Ascend Emojis & Symbols

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⣤⣠⣤⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁
⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣬⣉⣉⡛⠻⣟⣿⣿⣿⣿⠏
⢠⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣿⣯⣽⣿⠏⠀⠀⠀⠀⣴
⢹⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣀⣤⣦⠻⣿⣿⣿⠟⠉⠀⠉⠙⠻⣿⢸⣿⠟⠉⠉⠉⠻⣿⣿⢯⣼⠿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣾⣿
⢸⣿⣿⣿⣿⣿⠁⢀⣠⣶⣿⠿⠛⠛⢷⣜⣿⡇⠀⠀⠀⠀⠀⠀⠉⠘⠁⠀⠀⠀⠀⠀⣸⢇⠞⠁⠀⠈⣿⣿⠋⠀⠀⠀⠀⠀⠈⣿⣿
⢸⣿⣿⣿⣿⣷⣶⣿⣿⣿⡏⠀⠀⠀⠀⠙⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⠀⠀⢠⣾⣿⠃⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠈⣿⣿⣿⣿⣿⣿⣿⣯⣈⢙⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⢰⣾⣿⣿⣿⣇
⢰⣿⣿⣽⣻⣿⢿⣿⣿⣿⣿⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⠏
⣿⣿⡇⠈⢣⠀⣾⣿⡏⠙⣿⣿⣷⣕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⣠⣶⣍⡛⠛⠛⠛⠋⢀
⣿⣿⡇⠀⠀⠀⢿⠟⠷⢄⡘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⣦⣙⠿⠿⠿⠛⣣⣤⣴⣿
⣿⣿⡇⠀⠀⠀⠈⠠⣀⠀⠙⠿⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠸⣿⣷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⡀⠀⠀⠀⠙⠀⠀⠀⢘⣿⣿⣿⠁⠀⠀⠀⠀⠐⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣼⣿⡏⢈⡿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⣿⣏⣼⣿⣽⣿⣿⣿⣿⣿
⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠛⠉⠛⣹⣿⣿⣿⣿⣿⣿⣿
⣆⠀⢿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢶⣤⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⣿⣿⣿⣿⣿⣿⣿
⣿⡀⢸⣿⣷⣤⣄⣀⠀⠀⠀⠘⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⢿⣿⣿⣿⣿⣿
⣿⡇⠈⠻⣿⣿⣿⡿⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢸⣿⠀⠈⣾⢿⣿⣿⣿⣿
⢼⣷⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠰⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣬⣿⣧⡀⣿⡾⣿⣿⣿⣿
⠘⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⢸⣷⣽⣿⣿⣿
⠰⣿⣧⡀⣠⣤⣤⣶⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣼⣿⠛⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠋⢡⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⠏⠀⠰⠆⣳⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⡟⣿⣣
⠀⢸⣿⣿⣿⣿⡟⠀⠀⠰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠹⣧
⠀⠀⣿⣿⣿⣿⠃⣼⠂⢠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⢄⢻
⠀⠀⢹⣿⡟⣿⢠⣯⠰⠃⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠄⢀⣼⡄
⠀⠀⠈⡟⣸⡿⣾⣿⠀⠀⣿⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣤⣩⣷
⠀⠀⠀⢸⣿⠃⣿⣷⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⢀⣾⣇⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⡌⣿⣿
⡇⠀⠀⢸⡿⠀⣿⣿⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠿⠁⢻⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠸⣿
⣿⠀⠀⠸⡇⢸⣿⣿⠅⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣷⡾⠋⠀⠀⠈⣿⣄⣠⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⢇⡋
⣿⡄⠀⠀⠀⢼⣿⡋⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡘⠃⠀⠀⠀⠀⠘⣯⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣰
⣿⣇⠀⠀⠀⠀⣿⣿⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⣿⣿⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⢸⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⡜⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣠⣄⣈⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡿⠿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄⠀⠈⢻⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⢿⣿⢿⣿⣿⣆⠀⡸⣿⣿⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣸⣿⣿⡆⢈⠙⢷⡀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣿⣿⣿⡇⢠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠁⠀⠄⠀⠀⢿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⣦⡀⢀⠀⣀⣀⠀⠐⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠟⠋⠁⠀⢰⣾⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠙⣿⣿⣿⣿⢿⣿⡟⠷⢰⣿⣿⢶⣾⡆⠀⠀⠀⢠⣿⣇⠀⠀⢀⣤⣤⣀⠀⠀⣆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢿⣿⣿⡟⣮⣻⣧⣾⣎⢻⣿⣿⣽⣤⣤⣴⣶⣿⣿⡏⠀⠀⣾⣿⡿⠉⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⣾⣿⡏⠀⣿⡿⢉⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠀⠀⢀⣿⣿⠁⠀⠀⠀⣿⣿⡟⡀
⠀⠀⠀⠀⠀⠀⣰⠀⢠⣿⣿⡏⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣶⠂⠀⠀⣼⣿⡿⠀⠀⠀⠀⢹⣿⠀⠹⡀
⠀⠀⠀⠀⠀⢀⠏⠀⣾⣿⠋⠀⠀⠀⠻⠟⠋⠹⣿⣿⣿⣿⣿⣧⣤⣶⠿⣿⣷⡇⠀⣿⣟⡀⠀⠀⠀⠀⣸⣿⠐⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠀⢀⣿⣟⠙⠳⠦⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣃⢹⣿⣇⣸⣿⠁⠀⠀⠉⠉⠻⠿⡏⠁⠐⠤⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋⠁⠀⢠⣌⣉⡁⢠⠀⢿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠤⢽⠶⢦⣿⣿⣿⣿⣿⣿⣿⣽⡇⣽⣿⣹⡃⠀⠀⣀⠀⣀⣀⣀⣀⡀⢀⣄⣠⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⡿⠋⠀⠁⠀⠀⠀⢙⡟⠙⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠴⠈⣿⣿⣿⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⡈⠙⠟⠀⠈⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⠀⠀⢀⣾⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣸⣧⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣾⣷⣾⣏⢀⠀⠈⢐⠦⣀⠀⠀⠀⠀⠀⠰⣆⣖⡷⣷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣶⣶⣷⠀⣸⣯⣠⣤⠆⠐⠀⠀⠄⢠⣽⣆⢀⠀⠀⠀⢰⡮⠓
⠀⠀⠀⠀⠀⠠⣄⡤⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠙⠟⠛⠃⢄⢀⣼⣿⣤⠹⣿⣿⣿⣿⣦⡀⠾
⠀⠀⠀⠀⠀⠀⢻⠃⣠⣠⡀⢠⡖⠀⠀⠀⠀⠀⠀⠀⣈⣁⡘⠋⠉⠀⣠⡶⠀⢉⠛⠻⣿⣿⣦⡤
⠀⠀⠀⠀⠀⣠⢃⡞⣋⣩⠾⠞⢀⣀⣠⣤⣤⣤⣦⣉⣩⣼⣯⡤⠤⠤⠿⠃⠀⠉⠠⠄⠈⠛⢿⣽⣶⣤⡾⠃
⠀⠀⠀⠀⡴⢋⣤⠆⠀⠀⠀⠀⣸⣿⣿⠿⠛⠉⣉⣷⣿⣿⠃⡴⢂⠾⠉⠉⢲⣾⣶⡦⠘⠂⠰⢿⣿⢿⣷⡄
⠀⠀⢀⡜⣵⣿⡿⠀⠀⢀⣠⣾⡿⠋⠀⣠⡴⣿⣿⠿⠋⢁⣀⠳⣿⣧⣤⣤⡿⠿⠓⢛⡥⠀⢀⠀⠈⠅⣙⠿⡦
⢠⣾⡟⢹⡿⠟⠁⠀⣴⣾⣿⢋⡠⠔⠋⠁⠈⠁⠀⠀⠀⠈⠻⠇⠈⠉⠁⣠⡖⠀⠀⠈⠃⠀⠀⠑⢴⣴⢬⣤⡙
⠘⣧⡀⣼⡅⠀⠀⡸⠿⠛⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠛⠛⠁
⠄⠈⣿⣿⡟⠀⠀⢳⠐⠀⢱⠁⣶⣖⠀⢀⠀⠀⠀⠐⠀⢸⠀⠀⠀⠀⠘⠄⠀⠀⠀⢒⣅⣶⠀⠀⠀⠈⢷⣄⡀
⠶⣶⣿⡃⠀⢾⠰⠟⡆⠀⠠⣄⠙⠛⠀⡎⠀⢀⡀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⠀⠀⢀⠀⠀⡈⢡
⠀⠀⣿⡳⣦⠀⣶⠀⢸⠀⠀⠿⣿⣮⠆⠳⣿⣿⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡇⠀⠀⠀⢘⠀⡇⠀⠸
⠀⠀⠈⠳⠙⠘⣿⠀⠀⠃⠀⠀⣛⣉⡀⣶⣌⣛⢛⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⡏⡀⠀⢀⡤⠎⢈
⠀⠀⣴⢃⣦⣄⡈⠁⠀⠀⠀⠀⣮⣭⣛⠻⠿⣿⣼⣅⡀⢀⣄⠀⢀⣤⣤⢨⣍⣅⣈⡁⠤⠒⠉⣤⣾⣿
⠀⠀⢹⣾⣿⢻⡿⣲⣤⣤⠖⢊⣙⠛⢻⠿⠦⠄⠈⠉⠁⠻⠿⠀⠿⠿⣟⣛⣻⣩⣥⣴⣾⣿⠀⣿⣿⣿⡄
⠀⠀⠈⢻⣛⣚⣉⠉⠉⡁⢰⣿⡟⢻⣿⣿⣿⣿⣷⣶⣦⣄⠀⠛⠛⠿⣿⣿⢿⢹⣿⣿⣿⣿⡆⣿⠿⣿⡇
⠀⠀⠀⠀⠉⠻⢿⣧⣀⡿⠊⠛⢋⣩⣭⣴⣶⣿⣿⠬⣟⠛⢹⠂⣦⣤⣄⣀⣀⣮⣿⣿⣸⠿⠇⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⢡⣶⣖⠀⢹⣿⣿⣿⣿⡧⣍⠀⠛⠣⠆⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣷⣦⣿⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣴⡿⢿⣿⣿⢏⣵⣿⠀⣿⡖⢀⠀⢠⣝⠇⢸⡎⣽⣿⣿⡏⣽⡿⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠋⢰⣿⣯⢒⣿⣿⣄⣙⣁⣦⣀⣸⣿⠤⠘⠟⠛⡹⠏⠀⢾⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠀⢸⣿⡿⠿⢻⣿⠃⠉⣹⠋⠀⠀⡗⠀⠘⠀⢰⠃⠀⠀⠸⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡁⠀⢻⣿⣿⣿⠿⠛⠛⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠠⠾⠟⠋⠀⠀⢈⡠⠀⠀⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡇⠀⠀⢸⡶⠤⠀⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠻⣿⣶⣿⣿⠁⠀⠙⠓⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣼⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣮⣵⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢼⣿⡿⠈⠛⣿⣿⡟⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⢀⣠⣴⠟⠉⠀⠰⣿⣿⠁⡄⢸⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣤⣾⠟⠉⠁⠀⠀⠀⣴⢏⡏⠀⠀⢸⣿⣿⣴⠀⣹⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠚⢁⡾⠀⠀⡄⠛⢿⡟⠃⢴⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⣠⡿⠁⡰⠀⣧⣴⣿⡿⠀⠘⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢥⣤⣠⣴⣉⣀⣤⣶⣧⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣽⣿⣦⡄⠀⠀⡀⠀⠈⡰⠐⠒⠜
