Percentile Emojis & Text

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠄⣀⣄⡤⣤⡴⣤⣤⣤⣤⣀⣀⠀⠀⡀⢀⠈⠈⠙⠮⡽⢭⡻⣝⡻⣏⠿⡭⢯⠝⡊⠉⡀⠀⠀⠀⠀⢀⣀⣤⣄⣦⡴⣤⣤⣄⣀⡀⠀ ⡾⣽⣳⢯⣟⣷⣻⡽⣯⣟⣿⣻⢿⣿⣶⣤⣄⠀⢀⠊⡀⠈⠃⠻⣜⢳⡭⡛⠑⠃⠀⠀⠀⢀⢂⣥⣶⣿⢿⣿⣻⢯⡿⣽⣳⢟⡾⣽⣻⣟ ⣟⡷⣯⣟⡾⣧⣟⣷⣻⡼⣾⢽⣻⢾⣝⣿⣻⣿⣶⣤⣀⠠⠄⠁⠈⢁⠂⠁⡀⠄⣈⣰⣼⣾⣿⣟⡿⣞⡿⣼⢯⡿⣵⢯⣯⢿⣽⣳⢟⡾ ⣯⢿⡵⣯⢷⡻⣜⠶⣭⢳⣭⢻⡜⣯⢟⣾⣷⣯⣟⡿⣿⣷⣦⡔⠂⢀⠐⢠⣱⣾⡿⣟⡿⣽⣾⡽⢾⡹⣝⢧⡻⡼⣭⠷⣏⡟⡾⣭⢿⡽ ⣯⡟⡽⣎⢷⡹⢎⡷⢎⣳⢬⢧⣛⡴⣫⢶⡹⣞⡽⣻⣷⣽⣻⢿⣿⣶⣾⣿⣟⣯⣿⣽⡟⣿⢳⡝⣣⡝⢮⣓⠷⣳⢎⡟⡶⢭⡳⣭⢏⡿ ⢷⡹⣳⡝⣮⢝⡫⢜⠫⠘⠌⠂⠁⠊⡑⠪⠱⢎⡵⢫⡞⣽⢻⣿⣾⣽⣻⣾⢿⣻⣙⢶⣹⢎⠳⠉⠓⠈⠁⠈⣉⠁⠋⢞⡹⢣⡟⣜⣫⢼ ⢧⣛⡵⣚⠕⠊⠐⠀⠀⠀⠀⠀⢀⣁⢀⠀⢀⠀⡈⠡⠙⣜⢣⠻⡼⢿⢿⡹⢧⣳⡽⠂⢁⠀⡀⢀⢁⣁⠠⢀⠀⡀⠄⠀⠀⠃⠙⡞⣬⢳ ⡻⡜⠶⠉⠀⠈⠁⠄⣠⣼⣶⣿⣿⡿⣿⣿⣿⣶⣦⣔⡂⠠⠌⠋⠵⣫⢎⠽⠋⠁⣀⣨⣴⣶⣿⢿⡿⣿⣿⣿⣶⣦⣤⡁⢀⠈⠀⠈⢱⢫ ⡳⠍⠀⠀⠀⢈⣴⣿⣿⣟⣯⢷⣯⣿⣷⣟⣮⣿⣽⢿⣿⣷⣦⣁⠂⡀⠂⢠⣱⣶⣿⢿⣻⣽⣞⣿⣿⣷⣟⣾⣿⡽⣿⣿⣦⣀⠀⠁⠀⠑ ⠓⠀⠄⠠⢡⣾⣿⢯⡷⣾⣽⡿⣟⢯⡻⣭⢻⣜⡻⢿⡾⣷⣟⣿⣿⣶⣽⣿⣿⣽⣾⢿⡻⡝⢯⡞⣵⢫⡟⣿⣷⣟⡷⣯⢿⣿⣦⠐⢀⠀ ⠁⠈⠀⢰⣿⡿⣯⣟⣾⡿⣏⢷⡹⣎⠷⣭⢳⠮⣝⣣⢯⣝⡻⢿⣿⣯⣿⣿⠻⣝⢮⣓⠷⣹⠳⣞⡵⣫⢾⡱⢯⢿⣿⣽⡿⣽⣿⣆⠀⠀ ⠀⠠⠀⣿⣿⣽⣳⣾⣟⡳⡝⣎⢷⣩⣛⡴⠫⠙⠌⠓⠺⠜⣭⢳⢮⣝⡳⢎⣿⣘⡧⠋⠞⠱⠛⠼⣧⣛⡼⡹⣏⠾⣹⣿⣟⣷⣻⣿⡄⠀ ⠀⠀⠰⣿⣳⢯⣷⣿⢭⡳⣝⡺⡜⣶⠋⢁⠐⠈⢀⠐⡀⢈⠠⠙⠶⣮⣽⠛⠉⠁⡂⠐⠀⠀⠤⠀⠈⠹⣞⡵⢭⣫⢗⡽⣿⣞⣷⣻⡖⠀ ⠀⠀⠱⣿⡽⣯⣿⡟⢮⡵⢣⣟⠼⠁⢀⠂⣤⣼⣾⣿⣿⣿⣶⣦⣄⡀⢠⣰⣾⣿⣿⣿⣿⣶⣇⡀⠆⠀⡙⢾⣣⠗⣯⢞⣿⣻⢶⣻⡕⠀ ⠀⠀⢩⢿⡽⣞⣿⡝⣧⡝⣳⢞⠁⠀⠄⣼⣿⡿⣽⣞⣳⣟⣾⣽⣿⣿⣿⣿⣟⣾⣳⣟⡾⣽⣿⣷⡀⠂⠄⢚⡧⣻⡜⣯⢾⣯⣟⡷⡍⠀ ⠀⢀⠂⣿⡽⣯⢿⣛⠶⣭⢳⣞⠀⠀⢐⣿⣿⣽⣳⣿⡟⣯⢻⡽⣻⣿⢿⡻⣏⢿⡹⣿⣿⣳⣯⣿⡧⠐⠀⢢⡝⣶⡹⣎⣿⣞⣷⣻⠄⠀ ⣃⠀⠂⢸⣿⣯⣟⣯⢟⡶⡹⢾⡄⠀⠌⣿⣷⢯⣿⡷⣹⢎⠷⡩⢓⢮⠳⡝⣎⠷⣹⢳⣿⡷⣯⣿⡧⠃⠠⢱⡹⢶⡹⣞⣿⡽⣞⡧⠐⠀ ⢧⡈⠄⡈⢿⣷⢯⣿⣯⢖⣯⢻⣧⠀⠈⣿⣿⢯⣿⣷⢫⢾⡁⢀⠈⠀⠁⠀⠌⣹⡱⣏⣿⣟⡷⣿⠏⡀⠡⢧⡛⣧⢻⣽⣿⣽⡻⠄⠁⠀ ⡳⣥⠀⠠⠙⣿⣯⢿⣿⡞⣜⣣⢿⡆⢀⠸⣿⣟⣾⣯⡟⣾⣧⠀⠀⠀⡀⠌⣰⡷⣹⣽⡿⣽⣿⡿⠀⢄⣾⢧⢻⡼⣻⣿⢷⣯⠛⠀⠀⢴ ⡝⡶⢣⠀⡁⠸⣿⣟⣾⣿⣧⢳⣎⡽⡄⠠⠹⣿⣾⡽⣿⣎⢿⣧⣀⠀⢄⣶⢿⣱⣿⣿⡽⣷⡿⢀⠀⣼⣏⢾⡯⣿⣿⣯⣿⡟⠀⢁⡘⢮ ⣯⡝⣯⢳⡀⠀⠙⣿⣯⣿⣷⡯⣽⡞⣽⣆⠠⠘⢿⣿⡽⣿⣷⣻⢬⡻⣜⢮⣳⣿⣿⣳⣿⠏⠀⢄⣾⠟⣼⢻⣼⣿⢯⣿⠟⢀⠠⣠⢏⡷ ⣷⡽⣎⢯⢷⣄⠀⠜⢻⣯⣿⢿⣧⣟⠶⣹⢷⡀⡈⠽⢿⣷⣯⢿⣷⣻⣼⣿⣿⣿⣿⠟⡁⢀⣴⡿⣭⢻⣼⣿⡿⣯⣿⠏⡐⠠⣐⡳⢮⣽ ⣷⣻⣮⢏⡾⣹⣦⠀⠀⢻⣿⣟⡿⣯⣟⡱⣞⣻⣆⠀⢈⠻⢿⣿⣻⣿⣟⣿⣾⠟⠁⠀⣤⣿⢻⡜⣧⣿⡿⣯⣿⡿⠃⡀⢠⢳⡭⣝⣳⢾ ⡷⣯⣟⣿⣞⡵⣫⢷⡀⠀⠉⣿⣿⡽⣿⣷⣣⢷⣹⢻⣦⡀⠈⠙⠻⣿⠿⠋⠁⠀⣼⠿⣝⠶⣫⣾⣿⡿⣽⣿⠛⠀⠀⣤⢛⡶⣹⢾⡽⣯ ⣟⡷⣾⣽⣻⣷⣣⢏⡿⣆⡁⠀⠹⢿⣷⣻⣿⣮⣳⢏⡶⢻⣳⣄⠀⡀⠀⣀⡾⣝⣣⠟⣼⣳⣿⣟⣷⣿⠟⠡⢈⢠⡿⣴⢫⢾⣽⣫⢷⣯ ⣯⣟⡾⣵⢯⣿⣿⣮⡽⣏⢷⣤⠐⠈⠻⢿⣾⣟⣿⣾⣵⢫⢶⡹⣟⢤⡳⣏⠿⡼⣥⣿⣷⢿⣽⣾⠟⠁⠂⣠⡶⡟⣧⢏⣿⡿⣶⢯⣟⡾ ⡷⣯⡽⢯⣟⡾⣽⢿⣿⣯⢞⡭⢿⣄⠁⠈⠹⢿⣾⣳⢿⣿⣧⣻⢬⣳⢣⣭⢻⣵⣿⣟⣾⣿⠟⠁⠀⢂⣵⢿⡹⣝⣾⣿⢿⣽⣳⣟⡾⣽ ⣟⣷⢻⣟⡾⣽⢯⣞⣯⢿⣿⣺⢵⣚⡷⣤⠁⠀⠙⠿⣿⣞⡿⣿⣧⣷⣫⣾⣿⣻⣷⡿⠛⠁⠀⣁⣼⢿⡹⣎⣷⣿⡿⣽⢯⣶⣻⢞⣽⣳ ⠙⢾⣻⢾⣽⣳⣟⡾⣽⢯⣟⣿⣷⣏⢾⡹⣻⣄⡀⠀⠉⠿⣿⣷⣯⢷⣟⣷⣿⡟⠋⡐⠀⢢⣵⠿⣩⡞⣵⣿⣿⢯⣟⣭⣟⡾⣽⣛⣮⣟ ⠀⠈⠹⣻⣶⣻⠾⣽⣏⡿⣮⢷⣻⢿⣷⣽⢲⡝⡷⢧⣀⠀⠀⠙⠿⣿⡿⢋⡁⠠⢁⣰⢾⢯⡝⣞⣳⣿⣿⣻⡽⡾⣽⠾⣭⣟⣷⡻⠞⠀ ⠀⠈⢀⠀⠻⣿⣟⣧⣟⡷⣯⢿⣭⢿⣽⣻⣿⣾⡹⣏⡽⣳⣤⡀⠀⠀⠄⢂⢤⣵⣟⡻⣎⣷⣽⣿⢿⡽⣞⣷⣻⣽⣳⣟⣷⣿⠾⠁⠀⠁ ⣏⢦⠀⠈⠀⠈⢻⣿⣾⣽⣳⡟⣾⣛⣮⢷⡯⣟⣿⣾⣵⢫⡝⡿⣶⣤⣴⡻⣏⠷⣎⣷⣿⣟⣯⣿⣾⣽⣿⣶⣿⣶⣿⣾⣿⣥⣦⣤⣤⣴ ⡽⢎⡷⣂⠠⠐⠂⠈⠻⣾⣷⣻⣳⣟⡾⣯⣽⣻⢾⡽⣿⢿⣼⣳⡝⣮⢳⡝⣮⣿⣿⣟⡷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣻ ⣽⣫⠼⣭⡓⢦⣁⣀⠄⢈⠻⢿⡷⣯⢷⣛⣾⣳⢯⣟⡾⢯⣟⣷⣿⣮⣷⣿⣿⡻⣧⢿⣽⣳⣿⣿⣽⣟⣿⣾⣿⣵⣿⣧⣟⣾⣿⣣⣿⣺

