⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣲⡿⠁⠀⠀⠀⠀⠀⠀⡆⠀⣿⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⢡⣸⣿⣀⣀⣸⣦⠤⠶⣦⠦⣽⣤⣼⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⣰⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⣠⣤⢴⡾⣿⣿⠫⠁⠀⠙⢦⡀⣿⠀⠀⠹⣼⡀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠋⠁⢠⡾⠋⠀⠀⠀⠀⠀⠀⢸⠇⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⣠⣴⡗⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⢶⡖⢺⡿⠛⣉⣽⡿⠉⢹⣿⡀⠀⢀⣠⣴⣿⣷⠀⠀⠀⢈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠶⠒⢶⣿⡷⠒⠶⠤⠤⣄⣀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⢻⣶⣿⣿⢫⣿⡿⠛⠉⡩⠍⣉⣿⠟⠛⠛⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠷⠛⠉⠀⠀⠀⠀⣹⡿⢇⣴⣿⡏⠀⣠⣼⣯⣙⣶⢟⣁⣀⣨⡏⢻⡀⠀⢸⠏⢻⡯⢽⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣠⣾⠧⢤⣄⠀⠀⢀⣤⢶⣄⠀⢸⡀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⠖⢋⣷⠏⠀⠀⢀⡴⡿⠋⠀⠀⠀⢀⡤⠞⠋⠓⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢀⣴⢿⣛⣦⣿⠟⠁⠀⠐⢠⣡⡞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢤⣾⣿⣠⣾⣾⠃⠀⠀⢻⣿⡷⠤⠟⢿⣭⡉⣹⣳⣌⡇⠀⢸⠇⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢠⡟⠻⠶⠚⠃⠀⠀⠻⠷⠤⠼⠀⢸⡇⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⣯⠁⣴⢫⡏⠀⠀⢀⡞⣼⠁⠀⢸⣦⠞⠋⠀⠀⠀⠀⠘⡟⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⣠⣴⡛⣵⣲⡿⡛⠀⠀⠀⠀⣌⣴⠋⠀⠀⠀⠀⠀⠀⣠⡼⣶⡒⠛⠛⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣫⡾⠻⣾⣿⠃⠀⠀⠀⠀⢀⣷⠀⠀⠀⠉⠉⣽⠁⢨⡇⠀⢸⠇⠀⡟⣇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣇⣈⣿⣃⡞⠀⠀⠀⡞⢠⢿⣿⡶⣿⣟⠂⠀⣠⣄⡀⠀⠀⢻⣼⡝⢿⡄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⣠⣾⡋⣆⣿⡿⠋⠀⠀⠀⠀⣄⣷⠟⠁⠀⠀⠀⠀⢀⣤⡾⠋⠂⠈⠻⣦⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣻⠋⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⢻⣦⠄⢀⡀⢀⡏⠀⣼⠀⠀⢿⠄⢠⠃⣿⡀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⠀⠀⣠⠏⠀⠀⠀⠀⣴⣧⣶⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣽⠁⣼⠁⠀⠀⣼⠁⢸⣸⣿⣵⣆⣿⠀⣾⡿⢉⠛⣦⠀⢸⡟⡇⠈⣷⡶⢻⣝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⡾⠫⣆⣷⡿⠋⠀⠀⠀⠀⣄⣶⠟⠁⠀⠀⠀⣀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠘⣿⢟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡤⣂⡤⠖⡾⢁⣠⠏⣠⢏⣾⠏⠁⠀⠀⠀⠀⠀⠰⣿⣿⢖⢹⢽⣾⠇⠀⠁⠀⠀⢸⠁⠈⢰⠇⡇⡇⠀⠀⠀⠀⠀⠀⠀⢠⢮⢾⠃⠀⣠⠏⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⢰⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡼⠁⢰⠇⠀⠀⣰⠃⠀⣿⠃⠀⠈⠉⠀⠀⠘⠳⢦⣄⣽⠠⠈⣷⡇⠀⠘⣯⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⡄⢀⣤⣤⡞⠁⢀⣰⡿⠋⣤⣿⡿⡋⠀⠀⠀⠀⣀⣶⠟⠁⠀⠀⢀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠸⣏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡰⠁⠀⠙⠉⠀⣰⠟⢹⠋⣲⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣈⡟⠀⢾⠁⠀⠀⠀⠀⢸⠀⠀⡾⠀⣧⡇⠀⠀⠀⠀⠀⠀⢀⡵⠋⡾⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⡾⠁⢀⡟⠀⠀⣰⠃⠀⡰⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⠆⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣾⡟⠉⠛⣷⣾⡿⢄⣟⣿⡟⢂⠈⠁⢄⢀⣴⢿⣁⡀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢹⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡰⠁⠀⠀⢀⡤⠚⠉⢂⡏⣴⠃⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡿⠀⠀