Maid Frog Emojis & Text

Copy & Paste Maid Frog Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠐⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠐⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢀⡉⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠔⢋⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣈⠑⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠢⡀⠀⠀⠀ ⠀⠀⡠⠎⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠢⡀⠀ ⢀⠔⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⢤⡑⠃⠀⠀⠀⠀⠀⡠⢂⣂⣀⣐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢄ ⠀⡴⠁⠀⠀⠀⠀⠔⢣⠀⢀⢎⣵⠾⠛⠉⠘⢷⡌⠆⠀⠀⠀⠀⢂⡞⢋⠉⠈⠙⢷⣌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀ ⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⡆⣼⠇⠀⢀⠤⡀⠀⠓⠚⠛⠛⠛⠉⠉⠁⠀⢠⢤⠀⠈⢿⠸⡆⠀⠀⠀⠀⠀⢀⠠⣀⡠⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⢻⡆⠀⠸⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠆⠀⣿⠺⡁⢄⡳⠀⠀⣀⢎⣱⡌⣴⢂⠇⢠⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠤⠇⢠⢡⡾⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢱⠀⠀⠀⠘⣴⡮⡯⠭⣷⡌⡄⠘⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡀⠀⠀⠰⣘⠻⡟⡾⢋⡴⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡰⢡⣤⣤⣤⣤⣴⣥⣵⠤⠤⣤⣤⣤⡌⠂ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⣷⣾⣿⣿⣿⣏⠀⠀⣨⠟⠒⠒⠒⢚⣡⠇ ⠀⠀⠀⠀⠀⠀⠐⠃⠃⠀⠘⢌⠿⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⢁⣴⣿⣿⣿⣿⣿⣿⣿⣧⡞⢣⠞⢁⠀⠀⠀⠀⠀ ⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢠⣾⣿⣮⣉⠙⠒⠒⠲⠤⠤⣤⣴⡚⠉⠀⠀⣠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡜⡀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⢸⢻⣿⣿⣦⣢⢾⡹⡽⣻⣿⣿⣿⣿⣿⣿⣿⠏⣜⠛⠀⢖⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠪⡼⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡞⣾⣿⡚⠈⠁⠈⣷⣻⣿⣿⢋⣨⣿⣿⣿⣿⣶⣶⣌⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠻⢿⣿⣿⣿⣿⣿⣿⣇⣧⢄⣈⡷⠴⠖⠚⢉⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣽⣷⠃⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⣃⣙⣿⠟⠛⠉⠙⡟⠟⢉⣁⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⡏⡜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣞⣿⣿⣿⣿⣷⡘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣮⢰⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⣽⠿⣿⣿⣿⣦⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣬⢿⢿⣫⣏⣻⡿⠿⠋⢹⢡⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣂⡬⢿⠷⠾⠻⠯⣹⡀⠀⠸⡿⣯⡽⢿⣟⣿⡟⠯⠼⣧⠬⢽⠭⠟⠉⢠⡀⣀⡾⣸⠄⠀⠀⠀⠀⠀⠀⠀ ⠐⡄⠀⠀⠀⠀⠀⠀⠀⢇⢧⡡⠈⠀⠀⠀⠀⠀⡇⠀⠀⡏⠉⠁⠀⠉⠉⠀⣀⣀⣇⡀⢈⣀⣨⣭⡿⠟⣋⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡈⢦⠀⠀⠀⠀⠀⠀⠈⠪⣙⠒⠒⠒⠒⠒⠙⠳⢤⠔⢛⣛⡋⠉⠉⠉⠉⠉⠁⠭⣉⣉⠩⠭⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡰ ⠀⠐⢄⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠁ ⠀⠀⠀⠑⢄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢁⠴⠁⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⡁⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⣡⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠗⠄⡉⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣁⠴⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⣉⠒⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⡀⣤⢰⣶⢈⣉⠀⠀⠁⠋⠉⠴⠖⣠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣲⣭⣦⣄⣌⣳⣠⣤⡤⠊⡕⣽⣼⢞⣷⣦⣤⣬⣭⣭⣥⣿⣿⣶⣦⣍⠐⢍⠶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣪⣷⣿⣿⣿⣿⡷⢋⣿⡙⡟⡻⣎⠀⣻⣿⣿⡿⠿⠟⠛⠻⠿⢿⣿⣿⣿⣿⣾⣷⠀⢱⡄⢙⠢⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣵⣿⣿⣿⣿⣿⡿⢋⣴⣿⣇⣀⣀⣥⣾⡦⣄⠙⠥⣒⠒⠒⠒⠒⠤⣀⠀⠙⠻⣿⣿⠟⣠⣴⣇⠀⠁⠈⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢗⣿⣿⣿⣿⠿⣓⣵⣶⣿⣿⣿⣿⣟⠿⢻⣿⣿⣮⣝⡶⠠⢬⠁⢀⣂⣀⣀⣛⣦⠭⣭⠖⢟⣡⣿⣿⢷⡄⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⣧⣨⣭⠵⣏⣡⣾⣿⣿⣿⣿⣿⣯⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣶⣶⣶⣴⣷⣿⣿⣿⣿⣿⡜⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠱⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣯⣽⣤⣤⣤⣤⣦⣶⣦⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢋⠅⠀⠀⠀⠬⣉⠉⠉⠉⢉⡩⠝⠛⠉⠁⠈⠉⠐⠒⠂⠤⠬⠽⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡁⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