⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⡻⢏⠿⣙⢏⡻⣙⢏⡏⢏⢯⡙⢯⡙⢯⡙⢯⡙⢯⡙⢯⡙⢯⡙⢏⡻⣙⡛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣮⢽⣫⢟⡜⢮⡱⣍⠮⣜⡩⢦⡙⢦⡙⢦⡙⢦⡙⢦⡙⢦⡙⢦⡙⣬⢱⢣⠽⡼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣵⢯⣳⢏⡾⣣⢟⣬⢳⣎⡵⢣⡝⣦⣙⢦⡙⢦⡙⢦⡙⢦⡙⢦⣙⠦⣏⢯⣻⣝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⠴⡴⡶⠴⣶⢦⠶⣶⠦⢶⡴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⢀⣀⣤⡤⠴⡞⢭⠛⡜⢣⠝⣪⠳⡙⢎⠞⡓⢮⡙⢧⡙⠶⡙⢮⡙⢎⡝⡲⡙⡎⡝⢣⠞⣙⠎⣏⠳⢎⡝⢲⠳⠶⡶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⢻⢝⢿⡙⣏⣯⡋⡯⡻⡆⡜⡱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣾⣿⣭⣧⣍⣳⣜⣦⣫⣜⣱⣚⣤⡳⣍⡞⣬⡱⢦⣙⢦⣙⢦⣙⢦⣙⢦⡜⣥⢳⡜⣬⢣⣞⣡⣞⣴⣩⢶⣘⣧⣭⣳⣵⣮⣭⣿⣷⠀⠀⠀⠀⠀⠀⠀⠿⣷⣉⣏⣛⣛⣋⣛⣭⣙⣫⣑⣴⡵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠉⠛⠛⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⢀⡭⢉⣿⡇⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡿⠉⢿⡍⠉⠉⠉⠉⠉⠁⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡤⢠⢤⣤⣤⡀⡄⢀⣤⠤⣤⣄⠀⠀⠀⣠⠤⡤⢄⢠⣤⠀⠀⣤⢤⢤⣤⣤⡄⠀⡠⢤⡀⠀⣤⠤⠤⣤⣤⠤⠤⢤⡀⢠⡄⢀⡤⢤⢄⣘ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⠆⡼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⠇⠌⡘⢿⣦⣀⠀⠀⠀⢀⣀⣹⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠿⠿⣅⢸⢒⢒⣒⡂⠀⢸⣓⣒⢲⣮⠀⠀⠸⣟⣅⣈⣭⢽⣬⠥⠏⣽⢸⣔⡒⣒⠀⣼⣝⣼⣳⡀⠀⢸⣷⠀⢸⣆⢽⡆⢿⡠⣧⢝⣦⣐⣪⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠢⡐⠘⠻⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠃⠌⡐⢀⠂⠌⡛⠛⠛⡛⠛⢋⠙⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⠈⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠁⠀⠈⠉⠀⠈⠉⠉⠁⠀⠉⠁⠈⠉⠉⠉⢹ ⠀⠀⠀⠀⠀⠀⠀⠐⣧⢑⢨⣁⠣⢌⡉⠙⣛⠿⠳⢷⢶⡶⠾⠿⠛⡋⢅⡐⢈⡐⢀⠃⢌⠒⠠⠉⡔⢠⢩⣦⣩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡀⢀⣀⡀⢀⣀⠀⠀⠀⣀⣀⠀⣀⣀⠀⣀⣀⣀⠀⣀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⠲⣌⢳⣮⣜⣵⣿⠦⣱⣈⠤⡐⢡⠊⢡⠐⢂⡐⠤⠐⠢⢌⠂⠬⣁⢣⣰⣥⣾⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢐⣞⢸⣆⢽⣆⣿⠀⠀⠀⠈⢾⣒⡟⠁⣞⣇⠈⣸⡇⣿⣇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢬⣳⢻⢿⣿⣿⣷⣶⣬⣶⣭⣦⣽⣦⣭⣦⣶⣵⣿⣾⣾⣿⢿⡿⣿⢿⣻⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠛⠛⠉⠘⠛⠀⠙⠛⠀⠀⠀⠀⠐⠛⠀⠀⠈⠛⠛⠛⠁⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣏⡿⢮⣗⣯⠿⣽⣻⣟⡿⣽⢯⡿⣽⣫⢯⣽⣚⡷⣳⣞⣧⣟⡾⣯⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣽⣟⣾⣳⣟⣷⣻⢾⡽⣯⢿⣽⣳⢯⣟⣾⣽⣻⢷⣻⣾⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢢⣠⣀⣤⡀⣠⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⡗⣷⡾⢷⡴⡶⢶⣶⡆⣶⠶⡶⠶⡶⠀⠀⠀⠀⠀⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡿⣿⣻⣿⣻⣽⣾⣟⣿⣻⣽⣿⣾⣯⣿⢿⣾⣷⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⡧⠀⠘⠙⠛⡉⠋⣩⠙⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣷⠟⠀⠀⣤⣬⣶⣦⣤⣴⡆⣽⣤⣤⣤⢸⣤⣤⣦⣤⣤⣄⠀⣺ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣯⣿⣟⣷⡿⣯⣿⣾⢯⣿⢿⣽⣾⡷⣿⣯⣿⢷⣯⣿⡽⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠁⠀⠸⠟⢿⠿⠿⠟⠻⠟⠻⠿⠿⠻⠟⠻⡿⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠉⠀⠁⠉⠀⠉⠈⠉⠁⠈⠁⠉⠁⠉⠈⠉⠀⢳ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⢯⣿⣟⣷⡿⣽⣟⣯⣷⣿⣻⣯⣿⣻⣾⣟⣷⡿⣽⣿⣽⡾⣟⣷⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢲⣿⣶⡧⣷⣶⣶⢶⣶⢼⣦⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⡦⣾⣤⣤⣤⣤⣤⣶⣤⣦⣤⣴⣤⢤⣤⣤⣤⠀⠀⢸ ⠀⠀⠀⠀⠀⣠⣿⣿⢯⣿⣻⣾⢯⣿⢿⣽⣻⣷⣻⣽⡷⣟⣯⣷⢿⣯⣿⣟⣾⣯⢿⣻⣯⣿⢾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣯⡿⠀⠀⣴⡉⣡⣄⣡⠁⣀⣄⣀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢠⣿⣿⣽⡿⣯⣿⡽⣿⢯⣿⣻⣽⣯⢿⣯⢿⣟⣿⡽⣿⣻⣾⣻⣽⣾⢿⣻⡷⣿⣻⡾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⡀⠀⣸⢼⣤⢶⡦⣤⣴⣤⢴⣴⣤⣶⢦⣴⣦⣶⣦⢠⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠛⠙⠘⠋⠛⠉⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⣿⣿⣟⣾⣟⣿⣳⣿⢿⣻⡿⣽⣷⢿⣟⡿⣟⣯⡿⣟⣿⣽⡷⣿⣻⣾⢿⣟⣿⣽⡷⣿⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠟⠀⢰⣤⣤⢀⣤⣤⣴⣀⣄⣠⣄⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣴⣀⢀⣀⣀⣀⣤⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⣸⣿⣿⢾⣟⣾⡿⣽⣾⣿⣻⣽⣿⢾⡿⣯⣿⣟⣯⣿⢿⣽⣾⢿⣻⣷⣿⣻⣿⢾⣷⢿⣻⡷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⡍⠉⠈⠉⠀⠉⠉⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣟⣧⠀⠀⠋⠛⡟⠉⠙⢋⢻⡛⠋⡙⠉⠛⠋⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⣿⣿⢯⣿⢯⣿⣽⣿⣳⣯⣿⣽⣾⢿⣻⣽⣷⢿⣯⣿⣻⣽⣾⡿⣯⣷⡿⣽⣾⣟⣯⣿⢯⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣄⡀⠀⢰⢼⣦⢶⣆⢤⣤⣤⣤⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠃⠀⠀⠿⠿⠟⠿⠷⠿⠷⠿⠗⠟⠾⠿⠇⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣼⣿⣿⣻⣯⣿⢯⣷⣟⣯⣿⣳⣯⣿⣟⣿⣻⣾⣟⣿⢾⡿⣽⣷⢿⣻⣷⢿⣟⣷⡿⣯⣿⣻⣽⣾⣻⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣯⡷⠀⢀⣦⣈⣦⣀⣀⣠⣍⣠⡀⣀⣀⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣴⣦⣦⣦⣤⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⢾⣿⡷⣿⣽⣯⣿⢯⣿⣻⣷⡿⣯⣷⡿⣯⣿⣳⣿⢯⣿⢿⣻⣽⣿⣻⣽⡿⣯⣟⣿⢿⣽⣯⣷⣿⣻⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⢈⣉⢉⡉⠉⡉⡉⠉⠍⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣿⣿⣿⣿⣷⣿⣯⣿⣟⣿⣾⣿⢿⣷⣿⣿⣽⣿⣯⣿⣿⡿⣟⣿⣾⣿⣽⣿⣟⣿⣯⣿⣿⣷⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⢛⠛⠻⠟⠟⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢰⣿⣿⣿⣾⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣯⣿⣿⣷⣿⣿⣽⣿⣿⣿⣽⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⢠⡄⢹ ⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⣆⠀⠸⠻⠿⠲⠷⠿⠯⠷⠿⠾⠾⠦⡶⠿⠷⠖⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣬⠇⠃⠞⡴⢿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠾⠋⠀⢠⣶⢦⣦⣴⣾⡦⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠿⠿⠷⡚⢲ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢲⠨⡿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃ ⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠒⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⠒⢦⣧⡄⣀⣄⢀⣄⣰⣦⣶⣤⣄⢀⣤⡄⢠⡇⠀⣷⣲⢀⣤⣀⣤⣠⣄⣼⢤⣰⡆⠀⡼⡄⢤⣤⣀⣤⣶⠀⣿⠒⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⢾⣳⠆⢰⣞⠶⡦⣠⣠⣤⣤⣀⣤⡀⢰⣆⣸⢂⣤⣸⢧⣤⡀⣴⠖⠲⣧⣄⣀⣤⣀⣤⣴⡦⢼⢤⣤⣀⣤⣤⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀ ⠙⠦⠞⠇⠸⠻⠽⠻⠿⠟⠶⠿⠇⠸⢿⣦⡗⠀⡇⠀⠧⠼⠐⠽⠏⠇⠗⠻⠹⠴⠛⠀⠸⠋⠹⠾⠐⠟⠦⠟⠀⠻⠤⠋⠯⠿⠲⠤⠦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠇⠲⠼⠃⠐⠦⠟⠇⣧⣾⠻⠈⠟⠿⠇⠸⠇⠸⠟⠯⠟⠸⠽⠃⠙⠦⠖⠇⠸⠙⠯⠛⠽⠏⠷⠸⠻⠀⠟⣷⡾⠀⠹⠼⠓⠦⠦⠴⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣸⣧⡄⠀⠀⠀⢠⢤⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⢀⢢⠂⠆⠀⠀⠀⣠⠤⡀⠀⡀⠀⡀⢀⢀⠀⣤⠀⢠⠀⢀⠀⢀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀ ⢸⣿⠻⢹⣧⠀⠀⢸⡟⢪⣟⡿⡏⢱⢮⣹⡖⣉⡛⡏⢹⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠓⢻⠛⠓⡂⠀⠀⢿⣀⡟⢾⣻⢾⣻⣿⠉⠁⣇⠳⢫⠰⣟⡷⣏⣹⢻⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣟⠀⠀⠀ ⠀⠙⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠑⠀⠀⠀⠈⠀⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