Bongo Cat Piano Emojis & Text

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╱|、 (˚ˎ 。7 |、˜〵 じしˍ,)ノ

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠓⠒⠛⠋⠛⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣀⡀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣿⢣⠀⠀⠀⠀⠈⠛⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢹⡞⡆⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠈⢳⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⡇⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢸⡄⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢳⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⣧⣀⣠⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠛⠓⠲⠤⣄⣠⡤⠤⠤⠤⠶⠒⠓⠓⠛⢋⣉⣹⡆⢹⣉⣉⣉⣉⣉⣉⠙⠓⠒⠲⠤⣄⡀⠀ ⠀⠀⠀⠀⠀⣶⠶⣶⣒⡿⠁⠀⠀⠀⠀⠀⠈⠉⠓⣶⠖⠒⠚⠉⠉⠉⣉⡉⠉⢳⠈⣇⠀⠀⠀⠉⠉⠉⠉⠒⢲⣤⣈⣿⡄ ⠀⠀⠀⠀⢀⣿⡀⠀⠀⠉⠙⠓⠦⢤⣀⡀⠀⠀⣰⠏⢠⣤⠖⠦⣄⠸⢟⣛⣻⠻⣆⠸⣆⢀⣀⣀⡤⡞⠛⠛⠉⠉⠀⢸⡇ ⢀⣤⡶⢺⣽⣼⣥⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠿⢄⣀⠉⠉⠛⠁⣀⣴⡿⠿⠖⠛⠋⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇ ⠈⣿⣿⣿⣭⣛⠙⠻⠻⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣤⠾⠁ ⠀⠛⠛⠯⣷⣻⣽⣗⣶⠤⣄⣙⠛⠫⣷⣶⣤⣄⣀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢻⡉⣹⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⢺⠯⣿⣳⡯⣟⣶⣤⣄⣉⡋⣽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠶⠒⠚⠁⢸⣇⣷⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢰⠃⡏⠉⠛⠿⣽⣟⣻⠭⣇⠀⣀⣀⣀⡤⠤⠤⠒⣻⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⡇⠀⠀⢠⣿⠀⠉⠙⣿⣏⠙⠛⠻⣷⡄⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⡿⣷⡇⠀⠀⠸⣿⠀⠀⠀⢻⡇⠀⠀⠀⢻⡇⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⣿⠀⠀⠀⢸⣯⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣦⠀⠀⢐⣿⣄⡀⠀⢸⣿⠀⠀⠀⢸⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠿⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⣿⡫⣌⣙⠓⢾⣿⡀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⣽⠷⣽⣗⢾⣟⡗⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠉⠙⠋⠀⠀⠀⢀⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⠛⠀⠈⢻⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠳⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡾⣷⣦⣠⡾⣟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⡀⠀⢀⣠⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠉⢗⢦⠈⣿⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠋⠉⢸⣷⠀⠀⠀⠀ ⢀⠀⠀⠀⢼⣿⡉⠻⠇⠀⠀⠀⠀⠀⠀⣾⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡀⠀⠀⠀ ⠺⠷⠦⢤⣼⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠛⢿⡶⠆⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡽⠿⠟⠛⠲⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⠀⠀⠀⠀⠀ ⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⠉⠛⠳⠶⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀ ⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠶⠛⠛⠛⠛⠛⣿⠓⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀ ⠀⠀⢳⡛⠷⣤⣀⣀⣀⣀⣀⣀⣤⠶⣿⡟⠁⠀⠀⠀⠀⠀⣰⠻⢦⣄⣠⣤⡤⠴⣾⡋⠙⠛⠲⠦⠤⣤⣀⣸⣇⠀⠀⠀ ⠀⠀⠈⣿⠲⣤⣭⣉⣉⣙⣹⣭⣶⣾⢿⡇⠀⠀⠀⠀⠀⠚⠁⣴⠃⢹⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⠆ ⠀⠀⠀⢹⡆⠸⡆⠈⠉⢹⠁⠀⣼⠇⢸⡿⣆⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠀⡇⠀⠀⢸⠀⠀⣿⠀⠘⣷⣌⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣧⢻⡀⠀⢸⠀⢰⣇⡀⠀⡇⢿⠳⢦⣀⣉⠛⠓⠲⠶⠶⠶⡚⣛⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣷⣶⣾⣿⠿⠋⠙⠻⡇⣿⠀⠀⠀⢹⠛⠛⠛⠛⢛⡟⠋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⠀⠀⠀⢀⡼⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣠⡇⠀⠀⠀⡾⢁⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣉⠁⠘⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢹⡄⠀⠀⠉⢢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⡷⠀⠀⠀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢱⢃⣀⣜⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⢤⣃⠉⠁⠒⢭⠉⠛⢓⣚⡞⡖⠒⠒⣋⣭⢲⠀ ⢀⣤⡶⣧⣀⡀⠈⠑⠒⠧⢝⡚⠬⠟⠐⠒⠀⠹⠀⠀⢨⠄ ⠀⠙⠛⠷⣾⣭⣟⣶⠤⡤⠔⠁⠀⠀⠀⢀⣀⡰⢪⣽⠃⠀ ⠀⠀⠀⠀⣿⡏⠉⡟⠿⡧⠴⣖⢂⠝⠉⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⡇⠀⣇⠀⢸⢸⠀⠀⠀⠀⠀⣼⡇⠀⠀ ⠀⠀⠀⠀⠙⠃⣰⣫⣂⣿⠀⢸⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠋⠋⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⣤⣀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣋⣽⣛⣯⣿⣯⣿⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠿⡿⣓⣤⣽⠟⠉⠀⠀⠀⠈⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣯⣭⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢋⣛⣃⣒⣘⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠑⠀⣶⣖⠚⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡆⠀⠀⠘⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠋⠉⠉⠀⠽⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣭⣭⠁⠐⠒⠀⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣃⣀⠀⠐⢻⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡙⠛⠛⠋⠤⠀⣈⣉⣹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣯⣀⣉⡉⠓⠒⠤⠤⣄⣀⣽⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣏⠑⠒⠢⠤⣀⣀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣰⣾⣦⣴⢾⣉⠙⠒⠭⢍⣛⡟⠋⠉⠒⠢⠤⣄⣀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠺⢿⣿⣿⣿⣿⣿⣷⣮⠙⠒⠤⣄⡀⠉⠙⠒⠦⢤⣀⡀⢈⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡉⠀⠈⠓⢤⡈⠙⠿⣿⣿⣿⠟⠓⢤⡀⠀⠈⠙⠲⢤⣀⠀⠀⢉⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⠀⠙⠲⢤⡀⠀⠈⠓⢤⡀⠉⠉⠳⣄⠀⠉⠓⢤⣀⠀⠀⠀⢉⣶⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⣦⡀⠀⠈⠓⢦⡀⠀⠉⠳⢤⡀⠈⠙⠦⣄⢀⣈⣽⣶⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠈⠳⣄⠀⠀⠉⣳⣤⣖⣿⣿⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠴⠛⢦⡀⠙⠻⣿⣿⣿⣿⣿⣿⣧⠙⠦⣀⠀⠈⢱⣶⣾⣕⡿⠕⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣠⣶⣾⣷⣎⠣⣄⠀⠀⠈⠳⢤⡀⠙⠻⣿⣿⠿⣅⠀⠀⠈⣳⣶⣵⣋⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⢦⡀⠀⠀⠉⠲⢤⡀⠁⠀⠀⠙⢦⡞⣡⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠔⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠳⢄⠀⠀⠀⠉⠳⢤⣀⡔⢩⠟⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠊⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠑⠂⠀⠀⠀⠀⠋⠛⠃⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠙⣷⡶⠶⢶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⣈⣷⣶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠞⠋⠀⠀⠀⠀⣀⣴⡾⣟⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢤⣶⡶⠛⠉⠀⠀⠀⠀⣀⣴⡾⠟⠉⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⢉⣠⡶⠛⠁⠀⠀⠀⠀⣠⣤⡾⠛⠁⠀⠀⠀⠀⠀⢻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⣀⣤⠶⠋⠁⠀⠀⠀⠀⣀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⣠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠟⠁⠀⣀⡴⠞⠋⠀⠀⠀⠀⢀⣠⣴⠿⠛⠁⠀⠀⠀⠀⠀⣄⣀⣀⣠⡤⠤⡶⠦⣤⣄⣠⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠋⠀⣀⡴⠚⠉⠀⠀⠀⠀⢀⣠⡶⠟⠋⠁⠀⠀⢀⣴⠿⠛⠶⢶⣿⠀⠠⠴⢦⣀⢳⠀⠰⠖⠶⠀⢻⡿⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠁⠀⠉⠁⠀⠀⠀⠀⣠⣴⠾⠯⠭⠤⠤⠤⠤⠤⣤⣤⣽⣷⠀⠀⠀⠹⣇⠀⠠⠀⠀⣼⣷⠀⠀⠀⠀⠀⣷⡀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠻⠦⣤⣀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠹⣆⠰⠖⠆⠀⠘⣧⠀⢿⣷⠤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⠉⠙⠻⠶⣤⣐⡀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠹⣷⡄⣀⣠⣴⣄⣻⣄⣨⣭⣭⣧⣼⣷⣀⢹⠧⡤⡭⠉⢙⠛⠿⢶⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢦⣤⣤⣀⣀⣬⣿⣿⣶⣶⣿⡤⡴⣶⣶⣾⣿⣿⣿⣛⣿⣯⣿⣯⣿⠮⠤⠶⠾⠿⠛⠛⠛⠛⠛⠛⠛⢻⢰⡞⠂⠀⠀⠀ ⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠸⠶⠷⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣇⠀⠀⠀⠀ ⠈⠛⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠙⠳⢶⣦⡀ ⠀⠀⠀⠀⠛⣷⡄⠀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣴⣶⡶⠿⠿⢛⢛⣛⣻⡷⠀⢸⡇ ⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠘⣷⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣶⣶⠾⢿⠿⠿⠟⠻⠏⢉⣉⣩⡤⠤⠶⠒⠚⠉⠉⣉⣁⣤⣴⣾⠃ ⠀⠀⠀⠀⠀⠀⠛⢿⣦⣄⠀⠀⠀⠀⠙⣷⣌⠳⣴⣴⣲⣶⣶⣿⣿⣿⠟⠛⠛⠋⠉⣉⣀⣩⣤⡤⠴⠖⠒⠚⠉⠉⢉⣀⣲⣦⣦⣶⡾⠿⠛⠛⠋⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣶⣄⡀⠀⠀⠙⢷⡀⠙⣿⠁⣀⣀⣠⠤⠤⠶⠒⠛⠋⠉⠁⣠⣤⣔⣶⣤⣴⠶⠾⠟⠛⠛⣻⠉⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡙⢿⣦⣀⠀⢸⡇⠀⣿⠉⠉⠁⠀⠀⣀⣠⣼⣿⣶⡶⢿⡿⣿⠉⠉⠁⠀⠀⠀⠀⣀⣀⡿⠶⠶⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣷⣭⣻⣷⣼⡇⣠⣿⣤⣤⡶⠾⠛⠛⢻⢹⡇⢡⡇⣸⣇⣿⣀⣠⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡇⠉⢠⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⣯⣷⣼⣷⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠋⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠖⠛⠉⠁⠀⠀⢀⣠⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠉⠛⠿⣦⣀⠀⣀⣠⡴⠾⠛⠋⠁⣀⡠⣤⣤⣤⡶⠿⠛⡟⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⢶⣤⡀⠀⠀⢹⡟⠋⠁⠠⠤⣴⣒⣽⣷⣾⠛⠉⠁⠀⠀⠀⣇⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣦⣼⣇⣠⣤⡴⠟⠛⠉⠀⣸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠿⠿⠈⠛⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

╱|、 (˚ˎ 。7 |、˜〵 じしˍ,)ノ search jsvicky on 'search for emojis' for more!

