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

⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢉⣕⡞⣼⣿⣿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⡀⢻⣤⣴⣴⣶⣶⣶⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⢧⣿⣦⠬⡜⣼⡝⣿⢹⣿⣿⡟⣁⡀⣴⣿⡟⣹⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⣿⢀⣿⢀⠨⢳⣷⢴⣧⣸⣟⡟⠉⢁⡾⠋⣀⡴⢃⡠⣠⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠋⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣾⣧⢸⣻⠀⢩⡏⠀⣸⣯⣿⡿⠒⣲⠟⠘⣩⠿⣠⠏⣴⣿⢯⣟⣹⣄⡿⣿⣿⣿⠏⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠘⢸⡇⣰⣿⠏⣿⣀⡼⠧⢶⣶⣳⡞⢳⠞⣿⣣⠏⠀⢠⣞⣀⣸⣿⣿⠀⢻⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⣿⣷⣿⢹⠀⣯⣞⣧⣔⣯⣿⣯⡾⢃⣾⠟⠁⢀⣴⡟⢀⣼⡟⣾⡿⣐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣧⢹⣾⣴⣿⠋⡇⢸⣸⣿⣿⣿⣿⣿⣿⣯⣶⠟⠋⢀⣴⣫⢏⣴⠟⣽⣿⡟⠀⠈⢹⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢳⠇⣿⣿⣿⣿⢹⡀⠃⢸⡜⣿⢹⣿⣷⣿⣿⡿⣷⠶⠚⠛⢛⡿⠋⣠⣾⣿⣿⣤⣦⣀⢸⡟⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⡞⣸⢻⣿⣿⣿⣾⣗⠄⠘⡇⣿⠚⠻⠿⠯⠿⠅⠀⠠⢄⠍⢨⡙⠊⠑⣿⣿⣯⣿⡿⠻⣿⢡⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣾⢣⡟⢸⠀⣿⣿⣷⣿⣦⠀⣷⣹⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠛⠿⠿⡿⣁⣼⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣇⣼⣿⣾⠀⣿⣿⣮⡛⢿⣧⣽⡿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠶⠆⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡼⣼⣿⡏⡟⣼⣿⣿⣿⡻⣿⠃⣸⡟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢰⢳⢻⡿⣠⡷⣿⣿⣿⣿⡏⢻⣴⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣼⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⡞⣼⣷⢻⡇⣸⣿⣿⣿⡿⡟⠅⣴⣿⡟⢤⣀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⢻⢁⡿⠇⣸⠇⣿⣿⣿⣿⣇⣿⠞⣡⣿⣧⣤⣽⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⣸⠃⢀⣿⢀⣿⣿⣿⣿⣿⢥⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠺⠷⣏⡀⣼⡿⢸⣿⣿⣿⣏⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⣿⣿ ⠀⠀⠀⠀⠈⠙⠳⢿⣿⣿⡟⢉⣰⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣷⣤⠖⠛⠉⠉⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠤⢄⣀⠀⣨⡿⠟⢋⣿⡿⢯⣶⣝⣛⣛⣿⠿⢿⣿⢥⣠⠼⠻⣿⣟⣿⣿⣿⢿⣿⣿⡋⢤⡀⠀⠻⣌⣉⣻⣦⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢀⣼⡟⠛⣛⣿⡿⠀⠉⢛⣻⣿⠿⠋⠀⢸⢹⠀⠀⠀⠀⠘⣾⣦⠉⠛⠷⢿⣿⣻⣦⡌⠢⡀⠘⣧⣙⡛⣿⣗⡚⠉⠉⠉⡇⠀⠀⢀⣀⣀⣠⣴⣿⣿ ⠀⠀⠀⢀⡤⡶⣿⠋⣽⠛⣿⡿⢁⣤⢶⡋⠉⠁⠀⠀⠀⢸⠾⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠛⣿⣦⡙⣏⠁⠈⣯⣙⠛⢿⣆⠀⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⡟⢸⣷⣿⠉⡇⢀⣯⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⢿⣟⢧⡤⠶⠛⠋⠉⠻⣿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣶⣿⣧⣿⢃⠏⠀⡇⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⢻⡝⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⢿⣯⣎⠤⠔⡇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢴⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⡄⢿⠦⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡉⢿⣻⡄⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⣾⣇⠀⠋⡏⠀⠀⠀⠀⣀⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣻⣎⠀⠹⣵⡟⠙⠛⢿⣿⣿⣿⣿ ⣴⣿⣿⣿⣻⣿⣆⢰⠁⠀⠀⠀⠘⠁⣶⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⢻⣠⣴⠀⣼⡟⠛⠛⠛ ⣿⣟⠙⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⠁⠀⠀⠀ ⡏⠁⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀ ⣄⠀⢀⡀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣤⣀⠀⠀⠀ ⣿⣷⣌⢿⣷⣍⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠈⠊⣙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣎⣻⣼⣷⡆⠀ ⣿⣿⣿⣷⣽⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⠛⠷⢶⣤⣄⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣷⣿⣿⡿⠿⠃⠀ ⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡦⢶⣄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠙⣄⠀⠀ ⣸⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀ ⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠁⠚⠉⠛⠙⠛⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⡟⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⣏⠀⠉⠓⠤⣄⣀⡠⠖⠋⢳⣀⣀⣀⣀⣀⣀⣾⣐⣈⣦⣀⣀⡤⠤⠖⠒⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⠇⠸⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠷⠶⠾⡊⠦⣄⣀⡤⠖⠉⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢧⠟⠀⠀⠙⢧⡵⠀⢀⣀⠠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⡴⠛⠉⠙⡆⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠒⠒⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠋⠀⢀⣴⡾⠃⢀⠇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣜⠁⢀⣼⠛⠛⠤⣰⣫⠖⠀⡄⢸⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠘⢄⢸⢑⡷⢿⡿⢶⣄⠀⢈⠳⡄⣴⡧⢸⡏⠉⠳⡖⠲⠤⠤⢤⣄⣀⣠⡤⠴⠚⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⣚⣿⠀⠀⢄⡀⠙⠲⣍⣠⠋⠐⣠⣾⣿⢧⣴⣣⠏⣰⡿⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠈⢷⡀⠐⠭⣗⡀⡴⢁⢀⣼⣿⠂⠉⠢⣴⣁⡾⠋⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠦⢄⣀⠀⠀⠀⠀⠀⢀⣠⡤⢒⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⢄⡀⠙⠧⣴⡋⣠⠟⠒⣤⣠⢀⠝⣄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣜⡽⠡⣤⣼⡯⣍⡉⢲⠊⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠟⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡇⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣤⢞⡞⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀( ͜. ㅅ ͜. )𝘚𝘦𝘹( ͜ₒ ㅅ ͜ ₒ)(‿ˠ‿)

