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⠀⠀⠀⢀⣀⠀⢀⡀⠀⣀⣀⡀⠀⢀⣀⠀⠀⣀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⣀⣀⠀⠀⣀⡀⠀⢀⡀⢠⣤⢀⣀⣀⣀⡀⠀⠀⢀⣀⣀⠀⠀⢀⣀⠀⣀⡀⠀⣀⡀⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⠘⢿⣤⣿⠁⣾⠟⠉⢿⣇⢸⣿⠀⠀⣿⠀⠀⠀⣿⡍⠙⣿⡆⢰⡟⠉⠙⣷⠀⣿⢿⡆⢸⡏⣽⠟⠉⠉⣿⠉⠋⠀⠀⣿⣏⠙⠃⢀⡿⢿⡆⠸⣷⣸⡿⠉⢋⣽⣿⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠃⠸⣿⡀⠀⣸⡿⠸⣿⠀⢀⣿⠀⠀⠀⣿⡇⠀⣿⡇⢸⣇⠀⢀⣿⠀⣿⡈⢿⣼⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⡈⠛⣿⡆⣸⣧⣼⣿⠀⢹⣿⠁⠀⠽⢿⠍⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⠀⠀⠙⠿⠿⠟⠁⠀⠻⠿⠿⠋⠀⠀⠀⠻⠷⠿⠛⠀⠘⠻⠿⠿⠋⠀⠿⠇⠘⠿⠟⠀⠀⠀⠀⠿⠇⠀⠀⠀⠿⠿⠟⠱⠿⠀⠀⠻⠇⠸⠿⠀⠀⠻⠿⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠋⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⢾⣫⠓⣦⠉⠁⠀⠀⠀⣀⣴⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠙⠾⣿⣣⠞⣡⠀⢠⠀⠀⠀⣀⣀⡀⠀⠉⠻⣦⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢀⡴⠃⢀⡏⠀⢠⡞⣵⣶⣽⢦⡀⠀⠘⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⡴⠋⠀⠀⢸⠁⠀⠀⠉⠻⠿⢥⠼⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣴⡋⠀⠀⠀⠀⠸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠎⠀⠙⠀⠀⣄⣀⡀⢨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠛⠉⢠⣽⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⠀⠀⢰⡶⢤⣀⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⡄⢸⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢿⣶⣤⣉⣙⡒⣦⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣧⡏⣼⣿⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⠿⠿⠿⠿⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠟⠓⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⣠⠞⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠲⡶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⡀⣀⡀⢀⠀⡀⠀⣀⠀⢀⣀⠀⡀⢀⢀⣀⣀⠀⢀⡀⢀⡀⡀⢀⣀⡀⠀ ⠀⠈⢿⢹⡁⡹⢸⢸⡆⠠⡇⡷⣎⢈⡇⡿⣼⠉⠀⡇⠀⡘⣦⣼⢷⢹⡏⢰⠃⠀ ⠀⠀⠈⠀⠉⠁⠈⠉⠀⠀⠉⠀⢈⣉⣀⣁⣉⣀⠀⠁⠀⠈⠁⠁⠈⠈⠁⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠛⠛⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡤⡹⠀⠀⣀⣀⡀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠛⡂⢠⢀⢴⡠⠈⠂⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⠊⠀⢆⠀⠉⠁⠁⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠟⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣤⣶⣶⣿⣿⠀⢻⣥⣂⡄⠐⠀⠀⠀⠀⢀⣨⢬⣿⣿⣁⣀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⢢⣶⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠠⠂⢀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢂⠀⠀⠀⡠⠔⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

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

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

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

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

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

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

⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⢀⣀⠔⠀⣀⠤⠀⢀⣤⣀⣀⣀⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⠤⠚⠋⠉⠉⠀⢀⠔⠓⠒⢄⠀⠀⠀⠀⢀⡄⠩⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⠕⠊⠁⠒⢦⡀⠀⣴⠃⠀⠀⠀⠀⢳⡀⠀⠀⠈⢿⣤⡇⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⠀⡴⠋⠁⠀⠀⡇⠀⠀⠀⠀⠘⣧⠀⢣⠛⢄⡀⠀⠀⣠⠳⠰⢶⡶⠀⠀⡔⠸⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⢀⠞⠉⢹⠳⡀⠀⣧⡀⠀⠀⣠⣾⡾⠀⠈⠳⣤⣿⣿⣾⣽⠏⠀⠀⠀⣦⣀⡇⢸⡈⠢⣽⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢠⠃⠀⠀⠸⠻⡇⠀⠛⢿⣳⣾⡿⠋⠀⠀⠀⠀⢀⣉⣉⣉⣁⣀⣀⣀⣤⣉⣉⣁⣸⡑⣄⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠀⢸⡀⠀⢀⣾⡶⠃⠀⠀⠀⠈⣉⣠⣤⣶⣚⠭⠭⡵⠒⢒⠛⠉⢉⣹⣍⡙⠒⠲⠶⡉⢿⣿⡷⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⢱⢶⣿⠏⠀⢀⣠⣴⣾⡟⠛⠉⢩⠇⡄⢀⣰⠁⢀⡎⠀⠀⣿⣤⣾⣿⡄⠀⠀⢈⣀⣹⣿⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣧⠀⠀⠸⡀⣀⣴⡾⠟⠫⠥⢄⡀⠂⠀⠙⢰⠀⣾⠃⠀⣼⡀⣴⡘⠻⣿⡿⠏⣤⡀⢸⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⡀⠀⠻⣿⢿⠶⠒⠒⠲⣄⠙⢷⡄⠀⡇⣼⠃⢀⣾⣿⠐⣻⣧⣴⣿⣧⣌⡛⢡⣼⡿⠿⠟⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢃⠀⠀⢸⠸⣀⣴⣦⡀⠈⢳⠘⣷⣼⡝⠁⡰⠃⡼⢿⣿⣏⠁⠀⠀⠀⠉⠛⠿⣿⣥⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠈⡆⠀⣼⡄⢻⣿⣿⡇⠀⠀⢇⣹⣟⡠⠊⠀⠈⢀⣾⣿⣿⣿⡆⠀⠀⠀⠀⣴⡯⣠⣄⠀⢰⣿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠘⠄⣿⡇⠀⠙⠢⠤⠤⢤⣾⣿⠋⠀⠀⣀⣀⣼⣀⠻⠿⠟⠁⠀⢀⣠⣾⡀⠀⠘⠛⢀⣾⢷⡤⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⢿⡇⠀⡀⢰⣏⢳⠀⠀⠀⠀⢠⣾⣿⡏⠀⠀⠘⠛⠁⣠⣼⣿⡋⠙⢻⠉⠁⢸⣏⣿⣷⡀⢀⡾⠋⠀⢱⠈⣷⡄⠀⠀ ⠀⠀⠀⠀⣼⠗⠊⠀⣼⣯⢾⡀⠀⠀⠀⠘⣿⠋⠁⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠿⠇⠀⠸⣿⣿⣿⡵⠋⠀⣠⣒⡻⢟⡼⢹⢦⡀ ⠀⠀⣠⡾⠋⠀⠀⣼⡿⡇⠸⣧⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠔⢉⢀⠀⠈⣷⠛⡆⠈ ⣠⡾⠋⠀⠀⠀⡼⠋⡰⢀⡇⢸⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣰⣦⠞⠙⡆⠘⠀ ⠋⠀⠀⠀⢀⠞⠀⢰⡷⠛⠇⢸⡽⡄⠀⠀⠀⠀⢤⣤⡤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⡇⠉⣿⢻⠀⠀⣇⠀⡰ ⣇⠀⠀⠀⠘⢆⠐⠋⠀⠀⡀⡌⢡⠸⢆⠀⠀⠀⠀⡤⠅⣉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢩⡇⠀⡇⢰⠉⢸⡀⠀⢸⡔⠀ ⠙⢧⡀⠀⠀⠀⠑⠄⢀⣀⡟⠀⠘⣼⡈⠳⡄⠀⠀⠘⠦⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⣰⡟⠀⢰⠃⡌⢀⣿⣇⠠⠞⠀⠀ ⠀⠈⢷⣀⠀⠀⠀⠀⠀⠀⠉⠲⢼⡛⢉⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠀⠀⠀⢸⠃⠀⢸⣠⠥⠚⠉⠁⠀⠀⠀⠀ ⠀⠀⢈⣿⠿⠓⠒⠤⣀⠀⠀⠀⠀⠉⠺⢄⡈⣿⡛⠷⣄⣀⣀⣤⣴⡾⠟⠋⠁⠀⠀⠀⠀⢀⣏⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⢀⠎⠀⠈⡑⢄⠀⠀⠀⠀⠀⠉⠻⣏⢣⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⠾⠃⠀⠀⠈⠀⠀⠐⠀⠀⠱⣄⠀⠀⠀⠀⠀⠈⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠈⠻⠳⠤⣀⡀⠤⠖⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀

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⣀⣀⣀⣀⣠⣤⣤⣤⠶⠶⠶⢦⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⠛⠿⢭⣛⣉⠉⠉⠉⠉⠉⠉⠙⢿⡁⠀⠀⠉⠉⠉⠉⠛⣦⠤⠖⠒⠚⠛⠛⠛⠛⠛⢓⣶⠶⠖⠚⠉⢙⣁⣭⠭⠿⠛⠛⠛⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢽⣄⢀⣠⡴⠛⠉⠉⠉⠉⠻⡗⠚⢻⡇⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠤⢤⡶⠊⠉⠀⠹⡄⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠀⠀⠀⠀⢀⣤⣴⣾⣥⣶⡾⣷⣀⣀⣠⣴⣿⠥⠤⣄⣀⣀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢹⣄⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠟⠻⠯⠥⣄⣄⣿⠓⠛⡛⢉⣭⣤⣤⣤⠤⠴⠚⠛⠁⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⣿⡁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣧⣀⢉⡽⠛⠛⢳⣦⡄⠀ ⠀⠀⠀⠀⢰⡿⣄⡀⠀⠀⠀⠀⢉⣹⡿⢻⣿⠿⣿⣇⡉⣑⣦⣀⣀⣀⡤⠤⠤⣤⣤⡶⠶⠶⠶⠷⠶⢾⣉⠉⠉⠉⠙⡏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⢹⢻⣿⠇⠀⣴⣿⣿⣿⣿ ⠀⠀⠀⢠⡿⠀⠀⠉⠉⠙⠒⣶⡟⢉⣿⡿⠁⠀⢸⣿⠋⠉⣿⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡄⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢰⣿⣿⣿⣿⢻ ⠀⠀⠀⢸⡷⣦⣀⡀⠀⠀⠘⢿⣧⠞⢫⣷⣄⣠⠏⣸⠀⠀⡏⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡦⣄⡀⠀⠈⢦⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⣿⣿⣿⣾⣿⣴ ⠀⠀⠀⢸⣷⡇⠀⠉⠑⣶⠀⠀⠀⠀⠀⠉⠉⠀⠐⡇⠀⢸⡇⣠⠟⠀⠀⠀⠀⠀⣠⣾⣿⡟⢀⣽⣧⡹⣟⣷⡀⠀⠈⣧⠸⡄⠀⠀⠀⠀⢀⣀⣠⣼⣿⠃⠀⢀⡇⠻⣿⣿⠟⠛ ⠀⠀⠀⢸⡿⢷⣄⡀⢀⡇⠀⣀⣀⣀⣀⣀⣀⠀⢀⠇⠀⠈⢻⡟⠲⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟⢷⢸⣹⣷⠀⠀⠘⣆⣧⣠⢤⣶⣾⣿⣿⣷⣿⣿⠤⠴⠚⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⢸⣿⣦⣍⡛⠻⠃⡜⠉⠉⠀⠈⠉⢹⡆⢸⠀⠀⠀⠈⢧⡀⠀⠀⢀⡝⢉⣿⣿⣿⣿⣿⣅⡀⣸⢻⢿⣿⠀⠀⠀⢹⡿⢷⣾⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⢿⣿⣷⣶⣧⣄⣀⣀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠉⠑⠲⡞⠀⠀⣿⣿⣿⡿⠿⣿⣿⠇⣼⡾⣹⠀⠀⣀⠼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢶⣭⣛⣻⣿⣷⡾⢿⣿⣿⣿⣷⣿⡦⠤⣤⣤⣀⣀⣠⣼⡇⠀⠀⠹⣿⣿⣿⠀⡨⢏⣼⣿⣧⣧⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠻⢯⣉⠙⣷⣼⣿⣇⣳⣿⠈⢧⠀⠸⣄⡰⠋⠀⠀⣧⣄⡀⠀⠈⠻⠽⢯⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⢧⣬⣷⣶⣞⣁⣤⣤⣤⡵⠀⠉⠙⠒⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⣿⣿⢻⠿⢿⡟⢻⠿⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⣀⣦⣤⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⣖⡒⠉⠉⠉⠙⢧⠀⠀⠀⠙⣍⠉⠙⠛⢶⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡚⠉⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢳⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⠀⠀⠀ ⠀⠀⣀⣼⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⠀⠀⢿⡷⡆ ⠀⠀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⡾⠷⠤⢄⡀⠀⠀⠀⠀⣼⣷⠇ ⠀⢺⠋⠉⠀⠀⠀⠀⠀⠈⠉⠐⣲⣦⣤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣀⣤⣶⢿⡀⠀⠀⢠⠇⠀⠀ ⣤⣶⡄⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⢀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⡁⠤⠜⠛⠛⡇⠀⢠⠏⠀⠀⠀ ⢻⣛⣻⡀⠀⠀⠀⠀⠀⡼⠒⠂⠐⠒⣻⣗⣛⣇⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⣄⠀⠀⠀⠀⡰⠁⡠⠋⠀⠀⠀⠀ ⠀⠀⠀⠑⢦⡀⠀⠀⠀⢩⠉⠁⠉⠉⠁⠀⢀⠏⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠉⠒⠒⢊⡠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⠤⡀⠀⠑⠤⣀⣀⡠⠴⠋⠀⠀⠀⠶⠤⣤⠤⣤⠶⠆⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠋⠑⣲⡒⢶⡒⣶⢶⣶⣗⡛⣏⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠉⠉⢹⣡⣾⠯⠿⢻⠛⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢄⣀⣀⣀⣀⣨⠿⢿⣇⣀⣸⣀⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣄⣀⡠⠜⢧⣤⠟⠒⠒⠚⠻⠤⠼⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⣀⣀⡠⠔⠒⠒⠺⢤⡤⠖⠊⠉⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⠀⢀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠁⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠷⣽⣻⢿⣿⣶⣤⣄⡀⠀⠀⠀⠹⣿⣷⣄⢶⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⡶⣠⣾⣿⠏⠀⠀⠀⢀⣠⣤⣶⣿⡿⣟⣯⡾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⠈⠛⢷⣮⣟⠿⣿⣿⣿⣶⣦⣄⡘⢿⣿⡎⣿⣷⡹⣿⣿⣿⣿⣿⣿⢏⣾⡿⢱⣿⡿⢃⣠⣴⣶⣿⣿⣿⠿⣻⣽⡾⠛⠁⡎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳⣄⡉⠻⢿⣶⣝⡻⢿⣿⢟⣼⣷⣿⣿⣿⣿⣷⣽⣿⡿⢿⣿⣯⣾⣿⣿⣿⣿⣿⣧⡻⣿⡿⢟⣫⣶⡿⠟⢉⣠⡞⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡹⣿⣦⣀⠈⠛⢿⡷⣠⣛⠿⣿⣿⣏⣍⢿⣿⣿⡇⣿⣿⢸⣿⣾⡿⣩⣹⣿⣿⠿⣛⣄⢾⡿⠛⠁⣀⣴⣿⢏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠳⡜⢿⣿⣷⡄⠀⢘⠻⢿⣿⣮⣝⡺⢿⣷⡽⣿⣿⢻⡟⣿⣿⢯⣾⡿⢗⣫⣵⣿⡿⠟⡃⠀⢠⣾⣿⡿⢣⠞⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣆⠙⢦⣙⠿⢀⣰⣿⣷⡀⠈⣝⡻⢿⣷⣯⣓⢹⣿⢸⡇⣿⡏⣚⣽⣾⡿⢟⣫⠁⢀⣾⣿⣆⡀⠿⣋⡴⠋⣰⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡺⢿⣿⣿⣟⣷⣄⠘⠛⠛⠈⠛⠻⢼⣿⡟⢳⣿⡧⠿⠛⠁⠛⠛⠃⣀⣾⣹⣿⣿⡿⢗⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣷⣬⣛⠿⣮⣝⣻⣿⣓⡍⣷⢸⣿⣿⡇⢸⣿⣿⡇⣶⢩⣚⣿⣟⣫⣵⠿⣛⣥⣶⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⠻⢿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⡿⠟⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⢻⣝⡻⢿⣿⣿⣿⣿⡿⢟⣫⡟⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⡶⠄⠸⣿⣿⣄⡀⠀⠀⢀⣠⣿⣿⡇⠠⢶⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢸⣧⢠⡀⠀⠀⢀⡄⣼⡇⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⠃⠸⠁⠏⠹⠈⠇⠘⡇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠏⠀⠀⠀⣿⡄⢀⠀⠀⠀⠀⡀⢠⣿⠀⠀⠀⠹⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⢹⠇⢸⣷⣄⣠⣾⡇⠸⡟⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣆⠀⠀⠀ ⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⢸⢸⣿⣿⣿⣿⡇⡇⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⡜⠰⣿⣿⣿⣿⠆⢣⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠈⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡷⢠⣤⣤⡄⢾⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⣬⣉⣉⣥⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠋⠁⢀⠀⠐⠂⠀⠉⠀⠀⠀⠆⠀⠉⣒⣤⡀⠀⠀⠀ ⠀⠀⠀⣰⡟⠁⠒⠀⠀⠀⠐⠃⠀⡀⠁⢠⠀⠀⠀⠙⠛⠊⣽⡀⠀⠀ ⠀⠀⢰⢻⡅⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠰⣏⠠⣇⠀⠀ ⠀⢀⣸⣿⣷⣄⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠤⠒⣽⣧⡄ ⠀⠘⣿⡏⠀⠈⢉⣭⠍⡉⢩⣟⣍⣯⢍⡉⢁⢤⡤⣠⣖⠲⣷⢧⠀⠀ ⠀⢰⡪⠿⠛⠉⠿⢛⡪⡼⠷⠤⠬⠤⠦⠙⢛⢛⡃⠤⢈⣥⣤⠟⠀⠀ ⠀⠀⣩⠴⠶⢞⣉⣜⣚⣆⣢⣼⣥⣒⣂⣨⣀⣰⣤⡤⠜⠋⠐⢣⡀⠀ ⣠⣺⢭⣷⣶⣶⣒⣶⣒⣲⣖⣲⣒⣶⣒⣂⣈⣻⣉⣭⠿⠳⣖⠤⠇⠀ ⠀⠀⣾⣯⠉⠹⠉⠉⠙⠉⠉⠉⠉⠃⠀⠃⠘⠀⠀⠀⢸⣛⣿⡆⠀⠀ ⠀⠀⠘⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠂⠒⠂⠐⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣇⣼⡄ ⠀⠀⠀⠀⢿⠓⢶⣤⣴⣶⣿⣿⡿⠋⠉⣝⢷⡀ ⠀⠀⠀⠀⠈⢿⣿⡟⠁⠀⠮⢿⡇⠀⠀⠀⣸⣧⣒⣒⡒⠤ ⠀⠀⠀⠀⢀⣈⣿⣧⡀⠀⠀⣸⣿⣶⣶⣾⣿⣿⠷⠦⣘⠁ ⠀⠀⠀⢊⠥⢒⡺⣿⣿⣶⣾⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⢀⠈⠁⠀⠈⢻⣿⣿⣿⣿⡿⠿⠋⠀ ⠀⠀⠀⣿⡇⠀⢠⣶⣿⣿⣷⡄ ⠀⠀⠀⣿⣧⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⣿⣿⡿⣿⡿⠿⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣴⣿⣿⣭⣭⣭⣭⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣯⣧⣀⣀⣀⣀⣀⣤ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡟⠋⢁⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡿⠿⢀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣙⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣦⠀⣰⣶⣶⣶⣶⣦⡀⠀⣶⣶⡾⠀⣰⣶⣶⢲⣶⣶⡖⠀⣶⣶⡶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⣿⣿⣿⣇⣿⣿⡿⢿⣿⣿⡇⣸⣿⣿⠇⢠⣿⣿⡟⣼⣿⣿⠁⣸⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣠⣿⣿⡟⣸⣿⣿⠃⣸⣿⣿⢧⣿⣿⡟⠀⣼⣿⣿⢱⣿⣿⣧⣤⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡍⢠⣿⣿⣿⣾⣿⡿⠋⣼⣿⣿⠃⢰⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⣿⡏⢉⣿⣿⣿⣾⣿⣿⢿⣿⣿⠀⢰⣿⣿⡏⢀⣿⣿⡿⣸⣿⣿⠏⢹⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠁⠀⣾⣿⣿⣶⣾⣿⣿⢿⣿⣿⠇⢸⣿⣿⠀⢼⣿⣿⣷⣾⣿⣿⢃⣿⣿⡟⠀⣾⣿⣿⣀⣤⡴⠖⠊⠁ ⠀⠀⠀⣠⣿⠃⠀⢸⠿⠿⠿⠿⠿⠛⠁⡿⠿⡿⠀⠸⡿⣿⡇⠘⠿⣿⣿⡿⠟⢁⣼⣿⣿⣷⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠛⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢸⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠉⢛⡾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠲⢶⠀⠀⠀ ⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⠟⠀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⡇⠀⠀ ⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠿⢴⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠦⢤⡤⠞⠁⠀⠀ ⠀⢸⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠒⠶⢤⣤⣀⣀⠀⣀⣆⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⣿⣠⡤⠴⠶⠶⢦⣤⡀⠀⠀⠀⢠⡾⠟⠁⠀⠀⠀⠀⢰⡄⠉⠉⠛⠉⠙⠛⠿⠶⣶⢾⣿⠀⠀⠀⢠⣿⡷⠖⢺⣿⣿⣿⠿⠿⠯⠭⠭⠉⠁⠀⠀⠀⠀⠀ ⠀⣠⡿⠋⣡⡴⢶⠲⠦⣄⠈⠻⣦⠀⢠⠏⠀⢠⣶⠀⣠⡀⠀⣸⠇⠀⠀⣠⣶⣶⢦⣄⠀⠉⠛⣿⣄⣀⣠⡟⠁⢀⣴⠞⠋⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⢠⡞⠁⠀⠸⡇⠀⠈⢳⡄⢻⡆⢸⠀⠀⠈⠉⠀⠻⠃⣠⡟⠀⠀⠀⣿⣻⣿⠟⣻⠀⠀⣀⣤⡀⠉⠻⢦⣤⡾⠋⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀ ⣿⠃⣼⠀⣤⠀⢰⣷⠀⣶⡄⣷⠘⣷⠘⢧⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠘⠻⠷⠶⠋⠀⣾⣿⣭⣙⣧⠀⠀⠙⠳⣄⠀⢀⣴⠟⠁⠀⣠⡴⢒⣫⠭⠔⠒⠒⠒⠀ ⣿⠀⠸⣦⠉⠀⢀⣄⠀⠀⢠⡟⠀⣿⠀⠈⠳⣄⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠋⢁⣿⠀⠀⠀⠀⠘⢿⣟⠁⢀⡴⢟⡥⠞⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠈⠳⢤⣌⣋⣠⡴⠟⠀⠀⣿⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠹⣿⣯⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢀⣤⣄⠀⡶⠒⣦⣸⡇⠀⠀⠀⠀⠈⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣟⡦ ⣿⡄⢠⡞⠉⣷⣿⣀⣼⠇⠓⠒⠋⢸⡇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢿⡀⠀⢀⣼⣿⠟⠋⠁⠀⠀⠈⠉ ⢸⡇⠀⠛⠚⠉⠀⢀⣀⡀⢠⠴⠶⣼⣷⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⠀⢠⠞⠓⡆⣾⣉⣽⠛⠦⠴⠋⢿⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⣼⠇⢸⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⠀⠈⠳⠞⠁⠈⢉⣁⠀⣴⠖⠲⣼⣇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠺⠿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣿⠀⢸⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡆⠀⡖⠛⢳⡤⣏⣉⡄⢷⣶⣄⡉⠻⣄⡀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠈⢧⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣷⠀⠛⠒⠛⠁⠈⠁⠀⣀⣀⣰⠋⠀⣄⠙⢄⠀⠀⠈⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⠀⠀⠀⠈⠳⣝⣷⣄⣀⡀⠀⠀⠀ ⠀⠀⢹⣇⠀⠀⠀⠀⢠⡶⠛⢩⣍⠙⠲⢤⡽⣷⡈⠳⣄⣀⣼⠛⢿⣷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡟⢻⡝⢦⡀⠀⠀⠀⠈⠙⠓⠒⠒⠂⠀⠀ ⠀⠀⠀⢻⣆⠀⠀⢰⡏⠀⠀⠈⣋⠀⢀⡈⢷⠘⣧⠀⢄⣹⡟⠀⠀⠉⠛⠿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠠⢴⣲⣯⠿⠻⣷⡀⠙⠦⣌⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣦⠀⠘⣇⠻⠇⠈⠛⠁⠛⠃⢸⠀⢹⣧⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠚⠛⠉⠁⠀⠀⠀⠸⣷⡀⠀⠈⠓⠢⢤⣉⣙⣒⣒⣒⣀⣀⠀ ⠀⠀⠀⠀⠀⠙⢷⣄⠙⢦⡀⠀⢶⠆⠀⣠⠟⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠷⢤⣉⣛⣒⣒⣛⣡⡶⠟⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠈⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢤⡤⠶⠋⠁⠀⠀⠀⠉⠉⠉⠉⠉⠓⠒⠶⠾⠿⢦⣤⣀⠀ ⠀⠀⣸⠇⢸⡄⠀⢀⡾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠄ ⠀⠀⣿⠀⠀⣿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⣿⢀⡞⠁⠀⠀⠀⠀⠀⢠⡤⣤⣴⠷⣶⠞⠋⠉⠓⠒⢿⣚⡿⠛⠉⠙⠒⠒⢶⡶⠒⢦⡾⠃ ⠀⠀⣿⢸⡅⠀⠀⢀⢀⣾⠟⠉⢣⠀⠀⠀⡏⠀⠀⢀⣴⣶⣦⢹⣇⣴⣶⣦⠀⠀⠀⣷⠀⠀⢻⠀ ⠀⠀⣿⡀⠻⠶⣶⠟⣹⠥⡄⠀⡏⠀⠀⠀⣧⣠⣄⡘⠿⠿⠟⣸⡋⠿⠿⠟⠀⠀⣰⠏⠀⢀⡾⠀ ⠀⠀⢹⡇⠀⠀⢸⠑⡇⠀⣵⠘⣆⠀⠀⠸⣍⣿⣞⢛⣧⡴⠞⠉⢳⡦⠤⠖⠚⠉⢉⡿⠀⣾⠁⠀ ⠀⠀⣸⣧⣀⣤⣼⣇⠙⠒⠁⠀⢸⠀⠀⠀⠀⢸⠛⠯⣅⣀⡀⠀⠈⠙⢒⣲⣖⡋⠉⠀⠀⢻⠆⠀ ⠀⣼⠏⠉⠁⠀⠙⣿⡇⠀⢀⡤⠼⣧⠀⠀⠀⣼⠀⠀⠀⠈⣏⣩⠏⣏⣙⡏⠁⢠⠤⠤⣴⡏⠀⠀ ⠠⣿⠀⠀⠀⠀⠀⣿⣿⣆⠘⢆⢀⣸⠀⠀⠀⢿⣀⣀⣀⣀⣀⠀⠀⣹⠀⠀⠀⢸⠀⠀⢸⣷⠀⠀ ⠀⠈⠷⠤⣤⣤⡼⠋⢀⡿⢶⡀⠀⠹⣤⠊⠱⣌⠧⣄⣉⠀⠈⢱⣤⢏⡀⠀⠀⣀⡑⠖⢡⡟⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠀⣼⠁⠀⢷⡀⢀⣁⣦⠴⠋⠑⣤⡭⠿⠛⠿⢤⣾⣁⣀⣘⣦⡟⣀⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⢶⣿⣿⣿⣯⣙⣳⣟⣻⣿⣿⣶⣶⡞⣻⣭⠽⠿⠿⣿⡿⢿⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡇⠉⠙⡏⠀⠉⠉⠉⠉⠉⠉⣿⣖⣾⡏⠀⠀⠀⠉⠉⢹⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣷⣤⣄⣇⢀⣀⣀⣀⣀⣀⣀⣹⣷⣿⣁⣀⣀⣀⣀⣤⣼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡑⣜⣦⠹⣭⣉⣉⣩⠏⠀⠀⠀⠀⠙⢧⣄⢠⠼⠁⣸⣿⣷⣉⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡿⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⠧⣯⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⡼⠿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣏⠉⠉⠛⠒⢦⠀⠀⠀⢼⣄⣀⡀⠀⢉⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢤⣤⣤⠞⠀⠀⠀⠀⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⢤⣤⠤⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣖⣛⣋⡉⠁⠀⠀⢀⣿⠀⢀⣴⣿⠿⢯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠉⠉⠉⠉⠉⠉⠛⠓⠛⣿⢿⣷⣿⠿⠥⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣷⣾⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⢯⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣠⣤⣶⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⢰⣿⠿⠛⠛⢶⣄⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⣹⡿⠛⠛⠻⢷⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠀⢀⡴⠛⠁⠀⠀⣀⠀⠹⣦⡀⠘⣮⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⢀⣾⠟⠁⠀⠀⠀⠀⠈⠻⣿⡟⠛⠀⠀⠀⠀⠀⠀⣿⡟⣿⠏⠀⣰⠏⠀⠀⠀⠀⠀⣿⠀⠀⠈⣻⣆⠘⢷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⡟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣈⣻⣦⡀⠀⠀⠀⠀⠀⠘⣷⣿⠀⢰⠏⠀⠀⠀⠀⠀⠀⠛⠓⠲⠶⠃⠙⣦⠀⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⣼⡏⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠉⠛⢷⣄⡀⠀⠀⠀⠘⠛⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢻⣦⠀⠀⠀⠀ ⠀⢰⣿⡇⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣛⣿⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⣿⣧⡀⠀⠀ ⡇⠈⣿⠁⠀⠀⢠⡟⠉⠙⢿⡄⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⡿⣧⠀⠀ ⡇⢰⠇⠀⠀⠀⠸⣧⡤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣀⣠⣤⣤⣤⣤⣄⣉⡳⢦⣤⣀⡀⠀⠀⠀⢀⣠⠾⠃⠀⠀⠀⢷⡘⣧⠀ ⣿⣿⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⣠⠾⣯⠀⠀⠀⢻⣄⠀⢉⠙⠷⣤⣉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⣧⢽⠀ ⣿⡇⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⣾⠁⠀⠘⢷⣄⡀⢸⠉⠛⠛⠁⠀⠀⠙⠛⠶⣶⣒⠲⣦⡀⠀⠀⠀⠀⠀⢹⣼⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⣀⣀⣠⡾⠃⠀⢠⡏⢻⣆⠀⠀⢸⡏⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⢻⡄⠀⠀⠀⠀⠈⣿⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⣿⠷⠦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢹⡇ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⢸⡇ ⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇ ⢿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⠛⠚⠁⠀⠀⠀⢀⣸⣷⣄⡟⠉⠛⢶⡀⣿⠀⠀⠀⢸⡇ ⠸⡆⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢀⣀⡀⠀⡾⠁⠀⢹⡇⠀⠀⠀⢁⡏⠀⠀⠀⢸⡇ ⠀⣷⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⣾⠋⠉⠹⡾⠃⣀⣤⠼⠧⠤⠴⠖⠛⠁⠀⠀⠀⠈⣿ ⠀⠸⣆⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⢸⡇⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠈⠷⣾⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏ ⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣠⡶⠛⢷⣄⣰⠇⠀⠀⠀⢀⣠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⠀⠀⠀⣿⠘⣧⡀⠀⠀⠀⠀⠀⠀⠿⢶⣾⣉⣀⠀⠀⠈⠛⢀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀ ⠀⠀⠀⠀⢸⡆⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠉ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢧⣀⡀⠀ ⠀⠀⠀⠀⠰⠿⢿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⡟⣹⣿⣿⣿⣿⠣⢸⣿⣿⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠓ ⠀⠀⠀⠀⢀⡴⠋⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠏⠀⠀⣿⣿⠏⠀⣿⣿⣿⣿⠃⠈⢸⣿⡏⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⡇⠈⣿⣿⣿⣿⣿⣿⣿⠏⢻⠿⢤⣀⢀⣿⠋⠀⠀⣿⣿⣿⠃⠀⠀⢸⣿⣠⠴⢊⣁⢠⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀ ⠀⢠⡎⠀⠀⠀⢰⠁⢠⣿⣿⣿⣿⣿⣿⡿⣾⠿⢿⣷⣶⣿⣟⡶⣤⣼⣿⣿⠃⠀⠠⣴⣾⢿⣿⣿⣶⣶⢶⡿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀ ⡰⠁⠀⠀⠀⠀⠸⠀⢸⣿⣿⣿⣿⣿⣿⠇⠘⢦⡈⠫⠭⠛⢿⡝⣆⣸⣿⠃⠀⢀⣾⡟⢱⣿⣽⣻⣟⡿⠎⠀⢹⣿⣿⣿⣿⠀⡇⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⡄⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠉⠉⠛⠛⠙⠋⠙⠃⠀⠀⣿⢻⠄⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⢸⣿⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⢸⠇⢸⣿⣿⣿⡊⣆⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠸⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⢸⣿⣿⣿⣷⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⡏⠀⠀⠀⡇⠀⠀ ⠀⠀⢇⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⠻⣷⡟⣩⢆⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⡤⣾⠇⠀⠀⠀⠀⠀⠀⢀⡾⢻⣿⣿⣿⠇⠀⠀⠀⢱⠀⠀ ⠀⠀⠸⡀⠀⢸⠀⠀⠀⠀⠀⣿⡟⠀⢿⣼⢟⠌⣣⡀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⣠⣿⡾⡟⢹⣿⡿⠀⠀⠀⠀⠘⠀⠀ ⠀⢀⠀⢇⠀⠀⡇⠀⠀⠀⠀⣿⡇⠀⠸⡟⢲⣪⠞⣻⣦⡀⠀⠀⠐⠈⣉⣉⣉⠩⠍⠉⠀⠀⣠⣾⣿⣟⡽⠀⢸⣿⡇⠀⠀⠀⠀⠀⡀⠀ ⠀⢸⣶⠘⣆⠀⢰⠀⠀⠀⠀⢹⠇⠀⠀⢋⡔⢱⣮⡆⢵⡽⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠃⠀⣼⣿⠀⠀⠀⠀⠀⠀⡃⠀ ⠀⠀⢻⣆⠈⣆⠘⡆⠀⠀⠀⠸⠀⠀⠀⠸⣿⣝⡝⡹⣯⢞⣕⡩⢳⣄⣀⠀⠀⢀⣠⣶⠟⡡⡾⡫⡫⡟⠀⢰⠋⡟⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⢻⡆⠘⣧⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⣔⡵⡣⠊⡽⢻⣤⠜⡹⡋⣹⠞⣡⢾⣾⠋⡨⣻⠁⣠⠃⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⡾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡿⣼⣦⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠇⣿⠘⣷⡙⣷⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣵⣦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢠⡟⢀⣼⡇⠘⣿⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣶⣦⣤⡿⢋⣴⠋⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠈⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡆⠻⣦⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣾⡟⢻⣿⠷⣦⡀⠀⠀⠀⠀⢀⣶⡟⢹⣿⣏⣹⡿⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠙⠻⠾⢿⣶⣾⡷⣀⠀⠀⠐⡾⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⣶⢄⣀⠘⢿⡟⠁⡀⢀⣔⢷⣄⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣭⣤⣾⢷⣤⣛⣈⣥⣼⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠉⠀⠀⢉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠶⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⣠⣶⣦⡀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡾⣿⢿⣾⠟⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⢹⣿⠋⠉⢻⣧ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠛⠈⠛⣾⣿⣷⡆⠀⠀⠀⢸⣧⢹⡇⠀⠀⠀⠀⠀⠈⣿⡆⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⣘⣿⢸⣧⡀⠀⠀⠀⠀⠀⢻⣧⠀⣼⡏ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢠⣶⣿⣿⢼⣿⣿⣷⡄⠀⠀⠀⢸⣿⠀⣿⡇ ⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⢸⣯⠛⠈⠀⠀⠛⢸⡇⠀⠀⠀⠈⣿⣄⣿⠀ ⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⣿⣿⠀ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠁⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣿⣿⠀ ⠀⠘⠂⠀⠀⠀⠀⠀⠀⠠⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠰⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠀⠀⠀⠀⠸⠿⠂⠀⠀⠀⠺⠿⠿⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠩⠍⠩⠍⢩⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⡲⠑⢈⣨⠵⠊⠁⠀⠀⠀⠈⠲⢌⡻⣿⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠊⠈⠉⠉⣑⣀⣀⠀⠀⠀⠀⠀⡶⢄⡈⢻⣿⠟⠻⣄⠀⠀⠀ ⠀⠀⡐⡑⠁⢀⠏⢠⢞⠕⠚⠉⢻⣏⠀⠀⠀⠑⠀⢱⠀⠉⢇⠀⢹⣦⠀⠀ ⠀⠰⣼⠀⠀⠀⢰⡎⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠈⠘⡟⢿⡇⠀ ⠀⢷⡿⢰⠓⠀⠀⢣⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⢄⠄⠄⢣⣸⡿⠀ ⠘⣸⠁⠸⠔⢀⡀⠀⠳⠦⢤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⡆⠀⣿⣷⠂ ⠀⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣀⢀⠿⢿⣿⠀ ⠀⠸⡇⢀⠀⠀⡀⠀⠀⠀⠀⢄⠀⠀⠀⡄⠀⠀⠀⠀⢀⡞⢁⠄⠀⣼⡇⠀ ⠀⠀⠻⡌⢆⠰⡠⠐⠈⠀⣤⠜⠒⢢⠀⠀⠀⠢⠄⢀⣈⣄⢾⢴⡿⡟⠀⠀ ⠀⠀⠀⠹⣌⡿⢄⠀⠀⠀⠣⣄⢀⠶⠃⠀⢀⣀⣀⣤⣿⢿⣶⣯⠊⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢷⣝⡢⢔⡀⠈⠂⠤⠤⠀⢉⣹⠿⣫⣴⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣷⣦⣶⣶⣞⣛⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⣽⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⣦⣄⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠈⠙⢷⣄⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠇⠀⠀⠀⢀⣼⣿⣿⣿⠍⠉⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⣿⡋⠀⠀⠀⠀⢀⣠⣤⡾⠿⠃⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡇⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠹⣧⣤⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠖⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⣿⠁⠀⠀⠀⣀⣤⣴⣾⠟⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⠀⠀⠀⠙⠠⣶⠶⠟⠛⠉⠁⠀⠀⠀⣀⣀⣤⣤⣶⣶⣟⣛⠛⠉⠉⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠾⠟⠛⠋⠉⠉⠀⠀⠈⠉⠉⠛⠳⢦⣄⠀⢀⣿⡇⠀⠀⠀⠀⠀⢠⣿⠏⠀⢀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣵⡿⠋⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⣾⡇⢀⣀⣤⣶⣦ ⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⢿⣶⣾⠿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣧⠀⠀⠀⠀⣿⢿⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⠀⣤⡈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠘⣿⠳⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣿⡇⠀⠙⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋⠀⠀⠀⠀⢻⡄⠘⢷⡄⣿⠀⠀⠀⠀⠀⠀ ⢀⣴⣾⣿⣿⣿⡇⠀⠀⢰⡏⣿⠿⢿⣶⣦⣤⣤⣀⣀⣀⣀⣠⣤⣤⣴⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⡿⠟⣿⠁⠀⠀⣾⠀⣿⡀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡇⠀⢸⡇⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢀⣿⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⢸⡇⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢴⣖⢤⣀⣼⠛⡚⣳⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡃⢸⣿⡷⣯⠀⣟⢿⠀⠘⡌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢗⣬⡮⠃⠘⠩⠝⠃⠀⢀⠇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⢠⡆⡰⠒⡞⠀⡰⠃⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠡⣀⣀⠔⢱⡰⠁⠀⢠⠊⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⡸⠄⠤⠒⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠒⠒⠒⡟⠀⠀⠀⠀⡠⠊⠉⢲⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⡀⢀⣠⠃⠀⠀⠀⢰⠁⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠉⡸⠀⠀⠀⠀⢸⣀⠤⢄⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⢄⣀⠠⢇⠀⠀⠀⠀⠈⠁⠀⠀⠘⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡘⣄⠀⠀⢀⡴⠉⠉⠓⢤⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠤⠐⠊⠀⡏⠉⠻⡉⠉⠳⡄⢀⠌⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⡰⠁⠀⠀⡇⠀⢀⠕⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠓⠉⠁⠀⠀⡀⠀⠀⢀

