Run text face Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢒⣲⣶⣾⣿⣟⠛⠛⠛⠛⠛⠛⣻⣿⣷⣶⣖⡒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠉⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢀⣤⣤⣤⣄⡀⠀⠀⠹⣿⣽⣿⣿⠀⠀⣿⣿⣯⣿⠏⠀⠀⢀⣠⣤⣤⣤⡀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣾⣿⣿⣿⣿⣿⣿⣶⡀⠀⠹⣿⣿⣿⠀⠀⣿⣿⣿⠏⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⠇⠀⠀⠸⣿⣿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⢣⣶⣶⣶⣶⡜⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣘⢿⣿⣿⡿⣃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠩⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣯⣭⣭⣭⣿⣭⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡰⢿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡘⢻⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡛⠎⠁

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣤⣀
⠀⠀⠀⣴⣿⡿⠿⢻⣷⡄⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⣿⣆⠀⠀⠀⠀⣼⠿⠿⠟⠛⠻⣷⠀⠀⠀⠀⢰⣿⡿⠿⡿⡿⣿⡇
⠀⠀⠀⡟⢡⠀⠀⢠⠉⣿⠀⠀⠀⠀⠀⠋⠩⠄⠁⠠⠌⠙⠀⠀⠀⠀⠋⠀⠄⠀⠀⠄⠘⠀⠀⠀⠀⠘⠁⠰⠀⠀⠠⠈⠃
⠀⠀⠀⣿⡀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣿⣿⢶⣰⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠴⣤⠦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣄
⠀⠀⠀⠀⠁⠀⠙⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠂
⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣴⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣤⡀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣶⣦⡀⠀⠀⠀⠀⣠⣶⣿⣶⣤⣀
⠀⠀⠸⠟⢛⠉⠉⢉⠛⠿⠀⠀⠀⠀⠀⡿⢟⠋⢁⢀⠻⠷⠀⠀⠀⠀⣿⡿⠿⠛⠉⠻⢿⡇⠀⠀⠀⢰⡟⠛⠛⠉⠉⢿⡇
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠂⠈⠁⠀⠀⠀⢈⠀⠐⠀⠀⠐⠀⡁
⠀⠀⠀⠀⠁⣠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⠀⣰⣿⡿⠛⠛⢿⣦⠀⠀⠀⠀⠀⣼⣿⣿⡿⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⣿⡆
⠀⠀⠀⣿⠁⠆⠀⠀⠆⠙⠃⠀⠀⠀⠀⠋⠱⠀⠀⠰⠆⠙⠀⠀⠀⠀⠴⠀⠄⠀⠀⠄⠰⠄⠀⠀⠀⠸⠏⠩⠀⠀⠠⠈⠷
⠀⠀⠀⠻⠄⠀⠀⠀⠀⠼⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⢧⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣴⠦⠈⠁⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠿⠗⠀⠀⠀⠀⠀⠀⠀⠻⠟⠻⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠞⠻⠿⣯⣤⣀⡀⠀⠀⠉⠙⠛⠷⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⢷⣤⣄⣀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣄⣀⣤⣤⡾⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠛⠷⢶⣤⣤⣤⣶⠶⠟⠛⠉⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣀⠀⠀⢀⣴⠶⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡿⢋⡙⢷⡄⢸⣇⣰⣦⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡦⠀⠀⠀⠀⣿⠀⠸⢷⣾⠷⠿⠃⠀⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡴⠶⢶⣦⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣯⡀⣠⡾⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣦⣀⣀⣠⣤⣿⠶⠛⠀⠀⠉⠛⠛⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⣦⣄⣀⠈⠉⠉⠉⠁⣿⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣦⣤⣀⣿⣀⣠⣤⡶⠾⠻⢿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠋⠉⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠶⠶⠶⠶⠶⠶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠖



⣿⣿⢛⢿⢛⠟⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠐⠒⠒⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠭⠛⠉⠀⠰⠊⢁⡎⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢂⡇⢠⠀⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠃⠀⣈⠀⢀⣀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠨⣉⢢⣴⡷⠁⠀⣠⡞⠉⠁⠀⣸⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⣢⠌⠁⠁⠀⢠⠋⠈⠋⠀⢀⠴⣻⡆⠈⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡯⢆⡤⠤⠶⠶⠶⠯⠅⠀⠀⠀⠀⠈⠑⠒⠚⢋⠉⠤⣉⣁⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⣇⣾⠀⢴⣊⣛⠺⢏⣖⣦⣀⠀⠀⠀⠀⠀⣀⠼⢄⠀⠀⠉⠉⠒⠢⠤⢤⣀⡀
⠄⠀⠤⠤⠀⡀⠀⠀⠀⠀⠀⠀⣀⠔⠖⠊⠁⡸⠀⠀⡇⠀⠁⠀⠙⠂⠭⣱⡊⠉⠉⠳⣄⡤⠒⠉⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⢻⠃⠉⠉⠑⠄⠀⢀⣏⠁⠀⠀⠀⠀⠀⠓⠒⠄⡇⠀⠀⠀⣀⣀⡤⠤⠌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣂⣀⣀⣠⠔
⠀⠀⠈⡄⠀⡠⠶⠓⠊⠁⠈⠣⡀⠀⠀⠀⠀⠤⠀⠈⠑⠒⠿⣏⠉⠀⢤⡄⣀⡠⢀
⠀⠀⠀⠑⢄⢰⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀⠀⠀⠑⣀⡠⢶⣿⣿⠤⢾⡶⠼⡀⠵⡴⢳⠀⢀⠼⣥⣼
⠀⠀⠀⠀⠀⠉⠒⠂⠠⠤⠄⣀⣀⠀⠀⠈⢉⠒⠒⠩⠽⣁⠀⠛⠙⠒⠂⠭⣁⠸⡱⢳⠆⠇⠔⡍⢠⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠥⡀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠙⠒⠉⠈⠂⡸⠙⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠑⢄⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣀⡴⣾⡤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠉⠉⠉⠉⠋⠙⠓⠛⠛⠛⠒⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣤⡀⠀⢠⡄⢀⡀⢠⡄⠀⡀⠀⢀⣤⢀⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠀⠂⠀⠐⠈⠁⠀⠀⠀⠑⠂⠈⠁⠈⠉⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠃⠀⡠⠄⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠈⠣⠔⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠒⠚⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⣄⢠⡄⠀⠠⠀⣀⠀⠀⢤⠀⠤⠀⠀⠀⣤⠄⠀⠀⠀⢠⠀⠀⢠⣄⠀⣠⠄⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠀⠀⠌⠁⠄⠀⠈⠀⠄⠀⠀⠀⠙⠤⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠤⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠐⠀⠒⠀⠒⠂⠀⠀⠰⠄⠀⠶⠀⠒⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣇⡤⠋⠈⠛⠉⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠚⢄⢻⡞⠛⠀⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢡⡀⠀⠀⠀⠀⢀⣀⠤⠤⣀⡀⠀⠀⠀⠀⣼⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢣⠀⠀⠀⣴⠟⠁⠀⠀⠈⠹⣦⠀⠀⠀⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠘⣦⠀⠀⠏⠀⠀⠊⠀⠐⠂⣸⠀⠀⢰⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⠈⢦⠀⠳⡄⠓⠄⠀⠀⠚⠻⠀⢠⡎⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠁⢤⠀⠀⠀⠀⠀⠀⠐⣴⠟⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠸⠤⠤⠀⠀⠀⠀⠤⠿⡄⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠓⢀⡀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠛⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⢶⣶⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢀⣴⠃⠀⠉⠙⠛⠒⠤⠤⣤⣤⣤⣤⣴⠾⠛⠉⠁⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣤⣁⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠋⠋⠠⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⣤⣤⠀⠈⠙⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠉⠀⠈⠉⠉⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣴⠾⠛⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢷⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣼⣟⣁⣀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⡁⠀⠀⢀⣀⣀⣀⣀⣀⣤⣶⡿⠋⠀⣼⠀⠀⠀⣀⣤⠾⠛⣷
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣶⣶⣾⡿⠋⠀⠀⢠⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣿⣶⣾⡿⠛⠁⠀⢠⠇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⠎⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⡞
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣴⠋⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣰⠏
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⣤⣶⣶⣴⣤⣤⣶⣶⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣦⣴⣴⣦⣴⣤⣤⣴⣤⣴⣤⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠃⢀⠀⠀⢀⠀⠀⢠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢽⠃⢀⣎⡄⢀⣏⠀⢀⠶⠄⠀⢠⣏⠀⢂⠒⠀⣶⡠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⣆⢂⡮⠡⠁⣘⠱⢀⠸⠎⠤⠠⠗⣐⠀⡐⣆⣤⡰⠉⠃⣘⠉⠐⡢⠄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠈⠁⠐⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⢦⣤⣄⣈⠈⣈⠉⠀⠴⠆⣀⡚⠴⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⣿⠋⠁⢀⠘⡺⠄⢬⠤⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⢄⢻⢉⡤⣢⠟⠀⠅⣀⡼⠐⠂⠀⠀⠀⠠⡀
⠀⢀⡠⠐⠈⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣂⠕⠀⣋⠂⠁⠩⢁⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰
⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠂⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠸⡠⠒⣀⠔⠃⠐⡰⢡⣅⢳⠊⡄⠈⠓⠄⣀⣀⡠⠔⠁
⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⢀⠜⣠⣿⠋⠈⠀⢃⢀
⠀⠀⠀⠀⠂⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠃⢠⠊⣰⣛⣉⡉⠉⠓⡌⠊⠀⡎⡔⢀⠁⢀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⣴⠰⠃⣰⣿⡇⢀⠝⠒⠒⠁⠀⠀⣰⠉⠁⢡⢡
⠀⠀⠀⠀⠀⡠⠀⠂⣈⠯⠄⠒⠲⠰⣲⠒⠀⠀⠀⠀⢀⡠⢄⠄⠊⠀⠀⠀⠀⢉⢩⠝⠁⡐⠀⢤⣐⠈⠁⠛⠒⠊⡌⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢠⡃⠀⠀⠀⣀⠊⢨⠀⠀⠀⠀⠀⠀⢠⠈⠉⠀⢀⠌⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠘⠢⠤⠄⣁⡀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠃⠈⡄⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠆⠢⢄⣀⣀⢛⡟⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢁⠀⢀⣀⡠⠭⠓⠁⠰⠆⠀⠀⠀⣀⡈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠋⠉⠁⠀⠐⠒⠒⠂⠈⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⡺⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣄⠀⠀⣀⠤⠄⣂⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴⣖⠁⣋⠡⠗⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠉⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⠈⠉⠁⠈⠉⠀⠈⠐⠒⠒⠒⠒⠶⠶⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣤⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢯⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣽⣿⣿⣯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣶⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣇⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠦⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣜⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠻⣿⡏⣉⣻⠻⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠛⠛⢻⣿⣿⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⣇⢻⣿⣷⢠⣹⣿⡿⠶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⠶⡏⣡⣽⡇⢸⣿⡇⣿⢠⠛⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠘⠿⣿⢸⣿⢸⡃⣶⢸⣿⠃⣿⠉⣿⡟⠈⣿⠈⣿⢸⡇⣿⣿⡇⢸⣿⢀⡟⢸⠀⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⢠⣿⣿⠘⣿⣾⡇⢹⣿⣿⡄⣿⠀⣿⠀⡇⢸⠀⡇⢸⠁⣿⣿⡇⠙⣻⢸⡇⡾⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠠⣿⣿⠃⣿⣿⠀⣿⣿⣿⡀⢿⣿⡇⠛⠂⣿⢸⡇⢸⡄⡇⣾⢠⣶⣿⡇⣿⡏⢸⠇⡇⣌⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣤⣼⡈⠋⣻⠀⣿⣿⠟⣷⠘⣿⡇⢺⡆⣿⢸⣧⢸⡇⠁⡿⢸⣿⣿⡇⣿⡇⠿⢠⠇⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣿⣿⣿⣿⠗⠿⣿⣄⠛⢀⣿⣇⢸⡇⣿⢠⡄⢸⠃⢀⣇⠘⢻⣿⣧⣿⣷⣤⣾⣤⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⣰⣿⣿⣿⠏⠀⠀⠀⠉⠛⠻⠿⠿⣼⣧⣿⣼⣧⣼⣧⣼⠿⠶⠛⠋⠁⠀⠹⣿⣿⣿⣏⢻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⠙⠻⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⡈⠙⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠰⠿⠋⠁⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣤⣀⠈⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⠀⠸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠃⠃⠀⡄⠆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠐⢓⣘⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⣉⣉⣉⣉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠩⠉⠉⡍⢉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢹⡏⠉⠉⠙⣶⠈⠁⠀⠀⠀⣿⡄⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⣇⣤⡴⠞⠁⢰⠀⣰⣧⠀⡇⢻⡄⠀⢠⡇⠀⢸⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡆⠀⢸⠿⣦⡀⠀⠀⢻⡼⠃⡇⢸⡇⠀⢷⠀⢸⡇⠀⢸⡇⠀⠉⠀⢀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠈⠛⢦⡀⠀⠀⠀⠁⢸⡇⠀⠘⣇⢸⡇⠀⠀⡇⠀⠀⠀⠘⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢸⡇⠀⢸⠀⠠⡄⠀⠁⠘⠀⠀⠀⠸⡇⠀⢀⠹⣾⠇⠠⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠀⠙⠀⠀⢀⠀⡔⠒⡰⠄⣖⡦⠀⠀⠀⠀⣀⢀⣀⢀⣅⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠞⠶⠴⠛⠦⠞⠓⠋⠀⡟⠀⣇⠆⡟⢄⣀⠄⠛⠚⠙⠛⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣴⣶⡄⢀⠀⠀⣀⣀⣀⠀⡀⠁⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⡀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢸⠀⢸⡏⠉⢀⠘⡇⠀⠀⠀⢀⣿⠀⢰⡷⡄⠀⠀⠈⡇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣾⠀⢸⡇⠀⠀⠀⣧⠀⡀⠀⡾⢹⠀⢸⡇⠹⣄⠉⠀⡇⠀⢸⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⢸⡟⠉⠀⠀⣿⠀⠀⣸⠃⢸⡀⢸⡇⠀⠹⣆⠀⡇⠀⢸⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠠⣦⠀⢸⡄⣰⠏⠀⢸⡇⢸⠇⠀⠋⠘⣶⡇⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⠀⢸⡇⠀⠀⣄⠈⠛⠃⠀⠀⠸⠇⠘⠀⠤⠀⠀⠈⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⡠⡠⠀⢠⢀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠃⡇⢸⠘⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢸⠀⠁