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⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⠲⠤⠤⠒⠚⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⢀⠖⠢⣀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢀⠴⠲⡀⣿ ⣿⢸⡀⠀⠈⠑⠲⢤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠤⠖⠚⠁⠀⠀⡇⣿ ⣿⠀⢳⡀⠀⠀⠀⠸⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⠁⠀⠀⠀⢀⡼⠀⣿ ⣿⠀⠀⠙⢤⡀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⡠⠋⠀⠀⣿ ⣿⠀⠀⠀⢰⠋⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⢯⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⡎⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⡄⠀⠀⠀⣿ ⣿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿ ⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢹⠀⠀⠀⣿ ⣿⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠦⡴⢦⠴⠂⠈⠀⠀⠀⠀⠘⡇⠀⠀⣿ ⣿⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣧⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠏⠀⠙⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠈⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠔⠚⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠁⠒⠢⠤⠄⣀⣀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠾⠆⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢚⣶⣤⠤⣀⣀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⢰⡦⡼⠁⠈⢳⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⣩⠗⠒⠻⢭⣖⣒⡤⠤⣀⣀⡀⠀⠈⠀⡇⠀⠀⠀⠁⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣉⡀⠀⠀⡴⠃⠀⠀⣠⠋⠀⠀⢈⡟⠙⠒⠫⢭⢗⣒⡳⠤⣄⣀⡀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠛⠒⠤⠤⣉⣉⠓⠒⠤⠼⣁⣀⠀⣠⠋⠀⠀⠀⡴⠃⠀⠀⣨⠋⠑⠒⢪⡍⠓⠒⠣⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠦⣀⣀⠀⠀⠀⠈⠉⠓⠒⠢⠤⢌⣉⡒⠒⠤⠾⢄⣀⡀⡰⠃⠀⠀⢠⢎⡗⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠢⠤⢄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠤⠤⣀⣀⠀⠀⠀⠈⠉⠉⠒⠒⠤⠬⣍⣑⡒⡲⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠤⠄⣀⣀⠀⠀⠀⠀⢸⣳⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠘⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⢀⣠⡄⠀ ⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⡇⠀ ⢀⡴⠋⠀⠀⠀⠀⣀⣿⠂⣆⣠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀ ⣾⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠈⠙⠁⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⣾⠀⠀ ⠻⠦⠤⠴⠖⠋⠉⠓⠒⠶⠤⣄⣀⡀⠀⠐⠺⡂⠀⠀⠀⠀⠀⠀⠘⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⡾⠁⠀⠀⠀⠀⢀⠀⠀⠹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢤⣤⠤⠴⠚⠛⠒⠦⢤⣷

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣿⣿⡿⢟⡿⢛⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⢋⡴⠋⣡⠽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣿⢷⠋⠰⠊⣠⠞⣩⡿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣷⣞⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢸⠀⢠⠞⢁⡴⠋⣠⠞⢉⡛⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣿⠙⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠈⡇⠐⠃⡴⠋⣠⠞⠁⣠⠏⠀⠘⠁⠀⠉⠙⠓⠶⠤⢤⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣏⡗⣒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣋⣟⡖⠀⢠⣿⣿⡆⢳⠀⠊⢀⡴⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀ ⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠀⣸⣿⡟⣇⠘⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⢀⣿⣿⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⣿⣿⣻⣋⣾⣃⣰⣿⣿⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⣿⣿⣇⠘⣿⣿⠙⣧⠤⣶⢶⣦⣿⣿⣿⣿⡿⢣⣾⣿⡿⠋⣩⢍⠟⡽⢋⣿⠟⣩⢳⡦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣄⣉⣉⣛⣓⣶⣯⣿⣿⣿⣿⠟⡼⣱⣿⢏⡞⢁⡼⣿⢫⠞⣠⡿⢃⡞⢁⠞⣰⣿⢫⣟⣶⣶⣤⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⣿⣿⠇⠀⠀⣸⣿⣿⣿⠛⡽⢋⡼⣵⢿⠋⠞⢀⠞⠙⠙⠋⠘⠛⣡⠏⢠⠏⡼⠛⠹⢻⠿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣟⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣷⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣿⣶⣶⣶⣒⣒⣒⡒⠒⠒⠒⠒⠒⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟⢿⣭⣻⣿⣿⣿⠛⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⠛⠛⠿⠿⠿⠿⠶⢶⣶⣖⣲⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣶⣶⣬⣙⣿⢿⢿⡛⢟⢛⣿⣿⣿⣿⣿⡆⠀⠀⢻⣿⣿⢯⣿⠉⢹⣿⠛⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣟⣿⣿⣟⣛⣽⣷⣼⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣾⣿⢠⡾⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⢿⣿⠛⠛⣻⡏⡻⣹⣿⣿⣿⣿⣿⣿⠀⠀⢺⣿⣟⣿⣷⡟⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⢸⣿⠀⠀⣿⣧⣹⣿⣿⣿⣿⣿⠘⣿⣧⠀⢸⣿⣿⣸⡟⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡟⠘⡟⠀⠀⡿⣿⣿⣿⣿⣿⡿⠸⠀⠟⣿⣦⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣷⠀⠀⠀⢠⣿⢟⣉⣿⣹⣻⣥⣤⣤⣴⡟⠁⣿⣿⣿⣚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠛⠛⠛⠉⠙⠉⠻⠿⠟⠿⢿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠁⠀⠀⠻⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⣦⣤⣤⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠁⠀⠀⠀⠀⢸⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠀⢀⣠⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠗⠒⠊⠁⠀⠒⠤⢤⣀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠟⠛⠉⣿⠀⠀⠀ ⣀⡀⠀⠀⣠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢠⣶⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀ ⠉⠉⣻⠿⢡⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠈⠉⠁⠘⠷⠶⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀ ⢀⡼⠁⠀⠈⢷⡦⠤⠤⠤⠤⠔⢋⣿⠿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⣀⣠⡴⠀⠀⣿⠀⠀⠀⠀ ⢾⡇⢀⠀⠀⠈⢳⣤⠤⠤⠤⠔⠋⠁⠀⠀⠈⠉⠙⠛⠓⠶⠦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠙⢷⡀⠀⠀ ⣸⠁⠀⠙⠢⣀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⢤⣤⣤⣀⡤⠖⠛⠁⡄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀ ⢹⡀⠀⠀⢒⣒⣸⡷⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀ ⠘⣇⠀⠳⣆⣀⣉⣹⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⣀⡤⠶⠶⠶⠶⢧⣀⣀⠀⠀⣀⡤⠟⣦⡀⠀⠀⠀⠓⠒⣶⣿⣤ ⠀⣿⡀⡀⢀⣈⠉⢉⣿⠞⠁⠀⠀⠀⠀⢀⣤⠾⠿⠛⠓⠒⠛⠒⠒⠩⣁⣀⣀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠈⠻⠶⢶⣤⣤⡾⠏⠀⠈ ⠀⡘⣷⣼⡀⣠⢌⣽⠇⠀⠀⠀⠀⠀⠀⢈⡧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡠⠒⢀⣠⡴⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⢷⡆⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⡠⠴⠿⠓⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢠⠄⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣀⣀⣠⣤⡶⠶⠛⠓⠒⠒⠒⠛⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠉⢻⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⢤⣤⣴⠟⠋⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣤⠤⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣄⣀⠀⠀⢸⣿⠽⣶⡘⣟⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠛⠛⠷⠤⢄⣘⡀⠈⠀⠓⠻⠶⠀⢴⣶⡞⣯⠽⣦⠀⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠤⠤⢀⣀⣿⣝⠁⠋⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠤⠬⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠂⠤⠤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠼⠃⠀⠀⠘⠦⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠳⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣠⠤⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠲⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠹⠆⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠤⠤⣀⣀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣷⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⣾⣦⣼⠁⠀⠈⠳⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠉⠑⢲⡿⠯⢭⣓⣒⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⡇⠀⠀⠀⠀⠙⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⡼⠋⠛⠒⠢⣭⣽⣗⣒⠦⠤⣤⣀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠦⢤⣄⣀⣀⡼⠁⠀⠀⠀⣠⠟⠀⠀⠀⠀⣴⠛⠀⠀⠈⠉⣻⠖⠶⠬⣍⣛⣒⠶⠤⣄⣀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠓⠲⠦⢤⣀⣉⠉⠛⠒⠲⠴⣧⣀⣀⠀⢀⡼⠁⠀⠀⠀⢀⡴⠃⠀⠀⠀⢠⡟⠉⠉⠓⠒⣾⡈⠉⠑⠚⠶⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠤⠤⣤⣉⡉⠛⠓⠢⠤⢤⣠⣞⡀⠀⠀⠀⣰⠏⠀⠀⠀⠀⡴⢋⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠲⠤⢤⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠦⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠦⠤⢤⣈⣉⠙⠓⠲⠧⠤⣄⣀⣀⡞⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⠤⣤⡟⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⣞⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠳⠦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⠶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢷⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠼⠧⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣁⠀⠀⠀⠀⠀⣀⠀⠀⢻⣧⣀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣤⠤⠤⠤⠤⠤⠤⡤⣿⣀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠉⠉⠉⠉⠉⠉⠉⠙⢃⣀⣽⣿⣿⣿⡽⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⡇ ⠀⠀⠀⠀⣾⣧⣿⣤⣄⣀⣀⣀⣀⣀⣈⣉⡙⠛⠛⠒⠒⠒⠒⠒⠒⠲⠦⠆⠀⠀⠀⠀⠈⣧⣀⣀⣀⣀⣀⣠⣤⣤⣤⣬⣿⣿⣿⣶⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⢹⡇⣹⡇⠀⠀⠈⠉⠉⠉⢉⣉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠒⠲⠶⠦⣤⣤⣤⣄⣼⣛⣞⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿ ⠀⠀⢀⣠⣿⣷⠟⣇⣠⣤⣶⣚⣩⣥⠤⢶⣷⣶⣶⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣀⣠⡿⠃ ⢺⠿⠛⠿⣿⣵⡶⠻⣿⠯⢿⣿⣿⣿⣿⣿⡥⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡿⠴⠖⠛⣻⠟⠉⠀⠀⠀⠀ ⢸⣤⣧⡀⠀⠉⠉⠉⠛⠛⠒⠿⠿⠬⣯⣉⣙⣛⣛⠰⠿⠿⠯⠭⠍⢀⣀⣀⡀⠀⠀⢀⣴⠏⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠁⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀ ⠈⠉⠙⠛⠓⠒⢶⣶⣦⣤⣤⣀⣀⡀⠀⠈⠉⠉⠉⠛⠒⠒⠲⠦⣤⣭⣉⡙⢻⡟⠚⠻⣭⠾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠴⣿⡆⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⢉⡿⠋⠛⠻⠶⢶⣦⣤⣄⣀⠀⠀⠀⠀⠈⠙⣷⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠋⠉⢹⡇⠀⠀⠀⠀⠀⢻⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⣾⠁⠀⠀⠀⠀⠀⣿⠀⠀⠉⠙⡟⣶⠶⠤⢤⣿⣶⠶⣿⠉⠉⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠈⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⠃⠀⠀⠀⠀⠀⢸⣿⠀⣀⡤⢚⣿⡇⠀⣠⠟⠃⠉⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⠀⠀⠀⠀⠀⢸⣿⠾⠋⠀⢰⣿⣷⡾⠃⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠃⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢸⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⢶⠶⣦⣿⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⡿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⠀⠀⠀⠀⢠⣶⣿⣿⣯⡶⣶⣰⣶⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⡿⠀⠀⠀⠀⠀⠁⠀⠘⠛⠻⠿⠟⠛⠙⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣿⡆⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹⠸⡄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢱⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠻⠤⢄⣀⣀⣀⣀⣀⡤⠤⠤⠴⠒⢻⡈⡗⠚⠓⠒⠒⠲⠤⠤⣀⡀⠀ ⠀⠀⠀⢰⡶⠶⣾⡃⠀⠀⠀⠀⠉⠙⢲⠖⠒⠉⠉⢀⣉⣉⢇⠸⡀⠀⠀⠉⠉⠑⢒⣦⡬⣧ ⠀⢀⣠⣼⡇⠀⠀⠈⠉⠑⠒⠤⣄⣠⠏⠰⠾⣹⠶⠘⢻⣿⣹⣄⡷⠤⠔⠒⡏⠉⠁⠀⠀⢻ ⢾⣯⣞⡻⠿⠶⣦⣄⣀⡀⠀⠀⠀⠈⠉⠒⠲⡴⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣠⡟ ⠘⠛⠿⣿⣽⣶⣦⣭⣘⠛⢷⣶⣤⣀⡀⣀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢿⢉⡿⠋⠀ ⠀⠀⠀⠀⠈⢹⢻⢿⢿⣿⣷⣶⣬⢽⠋⠀⠀⠀⠀⠀⣀⣀⡤⠤⠖⠒⠊⠉⠁⢸⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⢸⣶⢸⠀⠀⢹⡟⠛⢿⡦⠲⠶⣾⡉⠉⡼⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⢻⡇⠀⠸⣿⠀⠀⢸⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⠟⠀⢠⣿⡓⠢⣤⣿⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⠿⣷⣼⣿⡇⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠀⠀⠀⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠞⠛⠁⠀⣄⠀⠈⠻⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⠀⠀⠀⣴⠸⣦⡀⠀⡰⠀⠉⠙⠻⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣽⡴⠁⣀⡤⠊⠀⠀⠀⠈⠙⠻⢶⣄⡀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⢿⠇⠸⣾⣷⣿⣓⣲⣦⣶⡶⠿⠛⠚⠛⠷⣦⡴⠾⠛⠉⣿⠀⠀⠀ ⠀⠀⠀⢀⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠶⢔⢀⣀⡿⢿⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊⡑⠢⠤⣀⡀⠀⠀⠈⠱⣸⣿⡏⠛⢲⣦⣄⣀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀ ⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣦⣤⡈⠲⠤⣀⡄⠘⠉⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡸⢜⠉⠉⠙⢿⣿⣷⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠀⠀⠀ ⢿⣤⣀⣀⣀⣀⣤⣶⠶⠛⠋⠛⠛⠶⠶⣦⣤⣄⣘⣮⣑⠒⠒⣒⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀ ⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠷⢦⣤⣄⣀⡀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢀⣀⣤⡴⠶⠾⢿⣦⣄⣀⡀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⣛⣋⣭⣭⣭⠁⠈⠉⠉⠙⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⣫⣷⠞⠛⠉⠁⠀⢀⡇⢀⡆⠀⠀⠀⠀⠀⠉⠛⢷⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣶⠟⠉⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢫⣼⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⠿⣷⣄⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢰⠏⠹⠿⠛⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣟⣿⡀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡏⠀⠀⠀⠀⠀⠀⣿⣀⣤⣦⣀⣾⠄⠀⠀⠀⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣧⣼⡅⠀⠀⠀⠀⠀⠀⠈⠋⠉⠹⠿⠛⠀⠀⠀⠀⠘⠻⠟⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀⠀⠀⣠⣴⠟⡋⠉⠁⣨⠿⡌⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢶⡋⠀⢠⣾⢛⠺⠷⣦⣠⣾⠃⠀⠙⣦⣙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠁⢀⣯⣷⣴⣷⠶⠦⠟⠁⠀⠀⠀⠈⠉⠛⠻⢶⣤⣄⠀⠀⠒⠦⢤⣄⣀⣀⣠⡤⠤⠤⢤⣴⠟⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠛⣧⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣿⢰⡿⣶⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢼⣶⢾⣏⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⢸⡆⠀⠀⠀⠀⠀⣼⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⢹⣷⡅⠘⠂⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠠⣿⣷⣩⡷⢦⣀⣠⡴⠶⢛⡟⠉⠁⢸⡗⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠳⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠸⣤⣼⣆⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⠛⠉⠁⠀⠀⡾⠁⠀⠀⢸⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠈⠉⠛⠻⢶⣦⣤⡀⠀⠀⣳⣦⡤⠤⠤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⣼⣦⢀⡟⢹⣦⠀⣈⢳⡀⠀⠀⠘⣇⠀⠀⠀⢸⣿⠀⢸⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠒⠋⠁⠀⠀⠀⣀⠠⢤⣀⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠐⡷⠄⣿⡆⠋⠈⠳⠀⠀⠀⢹⡆⠀⠀⢸⣿⠀⣾⡄⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠙⠓⠒⠋⠀⠀⠀⠀⠀⠀⣿⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣧⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⣿⣸⠃⢳⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠳⠤⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⡠⠴⠒⢚⡁⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠈⠉⠳⢄⡀⠀⠀⠀⠀⠀⠘⣷⠀⢸⣿⠋⠀⠀⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣇⠙⡦⠤⠀⠀⠈⣉⠉⠉⠉⠁⠀⢀⣠⠴⠊⠉⠳⣄⣀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⢙⣆⠀⠀⠀⠀⠀⢹⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢹⠀⠀⠀⠀⠉⠉⠉⠉⠳⣴⠋⠁⠀⠀⢸⣀⣀⣉⣉⠛⠒⠒⠒⠶⠤⢤⡠⠤⠤⡤⣴⣫⣯⣄⠀⠀⠀⠀⢸⣿⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⡅⢠⠀⠈⠉⠓⠲⠤⣤⣄⠀⠀⢠⠞⠀⣏⡟⠈⠙⠻⢷⣶⣤⣸⣇⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣧⢷⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⣇⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣏⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠓⠦⢤⣠⠤⣤⣀⣤⡧⠤⠖⠋⠁⠸⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿⠙⠶⣤⣀⡀⠀⠀⠀⣸⢀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠙⠉⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⢶⠚⢻⠋⢹⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⢧⠀⢸⡄⣸⠐⠟⠀⠀⠀⠀⠀⠀⡇⠹⠀⠀⢀⡆⠀⠀⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡅⠈⢦⠀⠀⠀⠀⣼⡄⠚⠃⠁⢀⣀⣤⣤⣄⣀⣀⠿⠃⠀⠀⠀⠿⠇⠀⠰⠇⠀⠀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡄⠻⠃⠀⠀⠀⠉⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣅⣤⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⣸⠟⠃⠀⠀⠀⠀⣀⣴⠀ ⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣠⢴⣁⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⢆⣀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢿⠁⠀ ⠀⠀⠀⠀⠀⢀⣠⠔⠊⠉⠀⢀⣀⠼⠛⠛⠉⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠇⠀⣀⣤⡀⠀⠀⠀⢠⣾⠀⠀ ⠀⠀⠀⠀⠰⣯⣀⣀⡤⠔⠚⠉⠀⣀⡤⠔⠊⠉⢛⡩⢿⣾⡿⣿⢛⣿⣿⣿⠿⠛⢁⣀⣤⣶⣿⣿⣿⣿⣿⣤⡄⠈⠁⠀⠀ ⠀⣀⣤⡀⠀⠁⠘⡿⢦⢤⣤⠖⠋⠁⢀⣠⠴⠊⠉⠀⢀⡡⠔⠻⠾⠛⢉⡠⢴⡞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⡷⠂⠀ ⠈⠻⡀⠱⣄⠘⢷⣦⣈⠀⡏⠱⣶⣮⣁⡀⢀⡠⠔⠊⠁⠀⠀⣀⠴⠚⠁⢀⣾⣷⡿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀ ⠀⠀⢽⡆⠻⣤⡀⠉⠻⢿⣿⡦⣌⡟⠋⠿⡿⣦⢄⣠⠔⡊⠉⠀⣀⡤⠖⠉⠀⠀⣠⠽⠛⠋⢹⣶⣼⣿⡿⢿⠋⠀⠀⢀⠖ ⠀⠀⠀⠁⠀⠱⡝⡄⠀⠀⠈⠙⢻⣿⣶⣤⣇⡀⠙⡿⠲⢤⡶⣫⠅⠀⣀⠤⠒⠉⠀⢀⡠⠔⠋⠉⢉⡡⠔⠈⠀⠀⣤⡾⠀ ⠀⠀⠀⠀⠀⠀⢹⣇⣀⠀⠀⠀⠀⡉⠛⠿⣿⣿⣶⣧⣀⣼⠋⠀⢰⣏⣀⣀⡠⠤⠚⠉⢀⣀⠔⠚⠁⠀⢀⡠⠔⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⢸⣏⠙⡆⠀⠀⢹⠳⡀⠀⠉⠛⢿⣿⣾⣷⣤⣸⡋⠁⣿⠲⣦⣴⣚⠉⠀⢀⣠⠔⠊⠁⠀⠀⠀⢈⣧⡀ ⠀⠀⠀⠀⠀⠀⠙⢿⣚⣦⠎⠀⠀⢸⡀⠱⡄⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣾⣄⠘⡟⠹⣿⡾⢯⣀⠀⠀⠀⣠⠀⠀⢈⡉⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡆⠀⠀⣀⡇⠀⠀⠀⠀⣀⠀⠀⢀⢴⠉⠉⠉⠛⠛⠿⣷⣤⣌⡇⠀⠀⠀⠀⡰⠁⠀⠐⠿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠃⠀⠀⠉⠁⠀⠀⠀⠘⠿⠷⠊⠁⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣀⣀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⣻⣤⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⣀⣴⠾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⢒⡾⠟⠋⠀⠀⠀⣠⣴⠟⠋⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⣁⡤⠞⠉⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠶⠋⠁⣀⠴⠚⠁⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡴⠋⢁⣠⠖⠋⠁⠀⠀⢀⣤⠶⠛⠉⠀⣀⣤⣀⣰⡖⠒⢒⠊⢿⠙⣒⣒⠺⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡏⠀⠒⠉⠀⠀⢀⣠⣴⣾⣉⣀⣀⣀⣀⣘⣿⠀⠀⠙⣧⠀⠀⠁⢘⡆⠀⠀⠀⢹⡄⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠙⠲⢤⣀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢹⣆⠀⠀⠀⢹⡄⠶⢆⠀⢳⡈⢿⡶⠤⣤⣤⣀⡀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠉⠓⠾⢤⣤⠴⠶⠶⠲⢤⣄⣀⣸⡁⢀⣀⣀⣿⣤⣴⣶⣦⣷⣶⡿⢿⣾⣿⣶⣿⣶⣦⣤⣭⣙⣷⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠙⡖⠲⣿⠿⠿⠿⠿⠿⠿⠟⠻⠛⠓⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⢿⡅⠀⠀⠀ ⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡀⠛⠶⣦⡀ ⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣶⠶⠾⠿⢟⣛⣫⡯⠭⠟⢃⣸⠃ ⠀⠀⠀⠀⠹⣦⣄⠀⠀⠀⠘⣧⡹⣄⣀⣤⣤⣤⣴⣶⡾⠿⠟⠛⠛⠛⣉⣉⡡⠤⠴⠒⠒⠋⣭⣍⣤⣴⠶⠶⠞⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡀⠈⠙⣦⠉⢻⣉⣉⣠⠤⠤⠖⠒⠋⠉⣩⣥⣴⣦⣤⠶⠶⠛⠛⡏⠉⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡍⣻⣦⡀⣻⠀⣿⠁⠀⣀⣤⣤⡾⣿⢿⣿⡟⡿⠉⠀⢀⣀⣠⠤⠴⠛⠛⠛⠲⢦⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢻⠛⢻⡿⠖⠛⠋⠉⠉⠀⠀⣇⣧⣼⣿⡿⠷⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⡤⢿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠋⠉⠀⣀⣼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠉⠛⠶⣄⣤⠴⠚⠋⢉⣀⣤⣴⡶⠶⠛⠉⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⣀⣿⠀⢀⣠⠼⠟⠛⣿⠁⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠿⠏⠛⢻⣿⡏⠁⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⢘⡭⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⠤⠒⠁⢀⡴⠚⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠒⣉⠔⠊⠁⣀⠴⠚⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⡡⠔⠈⠀⣠⠴⠊⢁⡤⣠⡄⢐⢲⢒⣀⢷⣄⡀⠀⠀⠀⠀⠀⠀ ⢰⠧⣈⢀⡠⠒⠛⠒⠒⠒⠚⡆⠀⣧⠀⠐⢇⣠⠈⡆⢧⣀⣀⠀⠀⠀⠀ ⢸⠀⠀⠉⠐⠣⢖⢒⣒⣦⣤⡇⣤⣼⣶⣶⡾⠶⠿⠾⠶⠷⠦⢯⡵⠀⠀ ⠘⠦⣄⠀⠀⠀⢸⢸⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣱⠤⡀ ⠀⠀⠈⣆⠀⠀⠘⡼⡀⢀⣀⣀⣠⣤⠤⠶⠶⢒⣚⠛⠭⣍⣛⣂⡨⠴⠃ ⠀⠀⠀⠀⠙⡶⣄⠈⢪⢹⠩⠭⠒⢒⣈⣩⡷⠦⠖⠒⢹⣉⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣺⠛⡾⠼⠒⠒⠉⣿⣹⡿⠧⠔⠒⠉⠁⠀⢀⣉⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠈⣟⠛⠤⣀⢀⡠⠤⠒⣉⣁⡤⠼⠃⠀ ⠀⠀⠀⠀⠀⠀⣿⡄⡇⠀⠀⠀⠀⣿⣵⢦⣼⣁⠤⠔⢛⡏⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⣇⠃⠀⠀⠀⠀⡟⠉⠀⢹⡇⠀⠀⠀⠁⠀⠀⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠒⠒⢠⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠄⠀⠀⠧⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠉⠉⠁⢲⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣋⣀⣀⣀⣀⡀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣠⠞⠁ ⠀⠀⠀⠀⠀⠀⢀⠔⡩⠀⠀⠀⠀⠀⠀⠠⡊⠀⠀⡀⢣⡀⣀⠤⠊⠀⠀⠀ ⠀⠀⡶⡌⠉⣉⣙⣚⣂⣀⣠⡤⠄⠀⠀⢇⣀⣀⡀⠀⠶⠿⠯⡍⠉⠉⠉⢹ ⣀⣠⣷⣧⣤⣶⣤⡦⠦⠤⠀⠀⠉⠉⠉⠛⠓⠀⠀⠀⠀⠀⢀⣇⣀⣀⠠⠞ ⠧⠬⣉⣈⡓⠛⠙⠥⠭⠛⣂⡠⠤⣄⣠⡢⠃⠀⠀⠀⠀⣀⣜⠁⢰⠁⠀⠀ ⠀⠀⠀⠱⠀⢩⠋⠑⢲⠒⠤⣄⢈⣳⣠⠤⠐⠒⠈⡹⠀⠀⠘⡄⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⠇⠀⠀⢸⠴⠊⣇⠔⠁⠀⢱⠀⠀⢠⠁⠀⠀⠀⠃⡇⠀⠀⠀ ⠀⠀⠀⢀⢰⠀⠀⠀⣼⠤⠴⢇⠀⠀⠀⠀⠇⢀⠇⠀⠀⠀⠀⢠⠇⠀⠀⠀ ⠀⠀⠀⢘⡼⠀⠀⠉⠙⠛⠛⠚⠂⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠽⠖⠚⡿⠀⡀⠀⠀⠉⠳⠦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡵⠛⠁⠀⠀⠀⠀⡇⢸⠁⠀⠀⠀⠀⠀⠈⠛⢶⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣾⣯⡄⠀⠀⠀⠀⠀⠀⢳⣸⣆⠀⠘⡄⠀⠀⠀⠀⠀⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢙⣳⣶⣇⠀⠀⠀⠀⠀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠇⠀⠀⠀⠀⢸⣀⣤⣄⣴⠀⠀⠀⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⢱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⣷⢾⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠀⠀⠀⠈⠛⠋⢸⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⠆⠀⣠⣶⣿⣁⢀⡴⠋⢧⡳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠝⠀⣸⣧⣽⡤⠭⠟⠁⠀⠀⠙⠒⠶⢤⣀⡀⠀⠤⢄⣀⣀⣀⣀⠤⢤⣠⡏⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣦⡀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡳⣤⡤⠞⠋⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⣷⡛⢻⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢘⣿⡛⣤⡀⠀⢀⣠⣴⠶⠖⢸⡄⠀⠀⠀⣸⠃⠀⠀ ⢦⣤⣀⠀⠀⠀⠀⠀⢸⡀⠙⠁⠀⠀⠀⠀⠀⠛⠃⢰⣤⣆⢀⠀⠀⠀⠀⠉⢀⣹⣿⣷⠛⠛⠉⠀⡜⠀⠀⢸⡄⠀⠀⢰⠏⠀⠀⠀ ⠀⠀⠉⠙⠓⠶⣤⡀⣀⠷⠦⠒⠒⠒⠒⠤⠤⣀⡀⠀⠀⠈⠉⠀⠀⠀⣾⡄⡞⢹⡆⣨⢳⡀⠀⠀⡇⠀⠀⢸⡇⢸⠀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢴⠋⠀⠀⠀⠀⠠⢄⡶⠀⠀⠀⠈⠑⣄⣀⣀⣀⣀⠀⠀⠀⣟⠘⠿⠀⠀⠁⠀⠀⢸⡄⠀⢸⡇⡞⢧⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠢⠄⣀⣀⡀⠀⠀⣀⣀⣀⠠⠤⢖⠋⠀⠀⠀⠀⢀⣈⠉⠉⠐⠢⢄⡀⠀⠀⠀⠀⢿⡀⢸⡗⠁⠈⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡅⢱⠢⠀⠀⠉⢉⣉⣁⠀⡠⠔⠊⠈⠣⠄⣀⣀⣀⠈⠉⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠘⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⢶⠒⠒⠢⠤⣀⡈⠉⠐⠂⢀⠞⠹⡿⠳⢦⣄⣀⠀⣿⢹⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣯⢦⡆⠀⠀⠀⠀⠉⠳⡄⠊⠀⡾⠁⠀⠀⠈⠉⠛⠿⢾⣧⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⢧⡀⠀⠀⠀⠀⠀⡇⠀⢀⡤⣇⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢶⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠒⠒⡇⠉⠁⠀⠈⢸⠧⣀⠀⠀⠀⠀⠀⠇⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠑⠒⠒⢚⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠒⠒⠒⠲⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⣀⠴⠋⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀ ⠀⢰⠃⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⠀⠸⡆⠀ ⢀⡏⣞⡿⢩⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠔⠒⢹⠀⠀⢹⡀ ⢸⠸⡏⠹⠿⠀⠀⠀⠀⠺⠂⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡸⠀⠀⠈⡇ ⢸⠀⠓⠒⠤⠤⣀⣀⡀⠀⠀⠀⠈⠉⠁⠀⠰⡶⢰⢛⣃⠟⢆⠀⠠⡇⠀⠀⠀⡇ ⢸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠢⠤⠤⣀⣀⠀⢸⠀⠓⠃⠀⠀⠀⠹⡄⠀⢀⡇ ⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠦⠤⣀⣀⡀⢱⠀⣸⠁ ⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠇⠀ ⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⠤⠤⠤⠴⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⠤⠔⢲⢲⠀⠀⠀⢰⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢖⠣⡀⠀⠀⡆⠴⠚⠉⣀⡀⠀⡼⠈⠀⣼⠀⡸⠀⠀⠀⠆⠀⠀⠀ ⠀⠀⠠⡆⠃⠀⠀⡡⣴⣾⣿⣿⣿⣿⣤⣦⣄⢀⡀⠀⠀⡜⠃⠀⠀⢠⠆ ⠀⠀⠀⢀⡠⠔⠈⣁⠽⠞⢻⣿⣿⣿⣿⣿⣿⣿⣷⠷⠆⣀⡀⠀⠀⣸⠀ ⠀⠀⠀⡗⢤⡒⢉⡠⠔⠊⡀⠍⠛⣚⣏⣿⠟⣋⢤⣶⣿⣿⣿⣷⢆⣅⠀ ⠘⢏⢢⠐⣾⣅⡓⢶⣆⣁⡠⠐⠈⢀⠤⠒⢁⠾⠾⣏⣽⡿⣿⣿⡿⠋⠀ ⠀⠘⠃⢳⠄⠉⠛⠶⣯⣙⡙⢲⠬⣠⢔⠊⣁⠄⠂⢉⠡⠛⢛⠫⠁⢀⡌ ⠀⠀⠀⠀⢧⠤⡀⠀⣍⠛⠿⣾⣤⣏⠀⡯⢤⣐⢊⡡⠔⠈⡀⠄⠒⠀⡀ ⠀⠀⠀⠀⠻⣣⡄⠀⢃⠣⠀⠀⠙⠻⢿⣷⣼⣈⠟⢶⡶⡉⠀⢀⠀⢀⠳ ⠀⠀⠀⠀⠀⢤⠇⠀⠼⠀⠀⢠⣄⠄⠧⠀⠈⠉⠛⠚⠃⠀⡠⠊⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣋⠇⠘⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⡤⢤⡀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢒⣩⠷⡘⡆⠀⠀⠀ ⣄⡀⢸⡿⣷⢳⡯⠏⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠃⢣⠀⠀⠀ ⠀⠈⠛⠯⣈⠉⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠐⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠉⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡠⠮⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠀⠠⠤⠒⠉⠀⠀⠀⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⢿⡿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣷⣋⠖⡡⢝⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡟⡁⢈⡴⢋⠔⢙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢹⠀⢊⡴⢉⠔⢁⡔⠁⠘⠉⠉⠒⠢⠤⢄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣹⣿⣷⣊⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣭⣿⡂⠀⣿⣿⠘⡀⠊⠰⠃⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢄ ⠀⠀⠀⠀⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⠃⣸⣿⠋⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣧⠘⣿⡟⣇⣠⣤⣤⣾⣿⣿⡿⣻⣿⣿⠛⣛⡻⡿⢲⡾⢲⢠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣦⡭⠭⢽⣾⣿⣿⣿⡿⡱⣱⡿⡽⢁⣞⣟⢝⣴⠟⡴⣡⢋⣾⣯⣿⣷⡶⠂⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣁⣀⣸⣿⣿⣃⣉⣴⣵⣙⣀⣁⣊⣀⣀⣀⣡⣮⣀⣁⣋⣀⣹⣛⣉⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡿⣿⣻⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠿⠷⠶⠶⢦⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⢠⣶⣶⣭⣿⣟⣟⡟⣻⣿⣿⣿⣷⠀⠈⣿⣿⢫⡏⢙⡟⢛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⢦⡶⡿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣧⡏⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣆⣿⠀⢸⣿⣳⣿⣿⣿⣿⢿⣇⠀⣿⣿⣹⣋⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠁⠟⠀⢸⣿⣿⣿⣿⡟⠃⠘⣿⣦⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠃⠀⠀⠺⣽⣶⡷⠷⠿⠿⢿⣧⣤⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠶⢶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⢀⢜⠟⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⣿⣉⠇⠀⠀⠀⠀⢀⣀⡀⢀⣾⠁⠔⡡⠊⠂⠈⠉⠐⠂⠤⠄⡀⠀ ⠀⠀⣼⢿⣿⡆⠀⠀⠀⢠⣾⣿⡇⣼⡏⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⢻⣆⡛⢡⣶⣾⣿⣿⣿⢟⣽⣟⡽⠃⣶⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣥⣼⣿⣭⣵⣭⣥⣥⣤⣤⣬⣤⣅⣙⡉⠁⠤⠄⠀⠀⠀⠀⠀⠀ ⣤⣝⣿⢿⡟⣿⣿⡎⠙⣿⡟⢻⢿⡟⠃⠀⠈⠉⠉⠉⠛⠛⠒⠂⠀⠀⠀⠀ ⢸⢿⠛⣾⣿⣿⣿⣷⠀⣿⣷⠣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠘⠀⣿⢿⣿⣉⣻⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠴⣶⡶⣦⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣇⣿⡿⠛⠉⠉⠛⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢨⠁⢉⣘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⡍⠀⠸⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠛⠃⠀⠀⢹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⢿⡟⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⡒⠂⠤⠤⣉⣉⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣼⢿⣿⣿⣿⣿⡉⠒⠒⠠⢤⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣾⣿⣷⣿⣂⢄⣉⠒⠈⠧⢀⡈⠉⠒⠂⣾⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠚⠉⠢⢍⠻⢿⣿⣿⠿⠦⣀⠉⠒⠢⢄⣈⠉⠒⣶⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣧⡈⠑⠢⣄⠀⠑⠢⣈⠉⠓⢄⠈⠑⠢⣄⠀⠈⣱⣾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣄⠀⠉⠢⣄⠈⠑⠤⡀⠉⣢⣤⣴⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢎⡉⠻⣿⣿⣿⣿⣿⣟⠢⡀⠈⠓⢤⣤⣾⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣠⣴⣶⣶⡫⣄⠀⠉⠢⢄⠙⠻⣿⡿⢏⠀⠈⢳⣴⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣮⡑⠤⡀⠀⠙⠢⢄⠀⠀⢑⢶⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠐⠊⠁⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠦⠈⠢⠄⠀⠀⠙⠶⠥⢋⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠟⠛⠛⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⣻⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠄⠸⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡦⠀⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⠭⠁⡀⣹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡄⠟⢻⠿⠪⠁⣒⡾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠛⠿⣿⡷⢅⠐⠠⠁⠒⣴⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣤⡀⠀⠀⠀⠀⠂⣈⣠⣤⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣠⠀⠋⠛⢿⣿⣿⠀⠀⣠⡶⠙⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣮⡂⢀⠀⠈⡀⢰⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠈⠉⠉⠉⠉⠉⠀⠁⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠒⠢⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢢⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠒⢦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢐⡲⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢫⣀⣀⣀⣀⣀⠀⠘⣧⣀⣀⣤⣖⣋⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⣶⠒⠒⠒⠒⠒⠻⠤⣾⣥⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣟⡛⠛⠛⠛⠛⠉⠋⢻⡀ ⠀⠀⠀⠈⣿⢻⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⠤⠬⣥⣀⣀⣀⣀⣿⣶⠖⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⣧⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⣀⣴⣿⠿⣄⣤⣴⣶⣥⣤⣴⣶⣶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⣀⣀⣤⠞⠀ ⠐⡟⠉⠻⠿⠿⢹⣿⣛⣿⡿⢿⡿⣶⣶⢢⣤⣤⠄⠀⠀⠀⠀⠀⠀⢀⡟⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠗⠛⠉⡿⠁⠀⠀⠀⠀ ⠀⠛⠿⠦⠤⣤⣤⣀⡀⠈⠉⠉⠓⠒⠲⠮⠭⢭⣉⣁⡒⠒⢶⡤⢴⣟⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡆⠀⠀⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⠉⠉⣻⠟⠒⠲⠦⣤⢤⣀⣀⠀⠉⠉⠹⡇⠀⠀⣀⣀⡤⠤⠔⠒⠛⣹⠉⠁⠀⠀⢹⡀⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⠀⢰⠃⠀⠀⠀⠀⣿⠀⠀⢈⣿⠏⠒⣲⠿⠛⢻⡁⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣇⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⠀⠀⠀⠀⠀⣯⣴⠚⢩⣿⣠⠞⠁⠀⠀⠀⢻⡀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢸⢸⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⢰⠃⠀⠀⠀⠀⢰⣏⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢀⣾⡟⢒⠲⠾⠯⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢸⡾⠓⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⢃⣼⠀⠀⠀⠘⠛⠻⠿⢿⣿⠿⠾⣧⠄⠀⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠛⠛⣏⠉⠙⡏⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠀⠀⠀⠀⡆⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⠀⢀⣇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡇⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⠉⠈⢳⡀⠀⠀⠀⠀⠀⣘⡆⠠⣿⠂⠙⠁⠀⠀⣀⡄⣀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⢠⣾⠄⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢳⡀⢠⣿⡄⠀⠀⠀⠀⠿⠃⠀⠀⢀⣠⣴⣶⣿⣿⣿⣯⣷⣾⣿⣦⠁⠀⣀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣷⠀⠉⠁⠀⠀⠀⠀⠀⣠⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣷⣾⣷⣧⠀⢀⡄⠀⠀⠀⠀⠀⢠⣼⠋⠉⠀⠀⠀⠀⠀⠀⣴⣾⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⡤⠾⣇⣼⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⣀⣤⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⣀⡟⠻⠿⠏⠉⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠿⡅⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣬⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡖⠋⠁⠀⠀⢀⣠⡤⠖⠛⠉⠀⠀⣀⡤⠞⠳⠿⠿⢟⢿⡙⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⠟⠋⠉⠀⣀⣤⣶⣿⣿⣿⣶⣶⣂⠀⡀⠨⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡍⠲⢴⣖⠋⠉⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⣀⡤⠖⠊⠛⠿⠛⣩⣿⢰⣿⣿⠿⠛⠉⢁⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀⣤⡀⠀⠀⠀⠀ ⢀⣤⡾⢤⠀⠀⢣⠀⠘⡏⢿⠲⢶⣖⠋⠁⠀⢀⣀⠤⠖⠋⠁⠀⠀⢀⡠⠔⠊⠉⠛⠞⠋⢃⣠⠔⢋⣿⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⣼⣿⢿⠋⠀⠀⠀⠀ ⠈⠿⡀⠀⢳⣄⠘⠿⣶⡧⣀⠁⢸⡏⠹⣾⣾⣏⣀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⢀⣠⠴⠚⠉⠀⢀⣼⣿⣾⡿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀ ⠀⠀⢹⣦⡸⢿⡄⠀⠉⠛⢶⣭⣒⠧⣀⡈⢻⠹⠗⢿⣿⣫⣄⡀⠀⣀⡠⠔⠚⠉⠀⠀⢀⣠⠴⠚⠉⠀⠀⠈⣻⠿⠼⠟⠻⣥⣀⣿⣿⣿⣿⡿⠋⠁⠀⠀⢀⡦⠤⠤ ⠀⠀⠘⠻⠃⠀⢿⡑⣆⠀⠀⠈⠙⠻⢷⣽⣺⠦⣀⡀⢸⡌⠛⠯⣿⣣⢀⠓⢀⣠⠴⠚⠋⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⢀⡿⠿⠿⠿⠟⢋⡡⠏⠀⠀⠀⢀⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⣼⡀⠀⠀⠀⠀⠀⠈⠽⣿⣷⣯⣟⣧⣄⡀⣹⠉⠉⢹⣿⠢⠍⢂⣀⡤⠖⠋⠁⠀⠀⢀⣠⠴⠊⠁⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠺⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⢀⡀⠀⠀⠀⠀⢠⡈⠙⠻⠿⣿⣿⣯⣟⡦⣤⣼⡋⠀⠀⢼⣧⣀⣄⣀⡠⠴⠚⠉⠀⠀⣀⡤⠖⠉⠀⠀⠀⢀⡠⠴⠒⠉⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣏⠉⢳⡄⠀⠀⠈⡿⢦⡀⠀⠀⠙⠻⢿⣻⢷⣮⣷⣦⣀⢸⠿⠑⠠⣿⡦⣤⣄⣤⠖⠋⠁⠀⠀⢀⣠⡴⠊⠁⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⡻⣼⣆⢀⡇⠀⠀⠀⢧⠀⢳⡀⠀⠀⠀⠀⠈⠓⠯⣿⣿⣷⣯⣗⡦⣀⣿⠀⠘⢿⡟⢯⣖⢦⣴⡚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠾⣯⠀⠀⠀⠀⢸⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⣛⠿⣻⠿⣷⣭⣗⡦⣈⡇⠂⢻⢸⡍⠛⠳⠄⠀⠀⠀⣰⠃⠀⠀⣠⡿⠀⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣸⡆⠀⠀⢠⣼⣇⠀⠀⠀⠀⢀⣠⣄⠀⠀⣠⠴⣿⠀⠀⠀⠀⠉⠈⠙⠳⠯⣗⡮⡼⠇⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠻⣿⠗⠊⠁⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠀⠀⠐⠐⢀⢂⠐⠀⠒⠀⠀⠀⠀⠈⠋⠑⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠓⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢳⣄⡀⠀⠀⠀⠀⠀⠀⡹⠤⠀⠈⠳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠞⠀⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠆⠀⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⢠⣠⡄⠁⠀⠀⠀⠀⢀⣀⡤⠤⢤⣄⠀⠀⠐⠡⠆⠀⠹⡀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⢠⠞⠉⠒⠒⠒⢒⡟⠀⠀⠀⠀⠀⠀⠀⢧ ⡴⠒⠦⣀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢦⣀⣀⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢧⠀⠀⠈⠳⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⠣⡀⠀⠀⠉⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎ ⠀⠀⠙⠦⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀ ⠀⠀⠀⠀⠀⠉⠉⠑⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣒⣶⣖⠒⠒⠒⠒⠒⠊⠁⠀⠀

𝄢♫⋆｡♪ 𝄞⨾𓍢ִ໋

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

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣈⠵⠂⠹⠏⠀⠛⢄⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⡔⠃⠤⠦⠆⠛⡌⣆⠀⠀⠀⠀⠀ ⠀⢀⠴⠊⢁⣣⣀⡀⠀⠀⠀⢀⡠⣇⡉⠒⢤⡀⠀ ⢀⠎⢀⡴⠋⢠⠀⡉⠉⠉⠉⠁⠀⣄⠉⠢⡀⠱⠀ ⢸⠀⢘⠀⠀⣼⢻⣷⣼⢰⣿⢸⡧⠹⠀⠀⢸⠀⡃ ⠘⣄⠘⠦⣄⡀⠀⠀⠀⢼⡽⠀⠀⢀⡀⠤⠋⣠⠃ ⠀⠈⠓⠤⣀⠈⠉⠒⠒⠒⠒⠊⣩⠽⠷⠤⠒⠁⠀ ⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠈⠉⠉⠑⠒⠦⣄⡀⣠⢴⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢸⠀⠀⠀⠀⠀⠀⠀ ⠑⠒⠤⢄⣀⡀⠀⢘⠁⠈⣣⠠⢄⠀⠀⠀⠀⠀⣀⣀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠙⠒⠤⠬⣄⣈⡉⠓⠒⠀⠛⡇⠀⢱⡀⠈⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠷⠤⣀⣁⡀⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡠⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⢠⡖⣶⡾⢁⡀⠀⠀⠀⠉⠛⠒⢲⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠓⠂⠤⠌⢈⡙⠂⠴⡾⡟⠆⢸⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠒⠤⠄⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣴⠞⠋⠉⠛⣻⠆⠀⣾⠹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠹⠓⠀⠀⠀⠘⢯⣄⢀⡇⠀⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⢼⠏⠁⠀⠀⠀⠀⣴⣶⣰⠀⠀⠀⠀⠀⠀⠀⣴⣖⣠⠀⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠸⣄⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⣀⣀⣀⡀⠀⠻⠿⠟⠀⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠭⠝⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣀⣠⡴⠶⠦⣤⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⢸⣁⣀⣤⠶⠶⠃⠀⠀⠀⠀⠹⠶⣯⡀⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣀⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⢠⣱⡄⠉⠙⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⢾⣿⣷⠃⣰⡤⠄⣀⣨⣽⠶⢤⣀⡤⠴⣦⠀ ⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠐⠖⠸⢿⣿⣤⡤⠄⠀⠀⠀⠀⡟⠀ ⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣄⠢⠄⠈⠛⠀⠉⠉⠁⠀⠀⢸⠁⠀ ⢠⡀⠀⢀⣀⡤⠴⢤⣄⣀⡀⢙⠄⣈⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀ ⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠦⢤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣀⡠⠤⠶⢦⣀⣀⣡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠈⢫⡷⠦⡀⠀⠀⠀⠀⠀⠀⢸⡅⠙⢦⡀⠀⠀⠀⠀⡇⢹⡄⠀⠀⠀⠀⠀ ⠀⠘⡆⢀⣈⣳⣄⠀⠀⠀⠀⠀⢷⠀⠀⣉⣳⣤⡤⠤⠇⠈⢿⣄⠀⠀⠀⠀ ⠀⠀⠘⢯⡤⢿⣾⣷⡀⠀⠀⠀⣨⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀ ⠀⠀⠀⠈⠻⣄⠙⣷⡝⢦⣠⠚⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀ ⠀⠀⠀⠀⠀⠈⢧⡈⣿⣆⠻⣄⠀⠀⠞⡴⠃⢀⡇⢀⡀⠀⠀⠀⠀⠀⠘⣆ ⠀⠀⠀⠀⠀⠀⠀⠹⣏⠘⣆⠘⢦⡀⠀⠷⠷⠞⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣬⠆⠀⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠈⢹⠖⣧⡘⢦⢀⡴⠋⠀⠀⠀⠀⣀⣠⡤⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⢴⠋⠳⣌⢺⣰⠋⠀⢀⠀⠀⠀⠀⢿⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠘⢮⡉⠒⠊⠱⣄⠀⠀⠀⠈⢿⡹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠳⣄⠀⠀⠈⢣⡀⠀⠀⣞⣠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠈⢣⡀⠀⠀⠙⢦⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡲⢤⡀⢹⣄⠀⠀⠈⣳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠈⠳⣤⠴⡫⠙⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⣕⣜⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠓⡄⠀⢀⣤⢤⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣰⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡋⠀⠀⠀⠀⠀⠀

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢠⠀⠀⠀⠉⠂⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠶⡃⠀⠤⢌⠈⠓⠀⠤⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠁⠒⠀⡀⠇⠒⡶⣋⣀⢄⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠘⠑⠄⠀⠑⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀ ⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠣⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠂⠠⡐⠉⠀⠀⠀⠀⠀⠀⠈⠐⢄⠠⢄⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠐⠀⠀⠠⠀⣀⡀⠀⠁⠀⠒⠠⢄⡀⠀⠀⡠⢤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠈⠘⡩⠒⢠⠄⣠⠀⣀⠀⠋⡃⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠜⣀⠀⠴⢀⣀⠊⠀⡀⠉⠁⠞⠁⢳⠤⢄⠠⠼⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠄⣈⠁⠐⠀⠉⠨⠆⣀⠊⠤⢐⡁⢀⠔⠃⠀⠀⠈⠁⠒⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⠀⠠⢀⣀⠉⠐⠂⣫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡖⠒⠠⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⠝⠋⠁⠀⡇⡇⢀⠀⠈⠓⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣽⣷⠀⠀⠀⠀⠳⠧⣄⡄⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡌⠀⠀⠸⡤⣤⠆⠀⢾⣿⠃⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⣀⡢⢀⣤⣎⢉⠟⡱⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢀⡐⢁⡾⠞⠒⠃⠀⠈⠉⠒⠤⣀⢒⡤⠔⠒⠲⡅⠀⠀⢀⡆ ⠀⠀⠀⠀⠀⢰⣻⡞⠏⠀⠀⣄⠀⠀⠀⠀⠰⡂⣟⡥⣀⣀⢤⠖⣡⠀⠀⡜⠀ ⠈⠓⠢⢤⣀⠈⡤⠀⠀⠀⣀⠁⠑⠳⠂⠀⣠⠠⢾⢛⡁⠀⡆⠀⢸⢠⢰⠁⠀ ⠀⠀⠀⠀⢐⠁⠀⠀⠂⠂⠀⠈⣱⠤⠤⠤⠄⠨⣘⠀⠀⠀⠸⡀⢸⡜⢆⠀⠀ ⠀⠀⠀⠀⠇⠬⠁⠀⣀⡀⡨⠕⠐⠄⣀⣀⠒⠀⠀⠈⡂⠀⠀⢇⡈⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸⠀⠀⣏⡉⠀⠂⠠⡉⠝⠹⠉⠒⠦⢼⣸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠧⢄⣀⣀⢸⣀⠤⠇⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠓⠦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠋⠒⠠⠤⡆⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠛⠷⢦⣤⣄⣀⣀⣠⣤⡴⠾⠛⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢸⣿ ⣿⡇⠀⡿⠁⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⢿⡄⢸⣿ ⣿⡇⢸⡇⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣀⣠⣤⠶⠟⠋⠀⠀⠀⢸⡇⢸⣿ ⣿⡇⠀⣷⢀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⣿ ⣿⡇⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⢸⣿ ⣿⡇⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⢀⡿⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣿⠉⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⣸⠇⠀⠀⠈⠉⠛⠶⠶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠶⠶⠛⠋⠁⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣄⣼⢶⣄⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⣿ ⣿⣷⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣷⣤⣤⣤⣼⣿

