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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⣤⣤⠀⢠⣤⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⣤⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡏⢀⣤⣤⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠘⠿⠿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠦⠤⠤⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⡀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠉⠉⢉⣉⣉⣉⣉⣉⣉⡉⠉⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠻⠿⠿⠿⣿⡿⠿⠇⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⣤⣤⣤⣤⣾⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⢉⣩⣭⣭⣭⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⣿⡟⠋⠉⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⣾⣿⣶⣶⣶⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⣶⣶⣶⣶⣶⣶⣶⡆⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⣾⣏⠀⠀⣹⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠘⠿⠿⠿⠟⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢢⣓⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⡿⣝⣮⢳⣍⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠉⠀⠀⠀⠀⠠⢌⣉⠉⠓⠢⣄⠀⠀⡀⢀⣠⣀⢆⣬⡱⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣾⡿⣼⢯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⣀⠩⠖⠋⠉⠁⠉⠉⠁⠐⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣯⣷⢿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⡐⡈⢦⠱⣈⠂⡁⢀⠠⡀⢂⢀⡴⢋⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⣠⣤⣶⣧⣶⣯⣶⣦⣴⣮⠦⠉⣝⣯⣿⣿⣿⣿⣿⣦⣄⠀⠈⠻⢽⣿⣿⣿ ⠀⢠⠰⡡⢝⢢⢣⡔⢦⣱⢉⡐⡰⢢⠏⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠄⠀⠀⣀⣀⣠⣯⣅⣀⠀⠀⣠⣊⣠⣶⣿⣿⣿⣿⣿⣿⣿⣱⡞⣫⣥⡿⣿⣿⣿⣿⣿⣿⣮⢧⠀⠀⣠⢬⣫⠟ ⠈⠄⣒⡽⣎⢯⣳⣹⢦⡛⢦⢱⣱⠃⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢾⡿⢿⣿⣿⣤⣬⣙⡻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⡟⢷⣸⠷⠋⠁⠀ ⠖⠱⣈⡶⢯⡗⣯⢞⡶⡙⢎⢒⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠛⣿⣿⣿⣿⣿⡞⡛⠀⠀⠀⠀ ⠴⠳⣝⢾⡹⡽⣩⢞⣰⣵⠞⡟⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡹⠿⣿⣿⣿⢋⠩⠾⠟⢻⣷⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⡬⠓⡌⢣⣝⡶⣽⢺⡱⣎⣽⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠙⢄⠀⠀⢰⡟⠿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠄ ⢠⡱⢜⡳⢯⡽⣷⡿⣟⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⠀⠉⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⢣⠀⠀⢠⣶⠄⣩⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⢡⢓⣬⠷⣯⣟⣷⣿⣿⡻⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡾⠁⣾⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢃⠀⠀⠙⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠂ ⣛⢾⣼⣻⣿⣿⣟⢿⣻⣷⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⣿⡇⢸⣿⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠂⠀⠀⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠄⠀ ⠛⠛⠾⣟⣧⢷⡺⣭⢻⡽⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⣹⢻⢀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣰⠀⠀⠀⠀⠀⠀⠀⠀⠄⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⡸⡀⠀⠀⠀⠀⠀⠁⠀ ⢠⠀⠀⢿⣻⣼⢣⡟⣮⢳⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⢿⣾⡬⠚⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣀⠀⠀⠀⠀⠁⠀ ⣦⣝⢢⣂⢿⣳⣏⢾⡱⣏⠾⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⢨⠋⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠛⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⡷⣞⣳⡽⣾⡽⣾⢧⡻⣜⢯⣻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⢹⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⡿⣡⢣⡙⠵⡻⢽⣯⡗⣯⢞⡵⣇⠈⠙⠻⣷⣶⣦⣤⣀⠀⠀⣀⣤⣶⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣄⡰⠤⠀⣀⣤⡤⣾⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⢳⠰⣇⢮⡱⡙⢎⡷⣿⣎⠿⣜⢿⡀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢏⠿⡹⠟⠻⠛⣝⢧⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⢣⠙⡺⢯⡳⢍⠎⣼⣳⢯⣟⡼⣫⢧⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⠱⠈⠂⠁⠀⠀⠀⠀⠈⠙⢟⠦⣄⣀⠀⠀⠀⠀⣀⣤⡒⠾⠛⠃⢦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⡿⠂⠀⠀⠀ ⣧⠙⡔⠫⠜⡌⢺⢴⢫⢿⡽⣞⡵⣻⣆⠀⠀⠀⠀⠀⠀⠀⠉⠋⡝⣿⠿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣉⢜⣡⠳⣌⠳⣎⢻⣎⢿⣯⣟⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⠀⠈⠛⠿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⣌⠞⡴⢫⡜⣳⣮⣗⢾⣯⣿⡿⠿⠟⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣶⣦⣄⣀⣀⣀⣠⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢫⠔⣫⡕⣣⢞⣵⣯⠿⠋⠉⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⠀⠀⡞⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢛⣿⣿⣿⣟⡷⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⢻⣴⢻⣽⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢀⠀⢠⡼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣯⣟⣿⢳⢮⡵⣩⡛⡖⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⢷⣺⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣼⠏⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⢯⣟⡻⣽⢻⣮⢵⣣⢝⡹⣒⠦⣍⡹⣙⠶⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢮⣳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠐⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣟⣯⣟⡞⣯⢻⡽⣞⠷⣎⡷⣭⢳⣳⣬⡒⣍⠳⢮⣜⡲⣌⢳⣒⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀( • )( • )ԅ(‾⌣‾ԅ)
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠄⣿⣿⣿⡟⢩⠁⢆⡐⡀⢆⠢⡐⢄⢞⡱⢌⠂⢆⠰⡀⢆⡐⠢⡐⢄⠂⢆⠰⡀⢆⡐⢢⠐⢢⠐⡄⢢⠐⡰⢀⠒⡄⢂⠆⡰⠐⡄⠒⡄⢂⠆⡰⠐⡄⢂⠆⡐⢢⠐⡰⢀⠆⢢⠐⢢⠐⢢⠐⡰⢀⠆⠌⡳⡀⢦⡗⡈⢷⡘⡄⢂⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠑⡈⢼⣿⣿⣏⠦⣉⠂⡔⡈⠆⣂⢱⠎⡎⡔⠡⢊⠔⡀⠒⢄⠒⡡⠒⢌⡘⢄⠃⠜⡀⡞⢀⠃⠆⠱⠈⢂⡑⠄⢣⠘⡄⢣⠘⡄⠣⠌⡑⠈⢆⡘⠄⢣⠐⡡⠢⢑⠢⢑⠰⣈⠒⡄⠓⠢⡑⠢⡑⠄⠣⢈⠈⢄⡙⣎⡇⡘⢆⣿⠠⣁⣿⣿⣿⣿⣟⡾⣿⣿⣿⣿⠐⣻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢆⡘⢐⡈⣿⣿⣿⣖⡡⢎⡐⠤⠑⣰⠫⡜⠰⢈⡑⠢⡘⠤⢉⠢⠘⠄⡃⠆⡰⢈⠌⣂⠱⡇⢌⡘⠨⡁⠎⠰⡐⡘⠄⢣⠐⣂⠱⢀⠣⠘⡄⠣⢸⡐⠌⢢⠘⢠⠑⠢⡘⠄⡒⠄⡒⠌⡌⡑⠄⢣⠐⡩⢐⠡⠌⡄⢢⠘⣦⠑⣊⢼⣇⠰⣿⣿⣿⣿⢯⣿⣿⣿⣿⡇⡘⠤⢻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢪⠐⠌⠢⢄⠹⣿⣿⣿⣧⢊⡜⣌⡳⢡⠓⡌⡑⠢⡐⢡⠒⡄⠣⢌⠱⡈⠔⡌⡐⠌⡰⠀⣽⠇⢢⠐⡡⢂⠍⡒⠰⢠⠉⢆⠒⡄⢢⠁⢎⠡⡐⢡⢺⠐⡌⠢⠘⡄⢊⠅⡰⢁⠆⡱⠐⡌⠰⢠⠉⢆⡘⠰⡈⢆⠱⠐⣂⠡⠘⣦⠘⣼⣹⢼⣿⣿⣿⣿⢯⣿⣿⣿⣿⠠⢡⠘⡥ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢆⡉⠜⡐⢂⠡⢿⣿⣿⣿⣷⣶⣰⢣⢃⠣⡐⢄⠣⡘⢄⠒⠤⡑⢂⡢⠑⡈⠔⡠⢃⢰⣵⢻⡀⢣⠐⡁⢆⠢⣁⠃⢆⠩⢄⠒⡌⠤⡉⢄⠢⢑⠂⣼⢷⣄⠣⢁⠆⡡⢊⠐⠢⢌⠰⢡⢈⠱⢠⠉⡄⢢⠑⡐⠢⢌⠒⡄⢊⢁⠺⣘⣼⡘⣾⣿⣿⣿⣯⢿⣿⣿⣿⠇⡒⢠⠃⡔ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡸⢄⠢⡁⢆⡁⠎⣸⣿⣿⣿⣿⣳⢏⢢⠃⡔⠡⢌⠰⡐⠌⡌⠰⣀⠳⢄⠃⢌⠂⡅⣢⡟⣮⢻⢀⠃⡌⡐⢢⠡⡐⢌⠢⠌⡰⢈⠰⢠⠑⡨⢐⠢⠡⣼⢫⡞⣷⣌⠰⠐⡂⢩⠐⡸⡄⠡⢌⠂⢆⠡⡘⠤⡘⢠⢃⠢⢌⠰⡈⠤⢁⢳⡞⡌⣿⣿⣿⣿⡽⣿⣿⣿⡿⢐⠨⢄⠒⢨ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⡑⢎⠠⣁⠢⢐⠂⡄⣿⣿⣿⣿⡏⣆⠣⢌⡀⢣⠈⠤⡁⢎⠐⡡⡘⡍⢠⠉⡄⢊⣾⣝⡾⢧⢻⡆⣃⠰⡁⠆⡑⢨⠐⢌⡐⠡⢂⠡⢂⠅⢢⠡⡖⢡⣯⣷⠻⣶⢹⣳⣅⠘⡄⡘⠤⠸⣁⠆⡉⢄⠃⡌⠰⣈⠂⡄⢃⠌⡰⢈⠰⢁⠺⡗⣌⣿⣿⣿⣿⣽⣿⣿⣿⠣⢌⢂⠢⢉⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⣍⢂⠡⠄⢃⠌⠒⡠⠼⣿⣿⣿⢑⢢⠃⡔⢈⠤⢉⠂⠥⢈⠆⣡⡝⠠⠃⠜⣰⡿⡵⠾⠒⠛⣿⣇⠌⠒⡈⠔⢡⢂⡉⠤⢘⠔⠉⠉⢣⡘⢄⠒⡏⣼⣳⠋⠙⠛⠳⢷⣾⣷⣔⡨⣐⠡⣘⠤⡑⣈⠒⡈⠥⢀⠣⠘⢄⠊⡔⢁⠊⡔⠨⢿⡰⣿⣿⣿⡷⣿⣿⣿⡟⡐⠢⠌⢂⠅⡊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢣⡘⠄⢣⠘⡄⡘⠣⡀⠤⢿⣿⡟⡸⢄⠣⢀⠇⢄⠃⠼⡀⠇⡸⢠⡘⠇⢛⣸⡟⡿⠃⡀⠃⠄⠸⣿⡜⠣⢘⠸⡀⢄⠠⢣⠃⠀⠀⠀⠀⡇⠜⣀⢻⣧⡇⠘⡀⠣⢀⠘⠣⣼⡛⣧⡀⡄⠛⢧⡄⣀⠇⠸⡀⢇⡘⠣⠘⠤⡘⠄⢣⠀⠇⡼⢧⣿⣿⣿⢿⣿⣿⣿⠃⡄⢣⠘⡄⠸⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡱⡘⡌⡐⢢⠐⡡⢁⠆⡡⢊⢽⣃⠳⡌⢢⠁⠎⡄⢊⠔⡡⢂⠅⡟⡐⢨⡼⢧⠏⡀⢂⠤⡁⠌⢂⠙⣧⠓⣌⠰⠈⠆⠌⡏⠀⠀⠀⠀⢀⡏⡒⢠⣿⡞⠀⠂⠄⣁⠂⠌⡐⠈⠻⣜⡻⣦⠑⡈⢷⡀⢊⠅⡒⠄⢆⡡⢉⠒⠤⡉⢄⠣⡘⢌⣏⡿⣿⡟⣿⣿⣿⡟⢨⠐⡂⢅⠢⡑⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⢒⡱⢄⠡⢂⠅⢢⢁⠢⡐⢌⣾⡐⢣⠜⡀⢎⠰⡈⠆⡘⠠⠌⢲⠃⡌⣾⡽⠃⠐⠠⠈⠄⡐⠈⠄⡐⠈⢻⡄⣋⠖⣩⢰⠃⠀⠀⠀⠀⢰⠃⡅⢺⡟⠀⠌⡐⠠⠀⠌⡐⠠⠁⢂⠠⠙⢽⣳⣌⠘⣧⠨⡐⠌⡌⠤⡐⢡⢚⡰⢈⠔⡐⢌⠎⣧⠼⣆⡱⣉⠏⡛⢡⠂⠥⡘⡀⢆⠡⠌ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣃⢆⢣⠘⡄⢊⠔⡂⡁⠆⣼⡧⡘⢥⢊⠔⡨⢆⠡⡘⠄⢃⠜⡼⠡⣼⡟⠁⠄⣁⢂⠁⠂⠄⣥⣢⣄⣁⡂⠽⣄⠳⣄⢻⠀⠀⠀⠀⠀⠘⣧⠘⡞⢧⢐⣠⣤⣥⣾⠶⠀⠡⠈⠄⠂⠡⢀⠙⢽⣶⠸⣇⠘⡄⢢⠁⡜⢠⢊⣄⠃⡌⡐⢎⡜⣸⢒⣳⠴⣡⠒⡌⢄⠩⡐⠤⢑⡈⢢⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠜⡰⢊⢆⢣⠘⢄⠊⡄⠡⢎⡏⡧⣙⠢⡍⠤⣑⠃⠆⡡⠘⡄⢺⡇⣹⡟⢀⣴⣶⣿⣿⣿⣿⣿⣶⣦⣉⠻⣿⣷⠉⢷⣌⡏⠀⠀⠀⠀⠀⢰⢣⣙⠟⢯⣻⡽⠋⣁⣤⣤⣾⣶⣷⣾⣶⣧⣴⣈⡄⠹⣷⡹⣧⢈⠄⡃⢄⢃⡐⢎⠰⡐⢑⢎⡰⣉⠖⡸⣇⠦⡙⡄⢌⠂⡑⠌⢂⡘⠄⢃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡘⣅⠫⣘⠢⢓⠌⣒⢨⡑⡺⢌⡓⢤⠓⣌⠣⢼⠁⢎⡀⠣⢰⣟⣧⣿⡾⢟⢫⡑⢎⠴⣸⡔⣻⣿⣿⣿⣷⣤⠭⠠⢈⠙⡇⠀⠀⠀⠀⢀⣟⣢⡞⢀⢂⣬⣷⣶⣿⡿⢿⣿⣿⣯⡹⢍⡛⡛⡟⡿⣶⣌⢿⣽⣧⡘⡐⠌⡂⠄⣏⠆⡑⢎⢢⡑⠦⡙⡔⣧⢣⠱⣌⠢⠘⢄⡉⠆⢌⡘⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠱⡌⡓⣌⠣⣍⠚⡤⢣⢼⢇⠣⢏⢢⡙⢤⢋⣼⠈⢆⠰⢡⣟⢾⣿⢏⡼⠜⠒⠉⠉⢩⣿⢿⠿⣿⢻⣿⣯⠛⡃⠡⢀⠂⡹⣄⠀⠀⢀⡜⠛⠚⡁⠄⢠⠀⠿⡙⣾⡷⣾⡿⢿⣿⣷⡉⠉⠒⠳⢬⡙⣿⡧⢿⣞⣷⣌⠢⢑⠨⢸⢆⡹⠌⢦⡙⠴⡱⢌⣹⣆⠳⣄⢣⠑⠢⠌⡘⠄⢢⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠳⢌⡱⢂⠳⣨⠱⡌⣥⠿⣨⠓⡬⢢⢍⠲⡌⢼⢨⠂⠆⣿⣎⢿⣟⡄⠀⠀⠀⠀⠀⢾⡿⣯⡝⡶⣋⡾⣿⢣⠒⣡⠒⡌⣰⠇⠀⠀⡼⡁⢎⢡⠒⡌⡄⢃⠎⢀⣿⣽⢲⡹⢧⣾⣿⡇⡀⠀⠀⠀⠉⢿⡃⠈⡿⣾⡏⣦⡡⢂⢽⠢⣅⢋⠖⡬⡑⢆⠣⢼⡚⣕⠢⢎⡡⢃⠆⡱⠈⢆⠡ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡜⢢⡱⣉⠖⣡⢒⣽⢡⡗⣢⠙⡔⣃⢎⡱⡘⡜⡦⡙⣼⡿⣏⣾⠃⡵⡀⠀⠀⠀⠀⠘⣇⠬⠛⠖⠋⢄⢇⢧⣋⠴⣉⠖⣹⠀⠈⢠⣗⠩⢆⡣⢚⠴⣈⢇⢺⡀⢯⡈⠳⠿⠚⠁⢼⠃⠀⠀⠀⠀⠀⡜⡄⠣⢜⣿⡱⣂⠟⡮⣜⠣⡜⣌⠚⡴⣉⢌⠳⡌⣷⣾⠏⢦⠱⣉⠒⣤⢩⡐⢆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡜⣡⠒⡥⢚⠤⣃⠞⣻⡓⢤⢋⠴⡡⢎⡔⡱⢌⣗⢡⡿⣿⣽⣾⠑⡴⢻⠖⣶⢶⠖⣶⡚⣏⠻⣭⠿⣘⡯⢖⡱⢎⡵⣚⡟⠀⢀⡾⢥⣛⡬⢳⡍⢞⡡⢞⣡⢾⣫⡽⢻⡙⣶⢞⡓⢦⡤⣤⢤⣤⡾⣍⠲⡑⢮⣿⣇⠳⡚⠴⣉⠖⣡⢎⡱⢒⡌⢎⡱⢌⣷⢈⠞⡤⢓⡌⢳⢠⠣⡜⢢ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡘⢤⢋⠴⣉⠲⢡⠚⣼⡑⢎⡜⢢⡑⢎⠴⡑⢎⠼⣺⠔⣿⣟⣿⡸⢎⢣⣛⡵⣋⠿⣅⢻⡰⣟⡱⣹⢎⡳⣍⡞⡝⣎⣽⠀⠂⣿⣥⢳⢣⢞⣱⠺⣍⡞⣯⠗⣮⢓⣜⢗⡫⢞⡼⢺⣙⢦⣳⢯⢲⢹⣀⡷⣙⣶⢏⣯⢱⡉⢖⡡⢚⠴⣈⠖⡡⢎⢢⢱⡎⢽⣊⠜⡰⢃⡜⡡⢎⡱⢌⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡩⢆⡍⢲⢡⢋⠦⡙⣾⡘⢦⡘⣅⠚⣌⠲⣉⠎⡜⡹⢎⣿⡇⢿⣜⡼⢗⣝⢶⣙⠳⣬⠻⣜⠶⣫⢓⣮⢛⠬⣳⡝⢭⣚⣄⣰⠏⣏⢧⣛⡵⣚⡽⢲⡙⢦⡻⢴⣋⡾⣜⢫⢳⡜⣯⢋⣗⡼⢖⣫⠽⣚⣝⠶⣱⣞⣷⢢⡙⢢⠱⣉⠖⡡⢎⡱⢊⢆⣿⣟⠚⠧⡙⠴⣉⠲⡑⢎⠴⣉⠖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠱⣊⠜⡡⢎⡜⢢⡑⢿⣴⣧⣼⣶⣉⢆⠳⢌⡚⠴⣑⢊⣿⠽⣮⣎⠾⣜⢥⢳⡜⡻⣌⠷⣍⣣⠷⡙⣦⢝⠺⣡⠚⠮⡑⢎⠒⡏⢎⠭⣒⠳⡱⢊⡥⠟⣥⡫⢖⠭⣒⡥⡛⣍⡺⢔⣫⠦⡝⢭⣪⣵⣫⣥⣻⢧⣏⣿⡤⡙⢆⠳⠌⡎⣷⣮⢰⣉⣾⣯⢿⢌⢣⡙⠦⣡⢣⠙⣌⠲⡡⢎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢓⡌⢎⡱⢆⡜⣡⠚⡔⠲⣌⠲⣙⣷⡊⡕⢪⠜⣱⡌⢆⣻⢿⣞⣯⠙⡞⠽⢶⠵⣭⠥⢃⠍⢢⠑⢪⠁⠎⠰⠠⠉⠆⡑⠌⠱⢈⢂⠒⠄⠣⠔⠣⡘⢌⠡⠜⢌⠲⢡⠒⡱⢡⢚⠪⢅⠳⢸⢛⡻⢍⠲⣐⣮⢟⣯⣿⣧⡙⡌⢎⡱⣾⣿⡽⣧⣾⡿⣽⣻⢎⡒⣌⠳⣠⢣⡙⢤⢣⠱⣊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢣⠜⣢⠑⡎⡔⢢⡙⣌⠳⣄⠳⣸⡿⣿⣌⢃⣾⣿⣯⠒⣼⡳⣎⣷⠡⣘⡌⠒⢌⠠⢌⣂⣼⣶⣿⣿⣿⣿⣿⣷⣷⣶⣴⣾⣷⣿⣾⣿⣿⣶⣾⣶⣤⣈⡐⠈⡄⢂⠡⠌⡐⡁⠢⡁⠎⡰⠙⡡⠃⠎⡡⣽⣞⢯⣻⣯⢿⣆⡙⠦⣹⣿⡷⣿⣿⢿⡽⣷⣻⡇⠲⣌⠲⢡⠒⡜⢢⢃⠳⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⢋⠴⣉⠖⡩⢆⡱⢌⠲⣌⠱⣾⡿⣽⣻⣿⣻⢾⣽⣿⣜⣷⣣⠾⢋⠁⠌⢳⠈⣤⣶⣿⣿⣿⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠈⠉⠛⠻⣿⣿⣿⣷⣅⠀⢂⠰⢀⠐⠠⢁⠰⠀⠤⠁⠄⡑⣠⡿⣗⡟⣾⡿⣽⢯⣿⡜⣲⣿⡿⣽⣿⡽⣯⣟⣷⢯⣗⠱⣌⠱⣃⠝⣌⠣⢎⡱⢌ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣆⠉⡶⢁⡎⢱⠎⣰⠉⡶⣈⢱⣿⢿⣷⢿⣏⡿⣿⣾⣹⡿⠉⠁⠀⠆⡈⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⢈⠹⣿⣿⣿⡆⡀⠆⡀⠈⡰⠀⠆⠁⠆⠁⢆⣸⣷⠿⣸⣸⣿⢿⣹⢿⡾⣿⡿⣏⡿⣷⣿⣹⡿⣾⣹⣏⣿⢰⡈⢇⡸⡈⣆⠹⢆⠱⡎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠴⣉⠖⡡⢎⡱⢊⠦⡙⡔⢢⣹⣿⣻⢞⠫⡽⣟⡷⢋⣡⠔⠊⠍⡙⣆⣠⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠁⠀⢸⣟⣿⣿⠀⠒⠠⠁⠄⠡⠊⡐⠈⣴⣻⣿⣟⣷⣧⣿⢯⣟⣯⣟⣿⣳⠿⠽⣛⣿⣿⣳⢿⣽⣳⢿⡽⡆⡍⢦⢑⡱⢌⠳⢌⠳⢌ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢚⠤⣋⠔⡣⢜⡡⢎⡱⢌⡃⣿⠟⠡⢉⠑⣪⠟⠓⡉⠄⡈⠐⡠⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⢀⣼⠿⣽⠡⢈⠐⠡⠈⠄⣁⠂⣤⣿⣿⣿⣟⡾⢋⠭⣉⠏⢭⡉⢖⡰⢢⠙⠦⣽⢿⣿⣟⡿⣞⣯⣟⡿⣧⢙⢢⠣⡜⡌⠳⡌⠳⡌ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡜⢢⡑⢎⡱⢊⡔⢣⢂⠧⡼⢃⠘⡀⣢⠋⢐⡀⢂⠐⠠⣀⣡⡴⣾⣿⣿⣿⣿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⢀⣴⡾⣫⢿⡟⢀⠂⠌⠠⢁⣢⣴⣿⣿⣛⢛⡛⡍⢲⡉⢖⡡⢚⠤⡙⢤⠓⡬⡙⣼⡳⢁⠐⠋⠿⡿⣽⣞⡿⣽⡊⢆⠳⡰⢩⠱⣘⠱⡌ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⠱⡘⢦⡑⢣⢌⠣⢎⡼⢁⠂⢰⠞⢁⡤⠦⣤⢶⣞⡿⣿⣫⣵⠟⠛⠉⠄⡀⠀⠄⠠⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀⠀⢸⣯⡟⣵⢣⡿⢀⠃⢌⣤⣷⣾⢿⣿⣻⣟⡿⣾⣦⣽⣤⣭⣶⢎⡱⢊⡕⢪⠜⡰⣡⣿⠁⠂⠌⡐⠀⠄⡉⠛⢿⣻⡇⢎⡱⢡⢃⠳⣌⠓⣌ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⢣⡙⢆⡜⡡⢎⡱⡞⢁⢂⣼⠧⠚⠡⢀⠂⣸⣟⢮⡷⣏⡷⠁⡐⠈⡐⠠⢈⠐⡈⠤⢁⠂⠄⡀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⢣⣟⢮⣿⣡⣲⣾⢿⡯⣟⡾⣯⣞⡷⣾⣽⣻⣽⣟⡾⣽⡏⢦⡑⢣⢌⡃⢎⣱⣿⠇⢈⠐⠠⢀⠉⡐⠠⢁⠂⠙⣿⣢⢑⠣⢎⡱⢢⡙⠤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠧⡘⢦⠘⡥⢊⡼⢁⡢⠎⠡⢈⠄⢁⢂⣴⣿⢏⣾⡗⣾⠀⠂⢄⣡⣤⣷⣿⣿⣷⣶⣤⣈⡐⠠⢁⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣯⢳⣞⡿⣟⣿⣳⢯⣯⢿⣝⣷⣻⠾⣽⣳⣞⣿⣳⢯⡿⣽⡘⠴⣈⠇⢦⠙⣦⢣⡇⢀⠂⠌⡐⢈⠐⠠⢁⠂⠌⡐⠀⢳⡎⡱⢊⡔⢣⠜⣡ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⢣⡙⢆⡹⣐⢣⢏⡴⠡⢈⠐⣠⣴⡾⣿⡿⣙⠾⣼⡟⡼⣷⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣀⠀⣰⣞⢧⣛⡾⡱⢛⣾⣽⣻⢞⣟⣾⢳⣯⣟⣷⣻⣞⣽⣯⠿⣟⢯⣧⠓⣌⠚⣤⡟⠳⢦⡇⠂⠌⡐⢀⠂⠌⡐⠠⠈⠔⠠⢁⠂⢿⡡⢣⠜⣡⠚⡤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⠣⡜⢢⡑⠦⣽⠏⠀⠄⡁⣺⣿⢫⡗⣽⣷⣏⢏⣿⣼⣿⣟⣷⣿⣟⣷⣿⣿⣯⣿⣿⢿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⠷⣯⡾⣍⣿⣹⣞⣿⣏⠶⣉⢧⢚⣷⢯⣟⡾⣽⣻⣞⣳⣟⣶⣻⢞⣧⡟⣼⠞⠉⣳⡌⣱⠎⡄⠃⠤⠁⠌⡐⢀⠂⠌⡐⠠⠑⡈⠄⣁⠂⡐⠨⣗⢣⠚⡤⠓⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢌⠓⣌⠣⡜⢢⢿⠘⠈⡄⢰⣿⣧⢛⡼⢣⣿⢎⡟⣾⣾⣟⣾⡿⣽⣾⢿⣾⣿⡿⣟⣿⡿⣿⣻⣯⣿⣿⣿⣻⣿⣿⣿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣧⡙⢦⢣⢚⣿⢾⣽⣳⢟⣾⣳⣻⡼⣏⣿⡳⣭⡇⢀⠂⠄⣻⠱⣉⠤⠉⠄⠡⢂⠐⠂⠌⡐⠠⢁⠂⡐⠂⠄⠂⠄⡁⢻⡌⡓⣌⠳⢌ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⡉⢞⡠⢓⠬⡽⡞⢈⠐⠀⣿⢺⣧⢻⡜⢯⡗⣏⣾⣿⡿⣽⡿⣽⣟⣾⣿⢯⡿⣽⣿⢯⣿⣟⣿⣽⣿⣯⣿⣟⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢎⢇⢧⢚⣿⣞⡭⠟⠚⣉⠡⠐⡈⣿⣷⡝⣇⠠⢈⢰⣇⠳⡰⢀⠡⠌⡐⠄⡈⠰⠐⠠⢁⠂⡐⠠⠁⡌⠂⠌⢤⢹⣇⠳⣄⢋⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢣⠜⡢⢅⡫⢴⢣⠃⠂⠌⠂⣽⢣⡟⡶⣹⠿⠛⢩⣿⣿⣻⢿⣽⣟⣾⣻⣷⠿⣽⣿⡽⣿⣻⣾⣿⣟⣷⣿⣳⣿⣿⡟⠰⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠮⠖⠛⠈⢆⠰⢈⠒⡠⠡⡘⠠⣿⣿⡽⣹⡄⠤⠘⡴⢣⠅⢂⠰⠀⠆⡐⠠⠁⠌⡐⢀⠂⠄⡁⢂⠄⢡⡼⣿⠐⣯⠒⡌⢎⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣃⢎⡱⢌⠲⣽⢸⡇⠈⠄⢡⣯⡿⠝⠚⠡⢀⢢⣿⣿⣳⣟⣿⣾⢯⣷⢿⡯⣿⣿⣳⣿⣿⣿⣿⣿⢿⣻⡷⣿⣻⣿⣇⠀⣂⣾⣟⣷⣻⣞⣷⣻⣟⣿⣿⣿⣧⠀⠄⠀⠊⢇⠢⣁⠂⠥⡐⢱⣿⣿⣿⡱⣿⣦⡘⡵⣃⠎⡐⢠⠁⠆⡠⠑⡈⠐⡀⠂⢌⣰⣤⣦⠈⣼⡻⣼⠇⣽⡘⡜⢢⠜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠳⣈⠲⡰⣉⢶⠇⢸⡇⢈⠈⡘⢉⠠⠈⠄⡁⢂⣼⣿⣳⣯⢿⣾⣿⢿⣯⣿⣹⣿⢿⡿⣽⣳⡿⣾⣽⣻⣯⢿⣷⣿⡟⣼⣻⡿⣯⣟⣾⣳⣟⣾⣳⣟⣾⣿⣿⣿⣧⡈⠠⠐⠈⢧⠠⡉⠆⠄⣽⡿⣇⢻⣷⣹⣮⡝⢶⣩⡒⠈⡄⠨⠄⡁⠂⠄⢱⣶⢻⠸⣷⣣⢟⡆⠙⠏⣟⡆⢿⡰⣉⠦⣉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡓⠬⡱⢡⠒⣼⠛⢛⡀⠂⡄⢁⠂⠄⡉⣄⣴⣻⢿⣯⡷⣿⣻⣯⣟⣿⡿⢧⣿⣟⣯⢿⣻⣽⣻⢷⣯⡷⣿⣻⣾⣿⡹⣾⡿⣽⣳⣟⣾⣳⣟⣾⣳⢯⣿⣿⢯⣟⣿⣷⣄⠈⠄⡀⠳⡌⠰⢈⣾⠁⢜⡎⢿⣵⣳⡝⡾⣰⢧⠑⠠⢃⡐⠤⠑⡈⢸⡗⣟⠃⢁⢹⡞⣷⠈⠄⢿⢧⣾⡑⢆⡓⠤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢎⡜⣡⢃⠧⣉⣧⣸⣼⡇⠡⠐⠠⠌⡐⣾⢫⢶⣟⣿⢷⣿⣳⣿⣟⣾⣿⣛⣿⣟⣾⡽⣟⣯⣷⢿⣻⣾⡽⣷⢿⣿⢧⣿⣻⣟⣷⣻⣞⣷⣻⣞⡷⣯⣿⣿⢯⣟⣞⣧⣿⡿⠖⠒⡒⠋⡉⠩⢉⡙⠚⠤⣳⡸⣿⡷⣻⣷⢣⢿⡈⣁⠢⠐⠠⠒⠀⡄⡿⣽⠐⠠⠈⣟⣾⡀⠌⣼⡻⣹⡜⢢⢍⡒ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢢⡜⢰⠊⢲⣵⣿⣿⢫⡇⠂⠁⡆⠐⢠⠈⣿⣾⣽⣿⢻⣾⣽⢳⣿⡟⣯⣽⣿⡞⣯⡟⣿⣽⣾⣿⣽⡞⣿⣽⣿⣿⣾⢳⡟⣾⣿⣷⢻⣾⣷⣿⣿⣿⣿⣯⡟⣾⣽⠋⠁⠀⡌⠐⢠⠁⡄⠁⠂⡄⠈⡄⠉⢱⣿⣷⣯⣷⢫⡞⣧⠀⠂⠉⠐⢨⠐⠀⢹⡞⡇⢠⠁⣿⡎⡇⢸⡟⣴⠛⡏⢲⡌⠒ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡜⢢⡑⢣⣺⣿⣿⢟⣵⡿⣧⢈⠐⠠⢁⠂⠄⣹⣷⣿⣽⣻⣞⡿⣿⣿⣻⡽⣿⣳⣿⣻⣽⣷⣻⢷⣯⢿⣽⣻⣽⣿⢯⣛⡟⣾⣹⣭⣏⠿⠭⢷⣚⣖⢧⣛⣼⡳⠋⠀⠄⢂⣡⣤⠵⠒⠒⣀⠃⠂⠄⠡⢀⠁⢂⠙⢿⣧⢿⡞⡼⣹⡎⠄⠱⠈⠄⢂⠡⢸⡟⣵⡌⠸⣷⣹⠇⢈⣰⡿⢱⣿⢢⡑⢣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡙⢦⢉⣷⣿⡿⣡⣿⢯⡿⣽⡀⠌⡐⠠⢈⠐⣾⣽⣾⣳⡿⣽⣻⣿⢷⡯⣿⣻⢷⣯⡷⣟⣾⢯⣿⢾⣻⡽⣿⣿⢽⡳⡯⢊⡉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⡀⠌⣰⡾⠛⠉⢄⠠⢁⠂⠄⡈⠌⡐⢁⠂⡁⢂⠐⡈⢿⣾⣿⡵⢣⣽⠈⣂⠉⡐⢈⠐⡀⢿⣧⠿⢀⠋⢁⣤⣾⠟⢁⠮⣿⣧⢘⠥ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠣⡜⢢⢣⣿⡿⣱⣿⢯⡿⣽⣻⣷⠐⠠⢁⠂⢬⣿⢯⣷⢿⣽⣻⣿⣟⣯⢷⣻⣽⣟⣾⡽⣿⣽⣻⣽⣻⢯⣿⣿⡻⢶⣝⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡾⠋⠄⡁⠊⠠⠐⠠⢈⠐⡀⢂⡐⢀⠒⡀⢂⠐⠠⠘⡟⣿⣷⣋⠖⡇⡐⡐⠐⡈⠐⡀⣂⡄⢠⣦⢸⡿⠝⡁⠰⣸⢋⡟⣿⢌⠲ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢄⠫⡜⡡⢆⡿⣼⡿⣽⢯⣟⣷⣿⣿⡆⢁⠂⡐⣺⢿⣻⣯⢿⣞⣿⣻⢾⣽⣾⣻⢷⣯⢿⣽⢷⣯⣟⡷⣟⣿⣿⠿⢽⣫⣝⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⡉⠐⡈⠄⠠⢁⠂⡁⢂⠂⠌⡐⠠⠐⡀⢂⠁⠂⡌⠠⢁⠠⠉⠝⣯⣙⡲⣄⡁⠒⠠⠁⠄⡙⠳⠘⠛⠠⠐⠠⠐⢡⣏⡟⢠⢸⣯⡒ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣮⣵⡶⣷⣾⣷⣿⣟⣿⣻⢿⡿⣿⢿⣿⣶⣶⣶⣿⡿⣿⢾⣯⢿⣞⣯⣿⣞⡷⣟⣿⢾⣻⡽⣿⢾⣽⣻⣿⣿⡟⣆⠀⣿⠉⠈⠓⢂⠀⡒⠈⣄⣠⣤⠿⠋⠄⢂⠑⠠⢁⠐⠨⠐⠠⢂⠐⠤⢈⠐⠠⢁⠒⢀⠂⠌⡐⠠⢁⠂⠤⢁⠂⠌⠉⢻⣷⣍⢚⢤⡁⢂⠐⠠⠁⠌⠠⠁⠌⡰⢯⠞⡐⢂⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣟⡿⣯⢿⣽⣟⣾⣽⡾⣽⡾⣯⡿⣽⣯⢿⣞⣷⢯⣟⣾⣽⣻⣟⡾⣿⡽⣾⣳⣯⢿⣻⡾⣿⣽⣻⣽⣟⣾⣿⣿⡿⣽⡸⠄⢉⣐⡼⠖⠋⠉⠍⡉⠍⡉⠡⢀⠡⠌⠠⢈⠐⡠⠈⠄⡡⠂⠤⢈⠐⠠⢈⡐⣠⢈⠤⢈⠐⠠⢁⠂⠌⣀⠂⠌⠠⢁⠂⢿⣻⣧⡂⡙⠲⣌⠄⠡⠈⢄⣡⡾⢛⠡⠒⣈⣾⣿⣿⣿ ⣿⢿⣻⣟⣯⡿⣽⣳⣟⣾⣽⢷⣻⣽⣻⣽⣟⣾⣽⢾⣳⡿⣯⣟⣷⣟⡿⣞⣯⡿⣾⣻⣽⣾⣳⢿⣞⣿⣳⡿⣯⣷⣟⣿⣳⣿⣳⣯⣟⣾⣽⣻⣽⣻⢿⣷⣧⣟⣯⠋⢀⠰⠈⡐⠠⢁⠂⠌⡁⠄⠂⡌⠐⠠⢁⠠⢁⠂⡐⣀⣦⡴⠾⠓⢧⣼⣤⢧⠘⡀⠌⡐⠠⢈⠐⠠⢈⠄⡑⠠⢈⠘⣧⢻⢷⡈⢡⠐⡹⣦⣗⠊⠥⡐⢂⢡⣳⣾⣿⣿⣿⣿ ⣿⣻⣽⡾⣯⣟⣯⣟⣾⡽⣾⣻⢯⣷⣟⡷⣯⣟⡾⣿⣽⣻⢷⣻⡾⣽⣻⢯⡿⣽⣷⣻⢷⣯⣟⣯⢿⡾⣽⣻⢷⣻⢾⣳⡿⣾⡽⣾⣽⣳⣯⢷⡿⣽⣻⡾⣽⣻⣟⣿⣷⣦⣵⣠⣅⣦⣬⣔⣤⣬⣡⣄⣡⣬⣤⡶⠶⠛⣋⠉⠄⡐⠤⢁⠂⡌⣷⣯⢦⠐⠠⢀⠁⠂⠌⡐⠠⠂⠄⡁⠂⠄⣿⠭⡞⣷⣀⠣⢐⠹⣿⣿⣶⣤⣷⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⢤⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⠞⢩⣧⡨⠿⠿⢿⡝⠯⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⠟⠍⠁⢒⠿⡠⠖⠉⠉⢙⣷⠀⠀⠀⠈⠩⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢤⡿⣥⡖⣲⣿⣿⣞⣁⣀⠴⢚⣿⠛⣷⡈⣆⠀⠱⡌⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⢛⣶⣿⣿⣿⠋⣹⣟⣁⣴⣾⠃⢀⡏⠇⠸⡀⠀⢱⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⡘⣾⣿⣿⡇⣸⡯⠽⠟⢋⣉⠑⡞⠀⡼⢠⢧⠀⠀⡇⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⡿⢰⢁⡟⠀⠉⣰⠙⡿⣷⣶⢦⡄⢰⠁⢰⠃⣸⡌⠀⢸⠃⢀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⢸⢸⢧⡰⢼⣿⡀⠉⠀⠈⠀⠀⠀⢧⢇⣸⣳⠁⡰⢃⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⡸⣼⡝⢦⠣⠁⠀⠀⠀⠀⠀⠀⠘⠙⠻⢥⠞⢁⠜⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⢿⣼⣇⠘⣧⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣼⣧⣾⡷⠛⢿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠺⣿⣿⣇⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠶⠶⠿⢿⣿⡇⠀⠀⠈⠓⠤⣤⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠋⠀⠀⠀⠀⠀⠙⠓⠤⠄⣀⡀⠀⢸⣷⣦⡤⠤⠖⠒⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⢀⢆⡀⠀⠂⠒⠒⠒⠻⠦⣄⡀⠀⢀⠢⠤⠤⢄⡹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡚⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⢬⣱⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⡄⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠀⠀⠀⠀⠈⡦⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠖⠋⠈⠳⣄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⢸⠈⠉⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢥⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⠀⠀⠀⠀⡹⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠄⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠭⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡆⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡱⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠹⡄⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠹⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⡥⠀⠀⠀⠀⣠⠴⢀⣠⠤⢦⡀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⢸⠁⠀⠀⣠⢚⡥⠚⠉⠀⠀⠘⣗⡄⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⠇⡎⠀⠀⣰⡳⠋⠀⠀⣠⣤⠶⠢⡿⣸⣆⠀⠈⣧⣄⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⢳⣠⣾⡟⠓⠆⠀⠘⠙⢀⣤⣶⢿⣤⣹⡅⠀⣿⠈⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠸⡇⣾⡛⣶⡦⠀⠀⠀⠛⢱⢼⣷⠸⠋⢣⠀⡇⣹⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⠀⠹⣏⠉⢟⣻⣀⠀⠀⠀⠐⠛⠛⠐⠀⠘⣴⡽⣇⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢇⠀⠘⡄⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢹⡀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⠀⢻⢦⡀⠈⠰⠶⠒⠂⠀⠀⢀⡤⠀⡇⢘⡆⢇⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡼⡀⣟⡶⢄⡀⠀⢀⡠⠖⠁⠀⢀⡇⢸⢻⠸⡀⠀⣿⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⢳⠟⢀⠷⠈⣹⡇⠀⠀⠀⠀⣼⢣⡞⢸⠀⡇⢰⣼⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⣠⠋⢀⡼⠟⠊⠟⠀⠀⠀⠀⠀⣿⠀⠑⢯⣀⣇⣎⢏⡞⠀⠀⠀ ⠀⠀⠀⢀⡠⠾⠔⠓⢞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⡈⠛⠿⠯⣀⠀⠀⠀ ⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠉⠉⠉⠉⠉⣧⡀⠀⠀⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⢻⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⢸⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡼⠃ ⠀⠀⠘⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⣠⠇⠀ ⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡎⠀⠀ ⢠⠇⣠⣂⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡄⠀⠀⡸⠀⠀⠀ ⢸⡀⠛⠜⣛⢸⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣯⠽⡇⠀⡇⠀⢀⠇⠀⠀⠀ ⠀⢷⡀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠂⠷⠦⠃⣰⠁⠀⣾⠀⠀⠀⠀ ⠀⠀⠑⢤⣀⠀⠀⢀⣠⠴⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⡴⠁⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⡽⠀⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣾⠀⠐⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⠀⠀⢠⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢰⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡜⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀
