Eww Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠁⠈⠙⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣀⣴⣾⣿⣦⣄⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠒⠀⠀⢶⣤⣀⠀⠙⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⢁⣠⣶⣿⣯⣿⣿⣏⠙⠿⣿⣶⣤⣈⠙⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⢷⣤⣈⠀⠀⠺⢶⣄⡀⠈⡙⠳⣦⣤⣶⡿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⡀⠙⠿⣾⣿⣯⣉⠛⠿⣿⣶⣤⡙⠻⠋⢁⡀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⢹⣿⣿⣦⣄⡀⠈⠙⢷⣦⣶⣿⣿⠁⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣷⠀⠀⠉⠻⢿⣿⣦⡌⠙⠋⠁⠀⢸⣾⡇⢸⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⡟⠿⣶⡾⠟⢹⣿⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⢰⣄⡈⠁⣀⣤⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⠸⠟⠙⣿⡇⠅⢾⡇⠀⢸⡿⠙⠿⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣀⣴⡀⢸⣿⡇⢸⣿⣿⠀⣴⣄⣸⣿⡇⢸⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⣀⠔⠁⠘⠇⠀⢸⡇⠀⠘⠁⠑⢄⡀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⡿⣟⣵⣷⣸⣿⡇⢸⣿⣿⣼⣷⣝⢿⣼⡇⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠿⣶⣤⣴⣷⡀⠀⠄⢾⡇⠀⠀⢠⣷⣄⣤⡾⠟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⡈⠙⠛⠁⢻⣿⣿⡇⢸⣿⣿⡿⠉⠛⠟⠉⣠⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄⠃⢿⡇⢀⣠⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠻⢿⡇⢸⣿⠿⠁⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠁⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣮⣦⣭⣤⣮⣼⣮⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠟⠻⠛⢿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⡛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻
⣿⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠒⠒⢢⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⡄
⣿⠀⡌⠀⠀⠀⠐⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⣠⣞⣽⣿⣦
⣿⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠁⠀⠀⠀⠀⠈⠀⠀⢀⡽⣶⣤⡀⠀⣟⣯⣿⣿⣿
⣿⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠛⠀⢀⠞⠃⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⡖⣲⡄⠀⢹⣿⣿⣿⡏
⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡀⠠⠀⠊⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠶⠽⡧⢀⣾⣿⣻⡿⣧⢀
⣿⠀⣈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠊⠁⠀⠀⠀⠀⠀⠱⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿
⣿⢠⣿⣷⣿⣶⣤⣀⡀⠀⠀⠀⢀⣀⠤⡂
⣿⢸⣿⣿⣿⣿⣷⣾⣽⣏⢉⠉⣉⣡⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⣀⡀⡀⠀⠀⢀⢀⠀⣀⠀⣀⡀⢀⣀
⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠈⠉⠉⠑⠢⢄⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⣿⠀⠀⠀⠀⠀⠚⠀⠀⠀⠠⠗⠀⠀⠀⠀⠀⠀⠀⠉⠁⣢⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇
⣿⠀⠀⠀⢠⠀⠀⠀⠀⡄⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢋⣴⣓⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣆
⣿⣀⡀⠀⠀⠓⠀⠀⢀⣀⡤⠊⠃⠀⡀⠀⠀⢢⠄⢨⣅⠁⢸⡗⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿
⣿⣿⣿⣄⢠⣼⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢱⡌⢿⣏⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⢾⣷⣿⣿⣿⣿⡄
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⣿⣿⣵⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣷⣾⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣶⢤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⠛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣂⣤⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⢋⣽⠿⣿⣿⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⠀⠛⢋⡌⣿⣿⠏⣿⢋⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣶⣦⣾⡇⡀⢁⣾⣱⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⢠⠒⠒⠒⠈⠛⣿⡿⢿⣿⣿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⠀⠀⠀⠀⠀⠁⠀⡐⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣷⣶⣶⣄⠀⠀⠠⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⠄⠀⠀⠀⠈⠉⠙⠟⠛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡏⠀⠈⠑⠀⠰⢾⣿⣷⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⠿⠿⣟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣆⣠⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⣿⠿⣿⠿⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⢀⣀⠀⢀⣤⡀⠀⣠⣖⠀⠀⣾⣏⢢⡀⣴⣖⠢⣀⣾⣷⣬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣴⣾⣿⣷⣾⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⢿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣤⣀⣀⡀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⣶⡏⣿⣿⣿⣿⠛⠛⣡⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣤⣤⣝⣾⣧⣈⠀⠿⠾⠀⢠⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣧⠙⢻⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⢧⡀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⡟⠿⣿⣷⣄⠀⠉⠛⠻⠿⠿⣿⢻⣷⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡇⠀⣀⠸⠿⣿⣿⣿⣿⣦⣶⣿⣿⣸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⣻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠃⢰⣿⠿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢄⣨⡄⠴⠛⠁⠈⠃⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣻⣿⡖⣶⣿⣶⠠⢄⣀⠀⠀⠀⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠰⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣦⣴⣿⣿⣿⣿⡿⣦⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠀⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⡿⠃⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡿⠿⣿⡿⠿⠻⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣶⣦⠛⠁⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⣙⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣤⡴⠂⣤⣤⠀⡀⠀⠤⣤⣘⣻⣄⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⣤⣀⡀⠀⠸⠏⢤⠀⢰⣯⣿⣿⣿⣄⠃⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⣀⠉⠉⠉⠛⠛⠛⠛⠓⠀⠀⠘⠛⠚⠛⠛⠿⠿⢿⣦⠳⡄⠀⠀⠀⢀⣥⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠄⠠⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⢀⡀⢀⡀⠀⢀⣀⣀⡀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡌⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠠⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠂⡀⠀⠀⠀⠘⠖⡠⠃⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢠⡈⠁⢠⡄⢠⡎⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢈⠓⢊⣱⠟⡿⠀⠀⠀⠐⠂⠀⠀⡀⠙⠃⠘⠀⠰⣇⣨⠃⠀⠀⠀⣶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢻⣿⠇⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠃⠈⠁⠀⢰⣿⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢉⠀⢀⠀⣠⠼⠃⠉⠀⠀⠀⠀⠀⠠⡀⠀⡐⠀⠀⠀⠀⣿⣿⣷⣄⣀⣀⡀⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢳⣾⣻⣿⣠⣀⠀⠠⠄⢘⡃⠠⠀⠋⠐⠄⠐⠀⠂⠈⠉⢻⣿⣿⣿⣷⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠠⠀⠈⠉⠁⢨⠽⣿⣻⡿⢿⢿⠒⠈⠀⡁⢰⠀⠀⠀⢊⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠙⠒⠀⠀⡶⠟⣴⣿⣽⠇⣀⠀⠁⠠⢀⡀⠈⠀⠀⠀⠀⠀⢰⣦⣄⣴⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡀⠻⣿⣷⣼⣿⣶⣿⣿⣿⡇⠀⠀⠀⢢⣤⡆⠀⠻⠗⠈⡿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⢸⡿⠇⠀⠀⠀⠀⠀⠛⠶⢯⣭⣛⣛⠁
⠀⠀⠀⠀⠀⡀⠀⢰⣦⣄⣴⣶⣆⠀⠀⠀⠀⢀⠀⠀⢀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠐⠁⣠⣶⣿⣿⣤⡉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⡴⠛⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠇⠀⠁⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡈⢀⠀⠀⢀⣠⡄⠦⠀⣀⣀⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⣂⡼⠉⠀⠀⠀⠀⠀⠀⠡⠴⡀⠀⠀⠀⠀⢸⣿⣿⡏⢿⡇⠈⠳⠄⢨⠨⡷⡆⠃⠸⠟⢻⡄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠀⠀⠘⠿⠘⠗⠆⠀⠀⢀⡙⠀⠀⠀⠀⢸⣿⠿⢿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⢀⠠⡀⡀⠀⠉⡹⠀⠀⠀⠀⢸⣿⠀⠘⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠤⠀⠈⢀⠀⠀⠰⠷⠿⠿⠿⠷⠟⠀⣠⠁⠀⠀⠀⠀⢸⠟⠃⠀⠈⠁⠈⠀⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣧⠀⠀⢶⣤⣤⠄⢄⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣴⡋⠁⠀⠀⠈⣿⣿⠋⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢷⢣⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⣷⣤⣀⣀⣴⣿⠃⢀⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣄⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠘⠉⢿⡽⠋⠉⠀⠀⠀⠂⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠐⠀⢠⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠐⣣⠀⠀⠀⠀⠀⠀⠸⣵⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠁⠀⠽⠄⠈⠑⠛⠛⠁⠀⡂⠈⠳⢦⡄⢸⣿⣿⣿⣿⣿⣿⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⠟⠃⣠⣬⣤⣤⣤⣄⣠⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠂⡀⠀⠀⠐⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣷⣷⢸⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⠀⠓⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇
