Crisitano Ronaldo Real Madrid season 2017/18 Emojis & Text

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠛⠛⢻⣿⣿⠋⠉⠙⢿⠉⠀⠈⢿⣿⡀⠀⠀⠹⣿⣿⣧⡀⠀⠈⠛⣧⡀⠀⠀⠁⡆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢐⠂ ⠀⢹⣿⡃⠀⠀⠀⣹⣏⠀⠀⠀⢿⣿⣿⡀⠀⠀⠻⣿⣄⠀⠀⠘⢳⡀⠀⠀⠙⣷⣦⠀⠀⠀⣿⣿⢧⠀⠀⠀⢸⣧⡀⠀⢀⣴⢤⢀⡠⡘⡄⣠⢀⢲⢠⠄⠀⢀⡰⣄⢫⣜⢣⢎⡘ ⠀⠀⠙⢷⣀⠀⠈⠹⣿⣦⠀⠀⠈⢿⣿⣷⣆⠀⠀⠈⣿⢧⣀⣀⠀⣿⡀⠀⠀⣹⣿⣄⣀⣀⣾⣏⣻⢳⣴⡶⣿⢻⡝⢯⡛⣬⢃⢮⢱⣙⢲⡡⢏⣎⠗⣞⡰⣡⢷⣎⠷⣎⣟⠦⣑ ⣧⠀⠀⢸⣿⡆⠀⠀⣽⣿⣧⣀⣀⣸⣿⢿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣻⢿⡹⣎⢷⣫⠾⣵⢫⡗⣜⡣⡝⢦⣋⢮⣓⢮⢧⡻⣜⡮⣟⣮⠷⣽⣞⣾⣻⡽⣞⡷⣣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡗⢿⣿⣿⣳⣟⡾⣣⢿⣱⢟⣮⢷⡻⣵⢫⡞⣥⡳⣝⢧⣛⣮⡝⣮⡗⣯⣻⢼⣻⣼⣟⣷⣻⡾⣷⢿⣯⣟⡷ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣽⣻⣽⣿⣿⣿⣿⣿⣿⠿⠟⠋⢉⣠⣄⠀⠈⢿⣿⣾⡽⣯⢷⣛⣮⢷⣫⢷⣣⠿⣜⣧⣛⡾⣝⣾⣱⣟⣧⣟⡷⣯⣟⣷⣻⢾⣽⣟⣿⡿⣿⣿⣯⣽ ⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢋⣭⣥⣤⠀⠀⠉⠀⣠⣷⡄⠹⣿⣿⡿⣽⢯⣟⣞⣷⣫⣗⣯⠿⣽⠶⣯⡽⣻⡼⣷⣻⢾⣽⣻⢷⣻⣾⢯⣿⣻⣾⣿⣿⣿⣿⣎⢻ ⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣿⣷⣿⣟⣿⣿⣿⣷⡿⢟⣡⣤⣤⡿⢿⣿⣿⠛⠂⢳⣿⣿⣽⣻⣾⡽⣶⣻⡼⣞⡿⣽⣻⢷⣳⣿⣽⡷⣿⣻⡾⣟⣿⡿⣽⣿⣻⣿⣿⣽⣿⣿⣿⣷⡆ ⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣯⣿⣟⣿⣿⣿⣿⡯⢡⣾⣿⣿⣿⣧⠈⠛⠋⠀⠠⡈⣿⣿⠿⠛⠻⢷⣿⢯⣷⣟⣷⣻⣟⣾⣿⢯⣟⣷⣿⡿⣷⣿⣿⣷⣿⣯⣿⣿⢿⣿⣿⣿⣿⣯⡇ ⣿⣿⠉⠉⠙⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣟⣿⣷⠘⡿⠟⣋⢡⣿⣦⣀⡿⠷⢶⡃⢹⣿⡀⠀⠀⣸⣿⢿⣞⡿⣾⣟⡿⠛⠻⠿⢿⣻⣷⣿⠋⠉⠉⠙⢿⣿⣿⣯⣿⠉⠁⠉⣿⣿⡟ ⣿⣿⡀⠀⢀⣾⣿⢿⣻⣿⣿⡿⠟⠛⠛⢿⣿⣯⣧⢰⣾⣿⣾⣿⣿⣿⣶⣶⣷⣵⡊⣿⣿⡃⢈⣽⣯⣿⣾⡽⣷⣿⣄⣀⣀⢀⣼⣻⣟⣷⣦⣤⣤⣤⣿⣿⣟⣿⣯⣷⣶⣾⣿⣿⠣ ⣿⣿⡷⣀⣼⣿⣿⣿⣿⢿⣿⣦⣠⣄⣤⣼⣿⣿⢿⣇⢻⣿⣿⣿⣿⣿⣿⠟⡩⠄⠀⠈⠻⢿⠿⣿⣿⣽⣿⣿⣿⣷⣿⣿⣿⣿⣾⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠ ⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡶⢂⠀⠀⣼⣼⣧⣶⣮⣭⣟⣛⡻⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢿⣿⢿⣿⣿⣿⣷⣍⠂⣴⣿⣛⣟⣻⣿⣿⣿⣿⣿⣿⣿⣟⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣿⣿⢮⣻⣷⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣶⣾⣴⣦⣶⣏⡜⡋⢧⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣟⡼⣿⣎⢻⣿⣿⣿⣿⣿⡿⣩⠓⢿⣿⣿⠟⢻⣿⠿⣿⣿⣿⢞⡌⣷⢆⡵⢷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⣿⣿⣿⣿⠉⠉⣻⣿⢿⣿⣿⡿⠙⣿⣥⣋⡾⠋⣁⠶⠋⣡⡶⢿⣿⡿⣼⣸⣿⢮⣽⣿⡿⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢽⣷⣯⣽⣿⣿⣿⡆⠀⣿⣿⡷⣤⣻⠃⢰⣿⠶⠋⢠⠜⢋⣴⠞⢋⣤⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣌⣻⣿⣿⣿⣿⣿⣷⣾⠟⣇⢧⢸⡏⠀⠈⠁⡀⢀⡀⠚⢋⣴⡶⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⢆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣽⣻⣿⣿⣿⣿⡿⠟⢴⡠⢽⡾⣿⡇⠀⠀⠀⢀⡰⠶⠖⠛⣡⡶⡟⣿⣿⣿⣿⣿⣿⣿⠿⢻⣾⣿⣿⡹⣎⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⠇⢀⣈⣿⣟⣶⡿⠃⠀⡀⠠⠎⡉⠷⣾⣿⣿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢈⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣄⣀⠀⠀⢁⣴⣷⣾⣿⣏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣟⣻⣾⣿⠫⢿⣿⣿⣿⣿⣿⣿⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡷⣬⢿⣿⣿⣿⠟⣡⡾⣿⣿⣤⣶⣿⣿⡿⣷⣿⣾⣿⣿⣿⣿⣿⣟⣋⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⠁⡜⣿⣿⣿⣿⣿⣿⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⢹⣿⢀⠶⣜⣿⣿⣶⡲⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣝⣙⣉⣋⡭⢭⣽⣿⠟⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣹⣈⡸⣿⣿⣿⣿⣿⣽ ⣿⣿⣿⣿⣿⢿⣻⣿⣿⢿⢻⣿⣿⡇⢘⣾⣿⣜⡶⣿⣿⡯⣿⣷⣝⡻⣿⣿⣿⣿⣿⢿⣿⢿⡟⢛⡟⣯⢻⡱⠾⡿⢋⣠⣶⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣝⠻⣛⣥⠽⣿⣿⣿⣿⣻ ⣿⡷⣿⣿⣿⣯⣟⣿⣿⢧⣞⣿⣿⣧⡾⠿⣶⣿⡟⣋⣼⣿⣽⣿⣿⣿⣿⣿⡿⢹⢳⡾⢛⡁⣇⢸⣇⠱⠿⣛⠁⣿⣾⣿⣿⡿⠋⣼⣿⣯⣿⣿⣿⣿⣿⡿⣿⣿⠥⢢⡜⣿⡿⣿⣽ ⣿⣿⣿⣽⣻⢟⡾⣻⢟⡯⣟⡟⣿⣦⠾⣻⣿⠉⣴⣿⣻⣿⣿⣿⣿⣿⣿⣏⣻⣸⣌⣷⣤⣤⣹⣦⣛⣹⣯⣷⣿⣿⠿⠟⢋⣤⣶⣿⣿⣧⢛⠽⢿⣿⣿⣷⡿⣿⣯⡵⣻⡜⢯⣿⢻ ⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣇⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠿⠿⠟⠿⠿⠿⠿⠿⠛⢉⣀⣤⣶⡟⢡⡿⡁⣿⣿⠎⣞⡌⡻⣿⣿⣿⣾⣿⡾⣽⣿⣎⢿⣽ ⣿⣿⣿⣿⣭⣻⣝⣯⢯⣝⣭⣏⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣶⣶⣤⣥⣷⣶⣾⣿⣿⣿⡿⢋⣰⡟⢠⣿⢽⣿⣿⢦⡝⡶⣙⣿⣿⣭⣿⣻⣿⣟⣿⣞⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣟⣿⣿⣿⣿⡿⠏⢐⣼⡿⢠⡿⢙⣾⡇⣿⣮⣝⣳⣵⣞⣿⣿⣷⣿⣽⣫⣿⠉⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⠟⡀⢼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣀⣴⣿⡟⢡⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠋⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣧⡹⣔⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣤⣴⣾⣿⣿⠟⣠⣿⣿⡗⣽⣿⠀⢸⣿⣿⣿⢿⣿⣿⣿⢿⣿⣟⡻⢿⡇⠈

ㅤㅤㅤ ⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⢿⣷⠒⠲⣾⣾⣿⣿ ⠀⠀⠀⠀⣴⣿⠟⠁⠀⢿⣿⠁⣿⣿⣿⠻⣿⣄⠀⠀⠀⠀ ⠀⠀⣠⡾⠟⠁⠀⠀⠀⢸⣿⣸⣿⣿⣿⣆⠙⢿⣷⡀⠀⠀ ⣰⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⠻⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠟⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀ ⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀ ⠀⠀⠠⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡿⠋⠉⠀⣿⡇⠀⠉⠻⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡛⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣷⣾⣿⡟⢻⣿⣿⣿⣿⣍⣹⣿⣿⣿⣿⠟⢿⣿⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⠾⢿⣿⣿⣿⠟⢛⣿⣿⣿⣉⣹⣿⣿⣿⠛⢿⣿⣿⣿⡿⠷⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣟⣻⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣻⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣿⣿⠿⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡛⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⢟⡥⠚⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠓⢌⡻⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⢠⣿⣿⠟⡡⠋⢀⣴⣶⣄⠀⢙⠦⠒⠒⠒⠒⠒⠒⠴⠋⠀⡰⠓⢆⡀⠙⢌⢿⣿⣿⡄⠀⠀ ⠀⢠⣿⣿⠏⡜⠁⣠⣾⣿⣿⠿⠃⢀⠀⠐⢶⠒⠒⡶⠂⠀⡀⠘⢦⡀⠀⠑⡄⠈⢣⡹⣿⣿⡆⠀ ⢀⣿⣿⡏⡜⠀⣰⣿⣿⡿⠋⢀⣴⣿⣷⣄⠀⠑⠊⠀⡠⠊⠙⢦⣀⣹⠆⠀⠘⡄⠀⢳⢹⣿⣿⡄ ⣸⣿⣿⢰⠁⢠⠏⠻⣿⠁⢀⣾⣿⣿⣿⣿⣷⣄⣠⣾⣄⠀⠀⠀⠋⠀⠀⠀⠀⢹⡀⠈⡏⣿⣿⣇ ⣿⣿⡟⠘⠀⢸⠀⠀⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⢻⣿⣿ ⣿⣿⣧⢠⠀⢸⠀⠀⡇⠀⢿⠻⣿⣿⣿⣿⠀⢠⣀⣀⣸⣿⣿⣦⡀⠀⠀⠀⠀⠀⡇⠀⡆⢸⣿⣿ ⢻⣿⣿⢸⡀⠸⡆⠀⢱⡀⠘⣆⠈⠻⣿⣿⠀⠸⠿⠿⢿⣿⣿⣿⣿⣦⡀⠀⠀⢸⠁⢀⡇⣿⣿⡿ ⠘⣿⣿⡆⢧⠀⠻⡀⠀⢳⡀⠘⢦⣀⠈⢻⠀⢠⣤⣤⣼⣿⣿⠟⢿⣿⣿⣦⣠⠇⠀⣼⢰⣿⣿⠃ ⠀⠹⣿⣿⡌⢦⠀⠱⣄⠀⠙⢦⡀⠈⠓⠚⠀⠸⠿⠿⠟⠋⠀⣀⣼⣿⣿⣿⠋⠀⡰⢃⣿⣿⡟⠀ ⠀⠀⠻⣿⣿⣎⠳⠖⠉⠀⠀⠀⠈⠓⠦⢤⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣦⠜⣡⣿⣿⠟⠀⠀ ⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣀⣸⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⣫⣾⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢋⣥⣾⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠿⣀⡸⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣟⢛⡽⠚⠉⢙⣛⡏⠉⠛⠺⣝⢛⣷⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣛⣭⣿⢱⠏⠀⠀⠀⢨⣯⡇⠀⠀⠀⠈⢧⢻⣯⣝⡻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣻⠞⠁⢿⠿⢇⡀⠀⠀⠀⣼⣭⣵⡄⠀⠀⠀⣨⠞⢿⠀⠙⢾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⡏⠀⠀⡾⣿⡿⡾⡞⢉⣧⣾⣿⣿⣗⢏⢹⣪⣺⢿⢟⡀⠀⠈⣯⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣷⡇⣈⡫⠿⠿⣏⣙⣛⣋⡼⢿⠧⢄⣛⣛⣉⠿⠿⠇⣊⡈⢰⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣄⡭⣕⠒⣯⡿⠏⢸⣃⣚⣛⣛⣀⣿⠈⢿⣯⣗⢒⡥⣅⡭⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣻⣤⣦⠴⠞⠓⠚⠛⠛⠛⠛⠚⠛⠶⢥⣄⡸⠁⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⣀⣀⣤⠤⠤⠶⠶⠦⢤⣀⣀⡀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣄⡀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣴⣻⠿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⢿⡳⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠁⢀⣴⣿⠛⠁⢀⠀⠈⠻⣦⡀⠀⣀⣀⣀⣀⣀⠀⠀⣠⠞⠁⠀⡀⠀⠙⢮⡷⣄⠀⠙⢦⠀⠀⠀⠀ ⠀⠀⠀⣴⠃⠀⣰⣯⠟⠁⢀⣴⣿⣷⣄⡀⠈⠛⠉⠉⠀⠀⠀⠈⢉⠛⠁⠀⣠⠞⠙⢧⡄⠀⠙⣾⣧⡀⠈⢷⡀⠀⠀ ⠀⠀⣸⠃⠀⣴⣳⠃⠀⣠⣿⣿⣿⡿⠋⠀⢀⠀⠀⠲⣖⠒⢲⡶⠂⠀⠀⠀⠙⢷⣄⠀⠙⣦⠀⠈⢷⢷⡀⠀⢷⠀⠀ ⠀⢠⡇⠀⣸⢳⠃⠀⣰⣿⣿⣿⠋⠀⢀⣴⣿⣷⣄⠀⠈⠷⠋⠀⢀⡼⠛⢧⡀⠀⣹⡇⠀⠘⣧⠀⠈⣿⢧⠀⠈⣧⠀ ⠀⣿⠀⠀⣏⡟⠀⢠⠟⢿⣿⠇⠀⢠⣿⣿⣿⣿⣿⣷⣄⠀⢀⣴⡋⠀⠀⠀⠻⠟⠉⠀⠀⠀⠸⡆⠀⠸⡟⡇⠀⢹⡄ ⢀⡏⠀⢸⢻⠇⠀⣸⠀⠀⡿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢧⣿⠀⠀⡇ ⢸⡇⠀⣿⢸⠀⠀⡟⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⠟⠿⠟⠛⠛⠻⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⢹⠀⠀⡇ ⢸⡇⠀⢻⢸⡄⠀⢿⠀⠀⣷⠀⠀⣇⠙⢿⣿⣿⣿⠀⠀⢴⣶⣶⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣼⠀⠀⣼⣿⠀⠀⡇ ⠘⣷⠀⠘⡿⣇⠀⠸⡄⠀⠹⡆⠀⠸⣆⠀⠙⢿⣿⠀⠀⠘⠛⠛⢻⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⡏⠀⢠⡇⡿⠀⢰⡇ ⠀⢻⡄⠀⢷⣿⡀⠀⢻⡄⠀⠹⣄⠀⠘⢧⣄⠀⢹⠀⠀⢤⣤⣤⣼⣿⣿⠿⠻⣿⣿⣿⣷⣄⡾⠀⠀⣼⣹⠁⠀⣾⠀ ⠀⠀⢷⠀⠘⣯⢳⡀⠀⠻⣄⠀⠘⢦⡀⠀⠈⠛⠺⠀⠀⢸⣿⡿⠟⠋⠁⠀⢀⣼⣿⣿⣿⠟⠀⠀⣰⣣⠏⠀⣸⠃⠀ ⠀⠀⠈⣷⡀⠈⢯⡻⣄⣠⠾⠁⠀⠀⠉⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣤⡀⡼⣻⠏⠀⣰⠏⠀⠀ ⠀⠀⠀⠀⢷⡄⠈⠻⣎⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⣿⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠁⠀⣰⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣄⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠿⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⣟⡽⠋⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡽⠞⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠈⠉⠓⠒⠦⢤⣤⣤⣤⣤⣤⣤⡤⠖⠒⠋⠁⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠉⠈⠉⠛⠛⢿⣿⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣿⡟⢁⡴⠶⠶⣶⣶⣤⡀⠀⠀⠀⢀⣤⣤⣄⣀⣀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡏⢀⣴⣶⣲⢿⣿⠆⠀⠀⢠⣿⣿⣭⣥⣄⡉⢳⡟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠹⠗⠙⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡺⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢶⣾⠿⠶⠷⣶⠀⠀⠀⠀⠀⠀⢠⣿⣵⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⣿⡋⢏⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⣿⣟⠀⠀⠀⠀⠀⢀⡴⠖⠚⠛⠓⠶⣤⡀⠀⠀⠀⠀⢸⣿⣦⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣤⡦⠈⠀⠀⠀⠀⠀⣸⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣶⣶⣾⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢿⡿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠈⠻⢷⣤⣀⡴⠚⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⢞⡅⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠃⠀⣌⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢴⣫⠾⠋⠀⠀⠀⠈⠛⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠟⠉⠀⠀⠀⠈⠳⢤⡉⠒⢤⣀⠀⠀ ⣀⠤⢖⣮⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣈⠑⠲ ⣷⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄ ⢽⣿⣿⠛⢻⣿⣿⣿⣿⠛⠛⠛⠛⢻⣿⣿⠿⠛⠛⠿⣿⡟⠛⠛⠛⠛⣿⡟⢿⣿⣿⣿⠛⢻⡟⠛⠛⠛⠻⣿⣿⣿⡇ ⢸⣿⣿⠀⢸⣿⣿⣿⣿⠀⢿⣿⣿⣿⡿⠁⣴⣶⣶⣾⣿⡇⠀⣿⣿⣿⣿⡏⢀⠙⢿⣿⠀⢸⡇⠀⣷⣷⣆⠈⢿⣿⡇ ⢸⣿⣿⠀⢸⣿⣿⣿⣿⠀⢤⣤⣴⣿⣧⠀⢿⣿⣤⠀⣿⡇⠀⣤⣤⣼⣿⡇⠀⣷⣄⠙⠀⢸⡇⠀⣿⣿⡟⠀⣸⣿⡇ ⢸⣿⣿⣀⣈⣉⣉⣉⣿⣀⣈⣉⣉⣹⣿⣷⣄⣈⣁⣤⣿⣇⣀⣉⣉⣉⣿⣇⣀⣿⣿⣷⣄⣸⣧⣀⣉⣉⣀⣴⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡎⠹⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣟⡿⠛⠉⢹⣿⠉⠉⠫⡻⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡫⢿⣿⡞⠀⠀⠀⣸⢿⠀⠀⠀⠙⣽⡗⠪⣻⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡟⠀⠸⣿⣷⡦⠂⣼⣿⣿⣥⠀⣤⣺⣿⠇⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣷⢉⣹⠻⣿⣉⣻⡯⢽⣿⠴⣿⣋⣻⡟⢫⠈⣴⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠙⢶⣿⠉⡻⣏⣸⣧⣽⣿⣤⣧⣘⡟⠋⠷⣶⠊⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠉⢁⣀⣀⣠⣤⣄⣀⡀⠉⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠖⠉⣀⣤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⣦⣄⠈⠓⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⣠⣾⠟⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠛⢽⣦⡀⠙⢄⠀⠀⠀⠀ ⠀⠀⡴⠁⢠⣾⠟⠁⣠⣶⣄⠈⠳⠖⠒⠒⠒⠒⠲⠖⠁⣀⠴⢦⡀⠙⢿⣆⠈⢳⡀⠀⠀ ⠀⡸⠁⣰⡿⠁⢠⣾⣿⡿⠋⠁⡀⠀⠲⡖⢒⡶⠀⢀⠀⠙⢦⡀⠹⣄⠈⢻⢧⠀⢳⡀⠀ ⢰⠃⢠⢻⠃⢠⣿⣿⡟⠁⣠⣾⣿⣦⡀⠈⠋⢀⡴⠋⠑⣄⣠⠗⠀⠘⡆⠀⢿⣇⠀⣇⠀ ⡾⠀⡾⡏⠀⡎⠈⡟⠀⢠⣿⣿⣿⣿⣿⣦⣴⣿⣦⠀⠀⠈⠀⠀⠀⠀⢹⠀⠸⣿⠀⢸⠀ ⡇⠀⣿⡇⠀⡇⠀⡇⠀⢸⣿⣿⣿⣿⠟⠿⠛⠛⢿⣿⣦⡀⠀⠀⠀⠀⢸⠀⠀⡏⡇⢸⡇ ⣇⠀⣟⡇⠀⡇⠀⢣⠀⠸⡈⠻⣿⣿⠀⠀⣶⣶⣿⣿⣿⣷⣄⠀⠀⠀⢸⠀⢠⣿⠃⢸⠃ ⢹⡀⢹⣿⠀⠸⡄⠈⢧⠀⠳⣄⠈⢻⠀⠀⣀⣀⣹⣿⣿⢿⣿⣷⣄⢀⡏⠀⡼⡿⠀⡼⠀ ⠀⢧⠀⢿⣣⠀⠹⣄⠈⠳⣄⠈⠑⠲⠀⠀⣿⠿⠟⠋⠀⢀⣽⣿⣿⠏⠀⣰⡻⠁⢰⠃⠀ ⠀⠈⢦⠀⠻⣷⡤⠞⠀⠀⠈⠓⠤⢄⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣦⣴⡿⠁⣠⠋⠀⠀ ⠀⠀⠈⠳⡀⠙⢦⡀⠀⠀⠀⠀⠀⢨⣄⣀⡇⠀⠙⢿⣿⣿⣿⣿⣿⣿⠋⢀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠙⠦⡀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠋⢁⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠈⠙⠒⠒⠤⠤⠤⠤⠔⠒⠊⠉⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠢⠤⠤⠤⠤⠤⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

