⠀⠀⠀⠀⠲⡅⠀⠀⠀⠀⣴⠋⠀⢀⡎
⠀⠀⠀⠀⠀⠀⢹⡄⠀⢻⡀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠹⠆⠀⢀⡴⠁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠈⢃⠀⠘⢣⠀⢠⠞⠁⠀⠀⠀⠛⠃⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠹⡀⠀⠀⡀⠀⢀⡞⠁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢀⣼⠦⠶⠛⢻⠇⠀⠀⠀⠀⠀⠀⡠⠒⠲⡄⠀⠀⠀⢀⣠⠾⠀⠀⠀⢫⡀⠀⢹⣦⠛⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠋⢁⣼⠀⠀⠀⠘⣇⡀⢸⡟⠀⠀⢀⠾
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢰⠀⠀⠀⠀⢸⣿⡗⠙⠛⠛⠛⠉⠀⢀⣀⣴⣿⡟⠀⠀⠀⠀⠀⠙⡿⢦⣀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠀⠀⠀⠀⠸⣿⣷⣤⣤⣤⣤⡶⠛⠋⠉⢹⡟⠁⠀⠀⠀⢷⡤⠛⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣷⠀⠀⠀⠀⠹⣿⣿⣿⠿⠟⠐⠒⠒⣴⠟⠁⠀⠀⠀⣠⠟⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⣆⠀⠀⠀⠀⠈⠻⠇⣀⣀⡠⠶⠞⠁⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠙⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠛⠉⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠳⠾⠙⠛⠛⠛⠋⠁⠰⠶⠶⠦⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠈⠙⠛⠛⠛⠲⠦⢤⣤⡤⠤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠐⠛⠋⣉⣁⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠳⣤⡤⠔⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⡤⠴⠶⢶⣶⠶⠖⠛⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠈⠉⠉⣿⠉⠙⠛⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⠤⣼⡁⠀⠀⠀⠀⠀⠀⡰⠓⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢘⡇⠀⠀⠀⢀⡤⠚⠀⠀⠀⢠⡇
⠀⠀⣀⠀⡀⣀⣠⡴⠖⠉⠀⠀⠀⠀⡀⠘⣧⣀⠰⠊⠉⠀⠀⠀⠀⠠⠺⡇
⠀⢘⠋⠤⠀⣀⣈⣡⡀⣀⡀⠀⢀⡠⠚⠛⠁⠉⢠⡀⠀⠀⠀⠀⡜⠁⣀⠃
⠀⠈⠑⠂⢤⣤⣤⣤⣤⣤⠀⠠⣏⠑⠂⠠⠀⠀⠀⣴⠄⢤⣤⠘⠓⢠⠌⠁
⣤⣤⣀⣤⣤⣤⣤⣤⣤⣠⣤⣤⣄⣉⣤⣤⣶⣶⣶⣤⣶⣤⣤⣌⣁⣠⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣠⣤⣤⣤⣄⣠
⣿⣿⣿⣿⠿⠛⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢷⣯⣿⣻⣿⣿⣿⣿⣿⣧⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣥⣿⣽⣿⣯⡿⡏⢿⣿⣿⡿⣷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡗⣿⣿⣿⣯⣿⣾⣏⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⢭⣲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⣿⣿⣾⣿⣿⣿⣿⢻⡟⣿⣿⣿⣏⣿⣿⣤⣀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣯⣷⣿⣣⣿⢻⣿⣿⣇⣿⣿⣿⣿⢿⣿⡾⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢛⣭⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⡛⣿⣯⣻⣿⣾⣶⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣟⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣫⣯⣾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⢶⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣷⣌⠻⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠛⠿⠟⣡⣿⣿⣿⣿⣿⣿⣟⣷⣿⡟⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣶⣶⣟⣻⣿⣿⣿⣹⣿⣿⣿⣿⣙⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⢛⣿⠟⠿⠫⠏⠃⠿⢿⠿⠟⠃⠋⠁⠻⠿⢿⡿⢿⣿⣿⡋⠙⠟⠋⠻⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠁


⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⣤⣌⣀⡀⠀⠐⠒⢭⡓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢛⣫⣭⣭⣭⣭⣇⣀⣀⣀⣐⣿⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡵⡺⠟⠟⠛⠉⠀⠉⠁⠀⠀⠀⠀⠉⠹⣟⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠏⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⢿⡆⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⢹⠆⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠀⠀⠀⢸⠱⠀⠈⠔⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⠙⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠃⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⠖⢣⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⢦⢀⣀⢄⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡆⠀⠀⠀⠀⠀⢴⠒⠚⠉⢀⡠⡾⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⢀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⢶⠒⠚⣉⢴⠇⠀⠀⠀⠀⢀⡾⠁⠀⠀⣀⠔⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠙⠲⠒⠁⠀⠀⠀⢀⣴⠏⠀⢀⡤⣄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣀⠀⠀⢀⣀⣠⠴⡟⠴⠒⠊⣁⡠⠟
⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⢉⡩⠝⠋⢅⣀⡠⠃⡖⠂⠉⠁
⠀⠀⠀⠀⠠⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠤⡏⠀⠉⢉⣠⢴⠆⠀⠈⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠞⠁⠒⠒⠒⠒⠉⠑⠒⠉⠉⢀⡞⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠤⠬⣉⠑⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠉⠓⠢⠤⣈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠺⣆⠀⠀⠀⠀⠁⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣯⠙⡖⠒⠒⠃⠤⠤⠔
⠀⠠⢄⠀⠀⠀⠀⠀⢀⡔⢉⡴⠊⠉⠹⠦⠖⠒⠒⠓⠓⠂⢄⡈⠉⠉⠛⠒⠒⠒⣃⣀⠀⠀⠀⢀⠏⣸⠁
⠠⡑⢄⠀⠒⠤⣀⢠⠎⢨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢇⠀⠀⠀⢀⡏⣀⠠⠔⣚⠖⠁
⠀⠘⢄⠳⣀⠀⠀⠉⠲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⡼⠒⠒⠒⠉⠁
⠀⠀⠀⠙⠢⡑⢤⡀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⠀⠀⠀⢀⠀⢐⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⣝⡀⠀⢀⠁⡊⠀⠀⠈⢻⢦⠀⠴⢂⡿⡄⠀⠀⠹⡦⡐⠐
⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠈⠓⢍⠓⢤⣁⠀⠀⠀⠀⡟⢀⠀⢀⠞⠀⡟⠀⠀⢠⠀⠹⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⢧⠀⠈⠳⡀⠐⣦⡙⢮⠢⢸⠁⢠⠃⠀⡠⠋⠀⠈⡇⠀⢀
⠀⠀⠀⠀⠀⠀⢖⠈⣀⣀⡀⠀⠀⢸⡤⠀⠀⢧⢠⣇⠹⡌⢳⠘⣆⡿⢀⡞⠁⠀⠀⢀⠆⢀⠎⢣⠀⡀
⠀⠀⠀⠀⠀⠈⠀⣈⠉⢳⡎⢢⡀⢸⠀⠶⡀⠈⠻⠂⠀⢱⠀⠀⡿⢽⣼⠀⢠⠀⢀⡌⢀⠠⡀⡏⠐⠁
⠀⠀⠀⠀⠀⠀⠈⢹⠙⠸⡇⢀⠱⣾⡄⢁⠈⠢⡀⢠⡄⡞⠀⢀⠇⡄⠋⡠⢁⢣⠏⠀⢸⢣⢰⠇⢀⢦
⠀⠀⠀⠀⠀⢀⣆⢺⡊⠀⠹⣇⠰⠠⢄⠀⠂⠀⠰⠂⢠⠃⢀⡞⡐⢸⠐⠀⢠⠃⠀⡰⠃⣸⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠘⡏⢦⣀⠀⠀⠈⠳⣝⢤⡈⠲⠀⠀⡄⢸⢠⠟⠐⠀⢾⠀⠂⡇⣠⠏⠀⣀⡎⠀⣠⢀⡸
⠀⠀⠀⠀⠀⠀⠱⣄⠈⠑⠢⢤⡀⠘⡄⠱⠀⠀⠀⠆⠈⠿⠀⠀⠀⠀⠀⡆⢹⠇⡄⢠⠎⢀⡰⣻
⠀⠀⠀⠀⠈⢻⠆⠈⠲⢄⠀⣄⡙⠶⣗⠀⠁⠀⠀⠘⢄⠈⠂⠰⠀⠀⠀⠐⡤⠊⢄⣮⠖⢋⡜⠁⣦⡀
⠀⠀⠀⠀⠀⠘⠒⠠⠱⠀⠱⡀⠂⠑⠄⠀⡄⠀⠀⠀⠀⠉⠂⣤⠀⠀⠀⠀⠄⠐⠎⠥⢈⠏⡀⠀⠁⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⡀⡇⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢐⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠈⠨⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠓⢤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠀⣀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠉
⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠂⢀⠁⠀⠀⡀⠁⠀⠔⠀⡀⠀⡀⠀⠀⢐⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠐⠀⠀⠈⠈⠀⠀⠁⠀⠈⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⣿⡄⣸⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠞⠁⠟⠹⡆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠞⠀⠀⠂⠀⠀⠀⠀⠃⠉⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣶⢦⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠶⡡⢿⡞⡏⠀⠀⠀⠀⢰⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡂⢀⠟⡉⠀⠁⣘⢳⢿⡄⢸⠀⠀⢨⠻⠻⣤⣇⢀⣖⠦
⠀⠀⠀⠀⠀⠀⣴⣥⠄⡀⠀⣹⡗⣡⣾⣿⠃⣰⡇⡸⠀⣿⠿⣄⣠⣿⢣⡀⠈⠹⣾⠁⠀⠈
⠀⠀⠀⠀⠀⠠⠋⠉⠛⠳⢾⣯⣾⣻⢳⠃⢠⣿⠇⡇⠀⢿⣾⡘⡈⢻⣇⢻⣤⠬⢶⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠉⠭⠙⠒⠋⠛⢻⣿⡄⠚⠛⠓⠓⠘⠻⡏⢁⡤⠔⠈⣷⣀⠄
⠀⠀⠀⠀⠀⠢⡀⠀⠀⡀⠘⠇⠀⠀⠀⠀⠀⠀⢸⢸⡇⠖⠂⠀⠀⠀⠀⣹⣀⠀⠀⠀⡸⠋
⠀⠀⠀⠀⠀⠀⠈⠑⠤⠷⠞⢀⣀⠀⠀⠀⠀⠀⡄⢸⠃⠀⠀⠀⠀⢀⠌⠀⢠⠋⠱⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⠉⠀⠉⠉⢉⡉⠉⢩⡀⠴⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣤⣼⣿⣿⣿⣷⣾⣿⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠟⣁⠀⠀⠀⠀⠀⠀⣀⠀⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠁⠚⠉⠀⠀⠀⠀⠀⠀⠉⠃⠀⠸⣿⣿⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⠋⠀⢠⣤⡀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠙⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣸⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⠀⠀⠀⠐⠀⠀⢀⢆⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠐⡶⠖⠻⠁⢀⡀⠔⠈⠀⠀⡠⠂⠀⠈⢞⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣠⠄⢴⡈⠠⠠⠠⣦⠒⠁⣀⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⢿⣧⣾⡇⠀⠀⠀⢹⡖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⠄⠺⣇⠀⠀⠀⠀⠋⠈⠀⠀⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠃⠈⠁⣀⠠⠄⠛⠒⢺⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠢⠐⠉⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣤⣤⣤⣤⣤⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢻⠛⠈⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⢰⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣆⣀⡇⠀⠀⠀⡀⣠⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⢯⣷⣿⠟⠀⠀⠀⠀⢿⣿⣴⣛⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡨⠊⠀⠀⠀⠀⠀⠈⢛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠁
⣿⣿⣻⣻⣛⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣻⣛⣿⣟⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢿⣿⣷⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⣿⣿⣷⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢙⣿⣿⣿⡆⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣹⣿⣷⣿⣯⡿⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣻⣻⣿⣹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢾⣿⣷⣿⣿⣾⣶⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣻⡟⣿⣿⣷⣅⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠾⣿⣫⣿⣿⣼⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣿⣿⢿⣿⣿⣽⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡵⢩⣿⣿⣧⣾⢿⣻⣿⣿⣿⣿⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⣽⣿⠏⣾⣿⣿⣿⣿⣼⣿⣾⣿⣷⣤⣈⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡟⢩⣟⡿⣿⣿⣟⣸⣿⣏⣿⣿⣿⣹⣿⣿⣿⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣺⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠻⠿⡿⠛⠻⠏⠈⠻⣿⣿⣿⠿⠛⠑⠹⢟⡿⢿⡿⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⢀⢄⡸⠀⠐⢅⡤⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠄⠀⠀⠀⠀⠄⡻⠦⠙⠁⡠⠚⠒⡄⠈⠃⢖⢠⡀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠑⠀⠀⣔⠦⠊⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⠪⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡮⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢕⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠉⡄⠀⢀⠀⠀⠂⠀⢢⠀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⠆⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡂⢠⡇⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠙⠛⠶⣄⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠂⠀⠀⠀⠀⠠⠁⢈⠀⠀⠀⠀⠛⢈⠇⠀⠀⢄⠄⢀⠏⠀⠀⠀⠀⠄⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⡀⡀⠁⠐⠚⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡰⠂⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡄⢴⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠈⠁⠄⠠⠀⠠⠀⠠⠤⠡⠈⢢⠈⠢⠀⠀⠄⠁⠀⠀⠊⠀⠁⠌⠑⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠤⠀⠀⠢⡀⠀⠀⠀⠔⠁⡀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠈⠲⠤⡤⠤⠴⡊⠀⠐⠂⢬⢶⢰⠎⢠⠆
