Silly face Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠟⠛⠛⠛⠛⠛⠿⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠻⠄
⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠛⠋⠉⠉⠛⠛⠻⢶⣦⣀
⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣤⡀⠀⠀⣿⡆⢀⠄⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡤⢤⣿⣿⠀⠀⢸⡷⣿⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢼⠿⠋⠀⠀⢸⡟⠈⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣄⣀⣀⣀⣀⣠⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠻⠿⣷⣤⣀⡀⢀⣀⣤⡾⠟⠋⠉⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠉⠉⠛⢿⣷⣦⣄⣠⣤⣾⡿⠃⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠈⠛⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣽⣬⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣾⣿⣷⣾⣶⣷⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣿⠀⡰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡆⠀⡠⠞⡟⣡⠋⠈⠷⡄⠈⢧⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡴⠁⠈⣧⠊⠀⠀⢯⠁⠀⠀⠀⠀⠀⢸⠃⠘⣦⠶⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣠⠏⠀⠈⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢦⣼⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠀⢀⡠⠶⠒⠒⠒⠒⠦⣄⠀⠀⣇⠀⠀⠀⢀⡠⠔⠒⠢⣄⠀⠀⠀⠀⠀⠀⢸⡶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠃⡀⡆⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢽⡶⠤⠒⠁⠀⠀⠀⠀⠈⢦⡀⠀⠀⢰⠀⠈⠀⣧
⠀⠀⠀⠀⠀⠀⠀⣀⡘⡄⠀⢣⡙⢤⡎⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⢠⡀⠀⠈⠙⢲⣼⡇⠀⠀⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠙⣏⠁⠀⡱⢭⣻⡇⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣤⣀⠀⠳⠄⠀⠀⠀⣟⡵⠀⡴⠓⣹
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠍⣲⣶⡇⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⢿⣿⣶⣤⠀⠀⠀⡿⣊⠀⢀⣴⣃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢑⣒⡶⠋⠀⠀⠀⠀⣀⣤⣶⣿⣿⡇⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠙⢿⠇⠀⠀⡿⠁⠴⠋⢁⠎
⠀⠀⠀⠀⠀⢀⣀⣸⠄⠀⠀⠀⡸⠁⠠⠶⠾⠟⠛⠛⠛⠻⣟⠋⠁⠀⠀⠀⠀⣠⣤⣤⣤⡤⣤⡤⠤⢤⡤⠀⢰⡇⠀⡰⢠⠏
⠀⠀⠀⠀⠀⠀⠉⢢⣄⣆⠀⢀⡇⠀⠰⡗⠒⢶⣖⣲⡶⠒⢻⡟⠛⠀⠀⠀⠀⢸⡄⠀⠈⠛⠛⠁⢀⣾⠁⠀⣸⠁⡼⠓⠻⣄
⠀⠀⠀⠀⠀⠀⢰⠋⣁⢹⡄⠘⡇⠀⠀⠱⣄⣀⠉⠉⣁⣠⣾⠁⠀⠀⠀⠀⠀⠸⣯⡓⠦⣤⣤⠶⢻⠏⠀⢀⡏⢸⠃⡤⡄⢹
⠀⠀⠀⠀⠀⠀⣿⢰⠁⠀⣧⠀⢷⠀⠀⠀⠘⠛⠿⠛⢛⡽⠃⢀⣤⠤⠶⠶⣤⡀⠙⠍⠂⠀⠀⠀⠁⠀⠀⢸⠃⣾⠰⠛⡷⣸
⠀⠀⠀⠀⠀⠀⢸⣼⡩⠗⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣟⠀⠀⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀⣰⡄⠀⢸⠀⡿⡀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢳⡝⢦⠜⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠚⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⢿⠼⣳⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣻⠁⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠴⠖⢒⣋⣡⣴⣾⡟⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠳⣶⣿⡿⠛⠛⢋⣠⠞⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠈⠛⠶⠶⢒⣋⡥⢠⣄⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⣄⡀⠀⠀⠉⢉⣡⡾⠋⠉⠁
⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠛⠛⠋⠁
⣿⣏⢭⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠛⠛⠳⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⣠⡴⠟⠋⠉⠀⠀⠀⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢶⣤⠀⠀⠀⠀⠀⣿⢀⡔⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠲⣾⣿⡇⠀⠀⠀⠀⣿⢸⡗⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣴⣶⣶⣤⡀
⠀⠀⣠⣴⣶⡶⣶⣤⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠟⠋⠀⠀⠀⠀⢀⡿⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢠⡏⠙⠻⠄
⠀⠰⠛⠉⣿⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠀⠀⠀⠀⠈⠙⠻⠶⠶⠶⠶⠶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣥⠶⠶⠚⠛⠛⠲⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣄⡀⠀⠀⠀⠀⠀⣿⠀⢀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣠⣿⣷⠀⠀⠀⠀⠀⣸⠀⣿⠤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⡿⠏⠀⠀⠀⠀⠀⣿⠀⠙⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⢀⣤⣶⣶⣶⢷⣶⣤⡀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠀⠉⠛⠷⢶⣤⣤⣤⡶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠘⠟⠉⠙⣿⣄⠀⠀⠉⠃⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⢀⡟⠈⠉⠛⠻⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠾⠛⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣾⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⡤⢤⣤⡤⠴⠾⠷⠶⠶⣶⠶⠶⠶⠶⠶⠷⠶⣶⠶⠶⠶⠶⠶⠿⠷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣿⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣿⣥⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠾⢷⣤⣤⣤⣤⣤⣤⡾⠷⠞⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣟⣻⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣭⣽⣿⣿⣯⣿⣿⣿

⣟⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⣀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠐⡀⠀⠄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠥⠀⠀⠀⢴⡈⠀⠀⠁⢁⣂⡴⠶⠤⠼⡂⠀⣀⠀⠀⠀⠀⠀⠀⣶⡆⠀⣤⠄
⠀⠠⠀⠀⠄⣀⠀⣶⠖⠀⡄⠀⠀⠀⠀⠈⢷⠊⠙⢿⠇⠸⡿⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⠒⠃
⠀⠀⠁⠀⠀⠙⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠠⠖

⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠁⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠘⢠⣴⠀⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣨⠀⠀⢸⠄⠠⠞⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠈⡍
⠀⢀⠀⠀⢠⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⢀⡀⠰⠖⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⡠
⠀⠃⠀⠀⠈⠄⠀⠀⠠⠀⠀⠰⠄⠀⠀⠀⠀⠀⢨⠟⠀⠈⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠⡁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⣀⠂⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠀⠒⡄⠀⠀⠀⠀⠀⠀⠐⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠂⠀⠀⠈⠃⠀⠈⠄
⠀⠀⠀⠀⡀⠀⠀⢅⢀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⡌⠁⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠴⠘
⠀⠀⠠⠂⠁⠸⢌⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣀⣀⣀⠠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡇
⠀⠀⠀⢸⠉⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⡆
⠀⠀⠀⠈⠓⠒⠒⠒⠓⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠚⠁
⠀⠠⠒⠀⣀⠀⠀⠀⠀⠀⠀⠠⠾⠛⠻⠿⠛⠛⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠿⠿⢿⣟⠷⢦⡄⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⠒⠄
⠀⠈⠉⠉⣀⣤⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠉⠉⠁
⠀⠀⢠⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠈⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠉⠛⠶⠦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠤⢤⣀⣀⣀⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣠⠴⠾⠷⢦⡀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⢀⡔⠉⠀⠀⠀⠀⠉⠳⠀⠀⠀⣠⡿⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦⣤⣄⣀⣀⣀⣤⡤⠶⠖⠛⠉⠀⠀⠙⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠿⠿⠿⣶⣦⣀⠀⢀⣠⣶⡾⠿⠿⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢁⡴⠚⠛⠛⠛⠲⣝⠻⠃⠻⢋⡵⠞⠛⠛⠛⠲⣤⡙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡀⠀⠀⠈⢷⣠⣠⠏⠀⠀⠀⡀⠀⠀⠈⢳⡀
⠀⠀⢀⣀⣤⠤⠶⠶⠒⠚⠛⣿⠀⠀⠀⣿⣿⡇⠀⠀⢸⡏⣿⠀⠀⠀⣿⣿⡇⠀⠀⢈⡟⠛⠒⠲⠶⠦⢤⣄⣀
⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⠉⠀⠀⠀⡼⠁⠸⣆⠀⠀⠈⠉⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⡤⠞⠁⠀⠀⠙⠶⣄⣀⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣦⣤⣀⣀⣀⣀⣹⣶⣄⣀⣀⣀⣀⣴⣾⣁⣀⣀⣀⣠⣤⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⡿⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⢏⢹⠉⢹⠀⢸⠀⠀⠀⡇⠀⡇⠉⡏⢙⠟⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠉⠒⠼⠤⣼⣀⣤⣀⣇⡠⠧⠔⠋⣁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣄⣀⣀⠀⢀⣀⣀⣤⠴⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⢶⣄⠀⠀⠀⠀⠀⣠⣤⠶⠶⠒⠒⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⣠⣤⣄⡀⠀⢀⣤⣤⣤⣄⠀⠀⠹⣿⠁⢀⣠⣤⣤⡀⢀⣤⣤⣤⣄⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣰⡿⠋⢹⣿⣿⣷⣿⣿⣿⣿⣿⣷⠀⠀⢻⣄⣿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣷⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣇⣽⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⢠⣴⣶⡶⣶⣄⠀⠀⠀⠀⢷⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⣿⠀⠀⠈⠙⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠉⠀⢀⡏⠙⠿⡄
⠀⠰⠛⠉⣿⡆⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠉⠛⠿⢿⡿⠟⠋⠀⠀⠀⣠⡾⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠀⠀⠈⠙⠷⣦⣤⣀⣀⣀⣀⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣤⣤⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⡉⠉⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣶⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣰⠶⠀⠀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠀⠀⠀⠀⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠂⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠈⠀⠁⠢⡠⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⠐⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠁⢰⠀⠀⢰⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⣬⠈⠁⠀⠀⡆
⠀⢀⣤⠀⠠⢀⠀⢀⠠⠓⠄⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠔⠃⠄⠀⠤⠂⠀⠀⠀⠀⠀⢴⠀⠁⠀⠀⠈⠙⠂⠀⠀⠐
⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠀⠆⣄⡀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⣈⠓⠂⠄⠀⠠⠐⠒⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠈⠢⡒⠁⠒⠀⠒⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠉⠈⠁⠁⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠰⠛⠉⠀⠀⠀⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⠀⠚⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠃⠀⠀⠀⠀⠻⢦
⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠈⠢⡤⠂⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⢄⡀⠀⠂
⠀⠀⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠖⢸⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢰⣿⣿⣿⡆⢷⣿⣿⠆⠀⠀⢀
⠀⠀⠀⠐⡄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢀⠠⠓⠄⣀⡠⠔⠀⠀⠀⠀⠀⢻⠀⠀⠀⠙⠛⢋⠔⠢⢉⡁⠔⠃⠀⠈
⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⢈⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⣠⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⡀⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⢠⣦⡀
⠀⠀⠀⠴⠶⢶⣤⣄⣀⢀⡀⣀⣤⣴⠶⠿⠒⠀⠀⠀⠀⢀⠤⠖⠋⠉⠐⡔⠉⠓⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⢀⠠⠐⠀⠁
⠀⠀⠀⠘⡀⠀⠉⠛⠉⡛⢋⠋⠋⠀⠀⡸⠀⠀⠀⠀⠀⠘⡀⠐⠘⠋⠀⡅⠉⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣤⡄⠈⣤⡄⠀⠀⢡
⠀⠀⠀⠀⠈⠐⠀⠀⠊⠀⠀⠁⠂⠐⠈⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠈⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠰⢄⡀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⣀⠀⢐⠂⠀⢐⠒⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⣠⠮⠧⢤⠘⠂⠠⠞⠒⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢏⡢⠤⠘⠒⠒⠘⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠆
⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠉⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠒⠒⠶⢤⣌⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡴⢋⣁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣴⠏⣼⢃⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠳⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣹⣿⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣿⣿⡿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⣠⣴⡾⠿⠗⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⡼⠋⢹⣧⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃⠀⠀⠀⠀⠙⠳⠦⢤⣤⣤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠁⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠙⠻⠷⢶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⠶⣾⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⢀⣀⣤⣄⣀⣀⣀⣀⡀⠀⢀⣠⠴⠛⠛⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣠⡶⠛⠉⠀⠀⠀⠀⠉⠉⠙⠛⠯⣀⠀⠀⠀⠀⠀⠈⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⡀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣄⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣀⣀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀
⠀⠀⠀⠀⠟⠁⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠒⠄
⠀⠀⠀⠀⠀⣀⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠓
⠀⢠⡄⠀⠀⠀⠀⠃⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠈⠑
⠀⠀⠑⠄⡀⠀⠀⠀⢀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⡀⠄⠂
⠀⠀⠀⠱⣤⠨⠄⠨⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠴⠒⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⠀⠶⡄
⠀⠀⠀⠀⠤⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⣀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡉⠀⠀⡀⠀⠀⠀⢀⠀⠀⠺⣿⡿⢘⠿⠿⠁⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠠⡤⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠠⣤⣤⣀⡀⢀⢀⣀⣤⠴⡦⠀⠀⠀⢀⡠⠴⠛⢡⠐⠲⠤⢀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠉
⠀⠀⠀⢄⠀⠙⢉⠛⢉⠋⠀⠠⠃⠀⠀⠀⠘⡀⠀⠃⢀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠡⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠴⢀⡠⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠦⣀⡀
⠀⠀⠀⠃⠄⠀⠂⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠋⠉⠉⠉⠉⠛⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⣴⠟⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠏⠀⣴⡏⠉⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣿⠓⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠹⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⢿⣶⣄⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣠⣼⣿⣿⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⣿⣿⣿⡟⢀⣾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⣠⣴⣾⡿⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠿⠋⢠⡾⠃⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⢠⣾⠿⣿⡄⠀⠀⠀⠀⠀⠀⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠈⠻⢦⣄⣀⣀⣀⣀⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⢰⠟⠁⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠁⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠈⠉⢻⠿⢷⣶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢸⠀⠀⠀⠈⠉⣻⠛⠛⠛⠛⠛⢿⠿⠿⠿⠿⠟⢻⠟⠛⠉⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠒⠢⠿⠤⣀⣀⡀⠀⣿⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⢸⣇⣀⣀⣠⣤⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠈⠉⠋⠁⠙⠋⠉⠉⠉⠉⢉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⣠⣴⠶⠛⠛⠛⠛⠛⠛⠻⠶⣦⣶⡛⠁⠀⠀⠀⠀⠉⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠘⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⢿⣷⣆⠀⠀⠀⠀⠀⢠⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢾⡿⠿⠛⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣖⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⣴⠋⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠉⢳⡄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢻⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⡀⠀⠀⠀⢀⣠⡴⢻⡟⣿⠀⣿⣿⠷⣤⣀⠀⠀⠀⣀⣤⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢯⣉⠙⠻⣿⡏⠁⣰⠟⠀⣿⠀⣷⠘⣧⡈⣽⣿⠛⢋⣩⠟⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠙⠳⠶⠤⠶⠟⠁⠀⢀⡏⠀⣿⠀⠈⠻⠦⠤⠶⠛⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠸⣇⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⢀⣠⠾⠁⠀⠀⠀⠙⢧⣄⣀⣀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢋⣡⡤⡴⠶⠒⠒⠶⢦⢬⣉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠉⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠉⣳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⣤⣄⣀⣇⣀⣀⣸⣤⣤⣤⣶⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡃⠀⠀⢀⡴⣻⣿⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣦⣤⣾⣿⣷⣿⠀⣰⣿⣾⣿⠃⠀⢀⣠⣴⣾⣭⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣛⣓⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣴⣾⣿⣿⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠋⠙⠛⠛⠛⠻⠿⣿⣟⠿⣿⣖⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠋⢁⣀⣀⣀⡀⠀⠀⣠⡴⠒⠋⠉⠉⠛⠲⢦⣈⠓⢤⡉⠉⠉
⠀⠀⠀⠀⠀⠀⣰⡿⣫⣾⣿⡟⢁⡴⠋⠉⠉⠀⠉⠉⠙⠺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠙⢄⠀⠀⠀⣠⡶⠾⠿⠷⣶⣄
⠀⠀⠀⠀⠀⣴⢫⣾⣿⣿⡏⢰⠋⠀⠀⠀⠀⠀⠀⣀⣀⠀⠹⡄⢀⡀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠈⠳⣠⡞⠁⢀⣤⣤⣄⡀⠙⢷⡀
⠀⠀⠀⠀⢰⣿⡿⢻⣿⡿⢀⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⣷⣿⣿⡆⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠙⠀⠀⠸⠟⠁⠙⢿⡄⠘⡇
⠀⠀⠀⠀⢼⠋⠀⣾⣿⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⣾⡈⠋⠁⠀⠀⣀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡟⠀⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠉⣛⣻⣿⡿⢿⡿⠷⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣧⠀⠀⠀⠀⠀⠀⢀⣠⣾⣯⠶⠚⡏⠉⠁⠀⠀⠈⣇⠀⠀⠀⠀⡇⠙⢦⠀⠀⠀⢶⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠻⣦⣄⣀⣀⣤⢶⡿⣟⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⣄⠀⣀⣠⣶⣤⣼⣷⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠇⠀⠀⠉⠉⠁⣠⠋⠀⢸⡀⠀⠀⠀⠹⣦⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢻
⠀⠀⠀⠀⠀⣼⠋⠀⣀⣀⠀⠀⠀⠀⠀⡼⢹⠀⠀⠈⢇⡀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⡇
⠀⠀⠀⠀⢰⡇⠀⣼⡟⠁⠀⠀⠀⠀⢠⡇⠘⣆⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠸⣧⠀⢹⣇⠀⠀⠀⠀⠀⠀⣷⣀⣸⣿⣿⣿⣿⣿⣿⣿⠟⢫⠟⠁⠀⠀⠀⠉⢻⣿⢿⣿⡟⠙⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⢻⣦⠀⠙⠷⠦⠀⢀⣀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⠀⠀⢀⡤⠶⣄⣟⠀⠀⠹⣷⠀⢸⡏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣤⠶⠋⠙⣆⠀⠹⣿⣿⣿⣿⣿⣿⠿⣤⡶⠞⠛⢷⣹⡄⠀⠈⢿⡄⠀⠀⢻⣆⠜⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⣿⣿⣿⢿⡇⠀⠘⡇⠀⠀⠀⢻⣧⠀⠀⠈⢷⡀⢀⡴⠋⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠙⢿⣇⠀⠙⣆⠀⠘⣄⠀⠀⠀⠻⣆⠀⣀⠬⠓⢁⣠⠞⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠳⣄⣈⣷⣄⣈⣧⡤⠤⠖⠛⢉⣤⠴⠞⣋⣤⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠉⠁⠀⠀⠀⠀⣀⣀⣤⣴⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠲⠶⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⢠⠾⠗⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠺⠦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡄⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠐⠀⡀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⡄⠀⠀⠐⡄⠀⠀⠀⠀⠀⢙⠛⠋⠁⠈⠑⣤⠂⠈⠉⠛⡂
⠀⠀⠀⠀⠀⠀⣤⠀⢡⡤⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠆⠀⡾⠂⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠰⠰⠆
⠀⠠⠆⠀⠀⠀⢀⠠⠓⠤⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠛⠦⣀⣀⠀⠁
⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⢀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠔⠉⠀⠐⠒⠀⠀⠉⠶
⠀⠀⠀⠀⠈⠢⡀⠀⠀⢈⠴⡄⠀⠀⠀⠀⠀⠀⠀⢁⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡧⠀⠀⠀⠀⣤⡀
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡁⠀⡀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠉⠻⠀⡀⠉⠙⠄⠀⠀⠀⠀⠀⢴⢶⣤⣄⣀⠀⡀⢀⣠⣤⡶⠶⠒⠀⠀⠀⠀⠀⠐⠁⣶⡶⣤⠱⢪⡼⠦⠖
⠀⠀⡆⠀⠀⠀⠀⢊⢀⡀⠀⠘⡀⠀⠀⠀⢀⠘⡄⠀⠙⠋⢙⠛⡙⠛⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⡦⢀⡀⣽⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠔⠀⠀⠀⠊⢇⠀⠈⠀⠀⠀⠁⠀⠈⠀⠀⠈⠀⢀⠄⠀⠀⠩⡁⠀⠐⠨⠭⠐⠁⠁⠂⠀⠊⠀⡠
⠈⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠈⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠑⣄⡀⠀⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⢉⡐⠀⠠⠀⠀⠄⠐⡂⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⠀⠀⠈⠁
⠀⠀⠀⠳⣰⠐⠀⠀⠰⠀⠓⡀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠠⠔⢂⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣬⠄⣀⠤
⠀⠀⠀⠀⠈⠁⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠞⠛⡁⠀⠀⠀⠘⠛⠆⠀⠀⠀⠀⠀⠀⠰⠛⠋⠀⠀⠀⠀⣤⣤⣄
⠀⢩⠉⠙⠿⠷⢶⡶⠾⠿⠉⠉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠠⠆⠀⣄⠀⠤⠖⠀⠀⡄
⠀⠀⠃⠄⠀⠤⠊⠈⠂⠀⠄⠐⠁⠀⠀⠀⠤⠀⠀⠀⠀⠘⠃⢸⠘⠀⠀⠠⠀⠒⠂⠀⠀⠈⠂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠂⠁⠁⠀⠀⠁
⠀⠀⠀⢀⡠⠔⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠁
⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⠀⢀⣠⣴⣾⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⡿⠿⠶⠤⡄
⠀⠈⠉⠉⠁⢸⡏⠛⠛⠿⠿⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⣶⣶⢀⣀⣤⣴⣶⣿⣿⣿⡿⠿⠛⠋⠉⠀⠸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡟⠻⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⣿⡿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠑⠚⠋⠀⠀⠀⠀⢨⡏⠸⣇⠀⠈⠣⠴⠛⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠉⠳⠶⣤⣤⣤⣤⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⣶⠛⠋⠉⠉⠉⠉⢹⡛⠛⠓⠲⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⡟⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠧⠤⠴⠿⠴⠶⢶⡶⠶⠶⠿⠒⠒⠒⠒⢾⠛⠛⠛⠉⠉⠉⢩⡿⠉⠉
⠀⠀⠀⠀⠀⠀⢠⣿⡁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡀⠀⣾⠋⢳⣄⠀⠀⠀⠀⠀⣀⣿⣀⣤⣤⣤⣤⣤⣤⣾⣦⣤⣤⣤⣄⣀⣿⡃
⠀⠀⠀⠀⡇⠀⠹⣆⡀⣙⣦⡴⠶⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒
⠀⠀⠀⠀⠻⣄⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠾⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⠿⠿⢿⣿⣿⠿⠿⢶⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠀⣀⠀⠀⠀⣼⣿⣿⣧⡀⠀⠀⣀⠀⠀⢀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣼⣿⣧⣴⣾⣿⣿⣿⣿⣿⣦⣼⣿⣷⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋⢁⣀⣠⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠉




