⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⣿⣎⠉⠙⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⠋⠉⠉⣩⡙⠛⠻⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠹⣆⠀⠀⠀⠀⠈⠙⠳⣦⡴⠚⠋⣉⡛⠓⠀⠀⠀⢠⣿⠿⣥⣀⡀⠛⣦⡀⠀⠉⠙⠳⠄⠀⠈⠙⠿⣷⣄⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢿⣆⠀⠀⣀⣠⣤⡾⣏⡴⠞⠋⠁⠀⠀⠀⠀⠀⣾⢃⠀⠀⠀⠙⠳⣮⡙⠛⠲⢦⣀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣽⣛⣯⢩⡿⣋⠀⠀⠘⠻⣄⢀⣀⣤⠤⠶⢶⣦⣀⡏⠊⠀⠀⠀⢀⣼⠙⠉⠒⠲⣤⡙⢷⡀⠀⠀⠀⠀⠀⠻⢷⡀⠀⠀⣀⣤⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠋⠉⣹⣿⢻⠃⠀⢀⣠⡴⠟⠉⠁⣀⣴⡶⣿⣿⣿⣧⢤⣤⣶⣿⣿⡝⠳⣦⡀⠀⠈⠻⣜⣿⠙⠛⠓⠒⠶⠤⣌⣇⡀⠀⠿⣿⣌⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣿⣿⠟⢋⡽⠿⠛⣡⡴⠛⠁⠀⣠⡴⠛⠉⠀⠀⠉⠁⠼⠟⠛⠛⠛⠿⢿⣿⣆⠀⠙⢷⣤⠀⢸⣟⡷⣤⠀⠀⠀⠀⠀⠈⠙⠓⣦⣌⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢁⡀⠋⢀⣰⡾⢫⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠘⢧⠀⠀⠁⠈⢷⡀⠀⢀⣠⣴⠶⢛⣿⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠻⣿⣿⣄⣴⡿⠋⣴⠏⠀⠀⢀⡾⢁⡤⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢧⡀⠀⣀⣸⣷⣾⠿⠭⠀⢠⣿⣇⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣮⣭⣭⣭⣿⣿⠏⠀⠀⠁⠀⠀⢠⡿⢡⡾⠁⣰⢇⡾⠁⣰⠆⠀⠀⡀⠀⠀⢰⡆⠀⡀⠀⠸⡆⠀⠀⠈⢧⣉⣻⡿⣏⠙⣶⣒⣶⣰⠏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⡿⠛⣺⣿⣿⠃⠀⢀⡾⠀⠀⢀⡿⢁⡿⠀⣼⡏⣾⠇⣰⡿⠀⠀⢠⣧⠀⡀⠀⣷⠀⣇⡀⠀⡇⠀⠀⠀⠘⣇⠀⠁⠘⣦⠀⠻⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣼⣯⣶⣟⣿⣿⠏⠀⢀⡾⠁⡄⠀⣼⠃⣼⠁⣰⡟⣸⡿⢠⣿⠇⠀⣼⢸⠹⣤⡇⠀⣿⠀⢻⣷⠀⢻⠀⠀⠀⠀⣸⡄⠀⠀⠀⢹⣿⣿⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⢻⣤⣖⣿⣿⡏⠀⠀⣼⠃⢰⠃⠰⣿⣰⣿⣤⣿⣷⣿⡇⣼⡟⠀⢰⠇⣼⣤⣿⢠⢰⣿⡀⢸⣹⠀⢸⡄⢰⠀⠀⣧⣿⠀⢠⡀⢈⣿⡿⢯⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣻⡷⠀⠀⠀⣼⣿⣿⠀⠀⢰⡏⠀⡟⠀⢠⣿⣿⢹⣾⢻⣿⢹⣧⣿⡇⠀⣿⢠⣿⣿⣧⣾⣼⣿⡅⢸⣿⠀⢸⡇⣿⠀⠀⣿⢸⡇⣸⣿⣿⣿⣶⣶⣦⡽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡿⠇⠀⠀⢰⡟⣿⣿⠀⠀⢸⠁⢰⡇⠀⣼⣿⣿⣸⣿⣾⣟⢸⣿⢿⡇⢠⡏⢸⣿⣿⣿⣿⣿⣿⣧⣾⣟⠀⢸⡇⣿⠀⠀⡟⠈⣷⣿⣿⣿⡝⠛⠿⣿⠀⢻⣷⣶⣶⣶⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢰⡇⠀⠀⠀⣾⢱⣿⣿⠀⠀⣼⠀⢸⡇⢠⣿⣿⣿⣿⣿⣿⣿⡾⣿⢸⣇⣼⣧⣿⣿⣿⣿⣿⣻⡏⠨⣿⣿⡀⣿⣧⡇⣸⠃⡇⣤⣿⣿⣿⣿⣿⣣⡼⠁⠀⢸⣿⠿⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⣿⡇⣿⠀⢰⡿⣼⣿⣿⣸⡄⣿⣄⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⠁⠘⠈⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⡿⢹⣿⠻⢁⡿⢀⡇⣿⣿⣿⣿⣷⣸⣿⢁⠀⠀⢨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇⣼⡟⡇⣿⠀⣾⡇⣿⣿⣿⣿⣧⣿⣿⡄⣿⣿⣿⠘⢻⣿⣿⣿⡇⠀⠀⠀⠘⣷⣿⠹⠋⢹⣿⣿⣿⣿⣿⣿⣷⣼⠇⢀⡼⠃⣸⢷⣿⣿⣿⢿⣿⡛⣿⡆⣧⠀⢸⡟⣷⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⢀⠰⣶⣄⠀⠀⠀⠀⠀⢰⣿⡟⠀⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠚⠁⣰⣿⣸⣿⣿⣿⠀⠸⡇⠛⣧⢸⡆⢸⡇⢸⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⣀⣭⣿⡇⠀⠀⠀⠀⢸⡿⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣻⡿⢋⣤⡶⠀⣴⣿⣿⣿⣿⣿⣿⡄⠀⣿⠀⣿⡆⠁⢸⡇⠸⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠈⣿⠿⠛⠁⠀⠀⠀⠀⢸⠇⠀⠀⢸⣿⢹⣿⣿⣿⠟⠛⠛⠿⢿⡿⢿⣿⣿⡿⣆⠀⠀⠀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠈⠙⠿⠋⡠⣌⣴⣿⣟⣡⣾⣿⡿⣻⣿⣿⢻⣿⡇⠀⣿⠀⣿⣿⡄⢸⡇⠀⡇⣿⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠸⣤⡀⣠⣿⡦⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣿⡿⠀⣿⣿⣷⠀⠀⠀⠀⠀⠙⠾⣿⣿⣷⣬⣷⣤⡀⠀⠀⢸⣆⣈⣿⠃⠀⠀⠀⠀⠀⠀⢺⣿⣯⣿⣿⡿⣿⣿⠟⣼⠋⣿⡏⢸⣿⡇⠀⣿⠀⣿⣿⣷⣾⠁⠀⡇⠀⠉⠁⣤⠆⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⢠⣿⡇⠀⠘⣿⣿⣴⡆⠀⠀⠠⠀⠀⠻⣿⣿⢿⣿⠏⠛⣦⣄⠀⠉⠋⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⠿⠞⠉⠀⠘⢁⣰⣿⢿⣿⣿⡇⠀⣿⢠⣿⣿⣿⣿⡄⢸⡇⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢸⠀⠀⠀⣸⣿⡇⠀⣰⡿⠋⣽⠇⠀⠀⠀⠀⠀⠀⣼⠟⢿⣁⠀⠀⠈⢿⣷⣦⣤⣤⣶⣶⡾⠋⠉⠀⢹⣿⣿⣟⠁⢀⣠⠴⠖⠛⠉⠀⣇⣼⣿⣿⣧⠀⢸⢀⣿⠻⣿⠇⠀⣸⠁⠀⣠⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⣿⠾⠛⠛⠉⠒⠲⣆⠀⠀⠀⠀⠀⠀⢶⡿⢡⣾⠟⠃⣀⣠⣬⣷⣮⣩⣤⣾⡋⠀⠀⠀⣠⣿⠟⠁⣨⡿⠋⠁⠀⠀⣠⣄⣼⣿⣄⣹⣿⣿⠀⢸⣿⣿⢸⠏⢠⣶⠏⠀⠸⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢀⣠⠶⢦⠹⣦⣀⠀⠀⠀⠀⣼⠀⣰⣿⠄⠸⠿⢿⣿⣿⣏⣻⣿⡿⣿⣶⣤⡞⢫⣿⠖⣸⡿⠋⠀⠀⠀⢠⣿⣿⠋⠀⠈⠻⣿⣿⠀⠀⣿⣿⣇⠀⣸⠟⢷⣤⡀⠈⠙⠷⢦⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠤⠤⠤⢤⣤⣀⣀⣀⣀⡀⣾⡿⣠⣶⡶⢛⣉⣙⠺⢷⣜⢿⠉⠙⠲⣴⡏⣰⠏⠘⢦⣠⣴⣿⣿⣿⣿⣿⣿⡇⠈⠛⢋⣴⣿⠏⠀⣿⠁⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠈⢿⣇⠀⣿⣿⢿⡄⠀⠀⠀⠙⣯⣛⠲⠦⢤⣄⣉⣁⠀⠀⠀⠀ ⠀⠀⠀⢠⡴⠶⢤⡀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣻⣿⢾⣋⣉⡉⠲⣄⠹⣾⡀⠀⠀⣸⡿⠃⠀⠀⢠⣾⠟⠋⠉⠛⠛⠻⣧⣽⠂⠴⠛⠁⠈⡇⠀⣿⠀⠀⢠⣶⠟⠀⠀⣠⣴⣳⣄⠀⠀⠀⠙⢷⣿⡿⣾⣧⠀⠀⠀⠀⠀⠉⠛⠒⣂⡬⢿⡏⠁⠀⠀⠀ ⠀⠀⠀⠘⣧⡀⠀⠙⢦⣀⠀⠀⠀⣰⡿⠃⣼⠟⠁⠀⠀⠉⠻⣿⣶⣾⣧⠈⠻⣄⣰⣿⡃⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⢷⢰⣿⠀⠀⢀⡏⠀⣠⡾⣋⣤⢤⡿⠻⣶⣶⣄⣸⣿⡇⢻⡿⣇⠀⠀⠀⠀⠀⣠⠞⠉⠀⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠓⠶⢾⣏⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⡾⢿⠋⠏⠀⠙⠦⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠸⡆⣿⠀⣰