⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠿⠿⠿⣶⣦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⣧⡀⠀ ⢠⣄⣀⣀⣀⣀⣀⣀⣀⣴⠋⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠘⣿⡀ ⠀⠙⠻⣿⣟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇ ⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃ ⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀ ⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀ ⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⡻⣟⠿⣯⢟⡯⣟⣻⢟⡷⣾⣴⣂⠒⠔⣂⢒⡰⢂⠖⣠⠣⡘⣄⠣⡜⡰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡡⢒⡰⢂⡔⢢⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⣿⣿⣿⣿⣹⢮⡳⣝⡳⢯⣝⣻⣳⣿⣞⣵⢫⡞⣵⣫⣞⡻⣿⢶⣀⢃⠲⣉⢆⡡⢂⡕⢄⡓⠌⡔⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣃⠆⢣⠘⠤⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣟⡻⣖⢯⡳⣭⣛⢧⣛⢶⣹⣮⣽⢟⢿⣾⣹⢴⡝⣿⠼⣿⣿⣮⠑⡌⢆⠒⣡⠘⣄⠚⡰⠌⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⠲⣈⠜⡡⢎⠱⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢯⡳⣎⢷⡹⣎⣷⣣⢟⣮⣛⢮⢿⡁⢻⣮⣽⢺⡽⣾⡽⣎⢿⡼⣹⢿⣷⣽⣦⣿⣴⣯⣶⣷⣦⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣦⣷⣵⣮⣾⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣛⢮⡳⣝⢮⡳⣝⡞⣿⡞⣶⡹⢮⣛⣽⢻⡭⣟⣿⣼⢳⠿⣯⡞⡵⣯⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢧⣻⡿⣱⠯⣞⡵⣫⢞⣵⣻⣷⣏⡷⣻⢿⣧⢻⡜⣧⠿⣿⣯⠽⣿⣳⢽⣻⡼⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⢻⣭⣟⢷⣭⢻⡜⣷⡹⢮⡽⣿⣿⣿⠳⣽⡞⡽⣿⣾⣱⣛⢮⢿⣿⣽⣷⣏⡞⣿⡽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⣟⣷⣿⣿⣾⣸⣇⣿⣿⣿⣷⣻⣾⣿⣿⣷⡘⠻⢷⣧⣿⣿⣿⣾⣷⣻⣿⣾⣿⣾⣳⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⣿⣟⢿⣿⣛⢧⣿⡽⣹⣿⡽⣯⣟⣻⡿⣿⠈⢻⡀⠀⢠⣬⡿⠽⣿⣻⢿⣯⣿⣯⢿⣧⡻⣿⣻⣿⣿⡛⢏⠻⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢏⠻⡙⢫⠛⠹ ⠀⠀⠀⠀⠀⠀⢸⣿⡫⣾⣿⡝⣮⢿⡷⡭⣿⣿⣿⣞⣿⠃⢿⠀⠀⢉⣿⣿⣏⣹⣦⡸⡷⣯⣽⣟⢿⣯⢷⣳⣯⢷⣯⣿⣯⡄⠣⡑⢯⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⢂⠡⠄⡡⠘⠀ ⠀⠀⠀⠀⠀⠀⢺⣿⣧⢿⣿⣝⣮⢻⣷⣛⣿⢿⣿⣾⠇⠀⡟⠀⠀⠘⠿⢿⣿⣿⣿⠇⢿⣽⣞⣯⣏⢿⣯⣿⡽⣿⣿⡽⣿⣿⣧⣌⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⡈⠒⡐⠠⠑⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣯⢟⣿⡾⣜⣻⣿⣧⡟⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠥⠒⢹⣿⣿⡷⣎⢿⣷⣻⡿⣽⣿⣿⣧⣟⣷⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡑⢀⠁⠡⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⡆⣿⣞⣿⣿⣱⢯⣿⣿⣧⣾⡟⢛⡳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣜⢯⣿⣿⣿⢶⣛⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠠⢀⠁⠂⠀ ⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⣾⣿⣿⣎⣿⣿⣿⣿⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⢻⣟⣮⢻⣿⣟⣿⡿⣼⡹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⡐⠀⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢿⣿⣿⣿⣾⣿⣆⠀⠙⠛⣋⡴⠂⠐⢆⣠⡤⠀⠀⠀⠀⠠⠋⠀⢸⣿⢾⣿⣿⣻⢼⣟⡶⣝⣻⣯⣏⠿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⠂⠀⡀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣟⡿⣿⡦⣄⠈⠉⠀⠀⠀⠀⠁⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣹⢾⣯⢷⡹⣎⣿⣞⡽⣹⢿⣿⣽⣿⣿⣿⣿⣿⣿⠀⠠⠐⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣽⣻⣿⣞⡳⣄⠀⠀⠀⠀⠀⠘⠋⢁⣠⠀⠀⠀⠀⣰⣿⣯⠟⣿⣯⢾⣟⣮⢳⢿⣿⡿⣜⢧⣟⣿⣽⣿⣿⣿⣿⣿⣿⠀⠀⢀⠁⠀⡀⠀ ⠄⠀⠀⠀⠁⠀⠀⠀⢀⠀⢸⣿⣿⡷⣿⣿⣽⣿⣿⣿⣿⣳⣤⣀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠞⢨⠏⠀⠀⢻⣿⣿⡿⣜⢯⣾⣿⣿⣽⡾⣼⡟⠉⠋⠉⠉⠛⠻⣷⠀⠁⠀⠀⠁⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⢈⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣯⣗⡮⣝⢿⣻⢶⣶⣶⣶⡒⠒⠉⠀⠀⠀⠀⠀⢸⣿⣿⡟⣼⢣⣿⣿⡿⣾⣿⣿⠁⣠⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠀⠞⠋⢸⣿⣿⣳⣿⣿⣿⣿⣟⣿⣿⣿⣿⡮⢷⣭⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢹⣿⣿⡹⢧⣿⣿⣿⣿⣿⡿⠁⣰⠃⠀⠁⣴⠋⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣿⣿⣿⣿⢿⣟⠿⣽⣿⣿⣿⣯⣾⡽⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣻⣿⢷⣫⢷⣿⣿⣿⣿⡿⠁⢰⠃⠀⠀⣼⠃⠀⠀⠀⠀⠀⠹⣷⣾⣷⣾ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡵⣿⣿⣿⠃⠀⠈⠉⠀⡀⠉⠉⠻⣽⣿⣽⣿⣿⣿⡿⣧⢤⣀⠀⠀⢀⣿⣿⡷⣭⣿⣿⣿⣿⡿⠁⠀⡟⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣻⣿⣿⠇⠀⠀⠀⠀⠀⢷⠀⠀⠀⣹⣿⣿⣻⣿⣿⡇⠙⣄⠈⠳⣤⡼⣻⣿⣳⣿⣿⣿⡿⡟⠀⠀⢠⡇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣻ ⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⡘⣿⣿⣿⣿⠀⠀⠈⢱⣿⢙⡟⢹⣿⣽⣿⣿⣿⢠⡇⠀⠀⢲⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣳⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣧⢿⣿⣿⠇⠀⠀⠀⠀⠙⠛⠃⢸⣿⣿⣿⣿⠃⢸⠆⠀⠀⢿⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿ ⠀⠂⠐⠀⠂⠀⠠⠀⠀⠂⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢸⣾⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⡾⠀⠀⢈⣾⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠋⠀ ⠀⠈⠄⢀⠁⢀⠐⢀⣠⣴⣾⣿⣿⣿⣷⡇⠀⠀⠀⠠⠀⠀⠀⠘⣧⠀⢀⣿⠁⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢀⣼⡇⠀⠀⠤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀ ⠀⠡⢈⠀⠄⠀⠀⣹⣿⣿⢿⡿⣿⣿⣿⡙⠀⠀⠀⠀⢳⡀⠀⠀⣿⠠⠈⠹⡄⠀⠀⠓⢄⡀⠀⠀⠀⠀⠀⠀⢻⡿⠊⢸⠁⠀⠀⣚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣤⣤ ⠀⢡⠀⠈⡄⠐⠀⣹⣿⢯⣿⣽⣿⣿⣟⣆⠀⠀⠀⠀⠀⢷⡀⠀⢸⡥⠀⠀⢣⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠉⣧⢀⡏⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢾⣽⣾ ⠀⠂⠄⢂⠠⢈⠀⢼⣿⣻⣽⣾⣻⣿⣯⣿⠀⠀⠀⠀⠀⠀⢳⡄⠈⢷⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣳⣿ ⠀⠌⢂⠰⢀⠂⠄⢸⣿⢯⣷⢯⣿⣿⢷⣻⡇⠀⠀⠀⠀⠀⠀⠹⣆⠘⣇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⡀⢸⣿⣯⣟⣯⢿ ⠀⠌⡀⠢⠄⡈⠄⢸⣿⣟⣾⣟⣿⣿⣟⡿⣿⠀⠀⠀⠀⠀⠂⠀⠘⢧⣹⡄⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡀⠀⠀⡏⠀⠠⠀⠠⠀⠀⠀⡀⠂⠀⣰⠁⣾⣿⢾⡽⣯⣿ ⠀⠜⠠⠡⠂⡐⠠⢸⣿⣞⡿⣞⣿⣿⣯⣟⣿⣇⡀⠀⠀⡀⠀⠀⠀⠀⢻⣷⣀⡀⠀⠘⢦⡀⠀⠀⠀⠀⠀⣰⢋⠀⠀⠀⢀⢰⠃⠀⠀⠀⠀⠀⠀⠁⠀⢀⢠⠃⢸⣿⡽⣯⡿⣷⣻