⠀⠀⠀⠀⠀⠀⠀⡤⢠⠀⡄⡴⠀⢠⡄⢠⠦⡄⠴⡄⡤⠢⡀⡄⣄⢠⠀⡤⠀⡄⠀⡴⢤⠀⢠⡔⠀⣄⣠⢀⠔⢤⠀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠃⠒⠃⠋⠙⠘⠉⠀⠉⠀⠑⠒⠁⠃⠃⠙⠀⠃⠀⠃⠀⠓⠊⠀⠘⠂⠀⠃⠘⠈⠒⠊⠐⠂⠘


⣿⢿⡿⢿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⠛⠓⠂⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷
⠀⠀⢰⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠈⢲
⠀⠀⠀⠉⠈⠉⠃⠀⠀⣠⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠋⡉⠈⠁
⠀⠣⠄⢂⣀⣤⠀⠀⠈⠉⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠓⠀⠀⠀⢀⡇⠀⠂⠤⠃
⠀⢀⡴⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⣿⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠉⠛⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⢤⡶⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⣰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢸⡇⢠⡇⠀⠀⠀⠀⠘⣇⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠶⢶⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢸⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢄⣠⠱⠀⠀⠀⠀⢻⡿⣿⣦⣀⠀⠀⢸⠀⠘⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⡇⠈⠻⢿⣷⣦⣬⣄⣥⣴⣿⣷⣄⣀⣀⣠⣴⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠉⠙⠛⠛⠛⠉⠈⠙⠛⠟⠛⠋⣿⣿⠁⠀⣤⠤⠴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣧⣀⠀⢻⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣆⣠⠞⠉⠀⠀⠀⠀⠉⢻⡿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⠀⢀⣿⣇⣀⣀⠀⢠⡶⢶⡀⠀⠀⠀⡏⠀⠘⣿⡅⣴⡾⢛⣻⣷⠶⠿⢶⣿⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣶⣶⡾⠛⠉⠁⠀⠉⠙⢾⣿⡧⠙⢦⡀⢰⡇⠀⠀⠹⣷⣏⠀⢿⠀⠀⠀⠀⢸⣿⣆⣀⣸⡓⠂
⠀⠀⠲⡶⠺⡄⠀⠀⠀⠀⠀⢹⣿⡠⢀⣤⣴⣦⣄⡀⠀⠙⣯⢂⠈⠳⣼⠀⠀⡀⠀⢻⣟⠦⣼⡷⠟⠁⠀⣼⠹⡏⠀⠈⣷⣤⣤⣀⡀
⠀⠀⠸⠓⢴⠆⠀⠀⠀⠀⠀⣾⣿⣏⣾⠋⠀⠀⠉⢷⠀⠀⢸⡷⣄⠀⠈⠀⢠⣧⠀⠀⢿⣄⠀⠀⣀⣤⡾⣣⠾⠷⠶⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣷⡀⠀⠀⠀⣸⠃⠀⢸⣯⣿⣷⡄⠀⢸⠙⣧⣠⣬⡿⠻⠛⠛⠉⠰⡏⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⣀⡤⠶⠾⠿⠿⠿⢿⣿⣿⣯⠻⠦⠤⠞⠁⠀⢀⣾⣿⣿⡈⠻⡶⠟⠀⠉⠉⠁⠀⢄⣑⣄⣀⣀⣹⣄⠀⠀⠀⠠⢎⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⡹⢿⣿⣧⣀⡀⢀⣀⣴⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠳⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣠⠞⠁⠀⢈⠿⠛⠛⠛⠋⠁⠈⠻⣧⠀⠀⠀⢀⡴⠞⠛⠓⠲⣄⡂⠀⠙⢦⠈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣰⠋⠀⣠⠴⠶⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠔⢃⡀⠀⠀⠀⠀⠀⣿⣰⠃⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣃⡀⢰⠊⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠛⠀⠀⠀⠀⠀⠀⠟

⣿⠋⠙⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⡿⡏⡌









⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣩⣩⣭⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⣭⣭⣭⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⠻⡉⠉⣙⡛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣠⠤⠤⠤⠤⠤⣝⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢰⢄⠀⠀⠀⠀⠀⣀⣠⢶⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⣄⠉⠉⠉⠉⠉⠉⣠⡎⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠘⣿⣿⣶⣶⣶⣾⣿⠟⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠻⠿⣿⠿⠟⠁⠀⠀⠀⠀⣼⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣃⠀⠉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣶⣄⣀⡀⠀⠀⢀⣀⣠⡶⠋⠀⠀⠙⠲⣄⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉⠉⠉⢉⣩⠟⠁⠈⠙⢦⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢀⠔⠊⠉⣄⠈⠉⣉⠓⠲⠤⢤⣤⠤⠶⠚⡿⠁⠀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⣷⡀
⡞⠲⠧⠴⣇⣀⣸⢧⡤⣾⣀⡀⢰⡖⠶⠶⠖⠒⠛⠛⠋⠉⠑⠄⠀⠀⠀⠀⠀⣠⡼⠋⢀⡠⠔⠋⠀⠀⠀⢹⡄⠀⠀⠤⠚⠀⢷
⠓⠶⠦⠤⠭⢭⣥⣄⣀⣀⣀⠉⠙⢷⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠱⡆⠭⣗⡶⢫⡀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣇⠀⠀⠉⠒⣽⡛⡻⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⢸⡇⢸⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⠀⠀⠀⠀⡇⠈⠳⠞⠁⠀⣀⣀⣀⣀⡠⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠈⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢻⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢸⠇⡼⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⡿⢀⡇⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢳⣄⡀⠀⠀⠤⠤⣤⣤⣤⡤⠤⠖⠚⠉⠀⠀⠀⢀⡾⣅⣼⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣰⠋⠀⠙⠳⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠙⠓⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⢩⠟⠛⠛⠛⠛⠛⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⣠⠤⣖⠒⠶⠧⠿⣤⠖⠛⠲⣿⠀⠀⡀⠀⠀⢀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣠⣼⠶⠋⠁
⠀⠀⠀⠀⠀⠀⡼⠁⣰⠽⣄⠀⠀⡾⠁⣠⢤⡀⢹⡙⠓⠻⠦⠤⠼⠷⠖⠛⠲⠶⠤⣤⣤⣀⣠⠴⠒⠦⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠙⠋⢙⠗⢾⡇⠐⣇⡼⠃⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡔⢢⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠋⠀⠘⣇⠀⠉⠀⢀⡾⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠶⢤⠤⢼⡇⠘⢦⠊⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣷⣄⣀⣀⣴⠏

