⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⡿⠋⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⠛⠓⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠟⠋⠉⠙⡿⣿⣿⣿⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠋⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⢻⠈⢢⣽⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣦⣿⣿⣿⣿⣿⠘⡀⠀⠀⠀⠸⡆⢹⣻⡿⡿⣿⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⡆⠀⠀⠀⠀⣧⡿⠈⣿⣿⡞⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⢻⣿⣿⣿⡿⣷⣷⠀⠀⠀⠔⢳⠁⢃⡟⡡⠷⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣼⣿⣿⣿⣻⣿⢿⡀⠀⠀⠀⢻⠀⢽⡟⠂⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣽⣿⣿⣿⡽⠈⢸⡇⠀⠀⠀⠘⠀⡿⣯⡒⠤⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢸⣼⣿⣿⣿⠁⠀⠈⠇⠀⠀⠀⠀⡠⠇⠛⢷⡖⢤⣿⣿⣿⣿⣷⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⣸⣿⣿⣿⣿⣄⡀⠀⣰⣠⠀⠀⠀⢧⠣⣸⠀⣳⡇⣿⣿⣽⠟⠻⣿⠟⠒⢒⣢⠖⡚⠛⠚⠛⠋⠿⡷⣶⣦⣤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢹⢽⣿⣿⣿⣿⣿⣍⢉⢣⢃⠀⠀⣾⠀⠈⡏⢸⣽⣿⣷⡟⡠⠊⠀⢀⡜⡉⢏⠀⠈⠁⠀⠀⠒⠤⡙⣄⠉⢢⠉⠐⢮⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡈⡿⣿⣿⣿⣿⠇⡿⡟⢿⣾⠀⢠⠃⠀⡰⢳⠿⣿⢿⠇⢰⠃⠀⢰⠛⢰⠇⠘⣆⠀⠀⠀⠀⠀⠀⠈⠺⣦⠄⢣⠀⠀⢣⡈⠺⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣩⣿⣿⡿⠃⡇⠀⢸⠱⡌⣷⡀⢫⢀⡾⠃⣸⣲⣿⣻⡀⢸⠀⢀⣯⣧⡌⠀⡄⠊⠦⠀⠀⠀⠀⠀⠀⠀⠘⣼⢾⡆⠀⠀⢻⣎⢎⠢⣄⠀⠀⠀⠀
⠀⠤⣠⣿⠾⢿⣇⣀⢱⠀⡞⡀⢰⡿⣇⣇⠎⠰⠃⠹⣿⡖⠛⠿⣿⣄⣸⠉⣼⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣳⢯⡀⠀⠀⢫⡻⣆⠙⣦⡀⠀⠀
⣀⡽⠋⠀⠀⣸⣏⠀⠀⢧⢧⣇⠀⠀⣿⠥⠀⡠⠢⠔⢹⡘⡀⠀⠀⠙⡿⣦⠋⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠉⠀⢸⡳⠙⢦⡀⠀⠳⡬⢦⡈⢳⣄⠀
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⢆⢹⠀⠀⢸⡖⠉⢀⡐⠴⢿⣇⠀⠀⠀⢰⢛⠏⢸⠃⠀⠀⠀⡼⡄⠀⠀⠀⠀⢀⡠⠔⢋⣿⢿⡤⠴⠿⢶⣶⣿⣠⣵⠤⡽⠗
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢿⡄⠀⠘⡷⡀⠀⠀⡷⠋⢦⠀⠀⣰⣣⡎⢀⣻⠀⠀⠠⠊⢀⣔⣒⣶⣶⠾⠛⠉⢙⣾⠟⠁⠀⠀⠀⠀⢹⠀⡨⠔⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢳⡳⡀⠀⡇⠀⡞⠀⡔⡹⡹⠀⠊⡿⣀⣀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠙⡋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠘⢳⠘⢆⢰⠀⣠⣎⡀⠧⡧⣤⠤⠾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣯⢦⡇⠀⠘⠳⣷⡍⠒⠭⣉⢘⡏⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡼⠃⣀⣀⡠⠤⠤⢔⣧⣀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣫⣷⣀⠀⠀⠈⢣⡀⠀⠀⠀⡟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⢤⣴⠓⠉⠀⠀⠀⠀⠀⠎⠁⠈⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠻⠽⠦⠤⠾⡇⠀⠀⢰⣧⢖⣒⡈⠁⢉⣉⠐⠒⠤⢄⣀⡼⡁⣠⠴⠒⠀⠀⠀⠀⡈⠉⠲⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡇⢀⠀⠀⢾⡇⠀⠀⢸⡜⠰⣏⣷⢠⠌⡹⣄⠀⠀⠀⡘⠀⢻⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣀⣀⣀⣉⡇⠀⠀⡏⠁⠠⣨⢿⠘⠂⣟⢳⡄⠀⠸⠃⠀⠸⣘⣠⣀⠀⠀⠀⠀⢸⠙⢷⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣗⣈⠻⢿⣦⣀⢧⣶⣾⢿⢺⡧⣞⣅⠃⠀⡰⠃⠀⠀⠀⣇⢌⠩⠿⢷⣧⣶⣺⡆⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⠂⣽⠟⣿⠘⢜⣮⣯⡿⣢⣨⡿⠀⡰⠁⠀⠀⠀⠀⠸⡏⢉⠉⣡⢻⢫⢮⣩⢾⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡗⠭⡝⢿⣿⣿⢰⣿⠛⠁⠈⠛⠚⢁⡴⠁⠀⠀⠀⠀⠀⠀⢫⠇⡰⢡⠋⢧⣿⠞⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⣼⡀⠀⠸⣿⠟⣁⣀⠀⠀⠀⡠⡻⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠍⠁⠀⠀⠙⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡀⢠⣿⣴⠛⣯⠷⠓⣴⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣦⢴⠽⡆⡇⢰⢹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿⣿⡟⢺⣿⣧⣣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⣧⡗⡑⡇⠘⣯⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠟⠛⢯⠳⡽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠉⢻⡷⡀⠀⢳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣤⣇⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣢⣼⠷⣧⡠⠀⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣫⠄⡠⠥⡝⢉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣢⣟⣂⣼⡉⠴⢳⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⡀⠱⢧⡴⣑⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠉⠈⠀⠇⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣌⣬⣤⠟⡧⠰⠁⣼⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀⣸⡀⡼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠚⠁⠀⠉⠉⠚⢀⢧⣏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⡎⡄⢉⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠱⠀⠀⠀⠀⣀⣼⡿⠙⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⠳⢩⣬⣶⢿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢈⢿⠝⠱⡀⢰⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣵⣭⠿⣻⡾⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⣶⠀⠀⢠⠫⠋⠀⠀⢃⠈⢟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠚⢁⣴⢶⣳⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⠛⠀⡴⡿⠁⠀⠀⠀⠘⡆⠸⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠞⠉⠀⣌⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀�

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠿⠿⠿⠶⢶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀
⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀
⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀
⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⡶⠶⠶⠾⠿⠷⠶⠶⠶⢶⣦⣤⣄⡀⠀⠀⠀⠎⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣠⣴⡶⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢶⡄⠀⠀
⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀
⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⠏⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⠀⠀⣠⣴⡶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠓⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀
⠀⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀
⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