Biotechnology Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣐⠡⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠒⠈⢁⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⠲⠦⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠤⠐⡒⠠⠀⠀⠀⡀⠄⠀⠀⠀⠘⠆⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡤⢒⠅⠀⠀⡠⠂⠀⠀⠀⢅
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣔⣊⣁⣀⣀⣀⣠⣊⣀⣀⣀⣐⣀⣈
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⢁⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⣤⡈⠛⢿⣿⣿⣿⣿⠏⠀⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣤⡈⠛⠿⠃⠀⠀⠈⠻⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⡉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣶⣄⡉⠻⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣶⣄⠙⠻⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦
⣰⣿⣿⣷⡄⠠⠶⠾⠂⠙⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠙⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧
⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣦⡈⠙⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠈⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⠿⠿⣷⣶⣦⣄⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡟⢁⣴⣦⠈⣿⣿⣿⣿⣦⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡀⠛⠋⣠⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠠⢘⠀⡄⠀⠀⠸⠁⡄⠀⠀⠀⡂⠀⠀⠠⠀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢳⣦⡀⠀⢀⣴⢾⣿⡷⢦⡀⠀⢀⣴⡞⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⣦⡟⠁⢸⣿⡇⠀⢻⣤⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⢟⣵⣿⡿⢋⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠁⠀⢸⣿⡇⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠿⣫⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢸⡇⢀⣿⣆⠀⢸⣿⡇⠀⢠⣿⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣧⠟⠁⠻⣦⣸⣿⣇⣠⠟⠀⠻⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣥⣶⣶⣬⠻⣿⣿⣿⣦⡀⠛⠋⠁⠀⠀⠀⠀⠉⣿⠋⠁⠀⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡦⣀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠈⠻⠿⠿⠟⢱⣿⣿⣿⡿⣫⣾⡿⣃⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣫⣾⡿⣫⡾⠋⠀⠀⠀⢀⣀⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠫⡾⠋⠀⠀⣠⡴⢛⠻⣿⣿⣿⠿⡛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠿⠗⣬⣭⣭⡸⠿⢃⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢣⣿⣷⡹⠿⠟⣴⣿⣎⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡏⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⡏⣴⣦⠙⠿⡛⢰⣿⣦⠙⣛⡛⣴⣶⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣷⣬⣅⢺⣿⣿⢌⣛⡁⣾⣿⡿⣨⣭⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⣙⡃⢾⣿⣿⢌⣛⠱⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖⠀⠀⠀⠀⠙⢿⣇⡻⢋⣴⣶⣶⣘⠟⣣⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠟⠛⠉





⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠸⣍⠉⠉⠉⣩⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠘⠰⠆⠀⠀⢸⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⣤⠤⠯⠤⡄⠀⢸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠾⠀⠀⠀⢐⡇
⠀⠀⠀⠀⠀⢸⠀⡀⠀⡇⢀⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⣀⣀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇
⠀⠀⠀⠀⠀⢸⠀⢉⠀⡇⣼⣿⣿⣿⣿⣿⣷⠸⣭⠍⠉⠉⣭⠽⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣇⡿⠠⠀⠠⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⡇
⠀⠀⠀⠀⠀⣸⢀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠘⠦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⡇
⠀⠀⠀⡴⠋⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣷⣶⣶⡶⣶⡶⣶⣶⣶⣶⡿⠿⠿⢿⣿⣧⣼⢧⡿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡇
⠀⠀⠸⣿⣿⣿⣟⣻⣿⣿⣿⣿⠃⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠈⠻⠿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣄⠀⢀⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡧⢸⣿⣿⣿⡿⢛⣦⠀⠀⢀⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣏⢸⡧⢹⣿⠿⣃⣿⣿⡆⢠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣧⣴⣶⣶⣏⠈⣡⣾⣶⣾⣍⢸⣿⣀⠘⠿⠋⢀⣹⡿⠁⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡁⢾⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣌⡻⠙⠟⠰⠿⢋⡙⢠⣾⡿⡫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣶⣿⣟⠛⠋⠀⠀⠙⢿⣿⣿⢿⡌⠡⠀⠛⠿⣿⣿⣿⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣷⢠⠎⠹⠆⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣦⣀⡀⠀⠀⠻⡿⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠋⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠰⣧⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠟⠿⣿⣷⣦⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⡀⢸⡇⢀⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠸⡇⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡷⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠀⠀⠀⢄⡀⠀⠀⢀⡀⠀⠀⢀⡴⢛⣤⡄⠿⠛⢿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠸⣿⣆⠀⢉⣴⠿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠈⠛⢠⢿⣵⡶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠙⠁⠀⠃⠀⠀⠀⠀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡙⠿⣛⡛⢿⣿⣿⣷⣤⣤⠀⠀⠀⢸⡇⠀⠀⢰⠇⠀⠀⠀⠀⣠⣤⣶⣶⣶⣬⣍⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⣤⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⡟⠀⠀⠀⠈⣷⠀⠀⠈⠀⠀⠀⣰⣾⠟⠉⠉⠉⠉⠉⠙⠳⠀⠈⠻⣷⡄
⠀⡀⠴⣬⣽⣷⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢠⣿⣿⡿⠋⠀⢀⡀⠀⠀⢹⣆⢀⡾⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠈⢿
⠀⠾⠟⠛⠉⠁⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣤⣬⣽⠋⠀⠶⢿⣿⣿⣿⣷⠀⢻⡟⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠘
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠛⣉⠉⣥⠀⣶⣷⣦⡜⣿⣿⣿⠇⢀⠙⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⣫⣶⣼⣿⣿⣇⣴⡄⢹⣿⣿⣷⡘⣿⣿⡄⠙⠻⣶⣾⡇
⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⣫⢞⣵⣿⣿⠿⠟⢋⣹⡆⢸⣿⣿⣿⣷⣌⠻⣷⠀⠀⣿⣿⠁
⠀⠀⠠⣾⣿⣿⣿⣿⠟⡜⣣⣾⣿⣿⡏⠀⠀⢸⣿⡇⣼⣿⣿⣿⣿⠿⠿⠀⠀⠀⣿⡟
⠀⠀⠀⠹⣿⣿⣿⡏⢳⣼⣿⣿⣿⣿⣿⠆⠀⢸⣿⠃⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢠⣿⣿⠏⢠⣿⣿⣿⠋⠉⠉⠁⠀⠀⢸⣿⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⣿⣿⡿⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⡏⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⣿⣿⡇⣸⣿⡿⠛⠋⠀⠀⠀⠀⠀⣰⡟⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⢿⣿⡇⠙⢫⡶⠀⠀⠀⠀⠀⠀⢰⢟⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠸⣿⣇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠹⣿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠙⠇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢻⠓⣄⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⡋⠀⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢁⡐⡜⠁⠀⠀⠀⠀⠀⠰⠶⡄⣣⠀⣠⠚⢉⡁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠜⣧⠀⠀⠀⠀⠀⠀⠀⠑⠻⣟⠔⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⢹⠴⠋⠀⠀⠀⠀⠀⠀⢠⡷⠺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢹⡀⠀⠀⠀⠀⠀⠀⠀⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⡎⢿⠭⠛⠉⠭⠍⠉⣽⢃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣍⠹⡄⠀⠙⣌⠳⣖⡒⠒⣒⡶⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣌⢩⣠⢡⠶⡢⠀⠑⢮⡵⢚⣭⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣅⠈⢾⣰⠁⢀⡔⣡⠞⠓⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠻⡇⢠⠏⡼⠿⠤⠴⠾⠷⡘⢦⠀⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢳⠇⣼⣢⣤⣀⣀⣖⣲⣿⡈⣇⡀⠀⢀⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣧⠀⢀⠀⠀⠀⢀⣠⡇⣿⢸⡖⣡⠴⣫⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡉⠁⠀⠁⠀⠈⡿⢁⠇⣈⡜⠛⣞⢟⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⠯⡥⢤⡽⠛⣡⡯⠎⡥⡀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢜⣩⢴⡋⠁⠀⠈⠢⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣰⡯⠹⢦⡘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡾⢁⣀⠀⢀⣹⣆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡟⠉⠉⠁⠀⠀⠁⠙⡆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡸⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡤⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⣣⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢬⢣⣵⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠔⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡯⣤⣝⠓⠀⠀⠀⠀⠀⠀⠀⠐⢥⠤⡪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡇⡰⢈⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈
⡿⠿⠿⢿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⢦⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⡼⠂⠀⢀⣤⠶⠚⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⢀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠐⢯⡁⠀⠀⠀⠙⣦
⠀⠀⠀⣰⠋⠀⠀⢀⡤⠞⠛⠓⠶⠶⠶⠦⡬⠷⠦⠤⠤⠤⣤⣍⡳⣦⣀⠀⠀⠀⠀⡞⠀⠀⠀⢀⣤⡖⣋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣀⠀⠀⣼⢧
⠀⠀⢰⡇⠀⢀⡴⠋⠉⠐⠚⠒⠒⠒⠒⠚⠓⠒⠒⠒⠶⠴⣦⠤⠟⠈⢻⠳⡀⠀⠀⡇⠀⣠⢶⣯⠤⠤⠭⠭⠭⠭⠭⣽⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣽⠃⢸
