⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠿⠿⠿⣿⣷⣦⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀ ⠙⠿⣿⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀ ⣾⣷⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀ ⣾⡟ ⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿ ⠀ ⣾⠏⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟ ⠀⠀⣾⠏⠀⠀⠀⢀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠼⠇⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⣠⣾⡷⠀⠀⠀ ⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠿⢶⣤⣄⡀⠀⠀⠀⠐⠟⠁⠀⠀⢀⣠⡶⠿⠋⠁⠀⠀ ⣠⣾⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠻⠶⣦⣍⡛⠷⣦⣄⠀⠀⠀⠐⠞⠋⠁⠀⠀⠀ ⣠⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢰⣷⠈⠙⠻⣶⣍⢻⣦⡄⠀⠀⢠⣴⠖⢒⣻⣿⣿⠟⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⣷⠀⠛⠀⡈⢻⣦⠹⣿⡄⠀⠙⠛⠛⠛⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⣦⡀⠿⠚⣛⠀⢻⡆⠹⠏⢀⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣴⣿⡿⠿⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⠃⠀⠈⠻⠷⣶⣤⣴⡿⠃⠀⣴⣿⣿⢻⣿⡇⠀⠀⠀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠟⠉⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢼⠟⠠⠿⠃⢨⡆⠀⠀⠀ ⣼⣿⣿ ⣸⣿⠇⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀ ⣤⡙⠃⠀⠀ ⣾⣿⣿⠃⢠⣿⠏⢠⣤⣤⣼⣿⣿⣥⣀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣾⣿⠿⠛⠻⢷⣾⣿⡿⠀⠀ ⣾⣿⣿⠃⢰⣿⠃⠀⠘⠛⣿⣿⣿⠋⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿ ⠀⠀⣠⣿⣿⡿⠀⠀ ⣾⣿⣿⢇⣴⡟⠁⠀⠀ ⣼⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣄⠀⠀⠀⠀ ⣾⣿⣿⡿ ⠀⠀⣰⣿⣿⣿⠃⠀ ⣾⣿⣿⡿⠟⠋⠀⠀⠀ ⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷ ⠀ ⣾⣿⣿⡿⠀⠀⢠⣾⣿⣿⣿⠃⠀ ⣼⣿⣿⣿⠀⠀⠀ ⣾⣿⣿⠇⠀⠀⠀⣄
⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿ ⢸⣿⣿⣿ ⢀⣴⡟⣿⣿⣿⡟⠀⣠⣾⣿⣿⣿⡇⠀⠀⣠⣾⠃⣼⣿⣿⡟⠀⠀⢠⣾⠟
⢠⣿⡁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠇⢸⣿⣿⣿⣴⣿⠏⠀⢿⣿⣿⣷⣶⡿⠋⢿⣿⣿⣿⣶⣾⡿⠃⢰⣿⣿⣿⡇⠀⣠⣿⠋
⠀⢿⣧⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠋⠀⠀⠙⠻⠟⠋⠁⠀⠀ ⠙⠛⠻⠋⠀ ⠉⠛⠿⠿⠋⠀⠀⠸⣿⣿⣿⣷⣾⡿⠁
⠀⠈⠻⢿⣷⣶⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⣴⠿⠛⠛⠻⠷⠾⠿⠟⠛⠻⣿⣶⠿⠛⠛⠻⠷⠶⠾⠛⢷⣄ ⠉⠛⠛⠋