Multiline ASCII Heart Emojis & Text

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⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣶⣤⡀⢀⣤⣶⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
ㅤ⠀⠀⠀⠀ ⠀⢀⣤⣄ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆ ⣠⣶⣿⣶⡀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⠀⣾⣿⣿⣧⠀⠻⣿⣿⠿⠉ ⣰⣿⣿⣿⣿⣿⣿⣿ ⠸⣿⣿⣿⣿⣿⣿⠏ ⠀⠈⠛⠿⣿⣿⡟
remember to downvote any posts that aren't symbols, social media exists for a reason, this website is for symbols not drama! ( ˶ˆᗜˆ˵ ) ༘ ⋆。˚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡠⡀⠹⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠄⡀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠆⡇⠰⠀⠈⠻⠦⠶⠶⠶⠶⠾⠶⠞⠋⠀⡌⠀⡇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⢻⣅⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣂⠀⠀⠀⠀⠀⠀⡿⣝⣺⣯⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀⠀⠀⠘⠫⣷⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠄⠀⠀⠀⠀⠀⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠠⠼⡦⠄⠀⠀⠋⢿⠉⠀ ⠀⣨⣧⠄⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠂⠠⠀⢠⠟⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠹⣧⣄⠀⠀⡒⠉⠉⠈⡃⠀⢰⣆⢠⣶⣄⣼⠀⠐⠠⠀⠒⢁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣄⣿⡆⠀⠀⠀⠀⠀⠘⢿⣇⠀⠈⠀⠂⠐⠁⠀⠀⠛⠛⠁⠈⠀⠀⣀⣤⡴⣷⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢞⣷⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⠴⢴⡤⢦⠤⡤⠤⠤⠶⠶⠚⠛⠉⠀⠀⢨⣿⣦⣀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠴⢖⡶⡿⡈⡹⡑⢢⠌⣪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣦⣷⠱⢌⡒⡌⡝⣜⠣⣑⠅⠎⠇⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠛⠻⢷⣤⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠉⣿⡐⠢⡔⡘⡡⢇⡡⢅⢡⡙⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣆⡀⠀⢻⣧⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⡿⠙⢧⣆⠵⡁⠦⠇⡪⢠⣜⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠹⢾⣀⡀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡾⣅⡎⢆⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠉⠛⠛⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠻⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢲⣶⣶⣤⣼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢾⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⣤⠶⠓⠋⠉⠁⠀⢈⣿⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠨⢿⣀⣀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ REPOST!! i love this website ngl ˖ ࣪⊹ anyways have sum stars bcs ur a star !!
⠀⠀⠀⠀⣀⡤⢤⣄⠀⣠⡤⣤⡀⠀⠀⠀ ⠀⠀⢀⣴⢫⠞⠛⠾⠺⠟⠛⢦⢻⣆⠀⠀ ⠀⠀⣼⢇⣻⡀⠀⠀⠀⠀⠀⢸⡇⢿⣆⠀ ⠀⢸⣯⢦⣽⣷⣄⡀⠀⢀⣴⣿⣳⣬⣿⠀ ⢠⡞⢩⣿⠋⠙⠳⣽⢾⣯⠛⠙⢹⣯⠘⣷ ⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁
⡟⠛⠻⠛⠻⣿⣿⡿⠛⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠐⡀⠂⢁⠟⢁⣠⣶⣿⡄⢹⣿⣿⣿⣿⣿⠿⠿⠛⣉⣉⡄⢹ ⣿⣦⣄⡕⠁⣴⣿⣿⣿⡿⢋⣀⣤⡤⢀⠄⣤⣶⣾⣿⣿⣿⡇⠀ ⣿⣿⡟⢠⣾⣿⣿⣿⣿⠁⢆⣾⣿⡁⢎⣾⣿⣿⣿⣿⣿⣿⡇⢠ ⡿⠟⢠⣿⠟⠻⣿⣿⣿⣿⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⣸ ⡆⢻⣿⡿⠖⠀⠈⢻⣿⢻⣿⣿⣿⣷⣟⠿⠟⠛⠙⢿⣿⣿⠀⣿ ⢁⣾⣿⣇⣤⣴⣾⣿⣿⣮⣭⣬⣭⣾⣧⢄⠀⠒⢶⣿⣿⣿⠧⠘ ⠀⣿⠛⠡⠂⠀⡀⠈⠙⠟⠉⠉⠀⠀⢍⠺⣷⣦⣾⣿⣿⣿⣦⡉ ⣧⠘⣈⣤⡀⠁⠄⡈⠄⡀⠂⠌⢐⣀⣀⠱⠘⣟⡿⣿⣿⣶⠉⣴ ⡟⢰⣿⣿⣿⠀⠚⠄⠠⠐⢀⠂⣿⣿⣿⣿⣶⣬⡺⣹⢲⡞⠆⢹ ⡇⢸⣿⣿⣟⠀⠀⠂⠁⠀⣂⠀⠹⣿⢿⣿⣿⣿⣿⣷⣭⡀⢴⣿ ⣷⡌⠻⡿⠋⠄⠀⠀⠀⠐⠀⠃⠀⠙⢷⣿⣿⣿⣿⣾⣿⣿⣦⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢦⣤⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠛⠃⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢳⣄⢀⡾⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⢿⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠹⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠛⢧⡀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠾⣧⡀⠀⠀⠹⣦⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⢷⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣤⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
.  +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⢥⠤⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠳⣄⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⠀⠀⠀⠀⠀⠤⣶⣛⠉⠀⠀⢈⡳⠖⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠀⣧⠇⠀⠐⠦⢤⣀⠀⠀⠀⠀⢀⣤⠖⠒⠛⠛⠓⠂⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡶⠋⢀⡀⠀⠀⢻⠀⠀⠀⠤⡀⠈⠳⣄⣀⡴⠋⢀⠔⠈⠉⢉⣱⠀⢀⠤⡄⠈⠳⣤⠠⠤⠦⢤⡀⠀ ⠀⠀⠀⠀⠀⣰⠋⢀⡔⠁⣸⠀⠀⠈⠀⠀⠀⠀⠘⢂⠀⠘⠋⠀⠐⠇⠰⠂⠉⠁⠀⠀⠈⠉⠀⠀⢠⠘⣧⠀⠀⠀⢻⡆ ⠀⠀⠀⠀⠀⡟⠀⡼⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⡄⠀⠀⣼⠇ ⠀⠀⠀⠀⠸⡇⠀⠣⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⠀⢀⣼⠋⠀ ⠀⠀⠀⠀⠀⣷⠀⢀⡄⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⣯⡾⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⢷⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢱⡀⠀⠀⠉⢰⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠆⠉⠀⢙⣷⣄⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣚⠁⠀⢙⡶⢃⡴⠋⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⣠⠄⠀⠀⢀⣴⠋⠀⠙⢦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠈⠳⡀⡜⡠⠊⠀⠀⣀⡘⣁⣀⠀⠀⠀⠀ ⠀⠐⠁⠀⢀⡏⡏⠀⠀⠀⠀⠙⠶⣌⠓⠄⣀⠀⠀⠀⠀⡀⠼⣀⣀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀ ⠸⣁⡇⠀⠸⡇⠣⣀⠀⠀⠀⠀⠀⠈⠻⣦⣉⣄⡤⠔⠂⠀⠸⠀⠀⠀⠀⢀⡴⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠶⢤⣭⣴⣦⣶⡾⠾⠟⠛⠙⢷⣄⡀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⢀⣠⣎⡁⢲⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡂⠀⠈⠛⠲⣄⡴⠞⠁⠀⠀⠀⠀⠀⠀⠨⡌⢪⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣖⡋⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⠆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠚⡛⢻⠑⢶⣄⠀⣠⠔⠋⠉⠙⠻⣷⣦⡀⢀⣴⣦⠀ ⢠⡟⠀⡴⠋⢸⡄⠀⣿⣶⣧⣤⣤⡀⠀⠀⢻⣿⣿⡀⠙⠉⠀ ⣾⡄⠀⣿⣄⡸⣇⣴⣿⠿⣿⣿⣿⠇⠀⠀⢸⣿⣿⡇⣢⣤⡄ ⢹⣷⡀⠈⠻⠿⡿⠿⠋⠀⠀⠈⠀⠀⠀⠀⣼⣿⡿⠀⠘⠛⠁ ⠀⠻⣿⣷⣤⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠻⣿⣆⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠈⠻⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⣠⣤⣤⣴⡿⠛⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠙⠀⢀⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡿⣦⣀⣠⡿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⡁⢹⡏⠂⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⢘⡇⠁⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣶⣾⢿⡿⣷⣶⣤⡀⠀⠀⠀⠀⢀⣠⣶⢾⡿⡟⠙⣶⣦⣄⠀⠀ ⠀⣴⣿⡟⣾⢽⣻⣽⢯⡿⣽⣿⢧⡀⠀⣰⡿⣯⣟⣯⠟⠁⠠⡹⢿⣾⣷⡀ ⣼⡿⣾⢽⣹⣞⣷⢿⣯⣟⣷⣻⣿⢷⣼⢿⡽⣷⣧⣤⣀⠀⢀⢤⣦⣴⣿⢷ ⣿⡽⣷⣫⣷⢿⣽⣻⢾⣽⢾⣳⡿⣿⢯⡿⡽⠷⣯⢿⣽⡆⢸⣿⢯⣟⣿⣿ ⣿⣟⣷⣻⣽⣻⢾⣽⣻⠹⣿⣽⣻⡽⣯⢿⣇⣀⣾⣟⡾⣿⣸⣟⣯⢿⣟⣾ ⠸⣾⡽⣯⡷⣟⣯⣷⡏⠀⢿⣞⡷⣟⣯⡿⣽⣻⢷⣯⣟⣷⣻⣞⣯⣿⢿⡍ ⠀⠹⣟⡷⣟⣯⡷⣯⠁⢰⠸⣿⣽⣻⢷⣻⢯⣟⡿⣾⣽⢾⣳⣯⣿⢯⡟⠀ ⠀⠀⠙⢿⠽⠗⠛⠁⠀⠀⠂⠌⠓⠻⢯⣟⣯⡿⣽⠋⠈⢻⣻⣾⣟⠏⠀⠀ ⠀⠀⠀⠈⠳⣶⣤⡀⠀⠀⡠⣶⣶⣾⢿⣯⣷⣟⣿⣳⣴⢿⣟⡷⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⡄⢸⣽⢿⡽⣾⣻⣮⣀⣽⣾⣳⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢣⢨⣿⢯⣟⣷⢯⡷⣿⡽⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠻⢯⣟⡾⣿⡽⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⣲⠤⠤⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⣥⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠛⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀ ⠀⠀⣀⡴⠋⣰⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀ ⢠⠋⠁⠀⢰⠉⢸⢠⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀ ⢸⠀⠀⠀⣼⠀⠀⠉⠀⠀⠀⠀⠀⠀⣆⣿⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⣧⠀⠀⠀ ⠀⠓⠤⠴⠤⢛⠜⠒⠒⢄⢀⠤⠤⣄⠉⡄⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠓⣄⠀ ⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠁⠀⠀⠀⣶⣀⣀⣠⡦⠺⡀⠀⠀⠀⠀⠀ ⠀⠀⢆ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢺⣐⠀⡗⢆⡀⠀⠀⠀ ⠀⠀⢸ ⠀⠀⠀⠀⠀⠸⡘⢦⡀⠀⠀⢀⣀⡖⠷⠶⠒⣺⣀⠖⠁⠀⠑⠲⣆⣀⣀⡠⠊ ⠀⠀⠀⠀⠀⠀⠙⠶⠷⠶⠖⢻⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⣀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡛⠛⢿⣿⡿⠛⡉⣍⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⠁⠙⢷⣤⠙⢁⠄⠀⠈⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠠⠀⠈⢉⣓⣶⣁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠁⠂⡀⠐⠺⠻⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢷⣄⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡭⣿⣿⣿⣿⣿⣿⠃⢠⣾⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣺⣿⣿⣿⣿⣿⠇⢀⣾⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠀⣸⣿⢃⣾⣿⣿⣿⣿⣿⠛⣿⣿⡿⠿⢿⣿⣿⠿⠿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠟⣡⣾⠏⠠⢈⡉⢿⣿⠀⢸⣿⠁⠁⣸⣿⠃⢀⠟⣠⣿⢿ ⣿⣺⣿⣿⣿⣫⠀⢠⣿⣿⡧⢀⣞⣈⠃⢘⣋⠀⠘⣿⡇⠀⣿⠏⠀⢸⣿⣿⢋⣼ ⣿⣿⣿⣿⣿⣿⠀⠸⣿⡿⣠⡈⠟⢁⣼⣿⣿⡇⠀⣿⢁⣿⣿⣇⠅⢿⡿⣣⣾⣿ ⣿⣿⣯⣿⣿⣿⡇⠀⠛⣱⣿⣿⣿⣿⣿⣿⣿⣿⣄⣥⣾⣿⣿⣿⣷⣶⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿hhgvl⣿⡟⣿⣿ ⣿⣇⠀⠹⣿⣿⣿⡟⣸⣿⣿⠋⢰⣿⣿⣦⡙⣿⣿⡯⠁⢰⣿⣿⣿⣿⣿⡇⢸⣿ ⣿⣿⣧⠀⠽⣿⡿⢰⣿⣿⡏⠀⣿⣿⣿⣿⣷⠸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣧⢸⣿ ⣿⣿⣿⣷⡀⠙⢣⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿ ⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⣿⣇⠀⢸⣿⣿⣿⣿⣿⡿⢸⣿ ⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⡇⣿⣿⡄⠈⣿⣿⣿⣿⡿⢃⣼⣿ ⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣦⡈⠿⣿⣿⠟⣡⣿⣿⣿⣶⣄⣙⣛⣋⣤⣾⣿⣿ ⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⢸⣿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀⠀⣼⣿⠀ ⠀⠻⣿⣷⣮⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
⠀⣠⠴⠚⡙⠙⠲⣤⣠⠖⢋⡛⠙⠲⣄⠀⠀ ⣴⠃⣰⠟⠉⠙⢦⡈⢁⣾⡟⠉⠳⣆⠸⣇⠀ ⣿⠀⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿⠄⣿⠄ ⠸⡄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⡏⠀ ⠀⠙⣆⠙⢧⡀⠀⠀⠀⠀⢀⡴⠃⣰⠏⠀⠀ ⠀⠀⠈⠳⣄⠙⠶⣄⣀⠴⠋⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢦⡈⢡⣰⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⠿⠛⠛⠛⠛⠛⢿⣷⣤⣾⠿⠛⠛⠙⠛⠛⠿⠗⠀⠀⠀⠀ ⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⡿⠁⠀⢀⣤⣀⠀⠀⢀⣤⣶⡆⠀⠀ ⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⣄⠀ ⠀⢹⣿⠀⣿⣷⣄⣀⣤⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷ ⠀⠀⣁⣤⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠛⠛⠛⠻⣿⣿⣿⠋⠉⠀⠀ ⠀⠘⠻⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⠟⢙⠛⠛⠀⠀⠀⠀⠀⣀⣴⡿⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠈⠻⢿⣦⣄⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⢦⣄⠀⠀⠀⠀⠀⣴⠟⠛⢧⣠⣶⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠦⠌⠛⠉⠉⠉⢹⠇⢠⣶⣼⣷⣞⢙⣧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠃⠀⠀⠀⠀⠀⠀⣿⠀⠈⢻⡃⠀⢸⡿⡄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⠛⠛⠛⢿⡗⢋⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠾⣷⠆⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⢺⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⡦⠀⠀⠛⠃⠀⠀⢠⢶⣄⠀⠀⠈⠛⠀⠀⠀⣺⠓⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣖⡀⣀⣀⡀⠀⠈⠉⠉⠀⠀⣀⣀⣀⠀⣲⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡆ ⢻⡈⠻⣦⣀⣀⣀⣀⣀⠀⠀⠀⠁⣴⠟⠉⠁⠀⠉⠛⢦⡀⢀⡴⠛⠉⠁⠈⠙⠻⣄⠀⠁⣀⣠⣤⣤⣤⣤⡤⠖⠋⣸⠇ ⡿⠳⣤⣀⡀⠀⠀⠉⠉⠉⠳⢦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣦⡞⠉⠀⠀⠀⠀⠀⢀⣠⠶⢻⡆ ⠻⣦⣀⠀⠀⠀⡴⠶⢦⡀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⠚⠳⡄⠈⢉⣀⣠⡾⠁ ⠀⠸⣍⣉⣁⡀⣇⠀⠀⠑⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⡀⠀⠓⠀⢀⡇⢤⣈⣭⠿⠁⠀ ⠀⠀⠀⠙⠷⠤⠿⠶⠦⠶⠞⠋⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠈⠻⠦⠴⠖⠻⠶⠶⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀꒰♡˃̶̤́ ꒳ ˂̶̤̀ ꒱꒰♡˃̶̤́ ꒳ ˂̶̤̀ ꒱😇😇𓆩♡𓆪𓆩♡𓆪𓆩ꨄ︎𓆪𓆩♡𓆪☆