⠀⠀⢸⡁⢠⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⡤⠤⠤⠤⠤⣤⣄⣱⣦⣠⠞⠀⡇⠀⠀⢧⢸⡁⠀⣉⣲⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣸
⠀⠀⠸⣇⠟⠒⠲⢶⡒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠲⢲⡶⠞⠁⠀⠀⡇⠀⠀⠈⠛⢷⣜⠧⠤⢤⣤⡤⣄⣉⣩⣯⣉⣉⣉⣉⡛⢉⣩⠷⠋⠀⠀⢠⠏
⠀⠀⠀⠙⣧⠀⣠⠤⠽⠦⠤⠤⠤⠤⣤⡤⠤⠤⣤⣤⡴⠚⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⣉⣳⣤⣄⣉⣩⡤⠟⠋⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠈⠳⣮⡖⠶⠖⠒⠒⠲⠶⣿⣴⠶⠚⠋⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣧⡤⠖⠛⠉⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣠⡤⠖⠛⠉⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⣀⡤⠴⠛⠣⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀⠀⣀⣠⠴⠶⡛⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⢀⣀⣤⣖⣿⣥⣀⣀⣀⣀⣀⣙⣦⡀
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⣠⠴⠒⠛⠛⠷⢖⡚⠁⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⣠⠴⠾⠯⠤⠤⠴⠧⠤⠤⠤⠤⣤⡤⠼⠃⠙⣦⡀
⠀⠀⠀⣴⠋⠀⠀⣀⣴⣞⣉⣉⣉⣛⡛⠓⢲⡞⠛⠓⠒⠒⠒⠶⠮⡝⢶⣄⡀⠀⠀⡾⠀⠀⠀⣠⡶⣭⣥⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣦⣀⣀⡼⢳
⠀⠀⢠⡇⠀⢠⠞⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⢿⡛⠃⠀⣷⢹⠀⠀⣇⠀⡠⠾⢷⡶⠶⠶⠶⠤⠴⠴⠼⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⣼⠃⢸
⠀⠀⢸⡇⢠⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⠒⠲⠶⠶⠤⠤⠤⠽⣦⡔⠃⠈⡇⠀⠸⡸⡇⠀⣠⣽⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⢀⡴⠁⠀⣸
⠀⠀⠈⣧⡟⠉⠙⢯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢉⡶⠞⠉⠀⠀⢠⠇⠀⠀⠉⠻⢦⣓⠤⠤⠤⠤⠤⣤⡤⠿⠤⠤⣀⣌⣉⣉⣩⠟⠉⠀⠀⣠⠏
⠀⠀⠀⠘⢷⡀⠀⣴⠛⠓⠒⠒⠒⠒⠲⡶⠒⠒⢒⣶⠶⠚⠉⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⣠⠭⠶⣦⣤⡤⠔⠋⠉⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠙⢦⣈⠉⠉⠉⠉⠙⢛⣯⣭⠿⠛⠉⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⡵⠶⠚⠉⠀⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣤⡴⠞⠋⠁⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⣀⣠⡴⠞⠋⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⢀⣀⡤⠖⠛⡍⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⣀⡤⠶⠾⣭⠷⠶⠤⠤⠤⠤⢤⡉⠳⣄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⣠⡔⠚⠉⠉⠛⠿⣉⠁⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡤⠖⠛⠓⠒⠒⠒⠛⠒⠒⠒⠒⠒⠶⣖⠃⠀⠈⣷⡄
⠀⠀⠀⢀⡞⠀⠀⢀⣴⢎⣁⣀⣈⣉⣉⣉⣙⣏⣉⣉⡉⠑⠐⠒⠒⣯⠻⣦⣀⠀⠀⣞⠀⠀⢀⡤⠾⠥⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠤⠤⠤⠬⢷⢤⣠⡏⣳
⠀⠀⠀⢸⠇⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣍⠁⠀⣹⠸⡄⠀⢣⠀⡴⠛⠳⣖⠒⠒⠒⠒⠒⠒⠚⠓⠒⠲⠶⠶⠶⠶⠶⠶⠲⢺⡟⠀⣽
⠀⠀⠀⢸⡀⣼⣋⣙⣛⣙⣛⣙⣛⣛⣛⣋⣷⣛⣛⣛⣒⣒⣒⡒⢚⣳⠞⠁⠀⡇⠀⠘⣜⣇⠀⡴⠾⠷⠦⠤⠤⠤⢤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡴⠋⠀⠀⡾
⠀⠀⠀⠘⣴⡃⠀⠈⠳⣄⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⡽⠋⠁⠀⠀⣠⠇⠀⠀⠈⠙⠷⣝⡒⠒⠒⠒⠲⠶⣦⠷⠶⠦⠤⠤⢄⣤⡴⠟⠋⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⢳⣄⢸⡓⠋⠙⠂⠙⠛⣓⣿⠛⢛⣐⡾⠟⠋⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡀⠀⣰⠚⠻⢶⣤⠤⠒⠋⠁⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠉⠳⣍⡉⠉⠉⠉⢉⣹⠿⠛⠉⠁⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠼⠗⠋⠁⠀⠀⠀⠀⢀⣠⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⠶⠊⠁⠀⠀⠀⠀⠀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠉⠙⠶⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⢀⣀⣤⣶⣚⣛⡧⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⢀⣠⡴⠖⠛⢻⡟⠒⠒⠒⠒⠒⠒⢺⡛⣦
⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⣴⣾⣉⣁⣀⣉⡛⢯⣁⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⡤⠞⠋⠉⠉⠉⠋⠉⠙⠛⠛⠛⠛⠻⣟⠋⠀⠈⢳⡄
⠀⠀⠀⢀⡟⠀⠀⣀⠴⠿⠤⠤⠤⠤⠤⣄⣩⣿⣉⣉⣉⣉⣉⣉⣉⣷⠙⣷⢦⡀⠀⠀⡇⠀⠀⣠⠞⠛⠒⠒⠒⠒⠒⠒⢲⡖⠒⠒⠒⠒⠲⠶⠾⠷⠤⢴⡏⢼
⠀⠀⠀⢸⡇⠀⣴⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣸⠀⡇⠀⠀⣗⢠⡞⠉⠻⢍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢱⠟⠀⣸
⠀⠀⠀⢸⡇⣾⣥⢬⣥⢬⣭⣭⣭⣭⣩⣉⣽⣏⣉⣉⣉⣉⣉⣉⣉⡽⠋⠀⠀⣷⠀⠀⠘⢾⣧⠠⣖⠚⠛⠒⠒⠒⠒⠒⡶⠒⠖⠦⠤⠤⠤⠤⣤⡴⠋⠀⠀⡿
⠀⠀⠀⠀⢾⡇⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⣠⠇⠀⠀⠀⠀⠉⠻⢮⣉⠉⠉⠛⠙⠻⢟⣛⠛⠓⠒⠒⣲⡶⠞⠁⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⣨⠗⠀⠀⠀⠀⠀⠀⠀⠰⣏⠁⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⡤⠶⠛⠉⠀⠀⢸⡋⠁⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠳⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣀⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⣀⣀⣀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢉⣉⣉⣉⣉⠉⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣌⡉⠉⠉⣉⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣋⣴⢞⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⣀⢈⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⣀⣉⣉⣉⣁⣀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⣭⣭⣭⣭⣭⣍⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⣤⣤⣤⡄⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠩⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣀⣀⣀⣈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⣤⣭⣭⣭⣥⣄⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣧⠀⠀⠀⠀⢀⣤⣴⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⣿⣇⠀⣠⣾⣿⣿⣵⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣝⢿⣦⡀⠀⠀⠀⣴⣾⣿⣶⣤⣀⠀⠀⣴⣶⣄⣼⣿⣷⣄⣿⣟⣼⣿⢟⣵⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡝⣱⣿⣶⣤⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⠛⣼⣿⣫⣿⡿⠟⢁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣙⡻⣷⢻⣿⣿⣿⣿⣿⢿⣿⡟⣿⣭⣄⡙⢿⣿⣿⣿⣿⢱⡄⣟⡵⣿⣽⠾⠿⣿⣟⣛⣛⣓