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⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⢪⣷⣟⣾⣿⣷⣧⣴⣥⣤⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢠⠚⢳⡄⠀ ⠀⢀⡀⠀⠐⠤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⢠⠏⠀⠀ ⠐⠇⢹⠀⠀⡠⢲⣿⣿⣿⣿⣿⡿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⡀⠘⠃⠀⠀ ⠀⠀⠨⠆⠀⠁⣸⣿⣿⣿⣿⠏⣀⣷⣿⡿⢋⣡⣿⠛⣿⣿⣿⣿⣿⣄⡈⠀⠀⠀⠀ ⠀⠀⠀⢀⡰⠟⢻⣿⣿⡿⢸⣀⣀⠀⢻⠁⢦⠊⣀⣀⡙⠽⢿⣿⣿⠋⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣏⡰⠁⢉⡛⠚⢏⠀⣨⠛⠚⣉⠀⠱⣈⣿⡃⢀⡤⠄⠀⠀⠀ ⠀⢠⠎⢱⠀⠀⢰⢹⣷⡇⠀⢶⡿⠗⣸⢶⣇⠰⢾⣷⠆⠀⠗⣯⡇⠀⢠⠂⠀⠀⠀ ⠀⠈⠁⠘⡀⠀⠈⢶⣹⠘⣦⣺⣤⡴⢋⠿⡎⢶⣴⣪⣶⡎⢸⢃⠇⠀⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⣤⣬⣻⣦⡥⠃⠃⡠⠄⠀⠀⢤⡈⠘⠮⢀⣾⣮⣤⣤⣤⣤⡀⠀⡜ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⣀⠘⠀⠒⠒⠒⠀⠘⠘⣦⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠄⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠂ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢂ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠔⠒⠙⢒⣲⣤⡀⢰⠀⢀⡼⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡠⣔⣾⣛⣽⣭⣭⣟⣾⣠⣿⣷⣭⣷⣖⢮⡉⠁⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡏⣿⣿⣿⣿⣿⣿⣦⢄⠀⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢄⡀⢸⣼⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⣿⠋⠉⠈⠉⠉⠉⠉⠛⣿⡿⣿⣿⣿⣿⣿⣟⠂⠈⠁⠀⡀⡀⠀⠀⠀⠀⢀⣀⡀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⡿⢿⣿⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠄⣠⡤⠖⠋⠉⠉⠉⠉⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠈⣿⡇⠀⠻⣇⠀⠀⠀⠀⠀⠀⢀⡿⠀⣼⡿⣿⣿⣿⣿⣦⡀⠀⠄⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠤⠴⢿⢻⣿⣿⣿⣿⠟⠉⢳⠶⠛⠛⠛⠷⡋⠁⠀⠀⠀⠀⠒⢞⣧⣤⣿⣇⣻⣿⣿⠃⠈⠉⠩⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⣿⣿⣿⣿⠀⡜⠁⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠔⠉⠀⠀⠀⠉⠯⣻⣟⠀⠀⢘⣷⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢹⡃⠀⢀⠀⡛⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⣬⣿⠹⡀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢤⣼⡀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠂⡀⣃⢆⠂⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡌⠉⡇⠀⠑⠄⣀⠀⠀⠀⣠⠴⠛⢡⡾⠸⢿⡀⠀⠀⠀⠀⠀⢀⣼⠋⣧⢀⠂⡰⡿⢥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⡀⢹⠀⠀⠀⠘⢍⣹⡹⠗⠀⠀⠀⠉⢀⠀⠙⢶⣤⣤⢤⡖⠁⡟⠇⡟⠱⣄⠈⠀⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠚⡄⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊⠁⢀⡧⢹⠇⠀⠈⢷⡗⣌⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⢷⡀⠁⠀⠀⠀⠀⡠⠊⠁⠀⠉⠈⠉⠒⡀⠀⠀⠀⠀⣼⣀⡾⠀⠀⠀⠀⠳⡅⡙⢈⠙⠲⢤⣄⣀⣀⠠⠔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠻⣦⡀⠀⠀⠀⠣⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⢀⣼⣛⣹⠁⠀⠀⠀⠀⠀⠘⢦⡁⡑⢊⠂⡶⡵⠌⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣇⠀⢴⡆⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢩⠶⣵⣬⣦⠀⠀⠀⠀⠀⠀⠈⠳⠀⠐⡀⢈⢂⡐⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠙⠓⠨⣷⣌⠁⠀⠀⠙⠟⢿⣶⣦⣄⡀⠀⣀⠤⠒⠉⠀⠀⠀⢀⣸⣾⣿⠲⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠁⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⣠⡆⠀⠀⠀⠙⢦⡀⠀⠀⠈⠢⡙⢿⣿⣿⣉⣀⣤⠤⢤⣾⠓⠊⢉⣾⣿⡏⠳⣤⡑⠢⣀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠋⠒⠚⠛⠁⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠈⠢⣽⡇⠀⣸⠇⢀⡞⡼⢀⣷⡾⡇⢹⠻⡄⠑⠙⢦⣀⠉⠐⠂⠀⠤⠷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⡄