Sobbing Face Down Emojis & Text

Copy & Paste Sobbing Face Down Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠉⠈⠉⠉⠻⣄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠉⠈⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⢄⠠⢒⡐⡒⡌⣽⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠔⣊⠑⡢⢑⠸⢰⡿⠀⠀⠀⢀⣠⠶⠚⠋⠉⠀⠈⠙⠟⢗⢒⠲⢒⠶⠤⢤⣄⣀ ⡘⢄⠣⡑⠬⣱⣎⡷⢦⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣟⡿⠛⠋⠉⠉ ⡘⢌⠱⡼⠟⠉⠀⠀⣀⣠⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠶⢤⣤⡀⠉⠛⠲⠦⣤ ⡘⠤⢋⡙⢛⠛⣛⠫⡙⢄⠣⠌⠭⣙⠛⡶⣤⣄⡀⠀⠀⠀⠀⣹⡧⣤⣄⣀⡀⠀ ⡘⠴⣁⠚⡌⡘⢄⠣⣑⠊⠴⣉⠒⠤⣩⠐⡅⡚⢿⣦⡀⠀⠀⢲⣷⡰⣈⠶⠉⠙ ⠈⠐⠂⠭⢰⡑⡊⡔⢢⢉⠒⣄⢋⡒⢄⠣⡘⡔⠢⢌⠹⠿⣤⡀⠙⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠚⢤⠣⡉⠔⢢⠑⡌⢒⠡⠬⠵⠌⣆⠣⢼⠙⠳⠾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠭⣘⣡⠚⡄⣃⠆⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀

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⡴⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠳⡆⠀ ⣇⠰⠉⢙⡄⠀⠀⣴⠖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠁⠙⡆ ⠘⡇⢠⠞⠉⠙⣾⠃⢀⡼⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠄⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠲⡄⠀⣏⣆⣀⡍ ⠀⢠⡏⠀⡤⠒⠃⠀⡜⠀⠀⠀⠀⠀⢀⣴⠾⠛⡁⠀⠀⢀⣈⡉⠙⠳⣤⡀⠀⠀⠀⠘⣆⠀⣇⡼⢋⠀⠀⢱ ⠀⠘⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡴⢋⡣⠊⡩⠋⠀⠀⠀⠣⡉⠲⣄⠀⠙⢆⠀⠀⠀⣸⠀⢉⠀⢀⠿⠀⢸ ⠀⠀⠸⡄⠀⠈⢳⣄⡇⠀⠀⢀⡞⠀⠈⠀⢀⣴⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⢧⠀⠀⢳⣰⠁⠀⠀⠀⣠⠃ ⠀⠀⠀⠘⢄⣀⣸⠃⠀⠀⠀⡸⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⣇⠀⠀⠙⢄⣀⠤⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣿⣿⣿⡿⠛⠁⠀⠉⠛⢿⣿⣿⣿⣧⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⢀⣀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⠉⠉⠉⠉⠉⠛⠒⠾⢤⣀⠀⣀⣠⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢭⡀⠀⠈⣷⠀⠀⠀ ⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢀⡟⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠀ ⣾⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠸⡇⠉⣷ ⣿⠀⠰⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣧⡴⠋ ⣿⠀⠀⢸⠛⢫⠀⠀⢠⠴⠒⠲⡄⠀⠀⠀⠀⡝⠛⢡⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀ ⢸⡄⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡼⣄⠀⠀ ⠀⢳⡄⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⢀⡼⠁⢸⡇⠀ ⠀⠀⠙⢦⣷⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⣀⡴⠟⠒⠚⠋⠀⠀ ⠀⠀⠀⠀⠈⠛⠾⢤⣤⣀⣀⡀⠀⠀⠀⠀⣀⣈⣇⡤⣷⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠩⣉⠉⠉⠉⣩⠍⠁⠀⢷⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠐⠦⠤⠼⠂⠀⠸⠥⠤⠔⠂⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣧⡟⠳⠒⡄⠀⠀⠀⡔⠲⠚⣧⣀⣿⠿⠷⣶⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣄⢀⠀⠀⡗⠀⠀⠀⡇⠄⢠⠀⣼⠟⠀⢀⣨⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢶⠬⠴⢧⣤⣤⣤⣽⣬⡥⠞⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠚⠛⠉⠉⠛⠛⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀ ⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠃⠀⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠘⡆⠀⠀⠀⠀⠀⠸⠿⠿⠟⠋⠁⠀⣰⣆⠀⠀⠙⠻⠿⣿⠇⠀⠀⠀⠀⠀⢠⠏ ⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣧⠀⠀⢠⠏⠘⣆⠀⠀⠀⠀⢀⡞⠀ ⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠛⠁⠀⢼⠀⠀⢸⠀⠀⠀⢀⠞⠀⠀ ⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠶⠋⠀⢀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⢤⣤⣀⣀⣤⢤⠤⠖⠚⠉⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⢀⣠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣡⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣷⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⡀⢿⣿⡿⣿⣥⣤⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⣿⠟⠛⠛⣻⣿⣿⣏⠁⠀⠹⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⠟⠁⢀⣠⣾⣿⡿⣿⣿⣄⠀⠀⠉⠙⠛⠿⠿⠿⠟⠙⠹⠿⠿⠿⢿⣿⣿⣿⣶⣄⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⢸⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠉⠚⠋⠀⠀⢀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀ ⠀⠀⢀⣠⣴⣶⣶⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠋⠓ ⠀⣴⣿⠇⠉⠉⠛⠛⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀ ⣴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡏⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠚⡄⢫⠉⢩⠃⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⡞⠳⡜⠦⠚⠘⠒⠋⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠉⠉⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡇⠀⡰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⢰⡆⢻⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⢰⠁⡰⠁⠀⠀ ⠀⠀⠀⠀⣶⣦⣤⠘⣿⣿⣆⠀⠀⢿⠇⣼⣿⣿⣿⣿⠛⢸⡇⠀⠀⠙⣿⣿⣿⣇⠀⠀⠀⠈⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣁⠀⠻⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣇⡀⣾⠃⠀⠀⢠⣿⣿⣿⡇⠀⡔⠒⠲⡄⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⠋⠉⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⠟⠀⠀⠱⠤⣀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⡀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⡗⡤⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣫⢸⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⡿⠿⠿⣷⣦⣠⣤⣾⠟⠛⠳⣦ ⡏⢀⢀⣠⣶⠟⣹⣿⠷⣦⡀⢀⢘⡇ ⢣⣤⣴⠿⠃⢀⡿⢿⡆⠈⠻⠿⠟⠁ ⠀⠀ ⠀⠀ ⣠⠃⠈⠳⡄ ⠀⠀ ⣰⡟⠁ ⠀⠀ ⣸ ⠀⠀⢰⡏ ⠀⠀⠀ ⢠⡟ ⠀⠀⠘⣇ ⠀⠀⠀ ⢸⡇ ⠀⠀ ⢿ ⠀⠀⠀⠀⠈⢷⡀