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢻⣯⣿⡊⢿⣟⣽⣿⢿⣷⠾⢻⣶⣷⣴⣶⣶⡝⠿⣛⢿⢸⡇⢠⣼⣷⣶⣝⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠃⢿⣿⣿⣿⣆⠰⢿⣿⠲⣡⣶⣬⡻⠿⣘⢿⣿⣿⣼⣿⡎⡆⣱⣿⣿⣿⣿⣿⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣾⣿⣿⣿⡏⣿⡇⠵⠿⢱⡟⣿⣛⢺⣿⣷⡍⣽⣶⡿⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣤⣤⣤⣴⣤⣤⣤⢻⣿⣿⣿⣿⣿⣿⣇⣿⣾⣿⣟⡌⣾⣿⣿⣷⣝⢿⡇⣿⣿⣇⣾⣿⣿⣿⣿⣿⡿⠿⣿⠋
⠐⢶⣶⣿⣭⣽⣟⣻⡮⠙⢿⣝⠣⣜⣿⣿⣌⠸⣿⣼⢳⣿⡿⠿⣿⣿⣎⢧⢻⡿⢻⣛⣿⣿⣛⣫⣷⠟⣁⡯⢿⣿⣿⣷⣦
⠀⠀⠈⠙⠻⠿⠿⢿⣟⣿⣦⣭⡃⠻⣾⣷⣮⣁⠙⠧⢨⣽⣿⣿⣿⣿⣭⣀⢛⣥⣭⣿⣿⣿⣭⣍⡰⢿⣿⣟⡿⣿⠿⠟⠛
⠀⠀⠀⠀⢀⣤⣾⢫⣾⣿⣿⣿⣿⣷⣮⣟⣿⢋⣾⣿⣮⣻⢿⣿⣿⣿⢟⡁⣎⢿⣿⣿⣿⣿⣿⣿⣿⣷⡝⡿⣿⣷⣄⡀
⠀⠀⠀⠰⣟⣿⣿⣶⡟⢿⣿⣿⣿⣿⣿⣿⣿⣎⠻⠿⠿⠟⣣⣶⣿⣿⣿⣧⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣷⣝⡻⣷⣄
⠀⠀⠀⠈⠉⠉⠉⢠⣶⣿⣿⣿⣿⣿⣿⣿⡿⣯⣶⣲⣶⣾⣿⣿⣿⣿⣿⣿⢊⠸⠿⡿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣮⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣋⣛⣿⣿⣯⡔⠛⣳⣿⣿⣿⣿⣿⣿⣏⣾⢃⣚⣛⣿⣛⣛⣛⣛⡉⠙⠉⠀⠀⠈⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣟⣻⣽⣿⢟⣯⣿⣯⡆⠻⣿⣿⣿⣿⣿⣿⣬⡽⢸⣿⡌⣻⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠿⠷⠿⠿⠿⢛⣵⣿⡿⣵⣿⣹⣠⠸⣿⠟⢻⣿⣿⡿⠁⠘⣿⣿⡙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢏⣾⣿⡏⣿⡟⣷⣶⡄⠈⠙⠉⠀⠀⠀⠘⢿⣷⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢫⣾⣿⡿⠁⢻⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢧⣿⣿⠟⠁⠀⠈⢿⡞⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡿⠟⠁⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⡙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⣄⠙⢷⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣌⠻⣦⡙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⠶⢿⡦⣬⣷⣶⠿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⣉⣹⡄⢿⠓⠈⠋⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⣦⡈⠳⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣤⡻⣷⣌⠻⡇⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⡈⠻⣦⡈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡙⢿⣮⡻⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣤⣤⣸⣇⣀⣙⣦⣬⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠛⠛⠛⡇⢸⠿⠦⠙⠛⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠺⢿⣍⠙⢦⡈⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣥⣄⠺⣦⡙⢿⠀⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠷⣄⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣌⠻⡦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀
⠀⢸⠀⠀⠈⠉⠲⢄⠀⠀⠀⠀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⢀⠴⠊⠉⠀⠀⢸
⠀⠀⢹⢹⠑⠢⡀⠀⠑⢄⡠⠊⠀⢀⠴⠒⡏⡏⠈⠩⢹⠒⢤⡀⠈⠑⢄⠔⠁⠀⣠⠔⢺⠹⠉⠈⡏⡟⠲⢄⠀⠈⠢⣀⠔⠁⠀⡠⠖⢹⢹⠁
⠀⠀⢸⢸⠀⠀⡏⡦⡀⠀⠱⣄⢴⢹⠀⠀⡇⡇⠀⢸⢸⠀⢸⠹⢦⠀⠈⠣⣠⠞⢹⠀⢸⢸⠀⠀⡇⡇⠀⢸⢱⢄⠀⠈⢦⡠⡎⡇⠀⢸⢸
⠀⠀⢸⢸⠀⠀⣇⠗⠙⢆⠀⠈⠺⣸⠀⠀⡇⡇⠀⢸⢸⠀⢸⣸⠞⠑⣄⠀⠘⢾⣸⠀⢸⠸⠀⠀⡇⡇⠀⢸⡸⠊⠳⡀⠀⠑⢇⡇⠀⢸⢸
⠀⠀⣸⣸⡠⠖⠁⠀⡠⠊⠑⢄⠀⠈⠲⢤⣇⣇⠀⣨⣨⠤⠚⠁⢀⡠⠊⠢⡀⠀⠙⠢⢼⣘⡀⢀⣇⡧⠴⠊⠀⢀⠔⠉⠢⡀⠀⠑⠦⣸⣸⡀
⠀⢸⠀⠀⢀⣀⠴⠊⠀⠀⠀⠀⠑⠦⣀⡀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠁⠀⠀⠀⠈⠲⢄⣀⠀⠀⢸
⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣬⠋⠀⠀⠒⠈⠁⠀⠈⠁⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠶⠲⠶⠶⠶⠶⠤⠤⠄⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⢀⣀⣄⣈⣉⡈⠀⠀⠀⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⡀⠀⠀⠀⠉⠉⠀⠀⢡⣲⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣦⡀⠀⠘⠻⢾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠛⠋⠀⠈⠛⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠋⠀⠉⠛⠛⠛⠓⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠘⠛⠛⠛⠛⠛⠛⠒⠒⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠿⠶⠿⠷⠶⠶⠆⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠉⠉⠉⠉⢉⣤⠀⢬⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠘⠿⣿⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⣶⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠓⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⠛⠡⠴⠶⠤⠶⠤⠈⠻⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⢀⣀⣀⣀⣀⣠⣀⣠⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠉⠉⠉⠉⠉⠁⠁⠀⠀⢿⡪⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡏⠀⠚⠛⠛⠛⠛⠛⠛⠂⠀⠀⠨⣐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡳⠻⣶⠀⠉⠛⠉⠉⠉⠉⠉⠁⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⢿⣿⣿⣿⣶⣦⣄⡀
