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⠀⠀⠀⠀⠀⠀⢀⣠⡾⠿⠛⠋⠉⠉⠉⠈⠉⠉⠙⠚⠫⢖⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⡷⡀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠀⠿⣿⡿⠃⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⢷⠀ ⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣧ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣧⠀⠀⣴⡶⢶⣦⡀⠀⠰⣿⡿⠿⠿⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⣿⡅⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⣿⡇⠀⠘⣿⣤⣤⣤⣤⣴⣶⣶⠶⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⢰⡿⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢀⣀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠙⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠟ ⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣁⣀⣀⣀⣠⣄⣤⣤⡴⠶⠾⠛⠉⠀⠀⠀ ⠀⠈⢿⣻⣆⡀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠋⣽⣿⣿⣶⣾⣷⣿⣛⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣾⣿⣿⣿⣿⣾⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⠃⠀⠀⠙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢹⣿⡆⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡟⢦⣀⡀⠀⠀⢀⣄⣀⣀⣠⣠⣤⣤⣴⣶⣦⣄⠠ ⠀⠀⢠⣿⣿⠇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠉⠉⠈⠙⣿⣧ ⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟ ⠀⣾⣿⣿⠀⠀⠀⢰⣾⣦⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣿⣿⣿⡯⠜ ⡀⣿⣿⡟⠀⠀⠀⠈⠛⠁⠀⠀⠀⠻⣿⠃⠀⠀⠀⠀⢻⣿⣻⣿⠿⠟⠛⠉⠀⠀ ⣗⣿⢿⣿⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⡛⣧⠀⢹⡆⠀⠀⠀⠛⠋⠉⣙⠛⢷⣄⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠈⠿⠶⠖⠒⠒⠛⠋⠉⣷⠀⠁⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⢶⣶⡶⠛⠁⠀⠀⢀⣀⣠⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣬⣷⣄⣀⣀⣀⣀⣠⣿⡿⠋⠙⠛⠋⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠻⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣷⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠿⢷⣶⣦⣤⣤⣀⠀⠀⢀⣠⣾⠿⠛⠉⠀⠀⠀⠀⠈⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀ ⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀ ⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟ ⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀⠀⠛⠉⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇ ⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⣴⡿⠟⠉⠉⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀ ⠀⠀⠀⠀⠀⠙⠿⣷⣦⣀⢀⣾⡟⠁⠀⠀⠀⢼⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡟⠀⠀⠀⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣴⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣀⣀⣀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⠖⠋⠉⠙⠓⠦⣄⣀⠴⠒⢉⣉⣉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣼⣵⣒⠭⠭⠤⠤⣝⡆⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⣀⠴⣾⡟⠉⠉⢍⠀⠀⢉⣿⣿⠿⠗⠐⠒⠒⠠⣄⡉⠆⠀⠀⠘⣄⠀⠀⠀⠀ ⡾⠁⠠⠤⠬⠷⢦⣌⣃⣰⠟⠉⠀⠀⢀⡀⡀⠀⠀⠀⠉⠳⡄⠀⠀⢸⡦⡀⠀⠀ ⠉⠉⠉⠉⠁⢿⣿⣽⡟⡟⠉⠉⠉⠉⠹⣿⣿⣿⠛⣗⣲⣶⡧⠖⠂⠀⠇⠈⢂⠀ ⣶⣒⡒⠒⠶⠤⠿⢯⣦⣿⣶⠖⠲⠶⠶⠾⠿⢛⣋⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⢂ ⠁⠙⢯⣄⡀⠀⠀⢀⣼⠁⠉⠳⢖⡒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⣴⡞⠁⠉⠉⠛⠉⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⡟⢦⣄⣀⣀⣀⣀⣀⣀⣀⣠⢤⢤⣴⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣃⣛⣛⣿⣿⣿⣻⣿⣿⡶⠾⠿⣿⠿⠛⠉⣹⠋⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⡷⣼⡟⠀⠳⡀⠀⢀⠴⠊⡁⠀⣠⠞⠁⠀⠀⠒⠋⠁⠀⠀⠀⢀⣠⣴ ⠀⠀⠀⠀⠀⠉⢷⠂⠀⠙⠚⠁⠀⢀⣴⣞⡀⢀⣀⢀⣀⡀⣤⣤⣔⣒⡽⠟⠋⠀ ⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠈⢀⡼⠷⣿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⠙⢦⣀⠀⠀⠀⠀⠀⠀⢤⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣳⣛⡉⢉⠉⢉⠉⠉⡙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠶⣿⠿⠛⠛⡉⠄⠌⠠⠁⠌⢂⠐⠄⢂⠀⡉⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⡱⢂⠁⡐⠠⢁⡐⠈⠄⠡⠈⢌⣤⡈⠌⠄⡂⠄⠡⠈⠳⡄⠀⠀⠀ ⠀⠀⣰⠋⡄⠂⡄⢂⣤⣥⣆⠠⠉⠄⠡⠁⠌⠻⣿⣦⣐⡈⠌⡐⢁⠂⡙⣆⠀⠀ ⠀⢰⠇⠢⢀⠃⠄⢿⣿⣿⣿⠇⡈⠄⠡⣾⣿⣿⣯⣙⠛⢁⠂⠌⣀⠒⠠⠘⡆⠀ ⠀⡾⢀⠃⡄⠡⠌⡈⠙⢋⠡⠐⠠⠈⠄⠻⣿⣿⠿⠁⡐⠠⢈⠐⠠⢈⠔⡁⢸⣀ ⢸⣧⠀⠆⡄⢁⠂⠄⡁⠂⠄⠡⢈⠁⠊⢄⠠⠀⡄⢂⠁⠆⠡⢈⠁⠢⠐⡀⢂⢱ ⠘⡇⠂⠆⡐⣦⠾⢦⡡⠿⠿⠿⢿⣷⣮⣄⢂⠡⠐⡠⠉⠤⢁⠂⠡⡁⠜⡀⠂⢸ ⠀⢿⠀⡃⠄⣷⠀⠀⢹⡔⡐⠢⡀⠄⡉⠿⣿⢆⡁⠆⡡⠒⠠⠈⡅⠰⠐⠠⠐⠑ ⠄⠸⣇⡒⠄⡽⠀⠌⠸⣇⠰⣡⣰⠼⠖⠛⠉⡈⢳⡆⠡⠌⡁⠂⠤⢁⡘⢠⠇⠀ ⠀⠘⣿⣆⡸⠁⠄⠂⠄⠉⢋⠉⡀⠄⠂⠌⢐⣠⠾⢁⠢⠁⠔⡉⠐⣠⢠⠏⠀⠀ ⠀⠸⣿⡙⡇⠐⡈⠐⡈⠐⡀⢂⠐⡈⠄⠘⢻⡁⠂⠆⠡⢉⠐⢠⢁⡴⠋⠀⠀⠀ ⠀⠀⣿⣇⡇⠐⡀⠁⠄⠡⠐⡀⠂⠄⡈⠐⢸⠠⠉⡄⠃⢄⣚⡵⠋⠀⠀⠀⠀⠀ ⠀⠀⢻⡿⣽⡀⠠⠁⠌⠠⠁⠄⡁⠂⠤⠁⢠⡁⠢⢴⡾⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⣟⣿⣦⣌⡠⠁⠌⠐⢠⣁⣤⠴⢋⣀⣤⢞⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢞⣭⡴⠒⠀⠒⣢⣬⠤⠀⠐⠒⠒⠒⠺⠦⠤⠬⣭⣿⣛⣛⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⣫⡿⠿⡞⢁⣠⡶⠖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⣮⣍⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠁⠚⠁⠀⣠⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣝⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⢀⡀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡝⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠞⠉⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠹⣆⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠹⣷⢿⡀⠀⠀⠀⠀ ⠀⠀⣷⣿⣿⠇⠀⠀⠀⠀⡼⠁⢀⡼⣫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢸⣆⢳⡀⠀⠀⠀ ⠀⢠⣟⣽⡇⠀⠀⠀⠀⣼⠁⠀⣨⡾⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⢻⡟⣧⠀⠀⠀ ⣸⣿⣿⣿⠁⠀⠀⠀⢰⣇⡤⠞⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠘⣧⢹⡆⠀⠀ ⣿⣿⡾⠃⠀⠀⠀⠀⣿⢉⣀⣀⣤⡀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠈⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠄⠀⠀⢿⢸⡇⠀⠀ ⣿⡋⠀⠀⠀⠀⠀⠀⡿⠛⣻⣿⣿⣿⣶⣾⣿⡀⠀⠀⣾⣄⢠⣟⠀⠀⣀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢸⠀⡇⠀⠀ ⣿⡙⢶⣤⣄⠀⠀⠀⣇⠀⡿⠟⣿⡿⠿⡿⠀⠙⠦⣄⣡⠈⠛⢻⣿⣶⣿⣷⣦⣄⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢸⡆⠃⠀⠀ ⠀⠉⠳⣦⣽⣷⣄⠀⠹⡆⣷⠐⠟⠓⣼⠃⠀⠀⠀⠀⠉⠀⢠⣿⠛⣿⣿⣾⣿⡟⣿⠟⢷⠁⠀⠀⠀⠀⠀⠀⣤⠀⣀⣴⠞⠉⡀⠀⠀⠀ ⠀⠀⢰⡿⣸⠏⠸⡟⠉⠁⠙⠧⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⠻⡅⢀⡿⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⠀⠀⠀⠸⣆⡑⠄ ⠀⠀⢸⢁⡏⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⡤⠞⠀⠀⢀⡾⠁⠀⣀⣤⠴⠃⣠⢾⣟⣀⣀⣀⣀⣀⣀⣈⠻⢀ ⠀⠀⡎⢸⡇⠀⢳⡈⢦⡀⠀⣠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣤⣤⣼⣅⠀⠀⣨⡵⢏⠀⠈⠉⠛⢿⣿⠭⣥⣶⠿ ⠀⠀⡇⣾⡇⠀⠘⡇⠀⢹⠟⠁⠀⠀⢀⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡙⡛⠛⡛⣯⠀⠀⠳⣤⣤⣤⣤⣌⠿⢸⡇⠁ ⠀⠀⡇⣿⡇⠀⠀⣧⠀⣿⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠁⠁⠁⠉⠁⢻⡄⠀⠀⠈⢷⣟⢦⣤⡴⠛⠁⠀ ⠀⠀⢳⢸⡇⠀⠀⠀⢸⡿⠲⣤⣄⣀⣀⣿⣿⠶⠶⣶⠦⣤⣤⠴⣶⣶⠶⣒⡋⢉⡿⠀⠀⠀⢀⠀⠀⣸⣿⣦⡀⠀⠀⠙⢶⣍⠳⢤⠀⠀ ⠀⠀⠸⣧⢻⡄⠀⠀⣼⡧⠀⠀⠈⠉⣹⣿⣿⠋⠉⢻⣤⣶⠶⠚⠋⠉⠉⠙⣿⡟⠁⠀⠀⣠⡟⠀⠀⣿⣿⡿⣯⣛⡲⠶⢶⣬⣿⢸⠀⠀ ⠀⠀⠀⠘⢯⣻⣦⣠⠟⠀⠀⠀⠀⠀⣿⢁⣹⣤⡞⣋⣁⣠⡴⠶⠛⠛⠉⠙⣿⣤⣤⣤⠾⠉⠀⠀⢠⣿⣼⠃⠀⠀⠉⠉⠛⠛⠛⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢀⡿⠻⣇⠀⠀⠀⠛⠛⠳⣄⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⣠⡾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡾⣧⡀⠀⠠⠴⠛⢙⡀⠀⠈⠓⢦⡀⠀⠀⠀⠈⢳⡄⠀⣠⣾⣃⣀⣀⠤⠶⣿⡿⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣎⡻⠶⠤⠴⣾⡿⢧⡀⠀⢤⣄⣻⡄⠀⠀⠀⠈⣷⠉⠛⠦⣌⣀⠀⠐⠺⡏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢛⡛⢓⣾⣉⢡⣤⣿⣷⣿⣭⡭⠽⠟⠛⠛⢻⣿⣦⣤⣤⣤⣬⡟⣓⣐⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠉⠉⠉⠉⠉⠛⠛⠳⠶⢦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⣺⣕⢦⠀⠀⠂⢀⡴⣶⣯⣟⠲⣄⠀⠀⠀⠀⠀⠀⠀⠘⣇ ⠀⠀⠀⠀⠀⠀⢸⠃⣿⣿⣿⣇⠀⠀⣼⢹⣿⣿⣿⣿⡌⢳⡄⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⢸⣦⢻⣿⣿⡯⠀⠀⠹⣾⣿⣿⣿⣿⡟⢀⡿⠂⢄⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⢸⡌⠙⠒⠋⠀⠀⠀⠀⠀⠙⠛⠿⠷⠚⠋⡠⡀⠀⠱⠀⠀⣼⠃ ⠀⠀⡞⢻⣾⣦⣀⠻⣤⣤⣀⠤⠤⠤⢤⣤⠀⠡⡀⠀⠀⠱⡑⠑⠀⢘⣠⠾⠁⠀ ⡔⢹⡷⣾⣄⠀⠈⠲⣏⠀⡿⠛⢳⣄⠀⠀⠀⠀⠈⢂⣀⣠⣤⠶⠞⠋⠁⠀⠀⠀ ⡷⢿⡀⠀⠉⠳⣄⠀⠈⠛⠷⠀⠈⡏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⣼⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⢽⡦⠄⡀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⠦⣀⣀⣀⣀⣀⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⠋⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀ ⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠤⣤⠞⠋⠁⠀⠀⢳⡀ ⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⡾⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⣸⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⡆ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠘⢧⠀⠀⠀⠀⠀⣀⣀⠀⠖⠚⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟ ⠀⠈⠳⢤⣀⣠⠞⠉⢨⣇⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁ ⠀⠀⠀⠀⠉⡟⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀ ⠀⠀⠀⠀⠀⠻⣄⡀⠀⣀⡼⠉⠛⠓⠒⠶⠶⠶⠶⠒⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠲⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⢦⡀⠀⠀⠀ ⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣦⠀⠙⣆⠀⠀ ⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢷⡀⠈⠧⡀ ⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠁⠀⠀⢳ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠀⠀⠛⣷⣤⣸ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸ ⡇⠀⠀⠀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⢸ ⡇⠀⠀⠀⠈⢧⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠙⢦⡘⠉⠀⢠⠖⡿⢸ ⡇⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢳⡀⣠⠋⣼⠀⡘ ⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠿⠁⠀⠉⠛⡇ ⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣽ ⠘⣦⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⡏ ⠀⠈⠓⠦⣤⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⡀⠀⠀⠀⡤⠏⠀ ⠀⠀⠀⠀⠀⠉⠉⠙⠶⠤⣤⣀⣀⣀⣀⡀⣀⣀⣤⣴⠋⠁⠀⠉⠑⠛⠉⠁⠀⠀

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⠙⢳⣌⢌⡻⢿⣷⡀⠀⣀⣤⣾⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣻⢿⣿⣿⣷⣿⣿⢿⡿⣿⣷⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠈⠳⣃⠌⣹⣷⣾⢿⣻⡽⣾⣿⣟⡷⣿⣿⣿⢿⣟⢯⣷⣹⢾⣹⢳⣟⣿⣿⣿⣿⣿⣟⡟⣾⢏⣿⢳⡿⣿⣜⣧⡀⠀⠀⠀⠀⠀⠀ ⣀⠠⠇⠀⠈⣿⡿⣽⣫⣟⣶⣿⣿⣻⣜⣿⣟⠿⣼⣫⣞⢯⡶⣫⣷⣯⣷⢺⣭⢿⣿⣟⢧⣻⢾⣭⡟⣾⣫⢷⣻⣿⣎⠳⠀⠀⠀⠀⠀⠀ ⠀⠉⣇⠀⣼⣿⣽⣿⣿⣿⣿⣿⣟⢶⡻⣮⢽⡻⢧⢷⣫⢷⣹⣿⣿⢿⣿⣿⣼⢫⣟⢮⣿⣿⣿⣷⣿⣱⢿⣧⢷⣻⣿⡆⠀⠀⠀⠀⠀⠀ ⢀⣀⣈⣾⣟⣾⣿⣳⣯⣿⢯⣟⢾⣫⢷⡭⣷⣻⣿⣎⢷⣫⣿⣿⢯⣟⡾⣽⢿⣷⣮⣿⢿⣯⢿⣿⣷⢯⣻⣿⣧⢯⣿⡧⡇⠀⠀⠀⠀⠀ ⡄⠀⣼⣟⡾⣿⣯⣿⢿⣯⣟⢾⣫⢷⣫⣾⣿⣿⣿⢿⡾⣿⡿⣽⢫⣾⡿⢾⣯⣿⠿⣿⣯⣾⣯⣟⣿⣯⣟⣿⢿⣳⢿⣧⡙⣦⠀⠀⠀⠀ ⣟⣾⣿⣿⣿⣿⣿⣽⣿⣳⢯⡿⣱⣿⣿⣿⣟⣿⣯⢿⣻⣽⣿⠾⢛⠛⠙⠃⠀⠀⠀⠀⠀⠈⠙⠿⣾⣿⣾⣿⣏⠿⣞⣽⣿⣎⡳⣄⠀⠀ ⣿⣿⣿⣿⣿⡿⣿⣿⣯⣟⣯⣽⣿⣿⣟⡷⣻⣟⡾⣏⢷⣿⠡⠎⠄⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⢿⣿⡾⣭⡟⡽⣾⣯⢿⣷⡝⢷⡀ ⣿⣿⣿⣿⡿⣽⣿⣿⠾⣵⣻⣿⣟⡷⣫⡽⣟⡾⣹⢮⣿⢃⠱⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠠⠐⠂⣿⣟⣧⢻⣵⣯⣿⣿⣞⣿⣦⠃ ⣿⣿⣿⡿⣽⣳⣿⣯⢟⣷⣿⡻⡼⣿⣷⣿⣵⣫⣷⡟⢡⠊⠀⠀⠀⢀⣠⣶⣦⠀⠀⠀⠀⣤⣄⠀⠀⠀⣼⣿⣾⣿⣿⢳⣻⣿⣿⡞⣿⣧ ⣿⣿⣿⣻⡵⣫⣿⢧⣻⣿⢣⡟⣵⢫⡝⣻⣿⡿⣿⣿⣿⣶⣶⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣟⣵⣯⠶⡭⣿⣿⣿⣹⣿ ⣻⣿⡿⣵⢫⣽⣿⢣⡿⢧⡻⢼⣩⠗⣼⣿⣟⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣧⡳⢽⣿⣿⣳⣿ ⣿⣿⣿⢭⡗⣾⣿⣹⣏⠷⣍⡳⣌⣿⣿⣿⣿⣿⠿⠿⣿⡏⢉⣁⣈⣩⣿⠏⠀⠀⠀⠀⠀⣿⣿⠿⣿⣉⣀⣤⣴⣿⣿⣿⣿⢩⣿⡟⣿⣿ ⠃⢿⣿⢮⣝⣿⡿⣜⣿⣙⠦⣿⣿⣿⣿⡉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⠟⣰⢫⣿⠱⢻⣏ ⠀⣸⣿⡗⣾⣿⣿⣎⢿⣯⢚⡱⢺⡟⢛⢧⣠⣤⣶⡶⢶⠿⠿⠿⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⣠⠤⡼⠿⢿⣿⣿⣵⣮⡙⢦⢻⣯⢼⡈⣁ ⣴⣟⣿⣿⣻⣿⣟⣿⣎⢿⣧⠎⣽⡏⡌⠭⡉⠀⠀⢀⡀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⡈⠙⢿⣿⣌⠿⣿⡰⠁⠀ ⣉⣿⣿⢿⣿⠿⣿⣿⣻⣮⢟⣿⣜⣿⡔⢡⠃⠀⣉⠲⢌⡋⡔⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠊⡴⢡⡃⠸⣿⣿⣯⣿⡇⠀⠀ ⣿⡏⣿⣏⠿⣃⠿⣿⣷⣻⣟⡞⣿⣿⣿⣄⠣⡐⠠⠉⠆⠱⢈⣂⣴⣤⣶⣶⣶⣷⣷⣾⣶⣶⣷⣦⣤⣤⣁⡀⠁⠂⢀⣿⣿⣿⢿⡇⠀⠀ ⠏⠹⣟⣿⣦⠀⠀⣿⣿⣷⣯⣻⣽⣇⠻⢿⠆⠁⠆⠀⠈⠀⠘⢿⠿⠟⠛⠋⠙⢉⣽⡿⢋⢭⡿⠻⣿⡙⢿⣷⡀⠀⣼⣿⣯⢻⡎⠁⠀⠀ ⠀⠀⠹⠿⣿⢿⣦⣿⣿⣻⢿⣷⣯⣿⣆⠢⠌⠤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢀⣳⡿⠁⢠⣿⡇⡜⣿⣧⣿⣿⢿⣿⣷⢻⡄⠀⠀ ⠀⠀⠀⠀⠉⠛⡿⣿⣿⣻⣿⣽⣻⣿⣿⣿⣮⣔⡠⢁⠂⠄⠀⠀⠀⠀⢀⣼⣿⠏⢠⣿⠏⠀⣰⡿⢙⣿⢠⢸⣿⡿⣽⣛⡾⣿⣏⢃⠀⠀ ⠀⠀⠀⠀⠀⠈⣼⣿⣟⣷⣻⢿⣷⡽⣻⣷⣍⣻⣿⣿⣶⣮⣖⣳⣄⣠⣾⣿⠃⣰⣿⠃⢀⢼⡿⠁⢠⣿⢌⢸⣿⣿⡱⣯⣝⣻⣿⢰⡀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣽⣿⣯⣛⠾⣿⣱⣻⣿⠻⣿⣿⡈⡝⢛⠛⣿⣿⣿⠃⠈⠋⠉⢠⢮⡿⠁⠀⢸⡏⠤⢘⣿⡿⣷⣣⣿⡜⣿⣼⡁⠀ ⠀⠀⠀⢠⣾⠿⠉⠞⣿⣿⡻⣯⣏⡗⣧⢳⣿⡗⢌⠻⣿⣶⣭⣼⣿⢹⡏⠀⠀⠀⠀⠽⠛⠀⠀⢀⣿⢏⠂⢹⣿⣷⣾⣿⣹⣿⣟⡯⠀⠀ ⠀⠀⣰⣿⠋⠀⠀⠀⠉⠻⣇⠹⣿⣞⡼⣻⣿⡁⠀⠁⠙⣿⣿⣿⣿⢠⣿⠄⠀⠀⠀⠀⠀⠀⠀⣾⡟⢢⠁⢸⣗⣻⠻⢩⣿⡿⣽⡃⠀⠀
⠀⠀⠀⠀⢀⢤⣔⠕⢂⣀⠴⠂⠀⠈⠉⠙⠒⠚⠯⠽⣒⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡨⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢵⣦⠀⠀⠀⠀⠀ ⠀⠀⠺⠒⡔⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣵⡄⠀⠀⠀ ⠀⣀⣤⡌⠀⠀⡀⠀⡠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⣷⡄⠀⠀ ⢀⣾⡟⠀⠀⠰⠀⡨⠎⡅⠀⠀⠀⠀⠀⢠⠾⠁⠀⠀⠀⠀⠀⠀⣆⠀⢸⣷⠀⠀ ⣿⡿⠃⠀⠀⣗⣈⣀⠀⢧⠀⠀⠀⠀⡰⠁⠀⢇⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⠇⠀ ⡿⣀⠀⠀⢸⠋⣿⣿⣿⡿⢦⡀⠶⢴⣥⣠⣄⡈⢆⠀⠀⠀⠀⠀⠀⠣⡀⢇⠇⠀ ⠉⠺⣽⣦⣀⡆⣆⠛⣱⠃⠀⠈⠁⢠⢟⣿⠿⡟⠿⢲⠀⠀⠀⠀⢀⣠⠔⢋⠀⠀ ⠀⢸⢻⠁⡇⠀⠈⠉⠁⠀⠀⠀⠀⠘⢆⣉⡴⠁⢀⠃⠀⣀⠄⣰⡟⠀⠀⠀⠑⡅ ⠀⣾⡏⠀⠍⢢⡄⠐⠒⢠⠀⠀⠀⠀⠀⠀⠀⠐⢳⠶⠧⠤⡴⠛⣀⣉⠙⢿⢿⠚ ⠀⣿⡇⠀⠄⣸⡀⠀⠀⣹⡀⠀⠀⠀⠀⠀⢀⣠⡼⠁⠀⠀⢰⡀⠈⠻⡿⣴⠊⠀ ⠀⠸⣿⡀⠀⡏⠉⠒⢒⣿⠏⢿⣉⡮⠝⠛⠷⡤⠃⠀⡐⠀⢸⣿⣦⢤⣬⣺⣷⠀ ⠀⠀⠙⣷⡾⠁⠀⠀⢸⣤⠷⠫⢥⣖⠂⠉⠉⢳⡶⠊⠀⢀⣿⠇⠀⠉⠁⠉⠉⠀ ⠀⠀⠀⢹⣧⡀⠀⢂⡏⠀⠂⠀⠀⠈⠳⡄⣠⠮⠤⠄⣲⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⢭⡟⣉⣦⣼⣶⡦⠤⢤⣧⣀⣁⣶⠄⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡬⠟⠛⠉⠙⠛⠫⢴⣀⣀⠀⠰⠒⠛⠻⢧⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⣠⠴⠒⠂⠐⠒⠢⢽⣧⠀⠀⠀⢀⡀⠀⢈⣙⣦⡀⠀⠀⠀ ⠀⠀⣠⡿⠃⢀⡴⠋⢀⡠⠖⠊⠉⠉⠉⠓⠿⣏⠉⢀⡤⠖⠒⠒⠛⠿⢿⣷⣀⡀ ⠀⣠⣿⢁⢶⠋⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⢈⠻⣟ ⣾⠟⡇⢸⣸⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠈ ⣿⠀⠁⠀⠁⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢠ ⢸⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠈⣋⣤⣧⣀⠀⠀⠀⠀⠀⠀⢈⣻⣶⣿ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⢖⡫⠟⠋⠁⢈⡙⠒⠂⠐⠒⠊⣩⣼⡟⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠻⣾⡀⠘ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣰⠀ ⠀⠀⠀⠀⠀⠠⡞⠁⠐⠢⠤⢤⣬⣍⣉⠙⠒⠒⠲⠶⠦⠤⠶⠖⠛⢋⣩⣼⣿⢷ ⠀⠀⠀⠀⠀⣄⠙⠒⠒⠒⠒⠶⠤⣤⣬⣭⣉⣉⣉⡁⠐⠂⠐⠀⢙⡿⠋⠀⣼⣿ ⣄⣀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢿⣅⡀⠉⠙⠛⠿⣭⣉⣩⣿⣿⡇⠀⠐⣇⠀ ⠟⠿⢭⣟⣒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣈⣉⡓⠶⣦⡄⠀⠈⠉⠛⠻⠗⠀⠀⠙⢾ ⠀⠀⠀⠀⠉⠉⠛⠚⠒⠶⠶⠶⠦⠤⠶⠖⠛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠈⠙⠄⢀⠴⠋⣽⠟⣽⣿⡶⠔⠒⠒⢶⣆⣩⣽⡶⠛⠉⠣⡕⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⡿⠁⠸⠋⠁⠀⠀⣠⣄⡀⠹⡿⠋⣀⡀⠀⠀⠹⡞⠀⠀⠀⠀ ⠀⠀⠐⣰⠋⢹⠟⠀⠀⠀⢀⡀⠀⣰⠏⠈⠻⣆⢀⡾⠻⣷⠀⢰⡀⣿⠀⠀⠀⠀ ⠀⣰⣀⡿⢀⡏⠀⠀⣠⣶⣿⠛⠀⣏⣠⡴⠒⠚⠛⠒⠢⣌⣧⢸⠁⠘⢦⢢⠀⠀ ⣰⣿⣿⢿⣿⠁⢀⣼⠟⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⣮⠳⣕⠄ ⢿⣿⠏⢸⡏⢀⡞⠁⣤⣀⠀⡴⠃⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣷⣤⡾⠚⣷⠘⣆ ⢸⡟⠀⢸⠇⡞⠀⠀⠈⣹⠟⣛⣳⣶⣖⣛⡋⠀⠀⠀⠙⣳⣟⣿⣭⣆⠀⢻⣇⢻ ⢸⡇⠀⣾⠀⠀⠀⢀⣾⣷⠿⠟⣿⣉⣉⣹⠋⠀⠀⠀⠿⢿⣏⣉⣹⣿⡷⢨⡟⣞ ⠀⣧⢠⣿⡄⢇⠘⢹⠻⢄⣀⠤⠼⠿⠿⠯⠀⠀⠀⠀⠀⠈⠿⢿⣟⡋⠀⢸⢀⠃ ⠖⣽⣿⣿⢱⠘⢆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣸⡌⠀ ⡶⣻⡙⠘⢿⡰⠀⢳⢵⡀⠀⠀⠀⢀⣀⣤⣤⡴⢶⣦⢴⣤⣤⣀⠀⢠⣿⡿⠇⠀ ⠀⠣⡷⣤⣼⡟⢦⡘⣆⠉⠀⠀⠀⠀⠉⠁⠀⣠⠞⢀⠎⢸⡄⢻⣤⡾⢿⡼⡀⠀ ⠀⠀⠈⠙⣿⢁⢢⡉⠻⡷⢤⣀⣀⠀⠀⢀⣼⠃⢠⠋⢠⠋⣷⠈⡏⠀⠀⢷⠁⠀ ⠀⠀⠀⣰⢿⢸⡄⠙⠄⢹⡛⢿⡉⠛⢻⣿⠇⠐⠃⣠⠋⢀⡇⠀⣿⢦⢰⢸⢸⠀ ⠀⢠⠞⠁⠀⠻⠘⢦⠀⢸⠀⠀⠻⣶⣟⢈⠄⠀⠀⠁⠀⡼⠀⠀⡿⠯⣷⢟⠆⠀

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