⢻⢭⡓⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⣏⢖⡲⣅⠀⠀ ⣣⢾⡛⣜⢫⣦⠀⠀⢀⣤⠴⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⢏⡝⣆⢀ ⢿⣧⢹⣬⡷⣚⣒⣶⡾⣍⡞⡱⣞⡇⠀⠀⠀⠀⢀⣠⢤⠖⣦⡤⠤⡶⠦⠤⣤⢶⠲⠤⣄⠀⠀⠀⠀⠀⢀⡤⠶⢶⢤⡀⢸⣛⣮⢞⡜⡚ ⠈⡷⣻⢏⠶⣙⢶⣼⠟⡼⣜⡵⠋⠀⠀⠀⣠⠞⡩⢴⣿⣿⣾⣹⠐⢢⢁⡾⡵⠚⢻⣷⣤⡙⠲⢄⠀⠀⢾⣍⡻⣌⢧⣷⡾⡞⣥⢫⡝⣃ ⠀⢻⣿⢊⣟⣾⢫⢇⡻⣱⢺⠁⠀⠀⠀⡼⣡⣿⣄⣀⡿⣿⣿⡏⡇⢢⢸⡿⣷⣤⣼⠿⢿⣿⣷⣎⣷⠀⠈⠳⣵⡩⢖⡻⣱⢻⣌⡳⢎⡵ ⠀⠀⢻⡧⢞⡧⣋⣮⣕⡣⢿⠀⠀⢀⡼⢃⣻⢿⣿⣿⣧⠾⠟⡙⣧⣂⣌⢣⡛⡿⠿⠷⠾⠿⠿⠣⣌⠳⡀⢰⢯⡱⣫⡶⢥⣛⢮⡓⣏⢶ ⠀⠀⠈⢯⡧⣓⢧⡚⣽⣞⡾⠀⢀⡞⠠⣿⠀⡰⢂⣖⣤⣯⣾⣿⣿⣿⣿⣿⣿⣇⠄⣎⣱⣉⢎⡱⣘⡇⠹⡞⣮⢵⢯⣱⠳⡬⢧⡙⣦⠋ ⠀⠀⠀⠈⠳⣭⢲⡹⢲⡞⠁⠀⣼⢐⠡⡙⠳⠗⡛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⡉⠛⣶⣵⠋⡐⢿⠈⠻⣆⢧⡛⢜⣣⠟⠁⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢰⡇⢊⠔⡡⢊⠔⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠡⣿⢹⡄⢡⢚⣇⠀⠈⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢊⠤⢑⠢⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⠃⢢⢻⡄⢊⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠌⢢⠁⢎⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣏⡄⢣⢺⡇⢼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡊⠤⠉⢼⣿⣿⣿⣿⠿⠋⡄⠒⡌⢢⠐⡌⠻⣿⣿⣿⣿⣯⠛⢓⠛⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⡏⣿⣿⣿⡿⠋⡄⠣⠌⡱⢈⠄⢣⠐⡡⠘⢿⣿⣿⣿⡐⣌⢒⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡅⠸⠿⢛⡡⠘⡄⠣⡘⠄⠣⡘⠄⢣⠐⣉⠂⠻⢿⠿⠁⢼⡲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣁⠦⠟⡁⢣⠐⡡⠂⡍⠰⢁⠎⡄⠣⢄⡉⠲⢦⣂⣉⢴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢲⢥⣂⠅⣂⠑⡈⢅⠊⡐⠌⢡⢂⣌⣡⠶⣛⣙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀ ⠀⡉⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⠈⠁⡸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⣶⠆⠰ ⠀⠀⡇⢀⡤⠤⣀⡀⠀⠀⠀⢠⣾⣯⠓⢴⡀⢸⠄⠀⠀⠀ ⠀⠀⡗⣞⠀⢠⡇⣹⣄⠀⠀⣏⣼⣿⡇⠠⡄⣸⠀⠀⠀⠀ ⠀⠀⠱⡀⡀⠘⢿⣿⣿⣆⠸⠿⠿⠛⠀⢠⣧⣳⠇⠀⠀⠀ ⠀⠀⠀⠱⢷⣄⡀⠉⠀⣯⠀⢤⢤⠤⣞⡷⡏⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠰⠹⡝⣏⠿⠤⠷⠿⠖⠒⠉⠀⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣞⠷⡄⠀⠀⠀⠀⠀⠀⣇⢸⠠⠖⠶⡄ ⠀⠀⠀⠀⠀⠀⢀⣹⣆⠙⠓⠀⡀⠀⠀⠀⣧⡈⠁⢀⡀⡿ ⠀⠀⠀⠀⠀⠰⡇⢀⣍⣀⢺⡄⠉⢹⡒⠀⠀⠳⠤⠛⠖⠁ ⠀⠀⠀⠀⠀⠀⠘⠒⠚⠉⠋⢳⡀⠀⠸⣆⠀⢲⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣠⠆⠙⠣⠦⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
.  +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀ ⢰⡿⠋⠙⠦⣄⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⢳⣄⠀ ⠸⣧⠀⠀⠀⠈⣷⣤⣤⠛⠋⠛⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣷⡄⠀⠀⠛⡆ ⠀⠙⣷⠀⠀⠀⠀⠀⡇⠀⠀⣴⠛⠀⠀⠀⠀⠀⣠⣴⡿⠓⠛⠛⢿⣟⠒⢤⣄⠀⠀⠀⠀⢾⡏⠀⠈⢿⣿⠃⠀⠠⠀⢸ ⠀⠀⢸⡄⠀⠀⠚⠋⠁⠀⣼⠁⠀⠀⠀⢀⡴⠛⠛⣋⣤⣄⠀⠠⠤⢤⣀⠀⠈⠳⢦⡀⠀⠈⢳⡀⠀⣾⠃⠀⣀⡀⠀⢺ ⠀⠀⠀⢿⡀⠀⠀⠀⡀⠀⣿⠀⠀⠀⣴⠋⠡⠂⠉⠀⠀⠀⣀⣀⡀⠀⠉⠙⠀⠀⠈⠱⣆⠀⢸⡇⢀⠀⠀⠠⠋⠁⢀⡿ ⠀⠀⠀⠈⢧⡀⠀⠀⠈⣰⠏⠀⠀⡾⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠙⡆⠸⣦⡀⠀⠀⠀⢀⣠⠟⠁ ⠀⠀⠀⠀⠀⠙⢦⣤⣴⠟⠀⠀⣸⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⡄⠈⠻⣦⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⣿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣷⡀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⣸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⡄⠀ ⠸⣧⠌⣹⢦⡴⠛⣶⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⣠⣤⣴⣷⢀⠻⡆ ⠀⢹⡏⢰⠖⠃⣾⠉⠀⣀⡴⢿⣏⣉⢭⣛⡙⢶⣄⠀⢻⡄⣸⠟⣌⡙⣷ ⠀⠀⢿⡠⠘⢦⡟⠀⣴⠋⡝⣡⣮⣶⣦⣥⡙⢢⠩⢷⡠⣗⠌⠒⣍⡼⠇ ⠀⠀⠀⠛⠶⠾⠁⢰⠇⡓⣴⣿⣿⣿⣿⣿⣿⣆⠱⡈⣧⠘⠳⠾⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡊⣱⣿⣿⣿⠿⠿⣿⣿⣿⡄⠡⣿⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⣽⣿⠏⠄⡂⠔⡈⠿⣿⣯⢱⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣧⠘⢢⠑⢬⠐⡡⢭⣇⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠻⠶⠻⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠋⠉⠉⠛⠛⠿⣿⣦⣶⣤⣤⡀⠀⠀⣀⣤⣴⣶⣾⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⡿⠁⠀⣤⠶⠶⢦⣄⠀⠀⠙⣯⡉⠙⠛⢿⣷⣿⡿⠛⠉⠁⣠⣶⣌⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠻⣧⠀⠘⣯⠀⠀⡀⢹⡇⠀⠀⠉⠑⢦⣀⡼⠯⠁⠀⢀⣠⣾⡿⣫⠿⣧⢿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⡀⠀⠻⣦⣄⠀⣀⢀⣠⡿⠃⠐⠈⡀⠃⠘⣿⡁⠁⠀⠂⣰⣿⣏⢷⣭⢻⣽⡾⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡇⠀⢀⡀⠀⢀⣠⡽⠿⠿⢯⣅⣀⠀⠈⢠⣄⠀⠀⠘⣧⠀⠀⢲⣿⣿⣾⣿⣜⡳⢾⡇⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣿⠿⠛⢉⠻⣦⡟⠀⣠⡿⠁⠀⠀⠀⠀⠈⠹⣆⠀⢀⠹⣦⠀⠀⣿⠀⠀⣿⡟⠁⠀⢿⣯⣝⣻⣇⣿⡇⠀⠀⠀⠀⠀ ⠀⢀⣤⣾⠿⠛⠁⣀⣠⣤⣤⠾⢶⣏⢠⡟⠀⠀⠀⢀⠀⠀⠀⢠⣿⠀⠈⠀⣿⣀⣼⠟⠀⠀⠟⠀⠀⣤⣿⣿⣮⣽⡧⣿⡇⠀⠀⠀⠀⠀ ⣶⡿⠛⢁⣤⣶⣿⣿⠋⠀⠀⠀⠈⣿⣾⡇⠀⠀⠀⠻⢧⡴⠶⠛⠁⠀⠀⢰⣿⣿⠝⠀⠀⠀⠃⠀⠀⣤⣦⣼⣿⣾⣇⣿⡇⠀⠀⠀⠀⠀ ⣿⠀⢰⣿⢏⡷⣹⢿⣶⠶⠚⣳⠄⠈⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡌⠙⠛⣿⣿⣀⡀⠀⠀⠀⠀ ⢿⣷⣄⠻⢿⣜⣧⣛⢿⣶⠶⠋⠀⠀⠀⠀⠙⢻⡶⣤⣤⣤⣤⣴⠶⠛⠁⠚⢻⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠙⡆⠁⠄⡹⣿⣧⠀⠀⠀⠀ ⠀⠙⢻⣷⣦⣍⡛⣹⡿⠁⠀⠀⠀⠀⠀⢀⣰⣿⣿⠃⢈⠁⠀⠀⠀⠀⠀⠀⢀⣨⣿⡿⢿⣿⣷⣷⣶⡶⠖⠀⠸⡄⢂⠐⡌⢿⣧⠀⠀⠀ ⠀⠀⠀⠈⠙⠿⣿⣿⠇⠀⠀⠀⣀⣤⣾⣿⣿⣿⣥⡀⢀⠠⢈⠀⡁⢈⠀⣘⣿⣿⡃⠀⠀⠈⢿⣿⣿⣶⡄⠀⠀⢣⠄⠊⠄⠻⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⡃⠐⠻⣿⣿⣿⠋⠁⠉⢿⣿⣷⡀⠆⢂⠐⠠⡁⠄⢸⣿⣿⣇⡀⠀⣀⠞⡉⡉⠙⣿⡀⠀⠰⡈⠌⡄⠁⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠀⢈⣾⣯⡿⣧⠀⠀⢀⣾⣿⣿⠀⢀⢂⣈⡀⠐⡈⠈⢿⣿⡉⠙⠛⡅⠢⠐⡥⠐⠼⣷⠀⠠⡁⠆⡠⢁⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠇⠀⢸⡿⣅⡀⢀⠒⠒⢏⡉⣿⠏⠀⢼⣟⣿⣿⠿⠀⠀⠈⠻⢧⣄⣀⣀⢡⠘⣄⣀⡤⠿⣧⡀⢡⠴⠡⠀⣾⡿⠀⠀ ⠀⠀⠀⠀⠀⣼⡟⠀⠀⢻⣦⠀⠉⠒⢁⣢⣰⡾⠋⠀⠀⠀⠉⠉⠁⡀⢀⣄⣀⡀⠀⠈⠙⠛⢧⡄⠀⠀⠀⠀⣬⡿⣌⠢⠄⢠⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⣿⡷⢄⣰⠟⠁⠀⠐⠀⢠⡟⠃⠀⠀⣀⡴⢦⣤⣤⡴⠞⠋⠉⠉⠛⠷⠀⠀⠀⠈⢿⡳⢄⢂⡤⣿⢿⡟⣧⢀⣾⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣼⡏⡀⠠⡈⠐⠠⣿⠁⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢦⠏⣟⣳⢯⣟⣿⡾⣿⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⡿⣷⢥⡐⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣂⢿⡮⣝⣞⣭⣿⠞⠉⡀⢀⠉⢻⣷⣤ ⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣯⣝⡳⢼⣷⠀⣀⡀⠀⣀⢀⡀⢀⣀⣤⣴⠶⣶⣤⣦⣛⠭⣩⡾⠛⠛⠛⠻⣿⣉⠉⡀⠤⢁⢰⡬⠞⠋⠉⠉ ⠀⠀⠀⠀⠀⣰⣿⠏⢁⠠⢉⠛⠿⣾⣿⣤⣴⠾⠟⠛⢻⡿⠟⠉⠀⡀⢀⠀⡀⠈⡙⢿⣏⠀⠀⠀⠀⠀⢲⡹⣇⢀⠂⠼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣰⣿⣧⣔⢦⠨⡐⡀⠆⢠⣴⠏⢁⠂⢀⣶⣿⡥⠀⠀⡁⠀⠠⠀⠐⠀⡀⠀⡝⣷⡀⠀⠀⠀⠀⣷⣻⡆⠜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣾⠟⠉⠀⠀⠀⠀⠀⠙⢎⡿⢁⡈⠀⢈⠠⢿⣟⠀⣴⠂⠀⢂⠁⠠⠈⠐⠀⣌⠱⡌⣿⡄⠀⠀⠀⡜⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠘⢷⣍⠒⡌⢿⣾⣧⠂⡄⢠⢀⣡⠐⠦⡙⡄⣃⠖⠸⣧⠄⠀⢀⠛⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠠⠎⣌⠹⠿⣶⣦⣬⣽⣻⠿⣿⣏⡥⣉⢒⡡⠒⠌⠀⠀⢻⣆⠀⠤⣹⣿⡐⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠉⠉⠉⣑⠂⠒⠊⠉⠶⡄⠈⠉⠓⠉⠉⠁⠁⢠⠖⠦⡉⠐⠒⠒⠊⠒⠐⢒⠢ ⡄⢂⡁⠸⠱⠉⡀⣁⣰⣟⠁⠀⠐⡀⢈⠐⢈⠁⠈⠘⣆⠀⠐⠈⢀⠀⠻⠣⠀⢀ ⠐⡄⣁⣐⣤⣲⣴⣿⣭⣈⡙⠲⣄⠀⠂⢈⠀⣠⡶⢛⣙⣿⣦⣥⣂⣌⣐⣀⡌⡎ ⣾⠝⣩⣿⣿⣿⣿⣿⣿⣟⣿⣦⠈⢳⡀⢠⡾⣣⣶⣿⣿⣿⣿⣻⣿⣿⣍⠉⢦⡁ ⡟⢰⣿⣯⣿⣿⣿⣿⠀⢨⣿⣿⣷⠀⢿⣟⣰⣿⣿⣿⣿⣿⣟⠉⢹⣯⣿⣧⠀⢻ ⡇⢾⡿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢸⡇⣿⡟⣾⣿⣿⣿⣿⣶⣿⣿⣞⣿⠀⢸ ⡇⢻⣷⡻⣿⣿⣿⣿⣿⣿⣿⣹⡿⢀⣿⡆⢿⣿⢽⣿⣿⣿⣿⣿⣿⡿⣻⡿⠀⣼ ⣿⣀⠻⣿⣍⣟⡿⢿⣟⣛⣾⠟⣡⣾⠏⣷⡘⠿⣷⣛⠿⡿⠿⢿⣻⣼⡿⠁⣴⠟ ⠈⢻⣦⣥⣋⡛⢟⠻⢛⣋⣥⡼⡟⣼⡃⡿⣹⢦⣍⡛⠿⠿⠿⠿⢛⣡⣤⠟⣿⠈ ⠀⢸⡯⣝⢻⢳⠾⠶⣾⢟⡏⢇⡱⣻⡇⣧⠉⠞⡻⠷⠶⣶⠶⢶⠞⡛⠩⣰⡟⠀ ⠀⢸⠇⠈⢃⠊⠁⠃⠂⢈⠐⠠⣜⣿⡀⢿⡀⠐⢀⠉⠑⣸⢿⡌⠐⠈⠀⢿⡁⠀ ⠀⢸⡇⠈⠈⠃⠐⠀⢂⠀⢤⡿⠽⣿⠀⡿⠹⣆⠀⠠⢱⠏⣞⢻⡄⣞⢀⠏⠀⠀ ⠀⢀⣿⡄⠰⡶⣬⡐⠀⣠⡟⡠⢙⣿⠀⡽⠀⡸⢦⠄⣿⠘⣾⣤⠇⠈⡞⡀⠀⠀ ⢀⡞⠈⢧⣤⣬⣥⣄⣀⣻⢾⣥⣎⣿⠀⢼⣀⣛⣏⣤⣭⣳⣞⣉⣀⣀⠇⢸⠀⠀ ⠀⠛⢾⢿⣄⣀⣤⣀⣉⣉⠳⢤⣞⡗⠀⢾⠙⣭⠖⠋⠀⠁⠉⠉⠉⣿⣶⠂⠁⠀ ⠀⢀⣾⢽⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⠀⠀⠀ ⠀⠀⣼⢫⣿⣞⣷⣯⣟⣾⣽⣾⣽⣿⣶⣿⣯⣟⣾⣳⣯⣿⣽⣳⣯⣟⣿⠀⠀⠀ ⠀⠀⡝⣠⢛⡟⠯⡿⣟⣯⣟⣷⠏⠉⠉⠉⠉⢻⡿⣟⣯⣟⢿⢏⡟⢤⣻⠀⠀⠀
