⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⠀⠀⢺⣿⣿⣿⣦⣀⣠⣤⣶⣶⣶⣶⣦⣤⣀⣀⣶⣿⣿⣿⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠘⢿⣿⣿⣿⣿⣿⣧⡀⠀ ⠀⠀⠀⠙⢛⡟⠉⠉⣰⣿⣿⠋⠉⠹⣧⠀⠀⣸⠛⠛⣿⡿⠿⠃⠀ ⢀⣤⠤⠤⣴⡇⠀⢠⣿⡟⢉⡷⢠⣾⡿⠀⠀⣿⣦⢰⣹⣷⠀⠀⠀ ⡞⠀⠀⣠⠬⢷⢠⡟⢁⠙⠻⠧⠾⡛⠁⠀⠀⠩⡙⡋⢡⠇⠀⠀⠀ ⠛⠖⠋⠁⠀⠈⡿⣄⠀⠐⠐⠈⠁⠀⠘⠔⠋⠀⢈⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣁⣽⡒⠤⣄⣀⣀⣀⣀⣀⣤⠴⢮⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡋⠁⠈⣿⣿⣿⡶⠃⠀⠀⠀⠀⡞⠀⢀⡇⠀⠀ ⠀⠀⠠⣿⠋⣢⣴⡇⢈⠟⠀⠀⠀⠀⠀⠀⠣⠤⠞⠀⠀⠀ ⠀⠀⢀⣹⠿⠛⠁⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣃⣱⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⠛⠉⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⣰⠠⣀⢠⣤⣀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⣞⠻⢯⢭⣱⢾⢦⣀⣹⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⢯⢓⢮⡛⣼⣮⢾⣛⠯⣭⢛⡼⡹⢏⣟⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⡜⣎⢶⣽⣏⢶⣷⣏⣗⣎⡟⢧⣫⣝⣺⣟⣴⢛⣦⡀⣠⠤⠒⠒⠦⣄⠀ ⣿⡹⣬⡿⠉⣸⣿⡏⠉⢻⡄⠀⠀⢀⣿⠉⢹⣿⣮⢇⢹⣡⠤⢤⣀⣀⣸⠂ ⠸⣷⢭⡇⣆⢹⣿⣷⣤⣼⡇⠀⠀⢸⣿⣦⣾⣿⣿⣺⢸⠀⠀⠀⠀⠉⠀⠀ ⠀⠹⣞⣻⡌⠦⣙⠛⠿⡻⢁⡀⠀⣀⠫⡛⠛⡉⠌⣿⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣷⣹⣶⣒⠒⠈⠀⠘⠿⠿⠋⠀⠈⠁⣲⡺⣿⢲⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣨⠟⠉⣬⠿⣶⣦⣤⣤⣤⣤⣴⡖⠋⠁⠸⠿⠗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣯⠀⠀⠘⢿⣼⢿⣁⣉⣄⣦⡤⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣳⠶⣶⡿⠃⠘⠧⠼⢣⠇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠟⠛⠉⠀⠀⠀⠀⢸⣿⣂⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠁

⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡔⣶⣾⣌⣇⣧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠧⣇⣎⢞⠣⣝⣞⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣠⠷⣚⠉⠉⢉⠓⠒⠤⣀⢠⢜⣧⡟⣦⣤ ⠀⠀⠀⠀⠀⠀⡾⠀⢠⡞⡕⢠⣾⣷⣶⣯⢄⣠⠇⠈⡙⣷⣖⠛⡼⡇ ⠀⠀⠀⠀⠀⣸⠃⠀⡾⢰⠀⣾⣿⡏⠀⢸⡆⠀⢩⣾⣧⡌⢟⠩⣇⠁ ⠀⠀⠀⠀⣴⣣⠶⠶⢿⠘⡄⠹⣿⣿⣶⣿⠃⢠⢣⣿⡇⢡⠈⣷⠋⠉ ⢀⣠⡴⠚⠁⢧⣤⣤⠬⣷⣈⡂⠬⢉⠭⡃⠀⢈⠈⢿⣿⡾⢀⠁⠀⠀ ⠸⢤⣤⣶⠴⠛⣡⡴⢾⣿⣙⠢⣄⡀⠀⠑⠂⠈⢪⣂⢽⠇⡼⠀⠀⠀ ⠀⠀⠀⢀⡴⠛⠉⢲⣤⡟⠻⣷⠋⠉⢙⡿⠟⠉⣹⡡⢊⠜⠀⠀⠀⠀ ⠀⠀⠀⣾⣷⣄⡴⠛⣿⣷⣤⠟⠀⠀⢸⣷⠤⣴⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣯⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⢟⡀⠀⠀⠀⠀⡛⠻⢤⣀⠀⠀⢀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢀⠊⣽⣕⠤⠤⡺⠁⢀⡴⠉⠻⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⣠⠶⣏⣿⠀⢸⢸⣿⡃⠁⢢⡁⠒⢪⠃⢀⡧⠘⣾⣿⠏⠀ ⣠⡤⠶⠚⠉⡹⣄⠈⠻⡕⢈⢌⠻⣷⣶⡿⠋⠀⢀⣈⣁⠧⣀⢸⡅⠀⠀ ⠈⠳⣤⢴⡶⠆⢈⠓⠦⢽⣆⠈⠉⠉⢡⣆⠀⠀⡞⣿⣤⣼⠿⢹⠃⠀⠀ ⠀⠀⠈⢻⡄⣀⣤⣶⡴⣿⣯⡛⢦⣀⠘⠿⠛⠁⠢⡈⠉⣁⣴⡏⠀⠀⠀ ⠀⠀⠀⠀⠘⢻⣿⠉⠑⣾⡏⠙⣿⠉⠙⠓⣶⣶⣶⣶⠛⠉⣤⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣇⣤⣾⣿⣱⣀⡜⠀⠄⠀⠀⠀⢈⣩⠟⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠃⠉⠻⢽⣷⠶⠒⠀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠋⠉⠀⠀

⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⡋⠈⣻⣿⣿⣿⣿⣿⣷⠦⡄⠀⠀⠀⠀⠀⠀ ⢀⡾⠛⣿⣿⢻⡁⠀⢩⠋⠈⣿⣿⣖⡩⢇⠘⣦⠀⠀⠀⠀⠀ ⢸⣦⣤⣿⣿⢡⡇⠀⢸⣶⣾⣿⡿⢣⠜⡏⠀⢸⣧⡤⢤⣄⠀ ⠸⣟⡻⣙⡬⠿⠃⠀⢀⠙⢭⣝⣌⠧⠊⢀⢰⣯⣀⡀⠀⠈⣇ ⠀⢻⣦⡐⠊⠀⠀⠐⠋⠀⠀⠈⠉⠉⠉⣠⣾⣿⣿⣿⡷⠤⠇ ⠀⠈⣿⣿⣶⣆⣀⠀⠀⠀⠀⣀⣀⡶⢿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢹⡃⠀⢿⣿⣿⣿⣿⣿⣿⣽⣾⣿⡿⠋⠛⢿⣿⣿⠀⠀ ⠀⠀⠈⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣟⡛⣧⣀⠤⣾⣿⣿⠁⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⠛⠶⣿⠟⠟⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⠀⠈⠓⣦⡀⠀ ⠀⠀⠟⠋⠘⠋⠁⠿⠛⠛⠛⠛⠉⠉⠀⠀⠈⠳⣶⣋⣹⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠃.

⠀⠀⠀⠀ ⠀⠀⠀⣀⠤⠔⠒⠒⡄⢀⣠⠤⠤⠦⡄⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⠴⠊⣡⣴⣾⡿⣣⠃⠀⠀ ⠀⠀⠀⠀⢰⠋⠀⠀⠀⡤⠊⠁⣠⣾⡿⠟⣉⠴⠁⠀⠀⠀ ⠀⠀⠀⡠⠓⠀⠀⠀⠘⠁⢒⣿⠍⠓⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀ ⢸⠘⠉⠀⠀⠀⣴⣶⢶⢀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⢷⣿⣵⣴⡆⢙⠉⡘⠟⠉⠁⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⢀⣾⡉⠣⠵⠶⠎⠉⠀⠀⠀⡠⠖⠛⠉⠉⠉⠙⢦⡀⠀⠀ ⠀⠊⠑⠂⠀⠤⣄⠀⠀⠀⠀⠀⠀⢀⣠⠄⠒⠀⠘⠁⠀⠀ ⣴⣒⠤⢤⡠⠔⡏⠀⠀⣀⠀⠀⠀⠀⠈⠙⠒⠢⢴⠑⢢⠀ ⠷⡀⠁⠀⠀⠈⡏⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⠁ ⠀⠈⠉⠉⠉⠉⠱⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡏⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⠉⠒⠤⠤⢤⡇⠀⠀⠀⠀⢀⢼⣇⠀⠀ ⠀⠀⠀⠀⠀⢠⠶⠿⠤⠤⠔⠛⡞⠦⣄⡠⡤⢊⣾⠟⠀⠀ ⠀⠀⠀⠀⠀⢱⣤⣤⣤⠠⢶⡿⠀⠀⠀⠙⠶⠽⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