⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⠢⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠄⠀⠀⢠⣴⣶⣤⣄⣠⣲⣶⢿⠛⣓⡶⣶⣃⡼⢽⣹⠌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠺⠀⠀⢠⣿⣿⣿⣿⣿⣽⣟⣾⣻⠇⣾⣷⡌⡁⠐⠀⢣⣼⣶⣤⣠⠒⡄⠀⠀⢠⠠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢰⠀⠀⢸⣿⣿⣟⣯⣿⣿⣾⣻⣽⢘⣯⣷⣿⢃⢀⣵⣾⡾⠷⣈⠥⢵⡴⢪⡥⡙⠖⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⢇⠀⢸⣿⣿⣻⣿⣯⣿⣟⣿⣽⣖⣟⣳⢿⣴⣿⣿⢻⣃⠀⠀⠀⠀⠑⠛⠳⢃⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡐⢀⡈⠑⢮⡿⠛⠛⢓⣛⠋⠉⠟⣛⣛⣟⣖⠧⣳⣿⢥⣷⢷⣥⠀⢸⢩⠆⠀⠀⢑⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠝⠋⠀⠀⡰⠉⡠⠀⠑⠐⠛⠒⠪⢝⣯⣿⣾⢭⣶⣝⣆⢙⢏⢴⢿⣠⣒⢲⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⡸⠀⠀⢀⠄⠀⠀⠀⢀⠀⠄⠘⠿⣿⣿⣼⣻⣄⡜⡄⠀⣼⠛⠿⡜⡧⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠰⠁⠀⠀⡌⠀⠀⠀⠀⠈⠁⠀⠈⠀⠈⠻⣿⣮⣝⣷⣝⣫⣎⣴⣯⣻⠏⠁⠠⡑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠆⠂⠀⢰⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠄⠙⠻⣯⢷⣷⣽⣿⣭⣷⣤⣀⡀⠀⠄⠢⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⡑⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠈⠒⠠⢌⣑⣚⣛⣛⡛⠟⢫⠓⡄⠉⠐⠚⡄⠀⠀ ⠀⠀⠀⠀⡠⠊⢠⠀⠀⠀⠀⢀⠔⠃⠀⠀⢀⡜⠀⡆⠀⠀⠀⠀⣄⠀⠀⠀⠈⠀⠀⣀⠀⠆⠀⣀⠀⠀⠀⠀⠀⢀⠎⡆⠈⠢⡀⠐⢘⠀⠀ ⠰⠒⣊⠁⠀⢀⠂⠀⢀⡠⠐⠁⠀⠀⠐⡲⠚⠀⠀⢡⢀⠀⠀⠀⢣⠢⡀⠄⠂⠉⠀⠀⡤⢀⠀⠀⠀⠀⠀⠉⠀⢉⡸⢹⠀⠀⠑⡄⠈⠦⠀ ⠀⠳⢄⣀⣠⠍⡀⠉⠀⠀⠀⣀⡠⠴⢺⡖⠀⠀⠀⠀⢣⠀⠀⠀⠈⡄⠈⠲⠤⡀⠀⠀⠀⠑⠾⣥⠶⠒⠒⠒⠲⣉⠀⡈⡆⠀⠀⢈⠒⠀⢳ ⠀⠀⠀⡜⠁⠀⠀⠍⢉⡭⠋⠀⣰⣵⣿⣿⣿⣿⣶⣶⣤⠢⡀⠀⠀⠱⠀⣠⣶⣿⣷⡶⡤⢤⣀⣄⣉⠥⠔⠀⠀⠹⡑⢄⣇⠀⠀⠘⡀⡠⣏ ⠀⢀⠎⠀⠀⢀⣠⠂⠁⠀⢀⠾⢿⡟⠉⠋⠑⡸⠓⠛⡆⠁⠑⢄⠀⠀⠱⢀⠉⡘⠁⠛⢿⠀⡿⠫⠎⠑⢆⡀⠀⠀⢣⠀⢼⠀⠀⡄⠒⠒⢺ ⡠⠁⠀⣠⠒⡡⡞⠀⠀⢀⢾⠄⠈⠁⠀⢲⡀⠩⣍⢀⡇⠀⠀⠀⠁⠢⢀⠑⢎⠀⠀⠈⠎⠀⠀⠀⢸⡄⠂⡑⠄⠀⢸⢀⢼⠀⡇⢰⠀⠀⡜ ⡇⠀⠞⠀⡜⢀⠁⠀⠀⣎⢸⠈⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⡀⢀⡀⠀⢀⠈⠀⠉⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⢼⡀⢸⠂⣸⠀⢸⠀⢊⢾⠀ ⠘⢤⡊⢰⠀⢸⠀⠀⢸⠁⠘⡄⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣠⢃⠦⠸⠀⠀⡎⡇⣜⡴⢹⠀⠘⠀⠃⠄⢧ ⠀⠀⠈⠘⣄⠘⡀⠀⢫⠦⡀⠘⠶⡒⢆⡀⠀⠀⠀⠀⠀⠀⠘⠄⠀⢀⠃⠀⠀⠀⠀⠀⣀⢔⡭⠋⢀⡌⠀⡜⠀⡳⠁⠀⢸⠀⠀⡆⠒⠙⡜ ⠀⠀⠀⠀⠀⢣⠑⢄⡈⠌⢡⠀⠉⠑⢄⠈⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠉⡐⠁⠈⠉⢠⠄⡎⠀⢠⡃⠀⠀⢸⠀⠀⣇⠀⡴⠁ ⠀⠀⠀⠀⠀⢠⠀⠀⡸⠉⢹⠀⠀⠀⡜⢠⢀⠀⠀⠀⣸⣿⣷⣤⣠⣶⣾⣟⢤⣀⣀⣀⠑⢤⡀⠀⠀⢣⠳⡀⠀⠑⡲⠀⢸⠀⠀⢸⠊⠀⠀ ⠀⠀⠀⠀⠛⠤⠄⠚⠁⠀⢆⠀⠀⠸⣄⡂⣸⣾⡟⠻⡯⠽⠛⠋⠉⠉⠛⠓⠾⡿⠋⢻⣿⠐⡼⠀⠀⣸⠀⠀⠉⠁⠀⠀⠈⡅⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⡖⣶⣿⢻⣽⡇⠀⠈⢢⠀⠀⠀⠀⠀⠀⡌⠀⠀⠘⣿⣶⣤⣤⠚⢡⠀⠀⠀⠀⠀⠀⠀⢹⡄⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣣⣿⣿⣛⣿⣿⡃⠐⠤⠤⠊⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁⠈⡇⢼⣿⣳⡌⢆⠀⠀⠀⠀⠀⠀⠀⠑⢄⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠂⢬⣿⣿⣿⢿⣿⣿⣿⡆⠀⠀⢰⠒⠒⢂⠀⠀⠀⡖⠐⠊⠇⠀⢰⠉⠰⢳⣿⣿⠮⠗⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠜⠊⠊⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⣐⢂⠀⡸⠀⠀⠀⢧⣀⣠⠃⠀⠀⡆⠀⢘⢻⣿⣷⣤⣘⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣁⠴⣶⣿⣿⣯⡾⡘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⡿⣿⣿⠉⢚⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⡬⠐⢸⣽⣿⣿⣇⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⣾⣿⣿⠿⢧⡦⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⢀⡰⢿⠛⠿⡿⣿⡿⠟⠳⢄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠞⠉⠛⢿⡇⠀⡤⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⠤⠚⠉⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⠤⠤⠤⠤⠤⠖⠒⠃⠉⠀⠀⠀⠀⠀⠈⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