Cute Cat💜💜💜 Hamster Copy and Paste (don't Search For Those Things) Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⢀⠠⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢸⠁⠉⠉⡀⣧⣿⣸⢀⠀⠏⡼⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠄⠤⠠⡍⡟⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣿⠐⠀⠀⠀⠀⡄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡇⠀⠏⣿⡿⣿⢸⠀⠀⢸⢱⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣤⣾⢸⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠔⣸⠞⢀⠀⠀⠉⠔⠤⠤⡦⠻⠃⠲⠙⠀⠀⠀⠀⠀⠀⡇⡿⣿⣿⣿⣿⢀⠀⠀⢸⡄⠘⠀⠀⠀⠀⠀⠋⠿⢿⠿⠈⠀⠀⠀⠀⠃⢠⣱⣀⣠⣅ ⠀⠀⠀⠀⠀⠀⠀⠊⡤⣀⢅⣾⠒⠞⡤⣉⣛⠛⠀⠀⠀⡀⣢⠙⠀⢦⢜⠑⠀⠀⠀⡇⣷⣀⣧⣿⣸⠀⠀⠀⠂⠉⢻⠙⠀⠀⠁⠋⡟⣛⢛⠓⠉⠀⠁⠊⠔⣴⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠁⠋⡠⠀⠀⠇⣠⠀⡼⠀⡧⣔⣠⣀⠀⠁⠏⠻⠛⠛⣙⠉⡞⡀⠰⠀⠀⠇⡶⠷⣿⣧⢠⠀⠀⠀⠋⣴⠳⠈⡀⣄⢳⣸⠐⠂⡇⠐⡁⣹⣀⣆⢀⠢⠟⡿⣷⢸⠁ ⠀⠀⠉⠟⣿⣿⠽⠤⠑⡀⠑⠀⣄⠳⠀⠂⠈⠃⡿⣶⣴⣥⣈⢄⠱⠀⣀⠤⠲⠽⢸⡇⣿⣿⣿⣟⠀⠀⠀⠀⢀⠀⠀⢆⠉⠋⡖⠲⠑⠈⡍⠉⠊⢦⠙⢨⠀⠀⠀⡜⠀⠀⡇ ⠋⡿⣿⣿⣿⣿⣿⠻⠙⢄⡑⠢⠉⡀⠳⠟⡾⡦⢙⠋⠟⣿⢲⠒⡖⣤⣿⠀⠀⡁⢸⡇⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠤⡒⢹⠈⠀⠁⠉⢩⠀⠀⠏⢿⣿⠿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡀⠢⡈⢦⠈⣧⢘⠆⣿⣴⢀⠀⠀⠀⠀⠀⣄⣤⠯⣰⢸⡇⣿⣿⣿⣿⣿⢿⠙⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢆⠈⣄⠓⣍⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢸⡇⣿⣿⣿⣿⣿⣿⣿⣄⣳⢤⠛⠈⠀⠀⠀⠀⠀⠊⢠⠀⠀⠀⠀⠋⠟⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⢸⠀⠀⡃⢸⠀⠀⠀⠀⠀⠉⠚⠴⠦⠳⠀⠃⢸⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⣅⢰⣀⢄⠤⠤⠤⡠⡀⠤⠤⠷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠔⢁⠊⠴⣀⢳⠀⠀⠀⠋⡴⢀⠀⠀⠀⡇⠻⣰⢸⡇⣿⣿⣿⣿⣿⣹⣹⠼⣀⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠴⣠⠀⠀⠀⡀⢢⠛⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣸⠀⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠁⡖⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠋⠀⠑⢸⡇⣿⣿⣿⣿⣿⣱⠀⣀⣇⠛⠚⠐⠁⠉⠉⠀⠢⠒⠟⣿⠀⢀⠁⣏⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣶⣿⣿⣿⣿⣿⣾⣻⡿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣄⡲⢸⡇⣿⣿⣿⣿⣿⡷⠘⠃⡿⣿⣿⣿⣿⣿⢛⡿⢿⣿⣿⣿⢻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣧⡏⣿⣿⣿⣨⠀⠏⣿⣀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠅⡸⢠⠳⢈⠀⠀⠀⠀⠁⢸⡇⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠔⣦⣶⣠⡀⣦⣿⣶⣠⠋⠉⠘⠀⣡⣉⢽⠒⠀⠁⠛⠛⠘⠀⠉⠛⠿⢼⡶⣤⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢤⠤⠤⠤⠤⠄⠤⠤⠤⡤⣤⣤⣤⡤⣤⣠⣤⠤⠤⡤⣤⣀⢤⠤⠤⣤⠤⠤⠤⠤⢡⡆⣤⣦⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⠀⠀⠀⢺⠉⠀⠀⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡠⠀⠀⣀⢆⠀⠀⡄⣠⣀⣀⣄⣷⢀⠀⠁⣰⠀⠀⠀⠀⠀⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡷ ⠀⠀⠄⢶⠙⠀⠀⠀⡀⠤⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡠⠀⠀⠀⠁⠋⢴⠤⠸⠀⠀⠀⠀⠀⡀⢦⠙⠠⠀⠀⠀⠀⠀⠀⠀⠀⢍⠒⠙⠈⠀⠀⠀⠀⠀⠁⠊⠔⡡⠟⣸ ⠀⠀⠀⠀⠀⣀⣏⢾⠤⡿⣛⠙⣉⣧⠱⣁⣉⡟⣩⢉⡛⣟⢽⠤⣽⣀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠟⣿⢿⠻⠛⠙⠉⠈⠁⠔⣪⠔⡠⠀⠁⣔⣀⣀⣀⣁⠋⠒⡤⢀⡜⠀ ⠀⠀⠀⠀⠀⠟⣿⣀⡋⣿⠀⠀⡀⣄⣷⢘⡏⣾⣠⢀⠀⠂⣺⡈⣇⢿⠙⠈⠀⠀⢸⠃⠀⠁⠈⠉⡟⣿⣿⣿⣿⣿⣿⣿⠼⢊⡠⠀⠀⠀⠊⡤⠦⠷⠿⣾⣡⠈⠀⠉⡏⢀⠀ ⠀⠀⠏⡿⢈⣿⣾⡊⠔⢀⠀⠀⠀⠀⠀⣧⣠⠀⠀⠀⠀⠀⢄⡲⡀⣿⣸⢀⠀⠀⢸⡇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠛⠔⣀⠀⠀⠀⣸⠀⣀⣿⣿⣿⣿⣸⠀⠀ ⠛⠉⣿⣿⣿⣿⢹⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⢿⠉⠙⠙⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠙⠁⡿⣿⣿⣾⢀⠀⠀ ⣿⣿⣿⣿⣿⣸⡆⠔⣁⣼⣇⠹⠀⠀⠀⠀⠀⠀⠀⠀⡟⣀⣱⢄⠆⢰⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡜⡁⣿⣿⢾⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠈⡀⢀⠒⡡⣰⠀⠀⠁⠞⠙⠀⠀⠀⢣⢪⠐⣀⠀⠃⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠋⡤⠋⣿⣼⣀⢰⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠽⠀⣤⢒⠈⠀⡄⢘⠀⠀⣇⠀⠀⠉⡜⢤⠀⡿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠈⠀⠀⠀⠀⠁⠋⠘⠤⠤⣁⠛⡟⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⠉⡉⠛⠙⢦⠒⠚⢡⠛⡟⣿⣯⠛⡿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠚⠁⡟⣿⣿⣿⣋⣒⣟⣾⣴⣤⢳⠀⠈⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣀⣊⣤⣤⣙⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢀⠀⠀⡀⣸⣀⡀⠀⠀⠀⠀⢀⢸⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠃⡿⢿⠘⠀⠟⣿⠻⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⡏⣿⢿⠈⠓⠉⠈⠀⢧⡟⢧⣼⢡⡼⢯⠗⢻⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣾⣶⢾⠟⣾⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⡿⣿⣿⡿⣤⣯⣿⠻⣿⣿⡟⣿⡿⣿⢘⠋⣟⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣴⣠⣉⣤⣶⣵⣦⣶⣡⣋⣤⣶⣶⣶⣷⣿⣿⣿⣿⣿⢸⡇⣿⣿⢻⠉⣉⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣤⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀

⠀⠀⠀⠀⡀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠏⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡼⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠸⠀⠀⠃⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠁⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡆⣿⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⡜⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠁⢰⠀⠀⠀⣄⠙⠀⠀⠀⠀⡀⢠⠀⠀⡄⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢠⠀⠀⡇⠀⠀⠀⠀⠀⡀⢤⠑⠀⠀⠀⠀⠀⠐⠀⣾⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠀⡽⠉⠒⠒⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⢠⠀⠁⡴⣀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠋⠴⣠⢀⠀⠀⣀⢤⠑⠀⠀ ⠀⠀⠀⠀⣾⠀⠁⣰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢷⠀ ⠀⠀⠀⠇⢀⠀⡇⠀⠀⠵⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠄⠛⡀⢸ ⠀⠀⠀⡸⠀⠀⡄⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡂⣠⠇⢠ ⠀⠀⡎⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀ ⠀⠇⢠⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡤⠘⠀⠀ ⠃⡼⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⢸⠀⠀ ⡆⢹⠀⠀⠀⠀⠀⠀⠀⠧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⠀⠀ ⠀⡄⠑⠀⠀⠀⠀⠀⠀⡀⣧⠉⠉⠉⠉⠉⠐⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠀⠀ ⠀⠀⠀⣀⠯⠿⠛⡈⣀⣀⣀⢻⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⢞⠓⠔⠾⡠⢀⠀⠀⠀ ⠀⠀⠀⡞⢏⣎⣇⣀⢯⠑⠀⣿⠀⠀⠀⠀⠀⠟⠊⠟⡼⢀⠋⣠⠎⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣼⢰⡇⠀⢸⡞⢣⣼⠀⠀⠀⠀⡇⣹⠈⠷⢀⠟⢳⠏⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⣿⠀⡀⠸⢻⢸⡇⢀⠀⠁⠖⡠⢀⠀⡀⢄⡶⣟⡀⡼⠳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠸⠀⢇⡆⢘⡇⠀⡤⢀⠀⠀⠂⠒⠶⠰⠈⡀⢦⢻⠀⢦⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠈⡀⢹⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸⠀⠀⡄⠘⠀⢇⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢸⠀⣇⡽⣴⠘⠀⠐⠛⠛⠐⠀⠀⠀⣀⣻⢟⠉⣏⠹⠀⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠛⣹⡇⠀⢣⠋⠸⣷⢼⢱⠛⠀⠀⠀⡦⣶⡛⣾⡇⠸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⠈⣿⠀⡅⣹⣤⢿⣶⣤⢀⠙⠘⠀⠆⠓⡟⣾⣠⢳⡄⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢸⣄⣧⠈⠀⣆⣸⡿⠢⠶⣤⣠⠀⠀⠋⡳⣰⠀⠀⡎⠇⢾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⡄⣗⠘⠀⠀⠉⠚⡥⢚⣠⠀⠀⠁⢸⡞⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⡀⢦⠤⣠⢀⠴⣠⠀⠀⠀⠀⡥⡞⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠉⠈⠀⠀⠀⠀⠀⠁⠉⠚⠴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢹⠄⡀⢀⠀⠀⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⠰⢉⡧⣿⢺⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡑⢂⡱⡜⢿⡀⠀⠀⠀⠐⠀ ⣿⠘⠤⣲⣰⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⡘⠆⠃⣇⣿⢺⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⡌⠡⡼⣏⠸⣠⣄⢈⠀⠀ ⣿⢿⠀⢀⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠃⢀⢩⡧⣿⢻⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡈⢱⡖⡍⢻⢀⠀⠀⠀⠀ ⣽⣿⠸⠐⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠤⢋⡧⣿⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⡃⠤⢚⣯⠘⠀⠀⠀⠀ ⣾⣟⢻⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡰⠜⡯⣟⣼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠘⣩⠖⣍⢻⠀⠀⠀⠀ ⣽⢾⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⡨⠖⣏⡃⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔⡃⠤⢚⣯⠈⠀⠀⠀ ⣻⣽⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡒⢎⣏⡇⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠒⣎⠇⣎⢹⠀⠀⠀ ⢾⣳⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⠴⢛⣯⡁⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⠰⢍⢢⡜⣿⠀⠀⠀ ⣟⣯⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⡱⢎⣿⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡨⠕⣊⠭⣗⠸⠀⠀ ⢻⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⣁⡓⢧⢸⠔⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠣⢆⡙⡧⢸⠀⠀ ⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠥⡂⡱⣾⠀⠀⡦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⢢⡜⡎⢽⠀⠀ ⡽⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠜⠃⣡⡿⢻⠟⠹⠋⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡉⠦⢃⢰⣾⠀⠀ ⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢂⡁⠆⠡⣿⣤⣀⣀⣯⣹⣄⣷⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡱⢆⡡⢽⠀⠀ ⣷⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢡⠠⡘⠣⣾⢀⠀⠀⠀⠀⢀⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⡰⢓⢡⡷⠀⠀ ⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠂⡁⠟⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠡⡱⠢⣑⡷⠈⠀ ⡿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠏⡴⢆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡡⠒⣡⡜⡯⠀⠀ ⡷⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡾⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⣦⠙⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠒⠌⣃⠠⢳⡌⣟⠀⠀ ⣻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢈⢠⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⣄⠹⠀⠀⠀⠀⠀⡘⠁⠄⡃⠄⡑⠢⣌⠚⢡⣾⠀⠀ ⡵⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠂⡀⢶⠈⠀⠀⠠⠄⠂⡐⠎⡁⠰⢎⡃⡔⢏⢸⠀⠀ ⣳⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢂⠁⣆⠑⠀⡐⠎⢁⡰⠎⢃⡄⠘⢱⡬⡟⢀⠀⠀ ⡾⣟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠌⠂⠁⠠⡐⡌⠆⡈⠱⢌⠡⠴⡈⠴⡓⣸⠀⠀⠀ ⣟⢧⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⠀⡐⠂⢁⢢⡐⠱⡌⠆⡈⠖⣈⡿⢀⠀⠀⠀ ⡼⢿⣯⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⡐⠌⠁⠤⡈⠢⡐⢌⡑⠦⢏⣰⠀⠀⠀⠀ ⣽⡞⣿⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠌⠂⠄⠈⢂⠔⢂⡡⠟⣼⠀⠀⠀⠀⠀ ⡳⣽⣸⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠁⢂⠄⢈⡐⢋⡷⣼⠀⠀⠀⠀⠀⠀ ⣼⡟⢰⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⢡⡀⠞⣫⣼⠀⠀⠀⠀⠀⠀⠀ ⣜⡿⢀⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠐⠁⡼⢏⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⣞⢰⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠃⢥⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⢠⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡱⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠈⠀⠀⠀⠀⠀⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠋⡷⣎⡞⢿⠈⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢑⡦⡟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠟⣾⣡⣸⢍⠂⣄⢻⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢨⠱⢂⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⡇⣩⠴⢋⠤⠒⣈⠑⣇⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⠆⡉⠤⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⢃⢆⠡⢶⠻⢉⠠⡐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠉⢢⡜⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢈⡱⢂⠤⡘⣆⢿⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⢋⢠⢽⡎⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠈⡰⠁⢂⠄⠩⣄⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⠇⣡⠖⢩⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⢸⠌⡀⠀⠀⠀⠐⠠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢾⡉⡰⢜⡻⣇⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡃⢸⠀⠀⠀⠀⠀⡁⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢿⠠⡱⢆⠳⣇⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠂⠀⣿⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⢊⠀⣿⣉⠤⣣⡕⡪⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠁⣼⠁⠉⠛⠛⠛⠿⠿⠛⠛⠉⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠋⠟⡿⣾⣛⣳⠾⣟⢛⢩⣿⠒⣈⡔⢻⢰⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠁⡿⣴⣠⣀⠀⢀⠀⢀⡀⣀⣄⢦⣷⢽⠻⠙⠈⠀⢸⠀⠀⠁⠛⡿⣶⣤⣀⢀⠀⠀⠀⠀⠀⠀⣀⣦⠻⢌⡑⡎⡼⡗⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠏⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣆⡶⣟⢯⠙⠋⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠻⠄⣯⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢿⣋⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡆⡍⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢦⠰⣿⠛⠀⠀⠀⠀⠀ ⠞⡿⢤⡷⠀⠀⠀⠀⣿⠀⠀⠀⠁⠛⠿⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠽⠽⠬⠙⠀⠀⠀⠀⣿⠡⣌⡷⣟⢹⠦⠷⠹⠀ ⡟⢠⠁⡿⠀⠀⠀⠀⣧⠀⠀⠀⡷⡇⣾⣿⡌⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠄⢠⡗⣿⣿⡼⠀⠀⠀⠃⢼⠡⡌⡗⣹⣼⠀⡃⣿⠀ ⣧⠈⡇⣿⠀⠀⠀⠀⡀⢹⠀⠀⡀⣦⣖⣠⣀⢀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣠⠀⠀⠀⠀⡟⣠⠐⡌⠓⣯⢩⠟⣿⢰⠀ ⠁⢄⠟⣹⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢲⢁⡡⠄⠣⣕⢻⡴⢠⠀⠀ ⠀⠢⡀⢸⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⣿⣸⣀⣀⣀⣇⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠌⠂⡀⠐⢊⡱⣷⠀⠀⠀⠀ ⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⣅⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡾⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠐⢀⠀⠀⠀⠐⣈⡷⠘⠀⠀⠀ ⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣯⣭⣯⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢸⡀⠀⠀⠀⠀⠀⠀⡐⡇⢸⠀⠀⠀ ⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣼⣤⣦⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⠀⠀⠀⠀⠀⠀⠀⡐⢂⢿⠙⠀⠀ ⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠁⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⣦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⠀⠀⢁⢸⣀⢳⠀ ⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⢀⠀⠀⠀⠀⣷⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⢧ ⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⡆⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡾⠀⠀⠀⡀ ⠀⠀⠀⠀⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⡄⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢙⠀⠀⠀⠀ ⠀⠈⠀⠇⣱⢾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠁⠋⠘⠀⠑⠉⠉⡏⢻⠉⠉⠀⠀⠀⠀⠀⠀⢆⠘⠀⠀⠀⠀⠀⠉⠟⣾⣻⣧⠹⠀⠀⠀ ⡰⠀⠀⡇⡀⢸⡇⢌⠻⠛⠉⠉⠁⠄⠈⠀⠀⠀⠃⠒⠒⠞⠤⡿⣠⣀⣀⢁⠋⢠⠀⠀⣃⢀⠀⣇⣸⣄⣦⣒⣝⢬⠶⠒⠀⠀⠉⠉⠋⠟⡿⣇⣽⣿⣷⢲⣿⠘⠀⠀ ⠀⠀⠀⡇⠘⢹⡏⠰⣇⢾⢹⡀⣆⣿⣿⣇⣿⢿⠻⠙⠈⠀⠃⣼⠀⠀⠀⡏⣰⠀⠀⠀⡄⠸⠂⡀⢿⠘⠂⠍⠒⠤⣠⣀⣄⠘⢀⠀⣿⣿⣿⠀⡡⣿⡇⣼⡿⣿⠀⡏ ⠀⠀⠀⠀⢳⣇⣿⠰⡇⢸⣻⠀⠀⣇⣿⠈⣿⣷⣿⣿⣾⢧⡿⢘⠀⠀⠀⣰⠀⠀⠀⠀⠀⢧⠁⠄⣿⢴⣠⢀⠀⠀⠀⠀⡇⢿⠀⡇⢽⣰⣿⠀⠀⣿⡇⣼⡟⣿⠿⣸ ⠀⠀⠀⠃⡷⠘⣷⢹⡀⢠⣿⠀⠀⡀⣾⣧⣇⡀⣿⣿⢿⣏⢠⣇⠀⠀⠀⠀⠀⠁⠜⠀⠁⡏⠰⡯⢀⠀⠀⠀⠀⠀⠀⠃⣾⣀⠁⣼⠀⠇⣸⠀⠀⣿⡇⣸⣿⣯⣼⠀ ⢳⠈⠀⣸⡇⢿⡌⣧⠘⠀⣆⡌⠘⠀⢸⡇⡼⠀⣿⣿⣿⣸⠀⡇⠀⠀⠀⠀⠏⣾⣫⠷⠹⣈⠐⣿⠀⠀⠀⠀⠀⠀⠋⣿⢀⠃⣾⠄⠁⡞⠀⠀⡇⣸⣄⡏⣼⣿⠙⠀ ⠂⢟⠟⢿⡆⡽⢻⡄⣷⠸⠀⢀⢸⠀⢸⡇⣸⠁⣿⢳⣾⠀⠀⡇⠘⠈⠋⡿⣼⣞⢯⣳⣽⢿⣋⣿⠀⠀⠀⠀⠀⠏⣯⢠⠃⡼⢨⠁⡿⢠⠀⠀⡿⢀⠃⣾⠏⣰⣿⠸ ⠀⡎⣻⣬⠳⣌⣳⢿⡈⢳⠘⠀⢿⠀⢠⡿⠡⡟⣣⣿⢠⠀⠀⡇⠿⣿⣿⣿⣶⣴⣤⣷⡿⣿⣿⣿⠀⠤⠀⠈⠇⣸⣸⠁⣼⣇⠀⡟⣰⠀⠀⠏⣰⠁⡾⢥⡼⠁⢹⢸ ⠏⣭⢞⣭⠶⣟⠻⣍⢶⠙⡀⢤⡉⢨⠇⣻⡟⢿⣯⣼⠀⠁⠋⡶⣤⣠⢀⠀⠀⠀⠀⠀⡀⣦⣷⣿⠀⠀⠀⠀⡧⣀⢹⡏⣂⡙⠀⣼⠀⠀⠏⣰⠃⡵⠟⣾⢀⡞⡟⢀ ⢾⣍⠽⣣⣜⠳⣌⣇⣤⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⠟⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢳⠈⠀⠀⡀⢹⡆⢹⠀⠄⠂⢁⠠⠟⣰⠀⢋⡿⣴⠋⡵⡞⢀⢸ ⢞⢣⡹⢧⡌⠳⣀⠰⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣽⠛⠀⠀⠀⠀⠀⠀⠛⠞⠤⠠⠒⠑⠈⠀⠀⠀⠀⣤⠛⠉⠀⡀⢻⣿⠙⠀⠀⠻⡷⣠⠋⡽⣾⣩⠿⢞⣠⠁⡟⢠ ⡜⢮⡙⢢⡜⠣⣀⠀⠋⡿⣿⣿⣷⣿⣿⣿⣿⣿⣻⢞⠤⠀⠀⠀⠀⠀⠀⣀⣀⠄⠤⠤⣤⠠⠀⠀⠀⠀⡀⣷⢿⠿⣿⣿⣿⣿⢿⠻⠿⣿⣿⣿⣾⣴⣠⠉⠟⣴⢀⠀ ⡖⢌⡱⢎⡌⠀⠃⡿⣿⣿⣿⢧⡟⣿⣵⣟⢿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⠶⡴⣤⣀⠀⠀⠀⠀ ⢣⣌⡓⠌⢀⠀⣿⣧⣾⢠⣾⡟⣿⣰⡰⡟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⢀⢧⠀⠀⠀⠀⠀⠀⡀⣄⠳⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⡌⠒⢀⠀⡇⣼⡟⢠⡁⢿⣽⣾⡀⠇⣿⢁⠈⠀⣋⣛⣛⠤⠀⠀⠀⠀⢤⠒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣻⢿⣿⣿⣿⣿⡿⣿⣿⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡜⠀⠀⠀⡇⢸⣟⠀⣿⣾⣇⢨⠀⣧⣿⣿⠸⡍⣯⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠏⠭⠤⠑⠀⠀⣷⡸⣖⣿⣿⣿⢧⣿⣿⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡜⠈⠑⠢⡇⣽⣿⠀⣿⢠⡄⠀⠠⡿⣿⣤⣿⣿⣿⣿⡿⣾⣷⠻⠙⠙⠀⠀⠀⠀⠁⠋⡶⣾⣿⢿⠈⢧⠈⡇⣿⠄⣇⣿⣿⡔⣿⣿⡧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⡀⡄⠀⢠⡄⣿⣷⠀⣽⠀⡀⠀⠃⣿⢠⠀⣿⣀⣄⣿⣿⠈⡇⣄⣷⣿⢽⠢⠎⠈⡄⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⢘⡡⣿⣿⡚⣷⢸⡿⢸⠈⠠⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⡟⠈⢹⠀⠀⠀⡇⣼⠀⠀⡇⢸⠀⢹⡄⣷⡟⢻⠉⣧⣿⢻⣯⣿⠈⡀⣿⣬⣾⣷⣹⣇⣹⡆⣿⢾⠈⣿⣿⡐⣾⠇⣿⢀⠀⠁⠂⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⠀⠀⠰⡇⢺⠙⠈⣤⣻⣈⣾⣶⣽⣦⣿⣦⡻⣤⣿⣿⡆⢹⠀⣇⢿⢸⡀⣯⣿⢢⠀⣷⢿⠀⣏⣼⡏⢣⣿⢠⠄⠀⠈⠀⠐⠀⠀⠈⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⣿⡇⠸⠀⠀⡇⢈⠀⣀⠦⣷⢿⢸⠀⡀⢷⡈⢤⣇⠸⣷⣿⠀⣯⠀⡿⣿⠀⠀⣟⣿⠀⢁⡤⣹⢀⡿⢃⣿⣾⢨⡀⠁⠀⠀⠐⠀⠂⠄⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⣳⣿⠀⠀⡆⠘⠀⠀⠀⡆⣿⣟⠸⠀⡇⢦⠘⠀⣷⠃⣸⠀⣟⠋⣿⢻⠛⠓⣿⢾⡤⠀⠇⢸⠏⣱⣿⣾⢁⠀⠂⠀⠀⠠⠀⠈⢀⠁⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣀⢱⠀⠀⢸⠀⠀⠀⡇⣷⢸⣇⠈⡃⠀⢧⠀⣇⠃⢰⣀⣿⣿⣾⠀⠀⡞⣏⢀⠃⢀⡞⠃⣻⡿⣴⠀⠀⠂⠀⠀⢀⠀⠠⠀⠂⠀⠀⠐⠄ ⠀⠀⠀⠀⠀⠀⠉⠛⡴⣀⢳⡀⠱⠀⡇⠀⠀⠀⡄⡼⢸⠀⢳⠀⠀⡇⢸⡇⡄⠀⠇⣿⣾⢀⠀⡞⣏⣸⠃⢰⠖⢫⣽⡿⢠⠀⠠⢀⠀⠂⠄⡀⠀⠈⢀⠂⠀⡀⠀⠄ ⠒⠒⠄⠤⣤⣠⣀⠁⠀⠀⡀⠳⡈⢤⠑⢠⠃⠀⠀⢣⢸⠀⡇⠈⠀⡼⠀⣼⠀⡅⡾⣿⠀⠀⡀⠟⣼⠃⣠⡁⠏⣿⡼⢀⡀⠀⠈⠠⢀⠀⠂⠄⠀⠀⠄⠀⠈⢀⠂⡀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢆⠑⡀⠠⠈⢣⠀⡄⢸⠀⠀⢸⠃⢠⡇⢀⠁⡴⢁⠠⠀⠃⡿⣰⠀⠀⠟⡿⣾⣠⠁⡀⠀⠐⠀⠁⠄⡀⠀⠁⠄⡀⠀⠐⠀⠄⠀⡁ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⡀⢤⠓⠈⠀⢄⠑⡄⠑⠀⢠⠀⠃⢡⠞⣠⠜⢀⠁⠞⣴⢀⠀⠋⡿⣴⣠⠄⡀⠀⠀⠠⠀⠀⠠⠀⠂⡀⠀⠀⠐⠠⠀⠠⡀⠀⠐ ⠀⠀⠄⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⣀⢤⠒⠙⢈⡀⠠⠐⠁⢋⣤⠀⡠⠀⠀⣠⠁⠉⠛⠶⣤⢀⠈⢀⠀⠐⡀⠀⠀⠠⢀⠁⠄⠀⠈⢀⠁⠂⠀⠠⠀⢀⠈⠄ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⢤⠿⠬⠶⡶⢶⠶⠴⣤⣤⣠⣄⠀⠀⠂⠀⠀⠀⠠⠀⠈⢀⠀⠄⠀⠈⠁⠀⠈⠁⠀⠈⠄⠀⢀⠈⠁⠀ ⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⢀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠄⠀⠀⠄⠀⠀⠠⠀⠄⠀⠀⠐⠠⠀⠐⠀⠂⡀⠀⠐⠀⠐⠀⠈⠐⠀⠈⠐⡀⠁⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠁

⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡍⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⡏⡉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⡞⢞⣤⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⡀⡇⢀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠋⠟⡰⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠊⢲⡉⣍⡯⣼⣤⠡⡽⣜⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢉⠉⠉⠉⠉⠉⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣄⠝⢀⣠⣤⠒⠟⣠⡋⣴⠧⠙⡀⢄⠦⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠯⢒⡤⣠⢀⠀⠀⠀⠀⠀⣀⢄⠦⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠋⡾⣁⣴⠢⠉⠂⣿⣼⢀⢁⡴⡀⣗⠭⠐⡀⢷⠈⠀⠀⠀⠀⠀⠁⠉⠒⠴⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⡿⣰⠏⣣⣴⢧⣿⣾⣠⠐⠋⣠⣍⠲⠙⡀⢄⠀⠀⣿⣚⠖⠤⡠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠚⠴⡤⣠⣀⣄⢤⠤⠤⠲⡖⠳⠉⡏⢸⡧⣴⡄⠳⢈⠀⣄⢶⡿⢿⡷⢑⢸⢄⠘⠀⠀⠀⡀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡦⢸⡄⠀⠖⣫⣰⠤⠛⠛⣼⢀⠁⣜⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠇⢀⠃⡾⣴⢀⠀⠋⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋⠒⠒⠒⠒⠛⠛⠛⠛⠚⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡆⠙⠉⠛⡴⣤⣤⠢⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠒⠤⠠⣀⢀⠀⡵⢧⠙⠀⠀⠟⢧⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣴⣀⠀⠉⠖⡤⣀⣄⠦⡊⠾⠶⠷⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⡇⡄⣿⠸⠇⢸⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠒⠒⠖⠤⡤⣀⣀⣦⣈⣐⣾⣀⣀⣀⣀⣀⣀⢳⠋⠖⡠⣀⣄⠤⠓⠉⠀⣏⢹⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⣿⣿⡟⢹⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⠛⠙⠛⠉⠚⠁⠀⠀⠀ ⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⠿⠿ ⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠈⡄⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣸ ⠀⠀⣄⠙⠀⠁⠉⠛⠟⠿⣿⣿⣿⢿⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⡤⣀⢀⠀⠀⠀⠀⠀⠀⣄⢶⡦⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿ ⠀⠃⠿⡿⣿⣿⣷⣿⣿⣿⣿⣼⣠⢀⠀⠀⠀⣄⣤⢶⠷⠛⠉⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⣿⣿⣿⣽⣷⣿⣿⣿ ⠀⡆⣷⣼⣻⣎⡟⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠷⣙⠊⠈⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣍⣷⢿⣌⣷⣿ ⠀⠀⠀⣀⣤⣷⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠻⠈⠀⠀⠃⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠈⡀⢀⠀⣄ ⠀⠀⠀⠀⠃⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢿⠘⠀⠁⡏ ⠀⠀⠀⠁⣿⣾⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⠙⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⠙⣟⣿ ⠛⠛⠛⡟⣼⠀⣴⣠⢻⠀⠀⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⣶⠁⠘⠀⠀⠀⠁⢰⣆⣿⣻⣿⣿⣿⣴ ⣿⣿⣿⣿⢿⠛⠙⡟⣵⠹⠀⣎⣻⣭⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⡤⣀⠀⠀⠀⠀⡏⠋⠀⣇⣾⣿⣿⢸⠀ ⣿⣿⣿⣿⣿⣿⣿⢻⡄⣻⢿⡉⢄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢠⠀⠦⢿⡄⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢻⣆⣿⣿⢴⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⡇⠔⠤⣎⣯⢿⣟⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡝⢻⠀⠀⠀⣀⠤⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣼⡇⠀⠏⢃⣿⣧⣿⣶⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣽⣿⠻⠉⠋⠛⠶⡤⢧⣟⢿⠻⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣴⣯⢀⡇⠉⣿⣷⢸⡟⢠⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣼⠀⣆⢿⠛⣙⣯⠈⠁⣏⡙⣦⣿⠛⠙⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠆⠾⢸⠀⠀⠀⠁⠉⡋⢶⣤⢁⡿⣿⠛⣽⠋⣿⡶⡤⢀⠀⠀⠀ ⣿⣿⣴⣠⣀⣀⢀⠀⠀⡇⠉⠉⠉⡚⣗⣿⡛⣙⣧⠘⡀⠢⡌⣦⣻⣿⢿⠷⠛⠉⣦⣾⠘⠀⠀⠀⠀⢹⢸⠀⠋⠿⣿⣻⢛⠉⠀⡿⣿⣛⠛⡟⣼⢀⠀⠀⠀⠀⠀⠀ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⣦⣻⣉⣌⠻⠀⡀⢤⡋⣿⣿⢿⣿⣿⣿⣟⣿⠻⠼⣠⢥⣿⢿⠿⣿⣛⣛⣝⣶⢯⡿⣿⢋⠟⡿⣨⠀⣀⢄⠤⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠁⡏⢸⠀⠀⠉⠉⠛⠖⣤⣷⣿⣿⢿⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣰⢉⡟⣿⣿⢿⠳⠙⠈⠀⠀⠀⠀ ⣿⣿⠻⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠀⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⣏⣿⣿⣿⢸⡿⣼⡀⣏⠷⠺⠒ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠁⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⣀⣄⣦⣷⣿⣿⣿⣿⣿⣿⣿⣾⢥⣿⣿⣿⣿⣿⢀⣿⢀⠃⣸⡞⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣽⣤⣧⣿⣡⠞⣿⣇⣿⣿⣿⣿⠇⣸⠇⡿⢁⢻⢠⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⡟⢿⠈⠀⠀⠀⠀⣀⢤⡟⣿⣴⠅⡟⡿⣿⣿⣿⣸⡇⢻⣷⣼⡞⡞⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣼⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⣴⢻⡏⣿⣿⣿⣿⡷⣠⡿⢻⢳⢰⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡟⣸⠃⣿⡻⣿⣿⣿⣼⡟⡏⣿⣼⡼⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣰⠆⠶⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡤⣷⣿⡿⣽⣧⢿⡛⣮⣿⣿⠀⣾⣿⣼⣇⢠⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⣿⣼⣁⡿⠿⠿⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣹⣷⠀⣦⣿⣷⣿⣿⠀⢸⡟⢣⣾⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠇⢡⣿⠻⡿⣿⣯⣿⣿⠑⠊⡙⢨⠍⢄⠠⠀⠅⠿⠯⠿⠻⠚⣿⡇⠘⠄⣗⣾⣿⣿⣿⢻⣸⡞⢠⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣠⡟⢸⣀⣦⣤⣿⣿⣾⣠⠋⡿⢛⠛⠚⠶⣷⡿⣿⣿⣷⣿⢹⣿⡜⢸⠃⡀⢹⣿⣿⣿⣿⠇⢳⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⢹⠈⠀⡟⣿⣽⠟⣴⢏⣫⣴⢀⠋⠟⣶⣯⣿⣿⣿⣿⣿⣿⣸⢸⡇⠋⣿⣴⣾⢹⣧⣿⣸⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣐⡿⣾⡟⣼⢀⡟⣴⢀⠁⠟⣾⢃⡾⣯⣿⣯⣔⣧⣞⣯⠀⢹⣿⣷⣿⡦⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⢻⠀⣿⣿⣸⣀⣞⢠⠀⠏⣣⣿⠞⢳⡞⣳⣶⢶⠧⡼⣀⣿⠏⣿⣰⡇⢸⠘⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⣧⣿⣿⣿⠏⣿⣿⣿⡿⣄⣹⣟⢯⣿⣴⠏⣠⠿⣩⠘⠟⣲⠒⡿⣿⣯⣸⠀⡏⢩⠀⣻⢸⣧⣾⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠋⡝⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣠⡠⢃⡴⣀⠋⡾⢁⠉⡟⣟⣸⣧⢴⣷⢳⠨⢀⣿⢀⣿⢰⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣗⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠈⣹⡟⣿⣴⡀⣁⡟⣿⣿⢹⣿⡝⣼⡜⠬⣦⣿⢧⣼⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣼⣤⣷⣿⣿⣶⣶⣶⣴⣴⣤⢻⡀⣳⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠛⠛⡟⣿⣿⣿⣿⣿⣼⡞⣕⢉⠟⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈ ⠀⠉⠉⠉⠛⠟⠿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀ ⡀⣄⣦⣿⣿⣴⣤⣧⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠛⠿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣼⠀⠀⠀⠀⣀⣦⣶⣷⣿⣿⢻⠈ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣶⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠟⠿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠿⠻⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣸⠀⠀⠀ ⠉⠉⠉⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⠀⠀⠀⠀ ⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣾⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣶⣿⣾⣠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠙⠉⠀⠀⠀⠀⠀⠉⠈⠀⢿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⣄⣤⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣷⣿⣿⣿⣿⣿⣿⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣶⣴⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⣿⢿⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣷⣾⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

SUCK IT UP LOSERS! THESE EMOTICONS R HOT AS FUCK!

