⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠶⢶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠀⢶⣻⣾⣟⠛⠽⣿⣿⣾⣷⣤⣀⠀⢶⣾⣿⣻⠟⡡⣨⣦⡙⣺⣿⣧⢠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡻⢧⠁⠌⣿⣟⠁⣶⣦⠏⢹⡿⠯⠿⠯⣯⢑⠛⠳⡕⡘⠋⢁⣵⠘⠛⠽⠎⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡾⠿⣿⣿⣿⣿⣽⠀⣿⠇⣺⣯⠡⣰⢸⡈⢰⣲⡀⢸⢠⣿⡆⡌⡄⢸⣿⡿⢧⠀⢸⣦⣼⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣥⢈⠙⠛⠛⠉⣠⡿⢐⣿⡇⠐⠿⢸⠀⠎⡉⣴⣾⡅⣯⡇⡇⣼⠀⠁⠶⢾⡷⣼⢿⣿⡇⠀⠀⠀ 
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣶⢲⣲⣶⣽⠆⣾⡗⠀⣞⡅⠛⠀⣾⡦⡈⢟⣧⠸⠃⢠⣾⣿⣿⣿⣾⣿⣿⠏⢸⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠚⣿⣿⣿⡟⡾⣿⡏⢸⣽⡃⣰⢐⢿⣿⣿⡄⣻⣠⣲⣽⣿⡷⢿⣿⣿⣿⣿⠃⢨⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠀⣿⣿⣟⠀⣹⣿⡿⡿⣿⣽⣬⣿⣻⣿⣾⢿⣛⣿⣿⠿⠛⢹⣧⡈⡻⠿⢻⠁⣼⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢹⣿⡇⣸⣿⠏⢸⣿⣿⡿⣿⣿⣻⠁⠻⣿⣷⡂⢤⢱⢾⣿⣿⢧⣶⠄⢠⣾⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⢹⣿⢸⣿⠃⠀⢯⣿⠋⢸⣿⣻⢇⠀⣿⢿⢽⡥⢸⠿⠛⢹⣿⡏⠈⣰⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣆⠸⠀⣿⡇⢸⡄⣿⡇⢰⣿⣿⣿⠀⣿⣿⣿⣿⠀⣰⣾⣿⢿⢇⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣄⢸⣇⠘⠻⠘⣿⠀⣿⣻⣯⡇⢸⣿⣿⣾⡆⢰⠞⠁⣹⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣾⣗⠀⣿⠀⣿⠀⣿⣿⣻⡇⢘⣻⣿⣯⣠⣠⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡀⣿⠈⡇⢸⣿⣿⣛⣀⠈⠋⢁⣉⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣬⣯⠀⠙⠛⢉⣹⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣶⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠶⢶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠀⢶⣻⣾⣟⠛⠽⣿⣿⣾⣷⣤⣀⠀⢶⣾⣿⣻⠟⡡⣨⣦⡙⣺⣿⣧⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡻⢧⠁⠌⣿⣟⠁⣶⣦⠏⢹⡿⠯⠿⠯⣯⢑⠛⠳⡕⡘⠋⢁⣵⠘⠛⠽⠎⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠿⣿⣿⣿⣿⣽⠀⣿⠇⣺⣯⠡⣰⢸⡈⢰⣲⡀⢸⢠⣿⡆⡌⡄⢸⣿⡿⢧⠀⢸⣦⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣥⢈⠙⠛⠛⠉⣠⡿⢐⣿⡇⠐⠿⢸⠀⠎⡉⣴⣾⡅⣯⡇⡇⣼⠀⠁⠶⢾⡷⣼⢿⣿⡇⠀⠀⠀  ⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣶⢲⣲⣶⣽⠆⣾⡗⠀⣞⡅⠛⠀⣾⡦⡈⢟⣧⠸⠃⢠⣾⣿⣿⣿⣾⣿⣿⠏⢸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠚⣿⣿⣿⡟⡾⣿⡏⢸⣽⡃⣰⢐⢿⣿⣿⡄⣻⣠⣲⣽⣿⡷⢿⣿⣿⣿⣿⠃⢨⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠀⣿⣿⣟⠀⣹⣿⡿⡿⣿⣽⣬⣿⣻⣿⣾⢿⣛⣿⣿⠿⠛⢹⣧⡈⡻⠿⢻⠁⣼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢹⣿⡇⣸⣿⠏⢸⣿⣿⡿⣿⣿⣻⠁⠻⣿⣷⡂⢤⢱⢾⣿⣿⢧⣶⠄⢠⣾⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⢹⣿⢸⣿⠃⠀⢯⣿⠋⢸⣿⣻⢇⠀⣿⢿⢽⡥⢸⠿⠛⢹⣿⡏⠈⣰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣆⠸⠀⣿⡇⢸⡄⣿⡇⢰⣿⣿⣿⠀⣿⣿⣿⣿⠀⣰⣾⣿⢿⢇⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣄⢸⣇⠘⠻⠘⣿⠀⣿⣻⣯⡇⢸⣿⣿⣾⡆⢰⠞⠁⣹⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣾⣗⠀⣿⠀⣿⠀⣿⣿⣻⡇⢘⣻⣿⣯⣠⣠⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡀⣿⠈⡇⢸⣿⣿⣛⣀⠈⠋⢁⣉⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣬⣯⠀⠙⠛⢉⣹⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣶⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