...ㅤㅤㅤ ⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⣴⣿⢿⣷⠒⠲⣾⣾⣿⣿⣄ ⠀⠀⠀⠀⣴⣿⠟⠁⠀⢿⣿⠁⣿⣿⣿⠻⣿⣄⠀⠀⠀⠀ ⠀⠀⣠⡾⠟⠁⠀⠀⠀⢸⣿⣸⣿⣿⣿⣆⠙⢿⣷⡀⠀⠀ ⣰⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⠻⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠟⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀ ⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀ ⠀⠀⠠⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⡶⣶⣤⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣯⣓⣿⣿⣿⣧⣿⣸⣿⡟⠶⢢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣟⠙⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⣿⣿⣾⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡷⣾⣷⣿⣿⣻⣿⣿⡞⣿⣽⣷⣿⡟⣿⣿⣯⣹⣿⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠛⠛⠉⠙⠛⠛⠞⠿⠟⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣥⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⡹⣿⠿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⣻⣿⣶⣾⣿⣳⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⡆⠀⠀⠀ ⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⣿⣿⡟⠀⠀⣠⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⢹⡟⠀⢀⠞⠋⠉⠉⢉⣛⣿⣿⣿⣦⠀⠀⠀⠀⠀⣰⣿⣿⡿⠟⠛⠛⠙⠻⢧⠀⠀⠘⢿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⢸⣇⠀⠈⠀⢠⣴⡿⣿⣿⡿⢿⣿⠇⠀⠀⠀⠀⣰⣿⣿⡿⣿⣷⣶⢶⣦⣀⢀⣷⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀ ⢠⠤⣼⣿⠀⠀⠐⠛⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢰⡟⠁⠉⠁⠈⠛⠁⠈⠿⣿⠛⢛⡀⠀⠀⣿⣿⣿⣿⣀⠀⠀ ⣿⡷⠄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠂⠒⠒⠂⠀⠀⠀⠃⠀⠀⣿⣿⠟⢉⣴⣿⡆ ⡇⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡴⠁⠸⣿⡇ ⢻⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠈⠃⠀⠀⣀⡇ ⠘⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠿⢿⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⢸⠃⠀⠀⠀⢀⡟⠀ ⠀⠱⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣵⠁⠀⢈⡞⠂⢀⡼⠋⠀⠀ ⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⢀⣄⠀⠀⢀⡼⠛⠁⠀⠀⣸⢲⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠠⠾⠿⣏⣁⣀⣈⣀⣈⣉⣍⣿⣿⡿⠅⠀⢀⡾⠁⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢰⡇⠀⠄⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⢠⡿⠀⢸⠀⢸⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⣠⣿⡥⠂⠈⠀⠘⣷⣵⣄⠀⠀⠀ ⠀⠀⠀⢀⠤⣾⣿⡆⠈⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⣿⣿⡿⢦⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣱⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⣿⡟⠁⢰⠇⠀⠱⣿⢗⣦⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡀⣿⡶⢦⢿⣿⣦⢾⣿⠀⣻⡇⠀⠀⠀ ⠀⠀⠀⠈⠙⢹⣇⣛⠹⠬⠧⠧⢛⡰⠧⠋⠁⠀⠀⠀ ⠀⠀⠀⢀⠄⢊⡡⠐⠒⠀⠀⠐⠂⠤⡁⠢⡀⠀⠀⠀ ⠀⠀⡔⢁⡴⢋⡉⠢⣀⠀⠀⣀⡠⢊⡉⠳⣌⠢⡀⠀ ⠀⡌⣰⠏⣰⣿⠟⢀⠀⢖⡲⠀⣀⠣⡈⢂⠙⣆⠱⡀ ⢸⢠⡏⢰⢻⠃⣰⣿⣷⣤⣠⣎⠀⠓⠁⠀⠆⢸⡆⠃ ⢸⢸⡇⠀⢸⠀⡿⣿⣿⠙⣉⣹⣷⣄⠀⠀⠀⢀⡅⠸ ⠸⠈⣧⠘⡄⢂⠐⢌⢻⠀⣉⣹⡿⢿⣷⣄⠃⣸⠃⡆ ⠀⠣⠘⣧⡸⠀⠑⠄⣉⠀⣋⣉⣠⣾⣿⣇⣰⠏⡐⠀ ⠀⠀⠑⢌⠢⢀⠀⠀⠸⠀⠃⠈⠻⣿⣿⠟⢁⠜⠀⠀ ⠀⠀⠀⠀⠑⠠⢉⡒⠀⠠⠤⠀⠒⣉⠤⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣴⢟⣉⣹⣏⣉⢻⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣯⣾⠿⣿⣿⣟⣻⣿⣿⠿⣯⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠸⣻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣛⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣳⣮⣽⣿⣿⣯⣵⣞⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⢿⠛⠉⠉⠀⠀⠉⠉⠛⡿⣿⣦⡀⠀⠀⠀ ⠀⠀⣴⡿⡫⠃⣁⠑⢄⣀⠀⠀⣀⡠⠊⣈⠘⢿⣿⣦⠀⠀ ⠀⣼⡟⡕⢠⣾⡿⠃⣀⠐⢖⡲⠀⣀⠘⢄⠑⡄⢪⢿⣧⠀ ⢰⣿⠙⢠⠻⡟⢀⣾⣿⣷⣌⣠⡊⠀⠱⠊⠀⠘⡀⠋⣿⡇ ⢸⣿⡇⢸⠀⡃⢸⣿⣿⣿⠿⠿⢿⣦⡀⠀⠀⠀⡇⢰⣿⡇ ⢸⣿⢁⠸⡀⢃⠸⡈⠻⣿⠘⠿⢿⣿⣿⣦⡀⢀⠃⡈⣿⡇ ⠈⣿⣎⢄⠡⡀⠢⡈⠢⠼⠰⠿⠿⠛⣉⣿⣿⠊⠠⣱⣿⠁ ⠀⠘⢿⣮⡒⠁⠀⠀⠑⢲⢠⠀⠲⣾⣿⣿⣿⢖⣵⡿⠃⠀ ⠀⠀⠈⠻⣿⣦⣄⠀⠀⠈⠉⠀⠀⠈⠻⣛⣵⡿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⠿⢷⣶⣶⣶⣶⣾⠿⠟⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡿⠿⠟⠛⠛⠛⠿⢿⣿⡧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣁⣤⣴⣶⣶⣶⣶⣦⣤⣈⠁⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠈⠙⠻⣷⣦⡀⠀⠀ ⠀⢀⣾⡟⠁⣠⣾⣶⣤⣀⢀⣠⣴⣶⣦⡈⠻⣷⡄⠀ ⠀⣾⡟⠀⣾⡟⠁⣨⣿⠿⠿⣿⣥⠈⠻⣷⡀⠹⣿⡀ ⢰⣿⠀⢸⣿⠀⣸⣿⠁⣤⣤⠈⠉⠀⠀⣿⡇⠀⣿⡇ ⠘⣿⡀⠸⣿⡀⠸⣿⡀⣿⣤⢀⣄⠀⠀⣿⡇⠀⣿⡇ ⠀⢿⣧⠀⢻⡷⠀⠙⠻⣿⠿⠿⠋⠀⠸⡟⠀⣸⡿⠀ ⠀⠈⢻⣷⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀ ⠀⠀⠀⠙⠿⣷⣤⣀⣀⠀⠀⢀⣀⣤⣶⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠿⠿⢿⣿⡿⠿⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡿⠋⠀⠀⠀⢸⣿⡆⠀⠀⠈⠻⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢛⣿⣿⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣅⣨⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⢿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣋⢉⣛⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⠿⠦⠞⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⠶⢞⣛⣛⣩⣭⣽⣯⣭⣭⣝⣛⣛⡲⠶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⢟⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⣋⡴⠛⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠛⢦⡙⠿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⠟⣡⡾⠋⠀⣠⡀⠀⠙⣦⡀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⡴⠋⠀⢀⣄⠀⠙⠳⣜⢻⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⡿⢋⡼⠋⠀⣠⣾⣿⣿⣦⡀⢈⠝⠋⠉⠉⠀⠀⠀⠉⢉⠙⠋⠀⢀⣴⠏⠉⠳⣄⠀⠙⢧⡙⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⣼⣿⣿⡿⢡⠞⠀⢀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠲⣶⠒⠒⢒⣶⠆⠀⠀⠀⠈⠳⣄⠀⠀⠘⢧⠀⠀⠳⡌⣿⣿⣿⣧⠀⠀ ⠀⣸⣿⣿⡿⢁⡟⠀⢠⣾⣿⣿⣿⠟⠁⠀⣠⣾⣿⣄⠀⠈⠳⣤⠞⠁⠀⣠⠞⠷⣄⠀⠈⢳⡄⠀⠈⢷⡀⠀⢻⡈⣿⣿⣿⣇⠀ ⢀⣿⣿⣿⠇⡾⠀⢀⡿⣿⣿⣿⠏⠀⢀⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⠞⠁⠀⠀⠙⣧⡶⠋⠀⠀⠀⠈⣷⠀⠀⣷⠸⣿⣿⣿⡀ ⢸⣿⣿⣿⢰⠇⠀⣼⠁⠈⢻⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣦⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡆⠀⠸⡆⣿⣿⣿⡇ ⢸⣿⣿⡟⢸⠀⠀⣿⠀⠀⢸⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡇⢹⣿⣿⡇ ⢸⣿⣿⡇⢸⠀⠀⣿⠀⠀⢸⡀⠀⢸⠿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⢸⣿⣿⡇ ⢸⣿⣿⣿⢸⡀⠀⣿⡀⠀⠸⡇⠀⠸⣆⠈⠻⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⡏⠀⢀⡇⣼⣿⣿⡇ ⠸⣿⣿⣿⡘⣧⠀⠸⣇⠀⠀⢹⡀⠀⠻⣄⠀⠈⠻⣿⣿⠀⠀⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣸⠁⠀⣼⠁⣿⣿⣿⡇ ⠀⢿⣿⣿⣇⠻⡄⠀⠻⡆⠀⠀⢻⡄⠀⠙⢷⣄⠀⠘⣿⠀⠀⣦⣤⣤⣼⣿⣿⣿⠟⠻⣿⣿⣿⣷⣦⣰⠃⠀⢠⡟⣸⣿⣿⣿⠀ ⠀⠘⣿⣿⣿⣄⢳⡄⠀⠹⣆⠀⠀⠙⢦⡀⠀⠉⠛⠶⣿⠀⠀⣿⣿⣿⡿⠿⠋⠀⠀⢀⣽⣿⣿⣿⡿⠁⠀⢠⡾⢠⣿⣿⣿⠇⠀ ⠀⠀⠸⣿⣿⣿⣆⠻⣆⢀⣼⠇⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣧⡀⢠⠟⢰⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⣦⡈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠀⠀⡶⠶⠖⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣴⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣇⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⢿⣿⡿⠛⣉⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣴⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣦⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠻⠋⠉⠉⠛⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠈⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠋⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡹⣿⣿⣿⠋⠁⠒⣉⣭⣭⣽⣿⡶⠀⢀⣤⣶⣬⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣿⠓⢻⡿⠀⠀⠀⠀⠛⠛⠛⠉⠀⠀⡿⢿⡿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠾⣆⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⣦⠤⠇⠀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣬⣄⠀⢠⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠣⣴⣤⣤⡼⠁⡎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡇⠀⠈⣿⠲⢤⣄⡀⠀⠀⠀⠀⠀⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢓⠇⠀⠀⠘⢇⠀⠉⠻⢿⣶⣶⡿⠛⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⠇⠀⠀⢸⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⠔⠊⠁⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⢸⢀⣿⣿⠑⠦⣀⠀⠀⠀⠀ ⠘⠁⠀⠀⡀⠀⠈⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⣿⡿⠀⠀⠈⠑⢤⡀⠀ ⠀⠀⣀⣴⠿⡄⠀⠀⠙⢿⣿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⠟⠁⠀⠀⢀⣀⣀⠈⠀ ⠹⣟⢉⡧⢤⡷⣀⡀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⡔⠉⠈⠉⢳⠀ ⠀⠀⡼⠁⣴⠋⠁⠉⢳⡄⢀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⣀⣠⣤⣌⣧⡀⠀⠀⣸⠁ ⠀⠀⠀⠀⢿⡀⠀⠀⣸⡟⢸⢷⡀⠀⢢⠄⠠⣤⡄⠀⠤⡔⠂⠐⢿⡀⠀⠀⠹⡏⠛⠛⠋⠀⠀ ⠀⠀⠀⠀⠀⠙⠒⠚⠋⢀⡇⠈⢷⡀⡎⠀⣼⢸⣇⠀⠀⣷⠀⠀⠈⢷⡀⢀⠜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⡿⠀⣰⡁⠀⢻⣆⣀⣿⡤⢴⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣾⣿⠿⠛⠛⠻⢿⣿⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣿⣿⡟⠁⠀⠀⠀⠀⠀⠹⣿⣿⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⢹⣿⣧⣤⣤⣤⣤⣤⣤⣴⣿⡿⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣾⣿⡿⠿⠟⠛⠛⠛⠛⠻⠿⢿⣿⣷⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣫⣥⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⣍⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⡿⠁⠀⣠⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⡀⠈⠻⣿⣷⡀⠀⠀⠀ ⠀⢀⣾⣿⠏⠀⢠⣾⣿⠟⠻⣿⣿⣶⣶⣾⣿⣿⣿⣶⣦⣾⣿⠟⠻⢿⣿⣄⠀⠘⣿⣿⡄⠀⠀ ⠀⣼⣿⠃⠀⣠⣿⡿⠁⠀⣴⣿⡿⣿⣿⣧⠀⠀⣨⣿⣿⢿⣿⣦⡀⠈⢻⣿⣦⠀⠈⣿⣿⡄⠀ ⢸⣿⡏⠀⢠⣿⡿⠁⢀⣾⣿⠏⠀⠈⠙⢿⣿⣾⣿⠟⠁⠀⠙⠋⠁⠀⠀⢻⣿⣇⠀⠸⣿⣧⠀ ⣾⣿⠇⠀⣼⣿⠇⠀⣸⣿⡏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⣿⣿⠀ ⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡁⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⣿⣿⡇ ⢿⣿⡇⠀⢻⣿⡆⠀⢻⣿⡇⠀⠀⠀⣿⣿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀ ⢸⣿⣇⠀⠸⣿⣷⠀⠈⢿⣿⣄⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⡏⠀⢰⣿⡿⠀ ⠀⢿⣿⡄⠀⠹⣿⣧⡀⠈⠻⣿⣷⣤⣿⣿⠀⠀⠀⢀⣠⣶⣿⡿⠃⠀⣰⣿⡟⠀⢀⣾⣿⠃⠀ ⠀⠈⢿⣿⣄⠀⠙⠛⠁⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠙⠋⠀⢀⣾⣿⠃⠀⠀ ⠀⠀⠈⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠘⠿⠟⠋⢉⣉⣉⣉⣉⡉⠙⠻⠿⠃⠀⠀⠀ ⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀ ⠀⠀⣴⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣦⠀⠀ ⢀⣼⣿⡿⠁⣠⡦⠀⠉⢉⠉⠉⠀⢴⣄⠈⢿⣿⣧⡀ ⣼⣿⡿⠁⣼⡟⢀⣴⣦⡈⢁⣴⣦⣠⣿⣧⠈⢿⣿⣧ ⣿⣿⡇⢰⣿⠀⣼⣿⡏⠉⣉⣹⣿⣿⣿⣿⡆⢸⣿⣿ ⣿⣿⣇⠈⣿⡄⠸⣿⡇⠀⠛⢻⣿⢿⣿⣿⠁⣸⣿⣿ ⠸⣿⣿⣆⢘⣿⣄⡈⠃⠀⠟⠛⢁⣠⣿⡃⣰⣿⣿⠇ ⠀⠙⣿⣿⣿⣿⣿⣿⣇⣀⣶⣾⣿⣿⣿⣿⣿⣿⠋⠀ ⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⣄⢼⣭⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⣽⣴⣐⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡰⣪⡸⣿⣿⣿⣣⠙⠢⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⡂⠀⠙⠟⣬⣻⡿⡟⣁⠈⡆⠐⢵⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣜⣯⣾⠚⠁⠀⠀⠀⠀⠀⠈⠀⠳⣄⡀⠁⠈⢆⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⣁⣄⡤⠖⠹⣷⣄⠀⠀⠀⡀⠀⠀⢀⣤⣾⣿⡳⣦⠀⠙⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢋⣃⠍⡏⠀⠀⠀⢻⢿⢛⠓⠂⠓⠠⠼⠻⡁⣘⠃⠈⠺⣧⡀⠊⠳ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠆⢱⠀⠀⠀⢸⠿⣌⣉⠀⢀⣒⢀⣬⡿⠏⠀⠀⠀⢠⠃⠠⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⠸⠀⠀⠀⢰⡀⢱⠄⠤⠀⠠⠜⠁⢡⠀⠀⠀⢀⡧⠀⡰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠃⢠⣤⠟⠽⢶⣂⡤⡤⢤⣄⡲⠕⣇⠀⢀⢎⣃⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡬⣦⣮⣏⠀⠀⠀⠠⠰⠗⣀⠀⠀⠀⣿⠉⠓⢤⠏⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣱⣿⡟⠀⠀⠀⠀⠀⡀⠈⡄⢠⡾⣫⣲⡠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠝⢧⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡟⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠁⢀⣠⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣦⠀⠀⠀⠀⢀⠇⢧⠄⠀⠀⠀⢈⡆⢣⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣷⣿⣿⡿⠛⠛⠉⠙⠛⠿⣿⣿⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠙⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⢹⣿⣿⣦⣶⣶⣶⣶⣶⣶⣶⣤⣿⣿⣿⠁⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣷⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠛⣉⣡⣤⣤⣤⣶⣶⣶⣷⣶⣶⣤⣤⣌⣉⠛⠿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⣠⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⡀⠀⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣦⡀⠀⣀⣠⣤⣤⣤⣤⣀⠀⠀⣠⣾⣿⣿⣿⣿⣦⡀⠀⠈⢻⣿⣿⣆⠀⠀⠀ ⠀⠀⢠⣿⣿⡟⠁⠀⢠⣾⣿⣿⠋⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠙⢿⣿⣿⣆⠀⠀⠹⣿⣿⣆⠀⠀ ⠀⢀⣿⣿⡟⠀⠀⣠⣿⣿⡟⠁⠀⢠⣾⣿⣿⢿⣿⣿⣦⡀⠀⠀⣠⣿⣿⣿⣿⣿⣷⣄⠀⠀⠹⣿⣿⣧⠀⠀⠹⣿⣿⡆⠀ ⠀⣼⣿⣿⠁⠀⢠⣿⣿⡟⠀⠀⣰⣿⣿⡟⠁⠀⠙⢿⣿⣿⣦⣾⣿⣿⠟⠁⠀⠙⡿⠛⠁⠀⠀⠹⣿⣿⣧⠀⠀⢻⣿⣿⡄ ⢰⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠘⣿⣿⣇ ⢸⣿⣿⠃⠀⢠⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⣿⣿⣿ ⢸⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⣿⣿⣿ ⢸⣿⣿⡇⠀⠸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⣿⣿⣿ ⠸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠸⣿⣿⣆⠀⠀⠀⢸⣿⣿⣧⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⢀⣿⣿⡏ ⠀⢻⣿⣿⡀⠀⠘⣿⣿⣇⠀⠀⠹⣿⣿⣦⡀⠀⢸⣿⣿⡿⠿⠿⠿⠇⠀⠀⠀⣰⣷⣤⡀⠀⠀⢠⣿⣿⡟⠀⠀⣼⣿⣿⠃ ⠀⠈⣿⣿⣧⠀⠀⠹⣿⣿⣧⡀⠀⠘⢿⣿⣿⣦⣼⣿⣿⡇⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⠁⠀⣰⣿⣿⡟⠀⠀⣠⣿⣿⠇⠀ ⠀⠀⠘⣿⣿⣧⡀⠀⠘⡿⠟⠁⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠙⠿⠟⠀⠀⢰⣿⣿⠟⠀⠀ ⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡐ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠴⠶⠋⠀⠈⠳⠚⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⠀⠀⠀ ⠈⠓⠲⡄⠀⠀⢀⡀⠀⣰⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠙⠀⠀⠉⠉⡆⠀ ⠀⠀⠀⠙⠓⠚⠋⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢹⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⣄⣀⣀⣤⣴⠟⠙⢶⡶⠞⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠳⠤⠴⠒⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠉⠀⡏⠀⣿⠟⠓⣶⣾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠛⠒⠛⢦⣤⠿⣇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣈⠓⠛⣻⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢻⡗⠂⠀⠻⠃⠀⢠⣶⡄⠀⠘⠛⠀⢈⣽⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠙⢳⣦⣤⣀⣀⣀⣀⣀⣤⣴⡾⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠾⠋⣽⣧⣌⠻⠿⠟⣫⣼⣯⠙⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⢠⣼⠏⠛⠋⠀⠀⠀⠙⠛⠙⣦⡀⣀⣬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⡉⠉⠉⡿⠉⠉⠉⣿⣋⣁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠉⠁⠈⠳⠦⠴⠷⠦⠴⠶⠋⠀⠈⠉⢐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠀⠀⠀⠀⠀⠐⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀by Lashpaige on roblox ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 9 dont remove creds