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

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⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠾⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣻⡿⠋⠉⠛⠷⢶⣤⣀⡀⠀⠀⠀⡴⠋⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⢀⣤⡞⠃⠀⠀⠀⠀⠀⠀⠀⠙⣯⡉⠀⠀⠀⢠⠟⢷⡄⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣄⡀⠀⠸⣄⣸⡷⡆ ⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⣤⣄⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠙⢲⣶⣾⠟⠃⠁ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⣤⣀⣀⠀⠀⠀⣀⣤⣴⣾⣏⠀⠀⠀⣟⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⢷⣴⠿⠋⠁⠀⠀⠈⠁⠀⣴⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣝⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⡉⠛⠻⢶⣶⣤⣤⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠈⠉⠙⠻⠶⢶⣤⣠⣧⣀⣤⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠉⠿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠹⣿⢦⡀⠀⠀⠀⠀⠀⠘⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⢻⡀⠻⣦⣠⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠻⣆⠈⠻⢧⣆⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠙⢶⡀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠲⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣿⣆⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠋⠘⢷⡀⠀⠀⠘⣟⠻⣦⣄⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⢹⡄⠈⠛⢿⣳⣄⡀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢧⠀⢘⣿⠀⠀⠀⠙⠾⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠛⠛⠛⠓⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⡴⠊⠁⠀⠀⠀⠈⠙⠢⣀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠉⠑⢤⡀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠋⠀⠀⠀⠀⠀⡠⠂⠁⠢⡈⢢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠎⢁⡈⢢⠱⡄ ⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡁⢰⣿⡆⢱⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠘⡀⠸⠿⢠⠀⢳ ⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠣⣀⠉⣁⠏⠀⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠑⠠⠄⠊⠀⣸ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⠃⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃ ⠀⡞⠀⠀⢠⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⠴⠁⠀ ⢰⠃⠀⠀⢺⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⠤⠖⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠓⠒⢺⠏⠁⠀⠀⠀ ⣾⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢳⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀ ⡇⠀⢰⣿⣿⡆⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢧⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀ ⣷⠀⠸⣿⣿⡇⠀⢠⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀ ⢹⠀⠀⠈⠉⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢱⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠸⡆⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢿⠀⢸⡀⠀⠀⠀⠀⠀⠀⡏⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⢿⣿⣧⣀⣠⣧⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡄⠈⣇⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠘⡇⠀⢻⠀⠀⠀⠀⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀⠀⠀⠀⢰⠁⢸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢿⠀⠀⣷⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⡾⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣄⠀⠀⠀⠀⢸⠀⠀⠀⢱⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢸⠀⠀⠀⠀⢇⠀⢰⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠉⠙⠛⠛⠒⠊⠋⠀⠀⠀⠀⠈⠲⠾⠶⠦⢼⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⡶⠴⠶⠒⠒⠒⠒⠒⠺⠿⠿⣿⣿⣁⣀⣀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⣴⡋⠉⠉⠉⠙⠦⣤⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣠⠤⠔⠒⠚⠉⠉⠉⠉⠒⠒⠤⠤⠤⠤⠤⠄⠂⠁⠈⠛⠒⢶⠄ ⠀⠀⠀⠀⠉⠛⠒⠒⠺⣦⣀⡀⣀⣀⣀⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣀⣀⣠⠖⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠻⠶⢤⣤⡤⠤⠶⠖⠛⠉⠛⠷⠶⠶⠖⠛⠋⠉⠛⠳⢦⣤⣤⡤⠤⠒⠒⠛⠛⠶⠶⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢶⣒⣒⣲⣶⣦⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⣤⠴⠚⣋⣭⣿⡿⠿⢶⣶⣯⣟⣷⣦⣭⣿⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⠤⠤⢤⣀⣠⠞⠁⣠⡴⠞⣩⣼⣿⣟⣛⣯⡿⠖⠛⠚⢿⣯⣟⢯⣿⡿⠋⠁⢀⣤⣞⡓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠉⠀⠀⢀⣠⠌⢙⣶⣞⣥⣾⡿⣋⣵⠿⠛⠉⠀⠀⠀⠀⠀⠀⠹⣿⡿⠋⢀⣠⡾⠟⠉⠙⠿⣶⣌⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⠖⠋⢁⣴⣿⣧⣿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣿⡋⡀⠀⠀⠀⣰⣿⣿⣶⣾⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠛⠁⠀⣰⣿⣿⣿⠋⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣁⠀⣐⣶⣿⣿⣿⢿⣿⡿⢻⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⡿⣿⡿⠁⠀⠀⢀⣼⣿⣿⣿⣾⣭⣲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣿⣿⣭⡌⠉⠁⣼⣿⡿⢦⠀⠀⠀⠀⠀ ⠀⣴⡟⠉⣠⡿⠁⠀⠀⠀⢸⣿⣿⡿⠻⣿⣿⣿⣷⣯⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡟⡆⢠⣰⣾⠟⠀⢨⣧⡀⠀⠀⠀ ⣾⢋⢠⣴⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣠⣾⡟⠁⠀⣠⡿⠿⣷⠀⠀⠀ ⡷⠈⣸⣿⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣉⠀⢀⣴⠿⠋⡠⢻⡇⠀⠀ ⠁⣠⣿⣇⣀⣀⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣿⣄⣀⣵⠸⣿⡄⠀ ⠀⣿⡿⠿⣿⣮⡹⣆⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣆⢠⣿⣷⠀ ⣤⣿⠀⠀⠈⢻⣿⣜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣯⣷⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⣿⣿⡄ ⣾⡇⠀⠀⠀⣠⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⣇ ⡟⠀⠀⢀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⡟ ⠀⠀⠀⣾⣿⣿⣿⠟⠓⢦⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠸⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣟⣿⠇⢰⠃ ⠀⠀⠀⠛⣿⠟⠙⢧⣀⠜⠳⣄⠀⠀⠀⠙⠉⢁⣾⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡄⠀⠀⣰⣿⣿⣿⡟⡦⡜⠀ ⠀⠀⠀⠀⠉⠀⣀⡔⠻⣆⣠⠿⠳⣤⣀⠀⠀⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣮⣿⣿⣿⡇⠀⡼⠉⣿⣿⣿⣡⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠹⣦⣠⠞⠳⣄⠀⡸⠿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣇⣰⣿⣿⢷⡾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⣈⠿⢧⡀⠀⡼⠿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁⢀⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⢙⡾⣧⣀⡼⠛⠣⣄⢤⣰⣶⣶⣲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⢀⣼⢻⣿⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢿⠀⢈⠟⢓⣦⣤⣿⣿⣿⣿⠟⠻⣿⣮⡙⢦⡀⠀⠀⠀⣀⣾⣿⣿⡿⠃⠀⣰⠟⠁⠘⡟⠀⠀ ⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣀⠈⠉⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⢮⣿⣄⠙⣂⣴⣾⣿⣿⡿⠋⠀⣠⠞⠁⠀⢀⣾⠇⠀⠀ ⣿⣿⣜⢦⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣿⣦⡀⠀⠈⠛⠛⠋⠀⠀⢀⣠⣤⡴⣿⣿⣿⣿⣿⣿⡿⠏⢀⣠⠞⠁⠀⠀⠀⡼⠋⠀⠀⠀ ⣿⣿⣿⣿⣮⣗⣲⠤⣄⣀⡀⢀⣈⣛⢿⣿⡿⢿⡦⣄⣀⣀⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣀⡴⢛⣁⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡔⢰⣿⣿⣶⣿⣾⡟⣯⣿⡸⣶⣿⣶⣄⠀ ⠀⠀⠀⠀⢠⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡆ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⣿⣿⣿⣿⣯⡆⠟ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⣿⠹⠇⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀ ⠀⠀⠀⠘⡀⠿⣿⡏⠀⠀⠠⠶⢶⣦⣤⠀⠀⣰⣿⣧⠀⠀ ⠀⠀⠀⠀⣧⡀⣽⡇⠀⠀⠀⠉⠉⠛⠀⠀⣼⣿⡟⠁⠀⠀ ⠀⠀⣴⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀ ⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠐⠦⣷⡟⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠀⠀⠀⠂⡀⠀⠀⠈⢀⣉⣹⡟⠀⠀⠀⠀⠀ ⠸⠿⠿⣿⣿⡇⠀⠀⠀⠈⢦⣀⠀⢀⣀⣩⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠿⡄⠀⠀⠘⠛⣽⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠛⠛⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀ ⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⠘⢿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄ ⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⡿⢿⠏⠙⢿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟ ⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⡆⠀⠀⣸⣿⣿⣿⡿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃ ⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠘⣿⣿⣿⣇⣀⣀⣀⣀⣀⣴⣾⣿⣿⣿⡿⠀ ⢸⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⡇⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠁⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⠛⠛⡿⠁⠘⠋⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠁⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀ ⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⢀⣤⣾⡿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀ ⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢠⣾⣿⡟⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⢀⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⠘⣿⣿⣿⣿⣧⠀⠀⠀⢀⣠⣤⣀⠀⠀ ⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠋⠙⠟⠉⠉⠁⠀ ⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣦⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⡇⠀⠀⣰⣿⡿⠛⣿⣿⣷⡀⢀⣾⣿⡏⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣷⠀⢸⣿⣿⠁⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣤⣤⣴⣾⣿⡟⠀⠀⠀⠀⣾⣿⣇⣀⣀⣀⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣧⣿⣿⡟⠀⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠋⠉⠛⠁⠀⠀⠀⠀⠿⠿⠿⣿⣿⠿⠃⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣦⡀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣾⣆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣨⣿⣿⣿⠿⠿⢿⣿⣿⣿ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠋⠀⣠⣾⣿⣿⡿⠉⠉⠻⣿⣿⣿⣿⠀⢀⣾⣿⣿⡿⠃⠀⠀⠀⣿⣿⣿ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⢀⣾⣿⣿⣿⠟⠀⠀⠀⠀⣿⣿⣿⣿⢧⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿ ⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣿⣿⣿ ⠛⢿⣿⠟⢋⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⣿⡿ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣿⣿⣿⠟⢸⣿⣿⣿⣿⡀⠀⢀⣠⣾⣿⣿⡟⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣧⣀⣀⣴⣾⣿⣿⣿⠏⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠙⠿⢿⣿⣿⡿⠟⠋⠁⢀⣀⣀⣤⣤⣤⣶⣶⣶⣦⠤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⣛⣛⡛⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⠿⠟⠛⣉⣉⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⠀⠀⠀⠐⠾⣿⠿⠛⠋⣉⣠⣴⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀ ⠀⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⡟⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠙⢿⡏⠀⠀⠀⠠⣾⢛⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠤⠀⢸⣿⡆⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⢶⣤⣀⠀⢠⡣⡒⠂⡆⣠⡿⠋⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡷⢰⡝⠀⢰⠋⠁⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣖⠢⢀⠀⢠⡟⠁⠀⢞⠀⠀⠘⡸⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠸⣧⡀⢈⡏⠀⠀⠀⠀⠀⡩⢴⠓⠃⠀⠀⠀⣠⣿⣏⣀⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢾⣿⠀⠀⠀⠀⡠⠊⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⢸⡻⡀⠀⠀⠸⠁⡼⢷⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⣰⠁⠈⡛⠋⡆⢀⣰⠀⠀⠀⠀⠀⣠⣴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠣⠤⠊⢃⣰⣷⢿⣿⣿⣿⣷⣾⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠴⠞⠋⠓⠒⠒⠳⠉⠆⢏⠙⠿⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠊⣿⣿⣬⣶⡀⡂⠀⡄⢸⣷⣄⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣆⠩⢚⣛⠛⠛⠻⠷⠐⠁⣸⠃⠀⠡⣠⡛⠐⠲⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠘⣿⣿⣷⣶⣶⡶⠛⢼⣧⡀⢸⡜⡠⠂⠉⠉⠙⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⠦⠂⢉⢻⣶⣿⠏⠀⠀⠀⠉⠓⠂⠻⠁⠀⠀⠒⢄⠀⠱⡄⠀ ⠀⠀⠀⠀⠀⢀⣆⣴⣁⣤⣤⡿⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⡖⠾⢆⠀⢡⠈⣌⠆ ⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣦⡀⠑⢄⠀⠀⠀⠀⣦⣴⠃⠀⠀⢧⣶⢠⣼⡏ ⠀⠀⠀⠀⠠⠚⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠃ ⠀⠀⢀⣴⣃⣴⣻⣿⣿⣿⡿⠋⣠⣾⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀ ⢀⡔⢀⣾⡟⢁⢽⡿⠟⣫⡴⣾⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⡿⠿⠶⠋⠁⠒⠉⠀⢠⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⣿⣧⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠹⣿⣇⠀⣾⠋⠉⠉⠉⠛⠻⠿⠛⠉⠀⢹⣹⣿⣿⣿⣧⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣿⣿⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏⢹⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠁⢘⡇⣴⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣷⣦⣤⣀⠀⢦⡀⠀⠀⣠⠶⠋⣿⣿⣿⣷⣶⣾⣷⣿⡿⣡⡞⠹⣾⣿⣿⣿⣿⣿⢗⣲⠖⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⣿⠿⣷⣄⠑⠀⡐⠁⠀⣠⣿⣿⣿⠟⣻⠟⠋⠁⢸⣯⡉⢸⢹⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢧⡈⢻⣿⣷⢳⣴⣾⡿⢋⣛⣫⠴⠋⣁⠄⠀⣴⣿⡿⢠⣿⣿⡿⠟⠛⠉⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠻⡄⠿⠷⠿⢋⡈⠀⠰⠿⠟⠛⠓⠛⡏⠉⠀⣀⣛⣩⣴⠟⣋⣽⣧⠆⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⡴⠋⠀⠀⢀⣹⡀⠀⠀⣼⠁⠀⠀⠀⢀⡀⠀⢰⡇⠀⣰⠋⠉⣡⠞⠋⠁⢀⣩⢿⣶⡄⠀⠀⡇⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠈⢉⠏⠀⠀⠀⣰⠋⠈⢧⡀⠀⠙⠻⡭⠤⠖⠋⠁⠀⡼⠀⣠⣏⡴⠊⠁⠀⢀⡴⠋⠀⠀⠈⠃⣠⠴⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⡰⠋⠀⠀⢠⣽⢧⡀⠀⠀⠙⣦⣀⠀⠐⠶⠂⠀⠀⣼⣣⠾⣿⠟⠁⠀⢀⡴⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⡴⠃⣀⣀⠠⣄⡀⣰⠁⠀⠀⢀⡞⠉⠈⣇⢀⣠⣾⣿⠘⢦⡀⠀⠀⢀⡴⠟⢁⣾⠏⠀⠀⣠⠏⠀⠀⠀⠀⣠⣞⣁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⣀⣹⣦⠀⠀⠀⠀⡸⠁⠈⠁⠈⠉⢒⣽⠇⠀⠀⠀⡾⠀⠀⠀⣼⡿⠛⠁⡟⢠⡈⢿⣷⠚⠉⠀⣠⢾⡏⠀⢀⡴⠃⠀⢀⡤⠞⠋⠁⠀⠈⠙⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⢿⡄⠀⠀⢰⠇⠀⠀⠀⠀⢀⡞⣹⠀⠀⠀⢠⡃⠀⠀⣼⣍⣀⠀⠀⠀⠘⡇⠈⠻⠧⢀⡶⣣⠟⠀⢀⡞⠙⢲⠞⠉⠀⠀⠀⠀⣀⡴⠖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠀⡄⢨⠀⠀⢀⣼⠀⠀⠀⠀⠀⡞⠀⢿⠀⠀⠀⢸⠉⢳⡾⠁⠀⠈⠙⣶⣄⠀⢷⠀⢀⡴⠿⡾⠁⠀⡴⠋⠀⣠⠏⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣠⠊⢸⠀⠀⠀⠙⢲⡦⣄⣸⡄⠀⠀⠈⣇⠀⡇⠀⠀⠀⠀⠈⣿⠳⣬⠔⠋⢀⡞⠁⣠⠞⠁⠀⢠⠇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⣇⠜ ⠐⠀⢀⠀⣀⡀⠀⠀⠀⠐⠶⢰⠃⠀⠀⡇⠀⠀⠀⠙⠙⢮⣿⣷⡀⠀⠀⢹⣰⠃⠀⠀⠀⠀⠀⠸⣴⡇⠀⢀⡞⢀⡾⠁⠀⠀⣠⠏⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⢀⠠⠐⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⣩⠝⠿⣕⣒⠒⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠡⠞⠉⣍⠻⠽⠘⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣠⠤⢼⡄⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠸⡥⢼⣿⡇⠀⠀⢠⠶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⡄⠀⠀⠐⠒⢉⠀⠀⠀⠘⣯⣛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠁⠀⠀⢠⠏⣀⡠⠤⣄⢹⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢀⡾⠊⠁⠠⡤⠼⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠈⠧⣌⠀⠀⠀⠀⠀⢀⡞⢸⢃⡤⠴⠲⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠻⣟⠷⣦⡲⢄⡀⠉⠀⠀⠀⠀⢸⣤⣿⠋⠀⠀⡄⡇⣨⠷⠤⣄⡀⣀⡤⢤⣀⠀⠀⢀⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⠳⡈⠹⣷⣝⡲⢄⡓⠒⠒⢫⣿⡈⢧⠀⠀⢰⡇⡇⠀⠀⠀⠙⠓⠤⣀⢈⢷⣚⢉⣀⣀⣈⠇ ⠀⠀⣴⡊⠉⢙⣦⣄⡤⠄⠺⣄⠀⠀⠀⠀⠀⠱⡀⠈⢪⡙⢶⠣⠤⢄⣁⣻⢳⠈⣆⠀⠘⣿⣿⢠⡀⠀⠀⣄⡠⢤⡤⠼⠯⠭⣉⡒⢦⡀ ⠀⢀⣤⠟⣉⠭⠲⣍⣈⠳⢆⣉⠁⠀⠐⢦⠀⠀⢱⠀⠀⠙⢦⡉⠒⠀⠀⠀⢸⠀⠀⠀⠀⠘⣿⡄⠈⢷⣦⣤⣭⣍⣉⣉⣉⣶⠦⣌⡙⠻ ⢠⠿⠒⡯⢴⡟⠛⠒⠚⠋⠓⠦⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⠙⢆⡀⠀⠀⠘⠁⠀⠀⠀⠀⠘⡇⠀⠀⠚⢹⣧⠀⠀⠀⠈⠉⠉⠉⠉⠉ ⠛⠔⠚⠓⠉⠉⠉⠉⠉⢹⡗⢾⠯⣉⠁⠈⣆⠀⠀⣿⡤⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡆⠀⠀⠀⠘⡆⠀⡟⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢤⣿⠀⠀⠀⠀⢹⣠⡇⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡊⢧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⣿⣶⣿⣿⣶⣤⠤⠛⠛⠓⠒⠒⠀⠠⠀⠐⢄⠀⠀⢸⠦⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣻⣞⣡⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠘⠆⠀⠀⠀⠀⠉⠉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠟⠉⠁⠀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⢀⣀⣠⣤⠃⡴⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠿⠿⠿⢿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣄⣀⣀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⢠⠆⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢠⠋⠀⠀⢀⡼⡖⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠘⣿⠋⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⡸⣹⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢿⣧⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⢀⣧⢇⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⢸⠘⢸⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠈ ⠀⠀⠀⠀⠀⠀⡒⠉⡰⠂⠀⠀⠀⠀⣠⠃⠀⠀⠀⢀⣴⠯⣼⣀⠀⠀⠀⢸⡄⢸⢿⡀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣶ ⠀⠀⠀⠀⠀⠀⢀⡜⢡⠆⠀⠀⠀⢀⡟⠀⠀⠠⠖⡿⠉⠉⡟⠀⢀⠇⠀⢸⡇⠸⣸⢣⠀⠀⠀⠀⢸⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿ ⣴⣂⣀⠀⢀⣠⠃⢠⠏⠀⠀⠀⠀⣸⠀⠀⠀⢀⡼⠁⠀⠀⡇⠀⢸⠀⠀⠀⣇⠀⢿⡌⠷⡀⠀⠀⠺⡆⢨⣿⣶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⠀⠀⠀⠀⡸⠁⢰⠏⠀⠀⠀⠀⢀⡇⠀⣄⠀⡜⠁⠤⣄⡀⠇⠀⠈⠀⠀⠀⢸⡄⠈⠳⡀⠙⢦⡀⠀⢷⠋⢸⣻⠙⠿⣦⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠻ ⠀⠀⠀⣴⠁⢀⡏⠀⠀⠀⠀⠀⣸⠁⡀⢸⣿⣷⣶⣤⣄⠉⢢⠀⠀⠀⠀⠀⠀⢳⠀⠀⠻⣄⠀⠙⣦⡸⡆⢸⣿⠀⠀⠈⠙⢦⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀ ⠀⠀⣰⠁⣠⡾⠀⠀⠀⠀⠀⠀⠸⡗⢿⣿⡟⠉⣽⣿⡿⣦⠘⣆⢸⠀⠀⠀⠀⠈⢣⣀⡴⠈⠁⡶⠓⠭⣟⣼⣿⠀⠀⠀⠀⠀⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⢰⠃⠚⢹⠁⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⡁⢸⣿⣿⣿⣿⣇⠙⡞⡄⠀⠀⠀⠀⣠⣞⣠⣾⣿⣿⣶⣦⣀⠙⡟⡆⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ ⡀⣿⠏⠀⢸⠀⠀⠀⠀⢰⡀⠀⠀⣿⡆⡼⠇⠸⡇⠻⠹⣿⠟⢀⡇⠹⡄⠀⢀⡴⠛⣩⠞⠁⣠⣟⣛⣿⡿⣷⣧⣷⣀⡀⢀⡞⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀ ⢿⡏⠀⠀⢸⠀⡄⠀⠀⢸⣧⠀⠀⢻⣷⠇⠀⠀⠳⡄⢠⡿⠀⡾⠀⠀⢘⡶⢋⡠⠞⠁⠀⢰⡿⢿⣿⣿⣿⣿⣿⣿⣧⠀⡜⠁⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀ ⠀⠹⣆⠀⢸⠀⡇⠀⠀⢸⣿⣧⠀⠘⣿⡆⠀⠀⠀⠉⠀⠀⣼⣥⠴⣚⡽⠞⠋⠀⠀⠀⠀⢸⡁⠸⠏⣻⢿⡿⣹⣿⢿⡟⠁⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣆⠀⠀ ⠀⠀⠘⡄⠸⡄⣷⡀⠀⢸⣿⣿⣷⣄⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠦⠀⠰⠚⡴⠟⢁⡞⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⡞⣇⢠⠀⠀⠀⠘⣆⠀ ⠀⠀⠀⢻⠀⣷⢿⡇⠀⠘⣿⣿⣿⣾⣷⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⣠⠇⠀⡼⠁⠘⡜⡷⣄⠀⠀⠘⢦ ⠀⠀⠀⠘⡷⠻⡿⣿⡄⠀⢿⣿⢿⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣠⠋⠀⣰⢳⠀⠀⠸⣿⡌⠓⢤⣀⡀ ⠀⠀⠀⠀⡇⠈⣿⣿⣿⣦⠘⢿⡀⠙⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢀⡴⠋⠀⣰⠃⡎⠀⠀⠀⠈⠳⣄⠀⢨⠙ ⠀⠀⠀⠀⡇⠀⣿⣿⣿⡋⣿⣮⣷⡀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⣴⡞⠁⢀⡴⠁⢠⡇⡀⠀⠀⠀⠀⠈⢳⣾⠀ ⠀⠀⠀⢠⡇⣤⢿⡟⠀⢰⣿⣿⣆⠙⠲⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠟⠒⢂⣴⡿⠟⠁⠀⠀⠀⣠⠆⢀⣴⣿⠏⠀⣠⠊⠀⠀⡼⣸⠃⠀⠀⠀⠀⠀⡈⠈⠀ ⠀⠀⠀⣾⠀⠈⢯⠳⣀⢸⣿⡇⠹⡄⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⣀⣀⠤⣖⡫⠴⣚⡿⢛⣁⡴⠋⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⡰⠀⠀⠀ ⠀⠀⠰⢿⣤⣤⣬⠷⣌⣻⣿⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⣀⣀⣀⠀⢺⠟⣡⠟⠉⠉⠉⠑⠛⠁⠤⠤⠞⢩⡾⠋⢹⠙⢦⣀⡴⢫⣿⢁⡤⣠⣶⠄⢀⡜⠁⠀⠀⠂ ⢀⡴⠋⠉⠉⠀⠀⠁⠉⠀⠘⢿⡀⣟⡇⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⠏⢀⣟⡾⠁⠀⢠⠄⠀⠀⠀⠀⠀⣴⣾⣫⠀⠀⣈⣧⡀⠈⠉⠛⠛⠛⠋⠉⢀⣤⠛⠀⣠⠆⠀⠀ ⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⢠⠀⠀⠀⢀⡀⣼⠛⣿⣿⣿⣿⣿⡁⠀⣿⠋⠀⠀⢀⡎⠀⠀⠀⠀⣠⠞⢻⣿⢁⣴⣾⣿⣿⣷⣦⣤⣀⣀⣀⣤⣶⠃⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠏⠀⠀⣠⢿⣿⡷⠖⠛⠛⠛⠿⡿⢈⡾⣷⠏⠀⠀⣿⠇⠀⢀⡴⠛⠁⠀⢸⣧⣿⡏⢁⣥⣀⡉⠻⣿⣿⣿⣿⣾⡏⢀⣀⣿⣷⣶⣶⣤⡀ ⠀⠀⠠⠐⠒⠒⠛⢿⡿⠿⠛⠛⣫⠟⠁⢀⣤⣞⡥⣿⠏⠀⠀⠀⣀⣴⡡⣇⣼⢇⡟⠀⢠⣹⣿⣠⠞⠉⡄⠀⠀⠀⣼⣿⣿⣷⣾⣿⣿⣿⠋⢿⣿⣿⣿⡟⠀⣼⣧⣤⣽⣿⠟⢩⠃ ⠐⠁⢀⡤⠀⠀⠁⢀⣀⣀⡠⠤⠄⠒⠒⠚⠛⠁⣰⠃⠀⢀⡴⠚⠉⠰⠀⢸⠃⡼⠀⠀⢸⣿⠟⠉⠀⠈⠀⠀⠠⠂⢹⣿⠿⢿⣿⣿⠛⣋⣠⡟⠙⢿⣿⠁⢸⣿⣿⣿⠋⠀⣰⣇⣀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⠟⠋⠉⠀⠀⠀⠉⠉⠛⠿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠁⠀⠈⠛⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀ ⢰⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⡦⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢹⡿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠉⠉⠉⠉⠁⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠛⠉⠀⠀⠉⢻⣆⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀⢀⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡦⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢿⣿⠿⣛⡿⠛⡉⣴⠾⢛⢩⣴⣶⣿⣿⣿⣿⣶⣤⡙⠻⢷⣄⡉⠻⢿⡻⢿⣿⢶ ⡟⣠⠞⢉⣤⡳⠛⢡⣸⣾⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣷⣆⠉⠻⠆⡄⡙⢤⡌⢷ ⠸⣁⢘⡞⢠⠡⡉⢄⠉⡩⢉⢡⣤⣾⣿⣿⣷⣌⡉⢩⠉⢃⠌⡑⢢⠘⢳⡄⠙⠆ ⠐⡄⢊⡐⠢⢁⣌⣴⣷⣶⡿⣿⣿⣿⢿⣽⢿⣿⣿⣷⣾⣶⣬⣔⠁⠎⡄⡘⠄⢃ ⠐⡌⢂⠔⣁⣾⣿⡿⣽⣺⢽⡳⣟⣿⣯⣟⣿⣿⢣⡟⣽⢻⣿⣿⣧⡘⠐⡌⡘⠠ ⠐⡌⠰⢈⣼⣿⣿⡱⢷⡹⣎⠷⣭⢻⣷⣯⣿⣧⢻⡜⣧⢻⡜⣿⣿⣷⡡⠐⡌⠡ ⣴⣬⣶⣿⣿⣿⢣⡛⡵⠹⣌⠻⡰⢫⣿⣿⣿⡆⢧⡙⢦⠳⡜⢲⢻⣿⣿⣶⣤⣥ ⣿⡟⣿⠞⣱⣟⠢⠱⣈⠣⠌⠢⠑⢸⣿⣿⣿⣧⠂⢍⠢⠑⡌⢡⢊⣿⣇⢻⢻⡏ ⢻⣇⠿⣘⢹⣯⠐⠁⢠⣴⣾⡄⠁⣾⣿⢿⣿⣿⡆⠀⣢⣡⣀⠁⠨⣿⡆⢣⣿⠇ ⠸⣿⡠⢃⢚⣿⡄⠀⣿⣿⣿⠃⣼⡿⢈⠍⡘⠼⣷⡄⢿⣿⡿⡆⢐⣿⡅⢣⡿⠀ ⠀⢹⣧⠣⡘⢿⣿⣤⣈⣉⣤⣿⠟⣀⠣⡘⠤⡉⢿⣿⣮⣉⣛⣠⣾⡿⢰⣿⠃⠀ ⠀⠀⠹⣷⣡⢊⠙⢿⣿⣿⣛⠣⡐⢄⠢⢑⠂⡅⢂⡙⠿⡿⢿⠟⠏⣧⡿⠃⠀⠀ ⠀⠀⠀⠘⢻⣦⣙⠠⠌⡡⢄⡑⠰⢈⠂⡅⢊⠄⣃⠐⡆⢔⡂⣼⡾⠏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢷⣮⣔⣢⠘⠄⡃⠜⡀⢃⠌⢄⣒⣬⣶⠿⠋⠀⠀⠀⠀⠀⠀ ⠡⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠶⡶⡷⠾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀ ⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣷⠀ ⢀⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣼⠋⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢸⣿⠀⠉⠸⣿⣿⣇ ⣸⣿⣿⡿⠋⠁⠀⠀⠀⢸⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⢿⣿ ⣿⣿⠟⠀⠀⠀⠀⢹⠀⠈⣿⣷⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢰⠀⠀⠈⢻ ⣿⠏⠀⠀⢀⣀⣀⡘⠆⠀⢹⣿⣇⠀⠀⠀⣴⡟⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⡟⣆⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁⠉⢻⣦⠀⠀⠀⠀⢠⣿⡿⠀⠀⣸⠀⠀⠀⠀ ⠏⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⢻⣿⣦⠀⠀⣿⠀⠀⣿⣏⣹⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⢻⣷⠀⠀⣿⡇⠀⠀⢀⣾⡿⠁⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠶⢶⣿⣿⣷⣤⣿⣇⣀⠈⠛⠻⠇⢠⣼⠏⠙⣻⣿⣿⣿⡿⠁⠀⠀⢻⣿⣿⣿⣿⡟⢻⣧⡀⠘⠿⢿⡻⠀⣠⣿⠃⠀⣰⣿⡟⠁⠀⢠⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣶⣶⣼⣿⣯⣴⣾⣿⠟⠉⠁⠀⠀⠀⠀⠀⠉⠻⠛⢿⣿⣦⣹⣷⣤⣀⣠⣠⣾⡿⣃⣤⣾⡿⠋⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀⣀⠐⠂⠀⠀⢤⣤⡤⠤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⠛⠁⠀⠈⠉⠙⠛⠻⠿⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠉⠛⠻⠿⣿⣿⣷⣶⣦⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⣦⣤⣤⣄⣀⣼⣇⠀⠀⠀⠀⠀⠀⠀⣠⡂⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣻⠿⠟⠙⠛⠋⠉⠉⠉⠉⠙⠋⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣆⠀⠀⠀⢀⣴⡾⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠿⠟⠋⠀⠀⣀⣴⣾⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀ ⣿⡀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠇⠀⠀⠀ ⢿⣧⠀⠀⠈⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣠⣦⠀⠀⠀⣀⣠⣴⣾⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀ ⠘⣿⣧⡀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣶⣾⣿⣿⣷⣾⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠚⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⢿⣷⣶⣦⣤⣤⣤⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠠⢀⣀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠳⠷⡻⠻⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢤⣶⣿⡿⠛⡻⠛⢻⡿⠿⠃⣽⣿⣷⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣬⣿⣧⡤⠞⠝⠤⠤⠦⠧⡴⠾⣽⣛⣋⣀⣀⡀⣀⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⢻⠻⠉⠀⠀⠀⢀⣠⣔⡂⠀⠀⠀⠀⠀⠁⠈⢙⢶⣬⣹⠀⠉⠛⠀ ⣦⠀⠀⡆⠼⠃⠀⠀⠀⣠⠞⢩⣿⣿⣿⣿⠟⠻⡔⣶⣾⣿⣷⣿⠓⢉⣿⣆⢀ ⠉⠑⢄⡏⠀⠀⢀⣸⣾⣿⣛⣻⣿⣿⣿⣿⣿⣿⡇⢼⣿⣛⡋⠁⠲⠅⣠⣼⠀ ⠀⠀⠀⠁⣠⠔⠉⡤⠞⠁⠀⠉⠉⠉⠉⠉⠉⢻⠟⠹⡿⡩⠔⠁⣄⣠⡿⣿⠆ ⠀⠀⠀⡴⠁⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⡤⡊⡀⠃⣠⣴⡿⢽⣿⡜⠀ ⠀⠀⣼⣌⡒⢌⣀⣀⡀⠀⠀⣐⠀⠀⠠⠊⣤⣞⣿⣿⣦⡯⢊⣨⡶⠛⠉⠀⠀ ⠀⢀⣿⣬⣍⣉⡓⠊⡉⡙⠛⠁⠀⢀⠖⡺⡟⣘⣿⡊⣿⣴⠟⠉⠀⠀⠀⠀⠀ ⠀⢳⡋⠋⠪⣻⠧⠀⣀⣿⣟⡿⢿⣿⣟⠗⢋⣼⣷⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠛⠛⠓⠶⠶⠶⠶⠶⢶⣭⣽⣴⡶⠷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⣿⡿⢿⣿⣿⣿⣷⣄⠀⠀ ⢀⣼⣿⡿⠟⠋⣁⡀⢀⣈⠙⠻⢿⣿⣧⡀ ⣸⣿⣿⠀⠀⠘⣿⣷⣾⣿⠃⠀⠀⣿⣿⣇ ⣿⣿⣿⠀⢾⣿⣿⣿⣿⣿⣿⡷⠀⣿⣿⣿ ⢹⣿⣿⠀⠀⢠⣿⡿⢿⣿⡄⠀⠀⣿⣿⡏ ⠈⣿⣿⣷⣦⣄⡉⠀⠀⢉⣠⣴⣾⣿⣿⠁ ⠀⣿⣿⢿⣿⣿⣿⣶⣶⣿⣿⣿⡿⣿⣿⠀ ⠀⣿⣿⠀⠈⠉⠙⣿⣿⠋⠉⠁⠀⣿⣿⠀ ⢰⣿⣿⣆⠀⠀⠀⣿⣿⠀⠀⠀⣰⣿⣿⡆ ⣿⣿⣿⣿⠀⠀⢀⣿⣿⡀⠀⠀⣿⣿⣿⣿ ⢻⣿⣿⡿⠀⠀⣼⣿⣿⣧⠀⠀⢿⣿⣿⡟ ⠈⠻⡿⠁⠀⠀⣿⣿⣿⣿⠀⠀⠈⢿⠟⠁ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⠁⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⢀⣠⣴⡶⠿⠷⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣴⠟⠀⠀⠀⣰⡾⠋⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠋⠉⠁⠀⠀⠀⠉⠉⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠀⠀⠀⠀⢀⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⠋⠁⠀⠀⠀⠀⠐⢺⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠷⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠚⠛⠉⠉⠙⠛⠲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢰⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⡾⠋⠀⠀⠀⠀⠀⣠⡶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⠂⠀⠀⠀⢠⡿⠰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠦⣤⣤⣤⣴⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠋⢻⣄⠀⠄⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠚⠛⠲⠶⠤⢤⣤⣀⣀⣀⣀⣀⣤⡤⠤⠶⠛⠛⠉⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠻⣫⣍⣉⣝⣉⣹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣼⣿⣦⣴⣿⣿⣿⣓