⠀⠀⠀⠀⠀⠀⠀⢠⡠⠁⠀⠀⠀⠀⠙⠒⡒⠂⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠄⠀⠀⠤⠀⠈⠧⠀⠚⠏⢈⣟⠚⠛⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⠀⠀⠀⠸⠁⠀⠁⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠄⣠⠐⠓⡂⠀⠀⢐⠀⢀⠂⠀⠀⢄⠀⠙⠃⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠃⠀⠘⠲⠄⠀⠀⠀⢀⠀⠀⢀⡤⠊⠁⠀⢀⠂⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠨⠀⢀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠐⠀⠃⠀⠀⠀⠀⠀⣆⠀⢀⡆⠀⠀⠀⠀⠀⠄⠀⠈⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠰⣀⠃⠀⠀⠀⠀⠀⡂⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠈⠳⠀⠀⠀⠀⠀⠶⠂⠀⠰⠤⠀⠀⠀⠀⠠⠬⠉⠀⠉⢥⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣵⢦⣀⡀⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⢾⣴⣶⡍⢭⣄⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⠒⠛⠛⣤⡹⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣻⣦⡦⠀⢸⡇⢀⠀⠀⠘⠻⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠛⠛⠉⠛⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⡬⣯⡱⠄⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⢋⣴⣿⣾⣿⡷⠃⠀⠀⠀⠶⣻⡿⢢⣾⣏⣴⣹⣏⣡⣤⡆⠀⣖⣨⡱⠂
⠀⠀⠀⠀⠀⠀⠀⠱⠛⠙⠉⠁⠀⠉⢦⡀⠀⠐⠉⠙⣢⣿⣿⠤⠾⠛⠛⠛⠻⠟⠛⢻⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣤⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣿⡿⣿⣷⣄⢀⣀⣠⡄⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⢀⣀⣴⣶⣿⣿⡿⠽⠯⢉⣭⠈⢫⣁⣩⣖⣐⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣉⣙⠋⢩⣥⠀⣠⣄⣴⡶⠦⢦⡁⢤⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠘⠒⠲⠆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠘⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⢺⣿⡆
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠻⣿⡄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣄⡀⣰⣿⡿⠃⠀⢠⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡼⣿⠁⠀⠀⠸⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠘⣿⣿⣷⠈⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣦⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⢤⡀⠀⢀⣿⣷⡀⠀⠀⣸⣿⣿⡟⠀⢤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢋⣼⣿⣿⣿⣿⡇⠀⠀⠀⢱
⠀⠀⠀⢤⡀⠀⣴⡿⠀⡀⠙⣿⣿⣿⣿⡆⠀⠀⢸⣷⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⠁⠀⠈⣿⣷⡄⠀⠀⠙⠻⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣷⣤⣀⣤⣿
⠀⠀⠀⠈⣿⣶⠟⠀⠀⣿⣦⣾⣿⣿⣿⠇⢀⣴⣿⠟⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⡀⠀⠀⠀⠀⠉⣰⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣇⠀⢀⣿⣿⠀⡀⠀⠘⢿⣿⣿⣿⢟⣴⣿⣿⠋⠀⢠⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣀⠀⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢿⣿⣿⣿⣿⣇⣀⣽⣷⡀⠈⠙⠿⢋⢸⣿⣿⣿⣷⣤⣾⡇⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⣿⣌⣿⣿⣿⣿⣿⡿⢡⣾⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⢠⠀⠙⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⡟⠀⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣷⣶⣿⣿⣿⣿⡟⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣘⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⡟⠛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠘⣇⠈⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣸⠀⠀⠀⠀⠀⠀⠀⠰⠋⡇⣦⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠰⡆⣨⢛⢥⡶⠀⠀⠀⠀⠀⠀⢸⢸⣄⣧⣠⠀⠀⠀⠀⠀⢀⠀⣲⠛⡏⠀⠀⠀⠀⠀⠀⡾⡿⠜⡄
⠀⠀⠀⣷⣼⢀⡾⣤⠦⡼⠀⠀⠀⠀⢸⣾⠈⡟⠙⢻⠀⠀⠀⠀⠀⠘⢟⢫⣿⣀⡀⠀⠀⠀⢀⠠⢇⠠⣤⢷⡄
⠀⠀⠀⠘⠦⠾⠇⠘⠃⠁⠀⠀⠀⠀⠀⠁⠰⠛⠖⠁⠀⠀⠀⠀⠀⠀⠀⠱⠐⢯⠃⠀⠀⠀⠘⣷⠛⠘⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠜⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⡀
⠀⠀⠀⠀⠘⡿⡏⡅⠀⠀⠀⠀⠀⢀⢀⠀⣿⢣⣀⡀⠀⠀⠀⠀⠀⠀⠎⣼⣿⢰⡀⠀⠀⠀⠀⠀⡄⣾⡼⣃⡋
⠀⠀⠀⠀⠸⣧⠛⣇⠀⠀⠀⠀⠀⠈⠉⢷⠾⡌⠛⢛⡁⠀⠀⠀⠀⢰⣜⣇⢹⡾⣧⡀⠀⠀⠀⠀⡁⢏⢁⢹⠠⠇
⠀⠀⠀⠸⣆⣿⢶⣼⠀⠀⠀⠀⠀⠀⣻⡛⠀⡿⣆⠛⠇⠀⠀⠀⠀⠸⣿⠹⢰⡀⠻⠀⠀⠀⠀⠠⣼⡾⢿⡘⢾
⠀⠀⠀⠀⠀⠰⠏⠋⠀⠀⠀⠀⠀⠀⠈⠃⠻⠅⠙⠋⠀⠀⠀⠀⠀⠀⠙⠘⠋⠃⠀⠀⠀⠀⠀⠀⠈⠃⡎⠻⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⡀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣄⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣽⡷⣷⡆⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢷⣿⠃⣀⣟⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣿⣅⣸⣧⡀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⡄⠻⣿⠇⣸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣷⡄⢠⣦⣾⡿⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⡟⠁⠘⣿⣿⣿⣿⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⣷⣾⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣏⠑⣿⣿⣿⠁⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⡅⢸⡟⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⢈⣿⣿⣿⣿⣯⣿⠟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡃⢸⣇⠀⢈⣿⣿⣿⣿⠏⣡⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠇⣸⣿⠀⠘⣿⣿⣿⠋⠘⣿⠋⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠘⠃⣤⡀⠿⣿⣿⠀⢸⣿⣆⣠⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣷⡄⠉⣧⣠⣿⣁⠀⢾⣿⣿⣿⣿⣏⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⢻⣼⡀⢛⡘⣿⡿⠀⠈⣻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⣤⡀⣿⡇⠈⠁⣿⣁⣠⠾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡁⠾⢇⣤⡀⣸⣿⣧⣼⣿⣿⣿⠀⣴⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠿⠃⢸⣿⡏⣹⣿⣿⣿⣿⣿⣿⣿⡿⠉⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣜⣣⣶⡀⢠⣶⣾⣷⢈⣿⣤⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠙⠇⠈⠧⢼⣿⣸⣿⣿⣸⣿⣿⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣧⢠⣶⡄⠸⣿⢿⡧⠸⣿⣟⣉⣿⠁⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡹⣿⣿⠁⠀⣻⣏⡴⣷⣴⣿⣿⣿⣶⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣄⣰⣷⣨⣼⣿⠙⢿⣿⣿⣿⣿⣿⣿⡟⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⣿⣶⠞⣿⣿⣿⣿⣧⣸⣿⣿⣿⢿⣿⣟⣹⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣾⣷⣿⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠙⠿⣿⣿⣿⡿⣿⡾⣿⣟⣱⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⢉⣿⣿⠛⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣎⡿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣹⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⣬⡻⢿⣷⣿⣿⡙⣽⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⢄⠙⣿⣏⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣀⣠⣤⣾⣿⣿⣿⣿⡿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠺⠿⠿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠱⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣤⠀⠀⢠⠀⠀⠀⡆⠀⠀⢠⠀⠀⠀⢠⠀⠀⢀⣤⡄⠀⠀⠠⡆⠀⠀⣤⠀⠀⠀⢤⣤⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⣿⠀⠀⣿⡆⠀⢸⣷⠀⠀⣿⡆⠀⠀⢻⡇⠀⠀⠙⣧⠀⠀⢰⡷⠀⠀⣻⡗⠀⠀⢶⣶⣄
⠀⠀⠀⠀⠀⠾⡗⠀⢀⡧⠀⠘⠛⠁⠐⠿⠂⠀⠘⠟⠀⢠⣿⡗⠀⠀⣿⣷⠀⠀⠀⠠⠀⠀⠬⣿⡂⠀⠿⠿⠀⠀⢻⡀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⠀⠀⢀⣤⣀⠀⠀⢀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⢐⣿⣿⣷⠂⠘⣿⠃⢐⣻⣿⡿⠆⠀⣼⠄⠀⢸⠀⠀⣿⠀⠀⠀⠀⢠⡆⠀⣷⠀⣷⠀⣿⠀⣶⠀⣷⠀⠀⠀⣰
⠀⠀⠀⠀⠙⠉⠇⠁⠀⠀⠀⠁⠀⠘⠛⠁⠀⠀⣿⠆⠀⣸⡄⢀⣿⡀⢠⣿⡀⢸⡇⠈⠟⠀⠿⠀⣿⠀⣿⠀⣿⠀⣶⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠉⠁⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⣀⠁⠀⠉⢰⡆
⠀⠀⠀⠀⠀⢠⣆⠀⠀⢰⡦⠀⢰⢦⠀⠠⣆⠀⠀⣶⠀⢰⣦⡄⠀⠀⠀⠀⠀⢀⣄⡀⠀⢀⣶⡄⠀⢀⣤⡄⠀⣟⠀⡀⠀⠸⡇
⠀⠀⠀⠀⠀⣺⣿⠀⠀⠊⠉⠄⠀⠀⠀⠈⠄⠀⠈⠙⠂⠈⠙⠳⠄⣠⣾⣿⡂⠼⠟⠛⠀⠿⠿⣿⠀⣺⣿⡷⠀⠉⢰⡇⢰
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⢀⠀⠀⠀⣨⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⣤⠀⠀⠀⢐⡆⡀⠀⠀⡇⠀⢰⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠝⠀⠀⠀⠸⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⡇⠀⠀⠀⠀⡟⠀⠀⠀⡇⠀⢨⡇

⠀⠀⣠⠖⠒⠒⢦⣀⣀⠀⠀⠀⢀⣠⣀
⠀⢰⠁⠀⠀⡞⠁⠀⠈⠱⡄⡴⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⣇⠀⠀⠱⡀⠀⠀⢀⡿⡇⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠉⠲⡄
⠀⠀⠈⠲⣄⣠⠟⠢⣤⠞⢀⣧⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⡆⢸⡄
⠀⠀⠀⠀⠀⠻⡇⠘⡟⠀⡽⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡴⠉⠀⠀⠀⠀⠀⠉⠲⡄⠀⡇⠀⠀⠀⠀⠀⢠⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣼⣣⠞⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⣾⠁⠀⠀⣀⠔⢁⣠⠔⠀⣹⠀⠸⡄⠀⠀⠀⠀⠆⢀⡞
⠀⠀⠀⠀⠀⡔⠲⡿⠋⢠⠔⠋⠉⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⢴⣮⠭⣿⡖⣊⣉⡀⣈⡩⠤⠔⠊⠟⣆⠀⠘⢄⡀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⢇⢀⣽⠀⡏⣠⠴⠖⠒⠒⠒⠒⠦⡀⢷⠀⠀⠀⢀⠀⠀⠀⠀⢯⡇⠠⠔⠲⠄⠀⠘⠉⠉⢸⠃⠀⠀⠀⢹⣻
⠀⠀⠀⣠⠔⣿⣿⠀⠀⣷⣟⠒⠒⠒⠒⠒⠒⠒⣇⣾⠀⠀⠀⠻⣉⡗⠀⠀⠀⠙⢄⠀⠀⠢⠤⠔⠂⣠⠏⠀⠀⠀⠀⢀⠧⣀
⠀⠀⠀⠁⠚⢹⢻⠀⠀⣿⢉⡭⡛⠒⠒⠚⠻⠥⠈⣽⡄⠀⠀⠀⠈⠳⢄⠀⠀⠀⠈⢑⡄⢤⠄⠐⠞⢹⣦⣀⣀⡠⠤⠺⣯⡼⠃
⠀⠀⠀⠀⠀⠛⠈⢧⠠⡻⡄⠀⢀⣀⠁⠀⣠⠀⣰⠃⠙⡄⠀⣠⡤⢤⠀⠙⠲⠤⣤⠚⠙⠪⡖⠐⡖⠁⠀⠙⣄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣇⠈⠒⣤⣬⣭⠥⣴⣊⣁⣀⣤⡿⠔⠓⠤⠼⠃⠀⢀⠔⢧⠀⢀⠀⡇⠀⠱⣀⡤⠴⠉⣆⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢪⡀⠉⠉⡇⠈⠉⠀⠈⣧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡉⠉⢹⠧⠤⠔⢻⣀⡴⠚⠁⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢹⠇⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡲⠊⠀⡀⠀⠀⢻⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣴⠛⣆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⢧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⠖⠋⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡦⠇⠘⠦⡤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⢀⣀⣀⣀⣀⣤⣴⠾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣇⠀⠉⠉⠉⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⣵⡇⠀⠀⠀⠾⣩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢇⣤⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⢠⠟⠙⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⡀⢠⡆⠀⠀⠀⠈⣧⠄⠐⠸⠀⡤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⠀⡰⠉⠷⠀⠐⠑⠀⠃⠀⣤⡠⠞⡷⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠸⢤⡇⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠐⡁⠘⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠈⠁⡐⠂⡰⠁⠀⠀⠀⠤⠂⡳⠀⠇⠆⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣦⡱⡄⠲⠇⠘⠀⠀⠀⠀⠀⠀⢀⠀⠞⠀⠔⢁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠌⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠊⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠈⡤⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢥⡀⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠮⠴⠖⠖⢤⣼⢶⡿⣷⣾⣷⠋⢻⣿⣷⡖⠦⢤⡄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣤⣤⣴⠞⠋⠀⣸⠁⢀⣿⢻⣆⠀⠙⢯⣟⠉⣷⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⣁⣀⣠⣶⡇⠀⠸⣿⠄⣻⡆⠀⠈⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠈⣿⠷⠏⠛⠉⠘⠶⠶⠞

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⣠⡇⠀⢠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠋⠀⢀⣾⠟⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢀⣴⣿⡏⠀⠀⣠⣴⡏⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⢳⣿⢀⠠⠾⢻⣿⠀⠀⢠⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⣿⡿⣱⣿⡿⠃⠀⠀⣼⣿⣼⠠⠄⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣽⣿⣿⣿⣿⣆⣠⣾⣿⢿⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢟⣿⡿⣿⣿⣿⣿⣿⢣⣼⣿⡎⢷⣇⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⢏⣾⡟⣸⣿⣿⣿⣿⡇⡾⣿⣿⢻⡌⠻⣆⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢀⢠⠁⣿⠟⣿⡿⣰⣿⣿⣿⣿⣿⡘⣇⢸⣿⣿⣿⠀⠙⣷⣄⠠⡱⣄
⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⣾⣿⡇⣿⢸⣿⣿⣿⡿⠧⠀⣼⡈⣿⣿⡇⢢⠘⣿⣧⠙⣿⣦
⠀⠀⠀⠀⠀⠀⢸⡀⣼⢿⣿⣿⠀⣿⣼⠳⠏⢠⣷⢀⣼⣿⠃⣸⢹⡇⣸⡄⠸⣿⡇⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠘⣧⢹⡜⣿⣿⡄⢹⣿⠀⠀⢸⣾⡈⠻⣿⢀⡟⣹⠇⣿⣥⠀⣿⣷⠀⢻⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠹⣿⣿⣿⣦⡿⣷⣄⡈⠻⠏⠀⡹⣾⣱⠏⣼⣿⣧⠀⣿⣿⠀⢸⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⣻⣯⣛⣿⣿⡝⢷⣂⠠⣼⣷⣿⢏⠼⠁⢸⡇⢰⣿⡟⠀⣸⢄