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠰⠟⠛⠃⠀⠀⠀⠸⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠀⠀⠀⠀⠘⠛⠆⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣆⠀⠀⠀⠀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡄⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠈⢢⠔⠉⠀⠉⠙⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣆⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰⠄⠀⡷⠆⠀⠀⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⡆⡴
⠀⠀⠀⣠⠄⠀⠀⠀⠈⠁⡠⠂⠀⠀⠀⠄⠀⠀⠀⠀⠈⢁⠀⠈⠀⠀⠀⠈⠑⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡴⠦⡀⠀⠀⠀⠂
⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠄⠂⠀⠀⠤⠤⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⢉⠁⠐⠂⠄⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠓⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⡀⠀⠀⠀⠀⠀⠙⠻
⠀⠀⠀⠀⠀⠈⠉⠙⠳⣦⠀⠀⠛⠲⠄⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠈⣤⣴⣀⡑⡤⢂⣬⣥⡤
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠠⠆⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠸⠉⠉⠹⣿⠷⠶⡷⠶⢿⠏⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣝⠁⠀⠘⢳⢶⡄⢸
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⡇⠀⠀⠀⡤⠆⠀⠑⠄⣀⣀⠠⠞⠀⠂⠄⠀⠀⠔⠁⠀⡀⠀⠀⠠⠄⠀⠁⡘⠻⡷⠟⡠⠓⢌⡙⣛⡡⠊
⠀⠀⢤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠠⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠹⠆⠄⢀⡀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠀⠀⠀⠀⠀⠀⠙⡦⢀⡀⠀⠀⠀⢀⡀⠠⠐⠂⠁
⠀⠀⠀⠀⢣⡙⠐⠂⠄⠀⠠⠒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠌⠁
⠀⠀⠀⠀⠀⠳⣰⠀⠀⠄⠘⠠⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠄⠓⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠄⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠈⠑⠠⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠂⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠀⠀⠀⠀⠠⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠷
⠀⠀⠰⡶⠶⣶⣤⣄⡀⣀⣀⣀⣤⡶⠾⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃
⠀⠀⠀⢣⠀⠀⠙⠋⠉⡛⢋⠋⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡀⠈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠙⠋⠀⡸⡀⠈⠙⠃⠀⠀⠌
⠀⠀⠀⠀⠁⠀⠀⠐⠊⠀⠀⠁⠐⠂⠈⠀⠀⠀⠀⠐⠖⠀⠐⠀⠀⠀⠉⠁⠠⡉⠀⠀⢀⠄⠀⠉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠐⠀⠐⠊⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢀⣀⠴⠒⠋⠉⠉
⠀⠀⠀⠀⠘⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣯⣭⣭⣽⣬⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠉⠉⠉⠉⠉⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠛⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠛⠛⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣼⠋⠀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⣼⣇⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢿⣭⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢉⣿⣿⡄⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣷⣿⣿⣿⠇⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⣀⣤⡄⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠋⢠⡿⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⣠⣾⣿⠛⠁⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣴⠟⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⣰⡟
⢀⡾⠋⠈⢿⣧⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⠀⠀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠜⠁⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⠛⠿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⡇⠀⠉⠉⠛⢻⡿⠿⠷⠶⠶⢶⣶⣶⣶⡶⠶⢶⡾⠿⠛⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡶⠶⢤⣧⣀⡀⠀⠀⢸⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠉⠉⠑⠛⠓⠒⠒⠂⠀⠼⠃⠀⠒⠒⠒⠚⠓⢹⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⢀⣠⡶⠾⠛⠛⠛⠛⠛⠻⠶⣦⣴⡟⠉⠀⠀⠀⠈⠙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢹⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⡿⠿⠿⠿⠿⠿⠿⣿⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠛⠻⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠷⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠿⠿⠿⣶⣄⡀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⠻⣄⠀⢀⣾⡿⠛⠉⠀⠀⠀⠀⠉⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⢀⣿⡿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢸⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⠀⢀⣠⣾⡿⠁⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠾⠛⢋⣿⡟⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿
⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠰⢶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠾⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣀⡀⠀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣉⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠉⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⣀⡴⠖⠛⠛⠛⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⠔⢲⣦⠀⠀⠀⠀⢸⡇⣠⠒⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⡗⣾⣿⠃⠀⠀⠀⢸⡇⠻⣙⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⣠⣴⣶⣶⠶⠶⣤⡀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⠈⠛⠷⠶⢤⡤⠶⠶⠛⠁⠀⠀⠀⠀⠀⢀⡤
⠀⠘⠉⠀⢻⣦⠀⠀⠉⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠈⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢠⡏⠉⠛⠳⠶⠦⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠶⠒⠛⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣈⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡛⠛⣿⠛⠛⠋⠙⠛⢻⠋⠉⠉⠉⠉⠙⣿⠉⠉⠉⠉⠉⠉⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣏⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⣀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠾⠷⢤⣤⣤⣤⠤⠾⠷⠛⠋⠉

⠀⠀⠀⠀⣀⡤⣤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢠⡖⢶⣋⣛⣧⣀⣄⡀
⠀⠀⠀⡞⠉⢀⣀⣀⢀⣷⠀⠀⠀⠀⣀⢶⣶⠿⢿⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⢿⡆⠀⠀⠀⡞⡡⠲⠤⠃⠐⠠⣞⡿
⠀⠀⠈⢻⣟⣁⠀⣀⣹⠁⠀⠀⣀⡼⠑⢦⠄⠚⣤⠌⢡⡀⡀⠀⢘⣃⠀⠙⠛⠋⠀⣠⠷⠀⠀⠠⢭⣃⢄⠀⠀⠤⠄⠄
⠀⠀⠀⢧⣀⣨⢹⡁⣂⡘⠀⠀⠣⡇⠀⠂⢄⣀⣨⠀⠂⢷⠁⠀⠐⠿⠗⢀⣀⣀⡼⢿⠇⠀⠀⠀⠸⠟⠸⠀⣸⠟⠡
⠀⠀⠠⣤⣷⣿⣬⣧⣧⣤⡀⠀⠀⢿⠄⠀⢴⡈⣥⠀⠰⡿⠀⠀⠀⢠⣴⣾⣿⣿⣶⣆⠀⠀⠀⠀⠀⢰⠀⣤⣄⢸
⠀⠀⠀⠀⢸⠈⠉⢉⠏⠁⠀⠀⠀⠀⠀⠀⠠⠈⠀⠠⠞⠀⠀⠀⠀⠀⠱⡉⠘⠋⡜⠁⠀⠀⠀⠀⠀⠀⠀⢈⡁⠔
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠒⠁
⠀⠀⠀⢰⣿⣟⣿⣷⣤⠀⠀⠀⠀⠀⢀⡠⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣒⡠⢄⣀⡀⠀⠀⠀⠀⠀⠀⣶⡳⠂
⠀⠀⠀⣸⣏⠙⠻⠿⣿⡄⡀⠀⢀⣰⠋⠉⠓⠈⠢⠺⠦⠀⠀⠀⠀⣠⣤⣴⣿⣿⣦⣶⠌⡆⠀⠀⠀⠀⡜⣿⡁⢳⡼⣄
⠀⠀⠨⣿⣽⣿⠀⣻⣯⣷⡄⠀⣺⡇⠶⢔⠀⠀⢰⢒⣶⠦⠀⠀⣺⡟⣏⢻⠛⠋⠯⡝⣶⡌⢣⠀⠀⠸⠄⠀⠈⠉⢁⣈⡀
⠀⠀⠈⡇⢸⣟⣶⣻⠇⡞⠀⠀⠀⢣⡀⠘⠦⠤⠜⠀⠠⠎⠀⠀⠸⠷⢾⠦⠀⠴⣶⠼⣿⣷⠞⠀⠀⠾⣷⡖⠂⠈⣱⠾⠛⠁
⠀⠀⠀⠳⠛⢁⡉⠙⣾⠃⠀⠀⠀⠀⢳⡀⠐⢮⡲⠗⠁⠀⠀⠸⠤⢷⠀⣀⡒⡂⠀⢀⣏⣹⠀⠀⠀⢠⡀⣬⣃⠤⣁⢀⡜⠃
⠀⠀⠀⠀⠑⠀⠉⠴⠃⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠞⠡⠎⠀⠀⠀⠀⠀⠀⠑⠙⠉⢈⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⢀⣶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣰⠻⣧⡀⠀⠀⠀⠀⢠⠂⠉⠉⠉⠉⠉⠢⡀⠀⠀⠀⠀⠀⠘⡿⠿⢿⡁
⠀⠀⢲⣾⠟⣉⠈⣉⠻⣿⠿⠃⠀⠀⠀⡞⠙⠦⠜⠉⡆⠀⠀⠀⡆⢀⡎⠉⠉⠉⠹⡄⢸⠀⠀⠀⠀⢻⢻⣟⣛⣿⣿⢩⠁
⠀⠀⢼⣻⡏⢳⠀⢸⣿⠽⡴⠀⠀⣠⣴⣧⣆⡄⣄⣴⣷⡆⠀⠀⠳⢶⣷⣦⠀⣷⣾⡟⠚⠀⠀⠀⠀⠀⢾⡙⡎⠛⣉⠓
⠀⠀⣸⣄⣤⣼⢶⣾⣤⣠⣧⠀⠀⠘⣸⣀⡤⣇⣴⢤⣯⠁⠀⠀⠀⢰⠍⠭⠀⡸⠉⠧⠀⠀⠀⠀⠀⠀⢸⡿⣅⡰⢿
⠀⠀⠉⠛⢯⡉⠛⠋⣠⠟⠉⠀⠀⠀⠨⢴⠤⠿⠶⢦⠗⠀⠀⠀⠀⠣⠴⡛⠛⠋⡹⠒⠁⠀⠀⠀⠀⠀⠸⣧⣿⣧⡼⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢦⣓⡠⠃⠀⠀⠀⠀⠀⠀⠀⠙⠠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⣁⠅