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⢠⠀⠀⠀⠀⠋⠟⠶⣠⣀⠋⠞⡶⣠⠀⠀⠀⠀⠀⠀⡀⢀⡀⣀⡉⢛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣾⣴⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣋⠈⠀⠀⠋⠟⡴⣠⠀⠋⠟⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠞⠤⠀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⢿⣿⣩⠉⠛⠿⣽⣉⠈⠀⠀⠀⠁⠋⠛⠟⠶⡤⣠⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣾⣺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢻⢈⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣶⣿⣹⡄⠸⠀⠀⠀⠀⠀⠀⠀⠁⠈ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡷⣙⠈⠀⠀⠉⠞⡴⣀⠀ ⠀⠀⠀⠀⠀⠀⠁⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⡿⣤⣀⠀⠀⠉⠛ ⠀⠀⠀⠀⠀⠃⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠙⠟⣿⣿⣿ ⠀⠀⠀⠀⠀⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿ ⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿ ⠀⠀⠀⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿ ⠀⠀⠀⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿ ⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢾⠲⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠈⢷⠈⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡴⣀⣯⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡙⢷⠜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⡇⣾⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣦⣷⡻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠀⠀⠀⠀⣯⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿ ⠃⡿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣰⠀⠀⠀⠀⠁⣸⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿ ⠀⠀⣀⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠀⠀⠀⠀⠁⡼⠀⠀⠁⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿ ⠀⠀⠀⡄⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⢹⠈⠀⠁⠋⠞⣠⠀⠁⠚⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⣿⣿ ⠉⠉⠉⠉⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⣀⣀⣀⠀⣀⣀⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣤⣦⣶⣿ ⠀⠀⠀⠁⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠀⠀⠀⠀⠉⠉⠋⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣭⢿⠉⠀⡀ ⠙⣿⣿⣿⣿⣿⠛⡽⢩⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡴⢤⠲⣒⣿⣷⣲⣒⣖⢤⣤⣀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⠿⠛ ⣾⣤⣠⢀⠀⠀⠀⠀⡀⣄⢤⠳⠙⠀⠀⠀⠀⠀⠀⠉⠖⡤⢀⠀⠀⠀⠁⡞⢀⡞⠀⠀⠀⠀⠀⠀⠉⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⣧⣯⣿⠻⠛⡛⣽⣭⣬⣦⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠸⠀⠀⠁⠛⡴⢦⠛⠉⠉⠀⠒⠖⣽⠀⡟⢡⠉⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠁⠉⠚⠒⠒⠒⠖⡶⣶⢶⠿⠻⠉⠙⣶⣶⣴⣤⣤⣶⢶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⣶⣶⣒⣴⢀⣆⢻⠀⠂⠐⣄⡶⢀⠂⣰⢿⠶⠷⠿⣿⠀⠀⠀⠀⠁⠞⠴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣦⠷⠿⠿⠿⠿⠻⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⣻⠖⠦⠐⠀⠀⠀⠀⠋⠙⠑⠀⠂⠛⠉⠀⠀⣄⢦⣻⣚⣟⠹⠀⠀⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣻⣙⣄⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡶⣻⢈⠀⠀⠁⠉⠋⠛⠟⡏⣿⣿⠀⢁⠟⣾⣿⣯⢻⠛⠈⠁⣏⣸⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠶ ⠀⠀⠀⠀⠀⠀⠁⠋⠗⣻⠉⠀⡁⢾⡤⣀⢀⠀⠀⠄⣧⣾⣶⣿⣾⡤⣀⠀⢸⠀⣦⣸⣄⣷⣶⡤⣤⣄⠦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⣀⠀⠀⠀⡀⢳⠈⠀⠀⠉⠚⠖⠤⢤⠤⡀⣤⠤⠀⠆⠀⡇⢠⠀⠀⢻⠘⠀⢦⠓⠈⠀⠀⠀⣀⢤⠶⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⢠⠀⠁⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⠶⠒⠓⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠙⠉⠀⠀⠀⠂⠴⣠⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣤⠦⠲⠓⠛⠉⠉⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠳⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⡖⠳⢻⠛⠿⠂⠒⠐⠀⣇⣟⣾⣶⣤⢴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

�🢦🝆🍑�tew lla uoy teg dna flesym yojne ot teg I dna naom uoy fo lla erehw emosevif a otni snrut ,hcihw emosruof a ni yssup dna stit slrig rehtona gnikcuf ,dna stit 'slrig rehto eht gnikcus dna ,ssa ruoy gnikcams yojne I dna kcid eguh ym gnikcus yojne uoy elihw emoseerht a evah ew ,dna lrig rehtona kcip I nehw gninrom lit pots non niaga dna niaga taht od I nehT .gninaom ylsselpleh ereht dnats uoy sa stit ruoy gnikcuf ot kcab og I neht stit ruoy revo lla muc I neht dna muc dna muc uoy litnu taht od I oS "��HHHA !YDDAD YM FO EDISNI YAW EHT LLA KCID RUOY TUP !REDRAH" ;naom dna maercs ot trats uoy drah os stit ruoy ezeeuqs I nehT .niaga naom uoy gnikam toof ym htiw ti gnibbur erofeb semit wef a skeehc ssa ruoy pals I os gninaom no peek uoY .syawedis uoy fo tuo lleh eht gnikcuf trats dna deb eht otno uoy worht dna riah ruoy barg I .etatiseh neve tnod I ,muc htiw derevoc erew taht stit ruoy ees I sa noos sa dna pu teg htob eW .uoy revo lla muc em gnikam ecaf ym revo lla gnitriuqs trats uoy nehT .yssup ruoy fo tuo gnippird strats muc sa deye-ssorc og ot trats uoY .enoyreve pu ekaw tsomla uoy taht ylduol os naom uoy sa yssup ruoy pu yot xes eht evohs neht I .steehs deb eht pirg uoy sa htuom ruoy ni muc ot trats I ylnedduS .kcid ym detaorht peed tsuj dah ehs sa denaom I ,ti debbarg I sA .kcid ym gnikcus ysub llits saw ehs sa ti debbarg I .ot erapmoc dluoc kcid ym neve ton hcihw gnol sehcni 03 tsaelta saw tI .nirg I dna yot xes reh ees I nehT .yssup reh kcil I nehw ylduol snaom neht kcid ym no gnikcus strats ehS .em no gnittis ssa yxes reh htiw em revo syal ehs sa nwod yal I .pu sdnats ehs sa ssa reh pals I nehT .yssem steg ti sa ot snaom ehs hcihw yssup reh edisni muc ot trats I nehT .t'nac ti hguoht neve reh otni rehtruf teg ot kcid ym teg ot thgim ym lla htiw hsup I dna tseuqer reh wollof I "!REDRAH OG DNA EM KCUF !YSSUP YM NI MUC !YDDAD EM NI MUC" ;smaercs ehs hcihw ot ssa reh kcams I .lrigwoc esrever a no reh edir I sa em otno reh hsup I .muc ot tuoba flesym leef I dna spil ym tsniaga snaorg ehS .reh gnissik yb pu reh tuhs I hcihw ot sa ylduol niaga snaom ehS .stit reh ezeeuqs I sa nwod dna pu kcab lla ti hsup I .ssa reh ezeeuqs I dna yssup reh edisni kcab kcid em evohs I sa reve neht no denrut erom m'I .kcid ym fo mottob eht otno gnimmuc si ehs litnu stit reh kcuf I .talf t'nsaw yletinifed ehs ,kceh ,ekacnap talf a naht regral erew taht stit suomrone reh neewteb kcid ym evohs em gnikam ,ylpeed snaom ehs dna ssa taf gib reh kcams I .sehtolc reh nepo pir dna deb eht otni reh hsup I nehT .no erom neve em snrut ti taht ylduol os snaom ehs dna yssup reh edisni peed saw kcid eguh sehcni 8 elohw ym litnu redrah dna redrah og I ,dias taht htiw dna '��yddaD-D' ;tuo spils drow eno sa gnilbmert em ta pu skool neht pil reh setib dna reduol neve snaom ehS .yssup reh edisni peed yrev muc I dna no denrut m'i dna ��snaom ehs ,nwod repeed dna redrah og i sa llaw eht no em skcuf ehS ~�🨫🝆�tumS

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⠻⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⡀⣀⣀⣀⣄⣤⣤⣿⣿⣿⢀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⢠⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⣿⣿⣿⣿⢹⠀⡇⣿⣿⣿⣿⣼⣤⣤⣤⣤⣤⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠛⣿⣿⣿⣿⣿⠀⡇⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣾⣶⣶⣡⣛⣝⣧⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⢸⠀⠀⠁⠋⠛⠛⡙⣈⣀⢀⠀⠀⠀⠀⣦⣿⣿⢿⣜⣷⣿⣿⣾⢠⡏⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⢸⠀⠟⣿⣿⣿⣿⣿⣿⠹⠁⡿⣿⣿⣿⣿⣿⣷⣿⣿⠻⣈⣀⠀⠁⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡀⣷⣿⣿⣿⣶⢀⠀⣦⣿⣿⣿⠹⠀⡟⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⠀⣷⣿⣿⣿⣿⣿⣿⣼⠀⠀⡀⣀⠀⠀⠀⠀⠀⣄⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣸⠀⠀⣄⣶⣶⣶⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠟⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⣿⣿⢀⡟⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣍⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣉⣬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠟⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣤⣶⣶⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠈⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠀⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⣄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠃⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣧⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⡼⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⡿⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⢽⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⣿⠉⠋⠒⠒⠒⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢰⠀⠀⠁⠾⣠⢀⠀⠀⠀⠀⠀⠀⣀⠦⠙⠀⠀⠀⠀⠋⠖⡴⣀⣀⣀⣀⣀⢤⠳⠈⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠃⣸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀ ⠀⠀⠀⠀⡇⢰⠀⠀⡼⠀⠀⠈⠉⠀⣄⠀⠀⠀⠀⠀⠀⠀⡀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⡆⢹ ⠀⠀⠀⠀⣾⠀⠀⠀⢸⠀⠀⣶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⠈⣿ ⠀⠀⠀⠏⢠⠀⠀⠀⢳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⢃⣼ ⠀⠀⠃⣰⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠀ ⠀⠀⣼⠀⠀⠀⠀⠀⠀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⠀⠀ ⠀⡏⢀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⣇⠸⠀⠀ ⠛⣼⠀⠀⠀⠀⠀⠀⠀⡄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⢀⠀⠀⢸⠀⠀ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⢹⢸⠀ ⣄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀ ⠀⡀⢢⠙⠀⠀⠀⠀⠀⠀⠉⠉⡉⣿⠛⠛⠒⠚⠒⠒⠴⠀⠓⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀ ⠀⠀⠀⠀⣄⢾⠿⠛⠙⣀⢀⠀⡀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣟⢲⠚⠤⠿⡤⢀⠀⠀⠀⠀ ⠀⠀⠀⠉⡼⣟⣧⣧⣸⢄⠳⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠘⠁⠋⠟⡸⣀⢀⡞⢀⠏⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⣹⢸⡇⢸⠀⣼⣅⠻⠃⣿⠀⠀⠀⠀⠀⠀⡟⠴⣀⡇⣮⢀⠋⡼⢀⠇⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⣿⢀⡀⢸⠀⢸⡿⠀⣿⢰⠀⠀⠀⠀⠁⠛⣴⠤⠳⡍⢰⠇⣿⣧⠻⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣻⣹⠀⠀⡇⠈⢿⣟⠀⣿⠀⠀⠁⠚⡴⣀⠀⠀⠀⠀⡀⣄⡳⢹⠀⣷⣄⠱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⠸⠀⡄⢹⡇⣈⠀⣹⠀⠆⣠⢀⠀⠀⠁⠉⠋⠒⠒⠀⠀⣀⠦⡟⠘⡀⢷⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⢿⠈⠀⡇⠘⢰⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡷⠈⠀⠀⡄⢻⠀⠀⢧⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⢸⠀⡀⢿⠁⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⠉⠙⠀⡄⠙⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⡇⣱⣼⣆⠀⠀⠆⠇⠿⠿⠾⠀⠀⠀⠀⠀⡞⢿⡿⠳⠛⣏⠻⠀⡄⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢹⠛⣽⠇⢸⠀⢻⠀⠾⡇⣿⢾⣷⠉⠙⠀⠀⠀⠀⣷⣿⠩⣛⣿⡆⢸⠀⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡀⢻⢸⠀⡇⣼⢶⠟⡛⢿⠾⣶⣀⠀⠀⠀⠁⠉⠉⡉⣿⢿⡴⣇⠀⡇⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣶⠻⣿⢸⠀⣄⣷⠛⡉⣿⢀⠁⠉⠛⢾⢠⠀⠀⡀⣏⣿⣼⢠⠀⡇⢸⡇⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡀⣄⢻⠀⠀⡀⢧⡇⣿⣄⣤⣠⣀⠀⠀⠀⠃⠞⣣⣼⠀⠀⠀⡇⢠⡏⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⣇⠀⠀⠀⡀⣧⣿⠘⠀⠀⠀⠁⠋⡴⣡⠞⣠⠀⠀⠀⠁⡼⠃⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⡆⢷⠊⠶⡴⣀⠉⠖⣠⠀⠀⠀⠀⠀⡶⢣⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠚⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⠤⠤⠶⠶⠶⠤⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡈⠰⢳⣌⡳⡷⣞⣽⡻⢖⢫⣑⢣⡠⠜⠃⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⡤⠚⣍⡲⡽⣾⣟⣳⣿⢞⡡⠲⣍⠐⢨⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠡⢃⠤⡙⢦⡹⣿⣳⣼⣻⣷⣻⠬⢒⡩⠔⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡌⠓⣌⡟⣽⢯⣿⣿⡻⣬⣷⠽⢌⡸⢎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢌⠡⡟⣯⣜⡯⣟⣿⣽⣻⡒⣍⢷⠽⢍⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠃⣿⣱⠼⣎⠇⣷⣿⣟⡭⢻⢈⡱⣇⣧⠽⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣮⡱⡶⠎⢃⣇⡸⣷⣿⢺⣿⡌⠙⢢⠱⣎⣮⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⣍⡱⢎⢃⠤⡑⣮⡝⣿⢞⣯⠖⠉⢠⠳⢆⢍⡧⠣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢓⣤⠜⠣⢁⠤⡘⠣⣣⢾⣻⣿⣖⡼⠌⡘⡁⠬⢃⡡⢧⢌⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢏⣠⢄⡀⠠⡀⡄⠂⢑⡧⣮⣟⣟⣿⢿⢂⠐⠠⠄⠂⡠⠔⣍⠧⢎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢂⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡮⣜⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⣟⡿⣿⣿⣿⢬⠀⠀⠀⠀⠀⣄⠑⢢⡔⣝⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠃⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠃⡇⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⢆⡘⡆⡞⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠌⠀⠀⠀⠄⠂⡌⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣗⣾⣿⣿⣿⣿⣿⣿⣾⣶⠀⠀⠀⠀⠀⠀⢀⠀⢉⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠁⢀⠀⠀⠀⢀⠀⢎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣄⣿⣿⣿⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠢⠉⠀⠆⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⡀⠀⠀⠀⠀⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣹⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⢦⣌⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⡌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡗⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡗⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠠⣀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠑⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠞⣳⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠷⣲⢌⡒⡌⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠉⡰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⡿⣿⠻⢎⠜⢣⡄⠘⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠃⡤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⠝⣦⣾⣿⣿⣿⣿⡿⠻⢧⡏⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠂⠈⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠔⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢎⡑⢪⢆⡈⡔⣃⣤⣾⣿⢻⢻⢢⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠻⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠆⢎⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠡⢂⢌⠱⢮⢌⡘⡄⠊⡄⠌⣇⣿⢻⢰⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠑⡉⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠔⣀⠀⣷⡈⠘⢌⡱⢏⢧⡘⢄⠘⢈⢆⡃⢸⢀⡐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠒⡠⢀⠀⠀⠀⡇⠽⠂⠌⠠⡑⣧⠻⢠⠜⠂⢁⡾⣋⡰⠆⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡏⢀⠊⢠⠀⠀⠀⠰⠀⠀⠀⠀ ⠚⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⡡⣿⠒⢀⡌⠁⠠⣷⢻⡙⢉⡼⠏⢐⡹⢆⡑⢯⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣿⠎⢀⠀⠀⠀⠈⡆⠀⠀⠀⠀ ⠂⡀⠀⠚⠀⠀⠀⠀⠀⠀⡀⠱⣮⠻⣈⠄⠡⢉⡟⣶⣿⣶⡞⣳⡟⠋⣡⠴⡚⣍⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⣿⣿⠀⠀⠀⠀⠀⣇⠀⢳⠀⠀⠀ ⠁⠔⢃⢸⠀⠀⠀⠀⠀⠀⡌⠒⣏⣿⣷⣶⣄⡈⡐⠄⠀⠠⢄⠡⠔⣂⣤⡷⠟⣉⡱⢶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⡿⣿⢸⠀⠀⠀⠀⠀⡇⠣⣄⠘⠁⠀ ⡐⡛⡿⠀⠀⠀⠀⠀⠀⠃⡔⢋⣾⢃⢠⡐⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠠⣄⣦⡻⡕⣎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⡿⡷⣿⢸⠀⠀⠀⠁⠉⡞⠷⡵⣪⡑⠠ ⠠⣇⢠⠀⠀⠀⠀⠀⠀⡹⡿⣬⢁⠢⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢶⡝⣎⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠁⢢⡘⣿⣯⣽⠿⠿⣿⣴⣾⣌⡔⢊⠡⢄⡘⠀ ⢞⡇⠈⠀⠀⠀⠀⠀⠃⣿⢴⠊⣸⠱⣈⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⣆⠘⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⢂⡈⡑⠦⢙⣽⢿⣿⣿⣴⠲⣌⠂⢀⢀⠌⠀⠡⠄⠀ ⣜⡿⠈⠀⠀⠀⠀⠀⡟⣹⠆⢋⢿⠻⢜⡩⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢷⣎⠘⠀⠀⠀⠀⠃⡰⠀⠀⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠌⠲⢌⡙⢶⡟⣿⣾⣱⢢⣁⠄⠀⢀⡀⠀⠄⠀⠈⡁⠀ ⢧⣓⢸⠀⠀⠀⠀⠀⣿⣁⠧⣿⣿⣯⢽⣊⠱⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢾⢯⠈⠀⠀⠃⡠⠐⠈⠁⡙⠰⠀⠀⠀⠀⠉⠄⠢⠌⡑⠢⢥⠐⢫⣕⠮⣟⣼⢞⡁⠠⡐⠀⠀⠀⠀⠌⠁⠂⢀⡁⠀ ⣱⡽⢸⠀⠀⠀⠀⠇⣸⠆⡡⣲⢾⣵⢢⢌⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠡⣆⢞⢯⠈⠞⢑⡨⠔⠃⡶⢈⡱⠄⠨⡑⠆⠁⠰⢣⡅⠂⢥⡋⡛⢏⡻⣟⣿⡜⠆⠀⠠⠀⠐⠀⠁⡿⢁⠠⠀⠀⠂⠀ ⡵⡎⢹⠀⠀⠀⠀⡇⢸⠠⢁⠤⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠠⠒⢈⢵⢺⣷⢍⡨⠞⣃⡹⢺⢆⡈⠱⢆⡁⠰⢙⡫⠞⠿⣦⣴⣦⣄⣡⣄⣀⣤⣤⣶⣟⠭⠛⠁⠠⡟⢡⠰⠀⠀⠀⠀⠀ ⡳⢍⡧⠀⠀⠀⠀⡄⢼⡀⠀⡀⠀⠀⠀⠜⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⡌⠄⠒⣉⡗⣣⢦⡝⠏⣩⠷⢚⢃⢅⡛⠾⡼⡶⣂⡐⢌⠂⢀⠠⢂⠁⠠⠀⠀⠀⠀⠀⠀⣀⢦⣳⡝⣿⡑⠠⠀⠀⠀⠀⠀ ⠄⡘⣇⠀⠀⠀⠀⠀⣧⠸⠀⠀⠀⠀⠀⠄⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⣉⠤⡑⠮⣋⢦⣙⠶⣙⡼⠛⢦⡵⣢⠄⡐⠌⢁⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⡑⠠⠀⠀⠀⠀⠀ ⡄⠘⡗⢸⠀⠀⠀⠀⡀⢻⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠒⣈⡰⠞⢋⣥⠲⣹⢖⡣⢑⣠⠘⠡⢂⠄⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡸⠘⠀⠀⠀⠀⠀ ⡂⠑⣯⢸⠀⠀⠀⠀⠀⡇⢸⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⠤⡘⢎⠣⢒⣩⡴⠓⣠⠰⡐⠌⠂⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠌⠀⠀⠀⠀⠀ ⢋⡾⣟⢹⠀⠀⠀⠀⠀⠂⣼⠳⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢢⡑⢃⢣⣌⠓⣠⠰⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠠⠀⠀⠀⠀ ⢾⣷⣮⣗⠈⠁⠀⠀⠁⠆⢴⠤⢦⠶⠻⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⡉⠤⠲⣑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠂⡀⣹⠀⠐⠠⠀⠀ ⣌⠲⢥⡟⢸⠡⠂⠄⠈⠠⡐⠀⠀⠴⠴⣥⣷⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀⠂⢁⡔⠋⣄⡘⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠃⡑⡌⠃⢡⢸⡐⠀⠈⠀⠀ ⣿⣶⣯⣿⣶⢹⠢⢌⠐⢨⠐⠦⠓⠈⠀⠀⣱⢻⠀⠢⠀⠀⠀⠀⠁⠊⠔⢀⠀⠀⠀⠂⠠⢒⡌⠑⡠⠜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠜⠣⡔⠫⡟⣸⠀⢈⠀⠀⠀ ⢱⣞⣎⠁⢫⡴⢳⡘⢆⡁⡐⠌⠁⡄⠳⠀⡇⡇⠻⠙⢇⠀⡀⣀⠀⠀⠀⠀⠀⠂⡁⢂⣁⠔⢊⠠⢄⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡿⢂⣯⠺⠀⠐⣈⠑⠠ ⡟⠣⢟⣾⡌⠑⠬⡈⢴⠦⠒⠙⠈⠡⡆⢿⠬⡷⢿⡻⣧⠻⠙⠉⠉⠃⠟⡰⠀⢈⠀⠐⠠⡐⠈⢁⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠥⠠⠀⠀⠌⢮⡽⢖⢰⢀⠀⠀⠀⡀ ⣿⣿⣿⢻⣛⠿⠶⠶⣤⣶⣟⡼⣖⣉⢦⡷⣹⣟⣿⢟⣳⣿⠸⣀⣁⣜⢀⠀⠀⠀⠀⠀⠀⠛⠄⠁⠠⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠌⡐⡠⠀⢸⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣼⣀⢀⠀⠀⠀⠀⠄⡊⣧⢿⡋⢛⡿⣿⣿⣿⣿⣿⣠⢺⠋⣰⠀⠀⠀⠀⠀⠈⠡⠐⣧⠙⠀⡀⠌⠁⠠⡈⠢⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠔⡀⠀⠀⠀⠇⠀⠀⠊⠠⠀⠀⠀⠀ ⣿⣿⢸⠀⠀⠀⠀⠀⠋⠳⢾⣶⣷⣼⣏⣿⣿⣿⣿⣿⣿⠋⢶⢨⠠⠀⠀⠀⠁⠀⠇⢁⡨⠒⣍⣦⠻⠉⠂⠄⠁⠞⠽⣿⣾⢶⠶⠻⠋⠐⠉⠀⠀⠀⠀⠀⠀⠀⠉⠊⠑⠨⢀⠀⠀⠀⠀⠀⠀⡃⠀⡰⠀⠀⠀⠀⠈⠀ ⣿⣿⣼⠘⠀⠀⠚⣤⣀⠠⠐⠠⠀⢿⣿⣿⣿⣿⣯⣿⣿⣱⢌⠁⠄⠈⠑⠠⠐⠀⡔⠃⣼⠖⡈⠖⡉⣔⢿⠙⡿⢯⣿⣸⠀⠀⠀⠀⣉⣖⠾⣲⠶⠷⠿⣉⢉⠓⠴⠆⠀⣆⠨⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠎⠀⠀ ⣿⣿⢹⣆⠹⡰⠋⡼⣄⢂⡀⠁⡿⣿⣿⣿⣿⣿⣿⣿⢾⡡⠜⡡⠞⠯⡱⡾⠙⢠⠡⡇⣛⢻⣞⠷⢛⡹⡝⣯⢿⣿⣾⢿⠹⠊⠲⢀⠀⠒⢉⠀⠀⠀⠀⠀⠃⡿⠻⡔⠀⠀⡀⠐⠣⠀⠀⠀⠀⠀⠆⠈⠄⠉⡾⢀⠀⠀ ⣿⣿⣿⠊⣧⠏⢠⠈⠕⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⢛⡶⣴⣤⣀⣀⣄⣦⣻⠇⣻⣷⣿⣿⢿⡹⣿⣿⣟⣿⣿⢸⡟⣠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠟⣾⣴⢀⠀⠀⠀⠀⡎⠎⠀⠀⠀⠀⠀⠀⢆⠈⠀⢱⣸⠑⢦ ⣿⣿⣿⢻⡇⣰⠛⣍⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣷⢮⣷⣿⣟⣷⣿⣿⣿⣿⣿⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣶⣶⣴⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣱⣤⢾⠲⢲ ⣿⣿⣿⣿⡿⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣌⢶⡼⣻⣾⣟⣽⣿⣿⣿⣼⢸⡀⠄⠻⠛⠛⠛⠛⠿⣿⣷⣿⣰⢀⠀⠀⠍⠒⢗⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⡥⢀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣼⢀⠉⠂⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠈⠀⠀⠀⡀⠡⡄⣝⢿⣧⣻⣿⣿⣿⢻⡆⠻⠉⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⠀⠀⠀⠀⣆⠸⣄⠹⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⠋⡾⢤⣀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⢀⠀⠀⠀⠀⠈⢂⡇⣏⣿⣿⣿⣿⣿⣿⠙⢧⣿⣿⣿⣿⣿⣿⣿⡿⣘⣿⢹⠀⠀⠀⠀⠀⡇⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⡎⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⡍⣮⣼⣿⣿⡾⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣾⢎⢃⡲⡠⠁⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠊⠊⠋⡔⢿⣿⡞⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣆⣿⣿⣿⠈⠁⠂⠄⠐⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣷⢁⢉⠈⠀⢀⠔⢀⠀⠀⠀⠀⠀⠀⣮⢄⠀⠀⠀⠔⣣⡪⡢⠰⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣧⣿⣿⢸⢀⠀⠀⠣⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟⣻⡱⠋⣿⣛⢟⠿⠂⠈⠀⠀⠀⠀⠀⢀⠀⠀⠁⠊⠐⢏⣘⠤⠙⡄⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠱⠋⡿⣿⣮⢀⠀⠀⠉⣸⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⡿⣿⣾⣿⣿⠹⠋⡿⢸⡿⠁⠛⠚⠿⢿⡟⣿⣿⣿⢿⠀⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠉⠛⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣿⣳⣼⣟⣿⣸⡼⡇⡼⢗⣻⣿⣜⢶⣿⣶⣴⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣫⠛⠿⡿⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡏⣿⡟⡟⣿⣹⣾⡝⣺⣽⡳⣯⡽⢿⠀⡇⢹⠀⡟⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣾⣣⣷⣟⡿⣿⣾⣴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠹⣿⣿⣿⣿⢿⣿⣿⣟⢿⣿⢯⣿⣽⡿⠹⡏⡿⡗⣳⣿⣿⣿⣿⣿⢎⣿⣿⣶⣩⠟⣿⣾⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣧⣿⣿⣿⣿⣿⣿⣿⣽⡯⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣸⣿⣿⣿⣿⣿⣢⣿⣿⢮⣏⣿⣿⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢇⣿⣽⢟⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⣎⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣟⣿⣿⣿⣿⣿⡑⢮⣉⠵⢊⡱⣄⣿⣿⣷⣿⣿⣿⣿⣿⣾⣨⢱⢪⠑⠀⣀⣧⣿⣵⣿⣿⣿⣢⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠤⠶⠶⠶⠶⠶⠖⠤⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⣄⣤⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢰⠀⠀⠀⠀⠀⠀⠀⡀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⠹⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣷⢸⠀⠀⠀⠀⠀⠀⠠⠋⣿⣿⠈⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⢻⠉⠋⠿⠿⣿⣿⣿⠈⠀⠀⠀⡏⢠⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢹⠉⠀⠀⠁⠟⡿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣽⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⡿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⣯⣿⣼⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⣿⣿⣿⢸⠃⢙⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⢿⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⢷⡟⣿⣿⣿⣿⢠⡀⣂⣀⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣾⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠟⣿⣿⡄⣿⣿⣿⠈⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣤⣿⢿⣇⣿⣿⢹⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣇⣿⣿⣿⣿⣿⣻⡟⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⢀⠃⣿⣿⢿⣿⣿⣿⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣰⡆⣶⣿⣿⣿⣿⣷⣿⣿⣿⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⠀⠀⡏⣿⣿⣿⣾⣿⣿⢹⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠛⡟⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⢿⠻⡌⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠇⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣼⣀⣀⣀⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣤⣤⣀⢀⡄⣄⣷⣿⣿⢶⡰⣀⣦⣷⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⣽⣿⣶⢠⠀⣧⣿⣿⣿⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⢷⡶⣀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⠹⢀⠀⡄⢷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣿⣠⠀⠀⠀⡇⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣯⣿⢘⠀⠀⠀⣀⣷⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⣿⣠⠀⠀⠀⠁⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣇⣿⠘⠀⠀⠀⠀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣿⣸⠀⠀⠀⠁⡿⣿⣧⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠘⠀⠀⠀⡇⣿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⣿⣿⢀⠀⠀⠀⡟⣿⢹⡈⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣷⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⢢⠀⠀⡀⡄⣿⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⣿⢠⠀⠀⠀⠃⣿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⡛⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢿⠈⠀⠀⠀⣇⣿⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⣾⢠⠀⠀⠀⠀⡇⣿⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⠹⠀⠀⠀⠀⣿⣿⠈⠀⠀⠀⠀ ⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⡿⣿⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣸⣿⣾⣦⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢸⠀⠀⠀⡆⣿⢹⠀⠀⠀⠀ ⠀⠀⡟⢰⠀⠀⠀⠀⠀⠃⣿⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡟⣿⣰⠀⣿⢸⠀⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⢸⠀⠀⠀⠀⣧⣿⠘⠀⠀⠀ ⠀⠃⣼⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣿⣶⢠⠀⣿⢀⠀⡄⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⢻⠀⠀⠀⠀⡄⣿⢻⠀⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⠀⡟⣸⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⣤⣤⣄⣿⠀⠀⠁⣿⢻⠀⠀⡇⣿⣼⣦⠶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢘⠀⠀⠀⠀⡇⣿⢸⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⠀⠀⣿⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣷⠀⠀⡇⣈⣿⠀⠀⡇⣿⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⡇⣿⢸⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⠟⡿⠸⠀⡇⢸⣿⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠹⠀⠀⠀⡀⣿⢸⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⠁⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢿⠈⠀⢹⣿⠀⠁⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠐⠀⠀⠀⣿⢸⠀⠀ ⠀⡆⢹⠀⠀⠀⠀⠀⡏⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢻⠀⣤⣤⠠⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠸⠀⠀⠁⣿⠀⠀⠀ ⠀⠀⣷⠘⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢻⠀⠀⡇⣸⠀⠀⠀ ⠀⠀⡀⢧⠘⠀⠀⠀⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠿⠙⡏⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠁⣼⢀⠀⠀⠀ ⠀⠀⠀⡀⢧⠈⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣩⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠿⣴⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣧⠙⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⢳⡍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⣿⣿⣿⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠿⣻⣟⠙⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣍⠈⠐⠀⠀⠈⠀⠀⠀⠁⠏⠿⡿⣿⣿⣸⣿⣿⣿⠿⡛⠙⠮⠳⠚⠀⠀⠀⠀⠀⠉⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠸⣀⣤⣷⣿⣼⣦⣷⣿⣷⣧⣿⢸⣿⣿⣿⣾⣴⡇⣾⣠⣟⣤⣠⣧⣼⣤⣬⣶⣿⣿⣾⢠⣇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀⡀⣷⢿⠈⠀⣧⣿⠀⣷⣿⡄⡀⣷⢸⠀⡇⢰⡿⣾⠀⠀⡿⢠⠀⠀⡟⣾⣧⢰⠀⠀⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⢠⠀⡄⣿⢻⠀⡀⣿⢻⡆⣿⠀⠀⡆⢸⠀⡇⠀⣿⢠⠀⡇⣾⠃⠀⡇⣿⢠⡖⠀⠀⠀⠀⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⡆⣿⠀⠀⡇⣾⢰⣿⠁⠀⠀⢿⠀⡀⡏⣼⠀⠀⡇⢸⣸⠁⣿⣸⡖⢠⠀⠀⠀⠀⡅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠘⠀⠀⠀⠀⠀⠀⣧⢻⠀⠀⢸⠀⡇⡏⠸⠀⢸⠀⠀⣇⢹⠀⠀⡿⠁⠀⡇⣿⠄⠀⠀⠀⠀⠀⠁⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠻⠈⠀⠀⠀⠀⡀⣿⠘⠀⢸⠀⠀⢸⢸⠀⢸⠀⠀⡏⣇⢸⠇⢻⣰⠁⡿⣾⠀⠀⠀⠀⠉⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠻⠙⠉⠀⠀⠀⣷⢹⠀⢸⠀⠀⣿⠱⠀⢠⠀⠀⣿⡇⢰⡇⣾⠀⡿⣿⢻⠛⠟⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⠶⠶⡇⣿⠀⢰⠀⠀⣿⡀⠘⠀⠀⠀⢸⠀⠀⡟⢠⠀⡇⣿⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⡆⠀⢻⠀⠀⡇⢀⠀⠀⣀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠄⠀⣶⠀⠀⡄⠀⠀⠀⠁⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠧⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡃⣿⠀⠀⠀⠀⡆⢘⠀⠀⠀⠀⠀⠀⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠻⠈⣟⠈⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣷⢸⣄⢶⡀⣀⣀⣀⣀⢀⢀⠀⠀⠄⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⢸⡀⣷⣿⣯⣿⣿⣿⣲⣗⣿⣯⣿⣰⠃⣿⣿⡑⣣⢟⢺⣿⢹⠟⣹⣟⢴⣡⣿⣿⣿⢴⢄⣤⠥⣩⣜⢋⣠⠋⠒⠤⣀⠊ ⠀⠀⠋⠒⡟⣾⢸⠀⡇⣹⣦⣿⣽⣷⣿⣿⣿⣿⣠⠁⣽⣾⣷⠀⢠⣷⡿⣿⣿⣾⣶⢷⠮⣽⣞⣯⢙⠀⠀⠁⡔⢋⡾⢁⠞⢀⠀⠁⡉⠈ ⢹⠏⣿⢸⡃⢸⢸⠀⡀⣻⣀⣀⣤⢠⡀⣧⣀⣀⠛⡶⣶⢛⠛⣿⠙⠀⣧⣽⢀⠀⠀⠀⢾⠘⣄⡦⡬⣄⢇⣿⡿⣿⠿⣾⠀⠀⠀⠀⠃⠙ ⣿⣿⣿⣿⡞⡇⢸⠀⠀⡿⠙⠈⠁⠚⠊⢠⠀⡜⠓⠖⠠⠀⠀⣀⣀⢦⡟⣻⢝⠳⠟⠸⢹⣿⠘⠀⡀⠀⣤⣿⣿⣿⣾⢀⠀⠀⠀⠋⣿⣿ ⣧⣿⣰⣄⣿⣿⢀⠁⠋⣿⠟⣷⣺⡴⠋⠀⡎⢀⠀⠀⠀⠀⠀⠀⠃⠀⡄⣻⣄⢷⣜⣤⣶⣿⢾⠀⠀⠀⠀⡀⣧⣴⠀⠀⠀⠋⠞⢻⣌⣦ ⡀⢀⠀⠄⣻⣾⡴⣀⠀⠁⡞⣠⠀⠇⣱⠏⢸⠉⠉⠀⠁⠀⠁⠋⣿⠀⠀⡄⢷⠘⢶⠿⠻⡙⣮⠿⠙⠉⠉⠉⡀⢦⠿⣿⣿⣻⣮⣿⢿⠈ ⠀⠀⠀⠀⣀⠀⠛⠏⣴⣠⣀⠀⠞⢣⡿⣶⣷⢾⣶⣤⣤⣀⣆⣴⢀⠀⠀⠀⡆⢳⠈⣧⣈⣤⣦⢷⡻⢛⠉⡉⢭⠭⣭⣋⡟⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠃⡾⣤⢀⠀⠋⠴⣀⠉⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⣄⠙⠀⠀⠀⣀⢤⠳⠟⡈⡀⣷⣿⣿⣿⣿⣿⣿ ⠀⠀⠄⡤⣠⠁⠉⠀⡿⣾⡤⣃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡑⢦⠙⠀⠀⠀⣆⣙⢧⠙⡄⣿⣿⣿⣿⣿⣿ ⠀⠉⠟⣿⢿⣡⣿⠙⣰⠀⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡆⠘⠀⠀⠀⠀⠀⠀⠒⢗⠙⢌⠠⠒⠒⡙⠹⣷⣿⣄⣿⣿⣿⡿⣿ ⡿⣿⣿⣾⡇⣾⣅⣼⠀⡁⣸⠀⠀⠀⠀⠀⢄⠙⣀⢄⠤⠲⠛⣿⠈⠀⣸⠃⠘⠁⠙⠈⠓⠛⠀⡇⣾⠻⠉⠀⠀⣄⡴⣿⢹⡀⣿⣷⣿⣿ ⣿⣿⣾⠀⠀⠃⡼⠆⠻⡟⠈⠀⠀⠀⠀⠁⠊⠋⢷⠠⠀⠀⠀⣀⢦⠑⢉⠁⡋⡟⣿⣿⣰⡁⠟⣿⢸⡄⣸⣄⠦⠒⣿⣶⣴⠤⡤⣤⣡⣯ ⣀⣄⢠⠀⠀⡿⢀⠄⡤⣿⣿⢿⠿⠿⣶⣤⢀⢶⠀⢧⠈⠀⠀⠀⠀⠀⣧⣿⣿⣟⣿⣿⠿⣿⣾⢠⣇⠀⢷⠀⠀⠀⡇⣬⣀⣸⣀⣀⣤⣿ ⠀⠀⠀⠁⡾⢀⠀⠀⠀⢹⡄⣷⠮⠹⣈⢀⠀⠳⠈⠀⢷⠀⠀⠀⠀⠀⠀⣆⣿⣈⣀⣀⣇⣿⠛⠖⣿⣸⣇⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣿ ⠀⠀⠆⣷⢹⠀⠀⠀⠀⣿⢿⠙⢦⠘⣇⠿⠛⠀⣧⠙⡄⢻⡟⢰⠀⠀⠀⠀⢆⣎⠙⠀⡤⢸⢇⠀⣻⢸⡇⠀⠀⠀⡍⢻⠈⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⣇⠳⠙⠀⠀⣿⣄⣿⢮⣿⠘⡀⣦⢿⡙⡸⢧⣏⣿⠘⠀⠀⠀⠀⠋⣷⣦⠘⠇⢸⡀⢻⣾⢹⡿⠻⠉⣞⣀⣄⣿⢤⠷⠰⠇⢀ ⠀⠀⠀⠀⠀⠀⡀⢦⠈⡇⢼⡀⢷⡌⣿⠈⡄⠳⣄⢿⠀⣧⣽⢸⠀⠀⠅⡿⢀⠀⠠⣿⡇⢰⠀⣿⠇⣾⢏⣾⣥⢰⠉⠃⡟⠸⡄⢹⠉⡞ ⠀⠀⠃⠈⠀⠀⠀⠀⣏⣿⣿⠈⡀⢧⡌⢷⠀⠀⠀⣆⢸⡞⣧⢰⠃⠀⠃⣼⢿⠀⠀⡇⣿⠀⠇⢿⣿⡿⣶⠖⠠⠀⢰⠏⣠⣧⠀⡁⣿⢀ ⠀⣀⡀⠉⣠⠀⠉⠔⢁⢰⣧⢿⠈⠀⢧⡄⢹⠀⠀⠀⣿⢀⡟⢸⡄⠄⡠⣗⣷⢳⠈⡇⢸⠀⡏⢀⠃⣼⠀⠀⠀⠀⡇⣾⣦⣾⠀⡔⠀⠀ ⠋⡰⠂⠃⠁⣏⢛⢠⡇⠛⣼⣿⣿⠙⠄⠀⡄⣴⠠⠁⣸⠇⢰⠀⠀⠀⠀⡆⠀⠀⢧⡇⢀⠇⢸⠁⡾⠀⠀⠀⠀⠏⣿⢀⡏⢻⠐⠀⠀⠀ ⠀⠀⠂⡄⠰⣿⢠⠀⡇⣿⢻⣆⣿⣿⠙⠀⠀⠀⠁⡞⢁⣿⠴⠰⠀⠀⠀⠇⠞⠉⡏⣿⠀⣿⢹⡿⢠⠀⠀⠃⡿⣿⢠⠇⣾⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⣠⢳⠈⠀⣿⣿⢻⣧⣿⣿⠰⠀⠃⣰⠁⡼⣀⠀⠀⠀⠀⠃⣿⡾⢀⠀⣟⡿⣿⣶⢶⠒⠛⠷⣿⣿⢠⠋⡴⢀⠉⠉⠀⠀⠀ ⠉⠀⠀⠀⠀⠁⠋⣹⠈⢇⡈⣄⢢⣿⡈⠀⠁⣰⠁⡼⠀⡀⠀⠀⠀⠞⣩⣙⢻⠉⠏⣿⣴⢀⠀⠀⠀⠀⠀⠀⣀⣦⣷⣠⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢀⠄⢀⣀⢦⣟⢴⠀⣄⢷⠉⣋⠖⣠⠀⠀⠀⠀⠀⠂⠄⠀⡀⣦⣚⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢣⠀⠀⠀⡀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠋⠻⠀⠀⠀⠀⠂⣰⠀⠀⠀⠀⠀⠀

