⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⢀⣤⣤⣤⡀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠁⣀⣴⡾⣟⢯⡽⣯⢿⣧⣄⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⣴⣾⣿⣏⡷⡽⣾⣿⣿⣿⣻⣿⣿⣄⡀⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⣿⣷⣻⣿⣯⢾⣝⣿⣯⡯⣾⣿⠛⠛⠟⠻⣆⡀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣿⣿⡟⣻⠛⢯⣉⡿⢻⡛⣿⣿⣿⣆⠀⡂⠀⢃⠙⢆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⢀⣾⣾⣠⣿⣷⣿⣿⢿⣿⣿⣿⣧⣼⣾⡱⠀⢡⠀⡅⠀⠆⢇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡠⠔⠊⠁⣠⣴⣿⣿⣿⠿⣿⣛⣺⣿⣿⣟⣺⠿⢿⣿⣿⣿⡁⠈⠂⠸⣈⡄⢈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡔⠊⢀⣤⠶⣿⣻⡿⣽⣷⣾⣿⡿⡿⣿⢻⣿⡿⡿⣿⣷⣶⣯⣽⣻⡷⣦⣀⠉⠘⠞⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⡀⠘⠓⠚⠛⠛⠳⠿⠷⡿⣟⣿⢡⣧⣭⠘⠾⢠⣥⣼⣿⣻⣿⢯⡷⣻⣽⢻⢿⣣⢤⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠒⠒⠒⠒⠤⡔⠈⠼⠛⢿⣿⣂⠘⠋⠀⠀⠈⠛⢀⣿⣿⠛⠍⠉⠉⠉⠉⠉⠉⠙⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡔⠀⢽⣿⡿⣦⣀⠐⠐⡀⣴⣿⣿⡇⠀⡤⠞⠉⠉⠉⠁⠉⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡀⠾⣿⣿⠿⠿⠾⢿⡱⢿⣿⣿⣷⡀⠘⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡠⠚⠀⣠⣿⣿⣷⠼⣻⡇⠀⠂⠤⢠⣿⣿⢙⣠⣷⣶⣤⠀⠑⠢⢄⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡰⠁⢠⠤⠞⠛⠋⣉⣤⣒⣻⣏⠑⡄⠀⣿⡿⡉⠛⢿⣿⣿⣿⣷⣦⣦⣀⣀⣀⡀⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡘⠁⡠⢃⣠⣴⣶⡻⣽⡿⡽⣭⣿⣳⣤⣾⣿⡻⣽⣳⣤⣈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠞⠀⣰⣟⢯⣻⣟⣶⣽⣿⣏⢷⡳⢮⣽⢻⣷⡺⣵⢳⣽⣿⣻⣷⣦⣄⡀⠙⠛⠛⠛⠿⠿⠿⣿⣶⣠⡀⠁⠑⠠⣄⠀⠀⠀⠀
⡰⠊⢀⣾⢻⣼⣟⣼⣿⣾⡿⣽⡞⣧⡻⣝⡾⣿⣟⣳⡭⣗⣻⣷⣻⢾⣽⣻⢿⣷⣦⣤⣀⣀⣀⣀⠀⠀⠈⠙⠛⠧⢤⠀⠘⢢⡀⠀
⡇⠀⣾⢧⡻⣽⢿⣾⣿⢯⣟⡿⣽⢲⣏⢷⣹⢳⣎⢷⣹⢞⣿⣳⢯⣟⡾⣽⣻⣞⣷⣻⢿⣿⣿⣿⣿⡿⠏⠈⢩⣶⣶⣬⣢⡄⠘⡄
⢇⠈⢻⡞⣵⣫⡟⣿⣯⣟⣾⣻⣧⡟⣼⢫⡞⣧⣛⣮⢗⣯⣷⣻⣟⣾⣻⢷⣻⣞⡷⣿⣿⣻⣽⣻⢿⣿⣢⡀⣿⣿⣿⣿⣿⣇⠀⠇
⠘⡆⠈⣿⢧⣳⠉⠈⠳⣿⣞⣿⣳⣽⣳⣯⡟⠉⣽⣶⣯⠸⣿⣷⣻⢾⡽⣯⢷⣯⣿⣿⣳⣟⡾⣽⢯⣟⡿⣿⣟⡿⣿⠿⢹⢱⠀⡁
⠀⡇⠀⣿⣯⡟⠀⢀⣮⣿⣿⣿⢿⣟⣿⣽⣿⠈⠻⠿⢟⣃⣿⣷⣯⢿⡽⣯⣿⣿⣟⣾⣳⢯⡿⣽⣻⢾⣽⣳⢯⣿⣯⣵⣷⠋⠀⡁
⠀⠄⠀⡿⣞⣇⠀⡞⣿⣿⣿⡿⣿⢯⣟⣳⡭⣟⡽⣫⢏⡿⣜⣿⣞⣯⣿⣿⣿⣟⣾⣳⢯⡿⣽⣳⣯⣟⡾⣽⣿⡿⣽⣳⡿⢀⠀⡁