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⢰⠇⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿ ⣸⣤⠚⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿ ⣿⡁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣾⣿⣮⢿ ⣿⢷⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⠞ ⣾⣿⣧⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⡽⠃⠀ ⡿⣿⣿⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⣷⡙⣿⠏⣽⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣭⣾⣿⣿⣿⠁⠈⠉⢉⣼⣿⣿⣿⢻⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣭⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣿⣿⣿⢟⣹⠀⣸⣿⡏⠙⢿⣿⣿⣿⣿⣿⣏⠁⠙⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⢗⠿⣿⠛⢻⡅⠸⡟⠀⠙⠧⠤⠀⠀⣿⣿⣿⠉⢿⣿⣿⣦⣈⠻⣝⢮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⡵⠏⢸⣏⡇⠈⣧⠀⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠘⣿⣿⡿⠻⣿⣿⣦⡉⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠄⠀ ⣿⣿⣿⣿⣿⣇⠁⠘⢂⣛⡇⠀⠸⣆⡇⠀⠀⠀⠰⠆⠀⠀⠈⠻⠄⠀⡟⠛⠁⠀⢈⠿⢻⣿⣦⣀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀ ⣿⣿⣿⣿⣿⣿⣆⠀⣨⣽⠁⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠃⠀⣸⣿⣿⣿⣷⣄⡀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿ ⠿⠿⠿⣏⣿⣿⡟⠉⢡⠇⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⠟ ⠀⠀⠀⣿⣿⣿⣿⣶⠏⠀⠀⠀⠀⠀⠀⢸⣿⣧⡒⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠟⢁⡤ ⠀⠀⠀⣇⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠳⣄⣀⣀⣁⣤⠤⠤⢴⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠏⣿⢃⢠⠋⢁⣀⠏⣀ ⠀⡤⢶⠘⢶⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠋⣹⣿⣿⣿⣿⡇⣿⣿⡿⢻⣟⣶⠓⡾⢹⠈⠁⢸⡤⠟ ⠋⠀⠸⡆⢸⠏⠈⡿⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⢰⡿⢿⣄⠀⢰⣿⣿⣿⣿⣿⠿⠛⢉⣤⡞⠉⠁⣰⣧⢸⣤⠖⠋⠀⠀ ⠀⠀⠀⢷⢸⢸⣿⠻⣟⣆⠀⠀⠀⠀⠀⡜⢿⣿⣿⣿⣄⣠⣤⠖⠋⠀⡏⣼⡄⣼⣿⣿⣿⣿⣿⡄⣠⣾⡟⠀⡀⣴⣣⠜⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣦⣻⣷⣿⣿⣧⡀⠀⠀⢰⠃⢸⣿⡿⠛⢯⣠⠃⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣿⣿⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠷⠾⠟⢀⣿⣿⣿⣶⣟⣷⠶⢦⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠋⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⣚ ⠀⠀⠀⠀⠀⠘⣿⣙⡻⣿⢿⣶⣶⣶⣾⡿⣿⡿⢿⣟⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⠇⠀⠀⠀⠀⣠⣤⣶⣿⣉⡟⢁⣬⠟ ⠀⠀⠀⠀⠀⠀⠘⣿⣧⡿⠾⠓⢻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⡾⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⠇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣭⣿⣿⣿⠇⠀⠀⠀⠀⣸⣿⣿⣿⠟⠉⠀⠀⠀⠀ ⣆⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡟⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠁⠀⠀⠀⠤⢤⡀⠀⡾⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⡇⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠈⠳⡀⠀⠀⠀⠈⠉⠓⠲⣄⠈⠚⠀⠓⣠⡴⠚⠉⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⠇⠀⢀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠹⡄⠀⠀⠀⣀⡠⠤⠾⠟⠒⠒⠈⠉⠉⠉⠓⠒⠶⠾⢦⣀⡀⠈⢷⡀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢸⠀⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢻⡤⠚⠋⠁⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣝⢦⣀⠀⠈⠀⠀⠀⠀⠀⢀⡞⠀⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢻⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣳⣄⡀⠀⠀⠀⠀⡼⠃⠀⡼⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⣸⠇⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠹⡄⠀⣠⡴⣶⣓⡒⢦⣤⡀⠀⠀⠀⠙⢯⡙⠒⠤⠤⠞⠁⠀⡼⠃⠀⠀⠀⠀ ⠈⢧⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢠⡎⠀⠀⠀⠀⢀⣴⠞⢉⣉⣽⣿⣦⠀⠀⢧⠀⡿⠟⠉⠉⠉⠙⠻⣿⣦⡀⠀⠀⠀⠹⡄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠈⢳⡀⠙⢦⣀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⡰⠋⠀⠀⠀⠀⢠⣾⡵⠞⠉⠁⠀⠀⠉⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠸⡖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⡀⠈⠛⠲⠤⠤⠴⠋⠁⠀⢀⣤⠞⠁⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⣀⣠⠤⣄⣀⠀⠳⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⣄⣀⠀⠀⢀⣀⡤⠞⢉⡟⠀⠀⠀⠀⠀⠀⢾⠃⠀⢀⣀⡤⠤⢤⣄⣀⠀⠀⠀⠈⠀⢠⠾⢋⣥⣤⣤⣤⣌⡙⠢⣄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡏⠁⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠈⣠⠖⢋⣡⣤⣤⣤⣀⠈⠑⢆⠀⠀⢠⣟⣴⣿⣿⣿⣿⣿⣿⣿⣷⣌⢷⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⢳⡄⣸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⡠⠷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⡿⠿⢻⠋⠁⢸⣿⣿⣿⣿⠀⠀⠀⠉⠓⠢⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⢹⣿⣿⡀⠀⠀⠀⢿⠀⠘⢧⡀⣼⣿⣿⣇⠇⠀⠀⠀⠀⠀⠀⠿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠄⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⡿⠿⠿⠛⠛⠋⠙⡁⠀⣷⡀⠀⣸⣿⣿⣷⣤⣄⡀⠈⢳⡀⢈⣽⣿⣿⡿⢋⣠⣤⣄⡀⠀⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⣀⡀⠘⣟⠻⣿⢿⣷⡀⠀⠀⠀⠀⠀⠳⣀⣨⣿⡿⠛⠁⠀⠀⠀⠀⠈⠉⠙⠛⠛⢻⡷⢮⣴⣿⣁⡀⠀⠙⠳⣄⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠛⠻⣦⡻⣯⣿⢿⣷⣤⣤⣤⡤⠞⢋⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣷⣯⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⠓⠦⠭⠭⠥⠤⢖⡟⠀⠀⠀⠀⠀⠀⣠⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⠏⠻⣦⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣶⡄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠨⡿⠏⢈⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠋⠀⠀⣹⠀ ⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠉⠉⠙⢦⣀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣷⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠀⠀⠀⢀⣻⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠹⣯⠑⢲⠷⢤⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡏⠀⢀⣀⣼⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠈⠛⠶⢤⣤⣤⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⡢⢧⡀⠉⣟⠲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⢻⣷⠛⢋⣩⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⢷⣀⠏⡶⠹⣄⠽⡝⠓⡖⠒⢦⠤⢤⡤⠽⣤⠤⡤⢤⣼⣿⠴⠞⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⡈⠙⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠺⠤⢽⣄⣙⡆⠘⣇⠈⢣⡴⠹⣤⠣⠔⢵⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣯⠀⠀⠀⠉⠙⠳⣦⡀⠉⠓⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⢺⣶⠛⠛⠛⢻⣿⣽⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⡀⠀⠉⠙⣷⠒⠶⠶⠶⠤⠤⠴⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣬⡉⠛⠒⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠛⠛⠛⠒⠒⠒⠤⠤⠤⠤⢄⣀⣀⣀⣀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠒⠂⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠤⠤⢤⣄⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣬⣷⣦⣀⡀⠀⠀⠀⠀⠀⣴⣋⣠⣤⡴⠶⠿⠛⠛⠋⠉⠉⠉⠙⠛⢶⡀⠀⠀⠀⣰⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠜⠁⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣶⠶⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⠴⠦⢄⣋⡳⢿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀ ⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠒⠈⠉⠉⠉⢉⣙⠒⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣤⣤⠶⠖⠒⠒⠮⣷⣾⣿⣿⣿⢑⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣶⣾⣽⣾⣿⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⢌⢉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⡿⠛⢿⣿⣿⣆⢆⠀⠀⠀⠀⠀⠀ ⠀⢸⣼⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⠿⠷⠋⠁⠀⠀⠀⣿⣿⣿⡘⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡟⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⣜⢿⡇⠀⠀⠀⠀⢠⣤⣤⣤⡼⠀⣶⣤⡔⠶⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⡎⡇⠀⠀⠀⠁⠈⠁⠀⠀⠃⠀⢸⠏⠀⠀⠉⠁⢸⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⡁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠠⠅⠀⠀⠀⠀⠀⠰⠀⢀⠀⣀⣿⣿⣦⡀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠒⠷⠾⠛⣺⡿⠋⣿⣿⡇⢲⣠⠄⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⢁⣼⣿⣿⣷⣿⣿⣷⣄⠀⠂⠄ ⠀⠀⠀⢀⡠⠖⠡⣿⣆⠀⠀⢀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒⠀ ⠄⠐⠉⠀⠀⠀⠀⠻⣿⣦⣀⠀⠈⠐⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠒⢀⣨⣷⠀⠀⠐⠲⠤⣤⣈⡑⢢⣤⣿⡀⠑⣄⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⠊⢡⡴⠖⡒⠒⠒⠛⠶⠒⠛⠻⢦⡀⠙⡄⠱⣼⣇⠀⣷⠀⠈⢣⡀⠀⠀⢀⡞⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠋⣴⣃⠔⢋⠔⠉⠀⠀⠀⠀⠀⢢⠀⠀⠀⠈⠢⡘⡄⢷⣿⣦⣽⡇⠀⠘⡝⢆⠀⢸⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⡀⠀⣠⢇⣼⠟⠁⢠⠎⠄⠠⠃⠀⠀⠀⠀⠀⡆⠰⡀⠀⠀⠈⢪⡀⢻⣿⣿⠀⣦⠀⢱⠈⢧⢸⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀ ⡾⠋⠉⠉⠉⡽⢻⠃⠀⢠⡏⠈⢠⠃⢀⡔⠀⡸⠀⠀⡆⢀⣧⠀⠀⡄⠀⢻⣄⣿⣧⣾⣽⠀⢸⠀⠘⡏⠁⠀⡸⠀⠀⡠⠒⠉⠀⠀⠉⢳ ⠀⠑⢒⣿⣥⡴⡇⠀⠀⡿⣀⠀⠈⢀⠟⠀⡰⠁⠀⡰⠃⢸⡟⡆⠀⢸⡀⠀⢻⡉⢣⣹⠏⠀⠈⢠⣾⡇⠀⠀⠇⢠⠎⠀⠀⠀⠀⠀⡠⠜ ⠰⡟⣩⣋⡿⣾⠃⠀⢰⡇⣿⢀⢿⡿⣶⡎⠀⢀⠞⢁⡠⠉⡤⢷⠀⠀⡇⠀⠀⢷⣼⣫⣔⡤⣾⠟⢹⠃⠀⠀⣸⡏⠀⠀⠀⣠⠖⠉⠀⠀ ⢸⡏⢉⠁⠀⡏⠀⠀⣸⣤⣿⣷⣾⡧⢬⣿⣶⠷⢺⠟⢁⣼⠃⢸⠀⣰⡇⠀⠀⠘⣯⡿⣿⣧⣤⡴⠛⠂⢀⠔⠁⠀⢀⡠⠊⠁⠀⠀⠀⠀ ⠀⠀⠈⠻⣶⣷⠶⠿⠏⠉⢛⣷⣾⡔⠊⠉⠀⠠⠷⣖⣫⣤⣄⣸⠞⣧⡇⠀⢰⡋⠀⠀⠀⠹⠯⡄⠀⠀⡞⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣷⡤⠤⠶⣾⠿⣟⣿⣄⠀⠀⠀⠀⠜⢻⣿⣿⣿⣿⠆⡿⠁⡄⡰⢉⡏⣷⡄⠀⠀⠘⡆⠈⢉⣀⡴⠀⠙⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⢧⠀⠀⢸⣆⢻⣿⣿⠇⠀⠀⠀⠀⠘⢿⣿⣿⣋⣜⣠⢾⣾⣷⡟⠃⣿⢿⡄⠀⠀⡹⠊⠁⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣟⠾⠀⠀⢰⠿⡎⠛⠛⠀⠀⠀⠀⠀⠈⠛⠉⠐⠋⡩⢃⣠⣴⡿⢁⣆⣿⡾⣇⠀⠀⡇⠀⢠⣤⡴⠖⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⣶⡄⠀⢧⠘⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⣾⣶⣉⣼⡿⣵⣾⣿⣿⠀⢨⣿⣶⠧⣀⡜⠉⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⡙⢷⣄⠸⣦⠀⠙⠢⣄⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠯⠞⠋⣿⣿⢸⣀⣿⠉⢹⡷⣌⡦⠤⠤⠤⣶⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⣿⢿⢷⠮⠷⣤⠴⢲⣿⠀⡛⡏⠩⡀⠀⠀⢸⠏⣾⠀⢻⣻⡀⠈⠳⣌⠓⠒⠒⠊⣠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⣿⠀⣸⢩⣄⣽⣿⣏⠉⢦⢀⡇⠀⢸⡀⠈⠻⣇⡀⠀⠈⠓⠦⣴⣞⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡇⣼⣿⡟⢿⡟⡆⠀⢻⠃⠀⠈⡇⠀⠀⠀⠙⠲⢤⣤⡴⠼⠿⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⠃⢸⡇⢻⢀⣾⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢀⠞⠻⡾⢯⡿⣦⡴⠒⠚⠁⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⢹⠿⣽⡜⢣⣴⡇⠈⠉⢓⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⢸⣓⢎⣑⠪⢼⠁⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⣷⡌⣧⠄⠉⠒⢿⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠙⠻⣿⣷⣤⣴⣏⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢰⡇⠀⠙⠯⣽⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠙⠲⠦⣄⣀⡜⠁⠀⠀⣰⣿⠁⠀⠀⢀⡾⠻⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠉⢉⣑⣶⣶⣿⡿⠖⠒⣶⣿⠀⠀⠙⣟⠙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣼⠙⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⡦⠖⠒⠚⠋⠉⠉⠉⣉⣵⣞⣿⡟⠁⠀⠀⠈⠉⠀⠀⢀⣾⠓⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⣾⠗⠋⢸⡀⢷⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⠤⠶⠖⠉⠁⠴⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢽⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢧⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⣶⠀⢀⡏⢻⣆⠀⠀⠀⠀⢸⠀⠀⠀⠘⡆⠀⠀⠀⣀⣉⡲⣄⠀⠀⠀ ⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠃⡇⠀⠀⠀⠀⠀⠀⢸⡆⢸⠇⠀⠻⣆⠀⠀⠀⢸⠀⠀⠀⠀⢿⠀⠀⠀⡿⠉⠉⠉⠛⠀⠀ ⠀⠀⣠⠞⠁⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣀⣠⣤⣟⣀⣀⢹⠀⠀⠀⠀⠀⠀⣼⣇⡏⠀⣀⣀⣽⡦⠤⣀⣏⠀⠀⠀⠀⠘⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠚⠓⠒⠚⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠏⠀⠀⠉⠙⣷⣤⡀⠀⢀⡾⢻⡿⠗⠋⠉⠁⠀⢱⡀⢸⡏⠀⠀⠀⠀⠀⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⠀⠀⣿⣠⣿⣤⣤⣤⣔⡒⢺⡀⠈⣠⠎⠀⡾⠁⠀⢐⣪⣯⣥⣼⣿⡟⡇⠀⠀⠀⠀⣦⣸⡀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⡸⢹⡀⠀⠀⢸⣷⠿⠉⢸⣿⣿⣿⡟⠃⣧⡴⠃⠀⠀⠀⠀⠀⢋⣿⣿⣿⣿⠊⢹⣇⠀⠀⢀⡆⣿⠙⢧⡘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢠⠇⢀⣧⠀⠀⠸⣿⣄⠀⢸⣿⠿⢹⡏⠀⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⢿⣽⡇⠀⢸⡟⠗⢀⣾⠀⢿⢸⣦⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⢀⣰⠟⣠⡟⢽⣧⠀⠀⢿⠈⠃⠈⠻⢥⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠿⠟⠁⠀⡏⠀⣠⣮⠞⣇⢸⣸⠁⠻⢼⡆⠀⠀⠀⠀⠀ ⠀⠀⣠⡼⠗⠿⠛⠋⠉⣇⣼⣿⣷⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⣾⣿⣿⣦⣹⣿⡇⠀⠀⠀⠣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⣷⣷⢆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⣸⣿⣿⡿⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢽⣯⠻⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠟⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠙⣧⣀⠙⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣼⠿⣟⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⣞⡿⠋⢹⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠙⡆⢹⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⢿⡝⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢳⣽⡇⠉⡓⠦⣄⡀⣀⣤⠖⠉⢹⣸⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡿⡇⣧⡑⣶⣶⡾⠟⠁⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⠇⠘⣗⠚⠋⠀⠀⠀⠀⠀⢸⢿⣷⢦⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⢲⡞⠹⣿⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠃⢉⠷⣌⠉⠛⠶⣖⣒⠒⠲⠤⢤⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠤⠔⠒⠊⠉⢡⡞⠀⢸⠳⡄⠈⠳⣄⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⣎⣀⠈⢷⡀⣠⣤⣬⣴⡂⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⣠⠞⣏⠀⠀⠀⠀⠀⢀⣰⠏⠐⠒⠺⠰⠞⠲⣀⠈⠳⣄⠀⠈⣧⠀⠀⠀⠀⢀⡼⠁⢠⠏⠀⠀⠉⠉⠓⡄⠀⠀⠀⠀⠀⠠⢄⡀⠀⠈⢧⠀⠀ ⠀⢰⡇⠀⠈⢧⣀⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠓⢄⡈⠀⠀⢀⡰⠋⢀⣴⠃⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠰⠁⢀⠀⠈⢧⠀ ⠀⣸⠁⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠉⠛⠛⠋⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⡄⠀⠈⠆⠀⠈⢧

⣿⣿⣿⠻⢿⣦⡀⠀⡠⠢⡀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠛⠉⢣⣄⡠⢠⠊⠀⡌⢀⠖⡏⠸⢇⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠋⠀⣘⠀⣰⡤⠁⠀⠰⡇⢸⠀⡀⡠⢳⢨⠱⣄⡀⠀⠈⢆⠀⠀⠀⠀ ⠉⠉⢹⠀⣤⡾⠙⣤⣻⢁⠤⠤⡀⣡⠮⠚⠋⠀⠤⠓⠗⠬⡑⠢⡄⢸⠀⠀⠀⠀ ⣶⣶⣾⣾⠁⣇⠀⢈⢹⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠸⡎⠱⠀⠀⠀ ⠩⠙⢛⠻⡀⣬⠦⠋⠠⢃⡎⣀⡈⡄⠀⠀⠀⠀⡜⢀⡀⠈⢂⠀⠀⠃⢀⢢⠃⠀ ⠀⠁⠀⠆⠐⡬⠍⣿⣇⣼⠀⢿⣧⡇⠀⠀⠀⠀⠀⣿⣽⠀⠜⠀⢻⠒⠚⠁⠀⠀ ⢔⡕⠒⠃⡔⠣⠼⣿⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⠢⡤⢠⡴ ⠀⠈⢀⣤⠻⡉⢰⣦⠭⠖⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢴⣏⠄ ⠀⢰⣿⣿⣧⣷⠞⠋⡆⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡠⠐⠉⠀ ⠀⠀⠻⣿⡿⠧⡀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠈⠀⠀⠀⠀ ⠀⠀⠀⠙⡒⠲⡈⠑⡄⠀⠈⡒⠤⣀⡀⠀⠀⠀⠀⢀⣠⣐⣉⣠⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠘⡄⢸⠀⣠⠋⠀⠀⠈⠙⠫⢝⣞⣁⡀⢤⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⠀⣶⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠒⢩⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⣰⡇⠀⠀⠀⢻⣿⣾⣽⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀

⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⣠⣤⣄⣐⣒⠒⠒⠉⠉⠛⠛⠛⠛⠛⠛⠿⠷⣶⣶⣤⣄⣀⡴⠋⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣱⠶⠖⠛⠉⠁⠀⠀⠈⠉⠉⠙⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠛⢿⡇⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠘⣇⠘⣿⠀⠀⢠⣤⣄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠀⠀⣀⣤⡤⠤⠤⠤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠘⠛⠋⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⣡⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠀⢸⠀⠀⠀⠀⢰⣿⣿⣧⢘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⢠⣾⡵⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠸⡄⠀⣀⣤⣯⣶⣇⠀⠀⠀⠀⠈⠻⠟⠃⠀⢻⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣠⣷⠞⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡃⣠⠴⠟⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡟⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠛⠉⣉⡥⠞⠛⠛⠳⢶⣤⣀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠈⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⣼⢳⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⡞⠃⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⠃⠠⡏⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠼⠇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠐⣆⠀⠀⣀⣠⣴⡶⢿⣿⣿⣿⣾⣷⠀⠀⢷⠀⠀⠸⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠹⠛⢹⣿⣿⣇⣴⣾⠿⠿⠿⢿⣿⡆⠀⢸⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣛⣋⣻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠋⠁⠀⠀⠀⠀⡿⠉⣿⣿⣋⠀⣀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⢹⣿⣾⠿⠋⠉⠉⠉⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣧⣼⣻⡟⠿⢯⣉⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣿⣼⡿⠁⠀⠀⠀⠀⢰⡇⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠙⡽⣿⣿⡿⠿⠿⢰⠛⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠘⣿⣾⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠿⠆⠀⣾⠀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⣷⡂⠀⠀⠀⠀⠀⠀⢻⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣀⣴⠿⠛⡙⠃⠀⢀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⣿⣿⣶⣄⡀⠀⠀⠀⠈⠻⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠛⠉⢀⠖⣼⠃⠀⠀⢸⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⣿⡛⠿⠷⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠆⡏⠀⠀⠀⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⠿⠭⠤⢦⣄⡀⠀⠀⢀⣤⣿⠟⠁⢠⠇⠀⠀⢠⡇⠀⣸⣇⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣻⣿⣿⣿⣶⣄⡀⠠⢀⡀⠀⠀⠼⠋⠀⠀⠀⠀⠀⢀⣀⣤⣾⡽⠟⠁⠀⠀⢸⠀⠀⠀⣼⠀⠀⣏⡟⠛⠿⠿⠶⠶⠤⣤ ⡀⠀⠀⠀⠂⢻⣵⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⡬⠍⠛⠶⠶⠶⠂⠀⠀⠈⣥⠞⠋⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡏⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⣧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣻⣿⠿⣿⣿⣿⣿⣿⡁⠛⠳⣄⣀⣀⡤⠤⢤⣠⡟⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⠁⠀⣾⣿⠹⢷⣄⠀⠀⠀⠀⠀ ⣥⣀⣀⠀⠀⠀⢹⣟⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡧⣹⣿⣿⣿⣿⡿⠛⣧⡀⠀⠈⢩⡁⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡞⠀⢠⡟⣿⡀⠀⢹⣧⡀⠀⠐⣋ ⠀⠉⠉⠛⠿⠶⢮⣿⣷⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢹⡘⢻⡏⢉⡿⠃⣰⣿⣷⣤⣀⠀⠑⣄⠀⢀⢾⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡇⠀⣼⠀⠈⠿⣄⢠⡏⢀⠶⠟⠋ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡇⢈⣷⡟⠀⢰⡿⢽⣷⠈⠙⠻⠶⢾⠉⠉⢿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠌⣷⡇⠘⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢷⢸⣹⡇⠀⣿⠇⠀⣿⡆⠀⠀⠀⠈⢱⣤⣸⡇⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡞⠀⢠⢿⡆⠀⠀⡀⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠦⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠓⣷⢸⣿⡂⠀⢹⣿⣄⠀⠀⢀⡾⠘⣿⡇⠀⠀⠀⠀⠀⠠⡇⠀⠀⢰⡇⠀⢸⣾⡇⠀⠀⢠⡏⠿⠀⠀⢄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢣⠀⠀⠀⠀⢀⠧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⡤⠤⡤⠤⡜⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣀⣰⠤⢀⣁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠋⠁⣑⡞⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡜⠟⣿⠃⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡋⢀⣀⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣷⣯⣧⣬⣽⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡾⣷⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣿⣰⣦⣴⣶⣾⣶⣶⣷⣶⣖⣀⠀⠤⢈⠳⣦⡘⢦⠀⠀⠀⠀⠀⠀⠀⠐⠐⠛⠛⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⡻⣿⣿⣿⣿⣿⣽⢿⣿⣿⢿⢿⡟⠓⠂⠀⠈⢾⡀⢣⠀⠀⠀⢀⡴⠊⣉⠓⠂⠀⠂⠘⢻⢿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⢿⠏⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⢳⡜⡆⠀⢠⢋⢔⣊⣁⢄⣀⡀⠀⠀⠀⠀⠀⠁⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣱⣱⣠⡷⢋⣉⣀⣀⣀⠀⠉⠓⠢⣄⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⠀⣀⣠⣖⣉⣀⠀⠤⣿⡭⢝⣫⡾⣋⡡⠤⠶⠒⠒⠮⢍⡑⠦⡀⠙⢶⣤⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣿⣿⣿⣿⣿⠛⠳⠶⢬⣅⣀⣀⣀⣀⡤⠤⠤⠬⣀⣻⣋⡴⠶⢆⣀⣄⡀⠀⠀⠉⠢⡘⢷⢄⢱⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⢠⡉⠩⠻⠿⣿⠷⢤⣀⠀⠀⠉⠉⡁⠀⠀⡠⠔⠀⠀⠉⠈⠙⠲⡒⠬⡑⠍⠢⣀⠀⠀⠈⠢⡹⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠐⠀⠀⠠⠈⠳⣲⠤⠏⢉⠗⠉⠀⣰⠟⠁⢀⡼⠃⡀⢶⡀⠀⠘⢆⠈⠳⡦⡈⢷⣦⣶⣶⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠋⠉⣱⠏⠀⢠⢾⠏⠀⢠⡾⠁⡸⣧⢨⡞⡄⠀⠈⢦⠀⠙⣌⠋⠻⣿⣿⣤⡙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢪⠇⠀⣰⠏⠀⣰⢃⠏⠀⣰⢣⠇⢀⣧⣿⣿⣧⣳⡀⠀⠈⢧⠀⠘⡄⠀⠙⣽⣿⢿⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡜⢁⡎⠀⣰⡟⠀⡸⢁⡎⠀⣰⢁⡾⠀⣼⠿⠋⠉⠁⣿⡇⠀⠀⢸⢧⠀⢹⣄⠀⠘⢽⢧⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣻⢃⡜⡇⢀⢏⠃⢠⠁⡞⠀⢠⠣⢻⡇⢠⠋⠀⢰⣾⣿⡇⡇⠀⠀⢸⣭⡇⢸⡻⣧⡀⠈⢯⢦⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡿⢣⡞⢀⡇⡸⢸⠀⡎⢸⠀⠀⡎⢸⣿⡇⢸⠀⠀⠸⣿⡿⢷⡇⠀⢰⣸⣥⣽⡞⢉⡙⢿⣦⡈⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠎⣰⠏⣠⡞⢰⡇⢸⢸⠀⡇⠀⡸⣸⣿⣿⡇⢸⣷⣤⣤⣄⣀⢸⡇⠀⡇⣇⡠⢶⣫⠝⠻⣄⠙⢾⣶⣄⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢁⡞⠁⣼⠃⡇⢸⢱⡈⡎⢰⠁⠀⣷⠃⣼⠟⢣⢸⢻⡟⠋⢀⠀⣾⢣⡼⣜⡵⣶⣿⣿⡇⠀⢸⠀⠀⣧⡇⣩⠻⣕⠒⡦⣤⣤⣤⡀⠀⣀ ⠋⠀⠈⢸⠀⡇⣸⠀⢿⡇⢸⣸⢸⢸⣀⣁⣀⡾⢾⡯⠤⠴⢌⣦⠃⢠⡻⢿⠀⢻⣿⣿⠇⠀⠸⠀⢰⠗⣠⢻⢶⢬⣳⢄⣈⡣⡙⠦⣀⠀ ⠚⣀⣠⠼⢳⡇⢿⣄⠘⣇⢸⣏⣿⣼⡶⠒⣶⣶⣶⣿⠙⣏⠁⡞⣴⡟⠁⠘⠆⠈⠉⠉⠀⠀⠀⠠⠾⠋⡼⢸⢦⣟⢮⡵⠦⢄⣈⠑⠈⠑ ⣉⣡⣤⣂⠠⢴⡘⢮⣟⣿⣾⣎⢯⠞⢆⠀⠙⢿⡿⠿⢀⣈⣼⡮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡄⠈⡝⢝⣇⠉⠓⠉⠉⠉ ⠈⠉⠀⠀⠀⣴⠏⢠⣾⠃⣿⡯⠷⠃⠈⠓⠀⣲⣂⠀⡩⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡜⢀⢾⣀⠈⠻⣆⠐⠠⠀⠀ ⠀⠀⠀⠀⣰⢃⠶⡿⠁⠀⣹⡗⢄⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⠘⣟⠏⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡷⡏⠉⠚⠉⠒⠮⠷⣄⠀⠀ ⡖⠀⠀⢰⣣⣮⠊⠀⣠⢾⡉⣇⠀⢳⡄⠀⠀⠀⠑⢄⠀⢦⣀⣀⣈⣉⣁⣀⡀⠠⠄⠀⠀⠀⠀⠀⣸⡿⡇⡇⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣂⣠⡾⢋⣠⠴⠊⠁⢀⠗⢼⠀⠀⡟⢦⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡁⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠿⠋⠉⣁⢀⡄⠀⣠⠋⣠⡞⣇⠆⣿⣶⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⢸⡎⢧⣿⠀⠀⠀⢀⣀⢀⣠⣥⣀⠀⠁ ⠁⠀⠀⢠⣸⣼⣿⣿⣯⣞⠁⠀⠹⣰⢻⠙⢷⣿⡗⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣿⡉⢺⠙⢾⣸⠀⢰⣀⣥⣿⣷⣿⣿⣿⣭⣮ ⠀⠀⢘⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣏⣾⠀⠈⣿⡝⡜⣿⡍⠳⣖⣠⢤⢤⡤⣤⣶⣿⡿⢁⡏⢳⢸⢰⡀⢹⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⣿⠀⡼⠀⣷⠙⡇⢻⠲⡀⠚⠮⠏⣹⠞⠉⠀⠀⡸⠀⢸⡿⣞⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣮⣴⣾⣿⣿⣿⣿⣿⡿⠿⠛⠀⠀⠀⠸⣷⠃⠀⠘⣴⡇⠀⢣⠙⠒⠒⠋⠀⠀⠀⠀⢠⠇⠀⠘⣿⡟⠀⠀⠙⢯⠻⠿⠋⠛⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⡄⠈⢤⣄⣠⡀⠀⢠⢯⠀⠀⠀⠙⢧⣀⠈⢣⠀⠀⠀⠀⠀⠀⠀⡞⠀⣠⠔⠋⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⡿⠛⠁⠀⠠⣿⠟⢛⣵⠇⠀⠀⠀⠀⠀⠀⠈⠙⠦⣇⡀⠀⠀⠀⢀⡜⠸⡏⠀⠢⡀⠀⠀⠀⠀⠀⢸⣦⣀⠀⠀⠹⠟⠅⠋ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⣀⣤⣶⣿⠃⠀⠀⠀⣠⢺⣿⢍⠉⢦⡀⢀⡏⠀⠀⠀⠈⠀⠀⡇⣧⡄⠙⣄⠀⠀⠀⠀⣼⣿⣿⣿⣶⣦⣄⡀⠀ ⠛⠿⠿⡉⠁⢀⣠⣴⣾⣿⣿⣿⠃⠀⠀⣠⠞⢹⢸⣿⡄⠳⢟⡇⣞⣀⠀⠀⠀⢀⡤⠤⢵⠙⢇⣠⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠁⠀⣠⠔⠉⣼⣿⣿⣿⣿⡇⠀⢀⣼⠁⠀⡆⠈⣿⣧⠀⠀⢠⠁⠀⠉⠲⠐⠋⠀⠀⢸⠐⡉⢠⣿⠁⡷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣠⠞⠁⠀⢀⣿⣿⣿⣿⣿⠀⣤⣿⣿⡀⠀⡇⠀⢻⣿⡆⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⡇⠔⠁⣼⡿⠀⠃⢱⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡴⠁⠀⠀⠀⢸⣿⣿⣿⣿⣧⣾⣿⣿⣿⣇⠀⠀⠀⠈⢿⣿⡀⠀⠀⠑⢄⠀⠀⠀⠀⡜⠀⠀⢰⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⢿⣷⠀⠀⣤⡈⡇⠀⠀⡼⣀⡅⢀⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⢿⣧⡀⢻⡄⢸⠀⠰⣡⠏⢠⣾⡿⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⣠⡾⢛⣦⣄⣰⠶⣆⣾⡙⣶⡤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⢤⣀⣿⡄⡟⠁⡇⢸⡅⠈⡿⠀⣿⡏⠹⡿⠀⢿⡏⠙⣆⠀⠀ ⠀⠀⢠⡖⢲⡸⡅⠈⣿⠇⢷⡇⢸⡇⠀⣇⠀⡇⠀⢻⣷⠀⢷⠀⣼⠀⢰⠇⠀⠀ ⠀⠀⠘⣧⠀⣇⢧⠀⢸⡄⠸⡇⢸⣷⠀⢿⠀⣷⠀⡿⢹⠀⢸⣤⡇⠀⣾⠓⢦⠀ ⢠⡞⠳⡿⣄⡸⣼⡆⢸⡇⠀⡇⠀⣿⡄⢸⠀⢹⢰⡇⢸⡆⠘⣿⠁⢀⡏⠀⣼⠀ ⠘⣧⠀⣟⠉⣧⢹⡇⠸⡇⠀⣷⠀⣿⡇⢸⡇⠸⣿⠀⣼⡇⢠⡏⠀⢸⠃⢰⠇⠀ ⠀⠘⡆⢹⡀⠸⡆⢷⠀⡇⠀⢻⠀⢸⣿⢸⡇⢀⡏⢰⣿⡇⣸⠁⠀⣾⠀⣿⣄⠀ ⢀⣴⢿⡄⢧⠀⢹⣼⡀⣻⣀⣘⣧⣀⣿⣼⣇⣼⣅⣾⣸⣧⡏⠀⠀⡏⢸⣧⠈⢳ ⣾⠁⣿⣷⡘⣦⡴⠿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⣰⡇⣿⡟⠀⢸ ⢹⡄⠙⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠟⠁⠀⣼ ⠀⢻⡄⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⡏ ⠀⠀⢻⡄⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢸⠇ ⠀⠀⠀⢻⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠈⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠀⠀⢻⡄⢰⣿⡏⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⣱⡄⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢸⡇⠘⠿⡿⠿⠁⠀⠀⣶⡀⢐⣶⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⣼⠁⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀ ⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⣿⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⢆⠀⠉⠉⠉⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠉⠉⠐⠒⠒⠊⠷⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⠒⠠⠤⠤⠤⠤⠊⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣄⣀⣀⣑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⡀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠦⡀⠀⠀⠁⠀⠀⠀⠀⠒⠒⠒⠒⠤⢄⠀⠀⠀⠀⣈⣁⣠⣤⣀⣀⠘⡄⠀⠀⠀⢠⠎⠈⢢⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠛⠋⠀⠀⠉⠉⠁⠀⠉⠑⠛⠲⢔⠁⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡀⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣠⠔⠊⠉⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠲⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠎⠀⠀⠀⠀⠔⠋⠀⠀⢀⣾⠀⠀⠀⢀⣠⣤⣤⣶⣶⣤⠄⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⢣⠀⠀⠈⠢⢄⡀⠀⠀ ⠀⠶⣎⠁⠀⠀⠀⠀⠀⠀⠀⣀⠴⢻⣯⠀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠙⠻⡀⠤⣄⣀⣀⠸⠟⠃ ⠀⠀⠈⠙⠒⢲⠄⠀⠀⢠⠞⣱⣲⠿⡧⠀⠀⠀⢀⣴⣒⡀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⢄⡀⡇⢰⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠋⠀⠀⢀⡤⠶⣿⠃⢠⠃⠀⣠⣾⣿⣿⣟⠛⠻⣮⠁⠀⠀⠀⠀⢼⣿⣿⣟⡛⠻⣦⣽⡇⠈⣏⠀⠀⠀⠀⠀ ⠐⠶⣎⣉⢀⣀⡄⢰⠋⣨⢷⡞⢀⡎⢀⣼⠟⣿⣿⡿⠿⣿⡆⢸⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⡄⢸⢿⢧⠀⠈⠢⣄⠀⠀⠀ ⠀⠀⠀⢠⠃⢠⠃⢸⠀⣷⠟⣠⠎⠀⠀⠘⢆⠻⣍⣛⣲⣿⠃⡸⠀⠀⠀⠀⠈⣇⢻⣛⣿⣿⠃⣾⣟⢻⠉⠒⠒⠛⠁⠀⠀ ⠀⠀⠀⣎⣴⠧⠤⠾⣆⠛⠛⠩⠤⣄⠀⠀⠀⠑⠪⠭⠽⠒⠊⠁⠀⠀⠀⠀⠀⠈⠢⠬⠽⠵⠚⢸⠙⢏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠃⠀⠀⢰⠀⢸⠓⢤⡀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⠄⣑⣦⠄⠀⠀⠀⠀ ⠀⠀⡏⠀⡀⠀⡸⠀⢸⠀⣸⠉⠙⡛⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠳⡆⠀⠀⡇⠀⢸⡴⠃⢀⠔⢻⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠃⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢷⡆⠀⡅⠀⡼⠟⠉⣁⡀⢸⡆⠀⠀⠙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⡄⢡⡴⠁⠀⡰⠁⠈⠻⢄⠀⠀⠀⠸⡄⠉⠒⠤⣀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⢄⣣⢀⡜⠁⠀⠀⠀⠀⠑⠦⡀⠀⠱⡀⠀⠀⠀⠉⠑⢒⠾⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠳⠀⠀⠀⠀⠀⠉⠀⡟⡆⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠢⡀⠀⠀⠀⠀⠀⢰⠳⣶⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠙⢆⠀⠀⠀⢀⡆⠀⡇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⠁⠀⠈⠑⢄⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠈⠢⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠑⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠛⢤⠖⠤⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣹⣦⣀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠈⠳⣄⠀⠉⠲⢤⡀⠀⠀⡇⠀⠀⣀⣀⡠⠵⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⠉⠉⠉⠉⠐⢢⣗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠐⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⡅⠀⠀⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⢆⢲⠊⠐⠪⠢⢄⡀⠰⣄⡀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢹⢚⢻⡆⠀⠀⢀⣨⣉⡉⠉⠱⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⠀⠉⡅⠀⠐⠥⠀⠿⠛⠂⠀⢜⡕⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⣜⠡⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢢⠀⠒⠀⠀⠀⠀⠀⢀⡠⢺⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡠⠄⠐⠒⠚⠀⠀⠁⠢⠀⣀⠀⠤⠒⠉⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠛⡀⠤⠄⠀⠒⡍⠤⠤⠤⠖⢻⠀⠀⠀⢀⡠⠔⡉⢢⣀⠀⠀⠀⠀⠀ ⣀⡠⠄⡲⠒⠛⡧⡀⠀⠀⡆⣸⡶⡍⠁⠀⠀⣰⢕⡡⠒⠉⠑⠦⡀⠀ ⠁⠀⢀⡡⠶⠊⠃⠷⣤⡀⠘⡝⢲⠙⠤⠚⠋⢀⠎⠀⠀⠀⠀⠀⠈⢂ ⠀⠀⢸⠈⣖⠀⠀⠀⠀⠈⢤⠓⡚⠀⠀⠀⠀⣜⠄⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣸⣾⢹⡄⠀⠀⠀⠀⠘⡉⠁⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣠⢾

⠀⠀⠀⠀⠠⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⢸⡁⠆⠀⠀⠀⠀⠀⠄⠀⢤⡄⠀ ⣤⣤⣌⠛⢶⡤⠀⢠⣤⣮⣤⣤⡾⠃⠀ ⡇⠀⠉⢷⣾⣿⣙⣿⡿⣿⣉⡴⠶⠶⡄ ⠛⠶⠶⠿⣿⣿⣿⡿⠛⠻⣯⡀⠀⣰⠁ ⠀⠀⠀⢰⣿⣿⣿⣷⡀⠀⠉⠛⠛⠁⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠸⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠿⠏⠀⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠶⣖⠚⠛⣛⡛⠛⠋⠙⠛⠓⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠞⠛⠉⠉⠀⠀⠀⢠⣿⢷⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⢀⣀⣀⣤⣶⣿⣿⣿⡇⠀⠘⣿⣿⣷⣿⣷⡶⠖⠒⠒⠶⢦⣤⡿⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠛⠉⠀⢀⡠⢀⣤⡶⠛⠋⠉⠉⠛⠿⣿⣿⠟⠀⠀⠀⠚⣻⡿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠻⣾⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠁⠀⠀⠀⠀⡟⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠸⣧⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠠⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢹⣧⣄⡀⠀⠀⠀⢸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⡴⠛⠁⠀⢹⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣼⠀⠈⠉⠛⢷⣤⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣼⠁⠀⠀⠀⣼⠃⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣄⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⣠⡟⢠⡿⠀⠀⠀⠀⠀⠨⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⣼⠇⠀⠀⠀⣸⠃⠀⠀⣿⡹⢿⡄⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⣠⡟⠀⠀⠀⠀⠻⣶⣄⡀⠈⠻⠟⠁⠀⣠⡴⠋⣠⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⠀⠀⠀⠀⡏⠀⠀⠘⠟⢷⣄⠛⢶⣄⡀⠀⠈⠙⠋⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠶⠒⠛⠉⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠙⢷⣶⡍⠛⠛⠒⠺⠛⠋⠉⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⠸⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⣠⣴⣶⠿⠛⠛⠋⠉⠛⠛⠛⠛⠿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢻⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠿⠿⠿⢷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠉⠓⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣆⠄⠀⠀⠀⠀⠀⠺⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⣄ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠈ ⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⣿⡀⢠⡿⠃⠀⠀⡀⢠⣦⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡾⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠘⢷⣿⡁⠀⢘⣾⠇⠀⠈⡟⣿⣿⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠲⣶⢤⣤⣤⣙⣿⣶⣾⣇⣀⣀⣴⡿⢻⡏⠀⠀⠀⠀⢸⣿⠿⠿⠿⣷⡷⠶⠶⠶⠶⢶⣶⠶⠶⠶⠿⠿⣿⠿⢿⡿⠛⠛⠛⢛⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠆⠀⠀⠉⠉⢸⣿⠛⠛⠛⠋⠚⣿⣇⣀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠁⠀⠀⠀⢀⣼⣿⣴⣦⣄⠀⠀⣿⠀⣿⡇⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⠉⠙⠻⣦⡀⢸⣿⠀⠀⠀⣿⣀⣀⣤⣾⠟⠋⠁⠀⠀⠉⠿⣶⣿⣤⣿⣧⣤⣤⣤⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⢾⠀⠀⣀⣀⣤⣼⣿⣤⣤⣤⣤⣿⣿⠀⠀⠀⠈⠻⠿⠿⠶⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠾⠧⢌⣽⣯⠉⠴⢟⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⢉⣶⡾⢋⡀⠀⠉⠉⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠑⣄⡀⠀⠀⠀⠀⠂⠀⠔⣫⠏⣢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠶⠋⣋⠋⡘⠉⠁⠀⠀⠀⠐⠛⢪⣣⣶⣧⣘⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠔⠕⠐⠱⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡷⣖⢗⡀⠀⠀⠀ ⠀⠀⠀⠀⡜⠌⠀⢠⡁⣘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢁⠸⡀⣿⡀⠀⠀ ⠀⠀⠀⣐⠌⢀⠂⢈⢎⣁⠉⠉⠛⠀⠀⠀⢠⣤⣤⣤⣸⡀⢸⠀⠇⢼⡇⠀⠀ ⠀⠀⠠⠋⣠⠇⢀⡞⡌⣶⣾⡇⠀⠀⠀⠀⢀⠤⠤⠄⣸⠘⠘⠀⠘⣄⢣⡀⠀ ⠀⠠⢡⣮⠂⠀⣼⡷⠉⠉⠉⠀⠀⠀⠀⠀⠪⢅⣿⣷⣾⠀⠀⡆⣷⡸⡖⠩⠵ ⠰⡱⠿⣣⠃⢠⡿⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⢎⠺⠗⣽⠀⠀ ⢷⢳⠿⡕⢴⣳⠁⠀⠀⠀⠀⠀⠝⢉⠗⠀⠀⠀⠀⠀⢇⣆⢠⠘⡀⣀⠹⠀⠀ ⢀⡏⣸⡇⡇⡏⣆⠀⠀⠀⠀⢄⠠⡤⠄⡀⠀⠀⠀⠀⠸⣏⣮⢾⣞⢼⡹⠀⠀ ⠈⢺⢓⢀⡁⠁⡎⣦⠀⠀⠀⠀⠈⠉⠐⠁⠀⠀⠀⡠⢳⠃⢃⢹⣧⡼⠀⠀⠀ ⠀⢸⣬⡱⡟⢀⢳⢻⣳⡄⠀⠀⠀⠀⠀⠀⣀⢤⢾⠀⡄⠄⢸⣸⠹⡆⠀⠀⠀ ⠀⠁⢽⡕⡇⢼⢘⡇⡇⢏⠑⠀⠀⠀⠂⠉⠀⣾⠸⠀⣧⡘⣼⡀⠁⡇⠀⠀⠀ ⠀⠀⠜⠰⢂⣿⡾⢿⡇⠈⡄⠀⠀⠀⠀⠀⠀⣿⣦⣷⠁⡇⡟⢉⣧⠃⠀⠀⠀ ⠀⠀⠐⠚⣾⣿⣰⡟⣾⠀⠀⠀⠀⠀⠀⠀⢸⣻⣽⣿⣿⢰⡷⠜⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠙⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣧⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠀⠈⡿⠦⣤⡤⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⡟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣰⡄⠀⠀⠀⠀⣤⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡄⠀⠀⠀⢸⡀⠀⠀⠀⠙⠁⡾⠛⠶⢤⣉⠁⠀⠀⠀⣸⠀⠀⠀⠀⢀⡆⠀⠀ ⢀⠀⠈⣧⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢹⠓⢶⠦⠬⠿⠀⠀⣰⠏⠀⠀⠀⠀⣼⠁⠀⠀ ⠘⠳⢤⣸⡆⠀⠀⠀⢈⣷⣄⡀⠀⠀⠈⠑⠋⠀⠀⠀⣠⡾⢷⡄⠀⠀⠀⢰⣏⣤⠞⠃ ⠀⠀⢀⣬⠿⠶⣤⣴⠞⠳⣌⠙⠲⠤⣤⣀⣤⠤⠖⠚⠁⠀⠀⢹⣄⣠⠶⠿⣥⡄⠀⠀ ⠀⠀⠈⠀⠀⠀⡼⠋⠓⠦⣈⡛⠶⢤⣀⣀⡀⠀⠀⢀⣀⣀⡤⢶⠿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠉⠓⠒⠶⣯⠭⠽⠿⠛⢛⣇⠀⠘⣇⠹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⠀⠀⠀⠈⣿⠀⠀⢹⡄⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡅⠀⠀⠀⠀⢹⡄⠀⠀⢳⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⠂⠀⠀⠀⠘⡧⠖⠚⠉⣹⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠸⢧⡿⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⡀⠀⠀⢀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠀ ⠀⠘⠚⠛⠚⠛⠻⠟⠛⠛⠟⠻⠛⠐⠛⠟⠛⠃⠀⠈⢐⠟⠓⠛⠛⠊⠐⠀⠂⠐⠓⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⢀⣤⡴⠶⠒⠛⠛⠓⠒⠿⠿⠳⢿⡷⣬⡷⣴⣦⣤⣤⣀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠋⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠋⠀⠈⠙⢦⡀⠀⠹⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠹⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣧⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣿⡀⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⡇⢸⡇⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⠀⠀⢹⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣧⢸⡇⢴⣾⠿⡟⠻⠿⠿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣾⣿⣿⣿⠿⠿⠿⠛⠛⠿⣿⡦⢼⠀⣿⡇⠀⠀⠀ ⠀⠀⣀⢸⣿⣼⡇⠈⠿⠀⢀⣠⣤⣤⣄⣀⣈⠙⡿⠀⠀⠀⠀⠀⢿⠇⢀⣀⣠⣤⣤⣄⣐⠀⠿⠀⠘⣧⣿⠁⣀⡀⠀ ⠀⣾⠟⠻⣿⡿⠀⠀⠀⠀⠿⠉⣿⣿⣿⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢿⣿⣿⡏⠻⠃⠀⠀⠀⣿⣿⠾⠻⣇⠀ ⠀⣿⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⣿⠀ ⢰⡿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡄ ⢸⣷⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢀⣿⠁ ⠈⣿⡇⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⢸⡏⠀ ⠀⠸⣷⣧⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⣿⡿⠃⠀ ⠀⠀⠈⢿⡏⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢻⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠛⠛⠛⠿⠛⠛⠛⠷⠤⠄⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣀⣤⣤⣤⣤⣤⣀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣽⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⢻⣿⢟⣛⠉⠉⠉⠀⠀⢩⣿⣯⣿⣷⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⠿⠟⠋⠀⣴⠚⠛⠉⢶⠀⠈⠉⠛⠛⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠏⣦⣄⠀⠀⠀⣷⠀⠀⠀⢺⡀⠀⣠⣶⣷⣌⢿⣦⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡶⠿⢷⣾⡏⣾⠿⢿⣷⡄⠀⢿⠀⠀⠀⠈⡇⢠⢿⣻⣏⠙⠊⣿⠟⠉⠉⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⢹⣿⠀⠐⠒⠚⣳⣤⣼⠄⠀⠀⠀⣿⢾⣶⣦⡀⠀⢸⣿⣦⡀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⠀ ⠀⣴⣿⠟⠛⠛⠿⣷⣄⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⢀⣴⣿⣿⣤⣤⣤⣿⡏⠁⠀⠀⠀⠀⠀⠀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠻⣿⣦⡀⠀⢠⣾⡿⠋⠉⠉⠙⢿⣧ ⠀⣿⡇⠀⠀⠀⠀⠙⣿⣧⣠⣾⡿⠋⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣦⠀⠀⠀⠈⠻⢿⣶⣿⠏⠀⠀⠀⠀⢀⣼⡿ ⠀⠹⣿⣦⡀⠀⠀⠀⠸⠿⠟⠋⠀⠀⠀⠀⡴⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⠿⠿⠿⠟⠛⠛⣿⠛⠛⢹⣿⠃⠀⠈⢳⡀⠀⠀⠀⠀⠉⠛⠀⠀⠀⢀⣴⣾⠟⠁ ⠀⠀⠈⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣸⣿⡁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀ ⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⣿⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀ ⠀⠀⣰⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⣸⣿⣿⣧⣄⡀⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣀⣿⣴⣿⣿⣿⣦⠀⠀⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⢀⡞⢻⣿⡄⠀ ⠀⢰⣿⡏⠀⢹⣄⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣼⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠙⢧⡀⠀⠀⠀⣠⠞⠀⠀⣿⣷⠀ ⢸⣿⠇⣇⠀⠀⠙⠷⣤⣀⠴⠋⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣉⣦⠶⠛⠁⠀⠀⣸⠃⣿⡇ ⣾⣿⠀⠹⣆⠀⠀⠀⢨⠍⠙⠛⠛⣹⣿⢿⣿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⣿⣿⡿⣆⠀⠀⠀⢳⡀⠀⢀⣴⠏⠀⣿⡇ ⠹⣿⡄⠀⠙⠳⣤⣀⣋⢀⣀⣤⠞⣽⣟⣿⠏⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢿⣿⣿⣌⠓⠦⠤⠤⠥⠶⠋⠁⠀⢠⣿⠇ ⠀⠻⣿⣄⠀⢀⡠⠈⠉⠉⠁⢀⣾⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠘⣿⡝⣿⣦⡀⠀⠀⠀⠘⢤⢀⣴⣿⠏⠀ ⠀⠀⠙⠿⣷⣯⣄⣀⣠⣤⣶⡿⠋⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡈⠙⠿⣷⣶⣶⣶⣾⠿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀ ⠀⢠⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠙⠻⣿⣿⣿⡄⠀ ⠀⣿⣿⣿⡇⢠⡄⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠶⠀⣿⣿⣿⣿⠀ ⢰⣿⣿⣿⣧⡀⠀⠀⣠⣿⣿⠿⠿⣿⣿⣤⣀⣠⣴⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⣿⣿⣿⣿⣿⠀⠙⢿⣿⣷⣤⣤⣾⣿⠿⠋⢀⣿⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⣿⣧⠀⢄⡉⠉⠉⠉⢉⣀⡄⠀⣼⣿⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⣿⣿⣧⣄⠙⠛⠛⠛⠛⢉⣠⣾⣿⣿⣿⣿⣿⣿⠀ ⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀ ⣼⡏⠀⠀⠉⣿⠉⠉⠉⠙⢿⡿⢿⡿⠋⠉⠉⠉⣿⠉⠀⠀⢹⣧ ⠙⠻⢶⣦⣼⣿⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⣿⣧⣴⡶⠟⠋ ⠀⠀⠀⠀⠀⢻⣆⠀⣀⣴⡿⠛⠛⢿⣄⡀⠀⣰⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⠛⠁⠀⠀⠀⠀⠉⠛⠿⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⡿⠿⠿⣿⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⡿⠿⠿⣷⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠉⠛⠻⢿⣷⣦⣀⠀⠀⣠⣴⣿⠿⠛⠋⠁⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠻⢿⣿⡿⣿⣿⢿⣷⣦⣀⠀⠀⠈⠙⠿⣷⡿⠟⠉⠀⠀⠀⣠⣶⣿⢿⣿⠿⣿⣿⠿⢛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⠻⣷⡀⠀⠈⠀⠉⠓⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠛⠁⠈⠁⠀⣰⡿⢿⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣄⠀⠘⣿⣯⠻⣷⡈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠉⣠⡿⢫⣿⡟⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⠀⠀⠈⠛⠿⣿⣷⣄⠘⢿⣧⡈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⣡⣿⡟⢀⣴⣿⡿⠟⠉⠀⠀⠀⣀⣀⠀⠀ ⠀⠀⠿⣿⣿⣿⣷⣶⣤⣀⡈⠛⢿⣧⠈⢿⣿⣄⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⣤⣈⢿⣧⣾⢏⣠⣤⣴⣶⣶⣦⣤⣄⡀⠀⠀⠀⢀⣴⣿⠏⢠⣾⠟⠋⢀⣠⣴⣶⣿⣿⣿⡿⠇⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⡇⠀⣨⣾⡿⠛⢿⣷⣦⣠⣾⠟⠋⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠈⠙⢿⣶⣄⣴⣿⠟⠻⣿⣦⣀⠀⢾⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀ ⠀⢀⣤⣶⣾⣿⣿⣿⣿⠿⢶⣴⣿⣿⣿⡂⡀⠀⢨⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⡀⠀⠀⣻⣿⣿⣷⣔⠾⢿⣿⣿⣿⣿⣶⣶⣤⠀ ⠀⠘⠛⠋⠉⠉⠀⠀⢀⣴⣿⢿⣿⣿⣿⣾⠅⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢨⣿⣿⣿⣿⢿⣷⣄⠀⠀⠈⠉⠉⠛⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠈⠙⠙⠋⠁⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠉⠙⠙⠙⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⡿⣋⣴⣶⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⣠⣬⡻⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣟⣵⣿⡿⢣⠆⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⢦⡹⣿⣿⣝⢿⣧⡀⠀⠀⠀ ⠀⠀⠀⣴⣿⢏⣾⣿⡿⣱⣏⡆⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣏⢷⡽⣿⣿⣏⢿⣷⡄⠀⠀ ⠀⠀⣸⣿⠏⠸⢻⡿⢹⡟⠞⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠘⠞⣿⡙⢿⠻⠈⢿⣿⡀⠀ ⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀ ⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇ ⢸⣿⠇⠀⠀⠀⠀⢀⣤⡶⠾⠛⠛⠶⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠴⠶⠛⠻⠶⣦⣄⠀⠀⠀⠀⠀⢻⣿ ⣼⣿⢀⡄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢠⢸⣿ ⣿⣿⣸⣷⢀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢻⣿⠛⠷⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠟⢛⣿⠇⠀⠀⠀⠀⠀⠀⣸⡏⠀⢀⢰⣺⣸⣿ ⢿⣿⣿⣿⣏⣦⠀⠘⢿⣦⡀⠀⠀⢀⠀⡈⢿⣆⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠿⠿⠛⠁⢹⡇⠉⠻⠿⠿⠛⠉⠉⠉⠁⠀⠀⠀⠀⢀⣾⡟⡀⢀⡀⠀⠀⣠⣾⠟⠀⢀⣾⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⡟⠆⠀⠀⠉⠙⠓⢲⣏⣴⠃⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⢹⣤⣷⠖⠛⠋⠁⠀⠀⠾⣿⣿⣿⣿⣿ ⠀⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠙⢿⣦⣄⣀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⢀⣀⣤⣾⠟⠁⠀⠀⠀⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⠇ ⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⢀⠀⡄⢸⣇⠀⠀⠀⠀⠀⠈⠛⠛⠿⠷⠾⠿⠟⠻⠷⣦⣤⣤⣤⣤⣴⠾⠛⠿⠿⠶⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⣿⠇⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀ ⠀⠀⠀⠙⢿⣿⣾⣷⣴⣷⣮⣟⡃⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀⣚⣯⣴⣾⣴⣶⣾⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡉⠀⠀⠙⠻⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀⢹⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣷⣶⣦⡀⠉⠛⠻⠷⠶⠶⠶⠶⠾⠿⠛⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⠶⠶⠶⠶⠿⠛⠋⠁⣠⣴⣶⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣶⡶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣦⣤⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠶⢶⢶⣶⣶⣶⣶⡶⡶⠾⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣟⢝⢟⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⢿⣿⡉⠀ ⠀⠀⠀⢀⠔⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣶⣿⣷⣄ ⠀⠀⢰⣿⣿⡟⣿⣿⣿⡟⠋⠉⢩⠀⠀⠀⠉⠉⠙⢻⠿⣿⣿⣯⣿⣿⣯⣿⡝⣿ ⠀⠀⠀⠉⢻⢱⣿⡟⠀⡇⠐⡀⠘⣇⠀⠀⣀⣀⠀⠘⡆⠀⢹⣿⣟⣻⣿⣿⠿⠉ ⠀⠀⠀⠀⣈⢻⡇⡇⣼⠻⡒⢣⡀⠸⡙⢍⠈⢮⣍⣁⡇⠀⡎⣗⡿⠀⣿⣿⡀⠀ ⢄⣀⣀⣀⣿⡘⡿⣿⣇⣠⣽⣴⣟⠦⣱⣀⣿⣾⣶⣽⡇⢢⣿⡿⠇⠀⣿⣿⣿⣶ ⠀⠉⠛⠿⡿⢇⣷⣿⣟⢼⣏⡏⠛⠷⣂⠉⠘⠧⠝⢊⣇⣼⠟⠁⠀⢠⣿⣿⣿⡙ ⠀⠀⠀⠀⢘⣼⣼⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⣚⣿⣿⣯⣭⣲⣼⣿⣿⣿⣷ ⠀⠀⠀⠴⠯⠟⣩⣷⣿⣷⣄⠀⠀⠠⠄⠂⠀⠐⡫⠋⣿⣿⣿⣿⣿⣿⣿⡿⣏⠙ ⠀⠀⠀⠀⣠⡞⢡⣿⣿⣿⡿⣿⣦⣄⣀⣠⣴⣵⣶⣾⡿⠻⠋⣿⣿⣿⣿⣧⠀⠈ ⠀⠀⢀⢞⡟⢰⣬⣼⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⠿⠋⠀⠀⡼⢿⣾⣿⣿⣿⡀⠀ ⠀⠀⠂⣾⠁⢨⣿⠟⢛⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⢀⣾⣷⣎⠙⠻⣿⡟⢆⠀ ⠀⠀⠘⡀⠀⣼⣇⣠⠾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣠⣿⠿⠛⠉⣧⠀⠈⠃⠀⡆ ⠀⠀⠀⠊⠦⠿⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠈⠆⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠙⠦⣄⠀⠀⠀⠀⣸⣧⠀⣰⡏⠙⣆⠀⠀⠀⠀⣠⡄⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⣿⠀⠀⠈⠳⣦⡀⠀⣿⢹⣠⡏⠀⠀⠹⣆⢀⣴⠞⣿⠁⠀⠀⠀ ⠀⠀⠀⢿⡄⠀⢸⠀⠀⠀⠀⠀⠙⢶⡿⠀⠛⠀⠀⠀⠀⠹⠋⠁⠀⣿⠀⠀⠀⠀ ⢶⣄⡀⢸⡟⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣀⡀⠀ ⠈⢻⡟⠷⣷⠈⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠛⣿⠁⠀ ⠀⠀⢻⡄⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀ ⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣆⠀⢀⡴⠟⠋⠉⠛⠻⢦⡀⠀⣴⠛⠁⠀⠀⠀⠙⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣦⡿⠁⠀⠀⠀⠀⠀⠀⢹⣼⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⣀⣀⠀⢸⠿⣇⢠⣴⣦⠀⠀⠀⢀⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⣦⣀⠀⢸⣿⣿⣶⣿⣤⣿⣿⣿⣿⣁⣠⣴⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⠛⣿⠟⠁⠀⠀⠀⠈⠙⢿⡉⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⣠⣾⣇⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣞⣭⡿⠶⠶⠶⠿⠿⠶⣽⣷⡀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠶⠶⠒⠛⠉⢈⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠈⠉⠉⠉⠁⠀⠀⠀⢀⡿⠻⣄⠀⠀⠀⠀⠀⠀⣾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠹⣆⠀⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢠⣿⡀⠀⠀⣿⣧⠀⠀⣰⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡼⠀⢻⣤⣤⣿⠈⢷⣠⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣰⠃⠀⢸⠇⠀⠘⣧⠀⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⢰⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡟⠀⠀⠀⠀⠀

