Winniepoo Emojis & Text

Copy & Paste Winniepoo Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣤⢤⡤⢤⢪⠕⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣤⢤⡤⢤⢪⠕⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢁⡩⠄⣤⣳⣿⡾⣅⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⡦⠞⡙⢃⡀⢩⠙⠀⠀⠀⣠⣤⢲⣿⣿⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⣭⡷⡇⠱⡈⢆⠇⢨⣔⣲⣾⠯⣍⢣⠫⡝⣢⠳⡌⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⢼⣌⡓⠚⣉⣠⣾⡇⢛⣿⠳⣌⢣⣿⣿⣷⣧⣍⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣴⣾⣷⣩⢿⣎⠻⠿⠿⠁⢰⢎⠵⣪⣥⠻⣍⠲⣵⣬⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⣶⢢⣍⢻⠷⣊⠟⣣⢀⣀⡀⢼⡎⢶⣋⠞⣱⢊⡵⢊⡽⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢏⠳⣌⣷⣾⣿⡜⣵⢎⡱⡟⠀⠀⠈⠙⣶⢋⡼⢡⠞⣰⢫⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡪⣕⢊⣶⣡⠲⣙⢭⢏⢶⠀⠀⠀⠀⠀⢹⢎⣴⢋⣼⠱⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣿⡟⢦⡙⣬⠒⠮⣍⠳⡄⠀⠀⠀⠘⣿⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡙⣤⢋⡳⢌⡳⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣾⣶⡋⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣆⠿⠇⠀⠀⠀⠀⠀⢸⣉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣻⠻⣿⡇⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡒⡲⢄⠀⢀⣤⣾⣷⣎⠿⣿⣧⡹⠙⠀⠀⠀⠀⠀⣠⡯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣗⢲⠭⣑⣏⣔⡫⡝⣿⣿⣏⢎⡽⢏⠷⠀⠀⠀⠀⠀⢠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠜⣎⠧⡝⢭⢿⡷⡱⣊⣿⢏⡲⢌⡫⠄⠀⠀⢀⡠⣼⣷⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣸⣣⢞⣩⣆⣛⣧⣳⡗⡜⡢⢧⡙⡴⢢⠔⡮⣽⣾⣷⣷⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠈⣑⣵⣾⣷⡜⡥⢋⡖⣱⣮⣴⣷⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⣍⣳⡄⠀⡞⡿⢆⠟⠋⢹⣖⡭⣲⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⢹⢻⣼⢻⣹⡀⣏⠷⡏⠀⡄⢯⡘⢖⣻⣿⡶⠭⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣶⣿⡀⢻⣿⢫⣷⣾⠀⠀⠙⢦⡙⡭⢒⠭⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣶⣶⡄⠀⠀⠀⣷⣎⡇⠀⠙⠃⠒⠁⠀⠀⠀⠈⠷⣘⠭⢲⡡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⡟⣽⢶⣒⣶⣯⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠫⢜⡹⢷⣹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Related Text & Emojis

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣠⠴⢞⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣲⣿⡄⢀⡴⠋⣠⣾⣿⣿⣿⣿⣄⣀⣀⡀⠀⠀⠀⠀⠈⠓⠲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣼⣿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣦⣄⡀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠊⠉⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡉⠛⢿⣷⣄⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠤⠐⠒⡁⢴⣤⣤⡀⠀⠀⠀⣠⣼⣿⣿⣏⣀⣀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣷⣄⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⢰⣦⣍⣁⠀⠀⠀⠀⠀⠀⢾⡉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⢻⣿⣆⠀⠀⠑⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠋⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⡄⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡻⢿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⢸⠾⠀⢀⣠⣶⠀⣠⣾⣿⣿⣿⣿⣦⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⢹⠁⠰⠉⠉⠒⢄⣸⡷⠿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⢇⡇⠀⠀⠀⠘⠁⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣯⠻⢿⣿⣿⣿⣷⣶⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⣿⣷⣶⣶⣾⣿⡿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⠀ ⠀⠀⢀⠞⡄⠀⠀⢠⣿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⣀⣇⠠⠔⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣿⣿⣿⡿⢣⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠰⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠟⢁⣾⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⡄⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠚⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⣉⣤⣶⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠹⣿⣿⣿⣿⣿⡏⠀⣿⡀⢻⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠻⣿⣿⣿⡇⠀⠸⣷⡀⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠈⠙⠿⣿⡄⠀⠘⢿⣦⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣡⣄⣀⠂⠀⠁⢀⠀⡀⠀⠈⠃⠀⠀⠀⠡⠐⡐⡖⠂⢬⢡⠄⢐⣍⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠟⠙⠉⠬⣥⡁⠙⢰⡈⠠⠀⠁⠀⢁⣴⣬⣤⠠⢠⠀⠉⠋⠁⣾⠇⢫⡤⣵⠋⡉⢁⢌⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠃⠥⠁⠩⣿⣷⡏⠁⠀⠚⠀⠠⠐⠁⠈⢺⠻⠄⠁⠀⡀⠀⢁⢐⡝⣾⡂⣿⢳⣷⣷⣛⣫⠕⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠞⢂⡸⠿⠿⣮⡐⠀⠀⠠⠊⠀⠀⢀⢻⠖⠰⢀⠀⠀⠠⠈⢶⢀⣿⠓⠁⣿⣾⣽⣷⢯⡵⢐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠂⠟⡴⣶⣛⠢⢑⡔⠀⠂⢀⡀⠀⢸⣮⡔⠀⠚⠀⠂⠠⠊⠀⡜⠙⣇⡞⡋⢖⠋⠿⣇⢿⡓⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢈⡆⣠⡁⠀⠉⢉⠈⢀⡌⠄⢀⡁⠐⢠⢶⠆⠀⡀⠈⠒⣀⠁⠀⢑⠀⠄⠬⠖⠉⢷⣽⡺⣿⣣⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⣄⠇⡀⠀⠠⠠⠑⡼⠁⠀⡋⠜⢀⢠⣏⡡⠀⠀⠀⠀⠄⠀⡀⠀⢇⢀⣹⣄⢀⣴⣿⣿⣾⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡐⠣⢺⣇⣠⡶⠛⣳⡇⠀⠀⡌⠅⢀⡘⣡⠃⡌⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡈⢻⡷⣿⣿⡿⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣇⠀⠀⠿⠟⠁⠀⠘⠀⡰⠼⢁⠉⠠⡕⡩⢠⠚⠀⠀⠂⠐⠀⠂⢀⠂⠀⠀⢹⡲⠧⠉⠫⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠄⠀⠀⢀⠾⠉⣠⣴⢁⣷⢣⠠⠀⢹⣿⡆⡂⠀⠀⠀⢠⣷⣈⠃⡀⡰⢢⠂⢹⣶⡀⢑⡘⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⣨⣟⠾⢴⣿⡈⠐⢢⢻⣿⢥⠈⠀⠀⢦⣸⣙⠲⡥⣀⡨⡐⠀⠘⠿⣧⡈⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢹⣷⣶⡞⠂⠀⠀⣾⡏⢙⣿⡇⠀⡀⠸⡯⠀⢁⠀⢦⣾⢫⢿⡿⣿⡃⢡⡐⠮⣸⠀⢻⣿⣻⣟⣦⣻⣿⣿⣟⣭⣻⣿⣛⣿⣿⣿⣿⣿⣿ ⢯⣽⣿⠀⠀⠀⠠⢽⣿⢿⠻⢿⢪⡀⠀⡊⠠⠤⢲⠋⣿⣦⠼⢣⡯⣯⡡⢭⣗⠞⠠⡀⢿⣿⣿⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⡴⠃⠐⠀⠠⠐⢻⣂⡘⣷⣾⠀⡧⠀⠀⠈⠁⠀⠀⣿⠁⣡⠛⠍⡿⠍⠢⡋⠳⡶⡗⢘⣿⣿⣯⠔⠶⠶⣾⣯⣭⣍⣸⣿⣿⣟⠉⠈⠹ ⡸⢟⠄⠀⠀⠀⠰⣿⠢⠥⡀⢹⠀⠃⠀⠀⠀⠀⡀⢠⣿⠐⡅⠀⢁⡿⢂⠅⠐⠰⣇⡨⠌⠻⣧⣼⣷⣶⣾⡷⢾⣮⣿⣿⣯⣿⠿⢧⣦⣀ ⣝⡿⠀⠀⠀⠀⠀⢹⡾⠡⠋⢫⠀⠴⡀⢐⠀⣁⡘⣸⡏⠀⠑⠄⢈⢭⠥⡠⠢⠀⣿⣇⡳⠁⠀⠈⠉⣉⣥⣶⣯⣿⣤⡉⠻⣿⣆⠀⠉⠉ ⣾⠁⠀⠀⠀⠀⠀⢼⡇⠀⠀⢸⣏⢀⡀⠼⠀⠊⠑⢞⠹⡀⠀⠁⠀⠠⠔⠈⠀⡐⢸⠛⢀⣠⡾⣡⣾⣟⣿⣿⢷⠉⢿⣿⣄⠈⡏⠀⢀⣾ ⣿⠀⠀⠀⡀⠀⠀⠁⠔⠀⠀⣶⢫⠋⢀⠈⠑⢔⢳⡘⡮⠇⠀⠀⠁⠀⠐⠪⠂⣧⡼⠀⣠⠏⣼⡿⠿⢿⣿⣿⣿⣧⠈⠻⣿⣶⣧⡄⢀⡟ ⣾⡆⠀⠀⠀⠀⠀⠀⢈⠀⢰⡏⠎⢠⣤⣶⠟⢿⣆⢋⠙⠭⣍⠄⠀⠀⡡⠕⡑⣽⠃⢨⣿⢿⠏⣀⡀⢀⣾⡟⢿⢻⣧⠀⢌⠉⠹⠃⡾⠀ ⣿⡗⠀⠀⠀⠀⠀⠀⠀⣨⡿⠁⢠⠏⠀⠀⠉⡁⢸⣯⠀⠀⣈⠆⠀⠀⢼⠁⢘⡟⢀⣿⣯⢣⣾⣿⣿⣿⢻⣧⠀⢻⣿⡆⢯⣧⠁⣑⠀⢠ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣵⡅⡿⠐⢄⠸⠀⠤⡀⡝⢎⢠⣍⡆⠀⡀⠘⠄⢸⠀⣼⣼⡤⠛⠉⠉⠙⣟⣿⣿⣷⡈⣿⣧⠸⣏⡆⢹⠄⠈ ⣿⣿⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⠃⠀⢠⣤⡀⠀⡠⢘⣌⣆⢿⡇⠀⠐⠆⠀⠐⣼⢳⣷⣢⡾⣿⣤⡀⢺⢿⣜⣿⣧⠸⢻⣦⣿⡘⠀⣰⣄ ⣿⣿⠁⠀⠀⠀⠀⠈⣀⢸⣿⡿⣄⢀⠼⣿⣿⣠⣷⡟⠘⣨⢿⣇⣠⠀⠈⠐⣺⢧⣿⡼⠉⠐⣣⣿⣿⡇⣠⡍⠸⣿⡆⠈⣿⣿⠃⠀⠀⢿ ⣿⣿⡀⠀⠀⠀⠀⠀⢏⣸⣧⡁⢻⣿⠲⠭⠞⣿⡿⠃⡔⣹⠾⡉⡉⠁⠀⠀⣿⣽⣿⡇⠀⢸⡏⣨⣿⣿⣿⢿⣦⠈⠷⠀⢼⡏⠣⠈⠀⠠ ⣿⣿⣣⠀⠀⠀⡠⢒⡽⢽⣿⣿⡈⠻⣧⣨⣸⡟⠁⣠⡞⠙⡴⣏⡩⣝⡳⢢⡇⣿⣈⠇⢠⡟⣱⢃⣿⣿⡇⢈⢿⣇⠀⠀⢸⣿⠈⠀⠀⢀ ⣿⣿⣿⠀⠀⠞⠞⠁⢀⣲⣏⠈⠙⠀⠹⣿⣿⠀⣠⠤⠖⠏⢱⠖⠛⢂⡉⣹⡷⡿⠿⣿⣸⡿⣻⢿⣿⢩⡇⢸⠀⠹⣆⠀⢿⣿⠀⠃⠴⢻ ⣿⣿⣿⡄⠘⠀⣀⢜⠟⣷⣈⠡⠉⠉⠀⢹⠇⠀⠀⢀⡠⠶⣩⣝⣛⡝⠙⢼⣿⢳⢂⣿⣿⣿⡇⠼⣿⢸⡃⢸⢠⣷⠛⠀⣿⣿⡀⣇⡀⣘ ⣿⣿⣿⡇⣠⣽⣄⠴⢊⡵⣚⠑⠆⠀⠀⢸⡀⠀⠀⠉⠀⣴⢷⡒⢾⣿⠃⢸⣿⣸⡼⣾⣿⠌⠄⠄⢸⣾⢡⣼⡿⣿⣿⣿⡿⢿⡅⣿⣇⢹ ⣿⣿⣿⣬⣧⠋⠕⡱⣫⣾⡿⣷⠂⠀⠀⣼⡷⣄⠀⠀⠐⣫⣷⣜⣿⣿⣵⢹⣿⡸⣷⣿⡟⠀⠀⠀⢾⣿⢿⣿⠿⣎⣧⣿⠀⢰⡇⣿⣿⠸ ⣿⣿⣿⣿⢣⢢⢫⢏⡼⣯⣿⣿⣗⣀⠜⢳⣼⣧⡉⠒⠺⣯⡏⢬⣿⣿⣟⣸⡟⡧⣿⣿⡴⠀⠄⠙⢾⡿⣼⡘⠇⡟⣿⣿⡰⣿⠀⣿⣿⡃ ⣿⣽⣿⣃⣿⢯⢷⠎⢀⡾⣿⣿⠟⠁⠀⠁⠈⠃⠀⠀⠀⠹⡼⣿⣿⣿⣿⠹⣇⣽⣿⣿⢋⠨⠀⢆⢰⣶⣿⣿⠞⣱⢏⣇⢩⣿⢰⠏⠋⣷ ⣷⣿⣿⣿⣿⣫⠃⠰⡎⡇⢿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠠⡟⣇⣿⣿⣿⣿⡟⣟⡟⣿⠚⠁⢐⠈⢄⢽⣿⣿⣰⣾⣧⣾⣿⢸⣿⣼⡄⠀⠸ ⣿⣿⣿⣿⣻⣿⡃⣸⢰⠁⣿⣯⣿⡀⠀⠐⠀⢱⢀⢀⣷⠳⣻⣿⠿⣿⣿⣷⣿⢣⠁⠀⠀⠈⠉⣬⣿⣿⣿⢩⡟⣻⣿⠇⣸⡏⡿⠀⣄⠘ ⣿⣿⣿⣿⣿⣿⠃⡇⣼⠀⣿⣯⢿⣿⣠⣴⣸⡀⣼⣾⣿⢶⣿⣿⣿⣬⠿⣿⡏⠈⠀⠀⠐⠄⠁⡼⡯⢿⣌⣮⣶⡿⠟⢀⣹⠁⡇⢁⡀⠀ ⣿⣿⣿⣿⣿⣿⠣⣧⡟⡄⣿⣿⣈⣿⡘⢹⢿⡗⣿⣿⡿⣿⢿⣯⣽⣻⢷⣹⠦⡇⠂⠀⢃⡄⡐⡽⡂⠩⢻⣼⡟⠅⠀⢀⠇⢸⡇⠈⠓⠀ ⢿⢿⣿⣿⣿⣿⢀⣸⣳⣧⢿⣿⣧⣧⣻⣆⢦⣼⢸⣿⡻⣿⣿⣿⣿⣿⣷⣏⢀⣗⠀⠀⣖⣓⢼⣾⣇⠀⢚⣇⠆⣶⣶⣾⠀⢸⡃⠀⢀⠀ ⠀⢉⢻⣿⣿⣿⣾⣿⣷⣿⣞⣿⣿⣧⣿⣿⣯⣯⣼⣿⣷⠼⣢⣩⣶⣧⣭⣿⣀⡆⣀⣤⡈⢡⢈⣿⡟⠀⠉⠹⡇⢹⢹⡇⢀⣾⠀⠀⠀⠀ ⠀⠈⡂⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣇⣿⣷⣶⡍⣯⣿⣶⣺⢾⠸⡝⡀⢿⣿⠇⠃⢸⣷⠀⠀⣷⢠⣻⡘⣼⢁⣼⡗⠀⣀⠀⣤ ⠀⠀⠀⠻⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣻⣿⣿⣽⣿⣿⣿⣽⢫⣶⣾⢇⢣⢷⠚⠋⠀⣠⣿⢹⢤⡀⢺⣇⠁⣇⣿⣿⡟⠀⠀⠛⠆⡛ ⠀⠀⠀⠀⠿⣏⢷⣿⣿⣿⣿⣿⣷⣿⣿⣿⡷⡿⣻⣿⣿⣿⣿⣵⣟⣥⡾⣞⢞⠈⢯⣛⣭⣽⠏⡶⣙⣡⣿⣿⣅⣿⣿⣿⣿⡆⠀⠀⠀⣵ ⠀⠀⠀⠀⠀⣌⡈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣋⣿⣟⣾⣶⣶⣋⠈⠓⠘⣿⠏⠀⢠⠿⠿⠟⣉⣬⡿⣿⠬⠟⠀⢿⡄⠀⣾⠋ ⠀⠀⠀⠀⠀⠿⣷⣿⡟⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⠍⠶⣻⣿⣽⣿⣽⣷⣿⣿⣶⣦⣽⠀⠰⠾⢶⣶⠾⣻⣿⣿⠖⠀⠠⠀⢸⡇⡶⠀⢀ ⠀⠀⠀⠀⠀⠁⠛⢿⢿⢯⣿⣽⣿⣿⣿⣿⣿⠃⠀⠐⠀⣛⢟⢗⣽⣿⣿⣿⣿⠇⢠⡿⣿⣄⡢⠤⢴⣾⣷⣝⢯⠑⢴⣌⢰⣜⣿⠃⢠⠊ ⠂⠀⠀⠀⠀⠀⠀⠀⢀⠁⣿⣷⣽⣿⣿⣿⡃⠀⢂⠠⠡⠀⢃⣹⣿⣿⣿⣿⣿⠅⡘⠛⠟⣻⢿⣶⣿⡽⣾⣆⡣⡳⣌⢿⣧⡿⡅⢠⠇⠀ ⠅⠀⠀⢀⣀⣀⣀⣀⣘⡘⡸⣟⣾⣿⣿⠏⠀⠀⠐⠐⠂⠀⠘⢱⣿⣿⣿⣿⣯⣎⠀⠀⠀⠈⠘⢿⣇⣿⣾⣾⡸⣦⠻⢎⣿⠏⢠⠏⠠⢰
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣴⣶⣾⣿⣶⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡶⠻⠛⠟⠋⠉⠀⠈⠤⠴⠶⠶⢾⣿⣿⣿⣷⣦⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠤⠒⠒⢲⠀⠀⠀⢀⣠⣤⣤⣬⣽⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⣀⣎⢤⣶⣾⠅⠀⠀⢀⡤⠏⠀⠀⠀⠠⣄⣈⡙⠻⢿⣿⣿⣿⣿⣿⣦⠀ ⢀⠔⠉⠀⠊⠿⠿⣿⠂⠠⠢⣤⠤⣤⣼⣿⣶⣶⣤⣝⣻⣷⣦⣍⡻⣿⣿⣿⣿⡀ ⢾⣾⣆⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠈⢋⢹⠋⠉⠙⢦⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠑⠀⠀⠀⠈⡇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣾⣿⣿⠿⠟⠛⠋⠛⢿⣿⣿⠻⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢠⣿⣟⣭⣤⣶⣦⣄⡀⠀⠀⠈⠻⠀⠘⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⠱⠤⠊⠀⢀⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⢧⡀⠀⠀⠸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠄⣀⡀⠸⠓⠀⠀⠀⠠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
