Cum Dot Art

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⣯⣻⣻⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⡿⣻⣻⣻⣻⣻⣻⡽⣯⣟⢷⠍⠟⠉⠛⢿⢿⣻⣻⢿⣿⣿⣯⣻⡽⣯⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣻⣻⡟⡅⠀⠀⠀⠠⠀⠀⠆⡹⣻⣻⡽⣯⣻⡽⣯⣻⡽⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟⡛⡜⡜⣎⢦⢶⣖⡴⡀⠠⣿⣿⣿⣟⣟⣟⣟⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣻⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⢆⢭⢎⢎⢞⡝⣝⡽⡽⡣⢂⣟⢯⢯⢯⣿⣻⣻⡽⣻⡽⣻⣻⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢧⡒⡔⢆⢯⢎⠚⡜⡇⣼⣿⣿⣯⣻⣻⣻⣻⢯⣿⣿⣻⣻⣻⣻⢿⣿⣿⣿⣿⡿⣻⣻⣻⣟⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⢧⢣⢣⠡⡋⡯⣫⢯⡹⣹⣿⣿⣿⣿⣯⣻⣻⣻⣿⣿⣻⣻⣻⣿⣟⣟⢿⣿⣿⣿⣿⣻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢣⢢⢌⣍⡹⡽⣹⣽⣿⣿⣿⣿⣿⡽⣯⣻⢯⣻⢯⣻⣻⣿⣿⣿⣿⣻⣻⣻⣻⢿⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⣍⢎⢎⢝⢏⢏⣝⢿⣿⣿⣿⣿⣿⣿⣻⡽⣯⣻⣻⣿⣿⣟⢿⣿⢿⣻⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣟⣟⡜⡜⡜⡝⡭⣫⢫⠂⢫⣿⣿⣿⣟⢯⣻⣻⣻⡽⣻⣿⣿⣿⣟⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⡽⡻⡿⣇⢣⢣⠱⡱⡱⣽⣿⠀⠀⠀⠀⠐⢉⠍⡛⢿⢯⣻⣻⣿⣿⡿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⡿⣿⣿⣟⢿⣻⣻⡿⣏⢋⠀⠀⠀⣹⣻⡇⢣⠱⣥⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣻⣿⣿⣿⣟⣟⣟⡽⣻⣿⡿⡿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣻⣿⢿⣿⣿⢿⣻⣻⣻⡃⠀⠀⠀⠀⠀⠀⠠⠠⡣⢢⠱⡉⠙⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡽⣻⣿⢯⣻⣿⣿⢯⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢿⣻⣻⣿⣟⣟⣟⣿⣿⣿⣿⣿⡿⣟⣟⠄⠀⠀⠀⠀⠀⠀⠀⢀⢆⡑⠡⠉⠋⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⢯⣻⡽⣻⣻⡿⣯⢿⣿⣿⣿⣿⣿ ⣿⣻⣟⣟⣿⣿⣿⣿⣟⣟⣟⣟⣿⣿⣿⣿⣟⣟⡽⡄⠀⠀⠀⠀⠀⠀⠀⢀⠁⣯⠚⠹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⢯⢯⣻⣿⣿⣻⣻⣻⣿⣿⣿⣿⣿ ⣿⣟⢿⣿⣿⣿⣿⣿⣻⣿⡿⣻⣻⣿⣿⣿⢿⣻⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣟⠖⡖⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣻⣿⣻⣿⣿⣿⣿⣿⣻⢯⣻⣻⣻ ⣿⣻⣻⣿⣿⣿⣿⣻⣽⣿⣿⣟⣟⢿⣿⣿⡿⣻⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢢⣠⣀⠀⠀⠀⠀⠩⡛⡝⡜⡖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣻⣻⣻⣿⣿⡿⣻⣿⣿⣻⣻⣿⣿⡿⣿⣻⣻⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⠈⠁⠀⠀⠀⠀⠀⠌⣌⢎⡜⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⡿⣟⢿⣿⣿⣿ ⣟⣿⣿⣿⡽⡽⡽⣻⣹⡽⣿⣿⣿⣻⣻⣻⣻⡽⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠣⠒⠀⠀⠀⠀⠀⠀⠎⢎⢎⢎⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡽⣿⣿⣻⣻⣻⢿⣿⣿ ⣿⣿⢿⣿⣯⣫⣏⢯⣫⣿⣿⣿⣿⣟⣟⣟⣟⡽⡽⠀⡀⠀⠀⠀⠀⢀⢀⠀⠰⡰⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⡽⡽⣿⣿⣿⣻⡝⡽ ⣯⣯⣯⣯⢯⣫⢫⣻⡿⣻⣿⣿⣿⣿⣿⣻⡽⡽⣭⠂⠀⡰⡱⠡⠢⢂⠆⠀⢠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⢫⣫⡿⣻⣿⣿⣿⣻⡹ ⡿⡿⣻⣻⣻⢭⣚⢧⢫⣻⣿⣿⡿⡽⡽⡽⡽⣹⣝⢇⠄⠀⠀⠄⠄⠄⡐⠀⠄⡐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⣝⡽⣹⢽⢯⡻⣻⣟⢯⢫⣚⣟⣟⣟⣟⣟⣟⡝ ⣯⣻⡽⣯⣻⡜⡵⡽⣎⢭⣻⡝⡽⣽⡽⣝⣝⣝⡝⣗⢭⢎⠀⠀⠂⠂⠀⠀⠀⡐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣝⣝⡝⣝⡽⡽⡹⣚⠵⡭⢯⢯⢯⣻⡽⡽⣣ ⣟⣟⡽⣯⢯⢎⢎⢯⣏⡗⡝⣝⡽⣻⢯⣫⢫⢫⣫⣻⢯⡳⡱⡱⡱⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡝⡝⡝⣝⡝⡝⡭⣫⢫⢭⣚⣝⣝⣝⡽⣹⣹⢧ ⢏⠯⢫⢫⢫⢪⢎⢯⢏⠳⡹⡹⣻⡿⡯⣫⢫⡹⡹⡽⡽⡹⡸⡜⡄⠀⠀⢀⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⡭⣫⡹⡹⡭⣫⢫⢫⣚⡜⡝⡝⣝⣝⢽⡹⡭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠶⢿⣛⣛⡻⢿⣿⣿⣷⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣯⣙⣦⡽⣯⢷⣻⣼⢯⡷⣞⡶⣭⢏⣛⠿⡾⣟⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢥⣻⢶⣻⡾⣽⣻⣯⣟⣾⢿⣽⣻⣽⢯⡿⣯⢿⣜⣧⡛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢻⡼⣯⣟⣯⣷⣿⣿⣷⣿⣾⣯⣿⣞⣯⣟⣯⣿⡽⣯⢿⡾⣽⣳⣬⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⢿⣽⣳⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡷⣟⡿⣯⢿⣽⣳⣯⢷⡹⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⣻⢾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣻⢯⣟⣷⢯⣟⡷⣫⢷⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣯⣿⣽⣟⣿⣻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣯⣟⣯⡿⣾⣻⣽⣻⣥⡛⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣿⣿⣿⣿⡟⡻⠿⡿⣿⣷⣿⣾⣽⣻⢿⣿⣿⣿⣽⣷⣿⣿⣿⣷⣿⣷⣿⣾⣵⣿⣿⠷⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢼⡱⣋⠶⡱⢎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣮⣽⡿⠧⣔⣲⠌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡙⢿⣦⣄⡀⠉⠻⣿⣶⣬⠱⡈⢳⡄⠀⠀⣿⣿⣧⡙⢶⣡⢛⣿⣿⣷⣧⣿⣶⣿⣼⡿⡟⣏⠞⣬⢳⡙⢦⣋⠶⣩⣾⣿⣿⣾⣿⣿⣟⡷⣯⣟⡿⣾⣿⣽⢆⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠛⠿⣿⣿⣿⣿⣧⡙⣎⢿⣏⠿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣈⣿⣿⣿⣿⣷⡀⠈⠻⣿⣧⠹⡌⣇⠀⠀⢸⡝⣷⡹⢆⢧⣋⠿⣷⣎⡭⡹⣍⢧⢣⢳⡹⣌⠻⣔⡣⣝⢣⢎⡳⣷⢿⡏⠛⠿⣿⣾⣽⣻⣽⣾⣻⢷⣻⣿⣿⣲⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⣀⢶⡸⣌⡛⢿⣛⣿⡷⢬⣿⢏⡞⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⣽⣾⣿⣿⣿⣿⣿⣦⠀⠹⣿⠡⡏⣿⠀⠀⠀⢻⣽⣿⣭⠲⡍⠞⠹⢻⠲⡕⡎⠎⢧⢣⢳⢬⠓⢮⠱⡍⠞⣼⡿⢫⡾⠃⠀⠀⠙⠉⡟⡿⠷⣯⣿⣿⣽⣾⡿⣿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣴⣭⣿⣿⣷⣿⣾⣿⣟⣜⣷⡟⢮⢼⡿⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⣶⣿⣿⣉⠉⠙⢿⣿⣿⣿⣿⣿⣆⠀⢻⣧⡿⣯⠀⠀⠀⣾⣿⣿⣿⣢⠝⣎⠳⣆⢶⡱⡹⡜⣜⠺⡜⣬⠳⣎⢧⣹⣾⠟⣷⠞⠁⠀⠀⠀⠀⠈⠑⠳⠶⠿⠛⠋⠉⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡱⣎⣾⡗⣺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣋⣀⡉⢙⣷⣤⣿⢿⣆⠀⢻⣿⣿⣿⣿⣿⡀⣸⣿⣿⡿⠀⠀⢸⣿⣿⡿⣿⣿⣾⣌⠻⡜⣎⠵⣣⠝⣬⢫⡕⣎⣳⣼⣾⣿⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣶⣶⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢳⣼⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣀⣡⢩⢟⣿⡮⢼⣿⣿⢯⣿⣧⣾⣿⣿⣿⣼⣿⣿⣿⢟⡏⠀⠀⠀⢈⣿⣿⣿⣳⣿⣿⣿⣿⣾⣬⣷⣥⣿⣴⣷⣾⣿⡿⣿⣻⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⢾⢭⠾⣟⡻⡽⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣤⣤⣩⢟⣿⣾⣹⣿⣧⣿⡿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠻⣽⣿⣿⣿⠿⠿⢿⣿⣿⣿⣳⣯⢿⣟⣿⣿⣿⡿⣿⢿⣻⣟⣯⡷⣟⣯⣷⣿⠋⠀⠀⠀⢀⣀⣀⣀⣠⡤⣤⠶⠾⣿⣟⣷⡶⢾⢟⡻⣩⢕⣦⣻⡼⣞⡿⣽⣻⣽⢷⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⢀⣟⡻⣿⣖⣻⣷⣿⡿⣙⠶⣽⣿⠏⠀⠀⠀⠀⢀⣴⣾⡿⠛⠁⠀⠀⠀⠀⢹⣿⣳⣯⣟⡿⣞⡿⣞⡷⣿⣽⣻⣽⢾⣯⣟⡿⣽⣿⣷⠿⠛⠛⠉⠉⠉⠁⠉⠀⠀⠀⠀⢠⣿⣻⢧⡽⣞⣮⢷⣯⣟⣾⣳⣟⣯⣿⡽⣷⢯⣿⢾⣻⢿⣿⣿⣿⡿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡷⠚⡿⣿⣧⡹⣿⣿⣿⣏⢶⣽⣿⣿⠏⠀⠀⠀⣀⣴⣾⠟⠉⠀⠀⢠⣿⠀⠀⠀⠀⠻⣿⣷⣯⢿⣻⣽⢿⣽⡷⣯⣟⣾⣟⣾⣽⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢯⡿⣽⣯⣟⡿⣾⣽⢾⣻⣾⡽⣞⣿⡽⣿⢾⣿⣿⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣨⣗⣤⢻⣼⣻⣿⣷⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⣠⣾⠿⠋⠁⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣾⣟⣾⣽⣷⣻⣷⣻⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣯⢿⣳⣟⡾⣟⣷⢯⣿⣳⣯⣟⣿⣳⣿⣿⣿⣫⣥⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣈⣀⣠⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⢿⣽⡾⣟⡿⣾⣻⢷⣯⣷⠿⢛⣯⠗⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⣿⣿⣯⢿⣽⣳⣯⡿⣿⣏⠉⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡽⣟⣾⣽⣿⣽⡷⠿⣛⡭⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣻⣾⣽⣳⡿⣽⣿⣦⡾⣟⣿⣦⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⣻⡭⠛⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣞⡷⣟⣾⣽⣻⢷⣯⣿⣿⣽⢯⣿⣷⡀⠀⠂⠀⢸⡟⠀⠠⣶⣶⣤⣤⣤⣀⣤⣶⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣶⡶⣶⣟⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢯⣟⣿⣳⣯⣟⡿⣾⣽⣿⣯⣿⡽⣿⣷⠀⠀⠀⣿⠇⠀⠀⣿⡉⢿⣿⣿⣿⣿⣻⣽⣿⣷⣿⣿⣿⣿⣦⣤⣄⣀⡀⠀⠀⠀⠰⠿⢻⣿⣿⣭⠽⠟⠈⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⣽⣳⣯⣷⣻⣽⢷⣯⣿⣿⣷⣻⣽⣿⡆⢀⣼⣿⠀⠀⠀⢸⣧⠘⣡⠀⠉⢙⡟⠻⠷⠿⢿⣿⣷⣽⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣿⣿⡽⣯⣷⢯⣟⣾⣟⣾⡽⣿⣷⣻⣷⣿⣷⢿⣿⡏⠀⠀⠀⠀⣻⣿⣿⣶⣶⡾⠀⣦⠄⠀⣀⠀⠟⠃⠀⠻⠠⣿⣷⡄⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⣿⣟⣷⢯⣿⣻⢾⣽⣾⣻⣽⣷⠿⣿⠞⠃⠘⢻⡇⠀⠀⢠⣾⣿⣿⣿⣿⣧⣤⣤⣬⣼⣛⠉⠁⠈⣿⣿⣶⣦⣤⣾⠇⠀⠀⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡈⠛⠷⢦⣤⣄⣀⣤⡴⠞⢋⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⢶⣦⣤⣤⣄⣤⣤⣤⣶⠿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

yes i caught you..⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⣮⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠙⢿⣿⣿⣿⣿⣿⣶⢻⡃⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡟⢥⡷⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣇⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠠⢀⣀⣤⣭⣿⣿⣿⣿⣿⡇⠄⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣶⣶⣶⡄⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢠⣴⣿⣿⢿⡷⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⣇⠀⠀⠄⣿⣿⣿⣿⡇⣾⣿⣿⣿⡷⠃⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀ ⣆⠀⡏⠉⠀⠀⣿⣿⣿⣿⡇⠈⠉⠉⠋⠁⠀⠘⣿⡏⢁⠃⠿⠛⢿⣿⣿⣿⣿⣿⡀⢸⠀ ⣿⢠⠇⠀⠀⠀⣿⣿⣿⣿⡇⠄⠀⠀⠀⢀⣠⣾⣿⣷⣌⠣⠀⠀⣸⣿⣿⣿⣿⣿⢧⢸⡆ ⣿⠈⠀⠀⠀⠀⢻⣿⣿⡿⢀⠀⠀⡀⣰⡿⠿⣿⣿⣿⣿⡄⢀⣶⣿⣿⣿⣿⣿⣿⢸⢸⢣ ⡇⠀⠀⠀⠀⠠⣿⣿⣿⡇⠸⠔⢤⢧⡿⢆⡀⠀⠈⠻⣿⡄⣸⣿⣿⣿⣿⣿⣿⣿⡜⢸⠸ ⠇⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠈⣼⡏⣴⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀ ⡦⠂⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⣿⣼⣿⣥⣬⣬⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣗⢸⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⢀⠀⠀⣽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢹⢸⡄ ⠀⠀⠀⠀⠀⢀⡘⣿⣿⣿⣇⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⣸⢸⡇ ⠀⠀⠀⠀⠀⠀⠂⠸⣿⣿⣿⡀⠀⢸⠘⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⡧⣄⡧⢸⣧ ⠀⠀⠀⠀⠀⠀⠠⡀⠸⣿⣿⣇⠀⠈⠀⣿⣤⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠧⠃⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠘⢆⢻⣿⣿⣧⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠐⠒⠒⠂⠈⢻⣿⡟⣿⠄⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠈⠉⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⣆⣴⠒⢀⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⢀⣀⡤⢄⡀⠀⠈⢹⠀⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⢈⣨⣟⣶⢉⣷⢼⡿⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⡁⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠸⠭⢟⣡⣾⡣⠞⡀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣘⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣀⠀⠀⢀⣠⡜⠀⠀⠀⢀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣿ ⠀⣤⣿⠟⠀⣰⠟⠃⠄⠀⠀⠀⢸⣩⣄⠀⢌⠉⠉⠉⠉⠉⠁⢀⣤⣾⣿⣿⠏⢻⣿⣿⣿ ⣾⡿⣧⣤⡴⠋⠀⠀⠈⠀⠀⢀⣼⣿⠟⠻⠷⠶⠒⠦⠤⢶⠤⠏⢩⣿⣿⣿⠀⠰⣿⢹⣿ ⡇⢐⣾⣿⣶⣇⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣿⣿⣿⣿⣧⡀⣿⢸⣿ ⣷⣾⣿⣿⣿⣿⡅⠀⠀⠀⠀⣸⣿⣷⣄⠀⠀⠀⠀⢀⣴⣮⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⣴⣿⣿⣿⣿⣷⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⣴⣴⡤ ⠀⣠⠀⢿⠇⡇⠀⠀⠀⠀⠀⠀⠀⢰⢷⡗ ⠀⢶⢽⠿⣗⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠂⠀⠀⣼⣷⡆ ⠀⠀⣾⢶⠐⣱⠀⠀⠀⠀⠀⣤⣜⣻⣧⣲⣦⠤⣧⣿⠶ ⠀⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣷⣤⣄⡹⣿⣷ ⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿ ⠀⠿⠃⠈⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿ ⠀⢀⢀⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⡀⡀ ⠀⣿⡟⡇⠀⠭⡋⠅⠀⠀⠀⠀⠀⢰⣟⢿ ⠀⣹⡌⠀⠀⣨⣾⣷⣄⠀⠀⠀⠀⢈⠔⠌ ⠰⣷⣿⡀⢐⢿⣿⣿⢻⠀⠀⠀⢠⣿⡿⡤⣴⠄⢀⣀⡀ ⠘⣿⣿⠂⠈⢸⣿⣿⣸⠀⠀⠀⢘⣿⣿⣀⡠⣠⣺⣿⣷ ⠀⣿⣿⡆⠀⢸⣿⣿⣾⡇⠀⣿⣿⣿⣿⣿⣗⣻⡻⠿⠁ ⠀⣿⣿⡇⠀⢸⣿⣿⡇⠀⠀⠉⠉⠉⠉⠉⠉⠁

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⠀⠀⠀⣴⣾⣿⣿⣶⡄ me⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣉⣩⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⠉⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣧⠀you⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡄⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣩⣝⢿⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡝⣿⣦⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⢻⣿⠟⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠻⠿⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣋⣁⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄ ⠀⠀⠀⠀⢠⣣⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⢧ ⠀⢀⢾⠟⣯⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⣁⣀⠘⢷⣦⣄⡀⢀⢀⠀⣀⣀⣹ ⠀⢸⢸⠀⠈⠃⠀⠀⠀⠀⠀⠀⣰⣾⡻⣭⣭⣽⣿⣾⡽⣿⡟⣼⣾⣿⣿⡟ ⠀⠈⠹⣿⡏⠄⠀⠀⠀⠀⠀⠀⠁⠙⢜⠿⣿⣿⣿⣿⡧⠈⣸⣿⣿⣿⣿⡇ ⠀⠀⣇⠘⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠿⠛⠋⠀⠀⢻⣿⣿⣿⡿⠀ ⠀⠀⠘⠤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠂⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡄⠀⠰⠄⠀⠀⠻⣿⣿⠇⠀ ⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣇⣤⡤⢄⠀⣴⣶⣿⠟⠀⠀ ⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⡀⠀⠈⢹⣷⣿⣾⣿⣿⠏⠀⠀⠀ ⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣶⣦⣤⣤⣬⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣍⣛⣿⣿⣿⣿⡟⠠⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢙⣿⣿⣿⣿⣷⣤⡀⠉⡢⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢆⡱⢫⡟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣻⢿⣟⡿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢂⡘⢦⡳⣏⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣳⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⣌⢣⡑⢦⣙⢮⣳⢻⡾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⢷⣿⢯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡳⢈⡒⡌⡖⣭⢺⡭⣞⡥⣏⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⡾⣏⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⢑⡣⢜⡜⡱⣌⢧⡽⣲⣽⢻⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣻⡽⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠐⢈⠐⡡⠊⢎⡳⣟⠾⣝⡾⣛⣾⢳⢯⡻⡝⣯⢟⡿⣻⢿⣟⡿⣟⣿⢻⠿⡿⣿⢿⡿⣿⣿⢿⣾⣿⣿⣷⡿⣽⣳⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣸⢮⣷⡱⣭⣞⡵⣏⢿⡱⣏⠷⣎⣟⢮⢳⡙⡴⢋⡴⢩⠞⡼⡙⢮⠘⣉⠣⡙⠤⢋⡹⢱⠫⣟⢿⣽⣿⣟⣿⣯⣟⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢭⣻⣽⣿⡷⣯⢻⣜⣣⢟⣼⡻⣝⣮⣛⢦⡙⡖⢣⠜⣡⠚⡔⣩⠂⢇⢢⠱⡱⢌⡒⠤⡃⠵⣈⠞⣽⣾⣿⣿⣽⣯⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣈⣶⣽⣾⡿⣽⢏⡷⣎⢷⣫⠾⣽⣹⢶⡹⣎⡵⣍⢳⢪⢅⡫⠴⣡⢋⡜⢢⢣⡑⢎⡸⢐⡉⢖⡡⢚⡜⣯⣿⣿⣯⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡸⣟⣿⡿⣽⣻⢎⣷⡹⣎⣷⣛⣧⢯⣗⡻⣜⡞⣬⢇⡳⢊⡕⢣⢆⢣⠜⣡⠆⡍⢦⠡⠣⠜⢢⡑⢣⢜⣱⢯⣿⢿⡽⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⢷⣻⣯⢿⣯⢷⣛⠶⣝⣳⢾⣹⢮⢷⡺⣝⢧⡻⣔⢫⡔⢫⠜⡡⢎⢎⡜⢢⡙⡜⠤⢋⡅⣋⠦⡙⢆⢮⡹⣟⣾⣿⡻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢬⢏⣷⡿⣟⣮⢳⣭⢻⣭⣟⣯⣿⣯⣿⣷⣯⣿⣳⣮⣳⣜⢣⢎⡱⢎⡖⣸⢡⠚⣄⠫⠔⡘⡔⢢⠍⢎⢲⡹⣽⢾⡷⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢆⢫⣞⢿⡝⣮⢳⢮⣟⣼⢻⣞⡷⢯⡳⣏⢿⡻⣟⡿⣷⢯⣟⣎⠖⣭⢞⡵⣎⡵⣂⠧⣙⠰⣉⠦⡙⡌⢶⣹⢯⣟⣿⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⢬⢷⡞⣯⡝⣮⢏⣷⣚⣮⢷⣻⣾⣿⣷⣿⣞⣷⣯⣟⣿⣻⡾⣝⠎⡜⢯⡾⣿⣽⢿⣻⣮⢷⡜⣦⣑⢚⢦⣻⣯⡿⣞⠥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⣓⡆⢀⠦⣄⠀⡀⢰⡠⡑⣨⠉⡝⢩⠛⣛⠻⡛⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣳⣟⣮⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠠⢈⠀⢂⠰⣿⣷⣿⣷⣿⣿⣷⣿⣶⣷⣽⣮⣵⣜⣶⡴⣮⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⡽⣾⡹⢾⣿⣿⣿⣿⣿⣿⡿⢣⣛⠜⡠⢉⠿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣌⠆⡐⢀⡈⠄⠂⠭⡙⢋⠟⡛⢟⠻⢟⠿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⡽⣧⢻⡹⣿⣿⣿⡿⣟⠣⣍⠣⢜⢢⡑⢦⣜⡽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣠⢀⢀⡈⢤⣷⣯⣿⣮⣷⣮⣷⣬⣮⣤⣳⣌⣦⣱⣊⡵⣩⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢾⣻⣽⢣⡳⡹⢿⡿⣵⢊⡱⢠⡍⢦⣣⣟⡿⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣙⠦⣹⣯⣀⡘⡿⢻⠿⡻⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⡽⣾⢯⣗⣯⢯⡝⣆⠳⣜⢧⡟⣷⣻⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡗⣯⣜⣿⣴⣧⣮⣵⣎⡶⣤⣃⣆⢦⡱⣨⢱⡩⢍⣋⢟⡹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣿⣽⣻⢾⣝⡾⣽⢎⡷⣈⠎⡝⣎⢟⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡙⣿⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣞⡷⢯⣟⡾⣽⣳⡟⡶⣥⢚⡘⣤⢋⠾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣧⣙⡯⢜⣳⣌⡖⣌⢦⣡⢋⡜⡩⢍⢫⡙⣋⠟⡛⢟⡻⢟⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⣯⣟⣳⢎⡳⢧⣏⠿⣽⢖⡯⣞⡶⣍⢏⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣼⣷⣽⣶⣳⣮⣷⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣽⣻⢮⡱⢫⡜⣹⢎⡽⢺⡵⢻⡜⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⡛⣷⢸⡏⣍⢫⠝⣋⠟⡹⢛⠻⡛⢿⠻⠿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣿⡽⣧⣻⡕⣮⡱⢎⡔⢣⢚⡕⢺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡷⢺⣿⣾⣿⣿⣾⣽⣷⣯⣷⣽⣦⣽⣜⣦⣳⣌⡶⣰⣎⡼⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣽⢯⡷⡙⢦⢻⡜⣬⡓⣎⡜⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡼⣯⢹⡟⢿⠻⡟⠿⡿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢫⣟⡯⣟⢾⡹⣏⠳⣉⠢⡙⡟⣶⡹⢆⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣧⢻⣽⣶⣷⣮⣷⣼⣎⣦⣵⣢⢦⡱⣌⣣⢍⡹⣩⠛⣝⣫⢟⡿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣫⢞⡵⣋⠶⡱⣍⠳⢄⠢⢱⡙⢦⡙⢮⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀ ⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡼⣝⢮⡱⢎⡵⣊⡕⣣⢎⡳⣌⢇⠾⣱⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢺⣧⢿⣳⣜⣦⣕⢮⣡⢏⣭⢫⡝⣋⠟⡛⡟⡻⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⢚⡶⣽⣺⢵⣫⢶⡝⣮⢻⡵⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⠀⠀⠀⠀ ⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣴⣫⣼⣍⣟⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣷⡿⣯⢷⣏⢿⣼⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣗⣿⣭⣋⣟⣹⢋⡟⡹⢛⡛⣟⠻⡟⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣾⣽⣿⣿⣿⣿⣿⣾⣿⣷⣿⣼⣷⣿⣮⣷⣵⣦⣧⣝⣮⣝⣯⣻⣽⣻⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡷⣯⢟⡛⣟⠻⣟⠿⡿⢿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀ ⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⣻⣿⣿⣾⣿⣾⣿⣽⣾⣶⣳⣭⣾⣴⣣⡽⣌⣯⣹⣙⣏⡻⣝⢯⣛⣿⣻⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣳⣿⢿⢻⠟⡿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡷⣿⣧⣿⣾⣵⣯⣾⣼⣳⣮⣷⣭⢯⣹⣍⣻⣙⡟⣛⡟⣛⢻⡛⡟⢿⡻⣟⠿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣞⣿⣦⣳⣴⣦⣵⣬⣖⣭⣞⣭⣏⡿⣹⣛⣟⣻⠻⣟⢻⠟⡿⣻⠿⣟⡿⣟⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⠃⠈⢻⣿⣦⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠘⣿⣿⣿⡏⣴⣿⣷⣝⢿⣷⢀⠀⢀⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⢿⣿⣿⡇⢻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣇⢸⣿⣿⡟⠙⠛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⡇⠀⠀⠀⠉⠛⣽⣿⣇⣀⣀⣀⠀ ⠙⠻⠿⠿⠿⠿⠿⠟⠿⠿⠿⠇⠀⠀⠀⠀⠀⠻⠿⠿⠛⠛⠛⠃