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⠀⠀⡖⢒⡖⢢⢀⠇⠐⠂⢤⡖⠒⡖⠢⣴⠒⡄⠀⡖⠒⠒⢲⠲⡒⠤⠒⡶ ⠀⠀⡀⢨⡇⠸⡙⠀⠻⠀⡌⠃⠀⡇⠘⣏⠀⢇⣀⡇⠘⠃⢸⢀⠕⢀⠹⡀ ⠀⠀⠁⠈⠈⠐⠋⠁⠀⠒⠁⠁⠀⠁⠈⠈⠀⠈⠊⠁⠀⠀⠈⠈⠀⠉⠀⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠶⠤⠤⠦⠤⠷⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠀⠘⣀⡤⠒⢺⣲⣶⣦⣶⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢴⣿⠻⠋⠢⢀⠀⡇⠀⠈⠁⠘⠛⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠌⠀⠉⠢⢀⠀⢠⠗⡇⠀⠀⠀⠀⠀⢸⣀⠠⠐⠒⠈⠢⡀⠀⠀⠀ ⠀⠀⠜⠀⠀⠀⠀⠀⣹⠏⠀⢻⠓⢦⡶⠶⠴⡞⠀⢢⠀⠀⠀⠀⠐⢄⠀⠀ ⠀⡼⡄⡀⠀⠀⠀⡜⣿⠀⠀⠀⡏⣹⠣⣴⣞⢇⠫⠣⠀⠀⠀⠀⠀⠀⠂⠀ ⠈⠓⢮⣘⢔⣤⠎⢠⡇⢀⡀⠀⠉⠸⠊⡆⠘⣎⢂⠡⡱⡀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠉⠓⠁⡔⠚⠃⠌⣀⠀⡤⠀⠨⡄⠀⠘⣦⠢⠑⡐⣄⣠⣔⡾⠃⠀ ⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆⠉⠉⡙⠲⡒⠚⠆⠀⢈⣷⢷⡾⣋⠱⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⡜⠀⠀⢰⠱⡀⠐⠄⠈⢤⡵⠥⢏⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣄⠀⢣⠀⠀⣸⠀⠱⡀⠈⢂⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠚⠉⠀⠀⠱⡀⠀⠢⡀⠀⠤⣰⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⡜⠤⠂⠈⠁⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣀⣀⡀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣠⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣟⣷⣶⣷⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⡿⠿⠃⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣯⣿⣿⣅⠀⠀⠀⠈⢯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⣵⡄⠀⢀⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣆⠈⢿⢄⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣧⡈⢎⢢⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡘⣆⠱⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⢆⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣧⡈⢿⢿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡵⡈⢫⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡝⢆⠳⡙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢄⠳⣕⡈⢮⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢢⠈⠳⠀⠑⠝⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢣⠀⠰⠠⡈⠺⣳⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠃⠀⢺⣿⣀⣼⣾⣿⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣆⣤⣾⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠿⣿⣟⣾⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⣻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣞⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣮⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⣴⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣷⣄⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣦⣈⠿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⠈⠻⣿⣿⡟⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠈⠛⠿⢿⣿⣿⠃⠀⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⡛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣤⠆⠀⣾⠏⢛⡇ ⠀⠀⠀⠀⠀⢻⣿⠀⠀⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢟⣿⣦⣄⣼⠛⠚⠁ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⢹⡄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡇⠀⠀⠀⠀⠀⠀⣼⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⡥⠿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠱⣄⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠟⠛⠉⠀⢠⠃⠀⠀⠀⠀⠀⢀⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⡿⠛⢿⣧⢠⡼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢸⡇⠀⠘⣿⠌⠁⡇⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⣀⣤⠖⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⢳⡄⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣾⠇⠀⢀⣿⣠⣰⡇⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣹⡿⠀⠀⣼⠃⣻⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡌⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⢧⡀⠀⠉⠙⠒⠶⠶⠶⠒⠋⠁⠀⣰⡿⠁⣠⡞⢁⣴⠟⠀⠀⠀⠀ ⣶⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠉⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⣀⡴⣾⣏⣭⣉⣹⢷⣄⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣅⠈⢛⣃⣿⠋⠀⠀⠀⠀⠀ ⠘⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⢒⣿⣿⠟⠛⠋⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠻⢷⣖⡒⠛⠛⠿⠿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠰⠐⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⣄⣤⣶⣿⣟⠛⣂⣰⣦⢆⡤⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⡉⣼⡛⣿⣶⢻⣏⠀⣡⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⣿⠏⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⠑⢟⣯⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⠛⠲⠦⠤⢀⠿⣏⠉⠻⢿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠿⠉⠉⠛⠉⢩⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢷⣰⠟⠀⠀⠉⠙⠛⢿⢹⢿⢹⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠤⠤⠤⣿⠀⠀⣶⣤⡴⠾⣿⠀⠛⢷⡄⠀⠀⠀⠀⢸⠸⢿⡿⣄⡀⠀⢀⡾⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠉⠁⢠⣿⠟⠀⠀⣸⣧⣄⣀⠀⠀⠈⠓⠛⣟⢿⣷⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⣿⠟⠀⠀⣴⣿⣿⣿⡿⠛⠓⠲⡶⠶⠼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⠃⠀⣠⣴⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⣛⡉⠉⠉⠛⠳⢦⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠄⠊⠀⢠⡾⠋⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⡉⠉⠷⡄⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢀⣼⡿⠋⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁⠀⢣⠙⣆⠀⠙⢦⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠋⠁⢀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⢀⣀⣤⠴⠛⢀⡤⠒⠛⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣧⡄⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢦⡀⠀⠀⠀⠀⠀⠻⠶⠟⠋⠉⣀⣀⣴⠋⣠⡺⡄⠙⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⢸⡌⠙⠳⢦⣤⣤⣄⣤⡤⠤⠖⠚⠉⣰⡇⠘⠏⠚⢉⠀⠉⠉⣙⣒⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠙⣇⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⣿⣿⣿⣕⣒⣭⣿⠚⢻⡉⢻⣻⣿⣿⡎⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢀ ⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠠⠀⣀⠀⠀⣿⣿⣿⡾⣿⣿⣿⣾⡿⡷⣄⠛⣉⣴⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠃⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁ ⠀⠀⠀⢀⣀⣀⣙⠻⠦⣾⣓⣦⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⠋⠀⣳⢄⡭⠥⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠛⠲⣶⠂⠸⠛⢓⠚⣛⡛⢛⡿⠛⠋⠀⣠⠞⠁⣠⠆⠀⠀⢀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢠⢷⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀ ⠒⣤⠀⠀⠀⠀⠀⣠⡶⠃⠀⣠⣶⡟⠉⣁⡴⠋⠀⠀⣠⠞⠁⣠⠞⣁⣤⠔⠚⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⠈⢇⠀⠀⠀⢠⠀⠀⢸⢿⣓⣤⡀⠀⠂ ⣾⣁⣤⡴⠶⠛⢋⡻⠶⠖⢋⣽⡿⠖⠋⠉⠀⢀⡴⠋⠀⣠⡾⠗⠋⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡞⠀⣸⠀⠀⠀⡸⠀⡀⢸⣄⢯⠉⠋⠉⠉ ⡇⠀⠀⠀⠀⠀⠀⠙⠓⢀⡞⠁⠀⠀⠀⡠⠖⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣸⠁⠀⣿⡄⠀⠀⡇⠀⢃⣸⠈⠛⠻⠶⠶⠒ ⠛⠷⢤⣄⡀⠀⠀⠀⣰⠏⠀⠀⣠⠔⠋⠀⣀⡴⢾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣰⠟⣆⠀⣿⣧⠀⠀⡇⠀⢜⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⢀⡾⠃⢀⡴⠊⠁⢀⣤⣾⠋⠀⢸⠙⡏⠽⣶⣲⣤⣖⡢⢄⡀⠀⠳⣄⢻⡄⣾⡄⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣴⠏⠀⠘⣤⣿⣿⠀⢀⡇⠀⠸⠻⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠸⣷⣶⡟⢀⡴⠋⢀⣤⣾⣿⠋⡏⠀⠀⢸⠀⢹⡀⣏⠈⢹⣯⣟⣷⣦⣅⠀⠈⢳⣿⠈⣿⡄⠀⠀⡿⠀⠀⠀⡼⢠⡾⠋⢠⠀⠀⠈⣷⣿⠀⢸⠀⠀⡇⢀⠀⠀⣻⣇⠒⠀ ⠀⠀⠀⠀⢡⡟⡴⠋⣠⣶⡿⣿⣿⠃⠀⢹⡀⠀⢸⠀⢧⢷⢿⡀⠘⠃⢀⣿⠋⠻⢶⡙⠲⠎⠦⠸⣿⡆⣰⠃⠀⣀⣾⣷⣋⣀⣠⣼⣤⣴⣶⣿⡏⢀⢾⡀⠀⡇⠈⢳⡏⠀⠈⢧⠀ ⠀⠀⠀⣰⣿⠟⣰⣾⢟⣿⣿⡇⣿⠀⠀⢸⢳⡀⠸⡄⠈⠻⣷⣽⣷⣶⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⢠⣿⡿⠿⢃⡾⠉⢉⣿⡟⣹⣿⠁⡄⢈⣇⣸⠁⠀⠀⡷⡀⠀⠘⡄ ⢄⣀⡼⠛⣃⡬⣟⡿⣼⣿⣿⡇⢹⡄⠀⢸⡀⢻⣄⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⣠⣏⠉⢁⣤⠞⠁⣠⣾⢏⣼⣿⠏⣠⡇⡸⠁⠹⣆⠀⠀⢹⣷⠀⠀⠱ ⣸⡿⢣⣴⠋⣠⣿⣷⣿⣿⣿⣷⠀⣧⠀⢸⡇⠈⠛⢿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠥⠔⠲⣿⠁⠩⢿⣟⣭⡤⣾⠟⢣⣾⣿⢋⣴⣿⡇⢹⠀⠀⢹⣷⣄⣼⠿⣇⠀⠀ ⣼⢡⣾⣿⠟⣿⣿⣿⣿⣿⣇⣻⡄⠸⣧⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠈⠉⠁⣶⣿⢟⣵⢿⡿⢱⠁⢸⡆⠀⠀⢻⣿⣿⣤⣹⣧⣀ ⣿⣾⠋⣿⡇⣿⣿⣿⠀⣿⣯⣉⣿⡄⠘⣇⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠤⠤⠤⣾⡿⠾⠋⣰⠟⠀⡼⢠⣷⠛⣆⠀⢸⣿⣿⣿⣿⣿⣿ ⢿⣯⡀⢻⡧⣿⣷⡿⠶⠟⢿⣿⣿⣿⣄⠘⢯⣿⣷⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠀⠀⠀⠀⣴⠏⠀⢀⡼⠃⠀⢀⡇⣾⠏⠀⡏⢷⠞⣿⠻⢿⣿⣿⣿ ⣼⡿⠟⣸⣿⣿⡿⣆⠀⠀⠀⠙⢿⣿⣿⣷⣮⣝⣳⣿⣦⡀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⣠⣾⡏⣀⡴⠋⠀⠀⠀⣸⢰⠏⠀⢰⡇⣸⣧⡿⠀⠀⢹⣿⣿ ⢿⢀⡴⠀⢹⣿⢡⣿⣷⣤⣤⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⠑⠢⣤⣀⡤⠔⠊⠁⠀⠀⣀⣤⠞⣿⣿⠞⠋⠀⠀⠀⠀⢠⢷⠏⠀⠀⣸⣱⡿⢿⣇⠀⢀⣸⣿⣿ ⢸⠟⠃⠀⠸⣿⣎⠻⣷⣯⣿⠿⠟⣋⣽⣧⣉⣻⣯⣯⡉⣠⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢶⣋⠛⢿⡏⠉⠀⠀⠀⠀⠀⠀⢠⡿⠃⠔⢰⡏⣹⠋⠀⢈⣿⡿⠟⠉⠉⠉ ⢸⠂⠀⠀⣰⣛⣻⣷⣌⡻⣿⡄⢾⣿⣿⣿⡿⣯⣿⣿⣿⣿⡇⣿⣿⣿⣷⣤⡀⠀⠀⣠⣴⣞⠉⢉⣀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣸⠀⡾⠁⠉⢳⡤⠾⠟⠀⠀⠀⠀⠀ ⡾⠀⠀⣼⣻⣿⣿⣿⠿⠟⠛⣛⣿⣟⣿⣿⣿⣿⣿⣿⣷⣿⢃⣿⣿⣿⣿⣿⣿⣷⣿⡇⠈⣿⠿⣿⢿⣷⡶⢴⣟⡦⢤⣤⡤⢤⣀⠘⠁⠀⢠⠇⣼⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⡄⢼⢯⣿⣿⡏⢠⣤⣶⣿⣿⠟⢻⡛⣿⣶⣬⡙⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⡇⠀⢹⡄⠀⠀⢹⡇⠀⢸⡍⠒⢦⣍⣳⣌⠳⣄⠀⡞⢰⠇⠀⠀⣀⣼⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⡰⣮⣿⣿⣿⣧⠸⡿⠋⣿⣿⠀⡌⢷⡜⠻⢏⣽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣼⡧⡄⠀⢸⡇⠀⣸⣿⡅⠉⠺⢿⣿⠀⢻⡷⣄⣼⣀⢀⡞⢡⡀⠙⢦⠀⠀⠀⠀⠀⠀ ⣼⣿⣧⠉⣿⣿⣿⣦⣹⣾⠉⢹⠀⣿⠀⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣴⣿⢢⡉⢀⣾⠂⠀⣷⢮⣉⣠⡠⣼⡟⠀⢸⣏⣧⡘⡏⢹⠀⠀⠙⢦⠈⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⣷⡼⣯⠙⣿⣿⣿⣿⠿⠿⠟⠃⠈⠛⠉⠉⠛⢷⣴⣿⣦⣀⣻⠇⠀⣰⣇⠀⠈⠋⠙⢿⡇⠀⣸⠇⠀⢰⡇⣸⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⣿⣟⠁⠀⠀⣿⠇⣰⠆⣰⣿⣾⣿⣞⣷⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⠟⠀⣰⣿⣽⣷⣄⣀⣠⡟⠁⢀⣿⠄⠄⣼⣡⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠂

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⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⠿⠿⠿⠿⢷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠋⠀⢀⣤⣶⠟⠁⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀ ⠀⠀⣴⣿⠋⠀⢠⣾⣿⠟⠁⠀⢀⣴⣿⣗⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀ ⠀⣼⡿⠁⠀⣴⣿⣿⠏⠀⠀⣠⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀ ⢰⣿⠃⠀⣸⣿⣿⣿⠀⠀⠐⠿⣿⣿⣿⣧⡀⠀⠀⠀⣀⣀⣤⣴⣾⣦⠀⠈⣿⡆ ⣾⡿⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⢸⣷ ⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢿⣧⠀⠈⣿⣿⣿⣿⡀⠀⠸⡿⠛⠛⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿ ⠸⣿⡄⠀⢹⣿⣿⣿⣧⡀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇ ⠀⢻⣷⡀⠀⠻⣿⣿⣿⣷⣄⠀⠀⠀⠻⠿⣿⣿⣿⣿⣷⣖⡀⠀⠀⠀⠀⣼⡟⠀ ⠀⠀⠻⣷⣄⠀⠘⢿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢀⣾⠟⠀⠀ ⠀⠀⠀⠙⢿⣦⣀⠀⠈⠛⠿⣿⣿⣿⣿⣶⣦⣤⣤⠤⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀⡀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣀⣤⣾⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢷⣶⣶⣶⣶⡶⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣏⡽⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⢹⣷⢤⡐⠈⣷⣄⣀⣀⣀⣀⡀⠀⠀⣀⣠⡼⢿⣿⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣶⣽⣍⢦⡉⠁⠈⠉⢩⡉⠁⠀⠀⠀⠀⠙⢷⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣾⣿⣿⣧⣭⡛⣿⠋⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠰⢄⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠓⢬⢿⣿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⢆⠀⠀⠀⠳⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⣷⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠈⢧⣰⣶⣶⣦⡄⠠⡌⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡃⠰⡿⢋⡏⠀⠀⠀⢀⣀⠀⠀⣤⣾⣟⡳⣮⣦⡀⠈⠇⠀⠉⠻⢿⠿⠁⡄⠈⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠶⠀⠑⡾⠁⠀⠀⠀⠀⠀⠐⣄⠙⠿⠿⠧⠼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢿⠊⠁⠀⠀⠀ ⠀⠀⠀⡟⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⠀⠀⠈⣧⣀⠤⡴⠆ ⠀⠀⣸⠁⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⠀⠀⢰⣤⣀⣀⠀ ⠀⢀⠏⢠⠀⠈⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⠀⢀⡀⣻⣿⣿⣿⣿⡇⠀⠀⣾⢟⡲⠌⠁ ⠀⡼⠀⠀⢀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣀⡈⡁⠀⣀⣿⣿⣿⣿⡿⠁⠀⠀⡏⠑⠏⠓⠀ ⢰⠃⠀⠀⡄⠠⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣹⡿⢿⠿⣿⣿⣿⠟⠁⠀⠀⢠⠇⠀⠀⠀⠀ ⢸⠀⣄⠀⠘⣦⡀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠁⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀ ⢸⠀⠘⠀⠀⢿⣹⣲⣄⣬⠑⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⡄⠀⠀⠀⠀⠀ ⣼⡄⠉⠐⠦⠈⢻⣧⣹⡟⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠏⠠⡿⠀⠀⠀⠀⠀ ⣿⢹⠀⠀⠀⠀⠀⠈⠛⠷⢄⠀⠀⠀⠀⠀⠙⠢⢍⡁⠒⠒⠒⠤⠄⠀⠀⠀⠒⡫⠖⠋⠀⠀⢿⠀⠀⠀⠀⠀ ⡏⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀ ⠻⠤⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠧⠤⠤⠤⠼⠦⠤⠤⠤⠤⠤⠴⠧⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢯⣽⣫⣬⡙⢦⣴⠞⠁⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠉⠑⠒⠒⡿⣄⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠐⠟⠹⡮⣿⣶⣤⣖⡒⢶⣲⣼⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⡿⢷⣿⠀⠈⠙⠻⣦⣝⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⣗⣳⡌⢻⢧⡀⠀⠀⠈⠙⠻⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉⣷⣾⣃⣈⢇⠙⠦⢤⠀⠀⠀⠀⠉⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⢿⡛⣯⣶⠟⠁⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠻⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⣄⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡿⠟⣁⣭⣾⠋⠀⠀⠀⢸⢻⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠖⠒⠈⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠈⠳⣄⠰⣌⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠿⢟⡥⠆⢰⡟⠃⠀⠀⠀⠀⢸⡟⠉⠙⠺⠿⠷⡆⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠙⠲⣄⠈⢧⠙⢷⡀⠹⣷⡀⠀⠀⠀⠀⠀ ⠀⣾⠃⢠⠏⢀⣴⡟⠁⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢢⡱⢄⡹⡆⠘⣷⠀⠀⠀⠀⠀ ⢸⡟⢠⠞⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⢤⠀⠀⠓⠈⠁⡇⠀⣿⠀⠀⠀⠀⠀ ⠈⣿⠋⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⠈⠉⠓⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⡇⢀⣿⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⡟⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣴⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠳⢾⡏⠀⠀⠀⠀⠀ ⠀⢹⣧⡀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣁⣠⠶⠟⠛⠛⣿⡇⠀⠹⣿⡀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀ ⠀⠘⠹⣷⢷⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠾⠯⠁⢠⡀⠀⠀⠀⢹⡇⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⡀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠯⠍⠁⠀⠀⠀⠐⢽⡄⠀⠀⠈⡇⠀⢀⡜⠈⢳⡀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⡄⠿⠀⠀⠰⢤⡀⠀⢀⣀⣀⣤⠴⣊⣵⣿⣥⠝⠂⠀⠀⠀⠀⠀⠦⣀⠀⠙⠲⣤⣌⣡⡴⣋⡤⠤⠈⢿⡀⠀⠀⠀⠀⠀⠹⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢍⣑⣀⡈⣀⣠⠾⠯⠁⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⠈⠑⠶⣄⣈⣉⣋⣩⠴⠖⠋⠹⡶⣷⣄⠀⠀⠀⠀⠀⠹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠉⠓⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣒⣲⣶⡒⣒⣀⠀⠀⠀⠀⠀⠉⠙⠻⠦⣤⣄⡀⠀⠀⣹⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠀⠈⠙⠒⠢⠤⢄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠤⠞⠋⠁⠈⠀⠀⠀⠀⠀⠀⣀⣀⠀⠘⢯⣭⣿⡿⠛⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠖⠒⠋⣡⡼⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠉⠉⠀⠀⠀⠀⣿⡿⢃⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠚⠉⠉⣀⣀⠀⢠⣯⣴⠋⠑⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⣀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⢀⠴⠋⢁⡴⠒⠋⠉⠁⣀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡟⣠⠀⠀⠀⠀⠀⠻⢿⢟⣿⣿⣷⣶⣶⣤⣤⣄⣀⣠⠜⢉⠟⠻⠿⡶⢧⣶⠴⠶⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣾⢃⠀⠀⠀⠀⠀⠀⠀⠈⢽⣯⣷⠟⢋⡠⠚⠉⠉⢙⠟⠛⠲⠶⠤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⢠⠀⠀⠀⣠⣶⠟⠉⠀⠀⠉⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⣇⣿⠁⢀⣾⠟⠂⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠋⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣰⡏⢸⡇⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣉⣉⣉⣉⣉⣉⣉⣀⡿⠀⠀⠀ ⠀⠀⠀⠰⣏⠁⠉⠉⠉⠙⣷⠀⠀⠀⠀⠈⠉⠉⢹⣏⣉⣉⣿⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢻⡟⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⣘⣧⣀⡀⠀⠀⠀⠀⠀⠀⢸⠇⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠉⠉⠛⠛⠛⠛⠓⠶⠿⠶⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠀⢠⡾⠛⠳⣄⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠙⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⢸⣇⣸⣦⡟⠀⠀⠀⠀⠀⠀⢿⣁⣨⡗⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣦⡀⠉⠉⠙⠷⠆⠀⠀⠀⠀⠀⠈⠉⠉⠀⣠⡟⠀⠀⠀⠀⠀ ⢰⡶⠶⠶⠶⠾⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠶⠶⠶⠶⢶⡆ ⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⢀⣠⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⡟⠉⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠛⠋⠀⠀⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠁⠘⣿⣿⣿⣿⣷⠀⠀⠀⣀⡀⠀⠀ ⠀⠀⣠⣿⣿⣿⣿⣿⠏⠀⠀⠀⢻⣿⣿⣿⣿⡆⣰⣿⣿⣿⣷⡀ ⠀⣴⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠛⠁⠀⠀⠀