⠀⠀⠀⢾⠀⣸⠃⠀⣿⡆⠀⠀⠀⠀⠀⣠⠎⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡾⠁⠀⣾⠀⢀⡼⠁⢀⡼⠁⢸⠀⠀⣴⢓⣀⣄⣶⠂⠀⠀⠀⠀⠀⣿⡇⠀⡼⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣟⡴⠿⣧⣤⣴⣿⡟⣐⣾⡿⠃⠄⠆⣨⣴⣾⠟⠛⠛⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⡇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣢⡤⠖⠚⠉⠀⠀⢀⣼⡿⠃⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡃⠀⠀⠀⠀⠀⣸⣰⠏⠀⢸⢻⠁⠀⠀⠀⣠⠞⠁⣠⠞⠁⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡼⠁⠀⢰⠇⣠⠏⠀⣠⠎⠀⠀⢸⡇⠘⠿⠻⡟⠟⠟⠀⠀⠀⠀⠀⢸⠇⡇⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⢐⣿⠟⠁⠀⣠⣾⣿⣿⡿⢷⡟⡉⢀⠂⡠⣧⣿⣅⠀⣠⠖⠋⠻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣯⣷⠀⠀⠀⡇⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠙⠒⠂⠀⠀⠀⢀⠞⢹⠃⠀⠀⣰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⢻⠟⠀⠀⡾⢸⠀⠀⢀⡴⢃⡴⠛⠁⠀⢀⡎⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠃⠀⠀⣾⡴⠃⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣷⢀⡇⢸⡇⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣰⡿⣿⣿⠯⣰⡟⠤⠁⣄⣲⡿⣋⣠⠼⠛⠳⠦⣄⣀⠈⠉⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠹⢿⣿⣿⣿⡇⠀⠈⣧⣴⠞⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠞⣆⠀⠀⣼⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⡴⠁⣼⠀⢀⠞⠈⠋⠀⠀⠀⢀⡞⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣸⠏⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⢰⡇⣸⠃⠀⠀⠀⠀⠀⢈⡏⠀⠀⢠⡿⡽⣼⠏⢰⡿⡀⢆⢳⣾⣿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⣟⠀⠀⠀⠀⠀⠀⠈⣹⡟⣿⠀⠠⣿⣇⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣎⣴⢟⡀⠘⢦⢀⡏⠀⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠞⠀⢀⡟⠀⠁⠀⠀⠒⠂⠤⠠⠾⠟⢉⣱⣶⡦⣭⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⠀⢀⢜⡏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⣿⢸⡇⣿⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣿⡵⣽⠏⢀⣾⠇⢲⣹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠳⠦⣤⣀⣠⡤⠞⠋⠀⢻⡄⠀⣿⡍⠉⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠃⡏⠀⠀⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⣡⠔⠋⠀⠀⡼⠁⠀⢀⠀⠠⣤⣴⡶⠦⠔⠒⠚⠉⢹⠯⡈⠑⢮⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠹⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢸⡷⠃⣸⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⡏⢸⡿⣷⠀⠀⠀⠀⠀⠀⡟⠀⠀⣼⣯⣽⡏⠀⢸⣟⣰⠟⢭⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⡿⣷⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⠃⡼⠁⠀⠀⠀⡿⠘⢦⠀⠀⠀⠀⠀⠀⠀⢶⣶⡤⠀⠀⠀⠀⠀⠀⢀⣼⢿⡁⢀⣀⣰⣾⡧⠤⢤⠬⠖⢺⡉⠦⢀⣀⡀⠀⠀⠀⠺⠀⠘⡆⢸⡇⠀⠙⠲⣄⡀⠀⠀⢀⣴⠋⠀⢸⠀⠙⣆⢾⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢷⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢻⡇⢹⠀⠀⠀⠀⠀⢸⠇⠀⢰⡟⣼⢻⡇⠀⣼⡏⠥⢬⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢹⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡇⣼⠇⢀⡀⠀⢸⠇⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣹⠃⢸⡟⠋⢁⡼⠃⠀⠀⠀⠀⠀⠀⠉⠓⣒⣲⡗⠛⠉⠉⢻⡄⠀⡇⠸⡇⠀⠀⠀⠀⠙⣓⡶⠛⠁⠀⠀⢸⠀⠀⠈⢿⡎⢃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡇⢀⡞⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠣⣸⡇⠘⡆⠀⠀⠀⢠⣿⠀⠀⣾⣹⡏⢸⡇⠀⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠇⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠋⡼⠀⠀⠀⠘⠷⠀⢼⡃⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⣰⠇⢰⡇⣷⢠⡞⠃⢀⣤⣄⣀⠤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⢰⡇⠀⠿⣠⡧⠤⠤⠤⠶⠒⠲⡀⠀⠀⠀⠀⠈⡇⠀⠀⠈⣷⣸⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣷⡾⡄⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣒⣺⣧⣄⣷⣤⣤⣤⣾⡇⠀⢸⣏⡟⠐⣸⡇⢀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⣧⢀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡜⢰⣇⡀⠀⠀⠀⠀⠀⢹⡍⠂⠀⠀⠀⠀⠀⠙⠦⣄⣀⡤⠚⠁⠀⠀⠀⣰⠃⠀⢸⣇⢹⣏⠀⠀⠀⠙⢦⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠤⣤⣤⣤⣬⡦⣄⠘⣷⡇⠀⠀⠀⠀⠁⠀⠀⢀⣼⣯⣤⣼⣿⡳⣿⣳⣄⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠂⠀⠀⠀⠀⢀⡰⠋⠀⠀⢰⠇⠀⢸⡏⠀⠀⠀⠀⠀⣸⠃⠀⣼⣻⡇⢠⣹⡇⣠⠞⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⣿⣾⠻⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠀⡯⡟⠁⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠈⣿⣻⠀⠀⠀⠀⠘⣧⡀⠈⢫⡓⢤⡀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣿⣿⣴⣼⣷⠤⠤⠶⠖⠒⠚⠛⡟⠙⡏⢠⢧⡟⣧⣯⠙⣿⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠀⠀⠀⢠⡟⠀⠀⣻⡀⠀⠀⠀⠀⢠⣿⠀⠀⣿⢸⡅⢠⣺⡟⠁⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣳⠇⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡄⠀⠐⠺⡇⢽⣧⣄⠀⠀⠀⠀⠙⢦⣀⠙⢦⡙⠢⣄⣀⠀⠀⡇⢠⣀⣒⣖⡒⡶⣦⡴⠶⡶⠖⠛⠛⢛⣿⣿⠯⠟⢻⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⠈⣿⠃⠘⠧⠀⠘⣏⠪⡳⣦⡀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⣿⠒⠒⢋⡏⠀⠀⠀⣿⠙⣗⠒⠒⠋⢙⡇⠀⢸⡏⢺⣇⡾⢹⠃⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢹⣆⣀⠀⠈⠑⢿⡎⠉⣶⣴⣖⢛⣙⣿⣯⣭⡛⠀⠘⢉⠙⣿⣏⣉⣁⣿⣋⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⣶⡿⢻⣿⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⠃⠀⠀⠀⠀⠀⢿⡀⡼⣦⣝⣶⢤⣤⡴⠊⠁⠀⣀⡴⠚⣹⠀⢀⣼⡶⠀⠀⠀⣿⠀⢻⠀⠀⠀⢸⡇⠀⣾⠇⣸⣯⢀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣧⠈⠁⠀⠀⠈⣧⠒⢭⣉⡹⠿⣟⣉⡹⢿⣿⡀⣞⠉⣩⡿⠉⠉⢿⣿⣿⣶⣿⣿⣶⣤⡶⠀⠀⠀⠀⠀⡀⠸⣿⡁⢀⣿⣠⣴⠷⠶⠶⠴⠶⠦⢤⣄⣀⢈⡟⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⣷⣬⡟⠉⣉⣉⣿⠯⠷⠖⠛⣿⠛⡿⠃⠀⠀⠀⣸⡇⠀⣿⠀⠀⠀⢸⡇⠀⣿⠀⠘⣿⣦⡿⠂⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢴⡇⠀⠒⠒⠒⠤⣀⠀⠀⠀⠈⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣀⣀⣿⠀⢰⠉⣳⣤⠞⠙⣤⢿⠛⡟⣿⣄⠏⠀⠀⠀⠈⢿⡟⣿⣿⣿⣿⠋⠉⠛⠛⠒⠒⠒⠟⠚⠛⠛⠋⣯⠉⠀⠀⠀⠀⠀⠀⢀⡜⠃⠈⣿⣿⡟⣧⡄⠀⠀⠀⠀⠀⢧⠀⠀⢻⢻⡉⠉⠁⠀⣀⡠⠔⠶⠟⡟⠀⠀⠀⠀⠀⠀⠘⠀⠀⡟⠀⠀⠀⢸⡇⠀⣿⠀⠀⠘⣿⡇⠈⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡇⠉⠁⠀⢀⣿⡅⠈⠉⠁⠀⠑⠦⣾⣻⣄⢸⠿⠸⣦⠀⠀⠀⠀⠈⠛⡿⣿⢳⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⡰⠏⠀⠀⠀⠈⠙⠇⠹⡿⠶⠀⠀⠀⠀⠘⠲⠄⣹⡀⠻⡚⠉⠉⠁⠀⠀⣀⣠⡷⢤⣀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠸⣷⠦⡀⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠥⡏⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣇⠀⠀⠀⣼⢣⡯⠀⠀⠀⠀⠀⠀⠻⠇⡈⢻⡦⡀⠀⠳⣄⠀⠀⠀⢰⣿⢿⠀⠹⣮⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⡇⠀⠙⣦⡤⢶⠛⠉⢉⡐⡇⠀⠉⠙⠂⠀⠀⠀⠀⢸⠃⠀⠀⠀⢨⡇⠀⢸⠄⠀⠀⢈⡗⢠⡇⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⢰⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢷⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⣏⢐⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠼⣇⠈⢳⡀⠨⢧⡀⠀⠘⠛⠋⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⢼