⢴⣤⣶⣾⣟⣇⠀⠐⠒⠂⠿⠛⢻⠳⡖⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠳⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠛⠓⠲⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠴⠂⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠁⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⠀⠀⠀⠈⠓⢦⠀⠘⢻⠀⠀⢠⡇⠀⠆⠀⠤⣤⡀⠤⢤⠤⠖⠚⠉⠀⠀⠈⢳⡀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣤⡤⣶⣷⣄⣸⣦⠀⢸⠀⣀⡤⣾⣿⣶⣾⣧⠄⠀⠀⢀⣀⡤⢾⡁⠀⠉⣻⠗⠋⠁⠀⠀⠀⠀⠀⠀ ⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣸⣏⠁⠈⠛⢻⣯⣿⣾⠟⢁⠀⣿⣿⡏⠟⠛⠋⠉⠁⠀⠀⢈⣻⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣄⣙⣻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠹⣟⣚⣻⢦⣄⠀⠀⠉⠛⠂⠀⠑⠙⠋⠀⠀⠀⠀⠐⠦⠖⣻⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠻⠿⠿⠿⠿⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠁⠀⠀⠀⠀⣿⠿⠷⠶⢿⣰⠂⢀⡶⣄⠐⠂⠀⢻⣆⢀⣴⣒⣶⣶⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⢶⣶⣤⣤⣴⣶⣶⠙⠉⠻⠿⢶⣶⡶⠖⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠉⢡⡟⠀⣽⠖⠒⠀⠉⠉⠛⢦⡴⠛⠁⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣦⣬⣭⣽⡛⠛⠻⣿⣯⣧⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⡞⢀⡞⠁⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡀⠀⠀⠀⠀⢀⣠⣤⣾ ⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣀⣤⢤⣖⣒⣲⣷⣿⣒⠲⢤⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢩⡽⠛⣿⣿⣿⣿⣿⠙ ⡀⠀⠉⢿⣭⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀ ⣿⣶⣦⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣀⣀⠀⣀⣀⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉ ⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠁⠀⣠⠞⠋⠁⠀⠈⢹⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀ ⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⡼⠁⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⠀ ⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣸⠁⠀⠀⠀⠀⣰⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠃ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣯⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡻⣷⣦ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣾⡇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠜⢷⡙⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣿⣯⣀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⢷⠈ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠲⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀ ⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀ ⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀ ⠛⠉⠀⠀⣀⣤⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀ ⠀⣀⡴⠞⠉⠀⠀⠈⣙⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄⣹⣿⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⢈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣺⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠟⠛⠋⠁⠀⠀⠀⠈⣉⣽⠿⠛⠉⣩⣿⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠤⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⣠⡴⠟⠋⠀⠀⠈⣋⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢛⡉⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠋⣀⣠⠶⠟⠋⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

ㅤㅤㅤ I just want to get fucked like this, pleasseeeㅤㅤㅤㅤㅤㅤㅤ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⠃⠈⢻⣿⣦⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠘⣿⣿⣿⡏⣴⣿⣷⣝⢿⣷⢀⠀⢀⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⢿⣿⣿⡇⢻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣇⢸⣿⣿⡟⠙⠛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⡇⠀⠀⠀⠉⠛⣽⣿⣇⣀⣀⣀⠀ ⠙⠻⠿⠿⠿⠿⠿⠟⠿⠿⠿⠇⠀⠀⠀⠀⠀⠻⠿⠿⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⡥⠀⠀⠀⠀⣠⠴⢀⣠⠤⢦⡀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⢸⠁⠀⠀⣠⢚⡥⠚⠉⠀⠀⠘⣗⡄⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⠇⡎⠀⠀⣰⡳⠋⠀⠀⣠⣤⠶⠢⡿⣸⣆⠀⠈⣧⣄⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⢳⣠⣾⡟⠓⠆⠀⠘⠙⢀⣤⣶⢿⣤⣹⡅⠀⣿⠈⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠸⡇⣾⡛⣶⡦⠀⠀⠀⠛⢱⢼⣷⠸⠋⢣⠀⡇⣹⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⠀⠹⣏⠉⢟⣻⣀⠀⠀⠀⠐⠛⠛⠐⠀⠘⣴⡽⣇⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢇⠀⠘⡄⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢹⡀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⠀⢻⢦⡀⠈⠰⠶⠒⠂⠀⠀⢀⡤⠀⡇⢘⡆⢇⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡼⡀⣟⡶⢄⡀⠀⢀⡠⠖⠁⠀⢀⡇⢸⢻⠸⡀⠀⣿⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⢳⠟⢀⠷⠈⣹⡇⠀⠀⠀⠀⣼⢣⡞⢸⠀⡇⢰⣼⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⣠⠋⢀⡼⠟⠊⠟⠀⠀⠀⠀⠀⣿⠀⠑⢯⣀⣇⣎⢏⡞⠀⠀⠀ ⠀⠀⠀⢀⡠⠾⠔⠓⢞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⡈⠛⠿⠯⣀⠀⠀⠀ ⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠉⠉⠉⠉⠉⣧⡀⠀⠀⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⢻⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⢸⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡼⠃ ⠀⠀⠘⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢠⠇⠀ ⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡎⠀⠀ ⢠⠇⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡄⠀⠀⡸⠀⠀⠀ ⢸⡀⠛⠄⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠵⠀⠀⡇⠀⢀⠇⠀⠀⠀ ⠀⢷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣰⠁⠀⣾⠀⠀⠀⠀ ⠀⠀⠑⢤⣀⠀⠀⢀⣠⠴⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⡴⠁⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⡽⠀⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣾⠀⠐⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⠀⠀⢠⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢰⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡜⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠉⠉⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⢃⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢸⡀⠀⢸⣦⢰⡈⡆⠈⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⢰⣿⣿⣄⢸⣿⣿⣟⣷⠀⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡸⣾⣿⣿⣿⣿⡿⠿⣿⡿⡏⢻⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠻⣿⠛⠿⠈⠀⠀⠈⠀⣇⠈⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⣹⣦⠘⣧⠀⠀⠀⠀⠀⢀⣿⣀⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣿⣿⣆⠘⡷⠢⢤⡴⠖⢉⡏⢹⢹⡗⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢹⡿⣦⡼⡔⠊⠀⢠⣾⠀⡧⠘⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⠟⢻⣾⠓⠛⡇⢳⠄⢠⠟⡇⢠⡁⢠⠃⢀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠛⢦⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠁⢴⢻⠈⣆⡀⣣⣸⡆⠀⠀⢹⣌⣷⡧⢼⣿⡀⠀⡇⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠘⡀⡆⢉⣿⣿⡏⠁⠀⠀⠀⠈⠙⠁⠀⠚⠛⡄⢸⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢹⡃⡾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣸⠷⢒⠟⠁⠀⠀⢰⠆⠀⠀⠀⠀⠀⡎⠀ ⠀⢀⡴⠒⠒⠲⠤⣀⣀⠀⠀⠀⠀⣇⠀⠀⠳⣇⠀⠀⠀⣀⠈⠀⠀⠀⠈⠉⠒⠚⢿⠏⢠⠔⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⠁⠀ ⢠⠋⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢄⣸⡀⠀⠀⠈⣖⢲⡚⠁⠀⠀⠒⠊⠁⠀⠀⠀⢸⡗⠁⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⢸⡄⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠈⠙⠒⢤⣀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀ ⠀⠱⣄⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⠀⢀⣤⡀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠼⡟⡅⠀⠙⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣸⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⣠⠃⠀⠀⠀⠀⠀⠀⠀⣸⠉⢦⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⠛⢠⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⢀⠆⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⢈⣧⣀⠀⠀⠀⢀⣴⣿⠀⠀⠀⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⠀⠀⠀⠀⠈⢳⣄⣀⣀⡠⠔⠋⠀⠀⠉⠉⠋⢉⡏⠙⣄⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠸⣧⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠹⣿⠉⣯⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⡟⢳⡿⠀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⢙⣿⣏⣩⠍⠿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⢿⠧⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⢀⣸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠥⠤⠐⠚⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠵⢶⠭⠽⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⢀⣀⡠⢔⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣘⣩⣅⣤⣤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⣻⣿⣿⢷⣾⣭⣯⣯⡳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠻⠿⡻⢿⠿⡾⣽⣿⣳⣧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡶⢈⠐⡀⠀⠀⠁⠀⠀⠀⠈⢿⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢅⢠⣥⣐⡀⠀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠡⠱⠒⠖⣙⠂⠈⠵⣖⡂⠄⢸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⠰⡈⢆⣑⠂⠀⠀⠀⠀⠀⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠀⠱⡈⢆⠙⠉⠃⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡡⢘⠩⠯⠒⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢔⡢⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠸⡁⠋⠃⠁⠀⢀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡰⠌⣒⠡⠄⠀⢀⠔⠁⣸⣿⣷⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣐⣤⡄⠀⠀⠘⢚⣒⢂⠇⣜⠒⠉⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣔⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⢀⢠⣤⣶⣿⣿⣿⡆⠀⠀⠐⡂⠌⠐⠝⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⡶⢐⡑⣊⠀⡴⢤⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠷⡈⠀⠶⢶⣰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠑⠚⣙⡒⠒⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠀⠀⠤⣬⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣙⠀⢠⠲⠖⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣰⢘⣙⣛⣲⣿⣿⣿⣿⡿⡻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⢾⡠⢤⣭⣽⣿⣿⣿⣿⡟⣱⠦⠄⠤⠐⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⡕⠶⠶⣿⣿⣿⣿⣿⣿⣗⣎⠒⣀⠃⡐⢀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣹⣏⣛⣛⣿⣿⣿⣿⣿⣿⣿⣞⣍⣉⢉⠰⠀⠠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢼⡧⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣣⣡⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅ ⡿⣷⣽⡿⠛⠋⠉⣉⡐⠶⣾⣾⣟⣻⡕⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗ ⢸⣿⣟⣥⡶⢘⡻⢶⡹⣛⣼⣿⣯⣽⢯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀ ⠘⢟⣾⣿⣿⣚⠷⣳⢳⣫⣽⣿⣛⣾⡷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢋⣿⣿⣯⣙⣯⣵⣿⣿⣯⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣡⣿⣿⣿⣿⡗⣮⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⢠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⢃⢸⠀⠀⠀ ⠀⠀⠀⣀⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣼⣿⠿⠧ ⠀⢠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠏⠀⢀ ⠹⣿⣿⣿⡏⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢆⠀⠀⣸⠃⢀⡔⠁ ⠀⠘⢿⣿⣧⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠏⠀⢀⣿⡶⡡⢀⠀ ⢠⠐⡀⢻⣿⣦⡀⠀⠀⠀⣀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⢀⢼⣿⠡⠁⡎⠀ ⡀⠇⢱⡀⣿⣿⣿⣦⣤⣀⡤⠞⠀⠀⠀⠀⠙⢦⣀⣀⠀⣀⡤⠋⣾⣿⣅⢼⠁⠨ ⡇⠘⢠⢇⢹⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⢸⣿⣿⣷⡘⠀⠀ ⢃⢀⠌⠀⠼⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠛⠚⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⢼⣿⣿⣿⣷⡀⠀⢀⣀⣀⠀⠀⢠⣿⣿⣿⣿⠤⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⢹⣿⣿⣿⣧⣬⣹⠓⠚⣭⣅⣽⣿⣿⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣿⣿⡏⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣹⣿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣿⣿⢊⣉⡀⡀⠀⠀⠀⠀⣀⣀⠉⢻⣿⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⣿⣿⠿⠽⠯⠽⢦⣀⣠⡚⠭⠿⠭⢯⣿⣿⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⣿⣿⣿⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⣿⣿⣿⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣼⣿⣿⣿⡀⠀⠀⠀⠀⠞⠢⠀⠀⠀⠀⢸⣿⣿⣿⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⡟⠓⢦⣤⣤⡴⢺⠁⠀⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢄⣀⡀⠀⠙⣻⢤⠇⠀⠀⠀⠀⠀⠘⢦⣸⠟⠋⢀⣀⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠡⡀⠀⠀⠀⠈⠉⠙⠓⠢⠤⠼⣄⡀⣠⠧⠤⠔⠚⠛⠉⠁⠀⠀⠀⢀⠀⢝⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠎⠀⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⢀⡇⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⡇ ⢸⡇⠀⠀⠀⠀⠀⠈⢍⣉⠗⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠐⢍⣉⠅⠀⠀⡀⠀⠀⠀⡇ ⠸⣷⠀⠀⢸⠀⠀⠤⠲⢄⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⢀⡐⢲⣄⠀⠁⠀⠀⠠⡇ ⠀⢻⠰⡀⢿⠀⠸⣍⣿⡿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣴⡟⡷⡀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢾⣮⣭⡿⠀⢠⠀⡀⢸⠁ ⠀⠈⢧⠀⠈⢧⣄⠈⠉⠀⠀⢀⣤⡾⠃⠀⠀⠀⠀⢀⡴⠋⣸⠁⢣⠘⠦⡀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠉⠉⣀⡴⠋⠀⣠⠏⠀ ⠀⠀⠈⠣⡀⠀⠀⠉⠉⠉⠉⠛⠋⠀⣀⡠⠤⠔⠊⠁⠀⣴⡟⠀⠸⣣⡀⠈⠑⠒⠤⠤⣀⣀⡈⠉⠉⠉⠁⠉⠁⠀⢀⡴⠃⠀⠀ ⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡜⠀⣸⠀⠹⣍⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢻⡶⠤⠤⠤⠤⠤⠔⠚⠁⣀⠴⠋⠀⠸⣧⡄⠀⠈⠳⢄⡈⠙⠒⠠⠤⠤⠤⠤⠤⣾⡉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠐⠢⠤⠤⠤⠔⠒⠒⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠒⠒⠤⠤⠤⠤⠀⠈⠟⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠦⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣿⣧⡀⠀⠀⠀⢸⣿⡏⠀⠻⣿⣿⣄⣠⠀⠘⠛⠒⠔⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⡏⠀⢻⣿⡟⠳⣄⢦⣿⣿⠁⠀⠀⠹⣿⣿⣇⠀⠀⠘⣂⠘⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠈⣿⣿⣶⣧⣸⣿⡿⠀⠀⠀⠀⠹⣿⣿⣆⠀⠘⡿⠟⢣⠀⠀⠀ ⠀⢀⡤⠀⠀⠐⠛⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⢹⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣆⣐⣛⣓⣻⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠖⠀⢠⠀⣿⢿⠟⠀⢀⠀⠀⢀⣹⣿⣦⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣉⣁⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⢸⣸⣧⡆⠀⠀⣨⠄⡾⠿⠛⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⠀⠈⢿⣿⣿⣿⣉⣹⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⣹⠀⢸⣿⠒⠷⣤⠖⠁⠈⠁⢀⣼⣿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡛⠛⠀⠀⠀ ⠀⠀⠠⡀⠀⢸⠁⢀⣿⣿⣆⡀⠁⠀⢀⡴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⣹⣿⣿⣿⣿⣿⡇⠀⠟⣵⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠿⠿⠟⠀⠈⠛⠉⠉⠉⠉⠯⣉⠉⠉⠉⠙⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣿⡟⠛⠻⢿⡀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⠏⠤⠁⠀⢄⠀⠀⠀⠀⠀⠀⢀⠏⠀⢀⣀⡤⠤⠔⠒⠒⠚⣧⠀⠀⣿⡇⠀⠀⠀⢳⡀ ⠀⠀⣼⣿⣿⣿⡟⠜⠁⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢼⢶⣿⣿⣿⣦⡀⠀⠀⠀⣰⡇⠀⣾⣿⣷⣤⣄⣀⠈⡇ ⠀⢰⡿⣿⣿⡿⢠⠀⢀⣠⣤⣤⣴⠒⢿⠀⠀⠀⠀⣸⠿⠿⠿⠟⠛⠛⠒⠚⠉⠀⠉⠉⣽⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠠⡿⣿⡇⠘⣏⠁⢰⣿⣿⣿⡷⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠈⠙⠻⣧ ⠀⠀⠀⠀⣿⡇⢠⣸⠓⠛⠛⠉⠁⠀⠀⣠⠞⠉⠓⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⢸ ⠤⠤⠄⣠⣿⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣤⣄⡀⠀⠀ ⠀⠀⢸⣿⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣿⣿⣿⣿⣦⡄ ⠀⠀⠘⠁⠀⢘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⢠⣾⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀ ⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣤⡄⠀⠀⠀⠐⣿⣿⣿⡿⠿⣿⣿⣏⠉⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⡿⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠛⢿⣿⣷⣦⣀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣈⠁⠀⠀⠀⢀⣸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣷⣄⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⡿⣋⡁⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠦⣄⣠⠤⡦⢤⣞⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⠞⣻⠀⢱⣄⡈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠ ⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⣧⣀⣿⠿⡎⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⡀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣏⢈⠻⠛⠙⢄⢹⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠁⠀⠀⠀⠀ ⠙⢄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣻⠷⣶⠶⠊⣇⣼⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠑⢤⣀⠀⠀⣠⠞⢆⠀⠈⠲⢄⠀⠀⠀⢀⡴⠿⠟⠛⠿⢷⠀⠾⠛⠛⠛⢲⠽⡄⠀⠀⠀⠀⢀⠴⠋⠀⢰⣆⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠑⢆⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠆⢀⡠⠊⠁⠀⠀⠀⠀⠙⠓⢦⡴⠒⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⠴⠀⠢⣀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠒⠋⠁⠀⠀⠀⠀⠉⠙⣲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠤⠤⠄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠬⡅⠀⡇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢰⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣬⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⢤⡴⠎⠀⠀⠀⠀⠱⣦⣀⣀⡀⠤⠔⠚⢿⣼⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠂⠉⠑⠲⣄⣉⣓⣒⣲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⡠⠤⠄⠒⢒⣤⣤⣼⠷⠦⣄⠀⠉⠺⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠈⢀⡤⣶⠞⠉⠀⠀⡇⠑⡄⠀⠙⢦⠀⠈⢪⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⠖⠁⡰⠁⠀⠀⠀⢀⡇⠀⠹⡄⠀⠀⠳⡄⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⢰⢏⠎⢰⠇⠀⠀⠀⠀⡼⠀⠀⠀⢷⠀⢢⠀⢡⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣟⡏⢀⡟⠀⠀⠀⠀⢀⠇⡀⢀⠀⢸⠀⠀⣇⠘⡴⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⢀⣿⠀⡸⡇⠀⡆⢀⡆⣼⠀⡇⠘⡄⠀⡆⠀⢹⢰⣇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⢰⣿⣷⣇⢧⡃⠇⢸⣿⠻⡄⢧⠀⢣⠀⡇⠀⢸⣼⣻⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠹⣻⡸⡈⣿⡛⣯⣿⣇⢸⣸⣷⣊⢿⠼⣄⠘⢰⠁⠀⣼⢼⣿⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⣀⣹⣿⣷⡹⡄⠻⠝⠛⠂⠙⠿⠾⣿⣿⣷⣧⡏⠀⢠⡏⣾⡈⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⡇⠀⣀⣠⠴⠊⠉⢉⣥⣷⣾⡈⠂⠀⠀⠀⠀⠀⠀⣳⠶⢃⠞⠀⢀⣾⣿⠁⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⣟⣷⣈⣿⡿⠀⢀⣴⠟⢹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠚⠯⣡⣤⠖⠛⠁⠘⣶⡻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠘⣿⢿⣿⣿⣧⣴⠟⠈⠀⠸⣿⣿⣿⣿⣷⣄⠀⢀⣀⡠⠔⠋⠁⠘⢦⡒⠦⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠈⢉⣿⣿⣿⡟⢻⢠⣧⣤⣻⣿⣿⣿⣿⠟⠉⢻⠉⠀⠀⢀⠠⠀⠀⠀⢹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⢀⣴⠟⠁⣠⣿⣻⣦⡈⢛⣿⠿⣿⣿⣿⡏⠀⠀⠀⣧⣣⠊⠁⠀⠀⠀⢀⣼⡟⣻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣀⣧⣾⣿⠿⠛⠛⠛⠉⢀⣴⣿⣿⣿⠁⠀⠀⠀⠈⠁⠉⠁⠀⠀⣠⣿⡿⣿⠋⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠀⠀⠀⠀⢀⡴⠛⠉⠛⢿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣱⡇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠠⢸⣿⡦⣂⣤⣶⡿⠿⠿⠿⢿⣿⣿⣿⣿⣥⡴⠶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⠀⠈⢿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢹⣿⣿⡿⠃⣠⡾⠋⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠠⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠚⠉⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣄⣲⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⣠⡖⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣦⡀⠀⠀⣀⠀⢀⣴⣿⡿⠟⠁⢀⣴⣧⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⣠⢿⣿⣏⢷⡌⠻⣷⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⠟⢻⣿⣿⣿⠋⠀⠀⠀⠋⣿⣿⢫⢻⡀⢻⡀⠈⠻⡟⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣴⣟⣿⡟⠁⠀⠀⠀⣠⣾⡿⣡⡟⢨⡇⠀⡇⠀⠀⣷⣽⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣼⣿⣧⣈⣀⣤⣾⣿⣿⠿⠋⠀⣼⣧⣰⡇⠀⢠⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣭⡉⠉⠉⠁⠀⣀⣴⠞⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡀⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⡀⠀⠀⢀⠇⠀⠀⠀⠀⣀⠀⢀⣘⣷⢄⡀⡀⠀ ⠀⠀⠀⢠⠃⠀⣠⣴⠯⠋⠀⠀⠤⣌⡉⠓⢤⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣸⣿⣧⠤⠓⠐⢤⠾⠤⣤⠋⠒⢤⣿⠉⠁⠀⠀⠀⠹⣇⠀ ⠀⠀⠀⠸⣤⠞⢁⠔⠀⠀⠀⠀⠀⠈⠙⢦⡀⠙⢦⡀⠀⠀⠷⣤⡀⠀⠀⣰⠟⠉⠀⠀⠀⢶⡁⠀⠀⠈⠦⠀⠀⠙⠒⡶⠲⡀⠀⠀⢿⡄ ⠀⠀⢀⣼⠃⠀⣇⡤⠊⠀⠀⠀⠀⠀⡼⠀⠙⣢⣤⣝⣒⣉⠦⣬⣝⣦⠞⠁⠀⢀⣀⠤⠴⠈⢓⣤⡤⠀⠀⠀⠀⠀⠀⠸⣤⠑⠀⠀⡀⠃ ⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⡤⠊⠉⡤⠊⠀⠀⠀⠀⠀⠉⠓⢶⡞⠉⠀⠀⠀⠀⠀⠀⢈⡓⠦⢄⡀⠀⠀⢰⡇⠑⠄⢸⣿⡀ ⠀⢠⠃⠀⠀⠀⠀⠀⠀⣀⣴⣾⠕⢺⠏⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢦⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⠑⢤⡀⡇⠀⠀⠘⢹⠇ ⠀⢸⠰⢤⣀⣀⠤⢔⣾⠿⠃⡄⢀⡏⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡳⡀⠀⢀⠼⠇⠀⠀⠀⠀⠀⠀⠀⢹⠣⢴⡆⠀⠸⠀ ⠀⢸⠀⢀⣠⠔⠊⠡⠖⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠱⡐⠋⠀⢆⠀⠀⠀⠀⠀⢀⠀⠈⣆⣀⠈⢓⣁⠀ ⠀⠼⠖⠉⠀⠀⠀⠀⢀⠤⢆⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠓⠲⠀⣀⠞⢁⣠⡒⠉⡀⠀⢀⣈⡿ ⠀⠀⠀⠀⠀⢀⣠⠔⠃⣠⢾⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡤⣴⠶⠒⠛⠛⠺⠯⣄⢠⣀⠈⠉⢿⡀⠀ ⠀⠀⣀⡤⠖⣉⡤⠖⠊⠹⢺⡷⣘⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡠⠴⠚⠀⣀⣀⣈⣷⣯⠑⢤⡀⢃⠀ ⠀⣀⣤⠖⠋⠁⠀⠀⠀⠀⡜⠀⠈⢻⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣠⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠋⠀ ⠚⣿⣿⣿⡄⠀⠀⠀⢀⡞⠀⠀⠀⠈⢧⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣤⠤⠖⠋⠀⠀⡠⠄⠀⠈⣆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣟⠉⡿⢿⣿⣿⣀⡿⢿⣛⠻⣟⠛⠛⠛⠛⣿⣚⢿⣶⣴⣂⣠⣤⣠⣥⣴⣥⡆⢀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠞⢩⣧⡨⠿⠿⢿⡝⠯⠛⠶⣤⢾⠀⠀⠀⠀⠉⠀⠛⢉⠉⠟⣉⣉⢉⣙⡏⣉⣁⣘⣈⠀⠀ ⣶⣤⣤⣤⣤⣤⣤⣄⣤⡴⠶⣶⣶⠟⠍⠁⢒⠿⡠⠖⠉⠉⢙⣷⠀⠀⠀⠈⠩⣳⣖⢶⠒⠒⠒⠒⢶⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⡖⣲⣿⣿⣞⣁⣀⠴⢚⣿⠛⣷⡈⣆⠀⠱⡌⠉⢧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠛⠛⠟⠛⠛⠛⠋⠉⢻⡿⢛⣶⣿⣿⣿⠋⣹⣟⣁⣴⣾⠃⢀⡏⠇⠸⡀⠀⢱⠀⢈⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡘⣾⣿⣿⡇⣸⡯⠽⠟⢋⣉⠑⡞⠀⡼⢠⢧⠀⠀⡇⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢰⢁⡟⠀⠉⣰⠙⡿⣷⣶⢦⡄⢰⠁⢰⠃⣸⡌⠀⢸⠃⢀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣶⣷⢸⢸⢧⡰⢼⣿⡀⠉⠀⠈⠀⠀⠀⢧⢇⣸⣳⠁⡰⢃⠀⣸⣿⣤⣶⣦⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡏⠀⣠⠆⠘⢿⣿⡸⣼⡝⢦⠣⠁⠀⠀⠀⠀⠀⠀⠘⠙⠻⢥⠞⢁⠜⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⣿⠏⡼⡰⠁⠀⠀⠈⢿⢿⣼⣇⠘⣧⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣼⣧⣾⡷⠛⢿⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡿⠀⠈⠰⠁⠀⠀⠀⠀⠸⠺⣿⣿⣇⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⡀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠿⢿⣿⡇⠀⠀⠈⠓⠤⣤⡤⠖⠊⠉⠀⠀⠀⠀⠀⠙⡄⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠙⠓⠤⠄⣀⡀⠀⢸⣷⣦⡤⠤⠖⠒⠒⠢⢤⡀⡇⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢀⢆⡀⠀⠂⠒⠒⠒⠻⠦⣄⡀⠀⢀⠢⠤⠤⢄⡹⣯⣀⠻⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⠉⠳⣤⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⢬⣳⣤⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣴⡿⡄⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣗⣷⠀⠀⠀⠀⠈⡦⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠖⠋⠈⠳⣄⠀⠀⠀⠀⠀⠀⢠⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣽⣿⡄⠀⠀⠀⠀⢸⠈⠉⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⠀⢀⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀ ⠀⠀⠀⠀⠀⢸⣷⣿⣿⣧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠛⠉⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠉ ⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⡄⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣧⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⠀ ⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣷⠀⠀⠀⠀⡹⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⢧⡀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀ ⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⠄⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣟⣿⡛⠭⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⢸⡇⢿⣁⣵⣾⡆⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⢸⣿⣦⣽⣯⣿⣿⣄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡱⡄⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠙⡄⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠹⡄⡇⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢸⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠋ ⢠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⠀⠳⠀⠀⠀⣿⣿⠂⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠀⠀⠀⣟⣿⣿⡆⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣯⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⢴⣨⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣽⢿⣿⡏⣾⣿⠏⢿⡘⢿⣆⠀⠀⢹⣿⡟⢉⢉⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⠟⣿⡁⠘⣿⡇⣻⢻⣷⠆⠀⢘⣿⡄⠀⠀⠙⠷⢼⣄⠈⠙⡗⠢⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡆⣿⣧⣀⣿⣿⡏⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⠀⠀⢉⠔⠲⢇⠀⠈⠒⣀⠤⠾⠿⠷⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⣷⣼⣿⣿⣿⢿⣧⡀⠀⠀⢀⣠⣴⡇⠀⣠⣴⢶⣮⣁⠀⠀⠀⣩⠖⠉⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⣿⣿⣿⡙⠿⣮⣯⠳⣄⠀⠀⠀⠀⡇⣰⠏⠀⠀⠀⠈⠑⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⢻⣼⣿⣷⣟⠛⠛⠓⠀⠀⠀⢀⣞⣿⢿⠘⣆⡀⠠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⡄ ⠀⠀⠀⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠹⣿⢅⡎⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⠁ ⠀⠀⢀⠜⠁⣿⣿⣿⣿⣦⠄⠀⠀⠀⣈⣶⠇⠀⠀⣠⠴⠊⠉⠀⠀⠀⠉⠓⠤⡀⠀⠀⠀⠀⡠⠞⢉⡿⠀⠀⠀⠀⠀⡎⠀ ⠀⠀⠀⠀⢀⠟⠉⣡⣼⣿⣠⡤⠖⠋⠀⠀⡀⠉⠉⠀⢀⣤⣆⣠⠀⠀⠀⠀⠀⠈⢏⠉⠘⠛⠢⠴⣊⡀⠀⠀⠀⠀⢰⡇⠀ ⠀⠀⠀⡠⣀⡴⠞⠛⠉⠁⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠇⠒⠢⠄⡀⠀⠈⠒⠤⣀⠀⢸⡇⠀ ⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀ ⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢧⠤⠬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀ ⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠐⠻⣄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⢫⠁⠒⠚⠓⠦⠤⢄⣀⣠⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢸⠇⢸⠀⡿⡟⡷⡇⠀⢠⣾⣉⣅⣿⣈⣧⡀⠀⢹⡇⠀⠀⠀⢸⣿⣿⣆⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⠀⣼⠀⢿⡇⡇⣧⠀⠸⣿⡍⢩⢿⠈⠉⢻⡝⢻⡇⠀⠀⠀⢸⣿⣿⣿⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⡄⣿⡴⢿⡇⣷⣿⣦⠀⢿⡇⣸⠀⠀⠀⠀⠙⣾⡇⠀⠀⢰⢸⣿⡿⡇⣧⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢫⠘⡇⣿⡇⢸⡧⢹⣿⣯⢊⣿⣇⠋⢀⣀⣀⣀⣀⣺⡁⠀⠀⣼⢸⣿⡇⢷⢸⡎⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠘⡆⢿⢯⣷⡌⠛⢸⡏⢿⠳⣇⠉⠐⠋⣿⣿⣿⣿⣯⢻⡇⢀⡟⣼⡇⡇⢸⢸⣷⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣹⣆⣧⠸⣧⣼⢿⣿⣿⣯⠈⣰⡏⠳⠄⠠⠿⠿⠟⠚⡅⣾⠀⣸⣇⣿⢻⡇⢸⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠸⡏⡜⡆⠹⡟⢾⣿⠿⡯⠀⢻⠁⠀⠀⠀⠀⠀⢀⣼⢱⠇⢀⣿⠙⣿⢸⡇⣾⢸⡿⢿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⡜⣷⢻⠹⡄⡹⡄⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣼⡏⢀⡿⣸⡇⣿⢸⣧⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⡇⢻⡘⣇⠹⣎⠻⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣇⣾⣿⣧⣿⠁⣿⢠⡟⠸⡿⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⣧⢿⣶⠿⣦⢮⠉⠃⠀⠀⠀⠀⠀⠀⠀⠘⢁⣾⣿⣿⣿⣿⡟⠀⣿⢸⣷⢰⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⣿⡌⣿⣿⣿⣥⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢀⡴⣿⡟⣿⡿⣿⣿⠃⢰⣿⣿⣹⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⢻⣷⣿⠿⣿⣿⣾⣿⣿⣿⣿⣿⠲⣤⡤⠞⠉⠞⠉⠰⣿⣣⣿⣿⠀⢸⣿⡏⣿⣸⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⣿⠀⣹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠘⠀⣿⣿⢹⣿⡏⠀⢰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠸⣿⣿⣼⣿⣿⣿⣿⡿⠿⠋⠀⠀⠙⠒⠒⠒⠛⢀⡴⠀⠈⠛⠷⣦⣿⣯⣿⣿⠃⠀⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠜⠃⠉⠉⠁⠉⠉⠁⠀⠀⠀⣀⣀⡐⡄⠀⠀⠀⢠⣏⡤⠴⠖⠂⠀⠀⠀⠀⠀⠈⠈⠳⣻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣼⠀⠀⠀⠀ ⠀⢀⠞⠀⠀⣠⠶⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⢀⡟⠀⢠⠞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⢸⠀⠀⡿⠀⠷⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⡀⠀⠈⢧⠀ ⢸⠀⠀⠛⠀⠀⠀⠀⠘⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢹⡄⠀⢸⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢡⡀⠀⢠⡇⠀⢈⡇ ⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢸⠃ ⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠚⠁⠀⢀⡞⠀ ⠀⠀⠀⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣡⠟⠀⠀⠀⠀⠀⠀⠙⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀ ⠀⠀⠀⠃⠀⠙⢷⡶⠤⣤⢤⠤⠴⠖⠋⣩⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⣿⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠈⠉⠓⠲⢶⡶⠶⣶⠞⠋⠁⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⣸⡁⡼⠁⠀⠀⠀⠈⡧⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⢾⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣄⡀⠀⠀⠀⠈⢻⣧⠈⠉⠻⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⡟⠻⢷⣦⣄⣀⣴⣿⣧⣀⣀⣬⣿⣿⣿⡷⠢⡄⠀⠀⠀⠀⠀⠀⠀⡿⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣦⡀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣦⡀⠀⠀⠀⠀⠀⢣⡀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣶⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠙⢆⠀⠀⠀⠀⠀⠱⢤⣾⣿⣿⣿⠏⠉⠉⢉⣽⣿⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⡤⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠉⠉⠙⠻⣿⠟⢢⡀⠀⠀ ⠀⠀⢰⡁⣿⣿⣿⣿⣧⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠱⡀⠀ ⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣧⠀ ⠀⠀⢻⢸⣿⡟⢻⣿⣿⠛⠛⠿⠛⢹⢿⣿⡿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀ ⠀⠀⢸⣿⣿⣿⠾⠁⣿⣦⠀⠀⠀⣇⡸⠏⠀⣿⣿⣿⠿⠢⢄⣀⠀⠀⠀⢀⡀⠤⠀⣤⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⢰⠛⠛⡏⠀ ⠀⠀⠀⢿⣿⣿⡆⠀⠙⠛⠁⠀⣀⠀⠀⢀⣼⣿⠟⡁⠀⠀⠀⠈⠉⠒⠊⠡⠤⠤⢼⣿⣿⣿⣿⣿⣿⠿⠷⣄⣀⣰⣇⣀⡴⠁⠀ ⠀⠀⠀⠈⠻⣿⣿⠀⠂⠤⠤⠤⠤⠖⠊⣿⣿⣿⠑⠌⣳⡆⢠⣤⠴⠊⠁⠉⠉⠉⠒⠢⢍⡻⣿⡟⠁⠀⠀⠈⢿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠈⢳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠃⠀⠀⠀⠀⣼⠯⠤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠞⠀⡀⢀⡜⠁⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢴⡿⠀⣮⠀⠀⠀⠀⠀⠀⠈⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡊⢁⠠⠃⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡀⠀⠀⠈⠑⠢⡄⠀⠀⠀⡼⠉⠉⠉⠓⠒⠉⠘⢦⡀⠀⠀⠀⠀⢀⠔⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡞⢁⣴⣾⣿⣿⣷⣦⣀⡤⢞⡵⠒⠓⢒⣦⡀⠀⠀⠀⠉⢲⡦⠤⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⠟⠛⠿⣿⡄⢸⠀⢀⣴⣿⣿⣿⣷⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⣴⣶⣆⠘⡷⣈⣰⣿⣿⣿⣿⡿⠟⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⠣⣛⣛⣁⣀⡆⠈⠻⢿⣿⣿⠏⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣥⣴⣾⣿⠀⠀⠀⠉⠛⢦⣄⣀⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡛⠛⠁⠀⠀⠀⠀⠀⠀⠉⢻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠇⠇⠀⣠⣿⡟⣱⢪⣧⣸⣶⡄⡼⣿⣿⣿⣿⡉⣿⣿⣿⣯⣵⣷⡧⡄⠀⠀⠀ ⠳⢸⡠⢪⣾⡟⣰⡇⢸⣮⣿⡿⣿⣆⣿⣿⣿⣿⣇⣧⡤⣽⣿⣏⣿⣻⣿⢧⡀⠀ ⡶⡛⢁⣿⡿⢠⣿⠀⠘⡏⠉⠀⢹⢻⢸⣿⣿⡿⡸⠊⠀⠀⠀⣿⢿⢿⣟⣧⡘⠗ ⡞⢱⢺⡇⠇⣼⡇⠀⢸⢎⡀⠀⠀⠀⢡⢿⣿⣗⣧⠃⠀⠀⠀⠙⠉⢊⠻⡎⢿⡌ ⢇⡇⣼⡖⢀⣿⠇⠆⢸⠘⡀⢀⠀⠀⠀⢞⣿⣿⢸⡶⠀⠀⠀⠀⠀⠀⠣⠘⡌⡞ ⣼⡇⡏⣟⠀⣿⠀⠁⢸⠀⠈⠀⠀⠀⡀⠜⢼⡿⡎⣧⡦⠀⠀⠀⠀⠀⠀⢃⠰⣸ ⣿⡇⠇⡟⡀⣿⢸⠀⠈⠀⠀⠀⠒⠈⢀⢀⠜⢆⠹⣨⡘⠢⣀⠤⣤⣤⡆⠘⡄⠉ ⣿⣧⠀⡇⠀⣿⡄⠀⢠⣧⣒⣠⣀⣐⣢⠄⠀⠈⢢⣐⢻⣦⣶⣿⣿⡟⠿⣿⣿⡀ ⣹⣿⡄⢿⣀⢹⣩⣶⢽⠛⣿⣿⢿⣿⡿⠆⠀⠀⠀⠙⢦⢻⡿⠦⢿⠇⠀⡟⣿⣷ ⡟⣿⣷⣯⡆⠙⡿⣇⠸⠀⠿⣟⣚⡿⠃⠀⠀⠀⠀⠀⠀⢧⡹⡄⠥⣴⡢⠀⢻⡏ ⣧⢻⣿⣿⣟⡀⢁⠈⠠⡀⢺⠰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⣮⡲⠇⠀⢸⣿ ⣿⣧⢫⣿⣿⣄⠈⣆⡀⠈⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠢⠀⠘⣿ ⢻⣿⣎⢿⡝⢿⣆⢻⣇⠀⠈⠀⠀⠀⠀⠀⠀⢀⣔⠦⠭⢥⣢⠀⠀⠀⠀⠀⠀⣿ ⢸⣿⣿⡜⣿⣦⡙⢧⣿⣆⡸⠀⠀⠀⠀⠀⢠⠶⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠠⠘ ⢸⣿⣿⣷⢹⣿⣿⡷⣝⢿⣧⡀⠀⠀⠀⠠⠉⢉⠇⠒⢢⠀⣽⡇⠀⠀⠀⡀⠀⠠ ⢸⣿⣿⡿⠎⣿⣿⡇⣿⠧⣻⡵⣄⠀⠀⠘⡄⠀⠀⢀⠴⠔⡱⠀⠀⢀⠔⠀⠀⠀ ⣼⢿⣇⢧⣿⡿⣿⣿⣿⣆⠈⠻⡈⢷⣤⢀⡈⠂⠔⠉⠉⠁⠀⡠⠔⠁⢀⠔⠀⠀ ⠥⢺⣾⠟⢸⣁⠀⣿⣿⣿⣷⣤⣜⣮⣿⣷⣾⣿⣳⣶⠀⠀⠊⠀⠀⢀⠂⢀⠀⢡

