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⠀⠠⠀⠈⠐⠂⠀⠀⡁⠒⡉⠂⣝⢣⡄⣌⡱⢜⠂⣏⣷⣿⡿⣿⣿⣿⢿⣿⢫⡼⠟⢣⣟⡿⣾⢀⡄⢠⠀⡀⣄⣶⡙⠹⠀⡷⠿⣿⢰⡁⠐⢠⣇⣿⣿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀ ⠀⠀⠀⡐⡈⢳⠀⢘⠃⠤⡙⠦⣙⡽⣾⠶⠻⡝⢎⡱⢿⡣⣿⣿⣿⣿⣿⣿⢿⣟⡿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠄⠁⣄⣷⠸⡇⣨⠀⠁⠀⠀⠀⡀⣿⣽⣷⣿⣾⣿⣯⣭⠲⠉⠀⠀ ⠀⠁⢀⠊⢄⠫⣇⠎⡁⠴⡙⢦⡍⡿⣎⣷⠯⣻⣿⣷⡿⢯⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡐⠀⠀⠀⠀⠀⠰⠀⣄⠠⣄⣦⠛⠐⠆⠀⠀⠀⠀⣿⣿⠀⣦⢙⠀⠀⠀⠀⡀⣦⣾ ⠂⠀⠠⠘⢣⢌⠣⢤⠘⡤⠑⢢⡟⣿⣜⠿⢧⡽⡾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡈⢧⠜⡷⢸⠀⠀⣷⣿⠀⠀⡄⠱⠀⠀⠀⠀⠀⠀ ⠀⡁⠄⠀⢱⡲⠀⣂⠑⠂⡡⢮⡗⣿⣟⡭⢾⡻⣽⢿⣾⣟⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠟⡿⢿⣿⠿⠻⠘⠀⠀⠀⢠⠀⣤⠳⣄⡷⣿⠀⠀⡇⣿⠀⠊⠠⡇⢆⠈⠀⠀⠀⠀ ⠀⠀⢀⠀⡀⠠⠐⠌⡡⠲⢎⡕⣯⣿⢳⣷⣟⢯⣿⡷⣞⣻⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣶⣽⣿⢿⠛⢈⠀⠀⠁⠀⢦⠑⣧⢸⠀⡇⣿⠿⢠⠀⢸⠀⣆⠠⠀⠀⠀ ⠈⠀⠀⠀⠀⠄⠈⡒⣍⢳⣌⡹⣿⣻⣽⣾⡽⣿⡿⣿⣿⣟⢯⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⡻⣙⣌⣙⣯⣟⣿⣿⢿⠹⠀⠀⠀⡀⠘⣆⠈⡄⣿⣾⠀⡇⢀⠀⠁⠔⣀⠀⠋ ⢓⠡⠀⠈⠀⠀⣅⠲⣎⡷⣝⠮⣿⣷⡿⣟⣿⣿⣷⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣹⠵⣮⣷⢿⠻⠈⠀⡀⠀⢀⡇⣿⢸⠃⣿⠀⠀⡰⠀⠃⡟⣯ ⡀⢳⢣⠀⢂⠄⡃⢿⣞⢫⣷⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⡛⣈⣦⣳⡰⢆⠙⡀⣤⣀⢿⠹⠀⠀⡇⣾⠀⡿⢠⠀⠀⠁⠟⣽⡾⣟ ⠀⡀⢦⠙⢂⠤⠘⡄⣿⢯⣳⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣯⣟⣯⣿⣾⣿⣶⣶⣤⢶⠛⣌⢶⠙⠄⠤⣧⠘⠀⠀⣿⢸⠀⠀⡇⢰⡏⣠⠀⠁⠟⣽⣿⡿⣷⣿ ⠀⠀⠀⡇⠸⢀⠀⠀⡄⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⢧⣼⡼⣤⣠⣀⢀⠀⠀⠀⠀⡀⣤⠻⡘⢤⠻⠛⢿⠀⠀⣠⢀⠀⠀⣠⠀⠀⠀⠟⣿⣧⣿⣿⣧⣿⣿ ⠀⠀⠀⡀⣷⠈⠃⠀⠀⡄⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡽⡻⢧⢌⠀⠀⠀⠀⠀⠁⠈⠀⠠⠀⠘⣄⣦⠻⡈⢧⡙⢱⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡀⢦⠈⠢⠉⠀⠀⣆⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⢾⣿⣯⢿⣿⡷⢭⡷⣯⣷⣿⣿⣿⣿⣿⣾⠳⢢⠜⠀⠀⡀⣄⠙⣄⠹⢀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿ ⠄⠃⠐⠈⠉⠀⣄⠱⠉⢢⠀⠀⡁⣿⣿⣿⣿⣿⣿⣷⣿⣿⣞⢯⣷⡽⢻⣻⣿⣴⡛⢿⣿⣶⣠⢀⠀⠀⠁⠉⠘⠀⠀⠀⠀⡀⠠⣆⢸⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣊⠱⢣⡌⣙⣽⠮⠻⡙⣈⣤⠲⡙⣿⢿⡉⣿⣿⣿⣿⣿⣺⢿⣞⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠾⠿⡿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⣧⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠞⣉⠶⣍⠳⢮⣝⣳⣝⣽⣾⢿⡿⣻⣛⣉⡍⣿⣿⣿⣾⢟⢳⣽⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠖⣋⢦⣙⡷⢎⣹⡷⣏⡳⣾⣟⡷⣞⣿⣿⣿⣿⣿⣿⡶⣞⡿⣟⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡼⢛⣮⡝⢳⣭⡷⢯⣫⣷⣟⣳⣾⣽⣿⣿⣿⣿⢷⣻⣭⢿⣷⣏⢢⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢰⠁⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢧⢳⣯⡟⢣⣵⡻⢶⣟⣯⡽⣿⣟⣿⣿⣿⣿⣿⣿⣽⣿⣯⡳⣝⣣⣿⣿⣿⣿⢻⣀⣦⠀⣀⣠⢀⢏⡿⢺⡑⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣵⡻⢶⡽⣫⣷⡟⣯⢷⣯⣞⡿⣿⣿⣿⣿⣿⣿⣻⣾⢷⣌⠴⡉⠣⣍⣿⣿⣿⣿⢈⠀⠀⠀⠀⠏⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣳⡽⣯⡷⣞⣽⡾⣟⣻⣷⣟⣿⣿⣿⣿⣿⣿⣿⣮⣟⢣⣙⠄⡂⠱⡏⣿⣿⣿⣿⢠⠀⠀⠀⠀⣿⣾⣠⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡆⣀⡀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣏⡳⣽⣻⣷⣟⣮⢿⣯⣳⣿⣿⣿⣿⣿⣿⣿⣡⢶⡟⢿⡿⣿⢿⡽⣞⣿⣿⣿⣿⠘⠀⠀⠀⠀⣀⠀⠉⠟⡹⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢲⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣹⢿⣯⡷⣽⡿⢯⣾⣟⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣷⣶⣻⣿⢻⣆⣿⣿⣿⢺⠀⠀⠀⠀⠋⡿⣿⣿⣹⣙⠋⠙⠈⠀⠀⠀⠀⠀⠀⠀⡄⠹⡈⠱⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡵⢞⣻⣽⡿⣯⣟⣫⡿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⠷⣭⣯⢿⡏⣿⣿⢠⠀⠃⣿⠟⣿⣿⣿⣿⠶⣛⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢿⡀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣞⣏⡾⣟⡿⢯⣿⢯⡿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⣿⣯⢹⡟⣿⣿⣿⣿⣿⠈⠀⡆⢿⣿⣿⣿⣨⠟⡿⢿⣈⠫⠟⡾⣶⢰⠀⠀⠀⠀⠃⣿⣶⠀⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿ ⢧⢣⣼⣻⢷⣯⢾⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⠛⠾⠀⠀⠀⠀⠀⠀⢧⠛⠇⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿ ⢣⢱⣮⡜⣻⢷⣯⢾⣾⣿⣿⣿⣿⣿⣿⣿⣎⡽⣨⡴⣀⣒⣀⣡⢞⣫⣶⢝⣫⣜⣿⣶⡞⢛⣥⣈⣤⣤⣦⣶⣳⣁⣩⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣷⣾⠃⣿⣿⣿⣿⣿⣿⣿ ⡖⡙⢮⣝⡼⣻⣷⣟⣿⣽⣿⣿⣿⣿⣿⣻⣽⠿⢧⡘⠃⠡⢃⣡⠾⣝⣩⣌⡄⢄⡹⢦⢎⠠⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠻⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿ ⠦⡜⢎⡳⣜⣻⣷⢯⢾⡿⣿⣿⣿⣿⣿⣿⣿⡹⢭⡯⢛⡹⡹⢯⡆⠐⠠⠀⢀⠐⠒⢡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢻⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢇⡎⢍⣲⡽⣞⣻⣷⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡹⠻⢊⠭⡂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⠹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠣⢆⣉⡼⡟⣧⣟⣯⣗⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢛⣀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡙⢧⢎⡭⢗⣫⢷⣯⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡎⠉⢳⣬⡝⣮⡗⢻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⡌⠳⣎⡗⣏⢯⣱⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡙⢬⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠎⣋⠵⣏⡱⢾⣟⣧⡽⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⠘⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣴⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠞⢣⡹⢶⣹⡼⢺⣯⣟⡾⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢤⠥⣿⢿⠼⠀⠀⠁⡿⣿⣿⣾⢯⣰⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡞⢇⡹⣶⡟⣏⠡⢯⣿⣟⢷⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣩⣟⣿⣿⠘⡷⣾⣀⣰⣞⢀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡜⢯⡱⣾⢫⣵⡾⣟⡽⣿⣯⡿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢛⣍⣯⣿⣿⣀⣿⢿⠹⡴⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡽⣟⡧⣟⣞⣳⣽⣻⣾⡿⣽⢿⣯⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣬⢠⡁⠭⢮⡙⣄⣷⢿⣿⣿⣩⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⡗⣯⠷⣟⣯⡷⢯⣷⢿⣯⡿⢿⣻⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠓⢉⠊⠺⡓⣉⣭⢮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡽⣻⣽⣿⡷⣞⣻⣿⣿⣯⣿⢯⣿⢿⣿⣯⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣤⣤⢤⣠⠤⢫⡛⣒⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢾⣿⣷⣿⣯⣿⣟⡿⣿⣿⣿⢿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣉⣏⣙⠨⡀⣀⠀⡄⣉⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣛⢛⠟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣯⣻⣽⢧⠰⡀⢄⠣⣘⢯⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣮⣻⢦⣲⣓⣻⢁⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠁⡾⢀⡇⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣻⠁⡾⢀⠟⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡄⣷⢸⠀⣆⠹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⡀⣷⠈⠀⣄⠙⠀ ⠀⠀⠀⠀⠀⠀⠁⠋⡷⣽⠦⠻⡟⢰⠀⠀⡀⢸ ⠀⠀⠀⠀⠋⠖⣀⢀⡅⣻⣴⢦⣝⠳⠙⠀⠞⢀ ⣢⣠⣤⢱⢺⠀⠀⠏⣽⠈⠉⠈⣌⢿⡄⢻⢹⠀ ⣒⣒⣒⢑⠏⠾⠴⢤⠤⠤⠳⣎⢸⡇⠸⡇⣻⠀ ⠀⠀⠃⢀⠀⣿⢠⠀⠀⠀⠀⣄⠹⡀⢁⠉⣞⠀ ⠀⠀⠀⣤⣠⣠⠀⠀⠀⠀⠀⠀⠀⠉⡗⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢺⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀

⠀⠋⠯⣻⣿⣿⣿⣷⣯⣟⣿⣿⡿⣿⣿⡿⣿⢿⣿⢿⣿⣷⣿⣿⡿⣿⢿⠿⠙⠀ ⡏⣟⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣯⣿⣻⢿⣿⣿⢻ ⣿⣿⣿⡿⣿⣿⣿⣿⣾⣤⣀⠀⠀⠋⡟⠻⠈⠀⠀⣀⣤⣷⣿⣿⣿⣷⣿⣟⣿⣿ ⣿⣿⡿⣿⣿⣿⣴⢀⠀⠀⠀⠋⡟⣿⣿⣿⣴⠀⠀⠀⠀⠀⡀⣦⣿⣿⣾⣿⣿⣿ ⣿⣟⣿⣿⣿⢠⠀⠀⠀⠃⠿⣿⣿⣿⣴⢀⠀⠀⠋⠿⠈⠀⠀⠀⡄⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢠⠀⠀⠀⡄⣷⣿⣿⣿⢙⠀⠀⠋⡿⣿⣿⣿⢻⠈⠀⠀⡄⣿⡿⣿⣿ ⣽⣿⣿⣸⠀⠃⠻⠈⠀⠀⣄⣷⣿⣿⢿⡿⣿⣿⣾⣦⣿⣿⣿⢻⠈⠀⣧⣾⣿⣿ ⣿⣿⣿⢸⡗⣿⣿⣿⠻⠈⠀⠀⣏⣿⣿⣿⣿⣹⠀⠀⡀⣦⣿⣿⣿⠰⡇⣿⣿⣿ ⣻⣿⣿⢹⠀⣄⣷⣿⣿⣿⠻⡿⣿⣿⣾⣷⣿⣿⢿⠙⠀⠀⡀⣧⢠⠀⡟⣽⣿⣿ ⣿⣿⣷⣿⠘⠀⠀⣄⣷⣿⣿⣿⣾⣠⠀⠀⣅⣿⣿⣿⢿⠘⠀⡀⠀⠃⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠘⠀⠀⠀⣄⣷⣠⠀⠀⠁⠟⣿⣿⣿⣴⢀⠀⠀⠀⠃⣿⣷⡿⣿⣿ ⣿⣟⡿⣿⣽⣿⠻⠈⠀⠀⡀⠀⠁⠟⣿⣿⣿⣴⢀⠀⠀⠀⠁⠟⣽⣿⣿⣿⣿⣿ ⣿⣿⣿⣻⣿⣿⣿⣿⠿⠛⠉⠀⠀⣀⣷⣴⢀⠀⠀⠉⠛⠿⣿⣻⣿⣿⣿⡿⣿⣿ ⣧⣿⢿⣿⣿⣻⢿⣿⣻⣿⣿⣽⢿⠿⡿⢯⠿⡿⣟⣿⣻⣿⣿⣟⣿⢿⣿⣿⣿⣼ ⠀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢐⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠈⣾⠁⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⣿⣿⣿⣿ ⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⠃⡿⢻⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿ ⡅⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⢿⣝⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿ ⡌⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⢿⣝⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿ ⣽⣆⣿⣿⣿⣿⣿⣿⣰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿ ⣿⢻⣆⣿⣿⣿⣿⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⣿⣿ ⣿⣿⢻⣦⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣷⣿⣿⣿⣿⣿ ⣿⣿⣿⢻⢎⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⠻⡄⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡻⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⣿⢹⣇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢻⣄⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢏⣿⣿⣻⣒⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⣿⣿⣿⣻⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡘⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢋⠀⢆⣿⣿⣿⣿⠈⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⣿⣿⣿⢻⡇⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⢀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⣿⣿⣿⣿⡚⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣠⢋⡿⣿⢿⠹⣌⣷⣿⣿⣿⣿⣿⣿⣾⣶⣵⣭⣭⣭⣶⣷⡇⣿⣿⣿⣿⢻⣆⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢠⡟⣿⣿⣿⣿⣿⣿⠻⣌⣷⣴⣩⣟⠿⣿⣿⣿⣿⣿⣿⣿⠿⢙⣷⣿⣿⣿⣿⠈⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⢻⣄⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⠸⣿ ⣿⣿⣿⣿⣿⣿⣿⠻⠎⡓⣿⣿⣿⣿⣿⣿⣿⢻⣦⣿⣿⣿⣿⣸⣄⣿⣿⣿⣿⣿⣿⣸⡟⣿⣿⣿⣿⣿⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⣌⣶⣷⣿⣿⣿⣿⣿⢻⣌⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣴⢇⣿⣿⣿⣿⣿⣿⢥ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⢆⡻⣛⣛⣝⡿⣿⢿⠻⣙⣄⣭⣭⣭⣽⣿⢿⡹⡿⣿⣿⣿⣿⣿⣼⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⣝⣭⣭⣩⣛⢛⠙⠈⡇⣿⢿⠿⣻⣛⣬⣦⣿⣿⣿⣿⣿⣴⢋⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣵⣩⢛⠛⣛⣬⣷⣿⣿⢸⠀⡀⣀⣉⣉⢛⡿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣴⢀⠃⡿⣿⣿⣿⣿⣿⣿⢿⡙⣦⠀⠸⠀⠀⣅⣇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡀⣤⢈⠁⠘⠃⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⢿⠘⣧⠸⠃⡀⡀⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠏⣣⡾⣡⡚⣄⣦⣧⣿⣿⣿⣿⣿⣿⣾⣜⡙⢢⠃⢇⠀⡀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠇⣿⡼⢏⣾⠌⠇⡸⡘⣿⣿⣿⣷⣿⣶⢿⠀⡃⢏⡘⡇⡇⠈⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡿⣼⡇⣿⢳⠇⣼⡏⣾⡏⢻⡙⠉⠈⢀⣦⠏⣶⣿⢠⡾⡏⢀⣯⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣷⢸⣿⣿⡘⡟⢃⣿⢡⣮⠶⡴⣠⣂⢐⠇⢸⠀⠀⠁⢧⢸⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡷⣿⡎⣿⢿⣇⣸⢰⡿⣼⠁⠋⠾⠠⠆⣴⠀⠀⠀⠉⡤⢀⡏⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣶⢳⣎⣿⠹⢷⠈⣤⠀⡥⣋⠿⠾⠡⠀⠀⠍⢩⠚⢀⡛⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠍⣖⣷⣿⣿⣿⠈⡦⣶⣶⣩⢟⣀⡭⣾⣲⣠⠉⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣉⣤⣐⢢⡀⣀⣀⢗⠘⡖⣡⡉⠟⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛⠿⡛⢛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