⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢩⣭⠉⢭⣍⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣨⢥⣤⡭⠅⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⠏⠀⠀⠤⠬⣢⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡒⡑⠉⠀⡤⠀⣤⠀⠀⠀⠉⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢫⣾⡞⠀⠠⠗⠒⠇⠀⠀⣮⣦⡑⢎⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢘⣿⠳⠀⠐⢲⠒⠒⠒⡶⣿⡿⠃⢸⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠺⣎⡁⢃⠀⠇⠀⢸⠀⠀⡰⠀⡸⠉⠒⠊⢀⡋⠑⠢⣀⣠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠖⡉⣹⠉⡶⢢⢄⡰⠁⠀⠸⢿⣿⣿⣷⣼⣄⣸⣀⣰⠥⠴⢃⣀⡠⠤⠊⠂⢄⠀⣩⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⢾⡀⠑⠬⡓⠷⣄⡈⢢⣢⠀⢠⠊⢁⠟⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣗⣿⡀⠀⠀⢠⡿⠤⠤⠄⣀⠀⠀⠀⠀⠀ ⠀⡴⡟⠀⠀⠻⣦⣀⣠⠃⠀⠈⠁⠈⣧⣸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⠮⠓⢩⣼⠇⢀⠔⢁⢤⣐⣢⣔⠪⠙⡒⢤⡀⠀ ⢰⣧⠁⠀⠀⠀⠀⠉⠛⠿⢤⣄⡭⢼⢧⢌⠉⠉⠁⠒⠒⠒⠒⠒⢖⠎⡲⡏⠉⠁⠀⠀⣀⢔⠝⢸⠒⠏⢠⣱⣿⣿⣿⣿⠆⠀⢡⠀⢱⡄ ⣏⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠮⣲⠤⣄⣀⠀⢀⣰⣟⣁⣀⣈⣢⣀⡴⣊⡔⠁⠀⡎⠀⣏⠝⢿⣿⣿⣿⠏⠀⢀⡎⠀⢸⢳ ⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣀⡀⠀⠀⠉⠒⠬⣉⡟⢡⠸⠿⡻⠿⠹⠁⡞⠁⠀⢀⡜⠀⠀⣝⣦⣀⡈⠀⢘⣤⣔⠟⠀⠀⠀⢾ ⠈⢢⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠘⠿⣿⣶⣦⣤⣤⣾⣃⠀⣑⣤⣤⣶⡃⢀⣿⡶⢿⡍⠀⠀⠀⠹⡿⢻⠿⠶⠗⠋⠁⠀⠀⠀⢀⡞ ⠀⠸⣉⠛⠿⠶⣶⣶⣶⡶⠞⠁⠀⠀⠀⠀⣿⠭⠟⡻⣿⣿⣿⣶⣿⣿⣿⣿⣿⢾⡋⠀⢈⡗⠀⠀⠀⠀⠙⢮⣿⣶⣦⣤⣄⣀⣀⡤⠎⠀ ⠀⠀⠙⠻⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣠⠟⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠹⣏⣁⠇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⠀