⠁⡟⣿⣿⣿⣿⣿⣶⣴⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿ ⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢷⠼⠾⠶⠶⠷⠿⠿⠤⣤⣯⣿⡋⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠙⣿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡿⣿ ⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⡟⣿⣠⢀ ⣶⣷⢿⠘⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⠿⣾⣶⣴⣤⣠⣤⣦⣿⣿⠙⠀ ⠀⠀⣿⣿⣿⣾⣶⣶⣿⣿⠿⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠻⠒⠀⠀⠉⠛⡿⣾⣴⣦⢸⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⠈ ⠀⡏⣿⣼⢀⠀⠀⠀⠀⠀⡀⣾⣤⣶⣿⠿⠛⠙⠈⠀⠀⠂⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣴⣠⢉⠋⠟⠿⣶⣤⣧⢻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸ ⠀⣿⣾⠀⠀⠀⠀⠀⠀⠼⡦⢸⠀⢹⠀⡀⣀⣤⣦⢷⠿⠛⠛⡉⣤⢳⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠛⠈⡁⢛⠿⣾⣴⣠⣇⠙⠀⠉⣿⢰⠀⠀⡟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸ ⡇⣿⢸⠀⠀⠀⠀⠀⠀⣧⠸⢧⠈⣆⢻⠈⠀⠀⠀⠀⠁⣏⣤⣧⣿⠿⠙⠟⣿⢸⠀⠀⠀⠀⠀⣄⣶⣿⣿⣴⣆⠻⠈⠀⠀⣀⣀⣀⠀⠀⠋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠃⡴⡏⣿⢀ ⠀⣿⢽⠳⠈⠀⠀⠀⠀⡇⢸⠀⣄⠳⡉⣤⠶⠲⠞⠶⣤⢁⠋⣴⠀⡄⣷⣿⣀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢰⠀⠀⣄⣦⠳⠙⠉⠉⠛⠖⡴⣠⠀⠀⠀⠀⠀⠀⠀⠁⠞⢠⠋⣿⣸⠋ ⠘⣇⣿⠘⢦⠘⡆⢶⠷⡾⢿⠾⠶⠰⡀⣄⢤⠶⠶⠴⡤⣠⢀⠀⠀⠀⡇⣿⠸⠀⠀⠀⠀⠀⠀⠀⡆⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⣀⠀⠟⣿⣽⠟⣿ ⢿⠈⣷⣿⠙⡀⠢⠀⡿⢀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠴⣠⠀⠀⠋⡿⣿⣿⣿⣿⣿ ⣿⣿⠻⣮⣿⠻⠈⠀⣄⢶⡗⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠐⢏⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⢻⠉⠀⠀⠀⠀⠀⠀⠀⠄⡠⣀⠀⠀⠀⠁⠛⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⡀⣀⢤⠤⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⣿⠿⠛⠙⠉⠉⠉⠉⠉⠋⠛⠿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠛⠉⠉⠀⠀⠀⠁⠉⠋⠛⠿⣿⣽⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠛⠾⣤⣤⣤⣤⣶⣶⣷⣭⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣀⠀⣀⣀⣤⢤⠤⠦⠴⠀⠀⠀⠀⠀⠀⡤⣤⣀⣀⠀⠀⠀⠀⠀⠉⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠉⠀⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢹⣀⠀⠀⠀⠁⠁⡁⣉⠀⠀⠀⠀⢀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⡰⠀⠀⠋⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠻⠀⠀⡇⠵⠤⡠⣀⢀⠁⡿⣿⢿⠼⠤⠤⠤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠁⠟⣰⠀⠀⠋⣸⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⠀⡀⡼⠀⠀⠀⠀⠀⣈⢀⡀⠉⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⡠⠀⠃⡴⡐⠀⠋⡴⣎⠀⠁⣴⠁⠉⠉⠉⠋⠙⠀⠀⠀⠀⠀⣦⠘⣄⠘⠀⣆⢹⠀⠹⠀⠃⢿⠈⠃⣿⠻⠛⢿⠐⠀ ⠀⠀⠀⠀⡀⢀⠀⠀⠃⣾⢠⠀⡴⢀⠎⢀⠁⡞⣠⣒⣄⣠⣀⣀⣄⣦⢷⠘⠀⠀⠀⣌⢷⠆⠈⡀⣏⠙⣿⠿⡿⣷⣿⣿⣴⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⠀⠀⠀⠀⠋⣠⠀⠀⠀⠀⠊⠤⣀⢄⠓⠀⢄⠑⠀⠀⠀⡀⡾⢿⣚⣖⢸⡇⢿⣿⡀⣿⣿⠀⣷⣿⢡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠃⠰⠀⠀⠀⠁⡜⢀⠀⠀⠀⠃⣹⠀⠀⠀⠀⠀⢇⠈⠀⢇⡄⠸⠀⢁⣧⠼⠀⢸⡀⣿⣸⠀⣷⣸⠁⡇⢸⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠟⣠⠀⠀⠀⠀⠀⡆⣿⢿⠛⠛⠉⠉⠛⠀⠀⠀⠀⢆⠈⡀⡄⢿⠄⢣⠘⣄⠀⠇⠸⠁⠸⠀⡿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠟⢫⠠⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣤⣶⣰⠀⠀⠀⠀⠀⣄⠈⠀⣿⠸⠀⠁⠋⠀⡷⢿⡿⣴⣣⣿⢹⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⢡⢿⢠⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⢎⡧⣾⣧⠀⡄⣿⣿⠀⡟⣸⣷⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⣱⡟⢰⠀⠀⠊⠒⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣸⣄⠇⠸⠀⠋⣿⣿⠮⣴⠀⡀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⣿⠈⠀⡆⣿⣿⢼⠀⠀⠘⠀⣇⠺⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⡟⣿⣿⢸⠂⡿⢿⡿⢿⣷⣿⠧⣿⢻⠈⡇⠘ ⠁⠀⠀⠀⠀⠀⠀⠀⡘⡀⣿⣿⠳⠉⡉⣉⠟⠸⡟⢻⢹⡿⠐⠸⠀⠃⠿⠽⠸⠀⠧⠟⣷⣼⣧⣿⠜⢠⡇⢿⣿⢀⡇⣿⠘⣿⣷⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⡆⠑⠉⣿⣿⠹⠈⠏⢿⣿⣾⣣⣿⣴⣷⠀⢸⢦⡙⣤⣤⢀⠁⡞⢁⡏⢀⡏⣿⣿⢀⡇⣿⢰⠀⡿⣾⢿⣿⠀⣆⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣽⣷⣿⢻⣿⣿⣿⢃⣿⣻⠀⡄⡿⢰⠁⡕⣏⠾⣡⣟⢠⡽⠊⠏⣷⣼⡄⠰⡆⣰⠁⡟⣿⢀⣧⣿⢸⠀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⣦⣿⣹⣿⠻⣮⢀⡿⣻⣿⣾⠃⣿⠛⣿⣹⡟⢟⣯⢡⡿⣟⠴⢁⡰⠀⠘⠀⠀⠁⡿⣤⢁⠉⠀⡇⠿⢉⡿⡟ ⠀⠀⠀⠀⠀⠀⠀⠆⢷⠘⠀⡀⢦⡿⣿⢿⡈⣦⣿⣧⢿⡿⣿⣿⠻⡉⣤⣿⣶⣴⣠⠁⠟⣷⣄⡥⣭⠀⠀⡟⣼⠀⡿⣿⠻⡯⣿⣀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣄⣶⣷⠻⣆⡻⣿⣿⣾⣶⣴⣤⣀⢀⠀⡀⣁⣛⣟⡶⣶⣤⣦⠀⠃⣿⢸⠀⣇⣸⣷⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⠉⠀⠀⠀⣄⣤⠶⠲⣇⠤⡒⠱⣉⣊⢀⠀⠀⠀⠀⠀⠀⠀⠤⣇⠹⠁⢌⠲⠛⢰⠀⡿⣿⢻⠀⣿⢸⡀⣿⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢄⠲⠙⠉⠀⠀⠀⠀⢱⠊⡴⢀⠀⠤⡤⣤⠀⠀⠀⠀⠀⠀⠀⢧⠒⠒⠂⡜⠀⡟⣿⣀⣿⠸⡇⢰⠀⣴⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠼⠢⠒⡒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁⣀⣀⣄⢀⠏⣿⢰⠀⣆⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠤⠤⡭⢤⠤⠠⣀⣀⣤⣀⣀⣀⣤⣠⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⣿⣿⢿⠲⡷⣿⣿⣿⡿⣿⣿⢶⠻⡙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣶⣶⣤⣤⠀⡀⣿⣿⣿⣿⣿⣿⣿⢿⣛⣽⢷⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣴⣀⠀⠀⠀⠀⠀⠀⠓⡈⣱⣀⣄⣤⣤⣤⣶⣶⣷⣿⡿⣟⢭⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡱⢧⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⢶⠷⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠒⠄⣡⣟⣾⣠⠀⠀⠀⡇⣮⠘⠀⠀⠀⠀⠀⠀⠀⢆⣎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠳⠙⠀⠀⠀⠁⠋⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣴⢀⠀⠀⠀⠀⠀⢸⢻⠉⠚⠒⠒⠒⠒⠛⠉⢩⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⡇⣿⣿⣿⣿⣈⢧⠻⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡿⣴⢀⠀⠀⠀⠀⠀⠀⠃⢿⡴⢀⠉⠐⠀⠀⠀⠀⡀⣄⢻⠈⡧⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠼⠷⠘⣀⢷⡍⣿⣿⡿⣿⢿⠈⣧⣿⢿⠿⠻⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠏⣿⣠⠞⣠⢀⠀⠀⠀⠀⠀⠀⠋⣿⢿⡈⣧⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⠙⠀⠀⣄⣷⣿⣿⣿⣻⣿⠻⣿⣿⣿⣿⣿⠰⠛⠒ ⠀⠀⠀⠁⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⢱⡼⠀⠀⠀⠀⠀⠁⠋⠞⣴⣤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠈⡀⣧⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⢙⠉ ⠀⠀⠃⣴⢀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣾⢰⡤⠀⠀⠀⠁⠋⠶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⡏⢋⠀⠀⣇⣿⣿⣿⣿⢿⣾⣿⣿⣿⢿⢻⣙ ⠀⠋⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡟⢻⠈⠀⠉⠛⠾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠟⣠⠁⡿⢟⢠⠀⠏⣠⡀⣧⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿ ⠃⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣄⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢠⠏⣿⡀⣿⠃⡴⢀⠀⠀⠀⡄⣿⣿⣿⣿⡞⣿⣿⣿⣿ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠞⠀⠀⠃⡰⠃⡽⢞⣧⠀⣾⢀⠀⠀⠞⠀⠀⠀⠀⣦⣿⣽⣿⣞⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠟⣣⡼⢀⡇⠀⢸⠀⠂⡴⢀⢈⠀⠀⠀⠀⣄⣷⣿⢿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠈⠀⠀⠀⠀⠋⠀⠀⠊⠀⢠⠋⡿⣴⠏⣠⠀⠀⣾⠀⢻⠁⠛⠛⡿⣺⠀⠀⠀⠀⠀⡇⣿⣿⠹⣿⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣴⠁⠞⣿⡴⢀⠀⡟⣠⠁⡿⣿⣰⠄⢀⠉⠞⡴⢀⠁⡶⣿⣽⣀⠀⠀⠀⠉⠟⣿⠁⣿⣿⣿⣿⡄⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠴⠦⠻⠀⠀⠃⠔⠁⠐⠀⠁⠞⢀⠏⡰⣄⢀⠀⠟⡟⣡⠟⣿⣿⣸⠁⠋⡿⣉⠉⠉⠀⠀⠀⠀⣁⢿⠀⠋⡿⣿⣿⣿⣷⣿⣿⣿⣿⢺⡸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢁⡜⢤⠷⠙⣇⠴⢠⠋⡴⠁⠞⣠⠋⡴⣧⢹⠀⠋⡤⡏⣿⡿⣿⣿⣿⢸⣀⣿⢠⠀⠁⠋⠛⠛⠿⣭⣻⣿⢟⣿⣿⣿⣾⣀⡏⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢠⠀⣠⠀⠁⠞⣠⢧⠉⡞⣁⠞⣠⠃⡜⢀⠁⡟⢹⡞⢀⠃⣿⣿⣿⣿⣿⣿⠈⠀⣄⣷⣻⣛⣋⣿⣿⣿⣿⣿⣿⣾⣴⣿⣿⢸⠉⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⠀⠀⠀⡀⠀⠀⠀⣄⠿⣰⠀⠀⢀⠀⠟⣴⣟⣿⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣖⣿⣤⣠⣀⠁⡟⣿⣿⣠⣇⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⣴⢀⠀⠀⠂⠛⡿⢈⠀⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠂⠓⡟⢀⠀⠁⠉⣿⠼⠤⣁⡿⣿⣿⣸⠀⡿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⣤⣠⣀⣁⣼⣧⣻⢈⠀⠁⠉⠀⡟⣀⢷⢧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠋⣴⣤⣀⣀⣀⠀⣇⢻⠞⣿⣿⣿⣿⢸⠇⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠂⠒⠛⠿⣾⣶⣴⣠⢀⠄⠤⢀⠉⠟⣿⢙⠟⡿⢸⠁⣸⠀⡄⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢸⠀⠀⠀⠀⠀⠋⡷⣸⡟⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠃⠛⠈⠀⠐⠀⡁⣸⠀⠁⠋⡿⣿⣿⣛⡿⣿⣿⣽⢀⠀⡟⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⠀⠀⠁⠟⡴⢀⡇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠘⠉⡈⣄⢦⠛⠉⡍⣯⣿⣛⢛⣿⣿⣿⣿⣿⣼⣠⠃⡼⠃⣼⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⠛⠞⣹⢀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⢻⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣇⣿⢻⠞⣴⠀⡟⢰⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡏⣿⣿⠈⡇⠈⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⢿⡈⣆⣽⣷⣿⣭⣤⣧⣙⢁⠋⠚⠴⡷⣿⣿⠀⠀⠀⣿⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢻⡄⢸⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿ ⣿⣿⣿⠙⡄⢿⣿⣿⠿⠙⡀⢷⠙⠀⠀⡇⣿⣿⠸⠀⡇⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠘⣧⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿ ⣧⣿⣿⣿⠻⡎⣿⣿⣿⣿⢿⠽⣦⠷⠾⡷⣿⣿⢿⠶⡷⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿ ⢿⣎⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⢿⡙⣦⡿⣿⣿⣿⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⣿⣿⣿⣿ ⣿⣿⣝⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⣇⣿⣿⣼ ⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⡇⣿⣿⢹ ⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⡟⣿⣿⡇ ⣿⣿⣿⣿⣿⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣿⣿⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠁⣿⣿⣸⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢹⠋⣿⣿⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⡏⣿⣿⢠⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡿⣿⣿⢸⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡇⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣷⣿⣿⣿⣿⣿⣿⣸⡿⣿⢿⣿⠀⠀⠀

⡇⠀⣄⢶⠻⠈⠁⣿⣻⠛⠛⠛⠛⠛⠿⠻⣘⢈⣀⣀⣀⣤⣴⣰⣄⠶⠶⢿⡶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣷⢿⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡄⣠⢰⠀ ⡟⠀⠀⠀⠁⣞⣴⣀⢀⠀⠀⠀⠀⠀⠀⡀⣀⣤⢶⠿⠛⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢹⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⡔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢶⠻⠈⠀⠑⢸⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠹⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⢳⠀⠀⠀⠀⠁⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⡇⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀ ⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡙⢦⠛⠛⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⣧⢸⠀⡆⠘⠀⠁⣯⡋⣿⣿⠈⠁⠀ ⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⢿⠀⠉⢿⡿⣿⣿⣽⣄⣤⣧⣾⣷ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣾⢣⢿⣿⣿⣿⣸⠀⠁⣏⠻⠞⣶⠙⠉ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⣀⢀⠀⣿⣿⣽⢀⠀⣏⢾⣠⢀⠀⠀⠁⣽⢉ ⣏⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣽⠩⠉⠉⡏⣼⣀⣀⣧⡴⣸⠀⠀⠁⠀⠀⡇⣹⡀ ⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡿⣿⣿⣿⢼⣿⣤⣤⠶⡿⣠⠀⢰⠀⠀⡆⠀⠀⣏⣿⢿ ⣵⣾⣷⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠀⠀⡀⣀⣄⣤⣧⠻⠓⡽⣿⠶⠤⣤⣤⣤⣤⠤⠦⢻⣿⢠ ⢖⣽⠉⣿⣾⣤⢦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⠀⠀⠀⠀⠀⠀⠀⡆⢻⠉⡞⣠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃ ⠀⠀⣀⣧⠈⠀⠀⠀⣀⢤⠲⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢧⣾ ⠀⠀⠀⡄⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⡿⢠⠀⠀⠀⠁⡟⣉⠈⠀⠀⠀⠀⡇⢙ ⠀⠀⠀⠀⡄⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠞⡤⢀⠀⣀⠦⠒⠖⠤⠤⠬⠯⠾⠓⠓⠛⠉⠀⠀⠀⠀⠀⠁⠋⡿⣴⢀⠀⠉⠛⡿⣇⣷⡾⢳⠀⠀⠀⠀⡇⣸ ⠙⠀⠀⠀⠀⡀⣦⢿⠁⠀⠀⠀⠀⠀⠀⠁⠋⠟⣿⡘⣄⠦⠑⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣿⠿⣿⣿⢿⣿⣿⣿⡿⣭⣿⣴⢀⠉⠞⣿⢂⡿⣿⠀⡇⢈⡄⠿⠷⠙⠀⡏⠀ ⡆⢿⠙⠀⠀⠈⠀⡀⣄⠦⠒⠓⠛⠟⡿⣿⣿⣿⣿⣿⠻⠈⡿⣻⠀⠀⠀⠀⠀⠀⠁⠞⡴⢀⠀⣀⣀⣀⣄⣤⣷⣿⣠⣇⣿⣦⣷⣿⣽⣟⡿⣿⠈⡄⣿⠘⡆⢸⠀⣆⡜⣠⠀⢻⠀ ⠙⡀⣦⠻⠈⣄⠳⠈⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣻⠈⣄⣷⣿⣟⢠⢷⠈⡀⢧⠈⣇⠉⠁⢸⠀⠀⣼⠉ ⣦⢻⠈⡀⣦⠻⠈⣄⠳⠈⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⣷⢿⠈⠀⣄⣿⠀⡁⣿⠙⡟⣼⣤⣿⣿⢰⠀⠏⣴⣠ ⠉⡄⢷⠙⠀⡀⣧⠻⠈⣄⠳⠈⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⡉⣬⡷⡿⣿⣿⠘⠀⡇⢼⡞⢀⠀⡾⢀⡏⣿⣸⠋⡴⢀⠀⠀ ⡁⢦⠙⣄⢷⠛⠀⣄⣶⠻⠈⣆⠹⠀⠀⠀⡀⣧⣿⣼⣿⡈⣿⣠⠀⣿⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣟⠻⣿⢹⣄⢷⠀⠀⣿⢠⠆⡾⢀⠇⣾⣼⠀⠀⠀⠀⠀⠀ ⡀⢦⣗⢿⡛⣮⢮⠙⠀⡀⣄⠳⡈⢣⠈⠀⠀⠃⣿⢸⡄⢹⣄⣧⠿⣼⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣷⣼⣤⣿⢻⠈⠀⠀⣄⢻⡾⢀⠃⣰⡇⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⣷⢿⣎⡻⢮⠙⠀⠀⣤⠻⣌⠹⠀⡇⣧⢸⠀⣆⠹⠏⣷⣿⡿⡆⠹⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⡟⢀⡄⣷⠛⣿⡇⢾⠙⢰⠇⣼⢀⠃⣼⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣦⡻⣿⡹⢄⠳⠈⠂⣧⡻⢮⣸⡇⢿⠀⠀⣆⣻⡂⢿⣄⠳⣿⠘⠀⠿⣸⣿⣙⢿⠋⡟⢻⠀⡟⢨⠀⠀⠆⣿⣿⠀⢻⣶⠞⣧⠀⠁⡾⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢿⠈⣄⠳⡉⣦⣿⣮⡖⣿⠹⠀⠀⣆⢿⣮⠹⠀⣄⢷⡟⣿⣿⣿⣿⣿⣷⣿⠠⡟⣱⢠⠀⠀⠀⡆⣿⠀⡁⡼⢀⡌⠋⡾⢀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣮⠻⠈⣄⢶⡙⢯⠙⡀⣄⢦⠙⠈⡀⣷⣿⢱⠀⠀⣄⣶⣿⣛⣉⠉⡟⣿⠿⣾⠀⠀⠀⠀⠀⠀⣽⠀⣠⠀⠁⡟⣼⢀⠁⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢳⣄⠻⠈⡀⣦⣹⢦⠙⠀⠀⣄⠲⠀⣄⣳⢪⠈⠀⠀⡀⣤⣳⣬⣷⠀⣿⢀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⡿⢀⢣⠟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⡀⢤⠁⠀⡄⠰⡀⢦⠙⠀⠀⠀⠀⠀⣤⢷⠘⠀⠀⠀⠀⣄⡶⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠐⠋⣷⢦⠃⣴⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠣⠀⠀⠀⠀⠡⡱⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡏⢈⠀⠀⠀⠃⠇⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠁⡐⠀⠀⠀⠀⠀⢰⡰⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠁⠜⢀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠪⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⠠⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡎⠹⡑⠠⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀ ⣤⠀⠀⠀⠋⡴⢣⠑⠁⠊⠓⠘⠀⢀⣼⡗⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⢠⠀⡙⡰⢀⠀⠀⡀⠃⡌⠀⡀⠢⠒⠒⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⣸⠀⡎⡼⠀⠀⠀⠀⠀⡅⢰⢀⡤⠑⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⠀⠁⢆⠀⠀⠀⠀⠀⠊⡿⠀⠀⠀⠀⢣⠁⠊⡕⠘⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⣧⠀⡏⠹⠀⠀⠀⠀⢱⢹⢣⢠⠀⠀⠀⡏⡉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⡆⠙⣴⣞⠀⠀⠀⠀⡇⣾⢠⠀⠀⠀⠀⣹⣸⠀⠁⢴⠢⠈⠀⠀⠀⠀⠀ ⣿⠀⠀⣷⠀⢱⠀⠀⠀⠀⡎⢀⠀⠀⠀⠃⠟⡘⠀⠀⡈⠇⠁⡄⠠⠀⠀⠀⠀ ⣿⠀⠀⡀⢤⡐⠣⠀⠁⠗⢀⠀⠀⠀⠀⡏⣕⠈⠀⠟⢈⡇⠀⡀⣊⠛⠨⠀⠀ ⣿⠀⠀⠀⠀⠀⡁⡋⣠⣆⠙⠉⠁⠂⡤⢁⠋⢼⡗⣿⢠⡇⠀⠀⡀⡢⣸⠑⠀ ⣾⠀⠀⠀⠀⠀⡇⢹⠈⠀⣻⣧⡳⣈⢑⣄⢹⣧⡜⣾⠈⠀⠈⠈⠀⠀⡄⠤⢠ ⢸⠀⠀⠀⠀⠀⡄⣷⣹⣴⠀⢽⢳⣌⠱⠣⣧⡄⠻⣰⠀⠀⢹⠄⠐⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣥⠘⣆⣿⠎⣿⠉⠈⡔⢱⠏⠛⢃⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⡪⣏⠇⣿⣿⢻⢛⡄⣢⣞⣿⠐⠀⠀ ⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡱⡴⢳⣿⣟⡌⢦⢟⣕⣩⠐⠀⠀⠀

⠀⢇⡿⠀⠀⠂⠂⠓⠛⡶⢠⠀⠄⣀⣒⣍⢨⢺⡞⠘⠀⢳⣧⠀⠀⢃⠠⠀⠀⠀ ⠁⠔⢀⢄⢔⡬⡼⣠⠄⠐⠀⠀⠀⠀⠋⡂⣶⣤⢤⢤⡇⡀⣦⠸⠀⡇⠀⠀⠀⠀ ⣨⠀⠀⠁⠾⢤⠆⠀⠀⡀⠊⠔⠠⢀⠀⠋⢖⠹⠒⡦⡙⠢⠘⣬⠱⡰⠡⠀⠀⠀ ⢸⠁⠟⣿⠉⡸⠀⠉⠔⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⢹⠏⠀⠀⢄⠈⢤⠓⠁ ⠂⢿⣿⣾⣤⡀⣔⢀⠀⠀⠀⠀⠀⠀⠀⡄⢤⠤⠂⡐⠓⣿⣿⠈⠀⠀⡀⢡⠀⢄ ⡿⣤⢊⠜⠉⡱⠠⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠰⠀ ⢸⡤⢅⠏⢃⡧⠊⠉⢉⠀⢡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⢸⠀⠂⢿⢻⡿⣄⣷⢙⠀⠋⡛⠟⠹⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠋ ⢿⠛⠟⣿⣿⣶⠹⠀⣼⣶⣷⠿⠿⣟⠻⠛⠀⠀⠀⠀⠀⠀⠉⠿⠹⠒⠂⢁⡇⢸ ⣿⣿⣿⣿⡆⠻⣾⢻⡏⠈⠂⠄⠤⡀⣒⡐⠀⠀⠀⠀⠈⡀⣦⠿⡟⢻⠉⡉⣿⣿ ⣿⣿⣸⣷⠘⣧⢿⡄⣿⢣⠙⢸⠐⠉⠈⠀⠀⠀⠁⡴⠋⠻⡿⣼⣀⣅⣼⢁⡟⣿ ⡆⣮⢺⡀⢸⡀⣿⠀⡆⡈⣍⣶⠻⠉⠀⠀⠀⠋⣻⡿⣿⣴⣞⠀⠃⡿⠛⡴⣟⣿ ⢢⢨⣧⠃⢀⡄⡏⠀⠁⢰⢧⠀⡀⣄⣶⠿⠜⣟⣿⣴⢀⡟⢿⡿⣿⣿⢩⡿⣴⣟ ⢀⣄⠈⣷⠘⠃⣇⡇⡀⠰⠏⠘⠋⡼⠟⣼⡏⣰⢀⠀⡟⣫⡴⣏⣜⢕⣮⢑⠏⣿ ⠀⡀⢒⡆⢳⠀⢰⡄⡀⠁⣿⢿⢟⣿⣿⠟⢓⠿⠿⣿⣴⣀⣏⣴⡉⡻⣿⠻⡴⢀

⠀⡄⠻⠀⠀⠀⠀⣷⠙⠀⠂⠀⡇⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⡽⠀⠀⠀⠀⣆⠻⠀⠀⡀⣀⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⠘⠀⠀⠀⠀⣄⢠⠀⠀⠀⠀⡀⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢿⠘⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠻⠉⠈⠀⠀⠀⠂⠒⠑⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⣸⠀⠀⠀⠀⡇⣸⢶⠙⠈⠀⠀⠀⠋⠛⠟⠿⠿⣿⣿⢽⠿⠛⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣦⠻⡈⣧⡟⣼⣠⣀⠀⠀⠀⠀⠀⠀⠀⣁⣿⣴⢀⣿⣐⣀⣀⣀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠁⠟⡴⣤⢦⠘⣆⢿⠈⠀⠀⠀⠀⠀⠀⠀⠟⣴⢀⠀⡟⢀⠀⠀⠁⠟⣿⣿⠚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀ ⠀⠀⠀⠀⠀⠀⡄⢻⠀⠃⡾⢀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠁⠋⡴⢀⠀⠀⠇⢿⠿⠿⠿⣿⣾⣰⣉⠋⠞⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢶⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠙⣿⢠⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠶⡴⣠⢀⠀⠀⠀⠁⣿⣿⣿⣿⣾⣴⣤⣠⣀⢀⠀⠀⠀⠀⣀⢦⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⠀⠀⠀⠀⠀⠀⠁⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠁⡭⣟⣿⣿⣿⣿⠟⠿⠲⠛⠛⠙⠈⠀⠀⠀⠀⠀⣄⢷⠙⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⠋⠟⣾⢠⠀⠀⠀⠁⠋⠐⠀⠀⠇⣿⣴⢀⠏⣴⣤⢀⠀⠀⠀⠀⠀⡀⣄⢤⠲⠙⠉⠀⠀⠀⣄⢷⠙⠀⠉⡞⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢹⠉⠋⠟⡿⣶⣤⣀⠀⠁⠛⠖⡴⣤⠀⠀⠀⠃⣿⣠⠀⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢾⠶⣶⣶⣴⣤⣇⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣾⣤⣠⣀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⣿⣽⠀⠛⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠟⢠⠀⠀⠀⠀⠀⠀⠋ ⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⡏⣴⠀⠀⠀⠀⠉⠟⡿⣴ ⠀⠀⠀⠀⠀⠀⠀⡿⣾⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠏⣼⠀⠀⠀⠋⡿⣸⡄⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢹⡄⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⠀⠀⠏⣿⣿⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣿⣦⡀⡀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⠀⡟⣴⢃⣰⠀⠁⠋⠶⡤ ⠀⠀⠀⠀⠀⠀⡇⢿⠛⣿⣾⢠⣗⣿⠿⠺⠒⠒⠤⠤⠤⠀⠀⠀⠀⠀⠀⡆⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⡿⣠⠁⣿⠚⡴⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢤⣦⢻⠈⠀⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⠀⡏⣿⡿⣨⢀⠀⠀⠁⠛⠔⣤ ⠀⠀⠀⠀⠀⠀⣹⠀⠃⣿⢠⠀⠀⡟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡟⣠⣀⣤⣦⣶⠷⡿⣿⣛⣛⣙⣏⠻⠉⠉⠀⣿⡄⠀⣿⣤⢀⣄⢦⡶⣴⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢸⠟⣷⢿⠘⠀⠀⣃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣄⣶⠿⣿⠀⠀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠟⣠⡟⣸⠀⠀⠀⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣠⠀⣾⠀⠀⠀⠀⠀⣧⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠈⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣼⠀⡏⢸⠀⠀⠀⠀⠀⡄⢻⢠⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠂⠒⠓⠙⠉⠁⠉⠛⠚⠴⣤⣀⠟⣿⣾⣿⢿⠙⣆⠙⠀⠀⠁⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠏⣠⢻⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⡏⣴⣿⣧⣈⣄⣶⣶⣽⠿⡿⣾⢠⠀⠀⠀⠀ ⠀⠀⠀⠇⢉⠈⢀⠀⣧⠈⠀⠂⠓⠙⠉⡁⣾⠁⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠁⠛⠴⡤⠤⠶⠶⠲⠛⠉⠏⣽⠁⣿⡄⢻⠀⠀⠀⠀⡀⣀⣦⠿⠻⠈⠀⠀ ⠀⠘⠀⡾⣤⣤⢤⠲⡓⢻⠀⠀⠀⡀⣄⣿⢹⠋⠛⠀⠀⠀⠀⠀⣿⢰⠀⠀⠁⠀⠋⣴⢀⠀⠀⠉⠋⠘⠀⠀⣀⣤⡶⡟⣾⠻⡌⠹⠀⠀⠀⠀⠛⡴⣠⡀⢷⠿⠾ ⠃⢠⠇⢠⠀⠀⠀⠀⠀⡅⢻⠁⠈⠀⠀⠄⣠⣄⣤⣤⠤⠤⠷⡦⣿⠈⠀⠃⣽⡿⢠⠋⠚⡤⣠⢀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⠻⠉⠟⣴⢀⠀⠁⡿⣴⢀⠀ ⡆⠉⣼⠀⠀⠀⠀⠀⠀⠀⡄⢯⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢿⠟⣻⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣷⢙⠉⠉⠟⣿⢀⠀⠀⠀ ⠀⡅⢛⠛⠛⠚⠒⠶⠷⠤⣠⣀⣀⣤⠿⠙⠉⠈⠀⠀⠀⠀⠟⣿⢦⣄⣿⣿⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⠭⠳⡉⣿⣿⣿⣿⣿⣹⣇⣹⢾⠁⠈⡀ ⠀⡄⣀⣄⣤⣶⠷⠻⠉⡄⠳⠈⠀⠀⡀⣄⣦⣿⢬⠦⠷⡿⣽⣿⠀⠄⣿⣿⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠳⡏⣷⣿⣿⠿⣼⣇⣻⣧⣷⣿⣿⡋⣼⠀⡟⢻⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⠳⠙⠈⠀⠀⠋⠒⢀⠀⠭⣿⣿⣹⠀⡟⣀⣿⣿⠁⠚⠽⣉⠀⠁⠁⠀⠇⣿⠘⠀⣉⣭⣯⣿⢻⠛⡟⣿⠻⡀⣿⣿⣿⢻⡿⣷⣼⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⣛⢬⠳⠿⣤⣠⣀⠀⡀⠛⢹⡟⣿⢻⣿⡿⣿⣿⣿⣿⣸⠁⡟⣿⣿⣸⢀⠀⡇⣿⣾⣿⣿⣿⣷⠉⣧⣿⣿⣿⢹⡌⢳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⣷⢿⠙⠀⠀⠀⣼⣧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣼⣇⣿⣿⣿⣿⢿⠛⣿⣿⢸⣶⣿⣼⡀⣿⡿⣿⣿⣿⣿⢠⡇⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⢷⠻⠈⢀⡏⣿⢠⣿⣿⣿⣿⣿⣿⣾⢻⡏⣹⠀⣆⣿⢿⣰⣧⣿⢸⠀⣧⣿⠀⣯⣿⣾⡿⣿⣼⠀⡟⡿ ⠀⠀⠀⠀⠃⠛⠛⠛⠛⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠿⣟⣿⠀⡇⣿⣿⣼⢀⣧⣽⣦⣿⣿⠸⠀⣿⣿⠹⠀⣦⢻⠀⠀⣿⠀⣿⣏⢹⡀⣿⢸⠁⣿⡇ ⠀⠀⠀⠀⠁⡋⢛⡏⠺⣴⣤⣤⣤⣤⣤⢤⠥⠲⠒⠓⠛⠛⠖⣷⣿⣿⣿⠸⠀⣿⣿⢰⠀⡀⣿⢸⡀⣧⢻⡟⣿⣐⣷⠀⠀⣿⠀⠀⣯⡟⣻⣼⣤⢳⡟⢸⡏⢸⡇ ⠀⠀⡤⣠⣀⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡟⠘⡇⡀⣧⣿⢿⠐⣧⣷⠈⠀⠀⡄⣷⠘⠀⣇⣿⣼⠀⡄⠀⠀⡇⠀⠀⣿⣿⣼⠀⠀⠀⣷⣿⣾⢁⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⡟⢻⡀⣿⣿⢹⠀⡀⢧⠘⠀⠀⡀⣧⠹⡏⣇⣿⠀⠀⠀⠀⠀⠉⡿⣿⣾⠒⠒⠙⠉⡟⣼⠃⡿⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢿⡷⣿⣿⣿⠿⠻⣯⠿⠛⠛⠙⣟⣠⣀⣿⠋⠉⠉⠉⠉⣻⣞⢶⠶⠤⠤⠤⣤⣿⢿⣿⣴⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠻⡌⣿⣿⣻⣛⣉⣉⠉⠉⠉⣯⠸⠀⡅⣿⣿⣿⣽⣤⢀⠀⠀⠀⠀⠀⠃⡟⣿⣼⣋⠉⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣜⣷⣝⢦⣝⣿⠻⠉⠀⠀⠀⠀⡀⣤⠤⣠⢀⡁⣿⣿⣿⠿⠛⠛⠛⠛⡾⣠⣀⣤⣤⣠⣀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠙⣄⢶⣙⣘⣙⣮⢿⠻⠛⠉⠈⠀⠀⠁⠉⠟⣶⣠⣷⠻⠛⠖⡶⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⣇⣿⣽⣦⣿⣿⣿⣢⣛⣛⣟⢟⣥⣻⣿⢴⠀⣻⣿⣻⡙⣧⣫⢔⢋⡿⣞⣡⠟⣴⢋⣻⢾⣴⣟⣿⣣⣽⢞⣰⡖⣺⠖⡭⣡⣞⢣⡾⢀⠋⠛⠖⠤⣀⠋ ⠀⠀⠀⠀⠀⠀⠾⣾⢸⠀⡀⢿⣦⢿⣛⣮⣿⣿⠿⠿⣿⡿⣛⣿⣠⠀⡟⣿⣿⢸⡄⢳⢥⣻⢋⡿⢿⣿⢟⣿⣷⢉⠋⡿⣵⢟⣾⣠⠀⠀⠀⠀⡅⣾⣡⠟⣴⠁⡞⣀⠀⠀⠁⠔⢀ ⠙⠀⠃⡿⣨⣦⣿⢠⢸⠀⠀⣾⠺⡙⣯⣿⠻⣌⣶⣿⣿⣾⣿⢘⠀⠏⣿⡼⣠⢦⠉⠀⡀⣷⣫⣿⣟⢶⣠⣀⣤⠷⡌⢶⣵⢋⣷⢮⠛⠛⠁⠞⣩⠞⣿⢠⠏⣴⢀⠀⠀⠀⡶⠲⠴ ⣿⠏⣿⣿⢹⠀⣾⠁⢸⠀⠀⢀⢻⠀⠀⡀⣀⢠⠀⠀⢸⠀⡀⠋⡶⣶⣒⢒⠿⠿⡿⢿⠈⠀⣦⣹⢉⠀⠀⠀⠀⡁⣾⠹⠀⣄⣦⣙⣀⠀⡿⣽⣿⣿⣽⣯⣾⠀⠀⠀⠀⠀⠀⠟⠙ ⣧⣿⣿⣿⣿⠻⢰⡏⢸⠀⠀⠀⣿⠉⠀⠀⠁⠛⠁⡞⢠⠀⡎⢉⠋⠚⠢⠐⠀⡀⣀⣀⣦⠹⡿⠪⣝⢦⠙⠛⠽⡀⢹⣿⠘⠀⠀⡀⣀⡄⣷⣿⣯⣿⣿⣾⢠⠀⠀⠀⠀⠁⡟⣿⣿ ⡇⣿⣿⣼⣷⣿⠇⣿⢠⠀⠀⠇⣾⣃⢽⠿⣴⢏⣰⠎⠀⠃⢰⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣽⣦⢿⡹⣦⣷⢻⣿⣿⢻⠈⠀⠀⠀⠀⠀⣧⢫⣿⣴⢀⠀⠀⠀⠀⠋⡽⣤⣷⣿ ⡆⣶⣲⠀⠀⣿⣷⢸⢁⠛⠶⣴⣤⣯⠻⣶⣠⢀⠏⢰⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⣧⢻⠈⣄⢻⠀⠀⣀⣦⣿⢙⠀⠀⠀⠀⠀⠀⡄⢻⠉⠉⠉⠛⠞⣿⣙⣞⢿⠈⣀ ⠀⣀⢀⠀⠀⢱⡿⣼⣠⠀⠀⠉⠉⠾⢠⠀⠀⡎⣧⠉⡿⢉⠋⠙⠈⠀⠊⠒⠁⠉⠟⡟⣼⠀⠀⠀⣆⢿⠒⣴⡼⣷⢿⠻⡍⣶⣿⠻⠋⠚⠒⠙⠀⡀⣧⣿⣿⣿⣿⠻⣮⣿⣿⢿⠀ ⠐⠀⠀⠀⠀⡀⠀⢀⠙⠍⣿⣴⣰⣠⠀⠁⠞⢡⡟⡞⣶⣿⢿⡶⣶⣤⣤⣤⣤⣦⣶⣠⠀⠀⠀⠀⠂⡗⠻⠀⣦⣹⣄⣤⣦⣷⠿⠛⠙⠉⠉⡉⢬⠤⡤⣥⣉⠛⣽⣿⢿⣯⣿⣿⢻ ⠀⠀⠀⠀⠀⠀⠋⠿⣾⣠⢀⠀⠁⠋⠴⡠⠀⡤⣠⢀⠀⡀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⡀⠣⠀⠀⠀⡀⣀⣤⣶⣛⣉⣃⣌⣠⣆⣿⣿⣿⣿⣮⣽⣿⣿⣿ ⠀⠀⠀⠁⠉⠟⣾⣠⠀⠀⠀⠏⣾⢡⠋⠖⠿⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⡘⢷⠙⠀⠀⠀⠀⠀⡂⣭⢷⢻⠈⠀⣇⣿⣽⣿⢿⣎⣿⣿⣿ ⠀⠀⡀⣀⣁⢈⠁⠋⠛⠘⡇⣻⡴⣀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠣⡈⢦⠛⠈⠀⠀⠀⡄⠷⡈⣷⠻⠀⣿⣿⣿⣟⢿⣦⣿⣿ ⠀⠀⠋⠟⣿⢸⣼⢃⣿⢸⡞⢀⠀⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢧⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⣉⠻⠈⣄⠶⠲⠒⠉⠉⢧⡜⣿⢿⣌⣷⣿⣿⣿⢸⣷⣿ ⠟⡿⢻⣿⡏⢀⢹⡾⣂⢻⢰⠀⠔⣾⠀⠀⠀⠀⠀⠀⠀⠓⠈⠀⠦⠒⠓⠙⠈⠀⣾⢸⠀⡇⣼⠀⠁⠀⠀⠀⠀⠀⠉⠙⠀⡀⣷⢿⠙⠈⠀⠀⡀⣄⢻⣇⣿⢿⠀⣦⣿⣹⣿⡇⣿ ⣇⣿⡇⣿⣠⠀⣤⢠⠏⣰⠀⠀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⠉⠉⠀⡀⣀⣤⢶⢿⠈⡇⢼⡄⣤⠐⠇⣿⠿⠛⣞⣦⠀⠃⡿⣸⣆⣽⠶⠛⠈⠀⡃⣜⢿⣷⠹⠀⣯⠉⣿⣿⣿ ⡿⣿⡿⣴⠀⠀⠀⡟⢸⠀⣦⢿⣿⠉⠀⠀⠀⠀⠀⠁⠛⠼⠣⣵⢳⠀⠀⠀⠀⠀⠀⡀⢦⠛⠙⠂⠛⡿⣿⣿⣿⣾⢀⠁⠟⣿⣾⢻⠀⣇⠀⠀⣀⢤⠶⣛⣬⣭⣉⣉⣉⣉⣉⠛⣟ ⢀⡀⣦⠀⠀⠀⡇⣿⠀⠀⠤⣦⣽⣾⣷⣿⣿⣿⣿⣶⣠⢀⢾⢠⡀⢷⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⢿⣻⣛⣛⣟⢿⣿⣿⣿⣴⢀⡇⠀⡆⢸⠀⠀⠀⠀⡇⣌⣀⣇⢀⣀⣀⣄⢰⣿ ⠀⠀⠀⠀⠀⠏⣼⢀⠀⠀⠀⡇⢸⣄⣷⢮⠛⠈⠦⣤⠀⠀⠱⠀⠀⠀⢻⠈⠀⠀⠀⠀⠀⠀⠀⢧⣾⣼⣤⣤⣤⣥⣧⣿⢈⠁⠏⡟⢾⠤⣿⠀⠀⠀⠀⡇⢸⢀⠀⠀⡄⢠⠀⠁⣿ ⢀⠀⠀⠁⠟⣿⠀⠀⠀⠀⠀⡇⢿⠙⡀⢧⡘⣤⠲⠙⠈⠀⡀⢷⠙⠀⡆⢻⠀⠊⠘⠀⠀⠀⠀⠀⣆⣞⠹⠀⠀⢁⡇⡸⣷⣈⠀⣾⣿⠀⣿⠀⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⡇⣼ ⠀⠀⠀⣤⣦⣿⠘⠀⠀⠀⠀⡇⣾⣿⣿⠻⣌⠹⠂⣿⣿⣿⠈⡀⣽⢷⠈⣇⠸⢸⣧⠀⠀⠀⠀⠀⠀⢆⡌⠿⠴⣀⡇⢸⡄⢹⠃⢸⣸⠀⣿⠀⠀⠉⠛⡛⣯⠻⠈⠀⠀⠀⠀⡇⢀ ⠀⠀⠀⠀⠀⡀⢿⠻⠈⠀⠀⠀⢿⡄⣷⡹⣧⡿⢻⠀⠀⣦⣿⠻⡇⠈⢦⡜⣿⢸⡿⠀⠀⠀⠀⠀⠁⠞⣷⣄⢻⠀⡇⢸⠀⣇⡏⢸⢸⡏⣶⠽⠡⣟⠰⡀⣄⣿⣘⣦⠿⠶⠠⡇⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠘⠀⣧⠿⠀⣧⠻⣆⣿⠸⠀⠆⡻⡄⢷⢻⠀⣆⣿⢱⣸⠀⠀⠀⡆⡞⣸⠀⡄⠸⣧⠸⡇⢀⠀⡇⣿⠁⣿⣼⠟⣿⣶⣻⢀⣀⡁⡏⣿⠀⡇⢹⠀⠸⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠓⡟⣿⠈⠀⣆⠹⡄⣿⠘⠀⡀⢀⡄⣿⠘⠀⣻⡿⢸⠀⠀⠈⡆⢱⢳⠈⠀⢀⡆⣿⡟⠀⠀⡏⢡⡟⣫⡿⣼⢁⠏⢠⠁⣰⣀⣿⣶⠸⠀⣆⡿⢿⣠ ⠀⠉⠈⡇⠒⠁⠐⠀⠀⠀⠃⡴⣾⣿⢿⠀⠀⣆⠹⡄⣿⠀⠀⠀⠀⡄⢻⠏⣠⡏⢀⠀⡬⠀⢽⡟⡟⢣⠀⠀⠀⣿⣼⠀⠀⣿⣤⢾⣯⣼⣄⣠⢀⠀⡆⠁⡟⢩⠈⢸⠀⠁⡟⢲⠀ ⠈⡀⢀⠀⠙⡀⠀⠀⠁⠜⢀⡇⠀⣇⣿⢻⠀⠀⣇⠸⡄⢻⠀⠀⠀⠀⣧⢰⠃⣿⢸⠀⢰⠤⣀⣇⣸⣼⢷⠈⠀⣿⢠⠀⡇⣸⠀⠃⣾⠀⠀⠀⠀⠀⠀⡟⣾⣠⣷⢰⠀⡷⢀⠀⠀ ⠁⡏⢠⠋⡃⡀⣀⣯⣁⣞⠀⡇⠁⣾⣿⣿⢿⠀⡀⠸⠀⣆⡿⠤⠰⠀⡾⠀⡟⢠⢸⠀⠀⠀⠀⡀⢸⢸⡀⣷⠘⣿⠀⠃⣾⠀⠁⡿⢠⠀⠀⠀⠀⠁⡟⣿⢠⠁⣾⠉⠈⠀⠀⠀⠀ ⣄⠈⠀⢈⡅⠈⣇⣻⣼⢀⠀⣟⣿⢻⡆⣿⣿⣿⢈⠀⠀⠀⠀⠀⠀⡏⢰⠇⢱⢉⠀⠀⠀⠀⠀⠀⢸⢹⠈⡀⢸⣿⠁⡿⣾⠁⡿⣸⠀⠀⠀⠀⠉⡿⣿⢰⠀⡿⣿⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⢦⡀⣀⡏⣹⠀⠀⠀⡇⣿⣯⠙⣇⣿⣿⣿⠘⠀⠀⠀⠁⠞⣠⠃⡿⣸⣁⣠⠀⠀⠀⠀⠋⢾⣛⠴⠦⢸⣼⡃⣿⢻⡿⣰⠀⠀⠀⠁⡟⣿⣿⣰⠀⠇⣾⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⣠⣀⢳⠙⠀⡇⣿⢻⣿⠙⣷⣻⣿⣾⠀⠀⠃⡾⢀⠁⡼⣀⠀⠀⠀⠀⠀⠀⠏⣷⢿⢸⠀⠀⡏⢻⣿⣿⣾⣴⠤⠶⠿⠾⣿⣿⣿⣸⠁⠟⣴⢀⠉⠉⠉⠉⠀⠉⠈ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⡏⠀⠀⢻⡀⣄⣦⡙⢷⣈⢀⠀⠀⡜⠀⠁⡾⢀⠀⠠⠀⠀⠀⠀⠞⣠⡍⣧⠸⠀⠁⣿⣿⣴⢀⠀⠀⠀⠀⡀⢀⠀⣀⣀⣦⣿⢾⠴⣠⣀⣀⠀⠈⠀⠀⠀ ⣄⠀⠀⠀⠀⠄⠶⡠⣁⣼⣆⠶⡙⢢⠛⠈⡀⣷⢿⠀⠀⠶⢠⠋⡴⠀⠀⠀⠀⠀⠀⠀⡀⠎⣠⣄⠶⣾⠶⣿⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣄⡿⣄⠀⠀⠀⣄⢿⠼⣶⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡎⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⠒⠀⠃⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⣄⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠊⠟⢿⠙⠀⠉⠉⠀⠐⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀

⡉⣄⢦⠚⡿⢊⢲⠒⠉⠀⠀⠀⡀⠦⠑⡄⠾⠘⠀⠀⠀⠀⠋⠠⡞⠡⡎⠀⠀⠀ ⠀⡉⣓⣿⣩⣔⣤⠿⠾⠒⠙⠌⠑⠈⠀⣀⡦⢷⠉⠀⠀⠇⣤⡶⣹⠋⣿⣟⣤⠢ ⣁⢷⢺⠚⡟⠸⠀⡛⠿⣾⣶⡲⢖⡲⠲⠈⠀⠀⣀⣀⣀⣆⢲⠌⠦⣞⣾⣱⢋⠀ ⢧⢃⢩⣌⣤⣶⡞⣄⣿⢀⠋⠀⠀⠤⠑⡀⠢⠉⠈⠒⠔⡨⠶⡅⠢⢊⣏⣿⡈⢳ ⢪⠋⣌⠤⢹⠑⢁⠀⢸⠀⣇⠀⠀⠋⡖⢢⠀⠀⢀⠀⡄⡑⣄⢿⡻⢻⡀⣾⢸⡀ ⢝⢢⠯⡺⡘⠡⡄⠛⠀⠁⠁⢗⡴⢤⢀⠀⠀⠀⠀⠁⡞⣝⣿⣱⣧⣿⠀⢃⢃⢸ ⣇⠉⢌⢁⡯⠯⠡⡇⠂⢎⢀⠀⠀⠀⠀⠀⠀⠀⠄⠵⡢⣐⢡⠶⢃⣦⠀⡀⠀⢿ ⣿⠿⣧⠟⠢⡈⠻⠳⢰⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠄⡦⠋⠀⢰⠀⠀⢸⣷ ⡄⡕⣦⣿⠟⡆⠀⡷⠃⠆⠀⠀⠀⠀⠛⠵⣯⠰⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡾⣿ ⠀⡄⠸⡇⣧⠛⠈⡇⡀⠈⢂⠈⠀⡹⡋⣾⣡⠉⠰⠈⠐⠀⠀⠀⠀⡇⢸⠁⢠⣿ ⠒⠉⢆⠈⢢⢌⢦⠓⢡⡂⠢⡁⣉⣭⡂⠐⠒⢀⡴⠠⠒⠙⠉⠀⠀⠀⢠⡘⠇⣿ ⠀⠁⣿⢿⠈⣀⠢⠁⣎⠔⣁⣂⠖⠤⠤⠤⠀⠀⠒⠀⠉⠀⠀⣁⠤⢰⠜⠀⡟⣿ ⠏⡇⣿⣿⣿⠙⠀⠃⢊⡤⢘⠠⠑⡁⠠⠒⠁⠈⠀⠀⠀⡀⠄⠁⠈⣃⠟⡾⣴⣤ ⡿⣿⣿⣿⣿⣿⢿⡈⠲⠀⠀⣀⣀⠑⡫⣌⢐⡍⣛⢋⠛⡚⣶⠴⠤⣠⢈⠀⠀⠟ ⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠂⠄⡠⢀⠀⠁⡟⣿

⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡏⣿⣾⣦⣸⣯⣿⣝⣷⣿⣿⣴⢀⡀⠪⡈⣦⠻⠈⠀ ⠀⠀⡀⢦⠙⠈⠀⠀⠂⡘⣶⣿⢳⢸⠇⢠⠀⡀⢨⣄⣷⠸⠀⠀⡀⡢⠠⡀⣦⠻ ⠀⠀⠀⠀⣼⣠⠁⠒⣾⠓⠉⡀⠀⠀⡄⠀⠀⠀⢸⠀⢄⡀⠁⠣⠀⠀⢄⠂⠪⡌ ⠀⠀⠀⠀⢱⡔⣾⡠⠋⠩⠀⢄⠐⠀⠀⠀⠀⠂⣒⠉⠈⠂⠗⡿⣉⣦⠳⠟⡘⠀ ⠀⠀⠀⠆⠁⣼⣟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡒⣄⣦⣷⣿⢶⠈⣄⣿⡙ ⢄⠂⠁⠀⣇⠄⢢⢉⠛⠐⠀⠀⠀⠀⠀⠇⠷⠹⡦⣤⠀⠀⠀⠴⣾⢧⡆⡼⣄⣹ ⠽⠉⠈⡖⣯⠤⠃⣜⢀⠀⠀⠀⠀⠀⠁⣹⡏⣼⠸⠁⠋⠈⠞⠄⠎⢂⠀⢈⣿⡼ ⣦⢺⠰⠞⢀⠀⡇⣻⠀⠀⠤⠸⠀⠀⡀⡄⣿⠰⢔⠿⣀⡠⠼⠐⠀⠄⢀⢀⡇⢰ ⠀⢀⡆⠀⠀⠊⡸⣀⢤⠑⠀⢸⠀⠀⠀⠀⣏⠿⡀⣂⣡⢤⢤⠘⡈⠄⠁⠇⣿⢣ ⠀⠀⠀⠠⠀⡱⠀⠀⠀⠀⣀⠀⠀⠂⠄⠀⣅⣿⢿⣙⠬⠰⠓⡡⢋⠘⠊⣷⣪⡯ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣶⣭⣿⣿⢿⢛⡛⢋⠚⣤⢝⢴⣠

⠀⠀⠀⠀⠀⣤⡭⡿⢟⣟⣟⣿⣻⣉⣽⣄⠡⡟⣿⡟⢿⣿⣿⣽⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⣿⣶⣤⣤⣤⣤⣦⣷⣿⠹⡟⣿⣿⢿⡽⣿⣿⣿⢿⠘⠀⠀⠀ ⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣾⣠⣀⠀⣀⣀⣀⣦⣷⠈⠀⠀ ⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠀ ⠀⠀⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀ ⠀⠀⠀⣾⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀ ⠄⠿⢀⣲⠒⡃⣦⠻⠙⠉⠀⠀⠉⠋⡹⠉⢙⠈⠀⠀⠀⠁⠋⠴⢀⠀⠀⠀⠀ ⠖⢴⠇⠐⠐⣿⠈⡎⣧⣷⣿⣿⣽⣯⣿⣿⣾⣶⣴⣤⣬⣈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠑⡞⣴⣄⠃⣿⣿⣹⣾⣿⣿⣿⣿⠃⣨⠀⠀⠏⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡔⠀⠖⠀⡿⣿⣿⣿⢸⣿⣴⣿⣿⣿⠚⠀⠉⣀⢡⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠆⠀⠃⠘⡄⣿⣿⣿⠄⠀⢠⠀⣿⣏⣾⢇⡤⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⢀⠀⠀⣤⣶⠲⠉⠉⠖⣴⣤⢂⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠤⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡯⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⣿⠀⣳⠈⠀⠀⠀⠀⠀⡀⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠇⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠶⡭⣾⣴⣤⣀⣇⠸⠠⣇⠿⠿⠿⠿⠿⠻⠛⠉⢎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠻⠈⠂⡿⣿⢰⠀⠀⠀⠉⠉⠛⠛⠿⡿⣿⣛⠛⠞⡴⣀⠀⠀⠀⠁⡾⠀⠀⠀⡆⣾⣷⣿⣿⣿⣿⣿⣿⣾⣶⠻⠙⠀⠀⠀⠀⠀⠀⠀ ⠉⡈⣷⠏⣿⣼⠏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠁⠔⣠⠀⠁⠈⠀⠀⢇⠀⣀⣦⣷⣿⣿⣾⠀⠏⣿⣿⣿⠿⠙⠈⠀⠀⠀ ⣄⣷⡸⣧⣿⢠⣿⣿⣿⣿⣻⡟⣿⣿⣾⣴⢀⠀⠀⠀⠀⣽⣧⣰⠁⠀⠀⡀⣸⠀⠀⡄⠀⠀⠀⠀⣀⣦⢹⠀⣷⢹⣭⣽⣭⣽⣿⢾⠶⠛ ⠀⠀⢄⣻⣰⠧⣀⣧⡿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⡄⣿⠴⢠⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣠⠀⠃⣾ ⠹⠀⠀⣧⠀⡄⢿⡿⣿⣿⣾⣠⠀⠂⠓⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⡿⠈⠀⠀⡿⠹⠀⠀⠀⠀⠆⣩⣉⣀⣤⣻⣉⣤⢳⠈⠀⣿⢼ ⡀⠀⠀⡆⠀⠀⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠸⠀⠉⠛⡿⣿⢻⠙⠏⣿⣿⠹⠀⠀⠀⠀⢦⡀⠀⠀⡀⣷⢿⠘⣀⢦⣿⠀ ⠀⠀⠀⠀⠀⠀⣧⣇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⢻⠈⠀⠀⡀⠀⠉⠉⠀⡄⣿⣿⠹⠀⡄⠹ ⠀⠀⠀⠀⠀⠀⡇⡆⢸⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⡏⣿⣿⣿⣬⣶⣷⣾⣶⣶⣤⣩⠞⣠⠀⠀⠀⠀⠀⠁⠐⠀⡞⣄⠻⣟⣿⣿⠘⠀⣇ ⢻⠰⠀⠘⠀⠀⡇⠏⢰⠋⠗⡾⣠⢀⠀⠀⠀⠀⠏⣰⢀⠀⠀⣀⣄⠤⠒⠔⠤⣠⣀⠀⠀⠀⠀⠀⠀⠋⡡⠃⡴⠏⢠⠆⣷⣿⣿⢸⠀⡀ ⣷⠘⠀⠀⠀⠀⡇⣾⣠⠏⣠⠀⠈⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⢏⣩⠟⣼⡝⠀⡆⢿⣌⢻⠀⠀ ⡵⢹⠀⠀⠀⠀⡇⠀⠟⢠⠀⡇⣇⢘⠀⠋⡰⠀⠋⠠⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⡳⣹⡼⢃⣶⢋⡾⢃⠼⠀⣦⢹⣇⠀⠀ ⡀⣿⠈⡇⠀⠀⡄⠃⢷⠘⠀⠋⣫⡿⣽⢎⢋⡴⢀⠁⠞⡡⠛⠟⣾⠠⠀⠀⠀⠀⠀⠱⠁⠞⢀⠆⣲⠖⣶⡴⣤⢀⡦⣿⠙⠀⣿⡌⠀⠀ ⠀⡀⢷⡏⠀⠀⠀⡏⡄⢿⡟⣴⢞⣯⣣⡴⢆⡠⠒⣱⠟⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠃⠶⠤⠳⠈⠀⠀⠁⣿⣿⢿⣿⢠⠀⠀ ⠀⠀⡄⣿⠸⠀⠀⢸⠀⣿⣧⡄⠷⠕⢛⡷⠿⠿⠿⣶⣴⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡿⣿⣿⠿⣿⠛⠿⣿⣴⣧⣷⣿⠈⠁⠛ ⠀⠀⠀⣇⢹⠀⠀⢰⠀⣼⡇⠀⠇⣸⠀⠀⠀⠀⠀⠊⡤⠦⠳⠟⣿⠀⠀⠀⠀⠀⠀⡿⠈⠀⡀⣦⣾⣶⣶⣶⣤⣠⢀⠀⡇⣿⣘⣀⣀⠀ ⠀⠀⠀⠀⣷⠈⠀⠀⠀⢸⡇⠻⣿⠹⠀⠀⠀⠀⠇⢁⠟⠿⡿⣴⢟⢉⠀⠀⠀⠁⠈⣄⢿⠀⠀⠀⠻⠉⠉⠋⢿⠙⠀⠁⡛⢸⢸⠀⠀⠀ ⠀⠀⠀⠀⡄⢹⠀⠀⠀⢀⠀⢹⡤⣦⣶⠿⠿⠛⡿⣾⣶⣥⣛⡿⣤⣀⣠⣠⣠⢉⡜⢷⡟⠹⠀⠀⡇⡘⢀⠀⡆⣼⣿⣼⣀⢸⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⠀⠆⠹⠁⣧⠈⠀⠀⠀⡀⠿⠚⠖⡾⣴⣤⣀⡄⠻⠿⠶⡴⣀⢧⡟⣸⣷⡀⣤⣦⢸⠀⠀⠀⢸⣇⣿⣿⢸⠀⠀⠀⠀ ⠒⠰⠀⠀⠀⠀⢹⠀⠀⣷⡿⡙⢹⠃⠙⠀⡏⣀⣽⠻⠙⠉⠋⠟⡿⣿⣬⠀⠀⠀⡆⣿⢸⡀⢳⠀⠀⢸⠀⠀⠀⠇⠀⢿⣾⠀⠀⠀⠀⠀ ⠀⠆⠀⠀⠀⠀⡆⠘⠀⡄⣿⣸⣄⣠⣇⠾⢸⠀⣧⣿⠀⣀⣀⠀⣇⡏⢹⠀⠀⠀⠀⣿⢷⠀⡄⢻⠈⢸⠀⠀⠀⡀⠀⡇⢀⠀⠀⠀⠀⠀ ⠀⠀⢠⠀⠘⠀⠀⢧⠈⠀⣇⣿⠘⠀⠀⢣⢸⠀⡇⣾⢹⠀⠀⠀⡀⣿⣿⠀⠀⠀⠀⣆⡇⠸⠀⣇⣿⢀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢣⠀⠀⢳⣄⠀⠀⡀⢷⠀⡆⣧⣌⠰⠀⠀⠀⡆⣸⢸⠀⠀⠀⠀⡀⢸⠀⡇⣿⠀⠀⠀⠃⢰⠀⡏⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠈⡀⢳⠈⠀⠀⠀⠀⠀⢰⢦⠈⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⢸⠀⡇⣹⠉⠛⠚⠶⠴⣤⣠⢀⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⠤⡀⢈⠀⠀⠉⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠔⠡⠆⠤⢀⠀⠁⠔⡀⠀⠀⠀⠀⣀⠢⠈⠡⠀⠀⠀⠀⠀ ⠀⠂⠄⡀⠄⠀⠑⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⡄⡈⠘⠀⠀⠀⠀ ⠌⠀⠀⠀⠀⠀⠀⠀⣀⢆⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⢃⡄⠈⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⠀⠀ ⠡⠀⠈⠀⠀⠀⠀⠀⠀⠀⡧⠑⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⠘⠸⠀⠀ ⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠤⠮⡠⠀⠀⠀⡆⣾⡙⡐⡇⠀⠀ ⠀⡄⢤⠙⠀⠀⠀⠀⠀⢀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀⣆⣻⡪⠰⢸⠀ ⠀⠀⢄⣿⢿⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⣦⣷⡟⠀ ⠀⠀⠀⢸⣾⢀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠹⠀⠀⠀⠀⠀⠀⠀⣇⠰ ⠀⠀⠀⡇⢸⠀⠃⢰⠀⠈⠒⡠⠈⠀⠀⠱⣇⠼⠠⠐⠀⠀⠁⠊⡰⠀ ⠀⠀⠀⡀⢡⠀⡏⠐⡠⠀⠁⠈⢶⠷⠙⠀⡧⢻⠉⠛⠼⣡⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⢿⠞⠤⣀⠀⠀⠀⣄⠲⡌⣿⣿⣿⣟⡸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⣾⢀⠁⠈⠀⠈⠀⠀⠀⣄⣿⣿⣿⢻⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⢀⠂⠦⣀⣤⠤⠀⠊⠈⡇⣿⣿⣷⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡟⢹⡀⢤⡠⠀⠀⠀⡓⠛⡔⡇⣿⣿⠉⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣘⡟⣃⠿⠿⠐⠛⠻⡟⠘⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⢿⣿⡿⣶⣿⠁⣼⣦⣷⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣼⣤⠀⣀⣸⢀⠀⠎⣥⣾⣄⣿⣿⣿⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⠈⠀⠀⠀⠀⠀⠀⡎⢠⠀⣿⣿⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢄⠐⠈⠀⠀⠀⡀⠀⠀⡁⡖⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠄⠤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠀⠄⠀⠀⠀⠄⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⡉⢋⣿⠀⡇⢙⠀⠀⠀⠀⠀⢀⣀⠀⣄⣶⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀ ⠄⠀⠄⠁⠄⠁⡏⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⡾⣿⣛⡿⣶⣤⣧⠘⠉⣌⠳⠉⠋⠛⠙⠉⠛⠛⠉⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⠙⠄⠁⠄⡁⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠟⠶⡤⣤⣉⢟⡴⣠⢀⠀⠀⠀⡟⣸⠀⠀⡠⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡛⢯⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠿⠉⠆⣿⣿⣿⢠⠀⠀⠁⠉⠉⠛⠟⠿⡿⣿⣿⣿⢿⠿⠿⣿⣴⣠⢀⠀⠀⠀⠀⠀⡏⣴⠀⠀⠀⠀⠀⣳⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠈⣆⣻⠏⣿⣿⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠁⠞⣤⢀⠀⠀⠉⠀⠀⠀⡄⠹⠀⡀⣄⣶⣿⣿⣿⡿⣴⠀⠏⣿⣿⣿⣿⢿⠻⠙⠈⠀⠀⠀⠀ ⣦⣿⠻⣌⣷⣿⡾⠀⣿⣿⣿⣿⣿⣽⣀⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠟⣶⠳⣼⠀⠀⠀⠀⠀⣯⢠⠀⠀⠀⣷⠀⠀⠀⠀⡀⣤⣷⣿⠀⠀⣿⣽⣄⣶⣶⣶⣷⣶⣿⢿⠛⠙⠈ ⠀⡀⣦⢱⡾⣿⢣⠈⣶⣷⣹⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⡄⠻⡼⠉⠎⠀⠀⠀⠀⡟⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣄⢦⠓⡏⣻⣿⡿⣿⣿⣿⣿⡾⣠⠀⡁⣿ ⠀⠀⠀⡀⣿⣤⠀⣿⠈⡇⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⢈⢀⠀⠀⠀⡇⣾⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣟⣿⣶⣶⣿⣿⣿⣠⠀⠀⠁⣿⣥ ⢳⠀⠀⠀⣇⠀⠀⡇⣿⡿⣿⣿⣿⣾⣠⠀⠀⠆⠦⠘⠀⠀⠀⠀⠀⠀⠀⠀⢿⠰⠀⠀⠀⠀⠁⡿⢻⠀⠀⠀⡇⣿⠹⠀⠀⠀⠀⠀⡄⣣⢛⠙⠀⣀⣆⠻⡙⣀⢦⠓⠈⠀⡇⣿⣠ ⡀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⡿⢿⠈⠀⠀⠉⠟⣿⣿⣿⠻⠈⠋⡿⣿⣿⠹⠀⠀⠀⠀⠀⡄⠾⣄⠀⠀⠀⣄⣿⣿⠻⠀⣀⣤⡿⣿⠀ ⠀⠄⠀⠀⡆⠀⠀⠀⣿⡇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⣿⡻⢷⠈⠀⡀⣷⠈ ⠀⠀⠇⠀⡀⠀⠀⠀⣧⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢁⣾⣠⣄⣶⠀⠀⠀⠀⠀⡄⣤⢤⠿⠙⠈⣇⣿⣻⢿⠀⠀⡀⣿ ⠀⠁⠐⠁⠀⠀⠀⠀⡇⠀⢿⠰⠀⠀⠀⠉⠋⠛⠖⠰⠀⠀⠀⠀⠀⡿⣿⣶⣶⣷⢉⣌⣦⣶⣶⣤⣤⣠⣁⠋⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠁⡞⢠⡌⣶⠿⣟⣿⣿⢹⠀⠀⡇ ⢿⡸⠀⡀⠸⠀⠀⠀⡇⠡⣸⠁⠋⠵⣿⣴⣀⠀⠀⠀⠀⠀⠀⠁⡾⣠⠀⠀⠀⠀⠀⣀⣤⢤⠲⠴⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡽⢈⠃⡼⠃⡽⠀⠆⣧⣿⣷⣿⣿⠀⠀⡄ ⣿⢸⠀⠀⢀⠀⠀⠀⡇⡿⢾⣠⠋⣴⢀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣫⡴⠟⣰⠋⣿⣵⡼⠀⡄⣿⡹⢰⣿⠀⠀⠀ ⡜⢻⠀⠀⠀⠀⠀⠀⡏⣰⠀⠏⣠⠀⠀⠟⠷⠐⠀⠀⠁⠞⣠⠤⠁⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡴⢞⣡⡾⢥⡿⣤⢣⡾⢤⠩⠀⡇⣿⠸⣧⠘⠀⠀ ⣆⣇⠸⠀⡃⠀⠀⠀⡇⠀⡇⣰⠀⠀⠀⢰⡿⠡⠊⠛⣱⠘⠀⠞⣠⠀⠐⠁⠚⠀⠈⡋⠑⠜⢀⠀⠀⠀⠀⠂⠈⠀⠀⡤⢏⣠⡔⢞⣠⠃⡽⣉⠟⣿⢩⡯⢛⠀⡀⡆⢻⡀⢸⠀⠀ ⠀⣧⢿⠀⡇⠀⠀⠀⡄⠀⣼⢿⠈⠀⠋⡱⢞⣣⡼⢋⡰⠋⡴⢉⠀⠃⠞⣠⠋⡿⡵⢞⣠⠀⠀⠀⠀⠀⠀⠀⣆⠙⠋⡴⢀⠄⡤⢤⠤⣤⣤⣠⣀⠀⡀⣥⣿⢻⠘⠀⣿⠘⢰⠀⠀ ⠀⠀⡇⢻⡏⠀⠀⠀⠀⡇⢠⡇⢿⠏⣾⣡⠞⣯⣴⢋⡴⢂⡠⢃⠟⣠⢟⡶⣷⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢘⠀⠀⠀⠋⠶⠴⠷⠙⠀⠀⠀⠀⡅⣿⣿⣿⡿⣿⢰⠀⠀⠀ ⠀⠀⠀⣇⣿⢸⠀⠀⠀⡟⠀⡇⣟⣴⢸⡳⡘⢋⡵⢋⠟⠛⠟⠻⠖⣷⡿⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣟⠿⠿⠻⡛⢿⠉⠉⠟⣿⣿⣷⣿⣿⣿⠈⠀⠀⠉ ⠀⠀⠀⠀⣷⣿⠀⠀⠀⣻⠀⡀⣿⠀⢸⠀⣁⠞⣠⢄⠤⠤⠤⣤⣀⣀⠁⠘⠈⠀⠀⠟⠸⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⡄⢷⣿⣯⣶⣶⣶⣷⣿⣿⣾⣴⢀⠀⢿⣧⣶⠶⠶⡴⣄ ⠀⠀⠀⠀⡆⣿⠘⠀⠀⣤⠀⠀⢸⠀⢸⠁⡿⢠⠀⠀⠀⠀⠀⠀⠃⡴⣀⣀⣄⢷⡿⣾⢩⠀⠀⠀⠀⠀⠀⠀⡇⢻⠈⠀⠀⠀⣧⣴⣤⣤⣤⣤⣈⠀⠀⠀⠀⡀⣿⡆⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢹⠀⠀⠀⠀⡇⢀⠀⣿⡟⣿⠹⠀⠀⠀⠀⠀⠀⣼⠁⠟⡿⣿⣿⣴⢏⣹⠉⠀⠀⠀⠀⠋⠙⡀⣆⢿⠀⠀⠀⡀⢿⠉⠉⠉⠋⣷⠻⠉⠀⠁⠛⡿⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠘⠀⠀⠀⡄⠀⠀⣿⠀⣴⣶⣿⠿⠻⠛⠛⠛⣿⣿⣿⣶⣤⢋⡿⣴⣠⣆⣤⣤⠤⣤⢡⡌⢷⠛⣯⠘⠀⠀⠀⡇⡘⣀⣀⠀⡀⣸⣷⢷⣴⣠⡇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠃⠈⠀⡇⢸⠀⠀⠀⣀⣀⣄⣭⣬⣈⣁⠛⠿⡿⣲⢶⠠⠛⠉⠉⠉⠋⠞⣴⢿⡀⣿⢮⣿⠂⠗⠿⡿⢸⠀⠀⠀⠀⢧⡀⣽⢷⠻⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⡇⢻⠇⠈⣷⠈⠀⠀⠀⠀⠁⡼⣻⣽⣀⣰⣀⠀⠀⠀⠁⡏⣿⣿⣀⣀⠀⠀⡆⣿⣿⢀⣦⠹⠀⠀⡀⢻⠀⠀⠀⠀⡇⠸⡇⡸⣿⣼⠀⠀⠀⠀⠀⠀ ⠴⢠⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⣿⡜⢿⡝⢹⠇⠷⠀⠀⡿⢀⣷⡘⣿⠳⠛⠛⠟⡿⣿⣾⣷⣄⠀⠀⠀⠀⠀⣿⣼⢸⠀⣇⠸⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⢷⣟⢰⠀⠀⠀⠀⠀⠀ ⠀⡀⠸⠀⠀⠀⠀⠀⣇⠸⠀⠀⡆⣾⣿⡀⣄⣠⡄⣿⠶⣼⠀⡄⣿⣿⠀⠀⠀⠀⠀⡄⢻⡇⢹⠀⠀⠀⠀⠀⣇⢸⢻⠀⠀⣧⠹⠀⣼⠀⠀⠀⠀⡇⢠⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠙⠀⠀⠀⠀⠀⣧⠈⠀⠀⢧⣎⢹⠀⠀⠀⣧⠸⢸⠀⠀⢿⣷⢹⠀⠀⠀⠀⠀⣧⡟⣿⠀⠀⠀⠀⠀⡄⢹⡇⠀⠀⡄⣿⢿⢠⠀⠀⠀⠀⡇⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢷⠈⠀⡀⢿⣆⠹⠀⠀⠀⣇⢻⠀⠀⣼⢻⣧⠸⠀⠀⠀⠀⡀⣿⡆⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⢳⠈⠀⡀⢳⠀⠀⠀⠀⠀⣦⠐⠀⣇⡄⢹⣄⠀⠀⠀⠀⠀⣆⠘⢸⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣇⣿⠀⠀⠀⠀⠃⢰⠀⠉⡟⠉⠉⠋⠂⠒⠒⠄⠤ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⢷⠘⠀⡄⢻⠉⠀⠀⠀⠀⠀⠀⡄⢱⣆⠹⠈⠀⠀⠀⠀⠀⣀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢹⠉⠛⠛⠶⠶⠤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⡌⣥⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⡀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣀⣀⣀ ⠄⠀⠀⠀⠀⠇⣾⣦⠰⣀⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠞⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⣀ ⠈⠂⠀⠀⠀⡀⣤⣳⣿⣉⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣶⠿⢰⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣀⣸⢤ ⣀⠀⠀⠀⣾⣧⠰⡟⣾⣶⣷⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⡃⣿⣿⣿⣿⣿⣿⣶⣿⣿⢶⠶⠤⠥⠯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⢀⠀⠇⢠⡸⠀⣶⠽⠿⠟⡛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣯⣿⣿⣶⣿⣴⣡⠟⣾⣠⢀⠀⠃⢞⣠⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⡼⡏⢉⠞⡤⣉⠟⣭⣉⣏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⣠⢋⡴⢀⠃⡿⣴⠀⠀⠀⠄⣠⠀⠀⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏ ⠀⠀⠏⢰⣠⢉⠖⣥⢈⣧⣿⢀⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡴⢀⠀⡴⢀⠀⠃⣣⣰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣟⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀ ⠴⣀⠋⠖⣠⢀⠀⡼⣀⣇⢸⠀⠀⡅⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⣠⠀⠀⠀⠀⠀⠀⠀⣹⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣷⣹⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣀⠀⠀⠀⠀⡞⢀⠁⣿⣿⣶⣒⣒⣗⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢀⠀⡿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⣤⢶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢠⠀⡼⠀⣌⠉⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠸⠀⡆⠘⠀⢷⠀⠀⠀⠁⠀⠁⡟⣶⠤⣤⣤⣤⢤⠲⠀⠀⠀⠀⠀⠀⠁⠚⡴ ⠀⠀⠀⠀⠃⣰⠀⡞⢀⠀⢿⣴⣀⣿⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠘⠀⢡⠀⡀⢻⠉⠟⢼⡤⣀⣄⠤⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣡⠞⡴ ⡞⣄⠳⠙⡼⠀⠏⢠⠀⠁⣼⠀⡏⢠⠀⠀⠀⢦⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠻⠉⣟⠾⣠⢀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⠀⠀⠀⠀⠃⣰⠟⣠⡀⠀ ⠀⠁⡼⣞⠀⠀⢶⠓⠉⡼⠀⠃⣰⠀⠇⠾⠒⠙⣄⢹⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠾⡠⢇⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⡸⠇⢀⠀⠀⠀ ⠁⡿⡴⢿⠛⠉⠈⠀⠀⢀⠁⡿⠙⠚⠉⣈⠣⡌⣦⡞⡜⣷⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⣠⣀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⢠⠀⠀⠋⢰⠀⢹⠋⠙⠀⠁⠛ ⡃⣰⠎⢀⡼⠀⣀⣇⠠⠀⡟⣾⣐⢦⡑⣄⠳⣇⠀⣧⢈⡇⢻⢆⠙⠉⠉⠙⠉⠋⠖⡥⣬⢀⠀⠀⠀⠀⠀⡆⡞⠘⠀⠀⠀⠀⠃⣿⣸⠁⣼⠀⠀⠀⠋⡿⢲⠒⠒⡓⣿⣿⣯⣿⣽ ⢠⠄⢀⡜⠀⠀⠏⢰⠀⡟⢀⢸⠀⠉⡉⢣⠀⣄⠀⠀⠁⡟⣿⠾⣡⣼⢀⠋⣴⢁⠟⣴⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠻⠈⠀⠋⣽⣿⠉⡿⢻⠓⠶⣸⢀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣼ ⠉⠁⡼⠀⠀⠇⣹⠀⠟⢠⠀⡜⠀⢳⠙⣀⢀⠀⠀⠀⡟⣾⣠⠿⣠⠀⡞⢀⠄⣀⠀⠀⠀⠀⠁⠀⠋⠚⠓⠞⠴⠤⣠⣇⣈⣷⣼⠀⠀⠀⠀⡉⡏⢚⠛⠴⠦⠭⠛⡿⣿⣿⣿⣿⢀ ⣀⣄⠀⠀⠁⠉⡉⣍⢩⠉⠉⢻⠉⠉⡉⢻⠈⠃⠋⡼⢀⠀⡞⢀⠀⠃⢸⠀⠀⠀⠀⠁⠚⡴⣤⣀⢀⠋⣠⠀⠀⠀⠀⠀⢣⠀⢤⠀⠀⠛⡿⢀⡿⠉⢾⠶⣠⠀⡏⣿⣿⣿⣿⣿⠘ ⠀⠀⠁⠜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⠀⠀⡄⢀⠀⠀⡀⢹⠀⠁⠋⠔⣸⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠁⠋⡖⠹⠀⠀⠀⢆⣴⣠⣀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠃⡴⢀⠀⠀⠀⠇⢠⠀⠀⠀⠁⠞⣀⠀⠀⡀⢦⠙⠈⠀⠀⠁⠀⠁⠉⠉⠛⠟⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠟⠰⠀⠁⠛⢴⣠⠀⠀⠀⠀⠀⡼⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⠤⡤⣀⠉⣞⣴⣯⣿⢿⠿⡋⣟⢿⠛ ⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠉⠉⠛⠒⠴⠤⣠⣀⣄⣤⣷⣾⢶⠴⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⣠⠀⠀⠀⠀⠀⠀⠀⠉⠚⠶⣴⣀⢤⡶⣶⣴⣀⠀⡆⣿⣿⣿⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⡀⣎⣧⣠⣆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇⣠⠀⠀⠀⠀⠀⠀⠃⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⡆⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢡⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⠂⣿⣿ ⠀⠀⠀⠀⠀⠀⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠃⣰⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠃⣿⣟⣯⣶⣶⠰⠀⠁⠋⠚⡶⢀⠀⠀⣀⣥⡈⣄⣦⣛⣖⣮⠶⠿⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠐⠄⠤⠤⠤⣨⣛⢉⠈⠀⠀⡀⣤⠦⠓⣛⣌⣦⣷⢴⢤⠤⠤ ⠀⠀⠀⠀⠀⠀⠁⡾⡀⣦⣶⣴⣤⣠⣧⣨⠀⠀⠀⠀⠉⠛⠿⣿⢿⠿⠿⠿⠙⠈⠀⡄⣿⣿⣿⣻⣛⣝⣩⣭⣿⣻⠉⠀⠀⠀⠀⢳⣆⣘⣀⣤⠷⠳⠙⠈⠀⠀⣀⣄⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⣿⣾⠮⠳⣌⠧⠙⠉⡟⠀⠀⠁⠏⡿⣿⣴⣀⣀⠀⠀⠀⠀⠀⡀⣄⠦⡓⣭⣿⢸⠀⡀⣀⣀⣄⣦⣿⣶⠳⠙⠈⡆⠘⢆⠙⠈⠀⢰⠀⣀⢦⠳⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⡞⣷⣿⢀⢳⠐⡀⢧⡙⣄⣷⠀⠏⡿⣝⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣵⠹⠀⡀⢹⠀⢧⠉⡄⣿⢿⠟⠻⠉⠀⠀⡀⢀⠀⠀⠂⠀⠀ ⠀⠋⡾⣤⠂⡟⣸⠀⡸⠀⠁⡽⣹⢤⠲⠗⣿⡿⣾⢢⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣌⠘⠀⡆⠸⠀⣧⣤⣦⣿⣿⣹⣷⢾⠻⠙⠀⠀⠀⠀⠀⠀ ⡀⡃⢿⠀⠆⢧⢠⠇⢀⠀⡻⡸⣿⠉⢸⡏⣿⣴⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⠸⠀⢧⠡⠀⢧⠈⠀⣄⣷⡜⣳⡝⣿⣿⠻⠙⠀⠀⠀ ⠐⡿⣸⠀⠃⣷⢿⣸⠀⡏⡼⠀⣧⣿⠠⣿⣰⠤⠲⠽⠤⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢦⠙⠀⠀⠀⠀⠀⠀⠀⡀⠸⡄⠘⡀⡽⠱⠀⢆⠙⠀⠀⢇⡘⣷⣠⣀⣄⣤⢶⠙⠀ ⡯⣿⢸⠀⠠⠀⣿⢀⠃⢹⢰⠀⡄⣿⠋⢰⠀⠀⠀⡀⢦⢧⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠟⣿⢳⠀⠀⠀⠀⠀⠀⠀⡆⠘⡄⠱⣇⡹⠀⠀⡄⠳⠀⠀⣆⡈⢳⠋⠜⣠⠀⠀⣀ ⣿⣿⢻⠠⠀⠀⣽⠀⡎⡇⠀⠘⠀⣿⣠⠀⠀⠀⠀⠀⠀⡏⣿⠘⠉⠀⠀⠀⠉⠉⠋⠘⣿⣿⣿⣿⡿⢿⠈⠀⠀⠀⠀⠀⠀⣆⠈⡁⣧⣿⠻⠀⠀⡀⣄⠙⠀⣧⠘⣧⢹⠀⠀⠀⡀ ⣿⣶⢠⠁⠀⠀⣾⠀⢸⠀⠀⢻⡏⣰⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣻⣾⣣⢻⠀⠀⠀⠀⠀⠀⠀⢧⡘⠀⣄⣷⢳⠀⠀⠀⡀⢤⠙⢇⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⣸⠇⠀⢠⠇⢀⢸⠁⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⢾⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠄⡙⣦⢿⠙⠀⠀⠄⡑⣯⣿⡜⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠀⡇⠁⢸⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⢀⣏⣷⣾⣿⣿⣿⣻⣶⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⡀⢦⣐⡄⢱⠀⠀⡀⣄⣦⢸⠀⠀⠀⠐ ⠀⠀⠀⠀⢀⠁⠀⡇⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢴⠶⠴⡤⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⠈⡄⠑⡄⠳⠈⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣵⠳⠈⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣼⠳⠉⠉⡉⢿⠙⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠘⠀⠀⢠⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠤⣤⠻⣏⣿⣿⣴⣀⠳⠀⠀⠀⠀ ⠀⣇⠙⠉⠀⠀⢸⠀⠀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠐⠋⠚⠽⠋⠟⡿⢶⣿⣿⢞⠐⠀⠀⢀⠀⠀⠀ ⠈⡄⣼⡶⠛⠉⢹⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⣤⣫⣿⣿⣾⣿⣯⣶⣤⣁⠋⡿⣴⣠⠀⠀⠁⠋⠒⠀⠀⠀ ⢳⠸⣇⠈⠀⣄⣧⠈⠀⠀⠀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⣿⣿⣻⣟⣶⣿⣉⠛⠾⣶⣤⣋⠔⠤⠤⡥⣭⣋⠒⠓⠘⠀⠀ ⡇⢯⠈⣷⠻⠙⡄⢸⠘⠀⡇⣇⣿⢻⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠄⠷⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⣶⣤⣤⣭⣤⣠⣀⠀⠀⠀⠀⢲⠛⠖⠤⣗⣘⣆⠘⠎⢀⠀⠀ ⠉⣹⢳⡀⣾⣿⢿⣟⢸⠀⡇⡀⣿⣿⠉⡿⠀⠀⣷⠛⠟⠿⠿⠻⠗⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⡄⢷⠈⡀⠹⠀⡈⢷⠈⣞⢀⠀⠉⠈ ⡀⣧⡜⠙⡆⢿⣷⣿⣏⠘⡇⢸⣆⣿⣿⣶⢿⠿⡿⣿⣾⣤⡤⣩⣏⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠹⡄⠸⠀⡄⣿⢠⠁⡼⢀⠀ ⠀⠀⢧⣆⠘⣆⡘⢻⣸⢳⡇⢸⠀⣧⣿⣦⣽⣤⣤⣤⣤⣤⣤⣀⡄⠻⠀⠀⠢⠙⠀⠀⠀⠀⠀⠀⠀⡄⢷⠙⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⣏⠀⠃⣰⠁⡼⡀⠐⠀ ⠘⠀⡀⢳⢧⠀⢃⡄⢻⡄⡜⣿⠀⠀⣧⠸⣄⠓⠀⠀⠀⠀⠀⠀⢱⡀⢳⠈⠈⡀⣄⠳⠛⠈⠀⠀⠀⠀⡀⣷⠫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣯⢿⣠⠀⡟⠀⠀⠀⠈ ⣿⠘⠀⡀⣳⢷⡄⠘⣇⠸⢆⣟⢹⠀⠀⣧⠘⡀⢦⠙⠀⠀⠁⠉⡏⠘⡀⣧⠈⠀⠀⠀⣄⣧⠾⠙⠀⠀⠀⠀⢧⢮⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠏⢠⠀⠀⠀⢁ ⣧⣿⠹⠀⡀⡹⢳⠁⠀⢧⠀⣆⡞⠘⣀⢤⢷⠙⠈⡀⣦⣙⢀⠀⠀⣦⠈⠀⢆⠘⠀⠀⠀⠀⣀⡳⢮⠙⠀⠀⠀⣦⡌⠳⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⣤⢾⢠⠃⡸⠀⠀⠀⠀⠀⡀ ⡄⣶⣿⢿⠙⡀⣱⣧⠘⡀⢸⠀⣆⢯⠀⠀⠀⢱⣄⡶⠽⡚⢯⠈⠀⠀⢧⠈⠀⡄⠳⠀⠀⠀⠀⠀⡀⡣⢮⠙⠀⠀⢇⡈⢳⠈⠖⠶⠴⡤⣠⣀⠀⠁⡼⠀⠏⣠⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣤⣷⢿⡙⢣⢯⠈⡆⠘⠀⢦⢿⠀⠀⡀⢱⠀⠀⣄⢦⣕⠺⠙⠈⢣⠀⠀⡀⢦⠙⠁⠀⠀⠀⠀⣄⡳⢮⠙⠀⢧⠈⢧⠈⠀⠀⠀⠀⠀⠋⣰⠀⠞⢀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣤⢷⣿⢫⠀⢆⠈⠀⣆⢻⠀⠀⡀⠱⠀⠀⠀⠀⣄⡳⣌⣦⠻⠀⠁⠋⡀⠳⣌⠓⠈⠀⠀⠀⢄⡙⠢⠈⢳⠀⢧⠈⠀⠀⠁⡴⢀⠀⡏⢀⠀⠀⡄⢸⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⡀⣄⠹⠀⣦⠈⠀⣄⢿⠈⠀⡄⠳⠀⠀⠒⠓⠛⡚⠲⡽⣷⣃⠈⠀⡀⣦⠻⢌⠑⠀⠀⠂⡈⠣⡌⣷⢹⠀⢧⠁⠞⣠⠀⠀⡎⢠⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠑⠀⠀⠀⠐⠈⠀⠀⡄⢱⠀⢇⠘⠀⡀⢷⠘⠀⡀⢣⠈⠀⠀⠀⠀⠀⡀⢤⢷⢎⠙⠀⠀⡄⣷⠻⢌⠐⠀⣄⠰⢦⡈⣧⠘⠋⣰⠀⠀⠁⠞⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⠑⠈⠀⡀⢦⠑⠈⡄⠻⠀⣄⠘⠀⠀⣆⠘⠀⠀⢆⠙⠀⠀⠀⠀⠀⠀⠀⣆⡝⠳⠀⠀⠀⣆⣿⠓⠈⠀⠀⠀⡆⠙⣼⢀⠀⠀⠋⡰⠀⠀⠀⠀⠋⠟⡿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠲⠉⠀⠀⣀⢤⡖⠻⠈⡄⠱⠀⠀⡀⠢⠈⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⡄⠱⢆⠙⠀⠀⡀⣶⣭⠷⠛⠞⡴⣠⠀⠁⠛⡼⢛⠛⠻⠾⠿⣷⣵⢸⣏⣿⠀⠀⠀⠀⠀

