⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⣤⡖⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣎⣿⣮⣙⢿⣝⢿⡸⣿⣿⡌⣿⣶⣄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣢⣥⣶⣿⣿⣿⢇⡟⣹⡟⢹⡟⣷⣹⣿⣿⣿⡳⣝⢿⣿⣿⣆⠹⣦⣳⢻⣷⣕⢻⣿⣿⣷⣮⣔⣈⠔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⣿⢟⢸⢸⠟⢹⠈⣧⢊⠜⣿⡜⣏⠃⢿⣾⢿⣿⣿⡿⠜⢿⡌⣿⣷⢸⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣱⣿⢸⢸⠰⠀⠆⢨⡣⡈⢎⠺⢌⣧⡈⢏⣢⡙⢦⡻⡔⡼⡇⣿⣿⢸⣿⣿⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢸⣼⢃⠆⠎⠂⠹⠦⠀⠑⠄⠙⢿⣆⠙⠿⣦⡙⣧⣀⣧⡟⣿⠘⣿⣿⣿⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⣛⠛⢸⣿⠸⡆⠸⠟⠏⠅⢊⠙⣿⣶⣶⣶⠇⠠⠄⠉⠈⠃⣹⢁⢫⠀⠈⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⠀⠸⡟⡄⠀⣤⡿⠀⠄⠄⣾⣿⣿⣿⣷⡷⠠⠰⠀⢿⡄⡇⡼⡀⠀⠀⠀⠈⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠱⡰⢸⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠥⡘⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢡⠘⣿⣿⣿⡟⢩⣭⣭⣍⢹⣿⣿⡏⠀⡸⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠉⣆⡀⠈⠙⠿⣷⣝⣛⣛⣫⣼⠟⢋⠀⣼⣱⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣿⠀⠀⢰⣇⢠⠸⢿⠀⢠⡖⢈⠙⣛⣛⡩⢀⠘⡀⠀⡽⡹⠁⠀⣤⠀⠀⢸⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⣿⠀⠀⣾⡆⡸⣆⠸⠄⠠⣻⣦⡝⠢⣵⢖⣵⣾⡇⠀⣇⠃⢄⠀⡿⡄⠀⢸⣿⠀⠀⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠢⠀⣀⠘⠿⠀⢸⣿⠀⢰⣿⠀⢱⠸⠀⠄⢼⣿⣿⢣⡀⡟⡄⣿⣿⠇⡄⣜⢰⠈⣐⢱⣷⠀⢸⣿⠀⠸⣼⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣿⡇⢸⣿⠀⣾⡇⢸⡀⡇⢹⡄⠦⠁⠉⠈⢻⢡⡇⠟⠉⠠⢨⡉⡈⢠⣭⡎⣿⡆⢸⣿⠀⢀⡎⠀⢀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣽⣿⣾⣿⣿⣿⠱⡎⠃⣿⡄⠃⣸⡀⢪⣤⡄⠈⠠⣠⠀⢠⠀⣇⢠⣦⡙⠷⢸⣷⣼⣿⣤⣿⡇⣠⣦⠃⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⣤⢰⣿⣿⠀⢁⡃⠘⠋⠀⢸⠀⠈⠂⠈⠂⠁⢈⠉⠉⠀⢼⣿⣿⣿⣿⣿⣿⣿⢡⣄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠇⢘⣘⣫⣴⡾⢋⠀⡳⠾⠀⣿⡆⢸⠇⠲⣶⣌⡸⢿⡿⢀⣿⣿⣿⣿⣿⣿⣿⡏⣿⣟⠻⢦⣄⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠟⣡⣾⢸⡮⠢⠅⢰⣶⣆⠀⠅⡀⢦⡙⢿⣶⣶⣶⣮⣝⣿⣿⣿⣿⣿⡇⠸⣿⣿⡒⡈⠧⠀⠀⠀⡀⠈⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠤⢴⣶⣤⣤⣤⣤⣤⠠⡄⣴⣶⣴⣶⣦⢒⡒⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢶⣦⣶⣦⣤⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⣄⠀⠉⠉⠈⠉⠉⠀⠁⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠈⠈⠉⠉⠉⠀⢀⣬⣿⣿⣿⣿⣏⣉⣹⣷⠁⢹⣿⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣬⣴⡿⣿⣿⣿⣿⣿⣿⣿⣟⡓⠺⠶⠿⠿⢺⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣟⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠲⠈⠉⢉⠉⡗⠖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⣤⠼⠳⣯⢹⢿⣿⣿⡿⣿⣽⣥⠘⡿⣷⣿⣿⣿⣿⣿⣿⠐⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡇⠀⣆⠂⠈⡉⠁⠇⠉⠁⠀⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠶⠋⠤⠳⠙⠉⠿⠿⠿⠃⠿⠟⠯⠈⠃⠻⠿⠿⠿⠿⠿⠯⠿⠿⠿⠍⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠉⠫⠇⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