⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣰⣫⠼⠶⠶⠚⠻⠶⠾⠳⠶⠾⠷⠶⠛⠛⠛⠉⠐⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢱⣠⡘⢷⣝⡑⡄⢀⡤⠄⠒⠚⠃⠀⠤⣄⠀⠀⣀⣀⣀⣀⢄⡀⢤⡤⠤⢄⣀⡀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⣿⡱⡌⣎⢇⡟⠁⠀⠀⠀⠀⢀⣀⡀⢮⡳⣖⠯⣦⣄⠀⠉⠛⠷⣾⣵⣄⣄⡉⠉⠒⠦⣐⠤⣀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠏⢠⡇⠀⠀⠀⠀⠀⣿⠱⡘⡜⢿⡖⢬⣲⡛⠉⠀⠀⠀⠈⠙⢿⣌⢆⠀⠉⠳⣄⠀⠀⠀⠙⠙⠻⣿⣦⣄⠀⠀⢑⣦⡙⠢⣄⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠁⡠⡟⠀⠀⠀⠀⠀⠀⡿⠀⣷⢱⣿⡇⠀⠹⣵⠀⠀⠀⠀⠀⠀⠀⠙⣮⣇⠈⠑⢌⡳⣄⠀⠀⠀⠀⠈⠻⣏⠳⣄⡈⠙⢿⣦⣈⠛⢦⣈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⣡⡾⡇⡇⠀⢸⠀⠀⠀⡇⣧⢀⣿⢸⡿⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠙⠪⣳⡀⠀⠀⠀⠀⠘⢇⠈⠻⣦⡀⡙⢿⣦⡀⢙⣷⡜⣆⠀⠀⠀⠀⠀⠀⠀ ⡔⠁⠀⣇⡇⠀⢸⠀⠀⠀⣿⡟⢸⣿⣼⠀⢹⡄⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⡄⢱⢣⠘⢆⠀⢠⡈⠻⣦⠀⠀⠀⠀⠀⠳⣄⠈⠻⣮⠢⡈⢿⣦⠙⢿⢾⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⡇⠀⠀⢸⡟⢇⣾⣿⡿⣄⠈⣷⠀⠀⡄⣧⠀⠀⡄⠀⠀⠀⢣⠈⣿⣆⠀⠑⣄⠱⣄⠈⠳⣄⠀⢦⡀⠀⠈⢦⡀⠈⠑⢮⢦⡙⢷⢈⣻⣿⢷⡀⠀⠀⠀⠀ ⠛⠦⣄⠘⢿⢸⠃⠀⠀⡿⢽⣾⡟⡽⠁⢸⠀⣿⡄⠀⡇⠇⠀⠀⡆⠀⠀⠀⠸⡄⢸⣿⡀⠀⠈⠣⡌⢢⡀⠈⢦⡀⠑⣄⠀⠀⠑⢄⠀⠀⠱⣝⢌⢣⡙⣽⣧⢻⡄⠀⠀⠀ ⠀⠀⠈⢳⣼⡇⠀⡼⡼⣡⣿⣿⠞⠁⠀⢸⠀⣿⡇⠀⡇⢀⠀⠀⡇⠀⠀⠀⠀⡇⢸⣿⡇⢀⠀⠀⠘⠦⡙⢦⡈⠻⣦⡈⠳⡀⠀⠘⢷⣄⠀⠙⣯⣦⢡⡜⣿⡀⢷⡀⠀⠀ ⠀⠀⠀⢀⡟⢁⣼⣵⣾⣸⢹⡇⡘⠀⠀⣸⠀⡟⡇⢀⡇⣿⠀⢠⡇⠀⠀⠀⠀⠁⢸⣿⣷⡈⠳⣄⠀⠀⠈⠪⠿⣦⣈⠻⣦⣙⢦⡀⠀⠻⣷⣤⡈⢻⣿⡿⡘⣷⠸⣇⠀⠀ ⠀⠀⣠⢏⣠⡾⠟⣡⣇⣧⠟⡇⡇⠀⣠⣿⢀⡟⡇⣼⢃⣿⡆⢸⡄⠀⠀⠀⠀⡀⢸⣗⣿⢷⡀⠈⠳⣄⠳⣄⠀⠈⠻⢷⣬⡻⣦⡹⠦⣄⠈⢿⣟⠢⣿⣿⣧⣿⡇⣿⡀⠀ ⣠⣾⣶⠛⡹⢣⣾⣿⢾⣿⠀⡇⠀⠀⢿⡇⣸⠀⡟⣿⡼⣿⢣⣟⡇⠀⠀⠀⠀⡇⣸⣟⣿⣀⠹⣦⡀⠀⠑⢾⣗⢄⡀⠀⠙⠷⣯⡚⠓⢤⡑⠦⣝⢷⣌⠻⣿⣹⡇⣻⡇⠀ ⢰⡋⡏⡾⣧⣛⣿⡏⣿⢻⠀⡇⠀⣘⣿⢡⡧⢤⣷⡷⢥⣟⡎⢸⡇⡀⠀⠀⢠⣧⣿⣿⣿⣷⣷⣜⢿⣷⣦⣀⡈⠓⠾⣷⠤⣀⡈⠙⠳⠦⣍⣓⡢⢍⣓⠙⠙⣯⣷⡿⠃⠀ ⠈⠁⠻⡀⠘⠁⢸⣿⡼⣏⣆⢱⠀⣸⣼⡞⣀⣼⣿⣥⣼⡿⠃⢸⠇⡇⠀⠀⡾⣸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣭⣟⣿⣵⣲⡤⠀⠈⠉⠉⠉⣉⣿⣿⡋⠁⠀⠀ ⠁⠀⠀⠀⠀⠀⠈⢻⡟⢿⡜⣎⢷⢣⠟⣻⣿⡿⢿⣿⣿⣷⣖⢺⢺⠏⠀⢠⣷⢇⣿⣿⣻⡿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣾⡿⠿⢿⢿⡏⣰⣿⣿⡇⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢿⡀⡟⣾⣹⡧⠤⠿⢿⣿⣿⡆⠉⢿⡟⡛⣾⠀⢠⣿⡏⣸⣿⠉⢉⡿⢋⡴⠒⠲⡙⣿⣿⣿⡇⠀⡏⠉⡍⡏⠉⣽⠀⠀⣸⢸⡀⡟⣿⣿⡇⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⡧⣷⠛⣷⠀⠀⠘⣿⢿⠁⢀⠟⢰⣿⢻⣰⣿⣿⣷⡟⠈⣧⠟⢠⠞⠉⢳⠀⡇⣿⣿⡟⡇⢰⠃⢰⣧⡇⢀⡟⠀⢠⣧⢧⣷⣁⣿⣆⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣼⣿⠀⠀⠀⣘⣋⣴⡥⠀⣼⠷⡾⢫⣣⣿⡟⠀⠀⠉⠀⠻⡆⠀⠈⢧⠇⣿⣿⡇⡇⣺⠀⣸⣾⢁⣾⠁⢀⣮⣿⣼⢉⢟⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡻⣜⡽⠃⠀⠀⠀⠉⠁⠉⠀⣰⠏⢀⣧⣿⣻⠏⠀⠀⠀⠀⠀⢠⣇⡠⠔⢫⣾⣿⣿⢷⢧⢇⢄⠇⣮⣾⠇⢠⡾⠃⡎⠝⣼⢸⣿⣿⡇⢻⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⠋⢯⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠛⠁⢀⡔⣡⣳⣿⣟⣾⣏⡞⡼⣼⣿⢇⡴⢋⣾⢀⣇⣷⡟⣿⣿⡏⡇⠘⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡷⣄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠁⣰⣫⣿⣿⡿⣫⣞⣴⣿⣿⠗⢻⡔⠉⡾⡸⣼⡾⣷⣿⣯⣧⠇⢀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣀⣤⡾⢛⣽⡿⣡⣾⣿⣿⠟⡟⢡⢾⣿⠀⢠⢡⡟⣿⣇⣿⣹⠙⣷⡔⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠉⠉⠁⣠⣾⣿⣫⣟⣿⠟⣹⠀⡇⣏⣾⡇⠀⢀⣿⣾⢸⡿⣿⠇⠀⠀⠉⠒⠂⠀ ⠀⠈⠂⠀⠀⠀⠤⠤⠤⠄⣀⣀⣀⣀⡤⢤⡷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠠⣤⣠⣤⣾⣿⣿⣿⡟⣉⣄⣠⠏⢀⣿⢟⡿⣀⣴⠛⡷⢉⣿⣹⣯⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⢔⣟⣄⢹⡄⠀⠀⠀⠀⣀⡠⠤⠖⠒⠲⢤⡀⠀⣀⣀⣼⡏⠀⣰⠿⢋⡉⢹⣳⣾⣫⣿⢃⠼⣙⣜⡧⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠛⠁⠸⣸⢱⠒⡖⢎⠉⠁⠀⠀⠀⠀⠀⠀⣙⣾⠏⢉⣩⣷⣾⠿⢶⣾⡌⣪⡿⠹⠈⠙⣧⣤⣀⠙⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻⠀⣇⢧⠈⣆⠀⠀⠀⠀⠀⠀⠀⢹⣭⣾⠟⢉⡤⠖⠋⠉⠀⠀⠈⠉⠛⠦⣄⡘⡕⢬⡟⢶⡙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⣰⣿⣧⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣴⣏⠢⣱⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⢣⡀⠀⠀⢠⣶⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣦⠙⣿⣧⣀⣙⣳⣄⠀⠀⠀⠀⠀ ⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⣼⣿⣏⣩⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢻⡍⡗⢦⣳⡀⠀⢀⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣆⡾⣿⣿⡿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡞⣷⡓⠛⠞⡷⡄⢾⡋⠓⢄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣽⣿⠏⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⠈⠻⢷⣤⣹⣜⣿⣱⣀⡠⠜⢳