⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠛⢲⡀⠀⢀⡞⠋⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠛⠒⠋⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢿⣤⠀⠈⠉⠉⠛⠛⠛⠲⡦⠀⠀⠀⠀⣀⣤⣤⣤⣤⣙⢦⣄⣀⣀⣀⣠⣶⣯⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠲⣸⠁⠀⠀⠀⠀⠀⡴⠛⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠉⢉⡿⠁⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣿⢦⣀⣠⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⡄⠀⢸⡇⠀⢀⡾⠁⠀⠀⠀⠀⡄⠀⠀⣧⠀⠀⠀⠀⠀ ⢰⠋⢉⣯⣯⣳⣆⠀⣠⠶⠾⣥⣄⣀⠀⠀⠀⢸⣇⣀⣠⠇⠀⢸⡇⢀⡾⠁⠀⠀⠀⠀⠰⣇⣀⣀⣿⠀⠀⠀⠀⠀ ⡏⠀⣼⣿⣿⣿⣿⠀⡿⠀⣶⣶⣦⣽⡇⠀⠀⢸⣯⠿⠷⠶⠶⠾⣧⡟⠀⠀⠀⠀⣤⡴⠶⠦⠯⢭⣿⠀⠀⠀⠀⠀ ⠻⢤⣽⣻⣿⢿⣟⣾⡷⣴⣿⣿⣿⣿⠇⠀⠀⢸⠃⡌⠉⣹⣟⣿⣹⣀⣄⣠⣀⢼⣧⡉⢩⣟⢻⡆⢸⡇⠀⠀⠀⠀ ⠀⠀⢹⣯⢿⣻⣾⣽⣻⢷⣻⢾⢿⡛⠀⢀⣠⣿⣶⣿⣿⣟⣿⣻⣽⢿⣼⣳⢯⣾⣟⡿⣟⡿⣻⢧⣾⣇⠀⠀⠀⠀ ⠀⠀⣼⠀⠉⠙⠚⠳⠻⣯⣟⣿⣳⣾⣿⣿⣯⣷⠿⣞⣷⣻⣞⣷⢯⣿⢾⣽⣻⢷⣯⢿⣽⣻⢧⣟⣼⣿⡄⠀⠀⠀ ⠀⢰⡏⠀⠀⠀⠀⠀⢠⡏⠈⠉⠉⠉⠉⠀⡿⢸⡏⣿⣳⣟⣾⣽⣻⣞⣯⢷⣿⣻⢾⡯⢷⣫⠟⡬⢻⡏⣧⠀⠀⠀ ⢾⣋⣁⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⠇⢸⡇⠘⠃⠉⠈⠁⠓⠸⢌⣿⠁⢻⣿⡘⠁⠂⠁⠀⢸⡇⢹⡆⠀⠀ ⠀⠉⠉⠛⠛⠛⠷⠶⠶⠿⠃⠀⠀⣴⠖⠛⠀⠘⣧⡀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢸⣿⡀⠀⠀⠀⠀⢸⠇⠈⠓⠲⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣿⠛⢲⡶⠒⢲⡟⠁⠀⠀⢸⠃⠙⣶⠶⠶⡖⠋⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⣠⠟⠀⢸⡇⠀⢸⡇⠀⠀⠀⢸⠀⠀⣿⠀⠀⢷⣀⠀⠀⠀⣠⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢛⡵⠖⠛⠚⠃⠀⢸⡇⠀⠀⠀⢸⠀⠀⠛⠛⠛⠲⢭⡛⠛⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠶⠶⠶⠶⠶⠾⠇⠀⠀⠀⠸⠶⠶⠶⠶⠶⠶⠖⠛⠀⠀⠀⠀