⣿⣿⣿⣰⠟⣮⣠⣉⣋⣘⣤⣷⣾⣣⣦⠻⠀⠀⠀⠀⠀⠁⠛⣿⣻⣿⣿⣿⣿⣿ ⣿⣿⣿⡯⣺⠴⣀⠄⠫⠙⠭⢋⠛⠰⠀⣄⣦⠶⠶⠶⡷⣼⣀⢄⠀⣷⣿⣿⣿⣿ ⣿⣿⣿⣋⠿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠂⠄⢀⢰⠀⠀⠀⡄⣿⣿⣿⣿ ⣲⢀⣇⢿⠾⠶⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠇⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠙⠀⠀⠀⠀⠀⠁⠊⡻⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿ ⠷⠿⠣⠉⡏⢻⠸⠀⠀⠀⠀⡏⠛⠉⠋⠄⡠⢀⠀⣆⢻⠈⠀⠁⡿⣿⣿⣿⣿⣿ ⡀⣷⣠⡿⢟⣶⣤⠶⠩⠈⡠⢀⠀⡀⢸⠀⠋⠴⣠⣀⣀⣧⣿⣿⣿⣿⣿⣿⣿⣿ ⠳⡈⣅⣾⣹⠀⠀⠀⡅⣷⠿⠓⠑⠔⢀⠇⣄⢕⢖⠤⡥⣿⣿⣿⣿⣾⣷⣿⣿⣿ ⡟⢯⡙⣽⠷⣿⢘⠟⣿⣼⣏⡰⠀⠀⠀⡯⣤⢧⠼⡲⣮⣿⣿⣿⣿⠟⣿⣿⣿⣿ ⣿⢿⣝⣈⢤⣲⣽⣽⣻⡫⡿⢿⠘⠀⠀⣄⢹⡇⠀⠀⡀⣦⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠻⣙⢠⡿⣿⣿⢽⠀⣄⣾⠄⠠⡒⠣⡟⠀⠀⠀⠀⠀⡄⣸⣾⣿⣿⣿⣿ ⣾⣶⣿⣾⣶⢶⣷⣿⣴⠃⢰⠀⠀⠀⠀⠀⠀⠀⣀⠤⠢⠒⠑⠉⢹⢸⣧⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⠀⠀⣿⠀⢀⡾⠛⠋⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠀⠀⠀⣿⢀⣾⠁⠀⣰⠆⢹⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣧⠀⠀⢠⡟⢸⡇⠀⣰⠟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣆⢀⣸⣇⣸⠃⢠⡏⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⠾⠟⠛⠉⠉⠉⠈⠉⠉⠛⠁⢾⠁⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠾⠟⠛⠛⣻⣿⣙⡁⠀⠀⢾⣶⣾⣷⣿⣶⣄⠀⠀⠀⠀⠰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣶⣶⠾⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⣿⣻⣟⣻⣿⡦⠀⠘⣿⣿⣛⡿⢶⡇⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⣿⣿⡗⠀⠀⠿⠉⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣿⡿⠁⠀⠀⠘⢦⣿⣿⠇⠟⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠛⠆⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⢶⣶⣦⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣟⣯⣽⠟⠋⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⠀⠉⠛⠷⣮⣍⣩⡍⢻⡟⠉⣉⢹⡏⠉⣿⣹⣷⣦⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⠇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⣠⡶⠀⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣥⢠⣤⠼⠇⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡄⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠾⠷⠄⠀⠀⠀⢀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⣿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠉⠛⢿⣿⣯⣿⡟⢿⠻⣿⢻⣿⢿⣿⣿⣿⣿⣿⠿⠟⠹⣟⢷⣄⠀⠀⠀⢀⣼⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠘⢷⣌⡻⠿⣿⣛⣿⣟⣛⣛⣋⣉⣉⣉⣀⡀⠀⠀⠈⠻⢿⣷⣶⣶⢛⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠹⢯⣟⣛⢿⣿⣽⣅⣀⡀⠀⣀⡀⠀⠀⠀⠠⢦⣀⠰⡦⠀⢸⠀⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⠀⣸⠀⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⢦⡀⡀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠳⣝⠦⢄⠀⠀⠀⣟⣷⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⡀⠀⠀⠈⠙⠂⠀⠀⠀⢸⣿⡄⠀⠀⠘⢦⡙⢦⡀⠀⠀⠀⠀⢰⣷⣷⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢧⣤⣀⡀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⢿⡍⠛⠳⠶⣶⣤⣤⣤⣤⣤⣤⠼⠟⡟⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣷⣶⣶⣶⣶⣶⣶⣦⣀⣀⣀⣻⡀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠈⠻⣿⡆⢹⣯⣽⣿⣿⠟⠋⠙⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣟⠋⠉⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠈⢻⣆⣿⠀⠀⠀⢁⣶⣿⠿⠟⠛⠷⣶⣽⣿⣿⣻⣏⠙⠃⣴⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⠀⣀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣿⢀⣰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣤⣤⣤⣤⣤⣤⣾⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⣾⢿⣵⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⢹⣜⠷⠦⠤⠤⠤⠤⠤⠴⠶⠛⣉⣱⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⣦⣤⣤⣄⣠⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀

🔥😈💦

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢁⠟⠛⠛⣈⣧⣿⢿⠶⣶⠶⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⢿⡘⣾⢀⡟⣿⠿⠈⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣷⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⢠⢘⡿⣿⣿⣿⢿⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢁⠟⡿⣶⣶⠶⠳⣍⣦⣿⣿⡘⣅⣶⣿⣶⣠⠁⢸⣇⣿⣿⣿⣿⢸⡀⠁⠍⠈⡑⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣶⣶⣴⣤⣠⣤⠃⣿⣴⣟⣿⣿⣿⢿⡙⢧⡘⣷⢿⡘⣷⠟⡿⢹⡀⣿⡘⣷⣿⣿⣿⢀⡇⣿⣿⣿⡘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣦⣷⣿⣿⢂⠛⠛⠛⠛⠀⠻⡟⠿⠘⡇⣿⡇⣿⣿⣿⣿⣿⣿⢻⢧⡄⣿⢿⠀⣿⣿⣿⠸⣷⢸⠷⡛⣙⠘⠃⡆⣿⣿⣿⢿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠟⠿⡿⠈⣆⣿⠀⣧⣿⣿⢹⡆⣿⣿⣿⢿⡆⣿⡜⣿⣿⣿⣿⣿⣿⣿⡘⢸⣿⣿⠀⣧⣿⣶⣶⡀⠄⣿⣿⣿⢳⡌⢸⡁⣭⣭⢃⠀⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿⠸⣧⢿⡘⣍⣥⣋⠙⣄⣿⣾⣤⠈⣤⢿⣎⣿⣿⣿⣿⣿⣿⢸⢠⣿⣿⠀⠋⠿⣿⣿⣿⣿⣿⢿⠻⣛⢿⠈⡆⣿⣿⣶⠁⠟⠙⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣴⣥⣬⣷⣿⡙⣄⣭⣩⠟⡄⣾⢁⣿⣿⣿⣾⢠⠻⢁⡛⣿⠉⣇⢿⣝⣷⣿⣿⣿⣾⠁⠀⣀⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⡛⣹⠈⡧⣿⣿⢿⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢠⠁⠋⠛⣟⠙⡀⣦⠀⣆⣴⣤⢩⠋⡓⣛⣿⣿⣿⠈⢰⡿⣿⣿⣿⠻⣀⣤⢶⣄⣤⢋⡴⢋⡿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣦⣻⣿⣴⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢹⡆⣿⣿⣶⣀⣫⠟⠿⣿⣿⣿⣿⢃⡿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⢿⠘⡧⣰⡡⠟⣿⣿⠿⣿⣿⣿⣿⢿⣛⣍⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣛⡛⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⠿⠿⠀⡟⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⢹⣧⣿⣿⣿⣿⣿⣿⠘⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣸⠃⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⣌⣷⣿⣿⣿⣿⢸⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⠸⣥⣭⣭⣬⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠦⣙⣬⣶⣶⣶⡆⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⢸⣿⣿⣿⣿⣿⠻⣙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣧⣿⣿⣸⣿⣿⣿⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⣸⢿⣿⠸⣧⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⢿⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⣧⣿⢿⢿⣿⣿⣿⡘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢰⡙⣧⢻⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡇⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⣆⣿⣿⣿⣿⣩⣿⡹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣼⡏⣿⠻⣌⢷⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣴⣩⣛⡛⣙⣬⣷⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣅⣟⣿⣿⣿⣿⣿⠻⣎⣿⣿⣿⣿⣿⣿⣿⣯⣾⢇⣼⠏⣿⣿⣿⣿⠻⣙⣤⣇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢃⡿⣿⣿⣿⣿⣿⠻⣌⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣭⣽⣾⣶⣿⡿⣷⣿⣿⣿⣽⢟⣿⢥⣴⠋⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⣄⣧⣿⣿⣿⣿⣿⣿⣶⣥⣪⠒⠒⡖⣿⣿⣿⣿⣿⣯⣿⣿⢸⠛⣄⣷⣿⣿⣿⣿⣿⣿⣿⢿⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢶⠿⣛⠭⣦⣶⣿⣾⣿⣹⣠⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⣀⣧⣮⣿⣾⢀⣋⠞⠶⣭⣩⣛⣛⣟⣿⣾⣷⣿⣿⣿⢸⠏⠿⠙⣇⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠿⡛⣌⣷⣿⣿⣿⣸⣸⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⣧⣰⠞⣥⢋⠽⣿⣿⣿⣿⣿⣿⣿⣿⡹⣦⣿⣿⢹⣇⣿⣿⡶⣿⣿⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⡑⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⣿⣿⡆⣿⣴⠇⣿⣿⣿⣿⣿⣿⣿⢡⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡇⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⠘⢉⠋⡿⣿⣿⣿⣿⣿⣤⢃⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠋⣙⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⢚⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⣿⣿⣾⣶⣥⢋⠟⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⢏⣿⣿⣿⠿⡛⣝⣬⣦⣶⣶⣶⣶⣤⣩⢛⠿⣿⢡⢻⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣤⣋⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣍⣶⣿⣿⣿⣿⣿⣼⢀⠉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡟⣿⠈⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢩⠛⡛⣛⣛⠛⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⣿⣿⢹⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣡⠟⡿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⠘⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢿⠈⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡆⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢋⡵⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⣿⣿⣿⣿⣿⢿⠙⡄⣷⣿⣿⣿⣿⣿⣿⣴⣫⣾⣡⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣼⢋⡴⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢿⠛⣍⣤⣶⣶⣶⣥⣩⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣧⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣰⡟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢡⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠄⠀⡀⣀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿ ⣿⣿⣿⣿⣼⢋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠋⠀⢠⠃⠙⠉⠀⡀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣿ ⣿⣿⣿⣰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣰⠀⠊⠃⠹⣼⠀⠀⠋⣿⣨⢉⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿ ⣿⣿⣰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣍⣶⣿⣿⣹⠀⠀⠃⡿⡟⢺⡇⠀⣿⣸⡏⣼⠻⠘⡀⣿⣿⣿⣿⣿⣿⣿⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿ ⣿⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣦⢠⠀⠆⣿⣿⣿⢸⡀⠀⣿⣿⣄⣿⢀⣠⠀⣇⣾⣴⣩⣟⢛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿ ⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⡟⣿⣿⣿⢸⠀⡇⣿⣰⡇⣾⠿⡠⠒⣡⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⡆⣿⢿⣿⢸⠀⣿⣹⠈⡿⢰⣸⠀⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⣆⣻⣿⢸⠀⣿⣿⢻⢠⣠⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠠⠁⣦⣰⠟⠠⡿⣾⢠⠀⠁⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⡏⣿⣿⣿⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢻⠟⣿⣻⣿⣽⣏⠟⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣀⣀⣷⣿⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣓⣌⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠀⠀⠀⡀⣷⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣼⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣾ ⡜⣿⣿⣿⣿⣿⣶⣿⣿⣿⣼⠀⠀⣀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣆⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠁⠉⠋⠹⢀⢷⠿⡿⢿⡙⣧⣿⣿⣿⢸⡍⢀⡀⣷⣿⣿⣿⣿⣿⣿⢸ ⢻⣧⣿⣿⣿⣴⢩⣆⣿⣼⠏⠿⡼⠏⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠘⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⢻⡀⣧⣿⣿⣿⢿⣙⣷⣿⢸⣷⢻⠉⠉⣦⣿⣿⣿⣿⣿⢇ ⣿⡘⣿⣿⣿⠸⡇⢻⣀⡟⣿⣿⢃⣿⣿⣿⣴⢀⠤⠙⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢃⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣷⣿⣿⣿⣿⡹⣷⣿⣿⢿⠈⣌⣷⣿⣿⣶⠹⣧⣿⡘⣷⣿⣿⢿⡙⣇⣿⣿⣼⡏ ⣿⢿⡌⣿⣿⢃⡿⣼⡇⣶⣶⢸⡿⣿⣾⢡⠘⠀⠀⡀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀⠀⠀⣄⣷⣿⣿⣿⠹⣧⣿⣿⢿⡌⠹⠧⣿⣿⣿⡘⣷⣿⠸⣁⣉⢁⢸⣿⣿⣿⢡⣿ ⣿⣿⢿⡜⣰⡆⣭⣸⡇⣧⣿⢸⣿⣴⢋⣿⣿⣾⢋⡿⣿⣿⣿⣿⣿⣾⣴⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠉⡟⡙⣦⣿⣿⣿⠹⣧⣓⣟⠘⡔⠸⡄⣿⣿⣿⡙⣶⢃⡿⣿⡧⠃⣿⣿⣰⡟⣿ ⣿⣿⣿⣿⠻⡀⣅⢸⡀⡟⣿⢸⢋⡿⣿⣿⣼⠏⣿⣿⣿⣿⣶⣥⣀⠗⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣆⣿⣿⢻⣌⣿⣿⣿⡘⢸⣿⣿⠘⡷⠀⣧⣿⣿⣿⠻⡝⣷⣹⡼⠀⣿⣰⡏⣿⣿ ⣿⣿⣿⣿⣿⢻⡀⢠⣷⣿⣿⢃⢳⣝⣭⣤⠏⣿⣿⣿⣴⢋⡿⣹⠀⡀⣉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢿⡙⣣⠟⢿⡙⣦⣿⢸⢈⣧⣿⣿⡻⢙⡁⣿⣿⣿⣿⣿⠻⣆⢠⠀⣰⡟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠘⠛⡆⣿⣿⡇⣿⣿⣿⡉⣦⣶⣩⠟⣦⣿⣿⣴⢋⡿⣿⣿⣿⣴⣯⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⡂⣍⣦⣿⣿⣿⣿⢿⣌⣷⣿⢿⡻⢛⢫⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣴⢉⡼⠀⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢻⡆⢿⡙⣦⣿⣿⣿⢺⢃⠿⣿⣿⣿⢿⡴⢋⡿⣾⣵⣩⣚⠒⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠂⣿⢿⡛⣭⣬⣶⣷⣿⡸⣄⣿⣿⣿⣿⣼⣿⣿⣿⣿⢸⣿⣿⣿⣴⢋⡰⠋⢿⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⣧⣿⢿⡙⣦⣷⢛⣿⣿⣿⣿⣵⢛⡋⣛⠟⠿⣿⣹⠀⠁⡉⡟⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣧⣼⣋⣛⣟⢭⠩⠉⡌⣷⣿⣿⣿⣿⡿⣿⣿⣿⢿⡾⣡⢟⡴⢋⡰⡟⣿⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣭⠢⣙⣭⣤⣶⢃⡿⣿⣿⣾⣴⣥⣫⢛⠿⣿⣿⣿⣿⣿⣿⠛⣿⣾⣴⣢⣿⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⣝⣮⣷⣿⣿⣿⣿⠹⣦⣷⣿⣿⣿⣿⣶⣥⢋⠾⣥⢊⡡⢛⡿⣿⣿⡇⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⣷⣿⣿⢿⠿⡛⣍⣭⠤⠿⠻⠚⠁⣍⣦⣶⣶⣶⣶⣶⣶⣶⣥⣩⣋⠛⠽⣤⢦⠶⠲⠓⣉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡀⣭⣦⣶⣶⣶⡶⣥⣩⣋⠖⡴⣩⢛⠿⣿⣿⣿⣿⣸⣿⣰⡟⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⡉⣬⣶⣷⣿⣿⣿⣿⣿⣿⣀⠋⣶⣶⣶⣶⣤⠠⠗⠿⠛⡛⣙⣭⣬⣶⣶⣷⣿⠿⠿⠿⣿⢿⡛⣍⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣍⣷⢿⠽⡭⣫⣛⣛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠨⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⡁⣾⣿⣿⠿⡿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⠿⠻⣛⣍⣬⣶⣶⣶⣶⣶⣶⣶⣶⣴⣤⣩⣛⠛⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣛⠟⡿⣿⣾⣴⣩⡙⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣋⢛⠿⣾⣴⣩⢋⡙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢸⣇⢻⣇⠘⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣧⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⢠⣾⣇⣿⣿⢸⡏⣿⠹⣧⠻⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢻⣆⣿⣿⣿⣿⣿⣾⣧⣿⣿⣴⠋⢠⡞⢣⡿⣿⣹⠏⣿⣿⣾⣶⣴⢡⣍⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣆⣿⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠹⣦⣿⣿⣿⣡⠋⣿⣾⢱⠔⢀⡉⠛⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⢿⠿⡻⣙⣀⣉⣭⣭⣭⣩⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⣿⠀⣿⢸⣷⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡛⣛⣛⢛⠟⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⣷⣿⣿⢿⡌⠹⣧⢻⡇⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠦⡛⣍⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⣿⢿⡙⡈⣷⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡌⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣧⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣆⢿⠻⣍⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⠹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡐⠠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⢀⠋⡟⠻⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣡⡟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣡⢋⠟⣿⣿⣿⣿⣿⠿⡛⣌⣶⣶⣿⣿⣾⣴⢁⠟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣛⣝⣭⣬⣶⣶⣶⣶⣶⣶⣶⣽⣭⣭⣋⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣛⠟⠿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

🌡️📈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣹⢦⠆⡈⠱⢆⡈⣿⣷⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⡇⣻⢿⣽⣯⡷⢯⡽⢿⣯⣞⣽⣻⣷⢟⣺⣽⢳⣬⠳⣘⠶⢋⢦⡙⢧⣌⠳⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣽⣻⣿⣿⣿⢿⣿⣿⣷⣿⢯⣿⣻⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⡙⢢⢌⡑⠢⢌⡑⣿⣿⣿⢿⣾⢿⣿⣿⣯⢿⣿⣿⣷⣯⣿⣿⢀⠀⠀⠀⠀⠀⠀⡇⣿⡟⣛⣹⣮⡶⣛⢷⣮⢗⣦⡱⣴⠞⢡⣳⠦⣑⠹⢦⣉⠲⣌⠚⢥⡜⣊⠵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⣷⣽⣿⢿⣾⣿⡿⣿⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⠣⢆⡈⠱⢆⡁⠰⣿⢿⣿⣻⣿⣷⢿⣿⣿⣯⢿⣿⣽⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⢿⠻⢻⡽⡛⢭⣊⡭⠖⣊⡱⣜⠧⡉⢦⡘⠴⣋⠤⣙⠧⣌⡹ ⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⡿⣿⣾⣿⣿⣿⣷⣿⣻⢿⣿⣾⣿⣽⣿⣟⡿⣿⣟⡿⣿⣿⣿⣿⣾⢽⠩⢍⡉⠩⢛⡿⣿⣿⣿⣿⡿⣾⣿⡿⣽⣿⣿⣯⡿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⠿⢏⣫⡜⢫⡤⢚⣎⡇⠆⣉⠱⢢⡼⡛ ⣿⣿⣿⣯⣽⣿⣾⣿⡿⣿⡿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣷⢯⣿⢿⣿⣷⡿⣿⣿⣽⢿⣿⣻⣿⣿⣯⣻⣿⣿⡿⣿⣿⣿⣿⣾⣬⣰⣠⣠⣀⣀⣦⣿⣿⣷⣿⣿⣿⡿⣿⢿⣿⡿⣻⣿⣻⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣽⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⢋⢱⢮⣙⡹⢧⣜⠿ ⣿⣿⣿⣷⣯⣿⣾⣿⣯⢾⣿⣟⣿⣿⣯⣿⣿⣟⡿⣿⣿⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⡿⣾⣿⣟⡿⣿⣿⣿⣿⡿⣿⣾⡿⣽⢿⣿⣻⣿⣾⣿⣟⣿⣿⣬⠰⢀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⡀⣀⣦⣿⣻⢿⣿⣟⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡷⣿⣟⣽⣿⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⣷⣯⢿⣯⢷⣾⣟⣽⡿⣷⣿⣾⣿⣟⣾⣟⢿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣻⢿⣿⣟⡿⣿⣻⣷⣽⣿⣻⣿⣯⡿⣿⣿⣿⣿⣳⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠸⠀⠀⠀⠀⠀⣄⣷⡿⣟⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣯⣿⢯⣿⣯⣟⣿⣟⣻⣿⣯⣿⢾⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⣽⣿⣽⢻⣽⣿⣯⢳⣾⣽⣿⣷⣯⣿⣿⣿⣾⡟⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣷⢻⣿⢻⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡟⣿⣯⣿⣿⣾⣽⣿⣽⣿⢻⣿⣾⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣯⡷⢯⣽⡾⡽⢾⣹⣾⣟⣳⣿⣾⣽⣾⡿⢷⣽⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⠀⠀⣾⠹⠀⠀⠀⠀⠀⠀⡀⣷⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣽⣻⢿⣽⣿⣻⣿⢯⣾⢿⣿⣯⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⣽⢾⣫⡼⢟⣫⢷⣣⣼⣟⣯⣟⣽⣾⣟⣯⣼⡾⣟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⣯⢿⣻⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠚⠖⠶⠶⠶⣿⠲⠒⠙⠈⠀⠀⠀⡆⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣷⡿⣾⣿⢯⣿⣯⣟⣾⣟⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣜⡿⢎⣯⠶⣛⣱⢿⣎⡳⣜⡻⣼⣟⢧⣹⣶⣗⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢬⠀⠀⠀⠀⠀⠁⠛⠶⣠⣀⠀⠀⠀⠀⠀⠣⣿⠀⠀⠀⣀⢦⠳⠛⠒⣿⢸⠀⠀⠀⠈⠀⠀⠀⠀⠁⡇⣻⣷⣟⡿⣯⣻⣿⢷⣿⣯⢿⣿⣷⣻⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⡮⢟⣣⢖⣭⡵⡮⠵⣎⡳⣜⠿⣎⡹⣶⡝⣣⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠀⠀⡀⣀⣠⣄⣀⣀⣀⣄⣤⣶⣾⣷⣶⣶⣶⣤⣤⣠⣄⣤⣤⣶⣿⢊⢄⠳⠚⠗⡾⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠻⠙⠀⠀⠀⣄⠳⣇⢸⠀⠁⡞⢀⠀⠀⠀⠁⠰⡟⣯⣻⣿⢯⣿⣟⡾⣿⣯⣻⢿⣷⣾⣻⣿⡷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡽⢮⣛⣱⢾⣋⡱⢞⣩⠶⣙⣶⠞⢧⣛⢧⡱⢿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⢛⣜⢮⠲⠏⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠻⠈⠀⡄⣿⢸⠁⡾⢀⠀⠀⠣⠀⡰⠏⣿⣳⢿⣷⣯⣟⡾⣽⢿⣾⣿⣯⣾⣿⣾⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡵⢎⡼⣛⡭⢎⡭⠖⣉⢶⡘⢾⣍⢳⡹⣳⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡠⣀⠄⠈⠠⢐⡏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⠻⠀⣿⢠⡞⢀⠀⠀⠀⠀⡌⠇⣽⡿⣿⣳⣾⣿⢯⣿⣻⣷⣟⣾⣽⣿⣿⣟⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡻⢧⣎⠵⢫⢦⡙⢣⣇⡤⣛⢧⣓⡮⡝⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠀⠀⠀⢼⡈⠇⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣴⣤⣀⣀⢀⣄⣿⣾⠀⢰⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣽⣿⢯⣿⢯⣾⣻⣿⣟⣻⣷⡿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢚⣳⣎⡱⢞⣣⠜⢩⡱⢦⡜⢧⡮⢒⣭⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠊⡠⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢺⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠁⣿⢠⠀⠀⠀⠀⠀⠀⠀⡇⣿⣷⣿⣿⣿⣿⣿⡿⣿⣟⣻⢿⣻⣽⣿⣯⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡜⢳⣍⡦⠝⢢⡝⢊⡱⢎⡌⠳⢌⡱⣟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣎⠥⡓⢬⡓⠤⡚⢅⠢⡜⢎⢑⡬⠓⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⠀⠀⠀⠀⠀⠀⠉⠟⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡌⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣷⣿⣾⣿⣯⢿⣾⣿⣳⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢎⣩⠦⣊⢱⢦⡃⢁⢨⡜⠥⡊⠕⣏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡲⠉⠉⠉⠒⠖⡶⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⣹⣿⣿⣿⢷⣿⣟⣻⣷⣟⣳⣟⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢎⡑⢎⢅⡨⠜⢣⡠⠕⡘⢣⢌⠪⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡱⠞⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⠀⠀⠀⠀⠀⠀⠇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣦⡝⣿⣿⣿⡿⣿⣿⣿⡿⣽⡿⣟⣷⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢍⡡⠜⢡⡜⠆⠡⣆⠌⡒⠓⢂⢑⢡⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣠⠀⠈⠀⠁⠋⠿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⣇⡈⣏⣿⢾⠵⠮⡽⠶⢋⣭⣖⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡈⠸⡎⠆⡈⢶⡈⠇⢁⡰⠎⡱⡆⠰⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠁⡰⠁⠏⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆⠉⣿⣹⠉⣷⣿⣿⡾⣹⢿⡿⣿⡿⢿⡹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠌⠱⢣⢀⣬⠒⢃⢠⡉⠰⢂⡐⠲⣉⡆⢹⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠀⠋⣴⢀⠂⠥⣈⠀⠀⠀⠀⠀⠀⠈⠀⠁⡟⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠉⡟⡤⢀⠀⠀⠀⠀⠁⠀⠀⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣀⣀⠀⡀⣀⢤⢤⣤⣤⣦⣷⢿⡻⣖⣎⣵⣾⢿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⢊⠱⣈⡑⠥⠀⢢⠌⠰⢊⡱⢆⡑⠬⡆⠹⡀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⡞⢀⠀⡀⡀⢀⠁⠉⠚⠒⠛⠖⠤⡴⣧⣿⣿⠒⡒⣶⣿⢹⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⣿⣼⢀⠀⠀⠀⠀⠁⠞⢀⠁⠊⡠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠅⠺⠳⡛⡒⣿⢿⣳⡝⢎⣧⣷⣻⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠱⢎⡡⠔⡉⡒⡈⢆⠈⡑⠄⠣⢤⠸⡘⢧⡌⠳⠈⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⢰⠀⠀⠁⠚⠷⣠⢀⠀⠀⠀⠀⠀⠃⣿⣿⣾⢀⠀⠀⠀⠀⠀⣀⣀⢄⠤⠤⠲⠓⠉⠈⠀⠀⠀⠀⠁⡽⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⠀⢄⠢⠈⠀⠀⠃⣿⠁⡰⢀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠒⠑⠋⠛⠶⠶⠦⣶⢾⣲⣽⣯⣶⢿⡹⣽⣦⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡑⠦⡌⠓⡠⠔⠂⠄⢈⠢⡐⠒⣉⢖⡈⢳⡎⠒⣍⠲⠈⢄⠢⠈⠀⠀⠀⠀⠀⠀⠁⡍⢫⠒⠖⠤⡠⣀⠀⡀⢄⠤⠂⠒⠀⠀⠀⡇⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠦⠓⡿⣿⢿⠛⠈⠢⠑⠈⠀⠀⠀⠀⠀⠀⠉⠞⡤⢀⠀⠀⠀⠀⠀⡄⠘⠀⣸⢻⡸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠄⡤⣤⠻⠛⠛⠋⠿⠛⠿⣭⣬⣦⣮⢿⡛⣭⢿⡍⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡱⢌⡘⠢⣐⡉⢂⢦⠈⢢⡑⢌⡓⠦⣉⠳⢍⢢⡘⠵⣊⢷⠛⡉⢄⠢⠈⠀⠀⠀⡗⣧⢻⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣷⠻⠙⠈⢈⠉⠋⠒⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢸⡟⢀⠀⠁⠟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠅⠀⠀⠀⠀⠀⠂⡴⣤⡦⣵⣬⢲⡙⣉⣤⣤⢶⢙⡀⣇⣌⡷⢯⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢋⠤⡘⢈⡔⠈⠥⢊⠄⢈⡰⡌⢣⣔⠚⠰⡓⠤⡎⠁⢦⢊⡐⣮⣑⢧⠬⠶⠻⠚⡓⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣷⣝⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡇⠀⠄⢃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠲⡙⣈⢤⠰⡀⣄⠛⣍⠮⣗⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠱⢢⠌⢂⠙⢄⠩⠂⢈⡑⢂⣁⢠⡵⠦⣈⠑⢢⢒⠡⢬⠆⡄⢇⡤⠦⣑⡸⢏⡔⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⡲⢝⠩⠒⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⡄⠘⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⣷⢮⠙⠀⠀⠀⠀⠀⠊⠒⠛⠛⠛⡙⣍⠫⠙⢄⠰⡀⢮⣛⢬⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣈⠰⢘⢢⠃⢠⠒⢡⢂⠐⠣⡐⡑⠠⠘⢇⡀⠄⠡⢂⠄⠱⣊⠄⠲⣈⠷⠃⢌⡧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⠳⠙⣉⢀⠤⠤⠀⠂⠐⠁⠎⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣦⢻⠀⣦⡙⢦⠙⠈⠀⠖⡶⣋⣙⠙⡉⠉⠉⡀⣀⣤⠦⠚⠑⢧⣍⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⠪⣑⠣⢀⠰⡔⠉⢂⠡⢀⡱⠈⡰⠜⠂⢌⡀⢐⠌⡑⠢⠔⣂⠌⡐⢒⠱⣅⡧⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⢷⠻⠛⠙⠉⠈⠀⢄⢻⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠉⡖⣌⠈⡄⢳⠈⡀⢦⡉⣯⠶⡽⣤⣀⣀⡀⣀⠀⣀⣀⠤⠤⠠⠄⡈⠱⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠣⢄⡘⠩⣠⡜⠂⠁⢂⠡⡅⠈⠦⡁⡐⢍⠀⣈⠒⠡⠐⢡⣌⠌⠓⣁⡆⡐⡜⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⢳⡽⣯⣧⢙⠤⢦⠚⠒⣒⢂⠓⠒⠓⠄⡧⠀⢰⢄⢳⠈⡀⣷⠑⠈⡀⣦⣘⣄⣦⣦⣶⠽⠮⠂⠒⠒⠒⠓⠓⠞⠞⠾⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢃⢡⡌⠓⢤⠒⢀⠠⡐⠒⡑⠆⢈⡑⠦⡇⠌⡐⠌⠂⡀⢡⠢⣅⠈⡱⠂⢡⡐⣌⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⣻⡿⢿⠙⢆⠘⢪⠀⠀⣦⠙⢻⠀⠡⡄⠈⡀⢆⠈⠀⢢⢌⠢⠙⠈⠀⠂⠐⠀⠀⣀⢄⠦⠀⠀⠀⠐⠃⠄⠚⢇⣾⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿ ⢠⡜⢣⡌⠤⡘⢌⡈⠆⠁⠰⢣⡒⠌⡠⢇⡀⠁⠄⢀⡀⠒⣈⠒⡍⠀⢰⡈⡔⠃⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣸⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⡿⢮⠟⢮⢈⠀⠀⠀⣧⠘⠀⠡⢆⠀⠀⡀⠢⠈⡀⠤⠑⣄⢤⠷⠩⠒⠒⠀⠀⠀⠀⠀⠀⠀⠡⠄⠋⣿⣽⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿ ⡱⢌⠢⡑⢨⠌⠐⢁⠠⠁⠠⠄⠈⠁⢠⠀⠈⠀⡀⠈⢂⠁⠄⠊⠁⢡⠈⢈⡔⢊⡐⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⣟⣷⠙⠀⠀⠀⣀⠓⠈⠀⢂⠈⠀⠀⡀⠄⠒⠉⠀⠀⠀⠀⣀⢀⠄⠤⠀⠀⠀⠀⠀⠋⡽⣿⣯⡷⣾⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⡜⢃⠠⠜⠀⡄⠀⠀⠘⠣⢃⠀⠀⠃⠀⠀⡀⠠⠀⠀⠄⠠⠄⠠⠃⠘⢃⡄⠀⢠⡸⢻⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟⠠⠀⠀⠀⡀⢻⣇⢿⠻⠀⠀⠀⠀⠣⠀⡀⠘⠀⠃⠜⠤⣀⠀⠄⡤⠀⠀⠀⠀⠀⠀⠃⠀⡀⣟⣼⣿⡿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿ ⡠⠖⡈⠓⠒⢈⡐⠂⢀⠁⠠⠐⠁⢀⠡⠂⠀⠀⠉⠄⠂⠀⠠⢈⡘⠀⠌⡈⠐⣈⠄⠌⡤⠳⡈⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣈⣠⣐⣄⣡⣌⣍⢭⠯⠿⠻⠛⠙⠋⠉⠙⠋⠋⠒⠒⠒⠖⠤⡠⣀⠀⠀⠀⠀⠀⠀⡄⢳⢦⣿⢾⠻⠙⠀⠀⢀⠠⡑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠋⡿⣯⣗⢮⣳⣾⣿⣿⣳⢿⣯⣿⣿⣿⣿⣿⣿⣿ ⣂⠄⡉⠐⠡⠀⠔⠀⠁⠂⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⢀⠈⠀⢁⠄⠁⢢⠁⢂⠁⣂⡑⣆⠳⠈⢄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠁⢋⠖⠬⡴⣤⣠⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⣤⢷⣯⣟⠯⠛⠉⠉⡀⢁⠤⠲⠒⠒⠒⠒⠤⠤⡀⢉⠞⡽⣷⣜⡽⢻⣷⣏⣳⣿⣞⡽⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⢠⠐⡈⠐⠐⡀⠂⡀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠂⣄⠀⠈⡄⠂⠠⠠⠊⡀⠜⠣⣄⢣⣎⢦⠓⠉⣀⠤⠒⠁⠉⠀⠀⠀⠀⡀⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠼⣰⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⠄⠠⡀⣀⣀⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣠⣌⠓⣭⡳⣞⡯⣝⡼⡻⣽⣯⡷⣞⣻⢷⣯⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⡀⠢⠄⡀⠂⠄⠀⠀⣀⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠄⠀⠄⠀⠈⢡⠉⢂⠡⡔⢈⣱⠆⢩⣖⠌⡳⣌⢶⠿⠲⠓⡛⢉⠭⠈⠛⡌⣷⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠁⡔⠀⡇⢘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⢇⠣⣳⢮⢷⣎⡽⣞⢯⡾⣟⣯⣽⣻⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⢂⠄⠂⢄⠠⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠰⠁⠄⠂⠈⢎⡀⡑⢆⡈⠵⡊⠵⢋⢣⣕⣦⠙⣬⠳⢌⣓⡬⣋⣔⣜⣶⣿⣿⠳⠛⠉⠈⢀⠀⠉⠞⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠀⠁⡼⢀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠁⠂⡄⡝⡣⢷⣏⢭⣾⡟⣯⢟⣯⢷⣾⣟⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡁⠤⢂⠀⣀⠁⡀⠄⡀⠀⠁⠄⠀⢈⡀⠀⢀⠀⢀⡀⠀⠠⠄⡌⠂⠁⠠⡀⠔⠀⠠⣈⠒⢥⡜⠣⢎⡇⠎⢣⡵⣎⡝⣌⠲⡎⠉⣰⠹⣦⠏⢁⢤⠓⡤⠽⣋⣿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⡠⢀⠀⠀⠁⡽⠂⢁⠌⠀⡐⡀⠀⢀⢀⠀⠀⡐⢌⠂⠁⠀⠀⠤⢌⡹⣲⡽⢮⣻⢷⢯⣽⡾⣟⣽⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢂⡅⠂⢀⡀⠠⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⢀⠀⠀⠀⢀⡀⠰⠄⠐⢀⠠⡀⡀⠒⣀⠌⡑⠦⡉⢆⠌⢲⡆⢝⡫⢆⡹⢏⢄⠞⢁⡤⠚⢧⢂⡰⣈⠿⢞⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⣠⠀⠀⠢⠐⠄⠂⢀⠀⠠⠀⢀⡄⠒⠄⠐⠄⡀⠁⢢⡍⡝⣯⡟⣯⣟⣯⢻⣿⣟⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⠄⡄⣩⠛⠿⣿⣶⡐⣶⣶⣿⣿⣿⣽⣿⣿⣿⢿⣶⢶⡑⣷⠄⠇⣿⢠⠄⠳⠛ ⢋⠿⣿⣿⣾⣡⠟⡿⣿⣿⢿⠻⣌⣷⣿⣾⣥⢋⠿⡿⣿⠿⠙⠄⡇⣿⠄⢿⠈⡀ ⣿⣿⣿⣿⠃⣴⣈⣆⣿⣿⣿⣿⣿⠻⣄⠏⣿⣿⣿⣿⣿⣠⣈⢣⠈⣤⠄⡆⣿⠻ ⣿⣿⣿⢡⡆⠙⢁⡟⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⠹⡉⠋⢰⠄⠿⠛⣍⣭ ⣿⣿⣿⡎⠹⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠏⡇⣿⣿⣿⣿ ⣿⣿⣿⢿⡄⢰⣄⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣵⠟⣸⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⢻⠄⠃⢿⣟⣿⣿⣿⣿⣿⢫⣮⣿⣿⣿⣿⣿⢟⣿⣿⢃⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢸⡁⡽⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣾⢃⣿⣿⣿⣿⣿⣴⣄⡿⣿⣿⢴⠠⠄⣀⣄⣡⣛⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣾⢃⣿⣿⣿⣾⣤⢀⠄⠄⢀⠄⣄⠄⠄⠄⠄⠄⡟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢡⣿⣿⣿⣴⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣼⡏⣿⣿⣸⠄⠄⠄⡆⣿⠷⠙⠛⠕⠤⠸⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢸⣿⣿⣿⢡⠈⠄⠄⠄⣄⣦⣿⣿⢯⠼⠰⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢸⣿⣿⣿⡋⢙⠈⠄⠄⠄⠄⡀⣧⣰⠄⠄⠄⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢹⣬⣦⣶⣶⣿⣿⠹⠄⠄⠄⠄⠄⠄⠄⠄⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠿⠻⠙⠉⠋⠛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠁⠉⠉⠉⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠚⠒⠉⠉⠉⠀⠀ ⠆⡿⣿⣿⣽⣦⢿⠙⠀⡀⣿⢻⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⡿⣿⣿⠿⠿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⢋⠒⠒⠒⠒⠴⡤⣠⢀ ⠀⡀⣄⣦⣿⠀⡀⣦⣷⠻⡟⣿⢿⠙⠀⡄⢿⠀⠀⠀⠀⠀⠀⠀⠃⡿⣶⣠⢀⠀⠀⡀⣄⣶⣿⠻⠃⠿⠿⠿⠿⠛⠛⠀⠁⣼⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢧⠘⠀⠀⠀⣄⣦⣿⣾⢿⠻⣏⢿⠘⠀⠀⠀⠀⠃⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣸⣀⣀⠀⠀⡏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⠹⠀⠀⠀⠀⣿⠀⡀⣀⣀⣧⣿⠸⠀⠀⠁⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⢸⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢧⠘⠀⠀⣿⢿⠙⠀⠀⡅⣾⠀⠀⠀⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⠈⠀⠀⡇⢀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⡄⢻⡌⢳⠈⡄⢳⠈⠀⡏⣰⠀⠀⠀⠀⠀⠀⠀⠋⠙⠉⠈⠀⠀⠀⠀⠀⡀⣷⠘⠀⣾⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⡄⢷⡘⢷⠀⠀⢧⠛⣸⠀⠀⠀⠀⠀⠀⠁⡞⣧⣾⣷⣿⠘⠀⠀⠀⠀⠀⡄⣿⡟⢸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⣦⡹⢻⠀⡏⣾⠀⠀⠀⠀⠀⠀⠃⣼⠀⡇⢸⡄⣿⢿⠀⠀⠀⠀⠀⠀⣷⣴⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⡄⡿⢿⣿⢠⠀⠀⠀⠀⠀⠏⣼⠀⠀⣿⠀⠀⣧⣽⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡄⣿⣸⠀⠀⠀⠀⠀⡟⣰⠀⠀⠃⣼⠀⠀⡏⣿⠒⠐⠀⠀⠀⠀⣼⠀⠀⠀⢿⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⣼⠀⠀⠀⠀⠁⡾⢠⠀⠀⠀⡟⢠⠁⡟⣿⢠⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⣇⣿⣿⠉⠚⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠀⠀⠀⠀⠀⠀⠀⠋⣴⢀⠀⠀⠀⠇⣸⠀⣿⣿⣽⠰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢻⠀⠀⠀⠀⠀⠋⡾⣸⠀⠀⠀⠀⠀⡾⠀⠀⡀⣧⣿⢿⠿⠛⠉⠀⠀⢀⠀⠀⠀⠀⡇⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⠛⠛⠾⡴⣀⠀⣆⠙⠀⠀⠁⡞⢀⠀⠀⠀⠂⣿⣿⣿⣿⣿⢿⠛⠀⠀⠀⠀⠀⡟⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣶⣶⢸⠀⠀⠀⠏⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢿⡏⣿⣿⣿⣶⠒⠀⡀⠣⠿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣿⣿⣿⣿⢻⠀⠀⠀⠉⡟⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣸⢀⠇⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⢻⠛⡿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣴⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

KITTEN?? W-WHY ARE Y-YOU H-HANGING W-WITH OTHER-ER ALPHAS??? 👿👿👿👿👿👿👿👿🐺🐺🐺🐺🐺 I-I T-THOUGHT I W-WAS T-THE ONLY ALPHA THAT H-HIT THE GRIDDY W-WITH YOU, WATCHED SKIBITI T'TOILET AND LAUGHED AT EDGY M-MEMES IN Y-YOUR LIFE🔪🔪🔪🔪🔪😭😭😭😭😭 RAHHHH 👿👿👿🐺🐺🐺 *i accidently attack you and u die cutely* WAIT N-NO KITTEN!!! I-I WANTED T-TO K-KILL T-THE OTHER ALPHA!! NOOOOO MY OMEGA CHICKEN NUGGET HONEY BUN SKIBTI TOILET!!!😭😭😭😭😭🔪🔪🔪 *kills himself cutely*