⠀⠀⡀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡋⠛⢿⠥⠖⠦⠓⢶⠂⢝⣫⣶⡖⢂⡖
⣀⣬⣵⣷⣯⣴⣵⣥⣀⣀⡀⠂⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠂⠀⠀⢹⣦⡈⠘⢿⣯⣷⣾⣷⡶⣶⣶⣷⣿⣶
⣿⣿⣿⣿⣿⣿⡿⣿⡿⡿⠿⠿⠖⠀⠀⠀⠀⠀⢐⣾⣿⣟⠁⡏⠀⠀⢀⡿⡗⠀⠀⢿⣿⣿⣙⠋⡉⠉⠉⠉⠉
⠉⠻⣿⣻⠿⠉⠛⠛⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠈⠻⣿⣿⡈⣇⡀⠀⠀⠀⠈⠀⠀⠈⠉⠙⠛⠛⡻⣿⣿⣿⣿
⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⡎⠀⠀⠀⠀⢻⣿⣷⣽⠳⣴⡬⢰⣾⣷⡖⢤⣤⣤⣿⣿⣿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠠⠀⠠⠾⠿⣏⠀⢙⡇⠀⡾⣿⣿⣮⣻⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢀⣶⡀⠀⠀⠀⠈⠁⠘⢿⣄⠈⠉⠙⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⡻⣿⣿⡿⡿⠟⠛⠛⠛⠛⣛⣿⣿⣿⣶⡄⠸⢯⣬⣤⣀⠠⠀⠀⠀⠠⡠⢞⢿⣖⣀⠘⠀⢪⣽⣿⣿⣿⣿⣿⣿
⠸⢿⣿⣿⣧⣠⣤⠐⠀⠛⠿⢿⣿⠿⠿⠿⠿⠝⠻⢿⡻⣟⠆⣠⡀⠀⠉⣽⣽⣷⣭⣶⣶⣿⣿⣿⣯⣿⣿⣿⣿
⠀⣈⣼⠀⠁⣊⠁⣙⠶⣤⣄⢀⣤⣵⣶⣶⢿⡶⠤⠤⠿⣿⣶⣤⣬⣥⣤⣥⣯⠹⠿⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿
⠀⠀⠸⠻⢷⣯⣸⣿⣿⣿⣬⣩⣗⣀⣀⢀⣠⡦⠄⠀⠸⠿⠿⠿⠿⠿⠶⢿⣿⣷⣷⣎⡛⠿⠿⠿⠿⠿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠉⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣣⣿⣿⣷⣤⢠⡆⠀⠀⣀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣶⣶⡿⢿⣶⣿⣿⣿⣿⡿⠿⠿⢿⣿⡯⣵⣾⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣤⠀⠀⢀⡀⠀⠿⠇⠀⠀⢀⡀⠘⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠛⠀⠀⠘⠃⠀⠀⢶⡆⠀⠘⠛⠀⢿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠀⢠⣆⠀⠘⠃⠀⠁⠀⠀⠰⣿⢸⣇⠗⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⠈⠛⠀⠀⠀⠸⡷⠠⣶⠀⢀⢻⡿⣤⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣦⡀⠀⣤⡄⠀⠀⠀⣷⠀⠿⢸⡇⢈⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠉⠀⠀⠉⠁⠀⣀⡄⠁⠀⣀⢸⡇⢠⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠃⠀⠀⣤⡄⠀⠀⠀⠛⠁⠀⠀⠉⢹⡇⠀⡆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣠⠀⠀⠉⠁⠀⠀⢠⣤⠀⠙⢀⡤⢸⡇⠀⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠉⠀⠀⠀⢾⣶⠀⠈⠁⠀⠀⠀⠀⣸⡇⢨⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢂⣶⡆⠀⠀⠁⠀⣀⠀⢳⣤⠀⠐⢿⡇⣴⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠀⠀⣴⡆⠀⠛⠀⣤⠀⠀⢠⣼⣏⠶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠴⠀⠀⠀⢠⡆⠀⢀⣀⡄⠀⠀⠉⢹⣯⠐⡌⣿⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢸⡇⣦⠀⣶⡄⠈⠀⠀⠈⠙⠁⠀⠀⠆⢸⣟⠃⢡⣿⡇⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢸⡇⠟⠀⠈⢡⡄⠀⠀⠷⠄⠀⢀⡀⠀⢾⣿⠈⣿⣿⡇⠀⠀⠀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣆⣠⣿⣷⡄⠀⢸⣧⡆⠰⠀⠀⠀⣀⡀⠀⠀⠀⠈⠀⠀⠀⣿⢰⣿⣿⡇⠀⠀⠀⠀⣪⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣏⣿⣿⣿⣇⢀⣸⠇⠀⡀⠀⠀⠀⠙⠃⠀⠘⠃⠀⠘⠃⠀⣿⢙⣿⣿⣇⠀⠀⢀⣤⣿⣿⣿⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠻⣿⣿⣿⠀⢸⡇⠘⢷⠆⠘⠛⠀⠀⠀⠘⠀⣠⡄⢀⣀⣿⠽⠇⣹⣿⠉⠉⠈⠉⢻⣿⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⠛⣿⣿⣿⠀⢸⡧⡆⠀⠀⡤⠀⢀⣴⠆⠀⠀⣀⠀⠈⠉⣿⠚⣋⢾⡿⠀⠀⠀⠀⠾⢿⣿⡿⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⠀⢸⡇⠀⢀⣄⠀⠀⠀⠀⠠⣤⡄⠀⢰⡆⠀⣿⣏⠷⣟⡿⠀⠠⠐
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⢹⣿⣿⡀⢸⣧⣃⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⠀⠉⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠈⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠐⠉⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠒⠋⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠻⠓⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣦⣶⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⢿⡷⢾⡂⠀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠀⢠⣤⣶⠶⢂⣸⢜⣿⡿⠗⣈⣿⣟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣿⣁⣾⣧⠜⢳⣾⠢⡀⢰⣞⣹⣿⣿⣿⡆⢀⣠⠜⣿⣏⢈⣿⣿⣓⣽⡿⠁⣙⣥⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣿⠫⢿⡷⠲⣮⠘⠷⣤⣼⡿⠋⠉⠉⡿⠃⠀⠀⢺⡛⣤⣼⠟⣩⣽⠆⠄⠘⣷⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠛⣧⠘⣿⣃⣸⣷⡆⣰⠟⠀⠀⠐⠶⡁⠀⢠⣀⠀⠙⣿⣀⣶⣮⢁⣤⡾⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠉⠠⢾⡋⢴⠞⠋⠀⣠⣴⡾⠂⠐⠷⠖⠋⠈⠁⠀⠈⠳⠛⠓⠈⠁⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠒⠚⠀⠘⠃⣘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠔⣮⢀⠔⠓⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣤⣮⣿⣷⣆⠀⠈⠀⠄⠀⠀⠀⠙⠉⠀⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⠀⢻⣿⠉⠹⢉⣴⣤⠀⠈⠁⠀⠀⠀⠀⠉⣡⠞⠁⠀⠀⠀⢠⣤⣠⣴⣾⣟⣧⠔⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣙⢧⣶⠀⠉⠐⠺⡮⢹⣿⣷⡄⠀⠀⠐⠂⠀⠨⠃⠀⠀⠀⠀⢰⣿⢯⣽⣜⣿⣿⠋⣰⣿⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣈⠛⣻⣾⣧⠀⠤⠀⠀⠀⣻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡙⠛⢋⣠⣾⣿⣋⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⢹⣿⣿⡟⠁⠒⢶⣃⣄⠄⢋⡉⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠈⣿⣻⣿⣿⣾⣧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⡿⠉⠙⠳⠴⠛⢃⡀⠈⠛⡄⠰⠀⠀⠀⠀⠀⠄⠀⠇⠀⠀⠀⠀⠀⠈⡷⡀⠉⣌⣿⣿⣷⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣀⢠⡄⢉⠀⠐⢀⣥⣀⣤⣄⣀⠀⠀⠀⠲⠤⠆⢠⠀⠠⢤⣼⠗⠿⠄⠹⣿⣿⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠋⢁⡀⠀⢸⠆⣰⠆⣿⡁⢼⣿⣍⠁⢀⣈⠣⠀⢤⣾⣿⠃⠀⣼⣷⠾⣽⣤⢾⣿
⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣀⣫⠏⢁⣴⣿⣷⣦⠘⣶⣷⣼⡿⠻⣿⢿⣿⣤⣈⣁⠐⠀⢄⣀⠰⡆⠀⣭⣽⠒⢼⣷⢿⣿
⠀⠀⠀⠀⠈⣙⣇⣌⣡⣴⢾⣿⣶⠿⢼⠟⣿⣷⡴⠈⠛⠛⠃⠰⣿⣶⣷⣿⡻⣿⣷⣶⡿⠿⢤⣤⣦⠘⣿⣿⣾⣿⣦⣿
⠀⠀⠀⠀⠀⠈⠋⣫⣾⠦⣿⣭⠟⣷⡈⢻⣷⡿⣿⡿⠆⠀⠀⠀⠉⠘⠻⣿⣷⣏⠙⢩⠶⡶⣦⣤⣉⠳⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠠⣄⡀⢸⣟⡹⣷⣎⡘⣿⣦⣿⡿⠻⡃⠀⠀⠀⠰⣤⡀⠘⢿⣿⣿⣿⠤⢻⣾⣿⡿⢿⣿⣶⣭⣿⣟⣻⣿⣶⣠
⠀⠰⠿⠶⠦⣤⣌⣠⣤⣿⣴⣯⠽⣷⣎⣿⣿⣷⣂⣱⠄⠀⠀⠀⠋⢙⣦⣤⠁⣿⣯⣤⠺⢿⣿⣿⣻⣷⣿⣿⣿⣯⣿⣻⡟⠁
⠀⠀⠀⠐⠋⠁⠀⠋⠠⠎⠀⣯⣶⣿⣿⣿⣏⣻⣿⣿⣦⡀⠀⠀⡰⢿⢻⣾⡀⣿⣿⣿⣿⣿⣻⣿⣿⣷⣹⣟⣿⣿⣿⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠊⠀⠀⠎⢿⡄⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⡛⠛⠛⣻⠛⠻⠛⢛⡻⠛⠛⠃⠀⠀⠀⠘⠻⠟⠛⣿⣟⠛⠛⢿⠛⠛⣿⠛⠛⠻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠈⣧⠀⠀⠙⠳⢦⡀⣿⡁⠀⠀⠄⠀⠀⠸⡀⠀⠀⠀⠻⠈⢷⣄⢸⠀⠀⣿⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠸⠇⠀⠳⠄⠘⠃⠈⠓⠄⠀⠂⠀⠀⠀⠘⠳⠖⠐⠶⠀⠀⠉⠛⠀⠀⠿⠀⠀⠒⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠘⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⡀⠀⠀⠀⠀⢠⠑⠂⠀⠙⣿⣦⣤
⠀⠀⠀⠀⢠⠤⠴⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠖⠀⠀⠣⠀⡄⠀⠀⠀⠽⠋