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣷⣾⢡⡶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠶⡟⣻⣦⣿⣧⣙⣲⣯⠶⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠐⠦⣼⣸⢿⣵⠊⠁⠀⠈⣙⢯⣔⡃⠄⠀⠀⠀⠀⣷⢀⡟⠀⡀
⠀⠀⠀⢀⡀⠈⢷⣠⡟⠀⠀⢸⡛⣦⢼⡿⢋⡀⠀⠀⠀⢊⡥⢄⢻⡿⠗⠀⠀⠠⣀⣸⣾⡶⠋
⠀⠀⠀⠀⠉⢓⣬⡟⢻⡄⠀⠐⠒⣨⡿⠁⢾⣿⠀⠀⠀⡋⣶⠀⠘⣷⠀⠀⠀⠀⠈⣿⡼⠋⠛⠒
⠀⠀⠀⠀⠛⠛⢉⡿⠛⢷⢦⡀⠀⣿⡇⠀⠠⠤⠂⠒⠀⠘⠒⠁⠈⣿⡆⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠣⡱⣄⠹⡅⡄⠀⠀⣶⡟⠿⣷⡄⠀⣼⠿⠁⢀⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠳⣝⢌⡲⣜⡛⠾⠟⢛⣠⡾⢋⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠘⠋⠹⣿⠮⠵⡶⢾⣁⣴⠏⢉⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠘⢧⣼⠁⠀⠙⠃⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠉⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⠀⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⣩⢿⣖⠒⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⣴⠏⠸⣿⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣰⡟⠀⠁⠀⠀⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠢⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣰⣶⣄
⠀⠀⠀⠀⠀⠀⠸⠿⠶⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣏⡁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠻⠿⣿⣿⣶⣄⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⠒⠢⢤⣀⠘⢿⡇⠀⠀⠀⣀⡤⠶⠒⠒⠒⠒⠦⣤⡉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡁⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣇⣨⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢎⢀⡀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠲⢤⣀⠀⠀⠀⣼⠃⠈⠧⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠐⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⢰⡿⠿⣿⡛⠛⠓⢦⠀⠀⠀⠈⠙⠒⠦⠤⠤⠤⠴⠖⠋⠁⠀⠀⠀⠀⠈⠛⠲⠦⠤⠤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠉⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣤⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⡼⠁⠉⠉⠛⠓⠶⣶⠶⠶⠦⠤⠶⠶⠶⣶⠖⠒⠛⠁⠁⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠉⠙⡟⠉⠉⠉⠉⠉⢻⠉⠉⠉⠉⠉⠉⢻⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⢀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠾⠧⣤⣤⣤⣤⣤⠴⠷⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠟⠻⣄⠀⠀⣈⠿⢿⣷⣄⡀
⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠀⠀⠀⠘⢧⡾⠃⠀⠀⠈⠉⠛⠷⢦⣤⣀⡀
⠀⠠⠔⢺⡟⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣘⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢹⡉⠁
⠀⠀⠀⠘⡷⠒⠒⠊⠙⢏⣹⣯⠿⠁⠀⠀⠀⣿⠀⠙⠭⠯⠟⠉⠉⠉⠀⠒⢺⠇
⠀⠀⠀⠀⢿⡤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠠⠀⠀⠀⠀⠀⠀⣀⠀⢀⡟
⠀⠀⠀⠀⠈⢳⣄⠀⢀⡮⠀⠀⠀⠀⠘⣠⠞⠙⠦⣀⠀⡇⠀⠀⠀⢈⡽⠏
⠀⠀⠀⠀⠀⠀⠉⠳⠶⣇⣀⣀⡤⠴⠚⠁⠀⠀⠀⠈⠉⠓⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠴⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⣯⣛⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠈⠙⠻⢯⣿⣻⣶⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣿⣻⡽⣲⢤⣀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢽⣞⠯⣡⣴⠦⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠹⣿⣷⠇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠴⠚⠁

⠀⢠⣤⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⢀⡤⠾⠀⠀⠀⣀⡀
⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠉⠙⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠰⠀⠀⠀⠀⠆⡀⠀⠀⠄⠀⠠⢶⢶⣤⣀⣠⣀⣠⣤⡶⠟⢻⠉⠀⠃⠀⠀⣀⠙⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⠘
⠰⠀⠸⠇⠀⡇⠛⠀⢀⠂⠀⠀⠀⠀⠀⠉⠉⠩⡁⠈⠁⢀⠌⠀⠀⠇⠀⠀⠿⢠⠙⠁⠀⠌⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠈
⠀⠑⠀⠀⠔⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠂⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠒⠀⠀⠀⠀⠀⠀⠉⠓⠀⠙⢒⠀⠀⠀⢠⠴⠒⠀⠀⠐⠢
⠀⢀⣠⠾⠛⢁⡐⠳⣄⡀⠀⠀⢀⣤⣤⣀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠠⠂⠀⠀⠐⠂
⠐⡏⠁⣤⠄⠨⠄⡤⠀⠈⡃⠀⠀⠀⠀⠉⢻⡆⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠠
⠀⢳⠀⠀⠀⢠⡄⠀⠀⢠⠁⠀⠀⠖⠒⠬⣆⠀⠣⠘⠃⠀⠄⠀⠀⠡⡀⠀⣠⡄⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠈⠁
⠀⠀⠑⠄⠀⠃⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⣀
⠀⠀⠀⠐⠶⠐⠁⠀⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⠴⠂⡘⠛⠦⣄⡀
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂⠀⠀⠀⠠⢡⣶⢦⡄⠁⣴⣶⠆⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋⠀⠀⠴⠱⠆⠀⠀⡉
⠀⠐⠀⠀⠠⠇⠀⠀⠐⠖⠀⠀⠀⢀⠤⣿⡷⠀⡄⠭⢿⠟⠀⠀⠀⠆⠀⠒⢀⡆⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⣀
⠀⣰⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠤⠄⡀⠀⠙⢛⡢⠀⠀⠀⢘⠩⠅⢀⠀⠈⠍⢃⠀⠀⠀⠀⠨⠀⠠⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠟⠛⠷⠆⠀⠀⢄⣀⣒⡂⠀⠄⠀⠀⠀⠀⠀⢀⠂⠀⢀⣤⢶⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣀
⠃⠀⠐⠛⠀⠰⠀⠘⠛⠉⣀⠂⠀⢠⠀⢉⡀⠀⣣⣼⡁⣰⡇⠀⠘⡀⠀⠈⠛⠸⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠈⠣⣙⣋⠼⠓⠉⠉⠚⠀⠀⠀⠻⢄⢀⡴⠋⠲⠤⠚⠁⠀⠀⠀⢦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⠀⠀⠀⠀⠀⠹⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠰⠛⣽⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣧⢀⢁⣤⠄⢀⣀⡀⢀⣤⡄⣠⣤⢀⣄⣀⡁⣀⡄⠰⢶⠷⠒⣤⣄⢀⣀⣾⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢠⣏⠀⠀⣀⡏⠚⠰⠿⠇⠻⠾⠛⣾⠛⢣⡟⠋⠘⠻⠛⠛⠋⠹⠶⠘⠶⠂⠛⠗⠘⠞⠛⠒⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠶⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⢠⣤⠀⢀⣤⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⣤⣄⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠐⠋⠀⠈⠧⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣤⠤⠴⠶⠛⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠘⠻⠆⠀⠀⠀⠀⠀⠀⠰⠟⠓⠀⠀⠀⠈⢙⠃⠀⠀⠀⠀⠀⢠⣤⣴⠿⠇⢀⠀⢀⠰⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⡀⠀⠀⢱⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠑⠁⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⠚⠀⠀⠀⠀⠀⠀⠀⠤⠀⠡⠀⠉⠀⠎⠁⠀⠀⠌⠀⠀⠀⠀⠀⠐⡀⠀⠀⠙⠃⢠⡉⠋⠀⠀⡰
⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠠⠤⠤⠐⠁⠉⠂⠐
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⡐⠀⠀⢠⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⣒⠒⠂⠄⡀
⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⡀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠛⠀⠀⠀⠀⠾⣦
⠀⠀⠀⠀⠠⠶⠦⣤⡀⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠀⠄⡀⠈
⠀⠀⠀⢀⠀⠀⠀⠈⢁⠔⠀⠀⠡⡀⠀⠀⠀⠀⠉⡟⠛⠷⣶⢤⣴⣤⣶⠞⠛⠉⡉⠀⠀⠀⠀⠀⠐⠀⠿⣽⡻⠂⠁⠿⣯⣏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⡇⠀⠀⢀⡤⠀⠡⢀⠀⢀⡠⠂⠢⢀⡀⡀⠔⠀⢀⠀⠀⢠⠄⠀⠐⠺⠿⠟⡠⠧⡚⠻⣋⠄⠀⡀
⠀⠠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢢⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠈⠓⠀⠄⠀⠀⠀⠀⣀⠠⠐⠊⠀⠀⠀⠀⠀⠀⠱⠀⢄⣀⣀⡀⠠⠄⠐⠊
⠀⠀⠀⠈⢆⠁⢀⡀⠀⡃⠀⣁⡀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸
⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⢁⡀⠤⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠔⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠴⠶⣦⣤⣀⡀⣀⣀⣠⣤⠶⠿⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠚⠛⠓
⠀⠀⠀⢄⠀⠉⠋⢉⠛⠉⠙⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⢁⡄⠀⠀⠀⢀⡀⠀⠀⠘⠄⠀⠉⠋⠀⠸⠀⠈⠉⠀⢀⠜
⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠹⠁⠀⢀⠀⠀⠁⡐⠂⣀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠄
⠀⠀⠀⠀⣤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠲⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠀⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⣶⣦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠰⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠆⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠻⣷⣤⣀⣀⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⣀⣠⣼⠟⠁⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⢁⣀⣀⣀⣀⣀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⠿⠟⠛⠛⠛⠛⠛⠿⢷⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠿⠿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠟⠛⠛⠛⠛⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⢀⣀⡙⠟⠋⠁⠀⠀⠀⠀⠀⠐⣲⣶⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⢙⣲⣦⣤⣤⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⡇⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠧⠔⠃⠀⠀⠀⠀⠀⠀⢏⣙⣿⣿⣿⠆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣤⣤⡴⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣯⣭⣿⣿⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠁

⢀⣠⣤⡀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⠀⠀⠀⠀⡄⣄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⣠⣤⣤⣄
⠈⠉⠁⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠪⠟⠀⠀⠀⠀⠪⠟⠀⠀⠀⠀⠀⠀⣿⠥⠾⠯⢵⡀⠀⡎⠤⠟⠯⣿
⣴⣶⡄⠀⠀⠀⠀⠀⠀⣾⣳⡆⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⠁⣤⡀⠀⠀⠁⠈⠀⠀⢠⣤⠈
⠙⠛⠃⠐⣦⣀⣠⡞⠀⠉⠋⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⠀⢠⣄⠀⠀⠀⠀⠀⠈⠁⠀⠠⡀⠀⠀⡠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⢦⡀⢀⡰⠀⠈⠁
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑⠤⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉



⠀⡴⢦⡴⣆⠀⢠⡶⣤⢲⡄⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⢠⢤⡀
⠀⠙⢎⡴⠁⠀⠀⠳⠤⠊⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠉⢁⣀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠐⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳⠽⠃⠀⠀⠀⠳⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠀⠀⠀⠀⠀⠀⡀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠐
⠀⠀⠀⠘⠧⣤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁



⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠙⠁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠢⠤⠄⠀⠀⠀⠢⡤⠖⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⣈⡵⠆⠀⠀⠀⢮⣁
⠀⠀⠀⡤⣀⣀⣀⣤⠄⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⣾⢷⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠬⣭⠥⠊⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠈⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠊



⠀⠀⣠⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠘⢜⠟⠀⠀⠀⠘⢜⠟⠀⠀⠀⠀⠀⠀⠐⠦⠤⠆⠀⠀⠀⠦⠤⠒⠀⠀⠀⠀⠀⠀⠀⡎⣷⠀⠀⠀⠀⡎⣷⠀⠀⠀⠀⠀⠀⠀⠀⣟⣹⠀⠀⠀⠀⣟⣹
⠀⠀⠀⠀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡙⠉⠀⠀⠀⠀⠉⢉⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠠⣟⣡⣤⣤⣄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠇⠀⠀⠢⠔⠂⠀⠘⠯⠋⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⣠⠖⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠒⠒⠒⠒⠶⢤⣄⡀⠀⠀⠀⠈⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⢸⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣁⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣣⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣤⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⡲⠞⣁⡴⠖⠛⠉⠉⠉⠉⠉⠛⠓⠦⣄⡀⠀⠀⠉⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⣠⠖⠉⠀⠀⢀⣾⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⡶⠒⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⣻⠁⣴⠷⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢿⡄⠀⢀⡞⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡰⠋⠀⡇⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⠃⠀⠀⠀⢀⡿⢄⡀⠀⠀⠀⠀⢀⡠⣄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠂⢀⡀⠙⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠙⣦⠀⠀⠀⣾⠁⠈⢧⠀⠷
⠀⠀⠀⠀⠀⠀⠀⢠⠖⣉⠭⢍⡀⠀⠀⢿⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠓⠦⡀⢸⠀⠀⠀⠀⠈⠳⣄⠀⣼⠋⠉⢢⣏⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠙⢦⠀⢸⠀⡴⠋⠀⠀⠙⣆⢀⣤⢤⣄⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⡇⠘⣇⠀⠀⣠⣀⣤⣈⡄⣏⠀⢀⡏⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣷⡀⠀⠸⣇⠤⣇⢧⣠⣤⣤⣄⠀⢾⠀⠀⠘⠃⠀⠠⠴⠖⠛⠛⠛⠿⢿⡷⠀⠙⢦⡜⢡⡏⠀⠈⠁⢉⡒⠋⠀⠀⢀⡜
⠀⢰⡆⢀⡴⠞⠓⢶⠋⠀⢀⠙⠀⠀⣇⠀⢸⠛⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⢸⠁⠈⢳⡖⠓⡆⠘⠃⠀⢠⡴⠋
⡄⠀⠀⢸⠀⠀⢀⣼⡀⠀⢹⡄⢠⠀⠉⠀⡇⠀⠀⢀⠔⠚⠉⠉⠉⣱⠶⠤⢄⣀⡀⢀⣀⡡⠏⠀⠉⠁⠀⠀⠀⣤⠤⠚⢀⡜⠀⠀⠀⠀⢸⠁
⢱⡀⠲⡀⠳⠖⠁⠀⠙⣶⠚⠀⠘⢦⠀⠀⣇⠀⠀⠻⡀⠀⠀⠰⠋⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⠎⠀⠀⠀⠀⠀⡸
⠀⠹⢄⠙⠆⠀⠀⠀⠀⠈⠛⠒⡞⠀⠀⠀⠘⠦⣀⠀⠙⠲⠤⣀⣀⣀⠤⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣀⠜⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠈⠉⠒⠶⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣰⠖⠒⠙⠋⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠒⠀⠚⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⢀⣇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣐⢒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣌⠙⠲⠦⢤⣀⣠⠤⠤⠖⠛⠉⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠲⣶⠶⠄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⢤⣀⡀⠀⠀⠀⣘⢻⡀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡏⠉⠛⠶⣄⡟⠘⡇⣠⡴⠶⠖⠲⣞⣸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠳⣄⠀⠀⡟⠃⠀⠛⠒⣷⠀⠀⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⣤⣤⣬⠦⢤⣄⢸⡇⣸⡳⡄⠀⠀⠀⣷⠶⠚⠛⢛⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⣭⡟⠁⠀⣎⠩⠷⠤⣒⡶⠾⠷⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⠢⣤⡀⡀⠀⠀⠀⠀⣨⠇⣀⣠⠔⣫⠃⠀⠀⢸⣇⢠⡞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢌⣉⣑⣒⣒⣚⣉⣉⠭⠔⠊⠁⠀⠀⠀⠈⢯⡛⠧⣄⣀⠀⠀⠀⢀⣠⠼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⠉⠉⠉⠁⠀⣤⠖⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢳⠀⠀⠀⠀⠀⠀⡈⠒⠀⠀⠀⠀⠀⠀⠀⣿⠐⠂⠀⠀⠀⠀⠀⠀⠐⠏⠆
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠆⠐⠐⠀⠐⠠⠀⠀⠁⠀⠁⠁⠀⠀⠡⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠈⠁⠀⠆⠀⠄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⠀⠀⠀⠀⠀⣀⡔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠆⠀⠀⠀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠀⠀⠠⠘⠆⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⢄⠘⠀⠀⠀⠀⠀⠀⢢⠄⠤⠂⠲⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣠⡀⠨⠃
⠀⠀⠓⠀⠀⠀⠋⠀⠀⠀⠀⠃⡀⠀⣀⡀⠀⠀⠀⢠⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⢀⡀⡀⠅⠀⠀⠀⠀⠁⠀⠀⠝⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠲⡀⠀⠀⠀⠀⠀⠀⡒⢲⡄⠀⠀⡀⣠⡔⠦⡄⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⠀⠠⢤⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠑⠀⣰⠀⠀⠀⠀⡀⢦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠒⢀⠀⡦
⠀⠀⠀⠙⠀⠈⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⢠⠄⠀⠀⠀⠀⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀
⠀⠀⠀⡴⠢⠰⠀⠀⠀⠀⠀⠀⠐⠚⠲⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠂⠀⠀⠬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠒⠂⠐⠒
⠀⢀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢤⣤⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠈⠠⠀⠄⠀⠌⠁⠀⠀⠐⠀⠐⠀⠀⠂⠀⠚⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠀⠑⠖⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠢⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁
⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⢻⡿⠛⢿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⠛⠋⠻⣿⠟⠻⣿⣿⣿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠾⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠈⠃⠶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠃
⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠤⠤⠤⠤⠤⠴⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠒⠒⠚⠋⠉⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣠⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢀⣴⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣭⣽⣵⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣾⣷⣾⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠟⠛⠉⠉⠉⠁⠀⠀⠉⠉⠉⠙⠛⠿⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄
⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄
⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠛⠿⣿⣷⣤⣀⠀⠀⠀⣿⣿
⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡷⠀⢰⣿⡟
⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠛⠛⠛⠶⢦⣄⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⣘⡅⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠁⠀⠉⠀⠳⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠓⠒⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⣀⡴⠀⠀⠀⣠⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡠⠾⢥⣀⠀⠀⠀⡹⠦⣄⡀⠹⡆⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢳⡄⠤⠄⢀⡧⠚⠀⠀⠀⠙⡆⠀⡾⠁⠀⠀⠙⣦⢹⡖⠒⠲⠚⠁⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡸⡀⠀⠀⠀⠀⠀⢻⡸⠃⠀⠀⠀⠀⢿⠈⣇⠀⠀⠀⢸⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡄⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢾⣿⠀⠀⠠⢐⣀⣺⡇⣿⠀⠀⠀⣾⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡇⠀⠀⠀⠀⣯⡀⠀⠀⣰⣿⡛⣿⣿⠀⠀⣴⣿⣏⣿⡇⣿⡀⠀⠀⣿⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⡇⠀⣰⣿⣿⣿⡿⢸⡆⢰⣿⣿⣿⣿⠃⡿⢣⠀⠀⠏⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃⠀⠀⢀⡜⢣⢱⡄⢿⣿⣿⣿⣃⠀⢻⣿⣿⣿⣿⡟⢰⠇⠈⢦⡀⠂⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⢀⠔⠊⠀⠘⣄⠻⣿⡟⠟⢁⠈⠀⠀⠙⠛⠿⠟⢡⡟⠀⠀⠎⠩⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠀⠀⠱⡀⠀⠘⣆⠀⠀⠀⣄⣠⣄⡀⠀⠀⠀⣰⠏⠀⠀⢸⠀⠀⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠀⠀⠀⡇⠀⠀⠈⠳⣄⠀⠘⠀⠈⠉⢧⠀⠚⣧⠀⠀⡤⠚⢄⠀⡄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⡆⠀⠀⠗⠈⠑⠆⠀⠈⠳⡇⠀⢀⠀⠀⡇⠀⣿⡤⠶⡀⠀⠐⠀⣿⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣷⠀⠀⢠⠀⠀⠐⠂⠀⡊⠳⢤⣶⣤⣿⡇⠀⣿⠀⠀⠄⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⢹⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠿⣿⣿⡇⢠⡏⠀⠀⠀⠀⠀⠀⣿⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠀⠋⢻⠀⡾⠁⠀⠀⠀⠀⠀⠀⣿⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢸⡀⠀⠀⠀⠀⠀⠀⠀⢈⡄⢀⡴⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⡇⠀⠀⠀⠀⠀⠀⢰⡁⠿⠊⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡰⠀⠀⠈⡄⢧⠀⠀⠀⠀⠀⠀⠀⠑⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣠⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⣀⠤⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢀⡈⡠⢀⣈⠀⠳⣄⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⢠⡿⠠⡇⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠈⠘⢁⠈⠙⢧⣄⠈⢧⡜⠀⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⡘⠃⠈⠁⠀⠀⠀⢢⡀⠠
⠀⠀⠀⠀⠀⠀⠀⡖⠉⠳⢶⣄⣉⠳⠄⠁⢀⠃⣇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⠇⢀⠀⠦⠄⠀⠠⠖⠐⣢⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠒⠐⠒⠋⠀⢸⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡞⠀⢸⣀⣀⡀⠀⠀⠙⠉⠁⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢸⠁⠀⠀⠀⠀⠈⠛⠒⠲⠶⠖⠁
⠀⠀⠀⠀⠀⢀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⠀⡿⠙⠒⢰⡖⡶⠒⠒⠒⠲⠶⠦⣾⠁⠀⠇
⠀⠀⣰⠚⠉⢻⡆⠰⡈⢳⡀⠀⠀⠀⢀⠞⣡⠬⡇⠀⠀⡛⠤⠠⠜⡰⠁⠀⠀⠀⠀⠀⢰⡏⠀⢸
⠀⠰⠃⠀⠀⢠⡇⠀⠩⡄⢳⣀⢀⡰⣡⠎⠀⠀⡶⠀⡼⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢾
⢀⠃⡄⢠⠀⠸⡀⠀⠀⠙⢄⣉⣩⠾⠁⠀⢠⣞⠁⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠻⡀
⠘⠁⠁⣎⠘⣄⡙⠦⣀⡀⠀⠀⠀⠀⠀⠀⣠⠋⠉⠉⠙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠒⠒⠲⣬
⠀⠀⠀⠉⠀⠈⠙⠓⠉⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⡆⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡇⠀⠀⠈⢳⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣘⣷⣤⣤⣴⣒⣚⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣳⣶⣶⣒⣚⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣦⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⠿⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠚⠛⠛⠉⣿⠿⠿⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⢠⣤⡄⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⠿⠟⠛⠉⠉⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⣿⡿⢿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠙⠦⣴⠿⠋⠀⠉⠉⠛⣻⠏⣿⠋⠉⠻⣅⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⡟
⠀⠀⢀⣠⣶⡟⠛⠛⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⠀⠀⠀⠀⠙⢶⣄⣀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⢰⠇
⠀⢠⠟⠁⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⠙⠛⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠓⠒⠒⠒⠚⠛⠛⠛⢉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠉⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠀⠀⠐⠒⠒⠒⠒⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⣠⠖⠛⠉⠉⠛⠓⠶⡋⠁⠀⠈⠙⣷⣴⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣼⡁⠀⠀⠀⠀⠀⠀⠀⠈⣀⣠⣤⠾⠋⠁⢰⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠶⠖⠛⠛⠉⠉
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣰⠷⣄⠀⣠⠶⣄⠀⠀⣀
⠀⢀⡤⣾⢻⡏⣷⣀⠀⠀⢀⣀⠀⢸⠉⠳⢤⡏⠀⠈⠛⠁⠀⠹⠞⠋⢹⠀⠀⠀⠀⠀⠀⠀⣀⣴⠳⣄⣤⡀
⠀⠸⣄⡈⠀⠀⣉⣹⠆⠀⢸⡍⠙⠛⠀⣀⣀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠘⠛⢹⠇⠀⠀⠀⢸⣍⠛⠀⠋⠼⠷⡄
⠀⠀⠈⢧⣀⠀⠻⣅⠀⢶⠤⠇⠀⢠⢎⠏⣯⢱⠀⠀⠀⠀⡏⣼⢹⢹⠀⠀⠛⢲⠆⠀⠀⣀⡾⠁⢀⣠⠤⠞⠁
⠀⠀⠀⠀⠉⢧⡀⠀⠙⠾⠇⠀⠀⠘⢾⣦⡯⠞⠀⠀⠀⠀⠑⠿⠾⠋⠀⠀⠴⠯⠶⠶⠛⠁⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⠀⢠⠴⣞⡿⠉⠉⠉⠹⠽⠋⠳⡀⠀⠀⠀⣀⣀⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⡇⠀⠀⣀⣀⡀⣀⣤⣀⠀⠀⡇⠀⠀⢙⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠀⠀⠀⠳⣄⣞⡁⠀⠉⠁⢀⣈⡦⠞⠁⠀⢘⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠶⢶⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⣀⡀⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡇⠀⢤⣀⡤⣄⣀⡴⢶⠀⠀⣿⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠉⠀⠈⠉⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡇⠀⢸⠀⠀⠀⠀⠀⢸⠀⢀⠟⠛⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⠤⠭⠥⠤⠾⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣦⣀⣶⣤⣶⣴⣴⣆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡌⣷⣾⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣷⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣪⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠘⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⠃⢀⣠⣴⣶⠶⠤⢄⣀⣠⠴⠋⠉⠀⠀⠈⠻⣶⣄⠀⠘⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣻⣿⣿⠃⣰⣿⡿⠋⠀⢀⣀⣀⡀⠀⠀⣠⠤⠶⠦⣄⠀⠹⣿⡆⠀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠸⣿⠟⠀⣠⠾⠋⠉⠉⠙⢷⡞⠁⠀⣀⠀⠈⣷⠀⠀⠀⠀⠈⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⣼⠃⠀⠀⢾⡆⠀⠸⣧⠀⠀⠻⠃⠀⢸⡇⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣰⠿⣦⣄⡀⠀⣀⣾⠃⠀⠀⠀⠀⢸⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠻⣦⣤⣤⣶⣿⠁⠀⠈⢿⣿⣿⣏⣁⠀⠀⠀⠀⠀⢘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢔⡿⠏⣼⠀⠀⠀⠀⢿⣏⡑⠒⠀⠀⠀⠀⠀⡂⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⢀⡴⢿⠀⠀⠀⠀⢸⣿⠙⣦⠀⠀⠀⠠⠄⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⣇⠀⠀⢀⣼⣿⣤⡿⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡉⢙⢻⡿⡟⠋⠀⠁⠀⠀⠀⠀⠀⠈⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⠄⠀⠄⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⢀⠀⠀⠀⠀⠀⠀⢀⠐⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠳⣄⠀⠀⠒⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠤⢤⣤⣤⣤⣄⣀⣀⣝⣠⣿⣴⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉


⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠎⢉⡆⣀⣄⡀⢫⣿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢧⢀⣀⠀⠀⡠⢄⠀⡤⠒⢣⣀⡙⢾⡄⣸⠏⠁⣠⡷⣾⣏⠉⠀⠀⢀⡞⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠈⢾⡅⠑⡞⠀⠀⣹⣀⠀⢫⣀⣉⣵⣋⣹⣞⣉⠙⢲⣀⠞⠒⣆⣠⠞⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠱⢄⣳⡤⠒⢧⡟⠒⢻⠋⣀⢜⠏⢹⡀⢹⢝⣩⢻⠛⠻⡍⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⢠⠊⠛⣄⠀⢀⣇⠀⢈⠏⠁⠸⣀⡰⠉⠉⠀⢇⢈⢷⠐⠁⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣦⣜⢊⡟⠀⠉⠁⢈⡭⠥⢤⡀⠀⣠⠔⠒⠒⢄⠀⠁⠈⣇⣀⠴⠾⢥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢉⡭⠔⠚⣻⠀⠀⠀⢀⡏⠀⢀⣀⠱⣴⢁⣀⠀⠀⢸⠀⠀⠀⠸⣍⠙⠒⠦⣈⠑⢦
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠼⠥⠖⢋⣴⡇⠀⠀⠀⠀⣇⠀⠸⣿⡇⡇⣿⡿⠀⠀⡼⠀⠀⠀⠀⣏⠳⣍⠓⠺⠃⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠾⠤⠤⠤⠶⠚⠉⢸⠀⠀⢀⣀⡤⠼⠶⠖⠚⠒⠓⠚⠒⠒⠾⠧⢤⣀⡀⠀⢹⠀⠈⠙⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⣤⣄⣀⣀⣠⡤⠤⠴⠒⠋⠁

