⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⡿⣷⣄⠀⠀⣿⡵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠛⠛⠿⣧⣦⣿⣤⣄⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢤⣤⣴⣶⣶⣶⣶⣒⣒⣒⣲⡶⠦⠤⢤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⣦⣸⡉⡟⣉⠙⠛⣛⡛⠛⠟⣛⠛⠛⠛⠓⣒⣾⢯⡉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠒⠭⢍⣁⠐⠲⠭⣳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢷⣽⣿⣭⣷⡏⡀⠤⠀⣀⡉⠐⠤⣈⠙⢏⠈⠉⡿⡟⣁⡧⢄⣉⠀⠉⠁⠒⠢⠤⢀⡀⠀⠀⠈⠉⠒⠤⡈⠹⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣯⠊⣡⠜⣿⣉⡜⣧⡀⠀⠀⠀⠉⠒⢤⠈⠑⢄⠑⢄⠣⣭⠟⠁⠀⠀⠉⠑⠢⣄⠀⠀⠀⠉⠐⠦⡀⠀⠀⢀⣈⣢⣨⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⢳⠃⡜⠁⠀⢹⣋⠵⠀⣿⢦⡀⠀⠀⠀⠀⠱⡀⠀⠙⢄⠑⢄⠀⠐⠠⣄⣀⠀⠀⠀⠈⠓⠤⡀⠀⣠⡼⠦⠞⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣷⠋⢰⣏⡆⢸⠀⠀⠀⢸⡙⢾⠿⣿⡆⠙⢦⡀⠀⠀⠀⠙⡄⠀⠀⠑⢄⡈⠑⠂⠤⣄⣈⠀⠀⠀⠀⣀⣨⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣵⡁⡰⡇⢸⠂⢸⡀⠀⠀⢸⣀⠀⠻⣼⡀⡇⠀⡏⠓⢤⡀⠀⠘⢆⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⢉⣩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡾⡻⣱⢹⡿⣉⣫⢳⡇⠈⡇⠀⢃⠀⠀⢸⡇⠑⢄⠈⠳⣣⠀⢳⠀⠀⢫⠓⣦⣌⡢⣀⠀⠀⠀⠀⠀⠉⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⡩⠊⡰⣱⠁⢠⠓⢲⠊⠉⢸⠀⠇⠀⠘⡆⠀⢸⠇⠀⠀⠱⡀⠹⣆⠸⠀⠀⠘⣼⢻⣹⡍⢙⠛⡲⢶⣶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢞⣵⠊⠀⡰⢡⠃⢀⠏⠀⡏⠀⠀⢘⠀⠀⠀⠀⡇⠀⣸⠄⠀⠀⣄⠘⢆⠻⡀⡆⠀⠀⡟⠚⠛⠱⢫⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⣣⠏⡜⠀⣰⠁⡏⠀⡼⠀⢰⠁⠀⠀⡈⠀⡄⠀⠀⡇⢰⣧⣄⠀⠀⠈⠢⡀⢦⢷⡇⠀⠀⠇⠀⠀⠆⡴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⡵⠁⡸⠀⢀⠃⢰⠀⠀⠁⠀⣿⠀⠀⢀⡇⢠⠇⠀⢠⢧⢿⣯⣽⢽⣄⠀⠀⠈⢦⢫⣇⠀⠀⡀⠀⡀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⣸⠅⢠⠇⠀⣼⠀⡼⠀⠀⡀⠀⡇⠀⠀⠸⢀⡎⠀⢀⡾⢻⣀⠈⠹⡉⠀⠣⠀⢢⠀⢦⢿⠀⠀⠃⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠹⠀⢸⠀⠀⠇⠀⡇⠀⠀⢧⠀⢧⢀⣀⠧⠮⠤⠤⠾⢄⣘⠂⢀⡀⠙⡄⢄⢣⠀⠳⠈⡄⡇⢰⠀⢠⡎⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡈⠀⠀⠸⠀⢸⠀⢀⡇⣀⡤⠚⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠲⣼⡄⠓⣦⢀⢣⠸⣻⣼⠀⠀⣇⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⢀⠀⢰⣀⣮⠔⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢼⡈⠘⡦⡁⢧⠰⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡜⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣍⠈⣦⠏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡻⡄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡝⣆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⢆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⢯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⡽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢱⡝⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢻⢦⡀⠉⠓⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

𓆤⭒𓆑⭒𓆣⭒𓆨⭒𓆦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠸⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢤⡀⠀⢤⣀⠀⠀⠘⢶⣄⠀⢹⡆⠀⢸⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢢⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡈⢉⣻⡶⣴⠿⢷⠶⠿⢦⣼⣀⠹⣆⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡌⠒⢦⣄⠀⠀⣇⠀⠘⣇⠀⡇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣤⣤⣤⣶⣶⡒⣿⠛⢻⡀⠀⢧⡀⢸⡀⠀⡾⠉⣙⡷⢿⣆⠀⢷⠀⢸⠀⢰⠀⠸⡇⠘⣆⠀⠀⠙⢦⣄⣈⣷⣤⣷⣴⣤⣿⣀⡇⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⣉⣩⡽⣻⣷⣴⠟⠒⣻⡿⢏⣻⣒⣿⣦⣿⡀⡶⠛⠻⣾⣄⣸⠀⢸⡀⠀⢻⡄⠘⢷⡀⣠⣴⣟⠉⢻⡀⢼⣏⠀⡿⢉⣿⣾⣇⠀⠀⣤⠞⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣠⣤⣴⡾⠿⠚⠋⢁⡼⠏⠈⠉⠁⠀⠀⠀⠀⠁⠀⠈⠛⣧⣄⣼⠃⠈⣿⠷⣾⣥⣄⣸⡧⢶⠞⠛⣏⠀⠹⣦⣨⣿⠞⠛⣛⣷⢾⣧⡶⢛⣷⠞⠁⠀⣀⡤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠋⠉⠈⢛⣷⣾⣇⠀⢸⠁⠀⣏⠀⠘⣧⣀⣸⣷⣾⠿⠛⠁⠛⠛⠿⠥⣤⠿⢶⠋⣉⣳⣶⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠲⠭⠿⠿⠳⠶⢻⠓⠚⣻⠉⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢳⣿⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠏⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠈⠻⣿⠋⠋⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