Trolled Emojis & Text

Copy & Paste Trolled Emojis & Symbols

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

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