⣤⣴⣦⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠁
⣿⣿⣿⣾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣆⡀

⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠉⢉⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠒⠊⠹⣶⠀⠁⠀⢀⠀⢨⠉⣶⠆⢲⠀⠀⢀⠔⢠⠄
⠀⠀⠀⠀⠀⢈⣛⣀⣀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠠⠀⠈⢸⡇⠀⣤⠂⢠⡎⠈⡏⠀⠸⡴⠲⡁⠀⠌
⠀⠀⠀⢀⣾⠛⠉⠉⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⢐⢶⠚⠹⡀⠈⢰⠈⢀⡄⢰⠀⠀⠂⠀⠁⠠
⠀⠀⠀⠘⠿⣶⣤⣤⣼⠟⠁⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠃⠘⠑⢆⠱⣀⠆⡦⠼⠁⠀⠀⢄⣤⠀⢠⠂
⠀⠢⣶⣮⡓⠆⣀⡀⢀⣴⣷⡀⠀⠁⠀⠀⠀⠀⡀⠀⠈⠀⠷⠀⠀⡰⢄⠖⢆⠀⠀⠀⠸⠆⡀⠀⠀⠀⠏⠀⠠⠃⠐⠀⠀⠃⠊⠈⣒⡁
⠀⠀⠀⠙⢿⡾⠻⣷⠟⡉⠉⠁⠀⠐⠀⠀⠀⠀⠑⠦⠀⠀⠀⠀⠀⣩⠊⠀⠈⠧⢠⠘⢦⡀⡨⠋⢣⡖⠐⡆⠀⠊⠈⠉⠀⡄⢠⠉⠀⠈⢂⠐⠉⠁⠑
⠀⠀⠀⠀⢠⣤⡀⠁⢰⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠍⠁⢀⣀⣰⣀⡀⠀⠑⢆⠉⠀⠀⠀⠀⡄⠆⠀⡄⠀⠂⠀⣧⠏⠀⡀⠀⠈
⠀⠀⠀⠀⢸⡟⢷⣄⢻⡇⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣿⣷⡆⠀⢨⠀⠀⡤⠚⠀⠄⠸⡘⡇⠀⠀⠶⠿⠀⠀⠁
⠀⠀⠀⠈⢸⡇⠀⠻⠾⠇⠁⠀⠀⠀⠀⠀⢰⡄⠐⠀⠀⠀⢵⣴⣿⠿⠛⠛⠻⢿⡇⠀⢈⠀⠁⢃⡀⠀⠀⡄⢳⡇⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⢶⣶⣶⣶⣶⡶⢀⠀⠀⠀⠀⠀⠈⠀⢸⡆⠀⠤⣾⡟⢁⠀⣄⣤⢤⢞⣣⠀⠸⣄⠂⢸⠇⠂⠀⢿⠸⣧⠀⠀⠀⣺⠈⠀⠀⣾⡀⠡⠄⠴⠚
⠀⠀⠀⠀⠀⠐⣸⣇⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⣿⠆⠉⢀⡀⡄⠰⠿⢂⠆⡌⠱⠊⠀⠑⠘⠀⠂⠛⠤⠤⠐⠉⠑⠀⠞⠁⠈⠐⠁
⠀⠀⠀⠀⠙⠛⠋⠉⢛⣋⠐⠀⣄⣄⡤⠀⠀⠀⠀⠀⣠⠤⠈⠀⠀⠈⠀⢀⣀⡄⣽⣷⠢⠀⢀⠤
⠀⠀⠀⠀⠀⢸⡟⠛⠛⡉⠀⠤⠤⠔⠲⣀⡀⢠⣶⣾⣿⠷⠒⠓⠑⠲⢿⣿⠑⠀⣻⠟⢁⠐⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠂⢸⡟⠛⢁⣀⢠⠶⣀⣘⠠⢺⣥⣜⡻⠉⠀⠀⠀⠀⠀⠀⠀⠈⢡⠠⢋⣴⣷⠊⠐⢀⠀⠀⢴⠇
⠀⠀⠀⠀⠀⠸⢛⣛⣛⣋⡀⡄⡇⠀⢱⣿⣧⢾⠧⠀⠀⠀⠀⠀⠀⠠⡀⠠⠞⣀⣉⣉⣉⡆⠚⠁
⠀⠀⠀⠀⠀⠰⣿⣭⣉⡉⠀⠀⠿⠀⠀⡿⢣⠘⠆⠡⡀⠀⠀⠀⠀⠀⠓⢀⡼⣿⣿⣿⣿⣷⡆⣠⠀⣀⠀⢀
⠀⠀⠀⠀⢄⣬⣇⣀⣹⣿⠂⠀⠘⣥⠂⣾⠀⡆⠈⢣⢱⡄⡀⠀⠀⠀⠀⠀⢄⣿⣿⣿⣿⡏⠸⣧⡘⠋⠉⠉⠁
⠀⠀⠀⠀⠘⠋⠉⠙⠋⠅⠀⠀⢈⢛⠀⡏⢀⠇⠀⠀⣿⡏⠀⠀⠀⠀⢲⡀⠉⠉⠉⠁⢸⣁⣐⣀⣀⣀⣀⡠⠂⣄
⠀⠀⠀⠀⠰⡄⠀⠀⠀⢀⠔⡁⠈⠈⣼⡇⣸⠀⠀⢸⣿⣿⣦⣄⣀⡀⠀⢇⠀⠀⠀⠀⠀⢻⣿⠿⣿⠿⣛⡃⠀⣸⣗⡀
⠀⠀⠀⠀⠀⠹⣄⠀⡠⢁⠌⠀⠀⠠⠛⠉⠟⠀⠠⣼⡏⡏⠉⠁⠈⣷⠀⢸⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣐⠋⠠⢹
⠀⠀⠀⠀⠀⠂⠈⠃⢴⣅⡀⠀⠀⠀⠀⠀⢸⡤⢠⡿⡀⡇⠀⠀⠀⣼⠧⠼⠄⠀⠀⠀⠀⠛⣻⠋⠙⠉⠀⠀⠙⡯⠀⠁
⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⢙⣒⣤⡀⠀⠀⠰⠴⠛⠂⠑⠃⠀⡀⠀⠓⠒⠀⠀⠀⡀⠀⠀⠄⠀⠀⠓⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⣴⡀⠰⠁⠈⢀⡠⠌⠀⢀⣀⣠⠄⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠀⠈⠐⠶⠏⠄⠐⠒⠓⠀⠀⠀⠠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣄⠀⠘⠲⠶⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠁⠀⣸⠇⠀⠀⢠⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⠴⠚⠁⠀⠀⠀⣿⠀⠠⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⡇⠀⠀⠀⠀⠀⡞⠁⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠈⠳⣄⣀⣷⠀⠀⠀⡀⠀⠙⠶⠊⠙⠋⠀⠀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⢢⣼⣠⠃⠀⠀⠀⠀⠈⠀⠀⠀⣠⠏⠳⡄⠀⠀⠀⠀⠀⣮⠽⠃⢿⣳⢰⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢯⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠿⡗⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣅⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠒⠂⠀⠀⠀⣿⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⣠⠖⠚⠢⠤⠤⠤⠤⠤⠤⠤⠔⠒⠉⠁⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⡖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠖⠒⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠄⠒⠒⠒⠚⠛⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣤⠤⠴⠚⠋⠷⣤⣤⠴⠓⠦⢤⡤⠴⠛⠓⠒⠒⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⣏⠉⣿⠀⠀⠀⠀⠀⢠⠞⠛⢣
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠘⠦⡤⠞⠀⢀⠀⠀⠀⠀⢀⡞⢳⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠸⠤⣿⡀⣧⠞⠀⠀⠀⠀⠀⠀⠀⢰⣛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡿⠀⠀⠀⠈⠳⣬⢶⣯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡄
⠀⠀⢀⣀⠤⠴⠒⠒⠲⢤⣀⢠⡴⠶⠶⠒⠒⠒⠲⡆⠀⢸⡇⠀⠀⢹⠀⠀⣠⠴⠚⠋⠉⠛⢲⡴⠏⠉⠉⢳⢘⡋⠉⠉⠉⢹⠀⢠⡟⠃⠀⠀⠸⠃
⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠘⣾⡄⠀⠀⠀⠀⠀⠀⢳⠀⡸⠀⠀⠀⡸⢀⣾⠃⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠸⡇⢸⡇⠀⠀⠀⣤
⢸⡆⠀⠀⠀⠀⣤⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣤⡴⠞⠀⡧⠀⠀⠀⣧⡞⠡⠀⠀⠀⠀⠀⡞⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡃⡄⠀⢀⡇
⡎⢃⠀⠀⠀⠀⠀⠀⠀⣤⣾⡁⣶⠀⠀⠀⠀⢸⣇⣀⣸⠃⠀⠀⠀⣿⠀⢀⡄⠀⠀⠀⠀⠙⠒⠙⡇⠀⠀⠀⣠⢤⡀⠀⠀⠀⣧⠸⣧⣗⣲⡾⠁
⣇⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠈⠉⠉⠏⠀⠀⠀⠀⠉⠁⠈⠉⡂⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡆⡼⡏⠉⣳
⠸⡄⠻⠀⠀⠀⠘⠛⠀⠀⠀⢀⡿⠀⣀⣀⣀⣀⣀⣀⣰⠀⠀⠀⠀⠀⠀⠀⢈⠙⠢⢄⣀⣀⣀⡠⡴⠦⠀⠐⣧⠀⠀⠒⠈⠉⡟⠙⠧⠼⠛⠁
⠀⣧⠰⢇⠀⠀⠀⠀⠀⢀⠰⣻⠁⠉⠉⣉⣉⣉⣠⣿⠏⠁⠈⠉⠉⠉⠉⣩⡟⠶⣤⣀⣀⣀⣀⡴⠶⠶⠶⠶⠋⠳⠶⠚⠛⠛⠁
⠀⠸⣆⡀⠉⠉⠀⠉⣉⣠⠞⠛⠛⠛⠋⠉⠉⠉⠉⠘⠓⠛⠛⠛⠉⠉⠙⠉⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⣤⡴⠶⠶⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡖⠳⢶⠋⠉⠀⠀⣠⠞⠋⣠⣤⠴⠦⣤⣀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠙⣆⠀⠀⠀⠀⠘⠁⢠⠞⠁⠀⠀⠀⠀⠉⢣⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⡦⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣶⡆⠀⠀⠀⡇⠈⡷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠉⠁⠀⠀⢀⠇⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠤⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠐⠀⠀⠀⠀⠤⠀⠴⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⣠⡴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⣀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⡄⢠⡾⠉⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡷⠚⠁⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⢸⠀⠀⢀⡔⠛⠒⠦⣄⡀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠑⠀⠀⢀⡀⠀⢰⡂⠀⠀⠀⠀⠀⣼⠀⢠⠏⠀⠀⠀⠀⠀⠙⢦⡀⠀⢠⠁⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣄⠀⠀⠀⢰⡏⢹⠀⠀⠁⠀⣀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡘⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⡿⢹⡆⠀⠀⣿⠀⢸⠀⠀⠀⣼⠉⢳⡀⠀⡿⠀⢸⠀⠀⠀⠀⣀⣀⣀⣠⣤⣼⣿⠀⠀⠀⠘⠛⠛⠓⠶⢦⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣻⡇⢸⡇⠀⠀⡟⠀⢸⠀⠀⢠⡏⡠⠚⠧⡼⠃⠀⢸⢉⡏⠉⠉⠉⠉⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠠⣤⡤⠞⠁
⠀⠀⠀⠀⠀⢾⣋⠉⠀⠀⠀⠀⠀⠀⠈⠁⠟⢸⡇⠀⢰⡇⠀⠈⢇⣀⡼⠀⠓⠙⠳⠖⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣤⣤⠟⠳⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠉⠛⢶⡄⠀⠀⠀⣠⠤⠤⠦⠀⣇⠀⢸⠓⠢⡀⠈⠉⠀⡤⠤⠀⢀⡴⠀⠀⠸⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠇
⠀⠀⠀⠀⠀⣀⣠⠤⠴⠏⠀⠀⠀⠙⠲⠂⢤⠀⢿⣤⠞⠓⠋⠀⠀⠀⠀⠓⠒⠒⠒⠲⡆⠀⡖⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣤⣄
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣄⠀⠀⠀⠛⢶⡄⠀⠈
⠀⠀⠀⠀⠀⠛⠦⠤⠤⠤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠾⠤⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠖⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠶⠶⠦⠤⣤⣤⣀⣀⣀⠀⠀⠀⠀⢀⣠⡿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⣀⣀⣀⡈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⢀⢤⡀⠀⠀⠀⠀⢀⣀⠺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠎⠀⠀⠀⠀⣇⣈⡇⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠰⠭⣆⢼⠝⠀⠀⠀⠀⠀⣔⡦⠀⠀⠀⠀⠀⠀⠁⠀⠾⠆⠀⠀⠸⢤⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡤⠤⢤⠀⠀⠀⣀⣀⣀⡀⣀⣤⣤⠀⡤⠤⠤⡄⠀⣠⠖⠂⢰
⢀⡤⠒⠉⠁⠀⠉⠳⣼⠉⠉⠁⠀⠈⡅⢰⠁⠀⢸⢀⡴⠋⠀⠀⠀⠛⠁⠀⠈⠶⠂⠀⠀⢸⠀⡏⠀⠀⠈
⢸⠀⠀⠀⣤⠀⠀⠀⣿⠀⠀⠀⢠⡤⠇⣸⠀⠀⢸⡞⠁⠀⠀⠀⡔⠋⡀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡆
⡆⠆⠀⠀⠀⠀⠐⠺⢤⡆⠀⠀⠠⠧⢤⡇⠀⠀⢸⡄⠤⡀⠀⠀⠈⠉⠙⠀⠀⠰⠲⠀⠀⠀⡆⢳⡧⢞⠁
⢣⠸⠀⠀⠀⠦⠀⠀⢈⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠧⢀⠀⠀⠀⣠⡄⠀⣤⠀⠡⠠⢐⠇⣏⡤⠞
⠘⡄⢆⣀⠀⢀⡀⠄⣾⣉⣉⣉⣉⣩⣿⠓⠒⠒⣂⣀⡸⠳⢤⣀⣈⡠⠶⠶⠶⠊⠲⠒⠒⠊
⠀⠑⠦⠤⣤⠤⠴⠊⠉⠉⠁⠀⠉⠀⠈⠉⠉⠁⠀⠉⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⢤⡴⠚⠉⢉⡽⠛⣉⣁⣉⡉⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠙⡆⠀⠀⠀⠋⡰⠋⠁⠀⠀⠉⢂⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠻⠃⠀⠇⠀⠀⠀⠀⡅⠀⠐⠿⠀⠀⢸⠀⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡳⠄⠠⠄⠊⠀⠀⠀⠀⠀⠙⢤⣀⠀⢀⡠⠊⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠈⢳⡀⠀⢀⡴⠒⠒⠦⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠔⠒⠉⠉⠉⠉⠉⠉⠉⠉⠁⠒⠒⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡴⠁⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡦⠂⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠁⠀⠀⠀⠆⠀⠀⡀⠀⠀⢀⡁⠀⠀⣈⣀⠀⠀⠀⠀⠀⣰⠏⠀⡀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠆⠀⠀⠀⢀⠄⠀⠀⠀⢨⡀⣠⠌⠀⠉⠁⢠⣀⠀⣠⠁⠀⠃⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⠀⠀⢀⠞⡇⠀⠁⢀⡀⠀⢸⠀⡁⠀⠀⠀⠀⠀⠈⢆⡏⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⠁⡇⠀⢸⠀⡷⠀⠀⠏⢹⡄⡸⠀⣧⣤⣤⡤⠤⠤⠤⠼⠷⠀⠀⠉⠉⠙⢓⡆