⣤⣤⣤⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠛⠚⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠲⠦⣤⣀⡀⠀⠀⠀⣴⡿⠋⠁⢀⣴⠟⠁⠀⠘⢿⡄⠉⠻⣶⣄
⠈⢻⣏⠛⠲⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠮⠿⠷⠶⣾⡏⠀⠀⢠⡿⠁⠀⠀⠀⠀⠈⢿⡄⠀⠈⢻⣦
⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⣿⡆
⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣇
⠸⢿⣿⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣼⣿⣤⣤⣤⣤⣀⠀⠀⠀⠀⣿⡄⠀⠀⢸⣿
⠀⠀⠀⠉⠛⠷⣶⣿⣷⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⣿⣿⣿⣿⣿⣟⣛⣁⣀⣤⣴⡶⠟⠛⣻⠟⠀⠀⠀⠀⣿⣇⣀⣀⣸⣿
⠀⠀⠀⠀⠀⢰⡟⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⢉⣿⠏⠉⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⣿⣏⣉⣉⣹⣿
⠀⠀⠀⠀⠀⣾⡇⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⣸⡏⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⢠⣿⠉⠉⠉⢹⡏
⠀⠀⠀⠀⢰⣿⡇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣿⡇⠀⠀⠀⠀⢿⡇⢀⣴⡶⠟⢛⣿⣷⣄⡀⣠⣾⡇
⠀⠀⠀⠀⠀⠻⠷⣶⣾⣿⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠘⣿⣟⣁⣴⠾⠋⠁⠀⠈⠛⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠳⠶⠶⠶⠦⣤⣤⣤⣄⣀⣀⣀⡀⠀⢸⣇⣀⣻⣇⣠⣤⣶⣾⡿⠛⣽⡟⠁⣠⡴⠶⠛⠛⠛⠓⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⣿⣿⠟⠛⠉⣉⣥⣴⡿⠁⣼⢏⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⣿⠉⢹⡇⢰⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠻⣦⠸⣇⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢻⣦⡀⠀⠈⠛⠿⣦⣹⣟⢷⡀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠉⠻⢶⣤⣀⣀⠈⠛⢿⣦⣽⣶⣤⡴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⡈⠉⠛⢛⣻⣿⡿⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣩⣙⣉⣍⣉⣯⣉⣿⣏⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠤⠄⠀⠀⠀⢠⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠀⠀⠁
⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠐⠒⢞⠁⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣉⠡⠶⠀⠀⠀⣄⠀⠀⠠⠴⠶⠞⠃⠀⠀⠀⢀⡄⢀⡀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠶⠀⠈⠋⠰⠆⠀⠀⠀⠙⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⡀
⠀⠀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐
⠀⠀⠡⠦⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣺⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⢀⡛⠔⢍⡀
⠀⠀⠀⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡔⠧
⠀⠀⠀⠀⠉⢀⠑
⠀⠀⠀⠀⠀⠀⢀⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠂⠀⣀
⠀⠀⠀⠀⣴⣶⢿⡧⠤⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠼⠁⠀⣴⢉⠀⠀⠀⠀⠀⠖⠀⠊
⠀⠀⠀⠀⣿⣧⡈⠙⠋⠙⠁
⠀⠀⠀⠘⠋⠙⠛⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠴⠒⠄
⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⢠
⠀⠀⠀⢀⠅⠀⠀⠓⣶⣶⡄⢀⣆
⠀⠀⠀⢶⣤⣤⣀⡀⠉⢉⣴⣿⡏⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠻⠛⠿⠿⣿⣿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠂⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⢧⡤⠄⠠⠀⠠⢤⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⢠⣤⠀⠀⠀⠀⣯⠐⠐⠀⠘⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣐⣻
⠀⠀⠀⠀⠀⠀⠀⢶⡒⠒⠒⠒⢲⡆⠀⠀⡿⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡇⠀⠀⠀⠈⣽
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠀⢸⡀⢠⣿⣟⣾⣿⣿⣿⣿⣿⡆⢰⡟⠛⠛⠛⠛⠛⠛⢳⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠃⢸⠂⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⡈⢻⢛⠉⠉⠉⠉⢹⡏⢹⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡅⠀⠀⠀⢀⣻
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⠁⠠⠠⠀⠐⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣈⣽
⠀⠀⠀⠀⠀⣀⡴⠚⠁⠘⠃⠀⠈⠛⢽⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣏⢙⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⢿⣿⣿⣯⣽⣿⣏⣹⣿⣿⣿⣿⣏⡟⠉⠉⠉⠙⣿⣿⣿⣿⣯⣽⣯⣽⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⢯⡻⣿⣿⣿⣏⣹⣿⣿⣿⣿⢟⡞⠁⠀⠀⠀⠀⠘⢯⣛⣿⣿⣿⣿⣿⣿⣿⣿⣫⠞⠁⠀⠀⠀⠀⠀⠀⣴⣻⣿⣿⣿⣿⣿⣿⣿⣳⣦