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠚⠛⠉⠉⠙⠛⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⣰⠁⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀ ⣼⠇⡼⠁⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆ ⣿⢸⠁⠀⠀⠸⡿⠿⢿⣿⣿⣿⣿⠂⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⣿ ⣏⢿⠀⠀⠀⢀⡇⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⢸ ⢿⠈⠢⢤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣴⠀⠀⠀⠀⠀⠀⠀⣾ ⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀ ⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀ ⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⢤⣤⣀⣀⣤⣤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠁⠀⠁⠀⠁⣽⠟⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠈⣿⣿⠀⠉⠉⠉⠉⠋⢀ ⠀⠀⠀⠀⠰⣿⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡀⣴⣿⡏⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⠇⠀⣇⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⢠⣿⣿⣇⠀⠠⠚⠃⠀⠀⠀⠀⡏⠀⡾⢦⣀⣿⠀⠀⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀ ⠀⠉⣾⣿⠀⠀⠀⠀⣀⣼⠤⠒⠛⠉⠉⣱⣿⣿⣿⠀⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⠃⠀⢸⣿⡇⠀⣿⣿⣿⣿⡉⠉⠙⠓⠢⢤⣸⡆⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀ ⠀⢺⣿⠇⠀⠀⠀⠈⠀⡏⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⠀⡟⠀⠀⢸⣿⡇⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢯⠙⠢⠀⠀⠀⣿⣿⣷⠀⠀⠀ ⠀⣼⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⢀⣀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡏⡾⠀⠀⠀⣼⣿⣷⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣿⣿⢸⣇⠀⠀ ⣶⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣼⣼⠃⠀⠀⢀⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⣿⠈⢿⣄⣀ ⣿⣿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⠃⠀⠀⠀⢸⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⡆⠀⠀⠀⠈⣿⠀⠘⡿⣿ ⢻⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⡀⠀⠀⣼⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣼⣿⣯⣿⣿⣿⣿⣿⣧⣄⠀⠀⢹⣇⠀⠀⠀⠀⡏⠀⠀⢸⣿ ⣼⠇⠀⠀⠀⠀⠀⣠⣼⡾⢟⡟⠉⠁⢀⣠⣤⣤⣤⣿⣽⠻⢿⣿⣿⣿⣿⣧⠀⠀⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⣛⣯⣥⣤⣄⣀⠉⢛⠛⠳⢾⣿⡀⠀⠀⠀⠃⠀⠀⠘⣿ ⢹⠀⠀⠀⠀⠀⠛⢿⡽⡆⣸⠁⢀⣴⣿⢟⠙⣏⡉⢻⣿⣷⡄⠸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠁⣠⣾⣿⣛⣿⡛⣿⣿⣷⣌⢃⠀⢸⠸⡟⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⢸⡆⠓⡇⢠⣾⣿⡍⠁⠀⣽⡇⠈⠙⢿⣿⡄⢻⣿⣿⣿⣿⣆⠀⢹⡄⠀⠀⢸⣿⣿⣿⠇⢰⣿⡿⠀⠉⣿⡅⠛⢿⣿⣿⡾⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⢸⣿⣇⠀⠀⠀⣿⣿⠀⠀⠀⣿⡇⣸⣿⣿⣿⣿⣿⣆⢸⣿⡀⠀⢸⣿⣿⣿⡄⢸⣿⠀⠀⠀⣇⡇⠀⠀⠹⣿⡇⠸⡄⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⠀⠈⢿⣿⣀⠰⠖⠛⠟⠀⢠⣤⡟⣱⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡀⣼⣿⣿⣿⣧⠘⣿⣀⡴⠈⠿⠉⢢⡀⢰⡿⠁⠀⢣⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡈⠻⢿⣏⣀⣀⣀⣤⣴⣿⣶⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣾⣿⣤⣄⣀⣀⣀⣹⡟⣁⣠⣴⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠿⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⠋⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠃⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡽⢿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣇⠉⠉⠛⠲⠦⣄⣀⣀⣀⣀⡤⠶⠞⠛⠙⣿⣟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠐⠀⠒⠋⠙⠒⠒⠒⡶⠶⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠒⠚⠒⠂⠒⠒⠒⠒⠒⠀⠘⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⠽⠽⠿⢷⣒⠦⢄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡟⠀⠀⠀⠀⠈⢹⡛⢮⡻⣏⠙⢿⡿⠿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣸⠀⠀⠀⠀⠀⠀⠈⢧⣀⡙⡎⠳⣿⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣴⠾⠯⠤⠤⠤⠤⠤⠤⢤⣤⣤⠤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣞⣀⣏⣧⣄⣀⡈⠹⠖⠒⠛⠳⣍⣀⣀⡤⠤⠝⠛⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠛⠋⠉⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣀⡠⢤⠤⠖⠚⠛⢉⣉⠀⠀⠈⡇⠙⠋⠀⣀⣀⠤⠴⠒⠋⠉⡇⠀⠀⠀⣀⢀⡈⢧⠀ ⠀⠀⠀⠀⣠⣶⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠉⣉⠤⣶⣾⣠⠴⠚⠉⠉⠈⠳⣄⣠⡷⠖⠉⠉⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⣤⡿⢿⣿⣾⣿ ⠀⠀⣴⢿⡽⠋⠙⠒⠒⠒⠒⠒⠲⠤⠤⠤⠤⠀⠀⠤⠤⠤⠔⠒⠋⠉⣠⡤⠖⠋⣣⣤⡾⠛⠉⣀⣴⣶⣯⣖⣦⡀⠹⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢰⣿⣿⡿⣿⣿⠸ ⢠⡾⣩⡿⣡⣴⣶⣖⣒⣂⣤⣤⣤⣄⣄⣀⡠⢤⣀⠀⠀⠀⠀⣤⠖⡫⠑⠓⣦⣴⠟⣁⣀⣀⣴⣿⢿⣛⡉⠻⣷⣵⡀⢹⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⣿⣿⣧⣿⡽⠀ ⢸⣷⣿⣼⡟⠙⠻⠿⠿⡁⠀⢠⠾⠿⠿⠿⠿⠟⢛⡆⠀⠀⡼⠷⠶⠖⠛⠛⣿⠟⠉⠁⠀⣸⣿⣧⣾⣞⣯⠱⣾⣿⣇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⡀⠀⣿⣿⣿⣯⣿⡇⢰ ⣸⣦⣿⣿⠉⠉⠓⠒⠒⠚⠛⠓⠲⠶⠦⠤⠤⠤⢼⣷⠀⠀⡇⠀⠀⠀⠀⢸⡟⠀⠀⠀⢀⣿⡇⣦⢹⣷⢿⣀⢚⣻⡇⠀⠸⡄⠀⣀⣠⠤⠴⣞⣫⣯⠤⠖⠒⡿⣿⣻⣿⡏⠀⠘ ⣸⣻⣿⣿⣿⣽⠳⣶⣶⣦⣦⣤⣤⣤⣤⣤⠤⠄⣸⣿⠀⠀⢹⣤⣄⣤⣤⣾⡇⠀⠀⠀⢸⡟⣷⣿⣿⣿⠚⠛⢭⣿⡇⠀⢀⣏⠭⠽⠚⣛⣉⡥⠶⠒⠚⠛⠉⠁⠸⠿⠿⠀⠀⠀ ⢻⠠⢽⣿⡻⠿⣼⡿⣿⡿⣿⣿⣿⣿⣿⣿⡿⡀⣸⣿⠀⠀⠸⠿⡿⠿⠿⠋⡇⠀⠀⣠⣾⡇⡿⣋⣀⣏⢻⡦⢼⣾⠓⠋⣁⣴⠴⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⣿⣿⣾⣮⣯⣭⣿⣛⣻⣻⣿⠿⠿⠥⠼⢿⠛⣿⣧⣶⣶⣿⣥⣭⣉⡹⠽⠟⠋⠁⣸⡇⢧⢿⡏⢸⡆⢁⣼⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠙⠛⠓⠛⠿⠿⠿⠿⢿⣿⣾⣿⣿⣟⣿⣷⣖⣀⣀⣐⣀⣐⣒⣊⣉⣉⣁⣳⠘⢦⡣⠬⣵⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣻⣿⣿⠠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣭⠽⠿⣿⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡋⣷⠿⠀⢀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⢺⢦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠂⢀⢠⡌⢹⠀⢸⠀⠀⣀⣤⡴⠖⠒⠋⠉⠀⠀⠀⢸⡀⠙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡖⢺⣌⠉⢸⣿⣶⢾⡛⣿⣅⣿⣷⣶⠠⢤⡀⠀⠀⠀⢸⡇⠈⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⡟⢛⣿⣶⣾⣿⣿⡀⠸⣿⠟⠟⢿⡏⣦⣼⡆⠀⠀⢀⣸⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⢿⢹⡏⣉⠉⣻⣿⠈⣿⡶⠰⡷⢻⠏⠀⡇⣼⣴⣿⣿⣷⣶⣿⣿⣿⣿⣦⣿⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⡴⣶⡿⣏⣿⣿⣿⣿⣿⣿⡇⠁⠘⣻⡟⠘⣿⣧⣰⣷⣾⣼⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⢸⡟⣾⣷⣥⣠⣋⠻⢿⣿⡋⣿⢸⣇⣴⣾⡿⢄⢠⡿⣿⣿⣿⣿⣿⣿⠿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡷⡏⠃⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣼⡾⣟⣿⣿⢿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⣧⣦⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠀⠀⣸⣇⣹⣿⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⣿⣿⣿⠿⠛⠛⠋⠉⠁⠀⠀⠀⣿⠀⠀⣾⣏⠉⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡷⠾⠛⠙⠓⠾⢦⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⣶⣾⣿⣤⣤⠄⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣙⣿⣿⣿⣿⣶⡖⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣭⠟⠛⠿⣯⡈⢻⣿⣿⣧⡀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣀⣏⣦⢹⣿⣿⣿⣿⡯⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⠀⢉⣽⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⡿⠿⣿⣿⣿⣿⢿⣿⣯⣳⡀⠀⠀⠀⢹⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣿⣿⠿⣯⣽⣿⠘⣿⣿⣿⣿⣗⠄⠀⠈⠛⠻⣿⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⣿⡿⣿⠀⢿⣿⣿⣿⢿⠃⠀⠀⠀⠀⣇⣷⡸⡟⠶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⣾⠏⠀⣿⠀⢸⣿⠏⠙⢾⣄⠀⠀⠀⠀⡿⣿⣇⣧⠀⠀⠉⠳⢤⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢨⠘⠀⠀⣾⠀⢸⣿⣷⣄⣀⠙⢷⣤⣦⣠⡇⣿⡟⢻⠀⠀⠀⠀⠈⢻⠶⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⠀⠀⠀⣛⠀⢸⠉⠻⠿⣿⣶⣀⠙⢾⣿⠁⣿⣿⠘⣇⠀⠀⠀⠀⠈⣷⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⢹⡄⢸⠀⠀⠀⠨⣿⣿⣿⣾⣿⠘⣿⣿⠀⠋⠀⠀⠀⠀⠀⠛⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⢸⡇⠸⠄⠀⠀⣸⣿⣿⣿⣿⢃⣈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⢼⣿⣿⣿⣷⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢻⣧⣩⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣬⣿⣿⠃⠈⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣤⣶⣞⡛⠿⠭⣷⡦⢬⣟⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⣯⡙⠳⣍⠳⢍⡙⠲⠤⣍⠓⠦⣝⣮⣉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⢿⣷⣯⣷⣮⣿⣶⣽⠷⠶⠬⠿⠷⠟⠻⠟⠳⠿⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣁⣀⣈⣛⣷⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⣸⣯⣁⣤⣤⣀⠈⢧⠘⣆⢀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀ ⠀⢙⡟⡛⣿⣿⣿⢷⡾⠀⢿⣿⣏⣳⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⢀⡞⠸⠀⠉⠉⠁⠀⠀⣠⣼⣿⣿⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀ ⣼⡀⣀⡐⢦⢀⣀⠀⣴⣿⣿⡏⢿⣶⣟⣀⣀⣀⣀⣀⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣾⣿⣿⣿⣾⡻⠷⣝⣿⡌⠉⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣿⣿⡟⣿⣟⠻⣿⡿⢿⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⢿⣼⣿⣿⠿⣏⣹⡃⢹⣯⡿⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⣿⣿⢿⠹⣿⣇⠿⣾⣷⣼⠟⠁⠀⠀⠀⢀⣠⣴⣶⣾⣷⣶⣄⡀⠀⠀⠀⠀ ⠀⢿⣾⡟⢺⣧⣏⣿⡷⢻⠅⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀ ⠀⠀⠙⠛⠓⠛⠋⣡⣿⣬⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⣀⠄⠀⣀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠞⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠤⠤⠤⠤⠤⢄⣐⣄⣀⡞⠀⠀⠇⠀⢠⢃⡴⠋⠀⢀⡠⠤⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⢀⣀⠀⠀⠀⠀⠉⠛⢯⣉⣉⠑⠒⠺⡾⢄⣀⠔⠉⠀⠀⠀⠀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⣴⠾⢛⣛⣿⣿⣟⣶⣤⡀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠈⠑⠦⣤⡶⢛⣩⠼⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣠⡾⣫⠔⡪⠝⠛⠉⠉⠉⠛⠻⢿⣧⡀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠸⠻⣍⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣼⣯⠞⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠀⠈⢻⡉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣼⣟⠇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⡇⢳⠤⣀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⡼⢸⢀⡤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⢸⠀⢸⠒⠒⠤⠤⢀⣀⡀⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇⠀⡎⠀⢠⣀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢼⣿⠃⢎⠀⠀⠀⠀⠀⠀⠈⢹⡄⠀⠀ ⠀⠀⠀⠀⣠⠤⠤⡀⠀⠀⢧⠀⢻⣼⣸⣧⠀⠺⠿⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡄⢸⡀⣸⣀⣀⣀⣀⣀⣀⣀⣸⠃⠀⠀ ⠀⠀⠀⡞⠀⠀⠀⠘⡄⠀⠘⡆⠈⢿⣯⣿⡧⣀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⢁⡏⠛⠁⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀ ⢠⠔⠊⠳⢄⡀⠀⠰⠗⠉⠓⢿⡄⠈⠣⡙⢷⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⡰⢃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢨⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡜⢹⢦⡀⠈⠓⠿⣿⣳⣦⣤⣤⣤⠴⠖⠉⠀⠀⢀⣴⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠘⣤⠀⢀⡴⠁⢀⡽⠖⠒⠉⠀⣾⠀⠑⢦⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀ ⠀⠈⡏⠁⠀⠀⢀⡇⠀⠀⠀⣸⢸⠀⠀⠀⠈⠁⠒⠢⠤⠤⠤⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀ ⠀⠀⠹⣄⣀⠤⠊⢳⠖⠒⠉⢨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠸⡆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠲⡄⢱⡀⢣⡀⠀⠀⠀⠀⠀⠚⠉⠉⠙⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡼⠘⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢷⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢠⡃⠀⠈⠳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⡿⢿⣧⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣠⠏⠙⢦⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠴⠃⠀⠀⠳⠄⠙⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣀⢴⠟⠀⠀⢠⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠂⣀⠀⠀⠀⢠⡀⢀⣀⡀⠈⠙⠻⣶⣌⠻⣦⡙⢦⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢩⠀⣀⠀⠙⣧⠱⡀⠘⢿⣄⠑⢌⢦⡀⠀⠙⣿⡇⠈⢷⣄⠻⣆⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⡆⠀⣿⣆⡀⠘⣧⠑⡄⠈⣻⣦⠈⢢⢻⡄⠀⠈⢷⣤⠀⠻⡦⣿⡃⢀⡿⠖⠊⠉⠉⠑⠲⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣞⣷⠇⢰⣧⠀⢻⢿⣷⠀⠸⣆⠘⡄⠰⡙⡷⡀⠁⢻⣆⠀⠈⣟⢳⡀⢹⠹⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣯⣸⠀⢸⣿⡀⠘⡄⣹⣇⠀⢻⡀⢱⠀⠣⢱⣷⡀⠈⣿⡆⢀⣸⣿⣿⡀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠄⡉⠀⠸⣿⢧⠀⢹⣿⣿⡄⢸⣷⡌⣧⠘⠀⣇⢳⠀⢹⣿⠙⣿⠦⡏⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀ ⠀⠀⠀⠀⠀⢸⣿⡀⣿⠀⠀⢻⡎⣣⣶⢿⣿⡿⠿⣿⡯⣿⡆⠀⢸⡆⣇⢈⣿⠀⢸⣷⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠸⣿⡇⢿⣧⠀⠶⠿⡟⢿⣿⣿⣿⠀⣿⠀⢹⡇⠾⠾⠀⠛⠂⠸⡇⢼⡿⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣷⣼⣧⣁⠀⠀⠀⢸⣇⣉⣥⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠹⢿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠐⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⢤⡈⠁⢀⣀⣤⣤⡶⠂⠀⠀⠀⠀⠀⠀⣠⣞⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠹⣾⡯⠗⢋⡁⠀⠀⠀⠀⠀⠀⣠⠞⠉⠃⠀⠀⠀⠀⠀⠈⠑⢤⣄⣀⣀⣠⠖⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡉⠓⠊⠁⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣾⠀⠈⣷⠤⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⢀⣾⠃⠀⢰⣿⣾⣿⠟⠉⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠒⠊⠉⠉⠱⡄⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⣠⣾⡏⠀⢀⣾⣿⠟⠁⣀⣴⣾⡟ ⠀⠀⠀⠀⣠⠴⢤⡞⠉⠙⢶⠈⠑⢦⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡠⠞⠁⠀⠀⢀⣼⣿⣿⣇⠀⣸⣿⠃⢠⣾⣿⣿⡿⠁ ⠀⠀⢠⡎⣱⣀⡀⠈⠙⠗⡄⠙⣆⠀⠙⡎⠣⡀⠀⠀⠀⠀⣠⠞⢱⣇⠀⢰⣯⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣿⠃⣰⣿⣿⣿⡿⠁⠀ ⠀⠀⢸⡟⠉⢸⡇⠀⠀⠀⠈⠀⣿⡄⠀⠁⠀⡏⢆⢀⣴⣾⣿⢠⡸⣿⡄⣼⠏⢙⢆⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃⣰⣿⣿⣿⡿⠁⠀⢀ ⠀⠀⢘⠀⢿⠋⢱⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠳⠘⣿⣿⣿⣿⣸⢳⡈⣿⢿⡁⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⠃⠀⣰⣿ ⠀⠀⠀⠀⠠⢍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⣿⣿⡧⢰⡇⣸⠀⠁⢹⣿⣯⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⡏⣠⣾⣿⣿ ⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠈⠁⡌⠀⣴⣿⣿⡻⣿⣿⣿⣿⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⢀⡶⠁⣼⣿⣿⣿⣷⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⡜⢦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠀⢸⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣸⡇⠈⣣⠀⢀⣤⣶⣾⣿⣍⠉⠻⣿⣿⡇⠀⠀⡸⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⠀⠀⠀⠀⢼⠓⠠⢶⣿⣶⣿⣿⣿⣿⣿⣿⣷⡄⢻⣿⡇⠀⢰⠁⢸⣿⣿⣿⣿⣫⣾⣿⣿⠟⢸⡇⠸⢛⣩⣿⣿⣿⣿⣿⣿⣿⡿⣫

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢒⡞⠋⠉⠉⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⠀⠀⢀⣞⣀⡠⠤⠄⠒⠒⠠⢤⣉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣀⠴⠚⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⢀⠄⠀⠀⢠⠞⠁⠀⠀⠙⡤⢤⠖⠀⠁⠀⠐⠤⠤⣀⡀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⡎⠀⠀⣠⠋⠀⠀⠀⣴⠋⠀⡄⠀⠀⠀⠀⠀⠰⠞⠈⣏⠑⢦⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⡇⠀⢰⠃⠀⠀⢠⣾⣿⡀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠚⣁⣷⡀⠱⡀⠘⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣞⠀⠀⠀⡇⢀⠇⠀⠀⢠⢻⡿⠿⠋⣼⡏⢻⣦⡀⠀⠀⠀⠀⠀⠉⢩⡿⡄⢱⠀⣣⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⠉⠉⠑⢢⡀⡇⡜⠀⠀⢠⠇⠈⡇⢀⣼⠿⠒⠒⠛⢿⣦⣀⠀⠐⠒⠒⠦⠀⢰⡄⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⠀⣷⣷⠃⠀⢀⡎⠀⢐⡷⠊⠁⠀⣀⣀⠐⡄⠈⠛⠷⢶⣤⣤⣤⠀⣨⠿⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢆⠀⠀⠀⢀⠾⣿⠀⢀⣾⡇⠀⠘⣷⠀⢲⠟⠿⠟⠛⠁⠀⠀⠀⠸⠛⠛⣿⣴⠟⠀⢱⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠒⠒⠃⠀⠘⣀⡾⠻⡇⠀⠀⢹⠓⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⠀⠼⡿⢻⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⡇⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⡜⠁⠈⡆⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣣⠀⠀⠀⠸⡏⢢⣄⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⢠⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣧⣧⠀⠀⠀⣷⠀⠹⣿⣷⣦⣤⣾⣿⠟⠀⠀⢀⣼⡇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣉⣧⠀⠀⠟⢳⢄⡈⠻⢿⣿⣿⠙⢄⣀⣠⣾⡿⡇⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⠀⠀⠀⡷⢶⡉⠉⠀⢹⠀⠣⡀⢸⠸⠀⠈⠑⠒⠙⠃⠀⠀⠈⠛⣭⠛⡇⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⠲⣄⠈⢧⡀⠱⡀⠀⠀⠀⠀⢀⠾⣷⣄⣀⣀⡴⠃⢠⠇⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠳⣄⠉⠒⡿⢠⠦⠤⢴⡿⠧⢾⠷⠛⢧⠀⠀⣾⢰⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⠀⠈⢂⣴⢃⡞⠀⠀⢿⠁⠀⠈⢆⣀⣸⠂⠀⢿⠘⡄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⠀⠀⠙⢲⣿⡥⠊⣀⡀⠀⠘⠓⠔⠊⠉⠁⠀⢀⣤⠤⠧⢵⡄⠀⠀⣷⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠃⠀⠀⠀⠀⠈⠑⠢⠖⠛⠉⢠⣾⠔⠛⢄⠀⠀⠀⠀⣀⠀⢰⠚⡏⢠⠀⡨⠏⣑⣶⠏⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⠹⢤⣀⡀⠀⠀⠀⢀⣀⣀⣀⣴⠋⠠⠒⢊⡩⢷⡀⠀⠘⣏⣱⠨⡿⣀⡇⢠⢃⠜⢁⠘⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⣆⠀⠈⠡⠒⠉⣹⠀⠀⠀⠁⢰⣧⠀⠉⠉⣻⠒⠃⢰⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀ ⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠦⣀⠀⠻⠀⠀⢸⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠢⢄⣀⣀⣀⣀⡠⠤⠤⠔⣾⡏⢻⡄⠀⠀⠀⡵⠀⠀⠀⢮⣹⠆⠀⠈⢹⣆⠀⠀⠀⠣⣹⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣤⣀⣀⣠⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⡦⠤⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠴⢺⣦⡤⠴⠶⠶⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡰⢁⣀⡤⠀⠀⣀⠀⡴⢋⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠟⠁⣾⡶⠿⠛⢲⠎⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠘⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⢤⣀⡒⣾⣯⣽⠿⣖⠒⠒⠒⠒⣶⡶⢾⠛⠯⣌⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⢀⣿⣿⡁⠀⢣⠀⠱⡄⠀⣾⣿⡄⠀⠳⡀⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣾⣿⠙⢿⡄⠀⢣⠀⢸⣾⣿⠈⢿⣄⠀⠱⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⢩⣭⡟⠉⣿⡀⠈⢿⡄⠀⢣⡸⠀⣿⡄⠀⢻⡄⠀⢳⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⣼⠀⠀⠹⢷⣄⡈⣿⣀⣼⡁⠀⣈⡿⢦⣤⣿⠤⠞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢿⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡋⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠈⠳⡷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⡽⠋⠁⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠋⠉⠉⠉⠛⢷⣦⡀⠀⠀⠘⣯⠒⠢⠤⠤⢤⣤⡬⠿⠛⣀⣠⣴⡿⠟⠁⠉⠓⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠄⣈⣳⣄⣀⣴⣾⣥⣶⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀ ⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀ ⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀ ⠀⠀⠀⠈⠛⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⠶⠿⠟⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠀⣀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡠⠟⠀⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣀⠀⠀⠀⠀⢸⠀⠘⡿⠁⠀⠀⣠⠞⠁⠀⠉⠉⠓⠲⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⡎⢹⠉⡷⢤⠀⠀⠈⠳⣄⣀⡠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠸⠀⠃⡇⠸⣇⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠘⣦⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠘⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠘⡌⢷⡀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⠺⣧⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠹⣦⡀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠒⠦⠔⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣷⠀⢀⢠⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣤⠟⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠈⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠏⠙⠶⢤⣄⣀⡀⠀⠀⢀⣀⣠⡤⠞⠋⠁⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⠀⠀⠀⠀⠀⠈⠉⠉⡏⠉⠁⠀⠀⠀⠀⠀⢡⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣀⣀⣇⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⠔⠒⠉⠀⢈⣏⠀⠉⠑⠒⢄⣠⠏⠀⠀⠀⣤⣤⣤⣤⡤⣤⣶⣶⠀⣤⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠒⠋⠉⠙⠓⠒⠒⠛⠁⠀⠀⠀⠀⠙⣛⠉⠉⠉⠉⡛⡛⠁⠉⠉⠁

⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⢿⠉⠉⠉⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠸⠀⠀⣀⣀⣤⠤⠄⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣷⣦ ⠀⠀⢀⠷⣄⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢠⣾⣛⣉⡭⠤⠶⠒⠚⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿ ⠀⠀⠂⠠⡟⣯⣍⣛⠒⣒⣲⣶⡶⠶⠶⠚⠋⠉⠁⠀⠀⠀⢀⣀⣀⣀⣀⡀⠠⠤⠤⠠⠀⠀⠠⠤⠤⠴⠤⠤⠤⢤⣤⣀⣀⠀⠀⠀⠈⢻ ⠁⠀⠀⣀⣈⣻⣄⡈⠉⠉⠁⠀⣀⣠⡤⠴⠶⠒⠒⣒⣚⣭⠭⠤⠶⠖⠒⠒⠒⠂⠀⠀⠉⠉⠉⠛⠓⠒⠒⠲⠶⠦⢤⣤⣿⣿⣶⣄⠀⠋ ⠀⠀⡀⡇⠀⠃⠙⣍⡁⠀⠉⠉⣁⡠⠤⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠇⠀ ⠀⠀⠻⠇⠀⠀⣠⡇⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡿⠀⠀ ⠀⠀⠀⠀⣴⡞⠁⠙⣄⠀⠀⢀⣀⠤⠤⠒⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠻⠄⢀⣀ ⠀⠀⠀⠀⣿⠀⠀⢠⠏⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠙⣿⣿⣿⠷⣄⠀⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⣾⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠏⢀⣴⣿⡷⠀⣿⣿⡟⠀⠈⢣⠀⠀ ⠀⠀⠀⣾⠁⠀⣠⠿⣿⢦⠀⠀⠀⠀⠀⢀⣴⠟⠉⠐⢦⡈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢀⣴⠋⠁⠁⢀⢦⣿⣿⣦⣀⡀⠀⡇⠀ ⠀⢀⡔⠁⢀⡴⠃⠀⠘⣦⡇⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢳⣤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢀⠞⣼⣿⣿⣿⠁⠉⠓⠿⣄ ⠴⠋⢀⣀⣾⣦⡀⠀⣠⡟⣧⡀⠀⠀⣿⣿⣧⠀⢀⣠⠶⠋⠁⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠔⢁⣼⣿⣿⣿⣿⣄⠀⠀⠀⠈ ⠔⠉⠉⠀⠙⠿⣷⡾⠛⠉⠋⠀⠀⠀⠙⠿⠿⠚⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣴⣿⠟⠉⠛⠻⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡉⡷⢄⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⣴⣿⡟⠁⠀⠀⠀⠀⠈⢻⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀ ⠳⢤⣀⣀⡠⠔⠁⣇⠘⡄⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀ ⣆⠀⠀⠀⠀⠀⠀⠘⣆⠱⡄⠀⠈⠉⠉⠉⡻⢷⣶⣶⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀ ⠈⢣⠀⠀⠀⠀⠀⠀⠈⠑⠻⠦⠤⠤⢔⣫⣤⣶⣿⣿⣿⣿⣿⣿⠿⢿⣷⠀⠀⠀⠀⠀⠀⣸⠏⠀⢡⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀ ⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠫⣉⢛⣛⣛⣛⣛⣛⣓⣒⣚⡿⠟⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⢀⠁⠀⠀⢀⡴⠒⠒⠢⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠁⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⡴⠃⠀⠀⢐⠿⠿⠂⠀⠀⣿⠀⠀⢹⠿⣿⠿⠛⠒⠒⠉⠁⠀⠀⠀⠀⠀⢀⡠⠞⡟⣿⡟⢤⡀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣼ ⠀⠀⠀⠀⠀⢧⡀⠀⡠⢾⡝⠀⢠⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡚⠉⠀⠀⣹⡘⢷⡀⢻⡦⠀⠀⢿⠀⠀⠀⠀⠀⡰⠋⠀⢀⡾⢀ ⠧⣀⠀⠀⠀⠀⠉⠛⠚⠉⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠱⣄⡠⠖⠙⠛⢮⣻⣦⢱⡀⠀⡌⠀⢀⣠⠴⠋⠀⣀⣴⣯⠗⠋ ⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⣀⠊⢀⡤⠶⣆⠀⠻⡙⢻⣧⣠⠶⢋⣁⣀⣤⣶⣿⠋⠁⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⣆⠀⣀⣤⣴⣾⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⣩⣤⣶⣾⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠿⢛⣉⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣟⣛⣩⣤⣶⣿⣿⣿⣿⣿⣿⡿⠟⣻⠉⠁⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣟⣿⠿⠛⠉⡅⠀⠀⠻⣿⣶⣶⡶⠶⣶⣾⡃⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣶⣿⣿⣿⣿⠿⢻⣿⣯⡾⠛⢉⣤⣤⠀⢴⣿⠀⠀⠀⠈⣿⡡⠖⠛⠻⠛⡇⠀⠈⣧⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⡿⠛⠋⠉⠀⢀⣿⣿⠋⠀⣠⠋⣼⠋⠀⣼⡟⢷⠀⠀⠀⠸⢧⣀⣀⣠⠞⣀⣤⣤⣼⣧⡀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⢸⣿⡇⣀⣿⣯⣼⠃⠀⣼⡟⠀⣼⡇⠀⠀⣠⣤⣬⣯⣥⣾⣿⠟⠋⠙⡿⠻⠿⠛⠋⠀⠀⠀⠀⢀⡶⠒⠒⠒⢶ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢯⠉⠻⡏⠀⣼⡝⠀⣼⡾⠀⢠⣿⣿⠟⠛⠿⠿⠛⠛⢤⡀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡀⠀⠈⠛⠾⠤⠾⢋⡀⢀⣿⡟⠁⢰⡇⢴⣶⣶⠂⠸⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠘⡇⠀⠀⠀⠀⠀⠀⢿⣧⡾⠟⠀⠀⠈⠛⠊⠉⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠈⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠠⠤⠷⠦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣶⣶⠶⠶⢶⠶⢾⣿⠿⣯⣸⠀⣹⣷⣦⣄⣀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠈⢧⡀⠈⣷⣿⣿⡄⢸⠛⣇⠳⣼⣆⠉⠛⠿⢦⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠈⢻⠇⣿⠀⢹⣿⣿⣆⠘⣆⣸⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣷⠀⠙⢦⣸⠀⢸⣿⠀⠹⡆⠘⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠘⣿⡆⠀⠀⠻⣧⠘⣿⡄⠀⢻⠀⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡠⢤⠖⠒⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠕⠁⣞⣯⡆⢁⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠞⠊⠀⠀⠹⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠙⠸⠀⠀⠀⠀⢀⣼⡇⢀⡀⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⠀⠀⡀⣀⢴⣿⡟⢁⠜⠀⠘⢖⣇⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢖⣩⣾⣿⡻⡯⢺⠈⠀⠀⠀⠀⠈⠘⠚⠼⢜⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠭⣾⠤⢼⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢤⠀⠀⠀⢀⡠⣾⠿⠷ ⠀⠀⠀⠀⠀⣜⡻⢓⣤⡠⠒⡡⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣲⣠⡐⡜⣽⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠡⣿⡟⢧⡀⠐⢄⠀⠀⢠⠏⠀⠀⠀⠀⠀⠉⠓⢉⢜⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢳⡀⠀⠑⠠⠃⠀⠀⠀⣠⣂⣀⠠⠔⡡⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠄⣀⣑⣦⣄⠀⠈⡦⠐⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡏⠀⠎⢀⣼⠙⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠹⠤⠜⢰⣏⣣⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡻⠁⢂⠤⠄⠒⠊⠥⢖⡶⡒⠒⠒⠒⠖⠒⠚⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢕⠧⡫⠔⠀⠉⢩⡙⠀⣀⣈⠻⣢⡀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⡾⠁⠉⠊⠀⠀⠀⠀⠀⠈⠑⢄⠑⢾⣖⣷⠀⡃⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⢤⡮⡪⠈⠀⠀⠀⢤⣤⠤⣄⣀⠀⠀⠀⠡⠡⢣⠠⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢾⣕⠊⠀⠤⣐⣾⣿⣟⠋⠙⢛⡻⢿⠶⣄⠀⠀⣾⠀⠀⠁⠀⠀⠀⠀ ⠁⠀⠀⠀⠈⠫⡣⡀⠡⠈⠑⠁⢀⡈⠄⡁⢀⣤⣡⡇⢵⡇⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠕⡒⠄⠐⢄⣐⠾⠁⢳⠆⠛⢉⢸⠀⣛⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣟⣄⠆⣀⠀⠀⠀⡀⠄⠀⠀⢀⢮⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⢺⢆⢠⡀⠀⠀⢀⢔⣵⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣋⢶⡚⠫⡖⢷⣿⣶⣕⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣧⡉⠀⠀⢀⣼⣿⣿⣿⣮⣿⡄⠀⠀⠀⠀⠀⢰⠂⠀ ⠀⠀⠀⠀⠀⠀⢘⢮⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠉⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢋⡆⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⢀⣀⠀⠀⠀⣠⣄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⠘⣿⠀⠀⡀⠻⠟⠀⢀⣾⣳⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢄⣀⣨⣅⣀⣤⠴⣾⣵⣻⣿⣷⣆⠀⠀⠀⠀⠀ ⡖⠶⠶⠖⠒⠒⠲⠾⠶⠶⠖⠒⠶⠿⡎⢿⢹⣿⣿⣇⠀⠀⠀⠀ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⢸⣿⣿⣿⡀⠀⠀⠀ ⢸⠀⠀⠀⠀⡆⠀⠀⠢⠀⠀⠀⠀⠀⣿⢯⢾⠻⠽⠷⠿⢻⣄⡀ ⠘⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⢻⢬⣾⠀⠀⠀⠀⣾⣷⣵ ⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡽⠿⣀⠀⠀⢠⣹⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⠚⠛⠛⠲⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠙⠳⣄⠀⠀⠀ ⠀⠀⢀⡾⠁⠀⠀⣴⢿⣿⣿⣿⣦⡀⠀⠀⣠⡞⣹⣿⣿⣿⣷⡀⠈⢳⣤⡀ ⠀⢀⡾⠁⠀⠀⣼⠃⣾⣿⣿⣿⣿⣿⡀⢠⡏⠀⣿⣿⣿⣿⣿⣿⡄⠀⠹⡄ ⠀⣼⠁⠀⠀⠀⡟⠀⢻⣿⣿⣿⣿⣿⡇⠸⡇⠰⣿⣿⣿⣿⣿⣿⠇⠀⠀⣷ ⢠⡇⠀⠀⠀⠀⢿⡀⠸⣿⣿⣿⣿⡿⠁⠀⠹⣦⣿⣿⣿⣿⡿⢋⢀⠄⠀⣿ ⢸⡇⠎⡤⡜⡼⣀⠙⠳⠿⠿⠿⠛⢠⣀⣄⣦⠀⠉⠉⠉⠁⠰⣟⡟⠏⢠⡟ ⠸⣇⠀⠙⠰⠓⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⣼⠁ ⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀ ⠀⠀⠘⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀ ⠀⠀⠀⠈⠻⢷⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣴⠲⠿⠷⣦⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⣷⣿⠀⠀⠀⣿⣿⠀⠉⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠛⠋⠀⠀⠀⠉⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣧⠀⠀⠀⣀⣀⣀⣀⡀⠀⣾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡸⣷⣚⡉⠉⠉⠉⣽⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠤⠤⡜⠛⠿⢿⣿⠏⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠈⣿⠀ ⢀⣠⣤⣤⣤⣤⣤⣴⣿⠀⠀⠀⠀⠀⢀⣶⠶⠶⣦⡀⠈⣹⢟⣁⠀⠀⢄⠀⠀⢣⠀⣠⣶⣜⣧⡀⠀⢰⡟⠁⠀⢸⡇⠀⠀⠀⠀⠀⢻⠀ ⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⣷⣰⡏⠚⣛⣷⡀⢸⠀⠀⢸⣠⣯⠭⠉⢼⣷⣶⣾⡇⠀⠀⣸⣇⣀⣀⣀⠀⠀⢸⠀ ⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣿⠀⠀⢠⣿⣿⣷⣄⣠⣶⠋⠁⠀⠀⠀⠉⣙⣷⣶⣿⣿⣿⣿⣷⠀⠀⢹⡿⠯⢍⡉⠛⢷⣾⠀ ⠀⠀⠙⢿⣷⣤⡀⠀⣴⠟⠉⢀⠴⠚⣩⠟⠀⠀⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⡆⠀⠙⡄⠀⢹⡇ ⠀⠀⠀⠀⠉⠻⢿⣿⡏⠀⢀⠇⠀⢰⠁⠀⠀⠀⠀⠀⠀⢻⡏⢛⠉⠉⠉⠉⢿⠉⠉⠀⠀⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⡇⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠸⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⢀⣿⣄⠀⠀⠀⠀⠀⢠⠃⠀⣰⠃⣠⣾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⠻⣄⠀⢣⡀⠀⠀⠀⢀⣠⣿⣦⣼⣄⣀⣀⣀⣸⣀⣀⣠⣴⣾⣿⣿⣿⣷⣶⣶⣤⣴⣧⣴⡾⠷⠞⠋⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠛⠻⠿⠾⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡾⠧⣄⡀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⣀⡤⢿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⣼⠃⠀⠀⠉⠓⠦⣤⣀⡀⠀⠈⠉⠛⠛⠋⢁⣀⣠⠴⠖⠋⠁⠀⠘⣧⠀⠀⠀⠀⠀⠀⢠⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⡀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣀⣴⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠈⠙⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠀⣀⠀⣼⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⢀⣠⡦⠖⠀⠀⠀⠀⢠⠏⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡴⠭⠤⠴⠛⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠴⠚⢳⣤⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⠀⠈⠘⠋⠙⠒⢴⠒⠚⠓⢶⡤⠤⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀ ⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠴⠋⢹⠀⠀⠀ ⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⢠⣨⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⡇⠀⠀ ⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⣄⣇⠀⠀⡈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣨⣿⣷⠄⠀⠀⠀⢠⠇⠀⠀⠀⢀⡿⡄⠀ ⠀⠀⣧⠈⠓⢤⣀⣀⠴⠞⠁⠀⠀⠀⠈⠻⣧⡀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠉⠀⠀⠀⢀⡞⠀⠀⠀⢀⡾⠀⠹⡄ ⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠙⢦⣀⠀⠀⠀⠙⠛⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠖⠲⠤⣤⠞⠁⠀⠀⡇ ⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡀⠀⠈⠓⢦⣄⣀⣀⣀⣀⣀⣀⣀⣠⡴⠒⠒⠒⢺⠟⠀⠀⠀⠀⠀⠻⠄⠀⠀⡇ ⠀⠀⠀⠀⠀⠈⠓⠦⠤⣄⣀⣀⡤⠔⠊⠁⠀⠙⠢⢤⣠⠞⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⣀⣠⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⢷⣀⡀⠀⠀⠀⣀⡤⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠉⠉⠁⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡴⠶⠒⠦⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⢶⡿⡯⣿⣿⣷⣤⣄⠒⠶⣾⣧⡀⠈⠙⣦⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡴⠞⠻⠁⡴⣶⠿⠉⣡⠬⠋⠀⠙⢸⣿⢷⠞⠉⠉⡶⢤⡼⣽⣶⡌⢻⣤⠤⢤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⢾⣿⣿⡷⡖⠒⡤⠾⣡⠶⣻⠿⢀⡤⠶⠏⠉⠿⢄⠀⠀⠀⠛⣳⣤⠀⢹⠟⠖⠃⠐⢦⠙⣦⡀⠀⠀⠀ ⠀⠀⣴⣿⠏⢋⡘⠀⣀⡰⠧⠄⠈⠀⠻⡲⢟⣧⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠉⠀⠋⠑⡦⢤⣐⡻⠗⢣⠙⣇⠀⠀ ⠀⣸⡇⢠⠆⢻⡤⠟⠉⢰⠆⠀⠀⢠⠔⠀⠘⢧⣀⠄⠀⢀⡀⠈⠀⠘⠉⣷⣄⠀⠀⠘⢱⣟⡉⠋⡦⣬⠿⠛⢷⠀ ⣴⣿⣿⣿⢷⡇⠀⠀⠀⠙⠦⠄⣠⠌⠓⠒⣲⣿⡁⠠⣞⠙⠉⡋⢹⢶⡤⠀⠛⠲⣭⢷⣦⠈⠛⢦⣀⡸⣋⣦⣼⠇ ⢻⣿⡦⢴⠋⣳⡤⠀⠀⣼⡇⢠⣿⠄⢠⡾⣁⠈⠳⢂⡈⠉⢙⡉⠉⠲⡤⣀⣀⡠⠏⠉⠛⣦⡶⠚⢤⡤⣿⡟⣷⠀ ⠘⢷⣶⣿⣾⠛⠛⠋⠀⠉⠉⢀⡄⢀⡁⢀⣽⣿⡿⢻⢷⣶⣾⣧⣤⣴⣇⣀⡝⠀⠀⡀⠀⣻⠀⣀⠒⠃⢿⣿⠏⠀ ⠀⠀⠙⠧⡼⠗⢏⠀⣀⠀⠀⠀⢙⡛⠉⠉⣿⣿⣷⠀⣼⡌⡇⠙⣿⣷⠞⠉⠀⠀⠀⠈⠋⣁⣰⠟⠀⢹⠉⠀⠀⠀ ⠀⠀⠀⠀⠙⠦⣈⣉⣉⠉⠀⠀⠀⠓⠦⠈⠙⢹⣿⣿⣿⡇⡇⢸⣿⠇⠀⠐⠤⠶⠴⠃⠀⢠⣄⣀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠴⠺⣄⡀⢀⣠⣸⣿⣿⠀⡇⣇⣾⢸⣄⡀⠀⠀⣠⣄⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⣿⣿⡀⡇⣿⣯⢸⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠈⠁⠃⢿⣿⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣞⣟⢸⣼⣆⠀⣾⣿⣿⡷⣓⣦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣼⣿⣿⡿⠾⣿⠿⣶⠿⢿⡿⡷⠀⠛⣦⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣈⣿⡹⠿⡟⠀⠀⠀⠈⣱⡄⠀⣼⠆⠸⠟⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢍⣿⣦⣝⢶⣌⣳⣞⣁⡙⢒⣿⣶⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣷⣿⣷⡶⣶⣤⣈⣴⣿⣻⣿⣿⣿⠷⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⢿⣿⣾⣿⣷⡾⢿⣿⣿⣏⣻⣿⣿⣿⡿⠿⣷⡞⠷⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣿⠿⣿⠿⣿⣿⠏⠐⠻⢹⣟⣭⣍⡿⡿⠿⣷⣤⠞⠓⢶⠟⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠛⠛⠂⠀⠘⠀⠘⠁⠁⠀⠀⠀⠁⠀⠀⠸⠓⠋⠀⠻⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠲⠤⢬⣙⣒⠲⠤⣄⣀⡀⠀⠀⠀⠀⠐⠀⠀⠀⣸⠀⠀⠀⣰⠃⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣀⣀⡬⠽⠗⠲⠤⣍⣉⠒⠦⢤⡄⠀⢰⠂⡇⠀⠀⠀⠹⢠⢻⠀⠀⠀⠀⠀⡜⠀⢀⣶⠖⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⣌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢾⡇⢀⣿⢰⡧⣄⣀⢀⡇⡎⢸⠀⠀⠀⠀⢰⠃⠴⡿⠋⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡞⢹⡟⠳⠤⣍⣿⢻⣧⡾⠀⠀⠀⠀⡌⠀⠀⠘⣠⠟⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣇⠈⣧⣀⠀⠀⠀⠤ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡎⣸⠁⣿⠁⠀⠀⠀⡿⣾⣿⡇⠀⠀⠀⢰⡟⠉⠉⣩⠏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠙⣦⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣮⣤⣤⣶⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣾⣷⣀⡀⠀⠀⣧⠋⢿⡇⠀⠀⠀⣸⣧⡤⠖⠁⢀⡼⡇⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⢀⣼⣷⣼⣷⣶⣶⡟ ⠀⠀⠀⠀⠀⠀⢰⡋⠉⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⠋⠛⠿⢷⣶⣿⡀⢈⡇⠀⠀⢀⣿⣿⣷⡄⠰⠋⠑⢣⠀⡀⠀⠀⠀⠀⠀⢸⠄⠒⠉⢨⠁⣽⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢼⣿⣿⣶⡅⠀⠀⣸⣿⣾⣿⣿⣦⠀⠀⢸⠀⡇⠀⠀⠀⢰⡄⢸⠀⠀⠀⣨⡾⢻⣯⡿⠋⠀ ⠀⠀⢀⡆⠀⣸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⠁⠙⠻⡇⠀⠀⣿⡻⣏⠉⠈⢿⣇⠀⠘⡄⣿⠀⠀⠀⢸⣧⠘⡆⣠⡾⠋⣠⣿⡏⠀⠀⠀ ⠀⠀⡼⡇⢀⠇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠉⠇⠈⠳⢤⡘⣿⡆⠀⡇⢻⡀⠀⠀⢸⡿⡀⡇⠉⣠⠞⣡⠏⠀⠀⠀⠀ ⠀⢰⠃⡇⣸⣄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣀⣤⡇⠀⡘⠀⠀⠀⠀⠀⠉⠻⣷⠀⢹⡆⡇⠀⠀⢸⡇⣇⡇⠈⢁⠜⠁⠀⠀⠀⠀⠀ ⢀⠇⢰⢣⠇⠀⠓⢦⣀⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣠⡤⠴⠖⠚⣙⣽⣠⡼⢧⠀⡇⠀⠀⠳⢤⣠⣤⡀⠙⠀⢸⡇⢹⠀⠀⠸⡇⠸⣷⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⡜⠀⣸⡞⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⢻⠻⠛⠛⠛⠛⠉⢉⣩⣥⢔⣾⡿⢾⣞⣯⠽⠛⠉⠀⢸⠀⡇⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠘⡆⠀⠀⡇⠀⢻⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⣿⠁⠀⠀⠀⠲⢤⣀⡀⠀⠀⠀⠀⠹⠿⣿⣶⣶⣤⣶⡿⠿⠿⠟⠛⠚⠉⠁⠀⠀⠀⠀⠀⠸⣶⠁⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⢳⠀⠀⡇⠀⠈⠃⠀⢠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣿⡯⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⡄⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠟⢟⣾⠟⠙⠂⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠚⠉⠁⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠼⠷⠦⠤⠤⠀⠈⠉⠃⠉⠙⠟⠻⠀⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⣭⣯⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢾⣋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣞⣏⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣮⡥⢦⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⢠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢲⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣾⡇⣀⢰⠃⠀⠀⠀⠀⣠⣠⡄⠀⣰⣀⠀⠀⠀⢰⡆⠀⣄⡄⠀⠀⣄⠀⠀⡸⡀⢸⡆⠉⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀ ⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠖⢫⡿⢀⣟⡏⠀⢀⡄⠀⣰⡟⢹⡇⢠⠋⢿⣆⠀⢀⢸⡇⢠⣿⡇⢀⡟⣿⡷⡀⣷⣧⣸⣷⠀⠀⣀⣤⣴⣾⠋⠁⠀⠀⠀⠀⢀⣠ ⣿⡿⠁⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡏⣹⠁⣰⣿⠁⣸⡟⠀⣸⡇⣾⠤⠶⢿⡄⣿⣸⠁⣼⡟⠂⣿⣽⡇⡀⡇⡟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⡿⠟⠋ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣼⣁⣰⠟⣿⣶⡿⣟⠯⠽⣿⡻⢿⣿⣿⣿⣿⣿⢀⣿⣿⣴⢯⣿⣿⣿⡇⣇⣿⠟⠋⠉⠉⠉⠉⠙⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⢿⣿⣿⠟⡇⢀⣠⣼⡅⠉⠓⠛⠉⠁⠙⢹⡟⠈⠿⠟⠾⣿⣼⣿⡃⢻⡟⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⠁⠀⠀⠀⠀⠀ ⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣾⣿⡸⣽⣯⠀⡇⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣿⡿⣿⣿⣾⠇⠀⢀⣤⣶⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⣧⣿⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⢹⡟⢿⣤⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣿⣿⡟⠲⢴⡚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⣾⠁⠸⣿⣿⣿⣿⡿⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⣾⣿⡿⠛⠋⠀⠙⣄⠀⢭⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⢿⣯⠀⢸⠏⠀⠘⣿⠛⢻⣿⣶⣼⣁⣀⣀⠀⠀⠀⠀⠀⣀⣤⡞ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡁⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠘⢦⠀⠙⠻⠵⠶⠖⠀⠀⢀⣴⣿⣿⣿⣾⡟⠀⠈⠀⠀⠀⢿⡀⣿⣿⣿⣿⡟⠛⠋⠀⠀⣀⣤⣾⣿⡟⠀ ⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⣾⣭⣧⡀⠀⠀⠀⠀⢠⣾⣯⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢸⣧⠨⡿⠿⣿⣿⣶⣶⣾⣿⡿⠿⢿⡟⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣷⣀⣀⣤⣾⡏⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣷⠸⣿⣿⣿⣿⡟⠁⠀⠀⠘⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡗⠛⠛⣿⣿⣿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⣦⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⠋⢿⡴⡾⣿⠟⠁⠀⣰⠂⠀⠀⠀⠹⡆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠤⠀ ⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡏⡆⠈⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢹⡴⢊⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣼⣷⣧⠈⠁⠀⠀⠀⣰⠇⠀⠀⠀⠀⢀⡤⣋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡞⠀⠀⠙⠦⢀⣀⣤⡤⠹⠷⠶⠾⡿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠖⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢻⣿⡿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⣠⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣷⣤⣤⠄⠀⢠⡆⠀⠀⣠⡴⠋⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣀⣴⣿⠁⣠⠞⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣯⣄⡥⣄⠀⡀⣱⣾⣿⣿⣿⣿⣆⠀⢻⣧⢠⡾⣰⡶⠆⣰⡶⠄⠶⣶⣶⡄ ⠀⠀⠀⠉⠀⠀⣰⣾⣿⡟⣿⠉⠿⢽⢱⠀⠀⢻⣿⠃⣿⠷⠆⣿⠷⠆⠀⣿⠃⠀ ⠀⠀⠀⠀⠀⣰⠟⢿⣿⣽⣦⠶⠦⣞⠝⠀⡀⠿⠃⠈⠛⠛⠂⠛⠻⠂⠸⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠜⣀⡓⠷⠚⠈⠉⠢⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡆⠀⠀⠀⢸⡿⡡⠀⠀⠀⠐⠠⡀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣴⣿⣿⣦⣀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠈⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⢄⠈⠀⠀⠀⠀⠀⠐⢲⡴⢤⠀⠀ ⠛⠉⠀⠀⠀⠀⠀⠈⠙⣿⣿⣧⠀⠀⠀⠀⠈⠾⠛⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣆⠀⣀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⠻⡄⠙⠃⠉⡹⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⢿⣿⣿⣿⣿⣿⣦⡇⠀⠀⡠⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣏⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠑⣴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠻⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡶⢸⣿⣿⣿⣿⣿⡏⣻⡈⠻⣿⢸⠙⡟⠛⠀⠼⣿⡇⠸⠿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡧⢸⠸⣻⣿⣿⢿⣿⣾⣿⣯⣉⠀⠀⠁⠀⠀⣠⣿⣿⣶⡧⣿⣿⡿⢻⣿⣿⣿⠐⢣⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⢰⡇⢻⣿⣟⠘⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⢸⣿⣇⠀⣿⣿⣿⠀⠀⢀⣀⠤⠤⠤⠄⢀⠀⠀ ⠀⠀⢀⡟⢢⠀⠸⠘⢼⣿⣿⡄⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⢸⣿⣏⣴⣿⣿⣿⣆⠔⠉⠀⠀⠀⠀⠀⠀⠀⢄ ⠀⠀⠀⠹⠇⠀⡇⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⣾⡏⢹⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⠀⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢀⣾⣿⣿⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢀⣠⢶⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⢹⣿⣿⣿⣿⣿⣿⢿⣶⣤⣤⣶⠟⠁⢸⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠀⢧⠇⡇⣼⡏⣿⣿⣿⣿⢿⠈⠫⡉⠛⠁⣀⠔⠁⠈⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠞⠀⡼⣸⠁⣿⢃⣿⣿⡛⠁⣇⠀⠀⠈⢳⡊⠁⠀⠀⢠⢃⡏⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⢰⠁⣹⡠⠟⠉⠘⣜⢧⠀⢻⡀⠀⣠⣿⣷⡄⠀⣠⣇⣼⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⡀⠀⢀⠇⡰⠋⠀⠀⠀⠀⠈⠉⣷⢼⣝⡴⢻⣿⡿⠙⢴⡟⢋⠎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠺⠽⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢯⠀⢰⣿⡇⠀⣞⠀⡜⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⢡⣀⠤⠤⠠⠤⠤⢤⣄⣱⣈⣆⣿⣿⡇⡔⠀⡜⠁⠀⠀⠀⠀⠸⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣇⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣾⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠀⢿⣷⠀⠸⡄⠀⠀⠀⠀⢀⡞⠀⠀⣾⡟⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡆⠀⠉⠀⠀⠀⠀⠈⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠆⠀ ⠀⠈⠉⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⡶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠒⠢⠤⠤⣴⣴⠾⠿⠧⢤⡙⠟⠙⢧⡀⠀⠀⠀⢠⠞⠀⣿⣿⠿⠿⠿⠶⢖⣒⡛⠋⠀⠀⠀⠀⠀⠀⡀⠀ ⡀⠀⠀⠀⠀⠀⠘⢄⠀⡴⠋⢱⣶⠀⢀⣤⣾⠏⠀⠀⠀⠑⠀⠀⠀⣏⠀⠀⢫⡀⠀⠰⡿⠆⠀⠀⠈⢳⠖⠀⠀⠀⠀⠀⠣⠀ ⠀⠀⠀⡘⠲⣤⠀⠀⢻⢤⣤⡤⠶⠞⢛⣥⠏⢠⠖⠒⠦⠀⠀⠀⠀⢻⡤⢤⡈⢯⡻⢶⣦⡤⠤⠤⠒⡏⠀⣠⠔⡂⠀⠀⠀⠀ ⡄⠀⠀⠙⠂⠈⠁⠀⠨⠤⠤⠤⢴⡺⠟⠁⠀⢸⠀⣠⣤⣦⡀⠀⠀⠘⣧⠀⣷⣀⠙⠶⢄⣉⡉⠉⠁⠀⠘⠁⠚⠁⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⢡⣄⠠⣤⠀⠀⣀⣉⣿⣭⣳⡀⠀⠀⢸⣄⣀⠈⠛⠀⢶⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠻⠄⠀⠈⣀⣤⠶⢾⣟⠉⠁⢹⣿⠿⠶⣦⣤⡿⠛⠻⣶⣤⣤⣀⡀⠙⠒⣶⡄⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⠀⠑⢀⣠⡾⠿⢿⣧⣀⣼⣿⣷⣶⣿⣿⣿⣶⣿⣿⣷⣶⣾⣿⣇⡀⢸⣿⠿⢷⣤⣉⠀⠈⢻⣧⠄⠀⠀ ⠀⠀⠀⠀⣀⡤⠞⠈⣠⡶⠿⢿⣤⣠⣾⡟⠛⢻⣿⣁⣨⣿⣏⣀⣹⣿⣯⣉⣹⣿⡟⠙⢿⣿⢿⣦⡤⢼⣿⣷⡀⠀⠈⣷⠀⠀ ⠀⠀⣶⡶⠉⠀⢠⣾⣿⣀⣠⣿⣟⢉⣽⡷⠖⠛⠛⠉⠉⠉⠀⠀⠀⠈⠈⠉⠉⠉⠙⠛⠛⠷⠼⣿⣧⣴⣿⣿⡇⠀⠀⣸⡆⠀ ⠀⠀⣸⠁⠀⠀⣿⣿⣯⣤⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠀⢀⣠⡿⠀⠀ ⠀⠀⢻⠀⠀⠀⢿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠛⠛⠛⠛⠛⠓⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡄⠀ ⠀⣆⠘⢷⣄⡀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠠⠤⠞⠋⠀⠀ ⠀⠈⠉⠀⠉⠛⠛⠉⠀⢀⣠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠘⠦⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⣛⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⢇⡘⠷⠀⠀⠀⢀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⣤⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠟⠛⢉⠀⠀⠀⠀⣀⠀⠀⢀⣠⠔⠀ ⠀⠀⠰⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⡤⠴⠒⠚⠁⠀⠀⣀⣀⡭⠔⠒⠉⠀⠀⠀ ⠀⠀⠀⠀⠙⠒⠶⠀⠀⠒⠀⠀⢠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀