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢤⣀⢀⡟⢿⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⣷⠀⢸⡀⠀⠀⢸⡇⢸⡇⠀⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣟⠛⠲⠶⣤⣀⣺⡇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣼⡃⢹⠃⠀⠀⠀⠀⠀⠀⢀⣀⢀⠠⡏⠀⠀⣳⡀⠀⢿⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⠉⠃⠀⠙⠦⣄⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢸⡆⢸⡇⠀⠀⣸⡇⣸⡇⠀⢸⣿⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣿⣬⣿⠗⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠻⣧⡀⠀⠀⠈⣿⠁⢰⡿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡆⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢠⡟⠀⠀⠀⠀⠀⠀⠀⢿⡉⠋⢻⣧⣀⢶⢷⠧⠀⠘⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⠀⣿⠀⠀⣻⡇⢽⡇⠀⢸⣿⠀⠀⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣤⡾⠋⠙⣦⠀⠀⠀⠀⠈⢿⡄⠀⢰⡏⠀⣼⠃⠀⠈⠉⠛⠲⠶⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢳⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣈⣇⠙⠒⠁⡤⣷⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠘⡇⢹⡆⠀⣽⡇⢸⡇⠀⠸⣿⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⢀⣼⠃⠀⠀⠀⠀⠨⣿⣢⡿⠁⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠤⣄
⠀⠀⠀⠈⢳⡀⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣯⣿⡿⡷⢻⠿⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡖⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣀⣻⣼⡇⠀⣿⡇⢸⡇⠀⠈⣿⡗⠦⣤⣀⡀⠀⠙⠻⣦⣄⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⢘⣿⠁⢀⡟⠒⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢳⡐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠯⠟⠋⣩⣖⣻⢃⡞⠐⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢻⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣦⣤⠶⠾⠛⠛⠉⢀⣧⢰⡿⢷⢸⡇⠀⠀⢸⡇⠀⠀⠉⠉⠓⠶⣄⣈⠙⠻⠶⠶⠛⠉⠀⠀⠀⠀⣀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⠀⡾⠁⠀⠀⠀⠀⠈⠉⠛⠓⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⢘⣿⠏⠀⢀⠀⠀⠀⠀⠀⢀⣴⣾⠂⠀⠀⠀⠀⠀⠀⠾⣶⣴⣥⣽⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠰⣿⢸⡇⠸⣾⡇⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠦⠤⠴⠶⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢸⢲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠠⡄⠀⠀⠀⠀⠀⠈⡆⢀⣀⣤⣤⡤⡼⣤⣤⣲⣤⣴⠶⡾⣦⣄⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠁⠀⣌⢷⡀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣲⣿⣿⡆⠀⠀⠀⠀⢸⣷⣄⠀⡟⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⡴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⠀⠀⢿⡇⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢳⡀⠀⢀⣠⣤⠶⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣬⡓⡿⢦⣸⣻⠿⢓⣿⣦⠀⠀⠀⠀⠀⠀⣠⣴⣋⡹⢿⣻⡇⠀⠀⠀⠀⠀⠹⣆⠑⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡷⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠾⠋⢹⣿⠆⠀⢹⣇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠰⣶⣀⠀⠀⠀⢸⣇⣀⣠⣴⠷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡛⢻⡟⣿⣻⣿⠿⠟⠀⠀⠀⠀⠀⢸⣿⠾⢋⣰⣾⡟⠀⠀⠀⠀⠀⠀⠀⠙⣮⠁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣻⣿⠍⠈⠃⠀⠀⠸⢿⡇⠀⠘⣿⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋
⠀⠈⠉⠉⠙⠋⠻⣿⢹⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⢧⡅⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣍⣿⣿⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡘⡇⠀⠀⠀⠀⠀⡀⠀⣀⣠⣴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠶⠞⠛⠉⠉⠁⠀⣧⡨⠉⣉⣠⣦⠀⠀⠀⠀⢸⣷⠀⠀⣿⣇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠹⣦⠀⠀⣘⡀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⠳⣶⣌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⢰⣢⣤⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠟⠛⠉⠉⠁⠀⢀⠀⣿⡟⠋⠉⠙⠛⠛⠋⠉⣹⠇⠀⠀⠀⠀⢸⡿⣆⢸⡏⣿⡀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢾⡛⠒⠶⠶⣦⣤⣤⣀⣈⣷⡄⠙⢷⣤⡀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢹⣿⣳⡞⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠛⢿⠟⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠼⠞⠋⠉⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⢿⣯⣉⣀⣀⣤⣤⣤⣤⠴⠶⠚⠛⠛⠛⠇⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣿⠹⣾⠇⢹⣧⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⢤⣄⣀⡀⢩⣩⠉⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠚
⠀⠀⠀⠀⢀⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠳⣽⣿⡞⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠲⢦⣀⣠⣤⣼⣷⣷⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣠⡤⠖⠚⠋⠁⠀⠀⠀⠀⣀⣀⣤⣤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⣆⠐⢻⡆⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣦⣄⣀⣤⣄⣤⣤⣤⣤⡤⠤⠶⠖⠛⠋⠉⠉⠀⠀⠀⠀
⠀⠀⠀⢀⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⠒⠒⠤⠭⣻⣷⣤⣤⣤⣼⣿⡛⠲⢦⣀⠀⠹⣇⠈⠳⣾⣿⢛⡟⠁⠀⠀⢳⡀⢀⡀⠀⢀⣀⣤⡤⠞⠚⠋⠉⠀⠀⠀⠀⣀⣠⣤⡶⠶⢿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠸⣧⡇⠙⠛⠏⣿⡄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⡀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠈⢉⣓⣊⡉⠻⢦⣄⠉⠛⠶⣼⣦⡀⠙⠻⣏⣀⠀⠀⢀⣀⣷⠾⠷⠛⠉⠁⠀⠀⠀⠀⢀⣠⣤⡶⠞⠛⠉⠉⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠘⢆⣠⣤⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡃⢠⣤⣠⡾⠋⠁⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⣿⡉⠉⠉⠙⠳⠾⢽⣶⣴⡄⠈⠁⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠋⠉⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣸⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢲⣶⠦⣤⣔⣆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⡋⢉⡀⣳⡀⠀⠀⠀⠀⢠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠇⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠛⠛⠛⠋⠉⣁⣀⡄⠀⠀⠀⢀⣠⣤⡶⣿⣩⠟⠉⣉⣹⡧⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣞⠀⠀⣇⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠤⠤⣄⣇⣀⣀⡀⠀⠀⠀⡀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⠞⠛⢻⣯⠿⠛⠋⢁⣠⣴⣶⣿⣛⣿⣦⣹⣅⡴⠞⠉⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⠉⣟⠉⠉⢹⡏⠉⣿⠉⠉⠓⠒⠲⠶⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣴⡶⠿⠋⠁⢸⠃⠀⣰⣿⠃⢸⣯⣧⡀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢦⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⡟⠀⠀⣼⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