⠀⣼⠗⡟⢻⣻⣛⢻⣟⣿⣾⣛⡛⣿⢛⣻⣏⣨⣧⣿⢻⡟⣿⣛⡛⣾⢛⣛⣿⣟⣿⢿⠟⣇⠿⣻⠿⡟⢿⡿⢿⠉⡷⢨⡋⠍⠹⡇⠀⠀⣿⣿⣿⣿⡾⢷⠀⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣃⣇⣸⣏⣿⣹⡿⢻⣿⣻⣇⣷⣼⣻⣿⣛⣛⣿⣀⣇⣿⣹⣇⡿⣽⢵⣟⢻⣿⣸⣂⣟⣶⣙⣄⣛⡿⠀⠀⠠⢀⡾⠄⠢⣤⠇⠤⠀⢿⣍⠻⢏⣥⠸⠿⠇⠀⠰⠆⠀⠀⠸⠯ ⠀⠈⠛⠛⠛⠛⠋⠙⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠙⣯⣻⣆⣿⠆⠈⣿⣿⣿⣿⣿⣙⣯⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣾⣿⣦⣿⡛⠿⣿⢻⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⣿⣿⣿⣿⣿⣶⣿⣼⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⡿⡿⠛⠉⠛⠿⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣾⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠀⠠⢀⣄⣤⣀⡀⠀⢀⣠⣤⣤⣤⣿⡟⣡⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡾⠟⢻⣿⣿⣿⣿⡉⢉⣉⡉⣉⢉⣟⣏⣽⣿⣿⣿⢿⡟⣋⢉⣉⣙⣻⣿⣿⠻⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠋⣹⣷⠛⠋⠉⠉⠁⠀⠉ ⢉⣤⠾⠿⠿⠿⠿⡟⠛⠉⠉⠉⠉⠿⡿⢿⣿⣿⣿⣿⠟⠋⠻⠛⠙⠛⠛⠿⡿⣷⣦⣙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡾⢷⣿⣿⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣷⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⡾⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⣹⣿⠱⣿⣿⣿⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⠇⢠⣿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣏⣹⣿⢤⣾⣄⣀⠀⠀⠀⢀⡀⠀⠀⣤⣀⣀⣀⣀⣀⣀⡉⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣻⣿⠟⠛⠿⣻⠍⠭⣿⣿⣿⡀⠀⠀⠀⠀⠀⢠⣿⣿⢃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠚⡛⣋⣻⠿⢿⣿⣿⣟⣁⡆⠀⠀⠀⠀⠀⢈⣁⣤⣾⣶⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⣀⣼⣿⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣴⣄⣤⣦⣶⣾⣿⣿⣤⠞⠹⣯⡙⠿⠁⠀⣠⠀⠀⠀⠀⠿⣿⣿⣷⣿⣾⣷⣽⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⣨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣍⣿⣿⣿⣿⣿⡿⢿⡦⣇⣀⣁⡀⢀⣈⣿⣷⣄⣀⠀⠀⠈⠛⣿⣿⡿⣿⣿⣻⣿⡿⣦⣯⠁⠘⣿⣿⣿⡇⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⢿⣿⠻⠿⣷⣿⣷⣶⣿⣿⣿⣿⣽⣿⡿⣷⣦⡀⠀⠙⠃⠘⠻⠿⠙⠹⠛⠻⣿⣾⣿⣿⣿⣷⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠝⠁⠼⢻⡿⣦⠁⢀⣀⣴⡿⠟⢉⡿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⡯⢖⣾⣷⣌⠛⠉⡀⠀⠀⠀⠀⠀⢿⠟⠘⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⣻⣥⣿⣻⣿⣿⣷⣾⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⢸⣷⣷⣮⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣾⣁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢐⣿⣿⣿⣻⠷⣶⡾⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢿⣿⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢙⢿⣿⣷⣄⡨⣿⢿⣷⣀⡀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⠥⠟⠧⠞⣿⠿⠋⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢁⣠⡄⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠿⣏⢳⡈⢻⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣆⣀⣀⢀⠀⢀⠻⣿⠶⣴⣀⣀⢀⣤⣿⣿⡶⣵⣶⣶⣶⣖⣄⡒⣀⣁⣀⣀⣤⣿⣿⣿⣛⣾⣅⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⡿⢿⣻⣿⣟⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