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠀⠈⠋⣉⣿⣿⣿⣷⡙⠿⠿⠯⠁⠀⢀⠴⠋⣴⣿⠟⠁⣰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⣿⣿⣿⣿⣷⣦⣤⣤⣤⣷⣼⣿⣿⠗⢀⡴⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣹⣿⣿⣿⣿⣿⣿⣿⠿⢛⣡⠴⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣧⣴⣿⡭⠤⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠿⠟⢻⠟⢿⠿⢻⡿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢘⡇⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⢡⣾⣷⠋⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠘⢿⣦⣿⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡤⠘⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣤⣬⣽⣿⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠘⠳⠦⠀⣀⣨⣾⣿⣷⡶⠚⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⢀⣀⣤⣼⣿⣿⣯⣁⣠⣤⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣯⣿⣿⣿⠛⢉⡙⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⣀⠀⠀⠀⠻⠛⠛⠛⢿⣌⠙⠛⠙⠓⠋⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣷⣶⣿⣶⣦⣤⣤⣀⣿⣦⢸⣶⣾⣛⣀⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣸⡿⠛⠙⢻⠋⠹⣿⠟⠉⣉⣉⢠⣿⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠿⠿⠿⠛⠟⢢⣼⡷⠚⢋⣩⣤⣠⣴⣧⣀⣀⣤⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣀⣉⣁⣤⡾⠷⠶⠰⠶⢌⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡈⠉⣻⠛⠛⣟⣉⣉⣤⣀⣠⣤⣀⣀⢸⣿⣏⢁⣰⠂⠀⢰⣶⣀⣀⣀⢤⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠶⢾⢿⣿⣿⠿⠿⠿⠛⠻⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠰⠶⢶⣾⣤⣤⣶⣶⡦⣴⡶⡶⠾⠓⠈⠙⠛⠉⡙⢻⣿⠋⠉⠉⣁⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠰⣷⢀⣀⣀⣀⣽⣟⣿⣟⣽⣷⣿⣿⣧⣴⣶⣿⣷⣄⣀⣿⢸⣿⣷⣿⣼⣿⣷⣶⣾⣦⣴⣿⣾⣿⣿⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠟⠉⠁⣉⠉⠉⣉⠉⠙⠛⠛⠛⢿⣋⣹⣿⣿⣿⣟⣉⣉⣙⣿⣿⡟⢻⣿⠛⠟⣛⣉⣭⣄⣰⠶
⠀⠀⠀⠴⠀⠀⠀⡴⠆⠠⣦⡀⣀⠘⢋⡁⠈⠛⢻⣶⣶⠿⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣟⠛⠛⢛⠁
⠀⠀⠀⠀⢴⣶⣶⣦⡴⢷⣾⣿⣿⣿⣿⣿⡿⢷⣿⣿⣿⣶⡿⠶⢿⠿⢻⣿⡟⠛⢋⠉⢻⣌⣉⣉⣉⡙⠛⠛⠻⠿⠿⠛
⠀⣤⠄⣤⣤⣴⣆⣠⣤⣤⣉⣁⢹⣿⣥⣬⣷⣾⣿⣿⣿⣿⡷⠒⣠⡄⣿⣿⣿⠺⣿⡇⠀⣉⣉⡉⢉⣅⢙⡇⠀⣀
⠀⠀⠀⠀⣸⡏⠋⣻⣿⣿⣿⡿⣾⣿⣿⣿⣿⢿⣏⣽⣯⣼⣅⣾⡟⣾⡛⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠿⠿⠿⣿⡷⠒
⠀⠀⣠⡾⠛⠛⣛⣋⣿⣟⣿⣿⣿⣽⣷⣼⣷⣾⣿⣿⣿⣿⣿⡟⢻⠏⢿⣿⣿⣿⡽⢿⣾⣿⣿⣦⣼⣷⣦⣤⣴⣿⣷⣶⣶⡄⠀⠀⣀⣀
⠀⠀⠉⠀⠀⠈⠛⠻⡿⠟⠛⠿⢊⡛⠛⠋⢉⣭⣉⠉⠁⠀⠀⠀⠀⠀⣿⣿⡏⠈⢁⣦⣄⣠⣝⣟⡉⠛⠻⠿⣿⡿⠛⠛⠛⠛⠓⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢰⣾⣷⣶⣴⣿⣿⣽⣧⣄⠀⣀⠀⠀⢠⣿⣿⡷⠶⢿⣯⣉⡉⠛⣿⣿⣶⣶⡾⠋⠡⠄
⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⡀⠀⢈⣁⢀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⠙⠛⠛⠛⠋⢀⣀⢀⣀⠀⢠⣶⣶⡶⠦
⠀⡤⣤⣤⡀⣤⣴⣟⣶⣦⡘⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⠛⢻⣿⠿⣶⣶⠶⣶⣿⣶⣶⣶⣮⣿⣿⣿⣤⣼⣿⣥⣤⣄
⠀⠀⠀⠈⠀⠟⠙⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢻⣤⣤⣙⣧⣤⣿⣦⣼⣿⣶⢿⡿⠿⢿⣿⣿⠛⣉⠉⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⠛⢋⡛⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⣿⣏⢀⡀⢀⣤⣤⣴⣦⣤⣤⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠷⣾⣿⣾⣿⣻⣿⠿⠿⠛⠃⠐⠛⠛⣿⣿⡟⠉⠁⠀⠩⠤⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⢠
⣀⣀⠀⠶⠀⠀⣤⣤⡀⠀⢠⣴⣾⡿⣿⠏⣹⣥⣄⠀⣤⡀⢠⣤⡀⠺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠛⠛⠰⠆⠸⠿⠶⠶⣿⠷⣶⣿⣿⣷⣶⣾⣿⣿⣿⣿⣯⣉⢉⣙⣣⣴⣿⣿⣧⣤⣆⣶⣾⣇⣀⣄⢠⡴⠶⣦⣄⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠶⠞⠛⠋⡉⠩⡍⠁⡀⠀⠀⠈⠁⡀⠀⠀⣹⣿⣿⣿⠛⠻⠿⢿⣿⣿⢿⣿⣿⣿⡛⣛⢛⣿⣿⠟⠿⠿⠿⠆⠤⠄
⠀⠀⠀⠀⢦⣤⣄⣀⣤⣄⣀⣀⠊⡁⠛⠐⣶⣿⣤⡄⢀⣤⣤⠀⠀⣽⣿⣿⡏⠀⠀⠀⢀⣠⣄⡀⠀⣉⢙⠛⠟⠛⢻⡏⠸⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⠛⠿⣿⣷⢶⣄⣰⣦⣤⣀⣀⣀⣀⣄⠀⢸⣿⣿⣿⡆⠉⢁⣍⣡⣿⣿⣿⣯⣼⣧⣼⣷⣾⣷⣶⡿⠛⠁⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠛⠛⠋⠁⠈⠛⠿⠿⠟⠛⠙⠿⠿⠿⠿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠈⠉⠉⠉⠙⠛⠋⠉⠁⠿⠛⠋⠛⠃
⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠂⠒⠂⠀⠀⠀⠐⠛⠛⠓⠾⠶⠾⡶⠖
⠀⠀⠀⠀⠉⠁⠶⠀⠘⠛⠒⠒⠛⠿⢿⣾⡷⢶⣶⣶⣄⠀⣀⣀⣴⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠳⠾⠿⢿⣿⣯⣀⡀⠤⣾⣿⣿⣇⣀⣀⣀⠀⠀⠀⣀⣴⣶⣶⣆⢀⣀⣈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡾⠿⣿⣿⡿⢶⡾⠟⠋⠁⠀⠁⠀⣻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣾⣿⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣶⣄⣀⣀⣀⣀⣀⠀⠀⠀⢀⣴⣦⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣿⠿⠟⠃⠀⠀⠚⢻⡿⠟⣻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢋⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡀⠀⠀⠀⠀⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣀⢀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠔⠆
⢀⡀⠀⠀⢠⠆⠀⠀⠀⢀⠀⠤⠀⠖⠂⠀⠀⠈⠉⠁⠒⠒⠊⠋⠁⠀⠀⠁⢸⠠⠤⠐⠒⠈⠁⠀⠁⠈
⠆⠁⠔⠀⠘⠀⢀⠠⠀⠤⠤⠤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠴
⠀⠐⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⡀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⡀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⡔⡈⠰⠄⠀⠁⠌⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠤⠤⠤⠐⠒⢒⡔⠃⠀⠈⠐⢲⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢈⠀⠸⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢈⡀⠀⡆⠀⢀⣀⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡆⠉⡋⠉⠀⠀⠈⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⣃⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠹⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⢀⠒⠈⠀⢘⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⢦⣿⣿⡯⢀⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⠆
⠀⠀⠀⠀⠈⡳⢮⣿⣿⣿⣯⠖⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠶
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡷⠞⠁⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠠⢽⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠠⣔⣻⣿⣿⣿⣿⠿⠖⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢰⡾⣿⣿⣿⣿⣖
⠀⠀⠀⠀⠠⣬⣽⣿⣿⣿⣿⣖⡂⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣭⣤
⠀⠀⠀⠀⠀⠛⠛⠛⢻⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢸⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣇
⠀⠀⠀⠀⠀⠀⠰⣾⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣿⣿⣬⡀
⠀⠀⠀⠀⠀⠀⠐⢺⣿⣯⠍⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠆⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⣿⣯⣥⡀
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡤⠤⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣯⣤⡄
⠀⠀⠀⠀⠀⠰⠶⣛⣿⢷⣄⣀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⢈⣩⣿⣿⣿⣿⣿⣭⡄
⠀⠀⠀⠀⠐⠲⠞⠛⣿⢷⣬⣅⡀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏⠀⠀⠀⠉⠉⠿⠛⢿⡏⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣻⣿⣛⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣰⡆⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣤⣿⣿⣤⣶⣶⣶⣯⣴⣷⣭⣿⡆⠀⠛⢲⡀⢛⣒⣶
⠀⠀⢀⢸⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⡏⢿⣿⣿⠀⢀⢀⡐⢾⢈⣦⣠⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣰⣶⠟⣤⢿⡏⢈⡷
⠀⢀⣾⣿⣿⣧⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀⠀⠀⠋⠀⢀⡌⣦⣠⢷⣏⣿⣯⣯⣧⡐⠀⠀⠉⢈⣍⣉⣩⣍⣭⣥⣤⡄⠀⣜⣿⣶⣼⠟⢹⣏⣸⡅
⠀⣼⣿⠏⠀⢿⣿⣇⠀⠀⠸⣿⣿⢿⢿⣿⣿⠃⠀⠀⢀⣜⣾⣷⣿⣿⣿⣛⣿⣿⣼⣿⣿⣷⣦⡰⣼⣿⣍⠓⢺⣟⡋⠉⠉⠀⠘⠿⠞⢿⣶⣿⠿⠛⠁
⠀⠻⢧⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⣁⣸⣿⣿⡟⠛⠈⠑⠀⠀⠀⠀⡀⠀⠘⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⡀⣴⢠⡀⠀⠀⠀⠀⠀⠀⠆⡐⠂⡆⠐⠀⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⣿⠇⢀⠀⠀⠀⠀⣠⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⣸⢼⣠⢧⣟⣳⢼⡰⣅⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠉⠁⡄⣑⣘⣄⠀⣀⣙⣦⡴⣃⠀⠀⠀⢠⡀
⠀⠀⠀⢸⡆⠀⠀⣯⣻⣾⣾⣿⣿⣿⣾⣷⣿⣷⣿⡄⠀⠀⠀⠀⠀⢀⣼⣧⣶⡤⣄⠀⠀⠀⠀⢀⠙⠐⠀⠑⠿⠟⠀⢠⣞⣿⡻⣞⡽⠁⠀⢠⣤⣽⠆
⠀⣰⢠⡿⢁⡀⠀⠈⠛⠛⢉⠉⠉⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⢠⣼⣽⣿⣿⣿⣿⣿⣤⠀⠀⣀⡴⠛⢦⡞⠀⠀⠀⠀⠀⣹⣟⣿⣏⠀⠀⢰⣛⣦⣹⣦
⠀⢿⡈⢷⣼⣄⠀⠀⠀⣠⢿⣆⣤⠀⠀⠀⠀⣦⣷⡄⢣⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣞⠀⡄⡟⢷⡜⣮⣷⣴⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⢈⣽⣿⠁
⠀⢸⡿⢸⣿⣿⠇⠀⣰⣯⢾⣿⣏⣦⠀⠀⠲⣬⡟⣷⣦⡙⣷⠀⠁⢸⣿⣿⣿⣿⡟⠃⠸⣧⣿⣿⣵⣿⣟⣿⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢰⣿⡟⠋
⠀⣾⣷⣾⣿⣿⠀⠀⣿⡇⠀⠋⢹⡿⠀⠈⣧⣿⣷⣿⣼⣷⣡⣧⠀⠻⣿⡟⢽⣿⡅⠀⠀⣽⣯⣿⣿⣿⣿⣻⡇⠀⠀⣀⣤⣴⣆⡀⠀⠀⠀⠉⢻⣿⣦
⠀⠈⠛⠛⠛⠋⠀⠀⠈⠛⠀⠐⠋⠁⠀⠀⠙⠛⠉⠋⠋⠙⠛⠋⠀⠀⠘⠀⠘⠋⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠃⠀⠾⠿⠿⠿⠿⠟⠛⠗⠀⠚⠛⠛⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣟⣉⣉⣛⣉⣹⣹⣏⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢰⣷⠀⠀⣠
⠀⠀⠀⠀⠀⠰⣶⣄⣸⣿⢀⣤⡔⠀⠀⠀⠀⠀⠀⢠⠀⢸⣿⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⢻⣧⢸⣿⢀⣾⠏
⠀⠀⠀⠀⣠⣤⣽⣿⣿⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀⢸⣷⣸⣿⣧⣾⠇⠀⠀⠀⠀⠀⠙⢿⣦⣽⣏⣏⣾⣷⣾⠟⠁
⠀⠀⠀⠀⠈⠙⣻⣿⣿⢿⣿⣿⠟⠛⠁⠀⠀⠀⠘⣶⣿⣿⣿⣿⣿⠞⠁⠀⠀⠀⠀⠀⢤⡾⠿⣻⢿⣿⠷⠶⠄
⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠰⣄⡀⠀⢸⣿⠀⠀⣠⡞⠀⠀⠀⠀⡀⠀⠀⣾⣿⣧⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⡄⣾⣿⠀⣸⡄
⠀⠀⠀⠀⠀⠹⣿⣦⠸⣿⣠⣾⠟⠀⠀⠀⠀⠀⣿⡄⠀⣿⣿⣿⢀⣾⡇⠀⠀⠀⠀⢠⡀⢿⣧⣿⣿⢰⣿⠇⣠
⠀⠀⠀⠤⣤⣤⣬⣝⣷⣿⣿⣿⣶⠿⠟⠁⠀⠀⠙⣿⣆⢹⣿⢇⣾⡿⠀⠀⠀⠀⠀⠈⢿⣮⣿⣽⡏⣿⣿⡾⠃
⠀⠀⠀⠀⠀⠀⣩⡽⠛⠉⠛⠶⣦⡄⠀⠀⠀⠠⢤⣬⣿⣦⣯⣾⣯⣤⠶⠀⠀⠀⠀⠀⠑⠿⢿⠿⢿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⠒⠒⠊⠁⠀⠀⠀⠀⠉⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠄⡀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡠⠂⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠖⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠐⠀⠠⠁⠀⠀⠀⢠⠦⡀⠀⠐⠠⠀⡀⠀⠈⠉⠁⠀⠀⡩⠀⠀⠀⠀⠀⠰⠢⠔⠘⠐⢃⡮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠈⠑⠂⢄⣄⣀⣀⢀⣀⣠⡔⢺⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣠⣶⠤⢤⢀⠀⣀⣠⡛⢡⡌⢊⡷⠊⠀⣋⠏⠀⠀⠀⠀⠀⢀⠎⠀⠈⠁⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢒⢢⠤⡴⣽⠀⠶⠀⡩⠗⢀⠉⠶⡤⠤⣢⠃⠀⠀⡇⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠆⠀⠈⢓⡒⠚⠋⠀⠠⠴⠀⠀⠀⠮⠹⢀⡜⠀⠀⣀⠤⠒⠁⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡀⠧⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠪⠗⠲⡍⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣠⡜⠢⠤⣄⣀⣀⣀⡀⠤⠴⠊⢡⠃⠀⢀⡁⠘⡀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⠸⢀⡀⠀⠀⠑⢄⠈⢢⠄⠲⠀⠃⡤⠔⠉⢡⠀⢃⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠆⠀⠈⡗⠂⠐⠁⠁⠺⡀⠀⡏⢠⠂⠀⠀⠀⡀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠸⠀⠀⠀⠀⠀⠀⠙⠢⡝⠞⡐⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠄⠀⡆⠀⠀⠀⠀⠀⠈⠄⡇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡰⡇⠀⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡌⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠰⠇⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⣮⢀⠀⠠⠤⠤⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠆⠰⡘⠾⠁⠀⠀⠀⠉⠀⣀⣀⡀⠷⠠⠤⠤⠀⠒⠠⠜⠒⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠄⠀⣸⠀⠀⠈⢻⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⢢⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠐⠞⣰⢠⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠢⢄⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢱⡋⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⣠⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡎⠛⠛⠛⠉⠁⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠛⠉⠀⣀⣤⣀⣀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠻⠿⠃⠀⠀⠀⣠⡤⢭⠏⠁⣴⡟⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠓⠀⠀⠀⠀⠀⠀⠀⡠⢧⡤⠤⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠛⠸⣇⠀⠀⠀⠀⠰⠿⣄⠠⠤⢤⣶⡟⠀⠀⠀⠀⠀⠀⠀⢀⡆⠰⡆⣴⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡎⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⢿⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⣿⣿⣿⣿⢦⣀⠀⠀⠀⠀⢠⣄⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣩⣿⣾⣿⣿⣿⣷⣯⣝⠲⢤⣀⣀⣹⡷⠚⣯⡀⠀⠀⠀⠀⠀⠀⢀⠁⠊⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠧⣙⢻⣿⣿⣿⣦⣀⣩⣭⣤⣾⣿⣿⣶⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣫⣴⣶⣶⣶⣤⣍⡛⠿⣿⣿⣿⣿⡟⠁⠈⢻⣿⣿⣶⡀⠀⠀⠀⢳⡄⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠙⣿⣿⣿⣦⡀⠀⢻⣿⣿⣿⣦⠀⠀⠚⠀⡀⠀⠀⡠⠋
