⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢶⠚⢛⡯⠁⠀⠀⣾⡛⢻⠟⠷⠲⢤⣄⡀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡍⠁⣠⠴⠟⢋⣉⣉⣉⣉⣉⠛⠛⠦⣄⡠⠲⢦⠉⠳⢄⡘⣿⡀⠹⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠏⢀⡴⢋⣤⣖⡋⠁⠀⣠⠞⠁⠈⠙⣳⣦⡈⠻⣷⠚⠀⠀⠹⣿⣿⣷⠀⠸⣿⣿⡟⢶⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⣰⠋⣰⠞⠀⠈⠉⠓⠖⠃⠀⠀⣠⠖⠋⠀⠙⣆⠈⣧⡤⠦⡄⠈⠻⣿⣧⠀⠸⣿⣿⣆⠹⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⣼⡷⡞⢉⣾⠁⣼⠷⠤⠤⣄⡀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⢸⡆⠘⡷⠤⠿⠀⠀⠸⣿⣄⠀⠙⣿⣿⣧⣻⣷⡀⠀⠀
⠀⠀⠀⠀⣾⢿⣿⣄⣼⡿⠉⠁⠚⡇⢀⡇⠀⠀⢀⡜⠁⠀⢀⣶⣤⣤⣄⣀⣀⠙⣶⣼⡇⠀⡇⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⠛⢿⣿⡿⣷⡄⠀
⠀⠀⠀⣼⣿⠀⢸⣿⠻⠃⢀⡤⢶⡇⠀⣇⠀⢠⡏⠀⣠⠖⠋⠀⠀⠀⠀⠀⠈⠉⠉⠟⠷⢼⣏⠉⢷⠀⠀⠀⠀⢘⣿⣦⡀⠀⠈⠻⣿⣌⢳⠀
⠀⢀⣼⣿⣿⠀⠸⣿⠀⠀⢸⣇⡴⢳⡀⠹⣆⣸⡴⠋⠁⠀⠀⡼⡟⣞⣇⢸⣿⣧⠀⠀⠀⠀⠈⠙⠿⣦⠀⠀⠀⠈⣿⢿⣷⣦⣀⡀⣽⣿⣽⡄
⢀⣾⢻⣿⣿⠀⠀⣿⠀⠀⠀⠈⠀⢈⣱⣄⡼⠏⠀⠀⣦⣧⣼⣿⣿⣿⣿⣿⣿⡛⡶⣦⣤⣉⡈⣷⡀⣽⣷⠀⠀⠠⣿⡛⣹⣿⣿⣿⣿⡿⠋⠀
⢸⡏⢸⡇⣿⠀⠀⣿⡆⠀⠀⠀⠀⡏⢠⡟⠁⠀⠀⣀⣿⣿⣿⠿⠟⠉⠉⠉⠉⠛⠛⠻⠶⣭⣿⡿⢷⣬⣿⠀⢀⣼⠿⠟⠓⠺⣯⠁⠀⠀⠀⠀
⢸⡇⢸⣿⡿⠀⠀⣿⡇⠀⠀⠀⠀⣹⠋⢀⡀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⢖⣉⣀⡉⠛⣿⣿⠟⠀⢸⣷⣖⣶⣶⣿⣿⠃⠀⠀⠀⠀
⢸⣿⣿⣿⠁⠀⠀⣿⣧⡀⠀⠀⠀⡿⣀⢘⣷⠟⣹⡿⢅⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣿⣆⠸⣷⣴⣦⡘⣿⣿⠿⠷⠞⠁⠀⠀⠀⠀⠀
⢸⡇⣾⡟⠀⠀⣸⣿⡏⣷⠀⠀⠀⢹⣿⣼⣋⡾⠋⣠⣴⣖⣦⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⣸⠿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣷⣿⣷⣄⣴⣿⠟⠻⠿⣷⣦⣀⠈⠻⠿⢿⡇⠀⣿⣿⣿⣿⣿⠀⠀⢺⢿⠃⠀⢀⠉⠛⠛⠋⠀⡇⣤⣤⡉⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠿⠿⡿⠿⠟⢿⡿⠛⠋⢀⣽⣷⠀⢰⡜⣷⠀⠻⣻⣿⣿⠎⠀⢤⣀⣼⢶⣴⡏⠀⠀⠀⠀⠀⣇⡙⠛⢼⣿⣇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣥⣶⣾⡿⣿⣿⣧⣄⣷⢹⣧⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠀⠀⢀⣠⣶⣿⣿⣿⣶⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠈⠳⢿⣿⠀⣿⣿⢦⣀⣀⣀⣀⣀⣀⣀⣉⣀⣤⣾⣿⣿⣟⣽⡿⠋⢠⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⡿⠿⠿⠿⣿⣭⣿⣿⢿⣿⠛⣛⡛⢹⡟⣿⣿⠋⠀⠀⢸⣿⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⣰⣿⡟⢸⡇⠘⡟⡇⠀⢻⣜⣿⣷⡀⠀⠈⠿⣿⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠇⠀⠀⠀⣼⣿⣿⠃⣿⠀⠀⡇⣷⠀⠸⣿⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⡼⢳⣯⡞⠀⣿⠀⠀⡇⢸⠀⠀⣿⡇⠸⣯⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢀⡼⢃⣾⣸⡇⢀⣿⠀⠀⠃⠘⡀⠀⢸⣷⠀⢿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠛⢁⡾⣻⣿⡇⢸⢿⠀⠀⢀⠀⡇⠀⠘⣿⡄⠸⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣀⣤⣾⣿⠟⢿⣿⣀⣼⣼⡀⠀⢸⣄⣅⣀⣀⣷⠷⢾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⡿⠿⠟⠉⠀⠈⣿⣧⣄⣀⠉⠉⠉⠁⠀⢀⣠⣤⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣭⣁⣠⣴⠶⣿⣿⠋⣭⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣼⠿⠋⠁⠀⠀⡟⢻⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⢻⡄⠀⠀⠀⣼⠁⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣉⠀⠀⠀⣀⣿⠀⢀⣾⡷⣶⣿⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠟⠋⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