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡔⠁⠒⢂⠞⢆⠀⠀⠀⠀⠀⠀⠐⠀⠠⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⡀⠀⠳⣄⠀⠐⠚⠃⠀⠐⠄⢀⡀⠁⢌⡳⠂⡄⡀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⢀⡴⣒⠊⠰⣾⢤⠘⠦⡀⠀⠀⢰⡉⠀⡠⡀⢄⠜⠀⡀⠀⠈⢆⠀⠈⠈⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢋⠎⠀⢠⢘⠅⢀⡀⠀⢡⣀⠀⠀⠁⠀⠀⠉⠊⠄⠀⠀⠀⠈⠀⡱⡄⠀⠀⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⣠⠄⡀⢀⠵⠁⠈⠰⠂⠉⠀⠈⠀⠀⠀⠀⡇⠒⠀⠀⢐⡤⠰⢀⡄⠂⠈⠢⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠈⠀⠠⠘⠣⢄⡉⣓⢀⣠⠄⠄⠀⠔⠂⠀⠀⠀⠀⠀⠘⠄⡀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢲⠆⠀⠀⠀⠀⠀⠀⢕⢤⣀⠀⣠⡠⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠉⠉⠂⠀⠀⠀⠀⠀⠑⠀⣿⠟⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠉⣀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄⠀⠀⠀⠾⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠈⠙⠒⠊⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⡀

⠀⠀⢀⣤⣾⣿⣿⣿⣦⠤⢀⣆⠀⠀⣀⠄⠀⠀⢀⠀⠀⠀⠀⢀⣴⣆⠀⠠⣠⣠⣄⣀⣀⠀⠀⣀⠀⢀⠀⡀⠀⠀⠀⢀⠀⣀⡤⢄⣹⡶⣷⣓⣷⡀⠶
⠀⢠⣿⣿⣿⣿⣿⡿⣿⡿⣫⣹⠇⠚⣿⠰⢛⠙⢻⣶⣠⡴⡛⢮⢸⣯⢰⣼⣿⣿⣟⣿⣿⣿⠛⠳⠶⣿⣿⡖⣯⣦⡶⢛⡆⢻⡇⠈⢹⡿⣟⣿⣟⣿⣻⣴⡂
⠀⣾⣿⣿⣛⣿⣿⣇⣹⣿⠛⢳⣾⠀⣿⠀⣿⠓⢺⣿⣿⡋⡇⣠⢰⣿⠣⢴⣿⢻⣿⠿⡟⠛⣿⣿⣿⢸⣿⢶⡏⣹⡟⣫⠀⣾⡇⣄⢸⡧⢮⢻⡭⣭⣉⣿⣷
⠀⢿⣿⣯⠛⢿⣿⣿⣼⣿⣴⣾⣿⣾⣯⣾⣿⣿⣿⣿⣬⣿⣿⣥⣾⣅⣶⣤⣿⣾⣿⣶⣶⣭⣿⣿⣥⣾⣷⣬⣽⣿⣿⣿⣾⣿⣶⣿⣿⣶⣯⣿⣶⣾⣿⣿⠃
⠀⠘⢿⣿⡄⠈⠙⠏⠻⡿⠿⠛⠉⠉⠻⠿⠛⠛⠩⠉⠛⠛⠉⢿⠙⠛⠉⠉⠉⠛⡛⣶⣜⡿⠛⠋⠏⠛⣿⠿⠟⠛⠻⠙⠙⠛⠛⠋⠉⠻⠋⠉⠙⣿⣿⠃
⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⡿⢿⡿⠿⠆
⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡾⢷⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠺⣥⠟⠃⠰⠋⠱⣷⣭⡓⣄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠎⠀⢠⣤⡴⣜⣿⣿⣷⣿⣧⣍⢻⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⣰⣶⣿⣏⣴⣿⣿⠟⠉⢋⣴⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣿⣿⣿⣾⣿⢿⣿⣿⠏⣩⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣉⠾⣿⣿⣿⣿⠇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀⡉⠛⣻⣭⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⠟⣿⣧⢺⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠸⠀⠳⣿⠀⠉⠻⣿⣿⣿⣬⣿⣿⣿⣿⣿⡏⠛⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⣶⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⡙⣿⣽⣿⣿⣿⣿⡿⠋⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠿⠿⣆⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢺⣿⣴⢶⣠⣾⣿⣿⣿⣿⣿⣿⡟⠉⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⢾⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡨⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣳⡖⢤⣤⣤⡀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣻⣭⣅⡙⠊⣹⣿⣿⣿⢿⣧⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⡖⡙⠃⠀⠀⠀⠀⢻⣥⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢋⣸⣿⣿⣦⡿⢿⣿⣿⣿⡾⣿⠀⠀⠀⠀⢀⣸⣷⣦⣀⣀⣰⣶⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣽⣠⣴⣿⣿⣟⣿⣿⡿⠃⠀⠀⠀⠉⠀⡁⠀⢠⣶⣶⣿⢛⣿⣿⣿⣿⣭⣿⣦⣼⣶⣾⣿⡟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣝⢛⣿⣿⣿⣿⣿⢻⠿⠟⠂⠀⠀⠀⠀⠀⣀⠖⠀⠀⠀⠈⠉⠀⠀⠀⠙⠻⢿⣭⣉⡁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠈⠻⠛⣘⢇⣎⠀⠀⠀⠀⢀⠀⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡠⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣹⡄⠀⢀⡼⠡⠇⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡏⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣼⠗⠋⢹⠀⠀⠀⠀⢠⠴⠶⠶⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠇⠀⠀⣿⠀⠀⢸⣤⠶⡄⠀⣼⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣈⣉⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠛⠛⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡸⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠛⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠉⠉⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢰⣶⣶⣶⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣤⣤⣤⡄⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢋⣀⣀⣀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋⠁⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠛⠁⠀⣷⣿⣾⡆⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠁⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⣀⣀⣀⣀⣟⣛⣛⣃⣀⣘⣛⣛⣛⣀⣀⣛⣛⣛⣃⣀⣘⣛⣟⣛⣀⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⢰⡆⠀⠀⠀⠀⠒⠂⠀⠴⣶⣶⠦⡤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⢸⡇⠀⠔⠈⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣁⣩⣿⣿⣿⣿⣿⠟⢋⣁⣤⣤⣤⣤⣄⣀
⠀⠀⢸⡇⡄⠀⠀⠀⠀⠀⢀⣠⣤⣾⡿⠿⠟⠛⣛⣭⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⢸⡷⠃⠀⠀⠀⣀⣬⣴⣶⣶⣶⣶⣶⣿⣿⣿⢿⣿⣿⣟⣩⣤⣀⣀⣴⣤⣍⠙⢿⣿⣿⣿⣷⣄
⠀⠀⢸⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠛⠋⢉⣉⣉⣿⣿⣿⣃⠀⠻⣿⣿⣿⣿⣷⣄
⠀⠀⢸⡇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⣠⣴⣾⣿⠿⠿⢿⣿⣿⣿⣿⣷⣄⠙⣿⣿⣿⣿⣿
⠀⠀⢸⣧⣾⠋⠻⢿⣿⣿⠿⠿⠛⠋⠉⠀⠀⢀⣴⣿⠿⠛⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿
⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿
⠀⠀⢸⡍⠻⠿⣶⣶⣤⣤⣤⣶⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⢿⣿⣿
⠀⠀⢸⡇⠀⠀⠀⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠁⠀⠀⢸⣿⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⡤⠀⠀⠀⠘⣿⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢃⠀⠀⠀⠀⠀⣿⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣟⡈⠀⠀⠀⠀⠰⣿⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣟⠟⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠛⠛⠉⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡔⢆
⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⡇⣿⠇⠐⠒⠒⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠾⢿⣿⣿⣿⣿⣿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣿⣿⣿⣰⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠛⠈⠻⣷⣔⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⣤⠋⢀⣼⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠦⣄⠀⠀⠀⠀⣿⣿⣿⣿⡇⠈⠁⠐⠋⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣌⡂⢰⣤⣠⣿⣿⣿⣿⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣹⣿⣿⣿⣧⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⠈⠙⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⡿⣋⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠛⠛⠛⠛⠛⠋⢉⣼⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⢶⣄
⠀⠀⠀⠀⠀⠀⣾⣻⣭⣥⠴⠶⣦⣹⣦⣄
⠀⠀⠀⠀⠀⢰⡿⢃⡀⠠⠤⠶⠾⣿⠇⣹⡀
⠀⠀⠀⠀⠀⣸⠃⢏⣀⠀⠤⠤⣤⣾⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⠒⠒⠒⠒⠀⠀⣀⡤
⠀⠀⠀⠀⠀⣿⠀⠈⠁⠐⣦⣤⡤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠁⠀⠀⠐⠦⣤⣤⣤⠶⠟⠉
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠈⠙⣧⣴⢟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⣷⠀⣶⠀⠀⠀⢸⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⣿⠀⠛⠶⠶⠶⢋⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⡴⢒⡦⠖⣻⠓⠆
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠙⠻⡻⣌⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣿⣤⣘⣵⣋⡉⠉
