⠀⠀⠀⠀⠀⣀⣴⡶⠿⠛⠛⠛⠛⠻⢷⣦⣤⣴⡶⠞⠛⠛⠛⠛⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡿⠁⠀⢀⣠⠴⠒⠋⠉⠉⠉⠙⠓⠶⢬⣷⣤⠴⠒⠚⠛⠉⠉⠛⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡟⠀⠀⠐⠋⠀⠀⢀⣀⣀⣀⣀⠀⠀⠈⠓⢯⡻⣦⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⠀⠀⠀⠀⣠⠴⢛⣉⣤⣤⣤⣭⣍⡓⠦⣄⡀⠙⢮⣷⠀⢀⣠⢶⣫⣷⣾⡛⠛⠓⢶⣍⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠃⠀⠀⠰⢯⣵⠚⠋⠁⣼⣿⣿⣟⢙⣿⡓⠦⣭⡓⠦⢽⢷⣿⢿⣿⣿⣇⣹⣿⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢾ ⠟⠀⠀⠀⠀⠀⠈⢷⡀⠀⢻⣿⣿⣿⣿⡿⠁⠀⠀⠉⣷⣟⠋⠁⠘⣿⣽⣿⣾⡟⢀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡝⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢤⣍⣛⣛⣋⣀⣀⣤⠴⣞⡟⢮⡙⢳⡶⠶⠿⠿⠷⠚⢋⣵⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠛⠁⠀⢀⣤ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠓⠦⠬⠭⠭⠥⢖⣺⠿⠋⠀⠀⠉⠳⢭⣉⠉⠡⠤⠶⠟⢿⣄⠀⠀⠀⠀⢀⣴⣾⣿⠇⠋⠁⠀⣀⣴⣾⣿⣽ ⠀⠀⢋⣥⠤⠤⣄⡀⠀⠀⠀⠀⠠⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⢈⣿⣆⣠⣴⣾⡿⠟⠈⠀⢀⣤⠶⡿⢛⣹⣿⠟⠋ ⠀⠀⣾⠡⠀⣀⡀⠉⠓⠶⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⣋⣼⠟⡻⢱⠁⠀⣀⡴⠞⠉⠀⢸⢳⡟⠉⠀⠀⢀ ⠀⠀⠹⣦⠀⢻⣿⣷⣶⣤⣀⣀⠀⠉⠉⠉⠉⠛⠒⠒⠒⠒⠚⠉⠉⠉⠉⠁⢀⣠⡞⠋⣀⠤⢳⣸⠶⢛⣁⣀⡀⠀⢠⢹⡸⣇⣠⣴⡾⣟ ⠀⠀⠀⠘⢷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣟⢿⣿⡯⠖⣉⣤⠴⡿⠵⠞⠋⠁⢘⡇⠀⠈⣾⣷⣙⠻⠷⢛⣽ ⠀⠀⠀⠀⠀⠙⢦⡀⠈⠻⢿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠈⠙⣿⣿⣿⣿⣧⣼⠀⣼⠋⠀⠀⠀⠀⠀⠀⣠⡾⠃⣀⣴⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠿⣻⣿⣰⠇⠀⠀⣠⣤⣾⣿⣏⣭⣶⣿⣿⣿⣿⡿⠟⣿⠉⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣀⣀⠀⠀⠉⠉⠉⠁⠀⣀⣀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠋⠀⢀⣿⠀⠀⠀ ⠛⠷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⣛⣫⡽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠋⠀⠀⠀ ⠀⠀⠀⠙⢿⣟⠛⠿⠷⢶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠤⠶⠛⠉⣠⣿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠿⠶⣤⣀⡀⠀⠀⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠙⡏⠉⡏⣻⡶⠶⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠻⣶⣿⡇⢰⡷⡿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠙⠦⠤⠤⠿⣿⣤⢞⡼⠃⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡷⠤⣄⣀⡤⠤⢂⡾⠁⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀ ⠳⣦⣀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⢽⣿⣿⠿⣿⣷⣦⣴⣶⡞⠋⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⣶⣴⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣟⣡⣤⣹⣿⣿⣧⣽⣿⣿⣿⣿⠟⠛⠷⣦⣤⣤⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⣄⣀⣀⣀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠹⣿⣵⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