⣀⣀⣀⣤⣤⣦⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢟⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠉⢠⠀⠀⠀⠀⠀⡾⢯⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣶⣷⣿⣰⣄⣷⣿⣿⣷⣿⣿⠈⠉⠉⠉⠋⠟⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠤⠤⡀⣤⣷⣴⣉⡗⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢾⠳⠁⠈⠀⠀⠀⠀⠀⡇⠈⠀⠀⠃⠗⣿⣿⡿⣿⣿⣶⣴⣠⣄⣿⢹⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⢸⠀⠃⣝⣯⠦⠓⠛⠛⠿⣝⠲⠒⡅⣤⣤⣤⢀⠀⠀⠀⡇⢻⠒⡗⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⠈⠀⣷⣞⠀⠀⠀⣀⣦⣷⢿⠙⠉⠈⠀⠀⠀⠀⠋⠒⡷⣸⠀⡀⣿⣿⣿⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠦⠿⢙⠈⠀⠀⠀⠀⡀⣦⣿⢿⢿⠈⠀⠀⠀⠀⠀⡅⢹⠟⡿⣿⣿⣿⣿⣿⠹⠀⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⢤⠧⠀⠀⠀⠖⡹⣿⣿⣿⠙⠁⠛⠈⠀⡃⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⢤⠤⠦⠒⠗⠺⢝⡤⣤⣤⠶⡴⣠⢀⣄⣦⣷⣿⣿⣽⢤⣷⢰⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠉⠒⠄⠤⣦⠹⠐⠀⠁⠾⣤⣤⠸⠁⠈⡄⢻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠄⠠⠀⠄⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⠁⠉⡍⠻⣍⠟⡿⣨⠀⠀⠀⠀⠀⢀⠀⣆⡗⣾⣷⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⣏⣿⣿⣿⣿⣿⢹⠈⠀⠀⠀⠀⠀⠀⠀⡀⢦⡀⣦⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢥⣹⣄⣠⣀⣁⣉⣜⣷⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡽⣼⠀⠀⠃⠟⡿⣼⠒⡟⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⣗⣿⣻⣟⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠈⠀⠀⡄⣾⣷⢡⠛⠿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⡬⢦⡶⢻⡇⣾⣤⣁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⠻⠉⠉⠈⠉⠚⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠹⣌⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀⣦⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣾⣤⣖⣷⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠈⠇⣿⣿⣿⣿⢿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⡌⣷⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣡⠛⣉⣤⣷⣿⣿⣿⣿⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠶⣙⣦⣷⣿⣶⢀

): ☭reltiH⣿⣟⣿⣷⣯⣽⣿⣿⢾⣭⢶⣽⠢⡜⢻⠳⢎⡣⣽⠰⠈⠀⢀⠀⠀⠀⡀⠀⡔⢃⣠⡜⠠⢀⠁⡿⢻⡟⣿⢿⠻⠉⢦⣆⣿⢈⣀⠀⡏⢾⣯⡟⠸⠀⠀⠀⠀⠀⠀⡀⢀⣿⣿⣿⣿ ⣿⣿⣿⢯⢷⡌⣿⡧⣼⣛⢦⣙⠦⢂⠁⣉⣄⢢⡱⢎⡀⢜⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣻⣾⠻⠈⣇⢸⠗⣿⣾⣿⣿⣿⢿⠀⠂⠈⠀⠁⠀⠐⠒⣍⣶⣿⣿ ⣿⣾⡿⣵⡻⣔⠸⣱⢾⣋⢦⡙⢲⢀⠱⠈⣐⠄⠀⠈⢀⡐⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢯⣿⣿⣿⣿⣿⣏⣿⠻⣟⠻⠙⣤⣯⣹⣿⣿⣿⣿⠀⠀⣿⠙⡦⣿⣿⣿⣿⢿⠙⠁ ⣽⣿⣟⣧⡜⡳⣜⡛⣧⢛⣮⡝⢠⠀⠣⣀⡘⢂⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⢷⡘⣣⢈⡇⣿⣿⠈⠀⣿⣿⢻⣎⣿⣿⣿⣿⣿⣿ ⣿⢾⣻⣿⡎⢍⣿⠽⣮⣽⢞⡑⢨⠀⠠⢒⡁⢄⠂⡀⠁⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣠⢀⡀⠀⣀⣄⣧⣿⣿⣿⡟⣿⠛⣌⠻⢈⠀⣿⣿⢸⠀⣿⣵⣟⢸⡹⣷⣿⣿⣿⣿ ⣿⣿⡿⣿⢿⣟⣯⣳⢞⣍⡱⢪⠐⠀⡌⠈⠠⡐⠀⢈⠡⠄⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠉⠂⠀⡀⣤⡷⣿⣿⣾⣿⡙⣮⠘⡇⣿⢸⠀⣀⡟⣿⡇⣿⠹⣟⣿⣿⣿ ⣷⣿⣿⣿⣿⣻⣷⢭⠲⡌⠳⢆⠀⠄⠂⠁⢂⠀⢀⠀⠀⠠⡐⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⢄⠦⠳⠦⠐⠠⠀⠀⡀⣆⣿⣿⣿⢿⣧⠹⣷⢻⠀⠁⣿⢸⡿⣿⣾⣫⠿⣿⣴ ⡬⣞⣿⣷⣿⣿⠺⣍⠱⢈⠢⣑⠀⠈⢀⠠⠀⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⣊⠑⠈⡀⣄⣷⣿⢿⣿⡿⢸⠀⡇⣼⠀⣿⣿⢏⣿⣼⢠⠐ ⢿⡌⡜⣿⡽⣻⢼⡀⠡⡔⠈⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢤⠷⠙⠌⢏⡹⣦⢿⠛⠿⡀⣆⣿⣿⢸⠁⣿⢀⡟⣿⣿⣾⣠⠂⢁⠠ ⣿⢿⡙⣦⡽⣛⣧⢻⠀⡐⠌⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠐⠠⠐⠀⠁⠀⠉⠉⠛⡉⣤⠳⡉⣦⣻⣛⠘⣧⣿⣿⠀⡇⣿⣿⢸⡏⢰⠟⣿⣾⣠⠂⠀⢀⠈⠀ ⣿⣿⣿⢸⣇⡿⣿⣿⢻⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⡘⠃⢃⠛⠟⠿⡿⣿⣿⣿⣿⢿⠛⣄⢧⡛⣄⣤⡀⣿⣿⠟⡿⣿⣿⠟⣿⣿⣿⣠⠀⠘⠀⠀⠘⠀⠀ ⣿⣿⣿⢿⠈⣷⣼⣿⣿⢻⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⢄⡘⡳⣿⣿⣿⣿⣿⣾⣷⣿⣟⣿⣧⠻⠙⣄⢷⡘⢦⡎⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⡙⣷⣝⣶⣿⣿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠐⡀⠀⢈⡒⢈⠐⠈⠀⠀⠀⠀⠀⠁⣌⡝⣣⣿⣿⢿⠻⣦⠻⣆⡿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀ ⣻⣼⣯⣷⣶⣿⠻⣎⣶⡝⣿⣿⢾⠀⠀⠀⠀⠀⠀⠈⠀⠀⠡⡐⠈⢂⡄⠄⠀⠋⢤⡀⠀⠉⠟⡿⣿⣿⣾⣶⣧⣿⣿⣿⣿⢿⣟⠹⡇⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠵⣎⡜⢳⠦⠂⣑⣄⢦⠷⠛⣍⢦⠀⡀⢶⠀⠀⠀⠀⠀⠅⡀⠡⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣁⣀⢀⠀⠉⠟⣿⣿⣿⣿⣿⣿⣿⠘⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣡⠶⣉⠲⣌⡑⠢⠌⠢⠂⠁⡀⢀⠄⠤⠶⢲⠀⠀⠀⠁⡠⡌⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣩⠴⡙⠦⢈⡱⠆⢈⠰⢌⠁⠠⢈⠡⠀⠀⠀⠀⠀⠀⢉⠡⢀⠠⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢃⡤⠑⢢⡌⠒⢈⡐⠔⠈⠠⠌⠁⠂⠀⠀⠀⠀⡈⠄⠒⡀⠈⠰⡝⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡏⣾⣠⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡘⡌⠐⢠⡜⠊⢄⡉⠠⠐⢂⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠐⢌⠢⠜⠀⠀⠀⠀⡄⠿⠙⣿⠿⠟⡿⡰⢀⡅⢮⣷⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠊⢄⡉⢂⠔⠈⢠⠐⡈⠐⠡⢀⠀⠀⠀⠀⠀⠀⠄⠁⡈⠳⣋⢶⣜⠲⠀⠀⠀⠀⡷⣿⣿⣿⣿⣰⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⢂⠐⢈⠡⠂⢁⠠⠄⠈⠠⠀⠀⠀⠀⠀⠀⠀⠑⠠⡜⠦⣻⢽⣎⢰⠀⠀⠀⠀⡟⣿⣿⣿⣿⠀⠁⠟⡿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⢹⠿⢿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⢌⠂⠄⠈⠠⠑⡀⠐⠌⠀⠀⠀⠀⠀⠀⠀⠞⡉⢠⡀⢀⠀⡀⢂⠡⠀⠀⠀⠀⣧⣿⣿⣿⣿⠿⣿⣶⣠⢆⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡍⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⡀⠐⢈⠂⢀⡐⠁⠠⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠈⠉⠄⠀⡄⠹⠀⠀⠀⡅⣿⣿⣿⣿⣴⢀⠀⠀⠆⠦⣴⣦⣷⣿⣿⣿⣿⣿⣿⣿⢻⣆⢷⣎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢊⡡⠄⠂⢀⠐⠠⠔⢀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⣈⠒⠐⡀⢰⠀⠀⡟⣿⣼⠀⣠⠀⠀⠀⠀⣉⠤⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡀⢿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠡⠰⢁⠠⢀⡐⠀⡐⢀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠐⡆⢠⠀⠀⠀⠀⠀⣷⣿⢹⡀⠀⠀⠀⠗⣠⢀⡀⠷⣔⣠⢁⠉⡏⣿⣿⣿⣿⣼⠀⠉⣿⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⡘⡜⠃⠄⡈⠐⡁⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣤⣁⣿⣿⣿⣿⣿⣿⡘⣤⣸⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⡜⡎⠑⢣⠄⡈⠐⡁⠁⠀⠀⠀⠀⠀⠀⠀⠱⢂⠗⢋⠿⠭⠿⠞⡡⠔⠉⡢⠔⠣⠀⠉⢡⡤⠚⠷⠛⠛⠙⠉⠌⠾⠖⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠈⠁⣼⠀⠀⠀⠀⠀⠀⠀ ⢩⢦⡑⠢⢃⠄⠈⠠⠀⠂⠀⠀⠀⠀⠀⠄⠂⣀⡘⢧⣼⣞⡼⠞⣁⠢⠖⠳⢻⡻⢆⡙⡱⣟⢻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣄⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⣙⢣⡱⢌⠣⠄⠈⡐⡁⢀⠀⠀⠀⠀⠀⠀⠀⢆⡒⢐⡤⢆⢆⡐⢹⣯⣟⣿⡿⣯⣭⡞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡸⢱⡲⠍⢂⠡⠄⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⣄⡵⣒⢽⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡀⠀⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣜⡹⠶⢃⢠⠘⠠⠐⠨⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡘⡱⢒⡨⠔⡈⠐⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⣶⡌⠓⢢⠑⢨⡄⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⢳⣌⠱⢨⠰⡐⠎⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⡓⣄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣱⠴⣊⠰⢎⡁⠠⠘⢂⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣧⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣡⡜⢆⡉⠆⢃⡅⠐⠠⢁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡛⣚⠀⡀⣃⣿⣿⣾⢀⠀⠀⠁⡐⠏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢡⡸⢆⠉⢠⠰⣞⡐⠀⠠⡈⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠖⠠⠀⠀⣧⢈⠁⠿⠏⠡⡿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⡐⢎⠁⡔⠊⢁⠠⢂⠀⠐⢀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⠲⠐⠀⠀⠿⠀⡀⣆⢋⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⠠⢘⠠⠡⠌⠂⠄⠁⢀⠂⡀⠐⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⡟⢾⣒⡑⢦⠻⠈⡀⠀⠀⠖⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢨⠐⣈⠠⠐⢈⡐⠈⡀⠐⢀⡀⠄⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣬⡶⣵⣅⢬⠶⠒⡑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⠄⠂⠀⢈⠡⠄⠀⠀⠐⠀⡐⠀⡀⠀⠐⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠛⠛⡛⠟⣛⡔⢤⠭⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠈⠀⠐⠀⠠⢀⠀⠀⠀⡀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠶⠰⠦⣗⢿⠿⣿⢻⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⡤⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠈⠉⢆⠀⠀⠀⠀⠀⠀⠀⣀⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠕⣢⢄⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢧⠀⠀⠀⠀⠀⢠⡛⢳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣀⠀⠀⠀⠛⠤⣀⠀⠀⠀⠀⠸⣀⠀⠀⢧⠀⠀⠀⠀⡜⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠲⣀⠀⠀⠀⠀⠉⠐⠠⢄⠀⠹⡄⠀⠀⠳⣀⠀⢀⠃⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠂⠤⣀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠈⢷⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠘⢦⠀⠀⠈⢣⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠳⡀⠀⠈⢆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠒⠤⢄⡀⡘⢦⠀⠀⠀⠀⠘⢳⡀⠘⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠐⠋⠳⠄⢀⡀⠀⠀⠙⠦⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠏⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⡁⠀⠢⠤⠜⠁⠉⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⢀⠇⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣐⡇⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢌⣗⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢾⡀⠀⠈⢣⣀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⡆⠀⠀⠀⠀⠉⠁⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠐⠒⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠂⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠋⡿⢻⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡷⣿⣿⣿⣿⣿⢉⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⢻⠘⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠀⠀⠀ ⠀⠋⡿⠻⠉⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⣄⣷⣿⣿⣿⣿⠿⠙⠀ ⡷⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⢘⠀⠀⠀⠀⡄⣧⣿⣿⣿⣿⢴ ⠀⣄⣷⣿⣿⣿⣿⠿⠉⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⠀⠀⠀⠀⣄⣧⣴⢀⠀ ⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⣄⣷⣿⣿⣿⣿⠿⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⢴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⣷⣴⢀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠇⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣁⣋⣟⣿⣿⣿⣿⣴⢀⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠇⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣿⣿⣿⠻⠿⠻⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⠟⣿⢻⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣾⣠⣦⣿⡝⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⢿⣝⣩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠿⠻⠙⡄⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢠⡇⣿⣿⣿⣿⣿⣧⣿⣿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⢀⠀⡄⣿⣿⣿⣿⣿⠉⣿⣿⣾⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣩⣉⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣾⣴⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢉⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠁⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣼⢿⠚⠔⠤⡀⣀⣀⣦⠱⠀⠀⠀⠀⠎⡴⢤⠤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⠶⣠⢀⠀⠀⠀⠀⠀⠀⡀⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣬⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⢰⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⡅⠬⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⣀⠄⠤⠤⣀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣲⠙⠉⠀⠀⠀⠀⠁⠋⠒⢤⠑⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⣀⠢⠀⠴⢀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠒⡴⢦⠓⠙⠀⠀⠀⠀⠁⠊⡠⢀⠆⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⢆⠑⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⣆⢰⠀⠋⠴⢀⠀⠀⠀⠀⡄⠽⢲⠛⠛⠛⠾⠀⢷⠿⠛⠟⠿⡴⢀⠀⠀⠀⢄⠲⠈⠀⢆⠞⣠⠀⠀⣀⢤⠑⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠋⠶⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣼⣇⠊⠶⣶⠷⣻⢿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⢄⠙ ⠀⠀⠀⠀⠁⠂⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣶⢹⢄⠙⠛⠻⢈⣏⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠑⠈⠀⠀⠀⠀⡀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⡎⠿⣿⣀⣧⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠒⠉⠀⠀ ⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⡈⣄⢱⠀⣻⠞⣦⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⣞⢤⡦⠤⣠⣄⠦⡗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠛⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⠻⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⠐ ⡏⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣾⣴⣀⣀⣀⣀⣀⣀⠀ ⡆⣿⣿⣿⣾⠀⡀⣦⣿⣿⣿⣀⣁⣋⣞⣿⣿⣿⡏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣀⣀⠀⠀⠀⠀⣇⣿⢿⡿⣿⣿⢿⣯⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠋⠙⠈⣷⣿⣿⣿⣿⣴⢣⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⣿⣿⣿⣿⡸⣤⣤⣠⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠠⠀⠈⠐⠂⠀⠀⡁⠒⡉⠂⣝⢣⡄⣌⡱⢜⠂⣏⣷⣿⡿⣿⣿⣿⢿⣿⢫⡼⠟⢣⣟⡿⣾⢀⡄⢠⠀⡀⣄⣶⡙⠹⠀⡷⠿⣿⢰⡁⠐⢠⣇⣿⣿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀ ⠀⠀⠀⡐⡈⢳⠀⢘⠃⠤⡙⠦⣙⡽⣾⠶⠻⡝⢎⡱⢿⡣⣿⣿⣿⣿⣿⣿⢿⣟⡿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠄⠁⣄⣷⠸⡇⣨⠀⠁⠀⠀⠀⡀⣿⣽⣷⣿⣾⣿⣯⣭⠲⠉⠀⠀ ⠀⠁⢀⠊⢄⠫⣇⠎⡁⠴⡙⢦⡍⡿⣎⣷⠯⣻⣿⣷⡿⢯⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡐⠀⠀⠀⠀⠀⠰⠀⣄⠠⣄⣦⠛⠐⠆⠀⠀⠀⠀⣿⣿⠀⣦⢙⠀⠀⠀⠀⡀⣦⣾ ⠂⠀⠠⠘⢣⢌⠣⢤⠘⡤⠑⢢⡟⣿⣜⠿⢧⡽⡾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡈⢧⠜⡷⢸⠀⠀⣷⣿⠀⠀⡄⠱⠀⠀⠀⠀⠀⠀ ⠀⡁⠄⠀⢱⡲⠀⣂⠑⠂⡡⢮⡗⣿⣟⡭⢾⡻⣽⢿⣾⣟⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠟⡿⢿⣿⠿⠻⠘⠀⠀⠀⢠⠀⣤⠳⣄⡷⣿⠀⠀⡇⣿⠀⠊⠠⡇⢆⠈⠀⠀⠀⠀ ⠀⠀⢀⠀⡀⠠⠐⠌⡡⠲⢎⡕⣯⣿⢳⣷⣟⢯⣿⡷⣞⣻⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣶⣽⣿⢿⠛⢈⠀⠀⠁⠀⢦⠑⣧⢸⠀⡇⣿⠿⢠⠀⢸⠀⣆⠠⠀⠀⠀ ⠈⠀⠀⠀⠀⠄⠈⡒⣍⢳⣌⡹⣿⣻⣽⣾⡽⣿⡿⣿⣿⣟⢯⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⡻⣙⣌⣙⣯⣟⣿⣿⢿⠹⠀⠀⠀⡀⠘⣆⠈⡄⣿⣾⠀⡇⢀⠀⠁⠔⣀⠀⠋ ⢓⠡⠀⠈⠀⠀⣅⠲⣎⡷⣝⠮⣿⣷⡿⣟⣿⣿⣷⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣹⠵⣮⣷⢿⠻⠈⠀⡀⠀⢀⡇⣿⢸⠃⣿⠀⠀⡰⠀⠃⡟⣯ ⡀⢳⢣⠀⢂⠄⡃⢿⣞⢫⣷⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⡛⣈⣦⣳⡰⢆⠙⡀⣤⣀⢿⠹⠀⠀⡇⣾⠀⡿⢠⠀⠀⠁⠟⣽⡾⣟ ⠀⡀⢦⠙⢂⠤⠘⡄⣿⢯⣳⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣯⣟⣯⣿⣾⣿⣶⣶⣤⢶⠛⣌⢶⠙⠄⠤⣧⠘⠀⠀⣿⢸⠀⠀⡇⢰⡏⣠⠀⠁⠟⣽⣿⡿⣷⣿ ⠀⠀⠀⡇⠸⢀⠀⠀⡄⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⢧⣼⡼⣤⣠⣀⢀⠀⠀⠀⠀⡀⣤⠻⡘⢤⠻⠛⢿⠀⠀⣠⢀⠀⠀⣠⠀⠀⠀⠟⣿⣧⣿⣿⣧⣿⣿ ⠀⠀⠀⡀⣷⠈⠃⠀⠀⡄⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡽⡻⢧⢌⠀⠀⠀⠀⠀⠁⠈⠀⠠⠀⠘⣄⣦⠻⡈⢧⡙⢱⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡀⢦⠈⠢⠉⠀⠀⣆⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⢾⣿⣯⢿⣯⡷⢭⡷⣯⣷⣿⣿⣿⣿⣿⣾⠳⢢⠜⠀⠀⡀⣄⠙⣄⠹⢀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿ ⠄⠃⠐⠈⠉⠀⣄⠱⠉⢢⠀⠀⡁⣿⣿⣿⣿⣿⣿⣷⣿⣿⣞⢯⣷⡽⢻⣻⣿⣴⡛⢿⣿⣶⣠⢀⠀⠀⠁⠉⠘⠀⠀⠀⠀⡀⠠⣆⢸⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣊⠱⢣⡌⣙⣽⠮⠻⡙⣈⣤⠲⡙⣿⢿⡉⣿⣿⣿⣿⣿⣺⢿⣞⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠾⠿⡿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⣧⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠞⣉⠶⣍⠳⢮⣝⣳⣝⣽⣾⢿⡿⣻⣛⣉⡍⣿⣿⣿⣾⢏⢳⣽⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠖⣋⢦⣙⡷⢎⣹⡷⣏⡳⣾⣟⡷⣞⣿⣿⣿⣿⣿⣿⡶⣎⡿⣞⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡼⢛⣮⡝⢳⣭⡷⢯⣫⣷⣟⣳⣾⣽⣿⣿⣿⣿⢷⣻⣭⢿⣷⣏⢢⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢰⠁⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢧⢳⣯⡟⢣⣵⡻⢶⣟⣯⡽⣿⣟⣿⣿⣿⣿⣿⣿⣽⣿⣎⡳⣝⣣⣿⣿⣿⣿⢻⣀⣦⠀⣀⣠⢀⢏⡿⢺⡑⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣵⡻⢶⡽⣫⣷⡟⣯⢷⣯⣞⡿⣿⣿⣿⣿⣿⣿⣻⣾⢷⣌⠴⡉⠣⣍⣿⣿⣿⣿⢈⠀⠀⠀⠀⠏⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣳⡽⣯⡷⣞⣽⡾⣟⣻⣷⣟⣿⣿⣿⣿⣿⣿⣿⣮⣟⢣⣙⠄⠂⠱⡏⣿⣿⣿⣿⢠⠀⠀⠀⠀⣿⣾⣠⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡆⣀⡀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣏⡳⣽⣻⣷⣟⣯⢿⣯⣳⣿⣿⣿⣿⣿⣿⣿⣡⢶⡟⢿⡿⣿⢿⡽⣞⣿⣿⣿⣿⠘⠀⠀⠀⠀⣀⠀⠉⠟⡹⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢲⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣹⢿⣯⡷⣽⡿⢯⣾⣟⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣷⣶⣻⣿⢻⣆⣿⣿⣿⢺⠀⠀⠀⠀⠋⡿⣿⣿⣹⣙⠋⠙⠈⠀⠀⠀⠀⠀⠀⠀⡄⠹⡈⠱⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡵⢞⣻⣽⡿⣯⣟⣯⣿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⠷⣭⣯⢿⡏⣿⣿⢠⠀⠃⣿⠟⣿⣿⣿⣿⠶⣛⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢿⡀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣞⣏⡾⣟⡿⢯⣿⢯⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⣿⣯⢹⡟⣿⣿⣿⣿⣿⠈⠀⡆⢿⣿⣿⣿⣨⠟⡿⢿⣈⠫⠟⡾⣶⢰⠀⠀⠀⠀⠃⣿⣶⠀⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿ ⢧⢣⣼⣻⢷⣯⢾⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⠛⠾⠀⠀⠀⠀⠀⠀⢧⠟⠇⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿ ⢣⢱⣮⡜⣻⢷⣯⢾⣿⣿⣿⣿⣿⣿⣿⣿⣎⡽⣨⡴⣀⣒⣀⣡⢞⣫⣶⢝⣫⣜⣿⣶⡞⢛⣥⣈⣤⣤⣦⣶⣳⣁⣩⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣷⣾⠃⣿⣿⣿⣿⣿⣿⣿ ⡖⡙⢮⣝⡼⣻⣷⣟⣿⣽⣿⣿⣿⣿⣿⣻⣽⠿⢧⡘⠃⠡⢃⣡⠾⣝⣩⣌⡄⢄⡹⢦⢎⠠⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠻⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿ ⠦⡜⢎⡳⣜⣻⣷⢯⣾⡿⣿⣿⣿⣿⣿⣿⣿⡹⢭⡯⢛⡹⡹⢯⡆⠐⠠⠀⢀⠐⠒⢡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢻⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢇⡎⢍⣲⡽⣞⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡹⠻⢊⠭⡂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⠹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠣⢆⣉⡼⡟⣧⣟⣯⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢛⣀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡙⢧⢎⡭⢗⣫⢷⣯⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡎⠉⢳⣬⡝⣮⡗⢻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠆⡌⠳⣎⡗⣏⢯⣳⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡙⢬⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠎⣋⠵⣏⡱⢾⣟⣯⡽⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⠘⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣴⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠞⢣⡹⢶⣹⡼⢿⣯⣟⡾⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢤⠥⣿⢿⠼⠀⠀⠁⡿⣿⣿⣾⢯⣰⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡞⢇⡹⣶⡟⣏⡷⢯⣿⣟⢷⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣩⣟⣿⣿⠘⡷⣾⣀⣰⣞⢀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡜⢯⡱⣾⢫⣵⡾⣟⡽⣿⣯⡿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢛⣍⣯⣿⣿⣀⣿⢿⠹⡴⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡽⣟⡧⣟⣞⣳⣽⣻⣾⡿⣽⢿⣯⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣬⢠⡁⠭⢮⡙⣄⣷⢿⣿⣿⣩⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⡗⣯⠷⣟⣯⡷⢯⣷⢿⣯⡿⢿⣻⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠓⢉⠊⠺⡓⣉⣭⢮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡽⣻⣽⣿⡷⣞⣻⣿⣿⣯⣿⢯⣿⢿⣿⣯⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣤⣤⢤⣠⠤⢫⡛⣒⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢾⣿⣷⣿⣯⣿⣟⡿⣿⣿⣿⢿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣉⣏⣙⠨⡀⣀⠀⡄⣉⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣛⢛⠟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

) ㅅ (⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣆⠈⠀⠄⡠⠀⠀⠋⠖⠤⣤⣿⣿⣿⣿⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢍⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⢧⠈⠀⠀⠀⡞⢀⠀⠀⠀⡄⣿⣿⣿⠚ ⠀⠋⠉⠀⠀⠀⠀⠀⠀⠁⠉⠋⠖⣠⣀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡀⢻⠈⠀⡜⠀⠀⠀⠀⠁⠋⠖⣤⣀⠀ ⠀⢃⡀⢤⠑⣯⣷⣈⣀⣀⠀⠚⠴⡠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⣘⡷⢺⠹⠊⠖⡤⣉⠖⡤⣀⠀⠀ ⠀⡀⢿⠉⠈⣀⢠⣄⠯⠺⠛⠛⠒⠶⣴⡤⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢾⣠⠃⠔⣠⢀⠀⠀⠀⠀⠀ ⡿⣈⢀⠀⡀⠉⡒⣠⢁⠞⣀⠀⠲⠓⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⢆⠤⢀⠀⠀⠀⠀⠉⠖⠼⠀ ⠀⣁⢓⠈⣀⣆⠈⠀⢀⠀⠀⠀⠀⠀⢆⠀⠋⡐⠱⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠖⠡⠊⠔⣠⢀⠀⢸⠀ ⠀⠸⠀⡆⢴⠣⢹⠀⠀⠀⠀⠀⠀⠀⠇⠼⢀⠀⡀⡳⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡏⢀⡄⠃⠿⣾⢔⠤⣀⣀⢤⠰⢸⠀ ⠇⢹⠘⠀⠀⡇⡀⢤⠑⠈⠀⠀⠀⠋⣰⠀⠀⠀⠀⠀⢦⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢠⠀⠏⢺⠕⣾⣴⣀⠀⠀⠀⠀⠀⠀⠃⢠⠀ ⡀⣿⢸⠄⠑⡇⢰⠀⠀⡀⢄⠦⡓⢈⠀⠀⠀⠀⠀⠀⠉⡞⢶⠓⠉⠀⠀⠀⠀⠀⠊⡤⠉⠊⡤⢀⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠀⠀ ⠃⡀⠀⠀⠑⣤⠸⠀⠀⠀⠀⠀⠀⡤⣤⢓⠈⠴⠤⣀⢀⠀⠁⠞⣦⣝⣬⠦⣉⣒⣝⣤⣢⠙⠀⡼⠀⠀⠀⠀⠀⠊⡤⣇⠀⠃⣼⢀⠀⠀ ⡄⢿⠀⠀⡀⠲⡶⠒⠙⠀⠀⠦⠈⠀⠀⡁⢶⠀⠀⠀⠉⠟⣰⠀⠀⡀⣤⠷⠀⠀⡀⢦⠙⡀⢦⠙⠈⠀⠀⠀⠀⠀⠔⢁⠞⣤⠸⠀⠀⠀ ⠀⣇⠹⠀⠀⠀⠁⠉⣿⢤⠒⠋⣤⠤⠾⢤⠐⠓⠤⣧⣿⣸⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⡀⢤⠓⡉⣌⠤⠀⠀⠋⠯⣴⣠⠀⠃⢠⠀⠀⠀ ⠀⡀⡀⢄⣷⣘⢀⠀⣀⠀⠀⠀⠀⠇⢀⠀⠀⡀⠀⠀⣧⢈⠀⠀⠀⠀⠀⠀⢣⠈⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈ ⡿⣿⣿⠿⠙⠀⠀⠀⠀⠀⠀⠁⠋⠿⣿⣸⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣿⣿⣿⣿⢿⠙⠀⠀⠀⠟⣿⣿⣿⣿⣿⠻⣘⣋⣙⣁⣛⣭⣧⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡟⣿⣿⣿⣿⣿⣴⣤⣤⣤⣤⣤⣤⣤⣤⣀ ⠀⣄⣷⣿⣿⣿⣿⢿⠻⡿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⠸⣷⣸⡟⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣾⢡⡿⣿⣿⣿⣿⣿⣱⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣉⡉⡟⣿⣿⣿⡈⢃⣿⣿⣿⣿⠛⣛⣛⣙⣉⣉⣉⣉⢛⠟⣿⣿⣿⣿⣿⣿⣱⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣦⣿⣿⣿⣾⣴⣀⠟⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣾⢀⡀⣦⣶⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣿⣾⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣯⣻⣽⢧⠰⡀⢄⠣⣘⢯⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣮⣻⢦⣲⣓⣻⢁⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠁⡾⢀⡇⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣻⠁⡾⢀⠟⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡄⣷⢸⠀⣆⠹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⡀⣷⠈⠀⣄⠙⠀ ⠀⠀⠀⠀⠀⠀⠁⠋⡷⣽⠦⠻⡟⢰⠀⠀⡀⢸ ⠀⠀⠀⠀⠋⠖⣀⢀⡅⣻⣴⢦⣝⠳⠙⠀⠞⢀ ⣢⣠⣤⢱⢺⠀⠀⠏⣽⠈⠉⠈⣌⢿⡄⢻⢹⠀ ⣒⣒⣒⢑⠏⠾⠴⢤⠤⠤⠳⣎⢸⡇⠸⡇⣻⠀ ⠀⠀⠃⢀⠀⣿⢠⠀⠀⠀⠀⣄⠹⡀⢁⠉⣞⠀ ⠀⠀⠀⣤⣠⣠⠀⠀⠀⠀⠀⠀⠀⠉⡗⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢺⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀ ⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠇⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣁⣋⣟⣿⣿⣿⣿⣴⢀⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠇⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣿⣿⣿⠻⠿⠻⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⠟⣿⢻⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣾⣠⣦⣿⡝⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⢿⣝⣩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠿⠻⠙⡄⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢠⡇⣿⣿⣿⣿⣿⣧⣿⣿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⢀⠀⡄⣿⣿⣿⣿⣿⠉⣿⣿⣾⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣩⣉⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣾⣴⠀⠀⠀ ─▀▄▄▀▄▄▄▀───────────── ──▓▒▒▒▒█░░▒█──────────── ─▀▓▒▒░░░█░░▒█─────────── ─▓▒▒░░░░█░▀▄▄▀▀▀▄▄▀───── ▀▓▒░░░░█▒█▒▒▒░░█▀░░█──── ▓▒▒░░░▒▒█▓▒▒░░░░█░░░█─── ▓▒░░░░▒▀▓▒▒░░░░░░░░░█─── ▓▒░░░▒▀▓▒▄▀▒░░░░░░▀▄──── ▓▒░░▒▀▓▒▒▒▒▄▄▀▀▀▄█────── ▓▒░▒▓▄▒▒▒▒░░░░░░█─────── █░░▓▄▒▒▒░░░░░░▀▄──────── █░▒█▒▒▒░░░░░░█────────── █▒█▒▒▒░░░░░░█─────────── ─█▒▒▒░░░░░▀▄──────────── ⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸ ⡀⣀⣀⣀⣀⣀⣀⣄⣧⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣶⢰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⢿⣿⣿⢿⠹⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠸⠀⡇⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣴⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠉⠉⠈⠀⠀⡇⣿⣿⣿⣿⣿⢻⠀⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠉⠉⡉⣯⣿⣿⣿⣿⣿⣿⣶⣿⣿⣼⣋⣛⣙⣦⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠄⣿⣿⣿⢿⡙⣦⣿⣿⣿⣿⣿⣰⠁⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⠻⣌⣶⣶⣤⣀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⠻⠈⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⢿⠘⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣤⣶⣶⣿⣾⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣶⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠿⠿⠿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⠀⠀⠤⣾⢀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠭⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣣⠳⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣌⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠚⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡼⣶⠀⠀⠀⠀⠀⠃⠉⠉⠋⠔⡧⣼⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢰⠀⠀⠀⠁⡿⣻⡿⢸⠀⡄⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠋⣿⣧⣷⠀⢢⠈⠈⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣽⢂⠀⢔⠒⣍⡓⠫⡌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠊⡫⡷⣴⢷⠭⣞⢠⣀⣀⣀⣀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⡿⠉⠉⠉⠉⠂⠖⣡⠾⢟⣰⠀⠀⣼⢃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠋⡷⢻⠀⠀⠀⠀⠦⠬⠏⣳⡴⢀⠀⠁⡜⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠼⠤⣤⣦⣲⣉⠦⣿⠛⠛⠒⠖⡒⣐⠋⢿⠛⠛⠟⡿⣿⣿⠀⡄⠈⠀⠀⠀⠀⠀ ⣈⠢⠈⠀⠆⠘⢆⡌⡜⠸⠀⠀⠀⠁⣼⣡⣤⣠⣤⢷⣿⣿⠙⠀⢃⠈⠀⠀⠀⠀ ⢀⠀⣇⠀⠀⡇⠃⢣⢣⢹⠉⠉⠛⡿⡌⠤⢠⠀⠀⡎⣿⣿⣶⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠁⣽⢾⣶⣶⣿⣿⣿⣿⣈⡆⠀⡀⠃⡍⣶⣧⣙⢿⢧⠀⠀⠀⠀⠀⠀ ⠀⢱⡸⠋⡴⢀⠀⠀⠋⣷⣿⣿⣿⢿⠿⠿⠿⠧⠿⠻⣿⠣⣴⡇⠑⠀⠀⠀⠀⠀ ⡏⡶⣠⢀⠀⠀⠀⠀⣤⣤⣦⢷⣛⣯⣿⣼⢷⣶⣼⣷⣀⡯⠀⠺⠒⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠫⣀⣤⠶⢤⡤⣠⢋⡜⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⠷⠬⠧⡶⣤⣀⣢⠠⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢣⡿⠋⠉⠙⠙⠀⠀⠀⠀⠀⡀⢠⠆⢀⠤⢤⡀⠀⠀⠀⣀⣤⠶⠒⠀⡾⠉⠉⠑⣄⠀⠀⠀ ⠀⠀⢸⣸⡃⠀⠀⠀⠀⠀⡇⠀⠀⠀⣧⠘⣴⠃⠀⠀⠘⡆⢩⠁⠀⠀⠀⠀⢸⠗⠀⠀⠀⠈⡆⠀⠀ ⠀⠀⠀⠉⠛⠿⢶⣦⠀⠀⢻⠀⠀⠀⣿⠀⢿⠀⣀⣀⡜⠁⡘⠀⠀⢀⣀⡀⢸⢵⠀⠀⢀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢸⡀⠀⡴⡟⠀⣻⠀⠀⠀⠀⠀⡏⠛⠐⠉⠁⠀⢸⣻⢍⡁⠁⠀⠀⠀⠀ ⠀⠀⠧⠷⠦⠶⠞⠁⠀⠀⠈⠓⠛⠉⠀⠀⢸⠀⠀⠀⠀⠀⣇⢀⣠⣶⡧⠂⡼⡇⠀⠉⢆⡀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⢀⡀⣀⢀⢐⣀⣀⣀⣀⡄⣀⣄⡤⣠⢀⡉⣁⣀⢀⢀⡠⠿⣡⣠⡒⡂⠚⡳⣖⠆ ⡀⢮⢟⣺⣗⣱⣾⣞⣒⣷⢦⠗⣥⢦⢿⠴⣊⣮⣮⣯⠷⣾⡧⣶⣧⣿⣾⣾⠟⡾⡺⠷⡫⢐⢏⢞⡾ ⠀⠘⢻⡼⠬⠆⠂⠑⠐⠈⠈⠈⠁⠉⡈⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬛⬛⬛⬛⬜⬜⬛ ⬜⬜⬜⬛⬜⬜⬛ ⬜⬜⬜⬛⬜⬜⬛ ⬛⬛⬛⬛⬛⬛⬛ ⬛⬜⬜⬛⬜⬜⬜ ⬛⬜⬜⬛⬜⬜⬜ ⬛⬜⬜⬛⬛⬛⬛

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⠃⠛⠛⠛⠿⠿⠻⠀⠀⠀⠀⠀⠇⠿⠿⠿⠟⠿⠿⠿⠿⠿⠻⠙ ⠀⣀⣀⣀⣇⣿⣽⠛⠉⠀⠀⠀⡇⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣴ ⠀⠀⠀⠀⡇⣿⣿⣿⣿⠻⠛⠙⡟⣿⣿⢸⣇⣿⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⢻⡇⣿⣿⢿⠀⠀⠀⠀ ⠀⠋⡿⣿⣿⣿⣿⢀⠀⢀⣷⢿⣝⣷⣿⣴⡏⣿⣿⣿⠘⠀⠀⠀ ⠀⣷⣿⣿⣿⣿⣸⠀⠀⠀⠀⣦⣿⢻⠈⠃⣿⣿⣿⣿⢰⠀⠀⠀ ⠀⡀⣤⣶⣴⣠⠀⠀⠀⠀⠀⠀⣆⣿⣿⡿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣶⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⠀⠀⠀⠀⠀