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⠁⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⠁⡀⠐⠈⠀⠐⠈⠀⠐⠀⠐⠀⡀⠂⠀⠐⠀⠠⠐⠀⠀⠄⠀⠠⠀⠀⠄⠀⠀⠄⠀⠀⢸⡿⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⡀⠀⠀ ⠀⠁⠈⢀⠀⠄⠈⠀⠁⠈⠀⠁⠈⠀⠄⠀⢀⠈⠀⠠⠀⠀⠀⠂⠀⠀⣄⣠⣤⣤⠴⠶⢶⡶⠶⠬⠿⢤⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠄⠈⢀⠀⠠⠀⠂⠁⢀⠈⠀⠄⠁⢀⠠⠀⠀⡀⠐⠀⢀⠈⢀⣤⠶⠛⠉⠁⣠⠀⠀⡠⠀⣤⢋⠁⠐⠠⡀⢈⠙⠒⢤⣀⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⠄⠀⠀ ⠐⠀⡀⠠⠀⠠⠐⠀⠀⡀⠂⠀⠠⠀⠀⠠⠀⠀⡀⠄⣠⣴⡿⠋⠀⢀⣴⠞⠁⢀⠜⣠⠞⢡⠃⠀⢠⠀⠑⡄⠑⢄⠀⠈⠓⢤⡀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⡁⠀⠄⠀⠐⠀⡀⠄⠁⠀⡀⠄⠁⠀⠐⠀⡀⠁⣠⣾⡿⠟⠀⠀⣰⡿⠃⠀⠠⢁⡴⠁⢀⡇⢠⠃⢸⠀⠀⢸⡄⠀⢣⠈⠠⡀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⡀⠂⢀⠈⠀⠄⠀⠀⠄⠂⠀⢀⠠⠈⠀⡀⢀⡼⣿⠏⡁⣠⠃⣼⠟⡀⠀⠀⣿⡾⡅⠀⣼⠀⡼⠀⠈⡇⠀⢸⢣⠀⠀⠃⢠⠑⢤⡈⠳⡀⠀⠀⠁⣀⣠⣤⠤⠄⠒⠒ ⠄⠀⡀⠀⠂⢀⠈⠀⡀⠄⠂⠀⢀⠠⠀⢠⡿⣽⢫⠖⢰⠃⣸⣏⡞⠀⢀⣾⣿⠇⠀⡄⡇⢸⡇⠀⠀⢳⠀⢸⡼⡄⠀⠀⠀⡇⠀⠱⡀⢳⣀⡴⠛⠉⠀⠀⠀⠀⠀⠀ ⠄⠐⠀⠀⠂⠀⠠⠀⢀⠀⠀⠂⠀⠀⣴⡿⣻⠃⡞⢀⠃⢀⣏⡞⠀⠀⣾⣿⣿⣀⢰⠃⣇⠀⢧⠀⡃⠈⣇⢸⣷⡇⠀⠀⠀⢸⠀⠀⢱⣀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⠁⢀⠈⠀⠠⠀⠀⠂⠀⢁⣾⣿⣱⠏⢸⠇⠀⡤⢾⣿⠓⠛⢻⣿⠋⣟⠀⣸⠃⣷⠀⠘⢦⡇⠀⠸⣟⣿⡆⠀⠀⠀⠘⡆⠀⠀⣿⣳⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠄⠂⠀⠐⠀⠀⠁⡀⢨⣾⣿⢃⡿⢀⣹⡤⢁⠀⣿⣟⠀⠀⣿⡿⠀⣯⠀⣿⣷⠸⣇⢤⡈⢷⡀⠀⢸⢿⣷⠦⣀⠀⢈⡇⠀⠀⠸⡇⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠈⠀⠀⠐⠀⠈⠀⠄⢠⣿⢣⡏⣼⣏⠀⢿⣷⠀⢢⣿⣯⡀⢸⢿⣇⠀⢹⡆⣿⣿⣤⡻⣦⣿⣦⣽⣶⣾⣈⣻⣤⠈⠙⢺⡇⠰⠀⠀⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠂⠁⠀⢀⣿⠇⣾⡐⣿⣿⠈⢾⣿⡆⣹⣇⣹⣷⣾⣬⣿⡀⠈⣿⣯⢻⣿⣧⠉⢻⡟⣷⡄⢹⠀⢸⡇⠀⠀⣼⡇⠀⠀⠀⢹⠈⡟⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠠⠈⢸⡿⢸⣷⡚⣿⣿⡡⢘⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡄⠈⠎⠢⢽⣿⣷⣄⡇⠈⣿⣿⣄⣀⣿⠀⢠⣿⠃⠀⡀⠀⣽⠀⣷⣿⡄⢠⠀⡄⡀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡧⣿⣿⡔⣿⣿⣇⠄⣿⡇⠈⢧⠈⢿⣿⣾⡶⠋⠁⠀⠀⠀⠀⠙⠙⠻⣷⣾⡿⣿⣿⣿⣿⣤⣿⡿⠠⠀⡄⢠⣿⠀⣿⣽⡇⠢⠑⠈⡜⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⣿⢧⣿⣿⣿⣖⡸⣷⠀⠀⠑⠤⠭⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⡍⠸⣿⣿⣧⠀⢨⣇⣾⣿⠀⣟⢸⡇⠀⠀⠀⡜⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⣿⣿⡿⣿⣿⣿⣿⢿⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢤⠀⠀⠀⠀⠤⣛⣛⣋⠀⠈⢁⣿⠇⡀⣾⣽⢿⡁⢠⡟⣼⡇⠀⢀⠒⡌⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢨⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⠳⣄⡀⠀⠀⠀⠀⠀⠀⢧⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⡰⣰⣿⡟⣾⢠⣾⣧⣿⠀⢀⠌⡓⣌⢣ ⠀⠀⠀⠀⣀⣤⡴⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣟⣵⣿⡟⢧⣿⣿⣿⡿⠃⠀⡌⢎⡱⢌⡖ ⠀⢀⣴⠟⠉⣠⣴⣾⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⠿⢿⣷⡀⠀⠀⠀⠀⠠⣤⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠤⢞⣻⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋⠀⣀⠣⡜⢢⡙⢮⡜ ⢠⡟⠁⣠⢞⠿⣩⣾⡽⠋⣠⡷⠻⠀⠀⠙⣿⢻⡀⠀⠉⠛⣤⠀⠀⠀⠀⠈⠑⠒⠠⠤⠞⠛⠀⠀⠀⠀⠀⠀⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠰⣀⠳⡌⢧⡹⢣⢞ ⢸⢀⡞⡵⠋⣴⡿⢋⠀⣰⠟⠠⢁⠂⠄⠀⢹⡆⢹⡀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣤⣇⣌⠳⣜⣣⠽⣍⢾ ⢀⡟⡞⢀⣾⠟⡵⠃⣰⠏⠀⠀⣼⠀⡙⣂⡏⢹⣀⡧⠀⠀⠀⠀⣿⣷⣦⡀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠋⠁⠀⣼⣯⢿⡟⣻⠇⢨⡉⢤⡀⠙⢶⣍⠻⣟⠶⣭⢞⣭⠏ ⢸⢹⠁⡼⢥⡾⠁⣰⠏⠀⠀⣰⡟⠀⣇⣼⠁⣸⣸⠇⠈⠀⠤⠀⣿⣿⣿⡿⣷⣤⣴⣶⣿⣿⣿⠿⡇⠀⠀⢠⣿⣣⡟⠡⡿⢠⠀⢿⠀⠘⢳⡈⢿⣳⣌⠳⣬⣻⡎⠀ ⠸⣿⣰⠏⣾⠃⢀⡿⠀⠀⢠⡿⠁⢨⡼⠃⢠⣯⠏⠀⠀⠀⠀⠀⣿⣋⢿⣽⣳⢯⣞⣼⡿⠋⠈⠘⡇⠀⠀⣾⢳⣿⠁⣸⡇⢸⠀⢸⢀⠀⠸⣷⡄⢻⡽⡆⢿⠟⢟⠂ ⠀⠙⣿⣼⡏⣄⣸⡇⠀⠀⡞⠁⠄⣾⠃⢀⣿⠋⠀⠀⠀⠀⠀⠀⣿⠐⣈⠹⠷⣫⣾⠏⠀⠀⠀⠀⡇⠀⣸⣿⣿⣿⠀⡼⡇⢸⠀⠘⡌⣆⠀⠘⣧⡌⢿⡇⣸⠀⠈⢳ ⠀⣼⣯⣿⣸⡇⣿⠀⠀⣸⠇⠀⣼⠁⣀⣾⠃⠀⠀⠀⠀⠀⠀⢀⡯⠰⡏⠁⠀⠜⠁⠀⠀⠀⠀⠀⣇⢠⣏⢿⣿⣿⡀⣇⣧⣾⡀⠀⠀⣿⢠⡀⢹⣷⠘⡷⠃⠀⠀⠀ ⣸⠿⣿⡟⣼⡇⣿⠀⠀⣿⣰⢽⡇⠀⢿⡇⠀⠀⠀⠀⢀⣠⢴⣿⠄⠁⢧⠀⠀⠀⠀⠀⣰⠀⠀⠀⢘⡿⢧⣾⣿⣿⣷⣿⠈⣿⣇⠀⠀⣻⢸⡇⠰⣿⣇⢳⠀⠀⠀⠀ ⡏⠀⣿⡿⣼⡇⣿⡡⠀⣿⣿⣿⠀⢀⠘⣄⣀⣠⠤⠒⠍⠂⠘⢿⡀⠂⠸⡄⠀⠀⠀⣰⡏⠀⠀⠀⣼⠃⠀⠈⠙⠻⢿⣿⣇⣿⣿⣆⡀⢹⢾⣇⠰⡏⢹⠘⡇⠀⠀⠀ ⠀⠀⠘⣿⢲⣷⣿⣽⣇⡿⠟⠋⠉⠉⠀⠀⠒⠶⢬⣝⣒⣦⣄⣸⣇⠀⢀⣃⠀⠀⢠⠋⢁⣀⣀⣠⡿⠤⠞⠒⠒⠃⠀⠀⠀⠈⠄⠁⠉⠉⠛⠻⢌⡇⢸⡀⡇⠀⠀⡰ ⠀⠀⠀⠹⣧⣻⣾⠟⠉⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠉⠉⢻⡏⠉⠉⠑⠀⠘⠋⠁⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣱⠇⠀⠈⠀ ⠀⠀⠀⠀⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠀⠀⠀⠀ ⡀⠀⠀⠀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡆⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⢧⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⢳⣀⢸⢁⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀ ⠀⠀⠙⢿⢂⡐⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣤⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⢸⡇⡐⠀⠀⠀⠀⠀⠀⡀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣭⣯⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀ ⠀⠀⠀⠘⡷⣈⠐⠀⠀⠀⢀⠐⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡾⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀ ⠀⠀⠀⠀⣷⡱⢊⠐⡀⠂⠌⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⣀⣀⣀⣸⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢸⡀⠢⠀ ⠀⠀⢠⡴⢻⣕⠣⠄⡡⢁⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣹⠟⢄⠁ ⠀⢰⣿⠟⢩⣯⠓⡌⠐⣠⡟⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣠⣖⣦⡀⠀⠀⢹⡀⠀⠀⠀⠀⣿⡇⠈⣧ ⠀⣿⡃⠀⣼⣹⡗⡌⠡⢼⠃⠀⠀⠀⡼⣿⣿⡗⢠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣿⣾⡇⡷⠀⠀⠀⣧⠀⠀⠀⠀⡿⠁⢠⡟ ⠀⠹⠷⠦⢹⣟⡷⣌⠡⣿⠀⠀⠀⠀⠙⠬⠽⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠿⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⡷⢤⡿⠞ ⠀⠀⠀⠀⠀⠛⣿⠰⢦⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡍⡆⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⢿⡔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⣯⠄⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⢯⣟⡶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡗⡼⡎⡑⢌⠻⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠛⠁⠀⠀⢸⠀⠈⠙⠻⢽⣷⢦⣄⣀⡀⢀⠀⢀⠀⣀⣠⣴⡿⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢰⢻⡔⣈⠒⣿⢩⢛⣟⠾⣳⣛⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠛⠛⠛⠉⠁⣼⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡪⡕⣣⠤⣉⣿⠀⢊⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠳⢆⡱⠠⢿⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡁⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⡻⢜⡰⡉⢾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⠐⠀⠀⠀⡀⠌⢸⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⢩⠖⣡⠇⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠩⠄⢂⠁⡰⠈⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⢽⢠⢋⠴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣆⡘⠤⢂⡱⢈⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⡜⢢⠉⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⠠⢉⠻⢶⠡⢆⢃⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⠤⡉⠆⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣇⠑⣈⠒⠤⢋⠴⣩⡇⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢂⠱⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢻⣄⠂⢍⣸⣡⣾⠟⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⡦⢑⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠈⢿⡞⣎⡷⠋⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡱⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢥⠃⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢰⣞ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡼⠁⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢀⡿⣜ ⠀⠀⠀⠀⠀⠀⠀⣼⣫⠞⡀⢡⠂⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢰⡟⣼ ⠀⠀⠀⠀⠀⠀⣼⡷⢋⡐⢈⠄⢂⠁⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣸⣽⡳ ⠀⠀⠀⠀⠀⣼⠟⡡⢂⠔⢂⠈⠄⠂⠌⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⣿⡞⣽ ⠀⠀⠀⠀⣰⢏⠦⡑⢌⡐⠢⡈⠤⠁⠌⡐⢀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣯⢿⡼ ⠀⠀⠀⢀⡿⣈⠖⡈⠆⡌⠱⡐⢢⢁⠂⡐⠀⠆⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢧⣟ ⠀⠀⠀⣸⡓⠴⡈⠴⠡⢌⠱⡈⠆⡌⡐⠠⠁⠂⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡾ ⠀⠀⢀⡟⡬⢱⠘⡄⢃⠎⡰⢁⠎⡐⠀⠑⣆⠁⢂⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣳ ⠀⠀⢸⢏⡔⡃⢎⠰⡁⠎⡐⠂⠄⠠⠀⠀⠈⢶⡀⠂⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡵ ⠀⠀⣾⢡⠚⣌⠢⡑⠄⡃⠄⠁⡘⠀⠀⠀⠀⠀⠹⣄⠂⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⢠⢈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻ ⠀⠀⣟⡌⢳⠠⣃⠌⠒⡀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠙⣦⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣀⡾⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷ ⠀⠀⡯⡜⣡⠒⡡⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⡴⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿ ⠀⠈⡷⣑⠢⡱⠡⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⡁⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿ ⠀⠀⡷⢡⢓⡰⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⠀⠀⠀⠀⢀⣾⠣⡘⠠⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷ ⠀⠀⢽⡡⢆⡱⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⣹⣯⣀⣀⣤⣿⠡⠆⡁⢂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷ ⠀⠀⣾⢰⢃⠦⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠋⠹⠟⢻⡿⣡⠃⠜⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡽ ⠀⠀⢽⡎⡜⢢⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠀⠀⣾⡱⡂⠥⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽ ⠀⠀⢸⡧⡙⢆⠣⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠔⢸⢧⡓⣁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢻ ⠀⠀⠸⣗⠭⣊⠕⡨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⣿⢎⡱⠠⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣟ ⠀⠀⠀⣿⡜⢢⢍⠰⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⣯⢛⠴⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣳⢾ ⠀⠀⠀⢹⣎⠇⣎⠒⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⣏⢎⡒⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣽⣻ ⠀⠀⠀⠈⣯⢚⠤⡃⠔⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⣏⠖⡨⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⢾⣽ ⠀⠀⠀⠀⢻⣍⠖⣩⠘⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣟⡯⠜⡰⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢻⣟⣾ ⠀⠀⠀⠀⠘⣯⢚⠤⡃⠤⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⡧⢋⠤⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠐⠸⣿⣽ ⠀⠀⠀⠀⢀⢻⡍⡖⢱⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢻⣿⡧⢩⢀⠃⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⠀⢿⣿ ⠀⠀⢈⣄⣠⠸⣏⡼⠡⡌⡑⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢺⣿⣇⠃⠆⡘⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⣲⠤⠘⣿ ⠀⠐⠀⠀⠀⡀⢿⡜⡱⢂⡑⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢺⣿⡧⢉⠰⢀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⢀⡀⠄⢹
⠄⠄⠄⠄⠄⠄⠄⠄⣀⣠⣤⣤⣤⣄⡀⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⣴⣿⣿⣿⡿⣿⡿⣗⢌⢳⡀⠄ ⠄⠄⠄⠄⠄⣼⣿⡇⣿⠹⡸⡹⣷⡹⡎⣧⢳⠄ ⠄⠄⠄⠄⠄⣿⣿⠱⡙⠰⣢⡱⢹⡇⡷⢸⢸⠄ ⠄⠄⠄⠄⠄⢿⢸⡈⣉⣤⠠⣴⡄⡇⠁⠄⢸⠄ ⠄⠄⠄⠄⠄⠸⡆⡃⡙⢍⣹⡿⢓⠄⠤⣐⡟⠄ ⠄⠄⠄⠄⠄⠄⠙⠾⠾⠮⣵⢸⡔⢷⣍⠉⠄⠄ ⠄⠄⠄⠄⢀⣴⣾⣿⣷⡺⡋⢞⣎⣚⣛⣳⣴⣶ ⠄⠄⠄⠄⢘⣛⣩⣾⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿ ⠄⠄⣀⠺⣿⣿⣿⠟⣡⣾⠿⢿⣿⣿⡎⢋⠻⣿ ⠄⠄⣉⣠⣿⣿⡏⣼⣿⠁⠶⠄⣿⣿⡇⡼⠄⠈ ⠄⠄⣈⠻⠿⠟⢁⠘⢿⣷⣶⣾⣿⠟⡰⠃⠄⠄ ⠄⣴⣿⣧⢻⣿⣿⣷⣦⣬⣉⣩⣴⠞⠁⠄⠄⠄ ⠄⠘⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⠁⠄⠄⠄⠄⠄ ⠄⢤⡝⣧⢸⣿⣿⣿⣿⣿⣿⠟⠄⠄⠄⠄⠄⠄ ⣜⢧⠻⣀⢿⣿⣿⣿⣿⣿⠏⣾⣧⡀⠄⠄⠄⠄ ⠹⢂⣾⣿⠸⣿⣿⣿⣿⡏⣼⣿⣿⣷⠄⠄⠄⠄ ⠄⣿⣿⣿⣧⠹⣿⢻⡿⢰⣿⣿⣿⣿⣇⠄⠄⠄ ⢸⣿⣿⣿⣿⣇⢹⢸⢁⣿⣿⣿⣿⣿⣿⡆⠄⠄ ⢸⣿⣿⣿⣿⣿⣆⠄⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄ ⠸⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⡇⠄⠄ ⠄⣿⣿⣿⣿⣿⣿⠄⠈⣿⣿⣿⣿⣿⣿⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣣⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠀ ⠀⠀⠀⠀⢀⣀⣀⣸⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡤⠶⠶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡇ ⠀⠀⠀⣰⣫⡏⠳⣏⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⡅⡇ ⠀⠀⢰⡇⣾⡇⠀⠙⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠻⢿⣶⣤⣍⡙⢿⣿⣷⣤⣾⡇⣼⣆⣴⣷⣿⣿⡇⡇ ⠀⠀⢸⡀⡿⠁⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⠴⢲⣶⣶⣶⣾⣿⣿⣿⣷⠹⣿⣿⠟⢰⣿⣿⣿⠿⣿⣿⣿⠁ ⠀⠀⠈⡇⢷⣾⣿⡿⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣌⠳⣼⣿⣿⣿⣻⣿⣿⣿⣿⡇⠈⠁⢰⣿⣿⣿⣿⣶⣾⣿⣿⠀ ⠀⠀⠀⣷⠘⠿⣿⡥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠌⠉⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⡿⣿⣿⣿⣿⣿⣿⣿⡞⠀ ⠀⠀⠀⢸⡇⠀⠹⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠟⠉⠉⠀⠀⠀⠈⢃⣿⣿⣿⣿⣿⣿⡻⠀⠀ ⠀⠀⠀⠈⢧⠀⠀⠏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠈⢳⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠊⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⣿⣀⡰⠀⠀⣤⣄⠀⠀⠀⠀⢹⣿⣿⣿⣿⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢠⣤⣶⣤⣀⠀⢀⣶⣶⣶⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠻⣿⣿⣥⣤⣯⣥⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠠⠀⠀⠀⠀⠈⣿⣿⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣠⣰⣄⡀⠀⢀⣀⣀⣛⣟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠾⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠠⣄⣉⣉⣻⣿⣿⣿⣿⣿⣿⡟⠧⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠅⠀⠀⠀⠀⠘⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠉⠓⠢⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⡄⠀⠀⢀⡑⠢⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢉⣕⡞⣼⣿⣿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⡀⢻⣤⣴⣴⣶⣶⣶⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⢧⣿⣦⠬⡜⣼⡝⣿⢹⣿⣿⡟⣁⡀⣴⣿⡟⣹⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⣿⢀⣿⢀⠨⢳⣷⢴⣧⣸⣟⡟⠉⢁⡾⠋⣀⡴⢃⡠⣠⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠋⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣾⣧⢸⣻⠀⢩⡏⠀⣸⣯⣿⡿⠒⣲⠟⠘⣩⠿⣠⠏⣴⣿⢯⣟⣹⣄⡿⣿⣿⣿⠏⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠘⢸⡇⣰⣿⠏⣿⣀⡼⠧⢶⣶⣳⡞⢳⠞⣿⣣⠏⠀⢠⣞⣀⣸⣿⣿⠀⢻⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⣿⣷⣿⢹⠀⣯⣞⣧⣔⣯⣿⣯⡾⢃⣾⠟⠁⢀⣴⡟⢀⣼⡟⣾⡿⣐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣧⢹⣾⣴⣿⠋⡇⢸⣸⣿⣿⣿⣿⣿⣿⣯⣶⠟⠋⢀⣴⣫⢏⣴⠟⣽⣿⡟⠀⠈⢹⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢳⠇⣿⣿⣿⣿⢹⡀⠃⢸⡜⣿⢹⣿⣷⣿⣿⡿⣷⠶⠚⠛⢛⡿⠋⣠⣾⣿⣿⣤⣦⣀⢸⡟⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⡞⣸⢻⣿⣿⣿⣾⣗⠄⠘⡇⣿⠚⠻⠿⠯⠿⠅⠀⠠⢄⠍⢨⡙⠊⠑⣿⣿⣯⣿⡿⠻⣿⢡⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣾⢣⡟⢸⠀⣿⣿⣷⣿⣦⠀⣷⣹⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠛⠿⠿⡿⣁⣼⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣇⣼⣿⣾⠀⣿⣿⣮⡛⢿⣧⣽⡿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠶⠆⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡼⣼⣿⡏⡟⣼⣿⣿⣿⡻⣿⠃⣸⡟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢰⢳⢻⡿⣠⡷⣿⣿⣿⣿⡏⢻⣴⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣼⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⡞⣼⣷⢻⡇⣸⣿⣿⣿⡿⡟⠅⣴⣿⡟⢤⣀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⢻⢁⡿⠇⣸⠇⣿⣿⣿⣿⣇⣿⠞⣡⣿⣧⣤⣽⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⣸⠃⢀⣿⢀⣿⣿⣿⣿⣿⢥⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠺⠷⣏⡀⣼⡿⢸⣿⣿⣿⣏⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⣿⣿ ⠀⠀⠀⠀⠈⠙⠳⢿⣿⣿⡟⢉⣰⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣷⣤⠖⠛⠉⠉⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠤⢄⣀⠀⣨⡿⠟⢋⣿⡿⢯⣶⣝⣛⣛⣿⠿⢿⣿⢥⣠⠼⠻⣿⣟⣿⣿⣿⢿⣿⣿⡋⢤⡀⠀⠻⣌⣉⣻⣦⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢀⣼⡟⠛⣛⣿⡿⠀⠉⢛⣻⣿⠿⠋⠀⢸⢹⠀⠀⠀⠀⠘⣾⣦⠉⠛⠷⢿⣿⣻⣦⡌⠢⡀⠘⣧⣙⡛⣿⣗⡚⠉⠉⠉⡇⠀⠀⢀⣀⣀⣠⣴⣿⣿ ⠀⠀⠀⢀⡤⡶⣿⠋⣽⠛⣿⡿⢁⣤⢶⡋⠉⠁⠀⠀⠀⢸⠾⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠛⣿⣦⡙⣏⠁⠈⣯⣙⠛⢿⣆⠀⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⡟⢸⣷⣿⠉⡇⢀⣯⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⢿⣟⢧⡤⠶⠛⠋⠉⠻⣿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣶⣿⣧⣿⢃⠏⠀⡇⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⢻⡝⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⢿⣯⣎⠤⠔⡇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢴⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⡄⢿⠦⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡉⢿⣻⡄⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⣾⣇⠀⠋⡏⠀⠀⠀⠀⣀⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣻⣎⠀⠹⣵⡟⠙⠛⢿⣿⣿⣿⣿ ⣴⣿⣿⣿⣻⣿⣆⢰⠁⠀⠀⠀⠘⠁⣶⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⢻⣠⣴⠀⣼⡟⠛⠛⠛ ⣿⣟⠙⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⠁⠀⠀⠀ ⡏⠁⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀ ⣄⠀⢀⡀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣤⣀⠀⠀⠀ ⣿⣷⣌⢿⣷⣍⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠈⠊⣙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣎⣻⣼⣷⡆⠀ ⣿⣿⣿⣷⣽⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⠛⠷⢶⣤⣄⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣷⣿⣿⡿⠿⠃⠀ ⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡦⢶⣄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠙⣄⠀⠀ ⣸⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀ ⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠁⠚⠉⠛⠙⠛⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⡟⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⣏⠀⠉⠓⠤⣄⣀⡠⠖⠋⢳⣀⣀⣀⣀⣀⣀⣾⣐⣈⣦⣀⣀⡤⠤⠖⠒⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⠇⠸⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠷⠶⠾⡊⠦⣄⣀⡤⠖⠉⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢧⠟⠀⠀⠙⢧⡵⠀⢀⣀⠠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⡴⠛⠉⠙⡆⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠒⠒⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠋⠀⢀⣴⡾⠃⢀⠇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣜⠁⢀⣼⠛⠛⠤⣰⣫⠖⠀⡄⢸⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠘⢄⢸⢑⡷⢿⡿⢶⣄⠀⢈⠳⡄⣴⡧⢸⡏⠉⠳⡖⠲⠤⠤⢤⣄⣀⣠⡤⠴⠚⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⣚⣿⠀⠀⢄⡀⠙⠲⣍⣠⠋⠐⣠⣾⣿⢧⣴⣣⠏⣰⡿⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠈⢷⡀⠐⠭⣗⡀⡴⢁⢀⣼⣿⠂⠉⠢⣴⣁⡾⠋⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠦⢄⣀⠀⠀⠀⠀⠀⢀⣠⡤⢒⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⢄⡀⠙⠧⣴⡋⣠⠟⠒⣤⣠⢀⠝⣄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣜⡽⠡⣤⣼⡯⣍⡉⢲⠊⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠟⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡇⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣤⢞⡞⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣠⠎⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿ ⠘⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡄⣰⠏⠙⣿⣿⣿⣿ ⢆⠘⣿⣿⣿⣿⣿⣿⠃⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣉⢠⣾⡿⢿⣿⣿ ⠀⠣⡘⢿⣿⣿⣿⣿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠈⠳⠾⠽⡇⠀⢿⣿ ⠀⠀⠱⡈⢿⣿⣿⣿⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⠐⠒⠒⣒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⢞⢿⠀⠀⢿ ⠀⠀⠀⠐⡘⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡁⠄⢀⣀⣀⠀⣴⠉⠈⣝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈ ⠀⠀⠀⠀⠱⡸⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢄⡼⣤⡶⠗⠂⠉⠉⠈⠑⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡴⡶ ⠀⠀⠀⠀⠀⢡⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣀⢤⡄⠶⠒⠋⠉⠉⡹⠋⠐⠂⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣹⠃ ⠀⠀⠀⠀⠀⠈⡎⣿⣿⣿⣷⣀⠤⣔⠶⡝⠓⠙⠁⠀⠀⠀⢀⡠⡜⠠⠀⠀⡠⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⢉⣐⠢⠤⠤⠤⠤⠤⢄⣧⣀ ⠀⠀⠀⠀⠀⠀⠸⢻⢟⡫⠝⠊⠁⠘⠀⢀⠀⠀⠀⠀⠀⠤⠐⣼⡠⣤⠲⠶⠒⠒⠀⠒⠒⠒⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠐⠉⠀⠠⠀⠂⠁⢀⡠⣊⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠒⢄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢀⢤⣶⣾⣿⣿⣿⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠁⠀⢻⣿⣿⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⢸⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⢀⣼⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⡶⣶⢶⣶⣶⡆ ⢀⣀⣀⣀⠀⢀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡛⣯⣿⣏⡯⡏⠁ ⠘⠟⠛⠝⠀⠜⠘⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠻⡛⠛⠓
⣿⣿⣿⣿⠛⠛⠉⠄⠁⠄⠄⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠄⠄⠄⠐⠄⠄⠄⠄⠄⠄⠄⠠⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠄⢀⡀⠠⠃⡐⡀⠠⣶⠄⠄⢀⣿⣿⣿⣿⣿⣿ ⣿⣿⣶⠄⠰⣤⣕⣿⣾⡇⠄⢛⠃⠄⢈⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⢀⣻⠟⣻⣿⡇⠄⠧⠄⢀⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣟⢸⣻⣭⡙⢄⢀⠄⠄⠄⠈⢹⣯⣿⣿⣿⣿⣿ ⣿⣿⣿⣭⣿⣿⣿⣧⢸⠄⠄⠄⠄⠄⠈⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣼⣿⣿⣿⣽⠘⡄⠄⠄⠄⠄⢀⠸⣿⣿⣿⣿⣿ ⡿⣿⣳⣿⣿⣿⣿⣿⠄⠓⠦⠤⠤⠤⠼⢸⣿⣿⣿⣿⣿ ⡹⣧⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢇⣓⣾⣿⣿⣿⣿⣿ ⡞⣸⣿⣿⢏⣼⣶⣶⣶⣶⣤⣶⡤⠐⣿⣿⣿⣿⣿⣿⣿ ⣯⣽⣛⠅⣾⣿⣿⣿⣿⣿⡽⣿⣧⡸⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡷⠹⠛⠉⠁⠄⠄⠄⠄⠄⠄⠐⠛⠻⣿⣿⣿⣿ ⣿⣿⣿⠃⠄⠄⠄⠄⠄⣠⣤⣤⣤⡄⢤⣤⣤⣤⡘⠻⣿ ⣿⣿⡟⠄⠄⣀⣤⣶⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⡎⠝ ⣿⡏⠄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⠐ ⣿⡏⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⡟⣼ ⣿⡠⠜⣿⣿⣿⣿⣟⡛⠿⠿⠿⠿⠟⠃⠾⠿⢟⡋⢶⣿ ⣿⣧⣄⠙⢿⣿⣿⣿⣿⣿⣷⣦⡀⢰⣾⣿⣿⡿⢣⣿⣿ ⣿⣿⣿⠂⣷⣶⣬⣭⣭⣭⣭⣵⢰⣴⣤⣤⣶⡾⢐⣿⣿ ⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢃⣼⣿🍑👈🤤🍑👈🤤εつ▄█▀█●
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠉⠙⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠄⠄⠄⠄⠄⠄⠄⠄⠹⣿⣿⣶⣶⣦⣬⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠄⠄⠄⣰⣧⡀⠄⠄⠄⠄⠈⢙⡋⣿⣿⣿⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄⠰⠼⢯⣿⣿⣦⣄⠄⠄⠄⠈⢡⣿⣿⣿⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄⠸⠤⠕⠛⠙⠷⣿⡆⠄⠄⠄⣸⣿⣿⡏⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣴⣿⣿⣿⢡⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠄⠄⠄⠄⣄⠄⢀⠄⠄⢀⣤⣾⣿⣿⣿⢃⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⣛⣡⣄⣀⠄⠠⢴⣿⣿⡿⣄⣴⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⡽⡁⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢃⣿⣿⢟⣿⣿⣿⣿⣿⣮⢫⣿⣿⣿⣿⣿⣟⢿⠃⠄⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣸⠟⣵⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣄⢰⡄⢿⣿⣿⣿ ⣿⣿⣿⣿⡇⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⡎⣿⣿⣿ ⣭⣍⠛⠿⠄⢰⠋⡉⠹⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⡟⢁⠙⡆⢡⣿⣿⣿ ⠻⣿⡆⠄⣤⠈⢣⣈⣠⣿⣿⣿⣿⣿⠏⣄⠻⣿⣿⣿⣿⣿⣆⣈⣴⠃⣿⣿⣿⣿ ⡀⠈⢿⠄⣿⡇⠄⠙⠿⣿⡿⠿⢋⣥⣾⣿⣷⣌⠻⢿⣿⣿⡿⠟⣡⣾⣿⣿⠿⢋ ⠛⠳⠄⢠⣿⠇⠄⣷⡑⢶⣶⢿⣿⣿⣿⣽⣿⣿⣿⣶⣶⡐⣶⣿⠿⠛⣩⡄⠄⢸
⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀ ⢀⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⡀ ⢸⣿⡁⠀⢠⣦⠀⠀⣤⣤⠀⠀⣴⡄⠀⢈⣿⡇ ⠈⢿⣷⣀⠈⠁⠀⣀⣿⣿⣀⠀⠈⠁⣀⣾⡿⠁ ⠀⠀⣿⣿⣿⣿⣿⠿⠋⠙⠿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀ ⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀ ⠀⠀⢀⣿⡇⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⡀⠀⠀ ⠀⠀⣼⣿⠁⠀⠀⠀⠻⠟⠀⠀⠀⠈⣿⣧⠀⠀ ⠀⣼⣿⠃⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠘⣿⣧⠀ ⢠⣿⡇⠀⠀⠀⠻⣿⣦⣴⣿⠟⠀⠀⠀⢸⣿⡄ ⢸⣿⠁⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠈⣿⡇ ⠸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⠇ ⠀⢻⣿⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣿⡟⠀ ⠀⠈⢿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⡿⠁⠀