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠂⠀⣠⡖⠉⠀⠊⣡⠖⢉⣽⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⢷⡤⠔⠈⡿⠀⢠⢃⢞⣡⣴⣟⡟⡹⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠸⡆⠀⢘⡆⠀⣼⣾⣿⣛⠝⣱⣿⠃⠀⠀⡸ ⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸⡀⢰⠇⠀⢻⠤⠋⠁⠺⣯⠏⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢣⣾⣶⠀⢸⡄⠠⡤⢡⡍⠀⠀⠀⡌⠀ ⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠈⡇⢸⣼⠗⣦⣴⠾⠀⠀⠀⣼⠅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⣤⣜⣴⡋⠉⠋⠉⢀⠆⠀⠀⠈⡌⢠⠀ ⠀⠀⢀⠠⠐⠀⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣾⡇⢸⠀ ⡰⠛⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣾⡟⡟⡇⢸⠃ ⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⣼⣿⠃⡇⡇⢸⠀ ⢧⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣥⣿⣿⣿⠀⣇⡏⢸⠀ ⠈⠣⣀⠀⠀⣀⡵⠢⢄⣀⣀⢤⠔⠒⢹⣿⣿⣿⣿⣿⠰⡟⠀⠀⠀ ⠀⠀⠀⠈⠟⢹⡁⠀⠀⠉⠒⠺⠧⠀⡘⢿⣯⣿⣿⡟⢡⡄⡄⠀⠀ ⠀⠀⠀⠀⠈⠘⡅⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣼⢁⣦⠀⡅⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⠐⢄⠀⠀⠀⠀⠐⣤⣼⣿⣯⣄⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠀⠀⠀⠐⢶⣿⣟⣿⣏⣻⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⣿⣋⣈⣱⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⣿⣿⣿⡾⡿⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢺⡿⣟⡾⣋⡴⠂⣻⣾⡇⠀ ⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⡀⢠⣦⣏⣉⠉⢉⠉⣳⢿⠿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣄⠀⠀⠀⣀⣤⣶⣀⣀⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⣿⣶⠿⠛⠋⠉⠉⠉⠉⠉⠛⠾⡟⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠀⣠⣤⣤⢤⣮⠿⣧⣤⣀⡐⠳⢤⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡿⠀⢠⡟⠉⠻⣄⠀⣻⡀⢠⣯⠈⣹⣷⣄⠿⣿⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴ ⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠃⠀⣾⠳⣄⣀⣿⣷⣿⣿⠟⢿⣿⣿⣿⣿⣷⣬⣉⣛⣛⣛⣷⡶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣻⡟⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⠀⣦⣿⣀⣼⡿⣿⢽⣾⣧⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⠟⠁⠀⠀⠀⠀⢀⣴⡾⠉⢀⡿⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠈⣿⣇⣀⣽⠏⠨⣬⣬⠽⠙⠘⠋⠁⠈⠁⢸⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⣀⣴⣿⡿⠀⠀⢸⠁⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⡿⡅⢙⣿⣴⣲⣶⠀⠊⢁⠀⠀⠀⡎⢀⡀⣸⣿⣿⣷⣿⣿⣿⣷⣿⣿⡿⢿⢵⡟⠀⠀⠀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢷⣿⣿⣿⣇⡹⠃⠀⠀⠈⠀⠀⠀⠙⠾⣿⢿⣿⠿⠛⠛⠻⢷⡿⢡⠟⣰⠃⡾⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⣏⢿⣯⣷⠒⠀⠀⠀⠀⠰⡟⠉⡇⢠⡿⠋⠀⠀⠀⠀⠀⣼⠀⡏⢠⡇⠀⢻⡀⠀⠀⠀⣿⡀⠀⠀⢦ ⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⠀⠀⠙⢿⣼⣿⡿⣷⣄⣠⠆⢀⣀⡈⢂⣀⡞⠀⠀⠀⠀⠀⠀⠀⢹⡆⢷⡀⢧⡀⠀⠳⣄⠀⠀⠈⠻⣄⡀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⣿⣧⣴⣿⣿⣿⢟⣻⣿⣿⣿⡇⠀⠀⢀⣀⠀⠀⣀⣸⣧⣈⣷⣌⠛⢦⣀⡙⠀⠀⠀⠀⠈⠙⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⢿⣿⣛⡿⠟⠛⠉⠉⠛⠫⣟⠋⠀⡐⢚⡛⠓⠛⠛⠋⠉⠉⢻⣿⡿⢷⣀⠈⣿⣷⣶⣦⣤⡤⠖⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⠉⢀⡾⠃⠀⠀⠀⠀⣠⣾⣥⣶⠟⠙⣋⠁⠀⠀⠀⠀⠁⠀⢐⣿⣷⣤⡼⠓⠾⠟⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⡜⠁⠀⠀⠀⣀⡾⢋⣭⡞⠁⠒⠚⠛⢉⣉⣀⣀⠀⠄⠀⢀⣺⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⢿⠀⠀⠀⠀⣴⡿⢋⣻⠅⣠⣴⠦⠚⠋⠉⠉⠉⠉⠉⠉⢛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠿⣄⠀⠀⣸⣗⡴⠟⣡⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⣤⣞⡛⠒⠶⢿⣷⣴⣿⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⡛⠿⣍⠛⠯⣄⡉⢍⡐⠨⣍⠙⡲⣿⣿⣾⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡀⠉⠲⡈⠳⣄⠀⠙⢲⠀⢀⠀⣽⣿⣾⣿⡿⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣿⠀⠀⠙⠀⠙⢦⠀⠀⣧⢺⡇⡿⣿⡿⠃⠀⠀⠀⠀⡇⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡄⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢰⡃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⢠⠀⠀⠐⢠⣿⡿⣋⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⡇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢠⣟⡀⣠⡴⠿⠿⠾⠋⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡷⠿⠟⠋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢻⡝⠓⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣻⡇⠘⡆⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⠀⠹⡦⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢧⣼⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠈⢧⣧⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣠⡫⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢤⡀⠀⠀⠀⠀⠀⠀⣶⣿⡗⠾⠀⢀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⣤⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⣉⡤⠴⠀⣀⣈⣭⣁⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠗⠋⣀⡤⠤⠒⢘⡥⠤⡀⠙⢦⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⡤⠚⠁⣠⠖⠛⠻⠧⢤⡈⠳⣄⠑⡄⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⣿⠋⣠⠞⠁⢠⠎⠀⡖⢀⠀⢀⡄⡵⡄⠘⢦⢣⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⡿⠃⣰⠏⠀⣳⡏⠀⣴⠁⠀⣸⣇⠙⡘⢿⡄⠈⠋⢧⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠁⢰⠏⠀⣠⣿⣟⢺⣟⣚⣿⡟⠘⣦⣷⡈⣿⡄⢀⡞⣧⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⡿⠀⢸⣿⣿⣿⣿⡿⣶⡿⠁⠀⠈⢿⣷⣿⣷⠴⣷⣽⣇⣿⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣸⣇⢰⣿⢿⣾⣭⣿⠿⠋⢠⣐⡒⠀⠀⣹⣿⢃⠂⢸⣿⣿⣿⠎⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣿⣿⣿⡏⠀⠚⠉⠇⠀⠀⠙⢹⡿⡷⠦⡿⠙⢸⢠⣾⣿⣿⣿⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣏⣿⣧⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠞⠀⣰⣶⣿⣿⡧⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣟⢻⣿⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⡟⠙⢦⡀⠀⠀⠀⣀⡤⢞⢏⡟⢼⡿⣿⣇⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡼⣿⠓⣶⠟⠋⣠⣟⣉⣀⣤⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠒⠉⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⢣⡤⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⢀⣈⡗⠀⣰⣾⡿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣿⡿⣿⣿⢭⣭⣄⣆⠔⠬⢍⠉⢛⠛⠿⣿⣿⣿⣿⣿⡏⡀⠘⠿⡋⠙⢿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣧⣼⣾⣿⡻⠿⠿⢭⣭⣾⣽⣿⠃⠀⡠⠟⢠⣿⣿⣿⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠞⠋⠐⠂⢭⣙⠛⠛⠿⣿⣿⣿⣿⣷⣶⣶⣦⣶⣾⣿⣿⣿⣶⣼⣁⣀⣼⣿⣿⣿⣇⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢷⣶⣤⣤⣤⠤⠬⠉⠉⢭⣝⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠈⣿⣿⣿⣿⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⣠⠎⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⡊⠛⠶⠶⠖⠋⠁⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠁⢀⣤⠏⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠶⠶⠾⠉⠁⢀⡞⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⢱⠏⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⡿⠀⡇⣠⠗⢄⠉⠲⠦⠤⣀⣀⣀⣀⣀⣀⣀⡤⠶⠻⠋⢻⠀⠱⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣾⠇⣸⠁⠃⠀⠀⠉⢒⠦⠄⣀⣀⣀⠀⠀⣀⣀⣠⠴⠺⡀⠈⡇⠀⢻⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣽⣿⢠⠃⠀⠀⢀⡆⠀⠈⠀⠀⠃⠀⠀⠃⠉⡏⠀⠀⡀⠀⡇⠀⢸⡄⠀⢳⠙⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⢃⡇⢸⠀⠀⠀⣸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⡇⠀⣄⡇⠀⢸⡀⠀⢣⠀⠈⢷⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⣼⠁⡜⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣧⠀⠈⢧⠀⠘⣆⠀⠈⣧⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⢻⠀⡇⠀⠀⣼⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⢹⡄⠀⢸⡀⠀⠹⡄⠀⢸⣦⠹⣇⠀⠀⠀⠀ ⠀⠀⢀⣿⠁⢸⡏⢰⠃⠀⡆⣿⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠇⠀⠀⠸⣷⠀⠀⣷⡀⠀⢷⠀⠀⣿⣆⣿⡄⠀⠀⠀ ⠀⠀⠈⣿⠿⢿⡇⣾⠀⠀⣇⣯⠀⢸⠀⠀⠀⡇⠀⠀⠃⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⣦⣠⣼⡟⠋⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⢸⣷⣿⣦⡀⣿⡇⠀⢸⠀⠀⠀⡇⠀⠀⡇⠀⠀⢸⡀⠀⠀⣿⡆⠀⠸⣧⣤⣤⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣷⣭⣿⣷⡀⢸⠀⠀⠀⡇⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⡤⣺⣿⠿⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠙⢻⠿⣬⣿⣯⣍⣒⣿⢦⡀⣿⡦⣄⢸⣿⣉⣐⢾⣿⣿⠟⠁⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠙⠛⠈⠛⠿⢿⣿⣬⡿⣿⣶⣼⠿⡿⢿⠋⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⣀⣁⣿⣿⣇⣈⣉⣇⣀⣆⡀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⡿⠳⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡏⠁⠀⠀⠑⢦⣬⡙⠓⢦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠳⣄⣀⠀⠐⡌⠻⣹⠦⣄⠹⢿⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠀⠀⡿⢀⡞⠙⠲⢮⡁⠀⠑⣌⠻⣶⡂⢀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠃⠀⣾⠁⡾⠀⠀⣠⠖⠛⠳⢄⠻⢧⣬⣙⠿⠷⠶⠶⣤⣀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⢸⡇⢰⠇⠀⢸⠇⢠⠚⠙⢦⣀⠀⠻⣯⠹⠗⠒⠒⠶⣬⣅⠀⢠⣿⣿⣷⣶⡦⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢤⣐⣢ ⢸⣷⠀⢸⠇⢸⠀⠀⢸⠀⢸⡆⢀⠀⠈⠱⡄⠹⣧⢀⠀⢀⡼⢹⡇⠀⣾⣿⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣚⠙⢿ ⣿⡏⠀⠸⡄⠠⠀⠀⢸⡄⠸⣆⠈⢷⣄⠀⠙⢆⠘⢿⣦⠘⡇⣾⠁⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⢿⣿ ⣿⡇⠀⢸⠃⢠⠀⠀⠘⣇⠀⢻⡄⠀⠛⢦⡀⠈⠓⢦⡈⠙⠻⠋⠀⣿⣿⣿⣿⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿ ⢳⣿⠀⠈⡇⢸⡄⠀⠀⠸⡆⠈⣷⠀⠀⠊⢿⣦⣀⡀⣽⠀⠀⠀⣸⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿ ⠘⡟⢾⠀⢳⠈⢧⠀⠀⠀⢷⠀⠸⡆⠄⠰⢾⣿⣿⣿⠿⠃⠀⢰⣿⡼⠛⢻⣿⣿⣿⣿⣶⣶⣦⣀⣠⣤⣤⣤⣄⣀⣀⣿⣾⣿⣿⣿ ⠀⢹⡼⡀⠈⢦⡈⠳⣄⠀⢸⡀⢰⠃⠀⠰⣞⣿⡏⠀⠎⠀⣤⣿⠏⠀⠀⠀⢹⡟⢿⠛⠛⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠳⣿⣄⠀⠉⠂⠀⠀⣸⡇⢸⠀⠀⢀⣼⡏⣰⡇⠀⢰⣿⠏⠀⠀⠀⠀⢸⡇⣼⠃⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉ ⠀⠀⠀⠙⢿⡷⣄⣀⣀⡴⣋⠠⡈⠀⠀⢀⣾⠟⠛⠁⢀⣿⡏⠀⠀⠀⠀⠀⡾⢠⠏⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠹⠿⡿⠿⠉⠀⠀⠀⣸⡿⠀⠀⠀⠀⢀⡾⣱⠋⠀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠘⠀⠁⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣬⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢩⣝⢶⡳⡖⢲⠖⡖⠞⢭⠽⡏⢩⠉⣭⡦⠔⡲⢆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠛⢳⣿⡷⠛⠓⠓⠚⠒⠚⠓⠒⠒⠋⠂⠒⠒⣒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠶⠶⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⢣⡶⠀⠀⠀⠀⠀⣠⠖⠉⣀⡴⠶⠊⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⠃⡼⠁⠀⠀⠀⣠⠞⣡⡴⠋⠁⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⣇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡏⢠⡇⠀⠀⠀⣼⣣⠞⠃⠀⠀⠀⣀⣠⣤⣄⣿⡇⢧⡀⠀⠀⢻⣄⡀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⢸⡇⠀⢠⣼⣿⣏⡀⠀⠀⢠⢾⠛⠉⠁⢀⣿⡉⠛⣷⣄⠀⢸⣿⠻⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⠀⣇⡴⢿⣿⡉⠉⠉⠁⠀⠀⠀⣀⣶⠾⢿⡛⠟⢶⣼⡇⠀⢸⢻⡀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⠀⢸⡆⣿⣛⠩⣿⣷⠀⠀⠀⠀⠙⠉⣷⢾⣿⡇⠾⠀⢻⠀⢸⠇⣽⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠻⣏⠛⠳⡿⢿⡞⠀⠀⠀⠀⠀⠾⠿⠿⠇⠆⠀⠀⣆⣼⣱⡇⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠀⠙⡄⠀⠙⠉⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⢿⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⠀⠀⢻⡄⠀⠀⠈⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⠘⡇⠀⠈⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡀⠘⡟⠦⣀⠀⠀⠒⠒⠋⠉⠁⠀⠀⢀⣠⠆⠀⣹⠀⣈⡇⢹⡄⠀⠸⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣄⣷⠀⢹⡳⣄⡀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⣿⠀⣟⢿⠈⡇⠀⠀⣹⣻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣧⣿⠇⢰⡍⠳⠤⣴⠛⠁⠀⠀⠀⠀⢰⣿⠀⡿⢸⠀⢸⡀⢀⣿⡇⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠇⢀⡼⠋⢀⣮⡇⣀⠴⡟⠀⠀⠀⠀⠀⠀⣿⠃⠻⣅⣼⠀⢸⡇⢸⣹⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠏⢀⡞⢀⣀⡸⠟⠋⠁⠘⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠳⢄⣸⣧⣧⣟⡼⠉⠀⠀⠀ ⠀⠀⠀⠀⢀⡤⠿⠤⠚⢲⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⡀⠀⢀⣀⠙⠛⠿⢾⣄⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠀⠴⠒⠒⠚⠒⠛⠛⣿⡉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀ ⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄ ⠀⢸⢹⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⢸⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⣼⠛ ⠀⠀⠸⣇⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⣼⠀⠀ ⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣰⠃⠀⠀ ⣼⢃⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢳⠀⠀⠀⢠⠏⠀⠀⠀ ⣿⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⠀⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀ ⢹⡆⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠉⠈⠀⠀⡼⠀⠀⢰⡇⠀⠀⠀⠀ ⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠃⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢤⣀⣀⣀⣀⣀⡴⠖⠋⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠁⠀⠀⢰⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠋⠉⣿⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢽⣼⠀⠀⠄⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⡿⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡼⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠄⣀⢤⢴⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⡼⡀⣦⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⢀⡷⣩⠛⢣⡱⣾⠄⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀ ⠈⠢⡀⠀⢀⢄⠑⠄⡀⠀⢀⣼⠿⢿⡅⠥⠶⢷⢂⠀⠀⠀⡠⠒⢡⠀⠀⠀⠀⠀ ⠀⠀⠀⠩⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢀⠀⠀⠀⠁⢡⠀⠀⠀⠀⠁⠓⡒⠊⠀⠀ ⠀⠀⠀⠀⣂⡀⠀⠀⠀⠀⠙⢤⠄⠂⠁⠁⠒⢠⠔⠁⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⢑⡄⢒⠒⡔⠁⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢁⢸⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢀⡤⠚⢄⠀⠀⠀⠀⣠⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⠋⠀⠀⠀⢣⠀⠈⠁⠈⢛⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⢉⣀⠤⠤⠭⢟⣦⣯⣇⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⣠⠒⠉⣠⠒⠁⡠⠚⢻⡿⣿⢿⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢀⠎⠁⡰⠊⠀⣠⠊⠀⠀⣼⠇⢋⢇⣷⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⠏⣠⠞⢠⢎⣴⠃⡠⠀⢠⣿⠀⢸⢸⣿⠞⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣼⡟⡴⢁⡴⡣⠛⡿⢠⠃⢀⢿⡇⠀⢸⢈⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡟⡇⡼⢸⡟⢁⣾⣿⣧⣰⣧⠇⢀⣾⠏⣇⠀⢸⢸⣿⡆⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠁⠁⣇⢇⣸⢃⡞⠀⠫⠿⢹⡟⣠⢾⠏⠀⢸⡇⡆⡸⡌⣷⡼⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡏⣼⡇⠀⠀⠀⢸⠵⠋⠃⢸⣟⢿⣧⢣⡇⣿⡘⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣾⣸⢰⣿⣣⠀⠀⠀⠀⢀⣀⣀⣀⣠⣾⣧⣾⣷⣿⣿⣾⣯⣣⡀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠿⢧⣙⣆⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣦⡄⠀⠀⠀ ⢀⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⠁⠀⠀⠀ ⢸⣿⣿⣿⣿⣧⢀⡀⠀⢀⡄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢣⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣇⣤⣴⣿⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⣄⡌⣇⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣌⡀⢸⣣⠸⡄⠀ ⠀⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠙⠻⣄⡧⠀ ⠀⢈⣿⣷⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⣀⡒⠢⡠⠴⣮⡇⠀ ⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣷⣀⣈⣴⡟⠃⠀ ⠀⠀⢼⣿⡟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠏⢙⡇⠀⠀ ⠀⠀⣾⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⣀⡜⡇⠀⠀ ⠀⠀⠘⣿⣿⣧⠀⠀⠘⠢⠤⣄⣀⠀⠀⠀⣤⠞⡟⠢⡀⠀⠀⠀⠀⠀⣠⣿⢁⡖⣠⢾⣫⠃⡇⠀⠀ ⠀⠀⠀⠈⠿⣿⣗⠄⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⡇⠀⠈⠛⢲⣶⡶⢾⣿⡇⣼⡾⣽⣯⠃⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣾⡄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠐⣾⣿⣷⠏⣿⢠⡟⣰⣿⠇⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⣿⡞⢀⣿⡟⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⣿⠀⢸⠏⢣⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠳⡀⠀⢿⠀⢸⠀⠈⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠹⡄⠈⢇⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢀⠀⠀⠱⡀⠈⠳⢤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⡿⢹⣄⠀⠀⠀⠀⠀ ⠀⠀⡶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡞⠀⠀⠀⠀⠀⣠⡾⠁⡜⢇⡀⠀⠀⠀⠀ ⠀⣴⢧⣈⠓⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡜⠀⠀⠀⠀⢀⠔⢱⣣⠊⠀⠈⢧⢠⡀⠀⠀ ⠰⠃⠀⢸⠋⠒⠢⢤⣉⠉⠒⠢⢤⣄⡀⠀⠀⠀⢹⡟⠀⠀⠀⠀⣰⠇⢀⡏⠘⣄⠀⠀⠈⢧⠙⢄⠀ ⠀⠀⠠⠋⠀⠀⠀⣼⠀⠉⠉⠒⠦⠤⣈⡉⠓⢶⢄⣇⠀⠀⠀⢠⠧⠤⢸⠀⠀⠈⠢⡀⠀⠈⠳⡀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⣿⡟⢁⢀⡼⢡⣾⣿⡟⢹⣿⡇⠸⣽⣿⣿⣷⠻⠳⣄⢼⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⢰⣟⣴⣿⣿⣿⣿⡟⣿⢡⣿⣿⠁⠀⢻⣿⣿⣾⣧⣄⢻⣆⠸⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⢹⣿⣿⣿⣿⡿⢀⣿⣿⣿⢿⠀⠀⢸⣿⢹⣿⡇⣿⠸⣿⠻⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⣾⣼⣿⣿⣿⠟⠻⡿⣿⡇⠸⡀⠀⠘⣿⣾⣿⣇⢸⡇⣿⡀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⡏⢸⣿⠿⢛⣷⡾⣇⠻⡧⠀⠃⠀⠀⠃⣸⣿⣿⣾⣧⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⢀⣿⠃⠁⠘⢷⣰⣿⣿⣶⠋⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⢿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⢸⣿⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡼⠟⡸⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣿⠐⡄⢡⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠁⠀⠀⠀⢡⣿⣿⠀⡏⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢦⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣧⡀⠀⠀⠀⣴⣿⣿⠆⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠀⢸⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣄⠀⠀⠀⠛⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡇⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠳⣄⠀⠀⣠⠔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠀⠀⠀⠑⠋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⡈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡿⠛⠉⠀⠀⠀⠈⠉⠉⣿⡟⠋⠁⠤⠤⠤⠤⠤⠼⢧⡀⠀⠀⢠⡧⠤⣀⣈⣩⣿⠿⣿⡿⠿⠛⠛⠛⠒⠻⠿⣦⠀⠀⠀⠀⠀⠀⠀ ⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠓⠉⠀⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠐⡄⣄⠀⠀⠀⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣝⣢⣼⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣄⠀⠀⡿⡄⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⢀⣷⢳⠀⠀⠀ ⡇⠀⠀⢀⠀⠀⣸⡟⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡏⢧⠀⠀ ⣧⠀⠀⠈⠀⢠⣿⠁⠀⠀⠀⣠⣶⡖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡋⢩⠧⠘⣿⡜⣆⠀ ⣿⡄⠀⠀⠀⢈⡏⠀⠀⠀⠀⡏⠻⡟⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢱⠀⠀⠀⠀⠈⠑⠒⠒⠒⠀⠂⠈⠈⢻⣭⣉⣿⠀⢸⣷⡹⠀ ⣿⣇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠙⠲⠿⠿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⣿⣷⠀ ⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⣠⠔⢻⠀⠈⣎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⣿⢻⣧ ⣿⣿⡇⠀⢸⡟⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣠⠃⠀⠀⠈⢎⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠈⠈⢿ ⣿⣿⣿⠀⢸⡇⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⡄⠘⢄⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠈ ⣿⣿⣿⠆⢸⡇⠀⠀⠈⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⡸⠁⠀⠀⠑⠢⠀⠑⣤⣀⣀⣀⡀⠀⢀⡠⢴⣦⣶⣿⣿⣿⡆⠀⠀ ⣿⠋⠁⠀⢸⡇⠉⠉⠉⠉⠛⠛⠛⠓⠒⠲⠶⠶⠯⢍⣀⡀⢀⣀⡜⢁⣀⠤⠤⢒⣒⡉⠉⠁⠀⠉⠟⠒⢒⣚⠉⠁⣰⣿⣿⣿⣿⡇⠀⠀