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⠓⠒⠤⣰⠋⠹⡄⠀⣠⠞⣿⠀⠀ ⠀⠀⠀⢀⠄⠂⠙⢦⡀⠐⠨⣆⠁⣷⣮⠖⠋⠉⠁⠀ ⠀⠀⡰⠁⠀⠮⠇⠀⣩⠶⠒⠾⣿⡯⡋⠩⡓⢦⣀⡀ ⠀⡰⢰⡹⠀⠀⠲⣾⣁⣀⣤⠞⢧⡈⢊⢲⠶⠶⠛⠁ ⢀⠃⠀⠀⠀⣌⡅⠀⢀⡀⠀⠀⣈⠻⠦⣤⣿⡀⠀⠀ ⠸⣎⠇⠀⠀⡠⡄⠀⠷⠎⠀⠐⡶⠁⠀⠀⣟⡇⠀⠀ ⡇⠀⡠⣄⠀⠷⠃⠀⠀⡤⠄⠀⠀⣔⡰⠀⢩⠇⠀⠀ ⡇⠀⠻⠋⠀⢀⠤⠀⠈⠛⠁⠀⢀⠉⠁⣠⠏⠀⠀⠀ ⣷⢰⢢⠀⠀⠘⠚⠀⢰⣂⠆⠰⢥⡡⠞⠁⠀⠀⠀⠀ ⠸⣎⠋⢠⢢⠀⢠⢀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠷⣬⣅⣀⣬⡷⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣠⠤⡶⣲⢺⣴⣶⢭⣉⢲⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⢵⣶⣿⣿⣿⣾⣷⣳⣿⣷⣵⣈⠷⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠘⢾⣿⡿⠿⠿⠿⠿⠿⠿⢿⡿⣿⣿⣿⣾⣾⣦⠀⠀⠀⠀ ⠀⠀⣠⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⢿⣧⠀⠀⠀ ⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣳⢮⣧⠀⠀ ⢠⣧⠇⡠⠄⣤⣤⣄⡀⠀⠀⣀⣤⣄⣤⣀⠀⠀⣿⣿⣿⣯⣇⠀ ⠈⣿⠀⢀⣶⣾⣿⣿⠁⠀⢸⣿⣿⣿⣧⣌⣥⠀⠘⣿⣿⣿⣿⠀ ⢀⣿⠀⠈⠁⠀⠀⠁⠀⠀⠀⠉⠉⠭⠽⠿⠻⠁⠀⣿⣿⣿⡏⠀ ⡏⠆⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢋⣿⣆ ⡎⠀⠀⢀⡴⠂⠈⠉⠻⠿⠿⠛⣀⢲⣤⣄⣀⠀⠀⠈⠘⣏⢹⡿ ⠱⡄⠘⢻⣳⣤⡶⠖⠒⠶⠶⢶⣿⣷⣿⣿⣿⣟⠀⠀⠄⠠⣰⠃ ⠀⢹⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠛⠁⢨⣼⣿⣿⡀⣼⠖⠛⠁⠀ ⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢁⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⢀⣀⣀⣀⣠⣤⣶⣿⣿⣿⡿⣁⡎⢸⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠸⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿#byFCA⣿⡄⠀⡇⠀⠀⠀ ⠀⢀⣼⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⡟⣿⣿⣿⣟⡁⠀⢿⣷⡄⠀ ⠀⣸⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣝⣿⣿⡍⠁⠀⢸⣿⣷⠀ ⠀⣿⣿⡀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⢸⣿⣿⠀ ⠀⢿⢿⣿⣄⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡯⠀⢠⢒⣿⣿⡏⠀ ⠀⠈⢮⡻⣿⣷⣀⠀⢀⢸⣿⣿⣟⣿⣿⠿⠒⣀⣤⣿⣿⠏⠀⠀ ⠀⠀⠀⠙⠺⣿⣿⣿⣾⣾⣿⣭⣭⣭⣷⣾⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀ ​​ ⚫ CRISTIANO RONALDO ​​⚫

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣴⡾⠛⠛⠿⣦⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠋⢹⡟⠀⠀⠀⠀⢹⣯⠙⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠸⣧⣄⣨⣿⣶⣶⣶⣶⣾⣇⣀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣛⣭⣵⡶⠶⠶⢶⣦⣭⣛⠉⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀ ⠀⣰⡿⠋⣠⡾⣷⣄⣀⣠⣀⣀⣀⣴⢷⣤⠈⢻⣦⠀⠀ ⣰⡟⠀⣼⠟⢀⣼⠿⣿⣍⢉⣿⠿⣷⡄⠹⣷⡀⢻⣧⠀ ⣿⠃⣸⡟⢀⣿⠃⠀⠈⠻⠟⠁⠀⠈⠀⠀⢹⣧⠀⣿⡄ ⣿⠀⢿⡇⠸⣿⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⢸⣿⠀⣿⡇ ⢿⡆⠸⣷⡀⢻⣦⡀⢸⡷⠶⠆⠀⣠⡀⠀⣼⡏⢠⣿⠀ ⠘⣿⡄⠹⠗⠀⠙⠿⣿⣧⣤⣶⠿⠋⠀⠸⠟⢀⣾⠇⠀ ⠀⠈⢿⣦⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀ ⠀⠀⠀⠙⠻⢶⣤⣄⣀⣀⣀⣀⣀⣤⣶⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀

⢠⣶⠶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠒⠒⠒⠒⠒⠖⠒⠒⠒⠲⠶⠶⠶⢶⡶⠶⢶⡶⠶⠶⠲⠖⠒⠶⠶⠲⠶⠒⠲⠶⠶⠶⠶⢶⡄ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢠⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢦⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⠃⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⢀⣀⣤⣴⣾⠿⠛⠁⠈⢧⠹⡄⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⡇⠀⢀⣤⠶⠋⠀⢀⣠⣤⣶⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠈⢇⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⡛⢉⣀⣤⣶⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⠿⠟⠛⠛⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⣿⣦⣄⠀⠀⠀⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣯⣻⣦⡀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⢀⣀⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠻⡿⠻⣷⣄⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡋⠀⠒⠦⣤⣚⣿⣘⣄⠉⠈⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⢸⡇ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢀⠀⠘⢻⣆⠈⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠁⠀⠀⠀⠀⠀⠉⠙⠳⢽⣛⠷⢤⣘⠛⠇⠀⠀⠀⠀⠀⠀⢸⡇ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣇⢸⡀⠀⠀⢿⣆⠸⣿⣿⣿⣿⣷⠀⠀⠀⣠⣾⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⣌⣓⠄⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣦⣿⣿⣸⣼⣇⡀⠀⠀⠙⡆⢻⣿⣿⣿⣿⣇⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⢸⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠉⢉⣿⣿⣿⣿⣿⣿⡏⠉⣷⣶⣤⣿⣬⡿⠛⣩⢿⣫⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⢸⡇ ⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣤⣄⡟⠛⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣾⣵⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢸⡇ ⠀⡇⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣆⡀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢸⣟ ⢀⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⣿⣿⣶⣄⡀⠀⠙⢿⣿⣿⡿⣿⣿⣟⡈⠀⠀⠀⠀⠀⣀⣀⡤⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣗ ⢸⡇⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⠇⠀⠀⠀⠈⠙⠉⠀⠀⠀⠈⠙⠷⣌⡀⠸⣏⣛⢲⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠘⡃⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⡇⠀⠀⠀⠀⠀⢀⡤⠒⣮⣿⣾⢟⡁⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⡀⠀⠀⠀⠙⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗ ⢰⣇⠀⠀⠀⠀⣴⣿⣼⡀⢿⣿⣭⣾⣿⣶⡄⠀⠀⠀⠀⢀⣾⡿⢽⣿⡟⠀⠀⠀⠀⠈⠙⠒⠒⠦⠤⠤⠤⠴⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡗ ⠀⣿⣤⣤⣴⣿⣷⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣾⣾⣯⣿⣿⣿⣤⣤⣤⣶⣤⣤⣤⣤⣦⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣼⣶⢗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣂⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⣼⣷⠼⣞⣽⢏⣿⣆⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠛⠢⠐⡍⡉⣾⣾⣽⣟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣦⠀⠤⢶⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⡙⢻⣿⣿⣧⣽⣉⣁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡔⡉⣩⢋⡋⠩⠯⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣘⣶⣁⢙⢐⣄⡴⠪⠓⠁⠉⠃ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣿⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⢐⢝⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⢛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⣿⡿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣔⡋⣩⣴⣖⣊⣈⠢⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⡿⣁⢤⣾⢹⣭⢣⢤⣾⢙⠗⢤⡽⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠢⣼⠝⠊⠩⡽⡏⡎⡟⠺⢸⣼⣳⣣⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡸⣿⡰⡄⣦⢿⠿⠿⣿⡇⡙⣒⣽⢻⣼⣫⣯⢼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣵⣬⣿⠟⡜⠙⠘⣤⢱⣿⣷⠃⠹⠑⠃⣿⣋⡧⣆⡻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣹⠿⢟⠕⠁⠀⠰⡀⠁⢡⣿⡏⠝⠐⠘⠀⡐⣼⣿⢫⡴⣯⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣭⣾⣷⠔⠁⠀⠀⠀⠀⢻⢢⢠⣿⣟⠀⠀⠀⣀⣾⣿⡏⣇⠱⣯⠋⢯⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⢯⣾⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⢸⢫⢸⠞⣡⠥⣤⠮⣷⡯⣿⢳⢯⡄⠙⢄⡀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⢿⣻⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢙⡻⠍⢟⡲⢾⣽⠶⢮⣬⠜⣶⡀⠀⠙⢮⡈⢻⣿⣦⡀⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⣠⣾⣿⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⡶⣻⢷⣶⣤⠔⡂⠬⣬⣗⣞⠃⠀⠀⠀⠉⠢⣬⢿⣿⣗⢉⡟⠉⠁⠀⠀⠀ ⣸⣿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢸⡞⡜⣏⢻⠎⡼⢎⡿⢳⣼⡄⠀⠀⠀⠀⠀⠀⠉⢾⣿⣿⣟⠷⣦⠀⠀⠀ ⠛⠋⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢰⠀⡒⣱⣇⢆⡀⡮⢭⠥⣚⢞⡼⢟⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣻⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢖⢔⡃⠰⢁⠋⢈⠗⠍⢽⣮⣶⣛⡀⢊⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⠈⠻⡂⠄⡀⠘⣦⣤⣶⣵⣿⠭⡠⡲⠊⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡣⠋⡍⠳⣎⠷⠀⠒⣠⣜⣫⣏⠷⣲⣫⠔⣝⠄⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢇⠄⣴⠬⠔⠳⢒⣣⠏⠀⠀⠉⢶⢢⢗⡙⣦⣃⣶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢣⣾⣙⣦⠤⠤⢾⠎⠀⠀⠀⠀⠘⠿⢾⡉⠀⠈⢵⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⡗⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢟⣧⣀⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣴⡶⢿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⣨⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡥⠀⡨⡆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⣭⡀⢡⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠰⠒⠛⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢠⠉⣷⡯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡋⠐⠱⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠡⡼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡊⠵⠐⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣬⣲⣏⣱⣄⣀⡀⠄⠀ ⠀⠀⠀⠀⠐⠿⠶⣵⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣥⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⠋⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠙⢿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⣠⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣦⡀⠀⠀⠙⣿⣿⣿⣄⠀⠀ ⠀⢀⣿⣿⣿⠏⠀⠀⢠⣾⣿⣿⡿⠋⠛⢿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠟⠋⠻⣿⣿⣿⣆⠀⠀⠈⣿⣿⣿⡆⠀ ⠀⣼⣿⣿⡏⠀⠀⢠⣿⣿⣿⠋⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠈⢿⣿⣿⣇⠀⠀⠘⣿⣿⣿⡀ ⢠⣿⣿⡿⠀⠀⠀⣿⣿⣿⠇⠀⠀⢠⣿⣿⣿⠿⠋⠁⠀⠀⠙⠻⣿⣿⡿⠃⠀⠀⠈⣿⣿⣿⡆⠀⠀⢸⣿⣿⣧ ⣼⣿⣿⡇⠀⠀⢸⣿⣿⡿⠀⠀⢠⣿⣿⣿⠃⠀⢀⣤⣤⣤⣤⠀⠈⠋⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠈⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⡏⠀⠀⠈⣿⡿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿ ⢿⣿⣿⡇⠀⠀⢸⣿⣿⣇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣯⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⣿⣿⣿ ⠸⣿⣿⣧⠀⠀⠈⣿⣿⣿⡄⠀⠀⠻⣿⣿⣷⣄⢀⣿⡿⠿⠏⢀⣴⣷⣄⡀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢸⣿⣿⣿ ⠀⢿⣿⣿⡆⠀⠀⢹⣿⣿⣷⣀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠟⠁⠀⠀⣼⣿⣿⡿⠀⠀⢀⣾⣿⣿⠃ ⠀⠸⣿⣿⣿⡄⠀⠀⠹⣿⡿⠋⠀⠀⠀⠀⠉⠛⢻⣿⣿⠿⠿⠛⠋⠁⠀⠀⠀⠈⠻⣿⡟⠁⠀⠀⣼⣿⣿⡟⠀ ⠀⠀⠹⣿⣿⣿⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣼⣿⣿⡟⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡛⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⠏⢀⣼⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣀⠙⢿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⠛⠛⢻⣿⣿⡟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⠿⠛⠉⢿⣿⣿⡄⠀⠀⢸⣿⣿⣇⠀⠀⠀⣾⣿⣿⠋⠙⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣧⡀⢀⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⠋⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀ ⠀⣰⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣷⣄⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣠⣾⣿⣿⣿⣧⡀⠀⠀⢻⣿⣿⣧⠀⠀ ⢠⣿⣿⣿⠁⠀⠀⣼⣿⣿⠟⠻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠛⣿⣿⣷⡄⠀⠀⢻⣿⣿⡇⠀ ⣼⣿⣿⠇⠀⠀⣸⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣟⠉⠉⣹⣿⣿⣿⡿⠋⠀⠀⠘⣿⣿⣷⠀⠀⠈⣿⣿⣿⠀ ⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⠿⣿⣿⣷⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⢻⣿⣿⡆ ⣿⣿⣿⠀⠀⠀⣿⣿⣇⠀⠀⢸⣿⣿⣏⠀⠘⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⡇ ⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⡄⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⣼⣿⣿⠃ ⢻⣿⣿⡇⠀⠀⢹⣿⣿⣇⠀⠀⠘⢿⣿⣿⣶⣤⣀⣀⣠⣴⣷⣄⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⢀⣿⣿⣿⠀ ⠘⣿⣿⣿⡄⠀⠀⢻⣿⣿⣧⡀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣰⣿⣿⡿⠁⠀⠀⣾⣿⣿⠇⠀ ⠀⠘⣿⣿⣷⡀⠀⠀⠹⣿⡿⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠘⠻⣿⠟⠁⠀⠀⣼⣿⣿⡟⠀⠀ ⠀⠀⠘⣿⣿⣿⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣾⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣤⣤⣤⣶⣶⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡌⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠂⢿⡈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⣿⢿⣆⠀⠀⠀⢸⡇⣀⣹⣷⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⣷⡀⣠⣼⣿⣿⣿⣿⠟⢻⣿⣿⣿⣻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⡿⠋⢾⣿⣿⣿⠟⠀⠀⢡⡼⣿⢿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⣸⡿⠅⠀⠰⢿⣿⣿⣟⣡⡀⢸⣶⣿⣇⠹⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢦⣄⠀⣿⡏⠉⠁⠀⠀⣠⣿⠻⣿⣿⣷⡼⠟⠋⠁⡴⠛⠺⣿⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣧⣴⣀⢀⣤⣼⡿⠄⣙⣋⣁⠀⠀⠀⠰⣃⣠⠖⢹⡟⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠿⠖⢿⣿⡇⠀⡴⠋⠁⠀⢈⣱⡄⠀⠀⠻⠿⠓⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⣿⣷⢸⡥⣴⣶⣿⣁⡴⠟⠀⢀⣀⠀⠀⣼⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⠀⠀⣤⠀⠀⠀⢻⣶⣶⣶⣾⣿⣟⠓⠛⠋⠉⠁⠀⠀⠰⠋⠉⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠉⠀⠀⠀⠘⣆⠀⠀⠀⠸⣿⣦⠀⠀⠀⠀⣀⣀⣤⠴⢚⣻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⣾⣦⣘⣦⣤⣤⣤⣽⣿⣷⣶⡿⠛⠇⠀⠷⠃⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣀⣨⣿⣿⠟⢿⣋⡉⠉⢃⠀⠀⠀⠀⢀⠀⢸⡆⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠦⣤⣿⣧⡀⢸⠀⠀⠐⣂⠺⡀⢸⠛⣧⡄⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⢧⠀⡄⡇⠀⠀⠀⡇⢸⠞⣋⢍⠉⠛⠷⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠢⡀⠀⠀⢄⠀⠀⠀⠀⢀⣠⠬⢧⡀⠳⣷⣃⣀⣀⠀⢣⢸⢸⣁⠀⠙⠒⠲⡌⢻⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣘⢦⣀⠀⠁⠀⣠⡔⠉⠀⠀⢀⡼⠋⠀⠀⠀⠈⠑⢼⣿⣀⠈⢉⣓⣦⠤⠗⢨⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠈⠳⣄⠉⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠟⠁⠀⠈⢣⠀⢈⣟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠁⠀⠀⢀⡆⠈⠑⢆⡀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⡀⠀⠀⠘⡄⠀⠀⠈⠉⠉⠓⢤⠀ ⠀⠀⠀⢠⠇⠀⠀⠀⣞⠀⠀⠀⠀⠙⢦⡄⠀⠂⠐⡀⠀⠀⠀⡤⠊⠁⠀⠀⠀⢇⠀⠀⠀⢻⠒⠖⠈⠉⠲⣤⡞⠇ ⠀⠀⠀⡼⠀⠀⢠⣸⣿⣦⡀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⣠⣾⡄⠀⠀⠘⡇⢀⣇⣅⣀⡾⠂⠀ ⠀⠀⣰⠃⠀⠀⢴⡟⡟⠋⣽⡿⡄⠀⠀⠀⠛⠦⡄⠀⠀⠀⠀⠀⢠⣤⡮⢿⣿⣿⣷⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⣴⠋⠀⠀⠀⠀⣿⠀⠸⡔⣌⡼⣟⢦⡀⠀⠀⠀⢱⡀⠀⠀⠀⠀⣯⠿⡃⠀⣹⡿⠛⡆⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀ ⠈⠉⠓⠒⠒⠶⠃⠀⠀⠓⠾⠷⠋⠀⠉⠙⠓⠛⠋⠉⠓⠒⠒⠚⣈⣗⣡⠞⠋⠀⠀⠇⣀⣂⣀⣠⡬⠇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣶⡛⠉⣷⡶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣞⣿⡿⢟⣇⣽⣷⣮⣛⣙⡛⠾⢿⣗⣦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣯⣿⠏⣡⠞⠋⠉⢸⣿⣿⣿⠈⠉⠓⢮⡉⣿⡿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠏⣩⣴⣿⠏⣼⠷⠖⠚⠓⢾⣿⣿⣿⠒⠒⠒⠦⣿⡌⢿⣦⣮⡉⠿⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡟⣠⡾⠷⣿⠿⠠⢇⡀⠀⣀⣀⡾⣿⢯⡿⣄⣀⡀⠀⣨⠧⠿⣯⠷⢿⣦⠙⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢥⠏⠀⢠⡏⢺⣿⠄⣷⣏⠀⣹⣧⡳⠾⣧⣿⠁⢹⣾⡃⣿⣿⠈⡇⠀⠘⣇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣫⣿⡘⣶⠋⠙⣷⠖⣴⣾⠛⣉⣶⣦⣭⣾⣿⣌⣁⣲⣞⡛⢫⣶⠰⠾⠏⠉⢷⣯⣼⣏⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣞⣶⡃⠿⠃⠾⣀⣤⠶⣿⣟⣉⣹⣏⢩⣾⣿⣮⢉⣿⡉⣛⣻⡶⢦⣄⡲⠒⠻⢋⣷⣟⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣯⣿⡆⠾⣥⣞⣩⡭⠿⠤⠿⠿⠿⠬⢽⣌⣛⣾⠽⠂⣶⣉⣿⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡶⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⢀⣀⣠⠤⠴⠒⠒⠒⠒⠒⠒⠲⠤⢤⣄⣀⠀⠀⠀⠙⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⣠⡴⣾⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢀⡴⠛⠁⠀⠀⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠏⠀⠀⢀⡴⠉⠀⢀⡴⠚⠙⢦⡀⠙⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠦⣀⠀⠀⠑⣄⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⣰⠋⠀⢀⡴⠋⠀⠀⠀⠀⠙⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠈⠳⣄⠀⠈⢳⡀⠀⠀⢳⡀⠀⠀ ⠀⠀⡼⠁⠀⢀⡼⠁⠀⣰⠋⠀⠀⣠⠖⢦⡀⠀⠀⠙⠊⠉⠉⠉⠉⠉⠉⠙⠋⠀⠀⢀⡴⠛⢦⠀⠀⠈⢦⡀⠀⠹⡄⠀⠀⢹⡀⠀ ⠀⣸⠃⠀⢀⡾⣧⡀⡴⠃⠀⠀⡴⠃⠀⣠⠟⠀⠀⠀⠀⠀⣠⡤⢤⡤⠀⠀⠀⠀⠐⠻⡤⠀⠈⢳⡄⠀⠈⢳⡀⠀⠹⡄⠀⠀⢣⠀ ⢠⡏⠀⠀⡼⠁⠀⢹⠃⠀⢀⡞⠁⠀⡴⠁⠀⠀⣠⢦⡀⠀⠀⠙⠋⠀⠀⢀⡴⢦⡴⠊⠀⠀⠀⠀⠹⡆⠀⠀⢧⠀⠀⢹⡀⠀⠈⡇ ⢸⠀⠀⢰⠇⠀⠀⡏⠀⠀⣼⡀⠀⡼⠀⠀⢀⡞⠁⠀⠙⢦⡀⠀⠀⢀⡴⠋⠻⣦⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⡇⠀⠀⡇⠀⠀⢱ ⡟⠀⠀⢸⠀⠀⢸⠁⠀⢰⠏⠻⣶⠇⠀⠀⡞⠀⠀⠀⠀⠀⠙⢦⡴⠋⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⣇⠀⠀⢷⠀⠀⢹⠀⠀⢸ ⡇⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⢸⠃⠀⠀⠀⢸⠋⠉⠉⠉⠉⢹⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢹⠀⠀⢸⠀⠀⢸⠀⠀⢸ ⡇⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⢸⡀⠀⠸⣧⡀⠀⠀⢸⠀⠀⠀⣠⡤⣼⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⣼⠀⠀⣸⠀⠀⢸⠀⠀⢸ ⢷⠀⠀⢸⡀⠀⠸⡆⠀⠈⣇⠀⠈⣧⠀⠀⢹⡻⣦⡀⢸⠀⠀⠀⠛⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡇⠀⠀⡏⠀⠀⡾⠀⠀⢸ ⠸⡄⠀⠈⣇⠀⠀⢳⠀⠀⠹⡄⠀⠘⣦⠀⠀⠹⢮⡻⣾⡆⠀⠀⣀⣀⡧⠀⢀⣠⣀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣸⠁⠀⢠⠇⠀⠀⡎ ⠀⢷⠀⠀⠸⡆⠀⠈⣧⠀⠀⠹⣄⠀⠈⢷⣄⠀⠀⠙⠺⠇⠀⠀⣏⣀⡤⠶⠋⠁⠈⠳⡄⠀⠀⢠⠞⠀⠀⢠⠿⣦⣀⡞⠀⠀⢰⠁ ⠀⠈⣇⠀⠀⠹⡄⠀⠈⢦⠀⠀⠈⢦⡀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⢀⡴⠋⠀⠀⣠⠏⠀⢈⡿⠀⠀⢠⠏⠀ ⠀⠀⠘⣆⠀⠀⠹⣆⠀⠀⠳⣄⠀⠀⠙⣆⠀⠀⠀⠈⢹⠆⠀⠐⡶⠶⣶⠚⠉⠁⠀⠀⢰⠋⠀⠀⢀⡴⠃⠀⢠⠟⠀⠀⢠⡏⠀⠀ ⠀⠀⠀⠘⣧⠀⠀⠈⢧⡀⠀⠈⠳⣄⡀⡟⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠈⠳⣄⠀⠀⠀⢸⠀⢀⡴⠋⠀⢀⡴⠃⠀⠀⣠⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢦⣀⠀⠀⠙⠃⠀⠀⠀⠀⢸⡀⠀⢠⡇⠀⠀⠀⠈⠳⣤⡀⠘⠚⠁⠀⢀⡴⠋⠀⠀⢀⡴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⣄⣀⡤⠞⠉⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠈⠙⠒⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠖⠚⠁⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⢉⠁⠀⣀⠀⠀⣀⡤⢖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⠤⢤⣀⣉⣹⠁⢉⡇⢹⡏⠙⠛⣯⣫⣳⣱⢳⢄⢛⡛⠙⢁⠀⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠻⣿⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⢛⣿⣥⣶⣶⣿⣶⣶⣽⣿⡺⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⣿⣿⣧⢿⣿⣿⣺⣿⣿⠧⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠙⣾⣿⣻⣯⣿⣭⣯⣿⣛⡿⣾⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣿⡿⠟⠛⠛⠛⠛⠛⠿⢿⣧⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⡿⢋⣥⣄⠀⠀⠀⠀⠀⠀⠀⣠⣌⠻⣷⣆⠀⠀⠀ ⠀⢠⣿⠏⣴⣿⣿⣿⣶⣴⣶⣶⣶⣤⣾⠋⠻⣷⣌⢻⣷⡀⠀ ⢀⣿⠇⣾⣿⣿⣿⣿⣿⣿⣦⣤⣾⠋⠙⠿⠆⠘⣿⣆⢻⣧⠀ ⢸⣿⢸⣿⠈⢻⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠸⣿⠈⣿⡆ ⢸⣿⢸⣿⠀⢸⣿⠻⣿⣿⣿⣿⣯⣿⣦⡀⠀⠀⠀⣿⠀⣿⡇ ⠸⣿⡘⣿⡄⠀⢻⣧⡈⠻⣿⣿⣿⣿⣿⣿⣦⡀⣼⡿⢸⣿⠀ ⠀⢻⣷⡘⣿⠆⠀⠙⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⠇⠀ ⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠿⠀⠈⠻⣿⣿⠿⢋⣴⡿⠃⠀⠀ ⠀⠀⠀⠈⠻⢿⣦⣄⣀⠀⠀⠀⠀⢀⣈⣥⣶⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣖⣲⣿⣿⣿⣏⣿⣓⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣏⣿⡾⠛⠉⠉⢻⣼⠉⠉⠛⠳⣾⣍⣧⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣭⣿⡾⣷⡿⠋⢀⣀⣀⣀⣻⣼⣀⣀⣀⣀⡈⠻⣷⡿⣶⣯⣹⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣷⠿⠋⣠⠿⣿⣷⣾⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣷⣿⣿⢧⡈⠻⣷⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣶⣿⣿⡿⠛⢿⡿⣿⣿⢿⣷⣏⣉⣷⣽⣿⣻⣿⣿⠟⠻⣿⣿⣷⣮⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣼⣿⡿⣽⠷⣴⣿⣷⣿⠿⢿⣿⡿⠻⣿⣿⠿⣿⣿⣿⣧⡶⣿⣿⣻⣿⣽⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⢻⣿⣻⠿⢿⣷⣧⣬⣿⣷⡶⣿⣿⣿⣿⡿⣿⡷⠾⣿⣯⣤⣷⡿⠿⢿⣩⣿⡉⣻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣾⣟⣭⡿⠟⢛⣿⣏⣹⣿⣭⣈⣽⣿⣉⣿⣟⠛⠾⣯⣝⣿⢾⠏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⡿⣟⣻⣯⣭⣽⣿⣶⣿⣶⣶⣶⣿⣯⣭⣟⣛⡿⢥⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⢀⣠⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣀⠉⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⠏⢀⣴⣿⣿⡿⢿⣿⣿⣦⡀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣠⣾⣿⡿⢿⣿⣿⣷⣄⠈⢿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⡿⠁⣠⣾⣿⣿⣻⣿⣷⣝⢿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠛⠁⠀⠙⢿⣿⣿⣦⠀⠻⣿⣿⣿⡄⠀⠀ ⠀⠀⣸⣿⣿⡟⠀⣰⣿⣿⣿⣽⣿⣿⡿⣫⣾⣿⣿⣿⣿⣏⠉⠉⠉⠉⣩⣿⣿⣿⣿⣿⣷⣦⡀⠀⠈⠻⣿⣿⣷⡀⠹⣿⣿⣿⡄⠀ ⠀⢸⣿⣿⡿⠀⣸⣿⣿⣟⣾⣿⣿⣯⣿⣿⣿⢿⣿⡿⣿⣿⣷⣄⣠⣾⣿⣿⠟⠁⠈⠻⣿⣿⣿⠀⠀⠀⠹⣿⣿⣷⡀⠹⣿⣿⣷⠀ ⠀⣿⣿⣿⠇⢀⣿⣿⡟⢿⣿⣿⢫⣿⣿⣟⣵⣿⣿⣿⣯⡻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⢿⣿⣿⡇ ⢰⣿⣿⣿⠀⣾⣿⣿⠃⠀⠙⠟⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣮⡻⢟⣵⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⢸⣿⣿⣿ ⢸⣿⣿⡏⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⣿⣿⣿ ⢸⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⢿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣯⣭⣽⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿ ⢸⣿⣿⣧⠀⣿⣿⣿⠀⠀⠀⠈⣿⣿⣷⠀⠙⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⢠⣿⣿⣿ ⠈⣿⣿⣿⡀⢹⣿⣿⡆⠀⠀⠀⠹⣿⣿⣇⠀⠀⠙⢿⣿⣿⣿⣄⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣿⣿⣿⠀⢸⣿⣿⡟ ⠀⢻⣿⣿⣇⠀⢿⣿⣿⡄⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠙⣿⣿⡟⣛⣛⣛⣻⣿⣿⣿⢟⣭⡻⣿⣿⣦⡀⢀⣾⣿⣿⠇⢀⣿⣿⣿⠃ ⠀⠘⣿⣿⣿⡄⠘⣿⣿⣿⣄⠀⠀⠀⠘⢿⣿⣿⣶⣤⡀⣿⣿⡀⣿⣿⣿⡿⢟⣫⣷⣿⣿⡿⣹⣿⣿⢿⣾⣿⣿⠟⠀⣾⣿⣿⡏⠀ ⠀⠀⠘⣿⣿⣿⡄⠈⢿⣿⡿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⡿⢟⣽⣾⣿⣿⣧⣿⣿⣿⠏⠀⣼⣿⣿⡟⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣆⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⡟⠻⠛⠻⣯⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⠞⠋⢠⣾⣿⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣴⣿⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠛⠁⣀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣴⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣾⣿⢿⣷⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⠟⣿⣿⢋⣁⣀⣀⣀⣙⣿⣿⠻⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⢸⣿⣧⣶⣿⣿⠿⠿⣿⣿⠿⠿⢿⣿⣷⣬⣿⣷⠀⠀⠀ ⠀⠀⠀⢸⣿⣟⠉⢻⣿⣄⣤⣿⣿⣤⣄⣿⡿⠉⢻⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣶⣿⠿⠟⠛⠛⠛⠛⠛⠿⣿⣶⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀ ⠀⢀⣾⡿⠃⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠈⢻⣷⡄⠀ ⠀⣾⣿⠁⢀⣾⡿⠻⣿⣶⣶⣿⣿⣷⣶⣿⡟⢻⣿⡄⠀⢿⣿⡀ ⢸⣿⡇⠀⣾⣿⠁⢀⣿⡿⣿⣦⣴⣿⠟⠉⠀⠀⢿⣿⠀⠸⣿⡇ ⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇⠈⠻⡿⠁⠀⠀⠀⠀⣸⣿⠀⢀⣿⡇ ⠘⣿⣇⠀⢹⣿⣆⠀⠻⣿⣦⣤⣠⣴⣦⡀⠀⢠⣿⡟⠀⢸⣿⠇ ⠀⠹⣿⣆⠀⠻⣿⠆⠀⠈⠙⠛⠛⠛⠁⠀⠰⣿⠟⠀⢠⣿⡟⠀ ⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣴⣿⠟⠀⠀ ⠀⠀⠀⠈⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣷⣶⣶⣾⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠋⣿⣿⣿⣿⠟⠁⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠙⣿⣿⣿⣿⡍⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠁⠀⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⡀⠈⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠁⠀⢻⣿⣿⣿⡆⠀⠀⣀⣠⣿⣿⣿⣇⣀⡀⠀⢀⣿⣿⣿⣿⠀⠈⠙⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠙⢿⣿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⡿⠃⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⠀⠀⠀⠈⢻⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⡿⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⣠⣤⣤⣤⣤⣄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀ ⠀⢠⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⠟⠻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠛⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⣇⠀ ⠀⣼⣿⣿⣿⠇⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⡀⣠⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⡇ ⢠⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⠋⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇ ⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢈⣿⣿⣿⡇ ⠈⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀⠙⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇ ⠀⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠈⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⠇ ⠀⢻⣿⣿⣿⣆⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣶⣤⣴⣶⣿⣿⣿⣦⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⠀⢀⣿⣿⣿⣿⠀ ⠀⠈⢿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⣰⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⠇⠀ ⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠻⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⡿⠁⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣄⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⢀⣼⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⢵⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⢟⡿⣿⣼⢿⣛⢷⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡾⣛⣿⠟⡮⠥⠤⣿⣿⠤⠤⢵⡽⣯⣟⠷⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡽⠛⠟⣵⢢⡄⢴⢻⣿⣦⠠⡰⣯⡿⡛⢳⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣯⣯⣷⢈⠗⢱⣎⣱⡮⢽⣯⢥⣶⣛⣮⠒⣋⣲⣽⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠒⣞⣯⢹⣽⡲⠧⠽⠿⠼⠇⣢⡿⢩⣲⠖⠊⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠜⠋⠁⢀⡀⠠⠤⠤⠄⢀⣀⠈⠉⠋⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠉⢀⠠⠒⢏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⣀⠈⠢⣄⠀⠀⠀⠀ ⠀⠀⠀⡔⠁⢀⠔⠁⡠⠒⢦⡑⢦⠀⠀⠀⠀⠀⠀⡠⠒⢄⡀⠑⢄⠈⠢⡀⠀⠀ ⠀⠀⡞⠀⡰⠁⡠⠊⢀⠤⡀⠙⠦⠓⠒⠒⠂⠴⠊⢀⠤⡀⠙⢆⠈⢢⠀⠑⡀⠀ ⠀⡜⠀⡰⠣⡔⠁⡠⠋⡠⠋⠀⡀⠀⠶⠖⠀⢀⣀⡹⠂⠈⢆⠀⢣⠀⢣⠀⢱⠀ ⢀⠁⢀⠃⢠⠁⢠⣁⡰⠁⢠⠊⠈⠢⡀⢀⠔⠛⢮⡀⠀⠀⠀⠆⠀⠇⠀⡆⠀⡆ ⢸⠀⢸⠀⠈⠀⡈⠈⡇⠀⡆⠀⠀⡖⠚⠓⢲⠀⠀⠙⢦⡀⠀⢸⠀⢸⠀⡇⠀⡇ ⢸⠀⠸⠀⢰⠀⢠⠀⢇⠀⢳⣄⠀⡇⠀⠶⡾⠀⠀⠀⠀⠙⢦⡸⠀⡘⠀⡇⠀⡇ ⠀⡆⠀⡇⠈⠆⠈⢆⠈⢆⠈⠪⣳⡇⠀⡤⠇⣀⠤⡀⠀⠀⣠⠃⢠⡃⢠⠁⢠⠁ ⠀⠘⡀⠘⡄⠘⢄⠈⠢⡀⠑⠄⡀⠁⠀⠉⠉⢀⡠⠜⢀⡔⠁⢀⠎⢙⠇⠀⡌⠀ ⠀⠀⠱⡄⠈⢆⠈⠣⣀⢸⠀⠀⠀⡇⠀⡏⠻⣅⠀⠀⡇⢀⠔⠁⡠⠃⢀⠜⠀⠀ ⠀⠀⠀⠈⢆⠀⠑⠤⡀⠉⠀⠀⠀⠧⠤⠇⠀⠈⠓⢄⠃⢁⠠⠊⠀⡠⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⣀⠈⠑⠂⠤⢀⣀⣀⣀⣀⡀⠤⠌⠋⠁⢀⠤⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⢀⣀⡀⡠⢒⢲⠖⠦⣖⣏⢦⠠⡄⠄⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣟⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⠏⣀⣀⣀⠀⠀⠀⢀⡀⠀⠸⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡎⣴⠶⠿⠇⠀⠠⠿⠯⢭⣱⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢹⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢹⣷⡀⠀⠀⠀⠋⠉⠙⠃⠀⠀⠀⣼⡟⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠟⣿⠁⠀⠀⠠⢒⡈⢑⡢⠀⠀⠀⣿⡶⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⡀⠀⠀⠉⠉⠁⠀⢀⣤⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣤⣠⣤⣤⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⢿⣿⡿⠿⠿⠿⠿⠋⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢧⣀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⠀⠉⠳⠋⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣔⠜⠀⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠐⢬⡂⢄⠀⠀ ⢠⣔⠾⠚⠁⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠈⠑⠬⣐ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⢸⣿⠀⣿⣿⣷⠰⠶⣾⠏⣴⡦⢿⡇⠶⢶⣿⢈⠻⡇⢸⠀⣶⣄⢹⣿ ⢸⣿⡀⠛⠛⣷⠘⣛⢻⣦⣙⣋⣸⡇⢛⡛⣿⢸⣷⣌⣸⡀⢛⣃⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⡿⡀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⡉⠚⠙⣉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠙⢄⣃⣰⣖⣉⠜⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⡷⠶⠒⠺⢅⣀⡠⠾⣶⣮⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡴⠞⠉⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⣀⠀⠀⠀⠀ ⠀⢠⣤⡼⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣷⡀⠀⠀ ⡼⠋⠁⠀⠀⣰⠃⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀ ⠀⠀⠀⠀⢤⡇⢀⡸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠹⢤ ⠀⠀⠀⠀⠀⠙⣆⠸⠇⠀⠀⠦⠤⣄⣤⠀⠀⠀⠀⠻⠿⠃⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣦⣤⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠐⢍⣀⣈⡊⣧⠀⠀⠀⠀⠀ ⢦⡀⠀⠀⠀⠀⣸⡟⢹⡏⠀⠸⠛⠓⠒⠶⢶⡴⠚⠛⠛⠛⠶⣶⠟⣧⠀⠀⠀⠀ ⠙⠻⠷⠶⠖⠚⠃⠀⠘⢿⡦⠄⠀⠀⠀⢰⠏⠀⠀⠀⢀⣀⠀⠈⢷⠈⢷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢸⠀⠀⠀⣴⠋⠉⣷⠀⢸⡷⠈⠉⠓⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠸⣆⡀⠀⢧⡀⠀⠀⣀⣾⡃⠀⠀⠀⠀ ANNYEONG MARSEL ˖⁺‧₊˚ ♡ ˚₊‧⁺˖ Hari iki kamu kan utbk, entah aku ngesend iki di hari h-jam atau menit idk 😇 soale aku membuat text iki 1 Mei mwehehehhehe.. Perbanyak doa yaaa, inget Tuhan, oiyo jangan lali fokuss (ati" & teliti baca soale yaa) 🥰 nek kesusahan ngerjain minta petunjuk Tuhan 😇 wtshi selalu doakan anata dari jauh yaa 🫰🏻🫰🏻 semoga bisa ngerjain soalnya dan nanti bisa lolos ugm hehehe... aminn. GANBATTE MARSEL ₊˚⊹♡

