Pog Emojis & Text

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