⠀⠀⠀⠀⠛⠖⠶⠶⠶⠶⠶⠶⠸⠀⠀⠀⠇⠾⠶⠶⠶⠶⠶⠲⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠋⠛⡛⢭⠲⠛⠛⠛⠀⠀⢸⠀⠀⠀⡇⢸⠀⠃⠚⠛⠖⡵⢛⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⣠⠀⠀⠀⣀⢷⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⢸⠀⡇⢸⠀⠟⣠⠀⠀⠀⣀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠀⠀⠀⠀⠋⡖⠶⠶⣶⠙⠃⢸⠀⠀⠁⡟⢲⠒⡶⢲⠛⣿⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠲⠓⠈⠇⢸⠀⠀⠀⠀⡀⣿⢸⠀⠁⡾⢀⠀⠀⠀⠀⠀⡀⣧⠘⠀⠛⠖⣴⠀⠀⠃⠿⠶⠶⠷⠛⠛⠛⠉⠉⠀ ⠀⠀⡆⢹⡇⢸⠀⠁⠂⠁⡘⣿⢻⠁⣿⢌⠸⠓⠁⠈⠉⠃⠘⡇⢸⠇⢸⠀⠀⠀⠀⠀⣇⠸⠀⠀⠀⠀⡀⣁⣋⢾ ⠀⠀⠀⣧⡏⢻⡬⠟⣫⢷⡯⢾⣻⣿⢷⣯⣞⣻⣽⣾⣟⣳⣿⡏⢸⡿⠀⠉⠉⠉⠉⠈⡏⢠⠀⠀⠀⠀⠀⡏⢰⠀ ⠀⠀⠀⡄⣿⣼⣟⢧⣻⣽⢿⣯⢷⣻⣽⢾⣿⢯⣷⣞⣻⣷⣞⠿⣷⣯⣿⣿⣾⣳⣿⣟⣯⠻⠳⠚⠙⠉⠀⣼⠀⠀ ⠀⠀⠀⠀⣇⣾⢧⣻⡿⣟⡿⣟⣾⢯⣳⣼⢿⣽⣻⣿⣟⣿⣿⣶⣿⣠⢀⠀⡛⢿⢾⣻⢷⣻⣽⣾⣻⢿⣯⢹⠀⠀ ⠀⠀⠀⠀⡇⢸⡆⢻⣟⢩⡉⣧⢼⣀⣠⣄⣀⣹⣿⣟⣹⠉⡌⠃⢸⠀⠀⠇⣿⣿⣿⣿⣴⡷⣾⣟⢿⣿⣻⣽⢤⠻ ⠀⠀⠀⠀⠀⣿⢭⠯⠦⠶⡴⣤⠀⠀⠀⠀⡟⣧⠾⠶⠶⠷⠿⣯⢸⠀⠀⡇⣽⣦⣶⣶⠀⡿⠀⣿⣿⣿⣿⣼⠀⡏ ⠀⠀⠀⠀⠀⣿⣀⣀⣇⠰⠀⠀⠀⠀⠁⡾⢀⡇⢸⠀⠇⣠⣀⣇⢸⠀⠀⠀⣀⣄⣥⠾⠶⣠⠀⣆⣳⣯⣯⢉⠋⢰ ⠀⠀⠀⠀⠀⣧⠀⠀⡄⠀⠀⠀⠀⠁⡾⢀⠀⡇⢸⠀⡄⠀⠀⡇⢸⠀⠀⠀⠀⠀⡇⢠⠀⠀⣠⣀⢦⣿⣀⣀⢀⠀ ⠀⠀⠀⠀⠀⡇⠹⠀⠀⠀⠀⠀⠁⡿⢉⠉⠀⡇⢸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠋⠛⡴⠀⠀⠀⠀⠀⠁⣸⠲⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣯⣶⣠⣀⣀⣀⣄⢦⣙⣤⣤⣤⣤⣀⠀⠀⠀⠀⡦⠲⠛⠛⠛⠉⠉⠈⠀⣤⢿⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠋⠒⠛⠈⠀⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣤⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠉⠋⡞⢀⠀⡀⢲⠛⠚⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