⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢠⣿⢏⣯⣝⢯⡻⣝⣯⢻⡭⣟⣧⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢠⣿⢏⡾⣳⢮⣏⡷⣝⡮⣟⣼⢳⢿⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⠀⠀⠀⠀⠀⠀⠀⢸⡀⣰⡿⣽⣚⠷⣽⢺⡼⣹⢞⣵⡻⣼⢫⡾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢠⠞⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⣵⣟⣳⢧⣛⣯⢳⣏⠷⣏⡿⣼⣹⢳⣏⠷⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⣰⠋⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣸⣟⡮⣗⢯⣳⢞⡯⣞⢯⣽⢺⡵⣫⣟⡼⣻⢽⡀⠀⠀⠀⠀⠀⠀⠀⡎⠀
⠀⠀⠀⠀⢰⠇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣿⢏⡾⣭⣛⡮⣟⡼⣽⣚⣮⢷⣫⢗⣮⠳⡝⢺⠅⠀⠀⠀⠀⠀⠀⣸⠁⠀
⠀⠀⠀⠀⣼⠀⠀⠀⠈⡇⠀⠀⠀⢀⡀⠀⣸⣟⢾⣹⡞⣵⣻⠼⡽⣖⢯⡞⣧⣛⠾⣌⠣⡉⠌⡀⠀⠀⠀⠀⠀⢀⠇⠀⠀
⠀⠀⠀⠀⣯⠀⠀⠀⠀⡇⠀⠀⣠⠞⢣⡀⣿⢾⡹⣶⣛⣧⢯⣛⡷⣫⢷⣹⢎⣧⠫⢄⠡⠀⠀⠄⠀⠀⠀⠀⠀⠸⠀⢀⡴
⠀⠀⠀⠀⢻⡀⠀⠀⠀⡇⠀⠈⠙⡄⣠⢻⡟⡾⣝⡶⣏⣞⣧⢻⣼⣝⣮⢳⣏⠶⣉⠆⠠⠁⡀⠆⠀⠀⠀⠀⢀⡤⠚⠁⠀
⠀⠀⠀⠀⠘⣧⡀⠀⠀⣏⠀⠀⠀⠹⠁⢸⣟⡽⣞⣵⢻⣜⢾⡟⠉⣷⡞⣯⢞⡵⢣⡘⠠⢁⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠿⣆⣀⡿⠀⠀⠀⠀⠀⠸⣯⣞⣳⢾⡹⣞⣿⠀⠀⢸⡿⣜⡯⣞⡵⣊⡕⡠⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⡾⣱⣏⠷⣭⢿⡄⠀⣼⡿⣹⢞⣵⣛⢶⣱⢣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠘⣿⣳⢞⣯⢳⣻⠇⠐⣿⣝⣳⡻⣼⡹⣮⢳⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⢤⡻⣟⡾⣜⢧⣿⠀⠀⢻⣮⢳⣝⡧⣟⡵⣯⣯⠤⣶⠆⠀⠀⠀⠀⣀⣠⠤⠤
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⣆⠙⠻⣷⢎⢎⡿⠀⠀⢸⡗⣯⣞⣵⠿⠛⠉⣤⠞⠁⠀⠀⠀⠀⠛⠉⠀⠀⠀
⠒⠒⠲⠶⠾⢧⣄⡀⠀⠀⠀⠀⢠⠞⢁⣤⣾⣷⡀⠈⠻⢦⣇⠀⠀⢀⡿⠞⠉⠀⠀⣠⣾⡙⢦⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠛⠀⣀⣀⣀⡟⢀⣾⣿⣿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡄⢳⣴⣶⣿⡿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠶⣿⣿⣿⡇⣸⣿⣿⡿⠁⢻⡽⣶⡄⠀⠀⠀⠀⠀⣠⢾⣿⡟⠉⣿⣿⣧⢸⣿⣿⠟⠁⠀⠀⠐⠲⠶
⠓⠲⠶⣤⣤⣤⣤⠀⠀⠀⢸⣿⣇⠸⣿⡹⢿⣀⡾⢛⡟⠈⠳⣤⣠⣴⠛⠁⣾⣿⣷⣀⣿⡿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠈⠻⣿⣆⠹⣯⣳⡝⣜⡿⠁⠀⠀⠉⣷⠃⠀⠀⠘⣷⣭⡻⣵⣻⢃⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠛⠛⠉⠀⠀⣆⡀⠀⣇⠀⠀⢀⣤⠈⠙⠻⠿⠵⢋⣡⣶⣿⡷⣄⡀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⢴⣾⢿⣅⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠋⠋⠉⠀⠀⠀⠀⢀⣴⣿⣿⣿⣟⡄⠈⠉⠓⠒⠶⠶ i love apples
⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢾⣿⠧⠙⠗⠛⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⢿⣤⣄⣀⣀⣀⣀⣤⡤⣴⠚⣻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠈⠙⡿⠂⠀⠀⢸⣼⣿⣿⡎⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣹⢛⣿⣿⣿⡄⠀⠀⠰⠋⣿⣿⣿⣿⣗⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢼⢸⣿⣿⣯⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣸⠸⣿⣿⣿⣆⠀⠀⢰⣿⣿⡿⣏⢯⣻⡄⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣆⢀⣿⣿⣿⣟⡼⣣⡿⣧⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣹⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠘⢷