⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀Так блэт,что тут происходит!⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠉⣙⡒⢻⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⢀⣴⣀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣓⣻⠟⠒⠶⣶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠁⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠷⠿⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⡿⠋⠀⠀⠠⡾⠀⠘⠋⠹⣿⣿⣿⠟⢉⣉⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⢋⡥⠞⠀⠀⠀⠐⠁⠀⡤⡀⣀⣿⠿⡏⢰⣾⣿⣿⣿⣟⣿⣯⡙⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡀⠀⣀⣠⣤⣶⠿⠛⠋⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⣿⡟⢸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⣯⣉⣁⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡀⣼⠁⣾⣼⣿⣽⡟⢈⣿⣿⠁⣿⣿⣿⣻⣿⣿⣿⣧⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣄⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠙⠛⠿⢿⣷⣦⣤⣀⡀⢸⠀⠀⠀⠀⠞⠀⣧⣼⣿⣿⢸⣿⢁⣾⣿⣿⢠⣿⣿⣯⣿⣿⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣻⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠻⢿⣿⣦⣄⣀⠀⠀⠀⡏⣙⣿⣿⣿⢣⣿⣿⡿⣿⣿⣿⡟⣼⣟⣿⣿⣽⡇⠀⢀⣀⣀⣤⣴⣶⣶⣿⡿⠿⠿⠛⠛⠋⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣷⣦⣄⣉⣿⣿⡷⣶⠤⣶⣿⣿⣿⢿⣿⣿⡿⢠⣿⣿⣿⢣⣿⣿⣿⣿⣿⣷⣾⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣟⠋⣴⣋⣀⣉⣿⡉⠁⣾⣿⣿⠇⣸⣿⣿⣿⣿⣻⣿⠘⣿⣿⣧⣄⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⡼⢈⣿⣿⣿⣿⣿⡉⠀⣰⣿⣿⠇⣴⣿⣿⣿⡿⣿⣿⣿⣷⠉⣿⠿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣤⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣴⣿⣿⠿⠛⠿⣁⡄⠨⡙⢻⠿⣿⣿⣿⣯⣥⣴⠿⠟⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣼⣿⡟⠑⠀⠀⠀⠀⠙⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣳⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣿⡶⠀⠀⣀⠠⣠⣀⡀⠀⢤⣀⣀⣀⣀⣀⠀⠀⠚⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⣀⣀⡃⢻⣧⣀⣄⣈⡉⠉⠉⠙⠛⠛⣻⡷⢶⠛⠟⠛⠉⢿⣿⣿⣿⠟⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠿⠿⢿⡿⠓⠒⠲⠶⢤⣷⣿⣿⡏⢽⣿⣼⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠿⣶⣶⣥⣄⣨⣭⣤⣤⣤⣴⣶⡿⣯⢉⣥⣄⡠⠶⣤⣤⣤⣶⣶⣶⣆⣾⣟⣟⠛⣈⠹⣿⣩⣭⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣷⣦⣬⣉⣹⠿⠛⠛⣛⣶⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣻⣷⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⠓⠀⠀⠉⣤⣤⣶⡿⣿⡟⠛⠛⠛⠻⢿⣿⡿⠿⠿⣽⣿⣿⣿⠏⠀⠀⠐⠲⠦⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⢠⢷⠄⠀⠘⢩⣽⡶⠶⠶⣶⣾⣿⣷⣶⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀Так блэт,что тут происходит!⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠉⣙⡒⢻⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⢀⣴⣀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣓⣻⠟⠒⠶⣶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠁⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠷⠿⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⡿⠋⠀⠀⠠⡾⠀⠘⠋⠹⣿⣿⣿⠟⢉⣉⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⢋⡥⠞⠀⠀⠀⠐⠁⠀⡤⡀⣀⣿⠿⡏⢰⣾⣿⣿⣿⣟⣿⣯⡙⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡀⠀⣀⣠⣤⣶⠿⠛⠋⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⣿⡟⢸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⣯⣉⣁⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡀⣼⠁⣾⣼⣿⣽⡟⢈⣿⣿⠁⣿⣿⣿⣻⣿⣿⣿⣧⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣄⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠙⠛⠿⢿⣷⣦⣤⣀⡀⢸⠀⠀⠀⠀⠞⠀⣧⣼⣿⣿⢸⣿⢁⣾⣿⣿⢠⣿⣿⣯⣿⣿⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣻⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠻⢿⣿⣦⣄⣀⠀⠀⠀⡏⣙⣿⣿⣿⢣⣿⣿⡿⣿⣿⣿⡟⣼⣟⣿⣿⣽⡇⠀⢀⣀⣀⣤⣴⣶⣶⣿⡿⠿⠿⠛⠛⠋⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣷⣦⣄⣉⣿⣿⡷⣶⠤⣶⣿⣿⣿⢿⣿⣿⡿⢠⣿⣿⣿⢣⣿⣿⣿⣿⣿⣷⣾⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣟⠋⣴⣋⣀⣉⣿⡉⠁⣾⣿⣿⠇⣸⣿⣿⣿⣿⣻⣿⠘⣿⣿⣧⣄⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⡼⢈⣿⣿⣿⣿⣿⡉⠀⣰⣿⣿⠇⣴⣿⣿⣿⡿⣿⣿⣿⣷⠉⣿⠿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣤⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣴⣿⣿⠿⠛⠿⣁⡄⠨⡙⢻⠿⣿⣿⣿⣯⣥⣴⠿⠟⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣼⣿⡟⠑⠀⠀⠀⠀⠙⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣳⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣿⡶⠀⠀⣀⠠⣠⣀⡀⠀⢤⣀⣀⣀⣀⣀⠀⠀⠚⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⣀⣀⡃⢻⣧⣀⣄⣈⡉⠉⠉⠙⠛⠛⣻⡷⢶⠛⠟⠛⠉⢿⣿⣿⣿⠟⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⠿⠿⢿⡿⠓⠒⠲⠶⢤⣷⣿⣿⡏⢽⣿⣼⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠿⣶⣶⣥⣄⣨⣭⣤⣤⣤⣴⣶⡿⣯⢉⣥⣄⡠⠶⣤⣤⣤⣶⣶⣶⣆⣾⣟⣟⠛⣈⠹⣿⣩⣭⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣷⣦⣬⣉⣹⠿⠛⠛⣛⣶⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣻⣷⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⠓⠀⠀⠉⣤⣤⣶⡿⣿⡟⠛⠛⠛⠻⢿⣿⡿⠿⠿⣽⣿⣿⣿⠏⠀⠀⠐⠲⠦⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⢠⢷⠄⠀⠘⢩⣽⡶⠶⠶⣶⣾⣿⣷⣶⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