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⠀⠀⠀⣴⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣉⣩⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⠉⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡄⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣩⣝⢿⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡝⣿⣦⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⢻⣿⠟⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠻⠿⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣋⣁⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣯⡿⣝⣯⠿⣽⢯⣟⡿⣻⣟⣿⣿⣿⢿⣿⣿⣿⣿⣻⣿⣶⣾⣷⣬⡁⠈⢀⣀⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢯⣽⢯⣟⢾⣵⣻⡽⣾⡽⣽⣳⢯⣟⣿⣿⣯⣿⢾⣿⣿⣟⡾⣯⢿⣿⣿⣿⣷⣤⣿⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠁⠊⠀⠁⠀⠀⠀⠀⠀⠂⠘⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣏⣿⢯⣿⢾⣟⡾⣳⣟⣳⣟⡷⣯⣟⣾⣿⣿⣿⢾⣿⣟⡾⣿⣿⣽⣿⣿⣏⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡳⣞⣿⣿⡯⣿⢾⣽⣳⢯⡷⣯⣟⣷⣻⣽⣿⣿⣿⣿⡽⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⣗⣻⣿⣟⡾⣽⢿⣛⣾⡽⣯⢟⣷⣻⢾⣽⣿⣿⣞⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⠿⣻⠿⠛⢹⣿⢿⠟⠛⠉⠐⣌⢻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣝⣾⣿⡟⣼⣻⣏⣿⣹⢺⣟⣵⣫⣶⡿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⢀⣠⣴⡾⢋⣽⣿⣯⣿⠋⡔⠉⣼⣿⠇⠀⠀⠀⠣⢌⣻⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣽⣿⣟⢾⣿⡵⣯⢾⣱⣯⣿⣷⢯⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣴⣿⣿⣿⣿⠃⢌⠀⢰⣿⡏⠀⠀⠀⠀⠱⢨⠼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣿⣿⣯⢿⣿⣟⣯⣿⣯⣿⣿⣿⣯⣿⣟⣿⣿⣳⣿⣿⣿⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⢣⠘⣀⡞⢸⣿⠁⠀⠀⠀⠀⢀⠃⢾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣽⣿⣿⣯⢿⣿⣻⣾⢿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣿⢋⢆⠃⣾⠀⣸⡟⠀⠀⠀⠀⠀⠀⠎⡽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣽⣿⣿⣿⣯⣿⣿⣏⣿⣿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⢣⢍⣢⣭⡇⢀⣿⢃⠀⠀⠀⠀⠀⢈⢒⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡟⢰⣿⢾⣿⣯⣷⣿⣿⣿⣞⣿⣿⣿⣿⣦⣛⢿⣿⣿⣿⣿⣿⣿⣽⠏⠉⠗⣚⣩⣾⠟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣷⣿⡏⢠⠃⢸⡟⠰⠀⠀⠀⠀⠀⢌⣺⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠀⣾⡏⣿⣿⡷⣿⣿⣿⣿⣧⣧⣼⣿⣿⣿⣿⣶⡹⢿⣿⣿⣿⣿⡸⢄⠉⠉⡙⣉⠡⣚⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣇⡞⠀⣼⠁⠁⠀⠀⠀⠀⠈⡴⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠁⢸⡟⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢾⣫⣼⠗⠀⠙⢟⡻⣿⣷⡂⠀⠀⠐⠀⠂⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠃⣿⣿⠟⠀⢠⡇⠀⠀⠀⠀⠀⠀⣘⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢀⣿⠁⠀⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣬⠉⡒⠋⠁⠀⠀⠀⣤⠙⠌⠻⢆⡀⠀⠀⢀⣰⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠋⠀⠀⣸⠁⠀⠀⠀⠀⠀⠐⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢀⣾⠏⠀⢰⡿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢡⣁⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠤⠚⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⠇⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⣹⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣾⠟⠀⢀⣾⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢎⣀⣀⠄⠀⠀⣤⣠⣤⡀⠀⠀⠀⣠⡿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠏⠀⠀⢠⠏⠀⠀⠀⠀⠀⠠⣜⡾⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣟⡞⠀⠀⣼⣿⣞⡿⣾⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡼⢏⣵⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠋⠀⢀⣴⠏⠀⡄⠀⠀⠀⣀⢳⡞⠀⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣟⣷⣇⢀⣼⠏⢸⢾⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡲⢤⣄⣀⣠⠖⣏⣱⣾⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠓⢶⣾⠟⠁⠀⡜⠀⠀⠀⡰⣬⠟⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⡳⠋⢸⢾⡾⡟⠀⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣃⢎⠲⣁⠏⣴⣿⡿⢻⢽⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠈⣆⠀⠀⠀⣠⠞⠀⠀⢀⡰⣳⠋⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀ ⣰⣻⠞⠀⢀⣼⣿⣿⠀⢰⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡜⣻⣆⠣⠜⡒⢼⡿⣈⠗⣚⣏⠿⣼⣿⡿⣿⣿⣿⢿⣙⢮⡿⠃⠀⠈⠒⠶⠾⠋⠀⠀⢀⢦⡟⠁⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀ ⡗⠁⠀⣠⡾⢃⣽⡾⣧⡾⣽⣯⣿⣿⣿⣿⣿⡿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣯⣇⠎⡴⢡⢎⠳⡜⢺⣄⢛⣦⢙⡴⢪⠜⣆⣛⣷⣿⣿⣟⢣⠎⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⣯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀ ⠀⢀⣾⢋⣴⠟⠁⠻⣽⡿⣿⣾⣿⣿⡟⠉⠉⢿⣄⠀⡸⠛⢉⠛⣿⣿⣿⣷⣮⣛⠍⠲⢌⠣⡜⡄⠛⡷⢏⠲⡌⣧⣻⠞⣋⢶⣿⣿⣏⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⣳⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⣴⣿⣵⠟⠁⠀⢀⣼⣿⣿⢷⣿⣿⡟⠀⠀⠀⠀⠙⣏⠀⠁⢢⡀⠸⣿⣿⣿⣿⠿⣿⣷⡾⠶⢶⣌⢓⡰⢊⣕⡾⢛⠤⡙⡔⢺⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄⣣⣼⡏⢽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀ ⠟⢏⠀⠀⠀⢀⣾⣿⣟⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠂⣿⣿⣿⣿⣿⣷⣤⡙⣷⣬⡘⠳⠐⢃⠌⡰⢉⠆⡱⢈⣽⣿⡎⢿⡆⠰⣇⠀⡀⢄⠢⣍⣶⣿⣿⡅⢺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀ ⠀⠀⠉⠒⢀⡾⠛⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢠⣿⣿⣿⣇⢻⣿⣿⢿⣾⣿⣷⠀⠁⠂⠌⢀⠁⠂⠁⢰⣿⣿⣷⡈⢻⡄⢹⡖⣈⠦⡿⣾⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀ ⡰⢪⡕⡴⠃⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⣼⣿⠟⣹⠇⠀⢿⣿⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣻⣿⣿⣦⣽⣾⣧⣝⣾⣷⢻⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀ ⢡⣣⠞⠀⣰⣿⣿⢋⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⠟⠊⠁⠀⣠⣿⣏⣾⣿⣾⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀ ⠚⠁⠀⢀⣿⣷⠏⣼⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢀⣠⣶⢿⡟⠀⠀⢀⠄⢊⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠒⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣟⣴⣿⣿⣿⣿⣿⡏⠀⠀⠀⣀⣤⣾⣿⠟⣉⢾⠇⠀⠐⣁⢶⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡆⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣟⣾⣿⣿⣿⣿⣿⣿⣿⠇⢀⣤⠾⠛⠋⠁⠀⠈⡔⣾⠖⢀⠜⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢄⡀⠻⣿⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⣟⡷⣯⣿⢿⣿⣿⡿⣿⣿⣿⡴⠋⠀⠀⠀⠀⠀⠀⠐⣸⡿⠀⠘⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢿⣷⡀⠀⠻⡷⣄⠀⠀⠀⠀⠀⠀ ⡸⠋⠉⠙⢣⣿⣿⣿⣇⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢰⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣦⡘⣧⡀⠀⠉⢌⠳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡛⠁⢣⠀⠀⠀⠡⡘⢆⠀⠀⠀ ⣦⣀⣀⣤⢾⣿⣻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡚⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⢸⠀⠀⠀⠀⠐⣌⡆⠀⠀ ⢿⡟⠏⠻⢿⣷⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡝⡔⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⡇⠀⠀⠀⠀⢸⡷⠀⠀ ⡏⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡹⢬⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⢀⣾⣿⠀⠀ ⢇⡀⠂⠀⠀⠀⠈⠙⠿⣯⠀⠀⠀⠀⠀⠀⢀⠑⡂⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⣽⡝⢦⡃⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣷⣄⠀⢀⣾⣿⡇⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠠⢃⡕⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⢼⡟⡼⣩⠿⣦⡡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣌⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⠁⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⢳⡄⠀⢠⠡⢣⠜⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠣⣹⢾⡙⠶⡡⢞⡩⢷⣯⡰⠡⢄⠠⣀⠀⡄⢠⢂⡜⣬⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢄⢻⡄⢣⠜⣡⢞⣿⣿⣷⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢤⡷⢏⢧⡙⣣⠕⡪⠜⡡⢞⡹⠿⣮⣵⣦⣹⣬⣷⣾⣾⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢦⡙⢦⡙⢦⣻⢡⣿⣿⣿⣦⣐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣈⣦⢽⢫⠜⡩⢆⡱⢢⠙⠄⠃⠁⠊⠔⢫⠔⢦⠣⣝⢲⣿⠿⣿⡅⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⣿⣿⣿⣇⢤⠀⠀⠀⠀⠀⠀⠀⢈⠒⡜⢦⣹⣳⣿⣿⣿⣿⣿⡿⢠⣷⠶⢤⣤⣀⣀⣀⣄⣠⣤⣬⠶⢓⢋⠆⢣⠊⠌⠑⡀⠂⠁⠈⠀⠀⠀⠀⠈⠐⣊⠦⡙⢦⣿⣿⣨⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⣿⣿⣿⣿⣿⣶⢄⡀⠀⠀⠀⠀⠠⢩⢜⣣⢷⢃⣿⣿⣿⣿⣿⣇⣿⣿⣧⠀⠀⠈⠉⠉⠈⠁⠀⠀⠐⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢎⣹⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⣿⣦⣿⣥⣤⣀⣀⠂⡇⣞⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣨⡿⢻⣿⣿⠏⠀⣸⣿⣿⣿⣿⣿⡿⠀⣿⢿⣿⣿⣿⣿⣿⣿ ⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣾⣾⣿⣯⣿⣿⣿⣏⣼⡿⠛⠙⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⣿⣿⣿⡿⣏⠀⣰⣿⣿⣿⣿⣿⣿⡇⠀⡿⢸⣿⣿⣿⣿⣿⣟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣿⡿⠟⠛⢫⡹⠖⠉⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⡿⢻⡇⠉⣹⣿⣿⣿⡟⣿⣿⡿⢀⣼⣡⣿⣿⣿⣿⣿⣿⣯ ⡿⢿⠟⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣁⡤⠒⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⡀⠘⢛⣿⣿⣿⣿⡟⢀⣿⣿⣅⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⢰⣿⣿⣿⣿⣿⠛⢣⠐⢌⣖⠡⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠙⢿⡿⠿⣻⣿⣿⣿⠟⣠⣿⡿⣻⣿⣿⢟⣋⣱⣿⣿⣿⣿⣿⣿ ⣿⢿⢿⣿⣭⡿⠃⠄⠀⡠⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣹⣾⣿⣿⣿⣿⣾⠿⠋⠀⠹⡸⣏⡉⠉⣿⣿⣿⣿⣿⣿⠋ ⡟⠁⢸⡾⠋⠀⢡⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢽⠂⢀⣼⣿⠟⠉⠉⠋⠉⠀⠀⠀⣆⣠⠇⠀⠀⣼⣿⣿⣿⣿⣿⣧⡀ ⣇⠀⠋⠀⠀⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢻⡇⢸⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠏⠉⠉ ⣿⡀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡑⣇⠘⣿⠈⢆⡀⠀⠀⠀⣀⠀⠀⣀⠤⣊⡽⢟⠿⠛⠉⠁⠐⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⣿⣦⠀⢀⣶⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣈⠻⣿⣿⣷⣿⣿⣿⣿⣿⡿⠁⠹⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣷⣜⢿⣿⣿⣦⠀⠀⠀⠀⢀⣀⣈⡙⠛⠛⠋⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⣝⣛⣡⣶⣶⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⢀⣿⣿⣿⣤⣤⣄⣀⣀⣀⡀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠠⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⢀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠈⠈⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠂⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⡀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠂⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠁⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠈⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢼⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠈⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠰⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⡿⠛⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠛⠁⣄⣾⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣿⠁⠀⠀⠙⠻⢿⣧⠀⢠⠋⠀⢱⡄⠒⠉⢲⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠼⣿⠀⠀⠘⠀⠀⠀⣿⢃⠇⠀⢠⠂⠀⢀⠀⠀⢃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⡅⠀⡆⠀⠈⢹⡅⢸⠀⡰⠃⠀⠀⣾⡆⠀⠘⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡰⡇⠀⠀⠘⣷⣮⠔⠁⠀⠀⡼⡇⢹⢦⠀⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠘⢄⠀⠀⠀⠉⠀⠀⠀⣰⠁⢈⡀⠣⣷⠀⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠀⠀⣸⣧⡀⠀⠀⠀⠀⣰⠃⠀⠘⣷⢤⣼⣀⠀⠱⡀⠀⠀ ⡀⡄⠀⢀⠃⠈⠙⠛⠃⠙⠶⢤⣤⠴⠃⠀⠀⠀⠘⠀⠙⢿⠙⢦⣸⣶⡄ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠩⠄⠤⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣶⠶⠟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠋⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣄⠻⡄⠀⠀⠀⠀⠀ ⠀⠀⣿⠐⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢄⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠑⢄⠀⠀ ⠀⠀⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢁⣈⠙⣦⡈⢆⠀ ⠀⠀⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠰⡄⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⡇⠈⠀ ⠀⠀⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣠⢤⣄⠀⠀⠀⠀⠈⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠉⠹⠛⠛⠁⣰⠀ ⠀⢸⠁⠀⠀⠀⢺⣿⠀⠀⠀⠀⣠⠞⣿⡝⢿⡇⠀⠀⠀⠀⢻⠀⠀⢻⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀ ⡀⢸⡇⠀⠀⠀⣿⣿⣏⠂⠀⠀⠸⣿⣿⣿⣽⠇⠀⠀⠀⠆⡟⠀⠀⠀⠹⡿⣦⣄⢀⢀⠀⢀⣨⣴⡇⠀⠀ ⠳⣼⣧⠀⠀⠀⠟⣿⢻⣦⠀⠀⠀⠍⠛⠛⠁⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠈⠓⢯⠛⣿⣿⡿⠛⣿⣧⠀⠀ ⠀⠘⠿⣷⡆⡀⠀⣿⠈⢿⣿⣦⣄⠀⠀⠀⠀⠀⣠⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⡿⡇⠀⠹⣿⡀⠀ ⠀⠀⠀⠘⢿⣷⡰⣿⠀⠘⣿⠿⠿⠛⠛⠛⠛⣫⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⡇⠀⣄⢻⡇⠀ ⡀⠀⠀⠀⠀⣿⢻⡏⠀⠀⠻⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⢻⣠⠀⠏⠘⢿⡄ ⢷⣟⠒⠀⠐⠋⣺⠃⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠄⠘⣧⠈⠄⠀⠈⢻ ⠀⠙⢷⣤⣀⣢⡿⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⠀⢻⡄⠀⠀⠀⢸ ⠀⠀⠀⠈⠉⠋⠃⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢳⡀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠹⣄⠀ ⠀⠀⠀⠀⠀⣠⡾⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠘⢦ ⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠨⢿⣇⠀⠀⠀⠀⠈ ⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀ ⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀ ⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣫⠄⠀⠀⣦⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣎⡄⢼⡟⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣹⠶⠛⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⠀⠀⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀
⣿⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣿⢿⣛⢯⡿⣽⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣿⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⡟⣧⣻⣞⣯⣟⣷⣻⣞⣷⣻⣾⣷⣿⣾⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢿ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⢧⣟⣷⣻⣞⣷⣻⣞⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣾⣳⣟⣾⣳⢯⡿⣽⢯⡿⣽⢿⣾⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⢿ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣿⢣⣟⡾⣽⣞⣷⣻⣞⡷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣳⣟⡾⣽⣻⡽⣯⢿⡽⣯⣟⣾⣻⣷⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⢿⣽⣻ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⠿⣜⣳⣯⣟⣷⣻⣞⡷⣯⣟⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣳⢯⡿⣽⣳⢿⡽⣯⣟⣷⣻⣞⣷⣻⣞⣿⣾⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⢿⣽⣻⢾⣽ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣿⣛⣾⡽⣾⡽⣞⣷⢯⣿⣳⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡷⣯⡿⣽⢷⣻⢯⣟⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣷⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⢿⣽⣻⢾⣽⣻⢾ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢿⣷⣿⣳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣿⣾⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣟⣿⣿⣿⣛⣉⣩⣍⣩⣉⣉⣉⣉⣉⣉⣉⣉⣉⠙⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣻⣞⣷⣻⢾⡽⣯⢿⣽⣻⣿⣷⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⢾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣈⠉⠉⠛⠻⠿⢿⣿⣿⣿⣾⣯⡿⣽⢯⣟⡾⣷⣻⣿⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠈⠙⠻⣿⣿⣿⣯⣿⣞⣿⣽⣿⡿⣿⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⡾⣽⢯⣟⡷⣯⣟⡷⣯⣟⡾⣽⣻⢾⣽⣻ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣌⠉⣻⣿⣿⣿⣿⣿⢿⡿⣿⡽⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⢿⣽⣻⢾⣽⣳⢯⣟⡷⣯⣟⡷⣯⣟⡾⣽ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡿⣯⣟⡾⣯⣟⣷⣻⡽⣞⣷⣻⣞⣷⣻⣞⡷⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣳⢯⣟⡷⣯⢿⣽ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⢾⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣳⢯⣟⣷⣻⣞⣷⣻⡽⣞⣷⣻⣞⡷⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⡽⣯⣟⣾ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⢯⣟⣾⣳⣟⣾⣳⢯⡿⣽⣞⡷⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⡽⣯⣟⣷⣻⢾ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡋⡍⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣽⣻⣞⣷⣻⣞⡷⣯⢿⣽⣳⢯⡿⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⡽⣯⣟⣷⣻⢾⣽⣻ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⢱⣈⣤⣼⠄⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢷⣻⣞⣷⣻⢾⡽⣯⣟⡾⣽⢯⣟⡷⣯⣟⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⡽⣯⣟⣷⣻⢾⣽⣻⢾⣽ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⢾⣿⣿⣿⡿⣯⢷⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠋⢉⣉⣙⠋⠁⠀⠀⠀⠀⠀⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡾⣽⢯⣟⡷⣯⢿⣽⣻⢾⣽⣳⢯⣟⡷⣯⣟⡾⣽⣻⢾⡽⣯⣟⣷⣻⢾⣽⣻⢾⣽⣻⢾ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⡷⣯⢿⣿⣿⣿⢿⣽⣻⣞⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠛⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⣀⣉⣌⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣽⣻⢾⡽⣯⣟⡾⣽⣻⢾⣽⣻⢾⣽⣳⢯⣟⡷⣯⢿⣽⣳⣟⡾⣽⣻⢾⣽⣻⢾⣽⣻ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⢾⡽⣯⢿⡽⣿⢿⣟⣾⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⠧⣁⣀⢿⣿⣿⣟⡁⠀⠀⠀⠘⣿⣿⣿⣿⠙⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣾⣻⣿⣿⣳⢯⡿⣽⣳⢯⣟⡷⣯⣟⡾⣽⣻⢾⣽⣻⢾⡽⣯⣟⣾⣳⢯⣟⡷⣯⣟⡾⣽⣻⢾⣽ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⣾⣳⣟⡾⣽⣳⣟⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠛⠉⡁⠀⣄⢀⠘⠘⠿⣿⣿⣟⣀⣠⣸⡿⠟⠛⠛⠿⠉⠋⢿⣿⣿⣿⣿⣿⣿⣿⣾⣳⣟⣯⢷⣯⢿⣽⣳⢯⡿⣾⣽⣳⢯⣟⡷⣯⣟⡾⣽⢯⣟⣷⣻⢾⣽⣻⢾⣽⣳⢯⣟⡷⣯⣟⣾ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⢾⡽⣯⢿⡽⣯⢿⣽⣿⣾⣳⣟⡾⣽⣳⣟⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠐⠠⣽⣿⠂⠌⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⢿⣿⣷⣿⣞⡿⣞⡿⣾⡽⣯⣟⡷⣯⣟⡿⣾⣽⣳⢯⡿⣽⣻⣞⡷⣯⣟⡾⣽⣻⢾⣽⣻⢾⣽⣳⣟⣾ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⣾⣿⣿⣷⢯⣟⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⣰⣿⣿⣿⣿⣿⣳⢯⣟⡾⣽⣻⣽⣻⣽⣻⢷⣻⢷⣯⣟⡷⣯⣟⡷⣯⣟⣯⣟⣷⣻⢾⣽⣳⢯⣟⡷⣯⣟⡾⣽⣻⣞⣷⣻⢾ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⢾⡽⣯⢿⡽⣯⢿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⣾⣶⣾⣾⣿⣿⣿⣿⣿⣿⣽⣻⢾⡽⣯⢷⣯⢷⣯⣟⣯⣟⡿⣾⣽⣻⢷⣯⣟⣷⣻⢾⡽⣾⣽⣻⢾⣽⣻⢾⣽⣳⢯⣟⣷⣻⣞⡷⣯⢿ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⣾⣳⢯⡿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⢗⡒⠒⠒⢚⣉⡽⠋⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣯⣿⣽⣻⣞⡿⣾⡽⣾⣽⣻⢷⢯⣟⡿⣾⡽⣾⡽⣯⣟⡷⣯⣟⡿⣾⣽⣻⢾⣽⣻⣞⣷⣻⢾⡽⣯⢿ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⢾⡽⣯⢿⡽⣯⢿⣽⣳⣟⡾⣽⢯⣟⡷⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠉⠒⠚⠚⠉⠀⠀⠀⢀⡠⠞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣷⣯⣟⣷⣻⢷⣯⣟⣾⣻⢾⣽⣳⣟⣷⣻⢷⣯⣟⡷⣯⣟⡷⣯⣟⡿⣞⣷⣻⢾⡽⣯⢿⣽⣻ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⣾⣳⢯⡿⣽⣻⢾⣽⣳⣟⣾⣳⣟⣿⣻⣟⣿⣻⢿⡽⣯⣟⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⢾⣽⣻⢾⡽⣾⣽⣻⣞⣷⣻⢾⣽⣻⢾⣽⣻⢷⣯⣟⡷⣯⢿⡽⣾⡽⣯⢿⣽⣻⢾⣽ ⣿⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⢾⡽⣯⢿⡽⣯⢿⣽⣳⣟⡾⣽⢯⣟⡷⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⢿⣶⠔⠒⠚⠉⠁⠀⠀⠀⠀⠀⢸⣿⣟⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣞⡷⣯⣟⡾⣽⢯⣟⡷⣯⢷⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⡽⣯⣟⣷⣻⣽⣻⢾⣽⣻⢾ ⣿⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⣾⣳⢯⡿⣽⣻⢾⣽⣳⣟⣾⣳⣟⣾⣳⣟⡾⣽⣻⣞⡷⣯⢿⡽⣯⢿⡽⣾⣽⣳⠯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡾⣽⢯⣟⡾⣽⢯⡿⣽⢯⡿⣽⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣷⣻⢷⣻⣞⡷⣯⣟⡿⣾⣽⣻ ⣿⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⢾⡽⣯⢿⡽⣯⢿⣽⣳⣟⡾⣽⢯⣟⡷⣯⣟⣾⣳⣟⣾⣳⣟⣾⡷⠏⠛⠓⠛⠾⠽⣯⠿⡽⠯⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢾⣽⣯⣿⣽⣯⣿⣽⣳⣟⣾⣳⢯⣟⡾⣽⢯⣟⡷⣯⢿⡽⣯⣟⡾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣷⣻⢾⡽⣯⢷⣯⣟⡷⣯⣟⡷⣯⢷ ⣿⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⣾⣳⢯⡿⣽⣻⢾⣽⣳⣟⣾⣳⣟⣾⣳⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠤⠄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠔⠂⠀⠀⠀⠀⠀⠉⠙⠚⠷⣯⣟⡾⣽⢯⣟⡾⣽⢯⡿⣽⣳⢯⣟⡷⣯⣟⡾⣽⣻⣞⣷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢷⣯⢿⣽⣻ ⣿⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⢾⡽⣯⢿⡽⣯⢿⣽⣳⣟⡾⣽⢯⣟⡷⣯⣟⣾⣳⣟⣾⣳⣟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⡠⠄⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣽⣻⢾⡽⣯⢿⣽⣳⢯⣟⣾⣽⣳⢯⣟⣷⣻⣞⡷⣯⢿⡽⣯⣟⡾⣽⣻⢾⣽⣻⣞⡿⣾⡽ ⣿⣞⡷⣯⣟⡾⣽⢯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⣾⣳⢯⡿⣽⣻⢾⣽⣳⣟⣾⣳⣟⣾⣳⢯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢯⡿⣽⢯⣟⡾⣽⣻⣞⡷⣯⣟⡿⣞⣷⣻⢾⡽⣯⢿⣽⣳⢯⣟⡷⣯⣟⣾⣳⢯⣟⣷⣻ ⣿⢾⣽⣳⢯⡿⣽⣻⢾⡽⣯⢿⡽⣯⢿⣽⣳⣟⡾⣽⢯⣟⡷⣯⣟⣾⣳⣟⣾⣳⣟⡾⣽⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢯⡿⣽⣻⢾⣽⣳⣟⡾⣽⣳⢯⡿⣽⢾⡽⣯⢿⣽⣻⢾⣽⣻⢾⣽⣳⣟⡾⣽⣻⣞⣷⣻ ⣿⣻⢾⡽⣯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⣾⣳⢯⡿⣽⣻⢾⣽⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⣿⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⣳⢯⣟⣾⣳⢯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⡾⣽⣻⢾⣽⣻⣞⡷⣯⣟⣷⣻⣞⣷⣻ ⣿⡽⣯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⣷⣻⢾⡽⣯⣟⡷⣯⣟⣾⣳⣟⣾⣳⣟⡾⣽⣻⢾⡽⣿⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢻⡀⠀⠀⠀⠀⠀⠀⢸⣿⢾⣽⣻⣞⡷⣯⣟⡾⣽⢯⡿⣽⢯⡿⣽⣳⢯⣟⡷⣯⣟⣾⣳⢯⣟⣷⣻⣞⣷⣻⢾⣽ ⣿⣽⣳⢯⡿⣽⢯⡿⣽⢯⣟⣷⣻⢾⡽⣯⣟⡷⣯⣟⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⢿⣽⡇⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠃⠀⠀⠀⠀⠀⠀⠈⣿⣟⣾⣳⢯⣟⡷⣯⢿⡽⣯⢿⡽⣯⣟⡷⣯⣟⡾⣽⣳⣟⡾⣽⣻⣞⣷⣻⣞⡷⣯⣟⣾ ⣿⢾⡽⣯⢿⡽⣯⢿⣽⣻⣞⡷⣯⢿⣽⣳⢯⣟⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⢿⣽⣻⣾⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⣿⣞⡷⣯⣟⡾⣽⢯⡿⣽⢯⡿⣽⣳⢯⣟⡷⣯⣟⣷⣻⢾⣽⣳⣟⣾⣳⣟⡾⣽⣳⣟⣾ ⣿⢯⡿⣽⢯⡿⣽⣻⣞⡷⣯⢿⣽⣻⢾⣽⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⣞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⣿⣽⣻⢷⣯⢿⡽⣯⢿⡽⣯⣟⡷⣯⣟⡾⣽⣳⣟⡾⣽⣻⣞⣷⣻⣞⡷⣯⣟⣷⣻⢾⣽ ⣿⢯⡿⣽⢯⣟⣷⣻⢾⡽⣯⣟⡾⣽⣻⣞⣷⣻⣞⣷⣻⢾⣽⣻⢾⡽⣯⣟⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⣿⣳⢯⣟⡾⣯⢿⡽⣯⣟⡷⣯⣟⡷⣯⣟⣷⣻⢾⣽⣳⣟⣾⣳⣟⡾⣽⣳⣟⡾⣽⣻⢾ ⣿⢯⡿⣽⣻⣞⡷⣯⢿⣽⣳⢯⣟⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⣷⣻⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣿⢯⣟⡾⣽⢯⡿⣽⣳⢯⣟⡷⣯⣟⣷⣻⢾⣽⣻⣞⣷⣻⣞⡷⣯⣟⣷⣻⢾⣽⣳⢯⣿ ⣿⢯⣟⣷⣻⢾⡽⣯⣟⡾⣽⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⣞⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢸⣿⣽⣻⡽⣯⣟⡷⣯⣟⡾⣽⣳⣟⡾⣽⣻⣞⣷⣻⣞⡷⣯⣟⣷⣻⢾⣽⣻⢾⣽⣻⢾ ⣿⣻⣞⡷⣯⢿⣽⣳⢯⣟⣷⣻⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⣷⣻⢾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⣷⢯⣷⣻⢷⣯⣟⡷⣯⣟⣷⣻⢾⣽⣳⣟⣾⣳⣟⡾⣽⣳⣟⡾⣽⣻⢾⣽⣻⢾⣽⣻ ⣟⡷⣯⢿⣽⣻⢾⣽⣻⣞⣷⣻⣞⣷⣻⢾⣽⣳⢯⡿⣽⣻⣞⡷⣯⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⡀⠀⠀⣿⣟⡾⣽⣻⢾⣽⣻⢷⣻⢾⣽⣻⣞⣷⣻⣞⡷⣯⣟⣷⣻⢾⣽⣳⢯⣟⡾⣽⣻⢾⣽ ⣿⣽⣯⣿⣾⣽⣻⣞⣷⣻⣞⣷⣻⢾⣽⣻⢾⡽⣯⣟⣷⣻⢾⡽⣯⢿⡷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠄⠀⠀⣿⣯⣟⡷⣯⣟⡾⣽⢯⣟⡿⣞⣷⣻⣞⡷⣯⣟⣷⣻⢾⣽⣻⢾⣽⣻⢾⣽⣳⢯⣟⣾ ⣿⣿⣿⣿⣿⣷⣿⣞⣷⣻⣞⡷⣯⣟⡾⣽⢯⣟⣷⣻⢾⡽⣯⢿⣽⣻⡇⠀⢠⣾⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣿⡷⣯⣟⡷⣯⢿⣽⣻⢾⣽⣻⣞⡷⣯⣟⣷⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣳⢯⣟⡷⣯⢿⣽⣻⣞⡷⣯⢿⡽⣯⣟⡾⣽⣿⡀⠈⠙⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡺⣁⣤⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢹⣟⡷⣯⢿⣽⣻⢾⣽⣻⣞⡷⣯⣟⣷⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡾⣽⢯⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⣟⡷⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠸⣯⢿⣽⣻⢾⣽⣻⣞⡷⣯⣟⣷⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣽⣻⣞⡷⣯⢿⡽⣯⣟⡾⣽⣳⢯⣟⡷⣯⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⣿⣟⡾⣽⣻⣞⡷⣯⣟⣷⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢾⡽⣯⢿⣽⣳⢯⣟⡷⣯⣟⡾⣽⢯⡿⣽⡟⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣟⣷⣻⢾⣽⣳⣟⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⣿⣽⣯⣟⣾⣽⣻⣾⣽⡷⠯⠿⠽⠯⠿⢽⣃⠀⠀⠀⠉⠑⠒⠢⠤⣤⣠⠤⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣻⢾⣽⣻⣞⡷⣯⣟⡷⣯⣟⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠒⠒⢙⣿⣟⣯⣟⡾⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣿⣞⡷⣯⣟⡷⣯⣟⡷⣯⣟⡷⣯⣟⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣞⡷⣯⣟⣷⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣽⣳⢯⣟⡷⣯⣟⡷⣯⣟⡷⣯⣟⡷⣯⣟⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢯⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⣯⣟⣷⣻⣞⡷⣯⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣟⡾⣽⣳⢯⣟⡷⣯⣟⡷⣯⣟⡷⣯⣟⡷⣯⣟⡾⣽⣻⢾⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡠⠀⠄⠠⠀⠄⠠⢀⠠⢀⠀⡀⢀⠀⡀⠀⠀⢠⣿⣯⢿⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣽⣳⣟⣾⣳⢯⣟⡷⣯⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⢷⣯⣟⡾⣽⣳⢯⣟⡷⣯⣟⡷⣯⣟⡷⣯⣟⡷⣯⣟⡾⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣮⣤⣥⣤⣀⣂⣐⣀⣂⣤⣤⣴⣶⣿⣟⡾⣯⢿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣟⣾⣳⢯⣟⡾⣽⢯⣟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢾⣽⣻⢷⣯⣟⡾⣽⣳⢯⣟⡷⣯⣟⡷⣯⣟⡷⣯⢿⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣟⣿⣻⣟⣯⢿⣽⣳⣟⡾⣽⢯⣟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣽⣻⢾⡽⣯⣟⡾⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡾⣽⣻⢾⣽⣻⢷⣯⣟⡾⣽⣳⢯⣟⡷⣯⢿⣽⣻⢾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣾⣳⣟⣾⣻⣞⡷⣯⢿⣽⣻⣞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣯⡿⣽⣳⢯⣟⣷⣻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣟⡿⣾⣽⣻⢾⣽⣻⢷⣯⣟⡾⣽⢯⣟⡾⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣾⣳⢯⡿⣽⣻⣞⡷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣯⣟⣾⣳⢯⡿⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⣳⢯⣟⡿⣾⣽⣻⢾⣽⣻⣽⣻⢾⣽⣳⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣳⣟⡾⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣳⢯⡿⣽⣳⢯⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣻⢾⣽⣳⢯⣟⡿⣞⡷⣯⣟⡿⣾⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⢿⣯⣷⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣟⡷⣯⢿⡽⣯⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣟⡾⣽⣻⢾⡽⣯⣟⡷⣯⣟⡷⣯⢷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣷⣿⣻⣿⣟⣯⣿⣿⣿⣽⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣾⡽⣯⢿⡽⣯⣟⡾⣿⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⡷⣯⢿⣽⣳⢯⣟⡷⣯⢿⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣾⡿⣿⣽⣿⣻⣯⣷⣿⣟⣯⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡽⣯⣟⡷⣯⣟⣷⣻⣟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣽⣻⢾⣽⣻⢾⡽⣯⣟⡾⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣿⣿⢯⣿⣟⣿⣽⣯⣿⣿⣯⣷⣿⣿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣳⢯⣟⣷⣻⣞⣷⣻⢾⡽⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⢾⡽⣯⣟⡷⣯⢿⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣿⣟⣿⣯⣿⣟⣷⣿⣻⣽⣿⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣻⣞⣷⣻⣞⡷⣯⢿⣽⣳⢿⣿⣳⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⣟⡷⣯⢿⣽⣻⢾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣯⣿⣿⣽⣷⣿⣟⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣞⣷⣻⣾⣽⣯⣿⣾⣿⣿⣾⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣻⢾⡽⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⡿⣿⣻⣿⣾⣿⣽⣾⣿⣯⣿⡿⣿⣻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣟⣷⣿⣯⣿⢿⣾⡿⣷⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣿⣿⣻⣷⣿⣻⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣻⣿⣽⣿⣻⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣽⣿⣾⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢾⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣷⣿⣻⣾⣟⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢯⣟⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣻⣿⣽⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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STOP IT 🚫⏹🚫🚫 DON'T MAKE THIS KIDS ARE TRYING TO FIND NICE EMOJIS AND YOU MAAKE THIS GO FUCK YOU MAN ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⠉⢯⣒⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢡⡐⡄⢀⡀⠈⢙⢮⡳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⠀⠂⠀⠈⠀⠀⠈⣈⠷⢉⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡐⡀⠀⠀⠀⠀⠀⣐⠼⢁⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠣⢁⠐⠈⠆⣀⡈⠀⠲⢃⢠⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡅⠂⠄⠂⠈⠐⢠⠓⢢⠱⣨⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠤⣤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠀⠀⠀⠀⠂⠈⠀⠈⠄⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣬⠛⣭⢫⡍⣶⢳⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⠀⠀⠀⠀⢢⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡓⠤⠁⠎⠱⡈⡜⢥⢻⣹⢻⠷⡶⣶⡶⢶⣶⣦⣤⡀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠐⠠⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠙⢢⠁⡈⠀⠀⠈⠀⠁⠋⠄⢊⠑⠄⠘⡀⢎⡝⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⢤⡁⢂⠡⠀⠀⠀⠀⠀⠀⡈⠁⢁⠊⠴⠓⠁⡜⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⢟⡽⣂⠖⡄⢂⢀⣴⠼⡞⡿⣛⡝⠛⠛⠾⣦⣤⣾⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣏⠳⢎⣖⠹⣎⡜⣧⡿⠡⢎⠱⠑⠨⠈⠁⠀⠀⠈⠉⣻⡏⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡗⡮⣙⠦⡸⡙⣼⡿⢋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣇⡳⡵⣊⠕⣩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣟⣡⢦⣽⡟⠐⠁⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠃⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠏⡉⣤⣿⠡⢈⠤⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢡⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣿⠾⠃⠒⠘⠳⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣞⣵⠶⣿⣿⢁⡞⠤⠒⠠⠁⠂⠀⠀⠀⠀⠀⠀⠀⢰⡏⢆⠂⠄⠀⠀⠀⠀⠀⠀⠩⢄⣿⠋⠁⠀⠀⠁⠁⠡⡘⣿⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⡟⢡⣾⢿⣌⠳⡘⠤⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡑⠌⡐⠈⠄⠀⠂⢁⠐⢌⢂⣿⢃⠉⠀⠀⠠⢈⠠⡑⢆⢽⠀⠀⠀⠀⠀⠀ ⢀⣿⡟⢡⣿⡟⢮⢌⢣⠐⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⠱⠈⠄⠡⠀⠌⡐⢀⠋⢤⣫⠇⠂⠀⠀⠀⠁⡀⠤⠱⣈⡟⠀⠀⠀⠀⠀⠀ ⢸⣿⣇⣳⡯⡝⢮⡘⢄⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⡌⠢⠁⠌⠠⢁⠂⠔⡈⠜⣲⠏⠀⠀⠀⠀⠠⠁⢀⢀⠂⣵⡷⠤⢤⡤⣀⠀⠀ ⢸⣿⣟⡶⡹⣍⠦⡑⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⣹⠣⡘⠠⠁⠌⠀⡁⢂⠌⡠⢉⣼⠇⠀⠀⠀⠀⠀⠂⢈⠀⡠⠘⣴⠏⠈⠀⠈⠺⢵⡆ ⢸⣿⣿⢶⡹⢆⠳⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠁⠄⡁⠌⠀⠐⠄⠊⠤⡁⢧⡾⠁⠀⠀⠀⠀⠀⠀⠄⠐⠠⢹⡏⠀⠀⡀⠄⡑⢠⡇ ⠸⣿⣿⣏⡳⢍⡚⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠂⣁⠂⠀⠀⠀⠌⡐⢉⠐⡌⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⢰⡟⠀⠀⠀⠀⢂⠐⢯⡜ ⠀⢻⣿⣯⣗⡪⢐⠂⠄⡀⠀⠀⢀⠀⠄⡀⠠⠐⠠⡈⠄⠌⡐⠀⠐⠠⠈⠄⢂⠜⣹⠄⠀⠐⠀⠀⣀⠁⢂⠐⢠⡿⠀⠀⠀⠀⡀⠌⡈⠵⡇ ⠀⢸⣿⣿⣿⣷⡠⢌⡐⢀⠁⠄⠂⠌⡀⠀⠀⠄⠡⢐⠨⠐⠀⡐⠈⠄⠡⢈⠆⡹⢜⡀⠂⠀⠀⡐⠠⠈⢃⠀⣾⠀⠀⠀⠀⠀⠠⢀⠓⡸⡇ ⠀⠈⣿⣿⣿⣿⣿⣶⣌⣦⡘⡬⣑⢢⠐⡀⠂⠌⡠⠁⠂⠁⠄⠄⠁⠌⡐⢂⠬⡑⢆⠀⠠⢀⠂⠡⢀⠂⠌⣸⠧⠀⠀⠀⠠⢀⠁⢢⠘⣼⠁ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⡼⣧⢧⣣⠜⣄⠣⡘⠤⡠⠀⠀⠘⡀⠀⠄⣀⢃⡘⢤⠛⠄⠘⠠⢄⠃⠤⠀⠄⡀⣿⠀⠀⠀⠠⠀⠀⡘⠄⣻⢻⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣳⢿⣤⡓⡜⡐⠀⠀⡄⢃⠄⠠⡀⢄⠢⢜⢢⡉⡐⢈⠐⡈⡘⠤⢉⡐⢡⠏⡐⠠⠁⠂⡀⠡⢐⢨⢴⠏⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⣿⣽⣳⣍⢶⣱⣌⠂⠌⢁⠰⣈⠲⣍⠢⡐⠁⠀⠀⠐⠀⢀⠂⢄⠣⡘⠠⢁⠂⡐⠠⢁⢢⢎⡿⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣶⣮⣶⣼⢳⣎⡱⢌⠢⡁⠄⣁⠀⠂⢌⠂⢆⠁⠂⠄⡂⠥⢑⡈⢲⡾⠃⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣵⣯⣶⣝⡲⢌⡘⢡⠂⢍⠠⠌⡐⠠⠘⡄⢣⢼⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣶⣭⢦⣉⠦⡘⢄⠢⣑⢣⡜⣱⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣷⣻⢯⣟⣿⣿⣷⣟⣾⣵⣮⣵⣺⣦⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠙⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⡿⠟⠛⠉ GO FUCK YOU, GO FUCK YOU
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠛⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠇⢀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠣⡀⠀⠒⣶⣿⣿⣿⡏⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⢸⣶⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢀⡞⠁⠀⠀⠙⣆⠀⣀⡴⠾⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠉⠛⠿⢿⣿⣧⡀⠀⠀⡾⠀⠀⠀⠀⠀⣸⡾⠋⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣽⣿⣿⠀⣸⠇⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠚⠉⣿⣿⣇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⣿⡟⠁⢠⡟⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢿⠀⠀⠀⣼⠀⠀⠀⠀⠐⠒⣿⡏⠀⠀⣼⠃⠀⠀⣰⡟⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣽⣧⠀⠀⣿⠀⠀⣼⠏⠀⠀⠀⠀⠀⢠⣿⢿⡿⡄⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣴⣷⠀⠀⠀⠀⠀⠀⢿⣿⡄⢸⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⣾⡏⠀⢻⡹⣦⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⡟⣿⡄⠀⠀⠀⠀⠀⠘⣿⣷⣾⣧⡞⠁⠀⠀⠀⠀⠀⠀⣸⠛⢧⠀⠀⢷⡘⢷⡄⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣾⠀⠘⣷⡀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠈⢳⡄⠈⢳⡌⢻⡄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡇⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⣾⡅⠀⠀⠙⢿⣿⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠸⣿⣧⣀⣀⡀⠀⣿⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡏⠀⠀⣀⣀⣸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠘⢿⣏⠻⢿⣾⣿⣦⣄⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣼⠁⠀⠛⠛⠿⠿⠿⠿⠃⠻⣿⣶⣄⡀⠀⠀⢀⣠⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⢿⣿⡟⠻⣷⣦⡀⠀⣿⣦⣄⡀⠀ ⢀⣠⡤⠴⠒⠒⠒⠒⢋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢻⣿⡀⠀⠙⢿⣦⣽⣿⣿⡿⠆ ⠀⠀⠉⠉⠉⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀
⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⠀ ⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆ ⣿⣿⣿⡏⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢹⣿⣿⣿ ⣿⣿⣿⣇⠀⠀⠀⠰⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⣸⣿⣿⣿ ⠸⣿⣿⣿⡄⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⢠⣿⣿⣿⠇ ⠀⠹⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠏⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⠿⢿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀ ⠀⢀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀ ⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀ ⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣄⠀⠀⣠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆ ⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟ ⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇ ⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀ ⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀ ⠀⠀⠘⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠀⠀⠀⣀⡴⢉⣿⠧⠿⢭⣒⣦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠘⣧⢴⣾⠁⢋⣴⣵⡶⢿⣶⡖⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⢴⣞⣡⢿⠿⢩⢽⢿⢚⣽⣶⣼⡟⢇⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡾⠗⠂⠈⠻⣤⠘⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⣀⡀⢹⠸⡀⢸⡼⣤⠻⢷⣧⣼⡄⢸⡄⠈⡇⠀⠀⠀⠀⠀⠀⢰⡿⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠃⠀⠀⠀⠀⢻⠳⡄⡃⢹⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⢻⡄⢹⣾⣓⣿⣗⣞⣈⡽⢳⢯⢇⣼⣃⡀⠀⠀⢀⣠⣴⡿⣸⣻⠀⡀⠀⠀⡀⠀⡦⢀⠀⢠⠀⠀⠀⠀⢀⢴⡿⠃⠀⠀⠀⠀⠀⠀⠈⣿⢯⢹⣸⡆⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣏⠺⣜⠒⠻⣷⠾⠋⢁⣼⣿⠿⠧⠶⠖⠒⠋⣩⣾⢯⣿⣿⡇⢸⠀⢠⣶⠇⣄⢀⣴⣤⠉⢀⡀⠀⠀⢡⡟⠁⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣇⣧⣿⣄⠀⠀⠀⠀⠀⢧⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣤⡙⠛⠿⣭⣽⣿⡿⠿⠆⠀⠀⠀⠀⠚⠋⠁⣸⡿⣿⣿⣾⠀⣿⡏⣸⡿⢸⡿⣿⠇⣼⣧⢀⢀⡼⠁⠀⠀⠀⠀⠀⣠⠴⠏⢀⡏⢿⣿⣾⣸⣌⠃⠀⠀⠀⠀⢸⣶⣷⣾⣿⣿⣷⣦⠢⠄⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣿⠛⠻⣴⢿⣷⣿⣧⣿⣷⣿⣠⣿⣇⡞⣾⡟⠀⠀⠀⠀⢀⡞⣡⣤⣦⠀⠀⠈⣿⣿⣏⣿⣦⣀⠀⢀⣤⣼⣿⠙⣿⣿⣿⣿⣿⣾⣦⡶⠃⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⢀⣸⣿⣿⣿⣿⣿⠟⡯⢀⡄⣯⣾⣟⣽⣿⣿⣿⣿⣿⢻⣿⣽⣽⠇⠀⠀⠀⠀⠀⣰⣿⢟⡅⠀⠀⠀⠈⠻⣿⣿⢿⠈⣰⣿⣧⣊⣻⣧⣬⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣧⣾⡇⡿⠛⣿⢿⣿⡟⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⠟⠛⠁⠀⠀⠀⠀⠀⠀⣰⣿⣸⡦⠖⠛⠻⣿⡿⠿⠉⠋⣿⣽⣿⣿⡎⠀⠀⠀⠀⠀ ⣤⣀⣀⡀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⣴⡃⣰⣿⣿⣿⣾⣿⣧⣿⣛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣁⡀⠀⢀⠆⢻⣷⡄⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⡾⣵⣿⣿⣿⣿⣿⣿⣿⣯⣴⠟⣿⣼⡷⠯⣧⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡇⢹⡇⠀⠈⠃⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣞⣯⠞⣿⠟⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣻⣯⣳⣼⣦⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⠶⣿⣁⣀⣠⣾⣿⡍⠀⠀⢀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⣬⣙⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⣠⡾⠋⢰⣾⣿⣿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣻⣷⣴⣿⡧⣄⠀⠀⠀⠀⠀⠀⢠⠖⠚⡟⣶⢻⣿⣿⢹⠉⣨⣿⡟⠿⢿⣶⣶⣿⣿⣿⣿⠿⣿⣿⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⣠⣾⠟⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣧⣯⣿⣷⣌⣗⠲⣤⣤⣀⠤⢤⣀⣀⣼⣿⣾⣿⣿⣾⣿⣿⣿⣧⡁⠀⣹⠿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡞⣡⡾⠛⠁⢀⡄⣸⣿⡿⣿⡟⣩⣴⣾⠗⠋⠁⠀⠀⠀⠀⠘⠛⠋⠉⣉⣻⠿⢛⡍⢠⢴⢶⣤⣀⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠛⠃⠙⣿⣿⣧⠀⠀ ⣿⣿⣿⣿⣿⡿⠋⠉⠙⠻⢿⣿⣿⣿⣿⢿⡞⠉⠀⢀⣴⣫⣾⣫⣽⣾⣿⡿⠿⠯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠐⠉⠀⣸⡄⣼⣏⣿⣷⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢻⡏⢹⣧⠀ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣿⣿⣿⣫⡏⢠⡴⣲⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢯⣿⣶⣟⣁⣤⣄⣠⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣧ ⡉⠛⠿⣿⣿⣿⣦⣄⣠⣾⣿⣿⣿⣿⡿⣰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠹⣟⣶⣻⡞⣿⠄⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣼⣿ ⣿⣶⣄⡙⢿⣿⣿⣿⣯⣿⣼⣇⣾⣿⣳⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⠷⠋⣶⣶⢶⣶⣦⠀⠉⠙⣿⠿⠿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⣿⣿⣷⣿⠟⠀⠀⣼⠃⠀⠀⠈⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡏⢿⣿⡇⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢀⡭⢤⣄⠀⠀⠴⣟⣿⠟⠃⠀⠀⣼⣿⣧⠀⠀⠀⠀⠘⣿⣿⢿⣿⣿⣿⣿⡿ ⠟⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢈⣧⠸⣿⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠰⠋⢰⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⢯⡻⣿⣧⠀⠀⠀⠀⠘⠿⠁⠈⢻⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⣿⣿⡆⣿⣧⢿⣿⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢿⣿⣿⣿⣿⣶⣤⣀⠀⢴⠤⠬⢯⣽⣦⣄⣠⡀⠀⠀⠀⠀⠸⠿⠉⠻ ⠀⠀⠀⠀⠀⡞⢿⣿⣿⣿⣿⣿⣿⡇⠈⠿⣿⣿⡄⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠈⠙⠛⠛⠁⠀⠀⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣬⣙⣛⣿⡿⠟⢿⡟⣰⢲⣿⣿⡇⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠏⠸⢦⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣿⣟⣿⣥⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠟⢁⣠⡶⠾⣻⢁⣾⣿⡟⢹⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠭⠡⣃⡀⠸⣄⣼⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠉⠛⠿⣿⣿⣿⣿⣷⣶ ⠀⠀⠀⠀⠀⢰⣿⣿⣠⣿⣿⣶⣿⣿⣿⣿⣿⠀⠘⠂⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠉⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉ ⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⣀⣀⣴⡷⠋⢆⡇⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣻⡟⢟⣿⢾⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀ ⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⣿⣿⡯⡤⠂⠀⠀⠙⠻⢧⣄⠸⡌⣷⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣟⣤⡗⣯⣾⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⠓⠦⣤⡀⢠⣶⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠀⠁⢸⣿⠄⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⢸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣾⣿⣡⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⣠⣤⣤⣤⣤⣀⣀⣀⣀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⠇⠀⣀⣀⣤⣤⣶⣶⣶⣤⣤⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠉⠙⠋ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢛⣻⢿⣻⠿⠖⠚⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠈⠉⠛⠷⣶⣄⡀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⠟⠉⠀⢀⣴⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠟⠛⠛⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠊⠉⢿⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⣿⣿⡏⠀⠀⢸⣆⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠏⠀⢹⣼⡇⢠⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣠⣦⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⠋⣿⢹⡄⠀⢿⡿⠀⠀⢳⡘⣇⠀⠀⠀⠀⠀⠀⢀⡤⠶⣖⠋⠙⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⢧⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⣿⣿ ⣿⣿⣿⣿⣿⠀⠸⣿⡘⡿⠀⢸⡇⠀⠀⠈⣿⣿⣄⠀⠀⠀⣠⡴⠋⠀⠀⢸⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠘⣿ ⣿⣿⣿⣿⣿⣆⡀⡿⣟⠃⠀⠀⠀⠀⠀⠀⠘⣿⣛⣫⣽⠿⠋⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠂⠀⠘⣖⠦⠄⠀⠀⠀⠀⢹⣧⡀⣀⣴⡾⠉⠀⠀⠀⠀⣼⢿ ⣿⣿⠫⣿⣿⡇⡇⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹⣦⣀⠀⠀⠀⠀⣨⣿⣿⡟⠋⠀⠀⠀⠀⢀⡾⠁⠘ ⣿⣿⣀⡀⠁⠈⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠻⡌⠉⠗⠒⠋⣩⠞⠈⢿⡄⣠⣤⠶⣿⡟⠀⠀⢀ ⣿⣿⣿⢱⠀⢠⠟⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⢧⣴⣿⣁⣠⠄⠀ ⣿⣿⣿⡇⠀⣏⣠⠿⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⡮⠇⠻⠛⠋⠀⠀ ⣿⣿⣿⡀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⡀⠑⣄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣧⠀⢀⣤⢤⣤⠞ ⣿⣿⣿⣆⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠁⣾⣷⣤⠘⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣉⡿⠛⠉⠉ ⣿⣿⠁⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⡼⢣⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠞⠛⠋⠑⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠒⢿⠁⠀⡀⠀⣠ ⣿⣿⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠂⠀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠲⡀⢀⣀⣸⣷⣾⠅⣜⢉ ⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠉⠉⠀⠈⢿⠁⠀⠉⠉ ⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡍⠀⢷⣤⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⢸⠀⣶⣿⣤ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠱⡽⣿⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢀⣾⡴⢋⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡭⠧⣼⡉⠙⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣤⡾⠃⢀⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣶⡟⠲⣽⣤⣄⡹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⢀⣴⣿⣿⣏⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢠⣿⠇⠀⠘⣿⣍⠓⠺⣯⣇⠀⣠⣤⣶⣦⠀⠄⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣿⣿⣿⣿⣏⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣴⣿⣿⢻⡁⠀⠀⢀⣾⠇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣸⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠁⠈⠁⠀⠀⠈⣿⠀⠀⠑⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢁⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣾⣿⣿
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⣿⣟⣿⣻⣟⣿⢻⣟⣿⣻⣽⣻⢯⣟⡿⣽⢯⡿⣝⣯⢿⣹⢯⣟⡿⡽⢯⡿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡻⡜⡼⣿⣿⡗⣷⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⣿⣞⣷⣻⢾⣭⢿⣞⣷⣻⢶⣯⣟⡾⣽⣳⢯⣷⣻⡼⢯⣯⡟⣾⡝⣿⣹⡽⣞⡿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⠿⢿⠿⠛⠉⠉⠉⠉⠉⠛⠻⠿⣿⡿⢿⢿⡿⢿⠿⣳⢙⠼⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣾ ⡿⣞⡷⣯⣟⣾⣻⣞⡷⣯⣟⣮⡽⣽⡞⣽⣫⢶⣯⢽⣻⢶⣛⣧⡟⣧⢷⣛⣮⢽⡳⣽⣚⣷⢫⣟⣷⣬⣙⠋⣡⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⡙⢎⡓⣦⠟⠚⠉⣀⠤⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡽⢯⣷⢻⣞⡷⢯⢿⣵⣻⣼⢻⣵⡻⡷⢯⣻⢮⣟⣳⢯⣛⣶⢟⣉⣉⠉⠉⠉⠉⠉⠓⠾⣟⣾⡭⢖⡾⠛⡱⠋⠉⠭⣁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡳⠊⠁⠀⣠⣞⣵⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣷⡻⣟⣾⢻⡾⣽⢯⣟⢮⡷⣞⣟⠾⣽⣛⣯⡽⢯⡾⣭⣻⢭⣿⠸⣿⡿⠛⠲⢄⡀⠀⣠⣾⢟⠕⣸⠋⠀⡼⢰⠀⠀⢰⠀⠉⠐⠤⡉⠢⣄⠀⠀⠈⠂⢄⠈⠢⡁⠀⠀⢀⡼⠁⠀⠀⢀⣠⣄⠀⢸⣬⡿⣟⣿⣿⣿⣻ ⣷⣻⡽⣞⣯⢷⡯⣟⡾⣫⢷⣛⣾⢻⣳⡟⣼⢯⡟⣞⢧⡟⣞⡿⣏⠙⠛⠟⠆⠀⢻⣾⠟⡵⠋⣸⠃⠀⣸⢱⢠⠀⠀⢿⠀⠀⠀⠀⠈⠂⢌⠫⡂⢄⠀⠀⠁⡄⠐⢄⠀⠉⠉⢢⣀⠀⡇⠻⣉⣻⣿⣿⣿⣹⣿⢽⢽⣿ ⣷⢯⣽⣻⢼⢯⢾⣽⣹⢯⣻⣽⣚⣯⢗⣻⣝⣮⡽⣫⢟⡼⣏⡾⣽⡆⠘⣺⢛⣳⣾⡇⡾⢁⠞⡏⡀⠀⡏⠈⡎⠀⠀⢸⡄⠂⠀⠀⠀⠀⠀⠐⠈⢆⠑⠄⠀⠈⢂⠀⢳⡀⠀⠀⠀⡳⢿⣿⣦⣸⣿⣼⣿⣭⣿⣿⣿⣿ ⣯⣟⡶⣯⢯⣛⣯⣞⣽⣳⢯⣶⣛⣮⢟⣳⢞⡶⣽⡹⣞⡽⣺⣝⣾⢻⣮⠳⢯⣿⡻⢱⠁⡼⢸⢹⠃⠀⡇⠀⢧⢆⠀⠈⣟⡄⠀⠀⠀⠀⠀⢠⡀⠁⠣⡀⠑⢀⠀⠃⠀⢱⡄⠀⠀⢱⣼⢹⠻⠿⠿⠃⢻⣿⣾⣾⣾⣿ ⣷⣫⢷⢯⣏⡿⢶⣻⢮⡷⣛⣶⢻⡜⣯⡽⢾⣹⢶⣫⢷⣹⢳⡾⣩⢏⣿⣆⡟⣼⠁⣾⠃⠁⣯⢸⡆⠀⠃⢀⢸⣎⠀⠀⠈⠞⢄⠀⠀⠀⠀⠀⠑⡀⠀⢣⠀⠈⢂⠀⢡⠀⢳⡀⠀⠈⠟⠁⠀⠡⡀⠀⠘⡍⢎⠥⣫⠝ ⣷⢫⣯⠿⣼⣻⢯⣛⡷⣻⣝⡮⣟⡽⣳⢽⣛⣮⢷⡹⣎⠷⡿⣰⡏⡷⢧⣿⠁⡇⢸⡟⠰⢰⡏⠸⡇⠀⠀⠸⡈⡏⢆⠀⠀⠸⡆⠣⡀⠀⠀⠀⠀⠘⡄⠈⢆⠀⠀⢣⠀⠀⠀⡗⡀⠀⠂⢠⠀⠀⠑⡀⠀⡗⣌⡓⢦⢛ ⣯⢟⣼⣻⣳⡽⣫⣽⢳⣏⡾⣵⢫⡾⣝⡮⣗⢮⣳⡝⣾⣹⣷⢿⡇⣿⣧⣿⠸⣏⡿⡅⢸⢸⢷⡀⢿⠀⠀⠀⠃⢧⠀⠑⢄⠀⣿⡳⡀⠀⠀⠀⠀⠀⠘⣆⠘⡀⠀⠀⢆⠰⠀⠸⡘⡄⠀⠸⠀⠀⠀⠠⠀⣗⠤⣋⢮⠱ ⣯⣟⣞⣳⢧⣟⣳⡭⣷⢺⡵⣫⢷⣹⢎⡷⣭⣛⠶⣽⢲⣿⣿⣻⡜⣿⣷⡇⡸⡇⣿⠀⡌⣮⠘⣇⠘⣇⠈⣆⠀⠘⡆⠀⠀⠡⢹⠱⡹⣧⡀⠀⠀⠀⠘⡸⡄⢇⠀⠀⠈⠆⠃⢀⠡⡘⡄⠀⠀⠀⠀⠀⡇⢸⡖⡭⢲⡍ ⣷⣛⣮⢯⢷⡺⣵⡻⣜⣧⢻⡵⣫⢞⡽⣺⢵⡫⣟⢮⠷⣿⢧⢿⣼⢻⣽⡇⣽⡇⣿⠀⡃⡇⢠⣿⣣⠸⡄⠸⡄⠀⢱⠘⡄⠀⡚⡄⠱⡜⣯⡷⢄⡠⠀⠀⢹⢸⠰⠀⢠⠀⠀⠈⡄⠑⡁⠀⡆⠀⠀⠀⢻⠀⣧⠹⣥⢚ ⣷⢻⣜⢯⣞⣳⢧⡟⣵⣚⣧⢻⡵⣛⢾⡹⣎⡷⣹⣎⡟⣿⣏⣾⣼⣛⣿⣷⣹⣿⠥⡇⡅⢇⢸⠈⢿⡄⣷⠀⠹⡄⠀⠀⢳⠀⡇⢳⠀⠘⣌⡼⠻⢝⠲⣤⡀⣿⠀⡆⠈⠀⢠⠀⠸⡦⣈⠢⠀⠀⠀⠆⠘⡀⠸⡳⡼⢭ ⣯⢳⡞⡽⣎⢷⣫⢞⣳⣝⢮⡳⣽⡹⣎⢷⡻⣜⠷⣮⡝⣶⢻⣼⣿⢧⣿⣿⣾⣿⡇⢿⡤⢙⣻⠠⢈⣿⣌⢧⠀⠙⣄⠀⠈⣧⢻⣤⠦⠚⠁⣡⣤⣶⣿⣿⢿⣿⣷⠇⠀⠆⠀⠀⢀⠱⠈⠁⠒⡄⠀⠰⠀⢱⠀⢻⡱⣏ ⡽⣣⢟⣵⢫⣞⡵⣫⡗⡾⣭⢳⢧⡻⣝⢮⡳⣝⡻⢶⡹⣎⠷⣎⣿⡧⣿⣿⢫⡗⣿⢌⣷⠐⢾⣐⣀⣀⣙⣿⣷⡄⠘⢦⡀⠘⣾⠙⢆⢰⣾⣿⣿⣿⣿⣿⡞⣼⢻⠀⢸⠀⠀⠈⢸⣆⠱⡄⠀⠇⠀⠀⡇⠀⢧⡈⢷⣹ ⣻⢵⣫⢞⡽⢮⣝⣳⢽⡳⣭⣛⢮⢷⡹⢮⣳⢭⣛⢧⡻⣜⡻⣼⣹⣇⡿⣡⣿⣿⢹⡖⣼⣷⣾⣿⣿⣿⣶⣿⡿⣿⠳⣄⠻⣄⠘⣧⠀⠈⠙⢄⣙⠧⣜⣫⠞⠋⡜⢀⡾⢘⠈⠀⠸⡏⠣⣹⠀⢸⠘⡀⠰⠀⠸⣻⣌⢳ ⡽⣎⢷⣫⢞⡯⣞⡵⣫⢗⣧⣛⢮⡳⣝⢧⣛⢮⡝⣮⢳⣭⢳⡧⢟⣫⣾⡏⢸⣿⢸⢷⣷⡘⡟⣷⣄⠉⢿⣿⠿⣻⡇⠀⠙⠪⠷⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣼⠃⡆⢆⢣⠀⢧⠀⢸⡘⠸⡄⢁⠀⡇⠀⢷⢭⢳ ⡽⣎⢷⡹⣎⢷⡹⣞⡵⣏⠶⣭⡳⣝⢮⡻⣜⢧⡻⣵⢫⣞⢳⡞⣯⢻⡧⡇⢢⣿⣹⡼⣷⡹⢶⣊⢿⠓⠒⠊⠉⠁⠀⠀⠀⢀⡀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⣸⢾⠏⣴⠏⣞⡀⠄⢸⡀⠘⡏⡀⣷⠈⠆⢱⠀⣸⣎⠳ ⠹⣎⡷⣹⢎⡷⣹⢎⡷⣭⣛⢶⡹⣎⢷⡹⣎⢷⡹⣎⠷⣎⢷⡹⣞⣽⢱⡇⢒⣿⣿⡇⣿⣷⡌⢻⣯⣷⣌⠀⠀⠀⠀⠀⠀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⢎⣼⠏⠀⣹⣆⠈⠀⢳⠀⡗⠀⠸⣇⠈⠈⣧⠸⣇⢏ ⠀⠹⡾⣵⢫⡽⣣⡟⣼⣓⢮⡳⣝⢮⡳⣝⢮⡳⣝⢮⣛⣮⢷⣹⢎⡟⡦⡁⢼⣿⡟⣠⡟⣿⢿⣆⠹⣧⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡵⠊⡾⠀⡃⣷⣿⣦⠡⡀⠱⣇⠀⠀⢻⡆⠡⠸⡷⢏⡜ ⠀⠀⢻⣾⣹⣾⣵⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠄⣿⡿⣱⣿⢸⣿⡄⢻⣿⣮⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⣫⢿⠏⢰⠃⠴⠁⣿⡷⡏⢱⣌⠑⣬⣖⠀⠘⡞⢄⠀⠹⣖⣸ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣏⣸⣯⣾⣿⣇⣿⣿⡇⠀⣿⢹⡙⢾⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣱⣿⠀⡸⡄⠸⠀⣿⡷⣿⠘⡇⠈⣖⠯⡇⢠⠘⡌⢆⠈⢿⣿ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⡇⣼⠿⢛⡿⠯⢍⣹⣿⠀⣿⢸⣿⣸⣿⣿⣿⣿⣶⡦⢄⡀⠀⠀⣀⠴⢋⠆⠃⡼⣧⠀⡇⡇⠈⠀⣿⡿⣽⡄⠁⠀⣿⢒⠼⡠⡇⢱⣈⠳⡀⠻ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⠟⠁⠴⠊⠀⣀⠀⣿⡟⢠⣷⢹⣾⣿⣿⣿⡿⠛⡛⣧⠀⠈⠉⣉⠡⢂⠅⠠⣰⡇⡇⠂⠇⡁⠀⠀⣿⣿⣿⣧⠀⠀⣿⣭⠚⣧⣻⠀⢧⢂⠹⣆ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡿⠁⠀⠀⠀⠀⡸⠀⣠⡿⡕⣸⠏⣾⣿⣿⣿⠋⢠⡑⢬⣟⠀⠀⠀⠀⢂⠁⠂⣴⠃⡇⢻⢂⢸⡇⠀⠀⢿⡿⣿⣿⣤⣤⣿⣎⣏⢿⣿⡄⠘⣦⠀⢹ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⣿⣿⢿⣽⠏⠀⠀⠀⢀⣠⡶⣟⣻⠋⠘⡰⢃⣾⣿⣿⠟⠁⢤⣁⢂⠂⣿⣷⠀⠀⡈⢀⣠⡞⠁⠈⢻⢸⠈⡇⢧⠀⢠⠸⣵⣿⣿⡿⠋⠉⠉⠉⠉⠉⠁⠢⢽⣆⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⢿⢇⠉⠳⠘⠀⠙⠂⣼⣽⣿⠃⢀⣀⣤⣶⣿⣟⣿⠟⠁⣠⠜⢀⣾⢿⣿⣿⣤⡀⠀⠈⠙⠻⠏⠁⠀⠀⠠⡞⠉⠀⠀⠀⣸⣿⡀⣿⣎⠀⢸⡄⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇ ⠀⠀⠀⠀⠀⠀⢸⣓⠋⠉⠀⠀⠀⠁⠀⠀⠀⢀⡞⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⢁⣤⠞⢃⣠⣿⣫⣾⣷⣿⣾⢿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣉⣥⣤⡴⢾⡿⣿⡇⠐⠹⣆⠀⣿⢤⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣾⣿⣫⣷⣿⣗⣒⣀⣤⣴⣶⣯⣷⣾⣻⢟⡛⠿⠿⣿⣿⣿⣿⣿⣷⣾⣾⣵⣯⣝⣻⢶⡾⢯⣭⣙⡛⡿⣧⣷⡘⣄⠙⡄⠸⣄⣹⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⣠⠴⠛⠛⠉⠉⠉⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣯⣾⣶⣶⣤⣐⡌⣉⠛⠾⢷⣭⣯⣭⢯⣝⣛⣛⠳⠯⠯⠽⢿⣱⣤⣣⡀⢧⠘⣦⡈⠻⣇⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡠⢒⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢝⠛⠻⠿⢿⣿⣿⣿⣿⣶⣾⣽⣿⣯⣾⣱⣞⡽⣛⠿⣿⣶⣿⡻⣭⣷⣎⡄⢸⣿⣷⣯⣄⡀⠘⢖⣤⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⡮⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⢀⡽⠋⠉⡙⢛⠻⠿⠿⣿⣿⣿⣿⣿⣶⣧⣯⣽⣯⣿⢿⣷⠘⣿⣿⣿⡆⠀⠁⠸⡞⢀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⠋⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠉⠉⠛⠛⠻⢽⣟⡿⣿⡿⢸⣿⣿⣿⣿⡄⠀⠀⣴⡷⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠀⣼⣿⣏⡳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣇⣼⣿⣿⣿⣿⣷⠀⠀⡏⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢨⣟⡿⣟⠋⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢀⣠⣤⢄⣠⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠆⣰⢋⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠿⡜⢬⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡘⣞⣿⣼⡼⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⠟⡠⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣾⡅⢈⠍⠓⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢏⣎⠱⡐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠂⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡮⣌⠳⣌⠡⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠰⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣭⢳⡘⢦⡁⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⢂⠔⠠⠐⠠⡀⠄⡀⢀⠀⡀⠀⠀⢀⠀⡀⠠⢀⠂⠌⢂⡔⣱⣿⡄⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⢷⣛⢦⣹⡘⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢍⢢⡑⢌⠡⠒⡌⡐⢢⠐⠤⠡⠌⡀⢂⡐⣀⡦⠞⠚⠓⠚⠛⠓⠻⣄⠑⡈⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣯⢾⣹⢮⡵⣙⢮⡑⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣎⠲⡌⢎⠒⣍⠰⡡⢆⡉⢆⠱⡈⠔⣡⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣌⣐⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⡽⣏⡷⣯⡽⣏⡶⣳⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⢘⣷⣍⡮⠱⣌⢣⠱⡌⠒⡌⣂⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣻⣽⣞⣧⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⡙⢎⡙⢛⠲⠖⠷⢖⠻⠟⢋⠄⣠⠀⡄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣐⡀⠂⠄⡀⢀⠀⢀⠀⡄⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣳⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣔⠉⠆⡌⢢⠑⡌⠒⡌⢢⣉⣦⡼⢤⠧⠼⠤⢧⡤⠧⠼⠤⠤⠤⠴⠖⠚⠒⠓⠒⠻⢿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠙⠲⡶⢤⣬⣦⣼⣶⣿⡿⣻⢿⣿⣿⣿⣿⣿⣟⡻⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣟⠟⠛⠶⠾⠴⠳⠚⠓⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠢⡑⢴⡬⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⡚⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠋⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⠁⠪⣉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⡄⠈⠪⡓⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠐⣬⡟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡿⠶⠒⠖⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢢⣄⠘⢾⣶⣤⠈⠉⡟⠇⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣀⣀⣀⣈⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡇⠀⠀⣾⣟⠛⠋⠉⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣴⣶⣿⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⢀⣀⢹⡆⠀⠀⠀⠀⠀⠀ ⢸⡏⠀⢸⣿⠀⠀⠀⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⣼⡇⠀⢸⣿⠀⠀⠀⠈⠻⠿⣿⣿⠿⠿⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣷⣶⣶⣶⣤⡀⠀⠀ ⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⢻⡇⠀⢸⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡇ ⠈⠻⠷⠾⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣇ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⡿ ⠀⠀⠀⠀⢿⣧⣀⣠⣴⡿⠙⠛⠿⠿⠿⠿⠉⠀⠀⢠⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⢈⣩⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠉⠁⢤⣤⣤⣤⣤⣤⣤⡀ ⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠙⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⡥⠀⠀⠀⠀⣠⠴⢀⣠⠤⢦⡀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⢸⠁⠀⠀⣠⢚⡥⠚⠉⠀⠀⠘⣗⡄⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⠇⡎⠀⠀⣰⡳⠋⠀⠀⣠⣤⠶⠢⡿⣸⣆⠀⠈⣧⣄⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⢳⣠⣾⡟⠓⠆⠀⠘⠙⢀⣤⣶⢿⣤⣹⡅⠀⣿⠈⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠸⡇⣾⡛⣶⡦⠀⠀⠀⠛⢱⢼⣷⠸⠋⢣⠀⡇⣹⠛⡇⠀⠀⠠⠀⠀⠀ ⠀⠀⠀⢱⠀⠹⣏⠉⢟⣻⣀⠀⠀⠀⠐⠛⠛⠐⠀⠘⣴⡽⣇⠀⢸⡎⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⢇⠀⠘⡄⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢹⡀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⠀⢻⢦⡀⠈⠰⠶⠒⠂⠀⠀⢀⡤⠀⡇⢘⡆⢇⠐⠸⣷⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡼⡀⣟⡶⢄⡀⠀⢀⡠⠖⠁⠀⢀⡇⢸⢻⠸⡀⠀⣿⢇⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⢳⠟⢀⠷⠈⣹⡇⠀⠀⠀⠀⣼⢣⡞⢸⠀⡗⢰⣼⢸⠀⠄⠁ ⠀⠀⠀⠀⠀⢀⠎⣠⠋⢀⡼⠟⠊⠟⠀⠀⠀⠀⠀⣿⠀⠑⢯⣀⣇⣮⢏⡞⠀⠀⠀ ⠀⠀⠀⢀⡠⠾⠔⠓⢞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⡘⠛⠿⠯⣐⠀⠀⠀ ⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠉⠉⠉⠉⠉⣧⡀⠀⠀⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⢻⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠂⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⢸⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⠀⠀⠀⠀⠀⠀⡼⠃ ⠀⠀⠘⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⡀⠀⡀⠀⠀⢠⠇⠀ ⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠂⠀⠀⡎⠀⠀ ⢠⠇⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠸⡄⠀⠀⡸⠀⠀⠀ ⢸⡀⠛⠄⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⢀⠵⠀⠀⡇⠀⢀⠇⠀⠀⠀ ⠀⢷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣰⠁⠀⣾⠀⠀⠀⠀ ⠀⠀⠑⢤⣀⠀⠀⢀⣠⠴⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⡴⠁⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⡽⠀⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣾⠀⠐⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⠀⠀⢠⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢰⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡜⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀
ㅤㅤㅤ I just want to get fucked like this, pleasseeeㅤㅤㅤㅤㅤㅤㅤ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⠃⠈⢻⣿⣦⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠘⣿⣿⣿⡏⣴⣿⣷⣝⢿⣷⢀⠀⢀⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⢿⣿⣿⡇⢻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣇⢸⣿⣿⡟⠙⠛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⡇⠀⠀⠀⠉⠛⣽⣿⣇⣀⣀⣀⠀ ⠙⠻⠿⠿⠿⠿⠿⠟⠿⠿⠿⠇⠀⠀⠀⠀⠀⠻⠿⠿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⢤⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⠞⢩⣧⡨⠿⠿⢿⡝⠯⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⠟⠍⠁⢒⠿⡠⠖⠉⠉⢙⣷⠀⠀⠀⠈⠩⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢤⡿⣥⡖⣲⣿⣿⣞⣁⣀⠴⢚⣿⠛⣷⡈⣆⠀⠱⡌⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⢛⣶⣿⣿⣿⠋⣹⣟⣁⣴⣾⠃⢀⡏⠇⠸⡀⠀⢱⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⡘⣾⣿⣿⡇⣸⡯⠽⠟⢋⣉⠑⡞⠀⡼⢠⢧⠀⠀⡇⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⡿⢰⢁⡟⠀⠉⣰⠙⡿⣷⣶⢦⡄⢰⠁⢰⠃⣸⡌⠀⢸⠃⢀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⢸⢸⢧⡰⢼⣿⡀⠉⠁⠈⠀⠀⠀⢧⢇⣸⣳⠁⡰⢃⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⡸⣼⡝⢦⠣⠁⠀⠀⠀⠀⠀⠀⠘⠙⠻⢥⠞⢁⠜⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⢿⣼⣇⠘⣧⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣼⣧⣾⡷⠛⢿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠺⣿⣿⣇⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠶⠶⠿⢿⣿⡇⠀⠀⠈⠓⠤⣤⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠋⠀⠀⠀⠀⠀⠙⠓⠤⠄⣀⡀⠀⢸⣷⣦⡤⠤⠖⠒⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⢀⢆⡀⠀⠂⠒⠒⠒⠻⠦⣄⡀⠀⢀⠢⠤⠤⢄⡹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡚⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⣾⣵⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⡄⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠀⠀⠀⠀⠈⡦⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠖⠋⠈⠳⣄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⢸⠈⠉⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢥⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⠀⠀⠀⠀⡹⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠄⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠭⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡆⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡱⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠹⡄⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠹⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢹⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣇⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣺⣪⢯⢯⢞⡮⣗⢯⡫⡯⣳⢝⣗⡽⡵⣻⡪⣗⢯⡫⣗⡵⡯⣳⢽⢝⡮⣗⢯⡳⣝⢞⡽⣽⡺⣺⢝⡮⡯⣳⡳⣝⡽⣪⢯⣺⢵⡻⣪⢯⣳⢽⡺⣕⡯⡪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣳⡳⡽⡽⡽⣕⡯⣞⡵⡯⣫⢾⢝⣞⢮⣻⡪⣯⣺⡳⡽⣕⢯⢞⣗⢽⡳⣝⡮⣗⢯⢇⢿⣝⣞⣞⡵⣻⡪⣟⢞⡮⣳⢽⢵⣫⢞⣵⡫⣗⢯⡺⣕⡯⣞⣝⢎⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣗⢯⢯⢯⢞⣵⡫⣞⢮⣻⡪⡯⣳⡳⣝⡮⣞⡵⣣⢯⣫⢞⡽⣕⢯⡳⣝⣞⢮⣳⢽⢕⣟⣞⣞⢮⢞⡵⣻⡪⣗⢯⣳⢽⢕⣗⢯⡺⡮⣳⡫⡯⣞⢮⣳⡳⡣⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡽⡽⡽⣝⡽⣪⢾⣹⢵⡳⡽⣝⣞⢞⡵⣫⣞⢞⡽⣕⢯⡳⡽⣺⢝⣞⡵⣳⡫⣞⡵⣣⣳⣳⣳⡫⡯⣞⢗⡽⡵⣫⣞⢽⢝⡮⡯⣞⡽⣕⢯⢯⡺⣝⢮⣞⣝⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢯⣻⡺⡽⡮⡯⣺⡳⣳⢝⣞⢽⣪⢞⡽⣺⢕⣗⢯⢞⡵⣏⢯⣫⢞⡽⣺⡪⡷⡽⣕⢯⢎⣞⣞⢮⣏⢯⡺⣝⡮⡯⣳⢵⡫⣗⡽⡮⣳⢝⡮⡯⣳⢽⡺⡵⣳⢵⢱⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢽⢮⢯⢯⢯⢞⣗⢽⡺⣝⢮⢗⡽⡵⣻⣪⢯⢞⡽⣝⢮⢗⡯⣞⢽⡺⣕⢯⣫⢞⡵⡯⡇⡷⣝⣗⣗⢽⣝⢞⡮⣻⣪⢗⡯⣳⢝⣞⢽⢵⡫⣯⡺⣵⡫⡯⣞⢽⢜⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢯⢯⢯⡳⣯⡳⣳⢽⡺⡵⣫⢯⢞⡽⣺⡪⡯⣳⣝⢮⢯⡳⡽⣺⢵⡫⣗⢯⢞⡽⣪⢯⢇⢯⣗⣗⣗⢽⣪⢯⢞⣗⢵⣻⡪⣗⢯⣞⢽⢵⣫⣾⣮⣷⣽⡽⡮⡯⣇⢯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⢝⣗⣟⣞⢮⢗⡯⣞⢽⢵⡫⡯⣞⡵⣫⢯⡺⡮⣫⢗⡽⣝⡮⣗⢯⣞⡽⣵⡫⣗⢯⣫⡪⣗⢷⢵⡻⣪⢯⡳⡽⣕⢷⢽⢵⣻⣾⣻⢿⡽⣾⣺⣞⡾⡽⣯⢿⢽⣝⣮⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣝⣞⣞⢮⢯⡳⣝⡮⡯⣳⢽⢝⣞⢞⡵⡯⣺⢽⡵⣯⢿⣺⡯⣟⣯⢯⣟⣷⣻⢷⣻⢮⣎⣯⢯⣗⡽⡵⣫⢾⢝⣾⡽⣟⡿⣽⢾⢽⡽⣽⣳⣗⣯⢿⢽⢯⣻⡽⣞⣾⣺⣝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣵⣳⡳⣯⡳⡽⣕⢯⣫⢞⡽⡵⣳⣫⢯⣾⢯⡿⡽⡯⣟⣗⡿⣽⢞⣯⢷⣳⡯⣯⡯⣟⡾⣝⣗⡷⡽⡽⣽⡽⣯⡷⣟⣯⢿⢽⡽⡯⣯⢷⣗⣟⡾⣽⣻⣽⣳⢿⢽⣞⣗⣯⣗⢯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣳⢵⣻⣺⡺⣽⡺⣝⣮⣻⣺⣽⣵⣟⣿⣺⢯⡯⣿⢽⣻⣺⣽⢽⢯⡯⡿⣵⢟⣷⣻⡽⣽⣳⢷⣝⢿⣟⡷⣟⣷⣟⣟⡾⡯⡿⡽⡯⡿⡽⣞⣷⣻⡽⣞⡾⣽⢽⣻⣺⣳⣗⣯⢷⣕⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣟⡷⡷⣿⢾⡾⡷⣷⣻⣞⣷⣳⣟⢾⣺⢯⡯⣯⡯⣷⣻⣞⣯⢿⢽⢯⡯⣟⣞⣗⡿⣽⢞⣟⣾⣳⢝⣿⣽⢾⣺⣳⢿⢽⣻⡽⣯⣟⣯⣟⣾⣺⡽⡯⣟⡽⣯⢷⣻⣞⣗⣯⣟⡮⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣽⣻⡯⣿⢽⡯⣿⡽⣞⣷⣻⣺⣞⣯⢯⡯⣟⣗⣟⣷⣳⣗⣯⢿⡽⡯⡿⣽⢽⣞⣯⢯⡿⡽⣞⣾⣝⢾⡽⡯⣟⡾⡯⣟⣷⣻⣳⣗⡷⣗⣷⣻⣞⡿⡽⡯⣯⣟⣾⣺⣳⣗⡷⡯⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣟⡾⣯⢿⡽⣯⡷⣟⣟⣞⣗⣟⣾⣺⢯⢿⡽⣞⣷⣳⣟⡾⣽⢽⣞⡿⡽⡯⣟⣾⣺⢯⢿⢽⣻⣺⢮⣫⡿⣯⢯⡯⣿⢽⣞⣾⡳⣗⡿⣽⣞⣾⣺⡽⣯⣟⣗⣯⣞⣷⣻⣺⡽⡝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠽⢯⣿⡽⣷⣻⡯⡷⣯⢷⣻⣺⡽⣽⢯⡯⣷⣻⣺⢾⢽⡽⣽⢾⡽⣯⢿⡽⡾⣝⣯⣟⣯⢷⣻⣳⡝⠙⠫⠫⠻⠽⠟⠾⠾⠯⠿⠽⠷⠻⠾⠳⠿⠳⠳⠫⠓⠛⠊⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠗⢟⢯⢯⣯⡷⣯⢯⣯⢯⣯⢷⣻⣞⣯⢿⡽⣽⡽⣾⢽⣽⢽⢯⣟⣾⡺⡷⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠙⠙⠙⠚⠯⠷⠷⠻⠽⠯⠷⠻⠽⠻⠚⠝⠋⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠿⠛⠋⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣴⣿⣿⣦⣄⡀ ⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠀ ⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⢼⣿⣿⣿⣷⡀⠀⢀⣀⣀⠀⠀⢠⣿⣿⣿⣿⠤⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⢹⣿⣿⣿⣧⣬⣹⠓⠚⣭⣅⣽⣿⣿⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣿⣿⡏⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣹⣿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣿⣿⢊⣉⡀⡀⠀⠀⠀⠀⣀⣀⠉⢻⣿⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⣿⣿⠿⠽⠯⠽⢦⣀⣠⡚⠭⠿⠭⢯⣿⣿⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⣿⣿⣿⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⣿⣿⣿⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣼⣿⣿⣿⡀⠀⠀⠀⠀⠞⠢⠀⠀⠀⠀⢸⣿⣿⣿⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⡟⠓⢦⣤⣤⡴⢺⠁⠀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢄⣀⡀⠀⠙⣻⢤⠇⠀⠀⠀⠀⠀⠘⢦⣸⠟⠋⢀⣀⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠡⡀⠀⠀⠀⠈⠉⠙⠓⠢⠤⠼⣄⡀⣠⠧⠤⠔⠚⠛⠉⠁⠀⠀⠀⢀⠀⢝⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠎⠀⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⢀⡇⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⡇ ⢸⡇⠀⠀⠀⠀⠀⠈⢍⣉⠗⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠐⢍⣉⠅⠀⠀⡀⠀⠀⠀⡇ ⠸⣷⠀⠀⢸⠀⠀⠤⠲⢄⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⢀⡐⢲⣄⠀⠁⠀⠀⠠⡇ ⠀⢻⠰⡀⢿⠀⠸⣍⣿⡿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣴⡟⡷⡀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢾⣮⣭⡿⠀⢠⠀⡀⢸⠁ ⠀⠈⢧⠀⠈⢧⣄⠈⠉⠀⠀⢀⣤⡾⠃⠀⠀⠀⠀⢀⡴⠋⣸⠁⢣⠘⠦⡀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠉⠉⣀⡴⠋⠀⣠⠏⠀ ⠀⠀⠈⠣⡀⠀⠀⠉⠉⠉⠉⠛⠋⠀⣀⡠⠤⠔⠊⠁⠀⣴⡟⠀⠸⣣⡀⠈⠑⠒⠤⠤⣀⣀⡈⠉⠉⠉⠁⠉⠁⠀⢀⡴⠃⠀⠀ ⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡜⠀⣸⠀⠹⣍⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢻⡶⠤⠤⠤⠤⠤⠔⠚⠁⣀⠴⠋⠀⠸⣧⡄⠀⠈⠳⢄⡈⠙⠒⠠⠤⠤⠤⠤⠤⣾⡉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠐⠢⠤⠤⠤⠔⠒⠒⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠒⠒⠤⠤⠤⠤⠀⠈⠟⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠦⠀⠀⠀⠀⠀
Smut🍆😫🥵~ She fucks me on the wall as i go harder and deeper down, she moans😩 and i'm turned on and I cum very deep inside her pussy. She moans even louder and bites her lip then looks up at me trembling as one word slips out; 'D-Daddy🫦' and with that said, I go harder and harder until my whole 8 inches huge dick was deep inside her pussy and she moans so loudly that it turns me even more on. Then I push her into the bed and rip open her clothes. I smack her big fat ass and she moans deeply, making me shove my dick between her enormous tits that were larger than a flat pancake, heck, she definitely wasn't flat. I fuck her tits until she is cumming onto the bottom of my dick. I'm more turned on then ever as I shove me dick back inside her pussy and I squeeze her ass. I push it all back up and down as I squeeze her tits. She moans again loudly as to which I shut her up by kissing her. She groans against my lips and I feel myself about to cum. I push her onto me as I ride her on a reverse cowgirl. I smack her ass to which she screams; "CUM IN ME DADDY! CUM IN MY PUSSY! FUCK ME AND GO HARDER!" I follow her request and I push with all my might to get my dick to get further into her even though it can't. Then I start to cum inside her pussy which she moans to as it gets messy. Then I slap her ass as she stands up. I lay down as she lays over me with her sexy ass sitting on me. She starts sucking on my dick then moans loudly when I lick her pussy. Then I see her sex toy and I grin. It was atleast 30 inches long which not even my dick could compare to. I grabbed it as she was still busy sucking my dick. As I grabbed it, I moaned as she had just deep throated my dick. Suddenly I start to cum in your mouth as you grip the bed sheets. I then shove the sex toy up your pussy as you moan so loudly that you almost wake up everyone. You start to go cross-eyed as cum starts dripping out of your pussy. Then you start squirting all over my face making me cum all over you. We both get up and as soon as I see your tits that were covered with cum, I dont even hesitate. I grab your hair and throw you onto the bed and start fucking the hell out of you sideways. You keep on moaning so I slap your ass cheeks a few times before rubbing it with my foot making you moan again. Then I squeeze your tits so hard you start to scream and moan; "HARDER! PUT YOUR DICK ALL THE WAY INSIDE OF MY DADDY! AHHH😫" So I do that until you cum and cum and then I cum all over your tits then I go back to fucking your tits as you stand there helplessly moaning. Then I do that again and again non stop til morning when I pick another girl and, we have a threesome while you enjoy sucking my huge dick and I enjoy smacking your ass, and sucking the other girls' tits and, fucking another girls tits and pussy in a foursome which, turns into a fivesome where all of you moan and I get to enjoy myself and get you all wet🍑🍆💦🤤
⬛⬛⬛⬛⬜⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬜⬛⬛⬛⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬜⬜⬛⬛⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬜⬜⬛⬛⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬜⬜⬛⬛⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬜⬛⬛⬛⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧 ⬛⬛⬛⬛⬛⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧 ⬛⬛⬛⬛⬜⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬛⬜⬜⬜⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬛⬜⬜⬜⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬛⬜⬜⬜⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬛⬜⬜⬜⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬛⬜⬜⬜⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬛⬜⬜⬜⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧 ⬛⬛⬜⬜⬜⬜⬜⬜🟧🟧⬜⬜⬜🟧🟧
⣿⣿⣿⣿⣿⣿⢋⣴⡆⢰⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⣰⣿⣿⣧⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡘⠿⢟⣛⣡⣦⣝⠻⣿⠸⠿⢠⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣾⢺⣿⣿⣿⣿⣿⣷⣖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⢠⣹⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠿⠿⠿⣿⢸⡘⣿⣿⣿⣿⣿⡇⢻⡿⢛⣛⢻⣿⣿⣿ ⣿⢋⣴⣿⣿⣿⣦⢀⢇⢻⣿⣿⣿⣿⣯⠰⣿⣿⣿⣿⣦⢻⣿ ⢣⣿⣿⣿⣿⣿⣿⠘⢼⡸⣿⣿⣿⣿⣿⣶⢹⣿⣿⣿⣿⣧⢹ ⣆⢿⣿⣿⣿⣿⣿⣶⣌⣧⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⢟⣱⣾
🍹🍹️̸🍹️⃤🍹️⃠🥫🛢🔋🍨🍦𓆏𓃰𓄁𓃠𓅿𓃟ဪ𒀱𒈓𒈙꧅𒈙𒈙ဪဪ🍹 ﷽🏳️‍🌈⃠🥃️̸🥃️⃠🍫️⃠☕️̸̼͙̈́͆̈́ͯ̒̆̀̓ͧ͠🥲⃤⃞⃟⃝🥲⃤⃞⃟⃝🥲⃤⃞⃟⃝🥲⃤⃞⃟⃝🥲⃤⃞⃟⃝✞✞︻デ═一︻デ═一✞𓅓✞ඞ¬ඞ︻デ═一✞︻デ═一✞︻デ═一⃞⃤⃟⃤⃝☺︎⃢( -_•)╦̵̵̿╤─( -_•)╦̵̵̿╤─( -_•)╦̵̵̿╤─︻デ═一︻デ═一☻𓂸𓂸﷽𓆩😞𓆪𓆈𓆩😞𓆪૮ ˙Ⱉ˙ ა rawr!🤡̵̛͔͍̱͙̥͔̯͖̥͙̲͆ͬ̊̑̔̂╰⋃╯ (◕ε◕*)/̵͇̿̿/'̿'̿ ̿ ̿̿ ̿̿ ̿̿🔥⃤🔥⃤🚫 🏳‍🌈⚕🚫 🏳‍🌈🥭️̸🥭️⃤🥭️⃠🐠️̸🐠️⃤🐠️⃠
pls someone fuck me💦😫
🥺⃤🏳️‍🌈⃤🧲⃤🧿⃤🧪⃤🧸⃤🥟⃤🦧⃤🦕⃤🎅🏿⃤🦟⃤🦚⃤🧉⃤🥡⃤🥄⃤🧂⃤🥊⃤🥌⃤🧩⃤🧻⃤🧬⃤🥶⃤🦷⃤🧠⃤👨🏾‍🦰⃤🧶⃤🧵⃤🤑̶̢̼̲͐̓̾̅͜
