Melissa Bardin Galsky Emojis & Text

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⢰⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⣶⠶⢶⡶⠶⡦⢰⡶⢖⣶⣶⢶⣲⣶⣶⢶⠶⠖⠲⠶⠶⠶⣶⠶⠒⠶⢶⡆⢰⠖⠐⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠖⠒⠒⠶⢢⢰⡶⠖⠶⠶⣶⣶⡒⠒⠒⠒⠒⠒⠒⠒⡶⡖⠶⡆⠀⠀⠀⢶⣶⣶⠒⢒⡖⢦⠀ ⣸⢻⡾⠟⡀⢻⣧⡴⠛⢦⡞⢸⡏⠀⠀⠀⡝⠛⣿⡇⠀⡄⢸⡯⡍⣉⣌⣉⣁⣉⢹⣹⣤⣠⣤⣦⣤⣴⣿⠀⠀⠀⢸⡇⢸⠀⣀⣀⡀⠀⠀⠀⣀⣀⣄⣀⣠⣴⣶⣶⣶⡴⢿⢨⣇⣠⠼⠋⠉⢉⣙⣲⣄⡀⠀⠀⠀⠀⣯⡇⢀⡇⠀⠀⢀⡾⣥⡀⢝⣦⡄⢸⠀ ⣼⢸⣾⣦⣤⣾⣿⣤⣤⡄⠂⢸⡆⠀⠀⠂⠉⠒⠹⡇⠀⠈⢸⡷⡁⣏⠉⠉⢿⣿⢿⠛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⠈⣭⣶⣶⣿⣦⢰⣿⣿⣿⣿⣿⣟⣻⣿⣿⣷⣄⢸⢸⡟⠁⠀⠀⣴⣿⣾⣿⣿⣿⣏⣀⣴⣶⣇⣾⡟⡇⠀⠀⠀⣡⣼⣿⣻⣯⣻⢾⠀ ⣾⠔⠻⣿⣿⣿⣿⣿⡿⠀⠀⢸⣧⣠⣦⡀⠀⠀⣸⡇⠀⠀⢸⡷⡁⣟⢢⠀⣸⣽⡞⣀⣈⣛⣿⢋⣰⡋⣷⠀⣀⠀⢸⡇⢰⣿⡟⣿⣿⣃⡤⢙⣿⣿⣿⣿⣯⣬⣿⣿⣿⣏⢿⢸⣿⣧⣄⣘⡇⠉⠻⣧⣝⣿⣿⣿⢿⣿⣯⣾⣽⡇⢠⣶⣤⣸⣿⣿⣷⣶⣿⣾⠀ ⣹⣻⣶⢿⣏⢽⣯⣽⣷⠴⢳⣾⣿⣿⣿⣿⣾⣯⣽⡿⠶⢆⢸⡷⡁⣯⣷⠟⢩⡏⢧⡁⠉⠀⠉⣉⢿⣟⣿⠈⠟⣁⣼⡇⢸⠹⣿⡿⢷⣎⠳⢀⠻⢿⣧⣿⢻⣟⡭⢻⠇⠹⢻⠨⡟⠁⠘⠿⠻⣧⠀⣼⢿⣿⣿⣟⣶⣿⣿⠛⠃⡇⠈⢻⡬⠛⠟⣿⣿⣿⣿⣿⠈ ⣸⢿⢻⡄⣹⣿⡿⢻⠇⣰⣾⣿⣿⣿⡌⢿⡞⣿⣾⡇⢀⣎⢸⡷⡁⡿⠁⢀⡿⣷⣤⣭⣿⣮⣽⠉⠀⣿⣿⣿⣿⣿⣿⡇⢸⠀⠉⠛⣟⣿⡍⠀⢡⡄⢺⡽⠛⢛⣿⣿⣧⣖⣹⠀⡅⠀⠀⠀⠀⣸⣿⡁⠈⣙⣿⣿⣿⣿⡇⠠⠀⡇⣰⠟⡠⠔⠚⠻⢿⣻⣿⠏⠀ ⢹⣸⣞⣽⣾⣿⣷⣬⣇⣧⢻⡀⢁⡾⡸⡈⣿⣿⣿⣱⣥⣿⢸⣷⡁⡧⠀⣬⢲⣿⡏⣻⣿⣿⣿⣶⢀⣿⡏⣿⣿⣿⠟⡇⢸⢄⠀⠀⠘⢛⣫⠥⠖⠓⠒⢶⣿⠿⠋⠳⠿⠟⢻⢠⡇⠀⠀⠀⢀⣿⣼⣿⣿⣿⣿⣿⣿⣧⣤⣶⢦⣗⣸⡥⢤⣤⣾⡶⠾⣿⣿⡄⠀ ⢻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⢸⣷⣃⣿⡦⣤⣿⣿⣿⠿⣻⣿⣏⣉⣩⣿⣿⣿⣁⣀⣠⣇⢸⡦⣼⣿⣿⣷⠦⣴⣶⣶⠶⣲⡿⢿⠒⢺⡾⠿⡏⢰⡿⢿⡏⢹⡟⠛⣯⠉⣿⢋⣿⠀⣿⣉⣹⠀⢾⣏⣹⠇⣸⣧⣴⠟⣘⣷⣤⣧⠀ ⢸⣿⣿⣿⢿⣿⣿⣿⠽⢧⣿⣿⠿⣿⣷⣾⠗⢻⣿⣿⡚⢋⡬⠿⣏⢙⣿⠿⡏⠉⡟⠟⣻⠉⣻⢛⣻⡄⢺⣋⣹⡆⢰⣋⣍⡇⠀⣏⣴⠿⢀⣻⣦⣿⣀⣳⣤⣿⣂⣼⣷⣾⣥⣬⣷⡿⣥⣤⠿⡿⢷⣀⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠃⢹⠀ ⢸⣾⢿⡇⠠⣏⣉⡿⠀⢯⣉⡽⠀⢹⣤⡼⣀⣸⣤⣴⡃⣨⣷⣾⣋⣠⣿⣾⣧⣤⠿⠿⠯⠦⠾⣿⠻⠖⠞⢛⣛⠓⠒⠛⣛⡛⣿⡿⠛⢻⠍⠙⡇⣾⡏⡉⣿⡯⢟⡻⣲⣾⠛⠓⢦⣤⣤⣤⣸⣇⣼⠆⣿⣿⡟⠛⣿⣿⣿⣿⠿⣟⣻⣿⣿⣿⣿⣿⣿⣇⡁⢸⠀ ⣼⣿⣿⣿⣿⡟⣻⣿⣾⣏⣽⡿⣿⣟⣿⢯⣥⣡⡁⠘⡇⠁⠀⠀⠐⠻⣷⣞⣻⣿⣳⣤⠀⠀⠀⢼⠁⢠⡶⠚⠏⡷⠾⡛⠹⢿⠉⣓⠀⣿⠃⠠⡇⣙⠻⣥⣿⣷⣾⠛⠻⠬⢤⡤⢴⣿⣿⡿⠟⠋⢹⠃⣿⣿⣧⠀⠙⠃⣖⣳⡶⠚⢘⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀ ⢽⣿⠻⣽⣿⣿⣿⣿⣷⣿⣿⣴⡿⣿⣟⣿⣻⡏⣴⣾⡇⠀⠀⠀⣰⢋⣾⡉⡝⡉⡹⣎⢳⡀⠀⣸⠀⠀⢳⡄⠀⢀⣴⠷⠘⠉⠉⡟⠛⠉⠀⠀⡇⠰⠀⣀⠛⢿⡁⠉⠀⠀⠀⠀⣎⠉⢐⠀⠀⠀⠀⠀⣿⣾⠁⢴⢦⣤⣶⠶⣴⣦⣾⣇⣾⣿⣿⣿⣿⣿⣿⣿⠀ ⢺⣻⣿⣿⣿⣿⣿⣿⡿⠉⣯⠛⠓⢮⣙⡵⠋⠉⣌⢉⡇⠀⠀⠐⣇⢸⠧⣀⣿⣁⡵⡟⠀⡇⠀⢼⠐⠀⠈⠳⠰⠋⢳⡠⣤⣤⡴⠃⠀⠀⠀⠀⡇⠱⠀⠀⠛⠘⢷⣤⣤⣶⣛⡇⣟⠃⠾⣀⠀⠀⠀⠀⡏⣼⠧⣀⠀⠀⠀⠀⣀⡠⢿⠫⣽⣿⣯⣿⢿⣯⣿⣿⠀ ⢸⢽⣿⣿⣿⣿⣿⣿⣗⡀⢀⣤⣼⣾⣿⣿⣷⣆⡇⢠⡇⠀⠀⠀⢩⠘⣆⠀⠉⠀⢀⡇⣰⠃⠀⢺⠈⠀⠀⠀⠀⠀⠀⣣⣙⡿⠁⠀⠀⠀⠀⠀⡇⣩⠀⠀⠀⢀⡄⠂⠛⢢⡀⢠⢿⡆⠀⠉⠀⠀⢀⡀⡇⢹⡀⢀⣉⠿⠟⠻⢥⣀⢐⡧⡟⣿⠉⣿⢸⣁⣃⣻⠀ ⢸⣿⣿⡿⠿⣿⣿⣿⠛⣿⣿⣿⣿⣭⣉⣿⣿⣉⣿⣿⡧⣄⣀⠀⢨⣦⣿⢢⣤⣤⣾⡿⡆⠀⠀⣹⠀⠀⠀⠀⠀⠀⢰⡏⣼⣿⣄⠀⠀⠀⠀⠀⡇⣽⠘⠉⢍⣻⣿⣿⡿⠿⣿⣳⡟⣿⠿⠿⢝⡋⢿⠄⡇⠀⠓⠃⠈⠢⡀⠀⡴⠉⠙⠀⣛⠈⢯⡏⣔⠪⣅⣿⠀ ⢿⣿⣿⣇⠐⢧⣤⠿⠀⢿⣉⣻⠀⢾⣋⣽⠆⢹⡋⢻⡆⢸⡟⢻⣿⠹⡿⠿⡏⠉⡿⡿⢷⠲⣶⢿⡼⡶⣶⣶⣶⡦⢾⣿⣿⡿⢿⣤⣤⣤⣤⣤⡇⢾⣶⣎⣉⣹⣿⣽⠂⠀⡿⠳⣦⣮⠇⠀⠀⠈⢹⡂⡇⠀⠀⠀⠀⠀⢈⡾⡀⠀⠀⠀⣰⣴⡏⢙⠦⣙⡶⢻⠀ ⢸⠘⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠑⠚⠓⠒⠒⠒⠛⠛⠒⠂⠻⠭⠥⠤⠽⠷⠧⠤⠽⣶⣟⣀⣹⣶⣝⣃⣙⣧⣼⠇⠸⢥⣤⠇⠀⣯⣉⡿⠐⢿⣙⣿⠀⣾⠛⢻⡉⢹⣟⢻⡏⢻⡿⠿⡝⢻⡿⠶⣏⠁⣽⣶⣶⠶⣶⣶⣤⠟⢧⣤⣶⠯⢿⣼⣦⣮⣁⣀⣀⣼⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠒⠚⠙⠛⠓⠒⠚⠛⠛⠰⠬⠯⠯⠥⠬⠷⠶⣧⢬⠳⣟⣯⣠⣿⣤⣽⣀⢻⣤⡾⢀⡹⣦⣸⠇⢸⣏⣩⡷⢐⣿⣟⡧⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⣟⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⢿⠉⠑⠒⣺⠛⠛⢻⠀ ⢸⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠠⡇⠀⠀⠀⣀⡀⢰⣷⡶⢂⣀⡀⠀⠀⢸⡇⠀⢠⠇⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠶⠖⠲⠖⠶⠾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣐⡇⠀⣴⠛⠉⠙⠳⣄⡾⠋⠉⠉⠓⣦⠘⡇⣰⠏⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⣋⣁⣀⣀⣀⣀⣀⣀⣈⣙⣦⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⡧⠀⠀⣤⡄⣿⠀⣄⡀⠀⠀⢘⣿⡿⠁⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠈⣳⠦⠀⠀⠀⠀⠘⠛⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠚⠋⠋⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠛⠓⠦⡀⠀⠀⠀⠀⢻⡄⠹⣄⣀⣉⡼⢻⡄⠉⠁⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠸⣇⣀⡤⠶⠦⢤⡀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣠⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⣷⠀⠀⠈⠀⠀⠀⠑⠦⠤⠤⠖⢻⠇⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⣠⣤⠴⠖⠛⠉⢉⡿⠀⠀⠀⠀⠙⣦⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⢠⠞⠋⢩⡙⠉⣩⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣤⡄⠀⠀⠉⣽⣯⣍⣉⠉⠙⢦⠀⠀⢸⡆⠀⠀⠀⠀⠘⣇⡀⠀⠀⡠⠚⠄⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢺⠑⠀⠀⠀⠀⠀⠈⣇⠀⢀⣤⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡟⠀⢀⣼⡇⠀⣼⠆⢀⣾⠟⠛⢿⣄⠀⠀⢰⡟⢾⡄⣠⠿⢳⡀⠀⠀⣼⡏⠉⠙⠓⠀⠸⡆⠀⠐⡇⠀⠠⣦⣀⣠⠖⠈⠉⠉⠀⠀⠀⠈⠉⠉⠹⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠉⠀⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢠⡇⠀⠈⣿⠙⠛⡿⠇⣺⣯⠀⠀⠈⣿⠀⢠⢯⠁⠘⣎⢱⠃⢻⣓⠀⢰⣿⠤⠆⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠉⠳⣄⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠈⢹⣟⢃⣀⡄⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⡽⠶⠶⢦⣞⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢸⠀⠀⢀⣿⠀⢸⣯⠁⠘⢷⣤⣤⡾⠏⠐⡷⠃⠀⠀⠈⠁⠀⠘⣿⠀⣼⣧⣴⣶⣶⡄⠀⠀⡇⠀⠀⣷⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠳⢤⣀⣀⠀⠀⣀⣠⡽⠟⠋⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡀⠀⠘⡆⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢸⠀⠀⠈⠋⠀⠈⠁⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⢸⡁⠀⠙⠃⠀⠀⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⢠⡍⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⡇⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⢺⠲⠦⠤⢤⣤⣼⡇⠀⠀⠀⠀⢰⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠘⡆⠀⠀⣸⣿⡀⣠⣿⣷⠀⣠⣾⢿⣆⢻⡆⠀⢰⡿⠀⢺⡇⢰⣿⠛⠳⠀⣠⡾⠻⡇⠀⠀⡇⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠈⣏⠀⠙⠦⣄⣠⠴⠋⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⣇⠀⣴⡟⠈⡿⢽⠀⢻⣇⡿⡄⠀⡿⡜⣿⢠⡿⠁⠀⣸⡇⣻⡿⢶⣤⠀⠛⠶⠶⣢⠀⢸⡇⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⢠⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢹⢀⣿⠀⠀⠘⠛⠀⠀⣽⡜⢧⣤⠟⠁⣸⣟⠁⠀⠀⠸⠇⢙⡿⣤⣤⣦⢖⣆⣠⡿⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠘⣆⠁⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠙⠊⠁⢀⡼⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠹⣄⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠒⠒⠖⠲⠲⠖⠒⠒⠒⠒⠒⠓⠚⠒⠓⠚⠓⠒⠚⠉⠛⠉⠉⠉⠉⠉⠉⣻⠿⣿⡖⠒⣦⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠈⠘⢧⣠⡼⣦⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣃⣹⣿⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠛⣷⠒⠶⠲⠖⠶⠲⠶⠒⠦⠶⠖⠶⠶⠲⠶⠖⠶⠲⠖⠒⠚⠛⠛⠛⠋⠋⠉⠉⢧⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣠⣀⣤⣤⣤⣤⣤⣤⣦⣴⣶⣶⣶⣶⣶⡖⠲⠶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⢟⡉⣩⠟⠋⠉⠀⢀⣄⠉⠉⠓⢾⡋⢉⣉⡈⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠾⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣄⣀⠀⠀⠈⠋⠀⠀⢀⣠⡷⢤⣯⣄⣀⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⡆⠉⠉⠛⠙⠋⠛⠙⠉⠁⠀⠀⠀⠀⠉⠉⠉⠛⠛⢷⣶⣶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠛⣽⠋⠙⠉⠉⠉⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣶⠶⣶⣶⣶⠲⣲⠶⢾⡟⣻⡿⢿⣿⢫⣿⡟⣏⠀ ⣸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⣶⣶⣶⡷⢲⡶⠶⡖⢛⡿⠿⣽⠛⣿⠟⣿⠉⡽⠛⢻⠍⢹⢛⣻⡇⠸⣏⣽⡇⠸⣏⣡⠿⠀⣿⣤⡿⣀⣻⣤⣜⣀⣙⣷⣞⣣⣼⣷⣶⠥⠬⠿⠿⢵⠀ ⣽⣶⣶⣶⢖⣶⢶⣶⠒⣾⠿⢿⡛⣿⠿⢻⡍⢽⡛⣻⡏⢹⡟⢻⡿⠰⣯⣩⡷⠐⢏⣉⣻⠂⣽⣬⡼⠃⡙⣦⣼⣃⣘⣲⣶⣇⣤⣷⡶⠯⣄⢻⣿⣿⣶⣾⡿⠛⠲⢾⠛⠓⠓⠚⠋⠉⠈⠉⠉⠓⢺⡋⠉⠁⠉⠀⠀⠀⠀⠀⠀⢀⣤⠎⢡⣤⣬⣳⠀⠀⠀⣸⠀ ⢹⣿⣿⣟⣈⣿⡶⣿⣠⣿⣾⣿⣤⡿⠿⠿⣦⣾⣿⢿⠷⠶⠟⢛⣲⣿⣿⡿⢻⣟⣛⣿⡏⢹⡗⡋⠁⠀⢀⡠⠤⣄⣀⣄⡴⣎⣤⣤⣌⠙⠾⢺⣿⣿⣿⣿⣿⣶⠶⣺⢿⢦⡤⣤⣀⡀⠀⠀⠀⠀⠺⠟⣛⣿⠿⣭⣟⣻⣿⣿⣟⣿⠎⣥⣭⣝⣛⣿⢋⣹⣿⢻⠀ ⢻⣿⣿⣟⢣⡀⣽⣳⣾⣟⣛⣿⣿⣷⠀⠀⣿⣿⣿⢋⠀⠀⠁⢛⡿⣃⣿⡾⢷⣏⣄⠩⣽⣿⣏⠀⠀⠀⢻⡔⠛⣏⣹⠦⠿⣿⡛⡟⢾⡃⣠⢠⣿⣽⣧⠉⢹⣧⠉⣿⢺⠟⡧⣟⠢⠽⠿⠷⠆⠃⢀⣾⣷⢿⣶⣿⣿⣿⣿⣿⡿⡏⠀⢽⠚⢫⠟⣏⣀⣠⣉⣾⠀ ⣹⣿⣿⢟⠆⢘⣿⠚⢿⣿⣿⠿⡿⣿⡇⠀⣿⣷⢾⡹⠶⣴⣶⣿⡿⠿⣿⣿⣯⡟⠛⢾⠻⠛⡧⡷⡒⠴⢾⣽⣿⣽⠛⠆⣠⣼⣷⣦⡋⠁⢹⢰⣿⣿⡋⣶⣇⠻⣧⣗⠾⣷⢧⡟⠀⠀⠀⠀⢀⡄⢸⣿⣷⣾⣿⠏⣿⣿⣿⠈⢻⢀⢠⡼⣎⠁⢠⣿⣿⣿⣿⣿⠀ ⢾⢿⣿⣾⣄⡼⢿⢩⠀⠑⣴⢻⣷⣏⣰⣆⣿⡵⢻⣱⠀⣸⣿⣿⠀⠀⠈⣣⣈⡇⡀⠈⡀⠀⡱⣏⢀⡰⢻⢟⡀⢋⣠⠶⠟⠿⣿⡿⡇⠀⢀⢺⣿⣿⣿⠿⠿⣞⠙⠛⢷⣶⣾⣅⡀⢠⣶⠎⠁⠖⢸⢿⡛⣿⣤⠀⢻⣿⣉⣠⣾⣿⣾⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀ ⢺⣿⣿⣿⣿⡄⣺⣶⣶⣶⡿⢻⣿⣿⠿⠏⠙⠙⢻⣼⣦⣾⣿⠿⢧⣤⣴⣼⣿⢻⣄⣋⡇⠰⡇⡗⢦⣴⣏⣨⣟⠛⡅⠀⠀⢰⢁⡄⡇⠀⢨⢸⣿⣯⡟⢀⣴⠾⣀⣀⣴⠾⣿⢿⠛⠛⢇⠀⠀⠂⢾⣷⣦⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠬⣿⣾⣿⣿⣿⣿⣿⣿⠀ ⣿⣾⣿⡏⠘⡿⠛⣯⠙⣿⠿⢿⠛⣻⣶⣶⡶⢶⣾⣼⡿⢿⣿⣤⣼⣿⣿⣿⡿⠷⣿⣿⣃⣰⠏⣇⣸⣷⣿⣿⡃⠀⢸⠀⠀⠀⣽⣾⡇⠀⢰⠸⣷⠈⠶⠿⢅⣰⣿⡋⣈⣾⣇⣈⣲⣤⣈⡧⣤⡇⢺⣿⠿⠛⣿⣿⣀⣿⡿⠿⢶⣿⣏⣳⡭⣽⣿⣋⣿⣟⡻⣿⠀ ⣸⢻⢿⠷⣤⠿⠷⠭⣤⣽⣶⣿⣀⣙⣶⣼⣂⣘⣧⣼⣇⠨⢧⣽⡗⠨⣏⣉⡇⠀⣏⣉⣹⠁⣽⠛⠻⡆⢽⡛⢻⡏⢹⠿⠿⡟⠉⡿⠷⣶⠻⣬⣷⣷⠶⣶⣶⣶⠿⣾⣿⣯⡿⣿⣮⣭⣿⣼⣁⡆⢸⣿⣰⣶⣿⣿⣶⣋⣹⣶⣾⣏⣼⣟⠿⣿⡟⡻⡟⢛⠟⣹⠀ ⢿⢸⠩⢸⡿⣦⠀⣤⣍⣨⠗⠀⠀⠀⠀⢀⣩⣿⢿⡟⠻⣿⢸⣿⡭⠉⠛⠛⠛⠿⠶⠿⠷⠖⠚⠛⠻⠴⠬⠿⢿⡤⣼⡟⢲⣧⣀⣓⣶⠛⠀⠛⠤⠜⠀⠹⢤⡼⠀⢸⣉⣉⠇⠰⣯⣩⡇⠐⡏⠛⣧⠈⣿⠛⣻⠉⣿⠻⢿⠉⢹⡿⠿⡟⢛⡿⣿⡟⠳⣶⣶⡿⠀ ⢻⣨⠰⣸⣷⣬⣯⣿⠁⠀⠀⢀⣀⣀⠰⣏⣀⣀⣤⣄⣠⣶⠸⣟⠮⠑⣤⣶⣶⡀⠀⠀⠀⢀⠀⠀⢰⣾⣿⣿⣿⡴⢻⡇⢸⣿⣿⣿⣥⣴⡆⠀⠀⠀⣠⣶⣿⣶⣷⣿⣿⣤⠀⢰⡟⠓⠒⠚⢿⡿⠳⠶⠟⠻⠧⢤⣾⡷⠾⠤⣼⡷⢞⣣⣈⣷⣤⣟⣈⣿⣶⣇⠀ ⢼⢸⣿⣿⣿⣿⣿⢿⣦⣴⣾⣿⡿⣿⣷⣄⢹⣿⣿⡟⣿⡧⢸⣏⢥⣼⣟⢻⣟⠛⡄⢠⣀⣿⣶⣤⣾⣿⠧⢿⡚⣧⣸⡇⢸⣿⣿⣿⣿⣿⣿⡹⣗⣢⣿⣿⣿⣿⣿⣿⣿⠋⠀⢸⣷⣄⣰⣾⣿⣶⣤⣾⡷⣀⣤⡀⣾⡿⠀⢀⡀⠁⢸⠀⠀⣀⣀⣘⢿⠘⣁⣹⠀ ⢸⢲⣽⣿⢤⣤⣿⣷⢋⠼⣿⡿⢧⣸⣿⣿⡿⣉⣠⣷⡟⠶⢘⣯⠀⣿⣯⣀⣈⣽⣿⣾⠿⣿⣟⣫⢹⣧⣤⣼⣧⣿⣿⡇⢸⣿⣿⣿⣿⣛⣿⡇⠘⣯⣿⣿⣿⣿⣶⢧⡇⠀⠀⠘⣿⣿⠿⣿⣿⡿⠿⢿⣿⣿⣿⡿⣛⣑⣦⠿⠏⠀⢰⢠⣿⣿⢿⣿⣿⣶⣿⣿⠀ ⢸⢸⠹⣿⣿⣿⣿⣽⡆⠀⣸⣿⣏⠀⠈⢿⣿⡏⠉⠉⣇⡹⢸⡧⠈⢛⣿⣿⣿⣿⣿⡿⣀⣤⣩⣷⣾⣿⣿⣿⢿⣿⣿⡇⢸⢸⣿⣿⣿⣿⠟⣻⣾⣽⡟⣿⣿⣿⣿⣄⣀⠀⠀⠀⡟⣿⣀⣽⣄⡀⢀⣿⣋⠁⣿⣿⢻⣿⣿⡇⠀⡄⣹⣸⣿⣏⠈⠋⢹⣿⣿⣿⠀ ⣾⠸⠀⢘⣿⣯⡼⠿⢷⡾⢿⣿⡿⣦⣤⣼⡯⠥⠬⢽⣷⣿⢸⡇⠀⣸⠿⡃⠻⣤⣻⣿⠝⠟⣿⡿⠛⢿⣯⣀⣸⣵⣫⡇⢸⢸⣿⣿⣿⣮⣷⣿⣿⣿⡿⣿⢛⣿⣿⣿⡿⠷⠀⢈⣿⣿⣿⣯⣈⡿⠋⢹⡟⣶⠿⡁⢯⠅⡿⣷⠞⡇⣽⢭⠙⠻⣶⢾⠏⣟⣿⣿⠀ ⢸⣲⢒⢫⡿⠟⠀⠚⠿⠤⠼⠿⠇⠹⠿⠿⠁⠀⠀⠀⠛⢯⢸⡽⣷⣿⣦⣝⣯⣿⣗⣬⣟⠻⠻⠿⣿⣿⣿⣿⣿⣯⣷⡇⢸⢸⣿⣿⡟⣿⢼⣿⠳⢷⣾⣥⣾⣿⣿⣿⡇⠀⠀⢈⡿⣯⡟⣾⠋⠰⠿⠏⣷⣿⡆⣙⣶⣎⠱⣞⣾⡇⣿⢚⠀⠰⣷⡾⠇⣩⠟⢹⠀ ⢺⣹⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣖⣀⣀⣀⣀⡼⠸⣟⣉⣛⣲⣴⣦⣤⣤⣼⣍⣆⣡⣴⣧⣤⣤⣾⣛⣆⣀⡗⢹⣾⣿⣽⣗⣶⣶⣝⣶⣿⣿⣻⣿⣿⣿⣯⡵⡬⡦⠘⣇⣀⣇⣘⣇⣀⣀⣐⣿⣿⣤⣿⣿⣽⣴⣿⣿⡇⢿⣸⣀⣀⡞⠀⢛⣄⣁⣸⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡋⠉⠙⢿⣷⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⢀⣴⣾⣿⣿⣏⣉⣉⣉⣿⣿⣿⣿⣶⣆⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡆⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⠉⠉⠙⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⡙⠿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣜⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠛⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠙⠛⠛⠿⣿⣷⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠙⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⠀⠘⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⢿⣿⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠻⣿⡎⢿⣷⡀⠀⠀⠀⠀⢀⣼⣿⢿⣿⣿⠀⠀⠀⠀⠀⣿⡿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⣸⣿⣿⣿⡿⠿⠿⣶⣦⣤⣄⣀⠀⢀⣿⣿⠁⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠈⢻⣷⡄⠀⢀⣠⣾⠿⠋⣼⣿⠇⠀⠀⠀⠀⠀⢿⣷⡄⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣇⢸⣿⠿⠿⢿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣁⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠈⣿⣿⣾⣿⠿⠁⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠸⣿⣧⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣿⣿⡟⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠈⠉⠉⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠋⠈⠛⢿⣶⣦⣄⣠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢀⣤⣤⣴⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣸⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢁⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣄⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢉⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⠀⠀⠀⠀⣀⣠⣤⣾⡿⠿⠟⠛⡿⠛⠛⠻⠿⢿⣿⣦⣄⡀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡁⠈⢻⣷⠀⠀⠀⠀⠀⠀⠻⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⠻⢿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⣿⣿⡿⢿⣿⣦⣼⣿⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢃⣾⡿⠟⠛⠛⠉⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢁⣴⣾⡿⠋⠀⠀⠙⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠛⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠁⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⣰⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠈⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⢀⣾⣿⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⡄⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠻⣿⣷⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠁⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠈⣿⣧⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣸⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣤⣤⣤⣤⣤⣾⣿⣿⣿⣷⣤⣄⠀ ⠀⠀⠀⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠁⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣦⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⣿⣿⠀⠀⠉⠻⢿⣿⣶⣿⣯⣽⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠿⢿⣿⣿⣿⣶⣦⣀⠹⣿⣷ ⠀⠀⢰⣿⡟⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡄⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⡈⠉ ⠀⠀⢸⣿⢣⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣿⣧⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀ ⠀⠀⢸⠇⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀ ⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡾⢿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⣿⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣴⣶⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⣿⣦⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⣠⡄ ⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⢈⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠻⠿⠿⠃⠀⠘⢿⣿⣌⠻⢿⣶⣤⣤⣤⣤⣴⣿⠿⠟⣸⣿⠇ ⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠉⠉⠉⠉⠁⢀⣠⣾⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣶⣤⣴⣾⠿⠛⠉⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⣧⣿⣻⣿⣦⣤⣶⣿⣿⣿⣷⣦⣤⣶⣶⣶⣤⣀⡀⠀⠀⠀⢠⣴⣿⣿⣿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣯⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣛⣧⢿⣼⣯⣿⣟⢯⡟⡽⢯⣟⣿⣶⣄⠀⢿⣿⣿⣿⣿⣯⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡾⣽⢟⣿⣿⣿⣿⡿⣟⡷⣣⢿⣼⣳⢿⣾⠛⣿⣫⢾⣽⣛⣮⠷⣿⣻⣿⣿⣿⣿⣿⢿⣟⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣿⢺⣽⣿⢺⣽⣮⣽⣯⣷⡞⣯⣿⠃⠀⠈⠛⣿⡖⢻⣼⡟⢳⣯⣿⣿⣿⢻⣭⡟⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡿⣿⣿⠿⠟⠛⠛⠻⠿⢶⣿⡋⠀⠀⠀⠀⠀⠈⣙⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⠀⣤⣴⠟⠋⠁⠀⠀⠀⠀⠀⠙⠿⣧⣹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣾⡿⠀⢻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢲⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠹⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣷⡿⣾⠁⢲⡞⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⣶⣿⣽⡻⢿⣻⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⢯⢷⣻⢷⣿⠀⠀⠙⠟⢉⣿⠻⠶⢶⣤⣤⣴⠶⠟⠉⠀⠀⠈⠻⢶⣤⣄⣀⣀⣠⣤⣴⣞⠛⢷⠄⠀⢸⣷⢿⣯⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣻⢾⣽⣿⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠻⠓⠀⠀⠰⢸⣿⣻⣽⢿⣿⣷⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⢷⣟⡾⣽⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⢿⣾⣷⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⡟⣯⣏⣷⣾⣿⣿⣯⢿⣆⠀⠀⠠⢴⣀⣤⣤⠴⡶⣚⢟⢻⢲⢦⣀⣀⣤⠴⣖⡞⢶⢦⣀⠀⠀⠀⠀⠀⠀⣼⣯⢟⣿⣻⣿⢿⣿⣿⣦⣄⠀⠀ ⠀⣀⣤⣤⣽⣿⣽⢳⡾⣵⣻⣟⣮⢗⣯⢾⣦⡀⠀⠀⠹⢯⣛⢻⡛⡶⢾⠾⡶⡷⡾⢷⠾⡷⢾⠾⡾⢛⡟⣿⠃⠀⠀⢀⣾⣿⣝⡾⣳⣯⣿⢯⡟⣽⣟⣿⡇⠀ ⣾⣿⣿⣿⣟⡟⣾⣫⣷⣿⢟⡿⣼⣛⡾⣯⢿⣿⣦⡀⠀⠀⠙⠷⣥⣏⢎⡣⣕⢣⡝⣪⢱⡙⢎⡳⣩⣣⠞⠁⠀⢀⣴⣟⡯⣿⡽⣞⣳⠿⣿⣿⣽⣳⣾⣿⣄⡀ ⠸⣿⡿⠿⢾⣿⣵⣻⡿⣭⢟⡾⣵⣿⣿⢿⣿⣿⡼⣟⣦⣄⡀⠀⠀⠉⠙⠓⠺⠷⠼⠥⠧⠿⠞⠛⠉⠁⢀⣠⣴⣿⢻⡼⣿⣿⣽⣻⢿⣻⣷⢯⣿⡵⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠸⣿⠟⠛⠛⠿⠿⣶⣿⣯⣿⣻⣗⣻⢮⢷⣻⢟⣷⣶⣤⣄⠀⠀⠀⠀⣄⣀⣠⣤⣤⣶⢾⡟⣯⢟⣮⢟⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠉⠙⠛⠛⠛⠛⠾⠾⠾⢷⣿⠀⠀⠀⠀⣿⣟⣿⣽⣳⣾⣯⣾⠯⠿⠾⠿⠾⠛⢻⣿⣿⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠸⣧⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⣿⢣⣽⡿⢶⣿⣁⣀⣀⠀⠀⠀⠀⠀⠙⣿⡏⢉⡛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣅⣎⣟⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠷⠾⢿⣤⣘⠢⢝⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣫⢞⣙⣿⣿⠉⠉⠛⠒⠒⠒⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠉⠙⢻⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢿⡿⢿⠾⡿⢧⣤⣤⣤⣄⣀⣀⣀⣀⡀⠈⠒⠉⠉⠓⠒⠦⠤⣄⣼⡇⢈⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠑⢸⣕⢫⢳⡙⢮⢲⡱⢎⠶⣉⢮⡙⣭⢛⡽⣙⡛⢶⡳⢶⠶⡦⢤⣤⣽⡆⢈⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠰⢸⣏⢎⢧⢛⡎⢧⡙⣎⠳⣍⠶⣙⢦⣋⠶⣡⢛⠦⡝⣎⠳⣍⠳⣜⢣⣿⡀⠄⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠘⢠⣿⡚⡜⣎⠳⣜⢣⡝⣬⠳⣌⠳⣍⠶⣩⠞⣥⢋⡞⡱⢎⡳⣌⠳⣎⢳⢺⣷⡀⠄⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠐⣸⣿⡱⡹⣌⠳⣌⠳⡜⢦⢛⡬⢳⣌⢳⡱⣚⠴⣋⠼⣱⢋⠶⣩⠳⣌⢧⢻⣿⣇⠈⠄⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠂⣿⣿⡵⢳⣌⠻⣌⢳⡙⣎⠳⣜⢣⢎⣇⠳⣍⠞⣥⡛⡴⣋⢞⣡⢛⡜⣎⢳⣿⣿⠀⠐⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⠀⢂⢻⣿⣗⡣⢎⡳⢬⢣⡝⣬⠳⣌⠳⣎⡜⢳⢬⡛⣼⣷⢣⡝⡸⢆⠯⡜⣬⢻⣿⣿⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⡌⣿⣷⠙⣮⢱⠋⣶⢱⢪⡕⣮⢳⡜⡜⢣⡞⣼⡏⣼⣷⢸⢱⠋⡞⢱⡌⢳⣿⡇⢠⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⢤⡀⠛⢿⣬⡧⣛⡼⣾⢮⣵⢎⡖⣣⠝⣎⢖⣿⢁⣿⡥⣋⣮⣙⣖⣯⣽⣾⠟⢀⢈⣓⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣭⡐⠀⠌⠙⠛⠻⠾⠷⣬⡛⢾⣷⠿⠾⡞⠁⠀⠉⠉⣉⣩⣭⡴⠶⠛⠁⢈⠰⣲⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣒⡷⠶⠾⠒⠛⠋⠁⠀⠈⠙⠶⣷⠶⠒⡒⠛⠋⠉⢀⠀⣄⣂⣬⣷⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⠾⣭⣕⣒⣒⣺⠓⠀⠀⠀⠀⠀⢹⣄⣁⣤⣥⣼⡶⢿⡻⣛⠽⣩⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣙⠶⣹⢳⢶⡬⣤⢤⡤⢶⢶⡛⣯⢻⢫⡝⢮⡱⢎⡳⡱⢭⣚⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣾⣾⣷⣾⣷⣾⣷⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⢂⠘⢀⠂⠄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡗⢠⠂⡔⣀⢂⡐⢀⠂⠔⢠⠂⠔⡰⢈⠴⢡⢫⡝⣿⣻⣿⣟⡿⣽⢿⣿⣿⣿⣿⣿⣿⣿ ⠈⠄⡈⠀⠌⠀⠁⠠⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡏⢄⢃⡐⠄⠂⡔⠈⡈⠌⠠⢈⠂⡁⠊⡄⢣⢎⡽⣞⣿⡷⣯⣟⡾⣻⣿⣿⣿⣿⣻⣿⣿ ⠐⠠⢀⠡⢈⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡏⢄⠂⠠⣜⣰⣤⡳⣔⡈⢒⡐⠂⡅⠓⠌⣣⢚⡼⣻⣾⣿⣳⢯⣟⡽⣿⣽⣳⡟⡿⣽⢻ ⠌⡀⢂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣏⣄⡼⣯⣳⢯⣶⣻⣽⡁⢢⠀⢃⠤⢉⠢⡑⢮⡱⣟⣷⣿⣽⡳⣯⢽⣷⣻⢶⡻⣝⡾⣹ ⢂⠐⠠⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡽⣛⡶⣯⣟⣶⣻⡞⠁⠤⠘⣀⠂⡄⢣⠙⢦⡹⢯⣿⣿⣞⣽⡳⢯⣿⣽⣳⢯⣝⣞⣳ ⠂⡀⠡⠀⠌⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣽⣻⣽⣳⣿⠞⠋⡀⢊⢠⣁⡤⡦⠴⢆⢩⢒⡽⣯⢿⣷⣻⢶⣛⢯⣿⣞⡷⣯⢞⣮⢷ ⠐⡀⢁⠐⠀⡁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠋⣩⠝⠛⡒⠒⠩⣕⠢⣄⠀⠀⠀⠀⠀⠀⣽⣿⡟⡑⠛⠙⡉⠁⢀⠢⣰⣬⣷⣿⣿⣿⣿⣿⣿⣾⣽⣯⣿⣿⣳⢯⡽⣞⣿⣿⣻⣭⣟⢮⣟ ⠀⡐⢀⠂⠁⠀⡈⢀⣠⣴⣾⣿⣿⣿⠿⡿⠿⠿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⠴⠊⠁⠀⠀⠈⠓⢤⡀⠑⢌⠱⣄⠀⠀⠀⠀⢾⣿⡗⢐⠈⡀⢀⡐⣪⣿⣿⢿⣻⢷⣻⣞⡷⣟⣾⢯⣟⣿⣿⣿⣳⢯⣞⣳⢿⣷⣟⣾⣽⣻⣾ ⠀⠐⡀⠄⠐⢀⣴⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣷⣶⣮⣽⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣶⣾⣿⣿⣦⡀⠀⢀⣤⣴⣤⣄⣠⣤⣤⣤⣄⡀⠀⠀⢰⣿⣿⢿⣿⣷⡄⢸⣿⣿⠀⠀⠀⡴⠁⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⢧⠀⠀⠀⣻⣿⣏⠀⠆⡀⣖⣿⣿⢿⣽⣻⢯⣿⢯⡿⣽⡿⣽⣻⣟⣾⣽⣻⣿⣳⢾⡽⣿⣿⣿⣿⣾⣿⣿ ⠀⢀⠀⢠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣟⠉⣿⣿⣿⣇⣴⣿⡿⣯⢿⣿⣿⣻⣽⣻⣟⣿⣶⣤⣬⣭⣧⣾⣟⣿⠃⢸⣿⣿⠀⠀⡼⠁⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⣇⠀⠀⣽⣿⣧⡘⣰⣾⣿⣿⣿⠿⡾⣿⣯⣟⣯⡿⣯⢿⣽⢷⣯⡷⣿⣽⣻⣿⣯⣿⢿⡿⡿⣟⡿⣿⢿ ⠀⡀⠀⣴⣿⣿⣿⣿⣯⣸⣿⠿⠯⠿⣿⣿⡏⠙⠿⠿⠟⠿⣿⢻⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⢿⣶⣮⣽⣾⣿⣿⣷⣿⣽⣿⠃⠙⢿⣾⠷⠿⣾⣽⣯⣟⣯⣿⣳⡿⠋⠀⢸⣿⣿⠀⢸⣁⣠⣤⣾⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣽⣄⡀⢹⡀⠀⣽⣿⣷⣽⣿⣿⠛⠁⠀⠀⠀⠀⠉⠻⣿⣽⣻⣯⡿⠛⠛⠛⠛⠷⣿⣻⣿⣿⢯⣳⣟⣼⣳⣏⡿ ⠀⠀⣰⣿⣿⣿⣿⣿⡾⠉⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⢠⡴⠛⠉⠉⠉⠛⢿⣧⡾⠀⢸⣿⣿⠻⢿⣷⣯⣿⡿⠛⠉⠀⠀⠙⣧⠀⠀⣿⠀⠀⠀⠀⠈⠛⠿⣿⣻⣿⣄⠀⠀⢸⣿⣿⡴⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠳⡀⢀⣴⠯⠛⠋⠉⠉⠈⠉⠹⡚⠽⢷⡀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⣹⠃⠀⠀⠀⠀⠀⠀⠈⢿⣟⣿⣿⣷⣻⣞⣷⣯⣿ ⠀⠀⣿⣿⣿⣿⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⡟⠀⠀⠀⠀⠀⠀⠀⠹⣧⣴⢿⣿⣿⣀⡼⣯⡿⠋⠀⠀⠀⠀⠀⠀⠘⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠻⣷⣤⣼⣿⣿⣆⡀⠀⢀⡇⠀⠀⠀⠀⠀⢀⣠⠗⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠁⢹⣿⣿⣿⣿⣿⡀⠸⠶⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⣠⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢨⣿⣿⣿⣿⣿⠀⢳⡀⠀⠀⠀⠀⠀⠰⣷⠀⣼⠀⢧⠀⠀⠀⠀⠀⠀⠾⠆⣿⠾⢻⣿⣿⣿⠟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⣾⡛⢺⣿⣿⣻⣿⣿⣀⣏⠉⠚⠓⠒⠒⠒⠒⠉⢁⣤⠀⠣⣠⡆⠀⠀⠀⠀⠀⠀⠀⠸⢀⣤⠟⣻⣿⣿⣿⣧⠳⣄⡀⠀⠀⠀⠀⢀⣴⠷⠲⣷⡀⠈⠁⠀⠀⠀⠀⠀⡸⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⣿⣿⣿⣿⣿⡀⠀⢭⡲⢤⣄⣀⣀⣀⣤⠞⠃⠀⢈⡳⣄⡀⠀⠀⠀⢀⣴⡟⠀⢸⣿⣿⣿⠰⢿⣿⢶⣤⣀⣠⣶⣀⣤⡾⠋⠀⠙⠷⢦⣾⣷⡤⠶⠿⣯⠉⠃⢸⣿⣍⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣰⠃⠀⠳⡄⠈⠉⠓⠒⠲⠐⠦⠒⠒⢺⠁⠜⠀⣿⣿⣿⣿⡿⠀⠀⠉⠙⠒⠒⠉⣟⡵⠀⠀⠈⣏⠲⠤⢤⠤⡤⠴⠊⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢂⣿⣿⣿⣿⣿⣇⠀⠀⠙⠒⠒⠊⠉⠑⠀⠀⠀⠀⠀⠙⠳⣍⣛⡛⠋⢉⣿⣧⡤⣼⣿⣿⣿⠀⠀⠉⠸⠃⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⢻⣿⣿⢹⣿⣿⡇⠀⠀⠀⠀⠐⠷⠂⠀⠒⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣧⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠿⠿ ⠀⠂⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣤⢶⠾⡶⢮⣴⠷⡶⣤⡀⠀⠀⢸⣯⡶⠷⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⣦⣴⢟⡻⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⢻⣿⣿⠋⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⣾⣿⡿⣻⣿⣧⡤⠤⠤⠴⠶⠖⠚⠛⠛⠛⠛⠛⠒⠒⣲⣶⣶⣿⡿⢿⣿⣿⣿⣿⣿⣷⠄⢠⣤ ⠀⡁⢿⣿⣿⣿⣿⣿⣿⣌⠀⠀⠀⠀⣾⣙⣎⣳⣭⢯⣧⢿⣼⣱⣻⣄⠀⣼⣛⠛⠲⣼⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣠⣞⣧⣽⡾⣷⣾⣵⣯⣷⡤⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⣿⣿⣸⢛⣿⣿⡉⠉⠉⠉⠉⠛⠒⠲⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠘⡄⠀⠉⢻⣿⡿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⡶⠞⢋⣩⠞⠋⠁⢀⣾⣿⣿⢿⣿⣻⠏⠃⡠⠔ ⠀⠄⣹⣿⣿⣿⣿⣿⣿⣿⣮⡂⠀⠀⠿⣯⣝⣱⢎⠳⣌⠳⣌⠳⣍⣻⣾⠏⠈⡹⡆⢸⣿⣿⣿⣽⣻⣦⡀⠀⠀⠀⠉⠻⣟⡟⣰⢏⡳⢎⣶⠋⠀⠀⠀⠀⢀⣴⣿⣿⣯⣷⣿⣿⣿⠇⣼⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⢻⠉⠳⢤⠀⣿⣿⣇⣿⣿⣿⣿⡏⠛⠻⢿⣍⣉⣉⣉⣁⣠⡤⠖⠋⠀⠀⠀⣠⣿⣿⣻⡽⣿⣾⣁⣆⠮⢤⡶ ⠀⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣑⠄⠀⠈⠉⠉⠛⠉⠛⠉⢋⣭⣿⣯⣀⢀⣁⣿⢻⣿⣿⣿⣾⣽⣿⡿⣷⣤⣀⠀⠀⢨⢣⠯⣮⠵⠛⠁⠀⠀⣀⣤⣾⡿⣿⣽⣻⣿⣿⢿⣿⣿⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⣿⣿⣿⣟⠡⢉⠋⢁⠉⢳⣄⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⣀⣴⣾⢿⣻⠷⣯⣟⡷⣭⣇⣤⡰⢥⡴ ⢀⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀⠀⢠⣐⣤⣽⣾⣿⣿⣿⠋⠀⠀⠈⢿⣿⣿⢿⣿⣿⣽⣻⡽⣯⢿⣿⣷⣾⣸⡒⣒⣒⣶⣶⡾⢿⡻⠯⠷⠛⠛⠉⠉⠀⠳⣼⣿⣿⠀⢸⠛⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢣⠀⠀⢹⣿⣿⡇⠂⠄⠈⠠⠀⣰⠟⡗⠀⠀⠀⠀⠀⠀⠀⡶⣿⣟⣯⣟⣯⢯⣟⡷⡾⣽⣳⢽⣺⡵⣶⠖ ⠀⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⠲⣧⡿⢦⠑⡜⢨⢁⣿⠀⠈⡏⠀⠀⠀⣿⡆⡘⢢⠑⠌⢂⠡⢀⠐⠠⠐⣠⣿⣿⣿⡇⠸⡄⠀⠆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡛⢦⡀⠀⠘⡄⠀⢸⣿⣿⡏⢀⠈⡀⠁⣰⠏⢀⡇⠀⠀⠀⠀⠀⠀⠀⢷⠈⣷⢯⡾⣽⣳⠾⣽⣽⡳⢯⣳⣏⡾⣝⡊ ⡘⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢸⣿⣿⠐⢀⠒⠄⠊⠄⠁⢂⡼⠒⢋⣳⠤⠤⢤⠇⢷⡀⠀⠈⠀⠂⠐⠀⠈⠀⠁⣼⢻⣿⣿⣇⠀⢇⠘⣀⣀⡀⣰⠁⠀⠀⠀⠀⠀⣴⣖⠻⣍⢦⡙⣮⢹⢲⡄⠱⠀⢸⣿⣿⡏⠀⡀⠄⢰⡏⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢺⣯⣟⡷⢯⣟⡷⡾⣽⢯⣳⡽⣝⡳⠀ ⡜⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⢫⢭⣹⣧⣄⣦⣴⣤⣦⣄⣄⡻⣏⠝⣿⣿⣧⠀⠀⠀⢸⣿⣿⠀⠀⠀⠂⠁⣠⠞⢿⣠⠞⠛⣻⠆⢸⣻⡄⠈⢧⡀⡞⠻⣆⠀⠀⠀⠀⢠⡟⢸⣿⣿⣹⠀⢸⣷⣿⣿⡟⠁⠀⠀⠀⠀⢐⣴⠳⣌⠳⣌⠦⡹⣆⢇⠳⣺⣆⠡⡀⣿⣿⣏⠀⠄⢠⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢿⡾⣽⣻⢾⣽⣻⣭⣟⣧⢿⡝⡇⠁ ⢾⣿⣿⣿⣿⣿⣿⣿⡿⣙⣎⣳⡾⣋⠷⣘⠖⡦⣓⢦⡙⢮⡝⣻⢻⣼⣿⣿⣆⠀⠀⢺⣿⣿⠀⠀⠀⢀⡾⠃⢀⣾⡥⠖⢛⣻⠠⢁⣿⡷⣶⢶⣾⣇⠠⢹⡆⠀⠀⠀⣾⠁⣼⣿⣿⠻⡇⠀⢿⠃⠁⠀⠀⠀⢀⣠⡴⠻⣌⠳⣌⠳⡌⠶⣑⢯⢎⠵⣢⢻⣶⠠⣿⣿⡧⠀⢂⡾⠁⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢿⣳⢯⣟⡾⣵⣻⢮⣯⢟⡼⢁⠀ ⣿⣿⣿⣿⣿⣿⣿⠯⣕⣣⣾⢳⡱⣍⠞⣥⢛⡴⣩⠖⡹⢦⡙⢦⠳⣌⡛⣿⣿⣧⣄⣻⣿⣿⠀⠀⢠⠟⠀⢰⣾⠋⠳⣶⣏⣡⣢⣥⣿⣻⢞⡽⣞⣿⡄⠀⢿⠀⠀⣰⠇⢰⣿⣿⣿⠀⢷⠀⠘⣆⠀⠀⢀⣠⠼⣧⣍⠳⣌⠳⣌⢳⣘⢣⡍⡞⣏⠶⣡⢋⣿⡔⣿⣿⡗⢠⡿⠁⠀⣈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠛⣟⡾⣽⣳⢯⣟⡾⢍⠀⢐⡰ ⣿⣿⣿⣿⣿⣿⣋⢾⣱⣿⣮⡱⢚⡬⣙⢦⢫⡔⣣⠏⡵⢣⡝⣪⠳⣌⢳⣼⣿⣿⣿⣿⣿⣿⠀⢰⠏⡀⣼⣿⠃⠠⣵⣿⣻⢻⡽⣏⡷⣏⡿⡽⣾⡁⢷⡈⠘⢧⣴⠋⢀⡟⢸⣿⣿⠀⠸⣆⠀⠈⠙⠋⠉⠀⢀⣸⣦⣳⡼⣳⡘⡖⢬⣃⠞⣸⢹⡲⢡⢳⡘⣿⣿⣿⣟⠚⠁⠀⣐⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⢀⠈⠙⠳⢏⡟⠎⠑⠀⢀⣲⢽ ⣿⣿⣿⣿⣿⠳⣌⣷⣿⣿⣿⣿⡷⣮⣕⣮⡱⢎⡵⢪⡕⣣⢞⣥⣫⣼⢟⣻⣿⣿⣿⣹⣿⣿⢀⡟⠀⣸⡿⠃⢀⣽⣿⣣⣟⢯⡷⢯⡽⡾⣝⣷⣻⡇⠈⢷⡀⠠⢀⣤⠟⠁⢸⣿⣿⡀⢆⠨⢓⠲⠖⠖⠒⠚⠉⠀⠉⠁⢀⣿⠱⢎⡣⡜⢎⡥⣋⠷⣭⠶⠛⣟⣿⣿⡧⠀⢂⣰⢟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣐⠀⡁⠀⠀⠐⢀⠸⣴⢯⣟ ⠛⠛⣿⣿⢣⣛⣾⣿⣿⣿⣿⣿⡟⡴⢪⡜⡽⢫⡝⣣⢛⡭⣋⢾⣿⣿⡜⡼⢿⣿⠳⣼⣿⣿⢸⠃⢰⡟⠁⠠⣼⢳⣯⠷⣞⣻⣞⢯⣟⡽⡽⡶⢯⣷⠀⠀⠙⠛⠋⠁⠀⠀⢸⣿⣿⡘⣌⠣⢎⠔⡈⢆⢉⡐⠠⢁⠐⠀⣸⡟⡍⠶⣑⢎⡣⢖⡡⢏⣽⠀⠀⣿⣿⣿⣧⢐⡾⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣻⢞⣻⢶⡱⣖⣞⡾⣻⣽⣻⢾ ⠀⠸⣼⢏⢧⣿⡏⡜⡩⢏⡛⣿⡝⣜⢣⠞⣜⢣⠞⣡⢏⠶⣩⣿⡟⢿⢿⣜⢣⢎⠳⣼⣿⣿⢹⡄⠊⢀⢐⡼⢣⣾⢯⢿⣹⠷⣞⣻⣼⢻⡽⣽⣛⡾⣇⠀⠐⠓⠦⠀⢀⣀⣸⣿⣿⡱⢊⡕⢪⢌⡑⢂⠂⠤⡁⠂⠌⣠⣿⡛⡜⣱⢊⠶⡑⢮⡑⠮⢼⡆⠀⢸⣿⣿⣧⠉⠤⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣟⢧⣯⢳⣏⣾⡹⣗⣯⡽⢯ ⠀⠸⣾⣎⢻⣿⣷⢨⡑⢣⢜⣿⡜⣬⢣⡛⡬⢎⡝⢦⣋⠞⣥⣿⣏⠲⡌⡞⠻⡞⢻⣿⣿⣿⠈⠻⠶⠞⠋⢀⣿⢯⣯⣻⣭⢿⣹⢧⡟⣯⡽⣞⣭⡟⣿⣆⠀⠀⠀⠀⠂⠀⢹⣿⣿⡱⣃⢮⡑⢎⡔⡃⠎⡔⣨⠑⣌⣾⢏⠲⣉⢦⢋⠶⡙⠦⢭⡙⢦⣇⠀⠘⣿⣿⡧⠈⢄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣟⡼⣳⢞⡶⣫⢗⣮⢽⣻ ⠀⠀⠹⢷⣧⢚⣿⣧⡌⢡⢊⣿⡘⢦⢣⡝⡜⣣⠞⣱⢪⢝⡲⣿⡇⡓⠸⡌⠓⡬⠑⢾⣿⣿⡤⣤⣄⢦⣴⣿⢯⣟⡶⣻⡼⣏⣟⡾⣽⡳⢯⣻⣼⢻⣵⣻⣷⣤⣦⢴⡰⣆⣾⣿⣿⡳⣍⢖⡩⢖⡸⢌⠳⣘⠤⣓⣾⠏⣎⡱⢍⠦⣋⠼⣩⡙⢦⡙⢦⣹⠀⠀⣿⣿⣟⢈⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢼⡳⣏⢷⣫⢟⡼⣣⢟ ⠀⠀⠀⣍⠻⣧⣚⡽⣿⣄⠢⣟⡜⣣⢳⢸⡱⣃⠻⣔⣋⠞⡴⢿⣽⡈⠱⣈⠣⢐⠩⣼⣿⣿⠉⠉⣹⣿⣿⣿⣷⣾⣽⣳⣽⣫⣾⡽⣶⣻⢯⣷⣭⣿⣶⣿⣿⣿⣿⡍⠉⠉⢹⣿⣿⡵⣊⢮⡱⢫⣔⢫⢞⣥⡷⠿⠿⠾⠶⠵⠮⣶⣍⣶⣡⣎⣥⣙⣦⣽⠤⠀⣿⣿⣯⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠙⢌⠃⡉⢊⠡⢉⠈ ⠀⠀⠈⠀⠁⠁⠙⢶⣭⣻⡷⢿⣬⡑⢧⢣⡓⣭⠳⡜⣬⢛⠼⣹⣏⠛⠓⠀⠈⠉⠉⢹⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣷⣽⡶⣯⣷⣾⣿⣿⣿⣶⣶⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣄⣢⣄⡥⢢⣤⢦ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⣯⣽⠞⠻⣿⡌⢧⡹⣔⢫⡜⣆⢏⡞⡥⣛⣆⠀⠀⠀⠀⠀⠸⣿⣿⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⢸⣿⣿⣿⣟⣿⣏⣿⣿⣻⣞⣷⣻⢾⡽⣯⣟⡿⣿⣷⣾⣿⣿⣿⣶⣶⣶⣶⣿⢿⣿⣿⡇⠀⢀⣤⠶⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠦⣄⠀⠙⣿⣷⢿⣻⣿⢾⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⣤⣿⣽⡏⢶⡱⢎⡣⢞⡜⣜⢲⡱⢣⡾⣷⣄⡀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢾⣷⣹⣿⣞⣷⣻⢾⡽⣯⣟⡷⣯⣟⣷⣿⣟⣯⢷⣻⣞⣷⣻⢾⡽⣯⣿⣿⣇⡴⠋⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠳⣆⢘⣯⣿⣟⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⢛⡝⢦⡓⣭⢚⡵⢚⡬⢣⡝⢣⠞⡴⣩⢝⡳⢦⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣿⣷⣻⢾⡽⣯⣟⡷⣯⣟⣷⣻⣾⣟⡾⣽⢯⣷⣻⢾⡽⣯⣟⡷⣿⣿⡟⠁⠀⠂⠁⠀⠁⠀⠄⠀⠉⠳⠶⠶⠖⠋⠁⠀⠀⠀⠈⠀⠁⠂⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⡜⣣⠞⡴⢋⡴⢫⡜⣣⠞⣥⣛⣴⣣⣎⣵⣣⣽⣿⣿⣦⢖⡦⢶⡴⣲⣒⣖⣲⣒⢦⣒⢦⣒⢦⢲⡰⢆⡲⣔⢢⡲⣔⡲⣔⢦⡖⢶⣺⣿⣿⣿⢿⣳⣿⣳⢯⡿⣽⣳⢯⣟⣷⣻⣞⡷⣿⣯⢿⣽⣻⢶⣯⢿⣽⣳⢯⣟⣿⣿⡇⠀⠠⠐⠀⠀⠐⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡈⠀⠈⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⠥⣛⡜⣩⣼⢷⣾⣷⣿⣿⣍⠙⠛⠿⣿⣿⣿⣿⣿⠛⠞⠹⠓⠛⠳⠙⠚⠣⠛⠚⠙⠚⠙⠚⠓⠛⠋⠓⠋⠓⠛⠚⠓⠙⠚⠘⠃⢻⣿⣿⣟⡿⣯⣿⡽⣯⣟⡷⣯⣟⡾⣷⣿⠿⡛⣿⣯⣟⡾⣽⣻⣞⡿⣾⣽⣿⠟⣻⣿⡇⠀⠠⠀⠀⠠⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠖⠋⠁⠀⠀⠈⠙⠿⣿⣿⣧⠀⠀⠈⢿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢯⡿⣽⡿⣽⣟⡾⣽⣳⢯⣟⣿⠁⠑⠃⢻⣷⢯⣟⣷⣻⢾⣽⣳⣿⡋⢤⣿⣿⡇⠀⠂⠀⠄⠀⠄⠀⠀⠄⣸⡇⠀⠁⠠⢀⡐⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⢿⣽⣿⣳⢯⣟⡷⣯⣟⣾⣿⠀⡄⡀⢸⣿⣻⣞⡷⣯⣟⣾⣳⣿⡄⠁⣹⣿⡇⠀⠌⠀⠀⠀⠀⠀⠂⠀⣏⠀⠀⠀⢀⠀⢹⠆⠠⠀⠂⠄⠁⠀⠂⠁⢈⠀⢸⣿⣿⣿⣿ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣐⣀⣄⣂⣤⣡⣀⣌⣐⣿⣿⣿⣀⣐⣈⣿⣿⣿⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⠀⠀⣀⠀⢸⣿⣿⢯⣟⢾⣷⣯⣿⣾⣽⣳⣟⣾⣏⣖⣡⣒⣍⣿⣷⣯⣟⣷⣻⣞⣷⣻⣇⣀⣿⣿⣇⣀⣠⣀⣀⣁⣀⣀⣀⣀⣯⢀⣀⣁⣀⣀⣸⣇⣀⣀⣠⣀⣀⣀⣠⣀⣀⣀⣘⣯⣟⣼⣳
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡎⠀⠀⣸⣿⣿⣇⡀⠀⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⣊⠔⠂⠉⢸⣿⣻⡇⠈⠁⠳⢄⠣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣧⠄⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠱⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠃⣤⠀⠸⠂⠀⠀⢀⠄⠐⠀⠛⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⡀⢰⡄⠺⠆⠀⠀⠀⠀⠀⠀⠛⠀⢙⡰⠎⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⣿⣌⠀⠰⠆⠀⣀⠀⢀⡀⠀⠛⠁⠘⠁⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣤⣤⣀⡲⢥⣀⣬⠴⣊⣠⣒⡀⠈⠁⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠉⠁⣼⣿⣿⣿⠋⠀⡘⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡌⢉⠍⠀⡀⠀⠀⢍⡋⠁⠀⢠⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣴⠋⢀⣤⣥⣴⣦⠀⠙⣦⣠⣾⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣄⣿⣿⣿⣏⣠⣴⣿⣿⣿⣷⣿⣍⠢⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⢺⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢹⡀⠀ ⠀⠀⠀⠀⢀⠠⠊⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢎⣿⡿⠿⠿⣄⣀⣑⣄ ⠀⠀⠀⠀⣿⣦⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣾⣿⠁⠀⢀⣸⣿⣿⣿ ⠀⢀⡀⠴⣿⣿⣷⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⣸⣿⣿⣿⣿⣿⣿ ⡦⢃⣠⠞⠻⣿⣿⣿⣦⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⡿⠛⢿ ⡶⠋⠀⠀⠀⠙⣿⡻⢿⣿⣦⠻⣟⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣬⣆⣤⣾⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⢄⠀⠀ ⣇⣀⣰⡶⠶⢲⡾⢷⣦⡀⠀⠉⣿⣿⣿⣿⠿⠋⣡⠤⠤⠤⢀⣀⣀⡀⠀⠀⠀⡄ ⡏⢹⣆⣀⠴⢬⡇⠀⠙⠛⠦⡞⠛⢋⣿⡷⠋⠀⡿⣦⣤⣤⣤⣀⣉⣉⡽⠀⢠⣴ ⡗⠊⠁⠀⠀⣸⣇⡀⢀⢠⣿⡇⣖⡿⣧⠤⠀⢰⡇⠈⠉⢉⠉⠙⠻⣿⢁⡄⢸⣿ ⡇⠀⠀⠀⣰⣿⡿⡿⠘⣿⠛⡇⠈⢰⢱⡀⠀⣸⠀⠀⠀⠀⠻⠁⣰⠇⣾⣷⢈⣿
    ヽ``、ヽ`、ヽ     ◜◝--◜◝     ( 。・㉨・ ) ♡ ♡ ♡   ┌───────⊹──────┐ ⠀  ⚓️ ʸᵒᵘ'ᵛᵉ ᵃʳʳⁱᵛᵉᵈ ᵃᵗ⚓     ҉ astro's ─ mailbox ◠   └───────⊹──────┘     ヽ``、ヽ`、ヽ     ∩_∩   ☆(˵ㅤ•ᴗ•)☆ come ⛅ inside !   ⚓️︶︶︶// ╰⇢ drop a letter in the slot ▰▰▰ ㅤ◦ everyone is welcome here ♡ ㅤ◦ if you want, ask to be a curator! ㅤ◦ my frens help manage my mailbox, so you'll see them reply to comments          ── ── ──     ∩_∩   ☆(˵ㅤˊᗜˋ)☆ curator ᝰ rules :   ⚓️︶︶︶// ╰⇢ if you want to remove yourself as a curator, you must do it yourself ⚠︎ ㅤ◦ do not take advantage of this role ㅤ◦ expect LOTS of notifications! ㅤ◦ do not mess with the projects ㅤ◦ treat everyone with respect          ── ── ──     ∩_∩   ☆(˵。 •̀ ᴖ •́ 。)☆ studio ᝰ rules :   ⚓️︶︶︶//  ⤿ FOLLOW COMM GUIDELINES   ˗ˏ ⛧ no adding/deleting projs ˎˊ-         ▭▭▭   ˗ˏ ⛧ no spam/advertisements ˎˊ-         ▭▭▭    ˗ˏ ⛧ be respectful + kind ˎˊ-         ▭▭▭   ˗ˏ ⛧ interviews ―▹ follow rules ˎˊ-          ── ── ──     ∩_∩   ☆(-人-。)☆ interview ᝰ rules :   ⚓️︶︶︶//    ╰⇢ ASK ME FIRST!! ㅤ◦ keep interview within one comment ㅤ◦ post interview questions in a brand new comment at the top of the studio so i am guaranteed to see it ( ˙꒳​˙ ) ㅤ◦ please be patient, response time is not guaranteed!          ── ── ──     ∩_∩   ☆(˵๑•̀ヮ•́)☆ about ᝰ me :   ⚓️︶︶︶//    ˗ˏ ➛ call me astro! ⊂⊃ she/her   ―▹ im in middle school !! (12+)   ―▹ my fav color is pale yellow   ―▹ south-east asian american   ―▹ zodiac: libra (october)   ―▹ i have two guinea piggies   ―▹ i love rblx, it's my childhood  ✗ .. disrespectful, anti-aesthetic, impersonators, stealing, lettuce  ✓ .. kind ppl, laughter, sanrio, sunny days, BIRD CHIRPS <33 I LUVV ⛅  ⤿ personal info cannot be provided          ── ── ──     ∩_∩   ☆(˵੭ ˙ᗜ˙ )☆ faqs ᝰ for you :   ⚓️︶︶︶//   ˗ˏ ➛ can i use your content?   ―▹ ♡ go to link here : scratch.mit.edu/projects/825846350/   ˗ˏ ➛ thumbnail tutorial?   ―▹ ♡ I'm sorry no! ˶ᵔ ᵕ ᵔ˶    ʳᵉᵈᵘᶜⁱⁿᵍ ʰᵉᵃᵛⁱˡʸ ʳᵉᶠᵉʳᵉⁿᶜᵉᵈ ᶜᵒⁿᵗᵉⁿᵗ   ˗ˏ ➛ where do you make thumbs?   ―▹ ♡ https://pixlr.com/e/   ˗ˏ ➛ where do you find fonts?   ―▹ ♡ dafont.com ☆ I have a tuto   ˗ˏ ➛ face reveal?   ―▹ ♡ no thank you ˊᯅˋ   ˗ˏ ➛ can i interview you?   ―▹ ♡ follow rules above!   ˗ˏ ➛ how'd you get 13k followers ?!   ―▹ ♡ patience & hard work!   ˗ˏ ➛ can you accept my rblx req ?   ―▹ ♡ no im sorry ☆ i never remember and it wouldn't be fair   ˗ˏ ➛ can we be friends ? ( o´^`o)   ―▹ ♡ no requests, it happens naturally!   ˗ˏ ➛ who is your idol?   ―▹ ♡ any og aesthetic scratcher!   ˗ˏ ➛ can you rate my [___]?   ―▹ ♡ sorry but no... create what YOU enjoy and like! :) i dont want to accidently hurt anyone's feelings either...   ˗ˏ ➛ are you﹫[___] ?   ―▹ ♡ no, not unless i (or my managers) say so.          ── ── ──     ∩_∩   ☆( ˶ᵔ ᵕ ᵔ˶)☆ my ⚠ accounts :   ⚓️︶︶︶//  ╰⇢ MAIN ⊱ @ASTRO-TEARS  ㅤ◦ @kitten-- ⇣ main alt acc ㅤ ◦ @astrosets ⇣ aes sets  ㅤ◦ @astro-pears ⇣ the better me ㅤ ◦ @astro_reqs ⇣ requests ㅤ ◦ @stikyredbean ⇣ old  ㅤ◦ @tears-keyboards ⇣ asmr  ㅤ◦ @koibao ⇣ vacay  ㅤ◦ @mychums ⇣ friends + ty  ㅤ ˗ˏ ➛ ROBLOX ᝰ queenhidder https://web.roblox.com/users/547664069/profile  ㅤ ˗ˏ ➛ YOUTUBE ᝰ yumyo https://www.youtube.com/channel/UCrsGx90CW6B4Z7vHY7NP8Zw ㅤ  ˗ˏ ➛ P1N ᝰ @.astrote4rs          ── ── ──     ∩_∩   ☆( ˶ᴗ _ᴗ)☆ my ♡ friends :   ⚓️︶︶︶//   ╰⇢ IRL friend group ⇣ LUV U          ⁶ ʸʳˢ ᵒᶠ ᶠʳⁱᵉⁿᵈˢʰⁱᵖ!    ㅤ◦ ayid———@ayid_7345    ㅤ◦ butter—@bvttercreame-    ㅤ◦ evie———@evie_chloe ⠀ ⠀ ⚠︎ evie isn't active AT ALL ⚠︎   ╰⇢ IRL 5LC LEAFIES ✫    ㅤ◦ ayid———@ayid_7345    ㅤ◦ elise———@elisebearr    ㅤ◦ matcha—@milkymqtcha    ㅤ◦ stella———@strxwbrryy   ╰⇢ SCHOOL FRIENDS    ㅤ◦ echo———@-echoo_    ㅤ◦ oof——@oofedupyeet    ㅤ◦ prepp———@pr3ppy    ㅤ◦ astella——@academia-    ㅤ◦ cece————@luuvly    ㅤ◦ taffy———@taffywaffi   ╰⇢ SCRATCH FRIENDS    ㅤ◦ too many to list off, ilya     ヽ``、ヽ`、ヽ     ◜◝--◜◝     ( 。・㉨・ ) ♡ ♡ ♡   ┌───────⊹──────┐ ⠀  ⚓️ ᵗʰᵃⁿᵏˢ ᶠᵒʳ ᵛⁱˢⁱᵗⁱⁿᵍ ⚓     ҉ astro's ─ mailbox ◠   └───────⊹──────┘     ヽ``、ヽ`、ヽ✋
