⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢦⢤⣀⠀⠀⠀⠀⠀⢰⡏⡀⠘⢺⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠛⠻⢻⡆⠀⠀⠀⠀⠈⢷⣝⠒⣪⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡁⠀⠊⣾⢁⣀⣤⣤⠤⢴⡶⣷⢸⡿⠶⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⣆⢿⣏⣿⣧⣤⢶⣿⣗⡿⢸⡿⠶⠯⣽⣟⣉⡉⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢟⣹⣾⢿⡈⢿⠿⠚⠛⠉⠉⠉⠁⠈⠛⠛⠒⠶⣤⣍⡛⠻⣧⣤⡟⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣴⠿⣯⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠉⠻⣿⣤⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⡟⣧⣼⢿⣵⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠈⠻⣦⠀⠙⣷⡀⣹⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⣯⣼⡿⣡⡞⠁⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠘⠇⠀⠀⠀⠀⠘⢿⣄⣠⡿⡿⣿⣿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣧⣿⠟⣼⠏⠀⠀⡞⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⣴⣷⣶⣶⣤⣀⠀⠀⠻⣿⠄⢣⣧⣀⡽⣦⣄⡀⠀
⠀⠀⠀⠀⣾⠂⣿⡏⢰⡟⠀⠀⠀⠑⠤⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠉⣿⣿⣦⡄⢻⣿⡼⡿⡛⠀⢺⣿⣧⡀
⠀⠀⠀⢸⡿⠿⠿⣤⡿⠀⠀⣠⡾⢿⣿⣧⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣿⣿⣎⣿⣽⣟⢶⣶⣌⣿⣿⡇
⠀⠀⢠⣏⠁⠀⠀⢻⡇⢀⣼⣿⣄⣨⣿⡏⠀⠀⠀⠒⠈⣷⣯⡿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠛⣿⣶⣿⣿⣿⣿⢸⡏⡁⠀⠻⠿⣿⣿⡇
⢀⡴⣿⡇⢳⠀⠀⢺⡇⣾⣿⣾⣟⣿⡟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⢨⡟⠋⠀⠂⣄⣿⡿⠃
⢸⣿⣿⣧⠀⠙⠀⢻⡇⠛⢿⣿⡿⠋⠀⠀⠀⠀⢀⣴⣾⣿⡿⠦⢭⣄⠈⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢸⡗⠀⠀⠀⣼⡟⠀⠀
⢸⣧⣿⣿⡿⢷⣓⢮⣷⠀⠈⣩⠏⠀⠀⠀⢀⣶⠋⣿⠟⠁⠀⠀⠀⠀⠙⣆⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠘⣧⣾⡃⠀⣀⣵⡟⡇⠀⠀
⠀⢿⣿⣿⠀⢀⡉⣯⣿⡆⢠⠟⠀⠀⠀⠀⣾⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠘⣇⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠛⠋⢝⣵⠇⠀⠀
⠀⠘⠻⢿⣦⣿⡿⡟⡏⢻⣿⠀⠀⠀⠀⢸⡟⠀⠀⠑⢦⣀⠀⠀⢀⣠⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⠛⠛⠉⠀⠀⠀
⠀⠀⠀⠀⠹⣷⣾⣿⣥⣸⣿⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣭⢯⡉⠁⣿⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠻⠷⢿⣿⣧⠀⠀⠀⠀⠀⠈⠛⠶⣄⣀⠀⠀⡀⢀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢅⠙⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣤⢶⠟⡧⠘⢠⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿ ⣠⣧⠔⠀⠀⠀⠀⠀⠉⠻⠶⠶⠶⠶⠤⣴⡶⠶⠖⠒⠒⠒⣒⠚⠉⠉⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠛⠉⢻⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠒⠚⠋⠁⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⠁⠀⠀𝕝𝕖𝕒𝕧𝕖 𝕒 𝕔𝕠𝕞𝕞𝕖𝕟𝕥 𝕠𝕟 𝕞𝕪 𝕡𝕣𝕠𝕗𝕚𝕝𝕖 𝕒𝕟𝕕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠒⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠂⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀𝕨𝕒𝕝𝕜 𝕒𝕨𝕒𝕪... 𝕤𝕝𝕠𝕨𝕝𝕪...
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⡀⢠⣾⣧⠀⠀⠀⠀⠀⠀⠀⣴⠚⢻⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠿⠋⠁⣿⠀⠀⠀⠀⠀⠀⢸⡧⠴⠞⢻⡄⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠈⠻⣤⣀⣸⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⠀⡖⢀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