Lucy Chibi Reverse 1999 Emojis & Text

Copy & Paste Lucy Chibi Reverse 1999 Emojis & Symbols ⠀⠀⠀⢠⣶⣾⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯

⠀⠀⠀⢠⣶⣾⣷⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣮⣿⣟⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣯⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀ ⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀ ⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⢀⣾⣿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣷⣄⣄ ⢾⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣯ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⢸⣿⣿⡿⠛⣿⣿⡏⠉⠹⣿⣿⣿⣿⡆ ⠈⣿⣿⡆⠀⢸⣿⣇⠀⠀⢻⣿⠿⣿⠁ ⠀⠈⠁⠀⣠⣾⣿⣷⠀⠀⠈⠃⠀⠉⠀ ⠀⠀⠀⠀⠉⠉⠸⢿⠇⠀⠀⠀⠀⠀⠀

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

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣶⡤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢉⡼⠛⠁⣠⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠛⠉⠉⠽⠓⠒⠓⠒⠿⠉⠛⠒⠦⣤⡀⠀⣠⡶⠋⠁⠀⢠⡟⠀⠀⠴⠟⠛⢳⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣶⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⡀⠀⠀⢀⡏⡆⠀⠀⠀⢀⣼⣋⡅ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⣸⠁⠀⠀⠀⠀⠉⠀⣸⡇ ⠀⠀⠀⠀⣀⣠⠴⠞⠋⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⢀⣴⠏⠀ ⣤⡴⠒⠛⠉⠀⠀⠐⠒⠛⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣌⣛⣒⣤⠿⠟⣶⠆ ⢹⣧⡀⠀⠀⠀⠀⠀⠀⣼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠉⠀⠀⣰⠏⠀ ⠀⢿⡷⣄⠀⠀⠀⠀⢰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠛⣯⠀⠀ ⠀⠈⢷⣈⠙⢶⣒⠛⠋⢠⠞⠀⠀⠀⠀⠀⡴⠀⢠⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣿⡦⣴⠟⠁⠀⠀ ⠀⠀⠀⢹⡟⠂⠩⠛⢲⡏⠀⠀⠀⠀⠀⢰⡇⣀⣿⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⠐⢺⢷⠂⠰⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠹⣟⡁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠲⢶⠀⡾⠀⠀⠀⠀⠀⢠⢸⡷⠫⢸⡆⢸⣆⠀⠀⠀⠀⠀⢳⠀⢀⡿⠘⢧⡀⢹⣄⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⡆ ⠀⠀⠀⠀⠀⠀⠈⢹⠁⢰⠀⠀⠀⠀⢸⢸⡅⠀⠀⠻⣎⣿⢦⣀⠀⠀⠀⣸⡀⣼⣷⣾⣿⣿⣾⣿⢦⣿⠀⠀⠀⠀⠀⠀⠀⢷⠦⠴⠖⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡄⠀⠀⠀⣿⠸⣇⠀⠀⠀⠈⠙⠂⠙⠷⣄⣀⣿⠟⢿⣿⡏⣀⡀⢙⣿⣿⣏⡀⠀⠀⠀⠀⢸⡀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿⡀⠀⠀⢸⡷⢿⣶⣶⣦⣍⡢⠀⠀⠀⠀⠙⠀⠀⢸⣟⠉⠽⠿⠍⣻⣿⠟⠀⠀⠀⠀⠀⣸⠁⢰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣧⡿⢦⣄⡀⣷⠀⠀⠈⠉⠛⠻⢦⠀⠀⠀⠀⠀⠀⠠⠿⠤⠤⠤⢒⡿⠃⣠⡞⠀⠀⠀⣠⡏⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠟⠁⠀⠉⢉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡯⠴⣺⣿⠀⠀⢀⡴⣿⡖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡤⠶⠋⠁⠀⠀⠀⢀⡄⠈⢳⣄⠀⠀⠀⠀⠀⠠⣄⣠⣤⣀⡄⠀⠀⠀⠀⠀⢀⡴⠋⣯⣤⠖⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡶⠚⠉⢁⡆⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⠓⣶⣄⣀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⡀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀ ⢸⠟⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣴⣿⣿⣤⡉⠛⢿⡖⠦⠤⠤⠖⢛⣿⠋⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠹⣷⣄⡀⠀⢀⡀⠀ ⢸⠀⠀⢸⡿⠁⢠⡄⠀⠀⠀⠀⡇⠀⠀⢀⡼⠛⠻⣿⣮⣙⣦⡈⣿⣆⠀⠀⢀⡾⠛⢷⣤⡀⠀⠀⠀⠀⢸⠀⠀⠀⢰⡄⠙⣮⡉⠉⠉⠁⠀ ⠘⣧⠀⡏⡇⠀⠸⡇⠀⠀⠀⠀⢻⠀⢀⡏⠀⠀⠀⠘⣿⣿⣿⣷⣽⣿⣦⣤⣼⡇⢀⡿⢸⠿⣆⠀⠀⠀⠈⣧⠀⠀⠀⢳⡄⠈⠻⣆⠀⠀⠀ ⠀⠈⢷⣇⣧⡀⠀⢹⣄⠀⠀⠀⠈⣇⢸⠁⠀⠀⠀⠀⠨⣿⣿⣿⣿⣆⢹⣆⣸⢡⣿⣷⡟⣠⣿⡀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢆⠀⠘⢷⡀⠀ ⠀⠀⠀⠀⠈⠙⠲⢤⣹⣦⣀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⠋⠈⢷⡄⠀⢀⡟⠀⠀⠀⠀⢹⡌⢷⡀⠈⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠛⠓⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠹⣦⠞⠁⠀⠀⠀⠀⢸⡇⠀⢳⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠻⣏⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⣀⡾⠃⠀⢸⣇⡞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⠇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⠀⠀⠼⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣀⣀⣀⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣿⠿⣯⣝⣳⠷⣌⠳⣄⡞⣀⣠⣤⠟⣡⣿⡦⣿⣎⢯⡀⠀⡇⣈⢽⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⣽⣏⣿⠶⡿⣿⣿⣚⣿⣿⠿⠿⠿⠿⠿⣿⣿⣧⢿⣿⢶⡻⢷⡿⣤⣼⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣾⡿⠷⠛⢉⣉⠄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣼⠛⠿⢿⣋⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣠⢶⡫⢥⠲⣬⣉⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠤⡀⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣞⣻⡽⠯⠵⠞⠋⣰⡾⣟⢧⣛⢧⡛⡴⡞⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⡆⠀⠙⢾⡀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