⣿⣿⡿⠟⠛⠻⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠁⣠⣶⣶⣶⣤⡀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡉⠉⠛⠻⢿⣿⣿ ⡇⢸⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡈⠙ ⡇⠸⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣧⠠⣈⠙⠛⠋⣁⡄⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⠀⣿⣿⣿⣿⣿⣿⣄⠢⠲⠀⣍⣒⠛⠷⣦⣍⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰ ⣿⡆⢸⣿⣿⣿⣿⣿⣏⣀⠀⠀⠀⣀⡙⠃⠀⠈⠉⠓⡿⣿⣛⠿⢿⣿⣿⡿⠀⣼ ⣿⣷⡀⠻⣿⣿⣿⣿⣿⣿⣿⣄⠸⠟⣡⣄⣠⣤⣤⣄⠈⠀⢝⣿⣦⠙⢿⠃⢰⣿ ⣿⣿⣧⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡰⣻⣌⣉⡉⠃⠈⢠⣿⣿ ⣿⣿⣿⣧⠀⢴⣶⣶⣶⣤⣤⣀⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣾⣿⣿ ⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣿⣿⣿⣶⣤⡉⠻⣿⣿⣿⣿⣿⡿⠃⣠⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⠟⠁⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⠻⣿⣿⣿⣿⡿⠛⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣉⣉⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⡿⠿⠛⠛⠛⣛⡓⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⢯⣷⣾⣆⠀⠀⠀⣀⣈⣿⣿⠆⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣀⣀⡐⠛⠿⠿⣿⣿⠟⠁⠀⠀⠀⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠛⠛⢻⣿⣿⣿⣿⣶⣶⠿⠤⢤⣤⣤⣴⡿⠈⢻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠛⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣯⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠴⠷⠶⠦⣤⣄⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣶⣾⣿⣶⣶⣦⠤⣤⣀⡀⠀⠀⠀⠀⣀⣤⣾⣯⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠙⠛⠻⠿⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣹⣿⣿⡿⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿⣿⣿⣇⣠⣶⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢰⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⣴⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣠⣾⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣴⣾⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠁⠀⠀⠀⠠⠂⠀⢠⠆⠀⢀⡾⢁⣴⡷⣣⣾⣯⡾⢫⣞⣶⠞⢁⣴⣾⣿⣿⣒⡴⣲⡾⠗⢠⡾⠛⡠⠊⠄⠀⢀⢀⡆⠀⠠⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⣴⠋⠀⣰⡟⢠⢟⣟⣴⣿⡿⢋⣴⣿⠟⣁⣼⣿⣽⣿⣿⣿⣏⡾⠋⢀⣴⠟⢁⠞⠁⢠⣴⡅⢀⡼⡇⠀⡇⠀⠀⠀⠀⠀ ⢀⠀⠁⠀⢀⣼⠃⠀⣼⡟⣰⢏⣾⣿⣿⣋⣡⣞⣡⣿⣾⡿⢋⣼⣿⣿⣿⣿⠏⢀⣴⠞⢁⡴⠁⢀⠴⣿⡿⢐⣾⢿⠁⢰⠁⠀⠀⠀⠀⡇ ⠈⠀⠀⣰⣿⢃⡄⣸⣿⣿⣿⣾⣿⡯⢶⣿⣯⣈⣽⡿⢏⣰⣿⣿⣿⣯⡿⢁⡴⢣⠆⣠⠞⢀⡴⠁⣼⡿⢁⡞⢁⣾⠀⣸⠀⠀⡀⠀⢸⠀ ⠀⢀⣾⡿⠃⣾⢀⣿⣿⣿⢻⠟⠀⠀⣸⣁⡀⠙⣿⣄⠈⣿⡿⣿⣳⣋⣴⢏⣴⢏⣴⣿⣾⠋⢀⣼⣿⣷⣿⣷⣿⡏⡸⠃⠀⣸⠁⢰⣏⣸ ⣀⡾⠋⡀⣼⡇⢸⣿⣿⣿⡟⠀⢠⡞⣿⣭⣿⡆⠈⢹⣿⠉⣠⣿⣿⣿⣣⣿⣿⣿⣿⣿⠟⣰⣿⣿⡿⠋⣼⣿⣹⣿⠓⠀⣽⡿⠀⢸⡿⡟ ⢋⣴⡿⢡⣿⠃⣿⠛⣿⣿⡇⠀⠘⣿⡟⠟⢻⠇⠀⢸⣿⠿⢻⣿⣻⣿⣿⡿⣽⣿⣿⢳⣾⣿⣿⣏⡏⠰⣿⣇⣿⣿⡘⢰⣿⠁⢀⣿⣧⠇ ⣿⠟⣱⣿⡇⢰⣿⡆⠸⣿⣿⣤⣀⣀⣀⣀⣤⣶⣾⣿⡿⠀⣸⣿⡿⢻⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣟⣸⣿⣿⣇⣿⢃⠀⢸⣿⡿⠀ ⣿⣾⢏⣼⣇⣸⣿⣷⡀⢿⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⡾⣿⡿⠁⣾⣿⡿⢿⣿⣿⣿⣟⡁⠘⢿⣿⣿⣿⣿⣿⣿⣿⢃⣿⠃⠎⣽⠃⡸ ⣿⣷⠘⣿⣿⣿⡏⣍⠣⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠿⡟⠀⢠⡿⠛⠀⠀⠻⣿⣿⣿⣀⠀⣶⣿⣿⣿⣿⣿⣿⣧⣿⢁⠆⣰⡿⢠⠇ ⣿⣏⢠⣹⡇⢿⡇⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡘⠀⠀⠾⠃⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠿⠿⢻⣿⣿⣟⣿⡟⣰⣿⢁⡎⢠ ⣿⣿⣦⣹⡇⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠿⠟⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⡾⣰⢻ ⣿⣿⣿⣿⣧⠀⠈⢧⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣾⣳⣏⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣿⡿⣁⣴⣿⣿⣿⣿⡿⡾⣿ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠻⢿⣛⠲⠽⣶⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢷⣿⣿⣾⣿⣿⣿⣿⣿⡟⠁⠁⠾ ⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡈⠉⠓⠲⠤⣝⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣾⡿⠿⣻⣿⣿⣿⣿⣿⠀⠀⣴⣾ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠤⠤⢀⠈⠉⠒⠀⠀⠀⠀⠀⠀⣀⠔⠾⠟⢁⣼⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠇⠈⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠟⢿⣿⣇⠀⠀⠈⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣴⣿⣿⡿⠟⠙⠋⢠⣿⣿⣿⡀⠀⠀⢿⣟⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣌⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⢸⣾⡁⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣼⣁⣤⣤⣤⡤⣤⣿⣿⣿⡟⠀⠀⠈⣿⣧⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⠟⠋⠉⠻⠀⠀⠀⠀⢸⡿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠀⠀⠀⣧⠀⠀⠀⠀⣷⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⢸⡇⠀⠀⠀⢸⡏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⡟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣢⡷⠀⠀⠀⠸⠀⠀⠀⠀⠀⢣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠋⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸

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⣿⣿⣿⣿⣿⣿⠟⠿⠛⠃⠀⠈⠻⢿⡛⢛⠋⠉⠋⠛⢿⡿⢿⠉⠀⠀⠀⠀⠀⢐⣤⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣶⣤⣀⣐⣀⣀⡂⢀⣤⡀⠀⡐⣤⠀⠒⢪⣷⣆⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⠿⠐⣦⣿⠋⠉⠙⠷⣶⡷⠿⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢶⣄⡀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠋⢻⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣽⠼⣾⡇⠀⠀⠀⠀⠀⠈⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣷⣶⣾⣿⣿⣿⣿⡟⠁⠀⢸⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠦⠤⠤⣀⣀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡟⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⠟⠶⢤⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣾⣍⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠁⠀⠀⠀⠀⠨⠻⠿⠇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣠⣇⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠁⠀⠀⠀⢰⣶⣄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡄⠀⠀⠀⠀⠀⡝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⡟⢻⡿⠂⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠈⡇⠀⡆⠀⠀⠀⢧⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣸⣿⣧⠀⢸⠀⢣⠀⠀⠀⢸⡄⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⢿⡟⢷⡀⢧⠘⡆⠀⠀⠈⣇⠀⠀⠈⢢⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠘⣿⠈⢣⠈⣆⢻⠀⠀⠀⢹⣤⣤⣤⣤⣿⣶⡒⠚⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠸⣇⣼⣧⠘⣎⣇⠀⠀⠸⡏⡉⠁⠀⠀⠀⠙⢦⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡇⠀⠀⡆⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⢶⣦⣿⣿⣿⣇⠘⣾⣄⠀⠀⡇⡇⠀⣰⣾⣿⣶⣄⡙⢦⣀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⡟⡇⠀⠀⣿⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⢻⣿⣿⢿⡄⠈⠻⡄⠀⢸⡧⣴⣿⣽⣿⣿⣿⣷⣄⠈⠳⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡼⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠛⠿⠀⠀⠀⠀⢰⣿⡟⣿⠼⠃⠀⠀⠙⣆⠐⢿⣿⠿⢿⣿⣿⣿⣿⣿⣧⠤⠌⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡾⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⡀⠀⠀⠀⠀⠀⠀⢀⣿⣡⠀⠀⠀⠀⠀⠀⠈⢧⡘⡟⠾⣦⣸⣿⡿⠛⠛⠛⣲⡦⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸⠁⣷⠃⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢰⣿⣭⣤⣤⣀⠀⠀⠀⠀⠀⠀⠹⣽⡀⠀⠸⠀⠀⣠⠶⠚⣇⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⢸⡈⡿⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠸⣧⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠳⣄⢀⡴⠋⠙⣆⠀⠈⢧⣀⣸⠀⠀⠀⠀⠀⠀⠀⡿⢧⠁⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⢷⣌⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⡆⠀⣈⣧⣤⣾⣿⣿⡄⠀⠀⠀⠀⠀⣆⣧⠈⠳⣤⡤⠔⠚⠛⠉⢉⣙⠒⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠁⠀⣾⣿⣿⣿⣿⣿⡿⠿⣿⡆⠀⠀⠙⣷⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡟⠈⠦⣀⡀⠀⠀⢀⣀⣠⡤⠈⠙⢕⠒⠀ ⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⠿⠛⠉⠀⢠⣿⣷⡀⠀⠀⠀⠙⠿⣮⣀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣿⣝⣦⣀⣠⣤⠴⠒⢯⣍⠈⠉⠓⢤⡈⢳⡀ ⣿⣿⣿⣿⣿⠀⠀⠸⣿⠟⠁⠀⢀⣴⣾⡿⠛⠉⢹⡆⠀⠀⠀⠐⡀⠉⠛⢻⣟⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡇⠀⠀⣠⣾⢿⣿⠟⠉⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀⠑⣄⠁ ⣿⣿⣿⣿⣿⡆⠀⢀⡏⠀⠀⣰⣿⠟⠋⠀⢀⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣰⢿⣿⣿⣿⣿⣿⣿⠃⣿⡇⣠⣾⡇⠀⡴⣻⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠘⡆ ⣿⣿⣿⣿⣿⣿⣦⣾⣀⣀⣰⡿⠃⠀⢀⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣼⣿⣧⠾⠋⠘⣿⣿⣿⣿⣿⣿⡀⣿⢿⡁⢠⣇⡼⠛⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡇⠀⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣠⣾⣿⣿⣿⣿⣿⣷⣀⠠⠁⠀⢠⣿⠛⢧⣄⡀⠀⣿⣿⣿⣿⠟⠙⡇⣿⣠⠿⣾⠋⢀⡜⡿⠁⠀⠀⠀⠀⢀⣠⡤⠖⠒⠒⠒⠲⠦⠿⣇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⢉⣿⣄⣆⣀⣿⣿⠀⠀⠈⠙⢷⣿⠿⠋⠁⠀⠀⢷⣿⠁⠀⠉⢷⣾⣿⠟⠓⠒⠲⠶⣾⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣀⣀⣤⠶⠿⣿⣿⣾⡿⠋⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⡼⣹⡏⠀⠀⠀⠀⣤⠀⠀⠉⠛⠶⠶⣤⣶⣀⣀⣠⡴⠾⠓ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣤⠴⢄⣾⡿⠋⢀⡄⠀⠀⠀⢀⣾⢹⣿⠀⠀⠀⠀⠀⠘⣿⡗⠤⣼⡿⠋⠀⠀⠀⠀⢴⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢶⣤⣤⣠⡾⠁⣼⣿⠀⠀⠀⠀⠀⠀⢹⣧⣠⣟⡀⠀⠀⠀⠀⠀⡿⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⢁⡴⢨ ⣄⠀⢀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡏⠉⠙⠋⠋⠉⠛⠉⣿⠇⣸⡿⠋⠸ ⠉⠻⣏⣁⣈⣉⡉⣿⣛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠸⣿⠿⣿⡇⡼⠁⣴⠟⠁⠀⢀ ⡄⠈⣻⡟⠁⢸⠇⣻⣯⡲⢙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢡⠀⠀⣿⣄⣾⠙⠛⠛⢿⣿⣿⣿⣻ ⡇⠐⢹⠃⠀⢸⠁⣿⣟⢿⡨⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠷⠶⠒⠶⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⢸⠀⠀⣿⡉⣿⠀⠀⢐⣿⣿⣿⣿⣶ ⡇⠀⢸⠀⠀⢸⠀⣿⡿⣳⢽⣦⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⢸⣀⣄⣿⣿⣿⣦⣤⣤⣛⣿⣛⣻⣿ ⡇⠀⢸⠀⠀⢸⠀⡏⣟⡮⢰⣽⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢐⡾⣿⣼⡇⢸⠙⠻⣯⣯⣭⣯⠙⠛⣯⣭⣭⣿⣿ ⡇⠀⢸⠀⠀⣾⠀⡟⠂⣙⢪⡓⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⠀⠀⣿⡛⠛⢿⠀⠀⢻⣿⠻⠻⢿ ⡇⠀⢸⠀⠀⡏⠀⡇⠀⠂⡍⠀⢸⡢⡀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⠿⣿⢋⡇⠘⠀⠀⢸⣧⠀⢸⠀⠀⢸⣿⡆⠈⢻ ⡇⢀⢸⠀⠀⡇⠀⡇⠀⠅⠳⠈⢸⢭⠒⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⢸⣿⡿⡇⠀⡀⠀⢸⣿⣗⢻⠀⢀⠀⣿⣷⣶⣾ ⡇⠀⣻⠀⠀⡇⢸⠇⠀⠀⠀⠀⢸⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⡿⠶⠤⠤⠤⠀⠀⣄⠀⠀⠀⢠⡇⠀⠀⠀⢸⢨⣿⣃⡇⠀⡇⠀⣸⣿⣿⣿⡆⠠⢸⣿⣿⣿⣿ ⡇⠠⣿⠀⠀⡇⢸⠀⠀⡀⠀⠂⠛⠃⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣿⡏⡿⠙⠛⠛⠛⠉⠉⡉⣛⣿⣿⣶⣶⣿⡧⠀⠀⠀⣿⢸⣿⣽⡇⠀⡇⠀⠙⠛⣛⡛⠃⠈⠸⢿⠿⢛⣻ ⡧⠨⣿⠀⠀⡇⢸⠀⢀⡮⡓⢌⡀⠀⢐⣾⣳⣦⢄⡀⠀⠀⠀⣴⣿⣿⣿⡇⣷⣶⣿⣿⣿⣿⣿⡭⢭⣤⣼⣻⣻⣿⣿⣤⣴⡀⣿⢸⣿⠉⡇⠀⡇⣠⣶⣽⣿⣿⣷⡄⢸⣯⣽⣿⣿ ⡇⢸⣿⠀⠀⡇⢸⠀⠠⣝⠯⣒⠉⠀⢸⣿⣿⣿⣾⣿⣷⣦⣾⣿⣿⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣭⢿⣿⣿⢍⣻⣿⣿⣿⣿⣿⢸⢿⣷⡇⠀⡇⠈⣿⣿⡷⠿⡟⠉⢸⣿⣏⠁⢸ ⡇⢸⡇⠀⠀⡇⢸⠀⢘⡧⣅⠨⢓⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣧⣻⣿⣿⡏⣿⢿⠻⢿⣿⢼⣿⣰⣿⣿⣻⣟⣯⣿⢸⣾⡟⢧⠀⡇⠀⣿⣏⠙⠛⣧⠀⢈⣽⣿⣀⣈ ⡇⢸⡇⠀⠀⡇⢸⠀⠀⠉⡓⢠⡀⢹⣌⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⣯⣿⠁⣷⠗⣭⣿⣇⣭⣾⣷⣿⣻⢹⣿⣿⣾⣿⣹⣿⣿⣿⣼⣽⡇⢸⠀⡇⢀⣿⣾⣴⡀⡗⡄⢀⣾⡇⠀⠀ ⡇⢸⡇⠀⠀⡇⢸⠀⠀⠀⠅⣒⠠⢘⢿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣯⢽⡀⣗⠙⠛⠛⠒⠀⠃⠓⠛⠛⢹⣿⠻⢿⣿⠼⡿⣿⣿⡟⢻⣗⢸⠀⡇⠈⣿⡙⠛⠃⣿⣿⣿⣿⣷⠶⣶ ⠇⠐⡇⠀⠀⣿⢻⠀⠀⠀⠃⠈⢁⢸⢽⣿⣿⣿⡿⣿⣿⣿⠟⢿⣿⣿⢿⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣶⣿⢿⠏⢹⣿⢸⠖⢻⡄⣿⣿⣤⣀⡿⠿⣿⡄⠀⠀⠀ ⠅⠀⡇⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⡟⠛⠟⠻⡇⡟⠁⣹⠟⢹⡟⣳⠦⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣇⣽⣿⣿⣿⣿⢸⠀⢸⣿⣾⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣷⠀⠀⠀ ⠁⠀⠁⠀⠀⠃⠀⠀⠀⠀⣴⡖⠛⠛⠛⠛⠻⣾⣶⡇⠀⢃⣛⣆⣠⣇⣸⣬⣃⣀⣈⣧⣀⡉⣿⣠⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⣸⡟⠑⠀⠀⠀⠀⡹⡿⣏⢻⣷⣾⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣶⣶⣶⡿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣻⣿⣿⣿⡟⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢻⡇⣰⠀⠀⠀⠀⡇⢇⢘⣿⣷⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⣶⣶⣾⣶⣾⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⠿⠟⠋⠉⠀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠘⠃⠀⠁⢺⢰⢿⠀⠀⠀⠀⡇⢸⠰⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⣛⣻⣯⣭⣽⣻⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣿⣿⠟⣻⡏⠀⠀⠁⢀⣿⡟⢸⣦⣤⣤⣤⣿⣾⠀⠀⠉⢹⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠉⠉⠉⠉⠹⠿⠛⠋⠉⠁⢀⣀⣒⣒⠲⠤⠬⠭⠭⠭⠭⠭⠭⠭⢉⣙⡿⠛⠹⠶⠤⣤⣤⣤⣤⣼⣿⣧⣾⠀⢀⠀⠄⡿⣿⣆⠀⠀⢸⡦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⡴⠃⢻⡟⣻⣄⡾⡇⢸⡃⡿⢻⢹⠟⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠓⡒⣻⣿⡧⣧⠘⣄⣿⣿⣿⣶⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⢹⠇⠃⠹⠄⢟⣿⡟⣿⣿⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣷⣦⡀⠀⠀⣠⣴⣶⣤⣤⣀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣜⡻⢿⡄⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣤⣶⣾⣿⣿⣷⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⣷⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣌⣉⣛⣃⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠸⣿⣦⡀⠀⠀⢿⣷⣤⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠙⣿⣿⣶⣄⠈⠿⣿⣿⢆⣰⣿⣿⣿⣿⣿⣿⣿⢠⣿⡿⢛⣉⣉⡛⠿⣿⣿⣿⣿⣇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⡄ ⠀⠀⠈⠻⣿⣿⣿⣦⢀⣵⣿⣿⣿⣇⣠⣿⣿⣿⣿⢸⣿⢡⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣿⣿ ⠀⠀⠀⠀⠈⠻⢿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⣿⠸⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠉⠃⠈⠛⠿⣿⣿⣿⣿⣷⡈⠛⢿⣿⣦⡀⠹⢿⣿⣿⣿⣿⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠹⣿⣿⣿⣿⣇⠀⠀⠈⠉⠉⠀⠀⠙⠛⠻⠟⠛⠛⠋⣱⡄⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠇⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⣴⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠶⣤⣀⣀⣀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠟⠲⢦⣤⠤⠤⠤⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⣻⡷⠶⠒⠛⠉⠉⠀⢸⣰⢿⣦⡀⠻⡄⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣀⡤⠖⠀⣀⣤⠴⠖⠋⣉⣄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⣿⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⡴⠚⢁⣤⠶⠛⠉⠀⠀⠀⡼⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠙⠷⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣠⠾⠋⠁⠀⢠⠆⡼⠀⡼⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⡏⢠⠃⠀⡇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣤⠀⠀⠀⠐⡇⠘⣄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁ ⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀ ⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⢶⣶⡶⠶⣶⣶⠶⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀ ⠀⢠⠾⠉⠀⠀⠀⢀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣛⣯⣿⢻⣿⣴⣟⣿⣷⡾⢻⣿⣤⣶⣿⣁⣽⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀ ⣰⣯⡶⠞⠛⠛⡿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠉⠉⠙⠻⢿⣍⣿⡿⣿⣿⣃⣴⣷⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⢿⣿⡿⢋⡾⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠾⣿⡿⠛⠁⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠁⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⡤⠤⠶⠖⠚⠚⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠻⡏⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⣿⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⡾⢷⠀⠀⠀⠀⠀⢸⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠇⠘⣆⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⣁⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠙⠳⣄⣀⠀⠀⠀⠀⠀⠀⣠⢴⡶⠇⠀⠀⠀⢀⣀⡴⠚⠉⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠉⠛⠛⠛⠿⠿⠋⢡⠾⠦⠤⡤⠴⠞⠋⠁⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣀⣀⣀⣀⣀⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠹⡆⠀⠀⠀⠈⠉⠉⠙⠒⠦⣄⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣆⣀⠀⢀⣉⡉⠛⢛⣛⡯⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣿⠿⣧⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⣰⠃⠀⠈⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⢫⠇⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⠃⠘⣿⣂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠃⡞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⢷⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠇⢰⠃⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢿⡧⠀⠀⠀⠀ ⠀⠀⢰⡟⠀⢸⣤⣾⣶⣄⠀⠄⠀⣠⣴⣷⣦⣀⡌⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀ ⠀⢠⡿⠁⢀⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀ ⢀⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆ ⣨⡏⠀⢠⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⣿ ⣿⠁⠀⣼⣿⣿⣄⠀⣠⣿⣿⣿⣿⣿⠿⣧⡀⢀⣼⣿⣿⣷⡀⠀⠀⠀⠀⠀⢰⡏ ⣿⢀⣰⣿⣿⣿⣿⣿⣿⣦⡙⣋⡛⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢠⣿⠆ ⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡏⠀ ⠘⢿⣦⣄⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡟⠀⠀ ⠀⠀⠙⢧⡉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⣠⣿⡁⠀⠀ ⠀⠀⢠⡾⠉⠓⠀⠀⠀⠉⠻⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠚⠁⡨⣿⡄⠀ ⠀⢠⣿⠁⣄⠀⠀⠀⠢⣀⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⣠⠴⠊⢀⡤⠞⠉⠀⠀⠀ ⠀⠸⣷⡀⠀⠑⠦⣄⡀⠈⠁⠈⠻⣿⡟⠁⠠⠴⠒⠋⠁⣠⣴⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣷⡄⠀⠀⠀⠉⠛⠳⠶⠶⢾⡆⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣀⠴⢋⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡯⡻⣦⣄⣠⣬⣶⠿⢛⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠩⠛⠋⠈⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣾⣿⢀⡞⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⣿⣿⣿⡾⠀⠀⣾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠃⢀⣾⡇⢸⣇⠀⠀⠀⠀⠀⠘⣦⣀⣤⣾⣶⠦⢴⣧⣀⠀⠀⠀⠀⠀⠰⡴⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣀⣴⣇⣀⣴⠀⠐⠀⠀ ⣿⣿⡏⠀⣲⡿⠀⢸⣿⡆⠀⠀⠀⢠⠾⢭⡀⠀⠀⠈⢣⡀⠀⢿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠙⢏⠉⠉⢻⣦⡀⠀⠀ ⣿⣿⠇⢀⣿⠃⠀⠘⠛⠁⠀⠀⣰⠃⠀⠀⠙⢦⠀⠀⠀⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⣆⠀⠀⠀⠃⠀⠈⠁⠙⣦⠀ ⣿⣿⠀⢸⡿⠀⠀⠀⠀⠀⡄⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⣇⠀⠀⣦⠀⣰⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧ ⣿⣿⠀⢸⡇⠀⠀⠀⠀⠠⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠛⠀⢸⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⣾⠃⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢰⠇⠀⠀⠀⠀⠈⣷⣠⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⣿ ⣿⡇⢀⣿⠀⡀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⠀⠀⠀⠀⠀⠈⠛⣁⣀⣀⣼⣿ ⣿⣇⡼⠟⠛⠁⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄⣀⠀⠀⠀⠀⠀⣀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀ ⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠽⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⢀⣿⠃⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡟⣷⠄⠀⣠⣤⠶⠶⠶⠶⠶⠶⠒⠒⠛⠛⢛⡿⠿⣿ ⠘⠀⠀⠀⣼⠛⢷⣄⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡟⠀⠀⡟⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡾ ⣱⠄⠀⠀⢿⣇⠀⠈⠛⠦⣄⡀⠀⠀⠀⠉⠛⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣧⠀⢸⡁⢀⡧⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⡴⠋⢀ ⠁⠀⠀⠀⠈⠋⠻⣦⡀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣄⣀⡀⠀⠀⡟⠀⢹⡀⠈⠛⠉⠀⣀⣠⠴⠚⠉⠀⣀⣤⠞⠉⠀⣠⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠈⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⢻⠇⠀⠈⣿⠛⠛⠛⠉⠁⠀⣀⣠⡴⠞⠉⠀⠀⣠⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠉⠛⠲⠶⢤⣤⣤⣀⣀⣸⡄⠀⠀⢸⣄⣠⣤⡶⠾⠛⠉⠁⠀⠀⣀⡴⠊⠁⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣦⠴⠛⠋⠉⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣒⣂⣤⣤⣆⣠⢄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⢀⢴⣿⡿⠟⠋⠉⠉⠙⠻⢝⢿⣦⡈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⣟⣓⣯⢽⣺⢽⡻⢞⣴⡴⠀⠀⠀⣦⢀⡞⠁⠀⢀⡞⡥⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠄⠀⠈⠀⢀⣀⠀⠀⣀⢄⣠⣮ ⣿⣿⡿⢿⣿⣿⣿⣿⣿⣽⣮⣿⡭⠚⠡⠀⣸⣻⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣽⣿⣿⣽⣯⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠓⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⠛⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣰⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠀⠀⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠠⡿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⣾⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⠃⠀⠀⣸⣀⣀⣤⡤⠤⠔⠒⠒⠒⠶⠤⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣤⢸⡀⢀⣀⠘⡏⠀⣠⠔⠋⣡⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠥⠟⠿⣷⡄⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠿⢾⣇⡼⢧⣠⡧⡎⠀⢀⣼⡁⠀⠀⣀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢼⣆⠀⠀⠉⠁⣠⡟⢀⣇⣤⠿⠿⢿⠿⠟⠶⣄⠀⠀⣠⠋⢀⣠⠤⢤⡀⠀⠀⢈⣿⣿⡀⠀⡼⠁⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢳⡔⢁⣴⣿⡃⠀⣠⣿⡄⠀⣏⠀⠸⢷⣰⠟⠙⢻⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⡟⣿⣿⠟⣇⠀⠀⠀⠀⠀⠀⣠⣴⡟⢠⣿⣿⣿⣿⣿⣿⣿⠁⣠⠞⠀⠀⠉⠁⡀⠠⡾⠿⣤⣴⡆⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⢸⡇⠀⠀⢰⡅⠈⣋⠀⠘⢦⡀⠀⠀⣠⣾⠿⠋⠁⢿⣿⣿⣿⣿⣿⡿⠃⡴⠁⠀⠀⠀⠀⠀⠈⠀⢀⣀⡝⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⣏⢹⡧⡄⠤⢤⠽⢷⣯⣉⣀⣀⠀⠰⡀⠙⠛⠛⠛⠋⠀⢰⠁⠀⠀⠀⠀⢀⡀⢀⡀⠈⠻⣤⣖⠦⣤⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠙⢧⢽⣄⣸⣦⣾⠷⣤⣾⡏⠉⠉⢛⡟⠲⠦⠤⢴⣞⡇⠀⠀⠀⠀⠀⠀⠀⣹⠉⠒⢺⣿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠸⡄⣿⠋⣽⡀⠀⠀⠈⠛⢤⣤⠟⠳⠴⠻⣦⣾⣷⡇⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⢐⢺⡄⠀⠀⠀⠀⠳⣄⠀⠀⠀⢃⢻⡀⠘⢳⡄⠀⠀⠀⠀⢀⣀⣀⣰⠶⡟⠙⡏⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⢠⠳⣄⠀⠀⠀⠀⠈⢣⡀⠀⠈⢣⣧⡀⢸⠟⢧⣤⠦⣴⡟⠉⢻⡇⣀⠷⢾⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠸⡄⠈⢧⠀⠀⠀⠀⠀⠑⡄⠀⠀⡌⠫⣝⡢⠼⠧⠀⠽⠤⠔⢚⣩⠤⠖⠋⠀⠀⠀⠀⠀⠀⣠⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⡀⢣⠀⠀⣧⣀⠀⠀⠀⠀⢸⡇⡜⠀⠀⠀⣿⢍⡒⠒⠂⠉⠉⠀⠀⡏⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠳⢤⣄⣀⣀⣀⣄⡀⠀⠀⠀⠀⠀ ⠀⠳⡈⡆⢠⠁⢉⡿⠒⠒⠚⠉⠙⠓⠤⣀⠀⠙⢾⡇⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⡼⠉⠉⠀⠀⠀⢰⡿⠙⠟⠛⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠘⣼⣼⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⣈⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠘⣧⠶⡦⠀⣀⡀⠘⠁⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀ ⠀⠀⠀⢬⡿⢷⣴⡶⠖⠚⠉⠁⠀⠀⠀⠈⠙⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡇⠀⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡙⢦⡀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢱⡤⠤⠤⠤⠤⠤⠤⠶⠒⠒⠒⠂⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⣄⣀⣠⠼⠉⠑⠒⠒⠒⠾⠟⠋⣩⠓⠒⠂⠉⢶⡏⠒⠤⣤⣄⡀⣹⠤⢤⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⠀ ⢀⣾⣿⣿⡟⠉⠀⠀⠀⠉⠻⣿⣿⣷⡄⠀⢠⣿⣿⣿⠁⠀⠀⠈⢻⡿⠿⠇ ⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⠀⠘⣿⣿⣿⣤⣀⣀⡀⠀⠀⠀⠀ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠉⠻⢿⣿⣿⣿⣿⣿⣶⣄⠀ ⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⡇ ⠈⢿⣿⣿⣧⣀⠀⠀⠀⣀⣤⣦⠀⠘⣿⣿⣿⣦⣄⡀⠀⠀⠀⢀⣼⣿⣿⡇ ⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⢉⣽⡉⠙⠒⢦⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡤⠄⠠⡀⠀⠀⠹⣏⠒⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡦⡞⠁⠀⠀⠀⠀⡎⢀⡀⠀⠘⡄⠀⠀⠙⢶⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⣍⡟⠀⠀⠀⠀⠀⢷⡈⠁⠀⡰⠃⠀⠀⠀⠀⠙⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠾⣄⠐⠒⠢⢤⡶⣉⡀⠲⠀⠈⣿⢩⢸⣆⣀⣁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡜⠑⠲⢬⣏⣡⡌⠁⠰⡦⢀⣷⠴⠟⠢⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠠⠔⠊⢉⣽⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠠⠖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⡟⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⣠⡾⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡟⢸⠁⠀⠀⠀⠀⢀⣻⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⢀⡆⣠⠔⠁⠀⠀⣠⠾⠋⠀⠀⠉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⢀⡇⠀⠀⠀⣠⡾⠛⠉⠙⠦⣭⣉⣉⣶⠶⠛⠉⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⣀⣀⣤⠶⠛⠙⠛⠒⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠋⢧⣠⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⢻⣤⣀⣀⣀⣠⣤⡤⠴⠖⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠈⠁⠀⠉⠀⠀⣀⣀⣀⠐⠲⠤⣤⠔⠢⠤⣤⡄⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⢠⡄⠈⠐⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠃⠀⡇⠀⠀⣤⣤⣤⣄⡀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿ ⠀⠀⢸⣿⣷⣸⠄⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⠛⢷⡀⠀⡇⠀⠘⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⡿ ⠀⠀⢸⣿⣿⣿⠆⢀⣿⣿⣿⡿⠿⠟⠛⠋⠀⠀⣈⣷⡀⡄⠀⠀⣀⣀⣀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁ ⠀⠀⢸⢀⣿⣿⡄⢸⣿⠀⠀⠁⢀⣀⣤⣴⣶⣿⣿⣿⣿⠃⠀⠘⣿⣿⣿⣶⣿⣿⠿⣿⣿⣿⣶⣦⣤⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀ ⠀⠀⢸⠾⣿⣿⡇⠀⠿⣄⣴⣿⣿⣋⣿⠿⠿⢿⣿⣿⣿⠀⠀⠀⢿⡉⠈⣿⣿⣉⣙⣛⣛⣙⣋⣭⠿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣄⡌⠁⠀ ⠀⠀⠸⠀⠻⣿⣇⢀⠀⠘⢿⣿⣍⣉⣥⣤⡴⠟⠛⠛⣿⡄⠀⢀⡀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⡼⡄⠀⠀⠈⠉⠙⠉⠀⠀⠀⠀⠀⣿⠁⠀⢸⡷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⡇⠀⠀⢸⡇⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢐⣿⣠⡇⠀⠀⠀⢳⡀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾ ⠀⠀⠀⠀⠸⣿⣿⣿⠈⢹⣄⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⣶⣾⡿⢷⣶⣤⡇⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠈⠃⠀⡄⠀⠀⠀⠀⢀⣿⡿⣿⡿⢻⡇⢺⣯⣉⠀⠀⠀⠈⠓⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⢻⣼⡿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⢓⣠⣿⡿⣿⣿⣿⣧⡀⢀⣿⣷⢻⡿⠛⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡥⡀⠀⠀⠀⣼⣿⣿⣧⣴⣿⣻⣿⣿⣿⣿⣿⣿⣧⣼⣄⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠻⢿⣿ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣿⣿⡟⢻⣿⡟⠛⠛⠛⠉⠉⠉⢙⣿⣿⣿⡿⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⣠⣼⣿⡿⠀⣤⣄⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⣿⣿⣦⡀⢈⣿⢽⠁⠈⠛⢷⣦⣤⣴⣶⣶⣾⣿⠿⠛⠃⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃⠀⢸⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣼⣿⠸⣧⠀⠀⢀⣿⣄⣉⣉⣁⣤⢤⣴⡟⠁⠀⠀⢀⣿⣿⣇⠀⠀⣠⣾⣿⣿⡿⠃⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣆⠈⠳⣄⡀⠉⣉⣉⣉⣉⡁⠉⠉⠀⠀⠀⠀⣰⣿⣙⣿⣦⢠⣿⣿⣿⠏⠀⠀⠀⢀⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣽⣿⣿⣿⣿⣿⣦⡀⠀⠉⠉⠉⣽⣿⣿⡥⠀⠀⠀⠀⢀⣴⣿⣿⡿⣮⣶⣿⣿⡟⠁⠀⠀⠀⣰⣿⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣾⣿⣏⣿⠀⠠⢀⡀⣀⣤⣞⣹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣠⡿⠋⠀⢼⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⣾⠻⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⡴⠋⠁⠀⠀⠀⣼⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⡐⠺⢿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣴⣾⡿⠀⠀⠀⠀⢠⣼⡟⠀⠀ ⢀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⢟⠋⠀⠀⠀⣠⣠⣾⣿⠁⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣞⣭⣿⣹⣟⣷⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣜⣜⣝⡛⣿⢿⣿⢏⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡝⡏⢸⢟⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠃⠘⣿⡞⠘⣠⣿⡅⣳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣷⡿⠟⠛⠋⠙⠛⠛⠷⣦⣍⠷⣄⠀⠀⠀ ⠀⠀⣰⣻⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⢧⡀⠀ ⠀⡜⣳⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣖⠳⡀ ⢰⢡⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⢡ ⢸⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸ ⢸⢸⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡆⡸ ⠈⢧⠎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⢱⠇ ⠀⠈⢿⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡡⣳⠏⠀ ⠀⠀⠀⠹⢷⣬⡒⠤⢀⡀⠀⠀⢀⣀⠤⢒⣥⣾⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⠷⣶⣦⣤⣤⣤⣶⡾⠟⠋⠁⠀⠀⠀⠀

⡯⣙⣢⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⠒⠉ ⣇⠀⣸⣯⠀⠘⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣰⠁⢹⣿⡤⠴ ⠈⠲⢿⠉⠀⢰⣿⠉⠹⣄⡤⠶⠶⡄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⣄⣸⠁⢨⣿⠲⢤⡇⠓⠊ ⠀⠀⢹⡀⠠⣼⡏⠀⠀⣧⠏⠀⠀⠇⡞⠁⠀⢹⠀⣠⠔⠲⣶⠤⡀⠀⢠⡤⠤⠤⠤⣄⠀⡰⠋⠉⠙⣴⡀⠐⠻⡇⠀⠀⣿⣤⠋⡁⠀⠀ ⠀⠀⠀⠛⠓⠛⣿⠀⣄⣿⡰⠄⢸⢡⠓⠒⠊⠙⣶⠁⠀⠀⠘⣷⠟⣶⡏⠉⠉⠳⢄⠸⡄⡇⠀⢀⣼⣿⠉⠉⠙⣗⠒⠂⡅⠛⠻⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣖⣻⢿⢄⠀⢻⡾⠀⠀⠀⢸⣿⠀⠀⠀⡜⠣⡀⣿⢸⠀⠀⠀⢸⣷⢧⡇⠀⠘⠺⣿⡆⠀⠀⡿⡀⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠻⠷⠇⡟⠒⣤⣀⣼⡟⣇⠀⠀⢷⠀⠀⣿⠈⢣⡠⡤⠊⠈⢿⣷⢀⣠⡤⣿⠷⣀⠜⠀⠈⢀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠈⣧⣀⠀⠀⠀⠙⠒⠧⠤⠟⡏⠳⣄⠀⢀⡷⠀⣿⠀⠈⢆⠀⠀⠀⢨⡿⠭⠔⠚⠁⠀⠀⠀⢠⣤⣼⠾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣶⣟⠈⣳⣎⣲⡀⠀⠀⠀⠀⠉⠓⠢⠤⠼⢥⡤⠿⠤⠠⠼⠤⠔⠓⠉⠀⠀⠀⠀⠀⡴⠛⣿⣷⠋⡿⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⣿⠀⠈⣷⠋⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣸⠉⠉⣶⡧⠤⢾⡏⣹⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⠀⠠⣯⡟⠂⢹⣶⡒⠒⢲⡔⠲⠤⢤⣄⡤⢤⡤⢤⣾⠁⠀⢀⣿⡏⠉⢹⣇⠠⣸⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⣤⣿⠀⠀⢸⡇⣷⠂⢸⡇⠀⠀⠞⣿⠀⠘⢧⣸⣇⠀⣠⢼⣿⣇⢀⣸⣇⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠸⣄⠀⢸⣿⠘⣦⣸⡇⢀⡼⠲⣿⠀⠀⠀⢿⡏⠉⠀⣸⢻⣏⢉⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⢸⠀⡼⡇⢏⠛⢄⢸⢿⢢⠀⡀⡏⣿⠂⢀⡇⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠷⠃⠘⠦⡤⡝⠻⢼⣉⡭⠇⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⡤⠖⠒⠒⠲⢤⠀⠀ ⠀⢤⠋⠀⠀⠀⠀⠀⠀⠳⠀ ⠰⡧⣶⣿⣗⣢⢰⣿⣿⣷⡇ ⠀⢮⠛⠹⠋⠉⠉⠉⠿⢉⡇ ⠀⠀⠳⢤⣤⣀⣀⡤⠴⠋⠀ ⠀⠀⠀⠀⢀⠜⠣⡀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⣀⣀⣈⠐⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⣁⣴⣶⣿⣿⣿⣿⣿⣿⣷⣮⣕⠤⡀⠀⠀⠀ ⠀⠀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣕⢦⠀ ⢀⣾⣿⣿⣿⣿⣿⠟⠛⠋⠉⢹⠛⠛⠛⠿⣿⣿⡏⡟⢹⠀ ⣿⣿⣿⣿⠟⢻⠏⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠙⣿⡥⠊⠀ ⠘⢽⡟⠁⣠⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⣦⠀⢠⡀⠡⠀⠀ ⢀⠎⠀⢠⠃⠀⠀⠀⣰⠁⠀⢠⠀⠀⡰⠋⢯⠀⣿⠀⢡⠀ ⢸⠀⢠⠇⠀⠀⠀⣀⠃⢰⣆⠸⡤⠞⠁⠀⣞⡶⠋⢀⢸⡀ ⡜⣀⡎⠀⠀⠀⢰⣿⣶⡤⠇⠉⠁⣶⣶⠶⡟⢠⠀⣪⠞⠀ ⠐⠼⣀⠀⠀⠐⡟⠩⠍⠀⠀⠀⠀⠑⠂⢰⠁⣡⠚⠁⠀⠀ ⠀⠀⠀⠁⠪⢟⠳⣄⠀⠀⠀⠀⠀⢀⣴⢏⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠠⣙⠟⣶⣶⣴⠚⠉⠉⢿⣿⣇⢆⠀⠀⠀ ⠀⠀⠀⠀⡤⣒⣨⡟⢿⡟⠁⠀⠀⠀⠀⢘⠟⠘⣿⢇⠀⠀