⠀⠀⠀⢠⡶⠒⠒⠒⠒⠒⠒⠛⡆⡇⠀⣿⠀⢡⠀⡸⠰⠡⢍⡇⠀⠰⠊⠀⠀⠀⠀⠀⠀⠣⣀⣀⡦⣌⡽⠋
⠀⠀⠀⠀⠉⠓⢦⠀⠀⢀⠤⠤⠁⢇⠀⡗⢢⠀⠉⠁⠤⠤⠤⠆⠀⠰⠀⡄⠀⠀⠀⠀⠀⢀⣸⠇
⠀⠀⠀⢠⠔⠒⠊⠀⠀⠈⠁⠐⡆⠸⠖⠉⠁⠀⠀⠀⠉⠉⠉⠳⠀⠋⠉⠁⠀⠀⠀⠀⠀⠈⢧⣀⡀⠀⠀⢠⣖⠒⠲
⠀⠀⠀⠸⠤⠀⣀⣀⣀⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⣼⣧⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣤⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠺⡖⣤⣤⡄⠈⣣⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢙⡄⣈⣼⣷⣼⣺⣇⠝⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢘⣷⣿⣿⣿⣿⣿⣿⣧⡀⠀⠸⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣶⣿⠿⣿⠏⠁⣽⠻⣿⣿⣿⣷⡀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠉⠀⠀⠀⠠⠀⠀⠀⠩⠛⠋⠙⠃⠀⠸⣷⠀⠀⠀⠀⡐⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣠⠊⣽⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠌⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠉⢀⢠⠆⢈⣀⡀⢈⠛⠚⣡⠞⢹⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⢀⠀⠊⢀⠞⠀⣀⠾⠚⠛⠿⡖⢆⡀⢀⡀⣠⣶⣿⣿⣿⣷⣿⣧⣤⠏⠀⠈⢧⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠛⠀⢰⠇⠀⠀⣀⠀⢻⣤⣧⣤⣿⠟⠉⠋⠛⠿⣿⣿⡏⠀⠀⠀⠀⠀⣿⡼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡆⢀⣀⠀⠀⣴⢺⣿⣿⠋⠡⠔⠁⣀⠀⢉⣿⡇⠀⠀⠀⠀⠈⣿⠃⢈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢡⡈⠉⠀⢀⣿⡿⡟⣧⣜⠲⣤⡄⢨⣤⢞⣿⡇⠀⠀⠀⠀⠀⢷⣄⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣠⡴⠋⠑⠒⠊⠘⢷⣿⠟⠻⠦⢠⡶⠛⡫⠀⣿⣄⠀⠀⠀⠀⠀⡞⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⡷⢶⡆⠙⠻⡆⠀⠀⠀⣠⣿⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⠁⠈⠀⠀⠀⣦⠐⠆⠀⠀⠀⠀⠠⠤⡄⢀⠠⠁⠀⢹⡆⠘⣿⠀⠀⢰⢿⡏⡏⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⢄⠀⠀⠀⢸⠀⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡆⠀⠈⣿⡖⣿⡶⠏⢁⣿⣷⣦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣳⣿⣡⣠⠚⠃⢸⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⣼⡿⠁⠀⠀⠒⠀⠀⠀⠀⠀⢸⣿⣏⡀⣒⣟⡥⣮⡼⠁⠀⠀⢿⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣼⠀⠀⠈⠁⢀⡤⠊⠀⠀⠀⠀⢠⠄⡈⣙⣿⡇⠉⢩⡄⣾⠂⠀⠀⠀⠀⠹⣯⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠰⣯⠾⢻⡀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠐⠋⠃⣾⣷⣥⣠⣀⠀⠀⠀⣼⠏⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡂⢠⣏⣽⡆⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣛⣲⣶⣿⣿⣿⣷⣬⣷⣄⡀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢠⢲⡏⠁⠀⠈⠙⠛⠳⢾⡧⣤⣀⣄⠀⠀⢘⣷⣤⣷⣶⣿⡿⠿⠛⠉⠉⠋⣿⣿⣧⣟⣻⡿⣿⣫⣾⡇
⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠈⣶⣽⢦⣤⣀⣀⣄⠀⠀⠀⠐⠭⡛⢟⣋⣩⣥⠭⠉⠋⠁⢠⣤⣤⣾⣔⣤⡿⣿⣷⣿⣿⣷⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠚⠒⡅⠀⠛⠈⠉⠀⠀⠀⠈⠀⠀⠈⠙⠦⣤⣄⣀⠈⠛⠿⣿⡶⠶⠖⠛⠛⠛⠉⠙⠉⠉⠉⠀⠐⠛⠛⠛⠛⣏⣉⣉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠠⠤⠀⠀⠶⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠑⡀⠀⠠⠫⠹⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡎⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃⠀⡙⢿⣿⠀⠀⠀⢀⣀⠰⠄⠚⠻⡃⠀⠈⠁⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣀⠀⠀⡀⢀⠄⠀⢾⡿⠢⡟⠀⠐⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠚⠀⠀⠈⠀⢰⡇⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠣⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⠀⢀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠍⠁⠀⠀⠀⠀⠀⠐⠀⠀⢠⠀⢨⠓⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣃⠄⠁⠀⠀⠱⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⡠⢤⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠔⠀⠀⠀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡧

⠀⣼⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠄⠀⢀⡀⢀⠀⡀⠀⠐⠂⢀⢀⡀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠃⠐⠀⠀⠀⠀⠀⠙⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⡀⠀⠀⠂⠘⠂⠒⠒⠊⠓⠘⠀⠃⠚⠈⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣦⠀⠠⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⡃⠀⠀⠀⠀⠀⠿⠇⠠⠭⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⢶⢤⣤⣿⣼⠃⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠈⢀⠂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠠⣦⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠳⠆⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢶⠖⠒⠒⠂⠒⠆⠀⡀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠒⠠⠋⢻⠀⠀⠀⠀⠀⡒⠺⠋⠂⠰⣶⢤⣀⣶⣶⢚⣶⣛⣦⣤⣄⡄⠀⠙⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣤⠶⠖⠲⢶⡤⠶⠚⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⠿⡉⠙⠏⠀⠀⢀⡴⠋⣠⠴⠒⠛⠓⠦⣄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣀⠀⠀⢹⡄⠀⠀⠀⠈⠀⡜⠁⠀⠀⡀⠀⠀⠈⡆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠿⠂⠀⢰⠃⠀⠀⠀⠀⠀⡇⠀⠀⠸⠿⠂⠀⠀⣸⠀⠟⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠉⠁⠂⠀⢀⠀⢀⠀⠀⠀⠀⠈⠛⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⢻⡄⠀⣠⠞⠋⠁⠀⠈⠻⣆
⠀⠀⠀⠀⠀⢿⠀⢀⠔⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡴⠃⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠈⠳⣬⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⣤⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡆⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠁⠀⡀⠀⠀⠈⠀⠀⠀⠳⠀⠀⠀⠀⠃⠀⠀⡠⠛⠲⢤⣀⠀⠀⠀⠀⢀⡞⠁⢀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠀⠀⠀⡀⠀⢰⠂⠀⠀⠀⠀⢀⡇⠀⡞⠁⠀⠀⠀⠈⠓⢄⠀⠀⡾⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣤⡀⠀⠀⢠⡞⢹⡀⠀⠁⢀⣀⠀⠀⢸⡇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠳⣠⡇⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢰⠇⣷⠀⠀⣸⠀⢸⠇⠀⠀⡞⠉⣧⠀⢸⠃⢸⡀⢀⣀⣀⣀⣀⣀⣠⣤⡿⡇⠀⠀⠈⠙⠛⠓⠶⢦⡀
⠀⣀⣤⣤⣤⣤⣤⣤⣤⣭⣿⡄⣿⠀⠀⣿⠀⢸⡆⠀⢰⢃⠖⢙⠶⡏⠀⠸⣉⡏⠉⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠰⢦⡶⠚
⠘⢏⣀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢿⠀⠀⡏⠀⠀⢧⣠⠞⠈⠉⠙⠒⡇⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠞⠙⠒⠛⠁
⠀⠀⠈⠑⣦⠀⠀⠀⡴⠒⠒⠃⢸⡀⢀⣏⣙⠄⠀⠀⢠⡖⠲⠤⠴⠇⠀⠀⠓⠒⣦⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⣠⠤⠖⠚⠋⠀⠀⠀⠙⠛⠓⡆⠘⠷⠞⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⣳⠀⢟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⣴⠒⠚⠲⢤
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄⠀⠀⠉⣳⠀⢀⣸
⠈⠉⠉⠙⠛⠓⠒⠲⠶⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠟⠀⠀⠈⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⠤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣛⣓⣲⣶⣶⣤⣤⣤⣶⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣋⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡴⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛
⣤⠤⠦⠤⢤⡀⠸⡧⣾⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⢸⡇⠀⠸⡳⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢹⡄
⣿⠀⠀⠀⠀⠙⣦⡟⢳⣠⠞⠁⣤⡏⢀⡔⠋⠁⢸⣷⠶⣦⣰⠲⣆⣞⡉⢩⡿⢾⠈⣛⣷⣰⠋⢻⣤⠖⢶⠖⠒⢦⠀⣠⠴⠟⠉⢻⠀⡇⢰
⣿⠀⠸⠟⠀⢠⠙⠃⢸⠛⠦⠤⡄⠈⣾⡀⠻⠃⠀⣿⡀⠉⠁⠀⡏⡴⠚⠀⢙⠸⡄⠳⠶⣤⡀⠈⡇⡄⢰⢲⡀⠸⡏⢧⠀⠛⠀⢸⣠⣟⣿
⢿⣀⣀⣀⡤⢋⠀⠧⠼⢃⡏⠉⠁⣀⢇⠙⠚⡆⠀⡇⠙⠦⡤⠞⠀⠓⠒⠒⢋⡀⠙⠒⠚⠃⠙⠉⣀⠉⢉⣈⠙⢛⣁⣌⠉⡇⠀⠘⡏⢣⡼
⡼⠮⠭⠤⠔⠋⠲⠶⠞⠦⠭⠭⠭⠕⠋⠙⠒⣇⠀⢻⠓⠦⠤⠴⠋⠑⠒⠒⠋⠙⠒⠖⠊⠉⠙⠋⠉⠋⠋⠈⠉⠉⠀⢸⠀⡇⠀⠀⡟⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠤⣼⣁⡇⠀⢸⠃
⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠶⠋⠀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡾⣏⠀⠈⠉⠀⢀⣾⡀
⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⢠⠟⣗⠦⠤⠤⢞⣿⡀⣠⢄⠀⠈⢠⣄⠀⢀⠀⠀⢀⢦⣀⠀⡄⠉⢀⣀⣈⣃⣈⣉⣃⣒⣾⠿⢹⡇
⢸⡀⡠⣄⠀⢸⠁⡇⠀⢰⠻⡄⢸⠀⠀⠉⡟⠋⢉⡇⠓⠃⠸⡆⠄⡏⠈⠓⠋⠹⡆⢸⠀⠀⠀⣿⠀⢸⠉⠈⠉⢸⡇⠀⣿⢹⡀⢨⠇
⠀⠉⠀⢸⡀⣸⠀⢹⣀⡟⠀⠳⠎⠀⠀⠀⢳⠀⢰⠁⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⢸⠀⠀⠀⢸⡀⡸⠀⠀⠀⠘⣇⠀⡏⠀⠉⠉
⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠎⠀⠀⠀⠀⠳⡴⠁⠀⠀⠀⠀⠧⠏⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⢻
⣀⣠⣤⣤⣀⡀⠀⢸⣇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣷⠀⠀⢸⠧⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⡆⠀⢸
⢿⠀⠀⠀⠀⠉⢳⣈⣷⣾⡀⣠⠞⠋⠙⡗⠀⢀⠴⠞⠛⢳⣀⣤⣄⢠⣤⣤⢀⡖⠛⠛⣶⣸⠇⠻⢤⡄⢸⠷⢿⡀⣠⣤⣄⡤⢤⣀⠀⠀⢀⣠⡖⠚⣷⠈⡇⠀⣿
⢸⠀⠀⣖⡄⠀⠈⠿⡇⠈⡷⣇⠀⠘⠛⠳⣤⡏⢠⣤⠀⢸⣿⠈⠻⠼⠀⢸⠞⣓⣢⠈⠳⡸⡇⢴⣒⡓⠛⠀⠈⡏⡇⠈⢁⡀⠀⢹⡶⢾⠉⠡⡆⠀⢻⠀⣧⣤⡏
⢸⠀⠀⠉⠀⠀⡼⠀⡇⠀⡇⢈⣍⣩⠆⠀⡟⢧⣀⣁⠀⢸⡹⣆⠀⠀⠀⡜⢸⣁⡀⣀⡠⠃⢣⡀⠉⣹⠿⣄⣀⠇⠧⢤⠇⢹⣀⣈⡇⠘⠦⣤⠀⠀⢸⣶⡧⢾⡅
⢸⡤⣤⠤⠴⠋⣠⠀⠙⠛⡁⢾⣀⣀⣀⡴⢣⣄⠀⢹⠀⠈⣇⡈⠛⠛⠋⢀⣀⡈⠉⠉⣠⣄⠀⠉⠉⣩⣀⣀⣀⣤⣀⣀⡰⢦⣀⣠⠤⠶⡄⢸⠀⠀⢸⣇⣨⠟⠁
⡞⠓⠲⠶⠒⠋⠈⠓⠚⠛⠓⠶⠶⠶⠖⠚⠁⠈⠙⢻⡆⠀⣿⠙⠲⠶⠖⠋⠀⠉⠉⠉⠁⠈⠙⠓⠋⠁⠈⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⡏⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⡇⡼⠀⠀⢸⠁
⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠶⠾⠁⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⢠⢞⡏⠀⠀⠉⠀⠀⢀⣿
⢻⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⢠⠿⡷⢤⣀⣀⣠⢞⣏⠀⢀⣄⠀⠀⠃⢀⡀⠀⠀⠁⠀⠀⣠⡄⢠⢤⡀⠐⠀⡀⢀⡘⢦⣙⠒⠦⠤⠤⣒⡿⢹⡄
⢸⠀⠀⡀⠀⠀⢰⠛⡆⠀⠀⡴⣄⠀⢸⠀⠉⠒⣦⠥⠶⢻⠉⢧⡞⠈⡆⡀⢰⠏⠙⣤⡼⠶⡆⠀⡟⠈⠁⠀⢷⠀⠀⡟⠚⠙⠚⢹⡏⠛⢻⠻⡇⠀⢸⡇
⠘⠧⠞⠉⡆⠀⣟⠀⢧⠀⢸⠀⢸⣀⡿⠀⠀⠀⢹⠀⠀⢸⠀⠀⠀⠀⣧⠀⢸⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⠃⠙⠦⠼⠁
⠀⠀⠀⠀⢳⣀⡇⠀⠘⠳⠞⠀⠀⠉⠁⠀⠀⠀⠘⣇⠀⡾⠀⠀⠀⠀⢻⠀⢸⠀⠀⠀⠀⠀⣟⢀⡇⠀⠀⠀⠘⣦⡼⠁⠀⠀⠀⠀⠳⣤⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⠴⠶⠒⢶⣤⠶⠚⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠓⠚⢯⡉⠛⠀⠀⢀⡴⠋⣠⠴⠚⠛⠓⠲⣄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⡀⠀⠀⣧⠀⠀⠀⠀⠀⡜⠁⠀⢀⣀⠀⠀⠈⡆⠸⣆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠋⠀⢀⡏⠀⠀⠀⠀⠀⣇⠀⠀⠘⠟⠁⠀⠀⡇⠀⠋⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣳⣄⣀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠈⠀⠀⠄⠀⠄⠀⠀⠀⠀⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣠⡤⠤⢤⣄
⠀⠀⠀⠀⠀⡟⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⢷⠀⣠⠞⠁⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⢷⡀⢴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣸⠞⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⠀⠀⠀⠀⠸⠁⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⣜⡀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⡇⠀⣠⠊⠀⠉⠓⠦⣀⠀⠀⠀⡞⠀⠀⠂⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⢶⡀⠈⠇⠀⠀⠀⠀⢀⡇⠀⠃⠀⠀⠀⠀⠀⠈⠳⡀⢸⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⢳⡀⠀⢀⡏⠀⡇⠀⠀⣰⠶⣄⠀⢸⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡀⠀⠀⠶⣯⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣿⢸⡇⠀⢸⠇⠀⡇⠀⠀⡏⣠⢿⣄⡜⠀⢸⠶⡖⠒⠂⠊⠛⠋⠉⠋⣹⠁⠀⠀⠀⢀⣀⣀⣽⠇
⢰⡞⠋⠉⠉⠉⠉⠉⠉⠉⢻⢸⡇⠀⢸⠀⠀⢧⠀⡸⠁⠓⠲⢬⡇⠀⠘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠈⣤⣀⣨⠥⣤⣼⠟
⠀⠙⠓⢦⡀⠀⠀⢀⣠⠤⠼⠀⡇⠀⣸⠒⡄⠈⠉⠁⡤⢤⣀⣀⡇⠀⠈⠧⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⢀⣠⡤⠴⠃⠀⠀⠈⠒⠶⢤⠀⢷⣤⠟⠛⠁⠀⠀⠀⠓⠒⠒⠒⢢⠀⡶⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠀⠀⣠⠤⠴⢤⣄
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⠀⠀⠙⢲⠄⠀⢨
⠈⠓⠒⠒⠲⠶⠦⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡼⠂⠀⠀⠛⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⡍⠭⠭⢝⣽⡿⣿⠉⠉⠿⠭⠭⠉⢕⣒⣒⣶⡿⠺⠭⠭⠭⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠥⠴⠶⠚⠛⣛⣉⣉⣉⣉⡑⠒⠈⠉⠓⠒⠒⠒⠒⠛⠋⣉⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠋⠉⠉⠉⠉⠉⠙⠛⠶⠤⣤⠤⠴⠶⠚⣉⣩⣍⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⣇⣀⣀⠀⣀⣀⣀⠀⠀⠀⢀⡒⣂⣠⡤⠔⠒⠉⣉⡉⠠⠬⡭⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣤⣤⣤⣤⣤⣄⣉⣉⣁⣉⣀⣀⣀⣤⣶⠷⠟⠃⠈⠁⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠛⢋⣉⣁⣀⡉⠉⠙⠛⠳⠶⠖⠚⠑⣉⣠⣤⡴⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣻⣿⣽⣿⣿⣿⣻⣿⣿⣶⣶⣾⣿⣯⣿⣿⡻⣶⣯⣳⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣇⠀⠀⠀⠀⠀⠰⠖⠀⠶⠆⠠⠶⠶⣶⢾⠷⡿⣿⣻⣭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣴⣶⡶⣶⠾⡿⣟⣣⣤⣾⣿⣿⣿⡈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡏⡀⠀⠀⠹⣿⣿⣿⣿⡿⣿⣿⣧⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⢿⣿⣷⣮⣿⢧⣄⢠⢀⣜⣽⣿⣿⣿⡇⣿⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡛⡼⣏⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡙⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡉⡛⡌⠠⡻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣙⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⢗⡜⣦⡄⠡⡼⡟⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣷⣦⣍⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠰⡸⣽⡜⣿⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⣹⣿⣿⣬⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣹⣏⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣍⡻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠏⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⣠⡀⠀⠀⠀⠀⠀⣠⣤⡀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠟⠀⠀⠀⠀⠀⠷⠞⢁⣌⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣲⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣤⠴⣄⠀⠀⢺⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡝⣉⡀⠀⠀⠀⠀⠘⣧⣼⠇⠀⠀⠀⢸⡇⠀⢸⠂⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠈⢯⡽⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⠛⠋⠀⠀⠸⡽⠇⠀⠀⠀⢠⡖⢦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢿⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⣤⣀⠙⠋⠀⠀⠀⠀⣀
⠀⠀⣠⠶⠋⠉⠉⠉⠉⠉⠉⠛⢷⡀⠀⡴⠒⠛⢻⡴⠛⠉⠉⠙⢦⡀⠀⣠⠶⠛⠉⠉⠛⠶⣄⠀⢠⡞⠁⠀⠀⠀⠀⠉⢳⡀⢀⡴⠚⠉⠉⠙⠛⠲⢦
⠀⡴⠃⠀⠴⠀⠀⣀⣀⡀⠀⠀⢸⡇⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⣴⠋⢠⠄⠀⠀⠀⠀⠈⢳⡟⠀⠀⠖⠀⠀⠀⠀⠀⣷⡏⠀⠀⠀⠀⢀⣠⣤⡾
⣸⠁⠀⠀⠀⣴⠛⠉⠉⢻⣴⣆⣼⠁⠀⡇⠠⡄⠀⢠⣤⠀⠀⢀⣤⢿⡇⠀⠈⠀⣀⣀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣠⠤⠴⠒⠙⣆⣀⣀⣀⡀⠈⠛⠓⠦⣄⠀⣴⢲
⡏⠀⠀⠀⢸⠃⠀⠀⠀⠈⠁⠈⠁⠀⠀⣷⠀⠀⠀⢸⣸⠀⠀⠀⢷⣸⠀⠀⠀⢰⠁⢸⠀⠀⠀⠀⣿⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⢳⡀⠀⠀⠈⣧⠈⠋
⣧⠀⠀⠀⢸⡀⠀⠀⡟⠛⠛⠛⠛⠛⠛⠛⢻⠀⠀⠀⠉⠀⠀⠀⠀⢻⡄⠀⠀⠈⠓⠋⠀⠀⠀⢀⣧⣤⣤⣀⠀⠈⠛⠛⢶⣠⡶⠶⢤⣄⣤⠞⠐⣦⠀⠀⣻
⢹⡀⠀⠀⠈⢳⡀⠀⠛⢶⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠶⠤⠷⠀⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡿
⠈⢳⡀⠀⠀⠀⠉⠛⠒⠋⠀⠀⠀⠀⣿⢻⠉⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⡏⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁
⠀⠀⠙⠳⣦⠀⠀⠀⠀⢀⣤⡄⠀⠀⣿⢸⣀⣀⠀⠀⣿⠙⣦⠀⠀⠀⢀⣸⠟⣆⢠⣶⠀⣤⡇⠀⣇⡾⣇⠀⠀⠀⢠⡶⢾⠁⠀⠀⠀⠀⠀⠀⣤⡀⡿
⠀⠀⠀⠀⢸⠀⣀⠀⡀⢸⠀⣷⡆⣴⣿⠈⠉⢹⡇⠀⣿⠀⢹⠀⣤⡄⣿⠉⠀⣿⢸⡏⠷⠿⠇⠀⠀⠀⢻⢰⢷⡀⢸⠁⠘⣇⢸⢳⡄⣾⢧⠀⡏⠛⠁
⠀⠀⠀⠀⢸⢸⡟⠞⢻⢸⡆⠀⣿⢿⠀⠀⠀⠘⣿⣧⣿⠀⢿⠀⡇⠙⠋⠀⠀⢹⢸⠇⠀⠀⠀⠀⠀⠀⠈⠛⠘⡇⣸⠀⠀⠹⣾⠈⠷⠏⠸⣦⡿
⠀⠀⠀⠀⠘⠿⠀⠀⠘⠿⠀⠀⠹⣾⠀⠀⠀⠀⠀⢸⣿⠀⢸⣄⡇⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⡿⢿⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⣰⣿⠇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢿⣷⡀
⢠⣿⡏⠀⠀⠀⠀⠀⠀⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠃⠀⠀⠀⠀⠀⠈⣿⣧
⣸⣿⠁⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⢹⣿
⣿⣿⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠙⠛⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⢀⣤⣄⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠻⣿⣶⣿⠟⢿⣷⣾⡿⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁
⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⡿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⠎⠘⠀⠀⠀⠀⢀⠀⠀⡠⠒⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢄⡤⠁⠘⢄⠀⢇⠀⢀⡠⠤⠀⠺⣄⢀⡜
⠀⠀⠀⠀⠀⠊⠁⠀⠈⠉⠁⠉⠑⠊⢢⡀⢄⢡⠀⠑⢟⣀⣈⣙⡷⠻⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠈⠒⠁⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠉⠀⠀⠀⢀⠴⠊⠁⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⡀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡶⠀⠁
⣠⣤⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢋⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣿⠗
⠉⠁⠀⠀⢠⠏⠀⠀⣀⠀⡀⠀⠀⠀⠈⡄⠣⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡸⠱⡀⠀⠀⢀⢼⠔⢒⢼⡀
⠀⠀⠀⠀⣼⠀⠀⠈⠢⠥⠃⠀⠀⠀⠀⢱⠀⠑⣄⠀⠀⠀⠀⠀⠈⡡⠊⠀⠀⠀⠈⠒⠀⠆⢠⢇⣸⣭⠕
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠈⠀⠄⣀⡠⠤⠚⠀⠀⠀⠀⠀⠀⣀⡤⢦⣳⠄⠠⠛⠈
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢠⠦⠔⠃⠀⠀⠤⠴⠒⠒⠂⠀⠐⠲⢄⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⡶⣷⠄
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡞⠚⠫⢉⡉⠉⠁⠀⠀⠀⠀⠒⠂⠀⢀⣀⠜
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠀⠀⠖⠐⢂⡨⠟⠁
⠈⠑⠂⠠⢐⢉⣽⢮⠂⠀⢸⠁⠀⢈⡩⠟⠁⠒⡲⠛⢻⡟⣁
⠀⠀⠀⠀⠀⠀⠫⠭⠤⣠⡈⡗⠊⠁⠀⠀⠀⠘⠒⠚⠙⠛⠁⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠒⠒⠂⠀⠀⠐⠒⠒⠒⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠶⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠶⠶⢦⣤⡀⠀⠀⠀⠀⣾
⠘⣇⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣅⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⢠⡟
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠶⠶⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠶⠶⠶⠞⠋⠁⠀⠀⠀⣸⠃
⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠶⢶⣤⣤⣀⣀⣀⣀⣀⣤⡴⠶⠶⠖⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⣧⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⠇⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⣠⣴⠶⠶⠚⠛⠛⠛⠛⠛⠛⠶⢶⣤⡀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣾⣋⣁⣀⣀⣤⣤⣴⠶⠶⠶⣤⣤⣀⣀⡀⠙⣷⣄⣤⡾⠋⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣓⣒⣦⣔⣶⣤⣴⣶⣞⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣀⣀⡀⢀⣀⣀⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢋⣭⣭⣝⠛⠛⠛⣿⣿⠛⠛⠛⣫⣭⣭⡙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢱⣿⣿⣿⣿⣇⠀⠀⣿⣿⠀⠀⣾⣿⣿⣿⣿⡆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⣿⣿⣿⣿⣿⣿⣷⠘⠋⣾⣿⣿⣿⣿⣿⣿⡇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡌⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⢡⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣌⢿⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⡿⣡⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠹⣿⣿⠿⣿⣦⣴⣿⣿⣿⣿⡏⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢻⣿⡆⠀⢸⠁⠀⢸⣿⡿⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢸⣿⡇⠀⢸⠀⠀⢸⣿⡇⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠈⣧⠀⢸⠀⠀⡿⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠀⢸⠀⠀⣧⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⢀⡟⠀⢸⠀⠀⢻⡀⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⡄⠀⠈⠀⠀⢸⣿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠉⠉⠢
⠀⠀⣀⠠⠤⢄⡀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⡅
⢠⠊⠁⠀⠀⠀⠈⠢⡀⠀⠇⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠙⣄⠸⡀⠀⠀⠀⠀⢀⠁
⢱⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠱⡀⠀⡀⠀⡘
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠈⣆⠙⢦⠀⣠⠃
⠀⠀⠈⠓⠤⣄⣀⠀⠀⠀⣀⡸⠤⠇⠉⠁⠑⠒⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡽⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⠙⢂⠶⠴⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠸⠁⠋⠈⣋⣈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⠐⢣⠴⢄⣀⣀⢸⠃
⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠚⠀⠒⠁⠀⠀⠀⠀⢼⠃
⠀⠀⠀⠀⠀⢀⡔⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠦⣤⢤⢀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠛⢦⠀⠀⢱
⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⣀⡄⢶⠒⡎⠒⠤⡖⠲⠤⠞⠉⠁⠀⠀⠀⡱⠀⠀⢉⠆
⠀⠀⠀⠀⠀⠀⠐⢄⣀⣸⡌⢳⡙⣦⡓⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⡏⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡹⡿⣌⢲⠦⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⠈⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠃⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡤⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠥⢦⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⣷⠈⠳⡀⢠⠖⣉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⡇⠸⡷⡄⠈⠛⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⠃⠀⣷⠙⢄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⠀⠀⠑⣦⣄⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢭⡙⠲⣾⠀⠀⢸⡀⣧⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡘⠓⠶⣧⣦⠙⠆⢦⠈⢷⣌⠳⢾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⣁⠀⠀⠀⠀⠛⠂⠈⠳⢤⣈⡉⠀⠀⠙⠷⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⢀⡴⠋⠁⠠⠒⠉⠉⠉⠁⠀⣀⡤⠖⢒⣠⡤⠤⠄⠀⠀⠉⢙⡛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⣰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⠒⠒⠛⠛⠙⠛⠓⠂⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⡰⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠲⣄
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣆
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢻⡀
⠀⠀⠀⠀⠀⠀⡖⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡇
⠀⠀⠀⠀⠀⣸⠁⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢸⡇
⠀⠀⠀⠀⠀⣿⡄⠀⢸⠁⠀⠀⠀⠂⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⢀⡼⣡⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢢⡀⣀⢸⡇
⠀⠀⠀⠀⠀⣿⠃⠀⢸⡆⠀⠀⠀⢀⣤⣤⣤⣤⣤⠴⠖⠒⢾⡆⠉⠛⠋⠛⠁⠀⠀⣄⣀⣠⡴⢻⣿⣷⣦⣄⣀⠀⢹⡏⠘⡇
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠠⠟⠀⠀⠠⠤⠤⠔⡂⠔⠈⠁⠀⠀⡀⢠⡀⠀⠀⠈⣹⠟⠓⠾⠿⣿⣧⣄⣉⣷⠘⡇⢰⠇
⠀⣠⡴⠶⠶⣿⣤⣄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⠀⢠⠊⠀⠲⢤⣤⣤⣤⡄⠀⠀⠀⢸⣇⡾
⡾⠁⣀⣀⣀⠀⠈⣿⠟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⡴⠂⠀⠀⠠⠋⠀⠀⠀⠸⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠟⠛⠛⠳⢦
⠇⠚⠉⠉⠙⢷⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⡶⠶⣤
⠀⡀⠀⠀⠘⠻⣿⢀⠀⠀⢀⠄⠀⠀⠀⠀⣰⠟⠁⠸⣆⠘⠿⢷⡄⠀⠀⠀⠀⠀⣀⣀⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠂⠀⠀⢀
⠀⠹⣆⢀⠀⠀⢿⢸⡀⢠⡏⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⣀⠚⠋⠉⠉⠘⣿⠀⠀⠀⠀⠀⢸⠀⢀⡼⠀⠀⣀⠔⠁
⠀⠀⠈⠻⣆⠀⠼⢸⡇⣾⠀⠀⠀⠐⠁⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⡇⠀⠋⠀⠀⠉
⠀⠀⠀⠀⢹⡄⠀⠈⣿⡇⠀⠀⠀⠀⠀⢀⡴⠟⠛⠹⣄⣴⠉⠳⣄⡙⠒⠤⠤⡀⠀⠀⠀⠀⡟⠀⠀⠀⢸⣾⠃⢀⡤
⠀⠀⠀⠀⠀⠙⠶⠶⢻⡇⠀⠀⠀⣠⠞⠁⠀⠀⣀⣤⡴⠿⣄⠀⠸⡟⠒⠤⣤⣤⣀⠀⠀⢸⠇⠀⠀⠀⣾⡟⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢠⡞⠁⠀⠀⡴⠛⠉⠀⠀⠀⠀⠉⠀⠃⠀⠞⠙⢿⣿⡆⢀⡟⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢴⣻⠖⡼⠁⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠈⠁⢀⡼⠁⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠞⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣤⣤⣤⠶⠛⠉
⣿⣿⣿⣿⣷⡾⢿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣷⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⡿⡿⡿⠿⠿⣿⣷⠿⠿⣿⠿⢿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠒⠒⠒⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠐⠚⠋⠁⠀⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⠠⠄⢀⡈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣰⠃⡖⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢱⢀⠞⠁⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠱⠒⠉⢱⡨⠀⠀⠀⠀⣠⡀⠀⠘⡆⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠰⠄⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠄⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠠⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⢀⠀⠂⠀⠤⢀⣀⡄⢄⣸⠛⣯⡲⢂
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠔⡁⠀⠉⠱⠇⠀⢀⣀⠈⠀⠀⠈⠓⠈⠁⠁⡀⠈⣀⠀⠈⡀⠠⠠⠀⡄
⠀⠀⠀⠀⠀⢸⠀⢠⡰⠀⠀⠀⠂⠄⠀⠀⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠙⢠⡄⠁⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠱⡌⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠔⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠂⢀⠒⠁⠀⠀⠀⠀⢠⠀⠀⢀⠀⢤⢀⢲⠀⠠⠀⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠰⢸⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⣀⡀⢙⢚⢀⣀⢘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢙⢛⡟⠛⠛⠿⣛⠛⠻⢿⣉⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠔⠋⠉⠢⡀⠀⠀⠀⠀⢀⡴⠚⠉⠓⣆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⡌⠀⡀⠀⠀⠹⡄⠀⠀⣠⠋⠀⠀⠀⠀⢸⠀⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⡇⠀⠀⠀⢀⠀⢳⠀⢰⠃⠀⡀⠀⠂⠀⡸⠀⣇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢱⠀⠀⠐⠀⠀⢸⡄⡇⠀⠂⠀⠀⠀⢠⠃⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⠀⠀⣿⠀⠀⢀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡤⡌⢣⠀⠀⠀⠀⡇⠀⠀⠀⠂⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢌⢦⠀⠀⢸⢁⠇⠈⢢⠉⠀⢸⡇⠐⠈⠀⢀⡞⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠛⠃⠓⠒⠛⠘⠛⠉⠉⠑⠒⠚⣄⠀⠀⢀⠌⠉⠙⠋⠉⠉⠳⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⢀⡴⠉⠀⠀⢀⣀⠠⠀⠀⠀⡀⠀⡠⠄⠒⠢⢄⠀⠈⢦⡴⠃⠀⠀⠀⠐⡀⠀⢀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠈⠙⡄
⠀⠀⠀⡾⠀⢠⠦⡤⠤⡤⠵⡀⠀⠀⠁⠞⠒⠲⠰⠒⠘⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠁⠀⠀⠀⠀⠀⠓⠈⠒⠲
⠀⠀⠀⣧⠀⢇⣀⣐⣚⣁⣀⡇⠀⠀⠀⢦⠐⠒⠒⠒⢒⠇⠀⠀⠀⡀⠀⠂⢀⡎⠀⠂⠀⠀⣀⣀⣸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠤
⠀⠀⠀⢧⡀⠈⠢⣤⣠⡤⠊⠀⠀⠀⠀⠈⠒⠤⠤⢒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞
⠀⠀⠀⠀⢹⡀⠀⢀⡠⠄⠀⠀⠀⠀⠀⣀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠉⠁⢀⡞⠉⠙⠓⠲⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⢀⡤⠛⠋⠉⢀⣀⣤⣀⣄⠼⠉⠛⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⣀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⡤
⠀⠀⠀⡼⠀⢀⡔⠋⠉⠳⠤⢤⡄⢀⠀⠀⡤⡶⢋⠀⠀⡏⢹⠀⡆⣷⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢠⠇⠀⡼⠀⠀⠀⠀⠀⠈⠳⠋⠋⠛⢡⠃⡎⣼⠀⡇⢸⠀⡇⢸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠋⠁
⠀⢀⡞⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇⣿⡀⡇⢸⣠⢧⡎⢣⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⡤⢤⠀⠀⠀⠀⢀⡖
⣞⠉⠄⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣷⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⢄⣀⠘⠛⢻⣿⣿⣿⣿⡇⠇
