⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠚⣩⠄⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⢋⡤⠊⠁⠀⠀⠀⠀⣠⡾⢫⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⠴⠋⠀⠀⠀⠀⠀⢀⣴⠋⠀⠈⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡌⠀⠀⠀⠀⣰⣻⠃⠀⢠⠆⡠⢀⣴⢣⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⡄⢠⠄⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠬⠽⣿⡿⢿⣿⣿⣿⢿⠿⢿⣿⣿⣿⡿⠃⠀⠀⠠⣠⠀⠀⡀⡼⣹⡏⣴⣶⢃⡜⢁⣾⢸⡸⣼⠀⡇⣿⡀⢸⡀⠀⡄⠀⢟⡆⠀⠀⠈⣿⣿⡿⢿⢿⣿⣿⣿⡿⢿⠿⠿⣿⠿ ⠀⠀⢠⠀⢩⢀⠘⠉⠼⣄⠀⢀⣼⠃⡠⣹⠀⡠⠖⢩⠾⠁⡠⣪⠞⣦⡿⠀⣿⢧⠞⣰⣿⣽⣸⡇⣿⠀⣧⣿⣇⢸⣿⠀⡇⡇⢸⣧⠀⢸⠀⠘⣿⣔⠈⢚⠉⠆⠞⣄⠈⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠈⠘⢆⠀⡘⢀⠀⠀⡒⠀⣿⡁⢁⡴⡡⠦⢊⣴⣟⣶⣟⡇⣶⣯⣯⣾⣿⣿⠹⣿⣧⡟⡇⢹⣿⣿⢸⣿⢀⢷⣿⢸⣿⡇⢸⠀⠀⣿⣿⣷⡸⠀⢀⡰⠞⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡲⣿⣦⠞⠈⢀⣴⣿⣟⡾⣏⢛⢸⡿⣿⣿⣿⡿⠁⢻⣿⣿⢿⣇⣸⣹⣿⢸⣿⣣⣘⠮⣾⣿⠁⡾⠀⠀⣿⣿⣿⣿⣆⠈⠋⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⢧⡿⣣⣤⣶⣿⣿⣿⣿⣿⣷⢿⡿⡇⣿⣯⠯⠤⣀⣸⣿⣿⣿⣿⣾⣿⣿⣼⠿⠛⠋⠱⢯⣿⣦⣳⣋⠋⢸⣿⣿⣿⣿⣷⡀⠑⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⢻⡻⣿⢷⣞⣾⢼⣿⣿⣿⣿⣿⣿⣦⠤⣴⣶⢿⡏⣏⡊⠓⠴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⡄⠫⠾⠷⠤⢽⡗⢫⢿⣿⢹⣿⢯⣏⠑⢺⣯⢸⢃⣿⣟⣦⣠⣼⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⢦⣶⡤⠟⠚⢇⠀⠻⣏⢍⡿⣿⣿⣿⣿⣿⡿⣷⢻⣳⡠⠈⠁⠀⠀⠇⠀⢙⣿⡴⢿⣟⣛⣛⣻⣟⡟⣼⣿⡜⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠴⠲⠖⠛⠉⠉⠁⠈⢥⠹⡃⠐⢍⠒⠤⢕⣤⡈⠳⣄⠸⣟⣿⣿⣿⡡⡏⢏⣷⠳⡀⠀⠀⠀⠀⠀⡎⢻⠁⠒⠁⠂⢀⣼⣿⣳⣿⣟⣼⣿⡿⣟⣽⠏⢠⠀⠀⡀⠰⢔⠒⢶⡀⠀ ⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠑⢦⠀⠈⠉⠀⠈⠳⡌⠳⣍⢛⠷⣥⡘⣯⠂⢄⣀⠀⠀⡀⣰⣧⠖⠀⠀⠀⣠⣿⣿⣯⣿⣿⣾⡿⢋⡴⣿⠃⠀⠀⠀⠀⣧⠄⠀⠁⠀⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡀⠀⠙⢦⡀⠀⠀⠀⠈⠲⣮⣷⡹⣧⠛⣟⢷⣄⠈⠙⠒⠂⠛⠂⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⢻⡇⠀⡞⠋⣿⠛⠲⢿⣝⣟⢦⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡽⡄⠀⠀⠙⠢⣀⠀⢤⠀⠀⠈⠛⢎⢣⢹⡇⢻⣦⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⢸⢱⡞⠀⢰⠃⠀⠀⠀⠙⠪⢦⣈⠻⣷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢿⡄⠀⠀⠀⠀⠈⠳⢄⡙⠂⢀⠀⠀⠐⠎⣿⢸⣏⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠃⢸⠎⠀⢀⠃⠀⠀⠀⠀⠀⠀⣠⠟⠃⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠻⠶⣆⢆⣿⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡎⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠴⠋⠀⣠⠎⢀⡴⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣦⢀⠀⠀⠀⠀⠀⠀⢢⣍⠛⣿⣿⣿⣿⣿⣿⣿⠟⢋⡅⠀⡤⠎⠁⠂⠊⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⡼⣿⣿⣿⢟⣫⠶⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⢁⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