⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠒⠒⠒⠒⠲⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡾⡽⠄⠀⡄⠀⢠⢁⣴⣿⣓⣒⠦⣱⡖⠖⠒⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣤⣤⣴⣯⡮⣙⢉⡁⠀⠘⣢⠈⠀⠀⣘⣿⣷⣾⣿⣿⠀⣷⠀⢄⠀⠆⠀⠀⠉⠓⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⡽⣿⣿⣿⣻⡿⢺⢿⣾⣄⡠⢻⣆⠀⠀⣙⣯⢿⣿⣻⡻⢉⣿⣯⣿⣷⣦⢀⠀⠀⠀⠈⢸⣀⢄⡉⠛⠙⠛⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣒⣮⣿⣷⣿⡟⣟⣭⣽⣿⣿⣏⣵⣼⣍⣄⢱⠀⢩⠙⡟⠁⢴⣿⡿⣛⡛⡛⠑⠑⠀⢄⠀⠀⣯⠳⣝⢦⡀⠀⠀⠀⠉⠳⣗⠒⠓⠒⠒⠒⠀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀ ⠝⣪⢿⢿⣿⣿⣷⣽⣾⣪⢿⡿⣽⣿⣿⣿⢿⣷⠰⠙⠊⢲⣣⣿⡿⠑⢻⣿⣿⣄⣢⢘⠇⠑⢮⢽⠤⠘⠷⣄⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀ ⠘⢕⣿⢫⣿⢟⣿⣿⣿⢿⣾⣿⣺⣯⣻⣿⣟⣿⣿⢿⣫⣴⣾⠛⢡⢒⣴⡿⣿⣿⠣⠡⡱⡀⠠⠙⠁⠀⢀⢾⡄⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀ ⠀⢋⡮⣿⡟⣸⣸⣿⣿⠿⢿⣯⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣁⣥⣽⣿⣽⣿⡟⣯⢅⠬⡈⠷⢄⠀⠀⠀⡜⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠎⡟⣿⢳⣽⢻⣿⡿⡆⢺⡟⡸⣝⣿⣿⣿⣿⣿⣏⠖⢬⣯⣿⣁⣼⣿⣋⣼⢗⢉⢌⡈⠳⣾⡗⣮⡑⡆⣤⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢠⠏⡾⢇⠇⠻⠁⡇⢹⣷⠇⡇⣿⣿⣿⣿⡳⣦⢾⣿⣿⡿⠻⡟⣹⣯⡟⣟⢕⡀⠪⣆⣌⠿⣿⣧⣜⡄⠱⡿⡀⠀⢠⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠃⠈⠀⠀⠀⡇⠈⣿⠀⢿⣯⣿⣿⣼⣿⣿⣿⡋⢟⣠⢼⠛⡃⣴⣁⡮⣳⣍⠳⢶⣿⣽⣿⣯⡉⠘⢆⠘⠯⢦⡀⠈⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠑⠁⠂⠀⡀⠀⢱⠀⣿⡄⢼⣿⣿⠟⢿⣿⣿⣿⣗⣤⡭⢦⣀⡨⡛⡿⣿⣮⣉⣳⣿⣿⡿⣷⡟⡞⣆⠈⣿⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⢀⠀⠀⠀⠇⠀⢸⡄⣿⢡⢹⢹⣯⣟⠎⡙⢈⣟⠙⠙⢮⠈⢮⢗⣾⣿⣿⣿⣿⣿⣟⣎⣥⠲⠮⠿⡀⣜⠟⠀⠀⠈⣗⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠇⠁⠀