⠀⠀⠀⠀⠙⢤⠈⠢⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⠃⢠⠇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⣭⣿⣆⠴⢊⣵⡾⠿⠋⠀⠀⣀⠤⠒⠉⠀⢀⡀⡀⠀⠀⠀⣸⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠙⢼⠁⠹⣄⠀⠀⠀⠀⠀⠀⣤⠀⢠⠃⢠⠇⡠⠃⡠⠄⠓⠤⣐⢏⠳⣄⣀⣴⣟⣳⢛⣥⣾⠟⠋⣳⠆⠀⡀⠀⢱⠀⠀⠀⠴⠁⣼⠙⢦⡤⢤⣿⢇⠑⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠇⠀⠘⠢⣄⡀⠤⠤⠾⠼⣀⡣⢤⡮⠊⢠⠊⣠⣾⡿⣿⡌⢇⣷⡾⢧⠝⣫⣶⠟⣋⠀⠀⢰⡁⣠⠎⠈⠢⠤⠃⠀⢀⣀⡠⠇⠀⠀⠀⣸⡿⠀⠑⠶⠇ ⠀⠀⠘⢆⠀⠀⠀⠀⠈⠑⡇⡤⣺⣽⣶⣶⣾⣿⣶⣶⣶⣬⣍⡒⠤⡆⢰⣿⠋⠀⢸⣿⠘⣷⢌⣵⣾⠛⠓⠋⢉⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢯⣤⣀⡀⠀⢀⢀⣿⣇⡴⡶⠀⠀ ⠀⠀⠢⣀⣱⠀⠀⠀⠀⢀⠏⢸⣿⠛⠉⠁⠀⠀⠈⠉⠉⠛⠛⠿⣷⣦⣸⣿⠀⠀⠀⢿⣆⣵⢿⣁⣤⢤⠀⠀⣈⡙⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⠎⣽⣿⠏⡰⠁⠀⠀ ⠀⠀⡤⠬⢅⣀⣀⣀⡠⠞⡄⠸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⢇⠀⠀⠈⣿⡅⠀⣀⠀⢸⣀⡞⠁⠉⠁⢠⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠳⣤⠞⢠⣿⣯⠞⠁⠀⣀⠠ ⠀⠀⠣⡀⠀⠀⢀⡠⠔⢒⣈⣠⣽⣿⣿⣷⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠦⡄⠀⠸⣿⡓⠩⢄⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⢣⡀⠀⣸⣿⠁⣠⠖⣋⡤⠖ ⡒⠦⣄⢙⡴⠊⣡⣴⣾⠿⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣰⠒⠢⠓⠈⡥⢠⡀⡀⠀⠀⣀⠀⠀⠀⠖⠀⠀⠛⠀⠉⢉⣿⣿⣫⠔⠊⢁⡤⢄ ⠉⠓⢤⠋⣰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠘⢧⣎⣁⠁⣠⠋⠈⡇⠀⠀⠉⠒⠒⢲⠀⠀⣸⣿⠃⢀⡠⠔⢁⡠⠞ ⠀⠀⡜⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⣇⠀⠀⠉⠁⠀⠀⠳⠤⢄⣀⠀⠀⣇⡠⢊⣿⡿⠚⠁⠀⡰⠋⠀⠀ ⠀⠀⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠈⣳⠀⠀⠀⠀⠀⣀⣀⣀⡼⠀⠀⠀⠀⣸⣿⠃⠀⠀⡼⢅⠀⠦⠀ ⠀⠀⡵⡹⣿⣦⣀⣀⣀⣀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣁⡤⢤⢀⣠⣼⣷⣶⡆⠀⠀⠀⣀⣀⣿⡟⠀⠀⢠⠓⢦⡙⠂⠀ ⠀⠀⠑⠚⠮⣙⠛⠛⣻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠀⠀⢀⡔⠉⠑⠀⠀⠀⠀⠀⠈⠻⣿⣷⣾⣿⣿⢿⠛⠉⠑⢦⡀⠈⠁⢸⣿⣓⣒⣒⠚⢤⡀⠙⠦⡀ ⠀⠀⠀⣀⣠⠔⡟⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⠀⠀⢀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠿⢿⣷⣿⣤⣄⣞⣁⣀⣀⣴⣾⠿⠛⠛⠿⣿⣦⡈⢦⠀⠀ ⠀⠀⣸⡘⠳⢤⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⠰⣄⡠⠎⣀⣴⣾⣿⣿⠟⠋⠁⢀⣀⣀⣈⣉⡙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⣿⡇⠈⡄⠀ ⠀⠀⠓⠽⡄⣀⠵⢻⣿⡄⠀⢾⣾⣾⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀⠈⠒⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⣔⡒⠄⠀⠀⠀⠀⠀⣿⡇⢀⠇⠈ ⠀⠀⠀⢀⡝⣡⣾⠟⠛⢌⣢⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⢛⣿⣿⣿⣶⣦⠀⠀⢿⡿⠿⡛⠛⠋⠉⠉⠉⠉⠉⢩⣷⡆⠀⠈⠉⠉⢩⡾⣫⢊⡴⠊⠀⠀⠀⢀⣼⡿⢁⡜⠀⣀ ⠀⠀⠀⠸⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⠿⢟⠿⣉⣁⠙⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⢠⣤⣶⡿⢛⣵⡮⠒⠉⠀ ⠀⠀⠀⠆⢸⣿⠀⠀⠀⠀⢀⢖⡔⠖⣩⣤⣶⣿⣿⠿⠛⠋⠁⢀⡼⠗⢉⠔⣁⠔⠀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡳⡋⣀⡤⠂⠀ ⠀⣠⡧⢼⠸⣿⡀⠀⠀⠀⣮⢣⢃⠞⠸⠿⠛⠉⣠⣤⣤⠀⠀⠀⠀⠀⠈⠚⠁⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠋⣡⠔⠀⠀ ⠀⠣⣄⠀⢣⡹⣿⣦⡀⠀⠁⠘⠊⠀⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋⠙⠛⠛⠛⠛⠛⠛⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⢀⣾⡟⡏⠀⠀⠀⠀ ⠀⠀⠀⠛⢦⡑⢮⡙⠻⠷⢶⢶⣶⠀⠀⠀⠀⠀⠀⠹⢿⣷⣦⣴⣶⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣵⣦⣤⣤⣴⡿⣿⣬⣓⠤⣄⡤⠈ ⠀⠀⠀⠀⠀⠙⡄⠈⠑⢒⠆⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠘⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠉⠉⣀⠔⠋⠉⠻⢿⣶⣭⡺ ⠀⠀⠀⠀⠀⠀⢺⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⣀⡀⠀⠀⣀⣿⣿⢃⣠⣤⠀⣯⣆⡀⠀⠀⠀⣠⣿⡇⡠⠊⠁⠀⠀⠀⠀⠀⠉⠻⣿ ⠀⠀⠀⠀⠀⢉⠏⠀⠀⠈⡆⢿⣧⡀⠀⠀⢀⣴⡃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣦⣭⣛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣦⡿⠛⠿⠷⠾⠿⡿⣯⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⢀⣀⠤⠚⣁⠠⠄⢀⡀⡨⢢⣿⠻⠷⠾⠿⢻⣇⠀⠀⠀⠀⠀⣿⡟⠷⢶⣶⡿⠁⠉⢛⣿⣿⣿⡿⢻⠯⢍⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢰⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⣿⣤⢔⣭⣶⢿⣿⣷⣾⣷⣿⠁⣠⣴⡶⠶⢾⣿⣦⣀⣀⣀⣼⡿⠁⢠⣾⣿⣁⡀⣰⣿⣿⡿⠋⠀⢀⠀⠘⡇⠀⠀⠀⠀⢀⣴⠎⢠⠀⡿⣯⣶⣿⣿⡿⠷⣶⣦⣄⠀⠀⠀⠀⠀ ⠀⢠⢃⣾⠏⣰⡟⠁⠀⠀⠉⢿⣿⠟⠁⣀⣤⠶⠛⠿⣟⢻⣻⢫⣀⣴⡿⠃⠉⠙⣻⡿⡷⠉⠀⠀⠀⠀⠠⠒⢿⡄⠀⣀⢔⡿⣃⡴⠃⡴⡻⠋⠉⠉⠛⢿⣦⡀⠉⢻⣧⠀⠀⣀⣀ ⣶⣬⣼⣿⠀⣿⡅⠀⠀⠀⠀⢈⣿⡆⣴⡟⠁⠀⠀⠀⠈⢇⣫⣷⣿⠟⠁⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡨⣗⢯⣲⣵⠞⠋⠀⡞⡼⠁⠀⠀⠀⠀⠀⢿⣧⠀⠀⣿⣧⣾⠟⠋ ⠏⠀⠉⠻⣷⣿⣷⣄⠀⠀⣠⣾⣟⠰⣿⡇⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⢸⠁⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⢹⡇⠙⠻⠿⠿⠟⠋⡼⠀⢻⣷⣄⣀⣤⣾⣿⡿⣥⡄⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠐⠦⣄⠀⠀⢧⠱⣄⡀⠀⢀⣀⣴⣿⠏⠀⣸⣿⣿⡀⠀⠀ ⣧⣄⣀⣠⣿⢃⠀⠀⠀⠀⠀⠀⠻⠀⠐⣿⠛⠛⠛⠛⠛⢻⣸⠇⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⠇⠀⠀⠈⠙⢦⢳⠀⠀⢱⣿⠿⠿⠿⠿⠛⠁⠀⣴⠟⣼⣿⣷⣄⣀ ⡛⣿⣿⣛⣡⣀⣃⣴⡾⣿⢿⣦⣄⣀⣀⣿⠀⢀⣀⣀⣀⣹⣟⣀⣼⣿⣟⣁⢀⠀⠀⠀⠀⠀⡀⠀⣾⣏⣀⣿⣇⡀⠀⢀⢀⣀⣂⣃⡀⠀⣿⢀⣀⣀⣀⣀⣀⣠⣿⣾⣟⣁⣙⡛⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⡝⠻⠛⢛⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢬⣄⣀⣀⣘⠟⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣼⣿⣿⣿⣷⡀⠀⠉⠉⠉⠙⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⢰⢿⡀⠀⣾⣿⣿⣿⣿⣇⡙⠀⠀⠀⠀⢠⠸⣷⠀⠀⠀⠀⠀⠀ ⠀⡰⠚⢧⡀⠀⠀⠀⠘⡇⠙⠚⠿⠿⠿⣿⣿⣏⢹⡿⢶⠶⢦⡤⠤⣿⠀⠀⠀⠀⠀⠀ ⣰⠁⠀⠀⠙⠒⠤⠤⠤⠛⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠉⠁⠂⣠⣄⣸⣇⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣀⣀⣀⣸⡿⠾⢧⡀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠮⠤⠞⠋⠀⠀⠀⠙⢦⡀⠀⠀ ⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠃ ⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣁⡀⠀ ⡇⠀⠀⠀⠀⠀⣰⡶⢤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠉⡽⠁⠀ ⢧⠀⠀⠀⠀⠀⢿⣿⣾⠳⣯⣠⣤⠤⣤⣤⣠⣿⠆⠸⣿⣶⡿⠀⠀⠀⠀⠀⣼⠃⠀⠀ ⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣧⣶⠏⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀ ⠀⠈⠳⢤⣀⣀⠀⠀⠀⣀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣀⣀⣰⡎⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠔⠚⠋⠉⠀⠀⠀⠀⠀