Furry Emojis & Text

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