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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡊⠀⠀⠀⠀⣿⣾⣿⣷⣶⡆⠀⠀⠈⠙⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢞⢩⠞⠁⠀⣀⣠⠴⢿⣿⣿⣿⣿⡷⠦⣄⣀⢀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠓⠛⢋⡤⠒⠉⠁⠀⠀⢸⣿⡟⢻⣿⡇⠀⠀⠉⠙⠲⢤⡈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⠆⢀⠴⠋⠀⠀⠀⠀⠀⠀⠸⠿⠷⠿⠿⠃⠀⠀⠀⠀⠀⠀⠙⣦⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⡟⠁⣠⡀⠀⠐⢿⡷⠀⠀⠀⠀⠀⢀⣔⠁⠔⠁⠘⠿⠇⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠁⠀⠛⠋⠀⢀⣀⣀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⢀⣤⡄⠀⣤⡤⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡀⠀⠀⣷⡮⠊⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠈⠁⢸⣿⠄⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠐⠛⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡖⠀⠰⠿⠋⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠙⠉⠀⠀⢴⡦⠀⠀⢴⡶⠀⠀⣀⠅⠀⠀⠀⠀⠀⣀⠀⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣆⣀⣤⡀⠀⠙⢶⣤⣀⡀⠀⣀⣠⡴⠊⠁⣀⣰⠴⠀⠀⠈⠉⠂⢾⣻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠙⢿⡿⠛⠁⣠⣶⣿⣿⣿⣿⣦⡇⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠛⠀⠀⢂⡇⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡇⠉⠛⠋⠛⠁⠀⠀⠀⠀⠈⠫⡛⢛⡫⠟⠁⠀⠀⠀⣸⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠮⠀⣠⡴⠁⠀⠈⢧⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣯⢀⣴⠋⠀⠀⣠⣤⣤⣧⣤⣶⣤⠀⠀⠻⣷⣦⣀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⣿⣥⡀⠀⠀⢿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣬⣿⣿⣿⣿⣿⣙⣒⣒⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢦⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣻⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⠀⢹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣿⣿⣷⡹⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⡏⠀⠀⢻⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⣴⣾⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠜⢹⣿⣿⡿⠻⠿⠿⡵⠀⠀⠈⠙⢧⣄ ⠀⠀⠀⠀⠀⠀⢠⣾⣧⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠕⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠁⢷⣿⣿⣿⣶⣝ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠋⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⠀⢰⣿⣿⣿⠁⠀⠀⢀⣀⣠⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣦⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⡏⠀⣺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⣠⠤⠖⠉⠉⣡⣾⣿⣿⣿⣿⣷⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⡾⠋⢀⣴⡿⠋⢻⣿⣿⣿⣿⣿⣿⣧⡵⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿ ⡇⣠⠞⠁⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈ ⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣽⡗⠞⠛⠻⣿⣿⣿⣦⠙⠿⡄⠚⠯⠭⠟⢻⣿⣻⣷⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⣹⡆⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀ ⡏⠀⠀⠀⢠⣀⣀⡀⠀⠀⣠⣤⣄⡀⠀⠀⠈⠙⠿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀ ⡇⣀⣀⣀⣼⡿⠿⠟⠛⢻⣿⠻⣿⣿⣦⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⢠⡶⠶⠶⢶⡤⠤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢰⠀ ⡟⠋⣉⣭⠀⠀⠀⣀⣀⡞⣿⠀⠀⠙⢿⢿⣷⣄⢀⣾⣿⣿⡿⢻⣿⣯⣶⡿⠇⢠⣾⣷⣄⣀⣀⠀⠀⠀⠈⠉⠉⠋⠉⠙⣷⠀⠀⠀⢀⣀ ⡇⠀⢿⣿⡶⠞⠚⠉⠉⢹⣿⠀⠀⠀⠀⠀⠈⣉⣿⠁⠀⢀⣠⣼⡿⠟⠉⠀⠀⢈⣷⠘⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⠃⠀⠀⢸⣿⣿ ⣿⠖⠋⠁⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⢀⣾⣿⣿⢰⣖⣻⡟⣿⣤⣤⠤⠄⠀⢸⡿⠀⠈⠉⠉⠉⡉⠉⠉⠛⠻⠿⢿⡏⢀⡄⠀⢸⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣶⠀⣼⣼⣿⣿⣿⠀⠻⠛⠁⡿⡋⠁⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠻⣤⡦⠁⠀⣼⡟⠀⣼⣷⡀⠘⣿⣇ ⡟⠀⠀⠀⠀⠀⢀⣾⣿⡟⡟⠻⠿⠆⠙⣿⡿⠁⣼⠀⠀⠀⢰⠃⣿⡆⠀⠀⢀⣿⠁⢦⢀⠀⠀⠀⠀⠙⠂⠀⣰⣿⠁⣸⣿⣿⣧⢀⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⢤⣔⠕⢂⣀⠴⠂⠀⠈⠉⠙⠒⠚⠯⠽⣒⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡨⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢵⣦⠀⠀⠀⠀⠀ ⠀⠀⠺⠒⡔⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣵⡄⠀⠀⠀ ⠀⣀⣤⡌⠀⠀⡀⠀⡠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⣷⡄⠀⠀ ⢀⣾⡟⠀⠀⠰⠀⡨⠎⡅⠀⠀⠀⠀⠀⢠⠾⠁⠀⠀⠀⠀⠀⠀⣆⠀⢸⣷⠀⠀ ⣿⡿⠃⠀⠀⣗⣈⣀⠀⢧⠀⠀⠀⠀⡰⠁⠀⢇⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⠇⠀ ⡿⣀⠀⠀⢸⠋⣿⣿⣿⡿⢦⡀⠶⢴⣥⣠⣄⡈⢆⠀⠀⠀⠀⠀⠀⠣⡀⢇⠇⠀ ⠉⠺⣽⣦⣀⡆⣆⠛⣱⠃⠀⠈⠁⢠⢟⣿⠿⡟⠿⢲⠀⠀⠀⠀⢀⣠⠔⢋⠀⠀ ⠀⢸⢻⠁⡇⠀⠈⠉⠁⠀⠀⠀⠀⠘⢆⣉⡴⠁⢀⠃⠀⣀⠄⣰⡟⠀⠀⠀⠑⡅ ⠀⣾⡏⠀⠍⢢⡄⠐⠒⢠⠀⠀⠀⠀⠀⠀⠀⠐⢳⠶⠧⠤⡴⠛⣀⣉⠙⢿⢿⠚ ⠀⣿⡇⠀⠄⣸⡀⠀⠀⣹⡀⠀⠀⠀⠀⠀⢀⣠⡼⠁⠀⠀⢰⡀⠈⠻⡿⣴⠊⠀ ⠀⠸⣿⡀⠀⡏⠉⠒⢒⣿⠏⢿⣉⡮⠝⠛⠷⡤⠃⠀⡐⠀⢸⣿⣦⢤⣬⣺⣷⠀ ⠀⠀⠙⣷⡾⠁⠀⠀⢸⣤⠷⠫⢥⣖⠂⠉⠉⢳⡶⠊⠀⢀⣿⠇⠀⠉⠁⠉⠉⠀ ⠀⠀⠀⢹⣧⡀⠀⢂⡏⠀⠂⠀⠀⠈⠳⡄⣠⠮⠤⠄⣲⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⢭⡟⣉⣦⣼⣶⡦⠤⢤⣧⣀⣁⣶⠄⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⢩⡝⠢⢤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⡀⢸⠷⠀⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡸⠓⢦⣄⣀⡠⠞ ⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠿⣓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠢⣍⡓⠢⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⣶⠶⡦⢤⣄⣰⠃⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⢤⣈⡉⠙⠒⣶⠦⢤⣤⡤⠴⣞⡿⠉⠓⠋⠀⠈⠉⠁⠘⠶⠛⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⣌⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⡤⣄⣀⡀⠀⣀⣀⣤⠀⠀⠀⢀⡎⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡇⢺⠀⠉⠉⠉⠀⠀⡆⠀⠀⢸⠁⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣷⠚⠃⠀⠀⠀⠀⠀⣇⠀⠀⢸⡖⠦⠿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣃⡤⠒⠮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⠿⣷⡈⠛⣡⣾⣿⣿⣿⡿⢿⣿⣿⡄⣀⣠⡄⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢎⠻⣿⣿⣿⣿⣿⣟⢹⣿⠷⠤⢼⣷⣼⣿⣿⣿⣿⣿⣷⡶⠯⠉⣠⡛⠛⣴⣿⢏⣾⠁⠀⠀⣀⣤⡤⠤ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠁⠙⣿⣿⣿⡟⣿⣿⡹⣷⣠⣔⡙⢿⣁⣿⣟⢻⣟⣿⣧⢠⡄⣿⣄⣬⣷⣽⠿⠱⣠⡶⠛⠩⠒⠀⠀ ⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⢘⠟⢿⣿⣿⣿⣿⣷⣿⣿⢿⣅⣼⣿⢸⠿⣿⠿⢀⡀⣾⢻⡏⢻⣿⣼⠙⣳⠟⣫⠆⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢳⡌⢿⣿⣿⣿⣿⣿⣷⣈⣿⣿⣿⣴⡶⢿⡀⡈⣧⠉⣽⠇⠎⠟⣹⠿⣡⠾⠃⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣇⠰⣆⠀⠀⠢⠤⠄⠘⠿⠏⠉⠟⢻⠛⠛⠛⠿⠿⣿⡿⣿⣿⡿⣿⡇⣼⣦⣿⣞⣻⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢆⠘⣦⠀⠀⠀⠀⠀⠀⢠⢠⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣿⣧⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡶⠁⡀⠀⡀⠀⠀⠀⢸⣄⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣧⣖⣀⠀⠀⠀⠀⠀⠀⠀⢠ ⣿⣿⣿⣿⣿⣿⣿⣿⠙⢦⡈⠤⠀⠀⠐⢤⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠿⢿⣿⣿⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⣌⣒⣥⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣯⣽⣿⣿⣿⣯⡗⠀⠀⠀⠀⣰⠀ ⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣀⠀⠀⡴⠃⠀ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟⠳⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣿⣿⣿⡟⣹⡏⢻⢿⣿⣿⣿⣿⣦⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠛⠁⠀⢤⡀⠀⠀⠙⠛⠙⠛⠛⠻⠗⠋⠀⢼⢲⣿⣿⣿⣿⣿⡆⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣟⣂⠀⠀⠀⠀⠐⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⣿⣿⣿⡿⠀⠀ ⣿⣿⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠀⢀⠀⢶⣶⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠹⠿⣿⠄⠀⠀ ⡿⠿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠑⠒⠤⠤⠄⠛⣠⣇⠰⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣄⣀⣂⣀⣈⣴⣿⣧⣀⣩⣅⠀⠀⡀⠀⠀⠀⠀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣾⣚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠛⠛⠛⠿⠿⣟⠛⠓⣿⢿⣶⡶⠶⠾⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣯⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣟⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠲⠤⠤⢄⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⣿⣯⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣽⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢽⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠎⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡖⢲⡤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠞⠁⠀⠀ ⡼⢈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢻⠉⠉⠙⡏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⡇⡞⠀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠻⠴⠉⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡉⠓⠂⠚⠃⠀⠀⠀⠀⠀⠀⠸⡀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⡸⠁⠈⣱⠦⣤⣀⣀⣀⣠⠤⣞⠁⠀⠙⠢⠤⣄⠀⠀⠀⢰⡀⠀⠀⠀⠑⢶⣇⠀⠀⢸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⠀⡇⠀⠀⡇⠀⢡⠀⠀⠀⠳⡀⠈⠓⢤⣀⣠⠴⠋⠀⠀⠀⠀⠳⣄⣀⠀⠀⠀⠈⠉⠓⢻⣄⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠘⣆⠹⣄⣀⣹⠀⠈⠣⣀⠀⠀⠉⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠋⠓⠢⣄⠀⡼⣶⣀⢠⣌⢳⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⣀⠈⠁⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡠⠖⠁⠀⠀⠀⢀⡞⢳⣿⣾⡏⢻⡟⠻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢗⠲⠤⢄⣀⣀⣀⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⣠⠞⠀⠀⢿⡉⠻⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠦⣄⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣠⠤⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡼⠓⠒⢤⡀⠀⠙⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠚⠁⣀⡀⢠⠿⡄⠀⠀⢀⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢃⢸⢀⡇⠀⠀⡟⠇⣼⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠒⠒⠒⠾⠦⠞⠚⠋⠓⠒⠲⠷⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⣀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⠷⠸⡄⠀⠀⠀⢀⣀⣤⣼⠥⢤⣤⣄⣷⡀⠀⠀⠀⣠⠶⠛⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠁⠀⠀⢀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠓⢶⣏⠁⠀⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⣐⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠆⠀⠀⠀⠀⠀⠀⠈⢻⡅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠚⠉⠉⣻⠂ ⠀⠀⠀⢸⣧⣤⣤⡤⠶⠶⣶⠒⠒⣻⣿⠛⢛⣿⡛⠛⢻⡗⠒⢶⡄⠀⠀⠀⢿⠀⠀⣰⠏⠀ ⣤⣴⣾⣻⠿⣦⡟⠻⢦⡾⠉⠳⠞⠉⠙⢷⠋⠀⠛⠶⠋⢳⡶⠛⣇⠀⠀⠀⠘⣇⢠⠏⠀⠀ ⠙⠻⢿⡏⠀⢰⣶⡄⠀⢠⠀⡀⢠⡀⢴⣶⡆⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⠏⠀⠀⠀ ⠀⠀⢸⠁⢰⠨⡍⠁⠀⢿⡼⠿⠾⠃⠈⠉⠠⠰⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⢸⣀⣠⣤⡄ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡅⠀⣼⠀ ⠀⠀⠀⠙⣦⣀⣄⢀⡀⠀⢀⠀⠀⣀⠀⢠⣄⠀⢠⣄⣠⢶⣀⣼⠁⠀⠀⠀⠀⣀⣇⢠⡇⠀ ⠀⠀⠀⠀⢸⣿⣽⣏⣹⣴⣋⣳⣞⣉⣷⣏⣈⣻⡿⠬⠿⠖⠛⠁⠀⠀⠀⠀⠀⢹⣹⣾⠁⠀ ⠀⠀⠀⠀⠈⢿⣆⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠘⡇⢿⡀⠀ ⠀⠀⠀⠀⠀⠀⠻⣷⠶⠤⠤⣤⣄⣀⡤⠤⠤⠤⠤⠶⠶⠂⠀⠀⠀⠀⠈⢳⣄⣠⣷⠀⠻⣄ ⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⣁⣀⣈⣹
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣞⡹⣆⣠⠿⠛⡩⢉⠅⢢⠌⡒⠤⣉⠉⡍⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢟⣬⣓⢾⣅⠢⡑⢄⠣⡘⢢⠘⡄⢣⡐⢩⠐⡩⠐⠤⡙⢦⡄⠀⠀⠀⠀ ⠀⣰⢏⡞⣦⡝⢮⢽⣆⠘⡄⢣⠘⡄⢣⠘⠤⡘⢄⠣⢌⡑⠢⡁⠆⡙⢧⡄⠀⠀ ⣴⢏⡾⣱⠞⣜⣫⢎⣽⠶⠞⠒⠓⠮⣄⡉⢆⠱⣈⡶⠚⠉⠉⠙⠳⣬⠠⡙⣆⠀ ⣾⢪⢵⣣⠻⣜⡱⡞⣼⡇⠀⠀⢀⣠⣈⣳⡌⣲⠏⠀⠀⠀⠀⣠⣤⣬⣷⠔⡘⣆ ⠏⢺⣆⣏⡳⢭⢳⣹⡞⠀⠀⢠⣿⣿⣿⣿⡆⢿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠂⠥⢹ ⠈⢆⡙⠞⠷⠯⠿⣇⠀⠀⠀⠀⠙⠿⠿⢛⡎⠜⣆⠀⠀⠀⠀⠙⠛⢛⡽⢃⠜⡈ ⠘⠤⡘⢌⠢⡑⢢⠉⠶⣄⣀⠀⣀⣠⠴⠋⡄⠣⢌⠳⢤⣄⣀⣠⡴⠋⡔⢡⠊⠔ ⡌⢢⠑⡌⢢⠑⢢⢉⣴⣤⣉⣍⡩⡐⠌⡑⢨⠑⣈⠒⣄⢢⣐⣦⣴⣡⠘⠤⣉⢲ ⣷⢀⠣⡘⠤⡉⢆⢺⣿⣿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⢿⠿⠿⢟⣿⣿⢀⠣⡐⣸ ⠘⣦⠑⡌⢢⠑⠢⠌⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡏⢄⠣⣰⠏ ⠀⠙⣶⢈⠆⣉⠆⡱⢈⠿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⢋⠰⡨⣶⠋⠀ ⠀⠀⠈⠻⣔⢢⠘⡄⢃⠆⣉⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡋⠔⣈⢶⡝⠁⠀⠀ ⠀⠀⠀⠀⠈⠳⢎⡰⢁⠎⡐⢂⠆⠤⣉⠩⡉⢍⠡⡁⢆⠱⣈⣮⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⡓⠮⣴⣁⣎⠰⣀⢣⢘⣄⣣⡼⣴⢟⡏⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡆⣇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠄⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⢹⣸⡀⠀⠳⣤⣤⡶⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣴⠶⠶⠛⠛⠉⣉⡀⠤⠖⠂⠉⠀ ⠀⠀⠀⣀⣀⣠⣤⣾⡟⢻⣤⡀⠙⠶⠮⢉⣀⣀⠀⠀⣀⡀⠤⠴⠒⠊⠉⠁⠀⠀⠀⣀⣠⡤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠛⠯⠍⠓⠒⠉⠉⠉⠛⠷⣤⣀⣀⠤⠤⠚⠋⠉⠀⠀⠀⠀⢀⣀⡤⠤⠒⠚⢧⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢒⣺⠏⠁⠀⠀⠀⠀⣀⣠⣤⡔⠒⠻⠭⢼⣧⡀⠀⢀⣀⠽⠧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠤⠖⣒⡩⠴⠒⠈⠁⠀⣀⡠⠤⠒⠊⠛⢽⣢⣌⡻⣦⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⢐⣦⡀⠀⠀⠀⠀⠀ ⠸⢿⣓⠊⠁⢀⣀⠠⠴⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠭⢙⡖⣲⠄⣀⡀⠀⠀⠀⠀⠀⢰⣶⣯⣬⣽⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠉⠑⠒⢮⣵⣲⣦⣤⣼⣺⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⠃⠀⠀⠀⠀⠘⠿⠁⠀⠘⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⢒⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⣀⣀⣀⡀⠀⠀⢧⠀⠀⠀⠀⠀⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠒⠋⠉⠉⠀⠀⠀⠈⠉⠓⠾⢄⣀⠀⠀⢠⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣩⠏⠉⠒⢒⣲⡤⠤⣀⣀⠀⠀⠀⠀⠀⠈⠑⢤⡘⡄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠀⠀⠀⠀⢰⠾⣣⠴⠚⠉⠉⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣔⡿⡍⡇ ⠀⠀⠀⠀⠀⢸⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⢳⡀⠀⠀⠀⠀⠀⣀⡤⠞⠋⣡⠞⠉⠀⣇⡇ ⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠛⠓⠚⠉⠉⠉⠁⠀⣴⡟⠁⠀⠀⠀⣿⠁ ⠀⠀⠀⣼⣁⣠⡤⢴⠖⠒⠒⠦⠤⢴⣶⣢⠤⠤⠔⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡞⠀⠀⠀⠀⢰⢿⠀ ⠀⠀⠀⠉⠉⢙⣦⠞⠀⡠⠞⠉⢉⡷⡄⠉⢙⡶⠃⠀⠀⠀⢀⣠⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡼⠀⠀⠀⠀⠀⡜⡞⠀ ⠀⠀⠀⣤⡖⠛⠀⠀⡜⠁⠀⡴⢋⣀⣹⣠⠋⠀⠀⠀⠀⣰⣿⠿⠛⠛⠿⣿⣷⣄⡀⠀⠀⠀⠀⠀⡼⢰⠃⠀⠀⠀⠀⡼⢱⠃⠀ ⠀⢀⣴⠛⠀⠀⠀⢼⠁⠀⣼⢁⣿⡬⣿⠃⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⣸⢃⡏⠀⠀⠀⢀⡜⢡⠏⠀⠀ ⠀⠸⡿⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⣀⡜⠁⡼⠀⠀⠀⡠⠋⣰⠋⠀⠀⠀ ⠀⠀⣧⠀⠀⠀⠀⠈⢳⣀⣙⣦⡤⠋⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⢤⠀⣹⠌⢩⠏⢠⣇⣠⠴⠊⢀⡼⠁⠀⠀⠀⠀ ⠀⠀⠘⡆⢀⡴⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣾⣷⣿⣿⣿⣷⣦⡀⠀⢸⠀⠻⣾⠉⠀⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⣥⠤⠦⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠛⠿⣿⣿⣄⣸⠀⠈⠻⣇⠀⢀⣀⠤⠟⠓⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡆⢧⡀⠀⠀⠀⠀⠀⠈⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣸⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡄⠙⢦⡀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⣀⣉⣷⡚⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣦⣴⠚⢁⡾⠋⠉⠳⢤⣀⢀⣀⣀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠁⢀⣺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣷⡇⠀⡞⠀⠀⠀⠀⠀⡼⠋⠉⠁⠀⠀⣀⣀⠤⠴⠒⠊⠉⠉⠀⠀⠀⠀⠀⣼⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢯⡛⢦⡀⠀⠀⠀⢀⡾⠥⠤⠔⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣸⣹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠀⢹⣶⣶⣖⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⠿⠉⠉⠋⠀⠀⠉⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠹⢤⣀⣀⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠙⠋⠩⠿⢿⣁⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠉⠑⠶⢤⣀⣀⣠⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣅⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀ ⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀
+ carrd.link •• ★ sexuality . timezone . minor/age 𖤐 song - artist ! ✩ ♡ mbti ✶ eth/nationality ✶ bday
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣜⡀⠀⠀⠘⠁⠈⠳⡄⠀⠀⠀⠀⢸⠃⠀⠀⠀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⢿⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⠥⠤⠤⠤⠤⠤⠤⣄⣱⣄⠀⠈⠀⠀⢳⡀⠀⠸⠁⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⢉⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠒⠦⢼⣃⠴⠲⠊⢛⣂⣀⣤⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⣴⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣦⡀⠀⠀⠉⠓⢾⡉⠉⠀⠀⠀⠀⠉⢳⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢸ ⠀⠀⢀⡄⢰⡀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⡾ ⠀⢀⡾⠁⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠴⠻⣿⣿⠶⠄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣸⠃ ⠀⡼⠁⠀⠀⣻⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣿⠿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⠃⠀ ⠀⡇⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠘⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠈⠉⠉⠛⠓⠨⠿⠷⠿⠭⠭⠶⠶⠤⠤⠤⠤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠠ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠶ ⢸⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⡞⠀⠀⠀⠀ ⢸⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠙⡿⠀⠀⠀⠀⠀ ⠈⠻⣄⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠹⣦⡀⢀⠞⠁⠀⠀⠀⠀⣠ ⠀⠀⠈⠢⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⣨⢿⡋⠀⠀⠀⢸⡇⢐⣧ ⠀⠀⠀⠀⠈⠑⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠷⠖⠋⠁⠈⣁⣀⡒⠛⠛⠉⠙⠛ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠲⠦⣤⣀⣀⣀⣀⢠⣤⣤⡤⠤⠴⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀ ⠀⠀⠀⠐⠂⠙⠦⢀⠔⠓⡄⡠⠤⠄⠀⣠⠞⡟⠉⠀⠀⣰⣿⡿⠿⣿⡆⠐⠤⣀⣀⡴⢤⠀⠀⠀⠀⠉⠘⠒⠤⠀⠀⠀⠉⠉⠁ ⠀⠀⠀⢀⡴⠛⠉⢙⣇⢰⡃⠐⠠⠀⡴⠃⢠⡷⠾⠯⠭⣽⢻⣇⠀⠈⢧⠀⠀⠀⠙⣦⣸⠟⠲⠦⣐⠒⠈⠁⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠤⢿⣟⡽⠆⢀⡀⠀⠉⠲⢤⡞⠁⠀⣸⠃⠀⠀⠀⠀⠘⣿⡄⠀⠈⢧⣤⠴⠋⠈⢉⠁⢤⣰⣿⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠹⡄⠀⠀⠀⠀⡇⠀⣼⡏⠀⠀⠀⠀⠀⢀⡏⠸⡄⠀⣾⠀⠀⠀⠀⣸⡷⠶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⣼⡥⠞⢡⠇⠀⠀⠀⠀⠀⢸⠃⠠⠙⣤⣸⣄⠀⣠⡾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣛⡿⠿⠛⢯⠉⠉⣉⣩⠽⠛⠛⠻⠯⣍⣉⠉⢉⠟⠛⠯⣭⣙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠓⠋⠁⠀⠀⢀⣼⢷⡋⠉⠀⠀⠀⠀⠀⠀⠀⠉⣱⢿⣄⠀⠀⠀⠉⠙⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⢖⡟⢹⠀⠀⠀⠀⣠⠖⢫⠋⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠻⡗⢦⡀⠀⠀⠀⢀⡟⢟⣢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡶⢋⡵⠋⠀⠈⡆⢀⡤⠞⠁⣠⠋⠀⠀⠀⠀⠙⢦⡀⠀⣠⠞⠁⠀⠀⠀⠀⠹⡄⠉⢲⣄⠀⣸⠀⠀⠱⣌⠑⢦⡀⠀⠀⠀ ⠀⠀⢠⣾⡏⢰⣿⡶⠶⠶⠤⣷⠿⠶⠶⢶⠷⠴⠶⠦⠤⠶⠶⠶⢿⡿⠓⠲⠂⠀⠀⠀⠂⠤⢼⠶⠶⠿⢷⡿⠶⠶⠶⢾⣷⠘⣟⣦⠀⠀ ⠀⠀⠀⢿⣇⠀⢽⠷⣄⠀⠀⠘⣷⡄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⣴⡿⠁⠀⠀⣴⠟⡁⣰⣧⠏⠀⠀ ⠀⠀⠀⠀⠻⣦⡈⠳⣝⢷⣄⠀⠘⡞⢦⡀⠀⢳⡀⠀⠀⠀⠀⠀⡞⠈⡇⠀⠀⠀⠀⠀⢠⠏⠀⣠⠞⣴⠁⠀⣴⠟⢁⣾⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡄⠙⢧⡙⢷⡀⠹⡄⠳⣄⠀⢷⡀⠀⠀⠀⢀⡇⠀⢧⠀⠀⠀⠀⢠⠏⠀⡰⠃⣸⠁⣰⠞⢁⣴⡿⣻⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠙⢄⠙⢶⡻⡄⠈⢧⡈⢳⠀⠀⠀⢸⠀⠀⢸⡄⠀⠀⢠⡏⢠⠞⠀⣰⣿⠟⠁⡰⢫⠈⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⠳⡤⣽⣷⡀⠀⠙⣄⢧⡀⠀⡞⠀⠀⠈⣇⠀⢀⣏⡴⠃⠀⣰⠟⠁⣠⢞⠕⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠘⢮⡓⣙⢦⡀⠈⢿⣣⢸⠇⠀⠀⠀⢸⢠⣾⠏⠀⣠⠾⠁⢀⣜⡅⢋⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠙⢦⠢⣝⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⣴⣻⡏⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠈⠳⣄⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⠝⢋⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠳⣀⣑⣆⣀⣒⣒⣀⣀⣀⣀⣠⠞⡵⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠶⠖⠚⠋⠉⠉⠉⠀⠀⠀⠉⠉⠛⠻⠿⢶⣶⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠠⠀⢐⣒⡂⠠⠤⠄⣀⡀⠐⠀⠀⠀⠈⠙⠻⢵⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠏⠁⠀⠀⣀⣠⣴⠶⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⢦⣤⣀⠀⠀⠉⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⠟⠀⢀⣤⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠈⢻⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠿⠃⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠙⣿⣆⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠘⢿⣆⠀⠀ ⠀⢀⣾⠏⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠘⣿⣇⠀ ⠀⣼⡇⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⢹⡾⡆ ⢠⡟⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢣⢷ ⢸⠇⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠸⢸ ⣾⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⢿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⢸⡆⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢰ ⠘⣷⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡜ ⠀⢻⣧⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢠⠃ ⠀⠘⢿⣆⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣠⢀⡞⠀ ⠀⠀⠈⣿⣇⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⡰⢣⡟⠁⠀ ⠀⠀⠀⠘⢿⣧⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡼⣣⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣆⡀⠐⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⢀⣰⢻⡵⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⢆⡀⠁⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⣰⢟⣵⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡲⣄⡀⠀⠈⠙⠳⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠚⠋⠀⢀⣠⠴⣫⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢽⣳⠦⣄⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⣠⠤⠚⣋⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠬⣭⣛⣳⡶⠤⠤⠤⠤⠤⠤⠔⢒⣛⣛⡥⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡈⠉⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠃⠣⠈⠟⠋⠋⠚⠫⠫⠑⠀⠈⠓⠪⠉⠀⠀⠀⠝⠋⠁⠀⠘⠉⠛⠿⠙⠹⠯⠓⠓⠿⡚⠚⠻⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠤⣖⠁⠀⢀⡤⠒⢉⣉⣉⣉⣉⠒⢤⡀⠀⠀⠀⠀⠀⢀⡠⠖⢊⣉⣉⣉⡑⠲⢤⡀⢀⣠⠖⠀⠀ ⠀⢀⡴⠋⠀⠀⠈⠙⡶⢋⣴⠞⠋⠙⢿⣿⣿⣿⣦⡈⢦⠀⠀⠀⡴⢋⣴⣾⣿⣿⠟⠋⠙⠳⣤⠙⢯⠀⠀⣀⠀ ⢠⠎⠀⠀⠘⠒⠦⡞⢀⣾⡏⠀⠀⠀⠀⣿⠟⢻⣿⣿⡄⢣⠀⡜⢠⣿⣿⠿⢿⣏⠀⠀⠀⠀⣿⣷⡀⢳⠋⠁⠀ ⠈⠀⠀⠀⢠⣤⣴⠁⢸⣿⣿⣦⣀⣠⣴⣿⣦⣼⣿⣿⣿⠘⣶⠃⣾⣿⣿⣄⣠⣿⣦⣀⣀⣴⣿⣿⣇⠈⡖⠒⠂ ⠀⠀⠀⠀⠀⠀⢸⡀⢸⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⢀⣿⡀⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣀⡇⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠗⠋⠉⠉⠉⠉⠉⠓⠾⣿⣿⣿⣿⠇⡼⠀⢧⠸⣿⣿⣿⣿⡷⠚⠉⠁⣀⣀⠀⠀⠉⠙⠶⡄ ⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⣉⣑⡢⡀⠀⠉⠻⡟⢃⡜⠁⠀⠈⢣⡘⢿⣿⠋⠀⠀⣤⣾⠥⠤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠙⢷⡄⢰⡄⠹⡏⠀⠀⠀⠀⠀⠙⣶⠃⣰⠆⣽⠋⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⡆⢹⡄⢹⡀⠀⠀⠀⠀⢀⡏⢠⡏⣼⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡀⡇⢸⡇⣴⣿⣿⣦⢸⡇⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⡇⠉⢸⡇⣿⣿⣿⣿⠃⡇⠘⢸⠁⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣼⠁⠘⠛⠛⠋⠀⢻⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⡏⠀⠀⠀⠀⠀⠀⠸⡧⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠿⣆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⠿⠋⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡿⠛⠉⠹⣴⡤⠞⠛⢛⣛⣛⠛⠛⠛⠿⠿⠿⣿⣿⣿⡟⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⠟⠁⠀⠀⠐⣊⡽⠗⠚⠉⠉⠀⠈⠉⠲⣤⠴⠶⣤⣤⣤⣽⠁⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢿⡁⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣹⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠙⠦⣴⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡼⠁⠀⠀⠀⣇⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠿⠻⡀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢳⠈⣇⠻⣄⣀⢀⡼⠙⢿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠑⠀⠀⠹⣦⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣇⢸⢣⡀⠉⠉⢧⡀⠀⠻⣿⣷⣮⣝⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⡼⠓⣶⠒⣛⠁⠀⠀⠀⠀⠀⠀⢀⣯⠀⠀⠀⠀⠀⠀⢸⠘⠆⠱⡄⠀⠀⢿⠦⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠟⠁⠀⢀⣀⠀⢀⡞⠁⢠⡇⢰⠃⠀⢀⠀⠀⠀⠀⢀⣞⣹⡀⠀⢀⠀⠀⠀⠸⣿⡷⠒⠻⣟⠁⠈⣇⠈⡹⣶⣶⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠆⣠⠋⠀⠀⡼⠀⡏⠀⠀⡾⠚⠛⠛⠉⡽⠉⠉⣇⠀⢸⠀⠀⠀⢠⣿⠀⠀⠀⠘⢧⠀⠘⡆⢡⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⠞⠁⠀⢀⣴⡇⠀⠁⠀⣸⠁⠀⠀⠀⡼⠁⠀⠀⠸⡄⢸⠀⠀⠀⢸⠋⠀⣀⣠⣤⣾⣇⠀⢳⠘⡄⠸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣯⡥⠤⠔⣶⡏⢨⡇⠘⠀⢀⡏⠀⠀⠀⣸⣧⣤⣤⣤⣤⣽⡄⡇⠀⠀⡎⠀⣾⢿⡿⢿⠉⠹⣆⠸⡄⠿⣄⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠁⠀⣠⣿⡄⢸⠀⠀⠀⢸⠁⠀⠀⣼⡟⠉⠉⠉⠉⢿⠉⣿⣷⠀⣰⠁⠈⠘⡄⠀⠸⠀⠘⢿⡆⡁⠀⣿⣿⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠇⠀⣴⠃⣿⠁⢸⡇⠀⠀⡼⠀⢀⡾⣅⢱⡀⠀⠀⠀⠋⠀⡇⠈⣲⠃⠀⢀⠀⠱⢤⣼⣶⣦⣾⠹⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣟⣤⡾⠁⢠⡇⢠⣿⣇⠀⢀⡇⢀⡞⠀⠀⠁⠛⠒⠒⠚⠛⢉⡇⡴⠃⣀⣀⣤⣴⣶⣾⣿⣿⣿⡇⠀⢻⣄⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣡⣴⣟⢀⣞⠀⣹⡀⢸⣿⠋⠓⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣮⣧⣮⡸⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⡻⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣶⣤⣉⣿⡟⠛⠻⣿⣍⣉⣉⡟⠓⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠉⠉⠛⡟⠓⢺⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠂⠀⢠⠥⠤⡤⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⣿⠿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠠⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠙⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡤⠤⠴⠶⠖⠒⠒⠒⠒⠒⠒⠲ ⠶⠖⠒⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠉⠉⠛⠲⠦⣤⡀⠀⠀⠀⣸⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠲⠦⠤⣼⣽⣆⠀⠀⡟⠀⢌⣆⣀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠦⠤⣤⣄⣸⣭⡿⢸⠇⢀⣠⣿⠗⠀⠀⠀⠀⠀⣠⠏⠁⠉⠙⠓⠶⢤ ⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠲⠦⣤⣀⣀⠀⠀⠀⠀⠐⠊⠙⠒⠶⢦⣤⣤⣧⡾⠋⠀⠹⠶⠤⡼⠋⠀⢀⣠⠶⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠒⠲⠶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠴⡤⠴⠦⡴⠴⠦⠤⠤⡤⡤⠠⠤⡴⠶⣶⢶⠶⢶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⠁⠀⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢿⠖⠃⣐⡒⠤⢄⡀⠀⠀⢀⣀⡙⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠃⠈⢀⡾⠿⠿⣷⣦⣈⣦⠸⡉⠀⠀⡈⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠣⠀⠀⠀⠁⠀⢀⣼⣿⣿⣿⣿⣷⣶⣿⣿⣏⢧⠀⠀⠀⠀ ⠀⠀⣰⢣⡶⢶⣶⣦⣠⣾⡿⣿⣿⣿⣿⡿⠿⣿⣹⣿⠛⠉⢣⡀⠀⠀ ⠀⡴⠃⠟⠁⠀⠀⠀⠀⠉⣹⣿⡋⣉⣥⣤⢀⣀⣴⣮⣷⣤⣀⠑⡄⠀ ⡼⣱⠀⢠⣾⣿⣿⣾⣿⣿⣟⣿⣷⣿⣛⣯⣽⣿⣿⣭⣼⣿⣿⡆⠘⡆ ⣷⠀⠀⠸⠿⣿⣿⣿⣿⠿⢿⣟⣛⠿⠿⠿⢿⣻⣟⣋⠁⠀⠀⡅⠀⣧ ⣇⠀⠀⠀⠀⣿⣿⡟⠁⠀⠘⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⢀⡇ ⠈⢦⡀⠀⠀⠸⠿⠻⣧⣀⣠⣎⡿⣟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀ ⠀⠀⠈⠙⠲⠤⢤⣤⣌⣉⣉⣉⣁⣀⣠⣤⣴⡖⠒⠛⠛⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⢿⠉⠉⠉⠉⠀⠀⠀⣀⣿⣠⣴⠖⠛⠛⠲⣄⠀ ⠀⠀⠀⢀⣤⣶⣶⡇⠠⡄⠀⠀⠀⠀⠀⣠⣿⣿⣿⠇⢒⣠⠴⠛⣿⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣄⡙⣄⠀⠀⠀⣸⣿⣿⣿⣿⡷⠛⠁⠀⣠⠏⠀ ⠀⣼⣿⠛⠋⠙⠻⣿⣿⣿⡏⠉⠉⠉⠡⣿⡏⡼⠋⠀⠀⣠⠞⠁⠀⠀ ⠀⣿⡟⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠘⠿⢇⡠⠴⠊⠀⠀⠀⠀⠀ ⠀⠘⢷⣤⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢉⠙⠛⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⠁⠈⠉⠁⠈⠛⠟⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣤⣸⣶⠶⠶⠶⠶⣆⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣷⡏⠉⠀⢹⣧⠀⠀⠀⢷⣏⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣟⠁⠀⠀⠀⠀⢻⣷⡄⠀⠀⣻⣷⡄⢙⣷⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⣀⡏⠁⠀⠀⠀⠀⠀⠈⣹⣷⠄⠀⠈⣿⣧⢀⣹⣇⠀⠀⢠⣤⣰⣞⣿⣷⣆⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⣽⠀⠀⠸⢿⣿⣿⣽⣿⠟⠁⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡀⠀⠀⣼⣿⠀⠀⣿⠀⠀⠀⠀⠙⡗⠟⠁⠀⠀⠀ ⠚⡇⠀⣀⡀⠀⠀⠀⢠⣽⠯⠁⠀⢠⡿⡏⢐⢶⡟⠀⠀⠀⠀⣴⠧⠀⠀⠀⠀⠀ ⠀⢻⣆⣼⢹⡻⣶⢶⡶⠎⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣲⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣶⣭⣭⣽⠃⠀⠀⠀⠀⢀⣀⣴⠋⠂⠀⠀⠀⣬⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⠛⠛⣷⠤⠤⠤⢴⡖⠚⠋⠁⠀⠀⠀⢐⣴⡿⠀⠀⠀⡞⣼⣦⣄⠀ ⠀⠀⠀⠀⠀⢠⣾⠻⠶⢶⣄⣠⣤⣤⣤⣠⣴⡤⢿⠛⠛⠀⢺⢳⣦⣇⣯⣿⣿⠆ ⠀⠀⠀⠀⠀⣾⠟⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡾⠞⠛⠁⠀ ⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠉⠚⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣄⠀⠈⠉⠛⠷⢦⣄⣀⣀⣀⣀⣰⡶⠼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢲⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠾⡤⢀⢀⣀⣠⡶⠴⠿⠒⠒⠒⠒⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⣾⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣶⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⣛⢛⢛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠷⢒⡶⠖⠒⠛⠛⠛⠉⠉⢙⣶⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡻⠿⠃⠀⠀⢿⣇⣀⣀⣀⣠⠤⠤⠤⢬⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠻⣤⠀⠀⠀⠈⠛⠒⠒⠶⠶⣶⣶⡶⢾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢃⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣟⡙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡍⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣀⣴⢶⣳⡀⠀⠀ ⠀⠀⠀⠀⢀⡠⠤⠤⢤⣄⣀⣀⡀⣀⣀⡠⠴⠺⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠈⢸⣿⣿⡀⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠿⠿⢶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⢿⣗⡇⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠈⣟⡇⠀ ⢰⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⣸⠉⠀⠀⠀⠀⣀⣠⣷⣿⣆ ⡏⠉⠛⠷⣦⣤⣀⣀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⣤⣤⣤⣿⠶⣶⡶⠿⠿⠛⠛⠋⠁⢸ ⣷⣾⢿⡆⠀⠀⣩⡉⠙⠛⠛⠻⠿⠿⠿⠶⠶⠶⠶⣶⣦⣴⣶⣶⠶⠶⡿⡿⠿⠻⣻⡙⠉⠁⠁⢠⣄⠀⠀⠀⢰⣷⡀⠀⠀⢸ ⠈⠁⠸⠦⣀⣸⡿⠿⢳⡆⠀⠀⢠⣞⣷⡆⠀⠀⢠⣤⣦⠀⠀⠀⢰⢶⣿⣷⠒⠋⠉⢹⡀⠀⠀⣾⣿⡀⠀⢀⣸⡟⢧⣀⠴⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠤⠤⠾⠛⠁⢷⣀⣀⣸⠟⠛⡆⠀⠀⣸⡾⠋⠀⠀⠀⠀⠈⠧⠤⠶⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠁⡤⠒⠈⠉⠉⠒⢦⡀⠱⡀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⠧⣀⡀⠀⠀⣠⡴⠃⠀⢧⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⣠⠞⠉⠈⢳⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠳⣄⠀ ⢰⠃⠀⠀⠀⢈⡷⠀⠀⢠⠀⠀⢀⡇⠀⠀⠀⠈⡆ ⠈⠧⣀⣰⣀⡿⠧⣀⡾⠟⠛⣦⣨⢿⡀⠀⠀⣰⠏ ⠀⠀⠀⠀⠀⠁⠀⢸⠁⠀⠀⢹⡀⠀⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠚⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀

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

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