⣃⠇⡋⠋⢓⠭⢞⢘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡌⠳⣄⢶⣿⢿⡸⢕⢨⢀⠀⠀⠀⠀⡅⢿⠈⠄⣿⠀⠀⡇⠀⣇⣘⣧⢿⣿ ⠏⡧⢗⣚⣿⠵⠿⢠⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⡠⠒⠀⢆⢿⣷⠈⣄⢻⠙⠀⠀⠀⠀⣄⠀⠀⢸⠃⢸⡇⠀⡏⢿⡉⣿⣿ ⢉⣵⡺⡷⣿⣿⡲⣜⠃⠰⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⠔⢠⠁⠙⠀⣆⣼⠙⠀⡿⣷⠿⠙⠀⠀⠀⠀⢀⢰⡿⢿⡋⣿⣿⣿⣿⣿⣿ ⠋⣤⡟⣭⣿⣷⣜⢵⠢⣗⠄⢎⠁⠀⠀⠀⠀⠀⠀⠀⡳⢖⢠⠁⣿⣿⢿⠻⡌⢤⡛⡥⣿⣿⣿⢹⠂⠀⠀⡗⠛⣮⣿⣿⣿⣿⣿⣿⣿⣿ ⡘⣟⡡⢶⣗⢷⡬⡒⠌⠄⣠⠀⣭⠐⠂⠀⠀⠀⠀⡀⡀⠀⠀⡿⣿⣿⣿⣿⣿⠿⣙⣿⣿⣿⣿⣿⠀⣧⣿⣿⣿⣿⠿⠛⡿⣿⣿⣿⣿⣰ ⡘⢎⡡⡘⠔⣮⡑⢬⠰⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀ ⠹⢅⢲⡈⢣⠄⣓⡞⢁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣀⠁⠂⣥⣴⣿⣿⣿⣿⣿⠹⣁⢿⡄⣾⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀ ⢫⡡⠖⢈⢇⡠⠈⠷⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠃⢰⠚⡌⣀⣷⣯⣿⣿⣿⣿⠊⣿⢠⣟⣳⣾⢠⠀⠀⠀⠀⠀⠀ ⠄⡈⠢⣈⠐⢂⠄⡀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⠛⡻⣟⣿⣿⣿⢸⣼⠃⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀ ⠩⠀⢂⠌⡍⠁⢂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠉⠍⡂⣍⡵⡏⣿⣿⣿⣿⣿⣿⢻⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢹⠀⠄⠂⢠⠹⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠡⠿⡟⡿⣿⣿⣿⢿⡉⢎⡳⣦⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⡿⠻⡀⢅⡆⢹⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⡰⣀⣀⣀⠀⣃⣏⣟⡼⣿⠿⣿⡙⣷⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣷⠿⠙⣖⡽⣚⠹⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⡀⠀⠀⠀⠒⡶⣴⣠⢀⣟⣿⣿⣿⣿⡞⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣀⠄⡂⣒⣐⠠⠀⠱⠀⠀⠀⠔⠣⠀⠀⠀⠀⠀⠀⠀⠀⠄⠻⡿⣿⣿⣿⣿⣿⢿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠒⣉⠢⡑⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⢡⡖⠀⠀⠀⠁⠋⠿⠛⡻⠀⡹⡿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⢁⢸⣿⠸⠀⠀⡀⣿⣿⣿⢈⠆⣿⣿⣿⣿⣿⣿⣿⣿⢹⢿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣮⡟⢣⢼⠀⠀⠀⣿⣿⣿⢿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⢂⠐⢆⣂⠙⠀⠀⣟⣿⣽⣼⢀⠀⣧⣿⣿⣿⣿⣿⣿⣿⢿⡀⣰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡐⣔⠘⡐⢰⠀⡷⣻⠀⠀⠀⠚⠤⡧⣴⣤⣏⣿⣿⣿⣻⠃⡔⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠁⠀⡐⣀⠀⠀⠀⠀⠀⠀⠄⣉⡟⣿⣿⣿⣿⢿⠛⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠿⠿⠿⠿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⡀⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣯⣿⣿⣿⣿⣸⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡰⣠⣄⢨⡀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣃⠃⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⢄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠶⡁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣰⠀⠀⡀⣀⠆⠳⠉⠀⠀⠀⠀⣦⢸⡄⢹⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠁⠞⠠⠁⠉⠛⡁⣟⣶⠶⠛⠛⠻⠉⠈⠀⡄⣦⠙⠀⠀⠀⣆⠀⣿⢠⡼⠀⠀⠀⠋⠴ ⠀⠀⠀⠀⠀⠻⣿⠀⠟⣴⢀⠀⣀⢛⠿⣿⣤⣷⢿⠾⣳⣿⣶⣽⢮⠰⠀⡀⢦⠰⠙⠀⠀⣼⠇⢠⠀⠋⡾⢀⠀ ⠀⠀⠀⠀⠘⡇⢸⡟⣹⠀⠁⠋⣿⣿⣠⢀⠀⠀⠀⠀⠔⡀⣄⠲⣝⠳⠙⡄⠘⠀⣷⠀⡇⢣⣰⠉⡾⣠⠀⠀⠀ ⠀⠰⠀⠀⣄⡳⢻⣿⣿⠃⡿⣿⣢⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⡀⢦⡙⠣⠈⠀⠀⠀⡀⡁⠞⣠⠀⠀⠀⠀⠀ ⠀⠀⢢⠈⠀⠀⣧⣗⣿⣿⣾⢀⠀⠀⠀⠀⠀⡀⣀⣏⣾⣤⣤⢠⠈⠈⡀⢠⣆⠘⠀⠁⠟⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣑⢭⠮⡓⢹⣌⣿⢰⡟⠀⠀⠓⠛⠛⠛⠛⠛⠛⠛⠗⣾⣴⢀⠀⠀⠀⣇⠁⡾⡄⢃⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⡀⣀⣄⢤⠶⣿⠐⣠⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⡀⡏⢐⡁⣉⢿⠛⠈⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⣸⠀⠈⠀⠀⠃⣿⣿⣾⣾⣷⣿⣿⠃⡴⠀⠀⠀⠀⠀⠀⣷⠿⣿⣿⣿⣿⢸⠙⣯⣿⠈ ⠀⠀⠀⠀⠀⠀⠁⠿⣿⠶⠀⠀⠀⠀⡄⣻⣿⢾⠀⠀⠀⡏⣿⠈⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⡟⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⢿⠀⠀⠁⣿⣠⠁⠉⠀⠀⠀⠀⠀⡆⣹⣀⣧⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡏⣿⣿⣼⠁⠟⡿⣽⣿⠹⣧⣿⣿⠀⠀⠀⠋⠟⣴⢁⠈⠀⠀⠀⠀⠀⣧⢨⡌⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡿⣇⣿⣰⠈⣿⣿⣴⣿⡾⣿⠻⣟⢺⠀⠇⠿⣿⣿⣷⡚⣙⣁⠋⠈⠀⠀⠀⣿⡏⣏⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢷⡿⣿⠀⣯⣶⣿⣿⣿⢿⣿⣿⣷⣼⠚⡟⣿⣿⢿⣿⣿⡿⣽⣏⢰⠀⠀⣆⣩⡇⢯⣷⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣇⣿⠾⢠⠀⠀⡀⢀⠀⠀⢀⠀⠀⢀⡀⡀⣀⣤⣤⣠⢃⠒⢠⠀⠀⠀⠀⡉⣄⡶⡟⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡿⣿⠃⠙⠈⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡜⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⢻⡏⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠈⠉⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⠃⡿⣿⣾⢃⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣀⣦⣿⠙⠇⣾⣞⣾⢁⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣒⣄⣭⣻⣯⢻⡴⠋⣿⣿⣿⣿⣿⣿⣿⣿⢟⡙

people, please don't post weird/innapropiote stuff, some people are just trying to find some cute/aesthetic symbols/combos here, and there are CHILDREN as well! spread this message to help! ♡

⠀⠀⠃⣸⠀⠀⠀⠋⡴⢁⠉⠉⠈⡀⣤⡷⢨⠀⠀⠀⠀⠀ ⢶⠙⡿⠘⠀⠃⡾⣴⣤⣀⣀⣀⣀⣄⢦⡷⢹⠀⠀⠀⠀⠀ ⠀⡀⣤⢻⠏⣠⠀⠀⠀⠁⠉⠉⠀⠀⠀⡀⣦⠹⠀⠀⠀⠀ ⠀⠀⠀⡅⣼⠀⠀⠀⠉⠀⠂⠙⠉⠋⠰⠀⠀⣇⠘⠀⠀⠀ ⠀⠀⠁⡟⢠⠀⠀⠀⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⣧⢿⠈⠀ ⠀⠁⣽⠜⠀⠀⠀⠀⠀⣗⣶⣤⣤⢧⠀⠀⠀⠀⡀⣿⢧⠘ ⠀⡟⣇⢻⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⢸ ⠀⣷⠿⣻⣿⠀⠓⠛⠛⠃⠙⠘⠀⠻⠿⠿⠞⢩⠀⣧⣧⢈ ⠀⠀⣇⢸⣧⠀⠀⣓⣛⣿⣾⣴⡄⣶⣶⣤⣀⢀⠀⡤⡜⢻ ⠀⠀⡇⢸⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⣷ ⠀⠀⡀⣷⠘⡀⢦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⡾ ⠀⠀⠀⡀⢷⠈⠀⡀⣷⢿⠿⠛⠉⠈⠀⠀⠉⠉⠋⣿⣴⢀ ⠀⠀⠀⠀⠀⣆⢿⠈⠀⡀⣤⢶⠶⣖⣶⣿⣿⣿⣶⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣄⠶⠳⠛⠻⠛⠟⠿⠶⣴⢀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈ ⠀⠉⠉⠉⠛⠟⠿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀ ⡀⣄⣦⣿⣿⣴⣤⣧⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠛⠿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣼⠀⠀⠀⠀⣀⣦⣶⣷⣿⣿⢻⠈ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣶⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠙⠈⠀⠀⠀⠋⠛⠟⠿⠿⠿⠿⠻⠿⠿⠿⠿⠙⠀⠋⠿⠿⠿⠿⠿⠿⠘ ⣆⣿⣿⠻⠋⡿⣿⣿⡻⣿⣏⣟⣿⣿⣿⣿⣿⣿⣾⡟⣿⣿⣹⣀⣀⣀⣀⢀ ⠀⠀⣄⣷⣿⣾⣥⢟⡿⣿⢹⡟⣿⢿⠿⠿⠿⠿⡿⣿⣿⣷⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⣷⣿⣿⣿⣼⣦⣿⣿⣶⣶⣿⣿⣿⣿⣰⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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