🔥💦😈

🤪🤤⬆️👀🍆🍑

🐱💦

🥵🍆

👀💋💦

🧿🥵💦

💦🥧

🔥🥵💦

🔥🥵😏

🍑💨😍

🍆🍆⬆️👉

🔞🔥🥵

💻👀🤤💦

🍑💦

👐👖🥵

⠐⠀⠂⣲⣦⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⢈⠀⠀⠂⡀⠀⠀⠀⠀⢁⠈ ⠠⠀⠛⣇⣲⢸⠀⠀⠀⠀⠀⠀⠀⢢⠈⣿⣿⣿⣿⢺⠒⠛⢘⠀⠀⠀⠀⡄⢀⡀ ⠀⠇⠙⡕⣯⡭⠀⠀⠀⠀⠀⠀⠀⠁⡖⣪⣠⠞⢠⠀⡠⠀⠳⠀⠀⠀⠀⠀⠀⠛ ⠕⢂⠠⢄⣭⠉⢩⠀⠀⠀⠀⠀⠄⢀⠀⠀⡛⢀⠀⠀⠀⠠⡇⢻⠉⠀⠀⠀⠀⠀ ⢀⠀⠂⢀⣄⣉⣈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠔⠈⠀⠉⡟⣄⡤⣀⠀⠀⠁⠑ ⠴⠙⠠⡐⡌⠂⢀⡀⠓⠐⠀⠀⠀⠀⠀⠀⡀⢣⠛⣤⣀⠀⠀⣀⠠⠀⠀⠌⢔⢀ ⠏⠢⠚⣀⢁⠻⡚⡪⢦⣬⠘⠀⠀⠀⠈⠚⡠⢀⠁⠀⠀⠁⠘⠈⡀⠁⠰⣗⠙⠋ ⢀⢌⠁⡐⡀⠈⡒⡐⢠⢃⣾⢼⣈⣂⠠⠀⠀⠁⡉⠺⠓⡾⢖⢐⠤⣉⠈⡏⣿⣼ ⣀⠁⡒⣒⠒⠒⡒⠳⠲⣠⡀⠂⠀⠀⠊⠤⣀⠔⠀⠀⢁⢀⠆⡸⢲⢤⣃⣿⣿⢻ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⢌⢀⠀⡄⠀⠁⡀⠀⢄⠒⠁⠂⠓⡿⣿⣷⣼ ⠀⠀⠀⠓⠒⠐⠄⠠⣀⣀⣤⠤⢀⠀⠀⠀⠸⠂⠀⠀⠀⠚⠄⣠⠄⣠⣀⣷⣾⣿ ⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡀⢢⣿

🍆💦🍑

💦🥵

🥵🎯💦

🌶️🥵

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠿⢻⡞⢤⡭⠴⠀⠀⠀⠀⠀⠀⠀⢾⠠⠇⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⣼⣣⠜⣎⢀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢡⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠜⣄⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠘⠀⠄⠐⠀⠀⠀⠀⠁⡐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠣⠈⠀⠁⡘⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠙⠀⠐⡤⡔⠛⢠⠀⠠⠒⠄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠧⠙⠀⠁⡏⣽⠸⠈⠀⠀⠊⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠒⠠⣀⠀⠀⠀⡀⣌⢀⣀⢀⠀⠀⢢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠐⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠀⠀⠀⠒⠉⠍⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⡀⢹⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠸⠀⠀⠀⠀⠀ ⡅⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠀⠀⠀⠀⠀ ⡄⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀ ⠀⠄⠘⠀⠀⠀⠀⡀⡧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠢⠉⠀⠀⠀⠀⢆⠘⠀⠀⠀⠀⠀⠀⠁⠋⡨⢀⣧⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⠠⠀⠀⡤⠳⠓⠚⠒⠐⠽⣁⡵⣸⢢⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡘⠀⣀⠀⠀⠀⢀⠀⠁⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠓⠛⠛⠛⠞⠠⣀⣇⠹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣿⡿⣿⠹⠀⠋⡓⣟⣿⠿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣻⣿⣾⣿⡝⢭⡾⣰⡿⣿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢿⡿⣿⣿⣿⢿⣤⣶⡶⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣷⣙⣾⢠⠀⠀⡀⣀⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

.niaga ti od d’I .yssup ym skcil ehs elihw daeh reh gnivig ro ,seloh ym fo rehtie ni yssup reh gnitteg em semitemos ,elihw a rof taht ekil eunitnoc eW .seciuj ym pu skcil ehs dna ,neht muc I .kcid reh fo esab eht kcil ot gninnigeb ,rehtruf daeh ym evom i sa naom I .htuom ym otni smuc ehs sa yssup ym fo spil eht dna shgiht renni ym ta setib dna skcus ehS .yssup ym edisni stops eht lla stih ehs -em edisni llits s’taht muc mraw eht dna eugnot looc reh leef I .yssup ym ta skcil dna htuom ym otni stsurht ehS .noitisop 96 eht otni teg ew dna dnuora snrut neht ehS .nac i sa kcid reh no peed sa og ot yrt I .tnaig era hcihw ,stit reh barg I .kcid reh gnikcus trats dna drawrof emoc i sa yssup ym fo tuo gnippird muc fo sdaol s’erehT .naom i dna ,em ni muc kciht ,mraw fo not a s’erehT .em otni daol reh smuc ehs dna ,gnibborht kcoc reh ,em ni peed sllab ,spots ehs nehT .erom neve otni detsurht eb ot yssup ym fo edisni eht gnitacirbul ,tniop siht ta lleh sa tew m’I .em edisni ylluf kcid iranatuf gnol hcni-01 reh ,repeed neve dna retsaf neve seog ehS .em edisni muc ot reh geb ot eganam i tub ,erusaelp htiw ykahs si eciov yM ”!esaelp !em ni muc …hpm …hgn“ .tsurht yreve htiw em tsniaga gnimmals era ,em edisni desaeler eb ot gnitiaw muc fo lluf dna gib ,sllab reh dna ,won retsaf neve gniog s’ehS .tuo em gnihcterts s’ehs os ,kciht si kcid reh tub ,thgit yrev m’I .yssup ym fo sllaw eht no erusserp stup kcid reh fo pit ehT .doog os sleef ti dna ,em ni repeed neve seog ehS .tey em ni ylluf kcid reh htiw tub ,ecap eht pu skcip neht ,ylwols tuo dna ni gniog strats ehS .yssup ym otni ti stresni neht ,sinep reh sdloh ehs ,dnah rehto reh htiW .naom ot em gnisuac ,shgiht ym sbarg ehs ,ylnedduS .yalpsid lluf no era seittit dna kcid suomrone reH .oot ,em fo tnorf ni s’ehS .em ni reh deen dna ynroh m’i ,gnibborht si yssup yM .daerps sgel ym ,deb reh no dekan m’I ♡⊹˚₊ iranatuf a yb dekcuF

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠛⠛⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⣿⣿⢿⠈⡇⣾⢠⠀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⣿⣼⢻⣶⢀⠀⠀⡄⠃⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⣿⢠⣆⠀⠀⠀⠀⠿⡇⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⢸⠠⠀⠀⠀⡄⣷⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣿⢸⠈⠀⠀⠀⠀⡀⣿⠈⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⢻⠀⠀⠉⠈⠀⠀⣧⢸⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⣿⢻⠀⡇⣿⣿⠻⡙⢰⠀ ⠀⠀⠀⠀⠀⠃⣿⣿⣿⣼⠀⡄⣠⣄⣷⣿⠻⠈ ⠀⠀⠀⠀⠃⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⣿⣶⢸ ⠀⠀⠀⠁⡏⣿⣿⣽⢿⠸⠀⠀⠀⠀⡀⢀⠈⢀ ⠈⡒⢤⡠⣇⣿⣿⣾⢨⠀⠀⠀⠲⡿⣿⠿⠸⠀ ⠀⠀⠀⠀⡀⣧⣿⢸⠀⠋⣶⣿⣿⣿⣿⣿⢼⠀ ⠀⠀⠄⠠⣀⢀⡀⡀⠀⠀⠀⣖⣶⣷⣴⣠⢀⠀

⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀

⠀⠀⠀⠸⠀⠀⡇⠀⡇⠀⠀⠀⡞⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠁⢸⡱⠀⠀⠀⢸⠀⠀⠀ ⠀⠁⡴⢁⠴⠋⡴⠀⡀⠳⠌⠳⡄⠳⠈⠀ ⠀⢰⠞⢲⡴⢀⠀⠉⠉⠈⣄⠲⢴⠘⢧⠀ ⡇⠇⢀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⡇⠀ ⡇⡜⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡀⡿⠀ ⠀⠀⠀⠀⠃⠒⡖⠀⡆⠒⠒⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠉⠉⠀⠀⠉⠉⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠉⡏⠀⠀⠀⠀⠀⠀⠀ ︎☦ susej kees

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢉⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠁⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣼⢿⠚⠔⠤⡀⣀⣀⣦⠱⠀⠀⠀⠀⠎⡴⢤⠤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⠶⣠⢀⠀⠀⠀⠀⠀⠀⡀⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣬⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⢰⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⡅⠬⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⣀⠄⠤⠤⣀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣲⠙⠉⠀⠀⠀⠀⠁⠋⠒⢤⠑⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⣀⠢⠀⠴⢀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠒⡴⢦⠓⠙⠀⠀⠀⠀⠁⠊⡠⢀⠆⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⢆⠑⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⣆⢰⠀⠋⠴⢀⠀⠀⠀⠀⡄⠽⢲⠛⠛⠛⠾⠀⢷⠿⠛⠟⠿⡴⢀⠀⠀⠀⢄⠲⠈⠀⢆⠞⣠⠀⠀⣀⢤⠑⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠋⠶⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣼⣇⠊⠶⣶⠷⣻⢿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⢄⠙ ⠀⠀⠀⠀⠁⠂⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣶⢹⢄⠙⠛⠻⢈⣏⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠑⠈⠀⠀⠀⠀⡀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⡎⠿⣿⣀⣧⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠒⠉⠀⠀ ⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⡈⣄⢱⠀⣻⠞⣦⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⣞⢤⡦⠤⣠⣄⠦⡗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢟⣇⠤⠒⠂⠤⡀⠀⢰⠃⠀⠀⣀⠄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⢆⢺⠀⠀⠀⠣⣀⣀⡼⢤⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣸⡀⠀⢀⣴⣤⠀⡜⠘⢆⣠⠴⠋⣩⣴⡾⢟⣿⣿⣿⣿⣶⣾⣭⣝⡶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⠀⢸⣿⠃⠀⠀⣠⡼⠣⣤⣿⣿⣛⠤⠛⣿⣿⡿⣻⣿⣟⡿⠿⣿⣘⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣯⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠈⢺⣻⣄⠀⠻⣄⣀⣴⣋⢔⢪⡶⠛⠀⢑⣲⢶⣿⣿⠾⠛⢡⠁⠀⠰⢿⣿⣿⡽⡆⠀⠀⠀ ⠀⠀⣠⣾⡿⠛⣿⡿⣿⣿⡯⠭⣍⣛⠷⣿⣧⢀⣶⡿⠲⡀⢀⣤⣪⠭⠭⣉⠑⠢⡀⠀⠉⠚⠭⣶⢶⡞⠁⢁⣴⢻⠀⠀⢰⠁⠀⠉⢆⠀⠀⣀⠤⣁⠀⢰⣁⡈⠙⢿⢻⠀⠀⠀ ⠠⠊⠉⠉⠁⠈⢉⢼⣿⠏⣴⡄⠀⠈⠙⠯⣿⣷⠁⢀⣷⢡⡾⠋⠐⢀⡀⠈⢳⠀⢱⠀⠀⢠⣾⡟⡏⣇⣴⢟⣡⠼⡀⠀⠀⠁⠀⠀⡸⡰⠉⢀⣆⡤⢷⠼⡟⠋⠀⠸⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⢸⠉⠉⠉⠐⣦⣄⠀⠀⠈⢿⣧⡸⣿⢸⠃⠀⠀⠘⠯⠤⠋⣴⡽⠀⠀⠎⠁⣸⣼⢟⠁⠈⠀⠀⡹⠢⢄⣀⡠⠔⠁⡇⠀⠀⡟⠻⡷⣦⠇⠀⠀⢠⢧⠠⣾⣦ ⠀⠀⠀⠀⣀⠸⡂⠀⠉⠈⠀⠀⠈⠫⡄⠀⠀⠀⠘⢳⣽⣾⡆⠀⠀⠀⠀⠀⠱⠋⠀⠀⣠⣴⣾⣟⠁⣨⣖⠤⠤⣲⠥⣤⠤⣀⠀⠀⠀⠳⣄⠀⠑⢄⡀⠀⠀⢀⡴⢳⣣⠑⠛⠉ ⠀⠀⠀⠈⠿⠛⠣⡀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠿⣟⣦⡀⠑⠦⣴⣶⡾⣶⣿⠟⡏⣾⣿⣦⡤⠜⠀⣼⠁⢀⡿⠀⠀⠱⡄⠀⠀⠈⠓⠲⠤⠬⠟⠛⠉⠀⢺⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠞⠒⠛⠉⠀⣾⣷⠋⣿⣿⠟⣁⡠⠎⠢⠤⠝⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢻⡝⡟⣶⣦⣶⣦⣤⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⠢⣁⠀⠀⠈⠑⢄⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠊⠉⠁⠂⢼⣵⠀⠀⠉⠁⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠇⠀⠀⠀⠀⢾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠢⢄⣀⡴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⠀⠀⠀⠀⠀⡞⠀⠀⠀⡀⢀⠀⠀⢁⢛⡴⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠋⡤⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⡀⢷⠉⠟⣠⣈⢦⠑⠈⡀⠀⠀⠀⠀⠀⠀⡆⠹⠋⡴⢀⠀⠀⠀⠀⠀⠋⠶⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢘⡀⢤⠓⠈⠀⠀⠀⠀⠀⣿⡀⠘⠁⣿⢀⠀⢻⠀⠀⣄⠻⠀⠀⠀⠀⠀⠀⠀⣷⢁⠉⠉⠋⠚⠖⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢧⠘⠀⠀⡀⢤⠳⠙⠈⠀⣾⠀⢹⡿⣰⠀⠀⡏⠚⠓⠉⠀⣦⠑⠀⠀⠀⠀⠀⡄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠋⠹⠀⠀⠀⡇⣿⠉⢿⠽⠭⠯⠻⠘⡀⢄⠳⢹⠀⣿⣿⠛⡶⣶⣴⠤⠤⣤⢤⠶⡲⢟⠙⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⣯⣴⢀⠁⠛⠴⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣿⡿⣴⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠳⠙⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠆⢠⠁⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠈⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠘⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢦⠛⠈⠀⠀⠀⠀⠀⠀⠀⣧⠈⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⣮⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⠀⠀⠀⠀⠀⡆⢸⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠠⠀⠀⠀⢿⠠⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⣽⣯⠿⠒⡶⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢤⠒⡟⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣷⣿⢿⠙⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣧⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠿⢰⠀⣆⣝⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢿⣭⠈⠀⡀⠲⠙⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⣽⢠⠋⠀⠀⡀⢤⠳⠙⠀⠀⡀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⡃⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠟⣿⣶⣴⠀⠀⠀⠀⠀⡀⣄⢤⢒⠑⢭⠫⠒⠀⠀⠀⠁⠋⠟⣿⣿⣿⣿⠿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢄⠤⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⠙⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣘⢺⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⡍⣷⣿⢿⠒⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠏⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⢶⠶⠴⢤⡶⣿⣿⠈⠀⠀⣁⣞⣤⠥⠾⠶⠶⣶⣻⡉⣀⢦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣴⣧⢾⣹⠛⠴⣤⣭⣮⠦⠛⣿⢹⠉⠏⣰⠀⡥⣋⠛⠛⠙⠉⠀⡁⣯⠻⡈⢯⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣶⢠⣀⠋⠿⣾⢴⣤⣀⣀⣀⣀⣇⢩⠉⠋⡒⠒⡒⢖⠴⣠⣀⢁⡾⡀⢷⡟⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠡⠏⡿⣼⣁⠛⠀⠤⠤⠤⢠⠀⡄⣠⣀⠀⠀⠶⠀⠀⠀⠀⠁⡿⣍⠙⠉⣮⣇⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⠒⠓⠉⠀⠀⠀⠀⠀⠀⠀⡇⢋⡞⣷⣿⡴⣠⣄⠹⠁⠀⠈⠀⠀⠀⠀⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣧⠛⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⡴⢀⠀⠀⠀⡀⣄⣼⠀⠀⠀⠀⠀⡄⣠⠁⡾⢀⠀⠃⡿⣿⣿⠩⠀⠀⠉⠫⡋⣹⠿⠛⠒⠦⠐⠀⠀⠀⠀⠀⠀⠀⠉⠞⣿⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⣸⠀⠀⠁⣟⢻⠀⠀⡆⠸⠀⠀⠀⠀⠀⠃⣸⣞⠀⠀⠀⣆⣝⣠⣧⢙⠛⣿⣿⣿⣿⣺⣶⣿⣿⢈⠀⠀⠀⠀⠀⠀⣤⣤⣦⢳⠙⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣯⠀⠀⠀⣿⣾⣷⠻⠛⠀⣆⠈⠀⠀⠀⠁⣼⡧⢰⠀⠀⠀⠀⣆⠹⠀⣅⣷⣿⣿⣿⣿⢻⠛⡟⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠳⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⠘⠀⡇⣿⣷⣿⣿⣾⠀⠁⢸⠀⠀⠀⡟⣘⡇⠸⠀⠀⠀⠀⠀⣄⠳⠈⠀⣀⣦⣳⣙⣈⣤⣤⣤⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠙ ⠀⠀⠀⠀⠀⠀⠀⣄⢳⠈⣀⣀⣷⣴⠀⠋⡴⠀⠀⠀⠀⣾⠈⡇⢸⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⡀⣄⣤⠦⠓⠛⠙⠉⠀⠀⠀⠀⠀⠃⠛⠒⠒⠒⠴⠤⣤⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠲⠙⠉⠋⡴⢀⠀⠀⠀⠀⠀⣿⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠓⠉⠈⠀⠀⠀⠀⣄⠻⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⢷⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⡄⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠆⣯⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠳⣮⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠇⠾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣷⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠞⡴⣯⢾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠦⠶⠲⠒⠖⠶⠶⠴⣠⣀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣫⣀⢄⠠⠀⠀⠀⠁⠈⠀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡞⢀⠀⠀⠀⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⣇⢳⠉⠉⠚⠒⠖⣠⡀⣃⡿⢿⠻⠉⠉⠉⠋⠙⠚⠴⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠀⠀⠋⡼⢀⠀⠀⠀⢿⣠⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⡆⢸⠀⠀⡀⢹⢱⠀⠀⠠⠀⠀⠀⣿⣿⣦⣷⣾⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠟⣠⠀⠀⠞⣾⢀⠀⠀⠁⡿⢰⠀⣇⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⣇⠈⠀⠀⣇⡎⠈⠀⠀⠀⠀⠀⠃⠀⠀⡀⡇⠈⠂⠀⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠁⡼⢏⢠⠀⠁⠞⣠⡞⠀⠀⡞⢤⠀⠀⠀⠀⠁⠉⠉⠀⠀⡀⠀⠀⠀⠀⡇⠘⠠⢧⠈⠀⠀⢻⢹⠀⠇⠈⠀⠁⡿⠹⠀⠀⣿⢿⠘⠉⣿⠚⠐⠀ ⠀⠂⠀⠀⠀⠀⠤⠀⡀⠀⠀⠃⡿⠔⠀⠁⠞⣠⠀⡞⢀⠀⠇⢾⡤⡥⣯⣶⣴⣤⣤⣦⢷⢿⠻⠈⠀⠀⠀⠀⣄⡱⠸⢧⠀⠀⡄⡧⠈⡆⢻⠋⡟⣿⣿⠿⡿⣾⣿⣾⣿⣿⠀⠀⠀ ⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠁⣶⢠⠀⠈⡠⠀⠀⡜⢀⠀⠟⣤⢂⡠⢀⠀⠀⠀⠉⠉⠉⠀⣀⣦⡳⠈⠀⠀⠀⡆⡀⣧⡁⢻⠁⠊⠕⣬⣤⣿⣬⣿⢸⣷⢹⣿⢸⡇⣿⣿⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡀⠀⠃⡾⢀⠀⠀⠀⠀⠀⠊⡴⢀⠀⠀⣄⠳⠈⡀⢦⠙⠀⠁⠀⠀⠀⡌⡞⢿⠶⡤⢿⠀⣷⣿⣿⠀⡇⣿⣿⢠⠀⣿⣿⢣⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⠃⣹⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡀⢧⡄⢻⠀⠀⢣⣇⢿⠜⢀⣿⠀⡇⣿⣼⠀⡄⣿⣸⠀⠀⣷⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠋⡼⢀⠀⠀⠀⠀⠀⠀⡇⣿⢻⠙⠈⠀⠀⠀⠀⠙⢸⠀⠀⡀⠀⣦⠘⠀⡄⠸⣿⠹⠋⣷⠁⠀⣶⢠⠀⠛⣄⢀⠃⢀⡀⠟⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠋⡥⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣾⣿⣿⣿⢿⠿⡿⣿⢀⠀⠀⠀⠀⠀⣆⠙⠀⢠⡇⣫⠀⡇⡆⠀⠀⠀⠐⣿⠹⢏⣻⢋⠛⣿⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡟⢃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⢠⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⡆⣸⠸⡇⠀⠛⠟⠀⣄⣿⣾⣿⣸⣀⡇⣿⣿⠈⠀⠀ ⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⣿⢰⣽⡾⢀⠀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⢸⢮⡤⡿⣴⣷⢰⠀⣧⣿⣿⢀⠃⣿⢸⣧⢿⠀⠀ ⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⣸⠃⣿⢀⠀⠀⠀⠀⢄⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠏⣾⣼⣧⢂⡏⡀⠀⠀⡇⣿⣿⠘⡿⣾⠀⡄⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡏⣿⢠⠀⠀⠃⡿⣛⣙⢱⠀⠀⠀⠀⠀⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣻⢠⠀⠀⣿⠸⠁⡟⡏⣿⣟⢸⡋⠛⠸⠀⠀⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠻⠀⠀⡄⡿⢿⡿⣰⠀⠀⠇⠸⡃⠁⣿⡰⠀⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠇⠏⠿⣿⣿⣿⠀⠋⣦⣿⣾⣿⣾⣿⣣⡿⢀⣿⣿⢿⠙⠀⣿⠀ ⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡇⣿⡿⢮⠻⠙⠉⡉⠋⠟⠿⠃⣿⢻⡽⡏⢻⠀⠙⠀⠀⠇⡻⣛⢯⠀⠀⠀⢻⡿⣧⣾⡇⣿⣯⠜⣜⠀⣿⢿⣿⢰⠀⡟⣿⠸⣧⣿⣧⣿⡿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⡀⣯⣿⢻⠀⡀⣀⣾⠏⣿⣿⣾⣣⣿⣛⢷⢸⠀⣿⡇⠈⡄⢶⣶⣴⠀⠀⠏⣴⣈⡏⢠⡇⣿⣿⣉⢰⠀⣿⣿⣼⠀⠁⣿⣿⢻⡿⣿⠀⣦⣿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣿⡿⣷⣯⢿⠸⡇⣿⣿⣯⣼⠃⣿⣼⢀⡄⢹⠇⣾⠀⣄⠯⠓⠙⠋⠒⡷⣼⠃⢸⣰⠀⡿⣿⣼⣇⠈⠀⣿⣼⢀⠀⡟⣿⢸⣷⣿⣿⠀⠀⣇⣾⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡌⣿⣿⢿⣿⣧⣻⣾⢃⣿⣿⠟⠁⠈⣇⣿⢠⠁⡾⢋⠟⣼⢁⠺⣾⢀⡟⠋⡴⡟⣴⣞⢀⡆⢠⠀⣴⢀⠃⣿⣿⣾⠀⡄⣶⣿⠂⠋⡇⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⡀⣦⣿⣿⢸⣿⢿⡙⣷⠀⡿⣿⢇⢿⣿⢀⡟⣿⠛⣿⡿⢙⡿⠟⣡⣞⢃⡾⢋⢾⣴⢁⡾⢀⠀⠸⠀⠀⠀⠃⡿⣸⣀⠁⠩⠀⠀⣿⡟⢉⠟⢿⡻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣞⠹⠀⠀⡀⣦⢻⣟⣿⣿⠸⡀⣷⢿⣿⡷⢿⠏⣿⣿⣿⠳⠈⣄⣶⢿⣿⢿⣾⣤⣀⠀⠋⡿⠯⡲⣒⢤⠈⠀⠁⡇⣿⢀⠀⣿⣿⠻⠊⡿⣿⣠⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢰⠀⠀⠀⡀⣄⣷⣿⣿⠻⠙⣆⢿⡌⢿⣿⣿⣿⢿⣭⣿⢾⠲⣲⣒⢒⠒⠖⠴⣤⣻⣟⠭⠭⠿⡿⢠⠀⡇⣿⣸⠀⠀⣿⣼⣿⢿⡿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠉⠀⠀⡁⣌⣦⣷⠸⣆⢿⣿⣾⣶⣤⣤⣀⢀⠀⠀⠀⠀⠀⠁⠋⠜⠤⡷⣭⣀⣀⣀⣜⠀⠀⡿⣿⢺⠀⠀⣿⢸⡆⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠈⠀⠀⠀⠀⣀⣤⣶⢶⠲⣳⣄⠦⡒⢙⣉⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⣠⣆⢻⠉⠉⣉⢦⠛⠗⢠⠀⡇⣿⣿⣿⠈⡇⣿⢸⠀⣄⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⠙⠉⠀⠀⠀⠀⠀⠀⡄⠸⠁⠋⡴⣀⠀⠆⠶⡶⣶⢠⠀⠀⠂⠀⠀⠀⠀⠀⣴⠹⠉⠈⠀⠋⡰⠀⠇⣿⣿⡄⣿⢻⠀⣿⢸⠀⡇⣶⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣢⣄⠦⠓⠉⠉⠀⠀⣦⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠶⠶⠴⡼⠀⠁⣿⣿⢠⠀⣧⣾⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢹⣀⣀⣄⠤⠤⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠒⠙⠈⠀⠀⠀⠀⠙⠀⠀⠀⠁⠋⡟⣷⣙⠉⠉⡉⢉⠋⣿⠛⠛⠛⠛⠛⠛⠛⠛⠚ ⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠁⠉⠀⣀⣄⠭⠬⡡⣈⣀⣀⣀⣀⣀⢄⡤⣀⠀⠀⠀⡆⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠁⠇⣿⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⡉⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠱⠀⠀⡐⢀⠀⣆⣿⢺ ⠀⠄⠑⠶⠬⠤⠁⣂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡘⠙⠒⠅⡒⢠⠀ ⠈⢦⠐⢁⡈⠵⠶⠥⡤⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢈⠀⢀⠀⠀⠀ ⣀⠒⠈⢠⠀⢀⠀⠀⢄⠉⡔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠩⠐⡠⠀⠀ ⠏⠈⣀⣜⠢⠈⠀⠀⠎⢀⠀⡀⢵⠀⠀⠀⠀⠀⠀⠊⠀⠏⢑⠾⣤⡀⠀⠀⠀⠀ ⡄⢰⠧⡐⠀⠀⢀⡦⠐⠈⠀⠂⠔⢤⠛⠈⠉⠃⡘⠓⡠⢈⠀⠀⠀⠈⠀⠁⡐⠀ ⠇⠀⠀⡆⠒⠘⠀⠙⠀⣎⠀⠁⠋⡰⠀⢄⠳⢀⢄⠑⢆⠑⠀⠀⠀⠕⢊⠧⠀⠀ ⠀⢤⠗⠼⠄⣠⠀⣀⣘⢀⠁⣀⣼⠀⠀⠀⡄⠈⠀⠀⠀⠀⠤⠠⡀⣀⠀⠰⠀⠀

⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠹⠀⢰⠀⠀⠎⢀⠀⠀⡁⣘⣀⢀⠀⠀⠀ ⡀⠼⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⡄⠈⠌⠀⠀⠄⠂⡅⢻⠀⠀⠁⠈⠓ ⠀⣇⢸⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠀⢧⢀⠀⠀⠀⠀⡦⠘⡀⠁⠎⠂⠒ ⠀⡇⠙⠏⣠⣀⣠⠄⠠⠐⠁⠈⠀⠀⠀⡷⠰⡈⠀⠀⠀⠀⠀⠁⢋⠜⢋⡼⣀⠀ ⠀⡇⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⡏⠤⣷⠝⠁⠀⠀⠀⡀⢧⢆⢀⠀⠀⠀ ⠀⡀⠢⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠹⢼⠀⠀⠀⡇⠀⢇⠛⠐⠀ ⠀⠀⠀⣡⢩⠀⣆⠻⠀⡆⠀⠀⠀⠀⠀⠀⠀⡈⠀⠁⢩⠀⠀⠀⣎⠀⡄⣇⢿⠈ ⠀⠀⠀⡄⣰⠀⠆⣡⠖⢈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣇⠀⠀⠌⢀⠀⠁⡇⣾⢸ ⠀⠀⣀⡇⡪⣤⣻⡞⢦⠘⢤⠢⠔⠈⠀⠀⠀⠃⠀⠁⡔⣡⣳⠀⠂⠚⠄⡠⢟⢘ ⠀⠀⠀⠀⢠⡀⣷⢾⠈⠄⠓⠀⠀⡂⠶⠚⡓⠒⠄⢂⠁⡶⢄⠀⠀⡏⠺⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⡄⡑⠀⡀⠹⠀⠀⠀⢲⡞⢀⠀⠀⠀⢄⠂⠁⠝⢩⣨⠂⡔⣠ ⠀⠀⠀⠀⠀⠀⠁⠖⡫⣽⣊⠫⢈⠋⡫⠐⢤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⣿⠹⣦⢺⣠⣀⣀⣏⣿⠻⢒⠌⣤⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣶⢿⢿⠳⠫⠚⢦⡸⡀⠒⠳⢌⢸⢣⢄⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⡡⡉⣄⣠⢻⠁⢶⣎⢘⠦⡘⡈⠒⢖⡒⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⣳⣩⢍⠽⢤⡤⠤⢤⡒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⢸⠀⠀⠄⠚⣠⠀⠀⠀⠀⠈⠀⠀⠀⡏⢠⠁⠀⠀⠒⠒⠖⣒⢒⢳⠀⠀⠀⠀ ⡇⢘⠀⠀⠁⢰⠀⠃⠯⠈⠀⠈⠀⠂⠟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠀⠀ ⡁⠀⠀⠀⣼⣀⣄⣤⢧⣿⠻⢿⠶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀ ⡜⠀⠀⠀⢸⠃⠴⣀⠀⠀⣀⣧⢥⠒⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⣠ ⠀⠀⠀⠁⣰⣱⠈⠀⠀⠀⠀⡀⡘⣷⢻⢌⠑⠀⢁⠭⠭⠈⠂⠐⠠⣀⠀⠀⠀⠁ ⠸⠀⠀⡉⠀⠁⣴⠀⠀⠀⠀⠁⠄⠁⡍⣿⣩⣠⡀⢀⠀⠉⠉⠈⡀⢢⡈⠣⠊⢤ ⠀⠀⠀⢹⣔⢀⠀⠀⠀⠀⠀⡀⢣⡾⣠⣆⣿⠸⠐⠀⣄⢘⠢⠙⢀⠢⣇⠀⢸⠀ ⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀⠇⡰⠀⠀⠀⣀⢷⠀⡀⠢⣆⠻⡁⣌⠢⠋⡿⢨⠀ ⠀⠀⠀⡆⢻⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠃⡧⠑⠀⠀⢄⠠⠀⠛⢜⢢⢠⠀⠀ ⠀⠀⠀⠀⡆⠈⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠘⠀⠀⠀⢆⠿⡮⡄⣛⢑⡍⠀⠀⠀

⠀⠇⠀⠀⡇⠀⠀⠉⠀⠁⢠⠙⠀⡇⠀⠈⠒⠒⠲⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠈⡆⠠⢀⠀⠀⡉⠔⣀⠁⡀⡞⠀⠀⡐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⡠⠀⠀⢄⠀⠀⡞⣠⠛⠹⡀⢄⣷⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠀ ⠀⢰⠀⠁⠉⠛⠟⡿⢿⣿⣿⣶⢿⠉⡁⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀ ⠀⠿⡿⣿⣿⣴⣠⣀⠀⠀⠀⠀⡄⣿⠸⣆⣹⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠇⣿⣿⣴⠀⠀⠉⠉⠉⠋⡜⣯⣿⣿⢀⠀⡇⢼⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣴⢀⠀⠀⡀⠀⠀⠗⡿⡶⣷⣾⢀⠀⠀⡇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠋⠀⠊⠶⣠⠒⠀⡀⢰⠁⠁⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⢩⡴⠒⠀⠈⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠁⣿⡀⣾⣿⣷⣿⣿⣟⣰⡟⢼⣔⡽⡿⠟⢟⣩⣗⣞⣠⡄⡊⣫⡡⠔⠠⢄ ⠻⡿⡉⣇⠀⣧⡄⢤⣀⣸⢁⠖⣲⡓⠻⣄⣽⢀⠀⢪⢌⣦⢤⡟⡿⢿⢰⠀⡀⢛ ⣷⣴⣷⡼⠀⡏⠮⠝⡑⠀⢠⡀⠀⠀⠁⣄⡽⡷⣦⠷⢺⠀⠀⣄⣞⣠⠀⠉⡵⣶ ⠀⠀⡆⢴⢁⠚⡰⠁⡧⡟⠛⠙⠚⠓⡾⠀⡀⢹⢧⠶⡟⠯⠐⠂⡉⣾⣷⡻⣿⠹ ⠀⠀⠋⡴⣀⠋⠅⢉⣰⠀⢀⠀⠀⠀⠀⠀⠀⡀⠂⢌⠈⡀⣄⣣⣉⣄⣿⣿⣿⣿ ⠀⠋⠻⠧⠹⣠⠂⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⡫⠌⠐⠁⢫⢷⣾⣿⣻⣿ ⣿⡾⣤⣡⣱⡉⢠⠀⠀⡀⠣⣈⠄⠤⢱⡆⠄⠙⠻⠞⠱⣟⠧⠒⡈⣷⢿⡍⣿⣷ ⣀⢠⠁⣸⠀⣧⠿⠾⠷⣤⡴⢆⠈⠀⠀⣄⡿⣿⣿⢿⣾⣡⠙⠸⠀⣇⠤⠰⠈⣧ ⠀⠂⡹⠀⠀⡇⡙⣣⠣⠙⢄⠙⢇⠄⠀⠀⡀⢒⠈⡗⢧⣇⢸⢸⠀⡆⠈⠀⠀⡄ ⠀⠀⡄⠦⠑⡇⣌⣽⢻⡀⢼⢛⣢⢻⠀⠀⠋⡤⢇⡇⠀⡜⢻⢯⡗⡀⣇⢌⠸⢡ ⠁⠃⠁⠀⡁⠶⢻⡀⡱⢱⠀⡄⠛⣧⠃⠀⣝⠘⡀⣾⠁⢖⣿⢠⠠⡡⣝⢸⢅⣰ ⠊⠀⠉⠭⢸⠹⣿⠻⡎⡄⠒⠀⢸⡼⠀⠀⡇⣠⠘⢸⡜⠃⢠⠀⠁⡞⣁⢹⠀⠀ ⠀⠀⢁⣱⠀⣷⢻⣷⢻⠀⠁⡔⡎⠤⠀⠀⡟⠸⡇⢯⢻⣹⠉⠋⡾⢁⣼⢀⠀⠀ ⠀⠀⠁⠈⢘⡎⣍⣢⣸⠁⡰⠌⠀⠀⠀⠔⣑⠙⡞⣴⢀⠀⣀⣀⢄⣴⠠⣀⢀⠀ ⠀⠀⠀⠀⠀⡀⣸⠀⡀⠣⣀⠀⠀⠀⡀⢀⠀⣠⠀⠀⠀⠉⠙⠀⠀⠂⠠⠀⠀⠀

⠀⠀⠀⠁⠓⠛⠛⠛⠖⠷⠓⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠚⠓⠿⣿⣿⣿⣴⠋⡿⢻⢈⠀⡚⠵⡟⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⡆⡀⢘⠀⠉⠒⡿⡶⣣⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣀⣀⢀⣇⣽⣿⢠⡟⣀⡀⣿⣸⠟⣿⣿⣿⣿⣰⣆⣿⣿⣿⣿⠘⠀⠀⠏ ⠀⠀⠀⠀⢣⢫⠉⢸⣼⢀⠏⣿⣿⣿⣾⣤⣠⣀⣀⣀⣀⣀⣀⣀⢀⠀⡤⣶⣶⠓⣸⠀⠁⣿⡼⣤⣤⣿⣾⣠⠀⠁⣿⣿⣿⣿⢿⠟⡿⣿ ⠀⠀⠀⠀⠀⣁⢯⡿⢿⠾⣹⠔⣣⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⠙⡾⣠⠀⠀⠛⣾⣷⠿⠻⡿⣷⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠜⣀⠀⡀⣄⠗⢹⠞⢀⠀⠀⠀⠀⡄⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣛⣿⠚⠉⠛⡴⣀⣀⠧⣾⣠⠀⠀⡏⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠃⢿⠻⠙⠉⠉⠏⣰⠀⠀⠀⠀⠀⠀⠋⠠⣀⣀⣀⠤⠤⠢⠓⠈⠀⠀⠀⠀⣷⢿⣾⢠⠀⠀⠇⣿⣷⠿⠶⣷⣿⣿⣽⢿⠙⡈⣀ ⠀⠀⠃⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠁⡴⢀⠀⠀⠀⠀⠀⠀⠀⠏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣻⡾⢀⠀⠀⣄⣶⣿⣿⣿⣿⠻ ⠀⠋⣽⣛⣼⣤⣤⣥⣰⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠉⠞⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠛⡙⣿⣿⣿⣿ ⠞⣦⢀⠀⢷⠈⠀⡸⠀⠀⠀⠀⠀⠀⡿⠙⠈⠀⠀⠉⠟⠿⣾⢲⠴⣧⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⡻⣄⠀⠀⣄⣷⣿⣿⣿ ⢤⠭⡭⣿⡿⢿⡟⠈⠀⠀⠀⠀⠀⠀⣆⣿⣻⣍⣿⣴⣠⠀⠀⠄⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⡟⢠⠀⠀⣦⡿⣿⣾⢳⣇ ⣿⣿⣿⣿⣿⣷⣿⣿⠸⠀⠀⠀⠀⠀⠀⣄⣶⣷⢚⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⣏⡿⣿⠹⠀⠀⣿⣿⢺⡤⣿ ⣿⣿⣿⣴⢁⠟⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣻⡴⣀⣄⣷⣿⠈⠇⣿⣿⠋⠟⣾ ⣶⣻⠋⠏⣿⣿⣿⠿⠿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⣿⣸⠀⠿⠟⣿⡾⢁⡿⣿⣹⣄⠿⣿ ⣿⠿⣾⣤⣠⣀⣉⣟⣿⣟⣿⢯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣟⠿⣿⣶⣶⢋⣿⣿⣴⡈⢧⡌⣿ ⣿⣿⣿⢿⡿⣬⣤⣤⣤⣤⣦⣶⣷⢿⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢁⠋⡿⣿⣾⣠⠏⣾⠱⣧⡜ ⣝⣿⣿⣿⣿⣿⢿⠴⠶⠽⠭⠭⠠⠓⠛⢹⠉⠉⠉⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⣾⣶⣿⣶⣡⠟⣿⣹⠀⡆⢻⣷ ⣿⢿⣎⣿⣿⣿⣿⢿⠲⡏⢚⣄⣤⣠⣉⣉⣞⠤⡤⣦⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢒⠔⣋⣷⢀⡄⢻⠈⣏⣿ ⣿⣮⣿⣿⣿⣿⣿⣿⢻⣇⢹⠀⠀⡇⣿⣿⢈⠀⠉⠋⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡄⠳⡈⣷⣼⢠⠀⠀⠀⡇⣿⣿⣿ ⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢹⠈⠀⡀⣦⣻⣿⡿⣾⣷⢼⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⣦⢿⡘⣷⣽⠹⠀⠀⠀⠁⡟⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣄⣧⣿⣿⢿⠛⠙⠉⣉⣈⢀⠀⠉⠏⣩⠀⠀⠀⠀⠀⠁⠊⠛⠜⡦⣌⢻⠀⠀⣀⣷⣿⣼⣷⠸⠁⠛⣿⣿⣿⣿⣿ ⡄⣷⣿⣿⣿⣿⣿⣹⠋⡯⣸⣧⣿⣶⣶⣿⣿⣿⣿⣿⣿⣴⢁⠉⠛⠹⠰⠀⡟⢻⡄⢹⠀⣆⡜⣿⠹⠱⡄⣆⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⢿⡆⣿⠹⠀⡧⢿⠚⠒⣷⣿⣏⣹⢻⡟⣿⡟⠉⣇⣿⠹⡆⠘⠀⢆⡌⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠻⠈⢳⢿⠈⡄⣹⢧⠀⣇⠸⣷⣹⣧⣌⣿⡞⠘⣇⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢰⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⢿⠶⣿⣿⣿⣿⣿⢿⠻⡙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⣤⣀⣀⣀⠀⡄⣾⣶⣶⣿⣿⣿⣿⣿⠿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⣠⠀⠀⠀⠀⠀⠀⢄⡕⠙⠀⠀⠀⠀⣀⣀⣤⣤⢶⠳⠙⠈⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣾⣠⠀⠀⠆⠿⠀⠀⠀⠀⠀⠀⣦⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠳⠈⠀⠀⠋⡏⢿⠉⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡟⣴⢀⠀⠀⠀⠀⣽⢾⠤⠠⢀⠤⠤⠲⠙⡀⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡈⠢⠈⣷⣿⣿⢻⣄⢿⠛⠉⠈⠀⠀⠀ ⠀⠀⠀⠀⠋⣾⢀⠀⠀⠀⠀⠀⡟⣴⠚⡠⠀⠀⠀⠀⠀⡏⢿⡄⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⢦⢙⠀⡀⡷⣿⣿⣿⢿⡟⣿⣿⣿⠻⠁⠉ ⠀⠀⠁⡞⣠⠀⠀⠀⠀⠀⠁⡟⣴⡼⠀⠀⠀⠀⠋⠞⣤⣠⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠁⠀⣆⣿⣿⣿⣿⣿⣿⣿⢹⣳⠙ ⠀⠁⡤⠀⠀⠀⠀⠀⠀⠃⣿⣨⡀⠀⠀⠋⠖⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠁⡷⠰⠀⡎⣷⣿⣿⣿⣿⣿⣿⢿⠿ ⠃⣠⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠾⠿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠟⣬⢸⠁⡴⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠔⠋⡿⣶⠀⢼⢀⠀⠈⠀⠀⡀⣷⣿⣿⣷⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⣾⣠⠃⠀⢸⠀⡤⠉⠈⠀⠀⠀⣇⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠃⠙⠴⠀⠟⠰⠋⡿⣰⡄⢀⠋⡴⠁⢿⡿⣶⣤⢀⠀⠁⠘⡇⣿⣿⡼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠤⠑⠀⠁⠐⠁⠀⠁⠜⢁⠜⣤⢀⠋⠟⢡⠟⣿⣸⠉⠟⣩⠉⠀⡀⠀⣀⢯⠀⠋⡿⣿⣾⣿⣿⣿⢻⡝ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⡰⠊⣠⢤⠛⣜⣠⠊⢡⠞⣡⠞⣤⢻⠁⠔⢇⣿⣿⣿⣿⢠⣇⢩⠉⠛⠿⠿⡿⣿⣿⣿⣿⣿⣼⢃⣿⣿⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠂⡰⠀⢄⡽⠊⣠⠀⡠⠃⡷⣿⡠⠃⣿⣿⣿⣿⣿⠛⠛⣟⣿⠿⣿⣿⣿⣶⣴⣠⣏⣿⢺⡿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⡰⠀⠀⠃⠟⢈⡇⣿⠏⣿⣿⣿⣿⣿⣿⣿⠀⣁⣌⣠⣀⡁⢿⠒⠄⡿⣿⣿⠁⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠁⠉⠉⡌⣀⣀⣎⣦⣻⢀⠁⠈⠀⣸⣦⢰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡴⣀⣀⣀⠀⣯⠞⡿⣿⣿⣸⡇⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠤⡴⣤⣸⣀⠀⠉⣛⠛⡇⣿⠿⣾⢠⡇⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠋⠴⣧⠟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⡈⢤⠳⠉⠁⢿⠿⡿⣿⣿⣿⣿⣾⣤⠋⠁⢸⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠋⡼⢀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢻⣞⣿⣿⣿⣿⣿⣿⣿⣶⣤⣠⣿⢻⡴⢀⡇⢠⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢱⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⣿⢿⡈⣧⣿⣿⣈⣤⠛⠄⡤⣄⣿⣿⠀⠀⣿⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⠈⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠙⣷⣿⣿⢿⡛⢶⠛⠛⣿⣿⠻⠛⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣿⣿⣿⡿⣿⣿⣿⣿⢿⡘⡷⣿⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣧⣿⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⡟⣿⢳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣿⣿⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠁⣿⣿⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡟⣿⣸⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠇⣿⣿⢠⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣼⠀⠀

