⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠁⠀⠁⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣶⡶⢶⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢠⣷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⣷⣼⣁⣈⣭⣿⡿⠷⠅⡶⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⣤⣶⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⡈⠙⣿⣏⣭⣴⣿⣾⠀⡀⠃⠀⡆⠀⠀⠀⠀⠀⣾⣿⠿⠿⣯⠀⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣽⣿⣿⣿⣿⢿⣿⣤⢀⣇⡄⢸⠃⡇⠀⠀⠀⢀⣿⡆⡄⣦⣏⣼⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡙⣿⣆⠀⠀⢙⣿⣿⣿⣻⣸⣿⡟⢢⣸⣏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣜⣿⣧⣶⡿⠛⠙⣿⣿⢿⣿⡟⣿⣿⣿⣶⠶⠞⣿⡟⠋⢛⣿⣿⡟⠈⠻⢿⣿⣿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠿⣟⠻⣿⣷⣤⡀⠀⢟⣽⣾⣿⣧⣿⣿⣽⡇⠀⠀⡿⠟⠀⡾⣿⣷⠖⠀⠀⠀⠹⣿⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢀⣨⡇⠀⠸⣼⣿⡈⠻⣿⣶⣿⣿⣸⣟⣿⢹⢿⣿⡇⠶⠰⡇⠻⠈⢱⣿⣡⣔⠀⢀⠀⡄⣿
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣇⣒⣲⣿⣿⣷⣄⣠⣭⢾⣿⣿⣿⣿⣷⠿⣿⣧⡀⢰⡧⣾⡆⣼⣿⣿⠀⢠⡷⢠⡇⣿
⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⠿⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢸⣯⣿⣾⣧⣿⠀⠉⣿⣿⣳⡿⠁⣾⣷⠇
⠀⠀⠀⠀⠀⢺⣿⣿⣽⣅⣄⢸⠀⣿⠛⢹⣿⣿⢫⡟⠉⠀⠀⢀⣴⡞⠉⠉⢻⣽⣿⠿⣿⣿⣿⡟⢁⢸⣿⠟⠛⣻
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⣾⣶⣯⣀⠀⠉⢹⣿⣻⣗⣶⠶⠛⠛⠁⠀⠀⠀⣿⣿⣷⣿⣿⣿⣵⣿⣿⣶⣦⢴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣧⣎⣿⣏⠙⢧⠀⢸⢋⣿⣟⠁⠀⠀⠀⠀⠀⢠⣤⣿⣿⣋⣩⣿⢿⣿⣿⡟⣭⣜⣻⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⡆⠘⣿⣿⣿⣾⢦⡀⠀⠀⠀⢸⠟⣽⣿⢉⣩⣿⣿⣿⣻⡇⢸⡏⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠙⢻⠿⣧⠀⢻⣿⣽⣿⣿⣿⣶⣤⡀⣸⢄⣿⣿⢉⣽⣿⠟⣹⡟⢀⣾⡇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠀⢻⡀⠈⢿⡿⠉⢿⣾⣿⣿⡏⢁⡾⢹⣧⣾⣿⣯⣴⣿⢇⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣾⡇⠀⠸⠁⠀⣠⡞⢻⢟⣡⠟⠁⣸⠋⠙⠋⠉⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡟⢹⡄⠀⢀⣾⡋⠐⣿⣿⠃⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⡇⣼⣿⢶⣿⠹⣧⣀⠿⣿⣆⣠⣾⣥⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⠀⠀⣰⣿⣿⣿⢸⣿⣤⢤⡍⠁⣷⠟⢿⣸⣧⠁⠉⠉⠛⠻⢾⣯⣟⡳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⠾⠚⢻⣿⠾⣿⣿⢸⣿⡇⢠⣽⣿⣵⠀⢸⡏⢀⣀⣤⡄⢀⣀⣤⣶⣿⠟⠀⢰⡄
⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⢡⣥⣶⣾⡶⠳⢿⣟⣫⣭⣿⣇⣈⡽⣻⣧⣤⣬⠿⠉⠱⢿⣓⠚⠛⠋⠁⠀⠀⠀⢀⡷⣶
⠀⠀⠀⠀⢀⣿⠛⠛⠛⠛⠉⠉⣱⠏⠀⠀⠈⠁⠀⣤⣞⡋⠉⠸⠃⠀⠘⠉⠉⣽⢻⠙⠛⠀⠀⠠⡀⠀⠀⣀⣿⣿⠃
⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⢟⣽⢧⡾⢳⣄⣄⠀⠀⠀⢹⣸⠀⠀⠀⡶⠀⡇⣀⣼⣿⣿⡟
⠀⠀⠀⣘⣿⡇⡾⠀⠀⠀⠀⢸⠇⡆⠀⢀⡴⣛⡵⠛⠁⠈⠀⠀⠙⡳⣽⣛⠒⠚⡿⠀⢀⡼⠃⣼⣿⣿⠛⠁⠉
⠀⢀⣼⣟⣿⣇⣿⠀⠀⠀⠀⢸⢾⡧⣾⡿⠾⠋⠀⠀⠀⠀⠀⠀⠀⣼⠀⠉⠙⣻⢃⣴⣿⣷⡟⠛⠛⠋
⠀⠀⢳⣿⢽⣻⣿⣾⣷⣄⠀⠸⠟⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣾⣿⣻⣿⠟⠁
⠀⠀⠀⠙⢶⣼⡋⡿⣿⣿⣿⣿⣧⣴⢤⡶⣤⣾⣶⣷⣶⣶⡶⣶⠟⣿⣿⢾⠟⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⣿⠛⢻⣿⠗⡟⠋⠛⠓⠓⠛⠉⢰⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⡇⣇⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢿⡇⣿⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⣿⣿⠀⠀⠀⠀⢀⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡶⣿⣿⣿⠀⠀⠀⠀⠸⢻⣯⣹⡟⠛⠿⣿⣷⣶⣤⣤⣴⣾⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡼⠃⢹⣼⡆⠀⠀⠀⠀⢸⣯⣿⣿⠀⠀⠀⠀⠈⠉⠛⠛⣿⡿⠗⢻⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣤⣼⣿⣿⣧⣤⣤⣤⣤⣤⠤⠤⠴⢿⣧⣠⣾⡇⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⣿