⠀⠀⠀⠀⠀⠀⢻⡀⢢⡀⠀⠀⠙⣦⠙⣧⡀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠛⢿⣟⢷⣄⠐⢶⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢷⡀⠀⠀⠈⠃⠈⢷⣄⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⣆⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢷⠀⠀⠀⠀⠀⠀⠙⢷⣄⣾⠃⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⣧⣄⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣸⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠉⠛⠦⣌⠙⠻⠷⢶⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⢠⡿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⢸⠀⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⠸⣄⠀⣿⣿⢧⣀⣀⡀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢸⡇⣸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡎⠒⠀⢹⡄⠑⠚⠒⠊⠀⠀⠀⠀⠀⣿⣿⢯⠐⠦⣤⣤⣤⣴⠾⠋⠀⡠⣞⠄⠀⢸⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⣤⠾⠃⢹⡄⠀⠀⠀⠀⠀⠀⢄⠀⡼⡼⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠛⠷⠶⢶⣤⡤⠤⠄⠀⠀⠸⠃⢰⡄⠀⠀⠀⠉⠢⣭⣥⣷⠄⠀⢀⣾⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣾⠋⠀⠙⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠙⠦⣤⣤⠤⠀⠈⠁⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠉⠛⠛⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⡀⣀⣠⣴⠾⠛⠛⠋⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⢰⠋⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢱
⠀⢠⠒⢺⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡗⠒
⠀⢼⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⢀⣠⢤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢤⢄⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡶
⣤⢸⡀⠀⡇⠀⠸⣒⡒⢒⣒⣒⣇⢠⡠⠀⢗⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠂⡤⢠⡁⠀⠀⠀⢈⡇⠀⢸⡇⠀⡇
⠛⠀⡇⠀⡇⠀⠀⠁⠀⠀⠀⠀⠙⣆⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⣴⠋⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡇
⠀⠒⡇⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⣀⡤⢤⣤⡄⠀⢀⢤⡖⠲⠤⣀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠘⡇⠀⠉
⠀⠀⠣⠤⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠘⠉⠀⠈⢑⠈⠉⠀⠀⠈⠳⣼⠃⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⠒
⠀⠀⠀⠀⠣⠄⠤⠃⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠀⠀⣀⠀⠎⣤⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠓⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠈⠀⠀⠀⡄⠘⠛⠀⡆⠉⠁⢀⠃⠀⠀⠈⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠂⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⠀⡠⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡀⠀⠀⠀⠑⠠⣀⡀⠀⠀⠀⡀⡀⠐⠀⠀⠀⠀⠀⡀⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠀⠀⠀⠀⠀⠀⠖⠂⠀⠃⠠⠃⠀⠔⠀⠀⠀⠀⠀⠀⠼⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⣀⡉⠦⠀⠀⠀⠐⠤⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⣀⢀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⡤⡀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠑⠒⠒⠒⠉⣿⠀⢹⡏⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠀⢸⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⢂⠀⢀⡹⠂⢎⡀⠈⡐⠉⠈⠲⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣹⠳⡀
⠀⠀⠀⠀⠀⢀⡞⠁⡟⠀⢠⠃⠀⡇
⠀⠀⠀⠀⠀⡼⠀⢸⠃⠀⡎⠀⠀⠃
⠀⠀⠀⠀⢰⠇⠀⡟⠀⢰⠃⢀⢰
⠀⠀⠀⠀⣸⠀⢰⡇⠀⡾⠀⣾⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⠤⣀
⠀⠘⠀⠠⡿⠀⣸⠀⢀⡇⢠⡿⠧⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡸⠀⢸
⠀⠀⠀⠀⡇⠀⡿⠀⢸⠁⢸⣿⠃⠐⠂⠀⠨⢍⠋⣰⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢠⡇⠀⣸⠑⣆
⠀⠀⠀⠀⡇⠀⡟⠀⢸⠀⢸⢋⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠐⠚⠀⠬⢐⡂⠀⠄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠜⡤⠀⡼⠀⢠⡇⠀⡏
⠀⠀⠀⠀⡇⠀⡇⠀⣾⠀⠀⠆⠀⠀⠀⠀⠀⠸⡄⠀⠀⠤⣤⡉⣿⠆⠀⠀⠀⠁⠒⠇⡀⡐⠀⠄⠀⠀⡜⣼⠇⢰⠃⠀⡾⠀⢰⠃
⠀⠀⠀⠀⢃⠀⡇⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢄⡉⠈⠛⠑⠀⠈⠑⡄⠀⠀⢀⡴⠀⠀⠈⠑⠂⠨⣙⡟⢀⠏⠀⣸⠃⢀⡟
⠀⠀⠀⠀⠈⠉⢧⠀⢧⢠⠃⠀⠀⠀⠀⠀⠠⡀⠀⠀⠙⢄⠀⠀⠀⠀⠠⣼⡤⠔⠋⠀⠀⠀⠀⠀⢀⢱⡿⢀⡞⠀⢰⠏⠀⡼⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠙⢶⠢⢲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠞⠁⡜⠀⢠⠏⠀⡼⠁⠂⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠉⠉⣽⣦⣄⣀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡼⠁⢠⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠻⠿⣿⣿⠿⡇⠑⣄⠀⠀⡀⠈⠀⡎⠀⡜⠀⣠⠋⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⣿⣦⣤⣀⣀⣴⡇⠀⠈⡠⠊⠀⠀⠀⣇⠎⢀⡴⢇⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡈⠙⠻⠿⢻⠏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⠷⠶⠞⠁⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀

⠀⠀⠀⠀⣠⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⣴⣴⠀⠀⠀⠀⢠⣤⣄
⠀⠀⣠⣿⣿⣄⣄⣼⣿⣧⡄⠀⠀⠀⣰⠛⢻⣷⣶⣾⡇⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠿⣿⠁⠀⢸⡿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣶⣄⣀⣀⣰⣶⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⡇⠀⠀⠀⠀⠀⠀⢠⣥⡄⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⣤⡄⠿⠏⢉⣯⡹⠿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⢀⣹⣏⣀⣀⣀⣀⣀⣀
⠀⠀⣿⡟⠛⠛⠻⣿⠅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠈⢹⡏⠉⠉⠉⠉⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠘⢷⠂⠀⠀⢠⡾⠏⠀⠀⠀⠀⣀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣀⠄⢀⠤⣀⢰⣄
⠀⠀⣤⣾⣶⣶⣶⠾⢧⡀⠀⠀⠀⠈⣿⠀⠉⠉⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⢿⣯⣼⣿⣿⣄⣠⠇⠀⠀⠀⠸⠿⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⡇⠀⠀⠙⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠙⠋
⠀⠀⠀⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢠⣄⢀⣤⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⣤⣤⣤⣤⣿⣇⠀⠀⠀⠀⣿⣿⣤⣄⣾⣿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠙⢻⠉⢹⣿⡍⠉⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣄⣅⣸⣿⠀⠀⠀⠀⠀⢸⠀⢸⣿⡇⠀⡇
⠀⠀⢶⣶⣶⡶⡶⣶⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣍⠀⠀⠀⠀⠀⠼⠄⠨⠿⠄⠤⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠠⣤⣷⢛⣿⣂⣀⡠⢄⣤⣼⣿⠆⠀⠀⠠⠀⠤⠀⠀⠀⠀⢿⣶⣚⣁⣀⠀⣠⣦⣤⡄
⠀⠀⠀⠀⠀⠀⡇⢠⣶⣦⣿⣿⣶⣶⣿⢷⣆⣀⣀⣀⣀⣀⣀⣠⣄⣴⣾⣿⣿⣿⣿⠾⢿⡏⢀⣦
⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⠟⢁⣼⣿⣟⣿⡍⢹⣽⣿⣿⠿⠿⡿⠿⠋⠀⠀⠀⣠⡄⠀⡿⡇
⠀⠀⠀⠀⠀⣸⡇⢸⣿⣿⢿⠗⠀⢠⣾⡿⠛⢃⣬⣩⣿⣟⣿⠀⠀⠀⠀⢠⣶⣦⣄⣀⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⡷⠀⢸⠟⠁⠀⠀⢀⡿⠟⢁⣶⣤⣿⣿⣿⡉⣿⡇⠀⠀⠀⠻⢿⣿⣿⣿⣿⡇⠀⣿⢿⡇
⠀⠀⠀⠀⠀⠇⡆⢸⠀⠀⢀⠀⢸⠗⢀⣸⣿⣿⣿⣿⠟⠛⢿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠘⣿⣼⡇
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠓⠈⠘⠀⠚⠙⢿⡿⣯⣧⠄⣸⣷⠀⠀⠀⠀⠀⠉⠙⢻⣿⡇⢰⡟⡉⠁
⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠈⠁⠀⠂⠀⠀⢠⣿⣿⠍⢲⣿⡇⠀⣷⠀⠀⠀⠀⠀⠐⠛⠃⢈⡿⣧
⠀⠀⠀⠀⠀⢠⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⠟⠉⣀⠀⢻⣿⣇⣸⡆⠀⢠⣄⣠⣤⣶⡆⢸⣟⡿
⠀⠀⠀⠀⠀⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⣓⡼⠛⠁⠈⣿⢿⣿⣷⣶⣿⣿⣿⣿⣿⣯⢸⡿⠁
⠀⠀⠀⠀⠀⢀⡁⢸⠀⠀⠀⣀⣴⣶⣶⣶⢰⣶⡶⠀⣆⢰⡄⣿⣿⠋⡽⢿⣿⡿⣿⣿⣿⣿⢸⣅
⠀⠀⠀⠀⠀⢨⡇⢸⣶⣿⣾⠿⢿⣿⢿⣿⢸⣿⣓⠘⠿⠻⣿⣧⠃⢀⡿⢘⣿⢃⣿⣿⣿⣿⠸⣿⠁
⠀⠀⠀⠀⠀⠐⡇⢸⠟⠀⠁⣠⢸⣿⡿⣿⣼⣿⣿⠦⢠⡄⢾⡿⠀⢠⠀⢸⣿⣾⣿⣿⣿⣿⢠⣿