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡄⣀⠀⠀⠈⣿⣟⢸⡀⠀⠀⠀⠀⠀⣼⣟⢷⡇⠀⠀⠀⢀⣤⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣲⣽⣽⢳⡤⡒⡤⡸⣿⡞⢡⠀⠀⠀⠀⢀⣿⣞⢧⠁⠀⠀⣠⣶⡿⡷⣿⣧⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠫⠟⠛⠛⠿⢿⣬⣤⣛⡿⡼⢡⠀⠀⠀⢸⣾⣈⠎⠀⣠⡾⣿⣟⠻⠟⠛⠻⣻⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣾⢣⢏⢹⣆⠀⠀⣾⣿⣉⢇⣾⡿⣇⡟⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣟⣾⡞⠄⠀⡿⣷⣩⣼⣯⡇⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⢋⣾⣯⢏⡕⢠⣿⣷⡽⡯⢻⣪⠇⠖⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡻⣮⡏⣸⡏⣷⢯⣤⣽⣻⠿⠏⠠⢅⣄⣄⣦⡯⡪⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢿⣺⢭⢷⠁⣿⣧⣿⣿⣿⡿⡑⢄⣒⣢⣿⣛⣿⣿⣿⣿⣷⣿⣿⣆⣀⣤⣤⣴⣾⣿⣿⡲⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⢱⢍⣤⣾⣞⣾⣿⠕⠔⡌⣦⣿⣿⣛⣛⣛⣿⣿⣻⣾⣟⣟⢯⣻⣎⠟⠛⠘⠑⠋⣾⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣷⢟⣭⣏⡼⣿⣟⣯⡿⣝⠙⢼⣸⣿⣿⣿⡿⡿⠽⠿⠏⠛⠃⠁⠁⡀⡀⠤⣠⣤⣴⣶⣶⣿⣷⣿⠷⠀ ⠀⠀⠀⢀⣴⣿⡿⣽⣿⣽⣿⣻⣟⡯⣤⢑⣫⡭⠌⡿⣿⣿⣏⣿⣮⠀⠀⠀⢀⣄⡤⣶⣿⣿⡿⣿⠿⣟⡯⡿⠿⣾⣟⢿⢳ ⠀⠀⣰⡿⣿⣿⢿⣯⣷⣯⣿⣏⣿⣽⠶⠮⠒⠂⣈⣿⣿⢿⣿⣷⠭⠀⠀⠠⣶⢷⣿⠋⠹⢩⡽⣾⡽⡾⣽⣾⣿⣯⡝⠚⠛ ⠀⢠⣿⣿⣿⣽⣿⣿⡟⣟⣗⣮⣹⣞⣯⣿⡀⢠⣼⣷⣻⣟⣿⣭⡇⠀⠀⢸⣿⡏⠀⠀⠀⠀⠈⢳⣿⣿⡟⠉⢻⣿⣿⣿⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣧⣯⣿⣿⣿⣿⣟⣿⡇⢀⣴⣿⣿⠃⠀⠀⢠⣤⣤⣈⣿⣿⣷⠀⠀⠀⠉⠉⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠿⡿⢻⢿⣿⣏⣶⣶⣿⣿⠻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⢿⣿⡿⣟⣻⣹⡿⣿⣾⡿⠉⠉⠙⢿⡿⣿⣻⣿⡿⢋⠀⠙⢸⣿⣿⣻⣿⡿⣿⠟⠳⠀⠸⣿⡿⡟⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣽⣿⢟⣿⣿⣿⣿⡿⠻⢒⣓⠀⠀⠙⠻⣿⣟⢲⡡⠜⠀⢸⣾⣿⣿⣷⠾⣟⠆⡄⠀⢀⣹⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣽⣱⣿⡊⣘⣦⣂⣠⠀⠀⢀⡼⠉⠳⡾⠤⣀⠬⢾⣿⣿⣟⡸⣟⢓⠀⠀⢷⣾⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣽⣿⣿⢿⣿⡾⡁⣻⢋⢾⣧⢡⡇⠀⠈⠀⢇⠀⠀⠘⠄⡀⠈⠢⢹⣿⣿⣵⣺⣭⣾⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⢿⣭⡃⣿⡇⢘⢴⣾⣻⡿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠙⠿⣿⣿⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣯⣿⣶⣻⣷⢩⣏⢓⣥⢮⠄⠀⠀⡀⠀⠀⠒⠀⠁⠀⢰⣿⣿⡀⠀⠈⠹⢏⡿⡷⣿⣻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⡿⣟⣾⣽⣿⣨⠥⠈⠀⢠⠃⠀⠀⠈⣳⣀⠀⣀⣤⣴⣿⡧⠋⢿⣄⠀⠀⣳⣻⣻⢻⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣯⣿⡿⣾⣞⣷⣞⣮⣁⡄⠀⠀⠰⠀⠉⢁⣨⠟⠉⠉⣼⣷⢁⠀⠀⢳⡌⠁⠙⡱⣡⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣽⣯⡟⠡⢒⠲⠒⠋⣰⠋⠀⠀⠀⢰⣿⡇⠀⢲⢂⠀⣿⢂⠠⢭⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡿⣧⢀⠀⠇⢀⠔⠁⠀⠀⠀⣠⣿⣻⡀⢠⠼⣃⠀⠙⡄⢰⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢿⣽⣟⢧⢤⣄⣄⠢⠀⣠⣴⡽⠋⠈⣇⠀⠃⠒⡴⠀⢀⣹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣾⣷⣿⡿⡄⠜⠠⢵⣯⠁⠀⠀⡏⡆⠐⠓⣳⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⣾⣳⢗⣆⣵⣿⠃⠀⠂⠄⠁⠁⢞⣹⣿⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⡿⣿⣿⠷⡃⠀⣒⢀⢔⣴⣾⣿⡿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣟⢿⣵⣢⣨⢼⣔⣻⣻⣿⣞⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣯⣯⣟⣾⣽⢭⡷⣟⣫⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣯⣟⡿⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡱⢌⢢⡑⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⠰⡈⢆⠱⣊⠽⣿⣷⣄⣴⣾⣿⢟⡫⢒⠥⢒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢢ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣎⠖⡌⠱⢠⠡⢃⠔⡡⢃⠔⡡⢃⠔⡡⢃⠔⡡⢃⠔⡡⢃⠌⡱⢈⠆⡓⡌⢮⢹⣿⣿⣿⢟⡱⢊⠴⡉⢆⠣⡘⠄⢆⡉⢆⠰⣁⠣⡐⢡⠃⡔⢡⠃⡔⢡⠃⡔⢡⢂ ⣀⣴⣿⣿⣦⣄⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣤⠾⠿⣦⣄⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣯⡜⣡⠣⡜⢢⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⡄⢣⠘⡄⢣⠘⡴⣉⠞⣾⣿⡟⢣⠎⢲⠉⢆⠱⡈⢆⠱⡈⢆⡘⢄⠣⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⢊ ⠟⠟⠀⠀⠉⠛⠿⢷⣾⣶⠿⠿⠛⠉⠀⠀⠙⠻⢿⣶⡷⠾⠛⠋⠁⠀⠈⣿⠟⠳⠶⠶⠶⠶⠛⠉⠀⠀⠀⣹⣿⣿⣿⣔⣣⠜⣢⠘⡤⢃⠜⡠⢃⠜⣠⢃⡜⠬⡱⠱⣌⣣⣓⣬⢡⠳⡰⣥⣿⡿⢏⡜⡡⢎⠡⠚⡌⢢⠑⡌⢢⠑⢢⠘⡄⠣⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⠀⠀⠀⠀⢿⡃⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⠻⢿⣿⣦⡹⣄⠣⢜⢠⠣⣘⡐⠦⣜⣵⣿⡿⠿⠛⠛⠻⢿⣷⣿⣿⡿⡙⢦⡘⢡⠊⡔⢣⠘⡄⢣⠘⠤⡉⢆⠱⣈⠱⡈⢆⠱⡈⢆⠱⡈⢆⠱⡈⢆⠱⣈⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣦⡙⢦⠁⡞⢤⢚⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⢡⡙⢆⢌⠡⢊⠔⡡⢊⠔⡡⢊⠔⡡⢊⠔⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠄⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⢆⡹⣐⢣⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⢧⠘⡌⢢⠉⢆⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⢎⠔⡣⠘⣄⠣⡘⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⣭⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡜⢢⠱⡈⢆⡉⢆⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢬⡑⢮⣾⡇⠱⢂⠱⣈⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡃⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠛⠻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣎⢇⠲⣁⠦⡘⠤⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢢⡑⢭⣢⣽⣿⢋⡜⡡⢍⠒⠤⣉ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠲⡌⢥⢊⣵⣿⡿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣯⣢⡑⢎⠰⣁⠎⡰⢁⠎⡰⢁⠎⡰⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡓⡜⣢⢽⣾⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣌⡓⢤⠚⡄⢣⠘⡄⢣⠘⡄⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡴⢣⣾⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⡱⢌⢣⡘⢄⠣⡘⢄⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣣⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣘⢢⠜⡠⢃⠜⡠⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⢣⠱⢌⠢⡑⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠻⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣮⢘⠆⡱⢈⠜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣦⠀⠀⠀⠉⠻⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣇⢎⡱⢈⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⣀⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⡶⠾⠿⠋⠁⠀⠀⠀⠀⠀⢿⣿⠢⣅⠋⡌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡓⠬⡑⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⣀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠧⡑⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠛⠿⣿⣿⣶⣤⣶⣶⣿⣶⣶⣶⣦⣤⣄⡀⠉⠙⠓⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡉⢖⡉⢆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡭⢏⡽⣙⠻⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠣⡜⢢⠜⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢦⢡⠋⢖⡡⢎⡛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢣⠱⡌⢣⢎⣱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠠⢇⠚⢤⠘⢢⡉⠖⡬⢛⠿⣿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠻⣤⢣⣳⣼⣷⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡓⢬⡉⢆⡉⠆⠬⡑⠦⣉⠶⢨⢍⡛⠻⠿⠿⡿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⠿⠟⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣍⠲⡌⢢⠘⡌⢢⠑⡒⠤⢊⢅⠢⣉⠱⣉⢎⠱⢒⠬⠥⣋⠭⣍⢫⡝⣻⣿⣿⣿⡛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢲⢡⠣⡘⢄⠣⡘⢄⠣⢌⠢⡑⠤⢃⠔⡨⢊⡒⢌⡒⣡⠒⣌⠲⣜⣵⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠈⠛⠿⣿⣶⣤⣄⣀⡀⠀⠀⢿⣿⣧⡎⡱⡡⢎⠔⣡⠊⡔⡊⡔⢡⠎⡐⢎⡑⢆⡩⢒⠼⢤⣻⣼⣿⣿⣿⣿⠿⣟⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⠿⣿⣿⣿⣿⣿⣥⣓⣎⠚⡤⢓⡜⠴⣘⠆⡎⠵⢪⣜⣦⣵⣿⣾⣿⠿⠛⠉⠙⢿⣿⣝⣮⣽⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⢀⣼⣿⠿⠟⠛⠉⠉⠉⠛⠻⢿⣿⣦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣷⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣶⣞⣷⠟⠉⠀⠀⣟⡇⠀⠈⠛⣿⣷⣶⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⣻⣿⣧⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⠛⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⠛⣿⣿⣶⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⡟⢿⣿⣟⣿⣿⣭⣿⣿⣙⣿⡿⢻⣿⣿⣿⣿⡷⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠒⠛⣿⣴⣿⣿⠿⢿⣟⣻⣿⣋⣻⣟⣻⣿⠿⣿⣿⣶⣿⠛⠓⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⣟⣾⣯⣿⣷⣾⣷⣷⣾⣿⣯⣷⣻⡯⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠟⠛⠛⠋⠉⠙⠛⠛⠻⠿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⠟⢉⣤⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⣦⡈⠻⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⡿⠃⣴⣿⣿⣿⣿⣿⣶⣄⣀⣤⣤⣤⣤⣤⣄⣀⣴⣿⠟⠻⣿⣿⣦⡈⢻⣿⣷⡄⠀⠀ ⠀⢀⣾⣿⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢻⣿⣿⣿⣷⣄⠀⠈⢻⣿⣷⡄⠹⣿⣿⡄⠀ ⠀⣾⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⣿⡿⠋⠙⢻⣿⡷⠀⠀⠹⣿⣿⡄⢻⣿⣿⡀ ⢸⣿⣿⠁⣼⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠉⠀⠀⠀⠀⢻⣿⣷⠀⣿⣿⡇ ⣸⣿⡿⢠⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⢸⣿⣿ ⣿⣿⡇⢸⣿⣿⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿ ⢸⣿⣷⠈⣿⣿⡀⠀⠀⢿⣿⣇⠈⠻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣿⣿⠁⣸⣿⡿ ⠘⣿⣿⡄⢻⣿⣧⠀⠀⠈⢿⣿⣆⠀⠈⠻⣿⣿⢾⣿⡿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣼⣿⡟⢀⣿⣿⡇ ⠀⢻⣿⣷⠈⢿⣿⣧⡀⠀⠈⠻⣿⣷⣦⣀⣿⣿⣾⣿⣿⣿⣻⣿⣿⣿⣹⣿⣿⣾⣿⡿⠁⣼⣿⡿⠀ ⠀⠀⢻⣿⣷⡀⢻⡿⠋⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣼⣿⡿⠁⠀ ⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠟⠁⣠⣾⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⢿⣿⡿⠛⠁⣠⣾⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠛⠋⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⢀⣾⣿⡿⠋⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⡀⠀⠈⢻⣿⣷⡄⠀⠀ ⠀⢀⣾⣿⡟⠀⠀⣰⣿⣿⠿⠿⣿⣿⣶⣦⣤⣶⣿⣿⡿⠿⣿⣿⣧⡀⠀⠹⣿⣿⡆⠀ ⠀⣼⣿⡟⠀⠀⣼⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢻⣿⣷⡀⠀⠹⣿⣿⡀ ⢰⣿⣿⠁⠀⢸⣿⣿⠁⠀⣰⣿⣿⠛⠁⠀⠀⠈⠙⢿⠟⠁⠀⠀⢻⣿⣧⠀⠀⢿⣿⣇ ⢸⣿⣿⠀⠀⣾⣿⡇⠀⢠⣿⣿⠇⠀⢸⣿⣿⡷⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿ ⢸⣿⣿⠀⠀⢻⣿⣇⠀⠀⣿⣿⣇⠀⢸⣿⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⡿ ⠘⣿⣿⡄⠀⠸⣿⣿⡄⠀⠘⣿⣿⣦⣼⣿⣛⣃⣴⣿⣷⠄⠀⢀⣾⣿⡏⠀⠀⣿⣿⡇ ⠀⢻⣿⣷⡀⠀⠻⣿⡿⠂⠀⠈⠛⠿⣿⣿⣿⣿⠿⠟⠉⠀⠀⢾⣿⡟⠀⠀⣸⣿⡿⠀ ⠀⠀⢿⣿⣷⡀⠀⠉⠀⠀⠀⠀⠀⠀⠸⠿⠅⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣴⣿⣿⠃⠀ ⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠉⣩⠽⠗⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡮⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⢤⣤⣀⠀ ⣀⣀⣀⣀⣤⣴⣶⠿⠋⠉⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠙⢷ ⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⢀⣴⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠦⡤⠤⣝⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠈⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠹⣷⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢦⣠⣤⣄⠀⢀⣠⠿⣿⣭⣷⣀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⢻⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣤⠞⠋⠁⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣼⠎⠉⠁⠈⠉⠉⠛⠿⣟⠁⠀⠀⠀⠀⣠⣼⡶ ⣤⣤⣴⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣽⣶⠀⠀⠀⠀⠀⠀⠀⠈⠳⡶⢶⣴⠟⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠋⠛⠒⠦⡍⠉⣹⠛⠑⠚⠛⠉⠙⠛⠻⢿⣿⣦⣤⣄⣆⠀⠀⠀⠀⠀⣿⣾⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣼⡏⢛⣻⣿⡿⢷⣾⣷⠀⠀⣯⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣷⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢒⣶⣶⣾⡟⣙⣷⡼⠿⣿⠀⠀⠈⠻⣤⣾⠻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⣤⣶⣤⣼⡏⠀⠀⠀⠀⠀⠀⠺⣷⡏⠘⣿⣿⡿⣷⣤⣿⣧⣀⣀⣴⣏⣀⣀⠙⠦⣄⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢸⡏⠁⠃⢹⣷⡄⠀⠀⠀⠀⠀⣰⠿⠀⣠⣿⡿⠃⠹⢿⡞⢻⡏⢩⠟⠋⠉⢹⣧⠀⠀⠉⠉⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⢸⣧⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⡏⠀⣠⣟⡛⠇⠀⠀⣾⠷⣾⠟⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⠀⠀⠀⢀⡖⠀⠀⠸⣧⠞⠉⠛⠻⡆⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠻⢦⣄⣀⣴⠾⠿⢶⣶⠶⠶⠶⠶⠶⠤⠿⣶⣿⣶⠶⠶⠿⠷⠶⠶⠾⠯⠤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀

⣴⣿⣦ ⢻⣿⣿⠂ ⢀⣴⣿⣿⣀ ⣾⣿⣿⣿⣿⣿⣿⣦ ⣴⣿⢿⣷⠒⠲⣾⣾⣿⣿⡄ ⣴⣿⠟⠁⠀⢿⣿⠁⣿⣿⣿⠻⣿⣄ ⣠⡾⠟⠁⠀⠀⠀⢸⣿⣸⣿⣿⣿⣆⠙⢿⣷⡀⠀ ⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⠻⣿⡭ ⢸⣿⣿⣿⣿⣿ ⠀ ⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀ ⣼⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ‏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠟⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀ ‏⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀⠀⠀ ‏⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀ ‏⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀ ‏⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀ ‏⠀⠀⠠⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡤ siu🤏🤏🏻🤏🏿👃🏽👎🏿🖖🏽

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠈⣶⣦⣤⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣶⣾⠇ ⠀⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀ ⠀⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀ ⠀⠛⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠛⠃ ⠀⠀⠀⠀⠙⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠑⠄⡀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠋⠁⠀⢀⡠⠊⠀⠀ ⠀⠀⠀⠀⠈⠒⢤⣀⠀⠀⠀⠁⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣀⡤⠒⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠶⢶⣿⣿⣿⣿⡷⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⠀⢣⠀⠋⠻⣿⣿⣿⣿⣿⣿⣧⠳⣿⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣟⢀⡴⠊⠁⣀⣤⣶⣄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⠀⢸⢧⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⠿⣛⣯⣽⣷⣶⣿⣿⣿⣿⣿⣿⣿⡏⢩⣧⠴⠾⢿⣿⣿⣿⣷⣄⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠀⣼⢀⢳⣄⠀⠈⣿⣍⠉⠙⠿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⡷⣫⣿⣿⣿⣿⣶⣾⣶⣾⣭⣦⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢟⣿⣿⣿⣦⠹⣎⡘⡏⢦⡀⠘⢦⡉⠳⢤⠘⣿⣿⣿⣦⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣯⣷⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢼⣣⣿⣿⣿⢹⣿⣆⠘⠳⣼⡀⠙⡦⡄⠈⠢⠬⡇⢹⣟⠣⠙⠻⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣭⣶⣾⡿⢟⣻⣵⣿⢛⣿⣿⠀⠙⠻⡟⠛⠛⠛⠛⠛⠿⠿⠛ ⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣾⣿⣿⣷⡀⠹⢳⣀⣧⢨⢲⠤⣤⠃⢸⡿⠀⠀⠀⠈⠉⠈⠛⠛⠛⠛⠿⣿⣭⣭⣽⣷⣾⣿⣿⣿⣵⣿⣿⣿⣧⡀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⠦⣈⠙⠻⣤⣠⠶⠁⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀ ⣽⣾⣿⢿⣾⣿⣿⣿⣿⡿⠋⢨⣿⣿⣿⡇⣿⣏⠳⢤⣉⠉⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠛⠿⣿⣷⣶ ⣿⣿⣏⣿⣿⣿⣿⣿⡿⠁⣤⣾⣇⣿⣷⡻⣿⣿⠀⠀⠀⠉⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣘⠿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⠻ ⣿⣿⢸⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣷⡈⣻⡄⠀⣀⣀⣀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⣠⠴⠊⢹⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⣿⡇⢸⣿⣿⢟⣻⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣼⢿⣍⣥⣤⣤⣤⣤⣒⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⡖⢉⡴⠊⢱⠂⠀⣼⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣧⠀⠀ ⣿⡇⣿⣽⣾⣿⣿⣿⣿⣿⡿⣇⠐⣾⣫⣿⣿⡇⠀⠿⠟⣹⠋⣩⣩⠛⠿⣾⣿⣦⣄⠀⠀⠀⣀⠀⠀⢠⣞⣥⣦⣶⣋⣭⣈⣩⠟⠉⣽⣿⣛⣫⣿⣿⣿⣧⠀⠙⢿⣿⣿⣿⣿⣧⠀ ⣿⢸⣿⣿⣿⣿⣿⡿⠿⠻⡀⠈⠉⢉⣿⣿⣿⡇⠀⠀⠀⣧⢬⠷⣿⡚⠆⠈⣿⣧⣻⠋⠠⠞⠁⠀⢠⠟⣛⣽⠟⣩⢡⠟⣿⢿⣛⣹⡋⠈⣿⣿⣿⣿⣿⣿⡄⠀⢸⠻⣿⣿⡿⢹⣆ ⣿⡼⣿⣿⣿⣿⣿⡇⠀⠀⠈⠒⢤⣼⣿⣿⣿⠃⠀⢰⣄⡘⢞⡿⠛⡟⠃⣠⠋⢻⠉⠃⠀⠀⠀⠀⠉⠴⣻⢡⣒⣿⣩⠍⡌⠀⣿⠃⠀⠀⠹⣿⣿⣿⣿⣿⣇⠀⢸⣧⣿⣿⡇⣿⣿ ⣿⣧⢻⣿⣿⣿⣿⣷⠀⠀⠀⢀⣾⣿⣿⣿⡏⠀⠀⠈⠙⢳⣌⡓⠒⢒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢌⠙⠑⣣⠼⢁⣠⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣷⣿⣿ ⣿⣿⣟⣿⣿⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⣿⣳⡀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠤⣤⣌⣉⣥⡴⢋⣿⣧⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣸⣿⣿⣼⡟⠘⢿⣿ ⣿⣿⣿⡜⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠋⢳⠱⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠠⢞⡏⡱⢏⠘⣅⣼⣿⣿⡆⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⢿ ⣿⣿⣿⣿⣜⣿⣿⣿⣿⡹⣿⣿⣿⣿⣧⠀⠀⢳⣞⡩⢍⡛⢝⠛⠳⣖⡳⣄⣀⣀⠀⠀⠀⣠⠔⠋⠀⠀⣘⣴⣃⣈⣀⣼⠯⢼⣿⣿⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣮⢿⣿⣿⣷⡻⣿⣿⣿⣿⣷⡀⠀⠈⠳⣤⠙⡎⢷⠀⠹⡼⡞⡅⠈⠉⠉⠛⠛⠛⠓⠛⠛⠳⣌⠋⢶⠀⠈⢳⡄⠹⣿⣿⣧⣄⡀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣝⢿⣿⣿⣿⣿⣶⢦⣤⠞⠀⡇⣸⠀⠀⡇⣉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠈⡆⠀⠀⡇⠀⣿⣿⣿⣿⣿⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣷⣶⣖ ⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣶⡻⣿⣿⣿⣿⣧⠑⠦⠴⢖⡟⠀⢰⠁⢸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠃⡰⠃⠀⡰⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣮⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⣿⣿⣶⣝⡿⣿⣿⣿⣧⣤⣿⣶⢶⣦⣤⣾⣍⡉⠉⠉⠒⢒⣒⣶⣶⣶⣿⠿⠋⠉⠉⠒⠶⠊⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣾⣟⢿⣿⣿⣿⣿⣿⣮⣛⢿⣿⣯⠛⠛⠋⠁⠹⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⡟⠋⠁⠀⠉ ⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢿⣿⣿⣿⣯⣻⠿⢿⣿⣿⣿⣷⣝⢿⣷⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⣿⡿⠋⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⣷⣽⡻⢿⣿⣿⣿⣷⣶⣿⣭⣿⣿⣷⣟⠃⠀⠀⠀⢀⣀⡙⢻⡿⠛⠛⠿⠷⣄⡀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⢿⣿⣿⣿⣿⡆⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣋⡁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣈⡻⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⣭⣭⣿⠛⠛⠛⠛⠛⠛⠻⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣟⣻⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣟⡻⣆⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠉⢉⣹⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⠚⠁⠀⠀⠀⢀⣤⠔⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣀⣀⡔⠙⡇⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣀⡠⠤⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣾⡦⣀⠀⠀⠹⡄⢣⠀⠀⣴⠁⠀⠈⠙⠻⠿⣿⣿⣿⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿ ⠀⠀⠀⠀⠀⠀⠓⠀⠙⢁⠎⠀⡇⠈⠓⢤⣀⠹⣼⠀⡸⠁⢀⡤⢚⣀⣠⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢰⠞⠛⢷⠀⠈⠙⠳⠦⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠘⠒⠒⠋⠀⣠⣤⡀⠀⠀⠉⠛⢶⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⡴⠖⠶⢦⠀⠀⠀⢧⣬⠇⣀⣠⠴⠞⠋⠁⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠘⠧⣤⣀⡼⠀⢀⣀⡤⠶⢛⣩⣤⣀⠀⢠⡞⠋ ⠀⠀⠀⠀⠀⠀⣠⠞⣁⣀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁⠀⠀⣿⠁⠀⣹⠀⠈⢷⡄ ⠀⠀⠀⠀⣠⠞⠁⠀⠷⠿⣀⣤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠒⠃⠀⠀⠀⡇ ⠀⠀⣠⠞⣁⣠⡤⠶⠚⠛⠉⠀⠀⠀⣀⡁⠀⠀⠀⠀⢀⡤⠶⠶⠦⣄⠀⠀⠀⡇ ⠀⡾⠛⠋⢉⣤⢤⣀⠀⠀⠀⠀⣰⠞⠉⠙⠳⡄⠀⠀⡟⠀⢀⠀⠰⢺⡆⠀⠀⡇ ⠀⡇⠀⢰⡏⠀⠀⢹⡆⠀⠀⠀⡇⠀⠀⠄⠀⣿⠀⠀⠳⣄⡀⠀⢀⣸⠇⠀⠀⡇ ⠀⡏⠀⠀⢷⣤⣤⠞⠁⠀⠀⠀⢷⣀⣀⣠⡴⠓⠀⠀⠀⡈⠉⠉⠉⠁⣁⣠⠴⠇ ⠀⠻⣆⠀⠀⠀⠀⢀⣀⣤⣀⠀⠈⠉⠩⠁⠀⠀⠀⠁⠀⢀⣨⡤⠖⠛⠉⠀⠀⠀ ⠀⠀⡿⠀⠀⠀⢰⡏⠀⠀⢹⡆⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠃⠀⠀⠀⠀⠀⠀⠀ ⢰⠞⠁⠀⠀⠀⠈⢷⣄⣤⠞⠁⣁⣤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡎⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠀⣏⡁⡷⡇⣟⡃⣟⡃⣫⠁⣟⡃⠀⠀⠀⠀ ⢸⡇⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⢕⠀⡈⢹⢉⠀