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⠀⢀⣠⣴⣶⣦⣄⡀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡿⣷⢿⣿⠹⡹⣆⠀⢻⡟⠛⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣛⡄⢿⣿⠙⠃⠀⣿⡄⠈⠉⠣⣀⡍⠀⢄⢀⣴⣄⠀⠀⠀⠀⠀⠀ ⢻⣿⣷⣿⢿⡄⠀⠠⠼⠃⡤⠴⠌⡀⢈⠔⠈⠀⠀⠀⠙⢄⠀⠀⠀⠀ ⠸⢿⣷⣭⠟⠎⠂⠀⣠⣮⢂⡀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀ ⠀⢸⢿⣿⣦⡀⠀⠈⠻⡅⠈⠀⢀⠠⠤⠀⡀⠀⠀⠀⠀⡰⡄⠀⠀⢀ ⠀⠀⠠⠛⣉⡍⡠⠄⠊⠁⠒⠈⣠⣄⡀⠀⠀⠰⠒⠐⠬⢖⡁⠀⠀⣸ ⠀⢰⡖⠊⠉⠁⠀⠀⠀⠁⠀⠀⣿⣿⠇⠀⠀⠀⢁⠀⠒⠀⠈⠒⠤⡟ ⠀⠀⠇⠀⠀⠀⠀⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⢄⠀⠀⠀⠜⡀⠠⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠑⠄⠀⠀⠈⠃⠘⠒⠂⠤⠤⢐⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠈⠢⡀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⡴⢇⢱⣄⣀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡥⠚⠉⠀⠀⢐⡈⠉⠓⢶⣝⣦⠀⠀⢀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⢿⠀⠀⣠⣤⠶⡋⠀⠀⠀⠀⠉⢻⣷⠞⠉⠀⠈⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⡼⢠⣾⠋⠀⣀⣤⣤⡤⣄⣀⣀⡀⢣⠀⠀⠀⠀⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⢿⣿⣷⣿⣿⣯⣥⠤⢴⣾⣿⣿⡿⣌⡇⠀⣀⠔⠁⠀⠀ ⠀⢀⡠⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢻⡅⠿⠟⠇⠀⠀⢹⣿⣛⡏⠇⢹⣏⠉⠀⠀⠀⠀⠀ ⡼⠋⠀⠀⠙⢦⡀⠀⠀⠀⢼⡇⠀⠀⠀⢾⡟⢦⡠⣤⣤⣤⡠⠤⣀⠤⣼⢸⠇⠀⠀⠀⠀⠀⠀ ⡇⡀⠀⠀⠀⠀⠙⢆⠀⠀⢸⡇⠀⠀⠀⢾⣴⡶⠈⠙⠻⠏⠒⠉⠀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀ ⡇⢱⠀⠀⠀⠀⠀⠀⠳⡀⢼⡇⠀⠀⠀⣼⣿⠃⠀⠀⣠⠀⠈⠲⣆⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⢧⠀⠀⠀⠀⠀⠀⠙⣼⡿⡀⠀⠀⠘⠦⢤⠤⠀⢋⠀⠶⠆⡸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡆⠈⡆⠀⠀⠀⠀⠀⠀⠘⣷⣳⡀⣀⠼⠂⠀⠀⠀⠈⠑⢲⠞⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⠀⠸⡀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠞⠋⠀⠀⠀⢰⠋⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢣⠀⠱⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢇⠀⠙⢄⠀⠀⠀⢀⣡⠆⠐⠢⠄⡀⠀⠀⠀⠤⠗⠒⠚⠓⠒⠒⠒⠒⠤⠤⣀⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⠑⢦⣀⠘⡇⢸⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠸⠀⠉⠑⠢⣤⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀ ⠀⠀⠀⠀⠀⠱⡄⠀⠀⢇⣠⠊⠉⠁⠈⠑⠒⠤⢤⣀⣀⣀⣀⣤⣤⣤⣶⠦⠥⠒⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣄⠀⢸⠗⠶⠦⠔⠒⠒⠂⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠉⠉⢠⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢠⠀⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⡇⢠⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠈⠘⣿⣶⣶⣶⣖⡀ ⠀⠀⠀⠀⢀⡤⣲⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢰⣿⣿⡿⠋⠉⠙ ⠀⠀⠀⣴⣯⣏⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣼⢿⢻⠀⠀⠀⢀ ⣦⣤⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣿⡊⠀⠀⠀⣠⠞ ⠈⠿⣿⣿⣿⣿⣿⣿⠀⣰⣳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⣷⡏⢇⠀⠀⠀⠀⣿⡇⠁⠀⣠⠟⠁⠀ ⠀⠀⠙⣿⣿⣿⣿⣿⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣿⣿⡟⠀⠀⠀⢰⣿⣷⣶⠊⡅⠀⠀⠀ ⡀⠀⢀⠈⢻⣿⣿⣿⣆⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣾⣿⣿⠃⡼⠁⣰⠆⠀ ⠹⣄⠀⢧⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⠃⡰⠁⢀⡏⠀⢀ ⠀⢻⡄⠘⣆⠀⢻⣿⣿⣿⣯⣦⣀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⠀⠀⠈⢿⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣸⣿⣿⢠⠃⢀⣾⠁⠀⢈ ⡇⠀⢿⠀⢹⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣴⣶⣤⣤⣤⡶⠛⠁⢀⣿⣿⣿⣞⡆⢻⣿⠀⠀⠏ ⣷⠀⢨⠃⢠⣧⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢠⠀⣸⣿⣿⣿⣧⣿⠚⠻⠀⢸⠀ ⡏⠀⡸⠀⡾⠈⢧⣈⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣂⣀⡇⠀ ⢱⡀⢁⡰⠁⠀⠀⢛⡛⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⡿⠉⠉⢉⠁⠀

⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠤⡤⠄⠀⠀⠀⠀⠀⠈⠉⠉⠒⠂⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⣀⣴⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢤⡀⠀⠀⠀⠀⠠⢄⣀⡀⠀⠀ ⠀⠀⠐⣨⠁⣨⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣋⠒⢤⡀⡀⠀⠀⠀⠈⠀⠀ ⣤⡶⣾⣿⡞⠉⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡠⡶⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢍⢷⡖⠂⠀⠀⠂⠀ ⣽⣃⣽⠏⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀ ⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⢰⣡⡆⠀⢠⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⢍⢦⡀⠀⡟⢿⠸⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣄⠀ ⠛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠝⣄⠀⠘⡆⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀ ⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢧⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⠻⣿⢺ ⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠘⠄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡎⠀⣹⣿ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀ ⣿⠛⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠻⣗ ⠉⢙⣉⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿ ⢴⣾⣿⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡸ ⣘⠛⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⣿⣷⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⣿⣿⣿⣿⠛⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀ ⣿⠿⠟⠁⠠⠀⠸⢿⣟⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⠆⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣏⣁⣀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡟⠉⢻⣶⠻⡿⠶⠶⣄⠀⠀⠀⠀⠀⢀⡶⢀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⡠⠚⠁⠀⠱⡄⠀⠱⡀⠀⠀⠀⢀⣸⣯⣼⣇⡀ ⠀⠀⢀⡀⢀⢀⣼⡏⠀⣠⠴⠊⠀⠀⠄⠀⠀⠈⣆⠀⢹⡀⠀⠀⠰⡦⣶⢷⣤⠀ ⠀⠀⠙⠛⣛⣿⠋⣶⠟⠁⠀⠀⠆⠉⠐⡞⠀⡆⠸⣦⠀⣇⣠⡄⠨⠅⣿⠒⣿⠀ ⠀⠀⡠⠘⣿⣷⡞⡡⢀⣴⡇⠤⣧⡴⣻⢁⣰⢱⡀⢿⣷⣿⠛⠁⠀⠀⠟⠉⠿⠀ ⠀⡐⣡⡞⣼⣿⢀⣇⡿⣿⣷⣿⢿⠞⣹⣟⣿⣹⣷⡌⣿⣿⡇⠀⡠⢱⢚⣢⠀⠀ ⠄⣹⡏⣰⣣⡿⡞⢸⣧⠙⠂⠁⠀⠀⠀⠻⢛⠟⣻⡇⢸⣏⢿⣎⡀⠀⢙⣁⡀⠀ ⢱⣿⣷⣿⡟⣧⣇⡇⡿⠠⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⡰⣟⠀⢹⢽⡎⢸⣿⣇⠀ ⢘⡿⣫⡿⠁⠀⠹⡐⢡⢳⡄⡀⠈⢁⣀⣤⣶⣿⣷⣒⣋⣿⣷⣿⠚⢊⢿⣻⣾⠀ ⣼⠏⡸⠃⠀⠀⣈⣵⠀⠀⠰⣍⣸⣽⣾⡿⠟⠁⢀⣴⣾⣿⣿⣷⣄⣀⡴⢆⡀⠀ ⢿⣾⣃⣠⢶⣯⣡⣼⣤⣤⣠⣿⣿⣿⡿⠃⠀⠀⠘⠻⢿⣿⣿⣿⣿⣾⣭⡭⠷⠤ ⣾⣿⠯⠔⢽⣿⣷⡼⠛⠉⠉⠉⠻⡎⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⡜⢛ ⡏⡏⣶⣠⣼⠟⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣹⢿⡿ ⢣⣽⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣹⣾⣹⡷ ⣨⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡇⠃ ⠙⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠓⠢⡤⣀⠤⠔⣿⣿⣿⣿⣿⠇⠀ ⠀⠨⢻⣿⣿⣶⣤⣄⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⣿⣿⣿⡿⡏⠀⠀ ⠀⠀⠹⣏⠛⢜⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢦⠒⠴⠆⠀ ⠋⠁⠒⠪⢄⡀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉ ⢴⠒⡶⣲⠮⣦⠝⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢖⣿⣟⣿⠛⡇⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⠦⣄⣀⠀⠀⠀⠀⢠⢺⣞⣋⣍⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢳⠀⠢⡈⢯⡉⠉⢏⡉⢹⡏⢹⡴⢶⣼⠇⠋⠁⢤⣴⡤⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠉⠱⡖⠚⢣⠀⠈⠑⠧⣄⡀⠻⠈⢷⡏⠀⠈⢻⠀⣠⡄⠀⡀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠘⢶⠀⠱⡈⠱⣦⣤⣈⡉⠉⠚⣷⠀⢀⣾⡿⢻⣿⣻⣵⣯⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⠇⠀⡉⠢⣌⠁⠂⠤⢀⣠⡏⣿⠋⠉⠉⠋⠉⠓⡏⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣈⣠⢈⠻⠶⠿⣿⣿⡟⠛⠁⠀⠀⠀⠀⣴⣾⣦⡀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢣⡄⠒⠋⢀⣽⣿⣶⠾⡿⣻⣛⠓⣶⣿⣻⡇⢀⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠚⠉⢡⠟⠁⠀⢇⠑⢚⣁⣤⣿⣡⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡠⠤⠖⠒⢒⣒⡶⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠤⣴⡇⠀⠀⠀⠈⠳⡏⠉⠉⡇⠙⣄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀ ⠚⣿⠅⠀⠀⢸⣏⣸⠏⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⢀⠞⡇⠀⢸⠈⠀⠀⠀⠀⠀⠹⡄⠀⠈⠢⡘⣦⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀ ⠀⣷⠀⠀⠀⠺⢿⡋⠀⠀⠀⠀⣀⣿⡿⠁⠑⠢⣄⠤⠚⠒⠓⠒⠸⢿⣶⠆⠀⠀⠀⠀⠛⢄⠀⠀⠘⡞⣽⣶⠄⠤⢄⠀⠀⠀⠀⠀⠀ ⠀⣿⣦⡀⠀⠀⠘⢁⣀⣀⣀⣐⣮⣿⠀⠀⣀⠞⠁⠀⣼⠊⠀⠀⠀⠀⠈⠑⢤⣀⠀⠀⠀⠀⣷⡀⠀⣹⣿⣿⠓⢂⡸⢷⡄⠀⠀⠀⠀ ⠀⣽⠛⣥⠖⡚⠉⠁⠀⠀⠀⠀⣸⢧⡶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠒⠶⡚⠁⠹⣾⡛⣉⣻⣶⣊⣑⣾⡁⣀⠤⠄⠀ ⠀⣧⣾⣷⡀⠃⠀⠀⠀⠀⣠⠊⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⠖⢉⣰⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢿⣤⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⣾⡇⠀⠀⠠⣾⢻⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⡀⡄⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠿⣿⡀⠀⠀⢻⢄⣇⠀⠀⠀⠀ ⠀⠀⠀⣿⢿⡇⠀⠀⢸⡏⠀⠀⠀⠀⢀⠀⡇⣶⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠈⠙⠻⣆⠀⠀⠀ ⠀⠀⠀⠁⠀⠙⣄⠀⢸⠃⠀⠀⠀⠀⠀⠙⢧⠙⣷⣄⠀⠘⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡆⢸⣆⡀⠀⠀⠀⠀⠀⠀⠳⣈⠛⢵⣦⣄⣼⠋⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀ ⠀⠀⠀⠀⣠⣴⡟⢹⢨⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡏⠀⣼⡄⠀⠀⠀⠉⠒⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⣿⡇⠀ ⠀⠀⣀⣴⠿⠋⣠⠎⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠲⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⣄⣤⣄⣀⣤⡿⠀⠀⢹⡇⠀ ⠤⠤⠤⢤⠖⠋⠁⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣾⣇⠀ ⣀⠀⠀⣍⣠⢤⠤⠤⢤⣈⣏⠁⠀⠀⠀⠀⠀⠀⠀⣸⠉⡇⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⡿⢿⠀ ⠒⠊⠉⠀⠀⠈⠀⠀⠘⣻⡎⠉⠲⢄⠀⠀⠀⠀⣠⠃⠀⠸⡀⠀⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣇⣼⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠷⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢣⠀⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠈ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢸⡆⠀⠀⠋⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣇⠀⢻⣌⣧⣿⣆⠀⠉⢲⠉⣹⠤⠀⢀⡇⢹⡿⠿⠉⠉⠁⠉⠀⠉⠑⠲⣧⣰⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣹⣿⣿⣿⣭⠁⠀⠸⠟⠁⠀⠀⣼⣿⣷⠖⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⡿⠙⠊⠉⠉⢀⣄⢀⡠⠀⣠⠞⣹⢿⡿⢠⣾⣿⠶⣄⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣾⡏⣿⡓⢲⡤⢤⠤⢽⡿⠗⠋⡯⢩⣧⣼⣷⣿⣝⠇⠀⢉⠿⠋⢫⠑⣂⣠⣼⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣿⣷⠏⠀⠈⠲⠤⣵⣀⣤⡞⠁⠀⠀⣿⣧⠛⠀⠠⣾⠤⣤⡾⠊⠉⠀⢘⣻⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢭⡗⠋⠉⠉⠑⢦⠈⢰⠀⠀⠀⠀⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡭⠭⡖⠂⢀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠒⠒⢲⠄⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠇⠀⣰⣠⢾⣿⠄⠘⡆⠈⢦⡀⠀⠀⠀⠀⣰⣥⣀⡠⠞⠠⣤⠤⠔⠂⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡯⣖⡹⠃⣰⣠⠇⢷⠀⠈⠑⢲⠒⢻⠛⠛⠛⠒⠒⠉⠁⠀⠀⠀⡀⢱⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⠒⠮⢽⡁⠀⠘⣆⠀⠀⢸⠀⣇⠀⠀⢀⡠⠤⠒⠋⠉⠉⠁⠀⠉⠉⠉⠉⠲⡄ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⠴⠋⢱⢄⡀⣸⣄⠀⢮⠀⠈⣱⠖⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢰ ⠀⠒⠺⠿⣶⣬⣍⡁⠛⠬⠳⢄⡀⠀⠀⠀⢀⡜⠁⡠⠋⠁⠀⡰⠁⠀⢸⠋⠀⠀⠈⣆⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠃ ⠀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣤⠴⠞⠒⠈⠁⠒⠤⠄⡇⠀⠀⠇⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣵⡀⢠⣤⠋⡠⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏⠀⣤⠀⠀⢱⠎⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣼⠉⢳⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀ ⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢈⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢹⣿⠀⢸⢸⣦⣀⣀⣀⣀⡠⠤⠤⠾⣁⣸⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⣿⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠤⠤⠤⠒⠉⠉⠁⣾⢿⣇⠸⡘⢯⡇⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣸⠁⠳⣄⡀⠀⠀⣨⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⢰⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠹⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⠀⠀⢀⡴⡃⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡜⠀⠙⢦⡀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⢶⡰⠃⠃⠀⠀⠀⡆⣦⣄⠀⠑⣄⠠⡈⠢⣢⡐⢌⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⠜⢁⠔⢸⠀⠀⡸⢹⣷⣾⣷⢦⡹⡷⡈⢲⡬⢮⡢⡙⢷⡄⠀⠀⠀ ⠀⠀⠀⡆⡜⢠⠃⢻⣸⢧⠠⠁⠈⠐⠛⠁⠘⣽⣧⠳⡀⣷⠑⠕⢌⠘⢯⣳⣄⠀ ⠀⢀⢠⡿⡰⢋⡆⢠⣽⡿⡛⡀⠀⠀⠀⠀⠀⢃⣏⣵⣳⣷⡄⠈⠢⡑⢄⠙⢍⠧ ⢴⠁⡾⡕⡇⢆⢹⣄⠻⣶⡅⠀⠀⠀⠀⠀⡰⠉⠹⣿⣿⣿⣿⣆⠀⠈⠪⡳⣄⠳ ⠸⠠⣇⢰⢸⡄⡿⠝⣳⣿⣼⣶⣤⣤⡤⠊⠀⠀⠀⠟⡙⣿⠿⠛⠁⠐⢠⡀⠈⠣ ⠇⠀⠈⢻⠛⠉⢠⡎⠁⠀⠀⠈⠁⠁⠀⠀⠐⠀⠊⠉⠉⠀⠀⡀⠀⠀⠀⠐⡀⠀ ⢻⡀⠀⠀⠀⣠⢣⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⣠⡗⣄ ⢾⠋⠀⠀⢉⠯⣭⣶⣶⡦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿ ⢸⣀⡀⠴⣉⣶⣇⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠶⢥⡵⠶⠋⢹⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠈⠁⠀⠸⠀⣧⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢸⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀⢸ ⢀⡀⠀⠀⠀⠆⠘⣆⠀⠀⠀⠀⠀⠁⠀⠀⣀⣌⣀⣀⣉⡓⠢⠤⠤⠤⣴⠪⣄⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢩⠎⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣴⡋⢠⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠋⢁⠀⡀⠁⠑⢎⣀⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⡎⢀⠷⣄⠀⠀⠀⢀⡉⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⠏⠀⠀⢀⡜⠀⡸⠀⢹⣉⡵⢶⠦⣭⣢⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⡒⠊⢉⢩⠋⠀⠀⢠⠎⠀⡴⠓⢒⣿⣽⣒⠏⠀⠈⢹⡆⠀⠘⣆⠀⠀⠀⣀⢤⡴⠶⠏⠉⠀⣀⣀⣀⣀⣀⠈⠙⠓⠒⠤⣀⠀ ⠀⠀⠈⠻⣦⡀⠀⡎⠀⠀⢠⠇⣠⠻⡆⠀⠀⠛⠛⠉⠀⠀⠀⢸⠁⠀⠀⢸⡤⡖⠫⢊⣠⣴⣶⠾⠿⠛⠋⠉⠉⠉⠑⠛⠿⠷⣶⣄⣀⠃ ⠀⠀⠀⠀⠀⠙⠺⢇⠀⠀⡞⣾⣧⣿⡿⠆⢀⣠⡀⠀⢀⡀⠀⡸⡄⠀⢀⣸⠟⠛⠚⠯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻ ⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⣿⠀⡇⠀⠀⢀⡛⠋⣀⣴⡿⢻⢀⠇⠘⣶⡉⢀⡀⠀⠀⠀⠹⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⠄⠹⢄⣀⣀⣀⣉⠉⠻⣄⣸⡼⠿⠉⠝⠊⠙⠢⡀⢠⡖⠒⢿⣆⡴⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣀⠀⣠⠞⢉⡽⠉⠀⠀⠀⠀⠀⠀⠀⠘⡾⣹⣀⢤⡟⠀⡇⢻⣆⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⠊⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⠏⠉⣛⠀⡇⠈⠒⠛⢤⣀⠀⠈⠉⠙⠒⠤⣀⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣼⠇⠀⢹⡠⠷⣆⠀⠀⠀⣿⣄⡀⠠⠔⢀⡴⠏⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠚⠁⢸⡄⠀⠀⠈⣟⠪⢍⢣⠀⠀⠋⢹⠁⢀⡴⠋⠀⠀⠀ ⠉⠒⠤⣀⠀⠀⠀⠀⠀⢴⠋⠀⠀⠀⠀⠀⠀⠠⢡⠀⠀⠠⠒⠒⠉⠁⠀⠀⠀⠀⡏⡇⠀⠀⠀⠈⢆⠀⠳⣶⡒⡒⢂⡧⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠲⣀⠀⠀⢹⠁⠀⠀⠀⠀⠀⡰⠃⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢳⠀⠀⠀⢀⣼⣧⣀⡉⠏⣠⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠣⡀⠀⠀⠀⢸⠁⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣒⣇⣀⠴⣻⣿⣿⡇⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⠲⠤⢤⡇⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢄⡀⠀⠀⠈⠙⠿⡷⠛⢡⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣦⡀⠀⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠘⢦⣿⡾⠉⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠈⣢⡀⢳⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⣍⡀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢄⡤⠖⠋⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⣻⠋⠀⠀⠉⠲⢤⡙⠀⠀⠀⠈⠳⣄⠀⠀ ⠀⠀⠀⠀⣠⠞⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⣀⣀⣀⣤⢤⣴⠶⣺⡿⠟⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣅⠁⢀⠀⠀⠱⣄ ⠀⠀⢀⡼⠋⠀⠀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⠉⠉⠉⢁⡰⣶⡿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢔⠀⠀⠀⠛ ⠀⢠⠞⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠀⠀ ⢰⠋⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣄⠀⢀⠟⣳⣀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀ ⡏⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⣿⢠⣯⠋⠁⠉⢛⠶⣔⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳ ⣟⣄⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢿⢱⠀⠀⠀⠘⡄⠈⢫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⡠ ⠈⢻⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠸⠀⠀⠀⠀⠸⡄⠀⢷⠀⠀⠀⠀⠀⠀⠀⢠⠤⣀⠀⠙⠄⠀⠀⠀⢘⠁ ⣄⠀⠙⢦⡀⠀⠀⣀⡤⠔⠚⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⡇⠀⠀⠀⠀⢳⠀⠸⡀⠀⠀⠀⠀⠀⡤⢼⠀⠀⠑⢄⡀⣢⠀⠀⠀⠃ ⠀⠉⠒⢤⣽⠢⡴⠁⠀⠀⣠⠎⠀⢀⠤⢤⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠈⡆⠀⡇⠀⠀⢠⡀⢠⠈⠈⢧⡀⠀⠀⠉⠁⠀⢀⣴⠶ ⠀⠀⠀⠀⠈⠙⠻⣄⣀⡜⠁⡠⠞⠁⠀⣸⣠⡄⠀⠀⠀⠀⠈⡄⢸⣀⡤⠖⠒⠒⠶⢤⣱⣀⡀⢸⠈⠻⡀⠂⠀⠙⠃⠀⢀⡠⠖⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠬⣀⠀⢀⡴⠁⠀⢱⢀⡀⠀⠀⠀⣷⠊⠁⠀⠀⠀⠀⠀⠀⠙⡄⠉⠉⠳⠤⢙⣂⣀⣠⠴⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢍⡀⠀⠀⡸⠉⣇⣀⠤⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢞⣠⠖⠀⣀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠑⠛⠀⠀⢀⡞⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⠛⠛⠉⠉⠉⠉⠙⠛⠛⢛⣿⣿⣿⡉⠙⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠋⠛⠛⠋⢛⣻⣿⡛⠛⠙⠛⠉⠉⠉⠛⠛⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠈⢷⡀⠁⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⡼⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⣾⣻⠇⠀⠈⢷⡀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⡾⠁⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⢀⡿⣿⠀⠀⠀⠈⢻⡀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⡾⠁⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⣿ ⣿⠉⠓⢒⣦⣄⣀⢸⡇⡿⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⢻⣆⣀⣤⠤⠤⠤⢤⣄⣀⣰⡿⠁⠀⠀⣼⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⣰⣿⣿⣿⣿⣿⢁⡇⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠘⣿⡶⠰⠁⠀⠀⠉⠀⣿⡿⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣿ ⣿⢰⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠐⠹⣇⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⢀⣤⡾⠋⠀⠐⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠙⠃⠀⢿⣅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⢿⣼⡇⠀⠀⠀⣠⡿⢏⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣄⣈⠙⢷⣆⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣿ ⣿⠈⠉⠛⠻⢿⣿⢸⣿⡇⠀⣠⡾⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠉⢻⣿⣿⣿⣿⣿⣷⣶⣭⣻⣦⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠈⠛⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣧⡀⠀⠀⠀⣼⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⡏⠀⠙⠛⣿⣿⢿⣿⣶⡇⠙⠶⠶⠚⢹⡶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⣼⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣧⣼⣷⣭⣣⠀⠀⠀⠀⡞⢛⣽⣏⠀⣸⣿⣧⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⣸⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣧⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⣿⣦⣼⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣯⢧⡀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⢻⡟⢿⣧⣀⣿⣿⡅⠉⠛⠿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⠳⣄⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠹⣆⠉⠻⣿⣿⣷⣤⣤⣀⣀⣤⣄⣀⣉⠻⣍⠉⠉⠉⠉⠉⠉⠹⠛⣉⣉⣭⣍⣀⣀⣠⣿⣿⣿⣿⣿⠋⠀⢀⣾⠆⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠈⢻⡄⢹⣿⣿⡙⠛⢿⠛⠛⢛⣿⣿⣿⣶⣄⠀⠀⠀⠀⣠⣶⣿⣿⣿⡛⠛⠛⡟⢻⣿⣿⣿⣿⡏⣠⣴⣾⠏⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣇⠀⠚⠓⠢⠽⠿⠿⠿⣿⠅⠀⠀⠀⠐⠩⣿⣿⠿⠿⠥⠔⠚⠢⣼⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⢀⡴⠋⠁⠸⢹⣿⣿⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢹⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⢀⡴⠋⠀⠀⠀⡰⠋⠀⠙⠳⣄⠉⠑⢲⠲⠤⢄⡴⠶⠖⠒⠶⠶⠾⢯⡤⢴⠖⢺⠉⢀⡠⠴⠛⠹⣳⡀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⢀⡞⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠈⠓⢦⣼⠀⣰⠿⠓⠒⠒⠒⠒⠦⠤⣀⡙⣆⠀⢸⢞⡩⠀⠀⠀⠀⠑⢽⣄⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⢸⠁⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⢫⣞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣆⠘⢫⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⢾⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢀⡠⠔⠓⠋⠉⠑⠒⠒⠢⡀⠀⠀⠀⢄⣠⠚⠙⢄⠑⣄⢣⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣿ ⣿⠀⠀⠸⡆⠀⠀⢸⠃⠀⠀⣠⡴⣾⣻⠁⠀⠀⠀⠄⠀⠒⠤⠤⠬⣦⡀⠀⢀⣧⡀⠀⠀⠁⠈⠙⣧⣀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣿ ⣿⠀⠀⠀⢳⡀⠀⡞⣠⠴⠛⠁⣰⡏⡇⠀⠀⠀⢀⣠⠤⠖⢢⢄⣠⠞⠁⠀⡰⠁⠈⠉⠁⠀⠀⠀⢹⠘⣯⠓⠲⠤⣄⡀⠀⢳⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠳⣴⠿⠁⠀⠀⢉⣿⠁⡇⠀⢀⣀⣤⢤⣶⣲⣏⣁⠽⠚⠁⡰⠿⠶⣿⣧⡀⠀⠀⡀⡸⢠⡿⠈⡀⠄⢀⠍⠳⢾⡆⠀⠀⣿ ⣿⠀⠀⠀⠀⣰⡏⠀⢀⣀⣶⣿⣿⣧⣹⣿⣭⡥⣶⠚⢯⠀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠻⢷⡀⠀⣨⣧⣿⣅⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣿ ⣿⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⢸⠀⠸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣿⠀⠀⣿ ⣿⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠛⠲⣾⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠛⠙⢿⣿⣿⣿⣿⣦⣀⣀⣾⠃⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠁⠀⠀⠀⣿ ⣿⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣤⣤⣤⣤⣤⣤⣤⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣠⣄⣤⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣿

⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢼ ⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢏⠻⣿⣿⣿⣼⣿⣿⣟⢿⣿⣿⡟⣿ ⡛⠉⠩⠷⡘⣿⠿⠻⠿⢻⣿⣿⢏⣤⢆⣼⡜⣦⣈⢿⣿⡇⢿⣿⠟⠻⣿⣿⣿⣿ ⢷⣄⠀⠀⠱⣘⡖⠀⢠⢯⡿⠀⣾⣳⡟⠙⣿⣌⣿⡄⢿⣿⣸⡏⠀⢀⠘⣿⣿⣿ ⠀⠹⡶⠔⠲⢿⣼⣦⣷⣿⢁⣾⣿⡟⠐⠒⠛⠻⣿⣷⠘⣿⣿⣷⣯⠩⣻⣿⣿⣿ ⠀⢰⠁⠀⠀⢢⠈⢿⣿⣇⣼⣿⣹⠀⠐⡿⠿⠟⢻⣿⡀⢿⣿⡏⠀⠀⠀⠘⣷⣳ ⠀⠘⡀⠀⢀⣠⣷⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⣽⣿⡇⣾⣿⡇⣀⣠⣤⣀⣿⣇ ⠀⠀⠱⣴⣟⠡⠛⠙⢟⣿⣿⠀⠀⣀⣀⢀⡄⢴⣿⣿⢰⣿⣿⣿⣿⠿⠟⠿⢿⣿ ⠀⠀⠀⠹⠋⠀⢀⣠⣬⣿⣿⣷⡔⢷⣯⠏⠁⠨⣿⣇⣾⣿⣿⣿⠁⠀⠀⠀⠸⣿ ⠀⠀⠀⠀⠱⣠⣾⠗⠉⣽⠋⠙⣿⣦⡀⠀⣀⠐⣿⣿⣿⠟⡟⠁⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠈⢋⠀⠀⡇⠀⠀⠉⢟⡟⠛⠟⠈⣿⣿⢃⠴⠁⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠉⠀⠀⠀⠈⠐⠀⠈⠉⠿⢄⡀⠀⠀⠀⠀⠀⠀⢰⢿ ⠀⠀⠀⠀⠀⠀⠀⢀⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠢⠀⢠⡿⣼ ⠀⠀⠀⠀⡠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⠋⣿ ⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⣿ ⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⣿ ⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠀⣿ ⠀⠀⠀⠈⠐⠢⠔⠶⣦⠄⡲⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⢤⣴⣶⣿⣿⡷⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠃⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠤⡤⢰⣰⡒⠒⠒⠒⡢⠀⠀⣖⣎⣱⠀⣠⣄⣂⣒⣰ ⠀⠀⠀⠀⠀⢀⡤⢫⢊⠡⢠⠖⢹⣕⠁⢀⠖⠘⡙⢞⣶⠿⢉⣄⣨⡃⢤⠤⠤⠀ ⠀⠀⠀⠀⠀⢸⡄⠸⠁⢠⠁⠀⠸⡝⠀⠈⠑⣆⡀⢺⡿⢀⡆⢦⣠⢠⠤⠼⠀⡌ ⠀⠀⠀⠀⠀⠺⡣⢄⠀⢴⠀⠀⠠⣹⣴⣶⣮⣍⡘⡞⠀⠀⠙⠂⠉⠁⢈⠭⠑⠂ ⠀⠀⢈⣠⣴⠿⠻⡇⠢⣈⣆⡔⠉⠀⠀⠀⠀⠉⠛⢿⣆⠀⠀⠀⠀⠀⠸⠀⠀⠀ ⠀⢠⣾⠟⢁⠄⠂⠈⡟⠉⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡤⢴⠂⢶⣆⣤⠔⠰ ⢀⣿⠃⢀⠂⠀⠀⠀⠳⣿⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠆⢱⠀⢰⢻⡀⠀ ⢸⡿⠀⠀⠀⠀⠀⠀⠀⡀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣼⣤⠷⠚⠵⠶ ⠀⣇⠀⠀⠀⠀⠀⠀⠀⢃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠐⢂⣀⣉⣩⠉⠤ ⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠑⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠠⠊⠀⠀⠀ ⠀⠀⢣⠀⠀⠂⢀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠄⠀⠀⠀⠀⡌⢀⣀⣀⠀⠇⠀⠀⠀ ⠀⠀⠀⠱⡄⠀⠀⠁⠢⢀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⡏⢢⣄⠀⠀⠀⣀⠴⡛⣗⠢⠤⠤⠤⠔⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠈⠁⠀⢰⠀⡏⣏⡉⠉⠣⠞⡴⣿⡠⡀⠀⠀⣀⣜⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠂⢵⢮⡯⣼⡿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡌⡸⣜⣿⣟⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠇⠈⡔⠤⠠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣸⠀⠱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠼⠠⢄⡁⣠⠑⣢⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⢀⣆⡇⠀⠢⡋⠛⠠⡀⠀⠀ ⠀⠀⠀⠀⠰⠁⢀⣞⢻⠀⠠⠆⠈⣄⠀⢸⠆⠀ ⠀⠀⠀⢠⠃⠀⡎⠰⡈⢳⠥⠤⠛⢹⡖⠉⠀⠀ ⠀⠀⠀⠘⣅⠀⠁⠂⢧⣀⠀⠀⠂⡇⢃⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⡩⠟⢺⡄⠓⡦⢠⣇⠘⡆⠀⠀ ⢸⡑⠂⠤⢄⠎⠀⠀⠸⣸⣿⡿⣸⠘⢆⠘⡀⠀ ⢯⠉⢒⡒⡯⠅⠀⠀⠀⠉⠉⠁⠛⠢⢀⣣⢡⠀ ⠀⠚⠁⠴⢿⡈⠁⠒⠂⠀⠀⠀⠀⠀⢀⡈⠙⢤ ⠀⠀⠀⠀⠀⠙⠠⠤⠤⢤⣤⠖⠉⠉⠈⠀⡠⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠃⠀⣀⣀⣴⠊⢡⠀

⣿⣿⣿⣧⢸⢹⠉⠑⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣴⣿⣷⢶⣶⣾⣿⣶⣾ ⣿⣿⣿⣿⣾⣸⡄⠀⠀⠀⠀⠀⡟⠣⡒⠠⠄⣾⣄⠀⢽⣿⣿⡿⢠⣙⠻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⡇⢹⣄⠀⠀⠘⢿⡿⡫⣻⣽⣽⣲⢤⣈⣝⢿⣿ ⣿⣿⣿⣿⠟⣿⣿⣿⣿⣮⡲⠼⢧⣤⡯⠀⠀⠀⡰⣏⣼⣿⠟⢘⣿⠷⣽⡙⢯⡟ ⣿⣿⣿⣷⣾⣿⣿⣿⣿⡥⠤⢖⢕⣄⠇⢀⠔⠑⠓⠿⣷⡅⠀⠀⠀⣹⣾⣅⡈⠳ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣠⠴⠋⠀⢸⡀⠀⢀⡠⠈⠩⠶⣤⣶⢟⡿⣠⣷⡀ ⣿⣿⣿⣿⣿⡿⠁⠀⠈⢻⣆⠀⢀⡠⠄⠋⠉⠛⡏⠀⠀⠀⠀⠸⢻⡏⠉⠣⠿⠷ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡻⠊⠁⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠇⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠾⢿⣇⢀⣲ ⣿⣿⣿⣿⡄⠀⠀⠀⢰⢀⠄⠂⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⣋⣿⣿⣿ ⣿⣿⣿⣿⣷⠀⢄⣀⣼⡷⠶⠶⠶⣦⣄⠀⠰⠛⢋⠭⠙⠫⠄⣀⠴⣺⡯⣿⣿⣿ ⣿⣿⣿⣿⣿⣻⣿⠛⠁⠀⠀⠀⠀⠀⠻⣦⣣⣾⣷⣤⣘⣋⣉⣠⣮⠟⣰⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⢄⣸⠁⠈⡆⠐⠁⠀⠈⠀⠀⠀⢀⣔⠐⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⡴⠀⢻⠀⢀⡇⠢⡀⠀⠀⠢⢀⠰⡁⠀⡈⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠹⠓⠃⠀⠯⢵⠀⠀⠈⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢀⡀⠀⠀⠘⠆⣤⣎⢀⣖⢭⠍⠀⠀⠀⠀⠀⠔⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⠸⠄⡔⠱⡤⠤⡴⠋⠀⠀⠁⠑⠒⠒⠉⢀⣀⡤⠤⠤⢶⣁⠀⠎⠐⠀⠀ ⠀⠀⠀⢱⠀⢹⣠⠗⠚⠃⠐⠒⠧⣄⣀⣨⠴⠊⠉⠀⠀⠀⠀⠀⠈⠳⣎⠀⠀⠀ ⠀⠀⠀⠘⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀ ⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀ ⣶⣶⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⣓⣩⣧⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⢀⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⡨⢿⣰⡹⠁⣵⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠰⠁⢀⡏⠁⠘⠉⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠁⠀⠙⢄⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡸⡇⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢸⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠃⣧⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀⡞⠁⠀⢸⠀⠀⢲⡀⠈⣧⠀⠀⠀⠀⡏⠀⠀⠀⡇⠀⡗⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠁⠀⠀⠉⠑⠤⣰⠏⠀⠀⠀⢸⡄⠀⠀⢇⠀⢸⡇⠀⠀⢀⡇⠀⠀⠀⡇⢰⠃⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⢀⡇⠀⠀⣾⠀⠀⠀⢀⣧⡾⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡼⠀⠀⠀⡘⠀⢸⠇⠀⢀⠏⠀⠀⢀⡼⡹⠁⠀⠀⠀⣀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⣾⠁⠀⠀⠀⠀⣸⠗⠀⠀⣴⠇⢠⡟⠀⠀⡼⠀⠀⢀⠇⢰⠃⠀⠀⢠⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡰⠋⠈⠀⠀⠠⢔⣻⡃⠀⣀⠞⠁⣠⣵⣇⡀⣰⠃⠀⠀⠸⣴⠇⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠞⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠉⠛⠤⠤⠛⢻⢿⡀⠀⣀⣰⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⣠⠖⠏⢳⡀⠀⠀⠀⠀⠀⠀⢸⣾⢻⡷⢶⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢰⣧⣶⡞⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡇⠀⠀⠀⠀⠀⢠⣿⣿⣮⡀⡟⠰⠠⠊⠉⢦⡀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⢿⣿⣷⣭⡃⠀⠀⠺⠗⠀⢳⢆⢀⡴⣹⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⢳⣦⣄⠀⢀⠁⠀⠈⠙⠋⠐⡇⠀⠀⠀⢀⡞⣨⠏⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣹⣷⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡞⣠⠃⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⣿⠓⠀⠀⠀⠀⣰⣿⠀⢀⣾⣲⠃⠀⣸⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣋⡀⠀⠀⠀⣠⣿⡟⢀⠎⢘⡇⠀⢰⡇⠀⢸⡄⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⣥⣾⠁⠀⠀⣴⡿⠉⢹⠏⠀⣼⠀⠀⠘⡇⠀⠈⠓⠀⠀⠀⠀⢰⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢽⣧⣴⠒⠉⢹⡝⠀⣸⠀⣰⢿⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠸⡷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠁⣰⠇⠀⠀⠀⠀⢰⠏⠳⣄⠀⠀⠀⠀⠀⠉⠙⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢠⠏⠀⠀⠀⠀⢰⡟⠶⠺⠿⢷⣄⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⡞⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠱⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⣀⠴⠋⡽⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠉⠉⠀⣰⠃⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠑⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⢸⡇⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⡀⠀⠀⠉⠲⣔⠒⠈ ⠀⠀⠀⠀⠀⣀⡤⣴⠋⠉⢸⣆⠈⠳⣄⠀⠀⠀⡜⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⠇⠀⠀⠀⠀⢀⡭⠞ ⠀⢀⡴⢾⡽⣶⣿⣿⡄⠀⡜⠈⢳⣎⠭⠷⠚⢰⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡁⠀⠀⠀⣀⡠⠊⠀⠀⣀⡴⠚⠁⠀⠀ ⠀⣿⡄⠀⠙⠿⣿⣿⣿⠎⠀⠀⠀⠘⣦⢀⣀⡼⣧⠀⠀⠀⠀⠘⠤⠄⠀⠀⠀⡰⠁⠐⠚⣉⣀⡠⠴⠖⠛⠛⠲⠦⢤⣀⣀ ⠀⠹⣝⠀⠀⠀⢹⣟⠁⠀⠀⠀⠀⠀⠈⡟⠻⡬⠿⢷⣄⡀⠀⠀⠀⠀⣀⡤⠼⠗⠒⠛⠛⠛⠓⠷⠶⣦⡤⢤⣀⠀⠀⠀⠀ ⣀⣤⣾⠂⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⣰⠃⠀⡇⠀⠀⠈⣉⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⣛⡿⣦⣄⠀ ⣾⡏⠀⠀⢀⣶⣄⠀⠀⢯⢶⡶⣖⡒⠁⠀⠀⣷⣤⡴⠚⠁⣀⣀⣠⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠙⠽⣿⣦ ⠘⡇⠀⢀⣾⣿⣯⣇⠀⠈⣷⣍⠂⠀⠀⠀⣠⣿⠽⠚⠓⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠑⢲⠏ ⠀⢻⣄⣿⣿⢿⣿⣷⣀⣥⣿⣏⣷⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣷⠿⠟⠋⠀ ⠀⠈⣻⡈⠻⠶⠦⠭⠿⠿⠛⠉⠈⠉⠉⠉⠉⠓⠒⠒⠶⠦⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠴⠶⠟⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠛⠒⠶⠤⠤⠤⠽⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠐⠉⠉⠉⢻⣿⣿⣿⣿⣶⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⢄⡀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⡇⠀⣼⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠉⠓⢤⡚⠉⠉⠉⠛⢏⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⣧⢰⡏⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢱⠁⠒⣬⣢⢄⠀⠀⠀⠈⠢⡀⢀⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⣿⣿⡁⠀⢸⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠟⠋⠉⢳⡀⠑⢦⡀⠀⠀⠈⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⣶⣿⣿⣟⣉⡒⣼⠀⠀⠀⣿⣿⡦⠶⠶⠀⠀⠀⠀⠀⠀ ⠀⢨⠃⠀⠀⠀⠀⣇⠀⠀⠿⡖⡄⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣿⣥⣿⣋⣹⣿⡋⢙⣻⣆⠀⢰⣾⣿⣷⡈⣷⣤⣤⠀⠀⠀⠀ ⡿⠋⠀⠀⠀⠀⢠⢃⡀⢀⣸⡟⠸⡄⠀⠀⡟⠋⠁⢸⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢡⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣠⠯⣄⠙⢾⣿⠇⠀⢹⡀⠀⠸⡀⠀⠀⡇⠀⠀⠀⣏⠙⠛⠿⢿⣿⣯⣽⡟⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠦⠤⠤⠟⠁⠀⠀⠙⠷⠮⠧⢤⣞⣀⠄⣀⣇⠀⢀⡷⠔⠒⠂⠛⠿⣶⣶⣶⠈⠉⠃⠀⠀⠛⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠈⠀⢿⣧⣄⣀⣠⠀⣠⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡀⠀⠉⣦⣙⢦⡉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⣿⡙⠒⢿⠁⠈⠓⠢⠄⠧⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣸⣆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡿⠄⣉⣽⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢤⡷⣼⡟⣽⡞⢻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠀⠓⠒⠛⠤⠴⠧⢄⣀⣀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠘⠻⠟⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣠⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠉⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠁⠀⠀⠀⠀⢀⡴⠋⠀⢱⡼⠀⣠⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣦⡀⠀⠀⢀⠎⠀⠀⢠⠎⣠⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣠⣿⣿⣷⣄⢀⡞⠀⠀⣠⣇⡼⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠿⣿⣿⣿⣿⣿⠉⠉⠐⣏⠀⣰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡸⠔⠒⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⠛⢿⣿⡿⠀⠀⠀⠉⢲⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣨⡦⠠⠴⠦⠤⠜⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⠋⢀⠄⠀⠂⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⡟⢻⣿⣿⡶⠿⠛⠛⠛⠉⠛⡛⢮⣿⡷⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣤⣾⢛⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⣽⣿⣄⡛⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠂⠒⣶⠴⠚⠉⠉⠓⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⡿⣿⡶⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⢰⠁⠀⠀⠀⠀⢰⣿⡿⣷⡀⠀⠀⠀⢀⡤⠒⠿⣿⣦⠀⠀⢻⣷⠌⢱⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⡿⠃⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠙⣿⣻⡿⣷⠀⠀⢀⠋⠀⠀⢠⡾⠿⠀⠀⢸⠈⣾⡏⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣇⡀⠀⠀⣠⢞⠁⡄⠀⠀⠀⠀⠸⣿⣻⣿⣿⡇⠀⠘⣤⣤⣴⢿⡀⠀⠀⣠⢯⣾⣻⣍⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠈⠢⣀⡇⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⠀⠀⢻⡘⣏⣻⣯⣶⣾⣷⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⢴⣶⣿⣼⣿⠀⠀⠀⠙⠻⠿⣙⣿⣿⣿⣿⣿⣦⣤⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢾⣽⣿⣹⣿⡆⠀⠀⠀⠀⣠⣿⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣶⡄⠀ ⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀⠀⠀⢰⢷⣾⣟⣿⣿⣿⣿⣻⠿⠛⢾⡉⣉⡵⣄⡉⢛⢿⡇⠀ ⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠙⠿⣿⣷⣦⣌⣼⣿⣿⣿⣿⣿⣿⠃⢀⣼⣯⡞⠋⠀⣿⡘⠈⣾⠃⠀ ⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣩⣿⣿⡇⢆⠀⠘⠻⣻⡿⣿⣿⣿⣿⣿⣿⣿⣤⢺⡿⠋⠀⠀⣼⣻⢷⣠⠇⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣟⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣻⣿⣿⠇⠀⠇⠀⠀⠈⠳⣝⠻⠿⠿⢿⣿⣿⢿⣿⡀⠠⣀⣀⡹⠋⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⡧⠀⠀⠀⠘⡄⠀⠀⠀⢀⢸⣿⡿⣿⠀⠀⢰⠀⠀⠀⠀⠈⠑⠂⢬⡀⠀⠙⢻⣿⣿⣶⣖⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣀⣀⣀⣅⠀⠀⢠⠋⢠⣿⣳⣿⣖⠞⠁⠀⠀⠀⣠⠄⠀⠀⠀⠙⢄⠀⠀⠹⢿⣿⢾⣿⣶⡾⢧⠀⠀⠀⠀ ⠀⢀⣴⠾⠛⠛⢛⡿⠛⠉⠀⠀⠀⠈⠉⠐⠛⠀⣿⣿⣿⡟⠉⠙⠒⠤⡠⠊⠀⠀⠀⠀⠀⢀⣴⢷⣄⠀⠈⠹⣿⣿⣟⡵⠋⢿⣶⠄⠀ ⠒⠋⠁⠀⢀⠔⠁⠀⠀⠀⠀⢀⣠⢤⣴⣲⣤⣸⣿⣿⡎⢣⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠳⣄⠀⠈⠙⠻⣷⣶⣿⣿⣄⠀ ⠀⠀⣠⠖⠁⠀⠀⠀⠀⣰⣯⣿⣿⢿⣿⡟⣭⣿⣿⣿⣁⣀⣑⣄⣠⣤⣼⣤⣀⣀⣀⣀⣸⣿⣶⡦⠦⠤⠶⢿⣦⣄⣀⣀⠉⠛⠻⢯⡇ ⠀⠀⠀⠀⠀⠀⠀⠰⢢⣿⣷⣾⣷⣼⣛⣧⣾⣿⣿⠯⠤⠼⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠚⠿⠾⠟⠃⠈⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀ ⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠱⡀⠀⢀⢤⠎⠀⠀⠀⠀⠀⠀⣱⠠⠀⠀⠠⠂⠀⠀⠀⠀⠀⢀ ⢳⠀⠀⠀⠀⠀⠀⠐⠄⡌⠀⡕⡀⠀⠀⠀⠀⠀⡜⠀⠃⠠⠁⢀⠄⠀⠀⠀⠀⡄ ⠈⢣⠃⢀⡀⠀⠀⠀⠈⢂⠀⠈⣱⣴⠚⣿⣷⣦⡇⠀⡸⢃⠔⠁⠀⠀⠀⠀⡼⠁ ⠀⠀⠑⢄⣌⣀⠀⠀⠀⠀⠑⣄⣿⢿⠄⠱⠿⣿⡀⡔⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀ ⠀⠀⠀⣀⣬⡿⠟⠛⠛⠓⠤⠸⡟⠆⡀⢀⡼⠛⡻⠀⡀⣈⡥⠴⠾⣯⢀⡀⠀⠀ ⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⣵⠀⠈⡎⠀⢠⠁⠂⠉⠀⠀⠀⠀⠀⠁⠈⠃⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⢶⣿⠶⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠁⠀⠰⣿⠄⠀⠉⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⣯⡄⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠈⡿⠿⣾⢻⣛⣳⠀⠀⠀⠀⠀⠀⠀⠾⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠒⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠒⢄⠀⠀ ⡀⣐⠍⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⢂⠀⠀⠀⠀⠀⠀⠑⠄ ⡟⡍⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣤⠈⡆⠀⠀⠀⠀⠀⠀⠈ ⡰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢠⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⢀⡤⠊⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠣⠀⠀⠀⡀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⢀⣠⠴⢎⡀⣀⠤⡊⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣶⠛⢀⠄⢤⡎⠀⢰⠋⠀⠉⠁⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⠁⢠⡏⢰⣭⣇⣠⢾⠀⡀⢀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⢀⣼⡟⠀⣠⢃⠇⠀⣦⢹⠁⠀⡆⠉⠙⠄⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣠⣿⡟⠀⢠⠃⢸⣤⣄⡌⠑⠁⠀⠃⠀⢀⡤⠀⠀⢸⠘⢧⠀⠀⠀⠀⠀⠀⠀ ⣾⠟⣹⠁⢀⠓⠀⢘⣛⡿⠁⠀⠀⠀⡇⢀⡞⠁⠀⠀⡜⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⣼⣧⠀⠈⠀⠀⠀⠀⡇⠀⢷⡾⠀⣠⣄⣶⠃⠀⠀⣿⢷⡀⠀⠀⠀⠀ ⠀⠈⠀⢰⣿⡿⠀⢲⠤⠤⠤⠐⠇⠀⠸⠏⠙⠋⠛⡏⠀⠀⠀⣿⠀⣷⡀⠀⠀⠀ ⠀⠀⠀⣾⣮⡇⠀⢸⣦⣄⠀⢼⠀⠀⠀⡷⠂⠉⣹⠀⠀⠀⢠⡿⠀⠸⣷⡀⠂⠀

⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⢿⣿⣹⠀⠈⣉⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⡀⢀⠈⡋⠙⠛⣿⣿⣏⣸⣿⣼⡀⢠⣼⣿⡇⣻⣿⣿⠛⠋⡏⠂ ⠁⡈⠀⣿⣷⣤⡟⠁⠀⠉⠢⠀⠱⠂⢀⠖⠉⠀⠉⣿⣤⣾⡇⠙ ⡄⢠⠀⡇⠀⠉⢿⣍⠳⢶⡦⡇⠀⠀⣖⠶⡶⢞⣩⡿⠃⠀⡖⠄ ⠀⠀⠂⡘⣦⣤⣼⣇⠀⠉⠉⠈⠀⠀⠉⠉⠉⠀⣾⣇⣤⣶⠃⠀ ⠀⠀⠀⠀⠢⡈⠹⠛⠂⠑⠦⡔⠉⠉⢢⠴⠞⠘⠛⡝⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠂⣤⢠⠀⠀⣦⠄⠠⣴⠀⠀⡀⠀⠱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠟⠊⠀⠀⠈⢙⠞⠉⠀⠈⠁⢄⣸⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⠀⠈⣇⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢀⣿⣀⣀⣿⣀⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢠⡄⢄⣢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣯⡇⢘⣬⣿⣿⣿⡿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠙⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏⣼⣷⡆⢸⣶⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡆⠀⠀⣠⣶⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡯⢴⣿⠿⠿⠾⢿⣿⣿⣿⣇⢸⣿⣿⡏⠁⠀⢰⠀⣴⣤⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⣶⣶⣾⡷⡀⠀⢀⣶⣭⣥⣤⡭⠿⣿⣧⣤⣴⣾⠹⠉⡏⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠒⠢⡞⠉⠉⠙⠻⣤⣈⣛⣛⣡⡇⠀⢸⣌⠻⠿⠟⠁⣀⣿⡏⠉⢁⡠⠤⠗⠓⠒⠒⠒⠤⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⡀⢸⢷⣄⡀⠀⢀⠄⠀⢄⠉⠉⠉⣉⠽⠋⠑⢞⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠄ ⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠒⠓⠁⠀⠋⠋⡹⠓⠤⠤⠒⠉⢢⢠⠋⠀⠀⠀⢸⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠐⡏⢄⠰⡄⢣⠞⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡄ ⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡠⠀⣤⠀⢤⡾⠄⠀⠉⠉⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡇

⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣆⠁⠛⠁⠀⠀⠀⠀⠀⢀⢹⣿⣿⡇⢯⢻⣿⣿⡹⣄⣿⣧⠁⠀⠙⣿⢿⣿⣿⣷⠀⢻⡄ ⣿⣿⣿⣷⣿⣿⢸⣿⣿⣿⣿⣿⡿⡏⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣨⡿⣿⣿⣷⢸⡌⣿⣿⡗⠏⠀⢻⡆⠀⡀⠸⣿⣿⣿⣿⣇⠈⢿ ⣿⣿⣿⣿⣏⣿⠀⣿⣿⣿⣿⣿⡇⢣⢸⣿⣿⣿⣧⠀⡀⠀⠀⢠⣶⣿⣿⣷⣿⣿⣿⠖⢷⢻⣿⠁⢀⣀⣨⣿⣾⡁⠀⠈⣿⣿⣿⣿⡄⠘ ⣿⡏⣿⣿⣿⡟⠀⠘⢻⣿⣿⣿⠁⠀⠈⣿⣧⢹⣿⡶⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣷⠀ ⣿⡇⠸⣿⣿⣷⠀⠀⠘⣿⣇⢻⡀⠀⠀⢻⣿⣶⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣵⣿⣿⠛⠉⠁⠈⣿⣿⣹⣿⡄⠀⣿⣿⣿⣿⡇ ⣿⣿⣄⢻⣿⣿⡆⠀⠀⣿⣿⠘⣧⠀⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⣿⡟⠙⣿⠀⠀⠀⠀⣿⡉⣿⣯⣽⡄⢹⣿⣿⣿⣷ ⣿⣿⣿⠈⣿⣿⣿⠀⢸⣿⡽⡄⢹⣀⣼⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡼⣿⠿⠃⢰⠇⠀⠀⢀⣤⣾⠇⣿⣿⣿⣷⡞⣿⣏⡈⣿ ⣿⣿⣿⠀⡏⣿⡏⣇⣸⣿⣇⡡⠼⣿⣿⣿⡇⣧⠰⠸⣿⡆⣿⣿⡿⠟⠉⠀⠀⢡⣿⠆⡴⠋⠀⢀⡴⡵⠂⡟⠀⢸⣿⣿⣿⡃⣿⣿⡇⢈ ⣿⣿⣿⡆⠀⣿⣇⣸⣿⣿⡥⠤⠤⢿⣿⡿⠁⡞⠀⠀⢿⠀⠛⠉⠀⠀⠀⠀⠀⠘⠇⠈⠀⢀⠔⡫⢊⡡⢾⠂⠀⢨⡏⣿⣿⣿⣿⠿⡇⢘ ⣿⣿⣿⣧⠐⣿⣏⡼⣿⣿⣤⣶⣶⣾⣿⣷⣿⡅⠀⠀⢸⠀⠱⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠧⠤⠔⠋⠀⠀⢁⠀⣸⠃⣿⣿⣿⣿⣷⠀⢸ ⠘⣿⣿⣷⠀⣿⣿⣾⣿⣿⣯⡥⢬⠉⠁⣼⠏⠉⠒⠀⠀⠀⠀⠇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠊⠀⣹⣿⡟⣿⣿⠀⠘ ⡆⠉⢻⣿⣿⣿⣿⠟⠁⠀⠈⠠⠚⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣧⣿⡇⠀⠀ ⢷⡀⢨⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠿⣿⣿⣷⡀⠀ ⠓⠻⡍⠉⢿⣿⣿⣦⣀⡠⠀⠠⢤⡀⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣿⠀⣿⠏⠻⢿⣤ ⡤⠤⠿⣜⣎⣿⣷⣨⡙⠦⢀⡒⢂⡼⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢰⡟⠀⠀⠀⠈ ⣷⣶⣦⣌⣿⣿⣿⣿⡕⢄⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⡟⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡞⠀⠀⠀⠀⠀ ⡴⢿⣮⣿⠿⢿⣿⣿⣟⣆⢓⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠁⢿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⡃⠀⠙⢿⡀⢀⣿⣿⣿⣿⣦⡀⡄⠀⠈⠢⡀⠀⠀⠀⣶⡄⣴⣶⠶⠶⠿⢿⡏⠀⠀⠀⠈⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⠈⢇⠀⠀⠀⠀⡀ ⣿⣶⣶⣤⣽⣿⣿⣿⣿⣿⣿⣝⠾⣄⠀⠈⠿⠀⠀⠀⣿⢣⢧⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢣⠀⠀⢠⡾⠁⠙⠻⠿⣿⣇⣀⡠⠔⠒⠁⠀ ⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠣⣀⠀⠀⠀⠀⢻⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⡄⢰⣿⠃⣀⠤⠴⠒⠋⣉⡤⠔⠀⠀⠀⠀ ⣿⣿⣿⣀⣀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⢵⣄⣀⠀⠀⠑⠮⣁⠳⢄⡀⠀⠀⠀⣀⡤⠒⠋⣰⣏⡿⠋⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡻⣿⣌⠻⢿⣿⣿⣿⣿⣿⣿⣇⠲⢤⣈⠉⠙⠓⠒⠦⠽⠶⣛⣛⣉⣹⠁⠀⢀⣴⣫⠞⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢻⢿⣿⣧⢹⣿⡷⣨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠺⠦⢤⡀⣀⡠⠤⠚⠚⠛⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡅⠈⢇⢹⣿⡄⣻⢯⢸⣿⣷⡽⣿⣿⣿⣿⠁⠀⢀⠀⠀⢀⡤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⢆⠘⡂⠹⣿⠟⢾⠷⡿⣿⢿⣎⢿⣿⡏⠀⠀⠈⣡⢔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⡻⣷⣜⣢⠀⠀⠀⠀⠀⠉⡶⡛⠟⠙⡧⠈⠋⠿⣻⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⢿⣼⣇⠀⠀⠀⠀⠀⣿⡻⠾⣴⣲⠃⡾⢣⣭⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣯⡿⢸⠀⠀⠀⠀⢰⢹⠾⢷⣤⣿⣀⡻⡋⠏⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⡆⢢⣀⡀⠀⢰⠏⠉⠉⠑⠢⢄⠸⣿⣷⣡⡀⠀⠀⠀ ⠀⠀⠀⣀⣤⣾⡿⡺⠋⠁⠛⢼⠀⢉⠹⠥⠛⠁⠀⠀⠀⠀⠑⢄⢩⣤⠹⢦⡀⠀ ⢀⣾⣾⡇⣸⢃⠎⠀⠀⠀⠀⠈⠣⡘⣧⡈⡄⠀⠀⠀⠀⠀⠀⠀⡩⢁⣰⠿⣯⠀ ⡼⠋⠁⣸⠉⡈⠀⠀⠀⠀⠀⠀⠀⠐⣼⣷⢰⠀⠀⠀⠀⠀⠀⠀⠇⠙⠻⣶⡜⢡ ⡇⠀⣿⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢙⠀⠡⡀⠀⠀⠀⠀⠰⠀⠀⠘⠖⢀⡜ ⡆⠐⠛⠡⣦⠐⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡵⢤⢈⠐⠂⠤⡴⠡⡄⢰⠛⡆⢸⠀ ⢹⠀⢠⠾⢷⢄⠈⠢⡀⠀⠀⠀⠀⠀⡆⢸⣷⠀⢯⠂⢀⠤⠑⢪⡂⣘⣶⠇⠈⠚ ⡼⠀⢿⡀⣺⠀⢣⣠⠚⣢⣄⠀⠀⠀⣧⣸⣿⡇⡇⢠⠃⠀⢀⠋⢁⡀⠀⣠⡔⣢ ⣁⣄⡘⠛⢁⡄⠚⠓⠈⠉⠀⠀⠀⠀⢸⣵⣽⣿⠁⠈⠀⠀⡌⠀⠈⠃⢠⣇⣔⠟ ⡏⠈⢳⠀⡟⠷⢠⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣀⡠⠃⣀⡴⠶⢛⣹⠃⠀ ⢓⣦⡎⠀⣨⣦⣈⠋⠀⠀⠀⠀⠀⠀⣸⠿⠿⣻⠖⣚⣋⣵⠾⠿⠶⠚⠋⠀⣧⡴ ⠄⠛⠻⠟⢓⣚⣛⣿⣮⣶⡾⠯⠭⠹⠚⠄⠈⠉⠉⢀⣀⡀⢀⣀⣬⡴⠶⠛⣁⡐

⠀⠀⠀⠀⠀⠀⠀⠈⢳⡨⣮⣾⠆⠈⣯⠗⠀⣄⣝⠛⠉⠀⠀⠉⠺⢶⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⠛⠙⠃⣄⡀⢀⢜⠿⡇⣴⠗⡄⠀⡀⠀⢀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣏⠓⠢⣚⡉⣘⠜⠚⣿⡺⠀⣌⣁⡦⠖⠺⡶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡪⣊⡉⠑⠌⠀⠀⠀⠻⠶⡤⠀⠀⠀⣀⠼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢡⡠⡦⠘⡀⢄⠀⠀⢀⣄⣀⠼⢄⠠⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣝⣡⡷⠙⡀⠈⠉⡝⠉⠉⣉⠠⠤⠄⠬⠤⠤⡀ ⠀⢀⣀⣀⡘⣄⠀⠀⠀⠀⢀⠔⣀⠔⢱⠄⣰⠀⠆⢈⠖⠈⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⠭⠛⠓⠂⠁⠀⠢⢀⡠⠦⠴⠅⡀⠁⢠⠁⠀⠸⠁⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⢢⠼⠄⢴⡡⠂⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢇⡜⢢⡸⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠆⠀ ⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⣆⠀⠀⠀⣀⣠⢺⠀⠀⡠⠁⠀⠀ ⠀⢠⡸⡀⠀⠀⣠⡤⠤⠤⠤⠀⠂⠉⢸⠿⡰⠫⡏⠉⠀⠀⢀⡍⠀⡰⠁⠀⠀⠀ ⠀⢸⡇⠈⢲⡠⠊⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⠃⠀⠀⠀⡘⠀⢀⠉⢄⠀⠀⠀

⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⡶ ⠔⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⡟⢶⢚⣃ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⣛⢚⢼⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⡄⠀⠎⠀⠀⠀⠀⣸⠧⢸⠘⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⣚⡿⠋⠈⠀⠀⠀⠀⠀⡟⣴⣤⠐⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢀⣷⣾⠀⠀⠀⠀⠀⢠⣇⠉⣹⢀⣚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠏⠁⠀⠀⠀⠀⠀⣼⠙⡍⢻⢠⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣸⢉⢸⢠⢸⠨⠚ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⡟⡀⠬⠼⠼⠧⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⢴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠊⢡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⠉⠓⠢⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀ ⠀⠀⢠⢏⠆⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀ ⣿⣠⢏⠎⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠈⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦ ⣿⠋⡎⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⡆⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠁⡜⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣸⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢠⡿⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠁⠀⠀⠀⢀⣴⠛⠀⠀⠈⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠈⢱⠀⠀⠀⠀⢀⣄⠐⠲⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⣀⠼⠏⠉⠉⠉⠉⢻⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠛⠋⠲⢤⣀⣠⠴⠚⣧⣀⣀⣀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠃⢀⣠⠤⣀⣴⠋⠀⠀⢠⡿⠁⠀⠀⠉⠉⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⢰⡿⠖⣶⠼⣷⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⣰⣿⠃⠀⣧⣶⣿⣆⣀⣾⠿⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⣰⠃⣾⠀⠀⢀⣀⠙⢿⠉⠁⠀⣧⠀⠹⠒⠾⡀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⠀⣴⣿⡿⠃⠀⠀⣰⠇⢀⡟⠀⠀⠘⣿⣄⠸⡄⠀⠀⢸⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⢸⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⢠⣾⣿⣿⠃⠀⠀⢠⠏⠀⢸⣇⣤⣄⠀⡟⠈⠻⡇⠀⠀⠸⡇⠀⠀⠀⢀⡤⠀⠀⠀⠀⢸⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣴⣿⣿⣿⡇⠀⠀⢠⣏⠀⠀⠈⡿⣿⣿⣦⠇⠀⠀⠀⠀⠀⢠⡇⠀⠀⣴⡿⠃⠀⠐⠀⠀⡿⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠋⢀⡿⠀⠀⢀⡞⠘⠀⠀⠀⣿⣉⣻⠏⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⡟⠁⠀⠀⠀⠀⢠⡇⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⣾⠃⠀⠀⣼⣿⡄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⣆⣴⡟⠁⠀⢀⡀⢀⣤⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡟⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⣿⣁⠀⣾⣿⣿⣼⣿⠇⠀⠀⠀⠀⢸⣿⠌⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⢀⣾⣿⣿⡟⠀⠘⢲⡦⠄⢀⡀⠤⠴⠺⡇⠀⠀⠀⢸⡿⠉⠙⠛⠉⠛⢻⡟⠀⠀⠀⠀⠀⢸⣿⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡛⢿⡇⠀⠀⢸⣄⠀⠀⠀⠀⠂⢸⠃⠀⠀⠀⠸⡇⢀⣤⡤⠶⠄⣼⠁⠀⠀⠀⠀⠀⣼⡇⠀⠀⢻⣿⣆⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣾⠀⠀⠀⠈⣿⣿⣶⣄⠀⠒⣿⠀⠀⠀⠀⠀⡿⠛⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠈⣿⣿⣆⠀⣇⠀⠀

⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣻⣿⠿⣿⣿⣿⡍⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⢹ ⡇⣠⠶⠒⠲⠶⣿⣶⣦⣄⣈⣳⣀⠀⠀⠀⡠⣼⣟⣾⣾⣩⢷⣄⠀⣠⠤⢤⣧⣾⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣁⣀⣀⣠⣄⣀⣸ ⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠻⢤⣿⣿⣿⣿⠁⣰⡟⠀⢹⣆⣠⣿⣸⣿⣿⡿⡁⠉⠒⠒⠒⠒⠈⠙⠛⠛⠿⠛⠋⠉⠉⠻⣿ ⣧⠀⠀⠀⠀⠀⢀⠀⠀⠒⠒⠶⠶⣶⣶⣶⣦⣀⣸⣿⣧⠀⠀⣠⣀⣤⡀⠀⣾⡏⣿⣿⣷⣈⣑⣶⠶⠶⠒⠉⠐⠀⢀⡠⠄⠀⠀⠀⠀⢹ ⡿⣧⣀⠀⠠⡀⠀⠉⠒⠒⠠⠤⢀⣀⠀⠉⠙⠫⣌⠻⣿⣧⣄⠉⠉⠋⣠⣾⣿⣿⣿⢿⠿⠋⠉⠀⣀⡠⠤⠒⠚⠉⠀⡀⠀⠀⠀⠀⠀⢸ ⡇⣿⣿⣧⡀⢱⡀⠀⠰⣤⣀⠀⠀⠀⠉⠓⠢⣄⠈⠑⢬⣉⣭⣭⣷⣿⣉⣉⠙⣫⠖⠁⣠⠔⠚⠉⠀⠀⠀⢀⣠⡴⠊⠀⢠⠀⢀⠀⣠⠃ ⡇⢹⣿⣿⣍⠙⣿⡄⠀⠹⣿⡿⠷⣶⣤⣄⣀⠈⠙⢶⣤⡈⣻⠁⢰⡏⠀⢀⣟⣱⠖⠉⠀⣀⣠⣤⣴⡶⣿⡿⠋⠀⣠⣶⡟⠀⣾⣴⣿⠀ ⡁⠀⠻⣿⡏⡀⣿⣿⣄⠀⠙⣦⠀⠈⣿⠉⠙⠳⢦⣤⣌⢻⡇⠀⡾⢳⠀⢀⣏⣡⣶⣴⣾⣿⠉⣼⣃⣤⠏⠀⣤⣾⣿⣿⠄⢰⣿⣿⡿⠀ ⡇⠀⢸⣿⡇⡇⢸⡟⠻⣦⡀⠈⠳⣆⡏⠀⠀⠀⠀⠙⢿⠙⠻⣖⠧⠼⣳⠟⠋⣹⠋⢀⣿⡇⣼⣿⠟⢁⣠⣼⠿⢻⣿⡟⠀⣿⣿⡇⡇⢀ ⡇⠀⢸⣿⡇⡇⢸⡇⠀⠈⠛⢦⡄⠘⡇⠀⠀⠀⠀⠀⠈⠳⡀⠈⠙⠚⠁⠀⣴⠁⠀⣸⠘⣿⣿⣧⣤⣾⠟⠁⠀⠘⣿⣡⣰⣿⣿⡇⢰⣸ ⡇⠀⢸⣿⣿⣷⠈⣧⠀⠀⠀⠈⠻⣶⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠃⠀⢠⡿⠀⢹⠿⠿⠋⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡇⢸⣿ ⣇⣀⣼⣿⣿⣿⣴⣿⡆⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⢰⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢡⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⣡⣿⡍⠻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⡾⣿⣿⣿⣿⣶⣶⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣯⣾⣿⣿⡆⠀⢹ ⣿⣿⠟⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣄⠀⠀⠀⣀⣲⣿⣯⣠⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⢸ ⣿⣧⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⡥⣼⢿⠿⡿⡿⢿⣿⣿⣿⣿⣿⣧⣤⣵⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠉⠁⠀⠒⠠⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠴⣣⣤⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠉⠘⣷⠶⡄⠀⠀⠀⠀⡤⠄⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⡠⠂⠀⠀⢀⡀⠀⠀⠀⢈⡸⢞⣹⡄⠀⡐⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⢀⠂⠀⡜⠀⢠⠆⢠⠎⠑⢄⠴⠄⠘⡄⠈⢎⡧⡈⠀⠀⡸⠀⠀⠀ ⠀⠀⠀⠀⣈⠀⠸⡴⢥⠴⣆⠁⠀⠀⢠⣿⣶⣶⣿⡀⠁⠡⡸⡀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢂⠎⠉⣿⢰⣿⡆⠀⢠⠃⣿⣿⣿⡿⠆⠀⠀⢡⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠌⠀⠀⡺⡘⠿⠇⠀⠈⠀⡘⠯⣟⠣⠢⡀⠀⠀⢃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⢀⡄⠆⠈⠀⠀⠁⠀⠀⢀⠜⢁⣠⠄⢰⠀⣸⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠘⠇⠈⠢⠀⣀⠀⢀⣀⣮⠀⠈⠃⠀⠸⣿⡉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠆⠀⠀⢀⡄⠍⠙⢅⡠⠈⢁⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⠀⠀⣸⠀⠀⠈⠢⣀⠐⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢻⠀⠀⠻⠆⢠⠁⠀⠦⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢐⠒⢒⠎⠀⠀⠑⠢⠤⢖⠁⠀⠀⡄⠀⠡⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠌⠀⡘⠀⠀⠀⠀⠀⠀⠀⠑⢄⠔⠁⢠⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡘⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡂⠀⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠐⡤⠚⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡆⡄⠀⠀⠀⠈⠐⠄⡀⡀⡐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⢀⣠⠤⠒⠈⢀⣧⣤⣤⣀⠀⠀⠀⢀⠏⣧⣤⡶⠤⢤⣀⠀⡆⠀⠀⠀⠀⠀⠀ ⠀⠉⠁⠐⠀⢸⣿⣧⣶⣿⣿⣦⡠⠂⠀⣿⣿⣷⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⠀⠀⠀⡠⣚⢆⣌⠀⠺⣆⠀⡀⠰⠆⠡⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠀⠌⢣⣥⣽⣐⣉⡛⠀⠧⣭⣓⠰⠽⠘⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠹⣯⢿⠼⢹⠏⠀⠝⠀⠸⣁⣸⠟⢰⡆⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠈⡿⣱⢌⠄⠂⡂⠀⠈⠀⠀⢠⠎⡸⡺⡾⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠀⢃⢇⢤⣾⡐⣑⠄⠀⠤⠺⠯⢰⣟⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠁⠙⠐⠋⠪⠄⠀⠀⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠂⠉⠉⠁⠐⠊⠀⡐⠁⠀⠀⠠⢈⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠀⠘⠀⠀⢀⡄⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠡⠀⠐⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⢱⠁⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⢀⠀⠁⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡠⢂⡈⠀⠒⠈⠁⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢒⠒⠢⡄⡀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⢀⠠⠤⠀⢤⡄⠀ ⠀⠀⠈⣄⠑⠄⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢨⠂⠀⠀⠔⢁⢾⠁⠀ ⠀⠀⠀⠹⣄⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⠁⠀⠀⢀⠔⢃⠎⠀⠀ ⠀⠀⠀⠀⣈⠶⢬⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⣾⣤⣤⣤⡶⢥⢔⠁⠀⠀⠀ ⠀⠀⠀⢾⡀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢀⢜⡴⡹⣿⡿⢹⡟⠛⠁⠀⣨⡆⠀⠀ ⠀⠀⠀⠀⠁⠒⡲⠘⣦⠀⠀⠀⡠⠒⡡⠣⠁⠚⠛⠟⣏⠉⠺⡋⠓⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⣛⣥⣑⣄⠀⢀⣾⠮⠵⣦⡠⠜⣄⢘⠗⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠊⠁⠀⠀⠉⠺⣗⠂⠀⣝⡗⠒⢎⠉⠁⠢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡌⠉⠢⠀⠀⠀⠀⠀⠘⠆⠀⣿⠋⠀⠀⠈⠁⠢⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⢱⢀⠀⠈⢄⠀⠀⠀⡀⢸⡼⠁⠀⠀⢀⠄⠊⢩⠹⠡⡀⠀⠀⠀ ⠀⠀⢀⠾⣀⡏⢀⠼⡆⠀⠑⠠⢐⠀⡌⠀⠀⣀⠔⠁⠀⡠⢣⠒⢇⠑⡀⠀⠀ ⠀⡔⠁⠀⠈⠃⡊⣠⡧⠤⠤⢤⡀⢉⣁⡈⠉⠀⠀⠠⢪⣖⠈⢢⢈⡇⠙⠠⠀ ⠰⠀⠀⠀⡜⠀⠉⢿⠁⠀⠀⠀⢱⢸⠀⠀⠉⠁⠒⡠⢄⡄⠑⡜⠋⠀⠀⠀⠁ ⠀⠢⣀⣊⡀⠤⠊⠀⢑⣤⣠⣐⣁⠼⡄⡀⢀⡀⠔⠁⢀⠃⠒⢅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠸⠁⠀⢹⠂⢤⠀⠠⠔⠁⠁⢄⠀⠈⠁⠈⠁⠀ ⠀⠀⢀⡀⠀⠤⠇⠐⠒⠒⠒⠊⠀⠀⠈⠁⠘⠐⠒⠒⠒⠀⠤⠧⠀⢀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⡉⠛⠿⡷⣦⣤⣴⣶⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠈⢱⠀⢠⡀⢠⣬⡟⢙⣻⢁⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⢽⡇⢠⡿⣌⠻⣿⣃⣸⠟⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⠃⢸⢻⠈⢳⠃⢙⣹⣴⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣇⢸⡀⠀⡄⠀⠈⠓⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠛⡫⠛⠓⠶⣶⡒⣚⣛⣿⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⢀⡖⠑⣄⠀⡇⠀⣸⠀⠀⠀⣄⠀⡇⠀⠀⠀⠻⣽⠃⠀⠀ ⠀⠀⠀⠀⠀⠳⠚⠁⡆⠑⠦⣹⡄⠀⢠⡏⠣⢹⣄⠀⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠧⠔⠧⠄⣀⠀⡇⠐⠛⠛⠓⠾⠿⣷⠔⢈⠀⠀⠀⠀ ⠀⠀⠀⣰⣡⣇⣀⣀⣀⣰⡁⠉⣳⣄⣀⣀⣀⣀⣀⡍⣇⣠⠇⠀⠀⠀ ⠀⠀⢀⠹⠋⠉⠀⠀⠀⠀⡩⠛⠉⠁⠀⠀⠀⠉⠙⠛⠿⢀⠀⠀⠀⠀ ⠀⠔⠁⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀ ⡌⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆ ⢡⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶⡇ ⠸⡓⠤⣀⠀⠀⢀⣀⣹⡂⠄⠀⠀⠀⠀⠀⢀⣀⠤⠊⠀⠀⠀⠀⠙⡇ ⠀⢣⣠⣤⠼⠟⠛⠛⠉⢹⠛⠓⠒⠒⠚⠛⠷⠤⠤⣤⣀⡀⠀⠀⠰⠁ ⠀⢀⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⠁⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀ ⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀ ⠀⠀⠈⠢⢀⣀⣀⣀⡀⠔⠁⠈⠢⠀⣀⠀⢀⣀⠀⠤⠊⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢿⡶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡛⠶⣄⣬⣷⣄⣬⣿⣷⠂⠄⠀⠀⠀⠰⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣤⣼⡿⢿⣿⣿⣿⣷⣦⣾⠢⡀⠀⠀⠣⣠⣷⣤⠄⠐⢢⣤⣀⠀⠀⠀ ⠀⡸⣿⣿⣖⠸⣿⣿⣿⣿⣿⣿⣄⡇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⢻⠑⠄⠀ ⠀⣷⣿⣿⣿⣾⣿⡿⣿⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠀ ⠀⣿⣿⡼⢻⡄⠉⢰⡻⢋⣿⣿⠅⡀⠀⠀⢀⠀⣠⣤⣤⣀⠀⠀⠀⡼⢿⠀ ⠀⠸⣿⣧⢈⠉⠀⣄⢠⣾⣏⠄⣀⠀⡉⠨⠶⠖⣻⢿⣿⠟⠛⢢⣼⣤⠎⠀ ⠀⠀⠈⠙⠂⠀⠀⠀⠈⠿⠁⠈⠳⠋⠀⠀⠀⠀⠀⢁⠟⠀⠀⢠⠯⠅⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠁⠀⠀⠀⠀⠀⠀⠀⡎⡴⢠⠃⠀⠀⠈⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⡀⠀⠀⠀⣔⣊⡔⡠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡔⣠⣤⣤⣅⣀⢜⠤⠤⣈⠀⠈⠢⣄⠠⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣋⡛⢇⠃⣰⣾⣿⣷⡂⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡵⢛⠃⣄⠙⠿⣿⠋⠀⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠽⠟⠀⠀⠈⠑⢶⠾⠀⠀⠀⠀⠀