⠀⠀⠀⡰⠀⢀⡤⣀⣤⣶⣶⡦⠉⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠉⠁⢻⣿⣶⣮⡛⣦⡀⠀⠸⡆ ⠀⠀⠀⠁⢀⣟⣼⣿⣿⣿⡿⠁⢀⣤⣆⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣵⣿⣷⣄⠘⣿⡏⠿⢿⡜⢿⡀⠀⢻ ⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣧⣶⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠟⣿⣷⣿⣷⣦⣾⡇⢸⡇⠀⢸ ⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣼⣿⢽⣿⣿⣿⢃⣾⠀⠀⢸ ⠀⠀⠸⣆⠀⠙⠙⢿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣼⣿⠿⣯⠞⠁⠀⢀⡟ ⠀⠀⠀⠙⣦⠀⠀⠀⠨⣭⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢶⠚⠁⠀⠀⣴⠟⠀ ⠀⠀⠀⠀⠈⢛⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠚⢻⠁⠀⠀ ⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠖⠚⠛⠓⠳⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣆⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢹⣿⣿⡿⣿⣿⣿⢿⡄⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢠⣽⣼⣧⣼⣿⣯⣧⣿⣯⣏⣸⣇⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣽⣟⣉⣥⣤⣬⣽⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣥⣿⣥⣨⣿⠓⠃⣽⣿⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣿⡿⠷⠾⣿⠿⠛⢻⣯⡽⠛⠀⠀⠀⠻⢯⣿⣿⠛⠿⣿⠿⠷⣶⣾⡿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠟⠒⠒⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠲⠞⠛⡟⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⡄⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣹⠟⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡿⡄⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⠹⡄⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡹⣄⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⢹⣿⣄⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠉⠉⢶⣤⣤⣤⡬⠉⠙⠀⠀⠀⠀⢀⣴⠟⠀⠀⢀⡔⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⣴⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠺⣿⡟⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠈⢳⡀⠀⠈⠳⣄⠈⠻⢷⣄⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⠁⠀⣠⣴⣶⣶⣶⣶⣾⡟⢳⣄⣀⠀⠙⠳⣦⣄⡈⠙⠓⠒⠒⠛⠉⠀⠀⠀⠀⢀⣼⡿⣟⢶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢸⣿⣿⢿⣾⠇⢘⡗⣤⣀⠈⠉⠉⠉⠛⠒⠒⠊⠀⠀⠀⠀⠐⠋⠀⠣⢻⡞⢿⣿⡟⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣸⣿⡇⢀⣿⠀⣾⠁⣿⡏⠙⠲⢦⣄⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⡀⡂⠈⣿⣾⣿⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠇⢰⡿⢠⣿⠁⠀⠀⠀⠀⠀⠈⠁⠉⠃⠀⠈⢸⠁⠀⠀⣿⠀⡟⠀⣿⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⢀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⡟⢻⠻⣿⢀⣿⡁⢸⣿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⠀⣷⢰⡏⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠞⠛⠳⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠛⠒⠶⠶⠶⠦⠤⠶⠶⠶⠟⠳⢦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀ ⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀ ⠀⣼⠃⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⡶⠶⢶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠘⣧⠀ ⢸⡏⣠⣤⣶⡿⠿⠛⠛⢩⡽⠋⠉⠙⢷⣀⡴⠛⠉⠙⠻⣝⠛⠿⢿⣶⣤⣄⣸⡇ ⣿⠟⠛⠉⠀⠀⠀⠀⢰⠏⠀⠀⣴⣦⠈⣿⡇⢠⣶⡀⠀⠘⣧⠀⠀⠀⠉⠙⠻⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠁⣸⠋⢧⠈⠉⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⣿ ⢹⡇⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⣠⡾⠃⠀⠈⠳⣤⣀⣠⡴⠏⠀⠀⠀⠀⠀⢠⡇ ⠈⢿⡄⢠⣄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡴⠂⢀⡾⠁ ⠀⠈⢻⣆⠈⠻⣦⡀⠀⠀⠲⢶⣶⣶⣶⣶⣶⣶⣶⠖⠂⠀⢀⡴⠛⠀⣠⠟⠁⠀ ⠀⠀⠀⠙⠷⣄⡀⠙⠷⣤⣀⠀⠉⠛⠿⠿⠟⠋⠁⣀⣤⠞⠋⢀⣠⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡉⠛⠓⠲⠶⠶⠶⠚⠛⢉⣠⣤⠶⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣦⣄⡀⠀⠀⣀⣾⣿⠇⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⠋⠻⢿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣀⣀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⣾⡆ ⣰⢾⠁⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⠏⠀⠀⣰⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⢀⣴⠏⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠉⠉⠠⣬⡟⠻⢿⣿⣿⣿⣷⣶ ⠀⠀⣀⣠⠏⠁⠀⠀⣴⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠙⢻⣿⡿⠃ ⠀⠠⠟⠓⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠻⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣶⣿⣿⣶⣤⣤⣤⣶⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠟⠛⠛⠛⢧⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠹⣿⠛⠻⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣍⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠳⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠐⠟⣧⡀⠀⠀⠀ ⣰⡟⣛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣠⣄⡀ ⢿⡀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⠶⢯⣝⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⡶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡉⣷ ⠘⢷⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⣤⣤⣄⣀⣀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⣙⣧⡀⠀⠀⠀⠀⠀⠀⣀⠋⣠⡿ ⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠉⠛⠙⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⣯⣤⠶⠶⠾⠿⠛⠉⠹⣷⠀⠀⠀⠀⢀⣼⠛⠛⠋⠀ ⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣠⡟⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠸⣏⠉⠛⠛⠛⠛⠛⠛⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠈⢻⣟⠛⠋⠉⠉⠉⣉⡿⠁⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠙⠷⣤⣀⣀⣀⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠙⠳⠶⣶⡶⠾⠋⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠶⠚⠛⠛⢻⡿⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⢤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⡤⠶⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠤⠤⠒⠒⠀⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠊⠀⠀⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡄⠀⢀⣤⠠⢄⡀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠊⠉⠉⠉⠁⠐⣤⠆⠉⠉⠉⠱⡀⣴⠋⠉⠉⠉⠙⠷⢤⣤⣤⠔⡡⠔⠒⠒⠀⢰⢀⡖⠈⠁⠀⠀⠐⣠⡾⠁⠀⠀⠀⢉⠇ ⣿⠀⠀⠀⠀⠀⠀⠀⣤⡴⠶⠶⠟⢩⡏⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⢱⠀⠀⠀⠀⢸⠈⢷⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠊⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠧⠄⠒⢆⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠘⡀⠀⠀⠀⢸⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀ ⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡿⠀⠀⠀⠰⠆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡄⠀⠀⠙⣷⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣦⡀⣠⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠉⡇⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠘⣿⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⢸⠃⠀⠀⠀⡴⢶⡀⠀⠀⠀⡃⠀⠀⠀⡏⠗⠉⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⢿⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⢾⣤⣀⣀⣀⡇⠘⣇⣠⡴⠟⠷⠶⠶⠖⠁⠀⠀⠿⠤⠴⠶⠚⠛⠓⠒⠚⢻⣅⣀⣀⣀⣠⣤⣤⡤⠃⠿⠶⠶⠶⠶⠖⠁⠀⠀⠀⠀ ⠀⠸⣧⣀⣀⣀⣠⣤⡜⠀⠀⠀⠀⠀⠈⣉⠩⠄⠀⠋⠁⠤⢀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⢀⣀⠤⠀⠢⠀⠀⢉⣭⠃⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⢸⠀⢰⡏⠀⠀⠀⠘⡀⠀⠀⠑⢄⡾⠃⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⡴⢚⣛⣛⣛⣻⡎⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⢸⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⢻⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠻⢶⣦⣤⣤⠴⠊⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣤⣤⣤⠴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠒⠚⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⡏⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⡇⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣀⣠⣤⣧⣄⣀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣞⣴⠟⠉⠀⠀⡇⠀⠈⠙⢦⣻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢞⡾⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⡿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠏⢸⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢳⠘⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠃⠀⣿⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢈⡆⠈⢳⡀⠀⠀⠀ ⠀⠀⢀⡼⠁⠀⠀⢹⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣾⡇⠀⠀⢳⡀⠀⠀ ⠀⢠⡾⠁⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⡇⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢳⡄⠀ ⣼⣿⣁⣀⣀⣀⣀⣀⣀⣈⣛⣶⣤⣤⣇⣤⣴⣾⣛⣁⣀⣀⣀⣀⣀⣀⣻⣆ ⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡤⢤⣴⠞⠓⠶⠒⠒⣆⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠛⠉⠀⡴⠒⠋⠁⠉⠉⠦⠤⠴⣀⠀⠙⠒⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⣀⣋⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠈⢷⠀ ⠀⠀⠀⠀⢀⣀⣀⣀⣹⣦⡴⠛⣿⠉⠉⠁⠀⠀⢸⡇⡇⠀⠀⠀⠉⠉⣿⡆⠈⡧ ⠀⠀⠀⡴⡋⡠⠀⡈⢿⡏⡇⠀⣿⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⡟⢣⠀⢳ ⠀⠀⡞⢁⠇⡞⠛⢮⣾⢡⣧⡄⡟⠒⢻⠛⠓⠒⢶⡇⣷⢤⣤⠤⠤⠤⠤⢼⣤⠞ ⠀⢰⢧⣾⢸⠃⠀⠈⣿⢸⣿⠇⡇⠐⡏⠀⠀⠀⢸⡇⢸⠀⡇⠀⠀⠀⠀⡀⣇⠀ ⠀⣾⣸⡇⡿⠀⠀⠀⣿⢸⠸⠀⡇⢠⠀⠀⠀⠀⢸⣷⢸⠀⢻⠀⠀⠀⡇⡇⢻⠀ ⢠⡇⣿⢱⡇⠀⠀⢸⡇⣸⢀⠀⠀⠈⡄⠀⠀⠀⠸⢻⢸⡀⠀⠀⠀⠀⡆⢧⢸⡀ ⣸⠈⡟⢸⠀⠀⠀⢸⡇⣿⢸⠀⢰⠘⡀⠀⠀⠀⠀⢸⠈⠃⠀⠀⠀⠈⠁⢸⠘⡇ ⢻⡀⢣⠸⣄⣀⣀⣼⡇⣿⠸⠀⢸⠦⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇ ⠈⢧⡀⢠⣬⣭⣿⣿⠀⣿⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇ ⠀⠀⠉⠙⠒⠿⠟⣿⠀⠹⡇⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⠁⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⡿ ⠀⠀⠀⠀⠀⠀⠀⠘⣎⢿⡟⠋⠁⠀⠐⠒⠒⢒⣒⣒⣒⣂⣀⣀⣤⣭⣤⣤⣤⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⠷⠦⢤⣀⣈⣉⣉⣛⣉⣩⣭⣭⣭⣾⣿⠿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠤⠤⠤⣤⣤⣤⣤⣤⣭⣭⡭⠭⠴⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⡄⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣠⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⡛⠳⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣬⡛⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⡿⠟⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠠⣴⣧⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⣼⡿⣱⡟⠀⠀⠀⠀⠀⠀⣰⣤⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠻⢳⡟⠀⠀⠀⠀⢀⣠⡼⢿⣿⣿⣦⣤⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠛⠛⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⡾⠀⠀⠀⢀⡴⠛⠁⠀⠀⠙⠛⠿⠿⠿⢛⣿⣻⣦⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢻⡤⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣶⣶⣶⣾⣶⠆⣸⡇⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⡇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⢿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈ ⢿⣿⢿⣿⣿⣿⣿⣿⠇⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠ ⠀⠀⠘⣿⣿⣿⣛⣶⡾⠛⠋⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠿⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⢤⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⣄⣀⣀⣀⣤⣴⡶⠿⠗⣒⣾⠗⠛⠓⠒⢶⡆⠙⠷⣤⣀⠀⠀⠀⠀⠀⢀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠀⠉⢻⡟⠋⢉⣀⣀⡤⠴⠚⢦⣿⡄⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠒⠒⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⣸⣧⠀⠀⠀⠀⢲ ⣿⡇⣸⡇⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠉⢻⣿⠀⠃⠀⠀⠐⠐ ⠿⠀⠹⣿⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⣰⠏⣿⠀⠀⠀⠀⠃⠀ ⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠈⠻⣧⣀⡾⠋⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⣧⡀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⣀⡼⠛⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⡴⠞⠉⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⡀⠀⠀⢿⡝⠓⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡃⠁⠀⠀⢹⡇⠀⠀⠀⠉⠙⠛⠲⠶⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠲⢿⣿⠛⠉⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀ ⣤⣤⣴⣶⣿⣶⣶⣿⣿⣶⣶⣷⣶⣶⣶⣶⣶⣿⣶⣶⣶⣦⣶⠿⠁⠀⠀⢸⠀⠀⣀⣠⣴⠶⠞⢻⡏⠀⠀⠀⠀⠙⢿⣦⠀⠀⠉⠻⢶⣤⣄⣀⡀⣀⣀⣴⣿⣧⣶⣶⣦⠀⡀⠀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣅⠀⠀⠀⠀⢸⠟⠛⠉⣀⣠⡤⠶⠞⢻⡀⠀⠀⠀⠀⠀⢙⣷⣤⡀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣴⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠳⣄⡀⠀⣸⠶⠚⠋⠉⠀⠀⠀⠀⠀⢷⣄⠀⠀⣠⣴⠟⢁⣿⣿⣀⡶⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⢻⡿⠋⠀⠙⢷⣄⠈⢻⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⡞⠉⢀⣴⠛⠉⠹⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠈⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣶⠏⠙⠻⠟⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢿⡾⠋⠳⣦⠀⠀⠈⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠙⠳⣦⡴⠞⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠒⠶⣤⣠⡶⠛⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⢀⠀⣀⠀⠀⠀⠀⠀⣆⣀⣠⣤⣀⣴⣤⣉⠳⣦⣆⡀⠀⠀⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠈⢁⡀⠀⢀⣤⣾⡋⡠⠀⠀⠀⠀⢀⣀⠀⣀⣀⠀⢀⡀⠀⡀⠀

⣿⣿⡟⢰⠃⢀⣴⣫⣾⣿⣿⢿⡏⠉⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠁⠀⠀ ⣿⣿⣇⡏⣠⢯⣾⣿⣿⣿⢃⡟⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⢡⠏⢀⣴⠃⠀ ⣿⣿⢈⡶⣷⡿⠿⠿⠛⠋⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠙⠓⣢⡤⠤⠤⢤⢤⡤⠤⠤⠤⠤⠤⣴⢶⡄⢸⠏⠀⠀⡴⠋⣠⠟⠁⠀⠀ ⠛⠋⠘⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢷⡾⠀⣠⠞⣡⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⣴⡿⠿⣿⣿⣿⣿⠳⣶⣤⣤⣄⣀⣤⢴⠏⠀⠀⢸⢃⣜⣥⡾⠛⠉⠉⠉⠙⠻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⠏⢤⣴⣿⠟⠀⠀⢹⣿⣿⣿⡆⠘⣿⣦⠀⠉⣰⠏⠀⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⣼⣃⣠⣾⣿⡟⠀⠀⢀⣿⣿⣿⣏⣡⠀⠘⢿⢆⣴⠋⠀⣠⣾⠟⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡾⢁⡼⠋⢻⣹⣿⣷⣤⣾⣿⣿⢿⣿⡇⠀⠀⣠⠟⣡⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⢁⡞⠁⠐⢾⣿⣿⣿⠛⢿⡿⠏⢸⡿⠀⢠⡾⠗⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣧⡟⠀⠀⠀⢸⠙⠇⢻⣄⡀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣽⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣾⡟⠀⠀⠀⠀⣿⠠⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⣴⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠁⠀⠀⠀⢰⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡏⠀⠀⠀⠀⣿⠁⠀⢠⣧⡀⠀⠀⠀⠀⠀⢀⡴⢁⣀⣀⣀⣀⣀⠀⠀⠀⠀⢸⡟⢿⠻⢿⠿⢿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⢸⡇⠀⢀⣐⠚⢳⣦⣄⣀⣠⡤⠼⣿⠉⠉⠀⠀⠈⡉⠁⠀⠀⠀⠀⠻⣤⣀⡀⢀⣸⠟⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠃⠀⠀ ⣄⣉⣩⠿⠿⠶⠤⢤⣄⣀⠀⠀⣀⣴⣞⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⣀⡤⠶⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠛⠁⠀⠀⠀⠀⠀⢀⣩⠷⠛⠉⠁⠙⣧⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢀⣠⠾⠋⠀⣠⠀⠀⠀⠀⠸⣧⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡴⠊⠉⠉⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⢻⡆⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⢠⠀⡴⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⢀⣴⠟⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠘⠲⠤⣀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠁⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢧⡀⠀⠀⠀⠘⣦⠉⠛⠶⣤⣄⣀⡀⠀⠉⠓⠚⠋⠁⢀⣀⣀⣤⠶⠒⠋⠀⢠⠆⠀ ⠟⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⣷⠀⠀⠀⠀⠘⣇⠀⠀⠹⡄⠉⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⢸⣷⡄⠀⠀⠀⢹⣤⠀⠀⢻⡄⢸⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⣀⡴⣋⡠⣶⠂⠀

⡇⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⡀⡤⠑⠲⠦⠤⠤⣤⣀⡠⠒⠠⡀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠈⠁⠢⡀⠀⠀⢊⠇⠀⣤⠘⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡚⠅⠒⠈⠉⠉⠉⠉⠐⠢⢀⠀⠈⠄⠀⢸⡀⠀⠀⣶⠞⡄⠀⠀⠀⠀ ⠀⠀⡴⠋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠔⠊⠁⠁⠀⠀⠀⣔⠋⠆⠀⠀⠀ ⠀⡼⢡⡞⠀⠀⠀⠀⡠⠒⣩⠕⠋⠑⠒⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀ ⠀⡠⡛⠁⠀⠀⠠⠊⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⡂⢸⡄⠀⠀⠀ ⠀⠁⠃⠀⠀⠀⠀⠀⢠⣃⣀⣀⣀⣤⠖⠀⠀⠓⢲⣯⠽⠛⢿⣄⡁⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢸⡿⠛⠛⠻⢻⠀⠀⠀⠀⢸⠀⠀⠀⢧⣿⣲⣤⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢰⣿⠀⠀⠀⠀⠀⢂⠀⠀⣨⠿⠓⠘⡜⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠈⣿⡦⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⢉⡤⡆⠀⠇⡗⠀⠀⠀ ⠀⠀⢧⠀⠀⠀⢀⠀⠀⢹⣿⣦⣀⢀⣀⠰⠊⠉⢑⣠⠴⠋⢀⠁⢰⢀⡷⠤⠤⠄ ⠀⠀⠘⣇⠀⠀⢸⠀⠀⠀⡿⣿⣿⣿⠑⢌⠡⠤⢼⠀⠀⠀⡘⠀⡄⢸⡷⢄⠀⢀ ⠉⠐⠒⢿⡄⠀⠈⠀⠀⠀⢉⢋⡝⣰⡷⢤⣑⠠⡇⠀⠀⠀⠇⢀⠁⡇⠑⣼⠑⠒ ⠀⠀⠀⠀⢳⡀⠀⡆⠀⠀⠘⠸⡄⡇⢹⡀⠀⡱⡇⠀⠀⢰⠀⠸⢠⡇⠀⣼⠀⠀

⠉⠀⠀⠀⢿⣧⣀⣀⣀⠾⡷⠦⠤⠻⣕⠴⣄⣸⣗⢼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣠⣽⠟⢉⠔⠉⠀⠀⠀⠀⠈⠳⣬⣙⠯⣕⠚⠢⡉⠉⢫⣛⣿⣿⣿⣿ ⠀⠀⠠⠊⡏⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠉⠛⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⢂⢇⣧⣚⣥⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠆⠀⠀⣈⢾⣿⣿⣿⣿⣿⣿⣿⡿ ⢘⣸⣾⣿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡯⡁⣎⠠⠐⠚⣿⣿⣿⣿⡛⠋⠁ ⣟⢿⢯⡏⠁⠀⠀⠀⠀⡀⠀⢸⢔⠀⠀⠀⢀⠗⠻⠠⠄⡀⣀⢡⠻⣿⣿⣿⣦⡀ ⢧⣳⡏⡀⠠⠀⠈⠀⠀⢃⣴⣁⣨⠆⢀⢀⠌⣰⣷⡶⣤⡼⠀⢾⡳⣿⣿⣿⣿⠷ ⠒⠉⢀⡇⠀⠆⠈⢃⢸⣻⢽⡛⡾⡲⠗⠁⠀⠹⡚⣢⢾⢀⠂⠘⢻⡶⡿⠍⠀⠀ ⠀⠀⠸⢃⢰⠘⠕⠠⢙⣳⣂⡠⠀⠀⠀⠀⠀⠀⠀⠀⢶⠾⠀⠀⡆⣷⡌⠨⡀⠀ ⡀⠐⣘⡸⡔⠆⠈⠀⢸⢅⠀⠀⠀⢀⠒⠒⠠⡄⠀⢀⠌⠀⡆⠀⣷⢣⠙⣀⠁⢤ ⠀⠉⠙⠒⢳⣸⡄⠀⢠⣪⣷⡤⣀⠈⠂⠤⠐⢀⢔⠁⠀⣆⡇⠀⡇⠘⠀⠀⠀⠀ ⡦⡀⠀⠀⠞⠘⡌⠢⡀⠇⠹⣻⠶⣭⠶⣤⡒⠕⠊⠀⠸⣿⠁⢰⠇⠀⠇⠀⣕⣤ ⠑⡏⠁⠲⣦⡀⠈⠢⣎⠚⠄⠈⠑⡌⡚⢴⠤⠤⣤⣄⡠⢧⣴⣿⠀⢸⠀⡇⣿⣾ ⠣⠵⢄⠀⠸⠃⠀⠀⠈⠀⠀⠀⠀⠱⠋⠉⠀⠀⠈⠁⠀⠀⢹⡟⢠⢋⣼⣷⣿⣿ ⣍⣶⣄⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⣵⣿⣿⡟⣿⣿

