⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠉⠉⠉⠙⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠤⣄⡀⢀⠝⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡠⠚⣅⡬⣍⣠⠋⣈⠿⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠘⣮⣙⠧⣾⣶⣷⡬⣷⠀⠀⠀⢀⣴⣲⡿⠿⣓⡾⠡⠀⠉⠉⢿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⠀⡇⠀⠀⢸⠉⠙⠁⠀⢹⣷⢻⣇⢀⣿⣾⣿⣾⡿⠋⡅⠀⠀⢀⣀⣤⣤⣤⣬⣭⣉⡛⣶⣶⢦⣄⣀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⡰⢡⢿⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠻⣆⠙⣿⡿⢿⣹⡇⠀⢸⠃⣸⣷⡛⠉⠀⠀⠀⠀⠀⠀⢉⣨⣿⣿⡍⠀⣠⠈⢻⡄⠀⠀⠀
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⠇⠀⡴⢁⠎⡸⢀⡇⠀⠀⢸⠁⠀⠀⠀⠀⣠⣿⣽⣿⣡⡼⢿⣧⡀⣿⠀⡏⢿⣷⣤⠶⣒⣶⠛⠛⠋⠉⣩⢿⣿⡗⠀⠘⣷⣤⣿⣦⠀⠀
⠀⠀⠀⠀⢹⡄⠀⠀⠀⢀⣎⣠⣊⣰⡫⠴⣳⡞⠀⠀⢀⡿⢤⣤⣤⡆⣼⣻⣿⣿⣿⡇⠀⠈⠻⣷⣼⣆⣿⠈⣿⢃⡞⣹⢸⡦⣤⣠⣾⡯⠸⣿⡆⠀⠀⠈⢿⠻⡿⣿⠀
⠀⠀⠀⠀⡾⠀⠀⠀⣠⢏⣰⡙⡒⡶⠶⣿⠟⠀⣀⡴⣞⣋⣭⣼⡿⠅⢾⣿⡿⣾⡿⣿⢟⡷⠃⠀⠉⠻⣿⡄⢻⣩⠴⢃⣾⣿⣿⣿⠟⠏⠀⢿⣿⠀⠀⠀⠈⣷⢹⣽⡆
⠀⠀⠀⢰⠇⠀⠀⠀⢻⡟⣶⣝⢿⣧⠞⢁⣤⠟⠋⠙⠻⠿⠿⢿⡿⠀⠀⢡⡀⣿⠇⢹⠏⠀⠀⠀⠀⠀⠈⢡⠟⣡⣴⡾⠻⣫⡿⢃⣴⠋⢀⣿⣿⠀⠀⠀⢠⠟⣼⣻⠇
⠀⠀⣰⡟⠀⠀⠀⡰⠸⣷⣿⠯⢷⠁⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⢻⣿⣷⣿⣭⡾⣿⠟⣠⣾⣿⣿⢠⢀⣴⡿⣴⣷⡟⠀
⠀⣰⡟⠀⠀⠀⡰⠁⠀⠈⠻⣍⡉⢦⣯⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⡥⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠙⠿⣯⣩⣤⡶⣞⣿⣿⢿⣧⣿⣾⣿⣿⠛⠉⠀⠀
⢰⡟⡄⠀⠀⠀⡇⠀⡀⠀⠀⡄⡏⢹⣯⢻⣆⠑⢆⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⣴⣶⠞⠀⠀⠀⠀⠀⠀⣰⢻⠀⠀⠀⠻⣿⣿⣿⣿⠿⢫⣿⣼⣹⣿⣿⣿⡀⠀⠀⢠
⠈⢧⡳⣄⠀⢤⠱⡀⢳⠀⠀⣇⠘⣼⣿⣿⢿⣷⣤⣀⠀⠀⠀⠀⠈⠉⠹⠿⣿⢻⣟⠅⠀⠀⢀⠔⠁⣠⠞⢁⡏⠀⠀⠀⠀⠘⢿⣟⠉⠀⢸⣏⡏⢹⣿⣧⠙⠿⣦⣀⡞
⠀⠀⠙⠻⢦⡀⠳⣝⢦⡳⡄⣹⣄⠈⠻⣿⣶⡙⠀⠙⠛⠶⣤⣄⣀⣀⣀⣠⡿⢀⣽⡄⠀⠀⣀⣴⣾⣷⡄⠸⠀⠀⡆⠀⠀⠀⠈⠻⣦⡀⠀⢿⣿⣄⡙⢿⣿⣯⣾⣟⠀
⠀⠀⠀⠀⠀⠉⠳⠮⣽⣟⣻⣮⣿⣿⠶⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⡹⣟⣿⣯⠽⠶⢽⣖⣛⠉⠀⠉⠻⣿⣆⡄⠀⢱⠀⠀⠀⠀⠀⠀⠙⠳⢤⣉⡙⠉⠙⠛⠱⠞⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⢹⣽⡜⠤⠤⠀⢤⣔⣮⣿⣿⡿⠂⠀⠀⠀⣨⣿⣧⠶⠒⠋⠉⠙⣧⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣸⡎⡛⢧⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣥⣄⡀⠀⠀⣼⠋⠁⠀⠀⠀⢠⠃⡏⠹⢤⠀⠀⠀⠀⠀⠀⠀⣸⣿⢷⣿⣵⠟⠛⢷⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣤⣴⠞⠉⠀⠀⠀⠀⠀⠉⠉⣽⣿⣧⣴⣯⣽⣿⣆⢀⡇⠀⠀⠀⠀⠀⡜⢸⡇⠸⡎⠀⠀⠀⠀⠀⠀⢰⡏⠈⣾⡟⠁⠀⠀⠀⠙⠻⣦
⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠛⢷⣷⣦⡦⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡮⢿⣿⣿⣮⣿⣼⡗⠀⠀⠀⠀⡆⠃⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⡿⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣥⣟⣼⠿⢸⠇⠀⠀⠀⠰⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣹⣦⣠⣤⣤⠤⠤⠶⠖⠒⢾⣷⣌⠉⠉⠀⢀⣿⠀⠀⠀⠀⠀⡇⠈⡞⡄⠀⠀⠀⢀⡄⠀⠀⣸⠂⠀⢸⡇⠀⠀⡄⠀⠀⠀⠀⠀
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡽⣷⡄⠀⣸⡇⠀⠀⠀⠀⢠⡇⠀⣜⢌⣦⡀⢀⠎⠀⢀⡼⠁⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣶⣿⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⢍⣛⠻⠶⠖⠋⠀⠀⠀⠀⠘⣼⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⠀⠀⢀⣀⣤⠶⠶⣤⣀⠀⣼⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⠓⣚⣛⠋⠁⠀⠀⠈⠙⣷⢯⣟⣁⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