⣘⡊⢎⢻⣽⣿⣷⡀⡈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⡀⠀⠀⠀⢰ ⡈⠻⣿⡿⣿⣿⣿⣿⣄⠠⣹⣳⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⢠⣮⡞⠁⠀⠀⠀⠀ ⠑⢦⡈⡿⣿⢳⣿⣿⣿⣧⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀ ⠀⠀⠙⢧⡈⠻⣭⣿⣺⣿⠀⠀⠘⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⣾⣿⢿⣿⣿⢤⡄⠀⠈⢟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⠉⠀⣸⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⣴⣿⣿⣿⡆⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⢻⢻⠿⢠⢿⣷⣡⡀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢀⣴⣶⠜⠛⠉⠉⡭⠛⠛⠹⠩⣝⠉⠲⣶⣤⡀⠀⠀⠀⠀⠀⠀⣰⣿⠟⢁⣴⣿⠀⠀⣧⣿⣿⣿⡇⠀⠀⢐⠟ ⠳⣄⠀⠀⠀⢸⣿⡏⠀⣸⠣⡙⠻⣿⣆⠀⠀⢻⣷⠤⠀⢀⣴⣶⣿⣷⣿⣦⣤⣤⣤⣇⣀⣀⣀⣓⣊⣽⣤⣽⣷⣷⣶⣤⡄⠠⢤⣾⠏⢊⣴⡿⣉⣾⡄⠀⢹⣿⡿⠟⠁⠀⢸⢻⠈ ⣄⠈⠛⢦⣀⣾⣿⠀⠀⡇⠂⢨⠳⣾⣿⢧⡀⢨⣷⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣴⢸⢿⡀⣿⢋⣻⠈⠈⡇⠀⠘⠛⣠⡾⢿⠀⢸⣿⡀ ⡙⢽⡢⣄⢈⢿⡏⠀⢠⠀⠀⠀⢰⠀⢿⣼⢹⡞⠁⢀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠈⡇⣿⡼⠗⠀⠀⣿⠀⠀⢾⣿⣿⣿⡇⠈⣿⡇ ⠙⠦⣌⠓⠍⣸⡵⠀⣸⡀⠀⠀⠀⣼⡜⡏⠘⠀⣠⣼⡿⠿⠛⠛⠉⠉⠉⠁⣀⠠⠙⢆⡿⢯⠊⣁⠀⡠⠀⠀⠀⠀⠈⠉⠛⠳⢦⣀⡇⢹⠰⢀⣥⡆⣿⠀⠀⢸⣽⡿⣾⣧⣧⢿⣷ ⠀⠀⠈⠙⣿⣿⠁⠀⡏⠙⠲⣄⣰⣇⡇⠃⣴⢾⡋⠡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠉⢾⡄⠀⠇⣴⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣄⠸⠿⡇⣿⡆⠀⠘⣿⣟⣙⣿⣿⣷⢻ ⠀⠀⠀⠀⡿⠃⠀⢀⠁⠀⠀⠉⡯⣇⡼⡫⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⣵⠇⠀⠀⢿⠋⣻⣿⣿⣇⣾ ⣀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢀⡴⡫⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠸⠛⠉⠓⣾⣿⣿ ⠠⢍⡓⠪⣄⠀⠀⠀⠀⢀⣴⣫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢸⣯⣿⣿ ⠦⣤⣄⣷⡏⠀⠀⠀⣠⡟⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⣿⣿⣿ ⠀⠀⠉⢾⠇⠀⠀⣴⢟⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣖⣶⣾⣿⢻⣿ ⠀⣐⡒⠖⠂⠀⣼⡟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡟⠋⠃⢸⣿ ⠀⠀⠈⠉⠐⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣀⣨⣿ ⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠉⣡ ⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⡀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿ ⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿ ⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣹⣿⣿⣿⡿ ⠀⠀⠀⠀⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣿⣏⣁⣈⣀ ⠀⠀⠀⠀⠈⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⡀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣯⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢿⣿⣿⣿⣿ ⣷⣾⡋⡁⠀⠀⠨⢽⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣫⣿⣿⣿⠙⠻⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣸⣿⣿⣿⣿⣿ ⣿⡿⠟⠋⠀⢀⡀⠄⠛⠿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣴⣶⠿⢿⠟⣩⣿⣿⣿⣿⣿⣿⣦⣌⡙⠻⠿⢶⣦⣤⣄⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⠛⠷⠶⣬⣹⣿⣿⣿⡿⣿ ⣿⣷⣶⣶⣎⠉⢀⠀⠒⠂⠉⢻⣿⣶⣶⣤⣄⣀⢀⠀⠀⠀⠘⣩⣭⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣄⣤⣤⣴⣴⣶⣿⣿⣿⣿⠿⣡⠷⠶⠤⣈⣻⣿⣿⣿⣇⣿ ⣿⣿⣿⣿⣷⡋⠁⠦⣀⠃⢀⡀⣹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣄⠀⠈⠓⢦⣀⣈⠳⠿⠿⣿⣿⣿ ⣿⠿⣿⣿⣿⣿⠃⠀⣠⣿⡷⠚⠠⣄⣈⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡁⡀⠀⠉⢳⣄⠈⠓⠬⠙⠿⣧⣤⡀⠈⠳ ⢓⣠⣴⣿⠟⠀⣠⣾⣿⣟⠀⠀⣠⡿⣿⣁⠰⢦⣼⡏⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠒⣷⣮⢦⣌⣶⣷⣿⣿⣤⣓⣱⣄⣈⣙⣦⡤⣦ ⣿⣿⣋⣡⣶⣾⣿⣿⣞⠁⣀⣴⣿⣤⢞⡝⣋⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