⣿⡏⢸⣿⣿⣿⣿⡆⣿⣿⣿⣾⠋⣿⣿⣿⣿⣿⣿⣿⡆⠉⠉⠉⠻⣦⠻⣶⣦⣤⣲⣞⣷⣷⣶⣤⣀⠈⠻⢿⣷⣄⢶⣄⠹⣿⣄⢠⡴⣾⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⣿⠏⣺⣿⡏⢰⡿⢻⣿⣏⢀⣿⣿⡏⣿⢺⣿⣿⣧⢀⡠⠋⠀⠹⣷⡘⣷⣉⣿⣿⣿⣿⣿⣿⣿⣦⣦⡀⢻⣿⣿⣿⣿⣿⣿⣮⣷⡀⠉⣧⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣼⠏⠀⣿⣿⢁⣿⠃⣸⢸⣿⣼⣿⣿⢧⣿⡿⠙⡏⣿⣿⣇⠀⠀⢰⣟⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⡄⢻⡿⣿⣿⣿⣿⣿⣿⣿⣶⣌⣷⡀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡏⠀⣸⣿⢿⣼⢇⣰⣧⣼⣿⣿⣿⣿⣼⣿⣷⣄⣿⣼⣿⣿⣆⠀⠀⣿⣿⣿⡹⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣷⡄⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀ ⣻⠃⢠⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣻⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⡄⠀⢹⣆⠀⠀⠀⠀⠀⠀ ⣿⣶⡾⠋⠞⠁⣸⣿⣿⣯⢿⣿⣿⣿⣿⢸⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⡀⢀⣽⣆⠀⠀⠀⠀⠀ ⠠⡟⠀⠀⠀⠉⠉⠉⠀⠠⢾⡿⣿⣿⣿⣿⣿⡾⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡇⢸⣿⣿⣧⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⢿⣿⡇⠐⣿⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⡏⣻⣿⡙⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣿⣯⣻⣧⣀⠙⣧⣹⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠹⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣧⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠆⠀⢀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠙⡽⣿⣧⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣆⠈⢷⠀ ⠀⠀⠀⠀⠀⠰⠃⠀⠀⣼⣿⣿⣷⢿⣿⣯⡻⣿⣿⣿⣿⣿⢻⣇⠹⠜⢿⡧⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡿⣿⣿⣿⣿⡄⠈⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠘⣝⣿⣷⡈⣿⣿⣿⣿⢧⠙⠇⢀⣠⣶⣶⣦⣌⣻⣷⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⣈⢿⣿⣷⡀⢤ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⢹⣿⣿⠀⠙⢸⣿⣷⠾⠇⠀⠀⠀⠀⢀⣿⢿⣿⣿⣿⣿⡟⣿⢿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣇⢸⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⣹⣿⡿⣟⣁⠈⣇⢹⠿⣿⣿⣿⣿⣿⠂⣿⠈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣞⣿⣿⣿⣧ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⠀⢸⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⢉⣬⡿⠀⠘⡟⠐⢻⣿⣿⣿⣿⠀⣿⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣯ ⠀⠀⢠⠟⣿⣿⣿⣿⣿⣿⠸⣸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡶⠟⠃⠀⠀⠹⣞⢠⢿⣿⣿⣿⠁⣿⠀⣿⣿⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⠋⢰⢹⣿⣿⣿⣿⣿⡈⢻⠀⢿⢿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠸⣿⣿⣇⡀⠙⠀⣼⣿⠀⠆⠻⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠾⢁⣀⣸⣿⣿⣿⣿⣿⣿⣷⠛⢧⢸⣢⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣽⡏⡇⠀⠀⣸⣿⡀⠘⢠⡿⣿⣧⣸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⡆⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⢿⣿⣇⣷⡇⠀⢹⣿⠁⣠⠟⢧⡘⢿⣏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣿⣿⣿⡼⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⣿⣿⣿⣷⣤⣼⣿⡟⠳⣤⡈⠻⣮⣻⣷⣝⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣇⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⣿⣿⣿⣇⣹⣿⣷⡀⢈⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⢸⣏⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⡠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣞⣟⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠷⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⡇⠀⢾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠈⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠸⡉⠛⢿⣿⣿⣿⣯⣿⣿⣟⡋⠉⠻⣿⣿ ⣿⣿⣶⣾⡇⠛⠻⢿⣧⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢄⡀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣽⡿⠿ ⠛⢿⣿⣿⣿⢶⣤⣀⢸⣿⣿⣯⣙⡇⠻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣿⣶⠶⠾⠟⠋⠉⠉⠉⠉⠉ ⠀⠀⢻⣿⣿⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡖⠛⣟⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⣿⣿⡟⠙⣠⣴⡴⠶⠛⠀⠀⢀⡴ ⣤⣠⣾⣿⡟⣷⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣦⠈⢻⡝⢿⡇⠻⣿⣿⢦⡄⠀⠀⠈⡿⣽⣿⣿⢹⣿⣿⠀⠀⠀⠀⣸⣿⡿⠼⠋⠉⠁⠀⠀⠀⢀⡴⢋⣤ ⣿⣿⣿⣿⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢯⣷⡄⢻⡾⡇⠀⣹⡟⠀⠘⢢⡀⠘⠃⣿⣿⣿⡘⢿⣿⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⣰⠟⣡⣾⡅ ⣿⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⠀⠘⢿⣧⣩⡿⣻⡿⣿⣿⣿⣿⣿⣯⣿⣿⣎⣷⡏⣀⣿⠃⠀⠀⠀⠙⢲⡇⠸⣿⣿⡇⠀⣿⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⢀⣴⠃⣴⣿⠋⢀ ⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⡿⣿⣿⡀⠀⠀⠻⣿⣦⣍⣾⡽⢿⣿⣿⣿⣿⣿⢹⣿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⣇⠀⣿⣿⠄⠀⣿⠀⠀⢠⣿⣿⣿⠁⠀⠀⢀⣠⠞⢁⣾⡿⠁⣴⢋ ⣿⣿⣿⣿⣿⣿⣦⣹⣿⣿⠃⠘⣿⡿⠛⠛⠷⠾⢯⣄⣘⣷⣀⣺⣿⣾⠇⢻⢸⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠁⢼⡂⢸⣿⢠⣶⣿⠀⠀⣼⣿⠈⠻⠀⢀⣠⡾⠋⣠⣿⠟⢀⡾⣻⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣏⠛⠛⣙⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⢹⡟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⠉⠙⡃⠀⣿⠀⠘⣿⣿⡏⣾⡿⣿⣿⡁⡸⣯⠿⣿⡉⠱⢺⣿⣿⣿⣿⢻⣿⣿⡟⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⣷⣿⡟⣝⣶⣿⣥⣾⡿⠑⣼⣿⢣⣿⡿⠃⢿⡜⠃⣿⣿⣾⠋⠉⢻⣿⣿⡜⠛⢿⣿⣿⡏⠑⠫⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣇⢠⣿⠇⣨⡟⣴⠿⡟⣧⠶⡀⢸⣿⠾⣿⡇⣠⢸⡇⡾⢹⣧⣱⣿⢦⣘⣹⡟⣿⣄⣠⣿⣿⣧⠀⢴⡿⣎⠉⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⣇⣾⢂⢿⣿⠋⣴⢏⣾⠻⡂⠀⠙⣤⣧⣾⡟⣆⣿⣇⠉⠈⣁⢣⣼⣿⠘⠉⠀⢮⣀⠿⣽⣷⣀⠛⣸⣿⣏⣷⣿⠽⢷⣿⣿⡿⠿⠿⠿⠗⠂⠀⠀ ⠀⣀⣀⣤⣴⣿⣿⣿⠏⠁⠉⠀⣠⣿⣿⣷⡅⣚⢃⢘⡛⠂⠀⠀⣾⣿⠁⢠⣽⣟⣰⡾⠁⠀⠘⢛⠓⣦⣖⣬⠁⣴⠃⣙⡁⠀⠀⢽⣿⣧⠘⠆⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⣩⣿⢟⠴⠟⢷⣟⣿⣿⣿⠉⠁⠉⠈⢺⠁⠀⡀⠀⢻⣿⡷⠘⢿⣿⠺⡇⠀⡀⠀⠾⠰⢸⣿⡏⠀⣲⠀⣿⣿⡀⠀⢸⢿⣿⣗⠺⠃⠀⣻⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠊⣸⣿⡟⠀⠀⣸⣿⣿⣿⠃⠓⠀⢠⡄⢽⡄⣰⣿⣤⢸⣿⣥⢰⢸⣿⣧⡆⢬⡅⣠⣤⢠⠀⣿⡇⠀⠉⠀⠛⢿⣷⣰⠀⠀⢹⣿⡒⠀⠀⢈⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣟⠡⠀⠀⢷⣿⣿⠃⠸⢷⣿⡇⠀⣾⢺⣿⣿⣿⢾⣿⠿⠀⠸⢻⣿⣿⢾⡃⢻⣤⡄⠀⣿⣧⢠⣤⠀⠀⢘⣿⣽⠆⠀⣸⣿⣿⠄⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⡇⠘⠀⠀⢰⣿⣿⣎⠀⠀⣿⡟⣧⠀⠈⣾⣿⣿⣿⣿⣿⣠⣶⣶⣾⣿⣿⡇⣁⢸⣿⣧⣦⣿⣿⣾⣿⡄⠀⠀⣿⣿⠀⠀⣨⣿⣿⡄⣶⣠⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⢀⡾⢻⣿⣱⣤⣠⣾⣿⣿⡿⡉⣧⢱⣿⢳⡄⣤⣾⣿⣿⣿⣿⣿⣿⢿⣾⣿⣇⢻⣿⣷⡟⠁⣿⣿⣿⣿⣿⣽⣿⣿⢱⣶⣹⣿⡇⠀⣈⢿⣿⣷⠿⢳⡄⠘⣿⣿⣧⣀⠀⠀ ⠐⠉⠀⣾⣿⣿⣯⣿⡿⢿⣿⡇⢱⢿⣿⡟⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⡏⡿⣿⣿⣧⠾⣿⣯⣿⣿⣿⣿⣿⣿⣟⠋⡿⢿⣷⡇⡙⢺⣿⣿⣷⣼⡏⢘⣾⣿⡿⠿⠷⠦ ⠀⠀⠀⣿⣿⣿⣳⣿⣿⣿⣿⠀⡜⢣⣿⠁⠀⣸⣿⣿⣿⣿⣿⣿⠛⣿⣿⠛⣿⣇⠘⣿⢻⣿⣆⣿⣿⣿⢻⣿⢻⣿⣿⣿⣧⡀⡾⣿⣇⠃⠻⣿⣿⣿⣹⣇⠈⠓⠹⣿⣦⡀⠀ ⠀⠀⠀⣿⣿⣏⣿⣿⡿⣿⣿⠀⢧⢸⣿⢸⢷⣿⣿⣿⡿⢹⣿⠏⠀⣿⣿⣿⣿⣿⠀⣿⢺⡏⠿⣿⣿⣿⢸⣿⠘⣿⣿⣿⣿⣧⣥⣿⣿⡀⠀⢸⣿⣿⣿⣿⡇⣤⣸⡿⣿⠙⠂ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡄⢸⣼⣿⢯⣿⣿⣿⣿⢁⣿⡟⠀⠀⢹⢹⣿⣿⣿⡄⡀⢸⣷⣦⣿⣿⣿⣼⣿⠒⠛⣿⣿⢿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣧⢸⣿⡇⣿⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣾⣿⣿⣿⠋⢹⡿⠋⠙⠳⣾⡷⣿⣿⣿⣷⢃⣾⣿⣷⣿⣿⠏⢿⢻⡀⠀⣜⣿⣟⢿⣿⣿⣿⣧⢸⣼⣿⣿⣽⣿⣿⣿⡿⠁⠁⠀⠀ ⠚⠋⢡⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢹⣿⣿⣿⣯⠟⢀⡿⠋⠀⠉⢳⣌⣷⣿⣿⣿⣿⣿⡿⢹⣿⣿⡏⠀⠺⣟⠇⠀⠙⢾⣿⣄⢻⣿⣿⣿⣸⣿⣿⣿⣽⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣁⣀⣿⣁⣀⣤⣄⣀⠸⡌⢸⣿⣿⣿⣿⣧⣼⣿⣿⣇⠀⠀⣼⣇⣀⣀⣈⣓⣿⣆⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⠀⠉⠉⢻⣿⣿⣯⣿⡟⠓⠳⢰⡿⢯⣿⣿⣿⣿⣿⠙⢿⡖⠻⣿⣿⣿⣿⣿⠉⠉⠋⣽⣿⣿⣿⣿⡇⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⢻⣿⡿⢻⡇⠀⣿⣿⣿⣿⣿⠀⠀⠢⠈⠿⠷⠿⠋⠀⠀⠀⢸⠇⠘⢻⠹⣿⣿⣿⣰⡀⠙⠂⠈⠛⠺⠟⠃⠀⠀⠀⠟⡏⣿⣿⣟⡇⢸⢿⣿⣿⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠘⣿⣧⡘⠁⠸⡀⢻⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳⣿⡿⠙⠁⠈⢠⣿⠉⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⢷⣤⣄⠀⠘⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣵⣁⣀⠀⣠⠿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡛⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢠⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡴⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⣿⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⢸⢻⢅⣰⡦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⠁⣀⣼⡇⠀⠀⠀⠈⠛⠦⢤⣀⣠⡤⠞⠋⠀⠀⠀⢀⣾⠘⠳⠤⣌⡉⠒⠫⢿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠁⠀⣀⡴⠒⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠉⠙⣦⡴⣩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣭⡓⠾⣅⡀⠀⣀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠱⠀⠀⣀⣤⠖⣻⣽⠾⢟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡿⠍⡙⠻⠷⣯⣽⣚⣯⠶⠿⠦⣄⣀⡀⠀⠀⠀⠀⠀⢀⡴⠞⠁⢀⣀⡤⢶⣚⣭⡵⠾⠛⠉⠀⠀⠀⢸⡟⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢾⢿⣿⠣⠐⠋⠂⠠⠀⠨⠉⠙⠛⠲⢲⣆⠈⠉⢻⡄⣀⡤⠞⠋⠀⢠⡾⡏⣷⣿⣟⣉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠙⠛⢦⣄⡀⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⣶⣿⣿⣯⣏⣠⠘⣿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣿⠀⢰⠏⠻⢁⣀⣠⣠⠴⠏⠀⡇⣿⣿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⢀⣨⣛⠳⢦⣄⣀

⠀⠀⠀⠀⠀⢳⡤⣄⣀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡌⡉⠓⠶⣤⣀⡀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢐⣀⣤⣤⣤⣆⣧⣰⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣶⣦⡀⠀⠉⠙⠶⢤⣄⣠⠀⠀⠂⠀⠀⠀⡀⠀⡄⣤⣤⣷⣾⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢲⡀⠀⠘⢿⣿⣄⡀⢠⡀⠀⠘⢛⣷⣀⣀⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢳⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡀⠀⠀⢳⡀⠀⠀⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠏⣿⡿⠛⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⠀⠀⢣⡀⠀⠀⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣿⠋⠈⢁⣀⡀⠀⠀⠺⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠉⠛⢷⡀⢀⣠⣿⣷⣶⣶⣼⠏⢿⣿⣿⣿⣿⣿⣿⣛⠿⠿⠿⠿⣿⡿⠁⠀⠁⠀⢀⡾⠉⠉⠉⠒⠂⠘⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢺⣧⠈⠉⠓⢿⣏⣤⠾⠻⣿⣿⣿⣷⣮⣿⣿⣿⣿⠿⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⣀⣤⣤⣄⡀⠀⠺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⢦⡖⠊⢿⡀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠋⠉⢻⠆⠀⠀⠀⠀⠀⠀⠏⠃⣾⣿⣶⣄⠈⠳⡄⠀⠘⣿⣫⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠄⠀⠀⠀⠙⠲⠞⠃⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⡞⠀⠀⣠⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⡏⣁⣽⣿⣧⠀⢹⠀⠀⢿⣿⡌⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⣿⣿⣿⡿⠀⠀⢸⡏⣠⠴⣶⣶⣄⠀⠀⠀⠀⠀⠣⡙⢿⣿⡿⠀⣠⠇⠀⢸⡷⣳⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⣤⣀⠀⠀⠀⠀⠀⠀⢠⡿⢻⠁⠈⢻⣿⣿⡁⡀⠀⣠⡀⠀⠀⠒⠦⠖⠊⠁⠀⠀⠨⣷⢇⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠗⠃⣠⡴⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡀⠐⣾⣿⣿⣷⠀⠀⢿⣷⡆⠀⠀⠀⠀⢀⡄⠀⠀⠀⢹⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⢷⡀⠈⠻⠛⣣⠀⠀⠈⠉⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⣼⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⡼⢽⡷⣄⠙⠲⠖⠊⠁⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⢀⣾⠃⠁⠀⠀⠀⠀⠀⣀⣠⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀ ⣤⣄⠀⠀⢠⡾⡷⠚⠉⠉⠉⠁⠀⠹⣄⠀⠀⠀⢀⣠⠞⠁⠀⠉⠛⠦⣄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⡆⢀⡴⠞⠉⠛⢧⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⢏ ⠀⠈⠙⠳⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⢞⣻⠇⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠹⢷⣴⣤⣿⣿⠛⣇⠀⠀⠈⠓⣄⡀⠀⣾⠃⠀⠀⠀⠀⣡⡿ ⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⡽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠾⠏⠀⢀⡄⠈⠋⠉⢿⣾⣿⡀⠀⠀⠀⠀⠙⢦⡯⠀⠀⣡⡴⠟⠙⠃ ⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⣀⣠⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⣠⣶⣿⣷⣄⣀⡀⠀⠀⣠⡾⠁⠀⢀⡴⠋⢸⣿⢷⡄⠀⠀⠀⠀⠀⠙⢿⣿⡋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣟⠻⠭⠾⠿⣿⡟⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠳⣍⢭⡻⢷⣮⣉⢉⣉⣉⣠⡶⠄⠈⠀⣸⣟⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⣟⢧⡀⠀⠀⠀ ⠀⠀⠀⢀⣤⠞⢋⣠⠾⠓⠺⠳⠟⠛⠛⢶⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⢷⣝⢦⡙⠻⢿⣧⣄⡀⠀⠀⠒⣾⡿⠻⣿⣦⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⣷⡀⠀⠀ ⢀⣠⡾⠋⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠴⣿⠿⢿⣿⣶⣤⣀⣀⣤⣤⠤⠴⠚⠉⠀⠀⠀⠀⠈⢿⣯⠻⣄⠘⠲⠿⠿⣿⣿⡿⣿⣧⡀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢧⠀⠀ ⠛⠅⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠹⠆⠀⠙⣿⣿⠏⠛⢦⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠘⢧⡀⠀⠀⠀⠀⠉⢻⡿⣿⣿⢿⡓⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⠀⠀⠀⠀⣼⣿⡏⠀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠘⠋⠀⠻⡀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠘ ⠇⣀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃⢀⣤⠀⠀⠀⠀⠀⠙⢷⣄⣀⡀⠈⠙⢷⣶⣖⡦⠤⠶⠾⣋⣿⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀ ⠆⣯⣽⠷⠀⠀⠀⠀⠀⠤⣴⡟⠃⠀⠀⠀⠙⢲⣀⣀⣀⠀⠀⠀⠈⠛⠶⣤⣄⢄⣿⣮⡳⠂⠀⠀⣿⣿⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀ ⢰⢤⣾⠛⠀⠀⠐⠛⡀⣼⣿⣤⠀⠀⠀⢠⠶⡆⢈⣿⡿⠆⠀⠀⠀⠀⠀⠈⠙⢿⣟⢿⡻⣦⡀⣀⣻⠇⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠿⠆⠀⠀⠀⠀⡀⠃⢧⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣳⡈⠛⢿⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠒⠘⠀⠀⠈⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⡰⠶⣖⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣽⡄⣸⠃⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠁⠀⢈⣄⠀⠀⠀⣀⡄⠀⠄⠀⠀⠀⠀⠀⠁⣠⣼⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣯⣤⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠒

⠀⠀⠀⣿⠁⠨⠴⠡⢞⢠⣿⡿⠋⢀⣾⣿⣿⣿⠁⠀⢰⠃⣿⣿⡼⣿⣷⣾⣾⣿ ⡄⣴⠞⣿⠀⢁⢴⣢⡿⣿⠟⠀⠀⣼⣿⣿⣿⠃⢄⣴⠃⣴⣿⣯⠈⣿⣷⡿⣿⣿ ⣠⣸⢤⣽⣌⣪⡿⢻⡟⠀⠀⠀⢀⣿⣽⣿⠇⡬⢊⡡⢊⢇⢿⣿⠠⢻⣿⣯⣿⣿ ⣟⡹⢽⣿⡿⡟⢀⣨⢁⠀⠀⠀⢸⣷⣿⣿⢊⠔⣋⠰⠋⠁⣘⡷⠁⠈⠟⢁⣟⣿ ⣿⣳⣿⡿⢄⠀⠀⡟⡌⠀⠠⠀⣺⣿⡟⠍⠐⣊⣽⣿⣿⠉⠁⠀⠀⣫⣝⢻⣿⣿ ⢐⡿⣫⣷⣏⠀⡘⣸⠀⠀⡗⢰⣿⡻⡘⠀⠀⠿⢸⣿⠏⠀⠀⠀⠞⢿⠟⡟⣻⣿ ⢋⡹⣿⣿⢋⡔⠐⡇⠀⢸⠁⣸⡘⠧⠱⠀⠀⡆⠀⠀⠀⠀⠀⠀⢘⠀⢸⣶⣿⣿ ⣾⣿⣿⣿⠎⡌⠀⠀⠀⠆⢠⠏⡔⠄⣀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⣼⣿⣿⣿ ⣿⣿⢏⣼⢰⢀⢸⠀⣸⠘⡈⣰⢠⠕⡸⠈⠢⡀⠢⠀⠀⠐⣚⡛⢀⣾⡃⡿⢻⣿ ⣿⣿⡆⢸⣼⡸⡄⢠⡹⡀⢁⢧⢏⠉⠣⡀⠑⠈⠐⠅⣀⠀⠀⣠⣾⣿⣿⣷⣿⡟ ⣿⡟⣠⣊⡿⠯⢴⣿⡥⠟⢘⡤⠜⠈⠑⢀⡉⠒⢄⠀⡰⠙⣬⣣⣿⠟⣿⠃⢺⠁ ⣿⠟⠋⠀⠐⠚⠁⠀⠈⠢⣀⠀⠀⠑⠤⣀⡁⠉⠢⣝⣴⠚⠛⠛⠛⣚⣧⠃⠈⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡠⠊⣼⣯⣰⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠬⡄⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⣰⢿⡧⢳⠘⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⢀⠴⠟⠊⠀⠘⠀⣰

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⢁⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⡿⣿⣿⣿⣿⣿⡿⠿⠿⣿⡿⠧⠄⣠⠤⠤⢀⡀⠼⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⣷⣤⣤⡛⡀⡆⠀⣠⣤⣤⣄⡀⠀⠰⠖⠚⠷⣄⠰⠀⢤⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⣿⠋⢡⡇⡇⠁⢾⠋⠀⠀⢂⠀⠀⠀⠀⢀⠄⠙⠀⠃⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⡏⠀⠈⠗⢃⠀⠀⠀⠀⡈⠵⡀⠀⠀⡄⡡⠠⡄⠀⣶⣼⣀⡀⠀⠀⠀⠀⢸⠀⠀ ⡇⠀⡰⠐⡄⡆⡐⠀⠀⠑⠒⠁⢀⠀⢸⠉⠈⠀⠀⠹⣿⣿⣿⣿⣿⣶⣶⣾⣤⣤ ⣧⠀⣇⢄⡇⡇⢇⠀⠀⠀⠀⢠⣄⣀⣠⢧⡀⠀⠀⢰⡇⠁⠈⠀⡉⠙⠻⠿⠻⣿ ⡏⣇⢸⡆⣆⢸⠀⠢⡄⠀⢀⣦⣵⠹⢙⣶⣧⠀⢠⡈⣿⠶⠾⣦⣤⡦⣦⡶⠶⠾ ⣷⣿⡄⠇⠙⢸⠀⢀⠀⠀⢆⠹⢿⣿⡿⠏⡇⠂⠘⠂⣘⠀⠀⠀⠉⠩⢛⣳⣮⣤ ⣧⣿⡇⠀⠀⠀⡆⢺⡄⠀⠀⠀⠕⠒⠀⠒⠀⠀⠐⠀⢹⠙⠢⡀⠄⠀⠀⠀⠈⠁ ⡇⡜⠀⣙⡄⡀⠤⡀⠄⠠⡤⠄⢀⢤⣴⠆⡐⡲⠊⠉⢹⢭⣀⡨⠢⢄⣀⢀⠀⠀ ⠓⠓⠚⠛⠀⠀⠀⠃⠀⠀⠈⠓⠒⠚⠛⠒⠛⠛⠛⠛⠛⠒⠒⠛⠓⠒⠚⠛⠓⠒ ⠀⠪⠵⠶⠶⠶⠶⠰⠖⠶⠶⠖⠶⠂⠩⢷⠰⠶⠲⣶⠶⠷⠶⠾⠆⠀⠀⠀⠀⠀ ⠀⢰⡦⣤⣤⢤⢤⣤⣄⣤⡦⢰⣂⣄⣤⣤⣤⣤⣤⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣍⠈⠀⠈⠉⠀⣁⠁⢉⡀⢈⡁⠁⠀⠉⠀⠈⡈⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠛⠟⠛⠋⠻⠟⠛⠛⠛⠛⠘⠻⠛⠋⠙⠟⠛⠛⠙⠙⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⠆⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠼⠛⢪⠁⣧⣧⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣃⣐⢸⡉⠀⣻⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠒⢿⡋⠸⠼⠐⠾⣛⣛⡇⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠰⣞⣁⠠⣝⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡔⠂⢩⠀⢀⢧⡐⢹⢿⡇⡄⠀⠀ ⠀⠀⠀⠰⠁⣿⣷⡀⣰⠹⢧⢀⡏⠀⢸⡕⠰⠀⠀ ⠀⠀⠀⡦⠀⢻⣿⣿⡇⡗⢣⣿⣇⠠⢼⠁⠀⠑⠀ ⠀⠀⣰⣀⠑⠸⣿⣿⣿⡀⣾⣿⣷⡀⠀⡑⢠⣘⡀ ⠀⣰⠠⠐⠂⠀⣿⣿⣿⣿⣯⣿⡏⠑⠂⠀⠀⠣⡇ ⢰⢁⠀⠀⠀⠀⢠⠽⢻⣿⣿⠿⣧⠀⠀⠀⢠⢠⠇ ⠈⠔⡑⡀⠀⠀⡇⠀⠼⡻⡉⠐⢨⠑⠢⢀⡀⠜⠀ ⠀⠈⠓⠒⠂⠤⠚⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⠿⠿⠿⠿⠿⠿⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠛⠉⣁⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠉⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⢁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡈⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢉⣁⣀⣤⣤⣤⣤⣀⣈⡉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠉⣠⣴⡾⠟⠛⠉⠉⠉⠉⠉⠉⠛⠻⢷⣦⣄⠉⠻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⣼⣿⣿⣿⣿⣿⣿⡟⠁⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠈⢿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⢻⣿⣿⣿⣿⣿⣿⣇⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠃⢠⣿⣿⣿⣿⣿⣿⡟⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢻⣿⣿⣿⣿⣿⣿⡄⠘⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⠀⣸⣿⣿⣿⣿⣿⣿⠃⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠘⣿⣿⣿⣿⣿⣿⣇⠀⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣷⠀⢿⣿⣿⣿⣿⣿⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⣿⣿⣿⣿⣿⡿⠀⣾⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡀⢸⣿⣿⣿⣿⣿⣿⣇⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⣸⣿⣿⣿⣿⣿⣿⡇⢀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⣰⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠘⣿⣿⣿⣿⣿⣿⣿⣦⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠏⠀⣴⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠙⢿⣶⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠋⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⠃⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡈⠙⣿⡇⠀⠀⠀⠀⢸⣿⠋⢁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⣡⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡿⠿⠿⠿⠿⠿⠿⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡿⢁⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⡈⢿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣷⡀⠀⠀⠀ ⠀⠀⢠⣾⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠻⣷⡄⠀⠀ ⠀⢠⣿⠏⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠹⣿⡄⠀ ⣰⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣆

⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠛⠛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀

⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠂⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⢀⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⠁⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⣠⣾⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣀⠀⠀ ⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⠋⠉⠉⠉⠀⠀⠀⢻⠿⠿⠿⠛⣿⣿⣿⣿ ⣿⣿⣿⣷⣀⣤⣤⣴⣆⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