⠀⠀⠀⠘⡄⣧⣿⡝⠎⣿⣿⣿⣻⡶⣾⣿⣷⠿⣿⡾⣿⣫⣿⣿⣿⣿⠙⣿⣤⠾⡏⠀⢜⠑⣨⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⠀⠀⠀⠀⠀⣀⡀⢳⢸⡇⡦⢻⡯⣿⣿⡟⡷⣿⣾⣿⢿⠿⠟⢛⡫⣿⡞⢙⣡⠈⢁⣠⣤⣐⣁⡐⢀⣠⡦⣄⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡷⠀⠀⠀⠀⣀⣿⣇⢸⠘⣇⡞⣼⣷⣟⢿⣖⡤⣼⢿⠿⢗⣷⢾⠷⠩⠉⢁⣼⣋⢤⣲⣶⡛⢿⢾⢸⢼⣳⣏⠈⠇⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⢹⣇⠀⠀⠀⡄⠀⠀⠀ ⢰⢻⠡⠠⢀⠖⠋⢵⢻⠉⠎⡇⣿⣳⡃⣿⢼⣿⣷⣿⣿⣛⣿⠞⣳⣶⢿⣛⠙⡲⡿⣧⡵⣻⣿⣾⣿⣿⣿⣿⣞⣿⣤⢾⡄⠀⠀⠀⠸⢿⣷⡄⠀⠀⠀⣷⠄⠀⠀⠸⡀⠀⠀ ⢷⡯⡄⢀⠟⠀⢠⡇⠈⡆⠀⢣⢼⣗⠳⣿⠽⣾⣿⣿⣿⣾⣱⣴⣇⣿⣾⣷⣤⣼⣾⣿⡿⡿⣿⣾⣿⣿⣿⣗⣍⠯⣜⠀⠀⠀⠀⠀⠀⠀⠡⣻⣆⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀ ⢸⡷⡛⠁⢇⣤⢞⡸⣶⣜⡤⡜⡼⣿⡷⣾⠀⣿⡿⣿⣽⢿⣿⡩⠿⢿⡿⡟⢯⣻⡿⢻⣻⣿⢻⣿⣿⣿⣮⣧⡲⠦⣈⠚⠨⠄⠀⠀⠀⠀⠀⢆⠻⡆⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⠘⣾⣌⡕⣎⡷⢙⢹⠹⣧⣳⢳⡇⣿⢴⣽⠀⣿⣿⣿⢙⣟⢏⠅⠀⠀⢀⣄⣌⣿⣷⣿⣻⣿⣯⣿⣿⢿⡽⣧⠁⢰⡙⢆⠀⠀⠀⠐⡄⠀⠀⠈⣆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣼⡍⣧⣯⣿⣷⣿⢯⣿⢧⢻⣾⣿⠀⡿⣿⣿⡴⡼⣨⠀⠀⢠⢚⡎⣙⠏⡉⢚⣞⢵⣯⣫⢻⣆⢿⢽⣱⣄⠃⠀⠃⡀⢀⠇⠈⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣾⣦⣿⣿⣾⣿⣯⣿⣿⣾⣿⣾⣸⣿⣿⠀⣿⣿⣿⣿⡋⢦⠄⣠⣿⣿⣿⡻⡙⣹⣺⠹⢹⣾⣌⣿⣿⣽⣻⢣⣎⡤⢀⠀⠑⢺⠈⡄⠀⠀⠀⠀⠈⣷⡀⢀⡄⠀⠀⠀⠀⠀ ⠀⢿⡈⢲⣹⠟⠿⡿⢿⣻⣿⣯⡟⣏⣷⢿⡘⣿⣿⣿⣿⣿⣿⢹⡝⢾⣿⣽⣎⣏⠀⡟⢹⣯⠿⣿⣟⣇⣿⣿⣻⢋⢀⠀⢀⢠⡋⢠⠃⠀⠀⠀⣰⢸⢻⢦⠺⠀⠀⠀⠀⠀⠀ ⠀⠘⢱⠠⢽⠀⠀⢼⡜⠉⠙⣿⡟⠙⣿⠈⢻⣿⠌⢹⣿⡿⠿⢿⢦⡾⢿⢾⣿⡧⣴⣇⡼⣇⣾⣻⠕⠻⣿⣿⣟⢢⢸⠉⠤⠜⡄⠉⡌⣀⣀⣠⣇⢠⣹⠉⠙⣢⢠⡄⠀⠀⠀ ⠀⠀⠀⠃⠛⠀⠀⠀⠀⠈⠃⠁⠉⠀⠴⣦⠀⠀⣽⠞⠚⠣⢀⣿⠩⠁⠩⠇⡼⡿⠟⠇⡸⠋⠊⠹⢸⡀⠁⢹⣹⡘⣾⢇⣀⢨⡿⡟⠋⠉⠛⠉⠈⠸⠃⠀⡘⠭⣎⡁⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡞⠓⠄⠀⠀⣠⠄⠁⠀⢀⠀⠈⠉⠙⠯⠤⠧⠧⠋⠑⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠁⠀⡀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠳⠃⠁⠀⠀⠀⠀⡀⠀⠀⣠⠣⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⠿⠇