⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣽⢋⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠻⢕⣿⠏⠀⠀⠀⠀⠀⠀⣠⣖⢾⡯⠇⡇⡀⠑⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡍⢷⣾⡏⠀⠀⠀⠀⠀⡠⣪⣜⣝⢧⠭⠶⠋⣀⠜⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡼⣩⡿⠇⣀⠀⠀⢀⣜⢯⡫⢆⡬⢋⡠⠔⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠃⢁⠀⠈⠀⠀⠀⠈⢾⡫⡽⢋⡔⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⣶⣿⣿⣮⣤⣆⢀⠀⠀⠀⠉⠡⠂⠈⢂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡕⡀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡰⣿⣿⡷⣿⣿⣿⡿⢋⣭⡙⣿⣿⢰⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⡏⠿⣱⣿⣿⣿⣧⣿⣿⠇⣽⣿⡇⠄⠀⠀⠀⠀⠀⠀⡇⠀⣀⡤⠔⡶
⠀⠀⠀⣴⢟⣿⣿⣾⣿⣿⣿⣿⣎⠛⢋⣴⣿⣿⡇⡁⠀⠀⠀⠀⠔⢒⢓⣉⠡⢌⢳⠃
⠀⠀⢠⠃⣼⡄⠉⠿⡛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣧⣂⠀⣠⢂⡎⡴⣋⣞⡼⢁⢢⠇⠀
⠀⠀⠘⡆⣳⡃⠀⢦⡀⠀⢸⠀⠆⣤⠤⡤⢦⠴⣰⡒⡞⣳⣤⣻⣍⣭⣠⣦⠼⠋⠀⠀
⠀⠀⢰⣷⣣⠇⠀⣺⣽⠀⠀⡘⣞⠦⡛⠼⢃⣋⣥⢶⣟⡯⢿⡹⢿⣖⣣⢛⡆⠀⠀⠀
⠀⠀⣸⣿⣿⡇⢀⡑⣆⣀⡀⡓⡉⣴⣥⣶⡟⣿⣾⣿⢮⡽⣏⣙⠋⣹⡏⠛⠳⠀⠀⠀
⠀⠀⣿⣿⣿⣿⡖⡤⢠⣴⡴⣿⣻⡽⣞⣵⡻⣧⣟⣿⣿⡽⣽⣊⣠⢮⣇⠀⠀⠀⠀⠀
⠀⢠⣿⣿⣿⣿⣿⣿⣟⣳⢿⣱⠷⣏⡿⣼⡻⣵⣞⣳⣟⣿⢧⡟⣽⣫⣟⢆⠀⠀⠀⠀
⠀⣼⣿⣿⣿⣿⣿⣿⣾⡽⢾⣹⢿⣹⡽⣳⣛⣷⣞⠓⣾⡽⣿⣽⣳⡽⣾⡸⠀⠀⠀⠀
⢰⣿⣿⣿⠟⢿⠿⣿⣿⣿⣿⡽⣞⣷⣻⣗⣟⣾⣻⣿⣳⣿⣿⣿⣷⣿⣿⣿⡄⠀⠀⠀
⠈⠙⠉⠀⠀⠀⠙⠢⡀⠨⢉⠉⠉⠛⠓⠛⠛⠚⠛⠛⠛⠓⡻⠛⠙⢿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡎⠘⡄⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠠⠔⠃⠀⠸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