⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⡠⠔⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣹⠔⠁⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡰⠁⠃⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⠢⣀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⣇⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⠾⠀⠀⠀⠀⠀⠉⢳⡑⠢⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠑⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠑⠢⣴⡀⠀⢰⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠖⠒⠓⠒⠓⠒⠛⠻⠟⠓⠒⠈⠐⠚⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠷⡤⠤⠋⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢂⠀⠀⠀⠀⢀⣴⠋⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠀⣤⣶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣇⢸⣄⠀⣇⠀⡀⠀⠀⠀⠀⠀⠀⣈⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣹⡠⡆⠀⠀⡏⡾⠸⣀⡿⡄⡇⠀⠀⠀⠀⠀⠀⠈⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣞⣒⣠⡮⠄⢁⣴⡔⢀⣤⠷⣁⣉⣟⣀⣧⠇⠀⠀⢴⠀⠀⠐⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⣮⣥⣤⠄⠉⢸⡔⠉⢹⢿⠟⣿⣿⠛⢿⡇⠀⠀⢨⡇⣾⣀⠋⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⣷⣿⣿⣞⣿⣆⡀⠀⠀⢠⢉⠏⣽⡿⠟⡟⣻⣿⣿⣏⠉⠀⠀⠑⠀⠀⣸⣾⣿⣿⣧⠀⢧⠀⣰⣿⣷⣿⢿⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⢴⣿⣾⢿⣷⣦⠄⣌⠫⣦⣿⠀⠰⣿⣿⣿⡿⢻⠀⠀⠀⠀⠀⠀⠸⣍⠛⢃⡜⠀⠈⣦⣿⣿⣿⡿⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠀⠸⣟⡁⠈⣫⢻⣏⣽⠏⠀⢻⡀⠸⡜⡀⠀⠻⣌⣉⡠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣄⣆⣾⣭⢿⣿⣿⢁⣫⠉⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡍⢆⠀⠀⠀⠀⣻⣗⣾⡽⣿⣿⣿⣇⡀⠀⠁⠀⠳⡄⡰⡶⣰⡼⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠞⠏⠃⢺⠿⣥⣀⡀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢲⣯⡳⡄⠀⣼⡄⢹⣿⣿⣿⣿⣿⢷⣶⣀⡀⠀⠀⠘⠿⣑⠙⠚⠁⠀⠐⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢹⣘⣧⠭⡑⠶⢮⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣮⢷⣝⢯⡝⢧⣸⣇⢻⢿⣾⣾⣿⣿⠟⠷⡄⠰⠤⡤⠤⠍⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡄⡿⢇⡎⣱⣉⢞⣸⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢮⣽⣳⣽⢶⣥⢾⣯⡀⣍⠉⠹⡄⠀⠀⠉⠒⠤⠼⡿⢆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣞⢹⣆⣼⡿⠽⣦⣛⣒⣿⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠘⠛⠚⠋⠳⠯⠝⢲⡽⣟⣓⠦⡔⣶⣶⣿⣶⣦⣽⣿⣿⣿⣶⡶⢶⡶⣾⣿⣿⢷⣟⣾⡿⠿⠷⠿⠿⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣶⢻⡝⣯⣛⢶⣭⢻⣿⣷⣼⣾⡷⣞⡿⣿⡹⢾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⣽⢞⣧⣛⡶⠏⣣⢵⣿⠋⣿⣯⣻⣇⠀⠙⣌⢿⡳⣞⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⡛⠚⠈⠓⢉⠄⠚⠓⠚⠛⠾⠋⠙⠉⠃⢈⠽⠻⡵⡿⣜⡳⢧⣛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣫⢟⡽⠟⢰⢻⡅⠀⠀⠀⠀⠀⢀⢠⠴⢂⣁⠀⠀⠀⠀⣹⡽⣝⣣⢏⡛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⡱⣏⡗⡿⢡⣞⣲⣟⠀⠑⠒⠂⠀⠁⠀⢸⢌⡑⢺⠀⠈⠉⠀⢸⣷⢻⣜⣧⣛⣟⡳⣼⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣏⢾⡱⣏⠞⣰⠏⣶⣿⣿⣿⣿⣷⣶⣾⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠶⣝⢮⡳⣽⡂⣽⡝⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⡷⣎⠷⡽⢋⡴⢣⢾⣿⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡏⢻⡉⠙⢿⣎⠳⣟⡼⣳⢏⡾⣱⣎⣟⣳⣛⠾⣶⢳⣞⡾⠃ ⠀⠀⠀⠀⠀⠀⣀⣴⢻⡜⣯⢞⡭⡟⣡⢞⣵⣤⡀⠙⠛⠿⠽⣿⣥⣋⣿⣯⡝⣽⠳⢰⣶⡇⢹⣿⣿⣿⣻⠉⢙⠿⢋⣡⡌⢷⡝⣮⢳⡳⣞⡼⣣⢏⡿⣜⣳⡞⠁⠀ ⠀⠀⠀⢀⣴⢾⡹⣎⢷⡹⣞⢮⡛⣰⣿⣿⣿⣿⣿⣷⣦⣤⣈⠐⠀⠀⠀⢉⣿⣧⣤⣜⣠⣾⣟⠛⠋⢁⣀⣽⣿⣿⣿⣿⣿⣶⣹⢧⡻⣵⢫⡞⣵⢫⡞⡵⠋⠀⠀⠀ ⢠⣤⣞⢯⡝⣮⢳⡝⣮⢳⣭⢋⡰⢻⢧⣈⣉⣉⡙⠻⣿⣟⣿⣿⢿⣿⣷⣾⢿⣯⡿⣿⣟⣿⣿⣶⣿⢿⣿⣿⣿⣿⣯⣿⡿⠋⡔⠫⢳⡭⢷⡹⣎⡷⠋⠀⠀⠀⠀⠀ ⠀⠈⠙⠮⣝⢮⡳⣝⢮⡟⢢⠾⠓⠓⠮⠥⠿⠚⠛⠑⢤⣉⣉⣉⣋⡻⢿⣯⣿⣷⣿⣿⣽⣷⣿⣾⣿⣿⠟⢉⣛⠻⢟⣉⡴⠉⠀⠈⠣⠽⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠁⠉⠻⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣰⠉⠲⢤⣠⠴⢤⣄⣀⣀⡤⠖⠛⢶⡚⠉⢸⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