⠤⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣢⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣴⣿⡤⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣌⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠙⢿⢇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⢀⡠⣤⢤⡤⣈⠙⠻⣇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣧⡻ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣤⠒⠒⢯⡇⡀⠀⠀⠀⠀⢀⡾⠋⠀⢀⣼⠑⠁⣴⣮⢄⡁⠕⡄⠈⢷⡀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣼⠏⢰⣶⣆⣷⠃⠀⢄⣠⣿⡟⠁⠀⠀⣼⡷⠃⣾⣿⣿⣿⣤⠀⣼⠀⠈⢇⠀⠀⠀⠀⠘⣿⣯⠙⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢻⣇⣘⠿⠓⠁⠀⠀⠀⠀⠉⠣⡀⠀⠀⢻⠗⠀⢿⣿⣿⡿⠃⠀⣸⠀⠀⢸⠀⠀⠀⠀⠀⢹⣿⡅⢹⣿ ⠀⠀⠀⠀⠀⢠⠿⠷⠦⠀⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢕⣤⣈⢆⢀⢀⠟⢉⣕⣄⡨⢃⣀⡴⢎⡄⠀⠀⠀⠀⠀⣿⣇⠀⣿ ⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢹⣿⡀⢾ ⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⢸ ⠀⠀⠀⠀⠀⢀⡇⠉⠒⢤⣴⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠒⠠⠤⠤⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⣿⢸ ⠀⠀⠀⠀⣠⣾⠏⢰⣢⣴⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⡠⣀⠀⠀⠀⠀⠀⠀⡉⠉⢹⣿⣿⣷⣶⣶⣜⠀⠀⢹⣸ ⠀⣀⡴⠊⢀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣤⣬⣭⣖⣻⣷⣿⣿⣿⣿⣿⡿⠊⠀⠀⣾⣿ ⠉⠒⠒⠂⠈⠿⠟⠿⠿⢿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⣰⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣴⣾⣿⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣿⡀⠙⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣶⡄⠀⣠⡿⣗⠈⣻⠇⠀⠀⠉⠉⠛⠛⠉⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡶⢶⣿⣧⠸⣇⣼⠋⠀⣏⠈⠉⠀⠀⠀⠀⠀⠀⢀⣴⠶⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⣤⡙⠃⠀⠙⣇⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⡉⠁⠀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣟⠛⠛⠁⠀⠀⠀⢻⣦⠀⠀⠀⠀⠉⠙⠒⠒⠒⠚⠳⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⢳⣦⠀⠀⠀⢀⡆⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢷⣄⣠⠞⠀⠀⠀⢠⡟⠉⠓⠶⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠀⠀⠈⠛⠛⠶⠶⠶⢿⠃⠀⠀⠀⠀⠀⠀⢀⣤⠞⢡⡀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡛⠻⢶⣤⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢻⡄⠀⠀⠀⣧⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⢶⣤⣈⠙⠛⢶⣤⣄⠀⢸⡆⠀⠀⠀⢀⣴⠟⠁⠀⠀⠠⢤⣇⠀⣠⠞⠋⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⡀⠈⠙⠻⢶⣤⣌⠉⠛⢿⣿⣆⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⡟⠀⢀⣤⠶⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⢷⡀⢀⠀⠀⠈⠙⠻⢶⣶⣿⠿⣷⣴⣿⢿⠆⠀⢀⡀⠀⣰⠇⣰⠏⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣆⠀⠀⢀⣀⡀⠀⠙⠻⢿⣮⣿⣿⣄⣼⣿⡷⠀⣿⡴⠏⠀⠀⠀⠀⠀⣼⠏⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⣿⣿⠟⠛⢿⡉⠛⢷⣄⠀⠀⠀⠙⠛⠿⣼⣿⣿⣾⣿⣄⣰⠇⠀⣤⢠⣾⠋⠀⡀⣿⣿⣿⣻⣷⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠂⠀⠀⠀⠙⣆⠀⠹⣧⠀⠀⠀⠀⠀⠈⠉⠛⢷⣶⣿⡿⣷⣶⣧⣴⣷⣤⣾⡟⣿⣿⣿⡿⢟⡟⠋⠉⠉⠉⠉⠛⠷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⠋⢻⡀⠀⠀⠀⠀⠘⡇⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⡇⠛⠾⣿⣿⣿⠽⠟⠳⠦⠤⣄⣀⠀⠀⠀⠈⠻⣦⣀⣀⣀⠀ ⠀⠀⢸⣇⠀⠻⣄⠀⠠⠀⢠⣇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡏⢀⣰⣶⣿⡿⠷⠤⣄⣀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠹⠉⠈⠻⡇ ⠀⠀⠀⠻⣦⣀⠈⢙⣲⣆⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⣐⣾⣿⣿⠣⣄⠀⠀⠉⠛⠦⢄⡀⠀⠀⠈⠓⠀⠀⠀⢀⣾⠇ ⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉⠱⣶⢤⣴⣤⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⡿⡝⢆⠈⠳⢦⣄⠀⠀⠀⠙⠢⣤⡀⠀⠀⠀⠀⠉⢿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠾⠶⣾⠋⣉⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡻⡌⠳⣄⠀⠈⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡈⠦⡈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣆⠸⣆⡀⠀⠉⠙⠓⠂⠀⠀⠀⠀⠀⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣮⣅⣀⣀⣀⣤⠀⠀⠀⣶⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢿⣤⣀⣴⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
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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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