⠀⠀⠀⠰⠀⠀⢀⣾⣿⠿⠟⠛⣋⣹⡄⠀⡀⠹⠧⠅⢀⣸⣿⣿⣿⣿⠁⡂
⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠷⢛⠍⠁⠀⠈⠁⠀⢄⣼⣿⣿⣿⣿⣿⡿⣸⠃
⠀⠀⠀⠀⠀⢰⣿⠙⡿⣠⡶⠋⠀⠀⠜⠂⠀⠔⠘⠛⠉⢻⣿⣿⡿⠱⠃
⠀⠀⠀⠀⢸⣾⡿⢧⣿⣋⣀⠎⠀⠀⠀⢀⣠⠴⠤⠖⢰⣾⣿⠟⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⣟⣇⠈⠇⠉⠁⠀⡀⠡⣀⣤⣯⣶⣾⣿⡿⣫⠅⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠹⡝⣧⣿⣦⠀⠀⢍⢲⡿⠿⣏⡿⠋⠵⢿⡏⠀⠀⠀⠀⢸⡄⠘⠁
⠀⠀⠀⠀⠀⠀⠙⠾⣿⡿⣿⣿⣿⠿⠛⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣶⡀⠀⠀⠀⢿⡀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠢⢄⣀⠄⢻⡄⢀⡼⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⢼⣏⣀⡦⣛⠻⣿⣿⠵⠞⠛⣉⣛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠍⡅⠀⠀⣀⡞⠋⡇⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⢸⡄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⢻⡀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢁⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⣴⡿⠀⠀⠀⢀⣸⣦⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⠟⠁⠀⠀⠀⠈⣟⣿⡇⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠛
⣀⣤⡤⢤⣄⡀⠀⢻⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢸⠧⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢻
⣿⠀⠀⠀⠀⠉⢧⣨⣶⣇⠀⡴⠋⠉⣹⠂⢀⡤⠞⠋⠹⣆⣤⣤⠀⣤⣤⡄⡾⠛⠛⣷⣼⡇⠻⠶⡄⢸⠟⢿⣀⣤⣤⣤⠤⢤⡀⠀⢀⣀⡴⠚⢻⡇⢸⠀⢸
⣿⠀⢠⣶⠀⠀⢸⢿⠀⢸⠾⣁⣀⡉⠙⢦⣼⠀⣴⡄⠀⣿⡇⠘⠶⠃⢨⡟⣙⣲⠀⠳⡄⡇⢰⣚⣛⢻⠀⠘⡏⡇⠈⣡⡀⠀⢹⠖⡟⠁⠴⠄⠀⡇⢸⠦⣼
⣿⠀⠀⠀⠀⢀⠎⢸⠀⢸⡄⡨⠤⠽⠀⢸⠛⢤⣠⡀⠀⡏⢷⣀⠀⠀⡸⠀⣇⣀⣀⡴⠃⠹⣄⣈⣹⠟⢤⡤⠇⠷⠤⠇⠹⣤⡼⠀⠙⠤⡆⠀⠀⣷⢾⡖⣧
⢹⠦⠤⠔⠚⢁⣤⠈⠉⢉⠐⠧⣄⣀⡤⢊⡤⣄⣀⡇⠀⢳⣀⠉⠛⠋⢀⣤⣀⣀⣀⣠⢦⣀⠀⢉⡠⣤⣀⣀⢶⣀⣀⡖⢦⣠⠴⠶⢲⠀⣧⠀⠀⢹⣀⡽⠃
⠀⠙⠓⠚⠋⠁⠈⠉⠉⠉⠙⠒⠒⠒⠊⠁⠀⠈⠉⣷⠀⢸⡇⠙⠒⠒⠉⠀⠀⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡿⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⢾⣣⠇⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠙⠒⠃⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡁⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡒⠤⢤⡤⢞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣌⣙⡒⢒⣒⡽⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣶⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⡀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠶⠶⠶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠋⠁
⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⠤⣄⣀⠀⠀⠹⡄⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢈⡙⠿⣯⣉⠉⠛⢉⡉⠟⠛⠻⠿⣿⣶⣄⣽⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠖⠉⠉⠉⠁⠐
⠀⠀⠈⠻⡄⠀⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⣈⣹⣿⠇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣾⣁⡀⢤⠤⣤⣤⣀⣀⢀
⠀⠀⠀⠀⠙⢆⠀⠀⠀⠈⠙⠛⠿⠿⠟⠛⠉⠁⣴⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢙⡛⠻⠶⣶⣟⢿⡛⢿⣿⣷⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡈⣧⠀⠀⠀⠙⠷⣤⣉⠀⠀⠀⠀⣠⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣀⣀⠀⣀⣠⣴⣾⠿⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢷⣄⠀⠀⠀⠀⠉⠛⠶⠶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠫⠾⠿⡿⠿⠋⠁⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠻⣿⣿⣷⣶⡦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠙⠋⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⡶⠟⠛⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢠⣾⠉⠀⠀⠀⠀⢸⡟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡇⠀⠀⠀⠀⠀⠈⣧⠈⠙⠳⢦⣄⡀⠀⠀⠀⣰⡿⣤⣉⣁⣀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠈⣋⠙⣿⡷⠶⠟⠀⠀⠉⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣠⡶⠏⣡⠀⠀⢹⣇⠀⠀⠀⢹⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠁⠁⣊⡡⠀⠀⠀⠻⣄⠀⠀⣘⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠛⠉⠳⠞⠋⠙⠰⣶⣶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠙⢷⡀⠀⠀⣠⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⢀⢀⣀⠀⠀⢹⡇⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⢸⡇⢠⡾⠋⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠐⠁⠀⠀⠙⠃⠼⢿⣡⣿⢃⣀⠤⠤⠄⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⣿⢀⡤⠴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣿⡀⠀⢠⡔⠒⠐⠒⠀⢀⠀⠉⠉⠉⡠⠆⠒⠂⢠⠀⠀⠀⠟⠋⠉⠀⠀⠀⠁⠀⠙⠋⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⡒⠂⠁⠹⣧⠀⢨⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⢃⠀⠀⠀⠀⠀⢱⡀⠀⢰⡏⠀⠀⠀⢠⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠉⠛⠦⢤⣿⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⣻⠀⠸⡄⠀⠀⠀⠀⢨⡅⠀⠈⢃⠀⠀⠀⠠⠆⠀⢠⡎⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⣄⠀⠀⠀⣀⠔⠁⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠘⢇⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠿⠿⠿⠿⠻⡿⠟⣽⠛⢿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⣻⣟⣛⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣶⣶⣾⣶⣶⣶⣶⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠉⠛⠿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠟⠉⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⣠⣾⣿⠿⠿⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁⠀⣰⣾⣿⠋⠀⠀⠀⠀⣼⣿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀
⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⣼⣿⢿⣿⣦⣀⣀⣀⣴⣿⠏⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣇
⠀⠀⠀⢠⣿⣿⠏⠀⠀⢸⣿⠇⠀⠙⠛⠿⠿⠟⠛⠁⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⢀⣾⣿⡏⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⣼⣿⣿⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣷⣦⣤⣴⣶⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠸⣿⣿⠉⢻⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⣿⣿⡇⠀⠉⠛⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧
⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⢻⣿⡆
⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⣸⣿
⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠃⠀⢰⣿⡿
⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠀⠀⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋⠁⠀⣀⡀⠀⠀⠘⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣶⣤⣄⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣶⣾⠿⠟⠉⠁⠀⠀⠀⠀⠻⢇⣀⡀⠀⠀⠙⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⣤⣴⣶⣶⣶⣶⣄⡀⠈⠛⠁⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠻⠿⢿⣿⡿⠿⠛⠛⠛⠛⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡇⠀⠀⠀⠀⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⢀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣾⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⡿⠿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣶⣿⣿⡿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⣤⡄⠀⠀⠀⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠸⠿⠇⠀⢿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣦⣤⣤⣤⣶⣶⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠟⠉⠉⠉⠉⠉⠉⠻⣿⣿⡀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⣠⣶⣿⠟⠁⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⢠⣶⣾⡶⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠻⣿⣿⣤⣄⣀⣠⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣶⣦⣶⣶⣶⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⣿⣿⡿⠉⠀⠀⣹⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠁⠀⠀⠀⢿⣿⣿⣦⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⢠⣄⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠘⣿⣷⠀⠀⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⣿⣿⣧⠀⠈⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⢰⣿⣿⣿⡄⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠀⠀⣠⣿⡿⠻⣿⣿⣦⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣠⣼⣿⡿⠁⠀⠈⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣡⣬⡻⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⢠⡙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡻⣮⡻⠟⠑⠽⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢤⡙⢦⣠⣾⣗⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⣪⢻⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⡝⣆⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢾⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⡾⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠰⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠂⠀⠀⠀⠀⠀⠸⡀⠀⠀⠠⣀⢤⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢱⠃⠀⠀⢀⡐⠁⣀⠤⠒⠘⡞⠁⠀⠀⣇⣀⠆⠀⠀⢀⡠⠒⠉⠀⠀⢱
