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