Lovelin Flying Emojis & Text

Copy & Paste Lovelin Flying Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⣤⡤⡤⠤⣤⠤⠒⠉⠁⠉⠉⠈⢢⣀⣀⡀⣠⠠⢰⠢⡘⣯⣵⣶⠞⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⣤⡤⡤⠤⣤⠤⠒⠉⠁⠉⠉⠈⢢⣀⣀⡀⣠⠠⢰⠢⡘⣯⣵⣶⠞⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡲⠖⠛⠋⡉⣉⢈⣁⣀⣀⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⠾⠚⠋⠉⠁⠀⠴⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠓⢧⣁⠁⠁⠀⡟⠉⠁⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣀⠑⠀⠀⠀⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠪⣂⡘⠀⡄⠀⠀⠀⠀⢘⡇⣴⢎⣬⣎⠻⡯⡆⠀⠈⡄⢠⠊⠀⢠⠎⠑⡄⠀⡐⠁⢌⡈⡇⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠁⠀⠀⢀⠃⡀⡀⠀⢴⠈⡋⠀⠀⠀⠀⡀⢭⣐⢡⡍⠏⠘⠣⢸⢘⡀⡀⠇⠁⠀⠀⢸⠀⠀⢐⠊⢀⢁⡐⠰⠀⠀⠀⠀⠀⠀⠀ ⠒⠄⡐⠃⠂⠀⠀⠀⢀⠅⢀⠇⠐⠀⠆⠀⣴⡷⡨⡄⡕⣄⡇⠠⡢⣣⠏⠂⡊⠡⠁⠀⠀⠀⠘⡅⠀⠈⠁⠄⡐⡔⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠂⠂⠀⠂⠀⠀⢸⠐⢀⠀⠀⠎⡸⣡⠯⠁⠀⠹⢷⣟⠍⠤⠖⡐⢁⠃⠀⠀⠀⡀⡰⠊⠁⠉⠘⠁⠋⠉⠙⢭⠳⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠀⠀⠁⠂⣹⡒⠇⢀⡤⣒⣢⢄⠀⠁⠉⠁⡠⠃⠀⢀⠐⠈⠀⠀⠆⠀⠀⢀⡀⠀⡄⠀⠀⠸⡀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠒⠀⢩⣧⡂⠀⠀⠋⠛⠋⠉⠀⡀⠔⠈⠀⡀⢂⠤⠚⢽⠉⠁⣟⡟⢁⢽⡍⢹⢓⢄⢀⡠⡇⠸⡀⠀⠀ ⠀⠀⠀⠀⠀⡏⠉⠉⣮⢇⠁⠂⢀⣐⡳⠂⠀⠉⢒⢾⠒⠂⡇⡆⠀⠀⡀⢡⣺⠂⠀⢈⠶⡆⠀⡃⠅⢨⠇⡡⠵⠕⠀⠀⢥⡇⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠑⡀⠀⠸⢐⣠⠀⣸⣿⢁⡔⠒⠤⡀⠅⡇⠀⠇⢹⣂⠕⠙⢟⢄⠡⡀⠠⢘⠕⡀⢐⠱⠪⠄⠒⢍⠍⠂⠀⢹⠂⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⣄⢘⡦⠎⠁⠉⠁⠀⡆⠀⢈⡷⠼⠊⠉⠉⠀⢵⠀⠀⠉⠻⣎⠄⡙⡅⠑⠲⡀⠅⢱⣽⠥⠊⠁⢀⡟⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⢠⠀⡀⠒⠁⡉⠇⠄⡇⠱⣄⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠉⠻⠬⣱⣤⠧⠝⠗⡏⢷⣷⠖⣥⠏⡀⠀⡰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⠌⣅⠀⠹⠠⠗⡆⠁⡇⢰⠛⡄⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⣀⣨⡷⠁⠀⠜⠙⠓⠓⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣖⠀⠀⠏⡂⢸⠃⠑⡥⣀⢱⡃⠀⠀⠑⡀⠀⠀⠀⠀⠀⠈⣳⠤⠒⣒⡿⠷⢯⠁⢠⠈⠀⠀⡐⠀⠀⡔⠋⠀⠀⠀ ⠀⡀⠀⢄⠀⠄⢄⠀⢶⡀⠠⠀⢕⠎⢉⠁⢡⣐⠟⢱⠀⠀⠀⠐⠦⡤⢀⣀⠔⡉⠀⠀⠀⠀⠀⠀⠘⡂⢀⠔⠈⠀⡠⠒⠉⠀⢀⣀⠠⠐ ⠀⣎⢐⠠⠔⢤⡀⠈⢆⢿⡷⠚⠁⣖⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⠁⠘⡀⠀⠈⠠⢀⠀⠀⠀⠠⣠⠧⠠⠒⠊⠀⠀⠀⠀⡂⢍⠠⢵⠀ ⠀⢯⡇⠀⠈⠀⠊⣡⠌⠫⠃⠀⠀⠀⠀⠀⠀⠀⠀⢔⡉⠀⠀⠀⢸⡀⠂⠐⡀⠀⠀⠀⠀⡨⠅⠋⠓⠄⣥⣂⠀⠀⠀⠀⠀⠉⠑⠂⠁⠀ ⠀⠸⣧⠀⠀⠀⣀⠵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠅⠛⢇⣀⡐⣄⡤⠾⢍⡀⠀⠀⠀⡘⠁⠀⠀⠀⠁⠂⠲⡠⠤⠀⠀⠀ ⠀⠀⠀⠉⠂⠏⠔⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠉⠁⡒⠠⢀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀ ⠀⠀⠠⠀⠀⡀⡀⡀⠀⡀⡀⠀⠄⠠⡠⠠⣀⠐⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⡢⠊⠀⠀⠀⠈⠁⠂⢄⠀⠀⠀⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠢⡀⠀⠀⠀⠀⠐⠒⠚⠺⡉⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡂⡌⢀⡀⢄⠢⢀⠀⣆⡂⠀⠠⡠⠠⠄⣀⠤⠄⠠⠄⠈⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠈⠒⠤⣀⡀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠰⡊⠀⠈⠁⠀⠀⠐⠀⠠⡀⠀⠀⠄⠀⠀⠈⡀⠐⠁⠀⠀⠀⠂⠀⠀⠠⠀⠡⠆⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠎⠤⠄⠀⠄⠀⠄⠀⠀⠂⠀⠁⠀⠁⠀⠀⠈⠀⠃⠂⠂⠄⡐⠄⠀⡀⠄⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

Warning: This item may contain sensitive themes such as nudity.

⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to _ノヽ ノ\_ me or my son `/ `/ ⌒Y⌒ Y ヽ ever again. (  (三ヽ人  /  | | ノ⌒\  ̄ ̄ヽ ノ ヽ___>、__/ |( 王 ノ〈 (\__/) /ミ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>
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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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