⠒⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣤⣦⣤⣤⣤⣄⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠿⢟⡛⠻⡉⠏⣭⣏⡙⠙⠛⠛⠿⠿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠋⣥⣶⣯⠒⢨⠁⡔⡈⠘⣿⣿⣾⣴⣿⡄⢂⠄⠩⠙⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠛⠡⢠⢁⣣⣾⣿⡿⠈⡄⢃⠔⡡⠡⢈⠛⠻⣟⣛⣽⣦⣬⣁⡎⠡⡀⢍⠻⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⡄⡌⠱⠰⣿⣿⠿⠏⣁⠒⡈⠔⡨⢐⠡⢊⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠐⡄⠛⣿⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⡏⢄⠣⡐⠌⡁⢆⣵⣦⣶⣾⣶⣷⣶⣬⣄⠡⢊⢴⣿⣿⣿⣿⠏⠉⢻⣿⣿⣿⣿⣿⣷⣄⠑⡈⠻⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⡿⢁⠒⡌⠒⢠⣣⣾⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣷⣆⣾⣿⣿⣿⣿⣦⣄⣴⣿⡟⠀⠀⠈⠙⠿⣧⡐⠡⡘⣿⣷⡀⠀⠀⠀ ⠀⠀⣰⣿⡟⢠⠃⡜⠠⢱⣾⣿⣿⠿⢿⣿⣿⣿⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣧⠀⠀⠀⠀⠀⣻⣷⡡⠐⡈⣿⣷⡀⠀⠀ ⠀⢠⣿⡟⡡⢢⠑⡠⢳⣿⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⠛⠉⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠹⣿⣿⣷⣤⣤⣤⣶⣿⣿⣷⡡⠐⡜⣿⣧⠀⠀ ⠀⣾⣿⠡⣁⠃⡜⢰⣿⣿⡇⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⡧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠋⠙⣿⣿⣷⢁⠰⢹⣿⡆⠀ ⢠⣿⡿⢀⠄⡣⠘⣿⣿⣿⣷⣄⣀⣀⣴⣿⣿⣿⣯⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⠋⢻⣿⣦⣶⣿⣿⣿⡆⠂⢆⣿⣷⠀ ⢸⣿⡇⠂⡌⠥⢹⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⡀⢀⣀⣿⣿⣿⣿⣿⣿⠟⠁⠈⣻⣿⣧⣈⢂⣿⣿⠀ ⢸⣿⡇⠒⣈⡑⢺⣿⣿⣿⣷⣤⣿⣿⡉⢹⣿⣿⣿⣷⣄⣀⣤⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠈⠁⠉⠻⣮⣽⣿⠀ ⢸⣿⡇⢡⢀⡃⢌⣿⣿⣿⠉⠙⠻⢿⣿⣿⠿⠟⠛⠋⠙⣿⣿⣿⣿⣏⡷⣩⠿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀ ⠈⣿⣿⢀⠢⡑⣼⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⣿⡟⣼⡳⡝⡞⢫⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠈⢿⡟⠀ ⠀⢿⣿⡆⢡⠏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⣿⡞⣡⢧⣙⡬⢓⣼⣿⣶⢦⣤⣀⡀⠀⠀⢀⣀⣠⣴⢿⡿⣇⠀⠸⠇⠀ ⠀⠘⣿⣷⣌⠳⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⡈⢡⢢⣼⣶⣿⣿⣿⡿⠂⢌⠹⡛⢟⡻⡛⢿⠻⣑⢎⡴⣯⠀⠀⠀⠀ ⠀⠀⠸⣿⣧⡛⣼⡇⠀⢻⣶⣦⣤⣤⣤⣤⣤⣤⣴⠶⠛⠋⢄⠂⡜⣷⣿⣿⠟⢛⠋⡉⠤⠑⠌⡒⠌⢡⠃⡝⠢⠙⡌⠂⢌⡷⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣷⡼⠂⠀⣿⢣⠾⡛⣔⢣⠣⡝⡘⠤⡈⢌⠱⠈⡄⣿⣿⣿⠡⣈⠢⡘⢄⠃⡉⢆⡁⢎⠰⡈⢄⠣⡑⢠⢹⣾⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⡄⠀⣿⠃⠎⡱⢈⠡⠃⡔⢠⠃⢌⠢⣁⠣⢀⡉⠍⡐⢄⠢⡐⠡⢌⢂⠱⡀⠆⡌⠰⣈⠢⣁⢘⣴⣿⠟⠁⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢹⡆⠢⠑⡌⢢⠑⡄⠃⡌⢂⠒⠄⡊⠔⡠⠃⠜⡠⢂⠅⠣⡈⠆⢂⠅⡊⠔⡡⢄⡒⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢻⣧⣌⠐⣁⠒⣈⠒⢄⢃⡘⠤⢑⠨⠄⢣⠘⡀⠆⡌⡑⠄⠣⠌⢂⠡⢒⣰⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⣻⡆⠀⠀⠹⣿⣷⣤⣎⡠⠌⢂⠂⢌⠢⢁⠎⡘⠄⢃⡘⠰⢀⠅⢊⠡⣘⣤⣷⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⡶⢤⢦⣿⠋⠛⠿⢿⣿⣶⣮⣴⣤⣧⣴⣰⣬⣤⣦⣥⣮⣶⣾⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⡋⣁⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⢻⠛⣟⢛⡛⣛⠋⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⠾⡷⡶⣶⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡾⠟⢋⢉⠰⢀⠄⡒⢐⡐⢠⢂⢉⡉⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠋⠰⢈⠰⢈⡐⢂⠌⡐⠂⡌⠰⡀⠆⡰⢁⠊⣄⣩⣻⣷⣄⠀⠀⠀ ⠀⢀⣾⢏⣰⡼⢳⠾⣶⣦⣤⡃⢌⠰⢁⠢⠑⡠⠃⣔⣬⠟⣋⣭⣿⠽⢿⣷⡄⠀ ⢀⣾⡿⠚⠑⠾⢿⣿⣿⣿⣾⣽⢶⣌⠂⠥⠑⡠⢓⡾⠃⠈⠉⠉⠻⣿⠏⠈⢿⡄ ⣿⣟⠁⠀⠀⠀⠀⣻⣿⣭⣥⣭⣯⢻⡎⠄⡃⢄⣻⠇⠀⠀⠀⠀⠀⣸⣶⣤⣾⡇ ⣿⢹⣆⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣯⣿⠀⡅⢂⢾⡇⣦⣤⣤⣶⣾⣿⡟⠉⣿⢏ ⣯⣿⠿⣿⣿⣿⣿⣧⣿⡟⠛⠻⣿⡶⣿⠀⠆⡡⢘⣧⢻⣩⣿⣿⣿⣾⣿⣿⡏⠀ ⠛⣿⢿⣯⣿⣿⣿⣿⣿⣇⡀⠀⢸⣻⠇⡈⠆⠡⢂⢹⣎⢁⣼⡿⠿⠛⡉⢘⡿⠀ ⢿⣃⠠⢈⠉⠛⠛⠻⠟⠿⠿⠶⠷⠯⠶⠶⠾⠳⠞⠚⠛⢉⠡⠐⠠⢁⠸⢻⡅⠀ ⠈⠛⣿⡾⢀⠁⢊⠐⡈⠄⡐⢀⠂⡐⢀⠂⠄⡁⢂⠡⠈⣤⣶⡼⣶⠶⠟⠋⠀⠀ ⠀⠀⣿⡀⢀⠊⠄⢂⣐⣠⣐⣀⢂⠐⠠⢈⠐⡀⠂⢄⣡⣬⠷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠓⠚⢚⠋⠉⠉⠉⠉⠛⠛⠻⠶⠞⠶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⢛⣫⢛⡭⢩⡛⣛⢒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⢺⡱⣌⠳⢎⡴⢃⡞⢥⡙⢦⠫⡜⣆⠎⣝⠢⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡶⡝⡬⢓⠦⣑⢫⢎⡴⢋⡜⣡⠝⣢⠛⡴⣊⡝⣤⠫⣌⠳⡄⠀⠀⠀ ⠀⠀⣰⠏⡵⣊⡕⢫⠜⣡⢇⣮⣶⡭⡜⣡⠞⣥⣟⣰⠣⡜⢢⢛⡤⡛⡜⢦⠀⠀ ⠀⣸⢣⡛⠴⡣⢜⡿⠿⠿⠿⣻⢋⠶⣡⢇⠺⣙⣟⠿⠿⠿⠿⣎⠴⣙⢬⠣⢧⠀ ⣼⢇⠧⣍⢳⣩⠏⠀⢀⣠⣴⣿⣼⣒⣥⣊⣧⣵⣾⣧⣄⡀⠀⠙⢮⡱⢎⡓⢎⣇ ⣿⠨⠞⣤⡟⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⢳⡎⡹⢆⣿ ⣯⢱⢋⡞⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⡕⡎⢾ ⢿⣢⠟⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⢟⡛⡛⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠹⣜⣻ ⠿⡟⠀⠀⠀⠀⠀⣿⠬⠭⡭⣙⠴⣊⠵⣩⠳⣌⠭⡭⣉⠧⢿⠀⠀⠀⠀⠀⢻⠇ ⠀⢻⡀⠀⠀⠀⢠⡟⢬⡓⢥⢓⡎⣥⠛⡴⡩⠖⣍⠖⣍⠮⣹⡄⠀⠀⠀⢀⡿⠀ ⠀⠀⠱⣇⠀⠀⢸⣋⢦⡙⢎⢦⠓⡴⢋⡖⢭⡙⣬⠚⣜⠲⣡⡇⠀⠀⢠⠾⠀⠀ ⠀⠀⠀⠈⢦⡀⢸⡒⢦⡙⠮⣌⡛⣌⠳⣌⠧⣙⢤⡛⡌⢧⡱⣇⢀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢬⣃⠞⡱⢦⡙⡬⢓⡼⡘⣥⠲⡱⢩⢒⣡⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠦⣵⢥⣋⣔⣭⢦⢵⡗⡻⡉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢯⡽⢭⣏⡝⣿⣿⣿⣏⢾⡱⣟⣼⢫⣝⣻⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⢨⡙⣭⣛⠿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⡀⠀⠀ ⣿⣿⣿⣿⣿⢧⣛⡳⣎⣞⡹⣿⣿⣏⠾⣽⢻⠞⡿⢯⡓⠧⣍⠿⣿⣿⣿⣿⣿⠱⡘⣻⣷⡘⡰⢌⠛⣜⡻⣿⣿⣿⣿⣿⡛⠿⠷⣤⣄⡀ ⣿⣿⣿⣿⣟⢮⠷⣝⡞⡶⣭⢿⣿⣏⡛⢦⠏⡞⠴⢣⠛⡵⢨⢒⡙⢿⣻⣿⣿⡆⠱⣈⣌⣧⠷⣛⠛⡏⢟⡻⣿⣿⣿⣿⣿⣷⡄⠀⡀⠀ ⣿⣿⣿⣿⡝⣮⢛⡜⡹⢓⠧⢯⢽⡇⠻⣉⠚⠙⢶⣁⠉⡒⢡⠂⣴⠌⠹⣎⣻⣷⣵⣟⣍⣃⣓⣌⣑⠈⢎⠱⡹⣿⣿⣿⣿⣿⣿⣧⡀⠐ ⣿⣿⣿⣯⡛⡴⢋⡜⢡⠋⠜⡠⢂⠋⠔⢢⠓⣤⣦⣙⣆⣱⡈⢿⣼⣿⣿⣿⣯⢿⣼⠟⢋⣭⡉⠉⠙⠻⣦⣂⢱⠹⣿⣿⣿⣿⣿⣿⣿⣆ ⣿⣿⣿⣷⣭⣶⣥⣼⣤⣮⣴⣤⣦⣬⣴⣴⣶⡿⣟⡿⢏⡼⠿⣷⣶⣿⡟⠯⣼⡟⠀⠀⡌⠋⠑⠀⠀⣀⣈⣙⡋⢻⣿⣿⣿⣿⣿⡙⠿⢿ ⣿⣿⣿⡷⣒⢦⠒⣦⣽⠿⠿⠿⠿⣽⣽⣛⠾⣿⢻⢟⡻⣭⡳⣦⣿⡷⣩⢏⣿⠁⠀⠃⠀⠀⣤⡦⠿⢋⢉⣩⡟⣀⣙⠻⣿⣿⣿⣿⣦⡀ ⣿⣿⣿⢷⡉⣶⠟⠋⣶⣫⠆⢀⠀⠀⠈⠛⢷⣬⢉⠎⡵⢪⣷⣿⣿⣿⡷⣾⠏⠠⣤⣶⠶⣾⢿⣰⣱⣎⣾⠾⣷⣯⣿⣷⡹⣿⣿⣿⣿⣿ ⣿⣿⣿⢳⣾⠋⠀⢄⡀⠁⠀⠂⠈⠁⠄⠀⠈⠛⢾⣼⡐⣏⠾⣿⣤⣿⣿⣿⣾⠷⢿⣾⣿⡷⠾⠟⣛⣻⣧⣮⣿⣟⡿⢿⣷⢿⣿⣿⣦⡀ ⡽⣿⣿⡿⠏⣀⣌⣀⣄⣰⣤⣥⣦⣤⣤⡶⢿⣻⡷⢎⣿⡜⢯⣽⡟⡦⢿⣷⣹⡿⢶⣶⣍⣰⡟⠿⢻⡛⢿⣯⣧⢻⡞⢥⣻⢿⡿⣛⢿⡣ ⣷⢹⡿⣵⡟⢩⣩⢩⣽⡉⢥⡩⢞⣹⣿⣿⠟⣋⢖⣼⣿⣈⢾⡿⡟⠰⡉⢷⡙⢧⡀⠠⢉⠙⠛⢮⠥⣙⠢⣍⢻⡀⣿⢀⠻⢾⣟⣿⣞⣷ ⣿⣇⠰⣿⣻⣖⣿⣄⣿⣞⣧⣿⣿⠟⣍⠦⣩⣿⡾⠃⡌⠙⢫⣧⣹⣦⣵⣾⣧⡼⢷⢶⣦⣬⣧⣔⣂⠡⠓⢬⠩⢧⠏⣬⢑⢸⣿⠿⣣⡟ ⣿⣞⢰⣿⣡⢟⣿⡞⣿⢯⣏⠷⣎⢟⡐⣲⡿⢡⠰⠁⣌⣶⡿⠛⠉⠀⢀⣀⣀⣀⣂⣆⣰⣋⣓⣛⣷⣧⣽⣦⣙⡬⡛⡔⢎⠆⣿⣿⡖⣟ ⣿⣿⡈⣿⣎⢯⢷⡟⣿⢳⢎⡟⣌⠂⣼⠛⣼⠀⣡⣾⠿⠋⢀⣤⣡⣿⣿⠿⠿⠿⣿⣿⡿⠿⠟⠿⣟⠻⠻⠿⢿⣿⣷⡌⠎⡆⢻⣿⣹⣯ ⣿⢿⣧⢹⣯⠞⢬⢇⠸⡗⡊⢖⠠⡚⢅⠣⣼⣴⠟⣉⣴⣾⣿⠿⠛⢉⠠⣀⣦⣰⣀⡈⡙⢶⣤⡀⢻⠀⠀⢀⠀⢹⣎⣿⡎⢴⡈⣿⣾⠧ ⣿⡦⢻⣦⠻⣎⢲⡘⢎⡱⢡⢎⡸⡑⢮⡾⠋⣤⣿⡿⠛⣩⡟⢀⢆⣶⡿⢿⢻⠟⣿⢻⢶⣦⡌⠻⣮⡄⠀⠂⠀⡄⣿⣾⡇⢣⣿⣼⡏⠱ ⣿⣷⡣⣟⢹⣎⢱⡌⠲⣌⢣⢆⣧⣽⣟⣱⡿⠟⠁⠀⢠⡿⣀⢣⡾⢯⣉⡟⡌⢿⡄⠛⢦⡑⢹⠒⣌⠻⣶⣶⣷⢾⣿⣿⢂⣿⣿⢸⡇⠀ ⣿⣾⣷⣩⢂⡿⣎⢿⡱⢌⠖⢮⣷⣿⡞⠋⠘⠄⠀⠀⣾⣷⡼⠙⢣⠞⡴⢨⡝⠂⠽⡌⠂⠟⢦⠉⠜⡐⢂⠚⣽⠻⠿⢶⣰⣿⡿⣼⠃⠀ ⣯⣛⡟⣿⡆⢏⣿⢸⣇⢫⠜⣻⣿⢯⠀⠀⠀⠈⢆⣸⣧⣿⡑⠫⢄⡻⠀⢦⡉⠄⣉⠳⣌⠘⠢⢍⢂⠓⣈⠲⢠⢾⢠⣯⣿⢏⡱⡟⠀⠀ ⣷⡭⢞⡥⣿⡸⣿⢞⣯⢸⡎⣿⣿⡉⣔⠀⣀⢀⢰⣿⡿⡷⢈⠱⡂⢡⢉⠠⡓⢌⠄⡘⡘⢦⡑⡌⣌⡰⣡⡙⣶⡿⣾⣿⠟⣻⠴⠇⠀⠀ ⠻⣯⣳⡞⡭⢿⣞⣯⣿⣜⣷⡹⣿⣧⣾⣷⢶⣿⣿⣿⠃⢧⢍⠲⣱⢂⣬⢒⡭⢎⠶⡱⡝⣦⢳⡜⣆⡷⣡⢟⣿⣹⣿⣳⠄⣹⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣆⠻⣹⣷⠏⣿⡽⢿⡟⣹⠟⡴⡉⢞⡬⢳⡱⣞⣬⢳⡞⣬⢷⣹⣝⡮⢷⣹⣾⣷⣝⣾⡟⢉⣥⣿⣧⡟⠀⠀⠀⠀ ⠀⠈⣿⡿⠀⢙⡯⢿⣿⣿⣦⣍⣻⣦⣌⠲⢧⡹⣙⢶⡹⢼⣹⠳⡝⡞⣜⣣⠟⡽⣎⠷⢮⡝⣣⣿⣿⣼⣿⣿⣦⣭⣿⢸⡟⠃⠀⠀⠀⠀ ⠈⠀⡟⠁⠀⢸⣇⠸⣿⣾⡓⣿⠻⣿⡿⣿⣾⣿⣶⣭⡟⣷⣾⢯⣷⣬⡑⣧⣿⣵⣮⣽⣶⣾⣿⣿⢿⣿⡟⠼⣻⣿⣿⢨⡇⠀⠀⠐⠀⠈ ⠀⠀⠀⠀⠀⠀⣧⢵⡿⠀⠑⠸⠃⠹⠿⠙⣿⣯⢿⣿⣃⢻⣿⣻⣿⣿⣥⣿⣿⣿⣿⣿⣽⣿⢿⣿⣸⡗⡌⢣⠻⣿⣿⣴⣧⣠⣤⣴⣞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⢿⣻⢷⣿⣻⣷⣿⣻⣽⣿⣿⣻⣽⣯⣿⣽⣯⣿⢿⣿⣿⣿⣿⢿⣿⢿⣯⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠓⢶⣶⣶⣾⣿⣿⡿⣿⣽⢾⣋⡗⣿⣿⣽⣷⣿⣿⢿⣻⣾⣟⣯⣷⣿⣻⣾⣟⣿⣯⣿⣿⣾⢿⣯⣿⢯⣷⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⣻⣿⣿⣿⠿⣩⢶⡹⣜⢶⡙⣯⣿⣯⣿⣿⣻⣷⣿⣻⣽⣾⣟⣷⣿⣻⣾⣷⣿⣯⣿⣯⣿⠿⣙⣿⣾⣿⣷⣿⣿⣧⠀⠀⠀ ⠁⠀⠀⣠⣶⣿⣿⢯⣶⣯⣵⣎⣳⠭⣞⣱⡿⢧⡹⣍⣻⢛⠷⣹⣏⡽⢻⢾⢻⡛⡟⣭⢳⣿⣹⡛⣏⢧⣻⡱⣎⣿⣿⣻⣿⣾⢿⡆⠀⠀ ⣀⣴⣾⣿⣿⣻⣽⡿⣯⣿⢯⣿⡿⣿⣼⡿⣙⢮⡳⣝⢶⣫⣛⣼⡧⣏⡟⣮⢳⡽⣹⠖⣿⣏⢶⡹⢎⡳⣜⠳⡵⣚⣿⣟⣿⣯⣿⣷⠀⠀ ⣿⡿⣿⣽⣾⣟⣯⣿⢿⣽⡿⣯⣿⢿⣿⢧⣿⣶⣽⣜⠮⣕⢾⣿⡱⢮⡝⣎⡗⣺⢵⣻⣿⣏⣶⣿⣿⣿⢿⣿⣾⣥⢿⣿⣯⣿⡷⣿⡇⡄ ⠻⠿⣿⣷⣿⢯⣿⣻⡿⣯⣿⢿⣽⣿⣿⡿⣟⣿⣯⣿⣿⣯⣾⣷⣽⣶⣿⣶⣿⣷⣾⣿⣿⡿⣿⣽⣾⢿⣻⣯⣿⣻⣿⣟⣾⣷⡿⣿⣿⣇ ⢀⣾⣿⣟⣯⣿⢿⣽⡿⣿⣽⡿⣯⣿⣿⣻⣿⢯⣷⣿⡽⣿⣿⣟⣿⣯⣿⣿⣿⢯⣿⡏⣿⣿⣟⣯⣿⢿⣻⣽⣷⣿⣻⣾⢿⣾⢿⣻⣿⣿ ⣿⣿⢿⣽⣟⣯⣿⢿⣽⣿⣽⡿⣿⣿⡿⣽⣿⣻⡿⣾⣿⣿⡿⣽⡷⣿⣿⣿⣯⣿⠏⠘⡼⣿⣿⡿⣽⣿⣟⣿⣾⣻⣽⣿⣻⣯⣿⡿⣽⣿ ⣿⣿⣟⣿⣾⣟⣯⣿⣿⣿⣳⣿⣿⣿⢿⣻⣷⢿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⠿⠁⣀⢂⠘⡽⣿⣿⣿⣟⣾⣿⣳⣿⣟⣾⡿⣽⣷⡿⣿⣿ ⣿⣿⣽⡿⣾⣻⣯⣷⣿⣯⣿⡿⣿⣿⢿⣻⣽⣿⣿⣿⣟⣯⣿⠿⣿⣾⣿⡉⠀⠠⠐⠈⠄⠈⢿⣿⣿⣿⣻⣾⣟⣷⣿⣿⣽⣿⣽⢿⣟⣾ ⠰⣿⣯⣿⣟⣿⣳⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢩⡾⠛⠙⠛⠻⠿⢷⣶⣶⣤⣤⣬⣿⣿⣿⣽⡷⣿⣻⣾⣿⣟⣾⣿⣿⣿⣟ ⠐⣿⣿⣳⣿⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣞⣫⡀⢀⡀⠄⢂⠀⣐⣶⣾⣷⣾⣾⣶⣷⣾⣷⣿⣿⣿⣿⣯⣿⣟⣿⣳⣿⣿⣯⣿⣿⣿⣿ ⠀⣿⣿⢯⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⡟⠛⢻⣿⠀⡤⢉⠄⢂⠿⣟⣿⣿⣿⣿⣿⠋⠛⣿⡉⣽⣿⣿⣿⣟⣾⣟⣿⡯⠹⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢹⣿⣿⣿⣿⣶⣿⣷⠐⡤⢣⡘⠤⣚⣧⢻⣿⡿⣿⣿⣿⣶⣿⣰⣿⣿⣿⣯⣿⢯⣿⣿⠃⣸⣿⡟⠿⣿⣿ ⠀⣿⣿⡿⠉⣿⣿⣿⣿⣿⠀⡀⠛⠻⡿⣿⣿⣿⡟⢰⢡⠣⠜⡱⢂⠽⢞⣿⣽⠟⢋⠡⢀⠂⡈⠉⢻⣿⣟⣾⣿⣳⣟⣰⣿⣿⠀⠀⠀⠈ ⢀⣿⠟⠁⠀⢹⣿⣽⣿⣯⣀⣄⣥⣦⣴⠶⢋⠍⡰⢁⠂⠛⠌⡑⠌⠒⡠⢀⠛⠿⢶⣶⣦⣴⣤⣶⣾⣿⢯⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠘⣿⣯⣿⠿⠿⢿⡉⠄⠂⠌⡀⠂⢁⢂⣨⣤⣴⣴⣬⣤⣀⠁⠢⠄⠀⢀⠠⢀⠛⠛⢻⣿⣿⡟⢻⣿⣿⣿⣿⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡟⠁⠀⢰⠈⢻⣦⡁⣠⣤⣵⣶⠟⠉⠀⡀⠀⠀⠉⢉⠀⠌⡀⢌⣰⠃⠌⡀⢀⢂⣿⣿⣥⡌⠁⠹⢿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⡀⠊⠄⢃⣼⣿⡟⠋⢁⣠⢿⣦⣄⣁⣀⣈⣤⣬⣤⣤⣶⣾⣿⣿⣿⣴⣶⡟⠋⠙⣿⣿⣅⣤⣠⣬⣿⣷⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⠟⠛⢿⣿⣿⣻⣿⡄⢀⠀⡀⢻⣿⣿⣯⣟⡻⢿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⢿⣿⣿⣿⡿⣟⣯⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⣾⣿⣳⣯⢿⣿⡄⠀⠄⢸⣿⣿⣿⣿⣽⣸⣿⣿⣿⣟⣿⣟⣿⠻⢿⣿⣿⣧⣴⣿⣿⣽⡿⣿⣁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣟⣯⣟⡾⣷⣻⢯⣿⣧⣤⣶⣿⡿⣿⣿⣿⡟⢻⣿⣿⣿⡜⣻⠛⣵⣮⡼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣟⡾⣽⢾⣻⣽⢯⣿⣿⣿⣟⣯⣿⡽⣿⣿⢿⣿⣿⣿⢿⣇⣩⠷⠾⣿⠖⣯⡘⣿⣿⣿⣿⣿⣯⣿⣻⣿⢾⣿⣧⠀⠀
⣿⣿⣿⢯⡽⣩⢿⣿⢳⡽⣽⣞⠿⢿⣿⣿⣿⡟⢿⣧⠹⡹⢿⣿⣿⣿⣶⣄⣀⠀ ⣿⣿⣿⢣⡟⣵⢫⣿⢏⡞⣡⠎⡛⢤⠙⢿⣿⣧⢊⣽⠶⡛⣋⠿⣿⣿⣿⣮⡉⠀ ⣿⣿⣏⠳⡜⢡⠋⡜⠃⢬⣡⣚⡔⡸⣼⣦⣷⣿⡿⢖⡛⠳⢦⣌⢹⣿⣿⣿⣿⣄ ⣿⣿⡗⡳⢞⣶⣶⣶⡷⣶⣻⣿⣹⢛⣳⡿⣹⡞⠀⠌⠉⣀⡤⠬⡍⢿⣿⣿⣍⠛ ⣿⣿⢣⡽⠫⡝⠠⠉⠉⠳⣇⡚⡜⣯⡿⣷⣷⢃⣴⣦⢿⣱⣶⠿⣿⣷⡾⣿⣿⢷ ⣿⣿⡟⣁⣀⣠⣐⣤⣤⣴⣼⠿⣼⣹⣿⡹⣿⡿⣽⣛⣭⠿⣼⢿⡿⣭⢻⣿⢿⣧ ⣧⠟⣿⣩⠽⣧⣍⣾⡽⢏⣧⡾⠳⣼⢳⣁⣻⣱⣄⣉⣘⠣⠜⡌⢷⡹⣈⢿⣿⢳ ⣿⣸⣏⡿⣟⡿⣭⠳⢍⡾⡃⢔⣡⠞⢋⣉⣁⣥⣬⣭⣯⣻⣶⣼⣆⡳⢜⣸⣷⣻ ⣿⣖⣯⠝⣋⠿⣈⠇⡼⢡⡷⢞⣩⣶⠷⠛⣉⣉⡛⠯⣍⠹⡉⠉⠹⣿⣦⠘⣷⣯ ⣿⡜⣾⢣⡅⠳⡌⡼⣴⢟⡼⠟⢹⠏⣰⢿⣛⣛⠟⡳⢮⡙⣦⣀⣤⣿⡮⣽⢾⠐ ⣿⣷⡡⢷⣯⡑⢎⣿⡟⠋⠠⢀⣿⣜⠋⡶⢡⠎⢣⠙⢦⠑⡨⢙⡛⠿⣴⣿⡾⠀ ⣷⠭⣿⣼⣽⣍⢾⣟⢃⠀⡀⣾⣿⠂⡍⢒⡐⢎⢈⠳⣀⢣⢑⢢⣼⣷⡿⣇⠇⠀ ⠻⣷⣽⣾⣽⡞⣯⢿⣾⣿⢿⡟⢢⡝⡸⢦⡜⣎⣎⠷⣭⢖⣯⢞⡿⢟⣦⠇⠀⠀ ⠀⣿⠏⣹⢿⣿⣮⣷⣭⣜⣞⠼⣣⣞⡝⣣⠟⣼⠺⣝⣮⣿⣿⣿⣧⣿⢻⠁⠀⠀ ⠀⠁⠀⢼⣸⠟⠘⡏⠿⢻⡿⣿⡹⣿⣿⣷⣻⣿⣿⣿⣿⣏⡿⡐⣿⣯⣳⣀⣤⡴
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀ ⢰⣿⠋⠹⣷⣤⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡀⢉⢿⣄⠀⠀ ⠸⣷⣤⠏⠀⣸⣿⣤⣴⠟⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣎⠁⡈⠿⣇⠀ ⠀⠙⣿⡄⡟⠁⡀⢘⡯⢀⢆⣿⠟⠀⠀⠀⠀⠀⣠⣼⣿⠿⠟⠿⢿⣿⡖⣦⣄⠀⠀⠀⠀⣿⡟⠁⠙⣿⣿⢧⠃⠶⣎⣿⡀ ⠀⠀⢹⡞⡄⢣⠟⠋⢁⢢⣿⠃⠀⠀⠀⣀⣴⠟⣛⣫⣥⣤⣠⡤⣶⣤⣅⣈⠹⢻⣦⡀⠀⠈⢿⡆⠡⣿⠏⠸⣤⣀⠰⣿⡇ ⠀⠀⠈⢿⣆⢉⠂⢬⣄⢒⣿⠀⠀⢀⣼⠏⡽⠞⢩⢑⢢⣄⣡⣐⣄⢢⢉⠛⢆⠣⣜⢻⣦⠀⢼⡧⢡⡆⠤⠽⢋⠉⣴⡿⠀ ⠀⠀⠀⠘⣷⣌⠰⠀⢙⣾⠟⠀⢀⣾⠋⡔⡱⠊⣴⣾⣿⣿⣿⣿⣿⣿⣶⡌⠢⡁⢆⠡⢻⣇⠻⣧⣃⠠⢀⠣⣌⣽⠟⠁⠀ ⠀⠀⠀⠀⠀⠻⠷⣭⡾⠿⠀⠀⣼⠇⡘⡖⢡⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠱⢈⠆⠡⣿⡄⠈⠻⢶⣧⠿⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠭⡐⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠡⢊⠅⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⢣⣘⣿⣿⣿⣿⡿⠟⠛⠻⠿⣿⣿⣿⣿⣿⣀⠃⠆⣼⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠂⣾⣿⣿⣿⠋⡐⡈⠄⡡⠐⡈⢻⣿⣿⣿⣧⠌⣣⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⢿⣿⠟⣁⠂⡅⠘⢄⠡⡁⠆⢡⠚⢿⣿⣿⢈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣈⡝⢒⡌⠱⣈⠱⡈⣴⠈⡜⢡⠘⡤⣭⣂⢭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣬⣑⣢⡑⠴⣀⡓⣌⣆⣳⣶⠟⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡰⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣞⣟⣹⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡾⢛⢻⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡟⠛⢻⣷⣝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀⣾⣧⡿⢉⠰⢠⢨⣿⠁⠀⠀⠀⠀ ⠀⠠⣯⣹⣿⢀⠣⠠⡙⣿⣌⢷⣦⣤⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠿⣿⣿⣹⣿⣿⡟⡁⠆⡑⢂⡼⣿⣠⡀⠀⠀⠀ ⠀⢐⣿⡿⢟⣆⠢⠑⡄⢹⣿⣿⣿⣿⠛⠍⡛⣿⣶⣤⠂⠀⠀⠀⠀⠀⠀⠀⣯⣿⣇⠂⠌⢿⣿⢿⡟⠡⠐⡌⡐⢢⠳⢉⡉⢿⣦⠀⠀ ⣿⣿⡃⡐⡈⠻⣧⢈⠰⢀⠛⣿⣿⠃⠌⡒⣱⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣞⣿⣎⠰⢈⠙⡋⠔⣁⠣⡐⠡⡉⠔⠢⡐⢈⣿⠆⠀ ⣷⣿⣡⠐⠤⡑⡀⠆⡑⠢⠌⣈⢉⡐⢂⠱⣼⣏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⢷⡄⠊⡔⠡⢂⠔⠡⡁⠆⡉⢆⠁⣞⢻⣦⡀ ⣿⣾⣿⣶⠆⡑⠌⢂⠡⢃⠒⢄⠢⠘⢦⣷⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⣾⣿⣔⢀⠃⢆⡘⠰⠠⠑⡰⢀⠎⣀⠂⢸⣿ ⣿⣿⡋⠄⢢⠑⡌⠂⡅⢊⠔⡨⢀⢃⣾⡟⡛⠷⡴⣋⣭⣷⣶⣶⣶⣶⣶⣦⣶⣾⣭⣽⣚⢾⡿⣷⣬⡀⠌⣁⠣⠑⡐⠢⢈⠤⠑⣼⡿ ⣿⡹⣷⣌⠄⠃⡌⠰⡈⠆⢂⠡⣢⣾⣿⢃⣷⡿⠟⢛⠩⢉⣷⠔⡠⢶⣄⡐⡈⠌⣉⠙⢛⠻⢷⣮⣟⠻⢷⣶⣤⣧⣤⣑⣦⣤⣿⠟⠁ ⠀⠉⠻⣽⣻⢷⣄⣃⣐⣨⣴⣿⠟⣃⣴⡟⠩⢐⠨⣤⣾⡿⢋⠰⠀⢭⠻⢿⣶⣬⣤⣘⣠⣈⠄⡉⠻⢿⣮⠻⡿⠿⠉⠉⠛⠋⠁⠀⠀ ⠀⠀⠀⠀⠈⠙⠽⠿⠛⢻⣭⣷⣾⡟⠳⠶⢷⠾⠟⢋⣱⣶⢆⢣⡙⢾⣷⣤⡈⢉⠍⠛⠛⢋⡐⠌⡐⢂⠹⣿⣌⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢃⠐⡢⢁⠆⠰⣨⣿⣿⢏⡜⣢⢝⣚⣿⣿⣿⣤⠊⠔⡑⠢⠌⢢⠁⢆⠡⢈⢿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⡿⠁⢆⠱⢀⢃⣬⣷⣿⡿⢯⡟⡼⠥⡏⢞⠳⣟⣿⣿⣷⣮⣤⣁⠊⡄⠡⢊⠐⡂⠌⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⠃⡜⠠⣳⣾⣿⣿⢿⡻⡵⢏⠞⡴⢫⢜⡣⡝⡸⢧⣟⣻⠿⣿⣿⣿⣿⣇⠂⡱⢈⠰⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣻⡟⢰⠠⠉⣿⡯⡝⣜⡲⣿⠈⠎⡽⢌⡳⢌⡖⡍⠖⡃⠌⣹⡿⣔⡲⡱⢾⣧⠂⢡⠊⡄⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢪⠇⡈⣿⣱⢹⢦⡹⣿⠀⢍⣰⣦⣶⣷⣶⣾⣴⣀⠃⠼⣿⡰⢳⣍⢻⣷⠈⢢⠑⡠⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠥⡙⢆⠡⣿⣥⢫⡖⣭⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⡱⣏⠼⣹⣯⠐⢂⠱⣀⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡘⡅⢂⣿⢖⡳⣚⢴⣻⣿⣿⣿⣻⢏⡿⣽⣻⣿⣿⣿⣿⡼⢳⢭⡚⡽⣷⠈⢌⡒⢤⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠐⡌⠄⣿⢎⡵⣍⢮⣽⣿⣿⣷⠿⠿⠿⢷⣷⣿⣿⣿⣿⡗⡹⢶⡹⣜⣿⠀⢊⢥⣾⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠌⢂⣿⣚⠼⡜⢦⣿⠟⡉⠄⣒⠨⣐⠄⡠⠌⡙⠛⢻⣭⡓⣧⠳⣼⡏⢰⣡⡿⣋⠄⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢺⣥⢻⡙⣎⣿⠀⡔⠡⣈⡇⠘⣆⠐⢢⠐⡉⢸⣷⡹⣜⠳⣜⣧⣿⢋⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⢷⣮⣧⡙⡖⣿⠐⠨⠑⡠⠉⡔⠠⡉⠄⠃⢌⠘⣷⣳⣼⡿⢿⡋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠯⠛⠿⢷⣧⣬⣥⣆⣡⣒⣤⣁⣦⣭⣼⣶⠿⣟⣏⠷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⢸⣉⡍⠛⠙⠛⠛⢻⡙⡏⢡⢒⣼⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢛⢻⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣟⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠋⠰⡀⢎⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠎⠠⡙⣿⡄⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣷⣦⣴⣏⣽⡟⠡⠌⡱⠈⡼⣿⣀⡀⠀⠀⠀ ⠀⢀⣴⡾⢿⣌⠌⡁⢆⠹⣿⣄⣠⣿⠛⠯⣝⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠐⡈⢿⣿⣿⡟⠁⢆⠱⢀⡱⡝⢉⡉⢿⣦⠀⠀ ⢀⣿⠇⡐⡈⠻⣦⠁⢂⠆⠻⣿⣿⡃⢉⠔⣫⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣎⠰⢈⠙⡋⢅⠊⡄⠢⡁⡑⢠⠂⠔⣈⣿⠆⠀ ⠐⣿⡜⢠⠐⡡⢠⠘⠤⡈⠔⣈⢉⠰⠈⡜⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡆⠡⠒⡌⠰⣀⠣⠐⢌⢂⠩⡐⢬⠿⣦⡄ ⠀⢙⣿⣷⠆⡑⢠⠉⡐⢡⠊⠔⢂⠙⣲⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣥⠁⢆⠱⠀⢆⠩⠄⢊⠰⠐⣂⠰⢘⣿ ⠘⣿⡏⢀⠢⡑⢂⠡⡘⢠⠑⡌⢂⠒⣼⡟⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣴⣤⣤⣄⣀⠈⠻⣷⣤⡂⢉⠢⠘⡈⠆⠡⠃⢄⠒⣼⡿ ⠀⠹⣷⣌⠄⡑⡈⠆⡑⢂⠢⠐⣬⣾⠟⢁⣤⣾⠿⠛⢋⢹⣷⠖⡠⢷⣆⡐⡈⢉⢉⡙⠛⠿⢷⣮⣝⠻⣷⣶⣥⣦⣬⣥⣼⣤⣾⠟⠁ ⠀⠀⠈⠙⠻⢷⣌⣄⢡⣢⣴⣿⠟⢉⣴⡟⠋⠄⣂⣡⣾⡿⢋⠰⠀⢭⡻⢷⣷⣬⣤⣀⣃⣐⠂⡉⠛⢷⣦⠈⠉⠉⠉⠉⠛⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⢀⣴⡟⠳⠶⢷⠾⠟⠫⣵⣯⡔⢎⡱⢾⣷⣤⡈⢉⠍⠛⠛⢋⡐⠡⢘⡀⠛⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠤⠡⠌⡄⠢⣬⣿⣿⣏⡜⣪⡑⢯⣿⣿⣿⣦⢈⠢⢑⠢⡘⢄⠃⠤⠑⡈⢿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⢎⡐⠡⢊⣤⣷⣿⣿⣻⠟⡭⠵⢭⡋⠿⣽⣿⣿⣷⣦⣆⣂⣁⠢⠘⢠⠃⠌⢊⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⡍⠰⣰⣿⣿⣿⠿⣿⢶⠏⡟⢬⡙⢦⡍⢧⡙⢷⣽⣻⡿⢿⣿⣿⣿⣇⠂⠜⡈⠔⣺⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢰⡈⠌⣿⡟⡭⢎⡽⣿⠀⠛⡬⢣⡙⣆⠞⡦⠙⠆⢌⢹⣯⡓⢶⡘⣾⣯⠀⢣⠘⡠⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢺⡐⡈⣿⡽⣘⢧⣚⣿⠀⢍⣰⣦⣷⣾⣶⣶⣭⡐⢨⠸⣷⡹⢲⡹⢼⣷⠈⢄⠣⢐⣩⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡣⠥⡃⢌⣿⡵⣩⠶⣩⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⣿⡱⣏⡜⣻⣯⠐⣈⠒⡄⢺⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠒⡅⠢⣿⢖⡭⢳⡱⣯⣿⣿⡿⣟⣯⢟⣽⣻⣿⣿⣿⣿⡽⣱⠞⡼⣹⣷⠐⢠⢃⢞⣽⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠁⡆⠡⣿⠞⣜⢧⡹⣾⣿⣿⣿⠿⠿⠿⢷⣷⣿⣿⣿⣿⣧⠹⣞⡱⢣⣿⠀⡡⢎⣾⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⡘⠠⣿⡛⡼⢢⣓⣿⠟⡉⠄⣂⠆⢒⠠⡀⠌⡙⠛⣛⣮⣓⠮⣕⣻⡏⡰⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣡⢹⡷⣩⠳⣍⣿⠀⡔⣈⠰⣎⠨⡇⢄⠣⡐⠡⢸⣿⢌⡻⡴⣹⣧⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣧⣝⡳⡜⣿⠐⡰⢀⠣⠉⢆⠉⡄⢂⠡⡘⢈⡿⣎⣷⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣾⣵⣬⣴⣄⣢⣉⣄⣒⣤⣣⣶⣴⢿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⡉⠛⠙⠛⢛⣻⣹⠏⢹⢲⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡹⡽⢤⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢲⢦⠀ ⢿⣱⡟⣲⢶⡻⣌⢿⠀⠀⢀⡤⣔⣦⠤⠖⢤⢴⣢⠄⡀⠀⠀⣤⠶⣤⢘⢯⣎⡳ ⠸⣿⢸⣱⡾⢱⡿⠁⠀⡰⣱⠉⣿⣿⢇⡈⣿⡁⣸⣿⣎⢱⠀⢷⠏⣶⡿⣇⠾⣁ ⠀⢻⡜⡧⣽⡣⡇⠀⡰⡓⠿⠿⡭⢟⣲⣄⣫⡻⠿⠾⠿⢫⡣⣠⢟⣦⠗⣭⠳⣭ ⠀⠀⠻⣜⠲⡽⠃⣰⠁⠧⠮⢗⣿⣿⣿⣿⣿⣷⣾⡒⠻⣤⠇⣹⠣⣏⠞⣥⠟⠁ ⠀⠀⠀⠈⠉⠀⠀⡇⡘⢌⢢⣿⣿⣿⣿⣿⣿⣿⣿⣷⢡⠏⣶⠘⡆⠈⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⡘⠄⣾⣿⣿⣿⠿⠛⠿⣿⣿⣿⣯⣔⣸⢒⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡀⣏⣿⣿⡏⠰⣀⠉⡆⡈⢿⣿⣿⠀⢁⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⡊⠿⣋⠄⠣⢄⠣⡐⢡⢂⠻⠿⠉⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⣅⡘⡐⢂⠡⡘⠄⢢⣉⠷⡮⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠉⠉⠉⠉⠉⠐⠠⡀⠀⠀ ⠀⠀⠀⠀⣤⣤⣠⣴⣶⣦⡀⠀⠀⢀⣀⠔⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠈⠢⠀ ⠀⠀⠀⢸⣿⠋⠛⠋⡈⢻⣷⣄⣠⣿⣿⠀⣀⣠⣴⠟⠀⠀⠀⠈⠳⣤⣀⡀⠀⢁ ⣾⣶⣤⣸⣿⣶⣦⣴⣶⡿⢟⣿⣿⣿⣿⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⢨ ⠙⢿⣿⣿⣿⣷⣦⣤⣤⣶⣿⣿⣿⡿⠃⡀⠀⠸⣶⣤⣶⠆⢳⣦⣤⡶⠁⠀⠀⢘ ⠀⠀⠉⡏⠛⠻⢿⣿⡿⠟⠛⣿⣇⠀⠀⠈⠄⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰ ⠀⠀⠀⢡⠀⠀⠈⠿⡇⠀⠀⠙⠛⠀⠀⠀⠘⡄⠀⠰⠶⠶⠶⠶⠀⠀⠀⠀⢀⠂ ⠀⠀⠀⠈⡄⠀⠀⣀⣀⣀⣠⣤⣴⠾⣷⠀⡤⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀ ⠀⠀⠀⠀⠐⠄⠀⠙⣯⣍⣉⣀⣠⣴⡿⠣⠁⠈⠑⠢⡤⠤⠤⠤⠔⠂⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⡀⠈⠛⠿⢿⡿⢿⠁⢠⣆⠀⠀⠀⠘⠤⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⣀⠀⠀⠈⢒⣈⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠣⢀⣀⣀⢀⠀⢀⡘⠁⠀⠀⠀⠀⠀⠀