⠀⠀⠀⠠⢦⠀⠀⠀⠀⢇⡀⣀⠔⢊⠩⠿⡏⠀⠠⢤⠄⠑⠦⡤⠊⡩⠋⣱⠄⠒⠉⠀⠀⠀⠀⣠⠃⡴⠞⠁⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠚⣉⠀⠀⠓⠾⣄⠀⠸⢤⣋⡠⠴⠳⣆⣀⣀⡀⢤⣐⡨⠔⠚⠣⡀⠀⠀⠀⠀⠘⠤⠠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠁⠀⠀⠀⠀⠙⢆⠀⢀⡁⢀⣴⡆⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠾⠂⢎⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⡀⠀⠀⠰⡰⠀⠀⠀⢀⠤⣄⢀
⠀⠀⠀⠀⣠⢬⡗⣎⣠⠤⠤⠊⠃⠀⠉⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣐⠀⠙⢶⣄⢀⠀⠀⠀⠀⢈⠂⠠⠄
⠀⠀⠀⠀⢯⣉⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⣀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡋⠻⠷⠿⠫⢥⢾⣕⣒⣒⢒⠒⢒⢒⣒⣒⣾⠡⠮⠢
⠀⠀⣀⠀⢈⣿⡿⡟⡆⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⢸⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⡎⠘⢷⣺⡿⠁⡅⠈⠄⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠈⠁⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤
⠀⠀⠀⠀⠠⡇⠀⢀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠐⠚⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣽⠲⢋
⠀⠀⠀⠀⠀⢀⡀⠀⣆⠀⠈⠻⠮⣄⠀⠀⠀⠀⠀⠁⠢⠠⠄⠀⠄⠤⠊⠉⠒⠦⠤⣤⠤⣤⠀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠑⠁
⠀⠀⠀⠀⢀⣀⢴⠉⠁⠀⠀⢀⠇⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠁⠠⢀⠔⠁⢰⠾⡀⠀⠀⠀⠳⢤⣴⣀⡑⠈⠑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠈⠒⠒⠁⠀⠑⠤⠀⠀⠠⠴⠶⠯⢝⡛⠲⠶⣤⣄⣈⠉⢒⠲⠦⠖⢒⡒⠢⢠⠴⠓⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠴⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣚⠛⠭⠿⠿⠶⢦⡤⠄⠄⠴⠁⠀⠀⠀⠀⠀⠉⠁⠐⠒⠒⠒⠀⠐⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠐⠒⠒⠾⢗⣒⣒⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣤⣤⣤⣤⣤⣶⣶⣿⣶⣿⡷⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣦⣾⡟⢻⣟⣿⣿⣿⣿⣿⣿⡉⠹⣿⣿⣟⠉⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣿⣿⣿⢿⣿⣧⠈⢻⡿⠛⠛⠛⠿⠿⠇⠀⢈⣿⣿⣆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠟⠋⠻⣿⠟⠻⣦⢻⣿⠀⠀⢀⣾⣦⠀⢠⡀⠀⠀⢸⣿⣿⣿⣆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣶⣤⣦⡀⠀⠈⣿⣶⣿⡇⠀⢸⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⡆⠀⣠⠀⠀⠀⠀⠀⠀⠉⠿⡇⠘⣟⣿⣿⣿⣿⣿⡄⠀⢿⣟⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠒⠛⠁⠉⠀⠀⠀⠀⠀⠀⣄⠀⠇⠀⣿⣿⣿⣿⣟⠃⠇⠀⢹⢿⣿⠃⠀⠀⠙⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡃⠺⠀⠐⠋⠛⠋⠀⠀⢰⣿⣵⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣟⠻⣿⣠⡤⠀⠙⢿⣿⣿⣿⣿
⣭⡿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢀⡄⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠛⠻⠀⠀⠼⠿⠏⠘⢿
⣿⣿⣿⣶⣭⡓⠶⣤⣀⠀⠀⢄⢠⠥⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠿⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⣿⣿⣿⣿⣿⣿⣶⣌⠙⢿⣧⣄⡄⠀⠀⠀⠤⠖⠁
⢿⣿⣿⣿⣿⡿⠛⠁⠀⣼⣿⣿⣏⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⠟⠀⠀⢀⣰⣿⣿⣟⣭⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣧⣽⠖⣥⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣾⣧⣲⣦⣤⣄⡀
⣿⣿⣿⣿⡗⠀⠀⢸⣿⣿⣯⣷⢟⡹⡇⡩⢬⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠈⠀⠀⠈⠁⠔
⣿⣿⣿⣿⠂⠀⠀⠀⢙⣿⣯⣾⣊⣵⣆⢓⣫⢴⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠶⠂⠀⠀⠀⠀⢀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⢀⣰⣶⡆⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠈⠿⣿⣷⣶⣶⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣾⣿⠿⠋⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠛⠉⠉⠉⠉⠉⠉⠙⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⣼⣿⣏⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣙⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⢸⣿⣿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⣿⣿⡇⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⠀⢸⣿⣷⠀⠀⠀⣤⣦⡀⠀⣾⣿⡇⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣾⣿⣿⠀⠀⠀⣿⣿⣿⣾⣿⡿⠀⣀⣠⣴⣾⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⣾⣿⡟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⢳⣀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣠⣎⠈⢂⠀⢀⣀⣠⠤⠔⠚⣁⣠⠄⣿⣌⣿⣄⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⠿⠛⠉⠀⢘⡏⠤⣴⠾⠟⠛⠉⠀⠙⠛⠛⣏⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠶⠛⢩⣿⡇⣠⣤⣶⢿⢉⠹⢛⠓⠶⠤⢤⣤⣀⣀⡀⠘⣿⣯⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⡁⠀⠀⠀⠀⠄⢹⠵⠛⠒⠚⠛⠻⠧⠾⣄⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠃⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣴⣿⡇⢀⣀⡤⠴⠚⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠋⠉⠀⠀⠀⠀⢿⣶⣶⣦⣤⣤⣤⣀⡀⠀⠠⠀⠀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡋⠀⠀⠀⠀⠀⠉⠁⠒⢴⣾⣿⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣀⡀⠀⠀⣀⠀⠀⠀⠈⠙⣿⡈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⠀⠀⠀⠀⠁⠢⢤⣴⣿⠟⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣄⣀⣀⣀⣀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠨⠿⣿⡿⢻⣿⢿⣟⣥⡴⣣⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣭⣀⣘⡋⠛⠛⠿⣿⣷⣿⣿⣶⣶⣶⣶⣦⣶⡾⢟⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⠦⣤⣬⣭⣽⣿⣿⡛⠛⠟⠿⣛⡵⣣⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡈⠩⠾⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣽⣯⣿⣽⣬⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠲⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣳⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⣶⠀⠀⠀⠀⢠⣖⡶⠰⠾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⠈⠉⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠿⠃⠀⠀⠀⠀⢰⣟⣷⠀⠀⠀⢰⡏⠉⢷⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠟⠸⣟⡆⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠳⠶⠋⠀⠠⣏⡇⠀⠀⠀⢠⠤⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⣯⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡈⠛⠃⠀⠀⠀⣀
⠀⠀⢀⡴⠛⠉⠉⠉⠉⠉⠙⢳⡄⢀⡴⠚⠛⣷⠞⠉⠉⠙⢦⡀⢀⡴⠛⠉⠉⠛⠶⣄⠀⡴⠋⠀⠀⠀⠀⠙⢦⠀⡠⠞⠉⠉⠉⠛⠲⡄
⠀⣰⠋⠀⠸⠁⣀⣤⣤⡀⠀⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠀⡖⠀⠀⠀⠀⠈⢿⠃⠀⠘⠁⠀⠀⠀⢈⡿⠁⠀⠀⠀⢠⣤⡴⠃
⢠⡏⠀⠀⢀⡾⠉⠀⠀⢷⠷⣼⠃⠀⡇⠐⠀⢀⠶⡄⠀⠠⡞⢹⠀⠀⠀⡠⢤⠀⠀⠀⠘⡆⠀⠀⠀⡔⠒⠋⠉⠱⠤⠤⠤⣤⡀⠉⠉⠲⣄⢸⣿
⢸⡇⠀⠀⢸⠁⠀⠀⣤⣀⣀⣀⣀⣀⣧⣀⠀⠀⠷⠃⠀⠀⠹⣿⠀⠀⠀⣇⡸⠀⠀⠀⢀⡇⠀⠀⠀⠧⣀⣀⡀⠀⡀⠀⠀⠀⣹⠀⠀⠀⢹⡄
⠘⡇⠀⠀⠘⣇⣀⣸⣧⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⠁⠀⠀⠀⡼⠻⢿⣶⣄⠀⠀⠀⠹⡏⠉⠉⠛⠋⠁⠨⠃⠀⢸⣧
⠀⣿⡄⠀⠀⠈⠻⠭⡽⠇⠀⠀⠀⣴⢶⠚⠀⠀⢠⣄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⡞⢳⠀⠀⠉⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⢸⡄
⢰⠃⠙⠶⣄⠀⠀⠀⠀⢠⣄⠀⠀⣿⢸⠀⠀⠀⢸⡟⣆⠀⠀⠀⠀⣶⢦⠀⣤⠀⣸⡇⢸⣠⣦⠀⠀⠀⢀⣤⡔⠁⠀⠀⠀⠀⠀⣀⢸⡇⠀⢸⡇
⡿⠀⠀⠀⢸⠀⡀⠀⠀⣏⢹⣤⢠⣼⠈⠛⢻⠀⢸⠀⢸⠀⣠⡀⡟⠁⢸⢰⡟⠷⠿⠇⠀⠉⠸⣄⣶⡀⢸⠀⢻⡀⡶⡄⣴⢦⠐⡟⠛⠀⠀⠘⡇
⡇⠀⠀⠀⢸⣸⠟⠞⣇⣿⠀⢸⢸⠀⠀⠀⠸⢾⣼⠀⢸⠀⡏⠛⠁⠀⢸⣆⡇⠀⠀⠀⠀⠀⠀⠛⠁⣇⣼⠀⠀⢿⡇⠳⠟⠸⣦⠇⢀⠀⠀⠀⡇
⡇⠀⠀⠀⠈⠟⠀⠀⠙⠃⠀⠘⠿⠀⠀⠀⠀⠀⣿⠄⠸⣦⠇⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⣇
⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢀⡀⠀⣿
⣿⠀⠀⠀⠂⠀⠀⠘⠆⠀⠀⠐⠄⠀⣰⣆⢀⡀⠰⠄⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠈⠃⠀⠀⠀⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢻
⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⢸⠞⣧⠀⠀⠀⣴⠀⢠⣦⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⣿⣀⠞⣧⠀⠀⣤⠀⡄⠀⣴⠀⣀⢀⣄⠀⠀⢸
⢻⠀⠀⠀⠀⠀⡼⢻⠀⠀⢀⣄⠀⢰⠃⠀⠀⣿⠀⠀⢰⡏⡇⡾⠸⡄⠀⢸⠇⢳⡀⣷⣴⠀⢸⠉⠛⠀⢸⠀⠀⢸⠶⠻⠞⢹⡆⠉⢸⢹⡄⠀⢸
⢸⠀⢠⣤⠀⠀⡇⢸⠀⠀⣸⢹⡄⢸⠀⠀⠀⢸⠀⠀⢸⠀⠙⠁⠀⡇⠦⢸⠀⠈⠻⠁⢹⡆⢸⠀⠀⠀⢸⡆⠀⢸⠀⠀⠀⢸⡇⠀⢸⠈⣇⠀⢸
⠘⢷⠏⢸⠀⠀⡇⠈⡇⠀⡁⠀⡇⢸⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠸⡇⠀⢸⠀⠹⣦⡞
⠀⠀⠀⠀⡆⠀⡇⠀⣧⠀⡇⠀⠹⠟⠀⠀⠀⠈⡇⠀⢸⠀⠀⠀⠀⣷⠀⣿⠀⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⡇⠀⡏⠀⠀⠀⠀⣇⠀⢸
⠀⠀⠀⠀⢷⣸⠁⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡾⠀⠀⠀⠀⣿⠀⡻⠀⠀⠀⠀⠸⡇⣸⠀⠀⠀⠀⢻⡼⠁⠀⠀⠀⠀⠘⢦⡟
⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠃⠀⠀⠀⠀⠸⣆⡇⠀⠀⠀⠀⠀⣷⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠲⡀
⠀⠀⢀⡠⠤⢄⡀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠗
⢀⠞⠁⠀⠀⠀⠈⠢⡀⠀⢸⠀⠀⠀⠀⠄⠀⠤
⠄⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⡄⠀⠀⠀⠀⠀⡄
⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⣄⠀⠀⠀⢰
⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢢⡀⢀⡇
⠀⠀⠀⠑⠦⢤⣀⡀⠀⢀⣀⣘⠦⠎⠈⠁⠘⠒⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠉⢉⡹⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠒⡲⠖⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⡀⠀⠐⠠⠄⠐⠁⠋⠀⢉⠈⡉⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠦⠄⠃⡴⠔⣁⢀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠂⠐⠊⠀⠀⠀⠀⢢⡇