⠀⠀⢀⣾⣿⣷⣤⣤⣤⣤⢤⣄⡀⣠⣒⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣵⣯⡁⢧⠂⣽⣿⡟⣟⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣷⣿⣿⣿⣾⣿⣾⣷⢱⢸⢇⣣⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠟⢹⣟⣻⣟⠛⠟⣛⣿⡿⢸⠘⠿⣿⣷⡀⠀⡠⡀⠀⠀⠀⠀ ⠀⠘⢻⣿⡎⡏⠉⠉⢀⠙⠋⠹⣧⡇⠀⣼⣿⡿⠳⡀⠇⢧⠀⠀⠀⠀ ⠀⠀⢸⡟⠁⢣⡄⢬⣭⡄⢀⣞⠋⠀⠀⠻⣿⡀⢃⠱⠰⠸⣀⢀⡀⠀ ⠀⠀⠈⠇⠀⠈⠊⣞⠛⣰⢯⠀⠀⠀⠀⠀⢽⠃⠈⣆⠙⠀⠓⢆⡏⡇ ⠀⠀⠀⠀⠀⠀⠀⠏⠩⢤⣾⡶⠤⣀⡀⠠⠈⡀⠀⢐⣱⡀⠒⠘⠑⡅ ⠀⠀⠀⢀⡀⠄⢊⡭⠟⢛⢲⠧⢭⣛⡪⠄⢀⠈⢢⠀⠣⡁⢀⣸⣶⠃ ⠀⠠⠊⠀⣠⠶⣉⣀⣀⣓⠧⠔⠋⠈⢷⣷⡇⠀⢸⠀⠈⣚⡿⣿⡏⠀ ⠀⡇⣠⡔⡅⠀⠀⠈⣇⡇⠀⠀⠀⠀⠀⣿⡇⡀⠠⠀⠀⡘⠸⢳⠛⠀ ⠀⠃⢸⠸⡄⠀⠀⠤⠄⠀⠀⠀⣀⣴⣾⣿⡇⠀⠀⠡⢀⠁⠀⢸⠀⠀ ⠀⠆⢨⡆⢿⡷⠀⠀⠀⠀⠐⠾⣿⣿⣿⡟⠘⣄⠀⠀⠉⠀⠀⡇⠀⠀ ⢸⠀⡜⠀⠀⣠⠤⠶⠶⠤⠤⣤⣸⣿⡿⠀⠀⠘⠄⠀⠀⠀⢀⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠐⢝⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠀⠀⠀⠀⠁⢆⠀⢀⠀⠀⠀⠀⠐⠽⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡄⠀⠇⡇⠀⢠⡆⠀⠀⠘⡆⠈⡎⣧⡐⡄⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠸⠀⡸⢰⠁⠀⣸⠃⠀⢸⠀⡏⠀⢃⠸⣧⢰⠀⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡀⠀⡄⠀⠀⡀⠄⢠⣿⠃⠀⡇⢀⠃⡎⠀⢠⡿⠀⠀⡌⠀⣧⠀⢸⠀⣿⢿⡇⠀⠀⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⡞⢠⠃⣰⠁⠀⢠⠃⠀⣼⢿⠀⢠⠁⡜⡰⠀⠀⣾⠃⠀⢠⣷⢰⡿⠀⢨⠀⢹⠘⡇⠀⠀⢰⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⣇⡆⢠⡟⠀⠀⡸⠀⠀⣿⢸⠀⢸⣴⣁⣁⣠⣼⣿⠶⠖⠚⠓⠚⠷⠦⣼⣀⣸⠀⠃⠀⠀⠈⡆⠈⣆⠀⠀ ⠀⠀⠀⢠⠏⡇⣾⡇⠀⠀⡇⠀⠀⣇⣸⣶⣞⠛⠋⠉⢠⠛⢁⣤⡶⠖⠒⠒⠒⠠⢄⡈⠙⠦⡀⢰⠀⠀⣷⠀⢹⡀⠀ ⠀⠀⠀⣾⣰⢹⣿⠁⠀⢸⣁⡠⠖⠋⢉⣀⣬⣷⡄⠀⠀⠈⠉⠛⣥⣤⡶⢶⣶⠶⣦⡽⠀⠀⣿⡇⠀⠀⣿⡆⠈⡇⠀ ⠀⠀⠀⣿⣧⡎⢹⣂⣠⠞⠉⢀⠔⠊⣁⣤⣼⣿⡇⠀⠀⠀⠀⠀⠙⠷⠚⠛⠋⠉⠉⠀⠀⢸⣿⠁⠀⠀⠇⡇⠀⢹⠀ ⠀⠀⢀⣿⡇⡇⡜⠙⣿⠀⠀⢡⣴⠟⣻⣥⠿⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢰⠀⣷⠀⢸⡄ ⠀⠀⡸⠁⠀⢰⡇⠀⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢸⠀⠻⠆⠀⡇ ⠀⢠⠃⠀⠀⣼⡇⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⡆⢀⠀⡇⠀⣧ ⠀⣼⠀⠀⢠⠟⡇⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⡀⠀⢰⠁⠸⠀⠇⠀⣿ ⢀⡏⠀⠀⡸⠀⡇⠀⡿⣷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣷⣄⣿⣄⡆⢀⣿ ⠸⡇⠀⠀⣧⠀⡇⠀⠃⡏⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠤⠤⠤⠤⢀⠀⠀⠀⠀⠀⠀⢠⡞⢹⢸⡇⠁⣹⣾⡿ ⢸⡇⠀⢰⡇⠀⡇⢸⠀⣷⠀⢀⠳⡀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⡇⢸⠀⡇⣼⣿⠃ ⠈⡇⠀⢸⡇⡄⠃⣸⠀⣿⠀⢸⣤⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⡏⠀⡇⣾⣤⠟⠋⠀⠀ ⠀⢳⠀⢸⡇⡇⢸⡟⠀⣿⠀⠈⣿⠀⢸⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⡼⠀⠀⣿⠟⠁⠀⠀⠀⠀ ⠀⠈⠙⠚⠷⢾⣜⡇⠀⣿⡀⠀⣿⡄⠘⣷⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢰⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⢦⣧⡇⠀⢸⣧⠀⣿⠀⢸⠹⣏⠢⡀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢠⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠾⠧⠤⠿⠧⣤⡇⠘⢆⠈⠓⠶⠿⠛⠁⣀⣀⣀⣤⣿⣤⣄⣀⣀⣇⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣀⣼⣷⣶⡴⠶⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⢋⡶⠟⠛⠷⣮⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠿⠿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠛⠉⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⣀⣤⣿⢷⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⣿⣠⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣾⣿⣿⠟⠉⠉⠉⠉⠫⡉⠛⠻⢷⣦⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⢾⣏⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣾⠋⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⢹⣇⠀⢀⣀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀ ⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣿⠚⠁⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀ ⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣻⡏⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡟⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠔⠚⢉⣴⠟⠀⠀⠀⢀⠞⠁⠀⠀⠀⠉⠲⡄⠀⠀⠀⢧⠀⠀⠀⠸⢿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠙⠻⣯⣍⣉⠉⠁⠀⠀⠀⢀⣀⣴⠿⢻⠀⠀⠀⠀⡞⢀⠴⠒⠒⢦⡀⠀⠘⣆⠀⠀⠈⢇⠀⢀⡠⠼⢿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢿⡟⠛⠉⠀⠀⠀⢇⠀⠀⠀⢷⠃⣴⣿⣿⣷⣷⠀⠀⣼⠀⠀⢀⣼⠔⠉⠀⠀⣸⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠈⠣⣀⠀⠈⠣⣿⣿⣿⣿⡽⠤⠊⢁⡠⠔⢻⠻⣆⣀⣀⣼⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠈⠓⠦⢄⣀⣀⠡⠤⠤⠒⠊⠁⠀⠀⡇⠀⣈⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⡷⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⡟⢹⣇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⢶⣶⣶⠶⠶⠾⠛⢻⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⣷⠀⢻⣆⠀⣀⣠⣤⣤⣤⣤⣤⣤⡾⠟⡰⠁⡇⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠘⢦⡀⢙⠟⠋⠉⣀⣀⣀⣀⣀⡤⠤⡚⠀⣸⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠹⡝⠒⡟⠉⢁⢦⠀⢸⡀⠀⢀⣇⠴⠁⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⠀⠘⠦⠽⠶⠶⠯⠤⠜⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⡄⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢘⡇⠀⠀⠀⠀⢸⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⣧⣶⡶⢾⣇⠀⠀⠀⠀⣾⡇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⢀⣤⠾⠟⠋⣶⠟⠋⠀⠀⣿⠀⠀⠀⠀⣿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⡇⠀⠀⠀⣿⠀⠀⠀⠀⢻⡆⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣿⣿⡄⠀⠀⢹⣇⠀⠀⠀⠸⣧⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣿⡈⢿⣆⠀⠀⣻⡆⠀⠀⠀⢿⡆⣀⣠⣿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣿⣿⣧⠀⠻⣷⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡿⠀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠈⠻⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣾⡗⣄⢦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⣾⣿⣿⣷⣿⣿⣿⢢⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠃⠀⠀⠀⠀⠈⠛⠿⢿⠻⢿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡛⢿⣿⣿⣿⣿⠛⠙⢀⡴⠞⢛⣙⣛⣳⣶⣤⣄⠀⠀⠀⣀⣀⣐⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⡻⣆⣟⣿⣿⣿⠀⠀⠀⠰⠖⡿⢭⡿⣿⡿⠟⠉⠀⣴⣿⣿⣿⣯⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣧⣿⢿⠉⠙⣿⡙⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⣏⠻⠿⠟⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡳⠾⣇⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⣼⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⣤⣀⣀⣽⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠾⢷⣶⣦⡀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣴⣦⣀⣀⣼⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡇⠀⠀⢻⡷⢦⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣱⡇⠀⠀⠈⢿⡀⠙⠻⢷⣦⣤⣀⣀⣀⣤⣤⣄⣠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡽⠀⠀⠀⠀⠈⠳⠄⠀⠀⠉⠻⢿⣿⣿⠟⠉⠉⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⠇⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠛⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡏⠀⠀⠀⠀⣸⠈⣿⣿⡦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⠴⠚⠉⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠸⢀⣿⣿⣷⠈⠙⠲⣤⡀⠀⠀⠀ ⠘⠋⠀⠀⠀⢠⡀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠈⠙⢦⣄⠀ ⠀⠀⠀⠀⣀⣼⣷⡀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁ ⢰⣤⣴⠿⣟⠁⠀⣧⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣶⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⡴⠟⠻⠿⣶⣄ ⠀⠹⠥⢀⣿⠛⠛⣯⡤⠤⣄⡀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⢿ ⠀⠀⠀⣼⠁⢠⣿⠋⠀⠀⠈⠻⣦⢀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣤⣤⣤⣌⣿⣄⠀⠀⠀⣠⡞ ⠀⠀⠀⠁⠀⠸⣿⠀⠀⠀⠀⢀⣿⠀⡽⣷⡀⠀⠤⣤⣀⠀⣀⣀⡀⠀⢠⣤⡤⠤⠐⠲⣯⠁⠀⠀⠈⢹⣏⠛⠿⠶⠞⠉⠀ ⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⣴⠿⠃⢰⠇⠹⣧⠀⢀⡟⠀⠀⡟⢿⡄⠀⠀⢸⣇⠀⠀⠀⢹⣷⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⢹⣧⡼⠁⠀⣸⠂⠺⣿⡀⠀⠸⣿⠀⠀⣀⠀⢻⣧⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣻⠃⢀⣰⣃⡀⠀⣻⣇⣀⣀⣿⡦⠴⣿⠐⠛⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢰⡆⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠡⡄⠙⢦⠀⠀⠀⠀⠀⢠⣆⠀⠀⢸⡏⠉⠋⠉⢸⠀⠀⢀⣦⠀⠀⠀⢀⢰⠃⢠⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣥⣽⣦⡼⠁⠀⠀⠀⠀⡞⠙⣆⠀⠈⢷⣀⡇⠀⣯⠀⠀⡼⠈⢷⡀⠀⠈⢻⣄⣾⣦⢞⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡶⣿⣿⠿⢿⠇⠀⠀⠀⣰⠃⢠⠈⢳⡤⢾⡿⣇⠀⢸⠦⢼⡇⢰⡀⠹⣄⠀⢈⣿⠿⠿⠿⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣇⠀⣀⠀⣾⡤⠔⠒⠋⠹⣦⣼⣶⣼⡃⠀⣿⠸⣆⣼⡆⢈⣳⣤⣷⣼⣋⠓⠺⣧⢠⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⡆⣻⠀⣿⠀⠀⠀⢀⡶⠿⠿⠿⠛⡇⠀⠈⠛⢛⠉⠀⣼⠛⣛⠛⠋⣹⢦⡀⠹⡿⡀⠀⢸⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠋⡇⠈⢷⢿⡀⡆⠀⠘⣧⢠⠀⠀⢸⠁⠀⠀⢠⠇⢰⠀⠸⡄⢸⠀⠠⡇⠀⢳⡀⢹⡇⠀⠸⡄⠈⠳⣄⠀⠀⠀ ⠀⠀⣸⠁⠀⠷⣤⠤⠞⠃⡇⠀⠀⠸⣿⡄⠀⢸⠀⠀⠀⠸⡀⠘⢦⡀⢹⠈⡇⠀⡇⠀⠀⠇⠹⠦⠤⠔⠋⣇⠀⢸⡆⠀⠀ ⠀⠀⡇⠀⠀⠀⠱⣄⠀⠀⠙⠲⢤⠀⣿⢳⡄⠈⣇⠀⠀⠀⣹⠀⠀⠃⢸⡄⠁⠀⣹⠀⠀⠀⠀⠀⠀⣀⡤⠿⠀⣸⠃⠀⠀ ⠀⠀⠙⣶⠲⡄⠀⠘⢦⣀⣀⣀⣸⠁⢛⠦⠤⠞⠃⠀⠀⠘⠁⠀⠀⠀⠀⠛⠒⠒⠋⣀⣀⡤⠤⠚⠉⠁⠀⢀⡴⣯⠀⠀⠀ ⠀⠀⠀⢸⠀⣇⠀⠀⣠⠷⣄⠀⠀⠀⠀⠙⠢⣄⣀⣀⠤⠖⠦⠤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⠨⣿⠀⠀⠀ ⠀⠀⠀⣸⠀⠙⢦⠼⠁⠀⢸⡀⢠⠖⠋⠉⠒⠢⣄⠀⠀⠀⠀⣀⣀⣤⠾⢦⡀⠀⠀⣰⠊⠉⠓⠦⠤⣤⣞⣥⠾⢻⠆⠀⠀ ⠀⠀⢸⠉⠉⠓⠦⣄⡀⠀⠈⣧⠼⠁⠀⠀⠀⠀⠈⢧⡀⠈⠉⢡⠞⠁⠀⠀⠙⠦⠞⠁⠀⢀⣠⠤⠞⠋⠁⠀⢀⡼⠀⠀⠀ ⠀⢠⡇⠀⠀⠀⣀⠀⠉⠑⠒⠦⠤⢄⣀⣀⡀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⣀⣠⠤⠔⠒⠋⠁⠀⠀⠀⠀⣀⣀⡼⣿⡀⠀⠀ ⢀⡼⠳⢶⠞⠉⠉⠙⢦⡀⠀⠀⠀⠂⠒⠚⠿⢍⣙⣶⢶⣶⣶⣶⣖⣋⣉⣁⣠⠄⠀⠀⠀⢀⡴⠦⠤⠞⠁⠀⠀⡇⠙⢧⠀ ⣿⡇⠀⠈⢧⡀⠀⠀⠀⠙⢦⡤⠴⠒⠒⠲⠤⣄⡀⠀⠀⠀⢀⡽⠛⠯⣍⡉⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢀⡴⠃⠀⢸⡇ ⠈⢧⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡤⠞⠀⠀⠀⠈⠉⠓⠒⠒⠋⠁⠀⠀⠀⣀⡤⠞⠁⠀⠀⢀⡾⠁ ⠀⠈⠑⠦⣀⠀⠀⠀⠉⠓⠲⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠴⠒⠋⠁⠀⠀⢀⣠⠖⠋⠀⠀ ⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣀⣠⠤⠖⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣾⣿⣿⡿⠋⡴⢫⣾⡿⣻⣿⠋⠉⢹⡉⢻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⣿⣿⢿⣿⢿⡿⠁⡜⢠⣟⣿⣽⠟⡼⠀⡀⠀⢣⠀⠙⣿⣿⣷⡻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⢫⣿⣿⡟⠁⡼⢡⣿⣿⣿⠏⣟⡇⠀⢰⡀⠈⢧⠀⠘⣿⣿⣿⡽⣿⣿⣧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⣸⣿⢣⣿⣿⣿⠁⢠⣧⣾⣿⣿⠏⡼⣸⠁⠀⠀⠙⣄⠈⣦⠀⠘⣿⣿⣷⣿⣿⣿⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⢳⣿⢧⣿⣿⣿⠇⠀⣼⣿⣿⣿⣏⡤⠀⡿⠀⠀⠀⠀⠸⣆⠈⣆⠀⢻⣿⣿⣿⣿⣿⣞⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⢠⡏⣽⣿⢀⣠⣿⣹⣿⣿⠟⠁⢰⠃⠀⠀⠀⠀⠀⠘⠀⠘⢦⣸⣿⣿⣿⣿⣿⣿⢵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⡀⣿⠘⠋⢁⣿⠋⢱⠃⠀⠀⡼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⠁⠀⣀⣼⣿⣴⣶⡉⠀⠠⠏⠀⠀⢠⡇⠀⠀⣀⣤⣴⣶⣾⣍⡀⠀⡟⠿⣟⣿⣿⣿⣿⣯⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⣿⣿⠁⣄⣾⡿⠿⠿⢿⣿⣿⣿⣆⠀⠀⠀⠈⠁⢲⣾⣿⣿⠟⠛⠛⠿⣿⣆⣇⠀⠙⣿⣿⣿⣿⣿⠣⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡏⠀⣿⣿⠁⣴⣶⣶⣌⠻⣿⣿⡆⠀⠀⠀⠀⣿⣿⡟⠁⣠⣤⣄⠀⠘⣿⢻⠀⠀⢹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡇⠀⢻⣿⣄⠻⣿⣿⢯⣴⣿⣿⠀⠀⠀⠀⢸⣿⣿⣇⢸⣿⣿⣿⠦⣰⣿⡼⠀⠀⣸⣿⣿⣿⣿⡏⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠒⠾⣿⣿⠀⠀⠻⣿⡷⣶⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠻⣿⣿⣷⣿⣻⣥⣶⣿⡟⠁⠀⢰⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⣿⣇⠀⠀⠘⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠀⣴⣷⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣾⠟⢩⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣿⡼⣆⠀⠀⠀⠀⠀⢻⡿⠙⠹⢿⠏⠛⠀⠀⢀⣴⠟⣁⡴⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠃⣿⣿⣿⣿⣿⣆⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣡⣾⠟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣸⣿⣿⣿⣿⣿⣿⣧⡀⠙⣷⣄⠀⡀⠀⠀⠀⠀⢀⢠⣴⣴⡿⠛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⣿⣦⣴⣲⢖⣠⣴⣿⠟⠉⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠙⠛⠛⠋⢉⣠⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⠷⠶⠟⠉⣠⣴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠶⠶⠟⠋⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣧⠀⠀⠀⠀⠀⢘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠶⢿⣿⣦⡀⠀⠀⠀⠒⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡄⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣧⣤⣄⣀⣠⣾⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣏⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡀⠀⠀⣧⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠿⡏⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⠛⢦⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠀⠀⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⡸⣞⣆⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⣻⡿⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⠤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⢧⡵⠚⡛⠛⢶⡞⠮⣝⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢟⡴⣿⡿⠿⣿⡿⡼⣷⣭⣳⡳⣌⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢁⣿⣴⡿⢟⣿⡳⣿⣿⣦⣠⡿⣻⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢡⣾⢃⣟⣤⣿⣿⠉⠛⠻⠿⠧⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣿⣿⣿⡾⢋⣼⠃⠀⠀⠀⡇⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⣷⠏⠁⣠⠤⠤⣄⣇⠀⢀⠀⢘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠇⠀⠘⠿⣿⣿⣷⣾⠇⠘⣶⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣧⣽⣿⠀⠀⣀⠀⠀⠀⢸⣿⠀⠹⠿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣦⣯⡿⢷⣄⣿⠀⠀⢠⣾⣿⣿⡆⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢯⣼⣰⣿⢿⣷⣾⣿⣿⡋⣥⣃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣛⡳⢿⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⣤⣴⣶⣶⣶⣶⣤⣾⣿⡇⠈⠻⣿⣿⣹⢿⣿⠇⡐⠲⠮⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣯⣽⣿⣿⣿⠿⠛⢿⣿⠃⠀⠀⢻⣿⣿⣾⣿⣇⢳⡖⣧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⠟⠿⣿⣿⣿⣿⡿⠿⢿⣯⣿⣟⣿⣿⣿⣿⠁⠀⠀⠀⣿⡆⠀⠀⠀⣿⡟⠉⠉⠟⠛⠊⠯⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⠟⠁⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣇⠀⠀⠀⢸⡇⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣟⠁⠀⠀⢲⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣖⠀⠀⠀⣿⡄⣰⣿⠁⠀⢀⣤⠶⣂⡶⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣰⣿⣿⣿⠁⢀⡴⣟⣁⣴⣿⣡⠤⢤⣀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣆⠀⠀⠀⠀⠏⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀ ⠀⠹⣿⡀⠀⠀⠀⠠⢈⣻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⢣⡀⠀⠀⠀ ⠀⠀⢸⣷⠀⠀⠀⣖⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠳⡄⠀⠀ ⠀⠀⢸⡿⠃⡆⣶⣿⡿⢉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢹⡀⠀ ⣀⣴⠟⠁⠀⢗⣾⣿⠁⢺⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇⠀ ⡏⠀⠀⢠⣶⠟⠉⢿⣤⣋⣿⣗⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⡇⠀ ⣅⣀⣾⡿⠋⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⢸⠃⠀⠀⠀⠀⡼⠀⠀ ⠿⠛⠉⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢹⣶⡟⠀⠀⠈⠶⣄⠀⠀⢰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣷⣶⣤⣤⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣴⣿⣿⡇⠀⠀⠀⠀⠈⣦⠀⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠙⠻⣿⣾⣿⣿⣿⣿⣿⣿⢷⣽⣿⣦⣄⡀⠀⠀⠀⠀⢀⠞⠁⣴⡾⣿⠏⣿⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢿⣦⣴⣿⠿⠛⠛⠛⠻⣿⡿⠿⠿⠿⣿⣿⣿⣷⣶⣤⣤⣯⣴⢿⡏⢹⡏⠀⢿⡇⠀⠀⠀⠀⠀⠀⡼⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢹⣿⢁⣠⣤⣄⡀⠀⣿⠀⠀⠀⠀⠈⠙⢿⣿⡛⠛⢉⣩⠞⠉⢀⣼⡇⠀⠀⣿⡀⠀⠀⠀⠀⡼⠁⠀⢀⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⠳⢼⡿⠋⠉⠉⠉⠛⢷⣿⡶⠿⣶⣤⣤⣤⣾⣿⡅⠀⠟⠁⡰⢶⠃⠸⣿⣀⣀⣻⣧⠀⠀⠀⣴⠃⠀⠀⢰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣆⢸⡇⠀⠀⠀⠀⠀⣨⣿⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⣴⠋⣠⢼⠀⠀⠹⣿⣿⡀⠻⣦⡀⠀⠻⡄⠀⠀⠈⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠻⣦⣿⣿⡷⠶⠾⠿⣻⣿⠛⠛⠒⠶⠶⠶⠶⢾⡇⠀⡤⠞⠁⡼⠀⠀⠀⢹⣿⣷⠾⣿⣿⠀⠀⢹⡄⠀⠀⣈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠾⠿⠟⠛⠉⠉⠉⠛⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣠⣶⣿⠟⠛⠿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠉⠉⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠜⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢸⣿⡇⠀⠀⠀⠀⠀⣷⡄⠀⢿⣿⠀⠀⣾⡿⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠘⣿⠁⠀⠀⠀⠀⠰⣿⡇⠀⢸⡿⠀⢠⣿⠇⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢠⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢿⣧⠀⠀⠀⠀⠀⠋⠀⠀⣹⡇⠀⢸⣿⣇⠀⠘⢿⠃⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⣼⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡈⣻⣷⣄⣀⠀⠀⠀⢀⣸⣿⠀⠀⠘⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⢀⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⢿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠻⣿⣧⣄⣀⣀⣀⣀⣠⣴⠟⠋⠀⠀⢠⣾⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣍⠙⠻⠿⠛⠃⠀⠀⠀⠀⠀⠀⠠⢤⣝⡻⠿⣿⣯⣿⢟⡥⠀⠀⣠⡼⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⡶⠒⢂⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⢠⣾⣏⣠⣾⣿⣟⣛⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢿⣿⢿⡟⠉⠀⡿⠉⣡⣿⠁⠠⠉⢛⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠈⠷⠀⠀⠷⠀⠈⠁⠀⠀⠀⠘⣷⡿⢷⣶⠦⠤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⣸⡏⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠶⢶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡀⠀⠈⢉⡉⠉⠛⠲⠶⢦⣤⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⡴⠟⣰⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠠⠴⠦⢤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢋⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⢀⡄⠀⠀⣿⡟⠛⠿⠶⠶⣦⣤⣭⣭⣍⣉⣙⣛⣛⣓⣛⣛⣩⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣤⣀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠿⣭⣄⣈⠉⠉⠑⠒⠢⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣲⡴⠛⠁⠀⠀⠀⠀⠱⠬⣍⣓⠲⣤⣄⣀⠀⠀⠈⠙⢻⣿⣶⣤⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢶⡶⢧⠤⠤⢬⣝⡻⣿⡗⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠖⠊⠉⠀⠀⠙⠻⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⠏⠀⠀⠀⡇⣳⠈⠙⢳⡄ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠋⠁⣠⣾⠿⠖⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡞⠀⠀⣀⡴⢿⡉⣠⠔⠋⡇ ⠀⠀⠀⢀⣴⣿⡿⣫⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣦⣤⣄⣀⣾⠃⣼⣤⣾⠭⠽⣦⢴⡟⠁⣠⣴⠇ ⠀⠀⡴⣿⣿⣋⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⡦⠀⠀⠀⠀⠀⠀⠀⣈⣩⡿⠛⢻⠋⢻⣿⠿⠚⠁⢰⠃⣰⣿⠏⠀ ⠀⠀⡇⠘⢡⠟⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣠⠤⠖⢚⣩⠟⠋⠀⠀⣸⡶⠊⠁⠀⠀⢠⠇⣰⣿⡟⠀⠀ ⠀⠀⣷⣴⣿⢦⣄⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠉⠁⢀⡤⠞⢉⣠⠔⠊⠉⣿⣿⠀⠀⠀⠀⣰⢋⣠⣿⡿⠁⠀⠀ ⠀⣸⣿⣿⣿⡈⠻⢿⣦⣄⠀⠀⠉⠓⠦⣄⡀⠀⢀⣠⠤⠒⠋⠁⠀⣀⣤⣶⣾⣿⣿⠟⠉⠀⠀⠀⠀⢸⡇⠀⣀⣴⣾⣿⠿⠛⠛⠀⠀⠀⠀ ⠐⡟⣿⣿⣿⣿⣦⣀⠉⠛⢿⣶⣤⣀⢀⣠⠽⠛⠯⣄⠀⣀⣤⣶⣿⣿⣛⣿⡿⠋⠀⠀⣠⡞⢻⡽⡄⢸⣶⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⠉⠻⣿⣿⣿⣿⣿⣦⣄⣈⣽⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣠⣾⡿⣿⣿⣿⢀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⢄⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣀⣀⠘⠛⠛⠛⠻⣿⠋⠑⠒⠚⣿⣿⣻⣿⣟⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠦⣀⠉⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠩⣥⣄⣉⡿⠁⠀⠀⠀⢰⣿⢹⡿⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠉⠻⢿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⢠⠟⣿⣟⣿⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠈⣹⡿⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⢀⡼⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠤⢤⣤⣤⣤⣤⣽⣶⣶⣿⣿⠿⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⡾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢿⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢙⣶⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠻⡷⣽⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⢷⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⠁⠀⠳⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⡿⣻⣟⣟⣿⣟⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣽⣏⣩⣯⣭⣧⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢹⡏⠀⠀⢰⡀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⣿⡇⠀⠀⠈⣧⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⢀⣿⠀⠀⠀⠀⢻⣆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⢻⡗⢛⠛⡟⠒⣶⠶⠶⣾⠿⢶⣶⣾⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠛⠛⠚⠚⠛⡒⠛⠛⠛⢻⠚⠚⢛⠛⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠙⣰⣇⣀⣀⣸⣃⣀⣠⣤⣾⠷⠤⢼⠦⢈⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠉⠉⠉⢀⣠⣼⣶⣶⣷⢶⣦⣄⣀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⣇⣀⣀⠀⣠⣾⣟⡽⠿⠚⠛⠛⠀⢤⣈⠙⠻⣦⣄⣀⣀⣈⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⠟⠁⠀⠈⢩⡿⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡈⢻⣯⠉⠀⠈⢿⣆⠀⠀⠀⠀ ⠀⣠⣾⣟⣥⣤⣀⠀⣰⣟⡀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⢿⣧⣤⣤⡌⢿⣷⡀⠀⠀ ⠼⢟⠁⠀⠀⠀⠀⠹⡿⢶⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⣾⡧⠀⠀⠀⠀⠻⣿⣆⠀ ⠀⠘⠛⠛⠛⠻⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠛⠻⠷⠶⠞⠻⠇ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀

⣴⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⣄⡀⠉⠉⣙⣿⠶⠀⠀⠀⠀⠀⣀⣠⡴⠶⠚⠛⠉⠉⠉⠀⠀⢸⡇⠈⠉⠉⢉⡛⠓⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣿⠉⠉⠹⣧⠀⠀⣀⣤⠶⠛⠋⠁⠀⠀⠀⠀⢀⣀⣀⣀⠀⢸⡄⢠⡴⢿⡋⠉⠻⣦⠀⠈⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠀⣀⣼⠿⠛⠛⠛⠒⠒⠲⠶⠦⣤⣀⠀⢸⣿⣿⣿⠀⢸⡇⣿⠀⢸⣏⠉⠋⠙⣇⠀⠀⢀⣀⣈⣙⣷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠛⠿⣿⣟⠛⠀⠀⣧⢻⡄⠀⠙⠷⢤⣤⡿⠀⢰⡏⠉⢉⣭⢿⣿⣟⣉⣉⠛⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠓⠲⢶⣬⣍⣛⠒⠲⠿⠦⠿⠦⢤⣤⣤⣼⣧⣤⣼⠶⠞⠋⠁⠈⠁⠉⠉⠉⠉⠛⠒⠶⣬⣍⡛⠶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣩⡿⠃⠀⣀⣠⣤⠤⣤⣄⣀⠀⠀⠹⣷⠶⠦⢽⣆⠉⠙⠛⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠛⠛⠛⠶⢦⡀⠀⠈⠙⠳⣦⣙⠷⣄⡀⠀⠀⠀ ⠀⠀⠀⢸⡇⢀⡴⠛⠉⠀⢀⣀⠀⠀⠙⢳⡄⠀⠸⣧⠤⠤⣽⣆⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⢤⣄⣀⠀⠀⣴⠋⠁⢀⣀⣤⣤⣀⠀⠀⠻⣆⠀⠀⠀⠀⠙⠳⣮⣿⣦⡀⠀ ⠀⠀⠀⠈⣷⡾⠁⠀⣴⣾⣿⣿⣿⣦⠀⠀⢻⡀⠀⣿⠀⠀⠀⠛⠶⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠙⢻⡇⠀⢠⡿⢿⣾⣿⡿⢷⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠉⣩⣿⡄ ⠀⠀⠀⠀⢹⡇⠀⠐⣿⢿⣿⣿⣿⣾⡇⠀⢸⡇⠀⠙⠓⠒⠶⠶⠶⠦⢤⣤⣭⣍⣛⣛⣶⣶⣤⣤⣀⣀⣸⡇⠀⠸⣟⣿⢻⣯⣟⣿⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢿⣏⣿ ⠀⠀⠀⠀⠀⢷⡀⠀⠻⣾⣰⣏⣹⡿⠁⠀⣼⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣙⣛⣿⡄⠀⠙⠷⢼⡷⠞⠋⠀⣠⣟⣀⣀⣀⣀⣀⣀⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠈⢷⣄⠀⠈⠉⠉⠁⠀⢀⡾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣦⣀⠀⠀⠀⠀⣀⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢤⣤⠤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣤⣿⣯⣻⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣷⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣿⣿⣿⣿⣿⣿⢋⡴⢚⣹⠗⢦⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢻⣿⣿⣿⢿⣤⠔⢉⡤⠒⣫⡿⠛⢲⣤⣞⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠋⠀⠙⠋⢣⡤⠋⡠⠛⣡⣴⣾⡿⠗⠚⣷⠢⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣘⣷⣞⡠⠞⣡⠞⠋⠀⠀⠀⠘⢷⠀⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⡏⠀⠈⠻⡎⠀⠀⠀⠀⣴⣷⠀⠈⠛⣷⣦⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠁⠀⠀⠀⠀⠛⢹⣿⣶⡖⠋⢽⣿⣿⢧⠙⡏⠙⢷⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⠂⠀⠀⠀⠀⠀⠀⠈⠉⢹⡀⠀⠀⠉⠉⡼⠀⡿⠀⠀⠙⠷⢿⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⢀⡴⠃⣴⠇⠀⠀⠀⠀⠸⡟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡄⣴⠇⠀⠀⠀⠀⢀⣰⡇⠸⡷⠶⠶⡦⠤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠺⠷⠶⠶⠶⢶⠶⠶⢤⣀⡀⠹⢏⡼⣹⠀⣀⡴⣾⢿⣿⡼⣇⢀⡷⠒⣲⣶⠶⢋⣹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⠀⠀⠀⠀⠉⠓⠦⣄⡀⠉⣳⠯⠼⣏⣿⣷⣶⣿⣿⣾⢟⠛⠛⢉⣉⣡⡤⠾⠋⢭⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠉⣹⠿⠿⣆⣀⣘⣮⢿⣿⣿⣿⡟⠛⠒⠋⠉⠁⠀⠀⠀⣀⡾⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠳⡀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⣦⢀⣀⣀⣠⠤⠖⠋⣁⣼⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢴⣯⣀⠀⠀⠙⢦⣄⢀⡀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣋⣿⣿⣴⣤⡴⠖⠋⠁⢨⣿⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠛⠦⣀⠀⠈⠉⠙⢶⣉⠿⠲⠶⢤⣤⣤⣤⣀⡤⠶⠋⠁⠀⠉⠀⠀⠀⠀⣀⣠⠔⠋⣸⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠉⠛⠒⠒⠶⠶⠷⠶⠒⠛⠉⢸⠀⢾⣷⣶⣤⣤⣴⠶⠶⠶⡖⡚⣋⣀⣴⠾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⣿⠿⠿⠾⠷⠿⠧⠶⠿⠟⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢨⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡶⠛⢦⣀⣷⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠙⠓⠦⣤⡀⠀⠜⣰⠃⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠋⡀⠀⠀⠉⠛⢧⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠁⣠⠋⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠁⠠⢳⣄⠀⠀⠀⠀⠙⠦⣄⡘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠇⢠⠇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠈⠉⢻⡦⣄⣀⠀⠀⢀⣀⡬⠿⠛⠛⠲⠤⢤⣀⡀⠀⠀⠀⠀⠸⡀⣿⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⡀⠀⢀⡾⠀⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠢⢄⡀⠀⠀⣿⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣶⣾⣷⣾⣿⣿⠿⠿⢿⠟⠿⠛⠛⠛⠛⠛⢻⢾⠿⡿⡿⠛⠛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⣶⠞⠋⠉⠀⠉⠩⣇⡉⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣫⠁⠀⣰⠋⠀⠘⢳⡀⠀⠀⠈⠙⢦⣀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⢋⡾⠁⠀⠀⡏⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠙⢧⡀⠀⠈⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢃⡼⠁⠀⠀⢸⠁⠀⠀⢸⡂⠀⢷⠀⠀⠀⠀⠀⠀⠹⣆⠀⠄⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠇⣼⠃⠀⠀⠐⢸⡀⠀⢸⠉⢹⣀⣘⣇⣀⣀⣀⣀⠘⠀⠘⢧⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⢠⡧⠤⠶⠖⠒⠚⠛⠛⠉⣇⣸⠉⠉⠉⠉⠉⠉⠉⠉⠙⢲⡜⣇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢻⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⢠⣾⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⢰⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀ ⠐⣿⡄⠘⣇⡇⠀⠀⠀⠀⣶⣶⡄⠀⢠⣤⣤⠀⠀⢴⣶⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⠘⡇⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⣷⠀⠰⡄⠀⣾⠀⠀⠀⠀⠀⠀ ⢠⡟⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡇⠀⢺⠀⠀⠀⠀⠀⠀ ⠘⣧⢿⡆⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡇⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⣿⣸⠀⠠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⡇⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⢻⡏⡇⡀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠘⣿⡇⢹⣧⣷⠶⢶⠶⠶⠶⡶⠲⣶⣶⣒⢒⣯⣿⣿⣿⡏⡟⣿⠿⢻⠁⠀⡇⠀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡆⣧⠘⠀⠸⡄⢰⡄⣷⣀⣿⣿⣿⣿⣿⣿⡿⢹⣇⠇⡼⠁⡞⠀⠀⡇⠈⠛⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⢿⠀⢷⠀⣧⠰⣷⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⣿⣷⡇⢰⠇⠀⢰⠃⢠⣰⢻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⢸⠀⠘⡆⣿⣴⣿⣿⡟⠃⠈⠉⠁⠀⠀⠀⠀⠛⣻⡇⣿⣦⣤⣄⣀⠀⠈⣇⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⣼⣤⣶⡟⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣽⣄⠀⠀⠀ ⠀⣠⣴⣖⣛⠻⡿⠿⣿⣿⣿⣿⣿⣿⣧⣀⣤⠶⠶⢶⣤⣀⣾⣿⣾⣿⡿⣟⣿⣿⣿⣷⣶⣾⣿⣿⣦⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣾⡿⣭⣛⠿⣿⣿⣷⣶⣶⣶⣶⣦⣽⣿⣿⢟⣩⡾⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⠻⣯⡿⢿⣿⣿⣿⣿⣿⣿⢟⣴⠟⠉⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠙⢶⣝⣿⣿⣿⣿⡽⠟⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠐⠀⠉⠻⣿⡿⠋⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣈⣡⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠲⠶⠖⠒⠛⠙⠲⠤⠖⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⢠⠀⣰⠀⠀⠀⣴⣀⣠⠀⠀⢀⡀⠀⠉⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⣠⠀⢠⣟⣷⣿⣤⣶⠾⢁⡿⣾⠀⠀⡿⣿⣄⠀⠀⠀⠈⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⢋⡅⠀⢸⡿⡏⢀⡾⢤⣿⠟⠉⣿⠀⣼⣿⣿⣦⣰⣇⡇⡇⠀⠀⠀⠀⠀⢠⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠾⣵⡂⠀⢹⣶⣈⢻⡇⠉⠀⣖⠃⠀⠀⠉⠘⠃⠟⢻⢻⡟⣽⠀⡇⠀⠀⠀⠀⠘⠋⣁⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠀⠈⠙⠲⢾⣿⠛⠛⠲⣄⠀⢿⠀⠀⠀⣰⠀⠀⠀⣠⡾⠘⠁⠀⣡⡶⠓⠲⢦⡐⣿⣥⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡄⠀⠀⠀⣸⠁⠀⠀⠀⠈⠳⠤⢤⣀⣠⣇⣀⣀⣼⣧⠤⠤⠶⠞⠁⠀⠀⠀⠀⢹⡄⠈⠁⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡏⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡆⠀⠀⣼⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⢠⡾⡃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡸⣧⣿⠛⠀⢠⣴⢻⠉⠉⠙⠓⠦⢤⣀⠀⠀⠀⠀⠀⠈⣯⠉⠉⠉⠉⠉⠉⠛⠦⣄⠀⠀⢷⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠯⢽⡿⠃⠀⠀⠛⣿⣿⣷⣶⣶⣤⣤⠴⠛⠀⠀⠀⠀⠀⠀⠙⠳⣶⣶⣶⣶⣾⣓⡖⠪⠿⠍⢿⡇⣼⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠀⠀⠀⠀⠀⠀⢸⡟⢯⣽⣿⣿⣏⣙⣟⢦⡀⠀⠀⠀⠀⢤⣴⣾⣟⣻⣿⣿⣿⣿⡿⠂⠀⠀⠀⢷⠁⠘⣆⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠥⢤⣤⠿⢊⡇⠀⠀⠀⠀⣼⡌⡷⢤⣀⣐⠦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠉⠀⢸⡀⠀⠀⠀⠀⢹⡇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠀ ⠀⠘⣦⠀⠘⢧⡀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡇⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⣸⠇⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡀⠀⠳⣄⠀⡤⠞⠁⠀⠀⠀⠀⣤⠼⠛⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⢳⡀⠀⠀⠀⣰⠟⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢨⡧⠀⠀⠀⠀⢹⠀⣠⠞⠁⠀⠀⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠀⠀⠙⢧⣀⣀⣀⡤⠴⠞⠋⠲⠶⠶⠶⠒⠒⠋⠙⠳⣄⠀⠀⣨⠞⠁⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠈⠳⠞⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣖⣒⣋⣉⠙⠒⢉⡉⣓⣲⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠉⠉⠉⠉⠉⠉⠉⠉⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⠤⠤⢀⣀⣀⠤⠤⠤⠖⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀ ⠀⣀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠦⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠶⠶⠶⠛⠳⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⣶⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⠻⣿⣿⣿⣿⣦⡀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣃⠀⠀⠀⠀⠀⡈⣙⣳⣤⣀⠀⢀⣼⣦⣤⣀ ⠀⠀⠀⠘⣿⣴⣦⣻⣿⣿⣿⣿⣷⣴⡟⠁⠀⠀⠀⠀⠀⠀⣠⡶⢛⣉⣠⣤⣤⣉⡙⠻⠶⣶⣦⣶⣿⢿⣭⣙⣿⣴⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠛⠋⠉⠉⠉⠉⠉⠉⣹⡏⢁⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡿⠿⠿⣿⣿⣿⣾⡀⠀⠉⣻⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⡏⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠉⢀⣠⣤⣠⡈⠙⢿⣿⠀⠀⣿⡟⢋⣥⣹⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⡀⠀⠀⠀⠀⠀⢘⣿⡟⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⣿⡆⢠⡿⠀⣼⣿⣿⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠇⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢿⣿⣿⣿⣿⡿⠁⣀⣿⡇⢸⡇⠀⢿⣿⡿⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣆⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠉⠉⠉⠉⢁⣀⣿⣿⠁⠀⣿⣄⡜⢉⣤⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣅⠀⠀⠀⠀⠘⠙⢿⣿⣶⣶⣶⣶⣶⣾⣿⡿⠟⠀⠀⣻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠈⢻⣿⣷⣤⡀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠉⠉⢀⣴⣿⣿⣿⠋⠀⣹⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣤⣤⣶⣿⡿⠷⣿⣿⣷⣤⣀⣀⡞⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⢀⣴⣟⣷⡶⠶⢶⣒⠀⠀ ⢀⣀⣀⣀⣀⣤⣴⠿⠛⠙⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠠⠄⠀⠀⠀⠀⠀⠀⠈⠩⠀⠀⣸⠋⠉⠀⠀⠀⠀⠈⠁⠀ ⠈⠉⠉⠽⠛⣿⣿⣶⣶⣶⣶⣶⣤⣤⣠⣦⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠈⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⡇⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣤⣤⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠋⠉⠉⠙⢿⣿⣴⡾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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