⠀⠀⠀⡀⠄⠒⠉⠉⠉⠉⠚⢷⡀⠀⠀⠀⣿⢁⣰⢛⢀⡾⣹⣧⢿⢣⠇⣿⠘⡇⠘⡄⠀⠀⠉⠻⠗⣄⠀⠀⢀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⡘⡇⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⢀⣾⣯⡜⠁⣿⣿⣧⡿⠋⣤⡿⢰⠃⠀⠑⠀⠈⠢⣄⠀⠀⠀⢀⡀⠔⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠁⢰⠀⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣯⣽⠋⣡⣾⠛⣹⡟⢀⣴⣿⠁⠀⠀⠀⢀⣀⠤⠔⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠃⢰⠈⢘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣸⡾⢻⡟⣸⡇⡁⢾⣿⣃⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⢸⡀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡹⣟⢴⣯⣓⠿⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡜⠀⠀⠀⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠵⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣘⢆⣈⠡⠤⠬⠭⠴⣤⣃⢀⠔⣁⣀⣀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣶⣿⣮⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⠀⠀⠞⠁⠈⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⡤⠊⠀⠀⠀ ⠀⢀⡤⠦⡀⠀⠀⠀⠉⠁⠒⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡤⠤⠀⠂⠀⢀⡃⠀⠀⠀⠀ ⠀⠸⠀⠀⡇⠀⠀⠀⢀⠄⢊⢺⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠒⠄⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠄⣿⣿⣿⣿⣿⣿⣿⡿⠋⢈⠄⢀⣼⣿⣿⡿⠋⠉⣩⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠐⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠘⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡏⡿⠁⠤⢤⠾⠟⣹⡿⠋⢀⡠⠾⡛⠋⠀⠹⡟⢻⣿⣿⣿⣿⣿⡿⡦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠄⢒⠫⠑⠁⣿⣿⣿⣿⠿⠀⠇⠀⠀⠀⠀⠀⢻⠃⠀⠄⠀⠀⠀⠀⠀⠀⠁⢨⢿⣿⣿⣿⣿⠇⠈⠐⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠃⢀⡠⠚⠛⣭⣁⠂⢄⡈⠀⠀⠀⣀⡔⢂⣡⠼⠋⠀⢄⠀⠹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀⠂⠀⠀⠀⣄⠈⠉⠉⢂⠀⠀⢰⠁⠉⠁⢀⡤⠀⠀⠀⢣⠠⢟⢏⠀⠀⢠⠒⠒⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠊⠑⡄⠀⠀⠀⠀⠆⠊⢣⠴⠀⠀⣠⣤⣬⣽⡦⠀⢈⡠⠠⡀⠀⢠⣴⡭⠤⠤⠀⠀⢨⠐⡪⠀⡇⠀⠀⢀⡠⠇⠀⠀⠀⠀⠀ ⠀⠀⠘⠦⠀⢰⡃⠀⠀⠀⠀⡇⠆⢹⠀⢆⠀⠀⠰⠚⠁⠀⠠⡼⠀⠂⠰⡂⢀⠈⠙⠓⡀⠀⠀⠜⢀⢠⠁⠇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠀⠱⡰⠘⡄⠀⠑⠡⣄⣀⠀⡄⠊⢀⠁⠁⢂⠈⢪⠄⣈⢠⠠⡴⠋⠀⢸⠃⡸⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⢣⠀⡈⡀⠂⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠊⠘⢠⠡⠀⠀⣆⠔⣁⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⣠⡺⣿⠻⠍⡛⢷⣾⣿⣧⡐⠁⠀⠀⠠⠂⠉⠀⠀⠀⠀⠀⠁⠢⠀⠀⢀⠁⢀⣾⣿⣿⡟⡰⢩⢣⣿⣿⣿⣆⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⣾⣿⣇⢻⢦⠘⣧⠀⢸⠿⣿⣷⣄⠀⠀⠐⠀⠒⠀⠉⠉⠁⠐⠂⠐⠁⠘⢈⣴⣿⣿⣿⡟⡰⢡⢣⠿⣾⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣟⡧⠺⣛⢀⡴⢆⣽⡿⣿⣿⣿⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡿⣟⡕⡡⣱⣿⡑⢾⣿⣿⣿⣷⠀⡀⠄ ⠁⠐⠢⢀⣿⣿⣿⣿⢌⠣⡹⡾⢯⣿⣿⢾⣿⣿⣿⣿⣿⣶⣭⣄⣐⢂⣀⣭⣷⣿⣿⣿⣿⣿⣿⡳⣷⣷⢓⣭⣳⣟⢾⣿⣿⣿⣿⡟⡀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⡆⣿⠳⣹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⢣⡫⣸⣿⣻⣿⣿⣿⣿⠃⠐⠄ ⠀⠀⠀⠀⢸⣿⣿⣿⡕⣿⡱⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣓⣽⣗⢾⣿⣿⣿⣿⠀⠀⠈ ⠀⠀⠀⠀⠀⣿⣿⣿⡾⣿⣧⢣⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⢤⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢝⣿⢷⣽⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣷⡜⣿⡇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⢷⣿⣿⣿⣿⣿⠀⠀⣄ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣣⢻⣷⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣽⣿⣿⣿⣿⣿⡄⠀⠓ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣗⡭⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢥⣺⣿⣿⣿⣿⣿⡇⢁⠀

⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⡲⡢⢤⣀⠀⠀ ⠀⠀⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⡀⢧⡜ ⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⡇ ⠀⠀⡇⢀⡼⢖⣶⣄⠀⠀⠀⠀⠀⠀⣠⡤⢶⡀⠀⠀⠀⠀⠀⡇⠸⢱⠃ ⠀⢀⡇⡞⢰⣿⣿⣿⡄⠀⠀⠀⢀⣾⣿⣿⡆⢻⠀⠀⠀⣠⠃⠀⢠⠇⠀ ⠀⢸⠀⢇⠸⣿⣿⡿⢠⣤⣀⠀⠸⣿⣿⣿⠇⣸⠀⠀⢠⠇⢸⢠⠃⠀⠀ ⠀⣸⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠑⠈⠀⠀⠀⢰⡜⠂⠀⡼⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⣆⢿⠀ ⠀⣻⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢘⣻⠀ ⠀⠀⠀⠀⣹⣶⣾⣿⣷⣦⣠⠔⠢⣀⣠⣀⡀⣈⣀⣤⣶⣎⡁⡠⠀⠀⠀ ⠀⠀⠀⠉⢉⣼⣿⠏⢹⣧⡙⠀⠀⣠⣾⠿⠄⠀⠛⣿⣿⣷⣬⣄⣀⠀⠀ ⠀⠀⣀⣴⣿⣿⣧⣀⠀⠐⢀⠐⠉⠁⠀⠀⠀⢀⣶⣾⡿⢿⣿⣿⣿⣷⣄ ⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡼⣤⣤⣤⣶⣷⣾⣿⣿⣿⣿⣄⠻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠖⠒⠒⠋⠉⠉⠙⠛⠊⠉⠙⣿⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣴⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⣆⠀ ⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡀⢹ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡸⠁⡞ ⠀⠀⢸⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡧⠊⣠⣤⣶⠾⢿⠀⢀⡇⡞⠀⡇⠀⠀ ⠀⠀⠸⠀⡟⠉⣹⠻⢻⣶⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⡜⠀⡞⢰⠃⠀⠀ ⠀⠀⢸⢀⣱⣀⣝⠶⠟⠃⠐⠚⠛⠿⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⢸⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⡇⠀⡇⠀ ⠀⠀⢸⠀⠀⠀⢸⢰⠃⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠛⢯⠀ ⠀⠀⢸⠀⠀⠀⡏⢸⣠⠞⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠤⠖⠤⣄⣘⡆ ⠀⠀⢸⡄⢐⡏⠁⡋⢂⡼⣁⡄⠊⠂⣤⡤⣻⠓⠢⠤⢾⠉⢳⠢⡤⠭⡇⠀ ⠀⠀⠀⢱⣿⡗⠀⠀⠘⣏⡷⢇⠠⠆⠀⣀⣇⠐⠁⢀⠀⠾⡀⠱⡌⢺⣔⣀ ⠀⠀⠠⠋⢹⠁⠀⠀⢀⡇⣲⢿⠄⠤⠬⠉⠁⠒⠈⠀⠀⠀⠈⠢⡈⠢⣄⠐ ⠠⣝⣡⠾⠃⠀⠀⡰⠋⠀⡾⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣿⣿⣟⡗⢀⣀⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⣤⣤⣤⣄⣤⣤⣀⣀⡀⠀⠀⠸⣿⠈⠉⠀⠻⠿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠁⠁⠁⠙⠛⠛⠋⠛⠳⠟⠷⣦⡤⣄⣀⣼⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢶⣴⡦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣠⣿⣟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠞⠁⢸⡹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡔⠁⠀⠀⣾⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠹⠿⠃⣆⣀⣀⠀⠀⢸⣻⣿⣿⠀⠀⠀⠃⠀⠀⠀⡎⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡹⠀⠀⠀⠀⠀⠀⠸⣤⠏⠀⠀⠀⠹⠿⠛⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣠⣟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡻⠶⠒⠋⡳⣄⠀⣀⡤⢶⣄⠀⠀⠀⢀⡀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⢠⡞⠑⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⣿⣿⢅⠀⠻⣷⣤⣶⡫⢿⣶⣄⣤⣖⡶⣶⣤⣄⣀⣤⣬⣇⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⡑⠮⣥⣾⣁⣀⣄⣼⣿⠿⠋⠁⠀⠈⢻⣿⣷⣝⡻⢏⡥⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣾⣧⣴⣾⣿⡏⢻⣦⣞⠋⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⡙⠛⠺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣵⣿⣿⠉⠉⢹⠉⣷⣿⠛⠛⠓⢦⣄⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣮⣢⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢪⣾⣿⣿⣿⠀⢔⡼⢄⡟⢻⡠⢄⣠⢮⣀⠉⠳⣦⣄⣀⠀⠈⢿⣮⡻⢿⣿⣷⣕⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢾⡟⢱⣿⢿⠀⠉⠀⠲⣿⣿⠃⠀⠾⠈⠾⠀⣠⣿⣾⣾⣷⣦⣌⣿⣿⣦⡉⠛⢿⣷⡵⡀ ⠀⡠⣐⣆⣢⢄⠀⠀⢪⢧⣟⠍⠏⣧⣤⣤⢠⣿⣿⣄⣀⡀⠀⢀⣼⡞⠛⠛⠛⡿⣿⣿⣿⣿⡛⠿⢦⣄⠈⢿⣵ ⢸⣾⠃⠀⠈⢳⣣⠀⠀⣉⣀⠘⣷⣾⠟⠻⢿⣽⣟⣻⣉⣽⢿⠺⢿⣦⣤⣀⡀⠘⢿⣿⢿⣿⢿⣦⡢⡪⣳⡀⡇ ⠸⢻⣆⠀⠀⠈⢗⠛⠒⣖⠉⠉⠁⣿⠀⠀⠀⠹⡟⢶⡚⠛⠛⢿⣾⣿⣿⣿⣿⣷⣾⣇⡀⠀⣈⣿⣿⣮⣅⠿⡣ ⠀⢫⢻⡆⠀⠀⠈⠀⠀⢸⡀⠀⠀⠹⣆⠀⠀⠀⢣⠀⢳⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠛⠛⠋⠂ ⠀⠀⢣⢿⡄⠀⠀⠀⣀⡠⣧⣄⣀⣀⣻⡄⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⢟⣛⣛⡻⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠛⠓⠒⠒⠉⠉⠁⠀⠀⠀⠘⠿⡤⠤⠤⠌⠛⠓⠒⠒⠛⠛⠛⠛⠋⠉⠉⠉⠓⠒⠂⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠶⣦⣀⣠⡤⠴⠶⠶⠶⠦⢤⣞⠉⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡴⠞⠉⠁⠀⠀⠀⢠⠤⠄⠀⠈⠙⠲⢤⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣰⠋⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠠⣄⠀⠀⠙⢦⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⠭⠤⠤⣀⠀⠀⠀⡜⣱⡿⠿⣷⡄⠀⠑⡄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠤⠤⣤⣶⣼⣿⣿⡏⢹⣾⣩⣿⣝⣿⡵⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⡵⢁⣤⡶⣤⡈⢦⠀⢰⣿⣏⠀⣰⣿⣿⠀⠀⢸⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⡠⠤⠔⣃⣶⣷⠀⠿⠟⠋⠛⢃⣼⡛⠙⢙⣛⣛⢣⡿⠟⠘⡐⠠⡀⠀⠀⠀⠀⣿⠁⣾⠁⢀⣼⣿⡜⡧⠄⢻⣿⢿⠋⠀⢸⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⢸⣰⡿⠋⢉⣒⠀⠹⣴⠁⠿⢣⢷⠛⣾⣰⠁⣥⣈⠃⣠⠖⠑⠪⡇⣵⠀⠀⠀⢀⡿⡀⣿⣶⡞⠉⠙⣧⣧⢾⢯⠻⣿⡷⠴⠋⢀⡠⠋⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀ ⠘⢾⠻⡀⢻⣀⠇⣰⢻⠀⣿⢸⢉⢿⣁⡟⢹⡋⡴⡟⠁⣀⠤⡺⡫⠃⠀⠀⠀⢸⠁⢳⡻⣾⣇⣀⣼⡝⠘⣏⠸⡆⠀⠉⠁⠈⠉⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢇⢳⠉⡥⢠⠈⢹⠦⠥⣫⣿⠷⣿⣵⣶⣷⣄⡣⡄⠉⢱⢘⠀⠀⠀⠀⠀⠸⡆⠀⠙⠪⠭⠗⠋⠀⠀⠘⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⢶⣄⠀⠀⠀⠀ ⠀⠀⢼⢠⡇⠙⠋⣠⣮⠋⠉⠑⣶⣶⣶⡏⠀⠈⡩⣊⡤⣲⢝⠜⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⣄⣠⠖⢋⡉⠙⢫⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠘⠝⣻⣭⣿⡫⠵⠢⢄⢼⠷⢿⠟⢃⠀⣸⣽⡳⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠀⢀⣀⡴⠖⠋⠁⢰⠋⠙⣾⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠰⠋⢹⠖⠋⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⡀⠀⠀⠀⣀⡴⠛⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠉⠉⠉⠉⠉⠁⠀⣀⡀⢻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⡇⠈⠑⠶⢤⣄⣀⣠⡤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⣤⠖⠉⢙⡏⠙⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢈⠀⠀⠏⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡴⠉⠀⠉⡆⢀⡟

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡶⠛⠙⢦⣀⣀⣤⣇⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⠀⢀⣀⠤⢤⠀⠀⠀⠀ ⠸⣇⠀⠀⠐⠋⠁⠀⠀⠀⣀⠘⠳⣄⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⠙⣧⣀⣀⣀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠤⠤⠽⢧⣄⡀⣴⡏⠀⠀⠀⠀⡗⢤⡀⠀ ⠀⣸⠇⠀⣤⠀⠀⠀⠀⠈⠋⠀⠀⠈⢧⡀⠀⠀⠀⠀⠸⣇⠠⢔⣋⠉⠀⠈⠉⠙⠓⢿⡀⠀⠙⡇⠀⠀⢀⣠⣤⡴⠛⡥⠄⠀⠀⠀⠀⣠⠽⡟⢱⠐⢖⣀⠋⢱⡜⠃⠀ ⢠⡏⠀⠀⠁⡀⠀⠀⠀⠀⣖⣦⠀⠀⠈⢧⠀⠀⠀⢀⡼⠋⠀⢀⣬⠀⠀⠀⠀⠘⠛⠂⠁⢀⣠⠇⠀⢰⡏⠀⡜⢁⡔⠋⠉⠓⢤⠀⢸⠋⣼⣍⣇⡆⡀⡄⢆⡆⢡⠀⠀ ⢸⡇⠀⠀⠸⣾⡄⠰⠶⠀⠙⠋⠀⠀⠀⢸⡄⠀⠀⡞⠀⠀⠀⠸⡿⠁⠶⠆⠀⣿⡇⠀⠀⠈⢷⠀⠀⠘⢧⣸⠁⢸⡀⠀⢰⣿⣌⡆⡼⠿⠯⠭⠼⣳⠈⢧⣴⠛⠻⠳⡄ ⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠓⠶⣼⡇⠀⠀⠀⢰⡿⠋⠓⠒⠒⣌⠁⠀⠀⠀⢸⣧⠞⠛⠻⠻⣄⠀⠉⣀⡉⠙⠏⣗⠛⢻⠀⠀⠀⢧⡄⢼⠈⠁⠀⠀⣹ ⠀⠘⢦⣠⢴⠖⠲⣄⠀⠖⠀⠀⠀⣾⢁⠕⠒⢢⠘⢇⠀⠀⠀⠸⡁⠀⠀⠀⠀⡏⠀⠀⠀⠀⡼⠁⢰⠋⠉⢢⠼⡶⢫⠀⠩⠙⢦⠘⠤⠞⠀⠀⢀⡼⠋⠹⠀⠀⠀⢠⠏ ⠀⢀⡞⠁⠀⠀⠘⠀⢧⠀⠀⠀⠀⢧⠘⠆⡠⠞⠀⠘⢆⠀⠀⠀⠱⣀⢀⣠⠞⠀⠀⠀⠀⡴⠁⠀⠘⠢⠤⢊⣼⢣⠀⠀⠀⠀⠈⡤⠤⠤⠴⠲⡏⠀⠀⠀⠀⣀⡴⠋⠀ ⠀⢸⡁⠀⠀⠀⠀⢀⠏⢰⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣴⢶⡿⢿⡀⠀⠀⠀⠀⢰⠡⠤⠤⠤⠤⢽⣤⠤⠶⠋⠉⠀⠀⠀ ⠀⠘⢧⣀⣀⣀⠤⠋⠀⡞⠀⠀⠀⠀⠀⡄⠀⠉⣦⣠⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⢀⡀⠀⠀⢀⣴⡿⠛⡟⠀⠀⠣⣀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⡀⢀⠀⠀⣠⠃⠀⠀⡟⡏⠀⠀⠀⠀⠀⢰⢻⠀⠀⠇⠀⠙⡄⠀⠉⣇⣇⠀⡇⠀⠀⢀⡠⣭⣍⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡀⠀⠀⠀⠀⠙⠧⣼⠤⠖⠁⠀⠀⢠⠇⡇⠀⠀⠀⠀⠀⢸⠈⢀⠔⠒⠦⠀⢹⡀⠀⣿⠈⠙⠻⣄⡔⠁⠀⠈⠇⠹⡆⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠒⣧⠀⠀⠀⠀⠀⠈⢧⡸⡀⠀⣠⠃⡼⠀⢠⢿⡄⠀⠀⢸⡇⠀⡔⠊⠉⣳⠇⠀⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠏⠁⢀⠈⠀⠒⢶⠲⣶⠒⠀⠀⠈⠁⢹⡆⠘⣇⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠉⢀⡴⠋⢀⡟⠀⠀⠀⠙⠓⠓⠒⠛⢻⡟⠋⠉⠉⠈⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⢦⣿⣤⣤⠤⠟⠀⠻⢦⣄⣰⣀⣼⠞⠁⠀⠘⠣⣄⠀⠀⠀⠀⠀⣀⣤⡤⠞⠛⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⣠⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠈⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡆⢀⡄⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠿⠷⣆⠀⠀⠀⢠⡾⠟⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠻⣶⣄⣤⡾⠁⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠴⠶⠶⣤⣍⠳⣦⣄⣀⣀⣀⣀⣤⣾⣟⣠⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⢹⣧⠀⠈⠉⠉⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡷⠶⠲⠟⡛⠛⠻⠾⣿⡾⠁⠀⠀⠀⠀⠀⣤⠶⠶⠶⠶⠶⠶⠶⢾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⢰⠀⠀⢹⣿⣿⣷⢸⡇⠀⠀⠀⠀⠀⢸⡏⠃⠀⠈⣿⣿⣷⡆⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣽⠁⢸⣦⣤⣾⣿⣿⣿⣞⡿⠀⠀⠀⠀⠀⢸⡇⣦⣤⣴⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡀⠸⠉⠹⠿⠿⠿⣿⢿⡷⠀⠀⠀⠀⠀⣾⡇⡏⠉⠿⠿⠿⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣺⢿⣦⣄⣉⣉⣀⣀⣈⣉⣼⡇⠀⠀⠀⠀⢰⣿⣧⣈⣉⣀⣀⣀⣉⣀⣠⡿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡿⠠⡏⣽⣿⣍⣉⠉⡉⠉⠁⠀⠀⠀⠀⢠⡿⢹⣿⡏⠉⠉⠉⠉⠉⠉⢉⡇⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠃⠐⡇⢿⣿⣿⣿⣿⢿⣿⣶⣤⣤⣤⣄⣿⠃⣸⣿⡇⠀⠀⠀⠀⠀⠀⠠⡗⠈⣷⠄⠀⠀⠀ ⠀⠀⠀⣰⡏⠀⠀⡇⠘⣷⡀⠙⣿⡿⣽⣻⡿⠋⢀⡾⠁⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠰⡇⠀⢸⣗⠀⠀⠀ ⢀⣴⠟⠛⠁⠀⠀⣿⡀⠈⠻⠶⠾⠿⠛⠉⠀⢀⡾⠋⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠛⠺⢶⡄ ⣿⠃⠀⠀⠀⠀⠀⠈⢻⣷⣶⡶⣤⣤⣤⣤⣶⠟⠁⠀⠀⠀⢸⡇⠙⠷⣦⣤⣤⣤⣴⠾⠃⠀⠀⠀⠀⠈⣿ ⢻⡄⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠂⠀⠀⣿⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢀⡿ ⠀⠙⠷⣦⣤⣤⣤⣾⢋⣀⣀⣀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣽⠀⠀⠀⣿⣀⣀⣀⣘⣷⣦⣤⣤⣤⠶⠛⠁ ⠀⠀⠀⠀⠉⠉⢰⡞⠋⠉⠉⠉⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⠀⠀⠀⠉⠉⠉⠉⠙⠻⣤⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⠇⠀⠀⠀⠀⠀

⢃⣀⣠⡬⠧⠤⣤⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⣆⡤⠖⠊⠉⠉⠉⠉⠉⠉⠑⠚⠧⣀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠀⠀⠈⢛⢷⣤⢄⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢤⣄⡀⠀⠀⠀⠀⠀⢹⣄⠙⢮⣇⡞⠁⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⢀⣤⡄⠀⣷⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⠀⣀⣠⣀⠀⠀⠀⠉⠈⢿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠿⣿⡿⠿⠈⠳⣄⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠒⠒⣖⡒⠛⠤⢤⣹⡀⠀⠀ ⣀⡠⢄⣀⡀⠀⠀⠀⠸⢿⣿⣿⣾⠉⠹⣶⠀⠘⡇⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢇⢠⠴⠶⢤⡤⢖⣉⠟⠀⠀⠀⠀⠀⠀⡩⠭⠤⣀⠈⠙⠢⣄ ⠁⠀⠘⢮⣙⣦⡀⠀⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⢀⡴⠋⠀⢀⠴⠒⠙⠲⡄⠀⠀⢼⢡⣤⠀⠈⢳⠀⠀⠈ ⠀⠀⠀⠀⠂⠻⠽⣦⡀⠀⠀⢀⣀⣀⡞⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣷⠏⠀⠀⢰⠃⠀⠀⣶⠀⡽⠀⣀⣼⣶⡿⠤⢄⡸⠀⠀⠀ ⠀⠀⠲⣄⠀⠀⠀⠉⠿⠉⠋⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⢠⡀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠸⡄⠀⠀⢀⡴⠁⠸⠿⠿⠛⠁⠀⠀⠉⢢⡀⠀ ⡄⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠊⠀⠀⠀⠉⠉⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀ ⠱⣄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣠⣷⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⣠⠤⢀⣀⣀⣀⣀⣀⡠⠴⠶⣦⡀⠀⠇ ⠀⠈⢳⣄⡀⢸⠁⠀⠀⣀⣤⠞⠉⠈⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣖⣒⣲⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⣭⠷⠾⠷⣶⡛⠒⠚⠀⠀⠀⢨⠇⠀⠀ ⠤⠤⠤⠁⠈⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠫⠤⣄⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠓⣤⠀⢀⣴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠛⢻⡄⢀⡠⠖⢊⡽⠋⠙⣦⣴⠖⠚⢧⡒⠤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠄⣀⣀⣀⠬⠷⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡷⠋⠀⠀⠈⠀⠀⡴⠋⡇⠳⡀⠀⠑⠀⠙⢦⡜⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⢈⣧⣀⣸⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⡴⠚⠯⢤⠀⠀⠀⠈⠉⠉⠑⠒⠲⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⢀⣀⠠⠔⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣾⠥⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠒⠀⠀⠀⠀ ⠓⠶⢤⣤⣤⡤⠤⠤⠴⠖⠚⢹⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠘⣄⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