Tohru Text Art

⣾⢿⠀⠐⢺⡀⠀⠀⠀⣀⠤⠔⠒⠋⠉⠉⠉⠛⠒⠣⢬⣀⠀⠈⠀⠀⣿⡝⠁⠀ ⡀⡤⠀⡤⢼⣿⠦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢾⣄⢀⣻⠁⠀⠀ ⠙⢦⣠⢀⣤⠟⣒⣯⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⡀⠐⡄⠀⠀⠑⢾⡾⡐⠀⠀ ⠀⠀⡼⠻⡆⣹⣭⡟⠃⠀⠀⠀⢠⠀⡇⢠⠂⠀⠀⣷⡀⢰⡀⠀⢠⠀⡙⢥⡀⠀ ⠀⢰⠁⡜⣄⠷⣏⠕⠀⢀⢀⢤⠞⢨⢣⠀⢳⡀⠀⡟⣇⠂⣧⠀⠀⠆⠈⡵⣬⢢ ⢣⠸⢠⢰⡀⡏⠁⠀⠀⠘⠁⠌⢨⠌⠀⠆⠀⠣⡀⡇⠘⡄⡏⡇⠀⢠⠀⣏⠌⠂ ⠀⠃⠀⢳⢴⢳⡀⠀⠀⢀⣌⣀⣜⣀⢄⠈⡄⠀⡗⡡⢀⣰⣃⠸⠀⢸⠀⠈⠆⠀ ⠀⠀⠀⢸⢸⠠⣺⡀⠀⢸⢡⠮⡇⢹⠳⠀⠘⣠⢻⣞⣟⠳⡈⠉⠃⠸⠀⢠⠀⠀ ⠀⠀⡄⢸⢸⢴⢼⢃⠀⠸⠈⠦⠅⠝⠀⠀⠀⠈⠈⠇⣈⡸⠃⢁⢆⡆⢀⠸⠀⠀ ⠇⢰⠁⠸⢸⢸⣜⡽⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡘⠀⢸⠀⠀⠀ ⢠⡟⠀⢂⢾⢸⠿⡷⠾⣄⠘⡀⠀⠀⡠⠖⠀⢤⠀⠀⠀⠀⣰⢥⡇⠀⠘⣷⡀⠀ ⢾⠃⠀⣈⠖⠁⠰⠀⠀⠈⠣⡗⢦⣄⡘⠂⠀⠊⢀⡀⠤⠊⢠⠇⢳⠀⡇⢡⠁⠀ ⠈⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠪⡢⡉⢹⠛⢴⡀⠀⠀⠊⠀⢸⠌⠈⠺⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣺⢠⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⠀⠀⢈⣼⠏⠀⠐⡿⠉⠀⠀⠀⠀⣰⡏⠀⢰⡟⠀⠀⠀⠀⠀⠀⢘⠀⢀⠀⡇⠀⣿⣇⠀⠀⠀⠀⠈⠷⠀⠀⠈⢿⣇⠀⠉⠉⠉⢀ ⠀⠀⠀⢠⣽⠇⠀⠀⢰⡇⠀⠀⠀⠀⣰⣿⠁⠀⣿⣷⠀⠀⠀⠀⠀⠀⠘⠀⣸⠀⡇⠀⢿⣿⡀⠀⠀⠀⠀⢲⡀⠀⠀⠈⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⣾⡏⠀⠀⠀⣼⠀⠀⠀⠀⣰⣿⡟⠀⢸⣿⣿⠀⡠⠖⠀⠀⠀⡟⢠⡧⣀⣷⠀⣿⣿⣧⣀⡀⠀⠀⠀⣇⠀⠀⠀⢹⣿⠀⠀⠀⠀ ⠀⠈⢽⡿⠀⠀⢀⣤⡷⠒⠋⠉⢱⣿⣿⡇⠉⣿⣿⣿⠀⠀⠀⠀⠀⢰⡇⡼⠀⢸⣿⠀⢹⣿⣿⣏⠉⠙⠒⠦⢼⣄⠀⠀⠀⣿⣇⠀⠀⠀ ⠀⠀⣿⠃⠀⠀⠀⢸⠃⠀⠀⢠⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⣸⢰⠃⠀⢸⣿⡇⢸⣿⣿⣿⣆⠀⠀⠀⠈⣇⠉⠂⠀⢻⣿⣷⡀⠀ ⢠⣼⡟⠀⠀⠀⠀⣼⠀⠀⢀⣾⣿⣿⣿⡇⢹⣿⣿⣿⣧⠀⠀⠀⢀⣿⠏⠀⠀⣿⣿⣧⢸⣿⣿⣿⣿⣆⠀⠀⠀⢿⡀⠀⠀⢸⣿⠸⣇⡀ ⢸⣿⠇⠀⠀⠀⠀⣿⠀⠀⣼⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⡄⠀⠀⢸⠏⠀⠀⢀⣿⣿⣿⣸⣿⣿⣿⣿⣿⣆⠀⠀⢸⡇⠀⠀⠀⣿⠀⠻⣿ ⠀⣿⠀⠀⠀⠀⠀⣗⣤⣾⠿⠿⠟⢛⣛⣿⢿⣿⣿⣿⣿⣷⠀⠠⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢶⣤⣸⣿⠀⠀⠀⡇⠀⠈⣿ ⠈⡇⠀⠀⠀⠰⣾⣿⢡⡏⢀⣴⡿⠿⡟⢻⣿⣮⠙⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⡟⢉⣵⣿⣿⡿⣿⣦⡘⡄⢸⡿⡧⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⢸⡌⠻⢠⣿⡯⠁⠈⣿⡉⠙⢿⣧⢹⣿⣿⣿⣆⠀⣧⠀⠀⣿⣿⣿⠀⣿⡿⠉⣹⡏⠻⢿⣿⡿⣸⠀⣷⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⣿⣧⠀⠸⣿⡇⠀⣀⣿⡇⠀⢸⡿⣼⣿⣿⣿⣿⣆⣿⣆⠀⣿⣿⣿⡀⣿⠄⣀⢿⣇⠀⠈⣿⠇⢹⢠⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⠙⢷⣖⠁⠈⣀⣸⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣽⣿⣁⣈⣀⠐⣶⠟⣀⣼⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣿⠿⠿⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⡇⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣯⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⢀⡇⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠤⠾⣿⣷⡦⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣥⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠞⠻⢿⠆⠀⠉⠙⠓⠒⠒⠒⠛⠉⠉⠨⡿⠮⣍⠁⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠲⠖⠲⠶⠶⡶⠶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⠶⠶⠲⠲⠶⠶⠒⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡤⠧⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀ ⠀⠀⢸⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠙⠿⢿⣶⠀⠁⠀⠀⠀⠀⠀⠐⠚⠉⠉⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡴⣛⡡⠄⠀⠀⠀⠈⠙⣶⣤⣄⣠⣄⣴⣾⣿⣄⣀⣀⠀⠀⠀⠉⠓⢤⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠀⢠⠀⠀⠀⢰⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⡻⠷⠿⠿⠉⠉⠉⠻⢟⡳⢦⣀⠀⠙⢢⣀⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠜⠀⠀⠀⢸⠀⣰⠟⠁⠀⢀⠀⠀⠀⢀⣤⠞⠋⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀⠰⡇⠀⠀⠀⣵⡂⢀⢿⣿⣦⡔⠀⠀⠀⠀⠀⡀⠀ ⠀⠇⠀⠀⠀⠘⣤⡇⣠⡴⠞⠁⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢹⣂⣠⠤⠃⠈⠙⢷⣿⡽⣷⣦⠀⠀⠀⠀⡇⠀ ⢸⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⣴⠏⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⠂⠤⠄⢆⠀⠀⠀⠻⣿⣿⣿⣤⠀⠀⠀⡇⠀ ⢸⠀⠀⠀⠀⠀⠀⠑⠦⣬⣤⡾⠁⠀⢠⠎⠀⠀⡇⣀⡠⣼⠤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠣⠀⠀⠀⠘⡄⠀⠀⢢⠱⠻⣿⣏⠇⠀⡼⠁⠀ ⠘⡇⠀⠀⠀⠀⠀⠀⢺⣿⡏⠁⠀⠀⣾⠂⠀⢸⠋⠁⠀⢸⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠸⠀⠀⠀⠀⢡⠀⠀⠀⣧⠀⢿⡿⢃⡾⡁⠀⠀ ⠀⠱⡀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⡟⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⢸⡆⠀⠀⢸⣇⢸⣿⢋⠻⡇⠀⠀ ⠀⠀⠱⡄⠀⠀⣀⣼⣿⣿⡇⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⠀⢻⡀⠀⠆⠀⠀⠈⡄⠀⠀⢀⣇⠀⠀⠀⠀⣿⠀⡀⢸⣿⠀⡗⠀⠀⢱⠀⠀ ⠀⠀⠀⢸⣾⡿⢿⣿⣿⣿⡇⠀⠀⠀⡇⢰⠀⢸⡇⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⣧⠀⠀⣸⣿⣿⣷⣶⣶⣿⣇⢹⣸⡟⠂⣿⠀⠀⠀⢀⠇ ⠀⠀⢀⡏⠈⠻⠿⣳⣿⣿⣇⠀⠀⠀⠃⢸⠀⢸⣰⣤⣤⣼⣿⣿⣵⣄⠀⢸⠂⣿⠀⠘⣻⣿⣿⡿⡿⠿⣿⣿⣟⣿⠁⠀⣿⡆⠐⠒⠁⠀ ⠀⠀⢸⡇⠀⠀⠀⠛⢼⣿⣿⣷⠀⠀⢰⢸⣴⣿⣿⣿⣿⣿⣿⣿⣏⠈⠒⠘⠓⠁⠀⠀⣏⡁⠘⢤⠇⠀⠈⡿⢻⣿⠀⠀⡇⣇⠀⠀⠀⠀ ⠀⠀⠀⢃⡀⠀⠀⠀⠘⣿⣿⠀⠀⠀⢸⣿⠏⢸⠋⠁⠸⣄⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⣀⠜⠁⣾⡇⠀⠀⣷⣾⠀⠀⠀⠀ ⠀⠀⢀⡴⠃⠀⠀⢀⣾⡇⢻⡀⠀⠀⠈⡿⡄⠘⣇⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⢰⣿⡇⠀⠀⡟⢹⠀⠀⠀⠀ ⠀⢰⣋⠤⢤⡴⠚⢹⡜⠀⣾⣧⠀⠀⠀⢳⠀⠀⠀⠉⠙⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⢰⢷⡜⠀⠀⠀⠀ ⠀⠉⠀⣠⠞⡁⠀⣿⠁⢀⡇⢫⠁⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢼⠀⠀⣾⡼⠁⠀⠀⠀⠀ ⠀⠀⢰⡇⢰⠁⠀⡇⠀⠈⡇⠈⣧⠠⡀⠀⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡋⣽⢇⠇⠀⣼⠛⡇⠀⠀⠀⠀⠀ ⠀⠀⠘⢧⣸⡄⠀⣳⠤⠴⠿⣞⠀⢣⡱⡀⠀⢧⠈⢳⠶⠤⢤⣄⣀⣀⣀⣀⣀⣀⣠⠤⠴⠒⠉⠙⣦⢿⣿⣮⣠⢾⡥⠞⠁⠀⠀⠀⠀⠰ ⠀⢄⠀⠀⠉⢧⣴⣿⣦⣼⣿⣿⡷⢲⡷⣿⣄⠈⢣⠈⢳⡀⠀⠀⠈⠉⠉⢹⣶⣏⠀⠀⠀⠀⢰⠞⠁⢠⣿⣿⣵⣿⣷⠀⠙⠢⣄⠀⠀⠀ ⠀⢀⡝⢦⡀⠀⢸⣿⡟⠛⠻⣿⣿⡟⢦⠈⠻⠳⢄⣣⠀⠉⠢⠤⢠⡤⠴⢿⡇⣉⡧⢤⣀⡜⠁⠀⣠⣾⣸⣯⣤⣾⣁⠀⠀⠀⠀⠁⠀⠀ ⠉⠛⢧⣀⠈⠲⣄⠙⢧⣀⣀⣼⣿⡗⣾⡗⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢣⣄⣠⠤⡤⣖⣾⣽⣿⡿⣧⣬⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣦⠀⠈⣼⣍⣼⣶⣿⠯⣿⣤⣇⣸⣧⠝⢩⡋⣩⣭⡏⣿⣿⣿⣟⠛⣿⣤⡏⢸⣷⡿⣤⣟⣻⠀⣸⠋⠉⢘⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⠀⣿⡟⢹⠉⠋⠙⠛⠦⠤⣬⣉⣉⡉⢛⣛⡛⠛⣛⣛⣻⠛⠛⡯⠭⠭⣤⡖⠒⠊⠁⠁⠀⣋⢉⣟⡉⣿⣿⣦⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⠤⠀⠄⠀⠀⠒⠒⠠⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⢀⡴⡆⢘⠴⠊⠉⠑⠂⡈⢉⠁⠚⠌⣰⠒⢕⢄⠀⠔⠀⠀⠀⠀ ⠀⠀⠀⠔⠃⣠⣃⠆⠉⠁⠀⠘⢀⠀⠀⠘⡀⢂⠈⢂⠀⠑⢤⠓⣌⠓⠀⠀⠀⠀ ⠀⠀⠀⢀⠚⡤⠋⠀⢀⢁⣠⡇⢸⡄⠀⢀⢸⡞⣦⠠⠆⠀⠀⠙⢤⢵⠁⠀⠀⠀ ⠀⢀⠀⢧⣸⠀⠀⠀⡺⠁⡜⠀⠿⡇⠀⢸⢸⠐⡎⢣⢸⠠⠀⡄⠲⠹⢦⠀⠀⠀ ⠀⠀⠠⠅⡜⠰⠀⢀⣇⠰⠀⣴⠀⠃⢀⠃⡄⣀⢕⣀⢢⢆⢣⠀⠀⢡⠘⠀⠀⠀ ⠀⠀⡙⢂⠃⡆⠀⣸⣹⣦⣾⡿⡀⢰⠁⡐⠀⢞⣻⢯⡍⢛⢾⡇⠀⡀⢃⠃⠀⠀ ⠀⠀⠈⠛⣀⡜⢀⡟⡁⣴⢻⡿⡆⢸⠜⠀⠀⠸⣽⢳⠇⠀⣿⠁⢃⠗⢄⡜⠀⠀ ⠀⠀⠀⣷⡿⠀⡌⠀⠀⠈⠛⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⡏⡇⠈⡾⡀⠙⢧⠀ ⠀⠀⢰⡏⣇⠈⠀⢸⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⢰⣿⣷⢀⢡⠱⡀⠀⠀ ⠄⠀⢸⢁⣿⠀⠀⢸⣣⡀⠀⠀⠰⠋⠀⠀⠀⠙⡄⠀⣠⣿⣿⣿⢸⣾⡀⢣⠀⠠ ⠀⠀⡏⢸⡟⡇⡄⢸⠻⡿⣦⣄⣐⢄⣀⣀⣠⣴⣤⣾⡿⠛⢿⣿⣾⣿⣷⣧⢡⣂ ⠀⢰⢱⠟⠰⠝⣷⡄⡤⠊⠈⠫⠙⢻⠉⠉⡩⡪⠒⡿⠣⠤⡼⠿⣁⠀⢹⠿⣆⠣ ⠀⠈⡜⠀⠂⠀⢈⡯⠿⣀⣀⡔⡻⢉⠷⠚⠉⠀⡐⠑⡤⠊⠀⠀⠀⠳⡹⠢⠘⠆ ⠀⠀⠀⠀⠀⡐⠁⡀⠀⢀⡟⣴⢵⠋⢹⢆⠀⡴⡃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠒⣲⠒⠂⠠⢀⠈⠢⠀⠀⠈⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠀⣠⣆⣁⣤⣾⣿⠲⠫⠤⣀⠀⠀⠈⠂⡇⠀⠀⠈⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢊⢿⡿⠋⠉⠉⠉⠀⠁⠀⠀⠙⢦⡀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⡖⠁⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠘⡈⢯⣀⠀⡀⣤⡼⠒⠄⠀⠀ ⠀⡀⠀⣸⠎⡄⠀⠀⡀⠀⠀⠀⠆⠆⠀⠀⡦⠀⢰⢁⠈⢗⣳⣾⣟⠀⠀⠘⡀⠀ ⠀⠡⠠⡟⠀⠀⠀⠀⡆⠀⠀⠀⢸⠸⣄⠔⢱⢁⠀⡼⠀⢰⠙⠎⠁⠤⠤⠄⠐⢴ ⠀⢀⣿⡇⠀⣇⠀⠀⠳⠀⢠⠀⠀⣗⣷⠀⠈⣼⣀⢅⠀⠈⣇⠀⠀⠀⡆⠀⠀⠘ ⠀⠊⠈⣇⠀⢻⡀⠀⢠⢧⠀⢣⠀⣟⡥⢗⣮⠯⠶⣿⠀⠀⠝⡀⠀⠀⠐⢀⠀⠀ ⢀⢂⡠⣾⠀⢸⣵⣤⢼⣶⣷⡔⠉⠀⠉⢹⠉⠢⠀⡬⢀⠀⠈⡧⠀⢸⠀⢄⢂⠀ ⠀⠀⠀⣛⡄⠀⡷⡏⢻⠃⢨⠑⠀⠀⠀⠀⠉⠀⠁⠀⡼⠀⠀⡇⠣⣸⣴⣞⡀⢨ ⠀⠀⠀⢸⢁⠀⠃⢸⢂⠁⠒⠊⠀⠀⠀⠀⠀⢀⣴⠞⣣⡄⡦⣃⠚⣿⣿⣿⣷⠀ ⠀⠀⠀⠘⡇⠀⢸⠀⣿⣕⠀⡤⠤⠀⠜⡂⠚⣕⣁⡠⠀⠁⠀⠈⢂⠘⠛⠛⣿⣿ ⠀⠀⠀⠀⠉⡄⢄⠶⠭⣿⣿⣯⣿⣢⠀⠀⣹⣽⡀⠀⢀⣠⣶⣷⢾⡀⠀⠀⠻⢿ ⠀⠀⠀⠀⠀⠈⠁⠀⢠⣿⣿⠛⢿⣽⣺⡦⣯⢹⢶⡾⣟⡿⣟⠿⠌⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣼⠟⣁⡀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⢺⢁⣨⠶⠚⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠁⡟⠁⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⢲⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡏⠀⠈⢶⠀⠀⠀⢀⡟⠀⠀⡆⠀⠀⠀⣼⠀⠀⢸⡇⠀⠀⢷⡆⠀⠀⠀⢰⢸⣇⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣣⢤⣤⠟⠀⠀⠀⢸⣃⣤⢼⡧⢤⣄⣸⣿⣀⣀⣾⣷⠤⠄⠸⣷⠀⠀⠀⣼⢸⢸⡄⣀⣸⣾⡦⢄⡀⢲⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⣰⠚⠁⠀⠀⠀⠀⣼⠁⢀⣿⠀⠀⢠⡏⢻⠀⢹⡏⢸⡄⣄⠀⢻⡆⠀⠀⣿⣾⠉⢿⠁⠈⣷⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠙⢦⡄⠀⠀⠀⠀⣿⠀⣼⡏⠀⢠⡟⠀⢸⠀⡿⠀⠈⣇⢸⡆⠀⢷⠀⠀⣿⡟⠀⠘⡇⠀⡟⣿⡇⠀⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣧⣤⣴⡇⠀⠀⠀⠀⡏⠀⣾⡇⢀⡞⠀⠀⣼⣼⠁⠀⠀⢹⡼⣿⡀⠈⣧⢀⡿⠀⠀⠀⢻⡀⣧⠸⣿⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣧⣀⡇⠀⠀⠀⠀⡇⢠⣿⣧⣾⠶⠶⠿⣿⣿⣕⡂⠀⠀⢧⠉⣧⠀⠈⣸⣧⣶⣶⣿⣾⣷⣿⣤⣿⠄⢸⠇⠀⠀⠀⠀⠀ ⠙⠢⠀⠈⣿⣹⠿⡇⠀⠀⠀⠀⣷⢾⢿⡟⠀⢀⡀⣶⣤⡀⠹⣿⠀⠀⠘⣇⢹⠀⢀⣿⣼⠋⡋⣤⣤⣻⠀⠈⣿⡇⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⣀⣘⣿⣄⡇⠀⠀⠀⠀⢹⣿⡈⠀⢰⣿⡿⣿⣿⣿⡄⣿⠀⠀⠀⠙⢸⡇⣸⠋⡏⣼⣿⣿⣿⣿⡆⠀⣿⣧⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡉⢨⠏⣧⠀⠀⠀⠀⠸⡏⢳⡀⠘⢿⣾⠛⣷⡾⠃⠋⠀⠀⠀⠀⢸⡿⠃⠀⠃⠻⣿⣿⣿⡿⢁⡴⠉⣿⡟⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⣾⠀⢿⢠⡀⠀⠀⢀⡇⠀⠙⠲⠦⠭⠿⠭⠶⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠲⠬⠭⠭⠖⠉⠀⠀⣹⠃⣿⢀⡔⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⠐⣿⡈⡇⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣏⣼⠀⡆⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⠹⡇⢻⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⠟⡟⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⡆⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢰⡇⠀⢻⠀⠀ ⠀⠀⣀⢀⣀⣀⣀⣀⣹⣿⡇⠀⠀⠰⣷⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⣼⢸⠁⠀⠸⡄⠀ ⠀⠀⡿⠤⠬⠭⠤⠤⢿⡿⣷⡀⠀⠀⣿⢦⡀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠈⣻⠇⠀⠀⠀⠀⠀⢀⣤⡞⠁⠀⢠⣏⢸⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠀⢸⡇⢹⣧⠀⠀⣹⠚⣿⣷⣤⣀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠉⠀⠀⠀⣀⡤⠒⠉⣿⠁⠀⠀⣼⣿⢺⠀⠀⠀⠀⠀ ⢀⠾⠶⣶⢄⠀⠀⠀⣸⠁⠈⣿⡆⠀⢻⠀⢠⢿⡇⠈⠙⠒⠦⣄⣀⠀⠀⠀⣀⣠⠴⠒⠉⠁⠀⠀⢀⣿⠀⠀⢠⡏⡿⣾⠀⠀⠀⠀⠀ ⠎⠀⠀⠈⣳⠙⠦⡀⠟⠀⠀⢸⣷⠀⣾⠀⡾⠈⠳⣄⡀⠀⠀⠀⠈⠉⣿⢙⢣⡀⠀⠀⠀⠀⠀⢀⠜⢿⠀⠀⣾⢧⣷⠹⡄⠀⠀⠀⠄ ⠀⠀⠀⠐⠁⠀⠀⠈⠢⣀⠀⠀⣿⣵⣯⡞⠁⠀⠀⠀⠙⠲⢤⣀⡀⠀⡸⠋⠀⢷⣄⣀⠀⢀⡔⣁⠔⠻⡇⢠⡏⠈⣿⡄⡙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣀⠀⠈⢻⣿⣿⢈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢧⡀⠀⠈⣿⣿⣿⣿⣾⣅⠀⠀⢻⣼⠁⢠⣋⣷⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠒⠒⠀⠉⠲⢼⣿⣿⣿⣏⣿⡿⡑⠒⠦⠤⣄⣀⢠⣟⣁⣀⣻⣆⠀⠸⢻⣏⠀⠀⢹⣷⣀⣈⣿⠔⠊⠉⣿⣌⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠁⢸⣷⡙⣆⠀⠀⠀⢠⢿⡍⠉⠉⢩⡏⠦⠀⠀⢻⣷⣄⠀⢿⣿⣤⠖⠒⠒⠒⠛⢿⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠛⠛⠉⠉⠀⣹⣿⠉⠉⠙⠛⠲⠤⣄⡀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⣀⣤⣶⣶⠀⠀⡼⡻⠄⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠹⡄⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⣤⣴⣋⠀⠀⢀⣠⣾⣿⣿⣿⣿⡷⢶⠶⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠇⠈⠳⡄⠀⠈⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡴⠋⣸⣿⣿⣿⡿⠏⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢛⢷⣄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠀⠀⠀⠀⠀⢾⠀⠀⢀⠞⣠⡾⠋⢿⡿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣏⠳⣄⣠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⠀⠀⠀⠀⠘⣇⢀⣞⣾⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢸⠀⠙⢿⣿⠓⠀⠀⠀⠀⠀⠀⠀⣠⡀⣿⣵⢦⡄⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⢰⣿⣾⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠰⡀⣧⠀⠈⢿⣶⣠⡄⠀⢶⡖⢸⣯⡿⣿⠏⠁⠀⠙⣆⠀⠀⠀⠀⠀ ⠀⢸⡄⠀⠀⠀⠀⠀⣶⣬⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⡇⠹⡀⠀⠈⢿⠋⣽⢿⡆⣼⣯⣾⡿⠃⠀⠀⠀⠀⠘⡆⠀⠀⠀⢠ ⠀⠘⣇⠀⠀⠀⠀⣴⣿⠏⠀⡇⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢳⡀⠸⣆⠀⠀⠀⠀⠀⣇⠖⠀⠀⠀⢸⠀⣇⠀⠀⠘⣿⣁⡼⣿⠿⣻⣟⣇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠘ ⠀⠀⢸⡀⠀⠀⢰⣿⡏⠀⢠⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢻⡄⠀⠀⠀⣤⢻⡄⢣⠀⠀⠘⡆⢸⠀⠀⠀⢻⡍⢻⣿⣍⢯⠲⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⡆ ⠀⠀⠀⢳⡀⠰⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠸⣿⡀⢠⠞⠁⠘⡇⢸⡆⠀⠀⣷⠸⡀⠀⠀⠸⣷⠀⠙⢿⣌⣓⣂⣒⣦⡤⠴⠒⠒⠂⠠⠥⠤⡇ ⠀⠀⠀⠀⠱⣤⡿⡏⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢠⠀⠀⠀⠀⠘⣷⠀⣿⣿⠁⠀⠀⠀⢿⠈⣇⠀⠀⢹⠀⡇⠀⠀⠀⢯⡆⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⠀⠀⠀⣼⣿⣳⡇⠀⠀⠀⣇⡀⠀⠀⠀⠀⠘⡿⡄⠀⠀⠘⣆⠀⠀⠀⠀⣿⡗⠹⡼⡄⠀⠀⠀⢸⡆⢻⠀⠀⣀⡷⣿⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠐ ⠀⠀⠀⣰⠟⠘⣿⡇⠀⠀⠀⢸⢻⡀⠀⠀⠀⠀⡇⢳⡀⠀⠀⠹⡀⠀⠀⠀⢇⢸⡴⡟⢷⠀⠀⢀⣠⣧⡾⠖⡛⣉⣇⠏⠀⠀⠀⠘⡾⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠐⣿⠀⠈⣽⣷⠀⠀⠀⢸⣟⡏⠉⠉⠉⠉⢿⢉⣧⡀⠀⠀⢳⡀⠀⠀⢸⠘⡆⣸⣼⣶⡾⣟⣋⣵⣬⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⡄⠀⢹⠢⣄⠀⠀⠀⢸⠀ ⠀⠀⠀⡿⠀⠀⢹⣿⠀⠀⠀⢸⣻⢳⠀⠀⠀⠀⢸⠈⠉⢿⡀⠀⠈⢷⡀⠀⣸⣤⣿⡟⢉⣥⣶⣿⣿⠉⢱⠛⠃⣿⣿⠀⠀⠀⠀⠀⢻⢸⡄⠀⠀⠀⠀⢣⠀⠈⠀⠈⢦⠀⠀⢸⠀ ⠀⠀⢰⠃⠀⠀⣸⣿⡀⠀⠀⠀⣧⡏⣷⠀⠰⡀⣈⣧⣤⣤⣷⣄⣀⣴⠗⠋⠁⠀⠸⠛⠋⢿⡟⠁⠸⣄⢸⠀⠀⠀⡏⡇⡄⠀⠀⠀⠈⠈⣻⡀⠀⠀⠀⢸⡄⠀⢀⠀⢸⠀⠀⠀⠀ ⠀⣰⣃⣀⠤⠞⠁⣷⡇⠀⠀⠀⢿⣿⡿⢿⡿⣟⣛⣩⣭⣽⣵⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⠉⠀⢀⣼⠉⡇⢸⠀⠀⠀⠀⠀⡇⢳⡀⠀⠀⢸⡇⠀⢸⠀⡼⠀⡠⠊⠀ ⠈⠁⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⢸⣿⣧⡼⠟⢿⣿⣿⣿⠀⠈⡛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠤⠴⠚⠁⠀⠀⣿⢸⡆⠀⠀⠀⠀⡇⠀⢳⡀⠀⢸⠁⢠⣧⣾⠇⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⣼⢸⡆⠀⠀⠀⣿⠙⢷⠄⠀⢸⡃⠀⠳⣄⡇⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⡇⠀⠀⠀⠀⡇⠀⠀⠣⣠⣯⣶⣟⣓⡧⣄⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⠀⠀⢿⡆⢧⠀⠀⠀⢹⠀⠈⣳⣄⠀⠙⢦⣀⠈⠁⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡄⣧⠀⢰⡀⠀⡏⠓⣒⣶⣿⣿⣿⣿⣿⣤⣿⣷⡄⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡀⠀⠀⠸⡆⠀⢻⡘⢧⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⣿⠏⠀⡇⡿⡄⠀⣧⣰⠋⢉⣡⠞⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠇⠀⠀⠀⣧⠀⠘⣷⣸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⣀⣠⣴⡾⢋⡾⠋⠀⠀⠀⢟⡵⠷⠖⠋⠀⠙⢯⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⠀⣿⠀⠀⢿⣟⡄⡙⣳⠦⠤⢤⡤⠤⣤⠤⠴⠒⣖⠛⠋⠉⠻⢯⣰⠏⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠛⠿⠿⠿⢻⣿⣶⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⡄⠀⠀⠀⠸⡄⠀⢸⣿⣟⣷⣯⣤⣴⣟⣀⣴⣯⡀⠀⠀⠈⠓⠦⢤⣀⣨⣿⣷⡶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣣⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⡀⠀⡄⠀⣧⣴⣋⣠⣽⣿⣿⣶⣽⣿⡙⣿⣼⡷⣄⠀⠀⠀⠀⠀⢹⣿⣉⣽⠄⠀⠀⠀⠀⠀⠀⢀⣠⣖⢻⣿⢰⣶⡿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡶⠏⠀⠀⠀⢺⣿⣿⣿⣿⣿⡷⡿⢿⣯⣹⣦⡀⠀⠀⠀⣾⣾⣽⣿⡆⠀⠀⠀⢀⣠⣶⣻⣿⠿⡴⣟⣒⣣⠧⣷⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⣨⠿⣿⣿⣿⣿⢷⣿⣿⣟⢻⣦⢿⣦⣄⣀⡗⢻⢻⣿⣠⢤⣶⡿⢿⣿⣇⡿⢏⡯⢗⣫⠤⢚⣋⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⣿⠞⠀⠀⠘⠺⣿⣿⣓⣼⡇⡷⢺⣯⣿⠺⣿⠿⢹⣿⠫⢟⣧⣼⠿⣓⣯⡥⠒⡛⠛⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡠⠌⠀⠀⠀⢀⣀⣰⠧⠤⠤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⢠⠴⠊⠉⠉⡟⠻⣄⣠⠤⣴⡛⠻⡇⢀⡀⠉⣶⣄⣀⣄⡐⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠀⢀⡠⠿⣤⠴⠋⠉⠉⢉⠗⠀⠀⠀⣮⠉⠉⠉⠙⠶⢍⣩⡁⠈⠱⣄⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⣄⣀⣸⠀⡔⠓⡴⢉⡵⠒⠁⠀⡰⠃⢠⠏⠀⠀⠀⠀⠉⠁⠀⢃⠀⠀⢀⠀⠉⠑⣶⠾⣷⢤⣀⠈⠒⢄⠀⠀⠀⠀⠀⠀ ⢳⡶⠟⠋⠙⣍⡹⠋⣁⢿⡶⠋⠀⠀⠀⡼⠁⠀⡜⠀⣼⠀⠀⠀⠀⡄⠀⠸⡀⠀⠈⣆⠀⠀⠈⠲⢧⣀⠈⢢⠀⢈⡇⠀⠀⠀⠀⠀ ⠀⠳⡀⢀⣤⣾⠁⡜⡱⠊⠀⠀⠀⠀⣾⠃⠀⢠⠇⢀⠏⠀⠀⢀⢀⠇⠂⠀⣇⠀⠀⠸⡄⠀⠀⠀⠀⠈⢦⢼⣤⠘⣤⣀⡀⠀⠀⠀ ⠀⠀⠙⢿⠉⢈⡿⠋⠀⠀⢠⠀⠀⣸⣟⣀⢠⣿⠀⢸⠀⠀⠀⣸⡜⣶⣾⡤⣿⣦⣀⡀⣷⠀⠀⠀⠀⠀⠘⡖⠻⡀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⡠⢟⣩⡄⠀⠀⢠⡏⠀⠠⡿⡏⠀⡞⢸⠀⢸⣇⠀⢀⣿⠁⣿⢻⡀⢸⠘⡄⠈⢹⣇⠀⠀⠀⠀⠀⠹⡀⢇⠀⢳⣀⡠⠔⠂ ⠀⠒⠋⠉⠀⡾⠀⠀⢀⡟⡇⠀⣼⠁⡇⡸⠀⠀⡇⢸⢻⡄⣸⠃⠀⣿⠀⢧⠸⠀⠹⡀⠘⢟⠰⠀⠀⠀⠀⠀⢷⢼⡄⡾⠉⠁⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⢸⠀⡇⠀⡏⠀⣧⣧⣤⡤⣵⣤⠘⣷⠃⠀⠀⡜⠀⠸⣾⣤⠀⢣⢠⠘⣧⠀⠀⠀⠀⠀⢸⠚⡏⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⠎⠀⠀⠀⠈⠀⡇⢸⣶⠞⢿⠛⣿⣿⣿⣿⠀⠙⡄⠀⠀⡇⢴⣾⠿⣿⣟⡛⢿⣤⣹⡆⠀⠀⠀⠀⠘⣦⡷⠃⠀⠀⠀⠀ ⠀⠀⢀⠎⢀⡇⠀⠀⢠⢀⣧⡞⢣⢠⣿⠒⣻⣿⣷⠈⠀⠀⠙⣄⠀⡇⠋⣿⢤⣾⣻⣿⡄⢸⠉⡇⠀⠀⠀⡀⠀⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠃⣠⠊⡇⠀⠀⢸⣾⠈⡿⢢⠘⣷⡜⠛⢋⣹⠀⠀⠀⠀⠈⠳⣇⠈⣿⣿⠛⠛⣿⠃⠘⢰⡗⢻⡀⠀⣷⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡸⠀⡇⠀⠀⡼⢃⡰⠃⢸⠀⠈⠙⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⠁⠘⠉⣾⡇⠸⣧⠀⢹⣆⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⡇⢸⢸⠁⠀⠀⢠⠃⠀⢀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠢⣀⠀⠸⡀⠘⡇⠀⡟⢧⣯⠟⢾⡆⠀⠀⠀⠀⠀ ⠀⠀⢀⠁⠀⡇⣸⣼⠀⠀⠀⢸⠖⠉⢁⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀⠱⣄⡇⠀⡕⢀⠏⣿⠋⠀⠘⣷⠀⠀⠀⠀⠀ ⠀⠀⠸⠀⠀⣷⡇⣿⠀⠂⠀⠞⠀⢰⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣧⠀⠹⣄⠀⡇⡘⢠⣿⠀⠀⠀⣟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠸⣧⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢿⡁⠀⠀⢉⣿⠀⠀⠀⢀⠏⠀⠀⠀⠀⠁⢋⡏⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⢠⣷⠀⣼⠇⣀⣀⣿⢣⡀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠉⠉⠉⠉⠁⠀⢀⡔⠁⠀⠀⠀⠀⠀⢀⡞⢧⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⣼⠇⢰⣿⢰⠁⠀⢹⣄⠳⣄⠀⠀⠀⠀⠀⠈⢯⣿⣶⠤⠤⠤⠤⢴⣾⠏⠀⠀⠀⠀⠀⠀⢀⣾⠤⢼⣿⡄⠀⠀⢸⡄⠀⠀⠀⠀ ⢀⡏⠀⣼⡇⢸⠀⣀⠀⣿⣆⣻⣦⣀⠀⠀⠀⠀⢸⠞⠙⠦⣀⣀⠴⠚⢹⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⢸⡙⢻⣀⠀⠀⣇⠀⠀⠀⠀ ⡜⠀⠰⡿⢀⡏⠀⠀⠉⡟⢿⣿⡏⠬⠷⠤⠤⢴⡇⠀⠀⢠⣾⡄⠀⠀⠘⣆⠀⠀⢀⣴⠊⢹⣿⣀⢀⢯⡈⠙⢏⢡⠀⢿⠃⠀⠀⠀ ⠀⠀⢰⣇⠎⠱⡄⠀⠘⢀⡜⠁⠀⠀⠀⠀⠀⡼⢧⠀⡴⠋⠈⢣⡀⢀⡴⢹⠀⠀⠀⠀⠉⠻⢿⠁⢀⣤⠃⠀⠈⢣⠀⢸⡀⠀⠀⠀ ⠀⢀⣾⠏⠀⢰⢹⠀⢠⠊⠀⠀⠀⠀⠀⠀⡰⠁⠈⠉⣇⡀⢀⠎⠉⢉⠀⢸⡇⠀⠀⠀⠀⠀⠈⢷⠃⠀⠀⠀⠀⠀⡆⠈⡇⠀⠀⠀ ⢀⡜⠈⠀⠀⢸⣸⠖⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⠏⠉⢻⠤⠒⠁⠀⣽⣧⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢠⠀⠇⠀⠀⠀