⠀⠀⠀⠀⠀⠀⡴⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⢱⢦⢤⠄⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⠞⠳⡀⠀⠘⡀
⠀⠀⠀⠀⠀⠈⢳⠆⠀⠀⠀⡀⣄⠲⡒⢲⠰⠶⡖⠒⠲⠖⠉⠁⠀⠀⠀⢸⠄⠀⢈⡅
⠀⠀⠀⠀⠀⠀⠈⢆⣀⣀⣅⠳⣌⢧⣙⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢯⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡙⣿⣮⠓⡾⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠎⠁⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡠⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠶⣄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢻⡄⠙⢄⢀⡔⢉⡉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⣣⠈⣿⢆⠀⠉⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠋⠀⢸⠈⠣⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠅⠀⠈⢲⡤⡤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠠⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠓⠋⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢯⣬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⢰⣿⠗⡘⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣠⢤⡀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⢉⣄⠀⠀⠀⠀⠿⡼⠃⠀⠀⠸⣇⠀⡿⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠘⠾⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠈⠉⠀⠀⠘⠛⠁⠀⠀⠀⣟⡷
⠀⠀⠀⣀⡤⠴⠶⠶⠶⠤⣤⡀⠀⢀⣠⣤⣄⣤⠤⠤⣄⠀⠀⠙⣫⠤⠤⢤⣀⠀⠀⣠⠖⠛⠛⠛⠶⣄⠀⠀⣠⠤⠤⠤⣄⣀
⠀⢀⡞⠁⡠⠀⠀⠀⠀⠀⠀⡇⠀⡏⠀⠀⠋⠀⠀⠀⠈⢳⣤⠞⢁⠀⠀⠀⠈⠳⣴⠇⠀⡤⠀⠀⠀⠘⣦⠞⠁⠀⠀⠀⣀⣸⠇
⢀⡟⠀⠀⢀⡴⠛⠉⢳⣤⣀⡇⠀⡇⢠⠀⢀⣤⠀⠀⣀⠼⡏⠀⠁⢀⣀⠀⠀⠀⢹⠀⠀⠀⢀⡤⠤⠴⢻⡀⠀⣀⠀⠘⠻⠧⣄⠀⡴
⢸⠃⠀⠀⣼⠁⠀⠀⠈⠁⠉⠀⠀⣇⠀⠀⠸⣼⠀⠀⠸⣦⡇⠀⠀⣎⢸⠀⠀⠀⢸⠀⠀⠀⢸⡀⠀⠀⠀⠈⠉⠉⠉⢣⠀⠀⠈⣧⠉
⢸⡆⠀⠀⢻⡀⠀⣾⡉⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⠋⠀⠀⠀⡼⢶⣦⣄⠀⠈⠉⠑⡶⠚⠒⠶⠖⠃⠰⠀⠀⢸⡄
⠀⣧⠀⠀⠀⠻⢯⣹⡿⠀⠀⠀⢠⣤⠼⠀⠀⢀⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⡼⣧⠀⠉⠉⠁⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⣠⠏⣧
⢰⠋⠳⢤⡀⠀⠀⠀⢀⣀⠀⠀⢸⢸⠀⠀⠀⢸⢷⡀⠀⠀⠀⢰⢤⠀⣀⠀⢸⡇⢿⣠⡄⠀⠀⠀⣠⣤⠂⠀⠀⠀⠀⠀⡀⢸⠁⠀⢻
⡾⠀⠀⠀⣿⢀⠀⠀⢸⢹⣦⢠⣼⠘⠛⣷⠀⢸⠀⣷⢀⡄⢸⠋⠸⡇⡟⠷⠿⠃⠈⠉⢹⢰⣆⢰⡇⠸⡄⡴⡆⢴⣆⢸⡟⠛⠀⠀⢸
⡇⠀⠀⠀⢸⣾⠓⢻⣸⠀⢸⣿⡀⠀⠀⠸⢷⣾⠀⣏⢸⠙⠋⠀⠀⣇⡇⠀⠀⠀⠀⠀⠈⠋⢸⣸⠇⠀⢹⣧⠹⠟⠸⣶⠇⢀⠀⠀⢸
⡇⠀⠀⠀⠘⡃⠀⠈⠛⠀⠈⠿⠃⠀⠀⠀⢸⣿⠀⢻⡼⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⠀⠸
⣿⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠃⠀⡼⢧⢠⡀⠑⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠀⢀⡀⢀⣀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠉
⣿⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⡇⠘⠋⣇⠀⠀⢰⢧⢀⡿⡄⠀⠀⡶⣆⠀⡀⠀⠀⢸⢷⡜⠹⡆⠀⢸⣀⣦⣀⣿⠀⠆⢰⣆
⢹⠀⠀⠀⠀⢰⠃⡇⠀⢠⡶⡄⠀⡇⠀⠀⣿⠀⠀⣾⢸⣼⠀⣧⠀⢰⠇⠹⣤⠟⢿⠀⣸⠀⠀⠀⡇⠀⢸⠛⠉⠉⢸⡇⠀⢸⢸
⢸⣀⡞⢣⠀⢸⠀⣇⠀⢸⠀⡇⢀⠁⠀⠀⢹⠀⠀⣿⠀⠀⠀⢸⠈⢸⠀⠀⠉⠀⢸⠀⣿⠀⠀⠀⣿⠀⢸⠀⠀⠀⢸⡇⠀⢸⠘⣇⢀
⠀⠉⠀⢸⠀⢸⠀⢸⠀⢸⠀⢻⣼⠀⠀⠀⢸⠀⠀⡏⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⡃⠀⠀⠀⢻⠀⢸⠀⠀⠀⠘⡇⠀⣸⠀⠈⠛
⠀⠀⠀⠸⡆⣼⠀⠘⢧⠎⠀⠀⠁⠀⠀⠀⠘⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢸⣀⡟⠀⠀⠀⠀⢳⣀⡇
⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⠁⠀⠀⠀⠸⡆⣸⠀⠀⠀⠀⢸⣤⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠓⠎⠀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⠀⣹⠦⢘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡀⠀⠉⠉⢉⣱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠶⢾⣦⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠓⣶⠶⠒⠉⠉⠉⠻⠶⠶⠒⠊⠙⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⣄
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠸⡇⠸⠃⠀⠀⠀⠀⠀⠀⠈⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⡀⠀⣿⡆
⠀⠀⠀⠀⠀⠈⣿⣧⠀⢰⡟⣠⠇⢠⣤⠤⠀⠀⠀⠀⠀⠁⠠⠀⠠⠀⢀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⢠⡿⡷⠀⣹⣧
⠀⠀⠀⠀⠀⠀⢿⣿⣧⣿⠂⠄⠀⠼⢯⣤⣄⠐⠀⠀⣦⡀⠃⠀⠁⠀⠈⠀⠀⠀⠸⠋⣀⢀⣠⣶⠞⠋⠁⣧⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⢿⡁⠀⣀⢤⣐⠉⣡⡼⠃⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⡟⠙⠋⢡⡄⠀⣴⣷⠈⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⠉⠁⢀⣀⠉⠁⠉⠒⠒⠙⠦⡀⠀⠀⠀⢰⣤⠞⢉⣥⡁⠰⠇⣀⣤⠶⢺⠿⣿⠀⣿⣯⣿⠘
⠀⠀⠀⠀⠀⠀⣿⣿⠃⣤⣤⡴⢦⣉⠀⠾⠇⢸⣿⠇⡀⢹⡇⠀⠀⠘⣿⠀⣈⣟⣁⣤⣼⣿⣿⡴⣯⡼⠃⢠⣿⢰⡟⢰
⠀⠀⠀⠀⠀⠀⡇⣿⡄⢿⣿⣷⣿⣿⣷⣤⣤⣴⣾⠃⠀⣾⡇⠀⠀⠀⣿⢻⣿⡈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⢠⢸⣧⠀⠹⣿⡷⣿⣿⣿⣿⣿⣧⣾⣿⡿⠀⠀⠈⠀⣿⣾⣿⣿⡶⢮⣿⣶⡿⢯⣿⠀⠀⠀⠀⣿⣡⡌⣦
⠀⠀⠀⠀⠀⠀⠈⢸⣿⡀⠀⢻⣿⣾⣝⣋⣙⣽⡟⣱⣿⠃⠚⠀⠀⠀⢻⡘⢿⣿⡄⠲⣬⣭⣵⠾⠃⠀⠀⠀⠀⠈⣿⡟⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠈⠙⠛⠋⠉⠁⢰⣿⡏⡨⠇⠀⠀⠀⠈⠳⠾⢿⣷⡄⠀⠀⠀⣠⣾⣷⡆⠀⠀⠀⢸⡧⢸⡇
⠀⠀⠀⠀⠀⠀⠸⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⢀⣀⠀⢈⡿⠁⠀⠀⣸⣿⣿⣿⡇⡆⠀⣠⣟⡇⢨⠃
⠀⠀⠀⠀⠀⠀⠂⢸⣿⠀⠀⣰⣿⣷⣦⡀⠀⠀⠀⠣⠄⣤⣾⣷⠀⠀⣾⠿⠛⠋⠀⠀⠀⢘⣿⣿⣿⣿⠯⠁⣠⣿⣽⠃⡟
⠀⠀⠀⠀⠀⠀⢸⡼⣿⠀⠀⠹⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢰⣷⡀⠀⣽⣷⡀⠀⢀⣠⣤⣾⠟⣹⡿⠟⠁⢰⡏⣿⠏⡜
⠀⠀⠀⠀⠀⠀⠀⢴⢿⣷⡄⠀⠸⢿⣿⣹⢯⣷⣦⡤⣄⣀⣘⣿⣷⣛⣻⣿⣧⣾⣿⣿⡏⠁⢰⠋⠀⠀⢠⣿⢱⣿⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡼⣶⣿⠤⢀⠀⠉⠻⣆⢹⣿⡛⢿⠿⣭⣋⠛⠛⡛⣿⣿⡿⠏⣀⣷⣿⠃⠀⠀⢀⣼⢿⠘⣇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣾⡇⠘⣷⡄⠀⠙⠋⠙⣿⣷⣤⣉⠋⠛⢿⠟⠛⢩⣴⠿⣿⠿⠁⠀⠀⠀⢠⡏⠸⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⣿⣿⣄⠀⠀⠀⠘⢷⣌⠙⠷⣦⣴⣤⣶⣿⣥⡿⠋⠀⠀⠀⣠⣶⡿⢧⠀⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⡁⠙⠉⣉⠻⢶⣄⡀⠀⠛⢷⣴⣫⣤⣇⣰⣾⡿⠁⣀⣤⣶⣿⡿⢋⡔⠁⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣅⠀⠂⢉⠀⠈⢻⣿⣿⣶⡄⠈⠙⠛⠛⠋⠁⠀⢰⣿⣿⡿⠏⢠⣾⡁⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢼⡄⠀⠀⠀⠘⠻⣿⠇⠀⠀⠀⠀⠀⠀⣀⠈⢿⡏⠀⠀⠈⠻⣿⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⣼⣿⣦⡀⠀⠀⢠⡎⠀⠻⠇⢀⠀⠀⠸⠿⠀⣸⠃⠀⠀⠀⠀⡀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢳⡄⣼⢿⣿⣿⣿⣦⣄⣀⠈⠦⣤⣤⡰⠶⠾⠶⠶⠖⣿⠀⠀⠀⠀⠀⣠⣤⠞⠡⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣧⡟⠀⠀⠀⠈⠙⠛⠻⠿⣶⣶⣤⣤⣄⣀⣀⣀⠀⠻⣤⣀⠀⣴⣿⣟⡁⠈⠀⠀⠀⠀⣅
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠐⠀⠀⢻⣴⣴⣶⣅⠀⠀⣠⠄⠀⠀⠉⠉⠛⠿⢿⣿⣿⣶⣤⡙⢠⠻⣿⠉⠁⠒⠉⠉⠀⠀⠈⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠉⠉⢿⣿⣇⡼⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠙⣿⡄⠀⠹⣷⡀⠃⠀⠀⠀⠀⠀⠀⠎⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢨⠀⠀⠀⣿⠿⠋⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢺⣇⠀⠀⠘⣷⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢿⣀⢀⣀⣠⣤⣴⣶⣾⡿⠿⢿⣿⣿⣶⣶⣤⣸⣿⣆⠀⣠⡌⠀⣐⠀⠤⠀⠀⢘
⠀⠀⠀⠀⠀⠠⠔⠀⠐⠀⠀⠀⠀⣀⡀⠀⠈⢛⣟⣿⡿⠛⠛⠷⠟⠀⠀⠚⡉⠀⣠⡿⡿⢻⣿⣿⠟⠋⠀⠀⠉⠙⣀⠠⠶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠤⠂⠀⠀⠈⠉⠀⠀⡀⠃⠈⡟⠁⠲⠄⠀⠀⠀⠀⠤⠀⠀⠙⠧⣤⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡆⢀⢄⣸⡿⠖⢁⡀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣘⣵⣾⡿⠛⠙⢛⡛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢻⣿⠀⣰⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢦⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⣰⠷⣄⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⢠⡟⠙⢷⣄⠀⣰⡏⠀⠈⠻⣦⠀⠀⣼⠃⠈⠻⣦⡀⠀⠀⠀⣴⠟⠁⠙⣧⡀⠀⠀⢀⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠳⢦⣄⢀⣾⠁⠀⠀⠙⢷⡟⠀⠀⠀⠀⠘⢷⣾⠃⠀⠀⠀⠈⠳⣤⣠⡾⠁⠀⠀⠀⠘⣿⣤⣶⠟⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣿
⠀⠀⠀⢻⡟⠛⠲⠶⠼⠇⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣶⠒⠒⢻⣿⠂
⠀⠀⠀⠘⣧⣠⡤⠤⢤⣀⠀⣿⢼⡇⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⠀⠀⢿⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⡆⠀⣿⡏
⠀⠀⢀⣠⣿⡇⠀⠀⠀⠈⢧⣼⠾⡄⡴⠋⣉⣽⠀⡴⠚⠋⠹⣧⡶⣦⢴⠶⣆⣞⠉⢹⡷⡇⠘⢲⣆⣼⠛⣧⡴⢶⡶⠒⢦⡀⢀⣤⠼⠉⢻⠀⡇⢠⡟
⢶⡟⠋⠉⠀⡇⠀⠿⠂⠀⡘⠃⠀⡟⠧⠤⢄⠉⢷⡇⠺⠇⠀⣿⡀⠙⠋⢀⡏⡬⠕⠈⢓⢡⠘⠭⢭⡉⠀⠋⢡⠀⡴⡄⠀⡟⢻⠀⠚⠂⠸⣂⡟⣺⠛⣷⡦
⠀⠙⢦⡀⠀⣇⠀⢀⣀⠔⠁⠳⠤⠇⡜⠀⠈⢀⡄⠙⠒⡆⠀⡇⠳⢦⣤⠜⠈⠓⠶⠒⢁⠈⠳⠤⠞⠉⠒⢁⠈⠉⣁⡙⠒⣃⣀⠉⡇⠀⠀⡟⢫⣽⡶⠟
⠀⠀⠀⢹⣦⠿⠭⠭⠤⠖⠳⠤⠴⠦⠭⣅⠬⠭⠚⠙⠲⣧⠀⢻⠒⠤⣤⠴⠋⠒⠒⠒⠉⠓⠦⠐⠋⠛⠒⠋⠓⠒⠁⠉⠉⠉⠈⡇⣏⠀⠀⡟⠻⣿⣁
⠀⢀⣴⠟⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣇⡏⠀⢠⡇⠀⠀⠙⢷⣄
⢠⣾⣋⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⠶⠋⠀⣼⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⡴⣟⠀⠀⠉⠀⠀⣼⠁⣤⣤⠶⠾⠛
⠀⠈⠉⠛⠻⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⡟⢗⡲⠤⠤⢞⣿⡀⢠⢄⠀⠀⣠⣄⠀⡀⠀⠀⣰⢆⡴⢦⠀⠁⣄⣠⣙⣦⣍⣒⣒⣒⠿⠋⡇⢿⡄
⠀⠀⠀⠀⠀⣇⢀⠤⡀⠀⡏⢸⠀⢠⠛⡆⠘⠃⠀⠉⡟⠋⠉⡇⠓⠃⢘⡄⢀⡇⠈⠒⠋⢻⠀⡇⠀⠀⠸⡇⠀⡏⠁⠈⠀⡇⠀⢹⣹⡄⢀⡇⠈⢷⡀
⠀⠀⠀⠀⣼⡏⠁⠀⣇⢀⠇⠈⣆⡸⠀⠙⠞⠀⠀⠀⢹⠀⢸⠅⠀⠀⠸⡇⢸⡇⠀⠀⠀⢸⠀⡇⠀⠀⠀⣇⢠⠇⠀⠀⠀⢧⡀⣸⠛⠛⠻⠶⣦⣼⣷
⠀⠀⠀⠀⠛⠛⠛⠛⣻⡟⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠳⠎⠀⠀⠀⠀⠳⠼⠀⠀⠀⠀⠘⠶⠃⠀⠀⠀⠈⣹⡿⠶⣤⣀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣀⣤⡶⠟⢻⣿⡇⠀⠀⠀⢠⣶⡄⠀⠀⠀⢠⣾⠷⣦⣀⠀⠀⠀⣠⡾⠷⣦⡀⢠⣿⠀⠀⠀⠉⠛⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠉⠁⠀⠀⠈⣿⡅⠀⠀⠀⣸⡏⠙⢷⣄⣰⡿⠁⠀⠀⠙⢷⣄⣴⠟⠁⠀⠈⠙⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⠁⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⢹⡇⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠲⣾⡇⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣠⣤⣀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣰⡟⠉⠙⠻⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