Moisture Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠏⠁⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢈⣽⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡙⠻⠟⢋⣤⣤⣌⠙⠿⠟⣉⣤⣤⣉⠻⠿⠋⣡⣤⣤⡙⠻⠟⢋⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⣿⣿⣏⣉⣩⣿⣿⣏⣉⣩⣿⣿⣏⣉⣹⣿⣿⣀⠀⠰⣶⠾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⣿⣿⣿⡿⢿⣿⣿⣿⠿⠿⣿⣿⣿⡿⡿⣿⣿⣿⢿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣾⣿⣷⣶⣶⣾⣿⣷⣶⣶⣾⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠻⣿⣿⣿⡿⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣱⡟⢎⢻⣿⣿⣿⣦⡙⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢰⣿⣿⣬⡇⣿⡿⠻⣿⣿⡎⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣝⣛⣩⣾⠟⣴⠿⣌⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢻⣿⣿⣿⣿⣿⣿⠏⣾⣿⣷⡙⣧⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣎⢿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⡟⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣀⡙⣦⡻⢿⣿⣿⣿⣿⣦⣍⣉⣭⣾⠟⣣⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠟⣩⣶⣿⣿⢿⣿⣿⡶⣭⣛⡛⠿⠿⠟⣛⣫⣥⡘⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏⣼⣿⣿⡿⠃⣾⣿⣿⣷⠘⢿⣿⣿⣧⢻⣿⣿⣿⣿⣦⠙⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡐⢛⣛⣭⣾⡇⣿⣿⣿⡿⢸⣷⣭⣛⡛⢈⣿⣿⣿⣿⣿⡇⠀⠙⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣣⠞⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣠⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢼⣿⡏⣵⣶⡆⣠⣾⣿⣿⣿⣷⣦⢰⣶⣮⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣇⢻⣿⣷⣜⣛⢻⣿⡟⣛⣫⣾⣿⡟⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣍⡛⠿⣿⣿⣿⣿⣿⣿⣌⢿⣦⡙⢿⣿⣿⣷⣶⣾⣿⣿⡿⢏⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣶⣤⣭⣿⣿⣿⣷⣝⠿⣶⣭⣛⣛⡛⣛⣛⣭⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠉⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣤⠀⠀⠀⡄⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠻⠿⠏⠈⠻⡿⠋⠘⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠁⠀⠀⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⣠⣦⡀⢀⣴⣦⡀⠀⢀⣴⣶⣦⡄⠀⠠⠀⠀⠀⢠⣶⣶⣤⠀⠀⠄⠠⠀⠀⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠈⠉⡏⠉⠈⢹⡏⠁⠀⠸⣿⣿⣿⡟⠀⠀⠀⠁⠀⢿⣿⣿⣿⠃⠀⠀⠈⠀⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠇⠀⠀⠸⠇⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⣿⣷⡄⠀⡀⠀⡀⠀⣴⣾⣿⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣿⣿⠇⠀⠀⠈⠀⠀⢻⣿⣿⡿⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⡄⠀⢀⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⢠⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠾⠟⠉⠀⠀⠙⠿⠶⠾⠟⠉⠀⠈⠙⠿⠶⠾⠟⠁⠀⠈⠙⠿⠶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠆⠀⠀⠸⠿⠿⠆⠀⠀⠺⠿⠿⠆⠀⠀⠾⠿⠿⠂⠀⠀⠾⠿⠿⠀⠀⠀⠾⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠺⠿⠿⠃⠀⠀⠺⠿⠿⠂⠀⠀⠻⠿⠿⠂⠀⠀⠻⠿⠟



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣠⠦⣤⣤⣦⠰⡆⡄⢠⢰⣦⢴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠙⠛⣈⠁⣙⠋⡘⠙⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡟⡾⢧⢹⠹⣿⢸⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⠙⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣋⠀⣀⠜⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡡⠚⠉⠲⡄⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⠴⠖⠻⡇⠀⠀⢀⡿⢁⣨⣿⡶⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⣘⡦⠤⣞⣰⠋⡰⢦⠈⡀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⢠⠀⠈⠁⠀⠀⠀⠙⢦⣙⣚⡰⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠄⣈⠁⠀⣤⣄⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢦⡼⠁⠳⡀⠀⠀⠀⠀⠀⡐⣒⠂⣠⠿⠼⣔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡰⢒⢢⡹⡀⠀⠀⠀⠀⠀⠀⡤⠟⢲⡖⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⣇⠹⠤⠞⢠⣇⣀⣀⡀⠀⠀⠀⡗⣒⣚⣓⣒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣈⡓⠒⢚⣉⡀⠀⢀⡀⠀⠀⡀⡇⡇⢴⡦⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣋⡀⠈⣓⡋⠀⣉⠓⠉⠀⣀⡼⠃⡇⣇⣒⣒⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠳⠶⠶⠶⠶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⣀⠀⡀⣀⡀⣀⣀⢀⠀⡀⣀⡀⢀⣀⠀⠀⣀⠀⡀⡀⢀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠫⣨⠇⡇⢝⡦⠈⠇⠸⣠⠇⠗⢯⢸⣒⠀⠨⣓⠆⠟⢧⢸⠸⠳⡇



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⡴⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣱⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⢸⠁⠀⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢹⣿⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣐⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠯⠾⠃
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠐⠦⡠⠔⠲⢤⠤⠒⠦⡤⠔⠲⢤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣛⣛⣭⣍⣛⣫⣭⣝⣛⣭⣭⣛⣋⡅
⠀⠄⠀⠀⠀⠀⠠⠄⠀⠤⠀⠠⠤⠀⠤⠄⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣛⣿⣟⣻⣿⣟⣿⣿⣛⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂⠀⠒⠀⠐⠂⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣽⣿⣯⣽⣿⣭⣿⣯⣽⣿⣯⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣆⠀⠀⠀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠿⠿⠀⢹⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠻⣷⣌⡙⠻⠿⢿⣿⣿⠟⢀⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠛⠋⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⢀⣾⡏⠙⣿⡆⠀⠀⠀⣰⡟⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢸⣿⠆⠀⣿⣷⠀⠀⣼⠏⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⣿⡆⢀⣿⠇⢀⣾⠋⣀⣤⣤⡀⠀⢸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⠉⠛⠁⣠⡿⠁⣸⣿⠀⢸⣿⡄⠸⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⣴⠟⠀⠀⣿⣿⠀⢸⣿⡇⠀⠻⣿⣦⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⢀⣼⠋⠀⠀⠀⠘⢿⣄⣼⠟⠀⠀⠀⠙⢿⣷⣤⣀⠀⠉⠛⠛⠿⠿⢛⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠙⠻⢿⣿⣷⣶⣶⣶⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⡿⠏⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣶⣶⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠉⠀⢈⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢿⣿⣿⠋
⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠐⢾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠉⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠈⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣶⡾⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⣴⠏⢻⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣶⠄
⠀⠀⠀⢸⣿⢠⣿⣿⢟⣼⠟⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡉⠉⠁
⠀⠀⠀⠘⣿⡈⢿⣏⢸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠶⣾⣷⡶⠄
⠀⠀⠀⠀⠘⠻⢶⣤⡤⠿⠿⠿⠶⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⣴⣾⣯⣽⣤⣤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⡴⢿⣿⠟⣿⠿⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⣿⣿⣿⣿⠟⠿⢿⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⢰⡇⢸⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠙⠉
⠀⠀⠀⠘⣧⡘⣧⡻⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠈⠛⠦⢭⡬⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡄⠀⣸⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣠⡄⠠
⠀⠀⠀⠀⢀⡄⣀⠈⠹⢿⣧⣾⣿⡿⡎⠀⠀⡠⣠⣦⢠⣤⣤⣤⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠐⠀⠂⠑⠀⡀⠂⠀⣄
⠀⠀⠀⠰⠿⣿⣷⡄⠄⠀⠈⣿⣯⡕⠆⠀⠀⠙⣿⣦⣺⣿⣿⣿⣤⣔⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣀⠸⢀⠀⢀⠘⡆
⠀⠀⠀⠀⠀⠈⠐⠻⣾⣥⣢⡽⣋⠛⢷⣦⡆⠀⢿⣷⠻⣿⣿⣗⠉⣉⣿⡍⠀⠀⠀⠀⣶⣶⠄⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⢀⠀⡈⠋⡆⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠐⠢⠄⠙⢿⣯⣴⡀⠈⠙⠛⣿⣿⡁⠀⠹⢿⣿⣧⢰⣿⣷⡄⠀⣀⣀⣻⣿⣦⠀⠀⠀⠀⠰⣁⡀⠀⠀⠼⡆⠠⠀⠀⢠⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠂⠀⠀⠀⠹⣿⠇⠀⠀⠀⢞⠛⣿⣿⠀⣿⡾⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣳⣤⠀⠀⠀⢸⣧⠁⠀⠀⠀⣾⠆⠸⣿⡇⣿⡖⣎⠸⣿⡯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠊
⠀⠀⠀⠀⠀⠀⢈⣿⠗⣤⣤⡀⡡⣯⠤⠀⠈⣸⣿⠂⠃⠀⢠⠉⠀⠈⠹⣿⠙⠛⠐⢼⣿⠡⠁
⡀⣤⡀⣀⡀⣶⡿⠏⠀⠉⠉⢻⣿⢻⣷⢶⡴⢿⣿⣦⣄⣨⡉⠁⠀⠀⠀⢹⣷⡇⠀⢸⣿⠙⡀
⠉⠻⢷⣿⣿⡿⠗⣶⣧⣦⣤⣠⠀⠁⠈⠉⠀⠒⠂⠍⢻⠿⡿⣿⣴⣄⡀⢪⣿⣷⣈⢻⣿⡆⠋
⢰⣼⣏⠉⠩⣻⡳⠂⠀⠋⠗⠐⢿⣂⣄⡀⠀⠀⠀⠀⠀⠀⢐⣻⢺⢿⣿⣿⣾⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠐⢤
⠙⠻⣿⣂⠀⣸⡯⣦⣄⣀⣀⣀⡼⠋⠉⠛⠷⠶⣤⣦⣰⣾⣵⣿⣶⣾⣶⣷⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⠀⠀⠀⠀⢦⢠⡀⠄⢄
⠀⠸⢿⣿⣿⠟⠁⠈⠈⠉⠘⠛⣃⣂⡀⠀⠀⠀⡺⢿⠟⠅⠠⠍⠙⡍⠑⠱⠸⢩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡀⣾⣿⣷⠀⠂⠐⢀⡈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠋⠚⠗⠇⠘⡈⡳⠀⠀⠀⠀⠁⣠⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢑⢈⡋⠁⠈⢀⣠⡘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠓⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡸⠿⠄⠀⠀⠵⠎⠀⠛⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠂⠠⠀⠃⠀⢀⣈⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⠀⡔⠀⢁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⣀⠀⡀⣀⡀⣀⣀⢀⠀⡀⣀⡀⢀⣀⠀⠀⣀⠀⡀⡀⢀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⢫⣨⠇⡇⢝⡦⠨⠇⠸⣠⠇⡗⠯⢸⣒⠀⠨⣓⠆⡟⠇⢸⠸⠳⡇



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠈⡰⠋⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢸⠁⠀⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣐⣫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠤⣄⣀⡤⢤⣀⣠⠤⣄⣀⡤⠤⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⠤⢤⣀⣠⠤⣄⣀⡤⢤⣀⣠⠤
⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⢀⣀⠀⢀⡀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⢀⡀⠀⣀⡀⠀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠄⠀⠤⠀⠠⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠄⠀⠤⠀⠠⠄⠀⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⢠⣦⣠⠴⢦⢠⣄⣴⠦⠰⣶⠆⣤⠀⣦⢴⠶⣄⣴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠟⠿⠹⠦⠼⠹⠇⠭⠿⠀⠿⠀⠿⠤⠏⠼⠻⠇⠿⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡄⣠⢀⣤⠀⣤⣤⢠⣤⡄⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⢳⡏⣼⠿⣧⢸⡇⢸⣟⡃⡿⢾⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⡤⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⠁⠀⠀⣰⠟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣴⠋⣡⡴⢿⣅⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡞⠁⠀⠀⠈⢳⣠⡇⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣤⠶⠶⠘⣾⡇⠀⠀⠀⠀⣸⡿⠁⣀⣈⣛⡶⢶⣴⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠖⠋⠉⠀⠀⠀⠀⠀⠀⠻⣄⡀⢀⣰⠏⢠⠞⠉⣠⡈⠙⠦⠀⠈⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠏⠉⠉⠻⢦⣿⠀⢸⡋⣻⠄⠐⠂⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⡙⣉⣠⠞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣀⡀⠀⠀⠀⢠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⡀⠀⢀⡼⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣁⣘⣛⡀⠀⢸⣏⢹⡆⣀⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢃⡾⠁⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⡈⢩⣭⠁⢠⡾⠷⠾⢷⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⡶⠶⢦⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⢦⡴⠼⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢿⡄⠂⢨⠇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣀⣸⣇⣀⣀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠠⠼⣧⡀⠙⠛⠋⣀⡾⠤⠤⠤⠤⠤⠀⠀⠀⠀⢸⡇⣤⠴⠦⠤⠦⣤⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡙⠓⠒⠛⣉⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⡇⣿⠀⣞⣳⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠴⠋⠁⠙⠷⠤⠞⠉⠈⠻⠦⠴⠋⠁⠀⠀⣠⣾⢸⡇⣿⠠⣬⣥⠄⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠐⠒⠂⠀⠐⠛⠂⠀⠀⠀⠰⠞⠋⠀⢸⡇⠻⠶⠶⠶⠶⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛


⠀⠀⣀⠀⠀⠀⠀⡀⢀
⣿⡟⡉⣻⠟⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠀⣾⠟⠉⠑⠂⠀⠠⣴⣿⣷⣦⣤⣤⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣽⣿⡇⠀⠀⠀⠀⠀⠐⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠟⠈⠁⠀⠀⠀⠀⠀⢰⣾⣟⣛⡿⢿⣯⣽⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣴⣯⣽⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢠⠟⠋⣽⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀
⠀⠀⠀⠀⠸⠺⣇⣈⣭⣩⡇⠀⠀⠀⠀⠀⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠹⡟⠃