⠀⠀⠀⠀⠀⠙⢮⣟⣿⠿⠿⠿⣿⣻⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠄⡂⠀⠐⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣨⠃⠀⠐⠀⠐⠀⠀⠑⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⣀⠑⡄⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⠄⠄⠀⠀⡎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠁⠂⠀⠀⡠⠓⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢀⠂⠀⠀⠀⢀⠄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠆⡁⠀⠀⣤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠀⠀⠠⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠧⡀⠄⠀⠈⢄⠉⡄⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠐⡆⠀⠀⡔⡁⠀⠀⠈⠐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠀⠤⠛⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⡰⠁⠀⠀⠀⠈⠀⠀⢇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠂⡅⠀⠀⠤⡊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡑⠀⠀⠀⢂⠌⠀⠀⡠⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠆⠀⠈⠤⠈⠄⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⣖⠂⠀⠀⠠⠁⠀⠀⠀⠣⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡁⠀⠀⠔⠉⠄⠀⠀⠀⠐⠀⠀⢠⠀⡀⠀⠀⡘⣣⠀⠀⠐⡀⡀⠀⠀⡔⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠄⠀⠈⠶⡉⠀⠀⠠⠀⠠⠀⠀⠈⠁⡁⠀⠈⡑⣚⡇⠀⢀⣞⣅⠀⠀⠳⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠂⠀⠈⠢⣀⠆⠀⠀⠀⠠⠀⠀⠘⠦⠀⠀⠀⢠⡄⠀⠀⢠⠤⢤⠀⠀⡞⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡁⠀⢀⠒⢉⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠏⠈⠀⠀⠀⡡⠂⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠄⠀⢀⠖⣁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠰⠀⠀⠀⠀⡆⠀⠑
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢐⠄⡂⠀⠀⠢⣀⠂⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⠣⡀⠀⠈⠄⠄⠀⠀⢈⠔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⡀⡆⢣⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡀⢄⠳⠘⡄⢂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⢿⣿⣿⣿⣧⡄⠆⠳⠘⡄⢇⠱⡈⣄⢡⡘⡄⢦⠱
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠿⠳⠾⣿⣿⣿⣷⠱⡈⠄⠡⠘⠀⠦⠉⠈⠀⠁⠉
⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢻⡿⢟⣥⡠⡈⡄⠣⠈
⠀⠀⠀⠀⠀⠀⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠋⠁⡀
⠀⠀⠀⠀⠀⠀⠘⣷⣤⠀⠀⠀⠀⠀⠋⠁⣀⣤⣶⣿⣿⣷⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡄⠀⠀⣶⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡖⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⢿⡿⠉⠻⣷⣦⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⢿⣿⡟⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣏⠁⠀⠀⠙⢿⣷⡀⠀⠀⠠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠙⢿⣷⣄⠀⠀⠀⠙⢿⣷⣄⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣏⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠙⢿⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣷⣄⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠈⠻⣷⣄⠀⠀⠀⠙⢿⣷⣄⣰⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠀⠀⠀⠈⠻⣷⣄⠀⠀⢀⣹⣿⣿⣿⣿⣿⡟
⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⢻⣿⣿⣿⣿⣿⡛⠛⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉
⠀⠈⠉⠀⠀⠙⢿⣦⣀⣿⣿⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⠤⠤⠤⠤⠤⠤⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠘⢷⣄⠤⠤⠤⢄⣴⠟⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣠⣼⣿⣿⣤⣠⣶⠍⣻⣶⢾⡋⠁⣤⣿⣿⣧⣄⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢏⣴⠟⠭⠤⠬⠝⢷⣌⢻⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⡟⠁⠀⠀⠁⣾⠣⠤⠤⠤⠤⠤⠤⢹⡆⠀⠈⢻⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣧⡀⠀⠀⡀⢿⡔⠒⠒⠒⠒⠒⠒⣸⠇⠀⢀⣼⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣎⠻⣦⣒⠒⢒⣢⡾⢋⣼⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠙⢻⣿⣿⠛⠙⠿⣂⣽⠿⢿⣅⡀⠛⣿⣿⡟⠋⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⢠⡾⠋⠓⠒⠒⠊⠻⣦⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠑⠒⠒⠒⠒⠒⠒⢹⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠈⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣿⣿⣿⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⣿⣿⣿⣿⢀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⣿⣿⣿⡿⢸⣿⣿⣿⡏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⢿⣿⣿⡇⣾⣿⣿⡟⣰⡟⣡⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⢸⣿⣿⠇⣿⣿⡿⢀⣿⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠸⣿⡟⢸⣿⡿⠁⢸⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀⠻⢁⣿⣿⠁⠀⢸⣿⡄⢿⣿⣇
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⡀⢻⣿⣿⣿⣿⡇⠀⢸⣿⡇⠀⠀⢸⣿⡇⢸⣿⣿⣦
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⠅⠀⠀⠙⠀⠀⠀⣼⣿⣧⠀⣿⣿⣿⡆⠀⠀⠀⢀⡀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⡿⢀⣶⣿⣿⣦⠀⢠⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⢾⣿⠀⣼⣿⠟⠁
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⢇⣿⣿⣿⣿⣿⠀⣾⣿⣿⡇⢠⣿⣿⣿⣿⣇⣤⡀⠸⠇⠀⠈
⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣿⣿⣿⠇⠘⡟⠃⢸⣿⣿⣿⣿⢟⣼⣿⣿⡿⢀⣾⣿⣿⣿⡿⠈⣿⡿⠀⠀⠘⠛⠛
⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣾⣦⡀⢺⣿⣷⠘⠿⠿⠟⢫⣾⣿⣿⠟⣠⣾⣿⣿⣿⠟⠁⠀⠹⠃⠴⣾⣷⣦
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣤⣄⠀⣠⡀⠀⢿⡿⢛⣥⣾⣿⠿⠟⢋⣀⡀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠋⠡⠾⠀⠘⠿⠻⠇⢹⣿⣆⠀⣀⣋⣩⣥⠄⣠⣾⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⣉⣩⣭⣤⣶⣶⣿⣿⣿⣿⣿⣷⣶⣄⡙⢿⠄⢻⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡆
⣀⣤⡶⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇
⠁⠀⠒⠒⠶⢶⣶⣦⣤⣬⣭⣭⣍⣛⣛⣛⣛⣿⣿⣿⠿⢿⣦⠀⠻⡿⠀⠙⠻⢿⣿⣿⣿⡿⠈⠿⠟⢛⣭⣭⣴⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠌⠁⠀⢰⣶⣶⣶⣶⣶⣤⠀⣠⣶⣶⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⣶⣶⣄⠹⣿⣿⣿⣿⣿⡄⠙⠻⢿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⠘⢿⣿⣿⡿⢛⣠⣤⣤⣤⡈⠻⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⡀⠈⢿⣧⠀⣴⣦⡄⠰⣿⣿⣿⣿⣷⡄⠻⣯⣶⣿⣿⣿⣿⣿⣿⣄⠹⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⡙⠀⠀⠋⠁⠀⠙⠛⠋⠙⠋⠁⢠⡜⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠋⠀⡀⣠⡞⠛⠂⠀⠀⠀⠀⠠⣦⠘⠿⡎⠻⣿⣿⡿⣿⠿⠟⠀⣰⡿⣿⢿⣿⣿⠿⢛⣻⣭⣶⣾⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠟⢀⣠⣤⣴⣶⣶⣶⠠⣾⣶⣶⣄⠀⠀⠈⠁⠀⠀⣠⣶⣷⣾⠷⢊⣠⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⣛⣛⣛⣛⠛⣠⣙⠻⣿⣿⣧⡀⠀⠀⠀⢠⣿⣿⠟⣁⣴⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢠⣄⠛⢿⣿⠋⣼⣿⣿⣷⣄⠙⢿⣷⡄⠀⠀⢸⡟⢁⣼⣿⣿⣿⣿⠋⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⣷⡀⠿⠄⠻⣿⣿⣿⣿⣷⣄⠹⣿⣄⠀⠘⢀⣾⣿⣿⣿⡿⠁⢀⣠⣶⣿⡿⢛⣥⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠚⣋⣡⣤⣶⣶⣤⣤⣉⡙⠻⣿⣷⡜⢿⣆⠀⢸⣿⣿⡿⠋⢀⣴⣿⡿⠛⣡⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣬⣛⠿⠿⣿⣿⣿⣿⣿⣿⣷⣦⣈⠛⠎⢻⡆⠙⠋⠁⢀⣴⣿⠟⢋⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣶⣶⣬⣭⣭⣉⣛⣛⣛⣻⣤⡄⠁⠀⠀⣴⣿⠟⣡⣾⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠙⠻⠿⢿⣿⣿⠿⠿⠿⠿⣛⣛⣭⡿⢠⡄⠀⠰⢟⣥⣾⠿⠟⠋⠁⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⡿⠿⠛⢉⣴⡟⠁⠀⠀⠙⠁⠀⠀⠛⢃⣀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⣠⣴⣿⠏⣰⡆⠀⣴⣟⠻⢶⣦⣤⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⢃⣴⣿⡇⠀⢿⣿⣷⣄⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⢡⣾⣿⣿⠁⠀⠈⠻⣿⣿⣷⣄⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢋⣰⣿⣿⡿⠁⠀⠀⠀⠀⠈⠛⢿⣿⣷⣌⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢁⣴⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⡿⠟⠋

⠀⠀⠐⠍⣡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡖⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠴⠶⠦⠀⠴⠶⠤⡆⠀⠀⠀⢰⠶⠒⣖⣖⣶⣲⡖
⠀⠀⢠⠊⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⡇⠀⠀⠀⠀⠀⠀⠴⠶⠶⠄⠠⠶⠆⡇⠀⠀⠀⢸⠀⠀⠻⠿⠿⠿⠁
⠀⠀⠀⠈⠩⠤⢀⠀⠀⠀⠀⠀⠀⠸⠿⢦⠸⠾⠷⠀⠀⠀⠀⠀⠀⠀⣇⡁⡁⡇⠀⠀⠀⠀⠀⠀⠶⠶⠶⠦⠀⠰⠆⡇⠀⠀⠀⢸
⠀⠀⠐⠌⣡⠀⠀⠀⠀⠀⠀⠀⠀⠎⣭⣥⢩⣭⠭⠀⠀⠀⠀⠀⠀⠀⣗⣶⣖⡇⠀⠀⠀⠀⠀⠀⠶⠶⠶⠀⠶⠶⠆⡇⠀⠀⣴⣾⠐⠓⣒⣚⣓⣒⠒
⠀⠀⠠⠊⡑⠆⠀⠀⠀⠀⠀⠀⢰⠃⠈⠉⠈⠉⠀⢆⠀⠀⠀⠀⠀⠀⠻⠾⠾⠃⠀⠀⠀⠀⠀⠀⠲⠶⠶⠀⠰⠶⠆⠇⠀⠀⢿⣿⠀⢘⣛⢛⡛⢛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣙⣎⣛⣛⣛⣛⠟⣛⠀⠀⠀⠀⠀⢘⡃
⢠⡖⣿⡳⣄⢀⣀⣀⠘⠀⠀⠀⣤⣿⡟⢩⣉⣉⢙⣿⠆⠀⠀⣰⣿⡷⠀⠀⡤⠤⠤⢤⡄⠀⢸⡏⠻⣹⣿⢹⣃⣻⣲⣿⠀⠀⠀⠀⠀⣿⡕⣴⣦⡀
⠈⢧⣹⣲⢧⣿⣿⣿⡆⠀⠀⠘⣿⣿⡇⢸⣿⣿⢐⣿⠿⠀⠀⢿⣿⡄⠚⠃⣧⣿⡯⣼⡇⠀⢸⡏⣦⢹⣿⢸⠋⢿⠽⣿⠀⠀⠀⠀⠀⠈⠀⠙⣿⡇
⠐⠀⠀⠀⠀⠒⠽⠟⠁⠀⠀⠀⠁⢿⣷⣴⣤⣴⣴⡿⠃⠀⠀⠘⠿⠏⠀⠀⠀⠀⠁⠉⠀⠀⢸⡷⢁⣾⣿⢸⣏⣿⠻⣿⠀⠀⠀⠀⠀⠒⠒⣤⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠧⠾⠿⠾⠿⠷⠷⠿⠀⠀⠀⠀⠠⠤⠄⠿⠷


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢻⣷⠀⣿⡆⣰⡾⠻⣶⡔⠿⣿⡿⠗⢸⣿⠛⠛⢠⣶⠟⠷⠆⢸⣇⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⣙⣿⠄⣿⡇⢿⣧⣀⣿⠇⠀⣿⡇⠀⢸⣿⣉⣉⠸⣿⣀⣠⡄⢸⡟⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠁⠀⠉⠉⠁⠀⠀⠉⠁⠀⠈⠉⠉⠉⠀⠈⠉⠉⠀⠈⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢤⣤⣤⣤⡤⣄
⠀⠀⠀⠀⢄⠀⢰⠀⢀⠄⠀⠀⣀⡴⣿⣿⣿⣿⢷⣄⠀⠀⠀⠀⠰⡦⠃⡿⠤⠓⠀⠀⠀⠀⠀⠀⢀⣀⠰⣃⠐⠁⡰⠃⠀⠀⠀⣷⠙⢸⡿⢿⡌⢣⣿
⠀⠀⣀⠀⠀⣁⣤⣤⡈⠀⠀⢀⡭⢑⢰⣶⣶⣶⠘⠭⡁⠀⠀⠀⠀⣾⢯⢙⣮⠻⢗⡆⠀⠀⠀⡰⣽⣯⣘⠧⣕⠀⠁⠀⠀⠀⠀⣯⣹⣼⣿⣿⣝⣆⡿
⣴⣿⣿⡶⢿⣿⢿⣛⣿⠀⠀⠈⣿⣿⣞⢟⢻⢏⣿⣿⡇⠀⠀⠀⠀⢖⣓⣺⣧⣉⣼⡇⠀⠀⠀⡿⣿⣿⣿⣿⣶⣽⡆⠀⠀⠀⠀⠀⠀⠀⢉⡁
⠉⠉⠉⠀⠉⠉⠨⠩⠡⠆⠀⠀⠈⠹⠿⢷⣲⠿⠿⠁⠀⠀⠀⠀⠀⠈⠻⣯⡟⢛⡿⠁⠀⠀⠀⠘⢝⡿⢿⠿⣫⠞⠀⠀⠀⠀⠀⠀⠀⠐⢶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢒⣒⣒⣒⣒⠂⠀⠀⠀⠀⢀⢀⡀⢀⢀⣀⣀⣀⠀⠀⠀⢠⡤⢴⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⣀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⣿⡟⠿⢿⣿⠀⠀⠀⠀⠀⣾⣶⡒⢂⣢⣶⣶⣶⡆⠀⠀⣿⣾⢫⣽⡾⡇⠀⠀⠀⠀⠀⠀⣴⣵⡏⡭⡟⠍⢷⡱⡄⠀⠀⠀⠀⠀⠀⠀⠰⠩⡄
⠀⠀⣯⣦⠈⣠⣿⠀⠀⠀⠀⠀⣿⡿⢷⡿⢿⣿⢙⣛⡂⠀⠀⣿⡰⣶⡦⣰⢥⣤⣤⣤⠀⠀⢰⢹⣿⣧⢃⠩⢂⣽⣾⣼⠀⠀⠀⠀⠀⠀⠀⢛⣤⠁
⠀⠀⣿⠯⠟⠿⢿⠀⠀⠀⠀⠀⣿⣛⣻⣟⣃⣿⣀⣒⡀⠀⠀⣿⣿⣾⣾⡿⠌⡉⠉⠉⠀⠀⠈⣎⢯⡊⡵⣇⡇⣿⡿⡌⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⣻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⢻⣿⣿⡿⡇⣶⣶⣶⣶⡆⠀⠀⠈⠺⠧⢼⣷⠦⠯⠊⠀⠀⠀⠀⠀⠀⣠⣤⣾⣧
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡀⠀⠀⠱⣬⣐⠆
⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⠄⠈⠐⡁⠄⠀⠀⠈⢟⣧⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⡈⠠⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠐
⠀⠀⠀⠀⢸⡀⠸⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠆⠀⠀⠀⠓⠰⠄