⠀⠀⠀⠆⠀⣿⠀⠀⠀⠀⠀⠀⠋⣸⠄⠀⠞⣠⠀⠀⠀⠀⠀⣷⣚⣛⣽⣄⡜⢱⣌⣷⠹⠀⠀⠀⠇⣇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⣾⠀⠀⠀⠀⠋⡴⣀⠀⠏⡼⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⣄⠶⣿⠻⣏⢻⠀⠀⣿⡀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠠⡄⠀⠃⢸⠀⠀⠊⡴⢀⠀⠇⠛⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣦⡷⢻⠀⣷⠀⣆⠈⠀⠀⠀⠀⢸⠀⠀⠰⠀⠀ ⠀⢀⠀⠀⡟⠁⠞⣠⠀⠀⠀⠀⡞⣄⢸⠀⠀⠀⠀⠈⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⡟⠀⠀⢇⠉⠀⠀⡇⢀⠀⠀⠀⠞⠤ ⠄⠠⠀⠏⣾⣠⠀⠀⠀⠀⠀⠇⢸⠀⣇⠙⠉⠉⠋⠙⠉⠉⠉⡴⡄⠀⠀⠀⠀⡀⠀⠀⠓⠉⠀⠀⣆⠸⠀⠀⣣⢌⠙⡇⠀⠀⠀⠀⢀⠀ ⢠⠀⠇⣴⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⣀⢀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⠿⠙⣆⠘⠀⠀⢧⡎⣿⠀⠀⠀⠀⠀⠀ ⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠳⣔⣷⠘⠱⠀⣦⣾⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⣀⠲⠒⠒⠖⠤⡡⣊⣔⠤⢠⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⠀⠀⠀⠈⢦⡟⢻⠏⢸⠀⠀⠀⠰⠀⠀ ⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠠⠄⠤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⡠⠀⠀⠀⠁⠈⣆⠘⡀⣷⣿⢀⠀⠀⠀⠀⠀⠀ ⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⣀⢀⠀⠀⠀⠀⠀⡄⣷⠿⣿⠸⠀⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣶⣤⢦⠷⠙⠀⠀⠀⣆⣿⣿⠘⡄⠸⠀⡄⠀⠀⠀⠃ ⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⢟⣠⣄⠤⠑⣇⠹⠀⠀⠀⡇⣿⣿⠈⢀⠀⠀⠀⠀⠀⡄ ⠠⠀⠈⠁⠉⠀⠀⠀⠁⠞⣴⣤⣤⣶⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢸⠀⠁⠈⡇⣿⣼⠀⠀⠀⡏⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡟⢸⠀⠀⠀⣿⠛⡾⣀⢄⠳⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣿⠿⣿⣿⣿⣾⢀⠀⠋⡿⣿⣾⣡⣟⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⣿⣿⢀⠀⠀⠀⣿⣿⢸⠁⠙⠉⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⡛⣟⣿⣯⣩⠋⠛⡿⣿⣻⣿⢿⡷⣿⠀⠀⠀⠀⠀⠄⠘ ⠀⠀⣿⣿⠛⠙⠉⠀⡄⣷⣿⣿⣿⣿⣿⢣⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣶⢷⣿⣿⣿⣿⣿⣿⣴⣬⣆⢻⡜⡄⣷⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⣧⣿⣿⠀⣏⠈⠀⠉⣉⣏⣿⣿⣿⣿⢗⣴⣾⣠⢧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⡀⣷⣿⡀⣣⠈⠀⢸⠀⠀⡇⠀⠀⠀⠀⡀⠀⠆ ⠀⠀⡆⣽⣸⠀⣿⣿⣿⣸⠀⠃⣿⣿⣴⢁⡼⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡄⣼⠀⠀⢧⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⣇⠀⣇⣙⣾⠀⠀⡇⣩⠉⠊⡾⠀⠀⠀⠃⢰⠀⠀⠃⠰⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠸⢻⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠑⠈⠀⡆⡿⠀⡄⠙⢸⠀⠀⡇⣀⠀⠀⢸⠀⠁⠀⡇⠀⠀⠏⣼⠀⠀⠀⠀⠄⠛⠙⠉⢸⠁⠉⠋⠿⣼⣧⢰⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⠲⠈⣄⠸⠀⣧⢸⠀⠘⡇⠀⠀⠀⢸⠁⣸⠀⣸⠀⠇⢠⢸⠀⠀⠀⠀⠀⠀⣀⣀⣸⡀⣀⣀⠀⢸⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⣄⢷⢼⠀⡀⢱⠀⢸⡄⠺⠒⠖⣼⡇⢀⠀⢸⠃⢰⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠈⠀⠀⢸⡄⠀⠀⡆⢀⠀⠂⠀⠀⠀⠀⠀ ⣄⠹⠀⠀⠀⣄⠻⠀⠀⠀⢁⠀⢹⠀⠀⢧⡇⠀⠀⢿⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣸⠢⠈⢸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠆ ⠪⡌⠹⠀⠀⠀⡀⢷⠈⠀⡆⠀⡆⠈⠀⡇⡇⠀⠀⣿⢰⠀⣸⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⡼⠀⠀⡄⢢⠑⠀⠀⠀⠀⡎⠀⠀⠀⠀⠁⢸ ⢆⡈⡧⠻⠈⠀⠀⠀⣆⠑⠀⢡⠀⢳⠀⡄⡞⢸⠀⣿⠀⠁⣿⠿⠟⠁⠋⡶⢫⡷⣿⣿⣾⢀⠀⠃⡴⠱⠀⣄⠹⠉⠏⢠⠀⠀⠀⠁⡿⢀

⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⠉⠉⠒⠔⣠⠀⠀⣁⢩⣀⣦⣖⣤⢦⠿⠿⠻⠛⠛⠛⠛⠛⠠⠄⠤⡠⣈⢛⠙⠉⠀⣀⢤⠢⣓⣍⣦⣤⣠⣀ ⠀⠀⠀⠀⠃⡿⠙⣪⣑⣈⠀⢼⠀⠀⠁⠟⡿⣶⣤⣤⣤⢤⠦⠓⡉⣿⣿⣼⣤⢶⣶⣷⠿⠛⠈⠀⢃⡄⠘⡀⣇⢤⠢⠙⠈⠀⠀⠀⠀⠀ ⠀⠀⠁⠞⣿⣸⢁⣀⠢⣝⣦⢸⠁⡟⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⠀⠀⠀⠀⠀⣧⡸⣀⢣⠀⢱⡄⢿⠛⠛⠈⠀⣀⠠⠀⠀⠀⠀ ⠀⠖⣠⠇⣿⢀⡈⠀⡟⣻⢄⠦⡿⣿⣴⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⡄⡜⠘⡀⠘⡀⣱⣤⣷⣿⣯⢿⠻⠙⠀⠀⠀⠀ ⠀⡿⢐⡁⣻⠏⢀⡏⣸⡇⡟⠇⣿⣠⠀⠈⡜⠀⠀⠀⠀⠀⠀⠀⠇⠲⠙⠀⠀⠀⠀⠀⠀⢇⡄⠘⣆⠩⡀⠡⠀⡀⢧⣦⣿⣶⣷⠻⠈⠀ ⡏⣿⠀⡀⣇⣸⠃⣧⠀⡆⣿⡎⢀⠀⡀⢢⢳⠀⠀⠀⠀⠀⠀⠀⡁⠀⡏⢿⠈⠀⠀⠀⠀⠀⢣⡄⠙⢷⢈⠀⢦⠈⠀⢣⢆⠉⠊⠀⣀⠤ ⣿⣿⠰⠀⡇⢈⡌⣸⠇⠁⣾⢀⠀⠀⠀⠀⡇⢿⠉⠉⠉⠉⠛⠛⡆⣿⣿⣿⣿⠘⠀⠀⠀⠀⡀⢱⡀⡧⢿⠈⠀⣀⠳⠈⢣⣄⢻⠀⠀⠀ ⣤⢠⠀⠁⡇⠀⢸⠀⡇⡞⢀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣾⣴⠀⠀⠀⠀⠀⡄⠻⠀⣌⢷⠙⠀⠀⡀⡳⢻⡀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⢀⠀⡟⢀⠀⠀⠀⠀⠀⠀⡇⣾⣥⣿⣿⣿⣿⣿⣾⣴⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⡈⡲⣤⠣⠀⠀⠄⣗⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⡄⢤⠤⡤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠙⠀⠀⢢⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢻⠈⠀⡀⠳⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡖⡳⠮⠿⡿⣴⠑⠀⠀⠀ ⠀⢳⠉⠀⡇⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠑⠋⠗⠛⠟⡶⣷⣿⢲⠀⠀⠀⠀⠀ ⠘⡆⣬⠶⡟⠘⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣛⣿⣿⣿⣾⣥⣉⠛⡾⣩⢈⠁⠊⠔⠀⠀⠀ ⣧⠸⢧⠙⠀⢳⠀⠀⡟⣿⠸⠀⠀⠀⠀⠀⠀⠀⠁⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣟⣿⣶⣶⣶⣴⡤⣠⢀⠀⢹⠉⠒⠽⡦⣈⣄⠀⠀ ⡉⣿⡈⣿⣿⡟⢹⠀⢸⣷⢿⠟⠸⡀⣻⠛⠛⠿⠛⠟⠿⣰⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠱⠈⢣⠀⡆⠸⣎⢀⠀⠀ ⡀⣧⢻⡄⣿⣷⣿⠈⢹⡄⣿⣿⣿⢿⣿⣽⣉⣋⣓⣬⢀⠀⠀⠀⠀⠀⠀⠀⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠘⢹⠀⣯⢠⠎⢀⠀ ⠀⠀⣷⠹⡄⡄⢹⢣⡗⠈⡄⢹⢆⠈⠀⠀⠀⠀⠀⢆⠘⠀⢄⠒⠉⠀⠀⠀⠀⣄⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠛⢠⠇⢀⠀⠀ ⢿⠈⡀⡵⠹⠀⣇⡈⡷⢹⠀⣄⠸⡀⠣⠉⠉⠉⡈⠘⡄⠱⠀⠀⡀⣦⠻⠈⠀⠀⡀⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⢀⠋⣰⠀⠀⠂ ⣧⢿⠙⡀⡷⠻⠀⢣⡀⣷⠘⣀⣤⠺⠉⣌⢳⠈⠀⡄⠘⡀⢢⠀⠀⠀⡀⣦⠿⠙⠀⡀⡱⠣⠈⠀⠀⠁⠉⠊⠖⡤⣞⠠⡟⢀⠀⠀⠀⠀ ⠀⣄⣶⢿⡙⣷⢹⡀⠸⡀⢷⠈⠀⠆⠈⣄⡢⣽⠑⠈⣆⠈⠀⢆⠙⠀⠀⠀⡀⣦⢿⠙⡀⠱⢆⠈⣀⢀⠀⠀⠁⡰⠁⡰⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⡀⣤⡶⣿⠸⡄⠘⡀⢷⠈⠀⠂⠀⠀⠀⢄⣳⠬⢷⠈⠁⡈⠣⢌⠙⠀⠀⡀⡳⠢⡌⠸⢆⠈⠀⠀⠞⢠⠁⡰⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⠘⡄⠘⠀⣦⠘⠀⢆⠘⠄⠤⠶⡴⠦⣵⢻⠈⠀⣄⡻⢬⠙⠀⠂⢎⡘⣷⠘⢆⠊⡠⠀⠃⡰⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠁⠀⡄⠙⡄⠙⠀⣄⠑⠀⡄⠑⠀⠀⠀⠀⠀⣄⣝⠑⠀⡀⣦⠻⢈⠀⢀⡄⠱⢯⡴⢀⠀⠊⢠⠀⠀⠀⠋⡟⠀⠀⠀⠀ ⠀⠀⠀⡀⠢⠑⠀⣀⠤⡖⠹⡀⠱⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⡢⢢⠈⠀⣄⣷⠺⠛⠚⡴⢀⠁⠋⡳⠋⠛⠷⠟⣿⣅⣿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠐⠀⠀⠀⠀⠀⣄⠧⢿⠀⠀⠀⠀⠀⣀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⣦⡘⣀⣁⣀⢄⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠂⠽⠬⠤⠤⠤⡶⠘⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⣆⠸⠀⢄⠘⠀⡀⢦⠜⠳⠓⠈⠀⠀⠀ ⣷⢤⠒⠑⠉⠉⠈⠂⠒⠒⣖⢶⠲⠉⠀⣆⠘⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⣄⡹⢣⡀⠣⠈⠀ ⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⡆⡿⠸⠀⢳⠀ ⠀⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⠀⠃⠟⠴⣿⠙⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⡄⢸ ⡇⣿⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡋⣿⣰⣀⣀⣤⣿⣸⠷⠊⠈⠀⠀⠁⡼⠀⠀⠀⠀⠀⠰⠀⠀⡇⢸⠀⠀⢸ ⡇⡆⠀⢆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢁⡜⢀⠀⠀⠀⠄⡤⡵⠳⠈⠀⠁⠋⡶⠘⠀⠀⠀⠁⡜⠀⠀⠀⡇⠀⠀⠀⢸ ⡆⠸⠠⠀⡀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡷⠀⠃⠀⠀⠀⠀⠀⡀⢇⣟⠾⣶⠙⡷⢀⠀⠀⠚⣠⠀⠀⠀⠀⢰⠀⠀⠃⢰ ⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⣠⠀⡏⠹⠀⠀⠀⠀⠀⠀⠋⢠⣿⢿⠘⡀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⡀⠦⠙⠀⠀⠀⠀⠀⠀⠀⠼⢀⠉⠒⡦⣟⣿⠀⠀⠀⠀⠀⠀⣆⠛⣼⣷⣗⠿⠘⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⠀⠀⠁⠔⡁⣉⠿⠙⠈⠀⠀⠀⢧⠀⢢⠉⠀⡁⣴⣤⠢⠙⠋⠴⠠⠤⣷⠈⡀⢳⡆⣿⠸⡄⠹⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀ ⠀⠀⣿⠴⢀⠀⠀⠀⡀⢤⠑⠀⡀⢷⣦⡬⢰⡇⠈⠀⠀⡀⢸⠀⠀⠆⠀⢳⠀⡇⢶⣴⢀⠏⢠⠀⠀⠀⠀⠀⠁⡜⠀⠀⠀⠀ ⠀⡆⣸⠀⠀⠀⠀⠀⠀⠀⡀⢦⠘⡀⢄⣤⠀⠇⣌⠢⠈⠀⡄⠀⠀⠀⠀⡄⠀⡇⣿⢉⠎⢠⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⢄⠢⠖⠷⠈⢄⠣⠙⠀⠀⠁⣰⢀⠀⠀⠀⠀⠀⠁⠚⡠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⡇⢚⠶⡷⢉⡈⣏⢳⠀⢿⠷⠙⠉⠊⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠃⠼⠣⠚⡠⢀⠜⠁⠀⠀⣀⣦⡼⢧⣿⠀⡀⣧⠈⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠂⠟⡼⠀⠀⠀⡏⠾⡦⢷⣴⣿⢴⡇⠋⠔⣠⠀⠀⠀⡆⣿⢸⠀⠀⠀⢻⠀⠀⡆⢿⣶⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠟⣿⢛⠾⢀⡇⣹⠉⠉⠀⠈⠀⠃⠿⣿⣿⣿⢿⠀⠀⠀⣸⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣴⣟⢙⠀⡷⣿⣿⣿⣴⢀⠄⣿⡙⣀⣎⣿⣠⠀⠀⠇⢫⣿⠀⠃⢠⡈⢧⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡀⣦⠻⡟⡚⢩⠀⠀⠀⠀⡇⡀⣿⣾⢠⠀⠀⠂⣴⢃⢰⠀⡄⡤⣄⠤⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣃⣖⠻⣉⢄⠤⠯⣰⠀⡏⢠⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠀⡎⠰⡀⣤⣤⣷⢈⠀⠖⢀⠀⠋⠗⡽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡦⠓⣿⢿⠀⠛⠛⣼⢥⠯⠴⣠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⢳⠀⠀⠀⢦⠘⠀⠀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣳⠀⠀⠀⣆⠸⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠹⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⣀⢤⠲⠙⠉⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⠀⠀⡄⡹⢤⠳⠋⠚⠖⠤⣤⣤⣤⡤⣦⢷⠾⠧⠒⠒⠒⠔⠬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⠀⠀⠋⡖⢶⡘⣧⠘⠀⠀⠀⠀⠀⠁⠞⣠⠀⡸⢀⠀⠁⡟⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⡄⢸⠁⡾⢀⠀⠀⠀⠀⣠⠀⠀⠀⠉⠞⣠⠀⠀⡏⠿⠿⡿⣿⣽⣋⠚⠴⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠀ ⠀⠀⠀⠀⠀⣿⡟⢀⠀⠀⠀⠀⠀⠋⠔⠤⣀⢀⠀⠀⠀⠏⣷⣿⣿⣼⡉⣉⠈⠀⠀⠀⠀⡀⣄⠳⠈⠀⠀⠀⠀⠃⢠⠀⠀ ⠀⠀⠀⠀⠀⣧⢰⠀⠀⠀⠁⠋⡾⢀⠀⠀⠁⠈⠀⠀⠟⣾⣠⣟⣶⣠⣀⢀⣀⣀⢤⠲⠙⠈⠀⠀⣄⠳⠈⠀⠋⣰⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠉⠛⠟⡶⣤⣀⠁⠚⠖⡤⣠⠀⠀⡟⣼⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢾⠴⠤⣤⣤⣇⣰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠃⣼⠀⠀⠀⠁⠛⡾ ⠀⠀⠀⠀⠀⡿⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⡼⠀⠀⠋⠿⣠⣠⠀ ⠀⠀⠀⠀⠀⣿⠘⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⢀⠃⡾⣧⢠⠀⠁⠋ ⠀⠀⠀⠀⠇⣽⠋⠛⡔⠳⠛⠉⠉⠊⠒⠒⠀⠀⠀⠀⡀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠋⣴⠁⢹⠚⠴⣠⠀ ⠀⠀⠀⠀⡏⢤⣧⠘⠀⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢟⠙⠉⠀⠀⠀⠉⠉⠈⠀⠀⠀⠇⢱⠁⣿⠿⣩⢀⠁⠋⠖⠤ ⠀⠀⠀⠀⢼⠁⡿⢨⠀⠆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢀⡀⣀⣤⣤⣦⠶⠶⡶⢶⠻⠙⡿⡀⡇⣹⠀⡀⣀⣀⠀⠀⠀ ⠀⠀⠀⠃⢳⣰⣿⢠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣸⠃⢰⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢻⡀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⡿⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠤⠤⠲⠛⠖⠤⡠⣀⠃⣿⣿⣷⢿⡛⠻⠉⠋⠘⠀⠀⠀ ⠀⠀⡇⢀⡄⡀⢸⠀⠁⠉⠀⡄⠸⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠁⠚⠒⠑⠉⠉⠀⠃⣼⡇⣦⠸⡀⣀⢄⣤⣦⢛⠈⠀⠀ ⠀⠀⡾⣤⠤⠒⣗⠈⠀⡀⣄⣷⢹⢛⠘⠀⠀⠀⣿⢀⠀⠁⠁⠜⢀⠀⠉⠋⠐⡀⣀⢤⣲⣿⢳⢎⠈⠀⠀⠁⠖⣠⡆⠿⠾ ⢰⠏⢀⠀⠀⠀⠀⢦⠛⠀⠀⡀⠀⣀⣀⣀⣄⣤⣿⠈⠋⣻⣰⠂⠤⣀⢀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⠻⡾⢀⠀⠋⣴⢀⠀ ⠄⢹⠉⠉⠉⠉⠊⠒⣴⢦⠑⠈⠀⠀⠀⠀⠁⡟⣱⣷⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠑⣆⣿⣿⢿⠿⣦⣾⠙⠀⠀ ⡄⣤⣤⣦⠶⠓⢍⠲⠈⠀⡀⣤⣶⠽⠦⠓⡿⣿⠀⡇⣿⢋⣠⠀⠀⠀⠀⠀⠀⠎⠃⡏⣿⣿⢻⣴⣿⣏⣷⣿⢹⣼⠁⣿⠋ ⠀⠀⠀⠀⠀⠀⡀⣄⠦⠓⠉⠉⠜⠠⠉⣟⣾⢳⠃⣰⡏⣾⠞⡯⢻⠙⠙⠐⡇⢿⠉⠚⣒⣿⢿⠾⣿⢿⡀⣿⣿⢿⡼⢿⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣲⣟⣙⠈⠀⠀⣼⠿⣿⣿⣿⣿⣿⣿⣿⠖⣿⣿⢿⠛⠈⣿⣸⣿⣿⣴⠿⣘⣿⣿⠞⡇⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⠻⠈⢀⡟⣼⡇⣿⣿⣿⣿⣿⠙⣹⡀⣷⣿⣤⣿⢸⡀⣿⠸⣯⢿⣳⣯⢸⠇⣿ ⠀⠀⠀⠒⠚⠓⠓⠛⠙⠉⠉⠈⠀⠀⠀⠀⡀⣿⢿⣿⢸⡆⣿⣿⢀⣧⣹⣦⣿⠈⡏⣾⠘⡀⢿⠀⡇⢹⣿⣟⠘⣷⢸⡟⡇ ⠀⠂⠒⠶⠶⠤⣀⣀⠀⠀⠀⡀⣀⣀⣄⠷⡹⣇⣦⣿⣿⠈⣴⣸⠀⡀⣧⠘⡄⣿⣿⠀⣦⠀⣇⠀⠇⣿⣿⢠⣄⡿⢻⣸⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⡿⠹⣇⣿⢽⡀⣦⠘⠀⠀⣧⠙⣸⣿⠀⠀⠀⡀⠋⡿⣾⢒⠓⠉⡏⣰⠟⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⢽⣶⣿⢿⠿⣝⠿⠒⠒⡟⣀⣇⠛⠛⠛⠛⣒⢴⠤⣤⣤⣤⣿⡿⣼⢁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⢾⣕⣷⢽⠤⠤⠤⠤⡦⠓⠚⣴⣧⣿⣓⠉⠉⠉⠉⠋⡶⣶⢲⠶⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⣄⠳⢿⣧⣯⠻⠛⠉⠈⠀⠁⠉⡟⣴⣷⣙⣛⣶⣤⢀⠀⠀⠀⠀⠀

⣼⣵⣤⣧⣿⣿⣿⣿⣿⢿⡿⡿⠿⢿⣼⡥⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣤⣧⣿⣿⣿⣿⣿⣿⣿⣿⣬⣤⣤⣧⣿ ⢸⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣯⣿⣲⣀⠀⠀⠀⣄⣿⣿⣿⢻⡆⣿⣿⣿⣿⣿⣿⣿⣿⢻⠁⠟⣿⣿ ⢹⠀⡆⣿⣿⣾⣯⣿⣿⣿⣿⣿⣾⣶⣴⣤⣦⣶⣶⣿⣿⣿⣿⡾⣰⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠻⡍⣿⣡⡿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⢡⡿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠁⠯⠛⠈⠀⠀⠀⠀⠀⠀⠀⣇⣀⣄⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢰⡟⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠆⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣾⠁⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡄⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⡆⣿⣴⣿⣿⣿⣼⣀⣇ ⣿⢸⡇⣿⣿⢿⠿⠙⠀⠀⠀⠀⠀⠋⠿⠿⢹⠀⡿⢠⠀⠃⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⣶⠻⠈⠀⠀⠀⣧⠈⣷⣿⣿⢸⠀⡇ ⣸⢰⡇⣿⣿⣰⣡⣿⠘⠀⠁⠟⣾⣤⣧⣿⣿⠘⣸⠀⠁⣴⠀⠁⠚⠙⠈⡀⠳⠈⠀⠀⠀⠀⠀⡇⠘⡄⢦⠛⠈⠀⡇⢸⡇⡇⣿⢸⠀⡇ ⢀⡇⡇⣿⣿⠀⡟⣿⢻⠿⣼⣠⢁⠟⣿⣼⡇⣿⢀⠋⣹⠋⠟⣳⠼⠧⣖⠻⠙⢿⠙⠀⠀⠀⠀⡏⣆⠳⠈⡀⣦⠻⡟⢸⡇⡇⣿⢸⠀⡇ ⠀⡿⣿⣿⢰⠄⣿⣿⣾⣤⠀⠏⣤⣃⣼⠉⣿⣾⣴⣶⣡⣏⢀⠀⢳⡾⠀⡇⢻⣌⣤⢦⠳⠙⠉⣿⠈⠀⣦⠙⠀⣄⣿⣿⡀⡏⣿⠻⠀⡁ ⠀⣿⣴⣾⠀⡟⣶⣠⠀⠋⡿⣿⡶⣴⣤⣠⣀⠀⠉⠖⣱⣟⢀⠀⡏⢰⠁⣻⡈⣤⢶⠙⠈⣀⣄⣤⣶⠷⡿⣿⠹⠀⡄⣿⠙⣍⣿⣿⢹⡇ ⠃⣠⠀⢀⠀⢠⠀⠊⡴⣠⢀⠀⠀⠀⠉⠚⠔⣠⠁⠖⣫⠙⣉⣉⣿⣷⣭⣭⣉⢬⠑⠈⣄⠢⠓⠉⠀⠀⠀⣀⣤⠰⠀⡀⢱⡀⣧⣿⣿⡇ ⢸⠀⠀⠀⠀⠀⡀⠀⠉⠚⠒⠤⡠⣀⠀⠉⠋⠿⢿⣿⣿⣿⣾⣠⠋⠉⠉⣄⣧⣿⠻⣌⠫⠙⠉⠀⣀⢀⠤⠠⠒⠒⠉⠀⡀⠠⠀⣀⣧⡿ ⢹⠀⠀⠀⠀⠄⡠⢀⠀⠐⠉⠒⠶⠶⣶⣑⣈⣷⣿⣿⡏⣾⠀⡀⣤⣀⣠⠀⠀⣧⣿⣸⣀⣦⣶⣶⣶⠶⠶⠒⠒⠀⠀⢀⠀⠀⠀⠀⠀⣧ ⣿⠻⠉⠉⠋⠛⠿⠛⠛⠙⠈⠒⠒⠒⠒⠉⡁⡿⣿⣿⣸⣿⣠⣆⢹⠀⡟⣰⠁⣿⣿⣿⣿⢤⠻⠒⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶ ⣸⣀⣄⣠⣀⣀⣁⡖⣤⢀⠀⠀⠀⠀⠀⠀⢀⠀⣧⣿⣾⣧⢤⠤⣠⠀⣄⢷⣩⣾⣾⣟⣼⡠⠀⠀⠀⣀⣳⣈⣄⣦⣶⣿⠶⠲⠒⠶⣠⡇ ⢹⠈⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⡍⣿⣿⣿⠿⣿⣻⡿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠉⠉⠉⠉⠉⠉⠉⡏

⡿⡀⣤⠲⠉⡟⢲⠒⠒⠒⠖⠶⡻⠙⣈⣀⣄⣤⣀⢤⠥⢾⣠⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣷⠸⠀⡀⠸⠀⠀⠀⠀⠀⡄⣄⠀ ⣿⠀⠁⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⠙⠈⠀⠀⡼⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⡈⢹⠀⠀⠀⠁⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⡀⠘⠀⠀⠀⠀⠈⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡑⠯⠞⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠸⠀⢸⠁⡋⢛⣿⢻⠉⠉ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣽⢿⠟⣿⣾⣤⣧⠙⠋⣼⣄ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⣀⡏⣿⣸⣀⢯⠴⣤⣀⢀⣏⣩ ⣟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⠻⠛⠛⣽⣀⣁⡴⢸⠀⠃⠀⠀⣿⣈ ⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡤⣤⣶⣶⣶⣹⡉⣟⣹⠋⢒⠒⠒⠓⠋⣯⣼ ⡦⠹⣟⣾⢶⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠀⠀⠀⠀⠀⣷⣉⣾⣠⠀⠀⠀⠀⠀⡀⣿⠁ ⠀⠀⣆⠘⠀⠀⡀⢄⠤⠒⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠁⠐⠀⠀⠀⡄⣼ ⠀⠀⠀⢣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⠦⠑⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠁⠋⣾⢀⠀⠉⠟⡿⠿⠈⠀⠀⠀⢾ ⠙⠀⠀⠀⢄⢳⠀⠀⠀⠀⠀⠀⠉⠛⠻⣤⣲⣁⣸⠀⠀⠀⠀⠀⠀⠁⠿⣿⢿⣿⣿⠻⠿⠿⠾⠯⣴⣀⠋⠷⣂⣿⣸⣇⣀⢳⠛⠈⠁⢠ ⡆⠻⠈⠂⠈⠀⣀⠤⠦⠷⠿⣿⣿⣿⣿⢿⠙⣿⢸⠀⠀⠀⠀⠋⠴⣀⠀⣀⣀⣀⣄⣶⣹⣏⣿⣦⣿⣻⣿⣿⠘⣆⢹⡄⠘⡀⣸⢀⡇⠀ ⠻⡈⣦⠻⡈⠢⠈⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣥⣷⠻⠀⣦⣿⢠⢦⠙⡃⠻⢗⠛⢸⠀⡏⠖ ⡉⢦⠙⡀⣤⠻⡈⠢⠈⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⢿⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠾⢻⣿⢿⠈⡄⢻⡞⣀⣏⢠⡟⣾⢃⡴⢀⠀ ⡁⢻⡉⢷⠙⡀⣦⠳⡈⠣⠈⠀⠀⣧⣿⣧⡘⣿⢈⣿⢁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠿⡟⡿⣿⣌⢰⠀⣷⢈⠿⢠⡏⣷⢀⠀⠀⠀⠀ ⠀⣄⡶⢿⣜⢿⠑⠈⣄⠳⢌⠑⠀⡇⣿⠀⢧⠀⣯⣻⡟⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⣧⢹⡏⣧⠹⠈⠁⣾⢀⠏⢠⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⢿⣜⠳⠈⣄⡻⢪⣼⣧⠘⠀⣧⢸⣿⣦⡟⠘⠀⠟⣧⣽⠻⠋⠹⠁⡼⠀⠀⣗⣿⠀⣿⢹⡶⢀⠃⢠⠁⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⣿⠻⡈⠢⡙⣦⢬⡦⢻⠈⠀⣦⣿⠹⡀⣦⡿⣿⣿⣿⣶⣿⢨⡟⣐⠀⠀⠀⣷⠀⡎⢠⠃⠟⢰⠁⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣦⣽⠳⡀⢤⣷⠺⠈⣀⠦⠑⣄⣷⢻⠀⡀⣄⣶⠾⠿⣼⣿⢰⠀⠀⠀⠀⡇⠀⠀⠃⡼⢸⠋⡼⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⣄⠀⠀⢆⣄⠲⠈⠀⠀⠀⣄⢷⠈⠀⠀⡀⢦⢰⡆⠀⠀⠀⠀⠀⡄⠸⠏⣾⠁⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣇⠀⣆⣿⣿⠈⠀⠀⡇⣿⢀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠛⡿⠀⠀⠀⠀⠀⣿⠒⠀⣄⣶⣿⣿⠈⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⣆⣿⢻⠀⠀⡇⣼⠀⠀⠀⠀⠀⠁⣼⠄⠶⡤⣤⢀⡇⠸⠀⠀⠀⠃⢸⠂⠀⠀⠀⠀⣄⢸⠀⠀⡇⢿⡛⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣿⠸⠀⣿⢸⠀⠀⠀⠀⠀⡟⢻⠛⠉⠛⠙⠉⡿⢸⠀⠀⠀⡇⠺⠴⠤⡀⢀⠄⡦⢲⠘⠀⡟⣿⣿⣾⢀⠀⠁⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⢿⠌⣿⢸⠀⠀⠀⠀⠇⣿⣼⣿⣿⣾⠀⣁⣿⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢰⠀⠀⡟⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢸⠀⠀⠀⠀⣿⣤⢀⡀⢀⠀⠁⡟⣴⣆⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⡄⣿⣼⠀⠀⠃⣾⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢿⠈⠀⠀⡇⢠⠀⠀⠀⠀⠁⡟⣴⠀⡇⢸⠀⠀⠀⠀⠀⠀⠏⣻⣉⣿⠀⠀⠀⠘⡞⢀⠀⠀⡿⢀⠋⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢹⠀⠀⡿⠀⠀⠐⠀⠃⡿⣴⠀⠀⡇⢠⠀⠀⠀⠀⠀⠇⣦⣿⣿⡿⠈⠀⠀⣏⢠⠀⠀⡇⣿⣿⣿⣴⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢻⠈⢸⠀⠀⠀⠀⡤⢀⠀⠀⠀⡇⠸⠀⠀⡇⠻⠈⡟⠀⣄⣤⣇⢸⠀⠏⢠⠀⠀⠃⣿⣿⣾⢠⡟⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⢸⠀⠀⠀⠀⠂⠙⠀⠀⠀⠀⢸⠀⠀⡄⠸⣄⣿⠘⠀⠀⡟⢀⠇⣰⠀⠀⠃⡿⣿⣴⠀⠃⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⠀⠀⠀⠀⠀⡀⠾⠒⠹⠀⣧⠀⠁⠉⢿⠙⣀⢀⠀⠀⣾⠃⣰⠀⠀⠃⣿⣿⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠿⣾⣀⣆⣿⣶⣧⠀⠃⣿⣰⠀⠀⠃⣿⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⠀⠀⠀⣷⠼⣶⠖⡿⢰⠀⠉⠟⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠉⠉⠉⠉⠀⠀⠁⡿⢠⠀⠀⠋⣴⣀⠤⣠⢀⠃⠛⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⣀⣀⣧⠚⠴⣠⣀⢤⠲⠋⠛⠶⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢻⠉⠉⠉⠉⠏⠼⣀⠀⠀⠀⠁⠋⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠲⠐⣄⢀⠀⠀⠀⠀⢱⠈⠀⠋⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠋⠰⠀⠀⠀⠀⠀⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡸⠈⠀⠀⠛⣴⢀⠀⠀⠀⠁⠊⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⡿⢠⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠁⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⣸⠀⠀⠀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡜⠁ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⡆⢰⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡎⠋⣿ ⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⠀⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠎⢏⣠⣿ ⠀⣄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠆⢏⢠⠀⠀ ⠀⠀⠀⢄⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠁⣼⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢤⠢⠓⠉⠉⠉⠉⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢡⠊⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⡏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡾⢴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢦⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠖⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⠚⣁⢫⠉⢿⡱⣈⣶⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡿⣿⢞⣤⣦⣷⣿⢰⣦⠷⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣰⠀⠀⠀⣸⡀⢤⢶⠙⣏⣹⣎⣷⣿⣿⣿⣿⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠋⠟⡿⣿⣿⣾⣠⠋⠔⠤⠤⠢⠙⠈⠀⠀⣀⣤⢶⡙⣦⣿⣿⣿⣿⢻⠀⠀⠀ ⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣠⠀⠃⢠⠁⠟⠩⠀⠉⡏⠻⠈⠀⠀⠀⡠⢦⣿⣿⣿⣿⣿⠺⠉⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⣾⣠⠀⠀⡟⠛⣿⣭⣊⣒⣄⣤⣀⣄⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⠈⠀⠀ ⠀⠀⠁⣿⣿⣿⣿⣿⣾⢀⠋⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠿⡿⣿⣿⣿⣿⣿⢻⠀⠀ ⠀⠀⡏⣿⣿⣿⣿⣻⠒⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢼⠀⡶⣶⣾⣤⣾⣤⣤⢀⣿⡿⣿⠀⠀ ⠀⠏⣿⣿⣿⣾⣿⣿⣻⣉⣉⢖⠶⠒⠈⠀⠀⠀⠁⠋⠑⢫⠟⠽⠺⡔⣤⣋⠏⠿⠻⣟⣿⣰⠀⠀ ⠀⣿⣿⣿⣿⠀⣆⣿⣿⣿⠻⠛⠌⠦⣾⢲⠈⠀⣟⢵⡿⣾⣷⢙⠍⠿⣯⣭⢻⡟⡟⣿⣶⣤⠦⠴ ⠃⣧⣿⣿⣸⠀⠀⡏⣶⣿⣿⣿⢿⠝⢉⠛⠒⡠⠀⣠⠀⠀⡀⠰⠀⡀⣀⣀⣀⣠⢀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⢹⠀⡜⣸⠉⣾⣷⢶⣎⣶⢸⢸⠁⠟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⣿⠘⢀⠯⣿⢉⡀⢄⡠⣏⡿⢾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⡞⣷⣶⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⣬⣿⢸⡀⣤⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢢⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣄⠤⠲⠉⣧⢿⠃⢹⠰⠁⠛⠘⣻⠂⡶⢳⢳⠀⠀⠤⣠⣀⣄⠤⠢⠙⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣸⡇⡏⠀⡃⣽⣾⡆⠹⠀⠀⢦⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠇⠸⠀⠁⠟⢀⡷⣻⠞⡧⣿⢸⠆⡙⢄⠳⠈⣧⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠛⣿⠀⠀⡟⣿⠋⡶⣦⠈⡞⣹⢻⠑⡆⢿⣻⣼⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⢲⠗⣿⣴⢀⠋⠻⣶⢸⡍⣿⠻⢻⡀⣄⢷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⣾⢀⠁⡿⣴⣧⠛⣿⢿⣿⣟⣾⠷⠙⠀⢳⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠏⡿⣠⠃⣿⣿⣿⣿⣵⣿⢻⠈⣦⠻⡇⠈⠀⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠇⣾⢉⠞⣿⣟⣫⣴⣷⣿⣶⣼⣾⠘⣆⢸⢧⠁⠀⡀⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⡞⡆⠈⡇⠀⣿⣿⢹⠀⡏⣼⠀⣧⣆⢿⠀⢸⠁⢶⢜⠑⠀⡀⢦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⠀⠞⢦⠙⢳⡟⡧⣾⣶⣿⢿⣿⢸⠀⡟⣼⡇⠋⢺⡖⠠⡁⠻⢌⠓⠈⠀⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠈⠁⡖⠒⠙⡈⡀⣿⣴⢛⣿⣿⢷⣮⢹⡟⣿⢈⡇⠁⠋⠟⣸⢀⠀⡀⠦⡈⠢⠀⠀⣄⠱⠀⠀⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡴⢀⡠⠎⣠⠀⡏⣷⣿⣿⣿⠀⣿⣟⢠⠃⣿⣿⣿⣿⢈⡇⣿⣿⣶⠀⠀⠀⠁⠈⡀⢧⡘⠀⠀⠀⢦⠟⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠞⢠⠀⠋⡴⠺⠑⠉⣀⠘⣀⣇⣸⠇⣿⣿⠿⣾⣧⣿⣿⣿⢸⡇⣼⢀⠀⠒⠔⡤⣀⠀⠏⣸⡀⢣⣌⠳⠁⢰⠀⠀⠀⠀ ⢀⠀⠀⠀⠁⡴⠀⠁⡔⢀⠄⢸⠀⡼⣀⣤⠹⡟⠿⣿⣹⣿⣿⠀⣷⡁⣿⣿⢼⡷⢺⠛⠛⠛⠒⠔⡤⢧⡟⣿⣠⣧⡉⠫⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠀⠟⣻⠀⠀⠀⢣⡇⢹⠉⠉⣲⣼⡠⣸⣷⣿⣸⠀⡇⡼⣿⣄⢹⡀⢸⡀⣄⢠⠈⠃⠿⣿⣾⣤⠘⡇⣿⣿⢀⠀⠀⠀⠀⠀ ⠀⠀⢇⠀⠃⡶⣖⣿⠙⠀⠀⡆⣿⢻⠒⠀⠃⢸⠃⢰⠀⣆⢸⠀⠀⣷⢰⠀⣧⠀⢹⠉⠀⠁⢟⣿⣿⣿⣟⡟⣿⡈⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⢺⠑⠉⡄⣻⢠⠀⠀⣆⣿⠙⠁⠏⢻⢻⠉⠈⠀⢀⠀⠀⠀⠀⠉⡍⠚⡖⡷⣿⣿⣿⣦⣿⣷⣹⣟⣴⣠⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠀⢱⠀⠀⣀⣤⢦⠒⠛⠟⡾⣠⢀⠀⠀⣭⠈⣀⣤⠾⠛⠛⠼⣠⣉⣉⢈⠀⠀⠀⡀⣤⢷⣿⠖⣤⢀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢷⡄⠸⠀⠀⠀⠀⠁⡜⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡿⣽⣞⣠⣀⠈⠂⠒⠒⠒⢄⠀⠈⣄⠸⠀⠀⠀⡰⠀⠀⠘⠀⠀⠀⠀⠀