⠀⠀⠀⠀⣄⡆⡇⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⣀⣠⣤⣦⣶⣶⣷⠀⢀⣀⠀⠀⠀⠀⡠⣀⡦⠶⠶⠷⠴⢤⣤⣂
⠀⠀⠀⡠⠞⠁⠉⣉⣭⣉⠛⠦⡼⠀⠀⠀⣶⣿⣿⠿⠛⣉⠭⡈⠉⡗⢼⠀⠀⠀⠘⡔⠁⢀⠖⠒⢢⡀⠀⠀⠑⢎⡠
⠀⢀⠞⣠⢴⣦⡜⠘⠿⠏⡆⡄⢱⠀⠀⠘⡿⠋⢀⡄⢴⡃⠀⣸⠀⢸⠀⡇⠀⠀⢸⠁⠀⠘⣄⣀⡰⣏⣉⠇⢀⠀⢗⣀
⠀⡸⢰⠁⠘⠟⡻⢄⡠⠔⢡⠇⡌⠀⢀⡤⡇⢦⢯⣀⠴⠉⠉⠁⣠⠇⢀⠇⠀⠀⠸⡄⠀⠀⠀⠀⠀⡀⠀⠀⣰⠀⣸⣨⠇
⣏⢱⠈⠲⠴⠚⠁⠀⢀⡰⢃⠞⠀⠀⠈⠢⠳⡀⠙⠒⠤⠤⠒⠊⠁⡠⠊⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠈⠑⠊⢁⠔⠁
⠈⠉⠳⢄⡑⠒⠒⢚⡩⠐⠁⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠤⠒⠊⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀
⠀⡠⣀⠴⠊⠉⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠁⠈⠁⠺⣥⠀⠀⠀⠀⠀⢠⣰⡿⢋⣉⠅⡉⣉⠙⠻⣃⢄
⠈⢳⠋⡄⠸⠋⢢⠔⠀⠳⣧⠘⡄⠀⠀⡠⢤⠎⠀⢠⠴⣤⡠⢒⡶⡄⠈⢯⡳⠀⠀⢀⣻⠋⠀⡴⠲⣌⠀⢈⢄⠀⠀⡔⠁
⠀⡎⠀⡇⠐⠀⠊⠢⠤⠞⠋⠀⡧⡀⠀⠙⡇⠀⠰⡑⠤⠽⠇⣀⠠⡧⠀⠀⡇⠀⠐⠧⣤⠀⡄⠙⠚⠀⠁⠁⠸⠀⠀⡇
⠀⢣⠀⠑⢄⡀⠀⠀⡠⠀⠀⡸⠦⠃⠀⠀⢇⠀⠣⡈⠀⠀⠀⠀⠈⢀⠆⢀⠇⠀⠀⠀⢧⠀⠸⣄⡀⠀⣀⠔⠁⠀⣰⠁
⠀⠈⢦⡀⠀⠀⠈⠀⠀⢀⠜⠁⠀⠀⠀⠀⠈⢦⡀⠈⠑⠂⠀⠀⠒⠁⡠⠊⠀⠀⠀⠀⠘⣄⠀⠀⠉⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠉⠒⠂⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠤⠤⠀⠂⠁
⠀⠀⠀⠀⣀⠤⠤⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣰⣦⣆⣴⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⢤⣤⣀
⡠⠤⣠⠎⢠⠔⠀⣀⡀⠀⠈⠑⣄⠀⠀⠀⠀⢀⣰⣿⡿⠛⠉⠉⠉⠛⠻⣿⣥⡄⠀⠀⠀⠀⣠⡞⡏⠆⠾⠘⠘⠘⠋⠓⣤
⠓⢲⠁⢰⠃⠀⡎⠀⣸⠒⢢⢢⠈⣇⣀⠀⠀⠀⢻⠋⢀⡤⢤⣄⡴⣶⢦⠀⠻⡟⡄⠀⡤⡼⠉⢠⡶⠤⣤⠞⠉⠳⣄⠀⢸
⠀⢸⠀⢸⠀⠀⠙⠒⠉⠒⠋⢀⠇⡯⡸⠂⠰⣉⡇⠀⢏⠀⠛⡻⢧⣉⠞⡀⠀⡟⠁⠀⠉⡇⠠⡜⣅⣀⠜⠦⠤⠞⠙⠀⡸
⠀⠸⡀⠀⢣⡀⠀⠀⠀⠀⣠⠞⡰⠁⠀⠀⠀⠀⡇⠀⠈⠙⠋⠀⢀⡠⠞⠁⢀⠇⠀⠀⠀⢱⡀⠘⠢⢤⣀⡠⠴⠃⠀⡴⠁
⠀⠀⠑⢄⡀⠈⠑⠒⠒⣉⡥⠊⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠉⠉⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⢀⣀⠤⠊
⠀⠀⠀⠀⠉⠉⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣾⣼⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠒⢒⣒⡒⠒⢒⣒⣂⣀⠀⠀⠀⣀⣠⣤⡀⠀⠀⢀⣀⠀⠍⠋⠀⣿⠹⠉⠀⣇⣀⣀⣤⣤⣶⣶⡀⠀⠉⢻⣿⣿⣿⠛⠙⡄
⠀⠀⠀⠾⢿⣿⣿⠿⠋⣥⣾⡿⠛⣻⣿⢀⣴⡿⠛⠉⣻⣿⢀⣴⣿⡟⣠⣾⣿⢀⠍⠜⠀⠀⠽⠿⠿⠟⠛⢻⣿⣷⡀⠀⠘⠻⠏⠉⠀⠀⣰
⠀⣀⣴⣾⣟⣋⡀⠀⣼⣿⣇⣀⣴⣿⠃⣾⣿⣤⣤⣾⡿⣷⣿⠛⣿⣿⠏⣿⡇⠈⠀⠀⠀⠀⠀⣀⣄⠐⣄⣠⣿⣿⣷⡆⢀⠐⠂⠀⢤⣀⠛⠒⠀⠀⠀⠀⢀⡀
⠸⠿⠿⠿⠛⠛⠃⠀⠘⠻⠿⠿⠋⠁⣀⣈⡛⠛⠛⢁⣀⣈⡁⠀⠉⠁⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⡀⠙⠿⣿⣿⡿⠁⣤⣦⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⢢
⠀⠀⠀⠀⠐⠒⠒⠒⠒⠉⠉⠉⢉⣉⡉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⠷⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⣽⣿⣿⣿⣦⣤⣶⣿⣿⡿⠿⠉⠉⠉⠉⣩⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠈⠙⠿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⢺⣿⣿⠛⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⣿⣿⣿⣷⣶⣶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣴⣶⣿⣿⣿⡟⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⡿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠛⠛⠉⠁

⠀⢸⣿⡟⣟⣿⢟⣟⣿⢻⣛⡿⣻⣻⢟⣟⢿⣛⣿⣿⣿⣿⣿⣛⣿⢟⣟⣿⣻⡻⣟⢿⣻⡟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣟⣶⣽⣜⣟⣿⣺⣚⣯⣻⣳⣜⣟⣼⣛⣟⣿⣿⣿⣿⣛⣿⣜⣟⣷⣻⣣⣟⣿⣹⣟⣶⣽⣿⣿⣿⣿⣿⣿⣽⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⣀⣴⣿⣦⣀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⢠⡶⣶⣦⠀⠀⠀⢠⡶⢷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡍⠉⠉⣱⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣆⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢠⠏⠀⠀⢀⣤⣴⣶⣤⣄
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣁⠀⠀⠀⠀⠁⠀⠁⠀⠉
⠀⠀⠸⠛⠛⠿⠀⠀⠀⠸⠛⠛⠛⠂⠀⠀⢰⠟⠛⠿⡆⠀⠀⠸⠛⠛⠛⠇⠀⠀⠀⠾⠛⠻⠇⠀⠀⠀⠟⠛⠛⠻⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡀⠀⠊⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⣀⢄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠀⠶⠾⠶⠾⠶⠄⠀⠸⠿⠗⠀⠀⠀⠀⠘⠿⠷⠂⠀⠀⠀⠀⢻⠿⠀⠀⠀⠀⠀⢺⡿⠆
⠀⠀⢀⣴⣶⣦⠀⠀⠀⢀⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⡀
⠀⠀⣌⠁⠈⢉⡀⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⡈⢂⢠⣌⡀⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⡄⠀⡀⠀⢰⣮⣷⣠⠤⣄⠀⠀⣴⣵⣄⣤
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠘⠋⠉
⠀⠀⠰⠿⠿⠷⠀⠀⠀⠰⠿⠛⠷⠄⠀⠀⢠⠾⠻⠿⠆⠀⠀⠰⠿⠿⠿⠄⠀⠀⠀⠾⠛⠿⠆⠀⠀⠀⠴⠶⠿⠦⠀⠀⠀⠠⠀⠠⠤⠄⠀⠀⠰⠿⠟⠿⠆
⠀⠀⣦⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠦
⠀⠀⠀⠀⠰⠶⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⢦⣤⣤⡆⠀⠀⠀⢀⣀⣀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢀⣤⣤⡀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠛⠉⠛⠛⠀⠀⠀⠘⠋⠈⠙⠀⠀⠀⢰⠋⠉⠛⠃⠀⠀⠀⠛⠁⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠙⠀⠀⠀⠛⠉⠛⠃⠀⠀⠀⠈⠁⠉⠉⠁
⠀⡀⠷⡄⢀⠞⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠙⠈⠉⠚⠛⠂⠀⠐⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠘⠇⠀⠀⠀⠀⠛⠒⠒⠃⠀⠀⠀⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠛⠢⡀
⠀⠀⠀⠀⠀⢰⠃⠈⠑⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢒⡒⢦⡀⠀⢸⡄
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠛⠿⣶⣶⣮⠿⠋⠁⠀⠘⠛⣪⢭⡤⣡⡾⣀
⠀⠀⠀⠀⠀⢠⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠚⠃⣪⠃⠤⠄⢤⡀
⠀⠀⠀⠀⡰⠇⠀⢀⡀⠉⠑⠒⠲⠤⠤⠒⠒⠋⢁⡀⡀⠀⢠⡄⣀⠁⠠⠿⢨⡿⣿⣲⣤⣀
⠀⠀⠀⡘⠀⠀⠀⠀⠈⠁⠒⠠⢀⠀⠀⢀⠔⡙⡀⢃⠑⡈⠂⠐⠠⢘⠰⢤⡈⠉⠽⣶⠶⠿⠱⠂⠀⣀⠀⡤⠄⠤⢠⡄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⡬⢐⡈⠄⠀⠂⠁⠨⡒⠠⡈⢀⠐⠱⠂⠀⢆⠉⠘⡁⢎⠡⣂⠔⠄⠆⠊⠁⠘⢆
⠀⠀⣠⠒⠒⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣈⠉⠙⠓⠒⠒⠀⠃⠀⠀⠀⠀⠀⠤⢈⣀⡁⠀⠈⠀⠀⢀⣀⠠⡴⠖⡏⠸
⠀⠀⡇⢀⠀⠀⢀⠀⠀⠈⠉⠉⠉⠉⠉⠹⣟⣛⠒⠛⠮⠭⠭⠄⠀⠀⠀⠀⠀⢀⠀⣀⠀⣀⣀⡀⠤⠤⠄⠒⠂⠁⢀⣀⠔
⠀⠀⠈⠢⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠉⠒⠄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠠⣉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠴⠀⠀⠹⣦⡀⠠⠤⠞⠁⠀⠀⠀⠈⠂⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠉⣀⠔⠁⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⠃⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠻⠆⠁⠀⣠⠤⠤⣀⡀⠀⠘⠱⠀⠀⠀⠀⠀⠀⣰⠃⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⠀⠚⢛⠿⠿⠦⠀⠀⠀⠈⠉⠒⠦⠤⣄⣠⣤⠴⠚⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣆⣘⢛⠷⠷⠦⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢺⣄⢀⣙⠛⠛⠑⠀⢀⣠⠔⠒⠀⠉⠉⠁⠤⠤⠤⠤⠤⠤⠤⣴⠞⠁⣠⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢻⡄⢀⣩⠌⠙⠁⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⣁⡤⠚⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠻⣦⡁⠉⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡡⠴⠊⠁⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⢦⠀⢀⠈⠪⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⠵⠚⠉⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠱⡀⠀⠀⠀⠁⢸⠀⠀⠀⢠⠏⠀⠐⠦⣄⠀⠀⠀⠀⢀⡤⣾⠗⠋⠀⠀⠀⣠⠴⠚⠉
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠉⠀⠀⠀⡾⠀⠀⠀⠀⠈⠙⠢⢄⣚⠭⠊⠁⠀⢀⡤⠖⠉
⠀⠀⠀⠀⡀⠐⠦⣄⣀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⠴⠚⠁
⠀⠀⠀⢀⠱⣄⡀⠀⠈⠉⠉⠓⠚⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⠖⠋⠀⢀⡤⠖⠁
⠀⠀⠀⠘⢦⡀⠉⠓⠶⠤⠤⣄⣀⣀⣀⡀⠀⣀⣠⡤⠤⠖⠒⠉⠁⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⣿⣿⣿⣷⣶⣶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣴⣶⣾⣿⣿⡟⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠛⠛⠉⠁
⠀⠂
⠀⡆

