⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠱⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢾⠃⠀⠻⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⠁⠀⣯⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⡇⠀⠀⠀⢹⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⣠⣾⡿⠁⡇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⠁⠀⠀⠀⠀⢫⠻⣮⣦⡀⠀⠀⠀⢀⣴⣎⡞⣤⣴⣦⣻⠟⢗⣒⠠⣇⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠏⣇⠈⠻⣿⣦⣀⣴⣿⣿⣾⡷⢿⣛⣃⡭⣅⣰⣶⢻⠋⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⡀⠀⠀⢸⢸⠀⠀⠙⠟⢷⣿⣿⣿⣿⣿⡟⣛⣛⠋⣿⣫⣭⠉⠒⠦⡀⠀⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⢡⠀⠠⠀⠿⡄⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣋⠉⢛⡽⠛⠵⣄⠔⠳⣌⢦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠿⠀⠀⢃⢆⠀⢳⠄⣇⠀⠀⢀⡠⠀⠀⠈⠻⢿⣞⣋⢙⣥⣴⣆⣛⣺⣧⣀⣿⣿⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣇⠀⠀⢾⣦⡀⢡⢧⢶⣶⠃⠀⠀⠀⠀⠀⠀⠙⠻⣿⣾⣿⣿⣿⣿⣿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣽⣦⡀⠁⠓⢔⡀⢸⡿⠇⠀⠀⣠⡴⠾⠛⢻⠄⠀⠈⠫⠻⡿⣿⠿⡇⢀⣼⡝⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⢇⠙⠲⠤⠄⢉⡞⠀⠀⠀⡴⠋⠀⣀⣀⠘⡀⢰⢴⡇⠀⣰⣶⣎⣿⣿⣯⡿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣽⣿⢒⣤⣤⡀⢸⠀⠀⠀⠀⢀⣴⣿⣿⣟⠻⣇⡸⠀⢱⣠⣿⣋⢻⢿⡿⣿⢽⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢵⣿⣿⣿⠶⣶⣾⠀⠀⠀⢠⣾⢿⣿⣷⡲⠀⢧⠃⠀⠀⠻⡿⡟⢸⢿⢿⣽⣷⡿⡂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣵⣟⣏⡩⠟⠇⠉⠉⠀⠚⢇⣫⣛⡻⠃⠀⢸⠠⠒⠀⠀⠫⢔⡁⠈⢳⡀⠙⢷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢾⣟⣭⠊⠀⠀⢁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣒⠳⡠⠀⢻⠆⠀⠀⠀⠀
⠀⠀⠀⢰⣯⣮⢇⠖⠠⠄⠸⡀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⢠⣮⣥⣴⣶⣾⠇⢸⠳⣚⠇⠀⠀⠀⠀
⠀⠀⠀⢸⣏⡤⡾⣶⢚⠤⠊⠱⣄⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢀⡀⠙⠛⠿⡿⢋⢀⡼⠀⢹⡃⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠁⣿⣹⡏⠀⠀⡠⠁⢗⠤⣀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣈⣀⠤⠴⡥⢤⣼⠶⠝⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠲⠶⠆⠈⠛⢻⡟⣿⣿⠿⣷⣶⣤⣄⣀⠀⠈⠪⣊⢉⡠⢟⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣶⢖⡇⢙⢿⠁⠠⢙⡻⢿⣿⣟⠷⢶⣤⣤⠲⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⢠⣜⠿⢿⣋⠀⠀⡆⠀⠀⠀⠘⠳⠋⠊⠁⢻⠿⡧⣖⣠⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣄⢶⠷⠟⠋⠀⠀⠀⠀⢘⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣏⡈⡽⠛⠿⢫⡶⣤⡀⠀⠀⠀⠀
⠀⢀⣶⡯⠛⠋⠀⠀⠀⠀⠀⠀⣯⡁⠈⠁⠲⠤⣀⡀⠀⠀⠀⠀⣀⣠⠈⠀⠐⠓⠂⠒⡄⢀⣽⢷⡦⡀⠀⠀
⠀⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⣦⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠈⠉⣡⡇⠀⠹⣾⢆⠀
⢸⡇⣇⠀⠀⠀⠀⠀⠀⠀⢰⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠋⠀⠀⠀⠀⠀⠀⠁⠺⣵⠀⠙⣿⣆