⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠠⡖⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠶⣴⣶⣄⠀⠀⠀⢀⣴⣞⣼⣴⣖⣶⣾⡷⣶⣿⣿⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠙⢟⠛⠴⣶⣿⣿⠟⠙⣍⠑⢌⠙⢵⣝⢿⣽⡮⣎⢿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢱⡶⣋⠿⣽⣸⡀⠘⣎⢢⡰⣷⢿⣣⠹⣿⢸⣿⢿⠿⡦⣄⠀⠀⠀⠀⠀⠀⡠⠀⠀⠂⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢧⡿⣇⡅⣿⣇⠗⢤⣸⣿⢳⣹⡀⠳⣷⣻⣼⢿⣯⡷⣿⣁⠒⠠⢄⡀⠀⠀⡀⠀⠁⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⣿⣧⡏⣿⣿⢾⣯⡠⣾⣸⣿⡿⣦⣙⣿⢹⡇⣿⣷⣝⠿⣅⣂⡀⠀⠡⢂⠄⣈⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⡟⣿⡇⡏⣿⣽⣿⣧⢻⡗⡇⣇⣤⣿⣿⣿⣧⣿⣿⡲⣭⣀⡭⠛⠁⠀⠀⣨⠁⠉⣂⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢻⣿⣇⣥⣏⣘⣿⣏⠛⠻⣷⠿⡻⡛⠷⡽⡿⣿⣿⣿⣷⠟⠓⠉⠢⢄⡀⢠⠇⠀⠀⠀⠁⠫⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢸⣾⣿⣽⣿⣏⣻⠻⠁⢠⠁⠀⠀⠀⠘⣰⣿⣿⢟⢹⢻⠀⠀⠀⠀⠀⠈⡒⢄⡀⠀⠀⠀⠀⠀⠀⠑⢄ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢸⣯⣿⣿⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⢿⣾⣸⠀⠀⠀⠀⠀⠀⣅⡠⠚⠉⠉⠁⠀⠀⠀⢀⠌ ⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢟⣿⣯⡟⠿⡟⢇⡀⠀⠀⠐⠁⢀⢴⠋⡼⢣⣿⣻⡏⠀⠀⠀⣀⠄⠂⠁⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠊⢻⣿⣜⡹⡀⠈⠱⠂⠤⠔⠡⢶⣽⡷⢟⡿⠕⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢿⠿⠿⢿⠾⣽⡀⠀⠀⠀⠈⠻⣥⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⠂⠠⠐⠋⠀⠙⠳⣤⣠⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠵⡐⠄⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠠⡀⠀⠈⠙⠶⣖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡥⠈⠂⠀⠀⠀⠀⠀⠀⠀⣼⠉⠙⠲⣄⠈⠣⡀⠀⠀⠈⢻⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⣷⡄⠈⠄⠀⠀⠀⢧⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⢠⣿⣤⣤⣶⣶⣾⣿⣿⡄⢸⠀⠀⠀⢸⣄⣤⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣼⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠈⠉⠙⠛⠿⠿⠽⠿⠟⠛⡉⠛⠲⣿⣿⠿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⣸⣿⣷⢷⠙⣻⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠉⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣏⠀⣿⣿⡘⣼⡇⠀⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢙⠓⠛⠘⣧⠾⢷⣄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣿⢟⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠀⠀⠀⢸⣧⠀⠹⣆⠀⠀⠀⠀⠈⢻⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢂⠙⢿⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⠀⠀⠈⠙⠀⠀⠻⡄⠀⠀⠀⠀⠸⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠐⠠⠀⠻⠬⠄⡒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠠⣲⡟⣯⣤⣮⣴⡦⣻⣵⣿⡿⣿⢿⡿⣿⣻⢿⣻⢿⣻⣿⢿⣿⣿⣿⢿⣻⡿⣿⢿⡿⣿⢿⣿⣻⢿⣿⡿⣷⣾⣦⣄⡙⠾⢱⠌⡥⣄ ⠽⡺⣝⡾⢩⡝⣴⣾⣿⣿⣿⣳⢿⣻⣯⢿⣻⣽⣟⣿⣻⣯⣿⢿⣳⣟⣾⣟⣯⣿⣻⢯⣿⣻⣯⢿⡽⣟⣾⢿⣯⣷⢿⣟⣿⣶⣒⣌⣾⠉ ⣼⣷⣿⣧⢻⣏⣿⣿⡿⣷⣾⣻⣟⡷⣯⢿⣯⣷⣞⣯⡿⣽⣾⣻⢯⣿⣚⣯⣷⣻⣽⣯⢷⡿⣝⣻⣟⣯⣟⡿⣞⣿⣯⣿⣻⣾⢿⣿⣆⠳ ⣿⢿⣿⣿⣿⣿⣿⣿⣟⣷⢯⣷⣻⣽⣟⣯⡷⣟⣾⣿⣻⣽⣞⣯⣿⣳⡿⣯⣟⣷⣻⢾⡿⣽⣟⡿⣾⡽⣯⣟⡿⣽⣷⡿⣽⣿⣻⢾⣿⡀ ⣿⣻⣾⣿⣿⢾⣿⣷⢿⣾⣻⣽⣻⣾⢯⣷⢿⣻⠛⢹⣯⣷⢿⣽⢾⣷⣻⢷⣻⣾⣻⢯⣿⣽⢾⣻⡷⣟⣯⡿⣽⡷⣯⣿⣷⣻⢿⣯⣟⣧ ⣿⣽⣟⣷⡿⣿⣿⣯⢿⣞⣿⣻⣿⣽⣿⣿⡿⢛⠫⠹⣿⡾⣟⣾⣟⣾⣻⢿⣹⡾⣯⣿⣳⣯⡿⣷⣟⣿⣳⣿⣯⡿⣷⣯⣷⣿⣻⢿⣞⣿ ⣿⣳⣯⣿⢿⣿⣯⣿⣿⣯⣿⣿⣟⡯⢟⣞⠔⠡⠈⠄⣿⣿⢯⣷⣻⣽⣯⣿⣽⣟⣷⢯⣷⢿⣽⣷⣻⣿⣿⣿⣿⣿⣷⣯⣿⣷⣿⣻⣿⢾ ⣿⣻⣿⡽⣿⣟⣾⣽⡾⣟⣿⣿⣿⣿⡿⣥⠤⠥⣌⣀⢹⣿⣯⣷⡿⣟⣾⡽⣷⢿⡾⣿⣿⣿⣟⣾⣿⣿⣻⣟⡿⣿⣿⡿⣿⣿⡿⣷⣻⣿ ⣿⣽⡷⣿⣿⣽⣾⣷⣻⢿⣽⣻⣿⡻⢚⣶⠒⢛⢒⠒⢺⣿⣯⢿⣽⢿⣽⡇⣿⡿⣽⢿⢿⣻⣿⣿⣿⣳⢿⣞⣿⣳⣟⣿⣽⣿⣿⣻⢷⣿ ⣿⢷⣿⣿⣳⣿⣟⣾⡽⣯⣷⣿⣿⣿⣿⣿⣿⣽⣿⣷⡄⣿⣯⣿⢾⣿⣽⢡⣿⣟⣯⡟⠀⡉⢿⣿⣷⡿⣯⢿⡾⣽⡾⣯⣟⣾⣽⣿⡿⣾ ⣿⣟⣿⡽⣷⣿⣻⣞⣿⣿⣿⣿⢛⣟⣿⣿⢿⣿⢿⡇⠉⢺⣿⣞⣯⣿⣿⠁⣿⣾⣻⠃⡠⡠⢀⠙⣇⠹⣿⣯⣟⣯⢿⣳⡿⣽⡾⣿⣿⣽ ⣿⢾⣟⣿⣿⣟⣷⣻⣽⣿⣟⣯⣸⣿⣿⣯⡿⣽⣿⡇⠀⠈⣷⡿⣽⣾⣿⠀⢻⣷⡟⡰⠁⠑⢄⠂⠹⡄⠹⣷⣻⣽⣟⣯⢿⣷⣻⡷⣿⣿ ⣿⣸⣿⣞⣷⣻⡾⣯⣷⣿⣯⡟⠘⢹⣿⢷⣻⣯⣿⡇⠀⠀⠸⣿⣻⡾⣽⠀⢸⣿⡧⠁⠀⠀⣠⣨⣒⣳⣢⣜⣿⢷⣯⣟⡿⣞⣷⡿⣿⣻ ⡷⣸⣿⣞⣯⣷⣟⣿⣿⣯⣿⣧⣦⠀⠿⢿⣻⣽⢿⡇⠀⠀⠀⣿⣿⢿⣿⠃⢸⣿⠁⠀⢶⣿⣿⣟⠿⠿⣿⣿⣿⣿⣷⣻⣽⣟⡷⣟⣿⢿ ⡗⣿⢾⣭⣷⣟⣾⣻⣿⣽⣿⠟⡞⣇⣶⣿⣿⣯⡿⠿⠀⠀⠀⢏⣧⢫⡧⠀⠈⣿⠀⠀⠹⣿⣷⡀⠀⠀⠀⢈⡟⣿⣿⢯⡿⣞⣿⣻⣽⣿ ⡧⣿⢿⡽⣾⣽⠟⣯⣿⡗⠯⣐⠆⡽⢛⡟⡛⠋⠀⠀⠀⢀⣀⡈⠋⠄⠻⠁⠀⢻⠀⠀⠀⠈⢿⣷⡀⠀⠀⢀⣿⣿⣽⣻⣽⣟⡷⣿⣽⣾ ⠷⣿⣯⣿⣿⣿⠀⢻⣟⣿⣶⣡⠾⠴⠧⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠸⣿⣿⡄⠀⣾⣹⣳⣿⣽⢾⣯⣟⣷⣿⣿ ⢀⠛⣿⣿⠿⣿⡅⠚⣿⣿⣿⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣘⣿⡿⠖⣏⣷⣿⣷⣯⣿⢾⣽⣾⣿⣿ ⡌⢊⠄⣤⢈⣿⣷⣀⡘⣿⣏⣿⣿⣢⡀⠀⠀⠀⠀⠀⠠⢤⡤⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢵⡢⢜⡡⣎⢿⣿⣿⣽⡾⣿⣽⣏⣿⣿ ⠙⣌⣼⢚⠉⠹⣻⢷⣿⠛⣿⣿⣯⠝⣿⣦⣄⡀⠀⠀⠀⢺⠁⡀⠋⠱⡄⠀⠀⠀⠀⠀⠀⠀⠰⢿⣡⣿⣿⢿⣧⣿⡿⣾⣽⣷⡟⡼⣽⣿ ⠔⠉⣲⠊⠀⡁⢸⡆⠈⢤⠄⠹⢾⠩⢀⣈⠳⢫⢖⣠⣄⡘⢆⠄⠡⢀⠸⠀⠀⣀⣠⣤⣴⣶⢻⣿⡿⣿⣽⣻⣿⣿⣟⣷⣻⣿⣧⢣⣿⣿ ⠀⢸⡅⠑⢦⡄⠄⢳⠀⠀⠉⢢⣀⠐⠂⢉⠚⣷⣞⠫⠾⢿⢫⡝⡛⢫⠱⢈⠉⡩⢿⣟⡛⠯⣿⡿⣽⣟⣶⣿⡟⣾⣯⣟⣯⣽⡏⣸⣿⡟ ⡥⢿⣷⣶⠾⢯⡤⢬⠿⣦⡤⡤⠵⠴⠶⠶⠶⠾⠷⠷⠾⠾⡆⣿⢿⠵⣥⣤⣮⢿⢙⣿⠁⣼⣿⣽⡿⣿⣿⠟⢸⣽⣿⣽⣿⡏⠱⣹⣿⢧ ⠘⢈⡿⢬⠥⣆⢘⡠⣶⡩⠵⠒⠁⠉⠉⠓⢵⡚⡌⣡⢊⠜⢻⢿⣹⡄⠀⠙⣺⣌⣯⣇⢣⣿⢿⣿⢣⢿⡇⠀⣬⣿⣷⣿⣿⡇⡄⣽⡿⡼ ⠆⠀⣶⣿⠤⡼⡼⠅⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⣯⠲⠞⡾⠿⡭⠍⠀⠀⠀⢁⢱⠚⣲⢹⣧⢸⣿⣏⠀⠀⡰⣽⣿⢯⣿⣻⠇⡇⡿⠰⠃