⠀⠀⠀⠀⠀⠀⠀⡸⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠤⠐⠉⠀⠀⠀⠀⠀⠀⠑⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⠀⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠤⡀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠁⠀⢸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⠀⠀⠀⠉⠄⠀⠐⠋⠁⠀⣠⣂⠰⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⠻⢮⣄⣀⣀⣀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠈⠐⠠⠤⢀⡀⠀⠀ ⠀⡐⠡⠀⠀⠀⠀⠈⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⡗⠀ ⠀⠀⠈⢑⠀⠀⠀⢀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣢⢾⠀⠀ ⠀⣆⠐⠀⠀⠀⠀⠀⠀⠀⢠⣷⡆⠀⠀⠀⠀⢀⣀⠀⠀⠀⡏⠁⠘⡀⠀ ⠀⡟⠢⡀⢀⠔⠉⠉⢺⡄⠂⠁⠀⠀⠀⠀⠀⠰⡿⠀⠀⢠⠁⠀⠰⠑⡀ ⠀⠱⡀⠀⠀⠀⠀⠀⠀⡏⠢⣀⠀⠁⠒⠀⠀⠀⣁⣀⣠⠗⠒⠲⡁⠀⡇ ⠀⠀⠈⠂⠄⢀⡀⠠⠊⠑⠤⠀⠏⠉⠀⠀⠐⣏⣀⡀⡇⠀⠀⠀⠁⡠⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣠⠔⠚⠉⠀⠀⠙⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣌⠡⠀⣀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢤⣀⡤⢴⡀⠀ ⣀⣀⡠⡖⠁⠀⠀⠀⠀⡸⠁⠀⢰⡆⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀ ⢀⠊⠑⣦⢀⣀⡀⢔⣾⣀⡀⠀⠀⠀⠈⠉⠓⠂⠀⢠⣄⠀⠀⠀⢀⡀⠀⡎⠀⠀ ⠻⠠⢀⠈⣶⠒⠒⠉⠀⠀⠈⠉⠑⠒⠲⠤⠤⣀⣀⠀⠀⣀⡤⠞⠁⠀⠀⠙⡄⠀ ⢃⠀⠰⢃⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠋⠁⠀⢰⠀⠀⠀⡀⠸⡀ ⢸⡀⢑⡒⢚⡿⠃⠀⠀⢀⠤⠶⠭⠦⠤⢐⣈⠉⠉⠑⣒⠆⠒⠁⠳⠤⣄⣠⠞⠓ ⠀⠳⢧⣖⡾⠀⠀⠀⠀⢼⡒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣠⣊⡤⠞⠉⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠳⣄⣠⠤⠖⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠘⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠤⠀⣀⠀⠀⠀⠀⡜⡍⢂⠁⢀⡀⠀⠀⠀⠀⠀⠈⠢⠊⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠐⠒⣳⣤⣀⣀⠈⠉⠒⠆⠀⣤⡶⠐⡄⢠⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠊⠀⡠⠋⢩⠟⠛⡶⠶⢤⣤⣆⡁⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡁⠚⠉⠵⢖⣃⠤⠎⣀⡠⠃⢀⠍⠉⡹⠁⠚⠂⠠⠄⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠤⠀⣀⠉⠀⠒⠩⠭⢒⣖⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠠⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣴⠂⠵⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⢄⣠⠊⠁⠀⠀⠀⠀⠀⠁⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠣⠊⠋⢀⣤⠀⡀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀ ⠀⡧⠀⠀⠀⠀⠀⠈⠓⠃⢰⣦⢏⢕⡆⠀⡇⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠌⠉⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀ ⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡜⡸⠁⠀⠀⠀⠀⠀ ⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡪⠊⣴⠣⠄⠤⢊⣭⣉⡆ ⠀⠀⠈⡇⠒⠠⢤⠤⠀⣀⣀⡀⠤⠒⢻⠈⠓⠒⠒⠋⠀⠀⠀ ⠀⠀⠀⠧⠠⠴⠃⠀⠀⠀⠀⠑⠂⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠢⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠗⢋⠁⠈⠉⠉⠒⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠔⡍⡀⠠⡄⠀⠀⠬⠧⢤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢎⣯⣄⢠⡀⣷⢙⢠⠈⣈⠉⡘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡿⡋⣤⠳⣷⣼⡸⣀⠥⠺⠁⠀⣀⠀⠀ ⠐⠠⢀⠀⠀⠀⠀⠀⠀⠈⠿⡄⠠⠤⠀⣏⠿⣿⣗⡽⠃⠀⠐⠁⠃⠀ ⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⢀⣮⠖⠀⠲⡊⠐⡛⠉⣿⣄⡀⠀⠳⡈⢂ ⠀⠀⠀⠀⠀⠀⠀⠁⢢⣲⢶⢧⡤⠎⠁⢁⣀⠝⢿⠑⡿⠶⡵⣦⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠠⢀⢀⡀⠀⠀⠔⢳⡀⠀⠈⣞⡊⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢗⣜⣵⣞⠁⢈⣗⠦⣈⡵⢁⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠄⡀⠈⣖⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⢇⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠤⠤⢀⡠⠖⢉⠀⢠⣤⡀⢀⠀⠑⢢⠐⡶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢡⠀⠀⠀⣠⡴⠋⣿⡔⠒⠪⡲⡑⡀⠀⡷⢡⡞⠑⠄⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠇⠀⠀⢉⠀⢩⡷⣴⠾⠯⠇⠈⠚⠀⢁⣟⢬⠢⡖⡊⠀⠄⠀⠀⠀⠀⠀ ⠘⡀⠀⠀⠘⡤⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠛⣁⠀⣀⠴⢤⡆⠀⡀ ⢰⠮⠶⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠈⠋⣱⣜⡋⠀⠄⠁ ⠘⢒⠒⢖⢖⠞⠂⠀⡀⠀⠀⠀⠀⠀⠀⠠⢊⢀⠎⠂⣢⣉⢀⣃⣉⣱⠀⠀ ⠀⠀⠢⡈⡲⠃⣠⠚⢄⠀⠀⠀⠀⠀⠈⠀⠉⢳⠚⠞⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠀⠁⠀⠀⠉⠒⠠⠤⠤⠤⠤⠒⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⠤⠴⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠎⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀ ⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠈⠢⣤⣀⡀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡟⠦⣤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠙⡆⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠆⢰⠃⠀⠀⠀⠀⠀⠀⠒⠒⠐⣫⡁⢀⠇⠀ ⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡼⠁⢀⡞⡀⣶⣀⡖⠀⠀⠀⠉⢀⠾⡆⠀ ⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⠁⣀⡑⠄⢻⣩⠤⠿⠀⠀⢀⡴⠋⠀⡇⠀ ⠀⠀⠙⢄⡀⠀⠀⠀⣠⠞⠁⠀⢿⠈⠛⠁⠀⠀⠀⠀⢀⣠⠖⡋⢠⠀⠀⡇⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠳⢤⠤⠤⠴⠖⠋⠉⠀⠀⡇⡜⠀⢸⠳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⡆⠀⠀⠀⠀⠀⠉⠁⠀⡸⣆⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣰⠁⠀⠀⠀⠀⣀⣀⣀⢀⡇⢸⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⣠⠖⠚⠉⠉⠉⠀⠸⡼⠀⠈⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠁⠀⠀⠀⠀⠀⠙⠓⠦⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠒⠒⠒⠒⠦⢤⡴⠚⠉⢠⣤⡄⠀⠲⣶⡿⠯⡄⠠⡀⠀⠀⠈⢳⡄⠈⣹⠳⢿⡆⢤⡀⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣇⠀⠀⠀⠀⠀⠀⢀⣴⡿⡟⣵⣶⠲⡴⠦⣤⣑⢢⡛⢦⡀⠀⠀⢿⣰⢇⣀⡴⠋⠢⡉⠢⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣆⠀⠀⠀⠠⣾⢿⡋⠀⡤⣯⡙⠀⠀⣀⣶⢬⡇⠓⢴⠳⡀⠀⡼⢃⣀⡟⠳⣄⠀⠙⣄⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡽⠂⠀⠀⠀⢯⣀⣇⠀⢳⡿⢿⣶⡷⠿⠟⢴⠟⠀⠀⠙⠥⠞⠁⣀⣾⣭⢦⡬⠷⡏⠉⣧⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠰⣄⣸⠂⠀⠙⠺⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣬⣧⣤⡷⠞⠋⠀⠀⠀⠈⠳⣄⣀⣀⠀⠀⠀⠀ ⠀⠈⢧⡀⠀⠀⠀⠀⢸⡁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⣠⡴⠒⠛⣯⠟⡀⠀⢠⠀ ⠀⣴⣮⣝⣶⡤⠠⠤⠤⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⣠⢤⠀⠀⠀⠙⠟⠙⣆⣸⡞⠙⡄⠘⡄⠀⠇ ⠀⣧⣇⣀⡀⣀⢀⣀⣀⣀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠑⣾⠀⢀⠀⠀⠽⠛⠻⡗⢷⢤⣹⡀⠱⠀⠀ ⠀⠈⠙⡍⠉⠹⡍⢫⣙⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢅⡀⢀⢞⠀⠳⣄⣱⣄⣀⣀⣀⣁⣀⣀⣸⣿⠀⠀⠀ ⠀⡇⠀⠘⣄⠀⠘⢄⣹⠯⠁⢀⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢐⡲⠞⢷⠤⠷⣤⣞⣏⠙⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠘⢆⡀⠈⠳⣤⡖⠋⠀⣠⠞⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠆⠀⢱⣈⣹⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠂⠀⠈⠛⢿⣚⠁⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⣀⣀⣀⣤⠿⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠰⣖⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣧⣽⠟⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡇⠀⠀⠙⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠸⣧⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣷⡀⣠⣤⣤⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣀⣤⣤⣽⠷⠶⠶⠶⠶⠿⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⣏⢀⣈⣙⣷⣝⢿⣆⠀⠀⠀⠀⠀⠀⠀⢈⣿⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣾⡄⠈⠻⣿⣷⡙⢷⣄⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠙⢿⣿⣆⠙⢷⣄⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠻⣿⣦⠈⠻⣧⠀⠀⠀⠀⠀⣠⡄⢀⣾⠏⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢻⡹⣷⡀⠙⣷⡀⠀⠀⠀⠛⢁⡾⠃⠀⠀⣼⠇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⠀⠙⣷⡀⠈⢻⣄⠀⠀⠀⢸⣿⣿⣷⡾⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠘⢷⡀⠀⠙⣷⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣬⠇⠀⠀⢸⢿⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠛⠲⣦⣠⣿⡀⠙⢦⡀⠀⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⣿⡉⠱⣝⢆⠀⠻⣆⣰⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣦⣴⡶⠶⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣀⣴⠟⠙⢿⣄⠘⢯⡳⢠⡿⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣿⠀⠀⠀⠹⣧⣀⣱⣿⣇⠀⣀⣠⣞⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⣦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⢻⣤⠀⠉⠛⠉⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠘⣿⣄⢹⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⣿⠃⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⣰⣟⣤⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠙⢷⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣤⣄⣀⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣭⡙⡶⣤⡀⠀⢨⢿⣄⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠈⠙⠷⠞⠀⠙⢷⣄⠀⠀⣠⣾⠋⠻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣋⠙⢮⠳⡀⠹⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠳⣝⢆⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣯⣷⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢦⡄⠀⠀⠀⠀⣀⣀⡀⠀⣼⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠟⠁⢸⡇⠀⠀⢠⣾⣿⠏⠙⠶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡇⠀⠈⠛⠛⠻⠷⠶⠶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⠷⣶⣤⣤⣴⣶⢾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠀⠀⠘⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⣦⣀⠀⠀⣠⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⡛⠛⠛⠻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠘⠃⠀⠀⠀⢰⣿⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢶⣦⣤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠻⠿⢿⣧⣴⣶⠀⠀⠀⣴⣶⣤⣿⠋⠀⠀⠈⠙⢿⣶⡄⢀⣼⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠻⠿⠇⣿⠀⠀⠀⠀⠀⠀⢿⡇⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⠀⠀⠀⠀⠈⠉⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀ ⠀⢀⣠⣴⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⣀⣤⣤⣶ ⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣿⠿⣿⣿⣿ ⢐⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⣴⣿⠟⢻ ⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢃⣰⣿⠟⠁⠀⠀ ⠀⠈⠻⣶⣦⣤⣴⣾⣷⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⢿⣿⠟⠛⠿⣷⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠉⠀⠀⠀⠀⠘⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⠀⠀⢀⣠⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣴⠾⠛⠋⣿⠀⠀ ⠀⠀⠀⠀⣠⡾⡋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡷⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀ ⠀⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠠⠮⢕⡿⠀⠀⠻⠶⠾⣧⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀ ⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⣰⣶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠠⠀⠀ ⢸⣇⠀⠀⠀⠀⠀⣀⣠⣤⡷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀ ⠈⠻⠿⠶⠶⠿⠟⠛⠉⠀⠀⠀⠀⠉⠙⠛⠿⠶⣦⣤⣄⣀⡀⠀⠀⠀⠹⠻⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⢶⣤⣤⡿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⢹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣐⣀⣀⣀⣤⣴⠶⠛⠛⠛⠷⢶⣤⣄⣈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⠄⠀⢘⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠆⢸⣿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⢦⠀⠀⠀⠀⠀⠀⠠⣯⣿⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⠉⣀⠀⠀⠀⠠⠽⠛⠁⠀⠀⠀⢠⠞⠀⣸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠒⠋⠁⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠴⠋⠁⠽⣻⣶⣂⡀⢀⣀⣀⡀⠀⠀⠀⢀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⡴⠃⠀⠀⠀⠀⠉⠀⠀⠹⠋⠀⠀⠙⣷⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠑⢶⡄⠀ ⠀⠀⡾⣙⣈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⣠⡞⠀⠀ ⠀⢰⡇⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⢠⢴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⢄⡰⣏⠀⠀⠀ ⠀⢸⡇⠒⠉⡩⠛⠁⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡴⠋⠀⢸⡀⠀⠀ ⠀⠈⣧⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠰⣦⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠸⡇⠀⠀ ⠀⠀⡟⢧⡀⠀⠀⠀⠀⢀⠴⠊⠉⠓⣼⡄⠠⣄⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⠹⡄⠀ ⠀⠀⣷⠀⠙⠲⢤⡤⠞⠁⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⣯⡍⠀⠀⠀⢀⡞⠀⠀⠀⢠⡏⠀⢸⡀ ⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠳⣄⠀⠀⠀⠈⠉⠓⠢⠄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠗⠒⠒⢤⡎⠀⠀⠀⡇ ⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣆⠀⠀⠙⢶⠤⠤⢤⣀⣀⣀⣀⣀⠴⠚⠉⠉⢋⠟⠈⠀⠀⠀⠀⠳⠀⠀⢸⠁ ⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⣀⡠⠴⠊⠁⠀⠈⠓⠦⠤⠞⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⢀⣀⣼⡀⠀⠀⠀⠀⠀⠰⠊⢠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠦⠀⠀⠀⠀⠀⠴⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠻⠶⠶⠶⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⣀⣤⠶⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠺⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⠛⠶⢤⣤⣄⣀⡀⠀⠀⣿⠁⠀⠀⠈⣷⡄⠰⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠾⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠿⣦⣄⣀⣀⠈⠃⠀⠀⠙⠷⠾⢦⣤⠄⠀⠾⢷⡟⠀⠀⠙⣦⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⠦⢤⣤⣀⣀⠀⠀⠀⢸⣇⠀⠀⠀⠸⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠲⠿⠦⣤⣀⣀⡀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠦⣤⣄⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⠿⠷⣶⣶⣶⡄⠀⠀⢀⣾⠋⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣄⣾⡿⠁⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⣾⡟⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠉⠈⠿⠻⠇⠀⠀⠀⠀⠀⠐⢿⣧⣄⡀⠀⣿⡇⠀⠘⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣿⠁⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣇⣈⣦⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⢠⣤⣤⣤⣤⣴⠀⠀⠀⠈⠛⠛⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠥⠤⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⠿⠛⠛⠛⠻⣷⣆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢀⣠⣤⣶⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣿⣱⠄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣄⣀⣤⣸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣦⢉⣧⣤⠤⠲⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⠟⠋⠁⣠⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁⠀⣠⢶⠁⠀⠀⢀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣱⢰⣰⡞⠀⡇⡠⠀⢠⢹⡀⠀⠀⠀⢖⠉⢉⣉⠉⡳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠃⣾⣿⣄⢸⠀⡇⠀⣿⠇⣿⠀⡄⠀⠘⡏⡡⠎⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡎⢸⣿⣿⡟⢸⢸⢹⣤⣿⠓⢺⠀⡇⠀⠀⠟⢀⡴⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡇⣾⣯⠛⣡⠈⢾⠀⢹⣿⣷⡿⣠⢃⡆⣸⠒⠉⡼⠀⠀⠀⢠⣤⡀⠀⠀⠀ ⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡅⠀⠀⣀⡀⠀⠐⣛⢩⣿⣷⣿⡡⢃⣸⡾⠁⠀⠀⠀⡏⠀⡇⠀⠀⠀ ⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⣦⡀⠀⠀⠀⠈⢙⡫⠁⣾⣿⡧⢾⣿⠀⠀⠀⠀⠀⢧⡀⠹⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⢀⣾⡤⠞⠛⠛⠛⢻⣅⠀⠸⣇⠹⠀⢸⣿⣷⣄⣀⠀⠀⠈⠳⡄⠈⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣠⣤⠬⣿⡀⠀⣠⠖⠊⠉⢹⠀⠀⢙⣶⣿⣄⡹⣽⣿⣄⣉⡲⣄⡀⠸⠀⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⣾⣋⢱⠞⠉⡅⠀⠀⠈⠦⠴⠋⠀⠙⢯⡉⠹⠌⠉⠙⠻⡻⣷⢀⠇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢻⡄⠀⠀⠀⠀⣃⣹⣾⠀⢰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣋⣭⡖⢤⡀⡾⠏⠀⠠⣿⣄⡀⠀⠴⠛⢡⠃⢀⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠮⣴⡮⠸⠇⣀⠀⠀⣮⠯⡙⠧⣤⡼⠃⣠⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢇⡀⠀⠀⠈⢳⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⣸⠛⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡳⢤⣀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠩⠻⣆⣀⡤⠤⠤⠤⢄⣀⡴⠛⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣀⡔⠋⠁⠀⠘⡛⠃⠀⠈⠉⠳⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⢾⠇⢰⣄⣴⡀⡄⠰⠟⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡤⢾⡄⠿⠀⠀⠀⠉⠉⠉⠀⠀⠀⠛⠀⢸⠦⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⠀⠀⢀⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣯⣀⡀⠈⠙⠲⣄⠀⠀⠀ ⠀⡼⠋⠀⠀⣠⠾⠋⠀⡀⠉⠙⠓⠒⠒⠒⠚⠛⠉⠁⠀⠀⠈⠛⢦⡄⠀⠈⢧⡀⠀ ⣼⠃⠀⢀⡾⠋⠀⠀⢸⡇⢰⡇⢀⠀⠀⠀⠀⠀⢀⣄⠀⢸⡄⠀⠀⠙⣦⠀⠀⢳⠀ ⡏⠀⠀⣸⠁⠀⠀⠀⣾⠟⣻⢃⣿⢠⡇⣼⣻⡇⡸⢿⣧⠘⣧⠀⠀⠀⠘⡇⠀⠈⡇ ⣧⠀⠀⠸⣆⠀⠀⠀⠛⠀⠙⠋⠙⠛⠃⣨⣿⣧⠙⠛⠋⠀⠉⠀⠀⠀⣸⠇⠀⢠⡇ ⠘⣦⡀⠀⠙⠷⢤⣀⡀⠀⠀⠀⠀⠀⠐⢿⡴⠏⠀⠀⠀⠀⣀⡤⠴⠚⠁⠀⣠⡞⠀ ⠀⠈⠻⢦⣄⠀⠀⠈⠉⠛⠒⠲⠶⠤⠤⠤⠤⠴⠖⠛⣿⢻⣿⠧⠀⣀⣤⠞⠋⠀⠀ ⠀⠀⠀⠀⠉⠙⠲⠶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠶⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠾⠋⠀⠙⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⡀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠀⠀⡄⠀⠀⠀ ⠀⠀⠀⣼⠟⣯⡙⣿⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡶⠞⠋⣿⠀⠀⠀ ⡀⠀⠀⣿⠉⠻⠀⠈⠀⠀⠀⢾⠆⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠉⠓⠒⢻⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀ ⠀⣠⠚⠉⠁⠀⠀⠉⠉⠻⢗⠲⠦⢤⣄⣀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠶⠒⠚⠛⠛⣻⠂⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠸⡇⠀⠀ ⠀⢻⣝⠓⠦⠤⢤⢤⠶⣚⣿⡇⠀⠀⠀⢀⡼⢛⡷⡖⠒⠒⠛⢅⠈⠉⠙⠒⠲⠤⢧⣄⣀ ⠀⠈⣏⠹⡟⠒⢲⠚⠋⡟⢹⣧⡀⠀⠀⠀⠀⠊⠀⠇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⢸⡄⡇⠀⢸⠀⢠⡇⠘⣷⡙⠢⣄⣀⠀⠀⠀⠀⠀⢀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⣼⣀⣸⣇⣸⡦⣤⡇⡏⠓⠦⣬⣍⣙⣛⣛⡯⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠈⣿⡇⠀⠀⡟⠀⠀⢀⡏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣰⠁⠀⢀⣞⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠙⢆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡠⠖⠊⠉⠀⠀⠀⠀⠀⠉⠑⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣍⠙⣖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡤⠖⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠓⠒⠦⠤⣀⣀⡀⠀⢸⡀⠹⠀⠈⠀⠀⠐⣿⠆⣄⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢚⣷⣦⣤⣄⣀⡀⠀⠀⠀⠉⠙⠛⠀⠀⢰⣦⡾⢯⠉⢧⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣩⠏⠛⠛⣿⢷⣶⣦⣤⣄⣀⠀⠈⠱⡇⠹⠂⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⢄⣀⣀⡴⠁⠀⢀⡼⠁⠀⠀⡼⠉⠙⠛⣿⠿⢶⣷⣦⣤⣄⣀⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠓⠒⠦⠭⣍⣓⡒⠾⠤⣀⣀⡞⠁⠀⠀⡴⠁⠀⠀⡼⠉⠉⠙⣻⠉⠙⠚⠓⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠤⢄⣀⡀⠀⠀⠉⠉⠐⠒⠺⠭⢍⣐⡚⠢⠤⢤⣜⡀⠀⢀⡼⡹⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠦⢤⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠤⠤⣀⣀⠀⠀⠀⠉⠉⠑⠒⠦⠭⣭⠏⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠤⢄⣀⡀⠀⢸⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⢿⡆⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢰⣏⣥⡼⠃⠀⢹⡦⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣠⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣤⣤⠶⠚⢋⣹⡄⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⡟⢿⠈⣉⣻⣦⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠁⠻⡆⢹⡀⠀⠀⠀⠀⠀ ⣄⡀⠀⠀⣾⣿⢿⣽⠟⠲⡿⠼⠇⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⣷⠘⡇⠀⠀⠀⠀⠀ ⠈⠙⠳⣦⣿⡷⠚⠛⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠿⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢶⣤⡄⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣀⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠳⢦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⠈⠙⠳⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠘⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢦⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣾⠉⠻⣦⢤⣤⣤⣤⣤⣤⣤⠶⠤⠶⠾⠇⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⡿⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠸⠟⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣠⠇⢠⡄⠀⠀⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⡴⢂⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠒⠛⠻⠷⣶⡄⠀⠀⠀⠚⠁⠴⠛⠁⠀⠀⠘⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⠷⣤⣤⣤⣤⣤⠴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⣠⠖⠳⠶⣦⣀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⣿⠀⠀⠀⠀⠙⢷⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠹⣆⠀⠀⠀⠀⠀⠙⢧⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠹⣦⠀⠀⠀⠀⠀⠈⠻⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏ ⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀ ⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠦⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣀⣴⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣲⣤⣤⣷⣶⣽⣿⣼⣿⣿⣾⣧⣄⣤⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠋⠉⠀⠀⠉⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠿⠀⠀⠈⠻⠷⠶⢦⣤⡀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣽⠛⢷⣄⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣦⡀⠀⠀⣿⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣠⡶⠆⠀⠀⣿⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⢋⣲⡀⠀⢰⡇⠀⠀⠀ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⣴⠟⠀⠀⢀⣼⠂⠀⣴⡶⠀⢀⣤⠀⠀⠀⠀⠀⠛⠋⠁⢠⣾⡅⠀⠀⠀ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣰⠏⠀⠀⣀⡾⠃⢰⣄⣼⡿⠶⢿⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠹⡇⠀⠀⠀ ⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢠⡟⠀⠀⠈⡘⠲⡀⠈⣯⣉⣠⣤⣼⡇⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣿⠀⠀⠀ ⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣸⡇⠀⢿⡿⠛⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⡏⠀⠀⠀ ⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⣀⣠⡶⠟⠁⠀⠀⠀⢹⣇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⢠⡆⢠⡆⠀⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⣀⣀⣀⣀⣤⣤⠶⠟⠋⠉⠀⠀⠀⢸⡁⢸⠇⠀⠀⢸⠿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣧⡟⠀⠀⠀⣾⠀⠹⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣷⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⣧⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⡇⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣼⠃⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠶⢶⡄⢠⡿⠀⠈⣷⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣤⣶⠾⠛⠋⠉⠉⠀⠀⠀⠀⠘⣷⣼⠃⠀⠀⠹⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠊⠁⠙⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⢠⡀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎⠀⠀⠀⠀⠸⠓⠶⣄⠀⠀⠀⠀⠀⠀⠉⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠊⠙⠛⣘⠆⢤⡖⠚⠳⢄⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠋⠀⠸⠇⠀⠀⠀⣳⠴⠖⣲⣲⠟⠀⠀⢀⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠉⣬⠓⣒⠚⠉⠑⢄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠀⠘⠂⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣀⣤⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣁⣀⣀⣀⣀⣀⣀⣀⡎⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢉⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⡖⡲⢦⡴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⣧⠡⠌⠻⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠉⠁⠀⠀⠀⠀⠿⠏⢰⣄⣄⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⣾⣦⣿⣇⢭⣻⣦⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⡃⠹⠆⠃⠋⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣠⠎⢀⡞⠀⠀⠀⠀⣀⡤⠶⠶⢦⣄ ⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣁⠞⢁⣰⣏⠙⠲⠦⠴⠚⠉⣤⡶⣤⣤⡟ ⠀⠀⠀⠈⢻⠳⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢿⠁⠙⠷⢤⣤⣤⠴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⢉⡿⠉⠛⠛⠒⠒⠒⢶⡒⠋⠉⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣤⣀⣠⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠏⠈⢿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣠⣴⡾⠟⠉⠁⠀⠀⠀⠉⠉⠙⠛⠿⣷⣦⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣏⣙⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠟⠋⠉⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠺⠶⠤⢤⣀⣀⢀⣿⣿⡛⢻⡿⠌⢻⡄⠀⢿⡿⣀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⠤⣤⣀⣁⠀⠀⠀⠉⠋⠻⠾⠃⠠⣾⣷⣿⢻⣯⠿⣧⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠶⠤⣄⣀⣀⠈⠈⢿⣏⠿⠁⠙⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠚⠿⠷⢦⣤⣄⣀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠷⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠦⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠂⠊⠿⠶⠶⠶⠶⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⣀⠀⠀⠀⢀⣤⡶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⢦⣾⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠾⠷⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠷⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠙⣷⣀⠀⢰⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⢦⣤⣄⣘⣿⡀⠀⠀⠀⠐⠘⢷⠀⠈⠁⢸⣤⣀⣠⡄⠀⠀⠀⠀⢀⣦⡄⣾⡟⠛⠻⣶⣄⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⣶⣤⣤⣄⣀⡂⠀⠀⠀⠉⠉⠙⠻⠷⠿⠃⠀⠈⠟⢹⡇⠈⠀⠀⠀⢻⣆⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠷⠶⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠶⠶⣤⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠶⢶⣦⣤⣄⡀⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠀⠈⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄⠀⠀⣀⣤⣶⡾⢿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠟⠋⠁⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⣀⣾⡟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⣴⡿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣠⣽⡛⠀⠀⣿⣧⣠⣿⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀ ⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠵⠋⠁⠀⠀⠈⠙⠋⠙⠿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⡿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣧⠀⠀⠀⠀ ⠘⠿⣷⣦⣤⣤⣴⣶⡶⠿⠟⠋⠉⠀⠈⠉⠙⠛⠻⠿⢶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⢻⢟⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢷⣶⣶⣤⣄⣀⡈⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⠀⠀⠀⠀⠀⢹⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡐⠠⠀⠀⠀⠀⣀⣤⣴⣾⠿⠿⠿⢿⣶⣤⣄⣀⠀⠈⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠶⠶⠶⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠶⣿⡇

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠛⠋⠀⠀⠀⠙⠓⠒⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢦⣤⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢱⡄⠈⢻⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⠚⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠙⠒⠶⠤⣄⣀⡀⠀⠀⠀⢸⡇⠈⢿⠀⠈⠁⠀⠀⠐⢾⡷⢂⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠲⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⡶⠗⠀⠀⠀⣤⣄⣾⢯⡉⡻⣆⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠓⠻⡯⢿⣶⣲⣤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠿⢛⡇⢨⣧⠁⠘⠃⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡾⠃⠀⠀⢨⡽⠙⠒⠻⠯⡽⣖⣲⣦⠤⣄⣀⡈⣇⠀⠉⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⠤⢤⣄⣀⣠⠏⠀⠀⠀⣠⠟⠁⠀⠀⢀⡾⠃⠀⠉⠉⢹⠟⠿⠯⢿⣿⣶⡦⢤⣄⣀⣀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠛⠓⠢⠤⢬⣍⣙⠓⠒⠶⠧⣤⣀⡀⢠⠏⠀⠀⠀⢀⡴⠋⠀⠀⠀⣰⠏⠈⠉⠛⢳⡇⠉⠙⠓⠛⠦⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⡀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠶⢤⣌⣉⡙⠓⠶⠤⣾⣀⣀⠀⠀⡼⠁⠀⠀⠀⣰⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⠶⠦⣄⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠦⢤⣤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠲⠤⣬⣍⣙⠓⠒⠦⢤⡼⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠉⠉⠑⠒⡾⢡⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠤⢤⣀⣀⡀⠀⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⣄⠙⢶⡀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⣽⣦⣶⠟⠟⠋⠉⠐⠒⠒⠚⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡿⠟⠉⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢀⡴⣿⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡄⣠⢠⣶⠋⢠⠇⢀⠀⠀⢰⠛⡄⠀⠀⠀⠀⢠⠤⠖⠚⠛⠓⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼⢃⢧⡿⠇⠀⡼⠀⡞⠀⢀⡏⡼⣇⡆⠀⠀⠀⠘⣆⡠⠤⢲⡆⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢾⠃⣾⣾⣿⣤⡀⡇⢰⡇⠀⣸⣇⡃⢹⡇⢐⡆⠀⠀⢹⢀⡴⠋⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡏⢀⣿⣽⣽⣿⠀⡇⢸⢹⣄⣿⣿⠛⢸⡇⠸⡇⠀⠀⢸⠏⠀⣠⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⣿⡺⠿⠋⠀⢳⢸⠈⠻⣿⣿⣦⣼⡇⢸⠁⣤⠀⣾⡤⠞⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣇⣸⡿⠇⠀⠚⠃⠈⠛⠀⢄⠿⣟⣿⣿⣡⢏⣼⡏⣸⠃⡄⣨⡞⠀⠀⠀⠀⣠⡟⠻⡆⠀⠀⠀⠀ ⠈⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠤⢤⣀⣀⠀⣉⣍⣰⣿⡷⢿⣿⡴⠃⣤⣿⡟⠀⠀⠀⠀⠀⢻⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⡀⠀⠀⠀⠀⠀⠈⢛⣋⠀⢸⣿⣿⣧⡶⣿⣿⠀⠀⠀⠀⠀⠀⠸⣆⠀⠘⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣈⣽⠶⠶⠶⠶⣶⣞⠋⠀⠀⣿⠙⢿⠀⠀⣿⡿⣦⡀⠀⠀⠀⠀⠀⠙⢧⡀⠈⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⣿⣾⠋⠀⠀⠀⣀⣠⠤⠾⣷⠀⠀⠹⣦⣈⣤⡀⠹⣝⢿⡯⡓⠲⢤⣀⠀⠀⠀⢳⡄⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡴⣾⣿⠛⣻⣳⣄⢀⣠⢾⠉⠀⠀⠀⣿⠀⠀⢀⣼⠻⣿⠶⠦⠝⢿⣽⣾⣶⡦⣌⡻⣦⡀⠀⡇⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣧⣼⣟⡍⢳⠟⠁⢸⠀⠀⠀⠀⠸⠦⠴⠛⠁⠀⠈⠻⣭⠩⠩⠆⠀⠀⠉⠳⣝⢿⣷⠀⡇⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠤⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠫⢷⡀⠀⠀⠀⠀⠀⢸⡆⢻⢧⡇⠀⢸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣠⠶⢤⣀⠀⠀⢀⣜⣵⠃⠀⠘⣿⡀⠀⠀⠀⠀⣸⣧⠏⡼⠀⢀⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢾⣶⠖⣾⠏⢙⡦⣌⡟⠃⠀⠀⢸⢹⡷⣦⣄⠐⠚⠉⢀⡼⠁⠀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠿⠵⣶⡯⠖⠻⢦⣀⠀⠀⢸⣦⠟⢦⡛⠳⣤⡶⠚⠁⣠⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢼⡏⠀⠀⠀⠀⠈⠻⣦⠞⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⣿⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢿⡈⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡛⠶⣤⣀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢩⡛⢷⡄⠀⣀⣀⣤⣤⣄⣀⡀⢀⣤⠾⠛⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⢀⣤⠟⠛⠉⠀⢰⣶⡤⠈⠉⠛⠻⢦⣀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠟⠁⢀⡄⠀⠀⠈⠅⠀⠀⠀⠀⣀⠀⠉⢳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⡀⣿⠇⠀⣿⣀⣼⡆⣰⠄⠘⠿⢁⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⡇⢸⡟⠀⠀⠀⠈⠋⠉⠉⠁⠀⠀⠀⠸⠇⠀⢸⡧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠋⠀⠀⠀⣠⣴⠾⠛⠷⣦⣤⣀⣀⡀⠀⠀⢀⣀⣀⣤⡶⠾⠋⠛⠷⣦⣄⠀⠀⠀⠙⢷⡀⠀⠀⠀ ⠀⢀⣾⠏⠀⠀⠀⣠⡾⠟⠁⠀⣠⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠻⣆⠀⠀ ⠀⣼⠇⠀⠀⢀⣾⠟⠉⠀⠀⢠⣿⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡆⠀⠀⠀⠙⢷⡄⠀⠀⠹⡆⠀ ⢠⡟⠀⠀⠀⣾⠃⠀⠀⠀⠀⢸⣿⣴⣿⡇⢰⡇⢀⣦⠀⣴⣶⡄⢠⣿⡳⠄⠸⣿⠀⠀⠀⠀⠈⢻⡄⠀⠀⢻⡀ ⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⡟⠀⣿⣡⣿⣧⣼⡇⢸⣧⣿⡇⣬⣝⣛⣷⠀⢸⡆⠀⠀⠀⠀⢸⡷⠀⠀⢸⡇ ⠘⣷⠀⠀⠀⢻⣆⠀⠀⠀⠀⠛⠃⠀⠙⠋⠈⠉⠙⠃⢀⣵⢿⣧⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⣼⠃ ⠀⠹⣧⠀⠀⠀⠙⢷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⡏⠀⠀⠀⠀⠀⠀⣀⣠⣤⠾⠛⠁⠀⠀⣰⠏⠀ ⠀⠀⠙⢷⣄⡀⠀⠀⠈⠉⠛⠻⠶⣦⣤⣄⣀⣀⣀⣀⣈⣉⣁⣀⣀⣤⣶⡶⢶⣿⣻⡂⠀⠀⠀⢀⣤⡾⠋⠀⠀ ⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁⠈⠷⣰⣿⣽⣗⣠⣤⠾⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⠶⠟⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠆⡲⠀⠀⠀⠂⠀⠀⠀⠎⢛⠿⠿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