Frog Dot Art

Copy & Paste Frog Dot Art Emojis & Symbols

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