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

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⢿⣿⢮⠻⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⡑⠌⠳⡀⠙⡄⢻⣿⠸⠟⣿⣿⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠯⣍⡙⠻⢮⡂⠀⠀⠀⠀⠀⢻⠀⠀⢿⡟⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⡛⠛⠒⠢⠄⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢻⢫⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣛⣫⣭⣭⡥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢣⠞⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣛⡫⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡄⣤⢄⠀⠀⠀⠀⠁⣠⡾⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡠⣀⣤⠔⠂⠀⠀⠀⠀⠀⢸⡏⡟⠻⠜⠧⠘⠋⠀⠀⠀⠀⠐⣉⣴⠿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣾⠟⣉⠀⠀⠀⠀⠀⠀⡄⢠⣶⣶⡇⢸⡇⠀⠀⠀⠀⠀⠠⠔⠋⠉⠚
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡾⠋⢀⠀⠀⠀⠀⠀⠑⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣪⣭
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⡴⢣⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣛⣛⣯⣭
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣣⡧⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠐⠢⠤⣤⣤⣬⣽⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣼⣷⠀⠀⣧⠀⠀⠀⠀⠀⠨⡳⣦⣬⣙⣲⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣿⣿⣴⡄⣿⣧⠘⣄⠈⢦⡐⢌⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⣼⣦⡳⣿⣷⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢃⣴⣿⣷⣾⣿⣷⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⡿⠉⡀⠛⢠⡤⠿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⣦⣣⣤⠒⠀⠀⠀⠀⠉⠉⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣿⣋⣤⠖⠀⢀⠀⠀⠲⢶⣤⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⢀⣽⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠧⠠⠶⠾⢿⣭⣭⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡛⠓
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠻⠿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⡻⣿⣦⡝⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⡿⣯⣍⠉⠉⠀⢠
⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠌⠛⠃⠠⣰⡆
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡟
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⡇⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⢠⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⢸⣿⡇⠀⡰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡸⠋⠁⣆⠀⠈⠀⢰⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣶⣤⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡟
⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠁⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢸⡇
⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⡇⠒⣿⠇⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⣿⣿⠀⠘
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⠀⠀⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠃⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⣿⠀⠀⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠂⠀⠀⠀⠀⠀⠀⠀⣾⠇⢠⣿⡇⠀⠀⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣾⣿⠃⠀⠀⢃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⢠⣿⡏⠀⠀⠀⣼⣿⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⣼⡿⠁⠄⠀⢠⣾⣿
⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⣿⠁⠀⠀⢀⣾⣿⡇⠀⠀⠆
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⣼⢟⣿⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠜⢁⣾⠋⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣰⡿⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⣶⡾⠋⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢀⣾⡿⠋⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠀⣤⡴⠟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠀⠀⠀⠀⠁⠀⡀⠀⠀⠛⠁
⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠒⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠁⠀⠀⠀⠀⢰⠇
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⣀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠒⠐⠲⡄
⠞⠃⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡿
⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢄⠀⠀⠀⠀⠀⡄⠀⡇⢀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠈⢷⠀⠀⠀⢰⡿⣄⠐⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⠜⠀⠀⠀⠈⡧⢈⠑⢄⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣧⠀⠀⠀⠀⠀⠘⢖⠁⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠈⢸⠀⡼⠀⠀⠀⠀⠀⠑⣤⠂⢀⠙⣆⠀⠀⠀⢀⠞⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⢀⠨⣸⠀⢇⠳⡀⢤⣀⠀⠀⠈⢢⠀⢐⡘⡆⠀⢠⢁⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠍⡂⠑⠄⢳⠀⠀⠁⠺⠌⡮⠳⡄⠀⢸⠂⡁⠁⢵⠀⠘⣡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡇⠀⠘⢄⠈⠢⡀⠀⠀⢠⠇⠂⣻⢠⠏⠀⠇⠠⡍⠀⢰⢻⡀
⠀⠀⠀⠀⠀⢯⠢⣄⡀⠀⠀⢳⠅⠘⡀⠑⢄⠙⣆⣠⠋⣠⠀⠿⠉⡠⠁⠂⢠⠃⠀⡼⠐⣇
⠀⠀⠀⠀⠀⠈⠢⡀⠙⡄⠀⠀⠱⡄⠑⡀⠀⠳⡈⠃⡐⠀⡄⢀⠎⠀⡐⢠⠏⢀⣴⠇⠀⢻⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠰⣤⣅⡚⠀⠀⠀⠘⣦⠐⡀⠀⠱⡐⠀⠀⡖⠁⠀⡐⢠⣮⡴⠛⢁⡀⠀⣼⠀⠀⢀⠜⣹
⠀⠀⠀⠀⠀⠀⠀⠈⠑⡌⠓⢤⠀⠀⢸⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⠛⣀⠄⠒⡉⠀⣴⠏⠀⢐⡡⠞⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢠⡀⢳⡀⢸⠁⡀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠊⠀⢀⠎⢀⡤⠁⠀⠀⢈⠔⢫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⡄⢷⠟⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡘⠀⡜⢁⣴⠏⡴⠉⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠐⠀⢠⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠘⣵⠯⢹⢰⠃⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⠃⢦⢘⠟⡌⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠈⢦⡰⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⠀⠀⠀⣀⣀⠀⠠⠌⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠡⠐⠈⠐⠠⠀⠠⠀⠤⠂⠄⠂⠀⠠⠀⠠⠤⠆⠑⠀⠀⠁⠒⠒⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⠴⠊⠉⠉⠙⠲⣄⠀⡠⠖⠋⠉⠓⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀⠚⠁⠀⠀⠀⠀⢀⣀⣈⣁⡀⠀⠀⠀⠀⠀⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠑⠮⡳⡍⠙⢒⣒⠂⠭⡀⠰⠤⢍⡓⠦⣄⣀⣠⢇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠡⣄⣀⡀⠩⢭⣉⡒⢬⠉⠙⠚⠀⠀⠀⠈⠑⠦⣄⡐⣡⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠉⠈⠳⠝⠆⠈⠓⠮⠷⢑⢦⣉⣉⣠⠴⠒⠒⠲⢤⣀⠀⠀⢀⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣐⡺⠦⣙⡌⠙⠿⠭⠷⢀⣠⠖⠉⠀⠀⠁⠀⠀⣠⠴⠒⣁⡬⠁⡴⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠨⢤⣀⡀⠉⠙⠒⠿⠆⣀⣠⠔⢋⠀⠀⠀⠀⠀⣀⡴⠊⠁⣠⣾⠁⠀⡾⠀⠀⢀⡤⠂⢰
⠀⠀⠀⠀⠀⢀⡤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠋⠁⠀⢄⠀⠉⠓⠦⠤⠮⠥⠴⠖⠛⠉⠀⠀⣼⣡⡤⠖⠋⠀⠀⢸⡇
⠀⠀⠀⠀⡴⠋⠀⠤⢤⣤⣤⠤⠤⠤⠖⠒⠒⠲⠤⣄⣀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢈⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠇⠀⠀⠀⠀⣀⡤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠁
⠀⠀⠀⠸⣄⠀⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠈⠓⠲⠌⠳⢭⣉⠛⠓⠒⠒⠒⠒⠖⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⠀⠀⣀⣠⡤⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠤⠶⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⠀⣠⣴⣶⣶⣶⣦⣄⣰⣾⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣾⢿⣿⣿⠟⠋⠉⠁⠉⢹⢠⣿⡟⠛⠛⠛⠛⢻⣿⣿⣿⡿⠹⠟⠻⣿⡎
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⡏⠹⡄⣀⣒⢀⡐⠢⡌⡝⣇⣀⠤⠀⣠⣰⣿⠻⣇⣰⠆⠠⠆⣿⢅
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠹⣦⡇⠀⠀⠀⠀⢸⠑⢤⡈⠀⠀⠀⠀⢸⣿⣦⡌⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢨⠱⣄⡀⠀⢀⠎⠀⢸⠳⣄⠀⠀⢀⢞⣴⢻⡣⣄⠀⢀⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⡁⠀⠀⠉⠉⡷⢤⣴⠚⣄⠀⠉⠉⡷⠾⣜⢄⠑⢄⡀⠏⡰⢳⣄
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⢷⡌⠓⠒⠒⠋⠀⠸⣿⠑⣌⠙⠒⠋⠀⠀⠀⠑⡄⢀⠉⠀⠑⠁⠀⠑⡄
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠸⣿⣄⣀⣤⣤⣤⣤⣿⡇⠘⡄⠀⠀⠀⠀⠀⠀⠸⡜⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠘⠶⠶⠶⠶⠶⠛⠟⠛⠛⠛⠛⠛⠛⠳⠶⠷⠶⠶⠶⠶⠶⠾⠶⠷⠶⠾⠶⠶⠶⠶⠶⠃





⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣟⣿⣿⣿⣟⣿⣿⣟

⢿⣿⣷⣦⣀⠉⠪⡳⣤⡈⠳⣕⢄⠙⢿⣧⡀⠳⡱⡱⠱⢱⡱⢻⡀⠀⠇⡇⠘⡇⠀⢸⠀⠸⠈⢀⡟⢌⣎⠎⢎⢎⠞⢀⣼⡽⡿⡫⣪⠞⢁⣴⢞⠕⠋⣀⣴⣾⡿
⣄⡀⠉⠙⠿⣗⣤⡀⠙⠝⢦⡈⠢⡑⢀⠙⣟⣄⠑⠄⠀⠁⠳⠈⢇⠀⢠⢻⠀⡇⠀⠘⠀⡆⠀⣸⠁⠜⠈⠀⠠⠊⡠⣻⠫⠊⠈⠜⢁⡴⠫⠃⢁⣤⣺⠿⠋⣁⣴
⢈⠙⠳⢤⣀⠈⠙⠪⣖⠀⠀⠙⠲⣄⠀⠀⠈⠻⡢⡈⠀⠀⠀⠁⠘⡀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠃⠘⠀⠀⠀⢁⢔⠝⠁⠀⠀⣠⠴⠋⠀⠠⣲⠕⠋⠁⣀⣬⣾⡿
⢄⡀⠀⠀⠈⠛⠦⣄⡀⠉⠂⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠐⠈⠀⡠⠔⠪⠛⠋⠁⢀
⣦⣌⣉⠂⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⣈⣥
⠀⠀⠉⠙⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠉⣁⣠
⠷⠶⢶⣤⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⣚⣋⡭⠥
⣉⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠈⠁⠀⠀⢀⣀
⠓⠶⠶⠭⠥⠄⠂⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠉⠁
⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤
⠶⠶⢶⣒⡒⠬⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⣀
⠉⠉⠀⠀⠀⢀⡀⠀⣀⣀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉
⣶⣖⣾⣿⡯⠷⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶
⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢄⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠋⠁⠀⠀⢀⡤⠖⠋⠀⡀⠄⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀⠀⠀⠢⢄⠀⠀⠂⢄⡀⢀
⢁⣠⣴⡚⠉⢀⣠⢖⠏⠂⠀⣠⠖⠋⠀⠀⢀⣴⠕⠀⠀⠀⠀⡄⢠⠁⠀⢸⠀⠀⠀⠀⡃⠀⠈⡄⢁⠀⠀⠀⠀⠨⣦⡀⠀⠈⠻⣶⣄⠀⠀⠹⡲⣄⡀⠈⢓⠯⣷
⡿⠟⢉⣠⣶⡯⠛⢁⢠⣪⠞⢁⠔⡡⠀⣰⡻⠫⡢⠂⠀⠀⡼⢀⡏⠀⠐⣼⡄⡇⠀⢠⣇⠂⠀⢹⡀⢣⠀⠀⠀⢔⠝⣽⣕⢄⠈⢮⡫⣷⣕⡄⡈⠛⢽⣶⣤⡉⠻
⣤⣾⡿⠟⠉⣠⢔⡵⠛⢁⡴⡻⠊⣠⣾⡟⡕⡵⡱⠀⠀⡼⡱⣼⠁⡀⡆⡇⣿⡇⠀⢸⢸⢰⢀⠈⣧⢎⢧⣆⢆⠈⢮⢪⢻⣷⣷⣄⠙⢮⡻⣟⢮⡢⣄⠉⠻⢿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢰⣮⡥⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢖⡎⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣳⡚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡮⠭⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠭⠭⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣭⣭⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠩⠭⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠔⣛⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠬⠽⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠒⣎⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠭⣟⡉

⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣼⣷⣭⣿⣷⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠙⢿⣶⣄⣀⣀⠀⣠⣾⡿⠋⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠟⠁⠀⠀⠀⢀⣼⣿⣆
⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠹⣿⡄
⠀⠀⠀⠀⢀⣾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡀
⠀⠀⠀⠀⣾⡟⠈⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠹⣿⣄
⠀⠀⠀⠀⠹⣷⣄⠀⠀⠈⠉⠛⠻⠿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⢿⣧⡀
⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣶⣦⣤⣀⡀⠀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣶⣤⣀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⡉⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣬⣙⠻⢿⣶⣤⣤⣀⣀⠀⠀⠀⢀⣀⣤⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣶⣭⣽⣻⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡺⠉⠩⢕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠀⠀⠀⠈⣆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠾⠳⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⣀⣠⡤⠶⠖⠛⠉⢁⣀⡤⠤⣄⠀⠘⢧⡀⠘⡜⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡥⠴⠚⠋⠉⢀⡠⠤⠔⠚⠉⠉⠀⠀⠀⠈⢆⠀⠀⠻⣄⠈⠒⠡⠙⠡⢐⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⠋⠁⠀⡤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠙⣆⠀⠀⠀⠀⠀⠙⡜⡄
⠀⠀⠀⠣⡀⠀⠀⠠⠀⠀⠀⠀⠌⠀⠀⣠⠏⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠘⣧⠀⠀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⢀⠎⠀⠀⡴⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡤⠚⠁⣷⠀⠀⠀⠘⣧⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠘⠀⢀⡞⠀⣠⣤⡀⠀⡇⠀⠀⠀⡠⠒⠉⠉⠀⠀⠀⣨⣧⠔⠋⠁⣀⡤⠚⠁⠀⠀⠀⣠⠾⡆⠀⠀⠀⢇⢇
⠀⠀⠀⠀⠀⠀⡀⢀⠊⢀⠄⢀⡞⠀⠀⠀⠈⢻⣤⡷⠤⣄⣀⣟⠶⠶⠶⠶⢒⣫⠕⣃⡤⠖⠋⠁⠀⠀⠀⢀⡤⠚⠁⠀⣿⠀⠀⠀⠈⠢⣕⡂⠤
⠀⠀⠀⠀⠀⠔⠠⠁⠰⠁⢀⡞⡴⠾⣯⠞⠉⠙⣿⢧⣀⣀⣀⣈⣩⠭⠭⠿⠛⠛⠉⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⠀⢀⡠⠟⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢈⠀⠱⠀⠀⠀⡞⠰⡁⢿⡏⠀⣾⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠉⠉⠳⣤⣬⣿⣡⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠑⠒⠒⠲⠦⠤⠤⠤⢤⠶⢶⣶⣖⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⡠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⣠⠃⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣸⠃
⠣⣈⠢⢄⡀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠶⠚⠋⠓⠚⠋⣡⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖⠛⣉⣠⠴⠊⠁
⠀⠀⠑⠢⠬⣙⡒⠲⠦⠤⢤⣤⣤⣤⣤⣤⣤⣬⣿⣿⠥⠤⠶⠒⠚⠋⣉⣁⡤⠴⠖⠋⠉
⣀⣀⣀⣀⣀⣀⣈⣉⣙⣒⣲⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣖⣒⣚⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⣛⢟⣙⠛⣛⢏⣿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⢀⣤⡶⠞⠛⠛⠳⣆⠀⣀⠀⠀⢀⣶⠿⣆⢸⡇⢀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠛⢱⡆⠀⠀⠀⣴⠏⢠⡿⣆⢀⣿⠁⠀⠉⢸⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠟⠛⠻⠶⣄⡀
⠀⠀⠀⣿⣀⣤⣾⣋⠀⣸⡇⣻⣸⡇⠀⠀⠀⢸⡇⠹⣦⡀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⣿⡟⠉⠉⢹⡇⣿⠛⠻⡿⣧⣤⣴⠿⢸⡇⠀⠙⢷⡄⠀⠀⠀⠀⣾⠁⠀⢸⡇⠀⢰⡆⠀⠀⢹⡇
⠀⠀⠀⣿⡇⣀⣴⡟⠁⠿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣤⠀⠁⠀⠈⢡⡀⠀⢸⡟
⠀⠀⠀⢿⠿⠟⠁⠀⣠⣤⣴⡶⠿⣢⡶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣿⡀⠙⢷⣤⣤⠶⠛⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⡀⢰⡟⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⣿⡄⠙⢷⣤⣀⡀⠀⠀⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣧⣠⣼⠟⠀⢀⡀⠀⢀⡶⠶⣦⣻⡇⠀⠀⠉⠙⠛⠛⠛⠛⠉
⠀⠀⠀⠀⣠⣤⣶⣦⡄⠀⢙⣁⠀⠉⡋⠁⣤⢠⡿⢻⣧⣾⠁⠀⢸⣿⣷
⠀⠀⠀⠰⣟⣁⠀⠙⠛⢠⡿⠻⠷⢸⣿⢈⣿⣼⡇⠀⣿⣿⡄⢀⣾⢹⣿⣶⠿⠟
⠀⠀⠀⠀⠙⠛⠛⠷⣦⣼⡃⠀⠀⣠⣿⠛⣿⠸⣧⣴⣿⠈⠻⡿⠃⠀⠉
⠀⠀⠀⠀⣶⣄⣠⣴⠟⠙⣧⣀⣼⠋⢿⡆⢻⡆⠈⠛⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠀⠀⠈⠁⠈



