Konata!!!! Emojis & Text

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡴⠛⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠬⣷⠄⠀⠀⠀⠀⢰⣆⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠐⢿⣬⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢠⣤⡀⠀⠙⣆⠀⠀⠀⠀⠙⠀⠀⠀⠀ ⠀⠀⣸⡄⠀⠀⠀⢀⡏⠀⠀⣀⡀⠀⠀⠀⠛⠀⠀⠈⣯⠀⠀⢞⣛⣯⡉⠀⠀⠀⣸⢦⣄⡀ ⠀⠺⢿⡿⠛⠀⠀⢸⡇⠀⡀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⢉⡏⠁⠀⠈⠛⡾⠋⠀ ⠀⢀⠈⠁⠀⠀⢀⣹⡷⣶⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢦⡄⠀⠰⠋⣹⡷⠛⠁⠀⠀⠀⠀⠀⣠⣤⡤⠤⣄⠀⠀⠀⠸⣧⡀⠀⣴⠛⣦⠀⠀⠀ ⠈⠻⠟⠁⠀⠀⠘⠋⠻⢶⣤⣀⠀⠀⠀⠾⠡⠸⣇⠀⠀⠀⠀⠀⠀⠈⠳⣆⡿⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠏⠃⠀⠀⠀⠀⠀⠀⠀⠙⣇⣸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⢀⣠⣤⠴⠶⠚⠛⠉⣹⡇⠀⢸⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠈⢦⢰⠀⠀⠀⠀⠀⠈⢳⡀⠈⢧⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⡏⠀⢰⠃⠀⠀⠀⣿⡇⠀⢸⡀⠀⠀⠀⠀⢸⣸⡆⠀⠀⠀⠰⣌⣧⡆⠀⢷⡀⠀⠀⣄⢳⠀⠀⢣⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⢀⣿⣇⠀⠸⡇⣆⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⢹⣾⡇⠀⢸⢣⠀⠀⠘⣿⣇⠀⠈⢧⠀⠀⠘⠀⢠⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⡀⠀⠀⠀⢸⠈⢻⡄⠀⢷⣿⠀⠀⠀⠀⢹⡏⣇⠀⣀⣀⠀⣿⣧⠀⢸⠾⣇⣠⣄⣸⣿⡄⠀⠘⡆⠀⠀⠀⠀⠆⠀ ⠀⠀⠀⠀⠀⣾⢿⠀⠇⠀⠀⠀⢸⠀⠀⢳⡀⢸⣿⡆⠀⠀⠀⣬⣿⡿⠟⠋⠉⠙⠻⣽⣀⡏⠀⠙⠃⢹⡙⡿⣷⠀⠀⢹⠀⠀⠀⠀⠰⠒ ⠀⠀⠀⠀⢸⣿⣿⣇⢸⠀⠀⠀⢸⣦⣤⡀⣷⣸⡟⢧⣀⡴⠶⠿⠻⡄⣀⣤⣴⡾⠖⠚⠿⡀⠀⠀⠀⠈⣧⠁⠹⠆⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢸⣀⣼⣿⣼⡆⠀⢀⡘⡇⠀⠀⠹⡟⢷⡜⢉⣠⣠⣠⣀⣤⡿⣛⣥⣶⣾⡿⠛⠿⠿⣶⣦⡤⢹⠀⢀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⢸⡛⠁⠀⠙⢿⠋⠉⠉⠻⠀⠀⠀⢿⣄⠈⠁⠀⠀⠀⢉⢟⣴⡿⠿⠟⢁⠇⠀⠀⠀⠀⠹⣿⠻⡇⢸⠀⠀⠀⠈⣷⠀⠀⠀⠀ ⠀⣀⣀⣘⣿⡇⠀⢀⣠⣤⣶⣶⣶⣾⣦⡀⠀⠈⡿⠀⠀⠀⠀⠀⠀⣿⠟⠳⠦⡤⠊⠀⠀⠀⠀⠀⣸⠇⠀⡇⣼⠀⢰⠀⠀⢹⣇⠀⠀⠀ ⠛⠁⠈⣿⣷⣧⣴⣿⠿⠛⣿⠿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣴⣶⠿⠿⠿⡷⢛⠕⠷⡄⣧⣿⠀⢸⠀⠀⠸⣿⡄⠀⠀ ⠀⠀⢠⣿⢿⣿⣿⠁⠀⠀⠈⠳⠤⠶⠃⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⣱⠒⡠⢆⡴⣣⣯⢞⣴⡟⢿⡄⡏⠀⠀⠀⡏⢷⡀⠀ ⠀⠀⡌⣿⠀⠙⣿⡦⢀⣤⡴⣶⠖⣲⠆⢀⠞⠁⠱⠀⠀⠀⠀⠀⠠⣾⠟⠛⡡⠞⠁⢀⡴⢋⢎⣽⡿⣫⠋⠀⠘⢷⠃⡄⠀⠀⡇⠈⣿⡀ ⠀⠀⣇⢹⣦⠀⠼⢃⡾⢋⣶⢃⡼⣹⡳⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠠⠋⠀⡰⠋⠀⢘⣇⡇⠀⢠⠟⠀⡇⠀⠀⠀⠀⢹⡵ ⠀⠀⢻⣌⢿⡆⠀⡝⣼⠟⣩⢏⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⠀⣠⠏⣠⣾⡇⠀⠀⠀⠀⠘⣷ ⡀⠀⢸⣿⣿⣷⠆⢠⠏⡴⠃⡡⠋⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠤⣄⣀⠀⠀⢀⣰⠏⠀⠀⠀⠀⢀⣠⡾⠗⠋⢰⠏⡇⠀⠀⠘⠀⠰⢻ ⣇⠀⠘⣿⣿⣟⠻⣄⡞⠀⠐⠁⠀⠀⠀⠀⠀⣠⠞⣩⣤⣶⣶⣾⣷⣶⣬⣿⣿⣿⡏⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⡆⡇⠀⠀⠀⠀⠀⠀ ⠹⡄⠀⠹⣿⣿⡄⠀⠉⠉⠀⡀⠀⠀⠈⢻⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣧⠀⠀⠀⠀⠀⠀ ⠀⣿⢦⣀⠘⢿⣷⡀⠀⠀⡀⢦⠀⠀⠀⠀⠹⣿⣿⠏⠙⢻⣿⡿⠛⠉⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⡆⠀⠀⡀ ⢼⣿⠀⠈⢳⣤⣉⣻⣤⣀⣉⣩⠆⠀⠀⠀⠀⠹⡿⠀⠀⠈⡿⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠓⠂⠀⣠⣾⣿⣿⡿⢿⡄⠀⣧⠀⠀⠹ ⣾⠃⠀⣠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢠⠴⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⣧⣀⠧⣰⣻⢄⠀⠀ ⠛⠶⢾⣿⣽⣭⣽⣭⢹⣷⠀⢹⣦⣀⠀⠀⠀⠀⡄⠀⠀⣸⡀⠀⠀⠁⣰⣧⣽⠀⠀⠀⠀⢀⣴⣾⣿⣿⡟⣻⣿⣿⣿⣿⢠⣿⣧⡸⣷⣄ ⠀⠀⠀⠈⠙⠿⣿⣿⣿⠏⠀⣾⣿⣿⣷⣦⣀⠀⢇⠀⠀⠈⠁⠀⣠⠔⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣼⣿⠏⣷⡈⠉ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⡆⠀⠀⠀⡾⠁⠀⠀⠀⣀⡴⠞⠛⣛⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⢰⣿⡿⠂⠈⠻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠉⠛⠻⠿⠿⠿⠿⠿⣇⠠⠸⣇⣀⣤⣴⣾⡭⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡀⠀⠀⠀⠀⠀⠈⣳⠀⣿⠛⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡯⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠉⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠛⣁⡤⠔⠀⠈⠛⠉⠀⢰⣶⣶⣤⠄⠀⠀⠈⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⣡⣴⣾⣿⣿⢿⣋⡥⠴⠚⠉⠀⠀⠀⠀⢀⣀⣀⣀⣙⣋⡁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣼⣿⣿⡿⠟⠋⠁⠀⠀⠀⢀⣀⡤⠴⠞⠛⠉⠉⠁⠀⠀⢈⡉⠛⠒⠦⢤⣀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⣀⣀⣠⡤⠖⠛⠉⢀⣤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠙⠷⣄⠀⠉⠉⠉⠉⠉⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⢳⣿⣿⣿⣿⠋⠀⠀⠀⣠⠋⠀⣠⠇⠀⠀⠀⠀⢰⠀⠀⢰⡀⢣⡀⠀⠀⠀⠘⢮⠳⣄⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⡾⣿⣿⣿⠋⠀⠀⠀⡴⠁⠀⡰⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⢣⠀⢳⠀⠀⢀⣀⣀⡆⠘⢧⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣧⢿⣿⠃⠀⠀⠀⡼⠁⠀⢠⠃⠀⡆⠀⠀⠀⠀⠸⠀⡇⠀⠈⡆⠈⢇⠀⢹⣿⣿⣷⣶⣮⣷⡀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣞⣿⣿⣿⣿⣾⠇⠀⠀⠀⢸⠁⠀⢀⡎⠀⢰⠁⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠈⢧⠀⣸⣿⣿⣿⣿⣿⣷⣤⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣯⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⡇⠀⠀⢸⠁⠀⡿⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⢰⡀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⡞⣦⠈⠁⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣿⠃⡜⠀⡆⠀⠀⡇⠀⢀⡇⠀⢀⡇⠀⠀⠀⠀⢸⠀⢸⣇⠉⠉⠲⡧⣄⠙⢿⣿⣿⣿⠟⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⡄⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⠃⠘⡇⢰⢧⠀⠀⡇⠀⠈⡇⠀⢸⠀⠀⠀⠀⢀⠇⠀⡿⢸⠀⠀⠀⣇⠈⠳⡄⠀⠀⠀⠀⢹⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⡇⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⣿⡿⠁⠀⠀⡇⢸⢸⠀⢠⡇⠀⢸⡇⠀⢸⡇⢰⠀⢰⠈⠀⢠⠃⠈⡆⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠇⠀⠀⠀⠀⠀ ⠈⢻⣿⣿⡿⢁⠀⠀⠀⡇⠘⡇⠀⠘⡇⠀⢸⣇⠀⠘⣷⢸⠀⢸⠀⠀⢸⣸⣖⣛⣢⣀⠁⠇⠀⡕⡀⠀⠀⠀⠘⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡟⡠⠋⠀⠀⠀⣇⠃⡇⠀⠈⣷⠀⠸⣹⡆⠀⠙⣼⡆⠈⣇⠀⠸⠛⠛⢻⣿⣿⣿⣶⣤⣧⠃⠀⠀⠀⢸⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⡴⠁⠀⠀⡠⢸⣿⠀⡇⠀⠀⣿⡀⠠⠧⠽⠄⠀⠀⢿⠀⠹⠧⠀⠀⠀⣤⣴⡿⣿⣿⠘⡿⠀⠀⢀⠀⠸⠀⠀⠀⠀⢻⣿⡿⣯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⢀⡏⣼⠁⢀⠀⡼⠁⢸⢸⠀⣷⠀⡀⣯⢷⠟⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣛⣿⠏⢰⡇⠀⠀⢸⠀⢠⡆⠀⠀⠀⠈⠻⡿⠋⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣼⣾⡏⠀⡾⡼⠁⠀⣿⢸⡇⢻⡄⢰⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⡄⠀⠈⠀⢸⡆⠀⠀⠀⡄⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣷⢻⡇⠀⣷⠃⢀⡜⢹⡄⣷⣨⠟⠛⠉⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⠃⠀⠀⠀⢸⢿⠀⠀⠀⢀⣸⡧⢰⠇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠿ ⣿⠀⢧⠸⣿⢀⡞⠀⠀⣳⠟⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⣾⠁⠀⠀⡇⠀⣾⣿⣆⠀⠀⣿⣿⠁⣾⠐⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠈⠃⠈⠧⣿⣾⠁⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠘⠀⠀⠀⡇⢀⠇⡼⠹⡄⢠⣿⢁⠀⣿⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠟⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠉⢙⣶⣤⣀⣀⣠⣴⣶⠿⠋⢸⠀⠀⠀⠀⠀⢸⠁⣸⡰⠃⡴⠻⣼⠘⡟⠀⡏⢸⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡿⠾⣿⣼⡏⠉⠻⡁⠀⠀⠘⢦⡀⢀⡆⢀⡎⢰⠏⢠⠞⠁⠀⠘⡿⢁⣸⣅⢸⠀⠀⠀⠀⠚⠓⢆⠀⠀⠀ ⠀⠀⠀⢀⣧⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⢦⣿⢿⣇⠀⠀⠀⠀⠀⠀⣠⠞⠋⢃⡞⢡⢧⡔⠁⡠⠀⢀⢼⡷⠋⠁⣝⣎⣄⠀⠀⠀⠀⠀⠀⠱⡄⠀ ⠀⠀⠀⠚⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠠⢻⠇⣰⠋⠹⣾⡛⠲⢦⣤⡤⠒⠋⠁⢀⣴⠚⠤⠚⠈⣳⠞⠀⢀⡴⠋⠀⠀⠀⠙⣽⢻⣆⠀⠀⠀⠀⠀⠀⠹⠀ ⠀⠀⠀⣰⠟⡜⠳⣦⣤⣤⣤⡤⠔⠒⠋⠉⠁⠀⠀⢾⣟⠁⠀⠀⠈⠙⢶⡤⣤⣤⣤⠖⠚⠉⠁⠀⢀⣄⡾⠋⢁⡴⢻⠀⠀⠀⠀⠀⠀⢸⡀⠱⠱⣄⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⣏⠀⡟⢦⣽⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⢠⠞⠛⢺⡀⠀⠀⠀⠀⠀⢠⣿⠋⠀⡰⠋⢀⡞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠇⠱⡀⠀⠀⠀⠰ ⠀⠀⣠⢿⡀⣸⠀⠙⠳⢦⣤⣄⣀⣀⣀⣤⣴⠞⠋⠀⠀⠀⠀⠀⠀⠘⣦⣤⠞⡀⠀⠀⠀⠀⠀⣼⠟⢀⡞⠁⠀⠸⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡯⠤⠗⠛⠀⠀⠀⠀⠀⠠⠀⠀⣇⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠜⠁⠀⠀⠀⠀⢠⢯⣠⠏⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⢀⣿⡴⡏⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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膩I嶮薤篝爰曷樔黎㌢´　　｀ⅷ膩I嶮薤 艇艀裲f睚鳫巓襴骸　　　　贒憊薤夢緻 殪幢緻I翰儂樔黎夢'”　 　 ,ｨ傾夢薤緻薤 盥皋袍i耘蚌紕偸′　　　 雫寬緻薤薤夢 悗f篝嚠篩i縒縡齢　　 　 Ⅷ辨f薤緻夢 輯駲f迯瓲i軌帶′　　　　　守I厖孩緻迯 幢儂儼巓襴緲′　 　 　 　 　 守枢i磬廛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⠊⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄ ⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⠀⠘⠿⠀⠀⢠⣀⢄⡢⠉⣔⣲⢸⠀⠀⠀⠀⠀⠀⢘ ⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠫⠭⠝⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊ ⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠉⠉⠀⠀⠀⠉⠉⠉⠛⠻⠶⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡐⣴⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⡄⠀⠀⠀⠀⠀⠀ ⣬⣿⠃⠀⠀⢠⣤⡄⠀⠀⠀⠀⠉⠲⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⣀⡀⠀ ⣿⣿⣄⠀⠀⣸⣿⡁⠀⠀⠀⠀⠀⣴⠀⠀⠈⠛⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡽⠇⠀ ⣿⣿⡛⠛⠛⠋⠈⠻⢦⣤⣠⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡄ ⠈⠛⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⢾⠛⠇ ⠀⠀⠀⠀⢭⡛⣷⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢿⣄⣀⣤⣤⣴⣶⠟⠛⠋⢉⣤⣶⣮⠀⠀ ⠀⠀⠀⠀⠀⣶⣇⠀⢀⣽⠟⠛⠛⠛⠛⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⢷⣤⣀⠀⢀⣠⣾⠟⠉⠁⠀⠈⢿⡟⠶⣶⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⢷⣾⠇⠀⢀⣤⣤⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣷⠀⠸⣏⠹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⢺⣿⣿⡇⠀⠀⣟⠀⢰⣆⠀⠘⣷⠀⠀⠀⢰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣦⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⢤⡌⠉⠁⠀⠀⠀⠻⠶⠟⠙⠷⠾⠋⠀⠀⠀⠘⠿⠿⠿⠁⣀⢠⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣷⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠚⠋⠀⠀⠀⠀⢠⡟⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠀⢿⣟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⢀⣆⣤⣀⣿⠀⢸⡏⠙⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣛⣿⡿⣿⡿⢛⡁⠸⢷⣀⠀⠀⠀⠈⠙⡛⠷⢶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠾⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣾⡳⣼⣆⠀⠀⢹⡄⠹⣷⣄⢠⠇⠻⣷⣶⢀⣸⣿⡾⡏⠐⠰⣿⣰⠏⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⡹⣟⡪⢟⣷⠦⠬⣿⣦⣌⡙⠿⡆⠻⡌⠿⣦⣿⣿⣿⣿⣶⣿⣿⡿⠾⣙⠄⡉⢳⣔⡀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣟⠛⠛⠙⠛⠉⠻⢶⣮⢿⣯⡙⢶⡌⠲⢤⡑⠀⠈⠛⠟⢿⣿⠛⣿⢟⣏⣃⣵⢯⣧⣽⣕⡟⡐⡿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⠯⣙⠛⢉⣉⣙⣿⣿⡳⢶⣦⣝⢿⣆⠉⠻⣄⠈⢆⢵⡈⠀⠀⢰⡆⠀⣼⣳⠼⡱⣯⣯⣷⢛⣷⣟⡵⣟⣯⡞⣧⡀⠈⣷ ⠀⠀⠀⠖⠉⠻⣟⡿⣿⣭⢽⣽⣶⣈⢛⣾⣿⣧⠀⠙⠓⠀⠑⢦⡀⠹⣧⢂⠀⣿⡇⢀⣿⠻⢏⣿⢟⣟⣿⣹⣾⡏⣖⡩⢿⣗⢡⡂⠀⠀ ⠀⠀⠀⠀⠐⠈⠉⢛⣿⣿⣶⣤⣈⠉⣰⣗⡈⢛⣇⠀⣵⡀⠀⠘⣿⡄⢻⣤⠀⢻⡇⣼⣧⣿⠁⢨⣜⢿⣱⡻⣵⣅⣫⢼⢿⣿⠽⡏⡀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⢍⡉⠛⠻⣷⡆⠨⣿⣭⣤⣍⠀⢹⣷⡀⠀⠹⣿⡄⠈⠀⢿⠁⣿⣿⢏⢂⠐⣷⡷⢿⣼⣾⣗⣭⢭⣿⣿⡕⠏⣇⠀ ⠀⣿⣇⣠⣾⣿⣛⣲⣿⠛⠀⠀⢀⣸⣿⣿⣟⣮⡻⣷⣤⡙⢟⡀⠀⠙⢧⠀⠀⠎⠀⠉⠁⠰⣿⠉⡽⣟⢿⣻⠽⣯⡷⣭⣟⣏⣿⢾⡿⠀ ⠀⠈⢻⣿⣿⣽⣿⣿⣿⣴⡏⠚⢛⣈⣍⠛⠛⠿⢦⣌⢙⠻⡆⠁⠀⠀⠀⣴⣦⠀⠀⠀⠐⢳⢻⣧⣥⡹⢫⢟⣗⣿⣿⣧⣯⣟⠾⠋⠀⠀ ⠀⠀⠈⠙⣿⣧⣶⣿⠿⣧⣴⣿⢻⡉⠀⢀⣠⣴⣾⡟⠿⠃⠁⣠⣤⡶⣾⡟⠅⠀⣀⡄⠀⣾⢸⣿⣿⢻⣾⣿⣯⣿⣿⣿⣿⣿⣡⣤⡄⠀ ⠀⠀⣠⣞⣋⣿⣿⣾⣿⡿⡛⣿⡟⣤⢰⡿⠟⠉⣀⣀⣤⣤⡠⠙⢁⣾⡿⠂⠀⣿⠟⣁⠀⣹⠀⣹⣿⡟⣼⣿⣿⣿⣿⣟⣿⣿⠁⠀⠀⠀ ⠀⢠⡿⢛⢟⣿⣿⣿⣿⣿⣿⡟⣼⣿⣟⢓⠛⣿⣏⣿⣵⣗⣵⣴⣿⢟⡵⣣⣼⣿⢟⣵⣶⢻⣶⣿⠀⠀⣈⢻⣿⣿⣿⢿⣾⢿⣧⠀⠀⠀ ⠀⠘⠃⢸⣿⡾⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣟⣾⡿⣫⣿⣿⣿⣽⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣴⡎⣻⣿⡏⣿⢿⣧⣿⡿⣿⡆⠀⠀ ⠀⠀⠀⠜⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣖⣿⢿⣿⡿⣿⣿⣿⡿⢡⢯⣿⣿⣿⣿⣿⣿⣿⣧⡿⣾⣷⣿⣿⣿⣿⡇⠉⠁⠀⠀ ⠀⠀⠀⠀⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⡇⣭⣿⣿⣿⣿⠃⠞⠟⣸⣿⠏⣸⣧⣀⠿⢿⣿⣿⣟⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⣹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢶⣦⣄⣿⠏⠀⣿⣟⣿⣶⠾⣿⣟⣋⣛⣿⣿⣿⣿⡇⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠛⠫⣿⣿⣿⣿⣿⡿⣧⠛⣿⠻⣿⣿⣿⣷⡌⠹⡟⠀⠀⠉⡟⠋⢠⣾⣿⣿⣿⡟⣿⣿⣿⣿⢀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠋⣾⣷⣿⣿⣧⠙⠀⠙⢣⠝⠛⠋⣽⣷⢦⠇⠀⠀⠘⠁⣤⣾⣿⠝⠛⠉⠘⢻⣿⣿⢿⣼⣷⡟⢻⣷⠉⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠟⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣾⠟⠀⢸⣷⣿⡇⠀⠛⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢹⣇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⣀⡄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⢻⣆⠀⠛⠁⠶⣶⣶⣶⣶⣶⣶⡶⠆⠘⠋⣠⡾⢫⣾⡟⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⣿⠛⠀⠙⣷⡀⠀⠀⠙⠛⠛⠛⠛⠋⠁⠀⢀⣴⠋⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣤⣿⣰⣦⡀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠐⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡄⢺⣿⡄⠹⣿⠻⢦⣤⣤⣤⣤⣶⣿⡟⢀⣀⠀⠀⢸⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⡀⠹⡷⣦⣀⡀⡀⢸⣿⠏⢠⣾⣿⠀⠀⣾⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣷⣻⡟⠀⡼⠁⣴⣿⣿⣯⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⣴⡾⠗⠛⢮⡑⢦⠄⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡞⠉⠁⠉⡇⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢲⡏⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣰⣟⡀⠀⠀⠀⢹⠀⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣠⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⣠⠂⠀⢀⢿⠏⠁⠀⠻⡶⡿⣅⣸⡖⢨⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡽⢧⠤⠤⣄⡀⢆⠀⠀⢀⡴⣫⡀⠀⠀⠀⠀⢳⣤⣤⠤⡤⠞⠁⠀⠚⠁⡌⠀⠀⠀⠀⢹⡉⠉⠛⠦⣸⠸⡆⠀⠀⠀ ⠙⢶⣤⡀⠀⢠⡇⠀⠀⢧⠀⠀⠉⠠⠕⣦⡾⠋⠁⠈⠓⠒⠒⠒⠉⠀⠈⠉⢣⡀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣇⠀⠀⠲⢾⣷⣷⠀⠀⠀ ⠉⠉⠉⠁⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠦⣄⣀⡞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡼⢹⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣇⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠉⠉⢻⡁⠀⠀⠀⢸⠀⠀⠀⠋⠁⠈⡇⠀⠀ ⠀⠀⠀⠀⠀⠞⢳⡀⠀⢠⡞⠁⠀⡔⠁⠀⠀⣴⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢷⡦⠤⠤⢞⡄⠀⠀⢤⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠃⣼⡴⢀⡞⠀⠀⠀⣰⢣⠃⠀⠀⠀⠀⠀⠘⣶⡀⠀⠀⡀⣆⢧⠀⠀⠀⢀⠘⣧⠀⠀⠀⠉⠛⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⠁⡜⠀⠀⠀⣰⡏⡸⡸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⠘⣼⠀⠀⠀⡼⡀⣎⠳⢄⡠⠖⠋⠹⣏⢹⡀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⢫⢿⣿⢁⢶⠁⠀⠀⢠⢿⠀⠁⠁⠀⠀⠀⠀⢠⠀⠈⣧⠀⠀⠈⠀⠛⡇⠀⡔⠀⢧⠹⣇⠀⠸⡄⠀⠀⢹⡆⠃⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⣿⣼⡇⣎⠊⠀⠀⠀⡎⡇⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⣧⠀⠀⠁⠘⠀⠿⠀⢠⠇⠀⠀⢸⣿⡀⣦⠘⡆ ⠀⠀⠀⠀⠀⠀⣸⣿⢰⡹⠀⠀⠀⣰⠃⣇⡇⠀⠀⠀⢀⡀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⣠⡿⣦⡤⣤⣼⣿⡛⠿⣦⢓ ⠀⠀⠀⠀⠀⣰⡟⡇⢸⡇⠀⠀⠸⣿⠀⣟⡆⠀⠀⠀⢸⡇⠀⠀⣿⣧⢻⠀⠀⠀⣠⣤⡇⠀⠀⠀⠀⠀⠀⢿⣾⠨⡇⣸⢻⡿⣿⡲⢈⡶ ⠀⠀⠀⠀⣠⣿⠃⣧⢸⣇⠀⠀⢀⡇⠙⠫⣇⣀⣀⣠⠬⠧⠶⠼⢹⡿⠾⢔⣒⣭⣁⣼⡇⠀⠀⠀⠀⠀⠀⣺⡟⢠⣇⢧⠸⣾⣿⡇⡫⢇ ⠀⠀⢀⣼⡿⠉⠀⣿⢞⡎⠋⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣿⣇⡾⢿⠘⢳⡬⢿⣗⢂⣄ ⠀⢠⡾⣽⠁⠀⠀⠈⠈⣷⣤⣼⣶⣷⣷⣶⡖⠃⠀⠀⠀⠀⠀⠀⠐⢾⣿⣶⣾⣦⣖⣾⣤⠄⠀⠀⠀⠀⠀⢻⡜⢷⡘⢮⠙⢷⠤⣽⣿⠋ ⢠⡿⢡⡏⠀⠀⢀⠀⠀⣾⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⣿⠭⠋⠀⠀⠀⠀⠀⠀⣧⠀⡷⡞⢿⢽⣖⠉⠀⠀ ⡞⠀⣾⠁⠀⠀⣸⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠁⠀⠀⠀⢨⠀⠀⢸⣿⡼⢹⠁⠀⠈⣿⡄⠀⠀ ⡇⠀⣿⢠⠀⠀⣿⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡼⠀⠀⢠⣧⠇⡾⠀⠀⠀⢻⡇⠀⠀ ⠁⠰⢿⣼⣄⠀⢻⠀⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢠⢏⡇⠀⠀⢸⣿⠠⠇⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠙⣧⣰⡿⣆⣴⡎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⡞⣸⠀⠀⣰⢇⣿⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠘⢿⡶⢿⡧⣿⣻⣯⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠐⠐⠛⢠⠃⠀⡰⠃⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠶⠤⣤⣍⡻⣿⠁⠀⠉⠓⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⡷⣀⡤⠶⣤⠏⠀⢛⣁⡴⣣⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠀⠀⣸⢀⡇⠀⠀⠀⠀⡼⠀⠈⠙⢲⣶⣶⠲⣿⣭⡤⠊⠀⡗⠛⢦⠤⣟⡋⣿⣽⠿⡏⠁⠘⡌⠹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⢠⣧⣼⡄⣀⡀⠀⣸⢃⣀⣀⣀⣸⢼⣏⣀⠼⠋⠀⠀⣸⠋⠉⠙⠒⠥⣟⠟⡁⠀⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⣀⡀⣾⣿⡟⠉⣩⣹⠞⠉⠉⠉⠁⡝⣣⢾⠋⢀⣀⠤⣖⣪⠇⠀⠀⠀⠀⢰⡃⠀⢧⠀⢇⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⠾⢷⢠⡤⣤⣹⣿⠉⡇⠀⠏⠀⠀⠀⠀⠀⡸⣷⣿⣿⣭⣵⡶⠿⢛⡏⠀⠀⠀⠀⢠⠃⠙⠦⣘⡄⠸⡄⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⢀⠄⠀⠈⠁⠈⣹⢻⣯⠀⢣⠀⣷⠃⡀⠀⠀⠰⠥⠿⣻⠟⠉⠀⢀⣠⡾⠶⣒⡤⣀⢠⠏⠀⠀⠀⠈⠛⠦⡷⠤⠤⠤⢤⠈⢇⠀⠀⠀⠀ ⠀⠀⠠⠔⠒⢋⡏⠀⡟⠀⢸⠀⡿⢤⡈⣂⠀⠀⠀⠈⠀⠀⠀⠀⢻⣿⣽⡒⢲⢬⣙⣯⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡧⢸⡟⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⢀⡸⢷⠀⢸⠀⣷⠀⠙⠚⠲⡐⠤⠀⠀⠀⠀⣴⣏⠀⠀⠛⠛⠷⣧⡿⠀⠀⠀⠀⠀⠀⠀⣸⠄⢀⣠⠿⠁⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⢰⢁⡞⠀⣼⡄⢸⡄⣿⠀⠀⠀⠀⠈⠒⣋⣧⣡⣶⠛⡌⢣⣀⣀⣠⢴⠧⠤⠴⠶⠒⠒⠒⣋⡭⠖⠚⠉⠀⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⢀⣣⠎⠀⠀⠈⡗⠀⡇⢸⠢⠠⠴⠒⠋⠉⢁⣀⣠⡇⠔⢚⠉⠀⠐⠂⣯⡤⠴⠖⠒⠚⠛⠉⢁⣀⣀⣀⢤⡄⡀⠲⠈⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⠿⠻⢶⣍⠳⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⠟⠉⠉⠈⢹⡇⢸⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⠙⢳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢀⣼⠏⠀⠀⠀⠀⠘⡇⠀⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣶⠞⠛⢶⣀⢀⣀⡀⠀⣷⡀⠸⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠨⣧⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⠟⡿⠁⠀⠀⠀⢻⡏⣿⣳⣤⡿⠟⢰⡾⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⠿⣶⠶⠤⣄⣀⠘⣦⡀⠀⠀⢀⡴⢚⣦⡀⠀⠀⠀⠀⠀⢘⣆⣴⣶⠶⢶⠶⠋⠀⠀⠐⠋⠁⣰⠁⠀⠀⠀⠀⠀⢻⡈⠉⠘⠛⠦⢈⡇⢻⡆⠀⠀⠀⠀ ⠳⢶⣄⣀⠀⠀⠀⢸⡏⠀⠀⠘⣇⠀⠀⠉⠉⢈⡳⣤⣠⣾⠗⠋⠉⠙⠶⠦⠤⠤⠴⠞⠉⠉⠉⠉⢿⣀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢴⣼⣿⣮⣷⠀⠀⠀⠀ ⠶⠶⠿⠿⠇⠀⠀⢸⠁⠀⠀⠀⢸⡄⠀⠀⠀⠈⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⠙⣻⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣠⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⠓⠶⠶⠧⢤⣀⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣾⠋⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢣⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠏⢷⡀⠀⠀⢠⡾⠋⠀⢀⡴⠁⠀⠀⠀⣠⢆⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⢿⣦⢤⣀⣠⡞⡇⠀⠀⠀⢠⡀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡶⠀⣼⢁⡆⢀⡞⠀⠀⠀⠀⢀⡟⡾⠀⠀⠀⠀⠀⠀⠀⠀⢷⢠⠀⠀⠀⠀⠀⣜⢻⡀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠛⠒⢦⡀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣼⢯⡟⠀⡼⠁⠀⠀⠀⢠⡿⢀⠇⡴⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⣦⠹⡌⣧⠀⠀⠀⠀⢷⠀⡹⢦⡀⠀⠀⢀⣠⠴⢿⣶⠶⡆⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣯⡏⠀⣸⠃⠀⠀⠀⢠⣿⠁⡼⢰⠃⠀⠀⠀⠀⠀⠀⢀⠀⣷⡆⠀⠀⠀⢹⡀⢷⣿⠀⠀⠀⠀⡞⡆⢻⡄⠙⠶⢶⡉⠁⠀⠈⢿⡆⢹⡄⠈⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢫⡿⣿⡞⢀⣇⡇⠀⠀⠀⢀⡟⡏⠀⠀⠈⠀⠀⠀⡆⠀⠀⠰⡀⠀⠈⣷⠀⠀⠀⠈⠁⠘⢹⠀⠀⢠⢳⠀⢷⠘⣿⡀⠀⠘⡇⠀⠀⠀⢸⣿⡌⠃⠀⠸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⢃⣞⡜⠀⠀⠀⠀⣼⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠀⠘⠀⢹⡇⠀⢀⡇⠀⠀⠀⠀⣿⣧⠀⢠⡀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⢸⢿⠀⠀⠀⠀⣠⡏⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⠀⠀⠀⠀⠀⠀⠄⡟⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣁⣀⠀⠀⢠⣿⣿⣷⣾⣧⡈⢇ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⡎⡏⠀⠀⠀⢠⣾⠀⣿⣾⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⣼⣧⢠⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⣾⢯⠏⣿⠉⢛⣿⣿⣹⣆⣉⡙⢷⠐ ⠀⠀⠀⠀⠀⠀⢀⣾⡏⣿⠀⡇⡇⠀⠀⠀⠙⣿⣄⢻⣼⡀⠀⠀⠀⠀⢠⣟⠀⠀⠀⡿⣿⣾⣿⠀⠀⢀⣀⣤⢶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⢺⢆⣼⢻⡿⠻⢿⡍⢃⣸⡟ ⠀⠀⠀⠀⠀⢀⣾⡿⠁⡇⡆⡇⣇⠀⠀⠀⢀⡇⠈⠛⠦⣇⣀⣀⣀⣠⠾⠿⠶⠷⠶⠇⣿⡧⠿⠶⣚⣩⣧⣀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⣾⡀⢧⠘⢿⣿⣿⣏⢉⡴⢆ ⠀⠀⠀⢀⣴⣿⡗⠃⠀⢳⣧⣹⡜⠖⠒⠋⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢠⣿⣿⠘⢷⣄⣸⣿⣷⠮⠀⠉ ⠀⠀⢀⣾⢿⡏⠀⠀⠀⠸⠏⠻⣇⠀⠠⣤⣠⣤⣤⣄⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣠⣤⡠⣄⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠹⣿⡀⢿⡰⢦⣿⡍⠙⠳⣶⣽⠗ ⠀⢰⣿⢇⣿⠁⠀⠀⠀⠀⠀⢀⢿⣻⣿⣿⣿⡿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⣿⣿⣿⣾⣿⣟⣁⠀⠀⠀⠀⠀⠀⠀⣸⡇⠘⢷⣀⡻⣦⣬⣛⣉⣻⠿⠇⠀ ⢰⣿⠇⣸⡇⠀⠀⠀⢠⠀⠀⢈⣿⡄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡟⠶⠁⠀⠀⠀⠀⡀⠀⠀⣿⣿⠀⣸⢿⡏⠹⠿⢿⣯⡁⠀⠀⠀ ⡾⠁⠰⡿⠁⠀⠀⠀⣸⠀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⠀⠀⠀⠀⠀⢀⠇⠀⠀⢹⣿⣴⡟⣼⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⡇⠀⢸⡇⢀⠀⠀⠀⣿⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⣯⡾⢀⡇⠀⠀⠀⠈⣷⢿⠀⠀⠀ ⡷⢀⣸⣇⢸⡀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⡆⡟⠀⠀⠀⢸⣿⡇⢸⠇⠀⠀⠀⠀⠈⢸⠀⠀⠀ ⠀⠈⠙⠿⣾⡷⠄⠀⣹⡄⠸⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡾⢸⠃⠀⠀⢀⣾⣿⠁⠚⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣄⣸⡿⣷⣠⣾⡏⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣠⡾⠁⡿⠀⠀⢠⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⡶⣿⣿⣸⣷⢻⣿⣹⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠆⠾⠿⠁⣼⠁⠀⢠⡞⠁⣼⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣹⣅⣈⣉⡘⠿⣿⡿⣿⠀⠈⠙⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⠀⠀⣀⣀⠀⣸⠃⠠⠶⠟⠀⣸⢇⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠁⠉⠉⠙⠻⢷⡞⢹⡇⠀⠀⠀⠀⠀⣩⠙⠲⠦⣄⣀⣀⣀⣀⣀⣀⡤⠴⠶⣲⠿⢹⣝⣶⡞⠉⠙⣿⣃⣤⣤⠴⣶⣚⣵⠟⢹⡿⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡾⠀⡼⠀⠀⠀⠀⠠⢠⡟⠀⠀⠀⠀⠉⡿⣽⣿⠙⠷⣿⣶⠶⠉⠀⢸⣍⣉⣙⡖⠻⡯⣅⣰⣿⣺⠟⡏⠀⠀⠀⠇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣸⣧⣶⣇⢀⣀⠀⠀⢀⡿⢀⡀⢀⣀⣀⣠⡵⣿⣏⣀⡤⠞⠉⠀⠀⢀⡿⠁⠉⠉⠉⠛⠦⣼⡽⢻⡁⠀⡇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⣿⣯⣿⠛⠋⣉⢻⡴⠟⠋⠉⠉⠉⠉⡽⢧⣴⣿⠋⠉⠀⣀⣀⡤⠶⣿⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣧⠀⢹⡀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣏⠀⠀⠀⠛⠶⣾⣿⠻⡇⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⣴⣀⣾⣷⡧⠴⣖⣚⡭⣷⣾⣿⠃⠀⠀⠀⠀⠀⢀⡞⠳⣄⠀⠹⡄⠘⣇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⢘⠤⠟⣛⣿⣾⣿⡏⠀⢹⠀⢸⡀⡠⠀⠀⠀⠀⠀⣰⠉⣿⣟⣿⣶⠿⠿⠚⠍⠉⣰⣏⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈⠙⢦⣿⡀⢹⡆⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⣿⡇⠀⢸⡄⢸⡏⠁⣀⠀⠀⠀⠀⠳⠒⠟⣿⠿⠹⠀⠀⠀⣀⣶⣛⠻⠿⢝⣶⣤⣀⡾⠁⠀⠀⠀⠀⠀⠈⠙⢶⡟⠶⠶⠶⠶⢶⣀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠴⠖⠛⢻⡏⠀⢸⡇⠀⢸⡇⢸⣟⣤⣀⢓⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣻⣏⣹⡒⠲⣦⣉⣉⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡆⢨⡟⠛⢿⡆⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⢀⡟⠀⢀⣾⡅⠀⠈⡇⠸⡇⠀⠛⠮⠿⢤⠀⣄⡀⠀⠀⠀⠀⠀⣀⣾⠉⠉⠉⠷⠶⢿⣤⣿⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⠀⣠⣾⠇⠀⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠁⣼⠃⠀⣧⠀⠀⡇⠀⡇⠀⠀⠀⠀⠈⠳⣌⣡⡴⣆⠰⢀⣀⣿⡙⢦⡀⠀⠀⠀⠈⢁⡟⠋⠁⢀⣀⣀⣀⣀⣀⣤⠴⠶⣛⣣⠶⠞⠋⠀⠀⠂⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⣼⠃⠀⠰⣿⡆⠀⣧⠀⣧⠀⠀⠀⠀⠀⣀⣀⣀⡤⠽⠶⠾⡿⠁⠻⣀⣷⠤⠶⠶⠖⣿⠃⠉⠉⠉⠉⠉⣉⣉⣀⡤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣈⡼⠃⠀⠀⠀⢸⡟⠀⢸⡄⣿⠠⠠⠶⠖⠛⠉⠉⠀⢀⣀⣀⣾⢁⠖⢋⡉⠀⢀⠂⠀⢀⣷⡴⠶⠶⠚⠛⠋⠉⠉⠁⢀⣀⣠⣠⣀⣆⣖⠆⡀⠘⠆⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣷⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣟⢀⡴⠋⠀⠀⣿⠖⠋⢀⡏⠀⠀⠀⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⡼⠀⢸⡟⡸⠀⠀⠀⠃⠀⠀⢸⡧⠜⠛⠛⣻⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢺⢾⡃⠀⠈⣴⠁⢻⡀⠀⠀⢀⡠⠀⠀⠀⠀⢸⣇⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡜⠂⠀⠀⣟⠀⢸⠑⠀⠰⠁⠀⠀⠀⠀⠀⠛⠉⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⣿⣿⣿⣿⣾⣶⣶⣤⣀⡀⢰⠕⠋⠀⠀⠸⠧⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣔⠈⣤⣶⡚⠁⠀ ⠀⠀⠀⠀⣠⣶⡀⢸⡟⠿⡿⠿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠋⠁⠀⠀⠀ ⠀⠀⠀⢰⢧⡷⡿⢘⡎⠀⠀⠐⣶⢶⣲⠈⠙⠋⠉⠉⠁⡘⡯⣿⡶⣆⡀⠀⠀ ⠀⠀⠀⢾⢈⣼⣿⣤⣿⣶⣶⣶⣿⣿⣧⣤⣄⣀⣀⣤⣾⣿⣿⢯⢇⣿⢳⠀⠀ ⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣷⣬⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⡀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣶⣴⣿⣿⣿⡧⠀⠉⠙⢿⣿⣿⣿⣿⣾⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠛⠿⣿⣿⡇⠀⠀⠀⠀⠻⣿⣿⣿⡿⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⢟⣭⣴⣾⣿⣿⠉⠭⠩⣤⡉⠻⠷⣦⣌⡙⠻⣶⣮⠙⠿⣿⣿⣳⣜⢦⡀⠀⠀⠀⠀⣀⡴⠋⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⢤⣄⡀⠀⠑⠢⢤⣀⠀⠀⠀⣠⣾⢟⣵⣿⣿⣿⡿⠋⢿⣆⣠⢓⡘⢿⡆⠀⠈⢹⣿⣶⡝⢿⣧⡀⠘⢷⣝⢮⢷⡕⣄⣀⡴⢚⣩⣶⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠑⠒⠢⣤⣌⣉⠒⣾⠋⢀⣾⣿⣿⡿⠃⠀⠀⠸⡏⠀⢸⣷⠘⣿⡄⠀⢲⡝⢿⣿⣦⣻⣿⣦⡈⢿⣦⠀⠹⣮⢳⣾⠋⠉⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠋⢉⡿⠁⢀⣾⣿⣿⡿⠃⠀⢀⣼⢠⣿⣠⢸⣿⡇⢸⣿⣆⣘⢧⠈⠻⣿⣿⣿⣿⣷⡀⠙⣧⠘⣏⢧⡙⣦⡀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⠁⠀⣾⣿⣿⠿⢁⠀⢀⡼⠁⣼⣿⣿⡈⣿⣷⡀⣹⣿⣾⣷⡀⠀⣘⠿⢿⣿⣿⣷⡄⠙⣧⠈⠈⢻⡜⢷⡀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣏⡶⣼⠇⣠⣸⢏⣿⡿⢠⡏⡼⣿⠃⢰⣿⣿⢿⡇⢿⡟⢷⣷⣿⣿⣷⣿⣆⠀⠐⣿⣻⣿⣿⣿⣄⠸⣧⡀⠀⢻⣎⢷⣤⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡏⣰⢣⡟⣼⣿⢃⡏⣼⣷⡏⢠⣿⣿⡇⠈⣧⠸⣿⡀⢻⣯⢿⣿⣿⣿⣧⠀⠈⢿⣿⣿⣿⣿⣆⠙⣷⡄⠀⠹⣧⡻⣷⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⢸⡿⣼⣹⣿⡏⡾⢱⡟⢸⡇⣾⣿⡟⠀⠀⠹⡆⣿⣇⠀⠙⢷⡝⢿⣿⣿⣷⣤⡀⠻⣿⣿⣿⣿⣧⡙⣿⣄⠀⠹⣷⣻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣧⣿⢇⣿⣿⣿⢱⠃⣾⠁⣸⣿⣿⡟⠀⠀⢀⣠⢿⡸⣿⡄⠀⠈⠻⣦⠉⠻⢿⣿⣿⣧⣽⣿⣿⣿⣿⣷⡘⣿⣧⡀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⡏⣼⣿⣿⡿⢸⠀⣿⢀⣿⣿⡏⣠⡤⠚⠉⠀⠀⢳⣽⣷⡀⠀⠀⠈⠳⢄⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡄⠈⢻⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡟⣸⣿⣿⣿⢇⡇⣰⡇⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⡵⢒⣦⣖⡊⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⢳⣿⣿⣿⣿⢸⣃⣿⠇⣿⡟⠀⢀⣠⢴⣂⣐⠦⠄⠀⠀⠹⣿⣧⠀⠀⠀⠀⢰⣿⠛⢻⣿⣿⣷⣮⡿⢿⣯⣿⣿⣿⣿⣿⣷⣄⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⢧⣿⣿⣿⣿⡿⣼⣿⣿⢀⣿⠀⣀⣼⣾⠿⣿⣿⣶⡄⠀⠀⠀⠈⢿⣧⠀⠀⠀⠚⣷⣤⣾⣿⣿⣷⠹⣿⣦⣿⣯⢹⣿⣿⣿⣿⣿⣧⣀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⢉⣿⢿⣅⣠⣿⣿⣿⡅⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⣿⠿⣿⣿⣿⣿⠀⣸⡿⢿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⡯⣿⣿⢸⣿⣿⡏⢸⣿⣿⣯⣿⠟⠷⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⢦⣐⣀⡢⢆⠀⠉⠀⢸⣿⡇⣿⣿⣿⣿⣿⡛⣿⢿⣿⣿⣿⣿⣷⣄⡀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⣿⡇⠀⣿⢿⢿⡿⠿⠷⣄⠻⣄⣉⣉⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠛⠛⠁⠀⠀⠀⢞⣿⡆⣿⣿⣿⣿⣿⣧⡹⡆⠈⠉⠛⠛⠿⠿⠿⣦⣄ ⠀⠀⢠⣾⣿⣿⠏⢸⣿⣿⣿⡷⢸⣿⠘⢸⣿⠀⠀⠀⠀⠚⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣿⣿⣿⣿⣿⣿⣷⣻⡄⠀⠀⠀⠀⠀⠀⠀⠈ ⢀⣴⢟⣿⣿⠋⠀⢸⣿⣿⣿⡇⣸⣿⡆⠩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⢾⣿⣿⣿⡌⠻⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠋⢁⣾⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣿⢸⣿⣿⣿⣿⣦⣤⣴⠟⠋⠉⠙⠲⣄⠀⠀⠀⠀ ⢀⣾⠋⠀⠀⠀⠀⢸⣿⣿⡿⠟⣿⣿⣿⠀⢸⡏⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⣧⣿⣿⣿⡿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀ ⠋⠁⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⣿⣿⣿⣇⠀⣷⡀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⢹⣿⣿⣿⡄⣸⣷⡀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣿⡈⢿⣿⣏⢸⣷⡄⠀⠀⠀⠀⠈⠻⣖⠤⢄⣀⠀⠀⠀⠀⣠⠖⢫⡏⠀⢀⡔⠀⠀⣸⣿⠟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠙⢿⣿⣿⣝⠶⣄⡀⠀⠀⠀⠈⠳⣄⡈⠉⠒⠒⠋⠁⢠⠏⢀⡴⠋⠀⠀⣰⡿⠋⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⢠⠀⠀⠀⠀⠘⢆⠀⠀⠉⠛⠿⢆⡈⠉⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⣰⣋⡴⠚⠀⠀⠀⡴⠛⠁⣸⢹⣿⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣇⠀⠀⠘⣆⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢷⠓⠢⣄⠀⠀⠀⠀⠀⠀⢰⠇⣾⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠘⠆⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⠟⠀⠈⢧⠀⠈⠳⣄⠀⠀⠀⢠⠇⠀⣿⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⢹⡆⠀⠀⠀⢦⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡎⠀⡔⠲⡌⢳⡀⠀⠈⠳⣄⣰⠏⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡟⢸⣿⣦⠀⠀⠀⠳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠟⠀⠀⢧⣀⡼⠀⡇⠀⠀⠀⠀⠁⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠘⣿⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡇⠘⣿⣿⣷⡀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⠃⠀⣿⣿⣿⣿⣦⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⢿⣿⣿⣿⣿⡟⣦⡀⢠⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⡰⠃⣠⠆⠀⠀⠀⣸⢻⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⢉⠤⠐⠋⠈⠡⡈⠉⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⢠⣤⠔⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠈⠱⡤⣤⠄⣀⠀⠀⠀⠀⠀ ⠀⠀⠰⠁⠀⣰⣿⠃⠀⢠⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢞⣦⡀⠈⡇⠀⠀⠀ ⠀⠀⠀⢇⣠⡿⠁⠀⢀⡃⠀⣈⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢢⠰⠀⠀⢺⣧⢰⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⠁⡘⠀⡌⡇⠀⡿⠸⠀⠀⠀⠈⡕⡄⠀⠐⡀⠈⠀⢃⠀⠀⠾⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⡇⠃⢠⠀⠶⡀⡇⢃⠡⡀⠀⠀⠡⠈⢂⡀⢁⠀⡁⠸⠀⡆⠘⡀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⢸⠀⠘⡜⠀⣑⢴⣀⠑⠯⡂⠄⣀⣣⢀⣈⢺⡜⢣⠀⡆⡇⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠇⠀⢸⠀⡗⣰⡿⡻⠿⡳⡅⠀⠀⠀⠀⠈⡵⠿⠿⡻⣷⡡⡇⡇⠀⢸⣇⠀⠀⠀ ⠀⠀⢰⠀⠀⡆⡄⣧⡏⠸⢠⢲⢸⠁⠀⠀⠀⠀⠐⢙⢰⠂⢡⠘⣇⡇⠃⠀⠀⢹⡄⠀⠀ ⠀⠀⠟⠀⠀⢰⢁⡇⠇⠰⣀⢁⡜⠀⠀⠀⠀⠀⠀⠘⣀⣁⠌⠀⠃⠰⠀⠀⠀⠈⠰⠀⠀ ⠀⡘⠀⠀⠀⠀⢊⣤⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢸⠃⠀⠀⠀⠀⠀⠃⠀ ⢠⠁⢀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠸⠀ ⠘⠸⠘⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢠⠀⠀⡇ ⠀⠇⢆⢃⠀⠀⠀⠀⠀⡏⢲⢤⢀⡀⠀⠀⠀⠀⠀⢀⣠⠄⡚⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀ ⢰⠈⢌⢎⢆⠀⠀⠀⠀⠁⣌⠆⡰⡁⠉⠉⠀⠉⠁⡱⡘⡼⠇⠀⠀⠀⠀⢀⢬⠃⢠⠀⡆ ⠀⢢⠀⠑⢵⣧⡀⠀⠀⡿⠳⠂⠉⠀⠀⠀⠀⠀⠀⠀⠁⢺⡀⠀⠀⢀⢠⣮⠃⢀⠆⡰⠀ ⠀⠀⠑⠄⣀⠙⡭⠢⢀⡀⠀⠁⠄⣀⣀⠀⢀⣀⣀⣀⡠⠂⢃⡀⠔⠱⡞⢁⠄⣁⠔⠁⠀ ⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⣀⠴⠚⠛⠉⠉⠉⠉⠉⠙⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣄⠈⢳⡀⠀⢇⠈⠉⡆ ⢰⠃⠀⠀⣠⠶⠚⠋⠙⠲⣄⠀⠀⡰⢁⣤⣄⡈⢳⡀⣧⠀⣀⡑⠊⠀ ⣼⠀⠀⡞⠁⢀⣤⢾⣿⣶⣬⣳⡄⣷⠛⢻⣿⣿⡄⣷⢸⡆⠣⠜⠀⠀ ⡿⡀⢸⠁⢠⣧⣀⡼⢿⣿⣿⡏⡿⣿⣷⣯⣿⣿⣷⡟⣼⡇⠀⠀⠀⠀ ⠰⢡⠈⢆⣿⣿⣿⣿⣿⣿⢿⡿⠃⢻⣿⣿⣿⣿⡟⠀⡙⠀⠀⠀⠀⠀ ⠀⠑⢄⠀⠛⠿⠿⣿⠿⠿⠛⠁⠀⠀⠙⠛⠛⡁⡠⠊⠀⠀⠀⠀⠀⠀ ⠀⡄⠒⠳⣴⡢⣄⣁⠀⠀⠀⠀⢀⣀⡤⣔⠏⠊⢁⡤⠒⢠⠀⠀⠀⠀ ⠀⠱⡄⠀⢿⣀⠉⣘⣛⣛⡛⠉⠋⢈⣁⣀⣀⣀⣸⠀⢀⡞⠀⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠈⠙⣽⠛⠉⠀⠀⠈⠉⠁⠀⠈⢿⠀⠀⠀⠀ ⠸⣿⠀⠀⠀⠀⠀⠉⠛⣧⠈⠉⠐⢺⡟⠉⠁⠀⠀⠀⠀⣸⡄⠀⠀⠀ ⠀⠀⠑⢄⣀⠀⠀⠀⣸⠇⠀⠀⠀⠘⣇⡀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠹⣧⡀⠀⠀⠀⡏⠉⠙⠋⢹⡆ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠛⠿⣦⡀⠀⠸⣷⡀⠀⠀⠹⣄⠀⠠⡹⠃ ⠀⢀⣿⠃⠀⠀⠀⠀⣠⣶⠾⠟⠛⠉⠉⠛⠿⣶⣄⠀⠀⠀⠀⣰⠃⢀⣠⣤⣄⠀⠈⢻⣦⠀⢻⣧⠀⠀⠀⠈⠓⠋⠀⠀ ⠀⢸⣿⠀⠀⠀⣠⣾⠋⠁⠀⠀⢀⣠⣤⣤⣤⣈⠙⣷⣄⠀⢠⣏⣶⣿⣿⣿⣿⣿⣦⠀⢻⣧⠘⣿⢀⢸⡛⠛⢲⠀⠀⠀ ⠀⣾⡇⠀⠀⢠⡿⠁⠀⠀⣠⣾⡿⢿⣿⣿⣿⣿⣷⣌⢿⣆⢸⣿⡋⠉⢉⣿⣿⣿⣿⣧⠈⣿⠀⣿⣿⠀⠹⠶⠋⠀⠀⠀ ⠈⡟⣿⠀⠀⢸⠇⠀⢀⣼⣄⠈⠀⣸⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣶⣿⣻⣿⣿⣿⣿⣤⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⢹⡆⠀⢸⡄⠀⣾⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏⣸⢧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⢳⡀⠈⢧⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢎⠃⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⡿⠟⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⡻⠿⢿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣀⡀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠬⣷⣄⡲⣤⣈⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢛⡵⠚⠁⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⢻⣿⠒⠭⣟⣷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣶⢾⣟⠯⠗⠊⠁⠀⠀⠀⣾⠟⠁⠀⢘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣧⠀⠀⠈⣿⡄⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠇⠀⠀⠙⠛⠛⠒⠒⠛⠛⠛⠻⠿⢷⡢⣤⣔⡶⠿⠟⠛⠛⠛⠻⠿⠽⠟⠁⠀⠀⢺⡿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⠒⠲⠛⠙⠲⠦⢼⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⠀⠀⠀ ⠀⠀⠹⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣴⢯⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⣖⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⠮⣷⣶⡤⡤⠴⠾⠟⠋⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⡤⠖⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠲⢤⡀⠀ ⢀⡟⢠⡖⠋⠙⢳⣤⠽⠖⠛⠉⠉⠉⠉⠉⠉⠙⠓⠾⣤⡖⠋⠙⠲⡄⠹⡄ ⢸⡀⣿⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⣹⠀⡇ ⠈⢧⣘⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣏⡴⠃ ⠀⠀⡽⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢹⡀⠀ ⠀⠀⡇⠀⠀⠀⠠⣯⣽⡇⠀⣠⠴⠚⠓⠲⣄⠀⢰⣯⣽⡇⠀⠀⠀⠀⡇⠀ ⠀⠀⡇⠀⠀⣀⣀⣉⠋⢁⡞⠁⠀⣤⣤⠀⠈⠳⡄⠉⣋⣁⣀⠀⠀⠀⡇⠀ ⠀⠀⣇⠀⠘⠻⠿⠟⠃⢸⠀⠦⣄⡼⢯⣄⡤⠆⣷⠘⠻⠿⠟⠃⠀⢰⠇⠀ ⠀⠀⠹⣄⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⣠⠟⠀⠀ ⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⠤⠤⣤⣤⡤⠤⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠚⠛⠓⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠓⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢀⣀⣤⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣆⠀⠀⠀⠀⠀⠀⣙⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⢠⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀⠀⣿⠉⠀⠀⠀⣰⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠹⣆⠀⢀⣼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠘⣏⠑⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢻⡄⠀⠈⠓⢟⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⢧⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣠⣶⣴⡿⠀⠀⠀⠀⠹⣆⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠙⡷⢤⣤⣸⣆⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⡄⢠⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⣷⡄⠀⢧⠀⠀⠀⠀⠀⢠⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⣧⡟⠹⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠹⣆⠀⢻⡎⠲⢼⣧⠀⠀⣀⡠⠾⣦⣤⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠷⣤⡹⣄⠀⠚⣆⠀⠉⢹⡢⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠙⠳⣄⢻⡇⠀⠈⠁⠈⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠲⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠀⠀⠀⠘⢿⠦⣤⣀⣀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠾⣟⡶⠂⡀⠀⠀⠀⠈⠘⠆⠀⢀⣄⠀⠀⠀⢳⡄⠈⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠖⢛⣿⠫⠢⠶⣏⠉⠹⢥⢶⣻⠜⠛⡗⠤⣠⢚⡇⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⠁⠀⢀⣿⠁⠀⠀⠀⠈⢧⠀⡞⠀⠀⠀⢀⡼⢆⠀⠉⠑⣢⣤⠀⠀⣘⣧⠤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠻⣁⠀⠀⠀⠛⠛⠛⡆⡞⠉⠀⣠⠶⠛⠛⠛⠛⢶⣄⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⣹⣧⡀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠻⣇⠀⠀⠀⠀⣿⠤⣴⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⠀⠀⢀⣿⢈⡇⠀⠀⣀⣀⣤⡴⠟⢉⣹⡟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠙⣷⡢⠴⠒⣹⡶⠟⠀⠀⠀⠀⠀⠀⠀ ⠠⣤⣤⣤⠾⠃⢀⣠⠟⠁⣾⢥⣀⠀⣻⡄⠀⢰⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠛⠒⠛⠋⠁⠀⠀⠙⠶⣬⣭⣽⣋⣒⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢻⠊⠁⢾⠀⠀⠀⠀⠀⠀⠗⡆⢠⡄⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠸⠀⡘⢸⠀⠀⠀⢠⠆⠸⠀⡇⡌⠃⠀⠀⠂⢸⠀⠀⢰⠀ ⠀⠀⠀⣠⠀⠃⢰⢀⠇⠸⠀⠀⢠⢻⢠⠃⠀⣧⢁⣰⠀⣸⣀⡀⠄⠀⠘⠀ ⠀⠀⠀⢃⣷⡾⠿⣾⣝⠂⠆⢠⠃⣨⠂⠀⢀⠗⣡⡼⢿⣛⠒⠯⣕⣆⣀⠀ ⠀⠀⢠⣿⠏⢀⣴⣿⣿⣦⠘⠃⠀⠁⠀⠀⠈⠼⣩⣾⣿⣯⡿⣦⠀⢫⢷⠀ ⠀⠀⣼⣿⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⡹⣿⢷⣸⠀⢸⣸⠇ ⠀⠀⢹⠛⢦⠹⡻⢋⣭⠿⠃⠀⠀⠀⠀⠀⠀⠀⠻⢿⣈⠕⢀⠜⠀⢩⠃⠀ ⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⡠⠤⠤⠢⢴⠶⣦⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡇⢀⠠⠤⠐⠩⠭⣇⠀⠠⠔⠢⠭⡄⠂⠀⠀ ⢀⡈⢆⣇⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠤⠊⠀⠀⠀⠀ ⠀⠈⠑⢭⡉⠒⠤⢂⣀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⢀⡙⣧⠤⠄⣀⡀⠀⠀ ⠀⠀⠠⢉⠆⡰⠑⠤⣀⣟⣍⠁⣒⡒⣒⡂⠀⠀⠉⢀⣀⢇⢌⡅⠀⡀⠀⠀ ⠀⠀⠠⠁⠈⠀⠀⡐⣪⠗⠊⠋⠁⡟⠗⠤⣍⠭⠔⠊⠉⠉⠑⢜⣄⡛⠀⠀ ⠀⠀⠀⠀⠀⠀⡌⣰⠃⢀⣀⡤⠖⠳⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢸⡿⣿⠇⠰⠟⠀⠀ ⠀⠀⠀⠀⣀⡤⣤⠶⠛⠉⠉⠀⠀⠉⠉⠛⠲⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⠀⠀ ⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧⠀⠀⠀ ⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳⡀⠀ ⡞⠀⠀⠹⣆⠀⠀⠆⠀⠀⠓⠊⠙⠚⠁⠀⠀⠀⠀⣰⠇⠀⠀⢻⠀ ⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸⠁ ⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠚⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢀⣀⡀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠀⣠⡶⣶⡀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣼⠋⢻⣦⠀⠀⠈⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⢀⣼⠟⠀⠘⣷⡄⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠁⢸⡏⠀⠀⠻⣧⡀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⠃⢀⣾⠋⠀⠀⠀⠘⣷⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⣸⠃⠀⠀⠀⠹⠷⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁⠸⠏⠀⠀⠀⠀⠀⠸⣧⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠃⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⣠⣶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠃⠀⠀⠀⠀⣰⡟⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⠹⢷⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡏⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⣀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⣤⣤⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢙⡗⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠸⣿⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡏⠀⣿⡆⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡇⠀⠀⠀⠀⣾⣏⣀⣀⡀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀ ⢸⣿⠁⠀⠘⣧⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠙⣷⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠿⣿⣿ ⢸⣿⠀⣤⡾⠛⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⣀⣤⣿⣿⠀⠀⠀⣀⣴⣿⣿⠟⠋⠁⠀⠈⣿⡏ ⢸⣿⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣴⣾⣿⡿⠛⠁⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⡇ ⣿⣿⣶⣤⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⡀⠛⠂⣠⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠟⠋⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠉⠙⠛⠿⠿⢿⣿⣿⣶⣶⣤⣀⣀⠀⠀⠀⠈⠿⣿⣶⣾⠿⠟⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⠿⠿⠟⠛⠋⠉⠁⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠀⠀⠀⠀⢸⣿⠃⢀⣤⠾⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⢸⣿⡶⠟⠉⠀⢸⠀⠀⠀⣠⣤⡀⠀⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣶⡖⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⢸⣿⠀⠀⠀⠀⠸⣧⣠⡾⠋⠉⣧⢀⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣤⣄⣿⣇⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⣀⣤⣤⣤⣤⣄⠀⠀⠙⣿⣷⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⢿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⠿⠛⠙⠻⣿⣷⠀⠀⢻⣿⡆⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠛⣿⣿⠳⣦⣄⣠⡾⠛⣿⣿⣀⠀⣠⣴⠟⠉⢩⣿⡿⠛⠁⠀⠀⠀⠀⢹⣿⡆⠀⠘⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⢹⣿⡇⠀⠉⠉⠀⠀⣿⣿⠛⠿⠋⠁⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⢰⣿⡇⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣤⣤⣿⣿⣧⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣼⣿⣀⣀⣀⣠⣴⣾⣿⣿⣀⣠⣤⣿⣿⣥⣤⣤⣶⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠉⠶⠤⠄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠀⠀⠀⠈⡢⢀⣀⠀⠀⠀⠀⢀⡠⠗⠂⡝ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡀⠀⠀⠀⠀⠀⠙⠢⣀⠀⢇⠀⢠⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀⠀⢩⡀⠀⠀⠀⣀⣰⠀⠈⢦⠀⠑⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⡦⠤⠥⠀⠀⢸⣿⡏⠀⠀⠀⢣⢰⡅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⡄⠹⡢⢰⡀⠀⣀⢆⡘⠟⠁⠀⠀⠀⠘⠇⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠈⠒⠵⣄⢱⡀⠹⠚⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣂⡀⠀⠀⠑⠇⠀⠀⠈⢳⠠⢄⣀⣀⣀⠤⠋⠀⠀ ⠀⠀⠀⣀⠤⢤⠔⠩⢟⠳⡤⡤⠴⡤⠠⡶⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠁⠀⡟⠀⠀⠀⢢⠃⠀⠠⠦⡄⠌⠑⣠⠤⠷⣖⠒⠢⡄⠀⠀⠀ ⠀⠀⣇⠀⠀⢧⠀⠀⠀⠀⢱⡀⠀⠀⠸⠀⠈⣀⡀⠀⠈⢧⠀⡷⠀⠀⠀ ⠀⠀⢸⠄⠀⡼⡧⠀⣀⣠⠴⢓⡶⠒⠒⠊⠉⠁⠘⣦⠤⢺⠽⠃⠀⠀⠀ ⠐⠶⠯⠴⠊⠀⢗⣂⣸⢤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⡿⠛⢿⣿⡆⠀⠀⢰⣿⡿⠛⢿⣷⡄⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣀⣤⣿⣷⣶⣶⣾⣿⣤⣀⣿⡿⠀⠀⠀⠀ ⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⢠⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⡄ ⢸⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠙⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀ ⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡞⢹⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠀⠀⣸⣥⣸⠇⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇⠀⣴⡟⢸⢻⣀⢾⡿⣿⡿⠀⡀⠀⣞⢆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡹⢇⣼⡿⠁⣼⡼⢣⡿⢁⢿⡇⢠⡇⠀⢹⡘⡆⢰⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⣸⠏⡇⢸⣿⠇⠀⡼⣯⡿⠁⢸⠀⡇⣾⠀⠀⠀⣿⢹⡞⢹⣇⠀⣠⢾⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⢧⢀⣿⢠⡇⢺⣿⠀⣸⢡⡿⣁⠀⡘⠀⡇⣿⠀⠀⠀⡏⣾⡇⢸⠸⡞⣍⣿⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣆⠀⠀⢠⣿⢸⠘⣾⣏⢸⢧⠸⣽⡤⣷⡟⢠⡇⠀⡇⢠⣽⡿⠀⠀⠀⣹⣿⠁⢸⠀⠹⣿⠇⡌⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢾⣿⢧⡀⣼⡇⠘⡄⢹⣿⣼⠸⠀⢳⣻⡟⠀⡾⠁⠀⡇⠀⣿⡄⠀⢀⣾⡿⢃⡄⢸⠀⠀⢏⣰⡅⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⢻⢿⣿⠀⠀⢹⡀⢻⣻⠀⠃⠈⢿⡗⢠⣿⠀⠰⠇⠀⢸⢧⣴⣿⠋⢡⣿⠀⣼⠀⠀⠸⣇⠇⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡄⢰⠛⡇⠀⠀⢣⠘⡷⡇⠀⠀⢸⣿⣿⣳⠀⠀⠀⠀⠸⣼⣷⠣⣀⡾⠋⢀⠘⠀⠀⠀⡟⢀⣼⠀⠀⠀⠀⢀⣠ ⢠⣄⠀⠀⠀⢱⣸⠀⡇⢠⠀⠀⠃⠹⡝⣄⠀⢸⣿⣿⡫⠀⠀⠀⠀⣸⣿⢧⣾⠏⠀⢁⡎⠀⠀⠀⢠⣇⡞⡞⣀⢤⣴⣾⢽⡟ ⠈⣿⣷⢄⡀⠈⢿⢸⣧⠈⢧⠀⠀⠀⠹⣎⠳⣼⣿⣏⣯⡆⠀⠀⢀⣿⣿⣿⠃⠀⠀⣼⠀⠀⡴⢠⣿⡟⣺⡯⠟⣩⠜⢁⡜⠀ ⠀⢸⡌⢢⣈⠒⢼⣾⣇⢳⡈⢧⠀⠀⠀⠙⢷⣼⣿⣿⠟⠓⣠⣶⣻⠞⠋⠙⡆⠀⣀⡇⠀⢰⠁⣾⠟⡰⠁⣠⠞⣁⠞⡽⠀⠀ ⠀⠀⢷⡝⣍⠳⣄⠸⣿⡀⢷⡈⢣⣠⣤⣤⣾⡿⠋⢁⣶⣶⣿⠋⢀⡤⠤⣀⣿⣏⡁⢻⣦⠃⡼⣼⡜⠁⠚⢁⡴⢁⡜⠁⠀⠀ ⠀⠀⠈⣿⣌⠣⡈⡑⢿⣧⡀⣷⣿⠟⢉⡿⠋⢀⡴⢉⡾⠁⣀⣴⠿⢀⣤⣼⣿⣿⡄⠘⣿⢷⢱⠟⢀⢴⡿⠋⣠⠎⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣶⡌⠪⡢⣻⣿⣿⠃⠀⣾⠁⠰⠊⢠⣾⡟⢉⠽⠋⡰⠛⠙⠻⣿⣿⡇⠀⢸⣸⡝⣾⠝⣡⣼⠟⠁⢀⣀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣝⢦⣌⣻⣿⠁⠀⣾⡏⢠⠃⡴⣻⡿⡰⠃⣠⠞⠀⠀⠀⠀⢹⡟⠃⢀⣎⣏⢇⢸⣮⣿⢥⣴⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⣌⣓⣿⣿⣿⡀⢸⣿⡇⣸⡿⠀⢸⡿⢁⡔⠋⠀⠀⠀⢀⡠⢾⣧⣆⢎⣾⣿⣿⣿⣀⣬⠝⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⡳⣢⣽⣿⣿⢿⣿⣷⣿⡓⢦⣸⣷⠺⡄⠀⠀⡠⠞⠁⣠⣼⣿⣿⣿⣿⣽⣯⡿⣽⣮⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠪⣙⢿⢹⣿⣿⣿⣟⠉⢳⣿⣧⣄⣸⡶⣎⣠⣶⣽⡾⠟⣫⠻⢿⣿⢀⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣳⣝⣿⣟⠻⠭⠭⠵⠶⠯⠟⡛⠛⡛⢒⣒⣉⡉⠁⢠⢟⣿⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⡱⡄⠀⠀⠀⢛⣦⣆⡀⠀⠀⠀⠀⡞⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡞⠀⢨⢿⣾⣄⠀⠀⠹⣶⠶⠁⠀⢀⣴⢯⠀⠈⡗⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣤⠴⠋⢁⡠⡇⠀⠈⣦⠳⡌⣷⢤⡀⠀⠀⣠⠖⣩⣳⠃⠀⠀⡇⠀⠈⠢⣤⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠞⢹⠛⠁⣠⠞⣁⣤⠇⠀⠀⣟⢇⠙⣍⠙⣎⠩⠍⠁⡴⣱⠃⠀⠀⠀⠿⣄⠀⡀⠈⣿⠃⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣎⣠⠛⢁⣀⡤⠤⠴⠧⢼⣆⣈⢣⡘⠆⣠⠞⢰⠃⣀⣀⣀⣀⡀⠈⠳⢅⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⣞⣉⣁⣀⣀⣀⡤⠤⠀⠀⠈⠉⠛⢺⡷⠒⣉⣉⣀⣀⠀⠀⠈⠉⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠈⠛⠓⡦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠬⠤⠤⠤⠤⠤⠤⠼⠭⠤⠤⠅⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠋⠉⠉⠉⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠉⠉⠉⠙⠻⢷⣄⠀⠀ ⠀⣴⡟⠁⢀⣤⡶⠞⠛⠷⢶⣄⠀⣻⣧⣴⠶⠞⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠷⢶⣴⣿⡁⣠⣴⠾⠛⠛⠶⣦⣄⠀⠹⣧⠀ ⢰⡟⠀⢠⡿⠁⠀⠀⠀⢀⣠⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄⠀⠀⠀⠈⢻⣆⠀⢹⣇ ⢸⡇⠀⢸⡇⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⣿⠀⢸⣿ ⠘⣿⡀⠘⣧⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣸⡏⠀⣼⡇ ⠀⠘⢷⣄⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⣼⠏⠀ ⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⣿⣇⣨⣿⣷⠀⠀⢀⣠⡶⠟⠛⠛⠛⠷⣦⣄⠀⠀⢰⣿⣅⣸⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠏⠀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠈⠹⣷⡀⠈⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⣾⠋⠀⠀⠀⢰⣶⣶⣶⠀⠀⠀⠈⢿⡄⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⢀⣿⠀⠀ ⠀⠀⠘⣿⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠀⣸⡇⢠⣦⣀⠀⠀⣹⣿⡃⠀⠀⣀⣤⠘⣿⠀⠿⣿⣿⣿⣿⣿⠿⠀⠀⠀⢸⡟⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠉⠛⠛⠛⠋⠉⠛⠻⠛⠋⠁⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⠶⠶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣶⣏⡁⣄⣀⣀⠀⣀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠤⠴⠻⢗⠋⠁⠀⠀⠈⠉⠛⠦⢿⣾⡳⠾⣤⣄⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡠⠤⠤⠬⣿⡶⢤⣠⠖⠉⠀⢀⠀⠀⠀⢁⣀⡠⠤⠄⠀⠀⠀⠤⠬⣻⠿⢦⣙⡋⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠶⠋⠀⠀⠀⠀⠀⢸⡅⠀⣧⠀⠀⢀⡤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠉⠒⠮⣷⣶⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⢠⡄⠇⢠⠟⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢹⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠀⣰⣿⠇⣠⢿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣤⣀⢀⣤⣼⣏⡟⠀⣇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⣿⣶⠿⣿⣿⣿⣄⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⢙⡿⣄⣀⣰⠇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⣼⢧⡀⢠⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⠀⠰⡄⠀⠀⠀⠀⣰⠀⢇⠀⣴⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⣸⡏⠀⢃⡸⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣸⠤⠄⠱⣄⠀⠀⢳⡄⠀⢀⡼⠃⠀⣸⣴⣿⡆⠀⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⢀⣿⠀⠀⠘⡇⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡿⠛⣛⡓⠊⠙⠒⠚⠉⠓⠋⠀⣠⡾⠿⠿⣿⠃⢀⡄⠀⡀⠸⡄⠀⠀⠀ ⠀⠀⠀⢸⣾⠃⠀⠀⠀⣿⣿⢰⠃⢀⡆⠀⠀⠀⠀⣀⣴⣿⠏⡐⠉⣠⣹⡆⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⣿⣖⢩⠇⠀⢹⣆⢣⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⠀⠀⠀⢸⡏⢿⠀⣼⠁⠀⠀⠀⠀⠉⢹⣯⠀⣏⣿⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣭⣿⣿⣤⣄⡄⠘⣾⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⢀⣿⣷⣎⡜⢹⠀⠀⠀⠀⠀⢀⠀⠹⣇⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⡉⠀⠀⠀⠀⠀⠀⠉⠳⣿⣀⠀⢀ ⠀⠀⠀⢹⠀⠀⠀⠀⡼⡽⠋⣿⠀⠘⡀⠀⠀⠀⠀⠈⢿⣶⡼⠗⠀⠀⠀⠀⠀⠀⠐⠒⣡⢴⡟⠋⣉⣽⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠈ ⠀⠀⠀⡏⠀⠀⠀⡼⢡⢧⢰⠋⢧⡀⡇⠀⠀⠀⠀⠀⠀⠻⣽⡯⠶⠶⠦⢤⡤⢤⣶⠛⠀⠼⠤⠯⠿⠛⠁⠀⣠⡤⢤⡀⠀⠀⠀⠻⠇⡀ ⠀⠀⢸⠁⠀⠀⡜⢠⠇⡸⠈⡇⠀⠉⠱⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡄⠙⢯⣿⣏⡀⠀⠀⠀⢀⡿⠃⠀⢠⡿⠀⠀⠙⢧⠀⠀⠀⠀⠉ ⠀⠀⡌⠀⢠⠎⣠⠃⢠⠇⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠒⠚⢽⣆⣰⠟⠉⠉⠻⣦⠀⠀⠿⠇⠀⠀⢸⡆⠀⠀⠀⣸⡇⠀⠀⠐⣶ ⠀⡰⢁⠔⢁⡴⠁⠀⡜⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠑⢢⡄⠙⣷⡄⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠻⢦⡤⠴⠟⠁⠀⠀⠀⠉ ⡴⡥⠦⠔⠁⠀⠀⣰⠁⠀⠀⠀⢀⣠⣤⠬⢷⣄⡀⠀⠀⠙⠻⣍⠁⠀⠀⠈⠷⣶⣄⣀⣽⢷⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣠⢟⣿⣋⣡⣿⣻⠛⠓⢾⣏⠉⠁⠀⠀⠀⠀⠀⠙⢿⠛⠛⣛⣷⣬⡝⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀ ⠀⠀⠀⠀⣀⡞⠀⡔⡶⠛⠉⠉⠉⣹⣧⣼⣿⠛⠀⣤⡴⢿⠷⣤⣀⠀⠀⠀⠀⠀⠀⢱⡾⠏⠁⠉⠉⠋⠉⠉⠉⠛⠻⣷⣶⣞⠁⠙⠢⢄

