⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠘⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⣄⠀⠀⠛⢿⡦⣄⠀⢸⡀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⠉⠓⠲⠤⣽⡌⠳⣸⠁⠀⠘⣦⢀⣀⡠⠤⠴⠶⣶⣶⠶⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠛⠁⠀⠀⠀⠀⠻⠥⠤⠄⣀⢤⠤⠤⠴⣷⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠤⠤⠤⠬⠽⠄⠀⠀⢣⡀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣀⠐⢻⣄⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡙⢦⡀⠀⠀⠀⠀⠀⣀⡴⠊⣉⡡⠴⠂⠀⢐⣆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⢀⣤⣾⡃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣕⠿⠷⠶⠄⠀⠀⢁⡴⠊⠁⠀⠀⠀⠀⠘⣌⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⣁⠴⠻⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠶⣦⡤⣼⠏⠀⠀⠀⠀⡰⠋⠀⠀⠀⢠⠆⠀⠀⠀⠈⠃⢈⠓⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢥⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⡽⠟⠀⠀⠀⢠⠞⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠙⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣰⠋⠀⠀⠀⡄⠀⣾⡇⠀⠀⠀⠀⠀⠀⣇⠀⢰⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⠻⢹⡝⠪⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⣼⢁⣀⣠⡶⠃⢀⡇⠀⠀⠀⢰⡇⢰⠷⡇⣦⠀⠀⠀⠀⠀⡿⡄⠸⡄⠀⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠈⠳⡄⢿⠀⠨⢿⣆⠀ ⠀⠀⠀⠀⢸⠟⠉⢀⡞⠀⠀⢸⠀⠀⢠⡀⣿⣇⣾⣇⣸⡘⢧⠀⠀⠀⢀⣇⠹⣄⣿⣯⢷⠲⠤⣄⣀⠈⢣⠀⠀⠀⠀⠀⠈⠺⣇⠀⠈⢞⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣤⠀⠀⢸⣦⡀⠸⢧⣿⢿⣿⣿⣿⣷⣼⣷⣄⠀⢸⣿⠀⣹⣾⣿⣿⣧⣀⡀⠀⢀⠸⣇⠀⠰⡄⠀⡀⠀⣈⣙⠿⠿⠃ ⠀⠀⠀⠀⠀⠀⢰⡟⣿⢠⢶⣿⠟⣷⣄⣿⣿⡰⣿⣿⣿⣿⡍⠳⠝⠳⣼⣻⣠⣿⣿⣿⣷⡽⢷⠣⠢⣸⣧⡿⣆⠀⢻⣴⣿⡋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣈⣉⣸⣿⣼⣿⣧⣬⡿⠿⢿⡃⢻⡷⠿⠟⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠃⢀⣧⠁⡼⣼⠳⡌⡆⠘⡄⠈⢻⡄⠀⠀⠀⠀ ⠀⢀⣠⠴⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⣲⠿⢿⣶⣱⡏⢀⠁⣷⡀⠹⣆⣴⡇⠀⠀⠀⠀ ⠀⢘⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⢀⣀⣠⠄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⣿⠛⠴⣋⡼⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣄⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠹⡿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢨⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠉⠀⠈⣻⣗⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣾⡏⠀⠀⠀⠀⠀⢹⡄⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⢟⡇⠀⠀⣠⠞⠉⠉⠀⠉⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⡇⠀⠀⠀⠀⠀⠀⡾⢸⡇⡠⠎⠁⠀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⡇⠀⠀⠀⠀⠀⠀⠀⠹⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⢠⣧⣼⣏⡀⠀⠀⠀⣷⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠁⠀⣠⣽⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⣆⠀⠀⣿⠀⠀⠀⠀⠀⠹⣿⣿⠟⠁⠀⢀⡾⣥⣜⣆⠀⠀⠀⠀⣠⠴⠒⠿⣿⣿⣭⠇⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠘⣹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢸⡇⢻⡿⣿⠀⠀⠀⢰⡏⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⡷⣇⣀⣽⣷⣼⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⢁⡟⠀⠀⠀⠀⢷⡒⠒⢂⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠈⢷⣀⣠⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠻⡶⢄⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠙⢮⠙⠲⢤⣀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⣠⠏⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠈⢦⡀⠀⠈⣩⠞⠁⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠳⠶⠦⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠦⠤⣄⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢺⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠓⠲⣀⣠⠞⠋⠀⠀⠀⢀⣀⣀⡼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