⣏⣈⣏⣽⣟⣯⣿⣹⣽⣻⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠠⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⢠⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡀⡜⠀⠐⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠉⣐⡉⠈⠀⠄⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠂⠀⠀⠀⠀⠀⠂⠀⡉⠃⠀⠐⢀⠀⠴⠁⠀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣯⣤⣬⣉⣁⣂⡐⠀⠀⠤⠿⠽⠛⠂⠴⢂⣄⣀⣀⣐⣷⣃⠟⠀⢀⣀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠉⠙⠋⠙⠉⠉⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⡏⢹⡅⢰⡊⠁⣀⣠⣄⡉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂⣒⣚⣻⣿⣽⡂⠨⡂⣼⡠⠊⠁⠀⠀⠹⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣚⣋⡭⠭⣖⠀⠆⣼⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠈⠥⠀⢒⣒⣛⡭⠅⢘⠁⡇⠀⠀⠀⠀⢀⠜⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠍⠩⠭⠵⣖⣒⠀⠐⠀⡇⢀⠠⠤⠒⠉⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⣨⡭⠭⠽⣒⠈⠥⢠⡗⢀⣠⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡀⣒⣺⠭⠭⠗⢀⠅⡼⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢂⣴⣾⣿⡟⠡⣡⠞
⠀⠀⠀⢀⣀⡠⠤⠤⣶⠒⠒⠒⢒⣈⣹⣦⣅⡀⠀⠀⠐⠄⠶⠀⢶⣾⣿⡟⣇⣡⣾⣿⣿⣿⣖⠒⠶⠶⠦⢤⣄⣀⡀
⠀⠀⣞⢉⢀⡀⠀⠠⡂⠀⠀⠀⠀⢄⠀⠉⠫⢉⣀⣀⠀⠀⠘⡛⢫⣭⣭⣍⣭⠽⠋⣀⠄⠈⡉⠉⠉⢓⡦⠀⣀⠙⡯⣷
⠀⠀⠈⠓⠿⣟⣒⠶⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣅⣉⣀⣀⣴⣶⣶⣦⣤⡤⠬⠴⠖⣚⣫⠽⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠦⠤⣤⣤⣤⣤⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣤⣤⣤⠤⠴⠶⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣵⣯⡜⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣄⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡿⠀⠃⣹⣶⣦⢀⡀⠀⠄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⣡⣿⡿⠁⠀⠀⡆⣾⣿⣿⡄⠙⢷⣶⣦⣌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣂⣩⢤⣴⣾⣿⠟⠁⠀⠀⡰⢰⣿⣿⣿⠁⠀⢸⣿⡿⠿⠖⠓⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⡤⢖⡟⠉⠉⠀⠀⠀⠀⠰⣁⣿⣿⣿⠃⠀⠀⣼⣏⠀⠀⠀⠀⠀⠠⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡵⣸⢡⣺⠃⠀⠀⠀⠀⠀⢰⣱⣿⣿⡟⠁⠀⢀⣼⢟⡼⠄⡒⢖⣺⣻⡃⠒⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢛⣷⢨⢬⡕⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⢀⣤⣿⠟⠘⡶⠜⡵⢃⢋⡹⣷⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⢠⠇⠨⣽⡁⠀⠀⠀⠀⠀⠀⢠⠟⠀⢀⣴⡟⠋⡏⡆⠀⢈⡼⡇⢸⠤⠶⢿⣧⠰⠦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡧⢋⣴⠥⠶⡆⠀⠀⠀⠀⠀⢠⡟⠀⣴⠟⢿⣘⢦⣙⠿⠋⠈⡿⢡⠷⠒⠀⣛⣿⣷⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⢱⠌⣴⡟⠁⠀⠀⠀⠀⠀⡿⠀⣼⠏⠀⠈⠻⣦⣈⠔⠒⡁⠐⣿⣾⣋⣁⡈⣽⣿⠻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠃⡞⢼⣄⣠⣼⡏⠀⠀⠀⠀⠀⣼⠃⣸⡇⠀⠀⠀⠀⣨⢵⡖⣿⠀⠀⠘⣻⣯⢡⠀⣰⡾⠁⣹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣠⡤⣥⢾⠏⠀⠀⠀⠀⡠⣰⠏⡴⠋⠀⠀⠀⠀⠀⠃⢠⣿⠸⡆⠀⠀⠙⠦⢬⠭⠿⠃⠀⠸⢿⣷⡀
⠀⠀⠀⠀⠀⣠⡾⠋⠘⠋⠙⠛⡁⠄⣠⣴⣀⣴⣵⢋⡼⠃⠀⠀⠀⠀⠀⠐⢸⣿⣿⠀⣷⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⡠⢊⣴⣾⣿⣿⣿⢟⣵⠟⣀⠤⠒⠀⠀⠀⠀⠀⠉⢻⣿⡆⣿⣿⣿⣷⣕⢄⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⢰⣯⠣⠀⠠⠄⣪⣾⣿⣿⣿⡿⣋⡵⠟⢛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡘⣿⣿⣿⣿⣷⣥⣆⡄⠀⣀⣴⣿⣿⠆
⠀⠀⠀⠈⢿⣿⣶⣾⣿⣿⣿⣿⣫⣷⣏⣽⣶⠎⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠉⠹⢻⣶⣿⣿⣷⠾⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣭⣛⠛⣻⣟⣿⣿⣯⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⢽⣟⡛⣛⣛⡻⣻⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⠿⠛⠻⢿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⢿⣯⣭⣍⡓⣆⣹⣆⡳⠞⣻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠿⢤⣄⡐⣦⡈⣿⣿⣧⣍⡉⢽⣿⣗⠨⠉⠛⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⢯⣙⡛⠶⠈⣷⣾⢷⣤⡁⠺⣿⡿⢂⣹⣿⢿⡟⣟⣋⣿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣐⠃⣬⣉⣟⠚⢷⣄⠐⢿⣟⣛⣃⣼⣿⡿⡇⣌⣳⣥⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡟⠻⣿⣿⣷⣬⡉⠻⣷⣄⣹⢳⣶⣼⠿⡏⢻⣎⣃⣿⣾⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣦⡈⢿⣿⡿⢻⡦⢼⣏⣽⡟⣭⣿⣷⣙⣦⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⢹⣿⠘⣷⣾⣿⣿⡛⣛⣸⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣦⣥⣾⣿⡹⠎⣧⣴⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣙⣢⣷⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣠⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠁⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⣀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣻⣿⣿⣿⣿⠀⠀⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⢹⣿⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡿⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣵⡅⠀⢠⡀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢀⣿⣧⣀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣮⣻⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡠⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⣿⣿⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣷⢿⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣽⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⣧⡈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣷⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠁⠀⢀⡙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣝⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠋⢺⣯⣿⡉⠀⠀⠀⠀⠀⢁
⠀⠀⠀⣠⠊⣠⢈⣵⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢾⣿⣿⣷⡄⢢⡀⠀⠀⠘⡄
⠀⢀⡜⠁⠀⠀⠜⠁⢀⠈⠉⠙⠓⠒⠲⠒⠒⠒⠦⣀⠀⠀⢨⠀⠀⠈⢻⣿⡿⠹⣦⡙⣦⣄⣀⣿
⢠⠋⠀⣤⣸⣶⠾⠿⠿⠿⠿⢿⣷⣶⣶⣤⣀⣤⣀⠈⠹⠶⠌⠀⠄⠀⣸⡿⠁⠀⠘⢷⣌⠛⠻⣿⣇
⣆⡼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣶⡶⠟⠃⢀⣴⣿⠃⠀⠀⠀⠘⣟⢦⠀⠘⣿
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣶⣿⡿⠃⠀⠀⠀⠀⠀⢸⡆⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⠦⠤⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣶⠞⠇⠙⠳⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠶⢦⣄⣀⠀⢀⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣤⣬⣭⣭⣄⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢀⡄⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣴⠏⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢿⣆⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠈⢿⣦⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢻⣇⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⠏⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⠋⠀⠀⠤⠤⠫⠤⠀⠀⠀⢉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢂⣉⣩⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣌⣉⣁⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⡷⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⢸⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡠⠊⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠐⠉⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠡⠤⠤⣔⣂⠁
⠀⠀⠀⠀⡤⠒⠊⠉⣁⣤⣴⣶⣶⣾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣶⣶⣶⣦⣤⣈⠉⠑⠒⢤
⠀⠀⠀⠀⠑⠢⠤⣀⣉⠛⠻⠿⠿⢿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⣉⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⢖⡐⠒⠀⠤⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠄⠀⠒⢂⡲⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠒⠂⠀⠀⠀⠀⠒⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⣠⢤⡄⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠀⢹⡷⣿⡀⣿⣤⣿⢼⣇⣿⡆⣼⠃⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣆⣹⣦⣾⠸⢗⣙⣥⠬⠭⠥⢬⣟⣋⠸⢿⣶⠀⠉⢠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⠇⢉⡥⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⢿⣿⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡞⢿⠛⡗⠒⠒⢶⣤⣤⡴⠒⠶⠻⡿⠛⢳⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⢰⡎⠀⡇⣶⠰⣾⠋⢻⡇⢸⡇⡆⢻⠈⢼⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠘⡀⢠⡀⠁⣿⢀⠋⠀⠀⢣⣸⡇⠁⡘⢸⡈⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⠙⠛⠚⠋⠁⠀⠀⠀⠀⠉⠙⠚⠓⠉⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡎⢣⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⢀⠋⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠑⢴⡀⢣⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⠎⢰⡴⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⡠⢂⠁⠳⡀⠳⣤⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⡰⠓⢐⠭⡰⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣢⠗⠯⠀⠀⣱⡀⠀⠉⠛⠒⠲⠒⠚⠋⠁⠀⢰⠁⠀⢈⠗⢮⣊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣔⢦⡚⠁⠙⠲⠦⣤⣀⣀⣀⣠⡤⠴⠚⠉⠑⢤⣖⣐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⢸⡟⢸⡇⢶⣦⣰⣶⠠⣶⣄⣾⡇⢻⡟⠻⠘⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣿⣸⣧⣸⡇⣼⡿⢟⣿⠀⣿⢻⢹⡇⣸⣟⣡⢀⣿⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠈⠻⠿⠃⠿⠇⠸⠿⠸⠿⠀⠺⠗⠿⠿⠿⠸⠿⠸⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⡤⣒⣢⠐⠆⣶⣰⠀⠀⠆⣶⡆⢰⠀⣶⡀⠀⣲⡐⡤⢐⢂⠀⠀⢰⠆⢦⡤⢒⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠁⠐⠂⠤⠀⠤⠊⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠐⠒⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡈⠠⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠄⠀⠐⠃⠀⠀⠀⠀⠀⠀⣠⠞⢁⠴⠁⠀⠀⠈⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⡀⡄⠀⠠⠁⠀⠀⠀⠀⠀⢀⠜⡁⠀⠁⡄⠀⠁⠀⢁⠀⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⢅⠀⠠⠠⠀⠥⠀⠀⠀⠀⠀⡴⠁⢀⠀⠀⠀⠠⡀⠀⢀⠈⢀⠢⠤⡀
⠀⠀⠀⠀⠀⠀⡀⠆⢈⣠⠀⠀⡹⠀⠀⠀⠀⢠⠎⢀⠔⠁⠀⠀⠀⠀⠰⠄⠀⠄⠈⣀⠲⠦
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⡰⠀⠀⠀⢀⡔⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠲⠆
⠀⠀⠀⠐⠚⠀⠀⠒⠠⢐⡀⠀⠀⡠⠔⠉⠀⡼⠁⠀⣄⠁⠢⡀⠀⠀⠀⠚⠂⠰⣢⡶⠾⠶⠾⣟⢦⡀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠵⠒⠉⠀⠀⢀⠜⠀⠀⠀⠈⠉⠐⠈⢢⡀⠀⠀⠓⢨⡥⠴⠶⠶⠶⠶⠿⠷⢦⠄
⠀⠈⠒⠄⠠⠄⠒⠊⠉⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠒⠠⠴⠁⠀⠀⠠⠤⠤⠀⠒⠈⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠂⠒⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠂⠁

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆
⠀⠀⢿⣿⣤⣀⣄⣀⠀⠀⠀⠀⢙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄
⢠⣄⠀⣿⣿⣿⡉⠙⢳⣀⠘⢧⣸⣿⣿⡿⡇⠀⠀⠀⠀⠙⢇⣿⣿⣿⡇⠹⡆⠀⠀⠀⠀⠰⢦⣀⣿⣿⣿⢻⡄
⠀⠈⠛⠋⠙⣿⣷⡀⠀⠙⠁⠀⠛⣻⣿⣷⠇⠀⠀⠀⠀⠀⠈⢛⣹⣿⣷⠀⠙⠃⠀⠀⠀⠀⠀⠙⠋⣻⣿⡇⠻
⠀⠀⢀⣤⣶⣿⣿⡇⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠃⡀
⠀⠀⠙⠿⠿⢦⣿⣧⡀⠀⠀⠈⠛⠛⢻⣿⡆⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⠻⣇
⠀⠀⠀⠀⠀⠀⠹⠋⠻⣄⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡁
⠀⠀⠀⠀⠀⣤⣄⠀⠀⣽⠟⠀⠀⠀⠀⠀⠀⢸⡿⠂⠀⣾⣷⠀⠀⠀⠀⢨⣿⠆⠀⠀⣶⣶⠀⠀⠀⠀⠀⢈⣷
⠀⠀⠀⢰⡄⣿⣿⣤⣴⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣽⣿⣿⠶⣄⠀⠀⠀⢀⣄⠀⣽⣿⣶⣶⣤⡄⠀⠉⠉
⠀⠀⠀⠘⣷⢿⣿⣿⡇⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⠀⠘⠓⠀⠀⠀⠹⣴⢿⣿⣿⠀⠈⢳⡀
⠀⠀⠀⠀⠉⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣥⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⡇⠀⠈⠛
⠀⠀⠀⢰⣾⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠛⠛⣿⣿⡀⠀⠀⠀⠀⢺⣿⠛⠿⣿⣇
⠀⠀⠀⠀⢿⡀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠻⣷⣄⠀⠀⠀⠀⠙⢧⣀⠙⢿⣄
⠀⠀⠀⢀⣼⣧⠀⣠⣤⡀⠉⠳⣶⠄⠀⠀⠀⠀⠀⠰⠾⠛⠀⠀⠀⠈⠙⢷⣄⣀⠀⠠⡿⢋⣀⡀⠙⢷⣄⡀
⠀⠀⠀⠈⠉⠀⠀⠸⣿⣆⠀⠀⠙⠁⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢿⣿⣁⡀⠸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠰⡆⣾⣿⣿⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠁⠀⠀⠀⠀⠀⠈⠻⠾⣿⣿⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠐⠷⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⣿⣇⢀⣀⣴⣷⢦⠀⣴⣿⠿⢿⣿⠀⠀⠀⢀⡀⠀⠀⠀⣿⡏⠉⠉⢿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠹⠿⠟⠋⠀⠀⠀⢠⡿⠀⠀⠀⠻⠟⠛⠛⠛⢷⠀⠀⢀⣿⠀⠀⠀⠀⠙⠿⣦⣄
⠀⠀⠀⠀⢀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣄⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠊⠁⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⣀⣀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠑⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠔⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀
⠀⠀⠀⡀⠹⣿⣿⣄⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⡟⠀⣶⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡏
⠀⠀⠀⢻⡀⣾⣿⣿⣿⣿⠉⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣿⣦⣹⡄⠀⠀⠀⠀⠀⢸⣶⠉⣿⣿⣦⣀
⠀⠀⠀⠘⣿⡟⠹⣿⣿⣿⡇⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⠙⠿⡷⠀⠀⠀⠀⠀⠀⢹⣦⣿⣿⡿⠻⣷⡀
⠀⠀⠀⠀⠈⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⢹⡇
⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣦⠘⠃
⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠛⠻⣿⡿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⠿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⢰⣿⠁⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠈⠛⢿⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠿⣆⣀⠀⠀⠀⢀⣀⣠⣾⠿⠛⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⢷⣶⣦⡀
⠀⠀⠀⠀⠀⠰⠾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠘⠋




⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⡀⢘⣿⣿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣷⣄⢹⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣿⣿⣶⣦⣄⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠛⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠋⠹⣿⣿⣿⣿⠛⢿⣿⡄⠀⠀⠀⠀⠀⠘⢷⠀⣾⣿⣿⣿⡏⠙⠛⣷⡀
⠀⠀⠀⠐⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⣿⣿⣿⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠙⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠙⠁⠀⠀⠀⠀⠀⠀⣼⠷⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣷
⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠐⢿⣿⣿⡛⠻⣿⣿⣆
⠀⠀⠀⠻⣿⣿⣧⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠀⠀⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣼⡿⣿⣦⡀
⠀⠀⠀⠀⠀⠙⢿⣧⡀⠙⠿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠈⠛⢿⣦⣄⠀⠀⠀⠀⠀⢰⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠒⢦⠀⣠⢫⠖⢆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⣳⣧⣤⣜⣠⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠶⢶⣦⢾⠓⠛⠛⠛⠋⠁⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠿⠿⢖⡚⡏⠀⠀⢀⣄⠀⠀⢀⡜⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠷⢶⣻⠁⠀⡴⠁⡨⢃⡴⢋⠜⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣛⡛⠛⠿⣞⡿⠀⡜⢀⠎⡴⢉⠔⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣛⣛⡛⢷⣻⠃⡸⢁⠎⡜⡰⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠒⢫⠟⠁⢰⠁⡜⡸⣰⡟⠀⣀⠄⢀⡤⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣠⠃⠀⠀⠀⠙⡰⣱⢳⠑⣊⠵⢊⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠕⠀⠀⢀⡔⠁⠀⠀⠀⢀⠔⡱⢃⠇⣫⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⢀⠎⠀⠀⣀⡤⢒⡥⠊⡠⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡭⣑⣒⣚⣒⡈⠭⠔⢊⡡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣶⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣈⠻⣦⣄⣀⣀⣀⣠⠴⣫⣾⣿⡿⣫⣿⣿⣇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡿⢛⣿⢋⣽⣿⣿⣿⣿⡉⠛⠷⣮⣷⣯⣭⣭⣴⣾⣿⡿⢋⡼⢵⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⢋⣴⣿⣷⣯⡟⣿⡿⣿⣿⡇⣷⣦⣄⣉⠛⠛⠛⠛⢛⣉⡴⠋⠐⠙⢛⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⠟⢻⡿⢀⡴⣿⣇⠿⣿⡷⠁⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠈⢽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢮⠇⣠⡾⠋⠀⢿⣏⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠙⠛⢁⡴⠊⠙⢳⣦⡀⠀⠙⠉⠈⠻⣦⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⢸⣿⣿⣿
⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠝⣿⣆⣀⣀⣀⣀⣹⣿⣦⠀⠀⠀⣰⢏⣽⣿⣿⡿⢻⣿⣟⣿⣿⣿
⢀⢀⣴⣾⣿⣼⣀⣀⣀⣤⣤⣤⠤⠤⠶⠒⠒⣛⣭⣭⣭⣁⣤⣤⣞⠳⣬⣙⣷⡤⢞⣵⣿⣿⣿⣿⠇⡿⣿⣿⣿⠋
⠘⣾⣿⣟⣟⣭⠭⠽⠀⠀⠀⠀⠀⠀⠀⣠⣺⠟⠛⢉⣿⣛⡿⣿⣿⠷⣌⡻⣷⣾⣿⣿⣿⣿⣿⡿⣸⢃⣼⣿⠉
⢰⣿⣿⣷⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⢰⣷⣏⣀⣴⣯⣿⠟⣷⣏⢿⡷⡄⠉⠻⣿⣿⣿⣿⡿⠟⣱⠇⢸⣿⣿⡇
⠈⠛⠿⢿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⢸⣿⣟⣛⣯⢻⠻⠋⠀⠀⢻⣿⢸⠿⠶⠮⣭⡤⠴⠞⠁⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠛⠛⠻⣽⣾⣯⢽⣿⣿⡟⣀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣾⣿⣾⣿⠇⠉⠛⠶⣤⣀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣉⣉⡉⢻⡅⣴⡇⠀⠀⠀⠀⠈⠙⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠻⠿⣿⣿⠛⢱⡿⣄⡀⠀⠀⠀⠀⠀⣿⣿⢿⣦⡀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠓⠶⣤⣈⣉⣀⡾⠁⠈⠻⣦⡀⠀⠀⠀⣸⣿⣧⢽⣿⣦⣮⣴⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢸⣿⡦⠶⠛⠉⢻⣿⢦⢈⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⣠⣾⢫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⢹⣯⡻⣿⢟⠝⠁
⠀⢀⣾⣿⣿⣌⣂⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣟⢿⣷⣄
⠀⣸⣿⡿⣿⣿⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠟⠋⠀⠀⠁⠙⣯⣧
⠰⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠈⠛⠿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣷⣦⣀⡀
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠄⠔⣀⡠⠤⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠁⣀⡨⢄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠠⠊⠀⢰⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠁⠀⡀⠸⠈⡁⡇⡠⠀⣠⣔⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠃⣀⢵⣄⠀⠃⢞⡈⢉⡽⠠⠔⠁⠀⠉⠉⠉⠉⠉⠁⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⣚⠳⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠈⠉⠀⠒⠤⠄⡀⠀⣀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣼⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⢊⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢑⠃⡠⠃⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⡀⠑⢌⡠⢁⣳⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠁⡀⡈⣿⣛⡠⠊⠁⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣉⠀⠐⠲⠖⠀⠉⠀⣰⢿⡵⡂⢠⠆⠀⠀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠑⣔⠀⠀⠀⠀⢀⡷⢛⡗⢞⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⢄⡀⠅⠋⠘⠤⠊⡶⢯⡶⠛⠹⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠈⠦⣙⣀⢠⠛⢄⠊⢃⠸⢷⠆⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣿⠀⠆⡡⢚⠀⣆⠤⠢⠊⡜⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠢⠀⠠⠔⠂⣡⣂⣤⣤⣾⣽⡾⠷⠔⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠒⠛⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢢⣿⣿⣷⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠏⠘⣿⡉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⢋⠁⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⡀⠴⣤⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠒⠛⠉⠀⠀⠹⡧⠀⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠺⣷⡀⠀⠀⢀⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣧⣄⡀⠀⠀⠘⠦⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢘⡠⠀⣼⣿⣯⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠰⠋⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢰⠐⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠈⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣧⣀⣀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣯⣴⣤⣽⣥⣾⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⢄⣀⠀⠀⠐⢴⡟⠆⠀⠰⣾⠧⠀⢰⢦⠀⡀⢂⠁⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠘⠤⠄⠞⠻⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⢀⠊⡇
⠀⠀⢀⡀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠚⠉⠐⠒⠲⠤⣀⠀⠀⢀⠄⣠⠄
⠀⠀⢸⡅⢸⡁⠀⠀⠀⢸⠀⠒⢒⠢⡀⠀⠀⠀⡠⠺⠷⠶⠀⠀⠀⠀⠀⠀⠐⠛⠺⡗⢦⡀⠐⠁⢀⡀
⢾⠀⢺⠀⢮⢠⠆⠀⠀⠈⠦⠼⠷⠤⡐⠀⢀⠞⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠑⡄⠀⠹⠛⠂
⢻⠀⣻⠄⡿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣷⠶⠸⠀⣰⠀⠀⠀⠸⠿⣆⣸⠀⠀⠀⠸⠀⠠⣤⣄
⣹⠀⢻⠀⠗⣧⠀⠀⠀⠀⠂⢤⣀⠤⠀⢸⠀⠀⠀⠀⡀⠀⢎⡀⢤⠄⣤⡀⠀⠀⠉⠒⠀⠀⠀⡇⠀⠛⠁
⢹⠂⡠⠲⡄⢁⣀⠀⠀⠑⢄⣤⡕⠀⠀⢸⠀⠀⡠⠚⠀⢀⡀⠀⠀⠀⣀⣙⠦⠤⢤⠀⠀⠀⠀⡇⠀⢠⢄
⠈⠁⢈⠟⠓⠚⢤⡠⢦⠀⠀⠀⠀⠀⠀⠈⡆⠀⠁⠈⠣⠤⣀⣀⣀⣀⣀⠤⠜⠃⠄⠀⠀⠀⢠⠃⠀⠲⠄
⠀⢰⡃⠀⢰⡀⠀⢣⠀⠀⠒⠤⣀⣀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠩⢂
⠀⠈⣧⠀⠈⣧⠀⠈⡆⠀⠐⢄⣤⡶⡀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠰⠽⠇
⠀⠀⠸⡆⠀⠺⡏⠀⠸⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⣀⣀⣀⡀⠀⠔⠊⠁⠀⠀⠀⣱⠒⠒⠄
⠀⠀⠀⢻⡀⠀⢻⡆⠀⢣⠀⠀⠀⠀⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠑⠂
⠀⠀⠀⠈⢷⠀⠀⢷⠂⠈⢆⠀⠀⡠⠉⠀⡣⠀⡐⡀⡀⠀⢀⠀⠠⠂⠀⠀⢠⡀⠰⣄⣀⣛⡃⢹⠀⠈
⠀⠀⠀⠀⠘⣇⠀⠘⣧⠀⠘⡄⠂⠀⠀⠉⠀⠀⡧⠁⢣⠀⡷⠷⣧⠀⠸⡿⠂⠃⠀⠀⠀⠀⠙⠈⣄
⠀⠀⠀⠀⠀⢹⡄⠀⢹⣄⠀⢱⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠈⠄⡀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠐⠄⠀⠑
⠀⠀⠀⠀⠀⠀⢷⠀⠸⠿⢇⣀⠇
⣀⣀⣀⣀⣀⣀⣘⣧⣴⣚⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣶⣿⣿⢿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢄⣀⠀⠀⠤⢤⡵⣫⣿⣿⣿⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⢀⣤⠴⠖⠒⠚⠋⣑⠉⠛⣒⣶⣶⣾⣧⣤⣤⣬⡩⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⢟⣋⠁⠀⠀⠀⠉⠉⠛⠛⠉⠙⠓⠦⠀⠠⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡩⠛⠁⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣽⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣟⠁⠛⠿⠃⠀⠀⢠⣶⣿⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢸⡟⡁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠾⠼⣧⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠛⠉⢉⡴⠶⡿⣤⣿⣿⣿⣿⣿⠛⠟⠋⠘⣿⣿⣿⡄⢠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣠⣧⡈⠀⢾⣶⣿⡟⠋⠁⠉⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢀⢸⣿⣿⣿⣾⣶⣬⣕⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣴⡾⠟⠃⢸⡌⢿⣿⡋⠛⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⠁⣀⣀⣤⣾⣟⡲⠭⠛⠓⠦⠙⢿⣟⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⣫⠞⠡⠖⠛⠛⣻⣿⡿⠋⠁⠀⠀⠀⠈⠉⠑⢈⣩⠤⠽⠿⢟⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠠⠶⠛⣛⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⣚⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢞⣀⣠⣤⡶⠟⠋⠀⠀⠀⢀⣀⣀⠤⢀⣠⡤⠶⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⡓⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠤⢤⡶⠋⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠠⣤⣶⡖⠒⣠⠴⠋
⠀⠀⠀⡈⠀⡴⠋
⠀⠀⢰⠃⣞⠁
⣀⣀⣙⣦⣨⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣯⣭⣭⣽⣿⣭⣭⣭⣭⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠁
⢀⣀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⢀⡀
⠀⠈⠙⠲⢤⣀⠀⠀⠀⠠⣄⡉⠲⢄⠙⠢⣄
⢄⡀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠉⠲⢤⡉⠂⠈⠑⢄
⠤⣄⣁⢦⣤⣀⠀⠀⠈⠙⠳⠦⣄⠀⠈⠓⠄⢀⡀
⠀⠀⠀⠉⠓⠛⠙⠒⠦⢄⡀⢀⣈⠙⠻⠿⣶⣤⣉⠲⢄⡀⢀⡀
⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⢄⣀⡈⠉⠒⠢⢄⡉⠛⠷⢦⣈⠐⠉⠢⢄
⠤⠬⢍⣉⡙⠛⠓⠶⠦⠤⣤⣀⡉⠉⠒⠢⠤⠀⠀⠐⢤⣌⡑⠢⠑⠢⢁
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣀
⠉⠉⠉⠉⠉⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⣒
⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠒⠂⠐⠒⠒⠒⠩⠭⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣀⠀⠄
⠤⠤⠤⠶⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⢊⣉⡉⠤⠀⠈⠉⠀⢀⠤⠔⠂
⠔⠒⣒⣀⡀⠄⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠟⠒⠉
⠉⠉⠁⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠁
⠀⣀⡤⠴⠒⣊⡩⠥⠒⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⠔⡀
⠀⣤⡶⠞⠋⠁⠀⠀⠀⠀⠀⣀⡤⠒⠉⢀⡠⠖⣩⠔⠋
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⠐⠊⠁
⠀⠀⢀⡠
⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠇⡟⢳⢼⠋⢸⡏⠁⡟⢻⠀⢸⠂⢸⡇⣿⣸⢸⡋⠱⣏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⡆⡟⠋⢸⡉⢸⡏⠁⣇⣸⠀⢸⡀⢸⡇⡏⣿⢸⡋⢠⣝⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠈⠉⠈⠉⠁⠉⠉⠀⠈⠉⠉⠁⠁⠈⠈⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠐⢃⣯⡀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣓⠠⠶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣂⡿⠉⠛⠋⠀⠀⢀⠀⠀⠄⠀⠀⠐⢶⣿⠿⠃⢾⠤⠀⢀⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣯⠘⣁⠤⠀⣀⠄⠻⣵⠈⣁⠀⡀⠀⠀⠀⠀⣍⠁⠼⡓⠀⢮⣻⡗⢮⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣁⠆⢠⣤⢣⡤⠛⡈⡀⠀⠈⠦⠁⠀⢁⢴⣢⣦⡴⠋⠀⠑⡮⠾⣿⠷⢉⠙⣷⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠴⠋⠉⣦⣟⣽⢆⣖⢫⠜⢣⠚⢁⠠⠀⣈⣠⣾⠋⠁⠀⠁⠀⠀⠘⢷⣌⢷⢩⡍⣿⣿⡿⣇
⠀⠀⠀⠀⠀⢀⣴⡎⢠⣞⣿⣾⣿⣷⣾⣟⣼⡆⠩⠛⠀⠰⣤⢾⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢳⣿⣻⣻⣧⢿⣦
⠀⠀⠀⠀⡠⢛⣿⡗⣨⣿⢟⣷⣿⡽⣧⢿⣯⠋⣄⢔⡪⣡⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣷⣷⣿⣤⣽⣿⣣
⠀⠀⠀⠘⡠⢿⣿⣿⣟⣿⢶⡟⣧⣿⡿⣿⣸⡷⣶⣬⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⣿⣿⣿⣧⣻⠂
⠀⠀⠀⢰⣷⣾⣿⡿⣷⢶⣾⠿⣷⣻⣤⣿⠿⢂⡿⣟⡃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢀⣿⣿⣿⣶⠛⡽⢧⣿⣴⣿⣿⣟⣉⡑⣟⣯⠋⡜⠀⠀⠀⠰⠾⡿⢿⣷⣶⣤⣀⠀⠀⠀⠀⠀⢠⣸⣿⣿⣿⣿⣿⣿⣿⣟
⠀⢀⡾⢿⣿⡋⣰⠟⣽⣿⣿⡟⣡⣿⣿⣿⣾⠋⡁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣭⠋⠛⢻⣷⠄⠀⠀⠀⢸⢴⣿⣿⣿⣿⣿⣿⣿⣎
⠀⠘⠁⣼⣿⠞⣻⣿⠜⠿⣣⣄⣙⠙⠃⣉⣿⣿⠇⠀⠀⠀⠀⠀⠐⠿⣭⣭⣍⡻⢶⣇⡂⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣸⢹⣏⣻⣭⣶⡇⡘⠹⡟⠿⠿⠿⠟⠗⠀⠀⠀⠀⠀⠀⢀⣤⣀⠘⣿⣿⡿⠳⡟⡓⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⣯⣽⣡⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠑⠚⠲⠞⠃⠁⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢣⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠀⠀⣠⣤⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣢⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠉⠠⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢨⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿
⠀⢀⣼⣿⣭⣿⡆⠀⠀⠀⠀⠀⠤⢿⡿⣿⣟⣿⣿⣿⣷⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠚⢹⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⢦⡄⡀⠉⠉⠉⠀⢉⣙⠓⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣰⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⣿⣯⣿⣿⣦⠀⠀⠀⠀⠀⠑⠲⠍⠛⣺⠛⢻⢫⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣭⣿⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⣿⣿⣾⣿⣿⣟⣿⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡎⣧⣿⣿⣿⡿⣛⣿⣿⣿⣿⣣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣻⣮⢻⣶⣌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠘⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡗⢛⣀⠀⠀⠄⠀⠀⠀⠀⠰⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣼⣿⡿⠛⠀⠄⠀⠀⠀⠀⠀⡈⠻⠂⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠠⢰⠆⠀⠀⢶⣆⢠⣦⢠⣤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⢿⣿⣏⡿⢧⡀⢰⡄⣀⢠⡛⣿⠤⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡁⣾⣶⢷⢼⡟⢧⢃⣴⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣴⡟⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣾⣿⣿⣶⣽⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡯⣯⣷⡰⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣿⢿⣿⡟⠋⢉⠏⢻⣿⡿⢿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣍⣹⣽⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠈⠒⠄⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠈⠂⢄⠀⠀⠈⠠⡀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠈⠂⢀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⠄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠶⠒⠒⠈⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡀⠀⠠⠤⠀⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⡀⠤⠐⠊⡡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠔⠀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⣠⠞⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⡠⠖⠉⠀⡠⠂⠀⠀⢀⠞⠁⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢀⡤⠚⠁⠀⢀⠔⠋⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⣿⣷⣶⣾⣾⡿⣾⣶⣶⣾⣿⣾⣾⣶⣶⣶⣶⣿⣶⣾⣷⣶⣾⣶⣶⣿⣶⣷⣾⣷⣿⣶⣶⣶⣾⣿⣶⣾⣷⣶⣶⣶⣾⣷⡷⣷⡾⢾⣾⢷⣶⣷⠾⠶⡿⠶⣷