⠀⠀⠀⠀⠀⠀⡇⢸⣰⣿⠀⣿⣿⣿⣇⠸⣏⣿⣾⣿⣿⣿⣼⡿⠀⠏⠠⢼⣿⣧⣉⠿⣿⣿⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⠀⣿⠛⣩⣿⡄⣸⣿⣿⣿⣿⣿⣷⡤⠁⣀⠀⠀⢿⣿⣿⣷⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠁⢸⣿⠁⠰⡇⠘⠁⢿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠾⣿⠀⢰⣾⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠆⢸⣿⣀⣴⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣿⣿⣿⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣿⢟⣻⣿⡟⠘⠛⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢀⣼⣿⣿⣿⣿⡿⠛⠛⠻⠿⠿⢋⠁⠉⠙⠛⢻⣿⣿⣿⣁⢠⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠇⠀⠿⡏⢸⡿⠋⣁⣿⣶⣦⡀⡀⢌⣳⣤⠲⣄⣤⣿⣿⣿⣟⢸⣿⣁⡀
⠀⠀⠀⠀⠐⠀⡀⢸⣽⠀⠠⠾⣷⣆⣛⣛⣷⣿⠿⠛⠻⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⠁
⠀⠀⠀⠀⠀⢰⡇⢸⣷⣶⣶⣾⣯⣉⣉⣉⣵⣶⣶⣶⣿⣿⣿⣏⣩⣤⠵⠤⡼⢿⣿⣿⣿⣧⠈⣿⡏
⠀⠀⠀⠀⠀⠈⡃⠀⣭⠉⠉⠩⠉⠭⠭⠍⠭⠭⠭⠭⠭⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⣉⡉⠉⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠳⠖⢉⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⠡⡴⠁
⠀⠀⠀⠀⠀⠀⠢⡀⠂⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠈


⣶⣶⣶⠶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣠⢀⣆⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⣰⣀⣀⣀⣀⣀⣶⡀
⠀⠀⠀⠀⠀⠙⠶⣾⣷⡶⠞⠁⠀⠀⠀⠀⠀⢰⣿⠻⠦⠄⣴⠂⠀⠀⠀⠀⠀⠠⠞⣿⢦⣠⢀⡿⠀⠀⠀⠀⠘⠐⣆⡶⣠⠆⠛
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣄⡀⠀⠀⠀⠀⠀⠀⢶⣭⣷⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣸⠟⢶⡀⣸⠇⠀⠀⠀⠀⠀⠀⢘⣿⡏
⠀⠀⠀⠀⠀⠀⢻⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢹⠶⠿⠻⣗⠀⠀⠀⠀⠀⠀⢠⣭⣥⣴⣾⣶⡿⠀⠀⠀⠀⠀⠀⠀⣼⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢉⡳⢄⠀⠀⠀⠀⠀⠀⠀⠐⢲⡂⢶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣸⣃⣀⡽⠂⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⡄⠀⠀⠀⠀⠀⠀⢈⣭⣀⣠⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣥⡀
⠀⠀⠀⠀⠀⠀⢹⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠟⠂⠀⠀⠀⠀⠀⠀⠻⣿⣥⣄⠈⣻⡇⠀⠀⠀⠀⠀⣠⠿⣿⣿⢷⣄
⠀⠀⠀⠀⠀⣤⣬⣿⣏⣿⣤⣄⠀⠀⠀⠀⠀⠀⣾⠁⢻⡀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⡟⣷⣿⡇⠀⠀⠀⠀⠀⠘⣿⠿⢿⣿⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⢠⡴⣿⣿⠦⡄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣷⣆⠀⠀⠀⠀⠀⠀⠠⡾⣿⢧⡀⢀⡾⠃⠀⠀⠀⠀⢶⠎⣷⣦⣤⣄
⠀⠀⠀⠀⠀⢰⠀⣿⣿⠀⡰⠀⠀⠀⠀⠀⠀⠀⠘⣼⣿⣮⡅⠀⠀⠀⠀⠀⠀⢹⡟⢳⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣮⡙⣷
⠀⠀⠀⠀⠀⠈⠢⡌⣿⠴⠁⠀⠀⠀⠀⠀⠠⠴⠚⠉⠀⠸⠁⠀⠀⠀⠀⠀⠀⢸⠃⠼⢤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠹⣄⡀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⡇⠀⠀⠀⠀⠀⠀⠰⡶⣻⠄⢀⣄⡀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣷⡘⠟
⠀⠀⠀⠀⠀⠀⠸⢿⣟⢻⠆⠀⠀⠀⠀⠀⠀⠀⠸⡶⢛⡇⠀⠀⠀⠀⠀⠀⠀⠐⠿⣷⣾⡿⢻⡄⠀⠀⠀⠀⠠⣔⣛⡯⠽⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠒⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠽⣏⣡⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⣡⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⠰⣶⠚⠃⠀⠀⠀⠀⠀⣀⣀⣀⣸⡏⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣧⠘⣇⠀⠀⣀⣀⣀⣸⠉⠉⠉⢉⡤⣦⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡟⢘⣷⣏⣀⣼⠉⠉⠉⠉⠀⠀⢸⡏⢀⣹⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠭⠤⠼⠃⠀⠀⠀⣀⣀⣠⡤⠶⠚⣩⡴⠋⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⣞⣛⣛⣉⣉⣩⣭⠤⠶⠚⠋⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠾⠿⠯⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠇



⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣁⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣣⠀⠀⠀⠀⠀⠀⠻⣿⣛⡁⠠⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡜⠋⠀⠀⠀⠂⠀⠳⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⡽⠁⠀⠀⠀⠰⣦⢀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣥⡾⠁⠀⠀⠀⠀⠀⠐⠛⠛⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠁⠀⠀⠈⠀⠀⠀⣀⡴⢟⣵⣿⣿⣿⣷⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⢠⣾⣿⡿⠟⠋⡼⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⢀⣾⣿⣿⣿⢆⡄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⣼⡿⠛⠉⢀⠘⠋⠉⠛⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠁⠘⢃⣤⣤⣥⢤⡞⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣧⣟⣴⠀⠄⠀⠀⠀⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⢉⣽⣍⠻⠛⠁⠈⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣅⠙⠛⠀⠠⠀⠀⠀⠀⠀⠁⢀⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠦⠀⠾⠛⠋⠰⣶⣦⠄⠈⠀⠀⠀⢠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⡀⠀⠠⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⢻⡤⠀⠀⠀⣠⡄⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠼⠃⠀⠀⠀⠀⠋⠀⠀⠀⠀⢈⣵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣆⠀⠻⠆⢠⡆⠀⠀⠀⠈⠀⠀⢻⣾⠂⢠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠿⣦⣽⣷⣄⣠⣤⣎⣠⣿⣤⣾⣁⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣻⣶⢏⣍⣠⣿⣿⡆⠀⣍⣿⣿⣧⡙⠛⣳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣻⣿⣿⣷⣶⣿⣿⣿⢿⣇⠀⢿⡿⢟⠁⣸⣷⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠁⠻⣿⣿⣿⣿⣷⣾⣧⡉⢿⣿⡆⠸⣏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⣾⣿⡿⣿⣿⣿⣿⣿⠙⣶⣽⣇⠀⣟⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠀⠙⢾⣿⣿⣿⡟⠀⢿⣿⣿⡄⠸⢷⡔⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣾⡟⢿⡟⠋⠀⠀⣨⣿⣿⣿⣷⣦⡴⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢨⡇⣼⡇⠀⠀⢸⣿⣟⠿⣿⣿⠀⠙⣆⠀⣠⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⣸⠃⢸⡷⡄⢰⣿⣿⡇⠀⣽⣿⠀⠀⠘⠟⠋⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡉⢰⣯⠀⢸⣷⣇⣼⡇⢹⣧⠐⠻⡎⠟⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠡⠀⠀⡟⢻⣿⣷⣾⠁⠀⠀⠠⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠇





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠟⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⣤⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⢸⠁⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⣠⣶⣔⣂⣰⣶⠖⠀⠀⠀⠀⡀⣴⡟⣻⣿⣿⣦⠀⣾⣭⣧⠀⠀⠀⠈⠀⠁
⠀⠀⠀⢤⣴⣾⠟⡛⠩⠁⠀⠀⠀⠀⠀⠀⠀⠼⠻⣿⣿⣿⣿⡇⠀⡹⢻⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢠⠀⠀⠀⠀⡠⢬⣿⣿⢟⠗⡁⢀⡼⠋⠀⢠⣤⣶⣤⡀⠀⠀⠀⠀⡎⣾⠀⣀⢀⡆⡄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠋⢀⣀⣆⠀⡔⠋⢱⡀⠀⠸⣬⣷⠶⡋⠀⠀⠠⣿⣿⣿⣿⡷⠄⠀⠀⠀⡟⣿⣆⣀⣾⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⠾⣵⣧⣴⡟⢳⣦⣴⣿⡿⠛⢿⣿⠀⠀⠙⢿⣿⠿⠃⠀⠀⠀⠀⡇⣿⣯⢨⣿⡇⡇
⠀⠀⠀⠀⢠⣀⣄⡀⠀⠀⠄⠰⠀⠀⠀⠀⠀⢸⣵⣸⣿⣿⡿⠖⠒⠚⢋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣇⣿⣇⠀⣿⣇⡇
⠀⠀⣤⠀⠀⠉⠛⠷⣶⣄⡀⠀⠀⠀⠀⢰⠀⠀⠹⣯⣀⣿⡇⠀⢠⣴⣄⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡿⣇⢀⡿⡧⡇
⠀⠀⢀⡀⠀⣴⠂⠀⠀⠈⠙⠻⠦⣤⣤⣾⡀⣄⡀⠀⠁⠹⣿⡊⠉⣻⡟⢴⣔⣄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⡧⠀⡇⢳⡇
⠀⣠⢾⡽⠛⠿⣇⠀⠀⠑⢤⣤⣤⣶⠟⠉⠙⠛⠣⠄⠀⠀⠹⣷⣂⢩⡝⢾⣾⡟⠀⠀⠀⠀⠀⠀⢀⡴⣣⣶⢣⣤⠷⣶⡝⣦
⠀⠈⣻⣇⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠗⠈⡟⠇⠀⠀⠀⠀⠀⠀⠺⢛⡟⣧⣼⣺⣆⡟⣿⠻⠃
⠀⠴⠿⠛⠳⢤⡀⢀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢰⣸⠠⣀⠀⠀⠀⠀⠀⠈⣶⡟⠹⠿⠉⢷⡎
⠀⠀⠀⠀⠀⠀⠙⠛⠷⢤⣄⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠛⠶⣄⡶
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠳⠦⣌⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠊⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠋⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠈⠙⠲⢬⣢⡀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⠀⠀⠀⣰⠋⠀⠀⠋⠈⠉⠰⠂⣀⠈⠀⢰⡄
