⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠇⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡸⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⣧⢿⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⣞⡿⣞⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣰⣟⢾⣽⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⢤⣶⡻⣞⣿⣺⢯⣽⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣀⣠⣤⣿⣽⣻⢾⣽⣷⣾⣽⣻⣞⣷⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣄⡀⠀⠀⠀⣉⣲⣴⢶⣞⡿⣽⣞⡷⣯⢿⡽⣞⣿⠟⠋⠁⠉⠈⠳⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢶⣾⣿⡽⣯⣟⡾⣽⡷⣯⣟⡽⡾⣽⡯⠁⠀⠀⠀⠀⠀⠀⢮⣭⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢞⣿⣿⢯⡿⣿⣯⣟⣷⣯⢿⣳⣟⡷⣽⣼⣻⣽⠀⠀⠀⠀⠀⠀⠀⢀⣼⡯⡗⠋⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣯⣽⣾⣿⣾⣗⡿⣯⡷⣯⣟⡷⣞⣼⣿⣀⠀⠀⠀⠀⢀⣠⡿⣏⡗⠈⠐⠈⠅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠏⠉⠉⠽⢟⢿⣿⣿⣿⣿⣷⣻⢾⡽⣞⡷⠄⡹⣶⢿⣻⢿⣻⡽⢯⣼⢦⠶⠁⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠇⠀⠀⠀⠀⠀⠁⣽⣿⣿⣿⣷⣯⣿⣽⣛⡦⠀⠀⢩⣿⣹⢯⣷⢻⣟⠺⢣⡖⣘⠤⠓⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡃⠁⠀⠀⠀⢀⣤⣾⣟⢿⣻⣿⣿⣟⡾⣽⡳⠄⠎⢳⣯⢯⣟⡾⢯⣞⣯⣓⠉⢀⠀⠀⡄⢢⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣷⣶⣳⣶⣺⣿⣿⣳⢯⣟⣿⣿⣳⢯⠛⠅⠃⠀⠀⣴⣿⡿⣬⢶⠾⠙⣊⣥⠾⡒⠊⢁⢠⠣⣌⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡽⣾⡽⣯⣟⣿⡿⣯⣿⣿⣾⢿⣿⠳⢏⣈⢠⠀⠀⣰⢿⡿⣽⣉⡶⠌⠋⠉⣀⡀⠁⠀⠀⠀⣘⡐⣂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣳⣟⣳⣟⣾⣽⣿⣿⣿⣿⣿⣦⣜⡻⡽⠆⠧⣴⡟⣯⢟⡳⣭⠲⠄⠐⠀⠀⠀⠈⠁⠉⠑⢊⡕⢃⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⢧⠀⠹⠾⡵⡞⡽⢢⣃⠐⠀⠀⠄⡐⠀⠀⠀⡘⢦⠘⣌⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⡈⠀⡀⠄⡑⠢⣉⠴⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣏⡴⣶⣵⣢⢤⢠⡀⡄⢠⠐⡰⢌⡱⠀⡁⡀⠆⡥⠆⡥⣛⡽⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣻⢷⣯⡽⣞⣷⣻⡼⣡⢋⡔⠣⠜⡐⢐⠠⡓⣤⣙⣲⣽⣻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣽⣞⣷⣻⡴⣣⢜⡱⣊⡕⣊⠠⡙⡰⣭⢷⣯⣿⢿



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