⠀⠆⠀⠿⣼⡿⣦⡿⣿⣿⢿⣼⢿⣧⣻⣷⣻⣎⣷⣯⣻⣜⡷⣺⣯⢿⣽⣿⣟⣾⣳⢯⡿⣽⣳⣟⡾⣽⣻⣿⢿⣽⣻⣿⠇⡌⠀⡆
⢠⡃⢀⣹⡿⣽⣻⢷⡼⣉⣀⣀⣉⣀⡉⠙⡳⠻⢿⠿⢷⣿⣽⣷⣿⣻⣿⣟⣾⣳⢯⡿⣽⣳⣟⡾⣽⣿⡿⣯⣟⣾⣿⡟⢀⡃⢀⠇
⢸⠂⠸⣦⡿⣯⣟⣿⣿⡟⠛⠛⠛⠽⠻⣽⣻⡷⣷⢲⣤⣄⣁⡙⢳⣿⣟⣾⣳⢯⡿⣽⣳⣟⡾⣽⣿⣯⣟⣷⣿⢿⣻⠃⢠⠁⢸⠀
⢸⠀⣸⣿⣟⣿⡿⣞⡿⣇⠀⠀⠀⠀⠀⠀⢸⣏⠉⠙⠓⠚⠽⣯⣟⣿⣞⡷⣯⢿⣽⣳⣟⣾⣽⣿⣻⢾⣽⡾⠋⠉⡔⠀⡞⠀⡝⠀
⡸⠀⢹⣹⣯⡿⣽⢯⡿⣽⠀⢀⠀⠀⢀⠀⢸⣿⣿⣶⣦⣬⣤⣿⣻⡽⣾⡽⣯⣟⣾⣳⣿⣾⣿⣳⢯⣿⠿⠁⡐⠀⣆⠜⠀⡴⠁⠀
⡝⠀⢸⣽⢾⣿⢯⡿⣽⣻⡎⠀⠀⠀⠀⠀⣾⣿⣻⣽⣳⢯⣿⡷⣯⣟⣷⣻⢷⣻⣾⡷⣿⣟⣾⣽⣿⠋⠀⡴⠣⣄⣀⣠⠞⠁⠀⠀
⡇⠀⡏⣾⢿⣯⢿⡽⣷⣿⣇⡀⠐⠉⡁⠀⣿⣿⣳⢯⣟⣯⣿⣽⣳⣟⡾⣽⡿⣟⢯⣝⣣⣟⣼⠏⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⡇⣿⣟⣯⣟⣿⡿⣽⣾⠀⠀⠀⠀⠰⣿⣽⢯⡿⣾⣽⡿⣞⣷⣿⢟⡷⠛⠃⣀⡀⠉⠉⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⢡⣿⣟⣾⣿⣻⣽⣳⣟⡎⠄⠑⠒⢴⡿⣿⢯⣟⣷⣻⢿⣻⡝⠊⠁⣀⠤⠚⠁⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⢹⣹⡾⢿⢳⠿⠾⡷⢿⠇⠀⠀⠆⢸⣻⣟⡿⣾⣽⠟⢁⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡀⢨⣸⠷⠫⠯⠾⠽⠵⠿⡀⠀⠀⠢⠜⠚⣿⣽⣳⣿⡇⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣅⠀⠿⠀⣤⠤⠤⢤⠊⠈⠀⠀⠀⠀⡇⠀⢿⣳⢿⣯⡇⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠢⠴⠖⠁⠀⠀⢸⠀⠧⠐⠀⠐⢔⠀⠀⢻⣟⡿⣞⡇⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢱⣀⢀⠀⢸⠀⠂⢸⣿⡽⣯⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡞⡭⡄⠈⠰⠄⡜⠿⣷⣻⣿⣀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠄⢸⡽⡖⢿⣤⣆⣸⡃⠀⠀⠋⢩⡟⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⢏⠖⡬⡹⠃⠱⣤⡀⢠⡛⠾⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠝⢄⢸⡍⢲⡁⠀⢠⢋⡽⢓⡇⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⣤⡶⢼⣜⡡⡶⠀⣸⠥⣊⣝⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⢐⡉⠢⡑⣭⢒⡇⢀⠷⡘⠴⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣇⠈⠳⡤⠬⠞⡮⡇⢸⢣⣙⠜⣹⡀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠈⠣⠤⠜⠁⢼⣣⣝⣪⣅⢳⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠴⠦⣀⡀⠈⠈⠉⠘⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