⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⢿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣬⣙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⢶⡿⢛⣭⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢮⣙⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣶⣋⡴⠋⠁⠀⠀⢀⣀⣤⣴⡶⣾⡯⠟⠋⠉⣯⡉⠛⠛⠛⠷⠦⣤⣀⠀⠀⠀⠀⠀⣿⢹⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⡿⠋⠀⠀⢀⣠⡴⠟⠛⢉⡴⠋⠁⠀⠀⠀⢰⠃⠙⢦⡀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣤⣾⡾⣿⣿⣀⣀⠀⠀⠀
⠀⠀⠀⣿⡟⠀⠀⢀⣾⠟⠉⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠳⡄⢀⠀⠀⠀⠀⠀⠸⡗⢿⣜⣿⣿⡟⢩⡷⠃⠀⠀
⠀⠀⠀⠘⢷⣤⣠⡞⠁⠀⣰⡿⠁⠀⠀⠀⠀⡀⣀⡴⠃⠀⠀⠀⠀⢶⠛⢿⣯⡙⢦⠀⠀⠀⠘⣄⠈⠻⣿⣷⢾⡇⠀⠀⠀
⠀⠀⠀⠀⢠⡟⣙⠔⠀⣼⡟⠀⠀⠀⠀⠀⢸⡋⠑⠚⠉⠉⠁⠀⠀⠈⠳⢤⣍⣛⣹⠃⠀⠀⠀⠘⡆⠀⠈⠻⣍⠀⠀⠀⠀
⠀⠀⠀⣰⠋⠋⠁⠁⣸⣿⢤⡀⠀⠀⢠⡀⠀⢧⠀⠀⠠⢖⡤⠴⠾⠟⠦⢤⣘⡍⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠳⣤⡀⠀
⠀⠀⢰⠃⡤⡔⠂⢠⣷⠃⠀⢙⠦⢄⡘⣌⠓⠮⠷⢀⡴⠟⢩⡟⠉⠉⢻⡉⠺⣟⠀⠀⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⠘⠟⣄
⠀⢀⡏⠈⣰⠤⠖⡟⡏⢨⣯⣽⠟⢯⡙⠒⠉⠉⠁⠀⠀⠀⠸⠒⠒⠚⠋⠁⠀⡟⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠈
⠀⢸⢁⠞⠇⠠⢸⣼⠁⡟⠠⡇⣠⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⣿⠀⠀⠀⠀⠀⠀⡧⢤⡀⠀⠀⠀⠀⠀
⠀⡿⠀⢀⣤⠴⠛⠉⢸⠁⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡏⠀⠀⠀⠀⠀⢀⠇⠈⢷⠀⠀⠀⠀⠀
⠀⣧⠞⣹⠃⠀⠀⢠⡈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⣸⠀⠀⠀⠀⠀
⠈⠀⢰⠃⠀⠀⠀⠀⡟⣷⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡜⢀⡴⠃⠀⠀⠀⠀⠀
⠀⢀⡟⠀⡀⠀⠀⠀⢸⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣠⠀⠀⣸⢋⡍⠀⠀⣀⠀⠀⠀
⠀⢸⠁⢰⡇⠀⠀⠀⠀⢣⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⣾⠃⠀⣰⢏⡜⠀⣠⠞⠁⠀⠀⠀⠀
⠀⢸⡀⡏⢻⡀⠀⠀⠀⠀⠳⡀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣡⠞⠁⣣⣀⣴⣃⣼⣾⣭⣤⡄⠀⠀⠀⠀⠀
⠀⠈⢷⣧⠀⠻⣄⡀⠀⠀⣄⣙⢦⡄⠀⠀⣩⣝⠒⢤⠀⠀⠀⣀⣤⣴⣾⣿⣕⣶⠾⠟⠛⠻⣏⣉⣀⣼⣼⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠃⠀⠈⠙⠲⢤⣈⣢⣈⠉⠓⠒⠛⣋⠙⣾⣷⣴⣯⣷⡋⠁⢀⡼⠋⠁⠀⣀⣀⡤⠿⡿⠿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢠⣿⣿⣦⣟⣉⣿⠞⠉⠀⢀⣤⠞⠛⠁⠉⠉⠛⠳⢯⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠁⠀⢠⣿⣿⣿⣿⣉⣻⠟⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢸⠁⠀⠀⢸⡿⠋⢉⡟⠉⠉⠀⠀⢲⡲⠛⠀⠀⠀⠀⠀⣀⡤⠖⠒⠦⣤⡈⢣⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⣀⣾⠁⠀⠀⠀⠹⠤⠞⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⣠⡴⢻⣥⡶⠛⠓⠲⢦⣙⣷⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⢾⣿⣟⡶⡄⠀⠀⠀⠀⠀⠀⣤⢤⣤⣴⢯⣀⢀⡴⢛⣥⡾⠟⣿⠃⠀⠀⠀⠀⠈⢻⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣱⣿⣿⣿⣁⣽⣆⡶⣶⣦⣀⣀⣿⠀⢳⣽⣷⣿⣿⣴⡟⠋⣠⠾⠃⠀⠀⠀⠀⠀⠀⠈⢷⡻⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢻⣻⡻⣿⣻⣝⢿⡋⣙⡇⢻⣏⢻⣿⣻⣝⢿⣉⣙⡟⣿⡟⣋⣽⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠙
⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⡟⢩⡿⢸⡇⣿⡇⣿⢿⡇⣇⢾⣿⣾⡇⣯⡇⣿⡸⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢀⣼⣿⢰⣶⠛⢹⠖⣺⠚⢹⡖⠛⠋⢸⡗⠛⠓⠲⣟⢻⠒⠛⢻⠛⠒⠚⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢠⣿⣋⣿⢋⡏⢠⠏⡴⠃⠀⢸⠃⠀⠀⢈⣇⠀⠀⠀⢟⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