Fantabulous Emojis & Text

Copy & Paste Fantabulous Emojis & Symbols 😍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⣀⣤⣦⣤⣦⣠⡀⠄⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⣰⠾⠛⠍⠁⠀⠐⠨⢉⠛⡷⣔⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢠⣶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢩⠳⣄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢠⡾⢋⠄⠀⠀⣀⣤⠶⠞⠛⠛⠛⠶⣤⠀⠀⠎⠹⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣲⢏⠁⠂⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠈⢳⡆⠈⠡⢻⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⣽⠓⠈⠀⠀⣼⠋⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⣿⠀⠐⡉⣇⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⡇⠌⠀⠀⢸⠃⠀⢀⣴⠞⠉⠁⠈⠙⢧⡀⠀⠀⢘⡇⠀⠀⣿⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠾⢧⣄⢸⣐⡀⠀⣠⡿⠟⠛⢾⡅⠀⠀⠀⠀⢀⡴⠟⠛⠛⠶⣧⣠⣤⣿⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠿⠋⠙⣾⠋⠀⠀⠀⢘⡇⠀⠀⠀⢀⡾⠁⠀⠀⠀⠐⠛⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣄⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣙⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⣘⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⢷⣄⣀⣠⡴⣿⠃⠀⠀⠀⠀⢸⢦⣤⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⡴⠛⠳⣤⣄⣤⣤⡴⠟⠁⠀⠀⠀⠀⠈⠉⠁⠀⣿⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣂⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⣼⣷⠼⣞⣽⢏⣿⣆⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠛⠢⠐⡍⡉⣾⣾⣽⣟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣦⠀⠤⢶⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⡙⢻⣿⣿⣧⣽⣉⣁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡔⡉⣩⢋⡋⠩⠯⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣘⣶⣁⢙⢐⣄⡴⠪⠓⠁⠉⠃ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣿⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⢐⢝⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⢛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠟⢛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⡄⠀⣀⡀⠨⣙⣏⣉⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢿⣿⣿⣿⡿⣟⣿⣯⣿⣷⣿⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣒⡛⢫⠤⣠⢤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣯⣿⢿⣿⢯⣿⣯⣿⣿⣻⣞⡷⣿⣽⣻⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⣭⣉⡓⠺⠊⢉⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣻⢿⡿⣯⢿⣷⢯⡷⣯⣟⠷⣯⡗⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣿⢿⣷⣄⡙⢮⠭⡁⢠⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣯⢿⣽⡿⣾⣻⣽⣳⣞⣟⡧⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡴⠹⢿⣿⣀⣿⣿⣯⣍⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡿⣯⣿⡽⣟⡾⣵⢫⣾⡱⢯⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣞⣰⣀⣾⡷⠘⣿⣿⣟⣩⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢷⣟⣿⢯⡷⣏⡟⣶⡹⢇⡞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⢯⣾⣿⣿⡿⠁⠀⠀⠼⢿⣿⠥⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡾⣟⣯⢿⡼⣹⢶⡹⢣⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡽⣯⣟⢾⡱⣏⠵⣋⠎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣳⢯⣏⡗⣎⠳⡌⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡗⣮⡝⣬⢳⠉⡎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣯⢷⣫⢗⡭⢎⢧⡙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⣟⣧⡟⡼⣉⢆⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⢿⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡂⠭⢊⠻⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣻⣞⡽⣲⢍⡎⢇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠒⠐⢀⠀⠠⠐⡆⢯⡹⡹⢛⡯⢭⡹⣿⣿⣿⣿⣿⣿⣿⡿⣾⢯⣷⣻⣜⡳⢎⡜⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢎⢦⡹⢄⡄⣌⣩⣝⠾⣡⢃⠡⠃⡘⢧⠿⣽⣻⣿⣿⣿⣿⣿⣽⣿⣟⣷⣻⡼⣝⢮⡙⡖ ⣿⣿⣿⣿⣿⣿⣿⠃⣾⣷⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢉⣩⣁⣳⣶⣦⣤⣤⣈⣥⢛⡞⣶⣿⣜⣫⢝⣶⣫⢞⣡⣀⣒⣀⡴⣨⡽⣎⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⢷⣻⡜⣮⢱⢣ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⢻⠇⠛⢧⠀⠀⠁⠀⠀⠀⠾⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⢾⣯⢷⣻⣼⢣⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⠀⣶⣿⠃⠀⠂⠀⠀⢰⣶⡾⠟⠫⣈⢿⡿⠟⣨⣿⣿⣿⢿⡆⠀⠈⣿⣿⣿⣿⣿⡟⢹⣯⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⢯⣿⢯⡿⣟⡾⣏⣞ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡀⢿⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣉⣛⠶⣿⣿⣿⣿⠟⣿⠃⠀⢠⣿⣿⡏⢿⣯⣭⠷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣯⣟⣯⡿⣽⣻⢞⡵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⡈⠹⡄⠀⡁⠀⠀⠀⠀⠀⠈⠙⠋⣙⣹⣿⣿⡿⠋⠀⠀⠀⠀⢺⣿⣿⣿⣆⢻⣿⣻⣶⣷⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⡿⣽⡷⣯⢿⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢲⡾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠜⡹⠟⠉⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣞⡽⢿⣿⡿⢿⡟⢶⣡⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣯⣟⣷⣻⣽⡳⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⣀⡆⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠱⠂⠄⣙⢣⣟⣮⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⣟⡾⣽⣞⡷⣯⡽⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⢈⣿⣿⣿⣿⣍⠣⡉⠴⣌⢷⣾⣻⣿⣿⣿⣿⣿⣿⡿⣞⣯⢷⣯⡟⣷⣫⡽⢶⡻⣵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢺⡿⢏⢀⣠⣀⠀⣦⣀⢻⣿⣿⣿⣿⣣⣝⡳⣎⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⡽⣯⣟⢶⡻⣵⢣⡟⣯⢳⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⢢⣏⣷⢿⣭⣻⢷⣿⣿⣿⣿⣽⣾⣳⣟⣷⣫⢯⡷⣭⢳⡝⣮⢛⡼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣞⡿⣎⡶⣿⣿⣿⣿⣿⣿⣞⡷⣟⣾⡳⣏⡷⣹⢎⡷⣙⢦⣋⠖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⢳⢏⣾⣿⣿⣿⡍⣉⣛⣻⡿⢿⣾⣽⣝⣳⣝⢮⠳⣍⠶⣉⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣞⢿⣺⣿⣿⣿⣿⣿⡉⢿⣿⡙⠲⣤⣈⡙⠻⠮⣽⣙⡌⢣⠱⣊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣆⠠⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⢀⣠⣶⣿⢿⡛⣴⣿⣻⢻⡽⣷⢯⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣡⡄⠀⢢⠉⠱⣄⠀⠉⠈⠐⠃⠄ ⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠹⣄⠙⣄⡀⠀⠀⠜⢢⠳⣾⣿⣿⣿⣿⣿⣷⣯⡷⢭⡷⣯⢿⣯⣿⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠉⠢⠈⢦⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢱⡙⢧⡈⠻⣦⣄⠘⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⢌⢧⡻⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⠀⠀⠃⠈⣷⡀⠀⠀⠀ ⣿⣿⣧⣿⣿⣧⣿⠟⠀⠀⠀⣠⠀⠀⢀⣠⠀⠀⢿⠛⠻⢤⡘⠻⣤⡀⠀⠀⠀⠀⢀⣀⣠⣤⡼⣼⢧⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡄⠀⠀⢀⠸⡇⠀⠀⠀ ⣿⣷⡿⣿⣽⠟⠁⠀⣠⡏⢰⡇⠀⠀⢸⣿⠀⠀⠘⣧⠤⠄⠙⢶⣌⠛⢶⣤⣶⣶⣿⣾⣿⣯⣟⣯⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣳⢯⣿⡄⠘⠤⢂⠙⢦⡀⠀ ⣟⡾⣽⠟⠁⠀⠀⢠⡿⠀⣾⡇⠀⠀⠹⢿⣀⣤⡀⠙⢆⡰⣳⣦⣈⡛⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣷⢫⣞⢿⡃⠄⢂⠀⢣⢳⡀ ⣯⡟⠃⠀⡰⠀⠀⣿⠃⢸⣿⡇⢀⠀⡀⠀⠈⠻⢿⣷⣮⠵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣿⣟⡿⣷⣿⠿⣝⡷⣎⠲⣅⠀⠀⠈⠀⠡⢓ ⠋⠀⣀⠔⠁⠀⢀⡇⠀⣾⣿⡄⠈⣆⠘⡀⠀⠀⠀⠹⢿⣿⣿⣟⣯⣙⣌⣙⡻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⢯⣟⣿⣿⡿⣿⡽⣾⣽⣻⣿⡹⣌⢳⣍⡒⠈⠄⠀⠀⠀⠀⠈ ⠀⠀⠀⠠⣆⠀⢸⠀⢠⠿⣿⡇⠀⢸⣧⠑⢦⠀⠁⠀⠀⢈⠛⢿⣿⣽⣶⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⣞⡷⣿⢯⣟⣷⢳⣿⣯⡕⢎⠲⡡⠌⠐⠠⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠈⢆⡇⠠⠊⠀⣿⡇⠀⠀⣿⡷⣄⠳⣤⠀⢠⠀⠀⠀⠘⠻⠿⣿⢿⡿⠟⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⣾⢿⣽⡻⢾⡭⣟⣿⡗⢮⡡⠂⠑⣂⠀⡲⢱⠀⠄⡁⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣿⣷⠀⠀⢸⡷⠜⢧⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡾⡽⢧⠿⣜⣿⡟⢢⠑⡤⠘⢤⠣⢌⢣⠘⠠⠀⠂ ⣾⣦⡀⠀⠀⠀⠀⢙⣦⠀⣿⣿⠀⠀⠀⠀⠆⠐⠛⣦⣄⠠⣄⠀⠰⠀⠀⠀⠀⠀⡐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⡿⣷⣿⣻⠯⣷⣎⡿⡍⢦⡙⠴⡁⠎⣇⠫⢄⠊⢀⠁⠀ ⠀⠀⠉⠲⣭⣯⣿⣾⣿⣷⣽⣿⡀⠀⠀⠀⠁⠀⣨⡇⠸⣷⣄⠁⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣟⢿⣿⣿⣿⣿⣿⣿⡣⢿⡱⢎⡝⠻⠶⣾⡽⣙⠦⡙⠤⠃⢘⠀⢳⡈⡐⠀⠀⠀ ⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣇⢠⠐⡁⢰⣿⠿⡷⠀⠹⡙⣶⣄⡀⠀⢠⡄⢀⣾⡿⣟⢣⠟⡼⢫⣿⢿⣿⣿⣿⡿⣿⣷⣏⠂⢜⡱⣌⡄⢣⣝⠂⡉⠒⡁⠀⠀⠂⠐⠈⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀ ⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⡄ ⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇ ⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠀ ⠈⢷⡀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⣿⠀⣼⠃⠀ ⠀⠈⢷⣼⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡾⠃⠀⠀ ⠀⠀⠈⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⢠⠀⣄⠀⠀⠙⢿⣿⣿⣿⡿⠏⠀⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣴⣿⠀⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⠳⣦⡀⠀⠀⠀⠸⣿⡿⠀⢻⣿⡟⠀⠀⠀⠀⣤⡾⢻⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⢻⠻⣆⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⡾⢻⠁⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⢹⠒⡦⢤⠤⡤⢤⢤⡤⣤⠤⡔⡿⢁⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⢸⠦⣧⣼⣀⡇⢸⢀⣇⣸⣠⡷⢇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠺⣄⣇⢸⠉⡏⢹⠉⡏⢹⢀⣧⠾⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠉⠙⠓⠚⠚⠋⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⣀⣄⡤⣤⡴⣤⣤⣤⣤⣀⣀⠀⠀⡀⢀⠈⠈⠙⠮⡽⢭⡻⣝⡻⣏⠿⡭⢯⠝⡊⠉⡀⠀⠀⠀⠀⢀⣀⣤⣄⣦⡴⣤⣤⣄⣀⡀⠀ ⡾⣽⣳⢯⣟⣷⣻⡽⣯⣟⣿⣻⢿⣿⣶⣤⣄⠀⢀⠊⡀⠈⠃⠻⣜⢳⡭⡛⠑⠃⠀⠀⠀⢀⢂⣥⣶⣿⢿⣿⣻⢯⡿⣽⣳⢟⡾⣽⣻⣟ ⣟⡷⣯⣟⡾⣧⣟⣷⣻⡼⣾⢽⣻⢾⣝⣿⣻⣿⣶⣤⣀⠠⠄⠁⠈⢁⠂⠁⡀⠄⣈⣰⣼⣾⣿⣟⡿⣞⡿⣼⢯⡿⣵⢯⣯⢿⣽⣳⢟⡾ ⣯⢿⡵⣯⢷⡻⣜⠶⣭⢳⣭⢻⡜⣯⢟⣾⣷⣯⣟⡿⣿⣷⣦⡔⠂⢀⠐⢠⣱⣾⡿⣟⡿⣽⣾⡽⢾⡹⣝⢧⡻⡼⣭⠷⣏⡟⡾⣭⢿⡽ ⣯⡟⡽⣎⢷⡹⢎⡷⢎⣳⢬⢧⣛⡴⣫⢶⡹⣞⡽⣻⣷⣽⣻⢿⣿⣶⣾⣿⣟⣯⣿⣽⡟⣿⢳⡝⣣⡝⢮⣓⠷⣳⢎⡟⡶⢭⡳⣭⢏⡿ ⢷⡹⣳⡝⣮⢝⡫⢜⠫⠘⠌⠂⠁⠊⡑⠪⠱⢎⡵⢫⡞⣽⢻⣿⣾⣽⣻⣾⢿⣻⣙⢶⣹⢎⠳⠉⠓⠈⠁⠈⣉⠁⠋⢞⡹⢣⡟⣜⣫⢼ ⢧⣛⡵⣚⠕⠊⠐⠀⠀⠀⠀⠀⢀⣁⢀⠀⢀⠀⡈⠡⠙⣜⢣⠻⡼⢿⢿⡹⢧⣳⡽⠂⢁⠀⡀⢀⢁⣁⠠⢀⠀⡀⠄⠀⠀⠃⠙⡞⣬⢳ ⡻⡜⠶⠉⠀⠈⠁⠄⣠⣼⣶⣿⣿⡿⣿⣿⣿⣶⣦⣔⡂⠠⠌⠋⠵⣫⢎⠽⠋⠁⣀⣨⣴⣶⣿⢿⡿⣿⣿⣿⣶⣦⣤⡁⢀⠈⠀⠈⢱⢫ ⡳⠍⠀⠀⠀⢈⣴⣿⣿⣟⣯⢷⣯⣿⣷⣟⣮⣿⣽⢿⣿⣷⣦⣁⠂⡀⠂⢠⣱⣶⣿⢿⣻⣽⣞⣿⣿⣷⣟⣾⣿⡽⣿⣿⣦⣀⠀⠁⠀⠑ ⠓⠀⠄⠠⢡⣾⣿⢯⡷⣾⣽⡿⣟⢯⡻⣭⢻⣜⡻⢿⡾⣷⣟⣿⣿⣶⣽⣿⣿⣽⣾⢿⡻⡝⢯⡞⣵⢫⡟⣿⣷⣟⡷⣯⢿⣿⣦⠐⢀⠀ ⠁⠈⠀⢰⣿⡿⣯⣟⣾⡿⣏⢷⡹⣎⠷⣭⢳⠮⣝⣣⢯⣝⡻⢿⣿⣯⣿⣿⠻⣝⢮⣓⠷⣹⠳⣞⡵⣫⢾⡱⢯⢿⣿⣽⡿⣽⣿⣆⠀⠀ ⠀⠠⠀⣿⣿⣽⣳⣾⣟⡳⡝⣎⢷⣩⣛⡴⠫⠙⠌⠓⠺⠜⣭⢳⢮⣝⡳⢎⣿⣘⡧⠋⠞⠱⠛⠼⣧⣛⡼⡹⣏⠾⣹⣿⣟⣷⣻⣿⡄⠀ ⠀⠀⠰⣿⣳⢯⣷⣿⢭⡳⣝⡺⡜⣶⠋⢁⠐⠈⢀⠐⡀⢈⠠⠙⠶⣮⣽⠛⠉⠁⡂⠐⠀⠀⠤⠀⠈⠹⣞⡵⢭⣫⢗⡽⣿⣞⣷⣻⡖⠀ ⠀⠀⠱⣿⡽⣯⣿⡟⢮⡵⢣⣟⠼⠁⢀⠂⣤⣼⣾⣿⣿⣿⣶⣦⣄⡀⢠⣰⣾⣿⣿⣿⣿⣶⣇⡀⠆⠀⡙⢾⣣⠗⣯⢞⣿⣻⢶⣻⡕⠀ ⠀⠀⢩⢿⡽⣞⣿⡝⣧⡝⣳⢞⠁⠀⠄⣼⣿⡿⣽⣞⣳⣟⣾⣽⣿⣿⣿⣿⣟⣾⣳⣟⡾⣽⣿⣷⡀⠂⠄⢚⡧⣻⡜⣯⢾⣯⣟⡷⡍⠀ ⠀⢀⠂⣿⡽⣯⢿⣛⠶⣭⢳⣞⠀⠀⢐⣿⣿⣽⣳⣿⡟⣯⢻⡽⣻⣿⢿⡻⣏⢿⡹⣿⣿⣳⣯⣿⡧⠐⠀⢢⡝⣶⡹⣎⣿⣞⣷⣻⠄⠀ ⣃⠀⠂⢸⣿⣯⣟⣯⢟⡶⡹⢾⡄⠀⠌⣿⣷⢯⣿⡷⣹⢎⠷⡩⢓⢮⠳⡝⣎⠷⣹⢳⣿⡷⣯⣿⡧⠃⠠⢱⡹⢶⡹⣞⣿⡽⣞⡧⠐⠀ ⢧⡈⠄⡈⢿⣷⢯⣿⣯⢖⣯⢻⣧⠀⠈⣿⣿⢯⣿⣷⢫⢾⡁⢀⠈⠀⠁⠀⠌⣹⡱⣏⣿⣟⡷⣿⠏⡀⠡⢧⡛⣧⢻⣽⣿⣽⡻⠄⠁⠀ ⡳⣥⠀⠠⠙⣿⣯⢿⣿⡞⣜⣣⢿⡆⢀⠸⣿⣟⣾⣯⡟⣾⣧⠀⠀⠀⡀⠌⣰⡷⣹⣽⡿⣽⣿⡿⠀⢄⣾⢧⢻⡼⣻⣿⢷⣯⠛⠀⠀⢴ ⡝⡶⢣⠀⡁⠸⣿⣟⣾⣿⣧⢳⣎⡽⡄⠠⠹⣿⣾⡽⣿⣎⢿⣧⣀⠀⢄⣶⢿⣱⣿⣿⡽⣷⡿⢀⠀⣼⣏⢾⡯⣿⣿⣯⣿⡟⠀⢁⡘⢮ ⣯⡝⣯⢳⡀⠀⠙⣿⣯⣿⣷⡯⣽⡞⣽⣆⠠⠘⢿⣿⡽⣿⣷⣻⢬⡻⣜⢮⣳⣿⣿⣳⣿⠏⠀⢄⣾⠟⣼⢻⣼⣿⢯⣿⠟⢀⠠⣠⢏⡷ ⣷⡽⣎⢯⢷⣄⠀⠜⢻⣯⣿⢿⣧⣟⠶⣹⢷⡀⡈⠽⢿⣷⣯⢿⣷⣻⣼⣿⣿⣿⣿⠟⡁⢀⣴⡿⣭⢻⣼⣿⡿⣯⣿⠏⡐⠠⣐⡳⢮⣽ ⣷⣻⣮⢏⡾⣹⣦⠀⠀⢻⣿⣟⡿⣯⣟⡱⣞⣻⣆⠀⢈⠻⢿⣿⣻⣿⣟⣿⣾⠟⠁⠀⣤⣿⢻⡜⣧⣿⡿⣯⣿⡿⠃⡀⢠⢳⡭⣝⣳⢾ ⡷⣯⣟⣿⣞⡵⣫⢷⡀⠀⠉⣿⣿⡽⣿⣷⣣⢷⣹⢻⣦⡀⠈⠙⠻⣿⠿⠋⠁⠀⣼⠿⣝⠶⣫⣾⣿⡿⣽⣿⠛⠀⠀⣤⢛⡶⣹⢾⡽⣯ ⣟⡷⣾⣽⣻⣷⣣⢏⡿⣆⡁⠀⠹⢿⣷⣻⣿⣮⣳⢏⡶⢻⣳⣄⠀⡀⠀⣀⡾⣝⣣⠟⣼⣳⣿⣟⣷⣿⠟⠡⢈⢠⡿⣴⢫⢾⣽⣫⢷⣯ ⣯⣟⡾⣵⢯⣿⣿⣮⡽⣏⢷⣤⠐⠈⠻⢿⣾⣟⣿⣾⣵⢫⢶⡹⣟⢤⡳⣏⠿⡼⣥⣿⣷⢿⣽⣾⠟⠁⠂⣠⡶⡟⣧⢏⣿⡿⣶⢯⣟⡾ ⡷⣯⡽⢯⣟⡾⣽⢿⣿⣯⢞⡭⢿⣄⠁⠈⠹⢿⣾⣳⢿⣿⣧⣻⢬⣳⢣⣭⢻⣵⣿⣟⣾⣿⠟⠁⠀⢂⣵⢿⡹⣝⣾⣿⢿⣽⣳⣟⡾⣽ ⣟⣷⢻⣟⡾⣽⢯⣞⣯⢿⣿⣺⢵⣚⡷⣤⠁⠀⠙⠿⣿⣞⡿⣿⣧⣷⣫⣾⣿⣻⣷⡿⠛⠁⠀⣁⣼⢿⡹⣎⣷⣿⡿⣽⢯⣶⣻⢞⣽⣳ ⠙⢾⣻⢾⣽⣳⣟⡾⣽⢯⣟⣿⣷⣏⢾⡹⣻⣄⡀⠀⠉⠿⣿⣷⣯⢷⣟⣷⣿⡟⠋⡐⠀⢢⣵⠿⣩⡞⣵⣿⣿⢯⣟⣭⣟⡾⣽⣛⣮⣟ ⠀⠈⠹⣻⣶⣻⠾⣽⣏⡿⣮⢷⣻⢿⣷⣽⢲⡝⡷⢧⣀⠀⠀⠙⠿⣿⡿⢋⡁⠠⢁⣰⢾⢯⡝⣞⣳⣿⣿⣻⡽⡾⣽⠾⣭⣟⣷⡻⠞⠀ ⠀⠈⢀⠀⠻⣿⣟⣧⣟⡷⣯⢿⣭⢿⣽⣻⣿⣾⡹⣏⡽⣳⣤⡀⠀⠀⠄⢂⢤⣵⣟⡻⣎⣷⣽⣿⢿⡽⣞⣷⣻⣽⣳⣟⣷⣿⠾⠁⠀⠁ ⣏⢦⠀⠈⠀⠈⢻⣿⣾⣽⣳⡟⣾⣛⣮⢷⡯⣟⣿⣾⣵⢫⡝⡿⣶⣤⣴⡻⣏⠷⣎⣷⣿⣟⣯⣿⣾⣽⣿⣶⣿⣶⣿⣾⣿⣥⣦⣤⣤⣴ ⡽⢎⡷⣂⠠⠐⠂⠈⠻⣾⣷⣻⣳⣟⡾⣯⣽⣻⢾⡽⣿⢿⣼⣳⡝⣮⢳⡝⣮⣿⣿⣟⡷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣻ ⣽⣫⠼⣭⡓⢦⣁⣀⠄⢈⠻⢿⡷⣯⢷⣛⣾⣳⢯⣟⡾⢯⣟⣷⣿⣮⣷⣿⣿⡻⣧⢿⣽⣳⣿⣿⣽⣟⣿⣾⣿⣵⣿⣧⣟⣾⣿⣣⣿⣺
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠁⠀⣴⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠻⠛⠒⣀⣴⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣶⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⢠⣤⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣧⣴⣂⣠ ⣤⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠛ ⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
m EMINƎMEMINƎMEMINƎMEMINƎMEMINƎMEMINƎMEMINƎMEMINƎMEMINƎMEMINƎMEMINƎMEMINƎM♍♍♍♍♍♍♍♍²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³²⁰²³·⁰¹·¹³ƦƦƦƦƦƦƦƦƦƦƦƦƦƦƦ(づ๑•ᴗ•๑)づ♡(づ๑•ᴗ•๑)づ♡(づ๑•ᴗ•๑)づ♡(づ๑•ᴗ•๑)づ♡(づ๑•ᴗ•๑)づ♡(づ๑•ᴗ•๑)づ♡εつ▄█▀█●
⠀⠀⠀⠀⠀⢠⡞⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⡁⡀⠈⣿⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡏⠀⡅⡇⠀⢹⣷⠀⠀⢀⣤⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠐⡇⢇⠀⢸⣿⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⡇⠸⡀⢀⣿⠏⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣄⣸⠀⢣⣼⡡⠒⢁⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠷⠶⠶⠶⠶⢤⣤⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣻⣧⡀⠋⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡄⠀⠀ ⠀⠀⠀⢀⣴⠞⠋⡩⠃⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀ ⠀⠀⣰⡿⠁⢀⠞⢀⠞⠙⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⡶⠿⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀ ⠀⣸⡏⠀⢀⠎⢀⠏⠀⢠⣿⠙⠻⠭⣉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⣀⣴⡾⠻⣷⣤⡀⠀⠀⠀⠀ ⢠⡿⠀⠀⣸⠀⡎⠀⠀⣼⣿⣄⠂⢤⣀⠉⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣶⣾⡟⠋⠁⠀⠀⠀⠙⠿⣷⣤⡀⠀ ⢸⡇⠀⠀⡇⢸⠀⠀⢰⡿⠈⠻⣷⣄⠀⠉⣲⣦⠠⠤⣈⡉⠐⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⡟⠀⠀⠀⠀⠀⠀⠉⣻⡷ ⠘⣇⠀⠀⡇⠘⠀⠀⢸⡇⠀⠀⠀⡽⠗⢋⣠⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋⠀⠀⠀⢀⣀⣤⡴⠚⠉⠀ ⠀⢻⣄⠀⡇⢰⠀⠀⣿⠃⠀⠀⣀⠵⠚⠛⠉⠙⢻⡿⠷⠶⣦⣤⣤⡴⠶⠶⠟⠛⠿⣷⠲⠶⠶⠚⢻⣿⠿⣿⣦⣄⡀⠀ ⠀⠀⢻⡄⢸⠘⡆⠀⣿⢀⠔⠋⢀⣠⣴⣶⣾⣿⣦⢱⠀⠀⠀⢀⡏⣹⣷⣶⣦⣤⣀⠀⠉⠢⡀⠀⢸⣿⣀⣤⠾⠛⠁⠀ ⠀⠀⠀⠹⣿⡄⠈⢠⣿⠈⠂⢾⠙⣿⣿⣿⡿⣿⣿⢀⠇⠀⠀⢸⡄⢿⣿⣾⣿⣿⣿⠉⡟⠒⠃⠀⣾⡏⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣆⡘⣿⠀⠀⠘⢦⡙⠿⠛⢋⣉⡡⠞⠀⠀⢀⠀⠳⠬⣉⣉⠙⠛⢃⡜⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀⠀⠀⠀⠉⠋⠉⠁⠀⠀⠀⣴⣟⣻⣻⡆⠀⠀⠀⠉⠉⠉⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣀⣤⠶⠒⠒⢲⣴⣞⠉⠀⠉⢳⣄⣀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢉⣹⣿⣦⠀⠈⣿⣁⣈⣷⣴⠚⢉⣹⡟⠛⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠛⠉⠀⣽⣷⣦⡼⠋⠉⠀⠉⣿⡛⠉⠀⢀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⢻⣧⡤⠤⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣼⠋⠀⠀⠀⢹⠏⠉⠉⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠿⣧⡀⠀⢠⠏⠀⠀⢀⣾⣯⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁
☺️☺️🙏(ㅅ´ ˘ `)
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⠤⣖⣾⣭⡍⠉⠹⣿⣗⣦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠶⢶⣶⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣾⣕⡦⣄⡀⠀⠀⠀⠀ ⠀⠈⣧⣧⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⣿⡿⣿⣿⣷⣯⣳⡀⠀⠀ ⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⠀⣿⡆⠀⢹⣿⣿⠛⣷⡀⠀ ⠀⠀⡴⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⣿⣇⣸⣿⠟⠁⠀⠉⣧⠀ ⠀⠀⣷⠂⠀⠘⣮⠙⠛⠒⠒⠛⠀⠀⢠⡏⠀⢰⣿⣿⣿⠏⠀⠀⠀⠂⢸⠀ ⠀⠰⡏⠀⠀⢰⣿⣷⣤⣄⢀⣀⣤⡜⠋⢀⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⠀ ⠀⢸⣇⡀⠀⠈⠛⢿⣿⣿⣷⣶⠯⢭⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⡄ ⠀⢺⣉⡍⢹⡆⠀⠀⠀⠉⠀⠈⠀⠀⠻⠛⠟⠛⠛⠋⣁⠀⠀⠀⠀⠀⣈⣿ ⠀⡟⠂⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠤⠀⠐⠀⢸⡟ ⢀⣧⡀⠀⠀⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⢸⡇ ⣼⣃⡀⠀⠀⠻⠻⢿⣿⣷⣤⣤⣤⣄⣀⠀⣀⣀⣀⣴⡆⠀⠀⠀⠀⠀⢸⣇ ⣿⢀⠁⠀⢠⡆⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⡏ ⢻⡜⠳⢶⣼⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇ ⢸⣿⡀⠀⠀⣿⣿⣿⣿⣿⢗⡶⢤⣤⣀⣀⣀⣀⣀⣀⡁⠀⠀⠀⠀⠀⠀⣿ ⠸⣏⢇⠀⠀⣿⣿⣿⣿⣿⠀⠉⠉⠉⠛⠾⣿⣿⣿⣿⣷⣤⣤⣤⡴⠤⢤⣿ ⠀⠘⢮⣁⣰⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⣸⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⡿⣿⡟⠁⣰⠇⠀⠀⠀⡀⣿ ⠀⠀⠀⡰⣻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⡽⣿⡿⠋⢀⡄⠴⣚⡵⠛ ⠀⠀⣾⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠖⠋⠉⠀⠀ ⠀⠀⠹⡽⣿⣿⣿⢏⠟⠀⠀⠀⠀⠀⠀⣠⢞⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠉⠛⠉⠀⠀⠀⠀⠀⠀⢸⣱⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⡿⠿⠿⠽⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⠿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡁⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠛⠻⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⡀⢀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⣴⣾⣶⣶⣿⣿⣷⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⢰⣿⣿⡆⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀ ⣠⣄⡀⠀⠀⢻⣿⣿⣿⣦⣾⣿⣿⣧⣴⣿⣿⣿⡟⠀⠀⢀⣠⣄ ⣿⣿⣿⣶⣤⣸⣿⣧⠙⣿⣿⡇⢹⣿⣿⠋⣼⣿⣇⣤⣶⣿⣿⣿ ⢻⣿⣇⠙⠻⢿⣿⣿⠀⣿⣿⠁⠘⣿⣿⠀⣿⣿⡿⠟⠋⣸⣿⡟ ⠀⠻⣿⣧⡀⠀⠙⣿⣿⣿⡏⠀⠀⢻⣿⣾⣿⠋⠀⢀⣼⣿⠟⠀ ⠀⠀⠈⢿⣿⡄⠀⠘⣿⣿⠇⠀⠀⢸⣿⣿⠃⠀⢠⣿⡿⠁⠀⠀ ⠀⠀⠀⠸⣿⣇⣀⣤⣿⣿⣤⣤⣤⣤⣿⣿⣤⣀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣦⡀⠈⠙⣿⣿⣿⣿⠋⠁⢀⣴⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⢿⣿⣿⡿⠋⠁⠈⠙⢿⣿⣿⡿⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠷⢤⣀⡀⠀⠀⠀⠀⣀⣤⠼⡟⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡾⠀⠀⠈⣧⠀⠀⠀⣰⠏⠀⠀⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠃⠀⠀⠀⢸⡄⠀⣰⠏⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠉⢙⣦⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣀⣀⣀⣷⢠⠏⢀⣀⣀⠀⢸⢀⡇⠀⠀⠀⠀⠀⢠⣿⡑⢾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣋⡼⢧⡀⠀⠀⠀⠀⠀⣿⢧⠘⢿⣴⠼⠇⣿⠈⣷⠯⢤⠼⠇⢸⣿⡇⠀⠀⠀⠀⣰⡟⢄⣨⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣴⢛⣷⡄⠀⠀⠀⠀⣿⠘⣧⠀⠀⣠⡞⠁⠀⠈⢧⡀⠀⢀⡾⢻⠇⠀⠀⠀⣰⠯⣉⢲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡽⢿⣄⠀⠀⠀⢹⡆⠈⢷⡴⠋⠀⠀⠀⠀⠈⠳⣤⠞⠁⣼⠀⠀⠀⣰⡟⠢⣬⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡞⣹⣆⠀⠀⠈⣷⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⡇⠀⣰⡏⠀⠀⣰⠣⣌⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣵⢛⣦⠀⠀⠘⣧⠀⢸⠀⠀⠀⠀⠀⠀⢸⣁⣰⡟⠀⠀⣰⣋⠀⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣡⠾⢧⡠⣼⣟⢷⡽⠀⠀⠀⠀⠀⢀⣨⡿⣫⣿⡄⣰⠓⠀⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣯⣿⢻⣯⣻⠿⣷⣤⣤⣴⣞⣛⣡⠖⣫⣾⡿⣯⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠶⠚⠉⠁⠙⣾⡏⠙⠓⠶⣬⣍⣉⣉⣭⡴⠞⠋⣿⠃⠀⠙⢿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠁⠈⠉⠻⣦⠀⢀⣤⡶⠛⠻⣦⣄⡀⠀⠀⠈⠉⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠉⢉⣷⡶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣤⣤⣀⣀⣀⣈⣙⡓⠶⣶⣶⣖⣻⠟⠁⠀⠀⠀⠀⠀⠀⣠⡟⠃⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣡⠟⠲⠤⠤⢤⣈⣉⡉⢻⣿⣿⠛⠛⢻⡄⠀⠀⠀⠀⠀⢠⡾⢻⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣼⠃⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⠀⠀⢈⡿⠶⣤⡤⠤⠶⠻⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡞⠋⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⠀⢰⠏⠀⣠⠟⠀⠀⠀⠀⢹⡆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠸⢻⠀⠀ ⠀⢀⣿⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⢹⣤⡏⠀⡼⠃⠀⠀⠀⠀⠀⠀⠹⠾⡿⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⢸⡏⠀⠀⠀⠀⢀⣿⣥⠶⢦⡉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡏⢹⡆⠀⠀⠀⠀⠀⠀⢸⡀⠀ ⠀⡿⢁⣠⡤⣤⣴⣾⣿⡈⠻⣦⠳⣄⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⡇⣿⠏⠀⡼⠁⠀⠀⠀⣀⡤⠴⠚⠋⠁⢠⣷⠛⢧⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⣼⣟⣫⣽⣷⣿⣲⢿⣌⠙⠦⣌⠻⣿⣦⣀⠀⢸⠁⠉⠛⠲⠤⢤⣷⠋⢀⣞⣁⣠⡤⠴⠺⡏⠀⠀⠀⠀⠀⣼⠃⠀⠈⣧⠀⠀⠀⠀⠀⢸⠇⠀ ⠹⣯⠞⠉⠀⠘⠛⠛⠛⠓⠒⠛⠛⠛⠒⠫⠷⢾⣤⣤⣀⣀⣀⣴⣧⣤⣾⡭⠽⠗⣾⠓⣦⣇⢀⣀⣀⣀⡀⡇⠀⠀⠀⠘⠳⠲⠦⢤⣄⣸⡆⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢼⡇⠹⡉⠉⢧⠀⠈⠙⡿⣄⢀⣠⠶⢖⣺⣗⡶⢤⡉⣻⡄ ⠘⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠴⠶⠒⠋⠉⠉⠀⠀⡼⠁⠀⡇⠀⠈⣇⣀⣠⠿⠾⠟⠚⠋⠉⠁⠈⠙⢳⣝⣯⠀ ⠀⢻⡿⣍⠛⠒⠦⢤⡤⠴⠒⠒⠒⠚⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢃⣀⣼⣥⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣾⠆ ⠀⠀⢳⠈⢳⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀ ⠀⠀⠈⠳⢼⣄⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡟⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠒⠶⢦⣤⣤⣤⡤⠤⠴⢶⣏⣉⡁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠓⠒⠶⠤⣄⣀⣀⣤⠤⠴⠶⠚⠉⣁⡴⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣸⠋⠙⠲⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣥⠾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣇⠀⠀⠀⣀⣀⣀⣠⠃⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠶⠤⠤⠤⠤⠴⠖⠒⠒⡖⠒⠚⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀
⣤⡤⣸⠑⣄⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢌⢄⠉⠙⣟⠛⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠿⠑⠐⠂⠉⠀⡀⠀⠀⠈⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⢸⠀⠟⠁⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠀⠀⠀⠀⠈⠢⡀⠀⠀ ⠀⢸⠃⠄⣀⠀⣠⢏⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠀⠘⣆⣀⡦⠏⠀⠀⠑⣄⢸⡧⠀⠀⠀⠀⢀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢄⡀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣷⠀⠀⠀⠀⠀⣆⠀⠀⣿⠀⠀⠀⠀⢀⣿⣧⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⠀⠀⠀⢨⠏⠀⠀⠈⢆⠀⠀⠀⣾⠁⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢠⠟⠒⠖⠒⠉⢩⢢⠀⠀⠱⡀⠹⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢆⠀⠀⠀⠀⡜⠀⡵⡀⢀⡇⠀⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⠠⡇⠀⠀⠀⢀⡇⠠⢷⠁⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⡜⠀⢣⠀⠀⢠⣏⣀⠜⡸⠀⢸⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣇⣠⠏⠀⠀⠀⠈⠁⣰⣧⡤⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠛⠛⠉⠉⠛⠛⠿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⢀⡾⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢿⡄⠀ ⠀⣾⠃⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠈⣿⡀ ⢸⡏⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⢸⡇ ⣼⠇⠀⢰⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠘⣿ ⣿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿ ⢻⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡟ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠘⢿⣿⣿⣿⣿⠟⠉⠀⠀⡐⠂⠀⠀⠀⠀⠰⢢⠀⠀⠉⠻⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠙⠻⣿⡇⠀⠀⠀⠀⣷⡆⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⢸⡿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠘⠿⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⢦⣤⣤⣤⣤⡶⠶⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠶⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠶⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣿⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠳⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣷⠶⠟⠛⠛⠛⠻⠷⠶⢶⣦⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠛⠋⠁⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠘⢻⡆⠀⠀⠀⠀⠀⢻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡿⠷⣶⣤⡀⠀⠀⠈⢸⣇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠘⣿⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠈⠻⣦⠀⠀⠈⠛⠛⠛⠟⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢹⡇⠀ ⠀⠀⠀⠀⠀⣿⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢸⡇⠀ ⣶⠶⠾⠶⠶⢿⣦⡀⠉⠉⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠿⢿⣶⣶⣶⣄⡀⠀⠀⠀⠈⢻⡇⠀⠀⠀⢸⣷⠀⠀⠀⠀⠈⣿⠀ ⠻⣷⡀⠀⠀⠀⠙⢿⣷⠶⠶⠶⠶⠶⠶⠟⠋⢠⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⢸⡇⠀⠀⠀⡈⣿⠀⠀⠀⠀⠀⣿⠀ ⠀⠘⢿⣆⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠻⣿⣷⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⢻⣿⣿⣿⣿⠟⠘⣿⡄⢀⣿⠗⠁⠀⣰⣹⣿⣀⣀⣀⡀⠀⣿⠀ ⠀⠀⠀⠙⠷⣦⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⡆⠀⢹⠟⠀⣿⡟⠉⢻⣿⣿⣶⣦⡀⠀⠀⠀⠀⠙⢷⣆⡀⠀⠉⠉⠉⠁⠀⠀⣸⣿⣾⡏⠀⠀⢀⣿⠛⠉⠉⠉⠉⠙⢻⣿⠆ ⠀⠀⠀⠀⠀⢘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣿⠀⢰⡿⠀⠀⢸⡿⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠶⠶⠶⠟⠋⣹⡏⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣠⡾⣿⠀ ⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣾⣷⣀⣠⣾⣷⣬⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⢸⡇⠀⠀⠀⣀⣴⠟⢱⡿⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠐⢸⣧⣶⣶⠾⠟⠁⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⢀⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⡿⠀⠀⠀⠀⠀⡀⣼⡟⣿⡄⠀⠀⠀⠀⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⢿⡟⠛⠛⣹⡟⠀⠀⠀⠀⠀⠐⣼⡏⠀⠘⢿⣄⠀⠀⢠⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⢻⣷⣦⣄⡀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⡿⠿⠿⠿⠛⣿⡿⠛⠛⠋⠉⠀⠀⣿⠇⠀⣼⠟⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠈⢿⡄⢀⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⢠⣾⠃⠀⠙⢻⣦⣀⠀⠀⠀⠀⢸⡟⠀⢸⣧⡀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢿⣦⣀⠀⠀⣀⣴⡟⠃⠀⠀⠀⠀⠀⠈⢿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣿⢀⣴⠄⠀⣿⠛⠿⣶⣤⣤⣾⡇⠀⠀⢹⣧⣠⣾⣯⣴⠶⣶⣄⠀⠀⠀⠀⠸⣷⣄⠀⠈⠙⠛⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠙⠛⠋⠀⣸⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⠿⠋⠀⠀⠀⢻⣇⣀⡀⠀⠀⠈⠙⣿⡀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢸⣿⠁⠀⠀⠀⠀⢀⣿⠛⠛⠛⠛⠿⣦⣄⣿⡇⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣄⣤⣴⠾⠿⠷⣦⣤⣀⣀⣀⣠⣿⠁⠀⠀⠸⣿⡀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⡟⠀⠀⠀⠀⠻⣧⣀⣠⣴⣾⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠶⣶⣶⣶⣶⣶⣶⣶⠶⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢔⡮⠒⠒⠒⠂⢌⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⢿⠆⣤⣀⠀⠀⠈⠪⡢⡈⠳⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⢠⣤⣸⠿⠓⠛⠦⢔⢄⡈⢟⢞⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⢫⡅⢠⠀⠉⢩⣭⡿⢿⣾⣼⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⡄⠀⢣⣌⣤⠀⠀⠈⠀⠈⢹⣿⠇⠠⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠙⡈⠐⢕⡅⠀⠀⣀⣔⠆⡜⠇⠀⠀⠔⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⠠⣙⡖⠀⠭⢄⡞⠁⠀⣴⠊⠀⠀⣧⠀⠃⠀⠀⠀⢀⠤⠄⠀⠀⠀ ⠀⠀⠀⠀⡐⠈⠀⠈⠤⣤⣤⠠⠀⠈⠁⠀⠀⠀⠘⢧⢸⠀⠀⠠⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡤⢈⡎⡄⢀⠁⠀⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⡄⠀⠈⢻⠀⠀⠀⠀⠘⡄⠘⠫⠧⠶⠻⠠⡈⡎⠀⠀⡄⠡⡀⠀⠀ ⠀⠀⠀⠀⠀⠈⢀⠀⠀⠣⣀⠓⠀⡴⠁⠀⠀⠀⠀⠐⠒⢲⠀⠀⠀⠘⢄⠈⠂⡀ ⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠉⠪⢄⠀⠀⠀⠀⡔⠁⠀⡘⠀⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠱⡆⠀⠚⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣧⡀⠀⠘⡄⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⠀⠀⡀⠄⠒⠉⠁⠀⠀⠀⠀⠈⠳⣄⠀⠈⢦⡀⠀⠀⠀⢣⠀⠀⠀⢀⠞⠀⠀ ⠀⠀⡌⠀⠀⠀⠀⡄⠀⢀⠀⣀⠀⠤⠉⢳⡄⠈⢌⢢⢀⢠⡤⣡⠔⠺⡧⠬⢶⠀ ⠀⠀⠁⠀⠀⢀⣴⣿⣿⣿⣿⣷⣦⣄⡀⠀⢻⢄⠀⠑⢿⣾⣿⣾⣷⣾⣧⣄⣀⣧ ⠀⠀⠢⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣵⠯⠜⢀⣠⣤⣝⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠄⣀⡤⢤⣤⣈⠁⣠⡔⠶⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠄⠄⠄⣼⣿⠁⡀⢹⣿⣷⢹⡇⠄⠎⣿⣿⣿ ⣿⣿⣿⠿⠛⠉⠁⠄⠄⠄⠄⠄⠄⠄⠹⣇⣀⣡⣾⣿⡿⠉⠛⠒⠒⠋⠉⢸ ⡿⠋⠁⠄⠄⢀⣤⣤⡀⠄⠄⠄⠄⠄⠄⠈⠙⠛⠛⠉⠄⠄⠄⠄⠄⠄⠄⠈ ⠄⠄⠄⠄⠄⢹⣧⡈⠿⣷⣄⣀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣠⢄⣾ ⠄⠄⠄⠄⠄⠈⠻⢿⣶⣌⣙⡛⠛⠿⠶⠶⠶⠶⠶⠖⣒⣒⣚⣋⡩⢱⣾⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠈⠉⠛⠛⠛⠻⠿⠿⠟⠛⠛⠛⠉⢉⣥⣶⣾⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠒⠶⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠻⣿⣿⣿⣿⣿⣿ ⣿⡿⠛⠛⠛⢻⣿⠿⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⢻⡟⠛⣿⡿⠛⣻⣿⣿⣿ ⡟⠄⣼⣿⣿⣿⡇⠄⣾⣿⣧⠄⢻⡏⠄⣼⣿⣿⣿⡇⠄⡟⢀⣴⣿⣿⣿⣿ ⡇⠄⣿⣿⣿⣿⡄⠄⣿⣿⣿⠄⢸⡇⠄⣿⣿⣿⣿⡇⠄⣀⠈⢻⣿⣿⣿⣿ ⣿⣄⠈⠙⠛⢻⣧⡄⠙⠛⠉⣠⣿⣷⣄⠈⠙⠛⢹⡇⠄⣿⣧⠄⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⠴⠋⠉⠉⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠚⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⢠⣤⣶⣾⣧⣤⣤⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡤⠴⠶⠤⢤⡀⣧⣀⣀⠀ ⠻⠶⣾⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢹⣿⣭⣽⠇ ⠀⠀⠙⠤⠴⢤⡤⠤⠤⠋⠉⠉⠉⠉⠉⠉⠉⠳⠖⠦⠤⠶⠦⠞⠁⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿ ⠈⠖⠉⠙⠩⠽⡻⢫⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⠹⠉⠃⠂⠰⠀⠍⠀⠴⠀⠙⠊⠡⠂⠀⠸⠑⠚⠛⠛ ⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣟⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⡟⠚⠿⢿⣿⡾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣦⣠⡤⠼⠛⠋⢩⡿⠋⠁⠠⠄⠈⠉⠉⠀⠸⣿⡽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠉⠉⢉⣠⣤⣶⡶⠀⠀⠀⠀⠀⢿⢻⣿⣷⣶⡦⣿⣿⣿⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣤⣾⣿⣿⡇⠀⣤⣾⣟⣿⡷⠂⡇⠀⠀⠀⠀⠀⠨⢌⣉⣁⠼⠄⣿⣿⣿⣿⣷⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣶⣿⣿⣿⣿⣿⣷⠀⠀⠈⠇⠤⠄⠚⠁⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡌⡑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⡷⣶⣷⣶⡶⠃⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣇⣻⡿⠛⠀⡀⠀⠀⠀⠀⠈⠙⠉⠀⠀⢀⣠⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠉⢣⡀⠸⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣠⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡜⣿⣿⣿⣿⣿⣿⣿⣏⣿⡙⠢⠤⢀⣀⣀⣀⣤⣤⡴⠞⢡⣾⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣷⢻⣿⣿⣿⣿⣿⡿⣯⣹⣿⣷⣶⣤⣬⡒⢋⢉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⢸⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣿⣿⣧⣤⣤⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡧⣿⣿⣿⣿⡿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣳⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⣀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠁⠀ ⠀⠀⠀⢰⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⢼⣿⣦⡄⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠼⠿⠿⠿⠿⠿⠆⠀⠀⠿⠿⠏⠀⠀⠀⠀⠀⠹⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄ ⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠃ ⠈⠻⣿⣿⣶⣤⣄⣀⣀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣿⣿⣿⠛⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
my little strawberry 🥺 ❤️ twt: 8taa2669 he's so adorable.. <3 i heared him whimper, he's soo adorable, eee (//>×<//) ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣛⣵⣾⣿⡼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣫⣾⣿⠁⠐⣻⣷⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢟⣵⣿⣋⣬⣿⣷⣾⣿⣿⡏⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠷⠿⠛⠉⠉⠉⠀⠀⠈⠉⣹⢟⡉⠉⠓⠶⢤⣀⡀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠵⠋⠀⠉⠙⡦⣤⣤⣉⠛⠧⣄⡀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⢻⢟⠻⠗⢲⣄⣤⣲⢏⣴⡞⠁⠀⢀⣠⡾⠃⠀⠀⠀⠀⣠⣽⡟⠀⠀⠀⠀⠀⢸⣿⠃⠀⠉⠛⠶⣄⡙⠻⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⣤⣀⢀⣼⣿⠙⠋⠁⣨⠟⠁⢀⣴⣿⠋⠀⠀⠀⠀⣠⡾⠋⢰⠇⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠈⠙⣦⡝⣶⣄⣠⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⣡⡿⠋⠈⠀⠀⣠⡾⠃⢀⣴⠟⣻⠋⢀⡔⠀⢀⡾⠋⠀⢀⡟⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⢎⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠋⠀⠀⠀⠀⢠⡾⢁⣴⠟⠁⣰⣏⡀⠘⠀⣠⠟⠀⡀⠄⣸⠁⠀⣰⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣦⠈⢶⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣦⡾⣿⢡⣿⣅⣀⡀⣿⢿⡄⠀⣰⠛⠛⠲⢤⣤⣿⠀⢰⡟⠀⢀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠘⢿⣷⡄⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣾⣧⣴⠃⢤⡀⠀⠀⢩⣿⠀⣾⠃⠀⣼⢿⡜⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣯⢻⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠁⠀⠀⡏⣿⠇⠀⠉⠙⠛⢿⣿⣿⣶⣄⠈⠳⣄⠀⣿⣸⢻⡄⠀⣹⠈⢷⡻⡆⢰⡆⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⢻⠀⢳⡌⣷⣶⣾⣿⣿⣿⣷⣶⣶⣶⣤⣄ ⠀⡾⠁⠀⠀⠀⠃⠉⠀⠀⣀⣠⣤⣀⡈⠙⢿⣷⡝⠆⠈⠙⢿⣿⠀⣿⠀⢻⠀⠈⠑⠀⣿⡆⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠘⠁⠘⣷⠸⣟⣉⣩⣭⣭⣍⣙⡻⣿⣿⡟ ⠀⠁⠀⠀⠀⠀⠀⢠⣠⣾⣿⣅⣠⣽⣿⣦⡀⠉⢿⡄⠀⠀⠘⢿⡆⣿⣇⢸⡆⠀⠀⢸⣿⡇⠀⠀⢸⣿⢿⡇⠀⣀⠀⠀⠀⠀⠀⢸⡄⢹⡍⡿⠻⠿⣿⣿⢹⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣼⣿⣿⣿⣿⢉⡧⠀⠀⠳⠄⠀⠀⠈⠃⠘⣿⣿⣿⡆⠀⣼⣿⣧⠀⢠⣿⠇⣸⠀⠀⣿⠆⠀⠀⠀⠀⠀⣿⡞⣿⠿⣦⣵⣿⢣⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣤⣿⢻⣿⡀⢸⣿⣄⣿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⣸⣏⣿⢿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢿⣤⣿⣷⣼⠏⢻⣇⣄⣼⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣴⢯⣿⣷⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠉⢻⣿⡄⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢏⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⢶⣮⣿⣦⡻⣧⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠈⠻⣿⣿⣦⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⢘⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣥⣀⣹⣷⣄⠈⢻⣿⣿⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢨⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣽⣿⣿⣿⣿⢻⡆⠀⠹⣿⡟⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡛⠿⣿⠃⠀⠀⣼⠇⠀⠀⢀⡾⣾⠇⠀⠀⠀⣸⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣇⣀⣀⣼⠋⠀⠀⢠⣾⢻⣿⠀⠀⠀⣠⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡾⠁⠀⢀⣴⣿⠃⣾⡿⠀⠀⢰⣟⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠟⠁⢀⣴⣾⣿⢇⣾⣿⠇⠀⣠⣾⣿⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣠⣶⣿⣿⡿⣽⣿⣿⡿⣠⣾⣟⣹⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⣫⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⡏⠀⠀⠀⠀⠀⠈⠁⠎⠀⣠⠏⠀⢠⠎⠀⠀⢀⣠⠞⠉⢀⣤⠖⠢⢄⠀⠀⠀⠙⢆⢻⡉⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⢿⡟⣼⠀⠀⠀⠀⠀⠀⠀⠂⠀⣰⡏⠀⢀⠏⠀⠀⣠⣿⠃⢀⢴⡏⠀⢀⡔⠋⠀⠀⠀⠀⠘⡷⠉⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⢰⠋⣼⢀⡏⠀⠀⠀⢀⠀⠀⠀⡁⢠⠇⢧⣀⣸⠀⠀⢰⠣⡇⢠⠋⣾⠀⢀⠎⠀⠀⣠⣖⡛⣗⢦⠇⠶⠶⠶⣖⠀⠈⠳⡤⠤⠦⢄ ⠀⣰⠃⢀⡇⢸⡇⠀⠀⠀⣸⡀⠀⠀⢳⡜⠊⠉⠀⠀⠉⠓⢯⡀⢳⣾⠀⢻⡀⠸⡄⠀⢰⠃⠀⠈⠻⣿⣶⣒⣤⠀⠈⠳⡄⠀⠙⣦⠀⠀ ⠀⠇⠀⠀⠃⠘⠃⠀⠀⠀⢿⠳⣄⢠⢏⠔⠙⡆⠀⠀⠀⠀⠀⠙⢦⠉⠁⠀⠙⠦⣇⠀⢸⡀⠀⠀⠀⠈⠉⠙⣿⠀⠀⠀⠀⠀⠀⠘⡆⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⡟⣸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠦⡀⠉⠉⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠘⠁ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⢰⡴⠚⠉⠀⠀⢀⡼⠁⠀⠀⠀⠀⠁ ⠁⢠⡴⢚⡛⠺⣟⡖⠒⠚⠋⠁⠘⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠒⠶⠤⢶⡿⢁⡤⠀⠀⠀⠀⠀ ⡾⠉⢚⣉⣉⣦⠘⠀⠀⠀⠀⠀⠀⢷⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠤⠤⠤⠤⣀⠠⣤⣖⣯⠴⠋⠀⢠⠄⠀⠀⠀ ⠀⣰⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐⠘⣇⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⠆⠠⡀⠀⠀⠈⠳⡘⢦⣀⠀⢀⣠⠏⠀⠀⠀⠀ ⠀⡇⠀⢀⡶⠋⠀⠀⠀⠀⠀⠔⠄⢷⣸⣧⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢃⠇⠀⠀⠇⠀⠀⠀⠀⢳⢀⣈⣩⠽⠃⠀⡰⢻⡄⠀ ⡀⢧⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⡏⠸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠻⢤⡤⠴⢚⣥⠟⠀⠀ ⣧⠀⢉⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣤⠤⠖⠚⠉⠀⠀⢸⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣺⠋⠀⢀⠀⠀ ⠘⠷⣼⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠸⡇⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠎⠀⢠ ⠀⠀⠸⣯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣧⠀⢩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠁⠀⢀⡏ ⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⠸⡄⠱⠴⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢠⡆⣠⠟⣀ ⠀⠀⠀⢸⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠠⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣷⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠇⢀⣤⣿⡾⠛⠛⠉ ⠀⠀⢀⣾⣋⣀⠙⢦⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠈⠹⡗⣖⠒⢚⣿⠛⠛⠛⠓⠛⠉⠀⢸⡇⠀⠀⠀ ⠀⣴⠏⠁⠀⠀⠉⣻⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠣⠌⠘⡇⣾⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⣴⠋⠀⠀⠀⣠⠞⠁⠀⠙⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠀⠰⢡⡏⣿⠀⠀⠀⠀⠀⠀⡼⢸⡃⠀⠀⠀ ⡏⠀⠀⢀⠔⠁⠀⠀⠀⣠⠼⠦⡀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⡁⢸⠀⠀⠀⠀⠀⡼⠁⢸⣷⠀⠀⠀ ⠀⠀⠀⠋⠀⠀⣀⡴⠋⢁⠤⠖⠛⠒⢾⡄⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⢸⡆⠀⠀⠀⡼⠁⠀⣼⠟⠁⠀⠀ ⡄⠀⠀⠀⠀⠚⠁⠀⠀⡏⠀⠀⠀⣰⢸⠻⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣇⢸⡇⠀⠀⡼⠁⠀⠀⣿⠀⠀⠀⠀ ⠻⣄⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠻⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠚⣿⡻⣿⡛⠛⣿⠿⣛⢾⡇⠀⠜⠀⠀⠀⠀⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠳⣤⡀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⢷⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀ ⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⣀⣤⠤⣤⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⢿⡶⠛⠳⢾⡃⠀⠀⠀⠙⣇⣸⣇⣤⡤⠤⠤⠤⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⢀⣠⠽⢤⡄⠀⢤⣿⣋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣦⡄⠸⢧⣤⡴⠋⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡟⠁⠀⠀⢠⡷⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠙⠷⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠲⠤⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡛⢦⣄⠀⠀⠈⣷⠀⠀⠀⠀ ⠀⢠⣿⠀⠀⠀⠀⢀⡾⠋⠀⢠⣾⡏⠁⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠈⢳⡆⠙⢧⠀⠀⢿⡄⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⢠⡟⠀⠀⠀⢾⡟⣷⣦⣴⣿⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣦⣴⣿⡇⠀⠈⣇⠀⢸⡇⠀⠀⠀ ⠀⢀⣿⣦⣀⠀⡿⠁⠀⠀⠀⠸⣿⣿⣷⡿⠃⠀⣰⣀⣀⣙⣃⣀⣀⠈⠻⢷⣿⡿⠁⠀⠀⣿⡄⣼⠃⠀⠀⠀ ⣼⠋⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣽⣏⢛⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⠟⠛⠓⢦⡀⠀ ⡇⠀⠀⠀⠀⠀⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢷⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⠻⢯⣿⡿⠟⠃⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⠀ ⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀ ⠀⠀⠈⠷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⢦⣤⣀⣀⠀⢀⣀⣠⣤⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀ ⠀⠀⠀⠀⠘⠶⣀⠀⠀⠀⠀⠀⠀⠘⢧⠻⠶⣿⡿⠃⠀⠈⢿⡽⠿⠋⣽⠇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠘⣇⣴⠟⠁⠀⠀⠀⠀⠙⢦⣴⡏⠀⠀⠀⢀⣴⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣇⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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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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