⠀⠀⠀⠀⠀⠉⠀⢄⠀⠀⠀⠀⠀⠐⢀⠠⠀⠐⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠘⡄⢨⠄⠀⠀⠀⠠⡄⠀⢱⢄⠀⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠈⠃⠀⢀⣀⡀⠀⠀⠰⠂⡀⠄⠣⠀⠐⠆⡀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢘⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⠂⣀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠙⢿⣅⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠳⡄⠀⠀⠀⠀⠉⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⣠⡎⠢⡀⠀⠀⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣁⣀⣀⣀⣀⣔⣉⣀⣀⣕⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣰⠏⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠁⠀⠀⠀⠀⠀⣠⡞⠉⠻⢦⣞⠁⠀⠀⠀⠀⠀⢠⡾⠉⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠉⠻⢦⣄⠀⠀⣰⠿⣄⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣸⠟⢶⣄⡀⠀⠀⠉⠳⢾⣇⠀⠈⢳⣄⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠙⠛⢦⡀⠀⠀⠀⣾⠃⠀⠀⠈⠛⢦⣄⠀⠀⠀⠉⢳⠄⠀⠙⣧⡀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠈⠛⣦⣄⣰⠏⠀⠀⠀⠈⢷⡀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⢻⡖⠛⠻⣦⣀⣀⣠⡾⠃⠀⠀⠀⢀⡾⠋⠙⣷⣤⡀⢀⡼⠃⠉⠁⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠟⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠻⣤⣀⡾⠃⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⣤⡉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠈⣿⠷⣤⡉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⡇⠀⠈⠙⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⡀⠀⠀⠀⣠⡶⠛⠉⠀⣀⣄⡀⠉⠙⠳⣦⡀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣧⡀⢠⡾⠁⠀⠀⠀⢸⡏⠈⣻⠀⠀⠀⠀⠙⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⢷⡟⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠙⠋⠛⠛⠛⠛⠉⠙⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠋⠙⠙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠊⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠂⢠⠀⢠⠀⠐⢂⠰⠀⠀⠂⢐⠀⠂⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂

⡖⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡖⠐
⠃⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⢀⡀⣀⠀⣤⠀⢀⡄⠀⢠⢀⡀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠠⡄⠀⡠⢀⡀⣀⠀⣀⢀⡀⣀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⢸⠀⠀⡇⣹⠀⢺⠀⡴⢹⡀⢸⠰⡅⠀⠀⠀⠇⠀⠀⠈⠳⡄⠀⡇⠀⡷⢼⠰⡇⠀⢸⢠⡷⡅⠐⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣼⣷⣾⣤⣶⣤⣾⣴⣧⣤⣶⣾⣶⣥⣾⣶⣶⣷⣶⣤⣴⣶⣧⣤⣧⣤⣧⣼⣦⣽⣶⣧⣼⣧⣼⣶⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⠉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠙⢿⣿⣦⣀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⡆⢸⣿⣿⡆⢴⣶⣶⣶⣶⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⣿⣿⡛⠛⠛⠛⠋⠈⣿⣿⡇⠸⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠁⠀⠈⠻⣿⣦⡀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢿⣷⣄⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠈⠻⡟⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⢸⣷⣄⠀⠀⠀⠀⠙⢿⣿⣦⡀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠙⢿⣷⣄⠀⠀⠀⠀⠙⢿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠙⢿⣷⣄⣀⣤⣶⣿⣿⡿⠋
⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣷⠈⣿⣿⡇⢰⣶⣶⣶⣾⣿⣿⣿⣿⠿⠛⠁
⢤⣾⣿⣿⣿⣿⣟⠛⠛⠛⠙⠋⠀⣿⣿⡇⠘⠛⠛⠛⠛⠛⠉⠉
⠀⠙⠋⠁⠀⠙⢿⣷⣄⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠒⢤⣀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠤⣄⡀⠉⠻⣦⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠻⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠑⠲⣄⡀⠙⢷⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⢁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠁⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⢶⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⡈⠻⣷⣄⠀⠉⠒⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⠿⣦⡀⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠈⠛⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠒⠤⣀⡀⠙⢷⣤⡀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠙⠷⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠑⢦⣄⠀⠙⣷⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⢷⠀⠈⢁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⠁⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⣦⡀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠈⠻⣦⡀⠈⠙⠢⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠘⢷⣄⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠉⠓⢦⣀⠀⠉⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⡿⠿⠟⠋