⢀⣴⡿⣽⣹⣮⣽⡲⣝⡼⠁⠀⠀⢰⠃⠀⢸⠁⠀⠀⠀⠀⠀⠀⣷⠀⠀⢺⣷⣄⡀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⡴⣖⣶⣲⣛⣯⣽⣭⢷⡶⣿⡱⢯⠇⠀⠀⢀⡏⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢹⡤⠿⢿⣿⣶⡟⠉⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⠉⠉⠀⢉⣿⡿⣾⢽⣫⢾⣵⣻⡿⠀⠀⠀⣼⠁⠀⣤⢞⣿⠀⠀⠀⠀⠀⠀⡟⢧⡀⠀⠙⣿⡀⠀⢸⡌⣹⠃⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣷⡶⡿⣿⣛⣛⣛⣻⣝⣭⣽⢿⡗⠀⡁⢠⡯⢀⡾⠧⠴⠻⣧⠀⠀⠀⠀⣸⠧⠬⢷⡀⠀⢻⡇⠀⠀⠹⢧⣀⣠⠀⠀⠀⠀⠀⠀ ⠟⠟⠓⢿⣟⣯⣟⡿⣻⡽⣫⣟⢮⣿⡇⠐⡀⢸⣷⠏⠀⠀⣀⡀⣘⣷⣄⠀⠀⢺⡁⣀⣀⠹⣤⡸⡟⠀⠀⠀⠀⢨⣽⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣹⣿⣾⡿⠷⣟⣻⣛⣯⣿⡇⠂⠄⣾⣯⣼⡿⣿⣷⣿⣍⠉⠻⣷⢤⣸⣿⣿⣿⡿⣮⣻⡇⠀⠀⣧⠤⠞⠁⠀⠀⠀⠀⠀⠀ ⡾⡿⠿⢝⣷⡾⣶⣟⣿⣻⢯⣟⣵⣫⣇⠡⠂⣿⣿⠁⣿⣿⣻⣿⡾⠀⠀⠈⠙⠻⢷⣿⢯⣷⠙⣻⡇⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣯⣟⣧⣟⣶⡿⠿⣞⡶⣏⣿⠀⠅⣿⡽⡇⢿⣿⣳⣿⡟⠀⠀⠀⠀⠀⡀⢿⣿⣿⠀⣿⡧⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⡷⣿⣿⡽⣽⢿⡶⣿⣻⢯⣳⢏⡾⣇⠀⣿⡵⢧⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⢻⡇⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡾⣽⣯⢷⡻⣽⣣⣟⣧⣿⣽⣻⡄⠹⣟⠮⣷⡀⠈⡀⠁⡀⠁⢰⡿⠿⠇⠀⠀⠀⢠⣿⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣿⣽⢷⡿⣷⣻⣻⣭⡽⣷⢶⣞⢧⢿⡀⣿⣿⣶⣟⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⢞⢫⠏⠀⠀⢠⠏⢰⡟⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠛⠛⢿⣻⣿⣯⣟⣳⢿⣽⢧⡟⣮⢻⡜⡽⡜⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⡥⣪⢏⠀⣀⡴⠋⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣻⣙⣺⣽⣯⣿⠾⣽⣭⢷⡹⣷⡹⣜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠁⠈⢳⢤⣤⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⣶⣶⣟⣾⣽⣭⣷⣶⣾⣿⣿⣮⣳⢻⡜⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣤⡶⠉⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠍⠉⠁⠈⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⣠⢼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣤⡴⣮⣟⣟⣯⣭⣵⣾⣶⣿⣿⣿⣿⣿⣿⠗⠋⠉⡟⠛⠟⠿⠟⠻⠛⠋⠳⣖⠚⠉⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⠿⠛⠛⠋⢻⣿⣿⣿⣿⣟⡿⣽⣷⢙⣿⡿⠛⠋⠁⠀⡀⠀⣹⣆⠀⠀⠀⠀⠀⠀⠀⡯⢧⣀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⡽⢿⣛⣯⣻⣭⣾⣿⣷⣿⣀⣁⠀⠁⠀⣰⡏⡞⣳⣄⡀⠀⠀⢀⣼⣙⣦⣭⡷⠴⠖⣟⡹⣇⠀⠀⠀⠀⠀⠀⠀ ⣾⣾⡿⢿⣿⢿⣟⣿⣻⢿⣿⣟⣯⡷⠿⠚⣻⢿⡙⠛⠛⠛⠛⠻⡛⡚⠓⠚⠛⠻⡉⡹⣹⢧⡀⠀⢷⠀⠀⠈⢻⡻⡓⣆⠀⠀⠀⠀⠀ ⠁⠁⣠⣿⢿⣯⣟⣾⣽⡿⣿⣿⢃⠆⡑⢨⣿⠭⡗⠀⠀⠀⠀⠀⠱⣌⣇⣌⣡⢲⠝⣡⠃⠀⠻⣗⢾⣧⣄⠀⠀⠉⢾⣎⠳⣄⡀⠀⠀

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

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