⠟⢡⣾⢣⡾⢉⣶⣶⡿⠛⠉⠛⠺⢿⣿⣷⠀⠋⣿⣦⣤⠴⠖⠋⠁⠀⣠⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢶⣀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⠇⢾⡓⠛⠃⠀⢀⡏⠙⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢻⣿⣾⡏⠀⠊⢸⣿⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠉⠻⣷⡴⠋⠁⠀⠀⠀⢀⡴⣞⣉⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⠂⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣏⣤⠾⢿⣤⣀⡐⡾⠃⠀⠀⠈⠻⣦⡀⢀⣤⠞⠓⠲⠿⠃⠀⠀⠀⠀⠸⣿⣏⡇⢀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠘⠻⣆⠀⠀⠉⠉⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⢀⣠⣾⣿⣋⣁⣀⠀⢘⣧⠀⢹⠷⣄⣀⠀⠀⠀⢘⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢷⣌⠁⠈⣿⣼⣟⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠂⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⠞⠋⣰⠟⠁⠀⠈⠉⠙⠛⠙⣷⣼⣄⠀⠉⠻⣄⠀⢿⣿⠗⠀⠀⢤⣤⣶⡤⠄⠀⠀⠀⣰⣿⡏⣠⣿⠷⠤⢽⣿⣻⡿⣷⣀⡀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀ ⠀⠚⠁⢀⣠⡴⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⡾⠋⠀⠀⠀⠀⠀⢠⠞⠋⠉⠛⢿⣷⣶⣿⣯⡿⣾⣿⣤⣤⣀⠀⢠⠏⠀⠀⠀⣀⡼⢿⣿⣿⡋⠀⠀⣀⣀⠈⠻⣿⣛⠹⠿⢛⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠦⣄⠀⠀⠉⠳⣤⡀ ⠀⡠⠶⠋⢁⡴⠋⠀⢀⣶⠀⠀⠀⠀⠀⠁⢀⣴⠏⠀⠸⠁⠀⠀⠀⣀⣠⡴⠟⠉⢛⣶⣶⣾⣿⣷⡌⠉⢠⡿⢿⡉⠛⠻⢿⡿⠶⠶⠶⠟⠋⠀⢻⣿⣿⡙⠳⢦⡈⠙⢷⣄⠀⠉⠛⠶⠾⠶⣄⣈⠻⣆⠀⠀⠀⠀⠀⢀⣦⡀⠀⠙⣦⠈⠙⢶⣄⠀⠀⠙ ⠀⠀⠀⢠⡞⠀⠀⣠⢿⡏⠀⠀⣾⣦⠀⠰⡟⠁⠀⠀⣀⣴⣶⣶⣾⣿⣋⢀⣠⠾⠋⠁⣼⠋⡇⠻⣿⡶⠋⠀⠋⢳⣄⠀⣿⡇⠀⠀⠀⠀⠀⣠⡟⣹⡇⢳⡀⢠⠿⠶⡶⠿⠷⠶⠤⣤⣀⡀⠀⠹⣦⡿⠁⢀⣼⡇⠀⢀⣿⣷⡄⠀⠈⢳⡄⠀⠈⠛⢦⣄ ⠀⠀⣰⠏⠀⠀⣰⠋⣾⠀⠀⢸⠇⢹⡆⠀⢷⡤⣾⡾⠋⠉⠉⠉⢉⣩⠟⣻⡟⠀⠀⣼⠃⠀⢻⡀⠈⠛⢦⣄⣈⠉⠙⠛⢹⠁⠀⢀⣠⡴⠟⠋⣰⢯⡇⠀⠙⣆⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠛⢲⡟⠀⢠⡾⣧⡇⠀⠘⡏⢻⣽⣦⡀⠀⠻⣦⠀⠀⠀⠀ ⠀⠀⠋⠀⢀⣾⡇⢠⡇⠀⢠⡟⢠⡟⢻⠀⠸⣷⡏⠀⠀⢀⣠⡾⠋⠁⣼⠋⠀⢀⡾⠁⠀⠀⠀⠻⣦⡀⠀⠈⠙⠛⠳⠶⠾⠛⠛⠉⠁⠀⣠⡾⠃⣸⠀⣶⠀⠹⣆⠀⠘⠳⣆⠀⠀⠀⠀⠀⠀⢸⠁⢠⡟⠢⣬⣷⠀⠀⣧⠀⢻⣿⡷⣄⠀⠘⣇⠀⠀⠀ ⠀⠀⠀⠀⠈⢸⡇⣾⠀⠀⡾⠀⣾⠀⠸⡇⠀⢻⠇⢀⣴⠟⠁⠀⠀⣰⠃⠀⠀⠘⢀⣼⣿⣦⣄⠀⠀⠉⠃⢤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢀⣿⣾⣿⠀⠀⠹⡆⠀⠀⢸⣧⣄⠀⠀⠀⠀⠘⠷⠟⠀⠀⠀⢹⣆⠀⢹⡇⠀⣿⣇⢹⣷⠶⣟⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⣇⣀⡼⠁⣴⢻⣤⡴⠻⣦⣿⠾⠋⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠈⠉⠛⠟⠋⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠴⠋⠀⠀⠀⠈⠿⠟⠉⠀⠀⠀⣿⠀⠀⢾⣇⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⣾⣇⠀⣿⣿⡀⣿⡀⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⡉⣽⡇⢾⠇⠘⣿⣠⠶⠋⠁⢀⣠⡤⠴⠖⠒⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⣿⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠉⣻⣿⢹⡅⡏⣇⠈⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⣿⡇⣼⠀⣾⢻⡇⠀⢀⣴⠟⠁⠀⠀⠀⠀⣿⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⢻⡙⣧⡀⠀⠀⠀⠙⠷⣄⣤⡀⠀⠀⢀⡟⠀⢰⣿⠃⣸⣿⠁⢿⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⡀⢹⡾⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⢈⣽⠗⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠈⢷⡄⠀⠀⠀⠀⠈⠙⢿⣷⣀⣾⠁⢀⡟⠁⢠⣿⠇⠀⢸⠀⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠻⣿⡋⠙⠉⠀⠀⠀⠀⣀⣠⠐⠀⠀⢸⣇⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⣿⠋⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠈⠛⢧⡐⢿⣤⣠⣾⠏⠀⠀⣾⣴⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⢷⣄⡀⠀⢀⣠⠶⡏⠀⠀⠀⠀⠀⠙⢧⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣼⠏⠙⠛⣲⣾⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⡉⡻⣷⠟⠁⠀⠹⡄⠀⠀⠀⠀⠀⠸⣆⣠⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡾⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠘⡏⠀⢀⡼⢋⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠃⢳⠀⠀⠀⣄⠙⣆⠀⠀⠀⠀⠀⣹⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣧⠞⠉⢠⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠘⣇⠀⠀⠈⠢⠘⢷⡀⠀⢀⡾⠁⠀⠈⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⣠⠾⠃⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢻⡀⠈⠳⣄⠀⠀⠀⠀⠉⡛⠛⢤⣀⠀⠀⠀⠉⠻⡷⠦⣤⣀⠀⣤⣤⣀⢀⣤⠴⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⣠⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣿⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⠀⠀⣀⣀⣀⣤⠿⠋⠉⠙⠻⣯⣅⠀⣼⠃⢀⣤⠖⠋⠉⠉⠉⠛⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢻⣄⣀⠀⠘⠷⠤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣏⣴⠋⣼⣦⡀⠀⢀⣠⣴⣷⣄⠀⠀⠙⠳⣤⣀⣀⣀⣤⡤⠴⠞⠉⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⢦⡀⢸⠉⠉⠉⠻⡆⠀⠈⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢘⣿⢣⣾⡇⣈⡽⣾⠿⠟⠉⠙⠿⢷⣖⢦⣤⡶⣏⡉⠁⠀⠀⣀⣴⠟⠛⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢿⣸⠀⠀⠀⠀⢿⣀⢀⣀⣀⠈⡉⠙⠒⠀⠀⠀⠀⠤⣤⡀⠀⠀⠀⠀⠀⠀⣀⡼⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣸⠇⠈⠙⠳⢶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⢻⣆⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⢦⡀⠀⠀⠀⣀⣴⡾⠻⢦⣄⡀⠀⠀⣘⣋⣤⣤⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠉⠉⠉⠘⢷⡀⠀⠈⣉⣉⣉⠉⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠙⠶⣤⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠛⢻⣍⠉⠛⠶⠞⠋⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⡀⠀⠀⠀⠀⠉⠻⡇⠉⠉⣿⠶⠛⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣤⣤⣤⣀⣀⣤⣶⡶⡟⠛⢷⣄⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠙⠻⢶⣄⡀⠀⠀⠀⢻⣶⣾⠿⠖⠚⠋⠀⠉⠛⢦⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠉⠉⠉⠛⣦⠀⠀⢹⣇⢽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠶⠤⣤⣄⣀⡉⠙⠳⠶⣶⠟⠻⢿⡶⣄⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠠⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠛⠛⠳⠿⢤⣤⣶⡿⠾⣷⣦⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢿⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣡⣀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⠀⠀⠉⠀⠀⠀⠀⢿⣿⠂⠀⠀⠀⠀⣿⣤⣄⣀⠈⣧⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⣠⡴⠒⠛⠛⣿⡋⠛⠛⣻⡏⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⢀⡿⠀⠈⠉⠉⠸⣇⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⣠⡞⢀⣠⠶⠋⠁⠀⠀⠀⠀⣿⠛⢳⣻⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠹⣿⣶⣤⣴⡿⠁⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠰⢋⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣀⠈⠋⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⠀⠀⠀⣿⣟⠛⠲⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣦⣀⣠⡴⠋⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠉⠁⠀⠀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣄⣀⣠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⢹⣿⠿⠿⠟⠋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⣿⢦⣤⣤⠾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