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢣⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣿⣷⠀⠀⠀⠀⣠⣤⣤⣤⣤⣶⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠾⠿⠿⠿⠿⠿⠟⠛⠋⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⡢⠄⠉⡁⠀⠀⠀⢀⠉⢀⠰⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢦⠁⡠⠐⠅⠀⡀⠔⠁⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⡄⠊⠴⠔⠐⣡⢠⠀⠀⢀⠔⢈⠉⠈⡦⠊⠐⠃⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⡔⢁⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠫⣀⡟⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠓⠲⠒⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠀⠈⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⢦⡇⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⠈⢨⠱⡀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⣀⠔⠊⠉⠀⠉⢆⢀⠾⡖⠋⠀⠀⠈⠢⣸⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠸⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠐⠊⠉⠀⢀⠀⠐⢉⡀⠑⠊⢈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢐⢰
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠉⠈⠁⢊⣆⠀⠀⠈⢯⡡⢬⠉⠑⢆⠀⡠⠈
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⠀⠀⠀⠀⢀⠆⠀⠀⠇⠰⡀
⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⣄⠠⠖⠁⠀⠀⠀⠈⠱⢰
⠀⠀⠇⠀⠡⠀⠀⠀⠀⠀⠡⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠆⠇⠀⠀⠀⠀⠄
⠀⠀⠀⡄⠀⢰⠀⠀⠀⠀⠀⠅⠒⠄⠠⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⠈⢠⠃
⠀⠀⠀⠱⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠐⣌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⣨⢁⠒⡁⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠐⠄⡀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⡠⠊⠁⡣⠀⠁⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣈⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀⣀⠤⠒⠁⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠤⠀⣀⣀⡀⠀⠀⣀⣀⠠⠤⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣪⣭⣔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⠛⠿⣿⣷⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣦⠀⠀⠈⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃⠀⠀⠀⠀⣐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣀⡀⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⢀⡞⣽⣿⣿⣶⣄⠀⠀⠘⠂⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢀⡀⠀⠈⠐⠀⠈⢷⣄⠁⠙⠻⣿⠀⣤⠀⠀⠰⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄⣀⡀⠀⠠⠤⠌⠐⢒⣀⣐⣐⣒⣒⡉⣆⢨⣸⠁⣀⠠⠤⡬⠁⠀⠀⣀⡀⢠⣀⣀⡀⢀⡀
⠀⠀⣀⠤⠖⣒⠭⠋⠉⠉⠀⡀⣠⡴⠶⠓⢛⣉⣉⠥⠤⠒⣀⡀⠀⢰⠇⢠⠷⠤⠬⣭⣉⣉⡉⠛⠒⠢⣤⣀⠀⠀⠉⠑⠐⠌⢁⡒⠒⠠⣄⡀
⠐⠉⠀⣠⠎⠀⠀⠀⠀⢔⠈⣞⠁⠀⢰⣾⠋⠁⠀⠀⢎⠀⠀⠐⠂⠁⠀⣀⣘⠢⡄⣀⠀⠬⡙⢿⢮⡅⠈⠛⢷⣤⡢⠀⠀⠀⠀⠘⣲⣄⠀⠈⠑⠦⣀
⠀⠀⠀⢯⡠⠀⠀⠀⠀⢕⡨⣷⠀⠀⠐⠽⣆⠀⡂⠀⠀⠁⠢⢤⣀⡀⣀⣈⣉⣑⡊⠎⠠⠔⠁⣼⠯⣻⠀⠀⠈⡍⣋⠀⠀⠀⢀⠢⡒⢽
⠀⠀⠀⠈⠲⣡⢂⢔⢄⠀⠈⠉⢶⡔⢄⠀⠈⠉⠒⠢⠦⣎⣦⣴⣮⣥⡤⢶⣲⣶⣆⣴⡶⣐⣑⠥⠚⠁⣠⢶⠕⣅⠎⠀⠀⢌⠢⠑⡬⠎
⠀⠀⠀⡀⠀⠀⠉⠉⠈⠊⢎⣆⡄⡈⠚⠊⠊⠃⠂⠠⣰⣒⡤⠤⢬⣭⣉⣊⣭⠉⡉⠉⡀⠠⠴⣶⣊⡪⠨⠖⠊⢁⢀⢊⣄⠦⠒⠉
⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠉⠉⠙⠓⠲⠦⠤⠄⣄⣄⡉⣉⣉⣹⣻⣬⣭⠝⠻⢇⢙⢉⣉⣤⣤⠠⠤⠆⠛⠚⠈⠉⢀⡀⠤⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠀⠀⠀⠀⠠⠤⠄⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠄⠀⠀⠒⠒⠀⣉⡉⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠐⠒⠀⠈⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⣡⠀⠀⠀⢸⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⢤⣶⣶⣦⡀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠔⠃⡀⠘⠆⢸⢿⣿⣿⢿⠋⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡠⠒⠂⡟⠂⢄⣟⡘⣙⠘⢻⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣇⣀⣀⣇⢀⠀⠀⡄⠀⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⡀⠀⠀⠀⠈⢋⣭⡉⠉⠉⠁⠀⠇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⡙⠢⣤⡤⠴⠋⡍⠒⠀⠀⠀⠀⠆⢪⣥⣌⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠷⠊⠁⣄⢀⠀⠁⠀⠸⠀⠀⠀⠀⣀⣸⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠖⠋⠙⠃⠀⠠⡏⢹⠀⠀⠀⢠⠀⠀⠸⠀⣶⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡅⠀⠀⠀⠀⠀⠀⠃⡎⠀⠀⠀⠀⡀⠀⣥⠀⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⡄⠀⢸⠃⢀⠀⡼⠀⠀⠠⠀⢀⠃⠀⠀⠀⡟⠀⠀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠇⠀⠰⠆⢁⡼⠁⠀⠀⡀⠀⠸⠄⠀⠀⠀⡇⣄⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠒⠺⠷⡶⠶⠒⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⢸⠇⢸⣀⠴⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⣇⣀⣀⡘⡇⠀⠀⠀⠀⠀⠀⠀⢨⣅⡾⠀⠋⢀⢠⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠀⠀⠀⡏⢸⠀⠑⠛⠲⣶⡄⣀⠠⠀⠀⠀⣼⠁⠀⠀⡼⠀⢠⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡿⠺⣇⠀⠀⠀⠚⠑⠫⡄⠀⠀⡜⠳⡧⠀⠀⠷⠀⢠⡿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡟⠀⢻⣆⠀⠀⠛⠀⠀⠀⣠⢾⠇⣾⠆⠀⠀⢀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⢰⠋⠀⡾⠋⡷⣄⣀⣀⣠⠞⢁⡎⣠⠁⠣⡉⢀⠙⡀⣨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠈⢯⣸⠃⠁⡗⠛⡁⡸⠣⣤⡞⡰⠋⢠⠀⣧⣰⣦⢧⣀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢇⣸⠀⠀⡧⢀⡟⣁⢠⣿⠃⠀⠀⢸⠀⡟⠁⠙⠚⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⢧⣄⡘⡇⣰⢂⡇⠀⣼⠀⠀⣀⠋⠀⣋⣠⠴⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠃⠀⠈⣧⠉⡱⠃⠸⢱⡀⠘⠳⠲⠟⠊⠉⠁⣤⢼⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠒⠒⣶⠒⣿⣤⣌⣳⡀⢚⣠⡗⠀⠀⠀⠃⠀⠀⠀⢹⣹⠦⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠴⠤⢤⣌⠭⠭⠥⠝⢙⠿⠭⠿⠶⠶⠶⠶⠂⠠⠴⠶⠤⢷⠤⠤⠤⠤⠼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⠤⠭⢤⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡤⠀⠀⠀⠠⠀⠀⠀⠂⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⣹⣿⣿⣿⡿⠿⠟⢿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⣀⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⡟⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⣨⣤⣶⡄⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣦⣄⡀⠀⠀⠀⠹⢿⡦⢻⣿⣿⣿⣟⢳⡄
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣷⡀⠠⣤⡀⠀⠘⠿⠙⢿⣿⣿⣿⣿⡆⣠⣤⠀⠀⢦⣄⣻⣿⣿⣟⠣⣿⣆
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣽⣧⣴⣺⣷⣦⡀⠉⢻⣿⣿⠀⠙⠁⠀⠀⠘⠯⠛⣿⣿⡇⢠⣽⣿⣆
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣼⣿⠆⠈⠿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣼⣿⣿⣿⡄
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣷
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼
⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡿⠉⠉⠋⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣇⠀⢀⡀⠀⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣇⣀⡀⠀⠉⠁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⢀⣠⣤⣤⣤⣤⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡿⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡞⢫⡌⣿⣿⡿⠁⠈⠀⠀⠀⠈⠉⠓⢲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠈⢸⣿⣷⣾⡟⠆⢻⡿⠃⠀⠀⠐⠆⠀⠈⠙⢄⠀⠛⡙⠿⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⣿⣿⣿⣿⠿⠂⠀⠃⠀⠀⠀⠀⠀⢀⣀⡆⠀⣠⣤⣿⣶⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⣇⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠁⠐⠂⠆⠀⠀⠀⠀⠀⠀⠤⠀⣾⣿⡿⠋⠉⡟⡬⢿⡿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣾⣿⣷⣽⡀⣈⣀⡄⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣿⣿⡟⠉⠉⠀⠛⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠿⣧⣤⣶⣈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠙⣿⡁⢀⣄⣀⡀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣟⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢐⠀⠀⠀⠀⠀⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⡿⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠉⠀⠐⢸⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⢁⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⢻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠂⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠁⠀⠀⠻⠳⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⠒⠴⢦⣾⣄⠀⠠⠄⠀⢀⣤⣶⣶⣾⣶⣶⣶⣞⡁⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠿⢿⣿⣷⣶⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢻⡟⠻⢵⣶⣮⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⢉⣥⣴⡾⢟⣴⣿⣏⣀⣴⣶⣿⣯⣿⣿⣿⠟⠁⣴⡀⠘⠋⠉⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⠹⠋⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣏⡻⠋⠚⠋⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⢀⣤⡤⡄⢀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠚⠛⠉⢿⡿⢿⢶⡦⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢰⠀⢰⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠳⠶⣤⣤⣠
⠀⠀⠀⠀⠀⠀⢸⣦⣬⣁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣯⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣰⣿⣃⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣰⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠋⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠼⠇⠀⠀⠀⠀⠀⢀⠀⣀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⡠⠔⠤⡐⠛⠀⠀⣰⠭⠏⡀⢀⢞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠉⠓⡄⠀⠀⠉⠀⠀⠱⠴⠖⠀⡠⠖⣋⠀⢀⠤⣈⢹⣗⡌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⣠⡗⠁⠀⢀⡔⠒⣢⣀⡠⠔⢫⠒⠛⡾⠃⣞⡶⡿⠀⠉⠰⠉⠱⡄⠀⣎⣱⠄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠖⠁⠀⡔⠁⣨⡷⠛⡇⠀⠀⠱⢤⡾⠃⣴⡌⠁⠀⣠⠔⠃⡤⠤⡘⣆⠌⢥⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢃⢌⣀⡳⠾⠃⡤⠒⣤⣤⡀⠀⢠⢄⠀⡞⠀⡠⠚⠣⣴⠃⠈⢦⣐⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢒⢦⣠⠴⠊⠁⠀⠳⠞⠉⡕⠀⡠⠗⠒⣿⠉⢀⡀⠈⠛⠀⡇⢨⡀⠀⡔⡐⠀⠀⠀⠻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡔⠚⢇⠀⡀⡰⠘⡘⠸⣰⠀⠀⣅⢀⣴⡟⠀⢧⠯⠀⠀⠀⠘⡄⠉⠀⠉⠀⠀⠀⢠⣄⠱⣤⡄⠀⠀⣀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠙⠛⠒⠋⢰⢡⢁⢣⢁⠗⢣⠀⠀⠈⠁⠉⢠⠶⣽⠂⠀⠀⢆⡆⢨⢀⡄⠀⠀⣔⣢⠀⢡⠠⡟⠀⣠⠼⣄⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢃⢁⢃⠆⡌⡐⡜⠛⠋⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⡠⠖⠶⡁⠘⠶⠀⠀⠉⠁⠂⢡⠐⢡⠀⢇⣠⢀⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠁⠀⠀⢢⠀⠈⡘⡜⡸⢠⢱⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠓⢄⣼⢂⠀⠀⠀⢀⠀⡂⡄⠈⠀⣸⠀⠀⠉⠠⣎⡶
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⡇⠀⠡⢂⠱⢁⢃⠇⡌⡜⡠⠀⠀⠀⠀⠀⣀⡀⠀⢠⣇⠀⢔⠌⠁⠿⠀⢀⢀⠰⠟⠁⠀⣶⠀⡼⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡄⡄⠙⢢⡀⠱⣂⠘⡘⢠⢡⢠⠃⠀⠀⠀⠀⠮⣀⡼⠀⡆⠈⠉⠉⠀⢀⠀⠀⠐⠈⠀⠀⠀⣀⠘⠤⠃⡉⣈⡇
⠀⠀⠀⠀⠀⠀⠀⡤⠠⡄⠘⣷⡀⠀⠱⡈⠡⡀⠁⡎⡈⡌⠀⡠⢊⡹⣄⠴⡌⢀⡴⠁⠀⠀⢀⠰⠘⣀⢤⡀⡎⠉⢧⡀⡧⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠘⠤⡨⠇⠀⠙⡇⠀⠀⠳⡀⠀⠀⠀⠁⠁⠇⡇⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⣨⠔⠋⠀⢰⠁⢰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⢇⠆⠠⡀⠘⣄⢀⠴⢦⡈⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⡇⠀⣦⠂
⠀⠀⠀⠀⠀⠘⠖⠃⠀⠀⣁⡀⠘⠊⠣⡑⡀⠈⠁⠀⠀⠓⠔⠋⠀⢀⠄⢂⡠⠖⡆⠰⡇⠀⠀⠀⠀⠀⠻⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢌⠂⠀⠀⠙⢌⠠⠀⠀⠀⠀⢀⠄⢂⡤⠚⠉⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠑⠢⡄⠀⢀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢸
⠀⠀⢀⡠⢄⣠⢄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⡴⠒⣢⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄
⠀⠀⠎⠤⠌⠽⣃⣃⣘⢤⠀⢉⣒⣒⣀⣩⣯⡑⣤⣤⠔⢒⣈⠉⢑⣲⣤⠤⠌⠉⣭⠥⠤⠤⠔⠋⠀⢙⠦⠤⠤⢤⢄⠀⣄⠈⠂⢒⣚⠂⠀⠀⡤⠠⡖⠒⣄
⠀⠀⠀⠀⣆⡀⣀⣀⡠⠤⠴⡖⠒⠒⠒⢲⣒⣒⣒⡒⠀⢘⣋⣀⣠⡼⠧⣄⣀⣀⣀⣀⣀⣈⠉⠀⠉⠉⠀⢀⠀⠵⣎⣷⢮⡭⡥⢤⣬⡌⣓⡌⣁⡚⠉⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠄⠒⠒⣲⡶⢤⣀⢱⠞⠣⢀⣀⣬⠿⢍⣁⡚⠛⣮⠔⠛⠛⠛⢮⡘⠃⢘⠉⠙⠮⡛⠓⡎⠀⠀⠉⠀⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⢤⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣯⢡⡴⣶⣤⠞⠛⠋⠉⠛⢳⡄⠀⠀⢀⣤⡴⠟⠛⠛⠷⣤⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠸⠧⠴⢬⣩⣽⡛⣦⡀⠀⠀⠈⢷⠀⠀⠘⠷⠶⠶⣦⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⡟⠀⢀⡤⠟⠀⢀⣤⣤⣤⠶⠟⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠳⠤⠟⠀⠀⠀⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢰⡇⠀⠀⢀⣠⣤⣤⣀⣀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⡛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⣼⠛⢶⡀⢸⠁⣠⣤⣈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⠁⠀⠉⠛⣯⠉⢿⣄⠀⠀⣴⠲⣄⠀⠀⠀⣧
⠀⣿⠀⠸⣧⣿⣀⣉⡙⠛⠃⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠸⠿⠶⣦⣻⣤⣤⡿⠀⠈⣿⠀⢀⣿
⠀⣿⠀⣰⠟⠀⠀⠈⠙⠦⣤⡀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⠇⠀⠻⡴⠋⡿
⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠈⠛⠛⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢠⡇
⠀⢸⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣶⠛⠀⠀⣠⠖⠒⢺⠇
⠀⠀⢻⡙⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⢿⣤⡄⢼⡋⠀⢠⡿
⠀⠀⠈⢷⡀⠀⠙⢳⡄⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣼⣿⡇⣸⡃⣠⡿⠁
⠀⠀⠀⠀⠳⣄⠀⠀⣿⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡟⢹⠟⠁⢉⡽⠋
⠀⠀⠀⠀⠀⠈⠳⣄⠹⣆⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡴⠟⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣳⣾⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠙⠢⡄⢀⡤⠔⠒⠚⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⠀⡰⠒⠋⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⢀⣀
⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠓⢤
⠀⠀⠀⣀⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⠢⡀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⣄
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⢲
⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠫⠽⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠁
⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠈⠉⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠉⠢⣄⣀⡀⠀⠀⠀⣀⣠⠞⠁⠙⠲⢤⣤⣀⣀⣀⡤⠴⠊⠁⠀⠈⠉⠙⠛⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⡼⢧⠀⠀⠀⠀⠀⠀⠀⡸⢳⠀⠀⡀
⠀⠀⠀⠀⢀⣴⡀⠀⠀⢯⣸⠇⠀⠀⠀⠀⠀⠀⡏⠸⡆⠀⠀⠀⠀⠀⣇⢸⡆⠀⠀⠀⡀⠀⠀⢇⣸⠇⢰⠻⡄
⠀⠀⠀⠀⢸⠀⣷⠀⠀⠀⠁⠀⠀⠀⢰⢧⠀⠀⠳⠼⠁⠀⠀⣠⡀⠀⠘⠛⠀⠀⠀⢰⠻⡄⠀⠈⠉⠀⢸⣀⡇
⠀⠀⠀⠀⠀⠙⠋⠀⠀⢠⡄⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⢠⡇⢧⠀⠀⠀⠀⣤⠀⢸⡀⡇⠀⢀⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠀⠀⠀⠙⠚⠀⠀⣠⡀⠀⠀⠘⢇⡼⠀⠀⠀⢸⠀⡇⠀⠉⠁⠀⢸⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠀⠀⠀⠀⠀⠀⢠⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠏⠀⠀⠀⠀⠘⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼
⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣄⠀⠀⢤⠀⠀⡀⠀⢀⠀⠷⠀⠀⠀⡄⠀⡦⠀⢀⠀⢰⡄⠀⢀⡀⠀⠀⠀⢆⠀⠀⢀⡀⠀⠀⡀
⠚⢰⡀⠈⠀⠀⠇⠀⠸⠆⠀⠀⡆⠀⠁⠀⠀⠀⠘⠀⠈⠀⣄⠘⠇⠀⠀⠀⠋⠀⣤⠈⠃⠀⠐⠖
⠀⠈⠁⠀⢸⠀⠀⢠⡀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣹⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⣆
⢲⠀⠀⡄⠀⠀⠀⠐⠃⠀⠀⣆⠀⢲⠀⠈⠀⠀⡄⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠴⠀⠗⠀⠸⠀⠀⢈
⠈⠀⠀⠋⠀⢰⡄⠀⢰⠀⠀⠁⠀⠀⡀⢀⡀⠠⣧⣀⡀⠀⠀⠛⠀⠀⠀⢲⠀⠀⠘⠀⠀⠀⡀⠀⡀⠘
⠀⢀⡆⠠⡆⠀⠀⣀⠤⢐⣠⠻⢛⠥⠢⠐⠀⠀⢈⡄⠂⠌⠉⠙⠒⠶⣤⡬⠀⣀⠀⠀⠀⠸⡥⠀⣥
⢀⠀⠋⠀⣠⣔⠚⠉⡴⡫⠡⢊⠩⡂⠈⠀⠀⠀⠀⠐⠈⠂⠉⠀⠀⠀⠈⠙⠲⡠⠈⠁⠢⢄⡀⠀⢠⡄
⠸⠀⡠⠊⠀⠁⠀⡜⢘⠨⡂⢑⢅⠂⠁⠀⠀⠀⠀⠀⠁⠁⡀⠀⠈⡀⠀⠀⠀⠘⢦⠀⠀⡀⠈⠢⡈⠁
⢀⢎⣢⠴⠀⠀⢰⢐⠕⠨⠞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⡀⢀⢀⠀⠀⠀⠈⣧⢐⠀⠀⡄⢝⡄
⠟⠉⠀⠈⠉⠀⣬⡵⠖⠓⠉⠈⠉⠉⠈⠙⠓⢦⣤⡀⢠⢠⣤⠴⠿⠓⠂⠡⠠⠤⠾⢜⡵⠚⠉⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣗⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣉⣁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠉⠀⠀⠁⠀⠂⠀⠀⠂⠔⠄⠠⠢⠠⠈⢄⠁⠌⠀⠨⠢⢀⠕⢔⢄⢀⢀⠀⡠⡂⡠⢀⢄⠔⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠄⢀⡀⠀⡀⠀⠠⠤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠐⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠂⠐⣀⡀⠀⠀⠠⠀⠀⠠⠀⠀⠈⠉⠄⡄⠀⠀⢐⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⢄⡀⡀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠰⠠⠀⢈⠀⠁⠐⠄⢔⠀⠉⠛⠲⠒⠺⠁⠀⠀⠑⢔⠀⠁⢅⠔⣐⡀⠁⠈⠁⠀⠈⠮⠤⡀⠀⠀⠉⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠞⠉⠱⠒⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣄⡴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡉⠣⠀⠅⠈⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠁
⠀⠀⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⣄⡤⠀⠠⣊⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠉⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡈⠀⡄
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢠⠀⠀⠋⠀⠀⠀⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠀⢀⠄⠀⠀⢀⠄⠀⠐⠀⠈⠉⠀⠀⢀⠀⢀⠄⠀⢀
⠀⠀⠀⠀⠤⠀⠠⠄⠀⠐⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠁⠀⠀⡀⢀⢀
⠀⠀⠀⠸⠔⠀⠀⠆⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⢈⡀⠀⣀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠂⠀⠀⢥⠀⠀⠀⠀⣀⠀⠀⡄⠀⠚⠀⠀⠁⠈⡁⠀⠀⠈⠀⠀⠁⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠃⠀⠉⠀⠀⠌⠀⠀⠘⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣀⣠⣤⣤⣤⣤⡤⣤⣬⣍⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠐⡿⠛⡟⠉⠏⢀⡀⠬⠷⣌⡉⣫⣹⢿⣿⣷⡒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡄⠀⠀⠀⠀⠀⠀⠁⠛⢿⣧⠀⠀⠀⠈⣿⣿⠛⣿⣿⣿⡝⣷⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⣀⣤⣴⠃⣨⡿⠀⠀⠀⣸⡿⣻⣿⣿⠟⠙⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡿⠋⠀⠀⠀⠀⠀⢿⡿⠁⢹⣤⣿⣇⣠⣴⣾⣯⣾⠁⣉⡸⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣷⠏⠀⠀⠀⠀⣴⡀⠀⠈⠁⠀⠈⢸⣿⡿⠉⠙⠛⠋⠚⢓⢿⣧⣤⢀⣾⠆⠀⠀⠀⠀⠀⣠⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠋⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⢰⠖⢙⣿⡗⠺⠇⠠⣤⣤⡎⣠⠹⠟⠈⠁⠀⡠⠃⢠⢆⡀⠈⢧⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⢠⡞⠀⢀⠀⠀⠀⠀⠀⠀⣡⣶⣷⡶⠞⠛⠋⠃⢀⠀⠀⠸⣿⣿⣿⡅⠀⠂⠀⠀⠄⠀⠘⠟⠋⠀⠀⠁⠀⠀⡀⡀
⠀⠀⠀⠀⠀⣤⠀⢀⣾⣇⠀⠀⣀⡀⠀⠀⣠⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠶⠀⠀⢘⣿⡟⠛⢀⣴⣿⣾⣕⣆⣰⣤⣴⡆⠀⠀⢦⡾⣧
⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⠁⢰⣿⣟⣹⡆⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⣿⣷⡤⠐⠛⠋⠉⣿⣿⡟⠛⠛⠡⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣄⠺⠋⣿⣭⣛⠿⢿⣿⣗⣀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣾⣿⠟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢢⡀⠀⣾
⠀⠀⠀⠀⠀⠘⠀⠛⠻⣿⣿⣷⡄⢹⡟⢿⣤⣄⣻⣶⣾⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠞⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠘⣿⣧⣘⠳⠛⠻⠿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⢀⣟⠀⢆
⠀⠀⠀⠀⠀⠀⢙⠀⠀⠐⠦⢈⢻⣷⠇⠀⢀⣀⢈⡙⠿⣿⡁⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣼⠃⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠈⣦⣢⡀⠀⠘⣿⠃⡤⠒⠃⠈⠀⠁⠀⠈⢹⡄⠀⠀⠀⠈⠁⠈⣿⡧⠀⠀⠀⣀⣠⣤⣀⡄⣶⣷⡟⠉⠣⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢈⠡⡈⠢⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⠲⢤⣔⣦⣦⠀⠀⠀⠻⠷⢿⣿⣿⣿⣿⠇⠋⣬⠀⠀⠀⠀⣛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠐⠿⣦⡀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠛⣧⣤⣄⠀⠀⠀⠀⠈⣽⢿⣿⣿⢸⣥⠀⠀⢸⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠢⠀⠀⠈⢳⡄⢹⡿⢶⡄⠀⠀⠀⠀⠀⣴⣾⣿⠋⠁⠀⠴⠂⠀⠈⠠⡜⣿⠏⠀⠙⠂⣠⢿⠁⡘⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡂⠀⠠⣌⣇⢾⠀⠈⢱⠿⠂⣀⣄⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⢀⡼⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⢈⣿⣼⠀⠀⠀⢁⣠⣿⣿⡟⠀⠀⠀⠀⢀⡠⠴⠒⠚⠋⠉⣻⣿⣡⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠳⢌⣿⣦⠀⢰⣾⣿⣿⣷⣦⣴⣊⣅⣀⣠⣄⣘⡁⢀⣦⣴⡿⠛⠙⠋⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠻⢾⣿⣿⣿⠿⠟⠛⠋⠉⠋⠉⠉⡉⠛⠙⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠂⠈⠉⠀⠠⢤⠔⡉⠉⠐⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠼⠃⠀⠐⠁⠀⠀⡆⣄⣶⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠴⠀⠀⢀⠔⡌⣡⠦⠂⠉⠈⠋⠀⠀⠀⠀⠀⠀⢩⡄⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢀⡄⢠⣯⣔⣐⠽⠚⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢸⡌⢂
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢚⣞⠄⠾⠁⠊⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⠉⠀⠀⠀⠀⠀⠀⠀⠠⡡⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⢀⡞⢁⡀⠀⠀⠀⠀⢀⣤⣠⠀⢀⢄⠦⠠⠆⠀⠀⠁⠀⠀⠀⠀⠡⠀⠀⠀⠀⠐⠱⡀
⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⢊⡯⠚⠉⢷⣗⢆⣀⣰⣈⣉⣑⠆⠈⢂⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⢣
⠀⠀⠀⠀⠀⠐⠀⠁⠀⡸⠭⠄⠐⡄⠀⠋⢸⠏⢯⣴⣤⠄⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡋⠈⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠼⠀⠀⠀⠀⠑⢄⣠⠤⡀⠀⡀⡸⠀⠀⠀⠀⣀⢀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠐⠉⠣⣄⢈⠀⡅
⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣶⣄⠀⠀⠀⠂⣉⣋⠗⢉⠉⠈⠻⠴⡄⠀⢀⠀⠀⠀⠘⡊⢁
⠀⠀⠀⠀⠀⠠⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢷⣀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠙⢏⠈⠀⠀⠀⠀⠘⠚⡆
⠀⠀⠀⠀⠀⠰⠈⢧⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠹⣧⡀⢀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠀⠉⢳⠁
⠀⠀⠀⠀⠀⠀⢃⠈⢿⣢⡀⣀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⢋⡉⡄⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⠷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠁⠀⠀⠈⡠⠄⠂⠀⠒⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡸⣀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⣈⠆⠀⠀⠔⠁⠀⠀⠁⢀⠠⠒⠁⠠⠒⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠢⡀⠈⢿⣶⣂⠀⠀⠀⣄⠛⠀⢠⡁⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⡄⠈⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡀⠀⣿⣹⠀⠀⠀⠈⠀⢦⠈⢢⠀⠀⠤⡀⠀⠀⠀⠀⠀⠠⢊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣌⡳⣎⣤⠀⠀⠀⠀⡴⠊⠀⣧⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⣶⣼⣃⣈⣀⣈⣀⠤⠤⠖⠊⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⢀⡖⢚⠀⣀⣀
⠚⠲⢤⣀⣀⣀⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⡆⢒⠀⠀⢀⡀⠀⠀⢸⡈⣁⠀⠀⢀⡘⡦⢶⢤⢾⡇⠿⠯⠋⠁⠁
⠀⠀⠀⠈⠀⠚⠠⠍⣅⡐⠒⠀⠀⠀⠀⢀⡶⢺⡗⣤⣀⣀⣀⣴⠀⠚⠗⢺⡩⠉⠩⢹⡅⠀⢘⠯⣬⢸⠛⠻⣇⠁⢠⠰⢸⣷⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡿⠀⠀⠀⣿⡇⢤⠚⠏⠀⠀⢠⣉⡣⠀⠀⠉⠛⢿⡀⢰⠿⡄⠈⢀⡽⡏⠀⣠⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢈⣇⠄⠀⠀⢀⡀⠀⠀⣠⠂⠀⠀⠈⠀⠀⠀⠉⠉⡄⠘⡀⣸⠀⢧⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠓⣾⣿⠛⠀⠀⠀⠐⠀⠀⠀⡀⠃⠀⢹⠇⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠖⠸⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢂⡉⠭⣀⠀⠄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠄⡅
⠀⠀⠀⠀⠀⠀⠀⢐⠁⣰⠒⡄⢱⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠠⠜⠉⠁⠀⠉⠙⢇⡇⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃
⠘⢌⡑⠒⠲⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⣀⠤⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣤⡦⠴
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠒⠂⡈⠀⠀⠃⠒⠂⠀⠚⠘⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣂⣀⡀⠄⠀⠀⠀⠄⠀⠴⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠛⠛⣛⠟⠁⣿⣿⡿⠿⠃⠀⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⡇⠀⠻⠟⠁⠺⠇⠀⠀⠀⠀⠀⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠀⢸⣿⣿⣿⣦⡀
⠀⠀⠀⡴⣿⣿⠋⠁⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠀⡜⠸⣿⣧⣀⡀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠈⠟⠿⣿⣿⡄
⠀⡸⠁⠀⠈⢹⣿⠁⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣤⡈⠉⢷⡀
⢀⠇⠀⠀⠀⠀⢹⡀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢣⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿
⠸⡀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿
⠀⢇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇
⠀⠘⡆⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟
⠀⠀⠘⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠈⢦⡀⠀⠀⢸⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠑⢄⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⡤⢀⣤⣠⣠⣶⣶⣶⣶⡶⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣡⣶⣶⢿⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠘⢋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⢛⣭⣥⣤⣤⣄⣀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣍⣿⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠻⣿⣿⣿⣿⣿⣿⣦⣼⢿⣿⣿⣿⠿⣷⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡿⠗⠋⠁⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣋⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣾⣿⠷⠰⢿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⢿⣧⢿⣷⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠷⠞⠋⠉⠀⠀⣚⡿⣿⣿⣿⣿⠈⠙⣿⣇⢸⡿⠁⠋⣥⣴⡿⣷⣿⣿⣃⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣷⠀⣀⡠⠐⠂⢎⣤⣿⣿⣿⣶⣽⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣻⣿⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣤⣄⣠⣤⣤⣴⣲⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⣀⣀⡤⢤⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠙⢋⡀⡙⠃⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣩⣻⡆⠀⠀⣀⣀⣠⠤⠷⣄⡘⢧⣐⣛⣦⣼⡵⠧⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⢇⡬⠖⠚⠉⠉⠀⠀⠀⠈⢻⣙⡞⠃⢹⠞⠉⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡴⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣦⠽⡶⠒⠒⠚⢛⡽⣿⠀⠀⠉⠀⠉⠉⣇⠀⠀⠰⡏⢭⡉⠉⠉⠉⢹⡛⠾⠟⠓⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⠊⢻⣦⠘⡇⠀⡔⠲⠋⢠⠇⠀⠀⠀⠀⡠⣄⢻⠀⠀⠀⢻⡀⠹⣄⠀⢀⣼⠇⠀⣦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⢸⣿⠀⣧⢸⠀⠀⠀⡾⠀⠀⠀⠀⠀⠓⠊⢸⠀⠀⠀⠀⢷⠀⠘⡆⣏⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡿⡏⠀⡏⢸⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣧⠀⣷⢹⠀⠀⠀⠸⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⢀⣿⠇⠰⣇⡼⠀⠀⣼⠀⠀⠀⠀⠀⠀⢯⡽⠀⡇⠀⠀⠀⠀⠸⡄⠘⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢠⡿⣄⣀⣀⣀⣀⣤⣤⠴⠶⠶⡶⠶⠶⠶⡶⠃⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⡄⠀⠀⠘⡇⡴⢡⠜⠛⠛⠛⢻⠀⠀⢰⠋⠉⠉⠙⢳⠀⠀⠀⠀⠀⠀⠀⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⠀⠀⢰⣧⡄⠀⢸⠃⡇⠈⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠘⠿⠁⠀⠸⣴⠃⠀⡟⠀⠀⠀⣸⠀⠀⣿⠀⠀⠀⠀⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢧⡼⠒⠒⠛⠛⠃⠘⠛⠛⠛⡟⠀⠀⠀⣠⠋⠉⠉⠹⣄⣀⠀⠀⠈⢯⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣭⣝⣛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠲⣄⣀⣀⣠⠖⠒⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠉⠕⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠜⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⡢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠐⠈⡄⡀⢀⢀⣀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠜⠒⠈⠁⠒⢄
