⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠢⣀⣿⣿⣟⣀⡼⠀⣞⠁⣾⣿⣿⡟⠢⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣀⣀⣀⣉⡉⠉⠀⠀⠀⠈⠣⣿⣿⣿⣇⡤⠃⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣹⡿⠟⢻⡟⢻⣿⠛⠳⣶⣶⣤⣤⣬⣉⣁⠀⠀⢳⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⣴⠃⣠⣿⢁⡾⡿⡄⠀⡿⠹⣆⢸⣻⣟⠻⣿⣷⡶⣤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠓⡠⠖⠒⠛⠓⠤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⣶⣿⣺⠋⡟⡿⠙⡇⢷⢀⡇⠐⠻⣿⡏⠻⣶⣿⢿⣿⣷⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠎⣀⡀⠀⠀⢶⡆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⡿⠟⣿⣿⡿⠇⠘⣿⠁⢶⢶⣿⣧⠤⣽⣿⠹⠏⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⠃⠀⣀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠏⢸⣿⣋⣻⠘⠋⠛⠃⠀⠀⢹⠀⠀⠘⠿⠟⠀⠁⡽⠆⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠙⠓⢃⡠⠴⣇⠀⠀⠀⠀⠀⠀⠀⣬⠔⠊⠋⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡤⠲⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡌⠙⣯⠽⠛⡇⢠⠋⠉⠓⠢⣄⠀⢀⡜⠀⢧⠀⠀⠀⠘⡄⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⢮⢿⠇⠀⢰⠈⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⠖⠉⢙⣿⠆⡞⣫⣉⠙⢟⠒⠢⢄⠀⠀⠙⠧⡙⠆⠘⡄⠀⠀⠀⠈⠓⢄⡀⠀⠐⠀⠀⠂⠀⣀⡱⠃⡼⠀⠀⣸⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡌⢹⡞⠁⠀⡴⢻⠃⣾⢇⠏⠙⠦⣈⣷⢤⣘⣿⢆⠀⠀⠙⢦⠀⢧⠀⠀⠀⠀⠀⠸⣏⠳⡤⣀⣀⡤⢾⠏⠀⢰⡇⠀⢠⠇⠀⠀⡠⠊⣡⠟⠳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⢇⠸⣿⠂⠀⡞⣱⣿⡾⢻⡞⠀⠀⠀⢈⣿⣶⡽⣿⣿⣷⡀⠀⠀⠱⡈⣆⠀⠀⠀⠀⠀⡏⠢⡙⡄⠀⡰⠋⠀⢀⡟⢀⠔⠁⠀⢠⠊⠀⡜⠁⠀⠀⡂⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢯⠘⣿⡇⠀⣼⡞⡟⣿⡿⢿⣯⠀⠀⠀⠀⣯⣿⣿⡈⣟⠞⡷⠀⠀⠀⠱⣸⠀⣀⣀⣀⣀⠷⠒⢒⣾⣿⠦⠤⠤⢾⡓⠁⠀⠀⡰⠁⢀⡜⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢶⣿⡟⠀⢰⣿⡿⢸⠀⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⠇⠾⠀⡇⠀⠀⠀⢀⣯⠞⠉⣀⣻⡀⣠⠾⣽⡿⣿⣿⡆⠀⡼⠁⠀⠀⣼⠃⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡿⠁⠀⠀⢸⠟⡇⠸⠆⠙⠿⠟⠁⠀⢀⠀⠀⠉⠁⠀⠀⠀⡇⠀⠀⠀⣸⡯⠤⣿⣿⣿⣯⣷⢿⣿⣷⠿⡿⣦⣽⢷⡀⠀⢸⡹⠀⡜⠀⠀⣠⠄⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠈⠀⢧⠀⠀⠀⠀⠀⢀⣀⡩⠥⢴⣆⠀⠀⠀⢰⠃⠀⠀⠀⢹⣤⣤⣿⠟⠙⠶⣇⣿⡏⡜⠀⢣⠘⣯⠤⠗⠀⢸⠃⢠⠁⣠⠞⡏⠀⠀⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣌⠣⡀⠀⠀⠀⢸⠀⠀⠀⠀⣹⠀⠀⣠⠏⠀⠀⠀⠀⠀⣿⣍⠁⠀⠀⠀⠈⢹⣁⡇⠀⠘⠛⠁⠀⠀⢀⠇⠀⠚⠊⠁⡸⠀⠀⣸⣿⣿⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠹⣷⣜⠢⣀⠀⠈⠢⢄⣀⠴⢃⡠⠞⠁⠀⣀⠴⢤⡀⠀⠹⣿⣷⣢⠤⢀⡀⠼⡉⡧⠤⠤⣀⠀⠀⠀⡘⠀⠀⠀⠀⢰⠁⠀⢠⣿⣿⣿⣇⠀⠀⠀
⠀⠀⠀⣼⣧⠀⠀⢠⠔⠀⢲⠓⠻⢮⣳⣦⡉⠁⠀⠀⠀⠉⢁⣀⠤⠖⠊⠀⠀⠀⠙⢆⠀⠈⢿⡇⠩⣍⡠⡀⡉⠉⠐⠲⠤⢌⣉⡸⠃⠀⠀⠀⠀⡇⠀⢀⣿⣿⣿⣿⣿⡀⠀⠀
⠀⠀⢀⡇⡏⢀⠔⠁⠀⠀⠈⠀⠀⠀⠀⠉⠉⠓⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢻⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣏⡤⠄⢒⡿⠋⡸⠀⠀⣸⣿⣿⣿⣿⣿⣇⠀⠀
⠀⠀⣸⢇⠖⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠕⠒⠤⠤⠤⢄⣀⢀⣘⠦⠤⠼⣦⠔⠒⠒⠒⠒⠒⠚⠉⠁⠀⠉⠉⠉⠀⢀⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⣰⠟⠉⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⠆⠀⠀⠀⠀⠉⠙⢄⠀⠀⠈⢏⠒⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢠⠏⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⡔⠲⢄⡀⠀⠀⠀⠀⢀⣠⠤⠔⠊⠀⢠⠇⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⣀⠤⡶⠀⠀⠀⠀⠀⠀⠀⡠⣤⢷⠀⡀⠀⠇⠀⠀⠈⠀⠀⠀⠈⣁⣀⣀⠤⣤⡴⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡚⢉⡴⠊⣠⡶⠀⠀⠀⠀⢀⠜⠀⣌⢾⠀⢿⠆⢰⢄⣀⠤⠒⠋⠉⠉⠀⠀⠀⢰⣿⠃⠀⢀⡀⣄⠘⢿⣿⣿⣿⣿⣿⡀
⢠⠀⣆⠀⠀⣠⣫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣠⡺⠋⣠⣲⠀⣠⠊⠁⠀⠀⠈⠉⠃⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⠀⠀⠀⠀⠘⣆⠈⢿⣿⣿⣿⣿⡇