⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡇⣰⣾⢦⢃⡾⣴⣿⣇⣀⡀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡝⢿⢹⣿⡏⠘⣇⡇⢻⠟⣿⡷⣶⠊⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣘⢷⡒⢳⣏⡏⣹⠇⣤⣯⣴⣧⣴⣿⠟⣟⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡆⡉⢻⡜⣇⣵⠟⠉⠉⠀⠈⠉⠋⠳⣾⣿⢋⣞⣛⣲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⣽⠦⢽⣿⣧⡿⠁⠀⠀⠀⠀⢀⡀⢀⡀⠈⢷⠞⣿⣩⣶⣆⠀⠀⢀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⡉⢳⣄⣿⡫⠀⠀⢀⣀⡰⣮⣭⣺⠍⠀⠀⠀⣿⠏⢉⣿⣉⢀⡀⢸⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡋⠉⢹⣿⠀⠀⣜⣯⣗⡿⠟⠉⡝⣾⠤⠄⠀⠹⣿⣯⣈⣽⠏⠀⢸⠒⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⢾⣷⣽⣥⣸⢏⡤⠟⠋⠉⠀⠀⡤⣰⡧⠈⠙⠶⢦⢻⡷⣟⣾⠿⡇⠀⣜⣠⣾⠾⣾⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣷⡟⠂⠀⠀⠀⣋⣝⡿⠻⢿⡿⠃⠀⠀⠀⠀⠀⣀⣈⡀⠀⠀⠀⠈⣿⡿⣶⣿⢦⡹⣄⢸⠀⠙⣞⣷⣒⣺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠃⠀⠀⠀⠀⢸⡿⢉⢿⢃⠀⠀⠀⣠⣾⡍⠒⠢⢬⣷⡄⠀⠀⣽⣷⣸⣿⣧⠀⣸⠿⠛⠛⢓⣂⠥⠚⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⣷⡞⢬⣿⡀⠀⠀⢿⣯⠄⠤⠤⠤⣿⡿⠂⠀⣿⣿⣹⣥⠿⣿⣧⠎⠈⠉⠉⠛⡗⠄⣤⢌⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠙⠿⠿⢾⣇⠀⠀⠈⠿⡇⠀⠀⠀⡟⠁⠀⣠⡿⠿⡿⠟⠋⠉⠁⠀⠀⠀⢀⡾⢻⡆⠿⠿⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠋⢷⣄⠀⠀⢸⠀⠀⡼⠀⣠⠾⢻⠟⠢⢄⣤⡶⠶⣄⣠⣤⣤⣠⡴⠋⠉⠀⠀⠀⠀⠙⠙⠶⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⡙⣷⠆⠬⠵⡾⢥⡞⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠏⡾⢻⢀⣄⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢳⡀⠀⠀⠊⠉⢠⠀⢠⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣇⢸⡈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠳⠀⠀⠀⢀⡼⠀⡌⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⠀⠀⣇⠀⢰⠃⠀⡸⠀⠀⠛⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠸⠇⡀⢀⡸⠤⡀⡆⠀⠃⡄⢰⠀⠀⢙⣿⣿⣶⣶⡾⠛⠛⢹⢿⡿⠷⢶⣮⣧⡀⠀⠀⠀⠘⣴⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣏⣀⣠⣶⡀⠀⣇⣀⢿⡇⠀⠁⠀⢀⣧⣀⣠⠴⠛⢉⡼⣿⠏⠀⠀⠀⣸⣿⠁⢠⡤⣿⣻⢿⡀⠀⠀⠀⢱⣣⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠉⠛⠛⠿⢯⣤⠝⢒⣺⠟⠛⠛⢛⣽⣳⠤⣲⡟⣹⠋⠀⠀⠀⠀⣿⣿⠀⣜⡜⣕⡳⠀⢙⣿⢦⣟⠷⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠛⢛⡲⠖⢚⣷⠾⠟⠁⠀⠜⠉⢠⠋⠀⠀⠀⠀⠀⣿⡇⣸⣟⣾⠋⡠⣰⠃⠀⠐⢶⡙⠪⣿⢷⡆⠀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⡔⣛⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⢻⡇⣿⣿⢃⠞⡴⠁⠀⠀⠀⠀⠑⠦⣘⠵⢧⠀