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠑⠒⠒⠢⡤⠒⠚⠀⢀⠂⠄⠔⡠⡠⢃⢊⠎⠀⠀⠀⠀⠀⠀⡄⢣
⠀⠀⠀⡠⠄⠠⢼⠀⠀⠀⢀⢀⠄⡠⢀⢀⢀⠄⢄⣄⣐⣆⣐⣀⣀⡀⣠⣠⡥⠚⠘⠺⡴⠋⠁⠳⡎⠀⠀⠀⠀⠀⠀⠀⠄⠸
⠀⠀⡜⠀⢀⢤⢀⢄⠔⡀⠡⢂⠜⡴⠥⠆⠚⠈⣩⠜⢋⢩⠉⠉⠙⠩⢍⣉⠒⠲⢤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠑⠤⠤⠤⠤⠀⠂⣒⠶⠂⠁⠀⠀⢀⡤⠊⠀⠀⠀⠂⢣⠀⠀⠈⠐⠀⢙⠢⣕⠀⡨⢉⠐⠤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠆
⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠈⡆⢁⠄⠀⠀⠂⠠⠈⠓⢄⠑⡡⢂⠄⢉⠑⠤⡀⠀⠀⠀⠀⠀⠀⠋⠐⠄
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⡐⢍⡀⠀⠀⠈⠒⠤⠀⠑⢄⠕⡨⠐⡨⢐⣌⣲⣄⠀⠀⠀⠀⠀⠀⠓⠢⡀
⠀⠀⠀⡠⠁⠀⠀⠀⠀⡠⢀⠜⠀⠁⠀⠀⢀⣀⣀⣀⣀⣀⠠⠀⠇⠀⡂⠤⠄⠒⠒⠒⠀⠠⢈⣢⣀⠕⠊⢁⠀⠄⠈⢀⠂⠄⡀⠠⠀⠀⠀⡅
⠀⠀⠀⠉⠉⠉⠁⠒⠠⢁⡬⠔⠒⠈⢉⠄⠍⠀⠀⠀⠀⢿⠁⠁⠚⠁⠀⠀⠀⢠⠀⠀⡠⢀⠀⠌⡙⡰⠡⠂⠌⡰⢠⠂⠎⡐⠡⢂⢂⠂⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣀⣀⣀⣀⣻⣏⣐⣁⣊⡐⠀⠁⠂⠈⠀⠀⣁⣊⣈⣀⣀⣁⣈⣀⣁⣁⣈⣐⣀⣁⣀⣈⣀⣀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇⠀⠀⠀⡤⠀⣠⠀⠀⠴⠀⠀⠀⡤⠀⠀⢠⠀⠀⠀⠄⠀⢀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣜⠇⢀⡀⢸⡃⠀⠀⠸⠁⢰⡌⠀⠰⠊⠀⠀⣢⠆⠀⢰⡁⠀⠀⠗⠀⠀⠗⢠⠃⠰⠂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⢀⡀⠁⢰⡥⠀⠸⢀⠀⢠⠚⠀⠀⠀⠰⠂⡜⠁⠀⢀⠀⠀⢀⠴⠀⣀⡒⠀⢀⡶⠀⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⢀⡀⠀⠀⢈⡸⠀⠘⠃⠀⠀⠸⠊⠀⠀⠀⢀⡭⠀⠀⠘⠃⠀⠉⡀⠀⠈⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⢸⢻⡀⢀⡀⢀⠴⠀⠀⣀⠀⢀⠄⢀⣈⠁⢀⠀⠀⠼⠃⢀⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡇⡀⠂⠈⠁⠀⢰⠄⠀⠛⠀⠈⠁⢀⡪⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠄⡀⠀⠠⢀⠀⡀⠀⢀⠀⡀⠀⠀⢀⠀⠀⢀⠀⡠⠀⠀⡀⢀⠀⡠⠀⡀⠀⠀⡀⠀⠀⡀⢀
⠀⠀⠀⠉⠂⠁⠊⠔⠨⠊⠔⠄⠈⠔⠡⠊⠔⡡⢂⠅⢊⠔⠡⢊⠄⡥⢊⠔⠨⠔⡡⡪⢂⠁⢊⠔⡡⢊⢔⠡⢊⠔⡥⢊⠂⠕⠊⠠⢊⠄⠔⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣼⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⣼⣧⣴⡄⠀⠀⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⣿⣿⣿⣿⣷⠀⠘⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠉⠀⠘⢿⣿⣷⣦⣤⣌⠻⠿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡇⠀⠀⠀⠉⢻⣧⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣶⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⠋⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠁⠀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣛⣛⣛⡛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣻⡿⣶⣿⣾⣿⣿⣿⣿⣆⢻⣷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣝⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣴⣦⣄⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣟⣯⣭⣶⣮⣭⣟⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⡝⣿⣆
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣸⡿
⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⢷⣝⢷⣭⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠈⠛⢷⣿⣿⣿⣿⠿⠋⠛⠿⢿⣿⣿⣿⠿⠛⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢆⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢀⣤⠤⣤⠤⠴⠖⠒⠛⠓⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠛⠉⠛⢲⡉⠋⠀⠻⣔⣀⡤⠤⣴⣒⣓⣲⡚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⣆⣀⣈⣡⠴⠚⠉⠁⠀⠈⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⣀⡤⠖⠚⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳
⠀⠀⠀⢰⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠙⠮⣭⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡇⢀⣀⣀
⠀⠀⠀⢰⣒⡦⠀⣀⣤⣤⣄⡉⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀⠀⠀⠀⣀⣴⣶⠿⠚⠀⠻⠶⠟
⠀⠀⠀⠀⠉⢀⣀⣓⣶⡤⠾⠃⠀⠀⢳⣤⣀⠀⠀⢀⠀⠀⢀⡴⠋⠉⣀⣤⡘⠮⠶⠭⡖⠃⠀⠀⠀⢀⣀⣤⣄
⠀⠀⠀⠀⢰⠋⠉⠁⠈⠙⠲⠤⠤⢤⣀⣈⠛⠛⠛⠛⠛⢫⠟⠒⠒⠚⠁⢰⠃⠀⢾⡭⠽⣀⣠⣤⡀⠘⠓⠒⠋
⠀⠀⠀⠀⠈⠳⣕⠤⣀⣀⡀⠀⣀⣤⣤⣭⡿⠀⠀⠀⠀⠘⠷⠶⢦⣄⣠⢿⡖⠛⠛⠒⠛⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠋⠁⢶⣛⣒⣶⠿⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⠗⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣀⡀⠤⠤⠄⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠄⠀⠤⠔⠋⠄⠀⠀⠀⠀⢀⠀⠀⠉⢁⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠈
⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠐⡀⠀⡀⠄⠠⢤⡔⠁⠀⠔⠈⠙⠀⠐⠀⠀⡀⠀⠀⢀⡌⠀⠀⠀⠠⠀⢀
⠤⠤⠄⠀⢀⠊⠀⠀⠘⡀⠄⠀⢴⡎⠀⠀⡀⠀⢡⠰⠅⠁⣘⠀⠀⢀⡀⠘⠀⠀⠠⠂⠀⠀⠀⠈
⠀⠀⠀⢠⠀⢀⠀⢠⡎⠀⠀⠀⠀⢧⠔⠁⠠⠀⢼⢠⠄⠋⠤⠀⠒⠄⠈⠐⢤⠀⠈⠆⠀⠀⠀⠀⡀
⠀⠂⠀⣼⠊⢀⠀⣀⠑⠉⠗⠀⠀⠘⣗⡂⠀⠀⢸⠪⠞⣨⡇⠈⠐⡶⡀⠀⠀⠑⠔⠄⠀⠀⠁
⠀⡄⠘⠋⠀⢸⠀⠉⢀⠀⡇⠀⠀⠀⠼⠇⠈⠉⢁⢨⠀⠉⠁⠀⠿⠇⡇⠀⠀⠀⡼⠁
⠀⠀⠑⠂⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠻⡇⢀⠸⢾⡄⢟⢒⠆⠙⡼⠁⠀⢀⠜⡎⠀⠁⠀⠀⠂⠊⠉⡑
⠀⠀⠀⠀⠀⠘⡤⠤⠄⠀⣀⣀⣀⣀⠢⠊⠟⢠⠀⣀⠙⢍⢃⣶⣎⠀⠤⢶⠍⢉⣀⣉⠠⢄⠀⡈⠀⠀⡀
⠂⠒⠀⠀⠀⠀⣀⡀⠀⠂⠠⠤⠀⠀⠱⢈⡀⢈⡗⠓⠀⠠⠄⠀⠀⠀⠀⠀⠁⠃⢀⠀⠀⢀⠀⠁⠀⠀⠤
⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠀⢂⠝⠒⠊⠎⠄⠀⠀⠀⠑⡦⡀⠀⡀⢀⠓⠀⢠⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠠⠤⢀⠔⠓⠐⠊⠌⠄⠀⠀⠀⠀⠀⡇⠤⠥⠒⢃⠤⠀⠼⠣⠂⠀⠀⠤
⣤⡄⠤⠀⠔⠀⢠⡔⠂⣄⠀⣀⣀⡀⠜⠢⢄⠀⡜⡀⠀⠀⠂⠉⠀⠀⣃⠀⠀⠀⢈⡐⠂⡀⠀⣤⠤⣤⠤
⠀⠀⠀⠀⠄⠀⢀⡛⠀⠊⠂⡁⠈⠀⢀⠠⠀⠙⠢⠄⡀⠀⠈⠒⠊⢠⠇⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠂
⠑⠂⠀⡀⠀⠁⠂⠘⠔⡤⠴⢄⡠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠰⠂⠠⠤⠄⠀⠡⠚⠉⠀⠀⠀⠀⠒⠀⠂⠠
⠀⢀⡀⠀⠈⠐⠀⠀⠈⠲⠒⢉⢀⣀⡀⠀⠀⠀⠈⠈⠁⣀⡀⠃⠀⠈⡀⠀⠃⠠⠀⠀⠀⠠⠤⠠
⠀⠀⠀⠀⠀⡠⠒⠐⠀⠊⠉⠊⠁⠉⡀⠀⠀⣀⣀⠁⠀⠀⠀⠞⠐⠂⠙⡕⡀⢀⡀⠠⠄⠀⡀⡀⠀⠀⠁
⠠⠐⠤⠂⠊⠁⠐⠀⠀⠃⠒⠂⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢀⠺⠀⠂⡄⢓⠀⠀⠀⠀⠀⠂⠀⠄⢉⣄⡀
⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣂⡀⠀⠀⢆⠸⠀⠠⠀⠙⠀⠀⠀⠀⠀⠠
⣤⣤⣤⣬⣬⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣥⣤⣤⣤⣤⣤⣶⣤⣤⣤⣴⣴⣶⣦⣬
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡤⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢻⣷⠈⢿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⢺⡀⠀⠀⣿⠟⠁⠘⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⢸⡇⠀⣀⠀⠀⡀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣀⠀⠀⠠⣿⣿⣿⡿⠀⠸⢇⣀⣿⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⢿⣿⣿⣧⢰⡿⠞⠛⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣶⠀⢸⣿⣿⣇⠘⠁⣠⠖⠈⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⡤⠀⠻⣿⣿⣶⣶⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣴⣿⣿⣿⣧⣿⣸⣤⣾⠿⠋⠉⠁⣾⠿⠿⠃⠀⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⣼⡟⠃⣿⠇⠐⠟⠃⠀⠀⢀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠈⢻⣿⣷⣾⣄⢁⡀⠲⠀⠿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣇⠀⣱⡟⠃⠉⠉⢙⣤⠜⢺⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⡿⠷⠾⣷⣆⣹⣧⣼⣿⣿⣿⡿⠿⠟⠛⠃
⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠘⠟⠙⢣⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⢸⡇⢠⣾⡅
⠀⠳⣄⡀⢸⣿⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⡀⢸⣿⣾⠟⠁⢀⡄⠀⣠⡆
⠀⠀⣿⡇⠘⣿⡁⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣀⣽⣧⡴⠞⠋⢀⣶⡟
⠀⠀⠉⢁⡴⠈⠉⠀⠀⠁⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠻⣿⣿⣿⣿⡟⠉⠁⣠⠶⣠⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠑⣄⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢿⣆⠈⠻⣿⣿⣷⣮⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⠃⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⣿⡇⠀⣹⠿⠟⠋⠉⠀⠀⡀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠘⠃⠀⠀⣶⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡜⢷⢀⣿⠀⠀⢠⡤⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣿⢁⣴⡗⠉⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⡀⠉⠀⠀⠀⠠⣤⡀⠀⢸⣿⣿⠉⢿⣿⣯⡘⠻⣧⣴⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣼⡿⣨⢻⣶⣌⣿⠃⠀⠀⠹⠁⣠⡾⢛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣿⣿⣠⣆⠀⠀⠿⠄⢹⣿⡏⠀⠆⠀⠀⣴⣟⣵⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣆⡀⠀⣤⡀⢻⣿⠀⢺⡆⠀⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠻⣿⠉⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⡟⠉⠉⠉⠉⠀⠹⣿⡾⣿⣇⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇⢰⣦⣤⣄⠀⠈⠁⢸⣿⣤⣿⠇⠀⠀⢀⣤⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣰⠁⣀⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⢻⣿⣿⣷⣤⡀⠈⠻⣿⠇⢀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡇⢰⡿⠻⣿⣿⡿⢡⠀⣿⢠⡜⢣⣾⠏⠀⠀⠀⠀⠀⢠⣄⡀⠀⠐⠀⠀⠺⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠜⠁⠀⠘⢿⠇⢸⡄⠸⣿⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⠈⠁⠀⣴⠁⠈⢠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄⠀⠀⢠⠆⠀⢀⣤⡀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡌⠙⢧⡀⢰⣈⣷⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⣾⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣶⣼⣿⠊⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠟⠀⠀⠀⠺⣿⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣏⠈⣿⣿⣇⣀⣤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⡀⠈⣤⠀⢀⣴⡀⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⣿⡀⢃⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⢷⣄⡹⡀⢸⣿⠇⢻⣿⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠘⡷⠗⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣤⠀⠀⠀⣉⠛⣿⠈⠻⠀⢈⡟⠀⠀⠀⠀⠿⠃⢠⠀⣀⠀⠀⠾⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣘⠿⣤⡄⠀⠀⠸⠟⠀⠀⠀⠀⠀⡂⠁⢠⣿⡆⠘⣀⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠿⣿⣷⣽⣿⣴⡀⢰⡆⠀⠀⠀⢠⣾⣿⣿⠀⢻⣿⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠈⠻⣿⣿⣿⠀⢸⡇⢠⡆⢠⡿⠋⠈⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠈⠻⣿⣤⣤⡆⢀⣶⠏⠀⣶⣾⣿⡀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠈⠙⣿⠁⠈⣡⡄⠘⣿⡇⢀⠁⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠸⡀⢀⣿⡇⢸⣿⣇⡈⣡⡭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⢰⣧⠘⣿⡇⠈⢻⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣄⠀⢸⣿⠀⠸⠇⠀⠏⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣿⣿⢈⣿⠀⠀⠀⠀⢸⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⢻⣿⣇⠈⠸⠿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣌⢹⣿⣆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⣼⣿⡀⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠐⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡔⣚⣮⢮⣠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢢⣀⢀⣜⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠦⠁⢸⣇⠠⠄⣤⠀⠀⠀⠀⡘⢫⢥⡈⡴⠆⡤⣸⠊⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢗⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣄⢄⡈⠒⢦⣸⡿⡛⠍⠂⠀⠀⠀⠀⠀⠓⠦⣴⣧⡄⡇⣏⡡
⠀⠀⠀⠀⠐⠀⠀⠠⠆⠘⠀⠈⠑⢤⡀⠀⠀⠀⠂⠀⠀⠀⠌⠓⢺⣵⡀⣍⣔⣢⣄⣀⢄⣀⠀⠀⠀⠙⠒⠋⠁⠟⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣐⣦⠤⠀⡀⣙⣉⠓⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⢀⣀⣀⣲⣂⢈⠟⠙⢙⠳⢕⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⢉⠻⡦⡈⠑⠀⠂⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠜⡇⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠑⠟⠷⠆⠀⠀⠀⠀⠀⣀⠀⠄⠠⠂⠄⣠⢳⠞⢀⡄⠉
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⡀⠀⠀⢉⡔⠊⣠⠃⡀⡑⡖
⠀⠀⠀⠀⢀⠐⠀⢀⠈⠣⡀⠄⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠓⠪⣽⣳⣶⠋⠀⠀⠀⠀⠈⠀⠀⢈⡻⠮⣱⣣⢰⣡⡊⠙⠂⠅
⠀⠀⠀⠀⠌⠀⡀⣀⡑⠤⠄⢲⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠓⢧⣈⣉⣩⣽⣇⠿⡃⠀⠀⠀⠀⠀⣀⠐⠒⣀⣀⣽⣿⣾⡁⠀⠁
⠀⠀⠀⠀⣩⠞⠉⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠺⠍⣀⣹⣆⠿⠋⡧⠚⣿⡏⠑⠀⠀⠀⠀⠈⠉⡵⢨⢟⠞⣹⢏⠃⠈
⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢒⡠⠔⢋⡏⡈⣢⣃⠄⠓⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⢛⠃⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑⠜⠠⠂⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣝⣫⣽⣩⣟⣹⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠁⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⠢⢶⣤⢀⢄⡀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠑⣇⣚⢡⡞⡥⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠬⢢⠃⠙⠙⢇⡇⢸⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⣸⠀⠀⠠⢀⡷⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠉⠉⠁⠓⠀⠁⠸⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠰⠁⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⡱⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠇⢠⠁⠀⠀⠀⣨⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⣄⡁⠀⣀⡤⠄⠗⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠗⠉⠀⠂⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣨⠀⠀⠀⠈⠊⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠁⠐⠠⠰⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠂⠂⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣧⠆⠀⠈⡇⠀⠀⠀⠀⠀⠀⡘⢀⠢⠃⠀⠀⢀⠄⠃⠀⢀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠉⠉⠛⠀⠀⢀⡇⠀⠀⠀⠀⡠⠈⠀⢼⣄⣀⢀⠔⠁⠰⠀⡸⡊⢰