“kids are on this site” why are they even on the internet.. like omg stop crying its not that deep move on and get your emoji combos/symbols. you search porn you get it you dont search it you dont get it so like..??? 💀 ⠀⠀⠀⣴⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣉⣩⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⠉⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡿⠛⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣩⣝⢿⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡝⣿⣦⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⢻⣿⠟⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣋⣁⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠿⠶⣶⣶⣿⣦⣄⡀⠀⠀⣀⣀⣤⣴⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣟⠁⠀⣀⡆⠀⠈⠙⠋⢻⡻⣯⡛⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠉⢳⡆⠀⠀⡀⠀⠀⢠⣤⡴⡿⠋⠹⠟⣯⠀⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠦⣀⡞⠀⠀⣼⡟⠶⢤⣸⡏⣷⡇⠀⣷⣺⣧⣰⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠳⢦⣼⠃⠀⣶⣿⠻⣦⡀⠽⣿⣞⢀⣠⣿⠟⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⣿⠆⢠⣿⣿⡇⠛⢿⣤⡇⠈⢻⠛⣿⣄⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣻⣿⡀⢀⣿⠈⠳⠤⠤⠿⠀⠀⢸⣴⠋⣻⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣇⠈⣿⡀⠀⠀⢰⠆⠀⠀⠈⠉⠉⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣍⣻⡷⠿⠿⣖⣤⣈⣂⣀⣀⣀⣠⣾⣏⣿⣽⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⠁⠀⣠⠖⠀⠀⠈⠉⠛⠶⣤⣀⣀⣀⠤⢭⣛⣧⡀⣠⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠳⣄⠀⠀⣾⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⡄⠀⠘⣧⠀⠀⠀⠀⠀⠐⢮⣁⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⣠⡾⢣⠀⢻⣄⢀⣠⠿⡇⠀⠀⠀⠀⣿⢳⣄⠀⣿⠀⠀⠀⠀⠀⠀⠈⣻⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠁⠀⠀⡆⠀⠉⠻⢦⣤⣧⠀⠀⠀⢰⣿⠀⠹⢦⡘⣷⢄⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣰⣃⠀⠀⠀⠀⠀⢸⠀⠀⣴⡿⠿⠶⠶⣶⣬⣿⣶⣷⣄⡠⠴⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠴⡾⠋⠉⠁⠈⠉⠉⠑⣶⢤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⢾⠒⠒⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⢁⢸⡃⠀⣀⣀⡀⠀⠀⣼⠀⠀⠀⠻⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢤⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⣿⠿⠟⠓⠋⠉⠉⠉⠉⠛⠳⢶⣶⠾⠗⠛⠛⠛⠋⠛⠛⠛⠛⠿⣿⣿⣾⡿⡍⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠣⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣢⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀ ⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣿⣿⡿⠿⠿⣿ ⠀⢸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠢⣄⣿ ⠀⠸⡆⠉⠳⢤⣄⣀⣀⣀⣀⣀⣠⢤⣼⣯⣑⡂⠤⠀⠠⠀⠀⠠⠀⠀⠀⣀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿ ⠀⠀⢳⡀⠀⣀⣀⣤⣭⣿⣿⠿⠿⠟⠛⠛⢿⠿⠿⠷⠶⠶⠶⠶⢾⣿⣯⣭⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇ ⠀⠀⠀⢻⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠶⣶⣤⣤⡀⣠⠋⠀ ⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠃⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠲⠤⣄⣀⣀⣀⣀⡤⠤⠞⠁⠀⠀⠀⠈⠓⠦⠤⣀⣀⠀⢀⣀⣀⠤⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠛⠉⠉⠉⠙⠛⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⠃⣠⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣇⡼⠁⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⡇⠀⠀⠀⢠⢮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⡼⠀⠀⢰⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⡀⢻⣿⣧⣠⡞⣿⠀⠀⠀⠀⣸⠀⣿⡀⠀⠀⠀⢠⣿⣰⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⡿⠀⠀⠀⠀⣿⡇⢸⣿⣸⡀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣤⣤⣿⠁⢸⣿⣿⣷⣶⣿⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⢻⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⢹⣿⣿⣿⣿⠋⡆⠀⣸⣿⣿⢸⣿⡿⠷⣿⡟⢻⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⠟⠛⠛⠁⢀⡤⠠⣄⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠛⠢⣿⡇⣸⣶⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠁⣿⣿⣿⣿⣿⡇⢀⣠⡶⠾⠿⠿⢶⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢻⣿⣿⠇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣧⠀⢻⣿⣿⣿⣿⡇⠈⠻⡀⠀⠀⡤⠀⠉⠀⠀⠀⠀⠀⠀⠴⠗⠒⡚⢿⣄⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣧⣘⣿⣿⣿⣿⡇⠀⠀⠹⠦⠼⠃⠀⣀⣀⠀⠀⠀⠀⠀⡄⠀⢠⠇⠀⠈⣱⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣾⣿⣿⣿⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠉⣝⠳⢾⣶⣤⣄⠻⠖⠋⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⠃⢸⢠⠇⡀⡘⠀⠀⠈⠛⠓⠀⠉⡉⠛⠳⠂⠀⠀⢀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⣿⣿⣿⣿⣿⣿⣿⢳⡀⠘⠂⠃⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⡇⡲⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⣿⣿⣿⣿⣿⣿⣿⡉⠻⣦⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠉⠁⣠⣾⣿⣿⠛⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⣿⢹⣿⣿⣿⣿⣿⣿⡇⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠾⠿⠯⣤⣾⣙⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⡿⣿⢸⣿⣿⠿⠛⣿⣿⣇⠀⠀⠀⠹⣿⣷⣤⣀⠀⢀⣤⣴⡿⠁⠀⠀⠀⠀⠀⢀⢿⣿⡇⠛⠻⣷⣂⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣞⢁⣶⣡⣿⠞⠋⠁⠀⠀⢹⣿⡟⣦⠀⠀⠀⠈⠻⣿⣿⣿⡏⠀⢀⠇⠀⠀⠀⠀⣠⡶⠈⢸⣿⠀⠀⠀⠈⣷⡄⠈⠁⠁⠉⠋⠙⠉⠓⠚⠛⠗⠛⠞⠲⠷⠗⠶⠳ ⠀⠀⠀⠀⣠⡴⠟⠋⠙⠋⠀⢤⣀⡀⠀⠀⠀⠘⣿⡇⠈⢧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⣀⡤⠞⠋⠀⠀⣿⡟⠀⠀⠀⠀⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠶⢄⣀⣹⣧⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⣸⠖⠋⠉⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⡶⠤⣤⣼⣧⡀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⣾⣿⠄⡇⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡞⣿⠎⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠ ⠀⢸⡟⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣯⣣⢿⣖⣀⣢⣐⣄⣆⢖⠆⠖⠫⠃⠙⠉⠁⠁⠁⠀ ⠀⠈⣷⣤⠿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⣾⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡄⢢⡜⢦⡙⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠱⣔⠟⣦⣹⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠁⠀⠀⠀⠀⣀⡤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡳⡀⠘⣦⠛⢿⡳⣝⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⠱⡆⠉⢦⡐⣷⣌⣿⡷⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠙⠒⠒⠶⢤⡀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⡆⠘⡦⠀⠳⡝⣿⡟⠁⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠘⢳⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠉⢠⣚⡽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⣰⠋⠁⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡹⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡶⠞⠉⠉⠒⠲⢤⡄⠀⠀⠀⠀⠀⢀⢇⡚⠉⠂⣮⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⣄⣀⠀⠈⣧⣳⡾⡞⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣦⣄⠀⠀⠀⢀⣾⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠉⠉⣻⡏⡇⡆⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⢘⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⡅ ⠀⠀⠀⠀⠀⠀⠀⡅⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣣ ⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠃⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅ ⠀⠀⠀⠀⠀⠀⠀⢝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⡀⡃⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⠀⠀⠀⠀⠀⡅⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⢑⡇⠀⠀⠀⠀⠀⠛⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⣟⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢰⢁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠈⣌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀ ⢀⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⡀ ⢸⣿⡁⠀⢠⣦⠀⠀⣤⣤⠀⠀⣴⡄⠀⢈⣿⡇ ⠈⢿⣷⣀⠈⠁⠀⣀⣿⣿⣀⠀⠈⠁⣀⣾⡿⠁ ⠀⠀⣿⣿⣿⣿⣿⠿⠋⠙⠿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀ ⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀ ⠀⠀⢀⣿⡇⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⡀⠀⠀ ⠀⠀⣼⣿⠁⠀⠀⠀⠻⠟⠀⠀⠀⠈⣿⣧⠀⠀ ⠀⣼⣿⠃⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠘⣿⣧⠀ ⢠⣿⡇⠀⠀⠀⠻⣿⣦⣴⣿⠟⠀⠀⠀⢸⣿⡄ ⢸⣿⠁⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠈⣿⡇ ⠸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⠇ ⠀⢻⣿⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣿⡟⠀ ⠀⠈⢿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⡿⠁⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠉⢻⣿⣆⣰⣿⣿⠁⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⢀⣠⡼⠟⠋⠉⠛⢿⣤⣀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣵⣾⣿⣿⡋⠁⠀⠀⣠⣉⣿⣿⣷⣶⣽⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⡿⠃⠘⠛⠛⠋⠁⠀⠉⠛⠛⠻⠎⠻⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣴⣿⠿⠋⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠈⠛⠿⣿⣷⡀⠀⠀ ⠀⠀⣼⣿⡇⣠⣤⣤⠤⢤⣤⠤⣿⡀⠀⠀⠀⣾⠧⢶⡦⠤⢤⣤⣤⡘⣿⣽⡄⠀ ⠀⣸⠟⣿⢸⣇⣀⣀⣴⣿⠿⠗⠚⠳⠄⠀⠴⠛⠲⠿⣿⣷⣀⣀⣀⣇⣿⠛⢷⠀ ⢰⡇⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⣠⠴⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡀⠘⡇ ⣼⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣄⠸ ⣿⠋⠁⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠙⢇ ⠇⠀⢀⣤⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣧⣄⠀⠀ ⣧⣴⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣷⣤ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⡀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠓⠒⠒⠀⠸⣿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠋⠉ ⠀⠀⠀⠈⠙⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⣛⠁⠀⠀⠀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⣷⡄⠀⠀⠀⠀⠀⢠⣾⡇⢱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⠚⣿⣿⡆⢠⠤⣤⢰⣿⣿⠓⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢹⣿⣿⣿⣄⣿⣿⣿⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⣿⣿⣿⠿⠿⠿⣿⣿⣿⣖⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⣿⣥⣤⡄⠀⡠⣤⢬⣿⣏⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⠀⠀⠈⢉⠁⠀⠀⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⣀⠀⠀⠁⢀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠻⣇⡏⠑⠒⠊⢇⣸⠟⠋⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢂⡩⠀⠀⠉⠉⠑⠂⠢⠠⠖⠒⠋⠉⠁⠀⠠⡁⠢⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠢⡀⠀⠸⠀⠀⠀ ⠀⠀⠀⠀⡧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢇⠀⠀⠀ ⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂ ⢰⠀⠀⠀⠠⠤⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠄⠀⠀⠀⠘ ⢸⡄⢀⠀⢠⣩⠁⠀⢣⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠊⠀⢈⣁⣄⠀⠀⢸ ⠀⢋⠈⢄⠑⠛⠀⢀⡼⠀⠀⠀⡠⢺⠻⠢⡀⠀⠀⠀⢦⡀⠈⠛⢋⠔⠀⡌ ⠀⠀⠢⣀⠈⠉⠉⠉⠀⠀⠀⠉⠠⡞⠀⢳⢄⠁⠒⠀⠀⠉⠉⠉⠁⡠⠊⠀ ⠀⠀⠀⠀⠁⣲⠤⠤⠄⠀⢂⠠⠊⠀⣧⠀⠁⠍⣐⠂⠠⠤⠠⢖⠈⠀⠀⠀ ⠀⠀⠀⢀⢾⠃⠉⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠀⠈⠱⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠉⠀⢹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣤⣼⠀⠀⠈⣦⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠚⢿⠿⠿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣍⣹⠀⠀⢠⣉⣩⣿⣿⠁⢻⣿⣿⣿⣿⣿⣿⠿⠿⡿⢧⠀ ⣤⠀⢠⡄⠀⣼⣀⠀⠀⠈⣿⣿⣿⣿⣤⣜⠿⠿⠿⠿⡆⠀⡼⠿⠿⠿⢿⣀⣬⣿⣟⣿⣿⠀⠀⠀⢀⡇⠀⣇ ⠉⠀⠉⡇⢠⣿⣿⣷⣦⣤⣿⠏⠀⠀⠀⠈⠙⢦⠀⠀⠘⡴⠁⠀⢀⡴⠋⠁⠀⠀⠀⠙⣿⣤⣴⣾⣿⣿⠈⠛ ⠀⠀⠀⠇⠈⣿⠉⠙⠻⢿⣿⣤⣀⣀⡀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⣀⣀⣠⣿⣿⠿⠛⠉⢹⠀⠀ ⠀⠀⢰⠀⠀⣿⠀⠀⠀⠈⢿⣷⣄⠘⠿⣿⣿⡶⢶⡇⠀⠀⠀⣸⡷⠶⣿⣿⠿⠋⣀⣼⣿⠋⠀⠀⠀⡾⣳⠀ ⠁⠀⠈⢄⠀⠉⢧⣄⠀⠀⢸⣿⡇⠉⠑⠒⠓⠒⠊⠳⠀⠀⠀⠛⠙⠒⠒⠒⠊⠉⢹⣿⡟⠀⠀⣀⣴⡏⠁⠀ ⠀⠀⠀⠀⠑⢄⠘⢿⣿⣷⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣶⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢄⠀⠉⢙⣻⠿⠯⠉⠱⣶⣤⠤⣴⠟⠓⠋⢣⡤⠴⣶⡖⠉⣸⠿⢿⣫⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢠⡇⠀⠀⠀⠀⠀⠈⡽⠁⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣶⡄⣄⠀⠀⠀⢸⣶⠒⠒⠲⠖⣿⠁⠀⠀⢀⡆⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⣿⢉⣹⠤⠤⠀⠘⠿⢤⣄⣤⡶⠿⠀⠤⠤⢼⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⠟⠉⠀⠀⠀⠀⠀⠀⢀⠝⠁⠀⠀⠀⠀⠀⠀⠈⠑⢄⣸⣀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣦⡄⢸⡏⢻⡙⠛⠒⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠁⢐⣴⣿⣴⣦⣤⣤⣤⣶⣦⣼⣤⣤⣧⣷ ⣿⣿⣿⣿⣿⣿⣧⢸⡇⢻⡇⠀⠀⠀⠀⠀⠀⢉⠑⠲⣦⣄⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠘⢣⣀⣾⣿⣿⣿⣿⢉⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠢⣍⠑⠒⠢⠤⣴⣿⣦⡀⠀⣤⣿⡟⢿⣿⡶⠶⣼⣆⡉⠙⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⣿⠀⣷⡈⠑⡄⠀⠀⠈⣹⣿⣿⣶⣶⢻⡿⣏⢻⣝⣷⣦⣀⠈⠉⠙⠻⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣄⠀⠀⢰⣿⠀⠸⣷⣦⡏⠀⠀⠠⠈⢹⣿⣿⡵⢋⣴⣿⣷⣿⣷⣾⣭⡛⣷⣮⣕⣤⠹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣓⣦⣼⣿⣤⣤⣿⡭⠄⠀⠀⠀⠀⢸⣾⠏⣰⣿⣿⣿⣿⠁⠞⣿⣿⠿⣮⣻⡍⠻⣷⣿⠿ ⣿⣿⣿⣿⣿⣿⣍⣀⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⢄⣐⢦⡩⡉⣹⠀⠀⠀⢀⣤⣔⣮⣸⣾⣿⣽⡛⠋⠀⠀⠈⠉⠑⢢⣅⣻⠹⠀⠈⢿⣇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂⠒⠒⢬⡙⢿⣶⡏⠀⠀⣰⠋⠁⠀⠀⠉⠻⢿⣿⣧⡀⠀⠀⠀⠀⢠⣾⣿⢛⡷⣤⡀⠈⠻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠠⡇⠀⠀⠀⠀⠀⣀⣠⠌⣉⡙⣷⣄⣀⣤⣾⠟⣡⡟⠁⣸⣿⡄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⢿⣿⣟⠛⠛⠋⠉⠀⠀⠀⠀⣰⣗⠦⣤⣀⣠⠞⠁⠀⡀⠀⠀⠀⠙⢻⣿⣃⣾⣿⣥⣼⡇⣿⣿⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⣀⡤⠴⠚⠉⠀⠐⠊⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⣿⡁⠀⠈⠙⠓⠻⠿⢷ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⠿⠿⠿⢻⣿⠁⠀⣉⣾ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡏⡠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⢟⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣇⣁⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣡⡼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡆⠰⣄⠀⠀⢀⣼⣯⣴⣶⣿⣿⣶⣶⣤⣀⠀⠀⠀⢠⡾⠟⠛⢉⣩⠤⠝⢒⣉⠀⠀⢀⣠⠴⢛⣿⡟⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⡞⢀⣤⣶⡋⠀⠀⣬⣡⡤⠴⠚⠋⣁⡴⣿⠞⢰⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆⣷⣿⣿⣿⣿⣷⣤⣤⣀⣀⣤⣤⣾⣿⡾⠃⢀⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠼⠛⠉⠉⠉⠉⠀⠀⠀⠀⠁⠈⠉⠉⠉⠓⡢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠩⢑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠪⢑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣴⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀ ⠀⠀⢀⠜⠓⠁⢠⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣶⣶⣤⣶⣶⣶⣿⣿⠆⠀⠱⡣⡀⠀⠀⠀ ⠀⢠⠎⠀⠀⠀⠀⠛⢿⣿⣿⣿⣷⣶⣦⣴⣶⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠛⠛⠁⠀⠀⠀⠘⡝⡄⠀⠀ ⣠⠎⠀⣠⠟⢧⡀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸⡀⠀ ⢼⠀⣰⠏⡰⠈⢷⣴⣶⣤⣤⣄⣀⣀⣤⣤⣤⣴⣶⣿⣿⡷⠀⠀⠀⠀⠀⢺⣿⣿⣷⣶⣤⣤⣄⣀⣀⣤⣤⣤⣴⣦⡄⠀⠀⠀⠀⠀⢳⠀ ⢼⢰⡏⢠⢁⠣⠄⣿⠻⠿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⠿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠈⣖ ⢺⠸⣇⠂⢌⠒⣈⡿⠀⣀⣤⣤⣀⣿⡉⠁⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣏⠉⠁⢀⣿⣿⣿⣆⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣻⠀⠙⠷⢦⡼⠞⢀⡞⡉⠤⠐⡈⢙⣿⣶⣶⡿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣾⠟⢿⡋⠐⡄⠢⠌⢻⡄⠀⠀⠀⢀⣄⠀⠀⢸ ⢺⠀⠀⠀⠀⢀⣀⡾⣟⣶⣶⣷⡾⡛⡝⡻⢿⣷⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⢖⠻⡹⢷⣶⣷⣾⣻⣽⣀⡀⢰⠟⡘⣧⠀⢸ ⣺⠀⠀⢀⡴⢯⣳⠹⣎⡳⣓⢮⣝⣻⢳⠷⣬⣘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢣⣼⠼⡳⣟⢯⢳⢎⡳⡝⣦⢯⣽⠏⡰⢁⠘⣇⢸ ⣺⠀⢀⡾⣩⠗⣮⠝⡶⡹⣥⢏⠶⣣⣛⣦⠀⠙⠳⡼⠗⠀⠀⠀⠀⠀⠀⠀⠸⢷⠼⠋⠀⣰⠽⡜⣮⠳⣭⢳⡹⢦⡳⣿⠐⢄⠣⠌⣹⡜ ⢼⠀⢘⡶⣍⣛⢦⡻⣱⢛⡴⣫⢝⡖⢧⣞⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⢳⡝⣲⣛⡴⣫⠵⣣⠷⣹⢷⣦⣴⠼⠣⣗ ⢻⠀⢸⢲⠭⣎⠷⣱⢫⡝⢶⣙⠮⣞⢳⣾⣿⡿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣿⢿⣿⣿⢣⡞⡵⢪⡖⢧⣛⣥⢻⡱⢞⡼⡇⠘⡾⠀ ⠈⢧⠀⢫⢳⣍⡻⢬⡳⢭⢧⣋⢷⣩⠾⢿⣿⡆⠀⠉⠙⠛⠉⠉⠉⠉⠉⠛⠛⠉⠀⢠⣿⡟⢧⡝⣚⢧⡝⡳⢎⡖⢯⡜⢯⡜⠀⣰⠁⠀ ⠀⠘⢆⡀⠑⠮⣝⣣⠽⡭⣶⢿⡶⠉⠁⠘⣿⣷⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⠃⠀⠹⠭⣞⠼⣹⠭⣞⣣⠝⠃⠀⣰⠃⠀⠀ ⠀⠀⠈⢣⡀⠀⠀⠈⠉⣹⠇⡠⢳⡀⠀⠀⠙⣿⣿⣿⣿⣻⣟⡿⣿⡿⣟⣿⣻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠐⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠑⢄⠀⠀⠀⣿⡠⠐⣹⡇⠀⠀⠀⠘⢿⣿⡞⣷⡽⣛⣷⣻⡽⣞⣳⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⢆⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⢻⣽⣳⠿⣽⣞⣳⢿⣹⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣯⣟⣷⣫⢯⡿⣭⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠙⠺⠷⠯⠿⠗⠋⠀⠀⠀⠀⠀⢀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣠⣦⠴⡴⡻⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⠀⢸⡟⠁⠀⢱⡀⠀⣠⠊⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⠖⠢⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠘⢧⣾⠁⠀⠀⠀⡇⠰⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢠⠔⠫⢤⡀⢀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡀⢠⡶⠀⠀⢻⡄⠀⠀⢠⡇⠘⢦⡀⠀⠀⠀⠈⠒⢤⡀⠀⢾⡁⠀⠀⠀⣨⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⢷⣤⣤⡏⠀⢀⣰⣋⣧⠀⠀⠈⠙⠒⠢⢄⡀⠀⠈⠓⠤⡈⠑⠒⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠑⠚⠉⣸⠁⠀⢸⠖⠒⢺⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣀⣠⡴⠃⠀⢠⢼⣁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠚⠳⣆⠀⠀⠀⠀⠀⠀⣠⡤⠚⠳⢶⡒⣿⠓⠶⠟⠀⠀⣀⡠⠤⠄⠒⠒⠋⠁⠀⠀⠀⣀⠜⠁⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣈⣧⣀⣠⡞⠹⣦⠤⠤⢄⣠⡞⠁⠀⠀⠀⠀⠈⠈⠓⠒⠲⠖⠉⠀⠀⠀⣀⣠⣤⣤⣦⣤⣶⣎⣁⠀⠀⢸⠁⠙⠆⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⠀⠸⣇⠀⠘⣧⣀⣴⣯⣤⣤⣄⣠⠆⠀⠀⠀⠀⢀⠎⠀⣠⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠉⠙⢷⣤⣨⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⢹⣶⡾⠛⠉⠁⠀⠀⠀⠀⠉⠛⠷⢦⣄⣀⣬⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀ ⣄⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣴⡟⠛⠿⣦⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣼⣿⣄⣡⣶⣾⣷⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠛⢻⢻⢾⠻⡙⠛⠛⠘⠒⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡒⠀⠐⠒⢒⠃⢰⣆⣈⠿⡼⠀⡇⠠⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⡘⠀⠀⢠⣶⣶⣴⢸⠚⡀⠈⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠡⠀⢀⣪⠃⠀⠀⡏⠉⠛⠽⠈⠱⣴⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠠⢆⠎⢹⠀⠀⠀⠡⡀⠀⠀⠀⢀⡿⡁⠠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠉⡔⠁⠀⢣⣀⠀⠬⠒⠒⠠⣾⠃⠧⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⣘⠭⣤⢬⣁⠋⢀⠀⠀⠀⠀⠀⠀⠙⢤⣘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣞⣵⠋⠀⢀⣜⠙⢦⠠⡀⠀⠹⣦⢄⠀⠀⢩⠁⠄⠀⠀⠀ ⠀⠀⠀⠀⢜⢿⠻⢑⢉⠭⠝⠋⣁⣀⣷⡀⠀⠀⠈⠑⠤⣙⠁⠀⠘⠀⠀⠀ ⠀⠀⢀⣼⣾⡜⣡⢾⠁⢀⢔⡫⠛⠉⠀⢀⠀⠀⠀⠀⠀⠀⠁⠢⡐⠀⠀⠀ ⢀⠔⠁⡎⡟⡗⠁⠸⢠⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀ ⣾⣶⣤⣽⡞⠀⠀⠀⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀ ⠙⠻⠿⣿⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⣲⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠣⢀⣀⡤⠤⠤⠤⠔⠒⠟⠯⢹⣹⣷⠶⠤⠤⠐⠒⠉⠤⡠⠊⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠉⠀⠈⠉⠉⠁⠉⠉⠉⠉⠉⠛⠛⠁⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣉⠀⠀⠀⣀⣤⠤⠖⠒⠂⠀⠀⠀⠀⠙⠓⠒⠒⠦⣤⣴⣶⠿⠿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⣾⠿⠿⠛⠛⠛⠻⠿⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⢀⣀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⣀⠄⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠐⠊⠀⠀⠀⠀⠀⠀⠀⠉⡵⠲⡄⠈⠻⣷⣝⢿⣿ ⣿⣿⣿⣿⠟⠁⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡆⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡇⠐⢦⡘⢿⣆⢻ ⠟⣱⡿⠃⡠⠊⠁⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⡠⠖⢊⣉⣉⣑⠲⢌⠉⠙⡟⠉⠛⠀⠱⣜⣿⡄ ⢰⣿⢡⠎⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠹⢆⢠⣾⣧⣄⠀⠀⠀⠀⢴⡿⠻⣷⣼⣁⡞⠁⠀⠀⠈⠳⣄⠱⡄⣷⠀⠀⠀⠀⠀⣿⡇ ⢸⡏⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣾⠉⠉⣣⣠⣴⠿⢟⠁⠙⠛⠀⠀⠀⠀⠈⠁⠀⢳⣍⡙⠛⠷⢶⣤⣀⡈⢹⠀⡣⠼⠀⠀⠀⠀⢠⣿⠇ ⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣨⣷⡶⠟⠋⣉⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠙⠻⢿⣶⣧⣄⣀⣀⣀⣠⣾⡟⠀ ⠈⢿⣧⣀⠀⢀⣀⣠⣤⣿⠿⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⢻⣧⣀ ⠀⣸⡿⠻⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⣟⢛⣛⣿⣿⣋⣩⣻⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿ ⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⡿⠋