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⡀⠀⢀⠞⢰⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠘⢰⡃⠔⠩⠤⠦⠤⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠄⢒⠒⠺⠆⠈⠀⠀⢐⣂⠤⠄⡀⠯⠕⣒⣒⡀⠀ ⠀⠀⢐⡡⠔⠁⠆⠀⠀⠀⠀⠀⢀⠠⠙⢆⠀⠈⢁⠋⠥⣀⣀ ⠈⠉⠀⣰⠀⠀⠀⠀⡀⠀⢰⣆⢠⠠⢡⡀⢂⣗⣖⢝⡎⠉⠀ ⢠⡴⠛⡇⠀⠐⠀⡄⣡⢇⠸⢸⢸⡇⠂⡝⠌⢷⢫⢮⡜⡀⠀ ⠀⠀⢰⣜⠘⡀⢡⠰⠳⣎⢂⣟⡎⠘⣬⡕⣈⣼⠢⠹⡟⠇⠀ ⠀⠠⢋⢿⢳⢼⣄⣆⣦⣱⣿⣿⣿⣷⠬⣿⣿⣿⣿⠑⠵⠀⠀ ⠀⠀⠀⡜⢩⣯⢝⡀⠁⠀⠙⠛⠛⠃⠀⠈⠛⠛⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡇⠀⠑⠀⠀⠀⠀⠐⢄⠄⢀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣷⣤⣀⠈⠲⡤⣀⣀⠀⡰⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣤⣙⣷⣅⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠟⠁⠙⠟⠛⠛⢿⣿⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⣠⡦⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣴⠋⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠎⡀⠀⠀⠀⡼⠁⠀⢠⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠃⡔⠀⠀⢀⣼⠃⠀⠀⡼⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢇⠞⠀⠀⢀⣾⠇⠀⠀⢠⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠑⠀⠀⠀⣼⣿⠀⠀⠀⣼⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⠣⢤⡴⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⢠⠏⡗⠀⡀⠀⢰⡟⣿⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡄⠀⢣⠀⠀⠀⠀⠀⢧⣠⠀⠀⠀⠀⢠⠀⠀⢿⡆⠀⠀ ⠀⠀⠀⡞⢸⠁⢠⠁⠀⣿⢁⣻⠀⠀⠀⢸⠀⠀⠀⡄⢸⠀⠀⠀⠘⡀⣸⡀⠀⢧⠀⠈⢣⢄⣀⠠⢴⠊⠙⡇⠀⠀⠀⠀⣇⠀⢸⣧⠀⠀ ⠀⠀⠀⡇⣸⠀⠐⠀⢸⡟⠉⣛⡇⠀⠀⠈⡄⠀⠀⢿⠈⡄⠀⠀⠀⢃⠈⠁⠁⠘⡆⠀⠈⡎⡇⠀⠘⡄⠀⢱⡀⠀⠀⠀⢸⠀⢸⣿⠀⠀ ⠀⠀⢸⡇⡟⡆⠀⠀⢸⠁⠀⢿⢸⠀⣦⠀⣇⠀⠀⠘⣇⠘⡀⡄⠀⠘⡆⡇⠀⠀⢹⠀⠀⠇⡇⠀⠀⡇⠀⠀⠑⢄⠀⠀⠀⡇⢸⢹⠀⠀ ⠀⠀⠈⣧⡗⡀⢰⠀⢈⢀⣤⣾⣿⢦⡽⠶⠼⣆⡘⣄⠘⢧⣀⠘⣤⢔⣺⣿⣶⣤⣄⣷⠀⠀⢇⠀⠀⡷⣄⠀⠢⡀⠑⠤⠄⣁⣇⣾⠀⠀ ⠀⢀⣤⣾⣷⡷⣸⣀⣾⣿⣿⣿⠿⢻⣿⡄⠀⠈⠉⠉⠁⠀⠉⠛⣿⣿⡿⠟⢿⣿⣿⣿⡄⠀⢸⠀⠀⡷⣌⠑⠢⣬⠶⣴⣾⣿⣿⣇⣀⣀ ⣰⡿⢻⠟⢻⡇⣿⣿⣿⣿⡿⠀⠀⠀⠰⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⠈⠬⢿⣿⣿⣧⣸⠀⠀⡇⠈⠑⠲⠤⢀⣷⣿⡿⣿⣶⣋⠉ ⠱⠁⣎⣀⡜⢇⠙⠛⣿⡃⠀⠀⠀⠋⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠂⠀⠀⣿⣿⠛⠻⠀⢸⣷⣏⠳⡄⠀⠘⣿⣇⣧⡏⠹⡉⠀ ⣳⣀⣽⠛⢁⣼⡆⠀⢸⣧⠀⠳⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣤⣀⡖⠚⢹⣿⠀⡄⠀⣼⢯⣄⣁⣷⣀⣸⣿⣿⠃⢱⡀⠙⠦ ⠳⠭⢤⡒⢁⣼⣿⡀⡀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠃⢠⣏⣤⡀⢀⠟⠋⡱⠻⣯⠀⠈⢿⣠⣠ ⠀⠀⣄⣀⡠⡞⠏⢷⣧⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⢀⣼⠋⠤⠔⠊⣠⠞⠀⠀⢿⣆⠀⠀⠉⠉ ⠀⠀⠈⠛⠋⠁⠰⡘⣿⡏⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢀⣾⡏⠀⣀⡠⠚⠁⠀⠀⠀⠈⠛⠒⠶⠶⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠘⣷⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢋⣿⠇⣠⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⡀⠀⠉⠓⠤⣀⠀⠀⠀⣀⣀⣀⠤⡴⠖⠋⡱⢃⣾⣏⡔⠁⠀⠀⣀⣀⣀⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠑⠲⢄⡀⠀⠀⠀⠀⠙⠛⠓⠀⠀⠀⣀⣈⣉⣉⣿⣅⣔⣁⣀⠒⠛⠓⠛⠉⠁⢉⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠄⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠤⠬⢣⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠋⠀⠀⠀⠀⠀⠀⠉⠉⠳⢶⣲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠉⠓⠲⢤⣄⠀⠀⠀⣀⣤⣤⣀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣧⣽⣆⠀⠀⠀⠈⠙⠲⢾⡏⠀⠀⠉⠙⠿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢟⣿⡏⢹⣿⣆⠀⠀⠀⠀⠀⡼⢹⡄⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡴⠚⠉⠉⠉⠳⣦⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣰⠟⢻⡇⢸⡇⠿⣆⠀⠀⠀⠐⠃⠀⢧⠀⠀⠀⠀⣀⣀⡤⣷⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⡏⢣⠀⠀⠀⠀⠀⠀ ⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠸⣦⠀⠀⠀⠀⢠⡾⠛⠀⣼⠏⠀⢸⡇⢸⡇⠀⠹⣦⠀⠀⢀⠀⠀⠸⣤⠶⠛⠋⠙⣿⡆⢻⣧⡀⠀⠀⠀⠀⠀⠸⡆⠀⠇⠀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⡀⠀⠈⢳⡄⣠⡾⠋⠀⠀⣼⡟⠀⠀⢸⣇⠸⣧⠀⠀⠹⣧⡐⠋⠀⠀⢀⡿⠀⠀⠀⠀⠀⢻⣼⠀⠙⢦⣄⠀⠀⠀⠀⠃⢰⠶⢤⣀⠀⠀⠀⠐⠀ ⢧⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠛⠶⢤⣤⡵⠋⠀⠀⢀⣾⣿⠀⠀⡀⠀⢿⡀⢹⡄⠀⠀⠫⠿⢶⣛⡛⠋⠁⠀⣿⡇⠀⠀⠀⢿⡆⠀⠀⠈⠻⣦⡉⠁⢀⡼⠀⠀⠉⡆⠀⡀⠠⠄ ⠈⢧⠀⠀⠀⠀⠀⣰⣻⡿⠁⠀⠀⠀⢀⣾⡃⠀⢀⣴⠟⢹⡏⠀⣸⠇⠀⠸⣇⠘⣷⠀⠀⠀⠀⢮⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠘⣇⠐⣄⡀⠀⠈⠻⣞⣋⣀⣀⣀⣀⡇⠀⠀⠀⠀ ⠀⠀⠱⡄⠀⠀⣸⠋⠉⠀⠀⠀⠀⢀⣾⠋⠁⣠⠞⠁⠀⣿⠁⢀⣿⠀⠀⠀⢿⡆⢻⡇⠀⠀⠀⣾⣿⡿⠀⠀⠀⠈⣧⠀⠀⠀⠰⣿⡀⠈⠛⠒⠋⠉⠉⠉⠉⠉⣉⣭⡟⠒⠀⠀⠀ ⠀⠀⠀⠙⢦⣀⣿⢠⣀⡀⠀⠀⣀⣾⠋⢀⡶⠁⠀⠀⠀⡿⠀⣼⡇⠀⠀⠀⠸⣿⡄⢿⡄⠀⢠⣿⡟⢳⠀⠀⠀⠀⢹⡄⠀⠀⢸⣿⣷⣀⣀⣀⣀⣀⣀⣤⡴⠞⠉⠀⠙⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣾⠇⠀⠀⠀⢹⡟⣠⡞⠑⠒⠲⠦⢴⣧⠀⣿⠁⠀⠀⠀⢠⡏⢿⣌⢿⡄⣼⡟⠀⢸⡇⢀⠉⠁⠈⣷⠀⠀⠀⢻⠀⠒⢦⠀⢲⠀⠀⠙⠷⣧⣀⡀⣀⣨⣧⣤⠶ ⠳⢦⣀⠀⠀⠀⢸⣿⡀⠀⠀⠀⣿⢱⠟⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡇⢀⠹⣷⣿⡿⠁⠀⣀⣿⡀⠈⠉⠀⢘⣧⠀⠀⢘⣆⠀⢸⣀⠘⡇⢀⣀⣀⣼⠷⠛⠛⠛⠻⠿⣦ ⠀⠀⠈⠳⣄⠀⢀⣿⡇⠀⠀⢸⣟⡟⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⠀⠀⠀⠀⣾⡇⣿⠀⠈⣻⣿⣆⠀⠀⠘⣿⠀⠀⠀⠘⣿⣧⠀⠀⢿⡄⣾⠀⠀⣷⡩⢭⣅⢀⠀⠀⠀⠀⠀⠀⠉ ⣆⠀⠀⠀⠈⠉⠀⢹⣿⡄⠀⣾⣿⠁⠀⢤⣤⣤⣭⣶⡤⣸⡧⣿⡀⠀⠀⠀⣸⣧⣿⠀⠀⣿⠀⠙⠧⡀⠀⠙⣦⠀⠀⠀⣿⠙⣷⡄⠘⣧⠟⠀⠀⣻⡄⠀⣿⢸⡞⣷⣄⠀⠀⠀⠀ ⠈⠳⠀⠀⠀⠀⠀⣼⣿⣷⠀⣿⣿⣄⣠⣾⠟⠉⣩⣿⣷⣌⢿⣿⡇⠀⠀⠀⣿⡟⣿⠀⠀⣿⠀⠀⣀⡀⠀⠀⠹⣦⠀⠀⢹⡆⢸⠷⣄⠙⣧⠀⠀⢸⡇⠀⢿⡌⢷⣻⡍⠛⢦⡀⠀ ⠀⠀⢀⠁⠀⢀⣼⣫⣿⣟⣇⢿⣿⡏⣿⡏⠀⣼⣁⢸⣿⣿⡎⢿⣿⡀⠀⠀⢸⣿⣿⡄⠀⣿⣀⣭⣽⣶⣦⣤⣄⠙⣦⠀⢸⣇⢸⡇⠈⣷⣿⣆⠀⠘⡇⠀⢸⣇⠸⣯⣷⠀⠈⠻⣦ ⠀⠈⠀⠀⣠⣾⣿⠏⣾⣿⣝⠻⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⠈⠻⢿⣄⠀⣈⣿⣿⢻⣶⠟⢏⣇⠈⢻⣿⣿⣿⣿⣿⣷⡌⣿⢸⣧⠀⢹⠙⣿⠄⢀⡇⠀⢸⣿⡀⢻⣿⣆⠀⠀⠈ ⠀⠀⣠⡾⠟⠁⣿⠀⣿⣿⠿⣧⢻⣾⣮⡇⠀⢻⣿⡿⢿⣿⡇⠀⠀⠀⠈⠛⠛⠛⠙⠃⠀⢠⣿⣿⣷⣿⣿⣿⣿⢻⣿⣌⠻⢿⣿⣿⣆⢸⡄⠀⠀⢸⡇⠀⢸⣾⣧⠀⢿⡙⢳⣄⠀ ⠀⠉⠁⠀⠀⠀⡇⠀⣿⠏⣠⡾⠻⣿⡿⠚⠶⠾⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡿⣿⣿⣿⠀⣿⣿⠟⢛⡿⠷⠙⢿⠁⠀⣠⣿⡇⠀⠘⡿⢹⣆⠘⣷⡀⠙⠧ ⠀⠀⠀⠀⠀⠀⣧⣼⢏⣴⡟⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⣄⣿⣿⣿⠇⠀⣿⣿⠀⢸⡇⠀⠀⠀⣠⣾⢙⣿⠁⠀⢰⡇⠀⢿⣆⠘⣷⡀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣾⣿⠁⠐⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠤⢤⠤⠚⣻⣻⡆⣼⠃⠀⠀⣾⠏⢀⡾⠻⣦⡀⠘⡇⠀⠈⢻⣄⠘⣧⠀ ⠀⠀⣠⣶⠿⠿⠛⣿⡟⣿⠀⢸⣿⠟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠿⣇⡿⠀⠀⠀⠀⣰⠿⠽⠶⢤⣻⢦⡇⠀⠀⠀⠙⣧⡘⣷ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⢻⡀⠀⣿⣆⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣻⣤⠴⠟⠁⠀⠀⢠⡼⠋⠀⠀⠀⢀⣈⡻⠝⢲⣄⢀⣀⠈⠻⢌ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡌⢷⡀⠹⢿⣷⣄⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣾⠃⠀⠀⠀⠀⣠⣿⣁⣒⣒⣲⣿⣭⣥⡴⠖⠚⠋⠉⠉⠛⣦⢠ ⠀⠀⠀⠀⠀⠀⣰⣿⠋⠹⣾⣷⣄⠿⣿⠻⣦⠀⠈⢻⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⠇⠀⠀⠀⠄⣠⣿⡿⢿⡿⠋⢛⣳⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⣼⡿⣿⠀⠀⠀⢻⣿⢦⣿⠀⠋⣧⠀⠀⢻⡄⠉⠛⣶⡤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠔⠚⠉⠁⣰⠏⠀⢀⣤⠶⣿⠏⠁⠀⣸⢠⠟⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳ ⠀⠀⠀⠀⠈⠀⠀⣿⣤⡀⠀⣸⣿⠀⠹⣏⣸⡿⢂⣀⣈⣿⣶⣾⣁⠀⢀⣴⠟⠛⢿⡄⠀⠀⠀⠀⠀⢀⣴⠋⣀⡴⠏⢁⡼⠃⠀⠀⢠⡇⣾⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡇⣇⠀⡿⣿⠀⠀⣹⠏⠀⠀⠀⠀⠀⠀⠀⠙⣷⡟⠁⠁⢠⢸⣿⠀⠀⠀⠀⣠⣾⣫⡾⠉⠀⣠⠟⠁⢀⣀⡤⣾⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆ ⠀⠀⠀⠀⠀⠀⠀⠸⣷⢹⣰⡇⠻⢀⡴⠋⠀⠀⠠⠤⠤⣤⣤⣄⠀⠈⠳⣤⡀⢸⣿⣿⠀⠀⣤⢾⣿⢛⡟⠀⢀⡼⢫⢹⣰⠏⠀⣰⠋⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠻⣷⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣈⡻⣾⣧⣿⠀⣠⡴⠋⠀⣼⠃⣰⠟⠁⢸⠈⡇⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⣐⠒⢒⢲⣦⣄⡀⠀⠈⠙⢻⣿⣿⠜⠁⠀⢠⠔⣿⣿⠋⠀⠀⢀⣿⡇⢀⣟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢀⣀⣀⣤⣀⣀⣾⣿⣟⣉⣛⣛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠤⠤⡀⠀⠀⠀⠀⠀⠻⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠋⠀⠀⠀⠘⡀⣄⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⡇⢳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⣀⡀⡾⢛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠉⢛⣋⡛⠁⢳⣾⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⣀⠀ ⠇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠁⠴⠒⠉⠀⠘⣿⣿⣿⣿⡎⢷⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠃⠀ ⠘⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠈⢧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠳⢄⣀⣀⣾⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣤⣀⠀⠀⠀⠻⣿⣿⠀⣴⣢⡤⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢻⣿⣿⣿⣿⡎⢀⣼⡿⠟⠋⠁⠀⠀⠀⠀⠈⠱⠀⠀⠉⠙⠛⢶⣼⣿⣹⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⢸⣿⣿⣿⣿⠓⢻⡽⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠸⠸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠳⣿⣷⣿⡇⠀⠀⠀⢀⡀⠀⡇⢀⡀⠀⠀⠀⢈⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⡄⠀⠸⣏⠹⣷⡀⠀⢠⠋⡈⢠⠋⡱⠁⣀⡀⠀⡼⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠘⡆⢠⠟⣷⢦⣿⠢⣬⠀⣧⠃⢸⡡⢊⡴⠃⠈⠀⠀⢀⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣡⠎⠀⢩⣸⣿⡄⠹⠐⠀⠀⠀⡀⠺⠚⣡⣾⠶⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠐⠁⣻⣿⣄⠀⠀⠀⠀⠀⢠⡏⠉⠁⢰⢻⣿⣟⣻⣿⣿⣿⣿⣿⡄⠀⢰⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠓⡏⢹⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣦⡏⢇⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣆⣸⡃⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣴⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠤⡀⠀⠀⠘⢶⣶⣾⣿⣿⣿⣿⣿⣿⣾⣷⣄⠀⠀⠀⠀⠀ ⡎⠀⠀⢰⢔⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⢠⣤⣤⣼⢻⣿⣿⣿⣿⠻⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠐⠀⢀⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⡇⡘⣿⣿⣿⣿⣿⣿⢄⡀ ⠆⠀⠀⢰⣿⣿⣿⡟⠐⠁⠀⠹⣿⣿⠸⡀⠙⣿⣿⣿⣿⣿⠔⠀ ⠘⠄⢀⣾⣿⣿⡿⠃⣀⣤⡄⠀⠘⢿⠇⢤⣄⡘⣿⢿⣿⠏⠀⠀ ⠀⠀⠘⡏⣿⣿⡿⢴⡏⠁⠀⠀⣀⣀⠁⠀⠀⠙⠛⣾⡏⠀⠀⠀ ⠀⠀⠀⡀⠿⡿⣇⠀⠀⠀⢠⠀⠀⠀⠰⠀⠀⠀⢀⡷⠀⠀⠀⠀ ⠀⠀⠀⠁⠈⢟⢻⡄⢀⢂⠨⠢⢀⡀⡰⠀⠀⢰⣿⡇⠀⠀⠀⠐ ⠀⠀⠀⠀⢃⠎⡏⣮⢲⠘⠃⠓⡔⢅⣄⣤⣶⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠢⢈⣸⣦⠀⠀⠀⠰⠉⢡⣻⣿⣿⣿⣿⣧⢀⡆⠀ ⠀⠀⠀⢀⣤⣾⣿⣏⡔⠀⠀⢀⠂⠀⠀⣿⡏⣿⣿⣿⣿⣿⣤⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀ ⠀⠀⣠⣾⡿⠀⠀⠀⠀⣴⣿⣏⣹⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣹⡆⠀⠀⠀⠀⢻⣷⣤⡀⠀ ⢀⡾⢡⣾⠃⠀⠀⠀⠀⠹⣿⣿⠿⠀⠀⣦⠀⠀⢠⡆⠘⢿⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⢿⡄ ⢸⣇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣧ ⣼⠿⣷⣟⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣿⣿⠟⣿ ⢿⡀⠈⠙⠻⢶⣭⣟⣿⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⢾⣛⣯⡷⠿⠋⠁⠀⣿ ⢸⡇⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠶⠶⠿⠶⠤⠴⠴⠾⠿⠟⠒⠛⠛⠋⠉⠁⠀⠀⠀⠀⢀⣿ ⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀ ⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀ ⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⡷⠶⣤⣤⣀⣀⣀⣀⣠⣤⠴⠶⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⠶⠶⠶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⣠⡾⢛⣦⣄⣰⠶⣆⣾⡙⣶⡤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⢤⣀⣿⡄⡟⠁⡇⢸⡅⠈⡿⠀⣿⡏⠹⡿⠀⢿⡏⠙⣆⠀⠀ ⠀⠀⢠⡖⢲⡸⡅⠈⣿⠇⢷⡇⢸⡇⠀⣇⠀⡇⠀⢻⣷⠀⢷⠀⣼⠀⢰⠇⠀⠀ ⠀⠀⠘⣧⠀⣇⢧⠀⢸⡄⠸⡇⢸⣷⠀⢿⠀⣷⠀⡿⢹⠀⢸⣤⡇⠀⣾⠓⢦⠀ ⢠⡞⠳⡿⣄⡸⣼⡆⢸⡇⠀⡇⠀⣿⡄⢸⠀⢹⢰⡇⢸⡆⠘⣿⠁⢀⡏⠀⣼⠀ ⠘⣧⠀⣟⠉⣧⢹⡇⠸⡇⠀⣷⠀⣿⡇⢸⡇⠸⣿⠀⣼⡇⢠⡏⠀⢸⠃⢰⠇⠀ ⠀⠘⡆⢹⡀⠸⡆⢷⠀⡇⠀⢻⠀⢸⣿⢸⡇⢀⡏⢰⣿⡇⣸⠁⠀⣾⠀⣿⣄⠀ ⢀⣴⢿⡄⢧⠀⢹⣼⡀⣻⣀⣘⣧⣀⣿⣼⣇⣼⣅⣾⣸⣧⡏⠀⠀⡏⢸⣧⠈⢳ ⣾⠁⣿⣷⡘⣦⡴⠿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⣰⡇⣿⡟⠀⢸ ⢹⡄⠙⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠟⠁⠀⣼ ⠀⢻⡄⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⡏ ⠀⠀⢻⡄⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢸⠇ ⠀⠀⠀⢻⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠈⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠀⠀⢻⡄⢰⣿⡏⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⣱⡄⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢸⡇⠘⠿⡿⠿⠁⠀⠀⣶⡀⢐⣶⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⣼⠁⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀ ⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⣿⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⣀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠞⠁⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠙⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠀⠀⠀⠀⠀⣰⠃⢠⡏⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⠛⠓⠶⠤⠤⠤⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡽⠀⢸⠀⠀⠀⠀⠸⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⢸⠀⠀⠀⠀⠀⢻⡀⢿⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⢸⡄⠀⠀⠀⠀⠀⠻⣌⢷⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⣸⡇⠀⢸⠀⠀⠀⠀⠙⠳⣿⣆⡀⠀⠀⠀⡟⣦⠀⠀⢀⡠⠖⠁⢨⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⡤⠞⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠠⣦⣩⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⡉⠉⠓⠀⢸⠃⠈⢧⡰⠋⠀⠀⢀⡾⣧⠀⠀⠀⠀⠀⠀⠀⢹⡖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⠈⢹⣹⡄⢸⣻⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⢀⣠⣌⡃⠀⢀⡴⠊⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠶⠦⣠⣠⠷⢷⡈⣿⢷⠀⠀⠀⠀⠀⣿⡄⠀⠀⢹⠀⠀⠀⠉⠙⢿⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⢸⠀⣠⡟⠀⠀⠈⢧⢸⡞⣷⡀⠀⠀⠀⢹⣷⠀⠀⢸⡆⠀⣀⣀⡀⠀⠙⢦⡀⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⣿⣰⠏⠀⠀⣀⡤⠬⢷⣽⡌⢧⡀⠀⠀⠈⣯⣇⠀⠀⣷⣶⣶⣦⣬⣭⣿⣆⡙⢿⡄⠀⠀⠀⠀⠀⡀⢸⡇⠀⠀⠒⠚⠉⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠋⣀⣴⣾⣿⣾⣿⣷⡛⠻⠤⠻⣦⣀⠀⠘⣜⢦⣶⣿⢽⣿⣿⣿⣟⣿⢿⣿⣷⣯⣤⠀⠀⠀⢰⡇⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⣀⣿⣼⣿⡿⣿⢛⡻⣿⣿⣏⠀⠀⠀⠈⠉⠉⠙⠻⠎⠛⠂⠈⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡷⠀⠀⢸⠃⢸⡷⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⣽⣿⣿⣗⠀⣿⣿⢿⣿⢷⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠘⠻⢧⣠⠏⡸⡏⠀⠀⠀⠀⣾⠀⢨⡇⠙⣆⠀⠀⠀⢸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣦⠀⢀⡈⢁⣀⣡⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠰⠞⠃⠋⢸⡇⠀⠀⠀⢀⡇⠀⢸⡇⠀⢹⡄⠀⠀⡟⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⢸⠘⢧⠀⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⣀⢸⡃⠀⠀⢰⣸⠀⠀⢸⡇⠀⣾⠁⠀⠸⠃⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⢸⠁⠀⠀⢰⡏⠀⢠⣸⠟⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠁⠀⠘⣾⢎⠗⠀⠀⢰⡆⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⣴⠃⠀⠀⠸⣿⠀⠀⠀⠀⢸⡇⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⡙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⡜⠁⠀⠀⢀⢠⡇⠀⠀⢀⠀⠘⡇⢀⡟⡇⢀⠄⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⢳⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣈⡿⠀⠈⠀⠀⠀⠀⠈⣼⠀⠀⠀⣿⠀⠀⣷⣼⣹⢃⡼⠀⠀ ⠀⠀⠀⠀⠈⣇⠀⠀⢸⠀⠀⠀⠀⠀⣀⠈⠙⠒⠶⠤⢶⣶⡖⠋⠉⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⡀⢰⡇⠀⣤⣼⢳⣷⠀⢸⣿⡿⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢀⣴⠟⢉⣼⡇⠀⠀⠀⠀⠀⠀⣠⢞⣡⠄⠀⠀⠀⠀⡼⡇⣼⣀⢸⡿⠷⠤⠽⠾⠷⠷⠀⠀⠀⠀⠀ ⠀⡆⠀⠀⠀⠘⡇⢀⣼⠹⡄⠀⠀⣀⡬⢶⣾⠟⢁⡾⠟⠋⠀⠀⠀⠀⠀⠀⠛⠋⢹⡏⠀⠀⠀⣠⡿⠁⣷⠋⠈⣙⣷⡀⠀⠀⠀⠀⠀⠈⠙⠲⣤⠀ ⠀⢳⡀⠀⠀⠀⢻⡀⡿⡆⢠⢾⡿⠋⣠⠞⢁⡴⢋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⣠⠴⠊⠁⠀⠀⠉⣠⠞⠉⣠⠝⢦⣀⢀⡤⠋⠉⠉⠀⠀⠣ ⠀⠀⠹⡄⢀⠀⠀⠻⣅⡀⣰⠏⠀⡴⠃⢠⣿⠞⠉⠉⠉⠓⢦⡀⢠⣤⣤⡤⠚⢓⡾⠉⠀⠀⠀⠀⠀⣠⠟⠁⢀⡼⠃⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠚⣳⣤⣀⡈⠙⣧⣀⡞⠁⠀⡞⣀⡤⠖⠦⣄⠀⠀⠙⢶⣀⡐⠙⠲⣏⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⡮⠂⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⠀⠤⡉⠉⠛⠋⠁⠀⢠⠏⠁⠀⠀⠀⠀⠉⠲⣄⣠⣿⣁⣲⡤⠈⢳⡀⠀⢀⡼⠁⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⢀⠘⢾⡄⢠⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⠜⣱⠃⠤⠤⠀⠀⠀⠘⢦⡟⢀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠑⢄⡉⠉⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢒⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⣀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡗⠋⠁⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢻⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⡇⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⡞⠀⢸⠀⢀⡟⡆⠀⠀⠀⢀⠀⠀⢃⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠃⠀⢀⡇⠘⡇⠀⠀⠀⠀⠀⢰⡟⠀⢰⠃⠀⢸⠀⡸⠀⣇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⢸⡄⠀⣸⠀⠀⡇⠀⠀⠀⠀⢠⠛⠃⢀⡟⠀⠀⢸⢠⠃⠀⢸⠀⠀⠀⡇⠀⠀⠘⡆⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⣼⢳⠀⡆⢀⣀⡇⠠⣏⣀⠀⢱⠀⠀⠀⣰⠏⢰⠀⡜⠀⠀⠀⣸⡎⣠⠔⢻⢀⣠⣼⡷⠶⢤⣤⣁⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠇⢀⣷⣿⣿⣿⣿⣾⣄⠙⠣⡘⡆⠀⢰⠏⠀⣼⡜⠀⠀⠀⢀⡿⠛⢁⣠⣾⣿⠿⠛⠓⠒⠿⢧⣝⢳⣦⠀⢸⠀ ⠀⠀⠀⠀⢸⣴⣿⣿⠟⠁⠀⣈⣽⣿⣷⡄⠀⢹⣤⠃⠀⠀⠟⠀⠀⠀⠀⠘⠃⣠⡿⢛⣡⣶⣾⣿⣷⣦⣄⠀⠉⢳⣝⣿⣩⠀ ⠀⠀⠀⠀⣼⣿⣿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢰⣿⣿⣿⣷⣿⣾⡟⢿⣷⠀⠀⢻⡜⣿⠀ ⠀⠀⠀⠀⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣿⣿⣟⣷⡀⢸⡆⠀⢸⡇⣹⡷ ⠀⠀⠀⢻⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⣯⣿⠟⡛⠓⣾⠁⠀⣼⣷⠟⠁ ⠀⠀⠀⠀⣇⠙⠿⣦⡈⢿⡛⢷⠁⢠⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣟⣀⡀⠰⠂⠀⡠⠋⠀⠈⢁⡞⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⠀⠁⠈⠛⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠈⠉⠛⠒⠒⠋⠀⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠒⠶⠾⠍⠛⠛⣛⠻⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⣀⣠⣌⣙⣛⡏⢧⠀⠀⠀⠀⠀⢶⣖⣚⣉⣀⣠⠄⠀⠀⠀ ⠀⠀⢠⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡴⠒⠉⠉⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠙⠁⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⣄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠙⠲⢦⣬⠵⠟⠦⣄⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠤⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢳⣦⠀⠀⠉⠓⠲⠭⢅⣀⡀⠀⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣿⡳⠒⠒⣀⣀⡤⠤⠀⠀⠀ ⠀⠀⠀⠀⢀⠏⢻⡀⠀⣠⠷⣦⡀⠀⠀⡿⣍⠙⠓⠒⠶⠦⠤⣤⡤⠤⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⠁⡴⢋⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⢠⠞⣧⡴⠁⠀⠀⠙⠒⣤⡷⠌⣳⣄⢀⡴⠳⣄⣴⡷⠤⢤⣤⣤⣤⠤⠤⠤⣤⣴⣿⣾⣤⠚⡄⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⠀⠠⠃⠀⠈⠀⠀⠀⠀⡰⠋⣩⡾⠛⠉⠙⠉⠀⢠⠟⠽⠳⠤⣤⣀⣀⡤⠔⠒⠉⠉⠀⠀⠁⠉⠢⡙⠆⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣼⠟⠀⠀⠀⠀⠀⢀⣈⣧⣀⣤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠄⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⡏⠀⢀⣠⣤⡶⠾⠛⠉⢹⠋⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠸⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢻⡄⠀⠀ ⢀⠀⠀⠀⠀⡞⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⠀⢰⢁⠀⣇⠀⠀⠀⠀⠀⠈⠀⠐⣄⡀⠀⠀⠤⢤⠊⢮⠢⡄⠀⠘⡇⠀ ⡀⠀⠀⠀⡎⡜⣄⣌⣆⠤⡂⡄⠀⠀⠆⢄⠙⡛⠲⡔⢳⢊⠁⢛⣾⠁⠀⠀⠁⠀ ⠁⠀⠀⠀⣧⣁⣈⡳⡀⠑⠜⠾⢔⡤⣘⡀⠉⠻⢍⡉⠉⠀⠺⡑⢼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠿⣽⣿⡀⠀⠒⠒⠂⠀⠉⠢⢴⣵⣶⣻⣷⣦⣬⢺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⢃⠀⡿⡯⣻⠀⠀⠀⠀⠀⠀⠰⣿⣽⣻⣽⡍⠛⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡆⠐⠪⠽⠉⠀⠀⠀⠀⠀⠀⠀⠀⣻⡥⠚⣀⡀⠁⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠉⢀⢜⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠰⡲⣟⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠏⠀⠀⠀⠀⠀⠀ ⢠⡀⡀⠱⣄⠹⢇⡑⠠⡀⠘⠏⠙⠽⠀⠀⠀⠀⠀⠀⡀⡴⠋⠀⠀⢀⠄⣀⠀⡆ ⠀⢳⣿⡦⣄⣁⣦⠤⡝⣫⣑⠤⣀⣀⡀⠠⠤⠐⠈⢡⡮⠀⠀⢀⣴⡫⠔⠉⠢⣱ ⠀⠀⠈⠉⠉⣁⠤⡰⠒⡩⡽⠋⢩⣿⠄⠠⠄⠄⢊⠩⠒⠒⢻⣍⣴⣤⡀⢀⣀⠀ ⠀⠀⠀⢠⠎⠀⢠⠁⡴⡱⠀⠀⠈⠅⠀⢀⠠⠂⠁⠀⠀⠀⡘⠘⠀⢀⠀⠁⠀⠑