⠁⠀⢀⠀⠀⡏⠀⠀⣿⠁⠀⠈⠁⠀⢳⡀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⡇⠀⢀⡏⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡜⠀⢸⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢲⡶⠶⠶⠤⢤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⢠⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢰⠃⢀⡇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣠⠞⠁⠈⠉⠒⠲⠤⠤⠖⡖⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠀⠀⣼⠂⠀⣸⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⠏⠀⢸⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠉⠙⠓⡶⠤⢤⣀⣀⣀⡤⢿⡀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢻⠀⠀⡿⠀⠀⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⣾⠀⠀⡎⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⣾⠀⢸⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠧⣤⣄⡏⠀⢠⠇⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠹⡆⢀⠴⠋⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⣸⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠽⣰⠁⡾⠁⠀⡼⡷⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⣽⠛⢶⣤⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠸⡗⠀⠠⡷⢇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡿⣾⠀⠀⣏⠁⠀⣸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⢰⠁⠀⢸⠇⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⢘⣿⡿⣀⣀⣟⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⠀⠀⢀⠇⠀⢀⡞⢰⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢹⢿⡏⠉⢙⡏⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠏⠀⠀⡾⠀⠀⡼⠀⢛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⠁⠀⣸⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⣼⠃⠀⢀⣧⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠀⠀⡟⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡅⠀⠀⢸⡇⠀⠀⣸⠀⢰⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣿⡀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡟⠀⣸⠃⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⡬⢽⣶⣤⣾⠁⠀⠀⡇⠀⣸⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠛⡇⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⢠⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣟⡽⠋⣽⠏⢀⣿⣷⡇⠀⠀⢰⢧⢹⡟⢑⡈⢿⣟⢯⠓⢲⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣧⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠾⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠈⠛⠰⣟⣉⣀⣿⣭⡿⠀⠀⠀⡞⠈⠛⠳⢾⠭⢧⣈⢛⣯⣅⣉⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢹⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⡇⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠙⠫⣗⢬⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠷⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠚⠉⠉⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⠼⠟⠻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠶⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