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠓⠂⠀⠹⣿⣿⣿⣿⣦⡈⢿⣿⣿⣿⣷⠀⠀⣦⣌⠀⠰⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠦⠀⠘⣿⣿⣿⣿⣿⣾⣿⣿⡿⠃⠀⣮⣿⣿⣷⣄⠐
⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠆⠀⠀⠈⢿⣿⣿⣟⠻⠟⠙⠃⠀⢀⣽⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣿⣿⡿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣁⠀⠀⠀⠀⠹⣿⣿⣿⣦⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡘⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠓⡀⠀⠀⠀⠹⣿⣿⡿⠁⢠⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠙⢿⣿⣿⣿⣿⣿⣿⣟⣻⣯⠥⠀⠀⠀⠀⢹⣿⠇⠀⣤⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢿⡇⣿⣿⣿⡉⢿⣿⣷⣤⣛⣿⣿⣿⣿⣭⣭⣥⣒⣢⠭⠂⠀⠀⣰⣿⡄⠠⣽⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠁⠙⣿⣿⡁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡤⠄⠀⢠⠏⣿⣷⠀⡙⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠻⣿⣿⣷⣌⣙⢻⣿⣿⣿⣿⣷⣶⣂⡘⠀⣿⣿⡆⠹⣮⡻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣍⡛⠿⣿⣿⣿⣿⣿⣉⡀⢿⠹⣿⢷⣌⢻⣮⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡍⠻⢿⣿⣿⣿⣷⣦⣶⣤⡈⢿⣦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠏

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠁⡈⣉⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣤⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄
⠀⠀⢰⣷⣿⠇⠀⢻⣷⡆⠀⠀⢰⣷⣿⠿⣿⣿⣆⡄⠀⠀⠀⠀⢻⣿⣿⣿⣶⣇⠀⠀⠀⠀⢸⣿⣿⠻⣿⣶⠀⠀⠀⠀⡄⣿⣿⠏⢿⣿⡆
⠀⠀⠸⣿⠁⣰⣦⠈⣿⡇⠀⠀⢸⣿⠿⠀⠘⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⣶⡿⠁⡀⠛⣿⠀⠀⠀⠀⣿⡿⠁⠀⢸⢿⡿
⠀⠀⠀⠙⠦⡙⢛⠴⠋⠀⠀⠀⠀⠻⠄⠀⠀⠠⠟⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟⠁⠀⠀⠀⠀⠹⠄⢾⡿⠀⠋⠀⠀⠀⠀⠙⠧⠀⠀⠀⠜⠁

⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⠀⠀⠀⣆⢸⣿⡄⡄⠀⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀
⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀⠀⠀⠀⢠⡄⣾⣿⢿⣿⣀⡄⠀⠀⠀⠀⣶⣻⣿⣷⢀⡄
⠀⠀⠀⢸⣿⣿⣿⣇⣷⠀⠀⠀⢈⣿⣿⠏⠻⣿⣿⣶⠀⠀⠀⣼⣿⣿⠋⢻⣿⣧⠀⠀⠀⣿⣿⣿⠟⠈⣿⣿⣿⠀⠀⢰⣦⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣷⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⡇⢀⣦⠀⣿⠇⠀⠀⠀⢻⣿⠁⠀⣼⢿⡟⠀⠀⠀⠸⣿⠉⢀⣆⠉⣿⠏⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠈⠁⠘⠟⠁⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠛⠟⠀⠉⠀⠀⠀⠀⠈⠙⠚⠛⠛⠋

⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⢀⢀⣼⣿⣷⡄⠀⠀⠀⠀⡀⠈⣿⣧⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⠀⡀
⠀⠀⢀⣿⣿⣿⢿⣿⣿⡄⠀⠀⢀⣿⣄⣽⣿⡟⢀⡀⠀⠀⠀⡀⢻⣿⠛⢿⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⣿⣿⣿⣾⣿
⠀⠀⠸⣿⡟⠉⠀⠹⣿⡇⠀⠀⢸⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⣿⣾⠋⢠⡀⢻⣿⠀⠀⠀⢠⣸⣿⡏⠿⣷⣾⡆⠀⠀⢸⣿⣿⣿⠛⢿⣿⣿
⠀⠀⠀⠻⣧⡀⠀⣰⠟⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⢿⣄⣿⣧⡼⠃⠀⠀⠀⠀⠻⡏⠁⠐⢻⡟⠀⠀⠀⠈⢿⡿⠷⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⣀⡠⠴⠒⠉⠉⢢
⡴⠋⠁⠀⠀⠀⠀⣀⣴⠗⢲⡀
⢧⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⢣
⠈⢇⣠⡾⠋⠁⠀⠀⠀⠀⠀⠈⢧
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⣿⠒⠒⠒⠒⢲⡄⠀⢀⣀⠀⠠⢶⡒⢦⡙⠒⢄⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⡧⣄⠉⢫⠓⡄⠀⠹⡄⠈⣆⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢈⡟⠋⣠⣞⡴⠃⠀⣰⠃⣀⠏⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠤⠴⠖⠚⠃⠀⠀⠁⠀⠘⠻⠥⠚⣥⡴⠊⢀⠔⠊
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠈⠉⠉⠉⠀⠈⠴⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠠⠀⣤⣀⠐⠆⢄⠂⠀⠀⠀⢀⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠈⠉⠁⠀⠑⡐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠂⠀⠈⢦⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢰⣧⠀⠀⠀⢰⣦⡄⠀⠀⠀⠑⡦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗⠀⠀⠀⡀⠀⠀⢀⠀⢨⠀⠁⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣦⡀⠀⠀⠉⠁⢠⡄⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠙⢥⠀⠺⣶⡶⠟⠁⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⣀⠈⠉⠁⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠘⠡⠀⠤⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⣀⠤⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠒⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠐⠄⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⡀
⠀⠀⠀⢤⡀⠀⢀⠠⠘⠈⠀⠀⠐⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⠀⠀⠀⠃
⠀⠂⠐⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠂
⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠤⠄⠤⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠲⡄⠀⠀⢨⠁⠀⡅⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠰⠶⠇⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠇⠀⠀⠀⡇⠘⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⢀⣠⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⠒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⡅⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⢲⠂⠋⠀⠀⠈⠳⠒⠲⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠘⠈⠁⡇⠀⠀⠀⠀⠉⠉⢋⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠎⠀⠀⢀⠀⠀⠀⣰⠀⠀⠀⡠⠀⠀⠀⠀⠈⢑⡦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣀⣀⣀⡀⢀⡀⣀⣠⠇⠀⢰⡋⠀⠀⠀⠀⠉⠀⣀⡠⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣴⣾⣿⣯⣶⣶⣶⣶⣷⣷⣷⣶⣿⣿⣶⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠁⠉⢉⡉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣦⡀⠀⠀⠀⣠⣶⠿⠟⠋⠉⠀⠀⠀⢀⣀⣠⣤⣤⣴⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠻⢿⣿⣶⣴⣿⣭⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣸⡿⢻⣿⣿⣯⡉⣩⣽⣿⠿⢛⣉⣭⣿⣿⠟⠛⣛⣉⣉⣉⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣿⡇⢸⡏⠛⢿⣿⣿⣿⣿⠿⣛⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣛⠿⠀⠿⠃⢠⣾⣿⣿⣿⣧⣾⠿⠟⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣶⣦⡔⢛⣿⣇⡰⢿⣿⣎⠋⣋⡛⠙⢿⣿⣦⣴⣶⣿⣿⣿⣿⣿⣿⣷⠶⠶⠈⠉⠙⠛⠻⠷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣥⣼⣟⠋⠾⢿⣿⣿⠿⣠⣵⣶⣾⣽⠻⡄⣾⣿⣿⣿⣯⣿⣿⣿⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣰⣿⠿⣟⣛⣟⣣⣶⣶⣶⣦⣼⡛⢛⣛⣻⣿⡷⠐⣋⡛⠿⣿⣿⣦⣤⣽⣿⣿⣿⠿⢿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠶⠷⠿⣿⣋⣹⣛⡻⠛⣻⣿⣿⣥⣀⣙⡻⢯⣵⣿⣿⣿⣷⡸⡏⢻⣷⣄⣉⡛⠻⣿⣶⣮⣍⡛⠻⠿⣿⣿⣿⡳⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣱⣿⣷⣶⣭⣟⣫⣍⣾⣿⡹⣿⣿⣾⣿⣿⣿⣎⢻⣿⣯⡛⠿⠃⠿⣼⡟⢿⣿⣿⣿⣿⣛⠛⠿⣿⣶⣤⣄⡀⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣿⣿⣿⣿⠟⣫⣞⣯⣝⣿⣿⢹⣿⡛⢻⣿⣿⣽⣿⣿⣭⡬⣁⣶⡜⣧⠀⣹⣷⣿⣛⡻⢷⣦⣄⠉⠻⢿⣿⣗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⡝⠛⣩⣾⣥⣿⣿⣿⣿⣿⢿⠜⣿⣿⣦⣍⡛⠛⠛⠉⢙⠾⢿⣿⢃⣿⡄⣿⣿⣿⣿⣿⠿⣿⣿⢿⣶⣤⡈⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⢁⣠⣾⡿⢫⣾⣿⣿⣭⣶⣶⣿⣷⣹⣿⣯⣭⣶⣾⣿⣿⡆⣿⣶⣦⢸⣿⣷⣿⣿⣿⣷⡙⢷⣌⠻⣷⣌⠙⠏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿⣿⣿⡾⢸⣿⣿⣫⣶⣵⡈⢹⡛⠿⣿⣿⣿⡇⣼⡇⢿⠀⢙⣛⠛⣻⡙⣿⣿⣌⠻⣷⡌⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⠛⠛⠛⢋⣡⣾⠟⢿⣵⣿⣿⣿⣿⣦⡙⣷⣮⣝⡛⠁⣛⠀⠈⠀⢸⣛⡋⢻⣏⢙⣃⠙⣃⠉⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣴⣻⡿⢟⠏⠀⢻⣿⣿⣿⠿⢿⠿⣓⣌⢻⣿⣷⣾⠃⠀⠀⠀⠀⠻⠃⠈⢻⡎⠋⠀⠙⣧⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⣽⣭⣾⣫⣾⣿⣎⣿⢧⡐⣿⣹⣧⡙⢿⣷⣮⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠛⣛⡟⣻⡋⣿⡷⣨⣧⠻⣿⣧⠙⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢟⣽⣟⣷⣹⣾⣿⣿⣷⣤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣟⣽⠞⣿⣿⣷⡈⠩⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡝⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⠀⠈⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⢀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠰⠳⣄⡎⠀⠀⠁⠠⠀⡜⢆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠈⠆⠀⠀⢀⠀⠰⠁⢸⠈⠰⠃⢰⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⡏⠲⢦⠀⠀⠀⠀⠀⠈⢄⠁⠀⢸⠀⠀⠀⡌⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⠀⡘⠘⡐⢚⡇⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⡀⠀⠳⠉⠀⠌⡰⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⣄⡀⠀⠀⠀⠀⠂⠄⠐⠂⠀⠀⠁⠄⠂⠀⠀⠤⠊⠉⠈
⠀⠀⠀⠀⠀⣼⠹⣭⢍⣠⢴⠚⢠⣀⣤⡤⡖⠢⣤⢼⣐⠒⣦⠀⢲⢢⡀⠘⠛⣻⣻⡄⢠
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠻⠼⠛⠛⠊⠳⣾⡴⠃⠰⣌⣠⡼⠷⣤⣸⡖⠲⠮⠯⠟⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢀⠄⢸⡀⡀⢀⢀⠄⡀⠀⢀⡏⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⣀⢄⢠⢰⣉⠀⡇⢁⢘⠀⣙⢈⣢⢸⠁⢸⢸⢸⠒⠁⠀⢸⠃⠀⡇⡈⢁⢀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⢸⠀⠘⠌⠠⠀⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠊⠈⠤⠌⠘⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⡤⠤⡤⠜⠙⠉⠓⢲⣀⠀⠀⠀⠀⠰⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⡀⢀⠔⠃⠀⠀⠀⠀⠀⠀⡤⣀⡀⠀⠀⠋⠙⠊⠳⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣃⠔⠋⠁⠀⠀⠀⠀⢨⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠠⡈⢩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠠⢌⣒⡲⠄⢺⠁⠀⠙⠀⠀⠀⣠⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣄⣀⠦⠬⠭⠹⣇⠀⠀⠀⢀⡠⠟⠁⠘⠤⡄⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⣸⢸⠀⡝⣿⢿⠀⠀⠀⠸⢤⣀⡶⠞⠀⠀⠀⠀⠀⠈⠉⠓⠋⠒⠩⡃⠀⠀⠀⢦⣀⠀⠀⢀⡹
⠀⠀⠀⠀⠀⠀⠈⡄⠀⢀⡏⡼⢠⠃⠉⠀⠀⠀⠀⠀⢸⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢅⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢰⠃⡾⠀⠀⠀⠀⠀⠀⠤⡄⡄⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⡆⠀⠀⠀⠀⠀⠀⢤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⠜⠀⠀⢴⠆⠀⠀⠀⠀⢁⠡⡀⠀⠀⠀⠠⣞⡀⠀⠀⠀⠀⣤⠀⠀⠈⢆⣀⠀⡀⢀⡖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣠⢷⢤⡀⠀⠀⠠⣀⠄⠀⠀⠀⠀⠀⠀⢀⠴⠩⢋⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢷⣦⠤⠤⠤⢤⢴⣖⠉⠁⠴⡄⠸⣗⡲⠤⠄⢤⡤⠤⠤⠤⢶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠡⠀⢻⡇⠀⠀⡾⠞⠉⠒⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠧⠴⠟⠁⠀⠀⠟⠃⠰⢷⠄⢀⡀⠀⢤⠄⢢⢄⡘⠚⠷⡀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠦⠀⣀⡀⠈⠙⠀⢸⠀⠀⠉⠉⠂⠼⠟⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠐⣠⠄⠀⠉⠀⡒⠦⢼⣀⢀⠀⡀⢀⠀⡀⠠⣐⠢⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠖⠩⠧⠤⠾⠦⡤⠴⠾⠳⠈⠀⠑⠚⠂⠈⠁⠈⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⢠⠀⠀⠀⢨⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⠀⠈⡀⠀⠀⠈⢂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡄⠌⠸⡄⡤⠂⠀⠀⠐⠤⢠⠃⠈⠢⡄⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⢄⠀⢠⣀⠧⡀⠀⠀⢠⠲⠴⠀⠀⡠⠆⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⢿⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠙⢦⣌⢷⣄⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠙⣆⠙⠷⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢛⡓⠦⡀⠈⢷⡀⠀⠀⠀⣿⠀⠀⠘⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⡄⠀⠻⡄⠀⢰⡇⠀⠀⠀⠀⠀⠀⣰⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡆⠀⣠⠟⠀⠀⠀⠹⣄⡀⢻⠀⠸⣇⠀⠀⠀⠀⠀⢰⡇⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣠⠟⢰⡏⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠘⢷⣄⠀⠀⠀⠀⠻⣄⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⡉⠀⠀⠻⢦⣄⣀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠳⢦⣄⠀⠀⠈⠳⡄⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡀⠀⠀⠀⠈⠉⢻⠓⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠃⠀⠀⠀⠀⢠⣸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢠⡞⠀⠀⠀⢀⣤⠟⣿⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠀⠀⢹⡆⢀⡤⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢁⡖⠉⠀⣀⡴⠞⠋⠀⣰⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠘⡇⢸⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠘⢧⣠⠞⠁⠀⠀⠀⠘⠁⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢰⠇⢸⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠁⠀⠀⠀⠀⠀⢠⢀⠞⠁⠀⣰⠋⣠⡾⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠃⢀⣠⠄⣀⣴⠆⢀⠀⠀⠀⠞⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠰⣶⣤⣛⠀⠈⢁⣾⣿⣷⣿⣿⠃⠀⠀⣀⠀⠖⢀⣀⡀⠀⠀⠀⠀⠀⣰⣯⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣍⣻⣦⣄⡀⠀⣀⠐⣀⣈⠛⠻⣟⣻⣿⣿⡿⠟⣋⠀⠀⣠⣤⣤⣤⡶⠿⠛⠁⠀⠀⠀⣀⡼⠯⠤⠤⠾