⠀⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠠⠄⡄⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠀⢀⢌⠈⠀⠀⢠⠘⠁⠰⠆⠀⠀⠀⠂⣼⡟
⠀⠀⠀⠀⠀⠢⢀⣀⠀⢀⢀⣠⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣠⣴⣯⠞⢐⡂⠀⠈⢳⣄⡠⢠⢤⣏⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⠷⠇⠀⠾⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠾⠛⠉⠀⣨⣴⣟⠁⠀⠀⠈⠻⠿⢿⣿⣿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠈⠠⠀⡀⢀⠈⠀⠀⡀⠀⠀⠀⠀⠁⣀⣤⡴⠚⠉⠀⢀⣤⣶⠿⠛⠿⠿⠟⠺⠤⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡰⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⢘⠄⠀⠀⢀⣜⠅⠄⢀⣠⣴⣿⣟⡭⠔⠒⠋⠉⠉⠉⠙⠉⠉⠀⣀⣀⣤⡤
⠀⠀⠀⠸⠀⢄⠀⡂⠀⠀⠀⡐⠀⠠⡘⠀⠀⣴⡟⢇⣠⣼⡿⠿⠛⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⣛⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠊⠀⡂⠀⠰⠈⠂⠊⠀⠀⠘⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢔⣀⡀⠀⠀⠀⡀⠈⡀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠈⠀⠠⠂⠀⠀⠀⠐⡀⠄⠐⠪⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⡀⠀⠀⠀⠐⠀⠀⠀⠢⡀⠀⠀⡀⠀⢀⠀⠤⠀⢀⠀⡠⠂⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⢀⠀⠤⣀⢀⡀⠀⢀⡒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠈⠁⠐⠜⡋⠈⠀⠌⠐⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠔⠉⠀⠈⠰⡀⠀⠈⢲⠚⠒⠂⢄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠘⡀⠀⠀⠀⢀⠃⠀⠀⠀⠳⡀⠀⠀⠡⡈⠀⠐⠀⠂⠀⠈⠂⠀⠀⠈
⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠣⡀⠁⠢⠠⠔⠁⢐⠂⢄⠀⠀⠈⢂⠀⠀⢈⡶⡀⠀⠀⠐⠀⠀⠁⢸⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠑⠄⡑⠢⡀⠀⣱⠐⠒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠈⠒⠂⠤⣀⠀⠀⠈⠂⢌⠚⢄⠀⡴⠚⠅⠦⠀⠀⢀⢠⠀⠚⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠘⠀⠀⠐⠒⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠉⠐⠤⠤⠋⠑⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠂⠠⢀⠀⠀⠀⠀⢲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⡀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠊⠁⠀⠀⠠⠠⠄⠀⠀⠁



⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣿⣟⣻⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⠒⠒⠲⢦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠠⠤⠀⠀⠀⠈⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣀⣠⣤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⠀⠐⠈⠁⠀⠀⠀⢄⢀⠀⡐⠀⠀⠀⢀⣿⢀⣤⠶⠛⠉⠸⡏⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠈⠳⠄⠀⠀⢠⠞⠃
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠘⠓⠶⡾⢛⡿⠋⠉⠉⠉⠙⠓⠠⣄⡀⠀⠀⠻⣦⠀⠀⠀⠀⠀⣠⠞⠳⡇
⠀⠀⠀⠀⠀⠀⢻⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠈⢷⡀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢀⡄⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠄⣣⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⣇⠀⠘⢧⡀
⠀⠠⠄⠱⡄⠀⠀⠀⠈⠢⡀⠀⠀⠈⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠉⠀⠦⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢷⡀
⠀⢰⠖⠇⠀⠀⠀⠀⠀⠀⠀⠙⢳⡷⢦⡄⠐⠀⠈⣷⠒⠂⠐⠀⠲⠒⠒⢦⡀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠸⡇⠘⠁⠀⠀⠀⢻⣄⣀⣠⢀⡄⠀⠀⠰⠉⠂⡖⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⣟⠀⢻⣾⡆⠀⠘⠀⣼⠻⡄⠀⠀⠉⠙⠲⠶⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢣⡀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⠈⣷⠀⠃⢠⡏⠀⢹⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡀⠘⢷⡀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⡀⢶⠀⠀⠀⠀⠀⢸⡇⠀⠈⣷⡀⠀⣿⠀⠀⠙⣆⠀⠀⠀⠀⢠⠄⠀⠀⣀⠀⠀⠀⢀⡾⠆⠉⠀⠖⠉⢿⣄⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢑⠠⡿⠂⠀⠀⠀⣸⠁⠀⠀⠘⡏⠰⡿⠀⠀⠀⠈⢷⡀⢀⠴⠐⠒⠢⠄⠀⠉⢂⢀⡞⠠⠐⠈⠀⠀⠀⠀⠻⢇⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠾⠙⣧⠀⠀⠀⠀⣽⠄⠀⠀⠀⠹⣄⣧⠀⠀⠀⡠⠤⢋⠌⠁⠀⠀⠀⠀⢁⠀⣸⡋⠠⠄⠀⠀⠠⠤⢀⡀⠀⠃⠉⢰⡶⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⠇⠒⠈⠀⠀⠀⠀⠙⣆⠀⠀⠂⡴⠁⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢴⠖⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠳⣄⣠⠁⡂⠀⡀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⠜⣿⡀⠁⠀⠃⠘⠀⣴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⢀⡧⠤⠤⠀⡀⠀⠀⠀⠀⢀⡜⠃⠀⡠⣡⠊⠀⡿⣀⢀⡁⣀⣰⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢰⠆
⠀⠀⠀⢀⣠⠶⠛⠀⠐⠤⠀⡀⠢⡀⢀⡴⠋⠀⠀⢠⡜⠁⠀⢠⠃⠈⠉⠙⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⢈⠓
⠀⢰⣉⠉⢀⡀⠀⠀⠀⠀⠀⠈⣴⠟⠉⠀⠀⠀⢀⡿⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡴⠊⠉⠁
⠀⠀⢉⡟⠁⠀⠀⠚⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢺
⠀⢀⡟⠀⡔⠁⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢿⡀⠀⠀⠀⠀⠀⠛⠁
⠀⢸⡅⠀⢀⠄⠀⠂⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡀
⠀⠘⢧⣤⡥⢶⠱⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⡀⠀⠀⠀⠀⣶⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⡀⠠⠀⡀⠀⠁⠀⠀⠀⠀⠀⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠰⡄⠂⠀⠁⠀⡀⠀⠘⣷⡀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠿⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠁⠈⠀⠀⠈⢷⡄⠀⠀⠈⠳⣄⠀⠀⢀⡀⠄⣀⡔⠉⠀⠀⠓⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⢀⠀⠀⢀⠀⠀⠘⣦⠀⠀⠀⠘⢯⣀⠀⠀⠚⠁⠀⠐⠉⠀⠴⠈⠲⡆⠀⠀⠀⠀⠀⠀⠠⠂⡀⠀⠀⠀⡿⣧
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢉⠀⠀⠀⠘⢷⡀⠀⠀⠀⠙⠢⣄⠀⠈⠀⠠⠀⠀⠀⡀⠀⠉⢲⡀⠁⠀⠄⠀⠁⠈⠃⠀⠀⡜⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⠳⢆⠀⠀⡀⠄⠀⠀⣀⠄⢫⡝⡟⠁⠀⠀⠀⠀⠀⣤⠜⣡⡟
⠀⠀⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⠀⠀⠙⠦⣤⣴⠶⠾⠉⠀⠈⢰⡟⠁⠀⠀⠐⢓⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⠴⠊⣠⠞⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⡂⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠀⣏⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠊⢤⡀⢰⡇⠀⠐⠊⣁⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⣄⡁⠐⠀⢀⣠⠤⠂⠁⠀⠀⠜⠒⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⡀⠄⠋⢉⡿⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣄⠀⣉⣠⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡗
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⡟⣷⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣷⠄⠀⠀⢸⣿⣿⣽⣿⣷⠀⣾⣿⣿⣽⣿
⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠘⢸⡿⢻⡇⠙⠀⠀⠀⢿⣿⡿⢿⣇⢹⣿⣿⠟⠋⠀⠀⠀⠀⠀⠈⠁⣷⣿⣿⣷⣿⠈⠁
⠈⠛⠻⣿⡿⠟⠛⠀⠀⠀⠀⠀⢺⠃⠘⡟⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⣤⠀⠀⠀⣤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢑⣶⣾⣶⣄⠀⠀⠀⠀⠀⢾⣿⣷⠄⣀⣠⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠠⣿⣦⣤⣶⣶⠤
⠀⠀⠀⠻⣿⣋⣿⡿⠃⠀⠀⠀⠀⠀⠙⢡⣾⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⣿⣿⣷⣊⣽⣷⠃
⠀⠀⠂⣸⣿⣿⣿⣿⡄⠂⠀⠀⠀⠀⠰⣝⠿⢋⣴⣿⣦⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣻⣧⣞⣹⠿⣿⠖⠁
⠐⠃⠀⠀⠀⠛⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠈⠙⠛⠿⠛⠋⠀⠀⠀⠀⠀⠈⠒⠛⠛⠐⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢐⠉⡆⠀⠀⠀⠀⠀⠀⢀⢶⣿⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣿⣿⣿⠀⠀⠲⢦⡄⢀⣤⣶⣤⡀
⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⣾⡆⣻⣿⠿⣃⣠⢼⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿
⠀⣾⠿⣿⠿⣷⠀⠀⠀⠀⣾⣿⣿⡞⠛⠒⠛⢽⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠼⢦
⠀⡏⠀⣿⠀⢹⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣦⣤⣀
⢠⣿⣿⣿⣽⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡿⢷⣦⣀
⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣠⣴⣶⣯⣽⣹⣽⣷⣶⣤⡀⠀⠀⠀⠀⠀⢀⠋⠂
⢸⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢀⣸⣟⠛⠟⠛⠁⠀⠀⠀⠈⢹⠟⠛⠻⡟⠛⠛⢿⠉⠀⠀⠀⠀⠀⢀⠂⠘⠘⠄

⠀⠀⠀⠀⢀⢰⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣆⣀⡆⠃⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠐⢻⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⣦⡀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢾⡷⡴⠂
⠀⠀⠀⠀⠀⣞⡷⠀⠀⠀⠀⠀⢀⣯⣍⠁⠀⣻⣇⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⢀⣀⡿⣇⢣
⠀⠀⠀⠀⡀⠘⠃⢀⠀⠀⠀⠀⠘⢿⡿⠃⠀⢏⠉⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⢠⡄⢠⣼⣼⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡟⠀⠀⠀⠀⠀⠀⡞⣿⡦⠓⠀⠀⠀⠀⠀⠀⣠⡾⣷⡄
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⣰⠿⣬⠁⠀⠀⠀⠀⠀⠀⠓⣿⡄⠀⠀⠀⠀⠀⢀⡼⢻⡄⠸⣿⡀
⠀⠀⠀⠀⠰⠁⢸⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠳⡄⠀⠀⠀⠀⠀⠰⠁⡇⠀⠀⠀⠀⠀⠏⠀⠞⠀⠀⠻⠇

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢈⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠐⣿⠂⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⣤⣾⣿⡇⠀⠀⠀⠀⠀⣀⣤⠟⠻⢿⠀⠀⠀⠀⠀⠀⠼⣿⠄⠀⠀⠀⠀⠀⣶⣾⣷⣶⣶⣦
⠀⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠾⠉⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢶⠠⢠⡄⡄⡦⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠙⢾⡗⠋⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠀⠀⠁
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⡎⠋⡇
⠀⠀⠀⠀⠀⡃⠃⠀⠀⠀⠀⠀⠀⣸⠀⠀⠓⠂⡄⠀⠀⠀⠀⠀⡞⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀

⠄⡠⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠉⢀⣄⡴⠀⠄⠀⠀⠀⠀⠀⣀⣀⣀⠀⠠⠀⠌⠀⠀⠀⢠⡄⠀⠀⠓⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠂⠔⠀⢄⡂⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠈⠓⠀⢀⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡀⠉⠢⢄⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠐⠆⠀⠀⠀⠀⠑⢄⠀⠰⡄⠒⠀⠏⢂⢸⡤⢢⡀⠀⠀⡠⠄⣀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠑⢄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠑⠦⠀⣴⢊⠔⢁⡼⡤⠊⢀⠤⢀⠈⠁⠒⢠⣤⡄⠀⠰⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣈⡁⢡⢁⡎⢠⢋⠜⠀⠀⡇⠀⢈⠀⠀⡰⢿⠞⠉⠐⠤⡇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠰⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠠⢧⠂⢀⢀⡀⠈⠀⠈⢀⡞⡷⠃⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠘⡀
⠀⠀⠀⠀⠐⠂⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠠⢣⠎⡜⡱⠀⢠⠛⠟⠀⠀⢀⣀⣀⣀⣀⡀⠀⠉⠢⡀⠀⠃⠀⠀⠄⠘⠤⠀⠀⠁⢀⠤⠠⠠⠄
⠀⠀⠀⠇⠆⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠂⢀⢡⠇⡞⡐⠀⢠⠿⠏⠀⣠⣾⠟⠓⠋⠙⠚⠿⣳⣄⠀⠈⠢⡄⠀⠀⠈⠐⠀⠀⠀⠀⠀⠁⠁⠐⠄
⠀⠀⠀⠀⠀⡀⠤⠤⠴⠀⠤⡁⠴⢲⠤⣀⡘⠀⢈⡜⢸⢡⠁⢀⢿⡟⠀⣮⠟⠠⠂⠁⠀⠀⠀⠀⠈⢻⣥⠀⠀⠈⢆⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠂
⠀⠀⢖⠈⠁⠀⠀⡄⠒⠒⠓⠈⠇⡏⢰⠃⠁⠀⠀⠀⠉⠂⠀⣼⣶⠀⢨⡟⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⣟⡆⠀⠀⠀⠱⡀
⠀⠀⠀⠁⠢⢄⣀⡀⠁⣐⣂⠴⠀⡇⢸⠰⠀⠀⢀⠀⠀⠀⢀⣧⡄⠀⠘⣣⠀⢄⠀⠰⠆⠀⠒⠀⠀⠀⠿⠇⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠠⠔⠇⠧⠘⠺⠀⠰⠁⠈⠂⠀⢸⣭⠁⠀⠀⠻⣦⡀⠀⠀⠀⠀⠐⠀⢈⢼⠟⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠂⠐⠁⠀⢸⣹⠀⠀⠀⠀⠙⠛⣶⣤⡤⣤⣤⡰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠢⠄⡀⠀⢸⠻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠦⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠤⠐⠂⠁
⠠⠀⡌⠀⠀⢀⢀⠀⠀⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰⠄⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠰⠀⠀⠀⡀⠉⠀⠀⠀⠈⠐⠂⠀⠠⠤⠄⠀⠀⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠂

⠀⠀⠀⢀⡀
⠀⠀⠀⣸⠷⠀⣠⡄⠀⠀⢠⣤⣤⣼⡏⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⣾⣶⢀
⠀⠀⠸⣿⣆⣠⠟⠁⠀⠀⠀⠉⠙⢿⣿⡾⡇⠀⠀⠀⣠⣶⡤⠀⣐⠶⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠙⠛⠺
⠀⠀⠀⠉⠚⠙⠓⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⣿⣿⡜⠋⠀⠀⠀⠀⠀⠀⠀⢸⡼⠟⡖⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣠⠄⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⢴⣟⣻⡇⠀⠀⠄⠀⠀⡀⠂
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⠦⠀⠀⠀⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠿⠿⠿⠁⢨⠷⠿⠛⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠞⠀⠀⠀⠀⠀⢐⡄⢠⡅
⠀⠀⠀⢸⡄⠀⠁⠀⠀⠀⠀⠀⢀⣀⠄⣻⣿⠛⣁⠀⣀⡙⣉⡁⠀⠘⣃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⢀⠸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢻⣧⠀⠈⠀⢹⣧⠀⠀⠈⠀⠰⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠
⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⡀⠀⠀⠈⠛⠀⠀⠀⠀⡀⠉⢁⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⡁
⠀⠀⠐⢦⢠⡀⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣈⠀⠀⠀⡀⢰⡇⠺⡖⡆⠀⠀⢀⡀
⠀⠀⠘⠋⠉⠃⠉⠀⠀⠀⠀⢠⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⢸⠁⠈⠡⠛⠀⠀⠈⡁
⠀⠀⢮⡄⠀⠀⠀⠀⠀⠀⠐⢨⠀⠀⠀⠈⠉⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠁⠀⠀⠀⢠⣦
⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⣀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠘⢷⡂⠀⠀⠀⢸⣤⠀⠀⠀⠀⣴⠟⠀⠀⠀⡄⡠⢿⣿⡇⠀⠀⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⣏⢠⡀⠀⢀⣴⠇⠀⠀⠀⠀⢼⠀⠠⠁⠀⠀⠀⠀⠀⠀⣠⡀⠘⣿⡀⡀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣷⣴⡿⠸⢿⣦⡾⡅⠀⠀⠀⠀⠀⢸⡆⠐⠒⢲⢀⠀⠀⢠⣤⣼⣿⡟⠋⠰⢱⣤⣤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣁⠀⣠⣿⣿⠄⠀⠀⠀⠀⠀⢘⣇⣊⠀⢸⠹⠀⠀⠈⠉⠉⣹⣷⣻⣿⣏⠉⠉⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣙⠻⠿⠛⠋⠙⠀⠀⠀⠀⠀⠀⠈⠛⣀⡄⠁⠀⠀⠀⠀⠀⢾⠟⠁⢸⣿⠻⠃⠀⠀⠀⢰⡄⣿
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠈⠁⠉⠁
⣶⣶⠶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡛⢶⣄
⠀⠀⠀⢠⡾⣿⣿⣿⣿⣿⣿⣆⢻⣧⡀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣄
⢶⣆⣚⠛⠛⠻⠉⠙⢻⣿⣿⣿⡇⢸⣿⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣷⡌⣷⡄
⠀⠀⢸⣿⣿⣿⣤⣾⣼⣿⣿⣿⡇⢸⣿⠀⢠⠋⠻⠿⠿⠿⠶⢶⣶⣶⣶⣤⣤⣤⣤⣀⣤⠚⢿⣿⣿⣿⣿⣿⣷⠸⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣧⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⡁⠀⢯⣀⣈⣿⣿⣿⢀⣿⣦⣤
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⣡⣿⠏⠀⡇⠀⢳⡀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⠀⠀⠀⠀⢷⠀⠘⣿⣿⣿⣿⡿⣸⡟⠉⠁
