⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣄⡤⣄⣤⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣔⣬⡞⣷⣫⢯⡽⡷⣭⣟⣻⢶⣥⣂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡴⣾⣝⣾⣽⡟⣟⢯⡻⣝⢭⡛⠽⢾⣧⣯⠷⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢻⣜⣷⢿⡹⢎⡽⢎⡷⣹⢾⠓⢏⡖⢲⠘⡙⢿⣗⡻⢾⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠄⠀⠀⢠⢾⡝⢎⣷⣟⣏⣾⣷⣯⣿⣯⣼⢣⡛⢧⡈⠙⠊⢣⣇⠀⠈⠻⣥⠳⡵⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣠⣫⡞⣼⣿⠏⣾⣿⣔⣿⣿⣿⣿⣄⢷⡉⢎⣩⣭⡘⣅⣈⡀⠀⠀⠙⢣⡘⢞⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠈⠀⠀⣰⡳⠥⣿⡿⠁⠀⣿⣿⣯⣟⣿⣿⣿⣿⢹⡆⢸⠉⠛⢃⣠⡛⢡⠀⠀⠀⠀⠱⡀⢂⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡕⠁⣾⠯⠁⠘⢧⣿⣿⣾⠿⢟⡛⣿⡟⠯⢲⠈⠑⣠⣀⣫⣔⣁⠀⠀⠀⠀⠀⠈⠄⠈⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡛⠀⡸⠁⠀⠀⠀⠘⠛⢻⣿⢿⣿⠿⣏⠀⣠⢰⠖⠛⣟⡃⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡎⠁⢠⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠋⠙⠦⠔⠘⠀⠘⣯⠿⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠆⠀⠀⠀⠀⠀⠀⣿⢀⣤⢤⣤⠀⠀⠀⠀⠀⢠⠄⠈⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢹⠀⠀⠀ ⠀⠀⠀⢠⢇⠀⡘⠀⢀⠀⠀⠀⠀⢀⣿⣿⡅⢸⣻⠟⢛⡧⣞⠛⢻⢴⣻⣽⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣇⠀⠀ ⠀⠀⠀⡾⠄⠀⣁⢴⣿⣤⣌⡖⡀⠘⠛⠈⠛⠚⠋⠃⠘⠃⠙⠒⢛⡂⠉⠚⠁⠉⠁⠀⢀⣠⣰⣴⡪⡄⠀⠀⠃⠀⢸⡄⠀ ⠀⠀⢠⡇⠀⠘⢻⣻⣯⣫⡿⠿⡷⠀⣤⠒⢒⣢⠀⢀⣀⣀⡀⢰⣏⠀⣆⡤⠒⡢⡀⡞⣯⢿⡻⣛⠯⠃⠀⠀⢰⠀⠀⡅⠀ ⠀⠀⢸⠮⠀⣼⠈⠠⣬⣭⣵⡤⠁⠀⢻⡆⢁⠸⡟⠀⠰⣦⠠⠉⣿⠀⠋⢀⡪⠊⠀⠸⠉⠂⠉⠀⠀⣠⡀⢀⡀⡀⠀⣻⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣇⠈⠀⡇⡀⠀⣿⠀⡆⡿⠀⢈⠏⢀⣶⡶⠀⠀⠀⠀⢶⣿⣿⣷⡿⠁⠁⠀⢉⠀ ⠀⠀⢸⣤⣤⣧⠤⣀⠀⠀⠀⠀⠀⢰⣞⣋⣀⣃⣇⠁⠆⡿⠀⢃⠧⡤⣎⣴⣥⣶⣢⠀⢀⠰⡶⠹⠟⠃⠁⠀⠀⢀⣀⣸⠀ ⠀⠀⢸⣟⣿⣯⠁⢰⠇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠛⠓⠒⠊⠁⠀⠚⠉⠉⠉⠉⠁⠀⠀⠐⠂⠂⠁⠀⣠⣴⢾⣻⣿⡻⠂ ⠀⠀⢸⣿⢾⣿⡄⠘⣄⠀⠀⢀⣤⣤⡴⢶⣖⣞⣖⣲⠀⠀⠀⠀⠀⣀⣤⡖⣯⣛⢦⠀⠀⠀⢀⣀⣴⡟⣿⣿⣿⣳⣿⣳⠀ ⠀⠀⢸⣯⢿⣿⠄⠀⡍⣞⢻⣏⡷⠋⠀⣞⡃⢀⡾⣹⣄⣠⣄⢶⡻⣝⢶⡹⣶⡹⣮⢷⣛⡷⣫⢟⣮⣽⣻⣿⣿⣽⣿⣏⠀ ⠀⠀⠘⣿⢯⣿⡧⠀⠘⣬⠳⣞⡄⠀⠀⡿⣝⢯⣳⢳⣎⡗⣮⢳⣝⢮⣏⢷⣣⢟⣼⢣⡟⣼⢫⣟⡼⣶⣿⣿⣟⣾⣷⣯⠀ ⠀⠀⠀⣯⣿⣽⣿⡀⠀⢧⢛⡼⢦⣀⣄⡿⣞⢧⣏⠷⣮⡝⣮⢳⣞⡳⢮⡳⣝⢮⡳⣏⡾⣭⢷⡺⣝⣿⣿⣿⢯⣿⡻⡆⠀ ⠀⠀⠀⢸⣷⢯⣿⣷⡀⠈⢧⢛⡭⣟⡽⡽⣞⣳⢮⡟⣶⡹⣎⠷⣮⡝⣧⢻⡜⣧⢻⣜⣳⡽⣞⣽⣻⣿⣿⢟⣿⣿⠳⠀⠀ ⠀⠀⠀⠀⢟⣯⣟⣿⣳⣄⣠⣉⠞⣵⢻⡽⣳⢏⣾⡹⢶⡝⣾⡹⢶⡹⣎⢷⡹⣎⠿⣜⣧⢟⣞⣷⣿⣿⣯⣿⣿⠦⠁⠀⠀ ⠀⠀⠀⠀⢸⣯⢿⣞⣿⣽⣻⢯⣷⣌⢷⡻⣭⣟⢶⡻⣝⡾⣱⢏⡷⣻⡜⣧⢟⣭⡟⣽⢮⣟⣾⣿⡿⣷⣿⣯⠋⠁⠀⠀⠀ ⠀⠀⠀⢀⢼⡯⣟⡾⣽⣻⣯⣟⡾⣽⣎⢷⡻⣼⢯⣽⣳⡽⣏⡾⣝⣧⢿⣹⡞⣧⢿⣭⢷⡻⢎⣵⣾⣿⡿⠉⠀⠀⠀⠀⠀ ⠀⠀⣠⠽⣏⢾⣱⣟⣳⣟⣾⣻⣿⣽⣮⣳⢝⡧⣟⢶⣻⡼⢯⣽⢻⡼⣫⠷⣝⡻⠮⢝⣫⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⡞⡽⣎⢷⡳⣞⣳⢟⣾⣳⣯⣿⣿⢿⣿⣾⣜⣧⢣⣛⡝⣊⢳⣉⣇⣹⣬⣶⡿⣿⣿⣟⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⡽⣳⡝⣮⢳⡝⣞⣻⠞⠉⠉⠉⠊⠽⢻⢿⣿⣿⣿⣿⣽⣻⣷⣿⣾⣿⡾⣽⡿⠟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⢣⣿⣼⣳⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠉⠙⠛⠉⠓⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