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠴⠶⠛⠻⢶⣤⣄⣈⣁⣰⣿⡿⣯⣥⣤⣀⡛⣿⣿⣶⣬⣍⠀⠻⠷⠶⢶⣆⣤⣴⣾⣿⣶⣶⣶⠤⠴⠶⠖⣶
⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣤⡤⠤⠶⠶⠚⠋⠉⠉⠉⠉⠁⣀⡤⣿⣿⣿⣿⣿⣿⣿⡿⠿⢶⠲⠶⣿⣿⣭⢤⣭⣍⣛⡛⠛⠶⠦⢤⣤⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠋⢑⣻⡿⠟⠋⢁⣀⡈⠉⠉⠉⠋⠉⠛⠒⠾⠭⣅⣀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⣯⣉⣀⠤⠖⠚⠉⠉⠀⠠⠖⠛⢉⣀⡙⠚⠙⠛⠶⠶⢦⣄⣠⣤⡴⠶⠯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠡⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠞⠀⢠⠀⠐⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⡡⠀⠐⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣀⠔
⠀⠀⠀⢰⡁⠀⣠⠶⠴⠁⠀⠀⢀⠀⠀⠀⡀⠃
⠀⠀⢀⡠⠁⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠠
⠀⠀⠫⠃⠀⠀⠀⠀⠉⠂⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⢀⡔⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠀⠀⠀⠂⠄⠀⠀⠐⠢⣙⢆
⠀⠀⠀⠀⠀⠠⣀⣀⠔⡀⠤⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠂⢀⠒⠚⠿⠇⣦⠀⢀⡀⠻⠄⡉⠳⢤⠆⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠒⠀⠀⠀⠀⢂⠀⣀⣴⠈⣼⣍⢀⠀⠀⠀⠀⠐⠂⢁⡐⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠰⠤⠀⠤⣄⠀⢀⠀⠀⢀⠀⠀⠆⠀⠀⡙⠀⠉⣻⡄⠀⢀⣤⣤⠀⠄⠈⠀⠈⠦⣆⠀⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰⠀⢰⠀⠌⡆⠀⠀⠀⠘⠋⠀⠀⢸⣷⣤⣯⡶⠀⠀⠀⠲⡌⣤⡄⣧⠀⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠂⠀⠉⠀⠀⠀⠈⠂⢠⡄⣠⠞⠃⠘⠳⣄⢀⠀⠀⠀⢸⠁⢯⣌⠉⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠔⠁⠀⢐⠈⠁⠉⠀⠀⠀⠀⠀⣀⢀⡤⠈⠙⠓⠀⢼⡆⣀⡾⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⡀⠀⠀⠀⠑⠠⠀⣀⣠⣤⡶⠏⠈⠉⢧⠀⠀⠀⠀⠀⡀⠀⢠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠀⠀⠀⠀⠀⠀⠁⠈⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠈⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⠤⠀⠂⠈⠀⠰⠴⡶⠀⠀⡀⠀⠚⠿⡀⠀⠀⠀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⡰⠁⢠⠐⢢⣿⡀⠀⠀⠀⣨⢿⣦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠀⠀⠀⠐⠛⣇⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢠⡿⠛⠁⢀⣶⠿⠛⠉⢁⣴⠿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⢀⠶⢀⣽⣷⣶⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⢻⠏⣿⣷⡦⢶⠅⠁⠀⠀⠀⠀⠀⢢⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢾⣄⣈⣗⡈⠄⠀⠰⡅⠀⠀⠀⠀⠀⡠⢋⠌⠠⡜⠋⠕⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠨⢙⡟⢣⠀⠀⠀⢰⠀⠀⠀⣀⠞⣁⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠠⣄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣸⠧⣀⣴⣄⠀⠈⡆⠀⠘⠁⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⠂⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡌⡇⠀⠸⡀⠀⢱⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠏⠀⢀⡀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠟⠟⠃⠀⠀⠀⠀⠐⠈⠀⠀⠀⠐⠚⠤⢠⣭⣥⣤⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠫⣠⠔⠁⠻⠿⠟⠁
⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⠀⢀⠀⢀⢀⠀⢀⠀⡀
⣿⠿⠿⠿⠿⢟⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣻⣟⣿⣿⣟⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡇⢠⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣜⣧⢜⡠⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣧⣹⡷⢪⠖⠚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠦⣽⡷⢠⢞⡡⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡐⢿⠶⣤⡀⠀⠀⠀⠀⠀⢾⣍⡛⢾⣿⠀⣫⠤⢾⠀⠀⠀⠀⠀⠀⣠⣴⣾⣩⠞⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡽⣄⠀⢆⢫⢷⣄⠀⠀⠀⣻⡷⣭⣻⣿⢈⡵⠒⣻⠀⠀⠀⢀⣴⣿⡟⣧⣿⠋⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢷⡈⠀⡎⡼⢳⡄⠀⢸⣟⠶⣽⣿⠀⢞⣉⣼⠀⠀⣴⣿⡿⣇⣷⡿⢣⢼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⣦⡈⢱⢣⢛⣆⢸⣯⣙⣾⣿⠀⣫⠤⢾⢀⣾⣿⣹⣿⣿⠟⡠⣭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠈⠎⡼⢻⣷⣭⣛⣿⠘⠱⠒⣿⣿⢿⣻⣿⡿⣁⢸⡽⠋
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣭⣽⣷⣄⢡⢫⢿⡶⢭⣿⠀⡘⣻⣿⣸⣮⡿⢋⡐⣬⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠙⢷⣬⣛⠭⠉⣙⠉⠛⠓⡶⢦⣤⣙⣯⡽⢿⣦⡈⠘⢿⡳⣿⢈⣹⢿⣿⡿⢋⣐⣦⣟⣡⣤⡶⡶⡟⡿⣿⣹⣻⠿⢿⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣶⣤⣌⣀⡑⠀⠂⠎⠿⠿⢿⣿⣿⢦⡀⠙⣿⠈⠁⠘⠥⣼⢖⣟⣟⣿⣿⣯⡴⠾⠞⠛⠋⣁⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣯⣟⣿⣻⣟⢿⡷⣶⡶⣶⣦⣤⡭⢉⠡⣼⡎⠀⠐⠛⢛⠛⠉⡉⡉⢀⠠⢠⣠⣐⣌⡬⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢛⡿⢿⠿⠛⣁⣴⣿⣇⠘⢀⣦⡙⠻⣿⣿⣷⣿⡞⠚⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⣈⡤⡶⣿⣯⡿⠁⣿⠀⢸⠉⠳⣀⠄⡌⠙⠓⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡵⠟⠛⠛⠛⠋⠁⠀⠀⢸⡇⣾⠀⠀⠈⠙⠒⠒⠓⠲⢌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⣤⣠⣀⢀⣀⡀⠀⢀⡀⠀⣀⣠⡀⢠⣶⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢰⣿⣿⠇⢈⡟⣻⡀⢸⡏⠀⣿⠙⡃⠀⣿⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠛⠿⠀⢸⣧⡾⠀⢸⣧⠀⠹⠾⠇⠀⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⣠⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠉⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠲⠂⠈⠉⠉⠉⠉⠉⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡁⠀⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠸⠇⢀⠀⢀⡠⠄⢲⡾⠉⠉⠉⠉⠉⠉⠉⠀⠒⠒⠂⠠⠤⢈⣳⠀⠀⠀⠀⢄⠀⠀⠃
⠀⠀⠀⠀⠆⠀⣾⠞⠁⠀⠀⢈⡴⢂⣈⠁⠢⡀⠀⠀⠀⠀⡠⢊⣡⡌⠑⢤⡈⠑⠤⣀⠀⠀⠀⢸
⠀⢀⡤⠞⠂⢴⡇⠀⠀⠀⠰⠋⣰⣿⣯⣴⣦⣸⡆⠀⠀⢠⣧⠼⠿⠷⠷⠤⣵⠀⠀⠘⡷⠀⠀⢸
⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠙⡗⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⠸
⠀⠀⠀⢇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠀⠀⠀⠀⢀⡏⠀⠉⢿
⠀⠀⠀⠘⢧⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠘⣏⠃⠠⠴⠦⠖⠘⢋⡼⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠈⠳⢤⣀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣤⣤⠴⠋⠁⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣐⠂⠲⡄⠀⢀⠔⠁⣠⠞⣠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠳⢦⣀⡀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢈⣤⡁⠀⠘⠣⠚⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⡶⠶⠶⣶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠓⠀⠀⠰⣉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⠇⠀⠀⢷⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠈⠯⣀⠀⠀⠀⢀⣨⠋⠈⠁⠀⠙⠛⠒⢶⡆⠠⠤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢤⣤⡤⣤⠞⠓⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠤⠤⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣸⡧⣤⣤⠤⠤⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⠘⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠘⢄⢸⣧⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⢶⡿
⠀⠀⠀⠀⣌⠁⠀⠀⠀⠀⠈⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⢃⠀⠀⠀⠀⠀⢀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢤⣀⡘⠀⣴⠀⠘⣧⣈⡄⠀⠀⠀⢀⡏⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠉⠛⠦⠻⡤⠚⠀⠈⠀⠀⠀⠀⣘⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠶⠒⠀⠀⠀⡟⠀⠀⠀⢸⡄⠀⠀⠠⠴⠶⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣀⣀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣰⠇⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣇
⠀⢀⠴⠚⠓⠠⣄⠀⠀⠀⠀⠀⠀⠀⡌⠉⢻⡄⠀⠀⠀⠀⠀⢸⠇⠀⣠⣤⠤⠴⠦⠄⢈⣦
⡰⠃⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠙⢒⠦⣷⠀⠀⠀⠀⠀⢸⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⣧⣀⣀⣀⣀⣀⣀⣀⣘⣁⢀⠀⠀⠀⢘⠋⠀⣼⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣽⣿⣷⣶⣶⣶⣶⣶⣾⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⢩⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⣊⣹⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⢆⢹⢨⡶⠄⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⠔⢊⣼⢚⡯⢤⣀⠀⠀⠀⠀⠀⠐⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⢤⢶⡶⠌⡴⣦⣧⡀⠀⠀⠀⠀⠀⠴⢫⡛⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣴⣷⡿⡧⢰⣿⣾⠪⢙⡁⠀⠀⠀⠈⠵⢷⣟⠃⠀⠀⠀⠄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⡛⠂⢠⣶⣿⣾⠓⢨⡉⠀⠀⠀⠀⠸⡫⣿⣯⡍⠀⠀⠀⣄⣾⡉⠀⠀⠀⠀⠀⠀⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⢠⣔⣿⡃⢿⣧⢈⢶⣷⠀⠀⠀⠙⡽⢻⣏⡒⠀⠀⠀⣨⣿⡆⠀⠀⠀⠀⠀⢀⣽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡚⠓⠛⠽⢱⢾⡟⣛⡿⡽⠀⠀⠐⠋⢟⡸⠿⠏⠀⠀⠀⣂⣿⡳⠀⠀⠀⠀⠀⠸⣷⡷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⢘⢸⡜⣋⡌⠃⠠⠀⠀⠘⠫⠏⣵⣓⠂⠀⠀⠠⣾⣿⣅⠀⠀⣦⠀⣠⠘⣿⣷⡂⢠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠞⠒⠐⠚⠋⢰⡓⠈⠤⠀⠀⠀⠀⠀⢶⣚⠿⢿⠥⠀⠀⠠⣜⣿⣇⠀⢀⣿⠞⣯⢥⣿⣶⢠⣾⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⠉⠈⠁⠀⠀⠀⡰⠾⡷⠿⠂⠀⠀⢹⢿⡿⣮⠁⢠⣼⣻⣿⠀⣿⣿⣸⡿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⣿⣿⣿⡤⠀⠘⢿⣿⡿⠀⢽⡏⢸⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠠⠄⢹⡇⠀⠀⠀⠀⠈⡾⠉⠀⠀⢀⡽⢾⠆⠀⢴⠇⢾⢛⠠⠐
⠀⠀⠀⢀⣀⠤⠄⠚⠻⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠼⠈⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆
⠀⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣰⣶⣶⠒⠒⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⡙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠹⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⡧⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⡍⢹⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⢤⡀
⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣛⣿⣿⣿⣿⣿⣟⣹⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⡏⣹⣿⣿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠟⠻⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡧⢘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣏⠀⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠟⣿⣿⣿⣿⣿⣿⠇⢀⣤⣸⡇
⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣥⣤⣠⣤⣾⣿⣿⡟⠉⠁⣰⣿⣿⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⢉⡛⢿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⢹⣿⠟⠹⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠛⠻⠷⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠭⣟⣋⣡⣤⣀⣀⠀⠀⠙⠐⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⡿⠋⡁⢠⣿⣷⣶⣦⠀⠀⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣇⠀⠐⢞⠡⣿⡏⢻⣟⢉⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⢹⣿⣿⣿⡆⠀⠈⠀⠙⠂⠤⢈⣉⡋⠛⠛⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢻⣎⣻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠍⢉⠀⠀⠀⠀⠀⢀⡘⢶⡀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠘⠙⣿⣿⡟⠳⣤⣀⣀⠀⠀⠀⠀⠙⠓⢶⡇⠀⠀⠀⠀⠀⠘⢃⣸⡇⣊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠻⢾⡽⣵⣾⠀⠀⠀⠀⠈⠉⠲⢤⣀⣀⡀⢀⡽⠀⠀⠀⠀⠒⠀⠻⣯⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣀⡐⠂⠢⣄⣀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣟⢠⣗⣤
⠀⠀⠀⠀⠀⠀⢠⣾⡿⢋⣿⣿⡑⠀⠀⠛⠋⠀⡀⠘⢷⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⢻⡇⢹⡇⠠⢐⣄⢠⡀
⠀⠀⠀⠀⠀⣴⡿⠋⠀⣿⣿⣿⣷⡄⠀⠀⣠⣶⣤⣀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡁⠀⢸⡇⡸⣧⠀⣿⠀⣴⠂
⠀⠀⠀⠀⠾⠋⢠⣴⣿⣿⣿⣿⣿⣷⡄⠀⢹⣿⣿⣿⡿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣸⣿⣿⣿⣠⣿⢰⣿
⠀⠀⠀⠀⠀⠀⠸⣯⣻⣿⣿⣿⣿⣿⣿⣦⠈⢿⠟⠋⠀⠀⣯⣥⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⠀⣿⣿⣿⣿⣧⣿⣽⡟
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠛⠿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣾⣷⣤⣌⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⣷⣈⣻⣟⠙⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⣿⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣤⠀⠈⠁⠰⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⢀⣾⣿⣿⣦⣄⣀⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠘⠛⠋⠻⠿⠿⡏⠃⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⢿⣿⠿⣿⣿⠿⠋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠉⠀⠀⠀⠈⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠿⣿⡿⢿⡿⢿⡿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣶⣼⣶⣾⣤⣾⣷⣴⣿⣥⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣤⢾⢅⡶⣠⣄⡃⠀⠀⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⠄⡠⠚
⠀⠀⠀⠀⠀⠀⠀⢀⠦⢌⣽⢞⣿⣖⣹⣿⢋⢳⣿⣤⠴⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡑⢢⣴⣤⣾⣷⠀⢊⡰⠖
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⡉⡱⠛⡣⠛⣫⣱⠯⡟⢿⡯⠃⠌⣉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡀⢼⠃⢿⡿⣿⢿⡉⠀⠠⡒⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠔⢠⣄⣁⣞⠇⠓⣬⠂⠱⠈⢃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠪⢀⡀⠊⢁⢁⣇⡠⠀⠈⢠⠂⠠⠤
⠀⠀⠀⠀⠀⠀⠀⢀⣅⡀⠰⡌⢠⡋⠉⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⣴⠀⠀⠐⠀⠀⠀⠀⠀⠀⡤⠔⣘⡙⠣⡀⢨⠋⠙⢃⡤⠀⠐⣄⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠘⠀⠈⠀⠀⠀⢠⠄⠀⠀⠀⠀⠰⠀⠀⡸⠂⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡤⠠⣐⡄⠀⢀⠛⢛⡁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠘⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⢁⠄⠂⡔⠀⡹⢶⣻⣋⠀⡀⠊⢀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⢘⠀⢒⡁⣀⣀⣈⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠒⡎⠉⢷⢻⣵⡨⢤⣥⣀⡀⠀⠠⠤⠤⠤
⠀⠀⠀⠀⠠⠒⡩⠋⢸⢧⡀⠒⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠟⠓⠀⠏⠁⠄⡀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠖⠀⠀⡆⠀⠱⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠂⠀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠒⠐⠛⢅⣽
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠐⠒⢫⢿⢶⣚⣿⠁⡄⡀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠳⣈⠁⢈⡁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠒⠀⠰⠀⠚⠻⠉⠀⠀⡠⡈⠈⠐⠀⠀⠀⠀⠦⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠀⣤⡿⠁⠀⠛⠁⠋⠖⠂⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠾⠁⠇⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠈⢵⠀⠀⠀⠀⠀⡤⠔⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣤⣓⣂⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠁⠈⠀⠀⠀⠀⠀⠈⢶⣆⣴⠂⠀⢀⠦⠬⠇⠂
⠀⠀⠀⠀⠀⢀⠄⡲⠂⡰⡍⠡⢌⠉⠉⠁⠀⠀⠀⠀⠠⣤⡞⡦⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠄⢐⣷⣠⡈⣾⡟⢿⣤⠄⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠞⠀⠀⠇⠘⣄⠀⠈⠆⠀⠀⠀⠀⠀⠀⢠⡽⣻⣿⢊⢻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⣰⡌⠻⠑⡏⡂⢉⠑⠂⠠⠄⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⠞⠛⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⡆⠀⠀⠑⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣤⣤⣄⣉⣉⠙⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⢹⣿⣭⣥⣤⣾⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⡀⠀⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠶⠖⠀⠈⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⠆⠸⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠⠄⠀⠁⠀⠈⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁



⣿⣿⡿⠿⣿⠿⢿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠑⠚⠷⡒⠶⣵⣄⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣻⣿⣿⡶⠞⢓⣲⡾⢦⣼⣿⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠉⠿⠿⣯⣹⣿⢯⡐⠿⢿⠿⢟⣛⣄⣤⠟⠛⠷⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠓⠶⢤⣀⡀⠁⠲⢤⣈⠳⠾⣏⡽⣿⠑⣌⠻⠛⠻⣷⣶⣪⣝⣿⣥⣤⣤⣴⣿⣷⡶⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣥⡍⣒⣾⣟⢿⡛⠛⢒⣮⣥⣾⣿⣾⢿⣿⣿⣿⡿⠟⣻⠋⣽⠋⠉⠟⠋⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢽⣶⣶⣿⣿⣾⣿⣫⣵⣿⡟⢻⣯⠟⠩⡾⠛⣇⢹⣯⣸⠃⠘⣧⡾⠥⣀⣠⢆⠐⢒⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢠⣬⣯⣿⣿⣿⣟⡉⣀⠀⠾⠏⣡⠊⢠⠇⠀⣸⣾⠋⣷⡤⢺⡗⠀⠀⣈⠋⣈⣩⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣶⣶⢟⣿⠿⢡⣼⣿⣧⡙⢣⡜⢞⠁⡛⣠⠋⠠⠐⠃⠇⠐⠁⢀⡎⠀⠀⠐⠒⣋⣠⣴⣿⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠲⠶⣖⣒⣾⣿⣽⡿⣿⢻⣧⣶⢿⣿⡿⣿⠿⢿⣿⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠔⠂⠩⠺⢋⣼⠇⢰⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣈⡥⣶⣿⡿⡟⣡⣣⣿⣿⣧⣟⣽⣿⣿⣢⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⣻⣿⢻⡟⡧⠀⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⠖⠾⢙⣻⣺⣾⣟⢸⡧⠋⢉⣥⣾⣿⣾⣿⣿⡗⣽⢆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⣒⣊⡵⣷⣿⡙⢶⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⢀⠠⢴⡶⠖⣩⢿⣿⣿⡽⡜⣿⡱⣫⣴⣿⢿⡌⣿⣷⠑⠈⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⢈⡉⢛⣛⡥⢸⣝⢿⣧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣵⣿⠃⢺⠁⢼⣇⠀⣰⣿⣿⣿⣟⢧⡇⡀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⣚⡿⠛⢣⣿⢻⣷⣿
⠀⠀⠀⠀⠀⠀⠤⠒⣉⡭⣰⣻⣿⡅⡇⢀⠆⠘⢈⣔⡿⣿⣿⡷⣽⠃⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⡊⠁⠊⢀⣼⠁⡧⡏⢳
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⣿⡟⡇⠀⣧⠨⢘⠀⢈⠋⣼⢿⡿⢷⣸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠄⠀⣴⣿⣏⡀⣿⠳⠸
⠀⠀⠀⠀⠀⠀⢀⣠⠾⣵⡟⣷⢰⡀⢸⠀⠀⠀⢀⣴⢋⢾⡇⠘⢱⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⢡⣿⣿⣿⡟⣇
⠀⠀⠀⠀⠀⠀⣐⣡⣾⣿⣯⠙⣦⠁⠸⠀⠀⠀⠀⠁⠈⠘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⣫⣾⢹⣏⡾⣧⡹⡄
⠀⠀⠀⠀⠒⣋⢴⣿⢿⣿⣟⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣸⣽⠃⣿⡾⠀⡎⢃⠉
⠀⠀⠀⠀⠈⡥⠪⠃⣾⣽⣿⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠻⣟⠸⣅⣇⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠁⡰⢸⣟⣹⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣛⣿⡟⢤⡝⠸
⠀⠀⠀⠀⠊⠀⠀⠁⣸⠟⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣼⣿⣇⠀⡀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢂⣰⠟⣼⣿⣇⠁⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠵⠋⠀⠜⠉⢣⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⢀⡤⠖⠤⡀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢳
⠀⠀⠀⣠⠋⠀⠀⠀⠈⢦⠀⠀⠀⡇⠀⠰⣍⣉⣉⣉⣉⣉⣉⣩⠇⠀⠀⠀⢺⣉⣉⣉⣉⣉⣉⣉⡹⠀⠀⢸
⠀⠀⢠⠃⠀⣠⣶⣦⡀⠀⢇⠀⠀⡇⠀⢀⠤⠤⠤⠤⠤⠤⠤⠤⡄⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⢤⠀⠀⢸
⠀⠀⡞⠀⠸⣿⠀⣸⡗⠀⢸⡀⠀⡇⠀⠈⠒⠒⠒⠒⠒⠒⠒⠒⠁⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⢸
⠀⠀⢇⠀⠀⣿⠀⣿⡇⠀⢸⠃⠀⡇⠀⠰⣉⣉⣉⣉⣉⣉⣉⣉⠆⠀⠀⠀⢾⣉⣉⣉⣉⣉⣉⣉⣹⠀⠀⢸
⠀⠀⠈⠳⢤⣿⠀⣾⣧⠴⠋⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣭⡑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢧⢀⡝⣸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⡆⠀⠀⠀⠀⠀⠈⢺⣹⠖⠁⠀⠀⠀⠀⠀⡖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⢯⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⡻⡼⠛⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠫⡳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢜⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠄⠈⠀⠀⠈⠂⠀⠰⠀⠀⠄⡃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⡠⠒⠀⠠⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠆⠀⠀⠀⠀⠀⠀⠁⠒⠋⠀⣋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣠⠐⡄⠀⠀⠀⡴⠾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠠⡀⢈⠄⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡆⢀⠖⠘⡀⠄⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠈⠀⠀⠀⠐⡀⠀⠀⠀⠀⠂⠀⠀⠰⣀⡀⠒⠒⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠉⠉⠀⠀⠀⠠⡀⠀⠀⠈⠑⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⡀⠅⠀⠐⠀⠀⠀⡞⠢⢄⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠂⠀⠀⡀⠁⠀⠘⢶⡀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠄⢴⠐⡀⠆⢃⠀⡀⢂⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀
⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠙⢾⡄⠱⠀⣄⢂⠐⠊⠰⡃⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⡀⠀⠉⠐⠀⠀⢠⢀⠂
⠀⠀⠀⠀⢀⠎⠀⠀⠀⡁⠀⠀⠈⢇⠀⢋⠘⢃⠀⣀⠒⠵⠲⢴⠃⠉⣱⠀⠀⠀⠀⠠⠤⠄⠀⣸⠀⠀⠀⠀⠈⠙⢥⠀⠠⠬⠧⠀⠀⠀⠠
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠉⠀⠚⣇⠈⠠⠀⢞⠡⠂⠎⠁⡼⠓⣞⡁⠉⠢⢤⠄⢠⣀⡀⡄⢠⡀⠀⠀⠀⢀⠄⠀⣤⣖⣂⣀⣀⣙⣓⡦
⠀⠀⠀⡞⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠠⠈⠠⡀⠀⡜⠀⢰⠁⠈⠉⠒⢲⡄⣸⠀⠅⢠⡼⠃⠀⠀⢰⠀⠉⠏⠀⠉⠉⣉⡉⠉⠁
⠀⠀⠘⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠑⢀⠀⢰⠁⠀⢸⠀⠀⠀⠀⠀⠉⠓⠚⠛⠁⠀⠀⠀⠀⢀⠃⠀⠀⠄⠣⠀⠉⠀⠀⠠
⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠁⠀⡐⠀⠀⠳⣄⡀⢰⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠐⠊⠁⠀⠀⠀⠤⠠⠄⠁⠈⠉⠠⠐⠂
⢰⡃⠀⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠊⣉⣉⠻⣿⣦⣤⡔⢊⣁⣉⣉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠉⠒⠤⢄⣀⠀⠀⠀⠀⡄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠘⠒⠐⠒⠀⠐⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠘⠄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠘⢆⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⢄⣿⡇⠀⢈⠀⠀⠀⠀⠀⠀⢠⡴⠋⡎
⠀⠀⠀⠀⠀⠀⠸⣧⡀⠈⠂⡀⠀⠀⠀⠀⢈⡰⣿⡇⠀⢘⡀⠀⠀⠀⠀⣠⡟⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⢀⠀⠀⠀⠐⢬⣿⠇⠀⢨⠀⠀⠀⣰⣼⠏⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠽⣿⣦⠀⠀⢣⡀⠀⠀⣰⣿⠁⠀⣚⠀⠀⢠⡿⠃⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣷⣄⠀⠱⡄⠀⣪⣿⠀⠀⡇⠀⢠⡿⠁⠀⡰
⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠈⠹⢿⣦⡀⠹⡀⢿⣿⠀⣰⠁⢪⡟⠁⣰⠚
⠀⠀⠀⠀⠀⠐⢮⣙⠛⢾⣷⣦⣌⠻⣷⡄⢡⠸⣿⠀⡏⢸⡟⢀⠔⢁⣤⣶⣾⠭⠿⣛⣺⠷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠙⠻⣷⣮⢻⣆⢷⣿⢸⣷⠟⡴⣣⣶⡿⠛⢉⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣙⠿⣿⣾⣿⣿⣯⣶⡾⢛⣡⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣨⣑⣚⣿⡿⣿⣿⢝⣊⣥⣀⣠⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉⠭⠭⢭⣭⢭⠿⠃⡜⠋⠉⠩⠥⠤⠤⠔⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⣿⣿⣿⣿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣾⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣩⣭⣿⣿⣿⣿⣯⣥⣤⣅⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠛⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠿⠟⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣌⣉⡁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⣛⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣻⣿⣿⣿⡿⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠈⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⡈⠋⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁

⠀⡁⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣖⣚⡋⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠉⠉⠉⠉⠙⠛⠻⠿⠿⠛⠛⠁⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠨⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣼⣷⣆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠻⣉⣤⣵⣦⣴⣤⣤⣤⣤⣴⣦⣴⠤⠤⡤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣴⡾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠿⠿⠛⠉
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⢀⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠻⢿⣿⣿⠀⠀⠀⠀⠀⠀⠄⠶⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⣀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢐⡂⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠙⣿⣿⣿⣿⣿⣷⡌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⢿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠀⠀⠀⠀⠰⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⠉⢸⡷⠑⢿⠇⠻⡄⠀⠀⠀⠀⠀⠀⠀⠉⣙⠃⠀⠀⠀⠀⢀⠂⣋⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣸⡓⠄⠀⠀⠐⠶⣦⣀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠠⠀⣹⣆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠉⣹⠟⠶⠦⣤⣤⡤⠁⠀⠀⠀⠀⠀⠀⠢⣈⠙⠄
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣷⣮⣝⣻⠷⣿⡑⣤⡀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⣀⠰⣿⣆⠈⠂
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠿⠛⠿⣿⣿⣦⣿⣾⣿⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡟⣳⣦⡀⠑
⠀⠀⠀⠀⣴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠿⣐⡉⢩
⠀⠀⠀⢸⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡳⣦⣄⠀⠀⠀⠀⠀⠀⠈⠈⠛⢁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣿⣮⣽⣷⡄⠀⠀⠀⠀⠀⠀⢶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿⣿⡳⠀⠀⠀⠀⠀⠐⢶⣉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠐⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⡀
⣿⣟⣉⡿⠿⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠀⠀⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣾⣿⡿⣋⠩⠤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⡀⠘⢿⣧⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⢀⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢃⠀⢰⣿⡇⠀⠐⢓⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠚⠀⠀⢹⡇⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠘⡄⠈⣿⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⣼⠇⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠘⢿⡛⢻⢰⠚⢛⣿⠟⠁⠀⠀⢀⣾⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠦⡀⠀⠀⠀⠉⠛⠆⠻⠳⢡⠀⠀⠀⡠⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠈⠓⠤⣀⡀⠀⠈⢸⡇⣁⢡⠔⠋⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡏⠉⠽⠘⠉⢸⠇⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠁⠲⠒⠒⠒⠒⠒⠒⠒⠒⠖⠉⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠺⢙⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢭⠼⡛⢞⢠⣶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣟⣿⣳⠹⢆⣩⡽⢉⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣯⣷⣿⣜⣋⣛⣓⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣭⣽⠿⣯⣽⣭⡤⠚⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡑⠲⣤⣰⠖⢶⣦⣦⣮⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣛⣛⣒⣿⠿⡤⣉⠛⣻⡿⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣀⣀⣸⢥⢉⣡⣶⣿⣮⣿⡿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠑⠻⣭⣿⡙⣎⡘⢻⣿⣗⣠⣠⣉⣔⣒⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣛⣿⣿⠻⢌⡟⣻⣷⣎⣷⣇⣤⣨⡬⣶⣖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⣿⣿⣿⣷⣤⡉⠙⢻⣤⣥⣿⣿⣪⣱⣿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⡿⢿⠿⢿⣳⣿⣷⣿⣿⠉⠀⠉⠉⠉⢁⡄⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣆⣀⣀⣤⡾⠟⣩⣵⣿⠏⣁⠹⣾⣷⣾⣷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢴⣦⡍⠙⠁⠀⣴⣿⣾⣿⡟⠻⢷⣯⣯⣴⣾⣿⣿⠟⠃⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢿⡿⢿⣿⣿⠿⣮⣾⣿⣿⣤⣧⣤⣻⣉⣻⣿⣿⣿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢹⠻⠻⠿⠛⠉⠉⠉⠙⠋⠻⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⡶⠚⠊⠱⠂⠖⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣿⣯⣿⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣬⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢴⣿⣳⡗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⣶⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣷⡾⢹⠏⢲⣿⣟⣛⢦⡀⠀⠀⠀⠀⠲⣿⣻⣿⣿⣧⠀⠀⠀⠀⠀⠘⢿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⢸⠉⠣⣼⣄⠀⠟⣧⣨⡷⠈⠀⠀⠀⠀⢀⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠠⢶⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⣈⣿⣆⣾⣿⣯⣶⠖⠂⠀⠀⠀⠉⠻⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⣸⣿⣿⠯⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣷⣂⡽⣿⠿⠿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠘⡟⢻⣿⡄⠀⠀⠀⠀⠀⠀⠉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣡⠈⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣆⡠⠀⠀⠀⠀⡙⢿⣿⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣨⣷⣤⠾⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⣹⣿⡿⢉⠉⡀⠀⣠⣀⡾⢿⡢⡿⠷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣿⣉⣿⡟⢡⣔⡂⠀⠀⠀⠀⠀⠀⠚⠙⠀⢸⠟⠀⠀⠀⠈⠀⢻⣿⠀⠈⢧⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠜⠛⠋⠉⣸⢻⡮⣮⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠛⠀⠀⢀⡘⢿⠃⣠⡶⠻⡟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣾⣿⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⢦⠙⠦⣾⣿⡿⡟⣾⣿⣦⡼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣘⣦⡄⢀⣿⣹⢀⣤⣈⣧⣤⣤⡤⠤⠀⠀⠀⠀⡷⠀⠀⠇⠀⠉⠙⣷⡿⣼⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣬⣽⣿⡷⢋⣿⣿⣿⣿⣿⡿⢷⣶⣄⡀⡀⠀⠀⠀⠇⠀⢤⣠⠄⠀⠘⡧⣶⣈⡇⠸⡶⠷⠗⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠁⣴⠟⢻⡿⣷⢀⣿⡄⠈⢻⡟⢷⣤⠀⠈⠉⠀⠀⠀⠉⠃⠀⣐⠡⡜⠆⠚⡿⠛⣩⡶⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢸⠇⠈⠘⣟⠁⠀⠀⠁⠀⠙⠇⢀⣀⠀⠀⠀⢠⠀⠀⠈⠀⠁⠀⠘⠁⣄⠸⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠼⣀⠀⢀⣿⣀⣶⣤⣶⣴⣤⣄⠀⠙⠳⣄⣰⠛⡇⠀⠀⠀⠀⠀⠀⢶⣿⣴⡟⠛⣋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⠞⠓⣿⠿⣿⣋⣉⡉⢿⣿⢷⣿⣉⠑⠚⣸⣿⡟⠉⠛⠠⠿⠖⠁⠀⠠⢻⡟⢹⡟⢀⡜⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣴⠏⠁⣼⠸⣿⣄⠃⠀⢻⡄⠈⠙⠂⢠⠁⠉⠀⢤⣦⡼⠀⠀⠒⠀⠀⠀⠧⣤⣿⣿⡿⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣿⠀⣿⠛⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣆⣀⠆⣀⠀⠀⠀⠀⠖⣿⣤⠛⠷
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⣙⣉⣶⣶⣴⡟⢀⣿⡶⣤⡴⠆⠈⠁⠀⠀⠀⠀⣴⡄⢠⡟⢻⣿⠿⠟⠲⢀⣄⠀⣾⣏⣦⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⣠⠶⠿⠟⣻⣿⣿⣿⣷⣮⣿⣶⣿⣤⣀⠤⣤⣀⠀⡀⠚⢉⠁⢀⠀⠀⠄⠃⠀⠹⣿⠿⣇⣈⠁⡴⠆⠓
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣼⠟⠉⢛⡥⠒⣴⡏⢸⡆⡙⢿⣆⠄⠙⢷⠀⢤⡌⠀⢸⣷⠀⠀⠀⠀⠰⠃⣘⠀⢹⡃⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⢸⠃⠀⣿⠁⠘⣿⡅⠀⠙⣿⣧⡀⠙⠛⢿⣴⣿⡿⢀⣸⠗⠀⠀⣤⣿⡿⠻⠟⢿⡌⠡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⢻⣧⠀⠹⣿⡆⠀⠈⠻⣧⠀⠈⣽⠃⣠⡇⢀⠉⠄⠁⠀⠘⠟⠷⣰⡆⠀⢉⢤⣀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⣿⠀⠀⠸⣷⡀⢀⡴⢛⡀⠀⠃⢰⢻⣟⠀⠀⠀⠂⠀⠀⢀⡾⠟⠀⣠⠀⠈⠛⡋⠀⠀⠀⢸⣠⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠒⢒⣒⣶⣄⣹⣿⣆⣴⠶⠚⢛⠀⢀⣠⠼⢷⣾⣿⣯⣛⠷⠀⢘⠈⠁⠘⠀⠀⠀⠀⠔⠁⡄⢻⡟⠉⠀⠀⠀⠃⠀⠀⡀⣺⠛⢿⡛⠆
⠀⠀⠀⠀⠀⠀⠐⠈⠉⣩⣽⠟⣿⣿⠛⠁⠀⠀⢸⡀⠞⠁⢠⡾⠹⣆⠉⠛⢲⡇⠈⢠⡟⠀⠀⠀⠀⠈⣦⣀⡇⠈⠇⣠⣴⣤⠀⠀⢠⡔⠠⢿⠀⠈⢧
⠀⢰⠀⠀⠀⠀⢀⣴⠟⠉⢀⣾⠃⢹⡆⠀⠠⢻⢸⣷⠀⠀⢸⠇⡀⠸⡄⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⡼⢻⡟⠅⠸⠤⠋⡏⠙⠀⠀⢋⠋⠀⢻⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣼⠃⠀⠀⠃⠀⠀⠈⢸⠇⠀⠀⠘⠀⣅⠀⢷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠈⠁⠀⢰⠀⠀⢀⠄⡔⢀⡜⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠀⢹⣄⣼⣦⣤⣤⣀⣠⣧⠀⠀⠀⠂⢠⡄⠀⠀⣾⡂⠀⢀⡼⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⢶⠀⠀⠀⢴⠾⣺⡇⠀⠀⣀⣡⣶⣿⡛⠛⠛⢭⣉⣹⣭⣴⣿⣛⡂⢌⡡⢉⠀⢿⣧⡄⣾⣥⢀⣸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⡏⢀⣜⣤⠀⠀⠀⠈⠛⠛⠛⣿⡿⠛⠛⠛⠛⠛⠛⢻⣾⣻⣿⣋⣧⢟⣱⣿⣇⣨⡄⢠⣉⣿⣟⣁⣸⣿⣧⣭⣿⣷⠾
⠀⠠⠀⠀⠀⢴⣍⡉⠙⠾⠿⠿⠉⠙⢷⣿⣷⣶⣾⣯⣥⣤⣤⣄⠈⠛⠛⠛⠿⢿⣿⣿⣿⣛⣽⣿⣿⣿⣿⣴⣮⣉⣉⡙⢻⣥⡴⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣷⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠖⣠⣶⣄⣤⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⠛⠛⠙⣿⠋⢠⡌⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣷⣄⣙⠛⣿⣿⣤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⢶⣄⠈⠁⢸⣏⠀⠉⠉⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣿⣿⣿⣿⣿⣯⣿⣿⣙⣷⣄⣤⣤⣶⡄⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠟⣿⡟⣩⣽⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣶⠿⠟⣉⡉⠀⣀⠉⠛⠋⠀⠉⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣤⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣷⣶⣤⣄⡀⠂⠀⠙⠒⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⢻⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠈⡉⠉⠉⠀⣀⣉⣈⣿⣁⠀⠈⠉⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⢷⡎⢹⣿⣿⣿⣽⣷⣆⠠⢺⣿⠆⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⣼⣿⣿⣿⠿⣿⣿⣿⠟⠻⠿⣿⡷⠐⠛⠛⠛⠛⠋⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⠋⠁⠉⠀⠘⢿⣿⣶⣿⣿⣿⣿⡄⠀⠀⠰⣤⣴⣄⣀⠀⠀⠀⠁⠀⠀⣀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣒⣤⣄⣿⣿⣿⣇⣀⣽⣏⠁⠀⠀⠀⠀⠈⠻⣿⣷⣴⣶⣾⣿⣿⣿⠟⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣯⣤⣶⣿⣿⠿⠿⠿⠟⡛⠛⡿⢿⣿⣿⣿⣿⣶⣿⣷⣄⣦⣀⣤⣠⡶⣾⠿⡿⣿⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⡷⢶⣾⠿⠿⠋⠀⠙⠋⠉⡙⣷⠤⠰⣦⣼⣿⣷⡿⠻⢿⣦⣼⣿⣿⣿⣿⡟⠋⣉⣠⡇⠀⣾⠿⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⡿⠃⠀⣠⣼⣿⣿⣷⣠⣤⣀⣾⡿⣋⡙⠛⠛⢛⣿⣛⣩⡎⠀⣰⣦⣴⣦⡄⠀⢠⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣶⡿⣿⣿⣯⣿⡿⠰⠟⠻⢿⡿⢿⣿⣿⣻⣿⣟⢻⣿⣿⣿⠈⠛⠻⠷⣶⡶⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠃⠀⠀⠀⠀⠘⠛⠛⠻⡿⠋⠀⠀⢀⡀⠀⠀⠀⠀⠙⠛⢋⣤⣄⢀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷⠟⠛⢹⣿⣶⣦⣤⡀⢰⡶⠐⣧⣄⢺⠟⠚⠓⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣦⣤⠀⢀⣀⣤⣴⣄⣀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⠾⣿⣿⣾⣿⡿⠋⣶⣶⣶⣾⣦⣴⣆⣀⡀⠀⠀⢠⡿⠛⢻⣿⣤⣿⣿⣿⣿⣿⣿⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⢀⣤⣶⣿⣿⣿⣿⣦⣬⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⡀⠀⠀⠻⠿⠿⠛⠛⠛⢿⣿⣿⣿⡛⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⡟⠛⣿⣿⣿⣷⣾⣷⣤⣄⣤⣤⣈⣀⠀⠠⣀⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⠻⠿⠛⣿⣿⣿⣿⡟⢛⣻⣿⣿⣇⣀⠀⠽⠛⢻⣿⣿⣿⣿⣿⣿⠛⣿⣿⡟⠛⠠⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠃⠀⠀⠀⣀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣛⠉⠷⣾⣿⣿⣭⠛⠛⠛⠛⢿⣿⣿⣿⣿⣶⣦⣬⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠛⠿⠿⢿⠀⠈⠉⠙⠛⢷⡘⢛⣷⣾⣿⣿⣿⣿⣿⣿⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⣿⡿⠟⢛⠿⣋⣁⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⡴⣦⣄⣀⡀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠉⠻⣿⡿⠿⠿⢿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⣴⡿⠿⠂⣉⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⡅⣠⡄⠀⠀⠁⠀⠀⡀⢰⣤⣤⣶⣤⣤⣤⡀⠀⠯⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⡋⠑⠶⢺⣿⣿⣿⣉⣽⣿⣿⣿⡀⠀⠀⠀⠀⠈⣤⣿⣿⣶⣶⣿⠷⠿⢻⡿⠿⢿⣿⣿⣿⣿⣿⣔⠆⠀⠀⠀⠀⠀⢠⣄⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⡘⠃⠀⢴⣿⣻⣿⣿⣿⡿⠿⣟⣉⣤⣄⠀⢀⠀⠈⢉⣿⣿⣿⣿⡏⠀⠠⠄⠀⠀⠀⠀⠉⠙⢛⣿⣿⣿⣿⣤⣶⣴⣶⣿⣿⣋⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣏⣽⠿⢿⣷⣶⣶⣿⣿⣿⣿⣷⣾⣧⡄⢀⣈⣿⣿⡀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠿⣿⠟⠉⠙⠉⠁
⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⠛⠋⠀⣀⣀⣠⠾⢿⣿⣿⣻⠟⠉⠛⠻⢷⣿⣿⣿⣿⣿⣿⣷⣿⣦⣴⣿⣷⣄⣠⣤⣄
