League of Legends Text Art

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⠀⡁⠄⠈⠀⠂⠄⠀⠀⠀⠀⠐⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠉⠂⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠐⠀⠡⢀⠀⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠠⠚⠄⠘⠤⠘⠣⢁⠢⡑⠌⠁⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⡁⠀⠁⠠⠀⠀⠠⠀⠀⠀⠈⠐⠀⠐⠈⠀⠀⠀⠀⠟⣿⣿⢿⣹⠿⢍⡱⢎⡑⢢⡙⠤⠱⡌⠒⣈⠱⢌⠓⠀⠘⠀⠀⠀⠀⠈⠠⠃ ⠐⠀⠀⠀⠀⠠⠀⠀⠉⠆⡈⠒⠌⡑⠌⠢⠑⢊⠀⠀⠇⣿⣿⣿⣿⣿⣿⣻⡿⢏⡱⢞⡌⡜⢊⡱⢎⢎⡡⡜⠣⣩⠖⢋⠁⠀⢀⠀⠃⡿ ⡀⠄⠀⠀⠀⠀⠝⢻⡽⠾⣋⠵⢊⡱⠎⢡⡲⠎⢃⠀⡧⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢏⢣⢜⡫⠥⢎⢣⡔⢫⡱⢯⢣⣧⠻⠀⠀⡟⣿ ⠀⠀⠀⠁⠛⣿⣿⣿⣿⣿⢿⣻⣽⠾⢫⣱⠯⢃⢡⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣏⠧⣘⠷⣊⡵⢎⡳⡗⣋⣵⡾⢻⠀⣿⣿ ⠻⠈⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠞⢩⠰⠀⠁⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⠵⣎⡱⢜⣫⠵⣫⡼⣟⣷⠊⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡻⠟⣭⣿⣙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⡳⣜⠯⣘⠾⣏⡱⣿⢿⡇⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⡀⣧⢸⡈⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢎⡽⢎⢳⣧⡞⣿⡧⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢹⠀⠀⡀⣿⢿⠈⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⠾⣗⡩⢷⣎⣿⢧⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⣿⣿⠹⠀⠁⣇⣿⢿⠹⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡹⢷⣎⣿⢣⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣄⣿⣿⠻⡘⠠⣿⣿⣽⢋⠙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡻⢧⣏⢰⡏⣿ ⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⢎⠙⣐⣀⣀⣥⣿⣿⣿⣿⣿⢽⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⢣⣼⠁⣿⣿ ⣿⣿⣿⢹⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢯⡱⢸⠀⠁⣉⣭⣿⣿⣿⣿⣿⣿⢿⣔⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣠⠋⣿⣿⣿ ⣿⣿⣿⣿⢹⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡶⠀⠃⣿⣿⣿⣴⣠⢂⣙⣀⣄⣦⣈⠀⢠⡀⣦⣷⣿⣿⣿⣿⣤⢒⠶⡵⣏⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⢻⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢰⠀⠀⡀⢀⠀⠀⠀⠀⠁⠀⠀⣄⢀⠁⠀⠀⠀⠈⣤⣿⣸⠆⣤⣶⣶⣻⣘⣧⣿⣿ ⣿⣿⣿⣿⣿⢿⣬⣿⠿⡙⣬⣶⣿⣿⣿⣿⣿⢿⣘⠰⠃⠀⠀⠀⠀⠀⠀⠟⣾⣠⢀⠑⠀⠀⠀⠀⠀⢡⢈⡄⠧⢿⡻⢑⠸⠓⠈⠳⡇⣿ ⣿⣿⣿⣿⣿⣿⣿⠿⣝⣶⣿⢿⠙⠧⠻⠛⣘⢖⡶⠀⡂⢀⠀⠀⠐⠀⡇⣿⢿⠹⡈⣇⢶⠠⠀⠀⠂⣀⢀⡏⡈⣿⣿⣿⡽⠞⡌⡚⢌⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣛⣍⢤⣁⢈⠃⠀⠈⠁⣿⠹⠐⠀⠂⠀⠀⣅⣀⣆⢋⠀⠀⠔⠀⠀⠁⠋⠔⣿⢻⣇⣿⣿⣿⢿⣞⠍⢢⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢁⡿⡿⡌⠳⢆⠈⡇⣿⣻⢚⠛⠀⠀⠀⡑⠈⠀⣀⣀⠄⢠⠀⠀⣴⢸⡇⣿⣿⠸⣷⣿⣿⣿⣿⢻⢥⡒ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⢿⣜⠫⢇⢀⡇⣿⣿⢿⠻⠯⠰⠀⡄⢠⡄⠄⠀⠀⠀⠁⣍⠀⠀⡧⣿⣿⣿⡘⣧⣿⣿⣿⢿⣺⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡗⣿⣿⡿⢓⡬⠘⡇⣿⣿⣿⣿⣿⠻⣭⣤⠸⠘⠁⠋⠳⠙⠉⠀⠀⠀⡄⣦⣿⣿⣿⡈⣿⣿⣿⣿⣿⢞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⠾⢏⠠⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡿⢿⡿⣿⣿⢿⠘⢃⠀⠀⡀⣦⣿⢿⡌⣷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⣿⣽⠒⢨⡇⣿⣿⣿⣿⣿⣿⣼⠇⢀⠁⣿⣿⣿⣿⣿⣿⣷⠻⡈⠐⠀⠀⡀⣧⢿⡈⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣿⠲⢀⡇⣿⣿⣿⣿⣿⣿⠀⡇⠐⠂⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⢀⠀⠀⠀⢦⢿⡈⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣶⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠻⠿⠿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⡀⠀⠀⠈⠛⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡐⢆⠲⣈⠭⣉⠛⠿⢿⣿⣷⣤⡀⠀⠀⠙⢿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡜⣌⠳⣌⠲⣡⢋⡜⢢⢍⠻⢿⣿⣷⣄⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⡿⠁⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡒⣌⠳⣌⠓⢦⠓⡜⢣⢎⢣⡃⢟⢿⣿⣦⠀⠀⠈⢻⣿⣆⠀⠀⠀ ⠀⠀⣸⣿⡿⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡱⣊⠵⣊⡝⢎⡹⡜⢣⢎⡳⢜⡣⢎⣻⣿⣷⡀⠀⠈⢿⣿⣇⠀⠀ ⠀⢠⣿⣿⠃⠀⠀⣾⣿⢏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡱⣍⢮⡑⣎⠧⣓⡜⣣⠞⡜⣬⢱⢫⡔⣻⣿⣧⡀⠀⠈⣿⣿⡄⠀ ⠀⣼⣿⡟⠀⠀⣸⣿⡿⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡱⢎⠶⣙⢦⡛⡴⣙⢦⡛⡜⢦⣋⠶⡹⣔⣻⣿⣇⠀⠀⢸⣿⣷⠀ ⢀⣿⣿⠅⠀⠀⣿⣿⣇⢳⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠵⣋⡞⡱⣎⠵⣣⠝⣦⢹⡜⣣⢎⡳⢵⢪⡼⣿⣿⡀⠀⠈⣿⣿⡀ ⠈⣿⣿⠀⠀⠀⣿⣿⢬⢳⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣋⢶⡩⢗⡜⣣⢧⡛⡴⣓⠮⣕⢮⠳⡭⢖⡳⣿⣿⡅⠀⠀⣿⣿⠆ ⠰⣿⣿⡀⠀⠀⣿⣿⣎⢳⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡱⢎⡵⢫⠼⡱⢎⡵⢣⡝⡺⡜⣎⢳⡙⢮⣱⣿⣿⠂⠀⠀⣿⣿⠅ ⠀⣿⣿⡆⠀⠀⣿⣿⣎⢳⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣱⢫⡜⣣⢏⡵⢫⡜⣣⢞⡱⡹⣌⢧⡙⢧⢺⣿⡿⠀⠀⢸⣿⡿⠀ ⠀⢹⣿⣿⠀⠀⠘⣿⣿⣪⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢆⡳⣜⡱⢎⡜⣣⢞⡱⢎⡵⠳⡜⢦⡛⣼⣿⣿⠇⠀⠀⣾⣿⡟⠀ ⠀⠀⣿⣿⣇⠀⠀⠹⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢎⠵⣪⢜⢣⠞⣡⢎⡵⢋⡴⢫⡜⡣⣝⣾⣿⠟⠀⠀⣰⣿⡿⠀⠀ ⠀⠀⠈⢿⣿⡄⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠎⡵⢢⢫⡜⢎⡵⢊⠶⣩⢒⣇⡚⣵⣿⣿⠏⠀⠀⣠⣿⣿⠃⠀⠀ ⠀⠀⠀⠘⢿⣿⣤⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⢜⣣⠳⡜⣣⠞⣩⠞⣡⠳⣼⣾⣿⡿⠁⠀⠀⣴⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣧⣀⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣧⣶⣽⣼⣵⣮⣵⣯⣶⣿⣿⣿⣯⣤⣤⣤⣾⣿⣿⣥⣤⣤⣄⡀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣾⣟⣾⣽⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣿⣻⠝⠁⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢛⡿⠟⠉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⣴⡿⢖⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡟⠀⠀⠸⡫⠞⠛⠚⠉⠉⠙⠓⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⠳⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⢋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣬⣧⣀⡀⠀⠀⠠⠤⠖⠒⠛⠛⠒⣺⠟⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣸ ⢰⡷⢶⣦⣄⣀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠀⠀⠀⠀⠈⠉⠛⠿⣶⣄⠀⠰⣦⣶⣶⡋⢁⣴⢷⠶⢄⡀⠀⠀⠸⣿⣲⠏⠳⠦⣴⡏⠀⠀⡟ ⢸⡇⣷⡦⣈⠙⢓⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡹⡟⠦⠀⣽⠳⣄⠓⠤⣽⢤⣄⣰⠃⠉⠓⠦⣞⡿⠁⠀⢠⡇ ⠸⡇⡇⠁⠈⢱⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⡏⠀⠈⠓⠾⣧⠞⠉⠙⠳⢦⣄⡴⢺⠇⠀⠀⣼⠀ ⠀⣷⢳⠀⣰⢋⣭⣙⣓⠶⢦⣄⣀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠤⠤⠤⣤⡀⠹⣧⢰⡇⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠈⣹⣿⠀⠀⢰⠇⠀ ⠀⠸⣟⣴⢯⢎⠏⢰⠏⢀⠏⢠⡿⠁⠀⣟⢹⢉⡤⣤⣄⣒⣒⣒⣒⣲⡆⢻⠀⠹⣿⠃⠀⠀⡼⠃⠀⠀⠀⠀⠀⣠⡞⢡⡇⠀⢀⡟⠀⠀ ⠀⠀⢻⣿⡟⡞⢀⠎⠀⡞⢀⣞⣀⡀⠀⢹⠘⡄⣏⠉⠉⠀⠀⠀⠀⠘⣾⠘⣇⣀⣿⠀⠀⣼⠃⠀⠀⠀⠀⢀⡾⠋⠀⣼⠀⢀⣾⠁⠀⠀ ⠀⠀⡟⢸⣸⠀⡞⢀⠞⢀⡟⠀⠀⠉⠉⢹⡄⡇⢸⠀⠀⠀⠀⠀⠀⠀⢧⡆⣇⠀⢸⠀⡼⠁⠀⠀⠀⠀⣴⠟⢬⡙⢲⡇⠀⡾⠃⠀⠀⠀ ⠀⠸⣧⣤⣈⣉⣁⡞⠀⡾⠉⠓⠒⠒⠒⠺⡇⢸⠈⠧⠒⠒⠒⠈⢉⣉⣉⣁⡟⠉⢹⣴⠃⠀⠀⠀⢠⡾⠃⠀⠀⠙⡾⠀⣼⠃⠀⠀⠀⠀ ⠀⣴⠞⠁⠀⠉⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠻⠞⠓⠒⠚⠛⠛⠉⠉⠉⠉⠉⣀⣠⣴⠟⠁⠀⠀⢠⡟⠀⠀⠀⠀⣰⠇⣰⠃⠀⠀⠀⠀⠀ ⠀⠈⠉⠛⢶⠶⣶⡶⣤⣤⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣤⠤⠶⠶⡶⠚⠋⠉⠳⣞⣀⡀⠀⣰⠏⠀⠀⠀⠀⣠⡟⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⣴⣻⣰⠋⠳⣄⠘⡆⠀⠀⠀⢸⠁⣠⠞⠉⠉⠙⠲⢄⠀⠀⣱⠀⠀⠀⢉⣩⣷⣶⣿⠏⠀⠀⠀⣠⢾⣏⣀⣸⡇⠀⠀⠀⠀⠀⠀ ⢐⣶⡶⠍⠀⠑⢄⠀⠈⢦⠇⠀⠀⠀⢸⠚⠁⠀⠀⠀⠀⠀⠀⣁⠔⠁⠀⠀⣀⣤⣶⣏⣡⠏⠀⢀⣰⠞⠃⢸⠀⢉⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠻⢿⡦⠄⠀⠀⠉⠲⣺⠋⠙⠒⠦⣌⠳⠦⠤⠴⠶⠖⠚⠉⠀⠀⠀⠀⣠⣞⡉⠀⠈⠉⠉⢳⠞⢉⢦⡄⡾⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢷⣄⠀⠀⠀⠙⠒⠤⢤⠴⠊⠀⣀⠴⠂⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣶⣤⢀⣀⣤⢿⣉⣵⠞⣹⠃⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣙⣶⣤⣀⠈⠑⠒⠒⠶⠒⠊⠁⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠰⣭⣟⣧⡸⢯⡉⠻⣍⠀⣰⡏⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⢾⡿⡉⠀⠉⢙⠳⠶⠶⢶⣤⣤⣤⣤⠤⠶⠶⠞⠋⠁⠀⢀⠀⣿⣮⣳⡈⢻⠀⠷⢦⣼⣶⣿⠀⢠⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠏⠀⣸⣺⠁⢀⣴⣏⡆⠀⠀⢒⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣄⡿⡇⠉⠁⣸⠀⠀⣸⡏⠀⠈⣟⠋⠀⣉⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠁⢧⡶⠉⢸⡼⣇⣆⠠⡘⢧⡀⠀⡀⠀⡀⠀⢀⠆⢠⣧⡟⠟⠁⠁⢀⣴⠃⠀⢠⠟⠁⠀⣰⡇⠀⢐⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⣤⣠⡟⠀⠀⠈⠁⠹⠟⣄⣏⡆⢳⣄⢘⣄⣸⣤⣾⣾⠉⣫⣶⡿⢿⣷⣋⡀⠀⠰⡻⢶⠶⣞⣁⡠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡞⠉⢻⣆⠀⠀⠀⠀⠀⠀⠈⠛⣫⣟⣼⣯⠾⠛⠛⠉⢹⡋⠉⠀⠀⠀⠀⠹⣯⣻⠾⠒⢺⡗⢦⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⣄⡀⢹⡶⢦⣄⣀⠀⠀⠀⢀⡽⠳⡄⠈⢣⡀⠀⠀⠈⣷⣄⣠⢤⣔⣦⠴⠟⠁⠀⠀⣼⢡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⢻⢿⡷⢶⣮⢍⣉⣛⡟⠀⠀⠙⣆⠀⢧⡀⠀⠀⢘⡶⠛⣏⣵⠀⠀⠀⠀⢀⡼⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣌⠓⠤⣌⣉⣉⣲⣷⡀⠀⠀⢹⢂⢸⣘⡾⠛⠉⣠⠞⠁⡇⠀⠀⠀⠀⡿⠤⣄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠉⣩⠟⠁⠙⠓⠒⢞⣟⣼⠛⣊⡤⠞⠁⠀⢸⠃⠀⠀⠀⠀⡇⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⢁⡀⢰⠃⠀⠀⠀⠀⠀⠈⠉⠉⠫⡁⠀⠀⠀⠀⡾⠀⠀⠀⠀⢀⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠥⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢰⡇⠀⠀⠀⠀⡼⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠙⢦⡀⠀⡼⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠶⠶⠿⢾⠃⠀⠀⣿⠀⣀⠀⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣴⠏⠀⠙⠘⠒⠓⠂⠢⠕⢚⠛⠳⠦⠄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠏⢸⡇ ⠸⣿⣶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠘⣷⡄⢀⣠⠶⣦⣤⣶⡶⠶⠶⣤⣀⣀⠀⣸⠏⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⣠⠏⠀⢸⡇ ⠀⠈⢿⣿⣌⠉⠛⠳⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢽⡟⣡⡴⣆⠉⠉⠉⠛⠛⠛⠉⠉⠙⣷⡄⠀⠛⢦⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠀⡼⠁⠀⠀⢸⡇ ⠀⠀⠀⠻⣬⠳⣄⠀⠀⠀⠀⠩⣛⠛⠶⣤⣤⣄⡀⠀⠀⠀⠘⠓⠒⠒⢶⡞⢠⠟⢀⣿⡴⠋⠉⠙⠦⡀⣸⡟⣦⢸⣿⠦⢤⡾⠀⠀⣀⡴⠚⠋⢶⠀⠀⣠⠞⠁⠀⠀⠀⢸⠁ ⠀⠀⠀⠀⠘⣧⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⢦⣤⣤⣤⣠⣞⣁⣺⣴⣟⠁⠀⠀⠀⠀⠀⠹⡿⣦⣸⢸⡁⠀⠀⢀⣴⠛⠉⠀⠀⠀⡄⣠⠞⠁⠀⠀⠀⠀⠀⣼⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣷⣴⡾⠿⢿⣦⣀⠀⠀⠈⢳⠀⠀⠀⠀⠀⣼⠟⠉⠛⠒⣿⣶⣾⣿⣬⣳⣄⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢳⡄⠀⠀⠀⠀⠀⢀⣾⠟⠉⢀⣠⡤⣤⣀⣀⠈⠙⢦⡀⠀⢷⠀⠀⠀⣸⠃⠀⢀⡴⠟⠉⠀⠀⠀⠀⠙⢻⣿⡞⠃⣼⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⣶⣀⠀⠀⠀⣼⢁⣤⠼⣶⣿⣿⣿⣿⣦⣅⢤⠀⠙⣤⠈⣇⠀⢰⠇⢀⡴⠋⠀⣠⣤⣭⣤⣤⣄⣒⣀⠹⣧⠀⢸⡇⠀⠀⠀⠀⠀⢀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠘⢿⣧⡀⠀⡏⢻⡇⠀⠈⢻⢿⣿⣿⣿⣿⣿⡅⠀⠈⠁⢻⣠⡏⠀⠈⠀⢰⡟⠉⠉⢻⣿⣿⣿⣿⣿⡛⢸⡇⢸⡇⠀⠀⠀⠀⢀⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⣼⠏⢷⡀⠇⣸⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⡟⠀⠀⠀⢠⣿⣧⣀⣠⣾⣼⣿⣿⣿⣿⡇⠸⣇⣸⣷⠀⠀⠀⣿⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠏⠀⣸⣷⠀⢿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣤⣿⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⣻⣿⣆⠀⠀⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣾⡿⠻⡃⠈⠛⢿⣿⣿⣿⣿⣿⠿⠟⠛⢻⣯⠔⢾⡯⠭⠿⣧⣄⣸⣿⠿⠿⠿⢿⣿⣿⣿⣿⡟⠀⠀⣰⣿⣟⣹⣄⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢴⡶⣶⠄⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢹⣿⣿⣿⣷⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠈⣹⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣇⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⣷⣠⠾⣄⣠⣶⡄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠉⠁⠀⠀⠉⠉⠁⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⣀⣀⣠⠴⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣿⠿⠶⣶⣲⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠿⣭⡁⠀⠀⠾⢿⣷⣏⠉⠉⠋⠉⠙⠓⠶⣤⣀⠀⠀⢀⣠⣴⣶⣿⣿⠿⠿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠈⠻⣶⠀⠀⠸⠿⢻⡾⢧⡀⠀⠀⠘⠀⠀⠹⠷⠞⠋⠉⠉⠀⠰⣀⣷⣴⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⡇⠈⢿⣶⣠⠀⣧⢠⠀⢰⡀⠀⠀⠀⣠⣠⣿⠿⠋⢿⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣤⣼⡇⠀⠀⣿⠻⠶⣼⣞⣆⠸⣇⡀⢲⢀⣿⠟⠁⠀⠀⢸⣿⣿⡿⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣟⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⣿⣿⣤⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⠤⣤⣟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡴⠋⢀⣤⡀⠀⣩⣧⠠⢤⠀⠀⠀⠘⣿⡟⠇⠁⠀⡇⠀⠀⠀⠀⣀⠲⣿⣼⣙⡇⡴⢺⡟⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⡾⣧⡇⠐⠓⢻⡆⠀⠻⠄⠀⠀⢻⣇⠀⠀⠀⡇⠀⠀⠒⠚⠉⢠⡇⠀⣀⣀⡐⠚⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⣰⢾⠀⠀⠀⠀⠀⢻⡛⠋⠀⢀⡤⠤⣄⠀⣧⠀⠤⠀⡤⠄⢼⣿⠀⠀⢸⡇⠀⠀⠀⠀⠁⣸⡇⡾⠁⠀⠙⡆⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⢀⣾⢆⠀⢰⡇⢸⠀⠀⠀⠀⢀⣀⣷⣄⠀⢹⡀⠀⠘⡆⢹⡀⠀⠀⠀⠀⠈⡿⠃⠀⢸⠁⠀⠀⠀⠀⠀⣿⣇⠇⠀⠀⣸⠃⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⠀⠀⠀⢿⠘⣇⢸⡅⠘⢧⣄⡀⢸⠟⠉⠉⢻⣶⣌⢧⡀⠀⢹⡄⣇⠀⠀⠀⠀⠀⢱⠀⠀⡜⠀⠀⠀⠀⠀⢀⣿⢹⠀⢀⡜⠃⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣄⠀⠈⢇⠘⣯⣧⡀⠀⠀⠙⠛⠀⠀⠀⠀⠙⢿⣇⢳⡄⠘⡇⢿⠀⠀⠀⠀⠀⢸⡆⠀⡇⠀⠀⠀⠀⠀⢸⣿⢸⣀⡼⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠳⣴⡛⠁⠈⢻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠹⣼⠇⣸⡀⠀⠀⠀⠀⠈⣇⠀⣇⠀⠀⣀⠀⠀⣿⣿⠀⠋⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠈⢿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⣠⣿⡿⢦⡀⣚⣀⣸⣿⣿⠟⣳⡿⠛⣶⣹⣛⣿⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣸⠛⢾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡙⢷⠛⠛⠳⡼⠓⠲⠿⠿⠉⠙⡾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠙⠳⢦⡀⠀⠀⣦⣄⠀⠀⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠘⣿⢳⡄⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣏⣨⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣁⡠⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠰⣠⡂⡐⠀⡠⠒⠀⠐⠦⡀⠑⣷⡇⠀⠀⢀⠔⢁⡤⠒⠈⣁⣤⣬⡄⠀⠀⠀ ⠠⡵⠋⢀⠃⢀⠃⡪⠕⡀⠀⡈⢆⠈⢆⠀⡠⢃⠔⠁⡠⠖⠉⢉⣁⣒⣾⠄⠀⠀ ⢺⠏⠀⡜⠀⠘⢀⡥⠂⢻⠷⠮⣢⡣⠘⣦⢡⣪⡴⢬⠆⣒⣈⢁⡒⠒⣺⡄⠀⠀ ⠃⠀⡸⠱⢠⠇⢸⡠⠊⢀⠔⡨⠝⢻⣧⡹⠋⠁⠀⠀⠀⠀⠀⢹⠤⣀⡐⣧⠀⠀ ⠀⡰⢡⢁⡞⠀⡎⠀⠰⠁⠌⡀⡐⠁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢗⠠⠮⣳⠃⠀ ⡰⠡⠃⣮⠀⣾⠡⢀⠁⡰⢠⣵⠁⣼⠁⠀⠀⠀⠀⠀⠠⠂⠄⠀⢨⢦⡾⠿⠀⠀ ⠀⢀⡾⠂⣼⠆⠆⡆⢀⣇⠇⡇⣰⠇⠀⠠⠀⠀⢀⣴⠟⠛⠒⠢⢸⣺⣧⡀⠀⠀ ⣴⡟⢁⣞⡟⢸⢠⠁⠈⣾⣸⣦⡞⠀⠀⠀⣠⡶⢛⣠⡴⠶⣴⡢⢰⡿⢿⠃⠀⠀ ⠏⢀⣮⣿⠀⠀⢸⠀⠀⡏⡿⣾⣇⠀⠀⠀⣩⣺⢛⠀⢸⠀⣿⡂⢸⡖⠁⠀⠀⠀ ⣴⠋⢸⠏⠀⡇⢸⡆⢸⠇⣷⣾⠀⠲⡄⠐⡏⠰⣖⡛⢓⣻⡿⢀⡏⢿⣴⡀⠀⠀ ⡇⠆⡿⢰⠀⠁⢸⠇⢸⢸⠉⣿⠀⢀⠇⣦⡈⠢⠀⠉⠘⠃⠀⢸⢅⡞⠝⣇⠀⠀ ⠸⢠⡇⣾⡀⠀⢸⠀⣸⢺⠐⡉⠀⠀⠀⠀⠩⡀⠀⠀⠀⠀⠀⡌⠀⠈⠘⡨⢁⣄ ⠀⣻⢰⡇⠀⡷⠈⠀⢧⣹⠀⠈⠢⢄⠀⣀⠤⠃⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀ ⢠⢯⢸⡇⠈⠰⡆⠀⣨⡟⠀⠀⠀⢀⡙⣁⣤⠴⠒⠂⢀⠎⢸⠀⠀⠀⠀⠀⠀⠀ ⢸⢺⡈⠃⢠⠀⡇⠀⣷⢷⢄⠀⠹⣯⣡⡉⢥⠀⢀⡴⠹⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠸⣼⠡⣣⠘⠀⡇⠀⡿⠈⢦⡢⡀⠁⠀⠀⠀⣠⠞⠁⡄⠀⢠⠔⠁⠀⠀⠀⠀⠀ ⡣⣋⢇⠹⠀⡄⡇⠀⡇⠀⠈⠮⠝⢳⡖⠲⠟⠁⠀⢠⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀ ⠘⣤⡁⠓⣆⡗⢻⡀⣷⠀⠀⠈⠄⠐⡄⠀⡰⠀⢀⠎⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀ ⠀⠈⣧⠀⠘⡅⠛⡳⡹⣃⠀⠀⠈⠢⠤⠤⠁⠂⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⠴⠶⠶⠶⠾⠭⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢈⣡⣤⠴⠒⠒⠋⠉⠉⠉⠉⠉⠳⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⣤⠞⠋⢉⣀⣤⠤⠴⠒⠒⠒⠚⠉⠉⠛⠒⠛⠲⣤⠄⠀⠀ ⠀⠀⠀⠀⠀⣠⡟⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⠅⣠⣿⣥⣶⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀ ⠀⢀⣤⡶⡞⢉⢾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡝⡜⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠁⠀⠀⠀⠀ ⠀⢸⠁⠶⣸⣾⣿⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣇⣿⣿⣿⣿⣿⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣠⣶⡾⠿⢯⠖⠀⠀⠀⠀⠀ ⠀⠹⣤⡴⢿⣇⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⡿⠿⠿⠿⠟⣛⣛⡻⠏⠉⠉⠁⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⣀⣻⡿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠛⠛⣿⣿⣿⣿⣷⣾⣯⣍⣀⣀⡀⠀⢀⣀⣀⡤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣤⠴⣿⣆⠀⠀⣄⠀⢠⣼⡟⣿⡏⠀⠀⣠⠞⣋⡭⠿⠿⠿⢿⡍⠙⠛⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣴⣿⣿⡄⠀⣿⢳⣿⠙⠳⣽⢧⢀⣾⡷⠚⠁⣀⠤⠤⠤⢭⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣏⢉⣽⣿⡿⡿⣿⢿⣢⣀⣹⣮⣿⡟⢡⣔⣮⣄⡀⠀⠠⣄⠈⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣟⣻⣿⡗⢻⣟⡆⢿⠉⠀⠈⠙⠛⠋⠁⠀⠀⠉⢦⡰⡀⠑⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡃⣼⣿⣾⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢽⣷⣤⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⢋⡿⠓⣻⠿⣇⠀⠉⠂⠀⠀⠀⠒⠉⠉⠀⠀⢸⣿⡗⣦⡟⠀⠀⢀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⡟⡿⢋⣠⡟⡶⠤⠄⠀⠀⠀⠀⢸⣋⣀⣀⠄⠘⠀⢸⡇⠀⢠⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⢹⣿⣻⣇⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⣀⣤⡴⣾⠟⢠⠏⠀⣿⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣿⡿⢧⠻⣦⣤⣤⣤⣴⣶⣿⠿⣿⣟⡻⢵⣺⠏⠀⡼⣆⢠⡟⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⠘⣧⢹⣖⣺⡷⣶⣶⡿⡭⣿⣲⡞⣿⠷⢲⣴⣇⣿⠞⡰⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣼⣿⣦⣻⣷⣶⣶⠶⠟⠋⢩⣿⢱⢛⣴⢏⣤⡾⢋⣴⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⠛⠓⣋⣻⣿⣿⣤⣴⠞⣿⣯⡿⢋⡤⣾⣿⣤⣿⡿⠛⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣾⣿⠟⠉⣻⡟⠉⣠⣾⣿⣿⢒⣥⣶⣿⣿⢛⣁⡠⠴⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⣿⣿⣇⣠⠶⣾⣷⣮⣿⠟⠁⢸⢉⣩⠟⣻⣿⣿⣖⣲⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣏⡸⣿⢫⣿⣿⣦⠹⣿⣿⠁⠀⠀⢸⣧⣴⣿⣿⣷⣶⣶⡎⣿⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣋⣾⣏⣿⡹⣿⠛⠓⠻⣿⣕⢶⣖⣒⣛⠛⢟⢿⣿⣿⣿⢣⡿⢸⣿⡽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⣴⣲⣯⣽⡿⣯⣻⣧⣶⢟⢃⣼⣿⣀⡬⡆⠀⠀⢫⣿⣧⡙⣝⣿⣿⣿⣾⣿⣿⠁⡿⢡⡏⢁⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣶⠂⣠⡼⠟⠓⠺⣿⣿⣿⣿⣿⣷⡀⠀⠈⣾⣿⣿⠛⡿⣿⣿⣿⣿⣿⠀⢇⠸⡇⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣧⣿⢋⣴⣿⣿⣶⣮⠉⠛⢿⣿⣿⣷⣴⣿⣏⢻⣏⣧⣤⣾⣿⣿⣿⡇⣶⡌⠲⡍⢲⠌⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⡀⢻⡌⢿⣿⣿⣿⣿⣇⠹⢋⣴⣟⡜⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣧⠈⣿⡌⢿⣿⣿⡿⢛⡴⢛⡵⢋⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⡾⣻⣿⣿⣿⣿⣿⡇⢸⣿⡜⣿⣗⡺⢭⣤⣻⣴⣿⣿⠓⡦⢤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⢿⣿⣟⡿⣿⡿⡄⣿⣿⣾⣿⣿⣿⣿⡿⣿⣟⢙⢿⣷⣾⣤⡇⢹⢹⡿⣿⣽⡆ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠿⠿⠿⡿⠿⠿⠷⠿⢷⣿⣿⢯⣿⣮⣝⢷⡸⣿⣿⠈⢿⣿⣿⠃⠈⢿⣿⣴⠙⡮⣍⠛⠛⠻⠷⠷⠶⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⢿⣿⢿⠟⢿⣿⣯⢀⡌⢿⣮⢆⠀⠀⠙⢿⣿⣇⣨⠛⡶⣶⣶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡏⠠⢿⢯⠻⡼⢿⡜⣿⡻⠷⡀⠀⠀⠉⠛⠿⣷⣇⢹⡧⢼⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣬⠏⠀⢳⣝⠾⡇⡅⣠⣴⠾⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠀⠀⠀⢻⣷⣶⡋⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢪⣟⣩⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠁⠐⠿⠚⠓⠒⠒⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠃⠀⠀⢀⣀⣠⣖⣩⠀⠀⠀⠀⠀⠀⠀⠀⡔⢹ ⢰⠤⣄⣀⠀⣀⡤⠖⠛⠉⠉⠙⠓⠶⣄⡀⣤⣤⢒⣱⡤⢀⠀⠐⣦⡖⠤⣸⠀⢸ ⢸⠞⠒⣬⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡅⢰⠙⠮⣰⡳⠶⢄⡉⣺⠇⠀⡎ ⠸⣦⣠⣭⢵⡖⡦⢄⠀⣀⡤⠤⠤⢀⣀⡠⠌⢳⣼⠀⢀⡞⠀⠀⠀⢈⣾⠀⡸⠁ ⠀⢹⡿⠎⡜⡰⢡⣃⠀⣃⡐⠛⠋⠁⠀⢻⣸⣀⡇⢀⠎⠀⠀⢀⡴⠁⠇⢠⠃⠀ ⠀⡎⠺⠴⡠⢡⠧⠀⣀⣹⢃⢇⡀⠀⠤⠼⠆⡦⣇⡞⠀⠀⣠⠊⠫⣽⢀⠏⠀⠀ ⠠⣞⡉⠉⠑⠃⠀⠀⠀⠘⠚⠒⠒⠂⠈⢉⣉⣠⡼⠁⠀⡰⠁⠀⢀⠇⠎⠀⠀⠀ ⠀⢀⣽⡹⠫⠙⠀⠀⢰⢒⠖⠒⠦⠉⠉⡇⠀⢘⣳⣦⡜⠁⢀⣠⣞⢸⠀⠀⠀⠀ ⠰⣞⡀⠑⠄⣱⠀⣀⡸⣈⠀⣀⣀⠠⠔⠁⢀⡴⠾⠴⢀⡠⡋⢰⢀⠟⠀⠀⠀⠀ ⠀⠈⠳⡀⠀⠘⡢⠤⠜⣀⠔⠀⠀⠀⠀⡰⠿⣿⡄⣀⣼⡢⢞⡎⡸⠀⠀⠀⠀⠀ ⠀⢀⣠⡾⠓⠦⠤⣉⣉⣀⣀⣀⠠⠴⠊⠀⢨⣾⠳⡕⣌⣢⡜⠀⣇⠀⠀⠀⠀⠀ ⢠⠎⠸⣏⡠⣾⡀⠀⢾⠀⠀⠀⠀⡀⠀⣤⠞⠉⢠⠁⢸⠋⢈⠏⢨⠇⠀⠀⠀⠀ ⠈⢢⣀⠏⠀⠋⠻⢾⣌⣆⣰⣰⣤⣷⣛⡼⠶⣖⡁⢀⢧⡤⠊⠀⡎⠀⠀⠀⠀⠀ ⠀⢏⠘⢦⣀⠀⠀⠀⢹⣗⠻⡉⠁⠸⡁⢀⣀⣈⠟⠋⢹⢩⠖⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⡟⣖⠿⢥⣴⡃⠈⢆⠰⣀⣀⠿⣻⡟⠀⠀⣠⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢌⠁⢒⡞⠑⠤⢼⣦⢞⡣⠞⠁⡇⠀⠀⡏⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡁⠤⠌⠀⠀⠀⠈⠀⠑⠄⠀⢸⠀⠀⠀⠇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠈⠢⣀⠞⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣀⣠⠃⠂⠴⠀⠔⠴⠴⠄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⡇ ⠈⢻⣷⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠹⣆⣠⠴⠲⣶⣶⣶⣶⣦⣤⣄⡼⠋⢈⡇⠀⠀⠀⠀⠀⠀⣀⡴⠋⡴⠃⠀⡇ ⠀⠀⠙⣿⣤⡉⠙⠓⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⣞⣁⣀⣸⢏⡖⢻⢀⡤⠬⣍⠁⣤⣌⢻⣆⣉⣱⠀⠀⢀⣠⢶⡛⠁⢀⠞⠁⠀⢠⡇ ⠀⠀⠀⠈⢧⠙⢆⠀⠀⠈⠑⠈⠉⠛⠓⠶⢤⣤⣀⣀⣰⣃⣸⣴⡛⠁⠀⠀⠈⢳⣯⣹⣼⠉⠉⢁⣤⠞⠉⠀⢸⢁⠔⠁⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠈⢧⡀⠳⣄⠀⠀⠀⠀⠀⢀⣤⣶⡷⠿⠿⠿⢭⡀⠈⠱⡄⠀⠀⢀⡼⠋⠙⣺⣷⡶⠿⢽⣦⣀⢀⣴⡏⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⠘⢦⡀⠀⠀⠀⡾⢋⣠⣲⣦⣶⣖⡄⡈⠳⡄⢹⡀⠀⡼⠁⣠⠞⠉⣠⣤⠤⢄⡉⢿⡋⠸⡇⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⢻⣦⠀⢸⢳⡏⠉⢻⣿⣿⣿⣿⣮⡀⠘⠂⣧⣸⠃⠚⠁⡴⠛⠻⣿⣿⣿⣿⡶⢿⢠⣇⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⡏⢳⡸⢸⣿⣶⣾⣿⣿⣿⣿⣿⣷⠀⠀⢸⡇⠀⠀⣼⣧⣤⣴⣿⣿⣿⣿⡇⢸⣦⣿⡀⠀⢼⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣠⣼⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣠⣾⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣹⣿⢧⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠋⢸⡀⠀⠉⠛⠛⠋⠉⠁⣠⠟⠁⠈⣩⢭⡉⠙⠻⣍⠉⠉⠉⠉⠉⠙⣄⠀⠻⣿⣿⣷⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠘⡏⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠺⠿⠔⠳⠤⠿⠂⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⣀⣤⠴⠛⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠿⠛⣻⣿⠷⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⠙⠳⣄⠈⢹⣿⣷⣤⡀⠀⠀⡎⠙⢶⡤⠶⠿⠛⢛⢫⣍⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣿⡀⠻⣦⡄⢳⣠⠀⣄⠀⠀⢠⣤⡿⠟⢹⡎⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣤⣴⣿⡇⠀⠛⠙⠺⣿⣆⢻⣤⣶⡼⠋⠀⠀⠸⣿⣿⡏⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⠟⢛⡛⠛⣿⡀⣀⠀⠀⢹⣿⣿⠛⢻⡇⠀⠀⠀⢠⣿⡿⢿⢙⣷⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢲⢿⡿⠘⠿⣇⠈⠦⠀⠀⣿⡇⠀⢸⠇⠀⠐⡚⢁⡇⢉⣉⣐⠺⣼⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⣀⠀⠀⡾⡇⠀⠀⠀⠘⣏⠁⢀⡖⠒⣄⢹⡀⠂⠐⠂⢹⣇⠀⢸⠀⠀⠀⠈⢸⣧⡏⠀⢈⡇⢻⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣇⠀⠘⣏⢧⢸⡃⢧⡀⠀⣴⠶⠿⣧⡘⣧⠀⠸⡌⡇⠀⠀⠀⠘⡇⠀⡿⠀⠀⠀⠀⣼⣿⠀⢀⠞⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣇⠀⠹⡌⢿⣧⠀⠉⠛⠋⠀⠀⠈⢻⣮⢧⡀⡷⢿⠀⠀⠀⠀⣧⠀⡇⠀⠀⠀⠀⣿⢻⣠⠏⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠮⣅⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠙⣧⡳⠃⣼⡀⠀⢀⠀⣸⣄⣧⣀⣤⡀⣼⣿⠈⣱⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⡿⣿⣦⠀⠀⠀⠀⠀⠀⠘⣷⣞⢻⣯⠷⢖⣶⢿⣿⣥⠿⣥⠿⠾⠿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠉⠳⢤⡀⠀⢠⣄⠀⢸⡿⡇⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣿⢳⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣠⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⣶⣶⣿⣿⣿⣿⣷⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠻⠛⠋⠉⠉⠉⠛⠿⠿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣶⣿⣿⣿⣿⣿⣿⣶⣦⣌⡉⠻⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡌⠻⣿⣿⣦⠀⠀ ⠀⣼⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣿⣿⣧⠀ ⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⡇ ⣾⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣷ ⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿ ⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿ ⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⡏ ⠸⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣰⣿⣿⠇ ⠀⠹⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣰⣿⣿⠏⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣸⣿⣿⠋⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⠟⠁⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⠁⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡇⠀⣠⠇⠀⢠⡆⠀⠀⠠⠃⣀⡴⠶⠶⠶⢤⣀⡀⠀⠀⠉⠱⢆⠹⣞⣎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⢀⣠⠴⢞⠋⠉⠁⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⢀⢏⢿⠀⠀⣸⠁⠀⠀⢰⡾⠉⠀⠀⠐⠀⠀⠉⠛⢶⣄⠀⠀⠈⢳⣿⡿⣄⠀⠀⠀⠀⠀⠀⣰⠞⠀⠀⢀⣴⠷⠋⠁⠀⠀⠀⣀⡠⣶⣒⣵⣲⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡸⢃⡾⣾⣾⡀⠀⡟⠀⠀⢀⡿⠀⢀⡴⠶⠦⣀⠀⠀⠀⠀⠙⢷⡄⡀⠀⠳⣷⠀⠀⠆⠀⠀⢀⡼⠃⠀⢀⡴⠛⠁⠀⠀⣀⣤⡶⠿⠿⠚⠛⠋⢉⣉⣉⣻⡄⠀⠀⠀⠀⠀⠀ ⠀⡰⢣⡿⡘⠀⠀⠀⣸⠁⠀⠀⢸⡇⠀⠁⣤⠶⢤⣈⠳⣀⠁⢦⡀⠀⠹⣆⠀⠀⠹⣷⠀⠀⠀⢠⠎⠁⢀⡴⠋⠀⠀⢀⣴⠞⢋⠁⠒⠀⠀⢀⠀⠐⣚⢩⣙⠿⡷⠦⠀⠀⠀⠀⠀ ⢐⣵⣿⡷⠀⠀⠀⢠⡟⠀⠀⠀⣸⠀⠀⢸⠃⣀⣀⣈⣳⣮⡢⡄⠙⢦⡀⠘⢧⠀⠀⢻⣄⠀⢠⠟⠀⣰⡟⠁⠀⣀⡴⠋⢀⣀⠀⣀⣠⠶⠖⠛⠋⠉⠉⠉⠉⠳⡏⠀⠀⠀⠀⠀⠀ ⠞⣹⢷⠁⠀⠀⠀⣾⠀⠀⠀⢠⡇⠀⠀⣯⡾⠛⠀⠩⠭⠭⢿⣿⣷⣤⣙⢦⡀⢷⡀⠀⢿⠀⡞⢀⡼⢋⣴⣦⣞⣫⣤⣺⡭⠚⠋⣡⣠⠤⠖⠒⠛⠛⠛⠛⠛⠳⢿⠄⠀⠀⠀⠀⠀ ⣴⢯⠃⠀⠀⢠⣾⠃⢠⠀⢰⢸⠃⠀⢸⡟⠉⠀⣠⠴⠚⠉⠀⠀⢀⣨⣭⣿⣾⣦⣳⡀⠸⣆⠁⣼⣵⡿⠛⠃⠀⠀⠈⠃⠀⠉⠉⠛⠛⢳⣤⡬⠕⠒⠒⠒⠚⠛⢾⡇⠀⠀⠀⠀⠀ ⢫⠇⠀⠀⠀⣼⠏⢠⠏⢀⣧⡏⠀⠀⡼⠃⣠⠞⠁⠀⠀⢀⡴⠛⠉⣀⡴⠖⠮⠭⣿⣷⡀⣿⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣤⣀⠀⠈⠩⠉⣻⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⡟⠀⢸⡽⠁⢀⢰⣧⡞⠁⠀⠀⠀⣴⠋⠀⣠⠎⠁⠀⠀⣠⠶⠞⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢉⠙⠓⠲⣤⣼⠈⢻⡀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⣿⠀⢀⣿⠃⠀⡈⢸⡏⠀⠀⠀⢀⡞⠀⠀⣴⠃⠀⠀⢀⡜⠁⠀⢀⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⣌⣉⣒⣀⣽⠳⣼⡇⠀⠀⠀ ⠀⠀⣰⡟⠀⣼⠁⢀⡾⡟⠀⢠⣇⡟⠀⠀⠀⢀⡞⠀⠀⣰⠃⠀⡜⠀⢸⠁⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⡀⠀⠀⠉⣿⣾⣿⠀⠀⠀⠀ ⠀⣰⠏⠀⡼⠁⢀⡾⠸⠀⢀⣼⢻⠃⢀⠀⠀⡾⠀⠀⢀⡏⠀⣸⢡⣤⠇⠀⠀⡾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⡌⢹⣆⣠⣼⣟⣿⡟⠀⠀⠀⠀ ⣼⠃⠀⠞⠁⠀⣼⢡⠇⠀⣸⣧⡏⠀⡄⠀⣸⠁⠀⠀⣼⠀⣴⡇⡜⡜⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⠉⠓⠀⠀⠀⢹⡁⢻⣿⡿⠋⣿⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢀⣾⢃⡏⠀⢰⡿⣸⠁⢸⠁⢠⡇⠀⠀⢰⡟⢰⣽⢸⣿⠃⠀⢠⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣤⣀⠀⠀⢸⣅⣨⣿⣒⠄⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣻⠋⠀⢠⣿⣧⡇⢠⡇⠀⢸⠁⠀⠀⡟⡇⣿⠏⢸⡇⠀⣀⣸⡟⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠈⠙⠳⣄⢸⣅⣾⣿⣿⣠⡇⠀⠀⠀⠀⠀ ⠀⢀⡼⣷⡿⠉⠀⣰⡟⣼⡞⠀⢸⠁⢀⡿⠀⠀⠰⢀⢃⣿⢀⣿⣅⠀⢨⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁⠀⢀⣀⣀⡄⢠⣤⣼⡀⠀⢈⣾⣿⣼⠚⣿⠇⠀⠀⠀⠀⠀ ⣴⡟⣱⡏⠀⠀⣴⡿⡴⡽⠁⠀⡞⠀⢸⠁⠀⠀⠀⢸⣾⡟⢸⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠋⣀⣠⣴⣶⠿⠿⠿⠿⣾⣯⣽⡧⠆⢸⣿⠿⡿⢞⡿⠀⠀⠀⠀⠀⠀ ⣹⡿⠏⠀⢀⣾⢻⢿⣿⠁⠀⢀⡇⠀⠈⡇⠀⠀⠀⢸⣿⠇⣿⣇⡉⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠿⠛⢁⣤⣾⣿⠟⠉⠙⠦⡄⠀⠀⣾⣍⣁⡀⠀⢸⠇⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀ ⡿⠁⠀⢀⣿⣡⣿⣻⢃⠀⠀⢸⡇⠀⢠⡇⠀⠀⠀⣷⢷⠀⣿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢩⡞⠁⣀⠀⠉⠀⠀⡧⠀⢀⣾⣯⣽⡇⠀⣸⡍⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⣴⣿⠿⢋⡟⡿⠆⠀⠀⢸⠀⠀⣿⢃⡇⠀⢸⣼⢇⢠⡿⠀⠙⢇⠏⡳⣄⠀⠀⠀⠀⠀⣠⣿⠗⠚⣁⡀⠈⠲⠤⠴⠞⣁⣴⡾⣿⣿⠉⢀⣰⣿⢻⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⣾⡏⠀⠀⣸⣸⡹⠀⠀⠀⡌⠀⠀⢿⢸⡇⠀⣼⡿⠘⢸⣿⣾⣶⣾⠀⠀⠘⣷⣤⣄⠀⣰⠙⣆⠀⠘⢿⣿⣟⠲⠶⠷⣿⠛⣻⣾⣿⡇⠀⢀⣿⠉⢯⣗⣯⡙⣦⠀⠀⠀⠀⠀⠀ ⣟⡿⠀⠀⠀⡿⡿⠁⣸⠀⢀⡇⠀⠀⣸⢸⠀⠀⡇⡇⠀⣾⣿⣿⣿⣿⠀⠀⠀⠈⢿⢈⠀⡇⠀⢹⡄⠀⠀⠙⠿⣷⣶⠄⠘⣞⡭⠟⠋⠀⠀⡼⡏⠀⠈⣿⣷⢹⣿⠀⠀⠀⠀⠀⠀ ⣿⠃⢰⠇⣸⣽⡑⠀⡇⠀⢸⠇⠀⢰⡟⣿⠀⠀⢳⠁⠀⡟⠉⠙⣻⣹⠀⠀⠀⠀⣼⢨⢻⣧⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⢹⡇⠀⣰⡿⣁⠼⠏⡆⠀⠀⠀⠀⠀ ⡏⢀⡎⠀⣿⡿⠁⣸⡅⠀⢸⠀⠀⢸⣿⡏⠀⠀⣼⡇⠂⡇⠀⢰⣿⢟⠀⠀⢀⡴⡏⠈⠸⢿⣷⣄⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠙⠺⢯⣖⠉⢀⣠⣷⡦⣀⠀⠀⠀ ⠀⢸⠃⢀⣷⢃⢀⢿⣧⠀⢸⠀⠀⢸⣿⠃⠀⠀⣿⢻⢸⠁⠀⡞⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠉⠺⢥⣈⠓⠈⢱⡀⠀ ⢀⡏⠀⣸⡿⡘⢸⣼⡿⠇⢸⠀⠀⢸⣿⢀⠀⣀⠋⣆⣾⢠⠀⠙⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠠⠌⠙⠲⠾⠷⠤ ⢸⠁⢸⣿⠇⣷⣾⡏⠀⠀⠊⢠⡀⢸⡇⢸⠀⢠⢳⠙⡟⡇⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⠀⣿⣿⡇⠀⢶⡄⢸⡇⢸⠇⠃⠀⡘⡘⡆⣯⠀⠀⠀⠀⠀⠀⠙⠓⢦⣄⠀⠀⣠⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣧⡟⠀⣿⡧⡇⠀⠸⡇⢸⣇⡸⠀⠀⠈⠗⡇⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⣿⠋⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠟⣷⠀⢿⣿⡇⠀⠀⡇⠀⢣⡇⠀⠀⠀⠀⢻⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣤⣴⣾⡿⠛⠛⠉⠀⠉⠁⠀⢠⣾⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⣿⡀⢸⣿⣇⠀⠀⡇⠀⠘⡇⠀⠀⠘⢠⡈⣿⣿⠀⠀⠀⠀⣠⣤⣾⣿⣦⣤⣤⣤⣿⠵⠋⠀⡀⠀⠀⠀⠀⢀⡴⠋⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠈⡟⣇⠈⡏⣿⠀⠀⡇⠀⢠⡇⠀⠀⠀⢸⡗⢧⢿⠳⣄⠀⠀⠀⠀⢡⣼⢦⢤⠀⠄⢀⣀⣴⣏⣀⠀⠀⠀⣠⡿⠁⢰⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⣷⢻⡄⣧⣿⠀⠀⣷⠀⢸⡇⠀⠀⠀⠀⣧⡛⠀⣷⠈⢳⡄⠀⠀⠀⢠⠟⠛⠛⠉⠉⠀⠀⠁⠀⠀⢠⣾⡿⠁⠀⣿⠀⠀⠀⢸⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣇⣹⡀⢻⡈⢸⠀⠀⢻⠀⢸⡇⠀⠀⠀⠀⣿⠁⠀⠈⣷⣄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠟⠁⠀⢠⠃⠀⠀⠀⢸⣠⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠈⢳⢧⣧⠀⠻⣌⡆⠀⢸⠀⢸⣷⠀⡄⠀⠀⣿⠀⠀⠀⠸⣏⠳⣌⡳⢦⣄⡀⠀⠀⠀⠀⢀⣀⣴⣻⠟⠁⠀⠀⠀⣼⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢦⡘⡏⢮⣧⠀⠙⣧⠀⢸⡄⢸⣿⡀⢃⠀⢹⣿⠀⠀⠀⠀⠘⣷⣄⣉⠛⠺⣿⣛⡛⠛⣛⣛⡿⠟⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⣀⠙⠶⣄⡘⢦⠀⢹⡀⢸⡇⢸⣿⣇⠈⡇⢼⣿⠀⠀⠀⠀⠀⠸⡆⠉⠉⠑⢒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣧⡀⠈⡉⠛⠳⢦⣧⠀⣿⣼⡇⣿⡄⠘⣼⣿⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠘⣆⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣽⣶⣿⣀⠀⠀⢿⡄⠙⠃⡇⢸⣧⠀⠸⣿⣷⠀⡀⠀⠀⠀⠀⠹⡄⠀⠀⠹⣄⠀⠀⢀⣾⠃⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀ ⠀⠀⠀⠈⢻⣷⠈⠀⠀⠈⢷⡀⠀⢇⢸⡼⣇⠀⢻⡙⡆⠁⠀⠀⠀⠀⠀⠹⢤⣀⡀⠹⠀⣀⢈⣁⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀ ⠀⠀⠀⠀⢻⣻⣆⠀⠀⠀⠊⢧⠀⠸⡌⣇⠻⣷⠈⣷⡹⣄⠀⠄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠙⠺⠒⠻⢧⣀⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠀⠉⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠙⣤⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠻⡀⠀⡀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠴⠶⠚⠋⠀⣀⡀⣀⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠈⢷⣦⠀⠀⠀⢀⣹⠞⠀⠀⠀⠀⠀⠘⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⡳⠦⣤⣀⣀⣀⣈⣙⣳⣶⣤⠴⠶⠒⣫⠽⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣋⣀⡤⣴⡿⠥⣤⣀⡀⠀⠀⠀⠀⠘⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠦⣄⡀⠀⠀⠀⠁⠀⠀⣀⣤⠄⠈⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣻⡿⠾⠿⠂⠀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠒⠦⣤⠾⠛⠁⠀⣠⣴⣾⠝⠛⠉⠉⠛⠉⠉⢿⣿⣯⣓⣶⠒⢛⣻⣷⣿⣿⡀⣾⡏⠀⠀⠀⢀⣴⣲⠆⠀⠀⠈⠻⣧⡀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⢞⠏⠁⠀⠀⢠⣾⠟⠋⠀⠀⠀⣤⣠⠂⠀⠀⠈⠛⣿⠙⣿⡻⠿⠭⠥⣿⣿⣧⠹⣄⠀⢀⡴⣻⠞⠁⠀⠀⠀⠀⠀⢹⣷⠀⢄⡎⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠾⠛⠛⠉⠛⠋⠀⠀⣰⡟⡱⠂⠀⠀⣠⡾⣵⠃⠀⠀⠀⣠⢿⣿⠘⣦⠔⠒⠛⠚⠻⣿⡚⠀⢩⡷⣯⣞⠁⠀⠀⠀⠀⣤⠀⢠⣼⢿⡄⢸⡇⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⢤⣤⣀⠀⠀⣀⠀⠀⠀⠘⢿⣽⠇⠀⠀⠘⡿⠟⠁⣀⣤⢴⣿⣵⠛⣽⣿⠟⠀⠀⠀⠀⢀⣼⠿⣶⠋⠀⢀⡿⡝⠛⣒⣶⡶⠻⣿⡋⢹⡜⣧⡞⠀⢠⢿⠙⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢸⡿⣿⣶⣷⣿⢛⡛⠉⠁⢿⠁⣀⣴⡿⠛⠀⠀⠀⠀⢀⣴⡿⢫⡤⠒⠛⣷⣾⣼⠁⢀⣿⡇⠄⠀⢿⣷⣬⣿⣏⠀⣰⣧⠋⢠⡿⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⠔⢃⡜⠁⠀⢀⡜⠁⢀⣼⢷⣀⢸⠇⠀⠀⣧⣀⣠⣼⣿⡿⣯⠟⠀⠀⠀⣠⣴⣿⠋⠀⠀⠀⠀⣼⣣⣿⠉⠉⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣴⠟⠁⢀⢻⡇⠀⠀⠀⠀⠀⠀ ⣾⣧⣤⣴⠋⠀⢀⡴⠋⠀⢠⣸⠃⢠⡟⠛⠛⠻⠻⣿⠟⢋⣵⢿⠟⠁⣀⠤⠚⣩⢿⠟⠀⠀⠀⠀⣠⡾⠞⣽⠋⠀⠀⠀⠀⠀⠀⠀⢻⡏⢿⣿⣿⡇⠀⢀⣰⣿⠁⠀⠀⠀⠀⠀⠀ ⠐⣫⡟⢁⣤⣾⠏⠀⠀⣰⣿⠃⠀⡾⠁⠀⠀⠀⣰⠁⣰⠛⠁⣠⠴⠚⠁⣠⣾⣡⠋⠀⠀⠀⣠⣾⠟⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⣿⣿⡇⢀⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀ ⠾⠛⠛⠉⣼⠏⠀⠀⡼⣿⠃⢰⢿⠇⠀⠀⠀⣼⣡⢞⠝⠀⠈⠀⠀⢀⡴⠋⢠⠏⠀⠀⠀⣴⠟⠁⠀⠋⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⢸⡿⢻⣿⣧⢘⢸⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠏⠀⢀⡜⢱⡇⢀⡎⡼⠀⠀⠀⠀⡷⣧⠋⠀⠀⠀⠀⡴⠋⠀⣠⠏⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⣀⣤⠾⠛⠁⠀⠈⠉⠀⠀⠘⢿⠋⣿⣿⡼⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡏⠀⢀⡞⢀⡾⠀⡼⢡⡇⠀⠀⠀⣼⡿⠁⠀⠀⠀⣠⠞⠁⣠⣼⣣⣶⡵⠟⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣭⣭⣭⣿⣶⣦⣴⡀⠀⢹⠀⣿⣿⣇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⢠⡏⠀⣼⡇⢰⡇⢸⠃⠀⠀⣸⠏⠀⠀⠀⢀⡼⣋⣴⣾⣿⣯⣿⠿⠥⠀⠀⠀⠀⠈⠋⠉⣽⠿⠟⠙⠿⢿⣿⣿⢉⣿⠋⠁⠀⢸⣷⣿⣿⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⢀⡞⠀⣼⣿⠀⡾⠀⣼⠀⠀⢰⠃⠀⠀⢀⣴⣿⠅⢉⣶⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣀⣀⣽⣿⡿⠅⠀⠀⠀⣿⣿⢞⣇⠈⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⢸⠁⢰⣿⡇⢰⡇⠀⢿⠀⢀⡏⠀⠀⠀⣹⣿⣿⣶⣀⣉⣳⣴⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠉⢩⣉⡉⠙⣡⢀⣤⠀⠀⢸⣿⠃⡞⢹⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⡏⠀⣼⢻⠃⣸⠁⠀⢸⣠⡟⠀⠀⠀⣰⣿⠁⠛⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⡿⠀⣿⠀⠀⣾⣇⡼⢃⡼⠇⡿⢡⣾⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⢰⡏⣾⠀⣿⠀⠀⢸⡿⠀⠀⠀⢀⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⠃⠀⡇⠀⢰⣿⣋⣴⣾⠶⣞⣡⣾⡇⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⣸⠃⣿⠀⡏⠀⠀⣼⢻⡇⠀⠀⣼⣿⠘⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠈⠁⢀⣾⠟⠉⣰⣿⣷⣾⣿⣿⢧⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡇⡟⠀⣿⠀⡆⠀⢰⡇⣾⠀⠀⠀⣿⣿⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣠⣾⣿⣿⣿⣿⡿⠉⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡷⠀⣿⣄⠃⠀⣸⢻⣿⠀⠀⠀⣿⣿⢠⣿⣿⢷⡀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⢀⣀⡤⢤⣄⡴⠖⠀⠀⠀⠀⠀⣴⠟⠉⣿⣿⣿⣿⣿⣿⡟⠇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠳⠀⠘⣟⠇⠀⣿⣿⣿⡄⠀⠀⣿⣿⢸⣿⣿⣌⣿⣦⡀⠀⠀⣀⡤⣿⣫⠿⠛⠻⠷⠖⠋⠉⠀⠀⠀⠀⠀⣠⣾⢿⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⡽⢻⡶⣶⣶⣦⣄⣹⡀⣸⣿⣿⢻⣷⡄⠀⣿⣏⣾⣟⣛⣙⣼⣿⣿⠖⣋⡽⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢟⣿⠀⠀⠀⣿⣿⣿⣿⡟⠁⢀⡸⠁⠀⢠⡖⠢⣄⠀⠀⠀ ⠀⠈⠁⠀⠘⠛⠛⠻⣷⣸⣿⡿⠄⠘⣿⡀⠟⠀⠈⣿⡿⡛⣫⣤⠶⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣷⢻⡟⠀⠀⠀⣿⣿⣿⡿⠁⢠⡾⠃⠀⠀⢸⡇⠀⠀⠁⠀⠀ ⡀⢀⣄⠀⠀⠀⠀⠀⠸⡏⣹⣧⠀⠀⢸⣷⡀⣾⠟⢥⠖⠟⠉⠀⢠⣿⣿⠿⠟⠻⠦⣄⡀⠀⠀⢀⣠⣴⠟⢛⣏⣉⠁⣿⡇⢠⠀⣷⣿⣿⣿⠁⣠⡞⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈ ⠛⢦⣟⣷⣄⠀⠀⠀⠀⢳⡘⢻⣧⡀⠀⢿⡟⢥⠀⡀⠀⢠⣶⡷⣦⣿⣿⣤⡀⠀⠀⠈⠉⠛⣫⡽⠋⠀⠀⠈⣹⣧⣼⣿⡇⣼⠀⢿⣿⡿⢣⣿⡟⠀⠀⢀⣠⣤⣾⡇⠀⠀⠀⠀⠀ ⠀⠙⠛⢟⣿⣷⣤⡀⠀⠈⠁⠀⠙⢷⡀⠈⣷⡀⠈⠀⣤⣾⠋⣻⣿⠃⠘⠻⣿⣟⣛⣛⣲⠟⢥⣴⣶⣲⣴⣿⣿⣿⣿⣿⡇⣿⡆⢸⡿⢱⣿⣿⠟⠲⢻⣽⣼⣿⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣽⣧⡀⠀⠀⠀⠀⠈⢿⣦⡈⢿⡀⣤⣿⣽⠾⠻⣟⡤⣠⠐⠚⠛⣦⡛⢿⣿⣷⣦⡤⢾⣛⡿⢛⣿⣻⣿⣷⢸⣷⠟⢸⡏⣾⡇⢀⢀⣿⣿⠿⠉⡇⠀⠀⠀⠀⠀⡜ ⠀⠀⠀⠀⠀⠀⠈⠙⢿⡀⠀⠀⠀⠀⠰⣿⣧⠈⢿⡁⠉⠀⠀⠀⠈⠻⣦⣔⣥⣾⣿⡿⠷⣈⣛⣷⣞⣯⣫⣴⣿⣿⣿⣿⡌⣻⡿⢰⡏⠀⢹⣧⣮⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠙⣟⣧⡀⠹⡄⠀⠀⠀⠀⠀⠀⠉⢛⣷⣷⣿⣿⢾⣿⣶⣭⣿⣿⣿⠿⠋⢙⣿⣿⡿⠁⡿⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⣀⡄⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⢧⡀⠀⠀⡀⡿⣿⣷⡀⠹⡆⠀⠀⠀⠀⢀⡴⠋⠀⠛⠉⣽⡿⣟⣿⣿⠉⠁⠀⠀⠀⠀⠘⢻⠃⠼⠻⣄⠀⠀⠸⡇⠀⠀⢀⣤⣶⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣧⠏⣿⣿⣄⠹⣤⠀⣠⠴⠋⠀⠀⠀⠀⢸⣿⣼⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠸⣄⠀⠀⢇⠀⠈⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡼⡝⣿⣄⠹⣿⡉⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠹⡄⠀⢸⡄⠀⠈⢯⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡅⡇⡏⢻⡀⠘⣟⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⢹⡄⠈⡇⠀⠀⠈⢿⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⠁⠀⣷⠀⣿⠀⠈⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⠀⠀⠀⠀⠈⢧⠀⢹⡀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠸⡄⣿⠀⣄⣀⣀⣀⣀⣈⣉⣻⣲⣶⣄⣰⡊⣿⠉⢹⢯⠉⠹⡄⠀⠀⠀⠀⠀⢸⡆⠸⢧⠀⢣⠀⠈⢿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠴⢻⡟⠀⠀⠀⣧⡏⠀⠀⠀⢀⠉⡉⢩⢿⣋⣻⣿⣿⣿⣿⢻⢀⣼⣾⣃⣠⡿⣆⠀⠀⠀⠀⠀⢹⡀⠘⡇⠀⢣⡀⠀⠹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡰⠋⠀⠀⠀⠀⣿⠠⠀⢀⣴⣿⣨⣷⢟⡾⣱⣿⣿⠿⠛⠛⠚⠚⠲⠞⠋⠁⠀⢿⣧⣦⢀⣶⡆⡸⡇⠀⢹⡄⠈⢧⡀⠀⠙⢧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣠⡞⠁⠀⠀⠀⠀⣠⡿⠀⣰⢟⠊⣵⣱⣋⢟⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⠋⠊⡜⠁⢷⠀⠈⢧⠀⠀⢣⡀⠀⠀⠱⢄

⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡀⡴⠁ ⠘⢯⡒⠠⠤⣀⡀⠀⠀⠀⢨⠂⢳⠪⠝⣛⡛⢓⡒⣅⠸⠀⠀⣀⠤⠊⡑⠀⡀ ⠀⠈⢋⠢⡀⠈⠈⠉⠒⣢⢤⣤⠧⠷⡋⠀⠀⢻⢽⣏⣉⢔⠈⠀⡡⠊⠀⠀⡇ ⠀⠀⠈⢢⠐⢄⠀⠀⡞⣉⣥⣤⡉⠢⡘⡀⠰⢁⠔⢉⡍⢉⠳⡊⡇⠀⠀⠀⠇ ⠀⠀⠀⠀⢂⠈⡷⣸⢹⣀⣿⣿⣿⣆⠈⢱⠃⠁⣎⢉⣿⣿⡏⢁⣇⠀⡠⠌⠀ ⠀⠀⠀⠀⠀⢹⣥⢷⠸⢿⣿⣿⠿⢿⠠⡾⢦⣸⡿⠿⣿⣿⡇⢈⣿⡄⠰⠀⠀ ⠀⠀⠀⠀⠀⢨⡟⠈⡄⠀⠀⠀⢰⠃⠀⠸⠃⠀⠑⡀⠀⠀⠐⠀⢻⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠘⣄⠘⠊⠐⢃⡰⠁⠀⠀⠀⠀⡸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⣀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠐⠚⢍⠐⣿⣍⡑⠐⡂⢄⡠⠴⠶⣛⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⠁⠀⠀⠀⠀⠄⠀⣧⠙⣦⣠⡀⡄⡀⡴⠛⢱⣤⢄⡀⠀⠀⠀⠀⠀ ⠀⢀⠎⠀⠀⠀⠀⠀⢜⠟⡛⢻⡀⡀⠈⣷⠟⢻⠀⠀⢸⣿⡖⠿⣄⠀⠀⠀⠀ ⠀⡜⠀⠀⠀⣠⠀⠀⢸⠙⠋⢈⢃⠀⠀⢹⠀⠈⠀⠈⢸⡔⠲⡱⡟⠀⠀⠀⠀ ⠀⢧⡀⢏⢄⡘⠄⣠⠚⢧⡡⡀⡎⡀⠀⠈⠀⡆⠀⠀⣾⠁⠜⡔⠀⠀⠀⠀⠀ ⠀⠀⠑⠔⡈⢧⡀⠀⠀⠀⠙⣗⠇⣇⠀⠀⣇⣇⣀⢠⡇⣪⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⡼⠛⢆⡀⠀⡀⠘⣯⠛⠛⠛⠛⠊⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢹⢢⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢆⠟⠀⡀⠀⠀⠀⠃⠀⠀⠀⢸⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠞⡞⢠⠁⠀⡀⣸⠀⠀⠀⠀⠀⣧⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⢀⣼⠋⠀⠀⢠⢃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⢀⣾⠞⠀⡟⢠⡾⣴⠻⣀⠀⢰⡄⠀⡾⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⢁⣿⠇⠀⠀⢀⡏⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠠⣿⠋⢀⢴⣿⠋⠀⠀⣡⣿⡟⠁⠀⣿⠀⠘⣷⠀⢸⢸⢸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⠀⡼⡟⠀⠀⢠⣾⢰⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣵⣻⡏⠀⢀⣾⡿⠋⠀⠀⠀⣿⠀⠀⢿⡄⠀⢫⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠀⣸⠷⠃⠀⠀⣼⡏⣼⠀⢀⡏⠀⠀⠀⠀⠀⠀⣠⡞⢁⣤⠞⣡⣿⢃⣠⠞⠉⠀⠀⠀⠀⠀⣿⡇⠀⢸⣷⡀⠸⠀⣿⡀⠀⠀⠀⠀⠀⠀ ⢰⡏⠀⢰⡏⠀⠀⠀⢰⢻⠁⡷⢤⣼⡶⠶⣤⣀⡀⢀⣴⡿⠖⠉⢀⣴⣿⠷⠋⠀⠀⠀⠀⠀⠀⢠⠆⢿⣧⠀⢨⡏⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⣿⠃⠀⡼⠀⠀⠀⠀⢸⣼⢀⡇⠘⡿⠧⣄⣀⣉⣿⠿⣯⣀⠀⣴⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⣿⣆⢸⡆⢹⡾⡇⠘⡇⠀⠀⠀⠀⠀⠀ ⣿⠀⢰⡇⠀⠀⠀⠀⠸⡏⢸⠻⣾⣿⣧⣴⣾⣿⣽⣒⣈⢙⠿⣷⣴⠆⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣀⣨⣿⣹⣷⣳⡘⡗⡿⠀⢻⡀⠀⠀⠀⠀⠀ ⢷⠀⢸⠇⠀⠀⠀⠀⠃⣇⣿⠀⡟⠈⢿⣮⡹⣏⠹⣝⡿⣷⣶⡦⠀⠀⠀⠀⠀⠶⣿⣿⣿⣛⣯⣿⢅⣈⣿⡆⢹⣿⣷⡇⡇⠀⠘⣇⠀⠀⠀⠀⠀ ⠸⡦⣼⠀⠀⢸⠀⠀⠘⣿⣷⢴⢃⡴⠃⠉⠻⠿⠶⠬⡵⠾⢿⣰⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠷⣦⣬⣽⣷⣼⠉⠉⠁⡇⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⢻⣹⠀⠀⢸⡄⠀⠀⣿⣞⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠀⠀⠀⠀⣼⡛⢧⣹⣷⣯⣉⣤⡿⠟⠁⣻⡇⠀⡀⣸⡇⠀⠀⠸⢷⠀⠀⠀⠀ ⠀⠸⣿⡆⠀⢸⡇⠀⠀⢿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠉⠀⠀⠉⠉⣽⠉⠀⠀⢠⡟⢹⣤⡇⢸⡇⠀⠀⠀⠘⣇⠀⠀⠀ ⠀⢠⣿⡇⠀⠘⡇⠀⠀⢸⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⢀⡟⠀⠀⢠⣿⠴⢢⡿⡇⢸⡇⠀⠀⠀⠘⣿⡇⠀⠀ ⠀⢸⣿⣷⠀⠀⢣⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣀⣀⠀⠀⠀⣄⣬⡀⠀⠀⠀⡞⠀⠀⢠⣿⠁⣠⢿⠀⡇⢸⡇⠀⠀⠀⠀⢸⣿⡀⠀ ⠀⠈⢹⡏⣇⠀⢸⡄⠀⢸⡏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣩⡤⠶⠛⠉⠁⠀⠀⠀⠁⢀⣴⣿⡟⠋⠁⡇⢸⠇⢸⡇⠀⠀⠀⠀⠘⣟⡇⠀ ⠀⠀⠸⣷⢸⡄⠀⣧⠀⠀⣷⠁⢿⣧⠲⠀⠀⠀⠀⠀⢀⣀⠴⢾⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⢈⣽⠿⠉⠀⢀⡇⣸⠀⡸⠀⠀⠀⠀⠀⠀⣿⢹⡀ ⠀⠀⠀⣿⡌⣧⠀⠸⡄⠀⢹⡀⠉⣿⢷⣄⠄⠀⠀⠶⢿⣗⠚⠶⠿⠿⢿⣿⡶⠄⠀⠀⠀⣠⡞⠃⠀⠀⠀⢸⠃⡇⢀⡇⠀⠀⠀⠀⠀⠀⣟⠈⡇ ⠀⠀⠀⢸⣧⠸⣇⠀⢻⡀⠀⣧⠀⠹⡎⢻⣧⡀⡀⠀⠀⠉⠿⠶⠶⠶⠿⠉⠀⠀⠀⣠⠞⣹⠇⠀⠀⠀⠀⡟⢸⠁⢸⠇⠀⠀⠀⠀⠀⢀⣷⠀⠃ ⠀⠀⠀⠠⣿⡄⠸⡄⠀⢳⠀⠸⡄⠀⣿⣶⡟⢷⣍⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⣿⠀⠀⠀⠀⣼⢡⡇⠀⡼⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⢸⣧⠀⢷⡀⠈⢳⡀⢷⢀⣿⠈⠛⠾⢯⣳⣤⣀⣀⣀⡀⠀⣀⡴⠟⠁⠀⠀⢸⣿⠀⠀⠀⢠⠇⣸⠁⢠⡇⠀⠀⠀⠀⠀⢀⣾⣿⢰⠀ ⠀⠀⠀⠀⢸⣿⣇⠈⢷⠀⠀⠳⡌⣷⣿⡇⠀⠀⠀⠉⠙⠻⠿⠿⠿⠟⠉⠀⠀⠀⠀⢀⢾⣿⠀⠀⢀⡟⢠⠏⠀⢸⡇⠀⠀⠀⠀⠀⢸⡟⣼⡞⠀ ⠀⠀⠀⠀⢸⣯⣿⡆⠈⣧⠀⠀⠙⣎⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⡟⠀⢠⠞⠀⡞⠀⠀⡼⠇⠀⠀⠀⠀⢠⡿⢱⡿⠃⠀ ⠀⠀⠀⠀⠀⣯⠙⣇⠀⠘⣇⠀⣀⣾⣿⣄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⣷⣠⠞⠀⣸⠁⠀⢠⡇⠀⠀⠀⠀⠀⡼⢡⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⣽⠀⣻⠀⢀⣸⣶⡿⠿⠘⠻⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⢿⡀⢠⠇⠀⠀⢸⠁⠀⠀⠀⢀⣾⣱⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣠⣿⡶⠋⠛⠋⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣄⡀⠀⡏⠀⠀⠀⢠⣾⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣗⠲⠶⠤⢄⣀⣀⣀⣀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣀⠾⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠈⠉⠉⠑⠲⠤⣍⣦⡀⠀⠀⠀⠴⣉⡤⠶⠖⠒⠒⠒⠉⠉⠉⠉⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠐⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⢁⣴⣦⣖⣋⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢗⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠏⠀⣴⢿⡿⣿⠿⣿⢷⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠳⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⢀⡞⠁⣸⢞⣥⣦⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢍⣳⣤⠀⣀⠤⢖⡠⢖⠩⠋⠁⠀⠀⠀⠀⢀⡾⠀⠠⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢒⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠲⢒⣒⠚⠳⠶⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡔⢊⡤⢒⣉⡥⠤⠐⠒⠒⠒⠚⠂⡄⠀⠀ ⠀⣠⡔⣫⡇⠀⠀⠀⠀⠀⠀⠀⣾⣥⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀ ⢸⢐⣷⢿⡇⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣤⣤⣤⣀⠠⠤⠖⠚⡛⠀⠀⠀⠀ ⠈⢿⣙⡿⡇⠀⠀⠀⠀⣤⡶⠖⢻⣿⣿⣯⣶⣂⣀⣁⣀⣀⠴⠊⠀⠀⠀⠀⠀ ⠀⠈⣿⣺⣷⡀⠰⣰⠿⣿⠀⣴⡯⠒⣋⣉⣧⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣯⣽⣿⢿⡟⣦⠽⢷⣏⠴⠧⢄⠀⢌⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣟⣸⣷⣇⡀⠀⠀⠀⠀⣈⢿⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢯⣽⣭⢟⣇⣈⠀⠀⠉⡠⠀⠘⠏⢾⠀⡠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡏⣿⣿⡀⠀⠄⠀⣀⣀⣠⣴⡾⢠⠁⣇⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⢣⢻⣿⣯⣭⣿⣿⡽⡿⢄⣞⡶⡱⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⢷⣿⡛⣉⣽⣿⠕⣡⢞⣴⣱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣷⡶⠛⢻⢋⣵⡿⣗⣼⣿⣟⠡⣴⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⢫⣿⣷⣎⢿⣿⠋⠀⣗⣭⣿⣟⡿⡿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣠⡤⣾⢋⡿⣿⠝⡏⠙⢿⣶⣶⣿⣿⣿⣿⢳⢇⠿⢣⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⡭⣩⠿⠋⢶⣿⣿⣷⡀⢸⣿⡟⠿⣿⣿⡿⢨⢸⠸⣿⣧⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣧⣾⣿⣷⡌⠹⣿⣷⣿⡏⣟⣶⣿⣿⡇⡧⣱⡱⣼⣿⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⠸⣞⣿⣿⡫⢚⢝⣽⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⡟⣴⣿⣿⣿⣇⢿⣿⣷⣿⣿⣿⡻⣮⣍⡖⣶⣶⣴⡀ ⠀⠀⠀⠀⠉⠉⠙⠛⠋⠙⠛⠻⣻⣿⣿⢿⣿⢘⣟⡇⠈⢷⣯⡞⢍⣉⣛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃⡼⢟⣼⣞⠿⢦⠀⠈⠛⠶⣜⣟⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠃⠈⣾⣭⠒⡋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠔⠒⠤⠤⣠⡤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠉⠲⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠑⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢉⡤⣲⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢦⡈⠳⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣯⣖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷⣀⣈⣶ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⡊⠉⠉⠀⠀⠀⠀⣀⡠⠤⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⡳⡀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠉⠀⠀⠀⢹⣿⣿ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠿⠉⠒⠒⠲⠤⠉⠀⢀⣀⠤⠀⢀⠄⠀⠀⢸⣾⣿⢿⡿⣿⡰⠶⠒⠒⠻⢧⣀⠀⠀⠀⠀⠀⠀⢸⡽⣹ ⠀⠀⠀⠀⠀⠀⢠⣧⣉⣀⡒⠒⠒⠒⠒⠛⠋⠁⠀⠀⠀⠠⠔⠊⠉⢈⣿⠹⡄⠀⠈⠁⠀⢰⣦⣤⣀⢹⣷⣄⠀⠀⠀⠀⣞⡱⣻ ⠀⠀⠀⠀⠀⠀⠈⠛⠻⢶⣶⣦⡤⠀⠤⠤⢤⣀⣀⠀⠀⠀⣠⣴⣾⣿⣿⡷⠇⠀⠀⠀⠀⠀⢿⣿⡿⢷⠙⠿⠂⠀⣠⣾⠟⣹⠃ ⠀⠀⢀⣠⡤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡗⢿⣿⠟⡰⣻⠁⠀⢦⠀⠀⠀⠀⠀⠀⠉⠵⠎⠀⠀⢠⢾⡿⠡⠚⠁⠀ ⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠀⣀⠠⠤⠐⠤⢽⡆⢪⣼⠟⢁⠎⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢁⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠖⢯⣤⣀⣰⠶⢖⣤⢴⣿⢻⣰⠃⣀⠀⢻⡷⡄⠀⠀⠀⠀⡀⠀⠀⢲⡴⢃⠜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡞⠀⠤⠈⠛⠓⠚⠉⠀⠀⢻⣾⠁⠀⣁⣠⣤⣿⠽⣦⡀⠀⠀⠙⣿⣿⣶⠷⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡽⠛⢉⣤⡖⠀⠙⠦⣀⠀⣀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⡟⠉⢀⣴⡿⠋⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣿⡶⢄⠀⠀⠀⠀⡠⠊⠇⢀⠃⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣻⣧⠀⠙⢦⡀⠀⠀⢸⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⡠⠈⢢⣤⣿⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠤⣶⠞⠀⠀⢠⡟⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⣾⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⡄⠀⠀⠀⡇⠀⠀⠹⡼⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠁⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣜⠆⡎⠀⢀⡇⠀⠀⠀⢳⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⣿⠀⠀⢴⠋⠀⠀⡦⠀⠀⠀⠀⠀⢀⣼⠏⢀⣼⠎⢸⢠⣞⡞⣧⠀⢲⠀⢬⡏⡆⠀⠀⠀⠀⠀ ⠀⠀⢠⠋⣼⠇⠀⢀⡞⡄⠀⡸⠃⠀⠀⠀⠀⠀⡾⠃⢐⣿⠇⠀⣠⣿⠋⠀⣿⠀⠈⡇⠈⡰⢱⠀⠀⠀⠀⠀ ⠀⣰⠋⣸⡽⠀⠀⣸⢇⠃⢠⠇⠀⠀⠀⠀⢀⡞⢁⡤⢫⡯⢀⡴⠛⠁⠀⠀⢻⡄⠀⣿⡀⢸⢸⡆⠀⠀⠀⠀ ⣰⠃⢠⠇⠀⠀⢠⢿⢸⢤⣼⠤⢤⣀⠀⣠⡿⠖⠋⣠⣿⠗⠉⠀⠀⠀⠀⡰⢿⣇⠀⠹⢇⠀⠈⣇⠀⠀⠀⠀ ⣟⠀⡜⠀⠀⠀⢸⡎⣼⢘⣟⠤⢤⣹⡿⢯⣄⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⡇⠸⣿⣆⢰⠘⡿⡄⢻⠀⠀⠀⠀ ⡇⢠⡇⠀⡄⠀⠈⡇⡏⢻⢿⣟⢿⠷⡿⣧⣌⣙⠓⠃⠀⠀⣀⣤⣤⣤⡼⡷⠒⣿⠻⣿⣇⡇⡇⠘⡆⠀⠀⠀ ⢣⣸⠁⠀⡆⠀⢰⡇⡅⡇⣰⠙⢷⣧⣝⣪⡽⣟⡀⠀⠀⠀⣰⣿⣶⣿⣿⣯⣑⣻⣄⡞⠛⠃⡇⠀⢳⠀⠀⠀ ⠘⣾⠀⠀⡇⠀⠀⣿⣳⡿⠁⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⢠⣟⢯⣿⣭⣃⣼⠟⠉⣿⡁⢰⣸⠃⠀⠸⡇⠀⠀ ⠀⢻⡇⠀⣇⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⡿⠁⠀⣰⠏⢷⡎⢸⠀⠀⠀⢸⡄⠀ ⠀⣿⣧⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⠀⠀⠀⢠⠃⠀⣰⠟⢉⡞⢹⢸⠀⠀⠀⠘⣵⠀ ⠀⢻⡟⡄⠘⡄⠀⢸⢻⣄⡀⠀⠀⠀⠀⠀⠈⠙⢗⣀⠴⠟⠃⠀⠀⠃⠀⣴⡿⠔⠋⡇⡏⢸⠀⠀⠀⠀⢯⡆ ⠀⠀⣷⢳⠀⢻⠀⠘⡎⢻⣦⠂⠀⠀⠀⢀⡤⠴⢿⣧⣤⡀⠀⠀⠀⠀⢨⡿⠋⠀⢠⢃⠇⡜⠀⠀⠀⠀⢸⢹ ⠀⠀⢻⡞⡇⠀⢇⠀⢧⠈⣯⢷⡀⠀⠈⠛⠯⣙⣛⣛⣿⡿⠂⠀⢀⣴⣏⠁⠀⠀⡾⡸⠀⡇⠀⠀⠀⠀⢸⠈ ⠀⠀⢈⣧⠸⡄⠘⡄⠸⡄⢸⣌⡿⣆⠄⡀⠀⠉⠉⠉⠁⠀⢀⡠⠊⣸⠁⠀⠀⣰⢁⡇⢰⠁⠀⠀⠀⠀⣾⠀ ⠀⠀⠀⣿⡄⢻⡀⠘⡄⢳⢘⡏⠓⠼⣕⣤⣀⣀⡀⠀⣀⡴⠋⠀⠀⣿⠀⠀⢀⠇⡼⠀⡼⠀⠀⠀⠀⢠⣽⢰ ⠀⠀⠀⢿⣷⡀⢳⠀⠘⣎⣾⣷⠀⠀⠈⠉⠛⠻⠿⠋⠁⠀⠀⠀⣰⣿⠀⠀⡞⢰⠁⠀⡇⠀⠀⠀⠀⣼⢻⡞ ⠀⠀⠀⢹⠾⣇⠀⢧⠀⠈⣯⡏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⣏⢀⡜⢀⠇⠀⢰⠁⠀⠀⠀⢰⢣⡟⠁ ⠀⠀⠀⢈⡇⢹⡀⠈⣧⣾⡟⠟⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣞⠀⡜⠀⠀⡜⠀⠀⠀⣠⢣⠎⠀⠀ ⠀⠀⠀⢸⣇⣿⡴⠛⠛⠁⠀⠀⠘⢵⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠳⣇⡀⠀⠇⠀⠀⣰⡷⠃⠀⠀⠀ ⠀⠀⠀⢿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣌⠉⠑⠒⠒⠶⠦⢄⣀⠱⡀⠀⠀⠀⡠⠊⢀⣀⣀⣀⠤⠤⠶⠒⠚⡹⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣷⣀⠀⠀⠀⠀⠀⠈⠉⠛⠂⠀⠼⠒⠋⠁⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢲⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣴⣴⣺⡵⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠃⠐⢟⠟⣏⡿⠚⡷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡲⢤⡀⠀⢀⡀⢀⠔⡾⠋⠁⠀⠀⢠⠎⢠⠏⠘⠛⠛⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠃⠚⠃⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠛⠻⢤⣀⠀⠀⠀⠉⢦⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⢳⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠋⠁⠀⢀⡠⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠳⣤⠀⠀⠀⣣⠆⠀⠀⠀⠀⢟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢟⠢⠤⠤⠤⠬⡽⠶⠤⠔⠒⡪⠝⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣏⣤⣤⡾⠥⢤⣀⠀⠀⠀⠈⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠢⠤⣀⣀⠀⢀⣴⠖⠀⢀⣠⢴⠶⠶⡶⠶⣶⣦⢄⣀⣀⣀⣀⣀⣴⢛⣽⠛⠛⠃⢀⣀⠈⠙⠢⣄⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡤⠟⠉⠀⢀⣴⠟⠋⠀⢀⣀⠄⠀⠘⢿⡷⢽⢴⣖⣛⣿⣿⡘⡇⠀⢀⢴⡿⠋⠀⠀⠀⠙⣧⠀⣠⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠖⠙⠋⠛⠂⠀⣰⢏⠆⠀⠀⣠⣯⠋⠀⠀⣠⢾⣇⣮⠔⠒⠒⠻⢷⠃⢨⠶⣵⣋⠀⠀⠀⣤⠀⣠⢿⡄⣻⠀⢹⣄⠀⠀⠀⠀⠀ ⠀⠒⠒⠠⠤⣤⠀⠀⠀⢻⢾⣀⣀⣨⣛⡡⠤⡲⠿⠺⣡⡿⠋⠀⠀⠀⣠⡞⢛⣥⣀⡼⡏⠉⣽⠟⠻⣿⠈⣇⡷⠁⡰⡻⢸⡄⠀⠀⠀⠀ ⠀⠀⣀⠄⡴⠁⠀⡠⠀⢸⣏⠻⡟⠋⢰⠀⠀⣳⣴⣿⡯⠀⠀⠀⣠⡾⠋⠘⠁⢠⢟⡿⠧⠴⠿⢤⣤⣿⣿⣿⣧⣴⠝⠀⣿⠁⠀⠀⠀⠀ ⣖⣉⣤⠞⠀⣠⠞⠁⣠⠏⢹⠓⠓⠶⠶⡿⢛⡽⡫⠋⣀⠤⣲⢿⠏⠀⠀⠀⣠⠿⡿⠃⠀⠀⠀⠀⠉⢿⡹⣿⣿⠁⢀⣨⡟⠀⠀⠀⠀⠀ ⢐⣵⣣⢴⡞⠁⢀⣾⠏⣀⡏⠀⠀⢀⡜⡠⡋⠀⠔⠊⢀⡴⣱⠁⠀⠀⣠⡾⢁⠜⠁⠀⠀⠀⠀⠀⠀⠈⣷⣻⣿⡇⣼⢻⡇⠀⠀⠀⠀⠀ ⠉⠁⢀⡟⠀⢠⢎⠏⢰⢹⠀⠀⠀⣞⢾⠎⠀⠀⠀⡴⠋⢠⠃⠀⣀⠜⠁⠀⠁⠀⠀⣀⡤⠒⠒⠦⠀⠀⢹⣽⣿⡇⣿⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠀⢠⠏⡼⢀⡇⡇⠀⠀⣠⡿⠁⠀⠀⣠⠎⢀⡰⣣⣴⠟⠁⠀⠀⢀⣠⣴⣟⣗⣒⣒⣦⣤⣠⠀⠸⡄⣿⣿⢸⡏⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⢠⠃⣰⠇⡼⢰⠃⠀⢠⠏⠀⠀⢀⡼⡣⢶⣿⣿⡟⠷⠀⠀⠀⠈⠋⢹⠟⠛⠛⠻⣻⣏⡽⠋⠀⢀⣧⢿⠿⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⢸⢀⠏⢰⣿⢀⡇⢸⠀⢀⠇⠀⠀⣴⣿⣂⠴⢇⣛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⢾⠛⠁⠀⠀⢸⡿⡻⣆⣹⣷⡀⠀⠀⠀⠀⠀ ⠀⢸⣼⠀⡾⡇⢸⠀⠸⣀⡟⠀⠀⢠⣿⠹⠛⠷⠒⠋⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⡖⢸⡇⣿⠀⠀⣿⣠⢇⡼⢹⢫⣷⡀⠀⠀⠀⠀ ⠀⠀⡏⢰⢷⠇⣿⠀⢀⣿⠀⠀⠀⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⠀⡟⠀⣴⣟⡥⣞⠶⣣⣾⢿⡇⠀⠀⠀⠀ ⠀⠀⢧⣼⢸⡇⠃⠀⣸⢹⠀⠀⢸⣻⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⣰⣿⢁⣴⣿⣿⣿⡿⡼⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⢸⡇⠇⠀⡏⣿⠀⠀⣿⣿⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠀⠀⠀⢀⡴⠿⣿⣿⣿⣿⣿⠟⢰⠃⠀⠀⠀⠀⠀ ⡀⠀⠀⠣⠀⢣⠆⢸⣿⣿⡀⠀⣿⣿⢸⣿⣞⣷⣄⠀⢀⣠⢽⣺⠿⠳⠯⠗⠋⠁⠀⠀⠀⣠⡾⡅⠘⣿⣿⣿⣿⠏⠀⡼⠀⠀⠀⠀⠀⠀ ⠟⡻⠿⢶⣦⣼⡄⣾⣿⠻⢷⡀⣿⠯⢿⣭⣯⣾⠿⣏⣭⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⡇⠀⠀⣿⣿⣿⡏⢀⡴⠁⠀⡞⠑⠄⠀⠀ ⠀⠀⠀⠀⠈⠉⢻⡿⣏⠁⠘⣧⡉⣡⡴⣛⣯⠞⠋⣻⣿⣿⣦⣄⠀⠀⠀⠀⢀⣠⢾⠭⠟⣽⠁⠀⡄⣿⣿⡟⠀⡾⠁⠀⠀⡇⠀⠀⠀⠠ ⠷⣼⣦⣄⠀⠀⠀⣏⠻⣦⠀⢹⣿⣏⠀⠁⢠⣤⢤⣿⣧⣀⠀⠈⠛⠒⢒⡾⠋⠁⠘⣿⣰⣿⢠⡄⢧⣿⡟⣶⡟⠀⠀⣀⣤⡇⠀⠀⠀⠀ ⠀⠙⠫⢿⢷⣄⠀⠈⠀⠈⢧⡀⢻⡄⠀⢰⣾⢉⣿⠃⠘⠻⣿⢻⣷⣞⡳⠶⠦⣴⣿⣿⣿⣿⡸⣇⣸⣏⣾⣿⠓⢊⣽⣾⣿⠃⠀⠀⠀⢀ ⠀⠀⠀⠀⠑⠿⣆⠀⠀⠀⠈⣻⣆⠻⡼⠷⠚⠉⠹⣮⡒⡨⣈⣷⣭⡻⣿⣟⡯⡷⣫⣾⣽⣿⠧⣿⢃⡾⠹⡟⡰⣼⠟⠉⠘⠀⠀⠀⠀⠊ ⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠙⣿⣆⠙⣄⠀⠀⠀⠀⠙⠻⢿⣯⣽⣷⣾⣝⣻⢾⣽⡿⠳⣿⣶⠏⡾⠀⠀⣿⡟⠁⠀⠀⠀⠀⡀⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⢳⣄⠀⢠⣸⣿⢧⡘⣆⠀⠀⠀⣠⠔⠉⠋⢩⡿⣟⣿⡏⠉⠁⠀⠀⠙⡟⠰⠳⡄⠀⠘⡇⠀⣀⣤⣶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣇⢿⣷⡈⢦⡠⠚⠁⠀⠀⠀⢻⣷⣿⣿⡇⠀⠀⠀⠀⢠⠃⠀⠀⠹⡄⠀⢣⠀⠈⡿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢹⢸⢷⠈⢷⣤⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠸⡄⠸⡄⠀⠸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡎⠈⣇⢸⠀⠉⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢳⠀⢇⠀⠀⠹⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⢸⢸⠂⠦⠤⠤⠤⢤⣽⣷⣖⣤⣏⡏⠉⣿⡉⢳⡀⠀⠀⠀⠈⣇⠘⡆⠡⡀⠙⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢩⠞⠀⠀⢸⡟⡀⠀⣠⢤⣦⣾⡷⣼⣿⣿⠿⠼⠾⣾⠖⠚⢻⣄⠀⢀⣄⢸⡀⢹⡀⢱⠀⠈⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣸⠇⢠⢾⢋⣯⢯⢮⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⡱⠁⡇⠠⢇⠀⢱⡀⠀⠙⢄

⠀⣠⣤⡤⣤⣤⢤⣤⠶⠚⠻⠿⢶⣄⠀⠀⣀⣀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣷⣯⡨⠉⢩⠄⠒⠒⠒⠤⡭⠛⢺⡟⠉⠁⡈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠀⡧⡜⠀⠀⣀⠀⠀⠛⠒⠢⠋⠐⠶⢧⣌⡻⢗⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⣿⠀⠀⠹⡀⠀⢹⣫⠉⠉⠉⠉⠉⠍⠉⢹⢨⡿⠿⣃⡘⡆⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣟⣿⠤⠟⠀⠇⢲⠀⢷⡵⡠⠀⠀⠀⠀⠀⢸⢀⣁⣉⣉⡉⠛⠳⠶⣤⣄⡀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣝⠻⠀⠀⠈⡐⠉⠀⣸⢿⣥⠀⠄⠀⠀⢀⣸⢸⣿⣿⣿⣿⣿⣶⣦⣤⣉⠛⢶⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⢿⣶⢢⠀⠀⣇⣠⠞⣹⢼⢞⣷⠀⠀⠈⠠⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡉⠻⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢿⣷⣼⡞⢁⣼⣿⢸⠐⢻⠀⠀⠀⠐⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠏⣰⣿⣿⣿⢸⡀⢸⠀⠀⠈⠂⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢳⡝⣆⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠇⣰⣿⣿⣿⣿⢸⠈⣾⠀⠀⠀⠠⢺⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⡘⣆⠀⠀ ⠀⠀⠀⠀⣿⡟⢰⡿⣿⣿⣿⣿⢸⠀⢽⠐⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠘⡆⠀ ⠀⠀⠀⢸⣿⢁⣿⣿⣿⣿⣿⣿⢸⠀⣾⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡀⢳⠀ ⠀⠀⠀⢸⣿⠿⣿⣿⣿⣹⣿⣿⢸⠒⣿⠀⠀⠀⠀⢸⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠘⡇⢸⡄ ⠀⠀⠀⢸⣿⠑⡿⠊⠉⠁⢹⣿⢸⠀⣿⠀⠀⠀⠀⢸⢸⠿⣏⣻⣿⠿⡿⠿⠟⢅⣴⣿⣿⣿⣿⣿⣿⣿⢀⡇⢸⡇ ⠀⠀⠀⢸⣿⡀⣧⡔⣶⡄⢀⣽⢸⠀⣿⡀⠀⠀⢀⢸⢀⣤⣌⣋⣤⣾⡿⠃⠾⢿⣿⣿⣿⣿⣿⣿⣿⡿⢼⠃⢸⡇ ⠀⠀⠀⠈⢿⣇⢹⡇⠻⢿⣿⢻⢸⠘⣾⠁⠀⠤⢚⢸⠐⢤⣀⡀⠈⠚⠒⢚⣥⣾⣿⣿⣿⣿⣿⣿⣿⠃⡾⠀⢸⠀ ⠀⠀⠀⠀⠀⢿⡄⢻⡀⠈⠀⢸⢸⠀⢹⠀⠀⣴⠋⢸⠘⠀⠈⠑⠀⠀⠉⠉⠙⠛⠿⠿⠟⠛⣿⣿⠏⣰⠃⢀⡏⠀ ⠀⠀⠀⠀⠀⠘⣿⣄⠳⣀⠰⢸⢸⡀⢸⠀⠜⠃⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⡠⠐⠀⢤⣶⣿⣿⠟⣰⠃⢀⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣦⡙⢞⢾⢸⢁⢸⠀⠀⠀⠀⢸⣀⣀⣁⣀⣀⣀⣀⣊⣀⣀⣀⣘⣿⣿⣣⣿⠃⢀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⡻⣤⣹⢸⢍⡊⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⢺⠖⠀⠀⠀⠀⢰⡘⠀⣺⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡾⢿⢊⣲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠀⠀⠀⠀⠀⠀⢧⠃⢠⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢣⢯⠢⣎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠱⡀⠸⡞⠀⣼⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣯⣃⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣐⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣷⠁⢠⠇⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠫⣦⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡾⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⡀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠇⠀⢫⡀⠀⠀⠀⠀ ⠀⠀⡰⡇⠀⠘⠀⡀⠀⠀⠀⢠⠏⣠⠃⢢⡶⡇⢀⠸⣳⠀⠀⠀⠀ ⠀⡰⣰⠃⢰⠷⢠⠃⠀⠀⢠⢃⢼⠃⡰⠋⠀⢇⠸⡄⠇⡄⠀⠀⠀ ⣸⢀⠃⠀⣾⡆⣼⠢⢄⡴⠓⣡⠞⠊⠀⠀⠰⢻⡀⡳⡀⠇⠀⠀⠀ ⡇⡌⠀⠀⡇⠓⢷⣿⠿⢯⣟⠓⠀⢀⣠⣤⣶⢸⡷⣧⣿⠸⠀⠀⠀ ⢰⡇⢰⠀⢳⣾⠌⠙⠓⠓⠻⠆⠀⣰⣿⣿⢓⡾⢷⢉⡹⠀⣇⠀⠀ ⠀⣇⠸⠀⢸⡯⠀⠀⠀⠀⠀⠀⠠⡀⠀⢉⠋⢠⡋⣾⠀⠀⢸⡄⠀ ⠀⣿⡀⡆⢸⣧⠀⠀⠀⠀⠲⣆⠠⠆⠀⠈⣠⡯⢺⠘⡀⠀⠀⣷⠀ ⠀⢸⣡⠰⠀⡌⣧⡀⠀⢴⡾⠿⣶⡄⠀⢠⠞⠁⠘⠆⠇⠀⠀⡟⡆ ⠀⠀⡏⠆⢃⢡⢸⢽⣄⠀⠈⠉⠁⣀⠔⣹⠀⢀⢳⢰⠀⠀⠀⡇⠀ ⠀⠀⣿⡘⡄⢢⢾⡄⠉⠓⠶⠶⠊⠁⢀⡏⠀⡌⠆⠈⠀⠀⢰⣿⠀ ⠀⠀⢹⢃⠐⣀⣽⡷⠀⠀⠀⠀⠀⠀⠘⣧⠜⡘⠀⠇⠀⢀⠷⠃⠀ ⠀⠀⣸⠼⠒⠋⠀⠈⢇⠀⠀⠀⠀⢀⠀⠀⠑⠧⡰⠀⢠⠟⠁⠀⠀ ⠀⠀⠙⢶⡂⠠⠤⠄⢀⠢⠀⠀⠠⢊⡀⡀⠀⠤⢄⠽⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣤⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⢀⠔⣀⢠⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⠄⡀⠀⠀⠀⠀⢀⡤⠞⠁⡺⢻⣟⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠢⠖⠉⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀

⠀⠀⢠⠇⣀⡞⠀⢰⠂⠀⠘⣠⠴⠒⠒⠲⢤⣄⠀⠈⠑⣌⢿⣾⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣀⡤⠖⠛⠉⠁⢀⣀⣘⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⡞⣰⣼⡇⠀⡟⠀⠀⣿⠁⢀⣀⡀⠀⠀⠉⠳⣄⡀⠈⢿⣟⠂⢀⠀⠀⢀⡼⠁⠀⣰⠟⠉⠀⢀⣠⣴⣾⣿⠿⠿⠿⣄⠀⠀⠀⠀⠀ ⠀⣜⣼⡛⠉⠁⣸⠃⠀⢰⡇⠐⣡⠤⣍⠢⡈⠠⣀⠈⢯⡀⠀⢻⡆⠀⠀⢠⠏⠀⡰⠋⠀⢀⣤⠞⠋⠍⠀⠀⠀⢰⡻⡻⢿⢤⠀⠀⠀⠀ ⣪⣾⡷⠁⠀⢠⡏⠀⠀⣸⠀⢠⠇⣠⢤⣽⣾⣲⣌⠳⣄⠹⡄⠀⢿⡄⢰⠃⣠⠞⠁⣠⠔⢋⡠⣄⡤⠴⠒⠛⣋⣉⣉⣉⢻⡁⠀⠀⠀⠀ ⢡⢿⠁⠀⢠⡾⢀⠀⣀⡏⠀⣼⡾⠉⢀⣚⠿⠻⠿⠷⠮⣷⡘⣆⠈⣇⡇⣰⣫⣾⠟⠱⠺⠟⠫⠥⡴⣾⣊⣩⣍⣉⣉⣩⣽⣧⠀⠀⠀⠀ ⢿⠃⠀⠀⣿⢃⡞⢠⣿⠁⢄⡟⢀⠔⠋⠀⢀⡤⠖⢋⣩⠭⣿⣿⣆⢹⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣒⡐⠒⢖⠒⣿⡀⠀⠀⠀ ⠁⠀⠀⣼⠇⡼⠁⣼⡏⢠⢸⡷⠋⠀⠀⡰⠋⢀⡔⠁⠀⣠⠶⠚⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⠉⣓⠲⢦⣏⢻⡀⠀⠀ ⠂⠀⣰⠋⣼⠃⣰⡟⠀⡼⡿⠁⠀⠀⡼⠁⢀⠏⢀⠄⣰⠃⠀⣰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡓⠶⠿⢶⣏⣿⠃⠀⠀ ⠀⡼⠃⡰⠃⣰⢿⠁⢠⣷⠇⠀⠀⡼⠁⠀⡞⠀⡞⣄⡏⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢈⡳⣄⣀⣾⣿⡿⠀⠀⠀ ⡾⠁⠘⠁⢠⢯⠇⢀⡿⡿⢠⠃⢰⠃⠀⣼⢃⣼⢹⡿⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣁⡉⠙⠂⠀⠈⣏⢹⣿⠟⢹⠃⠀⠀⠀ ⠀⠀⠀⣰⣿⠞⠀⣾⣿⠃⡞⢀⡏⠀⢠⣿⣸⡏⣿⠃⠀⣾⠏⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠛⠻⠶⣄⠀⡷⢲⣿⣟⣸⠀⠀⠀⠀ ⠀⢀⢾⡿⠋⢀⡾⣿⡏⢸⠃⢸⡇⠀⡼⡟⣿⢰⣟⠀⢹⣿⡀⠀⠀⠀⠉⠀⠀⣠⣴⡿⠋⠁⠀⢀⣀⣀⣀⡌⠃⣻⣿⣻⢿⡿⠀⠀⠀⠀ ⣴⣯⡟⠁⢠⣿⣽⡟⠀⣼⠀⣿⠀⠀⠀⣿⣿⣸⢿⣿⣿⠃⠀⠀⠀⠀⠀⣴⣿⠟⢋⣠⣴⡶⠿⠿⠿⣾⣯⡧⠂⣿⠿⠿⣺⠃⠀⠀⠀⠀ ⣿⠋⠀⣰⢏⣿⡟⠀⠀⡇⠀⣿⠀⠀⢠⣿⠇⣿⣦⣼⡟⠂⠀⠀⠀⠀⠈⠋⡡⣶⠟⡏⠩⠉⢳⠀⠈⣷⡦⡄⠀⣿⡤⠖⠁⠀⠀⠀⠀⠀ ⠃⢀⣴⡷⢻⣿⡟⠀⢠⡇⢰⡿⡄⠀⣬⣿⢣⣧⠙⢿⣟⢄⠀⠀⠀⠀⢠⣾⠵⢻⠀⠦⣀⣠⠼⢁⣴⣿⡟⠃⣰⡿⣅⡀⠀⠀⠀⠀⠀⠀ ⣤⣿⠉⠀⣿⣿⢁⠀⢸⠁⠘⡇⡇⠀⣿⠟⢸⣷⣶⣾⠀⠈⢷⣤⡀⢠⠛⡇⠀⢿⣿⡓⠶⠷⡟⣻⣿⣿⠇⢀⣿⠱⣿⣯⣳⡄⠀⠀⠀⠀ ⣿⠃⡄⢰⣿⡇⡼⠀⣼⠀⢠⣿⡇⠀⣿⠀⣿⠿⣿⣿⠀⠄⠀⢻⢤⡸⠀⠹⣄⠀⠈⠻⠿⠂⣽⣿⠋⠁⠀⢾⡇⠀⣼⡟⢿⣇⠀⠀⠀⠀ ⡟⢰⠃⣾⡟⢠⡇⠀⡇⠀⢸⣿⠃⢀⣿⠀⡇⠀⣸⣿⠀⠀⣠⡟⠓⣿⣦⡀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⣼⡫⠚⠉⣿⣄⡀⠀⠀ ⠁⡟⢀⣿⡃⣼⣧⠀⡇⠀⢸⡟⠀⠈⣟⢶⡇⢰⡏⠛⠀⠀⠁⠁⠀⠀⠉⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠉⠑⠻⣌⡓⠉⣆⠀ ⢸⠁⣼⡟⣅⣿⠻⠃⣧⠀⢸⡇⡄⢸⡹⣼⡗⠀⠱⢦⡀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠒⠈⠙⠛⠒ ⠎⢠⣿⠃⣿⣿⠰⡄⢹⣿⢸⢱⠃⠸⢧⣼⡇⠀⠀⠀⠙⠦⣄⡀⠀⢀⣠⠶⠚⠁⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣾⠀⣿⣿⠀⢻⠈⣇⡼⠀⠀⡇⡟⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⡿⠁⠀⣀⣀⣀⣀⡀⠀⠀⣸⠏⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣿⡄⣿⣿⠀⢸⠀⢹⡇⠀⢀⢡⢷⣿⠀⠀⠀⠀⠀⣀⡠⠤⠄⢴⡾⡿⠏⠉⠁⠀⠁⢀⣴⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣿⡇⢻⢻⠀⢸⡅⢀⡇⠀⠀⢸⣼⣿⣦⡀⠀⠐⠛⣟⣟⣛⢛⠛⠉⣠⠆⠀⠀⠀⣴⠋⣸⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⢻⢻⣸⣼⠀⢸⡇⢸⡇⠀⠀⢸⣿⠋⢧⠙⣄⠀⠀⠨⠿⠚⠒⠛⠉⠉⠉⠀⣠⣾⠏⠀⡏⠀⠀⣿⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣜⡇⢳⡹⡇⠈⡇⢸⡇⠀⠀⢸⡿⠀⠈⢷⣌⠳⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⢸⠁⠀⠀⢹⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⡘⡟⣿⡄⠳⣇⠀⣇⢸⣿⢸⠀⢼⡇⠀⠀⠘⢮⡑⠾⣷⣶⣤⣤⣴⣶⣾⠟⠋⠀⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡙⠮⣌⠳⡀⢹⠀⣿⢸⣿⡄⢧⢼⡇⠀⠀⠀⠘⣏⠓⠒⢾⠿⠓⠚⠉⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣄⡈⡉⠛⢾⣇⢸⡿⡿⣧⠈⢾⣿⠀⠀⠀⠀⠘⣆⠀⠈⣧⠀⠀⠀⣰⠇⠀⠀⢀⣯⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⡗⠆⠀⢹⡼⠁⡇⡿⣆⠸⣿⣇⠂⠀⠀⠀⠘⣆⠀⠘⣆⠀⠰⠋⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⠀⠀⠀⢾⣷⡀⠀⠀⢳⡀⢻⢹⡹⣦⢹⡼⣄⠀⠀⠀⠀⠈⠙⠓⠒⠚⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢰⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀⠀⠙⢄⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⣀⠠⠤⢐⣁⠠⠀⠀⠀⠀⠐⠠⡈⢤⠀⢈⠄⠀⠀⢱⡄⠀⠀⠀⠀⠀ ⠈⠫⢀⣀⠈⢉⠍⠀⣁⣤⣤⣤⣀⡀⣀⣀⡠⣷⠶⠏⠁⠂⢄⡀⠘⡄⠀⠀⠀⠀ ⠀⢀⣠⣤⡊⠁⣴⠋⠁⣤⠀⠈⣻⡻⢚⣹⣿⠣⣠⡴⠋⠀⠀⣳⢠⠗⡀⠀⠀⠀ ⠀⠀⠄⡄⠀⢸⣆⣀⡞⠡⡴⢾⡿⠊⠀⢀⣜⣮⣨⡗⢲⠚⣦⣫⡖⣠⢟⠀⠀⠀ ⣠⣂⠌⠠⠀⡰⠣⠯⣼⡤⣾⡟⢁⢠⡴⠋⠀⣰⡽⠉⠉⠒⢿⣿⡗⠁⣸⠀⠀⠀ ⠬⠥⡞⢀⡼⢡⠃⠀⣜⡼⠀⠊⡰⡓⠀⡠⠞⠌⠀⠀⣀⡀⠘⣿⣿⣸⡏⠀⠀⠀ ⠀⡜⢀⢢⢣⠹⠀⢰⠏⠀⡠⢊⣔⡤⠊⠀⣀⣠⣶⣭⣤⣄⡀⠏⣿⣿⠃⠀⠀⠀ ⠀⢁⢃⡞⡌⡇⢠⠃⢀⡴⢻⠻⠿⠁⠀⠀⠀⠋⣉⣙⡿⠏⠀⣾⣯⢪⡀⠀⠀⠀ ⠀⡞⣸⢃⠃⢣⠂⠀⣼⠛⠒⠊⠀⠀⠀⠀⠀⠀⠈⢆⡞⡇⢰⡧⣠⡹⣷⡄⠀⠀ ⠀⢇⡏⢸⠀⣾⠀⢸⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢁⡞⣩⣿⣿⠿⠁⠀⠀ ⠀⠘⠂⡎⢰⣿⠀⢸⣷⣿⣄⠀⠀⣠⣤⣤⡠⠄⠂⠀⣠⠊⣿⣿⣿⠃⡄⠀⠀⠀ ⠛⠒⠶⢥⣼⡟⢧⠸⠻⣯⣿⣳⣟⡉⠀⠀⠀⠀⣠⣜⡏⠀⣿⣿⠃⡌⠀⡆⠂⠀ ⢄⣆⡀⠀⠟⢧⠘⡶⠋⠊⣥⣼⣏⠉⠂⠠⡴⠊⢹⣡⡇⡰⣿⣧⡎⠀⣀⡇⠀⠀ ⠀⠉⠻⣆⠀⠀⢣⡘⣤⣼⠽⣧⠈⢿⣻⣯⡿⣾⢿⣿⣧⡧⡳⣿⣉⡿⠟⠁⠀⠀ ⠀⠀⠀⠈⢢⠀⠈⢳⡜⡄⠀⠈⠙⣿⣽⣿⣿⣿⠿⠻⣷⢳⠁⢸⠋⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⢾⣻⣌⢄⡀⠊⠀⠰⣿⣿⠀⠀⠀⡘⠀⠡⠀⡇⠲⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⡌⡗⠄⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢡⢰⠀⠱⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢠⡇⠀⠤⢭⡴⣦⣤⡏⣯⢱⡀⠀⠈⡄⠆⠀⠱⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢸⢀⡴⣿⣾⣿⠟⠉⠉⠈⠁⣹⡦⠖⢲⠸⡈⢄⠙⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠂⠒⠐⠖⡂⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡔⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢌⠢⡀⠀ ⠀⠀⠀⠀⠀⠀⠐⣡⡪⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠈⢆ ⠀⠀⠀⣠⣴⣆⡈⠉⠁⠀⠀⠀⠀⠀⠀⣤⣿⣵⡀⠀⣀⡀⠤⠂⠉⠉⢹⣿ ⠀⠀⠀⠀⣆⡉⠴⠮⠭⠔⠒⠈⠀⠥⠐⣻⢫⠋⠛⠁⣄⣉⢶⡄⠀⠀⣸⣽ ⠀⠀⠀⣀⡩⠷⠖⠂⠒⠒⠤⣤⣀⣴⢾⡟⢚⠀⠀⠀⠹⠟⠃⠛⢀⡴⡻⠋ ⠐⠈⠉⠀⠀⠀⠀⠰⢀⠠⠄⠬⡮⣫⠖⡑⢰⡀⠀⠀⠀⠀⠀⠀⢋⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⡏⠑⠦⠼⠝⠚⣯⠞⠐⢈⣿⣄⠀⠀⢤⣌⡮⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠀⠀⢼⣿⠏⢋⣵⠂⠑⠄⡨⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣷⡤⡀⠀⠀⠐⠇⡇⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠫⡇⠈⠢⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠧⠔⠁⢨⠿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⡾⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡻⠛⠀⠀⣀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣴⠁⠀⠀⠀⣿⢠⠀⠀⠀⠠⣽⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢿⠊⣩⡉⣾⣟⠁⠀⠀⠀⠀⢸⠰⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠉⣿⣿⡿⡿⣄⡀⠀⠀⣠⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⣼⣾⠛⠔⡩⣮⣷⢿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣿⠀⣼⢾⣠⡿⢯⣭⡝⠛⣲⣄⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠃⠀⠀⠀⠀⢀⣀⠀⢤⣒⣢⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣪⣶⣿⠿⢒⠋⠙⡻⢶⣯⡛⢳⣈⣁⡀⠀⠀⠀⠀⣠⡶⠋⡎⠀⠀⣀⣴⣖⠕⠈⢉⡵⠊⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣻⣫⣯⣓⣛⡯⢿⣿⣦⣘⡀⠘⠬⠭⣅⡘⡓⡤⠊⠙⠀⠀⠀⡴⠋⠀⣼⠤⣲⠯⡷⢺⠋⠁⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠻⣩⡀⡘⡏⢿⠷⠸⡀⠲⠙⠫⣽⣱⡤⠤⠤⠤⢴⣾⣧⠀⠀⣀⣠⡼⠃⠀⣰⠋⠁⠀⣴⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⣱⣿⣧⡀⢳⣾⢯⣉⠤⢽⣯⡖⠘⢤⣤⡷⣟⡹⠛⢆⠭⠗⣾⠃⠀⠀⠏⠀⠀⣰⠋⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡝⠘⠛⢿⡼⣽⣆⣻⡵⢋⣀⣨⠃⡜⠑⢦⠘⡍⢢⡾⢾⠟⢣⡀⠀⠸⣳⢶⣶⠃⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡦⠀⠘⢻⡿⣧⡰⣁⣾⣵⠿⡅⠰⢟⢢⢞⣁⣼⠀⠀⣾⡀⢸⢾⡝⣆⢰⡠⠵⡄⢰⢳⣿⢻⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠶⠞⢡⡟⠀⠀⣠⠟⢀⣼⢵⣿⣛⣾⣤⠶⠶⠒⠉⣁⣀⠼⣤⣾⢻⠈⢹⣹⠵⢻⡯⠤⠒⣳⢃⢯⣿⠙⣆⠘⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣿⠯⠒⠀⣠⣞⣄⡠⣾⡗⣲⡯⠬⠓⣉⢟⣿⣿⢷⣿⣶⣿⡷⠧⣶⣯⡀⢸⣠⠞⣡⢶⢹⣇⠀⣰⠃⣾⣿⠋⡷⠘⡀⠉⠉⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⣯⣤⡾⢳⡧⠾⠉⣛⣚⠥⠓⢛⣓⠯⠔⠚⣁⣼⢸⣽⣼⣸⣞⠄⠀⠀⣼⠻⣎⢏⡾⢃⡜⠁⣿⢸⣿⡾⢃⣼⣿⠃⠀⣹⡇⢧⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢴⢾⢽⡟⣵⣷⣿⢿⣿⠛⠉⣀⣀⣾⣆⡠⠴⢒⡽⢻⢹⠘⣿⣻⠟⢁⡀⡜⣼⠏⠀⡟⡞⢀⠎⠀⣴⢏⣼⣿⣷⣾⣾⡜⣀⡴⣋⡇⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠊⣠⢿⣾⣾⡿⢮⣭⣵⠞⣮⣄⣐⠷⠞⠋⠁⠀⠀⠋⠀⠸⢆⡠⠒⣵⡎⡽⢰⢰⡟⠀⠠⡟⢀⡎⠀⢸⣇⡼⠟⢇⣰⣾⣹⣾⣿⠞⣻⡇⡼⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⡗⣚⣉⡤⠤⠒⠚⠓⠙⢒⣪⠍⠚⠉⠀⠀⠀⢠⠔⠩⠔⠊⠉⠁⠀⠀⠀⣿⣀⡇⠘⡿⠇⠀⣰⠁⡘⠀⠀⣼⡟⠁⣴⣿⣿⣿⣿⣿⣿⣷⣷⣬⣧⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⢖⣶⠀⠘⢬⠃⠀⠇⠀⠀⡯⢠⡇⠀⢸⡟⢀⣼⠟⢻⡿⡏⢿⠙⢛⢿⠛⠏⢻⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