⠀⠀⠀⡄⠶⠙⠀⠀⠀⣿⣿⣿⣿⢀⠋⢾⢴⣥⣽⣾⣤⣀⠀⠟⡭⣉⠭⡛⣀⣦⢷⢬⠤⠤⣦⣿⣿⣿⣿⢻⠀⡀⢻⣷⠘⠀⠀⠀⠀⠀ ⢿⠙⠀⠀⠀⡀⢦⠙⠁⣿⣿⣿⣿⡼⣀⠀⠃⡾⣠⠀⠀⠀⠀⣄⣶⣤⣶⣴⢀⠀⠀⣦⠻⠉⠔⣦⣿⣿⣿⣿⢿⠈⣧⡾⢿⠃⠀⠀⠁⠟ ⣿⣿⢿⠙⠀⠀⠀⡀⣧⣯⣿⣿⣸⠀⠀⠏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠘⠀⣄⣿⣿⣿⣿⢿⡈⣿⣿⡿⠿⡿⣿⣿ ⣿⣿⣿⣿⣿⠾⠛⠋⣴⣟⣿⣼⠀⠀⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢛⡴⣁⠟⣿⣿⢹⠋⡿⡟⠞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠛⣏⠙⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣾⣤⣁⠛⡿⣿⣿⣿⣿⢹⡏⣿⣿⢹⠙⣋⡯⣿⠿⠟⠀⠀⠁⢿⠘⠀⠇⠛⡿⣽⣮⢙⣟⣿⣿⢻⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣤⣠⣤⣏⠁⠘⠁⡾⣇⣿⠹⠀⣇⣻⣖⣄⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣦⣿ ⣠⢀⢧⠈⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠺⠃⡿⢳⡿⢈⡟⣼⣿⣿⣿⢻⡏⣿⣿⠿⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⡀ ⠀⠀⠀⢧⠈⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢸⡟⣯⣇⣿⢿⣿⣿⣿⣿⡟⣿⣿⣿⢿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⡀⢦⠙ ⠉⠒⠴⡠⢇⠘⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡀⢦⠓⡈ ⣄⠲⠟⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠛⣿ ⠀⠀⠀⣇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣎⣿⣿⣿⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣠⣴⢀ ⠀⠀⠀⡆⠈⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣏⣼⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡞⢀⠀⠀⠀⠀⡆ ⠀⠀⠀⠁⢸⣁⣠⡇⢸⢸⢸⡄⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⢹⠉⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⡇⠀⡎⢸⠹⢂⠈⡄⣷⣪⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣸⡇⢠⣾⠀⡀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⢀⠀⢸⠃⢠⣆⡙⠢⡉⠢⠙⣌⣷⡻⣀⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢞⣡⠞⣡⠞⢸⠀⠀⡄⠹⠀⠀⠀⠀⡅ ⠀⠀⠰⠀⡏⠀⡼⠀⠈⠁⣜⠢⢝⠢⡑⠄⡢⣷⠺⠛⠉⠀⠀⡀⣴⢀⠀⠀⠉⠋⡛⣿⣪⣷⣫⠴⣩⠖⣠⠀⢇⠀⠀⠀⡆⠘⠀⠀⠀⡀ ⠀⠀⠀⠀⢰⠀⢸⠀⢻⣰⠀⠀⠀⣀⠢⣑⢌⠠⠒⠒⠀⣀⣉⣉⣉⣉⣉⣉⠉⠈⠒⠒⠤⣁⢿⡠⢦⠙⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠄⠀⠀⠀⠤⠦⠶⠶⠶⠴⡤⣠⣀⠣⠀⡀⠳⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢹⡞⢳⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣄⠤⠒⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠟⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣄⠤⠤⠢⠒⠒⠒⠒⠛⠛⠒⠖⠥⡭⣶⣴⣯⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠛⠴⣀⠀⠁⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠗⣾⢠⠀⠀⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⡞⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⠾⠒⠗⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠈⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⢀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⢸⠁⡿⣻⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⢿⡿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⢳⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⡇⠀⣶⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣼⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢳⠀⠀⢧⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⢀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣶⣶⣿⣿⣿⣿⣿⣿⢠⣁⣋⣀⣀⣀⣀⣀⢀⠀⠀⠀⢀ ⠀⠀⠀⡀⢧⠈⠀⣄⠱⠀⠀⠀⠀⡋⢰⠃⠈⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠁⡿⣴⢀⢀⠀⠀⡀⣄⣷⣿⣿⢿⡾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠻⠈⠀⣄⠦⠓⡜⢀⠀⡶⢀⠀⠀⢆⠙⠀⠀⠀⠀⠀⠀⠀⠉⠞⣠⠀⠀⠀⠀⠀⠀⠉⠟⣰⢀⠀⠀⠀⠀⠀⠀⠋⡟⣿⣾⣠⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣄⠲⠙⠉⡴⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠈⠁⠉⠋⠖⡤⢀⠀⠀⠀⠀⠀⠁⠛⡾⣠⠀⠀⠀⠉⠀⠈⠀⠀⠀⡏⣿⣻⠚⠒⠖⠿⠿⡾⣧⣽⣬⢦⠶⠒⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣦⠓⠉⠈⠀⠀⠁⠉⠛⠗⡿⣤⣀⢠⠉⠉⠀⠀⠀⠀⠀⠀⠀⡷⣿⣿⣾⠻⠖⡠⢀⡞⣤⣀⣀⣉⢦⠹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⡴⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣃⣸⣀⣀⠀⣆⡘⣷⠹⡇⣽⣿⠐⠀⠀⠀⠀⠀⠀⠁⡿⣷⣿⣠⠀⠀⠀⡍⢉⠋⠀⢉⠛⠞⣤⢀⠀⠀⠀ ⠀⠀⠀⠀⠋⡴⢀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⡞⠀⠀⠀⠀⠀⣧⠉⣏⣿⣿⣾⢐⠀⠀⠀⠀⠀⠇⡿⣼⠀⣿⢹⠁⠛⡽⣏⣿⣿⣿⣿⣿⣿⠻⠘⠀⠀⠀ ⠀⠀⠀⠏⣠⠀⠀⠃⢰⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠏⣼⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⡄⣸⣀⣄⣦⣿⠻⠈⠀⠀⠀⠀⡉⣿⢻⠀⡆⣿⣿⣿⣿⣖⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠇⢨⠀⠁⠋⡸⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠋⡴⣏⢠⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡀⣦⣿⠻⠀⠀⠀⢀⣧⣿⠘⠏⣿⣿⣿⣿⠻⠟⣿⣠⣧⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⡀⣀⣀⣁⣼⠀⠀⠀⠀⠀⠀⡇⠛⠚⠴⣠⢀⠞⢠⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⣦⢿⠙⠀⠀⡀⣿⢿⣿⣿⣿⣿⣤⣷⣿⢿⠀⡋⣿⣿⣿⣰⠀⠀⠀ ⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠋⡴⢀⠀⠀⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⠛⠛⣿⣀⣦⣿⢸⠀⠀⡀⣯⣿⢿⡿⣿⣴⢠⠀⠀⠀⠀ ⠀⠀⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠞⣠⠀⠀⠀⠁⠟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠦⣶⣶⣷⣸⠋⠟⣿⣿⣿⣿⣶⣿⣴⣤⣷⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡤⢀⠀⠀⠀⠉⠞⣠⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢟⣴⢀⠀⠀⠀⡇⠿⢰⠀⠁⡿⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠴⣠⠀⠀⠀⠁⠛⡴⣀⠀⠀⠀⠀⠀⠀⢄⠑⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣴⢀⠀⠀⠀⠀⠀⡄⣴⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠁⠉⠚⠴⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡄⣿⣿⣷⣾⣴⣀⣧⣿⣼⢀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⣀⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⠀⡀⣷⠻⠉⡄⣅⡿⣼⢀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣤⣀⣀⣀⣤⣶ ⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠛⠈⣀⣤⣶⣴⣠⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣾⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣴⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣴⣤⢶⠻⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣿⣽⢀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⣾⣤⢀⠜⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⠛⠛⠛⠛⠟⠿⣿⣴⣠⡄⣿⠘⠀⠀⡦⢳⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠈⡀⣦⢷⠻⠙⠉⠈⠀⠀⠀⠀⠉⠋⠛⠿⡶⣴⣠⢀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⡀⣀⣀⢋⣼⢀⠀⣄⢿⠈⠀⡆⢿⠉⠈⠀⠁⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠙⠀⠁⢸⠀⠀⠀⡀⣍⣾⣶⣤⣦⣴⣤⣤⣀⢀⠀⠀⠀⠀⠀⠋⠖⠲⠒⠛⠙⠈⠈⠀⠀⠀⠀⠀⠀⠁⡞⣠⣀⣄⣤⠤⡄⢷⠙⠋⣴⣀⣄⣧⣹⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣄⣀⠀⠀⠁⠞⣠⢀⠀⠀⠀⠀⠀⠁⠉⠉⠊⠒⠒⠴⡤⣀⢀⠀⠃⠛⠛⡙⢿⡉⢯⠛⠉⠉⠛⠶⣠⢀⠀⠀⠀⠀⠀⠀⡀⣷⢙⠉⠉⠛⡴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠁⠚⠴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣤⠦⠳⡏⣼⢀⠀⡁⣿⣾⠖⠶⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢴⠤⠤⡧⢀⠀⠀⠁⡼⢀⠀⠀⠀⠀⣇⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⣄⠢⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⢼⠤⠤⣿⠀⠀⠀⡿⢁⠋⠿⠢⠛⠓⡾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠈⣀⢦⠓⠈⠀⠀⠀⣀⢤⠲⠓⠉⠈⠀⠀⠀⡀⣿⣋⣶⣀⠀⠀⡇⣴⣤⣶⢶⠿⣽⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠞⡠⢀⠀⠀⡀⣄⠳⠈⡀⢤⠲⠉⠀⠀⠀⠀⠀⣀⣄⠲⠈⠀⡇⣸⠀⠀⠀⠆⣿⠀⠀⠀⠏⣾⣀⣄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡼⢤⠳⠉⠈⠀⠉⡴⣀⠀⠀⠀⠀⡀⣄⠢⠘⠀⠀⠀⠀⠀⣇⠀⡿⠀⠀⠀⠀⠀⣿⢻⠈⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡷⠈⠀⠀⡀⣏⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⣇⠈⠀⠀⠀⠃⣾⡀⣦⠻⠋⠟⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢤⠤⡤⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠞⢠⠀⠀⠀⢳⠈⠀⠁⡿⢹⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠁⠉⠉⠉⠚⠒⠓⠛⠛⠒⠙⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠓⠟⠿⣿⣿⣿⣿⣴⠃⡿⣿⠘⢐⢀⠑⢊⡰⡟⣿⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢈⠧⠤⡤⣀⣀⣁⣏⠫⣼⣷⣿⣿⣽⣿⣿⣿⣷⠽⠾⠶⠤⠦⠶⠴⠤⠤⠤⠤⠿⣿⣽⣏⢰⡇⣴⣤⣤⣿⣿⣰⠋⣿⣿⣿⣿⠻⠟⠦⠻⡿⣿⣿⣿⣿⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⢹⡇⠀⠀⠼⣯⣛⡶⣠⠋⡟⣿⣿⣿⣿⣿⣽⣹⠒⠒⠒⠒⠒⠓⠙⠉⠉⠉⠉⣏⢿⣿⣿⠀⣾⠠⠀⠀⣿⣰⠟⣿⣿⣿⣿⣿⣾⢀⠀⡆⣿⣿⣿⣿⣿⢸⠀⠁⠟⣿ ⠀⠀⠀⠀⠀⣄⠱⢳⠉⣞⡟⢰⠀⠟⣿⣶⣭⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⢴⠷⢳⠀⠀⠃⣿⡾⣀⣄⣌⣯⣿⣴⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣄⠿⡿⣯⣽⡾⣱⢋⣴⣋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣸⠛⠃⣾⣠⠀⠀⠀⠛⡾⣷⣿⠿⠻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠃⠞⣠⠀⣀⣦⣽⢏⣼⠀⡞⢠⠀⠀⠀⠀⠀⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣽⣿⣼⠁⠀⠀⠋⡾⣤⢤⠲⡙⣿⣾⣠⢀⠀⣅⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⣇⢿⡴⠀⠀⠀⠀⠀⠀⠀⠀⣩⢤⠒⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⣄⣧⢿⣡⡿⣾⣠⠀⠀⠀⠃⡿⣹⠉⠀⠃⠋⣿⣿⣿⣿⣽⣤⣶⣶⣿ ⠀⠀⠀⠀⡏⣿⣿⢿⠿⠿⠿⠿⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⡀⣀⣄⠷⠈⠀⠀⠀⠀⠀⡄⣷⣿⣶⢀⠀⠀⠀⠏⣿⣾⣫⣿⣴⣤⣷⣟⣶⣿⠙⣽⢿⠛⠈⠀ ⠀⠀⠀⠃⣿⣿⣷⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⣼⢀⠀⠀⠀⣀⣦⣿⣿⢿⣿⣿⣽⠳ ⠀⠀⠏⣼⣤⡏⣾⣶⠶⣶⣿⢠⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⣣⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠛⠙⠉⡈⣦⣿⣿⣿⣿⢿ ⠁⡞⣬⣤⣤⣿⠀⠀⠀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠁⠉⠛⠟⡼⣡⠛⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⠟⠳⠀⣀⣦⣿⡿⢿⣽⣿⣿ ⡾⢀⣤⠀⠀⡄⢻⠈⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠿⠛⠉⠉⠋⠟⣿⣾⢴⣤⣠⣀⣋⣔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠄⣀⣿⢰⡄⠀⠀⠀⠀⣏⣿⣾⣧⣿ ⣤⢤⣭⣋⣻⣿⣿⢿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢿⣛⣉⣭⣾⣤⣀⠀⠀⠀⠤⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠶⣨⠀⠀⠀⣄⣷⣿⣿⣾⢦⢛⣇ ⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣹⠉⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡼⣏⠋⣿⢿⠘⠀⠀⡇⣿⣿⢻⠔⣤⣿ ⢿⣿⣿⣿⣿⣴⣠⣫⡟⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡾⣡⠞⣶⣶⣿⣿⣿⠀⠀⡏⣿⣿⢠⠉⠋⣿ ⣯⣿⣾⣴⢀⠁⡿⣿⢹⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣽⣻⠿⣴⠁⠈⠀⡇⣼⣧⠐⠁⣿⣿⣾⠿⣬⣷⣙ ⣾⣳⡛⠍⠟⣿⣿⣿⣿⣿⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⠀⡀⢿⠿⣿⣻⣼⠃⡿⣿⣿⢳⡀⣷⢿⣝ ⣿⠻⠿⣶⣤⣤⣀⣀⣀⣃⣛⣛⣟⣿⣼⠷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣛⢿⡿⣿⣷⣿⣴⠋⣿⣿⣿⣤⡀⢧⠙⣦⣿ ⣿⣿⣿⢿⠛⠛⠟⡶⣶⣶⣷⣿⣿⣿⣿⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣠⠀⠋⡿⣿⣿⣾⢠⠏⢿⠸⣦⠹⣧ ⣿⣿⣿⣿⣿⣿⣿⠻⠉⠉⠉⠉⠉⠉⡉⣉⣤⣴⣠⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠟⣿⣿⣿⣾⣠⠉⠟⣾⢠⣆⠹⣧⢻ ⠻⣜⣷⣿⣿⣿⣿⣿⣿⣸⣄⣦⢻⠋⠑⣉⣍⢭⠿⣽⠉⠉⠉⠚⠓⠷⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣊⣔⣤⣯⣴⣠⠋⡷⣿⣶⠻⠀⡀⣿⢹⣷ ⣿⣿⠻⣮⣿⣿⣿⣿⣿⣿⢾⠳⡇⠺⡀⣤⣀⣀⣁⣉⣉⣟⠶⡶⣶⣷⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠒⠖⡤⢏⣷⢈⠀⣆⢿⠈⡀⣿⡿ ⣝⣷⣿⣿⡻⣿⣿⣿⣿⣿⢿⡈⣳⢿⠀⠀⠀⡇⣿⣿⣿⢀⠀⠠⠀⠀⣏⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠳⠈⣄⣿⠿⣾⣠⠀⢀⠀⠀⣆⢿⣽⣿⣿ ⣿⢿⣝⣷⣿⣯⣿⣿⣿⣾⣿⢿⡏⣿⠀⠀⠀⡄⣿⣿⣶⠻⠉⡟⢿⣿⣽⢨⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⠻⠀⣧⠙⡏⣹⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿ ⢮⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⡀⣦⣷⣿⣿⣿⣨⣧⣾⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⣤⢀⡄⣿⢧⡈⣿⢿⡏⠘⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣀⣄⣿⣿⣿⣿⢿⠻⠛⠙⠉⡈⣀⣀⢀⠀⠀⠋⡿⢉⠀⠀⠀⠀⠀⠀⠃⠙⠞⠛⠞⠤⣇⣈⣷⠚⠀⠀⡀⡆⣿⣼⢻⢧⣿⠘⠁⠛⡿⣿⣿⣿⣿⣿⣿ ⡄⡻⣯⣿⣿⣿⣿⣿⣿⣿⠀⠉⣷⣼⣇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠁⠋⠜⠘⠀⠃⣹⢹⡄⣿⠘⠀⣧⡘⣷⠿⡈⠹⠀⢤⣧⡞⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⣿⠀⣿⣿⢈⡀⣀⣿⣽⣤⣤⣤⣿⠿⠲⠟⠿⣿⣆⣿⢹⢧⠀⡇⣾⣾⠘⣆⠹⠀⠀⢧⡌⣷⢿⡜⢻⠈⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⣿⢿⠈⠀⣇⣎⣸⠤⠤⣧⣷⠽⣤⠤⣷⠼⣷⣿⡶⢿⠙⢹⣿⢧⠀⣆⠘⠀⠀⢧⡉⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⠙⡀⢷⣟⠹⠀⡄⠹⣄⢻⢁⡄⢻⡀⣿⢹⡄⠹⣧⣿⡸⢻⠀⣧⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣧⣿⣾⠀⣧

⢳⠀⠀⡀⣆⣠⠀⠀⡏⢀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠏⡿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣜⣷⣿⣦⣷⡿⣿⣾⣿⣿⡿⣿⣿⠚⣿⣸⠀⠀⡆⢸⢻⠀⠀⠃⡿⣻⣿⣰⢁⠋⠟ ⡀⠳⠀⠀⠀⠀⠀⠃⣠⠀⠀⠀⠀⠀⠁⠚⡴⣠⣀⣀⣀⣤⣤⣦⣾⣿⣿⣿⣿⣴⣤⣦⡿⣿⢿⡘⣷⢻⠈⠀⣀⣤⣷⣿⣿⣿⣿⠈⣿⣿⠀⠀⠀⢸⡇⠀⡟⣯⣷⣾⣡⡾⣠⠀⠉ ⠀⠀⢣⠈⠀⠁⠏⣠⠀⠀⠀⠀⠁⠟⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⣀⣤⢤⠲⡓⣯⣿⣿⠘⢀⢦⠙⠀⠀⠀⣄⣿⣮⣿⢀⣿⣿⢿⠿⢸⣿⡇⡿⣿⣠⡿⢳⡿⢁⠟⣿⣾ ⠀⠀⠀⣄⢦⣠⢀⠀⠀⠀⠁⠞⣠⣄⠀⠀⠀⠀⠁⠉⠉⠉⠉⠋⡰⣀⣀⠦⠙⠀⠀⠀⠀⠀⣄⣦⣿⠙⠎⣟⢿⠙⠀⠀⡆⣿⣿⠘⣿⣿⣿⣿⣿⣧⡇⣿⣰⠏⢰⡏⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢠⠀⠀⠀⠀⠀⠋⡴⣀⠉⠉⠋⣴⢀⠀⠀⠀⠀⡀⢣⠈⠀⠀⠀⠀⠀⡀⣶⢻⡈⣯⣝⢶⠛⠈⣇⣿⢸⣇⣿⣿⣿⣿⡟⠸⣹⠁⣿⠏⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠁⡞⣠⠀⠀⠀⠀⠀⠀⡎⢋⠞⣤⣧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⠀⠀⠀⠀⠀⠀⣄⣷⣙⢯⠻⡌⣷⣿⣿⢻⡇⣿⣿⣿⣿⣿⢹⡆⣿⢸⣿⣿⣿⣿⣿⣿⠀ ⠘⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⡇⢶⡁⢴⠀⡇⠈⠀⠀⠀⠀⠁⠛⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⣆⡙⣿⣿⠹⣄⣷⣿⡈⣿⣿⣿⣿⣿⣿⠘⣷⣿⣇⣿⣿⣿⣿⣿⠀ ⢀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣽⣉⠸⠀⡀⣧⠉⠛⠶⠤⣺⠉⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢿⠙⣄⢷⣏⣿⣿⣿⣿⣿⢹⡄⣿⡇⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣸⠐⠀⠀⡀⠀⠀⠀⠀⢹⣇⣀⣧⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢷⣎⣿⣽⣿⠙⣀⣦⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⠀ ⢛⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⣏⡖⠿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⢦⡝⣿⣹⣷⢿⠻⡈⣦⣿⣿⣿⢿⡀⣷⣿⣿⣿⣿⢸⠀ ⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣼⠻⠀⠀⠀⠀⠀⠁⠟⣿⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣄⡼⣿⠙⣧⣿⣿⠻⡈⣦⣿⣿⢹⡄⣿⣿⣿⣿⣿⠀ ⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⢤⠤⡤⣤⣥⣩⢚⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷⡝⣷⠘⡄⣿⣿⣿⠻⡌⣷⣿⠘⣇⣿⣿⣿⣿⠋ ⣿⣿⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠤⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣹⣄⠤⠀⠀⡇⣮⡹⢹⠀⡄⣿⣿⣿⣿⠹⣶⣿⡘⣧⣿⣿⣿⣿ ⣷⣿⢻⠀⠀⠀⢄⠓⡍⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢀⠈⠀⠀⡇⢀⣄⡿⠸⠄⡈⣷⣿⣿⣿⣿⣽⣿⡈⣧⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⣄⣷⠻⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠢⣿⠛⠚⠙⡄⡿⠀⠀⡆⢹⠀⣄⡙⣧⣿⣿⣿⣿⡿⢿⠈⣷⣿⣿ ⣿⣿⣿⠸⠀⠀⠄⠋⣒⠙⡌⣶⡛⢮⠘⠀⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⠴⣿⠉⠉⡔⢀⣸⠀⠀⠀⣇⠘⠀⣇⡹⣷⣿⣿⣿⣿⣿⢿⠀⣧⣿ ⣖⣿⣿⣿⠀⠀⠉⡂⣕⠬⠲⠒⣅⣿⣸⢦⡿⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠖⠷⣽⣠⣀⡆⡘⢀⠀⠀⢼⡇⠙⠀⡀⢻⠀⠀⣧⡼⣿⣿⣿⣿⣿⣿⢻⠀⣿ ⠈⣿⣿⣿⠀⠀⠀⣽⣤⡣⣟⠿⠛⡙⣯⠽⡰⣧⢼⠒⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟⣴⣀⣀⣄⣧⠻⢿⠀⠀⠀⢸⡄⣦⢿⠻⣿⠈⠀⡀⣷⣌⡻⣿⣿⣿⣿⣿⠘⡟ ⠸⣿⣿⣿⠀⠀⠈⣄⠤⢀⠀⠁⠞⠶⠶⡓⢿⠐⣖⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣾⣶⣿⣿⣿⣩⠀⠀⡇⢸⠁⠃⣿⣿⣿⢿⠛⠉⡄⢻⣆⡎⣤⣿⣿⣿⢹⡇ ⢹⣿⣿⣿⠁⡟⢸⠀⠀⠀⠏⣻⠛⠛⠉⠋⣞⢿⠹⣆⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠙⡆⢿⣿⣿⢹⠛⡉⣿⣿⣿⢻⠀⡇⢹⠟⣿⣿⣾⣧⣿⣈⣀⣄⣧⢻⢸⠀⡷⣿⣿⣿⡆ ⣧⣏⣿⣿⡟⣿⢈⠀⠀⡇⣿⣿⣾⢀⣄⣷⣿⣿⣟⢹⡄⣷⢿⠈⠀⠀⠀⠀⠀⠀⡄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣍⣟⣶⢲⠙⡏⣿⢹⠀⠀⡄⣿⠈⠀⡇⣿⣿⣿⢸ ⠚⣷⣿⣿⣿⣿⢿⠙⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢹⠀⢷⣌⠳⠀⠀⠀⠀⠀⠀⠂⠉⠤⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿⣿⣺⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⣿⢹⠇⡇⣿⣿⣾⢿ ⠀⠀⣧⣿⡋⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣾⣴⢀⡆⢸⣷⠹⠷⢀⡀⢧⠘⠀⠀⠀⠀⠀⡀⣄⠶⠲⠒⠒⠒⠒⠶⠶⠤⣠⣇⡘⢠⠀⠀⠀⠃⢸⣿⣿⠘⠃⠀⣇⣮⠇⡀⣿⣿⢿⣿ ⠀⠀⠀⣷⣸⠀⠓⡙⣿⣿⣾⣿⣽⣩⢉⠛⠟⣹⠈⢇⡂⣾⡘⢷⠚⠀⣆⠙⠀⠁⠖⠠⠞⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠀⠀⠀⠀⡇⢀⣿⣿⢸⡇⠁⡇⢸⡧⠈⣧⣿⣿⣿ ⢅⠙⠀⡄⢿⠀⠀⡆⣠⠀⣀⣀⠀⠀⠀⠀⠀⠀⣄⣷⢸⣆⣧⡄⢿⠘⠀⣆⠿⢠⠀⠀⠀⠀⠀⠁⠋⠚⠔⠀⠀⠀⠀⠀⠀⡇⠙⠀⠀⠀⣸⠀⣿⣿⢸⡀⡇⡇⢸⡇⢸⡇⣿⣿⣼ ⡼⣷⠘⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣦⠹⢻⣇⢿⠌⠿⡌⠹⠀⠀⠉⠋⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⡇⢸⠀⣿⣿⢸⠀⡇⡇⢸⡇⢸⡇⣿⣿⢹ ⢻⡀⣧⠈⠀⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⣯⡏⠘⣷⣿⡜⣿⡞⠿⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠸⡇⠀⠀⣿⣿⢻⠰⡿⡇⢸⡟⢸⡇⣿⣿⡄ ⡦⢻⠀⢷⠈⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⣿⢹⡆⣿⣿⣯⢿⡎⠸⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⠳⠈⠀⡇⢸⠀⢰⢸⠀⠇⣿⣿⢿⠀⣼⡇⢇⣿⢸⡇⣿⢰⠀ ⠻⣿⠹⡄⢿⡈⠀⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣷⣿⠈⣿⣿⣹⣷⢻⣦⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢧⠈⡇⣿⠀⡇⢰⠀⡟⣿⣿⢸⠀⠸⣿⡏⣿⢀⡏⣾⠀⡷ ⣧⠸⣧⠙⡆⢿⠈⠣⢧⠘⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣧⡈⣾⢸⣷⣿⣿⡏⣿⢹⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⡟⢸⡇⣿⠀⡇⠀⠁⣿⣿⣿⢀⠀⢸⠀⣿⣿⠀⣿⢠⠀⡟ ⠀⣧⣝⣿⠘⣇⣿⠙⠻⣆⠙⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⢹⢧⢿⡇⣿⣿⣼⣿⣿⠸⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡿⡆⠀⡄⠀⡇⣿⣿⣸⠀⡇⢸⡏⣿⢸⡏⢸⠀⡏⣿ ⢧⠈⣄⣷⣿⠙⣦⣿⣿⠹⣏⠻⡴⢟⠿⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⣿⡘⣿⣿⣿⡟⣿⣿⡄⢿⠈⠃⠀⠀⠀⠀⠀⠀⠄⠹⡆⠸⠀⠀⠀⡇⣿⣿⢀⠀⡟⠁⣿⣿⢰⡄⠁⢿⣠⠉ ⠙⣦⠙⡀⣧⣿⢻⣎⣿⣿⣿⣼⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣇⢸⣿⣿⣿⣸⣿⣿⠹⡇⢿⡙⢷⠀⠀⠀⠀⠀⠀⣧⢻⢻⠀⠀⠁⣿⣿⣼⠀⠇⣻⡿⣿⣼⠀⠀⡿⢛⡿⣿ ⡀⣤⡷⠻⠀⣆⣿⣿⡟⣿⣸⡟⣿⣿⣼⢀⠀⠀⠉⠛⠐⠋⡼⣇⢷⡄⢿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⢿⢻⠃⠛⠛⠬⠿⡿⣿⣿⠀⠀⡟⣿⣾⠀⠁⣿⣿⣿⣿⢀⠁⡿⣿⣴⣇⢀ ⠀⠀⠀⣀⣦⡿⡻⣾⣿⣿⣏⣿⣿⣴⣏⣿⣿⣷⣯⢖⡿⣿⣿⡿⡇⢸⣿⣿⣿⣿⣿⣾⣿⣿⢸⣇⣿⣿⣿⢻⣮⣿⣿⣾⣷⣿⣿⠀⡆⣯⣾⢠⠀⡿⣿⣿⣾⢁⠟⣴⣀⣾⠀⡼⠃ ⠀⠀⠀⠀⠀⡂⢶⣿⣿⣿⣷⣿⢻⡿⣿⣫⢟⣿⢛⠉⠈⡀⠀⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣸⣿⣿⡻⣝⣳⣦⢿⠉⣿⣷⠀⠇⣾⢠⠁⡿⣿⣿⣽⢟⣴⢀⠀⠇⢰⠇⢠⡞ ⠀⠀⠀⠀⠂⠀⠀⡞⣦⡛⡟⣿⣿⢞⣷⣿⣿⣿⣿⣿⣿⣿⠿⡿⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢷⡄⣷⣿⣿⣼⣤⣷⣿⣿⡟⠁⣾⢀⠋⡿⣿⣿⣿⣴⢀⠀⠀⠀⡞⠀⡾⠇⢸ ⠀⠀⠀⠀⠀⠀⡰⠀⠀⡀⣬⣣⣴⣶⠷⡛⣯⣵⣿⣿⣿⣿⣿⣿⢻⡉⣯⣷⣿⣿⣿⣿⣿⣿⣿⢸⡄⠰⡀⣄⣦⣿⠉⠀⣧⢹⣾⣴⢁⠟⣾⣵⣞⣿⢀⠀⠀⠀⠀⠇⢸⠃⢠⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣈⣇⡟⣶⣤⣠⠀⠀⠀⠀⡄⢶⣜⣿⣿⣾⢋⣼⠀⠃⠛⠈⠀⡀⣀⣀⣤⣷⢸⡆⢾⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣅⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣸⠁⠿⣰⡀⣥⠩⠉⠛⠟⠛⠛⣿⠹⣿⠀⠀⡆⢸⠀⠀⠀⠀⠉⠚⠖⠤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠉⠉⠉⠙⠙⠉⠋⠉⠈⣄⣷⣿⠰⡾⢁⠋⡞⣴⣠⢀⠀⠀⠀⠀⡀⣦⣿⠹⠀⠀⢿⠚⠖⡤⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣻⠾⣤⣠⣀⣀⢀⠀⡀⣀⣀⣤⣦⡳⣿⡿⢿⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⢰⠀⠀⠀⠀⠆⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠸⠀⠀⠀⠀⠀⠀⡀⢤⠲⠉⠀⠀⠀⠀⠀⠀⠀⣦⠻⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠋⠒⠒⠖⠶⠴⠤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠳⠈⠀⠀⠀⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀ ⠀⠀⣀⢀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠙⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠀⠀⢿⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡯⠰⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢮⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠹⠀⠀ ⠀⠀⠀⠀⠀⠋⠞⣡⢉⠉⠋⠛⠛⠒⠒⠖⠿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⣆⠘⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⠀ ⠶⠤⡤⣤⣾⣠⣤⣀⢀⠀⠀⠀⠀⠀⠀⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀ ⠛⠛⠛⠚⠒⠶⠴⠤⠤⠤⠤⡤⣁⣉⢋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀ ⠛⠛⠛⠷⠘⠀⠀⠿⠿⣾⣶⣿⣵⣠⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢿⠀ ⣀⣀⣄⡹⣿⣰⣀⣧⣾⠀⠀⣾⡀⠀⢸⣷⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡉⢏⣿⣾⠀ ⠉⠉⠀⡄⣷⠌⠇⣴⢀⠀⠀⢸⠀⠀⢹⡟⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠿⠿⠿⠿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣁⣟⣿⢰⠀ ⢀⠀⠀⠆⡍⢿⡏⢴⠀⠀⠀⣦⠙⠀⡄⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⠋⠟⣿⣌⣿⢿⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠁⡿⣿⣿⠀⠀ ⠁⠀⠀⠋⣿⣿⢾⠛⠽⠯⠛⠀⡀⣷⣋⣋⣝⣿⣿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣤⣠⣀⢠⣏⣿⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠋⣿⣿⣾⢠⠀⠀ ⣤⣤⣴⣼⣀⣀⢸⡄⢤⣤⣶⠒⣶⣴⢀⠀⠀⣆⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⢛⠉⠈⠉⠟⣿⢰⠉⠉⠊⠖⣠⢀⠀⠀⠋⡿⣿⣿⣴⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢽⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣾⣷⣹⣤⣤⣦⠙⠀⠀⠀⠉⠛⡿⣿⣿⣾⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⠿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡶⣠⠄⣶⠙⠀⠀⣄⠹⠁⣾⣷⣿⣿⣿⣿⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣼⣶⣶⣿⣿⠿⠻⠛⠉⠉⠉⠋⠟⠾⣠⢀⠀⠀⠀⠁⡌⢹⠀⠀⡆⠙⣇⣤⣷⣨⣀⠀⠀⠀⠀⡄⢤⠀⠀⠀⠀⠀ ⠉⠉⠛⠶⠴⣠⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⡿⣿⠙⠈⡀⣀⣀⣉⣿⣿⣶⣶⣷⣸⠃⢰⠀⠀⠀⠀⠀⣄⣜⢠⠀⠀⡀⣀⢳⠛⣏⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⠖⠴⠤⣠⣀⣀⣀⣈⢀⠉⠍⠇⠈⡄⢿⠙⠉⠀⠁⠟⢨⡀⢦⣳⣟⣿⣴⣀⠀⠀⠀⠀⡀⢷⣻⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠁⢏⣧⠠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⡏⠿⣾⡴⡤⢤⠄⣤⣀⣄⢿⠀⣇⠘⠀⠇⣿⣿⣿⠘⠀⠀⣄⣧⠹⠀⠀⠀⠀⠀⠃⡈⣧⣿⠠⠀⠀⠸⠀⡏⢠⠀⠀⠁⠾⠀⡀⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠖⡠⠀⠀⣤⠠⠀⠈⠀⠀⠀⠉⠉⡉⢊⠙⠀⢸⠀⡅⣿⣿⢸⣆⡖⠘⠀⡄⡠⣗⠿⠘⠀⠀⡈⢦⠾⣿⠀⠀⠀⢹⠏⢠⠀⠁⠞⣠⣿⠀⠀⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡄⣤⢦⠾⣤⣤⣧⠀⡄⣤⣤⣠⣀⣦⣸⢀⢧⠛⡿⡿⣻⣎⠛⠈⣆⠸⠀⠃⠇⣠⠀⠀⠀⣹⣤⣿⣿⠀⠀⡟⣶⢠⠄⡠⢀⠀⠟⢠⡇⠞⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢩⡸⢤⠀⠀⠉⠉⠈⠉⡯⣝⠠⠃⠛⠛⠟⠛⠿⣿⣸⣀⣧⣝⣦⣾⠝⣿⠀⡀⣤⠀⠀⠀⠧⡈⢭⡿⣿⠛⡴⢀⠀⠀⠀⠉⠛⡴⢋⠞⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣄⣤⣢⠴⣤⣄⣶⣶⣰⣤⠀⡄⣹⣀⡄⣷⣮⣇⢈⠀⠀⣄⠶⠙⡀⠉⠈⠀⠀⠀⠀⠁⡉⣦⠼⣠⣏⢉⠟⢲⠖⠵⡾⣶⠤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⡦⠤⠤⡼⡤⣤⢀⠀⠀⠀⠀⡀⣄⡤⣤⣤⠤⠤⡤⣀⣀⣀⣤⠰⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⢄⠤⠶⠲⠒⠙⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠒⠒⠴⠤⠠⣀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⡀⣀⣀⣄⣤⣤⠤⠤⠤⠦⠶⠒⠺⠀⠒⠒⠿⠀⠀⠀⠀⠀⠃⠚⠖⠴⠥⠭⠭⡮⣶⣴⣒⣀⠁⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⢄⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⢻⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⠀⡄⢀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⡀⠳⠈⠀⠁⠞⡴⣀⠀⠀⠀⠀⠀⡀⣄⠶⣝⠻⠀⠀⠀⠀⠁⣼⠈⠈⠀⠀⠀⠀⠀⠉⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⣀⣀⠀⠀⠀⣀⣀⢤⠳⠉⠀⠀⠀⣀⠯⣰⠀⠀⠀⠀⠀⠉⠚⠒⠒⠐⠂⡙⣦⢿⠈⠋⠟⣶⣶⢶⡲⣓⠿⠻⠚⡴⢀⠀⠀⠀⠀⠀⠁⠉⠋⠒⠒⠒⠒⠛⠈⠀⠀ ⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢾⠒⠛⠋⣰⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣰⠀⠉⠚⠤⣠⡀⣀⣄⠢⠙⠀⠀⠀⠁⠚⡴⣀⠀⠀⠀⠋⡰⠀⠀⣆⠙⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⣧⢻⠉⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢾⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠃⡰⠀⠀⠀⠀⠁⡜⢀⠀⠀⠀⠀⣄⠘ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣆⠹⠀⠀⡀⢻⣀⢤⠶⠲⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⡼⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠦⠈⠀⠀⠀⠀⠀⠏⡻⣶⣸⠀⡀⣦⠳⠙⣯⠀⠀⠘⠀⠀⣀⣀⢤⠶⠶⠒⠛⠉⠉⡏⢸⠀⡄⠷⠙⠈⠀⠀⠀⠀⠀⠀⡿⣟⣾⠤⠷⠈⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⢀ ⠀⠀⠀⣄⠣⠙⠀⠀⠀⣿⢠⠀⣧⠈⠀⠀⠀⣥⣿⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣤⢤⠤⠤⠦⠒⠒⠒⡒⣿⣸⠀⠀⡇⢸⠄⢸⠀⠀⠀⠀⠀⠀⠟⣠⠀ ⠀⠀⠀⠀⠀⡆⣿⢤⠤⣧⠘⠀⡀⣄⠿⠤⡤⣀⠋⡴⢠⠀⠀⠀⠀⠁⠉⠛⠒⠒⠒⠒⠔⠿⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⠏⣰⡄⡿⢿⠙⠀⠀⠀⠋⡶⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣳⠈⠀⣄⠻⠉⠁⡾⠀⠋⡴⢀⠀⠀⠀⠀⠁⠟⣴⣀⢀⠀⠀⠀⠀⠁⢰⠀⠀⣀⢧⠳⠉⠀⠀⠀⠀⠀⡇⣷⠛⡴⢀⠀⠀⡏⣸⣄⠷⠛⠾⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⣇⣌⣴⢀⠟⣠⠀⠀⠀⠀⠀⠛⡴⢀⠀⠀⠀⠀⠀⠀⠃⡿⠀⠀⠋⠴⣀⠀⡀⣄⠳⠈⠀⠀⡀⣦⢙⠉⠀⠁⠋⣷⣸⠀⡇⣾⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⡆⢻⠀⡇⢸⠀⠀⠀⠁⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠟⣷⣸⠀⠇⢸⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⡀⣀⣃⣿⢀⠀⠏⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⣧⠘⡉⠙⠋⠖⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣰⠀⢿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⣄⠻⡿⣾⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣞⣹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣼⠀⠀⣿⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡀⢦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⢸⠀⠀⡀⢷⡎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⡀⣄⣤⣦⢿⣤⣤⣤⡀⣿⣸⣧⠸⠀⠀⠀⡀⣷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢦⠙⠈⠀⠀⠁⡍⢺⠒⠒⠒⣟⢻⡙⣄⠤⠤⠢⠒⠒⣿⢯⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⡵⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣋⣞⣶⢳⠙⠀⠀⠀⡏⣿⣿⢩⠉⠉⠉⠉⠏⣿⣿⢀⣆⣤⠷⠾⠻⠚⠗⠿⡿⣩⢖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠛⡽⢓⠀⠀⠀⣆⠛⠴⣠⣀⣦⣳⣭⣬⣤⣭⣿⣿⣼⢀⠀⠀⠀⠀⣄⣳⠈⠄⣻⢧⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢼⣤⢤⡀⣷⢻⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⣋⣴⣤⣏⣠⠀⠀⠉⠚⠐⠀⠀⠀⣎⠻⣿⣼⣒⣀⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡉⢿⠙⠀⠀⠀⣷⢹⠛⣿⠉⠉⠉⠉⠀⠀⡎⢠⠋⡶⢀⠁⠎⡴⣀⠀⠀⠀⠀⠀⠀⡀⣷⠺⠀⠀⡏⢹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠟⣿⣽⠋⠚⠖⠴⡤⣠⢦⠳⠛⢟⣶⣷⢿⠿⠯⠶⣛⣌⠷⠉⠞⣠⠋⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣤⣀⣁⣉⣙⣍⠯⠻⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠟⣿⢠⠁⡿⣿⣿⣿⢾⡤⢳⡏⣴⢋⡼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠗⠀⣀⠀⠀⠀⡀⣇⣿⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢦⠹⠀⠀⠀⠉⠛⣟⣿⡿⣿⣿⢙⡉⣿⣿⣿⣿⣿⢿⣼⢡⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠸⠀⠀⠀⠀⠀⠋⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠦⠿⢿⣒⣒⣟⣿⣿⣶⣶⣶⣶⣶⣷⣿⣾⢠⠃⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠉⠋⠚⠖⣤⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡴⣀⢀⠉⠞⣤⣀⠀⠀⠀⠀⠀⠁⡟⣴⢀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢘⡑⣄⠦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠏⣴⢀⠁⠞⡴⣀⠀⠀⠀⠀⠀⠀⠀⠋⣴⢀⠀⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢸⠀⣄⣤⡳⣿⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⢰⠀⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢠⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢠⠀⠀⠀⠀⣄⣿⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣱⢋⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⠸⠀⠀⠉⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣠⠀⠉⠖⣠⠀⠀⠀⠀⠁⠟⣼⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⢀⠀⠀⠀⡀⢦⠙⠀⡀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⢰⠀⡤⢀⠀⠈⠀⠁⠋⠴⣠⠀⣄⠳⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⣀⢦⠙⠀⠙⠀⠀⠀⡀⠣⠘⡇⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣤⠤⠶⠒⠒⠴⠤⣤⣀⠀⠀⠀⠀⠀⠀⣄⠦⠙⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⣠⠀⠀⠀⠀⡀⣄⢦⡒⢻⠛⠛⠛⠛⡾⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢤⠲⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⠂⠔⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