⢠⠀⡇⢸⠀⠀⠀⢀⣼⣿⣷⡟⢁⡴⡏⣿⡀⠹⣷⣤⡀⢢⠸⣿⣿⣿⣿⣿⣿⣿⡍⢻⣿⣿⣿⣿⣿⣯⣛⢶⣾⣴⣅⠀⡠⠀⠀⠀⠀⠀ ⡜⢸⠀⡇⠀⠀⣠⣿⣿⣿⠏⢠⡿⠀⣿⡿⣿⣾⣿⣿⣿⡌⡆⣿⣿⣿⣿⣿⣿⣿⣇⢸⠛⠛⠿⢿⣿⣿⢿⣿⣿⣿⣭⣿⣇⡀⠀⠀⠀⠀ ⠃⡇⢸⢁⡤⠊⣽⣿⣿⠃⢠⣿⡇⠀⣿⣷⣼⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⢹⠸⣷⣶⡦⣴⣿⣷⣿⣫⣾⣿⣿⣿⣿⣷⣄⡀⠀⠀ ⣰⣤⣾⡟⠁⣼⣿⣿⠏⢀⣿⡿⠁⠀⣿⣿⠛⠟⠛⠃⢻⢿⣿⡈⣿⣿⣿⣿⣿⣿⡌⣷⡼⠋⠐⠋⠀⠀⢸⣿⣿⢯⣿⣿⣿⣧⡈⠻⡦⣄ ⠿⢫⡟⠀⢰⣿⡟⡟⠀⣼⣿⡇⠀⠀⢃⢻⡀⠀⠀⠀⠀⠶⠹⣇⢹⣿⣿⣿⣿⡿⣇⢻⠀⠀⠀⠀⠀⠀⢸⣿⢫⣿⢿⣿⣯⢻⣷⣄⠙⣄ ⣴⠏⢀⡷⣾⡿⢰⠃⢀⣿⣿⠀⠀⠀⣸⣦⠀⠀⠀⠀⠀⠀⠀⠘⡆⢿⣿⣿⣿⡧⢿⣜⠀⠀⠀⠀⠀⠀⢀⡵⠃⠘⢆⠿⢻⣆⠹⣿⣧⠈ ⡏⠀⣾⠀⣿⡇⠸⠀⣸⣿⡿⠀⠀⠀⣇⠈⡟⠀⠀⠀⠀⠀⠀⠀⠹⡜⣿⡿⣿⣷⢸⣇⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢷⠀⢻⣆⠹⡌⣧ ⠇⣸⡏⢠⣿⢻⢁⢀⣿⣿⡇⠀⡟⠀⣿⠀⠱⡀⠀⡠⠀⠀⠀⠀⠀⠱⡽⣿⣿⣿⡈⣿⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢻⡀⢻⡟ ⡀⣿⡇⢸⡟⣾⠏⠀⣿⣿⠁⢰⠁⠀⣿⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⢀⣷⣹⣿⣿⣇⢻⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢱⡀⢿ ⢹⣿⡇⢸⡇⣿⡆⠀⣿⣿⠀⡸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⢳⡹⠎⢿⡜⣿⡾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢳⡼ ⣿⣿⣇⠸⡄⣿⠃⡀⣿⣿⠀⡇⠀⠀⠑⡀⠀⠀⠀⠀⠐⠉⠀⠀⠀⡀⢀⡼⠳⡀⠈⣷⢻⣆⢹⠦⢄⣀⣀⣀⣠⣤⣤⣴⣄⠀⢻⡀⠈⠙ ⣿⣿⣿⠀⡇⣿⠀⠁⣿⣿⢸⠁⠀⠀⠀⢧⢀⣀⡀⠤⠤⠤⠤⣀⠉⠀⠉⠀⠀⠹⣄⠈⢧⢿⡜⡄⠈⣡⣴⣾⣿⣿⣿⣿⣦⣤⣾⣷⡀⠀ ⣿⣿⣿⡆⠂⣿⠀⠀⢸⣿⡏⠀⠀⠀⣾⣿⣿⣶⣶⣶⣶⣶⣦⣄⠍⠒⠀⠀⠀⠀⠘⢦⣦⠀⢧⣳⣾⣿⣿⣿⣿⣿⣇⠈⠻⣿⣿⣿⣷⡖ ⢹⣿⣿⣇⠀⣹⡇⠀⠈⣿⡏⣑⣶⣯⣽⠟⢿⣿⣿⣿⣿⣿⣿⣿⢿⣶⠀⠀⠀⠀⠀⠀⠹⣷⡌⢿⣿⣿⣷⣄⣿⣿⡇⠀⠀⣿⠿⣿⣿⢳ ⡇⣿⣿⣯⢀⣿⢿⠲⠶⣿⣿⣿⡟⠃⢸⠀⠘⢿⣿⣧⣀⣿⣿⣽⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢙⣯⣄⣀⡩⠟⠀⢀⠀⠋⠀⣿⣿⢸ ⡇⢻⣿⣿⣿⣿⣼⣆⠀⠘⡟⢿⣧⡀⠘⠀⠀⣿⢿⣉⣉⣉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣆⠹⢶⡂⠶⣶⡾⣉⡇⠀⠀⣿⣿⡗ ⣧⠈⣿⣿⣿⣿⣿⣿⡄⠀⢳⠀⠈⠇⡇⠀⢀⣸⡀⣤⡽⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⢄⣿⣤⠒⢭⣤⡈⠀⠀⣿⣿⣷ ⣿⣧⠘⣿⣿⣿⣿⣿⡳⡀⠘⣆⠀⠀⡇⠸⣀⣸⣗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠛⢷⣄⠉⠀⠀⠀⢸⣿⣿ ⣿⣿⣧⠘⣿⣿⣿⣿⣷⡁⠀⢹⣆⠀⠇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⠀⠀⠈⣿⣿ ⣿⣿⣿⣧⠹⣿⡿⣿⣿⣷⡄⠘⡟⣾⡇⠀⠀⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠸⣿⣿⣿⣇⠹⣿⣌⠻⣿⣿⣄⢹⣞⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⡵⠒⠒⠒⠒⣆⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿ ⠀⣿⣿⣿⣿⡄⢿⣿⣷⣌⠻⢿⣦⣻⣾⢦⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡏⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠿ ⠀⣿⣿⣿⣿⣿⠸⣿⣿⣿⣷⣄⡙⢿⣿⣿⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣅⣀⢁⠀⠀⣀⡀⠀⢐⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈ ⢰⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⡹⣦⡙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢠⠿⠒⠋⠉⢧⠀⢘⡬⢿⠃⠀⠀⠀⠀⠀⢀⠂⠀⠀⢠ ⢸⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⡇⢿⣿⣦⡹⣿⡿⣦⡀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⣸⣀⡸⢎⠏⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀ ⢸⣿⣿⣿⡿⢻⠋⣇⣿⣿⣿⣿⣷⢸⣿⡉⠳⢾⣿⡉⢳⣄⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣠⣚⣛⣉⠠⠊⠀⠀⠀⢀⡤⠞⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⢃⡏⣰⣿⢻⢿⣿⣿⣿⢸⣿⣷⠀⠀⠙⢿⠀⠻⣷⣤⣀⡀⠀⠀⠑⠢⠤⠊⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⢀⡤⠲⢄⠀⠀ ⠟⠋⣠⢏⣾⣷⡿⢹⠸⡌⠉⢻⣿⢸⣿⣿⣷⣄⠀⠈⠳⣦⠹⣿⣷⣌⢉⣲⣶⣤⣤⣄⣀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⠋⠀⠀⠀⠣⡀ ⠶⠚⣁⣿⣿⠟⠁⠘⣦⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠀⠀⠀⠀⠀⢀⡘⠀⢀⣄⠀⠀⢳

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⣠⣄⣠⡄⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠋⡀⢂⠕⢀⠜⢻⣿⣯⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⢀⠎⠔⣁⡴⠁⢀⡇⠀⣿⢥⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢼⢠⣿⢊⣼⠊⡧⠃⡾⡇⠀⣸⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢆⣇⠎⠙⠛⣧⡾⣁⣱⠀⣏⣧⡄⠀⠀⠀⠀ ⠀⢀⣴⣶⣼⣸⣼⡆⠀⠀⢁⣀⣛⣿⣾⣼⣾⣿⡀⠀⠀⠀ ⢠⣿⣿⡿⠛⠛⠛⠘⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⡷⠀⠀ ⣿⣿⣿⡄⠀⣠⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⡀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⣀⢲⢰⠀ ⠘⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⡿⠿⠿⢿⣿⣿⡇⠀⢉⣷⠀ ⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⢻⣿⣦⣥⡏⠀ ⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⣸⠟⠉⣀⡇⠀ ⠀⠘⢿⣆⠀⠁⠐⠂⠀⡔⠹⠑⠤⢀⣀⣴⢇⡧⣾⠏⡄⠀ ⠀⠀⠀⠙⠶⠀⠀⠀⠎⠀⠀⠀⠀⣿⡷⢻⡼⣹⡏⠀⠃⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢸⠀⡟⡀⢰⠀⠀ ⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⢢⠘⡀⠁⠀⠘⠀⠀ ⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠈⠂⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀ ⠀⠀⠎⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀ ⠀⣰⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⢠⠀⠀⠀⢀⠎⣧⠀⠀⠀ ⢠⠍⣒⠤⠀⡀⠀⠀⠀⠀⢡⣠⠂⠀⠀⡄⣿⠆⠈⢄⠀⠀ ⠁⠠⠁⠉⡒⠒⠨⠀⡒⠠⠄⣇⠀⠀⣌⢠⠀⠱⠀⠈⢆⠢

⠀⠀⢀⠚⠁⢀⣬⣴⣿⣶⣟⠯⠷⠶⢵⣀⡼⣍⠁⠈⣿⣼⣄⠀⠀⠀⠀⠀ ⠀⠀⡄⣠⣶⠟⠋⠉⠉⢐⣀⠈⠁⢰⣾⣟⠢⠄⣀⠉⠙⠻⢆⠱⠀⠀⠀⠀ ⠀⠀⢝⣿⠍⣠⢊⠉⠁⠀⠀⠀⠈⠉⠀⠉⠉⠁⠉⠉⠐⠒⠉⠷⢧⠀⠀⠀ ⠀⠸⢸⣇⢸⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡄ ⠀⢀⠸⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ ⠀⠸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⠀⢰⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠀⠀⠀⠀⠈⣯⣀⣀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢄⣀⣔⡾⠁⠀ ⠀⠀⠀⠀⠀⠘⣿⡰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡹⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⠀⠀ ⠠⠀⠀⠀⠀⠀⡈⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⠀⠀ ⠀⠀⠀⠀⠀⢀⠁⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀

⠀⠀⠀⠀⠀⢀⣄⠤⠒⠂⠈⠉⠀⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠁⡧⠀⠀⠀⠀⠀⠀⠀⠀⠹⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠰⣀⡀⠐⠂⠀⠀⠀⠀⠀⢡⢰⠀⠀⡠⢒⠂⢄⠀⠀⠀⠀ ⠫⢁⠀⠀⠀⠀⠀⠠⣤⣭⣴⣤⡈⢆⠀⠀⢠⡚⠀⢸⠠⣿⣷⠂⢣⠀⠀⠀ ⠀⠀⠉⣲⠄⠀⠀⠀⡝⢾⡿⠿⠩⣶⣦⠀⡾⠁⠀⠀⢂⠘⠋⢀⠊⠀⠀⠀ ⠀⠀⠈⢷⡄⢤⡄⠀⠠⠀⢁⡀⣈⡈⠣⣺⠟⡍⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠘⢟⢾⡒⠚⢭⡋⡰⢳⡶⠶⠫⢵⣴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⡞⠉⠉⠈⠒⠂⢿⣇⣽⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠻⣿⣾⣿⡿⠣⠀⢀⡀⠀⠀⠀⢀⣀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠃⠀⠀⠀⠀⠀⠈⠙⠅⡀⠀⠀⠀⠄⠁⠂⢀⠈⢵⠀ ⠀⠀⠀⠀⠀⠀⠘⢰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠬⣦⡐⠃ ⠀⠀⠀⠀⠀⠹⡐⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠃⠙⡷⠀ ⠀⠀⠀⠀⠀⠀⠐⡘⡀⠀⠀⠘⠤⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⠑⢄⠀⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⠀⡠⢊⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠑⢖⠠⢤⡤⠖⣿⢹⠪⣑⠒⠲⣺⠁⠀⠚⠀⠀ ⠀⠀⠀⠀⡠⠔⠂⠀⡹⡀⠀⠀⠑⢄⡀⡸⡁⢸⠀⠀⠁⠢⢽⠀⠀⠀⠀⠀ ⠀⢀⠄⠊⠀⠀⠠⠂⠀⢣⠀⠀⠀⠀⠈⠀⠈⣼⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣿⣷⣿⣜⡈⡲⡀⢀⡠⢖⠂⠀⠀⠈⠐⡆⠇ ⠀⠀⠀⠀⠀⠀⠑⡲⢤⣌⣡⣾⡙⠁⣶⣿⣿⣤⠞⡋⠔⠆⠀⠀⠀⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠄⣈⡝⠻⠇⠀⢙⠙⠡⣃⣁⠀⠜⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡑⠄⢬⢭⣽⢶⠮⠤⠊⠀⠀⠀⠀⠀⣠⠟⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠭⠖⠂⠥⡎⠀⣼⡀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⢰⠁ ⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⡀⠄⠊⠀⡜⠀⢧⣀⣀⣤⠞⠉⠀⠀⠀⠀⡠⠁⠀ ⢠⠲⠒⠁⠀⠀⠀⠀⠰⠯⠀⠠⠔⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠊⠀⠀⠀ ⠈⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡰⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢀⠎⡑⢲⠰⠁⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠆⡀⠀⠀⠀⢀⠀⡀⠔⠁⢸⡆⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡋⠉⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣠⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡏⠉⠉⠉⠉⠉⣽⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⡍⠉⠉⠉⠉⢹ ⡇⠀⠀⠀⠀⣼⡏⢫⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢫⠟⣿⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⣿⠁⠀⢣⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡼⠁⢀⠎⠀⢹⡇⠀⠀⠀⢸ ⡏⢉⣶⣦⣼⢸⠀⠀⠀⢣⠀⠀⢳⣄⡒⠒⠲⢤⡼⠁⠀⡎⠀⠀⠀⣧⠀⠀⠀⢸ ⣇⣿⣿⣿⡟⡏⠀⠀⠀⠈⣇⠀⣸⠃⠀⠀⠀⠸⣇⠀⡼⠀⠀⠀⠀⣿⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⡇⠀⠀⣠⠞⣁⣤⣤⣤⣤⣴⣤⣤⣀⡀⠳⣄⠀⠀⠀⣿⠀⠀⠀⢸ ⡏⠉⠙⠻⣼⣧⣠⣾⣿⣿⣿⣿⣿⡿⡋⠀⠈⣿⣿⣿⣿⣶⣵⣤⣠⡇⠀⠀⠀⢸ ⡇⠀⠀⠀⡰⣿⣿⣿⣿⣙⢛⣿⢿⣤⠑⠤⠔⣧⣿⡿⣿⡿⣿⣿⣿⣇⠀⠀⠀⢸ ⡇⠀⠀⡰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⡀⣠⣵⣿⣤⣿⣷⣿⣿⣿⣿⡀⠀⠀⢸ ⡇⠀⠀⣷⣼⠉⣿⡿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣷⡀⠀⢸ ⡇⠀⠀⠘⢌⠻⣿⣇⣄⣉⣁⣉⡛⢟⠛⠛⠛⠻⢛⣛⣟⣉⣩⣿⣿⡿⠋⢨⠆⢸ ⡇⠀⠀⠀⠈⢣⣿⣿⠉⠯⢉⣿⣿⣷⠀⠀⠀⣾⣿⣿⣉⣽⣹⣿⣿⣧⡾⠋⠀⢸ ⡇⠀⠀⢀⠔⠉⢙⠿⣷⠄⣀⡀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠄⢊⣿⡟⠁⠀⠀⠀⢸ ⡇⠀⡰⠁⠀⢠⠃⠀⠈⠒⢤⡇⡹⠯⠁⠠⠭⣉⣫⠁⣧⡂⠁⠀⠻⡄⠀⠀⠀⢸ ⡇⠀⡇⠀⠀⠎⠀⠀⠀⢀⠜⠿⠁⠀⡀⠀⠀⠀⠰⡧⡙⡄⠀⠀⠀⠘⠆⠀⠀⢸ ⡇⠀⢇⠀⠸⠀⣠⢴⡾⠁⠀⠀⠀⠂⠀⡆⠀⡭⢀⡈⠈⠲⢄⣀⠀⠀⠈⡄⠀⢸ ⡇⠀⠈⢆⡶⠋⠀⣸⢁⠀⣀⣨⣥⣜⡺⠔⢰⣥⣴⡀⠀⢀⢨⠇⠉⠑⠢⣵⠀⢸ ⡇⠀⠀⣾⣀⣤⣾⣿⣾⡿⠒⡏⠃⡜⠀⠀⠀⠀⠈⠳⣤⣾⣾⣄⡀⠀⠀⢸⠀⢸ ⡇⠀⠀⠻⣿⣿⣿⣿⡟⠑⠲⡇⠀⠁⠀⠀⠀⠀⠀⠀⣷⠛⠻⣿⣿⣦⣠⡞⠀⢸ ⣇⣀⣀⣀⣈⣙⣛⣋⣀⣀⣀⣱⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣈⣉⣉⣉⣀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣯⡿⠗⠛⠉⠉⠹⡻⣿⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠔⠂⠤⠒⠛⢻⣎⠀⠀⠀⠀⠀⡀⠈⠿⣷⡴⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠁⠀⡈⠀⠀⠀⢽⣽⣆⠀⠠⠊⠉⣿⠀⢸⢳⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠄⠀⢔⠑⠀⠀⠀⢻⣿⣾⡀⢠⣤⣾⢀⣀⡬⣾⡭⠁⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠀⠀⠀⢱⠀⠀⠀⢨⣽⣿⡇⠀⠚⠞⣻⣿⣿⣯⣀⣀⣀⣀⣀⠀⠀ ⠀⠀⢸⡗⠀⠀⠀⠈⠀⠀⠀⠘⣿⣿⣧⠀⠀⣐⣳⣿⣿⣿⣷⣿⠿⢟⠻⢿⡆ ⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠻⣷⣤⣹⣿⣿⣿⡟⢠⣾⠛⢁⣇⢠⠇ ⠀⠀⠀⢻⡧⠀⠀⢀⠀⠀⠀⢰⣿⡏⠂⠈⠹⡹⢿⡿⣿⣷⣽⢁⠀⢺⠛⠊⠀ ⠀⠀⠀⠈⣿⡂⠀⠘⠀⠀⡠⢿⣿⣁⡰⠀⠀⠀⠑⠢⡀⠉⢿⣷⣮⣀⡀⠀⠀ ⢀⡤⠖⠒⡺⠓⠀⠀⠑⠰⠀⣿⣿⠓⠢⢄⠔⠁⠀⠀⣨⢆⠈⠿⣼⣟⠝⢦⡄ ⠉⢀⠔⠁⠀⢀⣤⣴⣾⣵⣺⣿⠋⢄⠀⣘⡀⠀⠀⢠⣅⣀⣁⣢⣀⠉⠻⠿⣷ ⠀⠀⠀⠀⢐⣼⣷⢣⣿⡷⠿⠿⠉⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠒⠉ ⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢹⡏⠃⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢃⠀⢀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⢀⠖ ⠉⢦⡀⠀⠀⠹⡄⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⢠⠞⠁⠄⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡅⠀ ⢄⠀⠱⡀⠀⠀⠹⡀⠀⠄⠈⠀⠀⠀⠀⠀⢀⠴⡓⠀⠀⠀⠀⠡⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠘⢄⠀⠀⠀⠀⠀⠀⣸⠁⠈⡆ ⠈⠣⠀⠘⣄⠀⠀⢷⠀⠀⠀⠀⠀⠀⣀⠔⡁⣋⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠑⢄⠀⠀⠀⢀⠇⠀⡜⠀ ⠀⠀⢳⡀⠘⣆⠀⢸⡄⠀⠀⣀⡤⠞⠁⢀⠎⠁⠀⠀⠀⠀⠇⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠓⢤⡀⢸⠀⠠⠁⠀ ⠀⠀⠀⢣⠀⠘⡄⢸⣠⠔⠚⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠉⠪⣆⠇⠀⡀ ⠀⢣⠀⠘⡄⠀⢹⠞⠀⠀⠀⠀⣀⣄⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⣆⠀⠀⠀⠈⠳⣄⠁ ⣄⠈⢧⠀⢇⠔⠉⠀⠀⠀⣀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠈⠑ ⠸⠀⠘⡶⠋⠀⠀⠀⢰⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢃⡞⠁⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠋⠀⠀⠀⠀⠼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢰⡀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠈⡇⠀⠀⠸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠄⠀⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⠀⢰⡇⠀⢀⠀⠀⠈⢦⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⢸⡇⠀⠸⠀⠀⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠙⠳⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠿⠛⠋⠉⠉⠙⠓⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠒⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠒⠒⠒⠊⠉⠉⠑⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀

⡸⣭⣻⡝⣯⡝⣿⡿⠋⢿⣿⣿⣯⣽⡹⡼⣷⠹⣿⣟⢿⣦⡯⣝⣿⣿⣷⣌⢿⣹ ⣵⢣⡷⣻⣜⣿⣿⠁⠀⠘⣿⣿⣿⣶⡹⣷⣿⠀⠈⠿⣷⣙⢿⣾⡼⣿⣿⣮⡳⡽ ⢮⣻⡵⣳⣾⣿⡇⠀⣀⣶⠟⢿⣟⣿⣷⣻⣿⣧⠀⠈⡙⠿⣷⣟⡿⣿⣿⣿⣿⡵ ⣻⢼⡷⣽⣿⢉⣿⠞⠋⠐⠘⢉⢿⣮⢻⣿⣿⣿⡆⠀⣍⣂⡌⡙⡿⢿⣿⣿⣿⣿ ⣏⢾⣿⣿⠇⠀⢹⣇⣀⣤⡴⣾⠖⠹⠗⠊⠻⣿⣿⣆⣠⣿⣾⣿⣷⣮⡌⢻⣿⣿ ⣛⣮⣿⡿⠀⠀⠀⣹⣷⣾⣟⡿⠷⠂⠀⠀⠀⠀⠉⠙⠋⠀⠳⠾⠋⠁⠛⢛⣿⣯ ⡟⣶⢻⡇⢀⣴⣿⢟⡟⣯⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⡀⠈⣿⣿ ⡿⣜⣿⣷⠿⠋⠀⠂⠉⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠐⠀⠐⠀⣿⣿ ⣿⡜⣞⣿⡄⠀⠀⠀⠀⠠⢀⠀⠠⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿ ⣿⡽⣯⣞⣿⣄⠀⠀⠁⠀⠠⠀⠁⠀⢀⣠⣤⣶⣶⣿⣿⣿⠀⠀⠀⠁⠈⢰⣿⣿ ⣿⣷⢻⣷⣯⡻⢦⡀⠀⠀⢀⠀⠀⠀⠘⣿⣿⡟⠛⢿⡛⢯⡀⠀⠀⠀⢀⣾⣿⣿ ⣿⣿⣧⣏⡿⣿⣄⠉⠀⠀⠀⡀⠄⠀⠀⠈⢿⢠⢏⡄⢋⢃⡱⠀⠀⢀⣾⣿⣿⣿ ⣿⣿⣿⣾⣝⣯⠻⣿⣦⣄⠀⠀⠀⠐⢀⠀⠀⠫⣖⡍⢢⠏⡖⠀⣠⡿⣿⣿⣿⣿ ⢻⣟⣿⣿⣿⣾⣷⡣⢜⡹⢷⣦⣄⣀⠀⠐⠀⠀⠈⠦⣙⠞⡁⣼⣏⢷⣿⣿⣿⣿ ⣺⣟⡾⣿⣿⣿⣿⣿⣮⣕⣎⠦⣍⢋⢗⠺⣦⢤⣀⣄⣈⢤⡑⡯⣞⡹⣿⣿⣿⢈

⠀⠀⠀⠀⠀⡠⠁⠀⠀⠠⠆⡤⠤⠆⣁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠀⢀⠔⢒⠶⠿⢦⢤⣄⠀⠑⡀⠀⠈⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠃⠀⠀⡞⣾⢋⣠⢰⡇⠉⢎⣧⠀⠱⣀⡠⠄⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠁⠀⠀⡰⠀⣿⣸⠳⠟⣧⠹⡑⠻⣓⠔⠁⠀⢀⠎⢁⣀⣀⣀⠀⠀⠀⠀ ⢰⡇⠀⠁⠐⠣⢿⣄⣀⣤⣀⡏⣧⢳⣄⠈⠐⠄⡠⣂⣠⠀⠀⠀⠀⡸⠀⠀⠀ ⠈⠑⢄⠀⠀⠀⠀⠈⠁⠀⠈⢉⡹⢃⠩⡑⠄⡀⠀⠁⠚⠤⣄⠂⠉⠀⠀⠀⠀ ⠀⠀⠀⠈⠒⠤⣄⠀⠀⠀⠀⠈⠶⢾⢂⡟⠦⠌⡁⠒⠀⠄⢀⣁⡢⡀⠀⠀⠀ ⠀⠀⠐⣤⣤⠔⠼⣄⠀⠀⠀⠈⠛⠑⡚⠁⠀⠀⠀⠑⠦⢤⠤⣶⠏⡀⠀⠀⠀ ⠀⠀⠠⡖⡥⠋⠀⢇⠑⠤⠀⠀⣠⠌⠀⠀⠀⠀⠀⠀⠈⣷⣠⣞⣈⣆⡀⠀⠀ ⠀⠀⠰⡼⡇⠀⠀⢶⠇⠀⠈⢹⣿⠀⠀⠀⠀⠀⡆⠀⠀⣻⠇⠀⠀⠀⠀⠉⠢ ⠀⠀⠀⠑⠱⣀⡰⠁⡀⠠⠐⠒⠛⠒⠤⣀⠄⢤⠁⠎⣠⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣣⠗⠈⠀⠀⠀⠀⠀⠀⠀⠈⠲⡥⠾⠛⠃⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀ ⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣉⣇⠀⠀⠀⠀⢳⡀⠀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠢⢰⡟⡿⠣⣄⣀⣜⠜⠙⠀⠀⠀ ⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠆⠀⣿⢢⠛⡾⡁⠀⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⣴⠛⠀⢰⣿⣾⡄⡄⠀⠀⠀⠀⠀⠀ ⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣀⢐⣍⠻⠛⢉⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣽⣇⠄⠘⢄⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡉⠀⠀⠀⠀⠈⠐⠍⠢⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣀⠀⢠⠀⡜⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⡃⢀⠀⣴⡇⠀⣸⣿⡅⡀⠀⠀⠀⠀⡆⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⢰⡇⡎⢠⣻⣄⣠⣿⠛⣿⣿⠀⠀⠀⢠⣿⠶⡄⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⣾⣇⣿⣿⠿⣿⣿⡿⠾⢿⣿⢷⡶⢶⡾⣿⣿⣷⣿⣾⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⣿⣿⣿⣿⠀⣿⣿⠃⠰⣾⣿⠀⠃⠸⠀⣿⡇⢰⠄⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⣿⣿⣿⠀⠻⣿⠀⠰⢿⣿⡇⢰⠀⢰⣿⠇⢸⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⠛⠻⡿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠿⣶⣶⣶⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣾⣿⣿⣿⡄⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⠹⣿⣷⡀⢸⣄⡀⠀⢠⣤⠄⢀⣤⣾⣿⠀⣜⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠁⠀⣀⡀⠀⠀⡀⠈⢿⣧⠀⣯⠙⠶⢦⣴⣾⣿⠿⢛⡇⢰⠃⠀⠀⠱⡀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠘⣿⣆⣿⢿⣦⣼⡂⠀⣠⠞⢹⣧⡏⠀⠀⠀⠀⢃ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⡇⠀⢹⣿⣿⠑⠻⣏⠉⠟⠁⠀⣼⣿⣡⣿⠀⠀⠀⡟ ⠀⠀⠀⠀⢀⡼⡃⠀⠀⠀⠀⠀⠀⢸⣿⡤⠄⣿⣿⠀⠀⠀⠀⢀⠀⠀⡟⢻⢿⡇⠀⠀⠀⡇ ⠀⠀⠀⢀⣾⢿⣷⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⠀⠀⠀⠀⠸⡄⠀⢷⣾⠀⠙⢢⡀⠀⠃ ⠀⠀⢠⣾⠏⣾⣿⠀⠀⠀⠀⠀⠀⢹⣿⠀⢀⣿⣿⠀⠀⠀⠀⠀⠈⢆⠘⣿⡆⠀⠀⠙⢴⠀ ⠀⢀⡎⠊⣸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠈⢆⢸⡇⠀⠀⠀⠘⡇ ⢀⠼⠇⠀⠿⠿⠿⠿⠀⠀⠀⠀⠀⠻⠿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠼⠎⠁⠀⠀⠀⠠⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠠⠄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠃⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢵⠀ ⠀⠀⠀⠀⠀⢸⡏⢘⠀⢡⠇⣹⣇⡀⠀⠀⡆⠀⢸⠀ ⠀⠀⠀⠀⠀⢸⠳⣼⣧⡿⣶⡯⢼⣧⣤⣴⣿⣧⣬⡀ ⠀⠀⠀⠀⠀⠘⡆⣿⣿⡇⣿⡇⣻⣇⢁⠃⣿⢰⢸⡇ ⠀⠀⠀⠀⠀⢠⣏⣿⣟⠓⡞⠷⠾⠿⠾⠾⢷⢾⠾⠇ ⠀⠀⠀⠀⡠⠚⠘⠛⣿⡄⢃⡀⢀⡀⢀⣨⡎⣘⣀⠀ ⠀⠀⠀⠰⠀⠠⠀⢠⠈⢿⣸⣌⣲⠚⠛⣯⣧⠃⠀⠡ ⠀⠀⠀⣀⠀⠀⠀⠸⡇⠘⣿⠘⠟⠱⠊⢸⣏⡶⠀⢰ ⠀⠀⣰⣽⠀⠀⠀⠀⡟⠁⣿⡇⠀⠀⡄⢸⡏⠣⡀⠸ ⠀⡼⢣⣿⡀⠀⠀⠈⣷⢠⣿⠁⠀⠀⠈⠌⢷⠀⠈⢂ ⠴⠆⠚⠛⠃⠀⠀⠐⠻⠘⠁⠀⠀⠀⠀⠸⠌⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠠⣾⡟⢿⣦⡀⡀⣿⠃⠙⣿⣦⠂⢉⡐⡀⠀⠀ ⠀⠀⠀⣀⠀⠀⣸⣿⠀⠘⣿⡾⢽⡿⠀⠀⠘⣿⣆⠐⣷⢢⠀⠀ ⠐⠁⠀⡤⢸⢠⣿⠇⠀⠀⣛⣧⣾⡇⠀⠀⠀⠹⣿⣖⣛⣻⠀⠀ ⠀⠀⠀⢧⢸⣜⣆⢀⠔⠞⢋⣿⣿⣷⣶⣦⣤⣄⣹⣿⣯⡽⠀⠀ ⠀⠄⠀⣊⣸⣷⣀⠁⣠⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠈⢠⣾⣿⣿⣿⣤⣽⣿⡿⠇⠹⠟⠛⠛⣛⠛⠛⢿⣿⣷⡀⠀ ⠀⢠⣿⣿⣿⠹⠛⠋⠁⠀⠀⢀⠊⠀⠀⣀⣀⢡⠀⢸⡏⠙⢃⠀ ⢀⣿⣿⡏⠃⠀⠀⠑⡄⠀⠀⢄⣶⣿⣦⠀⣀⢼⣠⣾⣧⣤⣈⡆ ⠘⡹⣿⠰⡒⣲⣿⣯⠧⠀⠀⠊⠉⠉⠁⠀⠀⠀⢠⣿⠙⠛⠿⡇ ⠀⠀⣿⠠⠋⠉⠁⠀⢠⠊⠉⠒⠀⠀⠀⠀⠀⠀⣾⣏⣀⠀⠀⠀ ⠀⡾⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣿⣿⣶⡄ ⠀⠁⢠⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⡿⠋⠀ ⠀⠐⢿⣿⣿⣿⣿⣶⣶⣦⣤⡶⠀⠀⠸⠟⠛⠻⣿⣅⡀⡇⠀⠀ ⠀⠀⢀⣈⠉⠉⣉⠟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀ ⠀⣰⣿⣿⠓⠛⠁⠀⣀⣀⣤⣴⠂⠀⠀⠀⠀⠀⣰⠛⠛⠉⠀⠀

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⠈⠻⣿⣿⣿⣦⡀⠀⠨⣄⡠⣄⡈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀ ⡄⠀⠈⢻⣿⣿⣿⣦⡀⠀⠙⢦⡉⠓⠤⣀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠿⣷⣦⣄⣙⣷⡈⠻⣿⣦⡀⠀⠙⠲⣄⠈⠙⠦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠈⠙⠛⠿⣿⣆⠈⠙⠿⣦⣀⠀⠈⠙⠢⣄⡈⠐⢤⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠓⠶⣤⣀⠀⠉⠓⠦⣀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠳⣤⡀⠀⠀⠀⠀⠀⠀⡀⢤⣀⠀⠀⠀⠈⠹⣶⣦⡀⠈⠙⠀⠀⠙⢿⣿⣿⣿⣿⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠴⠞⠉⠀⠀⣼⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⡄⠀⣹⡷⠶⣤⣀⡀⠀⠈⠙⠲⠄⠀⠀⠀⠀⠈⠙⢷⣦⣄⠀⠀⠀⠀⠹⣿⣿⣿⣷⠘⣧⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⡀⠉⠀⠀⠀⠀⠀⡼⠛⡇⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⣿⣷⡐⠘⠳⣦⣀⠉⠙⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⣈⣿⣿⣯⣴⣾⡟⠉⠁⠀⢀⣤⣴⡶⣠⣬⣉⣙⠓⠲⢤⣀⣼⠁⣸⠁⠘⢁⣄⡤⢴⠖⣶⠏⠀⠀⠀ ⣿⣿⣿⣦⣀⡄⠙⠓⢦⣄⡀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⠋⡉⠙⢿⣏⠓⣦⡀⠛⢿⠩⠞⣡⣿⣤⡼⠋⠉⠓⠺⠿⣿⣿⠒⢛⡽⠟⠋⢉⣿⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠈⠛⠶⣄⡀⠀⣴⣿⣿⡿⠋⠀⠀⠀⠙⢦⡈⢿⣿⣿⣿⣦⣸⡀⠀⠋⠿⣫⡀⠀⠀⠀⠀⠀⠀⠉⠓⢾⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠘⠻⢷⣶⡄⠀⠀⠈⠙⣿⣿⡏⣿⠁⠀⠀⠀⠀⠀⠀⢉⣾⣿⣟⠛⢯⣿⣷⡄⠀⢸⡿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⠀⠀⠈⠛⠶⡄⠀⢠⣿⣏⣠⣿⣦⣶⣶⣶⣶⢲⣶⡿⠿⠿⠿⣿⠿⠿⠉⢻⣦⡈⠓⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⢀⣠⣾⣿⣿⣿⡿⠿⠛⢛⣻⣏⣭⠿⣿⣿⠋⣍⠛⠛⢓⡶⠦⢿⣿⣦⡈⢿⡿⠇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣴⠏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⣰⣿⡿⣿⣿⣤⣿⣿⣾⢻⣿⣴⣾⣥⣴⡄⣠⣬⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⠞⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠋⢀⣀⡤⠀⠸⠃⣾⠀⠀⠺⠏⠈⠟⢡⣿⠟⠉⣸⣿⢟⣿⠻⠿⠋⠛⠆⠀⠀⠀⠀⠀⠀⢰⠃⣠⠖⠋⠀⣠⠂⠀⠀⠀ ⣿⣿⣿⣿⣏⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠤⢶⡿⠉⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠺⠃⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⠋⠀⠀⠀⡴⠁⠀⠀⠀⠀ ⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠉⠭⢭⣛⣛⠲⠶⠤⠤⣄⣀⡀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⢀⠀⢀⡞⡠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⡄⠈⠉⠓⠲⢤⣀⣉⡓⠲⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠉⠀⣀⠤⠞⠁⢀⡾⠋⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⡀⠉⠳⣄⠀⠀⠀⠀⣀⠀⣀⡼⠋⠁⡀⠀⠉⡀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠁⠈⠁⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣿⡆⠀⠈⠥⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡌⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⣿⣾⣶⣆⠀⠀⢨⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⡈⠛⢿⣿⣿⡄⠀⢸⢊⣀⠈⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠉⠁⠀⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀ ⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠲⠤⢤⣤⡄⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣀⣐⠒⠒⠠⠰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠤⠤⠉⣉⣉⢸⣓⡲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⠒⠠⠤⢼⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣙⠛⠒⢸⠶⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠬⢍⣉⣹⣛⣓⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠲⠶⠶⡿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣙⣛⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣟⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠃ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁⡇⠟⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣯⣿⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢶⡀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣃⣛⡗⣼⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⣬⣷⣤⣤⣴⣢⣶⣿⣿⣿⢿⣗⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⠿⣿⣿⣷⠿⡿⣿⣷⣿⣿⣿⡟⠻⣿⡧⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣹⣿⡿⡿⡀⣧⣼⣟⠉⠙⢾⣷⣣⢘⣿⣿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣷⣧⣳⢿⣏⠁⣿⡿⠀⣿⣿⣿⣯⣿⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⣿⣿⠟⣻⠖⠋⠀⠀⠉⣿⣿⣟⣽⢿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢯⣷⣿⠀⠀⠐⠀⢀⣬⣶⣿⣬⣽⣿⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣏⡀⠀⣠⠖⠛⠉⠛⠹⠋⠙⠛⠉⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠟⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠐⢮⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⠥⠀⠀⠀⢀⣇⠀⢀⠀⢀⣀⠤⠆⠤⢄⣙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⡆⠈⠢⣀⠀⣿⣠⠎⠀⣩⣤⠤⠖⠒⠒⠚⠧⠼⣦⣀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠘⠷⢿⣻⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⡀⢠⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡽⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⠉⢻⣞⡹⠛⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡤⠤⠤⠤⣄⡀⡀⢀⣴⣁⣀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠲⠭⡛⣹⣯⠝⠛⠉⠉⠉⢷⣶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠤⠤⠤⣀⡀⠀⠀⡸⠻⣇⠱⣄⣤⠴⠛⠉⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠙⢦⡴⠃⠀⠘⢦⡞⠁⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠖⢺⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠟⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢳⡀⡠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⠞⢙⣣⣼⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠙⢓⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠋⠁⣠⣿⣿⡒⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠤⠤⠞⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢒⡒⢚⣛⠋⠀⢿⠿⠃⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡠⢺⢡⠃⡜⢀⠀⢀⢾⢠⡀⠀⢇⠀⠀⣶⡀⠱⡄⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡜⣱⡟⢡⢴⠃⡇⠀⣌⣀⣮⡧⠀⢸⠀⣄⣹⣃⠰⡰⣤⢀⠘⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡷⢹⢠⣧⣼⣸⡇⣸⣅⣀⡘⠛⠒⠚⠳⠖⣘⣩⠶⠧⠚⡿⠀⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠶⣇⢸⣸⠃⡜⢻⢿⣿⠁⠈⢹⡇⠀⠀⣴⠟⠉⢹⣷⣶⠆⣱⣲⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠛⣏⣿⠛⣷⠘⡅⠘⠖⠐⠊⠀⠀⡄⠘⠂⠤⠾⠋⡀⢀⡿⡏⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⡏⣸⢏⢙⡄⠑⡄⢣⠀⠀⠀⠀⠁⠀⠀⠀⢀⡷⠁⣸⡇⠻⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢙⢈⡏⢰⠙⣵⡀⣈⠺⣧⡀⠀⠀⠀⠀⢀⣴⣾⠇⣰⣧⡿⠑⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣾⢣⠘⣷⢿⣳⡌⢦⣈⡿⠢⠤⠒⢺⠋⠏⣿⣔⡱⠯⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠑⠧⠤⠷⠈⢻⣏⢁⠀⠀⠀⠊⠏⠛⠉⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠔⠋⠈⠈⢦⠀⠀⢃⡠⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⠉⠑⠣⣄⠏⠀⠀⠀⠀⠀⠑⠦⠄⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠠⢄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠑⠤⢄⣀⣀⣀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⡀⠀⠀⣀⡀⠀⠀⠀⢀⡠⠊⣀⢤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⢰⣿⠋⣟⣡⣴⣵⣿⢹⡿⠘⣿⣟⣍⢣⠳⡲⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣾⡹⣿⣿⣏⣿⣿⠇⠀⣿⢿⡟⡟⡗⣷⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⡇⡟⣿⢿⣥⡏⢗⠰⠀⠙⣻⣧⣇⣷⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⢸⡇⠁⠑⠾⠿⠃⠀⠀⠀⣾⣿⢻⢟⣿⠟⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣾⣇⡄⡄⠀⠀⠀⠀⡄⠀⠈⠉⢁⣠⣿⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣴⡀⠀⠀⣤⡥⠀⠀⢀⣼⣿⣿⡄⡏⡀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⠙⢆⠀⠈⠀⣠⣴⣿⣿⣿⣿⡇⢃⡇⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⡀⠉⠒⠁⢸⣿⣿⣿⣿⣿⣧⠸⢠⠀⠀⠀⠀⠀ ⢠⡿⠟⠛⠛⠛⢻⡿⠛⠁⠀⠀⠥⡀⠀⢰⠀⣙⣻⡿⡿⠿⠿⠤⠿⣆⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⣇⠀⠀⠀⠀⠈⢷⠀⠀⠀ ⠃⠀⠀⠀⠀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⢢⠄⠀⠈⡇⠀⠀ ⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⢿⣄⠀⣇⠀⠀ ⡇⠀⠀⠀⡺⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣯⡆⠀ ⡇⠀⠁⢸⠁⠀⢁⣴⡒⢄⠀⠀⠀⠀⠀⢠⠅⠂⠄⢀⠀⠀⠀⢀⢰⣂⣶⠹⡜⡀ ⣿⠀⠀⣼⠀⠀⠘⠬⡧⠊⠀⠀⠀⠀⠀⢸⢌⡀⠀⠀⠀⠉⠁⠀⠈⠳⠾⠄⣿⡅ ⣿⡆⠀⡟⡀⠀⠀⠀⠀⠈⠒⠄⠀⠠⠒⠇⠈⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠿⢷ ⣿⣧⢰⠃⠡⣀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠐⢈⠢⡀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠈ ⡿⠋⠸⡀⠀⠀⠵⠤⠤⠤⠤⢀⢊⠀⡠⢂⡀⠠⣅⠘⠒⠲⠦⣴⠚⣻⣿⣿⡇⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠉⠁⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢁⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣢⠋⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⠀⠀⢀⣎⡇⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⡀⢾⣿⡄⡔⡇⠀⠀⠀⡀⢸⠀⠀⠀⢈⣦⣌⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣶⡇⡀⠀⢸⣷⢸⣇⣇⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⡯⣿⣿⣷⣶⣾⡇⢸⣿⣿⣿⣿⠹⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧⣿⣿⣿⣿⣿⣿⣿⡟⢠⢻⣿⣿⣿⣧⠇⢸⣿⡏⣿⡿⠄⣿⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣽⠙⠛⠃⣀⣤⠤⡀⠀⠀⠀⠀⠈⠁⠙⠓⠲⡿⣸⣾⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠨⣿⣿⣿⣿⠰⣞⠛⠉⠉⠳⠄⠀⠀⠀⠀⢠⣐⣢⣄⠀⠈⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣄⣿⣿⣿⣿⠀⠘⢦⣠⠏⠀⠀⠀⠀⠀⠀⡉⠀⡰⠉⠓⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢻⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⡩⠓⢶⣦⣄⡳⠚⠁⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⠉⠉⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣼⣿⣿⣿⣿⣿⡏⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⣏⢹⣿⣿⣿⣿⣿⠀⠙⣷⣄⠀⠀⠀⠀⠀⢀⣄⠴⠾⠏⠥⣏⣿⡇⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⡸⢸⣸⠿⠛⠉⣿⣿⡄⠀⠈⠻⣷⣶⣤⡤⠒⢻⠁⠀⠀⠀⢀⠴⣿⠃⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠟⠺⠓⣉⡁⠀⠀⠀⢹⣿⠘⡄⠀⠀⠈⠙⠛⡇⠀⠀⠀⢀⣠⠔⠁⠀⣿⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠑⠲⢄⣈⣿⡄⠈⢦⡀⠀⠀⠀⠀⢀⠗⠊⠉⠀⠀⠀⣸⠃⠀⠀⠀⣸⢿⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠒⠒⠓⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⣿⠸⡆⠀⠀⠀⠀⠀ ⠸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣼⣿⡁⡇⠀⠀⠀⠀⠀ ⠀⡟⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢈⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣣⣷⠀⠀⠀⠀⠀ ⠀⢹⡐⡚⣛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠈⠐⠤⠀⠀⠀⠀⠀⠀⠀⠹⢧⡗⠑⡄⠀⠀⠀ ⠀⠈⣧⠘⣌⡷⡙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣷⠀⠀⠀ ⠀⠀⢹⣢⠈⢦⠻⣷⢝⣧⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢇⠀⠀ ⠀⠀⠀⢧⠳⡀⠳⡸⣷⣿⠀⠀⠀⠀⠀⠀⡴⠁⠉⠉⠑⠒⢄⡰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⣆⠀ ⠀⠀⠀⠘⡄⠛⢄⢽⣽⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⢞⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡀ ⠀⠀⠀⠀⢳⣠⠊⠁⡾⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⢌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠈⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠘⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠈⣞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁ ⠀⠀⠀⠀⠀⠀⢹⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡬⠓⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠑⠒⠤⣀⣀⠤⠔⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠱⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⣀⠴⠊⠀⣀⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢀⣀⠤⠒⠛⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⣀⡠⣤⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⣀⡠⠴⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣙⣦⣄⣹⡟⢁⣼⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⣿⠀⣿⣿⣟⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⣿⡈⢿⣿⣏⣙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠈⠻⢍⣉⠉⠉⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⢰⠋⠑⠾⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡇⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠤⠴⠣⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠦⠤⢤⣀⢁⣀⠸⠉⢳⡲⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣀⢙⣦⠈⠉⡐⢺⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣰⣿⣼⠏⠀⠀⠈⠲⡄⠀⠉⠑⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⣰⡿⣿⡏⠀⠀⠠⣤⠀⠈⣆⠀⠀⠀⢨⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢠⠿⡇⢸⣷⡀⢀⡈⠛⠀⣠⣾⣦⠀⢀⣼⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⡞⠀⢳⠀⠙⢷⠦⠬⡤⠼⠛⠁⢹⡟⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠚⠧⣀⠈⣇⠀⠈⡆⠀⠀⠀⠀⢠⡟⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠈⠹⢻⡦⣤⡃⠀⠀⠸⠀⣾⠃⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⣿⠶⠾⣧⠀⠸⢷⣤⡀⠀⣿⠀⠀⢿⡀⠀⠀⠀⠀ ⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣿⢧⣀⣸⣿⡋⢹⠿⣧⠀⠈⣧⠀⠀⠀⠀ ⠀⣿⡀⠉⠒⢢⣤⠤⢴⡞⠁⠀⠀⠀⠀⣧⢸⣿⣿⣿⡇⣸⠀⠘⢦⡀⠘⣆⠀⠀⠀ ⢰⠿⠻⢤⣄⣀⣀⣤⡿⠤⠀⠀⠀⠐⠒⠚⠛⠿⠿⠯⣬⣿⣄⠀⠀⠱⡄⠸⡄⠀⠀ ⠈⢷⣆⠀⢀⣩⠍⢸⡿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⣀⣿⠀⣷⠀⠀ ⠀⠀⠰⢿⣉⣁⡤⢾⣷⠀⠙⠒⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠯⣀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⡶⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠤⣤⣤⣤⣦⣤⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⣠⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠋⠀⠀⠀⠀⠀⠀⢀⣠⢿⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢚⡁⠀⠀⢀⣠⣤⡴⢾⣏⠀⠀⣧⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠎⡇⠀⡏⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣮⣶⣿⣿⣷⣮⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⢻⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⢸⠿⢿⣿⣿⣥⢨⣿⣻⣿⠿⠗⠀⠀ ⠀⠀⠀⢘⠳⣾⢠⣼⡄⠁⣬⣤⢸⠶⠃⠀⠀ ⠀⠀⠀⠀⠲⢼⣇⢀⣠⣤⣀⢠⣿⠴⠂⠀⠀ ⠀⠀⠀⠀⠀⡰⠔⠓⠫⡨⠓⠃⡼⣀⡄⠶⠗ ⠀⠀⠀⠀⠀⡀⠃⠠⠀⠀⠠⠀⠣⡘⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢀⠀⠐⠑⡀⢀⠐⡅⠀⠀⠀ ⠐⠀⠀⠉⠀⢁⠸⠖⠃⠀⠓⠲⢀⡁⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠤⠒⠒⠒⠙⠒⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠅⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢣⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⢹⡄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⠿⠀⠀⠀⠈⠷⠤⣄⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡇⠀⠀⠀⣠⠊⢠⡀⠉⠲⡄⠀⠀⠀⠀⠀⠀ ⠘⢯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣒⣦⣄⠀⠈⢦⡀⠀⠀⠀⠀⣇⢰⠇⠀⠀⡜⠁⣴⣿⣿⣶⡄⠘⢦⠀⠀⠀⠀⠀ ⠀⠀⠉⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠛⣿⣿⣿⣿⣦⡀⠳⡀⠀⠀⠀⣿⡟⠀⠀⠀⠸⡀⠙⢻⣿⡿⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡷⠖⠀⠀⠀⠀⠀⢚⠻⣿⣿⡿⣿⠏⠘⢷⣶⣷⡄⠀⢸⡟⠁⠀⠀⠀⠀⠱⡀⠈⠛⠀⠀⡠⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠾⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠙⣏⢀⣤⣾⡴⢻⠂⠀⠀⠀⠈⠉⠒⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣻⡉⠉⣽⠃⠀⠀⠀⠲⠀⣀⣠⡄⠀⠤⠤⠄⠈⣡⣾⠟⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠹⣤⡧⠤⠶⢾⣍⣉⠍⠀⣰⠧⣤⣤⡤⣶⠿⢋⣡⣄⡞⢁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⠑⢢⣤⡤⠤⣖⣠⡜⠁⠀⢻⣧⣍⣉⣉⣭⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠉⠉⠁⠺⢿⣿⣁⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠟⠉⠉⠁⠒⣒⠤⢄⣀⠀⠀⠀⠀⠀⣠⣴⡶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⡀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠑⠢⢄⠀⠀⠋⣹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⣆⠀⠙⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⣧⡀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡒⠤⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠶⠼⢿⣷⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠐⡇⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢹⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⢣⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠙⠲⣤⣀⣀⣀⣀⣀⣀⣤⣾⣿⠛⣧⡉⠓⢶⣤⣤⢤⡴⣶⡎⠁⠀⢴⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠘⢦⡈⠙⠛⢻⠉⠀⣼⠟⠀⡇⠈⠓⠤⣀⠀⠀⢣⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠉⠉⢁⣧⠀⠀⠀⠀⠀⠙⢦⡀⠸⠀⣸⣇⠈⠀⡇⠀⠀⠀⠈⠑⠦⣈⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢀⠞⠁⠘⡆⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠈⢳⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠀⠘⣷⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠆⢀⢻⠓⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠘⠿⣿⣿⣧⡀⠀⠀⠀⠺⣏⠉⠀⠀⠈⣹⠗⠀⠀⠀⢀⣾⡿⡿⠀⠀⠀⡸⣼⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠹⠛⠉⠻⠷⣄⠀⠀⠈⠓⢤⡠⠞⠁⠀⠀⣠⣴⡿⠟⢠⠇⠀⠀⢀⣷⣿⣄⡇⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠐⠦⣿⣿⣶⣄⠀⠀⠀⠀⣀⣴⣾⠿⠋⠀⠀⣼⡀⠀⢀⣾⡟⠈⣿⣷⡀⢿⡄⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠈⠙⠿⠿⣿⣶⡶⠾⠛⠋⠀⠀⠀⠀⢠⠏⠀⣠⠋⡿⠀⢠⣿⣿⢳⡘⣇⠀⠀⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡔⠁⡼⠁⠀⠀⣿⢹⡀⣷⣹⣷⣯⢉⡛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡴⠋⠀⡴⠁⠀⠀⠀⣿⣼⡇⠹⣿⣿⠈⠻⣭ ⠀⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠈⠀⠀⠀⠀⠀⡿⢹⡇⠀⢿⣿⣧⠀⠖ ⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⣿⠁⠀⠀⢹⡇⣇⠀ ⣀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣿⠀⠀⠀⠀⢻⣿⠤ ⡉⡛⠉⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⣏⠀⠀⠀⠀⢸⢻⣁ ⡟⠁⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⢇⠃⠀⠀⠀⠀⠈⢿⠹ ⢷⣄⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣞⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢣⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖ ⡈⣧⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⡄⣻⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿ ⡇⠉⢿⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡜⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀ ⢿⡆⠈⢻⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣠⢊⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣴ ⣿⣿⠀⠈⡎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⣠⢞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣼⢏ ⣬⣿⢿⣦⡸⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡶⠚⣡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⢇⡟⢡⡏ ⠙⢿⣄⡙⢷⣿⣄⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⢁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣠⠞⢀⠏⠁ ⠉⠉⠉⠉⠉⠙⠻⣦⡙⣿⣦⠀⠀⠀⠀⣀⣀⡠⢴⢒⣻⠿⠛⣉⠤⠾⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠋⠉⠉⠉⠉⠉⠉⠉⠙ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠿⣷⡿⠿⠯⠴⠖⠒⣋⣩⣴⠶⠭⠤⠤⠴⠶⠾⠦⠤⠼⠶⢒⣒⣞⣉⣉⣁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠓⠦⣤⣄⡀⠀⡇⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠉⠻⣼⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣷⣄⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢝⢿⣷⣄⠀⠀⠀⠀⠈⠦⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣈⠳⢿⣿⣷⡄⠀⠀⠀⠀⠈⣲⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣻⠋⠀⣾⡷⢿⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⣻⡄⣀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠟⠋⠉⠉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣤⣤⠼⠗⠚⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠒⠦⢄⡀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⢀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢼⣿⠁⠀⠀⠀⢾⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀⠘⢦⡀⠀⠀⠀⣸⣿⠦⠤⠤⠤⣌⡀⠀⠀⠀⠸⣿⡿⠻⠛⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠔⠛⠓⢤⣱⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠙⢧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣼⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⠀⢻⣆⢀⡠⠄⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⣄⣀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠉⠉⠀ ⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣶⠤⢄⣀⣀⣀⣀⣀⠠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣷⡙⠳⠶⣤⣤⣤⠤⠄⠠⠒⠉⠀⠘⢆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠈⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠢⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠖⢚⣹⡶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠉⠳⣄⣠⡿⠦⠤⠤⠤⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠀⢀⣴⣾⠟⢉⣡⠖⠫⣥⡾⢻⣄⡿⢳⣌⢿⣦⣄⠀⠀⠀⠀⠈⠻⣗⠀⠀⠀⣰⠇⠀⠨⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⢿⣀⣴⣿⠧⢤⣤⢏⣠⣼⡇⢠⣿⣿⣿⢿⣿⣷⣄⡀⠀⠀⠀⠘⢦⠀⡴⠁⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⢀⡝⣿⡅⣮⡿⢛⣻⡿⢹⣿⠋⣿⣿⣿⣿⣿⣿⡿⣷⣄⠀⠀⠀⢈⡿⠁⠀⠀⠀⠀⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠁⢀⡞⠀⠈⢿⣿⡇⡏⣸⣧⣾⣿⠂⣿⡏⣿⢿⣿⣿⣧⣿⣿⣧⠀⠀⡼⠁⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠢⣀⡇⢀⣿⠁⠀⠀⠈⢻⣧⣟⡿⢫⣿⣿⣴⡿⣷⡿⠈⠿⣿⣿⣿⣟⣿⣆⣸⠃⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⢇⠸⡏⠀⠀⠀⠀⠀⠹⣿⡿⣽⣶⠿⠅⠈⠎⠀⡾⡟⠻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⢹⡘⣷⠇⠀⠀⠀⠀⠀⠀⠘⢍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⡰⠂⠀⠀⠀⠀⣮⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢀⠇⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣫⣿⡟⠉⠀⠀⠀⠀⠀⡼⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡘⣄⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⣀⣠⣤⣤⣄⣠⣿⣿⡟⠁⠀⠀⠀⠀⠀⡼⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⡇⢈⣿⣿⣿⣧⠀⠀⠀⠀⣀⣠⢤⣼⣿⡿⠏⠉⣿⢿⠙⢿⡙⢿⣧⣀⠀⠀⠀⠀⠀⣹⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣧⡾⢸⡇⣿⡋⠉⠉⠉⠉⠁⠚⠿⣯⣭⣴⣦⣼⡃⠸⠀⠀⠙⠂⢭⡛⠿⣷⣶⣤⣴⣿⣿⣗⣹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⠙⣧⣯⠇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⠓⠊⠉⠁⠀⠀⠒⠒⠀⠛⣲⣶⣾⣿⣿⣿⣿⣿⣿⣯⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡇⠀⣷⣿⣼⣿⣿⣦⠀⠀⠀⠀⠈⠉⠉⠛⠛⣛⣻⣿⡶⠶⠤⠀⠀⠢⢀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⢳⠀⠸⣿⣿⣿⢿⣿⣷⡤⠴⠒⠒⠒⠒⠒⠒⠛⢾⣶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠶⠬⠿⣿⣿⣿⣿⣿⣿⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠈⢧⠄⠙⣿⣿⡇⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⠛⢻⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⢌⣳⡆⣾⣻⣷⣈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢎⠙⠿⣿⣷⣿⣿⣮⣻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⣀⣀⡤⠴⠚⢱⠀⠐⠒⠒⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢤⡈⠙⢿⣿⣿⣿⡳⢼⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠸⣹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣧⣿⢠⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣿⣘⢻⣿⣿⣿⣿⣿⣟⣸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠻⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠉⡈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠼⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⣼⣿⣿⣿⣿⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠸⡜⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣰⣶⠟⣿⣿⣿⣿⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠸⠘⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⠉⠉⠉⠙⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣀⡀⠀⠀⣀⣤⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀

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