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢋⣲⠟⠋⠉⠀⣴⣾⣯⣄⣀⣀⣠⣤⣶⣦⣤⣿⣿⣿⣿⣿⣇⣀⠉⠛⠋⠹⣿⡿⠿⣃⣴⡶⠀⣤⣴⣷⣶⣿⣾⣷⡀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⡾⠟⣹⡿⣇⡀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣠⣤⣿⡿⢿⣆⣀⠀⣠⣴⡿⣿⣿⣾⣿⣿⣿⡿⠿⣿⠋
⠀⠀⢴⣿⣿⣿⣿⣿⣻⣿⣿⣿⡷⠂⠈⣹⣷⣤⣤⡶⠏⠵⣦⠤⠤⣾⣿⣿⣿⣿⣿⡧⢤⣿⣿⣿⣿⡛⠀⣿⣫⣤⠀⠉⢠⡄⠠⠀⠀⠙⠉
⠀⠀⠀⣿⡿⠋⠠⠞⢻⣿⣿⣿⣢⣿⣿⣿⣿⣿⣿⣿⣷⣴⠀⠀⢤⣾⣿⣿⣿⣿⡿⡄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⣷⣄⢀⣄⣀⣤⣨⠿⠇
⠀⠀⠀⠀⠀⠀⢀⣬⣿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⣴⣇⣼⡟⢁⣠⣼⣿⠠⡦⢀⣨⣿⡛⣛⠻⠿⠿⢿⣯⣿⠟⣿⡶⣿⣿⠿⢋⣭⣥⣄⣀
⠀⠀⠀⠀⡀⠀⠈⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠛⠛⣹⠟⣫⣉⣽⣿⠴⣷⣼⣿⣿⣿⣿⣧⠀⠀⠘⠛⠁⣠⣤⠀⠀⢀⡀⠀⠉⠟⠛⠋
⠀⠀⠀⢿⣿⣾⣿⣿⣿⣿⣿⣿⡄⠙⠓⠾⠛⢿⣿⣿⣷⣴⠖⠞⣁⣠⣿⣿⡉⠀⠀⠀⠉⠀⠀⠛⠃⣿⣧⣀⠀⣶⣾⣿⢷⣿⡄⠈
⠀⠀⠀⠈⠋⠹⠿⠿⠛⠛⠛⠛⠁⠀⢠⣤⣴⣿⣿⠿⠛⢀⣼⣿⣿⣿⣿⠁⣀⣀⣀⣀⣼⣆⠀⣠⡀⢳⣎⣉⠀⠉⢛⠁⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣻⣿⣿⣿⣿⡆⠈⠛⣿⣿⢿⠿⣿⣿⣿⣟⣻⣿⣿⣿⣿⠿⣿⣯⣤⣶⣶⣮⣴⣦⣴⣋⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⢰⡿⣏⣁⠀⠀⠁⢀⣹⠿⠉⠻⣿⣿⣿⣿⣁⣈⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣿⡿⠛⠋⠉⠀⠀⠀⣸⣿⣦⣾⣿⣷⣀⣀⣨⣉⣠⣀⣠⡟⢁⣴⡟⠁⠀⠙⣿⣿⣿⣿⣿⣿⣍⣀⡄⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢐⡄⢿⣿⣿⣿⣿⣿⣿⣟⡛⠛⢿⣿⣿⠿⠋⠙⠿⠛⠁⠀⠘⠗⢰⣿⣿⣿⣿⣿⡿⠻⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠀⠉⠀⠙⠻⠿⠂⢸⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢻⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⣿⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣶⡶⠺⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠛⠁⠀⠉⠁⠸⠛⠻⠿⠛⠛⠛⠛⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡲⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣟⣫⣅⠤⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡽⢶⣒⣦⣶⣾⣿⣿⣿⣷⣶⣦⣀⣤⣤⣤⣤⣬⣥⣶⣶⣶⣶⣦⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⢻⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⡟⡿⠟⠛⠀⠀⠀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡟⡜⢙⡆⠙⢁⠐⠀⠀⠀⠀⠀⠀⠀⡠⣭⡟⠙⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠩⡻⢿⣿⣿⣿⣿⣿⣿⣿⡱⢈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠛⠏⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠏⠀⠀⠤⠤⠀⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠀⠤⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⡾⠀⣤⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠀⠀⠈⢣
⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠈⠂⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠻⠄⠀⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠀⢸⠇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠿⠀⠀⠀⠀⡆⢸⠇⠀⠀⢠⡀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⠀⠀⠀⢰⠃⠉⠀⡼⠀⠀⣇⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠁⠀⢠⡏⠀⠙⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⣶⠀⠀⢰⡀⠈⠁⢠⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⡟⠀⠀⠈⣷⠀⠀⢸⡄⠀⠇⠀⠀⣀⢠⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠸⠇⢄⠀⡄⠀⠀⠀⠈⠁⠀⠀⢠⠀⠛⠈⠀⣧⣰⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⠀⠀⢀⠈⠀⠁⡀⠀⠀⠚⠀⠀⣆⠛⠀⠀⡇⢸⢿⠋⠀⡀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⠋⢸⠃⠀⠀⠃⠀⢰⣆⠑⡆⣼⠘⠀⠀⠙⠀⠀⠄⢠⠀⠈⠀⠠⡇⠸⠁⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠈⣷⢈⡁⡀⠀⠀⢀⠘⠛⠀⠁⠻⠀⠀⢠⡀⠀⠀⣄⠀⠰⠀⠀⠀⠃⡿⠀⣆⠸⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⠀⠐⡋⢻⠃⣷⠀⠀⠚⡀⠀⠀⠀⠀⠀⢰⡌⡅⠏⢠⠟⡄⠀⠄⡀⠀⠀⣀⠠⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢸⡸⠇⠑⠴⡄⢡⣲⠐⣄⡇⠀⢀⠀⡄⢈⠀⡀⠿⠀⡾⠠⣠⡇⠸⠇⢀⡜⠃⠀⠀⢰⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢸⠂⠓⡆⣠⡄⠀⢧⣴⣾⡿⣶⡔⡌⠇⠀⠘⢠⡇⠀⠀⠀⠀⠋⡠⡖⣠⣸⣧⡘⠁⠀⠈⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡦⠘⣄⠀⠈⠛⠈⠃⠙⢟⠃⣿⠿⣦⠀⠶⠀⠈⠓⣦⠀⠀⠐⠈⣷⠏⣻⢁⣼⡿⠋⢀⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣤⣌⠀⡮⡄⢈⣗⣦⡼⢆⢠⡄⠻⠃⠀⠀⠊⡰⣿⠄⠈⠀⠰⢷⠠⠉⠈⠈⣴⢒⡊⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢈⣛⣠⠤⣿⣄⡧⢴⣾⣿⡹⠇⢸⣧⢱⣄⡶⠀⠆⠁⠁⠁⢠⣄⠀⢁⣈⡀⢻⣧⢀⣿⡌⠃⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⠁⠀⠀⠀⢹⣿⣆⡈⠯⠀⣀⣀⠀⠈⠛⢡⣿⣧⠤⠓⠠⢾⣿⣦⡈⠿⠃⢘⠡⢜⣿⡛⠁⠀⢉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⣀⣀⣠⣾⡾⠁⠀⠀⠀⣨⡿⠂⠒⠒⢿⠏⠀⠀⠀⠀⠀⠙⢿⡟⠈⠁⠙⣄⠀⠈⠙⢿⣯⡭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⡽⠯⠽⠿⣵⣠⢤⣄⣾⡿⣇⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⣠⣿⣷⣤⣠⢔⣿⡆⠀⣠⡴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠐⠾⠶⠛⠿⠧⢯⡥⠿⣿⣓⠠⠄⠂⠾⠛⣋⠿⠷⠿⠿⠳⢿⠶⠾⠾⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣎⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣓⣾⣯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣄⣉⣻⢿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢬⡤⠿⠗⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⡀⠀⠀⠀⠀⠐⠦⢽⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⢬⡄⠀⠀⠀⠀⠘⠓⠖⢧⣶⣮⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣿⠂⠀⠀⠀⠀⠀⠀⠀⢐⣼⠖⠀⢀⡗⠀⣈⣿⣽⣿⣽⣯⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣱⡄⠀⠀⠀⡀⠀⠀⠀⣐⣺⣃⠀⣸⣿⠀⣬⣬⣿⣿⣷⣷⠟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣋⠀⠀⢐⡄⠀⠀⠀⠀⠀⠀⠻⢦⡿⢇⠀⠀⢠⣧⡀⠀⠐⣾⡿⠿⠖⠿⣿⣗⣿⣿⣿⣿⣿⣿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢈⠻⣿⣃⠀⣼⡗⠀⠀⠀⠀⠀⣄⡓⠦⠶⢋⣀⠀⣼⣿⠗⠈⠀⠀⡀⠀⠀⢀⡜⣹⢿⣿⣿⣿⣿⡿⠟⠻⢶⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠈⡳⣶⡏⢐⣿⣿⡀⠀⠀⠀⠀⢈⡛⠻⣿⣿⠛⢐⡿⠃⠀⠀⠀⠀⠀⠀⢀⠎⣰⢃⠎⣼⣿⡉⢀⠀⠀⠀⠀⠉⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⡐⠾⣷⣖⠸⣿⣿⡇⠀⠀⠀⡀⡼⠉⣷⣶⣿⣤⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⢀⣴⣟⣿⣧⠀⠀⡀⠀⠀⠀⣄⢳⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⢌⣛⡟⣉⣸⣿⡿⠿⣤⣰⣾⡷⣿⣶⣾⣿⣿⣯⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⠟⢋⣼⢋⣹⢦⠀⢳⡄⠠⣄⠘⣿⠀⠛
⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠆⠋⢭⣽⣿⣿⣷⣶⣶⣦⠬⣿⣿⣞⠛⠛⠛⠛⠛⠀⠀⠐⠢⢤⣀⠀⣠⣀⣶⠚⣡⢀⡾⠋⠉⠀⠀⠑⠈⣿⠄⠻⡷⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⣀⣀⣤⣀⠉⣉⡁⠀⠀⠀⠀⠀⠘⠙⠛⠒⠀⠠⠤⠀⢀⣠⣶⡦⠉⠓⢿⣿⡋⡾⣳⠋⠀⡀⠀⢀⣴⡆⠀⠈⡀⣀⣀⣄⡀⠄
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠋⠁⠀⠉⠛⠀⣾⣿⣿⠀⠀⡀⠀⣠⣴⣶⣦⡀⠙⠻⠶⠦⠴⠤⠼⢿⠿⠾⢵⣶⠤⠀⠐⠉⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠉⠉⠉⠋⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⢀⢀⣦⣂⢈⠔⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠌⢦⡙⣿⣿⣿⡿⠂⠐⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⡙⠀⠙⡉⠝⠅⠀⠀⠁⠢⣠⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠬⡪⠍⠀⢲⠳⠷⠁⡀⠂⣗⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⡙⠐⠈⡆⠃⠀⡶⡾⠆⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠡⠀⠂⡈⠋⡃⠠⣾⣴⡿⠦⠀⠠⠊⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠊⠀⠤⡂⠚⣦⢝⣍⡑⣘⡁⠀⠉⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠃⠰⠻⠄⢸⠛⢁⠐⠂⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁⠀⠀⠆⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣈⢄⣼⡥⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⣀⠀⠈⢉⠗⢻⣿⣽⡷⢓⡃⠀⢀⡑⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠂⠉⠙⠀⠀⠐⠄⢂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣖⡏⣀⣀⣀⡀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠴⠂⡝⠁⡜⣄⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠐
⠀⠀⠀⠀⠀⠀⢠⠂⠀⢀⠃⠈⢆⠀⠈⠂⡀⠀⠀⠀⠀⠈⢙⣾⣯⣯⢠⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⡿⠏⠷⠗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⡀⡇⣆⢠⢀⠀⠀⠀⠈⠣⠀⡞⡤⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣛⣉⣛⠯⡅⣸⣾⣾⢀⠀⠀⠀⣱⣐⡿⢡⢚⠕⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣋⣭⠥⠭⠭⢱⡇⡟⣿⢸⢰⠀⠀⠨⡢⣕⡔⢡⢊⡠⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠛⣉⣙⣂⢿⣁⢇⡏⣸⢸⠀⠀⢝⠦⣹⡔⡵⢊⠵⣃⡀
⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⡀⢀⡘⣍⢉⣥⠴⠖⠂⢿⣸⠃⡟⡾⠀⠈⡢⣙⠮⣧⢾⢟⣋⣥⠤
⠀⠀⢀⠀⡐⢤⢰⡝⡎⢇⠹⡆⢳⡬⣯⠼⡷⢚⣋⣩⣹⣶⢱⡇⢳⣆⣝⠺⣗⢿⠕⣋⡤⠖⠛⡁
⠀⠀⡈⢧⠹⡌⢧⢧⠹⡌⢧⢳⡀⢷⠘⣶⢿⡋⣹⣬⣦⠬⠿⣄⡟⣸⡺⣟⠢⣿⣘⠥⠶⣒⣋⠀⢰⡄⣦⠀⠀⡀
⠀⠠⣘⣮⣳⣽⣪⣁⣵⣭⣮⣧⡿⢾⢷⡿⣼⣯⣥⣽⣎⣻⡙⠿⢧⡅⢹⠻⢗⣿⠠⠚⣉⣩⠴⠂⢸⡇⠘⣧⠀⣧
⠀⢀⣨⠝⣡⣫⣫⢞⡵⢣⢞⡞⡴⢣⢮⡞⢡⠖⢡⠎⣩⠏⣹⠛⠶⠿⣿⣀⡀⡿⠚⠋⠉⠀⠀⢀⡾⠃⠀⣿⢠⡏
⠀⠉⠴⣺⢟⡵⢣⣞⢔⡵⣫⢞⠔⡡⢋⡴⠡⠴⠧⠒⠡⢞⣁⣀⣀⡐⠒⠾⣍⠛⠶⣤⣄⡀⠀⠜⠁⠀⠀⡇⢸⠁
⠀⠀⠐⠑⠋⠚⠕⠉⠋⠀⠐⠉⠈⣠⣥⡴⠶⢆⣤⣤⣀⣀⡀⠀⠀⠙⣦⣤⠼⠶⠶⠶⠾⠿⠿⣷⠟⠛⣶⢶⣼⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⣤⣴⠛⠿⠷⣀⣈⡛⢯⣭⣄⡰⠛⠉⠀⠀⠀⠀⢠⡤⠖⢹⠇⢀⡾⣡⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠍⣭⣽⠿⢿⣾⣍⣛⠿⣮⠙⢻⣿⠾⣷⠀⠀⠀⣰⢋⡤⠖⢺⡖⣫⠾⣡⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣾⡿⠷⣀⣛⠿⣶⣟⢿⣿⣦⣿⣿⣶⣾⣷⡄⠀⠀⢠⠏⣀⡤⠊⠙⠔⢯⣵⣣⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢶⣂⣚⠿⡿⠷⣉⣛⡀⣾⣭⡌⢛⡿⢇⣻⠏⠀⠀⢠⠞⢁⡴⠚⣡⢂⠫⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⠿⠿⠿⢛⣓⣈⠻⣿⣿⡎⢿⣿⡞⣿⣷⣝⠧⠀⠀⠉⠀⡞⠀⢰⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣯⣾⣿⡷⣿⣿⣿⣇⣮⣭⡁⣶⣍⣵⣞⠿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣯⢍⣤⣝⢛⣛⣫⢹⣿⣇⢹⣿⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣅⢿⣿⣿⡊⢿⣿⣇⡿⣫⣶⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣵⣾⢤⣿⣮⡝⢻⡷⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠱⠆⠉⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⣉⣉⣭⢵⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣄⣀⣀⣀⣀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠭⣦⣤⠤⠒⢂⣈⠴⢦⡖⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⣁⡤⠤⠶⠦⠶⠤⠤⣀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠱⡀⠣⣀⠿⠗
⠀⠀⠀⠀⠀⠀⠀⢀⣯⠖⣩⠴⠒⠉⠉⣀⣀⣉⣉⠒⢬⣑⣺⠀⠀⠀⠀⠀⠀⢀⡀⠆⠃⠈⠀⡇⠀⠀⠀⠀⠀⢀⡀⠠⢄⣀⡀⠀⠀⠈⠙⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣡⠊⢁⡤⣖⣋⡩⠤⠴⠦⣀⠽⠲⡞⣇⠀⠀⠀⠀⠀⡀⠂⠁⠀⠀⠀⡠⠁⠀⣠⠴⠒⠉⠀⠀⠀⡀⠀⠈⠙⢦⠀⠀⠀⣰⢤
⠀⠀⠀⠀⠀⠀⠀⠈⣇⡾⠋⣠⠤⠄⠀⡀⠀⠚⠉⠂⠀⣷⠏⠀⣀⣀⡀⠀⠀⠀⠐⠂⣴⠞⡧⠀⢞⠁⠀⠀⠀⠀⢀⡦⠵⢄⡒⠰⣬⡇⠀⠀⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢏⢳⡀⠁⠀⠀⢀⠀⢠⠄⠀⠀⣸⠇⠀⣸⣡⡤⠟⠀⠀⠀⠀⠀⠈⠱⡇⠀⣾⠒⡲⠖⠈⠉⠀⠀⠀⠁⠈⠁⢸⣹⢤⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢄⡀⠀⠀⠉⠁⠀⣠⠴⠃⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⢿⡀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⢸⠁⠀⣸⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠙⢒⠒⡟⣯⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠉⠢⡑⢤⡀⠀⠀⠈⠲⠁⠀⣀⡴⢷⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠒⠼⣾⠤⠼⣦⠠⢾⣉⣉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠛⠯⣉⣱⠒⠿⠋⢯⡥⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣊⠀⠀⠀⠀⠀⢘⣦⡤⠼⠓⠶⠤⠤⢤⡄⠀⠀⠀⣠⣞⣉⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⡆
⠀⠀⢰⠒⢦⡀⠀⠀⠀⠈⠉⡳⠒⠂⢹⠧⣄⡀⠀⠀⠀⠀⠀⠀⡟⠒⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⡇
⠀⠀⠀⠑⠦⣼⠂⠀⠀⠀⡴⠁⠀⢠⡏⠀⠀⠈⠉⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠻⡖⠛⠁
⠀⠀⠀⠀⠀⠈⠳⡀⠠⡞⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠜⢦⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⢸⣿⠁⠀⠀⣁⣀⣀⣁⣈⣁⣀⣀⣀⡀⡀⠀⢹⣿⡄⠀⣿⡇⠈⠉⢁⣀⣀⣀⣀⣀⣉⣈⣉⡉⠁⠀⠀⣿⣷
⠀⠀⢸⡟⠀⠰⠺⣿⣿⣿⣿⣿⠋⣿⣿⡏⠋⡍⠀⢸⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡇⠀⣿⣿
⠀⠀⢸⡇⠀⢸⡾⠯⢒⠉⣿⡇⣠⣿⣋⣧⡸⣽⠀⢸⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⡟⢻⣻⣟⠁⠙⣿⣿⡇⠀⣿⣿
⠀⠀⢸⡇⠀⢠⡤⢒⣿⣷⣿⣋⡋⣼⢿⢶⣟⡤⠀⢸⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣷⣾⣿⡏⠀⢸⣿⣿⡇⠀⣿⣿
⠀⠀⢸⡇⠀⢈⠾⡯⣽⣿⣯⡻⣷⣄⣾⡞⢋⠁⠀⢸⣿⡇⠀⣿⡇⠀⣻⣿⣿⣟⣿⣿⣿⣇⠀⣼⣿⣿⡇⠀⣿⣿
⠀⠀⢸⡇⠀⢈⢳⡇⠘⢙⠛⡁⠚⢋⡿⠋⠐⠀⠀⢸⣿⡇⠀⣿⡇⠀⣽⣻⣿⣏⣹⣿⣿⣿⡄⣿⣿⣿⡇⠀⣿⣿
⠀⠀⢸⡇⠀⢨⣟⣱⠆⣀⣉⢀⣃⡃⣀⣤⡶⣧⠀⢸⣿⡇⠀⣿⡇⠀⠋⢿⣿⡿⢿⣿⣻⣿⣧⣼⣿⣿⡇⠀⣿⣿
⠀⠀⢸⡇⠀⠰⡁⠔⢶⠒⡞⠲⡰⠃⣟⣶⢐⡆⠀⢸⣿⡇⠀⣿⡇⠀⢆⢀⠒⠐⢲⡖⢆⠖⢰⣲⠄⣲⠄⠀⣿⣿
⠀⠀⢸⣿⠀⢸⢸⠓⢾⢸⠙⡦⡗⣎⠉⢠⠟⣇⠀⢸⣿⡇⠀⣿⡇⠀⡚⢯⣰⠻⡎⢹⠉⡆⢳⣸⢰⢻⡀⠀⣿⣿
⠀⠀⢸⣧⠀⠈⠀⠀⠀⠈⠉⠀⠁⠀⠉⠈⠀⠀⠀⢸⣿⡇⠀⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿
⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