A Cat Wearing a Cock Emojis & Text

Copy & Paste A Cat Wearing a Cock Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢚⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢚⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠠⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠅⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡠⠐⠀⠐⠀⠁⠈⠉⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⢂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⢠⠄⠂⠁⠈⠀⠀⠀⠈⠀⠈⠓⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀ ⠀⠀⠁⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠔⠁⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀

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