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡞⠁⠀⠀⠀⠀⢃⠀⢀⠊⠀⠙⠊⠀⢀⡶⢂⢫⡑⢄
⠀⠀⠀⠀⠀⠈⠒⠀⠀⡀⡀⠀⢀⣦⡴⠋⠠⢔⣶⣶⠒⣲⠗⠀⠀⠀⠀⣀⣀⠴⢏⣠⣈⣄⠝⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⡁⢤⣤⡤⢎⣉⣀⠿⠉⠓⠲⡦⢀⠀⠀⠀⠀⠀⠻⣭⣹⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠼⠿⠇⠼⢿⣏⣉⣶⡆⠐⡏⠀⠙⠛⠛⠛⠙⠻⠿⠀⠿⠧⠼⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠄⠄⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢈⠃⠀⠰
⠀⠀⠀⠀⠀⢠⠀⣠⣴⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢰⣿⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⢺⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡴⠊⠁
⠀⠀⠀⠀⣰⠏⠀⠆⠀⠀⠀⠀⠀⠀⠀⣠⠾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣤⡿⠏
⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠨⣗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⢡⣴⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠰⣀⣿⠿⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣦⣿⣯⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⢷⣦⣄⡁
⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣧
⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠘⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡤⣶⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣏⢁⣤⣤⣤⣤⣠⡶⠛⠛⠛⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⢀⣾⠏⠀⠙⠦⡿⠱⣯⣤⣄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢰⣿⣋⣁⣀⣀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠈⠛⠛⠛⠛⢷⡶⠿⢶⣆⠹⣦⣀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⠉⠛⠛⠛⠻⣷⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢠⡟⠀⠀⢀⣠⡾⠋⠀⠀⣀⣀⣀⣀⣤⣶⡿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠸⣧⡀⢀⡿⠁⠀⠀⠀⢸⣿⡛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⣼⣧⣀⠀⠀⠀⣴⡿⠛⠛⠛⠷⢶⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣦⣄⣻⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⢀⣿⠉⢻⣷⠀⢸⣿⠀⣠⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⡟⠀⠀⠀⠀⠉⠻⣷⡀⠉⣿⣆⠀⠀⠀⢰⡟⠛⣷⡀⠀⠀⠀⠀⣿⡀
⠀⢸⡿⠀⠀⣿⣄⢸⡿⠀⠙⠛⠻⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠉⠁⠀⠀⠀⠀⠀⣾⣿⣤⣤⣈⢻⣇⡀⠀⢸⡷⠀⠈⠙⣷⠀⠀⠀⢹⡇
⠀⢸⡇⠀⠀⠘⣿⡘⠳⠞⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⢿⣿⣛⣿⣯⣥⡀⠀⠐⣿⠀⣠⣴⣾⠇
⠀⢸⡇⠀⢀⣾⠟⠀⠀⠀⠀⠀⠘⠻⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣽⠃⠀⠀⠹⠷⠟⠀⣿
⠀⠸⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠛⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠀⠀⠀⠀⣀⣀⣀⣸⡏
⠀⠀⢹⣇⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⢠⡾⠋⠉⠉⣽⡇
⠀⠀⠀⢿⡌⠻⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣄⠀⣴⡟⠁⠀⠀⣰⡿
⠀⠀⠀⠈⢿⡀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⢙⣷⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠉⢿⡆⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⠀⣼⣇⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⢸⣿⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡿⠋⣿⡷⠋⠀⠉⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⣿⡀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⡀⠀⣠⣾⠃⠀⠈⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡘⢿⣦⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠋⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣍⠻⣮⡛⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⡶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⣶⠶⢶⡶⠶⠶⠶⢶⡶⠶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⡠⠒⢛⡉⠛⠒⢦⣀⠀⠀⠀⠀⠨⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠔⡡⣫⡟⢀⡤⠛⢦⡀⠈⠉⢳⡀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⣾⠫⠞⣵⣹⡏⢰⣿⣆⡇⠀⢰⠀⢷⣄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢀⡞⠁⠀⠣⣭⠽⠳⢤⣭⠞⠁⠀⢸⠀⢸⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⣰⠏⣠⠴⠒⠚⠋⠉⠉⠛⢲⡄⠀⠀⢸⠀⠈⣇⢸⣤⠖⠒⠒⠲⢤⣀⠀⠀⠈
⡏⠀⢧⣀⠀⠀⠀⢀⣀⣤⠾⠁⠀⠀⢸⠀⠀⢻⠘⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠐
⠻⡄⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⢸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠙⢦⣄⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⣏⠛⢦⣄⠀⠈⠢⠄⣤⠘⣆⣸⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⡟⠀⠀⢸⡟⠶⣤⣀⣠⣴⠏⣼⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠸⡄
⠀⠀⢠⡇⠀⠀⡼⠁⠀⠀⠈⠁⣯⢰⠇⠀⠀⠀⣰⠏⠀⠀⠀⣀⡀⠀⠒⢮⡁⢚⠄⢣
⠀⠀⠀⠳⠶⠚⠁⠀⠀⠀⠀⠀⠘⣾⢦⣤⠴⠞⠁⢀⡠⠖⠋⠉⠉⣧⡤⠤⢷⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠻⡄⡖⠒⠚⠉⠀⠀⢀⣀⣼⠁⠀⠀⠀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⢤⠇⡇⠀⠀⠀⠀⡞⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣠⠃⡇⠀⠀⠀⠀⠙⢤⡀⠀⠈⠳⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⡗⢀⡇⠀⢀⣀⣀⠀⠀⠉⠓⢤⡀⠈⢦⡀⠀⡐⠣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠁⠘⠣⡀⣇⠀⢌⠟⠉⠉⢁⣒⣛⡂⠒⠛⠢⠈⠓⢦⣍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣇⣀⡇⠀⠀⡇⠈⠑⢾⣀⡄⣞⠀⣫⠈⠉⠉⠙⠓⠒⠦⠾⠀⠳⣌⡑⠒⠠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣎⡛⣻⢿⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣽⣿⡟⠛⠛⠋⣹⣿⡜⣿⣝⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣒⣫⣿⣿⣿⣿⣦⣰⣿⣯⣭⠀⠀⠙⠛⠁⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠀⠀⠀⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⡿⠋⠀⠈⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣷⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣷⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠁⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢶⣤⣤⣿⣧⠤⠴⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡀⠀⠀⢠⠖⠋⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠉⠉⠳⡤⠇⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⣠⠴⠒⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠓⢆⠀⠀⠀⠀⣇⡀
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠙⡆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢃⡴⠃
⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠉⢦
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣄⠀⠠⠀⠀⠀⣸⠂
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⡤⠊⠉⠉⠁
⠀⠀⠀⢣⡀⠀⠀⠀⠀⣊⢤⣀⠀⠤⠠⠀⠀⣠⠞⠳⣄⡀⠐⠁⠀⠀⠀⣀⡠⠞⠦⠤⠴⠃⠀⠀⢀⡀
⠀⠀⠀⠀⠉⠓⠒⠚⠋⠁⠀⠈⠙⡒⠒⠚⠋⠁⠀⠀⠀⠉⠉⠙⠉⠉⠉⠁⠀⠀⠀⢰⠀⢠⡀⠀⠈⠃
⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⡆⠀⠀⠃⠀⠀⢶⠀⠀⠀⡇⠀⠀⠀⠀⢦⠀⠀⣦⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⡄⠀⠀⠀⡆⠀⣤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠀⢀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠘⠃⠀⠿⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄⠀⠘⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢀⠀⠰⠆⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠉⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⡖⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣰⡆
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠂⠐⠀⠀⠈⠁⠐⣄⢻⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢘⠆⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⢀⣈⣀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠆⣴⣆⣸
⠀⠀⠀⠀⠀⠀⢀⡴⢦⠀⠀⠀⠀⠀⠦⠀⠛⠤⠄⠀⠚⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⣿⣦⣞⣵⣿⣿
⠀⠀⢰⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣾⣿⡆⠀⠀⠀⠀⣀⣤⠞⠋⠀⢀⣸⣿⡿⣤⡀⢹
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⢀⣠⢀⢀⣠⠄⡄⠤⠀⢴⣴⡿⠿⣿⠿⢁⣠⠴⠋⠙⠏⠀⣀⣴⣶⢿⡟⠁⠀⠹⢿⣾
⠀⠀⢸⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣖⡛⠛⠽⠟⠒⠀⣨⣴⠞⠛⠟⠁⠀⠀⠀⠀⠀⠈⢻
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠋⡡⠛⠉⢀⣤⣶⣶⡿⠟⠛⠁⠀⠀⠀⠀⢠⣖⣦⣮⣿⡀⢸
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣂⣀⣠⠊⠀⢀⡶⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠟⠁⠀⣴⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣾
⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢉⡉⠉⣉⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠀⠀⠀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠦⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠑⠒⠒⠤⠂⠋⠀⠀⡀⠄⢀⠌⢈⠈⠀⠀⠀⠀⠐⠘⡀
⠀⠀⡠⠂⠐⠂⠀⡀⡀⡀⠠⠀⡀⣀⣠⠤⣤⣧⢦⣦⡤⢤⣴⠊⠉⠙⠎⠁⠈⠏⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠐⢀⣐⣀⡀⢀⣈⣈⠰⠐⠃⠁⢀⠔⠊⠀⡐⡄⠀⠈⢐⠢⢌⡁⢐⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡀
⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⡀⠄⡠⠉⠒⠤⡀⠀⠀⠀⠀⠀⠒⠠
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠂⡈⠢⡈⠀⠀⠠⣨⣰⣄⠀⠀⠀⠀⠀⠂⢄
⠀⠀⢀⣀⣀⡀⠀⡀⢀⠊⠀⣀⠀⣠⠀⠤⠄⣄⢆⡐⡀⠄⠐⠒⠀⠀⠒⠂⠼⣄⠓⠁⠀⠀⠀⠐⠀⠠⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠈⠐⠒⠉⠀⠀⠂⠁⠀⠀⠀⣽⡄⠈⠁⠀⠀⠀⠂⠀⠂⠄⠄⠌⠈⠄⠄⠄⠐⠀⠀⠡⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⠀⠀⣀⠀⡀⠀⣠⠀⠀⢀⠀⠀⢀⠀⠀⡀⠐⢂⠒⠒⡒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⠀⡀⢸⡇⠀⠠⠃⣠⠅⠠⠆⠀⢠⠚⠀⢐⠛⠀⠺⠂⠰⠿⡖⠸⢃⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠀⠁⠮⠀⢈⡀⠀⡘⠀⠀⠀⡆⠼⠁⠀⡄⠀⢨⡄⢠⡞⠀⢰⠆⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡠⠀⠀⢰⣇⠈⠁⠀⠀⠉⠀⠀⠀⠸⠀⡄⠈⠀⠀⡤⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⢸⠀⠢⠰⠃⠀⡰⠀⡼⠀⠖⠀⠰⠀⠈⠁⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠮⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠂⠂⠐⠁⠀⠂⠀⠄⠀⠂⠀⠀⠐⠁⠂⠐⠐⠐⠠⠂⠀⠔⠀⠠⠨⠀⠄⠐⠁⠈⠐⠐⠑⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⡇⠰⡇⣹⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⣇⢸⠀⠀⠀⠀⡇⠀⠷⢣⣏⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠙⢦⡑⠿⢸⠀⠀⠀⠀⣇⡴⠲⢤⠞⠲⣄⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡤⠾⡄⣀⣀⡔⠻⡇⠀⠸⡄⠀⠘⢦⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⢀⡔⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⠀⠀⡴⠛⢾⠁⠀⣿⠁⢸⡀⠀⢳⠀⠀⠹⡄⠀⠈⠳⢶⡛⠋⠉⠙⠻⢄⠀⠀⠾⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⠷⣸⠃⠀⡏⠀⠀⡇⠀⢸⢧⠀⠀⢧⠀⠀⠈⢦⡀⠀⠀⠈⠳⡀⠀⠀⠀⠳⡄⠘⢯⣉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣉⡽⠋⣹⠀⠀⡇⠀⠀⢻⠀⠘⡎⢧⡀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⠹⡄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⣿⡀⠀⢻⡀⠀⠈⢇⠀⠘⢆⠙⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⠀⢸⡍⠲⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⢏⢧⠀⠀⠱⣄⠀⠈⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⢧⢀⡘⢿⡛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡳⢟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡇⠀⠀⢸⣸⡏⢳⡉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠤⠚⢧⠜⠁⢹⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⢀⡉⠀⠀⠀⠀⣧⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡼⠀⠀⠀⠉⠙⠒⢲⠒⠒⠋⠁⠀⠀⠀⠘⡟⡟⠉⠉⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧

⠀⠀⢀⡀
⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣀⣠⠤
⠀⠀⠀⠀⢾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡟⠉
⠀⠀⠀⠀⠸⠻⣏⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣿⣿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠈⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀
⠀⠀⠀⠀⠰⠀⠈⢻⣇⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⣸⠀⠀⢸⠃⠀⢀⡿⠀⣀⣠⡤⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣶⡖⠉⣤⢤⡤⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣧⠀⠀⢿⠀⠠⠘⠿⢧⣍⣁
⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⣄⡀⠀⠠⡄⠀⠀⠀⢀⠀⠀⠀⣿⣷⣴⣷⣬⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢻⠀⡠⠚⠧⣤⡀⠀⠂⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠀⠀⠀⠀⠀⠀⠘⠢⠐⠊⠀⠟⠁⠀⠙⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⠸⣧⣀⣀⣀⣀⣉⣉⠓⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠉⠳⢤⡀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⣰⢙⡆⠀⡴⠀⡄⠐⡾⠒⢰⠀⣠⠀⡦⡠⡆⡠⣆⠀⡄⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠉⠹⡄⠧⠞⠧⠐⠧⠄⠺⠔⠻⠀⠟⠁⠻⠁⠸⠄⠟⠀⠳⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠆⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠰⠀⠀⠀⠀⠀⣼⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀⠀⠀⠀⢠⠇⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠁⠘⣇⠀⠀⠠⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣴⠃⠀⠀⠀⠀⠀⠈⠓⡄⠀⣸⠀⠀⣠⠔⠉⠀⠀⠠⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢠⡟⠀⠀⠤⠀⠀⠀⠋⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠉⠁⠀⠀⠀⠀⠀⠠⣄⡘⣦⣯⡴⠋⠁⠀⠀⢀⠀⠀⠈⠑⠢⣄⡀⠀⠀⢻⡄⠀⠀⢰⡟⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠛⣿⣏⡉⠉⠉⠉⠉⠁⠀⢀⡐⠀⠀⠙⢷⣄⠘⣿⠀⣠⡟⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⢸⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢿⣿⣦⡟⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⠿⠿⠿⢯⡤⣤⣀⣀⣀⠚