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢘⡆⠀⠀⠀⣀⣤⣤⣤⣂⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣆⠀⢀⢔⣾⣯⣶⣿⣿⣿⣿⣿⠛⠉⢉⠞⢀⣾⠀⠀⠀ ⠀⠀⠀⠉⠉⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⡟⠀⠀⠀ ⢀⣄⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⡀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄ ⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠕⠀⠀ ⠘⠁⢸⣿⣿⣿⣿⣿⣿⡟⠏⠀⢰⣿⣿⣿⣿⣿⠈⢿⣿⣿⣷⡈⠂⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⡏⣀⣈⣥⣄⢻⣿⣿⣿⣿⣐⠈⣿⣿⣿⡧⠔⠀⠀ ⠀⠀⠈⠙⢿⡿⢿⣿⢧⠀⠁⢀⠠⠀⠟⠁⠈⠉⠛⠋⢿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⠐⡶⠝⢀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠤⠍⠡⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠀⠀⡖⠒⠋⠁⠀⠀⠀⠰⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠎⠐⠠⢇⡀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠈⠑⠂⠽⠮⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀

૮( ˃ ꒳ ˂)ა ◟/づ🦴

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⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢉⣕⡞⣼⣿⣿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⡀⢻⣤⣴⣴⣶⣶⣶⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⢧⣿⣦⠬⡜⣼⡝⣿⢹⣿⣿⡟⣁⡀⣴⣿⡟⣹⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⣿⢀⣿⢀⠨⢳⣷⢴⣧⣸⣟⡟⠉⢁⡾⠋⣀⡴⢃⡠⣠⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠋⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣾⣧⢸⣻⠀⢩⡏⠀⣸⣯⣿⡿⠒⣲⠟⠘⣩⠿⣠⠏⣴⣿⢯⣟⣹⣄⡿⣿⣿⣿⠏⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠘⢸⡇⣰⣿⠏⣿⣀⡼⠧⢶⣶⣳⡞⢳⠞⣿⣣⠏⠀⢠⣞⣀⣸⣿⣿⠀⢻⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⣿⣷⣿⢹⠀⣯⣞⣧⣔⣯⣿⣯⡾⢃⣾⠟⠁⢀⣴⡟⢀⣼⡟⣾⡿⣐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣧⢹⣾⣴⣿⠋⡇⢸⣸⣿⣿⣿⣿⣿⣿⣯⣶⠟⠋⢀⣴⣫⢏⣴⠟⣽⣿⡟⠀⠈⢹⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢳⠇⣿⣿⣿⣿⢹⡀⠃⢸⡜⣿⢹⣿⣷⣿⣿⡿⣷⠶⠚⠛⢛⡿⠋⣠⣾⣿⣿⣤⣦⣀⢸⡟⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⡞⣸⢻⣿⣿⣿⣾⣗⠄⠘⡇⣿⠚⠻⠿⠯⠿⠅⠀⠠⢄⠍⢨⡙⠊⠑⣿⣿⣯⣿⡿⠻⣿⢡⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣾⢣⡟⢸⠀⣿⣿⣷⣿⣦⠀⣷⣹⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠛⠿⠿⡿⣁⣼⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣇⣼⣿⣾⠀⣿⣿⣮⡛⢿⣧⣽⡿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠶⠆⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡼⣼⣿⡏⡟⣼⣿⣿⣿⡻⣿⠃⣸⡟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢰⢳⢻⡿⣠⡷⣿⣿⣿⣿⡏⢻⣴⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣼⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⡞⣼⣷⢻⡇⣸⣿⣿⣿⡿⡟⠅⣴⣿⡟⢤⣀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⢻⢁⡿⠇⣸⠇⣿⣿⣿⣿⣇⣿⠞⣡⣿⣧⣤⣽⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⣸⠃⢀⣿⢀⣿⣿⣿⣿⣿⢥⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠺⠷⣏⡀⣼⡿⢸⣿⣿⣿⣏⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⣿⣿ ⠀⠀⠀⠀⠈⠙⠳⢿⣿⣿⡟⢉⣰⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣷⣤⠖⠛⠉⠉⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠤⢄⣀⠀⣨⡿⠟⢋⣿⡿⢯⣶⣝⣛⣛⣿⠿⢿⣿⢥⣠⠼⠻⣿⣟⣿⣿⣿⢿⣿⣿⡋⢤⡀⠀⠻⣌⣉⣻⣦⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢀⣼⡟⠛⣛⣿⡿⠀⠉⢛⣻⣿⠿⠋⠀⢸⢹⠀⠀⠀⠀⠘⣾⣦⠉⠛⠷⢿⣿⣻⣦⡌⠢⡀⠘⣧⣙⡛⣿⣗⡚⠉⠉⠉⡇⠀⠀⢀⣀⣀⣠⣴⣿⣿ ⠀⠀⠀⢀⡤⡶⣿⠋⣽⠛⣿⡿⢁⣤⢶⡋⠉⠁⠀⠀⠀⢸⠾⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠛⣿⣦⡙⣏⠁⠈⣯⣙⠛⢿⣆⠀⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⡟⢸⣷⣿⠉⡇⢀⣯⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⢿⣟⢧⡤⠶⠛⠋⠉⠻⣿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣶⣿⣧⣿⢃⠏⠀⡇⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⢻⡝⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⢿⣯⣎⠤⠔⡇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢴⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⡄⢿⠦⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡉⢿⣻⡄⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⣾⣇⠀⠋⡏⠀⠀⠀⠀⣀⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣻⣎⠀⠹⣵⡟⠙⠛⢿⣿⣿⣿⣿ ⣴⣿⣿⣿⣻⣿⣆⢰⠁⠀⠀⠀⠘⠁⣶⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⢻⣠⣴⠀⣼⡟⠛⠛⠛ ⣿⣟⠙⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⠁⠀⠀⠀ ⡏⠁⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀ ⣄⠀⢀⡀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣤⣀⠀⠀⠀ ⣿⣷⣌⢿⣷⣍⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠈⠊⣙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣎⣻⣼⣷⡆⠀ ⣿⣿⣿⣷⣽⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⠛⠷⢶⣤⣄⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣷⣿⣿⡿⠿⠃⠀ ⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡦⢶⣄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠙⣄⠀⠀ ⣸⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀ ⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠁⠚⠉⠛⠙⠛⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⡟⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⣏⠀⠉⠓⠤⣄⣀⡠⠖⠋⢳⣀⣀⣀⣀⣀⣀⣾⣐⣈⣦⣀⣀⡤⠤⠖⠒⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⠇⠸⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠷⠶⠾⡊⠦⣄⣀⡤⠖⠉⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢧⠟⠀⠀⠙⢧⡵⠀⢀⣀⠠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⡴⠛⠉⠙⡆⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠒⠒⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠋⠀⢀⣴⡾⠃⢀⠇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣜⠁⢀⣼⠛⠛⠤⣰⣫⠖⠀⡄⢸⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠘⢄⢸⢑⡷⢿⡿⢶⣄⠀⢈⠳⡄⣴⡧⢸⡏⠉⠳⡖⠲⠤⠤⢤⣄⣀⣠⡤⠴⠚⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⣚⣿⠀⠀⢄⡀⠙⠲⣍⣠⠋⠐⣠⣾⣿⢧⣴⣣⠏⣰⡿⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠈⢷⡀⠐⠭⣗⡀⡴⢁⢀⣼⣿⠂⠉⠢⣴⣁⡾⠋⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠦⢄⣀⠀⠀⠀⠀⠀⢀⣠⡤⢒⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⢄⡀⠙⠧⣴⡋⣠⠟⠒⣤⣠⢀⠝⣄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣜⡽⠡⣤⣼⡯⣍⡉⢲⠊⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠟⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡇⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣤⢞⡞⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣋⠹⠤⢤⣄⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠗⠛⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡼⠀⠀⡄⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣴⠞⣫⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠀⠀⠀⠀⣀⡾⠁⠀⣸⣇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡤⠶⠶⠾⠿⢿⣿⣿⣷⣶⣶⣾⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢤⣀⣤⣾⠟⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⡀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⢶⣽⣿⣿⣿⣿⣿⣟⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠗ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢁⡤⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠴⠞⠋⠀⠀⠀⠀ ⣴⡿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡿⣿⠟⠀⠀⠘⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠳⣄⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡟⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⡄⠀⠈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⠁⠈⣀⣤⡤⠄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣇⣷⠀⠀⠀⣤⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠉⢀⣀⣀⣤⣤⣀⡈⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠉⠓⠆⢻⣿⣿⣿⣿⣿⣿⣷⣶⣦⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠘⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠾⣿⣿⠿⠿⠟⠛⠛⠁⠈⢿⡿⣼⣿⠿⢿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢈⣿⠟⠁⠀⠀⠀⠉⠙⠛⠛⠛⠉⣹⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠉⠻⣿⣿⠈⠛⠷⠀⠀⠀⠀⢀⡴⠚⠉⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢠⠶⠶⣤⡈⢿⡇⠀⢀⠀⢀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢹⡇⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⢸⣍⠉⠁⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠤⠤⠤⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣶⡤⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⣾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢤⡀⠀⠀⠀⣸⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠈⠓⠦⣴⣏⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠉⠓⠲⣤⣀⠀⠀⠙⢷⣄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣤⣈⠛⢦⡈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⡀⠀⢀⣠⣤⣶⣶⣶⣷⣶⣶⣿⣿⣷⣶⣶⣶⣶⣮⣝⡻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠔⠒⢤⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡜⠉⠀⠀⠀⠀⢳⠀⢀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠈⡇⣼⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣇⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⡇⢀⣀⣀⣀⣀⣀⠀⡿⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⡆⠀⠀⠀⠀⠀ ⡇⠘⠙⠻⠛⠛⠛⠃⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⡄⠀⠀⠀⠠ ⡇⠀⠀⠛⠛⠙⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠠⠁ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣠⠄⠻⣿⣿⣿⣿⣿⣿⠹⣷⠠⠤⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠓⢤⠆⠀ ⢣⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢀⠴⠋⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⠻⡇⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⠞⠀⠀ ⠈⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡼⣧⠀⠻⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⢱⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢿⠀⠀⢙⣀⠀⠀⠀⢿⣿⣿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠙⠒⠦⠤⣼⣿⣿⣿⣿⣿⣿⣿⢻⡏⠀⢀⣤⣖⣲⣭⡶⠀⠀⠀⠀⠀⠙⢿⣞⠀⠼⠶⣾⣭⣤⣀⠈⢿⣿⡞⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡿⣻⣿⣿⣿⣿⣿⢸⠀⣠⣾⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠈⠉⠛⣿⣦⣿⡇⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠃⢿⣿⣿⣿⣿⣿⠸⠴⢫⣱⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣧⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⢸⠙⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡰⠊⠉⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣂⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠘⡇⣿⣿⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⢾⣿⣸⢻⣷⡄⠀⠀⠀⠀⣀⣀⠀⣿⠀⣀⡀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢿⡟⢙⢿⣆⠀⠀⠀⣴⠁⡸⠀⡼⠋⣱⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⣷⣤⣘⡛⣦⣀⠠⠃⠀⡇⡼⠀⣼⢁⡴⠊⣹⠀⠴⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡾⠀⣿⠙⣿⣯⠈⢿⣇⠀⡿⠃⠀⠷⠟⢠⠞⢁⡠⢤⡄⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢠⡿⣿⡆⠀⠛⠈⠀⠀⠀⠀⡄⠛⠚⣡⣴⣾⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠠⠊⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠋⠁⠀⡿⢿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⣤⣯⠽⠛⣇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡿⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣇⠈⢧⢠⠏⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠈⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣆⣨⢋⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠘⣿⣿⡗⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⣦⢴⠟⠋⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⢴⣾⡙⣻⡷⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠘⢿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠆⠀⠀⢰⣿⣦⠤⠔⠀⢹⣧⣀⣀⠀⠀⠀⠈⠀⡀⠀⠀⠀ ⠀⠀⣸⣆⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣀⡀⠀⠀⠀⠀⠾⠂⠀⠀⠀⢻⡏⠀⠀⢾⡛⠻⣯⣉⠁⠀⠀⠀⢀⡿⣤⣀⡀ ⠠⣴⣟⣻⡷⢶⠀⠀⠀⣾⠀⠀⠀⢰⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠀⠈⠛⠛⠛⣿⠛⠂⠀⠐⠻⣷⣼⠟⠉ ⠀⠀⠹⡿⠀⠀⠀⠀⠀⣿⣠⣀⣒⠀⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠔⠀⠀⠀⠀⠈⠋⠀⠀ ⠀⣠⠀⠀⠀⠀⠀⢀⣤⣿⠟⣿⡉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡿⢶⣤⡀⠀⠘⠟⢁⣿⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⡶⠤⣤⣄⠀⠀⠀⠀⠺⣧⡀⠀⠀⣴⠟⢿⡆⠀⠀⠀ ⠛⢷⣾⠋⠀⠀⠀⠀⣾⠛⢷⣤⣀⡀⠀⠀⠀⠀⠀⣼⠋⡁⢻⡀⢀⠀⠉⠀⠀⠀⠀⠀⠈⢻⣤⠀⣿⠐⢸⡇⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣷⠄⠀⠀⠀⠁⠀⢀⣸⡷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡏⠀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣇⠤⠂⠠⣱⣆⣁⡙⣑⡀⣠⡤⣤⣤⣤⣄⣄⡐⠇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⠿⣏⣏⣀⡼⣤⣿⡿⣿⠌⠁⢀⡂⢁⣀⡰⢡⠉⠩⡒⢄⡀⠀⠀⠀ ⠿⢿⡿⣅⠀⢸⢣⠁⡙⠩⣰⣿⣾⢷⡤⠛⠛⠒⡞⠉⠉⠒⠛⢳⠹⢶⣻⣆⣀⠀ ⡿⠅⣰⠋⢹⣿⡀⢳⠃⢱⢻⠛⠚⡯⡇⠀⠲⢶⣶⠀⠀⣀⣀⢰⣧⠄⢹⠋⢽⠁ ⠣⢬⣣⢄⣾⣇⣧⡜⠀⡏⠁⠀⢠⣿⣀⣆⡀⣿⣿⠀⢀⠀⠀⢸⡇⠃⢹⠉⢻⠀ ⠀⠃⠀⢹⣿⣿⣸⣇⠀⡇⠀⠀⢸⣿⠀⣷⠈⡟⣿⠀⡌⠀⣸⣾⡇⣿⣾⠀⢸⣇ ⠂⡀⠀⣸⣿⣿⣿⡏⡇⡇⠀⢠⢨⠉⠁⠙⠚⠃⠻⠦⠿⠠⠿⠯⠷⢿⡏⠀⣾⣿ ⠀⠂⢊⣿⣿⣿⡿⡇⣿⣧⠀⢸⣾⠗⠓⠒⠯⠀⠀⠀⠀⠀⠤⠴⣶⡼⡀⠀⣿⣿ ⠀⠀⣸⣼⣿⡏⡇⣿⣿⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠥⠐⠛⠛ ⠀⢠⡇⣿⣿⣇⡇⣿⣿⣿⡆⣧⣟⢧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠁⠀⠀⠀⠀ ⠀⣞⢱⣿⣿⣿⡇⡇⢿⣿⣿⣧⣿⢄⠁⠀⠀⠀⠀⠀⠀⠉⢀⣵⠀⠀⠀⠀⠀⠀ ⡼⢁⣾⣿⣿⣿⡇⡇⠘⣿⣿⣿⣿⣦⣈⡂⠄⣀⢀⣠⣴⣾⣿⡏⠀⠀⢀⣀⢠⡤ ⠃⢸⣿⣿⡟⠩⠁⠉⠉⠈⣻⣿⣿⣿⣿⣿⣿⢷⠞⣉⣉⣙⣿⠁⠀⠀⣸⠀⠈⡝ ⢀⣿⣿⣿⠇⠃⠀⠀⠀⠀⠈⢦⠙⣿⠻⠦⣳⣿⡤⠙⡄⢳⡄⠀⠀⠀⣿⠀⠀⠃ ⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢳⣹⠀⠀⢫⡤⣜⠀⢹⡜⠀⠀⠀⠀⡿⡆⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⡀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢠⣾⠕⠁⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡿⠃⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢰⡟⠀⠀⠀⡜⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢰⠃⠀⠀⠀⢠⡏⠀⠀⠀⢰⠃⠀⠀⡀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⣰⡿⠀⠀⠀⠀⡟⠀⠀⠀⡇⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⡴⠃⠀⠀⠀⣰⣻⠃⠀⠀⠀⢴⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⢜⡀⠀⠀⠀⢰⣫⡏⠀⠀⠀⠀⣾⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢊⠁⢀⡄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢿⡃⠈⠀⠀⠀⢀⣯⢏⡇⠀⠀⠀⢸⢻⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢰⠁⠈⠛⠛⠂⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⣼⠃⠀⡰⠀⠀⣾⡜⣼⡇⠀⠀⠀⡞⢸⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⢹⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠻⣦⣾⠀⠀⠀⠀⠀⠸⡆⠀⠀⢿⣧⠀⠀⠀ ⠀⠀⠀⠀⡿⠀⡏⠀⢠⡇⠀⢰⣳⠁⡿⡇⠀⠀⢀⠃⢸⠀⠀⠀⢸⡄⢸⡄⠀⠀⠀⠀⣧⠀⢸⡀⠀⠘⣇⠀⠀⠙⢦⣀⣀⣀⣀⣴⠚⠁⢻⠀⠀⠀⠀⠀⠀⢱⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⡇⢀⣧⠀⢸⠀⠀⣸⡿⠖⡿⣿⠂⠀⢸⠀⢸⠀⠀⠀⠈⣷⠈⣇⠀⠀⠀⠀⢸⡈⠙⡏⠓⠀⢹⡄⠀⠀⢸⠈⡇⠀⠀⠸⡀⠀⠈⣇⠀⠀⠀⠀⠀⠸⡇⠀⢸⣼⠀⠀⠀ ⠀⠀⠀⢰⡇⣸⢹⠀⠘⠀⠀⣿⠀⠀⣷⡟⡆⠀⣸⠀⢸⡀⠀⠀⠀⢿⡆⠸⡀⠐⠀⠀⠀⢇⠀⡇⠀⠀⠀⣿⠀⠀⠈⡆⣇⠀⠀⠀⣇⠀⠀⠘⢦⠀⠀⠀⠀⠀⢳⠀⢸⢹⡀⠀⠀ ⠀⠀⠀⢸⡇⡟⣸⠀⣧⠀⢠⡏⠀⠀⠸⣧⢻⠀⢿⡄⠀⣧⠀⠸⡀⠈⣷⡄⢳⠀⣧⠀⠀⠘⣆⢣⠀⠀⠀⠘⡆⠀⠀⡇⢸⠀⠀⠀⣿⠀⠀⢀⠈⠳⣄⠀⠀⠀⢸⠀⡼⢸⡇⠀⠀ ⠀⠀⠀⠘⣇⡇⢇⠀⣿⠀⢸⡇⢀⡤⣶⣿⣿⢦⡜⠿⢶⣽⣇⣀⢳⡀⠈⠻⣄⡇⠘⣦⡴⣖⣿⣾⣷⣶⣦⣄⢹⣦⠀⠃⢸⡀⠀⠀⣿⢦⡀⠈⠳⡀⠈⠳⠦⠤⢸⢀⢇⣾⡇⠀⠀ ⠀⠀⠀⣀⣼⣯⣼⡄⢸⡆⢸⣷⣿⣿⣿⣿⣿⠿⢿⣆⠀⠀⠈⠛⠓⠛⠛⠀⠈⠛⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⣿⡀⠑⠶⣄⣈⠳⢤⣀⣴⣾⣿⣿⡟⠀⠀⠀ ⠀⣠⣞⣻⣿⣿⣿⠃⡏⣧⣾⣿⣿⣿⡟⠋⠀⢸⠛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠃⠀⠀⠿⠿⣿⣿⣿⣦⣀⢸⡇⠀⠀⣿⠙⢦⣀⡀⠒⠉⢉⡽⣹⣿⣹⣿⠛⣲⡶⠶ ⡼⡽⠋⣰⠋⠀⣿⡀⡇⣿⣿⣷⡿⠟⠀⠀⢀⣀⠁⢹⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠒⠒⠛⣻⣿⣿⣿⢸⡇⠀⠀⡏⢀⣀⠈⠉⠑⠂⢸⢣⡿⢹⠟⣿⣿⣯⣄⠀ ⢱⠁⢰⠃⢀⣴⢻⡇⠃⠋⢹⣯⠓⠀⠀⠀⠈⠉⠀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠛⠀⠀⠀⣿⣿⡟⠚⢻⠃⠀⢸⣿⣯⡛⠱⡄⠀⠀⠸⣮⡇⢸⣤⡇⠘⣆⠈⠀ ⢸⠀⠉⣩⠿⠋⢀⣧⡇⠀⠘⡿⣆⠀⠳⣄⣀⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⡀⠀⢀⡤⠴⠋⣿⣿⠀⠘⠀⠀⣸⡿⡁⠙⠃⣿⠀⠀⣾⣿⢻⢿⠁⢧⠀⠈⠣⣀ ⣮⠽⠟⠋⣀⡴⠋⣿⢳⠀⠀⠛⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⣿⣿⡆⡇⠀⠈⣿⢉⠋⢙⠓⣿⣶⠾⢻⡟⡇⡇⠀⠸⡧⡄⠀⠀ ⠉⠓⠒⠾⣍⡠⠞⣿⡸⣇⢠⠐⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣧⠃⠀⣼⣧⡼⠴⠁⣰⠏⠁⣠⠎⠀⡇⡇⠀⠀⠙⢭⣲⣾ ⠀⠀⢠⣀⡀⣠⢼⡏⡇⢹⢾⢲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⡟⠀⣰⣽⢡⡤⠤⠚⠁⢀⡴⠃⠀⠀⢻⣾⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⠖⠋⠀⢹⡌⣾⣿⠏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡟⣷⠁⡰⣣⠇⠀⠀⠀⣠⠶⠉⠀⠀⠀⠀⠀⠳⠽⢦⣴⣶⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⣟⡇⠈⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⢹⣽⠇⠔⣱⠿⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⡀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⡟⢀⣯⡿⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⡀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⣀⣀⣠⣤⡤⢶⠖⠛⠉⣠⠎⢠⣾⣟⣤⠚⠀⠀⠀⢀⣀⣠⣤⣤⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠓⠂⠀⠀⠀⠀⠉⠉⠋⠙⠻⣯⡀⠴⠒⠀⠐⠒⠺⠷⠶⠛⠛⠋⠉⠓⡶⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠖⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠶⠦⢤⣀⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠈⠉⠁⠛⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠞⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠒⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⡴⠚⠛⠛⢦⡀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢀⣿⣤⠤⠤⣤⣼⣇⡀⢀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀ ⠀⠀⡇⠀⠀⠀⠀⢠⣖⠀⠀⣿⢸⠀⠀⢸⠈⡇⠀⣤⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⢀⡇⠀⡶⠶⠶⣼⣹⣦⠤⠗⠸⣤⣤⣼⠀⣧⣠⡿⣧⣤⣤⡀⠀⢠⡇⠀ ⢀⡾⠁⠀⣽⠀⣼⠋⠙⢻⣷⡀⠀⠀⠀⠀⠀⢠⣾⢿⣷⣦⠸⡇⠀⠈⢧⠀ ⢸⠁⠀⣼⠁⠀⣧⠀⣀⡾⢻⡇⠀⠀⠀⠀⠀⣿⠀⠀⡿⣿⠀⠳⡄⠀⠈⣇ ⠘⣇⠀⣿⢦⡤⠼⣿⠿⠿⠋⠀⢀⠀⠀⡀⠀⠙⠿⢿⠿⣯⠤⣤⢿⡇⢠⡏ ⠀⠈⢧⢸⡆⠳⣤⣸⠂⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⢼⣁⡴⠋⡼⢰⠏⠀ ⠀⠀⠺⠞⠀⠀⠀⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉⠀⠀⠹⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⡶⠄⠐⠂⢳⣤⠖⠋⠉⠙⠉⢦⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡸⢷⠒⠤⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣾⣁⡤⠀⠀⣨⠚⢻⣖⣲⣶⣦⡄⢲⡷⠴⠒⡞⠛⣻⠛⠟⠳⡛⢿⠿⣷⣴⣀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣩⡏⠀⢀⣸⡷⢤⣼⣿⣿⢿⣿⣇⠀⠁⠀⠀⠘⡄⠀⠀⠀⠀⢱⠘⡄⠀⠈⢫⡚⢵⡤⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠟⠋⠀⠀⢸⣏⠛⠓⠻⢿⣿⠖⠋⣿⣿⣻⣾⣿⠅⠀⣤⣶⣾⣟⣁⣠⡿⠿⠿⢿⣅⣙⣶⣶⣔⠛⣄⣈⢻⣷⡀⠀⠀⠀⠀ ⠛⠛⢿⣿⠟⢦⣀⠀⢀⣿⠸⣆⠀⢀⠏⠀⢢⣰⣿⣿⣾⡿⢿⣶⠖⠋⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⢻⡛⠛⠿⣦⣹⡳⣤⣄⠀⠀ ⣶⣶⠋⠁⢠⡿⠛⣿⣿⣿⡀⠙⣦⣾⠖⢒⣶⢿⡿⠯⢭⣍⣿⣿⣀⣒⣢⣤⣤⣼⣧⡄⠀⠀⣀⣀⣀⠀⢀⣸⣇⠀⠀⢈⣏⡷⢻⣿⡇⠀ ⡟⠉⠠⣠⡿⠁⠀⣿⣿⣹⣇⠀⢸⡇⠀⢸⣿⣸⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢉⣿⣿⡇⠀⠀⠐⠒⠒⠒⠀⣿⣿⠫⡤⢤⣧⣀⣀⣻⠇⠀ ⠓⠤⣀⡟⠣⣄⢠⣿⣿⡇⣿⣄⡾⠀⠀⣸⠀⠀⠀⠀⠀⣼⣿⣇⣀⣇⠀⠀⣸⣿⣿⡇⠀⠀⡄⠀⠀⠀⡄⣿⣿⠀⣧⠀⣿⠁⠈⣿⡆⠀ ⠀⢀⡞⠋⠑⠺⣿⣿⣿⣷⢸⣿⡇⠀⠀⣿⠀⠀⠀⠀⠘⣿⣿⠋⠉⣯⡙⠛⣿⣿⣿⣧⠀⠀⡇⠀⠀⢠⣇⣿⣿⣤⣿⣀⣿⠀⠀⢸⣷⠀ ⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⣿⣧⢀⠀⣧⠀⠀⠀⠀⠀⣿⣿⡄⠀⣿⡇⠀⣿⡇⡟⣿⠀⢸⡇⠀⠀⣾⣿⣿⣿⢰⣿⣿⣿⠀⠀⢸⣿⣴ ⡶⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⢸⠀⣼⠀⠀⠀⡀⢰⠛⠛⠛⠒⠓⠷⠤⣿⡇⠇⣿⡄⢸⡇⠀⢠⣿⣿⢿⣇⣾⣿⣷⡏⠀⠀⣼⣿⣿ ⠀⠠⠂⠀⣔⣼⣿⣿⣿⣿⣿⣿⡇⢸⣇⣿⠀⠀⠀⣧⢨⡇⡀⢀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⠁⠀⠀⣿⣿⣿ ⠀⠀⠂⠚⢀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡄⠀⠉⣿⣿⡿⠿⠛⠛⠻⠷⢶⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣖⣾⠇⠀⠀⢰⣿⣿⣿ ⠀⠀⠀⠀⣸⠟⣿⣿⣿⡿⡇⠘⣧⣼⣿⣿⡇⠀⠀⢸⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡿⣼⠀⢀⣸⣿⣿⣿ ⠀⠀⠀⢀⡿⢾⣿⣿⣿⡇⡇⠀⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠚⠉⠉⠉⠉⠉ ⠀⠀⠀⣾⠃⣾⣿⣿⣿⠉⡇⠀⣿⣿⣿⣿⣿⡀⢰⢤⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⢀⣿⣿⣿⣿⣼⡇⠀⡇⣿⣿⣿⣿⣧⣸⡿⣿⡇⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢚⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⡇⢸⣿⣿⣿⣿⣿⣇⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠉⠀⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⢿⣿⣿⣿⣿⣿⣾⣿⡀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠃⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠈⢿⣿⣿⣿⣿⣏⣿⣷⣤⣄⣈⣑⢲⣤⣀⣀⣀⣤⢶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⡤⢴⣶⡿ ⡏⠀⣀⣿⣿⣿⣿⣿⠛⢻⠗⠐⠉⠉⠑⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠼⠟⠋⠋⠉⠉⣿⣿⡟⠀⠀⠀⠀⠀⡟⠀⠀⠀⣏⢷ ⠁⠀⣼⣿⣿⣿⣿⡇⢀⠇⠀⠀⠀⠀⠀⠀⠈⢺⡟⢿⣿⣿⣿⣿⣿⠿⢿⠿⢛⢻⡟⠲⣶⡲⠤⣤⠞⢻⠃⠀⠀⠀⠀⢰⡇⠀⠀⠀⢻⠨ ⠀⢰⣿⣿⣿⣿⣿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠉⢻⣿⠛⠿⢷⣦⣲⡿⠿⡧⠤⠛⣷⠀⢻⣆⡎⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠸⠀ ⢀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠈⣿⠁⠀⠀⠈⡿⠋⠉⢻⡆⠀⠸⣧⠀⡟⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣧ ⣾⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣸⣆⠀⠀⠀⢙⣿⠿⢿⣄⡀⠀⢻⡶⠁⠀⠀⠀⠀⠀⠀⢸⠻⣧⠀⠀⠀⢹

