⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⢀⡲⢷⠷⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⠀⠀⠀⠀⢠⣣⡓⡉⣧⠎⠋⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⣻⣷⡦⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣔⠦⣤⣇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠸⣙⣯⣡⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⠀⠀⢹⣧⣢⠀⠀⠀⠀⡇⠀⠀⠀⣤⠂⡟⡟⣈⡳⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠛⠸⣻⡘⠀⡀⡀⣜⣇⡄⠀⠀⣧⡧⣿⣿⣿⣻⣇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠐⠂⠐⢓⣶⢾⡿⣵⣖⡓⣒⢈⠛⣁⣞⣭⣏⣿⣿⣿⣦⣿⡕⣘⣥⡀⢠⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠸⠂⠑⠋⠉⣳⣭⣿⡋⡹⠉⠠⠷⣿⣿⣶⣲⠓⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠟⣞⡌⠗⠀⢺⣞⢯⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣋⣂⣀⠀⠰⢷⠿⠁⠀⠀⣤⢺⢋⣁⠀⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⠛⠉⠀⣔⠛⣶⡟⡲⠀⠀⠀⢈⠸⣿⠃⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢰⠂⠀⠀⠀⡨⢭⢿⠋⡱⣀⡀⠀⢸⠀⡿⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠸⠀⠀⠀⠀⠉⠀⢳⣧⡛⠉⠉⠳⡘⠀⡽⠈⡄⠃⡀⠀⢀⣇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠜⢼⡤⠀⣠⠰⠳⠠⣸⢀⠃⠱⠄⠀⢏⣗⡑⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⠀⠀⢸⠔⢄⡀⠀⠀⡇⡻⠛⠀⠀⠉⠉⢹⣋⠇⢀⢀⠀⠀⠀

⠐⠂⠒⠒⠒⠒⠒⠛⠓⢫⠛⢻⡱⠛⠫⣺⢽⣧⡧⢾⠈⡈⠈⠉⢻⢸⢵⣈⠺⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⡄⠀⠀⠸⣲⡌⢿⣾⡰⡃⢀⡤⠼⣽⣮⢣⠅⠤⠄⢀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠥⡍⣿⠟⠱⣒⣬⣤⡃⠼⣥⡤⠄⠊⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠁⠀⠚⠀⠀⠈⢻⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣻⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⠄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