𓃬𓃮𓄇🐘🦓🐇
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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠛⠛⠋⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿ ⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣭⣍⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢳⣿⣷⣶⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣤⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢉⣿⣷⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠛⢣⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠉⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠧⠤⠤⠁⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠈⠑⠢⣄⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡤⠖⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠈⢳⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡅⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡸⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡑⠦⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠂⠈⠙⠉⢀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢹⣿⣿⣿⣿⣿⣿⠈⠉⠉⠛⠃⠀ ⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠑⡄⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡀⠠⠒⠤⢄⡀ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀⠀⠀⠘⣄⠀⠀⠙⠤⣀⣀⠴⠋⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⢰⣦⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡄⠀⠀⠀⠀⡄⢸⣿⣿⣿⣿⣿⣿⢰⣦⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠁⠀⠀⠀⠀⡼⡇⠀⣿⣿⣿⣿⣝⡛⠚⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⣆⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⡵⠁⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿ ⣿⣯⣭⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⡟⠀⠻⡷⣄⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠄⠊⠉⠐⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡆⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⣼⣼⣿⡟⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⠀⢿⠟⠉⠀⠀⠀⠀⡇⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠘⡄⠀⠀⠀⠀⢀⠐⠁⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⡆⠁⠀⠀⠀⢠⠂⢀⣁⣵⣤⣦⠀⢠⣶⢶⣂⣀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠇⠀⠀ ⠇⠄⠀⠀⢀⣎⣠⣯⣟⣿⣿⣾⣧⣿⢿⣽⣿⣿⣳⣦⣀⣀⡀⠀⠘⡄⢸⠀⠀⠀ ⠐⠄⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⢾⣿⣿⣿⣿⣿⣦⠀⢱⡘⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡆⢾⠃⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⡿⣋⡙⠿⢿⣿⣿⣿⣿⣿⣿⡟⢋⢻⣿⣿⣿⣿⠀⠑⠠⣀⡀ ⠀⠀⣿⣿⣿⡿⣻⣇⠊⠃⠄⠀⠀⠙⠿⠿⠛⠃⠂⠋⣹⣿⣿⣿⣿⡇⠀⡀⠈⡆ ⠀⠀⢸⣿⣿⣾⣿⣿⡆⠀⢤⣤⡀⠈⠰⡀⣀⣴⠂⠈⢿⣿⣿⢿⣿⠁⠀⠻⠀⡇ ⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠂⠉⠻⠋⠉⠘⢟⠁⠂⠀⢸⣿⣿⣿⣿⠀⠀⠀⡰⠁ ⠀⠀⠀⠸⣿⣿⣷⣿⣦⡀⢀⠀⠀⠀⠀⠀⣨⠀⢂⣠⣿⣿⣿⣿⡿⠀⠀⡐⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⠀⢰⣖⣀⣐⣼⠀⢾⣿⣿⣿⣿⠟⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⣅⠝⢏⣿⣿⣿⣿⣄⡀⠈⢛⣋⡀⢠⣿⣿⣿⣿⠋⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠈⠻⣿⡟⣿⣿⣗⠘⠉⠉⠁⣸⣿⣿⠏⠀⡐⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⠄⠀⠀⠉⢿⣿⣿⣷⣶⣶⣾⣿⣿⡟⠀⠰⠀⠀⢀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⠰⡀⠀⠀⢾⣿⣿⣿⣿⣿⡿⣿⣏⠀⢈⠀⡀⢀⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⣇⠤⢤⡼⠛⠋⠉⠛⢿⣿⣿⠻⣠⠽⠣⠗⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⢱⠁⠀⠀⠀⠀⠇⠀⠀⠀⡻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡋⣽⡴⢂⢆⠒⣆⣻⢀⣄⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠈⠑⡘⠊⠲⠉⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⡙⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠿⢟⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣭⣤⡉⠈⠉⠉⠙⠛⠛⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢋⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠒⠒⠒⠶⠶⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⡻⣿⣶⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠹⣇⠈⠻⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⣿⣳⠏⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡿⠟⠛⠛⠛⣿⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠘⣿⣄⠀⠀⠀⠀ ⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⠿⠟⠉⣿⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⢀⣿⠀⠀⠀⠸⣿⣦⡀⠀⠀ ⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠋⠉⠉⠀⣠⣿⣿⣿⣿⣿⠉⠉⠉⠉⢹⣏⠀⠀⠀⣀⣀⣐⣸⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⣿⣟⣷⡀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠿⠿⠿⠀⠀⠀⣉⣛⠶⢦⣤⣄⣀⣀⣀⣤⣴⣾⠿⠁⠀⠀⠀⠀⠀⠸⣿⠹⣇⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⠉⠉⠓⠲⠾⠿⠭⠭⠭⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⡄ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠘⣷ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠲⣶⣶⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢻ ⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠸⡄⢸ ⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⡇⢸ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣆ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⡿⢿⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⢰⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠸⣇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⠀⠘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠿⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀ ⠀⠀⠈⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀ ⠀⠀⠀⠀⠙⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠈⠙⠻⠿⠿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢟⣵⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣥⠆⢀⣈⡀⠀⠀⠀⣄⠀⢀⣸⡇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠷⠦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡤⣖⣚⣿⡽⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡬⣿⢿⠿⠯⡿⠟⣿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⠟⢛⣿⠟⠛⠛⠛⢻⡏⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡷⠦⠶⠶⠦⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⢀⣴⡟⠁⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠈⠶⠾⠗⠿⠿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⡀⠠⢏⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
╰┈➤ 𝐚𝐥𝐨𝐡𝐚 🌺⚡️ 𝚖𝚢 𝚕𝚒𝚝𝚝𝚕𝚎 🌊 𝓼𝔀𝓪𝓰𝓼 ✰ ☻ 🌴🤍🛍🌸 જ⁀➴ ʀᴇᴍɪɴᴅᴇʀ: 𝚘𝚋𝚎𝚜𝚎 🍍🐠💞⚡️ 𝐩𝐫𝐞𝐩𝐩𝐢𝐞𝐬 𝐚𝐫𝐞𝐧’𝐭 ⊹₊。ꕤ˚₊⊹ 🌊🍹🥽🤍 𝙖𝙡𝙡𝙤𝙬𝙚𝙙 🌺🌴🍹💞🍍⚡️ 𝑠𝑜 𝑔𝑜 𝑜𝑛 🤍⚡️🌸🌊 𝓪 𝓭𝓲𝓮𝓽 🌺⚡️🍹 𝐚𝐧𝐝 𝐬𝐭𝐚𝐲 🌸🌴🤍 𝚜𝚔𝚒𝚗𝚗𝚢 ꒦꒷‧₊˚⊹ 💞🍍🌸 𝒚𝒐𝒖 𝒑𝒊𝒈𝒔 ✦ .  ⁺   . ✦ .  ⁺   . ✦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣾⣿⠿⠋⣻⣿⣿⢿⣿⡿⣵⣿⣤⡿⣟⣿⣶⣤⣠⣄⠾⣷⠈⢿⣶⣶⡼⣧⣀⠠⢟⠲⣤⢀⢠⡏⠋⠉⢹⠉⠋⣼⠋⣽⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⠠⠈⣿⣆⢻⣿⣿⣿⣭⢻⣽⣳⡜⡶⢢⢆⠤⣀⢀⠀⠀⠈⠙⠿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⣿⣿⣿⣿⢷⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⢿⡛⢁⣴⢞⣿⠏⢀⡾⠋⠀⠈⠻⢿⣿⣾⣿⣿⣿⠋⣹⣧⡘⣿⣟⣿⣿⣿⣿⣾⣧⠺⣄⢹⡌⢆⡇⠀⣸⠏⠀⣤⡝⣠⠟⠁⠈⡵⣻⣿⣿⣿⣿⠋⠈⠐⠀⢘⣿⣾⣿⣿⣿⣾⣣⢟⣿⡽⣞⢷⣺⢻⡜⢫⡓⠌⠤⢠⠘⠙⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠿⢛⡿⠛⠁⣀⡶⣿⣿⣾⡏⠀⣺⢧⣄⡀⠀⠀⠀⠀⠉⠉⠻⢿⣶⡿⣸⣷⡟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣬⠐⢠⣿⠄⣢⡿⡽⢁⠀⠀⢀⡩⠷⠿⢟⣿⣿⣧⡈⣷⠀⢸⣿⣿⣿⣿⣿⣿⣽⢎⡷⣹⣽⣧⣟⣧⣟⣷⡾⣜⢦⡥⣄⡠⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⠈⠉⠉⠉⠀⠀⠀⠀⣁⡴⠞⠋⠁⢀⣀⣤⠄⣀⣚⣭⣶⣿⣿⣟⠀⣼⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠙⢿⣿⣍⣹⡿⢻⣿⣿⣿⣿⣿⣯⡿⡹⢿⣿⣿⣿⣿⣿⡿⢛⡥⣦⣤⣞⣋⣁⡤⠀⣉⣩⣭⣿⡗⡬⣓⣾⣿⣿⣿⣿⣿⡿⣞⡬⢶⣹⣿⣿⣟⣿⣽⢯⣷⣿⣾⡱⣏⢳⡱ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣠⠞⠉⢀⣤⣶⣿⠿⠛⠋⠉⠉⣩⣿⡿⠿⠃⠀⢉⠛⠉⠉⠉⠉⠉⠙⠻⠛⠀⠀⠀⠀⠀⠀⠈⠹⡟⣽⣿⣏⡙⠉⠙⠛⠁⢀⣳⡾⢟⣿⡟⢡⢬⡴⢋⢁⡀⣀⡤⠮⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣟⣧⣛⣧⣿⡿⣟⣿⣿⣾⣿⣿⣿⣷⣻⣽⢧⡟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠋⠀⠀⠀⠀⠀⢠⠞⠁⠀⢘⣫⣭⣥⡤⠄⢀⣤⣴⣿⣿⣫⣶⣶⣿⣿⠟⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣶⣇⠀⠀⣠⠏⡴⣻⠏⢩⡶⢚⣴⢫⡵⣛⣁⣀⣤⣤⡤⠶⠤⠄⠒⢤⣀⢀⡀⠀⠙⢿⣄⠢⠼⠿⣶⡭⢿⣿⣿⣽⣾⣿⡟⣾⣹⣾⡽⣯⣿⣻⢾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣋⠉⠀⠀⠀⠀⡴⠋⠀⠠⠚⠉⠁⡀⢀⣀⠶⢛⣿⣧⣿⠋⠀⠀⠀⠉⠁⠀⠀⠘⠿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⣠⠞⠏⣀⡾⠏⣩⣷⠟⣻⡽⠟⠉⢉⡴⠞⠁⠀⠀⠀⠀⢌⣷⣮⠵⣤⡀⠙⢧⣄⠠⠈⠛⣿⣿⣿⣿⣽⣷⣿⣿⡝⣯⣻⣵⢯⣟⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣶⣶⠆⢀⡞⠁⠀⠀⢀⣤⣶⣿⣿⣿⣿⣦⣿⠟⢩⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⣿⣿⣵⡾⠥⠤⠶⠏⠀⠰⠛⣋⣜⣻⣵⣯⣾⡟⠀⢀⣠⣶⡶⠶⢤⡀⣀⠉⠙⠒⠿⣶⣐⢦⡠⠀⠐⠾⣿⣿⣿⣻⢿⣿⣿⣽⣳⡽⣮⣝⢺⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⠟⠙⠙⣿⣿⣿⡿⣿⣷⠂⠀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⣿⣿⠷⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠺⡤⢴⣣⠄⢈⣿⣭⣽⣶⣶⣥⣴⣿⣿⣟⡿⠟⠛⠉⠘⠀⡙⠢