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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡴⠀⠀⡀⢀⠀⡤⠀⠀⡀⡄⠀⢠⣿⠋⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⠀⠀⢸⣰⢳⢃⡞⠀⣸⢰⣷⠀⠀⡇⡇⢠⣿⠃⢠⠀⣤⡄⠀⣿⡟⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠈⢯⢧⣀⠀⢻⢃⠞⠀⢀⡇⢿⡇⠀⠀⡏⠁⣾⠃⣰⠃⠀⣿⡇⢰⣿⣠⠋⡰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⢮⡱⣄⠀⠀⠀⠀⠈⢯⣹⣇⠉⠀⠀⠀⢸⠀⠼⠀⠀⠀⢀⡞⠁⠘⠁⠀⠀⡟⠁⢈⡏⢡⢞⡵⠁⠀⠀⠀⢀⣠⢆⡤⠖⠀⠀ ⠀⠀⠈⠙⢦⡙⢮⡳⡀⣰⡇⠀⠀⢿⣹⠀⠀⠀⠀⠋⠀⠀⠀⠀⣰⣻⠇⠀⠀⠀⠀⠀⠀⠀⣼⡇⠰⠋⠀⠀⠀⢀⠴⠋⠞⠉⠀⣀⡀⠀ ⡀⠤⣄⡀⠀⠉⠲⣍⢰⣟⡇⠀⠀⢰⣿⡆⠀⠀⢠⣧⠀⠀⠀⢀⣿⣯⠀⠀⠀⢸⢧⠀⠀⢀⣿⡇⠀⠀⠀⠀⣴⡏⠀⠒⠦⠭⠭⠽⠇⠀ ⠙⠒⠦⠬⣑⣲⠄⠀⢸⣿⣅⠀⠀⢸⠀⡇⠀⠀⠘⣾⡇⠀⠀⠈⡇⣿⠀⠀⠀⢳⣼⠀⠀⢸⠋⡇⠀⠀⠀⣸⡾⠃⠀⣄⣀⣒⡒⠒⠒⠂ ⢀⣀⣠⠤⢤⣤⡿⠀⢸⠋⢻⠀⠀⢸⠀⡇⠀⠀⢠⡿⣷⠀⠀⠐⡇⣿⠀⠀⠀⢿⢿⡆⠀⢸⠀⡇⠀⠀⢠⠟⣿⠀⢤⡣⠤⣀⡉⠉⠉⠉ ⠐⠒⠊⢉⣉⠥⠖⠀⠸⡆⢸⠀⠀⠸⡄⡇⠀⠀⢸⠀⢻⠀⠀⢀⡇⣿⠀⠀⠀⢸⠀⡇⠀⢸⠀⡇⠀⠀⢸⢀⡇⠀⠀⠈⠙⠲⢭⣃⣀⠀ ⠤⠒⠊⠉⠀⠀⠀⠀⠀⡇⢸⣇⣤⣴⡇⣿⡒⠒⢺⡇⢸⠉⠉⢹⡇⣿⠉⠛⠒⢺⠀⡿⢲⢼⠀⣧⣀⡀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⣷⢸⡇⠀⠹⠿⠿⠃⠀⢸⡇⢸⠀⠀⢿⣷⣿⡽⠀⠀⢸⠀⡇⠸⣾⣦⣷⣤⢸⡇⡼⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠁⢰⡿⣤⣷⡆⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣷⡀⠈⠛⠋⢡⢼⣁⣧⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢐⡇⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢿⣓⣿⡿⠆⠀⠀⠀⠀⠀⠘⢷⣽⠿⠟⠀⠀⠀⠘⠳⠽⠿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣯⣴⠞⡿⠁⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣄⣠⣤⡀⢀⣤⣤⣄⡀⠀⠀⢰⡞⠳⣄⣼⢹⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡇⠀⠉⠛⠉⠁⠉⠳⣄⣠⡴⠟⠋⠉⠙⢦⣀⣀⣼⠏⠈⠉⠀⠙⠋⠉⠀⠀⠈⠳⢤⣼⠇⠀⠀⠀⢘⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⣿⣷⣄⠀⠀⠀⠀⠀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣠⡄⠀⠀⢀⣠⣴⣿⣿⣁⡀⠀⠀⣀⣀ ⣀⡤⠖⠚⠋⣿⡟⠿⣿⣲⡲⢤⣤⣿⠁⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⣿⣿⣿⠿⠿⠏⠉⠁⣿⣤⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠐⣿⣆⠀⠀⠉⠉⠙⠉⠻⠟⠳⠿⣯⣟⣲⡶⠤⡤⢤⣤⡤⠤⠴⣶⣞⣻⣿⣼⣷⠋⠛⠃⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀ ⠛⠛⠀⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠛⠿⠿⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣞⡿⠛⠁⠀⠀⠀⠀⠘ ⣀⣀⣤⡤⠀⠀⠀⠀⠈⠛⠻⣝⣲⣦⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⣖⣺⡿⠷⠟⠉⠁⠀⠀⠀⠀⢀⣀⡀⢀ ⠉⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠚⠻⠭⠽⠿⣿⡽⠿⣿⡿⠿⠯⠭⠞⠛⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⠟⠉ ⠀⠈⠙⠳⠶⠶⣾⠛⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⡀⢀⣀⣤⡴⠖⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⠶⢿⣋⡀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⣩⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠒⠛⠛⣿⣅⣀⣀⣠⣤⡴⣟⣿⡤⣤⡤⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⣾⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣯⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣀⠀⠀⠀⠀⠀ ⠀⠀⠸⡿⢡⡿⠁⣰⡿⠛⣇⠀⢸⣷⡞⣿⡄⢻⣷⠛⣷⢸⣷⢸⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢾⣵⠞⠹⣧⣼⣿⣴⣺⣿⣠⡿⠟⣽⣧⣰⠟⠋⠙⠛⢸⣿⡾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⣿⠉⠀⣸⢻⣿⠀⠀⠀⠀⣰⢿⣿⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠸⣧⡿⠀⠀⠹⣦⡟⠀⠀⠀⠰⣿⣼⠏⠀⠀⠀⠀ ⢠⣀⣼⠟⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀ ⢨⣿⣟⡛⠉⣤⡀⠀⠀⠀⠀⣤⠀⣴⡟⣷⠀⢸⣿⢹⠆⠀⠀⠀⡀⢠⣄⠀⠀⠀ ⣾⠟⠉⣿⣽⡟⠠⣶⣀⡐⣾⡿⣴⣿⣞⠁⠀⠀⣿⡟⠀⣴⢶⡄⢻⡄⣿⣷⡄⣤ ⠙⠳⠾⢻⣿⣴⣶⢋⣿⢀⣿⠀⢸⣿⢻⡏⢰⡞⠛⣷⣼⢿⣤⢿⡼⠙⠉⢸⣿⠁ ⠀⠀⠀⠀⠉⠉⠁⠸⣧⠏⢿⡶⠋⠉⢸⡵⠋⠓⠚⠉⠁⠀⠀⠀⠀⠀⢰⡏⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀

⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣤⣿⣯⣻⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣷⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣿⣿⣿⣿⣿⣿⢋⡴⢚⣹⠗⢦⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢻⣿⣿⣿⢿⣤⠔⢉⡤⠒⣫⡿⠛⢲⣤⣞⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠋⠀⠙⠋⢣⡤⠋⡠⠛⣡⣴⣾⡿⠗⠚⣷⠢⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣘⣷⣞⡠⠞⣡⠞⠋⠀⠀⠀⠘⢷⠀⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⡏⠀⠈⠻⡎⠀⠀⠀⠀⣴⣷⠀⠈⠛⣷⣦⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠁⠀⠀⠀⠀⠛⢹⣿⣶⡖⠋⢽⣿⣿⢧⠙⡏⠙⢷⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⠂⠀⠀⠀⠀⠀⠀⠈⠉⢹⡀⠀⠀⠉⠉⡼⠀⡿⠀⠀⠙⠷⢿⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⢀⡴⠃⣴⠇⠀⠀⠀⠀⠸⡟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡄⣴⠇⠀⠀⠀⠀⢀⣰⡇⠸⡷⠶⠶⡦⠤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠺⠷⠶⠶⠶⢶⠶⠶⢤⣀⡀⠹⢏⡼⣹⠀⣀⡴⣾⢿⣿⡼⣇⢀⡷⠒⣲⣶⠶⢋⣹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⠀⠀⠀⠀⠉⠓⠦⣄⡀⠉⣳⠯⠼⣏⣿⣷⣶⣿⣿⣾⢟⠛⠛⢉⣉⣡⡤⠾⠋⢭⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠉⣹⠿⠿⣆⣀⣘⣮⢿⣿⣿⣿⡟⠛⠒⠋⠉⠁⠀⠀⠀⣀⡾⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠳⡀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⣦⢀⣀⣀⣠⠤⠖⠋⣁⣼⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢴⣯⣀⠀⠀⠙⢦⣄⢀⡀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣋⣿⣿⣴⣤⡴⠖⠋⠁⢨⣿⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠛⠦⣀⠀⠈⠉⠙⢶⣉⠿⠲⠶⢤⣤⣤⣤⣀⡤⠶⠋⠁⠀⠉⠀⠀⠀⠀⣀⣠⠔⠋⣸⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠉⠛⠒⠒⠶⠶⠷⠶⠒⠛⠉⢸⠀⢾⣷⣶⣤⣤⣴⠶⠶⠶⡖⡚⣋⣀⣴⠾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⣿⠿⠿⠾⠷⠿⠧⠶⠿⠟⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢨⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡶⠛⢦⣀⣷⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠙⠓⠦⣤⡀⠀⠜⣰⠃⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠋⡀⠀⠀⠉⠛⢧⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠁⣠⠋⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠁⠠⢳⣄⠀⠀⠀⠀⠙⠦⣄⡘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠇⢠⠇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠈⠉⢻⡦⣄⣀⠀⠀⢀⣀⡬⠿⠛⠛⠲⠤⢤⣀⡀⠀⠀⠀⠀⠸⡀⣿⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⡀⠀⢀⡾⠀⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠢⢄⡀⠀⠀⣿⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣶⣾⣷⣾⣿⣿⠿⠿⢿⠟⠿⠛⠛⠛⠛⠛⢻⢾⠿⡿⡿⠛⠛⡛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠀⢰⢰⡀⡄⡀⣆⠀⣰⢀⡾⠁⢀⠀⣤⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡀⡀⠀⠀⠱⣧⡈⡓⠌⠀⠷⠇⠀⠏⡼⡡⠃⣿⢠⣍⢊⠜⠀⠀⠀⠀⠀⠀ ⠀⠘⢍⠺⡢⢠⠀⠘⣿⠀⠀⠸⠈⠀⢀⡾⠀⠁⠀⠁⢠⡇⠕⠁⠀⡠⠲⠓⢁⠀ ⢔⡢⠄⡈⠪⣮⠃⠀⡞⡆⠀⢞⡀⠀⠼⡇⠀⢰⡆⠀⡽⡆⠀⢀⡺⠀⠘⢛⣒⡀ ⠠⢤⣬⡥⠂⡟⠇⠀⡇⡇⠀⡼⡇⠀⠂⡇⠀⢰⢷⠀⡇⡇⠀⡜⡇⠜⣩⢉⡀⠐ ⠠⠄⠂⠉⠀⢁⢰⣀⡅⡧⠤⡇⡗⠐⡆⡗⠤⢼⢸⢄⡇⣇⢀⢣⠃⠀⠀⠉⠑⠢ ⠀⠀⠀⢀⠔⣹⢸⡀⠛⠋⠀⠇⠇⠈⠛⠛⠀⢸⢸⠘⠧⠷⢸⢸⠐⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠑⠛⠁⠀⠀⠐⠶⠾⠆⠀⠀⠀⠺⠾⠗⠀⠀⠻⠿⠀⢸⡀⠀⠀⠀ ⠀⠀⠠⣇⠤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⡀⠀⢠⠤⣀⢢⡧⠀⠀⠀ ⠀⠀⠀⣼⠀⠉⠁⠈⠢⡔⠋⠁⠑⠤⠜⠁⠁⠈⠉⠀⡈⠑⠚⠀⠀⣸⡗⠀⠀⠀ ⡠⠔⠚⡿⠻⢶⣀⣤⣏⣳⣆⡀⠀⠀⠀⠀⠀⠀⣀⣶⢉⣿⠶⠾⠋⠉⣯⠁⠀⠉ ⠤⠀⠀⠻⣦⣀⠀⠀⠉⠉⠙⠻⠯⢯⠿⣯⠭⠷⠚⠋⠁⠀⠀⢀⣠⡾⠟⠀⠀⠠ ⢤⠖⠂⠀⠀⠉⠘⠑⠶⠦⣠⣤⣤⡄⣀⣤⣤⣤⡤⣄⠲⠦⠛⠊⠀⠀⠀⠠⢤⠤ ⠈⠓⠢⢴⡖⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⠤⠒⠉⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠓⠢⠤⠤⠤⢖⣃⣀⣀⣴⣞⣀⡀⠤⠔⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡶⢄⠀⣠⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣝⣾⣶⣧⣾⣅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠚⢿⣿⡿⠓⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠛⣆⠀⢸⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⢀⡞⠀⠈⠳⠬⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠉⠉⠉⠀⣠⠤⣄⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡁⠀⠀⠀⡞⠀⠀⠈⢳⠀⠈⢣⡀⠀⠀⠀ ⠀⠀⡼⠁⢹⠀⠀⠀⠳⣄⣀⣠⠏⠀⢀⠞⢳⡀⠀⠀ ⠀⡼⣥⠤⠋⠀⠀⠀⣀⣀⠀⠀⠀⠀⠘⣆⡀⢳⡀⠀ ⡼⠁⠀⠀⠀⠀⢠⠞⠉⠉⠳⡄⠀⠀⠀⠀⠉⠉⢳⡄ ⣇⣠⠤⠤⣄⠀⠘⣆⠀⠀⣠⠇⠀⢀⡤⠤⣄⠀⢠⠇ ⠈⠳⢤⣀⡈⡇⠀⠈⠉⠉⠁⠀⠀⡏⠀⣀⣨⠗⠋⠀ ⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠒⠒⠚⠋⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⡼⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠒⠒⠒⠢⢄⡀⠀ ⠀⠀⢠⠏⢩⠇⠀⢸⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠙⣄ ⠀⠀⡞⢀⡇⠀⠀⡇⢰⠁⢀⣀⣀⠀⡰⢻⡦⣄⢠⠏⣷⢤⡀⣠⢤⢠⠴⣄⢣⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⢸⠀⡼⠀⣀⡼⠀⡎⡰⠋⣴⠉⣽⠇⢈⣦⢸⡿⠀⣽⡆⣿⠃⣼⠏⢠⠋⠈⢆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⡇⠀⣋⡩⢴⠆⢰⡷⢁⣾⠃⢸⠏⢠⣯⠇⣼⠇⣼⡜⢠⣿⠠⠋⠀⡇⠀⠀⠈⢦⡀⠀⠀⠀⢀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜ ⢸⠀⡞⠀⠀⢸⣀⡌⣇⠸⣣⢧⣩⡆⡬⠥⠞⡿⢰⠤⠴⠃⠘⠒⡏⢸⠀⠀⠀⠀⠀⠙⡶⠖⠊⠁⠀⣆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀ ⡇⢰⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⢠⠃⠀⠀⠇⡎⠀⠸⡝⠦⠴⢃⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠘⢦⡀⠀⢀⣠⠤⠚⠁⠀⠀ ⠉⠁⠀⠀⠀⣠⠔⠒⠒⠢⣄⠀⣏⣸⠀⠀⠸⣄⣧⣤⡀⠈⡳⢻⡍⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⢀⡼⠋⠉⣩⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⣠⠒⠒⣲⠈⣦⠈⠁⠀⢀⡤⠤⠞⠀⠛⠚⠡⡎⠀⠀⠀⠀⡼⢉⡟⠀⠀⠀⠀⠀⢠⡞⠀⠀⡼⠁⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⢀⡇⢀⣃⣠⠞⣁⠼⡵⠒⣦⠤⣌⣗⣲⠃⡜⢩⠃⡞⣀⠀⠀⠀⢰⠁⡜⠀⡀⠀⠀⠀⢠⠟⠀⠀⢰⠃⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⠚⠉⠀⠙⢣⣠⠛⡏⡷⢠⠉⣰⡏⢰⢁⡏⣼⠟⢁⣧⠞⣩⡇⣸⡵⠋⣉⠓⢦⡴⢯⣤⠲⣤⡏⢀⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⢰⠋⠉⣠⠟⢠⡇⢠⣷⢡⡇⢸⡷⠀⣦⠞⠰⢣⠀⣾⠃⣰⡟⠀⡟⢀⣾⠃⢠⡿⠀⣾⠃⡰⢻⠁⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⢀⣇⡠⠞⢁⠴⠋⣇⢸⡵⠋⢧⣈⠷⢦⡽⣆⡴⠻⠤⢥⡀⢟⣤⣈⣇⠘⣡⣄⠚⣡⠘⡁⢠⣇⡼⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠧⣄⡥⠔⠊⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⠀⢀⣨⠽⠛⢹⢯⠈⢉⡇⢸⠻⣤⠾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢁⣀⡠⠴⠚⠉⠀⠀⠀⠘⢮⣙⣚⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⢋⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠋⣸⣿⠏⠀⢀⣴⣿⡿⣿⣧⠀⠀⠀⣶⣶⣤⣶⣷⣆⠀⠸⣶⣦⣾⣿⣿⣆⠀⣿⣿⠀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠛⠃⣰⣿⠏⢀⣤⣾⣿⠃⠀⣸⣿⠀⠀⠀⣿⣿⡿⠁⢹⣿⡄⣀⣿⣿⠏⠀⣿⣿⣠⣿⣿⣄⣼⡿⣿⣷⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣯⣴⣿⠏⠹⣿⣤⣴⣿⣿⢀⣶⢦⣿⣿⡇⢀⣾⣿⠿⢃⣿⣿⡀⣠⣿⠿⠋⠈⠙⠛⠛⠀⣿⣿⣶⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠉⠛⠛⢻⣿⣿⢿⣿⢿⣿⡷⠿⠋⠁⢠⣿⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡇⠀⠀⠀⣼⡏⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠃⠀⠀⠀⢿⣧⢈⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡿⠟⠀⠀⠀⠀⠈⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⣠⣾⣿⠟⢉⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣶⣿⣿⣁⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⢠⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⠛⠛⠉⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⢀⣾⣿⠋⣻⡷⠀⠀⢸⣿⡇⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀ ⣸⣿⣿⡿⠿⣿⣦⢴⣾⣟⠁⢀⣤⡄⠀⠀⣠⣤⣿⣟⠀⣼⣿⣇⣴⡿⠁⠀⠀⠘⣿⣧⣿⠇⠀⠀⣀⣠⡀⠀⢿⣆⠀⢻⣿⣷⡄⠀⠀⠀ ⣿⣿⠁⠀⠀⣼⣿⣿⣿⠉⠀⢹⣿⣧⣤⡄⠨⣿⣿⠿⢇⣿⣿⣋⣥⡀⠀⠀⠀⠀⣻⣿⡃⠀⠀⣾⡟⠛⣷⡀⠘⣿⣆⣸⡿⢿⣿⣄⣼⡟ ⠙⠻⣷⣶⣾⡿⣿⣿⢇⣴⣆⣼⠏⣹⣿⠀⢸⣿⡇⠀⠈⣿⣿⡿⢻⣿⠃⢀⣴⡿⠿⣿⣷⡀⣾⣿⣇⢀⣿⣧⣸⡟⠛⠛⠃⠈⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⡿⠃⢀⣿⡇⣠⣾⣿⠇⢀⣴⣿⣿⠃⣾⡏⢀⣼⣿⣄⠀⣸⡿⣿⠏⠈⠛⠛⠛⠻⠟⠁⠀⠀⠀⣴⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⣿⣿⡿⠹⣿⣷⡿⠋⠀⠀⠀⣿⣧⡿⠃⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢾⡟⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⠆⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⢠⡄⠀⠈⣏⡾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⢿⣁⢸⡷⢿⢀⡼⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⡋⢀⡴⠋⢈⠗⢤⣀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋⢀⠴⠁⢀⡼⠛⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠴⠋⢀⠴⠋⢀⠔⣉⣽⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣖⣩⡤⠶⣿⣯⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⢻⣿⣿⣿⣿⡛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣠⣶⣿⣿⣷⣦⡀⢠⠶⣴⠁⠈⡇⠀⢀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⢸⡅⠀⣠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⢸⠀⡿⠀⢠⡇⣴⠏⠉⡇ ⠀⢀⣠⣴⣒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠦⡄⠀⠀⠀⢸⣿⣿⠟⠻⠀⠟⠛⠲⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⠀⠃⢀⡾⠛⠁⢀⡼⠃ ⢠⣾⠛⡽⣿⡇⣽⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠙⣆⣀⣤⢤⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠙⢿⣿⣿⣿⣿⡿⣡⢧⢀⡄⠀⠀⠀⣠⠞⠀⠀ ⢸⣵⣄⠙⠚⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⡄⠹⡄⠙⢷⣄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣿⠟⠀⠀⢀⣉⣉⣽⣿⡛⠧⢽⡿⠃⠀⢠⠞⠁⠀⠀⠀ ⠈⠳⣄⣉⠛⠛⠒⠒⠶⡤⡤⣤⣤⡤⡤⡤⡤⡼⣷⡴⣷⣤⣸⣆⣠⣟⣻⣿⡿⣿⣟⣹⣂⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠠⠯⣄⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣍⠉⠀⠀⠹⡄⢁⣤⠤⠇⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠙⠒⠚⢷⠒⢤⡀⠈⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠄⠀⢠⡏⠀⢀⣠⣾⣿⣿⠏⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠦⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠉⠙⠻⢿⣦⡹⣍⣳⣴⣦⣄⡀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣯⣄⣀⣼⣿⣿⣿⣗⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣿⣿⡿⠿⠿⣿⣿⣿⣿⡿⠏⢹⡦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠉⠀⠀⠈⣻⡿⠟⢶⣿⣿⣯⠄⠀⠀⠉⠀⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⠀⣠⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣀⣀⣀⣀⡠⠤⠒⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢼⡿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⡟⠥⣛⠽⢢⣄⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⠿⣿⣷⠊⡡⢚⡽⠛⣉⣷⣮⣀⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⡴⢩⢖⡿⠟⠉⠀⢻⡍⠳⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠉⠙⢷⠋⠀⠀⢠⣦⠀⠹⢶⣼⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⢹⣿⡾⠉⠻⣿⢿⠈⡎⠙⢷⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡼⢠⠇⠀⠀⠉⣿⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢿⣶⣋⢠⠎⠀⠀⠀⠀⣼⠸⡧⠤⢤⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣟⠓⠖⠒⢲⡶⠦⠤⣀⠙⡣⣿⣆⣠⢶⣿⣿⣿⣀⣗⢒⣶⠶⣋⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠱⠦⣤⣝⠃⠹⣿⣿⣿⣿⣿⣏⣩⠥⠔⠒⠊⠈⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⠀⠀⠀⠀⠀⡴⠋⠉⠓⠒⠛⠛⠛⠛⢣⡀⠀⠀⣀⡀⠤⠊⣽⠃ ⠀⠀⠀⠀⠀⠀⠠⣯⡀⠀⠑⢤⣀⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣹⣿⣭⡤⠔⠒⠉⣽⣦ ⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⠤⣀⡈⠉⠳⢽⠓⢒⣶⠶⡶⣴⠒⠋⠀⠀⠀⠀⢀⣠⠴⠊⣡⠟ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⡇⢻⣿⣿⣿⣻⣏⣹⣥⡴⠶⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⢀⣀⡤⢄⣀⠀⠀⠀⢀⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠋⠉⠳⣼⡀⠀⠀⡖⠉⠀⠀⠀⠈⠙⠲⢤⣈⡜⢀⠴⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠁⣦⡀⠀⠀⠙⢦⣀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠉⢲⠇⡰⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠈⢻⢤⣀⠀⢀⣈⡹⠖⠛⠢⠤⢄⣀⠀⠀⠀⠸⢠⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⣀⣠⠏⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠸⠃⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣴⣶⣖⣶⣶⣶⠶⠾⠿⠿⠿⠿⢿⣿⣿⡿⠿⢿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢻⣷⡀⠀⠀⣴⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⢻⣷⠀⣼⡟⢀⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣙⣿⣾⣿⣴⣿⣱⡿⣫⣥⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣙⣻⣿⣿⣿⣿⣿⣿⣿⣟⣉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⢀⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢿⣦⡀⠀⠀⠀⣾⡏⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⢻⣷⠀⠀⠀⣿⡆⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⢸⣿⠀⠀⠀⠸⣿⣄⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢀⣾⡟⠀⠀⠀⠀⠈⠛⠿⣶⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣤⣴⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠉⠙⠻⣿⣆⡀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡿⢿⣦⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⣴⡿⠻⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⣶⡾⠟⠁⠀⠀⠀⠀⢸⣿⠁⠀⠹⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡟⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⣿⡄⠀⠀⠀ ⠀⠀⢀⣾⡿⣶⣶⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣄⠀⠀⠘⣿⣄⠀⠀ ⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠛⠛⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠶⠟⣿⡆⠀ ⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆ ⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⠸⣿⡀⠀⢀⣤⣤⣴⣦⣤⣀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⣸⡿ ⠀⠹⣷⣴⡟⠋⠁⠀⠈⠙⠻⣷⡄⠀⠀⠀⠙⢷⣦⣤⣀⣤⣴⡿⠋⠀⠀⠀⠀⢀⣾⠟⠋⠉⠉⠙⠻⣷⣄⢀⣼⡿⠁ ⠀⠀⠈⠻⣷⣦⣀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⢀⣨⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⠿⣶⣦⣤⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣀⣀⣤⣶⡾⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠷⠶⣶⣶⣦⣤⣤⣶⣶⡶⠶⠾⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡉⠛⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣀⠀⠀⣦⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠯⣀⡶⢿⡠⠛⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠔⢁⠜⠑⣦⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⠁⡠⠊⣠⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣊⠤⢾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠈⣿⣿⣿⣏⠉⠀⣀⣀⡀⠀⠀⡀⠠⠲⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡎⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣤⣾⣿⣿⣿⣧⢸⠉⡇⠀⡅⣠⠖⡆ ⠀⢀⣠⣤⢤⡀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⢸⣿⣷⠿⠀⠟⠦⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠠⠁⡰⠟⠁⣠⠃ ⢠⡿⠋⣿⣇⡇⠀⠀⠀⠀⠀⠀⠸⡄⠘⣤⢤⠠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠙⠿⣿⣿⣿⣫⢷⣠⡄⠀⢀⠔⠁⠀ ⠈⣟⠦⠍⠉⣀⣀⣀⣀⣀⣀⣀⣀⣘⣄⣸⡀⢣⡈⢳⠤⣀⣀⣰⢦⠀⠀⢀⣴⣯⣀⣤⣤⣤⣾⣿⣍⠚⠋⠀⣠⠃⠀⠀⠀ ⠀⠀⠙⠒⠒⠒⠒⠒⠒⠚⠒⠓⠒⠒⠻⡒⠋⠙⢿⠙⣉⣩⠍⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠧⠴⣦⠄⡈⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡄⠀⣴⣁⣀⣴⣿⣿⠋⠻⣿⣿⣿⡿⢋⡀⠀⠀⠀⠀⠀⢘⠆⠈⠲⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠈⢛⣷⣾⠮⢿⣷⣦⣄⣀⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣴⣶⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⢙⡿⠿⠾⣿⣯⡍⠀⠈⠀⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡜⠁⠀⠀⠀⠀⠀⠉⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠳⢄⣀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠐⠢⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠰⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠄⠄⠀⠄⠀⠀ ⠀⠀⠈⠂⢀⠃⠃⢀⠀⡰⡄⡀⣤⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠰⠠⠤⡊⡸⠜⡌⣹⢁⡆⡱⢸⢂⡇⡞⠠⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠆⠆⠉⣁⢻⠸⣵⡅⡜⠕⡇⠭⠊⠣⠆⠆⠀⠈⢲⠤⠐⠡⠀⠀⠀⠀⢀⠔⠀ ⠘⠀⠀⠀⠀⠤⠀⢀⢰⠀⢰⣸⡀⠘⣾⠐⠀⠀⢀⠎⠀⠀⠀⢱⠄⢀⠀⠀⠀⠀ ⠀⠀⠀⠆⡐⢀⠄⣀⡀⠀⣄⣚⠉⡌⡜⠀⠀⠀⡘⠀⠀⠀⠠⠁⢠⠁⠆⠀⠀⠀ ⠀⠀⠐⠠⠒⠁⢎⣵⡪⡙⣳⠂⠒⣼⢒⡦⢒⢖⠔⡒⢤⡰⡧⢄⠃⡜⠀⠀⠀⠀ ⠀⠀⠀⠊⠀⠈⠼⢠⡳⡁⣏⢰⠀⣅⢘⢡⣏⠈⠼⡁⡞⠰⠣⣹⡰⠀⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⢀⠝⠊⢁⠠⠚⢹⢎⣲⠘⠃⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠔⠒⠉⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢴⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⡪⡪⡵⠦⣠⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡫⡪⡲⠛⠉⢫⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢆⠘⠀⠀⢻⣦⠙⢿⡖⡖⢦⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢃⠀⠀⠀⠸⣄⡠⢂⠇⠀⠙⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⢞⠢⠀⣤⠠⢈⡯⣮⣠⣶⣾⣌⣁⠭⣳⠀ ⠀⠀⠀⠀⡸⡀⠀⠀⢉⠶⠦⠹⠿⠿⡟⠒⠈⢁⠸⡆ ⠀⠀⠀⠰⣅⡈⠢⢀⡈⡀⠀⠀⠀⣀⠮⠾⠭⠒⢈⢧ ⠀⠀⠀⢀⠃⠈⠐⠒⠛⠒⠊⢹⢻⣦⣤⣖⣖⡬⠔⠉ ⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠐⠴⠀⢠⠊⠉⠉⠒⠤⡨⢃⠔⢄⠀⠀⠀⠀⠀ ⡎⠸⢄⠀⠑⠢⡷⠄⣀⠀⠀⠈⢃⠃⢸⠀⠀⠀⠀⠀ ⠣⠠⠃⠈⠉⠁⠀⠀⠀⠈⠐⠠⣘⡠⠂⠀⠀⠀⠀⠀ ⣀⣤⣤⣤⣤⠤⠤⠤⣶⣤⠤⢤⠴⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⡁⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⢃⠜⠂⢄⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣀⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⣻⣿⣟⢋⣀⣀⠀⢀⠤⠀⠀ ⠀⢀⣀⠀⠀⠀⠀⢀⣀⠀⠠⣦⡤⠠⠀⢀⣿⣿⣿⣾⣿⣿⡇⠈⠠⠖⡹ ⠰⡏⡛⠒⠀⠀⠀⠈⢄⢣⢂⢧⡀⠀⣀⠀⠀⢹⠋⣙⣻⣿⡿⠆⠀⠀⠀ ⠀⠉⠀⠀⠐⠒⠒⠒⠚⢎⠉⠃⡩⠟⣹⣷⣾⣿⣿⡟⠛⠛⠃⠀⠈⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠷⠾⠟⠁⠉⠛⣯⠢⢤⣄⣀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠬⠿⣿⣻⣿⠖⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠊⠀⠀⠉⠁⢀⠔⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠐⠂⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠒⠒⢤⡀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣾⣾⠟⠛⠢⣄⠀⠀⠙⣦⣤⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⠋⠹⡟⠁⠋⠀⠀⠀⢈⣷⠶⠿⠭⣥⡤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⢸⡀⠀⠀⣀⠴⠚⠉⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⠀⠀⠀⣧⡴⠊⠁⠀⠀⠀⣼⣅⠀⣰⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣄⣠⡾⣋⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⣾⣿⣿⡷⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⢹⢷⣿⣶⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣾⣿⣿⣿⣿⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣡⠴⠊⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠀⠙⠲⠤⠤⠤⠤⢤⣶⣿⠋⠉⠁⠀⢻⡗⠀⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⡏⠙⠓⢦⡀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⢿⡇⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠻⠋⠀⠀⠀⠀⢻⣤⣴⣟⠉⠀⠀⠀⠀⡴⣶⣾⠿⠤⠷⠿⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠘⣆⠀⠀⢀⠶⣧⣼⠻⢿⣤⠀⣠⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠐⠢⠾⠿⠛⠛⠂⠛⣩⡗⢾⣿⠳⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⣀⡀⣥⣷⣀⣁⣀⣈⣣⡼⠀⠰⣤⣄⣢⡴⠋⣙⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠓⠒⠉⠉⠙⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣹⣿⢾⣗⣀⣍⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢻⢿⡧⠀⠙⠿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣆⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⠀⠀⠀⣤⠀⠠⡈⠙⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣋⣉⠽⠛⠉⠳⣤⠀⢠⡀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⡽⠖⠤⠦⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⣧⣀⣸⣦⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⡤⠒⠋⠉⠀⠀⠀⠀⠀⡀⢩⡙⢦⡠⡌⢳⡀⠀⠀⠀⠀⠀⠀⠻⣀⣿⣧⣤⠴⢤⣤⠀⠀⠀⠀⠀⠀ ⠀⠒⠾⠟⠛⠿⠿⠛⠛⠛⠳⠤⠤⠤⠤⢤⡤⢤⠤⡷⠤⠷⠖⠳⠟⠚⠡⠤⢶⡾⣿⡿⠿⠿⣿⡿⠶⠾⠽⣿⣿⣷⣦⡤⣤⡀⠀ ⠀⠀⠀⠀⠀⣠⣶⣾⣍⣥⣶⣶⣶⣤⣤⠖⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠶⠿⠿⠿⠶⠶⠶⠶⠶⠶⠿⠿⠷⠂ ⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⡴⡞⠃⢄⠈⣢⡤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⠁⠘⠀⠀⡠⠔⠋⡁⠒⠊⠉⠑⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⠀⣸⠔⠁⠀⠀⡦⠠⡇⠀⣀⣀⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢺⢿⣦⣄⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣧⠰⠀⠀⠀⠀⠀⠀⡐⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣈⡒⠤⠄⢠⣶⠊⠉⢐⡆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⠿⠏⠀⠈⢆⣠⠝⠃⠀⢠⣬⣇⠨⠧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡹⢁⣱⣀⣴⢲⢮⣳⣦⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣀⣀⡽⢈⣁⡹⠽⠠⠤⣠⠔⡢⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⠔⠒⢾⣿⠳⣦⠇⠀⠀ ⠀⠀⠀⠀⠀⡀⢠⣧⡀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠈⠢⢄⡀⡠⢀⠎⠂⠀⠀ ⠀⠀⠀⠀⠉⠀⠁⠀⣸⠀⢣⣈⣄⠀⣀⠀⠀⠀⠀⠀⡠⣻⠁⠉⠀⠀⠀⠀ ⠀⣠⣤⣤⣶⡤⣎⡉⠀⠀⠀⢠⡐⣝⣴⡱⢀⣠⣤⣤⣵⣿⣒⣤⣶⣀⠀⠀ ⠀⠀⠀⢠⡶⢬⡴⡶⢤⠨⠦⠤⠀⠀⠀⠀⠀⠈⠁⠒⠚⠓⠒⠚⠛⠛⠚⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡈⢻⡆⠀⣼⠏⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣉⣻⣾⣿⣼⣏⣾⣟⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⣿⣿⣿⣿⣿⣿⣯⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⠀⠀⢠⡟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠘⣿⠀⠀⢸⣇⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣿⠀⠀⠀⠻⣦⣀⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣁⣀⣤⡾⠋⠀⠀⠀⠀⠈⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠉⠉⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠈⠙⢷⡄⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⢻⡇⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⢀⣼⠏⠀⠀⠀⣴⡟⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠻⠶⠾⠛⠁⠀⠀⠀⢰⡟⠀⠈⢿⣄⠀⠀⠀ ⠀⠀⣴⣯⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠈⢻⣆⠀⠀ ⠀⣼⠏⠈⠉⠁⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⠾⢿⣆⠀ ⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆ ⣿⡀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⡿ ⠘⢷⣴⠟⠋⠉⠙⠻⣦⡀⠀⠈⠻⣦⣄⣀⣠⣴⠟⠀⠀⠀⢠⡶⠟⠋⠙⠻⣶⡄⣠⡾⠁ ⠀⠈⠛⢷⣦⣀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣿⠁⠀⠀⢀⣀⣼⠿⠋⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠷⢾⣷⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣿⣴⠶⠾⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