⠛⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁ ⠀⢀⠈⠳⡄⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡁⠆ ⠀⢐⡀⠀⠸⣏⠹⠿⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣖⣴⣿⢿⣷⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀ ⠰⠉⠀⠀⠓⠂⠀⠰⢸⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣿⠽⠷⢛⡛⢶⣯⣘⣻⠯⣽⣷⣦⣄⡀⠀⣠⣴⠂⠀⠀⠀⠀⠀⠂⠥ ⠂⠤⠁⡀⠜⢀⠰⢰⣾⣼⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠯⣄⣟⡃⠊⠉⠀⢀⠀⠀⠉⠉⢛⣦⡈⠓⠾⢿⣾⣿⣺⡄⠀⠐⠠⠀⠀⡉⠀ ⡈⢄⠃⠉⢀⠀⢆⣿⡿⠁⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡷⠛⢿⣿⣿⣷⡀⠀⠂⠄⡀⠻⣶⡟⠛⠻⣷⣦⡈⠉⣿⢯⣷⣄⠀⠠⢀⠀⠑⢢ ⡡⢈⠂⠄⠀⠀⣾⣿⡷⠀⠀⠀⠀⢠⡶⣿⠟⡁⣼⣿⣤⣤⣾⣿⣿⣿⡅⠠⠍⠠⢁⢸⣿⣧⣴⣾⠿⢿⣿⣦⠘⢿⣷⣿⠀⡁⢂⠐⠨⠄ ⡧⠀⠌⡀⢂⠠⠘⣿⣷⠀⠀⢀⣴⠟⢛⡵⢈⣴⡿⢿⣿⣿⣧⣼⡿⢿⠠⡐⣌⣶⣶⣎⠿⣿⣿⣿⣤⣾⠿⡛⣤⠘⣯⣿⡐⠌⠂⠁⠌⡐ ⣿⡌⡐⢀⠀⠢⣥⢽⣻⡆⢀⣾⣥⣴⠏⣐⣼⠿⣴⣣⣶⡼⠶⢣⣝⣮⣷⣿⣿⣿⣿⣿⣾⣴⣲⣜⠦⠧⢷⣹⡔⢂⠸⣿⣧⠎⢀⠈⠰⠐ ⠹⢦⣻⢦⣤⣐⣘⣻⡿⠀⣹⣿⢯⡏⢠⠛⠡⢐⡈⠡⢀⢰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⠠⢉⣏⠀⡇⣿⡿⣦⠈⠈⠀⡄ ⠀⠀⠉⠛⠮⣭⠿⠉⠀⠀⣿⢼⣹⢠⠃⢌⡐⢢⠈⣁⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠄⣽⠿⡂⣷⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢺⠆⠠⢃⠄⢢⠡⣘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⠏⣜⡹⢼⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠌⠐⡡⢊⠄⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⡞⢤⣛⣿⣿⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠠⠘⡐⠌⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣶⣭⣿⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⢆⡁⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢂⠔⣯⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡼⣆⠡⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣨⡇⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣟⡄⠉⢛⠩⡉⠔⢠⠀⡌⢈⠉⠙⠛⠛⠛⠟⠿⠻⢿⣿⣿⣿⣿⡗⠸⣱⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⣿⡦⣵⣈⠒⡤⠁⡄⠃⠌⡐⠄⡂⠤⠐⡄⠆⡄⢈⡙⢛⣋⠄⣱⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢽⣳⠦⣵⣂⡍⠰⢡⠘⡄⠢⡁⠆⡜⣠⢥⣖⣭⣴⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠙⢲⠯⣽⣿⠮⠿⠽⠯⠽⠿⠽⠿⢾⣯⡽⣫⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⢆⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄ ⡀⠃⠨⠁⠋⣷⡀⠀⠀⠀⠀⠀⢀⡴⣾⠿⡟⢯⣟⡷⢶⣤⣀⠀⣠⡀⠀⠀⠀⢂ ⠐⡠⠐⠁⣶⡟⠁⠀⠀⠀⣠⣶⣿⣼⣭⡀⠀⠄⢈⣉⣷⣬⡙⠷⣿⣆⠀⠀⠐⡀ ⡂⢁⠀⢸⣿⠄⠀⠀⣴⡾⢋⣿⣤⣼⣿⣿⠠⠌⠰⣿⣤⡾⢿⣦⢛⣿⡅⠒⠠⠘ ⣇⠄⡈⢄⡿⡇⢠⣞⡩⢆⣿⣙⣟⡷⣛⣧⣶⣿⣿⣝⣛⡟⠾⣍⡆⢹⣷⠁⠠⢁ ⠿⣾⣆⣈⣿⠇⣿⣿⠁⠏⡀⠉⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⢉⡇⣸⣿⡆⠁⠀ ⠀⠀⠉⠛⠀⠀⣿⠎⡘⢠⠡⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⢣⣽⡧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡃⠌⣂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣊⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣧⠐⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣉⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡌⢻⠿⠟⠻⠻⠿⢿⢿⣿⣿⣿⣿⣿⡇⣞⣽⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣮⣌⠡⠒⣀⠂⠄⡠⠠⠌⡙⡻⣁⣾⠏⠀⠀⠀⠀⠀ ⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⢷⣶⢽⡲⣥⠷⡯⣷⢿⡛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⡍⢩⢁⠒⡄⢃⠒⡌⢩⢁⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠴⢊⠔⡨⠑⡌⠢⢌⠒⡌⢢⠑⣌⣦⣦⣼⣴⣤⣙⠢⡀⠀⠀⠀⠀ ⠀⠀⢀⡔⢣⣸⣶⣿⠛⠛⣻⡇⢌⠒⡌⢢⠑⢺⣇⠀⠀⣿⣿⣿⣿⣮⣢⡀⠀⠀ ⠀⢠⣪⣼⣿⣿⣿⡿⣣⡴⠛⡌⢢⠑⡌⢢⠉⡌⠻⣷⣄⡹⢿⣿⣿⣿⣿⣾⡄⠀ ⢠⣿⠏⠿⠿⠟⠋⣰⡏⣔⢡⠘⡄⢣⠘⡠⢃⠌⣡⣶⢉⢻⣆⠙⠻⠿⣿⠿⣿⡄ ⡷⣿⣴⣾⠃⠀⢠⣿⠸⣯⣄⣧⣼⣾⣿⣿⣷⣿⠛⡡⢊⠄⣿⡄⠀⠀⢀⣠⣿⢴ ⢡⠉⣼⡇⠀⠀⣾⠇⡒⢌⢹⣿⢯⡷⣻⢷⣫⣿⡇⠰⡁⢎⢸⣇⠀⠀⢸⣏⢙⠂ ⢠⢹⣿⠀⠀⢠⣿⢡⠘⡄⢊⢿⣯⢷⣯⡟⣵⣻⡇⢣⠘⡄⢚⣿⠀⠀⠈⣿⡌⠒ ⡄⢺⡇⠀⠀⢸⡟⣀⠣⡘⢄⠊⡝⢿⣶⣿⣿⠟⡡⢂⠱⡈⠆⣿⡆⠀⠀⣿⡆⠡ ⢇⢻⡇⠀⠀⢸⡇⡄⢣⠘⡄⢣⠘⡄⢢⠁⢆⡘⢄⠃⢆⠱⡈⢼⡇⠀⠀⢾⡇⠡ ⠘⣾⣗⠀⠀⢸⣧⠘⡄⢣⠘⡄⢣⠘⠤⡉⢆⡘⠤⡉⢆⠱⡈⢼⣷⠀⠀⢾⣧⠃ ⠀⠈⢿⡄⠀⠸⣿⡐⢌⠢⡑⢌⠂⡍⢢⠑⢢⠘⠤⡑⢌⠢⡑⠸⣿⠀⠀⡻⠁⠀ ⠀⠀⠈⠳⡀⠀⢻⣧⠈⢆⠱⣈⠒⡌⢢⠉⢆⡉⢆⠱⡈⢆⠡⢃⣿⢀⡜⠁⠀⠀ ⠀⠀⠀⠀⠈⠲⢄⢻⣎⠄⠣⢄⠣⡘⠤⡉⢆⡘⢄⠣⡘⠄⣣⡸⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⢕⣈⣆⠑⢢⠑⠢⣘⣠⢣⠴⠓⠉⠀⠀⠀⠀⠀⠀⠀
⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⣀⣄⣄⣀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⣿⣟⣿⣭⣿⡿⢿⠷⡾⠿⠿⣿⣭⣿⣳⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣯⠿⢛⠛⡉⢉⠡⠐⡠⢐⠠⢂⠔⡨⢐⠠⡀⠤⢉⠉⡙⠳⢾⣭⣷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠾⠋⣀⠂⠆⡰⢀⠃⢂⠱⠐⢂⠡⢊⠐⡐⠌⠰⢈⠢⢁⠎⡐⢡⠂⠄⡉⠻⢾⣽⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠛⠠⠐⡔⠠⠉⡔⢠⢁⢊⠐⣂⠉⡄⠃⡄⠃⡌⢨⠑⡈⠔⣁⢂⠡⢂⡘⠠⠑⢠⠂⡄⣛⣯⡷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠟⠁⠌⡁⢒⣠⣁⣡⢐⠠⢈⠂⢅⠂⡜⠠⢡⠈⡔⡈⢄⠊⡔⢡⠀⠎⡐⢂⠌⣰⣽⡶⠿⠛⣟⣻⣿⣾⣝⢶⡀⠀⠀⠀ ⠀⠀⢀⡾⣿⠋⢄⣸⡶⠟⠛⠛⠛⡛⠻⠿⣶⣮⣄⠒⣀⠃⠆⡡⢐⠰⠈⠔⢠⠂⠜⡐⢬⣤⣿⠟⠉⣠⣶⣿⣿⠿⠙⠛⣿⣿⡻⣄⠀⠀ ⠀⢀⣾⣿⣣⣼⠟⢫⣴⣾⣿⣿⣿⣿⣿⣿⣶⣭⣛⢿⣦⣌⠐⢡⠂⡑⢨⠘⠠⡘⠰⠜⣾⡟⠁⠀⠚⠋⠙⠛⢿⣿⡼⣿⠏⠁⠻⡿⣆⠀ ⣰⣾⣿⣷⠏⠁⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⡧⢿⣷⡝⢿⣧⠂⡑⠌⠤⡁⢃⠔⡡⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡏⠀⠀⠀⢿⣽⡤ ⣿⣯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⣤⡇⣴⣬⣿⣆⢻⣿⡄⠊⡔⢈⠄⢢⠰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣤⣾⣿⡁ ⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⢾⣿⣿⣿⡆⣿⣧⠐⡈⠆⡘⠠⢸⣿⠀⣀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⢿⣿⢻⡧ ⣿⡃⣼⣿⣤⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣼⣷⠠⢘⠠⠑⡂⠥⣿⡇⢹⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⠃⠀⢀⣾⡿⠣ ⣿⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣹⣿⣿⡿⠿⠿⣿⣿⣧⣴⢼⣟⠠⢌⢂⠱⣈⠐⣻⣇⠸⣿⠛⢻⣿⣿⣿⣿⣧⣼⣿⣷⣦⣿⡿⠁⠀ ⣿⣦⣿⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠻⣿⡇⣿⡇⠰⢀⠆⠢⠄⠒⡘⣿⡄⢻⣶⠞⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣥⠀⠀ ⡟⠹⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣼⢻⣿⠁⠒⡈⠆⡱⢈⠒⠠⢹⣷⡈⠁⢀⣴⣿⣿⡿⠿⠛⠉⡀⠄⢸⣿⡄⠀ ⣦⣴⡿⠀⢉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣼⢣⡿⠋⢄⢃⡰⢐⣀⢆⣡⣅⣦⣿⣿⠶⠟⠛⠋⢁⠐⡀⠆⡑⠰⣼⣿⠋⠀⠀ ⢻⣿⣀⠌⠠⠐⠠⢀⡀⠠⠉⢉⠉⡙⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⠛⢉⠉⠉⡀⠠⠐⡠⠑⡈⢂⠡⠐⠠⠐⢘⣋⣿⠇⠀⠀ ⠀⠻⢿⣿⣷⣾⡇⠠⠐⠡⠘⡀⠒⠠⢁⠢⠐⠠⢁⠂⠌⠠⡁⠌⠄⡁⢂⠁⠂⠌⠠⠘⠠⠁⠌⡐⢠⣐⣠⣀⣂⣬⣄⣽⣶⠿⠋⠀⠀⠀ ⠀⠀⠀⢰⣾⠛⠀⢄⠡⢂⠡⢀⠑⠠⠂⠄⡁⠒⠠⠈⠄⠡⠐⡈⠄⡐⠠⢈⠐⡈⠄⡁⢂⠁⠂⢼⣿⡿⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢺⣧⠀⠌⢀⠒⢀⠂⠄⡈⠁⠌⡐⢀⠡⢀⠡⠈⠄⠡⠐⠠⠐⠁⢂⠐⡀⠂⠌⠀⠌⡐⣠⣬⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣶⣬⣄⣐⣄⣨⣴⡴⠷⠾⠿⠿⠷⠷⣶⣷⣾⣴⣦⣅⣢⣁⣢⣄⣤⣥⣬⣶⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠋⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⢤⣴⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢢⡀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⣿⠟⠋⠙⢿⣿⣵⡄⠀⠀⢰⣿⣿⣯⡀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠸⣿⣄⡀⠀⠀⠀⠀⠀⠱⡄ ⠀⣀⠀⠀⠀⠀⣿⣿⡇⠀⠓⠂⠀⠠⠠⣀⣿⣿⣿⣦⣴⣿⣿⣿⣿⡇⢠⣤⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣦⣤⡀⠀⠀⢳ ⣾⣿⣿⣦⣤⣀⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⠃⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⠁⠀⠀⠘ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⠛⠛⠛⠛⣉⣠⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣤⣀⣀⠀⢀⣀⣤⢠⣄⣀⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠐⢆⠀⠀⠀⠘⢿⣿⣿⣿⡿⠋⠀⠹⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⣿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣯⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠿⣿⠇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠞⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣦⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣿⣿⣷⣶⣿⣿⡿⠿⠿⠛⠋⣹⣿⡇⢰⡏⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠘⣿⣶⣤⣀⣀⣀⣀⣀⣤⣾⣿⣿⢧⣄⣱⠀⠀⠉⠓⠲⢦⡤⣄⣀⣠⣤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⡄⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠛⠻⠿⠿⠿⢻⡀⠀⡐⣿⡧⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠈⠳⠖⢱⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⠤⠤⠴⠚⣏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⢤⣤⣀⣠⣤⣀⡀⢀⢀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⢿⠓⠀⢀⡴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡒⠤⣀⡀⠀⢀⡴⠋⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⠀⠉⠑⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠵⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⢀⡤⠋⣀⣀⣀⣤⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠈⠉⠁⠀⠀⠀⠀⢧⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢐⣶⣆⠀⠀⢠⠈⢇⢰⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠀⠀⠀⣏⣧⠈⠟⠀⠀⠀⠀⠀⠀⠽⡿⠆⠀⠀⠀⢀⣿⣿⣦⣶⣶⠟⠀⠀ ⠀⠀⠀⠀⣀⣸⣿⣯⢧⠤⢤⣤⣴⠦⠀⠀⠀⠁⠀⠀⠛⠿⣿⣿⣿⣿⣿⡁⠀⠀⠀ ⠀⠙⠯⡻⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠰⣄⣠⡇⠀⠀⠀⠀⢸⣿⡿⠛⠛⠿⣆⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⢿⣿⠟⠒⠀⠀⠀⠸⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⣿⠿⠺⢝⡯⢧⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠓⠁⠀⠀⠀⠉⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡒⠒⠛⠁⠀⠘⠒⠒⢲⡶⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠈⢢⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⢠⠇⢀⡤⣀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠊⠁⠀⠈⠳⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣀⠀⠀⢀⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣟⠁⠀⠀⠺⡟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢉⠓⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚。⋆୨♡୧⋆ ˚。⋆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠗⡿⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⡞⢩⣯⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⡹⠁⢰⠃⣩⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⠿⣉⣩⠛⠲⢶⡠⢄⠐⣣⠃⣰⠗⠋⢀⣯⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣠⠬⠦⢤⣀⠈⠓⢽⣾⢔⣡⡴⠞⠻⠙⢳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⣳⠖⠉⠉⢉⣩⣵⣿⣿⣒⢤⣴⠤⠽⣬⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣟⠟⠋⢡⡎⢿⢿⠳⡕⢤⡉⡷⡽⠁ ⣧⢮⢭⠛⢲⣦⣀⠀⠀⠀⠠⡀⠀⠀⠀⡾⣥⣏⣖⡟⠸⢺⠀⠀⠈⠙⠋⠁⠀⠀ ⠈⠻⣶⡛⠲⣄⠀⠙⠢⣀⠀⢇⠀⠀⠀⠘⠿⣯⣮⢦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣥⡬⠽⠶⠤⣌⣣⣼⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣧⣤⡴⢤⡴⣶⣿⣟⢯⡙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣗⣞⣢⡟⢋⢜⣿⠛⡿⡄⢻⡮⣄⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⠮⠴⠵⢋⣇⡇⣷⢳⡀⢱⡈⢋⠛⣄⣹⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣱⡇⣦⢾⣾⠿⠟⠿⠷⠷⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠽⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⡿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣯⡿⣽⡷⣿⢿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣿⣽⣷⡟⣯⣿⣽⣯⣿⣽⠂⠀⢠⣶⣿⡟⣦⠀⣶⣶⣶⣶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣾⣻⠏⠀⠈⣿⣞⠟⢀⣴⣿⣻⢾⣽⣟⡿⣯⢿⣽⢯⣷⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⡀⢀⠻⣾⡽⣷⠀⠀⠸⣻⠀⣸⣟⠾⣽⣯⠷⣻⣽⣟⡿⣾⣻⢧⠀⠀ ⠀⠀⠀⢠⣾⣇⣀⢧⣨⣇⣏⡙⠯⣧⡄⠀⣟⠀⡿⠀⠀⠈⠀⠀⢀⣿⢾⣻⡷⣟⣿⠃⠀ ⠀⠀⠀⠘⢷⡏⠐⠊⠰⠃⠈⠛⢷⡷⣄⡀⠀⠀⡅⠀⢀⣠⣶⡿⠻⠏⢛⡓⠛⠋⠁⠀⠀ ⠀⠀⢀⣤⣦⣴⡶⣶⢶⣴⣤⣀⠀⠙⢟⡿⣦⠀⠀⠀⠛⣉⣴⡴⣞⡿⣟⣿⣻⣗⣦⠀⠀ ⠀⢀⣾⡿⣽⣯⢷⠛⠈⠉⠛⠛⠂⠀⠘⢷⣻⠀⠀⠀⠒⠛⠉⠁⢻⡷⣟⣯⡿⣽⢿⡄⠀ ⣠⣿⢯⣟⣷⣻⢿⣤⣤⡤⠤⠶⣶⠆⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠉⠙⢻⣽⣻⢯⣟⡿⡄ ⠙⠋⢿⣻⣞⣯⣿⣽⠚⢁⣤⡾⠁⠀⠀⠀⣾⠀⣿⣇⠀⠀⢰⣦⣀⣠⣼⢯⣟⡿⣽⣻⢿ ⠀⠀⠀⢿⣽⠳⠏⣠⡾⣟⣷⢿⣦⣤⠀⠀⢸⡄⢸⣯⢿⣶⣻⢾⣟⡿⣞⣿⣽⣻⢯⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⣿⡽⣟⣾⣯⡷⣟⣧⣤⣿⣻⡀⠹⣟⣾⡽⣿⣞⡿⣯⠃⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠻⢿⣧⣟⡿⣿⣻⢧⣟⣧⡇⠀⠘⠟⣿⣧⢿⠻⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣞⣿⣳⣿⣻⣽⢯⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣾⣽⡾⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⢀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀ ⠀⠀⠀⠀⠀⠟⠁⠀
ʕ•̫͡•ʔ
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠉⢳⣰⠋⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀ ⡀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠙⠷⠋ ⣰⠟⠉⠙⢦⡀⢀⣾⡟⠉⠳⣆ ⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠙⢧⡀⠀⠀⠀ ⠀⢀⡴⠃⠀ ⠀⠀⠀⠙⠶⣄⣀⠴⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡾⠲⠶⣤⣀⣠⣤⣤⣤⡿⠛⠿⡴⠾⠛⢻⡆⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⠀⠉⠁⠀⢀⣿⠐⡿⣿⠿⣶⣤⣤⣷⡀⠀⠀ ⠀⠀⠀⢹⡶⠀⠀⠀⠀⠀⠀⠈⢯⣡⣿⣿⣀⣸⣿⣦⢓⡟⠀⠀ ⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣍⣭⣾⠁⠀⠀ ⠀⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣤⡀ ⠈⠉⠹⣏⡁⠀⢸⣿⠀⠀⠀⢀⡀⠀⠀⠀⣿⠆⠀⢀⣸⣇⣀⠀ ⠀⠐⠋⢻⣅⣄⢀⣀⣀⡀⠀⠯⠽⠂⢀⣀⣀⡀⠀⣤⣿⠀⠉⠀ ⠀⠀⠴⠛⠙⣳⠋⠉⠉⠙⣆⠀⠀⢰⡟⠉⠈⠙⢷⠟⠉⠙⠂⠀ ⠀⠀⠀⠀⠀⢻⣄⣠⣤⣴⠟⠛⠛⠛⢧⣤⣤⣀⡾ Search '' kwroppiicafe '' for more!
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡶⣶⢻⣗⣻⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣦⡟⣷⢯⡷⠻⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢬⣿⣳⣿⠝⠉⠀⣠⣄⣤⣶⣤⣠⣄⡀⠀⠀⠀⠀ ⠀⢼⣿⣳⡯⠀⢀⣰⣿⣻⣽⣻⣞⣷⣻⡾⣽⢶⡄⠀⠀ ⢰⣿⣟⣿⠁⢀⣾⣿⣷⠟⠉⣠⣀⣀⠀⠙⢿⣟⣿⣖⠀ ⢸⣿⣿⡅⠀⣿⣿⣿⡖⣠⣿⣿⣿⣿⣿⣄⠀⢺⣿⣿⡇ ⢸⣿⣿⡧⠀⣿⣿⣿⢃⠉⠿⠿⠛⣿⣿⣿⡆⢘⣿⣿⣟ ⠘⣿⣿⣿⠄⠈⢿⣿⣿⣶⣤⣠⣴⣾⣿⡿⠃⢼⣿⣿⡏ ⠀⠨⣿⣿⣯⣂⠘⠻⢿⢿⣿⣿⣿⣟⠟⢃⣰⣿⣿⡿⠁ ⠀⠀⠈⢿⣿⣿⣾⣄⣠⢀⣀⣀⡀⣠⣴⣿⣿⡿⡟⠁⠀ ⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠛⠙⠉⠁⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⠛⠛⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣶⣿⡿⠃⣤⣶⣶⡄⠀⠀⣠⣶⣄⠀⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⣸⣿⡿⠟⠉⠀⠀⣿⣿⣿⡇⠀⢶⣿⣿⣿⠀⠀⣿⣿⡀⠀⠀⠀ ⠀⣤⣿⠏⠀⣀⣀⠀⠀⢻⣿⡿⠃⠀⢸⣿⣿⡿⠀⠀⠛⢿⣿⣆⠀⠀ ⠀⣿⡟⠀⣼⣿⣿⣧⠀⠀⠀⣀⣀⣀⣀⠉⠉⠁⣀⣤⣤⠀⣿⣷⠀⠀ ⠀⣿⠇⠀⣿⣿⣿⠃⠀⣤⣾⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⡆⠸⣭⠀⠀ ⠀⢺⡄⠀⠈⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⢽⣿⡿⠃⢠⣿⠀⠀ ⠀⣾⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣯⠀⠀ ⠀⣿⣿⠀⠀⠀⠀⢻⠿⠿⠟⠁⠉⢻⣿⣿⣿⠏⠀⠀⠀⣰⣿⠇⠀⠀ ⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀ ⠀⠀⢽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀ ⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀ ⠀⠀⠀⣹⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠱⣾⡽⠿⣿⡟⠙⠙⠛⠙⠛⠲⢶⣮⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠀⡀⢠⣴⣶⣾⣿⣥⡦⢥⣾⣿⣿⣿⣟⡾⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢃⣶⣷⣤⣥⣾⣯⣭⣿⠿⠯⠕⢚⣛⣋⣉⣭⢻⣱⡹⣿⣧⡍⣭⣭⣭⣭⣭⣭⣭⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⣻⡏⡏⣥⣦⣤⣶⣶⣿⣿⣶⣿⣿⡿⠿⢿⣇⢻⢷⠽⣿⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣮⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⢻⣹⣿⡄⠹⣿⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡬⣧⢿⣿⡇⢿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣎⠿⣿⣿⣆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠸⣿⢱⣿⣿⣷⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣙⠻⢿⢣⡀⠀⠀⠀⣀⠀⠀⠀⣀⣤⣴⣆⠀⠈⣿⢴⣧⣾⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣷⣎⢿⡀⠀⠘⣿⡟⡔⣛⡲⢬⡛⠿⠂⠀⢻⣮⢹⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⣿⡿⠌⢿⣄⠀⠈⢱⡇⣿⣿⣷⡎⣑⡀⠀⢸⣿⢠⣙⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⡿⢃⣴⣾⡜⣿⣦⡀⠸⢱⣿⣿⡟⣼⣿⣿⣶⣶⣭⣾⠿⠧⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⢡⣿⣿⣿⣿⣬⣿⣫⣴⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⡠⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣛⣛⣛⠻⠿⠛⠻⠿⠿⢿⣿ ⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⢥⣿⣿⣿⣿⢃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠼ ⡟⣻⣩⣭⣧⣾⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣜⠳⣭⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣴ ⣘⣋⣭⠹⣿⣿⣿⡿⢛⢿⣿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣷⣾⠖⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢱⣶⡿⢣⢹⡿⢱⣿⣮⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣛⣃⡎⣿⣯⢩⠹⣿⡄⣍⡻⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⢋⣾⣧⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀ ⠀⠀⡰⠁⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢣⠀⠀ ⠀⢰⠃⠀⠀⢠⣶⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠈⡆⠀ ⠀⢸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠱⠀ ⠀⣸⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⢙⡿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⢘⡇⠐⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⠐⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⠀⠀⠀⠠⡇⢈⠰⡃⠀⢀⣤⣾⣷⣦⡀⠀⠀⡗⢀⠈⡇⠀⠀⠀⠀⡇⠀ ⠀⠀⢳⡀⠀⠀⠐⡇⢀⠸⡁⠀⠘⢿⠿⠻⡿⠏⠀⠀⡆⢀⠂⡇⠀⠀⠀⡜⠀⠀ ⠀⠀⠀⠑⠦⡀⢈⡇⠠⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠂⣇⢀⡤⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣟⡁⠐⢨⡆⠰⣦⠀⠀⠀⠀⣰⡄⠀⣇⠠⠀⢼⠁⠀⠀⠀⠀⠀ ⣀⠤⠀⠒⠠⠘⠋⠄⠂⠉⠷⠛⠻⠒⠒⠒⠖⠛⠟⠚⢃⠠⠐⠘⢂⠀⠢⠐⠠⢄ ⠳⠬⢴⣅⣂⣄⣁⣠⠈⡀⢄⡠⣁⣠⣁⣈⣀⣡⣈⡐⢀⠂⢁⣈⣀⣄⣐⡤⠦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠇⣷⢶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡝⢚⣷⢿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠁⠉⠈⠀⠀⡀⢦⠉⣄⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣼⣫⠛⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⣭⣯⣹⣉⣉⣤⠤⣖⠻⡈⢦⠘⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠇⣳⠴⢯⡴⢀⠀⠀⡄⠤⠢⠛⠈⠀⠀⠀⠀⡟⠚⠒⡀⣦⣷⠿⠤⣶⣛⢍⠤⠶⢰⠀⣆⠘⠋⣿⣴⠀ ⠀⠀⠀⠀⠀⣧⣸⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠣⠋⠴⣠⢀⠀⠀⠀⠀⠀⡀⢄⠶⠓⠉⣀⠀⠀⠀⠀⣄⢹⡇⢀⠀ ⠀⠀⠀⠀⠀⡏⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡄⣷⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⡄⢳⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡀⠹ ⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠑⠀⠀⠀⠃⣾ ⠀⠀⠀⠀⠇⢀⡇⢸⠀⠀⠀⠀⠀⠀⠃⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⣀⣳⣾⠓⣴⠀ ⠀⠀⠀⠀⡟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡏⢠⠀⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠁⡿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀ ⠀⠀⠇⢠⠀⠀⠀⠀⡇⣼⠹⠀⠀⠘⡿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⡇⡾⠀⠀⠀⠀⠀⡇⢹⡀⢳⠀⠳⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⢦⠛⣿⣿⣿⣿⣿⣿⢿⠻⠙⠉⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⠈⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣥⣼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⢷⠀⡶⣶⡠⣤⢦⡴⡷⣯⡿⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠋⢰⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠘⠀⠀⠀⠀⠀⡄⢹⠀⠞⢠⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡼⢀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠈⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢼⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡆⠘⠀⠀⠀⠇⡼⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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