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⣴⣿⣿⣇⠀⠀⠴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠟⠛⠛⠛⠛⠛⠻⠾⠶⣽⣥⣈⡉⠁⠈⢀⠀⠙⠀⠀⠀⢸⣿⣭⡿⠃⠀⠀ ⠟⠋⠙⡇⠀⠀⠀⢸⣷⣆⠀⠀⠀⡀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣀⠀⣠⡀⠀⠀⢸⣿⡟⠀⠀⠀⠀ ⡀⠀⣠⠌⣀⣠⣤⣼⣿⣿⣿⣦⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⠀⠀⢘⣿⠁⠀⠀⠀⠀ ⢳⣜⠋⠀⡟⠋⠁⠀⢿⣿⡀⣈⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠘⢆⠀⠀⠀⠀⠙⢿⣁⣶⣋⢿⠀⢰⠀⠀⠀ ⠀⠛⢶⣄⣧⠀⣀⣤⡞⠉⢹⣛⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⡀⠀⠈⢆⠀⠀⠀⠀⠀⠈⢿⣼⢾⣤⠃⠀⠀⠀ ⠂⠀⠀⠈⢻⣿⣯⡤⠞⣶⡟⠛⣿⡿⠃⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⢸⢸⠀⠀⠀⠀⢸⣷⡀⠀⠘⡄⠀⠀⠀⢀⠀⠀⠉⢲⡇⠀⠀⠀⠀ ⠀⠀⠀⢰⠋⠀⣹⣧⣠⣼⣭⣿⡇⠀⠀⠀⠐⠀⠀⠀⢀⣿⠀⣸⡀⠀⢧⡆⠀⠀⠀⢸⣿⣧⠀⠀⢿⡀⠀⠀⠈⢆⠀⠰⣄⠙⠧⡀⠀⠀ ⠀⠀⠀⡟⠀⣰⢻⡀⣺⣶⣟⠁⡷⠀⠀⠀⠀⠀⢀⣠⡾⢿⠉⡿⣇⠀⠘⣹⡀⠀⠀⢸⠙⣿⡓⠢⢼⣧⠀⠀⠀⠘⡀⠀⠘⡗⣦⣈⠣⡀ ⣀⠀⢸⠇⢀⡇⢰⢿⣧⣀⠼⠛⠁⠀⠀⠀⣧⠔⠉⣰⠁⡈⢰⠃⠸⡄⠀⠹⣷⠀⠀⢸⠀⠘⢷⠀⠘⣿⣧⡀⠀⠀⢇⠀⠀⣿⠉⣿⡍⠂ ⠹⣄⢸⠀⢸⠀⣿⡸⢹⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⠃⠀⣆⡎⠀⠀⢣⠀⠀⠘⣧⠀⢸⠀⠀⠘⡇⠀⡇⢻⠀⠀⠀⢸⠀⠀⢸⣀⡞⠈⠀ ⠀⠻⡆⠀⠘⣆⠈⠀⣼⣆⠀⠀⠀⠀⠀⢸⠀⢠⠃⠀⢀⡟⠀⠀⠀⠈⠇⠀⠀⠈⢷⣸⠀⠀⠀⢸⢀⡇⠀⣇⠀⠀⢸⠀⠀⢸⢿⡀⠀⠀ ⠀⠀⠀⠀⠀⠸⡟⢻⡉⢎⢦⡀⠀⠀⠀⢈⣤⣃⣤⣤⣾⣤⣌⡑⢢⠀⠘⡄⠀⠀⡇⢹⡴⢊⣁⣠⣿⣀⡤⢸⡀⠀⢸⠀⠀⢸⠀⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⠁⣌⢦⡇⠀⠀⠀⠰⡟⠁⣤⣘⣏⠘⢿⠿⣶⠀⠀⠹⡄⢀⣿⡿⣾⢿⡿⠧⣍⠈⠙⡟⡇⠀⢸⠀⠀⢸⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⡀⢈⡷⣷⡀⠀⠀⠀⡇⢸⡇⡀⢿⠠⣼⡇⠈⠂⠀⠀⢹⣼⠘⣿⡗⠚⡇⠀⣸⡄⢠⠃⢸⠀⡘⠀⠀⢸⣇⠀⠀⠀ ⠀⠀⠀⢠⠂⠀⡇⢨⣧⡸⢠⡇⢣⠀⠀⠀⣷⠀⠻⣁⣈⣀⡽⠁⠀⠀⠀⠀⠀⠉⠀⠘⣧⠀⠃⢉⡿⠁⠀⢀⡞⠀⠇⠀⠀⠘⣿⠀⠀⠀ ⣰⠀⢀⡼⠀⠀⡇⢸⡇⢳⠀⡇⣾⡄⠀⠀⠘⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠉⠀⠀⠀⣼⠀⡽⠀⠀⢣⠀⠀⠀⠀⠀ ⡇⠀⣸⡇⠀⢰⠃⢸⡇⢸⣇⣳⣾⣷⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡄⠃⠀⠀⣼⡄⠀⠀⠀⠀ ⠀⢠⣿⠀⠀⢸⠀⣾⠇⢸⣿⣿⣧⣄⣣⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⣇⠀⠀⠀⡟⢧⡀⠀⠀⠀ ⢀⣾⡏⠀⠀⢸⡖⢻⢀⡼⠋⢹⠋⠉⠹⠷⣤⡀⢧⠀⠀⠀⠀⢠⡟⠉⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⢀⠼⣏⡼⣿⠀⠀⠀⡇⢸⢿⡄⠀⠀ ⣼⣿⠁⠀⠀⢸⢁⡿⠋⠀⠀⡜⠀⠀⠀⠀⠘⢷⣸⠷⣤⣀⠀⠀⠓⠦⠤⡤⠴⠋⠀⠀⠀⢀⣠⠔⠉⢀⣿⠃⢻⡇⠀⢸⠁⢸⡈⠳⠀⠀ ⠀⠎⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠈⢿⣿⡒⠤⢄⣀⣀⣀⣠⠤⠖⠚⠉⠀⠀⠀⢸⠏⠀⠀⡇⢀⠟⢦⡈⡇⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠱⣍⠢⣄⠀⢸⠘⡟⢶⣦⠀⠀⠀⠀⠐⠁⠀⠀⠀⣧⠎⠀⠀⠙⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠢⣸⠀⡇⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠈⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⣸⠀⡇⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠣⠤⣜⣉⠤⠛⢋⡉⠜⣛⠟⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⢤⣄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡉⠻⣆⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀ ⡰⠁⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢻⣦⡀⠑⢄⡠⠃⠀⠀⠀⠀⠀⠀ ⠁⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣼⣿⣦⡀⠀⡄⠀⠀⢻⣿⣦⡀⠳⡄⠀⠀⠀⠀⠀⠀ ⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⠀⠀⠀⠀⣰⡟⢻⣿⣷⣄⠘⣦⡀⠀⢻⣿⣿⡄⠙⣄⠀⠀⠀⠀⠠ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠏⣿⣿⣿⡇⠀⢠⣿⣿⠀⠀⠀⣰⣿⡇⠀⠙⢿⣿⣦⡘⣷⣄⠈⢿⣿⣿⣆⠘⣆⠀⠀⠀⢀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣿⣿⣿⡿⠃⠀⢻⣿⣿⣧⢀⣾⣿⣿⠀⠀⣴⣿⣿⠇⠀⠀⠀⠹⣿⣷⣿⣿⣧⡘⣿⣿⣿⣷⣿⡆⠀⣀⠘ ⠇⠀⠀⠀⠀⠀⠀⢀⣾⣽⣿⣿⣿⠟⠀⠀⠀⣸⣿⣿⣿⣾⣿⣿⣿⣠⣾⣿⣿⣿⢀⡀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣿⣿⡇⣿⢻⣦⠀⢹⡀ ⠀⠀⠀⠀⠀⠀⣰⣯⣿⣿⣿⠟⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠇⠀⠉⠓⠢⠤⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⠀⠳ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⢀⣀⣠⣤⣤⣶⣤⣿⣿⣿⣿⣿⣿⣿⡿⠋⢰⣏⣠⣤⣤⣄⣀⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⠀⠀ ⣶⣦⣤⣴⣿⣿⣿⡿⠑⣶⣿⣟⣻⣿⣿⣿⣿⡟⠃⢹⣿⣿⣿⣿⠟⠁⠠⠏⣼⣿⣍⣹⣿⣿⣿⣿⣦⡀⢻⣿⣿⣿⣿⣿⡯⣿⣿⡏⠀⠀ ⡀⠀⢬⣿⣿⣿⣿⡇⠸⠛⣿⣿⣿⣿⣯⣽⣿⣖⠤⡀⠿⠽⠟⠁⠀⠀⠀⢠⣛⣿⣿⣿⣿⣯⣛⣿⠉⠃⠘⣿⣿⣽⣿⣿⡇⣿⢹⡇⠀⠀ ⣷⣶⣼⣿⣿⣿⣿⢇⡀⠀⠈⣩⠤⠤⠤⠤⢀⣀⣠⠗⠠⠄⣀⠀⠀⠀⠀⠞⠉⠀⠈⠉⠉⢩⣹⡉⠁⠀⠆⢻⣿⣷⣿⣿⣧⡟⢸⠁⠀⠀ ⣷⣿⣿⣿⣿⣿⣿⠀⠑⢤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⡀⣀⠜⠀⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠈⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⠁⠀⠀⠘⣿⡿⣿⡀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢄⣀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢰⡉⡂⠀⠀⠀⣿⡇⣿⣧⠀⠀⠀⠀⠀ ⢀⣿⣟⣿⣿⣿⣿⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠉⠁⠒⠒⠒⠚⠳⣄⠀⠀⠀⠀⠀⠙⠁⠀⢀⣴⣿⡇⡏⣿⣆⠀⠀⠀⠀ ⢸⣿⣿⣹⣿⣿⣿⣿⣿⣦⡈⠢⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⡏⠉⠑⠒⠒⢄⠀⠀⠈⠢⡀⠀⢀⡔⠀⠀⣈⣽⢿⣿⢰⠃⢹⡽⡄⠀⠀⠀ ⣼⣿⣿⣧⢿⣿⣿⣿⠋⠀⣿⠦⣉⡶⠶⡼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠱⣾⣿⣶⣶⣿⣿⣿⢸⡿⣸⠀⠘⣷⢻⡄⠀⠀ ⣾⣿⣿⣿⣎⢿⣿⣿⡀⠀⠹⡄⠀⢀⠔⠋⠙⢦⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢱⠀⣠⠒⠒⠻⣧⣿⣷⣿⣿⣿⠸⢧⡿⠀⢠⣿⠀⢳⠀⠀ ⣿⣿⣿⣿⣿⠛⠛⠿⣧⢀⠀⢣⡔⠁⠀⠀⠀⡜⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣸⠀⠸⡀⠀⠀⠈⠻⡈⢿⣿⡿⠀⣼⡇⠀⢸⣿⡇⠈⣇⠀ ⣿⣿⣿⣿⠃⠀⠀⠀⠈⠙⠲⡏⠀⠀⠀⠀⣰⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⡇⠀⠀⢡⠀⠀⠀⠀⠹⡄⠹⣇⣼⣿⠇⠀⣸⣿⡇⠀⢹⠀ ⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⢠⠿⠦⠤⢤⣞⣀⣀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣣⠀⠀⠀⣸⡏⢾⣿⣿⣿⠀⢐⣿⣿⡏⠀⢸⡇ ⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠓⠒⠒⠈⠉⢹⠓⠒⠚⠉⠀⣸⠀⢹⡇⠀⣼⣿⣿⡇⠀⢨⠃

⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⣸⠁⠀⢀⣀⣤⠤⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⠴⠚⢿⣠⠆⠠⡓⠂⠀ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⢠⠖⢹⡇⠀⠀⠀⠀⠀⢽⠎⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡜⠁⠉⠻⣿⣿⣿⣿⣿⣦⠀⡠⠈⠁⠀⠀⢠⠞⠀⠀⢇⡄⠀ ⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡇⠀⠈⣇⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⣿⠟⠀⠀⠉⠙⠶⢄⠀⢀⠟⠀⣀⡤⠒⠋⠻⣿⣿⣿⣿⣯⠀⠀⢀⡤⠖⠁⠀⠀⠀⠐⠉⠢ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠈⢇⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠢⢴⣃⠀⠀⠀⠀⠀⠀⣠⠿⠏⢠⡞⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣧⠖⠋⠀⢠⠤⠔⠂⣞⠛⠀⢀ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠈⠳⣄⣀⣇⠀⠀⠀⠀⠀⢀⣠⠤⠒⢫⡉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⣿⡝⠓⢤⡀⠀⠀⠀⠀⠙⣿⣿⣿⣆⣠⠞⠀⠀⠀⠀⠹⣞⠀⠀ ⠀⠀⠀⠇⠀⠀⠀⠀⢀⡤⠒⢻⠆⠀⠀⠀⠀⣠⠽⠋⠀⠀⠀⣠⠖⠉⡀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠙⢦⡀⠀⠀⠀⠊⢿⣿⣿⠁⠀⠀⠀⣤⣦⣤⣿⠷⠀ ⠀⠀⠀⠀⠀⢀⣴⠚⠁⠀⠀⠸⣄⣀⣠⠶⠋⠁⠀⠀⢀⡠⠊⠀⠀⠀⢻⢆⠀⠀⠀⠘⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢠⡷⠶⠖⠀⠀⠀⢿⣿⡆⠀⠀⣰⠿⠋⣿⡏⠀⠀ ⠀⠀⠀⣆⡰⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⡠⠎⠀⢀⠀⠀⠀⠸⡏⢳⡀⠀⠀⠹⡌⠻⣆⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢳⡀⠀⠀⠀⢀⠾⢿⡗⠒⠋⠹⣄⡼⣿⡇⠁⠐ ⠀⠀⠀⠘⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⢳⡀⠀⢸⡀⠀⠀⠀⢳⡀⠹⣄⠀⠀⢿⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠙⢦⡀⡟⡽⢦⡘⣷⡀⠀⠀⠙⣿⢟⡇⠀⠀ ⠀⠀⠀⠀⠙⠤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⡀⠸⣿⡀⠀⠀⠸⡇⠀⠈⢦⠀⠘⣷⠀⠀⠘⠳⣄⠀⠀⠀⣀⡀⠘⣆⠀⢄⠀⠙⠛⠁⠀⢱⣏⣇⠀⠀⠀⠘⣯⡇⠀⠀ ⠠⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢳⡀⣷⢣⠀⠀⠀⣧⠀⠀⠈⠳⡄⠹⡆⠀⠀⠀⣨⣽⣾⣿⣿⣿⣿⠉⠳⣌⢆⠀⠀⠀⠀⠀⠉⢹⠀⢰⡀⠀⠈⢳⡖⠐ ⠂⡁⠀⢀⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⢳⣿⡎⢧⠀⠀⢸⡄⠀⠀⠀⠹⣄⣷⣠⣶⣿⣿⡿⠿⠛⠷⣬⣻⡀⠀⠈⠺⣄⠀⠀⠀⠀⠀⠸⡀⠈⢿⡀⠀⠀⠻⡄ ⠀⠙⠚⠉⠀⠘⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢿⠁⠈⡆⠀⠈⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣄⣀⣄⡀⠀⠙⠶⣄⡀⠀⠙⠲⣄⠀⠀⠀⠀⡇⠀⠸⣿⡗⠦⣀⡈ ⠀⠀⠀⠀⠀⢀⣷⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⢇⠐⠹⡆⠀⣧⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠸⡏⠛⠲⡤⣌⣛⣦⣄⣀⣇⣀⠀⣿⣧⠀⠀⠈ ⠀⠂⠀⠀⠀⠀⡟⢧⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡄⠀⢱⡀⢸⣞⣽⣿⣿⣿⣿⣿⡿⠛⠉⠉⠁⠉⣿⣿⣧⡴⠀⢹⡄⠀⡇⠀⡜⠀⠀⠈⡏⠉⠁⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠘⣆⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣧⣼⣾⣿⣿⣿⣿⣿⡏⠙⢦⣘⡄⠀⢀⣿⠿⠋⠀⠀⠘⣷⠀⡇⢀⠇⠀⠀⠀⡇⠀⠀⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠘⢆⠘⣯⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⢸⣾⣿⣿⢿⣿⣿⣯⠀⠀⠀⠉⣡⠾⠋⠁⠀⠀⠀⠀⠀⢸⣆⡇⡾⠀⠀⠀⢰⠁⠀⠀⣷⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⢻⡇⠀⠘⣆⢹⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⣿⡿⠇⠈⢿⣿⣿⣧⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⠁⠀⠀⠀⣸⠀⠀⠀⣿⣿⡉⠀⠀ ⠀⠀⢰⠀⠀⠀⢸⡇⠀⠀⠘⢦⣧⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠇⠀⠀⠘⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⢠⡇⠀⠀⢸⡛⠛⠿⡆⠀ ⠀⠀⠀⣧⡀⠀⢸⣇⠀⠀⢀⣈⣿⣦⠀⠝⣦⡀⠀⠀⠀⠀⠀⠀⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣿⡀⠀⠀⡞⠀⠀⠀⢸⣷⣄⣀⠉⠀ ⠀⠀⠀⢹⣷⠀⠣⣿⣴⣮⣷⣶⣿⣿⣿⣿⣷⣷⣦⣄⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢸⣇⠀⣸⠁⠀⠀⠀⣿⠀⢠⢖⣶⣾ ⠀⠀⠀⠀⢿⣆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⢸⣿⣠⡇⠀⠀⠀⠠⡷⠋⢠⣾⡵⠿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠛⢹⣿⣿⡿⠛⠧⣙⡄⠹⣿⣷⣄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢶⠋⠀⠀⠀⠀⠀⢀⣾⣼⡏⠁⠀⠀⠀⢸⠁⢠⠏⠁⠀⠀ ⡆⠀⠀⠀⠐⣿⣿⣿⡅⠀⠀⠈⢿⣿⣇⠀⠀⠀⣀⠴⠛⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠛⠈⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠀⢸⢀⣼⠷⢢⠀⠀ ⢽⡄⠀⠀⠀⢿⢳⣌⠛⠒⠀⠀⠈⠛⠿⢿⡶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⡇⠀⠀⠀⢀⡿⠋⠀⠀⢸⠀⠀ ⢸⣿⡆⠀⠀⠸⡄⢻⣿⣦⣀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠁⡇⠀⠀⠀⣼⣇⡤⣤⣤⡇⠀⠀ ⠈⣿⢿⡄⠀⠀⡇⠀⢿⡍⠻⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣻⣿⣿⠃⠀⢧⠀⠀⢠⢿⡇⣼⠉⠉⠁⠀⠀ ⠀⢻⢼⡿⡄⠀⢣⠀⠘⣿⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣝⣼⣿⠞⠁⠀⠀⢸⠀⠀⣸⢸⢠⠇⠀⠀⠀⠀⠀ ⠀⢸⣿⠃⢳⠀⢸⠀⠀⠸⣇⠀⠀⠀⣿⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⢁⣾⡿⠋⠀⠀⠀⠀⢸⡇⠀⡇⡈⢸⡀⠀⠀⠀⠀⠀ ⠀⢸⡽⠀⠈⣇⢸⡄⠀⠀⢻⡄⠀⠀⢸⣾⡀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⣖⣾⣿⡟⠉⢩⢀⣿⣿⡁⠀⠀⠀⠀⠀⠀⢧⢸⡇⣇⣸⠟⢹⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⣿⢸⡇⠀⠀⠸⣧⠀⠀⠀⣿⡇⠀⠀⢾⣏⣹⣖⣲⣶⣶⡶⠒⣶⣶⣾⣿⣿⣿⣟⡿⠷⠞⠋⠉⠛⠛⣛⣿⣿⡯⣿⣉⣷⣄⠀⠀⠀⠀⠸⣾⡀⡏⠀⠀⠈⠄⠀⠀⠀ ⠴⠁⠀⠀⢠⠏⣾⢳⠀⠀⠀⢻⠀⠀⢀⣿⣇⠀⣶⠞⠛⣆⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣧⡽⣄⠀⠀⠀⢠⣿⠟⠉⠀⠀⠈⢻⡧⣜⣦⡀⠀⠀⠀⣿⡇⡇⠐⢲⣶⠃⠀⠀⠀ ⠀⠀⢀⣠⣯⠚⡇⣾⡄⠀⠀⢸⡄⠀⢠⡏⢿⡼⠁⠀⢰⠛⠛⠛⠒⠒⠠⠄⢹⣿⣿⣿⣿⣿⡟⠀⠸⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⣿⠋⠀⢻⣦⣤⣤⣿⣿⡁⠀⠊⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⢸⠀⠸⠀⠀⠇⠀⠀⠀⠀⠀⠘⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⣠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡄⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⣆⠀⠙⢖⠐⠒⠒⠒⠒⠒⠠⢄⠀⠀⣶⠀⢠⣀⣧⣄⣀⢸⣇⣸⣄⣀⣧⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣧⣠⠷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⢱⡤⠶⢒⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⡷⢤⣀⡀⠀⢠⢸⠀⠀⣿⠋⠀⠸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠈⢧⡀⠀⠀⣀⠔⠊⠁⣠⡾⠟⠉⠀⠀⠙⠋⠀⠀⠀⠀⠀⠈⢁⠀⠀⠙⠲⢾⣸⠀⢰⡇⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠒⠺⠥⣀⣠⠞⠋⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠙⢦⡜⠁⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⢠⠀⢀⠇⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⢹⣀⡀⠀⠠⡀⠀⠑⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⡇⠀⢸⣠⠔⡊⠉⠀⣿⠀⠄⠀⠀⠀⠀⠀⣧⠈⠑⠢⣱⠀⠀⠘⣆⠐⢠⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣢⣀⠀⠀⠈⢿⠃⠀⠀