⠹⢌⡱⢌⠭⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠳⣌⠲⣌⠢⣅⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠠⠀⠀ ⡱⢠⢃⡄⠓⡌⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢌⠱⡈⠄ ⡡⢃⠎⠌⠳⡐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢎⠲⣡⠊ ⢡⢃⠚⡌⠱⠠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢎⡕⢢⢍ ⢅⠪⡐⠤⢡⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣎⠼⣡⢎ ⢢⠑⡌⢠⠁⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⠀⢀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣃⠿⣇⡳⢎ ⡂⢍⡐⠡⢈⠒⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠆⡃⢸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⡕⡺⢽⡷⣭ ⡘⠤⠘⡐⢂⠰⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⣇⡇⠎⣇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡳⢜⡱⢣⢟⣶ ⠔⡡⢃⠔⡠⢂⠁⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡿⢿⡒⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠱⣌⠧⣙⠧⣾⠽ ⡘⠔⡨⢐⡀⢂⠐⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡜⣰⡧⠽⣦⠈⡀⢀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢥⠛⣤⣛⢼⠫⡑⢌ ⢌⡘⢠⢁⠘⠠⠌⡐⢀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣿⠏⠉⢁⠳⣤⠈⢢⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣸⡬⠟⢩⠐⡌⢢⠑⣊ ⢂⠍⡒⢌⡘⡐⢂⡐⠠⢀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⠀⠀⠀⠁⡆⠝⠲⣽⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠚⡁⠆⡑⢢⠡⡘⢄⠣⠔ ⢌⠲⡁⠦⡐⢄⠂⡄⢁⠂⠈⠨⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡼⠀⢀⠀⠀⠃⢀⠃⠈⣯⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⡐⠌⡡⠘⠤⡑⢢⠑⣌⠢⢍⡊ ⠶⠥⠜⣤⣁⣊⠐⡈⠂⠌⡁⠆⠠⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡾⠀⠈⠀⠀⠀⠀⠀⠀⢼⡀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢋⠌⢢⠡⡐⢌⡐⢩⠐⡌⢢⠑⡄⠳⣈⠖ ⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠲⠬⠤⢅⣂⣈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⠌⡐⠠⢈⠀⠂⠄⠠⠀⠄⡀⢂⡐⢨⡴⡟⡉⢆⠡⢊⠔⢂⠡⢂⠜⡠⢃⠜⡠⢣⠜⡱⢌⢎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⣳⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡇⠀⠀⠀⠀⠀⠀⠈⣷⡀⠎⠤⢑⠠⡘⠰⡈⠔⡩⣐⣡⡶⢛⠍⡒⠤⡑⢌⠢⡁⠎⡄⠣⢌⠢⡑⡌⣒⢡⢃⢎⡱⢊⡬ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡌⢭⠓⡖⢦⠤⣤⢤⣤⣤⣤⣤⣷⣷⠀⠄⡐⢀⠀⠀⠀⢼⢿⡾⣴⢧⡶⣥⣷⡼⢗⡛⢩⡑⢌⡒⡸⢀⠇⡘⡄⠣⣌⠱⣨⠱⢌⡒⢥⢒⡡⢎⡜⢢⡕⢫⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⣙⡜⣌⠳⡌⠶⣘⢬⠹⣹⢻⣾⡍⡒⠌⣤⡆⠀⠀⠀⠻⣗⠎⢧⡙⣶⡛⡜⢢⠜⡡⢎⢢⠑⠦⣉⠖⡱⢌⡱⢂⠳⣄⠳⡌⡜⢢⢣⢜⢢⠞⣡⠞⣥⢛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⡚⣬⢣⡝⡱⢎⣎⣳⢏⡼⣹⣷⣉⡾⠋⠀⠀⠀⢀⠰⣹⡏⢦⣹⢇⡳⢌⠣⢎⡱⢌⠦⡙⢦⡑⢎⡱⢊⡴⣉⠶⣈⢳⡘⣜⢣⡍⣎⠳⣎⠵⣫⢼⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣖⢣⢞⣱⢋⣶⢏⡎⡱⢂⢻⣍⣓⠃⠄⡐⠠⢀⢒⡸⣿⢼⣏⠞⣜⢪⡙⢦⡑⢎⡲⣉⠦⡙⢦⣑⢣⠖⣡⢞⡡⢧⡹⡜⢦⡹⢬⡳⢎⡽⡲⢧⡳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡭⣞⣬⢻⡼⣏⡼⢡⠎⡬⡑⢦⡘⠤⡑⣂⠆⡎⡴⢻⣟⣬⣛⢬⢣⡝⢦⡙⢮⡑⢮⡱⣙⠦⣍⠞⡼⡱⢎⡵⣣⢳⢭⡳⣭⢳⣭⢻⡼⣹⢧⣛ ⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣜⢮⡳⣿⣣⡝⣦⡙⢶⣙⢦⣙⠶⡱⡜⡼⣸⢵⣻⡝⡶⣭⢞⣣⠞⣥⡛⢶⡹⣒⢧⡝⣺⣌⢟⣜⡳⢫⠶⣭⣛⢮⡵⣣⢟⡲⣏⢾⡵⣫⣞ ⡘⠤⡐⡈⡐⠠⡀⠄⠠⢀⠀⡀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢚⣯⡗⣯⡽⣷⣻⢶⣹⡳⣎⡿⣼⢫⣷⣹⢳⣝⣮⡿⣝⣳⡽⣎⢷⣛⢶⡹⢧⣛⡵⢮⡽⣱⢞⡾⡼⣹⢯⡝⣶⡹⣎⢷⡝⣾⣹⡽⣞⣽⣳⡽ ⠥⣓⠰⣁⠦⡑⡄⢣⡘⢄⠒⣐⠢⡐⠤⡁⢎⡐⠄⡡⠌⠤⠡⢌⠰⡀⢮⣳⣽⣳⡽⢯⡷⣯⣷⣻⣽⣳⢯⣟⡶⣯⣛⣾⣾⡿⣝⣧⣟⣞⣧⡻⢮⣽⢳⣝⡞⣧⣻⢵⣫⠾⣵⢏⣾⣹⢶⡻⣽⣺⠽⣧⢷⣛⡾⣧⢿⡽ ⡳⣌⠳⡜⣢⠵⣌⠣⡜⣌⠳⢌⠲⡑⢦⡉⢦⡘⢦⡑⢎⡜⡡⢎⠦⣙⣮⢷⣳⣟⡾⣯⣟⣷⣻⡽⣯⣟⣿⡿⣟⣿⣻⢯⣟⡿⣽⢾⡽⣞⣳⣟⢿⣼⣛⣮⣟⣳⡽⣾⣹⢯⣷⢻⣮⠷⣏⡿⣵⢯⡿⣽⢯⣻⡽⣯⢿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢛⡛⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠟⡉⣡⡖⠘⢗⣀⣀⡀⢢⣐⣤⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠉⣠⣲⣾⡭⣀⢟⣩⣶⣶⡦⠈⣿⣿⣿⣷⣖⠍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡛⢀⠚⢩⠍⠀⠀⠡⠾⠿⣋⡥⠀⣤⠈⢷⠹⣿⣎⢳⣶⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡏⢀⡤⠉⠀⠀⠀⣴⠆⠠⠾⠋⠁⣼⡿⢰⣸⣇⢿⣿⡎⣿⡷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⢸⢧⠁⠀⠀⢸⠇⢐⣂⣠⡴⠶⣮⢡⣿⢃⡟⡘⣿⣿⢸⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣯⢀⡏⡾⢠⣿⣶⠏⣦⢀⠈⠉⡙⢻⡏⣾⡏⣼⠇⢳⣿⡇⣼⡿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠈⡇⡇⡘⢏⡃⠀⢿⣶⣾⣷⣿⣿⣿⡘⡸⠇⠌⣾⢏⡼⣿⠇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡀⠀⢇⠃⢢⡙⣜⣾⣿⣿⣿⣿⣿⣿⣧⣦⣄⡚⣡⡾⣣⠏⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⡀⡀⠃⠸⣧⠘⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠃⠘⠁⢈⣤⡀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣇⣅⠀⠀⠸⠀⣦⡙⢿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⢛⣉⣉⣀⡀⠀⢸⣿⣿⣷⣬⣛⠛⢛⣩⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢋⣴⣿⣿⣿⣿⣿⣦⣬⣛⣻⠿⢿⣿⡇⠈⠙⢛⣛⣩⣭⣭⣝⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣼⣿⣿⣿⣿⣿⡿⡹⢿⣿⣽⣭⣭⣭⣄⣙⠻⢿⣿⡿⣝⣛⣛⡻⢆⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢥⣿⣿⣿⣿⣿⣿⢇⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣷⣶⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⡆⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⠁⠊⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣄⢻⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠈⣿⣿⣿⣿⣷⢙⠿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣩⣴⣷⣌⠻⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣆⢻⣿⣿⣿⣿⡇⣷⣶⣭⣭⣭⣵⣶⣾⣿⣿⣿⣿⣿⣿⣷⣌⠹⢿⣿⡿⢋⣠⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡚⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⢻⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⠈⣿⣿⣿⣿⢆⠀⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣤⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⣻⣿⣿⣿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣒⣻⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣇⢹⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣬⡻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⠻⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢎⢻⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣾⣦⢻⣿⣿ ⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣆⢻⣿ ⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣆⣿ ⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⡌ ⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⡆⢿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⠸⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣻⢿⡟⢿⡿⢿⣽⡌⣳⠀⠀⠀⠀⢻⢿⡷⢉⠛⠲⠶⠡⠀⢬⢅⠆⠤⢳⡄⠁⢆⠐⠈⢉⡙⢫⢟⡆⠀⠀⢈⠓⢉⢻⠀ ⠹⣄⡀⢈⡋⠥⣉⠀⢌⡠⢉⠢⠙⣌⢒⣦⣐⣢⣀⣆⣤⣲⣌⣴⣰⣠⠄⠀⠀⠀⠀⠀⠁⠈⠑⢢⣶⣤⣦⣼⣦⣦⣼⣧⣶⣦⣾⣶⣶⠀ ⣷⣶⣿⣶⣾⣷⣿⣿⣿⣿⡿⠋⠛⠛⠋⠉⠛⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⢿⣿⣿⣿⠃⠀⠀⢾⡹⣷⣿⣦⡄⠀⠠⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⡰⣿⣿⣽⣷⣤⠀⠈⢿⣿⠏⠀⠀⠸⠒⠿⣞⠿⠿⠿⢆⠀⠂⠀⠀⠚⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⠀ ⣿⣿⣿⣿⡿⡿⠏⠀⠀⠀⠀⠀⢴⡹⢾⣿⣿⣿⠿⠇⠀⠸⣿⡇⠀⠀⠀⠀⠈⣿⡀⠈⢍⣹⡆⠀⠀⢂⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣻⠟⠀⠀⠀⠀⠀⠰⠠⠐⢂⢀⢻⠷⠀⢉⡀⠀⢫⠁⠀⠘⡶⡞⠠⣿⣿⠻⣿⣿⣏⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⠀ ⠛⢿⣿⠗⠩⠄⠀⠀⠀⠀⠀⠉⢷⣶⣾⡾⡍⣿⡿⢿⣷⠀⠸⡇⡀⠀⢨⠀⠂⢀⣚⡃⢈⣿⡏⠠⠀⠀⠀⠁⢂⢙⢻⣿⣿⣿⣿⣿⣿⠀ ⠀⡠⠠⢍⠁⠀⠀⠀⠀⠀⠀⠈⠌⢻⠟⠦⠤⠜⠞⢊⡏⠀⠸⣯⠠⠀⠀⠂⣄⢒⣴⣿⡾⢏⡁⠀⠀⠀⠀⠀⠁⠹⢸⣿⣿⣿⣿⣿⣿⠀ ⠀⢡⠜⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢶⡤⣉⠚⣣⡿⠁⠀⣿⣿⣷⡀⠀⠀⠈⠛⢛⢫⡾⣹⠆⠀⠀⠀⡀⠀⠀⠀⠠⢪⣿⣿⣿⣿⣿⠀ ⠘⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⠘⠻⠿⠟⠀⠀⢠⣻⣿⣿⣷⣤⠀⠀⠀⡘⠦⡹⣽⣻⣴⢦⡤⢄⣤⢤⢤⣤⣅⢿⣿⣿⣿⣿⠀ ⣾⠗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡴⣢⣭⢿⡝⠀⠀⢀⠤⣿⠛⠍⡀⢱⠃⠀⠐⣀⠣⣕⢺⣱⣝⣴⣿⢣⣞⢯⣞⣿⣿⣷⡹⣿⣿⣿⠀ ⡿⣹⠠⠀⢀⣀⣄⣤⣒⡶⡜⣶⣹⢶⣽⣾⣿⣅⣀⠠⣌⡿⠃⠈⢀⠔⡀⠀⠄⡇⢆⡰⣏⣿⣹⢿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣻⣿⣿⠀ ⣿⠏⢄⠺⡽⣿⣿⣿⣿⣿⣿⣶⣿⣯⣿⣿⡿⣾⣼⣫⢻⣷⡁⠀⠎⠠⠀⠄⡘⡘⢦⣛⠾⣱⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠀ ⣾⠎⣀⠲⣉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣮⢇⠀⠈⢄⠩⡐⠴⣉⠶⡩⢎⡱⣏⣾⣿⣿⣿⣿⣿⣏⠜⣯⣷⡿⣽⢿⣿⠀ ⡿⢀⠢⡑⢮⡙⣞⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠈⢦⠳⣍⠞⡌⢣⠱⣏⡵⣿⣿⣿⣿⣿⣿⣿⡅⠀⢏⣿⣻⣽⣾⣿⠀ ⡇⠀⢆⡙⢦⠍⠀⠘⢧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣎⢼⣛⣮⡟⠠⡁⣞⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢖⡿⣯⣧⣿⠀ ⠀⠌⠰⣘⢧⠋⠀⠀⠀⢋⡾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⡽⣿⠇⢠⡱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠌⢺⣿⣿⣹⠀ ⠠⡈⠵⣩⠂⠁⠀⡐⢈⡐⣟⣿⣿⣿⣿⣿⣿⣿⣿⣟⡡⢿⣿⣿⣿⣿⡯⠙⠀⢆⡿⣽⡟⢭⣻⣿⣿⣿⣿⣿⣿⡇⠀⢠⠈⢂⠿⣿⡿⠀ ⢠⡙⡼⡁⠀⠀⠀⠐⡀⠐⢎⡿⣿⣿⡟⠜⠾⣿⣿⣿⡆⢹⣻⣿⣿⣿⣯⠁⠀⠘⡼⣃⠀⠂⣿⣿⣿⣿⣿⣿⣿⠀⡱⡜⡆⠈⢞⡽⣿⠀ ⢠⣛⠖⠅⠀⠀⠀⠀⡐⠈⠠⠙⡽⣻⣿⣄⣒⣽⣿⡿⣿⡄⠘⢿⣿⣿⡟⠀⠀⠈⠰⠩⡗⣿⣿⣿⣿⢿⣽⣿⡟⣰⣻⣶⣿⡈⢜⡲⢹⠀ ⢢⠍⣜⠊⠀⠀⠀⠀⠠⢁⠂⡁⠐⡉⠞⡻⢿⠿⣛⣿⣿⣿⡄⠈⠘⠁⠀⡀⠂⠠⠀⠁⠈⠐⣉⣬⣵⣿⣿⡿⠵⢔⣿⣿⣿⣧⠈⢿⣡⠀ ⠂⣼⡳⠡⠀⠀⠀⠠⠀⠂⠄⣑⢦⡠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣦⠀⠀⠠⢈⡁⠀⠡⠙⣾⣹⣞⣧⡿⣿⣿⣧⠒⣽⣿⣿⣿⣿⣷⡀⢣⠀ ⣇⣿⣧⣌⣠⣅⠧⠀⡀⢈⠰⡈⠦⡝⡶⣭⣿⣿⣿⣿⣿⣿⡿⡙⣆⠀⠀⢂⠐⠠⠁⠈⠄⢫⣟⡿⣽⣻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀ ⣯⣿⣿⣽⣾⣿⣶⣽⠇⢀⠢⣑⢻⠲⣍⢯⢻⡽⣯⣿⣿⡳⡇⣹⣿⠆⠀⠀⠌⡐⠈⡐⢄⠂⢌⡱⢿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⠀ ⣿⣽⣿⣿⣿⣿⣿⢋⢢⡀⢵⣊⢧⡻⣜⢮⣳⣻⣽⣟⢾⣳⢁⣿⣿⡆⠀⠀⠐⡠⠐⠠⣊⣝⠢⡌⢣⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⡧⣿⣿⣿⡿⢁⢎⢶⣙⠶⣽⣯⣿⣽⣳⢿⣿⣿⣞⣯⢷⢨⣿⣿⠃⠀⠀⠠⢑⠂⢀⠓⣎⠻⡄⢃⠎⡿⣿⣿⣿⣿⡓⠹⣿⣿⣿⣿⠀ ⢺⣿⣹⣿⠏⠠⠐⠊⢷⣫⢿⣽⣿⣻⢾⡽⣿⣿⣯⣼⣟⠯⡰⣻⣿⠀⠀⠀⠀⠀⡁⠂⠉⡌⠓⡄⠂⠌⡱⢫⢿⣟⡇⠚⠧⠹⣿⣿⣿⠀ ⠀⢿⣏⠋⠀⠀⠸⠴⠀⠍⡛⢿⣳⢯⣛⠾⣝⢯⣟⣟⢮⠃⠁⣿⡿⠀⠀⠀⠀⠀⠀⢀⠁⠄⢃⠐⠈⠀⣃⠨⡰⡣⣜⣲⠀⢜⣙⣿⣿⠀ ⡈⠆⣿⣆⠮⠵⠃⠜⡪⣏⠛⣳⠨⣅⣫⠙⢊⡧⢙⠈⡃⢠⠖⢽⡧⠠⢁⡈⠁⠀⠀⢀⣤⢀⢐⡠⠀⠙⢛⠌⢀⣿⠟⣯⣴⣿⣿⡿⣿⠀ ⣧⢈⠼⣿⣦⡒⣤⣐⣸⢼⣁⣉⣐⠿⠈⡳⠅⠰⡅⢁⢶⠟⠒⢿⣧⠀⠈⠐⠑⠠⠔⠈⡀⢀⣩⠭⠡⠀⡘⠀⠀⢀⣈⡽⣿⣿⣿⣿⣿⠀ ⣿⠀⠺⣽⣿⢿⡰⣌⢯⡝⡬⠢⠁⠀⡊⣉⠀⠈⠛⢍⣭⣟⡷⢸⡯⠀⢀⠢⡐⣀⠀⠀⠀⠀⠁⠁⠀⠀⢀⠰⣘⣦⢷⣿⣿⣿⣿⣿⣿⠀ ⣿⠂⡵⠺⣽⠑⣗⢽⣻⣿⣽⣭⠀⣆⡔⠾⡰⢐⢶⣯⣷⣯⢿⣼⣷⠀⠀⠦⣑⠦⡱⢀⠀⠀⠀⠀⠀⡐⡬⢯⣽⣾⣿⣿⣿⣿⣿⣿⣻⠀ ⣷⠀⢈⡄⣾⠀⢥⣚⣿⣿⣿⣯⣷⠈⠀⢀⡴⣫⣾⢿⣷⣿⡿⣴⡷⠀⠈⠲⣍⠞⡥⢃⠂⠀⠀⠀⢠⠱⣽⣻⣿⣿⣿⣿⣿⣿⣿⢷⣿⠀ ⣿⡄⠀⠃⠘⡆⣈⡟⣾⢿⣿⣿⣿⣇⠀⠮⣜⢷⣯⢿⣿⣿⣿⣹⣇⠀⠀⠓⣌⠛⠤⠁⠀⠀⠀⣀⢣⣛⣾⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⠀ ⢿⣳⠀⠈⠀⠇⠼⡸⣝⣿⣿⣿⣿⣿⠀⠳⣘⢯⡞⣿⣿⣿⣷⠹⡿⠀⠀⠑⠨⠌⢀⠀⠀⠀⠠⣐⢧⣻⣾⣿⣿⣿⣿⣿⡿⢏⣾⣿⣿⠀ ⣾⣿⣗⠀⠈⢠⢃⡓⠾⣼⣻⣿⣿⣿⠃⠠⠉⢖⡛⣛⣻⣛⡋⢀⣭⡄⠀⠀⠄⠂⠀⠀⠀⠀⡰⣉⠞⣻⣟⣿⣛⣿⣿⠛⠩⢸⣩⣯⣽⠀
⡘⠦⡑⡌⢆⠣⡜⠤⠣⢜⡠⠣⠜⠤⡓⢬⢣⡝⢮⡽⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢀⢲⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠹⣟⢿⣿⣇⠀⠀⠀⠀⢀ ⢌⡱⠘⡌⣌⠣⢌⢣⢉⠆⣡⠣⡙⢢⡙⢆⡣⢞⡱⣞⡵⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠄⣹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠀⠀⠀⠀⢨ ⠢⢌⠓⠬⠤⡙⢂⠎⡔⢊⠤⢃⠥⣃⠜⡢⢝⢮⡱⢏⣞⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⡜⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⣿⡇⠀⠀⠀⠀⢆ ⡑⢊⠍⠲⣁⠎⡅⢎⠰⡉⢆⠩⡒⢌⡜⡱⢎⠶⣙⢯⡞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣗⢀⢂⠀⠀⠀⠀⢡⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣜⢿⣇⠀⠀⠀⡈⠤ ⢨⠑⣊⠱⣐⠪⠔⣊⠱⡈⢆⠱⡘⢤⠚⡴⢩⠞⣭⢺⡝⣷⣿⣿⣿⣿⣿⣿⣿⣿⠡⡈⠄⠀⠀⠀⠀⠀⣍⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣽⣿⡄⢠⢁⠐⡈ ⢠⠓⡄⢣⠢⡑⠣⠌⢆⠱⡈⢆⡑⢢⡙⠴⣋⠞⣜⢧⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⡄⠡⠀⠀⠀⠀⠀⠀⠁⢾⣿⣿⣿⣆⠀⡀⠀⠀⠀⠀⠀⠀⢺⢯⣿⣿⣖⡠⠀⠠ ⢂⠱⡈⢆⠱⢌⠣⡉⢆⠡⡘⠠⠌⡅⢎⡱⢎⡝⣎⡳⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⠈⠂⠀⠀⠀⠀⠀⢣⢛⣾⣿⣿⡇⠀⠀ ⠈⢆⠱⡈⢎⠰⢃⠜⡠⠃⡌⠱⡈⢆⠣⡜⡜⣜⠲⣝⢯⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣆⠀⠲⣤⠀⠀⠀⡀⠀⢊⣿⣿⣿⣿⡒⠄⠀⠀⠀⠀⠀⢌⡳⣞⣿⣿⣷⡀⠀ ⠘⡄⢃⠜⡠⢉⠆⡘⢄⠣⢌⠱⣈⢌⡓⢜⡰⢎⡝⢮⣻⣿⣿⣯⣽⡳⢿⡽⣿⣿⣿⣿⣧⠀⠈⢠⠀⠀⠈⠄⡐⠸⣿⣿⣿⣷⡈⠠⠀⠀⠀⠀⠀⢱⢻⣼⣿⣿⣧⠀ ⠐⡈⢆⡘⢄⠣⡘⠌⢢⠑⡌⠒⣌⠢⠜⢢⡑⢮⡜⢧⣿⣿⣿⣳⡾⣙⢧⢻⣽⣿⣿⣿⣿⣧⡀⠠⠄⠀⠀⠐⠔⡩⢞⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠠⡙⣧⣿⣿⡟⠀ ⠠⢁⠆⡈⢆⡑⢌⡘⠄⠣⢌⠱⡠⢍⢪⠱⡌⣇⢞⣧⣿⣿⣿⡛⠆⢡⢊⡷⣻⣿⣿⣿⣿⣿⣆⠀⠈⠤⠀⠀⠐⠗⠬⣻⣿⣿⣿⣇⠠⡀⠀⠀⠀⠀⢱⢋⣿⣿⠃⠀ ⠐⠠⢂⠡⢂⠌⢂⠔⡉⢒⠈⢆⠱⠌⣆⠳⡸⢬⡻⣼⣿⣿⡷⢉⠐⠀⡌⢷⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠃⠀⠀⠀⠐⠳⣿⣿⡯⢿⣆⠀⠀⠀⠀⠀⢡⢪⣿⠏⠀⠀ ⠈⡐⠄⠢⢁⠌⠠⢂⠐⡈⠜⡠⢍⠚⡤⢓⣭⢳⡽⣿⣿⣿⡑⠂⠀⡀⠘⣧⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢣⣿⣏⡻⣿⣆⠀⠀⠀⠀⢠⣿⢟⡀⠀⠀ ⠐⠠⢈⠐⢂⠈⡐⠠⢁⠒⡈⠔⡌⢣⠜⣣⢎⣿⣽⣿⣿⢣⡑⠈⠀⡄⠱⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠠⢿⡇⣱⡟⣿⣆⠀⠀⠀⣿⡟⠸⠂⠀⠀ ⠀⠂⠄⢈⠀⢂⠠⢁⠂⠤⠑⡌⡰⢃⢾⣴⣿⣿⣿⣿⣯⠳⡉⠔⡰⢉⢶⣹⣿⣿⣿⣿⣿⣿⡿⣟⢣⡟⣕⠀⠀⠀⠀⣠⠈⣽⢃⠖⣿⣿⣿⣶⡴⢹⣿⠀⠀⠀⠀⠀ ⠀⠀⠄⠂⠀⠄⡐⠠⡈⠔⡡⢢⢑⣎⣷⣿⢿⣻⣿⡿⠧⠓⠄⡑⢤⡛⣮⣿⣿⣿⣿⣿⣿⣿⠳⡌⢧⡟⡾⣆⡀⢸⠝⠁⢸⡏⢸⠸⣽⣿⣿⣿⡇⣾⠉⠀⠀⠀⠀⠀ ⠀⠀⠠⢀⠁⢂⠤⠑⡈⢆⠡⡖⣭⣾⡿⣏⠾⣽⣿⣏⢰⠋⠑⡄⣣⢽⣿⣿⣿⣿⢯⡝⣿⡏⠱⡘⢄⠻⣵⣻⣆⠸⠀⠐⣎⠔⡘⢥⣛⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⡈⠄⠂⠤⢁⠂⢆⣽⣿⡿⡱⢯⣾⣿⣟⡿⠎⠀⡰⣡⢟⣾⣿⣿⣿⠉⢿⣷⣿⣽⠆⡀⠉⢆⡙⢧⣿⣆⢳⡼⠛⠠⡘⢆⡻⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠄⡁⠂⠄⡘⣸⣿⣯⠳⣍⢣⣿⠍⡾⠇⠀⡰⣱⣯⣿⣿⣯⣿⣿⡆⠹⣿⣿⣿⡿⣷⢯⣮⣝⣮⣳⣿⣷⠏⢁⠞⡠⢍⡞⣷⣻⣿⣯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⢈⠀⡐⠈⡐⠀⢿⣿⣳⡟⣼⢱⣿⣾⣋⣴⡶⣷⣿⣿⣿⣷⣿⡟⣾⣧⠲⡈⠉⠙⠿⣯⣿⣾⣯⣿⣿⣿⠋⠀⠀⡰⢁⠎⡼⣳⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⢀⠂⡐⠀⠤⢙⣿⣿⣳⡿⠃⢨⣿⣿⣿⣾⣿⡿⣿⣹⣿⡿⠛⡸⡽⣿⣇⢌⠒⢄⣀⡙⠻⣿⣿⣿⣿⠏⠀⠀⠤⢳⠊⡼⣵⣿⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠄⠂⡐⠠⢁⠂⣥⢾⣿⣿⠻⠀⠀⢻⣯⢻⡽⣭⣷⣿⡿⠋⢠⢜⡳⣝⣻⣿⣦⡝⢢⣌⢲⡀⢹⣿⣿⠏⠀⠀⠀⠐⢃⣾⣿⣿⠏⡐⠡⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢁⠀⠂⠄⢡⠂⣜⠶⣿⣿⡿⠀⠀⠀⠩⣿⢧⣿⣿⣿⠏⢠⡜⣣⣾⢻⣼⣻⣿⣟⣯⢱⢊⠖⡇⠸⣿⠏⠀⠀⠀⠀⣈⠰⣾⡿⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠂⠡⠈⠤⣸⣌⠘⣼⣿⡇⠀⠀⠀⠆⣿⣿⣿⣿⠇⢐⡳⣾⡽⣣⣟⣏⣿⣿⣞⡷⠎⣍⡾⠁⣸⠟⢀⠔⠀⠀⠰⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠠⠐⢀⢣⡖⢠⠐⠤⣹⣿⠁⠀⠀⠀⠀⠛⣿⣿⣏⠀⣬⢳⡝⣞⡵⣞⣿⣿⣿⢾⣳⢩⡼⠁⣴⠟⠀⠆⠀⠀⠐⢣⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠂⠄⢂⠓⡠⠍⣒⣹⣿⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⡣⣟⡼⣣⢿⣽⣾⣿⣿⡿⢁⡚⠀⢼⣵⠆⠀⠀⠀⠀⠀⡍⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠈⡐⠠⢡⠘⣤⡳⣿⡿⠀⠀⠀⠀⠀⢀⠸⣹⣧⣄⠀⡽⢷⡹⢾⣹⣿⣿⣿⠆⣷⢡⢠⣟⠃⡀⠀⠀⠀⠀⠠⡔⠋⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡀⠡⠀⡅⢢⡑⣞⣵⣿⡇⠀⠀⠀⠀⠀⠈⠃⠠⣿⣧⣄⠋⢿⡽⣯⢷⣿⣿⣿⣛⠬⡙⣿⠁⡐⠀⠀⠀⠀⠀⠰⣈⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠁⠂⢄⠡⢌⣳⡟⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠆⣯⣟⡿⣄⢚⡷⣯⢾⣿⣿⣿⣟⡦⠓⡏⠰⠃⠀⠀⠀⠀⢐⡢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⢂⠁⢆⡼⢋⡜⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠒⢷⢧⣏⢿⡽⣧⢻⡿⣿⣿⣿⣿⣏⡷⣾⡱⠁⠀⠀⠀⠀⢀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢈⠰⣈⠣⣐⠣⡼⡛⠀⠀⠀⠀⡀⠀⠈⠁⠀⠈⢀⠊⣽⡎⢿⡽⣿⣿⣿⣿⣿⡿⠉⣼⠏⠀⠀⠀⠀⠀⠠⢂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢈⠰⠀⢅⠂⡝⠂⠁⠀⠀⠀⢀⡃⠁⠀⠀⠀⠀⢸⠹⡞⣷⢈⠛⣷⣿⣿⣿⡿⢁⣾⠟⡀⠎⠀⠀⠀⠀⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⢀⠁⡂⠌⠠⢈⠐⡀⢁⠠⠀⠅⠠⢄⠀⠀⠀⠈⢦⠳⣹⣏⡄⠜⣿⣿⣿⠁⣼⣏⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⢂⠐⠈⡐⢀⢂⠐⡀⢂⠡⡘⠄⡩⠄⠀⠀⠀⢎⡀⢽⣽⣟⠀⠸⣿⣟⢸⡟⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠠⢀⠂⡐⠄⢂⢂⡐⢁⠂⡔⢡⠂⠀⠀⠀⠀⠈⠱⠘⣥⠿⣷⡀⠈⣿⣸⠡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠠⠐⠀⢂⠐⠌⠄⢂⠐⡠⢁⠒⠤⠘⠀⠀⠀⠀⠀⠀⠇⠘⣧⢻⣿⠄⣿⢧⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠌⡐⠈⠄⢂⠐⠠⢊⠄⡁⠀⠀⠀⠀⠀⠀⢩⣀⠿⣡⣏⡐⣿⡶⢋⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠁⡀⠂⠌⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⣯⢾⣜⣶⠁⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣞⣹⢹⡬⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⣦⣵⢦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢼⣽⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠛⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢈⠂⡐⡈⠄⡈⠠⠰⢀⠀⠠⡌⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠔⡠⢡⠐⠂⠄⣁⠒⣨⡇⢐⡏⣰⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡐⡡⢢⡁⠎⠐⠠⠀⡁⠻⡇⢈⠛⣦⠅⡘⡎⠡⠆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⠣⣅⠘⡌⠀⠁⠀⣠⣙⣿⣄⢫⡇⣹⡔⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢃⠌⡓⣯⠂⠈⠓⠢⠽⢻⣿⣿⣾⣿⡍⢼⡈⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⢴⢇⡣⠆⠁⠀⠐⢨⣾⢻⣿⡭⣿⠞⣤⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⠠⠍⡁⣤⠛⣉⠒⡜⡛⣷⢯⡟⢦⡩⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠤⠉⠤⢋⢎⡱⠮⡑⣎⢾⣹⢣⢳⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡉⠂⢅⠊⡔⢡⠓⡌⢖⡣⢏⠶⣡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠊⠔⠨⣀⠒⢨⠘⡸⢩⡒⢅⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⡀⠌⠠⠌⠰⡣⠜⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠱⠑⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⢀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢠⠃⢸⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡘⡶⣼⢰⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⡇⡧⠘⡆⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⣾⣷⣧⣀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠈⣿⡼⢿⣯⡛⠦⢬⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡟⢃⣼⠟⢿⣄⠀⠀⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢠⠏⢀⣾⣯⠤⠤⢿⣷⡀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠠⣿⣿⣿⡗⠒⠒⠬⣿⣆⠀⢀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣾⡏⠀⠀⠐⠤⡀⠙⢿⣦⣀⠀⠹⣦⡀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⡧⣿⠀⠀⠘⠀⠀⡆⠑⣄⠈⠙⠻⣶⣍⣿⡆⢆⠠⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⠀⠀⠸⡄⠀⡆⠀⡎⠀⢸⠀⠀⠙⣻⣿⡇⢀⠃⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢎⡷⠀⠀⠀⠃⠀⡇⠀⠃⠀⠸⡀⠳⠀⠈⢿⣧⠂⠌⡐⡀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠰⣿⢺⣗⠀⠀⠀⠇⠀⠁⠀⠀⠀⠀⠁⠩⠀⠀⢹⣿⠀⡘⠠⢀⠁⠂⠄⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠠⢁⠸⣿⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⡐⠠⡁⠂⠌⡐⠠⡀⠡⠐⡈⠠⢀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠂⠠⢈⠠⣿⣽⣯⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⢃⠄⣃⠰⢀⡁⢂⢁⠂⠄⣁⠂⠌⠠⢁⠐⡀⢂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠠⠁⡀⠂⡀⣿⢾⣿⡰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⢿⠐⡄⢂⠆⡐⢂⠤⢈⠂⡄⠌⡠⢁⠢⠐⡐⢂⠄ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⠀⡐⠀⠄⠀⣹⣏⣿⡦⢁⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⣿⡏⣆⠣⠜⢢⡘⢄⠣⢄⢃⠒⡨⠐⡄⠣⢌⠱⡈⠆⢎ ⡙⠷⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠂⢈⠀⠄⡐⠀⠂⠘⣿⣼⡷⡁⠆⡀⠀⠀⢂⠡⠀⠀⠀⠀⠀⠀⣿⣿⢤⡙⠬⣡⢘⠢⣑⠪⣄⢋⠴⣉⠲⣑⢊⠖⣩⢚⣴ ⠈⠳⣌⠲⣙⢻⢳⢶⣦⣤⣄⣀⣀⡠⢀⠠⢀⠈⣀⠠⢠⣐⣀⣻⣞⣿⣑⠢⢐⡀⠡⡈⠔⡀⠀⠀⠀⠀⠀⠼⣿⣷⣿⣵⣄⣣⢳⢬⡱⣤⣋⣦⣥⣳⣬⣾⡾⢷⣛⢛ ⠀⠁⢌⠳⣌⢣⠞⣲⡘⢦⡹⣙⢏⡟⣻⢛⠿⣻⠿⣿⣿⣟⡿⣿⣟⣾⣧⢃⠆⣄⠣⠘⠤⣁⠂⠀⠀⠀⠀⠈⢽⣷⣿⣜⣻⢻⡟⣿⢻⡟⣿⢻⣽⡿⢏⡱⡜⣡⠎⡜ ⠀⠀⠈⠱⢌⠶⣙⢦⡙⢦⠳⣍⠞⡼⣡⢏⡞⣥⢛⡴⣩⠏⣿⣟⣻⣞⣷⡫⢜⡠⢣⢍⡒⣤⣞⡤⠖⠂⠀⠀⠢⢝⣻⣧⣏⢗⡺⢥⡛⣜⢧⣿⠟⣍⢎⡵⡘⢦⡙⡜ ⠀⠀⠀⠀⠈⢞⡱⢎⡝⣎⡳⢬⣛⡴⢣⠞⣜⢦⣋⠶⣥⣻⡟⡴⣹⣯⣿⣟⢦⡱⢃⡖⣼⡿⠋⠀⠀⠀⠀⠀⠐⢠⢩⢿⣮⢎⠵⣣⠹⣼⣿⣋⠞⣬⠲⡜⣙⢦⡙⡜ ⠀⠀⠀⠀⠀⠈⡜⣗⣚⠶⣩⠷⣸⡜⣫⡝⣎⠶⣍⡞⣶⡿⣱⢣⢇⣳⢻⣿⣶⢩⠳⣼⠟⢀⠠⠀⠄⡀⠂⠄⠉⡄⢊⠾⣿⣬⠳⣌⢷⣿⢣⢮⣙⢦⡛⡜⣥⠲⣍⡜ ⠀⠀⠀⠀⠀⠀⠘⢿⣮⣛⣥⢻⡱⣞⡱⡞⣭⢞⡵⣺⣿⣱⢣⠿⣚⠯⣩⣟⡿⢷⣟⣥⣲⠄⠂⠌⡐⠠⠁⠌⠰⡈⢥⢛⣿⣧⡛⣼⣿⢫⢧⣓⢮⢲⡹⡜⢦⡛⡴⣊ ⠀⠀⠀⠀⠀⠀⠀⠣⣻⣷⢎⡷⣹⢎⡷⣹⠞⣎⢷⣿⢳⡎⢧⣋⠔⣣⡑⢎⣟⣯⣭⡷⠠⢌⡑⢢⢁⠱⠈⢆⠑⡘⢦⢩⠾⣷⣹⣾⣏⠿⣜⡎⣧⢳⡱⡹⢦⣙⠶⣱ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣯⡞⣵⢫⡞⣵⣫⠽⣾⣟⣧⢻⡱⢎⠼⢤⡙⡬⣩⡑⢦⡐⢣⠒⡌⢆⠪⠔⣉⠆⢎⡱⣊⠵⣫⣿⣽⣟⢮⡻⣼⡱⢧⡳⣍⠷⣓⣎⣳⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣜⣳⡽⣣⣏⠿⣽⡿⣜⣧⣛⢬⡓⣎⠶⣱⠱⣎⢧⡚⣥⢫⠜⣌⢣⡙⣤⢋⢦⢣⡝⣺⢵⣻⣿⠾⣭⡳⢧⣛⢧⡻⢼⣙⢮⢖⣥⣛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢣⡷⣝⣳⣞⣻⣽⡿⣝⣶⡹⢶⣙⢦⣛⡴⣛⡼⣲⡝⣦⢏⡾⣌⢧⣙⠦⣏⣎⠷⣜⣧⡟⣿⣟⣯⣳⢽⡻⣼⢣⡟⣧⣛⢮⣏⠶⣭ ⠀⠀⡀⢀⠀⠀⡀⠀⠀⠀⠱⡌⡿⣜⡯⢷⡞⣧⢿⣿⡿⣼⣛⣧⢟⡞⣶⡹⣎⢷⣳⡽⣎⣟⢶⡹⣮⢭⣛⡶⣹⡞⣽⢶⣻⣿⢯⡶⢯⡷⣻⡵⣯⠽⣶⡹⣞⡼⣻⢼ ⢀⠡⠀⠄⠠⢁⠀⢂⠁⡈⠰⡘⡵⢯⡽⣯⣻⡽⣞⡿⣿⣳⣟⣾⣫⡽⣶⡻⣝⣾⣣⢿⡽⣞⣯⢟⡾⣽⣣⣟⢷⣻⡽⡾⣽⡿⣯⡽⣯⢷⣏⡷⣏⡿⣖⢿⣱⢯⣳⢯ ⠄⡂⠍⡌⡐⢂⠡⢂⠔⡠⢡⢱⢫⣟⣽⣳⢯⡷⣯⢿⡽⣿⣞⡷⣯⣟⣷⣻⡽⣾⡽⣯⢿⡽⣞⣯⣟⣷⢻⣞⣯⢷⣻⣽⣿⣟⣷⣻⡽⣾⡽⣽⡽⢾⣹⢯⡾⣝⣮⣟ ⢌⡱⢊⡔⡑⣊⠱⢌⢢⡑⢦⡩⢷⣞⡷⣯⢿⡽⣯⢿⡽⣯⢿⣿⣷⣻⣞⣷⣻⢷⣻⡽⣯⢿⣽⡾⣽⣞⣿⣾⣽⣿⣿⣿⣿⣻⣞⣷⣻⢷⣻⢷⣻⢯⣟⣳⢯⣟⡶⣯ ⢎⡔⢣⡜⡱⢌⠳⡌⢦⡙⢦⡽⣛⡾⣽⢯⡿⣽⢯⡿⣽⢯⣟⣾⣽⣻⢿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿⣽⣳⣿⣟⣾⣳⣯⢿⡽⣯⣟⡿⣾⣽⣻⢾⣽⣳ ⢮⡜⣣⠞⣥⢋⢧⣙⢦⣛⣧⢿⣽⣻⡽⣯⢿⡽⣯⢿⣽⣻⢾⣳⣯⣟⣯⢿⡽⣯⣟⣷⣻⢿⣿⣽⣷⣿⣟⣾⣽⣻⡾⣽⣻⢾⣯⣷⢿⣯⢿⡷⣯⣟⡷⣯⣟⡿⣾⡽
i need my pussy licked so badly(¬`‸´¬)
⣯⣻⣭⡗⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⡀⠀⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠉⠻⣧⠜⣬⢳⣙⢮⡝⣾⣹⣿⢯⣟⣿⣻⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣻⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⣈⠩⠙⡓⠾⠦⣤⢦⣌⣔⣀⡀⠀⢀⠀⠀⠤⢤⣠⣊⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⢫⣜⣣⢽⡶⣭⣿⣿⣞⣷⣟⣿⢿⣿⡿⣿⣽⡿⣿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠂⠄⢂⠡⡐⠄⡒⢀⠂⢄⠠⢉⠙⠛⠲⠚⠶⠶⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠈⢳⡞⣦⢷⣺⡵⣞⣿⣿⡾⣽⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠆⣉⠰⢈⠰⠀⢎⠠⠃⡜⠀⠎⢄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠙⢾⣲⢧⡻⣝⣾⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡘⡰⢀⠒⡈⠤⢉⠤⢁⢃⠌⡁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠳⣯⡷⢾⣿⣿⣿⣽⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⠒⡡⠌⡐⢠⢁⠢⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣽⣿⣿⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⠊⠔⠠⠘⡀⢂⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⢃⠜⡠⢁⠒⡀⠂⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠑⡈⢆⠰⢀⠢⢀⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢡⠘⣀⠒⡈⠔⡀⠆⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠑⢄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠛⠛⠛⠻⠯⣿⣿⡇⠄⠒⠠⠑⡈⠤⠁⡌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠘⣏⠂⠌⡡⠑⣈⠰⠡⢡⠐⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⢀⠃⠤⠘⡀⠆⡈⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠁⡐⠠⠐⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠈⠿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠆⠀⠑⢀⠀⠙⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠰⡀⠈⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡞⢈⠀⠀⠀⠀⠀⠀⠀⡠⣾⢀⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡉⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣦⡤⢤⣆⣶⣶⣦⣼⣇⡈⢹⣿⣿ ⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣶⠟⠀⠀⠱⣄⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠄⠁⡀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡄⠀⢄⡙⢻⡿⠙⣟⠘⢧⣿⣿⣿ ⠙⠓⠶⠤⣦⣐⣠⠀⠦⠀⠄⡐⣈⣵⠚⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⠌⠐⠀⠀⠀⠀⠠⣈⣾⣿⣿⣿⣿⣿⣄⠀⠑⠀⢻⠀⢹⣀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠓⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠘⣆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⠢⠈⠄⡐⠀⣁⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣼⣶⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠳⣌⠠⢁⠠⢀⠠⠀⠀⠄⢀⠠⠀⠄⠠⢀⠠⠀⠀⣤⣿⣶⣶⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⡙⠲⢤⣂⡀⠂⠡⠐⡀⠄⠂⠄⠡⠀⠄⣢⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠒⢤⣈⠉⠛⠶⣒⡲⠦⣥⣈⣤⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⠈⠓⣦⡀⠀⠉⠑⠒⢽⣟⠛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣦⣥⣤⣥⣌⣐⣄⣠⣀⣄⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢂⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⣰⢶⢿⣶⠷⢶⣄⣀⠈⣳⣤⡤⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀⣠⣁⣂⣠⢈⠄⡁⠊⠄⡁⢂⢄⡡⢘⣠⣖⢾⣻⣦⣤⣄⣠⢹⠓⢯⠉⠙⣆⠈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠯⣍⢇⢫⢒⡱⢊⡔⢣⠚⣔⢣⢚⡔⢣⡚⡔⡣⢞⡘⢆⡣⢓⡬⢓⡌⢳⡘⡜⢢⠝⣢⠙⣆⢣⠓⡬⢓⣌⠳⣘⡌⠳⣌⠳⣌⠳⣌⠳⡌⢭⢩⠹⣩⢛⡛⡻⠿⡿⣿⣿⣻⡿⣿⡟⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡳⡽⡞⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠼⣌⢣⡚⠴⣩⢜⡡⢏⡆⢧⣋⠼⣱⡘⣖⡡⢇⢮⠱⣌⢣⡜⣡⢎⡱⡜⣌⢣⢎⢥⢋⡴⢣⡙⡴⢣⡌⣳⡐⢮⡱⢌⠳⣌⠳⢌⠳⡘⣆⢣⢣⢃⠮⢴⢩⣓⣜⣦⣽⣿⣿⣿⣟⠴⣫⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢳⣻⡝⣞⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⠳⣌⠧⡹⢜⡡⢎⡵⢋⡼⢡⢎⡓⢦⡙⣤⡙⢎⡆⢏⡜⣢⠜⣡⢎⠲⣑⢎⡱⢊⡎⡱⣌⢣⡜⡡⢇⠼⢤⡙⢦⡑⢎⠳⣌⠓⣎⠱⢣⡜⢆⣣⣏⣾⣾⣿⣿⣟⡯⢯⡽⢭⢿⣿⡮⣱⢋⡖⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣱⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⢷⠹⡜⣧⢳⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⢳⣌⠳⣍⢎⡵⢣⡚⣕⢪⡓⣬⡙⢦⡹⢤⢛⡬⢚⡜⡲⢥⠚⡥⢎⢳⡡⠞⡴⢋⡴⢓⡜⡲⢌⡓⡎⢞⡤⣙⠦⣙⡌⠳⣌⠳⢬⣗⣣⣼⣾⣿⠿⠟⠛⠋⠉⠉⠛⠳⢿⣎⣟⣿⣷⢥⡛⣼⢡⠣⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⡶⣷⢷⡞⡶⣙⢧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣝⡲⢬⢳⡜⢎⡖⣣⠝⣬⢣⡝⡴⣙⠦⣓⢭⢲⣩⢓⡼⠱⡎⢽⡘⡭⣒⠭⣓⢥⢫⡔⢫⠴⡙⣬⢱⢊⠧⡜⢦⡙⣦⣭⣳⣬⣷⠿⠿⠻⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣎⢷⣡⢏⡳⣜⢢⢒⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣲⣿⡟⠐⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⠛⡉⢋⠛⠳⠧⢎⠳⣁⠆⡀⠀⠀⠀⠀⠀⠀ ⡧⡝⣎⡳⣜⢣⠞⣥⢛⡴⢣⢞⡱⣍⢞⡱⢎⢧⠲⣍⠶⡹⡜⢣⠞⡱⢎⠵⣪⠜⢦⡩⢇⣚⣱⣢⣭⣾⣴⡿⣾⣿⠟⠋⠉⠁⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣾⣔⡫⠵⣎⢧⣋⠶⣑⠎⡔⢢⡐⣄⠢⡐⣄⠒⣄⢣⡜⣜⢾⣹⣿⣿⢿⣶⣬⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣊⠅⠣⠄⡡⠌⡐⠄⢂⡁⠒⡘⢄⢂⠀⠀⠀⠀⠀ ⡳⣽⡸⠵⣎⢧⢻⢬⣓⠞⣭⠮⣕⡺⣌⡳⣍⢎⡳⢬⢳⡱⣍⠧⣋⣵⣫⣜⣦⣽⣶⠷⠿⠛⠛⣭⠉⠀⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣷⣯⢽⣘⠶⣩⠞⣭⢞⡭⢧⡳⣬⢳⡵⣪⡝⢮⣓⠾⣙⣮⣿⣋⣩⣟⣯⣿⢻⣮⣕⡠⢀⡀⣀⢀⡀⢤⣰⣾⣿⡿⣇⢏⡫⡐⢡⠂⡔⣈⠘⠄⡰⠡⢈⠢⢁⠎⡠⠀⠀⠀ ⡷⣣⢟⡽⣎⡟⣮⢳⣎⢿⣬⣳⣭⣶⣹⣶⣭⣮⣷⣿⣶⡿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⡀⠈⠻⢿⣧⠀⠀⠀⠀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⢿⡷⣹⣿⣿⣷⣯⣞⡵⣛⡴⢫⣜⢣⣳⢱⡓⣮⠵⣚⢧⣫⣿⣿⣿⣿⣿⣿⣿⡻⣜⡳⢮⣝⡳⢧⡳⣎⢧⠻⡭⣏⣷⠟⠷⢾⣯⣷⣵⢂⡱⠐⡄⢊⠔⣁⠢⢁⠆⢡⠂⡅⠣⡐⠀ ⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣟⡫⢍⠩⡐⢄⢺⡄⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣻⣷⣶⣿⣿⣶⣶⣾⣿⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⣷⣾⣿⢯⣷⣻⣿⣿⣿⣿⣿⣿⣷⣾⣧⣎⣷⣬⣳⣝⣦⣿⣽⣿⠿⣻⢟⣿⣿⣿⣿⣿⣿⣧⣟⡼⣲⢹⢣⠟⣼⣩⣷⡿⠋⠁⠀⠀⠀⠈⠛⣿⣧⣆⢣⠘⡄⢊⠄⢆⠡⢊⠤⢁⠢⡑⢌⠡ ⢟⣛⣛⠻⣙⢏⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠖⣌⠱⣈⠶⣻⢀⣴⡇⠀⠀⠀⠀⠈⠁⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠉⠀⠀⢠⣦⣿⣟⣿⣻⣞⣿⣿⣳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣛⢻⣛⣯⠘⣿⣭⣿⣿⡱⢎⣿⣿⡙⡿⠿⠿⠿⠿⠿⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠻⣧⣋⠴⡁⠎⡄⢃⠆⡘⢄⠣⡐⠌⡂ ⢎⠴⣌⢣⢃⠎⡜⢿⣿⣿⣿⣿⣿⢛⡻⡱⠚⣄⠋⡜⡡⢍⢢⣿⢧⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠄⠀⠘⣿⣷⣿⣾⣳⣟⣿⣿⡽⣎⠿⣿⣿⣿⣟⣿⣿⡳⣎⠯⡖⡭⢶⣩⣷⢈⢿⡖⣿⣷⡏⢾⣱⣿⠈⢁⠀⠀⠀⠀⠀⠡⡱⡀⠀⠀⠀⠀⢰⣇⠀⢠⠈⣷⣤⣿⣿⣷⣕⢪⠰⡁⢎⠰⡈⢆⠱⡈⠔ ⠎⠑⡈⠆⡉⠒⡈⠈⠿⣿⣿⣿⣿⣷⣷⣿⣿⣀⣱⣠⣵⠞⢫⢁⠆⣙⠲⡆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣦⣾⣿⣿⣻⡟⣿⢻⣿⣿⡝⣮⢻⠼⣿⣿⣞⣿⣯⢳⢭⢳⡹⡜⣣⠖⣿⡘⣎⠟⣿⢾⣏⡳⣭⢿⠀⠀⠂⠀⠀⠀⠀⠀⠱⡜⡄⠀⠀⠀⣸⠻⣤⠋⠀⠹⣯⢳⣰⣿⢻⣿⣶⣉⢆⢣⡘⢄⠣⡘⢌ ⢘⡀⠈⢄⠡⠂⠄⠡⢀⠹⣿⣿⣿⣿⣿⣿⣿⠿⡟⡛⢎⡹⢦⡁⣎⡐⢂⣉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⡿⣭⣿⣿⣿⡞⣵⢫⡝⢾⣿⣿⣿⡞⣝⡎⢧⡓⢭⢲⢩⠷⣹⡼⢿⣿⣿⠧⣝⢮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸⡔⠀⢀⡿⢡⢻⡄⠹⢦⢹⣿⣸⣿⢎⣼⣿⢿⣾⣔⡌⢆⡓⠌⡆ ⠀⢆⡀⠐⡈⠡⢈⠐⡀⠄⠘⢿⣿⣿⣿⣭⢿⡃⠖⡩⣦⣴⣿⣿⣿⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣽⣳⣇⣿⣿⡽⣎⡳⡜⣣⣿⣿⣿⡽⡸⣜⢣⣙⣮⠵⠞⠫⡅⠀⠀⣿⢿⣜⠺⣼⡿⠀⢷⡀⠈⡀⠀⠀⠀⠀⠀⠑⡜⣄⠸⣡⠏⢆⡣⡝⣦⢣⣿⣷⢎⡳⣌⣿⢣⡻⢿⣿⣦⣉⠖⡡ ⠈⡄⢂⠀⠀⡁⢂⠐⠠⠐⠠⠈⢻⣯⣿⣷⣾⣷⣭⣔⠬⣹⣿⣿⡽⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡲⢯⣿⣿⣾⢿⣧⣛⡜⣥⡿⣿⠻⣾⡋⠉⠉⠁⠀⠀⠸⣀⠃⠀⢰⠃⠀⠙⢿⣾⠷⡀⢀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠘⡞⣷⢭⡻⣜⡶⣹⢜⡣⢿⣿⡧⢾⡖⣿⣿⣽⢷⡺⣽⣿⣮⡱ ⠐⡈⠔⠠⠀⠀⠄⡈⠄⠠⠀⠐⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣞⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡘⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠈⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⢿⣻⣿⢾⣁⠀⠘⡇⢷⣽⣦⠤⣀⠀⠀⣔⡹⠀⠀⣐⣦⠀⢀⣴⣿⡂⣁⠂⠠⠁⠀⠉⠀⠀⠀⠀⠀⠀⠰⡘⣧⡝⢮⡹⢱⢪⣼⣿⣿⢿⣻⣿⣾⣟⡿⣾⣷⣿⣿⣿⣿ ⢀⠐⡈⠐⡀⠀⠈⠀⠠⠁⡀⠂⠁⠀⠙⣿⣿⣿⣿⣿⣿⢿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠰⠡⡘⢿⡌⢻⣿⣿⣿⣿⣿⣿⣷⠏⣠⣹⣧⣸⣿⣿⣿⣿⣿⣿⣿⣳⣿⣷⢻⡿⠛⠻⣦⣌⡉⠒⠹⡈⢆⠙⠳⢬⡉⠓⠂⣒⣂⣭⠵⣻⢾⡿⣫⡞⠡⠄⢂⠁⠀⠂⠀⠡⠀⠀⠀⠀⠀⠀⢱⠹⣞⢣⣇⡯⣍⠯⣽⣿⣿⣲⢿⣿⣧⣛⣷⣻⣿⣿⣿⣿ ⡀⠆⢈⠐⡀⠀⠀⠀⠁⠠⢀⠠⠀⠐⠀⠘⣿⣿⣿⡳⣟⣿⡏⢾⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣬⣵⣴⣤⣭⣿⣾⣿⢻⣿⣿⣿⡟⣿⣿⣿⣿⣏⣥⢛⣿⣿⣿⡟⣿⣿⣟⣿⣷⡿⠁⠀⠀⠘⢯⣛⡂⠀⠱⡈⢆⠀⠀⢠⡖⠫⠬⠉⠁⣀⣀⠎⣴⣿⡄⢣⠈⠄⡈⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡶⣞⣷⣾⣻⣿⣿⣿⢭⠿⣿⣿⣿⣽⣿⣿⣿⡿⢿ ⡐⠈⠄⠐⡀⠁⡀⠀⠈⠀⢀⠀⠄⠀⠀⢀⠈⢿⡿⢷⣭⣿⣏⠽⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢘⡬⣷⣦⣮⣽⣿⣿⡝⡜⣌⢻⣿⡟⣘⣧⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⠿⣿⣿⢸⡅⠀⠀⠀⠀⢆⠙⠲⠆⠀⠘⡌⠂⠀⠀⣠⠛⣩⠚⠉⡅⠀⠀⢸⢹⡇⢢⠁⠂⠄⠁⠂⠁⢈⠀⠀⠀⠀⠀⢠⠏⠀⠀⢿⣩⣿⡏⣷⢩⣿⣿⢎⡳⣿⣏⠾⣍⠻⣿⣿⡝⢺ ⠄⡁⠂⠐⠀⠄⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠈⢷⡀⠀⢈⣍⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣟⠰⣣⢾⡛⢤⢻⣿⣿⣿⡿⢉⠛⣿⣿⣿⡿⣾⣯⣷⣿⡇⠈⣇⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠈⠂⠀⠀⢸⠀⡜⠀⠀⡇⠀⠀⡎⢸⡗⢠⠊⠡⠈⠄⠁⠂⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠘⣆⣿⣷⣜⣧⣿⣿⣻⠗⣿⣏⠾⣤⣳⣿⣿⠦⠷ ⢂⠠⠁⡈⠄⠂⢈⠀⠀⠀⠀⠀⢀⠂⠀⠈⠀⠀⠸⢳⡤⠤⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠉⠟⢛⣩⡿⢖⡱⣎⡽⣦⣻⣿⣭⣭⣖⣉⣤⡿⢿⣿⣿⣽⣿⡟⢹⣿⠦⡸⡄⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠘⠰⠀⠀⠀⠇⠀⠘⠀⣸⡇⢢⠈⡐⠁⢀⠈⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢻⡉⠈⠌⠀⣿⣿⣿⣏⢿⡂⠁⠉⠁⠋⠘⠋⠃ ⠂⠤⠁⡐⠀⠌⠀⡀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠁⢀⠘⣿⠉⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢾⡿⣛⣟⣣⢟⡼⣳⣿⠋⠙⡻⠋⠀⠀⠀⠀⢸⣿⣽⣇⠾⠑⢺⣿⡄⠱⡘⡄⠀⠀⠀⠀⢎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡠⢁⠂⠐⠈⠀⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡀⢰⣿⣿⣿⣿⣾⡇⠀⠈⠀⠀⠀⠀⠂ ⡁⢂⠡⠐⡀⠐⡀⢀⠐⠀⠀⠀⠀⠈⢀⠀⠄⠂⠀⠠⠙⣧⠀⠀⣼⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣎⠷⣓⢮⡳⣝⠳⣬⠓⣮⣿⣛⣿⡿⡶⠀⠀⠀⠀⢠⡤⣿⣿⣯⢿⡀⠀⢸⣿⡇⠀⠙⡌⠢⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⡯⢁⠂⠌⢀⠀⠂⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣷⣿⣿⣟⣿⡿⣋⣿⡖⠀⡀⠀⠘⣀⣸ ⠌⡐⢂⠡⢀⠂⠐⠀⠄⠐⠀⠀⠀⠠⠀⠠⠐⠀⠌⠀⡁⠛⣧⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣎⡳⡹⣌⠻⡔⢫⠔⣘⢫⡿⠉⠁⠀⠀⠀⠀⠈⠉⠁⡿⣯⣟⣧⠀⣾⣿⡇⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡱⠀⢠⣿⡇⢈⠐⠀⠀⠀⠀⣀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠛⠛⠛⠾⠃⠉⢩⠀⠃⠑⠁⠀⣱⢟ ⡘⠠⡁⠢⠀⠌⠠⠁⡀⠂⠄⠂⠀⠀⡀⠁⠠⠁⡀⠂⠄⠡⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿⣿⣟⡻⢟⠿⣩⠳⡑⢎⡱⢌⠡⠎⣴⣿⣿⣛⣻⡄⠀⠀⠀⠀⠀⢠⣿⣿⣽⣻⡶⠃⠜⢹⡀⠀⠀⠈⡆⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣎⣨⡏⠠⠀⢈⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣴⡿⢯ ⢌⠡⡐⠡⡁⠌⡐⠠⠐⢈⠀⠂⡁⠀⢀⠠⠁⠂⠄⠡⢈⢂⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⢋⡎⢥⢣⢙⡰⠌⣂⣷⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣼⣷⣿⣿⣽⣇⡟⠶⣦⢧⠀⠀⠀⠇⡇⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠴⢚⣿⡇⢐⠠⠈⢀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡀⠠⠐⠚⢛⣳⣮⢞⡟⣾⣱⢯⣿ ⡊⠔⡁⢒⡀⠒⠠⠁⠌⠠⢈⠐⡀⠡⠀⠄⡈⡐⢈⠔⠂⢌⡐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢢⢃⠆⢆⡱⢈⣿⣿⠿⢿⣿⡛⠻⡏⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠛⠀⠙⣆⠓⢄⡀⠀⡇⢀⢀⠹⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠃⠀⣼⣟⣿⠀⢂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢺⠀⠰⢀⠒⣛⢋⢋⠓⡈⠋⠙⠋⢁⠊⠉ ⡱⢊⠔⡡⠠⡁⠃⡌⠤⢁⠢⠐⡠⠁⠌⡐⠠⠐⠂⡌⠌⠤⣈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣜⠢⡔⢣⠘⣿⣧⠀⢾⡵⢸⠁⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣯⡘⠀⠀⠘⣇⠀⠀⠀⡇⠀⠣⣣⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣧⢻⣇⠐⣶⢀⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⣿⠀⠁⠁⠀⠀⠀⠀⠀⠀⠁⡀⠐⡀⢂⠁ ⡳⡡⢎⠰⡁⢌⠡⡐⢂⠤⢁⠊⡄⢉⠰⢀⠅⢃⠡⡐⢌⠒⡰⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣩⠼⣿⣗⣋⣴⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣐⡀⠀⠀⢹⠀⢀⣀⢣⠀⠀⢹⡗⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⢸⢧⡛⢿⣦⡙⣾⣦⣥⣶⣾⠶⠶⠶⠒⠒⠒⠒⢂⠤⣤⣹⠀⠀⠀⡾⡆⠠⠐⢀⠂⠀⠄⠡⠌⠐⠠⠡⠐⠠⠈ ⣳⠱⣎⠱⣈⠆⣂⠑⣂⠢⠌⢒⠈⡄⠣⣀⠊⡄⢣⠜⣌⢣⢵⣿⣿⡿⢟⢫⢙⠫⠟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⢿⣿⣿⣷⡿⢿⠿⣷⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⠹⣇⠀⠀⢸⠀⡎⠀⢣⠁⠀⢄⠳⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⡀⢻⣧⢛⡥⣿⡷⣟⡻⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢆⡀⠀⡼⢷⠀⡁⢂⠈⠄⡈⠄⡐⠈⠀⠀⠀⠠⠀ ⡱⢏⠶⣩⢒⠬⡄⢣⢐⠢⣉⠂⡅⢢⠡⣄⣣⣼⣧⣿⠾⣧⡛⣿⣿⡑⡊⠔⢂⡈⢜⡘⢇⡛⢿⣿⣿⣿⣿⣿⣿⣿⢷⡭⣿⣞⣿⣿⣿⣸⣷⠿⡞⠘⠛⠿⣿⣿⡿⠿⠛⠁⠀⠀⣿⣆⠻⣤⠀⣸⠀⡇⠀⠈⢧⠠⡰⠅⠀⠀⠀⠀⠀⠀⠀⡞⡰⢩⢿⣟⣷⣫⣾⡫⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢧⣸⡃⠐⠠⠌⡐⡀⢆⠠⢤⠐⢆⠲⡐⡣ ⢧⣋⠞⣥⢫⢖⡩⢆⡣⢖⣤⢳⣼⣶⡿⣟⣻⡽⠿⠷⠦⠽⠿⢯⣿⣶⣡⣊⡔⡈⠦⢭⣆⢩⠒⡌⡑⢻⣿⣯⠙⠛⠛⣓⡿⠿⠯⠌⢿⡼⣬⣙⣤⠖⠀⣉⣉⡤⠔⠀⠀⠀⠈⠑⣿⢈⡆⠨⠟⠃⠈⡇⠀⠀⠀⠳⣙⠀⠀⠀⠀⢀⡰⠀⢀⡏⢡⠃⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠨⡑⢎⡱⡉⠦⣉⠆⣍⠊⡕⡰⢃ ⡷⣎⠼⡐⢏⡮⣵⢫⣽⣯⣾⣟⡽⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣌⣉⣉⡛⠳⠾⣽⣷⣮⣔⣠⣹⣿⣿⠦⠗⠛⠓⠒⠒⠢⠤⢀⡑⠤⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣏⣤⣴⣄⠀⢹⡀⠀⠀⠈⠹⠀⠀⠀⠀⣿⠃⢀⣾⠠⠃⣸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠑⢢⠐⡑⠢⠁⠎⠠⠉⠐⡁⠃ ⣿⣎⡳⣉⠆⠌⠛⣿⣿⣿⠟⢉⠀⠄⠀⠀⠀⠀⠀⠀⣠⠴⢚⣉⠥⠔⠒⠊⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠤⣀⣀⡖⣹⡽⠰⢆⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠋⠀⠉⢣⡀⢧⡆⠀⡀⠀⠀⠀⠀⢰⡟⠀⢸⡏⠂⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠂⠀⠁⢢⠀⠁⠈⢄⠀⠀ ⣿⣯⡳⢥⠚⡌⠀⣿⡿⢃⠌⣀⠂⠄⠀⡀⠀⣀⡴⠋⡥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠯⢤⡚⠁⠀⠀⠀⠀⠀⠡⡀⠀⢄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠠⢀⡀⠀⢷⠘⡄⠐⠠⠀⠀⠀⠀⣞⠇⠀⣾⠁⣰⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠂⡀⠐⡂⠹⣢⢌⢣⠀ ⣟⣿⡽⣣⠝⡠⢡⡿⢃⠌⠒⠠⠀⠄⠂⢀⡞⢁⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠀⠀⣇⡀⠀⠉⠈⠒⠲⢤⣀⣀⣿⣿⣧⠃⣆⢻⡄⢸⡇⣷⠈⡔⠀⠀⠀⣼⡽⠀⢰⣏⣴⣿⣿⣯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⡐⠡⠐⠀⠀⠉⠀⠀ ⣟⣾⣿⡵⣋⠔⣸⢧⡉⢌⠡⠁⠌⠀⡴⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢍⡀⠀⣀⠤⠐⠂⢀⠉⣹⠿⢿⣧⣙⡞⣶⣻⡝⠃⡼⣡⠐⣈⠀⢼⢷⠃⡴⠿⣻⣻⣿⣿⣹⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⠡⢈⠀⠀⠀⠀⠀ ⣟⡾⣿⣷⡍⡖⢸⡆⠱⡈⠄⠃⠀⡼⠁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠔⠉⠁⠉⠻⣦⡀⠹⣶⢳⣿⣿⠇⢰⣏⡶⢁⠆⡈⢜⣺⡟⣧⣴⣷⠿⡄⠙⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢀⠠⢀⠂⣀⠀⠂ ⣿⣻⣿⣿⣯⢜⡡⢎⡑⠄⢃⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢄⡀⠀⠀⠙⢿⣐⠺⡟⠙⠛⢠⣾⣿⢇⣎⣶⣻⣪⠽⣪⣿⡿⠋⢠⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠄⢢⠀⡐⣼⡆⢀ ⣿⣟⣾⣿⣿⣎⠴⡂⢄⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠐⢄⠀⠀⠈⠿⣷⣧⠀⠀⠀⠛⠿⠾⠯⢿⣿⣽⣿⡿⠿⠃⣬⡟⠀⠀⠀⠘⡇⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣤⣷⣳⣿⣿⣼ ⣿⣿⣿⣿⣿⣟⢦⠱⣈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⢳⡄⠀⠀⠀⠉⠹⡗⢦⣤⡀⠀⠀⣀⠙⣿⣏⠠⢤⣶⣿⠁⠀⢀⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⠓⠤⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠈⠢⢈⠢⠈⠙⢂⢻⣭⣭⣍⡔⣾⣿⠟⡃⠀⠀⠈⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⣌⣿⣿⣿⣿⣿⣿⡟⣽⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡨⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠎⣐⣾⣿⣿⣿⣿⣻⡿⢃⠜⡋ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠡⢎⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢻⣾⣿⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠑⠠⣾⣿⣿⣿⡧⠟⡍⠰⢸⡀⢣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣈⠜⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⠍⣾⣿⡹⢎⡱⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠍⣂⢉⣼⣿⣿⡿⢃⢞⡰⢨⣑⠣⡜⠤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢤⠃⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢖⡡⢏⣼⡷⣙⢦⠓⡆⣍⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡒⢌⠢⠌⢠⣾⣿⣿⠟⡬⢍⣆⢣⠓⣌⡓⡘⢆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠤⣉⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⡙⢦⡙⠆⣾⣏⢳⢪⠝⣰⢊⡕⢪⠜⣐⠢⢄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠆⡱⢈⠆⡱⠈⠆⣼⣿⣿⡿⡑⢎⢖⣷⢊⣦⡽⢻⢇⡙⢆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣣⢆⡱⢈⠡⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢆⡱⢊⡜⢢⠑⢨⣿⣯⢓⡌⠚⢄⠣⠜⡣⢎⠥⣋⠦⡍⢦⠱⣈⠒⣄⠣⡐⡐⢢⠘⡄⢣⠌⡱⢌⠢⡑⢌⠢⠑⣬⣾⣿⡿⣫⠴⣉⢎⣾⢃⣾⣱⠏⡍⢦⡉⢎ ⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⠫⡔⡡⢌⠒⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠰⣈⠦⡘⠦⣑⠣⠘⡀⢨⣿⣿⣻⡜⠤⢉⠠⠈⠂⠱⡈⢦⣡⠟⡘⢆⠳⡌⠳⢌⠲⣡⠙⠆⡭⢐⠣⡘⠰⡈⢂⠅⡿⢠⣽⣿⣿⣿⡿⢋⢞⡡⣾⢫⢬⣭⣷⡟⣹⣦⠹⣌ ⣿⣻⣿⣻⣿⣿⢿⡿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣜⡴⢨⠜⡠⢑⠠⣁⠂⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⡐⢌⠢⣌⠲⣄⢣⡙⠔⢂⠁⠀⢰⣾⣿⣿⢧⡿⣼⣀⠆⠁⠂⠁⠀⣿⡟⠠⠑⡈⠒⣈⠱⢈⠱⡀⠍⢒⠠⢃⠂⠡⠑⣺⣦⣼⣷⣿⣿⣿⡿⠏⡴⢉⢆⡳⣍⢲⣛⠷⡶⢟⣛⠫⣕⢮ ⣿⣿⣽⢿⠃⣼⢏⢖⣙⠲⢬⢩⠝⣛⠻⣿⣿⣿⣷⢻⣿⢻⣿⣿⣿⣿⣿⣷⣧⢎⣱⣌⠒⠤⡑⢌⡐⠂⡌⠰⡈⠤⠐⡠⠄⢠⠀⠤⢀⠄⡠⢀⠄⡠⠄⡐⢠⠂⠤⢃⠜⡠⢣⠰⣑⠪⠱⢄⠃⢆⠢⠌⠐⠀⠀⣤⣿⣿⣿⢿⣿⣷⣧⣟⣾⣱⢂⠆⠸⣧⠇⠀⠀⠀⠁⠀⠐⠈⠀⠐⠈⢀⣠⣄⣌⣦⣵⣾⣿⣟⣽⡿⣙⡍⣲⢉⡖⣩⠦⣹⡇⠶⣉⣮⣱⠮⠖⠋⢉⣰ ⣿⣿⡏⢣⢘⡿⢌⠎⣆⢛⣤⡓⢎⠥⡓⡔⢢⠍⢯⠹⣿⢸⢫⣿⣿⣿⣿⣿⣿⣿⣾⣿⣮⠱⡌⢢⣾⠇⡌⠱⣀⠣⡑⠰⡈⢆⠩⡐⢡⠊⡔⢡⠊⡔⢡⠊⢤⢉⠒⣡⢊⡑⢢⠑⡄⠣⠑⡈⠌⠀⠀⠀⢀⣠⣾⣿⡟⢃⣠⠴⠚⠉⠉⠛⠿⣿⣿⣿⣷⠶⠒⠲⢤⣄⣀⣠⣀⣄⣢⣴⠞⠉⠁⠀⠀⠀⢩⣟⠻⣏⣁⣉⣉⡷⣡⢏⡴⣹⣒⣿⠵⠛⢉⣁⣤⢶⢚⡛⡭⣿ ⠰⣛⡘⡄⢊⢻⣮⡜⣠⣿⣉⡿⣿⡦⣙⡼⣟⣻⣎⣹⡇⠠⢻⢩⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣬⣿⡟⡜⣌⠣⡜⢤⠡⢃⡜⢠⠃⡜⢠⠃⡜⢠⠃⡜⢠⠉⠆⡌⡘⠄⣂⠘⠄⡈⠄⠁⠐⠀⠀⢈⣠⠞⠋⠉⢹⣧⠼⠋⠀⠀⠀⠀⠀⠀⠀⢈⡿⠞⠓⠢⠔⠀⠀⠚⠛⠋⠉⠉⠉⠁⠀⠀⠀⣀⡠⡔⠉⠛⠓⢻⣍⡳⢎⣵⣮⠞⠚⢭⣙⣶⣶⣿⣿⣩⣜⡦⠗⠊⠉⠙ ⡑⢢⡑⢌⡢⠄⢻⣿⢳⣶⠿⣿⣹⣿⣼⢿⣾⡷⢾⡓⣃⢆⠣⢆⡍⢻⢶⣌⡹⣛⢿⣿⣿⣿⣿⣿⣿⣿⣇⣳⡜⡜⣷⣧⣘⢢⠩⡔⢣⠘⡄⢃⠒⡈⠄⠃⠌⡐⠀⠂⠄⠐⠀⠀⢀⢂⣠⣦⣽⣾⢁⡀⠤⠒⠛⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣞⢻⡛⣟⡛⡿⢷⡤⡴⡖⢯⠳⣽⣟⣅⡀⠀⠄⠀⢸⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀ ⡜⢢⠜⡌⢻⣦⣸⣿⡏⢽⣻⣟⣛⠭⣊⡟⣛⡙⢦⣱⢃⡎⣹⢲⣜⡣⢎⢻⣶⡑⣮⠎⣝⡻⣿⣿⡿⣿⣿⣿⣿⣿⣶⣿⣷⣾⡕⣮⣥⢏⡴⣣⣼⣤⠷⠚⠓⠉⠈⠁⠚⠒⠈⡾⠟⢛⣛⣋⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠾⠾⠧⣽⢦⡹⣱⠧⣞⡱⡽⣩⢏⣿⣿⣿⣿⣧⣄⠢⣄⡀⠉⠓⠤⣄⡐⠀⠀⠀⠀⠀ ⣷⣃⡚⣄⡃⢿⣿⣿⣗⣃⢆⠣⣜⣾⣉⢓⣭⣪⢕⣋⢏⡱⣣⣇⢧⡛⡥⠳⣜⡻⣜⣻⢶⡱⣌⣛⠳⣍⢾⣹⢻⡟⣿⢿⣿⣿⣿⡿⣿⢿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣉⣭⣥⣤⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢶⠷⡶⢿⡷⣤⣤⢤⡴⣞⠧⣱⣬⢳⣜⡳⣽⣱⣫⣾⣿⣿⣿⣿⣿⣿⣶⣧⣔⡠⠀⢀⠈⠭⢓⠦⢄⡀ ⣿⣷⡈⢆⢲⣾⣿⣿⣧⣞⢺⣳⣿⣶⣤⢣⢖⠻⣷⣭⢦⢧⣿⡖⣳⢬⣳⠹⣴⣙⠶⣥⢧⠷⣜⣦⢷⣫⢷⣭⠷⣹⣎⣷⡹⣎⢧⡝⣶⡹⢮⣝⣻⣷⠖⠂⠀⠀⢤⢶⡶⣛⣯⣛⣮⡽⣭⣛⢿⡻⢿⡿⠓⠀⠀⠀⠀⠀⣠⣤⡶⣶⢶⢦⠀⢀⣀⢀⣾⡿⣹⢎⣯⣛⣭⢳⡹⢶⣹⣮⣵⣫⢟⡶⣭⢷⣛⠛⡉⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣔⣀⡄⠢⣌ 🌸⭐️🌈☀️
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣀⣀⣄⣠⣀⣒⣤⣡⣋⡽⣿⡏⠘⢿⣿⣿⣿⣿⣟⣯⣿⡾⣟⣯⢿⣽⣻⣟⣿⣿⣻⢿⣽⣻⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣛⣤⣶⣿⡿⣿⢿⡿⣿⠿⣿⢻⠟⣿⣻⣷⣿⢉⣼⣿⡙⣿⣿⣿⣻⢷⣿⣻⡞⣿⣺⢷⣻⣽⢾⣟⣯⣷⡿⣽⣿ ⣿⣿⣿⡿⣿⣻⣿⢿⣿⣿⣿⣿⢿⣾⣿⣤⠙⠻⠷⣿⣟⡻⣜⠹⠡⢋⠔⠁⠉⣄⢃⢌⡲⣽⣿⣇⢋⡭⠮⢳⣽⣿⡷⣿⣻⣞⣷⢻⣳⣭⡟⣷⢯⡿⣾⣟⣯⣿⢿⣽ ⣿⣿⣯⣿⣟⣿⣻⡿⣯⣿⣿⣟⣿⣳⡟⣿⡿⢋⡍⢫⣿⣵⡬⢔⣧⣲⣽⣦⣷⣿⣾⣾⣶⣶⣾⣿⣥⣀⣠⣾⢿⣿⣿⣽⣳⣟⡞⣯⢳⢮⡽⣞⢯⡟⣷⢯⡿⣽⣻⢞ ⣿⣿⡿⣾⡽⣞⣷⣻⣽⣳⢿⡾⣽⢯⣷⣕⡜⡁⣀⣧⠟⣿⣿⣿⣿⣿⡟⠿⣛⡛⣯⢻⡝⢻⣹⢿⣿⣄⠉⠿⣷⢜⢿⣷⣻⡼⣹⢎⡟⡮⢵⢎⡳⣝⢮⡳⣝⢧⣏⡟ ⣿⣿⣽⢳⣿⢹⡖⢳⣮⣽⡏⣷⢫⣿⣯⣿⢻⠛⢹⣿⢠⢻⣿⣿⡟⣥⠛⡕⢢⡔⡌⢳⡞⠋⡅⠊⣿⣷⣦⡄⢹⠂⢫⣿⣿⣷⣯⡞⢹⡜⢣⡞⣵⣮⢳⡝⣼⠚⡜⣾ ⣿⢧⢯⢷⡺⣝⣞⠳⣎⠷⣹⢎⣿⡿⣿⣞⣳⡹⣠⣿⣀⣼⡿⣿⣟⡻⠓⡝⡠⡄⠉⠼⡑⢢⠃⡸⣿⣿⣽⡈⠃⢈⢢⠑⢻⡌⢻⡿⣧⢯⡹⣞⣱⣞⡣⡽⢥⣛⡷⣹ ⣯⢟⣮⢳⣝⢺⡜⣝⠮⣝⣣⣾⢿⣿⡿⣿⣽⣧⡿⣷⣳⣿⣿⣷⣞⡹⢍⠁⠀⠈⠑⠦⡣⠎⡐⢁⣾⣿⣷⣿⢡⣀⠊⠄⢰⠱⣮⣷⠘⡉⠻⣯⠱⡮⣵⢽⣫⢞⣵⠓ ⣿⢺⢬⣓⢮⡳⡝⢮⡝⢮⣿⢭⢻⣿⣟⣿⣿⣿⣿⣻⣽⣿⣿⣟⢯⣋⠵⠊⢄⠰⠄⡀⢣⠊⡠⢾⣿⡹⣽⣯⠷⣑⣌⢬⣠⢿⣽⣿⡧⠁⠀⠀⠃⠈⠌⠏⢺⠛⠁⠀ ⣿⡭⢖⡭⢞⡱⣏⠳⣜⢯⣷⣮⣻⣿⣿⣿⣯⣿⡟⣽⢾⣿⣯⡻⣷⣮⣷⣾⣤⣈⠖⢦⣕⡢⣯⣿⢳⡳⣵⢻⣿⡵⡿⣿⣿⢿⡿⣿⢏⡱⠀⠀⠀⠀⠈⠀⠀⢂⠀⠀ ⡿⣇⠯⡜⣭⢳⣮⣟⣾⣿⡾⣇⠣⢿⣻⣿⣿⠋⣼⡏⠹⣜⡿⣿⣫⢟⠹⢿⡿⣷⣾⣴⣼⣞⣿⢿⣯⢳⡭⣏⡟⡿⣷⡹⣿⣧⣷⡐⡎⠴⡡⠀⠀⠀⠀⠀⠀⠀⠢⡀ ⡿⣝⢲⣹⢞⡿⢬⡟⣲⢯⠰⣌⢳⣿⣿⡿⠗⢩⠙⠀⣡⢷⣿⣽⣷⣞⡥⢊⣿⡶⣣⠽⣚⠌⣯⣟⢮⡓⣷⡹⣞⣵⣫⢝⡿⣛⢯⣿⣿⣶⡡⠳⣄⠀⠀⠀⠀⠀⠀⠐ ⡟⡽⣢⡟⢮⡱⢫⡜⢧⢋⠖⣬⣿⣷⣷⣾⣮⣵⣊⡰⣥⣿⠿⠿⡻⢿⠿⣷⡿⣽⢗⡫⢼⠣⢌⠩⠓⠉⠉⠀⠀⠀⠀⠉⠳⡹⠺⣟⣿⣽⡿⠑⠒⢧⡲⣌⠂⠀⠀⠀ ⣍⠷⣵⣫⠧⣙⢣⠞⡥⢊⡜⡰⣛⠿⣻⣿⣾⣿⣿⣿⡿⢡⠎⡑⠰⣈⠲⢡⠚⡔⢊⢴⠉⢎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⡏⠀⠀⡐⠀⢳⣌⠱⠀⠀⠀ ⢧⣻⡿⢥⠓⡍⣎⠳⣌⠣⡜⣱⣮⣶⣿⣿⢿⣻⣞⣿⢫⡕⢪⢌⡱⢀⠣⢃⡑⡨⠊⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠆⡥⠊⠀⠀⠀⢳⣡⠂⠀⠀ ⣷⡛⡬⢣⡙⡔⣊⠷⣌⢧⣽⣏⠷⣭⣛⡾⢯⡷⢾⡽⣷⣝⠧⣎⠴⣉⠦⡡⠊⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡆⠀⠀⢬⣇⡅⠀⠀⠀⠀⠀⠣⡙⠤⠀ ⢧⡙⡔⢣⠜⣰⠭⣟⠋⢸⣳⢎⣟⡲⡽⣜⡳⣝⢯⡽⡗⡾⢿⣮⢳⢡⠞⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠃⠀⠀⠀⠹⣌⠂⠤⠄⠀⠀⠀⠹⣡⢃ ⠣⡜⡬⠑⠈⢁⣼⢷⡣⠀⢯⠙⠺⣵⢣⠏⡵⢋⡞⡲⠽⡝⡽⢾⣣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⡏⠞⠀⠀⠀⠊⠀⠀⠁⠀⠁⠀⠀⠀⠀⠘⢎ ⠃⠀⠀⠀⠠⣼⢻⠷⣯⣳⢵⣅⠀⠈⢧⡛⣜⢣⢞⡱⣋⠽⣝⡿⣧⢫⠔⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠁⠀⠀⢠⢇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⣸⢷⢏⡹⣎⠹⣏⠹⡏⢷⢸⢱⠎⡸⢆⢇⡉⡎⢹⡿⣿⠹⣆⠀⡀⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⣸⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⣎⢧⡛⣬⢓⡎⣷⣽⣾⢏⢣⠚⠱⡈⠢⠐⠊⠀⡽⣿⣟⢤⣎⠔⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢎⣯⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⢲⢯⡜⡜⢦⡙⢦⢋⡜⠬⡘⠠⠈⠀⠀⠈⠀⠀⠀⠀⠀⢹⡿⣿⠞⡡⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠼⣸⡷⢣⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣤⡟⣦⢹⡘⢥⡙⢂⠣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⢺⢁⠂⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠙⢿⣹⣊⠔⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⡾⣙⢤⠣⠜⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⡋⠖⡀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢎⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠓⡜⠂⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡙⠦⠁⠌⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡵⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⡍⢃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡚⠅⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⡾⠑⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠣⡜⢡⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣍⢶⣟⢣⠅⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡘⠣⣄⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⢀⣠⡴⢡⠰⡹⣌⠿⣼⡎⠌⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠆⠀⠣⡀⠀⠀ ⠀⠉⠀⢈⡰⠊⢇⡰⣬⢳⡳⢭⠳⡄⠰⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠳⡀⠀ ⢢⢉⡼⠋⠀⠀⣆⡳⣿⣧⢻⣭⠳⡌⠱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⠀⠀⠹⡔ ⡀⠉⠀⠀⢀⠲⡼⣽⢿⣷⣯⢞⡳⣍⡑⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠂⠀⠀⠈ ⠀⠀⠀⠠⡘⢧⣿⣻⣿⣼⣿⣿⣻⣄⠻⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⣃⠀⠀⠀ ⠀⠠⢌⢣⡝⣯⣞⣷⣻⣾⣽⣿⣷⢎⡷⡑⢎⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⢆⣃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠯⢷⣃⠆⠀⠀ ⠰⣉⢎⣧⢻⡵⣫⣾⢿⡽⣯⣟⣿⣯⢶⣙⢦⡑⣎⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢹⣾⣯⢷⡌⣧⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⣇⡊⠀⠈⢫⠄⠀ ⢣⡝⣎⡞⣧⢻⡿⣝⢯⣞⡳⣏⣾⢻⣷⣟⣮⡗⣦⡱⣊⠴⣁⠦⡐⣄⠢⢆⡳⣼⣿⢾⣽⣯⣷⡱⣍⠦⡑⢠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠒⣴⡯⢀⠀⠁⠀⠀⢯⠄ ⡳⣜⣣⡝⡮⢿⣻⣽⣚⢶⡹⣞⡼⣯⡟⣿⣻⢿⣷⣿⣵⣻⣼⣳⡽⣎⣿⡭⢿⣿⣿⣛⣻⢳⣿⣽⣾⣶⣙⢦⣃⢮⡱⣌⢦⡱⢪⡜⢆⡦⠟⠉⠀⠀⠀⠀⠀⠀⠸⡜ ⣳⡜⢒⠩⡐⣿⣟⣧⡟⣮⢳⡝⣾⡱⣏⠷⣭⡻⢾⣽⣻⢿⣿⣿⣿⣧⣤⢤⡟⡯⢏⡽⣍⠟⡼⢫⠟⡲⠽⣷⣿⣮⣷⣞⣧⢿⡷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯ ⠡⡄⢃⠆⡐⣿⣟⡾⣝⣮⢳⡽⣖⣻⣜⡻⢶⣹⢳⢮⣝⣯⢾⣛⢧⠻⡜⢣⠚⢁⠃⠒⠈⠘⠀⠁⠈⠁⠐⠀⠘⠛⢛⠞⣩⠖⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢶⣛
⠀⢀⣠⣴⣷⣶⣖⠀⠀⠀⡀⡀⢀⣀⠠⠄⠀⠀ ⠀⢼⣿⣿⣿⣿⣿⣶⠋⠀⢸⣿⣧⡀⠀⠀⠀⠀ ⠀⠸⠿⣿⡿⠲⠀⠀⠀⢨⣾⣿⣿⣇⡠⢤⡒⠈ ⢀⠈⢀⡀⠀⠀⠀⠀⠸⢿⣽⣿⣿⡏⠁⠀⠀⠀ ⢸⣶⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀ ⠈⠻⣿⣷⣄⣠⡄⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⢰⡙⠻⣿⣿⡇⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⠀⠀⠈⠉⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⡀⠀⠀⠀⠀⠈⢸⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣷⡄⠀⠀⠀⠠⢸⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⡇⠿⠀⠀⠀⠀⣆⢠⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠃⡄⠀⠀⢀⣶⢻⣼⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⢠⣾⡇⠈⢿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠛⠛⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀
𒅒𒈔𒅒𒇫𒄆༒︎✞︎𖤐🃜🃚🃖🃁🂭🂺𒀱☭̼͙̈́͆̈́ͯ̒̆̀̓ͧ͠𒈓𒈙 ⃞⃤⃟⃤⃝☺︎⃢ ̶̿̀͊̍̈́͑̓̈́̃̆́ 𝄃𝄃𝄂𝄂𝄀𝄁𝄃𝄂𝄂𝄃𓁹‿𓁹⚝♛☻𒐫𓂀ﮩـﮩﮩ٨ـ🫀ﮩ٨ـﮩﮩ٨ـ𒋨☬⎛⎝ ≽ > ⩊ < ≼ ⎠⎞♱󠀽🃜🃚⛆✮❦⛧☾༺♰༻☽⛧♚▶︎ •၊၊||၊|။||||||||• 𝟎:𝟏𝟎▄︻デ══━一༒︎✞︎𓂋 ཐི❤︎ཋྀ📓༒�𒈔𒅒𒇫𒄆̦̘̼͔͈̲̝̺̰͗̋̅̈̚]̶̟̟͙͖̣̩͈̳̭̍͒͛̍ ूाीू㋛๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆ܻܻࣩࣩࣩࣩࣩࣩ࣯ࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩ݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅ࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤ์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋ືືືືືືືືືືືືືືືືືືືືືືືຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶຶ᪴᪴᪴᪴᪴᪴᪴᪴᪴᪴᪴᪴᪴᪴᪴           ︎︎ ︎︎︎︎ 𝟑 ︎︎           * ҈҈҈҉҉҉҉҈҈҈҈҈҉҉҉҉҈҈҈҉҉҉҈҈҈҉҉҉҈҈҈҈҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҉҈҈҈҈҈҈҈‌҉҉҉҉҈҈ًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًًٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍٍّّّّّّّّّّّّܑܑܑܑܑܑܑܑܑܑܑܑܑܑܑܑܑܑܑܑܑܑܑ๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊ܻܻܻܻܻܻܻܻܻܻ݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆ܻܻࣩࣩࣩࣩࣩࣩ࣯ࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩ֟֟֟֟֟֟֟֟֟֟֟֟֟֓֓֓֓֓֓֓֓֓֓֓֓֒֒֒֒֒֒֒֒֒֒֒֒֒֒֒֒֒֒֒֓֓֓֓֓֓֓֓֒֒֒֘֘֘֘֘֘֘֗֗֗֗֗֗֗֗֗֗֗֗֗֗֗ؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؖؕؕؕؕؕؕؕؕؕؕؕؖؖؖؖؖؖؖؖؖؖؖٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞٞ٘ۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛۛܺܺܺܺܺܺܺܺ݉݉݉݉݊݊݊݊݊݊݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅ࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤ ๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆ܻܻࣩࣩࣩࣩࣩࣩ࣯ࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩ݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅ࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤ์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์๋๋ ๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊๊݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆݆ܻܻࣩࣩࣩࣩࣩࣩ࣯ࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩࣩ݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅ࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣧࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣨࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤࣤ์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์์๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋๋ືືືືືືືືືືືືືືືືືືືືືືືຶຶ⃤ ⃤�‍⋆༺𓆩𓆪༻⋆⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤ ⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤⃤✩₊˚.⋆☾⋆⁺₊✧
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡽⢭⢳⡉⢧⠙⡌⠥⢋⠌⡱⠈⠆⢡⢋⡜⢯⣟⡿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡷⣹⢎⡱⡘⢢⠉⡄⠃⠌⡐⠠⠉⡌⡐⢂⠞⣱⠾⣽⠟⠺⠙⠀⠉⡤⢋⠠⠀⠉⠀⠛⠓⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⢣⢎⡱⠌⢢⠁⢂⠁⠢⢄⠱⣨⠰⣡⢋⡞⡭⠛⠀⠀⠀⠀⠈⠛⢛⣉⣀⣀⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣝⠮⡔⢃⠄⠈⠄⡈⠔⣨⢒⡥⣳⢥⣻⠞⠀⣀⣴⠾⣛⣭⣉⡁⠐⢪⣥⣞⣭⣻⢶⣤⡠⣀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣻⣽⢯⣿⣟⣿⡻⣟⢿⡿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⠁⠉⠙⠞⢬⠄⢂⠠⡐⡜⣢⢟⣼⣳⡿⢁⣤⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⢻⣿⣿⣿⣻⣽⣞⢯⣞⡹⢲⣙⢮⡓⠿⠙⠉⠀⡀⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠁⠂⠄⠀⠀⠈⠀⠑⠺⣵⣻⣯⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣠⣿⣿⣿⣿⣷⣻⣞⡼⠱⠉⠈⠀⠀⠀⠠⡌⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠙⢿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣾⢿⣿⣿⡿⠏⠁⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⢰⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠃⠀⠀⠀⠀⢂⠸⠢⢤⣀⡀⠀⡘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢛⠡⠀⢀⡀⠄⠐⠂⠈⣁⠂⠀⠀⠀⠀⠀⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣿⣻⢿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂⢇⠠⠀⠉⢉⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠄⠂⠁⠀⠀⠀⠄⢀⠆⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⣾⢳⢯⣟⡳⡝⢮⠻⣵⢻⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠼⡀⠡⠈⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡹⡐⢏⠞⡴⢹⡘⢣⡙⠤⢋⠝⡹⢞⡽⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣥⣺⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢂⠐⠀⢀⣠⠴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⡿⣟⡿⣽⢫⢷⢫⡟⣽⢿ ⡁⠜⡈⠜⣌⠣⡜⢡⠐⡂⠄⡘⢄⢃⠲⣩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⡻⣏⢧⢫⢡⠁⠀⠀⠀⠀⠀⠀⠀⡘⣾⣿⣿⣯⣿⡽⣺⢥⣋⢎⠳⡜⡹⣞ ⡘⠄⢣⠙⡤⠳⡜⢆⡳⡘⢤⠓⡬⢎⠳⢣⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⢿⣾⠇⠂⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⡷⡿⡵⢆⡇⢎⡱⢊⡵⢫ ⡜⣌⠣⢎⡵⢋⡜⣣⠖⡹⣌⠣⡝⡌⢣⡙⢺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢈⢿⣛⣹⣿⣿⣿⣿⣿⣿⣿⢧⣀⣴⣬⣷⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣻⡞⡈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⡝⣮⠜⣣⠜⡱⢎⡷ ⡼⢦⠿⡼⡜⢧⠞⡥⠞⡵⠬⡱⠬⠬⠥⠼⢱⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⠻⡿⣷⣾⠿⣿⣿⡿⣿⠙⠸⣛⡿⠿⠧⣏⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⠷⡿⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣯⢿⡼⡽⢦⡻⣭⠿⣼ ⣟⡻⣞⢳⣛⠞⣎⠵⣋⠲⣁⢓⡘⢂⡓⢌⠳⣜⡂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢀⠅⡉⡉⠅⠀⠉⢈⢁⠁⠀⢠⠤⢖⠲⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢃⡁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣻⣿⣿⣿⣿⣷⣿⣻⢷⣻⢷⣻⢷⣻⢿ ⡟⢳⡟⠻⡞⠻⡜⠳⢩⠓⡍⠲⡌⠣⡜⢩⠓⡞⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⣿⣿⣿⣿⣿⣧⠺⠑⠉⠎⠀⠜⠃⠀⠀⠊⠂⠋⠪⠁⣾⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⡷⡟⣿⢻⡟⣿⢻⣿⣿ ⣿⢻⡽⣳⢟⣳⢛⠷⣋⠾⡱⠦⡙⢦⠳⡙⡞⡵⢻⡄⠀⠀⠀⠱⠀⠀⠀⠀⢃⠀⠙⢿⣿⣟⣿⣿⣗⣄⡀⠀⠀⠰⠇⠀⠀⠀⠀⠀⢀⠴⢋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⢿⣳⢿⣻⢿⣻⢿⡿⣿⢿ ⣿⣻⣟⣿⣻⢟⣻⡟⣯⣛⠽⣩⢹⡉⢏⡝⡩⠝⣍⢳⡀⠀⠀⠀⡘⠀⠀⠀⠸⠀⠀⠈⢻⡽⣯⢿⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⣾⢻⣟⣿⢿⣿⣿⠟⠋⢁⡀⠁⠀⠀⠀⣀⠁⠀⠀⢠⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⣿⢿⡿⣿⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣟⣿⣻⣝⣻⣍⣳⢛⣍⢫⡝⣩⢍⣋⢧⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⣿⣝⢾⡽⣿⣷⣄⡂⠀⠑⠒⠶⠚⠁⠀⠠⢎⢻⠷⣩⡾⢯⣿⠟⠡⠐⠈⢠⠁⠀⠀⠀⢠⢹⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣯⣿⣯⣿⣯⣿⣭⣯⣭⣭⢯⣬⢭⡜⡭⢬⡍⣬⢇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠸⡹⣎⢿⡛⠟⡛⡹⣖⢤⢀⢀⢠⠔⡊⣠⡞⣸⢻⡴⢁⣶⠟⢀⠀⠀⢀⣏⢀⡀⠀⠀⠈⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣼⣷⣎⣷⣜⣲⡜⣴⢣⡜⣴⣊⣆⠀⠀⠀⠀⠀⠈⣴⢣⠀⠀⢰⡇⢹⣞⣧⡀⡴⢁⢫⣦⣋⠜⣢⡳⢊⣽⣠⣟⣷⢷⡿⠁⠠⣜⠀⠀⡼⢸⣸⡜⡃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣟⣿⣻⣟⣯⣻⣭⣳⣭⣚⣴⣉⣦⣙⣤⣃⣜⣐⣢⣜⣂⠀⠀⠀⣐⢀⢿⢈⡄⡆⣼⠁⠀⣿⡟⠈⠪⣄⠈⣦⠈⠉⠁⢀⠎⢻⣾⣿⣿⠁⠀⠀⠀⠀⠀⢰⠇⢯⡌⡇⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢾⡿⣾⡽⢶⢯⠶⡵⠾⡼⢷⢮⠿⣧⠀⠐⠃⠼⡂⠘⡧⠟⠁⠀⢀⣿⠃⠀⠀⠄⠙⢺⡄⠀⠀⢎⠔⢋⣿⡿⣿⡆⠀⠀⠀⠀⠀⢸⠰⠘⠾⠐⠠⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣷⣳⣽⢫⣎⡷⣭⢳⡝⣞⣮⣟⣾⣷⡀⠌⢃⠀⢈⠡⠀⠓⠰⠛⠁⠀⠀⠀⠀⠰⠀⠟⠀⠘⠎⠀⠨⣿⣇⠻⣿⣄⠀⠀⠀⠀⢸⡄⢠⣤⠃⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣯⢿⣮⢷⡽⣷⢿⣽⣾⣽⣿⣿⣿⡆⠈⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠙⠿⢤⠈⠙⠛⠉⠀⠀⠀⡇⠘⠁⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡾⣽⡿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⣞⣿⣞⣯⢿⣽⣻⣾⣯⣿⣿⣿⣿⣷⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣟⡿⣿⡿⣿⣿⣿⣿⣿ ⣯⡽⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣿⢿⣾⡿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢯⡻⡝⡮⢽⣩⢛⡵⢻⣝⡳⣟⣿⣻ ⣷⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣯⡷⡽⡼⢥⠣⢆⠧⡜⢥⠮⣵⢫⡶⣿ ⣯⡷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣟⢾⡱⢣⡓⠬⢁⠂⡐⢈⢂⠳⣌⠳⣝⡷ ⣿⣟⡿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣟⣿⣯⢷⣎⢷⣩⢓⠬⡱⢈⠔⡀⢂⠄⡣⢜⡹⢮⡽ ⣿⢾⡿⣿⢿⡿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢿⡾⣿⢞⡳⢮⡙⡖⣡⢃⠖⡠⠣⡜⡔⣫⡜⣷⣻ ⣯⢳⠯⣝⢯⡽⣳⢯⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢾⣟⣿⡳⣯⡝⣧⡝⡼⣡⢎⡜⣡⢳⡘⡼⣱⢞⣵⣻ ⠧⡍⡞⡜⢎⠶⣙⢮⡳⢯⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠔⢊⠉⠔⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠍⠒⠢⠄⠀⠀⢸⣿⣿⣿⣿⣾⢿⣻⢾⡽⢧⣛⢶⣹⠲⡕⡮⣜⡱⢦⢯⡵⢯⡾⣽⣻ ⢳⡘⡴⣉⠮⣱⠩⡖⡽⣛⡾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣿⠀⢀⡹⣈⣆⠎⠤⠊⢦⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⡾⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⢸⣌⡆⣩⠆⠀⢸⣿⣿⣿⡷⣿⢿⢯⡿⡽⢯⡽⢞⠶⣫⠝⣶⠹⣞⡽⣮⣽⣯⣿⣿⣿ ⢣⠜⣰⢡⠓⣌⠳⣌⡱⢭⡻⣽⣻⣯⣿⣿⡿⣿⡽⣞⠽⣍⠯⣝⢿⡃⠀⡵⢺⣼⣻⢄⠃⣆⠀⠀⠀⠀⠀⠻⠁⠀⠀⣰⡏⣷⠀⠀⢀⢺⠀⠀⠀⠀⠀⠀⢌⡡⣿⣷⡽⣒⠇⠀⣾⣿⣿⣳⢿⡹⣞⢧⡛⡵⢣⠞⣩⠞⣡⢛⡴⢻⣜⣳⡽⣞⣷⣿⣯⣿ ⢣⢎⡱⢊⡑⢢⠑⡤⢃⢧⠻⣵⣻⢿⣽⡿⣟⣷⢻⣌⠳⣌⠳⡘⢮⠽⣀⠈⠳⣌⠣⢎⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢃⢹⣧⡀⠸⠾⠁⠀⠀⠀⠀⠐⢮⡴⢩⣱⠮⠋⠀⣼⣿⣿⡷⣯⢏⡳⣍⠶⡙⡌⢇⡚⠡⢎⠥⢫⣜⡳⣞⣷⠻⠿⠿⠿⣿⣿ ⠁⠀⠈⠉⠑⠃⠽⢰⣍⢮⣻⡵⣿⣿⣿⣿⣿⣽⢣⢎⡱⠂⠥⡙⢆⡏⡷⣄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡻⠊⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣼⣿⣿⣿⡽⣎⣏⠶⡩⢖⠩⡘⠄⡈⠑⣈⡬⠇⠚⠉⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣻⢯⣏⠖⣍⠲⣉⠞⡼⣹⢯⣷⣦⣀⡀⠀⠀⠀⠀⢀⣀⢤⣼⢫⠗⠁⠀⢰⠀⠀⠱⣟⢧⣔⣀⠀⡀⠀⠀⠀⣀⢠⣴⣾⣿⣿⣿⣿⣿⣽⢫⡞⣭⢳⣍⢣⡱⡌⠆⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣻⣜⢯⡜⡱⣍⢞⡵⣯⣟⣾⣽⣿⡌⢷⢻⣛⢿⣣⢏⡿⠜⠃⠀⠀⠀⠘⠀⠀⠀⠈⠳⢮⣝⡛⣟⡻⣟⣳⡟⣸⣿⣿⣿⣿⣿⣿⣿⣞⣯⡽⣞⡳⠞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣜⡳⣜⢮⣳⣟⣾⣿⣯⠟⠁⠈⣯⠑⢎⡉⢣⢁⠂⠄⠀⠀⠀⢀⠀⡀⠀⢀⠀⣨⡞⡙⣘⠳⣉⡝⠀⠙⢿⣿⣿⣿⣿⣿⣷⡿⣼⠳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢎⣧⢳⣯⢿⡿⠋⠀⠀⠔⠈⠓⠤⡙⢄⠊⡔⢈⡐⠠⢁⠂⠔⠠⢈⠄⠢⡑⢣⢐⠢⡵⠋⠰⠀⠀⠀⠻⣿⣿⣿⣿⢯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣾⠏⠀⠀⠀⡌⠀⠌⡐⢂⠑⠌⡱⢈⠆⡰⢁⢂⠩⣀⢃⠢⠌⡑⣈⠦⠚⠁⠄⠂⠄⢡⠀⠀⠀⠘⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠳⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠌⡐⣼⠆⡈⠔⡀⠂⠙⠰⠃⢬⢶⡤⠆⠳⠘⠁⠁⠀⠄⠡⢈⢰⣬⠀⡆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣂⠁⢂⠁⢂⠘⠠⠁⠌⠹⢯⣳⣤⡐⠠⢀⠀⠀⠀⠀⠀⠠⢐⠠⢃⡌⢣⣬⡗⣹⣿⣇⣿⣯⢻⣼⠣⢼⡄⢃⡐⠠⢁⠌⢠⠁⠌⡄⠡⢄⡁⢆⣬⣞⡷⠋⠄⢒⠠⠃⡔⢨⢈⠒⡄⣉⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠀⠌⠠⠁⠌⠠⢀⠙⠲⣯⣳⢤⣌⡐⠠⢌⠢⡱⢌⡊⢥⣮⣵⡾⣽⣏⣾⣿⣷⣿⣯⡆⢗⡺⣳⠀⠄⠁⠂⠌⠠⠘⡀⠆⣑⡤⣞⣽⠞⣁⠢⠑⡌⢢⢁⠣⠌⡐⣢⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡽⢯⣟⡿⣦⣄⡁⢈⠐⠠⢈⡐⢠⠉⡟⣮⣽⣛⣦⢧⣵⡪⣜⣣⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⢶⣄⡘⣣⠀⠀⢀⠈⢄⡱⢜⡺⣵⣟⠟⢋⠐⡄⢢⠑⡌⠰⣈⢦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⠻⣝⢣⡛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣟⢷⣹⢳⢮⡽⢯⣿⣷⣦⡈⠐⠠⠐⣂⠱⡐⢢⡙⣯⡝⣻⢛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣯⢞⡭⣳⣷⣮⣤⡼⠆⣛⡬⢇⡟⠁⡈⠄⢊⠐⠄⢃⢰⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⢫⠗⣬⠓⡌⠣⠌ ⣿⣿⣿⣿⣿⣿⣿⣟⣯⢿⡾⣽⣞⣷⡻⣾⢽⣻⣾⣿⣿⡟⣆⡡⠒⢠⠃⡜⢡⡾⠱⣌⠣⢏⡼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣞⡷⣏⢶⣻⣹⣞⡟⢀⠘⠀⠄⠂⢧⠐⠠⠈⠄⡈⠐⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⡳⣏⠞⡴⢉⠆⠑⠀ ⣿⣿⣿⣿⣿⣿⣻⢾⡽⣯⣟⣷⡿⣾⣽⣯⣿⣿⣿⣿⣿⡇⢌⠙⡦⠅⠎⠴⡋⠥⢃⠴⡉⢎⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡯⣟⡽⢺⡹⣎⡳⡽⣞⣷⠀⠠⠁⠌⠐⠈⠓⠤⠁⠐⠠⠕⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⡳⡝⢮⡙⠴⡁⠊⠄⡀ ⣿⣿⣿⣿⣿⢷⣯⣟⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⢀⠊⠄⣉⠘⠤⡑⠬⡘⠤⣑⣮⣿⣿⣿⣿⣿⡿⣿⢻⡽⢎⠳⣏⠼⣘⢣⡑⢫⡕⣫⢽⡾⣷⣆⡡⠈⠄⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢷⡹⣙⠦⣉⠒⠄⡁⠂⠄ ⣿⣿⣿⣿⣽⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠠⠈⠐⠀⠌⠐⡈⢆⣱⣿⣿⣿⣿⣿⣿⣏⣿⡱⢈⠃⡐⠈⠀⡇⠐⠀⠀⠀⠉⣖⠡⢞⣹⣯⣿⣿⣷⣄⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣽⣏⣟⣳⣷⣌⠆⡡⠈⠐⠠⢁⠂ ⠀⠀⠀⠤⣀⠴⠊⠁⠀⠄⠀⠀⣠⠔⠋⠀⠁⠈⠀⣀⡧⠀⠀⠀⠀⠀⠀⠀⢐⠎⠁⡜⠁⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠳⡈⠑⡀⠀⠀⠀⠀⠀⠀⠈⡗⣄⠀⡀⠀⠈⡑⠢⣀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀ ⢀⡠⠖⠉⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⢀⠠⣠⠞⡡⠁⠀⠀⠀⠀⠀⠀⢀⡌⠀⡜⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠱⡀⠲⠀⠀⠀⠀⠀⠀⠀⠉⡄⠳⣈⠢⢀⠈⠀⠈⠑⠦⣀⠄⡀⠀⠀⠀⠀⠁⠂⢀ ⠁⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⢂⣡⢚⣡⠖⠁⠀⠀⠀⠀⠀⠀⠀⣸⠄⡜⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⡄⠇⠀⠀⠀⠀⠀⠀⠀⠐⣆⡈⡑⢄⡀⠀⠀⠀⠀⠀⠑⠪⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠞⠉⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⢯⠵⢊⡠⠁⣠⡴⠂⠀⠀⢠⡯⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡀⢄⠠⠠⢄⠹⣾⡂⠀⠀⠀⠰⠤⡈⠲⢈⢢⡹⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀ ⠤⠚⠁⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⣔⣋⣰⣏⣁⠆⣀⣀⣴⣾⣽⢃⠎⡄⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⠰⣀⠂⣵⡐⡌⢎⡜⡱⣊⠵⣨⣗⣄⣀⠀⠀⡀⢈⣙⣂⣢⣽⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⣂⣉⣩⠥⠬⢤⣉⣭⣌⡉⠒⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢋⣉⣩⣤⡴⣖⢲⠶⣦⣄⡉⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀What the sigma⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣭⠷⡚⣭⢩⣴⣣⣖⣶⣹⣦⣟⣼⡻⣿⢷⣦⣄⡉⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⡴⢞⢯⡿⣵⣻⣼⣏⣽⣳⢳⣎⢿⡷⣤⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡴⢋⡔⣣⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣣⢟⣦⡈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⣖⣻⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣗⡻⢦⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⢏⡞⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡽⣄⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⢃⡼⣵⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡯⣿⣦⠙⣄⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠒⣙⣉⣉⣍⣉⣉⣽⣛⣙⡓⠒⠒⠤⢀⣀⠀⠀⠀⠀⠀⠀⡼⢱⢏⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣆⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⣠⢏⣾⢟⡾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⠈⣦⣀⣠⠔⠒⣉⣡⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣌⣑⠒⠤⣀⡀⢰⠃⣾⣫⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⡀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⣡⢧⡾⢣⢟⡵⣻⢽⣻⢿⣻⣾⡽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣀⣠⣴⣾⣿⣿⡿⢿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣛⡛⡟⠿⣿⣷⣦⣌⡉⠐⣧⣿⣿⣿⣟⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢱⢣⡞⢡⢚⣼⡻⣵⢣⣏⢯⣳⢯⣿⣻⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣍⠲⢥⢎⡵⢊⣧⣙⢦⢻⠽⣿⣿⣿⣿⣟⠿⣼⡹⣶⣡⢷⡸⣱⢢⡙⣿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⡿⠀⡘⠬⣝⢶⡛⣼⢳⢮⡻⣜⡧⣷⢻⡾⣽⣻⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⡱⣚⢬⣛⢮⢞⡼⢳⢶⢩⡞⡽⣺⢥⣛⢿⣱⢞⡿⣣⣟⡶⣝⡶⣳⢥⢧⣹⢲⡻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣻⣯⣿⣿⣿⢿⣿⣿⣿⣳⣿⣿⡟⣿⣽⣿⣿⣿⣿⠇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⡇⣿⠀⢍⡺⢭⡞⣝⢮⣛⡾⣽⣹⢞⣭⢷⣫⢗⢯⢾⡽⢯⡿⣽⣿⣿⣿⣿⣿⠏⣿⡔⠩⠒⡍⠚⢮⡙⢣⠎⢓⠾⣱⢏⣾⣙⣮⣝⣾⣽⣳⣽⣾⣧⢻⡵⢫⢎⡳⢫⣽⣿⣿⣿⣿⣿⣿⣽⣾⣟⣷⣟⣿⣿⣿⣿⣽⣿⡿⣏⣾⣟⣿⢯⣝⣾⣟⣼⣿⣿⣿⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⣿⡆⢎⣝⣣⢟⣼⣳⣏⢾⡵⣫⢿⣜⣧⣛⢾⡹⢾⣹⢯⣿⣿⣿⣿⣿⣿⢇⡂⢼⣷⠀⢣⡐⣉⠒⡌⠃⠞⡩⠚⡍⢯⡙⢯⡹⢫⠯⡝⣯⢳⠿⣜⢧⣛⡟⣬⢓⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⢿⣷⣻⣽⢿⣽⡿⣛⣮⣿⣳⣾⣿⣿⣿⠇⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡆⣿⣿⣾⡲⢭⢾⡱⣏⣾⡻⣼⢯⡟⣼⢲⡝⡮⣝⡻⣜⣯⣿⣿⣿⣿⣿⣿⢘⣾⠟⠁⠈⡀⠰⠖⠛⠛⠛⠷⣶⢷⣼⢆⡟⢢⣍⣣⣯⣱⣎⣯⣽⡾⠿⡞⢾⡰⢫⡜⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡷⣯⣟⣾⣵⣻⣿⣾⣿⣿⣿⣿⡟⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⢻⣿⣧⣿⢏⣾⡱⣟⢮⢷⣹⢮⡝⣬⠳⣎⡵⣫⢗⡿⣾⣿⣿⣿⣿⣿⣏⣾⠏⠀⠀⢀⣀⣄⣦⣌⡽⣙⢣⢓⡎⠦⢓⣌⠣⠞⠫⢅⠫⡜⣱⣦⣿⣷⣿⣶⣭⣧⡜⡰⢣⢽⣿⣿⣿⣿⣿⣿⣿⣽⢾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡟⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡮⢿⣿⣿⣻⣶⡽⢞⣯⡗⣯⢾⣍⣳⢟⣬⡳⣭⣻⣽⣻⣿⣿⣿⣿⣿⡧⣿⡀⠰⠾⢟⡛⣛⠛⡿⠿⣿⣷⣾⣼⣶⣧⢸⣎⣱⢉⣾⣷⣿⣿⠟⣫⣭⣙⣻⣛⣿⢿⡿⣳⣾⣿⣿⣿⣿⣿⣿⣿⡾⣿⢿⣯⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢎⠻⣿⣿⣿⣿⣟⣶⣻⣽⣿⣾⣯⣿⣾⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣷⠘⣿⡧⣽⠶⠶⢇⠩⣴⣧⣶⡌⣹⠛⡟⢟⣾⠇⣿⣿⡿⢟⣫⣵⣾⣟⣟⣻⣛⡝⣫⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⢡⣴⣿⡿⠿⣿⡿⣿⣶⡿⢽⣿⡞⠶⠟⢨⣿⣷⣾⣿⡿⢿⣿⢿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠿⣿⣿⣿⠿⠿⠛⣛⣭⠦⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠬⣉⡙⠻⠿⢿⣿⣿⣿⣿⣿⡿⠿⠟⠋⡉⣿⣿⣿⣿⣿⣿⣿⡆⠂⠼⠿⣷⣤⣙⣿⣿⣿⠷⠟⡛⡐⣿⡇⠀⣿⣿⣿⡻⢶⣤⣟⣿⣛⣯⣴⠿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⠗⠚⠓⠒⠒⠒⠶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠢⠤⠄⠓⠤⠔⠓⠚⠛⣽⠃⣿⣿⣿⣿⣿⣿⣿⣿⣦⡁⠂⠄⡈⠁⠄⠂⠄⡈⠰⢠⠑⡸⣧⠈⣽⣿⣿⣿⣬⢻⠼⣭⡙⠲⣌⡳⣇⢿⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠏⢀⠀⢂⠡⣈⠑⣎⠹⣖⢮⡐⠁⠂⣰⡏⢀⣾⠋⠄⠡⠈⠔⠂⠤⡉⡙⠛⢛⠻⢿⢛⠛⡉⢍⡩⢐⠢⡉⢆⠨⡓⣌⡞⢿⣧⣻⣿⣯⢿⣿⢼⡻⣜⡟⣶⢳⢯⢻⣽⣿⣿⣯⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢉⣾⠃⠀⢢⡘⢄⠒⠤⡉⠤⡉⠼⠈⢿⣄⢠⡿⠁⠠⢀⠒⡈⠄⡉⢢⢉⡐⢡⢀⣁⣂⡑⢎⣆⣶⣶⣤⣥⣃⢂⠱⠈⢆⠱⢢⡙⣮⢳⣹⣿⣿⣿⣛⢮⡳⢯⡝⣮⢟⣮⢳⡽⢿⣿⣿⣧⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣡⡿⠁⠀⡸⢠⠓⡌⣘⠢⡑⢠⢁⠊⠁⠀⢹⣾⠃⠠⠁⢌⠒⢠⡑⣘⣴⣦⡿⢟⡛⢭⠻⣿⢿⡟⢫⠜⣛⡛⣛⢛⣷⣷⣬⣡⢣⡝⢦⣋⢾⣿⣿⢧⣟⢮⡝⣧⢻⡜⣯⢞⡧⣏⢻⣿⣿⣿⣷⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⠁⠀⠠⠑⡀⢣⠜⠤⠓⣌⠂⢆⢂⠀⠀⠀⢻⡇⠈⢌⠠⣌⣦⣷⡟⢯⣖⣿⣺⣝⣫⢳⡜⡲⣍⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⡝⣾⣿⣿⣿⣭⣳⢻⣜⢧⠿⣜⡯⢶⣩⢷⣟⣿⣯⣿⣷⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⢿⡀⠀⠀⠀⠀⠢⢌⢣⠙⡤⡙⢤⠊⡄⠀⠀⢸⡇⠈⠄⡚⠿⣿⡛⠛⠋⠉⠉⡉⠭⣙⡙⠿⣿⣾⢿⢟⡟⣫⠽⡹⠎⡱⢊⣭⣿⣟⡳⣼⣿⣿⣿⣿⣯⡗⣯⢞⣭⣛⡾⣽⣷⣻⣟⣿⣿⣿⣿⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡙⢷⣤⡀⠀⠀⠀⠢⠙⢤⠙⣢⠱⡈⠄⠀⠈⣷⠀⢈⠐⠤⠉⠻⢷⣤⡁⠆⠱⢁⠒⢨⠙⣌⠣⢍⡚⡜⢡⠂⠐⣠⣴⡿⣻⠱⣎⠵⣿⣿⣿⣿⣿⣿⣛⣼⡳⣾⣽⣽⣿⣿⣟⣿⣿⣿⣿⠟⣁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣬⠙⢶⣄⡀⠀⠈⠠⠙⣄⠣⡑⢂⠀⠀⣿⡄⠠⢈⠀⠂⠁⢀⠉⠻⠶⡁⠆⣉⠤⡑⢌⠚⢤⣑⣌⣦⣾⠾⣟⡽⣶⡷⡹⢼⣹⣿⣿⣿⣿⢿⣷⢿⣞⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣈⠛⢶⣄⡀⠁⠄⡓⢌⠢⠄⠀⢸⣧⠀⠄⠂⠀⠄⢀⡀⠂⠐⢈⠰⠙⣿⢿⣿⣿⣿⣿⣿⣹⣋⣵⣯⣾⠟⣡⢛⣼⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣿⡿⠟⢋⣡⡖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣈⠻⢦⣄⡀⢋⠄⡐⠀⣿⡿⠆⠐⡈⠠⠀⠈⠻⠖⠀⣀⣠⣰⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⠲⡥⣟⣾⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣟⣡⣠⣠⣀⣉⣉⣐⣒⡒⣒⠢⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠿⢇⣀⣩⣿⣦⣥⡐⢸⡿⠁⢀⠂⡔⠁⠌⡀⠀⠀⠂⠘⠋⠉⢉⠉⠩⠍⡉⠉⠽⣻⡛⠇⡰⣉⢾⣱⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⢟⣫⢟⣻⣾⢟⣽⣫⣟⣯⣙⡷⣶⣦⣤⣍⣉⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠖⣏⣩⡭⡵⠶⠖⢾⣿⢿⡻⢿⣿⣿⣿⣿⠃⠌⢠⠊⡐⢌⠠⠐⡀⠁⠠⠁⠠⠐⡀⠂⡁⠢⢄⠡⠂⣃⠱⢈⠴⣫⢞⣭⣟⣻⣿⣿⣿⣿⢻⡑⢣⢷⣿⠃⡽⢋⢱⡏⣮⢟⣽⠞⡿⣹⢶⣻⠿⣏⣉⣍⢛⠿⣿⣶⣤⣉⡉⠒⠤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⣊⣹⠷⠒⠚⠉⠁⢀⠠⣀⡐⢌⢂⡙⢿⣟⢾⣿⠆⣽⡏⠀⠐⢂⠱⣈⠂⡅⠣⢄⠡⣀⠡⢂⠡⠄⡡⢂⠅⠎⡰⠡⢄⡊⡔⡸⡱⢞⣮⣷⣿⣿⣿⣿⣿⠂⢌⣱⣿⡏⠰⢀⢂⠣⡜⡰⢊⢦⣛⠶⣩⢏⡵⣫⡟⡽⣎⢾⡱⣆⢯⣛⢿⣿⢿⣶⣤⣉⠒⠤⡀ ⠀⠀⠀⠀⠀⠀⣀⠴⣂⡯⠗⠋⠉⠁⢀⠠⣄⠆⠲⡘⢆⠣⡱⠜⡬⠒⡌⠦⡙⢎⣽⡆⣿⡇⠀⠈⠄⡃⢤⠘⠄⠣⢌⠒⡠⠱⢌⡘⢂⠱⢨⠌⡒⡅⢋⠦⡱⣍⢳⣙⣧⣟⣷⣿⣿⣿⣿⣿⠀⢂⣾⡿⢁⠃⠌⡀⠓⣄⢣⣙⢦⡻⡜⡵⣎⡷⣳⣝⡳⣽⢺⣝⣮⢯⡽⣾⢿⣿⣿⣻⢿⣿⣶⣮ ⠀⠀⢀⡠⢔⡭⠞⠋⠁⢀⣀⠰⠒⡙⠊⠑⣀⢊⡑⣈⠤⢡⠔⡢⢔⡡⢚⠴⣉⠖⡬⢷⢸⣷⠀⠀⠀⡓⢦⡉⣎⠱⢊⡔⠡⢆⢣⡘⡌⢣⠥⣊⢕⢊⢧⠞⡱⣜⣣⢝⣶⣿⢿⣿⣿⣿⣿⡟⠀⠜⡘⠁⡄⢨⠐⡌⡱⢰⣦⡟⣦⢻⡜⣳⡝⡾⡵⣎⢷⡭⣗⣞⢾⡭⢿⡽⣯⣿⣿⣿⣿⡿⣿⣿ ⠤⢞⡹⠞⠉⠀⠀⡀⠌⡤⠄⠦⡑⡴⣉⠳⡌⢦⠱⣌⠲⣡⠞⡱⢊⡔⡫⢜⡡⢏⠴⣩⠆⢿⣧⡀⠀⢹⣲⠹⣆⢯⢣⢼⡑⣎⢦⢱⡈⢇⢮⣱⢾⣯⢿⡿⣕⡾⣲⣿⣿⣟⣿⣿⣿⣿⡿⢁⡈⠐⣀⠢⠐⡅⢎⣰⣱⢏⡳⣌⠷⣙⡾⣱⠞⡷⣽⣹⡞⣷⣹⡞⣧⣟⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿ ⠴⠋⠀⢀⠠⡘⢤⡱⢋⡔⣋⢧⢳⡘⡥⢓⡜⢢⠓⡤⢓⢦⡙⠴⣋⠴⣙⢬⠓⣭⢚⡴⣛⢬⣻⣿⣦⣤⣯⣻⣜⣣⠟⣮⡝⣎⣞⣶⣽⣿⣾⣽⣿⣞⣿⣽⣯⣿⣿⣿⣻⣿⣿⣿⣿⠟⣁⠂⠤⣁⡆⠱⠡⣈⣶⠾⣍⢏⠶⣩⠞⣡⠷⡝⣯⢳⡽⣲⢹⢶⣭⣟⠷⣞⢷⣻⡼⣿⣾⣟⣿⣿⣿⣿ ⠀⡄⡘⣄⢣⠝⣦⣙⢧⢺⣭⢲⣭⣷⢣⠏⡜⣡⢋⠶⣉⢦⡙⠼⡰⢣⢍⠶⣉⠶⣩⠖⡽⣎⢷⡫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣦⡾⢢⢙⡰⠜⣀⢣⣵⣾⠟⣶⣚⣮⢷⣝⢮⡽⣹⣼⣜⣧⣶⣧⢿⣼⣶⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⡒⢬⠱⣎⢇⡻⢴⣙⣎⡳⣬⣷⣟⠮⡥⣋⡔⢣⢍⠲⣉⠖⣌⡳⢍⢧⡚⣌⢧⠛⡴⣻⢵⣫⢞⣭⣓⣦⣙⢎⡛⣉⠯⡭⣉⢧⡙⢆⠳⣌⢚⠭⣹⣿⡿⢭⣛⠽⣩⢋⡝⣤⣷⣿⠫⡐⢅⠢⣁⣣⡾⣟⣳⣭⣿⣽⣟⣾⣿⡿⣿⠿⣟⣟⡻⣏⣟⣻⣛⣟⣻⣟⣿⣻⣟⡿⣿⢿⡿⣿⣿⣿⣿⣿ ⣝⢪⡓⣮⢚⡵⣣⣞⣶⡿⣽⣾⣍⣣⣵⣢⣝⣮⣜⣵⣬⣺⣴⣙⣞⣦⣻⣜⣮⣳⣽⣧⣿⣼⣿⣼⣯⣽⣯⣿⣷⣧⣮⣑⣍⠲⢌⢣⠓⡌⢮⢡⢹⢟⡙⠦⣌⣳⣥⣿⣾⣿⣹⣬⣵⣬⣶⠾⣭⠿⠽⠛⠟⠋⣍⠩⣍⠳⣨⣙⡬⡽⢮⡼⣹⢷⣯⣷⢿⣾⢿⣿⣞⣿⣿⣽⣿⣿⣿⣿⣿⣯⣿⣿ ⣯⣳⣽⠾⣯⠟⠿⣛⠻⣝⠻⣙⢏⡹⢃⢏⡙⢏⠞⡽⢳⡭⣟⠿⣽⣻⠿⣽⣟⡿⣽⣷⢿⣿⣾⣧⣿⣾⣷⣿⣿⣿⣽⣿⣿⣿⣾⣶⣭⣘⡔⣂⢆⣬⣼⣷⠿⠿⢛⠛⡋⠍⢢⠐⣀⠂⠄⢂⠄⡐⢠⠉⡬⣑⠦⠳⣘⢋⠳⣉⠖⣙⠦⡻⣝⡻⢾⡽⡻⣿⢿⡾⢿⣻⣾⢿⡿⣿⣿⣿⣷⣿⣿⣿ ⡍⡱⢌⠲⢄⢫⡱⢎⠳⣌⠳⡍⢎⡖⡩⢖⡹⢎⡽⡱⢫⢼⣩⢻⣜⡷⣿⣟⡿⣿⢿⡿⣿⣻⡽⣯⣛⣯⣿⢿⡿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⠿⣋⠵⢊⠴⣁⠢⠌⡄⠣⠰⠠⠌⠒⠄⢂⠄⠣⢌⠡⠡⢎⠱⠠⣍⠒⣄⠚⡌⢲⠱⣌⠳⣣⣝⣳⢹⣏⡟⣿⣳⡿⣿⣻⣯⣿⢾⣿⣯⣿⣿ ⠜⡰⡌⢦⡙⣆⢳⡩⢖⡬⣓⢬⡓⣬⢳⡭⢎⡳⣜⣱⢻⡎⢷⠻⣞⡹⢧⣫⢽⡹⣎⢷⣳⢯⣷⣻⢯⡿⣽⢯⣟⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⢧⢳⡜⢚⠷⢶⠶⡶⣷⡼⢶⡷⢷⡾⠟⡞⢣⣜⣴⡾⣼⣳⣾⣼⣧⣦⣍⢢⡙⢌⠣⡙⢂⠳⢡⠲⣌⠳⣌⠿⡲⣽⣹⢿⢷⣻⢿⡿⣯⣿⣷⣿
“They only find bad stuff if they look it up” I searched up the word “cute”. I’m an 11 year old. We don’t wanna see that! It’s sad how kids are posting p0rn, and seeing p0rn. It ruins their mental health D: I can tell why you’re probably here. You wanted too see p0rn right? I know that lust might feel good but trust me: It won’t in the future. It can make you feel disgusting. And untrustworthy. This kind of behavior might even make you an assaulter/abuser someday. I promise you can get better. Or at least not look for p0rn on this cute site. It’s never to late to break free from lust. You are a good person ☆ You can feel happy. And free. It feels so much better i promise. The bad stuff you’re doing/seeing really isn't great. It can affect you’re health both physically and mentally. I’m serious. You might even be hypersexual/addicted to p0rn as a result of SA. If so, I’m very sorry! It is not your fault! It doesn't matter how long you have been addicted to it. You can still break free. Start by blocking 🔞 stuff. It’ll be hard, but you can do it. I believe in you. Try searching up cute stuff! Or spending time with a friend/sibling. You got this! You are strong and enough! You can win! You can! You will! And here are some cute symbols as a reward for reading this :) Not mine! ⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀:¨ ·.· ¨: ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ `· . 𐙚 ⋆˚✿˖° °❀⋆.ೃ࿔*:・ ฅ^>⩊<^ ฅ ପ(๑•ᴗ•๑)ଓ ♡ ゚𐦍༘⋆ ‧₊˚𖦹 ࣪.𓋼𓍊𖤣𖥧‪𖡼‬𖥧𖤣𓍊𓋼. ࣪𖦹˚₊‧ ૮꒰ ˶• ༝ •˶꒱ა ૮ • ﻌ - ა .☘︎ ݁˖ ˗ˏˋ༻ʚ♡︎ɞ༺ˎˊ˗ ⁺‧₊˚ ཐི⋆♱⋆ཋྀ ˚₊‧⁺ (*ᴗ͈ˬᴗ͈)ꕤ*.゚ (๑ᵔ⤙ᵔ๑) ⋆。゚☁︎。⋆。 ゚☾ ゚。⋆ 𓅰 𓅬 𓅭 𓅮 𓅯 ‧˚꒰🐾꒱༘⋆ (⸝⸝ᵕᴗᵕ⸝⸝) ( ˶ˆᗜˆ˵ ) And I know that you’re very strong! And i’m proud of you for reading this! So i’ll give you a cute little story to lighten the mood! Yet again, not mine! /)/) ( . .) "eatz" /づ🍪 /)/) (\(\ ( • •)? (• • ) can i pwease eat that too /づ🍪 vv \ (\(\ (\(\ ( • •)No.(• • ) 🍪⊂\ vv \ (\(\ (\(\ ( • •)(• • ) give me that! 🍪⊂\ ⊂ \ /)/) (\(\ ( 0 0) Noo! (. . ) / づ 🍪⊂\ "sad" /)/) (\(\ ( . .)"" (• • ) / vv 🍪⊂\ /)/) (\(\ ( • •)? (. . ) Ok fine, u can have it. / vv 🍪⊂ /)/) (\(\ ( ᵔ ᵔ)thx! (. . )"" / づ🍪 vv \ btw we can share if u want! /)/) (\(\ ( ᵔ ᵔ) (• • ) huh..? / づ🍪 vv \ /)/) (\(\ ( ᵔ ᵔ) (ᵔ ᵔ ) okay! / づ🍪⊂ \ Tysm for reading. I just want you to get better. I wish you the best life! ♡☆
me + you? (‿ˠ‿) Ɑ͞ ̶͞ ̶͞ ̶͞ ل
I would like to do something like that but for both genders but i dont have IG do you think we could figure something out?
(\ /) ( ≧ᴗ•) <3 ╭ ╯╰ ╮ │\ . . /│ ╰ | . \ ˊ ⎛ ⸌ᥩ⸍ ⎞ \ | / | 〡 〡
Please stop corrupting the generation with you adult content and please kindly go to mass, God still loves you ✝️
𝗧𝗔𝗞𝗘 𝗦𝗢𝗠𝗘 𝗛𝗢𝗟𝗬 𝗪𝗔𝗧𝗘𝗥 YALL ARE WAY TOO HORNY PLEASE STOP AND CALM DOWN. THIS IS A SITE FOR EMOJI COMBOS, NOT NSFW SO PLEASE CALM DOWN AND HAVE THIS HOLY WATER BEFORE I COME FINDING YOU: ✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞✞
FE!NFE!NFE!NFE!NFE!N FE!NFE!NFE!NFE!NFE!N FE!N FE!N FE!NFE!NFE!N FE!NFE!NFE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!NFE!NFE!NFE!NFE!N FE!NFE!NFE!NFE!NFE!N FE!N FE!N FE!NFE!NFE!N FE!NFE!NFE!N FE!N FE!N FE!N FE!NFE!NFE!NFE!NFE!N FE!NFE!NFE!NFE!NFE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!NFE!N FE!N FE!NFE!N FE!N FE!NFE!N FE!N FE!M FE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!N FE!NFE!N FE!N FE!NFE!N FE!N FE!NFE!N FE!N FE!N
🍒🔞 ...hey, are you feeling frustrated again? —no, i get it, really... sometimes it's hard to reach the...'release', you need. that, or it's just starting to get boring for you...? maybe we can try to fix that, if you'd like? ˖⁺‧₊˚♡˚₊‧⁺˖ let's start slowly. i want you to gently start to rub your thigh...slowly, and think about someone you really like...could be anyone, i don't judge. or just a situation that gets you in the mood. don't rush— there's no need to. this is time dedicated to you, and your needs. take it nice and slow. that's it, just gentle rubbing...slowly move down to your underwear. no— don't take them off yet. not until later. the idea is that you want to get yourself as worked up as you can. gently rub your fingers against the lips of your sex, just inching towards your clit. slowly, slowly...edge your fingers towards that spot. then slowly press down on it with your fingertips and breathe out... spread your fingers around it and slowly rub against it...up and down. you're doing such a good job.♡ look at how good you are at following directions, you're so perfect. now you can reach under your underwear, or take them off—whichever you prefer. spread the lips, and dip your fingers against your entrance, slowly sliding that finger up until you reach your clit. i wish i was there to help you. i'd love to kiss your thighs, your shoulders, your face... all over your body...and just watch you play with yourself. rub your clit in slow circular motions. really, now, pace yourself. spread your legs more, really lean into it. i want you to feel good. just imagine how good it would feel to feel a warm pair of fingers slowly tease into your pussy, pressing right in..down to the knuckles. or maybe a soft, wet tongue to lap up at that mess you're making. i'd love to lick every last inch of that loving mess, and taste just how horny you are. rub faster. press into your clit harder. you should even tease the edge of your entrance...but don't put anything in. i won't let you.♡ i'd just tease you all day, slowly sinking my teeth onto your nipples until they're nice and hard, and feel you shiver under my touch. i wanna finger you until you're sore, squeezing hard on my knuckles, begging for more. go faster. keep going, you're almost there. and then finally, when you're wet and your clit is sore and aching, i'd finally give you something bigger then just my fingertips. i'd rub my cock up and down your wet slit, feeling how pent up you are, teasing you all the while there...you'd have to beg more for it to be inside. rub faster, honey. i want you on the edge. do you think you can do that for me? really rub hard, spread your legs, give into the pleasure. don't be afraid to make noises, now. that's what i want to hear. i can't even act that teasing, because i want it just as much as you do. i'd slowly slide into your cunt, inch by inch, letting you feel the full length of my hard cock, letting you get used to the full length. i wanna hear you whine, whimper against my lips as i kiss you hard, tasting your mouth with my tongue, pushing all the way inside of your wet pussy. i want you on the edge, rub your clit as fast as you can. faster... faster. i want you to cum. don't think about it — just give into the pleasure. even when you're cumming, don't stop— overstimulate yourself. it feels so good. don't ever stop, just give into the pleasure. ...i hope that helped you out. that face you made when you came was adorable.♡
[HEYYY .HOUSE GUY HERE!! I STOLE THIS FOR ARCHIVAL PURPOSES!! THE OG POST THING DIDN'T HAVE AN ACTUAL TAG LIKE .LAVENDER OR STUFF LIKE THAT, SO IF YOU DID WRITE THIS ORIGINALLY PLZ PUT THAT IN THIS SECTION!!] so, you had a hard day today, mh? yeah, i know, ive been there before… you want to relieve some stress? i know how to… have you ever jerked off before? no? thats okay, i can show you how to… lay down on your bed, think of anyone you love sexually… imagine fucking/getting fucked by them… nice, isnt it? you hard yet? good boy… drop those pants down for me… damn…. its so big… slide down those boxers… mh, fuck… spit into your hand… and rub it all over your d.ck… perfect… youre doing good… now wrap your hands around it, and slide the f.reskin up… and down… wait… dont go too fast, i wont let you… yet… think about them, rub your thighs while doing so… now pick up the pace… mh… go a little faster… you like those wet noises it makes, dont you…? its okay… i do too… go faster… good boy… now let your self go, let the climax hit… good… that felt nice, didnt it…? [emoji tax; 🪼⋆.ೃ࿔*:・]
add me on discord im verry horny i wanna do a sex rp you can be a girl or a boy idc im bisexual so add me my user is kelly._.com
I am 😼 the Glob-glo-gab-galab 🪱🪱🪱 The shwabble🤑-dabble🪐-wabble🫂-gabble🎸 flibba blabba blab 🪱🔫 I'm😼 full 🥛of shwibbly 🤑liber-kind 🎙️I am 😼 the yeast t🦷🦷of thoughts🧠 and minds 🤯
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