⠐⢢⠐⢢⠐⣹⡷⣆⠐⢆⠒⡄⠒⡌⢶⡐⡐⢢⢉⠓⢆⠒⡌⡉⢍⡙⣿⣯⠁⠆ ⡉⢆⡉⢆⠱⡈⣿⠹⣎⠄⠣⢌⠱⡐⠌⣷⡡⢊⠤⣉⠆⡱⠤⡑⠢⢌⣿⢼⡣⠌ ⣿⣤⠘⡄⢣⡐⣹⡆⠹⣯⡐⡃⢆⠱⡈⠜⣷⢈⠲⡐⡜⢠⢃⠜⡡⣚⣯⠀⢿⡔ ⢿⣿⣷⣌⠡⢒⠌⣷⡥⢾⣿⣴⡉⠆⡍⠬⣹⡎⠔⡱⢈⡅⢎⢒⣡⣿⣇⣨⠘⣷ ⣎⢿⣿⢿⣷⣌⢒⠸⣏⠉⡈⠻⣿⣖⡌⢣⢜⡧⢊⣵⠊⡔⢪⢰⣿⡏⠙⠛⠷⠾ ⠈⠳⢿⣳⣍⠻⠿⣦⣽⣆⠠⠁⠘⠻⣿⡷⣾⠇⣭⡟⢸⡈⣵⣿⠟⠀⠡⠈⠄⠂ ⣄⠡⡈⢿⣾⣾⣿⣽⣛⣻⠷⣤⠁⠀⠈⢻⣿⢸⣿⢡⢃⣾⣿⢟⣺⣟⣿⣷⣮⡴ ⣘⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣓⠀⠈⠀⢰⣯⣿⢇⣾⣿⣟⣿⠿⣿⣿⣿⣿⣿⣿ ⣿⠛⠡⣾⣿⢿⣿⣿⣿⣿⠠⠉⠁⠀⣰⣿⢿⣽⣻⠟⠃⠈⠔⢺⣿⢿⣿⣿⣿⡎ ⠻⣇⠀⢻⣯⠟⢿⣯⠙⠋⠀⠀⢠⣾⠿⠛⠏⠋⠁⠀⠀⠀⠀⠘⣿⡏⢿⡋⠙⠃ ⠀⡉⠷⣌⣻⢦⣦⡼⠟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠘⠿⣤⣼⡧⠚ ⠀⡐⢀⠀⠈⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⡀ ⠀⠠⠀⢈⠀⠠⠀⢀⠀⠂⠀⠀⣴⣷⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠐⠀⠀⡀⠀⡀ ⡀⠁⡐⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⢀⢸ ⢧⡐⠠⠄⠡⠐⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠠⢈⣾

⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢃⠂⠄⣀⣸⡄⢣⠀⢀⡀⢤⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠠⠄⡃⠀⠀⠀⠁⠀⠁⠄⡐⠥⢀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠂⣄⢀⣪⠂⠀⠀⠀⠀⠀⠑⠀⠐⠓⢖⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡧⢞⡄⢃⡌⠘⢰⢠⣡⡄⣃⢰⡄⡀⣕⣤⡄⠀⠀⠀⠀ ⠀⠀⢀⣴⢔⢁⢺⢘⡦⢧⣇⢮⡸⡻⡳⠚⢣⣃⢿⣮⣢⡀⠀⠀⠀⠀ ⠀⠀⠈⠀⣸⣆⡎⢸⣗⣡⣴⣿⠗⠛⣴⣾⣿⠟⣾⠷⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⢻⣻⣿⡌⠻⠿⠋⠀⠀⠈⠉⠁⠀⣏⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠈⠻⣣⠀⢀⢔⣨⣥⣤⣬⡆⢸⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠻⠝⠂⠭⢚⣴⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡞⢕⢦⣴⣶⣧⢿⣿⣿⣯⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣷⣶⣯⡻⣿⡇⢀⠉⠚⠛⡍⠸⣻⣿⣿⣿⣿⠂⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⡻⣿⣿⣿⣿⣄⠣⠀⠀⠇⢠⣿⣿⣿⣥⣿⣦⣀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⡠⣿⣿⣿⣿⣿⣿⣿⠀⣯⡆ ⢀⢔⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡠⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⢠⡖⣶⡾⢁⡀⠀⠀⠀⠉⠛⠒⢲⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠓⠂⠤⠌⢈⡙⠂⠴⡾⡟⠆⢸⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠒⠤⠄⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠂⠐⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡇⠀⠈⠉⠁⠀⢉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀ ⠀⠀⣠⣾⢯⡓⠐⠂⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀ ⠀⢰⡿⠁⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡠⠀⠀⠀⠀⠀⢇⠀ ⢠⣿⢣⠂⠀⠀⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⠀⠀⠘⡄ ⢸⡷⢹⣤⡀⠀⡀⢸⠀⠀⠀⣀⣀⣀⣀⣤⡤⠖⠃⠀⠑⠄⠀⠀⠀⠀⠀⢣ ⢸⣷⡄⢻⡦⣀⣼⡿⠉⢹⣿⣿⡿⠋⣭⠹⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡄ ⠈⡏⣧⣌⠙⠛⣿⡇⠁⠛⣉⡻⢯⣂⠍⢼⠕⠉⠀⡀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠹⣿⣿⢳⠴⠛⡅⠀⣜⡴⠛⠓⠢⣍⣠⢔⠞⠄⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠹⣍⣇⣢⣀⢳⡴⢰⡀⠀⠀⢀⣠⠖⠁⢀⣼⡆⠀⠀⠀⠀⢀⡼⠁⠀ ⠀⠀⠀⠘⢿⡷⡜⢭⡉⠛⣛⡶⠏⠉⠁⠀⢀⡿⠋⠀⠀⠀⠀⢠⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢿⣆⢇⠀⠘⡄⠀⠀⠀⠀⠜⠀⠀⠀⠀⣠⠖⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠅⢀⣀⣀⣀⣀⣀⡤⠒⠉⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣾⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⢶⣛⣛⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠶⣶⠀⣰⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣼⣿⣿⣭⣟⣻⠿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢻⣠⡏⠀⣷⢶⠖⣷⠀⠀⠀⠀⣰⡿⣳⣿⣷⣿⣿⣿⣿⣭⣟⡿⣾⣝⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣘⠳⣄⠀⠸⡆⠈⣿⠁⠀⡏⢻⠟⢻⡇⠀⠀⣠⣿⢹⣿⣿⠘⢿⣿⣯⣟⡿⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣦⠙⢧⣠⣇⢀⣿⠀⣼⠇⣿⠀⢸⡇⠀⢠⣿⣿⣿⡏⠀⠀⠀⠉⠛⠿⣿⣷⣭⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢷⡄⠀⠉⠀⢀⣰⣾⣾⣻⣤⠀⢿⡄⢸⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣆⠀⣶⣻⡵⠈⠘⡿⠿⣯⣷⡿⠀⢹⣿⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⢶⡀⠈⢋⡇⠀⢸⣿⠀⢿⠛⣿⠷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠈⠙⢃⡜⠀⠀⠸⣟⠀⠘⣯⣷⣿⣷⡮⠤⣴⣚⣹⣭⣿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⢻⠀⠀⠹⠿⠿⠟⠁⠀⠸⣿⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣸⠀⢀⣀⣠⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⣿⣟⣿⠝⡓⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣶⠟⠙⠷⣤⡹⣆⣿⣿⡿⠻⠷⠾⢷⣶⣶⡟⠛⢿⣿⡳⢮⣳⣄⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⠛⢿⣧⣀⠀⢭⠉⠁⣠⡞⣹⠁⠀⠀⠙⣿⣦⣿⣾⣷⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠈⠻⢷⣶⣶⡾⠋⠀⡏⠀⠀⠀⠀⠈⢻⣷⡙⢿⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡇⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡖⠲⠄⠀⠀⠀⠀⠀⠀⣿⣧⠀⠱⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡇⠀⠸⡇⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠤⠶⠋⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⠹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠙⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣇⠀⠀⠘⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⣸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⢿⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢻⠁⠀⠀⠙⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢿⡀⠀⠀⠀⠈⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏⠀⠈⣷⠀⣤⢤⡀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠺⠿⠭⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⡽⠟⠀⠀⠀⠀⠻⣆⢹⠀⢳⡀⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠙⠛⠉⠉⠉⢀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⣇⣿

⠀⠀⣠⣴⣦⢤⡀⠀⠀⠀⡠⢲⡿⠿⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠋⠀⠈⠣⣝⢦⣠⠾⣾⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⡠⠴⠢⢤⣴⡇⠐⢻⣆⢘⣶⡒⠒⣤⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠒⠚⠉⢹⠿⠖⠛⢻⣿⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠾⣿⣿⣯⢳⡀ ⠀⠀⠀⠀⠀⡾⢻⡤⣤⣴⣷⣤⣤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠲⣶⡢⢄⡀⠀⠀⠀⠈⣿⣿⢡⡇ ⠀⠀⠀⠀⢠⠃⠸⣷⣒⣾⣿⡿⣿⠒⠂⠉⠒⠒⠒⠒⠒⠊⠉⠀⣀⣴⣿⣿⠟⠛⠛⠢⣀⣀⣴⣿⠟⠁⠀ ⠀⠀⠀⠀⣹⡀⠀⠉⠙⠿⠿⠚⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣹⡛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡧⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣧⣀⡄⠸⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢀⠋⢀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠘⣦⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠔⢁⣀⣾⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⣸⣿⣿⣶⣦⣴⣶⣶⣶⣿⣿⣿⡇⠀⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣇⠀⢸⣿⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⢹⠀⠀⢼⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⠀⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠐⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢿⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡘⣻⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡏⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡸⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⣤⣄⣀⣠⡾⣏⣽⣻⢋⣀⣀⣤⣤⣴⢞⣲⣤⣤⣤⣴⣦⣤⣾⣿⣿⣷⣶⣤⣤⣤⣤⣄⣤⠀ ⠀⠀⠛⠛⠛⠛⠋⠉⠉⠓⠿⠩⠜⠛⠋⠙⠋⠀⠀⠉⠉⠉⠉⠙⠛⠛⠿⡴⠏⠋⠉⠈⠁⠉⠉⠉⠀⠀⠀

⠀⣤⣄⣴⣶⣿⣿⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣀⣶⣆⣶⣦ ⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⠛⢿⣿⣿⣿⣿⣿⠛⡟⠛⢿⡿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣧⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⣤⡾⣶⠿⣷⡿⣷⣾⣧⣼⣆⣴⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣯⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠟⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣁⣠⣀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠉⠀⠀⠀⣹⠟⠃⠀⠀⠀⠑⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⠸⢷⠀⣏⠀⠀⠀⣴⠦⠀⢹⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⡤⠖⠲⠤⠽⣄⠀⠀⠀⠀⢀⠞⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⣄⣀⡀⠀⠈⠑⠒⠒⠚⠁⠀⠀⣾⣿⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠛⠿⣏⡉⠉⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⣀⣠⣴⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣽⠉⠉⠉⢀⡞⡋⢀⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢮⡇⡏⠀⠀⠀⡾⣀⠀⢹⣿⣀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣾⢸⠁⠀⠀⢤⣧⣭⠵⠶⠿⢽⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⡾⠀⠀⠀⠈⠉⡇⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣟⡝⠁⠀⠀⠀⠀⢸⠇⠀⠀⠠⢸⠙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⡟⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣾⣇⠘⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣁⠀⠀⠀⠀⠁⠀⢐⣿⠀⠀⠀⠀⡇⠹⣧⣻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡛⠒⠒⠒⠶⠶⡾⢯⣀⠀⠀⢸⠧⠤⠴⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣦⡀⠀⠀⠀⣧⡀⠈⠙⠓⠾⠄⢀⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣝⡂⠉⠓⠦⣤⠘⠳⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠓⠒⢻⠶⡤⠤⠤⠤⡤⠖⠚⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣽⠀⢇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣿⣍⣭⣍⣯⣷⠿⠤⠤⠤⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣻⠟⠁⠈⢽⡏⣻⠟⠓⠶⠶⠶⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⢽⣓⣒⣲⡶⣻⣏⡅⠀⠀⠀⠀⠀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⠭⢍⣚⣒⣺⡯⠭⠽⠓⠃⠈⠋⠁⠛⠋⠁⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠛⠉⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠛⠲⢦⣤⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠹⣧⡀⠀⠀⠀ ⢀⣼⠟⠅⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠑⠿⠃⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠹⣧⠀⠀⠀ ⣾⠏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢽⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣿⣆⠀ ⣿⣆⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⣶⡖⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⣶⣿⠟ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠈⠳⠤⠔⠒⠉⠉⠉⠑⠒⠤⠔⠉⠀⠀⢀⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠁⠀⠀⠀ ⢋⠒⠒⠤⠤⣀⣀⠀⠀⠀⠀⡘⢀⣤⢀⠀⠀⠀⠀⠀⢀⣤⣀⠈⡄⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠉⠉⠒⢲⠇⠈⠛⠛⠀⠀⢀⠀⠀⠈⠛⠋⠀⢃⠀⠀⠀⠀⠀ ⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⠀⠠⢠⠤⡄⠀⠀⢠⣾⣷⢸⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⢹⠂⠀⢀⠎⢆⠉⠀⠀⠀⠈⠂⠁⠀⠀⠀⠉⢉⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⢠⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠣⢄⡸⢠⠀⠀⠀⢣⠀⠀⠀⢀⠄⠀⠀⢠⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠢⠤⣀⠀⠇⠀⠣⡀⠀⠀⢆⠀⠀⢸⠀⠀⢀⠞⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢅⣸⠀⠀⠀⠙⢤⠴⠚⠂⠀⢮⣤⣤⠎⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠂⢤⠤⠤⠤⠤⢤⡤⠤⢤⡊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠒⠁⠀⠀⠀⠀⠀⠈⠒⢤⣷⠀⠀⠀⠀⠀⠀

⢀⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⡄⠀ ⠸⣧⠌⣹⢦⡴⠛⣶⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⣠⣤⣴⣷⢀⠻⡆ ⠀⢹⡏⢰⠖⠃⣾⠉⠀⣀⡴⢿⣏⣉⢭⣛⡙⢶⣄⠀⢻⡄⣸⠟⣌⡙⣷ ⠀⠀⢿⡠⠘⢦⡟⠀⣴⠋⡝⣡⣮⣶⣦⣥⡙⢢⠩⢷⡠⣗⠌⠒⣍⡼⠇ ⠀⠀⠀⠛⠶⠾⠁⢰⠇⡓⣴⣿⣿⣿⣿⣿⣿⣆⠱⡈⣧⠘⠳⠾⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡊⣱⣿⣿⣿⠿⠿⣿⣿⣿⡄⠡⣿⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⣽⣿⠏⠄⡂⠔⡈⠿⣿⣯⢱⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣧⠘⢢⠑⢬⠐⡡⢭⣇⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠻⠶⠻⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠛⠛⠛⠛⠛⠛⠛⠿⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠟⠛⠛⠛⠿⣦⣄⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⠈⢙⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⢱⡀⠀⠀⠀⠀⡜⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⢰⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀ ⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⡇⠀⠀⠀⢸⣿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀ ⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢠⣶⣶⣶⣦⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀ ⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀ ⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⣴⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡛⠛⠉⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠋⠁⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠈⠙⠻⣶⣄⠀⠀⠀ ⠀⢀⣴⣿⣯⣴⡆⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢰⣶⣬⣻⣷⡀⠀ ⠀⣾⠏⢸⣿⠿⠃⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠈⠻⢿⡿⠹⣿⡀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣤⣀⣀⠀⢀⣀⣠⣤⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇ ⠀⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣿⠟⠛⠻⣿⣯⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠃ ⠀⠀⠀⠉⠛⠛⠿⠿⠶⠶⠶⠶⠶⠿⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠶⠶⠶⠶⠶⠾⠿⠛⠛⠋⠁⠀⠀

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢴⠋⠙⠳⣤⡀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⡀⣠⡴⠟⠛⣷⠀⠀ ⠀⠀⠈⠳⢤⣀⢈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣀⣠⡴⠋⠀⠀ ⢀⣠⣤⣄⣄⣉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣡⣤⡴⣦⣀ ⢹⣅⡀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⢀⣠⠏ ⠀⠈⠙⠉⢋⣉⣇⠀⠀⣾⣷⠄⠀⠀⠀⠀⠀⠀⠀⢴⣿⡆⠀⢀⣿⡙⠋⠋⠀⠀ ⠀⠀⢤⠶⠋⠉⢈⣦⡀⠈⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠀⣠⣎⠈⠉⠛⢷⡀⠀ ⠀⠀⠻⣤⣤⠶⠋⠀⠈⠑⠠⠄⣀⣀⣀⣀⣀⣀⡀⠤⠐⠉⠀⠈⠻⠶⠖⠶⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠤⡀⠀⡠⠤⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠉⠁⠀⠉⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠤⡀⠀⡠⢄⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⣀⣀⣈⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡇⠀⣎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡇⣸⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀ ⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⡄ ⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇ ⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠀ ⠈⢷⡀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⣿⠀⣼⠃⠀ ⠀⠈⢷⣼⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡾⠃⠀⠀ ⠀⠀⠈⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⢠⠀⣄⠀⠀⠙⢿⣿⣿⣿⡿⠏⠀⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣴⣿⠀⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⠳⣦⡀⠀⠀⠀⠸⣿⡿⠀⢻⣿⡟⠀⠀⠀⠀⣤⡾⢻⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⢻⠻⣆⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⡾⢻⠁⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⢹⠒⡦⢤⠤⡤⢤⢤⡤⣤⠤⡔⡿⢁⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⢸⠦⣧⣼⣀⡇⢸⢀⣇⣸⣠⡷⢇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠺⣄⣇⢸⠉⡏⢹⠉⡏⢹⢀⣧⠾⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠉⠙⠓⠚⠚⠋⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⣀⣤⣤⣶⣶⣿⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠉⢉⣉⣉⣉⠉⠛⢶⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢠⡾⠟⢋⣉⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣭⣽⣿⣿⣿⣷⡌⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⣽⣦⣾⣿⣿⣿⡿⢿⣶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡿⠻⣿⣿⣿⣿⣿⢿⣧⠰⡇⠀⠀⣀⠀ ⠀⠀⠀⢻⣷⣿⣿⣿⣿⣥⣿⠇⢀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣌⣻⣿⣿⣿⡟⣸⠀⢣⢀⣽⣿⠇ ⢠⣶⠀⢸⣿⣝⠿⢿⣿⣿⣧⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠚⠁⠀⠀⠁⠀⣾⠀ ⠸⡆⠉⠛⠀⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡇⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⡠⢷⡀⠀ ⠀⠀⢀⡿⣙⡄⠀⠀⠀⢠⣤⣤⡀⢀⡤⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣶⠞⠋⠁⠀⠀⠀⠀⣾⠉⠀⣸⡇⠀ ⠀⠀⢸⡇⠈⠉⢇⠀⠀⠀⠀⠈⠙⠛⡷⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡸⢻⠀⢀⣽⠇⠀ ⠀⠀⠘⣇⠢⠀⢾⢦⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠉⠉⠁⠀⠀ ⠀⠀⠀⠈⠓⠚⠁⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣀⣤⡤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠉⠀⠈⣉⡓⠒⠚⠉⠴⢶⠀⠈⠉⠉⠂⠉⠉⠀⢠⡶⠶⣌⠙⠒⠒⠒⠋⠉⠉⠙⢷⣆⠀⠀⠀ ⠀⠀⠀⢿⠀⢀⡀⠘⠿⠃⠀⠀⣠⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣦⠀⠀⠀⠀⠀⠘⢿⡆⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠈⢣⡈⠁⠀⢀⣠⣴⣾⣏⣈⠉⠒⢄⡀⠀⠀⠀⠀⣀⡤⠖⠛⣳⣦⣄⣀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⢉⣿⣿⣿⣿⣿⣿⡿⢿⣦⡀⠱⣄⠀⢀⠜⢁⣠⣾⣿⣿⣿⠿⣿⣿⣏⠛⢻⡉⡇⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⢰⣿⢋⣿⣿⣿⣿⠋⠁⢾⣿⣿⡀⠸⣄⡎⣰⣿⢻⣿⣿⣿⣿⠛⠻⣿⢻⣷⡀⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣾⢀⣿⡇⣿⣿⣿⣿⣿⣦⣴⣿⣿⢻⡧⠀⡿⠀⣿⡇⣾⣿⣿⣿⣿⣄⣠⣿⡟⢻⡇⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⣿⠸⣿⣤⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⢀⣇⠀⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⡇⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠙⣿⣦⠿⣿⣿⣿⣿⡿⣏⣳⡟⢀⣼⢿⡀⠹⣿⣉⣿⣿⣿⣿⣿⣿⠟⣩⣿⠁⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⡈⠛⠷⣼⣯⣭⣥⣴⠟⠋⣠⠞⣿⢸⡷⣄⠘⠻⣷⣬⣟⣏⣹⣿⡷⠟⢁⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠙⠲⠤⣤⣤⣤⣤⣤⠴⠛⠁⠀⡟⢸⡇⠈⠓⠦⣤⣈⣉⣉⣉⣁⣤⠶⠋⣱⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⡇⠀⠀⠀⠀⠀⠉⣉⡍⠁⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢴⡄⠀⠀⠀⠀⠀⢀⡴⣿⡇⠀⡷⣄⠀⠀⠀⠀⡼⠙⢳⡀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⡀⠀⠀⠀⢠⠏⠀⢈⡇⠀⡇⠈⢧⠀⠀⡼⠁⠀⠈⡇⠸⠃⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⢻⠀⠘⢿⡿⠆⠀⢴⠛⡄⠀⢸⡇⠠⡇⢠⣈⡼⠀⢧⡘⢾⡷⠃⠀⢸⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⣈⡷⠖⠒⠲⠶⠤⢼⡛⠓⠶⣾⠃⠀⣷⡤⠭⢤⣶⠦⢬⣤⠤⢤⣀⡼⠀⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⡟⢻⣤⣤⣤⣤⣀⣀⣈⣓⣊⣽⠀⠀⣇⣙⣖⣋⣀⣀⣀⣀⣀⣀⣹⣿⠛⠉⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⢀⣀⣀⣇⢸⠙⠛⠛⠛⠁⠙⠿⠿⠿⣿⠀⠀⣿⠿⠿⠏⠉⠿⠿⠿⠿⠋⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠸⣦⢤⣄⣀⣀⣀⣀⣤⡤⣬⣿⣾⣁⣀⣀⣀⣀⣀⣀⣠⣤⣀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠣⡄⡇⠀⠿⢦⣄⣀⣀⣸⡆⠀⠀⠀⠀⠀⠸⣿⣿⣍⣿⣿⠈⢸⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⢻⠇⠀⠀⠀⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠀⢸⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦⣾⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣿⣇⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣘⣻⣿⣟⢛⣻⣟⣁⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀

⠀⠀⠀⠀⠀⢠⣿⣿⣟⣽⣿⣿⣾⢏⣾⣿⡟⣾⣿⠉⢀⡾⠁⣴⠏⣸⡟⣼⡿⡇⢸⠇⠀⠀⠀⠀⠘⣦⠀⠀⠙⣮⢿⡽⣿⣧⠹⣷⣾⣿⣷⡼⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣏⣾⣿⣿⣿⠃⣾⣿⡿⣿⡟⠁⠀⡼⠀⣼⡟⣰⡟⣰⡿⢡⠇⣿⠀⠀⠀⣆⠀⠀⠘⡆⠀⠀⠘⣿⣷⡽⣿⣷⡸⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⡇⠈⣼⣿⣿⢃⣼⣿⣿⣾⡟⠀⠀⣼⠃⣼⡟⣰⣟⣽⡿⠁⡿⢠⠇⠀⠀⠀⠘⢦⡀⠀⠸⡄⠀⠀⠘⣿⣿⣿⣿⣇⢻⣯⢹⣿⡿⡄⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⠀⣸⣿⣿⠃⣼⣿⣿⣿⣿⠁⠀⠀⡟⢠⡿⣱⣿⣿⡿⠀⣼⠁⢸⠀⠀⠀⠀⢀⠀⢳⡀⠀⠹⡄⠀⠀⠸⣿⣿⣿⣿⡆⣿⣿⣿⣿⣻⡄⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⢠⣿⣿⠃⣼⣻⣿⣿⣿⡇⠀⠀⢸⢣⡿⣡⣿⣿⡿⠁⣴⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠹⡄⠀⠀⢿⣿⣿⣿⣿⢻⣿⣿⣿⡇⢳⠀⠀⠀ ⠀⢰⣿⣿⣿⡟⣼⣿⠃⢰⢫⡏⣿⣯⣿⠀⠀⠀⢸⡿⢡⣿⣿⣿⢃⣴⠃⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠹⡄⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⠈⣇⠀⠀ ⠀⢸⣿⣿⣿⡇⣿⡟⠰⠁⠟⠀⣿⣿⣿⠀⢀⡴⣿⠀⣾⣷⣿⣯⠞⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢸⣿⣿⡿⣿⢸⣿⣿⣿⣿⡇⢹⡄⠀ ⠀⠸⣿⣿⣿⢻⡟⠁⠀⠀⠀⠀⣿⠏⠿⠚⠉⠀⢯⡾⠋⠋⡾⠋⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣿⣿⣧⡿⣿⣿⣿⣿⣿⣧⠀⡇⠀ ⠀⠀⣿⣿⣿⢸⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⡴⠛⠀⠀⣼⠃⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⢷⠀ ⠀⣴⣿⣿⣿⡼⠀⠀⠀⠀⢀⣼⣿⣀⣴⣆⡄⠀⠀⠀⠐⠏⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣶⣀⡀⠀⠀⠠⠋⠀⢿⣿⠠⣿⣿⣿⣿⣿⣿⣧⠈⠆ ⢸⣽⣿⣿⡽⠃⠀⣠⣶⣾⣿⠿⠿⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⣇⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⢸⣿⣿⣿⠀⠀⡆⣿⣿⠋⠀⠀⢀⡀⠀⠉⠻⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠁⠀⠀⠀⠈⠙⢿⣿⡆⢻⡄⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⢸⣿⣿⡇⠀⠸⣷⣿⠇⠀⣰⣿⣿⣿⣷⡄⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⢀⣠⣤⣤⣀⠀⠀⠀⢻⣇⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⢸⣿⣿⡇⠀⠀⣯⢿⣆⠀⢻⣿⣿⣿⣿⡇⠀⣀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⣸⣿⣸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠸⣿⣿⣇⠀⠀⠙⣿⣿⣆⠀⠙⠛⠛⠛⠀⣤⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠸⢽⣿⣿⣦⠀⢻⣿⣿⣿⣿⠃⠀⣰⣿⢿⡿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⣿⣿⣿⠀⠀⠀⠹⣿⡛⢿⣶⣶⣶⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣷⣤⣉⠉⠉⣀⣤⣾⡿⠃⠂⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⡀⠀⠀⠀⠉⢹⣿⣶⣿⣿⣿⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⢿⣿⣿⠿⢟⣉⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⠿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣶⣾⡿⠿⠋⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⢸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⢸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⢸⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⢸⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⢐⣒⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠋⠀⣠⡾⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠘⣿⣿⣿⣿⣿⣿⣿⣻⡀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⣠⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⠀⣠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠻⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠟⠉⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠉⠛⠿⣿⣷⣶⣶⣶⣿⠿⠟⠋⠁⠀⠀⠀⠐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠸⣿⠀⠀

⠀⠀⠀⢀⡴⠋⠉⢉⠍⣉⡉⠉⠉⠉⠓⠲⠶⠤⣄⠀⠀⠀ ⠀⠀⢀⠎⠀⠪⠾⢊⣁⣀⡀⠄⠀⠀⡌⠉⠁⠄⠀⢳⠀⠀ ⠀⣰⠟⣢⣤⣐⠘⠛⣻⠻⠭⠇⠀⢤⡶⠟⠛⠂⠀⢌⢷⡀ ⢸⢈⢸⠠⡶⠬⣉⡉⠁⠀⣠⢄⡀⠀⠳⣄⠑⠚⣏⠁⣪⠇ ⠀⢯⡊⠀⠹⡦⣼⣍⠛⢲⠯⢭⣁⣲⣚⣁⣬⢾⢿⠈⡜⠀ ⠀⠀⠙⡄⠀⠘⢾⡉⠙⡟⠶⢶⣿⣶⣿⣶⣿⣾⣿⠀⡇⠀ ⠀⠀⠀⠙⢦⣤⡠⡙⠲⠧⠀⣠⣇⣨⣏⣽⡹⠽⠏⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⢕⡋⠶⠄⣤⠤⠤⠤⠤⠂⡠⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⣄⣀⣀⣀⣠⠔⠁⠀

⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠾⣿⣾⣿⣾⣿⣾⣿⣾⣿ ⠋⡁⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠠⠐⠈⠁⠀⠀⠁⠀⠈⠻⢾⣿⣾⣿⣾⣟⣿ ⠊⠀⠀⠀⠀⢀⠔⠃⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠄⠀⠙⣾⣷⣿⢿⣿ ⠀⠀⠀⠀⡠⠉⠀⠀⠀⠀⠠⢰⢀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⡀⠀⠈⢿⣟⣿⣿ ⠀⠀⢀⡜⣐⠃⠀⠀⠀⣠⠁⡄⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠀⠀⠈⢿⣿⣿ ⠀⢠⠆⢠⡃⠀⠀⠀⣔⠆⡘⡇⢘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⢀⡆⠀⡼⢣⠀⢀⠌⢸⢠⠇⡇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⣼⣃⠀⠁⢸⢀⠎⠀⢸⠎⠀⢸⢸⡄⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠃⡏⠟⣷⣤⠁⠀⠀⠸⠀⠀⡾⢀⢇⠀⠀⠀⠀⠀⠄⠸⠀⠀⠀⠀⠄⠀⠀⠀⣿ ⠀⠀⣀⣿⣿⣿⢦⠀⠀⠀⠀⡧⠋⠘⡄⠀⠀⠀⠀⡇⢸⠀⠀⠠⡘⠀⠀⠀⢠⣿ ⠈⠀⢿⢗⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢰⠁⡇⠀⠀⢨⠃⡄⢀⠀⣸⣿ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣱⠀⠀⡎⠸⠁⠀⢀⠞⡸⠀⡜⢠⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣧⢰⣧⡁⡄⠀⡞⠰⠁⡸⣠⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠏⣿⠟⢁⠾⢛⣧⢼⠁⠀⠀⢰⣿⡿⣷⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠄⠀⡠⣚⡷⠊⠀⠀⠀⣿⡿⣿⡿⣿ ⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢸⠁⠀⠀⠀⢰⣿⣿⡿⣿⣿ ⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⡞⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿ ⠀⠙⢦⣀⠀⠀⠀⠀⠀⢀⣀⣠⠖⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⣿⣾⡿⣷⣿ ⠀⠀⠀⠀⠉⠉⣩⡞⠉⠁⠀⢸⡄⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿ ⡆⠀⠀⣀⡠⠞⠁⣧⢤⣀⣀⣀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣿⣷⣿⣷⣿⣿ ⣿⣷⠊⠁⠀⠀⡰⠁⠀⠀⠀⠀⣹⠶⢦⡀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣷⣿⣷⣿ ⣿⢿⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⡇⠀⠀⠀⠀⠀⠈⣿⣾⣷⣿⣿ ⠋⠈⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠻⣿⣽⣾⣿ ⢀⡄⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿ ⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⠀⠀⠀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⣃⡇⠀⠲⡀⠀⠀⠀⠀⠈⣿⡿⣿ ⣀⠤⠤⠤⡀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢬⠞⡇⠀⠀⠇⠀⠀⠀⠀⠀⣿⣿⣿ ⡁⢀⠀⠀⡇⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣸⠁⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿ ⠔⠃⠀⠀⡇⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⡃⠀⠀⠙⢄⠀⠀⠀⠀⣿⣷⣿ ⠒⠊⠀⠀⢸⠀⣸⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢅⠀⠀⡂⠸⡄⠀⠀⠀⣿⣟⣿ ⠓⠀⠉⠀⢸⣰⠃⠀⠀⠀⠀⠀⠀⡜⡆⠀⠀⠀⢸⠀⠀⡇⢀⠇⠀⠀⠀⣿⣿⣿ ⠉⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⠀⠀⡇⠀⠀⡇⢸⠀⠀⠀⠀⣿⣷⣿ ⡀⠀⢀⢿⣥⡤⠤⠤⠤⣀⣀⢠⠇⠀⢸⠀⠀⢰⠁⠀⢨⠀⢸⠀⠀⠀⠀⣿⣟⣿👉🤨