⠀⠀⠀⠀⣀⣀⣀⣀⢔⡊⠙⠟⢠⣄⠀⠀⣿⣉⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣮⣾⠿⠛⠀⣁⠠⠄⠒⠒⢒⠀⠄⣘⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣧⣶⠞⠁⡐⢁⠀⠀⠀⠀⡑⡀⠀⠳⢄⠀⠀⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⠏⠀⡐⢀⠃⠀⠀⠀⠀⠀⢠⣰⣷⣶⢆⠀⣿⣿⣄⠀⠀⠀⠀ ⠀⣰⣿⣿⠿⠀⠀⠀⡈⢰⠀⠀⠀⡇⢀⡈⢿⣿⣿⠀⢻⣿⣿⣿⣣⡀⠀⠀ ⢰⣿⣿⠏⠀⠂⢰⠀⡇⣀⡀⠀⠠⢣⠀⡏⢂⠉⠀⠃⣼⣿⣿⣿⣷⡇⠀⠀ ⠈⢻⠣⠀⢠⠀⢸⠀⣇⠹⡇⠇⠸⠶⣦⣵⣸⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀ ⢀⡳⠀⡔⣼⢠⢈⡧⠿⠆⠘⠈⠀⠀⣾⡿⡙⠀⠀⡀⠀⠹⡿⠇⠀⠀⠀⢰ ⣼⡇⡞⠠⠏⡼⠜⠣⡀⠀⠀⠀⠀⠀⠀⠠⡇⠂⠀⡇⠀⣠⢧⠀⡀⠀⠀⠸ ⠘⠐⠧⣡⡎⠀⠀⠀⢰⣄⡀⠀⠀⢀⣠⠗⠃⢀⢰⡙⡄⣟⢸⡘⠀⠀⠀⠀ ⠀⠀⡜⡜⠀⠀⠀⠀⠈⢣⡾⣷⠘⠋⠀⢄⡀⡘⢆⠜⠈⣎⢤⡇⠀⠐⢄⠀ ⠀⠀⣿⣀⠀⠀⣀⠤⠀⣊⠌⠻⣒⠄⢒⡡⠔⠈⡱⢁⠜⠁⠘⡿⣄⠀⠀⠃ ⠀⢸⡸⠺⣉⠀⠀⢀⡠⠘⠀⠀⣞⡺⠀⠀⢠⢏⠔⢱⠀⠀⠀⡇⠘⠡⠀⠘ ⠀⠃⠋⠀⠀⠀⠈⡞⠀⠀⠀⠀⢸⠊⠀⠀⣜⠎⠀⠀⢂⠀⢀⠇⠀⠀⠀⠀

⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⡠⠔⠒⠐⠉⠙⣆⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠐⠿⠃⠀ ⠀⣄⠀⠀⢸⠀⢀⡀⠀⠸⠀⠘⡃⠠⣳⣖⠀⢀⣦⣀ ⠈⠻⠉⠀⣿⣤⢘⠉⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠙⠀ ⢼⡦⠀⢊⢿⡋⠀⠀⠀⡴⢴⠒⠄⠀⠘⢄⢠⠛⡄⠀ ⠀⠁⠀⠀⠀⠉⢱⠂⠀⠀⠺⠂⠀⠀⠀⠀⢻⣰⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡴⠋⡉⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣶⣶⠶⠾⠿⠿⢿⣦⣦⡙⢶⣶⢦⣄⠀⣦⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠛⢿⡁⠀⠀⠀⠀⠀⠠⢀⡈⠛⠲⠿⢿⣟⠛⠻⣶⡦⢄⡀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣈⣟⣳⣤⣄⣀⡤⠞⠁⠀⠀⠀⣀⠀⠀⠈⠂⠀⢀⣠⠤⠤⠤⠠⠤⠤⢄⣈⣻⠿⢿⣆⣙⠛⠃⣬⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠙⡿⠀⠈⣏⠀⠀⠀⠒⠈⣉⡭⠶⠒⡒⠋⠉⠉⠀⠀⠀⠀⠀⠐⠤⡀⠈⠉⠓⠲⢬⣉⠻⣤⣩⣙⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣻⡤⠀⠀⡠⠛⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠙⠀⣾⠏⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠀⠈⣷⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡾⠀⢠⣿⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⣴⡟⣿⠁⣰⠋⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣿⢷⡤⢄⣠⡶⣾⣿⣴⠏⠀⣿⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠘⠿⣷⣶⡶⣿⣺⣿⣿⣧⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠿⣿⡇⠈⠉⠀⡿⠉⠁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠙⠒⢒⣾⠃⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣇⠀⠀⡀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⢠⢿⠿⣤⠀⢸⠁⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢹⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣰⡞⠀⢹⡀⢠⣿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⢀⡾⡏⠀⢸⡆⡿⠀⣴⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣰⠇⠤⠀⠹⣄⠀⠀⠀⢻⣆⠀⠀⢀⣸⡿⠁⠀⢸⣧⢿⡿⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⡸⣻⠀⠀⠀⢳⠃⢠⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⣿⣶⡶⠿⠦⡌⠛⠶⠤⠼⠏⠓⠤⠾⠃⠀⣀⣴⣿⣿⣿⣇⡇⠀⢀⡄⠀⡀⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⣷⠇⠀⠀⠀⢸⡇⡞⡟⢹⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⡠⠖⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠉⠉⠉⢸⣿⢀⣠⢾⠀⠀⢱⣄⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⡟⣷⡇⡏⠀⢀⡏⠀⠀⠀⠀⠀⣤⣤⣾⣿⡟⠀⡞⢁⣠⣶⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣼⣿⣯⣄⡼⠀⠀⢸⡟⣆⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣻⡇⠻⡇⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣏⢹⣿⡟⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣙⣬⣿⣿⣷⣤⣄⣸⠁⠹⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢠⣿⣷⣤⢃⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠻⢿⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠉⠉⠁⠉⠉⠀⠀⠉⠙⠳⣤⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⡇⠀⠀⠀⠀⠀⡼⣼⡿⣾⡜⠁⢸⡄⠀⠀⠀⠀⠀⠀⠹⣦⣄⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠆⢀⣴⣿⡿⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⠀⠶ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⢃⢏⠁⣿⣇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣭⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣠⠞⣹⡏⢁⣀⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⣰⠃⡼⢸⠀⡟⠘⢦⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣽⡭⠭⠽⣶⠶⢤⣤⠴⢶⣶⠟⠁⠀⠿⣦⣽⣵⠟⠛⠁⠀⠀⢠⣤⠶⣤⡀⠀⠀⠀⠀⠙⡿⢂⡀ ⠀⠀⠀⢼⠃⠀⠀⠀⡰⠃⡸⠃⡿⠀⣷⠀⠀⠉⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣀⡈⠓⢮⡙⣿⣿⠀⠀⠀⠀⠀⠀⢈⣾⡧⠀⠀⢠⡿⡃⠀⠈⠙⣧⡀⠀⠀⠀⢡⣀⠋ ⠀⠀⠀⡼⠀⠀⢀⡜⠁⣰⠃⢰⠇⠀⠙⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠲⣤⢀⣀⣀⡴⢾⠁⠀⣠⡿⠿⠿⡷⣦⠀⠀⠀⢰⢻⡇⠀⠀⠀⣾⣋⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⣄⣀ ⠀⠀⢰⠃⠀⣠⠏⢀⡜⠁⠀⡼⠀⠀⠀⠈⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠙⠾⣆⣾⠋⠀⠀⠀⠀⢹⣧⠀⠀⠈⠛⠃⠀⠀⠀⢻⣯⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠈⣿ ⠀⢠⠏⢠⠞⠁⣠⠟⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⣢⠄⠙⢷⣶⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⠶⠛⠋⠀⠀⠀⠀⠀⠉ ⣠⢏⣴⣁⡤⠞⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢀⣠⣄⣙⣦⡀⠀⠀⠀⠀⠙⠳⣶⠒⠉⠁⠀⠀⠈⠻⣦⣤⢀⠀⢀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢠⣾⢿⣪⠿⠀⣿⡿⡷⢤⣄⣤⡤⠴⠴⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⢾⡿⣿⣆⣉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣀⣰⣛⣱⣿⠶⠶⢾⣯⣼⡇⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠀⣠⣤⡼⢿⣿⣧⣨⣿⣶⣄⣀⣀⣀⣀⡀⠀⠀⣀⡀⣴⡙⠻⠶ ⠀⠀⠀⠀⢀⣀⣴⠇⠀⡴⣻⠟⠋⠉⠀⠀⢁⣰⣯⣖⢾⣶⠛⠁⢠⣴⡶⠿⣿⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡻⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⢹⢿⡟⣿⣏⠀⠈⠙⠶⢄

⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⡇⠀⢰⢰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢏⠉⠁⠀⠀⠀⠀ ⠀⠀⢰⠀⡇⢀⠀⠡⣧⡀⠀⣧⠀⠀⡀⠇⠀⠀⠀⡆⠀⢀⠀⠀⠀ ⠀⠀⠘⠐⣷⢸⡀⠀⠀⡉⠀⣇⡱⠁⡀⢻⠀⠀⠀⢱⠈⠁⠀⠀⠀ ⠀⠀⡌⡰⠊⢋⣧⡀⠀⢧⠀⡇⢀⠈⠢⣸⠀⠀⠀⢸⠀⠀⣀⠄⠀ ⠀⠀⡗⣡⣶⣼⡟⠕⢄⣘⣂⡽⣿⣿⣿⣮⣤⡀⢠⢸⠀⠉⢸⠀⠀ ⠀⠸⡿⠍⠷⠿⡵⠀⠀⠀⠀⠀⢸⡙⣭⣛⠋⠀⡀⢸⢣⠀⢸⠀⠀ ⠀⠀⡏⡆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠶⢼⠀⢠⠃⢸⡸⠀⠂⠀⠀ ⠀⠀⡇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⡟⠁⢠⠀⡄⠀ ⠀⠀⢃⠀⡅⠂⠄⡀⠀⠀⠀⢀⠀⠀⢐⠇⠈⠀⢀⠃⢠⠀⣴⣇⠂ ⠀⠀⢸⠀⣇⠀⠀⠀⡩⢙⡏⠀⠀⣀⣌⠀⠀⡰⣘⣰⠏⠷⠿⡁⠀ ⠘⠄⠀⢇⠏⠴⢊⢋⡔⠁⡀⠀⠀⣠⡂⠄⠊⢘⠡⢊⠂⢄⠐⠀⠑ ⠀⠈⡲⢤⠵⠥⠁⡮⠐⠠⢈⢢⡍⡲⡀⠀⡀⠀⠴⠁⠀⠀⠡⠀⠀ ⠀⠈⠀⠈⡢⠀⢠⠀⠀⠀⠀⠙⠃⠀⠈⠪⠠⠊⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⢀⡀⠙⣷⡀⠀⠀⠀⢀⡾⢋⡤⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠇⠙⣄⠘⠧⠤⠤⠤⣾⢡⠏⠀⢱⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡏⠀⢀⡖⠲⣄⠀⠀⠀⣀⠤⠊⠁⠀⢣⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣠⠤⠞⠀⠀⠈⠑⠦⠊⠁⠀⠀⠀⠀⠀⠙⠒⡂⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⢱⠀⢱⣶⡄⠀⢠⣤⣤⡄⠀⠀⣴⣶⡆⠀⠰⠥⡀⠘⣧⠀⠀⠀⢀⣀⣀⡀ ⢸⡇⡞⠀⠈⠋⠁⠀⢈⣩⣭⣁⠀⠀⠉⠉⠀⠀⠀⢠⢇⣤⡿⠀⣠⡶⠛⠉⢸⠃ ⠘⠷⠿⣤⣄⣀⡀⠀⠹⣏⣠⠟⠁⠀⠀⣀⣀⣤⡶⠟⠋⠁⢀⡾⠋⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠉⠉⡟⠛⠒⠒⠒⠚⠛⠋⠉⠁⠈⠻⣦⠀⠀⢸⢇⡠⡄⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡄⠀⠀⠀⣤⠀⠀⠀⠘⣧⠀⢸⠉⠀⠧⠴⠲⣸⡇ ⠀⠀⠀⠀⣾⠛⢷⣧⡀⢀⣸⡇⠀⣀⢤⣿⠞⠛⢻⡄⢹⣆⣿⠀⠀⠀⠀⣠⡟⠀ ⠀⠀⠀⠀⢹⡆⠀⢿⡈⠉⠸⡟⠊⠁⢸⡇⠀⠀⣸⡇⢈⡟⠁⠀⢀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠻⠶⠾⠷⠶⠶⠷⠶⠶⠾⠧⠤⠾⠿⠴⠾⠷⠶⠛⠋⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠾⢳⣦⡀⠀⢀⣠⣶⣦⡄⢠⣾⠟⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠙⣿⣷⡾⢿⣿⠀⣼⡟⠛⢿⣦⣿⠇⢹⣧⣼⣿⣦⣄⣿⡟⠙⣷⠀⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⣿⣦⡀⣿⡏⠀⢸⡿⠀⢿⡇⠀⠈⣿⡿⠀⢸⣿⣿⡀⠈⣿⣿⠃⠀⢿⣿⡟⠉⠻⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣀⠀⣿⡏⠀⠈⣿⣿⡿⠹⣇⣿⠁⠀⣼⡇⠀⢸⣿⠀⠀⣿⡇⠀⠀⣿⣿⡇⠀⢸⣿⠀⠀⢸⣿⠁⠀⢰⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠉⢻⣧⠸⣇⠀⠀⠸⣿⡇⠀⢻⣿⠀⠀⣿⡇⠀⠀⣿⡄⠀⣿⡇⠀⠀⣿⡿⣷⠀⠈⣿⡆⠀⣼⡟⠀⠀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⣿⡄⢿⡀⠀⠀⣿⡇⠀⠸⣿⠀⠀⣿⣿⠀⠀⢸⡇⠀⢸⣇⠀⢀⣿⠁⣿⠀⠀⢻⣇⢠⣿⠀⠀⢠⣿⣷⣤⣄⡀⠀ ⠀⠀⢀⣀⡀⢿⣇⠀⠹⣧⢸⣇⠀⠀⣿⡇⠀⠀⣿⡀⠀⢿⣿⡆⠀⢸⣇⠀⢸⣿⠀⢸⡟⠀⣿⡆⠀⠈⣿⣼⡇⠀⠀⢸⡏⠀⠀⢻⡇⠀ ⠀⣰⡿⠛⢻⡞⣿⡀⠀⢻⣆⣿⠀⠀⣿⡇⠀⠀⢻⡇⠀⢸⣿⣇⠀⠸⣿⠀⠈⣿⡄⣿⠇⠀⢹⡇⠀⠀⣿⣿⠀⠀⠀⣿⠃⠀⠀⣿⠇⠀ ⠀⣿⡇⠀⠀⣿⣾⠿⣿⡌⢿⣿⡆⠀⢸⡇⠀⠀⢸⡇⠀⢸⣿⣿⠀⠀⣿⠀⠀⢹⣷⣿⠀⠀⣸⡇⠀⠀⣿⡏⠀⠀⢀⣿⠀⠀⢸⡟⠀⠀ ⠀⠸⣷⡀⠀⣿⡁⠀⠹⣧⠈⢿⣧⠀⢸⣇⠀⠀⢸⣇⠀⠀⣿⣿⡇⠀⣿⠀⠀⢸⣿⡇⠀⣠⣿⡇⠀⠀⣿⠁⠀⠀⢸⡏⠀⢠⣿⠃⠀⠀ ⠀⠀⠹⣧⠀⢸⣧⠀⠀⢿⡆⠘⣿⠀⠸⣿⠀⠀⠸⣿⠀⠀⢸⣿⣇⠀⣿⠀⠀⠀⣿⠁⢠⣿⢹⡟⠀⣸⡟⠀⠀⠀⣼⡇⠀⣾⡏⠀⠀⠀ ⠀⠀⠀⣿⣧⠀⢿⡄⠀⠈⣿⡀⣿⡇⠀⣿⡀⠀⠀⣿⡄⠀⠀⣿⣿⢠⣿⠀⠀⢸⡟⠀⣼⡿⢸⡇⢀⣿⠇⠀⠀⠀⣿⠀⢰⣿⠻⢷⣤⠀ ⠀⢀⣠⣿⣿⡄⠘⣷⠀⠀⠘⣷⣿⣇⠀⢹⣧⠀⠀⢸⣷⣀⣀⣸⣿⣼⣿⣆⣠⣾⣇⣠⣿⡁⣸⡇⣼⡿⠀⠀⠀⢰⣿⠀⣾⢿⣦⠀⠹⣷ ⢰⣿⠋⣠⣼⣿⡀⢹⣧⠀⠀⣹⣿⣿⣶⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⢷⣿⣇⡀⠀⠀⣸⡇⢰⣿⣾⡟⠀⠀⢿ ⣿⡇⠀⣿⣿⣿⣧⠀⣿⣷⡾⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⣿⡇⣸⣿⡿⠁⠀⠀⣿ ⢹⣷⠀⠘⢿⣿⣿⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣿⣿⠃⠀⠀⢀⣿ ⠀⢿⣧⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠁⠀⠀⠀⢸⡿ ⠀⠈⢿⣧⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⡇ ⠀⠀⠈⢿⣧⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀ ⠀⠀⠀⠈⢻⣧⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡟⠀ ⠀⠀⠀⠀⠀⢿⣆⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⢹⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⣠⣶⣶⡶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢰⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣀⣸⣷⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠈⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣤⡄⠀⠀⢴⣶⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀

⠀⣾⡿⠿⣿⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⠿⣿⣶ ⢸⣿⠃⠀⠀⠀⠈⠉⠙⠛⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠛⠋⠉⠁⠀⠀⠀⠸⣿ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣴⣶⣾⠿⠿⠿⠟⠛⠛⠛⠿⠿⠿⢿⣶⣶⣤⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢻⣿⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⣿ ⠸⣿⡆⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢸⣿ ⠀⢿⣷⡀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢀⣿⡟ ⠀⠈⣿⣧⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣾⡿⠀ ⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀ ⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀ ⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀ ⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⢻⣿⡀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠀⠈⠙⣷⣤⢾⠂⠀⠀⠀⠀⣿⡟⠀ ⠀⠀⠈⣿⣧⠀⠀⠀⠸⢯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⠀⠀⠀⠸⠷⠞⠃⠀⠀⠀⣸⣿⠃⠀ ⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⢤⣀⣀⣦⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢯⣏⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⢿⣶⡀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠈⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⡇⠀⢰⡆⠀⠀⠀⢰⡄⠀⠀⠀⢠⡆⠀⠀⠀⢰⡆⠀⢸⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠙⣿⡀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⢀⣿⠉⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣶⣾⣿⣾⣷⡀⠀⢀⡿⠁⠀⠀⠀⠈⢿⡀⠀⠀⣾⣷⣿⣷⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠿⣿⣶⣶⣶⣶⣶⣿⣿⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠎⠀⠀⠀⢁⠀⠀⠈⠢⠀⠈⢢⡀⠀⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⠀⠐⠀⠘⠀⠀⠀⠀⠀⢃⠀⠀⠀⠡⢀⠙⣶⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⡌⠂⠀⡇⠀⡆⠀⠀⠘⡄⠀⢸⣄⠀⠀⠀⢃⠑⢴⡆⢀⡴⢳⠀⠀⠀ ⠀⢄⠀⠀⢻⠀⠸⣇⡀⢇⠀⠀⠀⡑⡤⠐⡙⡀⠀⠀⠸⡠⡙⡷⣏⣀⢀⠀⠀⠀ ⠉⠚⢆⠀⢸⠀⢰⢰⣈⣏⣇⠀⠈⡄⢼⠟⢍⢳⡦⠀⢀⠣⠜⠙⢌⠙⢻⠀⠀⠀ ⠀⠀⣀⠀⣾⡀⠘⡸⡏⣎⣇⠑⢄⢃⠘⣖⡺⠘⠁⠀⣿⠐⢰⡛⡘⠀⢸⠀⠀⠀ ⣠⢤⡿⠀⢹⢱⡄⠑⣧⡑⠃⠀⠀⠈⠀⠀⠀⠀⡆⡸⠃⠐⠚⡡⠁⢸⢸⠀⠀⠀ ⡠⢜⣠⠀⠀⠁⠙⠦⣷⠁⠀⠀⠀⠀⠀⠀⠀⠤⠜⠀⡐⣹⣿⡇⠀⠸⡄⠀⠀⠀ ⠀⠩⢧⣶⠆⠀⠀⠀⠀⠢⡀⠀⣀⣀⡀⠀⠀⠀⣠⠎⠀⣿⣿⣇⠀⠀⣧⠀⠀⠀ ⠀⠀⠀⠉⡀⢀⣀⣀⠠⡔⢾⢟⢭⣀⣀⣀⣤⡾⠁⠀⠀⢻⣿⣿⡆⠀⢸⠀⠀⠀ ⠀⠀⠀⣠⢋⠬⠉⢻⠇⠀⠈⣸⡘⣿⣿⡟⠋⠀⠀⢀⠔⠁⠀⠀⠙⢀⠀⠃⠀⠀ ⠀⠀⠀⡅⠁⢈⢰⠁⡠⠂⠈⢹⠋⡩⡻⠻⠀⠀⠀⠆⠀⠀⠀⢡⠀⠀⢂⠘⡀⠀ ⠀⠀⠀⠅⠀⢸⡆⠰⠢⡀⠸⠠⢋⠌⠀⠲⠠⠒⢨⠀⠀⡠⠄⠒⢄⠀⠀⡄⢡⠀ ⠀⠀⢀⣾⠀⢘⢿⠇⠀⠈⠗⢠⠂⠑⠤⠤⠐⠈⢹⠔⠡⠀⠀⠀⠀⠱⡀⠃⠀⡄ ⠀⠀⢪⣙⠐⡑⠹⠠⢀⡊⣠⡁⠀⠠⠂⠀⠀⢀⢿⢠⠁⠀⠀⠀⠀⠀⠐⡄⢰⢀ ⠀⠀⡙⣀⠠⠐⠘⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⢎⢷⢸⠸

⢀⡀⠀⠀⣰⣿⣿⠙⠁⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⢸⠇⠀⠀⠀⠈⠈⠻⢯⢷⡴⣤⣀⠀⣠⠙⠋⠙⢦⠀⠀⠀⢹⡷⠀⠀⠀⠉⠙⠿⣇ ⡿⠃⢠⣴⢿⣿⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠉⠁⠀⠀⠀⠈⠳⡄⡄⠀⢷⡀⠀⠀⠀⠀⠀⠈ ⠈⣿⣿⣷⣾⢿⠃⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠈⢷⡀⠀⠀⠀⠀⠀ ⠀⠻⠿⠿⡿⢸⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠐⠤⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⣀⠤⠤⠀⠀⠀⠳⡄⠀⠙⠒⠶⣿⡿⢂ ⠀⠀⠀⢰⠁⡞⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠔⢊⣩⣤⡴⠒⠒⠒⠒⠂⠤⣽⣦⣀⣠⠖⣁⠴⣫ ⠀⠀⠀⢸⣾⡇⠀⠆⠀⠀⡇⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⢋⣿⡾⠛⠉⠀⠐⠂⠈⠛⠛⠉⣿⣾⣟⣡⣴⣾⣿⣟⡁ ⠀⠀⠀⡾⣿⡇⠀⠀⠀⢰⣧⣿⠄⠀⠀⠀⠀⠀⢸⠀⠀⢀⡤⠖⣋⣥⢴⡾⠍⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠿⠛⣿⢻⣿⣿ ⠀⠀⠀⠉⣿⣿⢧⣀⠀⣼⣩⠟⠀⠀⠀⠀⠀⠀⣸⠤⢚⣥⣶⣿⣯⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣀⣠⣴⣏⣸⣿⠇ ⠀⠀⠀⠀⢸⣿⠶⣤⣙⡟⠣⢤⣀⣀⠀⠀⠀⠀⣿⡴⣿⣷⣾⣿⠏⢀⣶⡄⠀⠀⠀⢀⣶⢲⡄⠀⠀⠀⠀⠀⣼⠷⠶⠛⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠟⠒⠝⠟⠳⢶⣦⣤⣬⣭⣭⣭⣽⣿⣿⣿⣿⡇⠀⡟⠉⣻⠀⠀⠀⡸⠳⢴⠇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠘⡟⣿⣠⡇⠀⠛⠒⠒⠰⠃⠀⢸⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡞⠉⣀⣤⡀⠀⠀⢀⣠⡄⠈⠉⠒⢄⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢠⣄⠀⠀⠀⠀⣰⢤⠀⠀⠀⢰⠇⡇⠀⠉⠙⠀⠠⠀⠈⠛⠛⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣯⣼⡇⠀⠀⠀⡿⠤⡇⠀⠀⣾⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡏⠓⠶⠆⠀⣇⣀⠀⣀⡇⠀⠱⠔⠋⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣠⡄⠀⠉⠀⣠⣤⡀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠛⠁⠠⠤⠄⠉⠋⠁⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢀⣙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠘⣽⡆⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀ ⢁⡀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⢢⣸⣆⣀⠀⠀⠀⠈⣿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠀⢸⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣷⣦⣀⠀⠀⠀⣞⠉⢉⣦⣤⢬⣇⣀⣭⡿⠀⠀⠀⠸⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⢀⡟⢠⠟⡆⢸⡀⢱⣄⣠⣶⠀⢣⠀⠀⠀⠀⢸⡰⣄⠀⠘⣏⠛⠻⢶⡞⠙⢲⠏⡁⠀⠐⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⡇⠸⠀⠘⢿⣿⠛⠛⣄⠀⠳⣌⣧⠀⠀⠀⠀⣇⠢⠙⢶⣾⢧⡤⢾⡤⠶⠿⣤⣁⣤⠴⡎⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣇⢠⣦⣬⣙⠢⡀⠈⠑⠢⠿⠛⠳⢼⡗⠤⣸⣄⠀⠀⠈⠛⢳⣄⠄⠀⠀⠀⠀⠙⢦⡈⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⣷⣌⠂⠀⠀⠠⠤⣤⠴⠆⠀⠈⠉⠹⡄⢀⡴⣋⣤⣶⣶⣶⣶⣶⣄⡀⠙⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⣿⠟⠛⢻⠟⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣾⣿⣿⣿⣷⣧⣽⣿⣿⣿⣷⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡟⣆⠀⢸⣿⣿⣝⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⣿⣤⡾⢷⣤⣸⡇⠉⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⠀⣀⡁⠾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣽⡿⠋⠈⣿⠃⠀⠀⣸⠋⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣽⡀⠀⠉⠙⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣓⣒⣋⠁⣀⣠⡎⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠤⠼⠋⠉⠁⣆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠸⡗⣶⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡀⠀⠹⣦⢨⠙⢦⡀⠀⠀⠀⢸⣿⠗⠲⣖⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⣶⠀⣀⠀⠀⠳⣄⠀⠙⠿⢄⣀⠉⢲⣄⠀⠀⠙⠋⠉⠙⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣾⠏⠀⠀⠀⠀⠀⢀⡖⠀⣠⡄⠀⢸⠀ ⠀⠘⣧⣹⣷⣤⣀⠀⠉⠲⢤⡀⠈⢉⣹⢿⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡒⠋⢁⡤⣞⠁⠀⠀⠀⠀⢀⣴⡟⣁⡔⠃⠳⡄⠈⣶ ⠀⠀⠈⠿⣿⣮⣽⣿⣦⠶⠿⠛⠛⠻⠬⣮⡳⣤⣌⣙⣶⡶⣶⡖⠒⠛⠉⠁⠀⠀⠀⣀⣬⠞⠉⠀⢀⣀⣀⣴⡿⠷⠚⠉⠀⠀⠀⠈⠓⠾ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⣀⣤⠶⢶⠒⠒⢲⣯⣽⠟⠉⠀⡾⣯⣧⠀⠠⢤⣀⣠⠔⠋⠁⡠⠋⠉⠉⠉⠙⣷⠶⢶⡎⠤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⢰⠃⠀⣠⡏⡼⠁⠀⠀⠈⢿⠟⠁⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⢠⠏⠙⠛⠉⠉⠉⠀⠴⠛⠛⠲⣄ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢠⠏⠀⢰⡏⠰⠃⠀⠀⠀⠀⠈⣦⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⢀⡎⡠⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

