⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⡠⣪⢖⡲⣭⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣀⠙⣆⠀⠀⠀⠀⠀⠈⣾⢝⣚⡳⣆⣻⡜⡄⣀⡀⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⠶⠶⣄⠈⠳⣼⡇⠀⠀⠀⣀⣠⣕⡁⢀⡼⣸⡿⣡⡭⢖⡚⢏⡻⣒⢶⡥⣬⣒⣒⠤⢀⠀⠀⢠⣏⡴⠛⢁⣠⣄⡀⠀ ⠀⠀⠀⠘⠦⢤⣘⣧⠀⠈⠀⡠⣒⣭⢶⣶⣶⡭⢵⢾⣿⠛⡥⢊⡕⠊⠑⠒⡥⢎⢲⢡⠃⠙⢫⠳⣕⣄⠀⠋⠀⢠⠟⣀⣠⠇⠀ ⠀⠀⠀⣀⣤⣄⣈⠋⠀⡠⣪⡞⡱⢊⣦⢿⠱⣘⡥⢚⡌⣳⠈⠱⡘⢦⡀⠀⠀⠉⠢⣷⡲⠀⠀⠁⠻⣎⢇⠀⠀⠸⠋⠉⣀⠀⠀ ⠀⠀⢮⣡⠴⠞⠉⢀⢎⣿⠁⢀⣼⡟⠍⠒⣍⡞⠀⢠⡾⠇⠀⠀⢘⣷⡰⠀⠐⠀⠀⡘⣿⡅⣀⢆⢣⢻⡷⡕⡄⠀⠐⠯⣍⡙⢢ ⠀⠀⠀⠀⠀⠀⢀⢎⡿⣁⠠⣾⢟⠁⡠⢾⠏⡠⣴⣿⣇⢆⡠⡔⣣⣾⣿⢡⠤⣈⠰⣩⣾⣿⡴⣉⣶⣿⣯⠹⡜⡄⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⡸⣸⠃⢡⢯⡟⡌⠎⣵⡟⠬⣵⠟⣻⣿⣦⣵⡿⣿⠏⢻⣧⡳⢌⣣⣷⣿⣻⣿⣻⣟⣾⣷⣹⡇⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢆⣏⠳⣌⣿⡰⢡⠎⣽⣯⢷⡟⠀⣸⣿⣿⣷⣿⣿⠀⠀⣿⣿⢿⣻⣷⣿⣿⣷⣿⣾⣿⡽⣯⢇⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣸⡸⣿⡵⣾⣿⣧⢃⡞⣹⣯⡿⣧⠐⡟⠉⠙⠿⠈⠛⠄⠒⠛⠛⠉⠁⠀⠛⠛⠛⠙⢻⣿⡟⡕⠁⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⣁⢶⠓⡿⢭⣍⣙⣿⣮⡟⣴⣿⡿⠿⢟⣦⡴⠶⣶⣄⠀⠀⠀⠀⠀⠀⣀⣴⡶⠶⣦⡀⠀⣿⣧⢣⣀⠰⣱⠐⠀⠀⠀ ⠀⣠⡾⡯⣹⡎⣧⡀⠀⠂⠩⣿⣟⣿⣷⣻⣷⠀⣼⠇⣠⡶⣦⣹⡇⠀⠀⠀⠀⢰⡿⢀⣴⣶⣌⢻⣶⣿⣟⢓⣲⡹⡣⠃⠀⠀⠀ ⢸⢸⡡⣧⣬⠞⣻⣿⣦⣄⣼⠿⣿⢿⡿⢻⣾⣷⢿⣆⠻⣦⣥⢟⡃⠀⠀⠀⠀⠘⣷⡘⢿⣂⣿⣸⣷⡏⠛⣛⣪⠊⠀⠀⠀⠀⠀ ⠀⠑⢝⠷⠿⣛⠥⡼⣕⣻⡍⣿⢻⡀⠷⠀⢿⡄⢊⠝⣳⢶⡶⠾⠋⡔⡉⢌⠡⢃⠍⡻⢛⡛⠰⢻⣿⠻⡍⢳⠪⡢⡀⠀⠀⠀⠀ ⠀⠀⢀⣽⠻⠁⠀⡇⣯⠾⣟⢾⡀⠉⠀⠀⠘⡷⠈⠒⢄⠢⢌⠁⠁⠀⠀⣀⡴⠀⠈⠐⡡⠌⠑⠀⣿⠀⠓⠘⠂⡇⡇⠀⠀⠀⠀ ⠀⢰⢱⢻⢠⣀⣰⣵⠳⡜⣻⠞⣻⣤⠉⠀⠀⣿⡄⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣀⠀⠀⠀⠀⣼⡏⠀⠀⠆⣿⡱⠃⠀⠀⠀⠀ ⠀⢸⢸⣭⢓⡯⢞⠀⠀⠁⠪⡜⣽⡇⠀⠀⢰⣿⣿⣄⠀⠀⠰⣏⡁⠀⢈⣉⡉⢀⣽⠇⠀⠀⣰⠓⣿⠀⠀⠀⣧⢇⠀⠀⠀⠀⠀ ⠀⠀⠑⡝⣿⡙⢦⡐⠎⠀⣠⣽⠏⠀⠀⠀⣾⢿⣽⣻⣿⣦⣤⣀⠉⠉⠁⠀⠈⠉⢁⣠⠴⣾⣷⣾⣿⠀⠀⠀⠘⣎⢇⠀⠀⠀⠀ ⠀⣠⣪⢞⡱⣼⢆⡹⢬⢹⡿⠃⠀⠀⠀⢰⣿⡖⠈⢻⣿⢦⣙⠛⠿⣶⣶⣶⣶⠿⣿⣷⠚⢿⣫⣽⣿⡄⠀⠀⠀⠈⣮⢆⠀⠀⠀ ⢠⢣⣿⣮⢿⣷⣈⣾⢭⡟⠀⠀⠀⠀⠀⣾⣛⣿⡄⠀⣿⣿⣿⣿⣷⣤⣦⣴⣤⣾⣯⣿⡆⠈⢿⣛⠹⡇⠀⠀⠀⠀⠘⣎⢆⠀⠀ ⠈⢊⢿⡏⣆⢿⣽⡿⣿⠃⠀⠀⠀⠀⣴⣿⣿⣼⣧⠀⠸⣷⣍⡛⣛⢻⡛⣟⢻⠛⡝⣻⣿⡀⢈⣿⣿⢿⠀⠀⠀⠀⠀⣾⢠⠀⠀ ⠀⠀⠑⠕⠹⠑⢝⠅⡙⣆⠀⠀⢀⣰⣿⣿⣾⣻⡛⠛⠓⢛⣿⣿⣿⣶⣵⣬⣶⣿⣿⢿⣿⣉⣉⣤⢿⣾⣧⠀⠀⠀⣶⡇⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢁⢿⣿⣮⣷⣿⡿⣿⡿⠋⠉⣯⣽⠏⠁⠉⠛⠾⠽⠯⠿⠽⠷⠋⠀⠙⠦⠏⠀⣿⣿⣷⣮⡿⣿⢇⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⠛⣫⣅⢳⡄⠠⡄⢄⡠⢀⡀⠠⡀⢄⣀⣀⣀⣀⡀⢀⡀⡐⠤⠠⠄⣼⢃⣭⣝⠛⠛⠕⠁⠀⠀⠀