⠀⠀⠀⠀⠀⠀⡀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠒⠈⠁⠑⠀⠢⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠁⠓⠂⣄⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀ ⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡄⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀ ⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅ ⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁ ⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀ ⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⠀⠀ ⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⢿⡿⣁⠀⢆⡘⠤⡘⠠⢰⠃⡄⠂⠄⠀⠀⠀⠀⡀⡆⠌⢄⠀⠀⢠⡇⠂⡌⠄⠀⠀⠀⠀⠀⠀⠡⣖⠀⢃⠸⠀⠸⣟⡄⠘⡽⡜⡄⠀⠀⠀⠈⠦⠀⠀⠀⠸ ⣿⣿⣿⣿⣿⣿⡿⠁⠈⢻⡝⣟⣷⡿⢁⠤⢀⠢⢌⠰⡀⠂⡟⠠⡄⠈⠀⠀⣀⠤⠐⣰⠌⡈⢄⠂⡡⣺⠄⡇⠰⠈⡄⢃⠰⢀⠰⢀⠂⢽⠂⢼⠐⡠⠄⣿⡼⡀⠱⢹⡰⠀⠀⠀⠀⠀⣆⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠁⢄⠠⢀⣹⣞⡿⢁⢊⠰⢀⠎⡐⢂⠁⢳⠋⠴⠁⠀⣠⠞⡠⢁⣺⡇⠤⢁⠢⠘⢠⡿⢰⡏⠄⢃⡐⢈⠰⢈⠰⢸⠌⣸⠌⢺⡐⠤⢈⣽⣧⢩⡄⢉⢧⠡⠉⡍⠒⠤⣸⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⠩⡐⠌⢿⡯⣿⠇⡌⠢⢡⠈⡔⠈⠂⠃⢾⢈⠒⠀⡴⢁⡾⠑⣸⢻⢀⠒⢠⠂⡉⢼⡇⢸⡇⠌⠄⡄⢃⠰⢈⠰⠸⡂⢼⢈⢹⠆⠰⢸⢿⠸⡆⢷⢈⠸⣄⠃⠤⢉⡐⠨⣧⠀⡀ ⣿⣿⣿⣿⣿⣿⡟⣿⣻⢾⡷⣿⠐⡄⢃⠆⠈⠐⠁⠀⠀⣾⠸⠀⢀⡇⣼⠇⢡⡏⣇⠢⠘⡀⠆⢡⡎⡇⢺⣇⠘⢠⠐⠨⡐⢂⠢⢡⡇⠾⢈⢸⡃⡘⢼⢸⠀⢻⠈⣇⠌⣷⢈⡐⠂⠤⢱⢿⠀⠔ ⣿⣿⣿⣿⣿⣿⣯⡚⢧⡻⣽⡏⠰⡈⢄⠈⠀⡀⠀⠀⠀⣿⢸⢀⢂⢸⡟⡈⢼⢳⠁⢂⡁⠆⡑⢺⢱⡇⣼⢿⠈⠄⡈⠡⢐⠠⢁⢺⡄⡟⡀⢺⢁⡴⡿⢸⢄⠈⡇⢺⡆⢸⡆⠤⢉⠰⢐⣸⠈⠔ ⣿⣿⣿⣿⣿⣿⣿⣷⠁⢿⣹⡇⠡⠌⠀⠀⠀⠀⠀⠀⢀⡿⣸⠀⢂⣿⢃⠐⡞⡼⢈⣄⣐⣤⡴⡯⢼⠴⡿⢼⠾⠶⠶⠶⣤⠂⠌⣹⢰⡇⡐⡏⢸⢡⡇⡽⡀⠑⢳⠐⣷⠀⢿⡇⠌⡐⠂⡽⢈⡐ ⣿⣿⣿⣿⣿⣿⣿⡏⠠⣄⣿⠄⠀⠀⠀⠀⠀⡅⠀⠠⢠⡟⣧⠈⣰⣿⠀⣼⠴⡗⢉⠉⡐⢠⢷⠃⢸⢠⠃⢸⣿⠀⢀⠂⢸⠀⢂⡏⣼⠁⣸⠁⡏⡜⡇⡧⠬⣴⣼⣀⢿⢇⢸⣹⠀⠀⡁⠇⡃⠄ ⣿⣿⣿⣿⣿⣿⣿⣇⡷⠊⢸⠀⠀⠀⢠⣦⣄⠇⡈⢁⠆⣿⣧⠐⣽⡇⠐⣾⢰⡇⢂⠡⢈⡏⡞⠀⡼⣸⠀⠀⣿⠀⠀⠂⣏⠐⢸⢡⡟⢀⡏⣼⢱⠁⣧⠁⠀⠀⠈⡟⣻⠺⣤⣿⡆⠐⠀⡇⠄⡈ ⣿⣿⣿⣿⣿⣿⣿⣿⣄⠂⣿⠀⠀⢠⠃⢿⣣⠐⠠⠌⠠⣿⣿⠀⢿⠃⢌⣿⠸⡇⢀⢂⡼⡼⠀⢀⢧⡯⠄⡀⣿⠀⠌⢰⡇⠈⣼⡿⠁⡞⣸⢇⠇⢰⡟⠀⠀⠀⠈⡇⡝⠀⢇⡟⡧⣄⠂⡇⠀⢰ ⣿⣿⣿⣿⣿⡿⢭⢿⣿⣶⣻⡆⠀⡏⠠⠸⡽⣏⠐⡈⡐⢿⣻⡠⣿⠈⢸⡍⣆⣧⣾⣾⣿⣿⣶⣾⣾⣆⠄⠀⣿⡆⠀⣸⠁⣸⡿⢁⡞⡕⡹⡌⠀⣼⢁⠤⠤⢀⣀⡇⡇⠀⠸⣼⡇⠀⠑⣷⠈⣸ ⣿⣿⣿⣿⣿⡹⢎⣗⡻⣿⣷⣇⠘⣇⠄⡁⢻⣽⡆⠡⠠⢹⣿⡓⣿⣴⣿⣿⣿⣿⡿⣟⣿⢫⣟⣏⠉⠙⠛⠶⣿⢿⠀⡞⢀⡟⢡⣾⠊⣰⠟⠀⣼⠃⣐⣤⣴⣦⣤⣧⣇⣠⠀⣿⡇⠀⡁⡏⠀⡿ ⣿⣿⣿⡟⣧⣛⡭⢶⡙⣿⢻⣿⡄⢻⡔⠠⡈⢧⢿⡆⢡⠈⢿⣇⣷⣿⡿⠛⣯⢽⡳⢧⡞⡷⠎⣽⡀⠀⠀⠀⠛⠘⠻⢣⣞⣴⠟⠁⠠⠏⠀⠐⠁⢸⣿⢿⣟⠿⣿⡿⣿⣷⣤⣸⡂⠀⢸⠃⢰⠇ ⣿⣿⡿⣹⣧⡓⢾⢷⡟⢸⣯⢹⣷⡌⢻⣄⠱⣌⠳⣿⣦⠲⠾⣿⣿⣿⠁⠈⣟⠊⢿⡧⢿⠃⡜⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣟⡳⢾⡻⡴⢷⠈⠻⣿⣿⣟⠋⡟⢀⡎⠄ ⣿⣿⠳⣽⠲⣝⡿⢸⡇⣸⠙⣷⢺⣿⣧⡻⣷⣌⢢⡙⢽⣷⣤⠘⢧⠙⢦⡀⢻⡌⠠⢠⢁⠒⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⣹⡏⠵⡙⣺⠀⠀⠸⣿⣿⣾⢁⡾⠀⣲ ⣿⢫⡝⣾⢹⣾⢃⢹⡇⢼⠂⣿⣹⠋⢉⡿⣾⣿⣷⣌⠲⣽⢿⣿⣮⣷⣀⠈⠀⠙⠗⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢈⠩⠀⡥⠲⠏⠀⠀⣸⢟⣽⣫⡟⢁⣴⢏ ⣏⢷⣙⣮⠟⡐⠢⢼⡇⢸⡿⢧⣟⠀⡇⡄⣤⢩⢿⣛⢷⣤⣭⣛⢿⣮⠉⠳⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢷⡼⠆⠀⠀⠐⠁⣿⣿⣋⣴⣾⢋⣾ ⣞⢺⣼⠏⡐⠌⡁⣿⡇⢸⡇⠼⣿⠀⢷⠀⢹⡆⣿⡉⠚⠶⣭⣻⣿⡟⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢫⣿⡳⣵⡿⢿ ⣎⡿⢼⠂⡅⢊⠔⣿⣵⢺⡏⠄⣿⣧⡈⠓⢌⠷⢾⡇⢁⠢⢀⢹⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣬⡿⢣⡓⣸⣇⢻ ⣾⣃⡯⢼⣀⠣⣈⣿⡽⣺⠛⢠⠹⡻⣿⣦⡀⠑⠪⣇⠂⠔⡈⡾⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⠟⡞⠡⢠⢰⣿⠸⣸ ⣿⣿⣳⢯⣿⣿⣿⣷⣽⣹⡇⠌⣷⢳⢋⠻⢿⣦⣀⡟⡀⠊⢰⡇⠂⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠈⢺⡞⠠⢁⢂⣯⡏⠵⡘ ⣿⣿⡜⣿⣿⣿⣿⣿⢾⣻⣧⡂⢹⣏⣿⡄⠌⢻⣿⣧⠀⠡⣸⠠⠁⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠫⣦⠀⠀⢀⠔⠁⠀⠀⠀⡀⠀⠙⢦⢁⡞⣼⡙⢦⠑ ⣿⣿⡽⣹⣿⣿⣿⣿⡯⣷⣯⢿⣄⠻⣜⣷⡈⠄⢻⣷⠈⢠⡗⠠⠁⣿⢸⣄⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠀⠀⠀⠀⠀⠀⡰⠂⠤⣀⠀⠀⢀⣃⠀⣰⠁⠀⠀⡴⢴⣧⠀⠀⠀⠀⠙⢦⡏⡝⢢⠌ ⡿⣿⣿⣽⣿⢿⣿⣿⡷⣣⢿⣯⣻⢷⣽⢞⣿⡄⠂⣿⠀⣸⠃⠠⢁⣷⠸⡇⠑⢤⡀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠈⢧⡀⢿⣿⣾⡿⠁⡠⢊⣴⣿⢸⡷⣄⣐⠀⢀⠄⠙⠓⠧⣌ ⣿⣷⣿⣿⣿⣿⣿⣿⡿⣵⢫⣷⣏⣟⣾⣻⣾⣿⣆⢿⠀⡿⠀⠀⠂⣼⠐⣿⡀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠑⠮⠿⠛⠒⢈⣴⣿⣿⡏⡾⢁⠈⣿⠖⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣯⣟⣷⢯⣿⣿⣿⢰⠃⠀⠀⠐⢸⠀⣻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⡀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣃⠇⢂⢡⠏⠀⠀⠀⠀⢀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢾⡻⢷⣯⣿⣼⠀⠀⠀⢀⡼⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⡀⠀⠀⠀⠀⠈⠢⣤⣾⣿⣿⣿⣿⣿⣿⣿⢸⠠⡱⠃⠀⠀⠀⣠⣶⠋⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⣽⣯⣞⣽⡟⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣿⢀⡜⠁⠀⠀⣠⡞⡱⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⢿⣿⣿⣿⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡼⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣞⢾⡹⡿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⣠⣿⣿⣿⣿⣦⣄⠀⠀⠀⠻⣿⣿⡟⠀⠀⣠⠂⢺⣿⡣⢀⢀⠄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣾⣿⣧⢶⡶⣿⢿⣿⣦⣤⣀⣀⣀⣤⣀⣴⣶⣤⣤⣄⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢠⣾⣿⣾⡷⣰⠉⡆⣹⣿⣿⣶⣿⣆⡀⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣯⢷⣏⡿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⡿⠕⠉⢆⢱⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⣾⣹⡞⣷⡽⣞⡽⣯⢿⣹⢯⣿⣿⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢪⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡽⣶⢯⡽⣞⣳⢯⡽⣞⣯⣽⢫⣿⡟⣿⣻⢿⡽⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⣛⡾⣽⣹⡽⢾⣹⠷⣞⣞⠿⣼⣿⡘⣯⣾⣿⢿⣹⢯⣟⡿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠻⣿⣿⣿⣿⣿
⣀⡤⢤⡀⠀⣠⠖⣶ ⢻⡇⠀⠹⡞⢃⡼⠏ ⠀⠙⠷⠦⣤⠏⠁⠀
⠀⠀⠀⠀⠀⠀⢀⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⠀⠀⠀⢀⣄⠘⠀⠀⣶⡿⣷⣦⣾⣿⣧ ⢺⣾⣶⣦⣰⡟⣿⡇⠀⠀⠻⣧⠀⠛⠀⡘⠏ ⠈⢿⡆⠉⠛⠁⡷⠁⠀⠀⠀⠉⠳⣦⣮⠁⠀ ⠀⠀⠛⢷⣄⣼⠃⠀⠀⠀⠀⠀⠀⠉⠀⠠⡧ ⠀⠀⠀⠀⠉⠋⠀⠀⠀⠠⡥⠄⠀⠀⠀⠀⠀