⠀⠀⢀⣤⡞⠉⢀⣨⡿⠦⠖⠢⣼⣟⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠋⠁⠉⡿⠋⠁⠀⠀⠀⠀⣸⣏⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢿⡁⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠁⠀⢠⡞⠁⠀⠀⠀⠀⣠⠎⠀⠈⣻⠋⠀⠀⠀⣀⡴⠖⢋⡿⢋⡽⠋⠳⣶⣿⣉⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⣠⠄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠋⠉⣿⠀⠀⠀⠀⠀⣰⣧⣀⢠⠞⠁⣠⠴⠒⠙⠿⠴⡾⠋⡴⠋⠀⣠⠞⠁⠀⢸⣧⣀⣠⣈⣧⡀⠀⡀⣀⡼⠃⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⢻⡄⠀⠀⠀⠀⡏⠀⣽⡏⡰⠋⠀⠀⠀⠀⠀⢠⠇⡞⠀⢠⡞⠁⢀⡤⢶⡋⠹⡍⠉⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⡶⠚⠛⢦⡀⠀⠀⡟⠓⠛⡾⠁⠀⠀⠀⠀⠀⠀⢸⣿⣆⣰⣿⡆⣠⠋⠳⣄⠙⢦⡙⣦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠧⣄⠀⠀⠙⢄⢀⣸⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠛⠛⠁⠀⠀⠘⢦⠀⠳⡬⠷⣄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⣳⣤⠶⠺⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⡄⠈⠙⠦⣄⡀⠈⡆⠀⠀⠀⠀⢰⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡟⠋⠉⠉⠁⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⡄⠀⠀⠀⠙⠶⣵⡀⠀⢀⡠⠃⠀⠘⣇⠀⠀⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣅⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢳⡀⠀⠀⠀⠀⠈⢻⡉⠉⠀⠀⠀⠀⠸⣶⣿⣭⡉⠉⢛⣽⡷⣦⡀⠀⠀⠀⠀⠀ ⡖⠈⠹⣗⡒⠒⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⡇⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⢀⡇⠁⢈⣽⠞⠋⠁⠁⢀⣽⡄⠀⠀⠀⠀ ⠙⢆⡀⠀⢀⣸⠟⠃⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢹⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣠⣾⣃⠀⠘⢷⡄⢀⣤⢞⣯⠿⠟⢦⠀⠀⠀ ⡆⠀⠉⠉⢩⣿⡦⠀⠀⠀⠀⠀⠀⢤⠀⠀⠹⡄⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠀⠀⠀⠀⣿⠒⠒⠒⣶⠞⠋⠉⠉⠛⢶⣄⡙⢻⡿⠋⠁⠀⠀⣨⣇⠀⠀ ⢻⠀⢠⡄⠐⠛⠉⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠹⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠻⣤⣴⣛⠁⠀⠀⢀⣠⠼⢶⣻⣷⣾⣿⡄⣠⡴⠟⣙⣿⡀⠀ ⠀⢣⣌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢻⣿⡿⠷⢠⣖⡋⣸⣾⣿⣿⣿⣿⡏⠋⢹⡇⠐⢻⣿⡇⠀ ⠀⠀⠙⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣾⢿⣇⠀ ⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⠀⠀⠀⠀⠀⣼⣾⣷⡀⠀⠀⠀⣀⣤⡽⠿⠻⠁⣿⠀⠀⠀⠀⣿⠘⡟⡀ ⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡼⠀⠀⠀⠀⢀⣴⣿⡙⣿⣿⡄⠀⣼⣿⢿⣤⣤⣴⣶⣿⡄⠀⠀⣰⠏⠀⠇⠅ ⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢠⡗⢦⣠⠤⠒⠻⣿⣿⣿⣿⣟⣿⡾⠿⣿⣄⠀⠀⠉⢤⣼⡇⠀⣠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣺⠇⠀⠀⠀⠀⠀⠈⢛⣿⣿⢿⣿⣄⣀⣿⣿⡏⠁⠀⠘⣹⣇⣴⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⡗⠘⣆⠦⠀⣠⠶⠚⠉⠑⠦⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣤⣀⡀⠉⢹⣿⣷⣦⣤⣾⣿⡿⠛⠙⢿⣦⡀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⣄⠀⡤⠖⠋⠀⢦⡜⡆⠈⠀⠀⠀⠀⠀⠀⠘⢷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⡟⠛⠋⠉⣿⣷⠀⠀⠀⠙⢿⣷⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠁⠀⠀⠀⠀⠙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣉⣙⡒⠒⠶⠦⠤⠤⣰⣷⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⢀⠒⡡⠚⠈⢑⣏⡆⠀⠀⠀⢀⠀⠀⡠⢄⠒⠂⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⢺⠀⠀⡰⣁⢈⠤⠐⢬⠪⠊⠈⢋⣆⣈⣆⣀⡠⠃⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⡚⠢⡀⢗⠳⠁⠀⠀⠸⡧⣦⠔⢋⠪⣂⡀⠀⢡⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡬⠶⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠱⡈⠂⢌⡄⠀⡈⢃⠀⢀⡀⠀⠀⠀⠀ ⡜⢦⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢡⠀⠀⢸⠉⠀⠀⡞⣫⠝⠓⣢⠀⠀ ⡕⠒⣮⠁⠀⠀⠄⠡⠀⡆⠀⠀⠀⠀⠀⠈⠈⠀⠀⢸⠀⡤⠚⠒⢌⢲⠟⠉⣡⠀ ⠡⣥⠀⠀⠀⠀⠈⠐⢵⡀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠈⡿⠆⢔⣻⣿⣿⠓⠏⣺⡆ ⠀⠘⠄⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⢣⠀⠀⢀⡷⣄⢀⣬⣛⣁⡇⠀⡏⣧ ⠀⠀⠀⠢⢀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⠎⠸⠒⠂⠙⣿⢿⣚⣧⠄⠱⣇⣜⠀⠉ ⠀⠀⠀⠀⠀⠁⠒⠤⣀⠤⠣⣋⠐⠉⠈⠢⣇⠀⠀⠀⠉⠑⠂⢿⡷⠚⣯⠈⠳⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠙⠦⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⣀⣀⡀⡆⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣶⣶⡶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠹⣿⡍⣭⣭⠿⣿⣿⡿⠀⠀⠀⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣾⣿⡿⠇⠀⠰⠶⠒⠂⣤⡄⢶⣿⣿⠁⠀⠀⢠⣿⡟⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠿⣿⣿⣛⠿⠿⣾⣿⠿⠏⠀⠀⠀⠀⠀⡄⠀⠀⢀⣾⣿⠃⠀⠀⠀⣾⡿⠁⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣿⣿⣿⣶⣿⣿⢣⠀⠀⠀⠠⡄⡌⠁⠀⢠⣾⣿⠏⠀⠀⠀⣼⣿⠃⠀⠀⢀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⣦⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠻⠿⣿⣟⣛⠳⢿⡟⣿⣸⠀⠀⠠⠉⣿⣷⣴⣦⣨⣿⣿⣤⣀⠀⣰⣿⠃⠀⠀⠀⣾⣿⣿⡟⠀⠀⣶⠒⠓⠒⠒⢲⡄⠀⢹⣿⣿⣆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣏⡉⢠⣄⣀⣀⣛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⠋⠉⠿⣄⠀⠀⠈⠳⡄⠀⠀⠈⡇⠀⠈⣧⡴⠋⠁⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡆⠈⢿⣿⣿⣮⣼⣿⣿⠋⠈⠻⣿⣟⣿⣿⣿⣦⡀⢰⣟⠀⠀⢰⠀⢹⣿⢻⣆⣸⠀⠀⠀⢹⡀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⠀⢸⣿⣍⠙⠿⣿⡵⠚⠉⡽⠛⢿⣿⣿⣿⡟⣿⣿⣿⠀⠀⣸⠀⢸⡯⡏⠀⠘⡆⠀⠀⠘⡏⠁⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡶⣺⢿⣿⣿⣧⢤⣉⣿⣷⠀⢸⠁⢀⣾⣥⣀⡼⠈⢻⣿⣿⣋⣻⣿⠀⠀⡏⠀⢸⣿⠀⠀⠀⢳⠀⠀⠀⢹⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠿⡀⠙⣿⣧⣿⣿⣿⣁⠀⠈⠳⣾⣿⣿⠟⠁⠀⠀⠙⣿⣿⣿⢿⠀⠀⡇⢀⡟⣿⣴⢧⣀⣘⡆⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⢿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠘⣿⣿⠏⠀⠈⠓⠦⣄⠀⠙⠁⠀⢀⣀⣤⣠⡾⢿⡏⢸⠀⠀⡟⠿⠿⠿⠃⠀⠀⠉⢳⠀⡰⠁⠀⠀⠀⠀⠀⠀⣠⠾⡅⠀⠀⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠀⢀⣀⣠⣠⡬⠽⢿⣶⣾⣟⠛⠋⠁⠀⠸⠀⢸⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃⠀⠀⢀⡀⢀⡤⠚⠛⠤⣷⡀⠀⢸⠇⠀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣠⠔⢊⠽⠛⠉⠉⠉⠑⢦⠀⠀⠀⢉⡗⢦⣀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⡠⠼⣄⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠉⠓⠢⢄⡀⠈⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⡏⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠸⠦⠏⠉⢳⡀⡿⠿⣿⢀⡠⠴⠒⠋⠉⠁⠀⠀⠀⠈⢦⡀⠀⠀⣀⣵⡀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢠⣿⣀⣀⣈⣷⠦⠄⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠇⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⠿⣿⣷⡤⡄⠀⠀⠀⠀⠀⠀⢻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⠈⠈⠋⠉⠀⢹⡇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢩⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢻⣿⡿⠟⠻⡀⠀⠀⠀⠀⠀⠀⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣄⣀⣀⣈⣸⣷⣿⣿⣿⣀⡀⠀⠀⠀⢀⠀⠀⢈⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⡄⠀⠀⢇⠀⠀⠀⢀⣠⠼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉⠉⠓⠲⣞⠋⠉⠉⠉⠉⠉⠉⠛⠒⢶⡒⠒⠒⠒⠒⠂⠐⠂⠐⠒⠲⠶⠶⢶⡋⠀⠀⢀⣸⠗⠚⠋⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢽⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⣷⡄⠀⠀⢹⡇⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡇⠹⣦⣀⣠⣿⣾⣿⡿⢿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⣸⠟⠙⣿⣿⣟⡃⠀⠵⢿⡿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⢸⣾⠿⠀⠀⠙⣿⣿⣷⣄⣸⡿⠇⢉⣹⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢺⣇⣠⠀⣀⣼⣿⠙⠟⠋⠉⠀⢠⢁⡠⢿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠻⠛⢿⣿⠁⡔⠉⢉⣉⢶⠀⠀⠿⠗⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣀⣀⣘⣿⣼⣗⣾⠿⠴⠊⠁⡤⠄⢀⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠚⠀⠐⠀⠀⠀⢏⠉⠉⠙⣿⡄⠀⠀⠀⠀⣀⣠⠴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⣷⣌⣦⣤⣤⣽⣿⣶⣶⠚⠃⠙⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⠴⣿⣟⠛⣥⠀⢩⠀⠀⠀⣠⠀⣧⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⢳⠀⡀⠄⠒⠈⡀⣦⠿⠷⠷⢦⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡠⠙⢄⠑⣶⠀⢀⠀⢇⡗⣇⡀⠒⠲⡝⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠢⢄⠀⠀⠴⠋⠀⠀⡰⠉⠀⠀⠀⠁⠺⢧⣀⡨⠱⡖⠃⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠀⢀⠑⠤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠘⡀⠘⠂⠀⠦⢄⠀ ⠀⠀⢠⠃⠀⢀⡎⠀⠀⠈⠢⡄⠀⠁⠀⠀⠀⣠⠞⠁⠀⠈⡆⠀⠀⢳⠤⠀⠐⠤⡼⠇ ⠀⠀⡎⠀⠠⣾⣿⡦⣀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠘⡆⠤⠤⠴⠋⠀ ⡠⠚⠀⠀⢰⠋⢇⡸⣿⣆⠀⠀⠈⠑⡀⠀⠀⠀⡴⣿⠙⢻⣿⣇⠀⠀⠱⡀⠀⠀⠀⠀ ⠓⠂⠤⠤⠞⠀⠘⠾⡿⠃⠑⠒⠂⠒⠓⠂⠀⠐⣛⣖⡰⠚⠁⠸⢀⣀⣀⣈⠆⠀⠀⠀

⠀⠀⠀⠀⣄⠀⠀⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠳⣀⣷⣾⡶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣠⠏⠹⣿⣃⢰⣿⠻⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢂⣇⣄⡴⢟⣛⡋⠁⣎⣝⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡉⠹⣷⣥⣴⠺⢀⡈⢠⡿⠃⠀⠀⠀⠀ ⠀⠈⠀⠁⢀⢋⠉⢻⣄⣀⡀⣤⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠭⢽⡻⡟⠃⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⢌⡁⠀⠃⠞⠛⡓⣦⠀⠀⠀ ⠀⠀⠀⡰⠠⡁⠄⠉⠠⠊⠁⠁⠲⢭⠵⠚⠘⠇⠀⠀ ⠀⠀⠰⠀⠠⠈⠂⡀⠠⠀⠀⢀⠔⠁⠄⠐⣀⠩⢁⡂ ⠀⢀⠃⢐⠿⢦⡀⠐⢀⠀⠀⠁⣀⣤⣦⠀⠃⠈⠐⠀ ⠐⠥⠀⠈⠘⢿⠇⠤⠤⠦⠤⠼⠭⡨⠋⢀⣈⣢⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣝⣿⣯⣿⣻⡿⣷⣿⣴⣿⣿⣷⠾⣷⡿⣿⣿⣾⣧⠾⣧⣆⣨⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠁⡿⠀⠀⢸⡄⢀⡾⠋⢹⠁⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣼⠃⠀⠀⣧⠀⠀⠀⣿⣿⡆⠀⣾⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⠻⠖⠛⠋⠉⠁⠀⠀⢉⡇⠀⠀⢸⡟⢄⢀⣀⣿⣿⣧⢺⡟⠃⠸⣿⡟⠒⠤⢤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠘⠛⠋⠉⢉⡉⠁⠀⢻⡅⠀⢠⡋⣷⠀⠀⠈⢳⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣴⣿⣷⣥⣿⡌⣷⠀⣏⠉⠙⣆⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⣼⢷⣿⣶⣿⣛⣻⡟⠀⢿⣄⠀⠙⣆⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢠⠞⣩⡟⠀⠀⠀⠀⠀⢀⡏⠉⠉⠛⠿⢦⣉⣻⡀⠀⠙⢷⣄⠸⡆⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⣯⣴⣿⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⣿⣿⣿⡀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠹⡄⢀⡜⠋⠁⣿⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡙⠀⠀⠀⢠⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣀⡈⠉⠒⢧⡜⠀⠀⣠⡿⠀⠀⡀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠈⢻⠐⠒⢲⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡶⠾⠁⢀⡾⠋⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠙⢶⣦⣤⣠⣤⠀⠀⣴⣿⣿⠀⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣾⠀⠀⠀⠀⠀⠘⢷⣤⢤⣤⠤⠶⠛⠋⠀⠀⠀⠀⠙⠛⢿⣿⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠞⠛⠛⠛⠛⠓⠶⢤⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡆⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⠤⠖⢒⣦⣤⣤⣀⠀⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣠⡾⢟⢁⣤⠞⠋⠁⠈⠉⠙⡿⣶⣄⠀⠙⢆⠀⠀⠀⠀⠀⠀⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⡝⢾⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⡾⠋⣀⣾⠟⠁⠀⠀⠀⠀⢀⣼⡇⠀⠙⢷⣄⠀⠱⣄⠀⠀⠀⠀⠘⣟⢿⡦⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣴⣿⣿⣿⡿⣿⠹⢧⣀⣀⣀⣤⠴⢿⣿⣇⡀⠀⠈⠻⣷⡀⠘⡆⠀⠀⠀⠀⠘⠻⢧⣁⡙⠓⠤⣄⣀⣀⠴⠋⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⣿⡟⣰⠏⡶⠀⠀⠉⢀⣀⣠⠼⠛⠉⠁⠀⠀⠀⠹⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⢸⠏⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠛⣟⣠⡟⠀⣿⣀⡴⠚⠋⠁⠀⠀⠀⣠⣤⣴⣲⣶⣶⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣧⣰⡇⣠⡟⠉⠀⣨⣿⠏⠀⠀⠀⠀⢀⣶⢟⣫⣸⠾⠛⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⢿⣏⣿⣿⣿⠀⢠⡾⠋⣽⠀⠀⠀⢀⣾⠻⠤⣼⠟⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⡾⠋⠀⣸⠿⣿⣿⣧⣴⠏⠀⠀⣿⠀⠀⣰⠟⠁⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡾⠃⠀⠀⠀⡇⢠⡏⢀⡿⠁⠀⠀⠀⠙⡄⢠⠏⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⣥⣀⡀⠀⠀⣷⣞⣀⡞⠁⠀⠀⠀⠀⠀⢧⡟⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣶⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢁⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠙⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⠲⠖⢶⣿⣿⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣾⣿⣿⡿⠛⠋⡿⡻⢿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⣤⣴⣚⣋⣁⡀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣤⠶⠿⠟⠛⠛⠻⠿⠿⠿⠶⠶⠶⠶⠛⠁⠈⡙⠓⢾⣧⠤⣯⣿⣿⠿⢟⠛⠛⠛⠉⠁⠀⢀⣀⡀⠀⠀⠉⠓⢶⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡇⠸⡵⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣤⣷⣶⣷⣼⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⣿⣿⣿⣿⣷⡄⠀⠐⠄⣆ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣹⣧⣤⣿⣿⣿⣿⣿⣿⡄⠀⢠⡄ ⠀⠀⠀⠀⠀⠘⠛⢻⡿⣓⣻⡉⠛⣻⣟⡩⢿⣿⣀⡴⡼⡎⠀ ⠀⠀⠀⠈⠁⢀⠀⠈⢳⡉⠉⠂⠀⠪⠿⠇⢴⠟⡡⠐⠂⠁⠀ ⠆⠀⠀⠀⠀⠀⠑⠀⠀⠉⠒⠞⠀⠌⠂⡄⠁⠀⠀⠀⠀⠐⠀ ⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢀⡀⣰⠃⠚⠚⠁⠀⢀⠃⠀

Venus planet of love was destroied by global warming ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⢿⠿⠿⠿⠿⠿⡿⠿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠉⠉⢀⣠⣾⡆⠀⠀⠀⠀⣿⣦⠀⠈⠉⠙⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠉⠀⠀⠀⠀⣶⠿⠟⠉⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⡿⠉⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣦⣤⣄⡀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠀⣠⣶⣿⣿⠿⠛⠛⣿⣿⣷⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⡏⠀⠀⠀⣠⣾⣿⣿⣿⣿⣂⣤⡼⠿⢿⣿⣷⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣷⣄⠀⠈⢿⣿⡄⠀⠀⠀ ⠀⠀⠀⣿⡿⠀⠀⠀⣰⣿⣿⠟⠛⠛⠛⠛⠁⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⠁⠀⠈⠹⣿⣤⣦⣸⣿⣿⡟⣿⣦⠀⠘⣿⣷⠀⠀⠀ ⠀⠀⢸⣿⠇⠀⠀⢰⣿⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠉⠉⠁⠈⢹⣿⡇⠈⢿⣇⠀⢹⣿⡄⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⣼⡇⠀⣿⣦⣀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠘⣿⠀⠘⣿⡇⠀⠀ ⠀⠀⢸⣿⠀⠀⠸⣿⡇⠀⠘⢿⣿⣟⠛⢳⣶⣾⣿⣿⣿⡏⠀⠀⢻⣿⣿⠿⠻⣷⡄⠀⠀⣀⣠⣴⣿⠟⠀⠀⢀⣿⠀⠀⣿⡇⠀⠀ ⠀⠀⢸⣿⡀⠀⠀⢹⣿⡀⠀⠀⠉⠛⠿⠿⠿⠿⢟⣿⣿⠁⠀⠀⠘⣿⣿⣷⣦⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣠⣾⡿⠀⢀⣿⡇⠀⠀ ⠀⠀⠈⣿⣇⠀⠀⠈⢿⣿⣤⣄⣀⣀⣀⣀⣠⣶⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣦⣍⣉⠉⠉⠀⢀⣀⣠⣴⣾⣿⠟⠁⠀⣸⣿⠃⠀⠀ ⠀⠀⠀⢻⣿⡄⠀⠀⣰⣾⣿⣿⣿⡛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠛⢻⣿⣿⣯⣭⡀⠀⠀⢠⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣄⣰⣿⡟⠉⠻⣿⣷⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⠙⢿⣿⣧⣤⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⡿⠋⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠸⠿⠛⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠙⢿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀ ⢀⣾⣿⠟⠁⠀⠀⠀⣶⣴⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣼⣿⡿⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀ ⣼⣿⠃⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⣷⣶⣶⣦⣶⣶⡿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣦⣤⣤⣀⣀⣀⣼⣿⣿⣦⣤⣠⣤⣤⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠉⢻⣿⡏⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣶⣦⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠘⣿⣿⣆⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏ ⠀⠈⠻⣿⣷⣄⡀⠀⠀⢿⣶⣤⣄⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣤⣶⣆⠀⠀⠀⠀⢀⣠⣶⣿⡿⠋⠀ ⠀⠀⠀⠈⠙⠿⢿⣷⣶⣤⣽⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣯⣤⣤⣤⣶⣿⡿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⢀⣠⡖⡾⠛⣿⣷⠒⢠⡀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀ ⠒⢶⣶⠶⣶⠟⠁⠈⡁⠘⣸⠃⠀⡿⠁⢱⡀⠀⠀⠀⠀⠞⠟⠀⠀⠀⠀⠀⠀ ⠙⠿⢿⣻⣿⡇⠀⣶⣤⣸⢯⣀⣼⠃⢀⣿⠇⢀⠀⠀⡆⢲⢧⡀⣀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡞⢶⣦⣾⡟⢻⣿⣷⣄⣼⠈⠐⣦⢉⠀⠰⠘⠁⠀⠀⠑⠄⠀⠀ ⠀⠀⠀⢖⠿⣷⣜⡦⠉⣠⣧⠏⢻⣟⣿⢠⠀⡆⡀⡀⠀⡠⠂⠀⠀⢀⡆⠀⠀ ⠀⠀⠀⠀⠁⢹⠟⠁⠂⣍⣃⣄⠤⠻⠁⢸⠚⠋⠁⠡⡀⠀⠀⢀⣴⠁⢡⠀⠀ ⠀⠀⠀⠀⢠⡤⢐⠛⠀⢐⠈⠩⡢⢀⢸⡟⠀⠀⠀⠀⠃⠀⠑⡀⠀⠁⠊⢌⡡ ⠀⠀⠀⢀⡏⠧⠬⡔⠂⠁⠀⠀⠀⢔⠡⠉⠀⠀⠀⠀⠀⢱⢏⣿⠆⠀⠀⢈⠀ ⠀⠀⠀⠘⠓⠒⠆⠓⠛⠂⠤⡤⠀⠘⠠⠤⡤⠀⠀⠀⠀⠀⢨⠀⢈⠤⠀⠊⠀

⣿⣿⣿⠟⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⡩⠍⠘⠡⠿⠿⠿⡿⠏⠽⠿⠛⠛⠟⢿⣿⣿⣿⣿⢟⣩⡻⢿⣿⡟⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠻⣿⣿⣿⠋⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣅⣠⣇⣇⣀⣄⣀⣄⣄⣦⣤⣤⣴⣤⣼⢿⡇⣬⣥⣄⢻⣿⣶⡝⢁⡎⢰⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄⢦⠀⢹⣿⠇⣰⠐⢰⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢟⡋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡐⠞⠋⢑⣼⣿⣿⢣⢸⣤⣆⡂⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠘⣧⡜⣥⣾⣿⡆⠛⠧⣼⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⢋⡔⢿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣿⣿⡟⣥⢸⡜⠎⣸⣾⠠⡈⣿⣿⣿⣿⣿⣿⣿⣿⡧⡘⠸⢿⣿⡿⢿⣾⣿⡌⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⣱⣿⣧⡜⢇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⠟⢸⣿⣜⠷⠀⠁⠱⡡⠂⢸⣿⣿⣿⣿⣿⣿⣿⡷⠂⡀⣈⣩⡀⠠⠿⢋⡅⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⣸⣿⣿⣿⣿⣦⡂⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣷⣶⣶⣶⠿⠎⣿⣿⣿⣿⣿⣿⣿⣷⣄⡙⠌⠩⠶⠸⠏⠚⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣿⣿⣿⣿⣿⣿⣿⣷⡄⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⠿⠿⠿⠿⠿⠋⢞⣴⣿⣿⣿⣿⢛⣥⣶⣶⠦⠅⣠⡤⠈⣭⣥⣤⢍⣥⣶⣶⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣌⢿⣶⣬⣛⡛⠿⠿⠿⠿⢛⣍⣝⠃⣚⣻⣭⣭⣝⡂⢋⣴⣋⣿⣦⡁⣿⣿⠋⡴⠾⣿⣿⣷⣴⡿⢿⣿⣿⠸⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⡇⢹⣿⣿⣇⢷⣝⠻⢿⣿⣧⡙⣿⣿⣿⣬⣿⣿⣿⣶⣦⣄⡻⢿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡇⢿⢇⣾⡁⢠⠈⣿⣿⡇⢄⠀⢻⣿⡷⣱⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⠹⣏⠩⣭⣙⡈⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠋⣿⡹⣿⣿⣄⠻⣿⣿⡿⠷⣦⠘⣿⣷⣶⣾⣿⣿⣿⣶⢾⠿⣛⣃⣛⡻⣿⡿⣘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⡙⢷⣄⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⢻⣿⣿⣿⣿⣷⣍⠉⣶⣿⣿⣷⠘⢿⡿⢭⠏⣈⣉⡃⠀⣰⡝⣿⡿⠿⢋⠴⣿⢨⣷⣌⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣦⣔⠺⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⣛⣿⣤⣽⣿⣿⣿⣿⢄⡿⢟⣋⣭⣽⣦⣭⡀⠻⣿⣿⣿⣸⣿⣿⣷⠾⣿⣿⠇⠠⠉⣀⡥⢀⣾⣿⣿⣦⠘⣛⠿⠆⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⢖⣲⣤⣤⣤⣤⣤⣀⠀⢭⣽⣿⣿⣿⠏⣠⡾⠿⣿⣿⣿⣿⣿⣿⡄⣮⡙⢿⡿⢛⣥⡖⢿⣿⣶⣤⣤⡾⠏⢸⣿⣿⣿⣿⣿⣧⣿⣿⣶⣌⠻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⢛⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣜⠿⣛⣥⣶⣾⣿⣿⣷⣿⣿⣿⣶⣶⣬⣝⡛⢶⣶⣌⢻⣷⣾⡿⠟⣋⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿ ⣿⣿⣿⣿⣿⢋⣴⣿⣿⢟⢍⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣷⡨⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⡎⢿⣿ ⣿⣿⣿⡟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣝⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⡸⣿ ⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⡇⣿ ⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⢻ ⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⣼ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⢃⢿ ⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⣿⢃⣾⡇ ⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡴⠟⣱⣿⣿⡇ ⣿⣿⣿⣦⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣬⣟⣛⠻⠿⠿⣛⣛⣛⣛⣯⣭⣭⣭⣥⣴⣶⣶⣶⣾⣿⣿⣿⣿⠃⣾⣿⣿⣿⡿⠹⣿⣿⣿⣿⠿⠟⠋⢵⣶⣶⣧⠻⠟⣩⣾ ⣿⣿⣿⣿⣿⣷⣮⣭⣟⣛⢛⣛⣛⣛⣛⣛⣿⣯⣥⣭⣭⣴⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣴⣬⣙⣛⣛⣥⣾⣿⣿⣶⣶⣿⡌⣿⣶⣶⣶⣶⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢛⣫⣵⢎⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣍⣛⣛⣿⡿⢟⣿⣿⣿⣿⣿⣴⣶⣶⡶⣨⣭⣭⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠰⣛⣫⣭⣭⣭⣭⣭⣭⣍⡓⢟⣛⣫⣭⣭⣭⣭⣙⣛⣻⠿⢿⢃⡾⠘⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⡛⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣾⢣⣧⢹⣿⡿⢟⢛⣩⣶⣾⣿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣈⠻⣿⣿⣿⣿⣿⣿⣿⢃⣶⢄⣾⣿⡎⢣⣾⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⢃⣿⣷⣌⠻⣿⣿⣿⣿⡟⠸⢇⣾⣿⣿⣷⡘⠛⠈⠙⠛⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⡏⣼⣿⣿⣿⣷⣌⢿⣿⣿⠡⢆⣾⣿⣿⣿⣿⣷⢸⣿⡿⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣛⣣⣿⣿⣿⣿⣿⣿⣷⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡇⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣸⡇⠀⠀⢿⡉⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢸⣧⠀⠀⢸⡇⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢀⣀⣼⣿⣴⣶⣾⣷⣤⣄⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⡀⢠⠄⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⡟⠀⢸⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠘⠃⠠⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⣿⡟⡇⠀⢸⠛⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⢾⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⠉⠁⠀⢸⡄⠀⣶⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⣿⡷⠯⣥⣤⣈⣙⣦⠀⠀⠀⠀⣠⡽⠛⠉⠉⠓⢻⣟⣿⣿⠀⢀⣀⣼⠷⡾⠻⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠤⢤⣼⣿⡇⠀⢻⣿⣿⣿⠟⡇⠀⠀⢰⠛⣿⣿⣿⣿⡟⠉⠙⣿⣿⡿⠿⠿⠛⠀⢸⡀⣇⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠉⢻⣶⡤⠬⠭⠭⠴⠧⠀⠀⠰⠧⣌⣛⣛⣋⣁⣀⣴⣿⣟⠀⢀⣠⠴⠓⠚⠉⠉⠉⠉⠉⠉⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⣸⣷⣤⣀⠀⠀⢀⣠⠔⠂⢄⡀⠀⠀⠀⠀⣠⠞⠋⠉⠻⣏⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠤⠾⠔⠃⠀⠻⠻⠏⢹⠿⢤⣀⣀⡠⠟⠲⣄⠀⡼⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠘⡄⡇⠀⠀⠀⢤⢀⣿⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠙⢦⣘⣦⡨⠟⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣤⠄⢀⣤⡠⠤⣬⠟⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⡿⠿⢿⡿⠿⣷⣿⡿⡾⠻⠿⠿⠿⠷⠚⠴⠠⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡇⠀⠀⣧⣼⠁⢸⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠙⠢⠤⠒⠒⠊⠉⢓⠏⠀⠀⣷⡀⠀⣹⣿⣠⡿⠂⢸⡷⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠋⠉⢉⣉⢀⡘⡇⢀⣬⣿⡀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣴⣿⣟⣿⣷⣽⠸⡇⠈⢧⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⠔⣿⠀⠀⠀⠀⢸⠟⠛⠻⠿⣙⢻⡀⠙⢦⡀⢳⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢀⣮⣾⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠁⠀⠈⣿⣿⡇⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⢼⣄⠎⠁⢀⡇⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡀⣀⣠⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠢⡤⠝⠀⣰⠋⠀⠀⣆⠀⠀⠀⠈⠳⢤⣀⣀⣀⠀⢀⣼⣿⠀⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣼⣁⡀⠀⠀⠙⣦⡤⠤⠤⠒⠋⠁⠀⠈⠑⠻⢿⣈⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⠉⣉⡉⠉⠉⠓⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⡴⢊⣩⠜⠛⠛⠳⣶⣄⡈⠢⡄⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠈⠻⣦⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡞⢁⣼⠟⠁⠀⠀⠀⣠⡇⠈⠻⣦⠈⢢⡀⠀⠀⠀⢿⣷⣤⡀⠀⠀⠀⠀⠀⡇⠈⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣿⢋⠓⠤⠤⠒⠚⣿⡷⠄⠀⠈⢷⡄⠱⠀⠀⠀⠈⠙⠳⢌⡁⠒⢦⡴⠊⠀⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠉⡿⢿⢡⠇⢸⢀⣠⠴⠒⠋⠁⠀⣀⣤⣤⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠲⢼⡁⠀⠀⠀⠀⢁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣮⣼⣁⡼⠉⢀⣾⠏⠀⠀⠀⣠⠶⣋⡽⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠀⡎⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⢻⣿⣿⣿⢁⡴⠋⢸⠀⠀⣠⠞⢑⡶⠋⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀ ⠀⢠⡞⠋⠀⢸⢉⡟⢻⠟⠁⠀⠸⡄⢠⠋⢰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀ ⣰⣏⣀⡀⠀⢸⣞⣠⠏⠀⠀⠀⠀⢷⡏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⣿⣿⣿⣿⣷⣾⣿⠏⠀⠀⠀⠀⠀⠈⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠙⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠈⠙⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⢒⣿⣿⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⣿⣮⣷⣄⣀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠀⠀⠀⢀⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⣤⠶⠶⠶⠿⠿⠿⠿⠭⠭⠽⠋⠙⠓⠦⣧⣤⣽⣿⠿⠿⠟⠛⠛⠉⠉⠉⠁⠈⠐⠦⠖⠁⠀⠀

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⠿⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⣀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠴⠦⠤⢤⣤⣀⣀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣭⣷⣶⣶⣤⣤⣤⣤⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⠿⠛⠋⠉⠁⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠿⠛⠋⠉⠉⠉⠉⠉⠙⠛⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⡀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⢶⣄⠀⠈⠻⣿⣮⠻⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⠀⠀⣠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡿⠀⠢⡀⠙⣿⣷⠈⢿ ⣿⠟⣽⣿⠟⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢀⣠⡤⠴⠶⠶⢤⣄⡀⠰⠶⠾⢿⡾⠷⢶⡆⠘⢦⠘⣿⣇⠘ ⠋⣸⣿⠋⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠉⠉⠙⠳⣦⣄⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⡄⠀⣴⠋⢁⣤⠶⠞⠲⠶⣤⡉⠳⣄⠀⢸⡇⠀⠀⠀⠀⠈⠳⢽⣿⠀ ⢀⣿⡏⡴⠃⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣀⣀⣀⠀⠀⠈⠻⣆⣴⣿⣿⣶⣄⠀⠀⠀⠀⠀⢸⣿⠟⠙⠿⣿⣧⣤⣏⠁⠀⠀⠀⠀⠈⢻⣆⠈⢧⠸⣧⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢰⣿⠉⠀⠙⣇⣠⣴⣾⠿⢛⡁⠈⠛⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⢳⣤⡉⠛⠛⠿⢷⣦⣤⣀⡀⠀⢹⠀⢸⡦⠼⠀⠀⠀⠀⠀⠀⣾⣿⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣧⣤⣶⠿⠟⠋⢉⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠂⠀⠀⠈⠙⠛⠿⣿⣶⣤⣾⡀⠀⠀⠀⠀⠀⢀⣼⣿⡏⠀ ⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣴⣾⡿⠛⠉⠀⠀⠒⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣶⣶⣾⣿⣿⣿⠀⠀ ⠀⠙⣿⣿⣦⣤⣠⣤⣴⣶⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠘⢿⣷⣶ ⢀⣠⣿⡟⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿ ⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡋⣿⣯⣤⠤⠿⠿⠷⠶⠶⠾⠼⢷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿ ⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣿⣿⣿⣿⣿⡟⠁

⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⢉⠉⠀⠁⠀⠀⠀⠀⢉⣉⣃⣈⣹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣯⠿⠛⠛⠓⠶⣭⡀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠀⠀⠀⡈⠙⠻⣿⣿⣿ ⣿⣿⡿⠋⡠⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠰⢹⠄⡘⢿⢻ ⢫⢟⠀⠁⠀⠀⣠⠤⠐⠠⢄⠀⣸⠀⠀⠀⢀⣷⣀⠔⡨⠭⠥⡢⠉⡏⠉⠈⠺⡇ ⣼⠁⠀⠀⠀⡼⠁⡴⢉⣦⡴⢞⠉⠓⠀⠀⠈⠀⢮⣛⠲⠦⣄⣸⢀⠤⠀⠀⢠⡇ ⠸⣆⠀⠀⣀⣧⠶⠛⠉⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⢻⣀ ⣰⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾ ⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠛⠋⠉⠁⠉⠚⠃⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟

⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣸⣶ ⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⢠⣿⠿ ⠀⢀⣠⠾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢦⣄⣠⣴⣿⣿⠀ ⠐⠋⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⣻⠛⡟⢩⣭⣥⣤ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢸⣟⣃⣛⠀⡇⢸⣿⣿⣿ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣛⣛⠓⡶⢶⡒⡒⠚ ⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠈⠉⠀⡇⢨⣿⣇⢀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡾⣦⡀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣦⡤⢤⡇⠀⠛⠉⠻ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢀⣤⣾⣷⣿⡇⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⣀⢈⠃⠀⢸⢸⣾ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⢋⢹⣿⡿⠟⢷⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢩⣹⣇⣸⡆⠀⠻⣼⣿ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡧⠤⠞⠋⠙⣿⡀⠀⠠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢿⣿⣾⡇⠀⠀⢀⣿ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣇⠀⠀⠀⢀⣼⣿⣶⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠙⠛⠙⠛⠃⠀⠈⠙⠿ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣧⣀⣠⣾⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⢠⣄⣁⡴⣦⡇⣦⠶⣶⣶ ⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠙⠛⢛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⠘⣇⢀⡞⠙⡇⢀⣤⢄⣭ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢸⠀⣸⠉⣤⠄⡷⢮⣉⡉⣹ ⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠁⢸⢠⡇⢀⣿⠘⡇⠈⣳⣭⠿ ⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠶⢼⢰⡇⣘⣷⠀⡇⢈⡋⢁⣀ ⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⢸⠀⠁⠸⢶⠂⡏⡟⡿⢸⣿ ⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡍⢩⡅⢸⠓⠚⠛⠛⠛⡛⠛⡓⣚⠛

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

⠀⠀⠀⢰⣦⡉⠉⣄⠑⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡘⢿⡄⣼⣓⣞⣅⣉⣐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⢆⡚⣡⣿⣿⣿⣿⣿⡉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣣⣼⣧⠫⣳⣿⣿⠿⠿⢿⣇⠀⠀⠠⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀ ⠀⠀⠀⠀⡸⣿⣿⠿⢋⡀⠁⠛⣼⣶⣶⣿⣮⠀⢀⣶⣿⡦⡀⠀⠀⠀⠘⡀⠀⠀ ⠀⠀⠀⠀⠁⢹⣿⣴⡻⠃⠀⠀⢈⢼⣿⠿⢿⡀⢸⠟⠛⢣⣼⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣻⡿⣦⡤⠀⠐⠧⡠⢋⠀⠀⡁⠸⣀⣠⣀⣿⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⢀⢤⡎⠀⢀⠃⠀⠹⠿⠟⢸⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠙⢦⠎⠁⠠⣀⣴⣏⣀⠜⠀⠀⡌⠀⠐⠜⠀⠀⢈⣞⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠀⠘⡄⠀⣠⣿⣿⣿⠁⠀⠀⡐⠀⠀⠀⠀⠀⠀⢸⠛⡇⠀⠀⠀⠀⠀ ⠀⠆⠀⠀⢁⠀⢸⠙⠿⣿⡟⠛⠒⡈⠝⠁⠉⠀⠀⠀⠀⠤⠦⠔⠠⠤⠄⠀⠀⠀ ⠀⠈⠀⠀⠀⠄⠘⠤⠔⠺⣤⠲⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠈⡆⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠐⠢⠄⣀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⠀⠀⡀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠆⠈⣑⠦⠖⠊⠉⠓⠤⣀⠀⠀⣰⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⣿ ⣷⣤⡀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⣤⡤⣆⡦⣢⢤⢤⡠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣞⡽⣺⣝⣞⣞⡵⡯⣫⢯⡳⣝⣮⡳⣓⢦⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴⡯⣞⣗⡵⡯⣳⢵⡳⡵⣫⢯⡳⡯⡞⢗⠗⠏⢏⠏⠗⣏⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⢯⢯⢟⡞⢞⠾⠽⠳⡫⣫⢫⢃⡇⡅⠂⠌⠄⡂⢅⡢⢎⡋⣂⠣⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠯⣌⢻⡵⡯⣷⡐⠨⠠⡵⠭⠔⠔⠂⠊⠚⢪⢈⣐⡠⡒⢁⠁⣀⠀⠈⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢵⢡⠃⡒⠯⡯⡷⡯⠊⠮⠀⠂⠠⡆⠀⠀⠀⠀⢗⠐⠨⣊⠠⡀⡈⡀⠀⠀⢀⠫⠊⡐⠔⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡑⡅⡑⡁⡂⢂⠌⠨⠈⠌⡸⡈⠄⠀⠀⠀⠀⠀⢀⠇⠌⢂⠩⠈⢄⠡⠉⠒⢤⠪⠨⢐⢀⠂⠔⢀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠎⡌⡂⠔⡀⡂⡂⠌⡨⠨⢐⠠⠱⣐⢀⢀⠀⡀⡔⠜⠈⠄⠅⠂⠅⡂⠌⠨⢈⢸⠨⢐⠐⡀⡊⠨⢀⠂⡁⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⡑⢅⢐⢐⠠⠂⠄⠅⡐⡈⠄⢂⠡⢐⢈⠡⢉⠨⠐⡈⠌⡨⢬⡨⡐⡠⡁⡅⣆⠏⠌⡐⡈⠄⠂⠅⡂⢂⠂⠄⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣺⣪⢯⢯⢞⡮⣗⢯⡫⡯⣳⢝⣗⡽⡵⣻⡪⣗⢯⡫⣗⡵⡯⣳⢽⢝⡮⣗⢯⡳⣝⢞⡽⣽⡺⣺⢝⡮⡯⣳⡳⣝⡽⣪⢯⣺⢵⡻⣪⢯⣳⢽⡺⣕⡯⡪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣳⡳⡽⡽⡽⣕⡯⣞⡵⡯⣫⢾⢝⣞⢮⣻⡪⣯⣺⡳⡽⣕⢯⢞⣗⢽⡳⣝⡮⣗⢯⢇⢿⣝⣞⣞⡵⣻⡪⣟⢞⡮⣳⢽⢵⣫⢞⣵⡫⣗⢯⡺⣕⡯⣞⣝⢎⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣗⢯⢯⢯⢞⣵⡫⣞⢮⣻⡪⡯⣳⡳⣝⡮⣞⡵⣣⢯⣫⢞⡽⣕⢯⡳⣝⣞⢮⣳⢽⢕⣟⣞⣞⢮⢞⡵⣻⡪⣗⢯⣳⢽⢕⣗⢯⡺⡮⣳⡫⡯⣞⢮⣳⡳⡣⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡽⡽⡽⣝⡽⣪⢾⣹⢵⡳⡽⣝⣞⢞⡵⣫⣞⢞⡽⣕⢯⡳⡽⣺⢝⣞⡵⣳⡫⣞⡵⣣⣳⣳⣳⡫⡯⣞⢗⡽⡵⣫⣞⢽⢝⡮⡯⣞⡽⣕⢯⢯⡺⣝⢮⣞⣝⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢯⣻⡺⡽⡮⡯⣺⡳⣳⢝⣞⢽⣪⢞⡽⣺⢕⣗⢯⢞⡵⣏⢯⣫⢞⡽⣺⡪⡷⡽⣕⢯⢎⣞⣞⢮⣏⢯⡺⣝⡮⡯⣳⢵⡫⣗⡽⡮⣳⢝⡮⡯⣳⢽⡺⡵⣳⢵⢱⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢽⢮⢯⢯⢯⢞⣗⢽⡺⣝⢮⢗⡽⡵⣻⣪⢯⢞⡽⣝⢮⢗⡯⣞⢽⡺⣕⢯⣫⢞⡵⡯⡇⡷⣝⣗⣗⢽⣝⢞⡮⣻⣪⢗⡯⣳⢝⣞⢽⢵⡫⣯⡺⣵⡫⡯⣞⢽⢜⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢯⢯⢯⡳⣯⡳⣳⢽⡺⡵⣫⢯⢞⡽⣺⡪⡯⣳⣝⢮⢯⡳⡽⣺⢵⡫⣗⢯⢞⡽⣪⢯⢇⢯⣗⣗⣗⢽⣪⢯⢞⣗⢵⣻⡪⣗⢯⣞⢽⢵⣫⣾⣮⣷⣽⡽⡮⡯⣇⢯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⢝⣗⣟⣞⢮⢗⡯⣞⢽⢵⡫⡯⣞⡵⣫⢯⡺⡮⣫⢗⡽⣝⡮⣗⢯⣞⡽⣵⡫⣗⢯⣫⡪⣗⢷⢵⡻⣪⢯⡳⡽⣕⢷⢽⢵⣻⣾⣻⢿⡽⣾⣺⣞⡾⡽⣯⢿⢽⣝⣮⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣝⣞⣞⢮⢯⡳⣝⡮⡯⣳⢽⢝⣞⢞⡵⡯⣺⢽⡵⣯⢿⣺⡯⣟⣯⢯⣟⣷⣻⢷⣻⢮⣎⣯⢯⣗⡽⡵⣫⢾⢝⣾⡽⣟⡿⣽⢾⢽⡽⣽⣳⣗⣯⢿⢽⢯⣻⡽⣞⣾⣺⣝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣵⣳⡳⣯⡳⡽⣕⢯⣫⢞⡽⡵⣳⣫⢯⣾⢯⡿⡽⡯⣟⣗⡿⣽⢞⣯⢷⣳⡯⣯⡯⣟⡾⣝⣗⡷⡽⡽⣽⡽⣯⡷⣟⣯⢿⢽⡽⡯⣯⢷⣗⣟⡾⣽⣻⣽⣳⢿⢽⣞⣗⣯⣗⢯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣳⢵⣻⣺⡺⣽⡺⣝⣮⣻⣺⣽⣵⣟⣿⣺⢯⡯⣿⢽⣻⣺⣽⢽⢯⡯⡿⣵⢟⣷⣻⡽⣽⣳⢷⣝⢿⣟⡷⣟⣷⣟⣟⡾⡯⡿⡽⡯⡿⡽⣞⣷⣻⡽⣞⡾⣽⢽⣻⣺⣳⣗⣯⢷⣕⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣟⡷⡷⣿⢾⡾⡷⣷⣻⣞⣷⣳⣟⢾⣺⢯⡯⣯⡯⣷⣻⣞⣯⢿⢽⢯⡯⣟⣞⣗⡿⣽⢞⣟⣾⣳⢝⣿⣽⢾⣺⣳⢿⢽⣻⡽⣯⣟⣯⣟⣾⣺⡽⡯⣟⡽⣯⢷⣻⣞⣗⣯⣟⡮⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣽⣻⡯⣿⢽⡯⣿⡽⣞⣷⣻⣺⣞⣯⢯⡯⣟⣗⣟⣷⣳⣗⣯⢿⡽⡯⡿⣽⢽⣞⣯⢯⡿⡽⣞⣾⣝⢾⡽⡯⣟⡾⡯⣟⣷⣻⣳⣗⡷⣗⣷⣻⣞⡿⡽⡯⣯⣟⣾⣺⣳⣗⡷⡯⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣟⡾⣯⢿⡽⣯⡷⣟⣟⣞⣗⣟⣾⣺⢯⢿⡽⣞⣷⣳⣟⡾⣽⢽⣞⡿⡽⡯⣟⣾⣺⢯⢿⢽⣻⣺⢮⣫⡿⣯⢯⡯⣿⢽⣞⣾⡳⣗⡿⣽⣞⣾⣺⡽⣯⣟⣗⣯⣞⣷⣻⣺⡽⡝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠽⢯⣿⡽⣷⣻⡯⡷⣯⢷⣻⣺⡽⣽⢯⡯⣷⣻⣺⢾⢽⡽⣽⢾⡽⣯⢿⡽⡾⣝⣯⣟⣯⢷⣻⣳⡝⠙⠫⠫⠻⠽⠟⠾⠾⠯⠿⠽⠷⠻⠾⠳⠿⠳⠳⠫⠓⠛⠊⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠗⢟⢯⢯⣯⡷⣯⢯⣯⢯⣯⢷⣻⣞⣯⢿⡽⣽⡽⣾⢽⣽⢽⢯⣟⣾⡺⡷⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠙⠙⠙⠚⠯⠷⠷⠻⠽⠯⠷⠻⠽⠻⠚⠝⠋⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠙⢻⣶⣶⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠂⢄⠜⠛⠻⡏⠀⠈⢢⠀⠀⠀⠀⠀⠀⢀⡾⢸⢰⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡠⠎⠢⡀⠀⠑⢤⣾⣧⠀⠀⠀⠀⢀⣾⣃⣸⡿⢀⡀⠀⢠⣄⣀⡀⠀⠀⠀ ⣀⠎⠀⠀⡇⠈⣶⢄⠀⢻⣿⢧⠀⠀⢠⣿⣿⣽⣋⣿⣓⣷⠀⡼⢿⠔⠦⠄⠀⠀ ⡇⠀⠀⣠⡑⢤⡿⠈⡄⠘⡄⠀⡀⠀⢘⠿⠿⣿⣟⡿⢿⣿⠇⠐⠀⠀⠀⠀⠀⠀ ⠓⠒⠊⠁⠀⠙⠛⡲⠅⠂⠣⡠⠓⠀⠈⠛⠒⣇⠉⢀⠈⣡⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠹⡉⢙⣜⢌⡢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠄⣄⢂⠀⠀⠀⠀⠀⠱⢰⡗⣉⠦⡄⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⢠⠀⠀⠀⠀⠀⢚⢺⣥⠋⠂⠀⠀⠀⠀⠀⢸⠀⠈⠒⠓⠂⠠⠄⠀⠀⡀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢡⡐⡈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡠⠤⠀⠰⠁ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠈⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡰⠁⢀⢋⡔⠁⠀ ⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢐⠀⠃⠀⠀⠀⠀⠀⢠⣴⣿⣷⣤⠅⢠⠃⡛⠀⠀⠀ ⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⡸⠐⠚⡄⠀⠀⠀⠀⠆⠀⠙⠿⡟⠀⠈⢲⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠀⠀⠀⢰⠁⠀⠀⢡⠀⠀⠀⢸⠀⠀⠀⠔⡁⠉⠉⠁⣀⠀⠀⠀

remember to downvote any posts that aren't symbols, social media exists for a reason, this website is for symbols not drama! ( ˶ˆᗜˆ˵ ) ༘ ⋆｡˚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡠⡀⠹⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠄⡀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠆⡇⠰⠀⠈⠻⠦⠶⠶⠶⠶⠾⠶⠞⠋⠀⡌⠀⡇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⢻⣅⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣂⠀⠀⠀⠀⠀⠀⡿⣝⣺⣯⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀⠀⠀⠘⠫⣷⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠄⠀⠀⠀⠀⠀⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠠⠼⡦⠄⠀⠀⠋⢿⠉⠀ ⠀⣨⣧⠄⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠂⠠⠀⢠⠟⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠹⣧⣄⠀⠀⡒⠉⠉⠈⡃⠀⢰⣆⢠⣶⣄⣼⠀⠐⠠⠀⠒⢁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣄⣿⡆⠀⠀⠀⠀⠀⠘⢿⣇⠀⠈⠀⠂⠐⠁⠀⠀⠛⠛⠁⠈⠀⠀⣀⣤⡴⣷⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢞⣷⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⠴⢴⡤⢦⠤⡤⠤⠤⠶⠶⠚⠛⠉⠀⠀⢨⣿⣦⣀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠴⢖⡶⡿⡈⡹⡑⢢⠌⣪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣦⣷⠱⢌⡒⡌⡝⣜⠣⣑⠅⠎⠇⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠛⠻⢷⣤⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠉⣿⡐⠢⡔⡘⡡⢇⡡⢅⢡⡙⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣆⡀⠀⢻⣧⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⡿⠙⢧⣆⠵⡁⠦⠇⡪⢠⣜⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠹⢾⣀⡀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡾⣅⡎⢆⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠉⠛⠛⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠻⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢲⣶⣶⣤⣼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢾⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⣤⠶⠓⠋⠉⠁⠀⢈⣿⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠨⢿⣀⣀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⠇⠀⢸⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⣸⠀⠀⢸⡇⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⣶⣿⣿⣿⣿⣿⣶⣬⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠽⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⣿⡷⡇⠀⡷⣿⡿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡉⠛⣿⠿⠧⣿⠿⢷⣠⠿⠿⣧⠽⢿⣿⠋⢉⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠿⣶⡟⢲⣤⣬⣷⠀⠁⢀⣮⣤⣤⠒⣿⣶⠿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡀⠈⣿⡦⠽⠿⠵⠇⠀⠸⠬⠿⠯⢴⡿⠁⢀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠶⣿⣧⢀⣀⡀⠠⠤⠀⢀⣀⣠⣾⣷⠶⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⣹⡦⣼⡟⠛⢻⣧⢴⣉⠙⡆⠀⠀⢀⣠⣤⣤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡽⠀⠀⠀⠙⡶⠁⠀⠀⠈⣏⠙⢶⣿⠤⠛⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠀⢀⡀⢸⠁⠀⡀⠀⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡎⠀⠀⠀⠀⢈⣆⠀⠈⠁⠀⠀⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢠⠀⠀⢰⠉⠀⠑⠀⠀⢀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⠤⠤⠤⠤⠀⢸⣀⣸⣀⡀⢸⠀⠀⢸⡀⠀⣈⣀⣰⠄⠤⠤⠤⠤⠠⢤⡀⠀ ⡰⠃⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⣉⠀⠀⠈⠈⠙⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠘⡆

⠀⠀⢀⣤⠤⢶⣶⣶⣶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⠈⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠲⢤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⢸⠀⠀⣼⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠦⣀⡤⠾⠛⠛⠛⠻⠿⡟⠁⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⢸⡀⣰⡿⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠳⣄⠤⢌⣙⠦⣄⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⢸⣧⣿⠇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠳⣄⣀⡬⢗⡪⠓⢦⡀⠀⠀⠀⠀⠙⢦⣠⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⣀⣼⣿⣿⣄⡀⠀⣿⠀⠀⠀⢰⣤⣤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣰⠟⠁⠀⠀⠹⡄⠀⠙⢦⣀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡶⣿⣿⣿⣿⣭⣥⣍⠳⣿⠀⠀⠀⠠⣿⣿⡟⠾⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣽⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠟⣗⢢⡀⠀⠀⠘⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣯⣬⣿⡋⠉⣻⣶⠓⠙⠒⣿⡄⠀⠀⣶⣞⣭⣿⣆⠉⣷⣦⣤⡄⠀⠀⠀⠀⠀ ⣶⡾⠃⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⢸⢸⡖⣷⠀⠀⠀⠘⡿⠿⠛⠉⢣⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⠀⠛⠋⠉⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⣼⠉⠳⣄⢸⢸⣸⠀⢰⢧⠀⠀⠀⢧⠀⠀⠀⠸⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⢀⣀⡼⠛⠦⣄⣈⠳⣼⣏⠀⠀⢸⡆⠀⠀⠘⡆⠀⠀⠀⣧⠀⠀⠀⠀⢳⣄⡈⠉⠙⠛⠿⢿⣷⣶⠾⠏⠉⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠷⠤⠤⠤⠟⠋⠀⠀⠀⠀⠙⠿⠶⠿⠦⠤⢞⣀⡤⠤⣀⣿⠀⠀⢀⣹⠶⠒⠛⠒⠘⠻⠿⣿⣿⣶⣦⠀⠈⠙⠀⠀⠀⠛⠛⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⠀⠀⠀⠀⠈⠙⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⣐⣽⣆⡀⠀⠀⣠⠄⠀⣠⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠛⠓⠚⢷⡀⠺⣇⠈⠾⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢠⣿⣖⡎⠳⡄⣼⠙⢦⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⣿⣀⡉⠙⢻⡀⠀⠈⠉⠙⠒⠚⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣿⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢀⣿⣄⣉⣉⣽⠛⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣧⡀⡟⢿⢹⡴⢿⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⠀⠧⠤⠼⣏⣀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡉⠙⣿⣦⣾⠇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠲⠶⠤⣀⣀⣀⣀⠀⢀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠈⠛⣋⣀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡔⠀⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡖⠲⡄⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠷⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⡃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢳⣠⠇⠀⢀⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⡼⠋⣀⣴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⣿⣷⡄⠀⠀⠀⡞⠁⠀⠀⢀⡞⢁⡴⡿⠃⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣾⣿⣿⣿⣿⣧⣀⣼⣁⢠⠄⢀⡾⠤⠟⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠭⣿⣿⣿⣿⣿⣿⣿⡆⠉⠉⠑⢾⡀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⡤⠤⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠀⠓⠣⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠙⠻⣋⡀⠀⣀⡀⠉⠀⢸⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣠⠾⠻⠈⠉⠉⠹⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠂⠐⠈⠉⠀⣞⠁⢠⠖⠀⠉⠉⠀⢀⠀⣀⣀⠤⠔⠂⠀⠀⠀⢀⠀

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣷⣶⠖⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⢛⣙⢓⠒⡖⣛⣿⡏⠀⠀⣸⡿⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⢿⣿⡿⢿⣿⣽⣿⡟⠉⠀⠈⢉⠀⠈⠁⣿⡿⠀⠀⢠⣿⠃⠀⢈⣦⠀⠀⠀⠀⠀⠀⠀⡀⡾⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣶⣶⣿⣿⣷⣦⣿⡷⡄⠀⠀⠄⡔⠀⠀⣼⡿⠁⠀⢀⣾⠏⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠈⠀⢧⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠿⣭⣝⣻⣿⡗⡇⠀⠊⣿⣷⣶⣦⣿⣷⣤⣀⣼⡟⠀⠀⢰⣿⣿⠃⠀⢲⡚⠋⠉⢹⡀⠘⡿⢿⡀⠠⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢻⣿⡀⠸⣶⣶⣾⢹⣿⡿⠻⣿⣿⣿⣿⣄⠀⢠⡏⠀⢉⠢⣤⣤⡉⡆⠀⠈⡇⠀⡵⠋⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⢹⣟⠻⢿⣟⡥⠒⡾⢿⣿⣿⣟⢷⣾⡇⠀⢸⠀⣿⡹⠉⢣⠀⠀⢸⠚⠀⢠⠄⠀⠀⠀⠀⢸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣺⢿⣿⣧⣌⣹⡷⠀⢉⠀⣼⣥⣰⠋⢻⣿⣏⣻⡇⠀⠈⠀⣷⡇⠀⠘⡄⠀⠈⣆⠔⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⡄⠹⣷⣿⡿⠧⡀⠈⠺⢿⠟⠁⠀⠀⠹⣿⡿⠃⠀⣆⣸⣙⡷⠣⢤⣇⠀⢠⠎⠀⠀⠀⠀⠀⡠⠚⠻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⣽⠏⠀⠀⠈⢑⣢⣤⣄⣤⠶⠶⠚⢹⠃⣀⢀⡇⠉⠉⠁⠀⠀⠘⣤⠃⠀⠀⠀⠀⡠⢞⣹⡀⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⡤⢒⠞⠛⠐⠒⢌⠉⠉⢐⡦⣄⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣸⡀⠀⠈⠲⡏⠀⠀⠉⠑⠢⢍⡀⠉⢆ ⠀⠀⠀⠀⠀⠀⠀⣼⢿⠁⠰⡅⠀⠀⠀⢀⠜⠀⠀⠘⠶⠋⠱⡄⡿⢿⣁⠤⠒⠊⠉⠀⠀⠀⠘⢄⠀⣀⣼⡆⠀⠀⠀⠀⠀⠙⣶⠏ ⠀⠀⠀⠀⠀⠀⢸⠇⠞⣧⠤⠼⡇⠂⠈⠁⠀⠀⠀⠀⠀⠀⡴⣋⠥⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣹⣿⡖⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⢸⣟⡀⠀⠀⠄⣧⣤⣶⡆⠀⠀⠀⠀⠀⠘⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣏⠁⠸⡄⠀⠀⠀⣠⠞⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠉⠉⠉⠓⠢⢴⠚⠒⠚⠛⠛⠒⠲⢶⠦⠤⠤⠤⠀⠄⠠⠤⠤⠤⢴⠉⠀⢀⡷⠒⠒⠋⠁⠀⠀

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

⠀⠀⠀⠀⠀⢠⣤⡀⠉⠉⠉⢳⡀⠙⢦⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡟⣿⣷⡄⠀⠀⢳⣄⠀⠙⣟⡙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⠈⢿⣿⣦⢀⡴⣟⢒⣖⣡⣀⣀⣀⡉⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⣠⠋⢹⣿⠋⣸⣿⣿⣿⣿⣿⣿⣿⡿⠾⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠟⢢⡆⠙⣾⣿⡿⣿⣿⠿⢿⣿⣿⣷⣄⣀⣀⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠓⣀⣹⣿⣇⠱⡽⠳⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠏⠀⠰⠛⢿⣿⠇⣿⣀⣀⣀⣸⣿⠉⡆⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⣿⡿⠟⠋⣀⣀⠀⠀⠉⠁⣴⣿⣿⣿⣿⣿⣿⣦⡇⠀⠀⣴⣿⣿⣿⣿⠳⡄⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠚⠀⠘⣿⣿⣧⣀⡾⢿⠟⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⠿⠿⢿⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡷⠉⠀⠀⠀⠀⠀⣠⠞⠻⣿⡼⠋⠉⠙⢢⠀⠰⡏⠁⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢿⣶⣤⡤⠐⠒⠚⠷⣄⡠⠞⠁⠀⠀⠀⢀⠂⠀⢇⠀⣀⣀⣀⢸⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⡟⠉⠀⠀⠀⠀⠀⠈⠁⢀⡼⠀⠀⠀⣸⠀⠀⠘⣿⣿⣿⣿⡟⢹⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣈⠩⡇⠀⠀⠀⠀⢀⣀⡴⣚⣿⠃⠀⠀⢠⠇⠀⠀⠀⠘⠛⠛⠟⠀⢸⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⡀⠈⠻⣶⣄⡔⠋⠁⠀⢇⠀⠀⣠⣾⠉⠀⢀⣼⠃⠀⠀⠀⡜⠀⠀⠀⢆⠐⡄⠀⠀⠀⠈⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⡀⠀⠀⣟⠁⠀⠀⠀⠈⣳⣾⣿⣿⣿⠶⠋⠁⠀⠀⠀⣸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠸⣆⠀⠀⢀⣴⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡄⠀⠀⠀⠘⡆⠀⠀⠸⡷⠾⣿⣿⣿⣿⣿⡿⠷⠤⠤⠶⠒⣻⠟⠑⠒⠒⠒⠒⠒⠢⠤⣀⠀⠀⡞⢀⣠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⠀⠀⠀⠀⠸⡀⠀⠀⡇⠀⠈⠛⠛⣿⠏⠀⠀⣀⡤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢷⣀⡠⠔⠛⢧⣀⡶⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠐⠛⠒⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠑⠒⠦⣄⢀⣤⡤⠶⠛⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⡴⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⣼⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿ ⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣶⣤⠤⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠉⠉⠉⠍⢻⣆⠀⠙⢦⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠈⠁⠀⠁⠈⠀⠁⠉⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠸⣿⣦⡀⠀⠀⠀⠹⣦⡀⠀⠙⢿⡮⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣆⠹⣿⣽⣦⡀⠀⠀⠹⣷⣀⣀⣠⠷⠒⠒⠛⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⢿⣿⣿⣆⣴⣟⣯⣉⣽⣥⣴⣦⣤⣤⣤⣄⣀⠉⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡼⠋⢨⣿⡟⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠷⣤⡤⠘⢇⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣸⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣧⡀⠘⣿⣽⣷⠹⡜⢿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣴⣶⣾⣿⣿⡄⠈⡞⣈⣽⡿⣟⡏⢻⡿⠛⠛⠛⠛⣿⣿⡿⡆⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠿⠋⠹⣿⣿⠇⢸⣇⣄⣤⣤⣤⣿⣿⡁⢷⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣿⣿⣿⣿⣻⠟⠋⠀⠀⠀⠀⠘⠋⠉⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⠀⠀⠀⢠⣾⣿⣿⣿⣿⣝⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⣿⣿⣿⣧⡀⠀⣴⣏⣿⡏⠀⠀⠀⠀⠈⠱⠿⠛⢹⣯⣿⣿⣿⣿⣿⡿⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣾⣅⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡜⣿⡿⠿⢿⣇⠀⠀⠀⣿⡿⠛⠉⠉⠉⢻⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠀⠛⢿⡿⠃⠀⠀⠀⠈⣿⠀⠀⣏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⢿⠿⢽⣿⣶⣶⠶⠖⠒⠚⠛⠷⢦⣀⡴⠊⠀⣀⠀⠀⠀⠀⣾⠀⠀⢸⡄⠀⣀⣀⣀⣀⢸⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢻⣷⣶⣼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢠⠇⠀⠀⠀⠀⡏⠐⠀⠀⢵⣾⣿⣿⣿⣿⡿⢹⡇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⡟⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠈⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠀⢀⡤⠖⠚⣿⠀⠀⠀⠀⢀⣠⡤⠖⠛⠡⢶⡿⠁⠀⠀⠀⢀⡏⠀⠀⠀⡀⠀⢀⠀⠀⠉⠁⠀⠀⣷⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠅⠀⠀⠀⠀⠀⢦⠀⠀⠸⠿⢿⣦⡞⠁⠀⠀⠀⢻⡄⠀⢀⣴⣿⣇⠀⠀⢀⣰⡾⠁⠀⠀⠀⢀⡼⠁⠀⠀⠀⠸⣆⠈⢧⠀⠀⠀⠀⠀⢸⡟⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⢙⣶⣿⣿⣿⣿⣿⡶⠟⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣾⣗⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢻⡤⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢹⣦⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣀⣀⣤⢴⡿⠤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⠇⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⢿⠋⠉⢻⣿⣿⣿⣿⣿⡟⠛⠛⠛⠋⠉⢉⣡⡴⠏⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠑⠲⢄⣀⣀⣿⣤⡤⠾⠄⢤⢄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣼⡄⠀⠀⠉⠛⢛⣿⠗⠀⠀⢀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠘⣇⠀⠀⢹⣆⣀⣀⡤⠞⠻⣇⠀⣰⠾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠉⠁⠀⠀⠀⠈⠻⣯⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠈⠉⠙⠲⣦⣀⣨⣶⠶⠞⠋⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⣠⡶⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣦⣄⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣶⣿⣿⣿⣿⣿⣿⣿ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⡶⠶⠄⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢹⡇⠀⠀⢸⡏⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢸⡇⠀⠀⢸⡇⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⣿⣧⣤⣤⣼⣿⣀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠀⠈⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⣻⠀⠀⣟⣻⣿⡟⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠉⢹⣿⡿⠿⢼⣿⠿⠿⣆⣸⠿⠿⣿⡧⠿⢿⣿⡏⠉⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣶⣾⡿⢤⣤⣀⣉⣧⠀⠈⠁⠀⣼⣋⣀⣤⡤⢽⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠉⢻⣧⣀⠻⣿⣿⢛⡇⠀⠀⢸⡛⣿⣿⠟⢀⣼⡿⠉⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⣿⡏⠉⠙⠓⠛⠛⠀⠀⠉⠙⠛⠋⠉⢹⣿⠁⢀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⡤⣄⣀⣀⡀⠶⠶⠄⣀⣀⣠⣤⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠉⣳⣤⣼⡿⠛⠛⢻⣧⣤⣞⠙⠛⢧⠀⠀⠀⠀⠀⣀⣠⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⢶⠋⠉⠀⠉⠙⢦⡴⠛⠉⠀⠈⠹⡖⠺⢦⣠⣶⡋⣙⡿⠿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡟⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣿⠀⠈⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠇⠀⠀⣤⡄⠀⡇⠀⠀⢠⡀⠀⠀⠸⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡇⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠀⠀⠀⠀⢈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⢀⠀⠀⠀⣠⠞⠁⠉⠳⡄⠀⠀⠀⠀⠊⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡇⠀⠀⢸⠀⠀⠀⢰⠇⠀⠀⢸⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠴⠋⠉⠉⠓⠒⠒⠒⠒⠺⠦⠴⠧⢤⣤⣸⡆⠀⠀⢸⢤⣀⣤⠼⠦⠴⠛⠒⠒⠚⠉⠉⠉⠉⠉⠳⣄⠀ ⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠁⣀⡀⠀⠀⠈⠀⠀⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇

⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢠⣷ ⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⢠⣾⠋ ⠠⠖⢩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⠻⠿⡾⢛⣛⣀ ⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⣟⣛⡃⠇⢳⣶⣾ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢸⡯⢩⠍⡟⢻⣩⠉ ⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢸⣗⡀⠀⡇⠸⠿⣤ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⣤⣯⣿⠄⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠉⠉⠇⠀⡄⣦ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠔⣋⣿⡿⠛⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢣⣺⣹⡇⠀⢧⣿ ⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠊⠉⠹⣆⢐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣿⡿⡇⠀⣠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣆⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣇⠀⢀⣀⡅⣀⣀⣉ ⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠛⠿⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡗⡏⢩⠟⡇⢁⣈⣩ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⡇⡸⢨⡄⡗⢮⢍⣹ ⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡗⡇⢴⠃⡇⢨⡷⠛ ⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠈⠉⡇⠃⣮⡅⡧⡶⣤⣶ ⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡟⢒⠂⡗⠒⠒⠓⠓⠛⠒⠛

⠀⢀⡴⣎⣁⡠⠿⠒⠒⢶⡟⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠐⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠋⠀⡰⠋⠀⠀⠀⢠⠞⠳⣶⠃⠀⠀⠀⣀⢠⡤⢤⡤⣀⣠⡴⠋⠙⣆⠀⠀⠀⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠒⢺⠁⠀⠀⠀⣰⣁⢀⠔⢁⡠⠔⠺⢯⡴⢊⡔⠁⣠⠞⠉⢱⣀⣀⣘⣄⠀⠀⢀⡔⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⢸⣄⠀⠀⠀⣇⣸⣏⡔⠉⠀⠀⠀⠀⣇⠎⢀⡜⠁⣠⠲⣏⢫⡉⠉⠉⠉⠉⢹⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⠉⠉⠢⡀⠀⢏⠉⡍⠀⠀⠀⠀⠀⠀⠿⠧⠿⣧⠞⠈⠳⡈⠢⣙⣄⠀⠀⠀⠈⡆⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⣠⠬⣶⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠙⡄⠑⠦⣀⠀⢣⠀⠀⠀⢀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⠋⠉⠉⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠱⡀⠀⠈⠑⠾⣆⣀⣠⠎⠀⠹⡀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀ ⡀⠷⣄⣀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢳⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⢻⠟⠷⣄⡭⠞⠛⢢⡀⠀⠀⠀ ⢧⡀⠉⠀⣴⠆⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⡆⠀⠀⠀⢰⠇⠀⠀⠀⢀⡞⠀⠸⣅⠀⣠⣴⣾⡷⡄⠀⠀ ⡆⠈⠀⢸⣷⠀⠀⠀⠀⠀⢤⠀⠙⡄⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⢸⠒⠒⣲⠞⠋⠉⠑⢦⣌⢻⡟⠉⠀⢀⣸⡀⠀ ⢱⡀⢆⠈⠁⠀⠀⠀⠀⠀⠀⠳⢄⡘⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⣷⣾⣅⠀⣀⢴⣞⣿⣿⣿⣿⣤⡖⢋⣽⣧⠀ ⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠀⠀⠀⠀⢸⠉⠉⠈⠳⢶⣿⣿⣿⣿⡇⠀⠁⠀⣼⣿⠀ ⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣼⣷⣄⠀⠀⢀⣨⡽⠟⠋⣿⠀⠀⠀⡟⢻⡂ ⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⡃⠀⠀⣠⣼⣿⣽⣿⣆⣰⣿⠛⠶⠶⠿⢻⡀⠀⣸⠃⠈⠀ ⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⣠⠞⠀⣸⠉⠛⠉⠀⠙⢿⣿⣿⣿⡉⢹⣷⡄⠀⠘⢿⣁⣴⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⢀⠎⢣⠄⢀⡤⠖⠚⠳⢄⠀⡏⠀⠀⠀⠀⠀⠚⠻⢤⣉⣉⢙⣿⣧⣤⣴⣿⡿⠛⢿⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡠⠚⠁⠀⠢⣧⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣏⠉⠉⢿⣇⠀⠀⠙⠻⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠤⠬⠭⢉⡘⠃⠀⠠⠤⠤⠤⠀⠀⠤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠀⠀⠀⢹⡿⠁⠀⠈⢳⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠤⢤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠻⣦⡀⣾⠃⠀⠀⠀⠈⣇⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⡀⠀⠀⠈⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⡿⠀⣇⠀⠀⠀⠀⠀⠘⠢⣄⡀⠀⠀⠀⠀⣀⡴⠉⠀⠈⠉⠳⢤⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⣀⣾⠏⠀⠀⠀⣿⠆⠀⠀⠀⣸⡇⠀⠈⠲⣄⣀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠈⠳⣄⡀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣽⠿⢶⣶⣤⣴⡇⠀⠀⣀⣶⣋⣿⡀⠀⠀⠀⠈⠉⠓⠲⢤⣀⠀⠀⠀⠈⠓⢦⣀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠓⠛⠢⠿⠋⢁⡿⠀⠀⠀⣿⠤⠤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⡧⠤⠤⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠖⣾⣿⡁⠀⢀⣼⡏⠳⠦⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠉⢙⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠉⠛⢯⡉⢿⡙⠛⠛⠃⠀⢀⣀⡤⠴⠒⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣹⣧⣄⣀⣴⠋⠙⢷⡄⠤⣤⣄⣀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠈⠈⠙⠛⠒⠲⠖⠋⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣦⣤⣶⣾⣍⡀⠀⠀⠀⢸⠁⠀⠙⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⠉⢿⡆⠀⠈⢿⣄⠀⢀⣼⢋⣀⣀⡀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⣠⣴⡶⠿⠛⠋⠉⠀⠀⠀⠀⠈⠉⠙⠻⢷⣦⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡦⠀⠀⠘⣿⡄⣠⣴⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⣶⣤⣀⠀⠀⠀⠀⠜⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⣽⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢶⣤⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣠⣴⣶⣤⣀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⣶⣤⣀⣀⣀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣼⡿⣅⡄⠉⠻⣷⡀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣼⣿⣧⣀⣴⣾⣷⣿⣿⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿

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༼ つ ◕_◕ ༽つ🍰🍔🍕

⢘⠶⡀⢲⠆⣿⣿⣿⣿⣿⣿⣿⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢀⠂⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠘⢘⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣄⠀⠀⠀ ⢠⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⡆⠀⠀ ⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⣀⣤⣤⣭⣭⣭⣭⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⡿⡿⠡⠿⠎⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠀

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ᶠᶸᶜᵏme𓀐𓂸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠛⠛⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠈⠻⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣿⣟⠛⠻⢿⣷⣦⣠⣤⣾⣿⣿⣧⣀⣤⣤⣾⣿⣿⣿⣿⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣦⡀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢨⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣦⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⡟⢳⡀⠀⠀⠀⠀⠀⠀⠙⣆⠀⣠⣾⣿⣶⣦⣤⠤⠒⠒⠒⠒⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠉⠏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣏⣀⣀⣀⡤⠴⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⠞⠉⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠙⢦⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⢸⣿⣿⣿⣿⣯⣧⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⢧⠀⠀⠀ ⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⣾⡇⠀⠀ ⠀⠀⠀⣸⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⢸⣄⣿⣿⣟⠹⣿⣿⣏⠉⠉⠜⠛⠉⢠⠟⣿⣿⡿⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⡾⠁⢸⣿⣷⡄⠀⠀⠀⣸⣀⣸⠋⠀⣸⣿⣿⣿⣿⠷⠦⣀⡀⠀⠀⠀⠀⠀⢀⣀⡠⠴⢖⣤⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠛⡇⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⡇⠑⠸⠿⠿⠷⠀⠀⠀⠉⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠉⠛⠢⢤⠤⠞⢋⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⠞⠀⠀⣴⠃⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠘⠲⠆⣀⣤⣾⣿⣿⡿⣄⠲⣄⡀⠀⠀⠀⠀⠀⣠⣤⠭⠭⠭⢭⣍⡛⠻⢿⣿⣿⣿⣿⠟⠉⠉⠉⠻⢶⣶⣿⣷⣶⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⣀⡈⠻⣿⣿⣇⠈⣙⡶⠒⠒⠒⠚⠋⠁⠀⣿⣿⣿⡇⠈⠳⢬⣿⠉⢲⣶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⣍⠻⣿⡏⠀⠀⠀⠀⠀⠸⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⣠⠏⠁⠑⠄⣀⡩⣟⡿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⣿⡿⠀⠀⠀⠀⠘⢳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠃⠀⠀⠀⠀⠀⢸⣟⣥⢄⣀⠀⠀⠀⠀⠀ ⠀⢰⠡⠒⠊⢈⡡⠊⠂⠀⡜⡀⡀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⢀⡰⠂⠀⠀⠀⢠⠏⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⢸⠈⢶⡔⡁⡀⡀⡀⣔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢀⣤⡞⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀ ⠀⠀⠓⣏⠑⠢⡀⡤⡕⠋⠓⠂⠄⠠⠠⡀⠀⠀⠀⠀⠳⣄⣰⣄⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⢻⣿⠁⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀ ⠀⠀⠀⡇⠑⠤⠥⠵⠷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⡼⠁⠀⠀⠀⠄⠄⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠋⢀⡼⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠐⠀⡂⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣄⣠⣔⠋⠀⣠⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⣀⠀⠀⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⣰⠏⠀⠀⠈⠉⠛⠛⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡼⠏⢀⣴⣶⣿⣿⣿⣶⣬⡀⠀⣀⡼⢋⣤⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠙⠷⢤⣀⣀⠴⠚⠁⠀⠀⠀ ⠔⠋⠀⢀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢰⠋⠀⠀⢀⣴⣾⣿⣷⣄⠀⠀⣀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣖⣄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠁⠈⠙⠻⣿⡄⠸⡄⢀⣼⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⡇⠓⠛⢖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⢠⣾⣿⣶⡀⢙⣳⣄⢁⣾⣿⣿⣿⣿⣿⡿⠟⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⣇⡀⠀⠀⢇⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢱⡸⠿⠿⠋⠀⢠⠂⠉⠛⣿⣿⣿⣿⣿⠋⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠉⠉⠉⢩⠏⠁⠀⠀⠀⠀⠉⠑⠂⠒⠒⠂⠒⠊⠉⠉⠉⠉⠉⠁⠁⠉⠻⣆⠉⠓⠒⣋⡉⣿⣧⠀⠀⠀⠉⠻⢿⣧⡀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣼⣿⣹⣟⣿⡟⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣾⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠁⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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❤️💕❤️𝕚 𝕝𝕠𝕧𝕖 𝕪𝕠𝕦 🤍❤️💕❤️

⋆༺𓆩☠︎︎𓆪༻⋆ﮩ٨ـﮩﮩ٨ـ♡ﮩ٨ـﮩﮩ٨ـ★ ★ ★ ★ ★☠︎︎༒︎✞︎🕸𖤐𝓕𝓾𝓬𝓴PENİS╰⋃╯ love hope astetic

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

🍑𝓯𝓻𝓮𝓪𝓴𝔂🐉

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🍑🔥( ͜. ㅅ ͜. )

⠀⠀⠀⠀⠀⢠⣤⡀⠉⠉⠉⢳⡀⠙⢦⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡟⣿⣷⡄⠀⠀⢳⣄⠀⠙⣟⡙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⠈⢿⣿⣦⢀⡴⣟⢒⣖⣡⣀⣀⣀⡉⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⣠⠋⢹⣿⠋⣸⣿⣿⣿⣿⣿⣿⣿⡿⠾⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠟⢢⡆⠙⣾⣿⡿⣿⣿⠿⢿⣿⣿⣷⣄⣀⣀⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠓⣀⣹⣿⣇⠱⡽⠳⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠏⠀⠰⠛⢿⣿⠇⣿⣀⣀⣀⣸⣿⠉⡆⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⣿⡿⠟⠋⣀⣀⠀⠀⠉⠁⣴⣿⣿⣿⣿⣿⣿⣦⡇⠀⠀⣴⣿⣿⣿⣿⠳⡄⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠚⠀⠘⣿⣿⣧⣀⡾⢿⠟⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⠿⠿⢿⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡷⠉⠀⠀⠀⠀⠀⣠⠞⠻⣿⡼⠋⠉⠙⢢⠀⠰⡏⠁⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢿⣶⣤⡤⠐⠒⠚⠷⣄⡠⠞⠁⠀⠀⠀⢀⠂⠀⢇⠀⣀⣀⣀⢸⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⡟⠉⠀⠀⠀⠀⠀⠈⠁⢀⡼⠀⠀⠀⣸⠀⠀⠘⣿⣿⣿⣿⡟⢹⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣈⠩⡇⠀⠀⠀⠀⢀⣀⡴⣚⣿⠃⠀⠀⢠⠇⠀⠀⠀⠘⠛⠛⠟⠀⢸⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⡀⠈⠻⣶⣄⡔⠋⠁⠀⢇⠀⠀⣠⣾⠉⠀⢀⣼⠃⠀⠀⠀⡜⠀⠀⠀⢆⠐⡄⠀⠀⠀⠈⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⡀⠀⠀⣟⠁⠀⠀⠀⠈⣳⣾⣿⣿⣿⠶⠋⠁⠀⠀⠀⣸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠸⣆⠀⠀⢀⣴⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡄⠀⠀⠀⠘⡆⠀⠀⠸⡷⠾⣿⣿⣿⣿⣿⡿⠷⠤⠤⠶⠒⣻⠟⠑⠒⠒⠒⠒⠒⠢⠤⣀⠀⠀⡞⢀⣠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⠀⠀⠀⠀⠸⡀⠀⠀⡇⠀⠈⠛⠛⣿⠏⠀⠀⣀⡤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢷⣀⡠⠔⠛⢧⣀⡶⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠐⠛⠒⠦⣄⣀⡀⠀⠀⠀⢠⡀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠑⠒⠦⣄⢙⣦⡤⠶⠛⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⡴⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⣼⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿ ⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣶⣤⠤⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣶⣶⡶⠶⠶⠶⠤⠶⣶⣤⣄⠀⠀⠀ ⠀⠀⠀⡤⠶⡝⠿⣻⣻⣷⣦⡀⠀⠀⠀⡠⢀⣲⣮⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣿⣿⣶⣿⣿⣿⣿⠾⠻⣿⣿⡄⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠙⠛⠿⢿⢦⣔⣷⣿⡿⠟⠋⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢾⣏⡿⣻⣽⣴⣦⣶⡿⢻⣿⡄⣭⢾⣿⣧⢿⢸⣷⠀⠀ ⠐⢢⣴⣤⡴⠿⠿⠷⠶⠾⠾⣿⣾⣿⡟⠛⠛⠛⠛⠻⠿⠿⠶⠶⣦⣤⣍⣓⢤⣘⣦⡀⠀⠀⠀⢸⣿⣋⢐⣀⡙⢿⣻⢿⣿⠷⠛⠟⠞⣿⣿⣿⣟⣾⡇⢻⣇⠀ ⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⢫⡟⠽⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠓⠾⣿⣦⣀⠀⠈⠷⣿⣫⢿⣺⣏⣇⢳⣬⠮⣐⢸⠄⣿⣷⠞⢩⣿⡧⢼⠗⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣴⠸⢐⡑⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⣉⠛⣷⣾⣭⣛⣷⣦⣭⣥⣗⣲⣿⠂⠀⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⣷⠀⠘⢿⣬⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢿⡿⢿⣿⣌⡙⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⡈⣭⡄⠀⠈⣻⡧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣾⣶⣬⣿⣿⡻⣦⢶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣹⣿⣿⣀⣀⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣞⣿⣿⣿⠁⣸⣬⣿⣆⢀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣾⣿⣷⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⣿⣿⣿⣿⣿⣿⣿⢀⣼⡿⠁⣹⣿⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡴⡷⣿⣿⣿⣿⢋⣴⣛⣿⠿⢏⣠⣴⣿⡿⠿⠻⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣚⠉⣾⠣⠰⣗⠋⡧⣿⣿⣿⡿⠿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠈⠛⢿⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⢫⢿⣄⣼⣻⣽⣻⣿⣿⣿⣿⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣯⣹⣿⡿⠟⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡇⠀⠀⠀⠀⠈⠫⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀nah i'm leaving this site⠀⠀⠀ ⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ain't no way yall beefin⠀⠀⠀ ⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀over pixels💀💀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⢭⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢴⣞⣟⣻⣦⣤⣤⣖⣒⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣫⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡏⠀⠀⠘⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⡇⠀⠀⠀⣧⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⠿⢿⡇⠀⠀⠀⡿⠿⠿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⡟⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣦⣤⡇⠀⠀⠀⣧⣤⣴⣿⣿⣿⠀⠹⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⢻⡏⠛⠆⠀ ⢠⡆⠀⢠⣦⠀⠀⣴⣇⡀⠀⠀⠀⢸⣿⣿⣭⣽⣿⣤⣤⡿⠿⠿⠿⠿⢿⡀⠀⣸⠿⠿⠿⠿⠿⣧⣠⣤⣿⣯⣽⣿⣿⡇⠀⠀⠀⢀⣸⡇⠀⣸⡀ ⠟⠁⠀⠘⢫⠀⢀⣿⣿⣿⣶⣤⣀⣸⣿⠟⠁⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⢣⣠⠇⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠈⠻⣿⣇⣀⣤⣶⣿⣿⣧⠈⠻⠇ ⠀⠀⠀⠀⢸⠀⠸⣿⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠁⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⡇⠀⠀⠀ ⠀⠘⠀⠀⠈⠀⠒⣿⡀⠀⠀⠈⠹⣟⣿⡟⠲⠶⣦⣤⣄⣀⡀⠀⠘⡆⠀⠀⠀⠀⠀⢰⠃⢀⣀⣠⣤⣤⣶⡶⠶⢺⣿⣻⡏⠉⠀⠀⠀⣿⣀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠙⣿⣿⣦⣀⠈⠻⣿⣿⣿⠟⢻⡇⠀⠀⠀⠀⢀⣼⡟⠻⢿⣿⡿⠿⠋⢀⣠⣾⣿⠋⠀⠀⠀⠀⢸⡏⣽⠆⠀ ⠀⠁⠀⠈⢃⡀⠀⠛⢻⣄⡀⠀⠀⠀⣿⣿⣷⠈⠉⠓⠒⠺⠦⠴⠞⠻⡆⠀⠀⠀⠸⠟⠙⠒⠒⠒⠒⠚⠉⠉⣸⣿⣿⠀⠀⠀⠀⣀⣾⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⢿⣿⣶⣦⣤⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣤⣤⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠛⠿⣿⣿⣿⣿⣿⡦⢤⣀⡀⠀⠀⠀⠀⣠⣶⣿⣶⣄⠀⠀⠀⠀⠀⣀⣠⠴⣾⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⢨⡿⠙⠛⠃⠀⠀⠿⠿⣟⣒⣲⠟⠉⠉⠁⠈⢳⣖⣛⡿⠿⠇⠀⠠⠿⠛⢻⣥⠟⠁⠀⠀⠀⠀⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⣰⣄⠀⡀⠀⠀⠀⠀⢹⣦⣤⠤⠤⣤⣤⢴⣾⠁⠀⠀⠀⠀⡤⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣻⣿⠶⢷⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣰⣿⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣇⡤⠞⠋⠉⠉⠁⠈⠉⠙⠿⣷⣿⠟⠋⠉⠀⠉⠉⠙⠛⠦⣄⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣶⣶⡶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠹⣿⡍⣭⣭⠿⣿⣿⡿⠀⠀⠀⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣾⣿⡿⠇⠀⠰⠶⠒⠂⣤⡄⢶⣿⣿⠁⠀⠀⢠⣿⡟⠀⠙⢦⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠠⠄⣰⣿⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠿⣿⣿⣛⠿⠿⣾⣿⠿⠏⠀⠀⠀⠀⠀⡄⠀⠀⢀⣾⣿⠃⠀⠀⠀⣾⡿⠁⠀⠀⢰⣷⡀⠄⠀⠀⠀⠀⠀⡢⠄⡂⢸⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣿⣿⣿⣶⣿⣿⢣⠀⠀⠀⠠⡄⡌⠁⠀⢠⣾⣿⠏⠀⠀⠀⣼⣿⠃⠀⠀⢀⣿⣿⣧⠀⡀⠀⡀⠀⡄⠐⠀⠀⠘⣦⣠⣿⠀⠀⠀⠀⠀⣀⠂⠀⠱⡍⠠⡄⠀ ⠈⠙⠻⠿⣿⣟⣛⠳⢿⡟⣿⣸⠀⠀⠠⠉⣿⣷⣴⣦⣨⣿⣿⣤⣀⠀⣰⣿⠃⠀⠀⠀⣾⣿⣿⡟⠀⠀⣶⢒⠛⡗⠒⣲⡄⠀⢹⣿⣿⣆⢀⣀⡐⢐⣩⠳⡄⠀⠡⡀⠁⠀ ⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣏⡉⢠⣄⣀⣀⣛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⡀⠪⠀⣾⠛⠩⡿⣔⡀⠀⠈⠳⡔⡂⡀⠋⡇⠠⠉⣧⡴⠫⠁⠂⢀⢻⠳⣆⠀⡓⢃⢯⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡆⠈⢿⣿⣿⣮⣼⣿⣿⠋⠈⠻⣿⣟⣿⣿⣿⣦⡊⢶⣟⠁⠠⣷⠨⣹⣿⢻⣆⣾⠐⠀⠁⢹⡁⣤⡋⠄⠀⠀⠀⠕⡎⠀⠈⢱⣥⢴⡟⣉⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⠀⢸⣿⣍⠙⠿⣿⡵⠚⠉⡽⠛⢿⣿⣿⣿⡟⣿⣿⣿⠁⠠⣸⠈⢼⡯⡏⠈⠘⡎⠁⠀⠚⡏⡋⠀⣠⠖⠄⠁⠠⡉⡡⡄⣀⡓⣋⣁⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡶⣺⢿⣿⣿⣧⢤⣉⣿⣷⠀⢸⠁⢀⣾⣥⣀⡼⡯⣿⣿⣿⣋⣻⣿⡄⡜⡏⠁⢸⣿⠠⠀⠁⢷⠅⡄⠀⣹⣈⡞⠏⡢⠂⢼⠅⡄⢌⠑⣼⠕⣵⠠⡂⠗ ⠀⠀⠀⠀⠀⠀⠈⠻⠿⡀⠙⣿⣧⣿⣿⣿⣁⠀⠈⠳⣾⣿⣿⢟⡁⡀⠀⠙⣿⣿⣿⢿⠀⡀⡧⢈⡟⣿⣴⢧⣁⣘⡆⢀⠀⣢⠋⠘⡙⠌⢑⡇⢄⠈⣡⣏⣿⡦⣌⠘⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠘⣿⣿⠏⠀⠈⠓⠦⣄⠐⠹⠛⡀⢀⣈⣤⣠⡾⢿⡏⣻⠌⡂⡟⠿⠿⣿⠃⠁⠂⢉⢳⠀⡰⠃⡑⣀⠲⡀⣆⡑⣪⡼⡇⡯⣃⣷⡇⣐⠀⣡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠀⢀⣀⣠⣠⣭⡿⢿⣾⣿⣟⠛⢋⡣⢀⠸⠅⢸⣤⣥⡏⠁⠐⠀⠉⠅⢐⠤⡙⢿⡋⡅⣝⢂⡄⢀⡧⠺⠛⣯⢽⡠⣔⢹⣅⣜⢆⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣠⠖⢮⠽⡛⢉⠉⡉⡙⣮⡢⡁⠒⢋⡟⢮⣵⢥⣀⣸⣿⣿⣷⡁⡠⠀⡀⠊⣰⣐⣸⠼⣆⠑⢄⠉⠙⢿⡋⡠⠉⡁⠈⢉⡖⡪⡄⡙⠈⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠛⠉⡏⡁⡁⠊⠀⠄⢁⣼⣋⠠⠀⢽⣧⣿⠋⢳⡠⡿⡿⣿⢃⣤⣴⠶⠯⣟⡅⡅⡅⠀⡉⣧⡀⡈⢀⣑⣵⣀⢭⢃⢰⢮⡎⠅⡅⡸⣤⡻ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢠⣿⣀⣀⣈⣷⠿⢄⠑⠺⠍⡀⠃⠀⢨⡅⡣⠄⢁⣤⠿⠇⣁⡟⡋⢉⠡⠛⣃⡇⠗⠄⢀⠣⠈⠀⢹⣾⣿⡿⣿⣷⡍⡈⡀⠸⣜⡲⣇⣑⢻⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⠈⢈⡋⠙⡚⢻⡇⠀⢀⣁⡅⠀⠀⡠⠁⡩⠅⠀⣼⢹⠟⠉⡅⠀⠓⠀⠀⡁⡀⢈⡀⡀⠨⠄⠀⠀⠀⢟⢻⣿⡻⠽⢗⠢⡀⠀⠯⠇⠀⡗⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⣌⣀⣀⣈⣸⣷⣿⣿⣿⣀⡀⢂⠁⢆⢃⠀⠀⢈⣻⣄⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠀⣟⠅⠟⠀⢇⠇⠁⢁⣀⣠⠾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉⠉⠻⠲⣞⠋⠉⠉⠉⠉⠉⠉⠛⠒⢶⡒⠒⠒⠒⠒⠂⠐⠂⠐⠒⠲⠶⠶⠆⡋⠀⠀⢀⣸⡗⡚⠈⠉⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠛⠻⣿⣿⣿⡿⠋⠀⣴⣿⣿⠟⠻⠿⠿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠂⠀⣠⣿⣿⡏⠀⠠⠾⣿⣿⣿⣦⣤⠀⠀⣸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠚⠻⣿⣿⣷⣤⣤⣀⣠⣿⣿⠟⠁⠠⠾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣷⣄⠀⠈⠻⣿⣿⣿⣿ ⣿⣿⡿⠃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢈⣿⡟⠀⢠⣿⡿⠋⠉⣿⣿⣏⠀⢻⣧⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣷⣄⠀⠙⢿⣿⣿ ⣿⡿⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⠟⠁⠀⠀⠙⠟⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⢿⣿ ⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣿⣷⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣿ ⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸ ⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸ ⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸ ⣿⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣿ ⣿⣷⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣼⣿ ⣿⣿⣷⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣾⣿⣿ ⣿⣿⣿⣿⣷⣄⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⢀⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿ STOP.

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

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

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