⠀⠀⠀⠀⠀⢀⣀⣀⣀⢠⠤⠴⠶⢲⡖⠒⠒⠛⡟⠛⠛⠛⡇⠀⢰⡗⠒⠒⠲⡆⠀⠀⢀⣀⣄⣀⡀
⠀⠀⡖⠚⠉⠉⡁⠀⠈⢻⡄⡀⠀⣾⣷⡆⠀⢸⣿⠀⠀⢸⡇⠀⣼⣷⠀⠀⣴⡇⠀⢠⡏⠀⠀⢀⠙⠛⠓
⠀⠀⢷⠀⠀⠸⠟⠀⠠⣾⡿⡟⢤⣿⣿⠇⠀⢸⣿⠀⠀⢸⣧⣤⣿⣿⠀⠀⣿⣀⣠⣿⣧⠀⠀⠙⠿⣄⣀
⠀⠀⢸⠆⠀⢰⣶⡄⠀⢘⣧⠈⠓⠲⢬⡙⢢⣿⡟⠀⠀⠘⠛⠀⢸⡟⠀⠀⠿⠿⠉⢹⠋⠛⢶⣄⡀⠈⠙
⠀⠀⡼⠂⠀⠈⠉⢀⣠⣾⣿⣶⣤⡴⡟⣁⣸⣿⣓⣶⡶⠶⣶⣶⣾⣷⣦⣤⣤⣤⣤⣼⣀⣀⣄⠉⠁
⠀⠀⣧⣶⣶⣿⣿⣿⣿⣿⣿⣿⠃⣤⠙⠛⠋⠾⣿⣏⠀⠀⠀⠉⠛⢿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣶⣶⡾
⠀⠀⠈⢿⣿⣿⣿⣿⡿⢿⡿⠟⠚⣋⡀⠀⠀⠀⣾⣿⣿⣦⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠋
⠀⠀⠀⢠⠏⠀⠀⠠⣵⣾⡘⢁⢏⠈⡹⣠⣴⣾⣿⣿⣿⣿⣇⠀⡗⢀⠇⠀⠀⠀⠀⠀⣀⣿
⠀⠀⣠⠋⠀⣀⣀⡐⣚⣹⣻⣿⣷⣊⣴⣛⣋⣉⣛⢛⣽⣿⣿⣰⣗⡇⠀⠀⠀⠀⣆⠂⠛⠛⣄⠀⢀⢀
⠀⢀⣯⠀⠈⢀⡈⣹⠿⠁⠈⠀⠀⠈⠉⠉⠁⠈⠉⠉⠉⠩⠭⢍⠉⠁⠀⠀⠀⢠⡏⠈⢠⠀⠉⡇
⢠⠎⠀⠀⠀⠠⣾⣷⠀⠀⠠⣄⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⣴⣿⣿⠀⠀⢸⠀⠀⢹
⡏⠀⠀⠀⠀⠀⢸⡿⣦⣀⣠⣾⣿⣿⣷⣶⣄⣤⣄⡀⠀⢀⡤⠋⠑⣒⠒⠻⣿⣿⣤⣶⡏⠀⠀⢺⡀
⠘⣆⠀⠀⠀⣧⢞⣽⣿⣿⠿⠋⠀⠙⠻⣿⣿⣿⠛⠛⢉⡡⠊⠀⠀⠀⠙⠁⣿⢻⣾⠉⠀⠀⠀⢸⠃
⠀⠈⠣⢤⣾⠿⠚⠋⠉⠀⠀⠀⠀⠀⠀⢹⣿⠻⠠⡄⠉⣤⣶⠟⠋⠛⠃⠂⡇⠈⢿⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠐⠄⠠⣴⣶⠿⠋⠳⠃⢹⣧⠴⠚⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣀⣠⣠⣤⣤⣦⣴⢶⡿⢧⠄⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢷⡤⠄⢀⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣤⣶⣶⡶⠶⠶⣤⡀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠐⠋⠹⣇⣀⣿⠀⠀⠀⠙⠂⠀⢸⣿⡀⠀⠀⠀⠀⠚⠉⣯⣀⣸⠇⠀⠈⣿⡃
⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⢻⣦⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⠉⠉⠁⠀⣀⣠⠶⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣽⣿⣽⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⠟⣻⣯⣿⣿⣿⠿⠋⠁⠘⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣴⣿⣿⣿⣿⣟⣿⣿⣿⣾⣧⣼⣿⣿⢿⣟⠻⣿⣯⣹⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠙⣿⡿⣯⣷⣭⡷⣧⣼⣻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣾⣻⡿⣿⣌⣿⣿⡟⢷⣿⣿⠿⣿⣷⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣩⢺⣷⣿⣿⣿⣍⠛⣿⣌⡻⣦⣿⣿⣿⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡓⠿⢿⢻⣿⣏⣿⣿⣾⣿⣷⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣹⢟⣤⢼⣻⡿⠿⢿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣏⣱⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣡⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠾⠿⠿⠿⠿⠶⢶⣶⣤⣀⠀⠀⠀⢈⣱⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣄⣑⣴⣦⣄⣀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢋⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⡿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣥⣼⣤⣶⣷⣾⣿⣷⣶⣾⣶⣤⣤⣀⣀⣀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠛⠹⠋⠀⠀⠀⠇⠘⠓⡀⠈⢳⡌⠙⣿⣷⣦⣤⣶⣶⣿⡿⠏⣿⠉⢭⠛⠃⠀⠀⠙⡿⠋⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠈⣟⢻⣷⠀⠀⠀⠈⠉⠐⠂⠚⠛⠛⠓⠂⠉⠁⠀⢸⣿⡿⠿⠿⣿⣿⠀⠀⠈⠑⠚⠷⠊⠴⠒⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣏⠀⢻⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠸⣿⠀⠸⡆⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢹⡄⠀⣷⠀⠀⠉⠳⢶⣤⣤⣤⣀⣀⣀⣤⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⡶⢿⣿⣿⣿⣿⠿⢀
⠀⠀⠀⠀⠀⠐⠉⠉⣽⣿⢿⣷⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⠛⠳⠖⠛⠛⠛⠛⢉⣵⣶⣾⠄⣿⣿⣇⠀⠀⠙⢦
⠀⠀⠀⡴⠃⠀⠀⢀⡤⠤⠂⠰⠿⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡉⠉⠁⠀⠙⠁⠈⠃⡄⠀⠈⢷⡀
⠀⢀⡞⠁⠀⢀⡴⠃⠀⠀⠀⠀⣀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢀⠀⠤⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡟⠱⢾⣦⡀⠀⠀⠀⣆⠀⠀⢳⡀
⢠⡟⠀⠀⢠⠎⠀⠀⠀⢠⠞⠁⢻⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣴⡄⠹⣷⡄⠀⠀⠸⣄⠀⠈⣷
⢻⡄⠀⣠⡎⠀⠀⠀⣶⡏⠀⣿⣿⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣖⣶⡒⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠻⢿⣷⠀⢻⡄⠀⠀⠀⣻⡄⠀⣿
⠀⠻⣶⠋⠀⠀⠀⠀⣿⣧⡴⠛⠁⠀⢀⣴⣛⠀⠀⠀⠀⠀⠀⠰⢾⣿⣛⡋⠉⠛⠉⣉⣻⣿⠿⠒⠀⠀⠀⠀⠀⠀⣢⣾⣟⣿⡄⠀⠀⠑⣼⡿⢧⠀⠀⣿⣧⡴⠁
⠀⠀⠸⣀⠀⠀⠀⠀⢩⡏⠀⠀⠀⢠⡿⣿⣷⣆⠀⠀⠀⠀⠀⢤⣀⠀⠉⠉⠛⠛⠉⠉⠀⠀⢠⡄⠀⠀⠀⠀⢠⣴⣿⣿⣿⠿⣿⠂⠀⠀⢸⡇⡄⢀⣼⣻⠟⠁
⣀⣠⣤⡿⣆⠀⠀⠀⣾⠁⠀⠀⠀⠘⣷⣻⡿⣿⣿⣏⣀⠀⠀⠸⢛⡷⣶⣤⣤⣄⣀⣤⣴⡾⠛⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠟⢻⠀⠀⠀⠈⣧⣠⣿⡿⠃
⠻⠕⠂⢈⣙⣳⣤⣰⣿⠀⠀⠀⠀⠈⢿⣿⣷⣼⠻⣷⣬⣓⠄⠀⠀⠀⠈⠀⠈⠉⠉⠋⠁⠀⠀⠀⠀⣠⣼⣿⣿⡷⠞⠉⠀⠚⠋⠀⠀⠀⣸⣇⡿⠏
⠴⢢⣷⣿⣿⣿⣿⣿⠿⣦⠀⠀⠀⠀⠈⠋⠉⠛⠿⣧⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟⠁
⣟⣘⣿⣿⣿⣿⣿⣿⣷⣍⠛⢦⣀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣻⣿⣿⣦⣄⣄⣀⣀⣠⣤⣶⣾⡟⢫⡽⠿⠁⠀⠀⠀⠀⠀⠀⣀⣤⠶⢻⣿⡁
⢻⣇⣼⣿⣿⣿⣿⣿⣿⣿⣶⡀⠉⠂⢀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⣿⣿⣿⣿⡿⢹⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣸⣿⣿⣿⣟⡿⢷⣶⣤⣄⡀
⠘⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⣿⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣼⣿⣿⣿⣿⣿⣿⣧⣤⣟⠛⣿⣿⣶
⣽⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⠀⠀⠀⠀⡀⠉⠀⠀⠙⢿⣾⣿⢿⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⡷⣤⣭⡘⣿⡟⣿
⢱⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⣀⠀⠀⠀⠀⠀⠰⠀⢠⠤⠛⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠦⣬⣽⣟⣿⣿
⢻⣷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠂⣁⠀⠀⠀⠀⡤⠒⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢳⣧⣼⣿⣿⣿
⣻⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡐⠆⠈⢭⠄⠂⠀⠆⡭⠅⢸⣇⠀⠀⠀⠀⠀⠀⠆⠀⢁⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣦⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢉⠀⠶⢢⡌⢣⠐⢆⡀⣼⡏⢀⠀⠄⢰⠂⡈⠂⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡛⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠠⠦⠠⡾⠃⠈⠀⠜⠃⣾⡇⡴⣦⢠⡆⣰⠃⣾⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⢀⠀⡀⠀⡄⢰⠆⡴⠺⣿⣦⠀⡄⣨⠃⠘⠀⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⢰⡇⢐⡅⣾⡄⢠⠀⣄⢸⣿⠋⣼⡿⣿⢸⡇⢸⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠙⢶⣤⣤⣀⣀⣠⣤⡴⠞⠛⠉⠛⠛⠶⣤⡀⠀⠀⠀⠀⢀⡀⠤⠋⣢⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⢀⡄⠀⠀⠀⠀⠈⠛⠒⠀⠀⣠⡁⠀⠀⣸
⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⡿⠷⠾⠿⣭⣭⣽⣿⠿⠿⠿⣿⠋
⠀⠀⠀⠀⠈⠛⠶⠶⣦⣤⣤⡶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⣠⣼⠟⠀⡀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡶⠋⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠛⢿⠟⠙⠣⢄⣠⣄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⡰⠃⠀⠀⠀⠀⠀⠈⠙⣷⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⢖⣒⣋⣀⣈⣀⣉⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠒

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣯⠊⢻⣿⣿⣿⠸⠀⡇⢹⢸⣿⣿⣿⠟⠀⢰⢿⣿⣿⠟⣴⡿⣫⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡙⢿⣷⡀⠹⣟⣿⠀⠁⠁⢸⢸⣿⣿⡏⠀⢠⠏⣾⡿⢣⡾⢋⣾⢟⣫⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣆⠙⢿⣄⠙⡞⣇⠀⠀⠀⢸⣿⣿⠀⠀⠈⢠⠋⡴⢋⣵⢟⣵⢟⢽⡯
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣙⢷⣄⠙⢦⡈⠘⠄⠀⠀⠘⢻⠇⠀⠀⠀⠀⠊⡠⢋⠴⠋⠀⠐⠝⣋
⠀⠀⠀⠀⠀⠀⠀⢨⣁⠉⠛⠿⠿⣇⡈⠳⢄⠳⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣬⠷
⠀⠀⠀⠀⠀⠀⠀⠠⣬⣍⣒⠀⠀⠀⠈⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⣁⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠨⡥⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢠⠠⣦⠀⠀⠀⠀⠀⠐⠒⠭⠽⢷⣞⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠶⠶⠶⠤⠀⠀⠀⠀⠈⠟⠋⠙⣈⠀⣡⠀⠀⠀⠀⠀⠀⠨⠭⠽⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠯⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⠸⠟⠟⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠭⣙⡓⠶⠿
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡙⢦⣈⢷⣦⣄⡀⠉⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠐⣋⢀⣠⡶⣀⠔⡀⢀⡴⠁⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠹⣄⠙⢷⣽⣿⣿⣷⣦⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⢟⣭⢞⣵⣞⣵⠟⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠘⣎⣆⠘⢷⣄⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⡷⣛⣵⣿⣿⡿⠃⣴⠃⡼⠀⠀⡿⠀⣾⢠⠀⡄⠀⢹⣞⣧⠈⢻⣷⣌⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡟⢁⣼⣟⣼⢁⡾⢸⡇⣿⣿⢸⠀⣷⢀⢸⣿⣿⣷⡀⡹⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠇⠀⠘⣄⠀⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠎⠀⠀⠀⢸⠠⠘⠈⢣⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⣎⠀⠀⢀⡠⠎⠀⠀⠀⢸⡇⢰
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠏⠀⠀⠰⠀⠀⠀⠀⠀⢸⠃⢸
⠀⠀⠀⠀⣸⡀⠉⠉⠽⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⣠⢞⣹⠛⣠⡶⠖⢀⠀⠀⠀⠀⠀⠀⢀⡎⣰⣿⣦⡀
⠀⢸⣃⠀⠘⢷⡄⠰⠂⠀⠀⠀⠀⠀⠀⠀⣞⣴⣋⣀⣀⡀⢀⣀⣨⠢⣀⣀
⢀⠈⠉⠀⠀⣾⠻⣶⣄⠀⠘⠀⠀⠀⠀⣸⡟⠉⠫⣀⠴⠄⢀⣤⢞⣯⣽⣏⠓⢄
⠇⠀⠀⠀⢠⠔⢂⣽⡈⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⡜⢀⡜⡹⠉⠓⡛⠲⡎⡄⠀⠃
⠀⠀⠀⠀⣠⡽⢈⡁⠙⢷⠀⠀⠀⠀⢀⣟⢧⡀⠄⠀⢀⠼⢆⠀⠂⠈⢳⠀⠶⠒
⠀⠀⠀⢀⣉⠀⣌⢁⠀⠘⠆⠀⠀⠀⠈⡿⢍⡻⢴⡚⠋⠀⠀⢣⠀⠉⠀⢨⠩⢿⣝⣦⣀
⠀⠀⢈⡿⠍⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠙⢦⡀⠀⠀⠑⡄⠉⠀⢋⡉⣙⠿⢿⣵⣦⣄
⠀⠀⣎⠀⠀⠀⠀⢃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠸⡄⠘⠁⠉⠀⠀⠀⠀⠀⠈⠑
⠀⠀⡇⠀⠀⠀⠀⠀⠳⣄⠀⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⡗⠀⠀⢀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢇⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⣀⣀⣀⣠⡤⠔⡪⠝
⠀⠀⠈⠛⣒⣒⠒⢉⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁

⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠆⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠠

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⣂⢆⠀⡀⠀⡠⢄⠀⠀⠀⢀⣀⣤⣶⣴⣶⣇⣀⡀⡀⠀⠀⢀⠤⡰⠶⠒⠓⠳⠴⣔⡀
⠀⠀⡠⠞⠁⢈⢤⣦⣌⠑⢶⠁⠀⢠⣾⡿⠟⠋⡡⠀⢄⠘⡕⢇⠀⠀⢈⠎⠀⡔⠉⠑⣄⣀⡀⠙⢥
⠀⡰⢡⠪⣿⣿⠈⠛⢹⢰⢀⠀⠀⠈⡏⠀⡴⠉⡧⣀⠜⠀⡇⢸⠀⠀⢸⠀⠀⠘⠦⠔⠣⠔⠃⢠⠈⠧⡄
⡤⡇⠠⣀⣈⠜⠑⠊⢡⢎⠜⠀⠀⣏⡇⠳⢕⣊⣀⣀⠤⠊⢀⠎⠀⠀⠈⢆⠀⠀⠀⠀⠢⠤⠤⠂⡰⠓⠁
⠑⠚⢄⠠⠤⠤⠤⢒⠁⠋⠀⠀⠀⠀⠈⠢⢀⢀⣀⣀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠄⢀⠀⣀⠠⠔⠊
⠀⠀⠀⠉⠁⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⡀
⢀⠤⡠⠖⠉⠉⠈⠁⠐⢤⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⠈⠑⢪⡀⠀⠀⠀⠀⢠⣶⠟⠉⠉⠉⡉⠛⢿⠤⡀
⠈⡲⢡⠀⠋⢡⠄⠉⢹⡆⢃⠀⠀⡔⡲⠁⢀⠔⣦⡄⠲⠶⡀⠙⡽⠀⠀⣈⡟⠁⢰⠒⡮⡀⡨⠀⠀⢰⠁
⠀⡇⠸⡀⠁⠁⠑⠒⠉⠀⡼⢢⠀⠈⡇⢀⠫⠕⠂⠁⠄⠸⠃⠀⢸⠀⠈⠓⡆⠰⡀⠉⠀⠀⢀⠆⠀⡸
⠀⢣⠀⠑⠂⠠⠀⠒⠀⡰⠉⠁⠀⠀⢣⠀⠓⠄⡀⠀⠀⡠⠞⢀⠎⠀⠀⠀⢇⠀⠑⠢⠄⠐⠁⠀⡰⠁
⠀⠀⠑⠤⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠠⠄⠂⠁⠀⠀⠀⠀⠈⠢⢀⡀⠀⡀⠠⠊
⠀⠀⠀⠀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣄⣄⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⡠⢄⡰⠋⡡⠀⣀⡀⠀⠉⢢⠀⠀⠀⠀⣀⣼⣿⠟⠛⠛⠛⠻⢿⣯⡄⠀⠀⠀⢀⣴⠎⠏⠿⠸⠉⠛⠑⢦
⠓⡚⠀⡌⠀⠘⠀⣹⠒⡖⡄⢳⢀⠀⠀⣈⡟⢁⡤⢤⣤⢴⣶⡄⠙⡟⡄⢠⣔⠎⠁⡴⠤⢤⠊⠉⢢⠀⠈
⠀⡇⠀⢇⠀⠈⠉⠉⠉⠀⡇⡸⠔⠁⠸⢼⠀⠸⣀⣈⠝⠣⠔⡡⠀⢸⠀⠀⠈⡆⢢⡣⠤⠚⠂⢐⠉⠀⡰
⠀⠰⡀⠈⠢⢀⣀⣀⠠⢚⡴⠁⠀⠀⠀⠘⡄⠀⠀⠤⠤⠤⠊⠁⢠⠃⠀⠀⠀⠣⡀⠉⠒⠒⠒⠉⢀⠔⠁
⠀⠀⠈⠂⠤⠀⠠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⣀⡠⠔⠁⠀⠀⠀⠀⠀⠈⠒⠂⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠠⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⢉⣀⣀⣈⣉⣉⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⢉⣁⣠⣄⣀⣀⣀⡀⢨⣽
⠀⠀⠀⠀⠀⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠹⠟⠙⠿⣿⣿⡟⠉⣹⠿⣿⣿⣟⠛⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⢈⠛⠋⠴⠟⠀⠀⢼⣿⠻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣅⣀⣀⢻⣶⣮⣽⢞⣻⣏⣹⡧⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣤⣦⢤⣀⠀⠀⠀⠻⣾⣥⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢰⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⣸⡥⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣽⣿⣿⣿⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⡞⢩⢿⣿⠟⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⡿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠺⠇⣴⣾⡯⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⣸⣿⠁⠀⠀⠙⠉⠉⠀⠙⢿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣴⣿⣿⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣦⣴⣶⣶⣤⣼⣷⣾⣟⣿⣿⣧⣠⣼⣷⠶⣶⣶⣶⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢉⣉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣴⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠁⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⠤⠀⠄⠀⣀⠀⠀⠀⠀⣀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣟⣁⣀⣤⣤⣤⣤⣠⣀⣀⣀⣀⠈⠀⠒⠿⡞⢷⠺⡶⢷⡼⡴⠄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⠦⣄⡀⣽⣏⣹⣍⣻⣛⣟⣆
⠰⡒⠀⠠⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⡿⠟⠹⡃⠈⣻⣿⣿⣷⡷⠤⢧⡬⣭⢆
⠡⠁⠀⠄⡀⠀⠻⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷⡫⠋⠁⣿⣷⣿⣖⢳⡚⠶⠧⡀
⠀⠢⠀⡐⢀⠀⡀⠙⢧⣈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠟⣹⣾⢟⠕⠀⠚⠻⣿⣿⣿⣿⣿⡘⢓⠓⡄
⠀⠀⠑⠀⠤⣤⣤⠬⠿⠏⠑⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣛⠉⠀⠀⢶⡀⠀⠼⠿⣫⣾⣍⣹⣉⣉⣉⣄
⠀⠀⠀⠀⠀⠀⠙⠷⢤⡀⠀⠀⠀⠀⠐⠂⣠⣤⣤⣾⠿⠿⠟⢛⠯⠟⡫⠙⠁⠐⣹⣯⠽⡆⢷⡤⠵⡤⠭⡤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣶⢶⣶⠾⡿⠉⠉⠀⠀⡀⠤⠤⠒⠈⠀⠀⠀⠀⠀⠀⠚⠻⠿⠛⠛⠛⠛⠒⠛⠛

⣿⣭⣭⣍⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⠿
⣿⣿⣿⣿⣿⣿⠷⠶⠶⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⣶⣶⣶
⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣭⣭⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣽⣯⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿
⣯⣭⣭⣭⣭⣭⣍⣉⣉⣉⣉⣉⡉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉
⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠛⠛⠛⠛⠉⠙⠉⠙⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣐
⣟⡛⠛⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣒⣒⣲⣶⣾
⣿⣿⣿⣛⣛⣒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣻⣿⣿⣿
⣛⣛⣉⣉⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⠿⠿⠿⣿
⣿⣿⣿⣿⣿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶
⣿⣿⣿⣛⣛⣛⣛⣉⡉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣚⣛⣿⣿⣿⣿
⣷⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠛⠛
⣿⣟⣋⣉⣉⣉⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣉⣩⣽⣿⣿
⣿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣩
⣿⣿⣿⡷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶
⣿⣿⣿⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿
⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿
⣿⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠻⠿⠿⠿
⣿⣯⣭⣭⣭⣭⣭⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣬⣭
⣓⣒⣒⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠶⠶⠾⠿
⣿⣿⣿⣛⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣼
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢆⠀⣁⣀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡘⠑⣤⠀⠉⠋⠀⠉⠓⢷⡦⣀⡀⠀⠀⢀⡠⣾⠃⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢲⣆⠀⠸⣃⣠⠴⠒⠋⠁⢄⡀⢄⡀⠈⠒⠭⣍⣉⡭⠞⠁⣀⣠⠤⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠖⠒⠉⡀⠐⢆⣈⡥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⠦⢄⠀⢀⠤⠒⠉⠁⠀⠀⠈⡆
⠀⠀⠀⢠⠴⠒⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠐⠒⠲⠦⠤⠴⠒⠒⠀⠒⠢⣜⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⣀⣀⣀⣀⣀⣠⠤⠤
⠀⠀⠈⣞⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⠠⠤⠤⠐⠒⠒⠚⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠘⠦⣤⡀⠉⠉⠓⠒⠂⠀⠀⠤⠤⠔⠒⠂⠉⠉⠀⠀⠀⠀⠀⢀⣀⡀⠤⠐⠒⠈⠉⠉⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠉⠓⠖⠦⣄⣀⣤⣀⡀⠀⣠⡀⠀⠀⠀⢀⡀⠀⠐⠉⠁⢀⣀⠀⣀⣀⣀⣀⣀⢀⡀⢀⣀⣀⣀⣀⣀⡤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠁⠀⠉⠉⠉⠁⠀⠉⠉⠉⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠉⠙⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠵⠒⠋⠉⠉⠉⠉⠉⠉⠙⠒⢤⠊⠉⠉⠉⠙⠲⡄⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣤⠴⠶⢶⣾⣙⣛⠒⠒⠒⠶⠧⣄⣀⠀⠀⠀⠸⡄⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛⠒⠒⠒⠦⠤⣄⡀⠉⠑⠲⢤⣀⠀⠈⠙⠒⢤⣀⢳⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠈⠙⠲⢤⡀⠀⠈⠙⠢⣄⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡏⢿⡑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⡉⠓⢤⣀⠀⠀⠙⠢⣄⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⡇⠈⢳⡄⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢬⣑⡦⣄⡀⠀⠙⢦⡘⡆
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢸⠃⠀⠀⠙⣦⣀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣶⣤⣼⣿⡄
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣠⠋⠀⠀⠀⡰⠃⠙⠳⣦⣄⣀⠀⠀⠈⠙⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣖⡋⢁⣏⠹⡄
⠀⠀⠀⢀⡼⠁⠀⠀⢀⡔⠁⠀⠀⣀⠞⠁⠀⠀⠀⠀⠉⠛⠯⣖⡲⠤⠤⣀⣀⣀⣉⣉⣙⣒⣒⣲⠶⠶⠚⢋⣩⠥⠾⠟⠋⢁⡼⠁⠘⠦⣀⣠⠤
⠀⢀⡤⠊⠀⠀⣠⠔⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠦⠤⠬⠥⠤⠤⠤⠖⠒⢾⣉⡉⠓⠒⠒⠛⠉⢉⣩⠗
⠐⠫⢤⣤⣖⣋⣁⣠⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⡍⢫⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⡼⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡟⠲⠤⠖⠚⠉
⠀⠀⡰⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⡄
⠀⠀⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢠⠇
⠀⠀⠀⠑⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⡅⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣀⢀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⢤⣤⣈⣓⣒⣒⣒⣋⣤⡤⠤⠖⠒⠉⠁