⠀⣠⣤⣶⣶⣦⣄⡀⠀⢀⣤⣴⣶⣶⣤⣀⠀ ⣼⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠠⠤⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠐⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠀⠀:¨ ·.· ¨: ⠀⠀⠀⠀⢰⡿⠉⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⠃.⠀⠀`· . ꔫ⠀ ⠀⠀⠒⠒⠸⣿⣄⢀⣃⣿⣿⡟⠉⠉⠉⢹⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠚⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠠⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠁⠀⠒⠤⠀⠀⠀⠀ ⠨⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀ ⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⠀⠀⠀⣠⣴⣶⣿⣿⣶⣤⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⢀⣴⣾⣽⣿⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣄⣠⣤⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣠⣤⣤⡀⠀⠀⠀⠀ ⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⠿⠛⠉⠁⢠⣾⣿⣾⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠙⠻⠋⠀⠀⠀⠈⠃⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⢤⣴⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡌⠛⠻⢿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⡀⢀⣤⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣄⠀⠀⠀ ⠀⠀⢀⣤⣤⣤⣀⡉⠛⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣤⣤⡀ ⠀⣰⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣶⡄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠸⣿⣿⠿⠟⠃ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣤⣤⡀⣠⣤⣤⣄⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣸⣿⣿⣿⣷⣿⣿⣿⣿⡇ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⣷⣦⣴⣤⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠸⣿⣿⣿⠟⠀⠀⠈⠻⣿⣿⣿⣿⡿⠟⠉⠀⣾⣿⣷⣶⣦⠙⢿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⠀⠀⠘⣿⣿⠿⠋⠀⠀⠈⠛⠿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣲⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣷⣦⣀⣞⡿⠋⠉⠉⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠈⠻⣿⠃⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⡄⢀⣄⣤⣄⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⣿⣦⣀⠀⠀⠀⠀⢻⣿⣿⠿⠿⠿⢿⣶⠀⣰⣿⠀⣠⣖⣲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠁⠀⠀⠈⠻⣿⣷⣀⠀⣴⡿⡟⠁⠀⠀⠀⠈⣿⣷⣿⣷⣎⡿⠛⠋⠻⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⡀⠀⠀⠀⠀⠀⠹⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⢻⡟⡟⠈⠉⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⢿⣟⡅⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢨⣻⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣧⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⠀⠀⠀⠀⠀⠀⢀⣾⡏⢀⣴⡿⣷⣶⡿⣷⣦⡀ ⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣷⡄⠀⠀⠀⠀⢠⣶⡏⠀⢸⡏⠀⠈⡟⠀⠈⣿⡇ ⠀⠀⠀⠈⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠙⣿⡆⠀⠀⣠⣯⠏⠀⠀⠈⣿⡄⠀⠁⠀⢰⣿⠁ ⠀⠀⠀⠀⣜⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠹⣿⡄⣰⡿⠃⠀⠀⠀⠀⠻⣿⡄⠀⢠⣿⠋⠀ ⠀⠀⠀⠀⠀⠹⣿⡇⡀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠉⠹⠏⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⣿⣯⡄⠀⠀⡤⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣢⡎⢜⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡔⢒⠲⣒⣤⣲⡀⢒⣒⠢⢄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠖⢉⡤⣝⢶⡷⣿⡾⣟⡷⣫⣷⣻⣟⣷⣶⣤⡘⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢼⠿⠻⣟⣛⣛⠠⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠠⠛⡜⠇⡃⠇⠘⠻⠼⣇⠿⠧⠿⠃⠟⠿⡇⠿⣧⡿⣼⣟⣿⣿⡠⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⢽⣴⣾⣿⢿⣟⣿⣼⣻⢷⡶⣤⣤⣉⠢⢄⠀⠀⣠⠊⡁⣀⡶⣒⡲⣽⢳⢟⣻⡝⡷⣶⣤⣀⠐⠻⣒⠒⠲⠤⣤⠉⢿⣽⣿⣿⣿⡇⢸ ⠀⠀⠀⠀⠀⠀⢀⣔⣟⣶⣿⣿⢿⣾⡿⣿⣾⣞⢿⣿⢣⡿⡽⢮⣽⣳⣄⠁⠉⢂⣴⢛⣭⡻⣜⣳⢻⡽⣎⡷⣫⢻⢳⢜⣿⣿⣦⡈⢦⡀⠀⠈⣷⠂⣿⣿⢿⣿⢐⣾ ⠀⠀⠀⠀⠀⣠⣏⣾⣿⣿⣷⢟⡋⠔⡱⢀⡁⢏⠿⣾⣹⣝⣻⢧⢞⡶⣣⣟⣯⡽⣼⢣⣳⣹⠶⣪⢿⡰⣏⢷⠩⣞⢧⢛⣼⡝⣿⣿⣦⠘⣄⢤⡓⢨⣿⣿⣿⡏⣼⠃ ⠀⠀⠀⠀⢠⣿⣾⣯⣿⣿⢃⢎⠄⠸⠜⡄⢐⡆⠄⠸⡷⢮⣟⡮⣟⡼⣣⢯⣶⢫⠵⣏⠷⣵⢚⡵⠾⢗⡾⢭⡳⡽⢮⣼⢺⣿⢸⣿⣿⣧⠈⠏⢡⣾⢿⣿⠏⣰⠃⠀ ⠀⠀⠀⢀⡿⣿⣿⣿⣿⣯⢱⢊⠎⠄⢫⠀⠠⡌⠀⢠⣽⢯⣶⢻⡬⣷⠟⣮⣞⡙⡾⣭⢟⡞⢧⣺⣽⡡⢟⡧⠱⣟⣳⢩⢿⣳⡭⣿⣿⣿⢃⣸⠿⣿⡿⢋⡾⠁⠀⠀ ⠀⠀⠀⢸⣽⣿⣿⣿⣿⣻⣄⢣⢃⢚⡱⠄⢁⢣⢠⡾⣭⡟⣯⣻⣹⣎⡟⣷⢫⣳⢻⡕⢮⡻⣼⢲⠮⡕⣻⡵⢏⡗⣏⡞⣯⣗⢾⣿⡟⢁⣼⣳⣿⠏⣴⠋⠀⠀⠀⠀ ⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⣟⣿⣦⡼⣴⣣⣾⣻⣿⢽⣳⢯⣿⢾⣱⢯⡞⣯⣗⣏⡽⢯⣫⢷⣑⣫⢷⣍⢧⡽⡺⣜⢷⢸⣷⢫⠛⢁⣤⢿⣾⠟⢁⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⢿⣽⣳⡿⣼⢯⡿⣗⡿⣻⡼⣷⡏⣷⣾⣹⣻⡝⣶⢏⣶⢫⡟⣜⣫⢶⣹⣏⠯⡗⠋⢁⣠⣿⣾⠛⣁⢨⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣟⣿⣷⣯⣿⣾⡷⣿⣽⢯⣿⡷⣟⣧⢻⣳⣍⣷⣭⡗⣯⣽⡽⣾⡭⣗⣯⣜⡷⣗⡮⡯⠋⣀⣶⣿⡾⢋⣥⣾⠏⡺⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣟⣾⣿⣷⣟⣿⡾⣟⡾⣽⣹⢞⡷⣻⡗⣮⡷⣹⡾⣽⢺⣵⢯⣳⣞⣞⠯⠟⢁⡰⣦⡿⢟⣡⣴⣿⣿⠏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣾⣻⣽⣷⣻⢷⣻⣯⢾⣽⣳⣽⡳⣭⣿⣹⡾⣽⣞⡿⢞⢁⣰⣧⣿⠿⣋⣤⣿⣿⣿⣿⠋⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣫⡿⣿⣿⣿⡾⣿⣿⣷⡿⣟⡷⣯⣿⣳⣟⡾⣽⣓⠾⣽⡳⣿⠷⠟⣉⢁⣰⣮⣿⠿⣛⣡⣾⣿⣿⣿⡿⡟⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣻⡏⠛⢿⣿⢿⣿⣿⣿⢾⡿⣟⣿⣿⣳⣯⣿⡽⣞⣯⣟⡿⠙⢃⣥⣼⣿⡿⡟⣫⣴⣾⣿⣿⣿⣿⡟⢫⡵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠻⡽⣿⣿⣿⣿⣿⣻⣾⣿⣽⡿⠹⠟⣉⣤⣶⣾⣿⡿⠛⣥⣵⣾⣿⣿⣿⣿⡿⠿⣁⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣢⢀⣀⠀⣀⢈⣓⣯⣟⣿⣿⢿⢻⣍⣾⣴⣿⣿⣿⠿⢻⣹⣴⣾⣿⣿⣿⣿⣿⣿⡟⣫⡵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣽⣾⣷⣾⣿⣿⣿⣿⣿⠛⣭⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⢫⣥⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢭⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠞⠛⠃⠉⠁⠉⠚⠿⣛⢿⣿⠿⡟⣟⡭⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠑⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡻⣟⡻⣏⢿⡹⣏⢿⣹⣳⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡑⢂⠰⢀⠣⢎