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

⠀⢀⣴⣆⠀⠀⣴⣶⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣐⡀⠀⠀⠀⠈⠁⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⠝⢸⡭ ⢀⣿⣡⣿⠀⣾⣣⣼⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⣆⢦ ⣾⠋⠉⠹⢿⠟⣩⡙⢷⣤⠀⠀⢸⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠟⠹⢸ ⠇⠞⢻⠛⠛⢀⡟⠀⢸⡟⠀⠀⡿⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⣸⡃⢀⣚⠁⠀⢸⣥⢞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⠀⠛⠃⠈⠛⠁⢀⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣆⠙⢮⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣳⢯⡟⣿⡟⣿⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣧⣸⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⢀⣿⠁⣿⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠃⠀⣸⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢡⡀⣼⠃⢰⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⡏⣼⣿⡟⢀⡼⢱⠸⣿⣿⣿⡽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡾⣣⡟⠁⣿⣿⣿⣿⢻⣿⣿⢸⣾⣿⣿⣿⣿⣿⠇⣿⣿⢀⣮⣴⡾⡟⢻⣿⣿⢿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣷⣼⣿⣿⣿⡿⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡟⠋⠀⠀⠀⠀⠉⠙⠋⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢹⣿⣿⣿⣿⡇⢸⣟⠸⣿⣿⣿⣿⣿⣿⢧⢀⣴⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠓⢌⣿⠀⠻⠻⠿⠿⠿⠿⠈⠉⠀⣧⠀⠀⢿⣹⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠞⠛⠉⠓⢶⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠳⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣭⡿⠋⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣷⡈⣇⠀⠀⠀⠀⠀⠘⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠋⠁⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣠⣴⣾⣿⣏⣼⣿⣿⣿⣿⣿⣷⡼⣆⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣰⣇⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⣼⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⢀⣴⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢧⡀⠀⠀⣠⡴⠋⠀⠀⠑⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⣤⣾⡿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⢺⣿⣿⡿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⢀⣠⣤⠶⠒⠋⢉⡿⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀ ⢀⣿⣿⣿⠃⣼⡿⠿⠛⠉⠉⠉⠉⠉⠉⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⠖⠒⠋⢉⣠⠴⡶⠏⠉⠀⠀⠀⠀⢠⠏⠀⢸⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠚⣿⠟⣿⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⣿⣿⣿⣇⠀⠀⠀⡀⠀⣼⣆⡠⢞⣡⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⣤⠋⣴⣁⢸⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⣇⡀⢸⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⢡⠎⠁⠈⠙⢿⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠈⠁⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⡴⠛⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠉⠁⠀⠀⠀⠀⣿⣿⡿⣿⣿⣧⣀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣀⣼⣿⣿⠟⣡⣿⡿⡿⠛⠉⠀⣰⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠤⣄⣀⣛⠀⠀⢸⣿⣷⠸⣿⣿⣿⣿⣶⣤⣀⡈⠉⠓⠲⠶⠶⠶⠶⠚⠉⠁⣀⡴⢋⡽⠛⠉⠀⠈⢀⠽⠊⠀⠀⢀⡾⠁⢠⡆⠀⠀⠀⢀⡄⡈⠀⠀ ⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠉⠀⠀⠀⠉⠛⠺⠿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⣀⣠⣴⡿⠋⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⣠⠟⠀⠀⣼⠁⣀⣝⣷⣽⣿⡇⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣈⣻⢿⣿⣿⣯⠙⣛⡛⠻⠿⠿⠯⢩⡿⡟⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣴⠋⠀⠀⢠⡇⣺⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡏⠛⠂⠉⠈⠉⠉⠙⣋⠉⠁⠀⢀⣤⠖⠋⠀⡇⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⣸⠁⢀⡠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠰⣿⣧⣄⡀⣀⡀⠀⣠⠞⠁⢀⣀⣀⣾⡝⢦⠀⢰⠃⢀⡴⠊⠀⣀⠤⠴⠶⠶⠶⠖⠋⠉⢹⣙⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣮ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⡡⠖⢀⣀⢻⣿⣿⣿⣿⣿⣷⡄⡛⣷⣦⣴⣶⣮⣅⡸⢇⠘⠒⠛⡀⢘⣭⣶⣾⣶⣶⣶⣤⣿⣖⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣿ ⠉⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠜⢉⡀⠀⠀⠀⠀⠐⢺⣿⣿⣿⡿⠋⠛⠃⢣⣿⣿⣿⣿⣿⣿⣿⣷⣤⢤⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⢷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿

⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⢔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡜⠁⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠁⡎⠀⠀⢸⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠈⠙⡒⠒⠢⠤⠤⢤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⢧⠘⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⡇⠀⠀⠀⠈⢦⣳⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣧⠀⣆⠀⠀⠀⠙⢿⣄⡀⠀⢸⠹⡄⠀⡠⠔⠂⢸⡀⠀⠀⠀⠀⠀⣇⠀⣀⡠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⠘⢦⣿⡀⣿⡄⠀⠀⠀⠀⡀⠈⠀⢸⠀⠘⠎⠀⠀⡀⠛⡇⠀⠀⠀⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡧⣀⣀⣭⣧⢸⣧⠀⠀⠀⠀⣧⠀⠀⢻⠈⠉⠒⠶⣎⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⣸⠋⠀⠈⢆⣿⢧⡀⠀⠀⢻⣆⠀⢸⡀⢀⡀⣀⡈⠳⣄⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⡔⠋⠀⠀ ⠀⠀⠀⢸⡿⠃⢀⣤⣖⣞⣿⣦⠳⡄⠀⠈⣿⡄⣈⣿⣿⣿⣿⣶⣿⣬⣳⠀⠀⠀⠀⡀⢸⠀⠀⠉⠁⠀⡇⠀⠀⠀ ⠀⠀⢀⢸⣧⣾⣿⡿⢿⣿⣷⠀⠁⠘⠒⠒⠾⡟⠿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡦⠀⢀⠇⢸⣄⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⣿⣿⣇⢸⣾⢿⣿⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⠙⠫⣡⣏⣻⠉⠀⠀⢸⠀⢸⠉⣆⠀⠀⢰⠇⠀⠀⠀ ⠀⠀⠀⢸⢷⡀⠠⠅⠤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢘⡉⠁⣿⠀⠀⢀⡎⠀⢸⠀⢸⠄⠀⡼⠀⠀⠀⠀ ⠸⠀⠀⢸⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⡿⠀⠀⢺⠃⠀⣸⢄⡿⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢀⡟⠀⢘⣿⡛⠀⠀⡀⠀⢀⡄⠀⠀ ⠀⠀⠀⢸⡇⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡞⠀⠀⠀⡇⠀⠀⠀⢳⠀⣸⠇⠀⠀ ⠀⠀⠀⠈⡇⠀⢰⡈⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠋⠀⠀⠀⣸⠁⠀⣰⠀⢸⣠⣿⢀⠆⠀ ⠀⠀⠀⠀⣧⠀⠀⡇⠀⠀⠀⠈⠙⠒⠦⠤⣤⡶⠒⠉⠁⠀⠀⠀⡼⠁⠀⠀⠀⢀⢀⡇⢀⣤⢿⡆⣸⣿⠿⠋⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⣧⠀⠀⠀⠀⢀⣠⡴⢋⣵⠏⠀⠀⠀⠀⣠⣼⣥⠀⠀⠀⣠⢾⣼⠤⣸⡛⠂⠛⠛⠛⢀⣀⠀⠀ ⠀⢦⠀⠀⠀⣇⢸⡇⠁⣤⡴⢋⡽⢋⡔⠉⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡠⠞⠃⠸⠃⣠⠞⢳⣄⠀⢀⡠⠄⠀⠙⢆ ⠀⠈⢢⠀⠀⠈⢦⡁⣨⠋⣠⠊⢠⠿⠒⠉⠒⠤⡀⠀⣠⣤⠾⡷⠚⠉⠀⠀⠀⡰⠊⢀⡴⠁⠈⠙⠫⡀⠀⠀⠀⠀ ⠀⠀⠀⢉⡵⠦⠤⢉⣧⣴⠁⢀⣯⠴⠒⠒⢤⣀⠈⠢⡄⠉⠻⣄⠀⠀⠀⡴⠋⠀⣰⠟⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⠀⢠⠊⠀⠀⢷⡄⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠲⣾⠓⠚⠃⠈⠣⣀⠜⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠄⡙⠊⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠓⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣶⣶⣦⣤⣨⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣬⣿⣼⣷⣄⠀⠀⠀⠠⠀⡠⠀ ⠀⠀⠀⠀⠀⡺⣿⣿⣿⣿⣿⣿⣿⣿⢸⢇⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⡠⠊⢀⣶⢶⣷⣿⣿⣿⣿⣿⣿⣿⠟⠈⢑⢯⣛⠛⢡⠓⠛⣿⣿⣇⠀⠀⠀⠀⠀ ⣵⡷⣹⣧⢼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠀⠁⠀⠈⠃⢀⢿⣿⣿⡆⠀⠀⠀⣠ ⡿⡉⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡶⣒⡌⠀⠀⠀⠌⠉⣿⣿⣿⣷⢀⣀⠈⠻ ⣷⣁⠴⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⢸⡿⠷⣦ ⣇⠫⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠻⠁⠀⠀⠀⠠ ⣿⣷⠏⠀⠀⠀⢀⠽⢉⠀⠨⠉⡛⠳⡓⠨⠔⣲⣶⠾⣿⡍⠍⡈⠣⡀⠀⠀⠀⣀ ⣿⡿⠤⠀⠀⢀⠂⠀⠀⠆⠀⠀⠀⠉⠐⠱⣢⣤⣿⣍⣯⣿⡕⢌⡢⠘⡤⢶⣄⢀ ⡍⠁⠀⠀⠀⢸⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠙⢿⢷⡀⠈⠳⣹⣚⢿⠀ ⣇⣤⢄⣤⣠⠘⡄⠀⠈⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⢄⠈⠪⠫⡛⣳ ⣿⢋⠚⡿⢿⢠⠿⡀⠀⠈⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠀⠑⠹⢿ ⢧⢇⢤⡂⢹⠑⠠⣪⡢⠄⣸⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢳⠀⠀⠀⠀⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⢤⣀⠀⠀⠀⠀⢠⠞⠉⢧⢀⡴⠚⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⠦⣄⣰⠏⠀⠀⠈⠋⠀⠀⠀⠸⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⣸⡄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⢉⡿⠂⠀⠀⠀ ⠀⠀⠀⠈⠛⢶⡴⠶⢶⣶⣶⣾⣿⣾⣶⣶⣶⣶⣶⣶⣶⣴⣦⡁⠀⠐⡆⣠⣴⣿⣵⣶⣶⣶⡶ ⠀⠀⠀⠀⠀⣼⣀⠄⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⠟⠃⠀ ⠀⠀⠀⠀⠀⣿⡳⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣥⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⢲⣩⡔⢯⡀⠀⠀⡇⠀⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⢀⡾⠃⣿⣇⡠⠃⠀⠀⡇⠀⠀⢀⢰⠉⠀⡠⠜⢧⢰⠀⠈⢿⡙⠛⠿⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⣾⠁⠀⠘⠉⠀⡐⠉⠀⢱⣶⠀⡞⠯⠴⠛⡲⢀⡞⠀⢸⡶⢼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⡰⠀⡈⠉⠁⠈⠸⡜⠀⣄⠀⠊⣠⠞⢱⣤⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠶⣜⡁⠀⠈⠁⠀⠀⠀⠀⢀⡈⢻⡉⣽⢤⣀⣷⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⡶⢶⠋⠉⠉⠉⠉⠉⠉⢹⡆⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢼⡅⣯⢰⢀⠀⠀⠀⢀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡟⣿⣾⣾⣿⣿⣿⣿⢿⣿⣷⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢸⣿⣿⣿⣿⠿⣛⢿⣿⣓⣼⣻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⢿⣥⣿⢇⡿⡉⠭⡑⢄⠣⣙⣦⣍⡛⠧⠹⣏⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣯⣐⣉⣿⣿⢰⡇⡱⢂⠍⢢⡑⢄⠺⣽⣳⣬⣑⣤⠷⣋⢙⣳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠏⠀⣩⣾⣿⣿⣼⣧⣦⣵⣮⣥⣼⣌⣱⣧⣯⣽⣏⡰⢡⣶⠟⠛⠖⠲⣄⠀⠀⠀ ⠀⠀⠸⡇⠀⠀⣸⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⠛⠉⢻⠀⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠙⢲⡖⠋⠀⠀⠀⢸⡏⢹⠋⢩⣼⠉⡌⢩⠉⡍⣽⡅⢰⣾⠀⠀⠘⣧⣴⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡰⢉⣛⡾⢡⡉⢜⡠⢃⣾⡯⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡱⢐⣣⠞⡡⠒⣌⢢⣴⣿⣿⣿⣿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⢡⠌⣻⣶⣋⠔⣡⢓⣼⢿⣵⣿⡿⢿⣱⡾⢋⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⡾⡽⢃⠝⣷⣴⠟⠁⠀⠙⣿⠵⣋⠳⣝⢮⣲⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣻⣿⣿⣦⣾⣿⣧⣝⢷⣌⣒⣤⠟⠀⠀⠀⠀⠈⠳⣦⣱⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⣿⣿⣿⣿⣾⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢿⣿⣿⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⡠⠴⠒⠒⠢⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⣼⡧⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀ ⡞⠉⢠⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡀ ⣟⠒⠛⠢⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣣ ⠀⠉⣲⠤⣄⣀⣀⣀⣀⠀⠀⠀⡀⠀⠀⣦⠤⢴⣖⢊⣽⡄ ⠀⠀⠙⡾⠁⣴⡄⢀⢀⠀⠀⠀⢈⣅⠈⠁⠀⠀⣇⢹⣻⠀ ⠀⠀⠀⡇⠶⠉⠀⠈⠊⠓⠊⠀⠘⠛⢠⠤⠀⠀⡏⠀⠁⠀ ⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀ ⢦⣶⡶⠸⡈⠙⠢⠤⣀⣀⡀⠀⢀⣀⡠⡴⠊⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠹⣿⣿⠆⠀⠀⠀⠀⠀⠸⣿⡏⠉⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠔⣒⣶⣶⣶⠖⢋⡤⠖⠉⠀⠀⠀⠀⠻⠿⠗⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣡⣾⣿⡿⠛⠋⠉⠁⢀⣀⡠⠤⠒⠚⠛⠛⠓⡒⠂⠤⢀⡀⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⢃⣀⣠⣤⠔⠊⠉⡠⠄⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠑⣦⡈⠉⠉⠉⠉⢩⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⢀⠎⠀⡰⠁⠀⠀⠀⠀⠀⠐⡈⢣⠀⠀⠀⠙⠙⢦⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⢀⠎⠀⡼⠀⠀⠀⠀⠀⠀⢠⠀⢱⠀⢇⠀⣾⣷⣦⣤⣧⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⡿⠀⠀⠀⠏⠀⢰⠁⢠⠀⠀⠀⠀⠀⡌⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⢣⠀⣿⣿⣿⣿⣷⣤⠂⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⡿⡇⠀⠀⠸⠀⠀⡆⠀⡘⠀⠀⠀⠐⠀⣧⠠⢀⣀⠈⢿⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣏⢆⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⡟⢠⠀⡄⠀⢀⠀⠐⠇⠀⡇⠀⠀⠀⠀⢀⡿⠀⠀⢹⠑⠈⠙⠛⠋⠙⡆⠀⣼⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⠏⠀⠠⠀⢃⠀⣸⠀⢰⡀⢠⡇⠀⠀⡀⠀⣸⠀⡇⠀⢸⡄⠈⡄⠀⠀⠀⡇⠀⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠘⢿⣿⢏⠄⠀⠀⡀⠀⠀⢸⠀⢸⣇⠀⢳⣴⠀⡇⠀⣇⣷⣾⣦⣀⡁⠀⣧⠀⠀⠀⡁⠀⠸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⣸⢃⠈⠀⢀⢠⡇⠀⠀⢸⡇⠈⠿⡄⠈⠻⡆⢹⡄⠃⠁⢘⣻⣿⣿⢿⡎⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀ ⠀⢠⣳⠇⠀⢠⠋⢸⡇⢰⠀⢸⣷⠼⠛⠻⠄⠀⠁⠀⠀⠀⠀⢸⣟⣿⡟⢸⠁⠀⠀⠀⡄⠀⠀⠀⠻⡷⢻⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⣿⣿⠀⣶⠃⢀⣦⢿⠸⣆⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢠⠀⠀⠀⣧⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢿ ⢸⡟⢧⢀⡿⢠⠎⠸⣸⠖⠋⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣸⠀⠀⡀⢀⣿⡀⠀⢠⣾⠇⡏⣀⣠⠔⠀⠀⠀⠀⠈ ⠀⠛⠈⢦⣷⡎⢀⣴⠁⠀⠀⠀⠀⠀⢱⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠞⠛⠀⠀⡁⢸⢻⢷⠀⣸⢟⠀⡇⠺⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠟⣽⠋⠀⠀⠀⠀⠀⠀⠘⢿⠉⣳⣦⣄⣀⣤⣶⠞⠉⡇⠀⠀⠀⢠⠁⣞⠎⡴⢣⡟⡟⢰⠃⠇⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⡏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣟⢻⣿⡇⠈⠃⠀⠀⠘⢀⣴⢀⡌⡜⢡⠞⠀⠀⣹⣡⠞⣤⠀⠀⠀⠀⠉⠢⡀⠀ ⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡞⣨⠿⣯⣷⣄⣀⣀⡤⠖⠁⣀⠞⡸⠙⣅⠞⠀⡨⠋⠀⠈⢾⣷⡄⠀⠀⠀⠀⠹⡀ ⠀⠀⠀⢠⢿⡓⢦⣄⣀⠤⠤⠒⠛⠉⠀⠰⣿⠁⠀⠈⠓⣦⢤⣤⡤⠖⠚⠁⠀⣀⡔⠁⡠⢺⠁⠀⠀⠀⠈⡇⠻⢢⡀⠀⠀⠀⡅ ⠀⠀⠀⣯⠈⡻⢾⡉⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⢰⠋⢙⡇⠀⠀⠀⠀⣼⠋⢠⠞⠁⡎⠀⠀⠀⠀⠀⡇⠀⠈⠈⠄⠀⠀⠘ ⠀⠀⣰⠛⡦⠇⠀⠉⠁⠐⠒⢲⢒⡟⠁⠀⠀⠀⠀⠀⠈⣿⢫⠆⠀⠀⠀⢰⡏⡰⠃⠀⠀⠳⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣏⣽⠁⠀⠀⠀⠀⢣⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣷⣶⣶⣦⣤⣀⡀⠀⢈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡈⣿⣿⡘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣇⠀⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣖⠀⠀⠀⠀⠀⣠⢈⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⡏⢢⣸⢿⣿⣿⣿⣿⢹⡟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠠⠁⠀⠀⠀ ⣠⠜⠁⠀⢰⣶⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠛⣿⣼⣛⠛⠉⣡⡞⠋⠛⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀ ⠅⣠⣖⠴⣻⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣷⠈⢿⠉⠀⠀⠸⢳⡇⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⡷⣪⢽⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢻⣿⣿⣿⣿⣇⠀⠀⠀⢀⠀⢀⣲ ⣿⡵⠋⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣦⣤⣤⠶⠊⠀⠀⠀⠀⠀⠀⠐⢚⢡⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿ ⣿⠯⡖⠀⢸⣏⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠒⠈⠺⠾⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⢰⣶⣦⡀⠀⠋ ⣗⡯⢀⡠⢼⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠃⣿⣻⣿⣽⣷⣦ ⣿⣿⡟⠂⠀⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠐⠒⠒⠒⠒⠒⠒⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠁⠀⠉⠁⠀⠀⠉⠙ ⣻⠭⠔⠂⠀⠀⢀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠽⠏⠀⠀⠀⠀⠀⠀⠀⠒ ⣿⣿⣶⣶⠇⠈⠀⠀⠀⠈⠀⠈⣿⡟⠋⠁⠀⠉⠙⠛⠿⠿⣷⠼⢦⣉⡒⠢⠤⣤⣤⣤⣾⣿⣿⣟⣙⡙⠉⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⡀ ⣿⣟⣛⡛⠋⠀⠀⠀⠀⠀⢠⠎⠀⠉⠲⣀⠔⠉⠉⠑⠢⠤⣈⠑⢤⡀⠀⠉⠒⠮⣿⣏⣙⣿⣓⣢⣄⠉⠒⢄⠀⠘⢦⠀⠀⠀⠀⠀⠐⠢ ⠞⠓⠂⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠒⠜⢷⣯⣭⣭⣿⣯⣁⣹⣿⣿⣧⡙⠢⣄⠱⡄⠈⢇⣠⣰⣆⣀⡀⠈ ⠭⠭⠥⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣧⠀⠈⠳⣜⣶⠸⡦⢰⣿⡿⠤⠨ ⣿⡭⠁⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⠀⠀⠻⡟⠿⢆⠀⠀⠈⠙⢦⣿⠭⠽⢿⠭⠩ ⣿⣓⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠰⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠑⢤⡷⡀⠀⠈⠠⠙⢿⣻⣯⠥⠬ ⣿⣶⣭⠭⣺⣿⣷⣿⡇⠈⣿⡀⠀⠀⠀⠱⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡘⢄⠀⠀⠑⣄⠹⣄⣴⣿ ⡯⣝⡊⠉⢺⣿⠿⢾⡇⢠⣿⣧⡀⠀⠀⠀⠘⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⡄⠀⠀⠈⠆⠘⣿⡿ ⣿⣗⠬⠀⢸⡇⠠⢼⣷⣇⡄⡈⠳⢄⠀⠀⠀⠘⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡆⢣⠀⠀⠀⠀⠀⣔⣊ ⠿⡛⢯⡒⢼⣇⠁⢺⡇⠈⠑⢦⡑⣦⡑⠢⠤⣘⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠏⠁⡃⢸⠀⠀⠀⠀⠀⢰⣒

⠀⠀⠀⠀⢨⢊⠠⠐⠂⠈⢀⠤⢈⠉⠙⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠂⠁⠀⠀⢀⠔⠈⠀⠀⠈⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡔⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⠀⠀⠀⢁⢄⠀⡑⢄⠀⠈⡢⠀⠀⠀⠀⠀ ⠀⡆⣦⢄⠀⠤⠦⢅⠀⠀⠀⠀⠎⡄⠀⠀⢸⠀⢢⠑⡀⠁⠢⠌⣑⡂⠤⡤⠃ ⢪⡗⠻⢬⡦⠤⠔⢠⠂⠀⡀⡘⠀⣠⠠⠀⠀⠀⠐⢃⠐⡄⡀⢱⠇⢡⠀⠀⠀ ⢀⢘⡊⡜⡌⠀⠀⠇⠀⠰⡐⠂⠁⠘⠀⡇⢸⠀⠀⠀⡄⣯⢺⡆⠇⢸⠔⠀⠀ ⢸⣇⡰⠂⠰⡀⠀⠸⡠⠋⠀⠀⣀⠀⠜⣡⠂⡶⠶⠆⢰⣿⡌⢈⡴⠊⠀⠀⠀ ⡄⠎⢢⠀⠀⢑⠄⢄⠃⡠⠶⠛⠋⠁⠀⠁⠀⠀⠀⠀⣼⢸⢟⠜⠀⠀⠀⠀⡀ ⢀⠴⡁⠀⠀⢻⠐⣄⠑⢬⠢⠤⠖⠀⠀⠀⠀⡠⠐⠒⠛⠈⠀⠀⠀⡀⠐⠀⠄ ⠚⠀⢰⠀⠀⢠⠁⠚⣁⠀⢢⢀⡀⠀⠀⢀⠜⠀⠀⠀⠀⢀⡀⠀⠀⠈⠂⠊⠀ ⠀⠀⡈⠀⠀⠸⠀⠊⠉⠱⡈⢧⣀⠉⢧⡏⠀⠘⠁⠘⠭⠟⠁⠀⠀⠀⠀⠀⠀ ⠁⡰⠀⠀⠀⠆⡘⠠⢀⠀⠐⣸⡌⠣⡊⡇⠀⠀⠀⠀⠰⢤⡀⠰⠿⠃⠀⠀⠀ ⠠⠁⠀⢀⠌⡗⠀⠀⠀⠈⠐⣿⡁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⡠⢂⢼⠀⠀⠀⠠⢠⡊⣁⡈⠦⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡞⡰⠋⠀⢀⡠⠤⠔⠒⠉⠀⠀⠀⠈⠉⠛⠛⠽⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⣠⠔⠉⠁⠀⠀⠀⠀⠀⣠⠏⠈⠙⠲⢄⡀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⡀⠀⠀⠻⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠈⠢⡀⠀⠈⢢⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡰⣄⠀⠀⠀⠀⠀⢸⠈⠳⡀⠰⡄⠈⠲⣄⠀⠈⠢⣙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⢘⡏⣴⣶⣄⠀⠀⡤⠶⠶⣾⣄⠀⠀⠀⠀⠀⠀⠀⡇⠘⡀⠀⠀⠀⠀⠘⡄⠀⠙⡄⠘⣄⠀⠀⠑⠲⣤⣀⠉⢷⠒⠠⠤⢤⡴⠃ ⢠⢾⣀⢾⣯⠈⢧⠀⠀⠀⠀⡼⠈⣇⠀⠀⠀⠀⠀⣸⠁⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⢹⡄⠘⢆⠀⠀⠀⢱⡆⡏⠙⢗⠒⠒⠉⠀⠀ ⠁⢾⡃⠀⠻⡷⡿⡗⠒⠒⠊⠁⣠⠏⠀⠀⢀⡆⢠⠃⠀⢀⣸⠀⠸⡀⠀⠀⡇⠀⠈⠉⢳⠀⠈⢣⠐⣄⠀⢳⢹⠀⠘⡄⠀⠀⣀⠀ ⠀⢸⠸⣠⠎⡁⢧⠈⠓⠒⠒⠚⡇⠀⠀⠀⡜⢠⡷⠒⠉⠁⠠⡄⠀⡇⠀⢀⡇⠀⠀⠀⠀⢇⠀⣧⡑⢼⣦⠈⣿⠀⠀⡇⡠⠊⠀⠀ ⠀⣎⡰⠳⡀⠃⠘⡆⠀⠀⠀⠀⢧⠀⠀⣼⣡⠋⠀⠀⠀⠀⠀⡇⢠⢿⠀⡸⠀⠀⠀⠀⠀⠸⡄⣿⣧⢨⠿⣆⢸⠀⣠⠏⠀⠀⠀⠀ ⠀⡿⡇⠀⣹⡇⠀⠸⡄⠀⠀⠀⠸⡄⣴⠟⠁⠀⠀⠀⠀⠀⠀⣧⠎⢸⡤⠃⣰⣿⣿⠷⠶⠀⣽⡟⣿⡄⡇⢸⣄⠟⠁⠀⠀⠀⠀⠀ ⢠⠃⣹⣎⠀⡇⠀⠀⠘⣄⠀⠀⠀⢻⠀⠀⠀⣀⣴⣶⣿⡷⠂⠁⠀⠚⠁⠀⠈⠁⠀⠀⠀⠀⣹⠃⣿⢣⠃⡸⠋⠀⠀⠀⠀⠀⠀⠀ ⡜⢸⠁⠈⣳⡇⠀⠀⠀⣨⠆⠀⢢⡀⠁⡀⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⣟⣡⠜⠁⠀⠀⠀⠀⠀⠀⠀⡀ ⠁⢸⣠⠞⢡⠇⠀⠀⠸⣷⠂⢦⡀⠙⠦⣈⠓⢤⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠼⠿⠒⠋⠁⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀ ⠀⣾⠁⠑⢸⠀⠀⠀⠀⠙⢆⠤⢷⣄⠀⠈⢏⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⢀⡴⠁ ⠊⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠑⠋⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⠀⠀⡴⠮⠭⢧⠀⠈⣧⠈⠙⠲⠶⣖⡒⢲⠃⠀⠀⣖⡤⠀⢰⡶⢲⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⠀⡎⠀⢸⠀⠀⠀⠀⠳⡀⠸⣷⣦⣀⠀⠘⣷⡎⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠇⠀⢀⠏⠀⠀⠀⠀⢰⡇⠀⡏⠀⠀⠀⠀⠀⠱⡄⣿⡌⠻⣗⢦⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⣟⣽⠇⠀⠀⠀⠀⠀ ⠀⢀⡎⠀⠀⠀⠀⢠⢏⢇⡞⠀⠈⠁⠒⠤⣀⠀⢹⣿⡇⠀⠈⠳⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠆⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⡼⠀⠀⠀⠀⢠⠎⣸⠏⠀⠀⠀⠀⠀⠀⠈⠑⢺⣿⠃⠀⠀⠀⢸⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⣠⠋⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠋⠓⢄⡀⠀⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⠀⣀⠔⢁⡴⢻⠁⠀⠀⠀⠀⠀⠰⡘⣯⣀⣀⣀⡤⠄⠛⠊⡁⢢⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀

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

veri cutesie bio mωe made fur nyuu ! ! :3 baker themd ! ! 🍰🍓🍪🍭🎀🥞🧁 made baii @ cloudy_sodaz enjoyy ! ! ^__^ 🎀 ⌣⌣⌣⌣⌣⌣ ꒰ 🎀🍰🍭 ꒱ ⌣⌣⌣⌣⌣⌣ 🎀 . ☆ 🍰 ꒰ haii theree !! (๑╹ꇴ◠๑) ﾉ 🥞 🎀 me is calld _______ !! (๑ • ω • ๑) ꒱ 🍰 ♪ 。 ⌒⌒⌒⌒⌒⌒ 🍰 ⌒⌒⌒⌒⌒⌒ . ☆ 🍭 ꒰ welcome tuu mi cupcake shop !! :33 🧁 ︶꒦ ︶꒷꒦ ︶ ꒦ ︶꒷꒦ 🍰 ︶꒦ ︶꒷꒦ ︶ ꒦ ︶꒷꒦ 🍓 mi pronouns r ______ !! ( ﾉ ๑ ^ ω ^ ๑ ) ﾉ ꒱ 🎀 ♪ 。 . ☆ 🥞 ꒰ me lovv __________ !! (๑ ^ ω ^ ๑) 🍰 ⌣⌣⌣⌣⌣⌣ 🍭 ⌣⌣⌣⌣⌣⌣ . ☆ 🎀 _______ is mi best friend everrrr !!! ( ๑ > ꇴ < ๑ ) 🥞 🍓 (pronoun) is the best !! :33 🧁 🍪 aa cuteness overloaded !!!! (๑ > ω < ๑) ꒱ 🧁 ♪ 。 🎀 ⌣⌣⌣⌣⌣⌣ ⌒ ☆ ꒰ 🧁 ꒱ ⌣⌣⌣⌣⌣⌣ 🎀 . ☆ 🍪 ꒰ supa cutesie littl baker !! ( ๑ - ꇴ - ๑ ) 🍭 🍰 join mi littl grp calld ____ !! ( ๑ ╹ꇴ╹๑ ) ꒱ 🍓 ♪ 。 (onli if nyuu hav one ! ! :3) ⌒⌒⌒⌒⌒⌒ 🍪 ⌒⌒⌒⌒⌒⌒ . ☆ 🎀 ꒰ creds tu @ cloudy_sodaz fur bio !! ^__^ 🥞 ︶꒦ ︶꒷꒦ ︶ ꒦ ︶꒷꒦ 🍭 ︶꒦ ︶꒷꒦ ︶ ꒦ ︶꒷꒦ 🍓 heres sum cupcakes me baked !! ( ๑ ^ ω ^ ๑ ) ꒱ 🧁 ♪ 。 . ☆ 🍭꒰ thank u fur visitin mi cupcake shop !! 🍪 ⌣⌣⌣⌣⌣⌣ 🍓 ⌣⌣⌣⌣⌣⌣ 🍓 ꒰ buh . . baii !! (๑ > ω < ๑) ﾉ 🍰 ♪ 。 🎀 ⌣⌣⌣⌣⌣⌣ ꒰ 🧁🥞🎀 ꒱ ⌣⌣⌣⌣⌣⌣ 🎀

૮꒰◞ ⸝⸝ ◟꒱ა 💤 ♡

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⢤⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀ ⠀⢿⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢿⡿⠁ ⠀⢸⠀⠁⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⡿⠃⠀⢸⡀⠀ ⠀⢸⠀⠀⠀⠈⣎⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣟⡀⡇⠀⠀⠀⡇⠀ ⠀⢸⠀⠀⠀⠀⢸⣄⠹⣿⣿⣿⣦⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢠⣾⣿⣿⣿⣿⣫⣾⡇⠀⠀⠀⣷⠀ ⠀⣾⠀⠀⠀⠀⠘⡜⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⢽⠁⠀⠀⠀⣿⠀ ⠀⢸⠀⠀⠀⠀⠰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⣄⡀⠀⠀⣿⠀ ⠀⢸⡆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⢰⣿⠀ ⢳⡸⣿⣤⣄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⢴⣿⣳⠀ ⠠⣽⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣡⠏ ⠤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠄ ⠀⠰⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠄ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠊⢻⠈⢿⣿⣿⣿⣿⣿⣿⡏⠙⢻⡇⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡏⠘⡇⠀⠀⠸⡄⠈⣿⣿⣿⣿⣿⡏⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣶⣶⣤⣀⠡⠀⠈⢻⣿⣿⣿⠀⢀⣤⣶⣶⣦⣄⣿⣿⣿⡟⠛⢻⣿⣿⣧⠀ ⠴⠛⠁⠈⣿⡀⠉⢻⣿⣿⣿⣿⢹⣾⣿⣿⣿⡆⠀⠀⠙⢿⡄⠀⢿⣽⣿⣿⡏⣿⣿⣿⡟⠀⢀⣾⠇⠀⠉⠛ ⠀⠀⠀⠀⠈⣷⡀⠈⢿⣿⣇⠘⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡽⠛⣣⣿⣿⠃⢀⣾⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠟⠙⢦⣌⡻⣿⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣥⡶⠋⠛⠧⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣬⣁⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⢓⢤⣀⠀⠀⠀⠶⠿⠷⠀⠀⠀⣀⣤⣾⣿⢿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢃⡞⣰⠈⠓⢦⢄⣀⠀⣀⣠⣴⠞⠁⢸⠇⣿⡀⣿⠿⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⠀⠀⣿⣿⣿⠟⠋⠉⠉⠉⠣⣼⠃⣟⠂⣄⠈⠳⡍⠉⢉⡾⠁⠀⠀⡿⣸⡟⠋⠀⠀⠈⠉⠹⣿⣿⣿⡇⠀ ⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣦⠙⢇⠀⠉⣶⢿⠀⡿⣆⠈⠁⣰⣇⣿⣧⡀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀ ⠀⠀⠀⣿⣧⠀⠀⠀⠀⢠⠴⠶⢾⣿⠆⡌⠆⣰⣧⡄⣤⣠⣿⡀⣰⢻⣷⣮⣉⡀⠀⠀⠒⠲⠆⣰⣿⣿⠀⠀ ⠀⠀⠀⢻⣿⡈⠙⠛⠛⠛⣀⣐⣤⣶⣿⣯⠈⠀⠘⣿⣷⣿⠏⡟⠁⣸⣿⣿⣿⡟⠻⠥⠴⠶⠾⢻⣿⣿⣆⠀ ⠀⠀⠀⣸⣿⣟⠒⠠⠄⠂⣠⣿⣿⣿⣿⣿⡄⠀⠀⢻⣷⣿⠀⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀⢀⣴⣿⣿⣿⡏⠀ ⠀⠀⢠⣿⣿⢿⣷⣦⣤⣾⣿⣿⠙⢿⣿⣿⣷⡀⠀⣸⣿⡿⡄⠀⢰⣿⣿⡿⢋⣿⣿⣷⣶⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠘⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣷⠀⣟⣽⣾⣿⢠⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⡆⠀ ⠀⠀⢠⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⡿⣿⣿⣿⣿⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⣿⣿⠇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣵⣶⣿⣿⠉⢍⢠⡈⠻⠶⣬⡙⢷⣮⠙⠿⣿⣷⣶⣄⠀⠀⢀⣠⢖⡡⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠒⠤⠄⣈⡑⠢⠤⢀⡴⠛⣵⣿⣿⠟⠉⢹⡶⠈⣌⢻⡄⠀⠘⣿⣷⣹⣷⣄⠹⣿⠛⢻⣷⣶⡯⠶⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⠟⢲⡞⠁⣼⣿⣿⠏⠀⢠⢸⣇⡀⣿⡎⢿⣆⠸⡌⠻⣿⣿⣿⣧⠈⢷⡀⡿⣝⣧⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⢀⡞⠀⣼⣿⡿⢃⠀⣠⠏⣼⣿⡇⢿⣧⢘⣿⣿⣧⠀⠙⠿⣿⣿⣷⡈⢷⡀⠘⣞⢧⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣷⡾⢡⢤⣯⣿⢣⢎⣾⡟⢠⣿⡿⣿⢸⡏⢿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣷⡈⢷⡀⠘⣯⣳⣦⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣧⡟⣟⣾⣯⡟⣼⢻⢃⣿⡿⠁⠸⡌⣿⡀⠻⣟⣿⣿⣿⣄⠈⢿⣿⣿⣿⣌⢿⣄⠘⢷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⢿⢱⡇⢸⣿⡿⠁⠀⣀⣷⣿⣧⠀⠙⢦⡙⠻⣿⣷⣦⣻⣿⣿⣿⣎⣿⣦⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢧⣿⣿⡿⠈⢸⢇⣿⣿⣡⠔⠊⠁⠀⢳⣿⡆⠀⠀⠙⢦⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣧⡀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣼⣿⣿⣯⢇⣿⣸⣿⠁⠀⢀⠀⣀⠀⠀⠻⣿⡄⠀⠀⠀⢛⣽⢧⣤⣌⡿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⡇⣸⠃⢀⣾⣿⣿⣦⡀⠀⠀⠙⢿⡄⠀⠀⢼⣅⣼⣿⣿⡿⣯⣽⣿⢻⣿⣿⣿⣷⡀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⡇⣿⢙⣿⣏⣠⣿⣿⡇⠀⠀⠀⠈⠻⣆⠀⠸⡿⢿⣿⣿⠇⢹⠿⣿⡈⣿⣿⣿⣿⣿⣷⣾⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⠸⣿⣷⣿⣿⡇⢿⠿⢿⡟⡋⠀⠀⠀⠀⠀⠈⠣⡀⠑⢤⣤⣶⠀⠀⠀⣿⡇⣿⣿⣿⣿⢹⡟⠿⣿⣿⣷⣤⡀⠀ ⠀⠀⢠⣿⣿⠏⣿⣿⣿⢀⣿⡏⣿⠉⠛⠊⠳⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣷⣷⡀⠀⠈⠉⠉⠙⠓ ⢀⣴⣿⣿⠃⠀⣿⣿⣿⢸⣿⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⡏⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠋⣸⡿⠁⠀⠀⣿⣿⣿⣿⣿⡄⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⣿⣿⣿⣿⣦⣤⠟⠋⠉⠒⢦⡀⠀⠀ ⡴⠏⠀⠀⠀⠀⣿⡿⠋⢹⣿⣇⠘⣇⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⢸⣿⣿⡄⢹⡄⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⣿⠻⣿⣟⣿⣄⠀⠀⠀⠉⢲⡤⢄⡀⠀⠀⠀⡠⠞⡟⠀⣠⠀⠀⣾⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡄⠈⠻⣿⣿⠓⠤⠀⠀⠀⠙⠦⣈⠉⠒⠉⢀⡞⢀⠜⠁⠀⣸⠟⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢂⠀⠀⠀⠘⠆⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠉⢲⣤⣞⡊⠁⠀⠀⠚⠁⢰⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣇⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⢠⠋⠘⡄⠈⠢⡀⠀⠀⢀⠇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⡟⣆⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⢠⠃⠰⠲⡜⡆⠀⠈⠢⣠⠎⠀⣿⡟⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⣿⣿⠁⣿⣦⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠀⠘⠂⠃⠸⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⣿⣿⠀⣿⣿⣷⡄⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢠⣿⠀⠀ ⠀⠀⠀⣿⣿⠀⢻⣿⣿⣿⣦⣄⠀⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢀⡜⢁⠄⠀⠀⢸⣿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⠛⠛⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⠛⠛⠿⣷⣦⡀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⠀⣀⣀⣀⣀⣀⠀⠈⠙⢿⣦⡀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⡀⠀⠀⣰⣾⠟⠁⠀⢀⣀⣀⣀⣀⡀⠀⠀⠙⢿⣦⡀⠀ ⠀⣼⡿⠁⠀⣠⣶⡿⠟⠋⠉⠙⠻⢿⣦⡀⣀⣿⣷⣾⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⠿⣾⣿⣅⣀⣴⣾⠿⠛⠉⠉⠛⠿⣷⣄⠀⠀⠹⣷⡀ ⢸⣿⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⢀⣠⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣧⣄⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⢻⣷ ⣿⡇⠀⠀⣿⠇⠀⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⠈⣿⡇⠀⢸⣿ ⢻⣧⠀⠀⣿⡆⠀⠀⣠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡀⠀⠀⣿⡇⠀⢸⣿ ⠈⣿⣆⠀⠸⣷⣄⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣼⡟⠀⢀⣿⠏ ⠀⠘⣿⣦⡀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⣠⣿⠏⠀ ⠀⠀⠈⠻⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀ ⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀ ⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⣼⣿⣿⠀⠀⠀⠀⣀⣴⡾⠿⠛⠋⠙⠻⠿⣷⣦⡀⠀⠀⠀⢸⣿⣇⣀⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⢀⣼⡿⠋⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣤⣄⠀⠀⣾⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠂⠀⠀⠀⠀⠸⣿⡄⠀⣠⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⣾⡇⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⠀⢠⣧⡀⠀⠀⠀⢘⣿⣟⠁⠀⠀⠀⣠⣶⡄⢻⣷⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⣿⠇⠀⠀ ⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢸⣿⡀⠀⠙⠻⠿⣶⡾⠿⠋⠻⠿⣷⡶⠿⠟⠉⠀⣼⡿⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⠶⠶⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀ ⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⡄ ⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇ ⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠀ ⠈⢷⡀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⣿⠀⣼⠃⠀ ⠀⠈⢷⣼⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡾⠃⠀⠀ ⠀⠀⠈⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⢠⠀⣄⠀⠀⠙⢿⣿⣿⣿⡿⠏⠀⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣴⣿⠀⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⠳⣦⡀⠀⠀⠀⠸⣿⡿⠀⢻⣿⡟⠀⠀⠀⠀⣤⡾⢻⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⢻⠻⣆⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⡾⢻⠁⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⢹⠒⡦⢤⠤⡤⢤⢤⡤⣤⠤⡔⡿⢁⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⢸⠦⣧⣼⣀⡇⢸⢀⣇⣸⣠⡷⢇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠺⣄⣇⢸⠉⡏⢹⠉⡏⢹⢀⣧⠾⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠉⠙⠓⠚⠚⠋⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣇⣠⢖⣖⢦⡤⠴⢶⣶⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢤⡀⠀⠀⠀⠀⠀⢾⠀⠈⢁⡿⣿⡏⣆⠀⠈⠉⣷⡆⠀⡿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠉⠙⠒⠦⠤⣤⣼⡄⠀⡞⠀⠘⣿⢸⡄⠀⠀⠘⣆⡴⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡀⠀⠀⡴⠊⠁⡴⠒⠒⠒⠚⠙⢦⡀⢀⣀⣀⣯⣈⣿⢸⠁⠀⠀⠹⡇⢹⠀⣠⣾⣿⣶⠀⢀⣼⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⢋⣠⡍⠉⠉⠀⠀⠉⢳⠀⠀⠀⠀⠀⢀⡿⠏⠀⢀⣀⣄⡈⠙⣆⠀⠀⢀⣽⠸⣿⠟⠉⢠⣏⡤⠼⠷⠶⣏⡉⠙⠒⠒⠒⠚⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⣼⡟⢠⠞⠉⠙⠲⣄⡳⣄⠀⠀⡴⠁⠀⠀⠀⢀⣴⣿⢿⡦⠼⢦⡤⠿⠿⠷⣿⣀⡴⢟⣉⣤⣆⡀⠀⠘⠻⣄⠀⣠⠴⢤⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠴⠃⠀⠀⠀⠀⠀⠉⠁⠀⣼⡄⠀⠀⠀⠀⣸⣿⡋⠀⠀⠀⣇⠀⠀⠀⠀⣨⠇⠀⠈⢿⣿⣷⠤⠄⠀⠀⣸⡏⠀⠀⡼⠉⠃⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⣿⣿⣷⠤⣀⣀⣈⣹⣶⣿⣉⠁⠀⠀⢀⣠⣿⣿⡇⠀⠀⠀⢹⡁⠀⡼⠁⡠⠤⢄⠀⠑⠲⣤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⣿⣿⣿⣄⣼⣯⣿⣿⣿⣿⣿⣿⣻⡟⢉⣿⣿⣿⡇⠀⠀⠀⠀⢧⠺⠓⠋⠀⠀⠈⢧⠀⢢⡈⢿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢣⣀⠹⣶⠿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢹⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠞⠁⠀⠀⢀⡤⠞⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⣿⣿⡟⢻⣿⣯⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣩⣄⢸⣿⣿⠇⠀⣿⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣈⣿⣡⣿⡤⠤⠞⠁⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⢀⣏⢀⢀⣀⣀⣀⣀⡤⠴⠚⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠦⢤⣤⠤⢴⣿⣭⣭⣭⣿⣛⣉⣀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡿⠀⠀⠀⢹⡍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⠆⠀⠀⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠥⣄⣀⣈⣛⡲⠖⠒⢲⣯⣍⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⣄⣀⣈⡷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠙⢞⢎⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡠⠂⠀⠀⠀⠀⠀⠂⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⢣⡣⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠊⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡷⡄⠀⠀⠀⠀⠹⣕⠵⠄⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠙⢌⠢⡀⠀⠀⠀⠈⢮⡀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡚⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠑⢝⠢⡀⠀⠀⠀⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠑⠅⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠑⠦⢀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣼⣟⣾⣯⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣿⣝⡿⣾⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣹⣿⠱⣷⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⣿⣿⠸⣿⡇⠀⢀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⡀⠀⠀⠀⠀⠀⣾⣿⣯⣏⣼⣿⣿⣿⣿⠏⢧⢸⣿⣿⣿⣿⣿⣿⣿⡆⢿⣧⣠⠞⠀⢻⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡇⠀⠀⠀⠀⠀⣿⣿⡿⣰⣿⣿⣿⣿⣿⠶⢦⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⢿⣤⠶⠞⠛⠛⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡌⡆⠀⠀⠀⠀⠀⠀⠀ ⠶⠋⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⣟⢿⣿⣿⣿⣿⣟⣵⠟⠁⠀⠀⠀⠀⠀⠙⣿⣯⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⡇⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⢸⡟⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣤⡘⠆⠀⠉⠉⠁⢸⡏⠀⣤⡀⠀⠀⠀⠀⠀⢿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⠞⠛⠀⢸⠃⠀⠀⣾⠁⣿⣽⣿⣿⣿⣿⣿⣷⡁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⠀⣋⠀⠀⢠⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡸⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠁⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠛⠀⠀⠲⠤⠀⠀⠀⠀⠀⣠⠐⠖⠒⠚⠛⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡀⠀⠛⣷⠤⠤⠤⠤⠖⠒⠛⠛⠋⠉⣛⣦⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⣿⣇⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢫⠙⢶⣶⠢⢤⣤⣴⡶⠖⠛⠉⠀⠈⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠻⣿⠈⢿⣿⣿⣿⣿⣿⣿⣆⠀⠘⣄⠀⠐⠢⠖⠋⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⠂⠀⠀⠈⠳⠈⠻⢿⣿⣿⣿⣿⣿⣿⣶⣝⣦⣼⠁⠀⠀⠀⠀⠀⠀⣀⡴⣫⣿⣿⣿⣿⡿⣟⡿⣫⡾⣿⣿⡿⠟⠋⠁⠀⣠⠟⠓⠒⠶⠖⠒⠒⠂⠀⠢⢀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡝⠻⢿⣿⣿⠿⣶⣭⣟⣓⠒⣚⣛⡯⠵⢿⣟⠛⠿⠛⠁⡼⠁⠀⣠⠞⠁⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠉⣹⡿⠃⢀⡴⠋⠈⠳⣶⣠⠞⠁⣠⠞⠁⠀⠀⠀⠀⠀⡰⠫⠤⠤⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢰⣿⠁⣠⣏⣈⣡⢶⡄⢽⢁⣤⠞⣡⣤⠀⠀⠀⠀⣠⠞⠁⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠆⠀⣿⠇⢻⣿⣶⣶⣶⣝⣿⠉⢹⣵⣡⣴⣾⣆⠀⢀⠞⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣿⠀⠘⡄⢸⡏⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡴⠋⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠛⡄⠀⡇⢸⠁⠀⣰⣃⠀⢹⣿⣿⣿⣿⡟⢿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⡾⠀⣰⠟⠁⠀⠀⠛⢿⣿⠋⢠⠊⠛⢷⣭⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣇⡎⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢠⠇⠀⠀⠀⠀⢹⠀⢸⣇⡴⠋⠀⠀⠀⠀⠀⠈⣇⠀⢸⡤⠂⠀⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⠁⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢀⠞⠁⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠘⡆⢸⡿⠁⠀⠀⠀⠀⠀⠀⢰⠃⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⣠⠎⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣸⣁⣼⠃⠀⠀⠀⠀⠀⠀⢀⠇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡇⡄⢀⠇⠀⠀⠀⠀ ⣀⠀⠀⠀⣀⣀⡀⠀⢀⡴⠁⠀⠀⡀⠀⠠⠃⠠⠀⠀⠀⠀⠀⠀⠁⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡈⠀⠀⠀⠀⠀⠀⠀

⠄⡀⠠⢀⠀⢀⣴⣿⣾⠿⣙⠴⠌⠓⣮⡳⣍⢻⡷⣦⣀⢄⣪⠂⠁⠀⠀⠀⠀⠀ ⠀⠀⠈⡶⢲⠃⣾⡿⠁⡀⣇⢸⡼⣆⡎⢻⣿⣧⠱⡌⢟⢅⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣥⢇⣘⡿⣵⡶⢱⡿⡾⡧⣽⣿⣄⠩⣿⣷⡘⡄⢫⣦⡸⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣮⣽⠻⡜⣧⡿⠁⢣⣧⠙⣝⢿⣦⡙⣿⣷⡝⣄⠻⣷⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⣽⡿⣆⢧⣿⠥⠒⠉⢻⡆⠈⠃⢉⡛⠿⣿⣿⣿⣧⡙⣧⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣷⣼⢸⠁⣤⣦⡂⠀⠻⡄⠀⢰⣛⣷⣾⣻⡿⣿⣷⣌⠣⡀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⡝⣧⣿⠧⠀⠀⠘⢆⠘⡛⢛⠃⠛⣧⣿⣿⡿⣷⣿⣦⡀⠀ ⠀⣠⣿⢻⣿⡇⡿⣿⠓⠑⠮⠞⠀⠀⠀⠀⠁⠈⠉⠀⠀⣿⣿⣿⣷⣧⠈⠉⠙⠒ ⢘⡿⠁⢸⣿⣷⣇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣼⣿⣷⣙⡿⠃⠤⡀⠀ ⠚⠀⠀⡸⠛⢹⣿⡘⡌⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣿⣿⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⠈⡟⢷⣻⣄⠀⠁⢢⠄⣀⢀⠠⡚⢀⠀⣸⢿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⢀⠀⠘⠄⠙⠳⡅⠀⠀⠁⠂⢄⣴⠐⠁⠀⢃⢻⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢆⠈⢐⡀⠀⠀⠀⠈⠢⡀⠀⠠⢁⢃⠑⢄⢀⠌⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⢸⣦⠀⠳⡀⠀⠀⠀⠀⠈⠐⠁⠀⠂⠆⠀⠀⢰⡿⠀⠀⠀⠰⠁⠀⡇⠀ ⠀⠸⣿⠸⣿⣷⣄⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⢊⠀⠀⣿⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠀⠀⠀⠈⠉⠛⢲⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠈⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⡴⠶⢻⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⣠⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⣴⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣄⠀⠀⠀⠻⣇⠀⠀⠀⢀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠹⡷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠻⣷⡀⠀⠀⠙⢷⣄⣰⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⢿⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢿⣆⠀⠀⠀⠉⢋⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠘⢷⣄⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⠇⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠈⠙⢷⣤⣀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⢸⡄⠉⠙⠛⠛⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⢸⣿⢧⡀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠹⣧⡀⠀⢻⣆⠙⠶⣬⣷⡀⠀⠀⣀⣀⠾⠿⣦⣤⡌⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠷⣦⣀⠹⣦⡀⠠⠞⣷⠀⠀⠉⠝⡷⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠈⠙⠛⠿⣿⣦⠀⣹⣧⠀⠀⠸⠟⠁⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠙⠻⣦⢻⡄⠀⠀⠀⠀⠀⠘⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⠷⢦⣤⣄⣀⠀⠀⠀⢀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣟⣻⠿⠆⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⣀⠀⠀⠀⠈⢿⣆⠀⠈⠉⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⣶⡾⠫⢄⣴⡞⠛⠒⢾⣃⣠⣤⢆⣠⠶⣶⣤⣀⠀⣠⢿⡏⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⣼⠏⠉⠁⠈⠉⠉⢧⠀⠀⣹⠃⠙⠉⠁⠀⠘⣦⠉⠙⠡⢾⣇⣀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠈⢧⣠⡏⠀⠀⠀⠀⣠⡴⠛⢠⡀⠀⣀⣀⣽⡿⠆⠀⢀⣠⣼⣗⣚⠛⠛⠛⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠙⠉⠉⠉⣧⢸⠁⠀⠀⢠⡴⠞⠛⠉⠉⠉⠛⢷⣦⡀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣠⣴⣦⠀⠀⠀⠀⠀⠙⣿⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⣤⣤⣤⣤⣤⣤⡶⠶⠶⠿⠛⠋⠉⠈⢿⣆⡀⠀⠀⠀⣀⣿⡉⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⡟⢠⣿⠀⠀⠀⣠⣤⣴⣶⡾⠛⠁⢀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡛⠚⠛⠁⣿⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣄⣀⣠⣴⠟⠀⠀⣠⣾⠟⠀⣾⣧⡀⠀⠀⢸⣇⠀⠀⠠⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠻⠿⠤⠶⠾⠟⠋⠁⠀⠀⢿⣦⣉⠛⠛⢋⣿⠦⠤⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