⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡴⢧⣀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠏⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣶⣒⣶⠦⣤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠲⡌⠙⢦⠈⢧⠀
⠀⠀⠀⣠⢴⡾⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⢃⡠⠋⣠⠋⠀
⠐⠀⠞⣱⠋⢰⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢖⣋⡥⢖⣫⠔⠋⠀⠀⠀
⠈⠠⡀⠹⢤⣈⣙⠚⠶⠤⠤⠤⠴⠶⣒⣒⣚⣩⠭⢵⣒⣻⠭⢖⠏⠁⢀⣀⠀⠀⠀⠀
⠠⠀⠈⠓⠒⠦⠭⠭⠭⣭⠭⠭⠭⠭⠿⠓⠒⠛⠉⠉⠀⠀⣠⠏⠀⠀⠘⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⣰⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠛⠉⠁⠀⠀⠀⠉⢳⡞⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠀⣀⣤⣴⠶⠻⠏⠛⢋⣉⣷⢿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡄⠀⠀ ⠀⣠⣖⣫⢶⣿⣶⣚⣛⣛⣛⣙⣻⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⢠⠎⠀ ⣰⣫⠞⠉⠈⡩⣹⣠⣤⣀⣀⣈⢉⣿⣿⣿⠁
⠀⠀⣠⣴⣒⣺⣿⣯⣯⣿⣿⣟⡳⣶⣶⣤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡎⠀ ⣠⡾⠋⠀⠀⣠⣾⡛⠁⠀⠀⠀⠈⠙⢿⣿⣿⠟⠀
⠀⣼⣟⡿⠋⢁⣄⣤⠶⠓⢺⠟⠉⠉⠛⠻⢿⣿⣷⣦⣤⣀⠀⠹⣄⠀⡜ ⢀⣴⠟⠀⢀⣤⠞⠋⠁⠉⠛⠙⠿⢒⡶⠦⣿⣿⡟⠀⠀
⢸⣿⣿⣿⣿⣿⠋⣠⠴⠚⠋⠻⢷⣦⣦⣤⣀⣀⠀⢙⢛⣻⣿⣦⣜⣾⣥⣾⣯⣴⠾⠋⠉⢉⡉⠙⠓⠲⢦⣤⣀⣀⣠⣿⣿⠇⠀⠀
⠘⢿⣿⣻⣿⣷⡟⠁⠀⣠⣴⠿⠋⠀⠀⡀⢬⣿⠿⠛⠛⠛⣻⣿⣿⣿⣿⣟⢿⢒⠲⠶⠶⠤⠭⢴⣆⣀⡀⠈⠛⣻⣿⣿⣿⠀⠀⠀
⠀⠈⠻⣿⣯⣿⣷⣤⣾⡟⠁⠀⢀⣠⣬⠞⠉⣀⣤⡤⠾⣋⣉⣥⣴⣿⣟⣿⣿⣿⣍⡉⠙⢛⠒⠒⠮⣭⣏⣙⣺⣾⣿⡿⠏⠀⠀⠀
⠀⠀⠀⠈⠻⣿⣟⣿⣏⠀⢀⣴⡿⠏⢁⢴⣾⡿⣉⡴⠟⢋⣥⡾⢻⣿⣿⣿⡿⣦⡀⠉⢿⢯⣗⢶⣤⣀⡉⠉⠋⠻⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⡟⠁⣠⣷⠋⣡⠞⠉⠀⣠⣾⠟⢠⣿⠱⣻⣿⣇⠨⢻⣄⡀⠳⣌⠳⢦⣈⡻⠷⣦⣸⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠳⣿⣾⣿⣿⣷⣿⣥⠞⠁⠀⢠⣾⣾⠋⠠⢻⣿⡆⢻⣿⣿⠀⢼⠃⢻⠲⡝⢧⡀⠙⣷⣄⠀⣹⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⠿⠿⡾⠃⠀⣠⡾⣻⢿⣏⠀⢠⣸⣿⡇⠀⢻⣷⠀⢸⢆⣊⡇⡻⡄⣻⣷⣬⡛⡷⣿⢿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣄⣾⠋⣾⣷⣯⠁⠠⠀⣽⣺⣷⠀⠀⣿⡇⠸⣧⠠⢹⠈⣼⡎⢿⡌⠛⣿⣷⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡾⠋⣼⡏⣿⣇⠀⠠⣿⢻⡟⣿⡆⢀⣿⡄⠀⣏⡀⡿⡎⠞⣿⣌⣿⣸⣯⡟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⣿⣟⣿⣿⣽⣠⣾⡝⢸⣿⡹⣿⢀⢹⡧⡆⢽⣥⢰⣿⣘⠘⣿⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣷⣌⣿⣇⠻⣟⡰⠿⣿⡄⢷⡅⠁⠁⣀⡵⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠽⣿⣿⣿⣿⣿⣿⣏⡴⠋⠀⠀⠈⠛⠒⠚⠚⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