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⠒⠤⣀
⠀⠀⠀⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠠⢀⡄⣠⢔⣒⠰⢱⣦⣄⢄⠀⠀⠀⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡄⣴⣾⣿⣿⣦⣼⣿⣷⣿⣿⣿⣦⡀⠀⠀⠈⡈⠉⠂⠄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣦⣾⠇⠀⠂⠀⠈⠐⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⢨
⠀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠙⢿⣿⣏⡀⡀⠀⠁⠀⠀⣇⠀⠀⠀⡰⠀⠀⣀⠀⣠⢀⢀⡀⠀⠀⠀⠀⢀
⠀⠈⠢⣠⠸⣿⣿⠋⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠿⠿⣿⠀⠀⢄⠀⠸⡄⡀⢠⠃⠀⣠⡔⢊⣤⠲⣪⣍⢊⣿⣿⣿⣿⡑
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⣤⣾⣿⡂⢀⣀⣀⠀⠘⣆⢇⡤⠞⠁⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⠀⠀⠀⠹⠿⠛⠁⠀⠀⠀⡠⢁⠿⠇⠀⣀⠔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢠⣄⣧⡼⢸⡤⠿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠈⠢⢄⠀⢀⠔⠁⠀⠀⠀⠀⠀⠘⠂⢙⠛⢦⣒⣒⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠄⢹⠇⠀⠂⠀⠠⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⠀⠀⠉⠛⠛⠁
⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠂⠀⢰⠀⠀⠀⠈⢳⡄⠀⠀⠀⢀⣠⣿⡿⣿⣿⡿⠻⠿⠿⠷
⠀⠀⠀⠀⠈⠁⠀⠁⠀⠊⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢹⡿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠀⠐⠒⠒⠒⠂⠐⠒⠐⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠋⡡⠔⠋⠁⠈⣹⠀⠀⠀⠀⠒⠒⠀⢠⡞⠁⠈⠁⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢟⠆⢀⠔⠋⠑⠀⣀⠤⠊⠀⠀⠀⠀⣀⡀⠀⠀⠀⠧⢄⠢⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⡤⠚⠰⡧⠒⠒⢫⠄⢢⠀⠀⠀⢠⠖⠉⠈⠉⠹⣦⠞⠉⠚⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢠⠤⠜⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠰⣃⠀⣞⠧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠅⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⣘⡛⣋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠱⢼⠇⢀⡀⢀⣤⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢰⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢀⠴⠊⠉⠁⠀⠑⢆⠀⢠⢮⠒⠚⠀⠀⠀⠘⠢⡀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⣜⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠍⠥⠴⠒⠠⡄⠀⠀⠨⠗⠊⠈⠣⠤⠊⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⡀
⠀⠀⢠⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠘⠒⠄⡀⡴⠶⠤⢀⣀⡀⢇⠀⠀⠀⠀⢰⠦⡄⠀⣄⠤⣄⠀⠀⠀⠰⠘⡇
⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡆⢇⠀⠀⠀⠀⠳⠴⠊⢓⠀⠈⠙⣄⠀⡼⠀⡇
⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢳⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠆⠰⡄
⠀⠀⢠⠀⠷⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡑⢆⠀⢀⣠⠞⠁⠀⠀⠀⠀⠑⢂⡇⡆
⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⢄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡛⠥⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠇⠀⠈⢀⠀⠀⠀⠀⠀⠰⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠃⠊⠀⠀⠀⠀⠀⢠⠃⡘
⠀⠀⠀⠸⡄⠀⠀⡧⠀⠀⠀⠀⠀⠐⠦⡙⠒⠂⠀⠒⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠹⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠎
⠀⠀⠀⠀⠀⠱⡌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠘⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠤⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⡘⠁⡌⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⣎⡤⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠋⠉⠀⠀⠀⣀⠠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⡿⠛⣺⣷⣆⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⣾⣿⣿⣿⠏⠀⠼⣽⣿⣿⣧⡀⠁⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣃⠀⢀⣘⣻⣿⣿⣿⣧⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⣿⣿⠃⣀⣀⣀⣀⣉⣻⣿⣿⣿⡄⠀⠀⠈⠹⡄
⠀⠀⠀⠀⢀⣤⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⢸⠉⠃⠉⠙⠈⠁⠻⠻⠿⠍⠹⢽⠿⠻⣿⠙⠿⣿⣿⣹⣿⡿⠿⣿⡿⡿⠿⣿⠁
⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⠀⠸⠠⠀⠀⢸⠀⠀⣿⠀⠀⠀⠈⢸⠁⠀⠀⠀⠁⢰⠀⢻⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓
⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⢀⡤⠄⠀⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⠟⠿⣿⣆⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣾⣿⣿⣿⡟⠱⢖⣞⣿⣿⣷⡀⠁⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠏⠀⠠⠤⢿⣿⣿⣿⣿⡄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠏⠈⠀⠘⠚⠛⢻⡿⣿⣿⣇⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣡⡀
⠀⠀⠀⠀⠀⠛⠛⠛⠿⠏⠿⢻⣿⣿⣿⠻⢻⢿⣿⣿⣿⡿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠀⢹⠁⠀⣿⠀⠈⠉⠙⠛⡿⠛⠉⠉⠋⠋⢃⠈⢻⢡⡄
⠀⠀⠀⠀⠀⠀⠄⠀⢸⠀⠀⠀⠀⠀⢘⠀⠀⠸⠀⠀⢻⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠂⠀⢀⡗⠀⠀⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠂⠀⠀⠡⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠘⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠄⠀⠀⠀⠤⠀⢠⠀⠀⠀⠈⢄⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠰⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⣠⠤⠊⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠤⠰⠄⠂⠀⡄⠀⠀⣠⣀⣀⡀⠉⠙⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠐⠒⠂⢼⢛⠉⠉⠈⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠃⠀⠛⠁⢼⠀⠀⠀⠀⠀⠀⠐⠄⠐
⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⡘⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⡠⠳⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⡈⠢⠁⠀⠤⠀⠀⠤⠄⡄⠀⠐⠀⠀⠎⠰⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠠⠘⠛⠿⠤⢰⡖⢲⠇⠀⠚⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠒⠀⠀⠠⡄⠀⠀⡀⡀⠀⠐⢀⠀⠁⠀⠀⢀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠁⠀⠡⢒⡄⣁⣛⠄⠁⠀⠃⠂⠈⢄
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠁⠀⠀⡀⠀⠀⠀⠩⠁⠀⡫⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠈⠉⠉⠃⠈⣋⠁⠈⠉⠉⠘⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠀⠀⠉⠁⡀⠤⠤⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠐⢐⡒⠂⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡀⠄⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⠄

⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⡀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠄
⠀⠀⠀⠀⢀⠀⣴⠦⠀⢀⠂⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠳
⠀⠀⠀⠉⠊⠐⢋⠃⠂⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡐⠀⠈⡀⠀⠀⠤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠠⠐⠀⠀⠂⢰⠀⠀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠀⠀⣡⠘
⡳⠉⠔⠆⠀⠢⠐⠁⠀⠁⠉⠙⠀⠀⠄⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⠁⠀⠊⠁⠀⠠⡀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠠⠒⠉⠂⠀⠐⢤⠀⠀⠄⠀⠀⠈
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠘⠀⠈⠀⠂⠠⠀⢀⣠⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢁⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂⠀⠈⣀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠰
⠄⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠄⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡀⢈⠁
⠐⠀⠀⠈⠁⠀⠀⠀⠈⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡀⠄⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⢁⠀⠠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢸⠂⠀⠒⠐⠄
⠀⠀⠰⠀⠀⠀⠀⠀⢠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠⣠
⠀⠃⣄⠘⠂⡀⠀⠄⢨⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠉⠀⠀⣰
⠀⠀⠈⠀⠀⠑⠐⠄⢌⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⡀⢠⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⣆⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⢀⠇⠘⢀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠱⠄⠀⠁⠀⠀⠀⡀
⠀⠀⢴⣒⢆⢱⢝⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡈⠀⠀⠈⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠙⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠉⠁⠀⠀⠀⠀⠼⣏⣿⠿⠖⣲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠀⠀⠀⢠⣤⡘⡛⢁⠀⠰⠜⠛⠁⢶⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣤⣶⣤⣀⣤⣤⡐⠿⠿⠃⣡⠠⠾⢷⣄⠀⠀⠘⣿⣿⣿⣿⣿⡇⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⠖⠀⣀⣿⣇⠀⠀⣻⣿⣿⣿⣿⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣵⣾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢁⣤⣈⠛⠁⠀⠀⢿⣿⠋⠉⠁⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡼⠐⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣨⣿⣷⣶⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠈⢙⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣿⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⣁⡉⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠋⠉⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣀⡀⠀⠀⠸⣿⠁⠀⢀⣀⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛
⠀⠀⠀⠀⠀⠀⢀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠴⣦⢴⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠂⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠋⠄⡿⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⠀⠂⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢋⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠧⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⡈⠉⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠘⠀⢀⠀⠀⡀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⣐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠂
⠀⠠⠀⠀⠀⠴⠂⠈⠉⠻⢃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⢀⠀⠀⠀⠀⢈⠀⠘⠀⠀⠀⡁⠀⠀⠲⣶
⠀⠀⠀⠀⠀⠐⠊⠀⠰⠀⠘⠀⠀⠀⠀⠀⠀⡀⠉⠑⠒⢄⡀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡄⡀⠸
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠀⠀⠀⠀⠐⠈⢉⡀⢌⠠⠱⠃⠤⠂⡀
⠀⠁⠂⠀⢀⠀⠀⠀⠀⠀⠀⢠⠠⢀⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠶⠬⢾⣷⣿⣴⠤⠴⠄
⠀⠀⠀⠦⢬⡄⠀⠀⠀⠀⠐⣠⡴⡋⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⣍⠤⠖⢂⠖⠟⢟⢣⡀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠞⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢂⠀⠀⠠⠂⠷⠐
⠒⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⢀⠤⠠⠀⣀⡀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠄⠀⠀⣀⠄
⠀⠀⠀⠀⠈⠀⠈⡈⠰⡏⠀⠠⠂⠀⠀⣀⡡⠎⠀⠀⠀⠀⠀⠼⠛⠆
⠄⡄⠀⠄⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠛⠶⠤⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠁⠀⡀⠀⠀⠀⠀⠁⢒⠂⠐⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠈⠀⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣠⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠐⠀⠒⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⢀⠀⠐⠀⠀⠀⠒⢤⡀⠀⠶⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⡙⠳⣤⣄⡀⠢⠄
⣒⣖⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣈⣛⣂⣀⣁⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠁⢀⡤⠒⠉⠉⠻⡒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠘⡄⠀⠑⢦⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡄⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣨⠕⠢⣄⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡜⠁⠀⠀⠈⠛⠀⠀⡤⠤⢤⣀⣀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⢾⠁⠀⢀⠇⠀⠉⠓⠢⣼⠤⠔⠒⠒⠒⠺⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠠⢎⣁⣸⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⡰⠁
⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠀⣲⠄⢒⡼⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢸⠁⠙⠫⠧⠴⢏⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠈⢆⡀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⣉⠲⡖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⢴⠕⠁⢠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢀⡠⠴⠒⠳⣿⣷⠒⠲⣶⣶⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣀⡠⠟⠀⠀⠀⡿⠿⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⡇⠀⠀⠀⠀⠀⢆⠀⠀⠧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⡠⠔⠋

⠀⠀⡀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢿⣆⠀⢸⣆⠘⠋⣀⠀⠀⠀⣷⡆⢀⠀⢠⣄⠀⠰⠀⠀⠀⢀⠘⠇⠀⠀⠀⢠⣄⠁⣀⠀⠀⠠⣤⣁⣼⠂⠀⠀⢀⠛⢀⠂
⠀⠀⠈⠻⠆⠈⡛⠀⠾⠋⠀⠀⠀⠈⠁⡿⠁⠀⠁⠲⠀⠀⠀⢀⡘⢧⡶⠂⠀⠀⠀⣉⠾⠋⠀⠀⠀⣬⡙⠁⣀⠀⠀⠈⣈⠺⠈
⠀⠀⢶⣦⡀⣰⠆⢀⣴⡶⠀⠀⠀⠀⠃⠀⠀⠀⠰⡀⢀⡀⠀⠈⣿⣆⣴⡇⠀⠀⠈⢻⣧⡶⠀⠀⠀⠉⠛⣿⡟⠀⠀⠀⠉⠲