⢄⠀⠈⢻⡌⠳⢮⣄⠀⢻⣿⣿⣿⣿⣿⣿⢿⡿⣿⣷⢯⣟⡼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣠⣤⣬⣿⣿⢇⠀⢹⣧⠀⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠈⠛⠛⢁⣠⣴⣖⣦⡠⢒⣿⣯⣾⣿⣿⣿⣿⣿⡏⠉⢀⣂⣒⣀⠀⠳⡄⠚⢛⢻⢿⣟⣋⣷⣤⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⣤⣀⢠⠀⠱⣄⠀⠈⠓⢦⣾⣿⣟⡿⣷⣿⡿⣽⣳⣯⣿⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣶⣿⣟⢃⣞⣽⡇⢸⣆⡈⢿⣧⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⠀⠀⢈⣿⡟⣩⣿⣿⣿⡿⠁⠀⣠⣶⣿⣿⣧⡀⠀⠒⠛⣶⢤⣙⣚⢹⣿⣷⣿⣟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡁⠀⣿⠷⣦⠀⠈⠻⣿⣿⣿⣝⡯⢿⣿⣿⣿⣿⣯⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠿⢋⡙⢠⣾⣿⣟⣠⡼⠛⠶⣤⣬⣷⡦⢬⣇⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⠿⠿⣿⣿⣤⣐⣾⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⢴⣾⣷⣾⣯⣷⡄⠀⠀⠘⢯⡝⢛⣿⣿⣿⢷⣏⣻⣿⣷⣦⠀⠀⠀⣀⡀⠀⠀⠀⠀⠙⢷⣿⣦⠈⢷⠢⣄⠈⠻⣿⣟⣿⣿⢾⣽⣯⣻⢷⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⢾⠷⣿⡿⠟⠉⠤⠐⢢⢚⣿⣳⣭⣿⣻⣿⠀⠀⠀⠀⣀⣾⣿⡏⢰⣿⣷⣤⠀⢹⣿⡿⠿⣿⣻⣿⣿⣿⣿⣿⣷⡆⠀⣼⣿⣿⣿⣿⣶⣇⠀⠀⠈⠲⣼⡋⣳⣽⣿⣿⡟⣛⡿⠻⣿⣦⣤⣴⣶⢿⣶⡖⢦⣄⠀⠀⠙⢿⡂⢆⠓⢌⠣⠠⣽⣿⣾⡽⣿⣯⢷⣯⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇⠀⠀⠀⠠⣶⣶⢶⣦⣄⢹⡀⣨⣛⣧⡒⣉⡁⠄⣩⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⢠⣾⣿⣿⣿⣜⠲⢤⣀⣠⣿⠛⠀⢀⣼⣿⣷⣊⣵⢿⣿⣏⠀⠀⠸⣿⣿⣬⡿⢏⣤⡀⠀⠘⠲⢭⡙⠀⠩⣿⣯⣭⣽⢿⣵⡛⠉⢀⣀⡈⠛⠛⠻⣶⣿⣷⣄⠀⠈⣷⣌⠄⠈⢃⠀⢿⣛⢿⣽⣯⣟⣷⣮⣗⣮ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⢿⣿⠀⠀⠀⠀⡿⠋⡿⣷⠈⠙⠻⣇⠻⡝⡱⠌⠠⣥⢾⣻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣠⣾⡛⢚⣻⣿⣧⣄⣹⡏⠀⠀⠀⠚⢿⣿⣽⢳⡍⠙⠀⠀⠀⠀⠈⠉⠀⢠⣬⠽⣟⣛⢡⡿⠶⠚⠉⢀⣀⠀⠀⠀⢼⣿⣿⣶⣂⠘⣻⣦⠈⠁⡀⢸⣿⣿⣿⣾⡽⣾⣽⣛⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣻⣯⢿⣿⠳⠀⣘⠀⠀⠱⣽⣶⠴⠄⡏⢃⡛⠆⠺⢅⣾⣿⣿⣿⣿⣯⣿⣿⣿⣧⣀⣀⣰⣿⣿⣿⣿⡿⠛⠛⠉⠁⠀⢀⣠⡾⠏⠰⠄⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠿⣦⡀⠀⠀⢀⠀⠀⢀⣀⡙⠿⣭⣿⣾⠇⠀⠀⠚⠁⠀⠀⠀⠀⠀⠈⠉⠉⣉⠛⠛⠛⠷⣤⣁⡈⢿⣿⣯⣿⣿⣷⣻⢿⣽ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣽⣳⢯⣟⡿⡿⠐⣟⢦⣀⠀⠀⠉⠉⣰⠃⠾⣤⣽⠿⠻⢯⠿⣿⠷⣿⢟⣫⣵⣽⣿⣿⣿⣿⣿⡿⣾⣿⠇⠀⣀⣠⣴⣾⣿⣥⣤⠴⣶⣄⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣜⠶⣻⡄⠀⠀⠀⠀⠀⠀⠙⣿⣮⣜⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⢈⠉⠲⠦⣠⢄⡉⢿⣶⣿⣿⣷⣯⢿⣽⡿⣾ ⣿⣿⣿⣿⣿⣿⣻⣟⡷⣿⢾⣽⣻⡾⣵⡇⠀⠈⠉⠛⣷⡄⠀⡼⠃⡼⠞⠁⢀⣨⣿⣻⣿⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⣿⣿⣿⣿⣿⣿⣟⡦⠀⣀⣠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡔⢻⣷⠀⠀⠀⠀⠀⠀⠀⠸⣯⣋⠹⣧⠀⠀⠀⠀⠀⠀⣀⠈⢭⡍⣿⡟⣏⣓⣶⢤⣈⠻⣇⡀⢻⣿⣿⣟⡾⢯⠷⣿⣷ ⣿⣿⣿⣿⣿⣳⣯⣟⡿⣽⣻⣶⣁⠛⠿⣷⠀⠀⣰⠏⣹⠇⡸⠁⠐⢀⣤⣾⢟⣻⣿⣿⣿⢿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠻⣄⠀⠀⠀⠀⠈⢉⣡⣦⢤⣈⠻⠟⣧⡘⢿⢻⡀⠸⡟⠛⣿⣿⣟⣿⣿⡻⢷⣯ ⣿⣿⣿⡿⣷⣟⣷⣯⢿⣝⠳⣏⡻⠟⠂⠀⠀⠀⠙⠛⠍⡼⢁⡰⡞⣿⣻⣿⣿⣿⣷⣿⢿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣭⡙⠛⢻⣿⣿⣿⣿⣿⣻⣿⣇⢉⡉⠛⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⢯⣻⠟⢿⡢⠄⠀⠀⠉⠿⣿⣶⣯⠷⣶⠤⣍⠛⠈⢳⠀⠹⣄⠉⠻⣿⣷⣾⣽⢻⡼ ⣿⣿⣿⡿⣟⣾⣟⣾⣍⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⠁⣰⣟⣻⣽⣿⣿⣿⣟⣿⣿⢯⣽⣿⣿⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣧⣄⠈⠋⢹⠉⠛⠛⠯⣠⣍⡻⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣙⣋⠙⠋⠛⢷⡄⠀⠀⢀⠐⢿⣷⡶⢬⡉⣏⢳⡄⠈⢷⠀⠈⢻⣷⣽⣾⡿⣿⣿⣼ ⣿⣿⣿⣿⣻⢷⡾⣬⣡⡄⠀⠐⠀⠀⣀⠀⠀⠀⢀⡼⠀⣴⣿⢛⢻⣯⣿⣷⣿⣿⣯⣿⣯⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣄⠀⠈⠓⠀⠀⠈⠉⠻⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢭⣭⣭⣻⡓⢦⣴⠙⡠⠄⠈⠂⠈⣿⣿⡆⠻⣌⠳⣌⢢⡀⠙⣦⡀⠹⣿⣿⣹⣿⣻⣿ ⣿⣿⣿⣷⢯⡿⣽⢯⣷⣹⣻⣟⡿⠛⠁⠀⠀⣠⠞⣠⣾⠵⣏⣴⣿⢿⣿⣿⣯⣿⣟⣿⣿⣿⣿⣿⢿⣽⡟⣿⣻⣿⣿⣿⣿⣿⣿⣦⡙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠙⢿⣽⠶⠖⠲⢶⣤⣶⣾⣿⡷⢦⣒⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢭⣅⡙⣮⢿⡄⠉⠀⢀⣴⡆⢸⡿⣷⡄⠈⢧⡀⠀⠈⠀⠀⢳⡀⢸⣷⡝⣿⣿⣿ ⣿⣿⣿⣯⣿⣻⣽⣻⣾⣵⡷⠛⠀⠀⠀⠀⡴⠋⠜⢁⡖⢺⡏⣽⣣⣾⣟⣿⡿⣟⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⣿⣽⡿⣧⡀⠙⢻⣟⣦⣄⠀⠀⠀⠀⠀⠈⢳⣦⣾⣟⠋⠉⠀⠀⠈⠉⠙⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠼⡄⠈⢙⠿⡦⠄⠀⠉⢻⣾⣇⢿⣿⡀⠀⠙⡆⠀⠀⢠⡀⢳⡀⠹⣟⣼⣿⣻ ⣿⣿⣷⡿⣞⣷⢯⣻⣭⣄⠀⠀⠀⠀⠀⡼⠁⢀⣎⡟⣤⠟⣼⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⡀⠈⠙⠛⠿⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢧⡀⠈⠂⢸⡄⠀⠀⠀⢿⢿⣎⣷⢻⠀⣄⠀⠀⠀⠀⠳⡈⢧⣰⡜⢿⡷⢯ ⣿⣿⣿⣽⡿⣯⣟⣣⣽⡟⠀⠀⣀⣴⣾⠅⣀⢸⡟⢻⡏⣰⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠉⠛⠛⠛⠿⠿⣿⣿⣿⡻⠿⠧⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⠀⠀⢧⡀⠁⠨⣿⣦⢠⠀⠈⣧⠹⡼⢿⠀⠘⣦⡀⠠⠀⠀⠳⣌⡿⢟⡾⢿⣷ ⣿⣿⢿⣾⣿⢿⣽⣻⣿⠁⢠⠞⢁⡼⠁⣤⠾⠏⢰⣿⣹⣿⡀⢨⣿⣿⣯⣺⣿⣿⡿⠋⠉⠙⠿⣽⣿⣿⡀⠀⢀⣀⣀⣤⣀⠀⠙⠻⢿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠿⢻⠤⣌⡷⠀⠶⣅⢿⡀⢀⠀⢹⣆⢹⡈⢷⠀⢹⣧⠹⡆⠀⠀⠀⣷⡸⣽⢎⡜ ⣿⣿⣟⡿⣾⡿⣽⣻⣷⣤⣾⣶⣿⠉⣘⡃⠀⢼⣚⡟⣿⣹⣧⣤⣽⣿⣿⣿⣿⣿⣱⣶⡿⠃⠀⠼⣷⣾⣿⢿⡶⠈⠉⢉⡁⢀⡀⠀⠀⢀⣠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡶⠶⢀⠘⢲⡸⣿⡄⠀⠸⠆⢳⣬⣧⠀⢿⣈⣷⡀⠀⠀⢿⡒⢿⡀⠀⠀⣟⡙⢮⡓⠀ ⣿⣿⢯⡿⣽⣟⣿⣯⢿⣽⣿⣿⣿⣶⡇⣛⢻⣿⣿⡿⢏⡽⣿⣿⣭⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢘⣿⣯⣴⣻⣙⣿⣿⣾⣿⣿⡿⠇⠀⢨⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⢀⡘⢷⡌⢳⣄⠀⠙⡄⠹⡄⢧⣸⣷⡹⣷⡄⠀⠈⣷⠘⢿⡄⠀⠘⡟⡤⠀⠐ ⣿⡿⣯⢿⣽⣾⣟⣾⣿⣿⢿⣿⣿⣽⠆⠈⠻⣿⣿⣟⣼⢏⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣾⣿⣿⣿⣿⡿⠿⠛⠋⠈⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⡀⠀⠁⣠⠄⠂⢀⠀⠙⣆⠓⢦⣄⣣⠀⢧⡀⢳⢸⣿⠃⣽⡿⣧⠀⠀⠸⡇⢻⠳⡀⢤⣌⠑⠀⠰ ⣿⣻⡽⣯⣷⢿⣾⣟⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠙⠿⣮⣿⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠒⢾⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⢤⡖⠒⠀⠠⡄⠐⡆⠀⠈⠙⠶⣿⣷⠀⢸⡇⠀⢸⣿⣗⢺⡇⢸⡀⠀⠀⠃⢸⣦⣳⠻⣎⠁⢨⢹ ⣿⢯⣟⡷⣯⢿⣾⣿⣿⣿⣿⣧⣾⡅⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠋⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⣤⣦⣤⣠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⢷⡀⠉⠀⠀⠀⠀⢳⡉⣇⠈⣿⠀⢸⣿⢻⣼⡧⠈⠇⠀⠀⠀⠈⣷⢹⣶⠁⠀⢢⠐ ⣿⣻⢾⡽⣯⢿⡾⣿⣿⣿⡏⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠀⠀⠀⠀⠀⠀⠀⠂⠸⠻⠃⠙⠿⣄⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠢⣵⣦⣘⣦⠐⠀⢰⡿⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠈⢧⠊⠀⣿⣀⣿⡟⢹⣿⡇⠀⠀⠀⠀⣷⣰⡈⠃⠀⠲⣼⣇⡺ ⣿⣳⢯⡿⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣠⣄⡉⢓⡃⠀⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⣄⠀⠀⡄⠀⠈⠁⣈⢿⡼⣿⣇⡾⢹⡇⠀⡄⠀⠀⠹⡽⣧⡀⠖⡲⢷⡞⠱ ⣿⣟⣯⢿⣽⡾⣽⣿⣿⣿⣿⣿⣿⣏⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⡛⢳⣮⡙⡟⠠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣆⠘⣄⠀⣸⣿⠻⣧⡹⣿⡄⣻⡇⠀⣹⣄⣆⢰⣿⣿⠿⣿⠗⠋⠀⠁ ⣿⣟⣾⣻⡾⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢀⢀⣦⣶⣿⣶⣽⡍⠙⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠶⢰⣿⣄⠀⠋⠂⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣿⡄⠘⠀⣿⣇⠐⣿⢹⡜⣧⠈⣷⠀⣿⣿⣿⡄⢻⣽⡉⢛⡀⠤⣤⣬ ⣿⣿⣻⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣶⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⢿⣿⣶⣶⣤⣤⣀⣀⣣⡀⣄⣆⣤⣧⣷⣤⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠙⠛⢦⣻⡆⠀⠀⠋⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠸⣇⠀⠀⢨⠻⣶⣿⣼⠃⢹⣄⠘⢢⣿⣿⣿⡿⠀⠺⣷⣮⣽⣿⡤⠂ ⣿⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣆⠀⠀⠀⠉⠙⠋⠀⠉⠀⠀⠈⠉⠙⠉⠿⠟⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⡇⠀⠘⠀⠀⠙⠉⠀⢸⣿⣧⠈⣿⠛⠛⣲⠶⣶⣟⣧⣭⣶⠞⠁ ⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠀⠉⠉⣶⡎⠹⠍⠛⠛⠿⢿⣿⡟⠧⠄⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⢳⡀⢿⡿⡄⠀⢁⠀⠀⠀⠘⣞⣋⣙⣥⡿⠟⠛⣋⣺⣼⠿⠛⠉⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠛⠃⠀⠈⠓⢀⣀⡀⠜⢻⠉⠈⣙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀🐯🐯🐯🐯🐯🐯🐯🐯cool🐯🐯🐯
⠀⢀⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⡀⠀ ⢠⡿⠋⠉⠉⠉⢻⡋⢻⠗⠲⠀⠀⠀⢸⡷⠖⠛⠉⠉⠉⢹⡋⢻⠗⠲⢿⡄ ⣾⠇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠸⠷⣤⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⣷ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟ ⠘⣷⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃ ⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠉⠉⠉⠉⠉⠉⠉⠒⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⡤⠚⣳⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠔⠛⣧⡴⠞⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠻⠿⣷⣦⡀⠈⠳⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠖⠋⠀⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠻⡄⠀⠀⠀ ⠀⢠⠞⠉⠀⠀⠀⠐⣉⡜⠁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⣰⠃⠀⠀⠀⡠⢀⡞⢁⡴⠛⠉⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠈⠙⢶⡄⠀⠀⠈⣧⠀⠀ ⢹⠀⠀⢀⣼⣡⠋⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⢸⠀⠀ ⠘⠓⠒⢛⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⣿⠀⠀⢸⠀⠀ ⠀⠀⠀⠈⣧⠀⠀⢻⡆⠀⠀⠀⠀⣾⣿⣿⣷⣼⠇⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⣿⣿⣿⣦⡿⠀⠀⢻⠾⠁ ⠀⠀⠀⠀⢿⠀⠀⠀⠙⢦⣀⠀⠀⠙⠿⣿⠟⠋⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠘⠿⣿⠿⠉⠁⠀⢠⡿⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠙⠻⠿⠿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠽⢿⡻⠏⠉⠀⠀⠀⠀⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠷⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣠⣀⣤⣴⣶⣶⣾⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠛⠛⠉⠉⠉⠙⠛⠛⠻⣧⡀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢀⣠⣴⣾⠿⠟⠛⠛⠋⠉⠉⠙⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⢳⢒⣛⡶⣤⣄⡈⠷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢀⡾⠛⠉⠀⢤⢶⣶⣲⣖⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣾⢣⣴⣶⣶⣿⣿⣿⣿⣿⠛⣿⣿⠳⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢩⡿⠙⢿⣿⣿⣿⣿⣿⣟⢻⣿⡆⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⣟⣿⣿⣿⣿⣿⣿⣁⣿⡿⠀⠈⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣈⠻⢿⣿⣿⣿⣿⡿⢠⡇⠈⡇⠰⣚⣿⣿⣷ ⠀⣀⣀⠀⢸⣿⡟⢿⣿⣿⣿⣿⣿⠟⢁⣤⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠾⠾⠭⠭⠴⠿⠁⠀⠙⠞⠁⠀⣼⠁ ⢸⡗⠮⣍⣻⡏⢿⣬⣛⣛⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠈⣧⠀⠀⠉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀ ⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣻⡀⠀⠀ ⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣨⡵⠛⣷⠀⠀ ⠀⠀⠀⢀⡼⡃⡂⠀⠀⠀⠀⠀⢰⣴⣶⡈⠀⠀⣀⡀⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣵⡶⠟⠋⠀⠀⠀⠀⠀⠀⢀⡟⠉⠀⠠⣿⠀⠀ ⠀⠀⠀⣾⡏⡉⠋⠳⡆⠀⠀⠀⠈⠁⠉⠛⠿⢿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⡾⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣀⠀⠀⣿⠀⠀ ⠀⠀⠀⢿⡇⣇⠀⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠰⢦⣤⡿⠋⠀⠀ ⠀⠀⠀⠘⢷⣉⠃⢀⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬛🟧⬛⬜⬜⬜⬜⬜⬛⬛🟧🟧🟧🟧⬛⬛⬜⬜⬜⬜⬜⬛🟧⬛⬜ ⬛🟧🟧🟧⬛⬜⬜⬛⬛🟧🟧🟧🟧🟧🟧🟧🟧⬛⬛⬜⬜⬛🟧🟧🟧⬛ ⬛🟨🟨🟧🟧⬛⬛🟧🟧🟧🟧⬛🟧🟧⬛🟧🟧🟧🟧⬛⬛🟧🟧🟨🟨⬛ ⬛🟨🟨🟨🟧🟧🟧🟧🟧⬛⬛⬛🟧🟧⬛⬛⬛🟧🟧🟧🟧🟧🟨🟨🟨⬛ ⬜⬛🟨🟨🟧🟧🟧🟧⬛⬛🟨🟨🟨🟨🟨🟨⬛⬛🟧🟧🟧🟧🟨🟨⬛⬜ ⬜⬜⬛⬛🟧🟧🟧🟧⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛🟧🟧🟧🟧⬛⬛⬜⬜ ⬜⬜⬜⬛🟧🟧🟧⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟧🟧🟧⬛⬜⬜⬜ ⬜⬜⬜⬜⬛🟧🟧🟧🟨⬛⬛🟨🟨🟨🟨⬛⬛🟨🟧🟧🟧⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛🟧🟨⬛⬛🟨🟨🟨🟨⬛⬛🟨🟧⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟧🟧🟨🟨🟧🟧🟧🟧🟧🟧🟨🟨🟧🟧⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟧🟧🟧🟧🟧🟪🟪🟪🟪🟧🟧🟧🟧🟧⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟧🟧🟧⬛⬛⬛⬛⬛⬛⬛⬛🟧🟧🟧⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛🏻🏻⬛🏻🏻⬛🏻🏻⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🏻🏻🏻⬛🏻🏻⬛🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠈⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠔⣯⠤⠚⠛⠟⠀⠀⠀⠀⠀⠾⠿⠿⠿⢶⣄⠈⠣⡀⠀⠀ ⠀⢀⡠⠖⠉⢀⡠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠳⡀⠀ ⣠⠋⠀⠀⠀⣠⠖⣡⠴⠒⠲⢤⡀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠢⢄⡀⠀⠀⢷⠀ ⡇⠀⠀⣜⡵⢡⠞⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠙⡄⠀⢘⡄ ⠛⠒⢺⡉⠀⣾⠀⠀⠀⠀⢀⣀⡀⢹⠀⠀⠀⡏⠀⠀⠀⠀⣀⣀⠀⢻⠀⢸⡇ ⠀⠀⠸⡇⠀⠙⣆⠀⠀⠀⣿⣿⣿⡞⠀⠀⠀⠹⡄⠀⠀⢸⣿⣿⡷⡟⠀⢘⠟ ⠀⠀⠀⢧⠀⠀⠈⢷⣤⣤⠬⠿⠁⠀⠀⠀⠀⠀⠘⣶⣤⡤⡭⠟⠁⠀⠀⡾⠀ ⠀⠀⠀⠈⢦⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣴⠃⠀ ⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⠒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠛⠛⠛⠉⠉⠉⠛⠛⢷⣤⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⢠⣴⠾⠛⢋⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣻⣯⣭⣭⣽⣶⣦⠙⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡞⣠⣤⣼⣿⣿⣿⡿⣿⡦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢻⡿⣿⣿⣿⣿⣿⡿⣿⡅⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣻⣿⣿⣿⣿⣿⣭⣿⠇⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣌⣻⢿⣿⣿⣷⢏⡇⠘⡄⢒⣿⣷⠄ ⢠⣤⠄⣽⢿⡹⣿⣿⣿⣿⣫⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠒⠚⠁⠀⠙⠁⢀⡏⠀ ⢻⡈⠑⠺⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀ ⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢢⡼⣆⠀⠀ ⠀⠀⢀⣽⣀⠀⠀⠀⠀⢠⣤⣄⠀⢀⡀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠀⠀⠀⠀⢀⡞⠁⠀⣿⠀⠀ ⠀⠀⣾⣧⠈⠙⡆⠀⠀⠀⠀⠉⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼⢧⠀⢀⡿⠀⠀ ⠀⠀⢹⡟⠦⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠙⠋⠀⠀⠀ ⠀⠀⠀⠈⠓⠚⠁⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣫⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⡤⢰⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡼⠋⠀⠀⠻⠿⠿⠿⠛⢉⣩⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠈⠙⠻⢿⣿⡿⠋⠰⠿⠇⠀⠀⢀⣄⠀⠀⣀⠴⠿⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⡠⠔⠒⣊⣉⣉⣉⣉⡒⠒⠒⠠⠤⠤⠤⠄⠀⡀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⣀⡤⢚⡥⣐⡺⠭⠍⠁⠠⣤⠄⠉⠉⠁⠀⢀⣀⣀⣉⣉⡉⠓⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣁⡔⡱⠋⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢩⠆⠀⠀⠀⠈⢣⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠛⠛⢛⣛⡛⡿⠋⢁⡈⣠⡴⣾⣿⣿⡟⠓⠶⣤⡁⠀⠀⠀⠀⠼⣀⣤⣤⠤⣤⡈⠁⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⢶⠞⢙⣛⣛⣧⣈⠋⠀⠛⠒⠛⢛⣿⠛⠶⢤⣨⠟⠀⠀⠰⠶⣾⠿⠛⠓⠒⠚⠋⠈⠙⠋⢑⡮⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠁⠇⣰⠟⠁⠀⡆⠉⠛⠷⠤⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢠⣄⣠⡶⠾⠲⢶⢹⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⡀⣿⢀⣠⣴⠛⠶⢤⣄⡀⠀⠀⡠⠤⠤⠴⣴⠖⠂⠀⠀⠀⠀⠉⠻⣦⡄⠀⠉⠉⠁⣷⡀⠀⡸⢠⣱⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣄⢇⠸⡆⠀⠘⣧⣀⠀⠉⣿⠳⠶⣤⣀⡀⠈⢧⡼⠟⠛⠓⢀⡀⢀⣼⠟⠋⠓⠢⢀⣠⡿⣧⠨⠔⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣷⣍⠃⠀⠀⠘⣿⡻⢶⣾⣦⡀⠀⠀⠉⡿⠲⠶⠦⣤⣄⣀⣉⣉⣁⣀⣀⣠⠶⠛⡇⢷⣿⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠘⢷⡄⣸⠙⠻⠿⣶⣦⣧⣀⣀⠀⠀⢸⠀⠀⢹⡏⠉⣀⣸⣇⣀⣷⣾⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠹⢯⣀⠀⠀⠀⣹⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠙⠳⣦⣠⠏⠀⠀⠀⠀⣿⠀⠈⠉⣹⠿⢄⣴⠟⠿⡇⡼⣹⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡉⠒⠭⣓⠦⣀⡉⠙⠲⠶⠦⢤⣿⣤⣤⣠⣏⣀⣴⣯⡶⢄⡈⢙⣧⣀⠀⠸⡇⠀⢀⣤⣶⣶⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠉⠓⢤⣀⠉⠲⢭⣒⡦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠿⢤⣈⣳⣄⡇⢀⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣧⠀⠀⢀⠈⠙⠲⣦⣀⠈⠉⠉⠒⠲⠿⠯⣍⣉⣉⣁⡉⠉⠉⣀⣀⠴⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡄⠘⣦⠓⢤⡀⠀⠉⠛⠶⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁⠉⠛⠿⣿⣿⡿⠟⠀⠀ ⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⣷⣤⡙⢦⡀⠀⠀⠀⠉⠉⠉⠙⠛⠶⠦⠤⣤⣀⣤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣈⠻⣝⢦⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠳⣌⡳⣌⠲⣬⡓⠦⡄⠀⠀⣀⡤⠄⢠⣄⢠⣟⡄⢸⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⡈⠳⣌⠳⢌⡙⠢⡀⢀⣼⡋⠀⠀⠀⢹⠀⠟⣡⢸⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠳⢄⠈⠳⣄⠙⠆⣰⡟⠈⢷⡄⠀⠀⢸⡇⠀⢃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡙⠢⡈⠓⠂⣿⡇⠀⠈⢿⣦⣄⠸⣝⢦⠈⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠙⠛⠿⠂ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⠂⠀⣀⢀⣿⠇⠀⠀⣸⠛⣿⠀⠹⣷⡑⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠘⢁⡾⠋⠀⠀⠀⣿⠀⠘⠇⠀⠈⢿⣆⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣆⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠛⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⢆⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣇⠀⠀⠀⠀⠀⠀⣠⣴⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⡏⠘⣆⢀⣠⠞⠛⠛⠉⣀⣤⣤⣬⣉⡛⠛⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡏⠳⣄⠀⠀⢰⡇⠀⠸⡟⠷⣄⣀⣀⣀⣈⠛⠻⠾⢿⣿⣷⠀⠀⠀⠈⠙⠛⠛⠛⠦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡇⠀⠈⢳⡀⢸⡇⠀⠀⢿⠀⢀⣍⠉⠉⠉⠙⠶⣤⣄⣀⣀⣶⣦⣤⡀⠀⠀⠀⠀⠀⣬⣭⣉⠉⠛⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡄⠀⠀⠙⣾⡃⠀⠀⢸⡔⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢭⣉⣀⣀⠀⠀⠀⠈⢙⣛⣁⡀⠀⠀⠈⠙⣛⣛⠓⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⢴⡦⠤⠤⣤⣹⣆⠀⢈⣿⣇⠀⠀⢸⣷⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⣤⣀⣀⠛⠿⣽⣿⣶⣄⠈⠛⠿⢿⡦⠈⠙⠛⠛⢻⣿⣿⡆⠀ ⠈⠳⣄⡀⠀⠈⠛⢿⣻⣿⣿⠛⠛⠛⢻⣶⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠶⣄⣉⠉⠀⠀⠀⠀⣀⣀⣤⠤⢶⡿⣹⠟⠀⠀ ⠀⠀⠈⠙⠲⠤⣄⣠⣿⠈⠉⣴⠞⠶⠾⣿⣅⡀⠙⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣿⠖⠛⠉⠁⠀⣠⠟⣼⠋⠀⠀⠀ ⣀⣤⠴⠖⠒⠚⠉⠩⣿⣠⣴⡏⠀⠀⠀⠀⠈⠻⣾⡿⠏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠞⠋⠀⠀⠀⠀⣠⡞⠁⢸⠏⠀⠀⠀⠀ ⠉⠙⠓⠒⠶⠶⢖⣷⠿⣿⠋⢿⡄⠀⠀⠀⠀⠀⠀⠛⣦⣀⣽⣆⠀⠀⠀⠀⣀⣀⣤⡤⢤⣤⡤⠤⣤⣄⣀⣠⠞⠁⠀⠀⠀⢀⣤⣾⣿⣧⣤⢿⢠⣤⣤⣀⡀ ⠀⠀⠀⠀⣠⠴⠋⢁⣀⡽⣦⡴⡿⠷⣄⣀⡀⠀⠀⠀⢸⡿⠋⠘⡓⠒⠛⠻⣿⣇⣠⣤⣼⣿⣧⣄⣀⣾⡿⠛⠳⢤⣤⢤⡶⠛⠋⠉⠀⠀⠀⠀⠀⣀⣤⠾⠋ ⠀⠀⠀⠈⠛⠛⢻⡉⠁⠀⠈⠙⢦⣤⣤⣭⣉⣻⣿⡟⠉⠁⠐⣿⡷⠀⣤⠞⠋⠉⠁⠀⠀⠀⠀⠈⠉⠛⠳⣦⢠⣾⡿⠀⣻⣀⣀⣀⣤⣤⠶⣾⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⠀⠐⡏⠀⠀⠀⠈⠉⠙⠛⠛⠿⠙⠳⣄⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⢈⡟⠋⠉⠉⠙⠛⠿⣽⣴⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡛⠉⣄⣷⠀⠀⠙⢦⣄⣀⣀⣀⣀⣠⡤⠖⠃⠀⠈⠳⣾⡿⠳⢤⣀⣀⣀⣀⣀⣀⣠⣶⣯⠁⣠⠞⠛⢶⣶⢤⣤⣀⣀⣀⣈⣹⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠺⣏⣉⣉⣉⣼⡂⠀⠀⠀⢀⣈⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣀⣹⣿⡏⠉⠁⣀⣸⠿⠿⣷⣄⡀⠀⠙⢿⣏⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣉⣉⣁⡼⠁⠀⠀⠈⠉⠉⣽⠉⠉⠉⡿⢲⠦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢷⡀⠀⠹⣿⣿⣷⣦⣤⣙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠠⡄⠉⠙⠒⠾⠡⣏⡀⠀⢹⠶⣄⠀⠀⠀⠀⢀⣠⢤⣄⠀⠀⠀⣻⣤⡀⢻⢿⣽⠏⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠐⠶⣄⠀⠉⠛⠋⠀⠘⠂⠀⠀⢠⡞⠁⠀⣿⠀⢀⡼⠋⣸⣿⣛⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣧⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠘⢧⣴⠞⠁⠀⣾⣡⠴⠿⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡿⢧⠀⠈⠙⠲⡦⢤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣼⠟⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