⡍⢣⢍⡙⣌⠣⡉⢍⢩⠉⠭⡙⢋⠛⡙⡛⢿⣿⠻⢟⡻⢛⠛⡟⡛⡛⠟⡛⠿⠿⠿⠿⠿⠿⠿⢿⡟⠻⠿⡿⡿⢿⣿⠿⠿⠛⠛⠛⠛ ⡌⠥⣂⠜⡠⢃⠱⡈⢆⢩⠒⡡⢊⡔⡡⡑⠢⢌⡑⣾⣿⣦⡑⢨⠑⣌⠢⠱⢌⠢⡑⢢⠑⠦⣑⢊⠹⢦⣀⠔⡹⣄⠈⠳⢤⣀⣀⣀⣀ ⡌⢓⡐⢊⠕⡊⣅⠓⡌⢢⠑⣴⡿⣿⣦⡁⢇⢢⠐⣹⣯⠙⢿⣷⣌⡄⢣⣑⡈⣒⣿⠣⡘⢆⠰⣈⠒⡄⢢⠘⡀⢉⡙⠀⠀⠈⠉⣩⣽ ⡘⢢⡘⠔⣊⠴⣀⠣⡘⠤⣱⡿⠁⠈⢿⡏⡆⢆⠡⣛⣿⣀⣠⣬⣿⣿⣿⠟⣀⣿⣿⣶⣧⣌⠡⢶⣿⣶⣬⣃⡀⢀⣤⣴⠶⠾⠟⢫⠀ ⠌⡒⢌⠚⡄⠲⣁⠒⡡⣾⡿⠁⠀⠀⢘⣿⢲⣧⠘⠻⣿⣿⡿⠟⠋⠀⣻⣷⣿⣿⣿⣏⡈⠷⣿⣿⣹⣷⡈⠻⣷⠖⡌⣉⣿⢿⣶⡿⣤ ⣴⡡⢊⠒⡌⡱⢀⣧⣿⡏⠀⠀⠀⢠⣾⡿⣹⡿⣧⡉⢿⣇⠀⣀⣴⣾⣿⣿⣥⣿⣽⣿⣿⣶⠀⠈⠙⠛⠃⠀⢻⣿⠾⠋⠀⠀⠀⠀⠀ ⣿⠀⡇⢛⠠⣣⣿⣿⠇⠀⠀⢀⣼⣿⣿⣿⣿⠀⠿⣧⡸⣿⣼⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⡟⠰⢈⣦⣿⣟⣿⠇⠀⢀⣴⣿⠟⠋⢠⣿⠇⠀⠀⠹⣷⣿⡉⠈⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⢀⢠⡷⠀⠀⠀⠀⠀⠀⠀ ⣁⣧⣿⠟⡡⢼⣏⣤⣶⡿⢋⣁⣠⣴⣾⣿⡄⢀⣀⠀⠈⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⣠⣿⣁⠀⠀⠀⠀⠀⠀⠀ ⡿⢋⠄⡣⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠏⠀⠉⠻⢶⣤⠀⠀⠀⠀ ⠄⠣⡌⢡⢋⣿⠛⠉⣴⣾⣿⠟⠋⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⡌⠣⢌⠡⣾⡟⠠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀ ⡇⠱⣈⢲⣿⣿⠼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠈⢿⡀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀ ⡇⠱⣠⣊⢽⣷⡄⠀⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠ ⣇⣹⡿⢻⣧⡿⣷⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢀⡾ ⣿⡿⠻⠦⠻⣿⣿⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠙⠻⠷⠶⢤⣤⡤⡴⠶⠞⠋⠁⠀⠀⠀⠀⣼⣋⡀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢀⡾⠁ ⢿⣧⠤⠤⢦⣬⣿⣦⣤⣀⣀⣀⣻⣦⣀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠉⠀⠀⠀⠀⣀⣾⠏⠀⠀⢀⡾⠁⢀ ⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠉⠙⠛⠳⠶⢦⣤⣄⣀⠀⢠⣾⣁⣀⣀⣀⣠⣴⣾⡏⠁⠀⠀⠀⠘⠁⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⣿⣯⣭⣭⡍⠀⠀⡄⣤⣤⠀⠀⠀⠀⢰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⣏⡙⠉⠛⠛⠛⢶⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⢶⣤⡀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢷⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦ ⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠈⠀⠁⠈⢀⣁⣈⣀⣁⣈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