⠀⠀⠀⠉⠀⡿⠀⠈⠁⠀⠀⠀⠀⠶⠶⠂⠀⠀⠀⡹⠈⠁⠀⠀⠈⠉⠋⠀⠀⠀⠸⣇⣡⡄⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢈⡙⡔⠗
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⡀⠀⠀⠉⠀⠀⠀⠰⣶⡄⢠⡄⠀⠰⢾⣶⢄⢿⠄⠀⠀⠸⣶⣾⣯⡔⠀⠀⢀⡀⠀⡄⣧⡀⠀⢰⣿⠀⠀⡀⠀⠀⢠⡄⠀⠀⡀
⠀⠀⢈⡄⠈⠀⠃⣀⠀⠀⢠⣌⠃⢸⠇⢀⡀⠀⠺⠃⠙⢇⣴⡆⠀⠀⠁⠀⠀⠀⠰⣌⢰⣧⡿⠆⠀⢠⣜⣡⠀⠀⠙⠳⠀⠘⠃⠀⢚⡁
⠀⠀⢀⠀⡄⠀⠀⣨⠀⢰⣬⡛⠀⡆⢰⣿⠃⠀⠀⠀⠶⢌⣾⠀⠀⠀⣠⠀⠀⠀⢳⣶⡧⠍⠀⠀⠀⢦⡟⢋⠀⠀⢠⣤⣦⣶⣤⠛⠉⠁
⠀⠀⠉⠀⠀⠐⠀⠀⠀⠘⠿⣷⠀⠄⠈⣁⣀⠀⠀⠀⠀⠀⠁⠀⠐⢶⣿⣶⠆⠀⢸⠃⠀⠀⠀⠀⠠⣤⣷⣿⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠐⠛⠛⠛⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠿⠛⠛⠻⠷⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⢤⣼⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠉⠉⠙⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿
⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣿
⠀⠀⠀⠀⢻⡏⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⣽⡟
⠀⠀⠀⠀⠈⢿⣄⢅⡂⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⡠⢐⠠⢐⣼⠟
⠀⠀⠀⠀⠀⠈⠻⣷⣬⣄⡂⠀⠀⠄⣀⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⢤⣄⣅⣂⣌⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠛⠉⠑⢦⣥⣅⣐⡐⡀⠀⢂⠄⢅⣐⣐⡽⢿⣦⣄⠄⡀⡀⡀⠀⠀⠄⣄⡶⠟⠁⠀⠈⠉⠉⠉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠈⠙⠛⠷⠾⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢤
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣰⡟⠁⢰⡄⠀⠀⠀⠀⠀⠀⣠⡾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⣾⠋⠀⢱⡀⠀⠀⠀⢿⡄⠀⣸⠇⠀⠀⠀⠀⠀⢰⡟⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠋⠀⠀⢀
⠀⠀⠀⢿⣄⣀⡼⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⢀⠀⠀⠘⢧⣀⣠⠟⠀⠀⢀⣴⠞⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡞⠋
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠉⠁⠀⢀⣼⠟⠁⠀⠀⠀⠙⠷⠴⠟⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡾⠋⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣄⠀⠀⠀⠀⣿⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠻⣄⣠⡾⠁⠀⠀⠀⢀⡀⠀⠀⠀⣿⠀⠀⣸⠀⠀⠀⠀⠙⢦⡴⠟
⠀⠀⠀⠀⠀⢠⡾⠋⡀⠀⠀⠀⠀⠀⠹⢦⡴⠟⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠙⠶⠾⠋
⠀⠀⠀⠀⠀⣿⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⠏⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠻⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠐⣄⠀⠀⠀⠀⠀⠀⢼⡇⠀⢈⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⠷⠤⠾⠁⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣤⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⡰⠔⡒⣮⡍⠙⣯⡼⣮⣶⡦⠆⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠛⠋⠁⠈⠁⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡡⠖⠲⠶⢶⣄⠀⠀⣀⡀⣠⠤⡬⢤
⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠅⠀⠁⠀⠈⠀⠍⠍⣬⠉⡑⢶⠔⠊⠐⠑⣄
⠀⠀⠀⠀⠀⣠⣾⣸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠀⠐⠀⠀⠀⠀⠀⡀⠘⠂⠙⠒⣈⣁⡋⣟⠉⢁⣄
⠀⠀⠀⢀⠐⢿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠏⠀⣀⠀⠀⠐⠀⠓⠄⠀⠉⢂⠀⠋⠁⠉⠃⠀⠀⠀⠈
⠀⠀⠀⣤⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⡲⣄⠈⢀⠀⠂⠀⠀⠉⠀⠀⠠⠀⡄⡁⠀⠀⠀⠂⠀⠰⢶⡝
⠀⠀⠖⠠⠆⣛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢠⣞⠜⠋⠠⠀⠐⠐⢋⠈⠀⢘⠃⠠⠀⠀⠀⠀⡂⠀⡁⠁⡀⠠⠀⠰⡾⣳⢒
⠀⢠⣔⠛⠀⠀⡰⣍⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡷⡞⠀⠀⣈⠓⣒⣠⠀⠄⢁⠀⢁⣀⡀⠀⠀⠀⠀⠁⠐⠂⠀⡀⢀⠀⠀⠈⡋⠩
⢠⠞⢉⣉⣁⣨⠞⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡣⠤⢄⡊⡳⠓⠁⡄⢩⣁⢀⡱⠙⣁⠇⢼⠠⠞⠠⢀⠀⠀⠃⠀⠐⡀⠁
⢠⢤⡭⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⡵⠋⠀⣈⢳⡼⠲⣄⡀⠠⢤⠠⠀⠀⣄⢎⡁⠰⠇⠈⡑⠁⠴⠀⠒⠀⢄
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡶⡿⠞⠻⠛⡛⠻⣦⣤⣍⣳⢀⣄⠒⢁⠸⣟⠧⢼⡆⠰⠃⠀⠀⢠⡄⠘⡫⡃⠈
⠀⣳⢀⡀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠌⠀⠠⠀⢀⠃⠸⣝⣆⠀⢰⡆⠘⢀⠀⠙⢷⡀⣀⡦⢠⠼⢻⠇⣦⢆
⠻⠯⣯⣼⠤⢶⡆⠂⣤⡀⠀⠀⠀⠀⠀⣼⢹⡄⣀⣠⣃⣄⡄⠁⠀⠰⠀⠀⢆⡐⠊⣯⡳⡼⢷⣚⠉⠀⠀⠀⠉⢢⣿⠃⠀⠻⣸⡇
⠀⢠⣯⡚⢺⠃⡏⡛⣻⢦⣤⡀⠀⠀⠀⠻⡈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣫⠼⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⠻⣿⡀
⠀⠀⠙⣟⠢⠠⡅⡏⣛⣚⠴⢽⡄⠀⠀⠀⠙⠲⣴⡤⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⣠
⠀⠀⢀⡷⠊⣀⢌⢣⠱⣻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣍⠁⣻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠠⠂
⠀⠀⠘⢧⢁⣹⢠⢈⡧⢜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠠⢄⡠⠀⠖⣶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠘⣇⠙⠿⠾⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠂⠼⠔⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠘⡀⢀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⠍⠀⢠⡽⢁⡤⠄
⠀⠀⠀⠀⠀⠀⠻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣶⠟⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠤⣤⣴⣶⣶⡤⣤⣀⣀⣁⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠰⡀⢤⣶⣾⣿⣿⣿⣿⣿⣶⣴⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠀⠂⠀⠀⠀⢀⡽⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⣿⣿⣿⣿⠃⠀⠀⠀⠠⣶⠋⠀⠀⠉⠉⠉⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⢕⢄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠛⠁⠀⡄⠀⠀⠀⠀⠀⡟⢻⠶⣄⡀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣃⣠⣾⣦⠀⡀⣻⡇⠀⠀⠀⢸⡇⣾⠀⠈⠻⠃
⠀⠀⠀⠀⣠⠀⠀⠀⣴⣿⠀⠀⠀⠀⣰⣀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⣿⡇⠀⠉⠛⠛⠋⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⢀⣠
⠀⠀⠀⣼⣿⡆⠀⢀⣿⣿⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠐⠻⢧
⠀⠀⢰⣿⣿⣷⠀⣸⣿⣿⡇⣠⡄⣿⣿⣿⠀⢠⣾⡅⠀⠀⠀⠀⣿⠋⠁⠉⠀⢀⠀⠤⠤⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⢀⣿⢽⣧⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣇⣼⣿⡃⠀⠀⠀⠀⠉
⠀⠀⡗⡐⠻⣿⠟⠉⠉⢉⣿⣿⣟⠁⠉⠉⣿⡿⣿⡇⢀⣤⣤⠠⠀⠰⡄⢶⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⢠⣀⡀
⠀⠈⠀⠀⠀⠀⠀⠄⠀⢼⡡⣿⣿⠀⠀⠀⠈⠀⠁⠀⠙⠚⢻⣿⣿⣿⣿⣿⣿⡟⠋⠋⠁⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠿⠻⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣽⡿⠁⠀⠀⠀⠠⠤
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣮⣵⣦⣤⣮⣴⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢡⠀⠀⠀⣀⢀⡀⠤⠤⡀⠀⠀⢀⠐⠈⠉⠆⠀⠀⠀⠀⢀⠋⡍⠁⠀⠂⢄⡀⠀⠀⠤⡤⠂⠃⠀⠀⠄⠂⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠂⠉⠀⠀⢨⡇⠀⠐⠋⠀⠀⡌⠀⢠⠀⠀⢀⠀⠀⠀⢸⠀⠈⠢⡀⠀⠀⠙⡄⠀⠀⠀⡘⠀⠀⠀⡄⢀⠔⠁⠄
⠀⠀⠀⠀⠀⣤⠀⠀⠉⠀⠀⡃⠀⠀⠈⠀⠀⠀⠀⠀⢠⠊⠀⠀⢘⠀⡀⠈⠑⠀⠀⠀⠆⠀⠀⠐⢄⠀⠀⢰⠀⠀⠠⠜⠀⠀⠀⠘⠇⠄⠊
⠀⠀⠀⡰⠈⠿⠀⠀⠀⠐⠀⠅⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⢮⡔⠁⠀⠀⠉⠄⠀⠈⠢⠀⠀⠀⠑⢀⡘⠀⠀⠀⠀⠀⢀⠔⡀
⠀⠀⠰⠀⡘⠀⠐⣀⣀⠀⠀⠀⠀⠀⠐⠭⠁⠀⠀⡀⠀⠀⢄⠀⢸⠀⠀⡠⠂⠀⠤⠀⠀⠀⠈⠁⠀⠂⠈⠡⠀⠀⠀⠀⠐⠀⢀⠐
⠀⠀⠠⠊⠀⠀⡌⠀⠀⠀⠁⠆⡀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠂⣸⡀⠊⠀⠀⡐⠀⠀⠰⣅⠈⠰⡄⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⣡⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠈⠐⠂⠠⡭⠤⠀⠒⠈⠀⠀⠀⠇⠀⠉⠂⡼⠀⠀⠀⠀⠀⠀⣇⣀⡈⠠⠭⠛⠐⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⡢⠄⠁⠀⡠⠶⢄⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠃⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠏⠁⠁⠀⠀⡌⠁⢰⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢠⠈⢁⠛⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⡄⠀⠀⠀⣀⠀⠘⠤⡇⠀⠀⡄⠂⠀⠀⠀⡀⠂⡰⠀⠀⠀⠀⠀⠈⠖⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢆⠀⠀⡆⠀⢀⠃⠀⠀⠘⠄⠒⠀⠠⠈⣄⠀⠈⠃⠀⠀⠈⠛⠈⠀⠀⠀⠔⠓⠀⠀⠀⠀⠀⡇⠑
⠀⠀⠀⠀⡠⠐⠀⡀⠀⠀⢀⡠⠛⠄⠀⠀⠑⢄⣁⡀⠂⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⡐⠤⣘⡀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠱
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠃⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠉⠂⣄⠀⠀⠀⠀⠀⢈⠉⠁⠀⠀⠡⠀⠀⠰
⠀⠀⢸⡀⠤⠐⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠁⠢⢄⡀⠀⠀⠑⠀⠄⣀⡀⢉⡄⠂
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⠰⢠⠀⠀⠇⠀⠀⠸⠀⠀⣄⠀⠲⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⡠⠂⠀⠀⠀⠀⡄⠀⠈⠛⠀⠀⠀⠀⠋⠁⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣉⡉⠱⡦⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠠⠀⠀⠀⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⢀⠀⠒⠀⠀⢠⠂⢂⡠⠂⠉⠂
⠀⠀⠀⠀⠰⡁⠀⢌⡐⠢⢄⠀⠀⠀⠀⣄⠒⠈⠉⠀⠀⠀⣠⡄⠀⠀⠈⠉⠁⠒⢠⠀⠀⠀⠀⢠⠉⢂⡀⠀⠀⠀⢠⠊⢰⠄⠀⠀⠀⠀⣀⠂
⠀⠀⠀⢀⣀⡈⠢⠀⠀⠂⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⢐⠉⠀⠀⠀⣠⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠃⡀⠀⠀⡀⠀⠀⠀⠵⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠷⠀⠀⠠⠈⠃⠀⠀⠀⠁⠄⠀⡀⠀⠀⡠⠊⠀⠀⣤⡐⠁
⠀⠀⠀⢀⠠⠀⠀⢀⠀⢛⠀⠀⠁⡀⢁⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠠⠊⢠⠀⢰⠀⠀⠈⠂⡀⠆⠀⠜⠀⠀⢃⡠⠊⠀⠀⠀⠀⡠⠄
⠀⠀⠐⠁⠀⡠⠒⠁⠀⢸⠀⢤⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⢀⡠⠊⠁⠐⠂⠀⠈⠁
⠀⠀⠇⠀⠀⠀⡠⠂⢂⠀⠀⠀⠀⡀⡠⠀⠀⠀⣤⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⡷⠁⢠⠀⠀⠀⠀⠀⠀⠰⠔⠈⠀⠀⠀⠀⠀⠀⢀⣀⡔⠢
⠀⠀⠈⠁⠀⠉⠀⠀⠀⠉⠉⠀⠀⠈⠀⠀⠀⠀⠈⠢⠈⠐⡄⠀⠀⠀⡀⠀⢦⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠀⠁⠀⡆
⠀⠀⠀⠀⢀⡀⠤⠠⣀⠤⠤⢀⡀⠀⠀⠀⠀⠀⡄⠀⠡⣠⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⢰⠀⠢⡌⠈⠆⠀⠱⠀⠀⠀⠈⠢⢄⡀⠀⠇
⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⢡⠀⠈⠻⡄⠀⢠⠀⠀⠰⡶⠃⠀⠀⠀⠠⠄⠲⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠹
⠀⠀⠣⡀⠐⢀⠀⠇⠀⠘⠀⡐⠀⢀⠜⠀⠀⠀⠀⠂⠀⠐⠰⣦⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠁⠀⠆⠀⠐⢢⡠⡀⠀⠀⠀⢁
⠀⠀⠀⠈⠢⠀⠢⣀⠀⠀⠌⢀⠔⠁⠀⠀⠶⡄⢠⡀⠈⠒⢀⠀⢢⡀⠀⠀⠀⡠⠀⠀⠀⣄⠀⠀⠁⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠋⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠽⣶⠧⠐⠁⠀⠀⠀⠀⣀⠐⢄⠁⡀⠀⠀⠈⠈⠑⡀⠀⠀⠃⠀⡠⠊⡸⠀⠀⢀⢀⠀⠈⢃⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠣⠈⠶⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠃⡀⠖⠁⠀⠘⢦⡀⠀⠂⣤⣤⠀⠀⠀⠆⠁
⠀⠀⠀⢠⠲⠀⠀⠀⠀⠀⠀⠘⠁⠀⢉⠐⠢⢄⠀⠀⢀⠐⠈⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠣⣀⠁⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣰⡆⠔⡠⠞⠀⠀⡌⠡⢀⢀⡴⠚⠀⠀⠀⠠⠐⠃⠐⠺⠀⠀⠀⢀⡀⢴⠀⠀⠀⠁⠀⣀⠀⠌⣰⡄⠀⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⡙⠉⠁⠀⠀⠀⠘⣧⠀⠙⠁⠀⣠⠀⠀⠀⠓⢄⠀⠀⠀⢈⠀⢠⠉⢠⠁⡆⠀⠀⠀⠀⠈⢁⠈⠛⠀⠈
⠀⠀⢀⠂⠀⠉⠀⠐⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⣄⠄⢀⠇⠀⠀⠀⠀⠀⠁⢂⠤⠁⠀⠘⣠⣄⠔⠁⠀⠀⡟⠀⠐⣼⠦⠐⠒⡰⠆
⠀⠀⠰⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⢠⠪⠀⠘⠢⠀⠀⠄⡁⢀⠌⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠃⠀⡀⠋⠉⠉
⠀⠀⠀⠱⢀⠀⢀⠂⠀⢠⠆⠀⠀⠀⠘⢆⠘⠃⣄⠓⡀⠈⡷⠁⠀⠠⠐⠃⡰⠆⠀⠀⣀⠄⠻⢄⠀⠀⢰⢂⠐⠀⠠⠀⠾⠇⣀⠀⠀⠶
⠀⠀⠀⠀⠀⠁⠪⠀⠒⠁⠈⠀⡀⠀⠄⠀⠉⠓⠈⠰⠆⠀⠇⠀⠠⢇⡰⠟⠰⠆⠀⢰⡀⠀⠀⠀⡆⠀⢰⠈⡀⠰⣤⠎⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠐⡣⠀⠀⠀⠀⠀⠀⠑⡇⢀⣦⠋⠴⠚⠁⠀⠀⠀⡄⠀⢀⡘⠁⠀⠀⣄⣀⠘⠉⠒⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠆⢀⣀⠙⠀⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠀⠀⠀⠀⠘⠛⠒⠀⣀⡀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢉⡁⠤⠤⠶⠒⠦⠤⢌⠁⠀⢀⠀⠀⠀⣀⠠⠤⠐⠒⢒⣒⢂⣠⣤⣀⡀
⠀⠀⠀⠀⠀⣀⠤⠐⠒⠬⡀⠔⠁⠠⠒⢒⣋⠉⣁⡒⠂⠀⠀⠄⠀⠀⢀⣌⠠⠐⠈⠉⠀⠀⠀⠀⠀⣉⡹⠒⠚⡀
⠀⠀⠀⣀⠰⠁⠀⠀⠀⠀⠀⠁⠈⠑⠌⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠸⡅⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠈⡄⢕⠢⡀
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⢀⠔⠂⠒⢄⠈⢆⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡇⠈⢆⠈⢆
⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠁⠈⢄⠈⠀⡇⠘⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⡄⠀⢣
⠀⠀⠀⠀⠙⠢⠤⠖⠀⠢⠤⠤⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠱⢄⠀⠠⡞⠀⠀⠀⠒⠒⠂⠤⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⢢⠀⠀⢍⡀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⡇⠁⠰⠈⠢⣀⠀⠀⠀⠀⢀⠄⠉⠢⡀⠀⠀⡄⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠼⢀⢆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠝⠁⠀⠀⠀⡅⠀⠀⠀⠀⠀⠑⡆⠀⢀⠎⠀⠀⠀⠘⢄⢰⣀⠀⢀⣀⠀⠀⡠⠔
⠀⠀⠀⠀⠀⠨⣀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢢⠆⠺⠀⠀⡇⠀⠀⠀⢀⡠⠤⠁⡠⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠃⠀⠀⠈⠀⠀⠀⠀⠀⠘⠉⠁⠈⠁⠀⠀⡐⠁⠀⠀⠀⢀⠄⠐⠐⡢⠄⠀⠒⠒⡄
⠀⠀⠀⠀⠀⡠⠔⠒⠒⠤⡈⢉⠕⠘⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄⢠⢬⠀⠀⠀⠀⠀⠸⠡⠴⠀⡏⠤⠄⠨⠁⠁
⠀⠀⠀⠀⠰⠁⡠⠒⠂⡄⠘⡜⠀⠒⠂⠁⠀⠘⢀⣄⡠⠀⠠⢄⠀⠀⠣⣓⠱⠁⠀⠀⠀⠀⢀⡸⠀⠀⠀⡇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠰⡀⠦⡠⠀⡸⢀⠃⠀⠀⢀⠆⠀⠜⡃⡎⢠⠂⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⢀⠔⠊
⠀⠀⠀⠀⠒⠵⣤⠠⠴⠕⠋⠀⣀⠤⠊⠀⠀⢂⡀⠘⠄⣓⣤⡖⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠺⣂⣤⣄⠀⠀⠬⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠋⠉⠉⠉⠉⠉⠙⠛⠒⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣋⢁⠠⠤⠐⠒⠀⠀⠀⠀⠈⠉⠉⠀⢀⡐⡢⣼⠟⠦⣤⡀
⠀⠀⠀⠀⠀⠀⣴⠋⡠⣎⡸⠀⠀⠀⠀⢀⠠⠄⠒⠈⠁⠈⠁⠀⠀⢀⣴⡟⢢⠖⣄⠙⠶⣄
⠀⠀⠀⠀⢠⡞⣡⠊⠀⠀⠀⢀⠤⠐⠈⠀⠀⠀⠀⣄⠀⠀⠀⢀⣴⢿⡇⠙⢄⠉⠈⠳⡄⠈⢷⡀
⠀⠀⠀⣰⠏⡐⠁⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠘⠘⢀⣠⡴⠋⠀⠘⣇⠀⠀⠱⣄⠀⠘⢦⠀⢻⡄
⠀⠀⢰⠏⡔⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠁⠐⠒⠢⣄⠈⠳⣄⡀⠈⢆⠀⠀⠳⡀⢻⡀
⠀⠀⡟⢰⠁⠀⡜⠀⠀⠀⣀⣠⡴⣶⠟⠛⠛⠦⡄⢠⠒⠉⠉⠑⢄⣀⠄⠀⠀⠙⢦⠈⢆⠀⠀⢱⠘⣧
⠀⢸⠇⡆⠀⠸⢴⡶⢾⡋⠉⠴⢶⠁⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⢘⠋⠀⠀⠀⠰⢎⣧⠘⡀⠀⠈⡇⢹⡀
⠀⣾⢰⠀⠀⠇⢸⡇⠧⠟⠀⠀⠸⡄⠀⠀⠀⠀⢹⢯⡀⠀⠀⣀⠜⠀⠀⠀⠀⠓⠊⣿⠀⠇⠀⢠⣹⢸⡇
⠀⣿⠶⡀⢸⠀⢸⡇⠀⠀⣨⣃⠀⠈⠒⠒⠒⢚⠥⠤⠬⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠃⢸⡇
⠀⡟⡶⠃⢸⠀⠘⣇⠀⠉⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡿⠀⠇⠀⠀⠀⢸⡇
⠀⡇⠁⠀⢸⠀⠀⢿⠙⠶⣤⣀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠞⡛⠁⢰⡇⢠⠀⠀⢸⠀⢸⡇