⠀⠀⠀⢀⡤⠒⠉⠉⠉⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⠉⠉⠉⠑⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠉⠉⠒⢤⡀
⠀⠀⣠⠋⠀⡠⣀⠀⠀⢀⣄⡀⠈⢆⠀⠀⠀⠀⠀⢀⠞⠀⢀⡀⠀⠀⠀⢀⡀⠀⠳⡀⠀⠀⠀⠀⠀⡰⠁⣀⠀⣀⠀⠀⡀⠀⡀⠙⣄
⠀⢀⡇⠀⠈⠀⠈⠀⠀⠉⠀⠉⠀⠈⡆⠀⠀⠀⠀⡜⠀⠀⠸⠟⠀⠀⠀⠻⠇⠀⠀⢣⠀⠀⠀⠀⢰⠃⠀⠈⠓⠁⠀⠀⠉⠊⠁⠀⢸
⠀⠈⡇⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠤⠤⣀⠀⠀⠀⢸⠁
⠀⠀⠳⡀⠀⠈⠓⠢⠤⠒⠁⠀⠀⡜⠀⠀⠀⠀⠀⠘⣄⠀⠈⠉⠉⠉⠉⠉⠁⠀⣠⠃⠀⠀⠀⠀⠀⢣⠀⠀⠊⠀⠀⠀⠈⠃⠀⢀⠞
⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠦⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠙⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠀⠉⠉⠛⠲⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢠⡞⣡⠲⣦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡏⠸⣇⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢻⣷⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⣲⣿⣿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⣠⣶⠶⠿⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⣼⠁
⠀⢀⡞⠉⢿⡄⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠈⠙⠲⠤⠤⠤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠈⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⠛⠷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠙⠛⠛⠿⠶⠶⠶⠶⠶⠶⠾⠛⠛⠛⠉⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡖⠒⠦⠤⠤⠤⢤⣤⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠤⢲⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣠⡼⠷⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⣠⠾⠛⠉⠉⠉⠉⠉⠛⠛⠶⣏⠁⠀⠀⠀⠀⠉⠳⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠙⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⡶⠀⠀⣀⣠⡤⠶⠖⠚⠛⠛⠛⢛⣛⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⢁⣴⣫⡴⠞⠋⠉⠀⠀⠀⠀⣀⣤⣖⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣩⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢛⡽⢖⣠⡤⣤⣄⡈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢯⣥⠀⠀⠈⡼⠋⠀⠀⠀⠀⠙⠳⣄⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡐⠂
⠀⠀⠀⠀⠀⢀⣹⠀⠀⠀⠀⠀⢴⠚⠉⠀⠀⢀⠞⠛⠀⠀⠸⡇⠀⢀⣤⡀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠙⢦⡀⠀⡤⠤⢬⡀⠀⢌⠉
⠀⠀⠀⠀⢰⢋⣽⠀⠀⠀⠀⠰⣶⠓⠀⠀⠀⠏⠀⠀⣤⠖⠛⠛⠲⣥⣿⡿⠀⠀⠀⠀⣸⠃⠀⢀⣀⣀⡀⠙⣎⠣⣤⡞⠉⠙⣦⡤⣄
⠀⠀⠀⠀⠸⢣⡏⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⡆⠀⠀⠀⣀⡴⠋⠀⠐⠉⠀⠠⡟⠉⠻⣦⠏⠉⠉⠜⢁⣀⣸⠃⡴
⠀⠀⠀⠀⠀⢸⡇⣴⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⣧⡀⠀⠀⠈⣹⡟⠒⠚⠛⠉⠀⠀⠀⠀⠀⢀⣠⠟⠙⢲⡈⠀⠀⣠⠞⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠻⠙⣆⠀⠀⠀⣀⣀⡀⢹⠀⠀⠀⠀⠈⠙⠒⠒⢊⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡡⠤⠀⣸⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠋⢉⣉⣉⣉⠉⠃⠀⠚⢯⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢾⡉⠲⢤⡴⢣⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠛⠷⠶⠋⢁⣴⣄⠀⠀⠈⠙⠒⠦⠤⣤⣤⣤⡤⠴⠖⠛⠉⠙⣆⠀⠈⠣⡀⠙⢧⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⠴⠞⠋⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⢩⣷⡀⠀⠀⠀⢀⣧⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢻⡋⠀⠀⠀⠀⠀⢠⠖⠀⠀⠈⠉⠙⠓⠒⠒⢚⡿⠯⠭⢤⣤⣀⣸⠶⠿⠦⠤⠶⠋
⠀⠀⠀⠀⠀⢀⣰⡟⢻⡀⣠⣿⣶⣄⣀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢯⡀⠙⠜⠛⠁⣨⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⣾⡋⠑⢂⣠⠼⠉⠓⠶⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⠴⠞⠁
⠀⠀⠀⠀⡼⠁⠉⠉⠉⠀⠀⠀⠀⢀⡴⢋⡴⠋⠉⠉⢀⡤⠞⠁
⢀⣠⠤⠾⣧⡀⠀⠀⠀⠀⠤⠤⣴⣏⣴⣏⡀⠀⣠⡴⠋
⣟⠀⢠⠞⠧⠽⠛⠲⢤⣤⣄⣴⣋⣤⡤⠴⣶⣫⢿⠉⢳⡄
⢿⣓⣛⣓⣚⣛⣛⣭⠭⠵⠚⠯⢽⣓⣒⠒⠾⠶⠛⣒⣿

⠀⠀⠀⠀⠀⣠⣶⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⣠⠤⠶⠖
⠀⠀⠀⠀⣿⣿⡿⢿⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⢞⣡⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠉⣵⣾⣿⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀⣿⣾⡿⢋⠔⠒⠢⢍⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠘⠻⣶⣄⡘⣿⣷⡧⢊⠭⣑⢄⠑⡜⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣀⣿⣦⣶⠶⠿⠟⠛⠛⢛⣿⠿⠛⠿⢿⣿⠷⣶⣤⣦⡣⠈⠢⡙⢿⣆
⠀⠀⠀⣀⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣶⠦⢹⡆⠀⠈⠙⠻⣿⣢⡙⢦⢹⣷
⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣀⣈⣡⡾⠁⠀⠀⠀⠀⠈⢿⣞⢸⢸⣿
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⢸⣟⠣⠜
⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⢸⣿⣧⣿⣦⡀
⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣏⠁⠀⠀⣠⠾⠿⣿⣿⠿⠞
⠀⠀⠀⠉⠛⠿⠶⠶⣶⣦⣤⣤⣶⣶⡶⠶⠶⠀⠀⠀⢀⣴⠋⠀⢿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢀⣀⣠⣤⠶⠛⠁⠀⣠⣾⠀⠀⠀⠺⣶⣶⡿⠋⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢻⡄⠀⣀⣠⣾⠿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠻⣿⠟⠋⢀⡼⠃⡀⠀⠀⠀⢸⡏⠀⠀⠀⢴⣿⣶⣾⣿⣾⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠛⠉⣀⣴⠏⠀⠀⠀⣿⠃⠀⠀⠀⠀⢀⣼⡿⣿⠟⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⣤⣄⣀⣀⣀⡀⠀⠀⠈⠉⠀⢀⣀⣀⣰⡟⠀⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠒⠲⠶⠦⠬⠭⣿⣤⣾⣉⣉⣉⣉⣉⣉⣿⣧⡶⠿⠛⠉
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡇
⠀⣰⠋⠙⡇⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⢸⠇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⣠⣿⢀⡞⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠷⠴⠚⠛⠻⠶⣦⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠷⢶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⣶⠶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠲⢦⣤⣤⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡾
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢲⣤⣍⣉⣥⣴⠂⣿⣿⣿⣿⠐⣦⣬⣉⣩⣤⡞⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⡙⠻⠿⠛⣁⣼⣿⣿⣿⣿⣧⣈⠛⠿⠟⢋⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⣡⣴⣾⣿⣿⣿⣿⣷⣦⣌⢻⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠆⠀⡄⠀⠀⡂⡤⠀⢠⣦⠀⠄⠀⠠⠀⠀⠀⢰⠐⠆⠆⠰⠀⠂⡀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠿⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷
⠀⠀⠀⢠⠖⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⢆
⠀⠀⠀⠘⠦⣤⣤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⣤⡤⠏
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⡀
⠀⠸⢤⠤⠔⠂⠀⣀⣀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠂⠉⠙⠂⠀⠀⠀⠀⠀⢸⠀⠀⠒⠤⢄⠼
⠀⠀⠀⢀⣴⢾⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⢰⠟⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠉⠛⠲⠶⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢤⣄⣀⣀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣠⣽⣧⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⢠⠔⠋⠉⠉⠉⠉⠛⢏⠀⠀⠀⠈⣻⡾⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣏⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠟⠋⠀⠸⠿⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁

⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⣀⣀⣀⣀⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣄⣀⣀⣀⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣯⣀⣀⣠⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣀⣠⣤⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠋⠉⠉⠉⠛⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡧

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣛⣯⣭⣟⣻⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