⠀⠀⠀⠀⠀⠀⢀⣄⣴⣄⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡦⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⢿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠎⠀⢀⣀⣤⠤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⠤⠤⣄⣀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢞⠉⠀⠀⠀⠠⢀⠉⠙⢦⡀⠀⠀⢠⠞⠉⠁⠀⠀⠀⠀⠈⠙⢖⢢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣾⠃⠀⠀⣀⣀⣀⣤⣾⣷⣤⢾⣿⠛⠻⣿⣀⣤⣶⣄⡀⠀⠀⠀⠀⠀⢳⣷⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⢸⡎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⠇⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⢿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⡀⠀⠈⠒⠒⠛⠛⠉⠀⠀⣶⣿⣶⣶⣶⣶⣶⡆⠀⠈⠑⠒⠛⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠀⠃⠀⠀⠀⠀⠀⠬⢐⣄⠀⠈⠙⠛⣿⠟⠛⠋⠀⠀⠠⠉⠁⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢶⠿⣧⣞⣸⣾⡄⠀⠀⠀⠀⠀⠿⣗⠤⣀⣒⣿⣀⣁⣀⠄⠊⠀⠀⠀⠀⠀⢀⣴⣿⣦⣀⣄⠀⠀⠀⠀⠀ ⡐⢹⣿⣿⣿⣿⣿⣿⣶⣴⠀⠀⠀⠆⠌⠳⢤⣀⠈⠀⡀⠄⢘⠆⠀⡀⠀⢁⣴⣿⣿⣿⣿⣿⣿⣁⢀⣀⠀⠁ ⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣄⣰⣶⣟⣷⣿⣿⣷⣭⣧⣤⣽⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⢿⣿⣿⣿⡻⣿⣿⠿⠻⣏⣿⣿⣿⣿⣿⣿⣿⣿⢻⠷⠀⠀⠀ ⠈⢿⣿⣿⣿⣿⣿⠿⣿⣝⣿⣿⣿⣇⠘⡄⠁⣠⢾⡞⠛⠃⢻⠉⠀⠀⢁⢀⠣⡟⡏⣿⠭⠈⡇⠸⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⡯⣿⠓⠙⠀⢰⠉⢇⠀⠛⠃⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢻⠳⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⡇⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢲⡏⠀⠀⠀⠀⠀ ⠀⠀⠐⠿⠟⠀⣿⠀⢢⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠳⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡥⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠙⡝⢧⠉⠉⠓⠲⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣽⠀⠀⠀⠀⠀⠀⡇⡇⠀ ⠀⠀⢀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣇⠀⠀⠀⡃⢰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡧⣇⠀ ⠀⠀⣸⠀⣠⠔⠋⠉⠉⠉⠑⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢣⠀⠀⠀⡇⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⡇⣷⠀ ⠀⠀⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⡤⠀⠀⠀⢻⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣧⣿⠀ ⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡳⡀⠀⠀⠀⠀⠀⣧⠇⠀⠀⠀⢸⡇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣿⣿⠀ ⢀⡟⠀⢀⣀⣤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⠀⢰⡟⢀⣼⡴⠚⠋⢻⡄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡷⡿⠀ ⣼⡥⠞⠉⠀⠀⢀⣠⡴⠶⠒⠛⠛⢲⣤⡀⠀⠀⢻⡁⢠⠀⢠⣯⡴⠋⠁⠀⠀⠀⠀⠹⠄⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⣿⡀ ⠏⠀⠀⢀⡴⠞⠉⠀⠀⠀⣀⣤⡶⠋⠀⠈⠓⢤⡀⢳⡏⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡄⠀⠀⠀⠀⠀⠀⢸⡆⠉⠉⠁ ⠀⠀⣰⡿⠃⠀⠀⢀⣴⠞⢁⡞⠁⢀⡤⠂⠀⠀⠙⢾⡷⠋⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠿⡄⠀⠀ ⢀⣾⠟⠀⠀⠀⣴⡿⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢷⠀⠀ ⠈⠏⠀⠀⢠⣾⠟⠀⠀⣼⠁⣀⣠⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣖⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠘⣇⠸ ⠀⠀⠀⣰⣫⠏⠀⠀⠀⣿⣤⡿⠋⠐⠚⢿⣷⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⣿⣿⡆⠙⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢹⡀⠀⢹⡄ ⠀⠀⢰⢿⡏⠀⠀⠀⢀⣧⣾⠁⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⢀⣿⣿⣿⠀⠈⢻⣟⠛⠃⠀⠀⠀⠀⠀⢰⡇⠀⢸⡇⠀⠈⣧ ⠀⢀⡏⡼⠁⠀⠀⠈⠉⣹⡏⠀⢸⣦⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⣠⣾⣿⣿⣿⡀⠀⠈⢿⡦⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸ ⠀⠸⢀⠇⠀⠀⠀⠀⠀⣿⡙⠀⢸⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣿⡿⣿⣿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠸ ⡄⠀⢨⡄⠀⠀⠀⠀⠀⣸⠇⠀⠘⣍⠈⢀⡇⣀⣠⠤⣤⡀⠀⠀⠘⣯⠃⠈⠀⣹⠏⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠙⠦⣄⡇⠀⠀⠀⠀⣰⢏⡠⠴⠄⠉⠉⠋⢸⡁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⣉⡉⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡎⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠁⠀⠀⢀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠘⡉⠳⣤⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠃⠀⠀⠉⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠘⣿⠟⠁⠀⠀⠀⠀⣰⠃⠀⢀⠄⠀⢀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⠖⢶⣶⣾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣀⡾⠃⠀⠀⣾⠃⠀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢧⡀⠀⢀⣀⣴⠟⠀⠀⠘⣿⡇⠸⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣶⡿⠋⠀⢀⡾⡛⠀⣼⢡⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠬⠓⢚⣩⠞⠁⠀⠀⠀⠀⢿⣇⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⢻⡟⠋⠀⠀⣠⠞⡱⠁⣼⠃⢸⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠤⠤⠤⠦⠤⠤⠤⠤⣤⣤⣤⣀⣀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠉⠉⠛⡷⠶⢦⣀⣀⣸⠃⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⢀⣠⡴⢶⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⣿⡝⠻⣶⡀⠀⠀⠀⠀⠀⡝⠀⠀⠈⢹⠟⠶⣤⡀⠀⣾⠋⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀ ⠀⣰⠟⠁⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢡⣰⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠁⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀ ⣰⠏⠀⣸⡅⠀⣠⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⠻⠿⠷⠋⣴⠏⠀⠀⢀⡴⠟⣏⣭⣽⣳⣄⠀⠀⠀⠐⣿⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⢿⠧⠀⣿⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣤⠟⠁⠀⠀⢰⠟⠀⢰⣯⣿⣿⣛⣿⡆⠀⠀⠀⠈⠛⠲⢿⡋⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣦⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠷⣄⣀⣀⣀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠤⠤⠼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠻⠶⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⠗⠒⠒⠲⠀⢀⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⢠⠀⠀⢠⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢳⡄⠀⠀⠀⠀⠀⣄⠀⣧⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⡞⡆⠀⠀⠙⠳⠮⣤⣤⣀⣀⠀⠀⠀⢀⣀⣾⣥⡴⢿⠃⠀⠀⠀⠀⢻⡀⢹⡀⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢸⡇⡀⠀⠀⠀⠀⣀⠀⠈⣉⡉⠭⢩⠉⠉⠉⠉⠀⢠⡇⠀⠀⠀⠀⠀⠈⣷⠀⣧⠀⠀⠀⠀⢸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣰⢾⠟⠃⠘⣠⠀⣯⡟⠆⠄⠒⡇⠐⠲⠀⠰⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠙⠀⠈⠀⢰⡀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠋⠁⣾⠀⠀⠀⠀⠀⣵⢁⠀⠀⠀⠁⢤⡄⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⢰⡄⠀⠀⠀⠀⢀⡾⢿⣦⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣀⣴⠞⣯⡀⠀⠀⢀⣼⣷⡀⠀⠀⠀⢸⣤⠀⠀⠀⣠⡾⢷⣄⠀⢀⣴⣟⠀⠀⠉⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠲⠦⣤⣤⡤⠶⠛⢋⣽⡷⠞⠛⠉⠀⠀⠈⠻⢶⡶⠟⠁⠈⠿⣦⣄⣴⠟⠻⣦⣤⡾⠋⠀⠀⠙⠛⠛⠉⣿⠳⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠾⢻⡿⠋⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠙⢶⣄⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠴⠟⠁⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⣿⣍⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣸⡀⠹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣸⠃⠀⠀⢠⣄⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⣠⡄⠀⠀⣼⣇⣴⡶⠉⡃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡉⠛⠳⢦⣄⣸⡟⠳⢦⣄⠸⣎⠻⣦⡀⠀⠀⣸⣿⡇⢀⣤⡴⠛⢩⡟⢀⣠⡤⠶⣿⣟⣥⡤⠞⠛⣯⣟⣡⣴⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⢾⡿⠀⠀⠀⠈⠙⠿⠀⠀⠈⠻⢿⡤⠈⠛⢦⣤⡯⠾⠿⠋⠀⠀⠀⠿⠛⠋⠁⠀⠘⠛⠉⠀⠀⠀⠀⠛⠉⣠⡞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⢀⣾⡀⠀⠀⢸⣧⣀⠀⠀⢲⡦⢤⣀⣉⣙⣶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣾⣥⣴⠶⠶⠒⣺⡟⠁⠀⣀⠀⠀⠀⠀⣀⣴⠀⠀⢀⣴⠻⡆⠀⢀⣶⠟⠉⠳⣄⠀⣾⣿⡏⠛⢦⣼⡇⠀⠀⠉⠉⠙⠛⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣿⣧⣴⣾⠟⠉⠘⣦⡴⠛⠀⠀⣿⡶⠋⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣟⠋⠙⠛⢿⡿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⡿⠛⠓⠺⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠷⠶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣴⣟⣥⣶⣿⡯⢭⣯⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⣛⣭⣴⡞⠉⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⡿⢛⣵⣾⣿⠟⣉⣤⣶⣿⣿⣿⣿⣟⢿⣿⣟⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣡⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣦⡙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⡿⡿⠃⠉⠁⠀⠀⠀⠹⣿⣿⡉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡇⠀⢹⣿⠹⣿⣿⣿⣿⠟⣻⣿⣿⣧⡀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢷⠀⠈⣿⡇⣿⣯⣿⣯⣼⣿⡟⣿⢿⢱⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⡇⣿⣿⡒⠲⣶⣦⣄⠀⠀⠀⢀⣴⣿⣿⣟⠛⢻⡇⢹⣿⣿⠀⣿⠛⣹⣿⠀⠙⣇⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀ ⣸⠁⢸⣿⠿⣶⣾⣿⣿⣇⠀⠀⢾⣿⣿⣿⣯⣥⣤⡇⢸⣿⠁⠈⢏⣼⣿⣟⠀⠀⡟⡄⠀⠀⠀⠀⠈⠻⣦⡀⠀ ⠀⠀⣼⡟⠀⣩⣤⠀⠛⠛⠀⠀⠘⠛⠋⠀⠙⠋⠈⠁⣼⠇⢀⣷⡾⠛⣿⣽⠀⢀⢇⡇⠀⠀⠀⠀⣆⠀⠘⢷⣦ ⠀⠀⠞⠁⣰⣿⣿⡷⠶⠖⠀⠀⠀⠀⠀⠲⠦⣤⠾⡿⠋⠀⢸⠟⠁⠀⣸⠇⠀⢸⢸⠀⠀⢠⠃⠀⠈⠣⣄⠀⠙ ⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠲⣄⠤⠄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⢠⣾⠋⠀⢀⠇⡎⠀⠀⣿⠀⠀⠀⠀⠀⠙⠢ ⠀⠀⢀⡿⠻⣿⣿⡿⣿⣦⡀⢀⣀⠀⠀⠀⠀⠀⠀⣠⡶⠋⣠⣾⠟⠁⠀⢀⡞⡜⠀⢤⠀⢹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠇⠀⠈⠻⠁⢸⡜⣿⣿⡛⠛⠉⠉⠀⣠⣾⣯⣴⣿⣿⠁⠀⢀⣠⣾⠞⡀⠀⠀⠱⡄⠹⡄⠀⠀⠀⠀⠠ ⠀⢀⡿⠀⣰⠂⠀⠀⠀⠻⣿⣻⣿⣦⡤⢴⣿⣿⡿⣛⣉⠈⢿⡄⠀⠈⡻⠋⢀⡽⠀⠀⠀⠈⠂⠁⢀⡔⠀⠀⠀ ⠀⢸⡇⠀⠸⣄⠀⠀⠀⠀⠙⣏⠛⠛⡷⠟⠋⠀⣿⣿⣿⡷⠈⢳⡴⠋⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⣾⡇⠀⠰⣈⠑⠢⠤⠀⠀⠈⠓⢀⣀⣀⣀⣀⣀⣉⣭⣴⠆⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢠⠄⢸⠁⠀⠀⠀⠀ ⠀⢻⡄⠀⠀⠀⠉⠉⠉⠃⠀⠀⠀⠀⠈⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢶⣤⣀⠀⠀⢰⢻⠀⡏⠀⠀⠀⠀⠀ ⠀⢸⠿⡄⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⣀⡀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⠤⠄⠈⠛⠿⣂⢸⠸⣀⠇⠀⠀⠀⠀⠀ ⠀⣾⠀⠙⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣴⣶⣄⡀⢸⡏⠘⣆⣿⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⡿⡍⢿⣿⣿⡉⠉⢏⢹⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⣿⣿⣿⠀⢉⡙⣿⣿⣿⠈⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠰⡘⣿⣿⡇⠀⠘⡌⢿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⢤⣻⢿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⠐⠁⠀⣸⣿⣿⠒⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⡏⠑⠓⠾⣿⣧⣀⡀⢱⡘⣿⡇⢡⠀⠘⣿⣿⣿⣿⡇⠸⣸⡆⢿⣿⣿⣿⡏⡇⠄⡀⠈⣿⣿⡶⠞⣉⠁⢿⣿⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⠖⠀⠀⠚⣿⢙⡛⢻⣶⣿⣧⣀⢇⠀⠸⣿⣿⣿⠃⠀⣿⡆⠸⣿⣿⣿⡿⢁⣠⣶⢛⡩⢿⣏⣠⣤⠴⠶⣿⠶⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⠶⠖⠛⢛⣿⡿⣻⣷⣶⣭⣿⡛⣿⣷⣦⣿⣿⣿⠀⡸⢸⠲⡀⣻⣿⣿⣿⠟⣩⠔⣣⣶⢿⣏⢸⡷⡄⠀⢸⠀⣸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡀⠀⠀⣾⣦⣿⣟⣄⣽⠀⠙⢧⡀⠑⣈⠹⣿⣿⣟⣁⡬⠔⢣⠸⣿⣿⣿⢈⣡⡞⠁⣿⠋⣻⣝⠱⡷⠀⠀⢰⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⠙⣧⠀⠀⠹⣾⡅⢹⣧⠏⠀⠀⠈⢿⠄⠀⠀⠙⣿⠀⠀⠀⠀⠈⢆⢸⣿⣿⢞⠏⠀⠀⠘⢿⣿⣿⠟⠁⢀⣴⠏⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⢀⡈⠳⣦⣀⡈⠉⠉⠁⠀⠀⣀⣠⡾⠇⢀⠀⠀⢘⡂⠴⠖⢢⠔⠚⢇⣿⣿⡉⠙⠲⠤⠤⢀⣤⣤⡴⠶⣿⠿⡄⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⢨⣅⠀⠈⡙⠻⠟⠿⠛⠛⠋⠉⠀⡠⠖⠂⣉⡴⠧⣄⡀⡰⠋⢀⢡⠘⣾⣿⡗⢬⣄⠀⣄⣴⣚⣤⠶⠚⠁⠀⢂⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⠀⠈⠑⠢⠤⠤⢤⡀⠀⠀⠉⠁⠻⠕⠊⠁⠀⢠⣭⣛⡓⢂⡬⠰⣇⢸⠸⡇⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣞⢁⠋⢉⣷⢿⣥⡦⡹⣎⡆⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⡗⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢞⠻⢏⣠⠼⠟⠁⠹⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡎⢆⠀⢸⣿⣦⠄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠱⡌⢆⠸⠉⠁⡾⣶⡄⡘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢜⢆⠀⢸⠃⠛⡋⠀⠸⢷⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⢠⡾⠋⢿⡄⠀⠀⢀⣀⣤⣶⡾⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⣯⡛⢶⣄⠀⢠⡟⠀⠀⠀⢻⣀⡴⠋⣱⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣀⣀⠈⢳⡄⠙⢷⣼⠁⠀⠀⠀⠈⣿⠁⣰⠏⠀⠀⣀⣀⣤⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⢿⣟⠿⣿⣄⠀⣿⠀⢠⡾⣦⠀⢻⡆⣿⡴⠞⢛⣿⠏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⡅⠙⠳⣿⣠⡟⠁⠘⣧⣼⠟⠉⢀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⡄⠀⠘⣿⠀⠀⠀⢹⡏⠀⢀⡾⠁⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣶⣬⣷⠀⢰⡇⠀⢀⡀⠀⣿⠀⣼⣡⣶⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⢻⢷⣼⡇⣸⠟⢷⡀⢹⡷⠋⣱⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣄⡚⣧⠀⠹⣷⡏⠀⠘⣷⠟⠁⣰⣏⣠⣤⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡻⢷⣄⢸⡇⠀⠀⣿⣀⡴⠛⣽⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣠⣉⣻⣆⣀⣠⣿⢋⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠻⣿⠟⠛⠛⠛⠛⢿⠛⠛⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡋⠀⠀⡴⠻⣄⠀⠀⠀⢠⠏⠳⣄⠀⠀⡟⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠏⠀⢧⣠⠞⠀⠀⠈⢦⡀⣰⠃⠀⠀⠈⠑⣼⡀⠀⠙⣧⡀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⣠⠞⢧⠀⠀⠀⠀⢀⡽⢇⠀⠀⠀⠀⣰⠃⠙⠢⣄⡘⣷⡀⠀⠀ ⠀⠀⣼⢧⡴⠞⠁⠀⠀⠱⣄⠀⣠⠟⠀⠀⠳⣆⠀⡼⠃⠀⠀⠀⠀⣹⠻⣷⡀⠀ ⠀⢸⡟⠉⢣⡀⠀⠀⠀⠀⣹⢾⠁⠀⠀⠀⠀⢀⡟⢦⣀⠀⠀⠀⢠⠃⠀⠹⣧⠀ ⠀⣿⠀⠀⠀⢳⡀⠀⡠⠞⠁⠀⠑⢄⠀⠀⣠⠋⠀⠀⠈⠓⢤⣠⠇⠀⠀⠀⢿⡀ ⢀⡏⠀⠀⠀⣠⠽⣏⠀⠀⠀⠀⠀⠀⣹⢾⡁⠀⠀⠀⠀⠀⣰⠋⠙⠲⢤⣀⢸⡇ ⢸⣧⡤⠖⠋⠁⠀⠈⠳⣄⠀⠀⣠⠞⠁⠀⠉⠳⢤⡀⢀⠞⠁⠀⠀⠀⠀⢠⢿⡇ ⢸⡇⠙⣄⠀⠀⠀⠀⠀⣈⠷⣏⠀⠀⠀⠀⠀⠀⢀⡽⠛⠤⣄⡀⠀⠀⡰⠃⢸⡇ ⠀⣷⠀⠈⢧⣀⣠⠴⠊⠁⠀⠈⠳⢦⡀⠀⢀⡤⠋⠀⠀⠀⠀⠉⠙⡾⠧⣄⣸⠇ ⠀⢻⡤⠔⠚⠙⢦⡀⠀⠀⠀⠀⠀⠀⣉⠷⠯⣀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⣿⠀ ⠀⠘⣷⡀⠀⠀⠀⠙⠢⣀⠀⣀⠴⠊⠁⠀⠀⠈⠙⠒⠤⣤⣞⠁⠀⠀⠀⣼⠇⠀ ⠀⠀⠙⣧⠀⠀⢀⣀⡴⠞⠛⢦⣀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠈⠉⠛⠲⣶⠟⠀⠀ ⠀⠀⠀⠙⣷⣏⡉⠀⠀⠀⠀⠀⠈⠑⠢⣤⣠⠖⠉⠀⠀⠀⠀⢀⡤⣺⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⢧⡙⠢⣄⡀⠀⢀⣀⠤⠚⠉⠉⠙⠒⠦⢤⣀⡴⢋⡼⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢶⣴⠿⠺⢯⣀⠀⠀⠀⠀⠀⣀⠴⠊⣁⡼⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣌⣉⣶⣦⣶⣩⣤⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣄⠖⡚ ⠀⠀⠀⠀⠀⠀⠀⠠⣶⠤⢀⡩⠛⠛⠻⡛⠉⠷⠒⠉⠁⡠⠊⠀⡞⠀ ⠀⠀⠀⠀⢀⠤⠒⠉⠀⢀⡞⠁⠀⠀⡰⠀⠀⢠⠂⠀⠰⢔⡀⠰⠀⠀ ⠀⠀⣠⠞⠁⠀⡐⠀⠀⡜⠀⠀⠀⠀⡇⠀⠀⡌⠀⠀⢆⠀⣠⠁⠀⠀ ⠠⠊⣥⣐⣒⣸⡁⠐⠀⠃⠀⢀⠀⣰⣇⠀⠀⠀⢸⠀⠀⢃⢡⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢠⡄⠀⢈⠀⣷⠘⣆⣀⣄⡘⡇⠀⠘⠸⡇⠀⠀ ⠀⠀⠀⠀⠀⣯⠀⡀⣇⢱⡀⠘⠀⡇⠈⣩⣄⣀⡈⢻⠀⡗⡄⣿⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⣏⣷⣴⣷⡀⢃⣇⠉⠁⡾⣿⢯⢻⠀⡷⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⣧⢧⢨⣷⠜⠿⠏⠈⠾⠄⠀⠈⠉⠀⢸⢸⢳⠀⣽⠀⠀ ⠀⠀⠀⠀⠀⡿⠀⢎⢛⣃⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⢸⢀⣧⢹⠇⠀ ⠀⠀⠀⠀⣸⠃⠀⢸⠞⣦⢣⣀⠀⠀⠀⠐⢀⣴⡿⡀⡇⢘⠟⡈⡸⡄ ⠀⠀⠀⠀⠁⠀⠀⠈⢸⠈⡆⢦⠉⢐⡦⠴⠛⠁⢠⣥⠅⠞⣣⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢰⠸⡸⠔⠁⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡁⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠊⢁⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠎⠀⣤⠾⠻⠿⣷⣴⠃⠀⠀⠀⠐⢳⣴⡟⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠋⠀⣸⣇⠀⠀⠀⣸⣃⣀⠀⠀⠀⠀⢸⣿⡇⠀⣠⡀⠀⠀⣤⡀⢀⣤⠀⠀⣠⣄⠀⠀⣤⣀⠀⠁⠀⢀⣤⣄⡀⠀⡀⠀⠀ ⢰⠁⢠⣾⠙⠿⠿⠿⡿⠿⠛⠿⢿⣷⣄⠀⢸⣿⡷⠋⢿⣿⠀⠛⣿⣿⠛⢿⠓⠚⢿⣿⠋⠘⣿⡟⠁⠀⣿⣏⠉⠻⣿⠿⠿⠀⠀ ⠈⠀⠈⠿⣷⣶⣶⣾⣿⡿⢿⣿⡆⢹⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇⠀⠀⣿⡏⠀⠀⣿⠀⠀⠀⠀ ⠀⠁⢀⣠⣤⣤⣼⣁⡀⠀⣠⠿⢃⡼⠃⠀⢸⣿⡇⠀⢸⣿⠀⠀⣿⣏⠀⡀⠀⠀⣿⣿⠀⣠⣿⡇⠀⠀⣿⣇⠀⣠⣿⡀⠀⠀⠀ ⢸⠀⠸⣏⣉⣉⣛⡿⠿⢿⣷⠖⠋⠀⠀⠐⠺⡿⠗⠂⣼⡿⠀⠘⠻⣿⠖⠃⠀⠀⠹⠿⠟⠉⢿⠟⠒⠀⠙⢿⡗⠉⢿⣷⡀⠀⡆ ⠈⢦⣀⠉⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣮⡿⠇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⣀⡀⠀⠀⣤⢍⣁⣀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡟⠛⠻⢻⡿⢩⣿⡏⠀⡀⠀⠀⠀⣸⠏⠀⢀⣴⢿⣶⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠁⠀⢀⣾⡇⢸⣿⡆⠀⡀⠀⠀⣠⣅⠀⣀⣸⣿⣀⡀⠀⠀⢀⣤⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⢼⣿⡇⠘⣿⡇⠀⠀⠀⠘⣿⡟⠛⠉⢹⣿⠉⠁⠀⣾⡏⠻⣷⣤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠠⢤⣿⡇⣸⡿⠁⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⣿⣇⣤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⣿⣱⣋⣀⣀⡀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣤⠾⠛⠛⠛⠛⠿⣿⠷⠋⠀⢿⡿⠎⠈⠻⢿⡷⠃⠘⠿⢿⡷⠞⠁⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⠀⠀⠀⠀⠠⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠠⢤⣦⡀⠀⠀⣀⣼⣿⣧⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠘⣿⣤⣾⣿⣿⣿⣿⣿⣧⣀⣾⠏⠉⢁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⠛⠉⢹⣿⣿⣿⡏⠻⠿⠁⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠆⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⠇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣾⣿⠀⠀⠈⣿⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣴⣿⡏⠀⠀⠀⢹⣿⣄⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠉⠉⢀⠀⠀⢦⣀⠉⠉⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠟⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠉⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡁⠀⠀⠀⢀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠝⢿⣬⣽⠲⢤⣀⢸⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠌⠀⠀⠀⠈⠻⠦⣼⣇⠙⢿⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⡊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢃⣠⣷⠾⣿⠶⠦⣄⡀⠀⠀⠀⠀⣿⠏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⢩⣿⣏⣿⠷⠛⠻⢷⣴⠏⢧⡀⠀⠀⡏⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢀⣾⣽⡟⠁⠀⠀⠀⠀⠹⣷⡴⡧⠀⢰⣆⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⣹⠀⡜⢠⡿⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢻⣿⡿⠃⠀⢹⣷⣿⣦⣀⡀⠀⢀⣴⠿⣶⠇⡼⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣽⠇⣿⠏⠀⠀⠀⠀⠙⠳⣿⡙⠛⢻⡟⠋⣠⣟⡶⢧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠙⢏⣿⠁⢺⣿⣄⡀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠋⠉⣥⣿⣫⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠷⠤⢤⣤⣙⣰⣿⣿⣃⠙⢳⣤⣄⠀⠀⠀⠀⠀⠀⣰⣾⠛⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠉⠙⠿⣿⣿⡈⠙⢲⣦⣄⣀⣨⣿⣏⡴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠈⠙⠲⢼⣟⡀⣦⣭⣹⠏⢸⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡛⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢉⡿⡅⠙⠂⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣍⠓⠦⣄⡀⠀⠀⣤⡿⢛⣤⠋⠙⢷⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠛⠉⠉⠙⠶⣤⣉⡙⠿⣏⡱⠊⠀⠀⠀⠀⠉⠳⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⡄⠀⠀⠀⠀⡲⠸⠈⡻⢻⣶⠄⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⣠⢾⡇⠀⠀⠀⠀⠀⠀⠘⢉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡦⠀⠀⣰⠦⢾⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣰⠃⠀⠈⣧⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⡼⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣙⢀⠀⣹⣋⣛⣋⣉⣛⡋⣟⣏⣙⣉⣙⣙⡋⣉⢙⢉⣿⣄⣠⣀⣀⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣬⣉⣉⣉⣉⣉⣉⣙⣙⣙⣋⣉⣉⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⢟⠩⠒⠀⠀⠀⠒⠩⢛⣟⡉⠉⠉⠉⠉⣙⣣⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⡠⢤⣀⣀⣀⠵⢄⡀⣀⡀⠤⠤⠤⠬⠑⣄⠀⠀ ⢀⣿⣿⣿⣿⣿⠁⠀⣀⣔⡪⠕⠈⢁⣀⣤⣤⡍⠱⢯⣒⠨⠍⣭⣭⣽⣗⠶⣧⠀ ⢸⣿⣿⣿⡿⠃⠀⠀⠑⠒⠶⣂⠈⢸⣷⣿⡟⢻⣆⣸⠀⠀⢰⣿⣾⣟⣻⣆⣠⠃ ⡘⢿⣿⠋⠁⠀⠀⠀⠀⠀⠑⠊⠥⠞⢛⣿⣷⣛⠭⠊⠉⠉⠉⠙⠛⠋⢉⠜⠁⠀ ⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠊⠁⠀⠀⠑⠂⠄⠐⠒⠪⡁⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣤⣤⣴⣶⣶⣿⣷⣀⣶⣦⣤⣄⣀⡘⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡔⠩⣏⡀⣆⠀⠙⡿⠿⢛⣿⡿⠿⠿⠿⠿⢿⣛⠻⠟⢓⠀⠀ ⡀⠀⠀⠀⠀⠀⢳⡈⠒⠤⢀⣉⡁⠐⠚⠂⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢰⠉⠀⠀ ⣣⡀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠉⠉⠀⠒⠒⠒⠀⠀⠤⠤⢤⠤⠐⠋⠀⠀⠀ ⣿⣷⣯⣖⡢⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣭⣭⣭⣭⣭⣵⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣣⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⣱⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣭⣛⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢟⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣮⡻⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣷⣦⣄⣀⣠⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⠟⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⠿⣿⠿⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠁⠈⢿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⢀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢏⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⠿⠿⠟⢿⠉⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⣿⣿⡿⠟⢿⣿⣿⣿⡟⠛⠛⢻⣿⡇⢀⣠⣤⣤⣽⣿⣇⠀⠀⠈⠳⣿⣿⣿⡿⠃⠀⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢧⣀⣼⣿⣿⡿⠃⠀⠀⣼⡿⣾⡿⢤⣠⠟⠛⠻⠿⣷⣄⣀⡀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠀⠀⠀⠀⣀⣀⡀⠀ ⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⠈⠙⠛⠛⠋⠀⠀⣀⣼⠟⠁⢀⣠⠶⠛⠉⠙⠲⢤⡈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠦⠤⠤⠤⠖⠋⠉⠉⠉⠁ ⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣿⡿⠁⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⠖⠒⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢻⡇⠈⠓⠦⠤⢤⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠒⠋⠁⠈⠉⠛⠋⠁⠀⣠⣿⡎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢹⣧⠀⠀⠉⠛⠿⠿⠿⢿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠚⠉⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢸⣿⣿⣿⡿⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣶⣶⣶⣶⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠸⣿⣿⣿⣿⠉⠻⣿⣿⣿⣷⢸⣿⣿⣿⣿⣤⣴⣶⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⠀⠀⢻⣿⣿⣿⡇⢠⣿⣿⣿⣿⠟⠋⠙⠻⣿⣿⣿⣿⡆⣿⣿⣿⣿⣦⣼⣿⣿⣿⡿⠈⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⡄⢸⣿⣿⣿⣇⢸⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢻⣿⣿⣿⣇⣀⣀⣠⡦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣿⣿⡆⠀⠀⠀⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡝⢿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠙⣿⣿⣿⣿⣿⡇⠀⠙⠿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠈⠻⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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