⠀⠀⠀⠀⣴⣾⣿⣶⡀⠀⠀⢀⣤⣶⣦⣄
⣶⣦⡀⠀⢻⣿⣿⣿⣷⣦⣾⣿⣿⠋⠛⠿⣷⡄
⠘⢿⣷⡀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣧⣄⠀⠈⢿⣿⣶⡆
⠀⠀⠙⢿⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠉⠁
⠀⠀⠀⠀⠙⠿⠿⠋⠁⠙⠻⢿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠋⠉⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣾⣿⣷⣄⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣻⠟⠁
⠀⠀⠀⠀⠀⠀⣠⠊⣡⠔⠁
⠀⠀⠀⠀⡠⠊⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⣠⠊⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⠛⠛⠉⠙⠛⠓⠦⡀
⡠⠊⣙⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣤⡿⠻⣦⣀⣤⣶⣶⣶⣶⣶⣾⣆
⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣩⣿⣿⣿⣶⢿⣿⣿⣿⣟⣿⣾⣷⣿⣿⣇
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢏⠠⠀⢨⡹⣏⢉⠉⣸⣿⡏⡍⠩⣟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡘⢆⠀⠀⢠⠑⡌⠀⠀⣸⣷⡀⠀⢀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⣽⣀⠉⣐⢾⣟⢆⡁⡰⠾⢀⠂⠀⠩⢦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣸⣆⣉⣀⣀⣷⠡⠈⠀⠀⠀⢂⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡄⡆⠀⠀⢀⣸⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠳⠒⠒⠒⠉

⣿⣿⣿⣿⣿⣿⣿⣷⡝⣆⠹⣿⣿⣿⣿⣿⣿⠀⣷⠀⢻⡆⢸⣿⢸⣿⣿⣿⣿⣿⣿⣼⠁⠏⢠⣿⡟⣾⣿⣿⣿⠟⢀⣾⣿⡿⢋⣾⣿
⣿⣿⣿⣿⠋⠻⣿⣿⣿⣌⠣⠘⣿⣿⢿⣿⡿⡆⠘⡆⠘⡇⠀⣿⢸⣿⣿⣿⣿⣿⠇⠇⠈⠀⣾⠏⣼⣿⣿⣿⠋⣰⣿⣿⢟⣵⣿⣿⠿
⣿⣿⣿⣿⣷⣄⠈⠻⣿⣿⣦⠀⠈⢿⣯⢻⣷⠑⠀⢁⠀⠣⠀⢿⠸⣿⣿⣿⣿⡟⠈⠀⠀⣸⠏⡼⣻⣿⡿⢁⣾⣿⠟⣡⣿⣿⠟⣡⣾
⣿⣿⣿⣿⣿⣿⣷⡄⠈⢿⣿⣷⡀⠀⠻⣆⢻⣇⠀⠀⠀⠀⠀⢸⠀⣿⢻⣿⣿⠁⠀⠀⢠⠏⠘⣱⡟⠁⣠⣿⠟⣡⣾⡿⠋⣡⣾⠿⣫
⣿⣿⣿⣷⣝⠻⣿⣿⣦⡀⠙⢿⣿⣄⠀⠙⣆⢻⡆⠀⠀⠀⠀⠘⠀⣿⢸⣿⡏⠀⠀⠀⠈⠀⣰⠋⢀⡼⠋⢀⣼⠿⢋⣴⡿⢛⡵⢚⣥
⣿⣿⣿⣿⣿⣷⣮⡙⢿⣿⣦⡀⠙⢿⣦⡀⠘⢆⢻⡀⠀⠀⠀⠀⠀⣿⣾⣿⠀⠀⠀⠀⠀⠐⠁⡠⠋⢀⣴⠟⢁⣴⠟⠩⢒⡡⢞⣫⠴
⢽⣛⠿⣿⣿⣿⣿⣿⣦⡈⠻⢷⣄⠀⠙⢷⣄⠀⠀⠳⠀⠀⠀⠀⠀⡇⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⡠⠊⢁⠴⠋⠀⠀⠐⠩⠐⠉⣀⡤
⣤⣈⠉⠀⠉⠛⠿⣿⢷⣽⡢⠀⠙⠳⣄⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢒⣩⣵⣾
⣉⠙⠛⠶⢤⣀⡀⠀⠀⠈⠉⠓⠄⠀⠈⠑⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⠁
⣻⠿⠷⣶⣤⣄⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣠⣤⣶⡾⣿
⣉⣉⡁⠀⠀⠈⠉⠙⠓⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⠄⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⣚⣋⣩⣭⣴⣶⠿⠿
⣿⣭⣭⣭⣍⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡿⢻⡽⣿⢂⢿⣂⢸⡼⠃⠀⠀⠀⠀⠀⠀⠐⣀⣉⣉⣩⣥⣤⣴⣶⣶⣾⣿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠖⠒⠒⠀⠀⠀⠀⠀⠀⠹⠟⠘⠀⠈⢁⣈⡅⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠲⠿⠿⣿
⣿⣿⣿⠿⠿⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣷⣿⣾⢻⣂⢙⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⣓⣶⣶⣿
⡿⠶⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠙⠉⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⣀⡀⠀⠀⢈⣉
⣤⣴⣶⠆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠈⠐⠒⠤⣄⣉⠙⠛⠷⢶⣶
⠛⠉⢀⣀⣤⡴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠙⢦⡀⠀⠐⢤⣀⠀⠀⠀⠈⠙⠓⠶⣤⣄
⣶⡿⠟⣋⠥⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠙⢷⣌⡓⣮⣛⢶⣦⣤⣀⠀⠀⣀⠉
⡵⠖⠋⣀⠄⢀⡤⣒⠅⢀⠴⠊⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢷⣄⠀⠻⣿⣮⣝⢿⣿⣿⣿⣷⣦⣄⣉
⣠⠴⣊⣵⣞⡽⢊⣡⠞⢁⣴⡄⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⠀⠀⠀⠀⠀⠈⢧⠰⡄⠀⠻⣷⣄⠈⠻⣿⣷⣿⡻⣿⣿⣿⣿⣿
⣵⣿⣿⠞⣡⣴⠟⣡⣴⡿⣫⣾⡿⠃⠀⠀⠀⢠⠀⠀⠀⢸⡇⠀⢸⠀⡆⠀⡀⠀⠀⠘⣧⠹⣆⠀⠙⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿
⡿⣋⣴⣿⠟⣡⣾⣿⢟⣵⣿⡟⠁⣠⠆⠀⣰⠇⠀⠀⢀⣿⠀⡄⣼⡀⡇⠀⣤⠀⠀⠀⢹⣧⡹⣦⠀⠈⢿⣿⣦⡐⢌⠻⣿⣿⣿⣿⣿
⣾⡿⢋⣵⣾⣿⢟⣵⣿⣿⠏⠀⣰⣯⠎⢰⡏⠀⠀⡆⣸⡟⢠⡀⣿⡇⣧⠀⢹⡆⠀⠀⢀⢿⣷⣹⣷⡀⠀⠻⣿⣿⣦⡳⣝⢿⣿⣿⣿
⣫⣴⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⣿⡟⣰⡿⠀⣸⡿⢀⣿⡇⢸⣿⣿⡇⣿⠀⢸⣷⠀⠄⠘⣾⣿⣷⣿⣿⣄⢢⡙⣿⣿⣿⣮⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⣾⣿⡿⣱⣿⠇⣰⣿⠇⣸⣿⠁⣿⣿⣿⡇⣿⠀⠘⣿⣇⢸⡀⣿⣿⣿⣿⣿⣿⣦⠹⣌⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣀⣤⣤⠶⠶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠏⠡⢀⡼⠋⠀⢠⡖⠋⠉⣩⡟⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡿⢰⠁⣿⣧⣤⣤⣤⣹⣦⣀⣿⣃⠀⠐⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠳⣜⣦⣀⠉⣡⣤⣼⣟⠿⠿⢿⡹⢻⣦⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣦⠄⠈⠛⡦⠶⠟⠛⠛⢟⢻⣦⠀⠈⣦⢹⡆⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⠞⠁⠀⠀⠀⠀⠀⢻⣿⠆⠀⣽⣿⠁⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡔⠋⢉⣽⠃⢸⡀⠀⣚⢂⠦⠀⢠⣾⡟⠀⣠⣿⠉⡀⠡⠄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣰⡿⠡⢹⣾⣧⡈⠉⠉⠀⠀⢸⡟⠀⢰⣿⡿⣷⡙⠶⣾⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⢼⠛⣿⡿⠀⠀⠀⠀⠜⢣⡆⢸⡟⢀⢉⢻⣶⣤⣄⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣿⠷⣄⠀⠀⢶⠆⢈⣧⣀⠑⠀⠠⣤⣝⢿⣍⡙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠒⠒⠲⠶⠶⠾⠛⢹⡆⠈⠂⠀⢀⣤⣿⣿⣿⣿⣷⣦⠠⡙⢷⡈⠙⢦⠘⠆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠲⣤⡀⢿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠄⣸⡇⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠇⢀⠀⠙⠛⠉⠁⠀⢸⣿⡯⠀⣰⡟⢠⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠁⠠⠟⠀⠻⣿⡏⠑
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⣄⡑⢀⠠⠀⢉⠛⠳⣎⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣯⡙⠀⠸⡇⠀⠛⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣄⡀⠀⠀⠀⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣦⣀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⡀⢷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠉⠓⠤⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⣤⠤⠖⠒⠒⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⡾⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣿⡁⠀⢸⠟⠛⠉⠀⠀⠀⠀⠀⠐⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡧⠀⢠⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣾⣿⣿⣿⠇⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠉⠻⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠆⠁⠀⠀⣸⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠀⠀⠀⢀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠢
⠀⠀⠀⠀⠀⠀⡴⡚⠒⠄⠀⠸⡆⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠸⡇⡷⠀⠀⠀⠀⣹⠿⠾⠿⠿⠿⣦⡤⠖⠋⠉⣠⠤⢀⠈⠹⣶⡄⠀⠀⠀⠀⠀⠐⠒⠄
⠀⠀⠀⠀⠀⡠⠿⠷⠶⠶⣶⣮⡀⢦⣀⣀⣀⣀⣸⣁⠀⠀⠀⠈⠓⠦⣌⡀⠸⣿⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢙⡗⠋⠉⠁⠀⠀⠈⠙⢳⣄⠴⠚⢦⡀⠀⠈⣠⣿⣷⠦
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠙⢀⡼⡫⠖⢚⣃⣤⣀⠉⠒⠤⠤⠤⠤⠄
⠀⢀⠂⠀⠰⣄⠀⠀⣟⠀⠀⠀⠀⣠⠴⠚⠳⡄⠀⠀⠀⢸⣿⠀⠀⠀⠎⠁⠀⠈⠁⡠⣲⠟⢛⣷⣄⡀
⠀⡾⠀⠀⠀⠈⠙⠆⠿⣤⡤⠖⠋⢁⣤⡶⠖⠛⠒⠂⣀⣨⣷⣖⣶⣤⣀⣦⠀⠀⠀⠈⠀⠔⠉⠉⠩⠿⠷⣦⣀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠐⡊⠕⠊⠉⢹⣍⣀⠉⠳⣄⠂⢀⡀⠀⠀⠀⠀⠀⠠⢤⡶⠛⠉⠀⠀⠉⠒⠦⣄
⠀⠃⠀⠀⠀⠀⠀⠀⠠⠤⢤⣈⡓⠋⠁⠀⠀⠐⠃⠀⠀⠴⠚⠛⣻⣿⣛⠀⢬⣳⠀⠉⠀⠐⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⢠⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠘⠃⠀⠀⠒⠙⠛⣩⢿⣿⣥⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠉
⠘⢧⡀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠈⠻⣦⣄⠀⠀⠓⠀⠀⡀⠊⠀⠀⠈⣻⣷⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏
⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠛⠂⠀⠀⠈⠈⠡⠚⠛⠋⠉⠐⣦⣄⣤⠤⠖⠚⣩⡾⢃⡠⠊
⠀⠀⠀⠀⠈⠛⠷⠶⢶⣦⣤⣀⠈⠙⢶⣄⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⣴⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡀⠈⠳⢦⣀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠬⠽⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠻⢿⣤⣀⣀⠀⠀⠀⢀⣀⣀⣤⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⠀⠉⠉⠉⢉⣉⣤⡾⢛⣁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⣴⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⢳⡄
⠀⠀⠀⠰⣷⣷⣫⠛⠒⠚⢂⠀⠀⠀⠀⠀⠀⠀⡉⠻⣆⠙⠻⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡈⢿⠃⠶⡶⡄
⠀⠀⠀⠀⠘⠻⣿⣷⡶⠿⠆⠆⠀⠀⠀⠀⠀⠀⠈⠳⢬⡷⣄⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⡲⠷⣤⢼⡇
⠀⠀⠀⠀⠀⠀⠈⠙⣮⡛⠿⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢌⠣⡰⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⢜⢇⠙⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠠⠤⠬⠷⠖⠒⠶⠶⠗⠀⠀⠀⠀⠀⠀⠠⠤⠕⠬⠒⠨⠽⠆⠀⠀⠀⠀⠀⠀⠠⠤⠤⠦⠕⠓⠒⠲⠋


⠀⠀⠀⠀⠀⣀⣴⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡇
⠀⠀⠀⠠⡾⣿⣎⠢⠷⢶⡴⡄⠀⠀⠀⠀⠀⠀⠀⢀⠺⣇⢇⠲⢶⡒⡄⠀⠀⠀⠀⠀⠀⠀⡈⢧⡀⠻⣿⠒⠢⡀
⠀⠀⠀⠀⠈⠪⣯⣀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡓⢵⣄⠹⡜⡄⠀⠀⠀⠀⠀⠀⠈⠂⢌⠳⡌⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠫⡫⡵⢖⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢝⢷⡘⠪⢠⡀⠀⠀⠀⠀⠀⠀⠀⠑⢜⢶⠤⢘⠄⣀
⠀⠀⠀⠀⠀⠀⠤⣤⣼⠮⡲⣿⣷⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠤⢤⡤⣑⣂⣀⡠⠇⠀⠀⠀⠀⠀⠀⠠⢤⣭⠒⣂⢤⠬⠞