⠀⠀⠀⠀⠈⠛⠿⣿⣯⣵⣾⠟⠁⠀⠀⢸⠀⠀⢳⡄⠀⠀⠀⣾⣿⡟⠁⡤⠙⡄⠀⠀⠀⠸⠁⠀⣿⣿⣿⢟⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠻⣄⡀⠀⣿⠋⠁⠀⠁⠈⣧⠀⠀⢀⣇⡀⠀⡝⠻⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠱⣄⣘⡇⠀⣀⡀⢈⣧⣠⡔⠁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⣀⡀⠉⠑⠲⣤⡙⠛⢷⣄⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠛⠛⠆⠀⠀⠸⣷⡀⠀⠙⣦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢠⡀⠀⣿⣿⣿⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣿⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⠟⠉⠀⠀⠀⠙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠀⠀⠀⠀⠀⢰⠂⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⣠⣾⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡦⠰⣤⣀⣀⡀⠀⢠⠛⠙⠒⠉⠉⠀⢸⡀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢧⡸⣇⠀⠀⠉⠗⠁⠀⠀⠀⠀⢀⡴⠻⣓⢀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡏⠉⠉⠳⢤⡀⠀⠀⠀⠀⣠⠖⠉⠀⠀⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⠿⠿⠟⠉⠉⠉⠉⠉⠓⠶⠶⠊⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠛⠉⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⡴⠦⠀⣠⣼⣯⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⢀⠀⠀⠀⠀⠀⠀⡀⣠⡉⠹⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠁
⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡠⠄⢹⡆⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⢔⢒⢒⠘⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠋⠂⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠁⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠒
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⣶⠧⢀⣀⠀⠀⡎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠎⠀⠀⠀⣧⠞⠉⠙⡿⠇⠀⣶⠞⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡼⡇⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠴⠋⠀⣇⠀⢰⠃⠀⠀⢀⠄⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠙⠁⢅⣀⡔⠀⢆⠘⢛⠽⡄⢀⡤⠊
⠀⠀⠒⠢⠐⠀⠙⠆⡀⠈⢅⠀⠀⠈⠱⢤⣰⠛⠉⠒⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⡰⢀⠆⠐⠲⠤⢄⠉⠀⢇⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣽⣯⠉⣹⣿⣟⡀⠀⠀⠀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⢋⣽⣿⣿⣧⡈⢣⣶⣤⣼⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣴⣾⣿⣿⣿⣿⣧⡾⠛⠿⢿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣷⣆⠀⠈⠻⣇⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡃⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡇⢧⣾⢗⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⡿⡟⣻⠱⠀⠀⠀⠙⢚⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢾⣿⡿⠙⢿⣿⣿⣏⣉⢛⣀⣉⣍⣿⣙⣟⢲⣾⣶⣶⣤⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠶⠽⠶⠺⣿⣿⣯⣹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⢭⣯⣿⣿⣿⣿⣟⣿⣿⣿⣏⣽⣿⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣾⣯⣿⣿⣿⣿⣿⡿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡍⢿⣿⣿⢿⣷⣿⣿⣿⣿⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣻⣿⣿⣿⣿⢻⣯⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣻⣿⣿⣿⣿⠇⠀⠙⢿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣿⢿⣿⣿⣀⠀⠀⠀⠙⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣶⣿⣿⣿⣯⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣼⠿⣿⢟⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠗⠋⢿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠛⠛⠳⢦⡄
⠀⠀⠀⢀⣠⡶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⡆
⣼⠃⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠛⠛⠋⠉⠉⠀⠸⣇
⣿⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣤⠀⠀⠀⢸⡆⢸⡆
⢸⡇⠀⠀⠀⣀⣤⣤⠿⠀⠀⠀⠀⠹⠂⠀⠀⠈⠁⠘⣧
⠀⢷⡀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢿⡀⠀⠀⠀⢀⣠⡴⠶⠞⠛⠶⠶⣤⡀
⠀⠘⢷⡀⠈⠷⣤⣄⠀⠀⠀⠀⢀⣤⡴⠞⠛⢉⣿⠀⢸⡇⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠙⠢⣤⣤⣿⡀⠀⠀⠀⠀⠹⢦⣤⣤⠞⠃⠀⣿⠀⠀⣼⠃⠀⠀⢀⣤⠶⠶⢦⣄⠀⠀⠈⢿⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢀⡟⠀⠀⠀⣾⠁⠀⠀⠀⢻⡆⠀⠀⢸⡇
⠀⠀⣠⠀⠀⠀⠀⠀⣠⠿⠳⢦⣤⣤⣤⣤⡴⠾⢯⡀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⣀⡾⠁⠀⠀⢸⡇
⠀⣼⠋⠀⠀⠀⢠⡾⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠙⣦⡀⠀⠹⣆⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⣠⡟⠀⠀⠀⣸
⢰⡏⠀⠀⠀⢠⡟⠀⠀⠀⣠⡾⠛⠉⠉⠉⠙⠷⣤⡀⠘⣧⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠉
⣼⠁⠀⠀⠀⢸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣿⡀⠀⠀⠀⠈⢹⡟⠛⠛⠛⢻⡍
⣿⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⣨⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠸⣇
⠉⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧⡀⠀⠀⠀⢀⣴⠏⠀⠀⣴⠏⠁⠈⠉⠙⢷⣼⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⢦⣄⣠⡾⠁⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⣰⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠙⢷⣶⣤⣀⠀⠀⠀⢰⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡇⠈⠉⠛⠳⠶⣼⣧⣀⣤⠾⠃
⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠶⠶⠶⢾⡃
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⣿⣿⡇
⠀⠘⢿⣿⣿⡟⠻⣏⡉⠉⠉⣉⠉⠉⢉⣩⡟⠹⣿⣿⣿⠏⠁⠈⢻⣿⣿⣿⠙⣯⣉⠉⠉⣉⡉⠉⠉⣩⡿⠉⣿⣿⣿⡏⠁
⠀⠀⠈⠛⠛⠁⠀⠙⢿⣦⣸⣿⣆⣴⡿⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠈⢻⣷⣤⣿⣧⣤⣾⠋⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⠃⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠑⡀⣉⠀⠀⠀⠀⠀⠀⠀⠀⣈⢀⠊⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⡀⠀⠉⠁⠀⠀⠀⠈⠁⢀⡎⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣄⣀⠀⡼⠁⠈⢇⠀⢀⣠⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⣶⣶⠤⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠐⠃⠀⠊⠎⢁⡈⡀⠰⠀⠐⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⡤⠄⠠⠀⠀⢤⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠄⣴⡇⠀⠀⠀⠀⢸⣤⠠⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠒⠒⠒⠂⢺⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡟⠀⡇⠀⠀⠀⠀⢸⠀⢻⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡽⠀⠚⡏⠀⠈⠉⠀⢹⠛⠁⢯⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠴⡫⠃⠄⢀⡇⠀⠀⠀⠀⢸⡀⠀⠘⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠊⡠⠐⠀⠈⡏⠈⠉⠀⠁⢸⠁⠈⠂⢄⠑⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠊⡠⠊⠀⠀⠀⢀⣇⠀⡀⢀⠀⣸⡀⠀⠀⠀⠑⢄⠑⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⢠⢏⡔⣁⢀⣀⡀⣀⣀⣀⣀⡰⠃⠀⢰⡆⠀⠘⢆⣀⣀⣀⣀⣀⣀⣀⣈⢢⡹⡄
⠀⠀⠀⠀⠀⠀⠸⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⢸⡇⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠴⠀⢀⠀⢀⠀⡀⠀⠀⢸⡇⠀⠀⢈⠀⡀⠀⡀⠀⠦⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠲⠒⠂⠏⠹⣒⣒⣿⣟⣖⣒⡋⠸⠒⠒⠖⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠻⠿⠟⠛⠿⠿⠃⡀⠀⠀⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠒⠚⠓⠒⠺⠂⠀⠀⠀⠀⠀⠀⠀⡗⠒⠚⠓⠒⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⢤⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⣄
⠀⠀⠀⣴⣮⣿⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢿⣯⣶⡄
⠀⠀⢸⠉⡇⢸⠀⣿⣿⣿⣿⣷⡀⠤⠤⠤⠐⠒⠒⠒⠒⠒⠒⠠⠤⠤⠄⣰⣿⣿⣿⣿⠇⢸⠀⡏⢹
⠀⠀⣸⠀⡇⢸⠀⢸⣿⡟⣧⣴⣶⠶⠿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠷⢶⣶⣤⡟⣿⣿⠀⢸⠀⡇⢸⡀
⠀⠀⢳⡆⢡⠀⡆⠈⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⡏⠀⡆⢠⠁⣾⠃
⠀⠀⠀⠱⡈⣆⣰⣠⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣰⣀⡎⡰⠁
⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠋⠁