⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠤⠐⠒⠀⠀⠀⠀⠀⠒⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⡜⠅⠀⠀⠀⢀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡔⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢠⢱⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⡅⠀⠀⣶⣆⡔⠠⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠎⠀⠀⠀⢠⢿⡀⣄⠀⠀⠂⠒⡓⢺⠒⠒⠂⠠⠀⠀⢣⠀⠀⠀⠀⠘⡀⢠⣿⠻⢓⠀⠠⣁⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⡞⠀⠀⠀⢀⣆⠿⢚⠅⠀⠀⠀⢀⠃⠸⣄⣀⣀⣀⠀⢠⣈⡆⠀⠀⠀⠀⡏⡸⣡⡼⣞⡀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠔⠻⠀⠀⠀⠊⡝⠀⢸⡡⢚⣂⠀⠀⢸⡰⢊⣷⠀⠀⠀⠙⠃⠐⢸⠀⠀⠀⠀⢰⣁⠘⢏⡇⠈⢄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⡆⠀⠀⠀⠀⡇⠀⠈⠧⣎⡭⢦⢤⡚⢇⠘⠟⠀⠀⠀⠀⠀⠀⠞⡀⠀⠀⠀⢸⠹⠀⠈⠁⠀⠨⡀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢣⠂⠀⣀⠞⡔⢊⢏⠛⣴⣿⣿⣷⢏⠮⣤⡀⣀⢀⢀⣀⠀⠀⠐⡇⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⣇⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠶⠊⡽⡘⠁⠀⠃⠘⡼⢻⣝⢦⢏⠖⠦⠹⠬⠏⠞⠴⠃⠀⠀⢃⠀⠀⠀⠀⡧⠁⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡅⢢⢣⡀⢠⢴⠹⠘⠑⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⢣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢡⠀⢃⡆⠀⠀⠀⠀⠀⢀⣀⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡥⠂⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡴⠈⡃⠀⠀⠀⠀⠸⠛⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠠⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠠⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⡐⢇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢀⠀⡄⠀⣋⣷⠀⠀⠀⠀⠀⠀⠀⠀⡅⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠃⡃⠀⠈⢾⢤⣂⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠠⠀⣰⣿⠛⡄⠀⠀⠀⠀⠀⠀⠀⢸⡈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠳⡀⠀⣎⢧⠌⣍⢓⡶⢦⣥⣴⡆⢀⠠⠀⢄⠂⣼⠐⠀⡔⡰⢋⠡⠞⠣⠄⠀⠀⠀⠀⠀⠀⠈⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠀⠡⡄⠘⣝⠷⡌⣼⠛⡁⣿⡿⡇⢨⠐⡉⢄⢮⠃⠀⡐⡴⠁⡆⠂⠂⠀⠈⠆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣟⢦⡘⣼⢐⢳⢄⡡⠘⣿⣷⢴⣞⠞⣉⠎⢀⡴⣋⣐⣁⣀⣀⣀⣀⣀⣰⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⣯⣳⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣹⢆⡙⡚⣮⣷⣠⣥⣵⣶⣿⣿⡿⣿⣣⣶⣿⢿⣻⣟⣿⣻⣟⡿⣿⣿⣿⣿⣄⠀⠀⠀⠃⢀⣀⣀⢶⡹⣒⠶⣹⢛⡏⢶⣟⣧⠃⠀
⠀⠀⠀⠀⠀⠀⠀⡼⠉⢦⠱⣱⡿⠋⠡⠤⢿⣿⣽⣳⢿⡽⣯⢿⣹⣯⢷⣻⢮⡷⢯⣟⣳⣟⡾⣽⢿⣆⢀⡾⡞⢯⡹⡝⡮⢵⡙⣮⡕⣯⢞⡻⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠓⣿⡇⠀⠀⠌⠤⣿⣳⢯⣟⡷⣯⣧⠾⣽⢯⣻⣽⣻⢟⣾⣳⢯⡿⡽⣯⢿⣯⢳⢭⢳⡱⠝⣸⢣⡽⡖⠛⠊⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡇⠀⠀⢀⣦⣿⣽⣻⢾⣽⣤⡤⣆⡨⠛⣷⢿⣿⣟⣾⣽⣯⢷⣻⡽⣯⢿⣏⣎⠧⣝⠼⣡⢧⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡜⡇⠀⠀⢘⣿⣾⢷⡯⣟⡾⡏⢳⡿⢀⠋⠙⢿⣿⣿⣿⣿⡿⣯⢷⣻⣽⣻⣿⡬⢓⡼⣍⢧⣟⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡱⠃⠀⢀⣸⣿⣽⣞⣷⡻⣷⣇⠈⢣⡞⢀⡦⠊⠻⣛⡙⢿⣷⣻⣞⣯⣟⣯⣿⡓⢼⣡⣛⡼⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠨⠀⠀⢠⠔⣿⣿⣽⣻⣼⣻⢧⣟⣆⠀⠧⡮⢁⠄⠀⢣⣚⡆⠱⣻⣞⡷⣞⡷⣿⢣⠞⣴⢫⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡄⣤⠞⠁⢂⣿⣿⣞⡷⣽⣳⣟⡾⣽⣶⡁⢡⠉⡄⠃⠌⢃⢃⠀⢱⢯⡿⣝⣿⢧⣛⡾⣭⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢛⢥⠀⠌⢰⣿⣿⣯⣟⣷⣻⣾⣽⡗⢋⣿⣆⣒⡈⠜⡈⢢⢸⠀⠈⣯⢿⣽⡞⣯⢞⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠌⣆⢈⡼⣿⣿⣿⣽⣻⢿⣧⣞⣷⣞⡿⣻⢿⡏⢉⠉⢯⡹⠀⠀⣿⣻⢧⣛⡮⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣻⡰⠊⠠⣿⣿⣿⣷⣯⢿⡽⣿⣄⣯⡿⠋⢿⣇⠠⢈⠦⡇⢀⣤⣟⡧⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⠻⠿⠯⠟⠷⣻⣟⣷⣶⣼⣿⡀⡼⡡⠗⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