⠀⡇⠀⠀⢸⠀⠀⠸⡆⠀⠸⠉⠉⠙⢋⣿⣿⡛⠻⢿⡿⠟⠋⣿⠳⣄⠀⢌⣻⠀⣸⠃⡈⠀⢎⡿⠀⢸⠇
⠀⣷⢸⠀⠈⣤⡄⠀⣷⠀⡄⠀⢀⣴⠋⢸⣿⠇⠀⠀⠀⠀⠀⢸⡄⠈⢳⣄⠇⠀⣿⠀⠇⠀⠀⠇⠀⣿
⠀⣿⢸⠀⠀⠷⠃⠀⢸⡄⠇⢀⣾⡁⠀⢸⠏⠀⠀⠀⠀⠀⠀⠈⣧⣤⢾⡏⠓⢶⡏⡘⠀⠀⠰⠀⢠⡏
⠀⣿⠀⡀⠀⠈⡇⠀⠘⣷⠞⠋⢹⡟⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢳⠀⠸⣧⡧⠦⣤⣧⣄⣸⠇
⠀⠸⣦⣧⠤⢤⣧⣤⡴⠏⡠⡀⣾⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠸⡇⠀⠀⠀⢠⢲⡄⠈⠉
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠓⠉⢷⡀⠻⠶⣤⡤⠤⢤⣤⡤⠴⢾⡟⠋⢀⡼⠃⠀⠀⠀⠀⠉
⠀⠀⠐⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⠟⠀⠀⣀⣉⣁⠀⠀⠹⣶⠋⠀⢜⠇
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⢿⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠲⡀
⠀⠀⠀⠀⠀⠀⠛⠜⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡦⡀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⡟⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡶⠶⡶⣶⣤⣀⣿⣀⡤⠶⠒⠛⠚⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠏⠓⠀⠀⠀⠀⠀⠙⢿⠋⠀⠀⠀⠀⠀⠀⣄⣿⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡻⠛⠷⠤⣤⣄⣀⣀⣀⣀⣼⣦⣤⣤⣤⠴⠶⢞⣛⣭⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⠶⠶⠦⠭⢭⣭⣼⠷⠴⠶⠶⠚⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠾⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⣇⣠⣾⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⢶⣖⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠿⠿⠿⣿⣿⠭⠅⠀⣈⣉⣤⣤⣴⣶⣦⣄⡀⣿⣿⠟⠋
⠀⠀⠀⠀⠈⠁⠒⠒⠂⠀⠠⠄⠀⢼⡗⣧⣤⣤⣤⣤⣤⣶⣴⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⢰⣶⣴⣾⣿⣦⣤⣴⣦⡀⠀⠀⢨⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⢻⣿⣿⡿⠂
⠀⢸⣿⡟⢸⣿⣿⣿⣿⠏⠀⠀⠀⠸⠇⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⠃
⠀⢸⣟⡇⠈⠈⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⠿⢿⣿⣿⣯⣿⣿⣶⣄⠀⢸⠃
⠀⣸⡏⣗⣖⠒⡒⠒⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠛⣿⣿⣧
⠀⢻⣃⣿⡏⡆⣷⡆⣷⠀⢀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⠀⣿⣿⣿⡀
⠀⣦⣿⡿⠃⠃⡿⠇⣿⣄⣾⢣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣿⣿⣿⡆⠈⣻⣿⠇
⠀⢟⣿⡏⣴⡆⣀⡀⣿⣿⣿⣾⣧⡦⠀⣀⠀⠀⠀⠀⠀⠠⠙⠀⠀⣼⣿⣿⣿⣷⣿⣷
⠀⢹⣿⡇⠘⠁⠁⢀⣿⣿⣿⠯⢿⣿⣿⡟⠗⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠸⣿⣷⣤⣶⣟⣉⣀⣴⡞⣦⡾⠋⡽⡀⠘⡀⠀⠀⠀⠀⠀⠀⠘⠛⠉⣽⣿⣿⡇⠹⠃
⠀⠀⢹⣿⣿⣿⣿⡀⢸⠏⢻⣼⠃⠀⣁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢹⣿
⠀⠀⢹⣿⡿⠋⠀⠳⣼⠀⠀⠹⣦⣶⡿⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇
⠀⠐⠉⠁⣀⣠⠤⠂⠁⠀⠀⠀⠈⢿⣴⣛⡤⠁⠀⠀⠀⠀⠀⠠⠀⠙⢿⡄⢺⡗
⠀⠀⠾⠿⣷⣶⡀⢲⠰⡀⠀⠀⠀⠀⢻⣿⣦⠂⠀⠀⠠⠀⠀⡀⠀⡀⢠⣴⠏
⠀⠀⠀⠀⠐⣿⣷⡀⢳⡹⡄⢀⡤⠞⠃⠈⠌⢁⠀⢠⠆⠀⠔⠤⡀⣁⣿⡟⠂
⠀⠀⠀⠀⠈⢙⣿⣿⣤⣿⠿⠉⢁⠐⠀⠲⠀⠨⠎⠁⠀⠀⢄⣰⣾⣿⣿⡇⢀
⠀⠀⠀⠀⡠⣬⣥⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣶⣾⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⣴⢶⡶⠶⢶⣟⣿⣿⣿⣿⣗⣲⣐⠐⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢿⡽⠯⠾⠧⢷⡂⢀⣀⣩⣯⣣⢿⣿⠟⠉⠛⢿⡿⢛⢤⣌⠑⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠃⠉⠘⠿⢋⣶⠦⡀⠙⣿⠷⣻⡄⠀⠐⡩⡢⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠁⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⡘⣿⢵⣚⠁⠠⣉⢞⡡⡷⠀⠑⠌⠉⠀⢶⣀
⠀⠀⠀⠀⠀⢀⢴⠋⡤⢾⣲⠀⠀⠀⠀⢒⣈⠡⠄⠀⠀⠀⠀⠀⣜⢕⠙⡡⡢⣲⠉⠙⢷⢷⣟⡟⣫⡽⡆⠀⠠⠤⡶⡚⠛⢢⡀
⠀⠀⠀⠀⠠⡡⢪⢔⡫⢐⠬⡆⠀⠀⠩⠄⠒⠀⠈⠁⠀⠀⠀⠀⠈⠲⢜⣨⣪⡇⠀⠀⠘⠋⢹⣯⣻⡯⢕⣢⡼⠛⠜⡀⠫⡱⠑⢄
⠀⠀⠀⡐⠘⡁⢜⢕⡪⠔⡓⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣏⠇⠀⠀⠀⠀⠀⠈⠳⡥⢞⠫⡐⠄⠀⡁⠄⢀⠠⠀⠈⢢
⠀⠀⡜⠠⡐⠨⡑⢌⠛⢶⡌⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢤⠤⢤⠤⣏⠐⡉⠤⢒⠡⠐⢈⡠⠔⠀⢰⢆⢡
⠀⡰⠀⠐⠨⠑⡢⠑⡪⢒⣈⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠒⡎⠐⠺⠀⠒⢉⡠⠔⢊⠡⠄⠀⠀⠐⠾⣤⢆
⢀⠁⠀⠉⠒⠂⠤⣁⠊⠲⢷⠀⠀⠀⠀⠐⣩⠔⢀⠠⠐⠀⠀⠀⠐⡂⠅⠀⠀⡀⡎⡉⠍⣒⠌⢒⡡⠔⢊⠥⠒⢈⡠⠄⡂⠁⠠⠀⠀⡇
⠈⠀⠀⠀⠈⠀⠀⠀⠀⠁⠸⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠒⠀⠁⠀⠚⡂⠄⢂⠡⠐⣉⠡⠐⢈⡠⠔⡊⠥⠒⠁⡀⠄⠨⢀⡅⠁⡖
⡆⠀⠀⣀⡀⠩⠄⠐⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⡠⠔⢀⠤⠐⢈⠠⠐⡊⠅⠒⢉⡠⠄⣂⠥⠐⢀⠨⠁⣛⠼⠦
⡇⠀⠠⠄⠒⣀⡈⠅⠂⠀⠀⠀⢦⣆⠀⠀⠀⠀⠀⠠⢠⠤⡂⠒⠄⠣⠀⠄⢂⡨⠄⣂⠩⠔⢂⡁⠤⠒⣈⠥⢒⡉⠄⠂⠀⢐⡀⠅⡀⠀⡀
⡇⠀⠀⢒⡉⠤⠐⣊⠤⡐⠀⡀⠈⢯⠱⡀⠀⠀⢰⠣⢐⠨⣒⠅⡑⡔⠐⢊⠅⠐⢁⠤⠐⢊⡡⠄⢒⡩⠔⢊⡁⠤⠒⢁⢀⠥⠂⠜
⠀⠀⠈⠀⠒⡀⠍⢂⠡⢒⡩⢐⡠⠀⠀⢀⡀⠀⠈⢆⡡⠚⣳⠜⢂⠔⣍⣦⠨⠄⠀⠀⠈⣠⠖⠈⠡⠐⢈⡁⠄⢂⠨⠄⠀⡀⠀⠀⠀⠬⢄
⠨⠀⠀⠀⠠⠔⢈⠤⢂⡡⠒⡡⠐⡠⠀⠀⠈⠒⠄⠤⢀⡀⠢⠻⠕⣉⢔⠹⢊⠕⢋⠔⣊⠔⡩⠀⠀⣈⠥⢒⡉⠤⠂⠀⠀⡂⢸⠀⠰⠛⠉
⠀⢂⠀⠀⠒⣈⠄⠂⣁⠔⢉⠤⢊⠤⢂⠴⢂⡴⠀⠀⠀⠈⠣⡐⣉⡂⣁⠔⠓⠒⠡⠜⠠⡙⠪⢐⠅⡀⠀⠡⠒⠊⠀⠀⠄⢂⠄⠑⣀⠤⢠
⠀⠈⡄⠀⠈⣀⠔⠊⡠⠒⡡⠔⢁⠔⢁⠔⠋⡠⠀⠀⡀⠀⠀⠀⠉⠑⠀⠀⠀⣀⠤⠀⠀⠈⠀⠢⡈⠐⠀⠀⠉⠀⠀⡀⠭⣐⠡⢀⠀⢠⠁
⠀⠀⠰⡀⠀⠠⠒⢁⠤⠊⡠⠞⢁⠔⢁⠴⠊⣀⠔⠁⠀⣈⠔⡀⢀⠜⠀⠔⡪⢒⠉⠀⠀⠀⠀⠀⠐⠆⢄⠀⣀⠀⠀⣒⠩⢐⠪⡐⢠⠃
⠀⠀⠀⠱⡀⠀⠀⣁⠔⠈⡠⠊⡡⠔⢁⠠⠊⡠⠂⠀⠀⠔⡩⠀⢜⠀⠀⠀⡪⠐⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢇⠠⢐⡈⢐⠜⡠⠃
⠀⠀⠀⠀⠘⢆⠀⠀⠐⢊⠄⠊⡠⠒⣁⠔⡊⠔⢁⠔⠀⠀⢒⡡⠂⡱⡀⠀⠀⠭⠐⠀⠀⠀⢐⠪⠀⠀⠀⠐⠁⢐⡪⠕⡪⢐⠔⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢉⠔⢊⠠⢊⠤⢊⠡⢊⠀⠀⠁⠔⡨⢒⠈⠒⢄⠀⠑⠀⠀⢆⡢⠁⠀⢀⣀⠎⠀⠤⠂⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠁⠊⠡⠒⡡⠒⣁⢔⡡⢂⢀⠀⠑⠠⡀⠨⠀⠄⠀⠀⠀⠀⠀⡜⠁⣀⠠⠄⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠈⠐⠊⠒⠡⠊⢔⠕⡠⢀⠀⠀⠈⠀⠀⠀⠀⢀⡰⠊⠀⠐⢂⠥⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⡤⠊⠁⣀⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠶⣄⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⡏⠀⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⣀⠜⠀⠈⣼⡀⡀⡄⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⢨⣄⠀⠀⠀⢰⢃⡏⠀⠀⠑⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠙⠳⢤⣸⣯⣀⡠⣦⢦⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠞⡐⠐⠀⣀⠄⣹⡪⠑⠒⠨⠴⡿⣆
⠀⠀⠀⡀⠀⠀⠀⠀⣠⣄⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢹⠂⠅⠥⠈⠀⠀⢾⢠⡌⢫⣦⡔⡱⢫⠂⠀⠀⠀⠀⣤⡀⠀⠀⡷⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠉⠩⡉⣋⠋⢰⠀⠈⠉⢁⡔⢦⡀⠀⠀⠀⠀⠀⠀⡏⠈⠀⣠⠖⠂⢾⢸⡁⡗⠈⡴⢣⠃⠀⠀⠀⠀⣰⠻⡝⠒⠫⠄⠀⣉⡭⠙⢉⠋
⠀⠀⠀⠀⠀⠐⣌⣗⢶⠤⡀⠀⠀⠱⡀⠉⠉⢳⠤⢶⡑⢤⡇⠡⣸⠁⠀⠀⣮⡸⠉⡰⠥⣴⣉⡀⣀⠜⡃⠋⠰⠀⡃⢀⠞⠀⠈⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢃⠃⠈⠀⠉⠓⠤⠌⡁⢄⠀⡐⠛⢰⡯⠁⣀⢘⢊⣲⣀⣴⣿⢀⠞⡠⠺⠰⠦⣝⡄⢸⡇⠀⠇⣲⣄⠡⠠⠤⡤⠀⢀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⢳⣤⡀⠀⠀⠀⠀⠀⣠⠚⣆⣄⠀⠺⠀⢨⡧⢃⠟⢹⠃⣷⠀⡴⠃⡀⠀⠀⠈⡷⣽⢖⠗⠊⡠⠬⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⢠⡟⠚⠃⠘⠂⠚⠘⢁⠁⠀⢀⢁⡷⠾⣧⣀⠁⢸⠉⣧⠀⣿⠊⠁⠘⠀⠀⢀⣴⠛⠀⠀⢗⠟⠀⠀⠄⣦⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⢀⡀⠔⡁⢠⠈⠀⡩⢶⢻⠎⠙⠳⡄⠳⣜⢦⣹⠃⠀⠀⣀⣰⣈⠕⣮⡁⢤⠀⣉⣀⡴⢹⠟⣋⡶⠒⠂⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⣈⠂⡌⠀⠀⠏⣏⠉⡭⠘⠷⣤⣈⠭⠅⣀⣰⡏⠉⠁⠀⡘⢷⠸⠇⠝⠽⡶⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠈⢧⠜⣂⣠⢄⠭⣺⠧⡤⢶⠔⢶⣯⣤⣧⣎⠹⠀⣀⣄⢀⠠⡘⢽⣄⢀⢀⣘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⡤⢿⡿⢹⠁⡘⠁⠀⠑⠐⠑⣃⠘⣁⡽⠃⠀⠈⠦⣄⠀⠀⡠⢛⠻⠀⠘⡻⢗⠲⢦⣵⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣴⣊⡁⠀⠎⠀⠹⢄⠀⣄⠀⡠⢴⠈⣧⡶⠟⠀⠀⠀⠀⠀⠈⠻⡛⡩⠴⢒⠞⠐⠣⠠⠝⠛⠃⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠒⠚⠛⠲⣤⣍⡥⠥⣌⣯⠔⠉⠀⠀⠀⢰⠇⠀⠀⠀⠀⠱⡰⠞⠋⠁⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣶⣿⣿⣿⣷⣾⡿⠿⠗⢠⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣗⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠛⣫⡟⠋⠁⠀⠀⠀⠀⣻⠿⠛⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢹⡟⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠑⠄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⢫⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠈⢢
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡯⢿⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢂
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⣿⣿⠀⠀⣙⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢸⡿⣼⠃⣿⣇⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣟⡀⠙⠦
⠀⠀⠀⠀⢸⠁⠏⠀⢋⠋⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⢠⣦⣀⠀⠀⠀⡆
⠀⠀⠀⠀⢸⠀⠀⠀⢺⢀⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣦⠀⠀⠇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⢆⠛⠻⠀⠲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⣀⠘⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠰
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⣴⣿⣧⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢁⠃
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢻⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠄⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣉⠤⠒⠒⠂⠐⠒⠒⠤⢁⠂⠄⠀⠀⠀⠀⠆⠢⠠⠤⠆⠤⠄⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⢀⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠊⡠⠊⣀⠔⢊⡩⠥⠤⠭⣉⠐⠠⠈⠢⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢔⠡⠊⠁⠀⠀⠀⠀⠀⠈⠀⠀⠢⠈⠄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣀⠠⠀⠔⠀⠊⠀⠀⡅⠀⠀⠀⠀⠀⠈⠓⢢⡀⠀⠀⢰⡀⠀⠀⠀⠈⠂⠁⠘⠀⠂⠀⠀⠀⣜⣝⢍⠑⠠⠤⢄⡀⠀⠀⢀
⠀⠀⠀⠈⠈⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⢆⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣄⠀⠀⠀⢿⡀⠁⠑⢄⢀⠀⠹⠀⠀⠙
⠀⠀⠀⡀⠀⠀⣀⠤⠔⠚⠒⢒⡒⠠⠤⠀⠀⠀⠈⠑⠢⠔⠁⠀⠀⠀⠀⠀⡤⠐⠁⠀⠀⠀⠀⠀⠁⠂⠀⠈⢳⡄⠀⣸⠀⠀⡰
⠀⠀⠀⠂⡠⠺⠑⢢⠈⢀⣰⠀⠈⠳⠆⠀⠈⠢⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠦⠀⠤⠤⢤⡀⠀⣀⠀⠀⠀⠀⣠⡇⢔⠋⠀⢺⡀
⠀⠀⢀⡾⠁⠀⠀⡘⠤⠂⠈⠓⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⢺⢩⣹⠈⠀⠀⠀⠑⢄
⠀⠀⡼⠀⠀⠀⠀⠁⢀⣀⣀⠀⡠⠄⠀⢄⢠⠔⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠂⠂⠒⠁⡠⠊⠀⡇⠚⠇⠐⠀⠀⢄⠐⠈⠣⡀
⠀⠀⠗⠈⠀⠁⢢⡞⠁⠀⢨⢹⠃⠀⠀⠀⠿⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⠶⣶⣶⣤⣄⠀⠀⡠⠊⠀⠀⢸⢁⢱⠀⠀⠀⠀⢀⠀⠀⠀⠈⠢⡀
⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⡆⡄⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠻⢧⣄⣀⣀⡼⠄⢇⠀⠘⢂⡼⠘⣤⠀⠀⢀⡀⠈⢢⡀⠀⠀⣠⠜⡄
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢳⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠑⠔⠃⡇⠀⠉⠀⣆⠀⠀⠀⠀⠙⠆⢀⠁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡤⠀⠀⠀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢰⡆⠀⠀⠄⠠⠄⠂⠈⠀⠁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣀⠠⠤⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⢀⡀⠀⠀⠀⠀⢰⡉⡕⠒⠈⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠅⠀⠂⠀⡇⠁⠈⠁⠀⠅
⠀⠀⠀⢰⠄⠀⠀⡀⠀⠀⠀⠀⠀⠧⣑⡡⠇⠀⠀⢈⠂⠀⠙⠳⢤⣄⣀⣠⡤⠤⠒⠒⠂⠀⠀⠀⠀⠘⢀⡀⠄⠀⠈⠒⠂⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠭⠉⠀⠊⠁

⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⢀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⢀⠀⢰⣦⡄⠀⠀⠀⠠⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠆⠀⠢
⠀⠀⠀⠘⠆⠀⠜⢃⠠⠈⠁⠀⠁⠀⠈⠀⠀⡄⠀⠀⠀⠀⠠⠠⠀⠀⠄⠀⣠⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠰
⠀⢀⠀⠐⠂⠀⢀⠘⠄⠈⠠⠀⡃⠀⠐⠀⠀⠆⠀⠀⠂⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠆⠐⠀⠀⣁⡼
⢢⠓⡖⣄⠀⢦⡀⠊⠀⠑⠐⠓⠃⠀⢈⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠐⠂⠀⠀⡈⠀⠀⠀⠀⠀⠀⠋
⠁⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠈⠀⠀⠠⠆⢠⠀⠈⢢⣀⠀⢀⡀⠀⠀⠘
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠀⠀⠀⠀⠀⠐⠆⠐⠂⠀⠀⡈⠀⠀⡀⠉⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⠐⠠⣀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠄⠀⠀⠂⠈⠃⠤⠀⠂
⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠉⠀⢀⡜⠀⠈⠂⠀⠘⠀⠀⠀⠀⠀⠈⢨⡀⠀⠀⠀⠀⠠⠂⠈⠁⠀⠐
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠁⠀⠀⠀⠀⠀⠠⠴⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⠀⢰⠀⠀⠀⠈⠁⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠜⠀⠀⠀⠀⠀⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠴⠄⠀⠈⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠐⠄
⠈⠈⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⠀⠀⠁⠀⠀⠁⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠖⠂⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠙⢀
⠀⡀⢀⢀⠀⠀⠀⠀⠀⡆⠀⠀⠄⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠈⢀⠀⠀⠡⠆
⠀⠀⢧⠈⠐⢤⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠁⠒⠐⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠡⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠄⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⢃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣮⢶⠄⠠⠂⢀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⢄⡀⠠⠄⡀
⠀⠀⠀⠀⠈⣄⣸⠿⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠄⠀⠀⠁⠃⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⠄⠄⠀⠀⠀⠤⠄
⠀⠀⠶⣍⢷⣘⢝⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠐⠆⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢀⠀⣀⠙⠀⠉⠀⠀⠀⠀⠀⢀⠀⡀⠈⢀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⢌⠎⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰
⠀⠀⠀⠀⠁⠀⢸⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣷⣣⠂
⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠄⠜⢂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥
⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⢀⡀⠉⣀⣼⢏⡴⠒
⠀⠀⠀⠀⢡⠈⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡌⠀⠆⠀⠀⠀⠀⠀⢀⡡⣼⣿⣷⡈
⠀⠀⠀⠀⠀⢣⡉⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠐⠀⠀⠀⠀⢀⣵⡿⠉⡄
⠀⠀⠀⠀⠀⠀⠳⡀⢣⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⢹⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⡁⠈
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