⡝⢮⡹⣝⢯⢯⡑⠈⠀⠀⠈⠙⠯⠉⠉⠉⢻⡉⠉⠉⠉⠹⡖⢆⡀⠢⡜⣱⢖⡀⠀⠀⠈⠀⠀⠉⠉⠈⠉⠩⠉⠁⠀⠀⠈⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣶⠸⣿⣆⠀⠀⢀⣾⣋⣿⢧⡀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣗⣯⢳⣯⢳⣻⣼⣫⢶⣏⠾⣥⡀⠀⠀⠀⠀⠀⠀⢠⢉⠆⡁⠀⠀⠀⠉⢎⣜⢣⡕⣫⢞⢢⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠉⠀⠀⠀⠑⠈⠂⠀⠡⢌⡱⢊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢜⣂⢹⣿⠀⠀⣸⣿⣿⣿⠢⡵⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⡼⣭⢿⣜⡯⣗⢯⡽⣣⣟⡻⡜⡵⠀⠀⠀⠀⠀⠀⠄⡊⠔⠀⠀⠀⠀⠀⠈⠌⠦⣙⠦⣋⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢏⣼⢻⣿⠀⢀⣿⣿⣿⡳⠽⣜⡣⠄⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡝⣧⡟⣮⢷⣹⢧⣿⣱⢯⣳⣙⢮⡁⠀⠀⠀⠀⠀⠐⠐⠆⡀⠀⠀⠀⠀⠀⠀⠂⠱⢊⠄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢹⣿⠀⠈⣿⡟⣷⣏⠿⣼⡹⣖⡀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⠾⣵⢻⣝⡾⣹⡞⡶⢯⡟⣶⡹⡞⡄⢀⠌⠀⠀⠀⠀⢳⡀⢆⡁⠀⠀⠀⠀⠀⠀⠁⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡀⠀⠀⠀⠀⠡⢘⠸⣿⣄⣰⣿⣷⣿⢾⡹⢶⡹⢖⡽⣀⠀⠀⠀⠀⠀⡀⠸⢿⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢻⡭⣟⣮⡝⣧⢿⡹⢧⡻⢶⣏⡳⢠⡾⠀⠀⠀⠀⢀⣼⡃⠖⠤⡀⠀⠀⠀⢀⠐⠈⠀⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠂⡌⠠⠐⡀⠂⠌⡀⢈⢀⣙⣻⣿⣿⢿⡹⣞⡽⡳⣝⣫⢞⡥⠀⠀⠀⠀⠀⠟⠀⢬⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢫⣷⣛⠶⣝⡧⣏⡟⣧⣝⢣⠚⣡⡿⠁⠀⠀⠀⠀⢮⣼⢁⢎⡱⡱⢠⣀⠂⠄⢀⠀⡈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠠⢎⠰⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡄⣂⠀⠀⠀⣄⢣⡝⡼⣡⠣⢄⠁⠄⡐⠀⡀⢤⣿⢿⣛⡮⢷⡹⣞⡵⣫⡜⡯⢶⡁⠀⠀⠀⠀⢈⠀⠈⢿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢳⣏⣾⢻⣜⡳⣽⣞⡷⢊⠇⠄⣿⡧⠁⠌⠀⠀⣠⢳⡿⣘⠦⡱⢡⠇⣌⢳⢊⠀⠠⠀⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⡘⢦⠱⡀⠀⠀⠀⠀⠀⢂⠡⢌⡳⣜⣱⢊⡄⡘⠴⣋⢾⣱⢃⡳⢌⠂⠔⡀⠁⠀⠈⣿⣾⢭⡟⣧⢟⡵⣚⣥⢻⡜⣧⢓⡀⠀⠀⠀⠘⠀⠀⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢣⡿⣜⡳⣎⢷⣹⢾⡝⠀⠀⣠⡟⣡⢉⠀⠈⡐⢦⣛⠦⣍⠶⣭⢓⠚⣌⠳⣎⠤⢁⠘⠠⡁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡈⠴⣚⢴⣋⣆⠀⠀⠀⠀⠀⡀⢂⠱⠸⣔⣫⠖⡴⣡⠣⡝⣎⢧⢏⡜⠢⠌⠀⠀⠂⠀⠀⠘⣿⣧⣻⡝⡾⣽⡹⣎⢷⣙⢮⡳⢆⠀⠀⠀⠀⠁⠀⠀⢸⣿⣳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢣⣟⣭⢳⡭⣞⣽⣿⠈⠀⢀⡿⢰⡁⢎⠀⢂⠘⣷⣫⠗⣼⠳⣌⢇⡞⣬⢻⡜⣆⠣⠌⠡⠄⠄⠀⠀⠀⠀⠀⢠⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠣⡝⢎⡷⣺⠄⠀⠀⠀⠀⢰⢡⢊⡵⢫⣜⢯⣳⢣⢳⣉⢎⡿⡼⣘⠱⣈⠐⡀⠀⠀⠀⠀⢸⣿⢧⣻⢵⣣⢿⡜⣧⢯⣏⢷⢫⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡝⣾⣱⢯⡞⣵⡿⣞⠅⠀⣸⠃⠢⡝⡠⢊⠀⡜⣣⣟⡼⣣⢟⡼⡮⡝⢮⣟⣽⢮⡧⣉⠆⡈⠀⠀⠀⠀⠀⠀⡲⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢈⢢⡙⡾⣙⠾⣱⢋⠀⠀⠀⠀⢈⠆⡧⡜⣧⢏⡷⣭⣛⢦⡝⣸⢞⡱⡍⠶⣠⠣⠄⠀⠀⠀⠀⠠⣟⣯⢷⣫⢞⣭⣻⣜⡳⣎⢯⡝⣀⠀⠀⠀⠀⠈⠄⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣜⣳⠽⣎⡿⣜⣿⡽⠀⠀⣿⠀⠓⡬⡑⠄⠢⣜⣳⣟⡾⣵⢯⣷⡻⣝⣻⢾⡽⣯⢷⡍⡖⢡⠈⠀⠀⠀⠀⢀⡿⣾⡅⠀⠀⠀⡄⠀⠀⠀⠀⡸⣔⠀⠀⠀⢬⡳⡽⣱⢫⡝⣧⢏⠄⠀⠀⠀⠀⡻⢴⡹⢾⣽⡺⣵⢫⢶⣩⠳⣎⠷⣙⠶⣡⣙⣮⠕⡢⢄⣢⣽⡿⣯⣳⢏⣞⢾⡱⣎⠷⣙⢮⡽⢤⠀⠀⠀⠀⠀⠃⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⠾⣭⡟⣾⣱⢿⣾⣓⠀⠀⢳⡈⠰⣡⠝⡨⢐⢮⣳⢯⣟⣾⣳⡞⣷⣭⣟⡿⣿⣽⣟⣾⡹⢦⡁⠀⠀⠀⠀⣼⣻⣷⣻⡄⢀⠰⣌⠀⠀⠀⠀⣼⢮⣇⠠⣄⢣⣛⢷⣣⢷⣹⣎⠯⠄⠀⠀⠀⠀⢻⡆⡝⣧⣏⣷⣭⣿⣾⣷⣿⣮⣵⣥⡞⡵⠏⠁⠊⠐⠉⢶⣿⣽⣳⡽⣺⡝⣮⢳⣭⢻⡝⡮⣝⠶⠀⠀⠀⠀⠀⠰⡄⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⡟⣶⢻⡖⣯⣿⣟⣧⠀⠀⠀⠳⣄⣣⠛⡴⢩⢾⣽⣻⢎⡷⢡⠛⡶⣹⢾⣿⣿⣿⢾⣯⣟⡷⣘⠤⠀⠀⡰⣯⣿⣷⣿⡾⣤⣓⢮⠆⠀⠀⢨⣟⡿⣞⢷⡨⢷⡹⣎⢷⣫⢶⡻⡜⡄⠀⠀⠀⠀⣠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢾⣿⣯⡳⣝⢧⡻⣞⡳⢮⡳⣝⡞⣥⣛⠀⠀⠀⠀⠀⠀⠁⠀⢾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⡿⣽⣫⢽⡳⣟⣿⣯⠂⠀⠀⠀⠀⠉⠛⠚⠓⠚⠃⠻⡙⢎⠡⡈⠔⣯⣿⣿⣿⣿⣿⣯⣿⣿⣵⣮⣵⣌⣳⣿⣿⣿⣿⣿⡷⣯⢿⡶⣠⠀⣸⣿⣿⢿⣳⡝⣧⢿⣜⡧⣟⣮⢷⣹⢇⡆⣀⣤⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⡉⠉⠈⠙⣿⡀⠀⠀⠀⠀⢾⣿⣳⡝⣮⢳⡻⣼⡹⢧⣻⠼⣹⢧⣛⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢻⣷⣿⣯⣷⣻⣯⣷⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢧⡻⣼⣿⣿⣿⣿⡽⣭⣟⣾⣽⣻⡾⣽⢯⣛⣾⣿⣿⡿⢟⣯⣷⣿⠛⠭⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⣳⡝⣮⢳⡝⣧⣛⢧⢏⡟⣶⢫⢷⣩⠀⠀⠀⠀⠀⠀⠀⢸⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⡟⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣿⣿⣿⣿⣽⢷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣋⠰⣻⣟⠧⠀⠁⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣤⠀⠀⠀⣹⢾⣿⣟⡳⡽⢎⡷⣹⢶⡹⣎⠿⣜⢧⣛⡶⢣⠂⠀⠀⠀⠀⠀⡄⢈⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣮⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠁⠈⠀⠉⠋⠛⠙⠃⠏⠹⠙⠛⠛⠻⠿⢿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⡃⠄⠀⠀⠀⠀⠀⣀⣴⣧⢆⢻⣿⡁⢀⣠⣾⡋⠀⠀⠀⣿⢾⣿⣟⣷⡹⣏⢾⡱⢧⡻⣜⣻⡼⣫⢞⡽⣣⠄⠀⠀⠀⠀⠀⡅⠠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣧⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢠⣄⠠⣃⠴⣨⣆⢤⠀⠀⠀⠀⠀⠀⠀⠉⠉⠍⠻⣝⡻⣟⠿⣿⣿⣿⣿⣛⣾⣿⣿⣿⣿⣿⣿⣿⠝⠂⠁⠀⠀⢀⣤⣄⣤⣿⠏⡏⢸⣿⢾⣿⣿⣿⣿⣇⣴⠃⢰⣿⣿⣿⣛⡶⣝⢮⡳⣝⢧⡻⣜⢧⡳⣝⡮⡗⢧⢂⠀⠀⠀⠀⠀⠀⠐⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡘⢿⡆⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢀⣿⣄⡒⣬⣽⣿⣷⣭⣿⣛⣿⣯⣿⣗⣦⣼⣆⡀⠀⠀⠀⠀⠀⠈⠁⠈⠌⠑⠌⠓⠣⢋⠜⡯⢟⡻⠏⠗⠋⠀⠀⠀⠀⢠⣤⣿⣿⣿⣟⢁⣨⣜⣻⠋⠮⠿⣿⣾⣿⡟⠋⠀⢸⣿⣿⣿⡹⣞⡽⢮⣝⢮⣳⢳⡭⡞⣵⢫⢞⡹⣭⠆⡀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡑⢂⠀⠀⠀⡀⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⣄⣠⣼⣿⣷⣿⣿⣿⣿⣿⣿⢧⣈⣹⣿⣿⣿⣿⣿⣷⣝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣫⣺⡷⢾⣿⠏⠀⠀⠀⢘⣿⣿⣷⡄⢠⣿⣿⣿⣳⡟⣼⡹⣞⡼⣣⢏⡷⣹⠽⣘⢯⣚⠵⡣⢍⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡄⠆⠠⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣭⣷⣶⣿⣾⣿⣤⣇⣺⣍⡽⣻⣿⣿⣿⣶⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢿⣿⢺⡁⠈⠉⠀⠀⠀⢀⣾⣟⡋⠛⠀⢸⣿⣿⡳⣏⢾⣱⠻⣜⡳⣝⢮⡳⣝⠾⣙⠾⣌⠷⣱⢊⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡈⢇⢧⠀⠆⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⡏⢿⣿⣿⣿⡗⠨⠉⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠹⠿⠗⠟⠁⠀⣠⠀⠀⢀⣾⣿⣿⡏⠀⠀⢨⣿⣟⡷⣫⢎⢷⡛⣬⢳⢎⡷⣹⢎⡽⢭⣛⡬⣛⠴⡃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢋⢬⣓⠀⠀⢂⠠⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⢿⣿⣿⣿⣆⠀⠘⠋⠀⠈⢿⣿⡝⠿⢛⢳⠄⠀⠀⠉⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢠⣄⡀⠀⠀⠀⣠⣾⠋⣀⣤⣾⣿⣐⠄⠀⠀⠀⢸⣿⣿⣿⢧⡻⢮⡝⢮⢏⡾⣱⢧⣛⡜⣣⢞⡱⣭⢚⠅⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠸⢬⣻⡆⢄⠂⠡⠘⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⢿⣿⣿⣷⣤⣾⣧⠀⠀⠀⠙⠳⠗⠞⠋⠀⢠⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣟⢛⡴⠚⠛⠀⠀⠀⠀⢸⣿⣻⣿⣳⢭⣓⠾⣭⢞⡵⡹⣎⠷⣽⢣⣏⠾⣐⠫⠄⡀⠀⠀⠀⠀⠀⠀⣻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⡄⠀⠀⠀⠀⠀⠈⠽⣿⣢⢡⠂⡁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⡀⣀⣀⣴⣿⣤⣤⣄⠀⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⡀⠀⠀⢸⣿⣿⣿⢧⡻⣬⢻⣜⡳⡞⡵⣭⢻⡜⣷⢪⡟⣥⢃⠒⠀⡀⠀⠀⠀⠀⠀⣽⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⡦⠀⠀⠀⠀⠀⠀⠙⣷⣎⡱⡱⠌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠿⠿⠻⢿⡿⠿⠿⠿⠟⠛⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⡟⠃⠀⢸⣿⣿⡟⣮⢵⣋⠷⣞⡵⣫⠷⣭⡳⣝⢶⢫⡜⣧⢊⠐⠄⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⢿⣿⣿⣴⡀⠀⠀⠀⣬⢽⣻⣷⣧⣋⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣝⠾⣸⢭⣛⡼⣱⢏⡾⣱⢻⣜⡣⢏⡾⣡⢏⡐⠀⠂⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⡟⡾⣽⣷⣿⣳⢆⣾⣿⠗⡜⣮⢟⡿⡻⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⢯⡝⣖⡣⢧⡹⢧⣛⡼⣫⢗⡮⣝⡏⢶⡱⣊⠔⠀⠀⠀⠀⠀⠀⠀⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣳⡽⣏⢷⣫⢿⣿⣿⣿⣿⡨⢱⣞⡽⣾⣵⣣⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠛⢿⣮⣤⣵⣂⠱⢣⠞⣵⢫⡟⣼⢣⠟⣦⢳⡱⢊⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⡼⢯⡳⢯⣯⢟⣿⣿⣿⡅⣯⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠿⠿⠛⠋⠙⢻⣿⣶⣯⢞⣧⢻⡜⣯⢛⡴⢧⢳⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⣳⢮⡗⡾⣝⠾⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣇⢀⣤⡀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⢠⣴⣾⠿⢟⣿⡞⣽⢪⠷⣭⠞⡵⣚⢮⢇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣜⣻⣼⢻⡭⣿⢽⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⠀⠀⠀⠀⠛⢿⣦⣾⡿⣜⢧⣏⠷⣭⢻⡴⢫⡞⣎⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⢫⣷⢫⣷⠻⣌⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠏⠀⠀⠀⠀⣀⣀⣴⣾⠿⣿⣝⢮⡳⣞⡽⢪⢷⡩⢷⡸⣌⠧⠀⣀⣤⣶⣶⣶⣾⣷⣦⠀⠀⠀⠘⢧⡄⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⣮⣷⣘⣿⣜⣳⣿⣿⣿⡹⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣄⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⣼⣿⡿⢋⣠⣼⡿⣹⣎⢷⡹⣞⡽⢮⡝⣶⣹⣼⣾⣷⣿⠟⠁⠉⠁⠀⢻⣟⢷⣄⣀⠀⠈⠙⣦⡈⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⡿⢿⡿⣿⣿⣻⣾⣟⡳⣎⢏⠟⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠈⠻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢮⣷⣟⣷⣿⣿⣭⣿⣭⣇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⠟⠁⠀⠀⠀⠀⣠⣿⡿⣵⣫⡝⣧⢿⡱⣎⡷⣹⠼⣹⢧⡻⣴⣿⡏⢹⣿⡏⠀⢀⣤⣄⣤⡾⠛⠿⣿⡿⢿⣿⣆⠈⣳⣆⠀⠀⠀⠀⠀⠀ ⣿⣽⣹⠶⣹⢯⣷⣿⣯⣿⣳⣍⠎⡌⢰⠹⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠈⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⣀⣠⣴⣮⣿⣿⡻⡿⣛⡉⠉⡛⠿⣽⣿⣝⢶⠞⠂⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⢰⣶⣤⣀⣴⣿⣿⣝⣯⣷⣽⣾⣧⣽⣮⣵⢫⡝⣧⢏⡳⣾⣿⣧⣾⣿⠁⢠⣾⢿⠙⢿⣄⣠⣴⣿⣤⣾⠻⣿⣶⣿⠈⠹⡇⠀⠀⠀⠀ ⣿⣿⣽⣯⣗⣯⣾⣷⣿⣿⣿⣾⣿⣌⢧⡚⣌⠻⢿⣿⣿⣿⣿⣿⡿⣿⣶⣤⡀⠀⠈⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⠻⢟⡻⣿⡂⠙⣾⣿⣿⣿⣿⣟⢀⣜⣥⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⢟⣿⣷⣤⣼⣿⢹⣿⣿⢏⣷⣾⣿⠟⠛⠉⠛⠛⠿⣿⣷⣽⣮⣻⣽⣿⣿⣿⣿⣿⣥⡾⠁⠈⢣⠀⠉⠛⢻⡟⣿⣿⣀⠀⣹⣿⡇⠀⢻⡀⠀⠀⠀ ⣿⡿⣿⢿⡿⢿⣿⣽⣟⣿⣿⣿⣿⣿⣿⣿⣾⣍⡳⢢⠱⢎⠠⠀⠀⠑⣿⣿⡟⠀⠀⠀⠈⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢝⣔⣹⣿⣷⣾⣿⣿⣿⣿⣿⣷⣛⣳⠄⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠰⣿⣷⣭⣯⣭⣿⣿⡿⢧⣻⣿⣟⣁⠀⣼⠿⢿⣧⣀⣀⡙⠿⠿⣿⣿⣃⡀⢠⣿⣿⣿⣿⣦⡀⠈⠇⠀⠀⠀⠓⠘⠟⠀⠤⠟⠿⣿⣦⠀⠳⡀⠀⠀ ⣟⢷⡹⣞⡵⣣⢿⣿⣾⣳⢿⣿⣹⣿⡿⣿⣿⣿⣿⣧⣣⠈⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠳⢭⣫⣿⣿⣿⠿⠿⠿⠿⠬⠉⠀⠀⠀⠀⢀⣔⡾⠟⠁⠀⠀⠀⣿⣿⣷⣯⢞⠶⣹⣾⣿⣿⡿⠛⠓⠚⠁⠀⠀⠉⣙⢛⠛⠿⣿⣿⣿⠿⣿⣿⣿⣿⣻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣧⠀⠈⢆⠀ ⣿⢧⣟⣳⢏⡷⣎⠻⢿⣿⣿⣿⠿⢋⠁⡄⡰⣹⣿⣿⣿⣷⣶⣶⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡶⡺⠕⠁⠀⠀⠀⠀⢹⣿⣿⡞⢮⣿⣿⡟⢛⣥⣴⣶⣤⣤⣤⠀⣠⣄⡀⠈⣉⣹⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⢿⡇⠀⠈⠃ ⣯⡟⣾⢭⣟⣾⣱⢏⡶⣲⠶⣜⡲⣭⢖⣬⢱⣣⢞⣵⣿⣿⡿⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⡆⠙⠛⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣝⣻⣿⣿⣿⠿⠛⠋⠀⠉⠀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣿⠿⢟⣾⡾⡟⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣿⡀⠀⠈ ⣿⣹⢎⡿⣮⢷⣯⠾⣝⡷⣻⢭⢷⣫⠾⣜⡧⢯⣛⢾⣿⣿⡯⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡛⣿⣿⣿⣿⢀⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢮⣽⣿⣿⠁⠀⠀⠀⢴⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠗⠯⠉⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢻⣷⠀⠀ ⣿⣜⣯⢾⣹⣻⣼⢻⣽⡺⣵⢯⣞⣳⢻⣝⢾⣫⡝⢮⣻⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢿⣷⣷⣎⣾⣱⡟⣿⢶⣴⣤⣦⣐⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡿⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢯⣿⣿⡇⠀⠀⠐⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⣿⣇⣠ ⡿⡼⣭⣟⣧⣟⢮⡟⣶⡻⣵⡻⢮⣽⣳⡞⣯⣳⢟⣧⠽⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣩⣙⠻⣿⣷⣿⣯⣿⣞⣷⣹⡟⣿⣿⢿⣶⣤⣄⣀⣀⣀⣀⣴⣾⣵⣿⣿⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢾⣿⣿⡇⠀⠀⠀⠉⢻⣿⡄⠀⣿⣿⣿⣿⣿⣿⣶⢀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣹⣿⠁ ⣿⡵⣫⢞⣷⣫⢾⡽⣳⢟⣵⡻⣟⡶⣭⣻⢧⣻⢏⣾⡹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⡇⠑⠂⠈⠉⠋⠛⠛⠿⠿⢿⣷⣿⣿⢾⣽⡻⢿⣿⣿⣿⣿⢿⣿⣿⠃⠀⠀⠀⠀⢹⡙⡶⠀⠀⠀⠀⠀⠀⢨⣿⣿⣡⣾⣿⣿⡇⠀⠀⠀⠀⠀⢹⡇⠀⣿⣿⢿⣿⣿⣿⣿⣿⣶⣀⣠⣴⣿⣿⣿⣿⣿⡋⠙⠁⠀⠀⠀⠘⠟⠒⢄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀ ⣿⣜⣯⢟⡶⣯⣻⣼⢻⣞⡳⢿⣱⢯⣳⣏⣞⣳⡟⣶⡹⡹⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⢿⣇⠉⠳⣹⣻⠾⣝⠂⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠙⢳⡄⠀⠀⠀⠀⠀⢠⣿⡿⠟⢉⣿⣿⠀⠀⠀⠀⠀⠀⣾⡇⠀⠞⣹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠁⠀⠀⢀⢀⣀⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⡽⠛⠀⠀ ⣿⢞⣮⢻⣝⣳⡟⡾⣽⣺⠽⣏⣟⡮⡷⣞⡵⣧⢻⣖⡳⣽⡹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⣀⣀⣄⣂⡲⣌⣒⢦⣀⠹⣷⡦⡐⠯⠛⠐⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⢶⡶⢶⡶⢾⡿⠏⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⢈⣿⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⡀⣠⣴⣶⣾⣿⣿⣿⣧⣤⣾⠋⠀⠀⢀⡠⠐⠋⠁⠀⠀⠀⠀ ⣿⡞⣭⣟⡾⣱⢿⣹⠶⣭⣟⡽⣺⢽⣳⡽⣺⢵⣛⡾⡽⣶⡹⣞⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⢆⠛⡙⠫⠍⡜⣱⣛⠶⡛⠞⣎⠓⠚⣿⡇⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠁⠀⠪⠁⢈⣉⣛⣷⠚⢹⣿⣿⣿⡿⢿⡟⣭⢻⣿⣿⣿⣿⣶⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣻⢳⠾⣝⣯⣳⢯⡻⣵⢮⡷⣝⣮⢳⡝⣯⢏⡷⣽⢳⣧⢻⡜⡮⣽⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣛⣿⣿⡻⣏⡟⣄⢣⠈⠄⠁⠈⠔⠀⠌⠀⠀⠀⠈⢻⣶⣤⣤⣾⣿⢻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡸⠃⠀⢀⣴⣦⣶⣿⠛⢻⠿⠿⡿⣿⣿⡿⢋⠞⡽⢌⣧⢹⣿⣿⣯⣈⠁⠂⣀⣀⠀⠀⠀⠀⢀⣾ ⣿⢣⣟⢯⣛⡶⣯⡗⣯⣗⣻⡼⣳⣭⡟⡽⣎⡿⡼⣭⢷⢮⢧⡹⠵⣎⡝⢻⣿⣧⠀⠀⠀⠀⠀⠀⣹⣿⣿⣷⣯⡹⣜⡱⠎⠂⠀⠀⣀⠀⣴⣦⣤⡀⠀⠀⠀⠛⢿⣿⣋⠀⠛⠛⢻⣷⣤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠀⠀⠀⠀⠀⠀⢀⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢳⣤⠲⣿⣿⠟⡭⢲⡝⢧⠞⡤⡀⠄⠠⠀⠍⣚⠜⣪⠔⣋⣿⣯⣿⣾⣿⣿⣯⣽⣷⣶⣶⣾⡿⠛ ⣯⣟⡞⣯⣏⣷⣳⡟⣷⣞⣳⣛⣧⡻⣼⡻⣵⢫⢷⡽⣞⣯⠧⣙⣷⡸⣜⢣⢿⣿⣷⣄⠀⠀⠀⢀⣿⡏⠡⣉⠟⡿⢿⣿⣶⣄⠀⠀⠈⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⠉⠻⠶⣠⣠⣾⠿⠋⠀⠀⠀⠀⠀⣠⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢁⣸⡇⠈⢄⠀⠀⠀⠀⠀⠀⡘⠀⢀⣸⣿⡷⣾⣿⣿⣾⣷⣾⣧⣟⡴⡁⢂⠁⠂⠀⠈⢿⡔⣫⢔⠻⣿⣿⣿⣿⡟⠛⠻⠿⠿⠿⠟⠀⠀ ⡿⡼⣝⣳⢯⢶⣛⡾⢧⣻⡵⣻⣼⣳⢯⡽⣞⢯⣗⣻⡽⢎⠁⠈⠩⡙⠢⠝⠾⢿⣿⡏⠀⠀⣀⣾⡿⢁⡵⣺⢯⡟⡆⠀⠉⠛⠗⠶⠷⢶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣏⣡⣴⣿⣷⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠑⢄⠀⠀⠀⡰⠁⣠⣾⣿⡿⠀⠙⠀⠈⠙⠛⠿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠈⢳⡵⣊⠷⣈⠟⣬⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⡝⣯⡽⣞⣯⡽⣞⣯⢷⣻⢵⣎⠷⣯⡽⣞⣽⣺⢳⣟⡆⠀⠀⠢⡀⢈⠴⠶⠦⡈⣽⠷⠿⢿⣿⣥⣦⣞⣻⠿⡽⠁⢀⢀⣠⡤⠶⠓⠛⠉⠁⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⢀⡀⣀⣀⣀⣀⡀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣷⣶⣽⣷⠊⠴⠉⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⢞⡷⣝⣳⠾⣽⣹⡞⣧⣟⣮⢏⡿⢶⡹⢾⡵⣫⢟⡼⣓⠦⠀⠀⢘⠧⡀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠈⠉⠙⠛⠓⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣟⠁⠀⠀⠨⣿⣿⣿⠀⢸⡇⣤⣽⣿⣻⣿⣿⣿⡿⠛⠁⣀⣤⣴⣶⣶⣤⡀⠀⠀⠀⠀⢿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⢿⣿⣶⣤⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⣯⣛⡾⣽⡳⣟⡾⣧⢟⣧⢟⡮⢿⡼⣏⢿⣳⢯⡗⣯⢽⡹⣞⣴⣦⣼⣄⠀⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠈⠻⣿⣿⣿⣶⣀⣤⣰⣿⣿⠗⢀⣾⣿⣿⣿⣿⣿⣿⠟⠉⢀⣴⣾⣿⣿⠋⠀⠈⠙⢿⣦⣀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣦⡉⠉⢻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀ ⣿⣣⣟⣶⣻⣽⡳⣽⣞⣮⢿⣹⢷⣹⠾⣝⡾⣣⢿⡼⣣⣟⡾⣜⠳⣯⣽⣿⣾⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⡶⠶⠶⠶⠾⢿⣯⡀⠀⠀⠀⠀⠀⣠⠿⢻⣷⣤⡀⠀⠉⠛⢿⣿⣿⣿⡿⠋⢀⣼⣿⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⣿⡵⢯⡶⣏⣶⢻⡵⣾⡱⣟⢮⡗⣯⢻⡹⠚⠝⠪⠜⠵⣊⠳⢉⣼⣿⡿⠙⣿⠇⠀⠀⠀⠈⠉⠹⠉⠀⠀⠀⠀⠀⠂⠀⠛⣨⣾⡟⠁⠀⠀⠀⣤⢞⣣⣾⣿⣿⣿⣿⣷⣄⡀⠀⠀⠈⠛⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⢿⣧⣀⣀⠀⠰⣯⡛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⣿⢞⣯⣳⢟⣼⡻⣜⡧⢿⣜⡯⣞⡱⢣⠀⢀⡴⣲⣆⡀⠀⣠⣾⡯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠿⠛⠉⠀⠀⢠⣤⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣦⣀⣯⣻⣷⣿⣿⣿⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⣿⡺⣵⣛⢾⣣⢿⡹⣞⣯⢾⣹⢷⣹⢣⡀⠙⣿⡟⠋⠉⠳⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡶⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣍⣿⣿⣿⣿⣿⣶⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⡇⠀⠀⠀ ⣿⡵⣻⡼⣏⠾⣧⢿⣹⢮⢯⣳⢯⣞⢧⡳⣌⣻⣄⣠⣦⣤⡀⢀⠀⠀⠀⠙⠛⠻⠟⠛⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠛⠻⣿⡿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⡀⠀⠀⠀ ⣿⣞⣷⡽⣞⣿⡹⣯⢽⣫⢷⣫⢷⣞⣧⣿⣿⣿⠟⠻⠋⠙⢛⣃⣀⣶⣄⣀⣀⣀⣀⣀⣀⢀⠀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣇⡀⠸⣷⡄⡉⢙⢛⡻⠿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣯⡂⠀⠀
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⢈⣷⡿⣿⠿⢷⣦⣆⠀⣰⣤⣶⠿⢿⣿⣷⡇⠀⠀ ⠀⣾⡿⠃⠈⠀⠀⢈⣿⣿⣿⡁⠀⠀⠀⠀⢻⣿⡀⠀ ⠲⣿⡷⠀⠀⠀⠀⠘⢀⡿⡅⠙⠀⠀⠀⠀⢺⣿⡿⠂ ⠛⢻⣿⡃⠀⠀⠀⠀⠘⢀⡇⠀⠀⠀⠀⠀⣿⡿⠛⠀ ⠀⢈⣿⣿⣁⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣽⣿⣃⠀⠀ ⠀⠀⠀⠿⣿⣷⡀⡀⠀⠀⠀⢠⡀⣴⢿⡟⠇⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⡞⠀⢲⣾⡿⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠉⠛⣷⡛⠁⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠖⠲⢤⡖⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⣄⠀⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⠀⠀ ⠀⡞⠉⠻⠁⢹⠀⠀⡏⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠋⠀⠀⠀⠀⣀⡤⠴⠒⠊⠉⠉⠀⠀⣿⣿⣿⠿⠋⠀⠀ ⠀⠳⢤⡀⠀⡞⠁⠀⡇⠀⠀⢀⡠⠼⠴⠒⠒⠒⠒⠦⠤⠤⣄⣀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠷⡏⠀⠀⣇⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⠤⢴ ⠀⠀⠀⠀⠀⠀⣸⠁⣾⣿⣀⣽⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⢿⣦⠀⠀⠀⢸⡀⠀⠀⢀⣠⠤⠔⠒⠋⠉⠉⠀⠀⠀⠀⢀⡞ ⠀⠀⠀⠀⠀⢀⡏⠀⠹⠿⠿⠟⠁⠀⠰⠦⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⢘⡧⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⠀⣼⠦⣄⠀⠀⢠⣀⣀⣴⠟⠶⣄⡀⠀⠀⡀⠀⠉⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⢰⡇⠀⠈⡇⠀⠀⠸⡾⠁⠀⠀⠀⠉⠉⡏⠀⠀⠀⣠⠖⠉⠓⢤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⢧⣀⡼⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣧⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⠳⠤⠖⠃⡟⠀⠀⠀⢾⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠈⠦⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠙⢦⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠸⡇⠈⢳⡀⠀⢹⡀⠀⠀⠀⢀⡞⠁⠉⣇⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⣀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣷⠴⠚⠁⠀⣀⣷⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣳ ⠀⠀⠀⠀⠀⠀⡴⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡴⠚⠉⠉⠀⠀⠀⠀⢸⠃⣀⣠⠤⠤⠖⠋ ⣼⢷⡆⠀⣠⡴⠧⣄⣇⠀⠀⠀⠀⡴⠚⠙⠲⠞⠛⠙⡆⠀⠀⠀⠀⠀⢀⡇⣠⣽⢦⣄⢀⣴⣶⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣼⣽⡞⠁⠀⠀⠀⢹⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⢠⢟⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠉⠁⢳⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠙⢦⠀⠀⠀⡠⠁⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠏⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⡆⠀⠈⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠹⣧⠞⠁⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡀⠀⠙⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢀⡄⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⣰⣀⣀⣀⠀⠀⠀⠘⣦⣀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢸⡇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠀⠀⠈⠉⠉⠉⠙⠻⠿⠾⠾⠻⠓⢦⠦⡶⡶⠿⠛⠛⠓⠒⠒⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠠⠄⣤⢀⠀⠀⠀⠀⠀⠐⠷⠀⠀⠀⡀⢠⠤⠤⠤⠀⠀⠀⠀⠀⠀ ⢰⠐⠆⠖⠐⠂⣆⢠⡆⣄⠀⠀⠀⠀⠀⠀⢀⡄⢆⢠⡆⠖⠐⠃⠶⢰⠀⠀⠀ ⡋⠀⠀⠀⠀⠀⠀⠈⠁⢊⣐⡀⠀⠀⠀⣂⢈⠃⠉⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠐⠂⠢⠸⠃⠁⠈⠀⠻⠠⠂⠒⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⡅⠀⠀⠀⠀⠀⠀⢀⡀⡥⠴⡀⠀⠀⠀⡠⠨⡄⣀⠀⠀⠀⠀⠀⠀⢨⣀⠀⢀ ⡃⠀⠀⠀⠀⠀⠀⠀⠀⡰⢺⠃⠉⠈⠉⡛⠐⡀⠀⠀⠀⠀⠀⠀⡐⣸⡂⠉⠁ ⠹⢠⡄⣤⢠⡄⠶⠈⡅⠏⠀⠀⠀⠀⠀⠀⠈⠇⡍⠐⡆⣤⢠⡄⣴⡺⠁⠀⠀ ⠀⠀⠀⠢⠠⠄⠔⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠆⠤⠠⠃⢎⢅⢂⠦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠩⠤⠬ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠵⠷⠾⠧⠇⠲⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠒⠒⠒⠒⠓⠉⠉⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢖⠤⣀⠇⠙⠉⠉⠉⠉⠈⡁⣉⣉⢭⠻⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠏⠀⠀⠀⣀⣀⣀⠀⠉⣉⣟⣷⣯⣒⢴⡤⣀⠀⠀⣄⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇⠈⠇⣾⠀⠀⠀⡏⢠⠀⠀⠀⠉⠋⠵⣭⢒⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⣀⢹⠀⠀⠁⡸⠀⠁⠋⡯⣪⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠀⠀⠀⠀⣦⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⠉⠀⡾⠁⠏⣮⣠⠀⠀⠀⠀⠀⠄⠧⠀⠀⠀⠀⠀⠀⠀⠀⣄⠦⠘⠀⠊⡗⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢧⢿⡿⢠⠀⠀⠀⠀⠀⠀⠀⠉⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⣾⣤⣆⠙⡀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠋⠗⢸⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⣄⠦⠒⠙⠀⠁⠛⡿⣨⠀⠀⠈⠀⠀⢦⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠇⣿⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣄⠹⠀⠀⢏⣷⣴⠀⡄⠹⠀⡄⠸⠀⠀⢇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⠀⠀⣽⠀⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡯⡮⠆⠻⠀⠀⡄⠘⠀⡀⠘⠀⠀⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⠀⡏⣯⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡿⢠⠀⣇⢸⠀⠀⢩⠀⠀⡇⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣸⠀⡀⢷⠉⠀⠉⠚⠛⠒⠀⠀⠀⠀⠀⠀⠀⢿⣸⠀⠀⡇⢸⠀⠀⡇⠀⠀⡇⠀⠀⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⡿⠟⠏⣾⣠⠀⠀⠀⠀⠀⠀⠇⠥⠻⣿⠀⠀⠀⡇⢠⠀⠁⡼⠀⠀⡇⠀⠃⣱⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⢹⠀⠀⠀⠀⠀⣼⢿⡼⠀⠀⠀⠀⠀⠀⠀⠋⡗⡽⣉⡄⣿⠛⠈⡆⠀⠀⡏⢀⠉⠞⣠⠚⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⡼⡀⢦⠓⠉⠉⠉⣏⢠⠀⠁⠀⠀⠀⠇⢡⠏⢛⡽⢿⠓⠀⡏⠇⣦⠻⡇⠊⡴⠀⠀⠀⢇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠶⠓⡟⡍⢦⡗⣶⠥⣾⡇⣽⡿⡏⣏⠸⢧⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⢁⠟⣿⣿⣹⣿⢻⣿⠀⣿⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢦⠙⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠁⠊⠖⣠⡄⢿⡿⣿⣿⣹⡟⠸⡏⢸⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠈⠉⠏⡴⢀⡀⣀⣇⣿⣿⣿⢿⠙⠈⠀⠀⠀⠇⣿⣧⠿⣿⣟⣿⢡⡽⢿⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠁⣿⠿⢼⡿⣿⣷⢿⠛⠛⡿⣿⣿⣿⣿⣿⢹⣟⣽⣸⠀⠀⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠟⣿⣽⣷⣿⣿⣿⣿⡿⣿⣿⣟⡿⣮⣻⣻⣾⡰⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡿⣶⢴⡤⣦⣷⡭⣯⣿⡿⡯⡭⠿⣾⠴⡤⣴⢠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⠖⠤⠤⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠁⠉⠉⠉⠚⠴⣧⠀⠀⠃⠛⠉⠉⠉⠉⠉⠋⠒⠿⡿⣹⢸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⡼⢡⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣃⠟⣿⢾⢠⠀⠀⠀⡎⠀⠀⢿⣯⣿⢰⠀⠀⠀⠀⠀⠀⡄⣽⣽⣽⠹⠀⠀⠁⠋⠙⠉⠉⠉⠉⠉⢞⡖⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⣷⣿⣶⡠⠀⠀⠀⠇⢠⠀⡇⡏⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⣳⣷⣷⠳⠀⠀⡇⣹⣛⣽⣿⣻⠿⠷⠀⠀⠀⠀⠀⠀ ⠁⠁⠉⠉⠁⠀⠀⠀⠀⠀⣚⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⡏⡇⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡏⣿⠀⠀⠀⣸⣀⣀⣄⠤⡤⣀⠀⠀⠀⠀⠀⠀ ⡇⡄⠙⡟⠀⢹⠉⠸⠀⡇⠤⠸⠼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠃⡽⠉⠋⣷⣿⡯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣗⡿⢿⠭⠯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡀⢹⢸⠀⠀⡀⠀⢀⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡄⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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