⣾⠇⠀⣼⠀⢰⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⡄⢸⢣⠀⡀⠈⢧⡀⠀⠸⡖⢏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠁⠈⠉⠒⢲⡇⠀⠀⢸⣿⠀⠀⡇⠀⣼⠀⠀⢠⣿⠀⡇⢀⠀⠀⠀⡇⠸⡌⡆⢰⠀⠸⣧⠀⠘⣷⠈⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠁⠀⠀⢀⣤⣾⠀⠀⠀⢠⣿⠀⢰⡇⠀⣿⠀⠀⢸⢻⠀⣇⢸⠀⠀⠀⡇⠀⡇⠘⡀⡆⠀⣿⠀⢰⣏⣧⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣞⠋⠉⠀⠀⢀⣪⡝⡉⠀⠀⠀⢸⡇⠀⢸⣇⠀⣟⢀⣀⣾⡼⠤⠿⠼⠤⠤⣼⣷⡤⠧⢀⣧⢸⡄⢸⣸⠈⣯⢸⢳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⣹⡟⠉⢡⣿⠃⡇⠀⠀⠀⢸⣇⣀⣼⣹⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣶⣶⣦⣭⡝⢺⡇⠘⣿⡼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠚⠋⠀⠀⢠⠇⢀⡇⠀⠀⠀⠈⠉⠠⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠈⢧⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀ ⠉⢿⣇⠀⠀⠀⢠⠋⢀⡞⡇⣤⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⠘⡄⢒⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢳⡀⠀⠁⣀⡼⣇⣧⡽⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢹⡀⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⡴⠚⣫⠴⣻⠏⠀⢸⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⡀⠣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣏⣉⡡⠞⢁⡤⠂⣸⠀⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠒⢿⣦⣈⣳⣤⡄⠀⠀ ⠀⠀⢀⡼⠁⢸⠋⢀⣿⣿⣤⣞⣁⣀⣠⠟⠛⠒⠲⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠶⠚⠛⠓⠒⠶⠶⣿⣿⣽⠟⠃⠀⠀ ⣠⣶⣋⠀⠀⠈⠛⢿⣤⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣷⣶⣦⣄⣈⡁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠉⠈⠻⣿⣿⣿⡿⠿⢿⣿⣿⣿⣝⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠙⠻⣿⠿⢷⣬⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⡀⠀⠀⠀⢀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠉⢻⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⡔⠁⠀⠀⢠⠃⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⡜⠀⠀⠀⢠⡏⢀⣏⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⠀⠀⠘⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡣⠀⠀⠀⠀⠇⠀⠀⠀⠀⡜⢠⠂⠀⣴⣿⠉⡽⢹⠋⢰⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡀⠸⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠸⠀⠀⠀⠀⢸⢠⠇⠀⣼⠏⡇⢠⡗⢾⠀⡇⠀⠀⠀⠀⡄⡾⠀⢠⣀⣼⠀⠀⠀⠀⢰⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠁⡀⠀⠀⢠⡇⠀⠀⠀⠀⣏⡜⣀⣼⡽⠀⣀⣏⠀⡇⢠⡇⠀⠀⠀⢸⢠⡇⠀⡼⠀⡟⠀⠀⠀⠀⢸⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⣰⠁⠀⢠⣿⠁⠀⠀⠀⢸⣿⡿⢻⡿⢿⣿⣿⣷⣬⡇⣸⠀⠀⠀⢀⣿⣾⠃⢠⡇⢸⡇⠀⠀⢸⠀⡌⠀⢸⠀ ⠀⠀⠀⠀⢀⠜⠀⢰⠇⠀⢠⡿⢿⠀⠀⠀⠀⢸⣿⢀⣾⣷⣾⣿⣿⣯⠙⠛⠋⠣⢄⣀⣼⡟⡿⠀⣾⠃⣼⡇⠀⠀⡘⠀⡅⠀⣿⠀ ⠀⠀⠀⢠⠏⠀⠀⡞⠀⢠⡟⢀⣾⠀⠀⠀⠀⢸⡇⠸⣿⡛⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣴⣽⠁⠀⢀⠇⢸⡄⢰⢹⠀ ⠀⠀⠀⢸⠀⠀⢰⡇⢀⣿⠇⠀⢻⠀⠀⠀⠀⢸⡇⠀⠉⠣⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣼⣿⣿⠻⣿⣦⡼⠀⣾⠁⣸⢸⠀ ⠀⠀⠀⠈⢇⠀⠈⡇⢸⠁⠘⣄⠸⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠎⣼⣇⡼⡛⠀⠿⡀⡀ ⠀⠀⠀⠀⠈⢣⠀⢳⠀⢀⣼⠟⠛⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣠⠿⠃⢀⡼⣿⠁⢠⣧⢸⠀⢳⡇ ⠀⠀⠀⠀⣠⣤⣷⣌⣧⠎⠀⠀⢀⡇⢠⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⠇⠀⡼⠙⠊⠀⠀⠀ ⠀⠀⢀⣾⣿⣶⣿⣿⣿⣶⡿⢍⣉⢹⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡎⠀⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡧⠔⠛⠙⣆⣷⡀⠀⢿⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢰⢁⠂⡜⠀⠀⠀⠀⠀⠀ ⢀⣤⣴⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣧⠀⢸⠀⠀⠈⠓⠢⠤⣀⣀⣀⣀⣀⣀⣀⣠⢤⣾⡿⠁⢀⡇⡸⢠⠇⠀⠀⠀⠀⠀⠀ ⣿⣯⣼⣿⣿⣿⡽⠁⠀⠀⠀⠀⠀⠀⠘⣿⠸⡆⢸⣇⠀⠀⠀⠀⠀⢀⣀⣼⣏⡉⢻⡇⣠⠟⣽⡇⠀⣼⢠⣷⡼⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢷⠈⡏⠻⣖⠦⡤⠼⠛⠋⠁⠘⢿⣿⣿⣿⡏⢹⣧⠀⠇⡜⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡏⢤⠄⠒⠒⠒⠢⠤⢤⣀⣀⠀⠻⠘⣷⣷⠒⠙⢦⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⠁⢸⣿⡄⢰⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠿⠄⡎⡔⣸⠋⠉⢑⠖⡞⢠⢠⣍⣑⡲⣼⡟⢢⡴⠚⡇⠀⣻⠦⣄⡄⠀⠘⣿⠁⠀⢸⣿⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢇⠌⡜⠠⣍⣁⣀⣀⡼⢰⠁⡏⠈⠀⠀⡟⢸⡖⠁⠘⢦⡟⠲⣿⠓⡶⣷⡀⠀⢿⠀⠀⠸⠟⣿⣼⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⠨⢴⡗⢲⡖⢒⣒⠒⠢⠿⠤⣉⣉⠐⠒⠇⢸⠈⠲⡤⠚⣷⠰⠿⡇⢁⢸⡗⢤⣸⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠴⣶⡶⠒⠀⠤⠴⠖⠠⢀⠀⠀⠀⢂⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠙⠂⠀⠈⣱⣶⣶⣾⣿⠦⢤⣤⡉⠢⡀⡸⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⢁⡠⠀⢀⠔⠋⠈⠉⠀⠀⠀⠠⡐⡅⠀⡗⢾⣿⣆⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⢀⡔⢁⠀⡀⠀⡀⠀⠀⠀⠀⠰⡘⠁⡆⠀⠹⣿⡷⡆⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⠀⡼⠀⡗⠈⠇⠸⠃⠀⠀⠀⠃⠀⠸⠀⠘⡝⣿⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠄⠀⡇⠀⡇⠀⢰⠀⡇⠀⡇⠀⢠⠀⠀⡇⠀⣧⠻⠊⣇⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⡇⠀⣧⣀⣤⣷⡀⢠⣧⠠⣿⣿⣿⣿⣾⡏⢸⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⡗⠀⢳⣿⡿⢿⠻⠻⠈⠈⠉⠀⡇⠑⠁⡸⢹⠃⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⣇⠀⠹⠇⠣⢀⣁⠜⠀⠀⠀⠀⠈⠐⠋⠀⣿⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢡⠹⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣦⠳⣦⠘⡐⡤⠤⣀⣀⣀⣀⠠⠄⠒⡵⣿⣡⡪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⢿⣿⠟⠷⢐⡈⠢⢄⡀⣼⣧⢀⡠⠊⢠⣿⣛⡏⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀ ⣲⣼⣿⣻⢰⡠⡤⣤⣤⣤⣮⣽⣴⣶⣾⣿⢻⡾⢿⠆⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀ ⣿⠉⠉⠛⠋⠉⠭⠿⠿⢻⣯⣟⠛⠙⠚⠉⡸⢹⣽⣿⡆⠀⠀⠀⠀⠀⠈⠂⠄⡀ ⣿⢣⣀⣀⠀⠀⠀⠀⢀⣸⠓⡧⢤⢄⣰⣞⣄⠈⠓⠜⡁⠢⢀⠀⠀⠀⠀⠀⠀⠈ ⣱⠺⣟⣺⡟⣖⣿⠒⢏⢃⠔⠸⢼⠴⠇⢣⢸⠗⠠⣸⠨⡐⢀⠑⠠⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⣠⠦⠂⢸⠃⣀⣤⠒⠦⠂⠀⢐⣦⢢⡄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⢋⠜⠈⡠⠒⡨⠉⡉⠙⡿⠛⣷⣧⡳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⡱⠊⢀⠈⠀⡰⠁⠠⠀⠀⢸⠀⠉⢊⢓⡀⠀⠀⠀ ⠀⠀⠀⠀⡀⠉⣄⢀⢀⡞⠀⢠⠃⠰⣲⠃⢀⠇⢱⠀⢸⠀⢡⠀⡡⠷⠀⠄⠀ ⠀⠀⠀⠀⠀⢰⠀⠑⡿⠀⠀⡆⠀⠷⠉⠀⢦⢸⢸⠀⢺⠠⣸⠀⢡⢫⠁⠀⠀ ⠀⠀⠀⠀⠢⠉⣀⢠⠇⠀⣾⣶⣾⣦⣧⡸⢸⣾⡏⠀⢿⠀⢸⡆⠸⠘⡆⠀⠀ ⠀⠀⠀⠀⠠⡐⠁⢸⠄⢆⠁⢟⠻⣿⠋⠀⠈⠙⠣⣶⣬⡀⣾⡇⠀⠀⡧⡄⠆ ⠀⠀⠀⠀⡿⠀⠀⣿⠀⢸⠀⠀⠉⠀⠀⠀⠀⠀⡾⢿⣿⡟⢷⢣⣶⠀⣿⡁⠀ ⠀⠀⠀⠀⠈⠕⣆⢼⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⢁⣾⣾⢿⣰⡆⠋⠀ ⠀⠀⠀⠀⠀⣱⣯⣿⡇⣾⠴⠤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡚⠟⡇⣀⢹⣧⠀⠀ ⠀⠀⠀⢐⣬⢼⣿⣿⣇⣿⠈⠕⠌⡣⡒⠆⠀⣤⠒⠈⣼⠀⢘⢃⡿⡠⠋⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⠋⠘⠋⠁⠈⡵⡬⢧⡤⠒⠥⠉⢍⣹⣿⣿⢸⠈⠀⠀⠀⠀ ⢀⣴⣺⣿⣿⣿⣏⡦⢀⡀⠀⢀⡇⠊⢣⡇⠀⠀⠀⠀⣻⣿⣿⣸⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣯⢫⠺⡱⣆⡛⣉⢸⠡⠒⢽⡇⠀⢐⠂⡩⢿⣽⣿⣷⣦⠀⠀⠀⠀ ⠀⢈⠛⠛⠀⠁⠫⢶⡢⠗⢊⣿⠱⢔⢹⠧⠇⢿⠰⣑⠸⢛⣿⣿⣿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠶⣿⠟⠓⠚⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⣫⠄⢠⡾⠁⠀⢀⠀⣴⠂⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡀⠀⢀⣠⣾⠟⣿⢋⣼⠃⣰⣿⡆⠀⢠⠋⢰⡇⠀⣸⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢹⣶⣿⠟⠁⡼⢁⡾⠁⣰⣿⡏⠀⢠⡟⢀⣿⠀⠀⣿⠀⢀⠀⠀⠀⢨⢷⡀⠀⠀⣠⠚⢩⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡴⠋⣸⠃⠀⣼⣵⣾⠓⣰⢯⣿⠀⠀⣾⠃⣸⢻⠓⢦⣿⠀⠘⡇⠀⠀⠈⣧⢳⡄⣸⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢉⡀⣼⡟⠀⣰⡇⣼⣿⢠⣿⡎⣏⣀⣠⣿⣀⡟⠸⣦⣸⣿⠀⠀⡿⡇⠀⠀⠹⡶⠿⠃⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡵⢾⡟⢠⢿⠁⢰⡏⠛⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠒⠀⠈⠷⣄⣇⣇⠀⠀⠀⣷⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣀⣾⠁⣾⣿⡶⢛⢀⣀⣰⣿⣿⣅⠀⠀⠀⠀⠀⠀⣰⣿⣒⣂⡀⠀⠈⢻⣼⠀⠀⠀⢸⣷⣄⣀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⣿⣿⠁⠸⣟⠻⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢶⣦⣶⣹⠀⠀⠀⢸⣿⣛⣯⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⣿⣽⠐⠰⣾⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣍⣽⣿⠀⠀⠀⢸⡇⠀⠁⠸⣳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⢰⣿⡇⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠉⠀⡇⠀⠀⠀⢸⠿⠃⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⣿⠀⠀⠀⠀⠀⠈⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣾⡄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⢿⣿⣧⠀⠀⠀⠀⢸⡇⠀⣼⢠⣿⠟⣦⠤⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷⢠⠹⣿⡄⠀⠀⠀⣼⠀⢰⡟⣿⡝⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⣄⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣤⣿⠃⠀⠀⢰⡿⠀⣿⢳⣿⠁⣄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⣷⣸⣿⣿⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏⠀⣀⣴⢿⣇⣸⣿⡿⢸⠀⣿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣹⣾⣫⡤⢤⡤⠟⢻⣷⣶⣶⣶⣿⣿⣻⣻⣿⣤⣀⣤⣴⣾⣿⣷⡿⠷⣶⣟⠉⢀⣾⣿⣿⡟⠁⠀⢠⡿⠇⣼⠃⠀⢀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣷⣿⣿⠟⠛⠛⠛⠋⢁⣴⠏⣹⣿⣇⣻⡿⠿⠛⣿⣧⣀⠙⣷⡽⠟⠛⡛⠀⠀⣸⣿⣆⢸⣿⣿⡿⠁⠀⢠⣾⣤⣾⡿⠟⠻⠛⠛⠛⠛⣿⠉⠉⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣾⣿⣿⣿⡀⠀⠀⠀⠀⠈⢠⣾⣻⣿⣿⠉⠀⠀⠀⠻⣌⡙⠻⡿⠶⠶⠋⠉⣀⣤⠟⠀⣹⣿⣿⣿⣁⣠⣴⣿⣿⣿⡏⠀⠄⠀⠀⠀⠀⠀⣿⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠻⠷⠆⠀⠀⠀⠀⠚⠛⠿⣏⣹⡄⠀⠀⠀⠀⠀⣽⣶⢶⣶⣶⠶⠚⠁⠀⠀⠀⠉⠉⠹⣿⣟⠛⠙⣿⣿⣿⣧⣄⣡⣤⣤⣤⣤⣾⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠹⢷⡀⠀⠀⠀⢸⣯⠼⠯⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣶⣾⣿⡟⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣀⠀⡿⠳⣄⡴⣿⡇⠀⠀⠀⢀⣀⣠⣤⣶⣻⣿⣿⣻⣼⣿⣡⣤⡤⠤⠤⠤⠤⠤⠄⠐⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣷⠔⠙⢷⣿⣷⣲⣲⣿⣯⣽⣿⣿⣿⣿⣭⣼⣻⣿⣟⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢯⣽⣽⠟⢳⣤⡚⣿⡟⣿⣯⣍⣏⢛⣻⣿⣿⡿⠿⠛⠛⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡴⠋⠈⠙⣿⣷⣾⣷⠿⣟⣛⡫⣭⣤⣀⣀⡀⠀⠀⠹⣿⣃⢿⡄⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡟⣿⡏⠛⠚⣷⠒⠶⡖⠋⠉⢻⢿⢻⠋⠉⣿⣟⣻⣿⡿⢋⠉⣉⠉⡛⣖⢺⡷⢿⡋⠏⠉⠻⣷⣾⣿⡷⣄⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⢀⣠⠬⠳⠀⢷⢸⡇⠀⠀⣿⠀⠀⡇⠀⠀⢸⣻⣿⣦⣚⡋⠉⢙⣿⣷⣠⣬⣿⢽⡶⠾⠮⣥⣸⡿⣟⠿⣟⠉⣙⡋⢳⣬⣳⠼⣧⡹⠿⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⣀⣀⣀⠀⢀⡰⠏⠀⢰⣢⣀⠸⡇⢷⡀⠀⢹⡀⠀⡇⠀⣾⠉⣉⣉⡉⠉⠁⠀⣿⣁⠺⣍⠳⣿⣭⣷⣤⠵⣿⣽⣿⣿⣷⣾⣷⣿⣫⣾⣿⣿⣀⣙⢳⣀⣷⣀⣀⣀⣀⣴⡄⠀⠀⠀ ⠉⠈⠉⠀⠀⠉⠂⣰⠿⠏⠉⠀⢻⣮⣷⣀⠈⣇⣀⣇⠀⡘⣷⡦⣭⠉⠀⠀⠀⢀⣿⣷⣿⣗⡋⣻⣉⣽⠷⠿⣿⣝⠿⢳⡒⢛⣍⣭⣿⠟⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⢆⠀⠀⠀⠾⣿⣿⠅⠀⢀⠀⠈⠙⣿⣶⣿⡿⠷⠴⣾⣿⠿⢿⣤⣤⣤⣶⡿⣩⣾⡿⢾⣭⣭⣽⣶⣶⣶⣷⣿⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠫⡳⠄⢀⠀⠙⠃⠀⡠⠌⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠹⠿⣿⠟⠋⠙⠛⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⡉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠇⠀⠀⣀⣀⣤⣤⡄⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿ ⠀⢰⣿⣿⣿⣿⡟⢿⣿⣿⣿⡿⠿⠿⠟⠷⠶⠿⣿⢿⣿⣿⣿⣿⣀⠎⡹⠀⢿⣿ ⠀⠜⠿⠿⣿⣿⡿⠀⢹⠟⠩⠂⠀⢠⠀⠀⠀⠀⡈⠑⡈⠙⢿⡿⠋⠀⡏⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⡇⣠⠊⢠⠗⠀⢰⢸⠀⠒⡄⢀⠁⠀⠘⡔⠉⠀⠀⠀⡿⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⡝⡇⢠⠛⡀⠀⡄⡄⡄⠀⣧⢨⢸⠀⠀⢡⠄⠂⣀⡜⠁⠀⠀⢹ ⠀⠀⠀⠀⠀⣰⢣⣆⣤⣷⣇⠀⣷⡇⣷⣶⣍⣄⣬⠀⠀⢈⠏⠁⠈⢇⠀⠀⠀⢸ ⠀⠀⠀⠀⠘⡞⡞⡟⢱⣿⡇⠀⠀⠈⣷⣿⣿⠩⠻⠀⠀⢸⠸⡂⠀⠘⣆⠀⠀⠈ ⠀⠀⠀⠀⠀⡇⣇⠃⠈⠋⢀⣀⣀⠀⠙⠒⠋⠀⠀⠀⠈⢸⡀⡇⣷⣶⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⡟⡀⠀⢰⣿⡿⠋⠑⢄⠀⠀⠀⢸⠀⢸⣀⠇⠀⢸⣿⡇⠀⠀⠀ ⡀⠀⠀⠀⠀⢸⡇⠘⣄⡸⡟⠀⠀⠀⠈⠆⠀⠀⣸⠀⣸⢫⠀⠀⡼⣿⠇⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⡇⢀⢹⣎⢙⠂⣤⠤⢮⡤⠒⡩⠛⢀⣇⣜⣀⣼⣾⣿⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⣿⡸⣸⡿⡿⠚⢪⣤⡤⠢⡔⠀⡆⠎⠈⢻⣿⣿⣿⡏⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⣾⣷⠋⠕⠇⠀⢸⡐⡆⠀⢈⡎⠏⠐⢖⣤⢿⣿⣾⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⡟⠀⠈⠉⠃⢳⣽⣝⢖⡃⠁⠀⠀⠢⢿⣿⡿⢿⣯⡧⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢸⠀⠃⠈⠀⠀⠀⠃⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠒⠢⡐⠠⠠⠤⠤⠤⢀⠀⣠⠀⣸⣀⢸⡆⣇⣸⠀⠀⠀⠇⠀⢸⣇⣇⠀⠀⠀ ⠀⠀⠃⠀⠡⠀⠀⠀⡀⠕⣊⡼⠟⢿⠟⠋⠙⠻⠒⠢⢄⡇⠀⣸⠁⠈⠀⠀⠀ ⠀⠀⡇⠀⠀⠑⠒⠭⣠⠞⠁⠠⠀⠀⢰⠀⠀⠀⢡⠀⠀⠉⠢⠃⠀⠰⠀⠀⠀ ⠀⠀⢣⠀⠀⠀⠀⡠⠃⢠⠀⣆⢠⠐⢺⢀⠀⠀⠀⢗⠢⢐⡀⠑⡀⢠⠀⠀⠀ ⠀⠀⠀⡡⠢⠀⣹⠃⢀⡟⢀⠇⡄⠀⢸⢠⠀⠀⢰⢸⠆⠄⢱⠀⢰⢣⠀⠀⠀ ⠀⢀⣰⠀⠀⣠⡎⠀⠈⡇⢸⠀⡇⠀⣟⢸⢠⠀⢸⠘⠘⡰⠈⣿⢸⢧⠀⠀⠀ ⠀⠑⢠⠄⢒⡎⡇⠀⠀⣇⣘⣦⣷⣶⣯⠉⠈⠀⠻⣮⣴⣓⡣⣿⢸⡸⠃⠀⠀ ⢄⡔⠉⠀⡰⠠⡇⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠹⠀⡇⠀⠀⠀ ⠀⠙⠄⠀⡠⢇⡯⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢣⢳⠀⠀⠀ ⠀⠀⢸⡋⣒⠝⡠⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⢦⣑⣄⡀ ⢀⠴⠃⠪⣤⢻⡶⠁⠐⠋⠁⠒⠒⠒⠒⠂⠀⠀⠒⠒⠒⠒⠊⠉⠐⠚⠛⠚⠁ ⠋⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⣴⠋⠁⢀⣟⡆⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠄⠒⠠⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣵⠟⠁⠀⠀⣸⡽⠁⠀⣀⣤⠖⣺⡭⠽⠒⠒⠉⠉⠉⠉⠉⠉⢁⣒⣒⠮⣭⣓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣰⠟⠀⠀⠀⠀⢰⡇⣇⠰⢋⡥⠞⠉⠁⠀⣀⣠⡴⠶⠶⠾⠿⠿⢿⣿⣿⣿⣿⣶⣶⣭⣓⠮⣛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠈⢳⣀⠞⠋⠀⠀⣠⠖⠛⠁⠀⣀⠤⠀⠀⢀⡀⠀⠙⠿⡟⠋⠈⣿⣿⣿⣷⣌⠳⢽⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⣠⡞⠃⠀⠀⢠⠞⠁⠀⠀⣠⠏⠀⠀⢀⡞⠀⠀⠀⠈⣿⠿⠋⠙⢷⣄⠙⢮⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠃⠀⠀⠀⡴⠋⠀⠀⠀⣰⠏⠀⠀⠀⣼⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠙⢷⡀⠳⡝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣇⠀⠀⠀⠀⠀⠀⠐⢦⣽⠋⠀⠀⠀⢠⡞⠀⠀⠀⠀⣰⡏⠀⠀⠀⣸⠇⢀⢠⠀⠀⠀⢸⠂⠀⠀⣀⠀⠀⠹⣄⠸⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⣆⠀⠀⠀⠀⠀⢴⡿⠃⠀⠀⠀⢠⢏⣀⣠⢴⠶⢶⣿⣀⣀⠀⢰⡟⠀⡟⢸⠀⠀⠀⢸⠀⠀⠀⢹⡀⠀⠀⠙⣆⠹⣸⡆⡀⠀⡠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠁⢀⡞⢦⡀⠠⣄⠻⣿⠃⠀⠀⠀⢀⡟⠀⠀⢀⡞⢀⢿⠃⠀⠀⢀⣟⠇⢸⠁⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⣧⠘⣧⣇⠹⣠⠼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠙⢦⣽⣿⠇⠀⠀⠀⠀⣸⠀⠀⠀⣸⢃⡏⣸⠀⠀⠀⡼⢹⠀⣾⠀⣾⠀⠀⠀⣾⣧⡀⠀⢸⣷⠀⠀⠘⡄⠘⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⣠⡇⠀⠀⢀⡇⡸⠀⡇⠀⠀⣰⠃⡞⢰⣿⢀⡇⠀⠀⠀⣿⡆⠙⠲⣼⡿⠀⠀⠀⢇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠻⠀⠀⠀⠀⣾⠇⠀⠀⠀⣀⣿⣤⣄⣀⣼⣳⣇⣠⡇⠀⢀⡟⠀⡇⣸⣸⣸⡇⠀⠀⢀⣿⡇⠀⠀⢸⣿⡆⠀⠀⢸⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠲⠦⠤⢤⣤⠴⢾⡟⠀⠀⠀⠀⣿⡿⢻⡛⣿⣿⣿⣿⣾⣿⣟⣸⠁⢘⡇⡇⣿⣿⡇⠀⠀⣼⢹⡇⠀⠀⢸⢿⡏⠀⠀⢸⠆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡞⠁⠀⠾⡇⠀⢀⡀⢸⠇⠃⣿⣿⣿⣿⣿⣿⣿⠟⠆⠀⠀⠀⠷⡇⢸⣿⠀⢀⣀⡟⢸⠇⠀⠀⣸⣾⡧⠀⡀⢸⠀⠀⢻⡃⠀⠀⠀⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⠟⠀⠀⠀⣰⡷⠀⠰⠀⣼⠀⠀⢿⡁⠙⢿⡿⢻⡿⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣾⣿⣺⡀⠀⠀⣿⢿⡏⠀⡇⢸⠀⠀⣸⣥⣤⣖⣪⠗⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡼⠃⠀⠀⠀⢠⣿⡇⠀⡎⠀⡟⠀⠀⠈⠛⣶⠦⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣿⣿⣿⣿⣶⣶⡟⢸⡇⢠⡇⢸⠇⠀⣿⢠⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⡇⠀⢀⠁⠀⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⣿⣿⣿⣿⢻⡷⣿⠃⢸⣷⢸⠀⠀⣿⡿⣏⠀⠀⠀⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡹⣄⠘⡀⠀⡟⢸⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⢯⢻⣿⠏⠘⠀⡿⠀⣏⣿⢸⠀⠀⣯⠓⢮⣳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠻⣇⠀⢇⢸⡇⠀⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠒⠚⠛⠁⠀⢀⣾⣧⣾⣻⢻⢸⠀⡷⣿⡛⠻⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣨⣷⣜⣷⡇⠀⣧⢰⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⡇⠘⠾⢰⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣾⣿⠛⣿⣿⣟⠀⢨⡈⣧⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⣫⣿⢷⠇⠀⠀⡞⢻⢳⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⠀⢸⣇⣿⠙⠚⣻⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣯⠶⠞⠉⢸⣾⠀⠤⢸⡇⢸⣾⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠃⢸⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⠀⢿⠙⣄⠈⠻⣟⡲⠤⣄⣀⣀⣀⣀⠀⠀⢀⣀⣠⠴⠾⡍⣽⡅⠀⠀⠀⣾⡏⠀⡓⣟⡏⠀⣿⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⢿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⠀⠙⢇⠈⠣⠄⡈⠙⢦⣤⠴⠟⠉⠉⠉⣿⣯⡉⠀⠀⠀⢷⡼⣇⠀⠀⡘⢹⠁⢸⣿⠟⣁⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣾⣿⣿⣿⣿⣯⠏⢹⣾⡏⣿⡆⠀⠈⠓⢦⡀⠘⢦⣼⠇⠀⠀⠀⢀⡴⠏⠈⠛⣶⡲⠶⠦⣝⣿⣶⣾⣷⣿⠀⣼⢣⣴⣧⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠉⠁⠉⠁⠀⠀⠀⢸⣯⡑⠶⠿⠶⣶⣶⣟⣉⡠⠴⠖⠋⠀⠹⡄⢀⣾⣿⣿⣿⣭⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙⢦⣤⠚⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⡟⢛⣿⣿⣿⣿⡿⢿⣿⣷⡆⣹⠦⣄⠀⠀⠀⠀⠀⠀⠀⢸⣹⡤⠞⠁⠈⠳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠠⣿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣋⠟⣼⣳⠋⠈⠙⠲⣦⣄⣀⣀⠀⣿⡟⢧⡀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣏⡙⢧⢁⡞⣽⠁⣴⢻⡆⣼⢣⠆⠉⠉⢙⣯⡇⣀⡽⢾⣁⢸⣿⠤⠤⠤⠤⢤⡔⠒⡊⠉⢁⢹⣾⣇⣴⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⣥⣈⠻⢇⡙⠶⣍⡾⢰⢃⡏⣠⠟⡇⢸⣼⡏⠁⠀⠀⠈⣻⣿⡇⠀⣀⣀⣸⡇⠀⡇⢾⠉⡇⢿⣿⣿⣿⣿⣿⣧⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠻⠿⠿⢿⠏⠀⠀⠙⠒⢺⡟⠳⢤⣠⡏⠘⠧⠤⠼⠃⡼⡿⠈⢢⣀⡴⠛⢻⣿⡇⠀⡧⢈⡇⡇⠀⡇⣘⣣⠇⠘⣏⡽⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣦⣍⠛⠒⠦⠤⢴⢧⡧⠖⠋⠉⠲⡄⣼⡟⠛⠲⠟⠚⠃⣧⠀⢉⣁⣤⠴⠚⢁⣀⣶⣿⣿⣿⣿⣿⡿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠇⠀⠀⠀⠀⣦⣤⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠶⣶⠀⢸⣿⣿⣿ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠉⠛⠛⠛⠛⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣆⣼⠃⢠⡟⠀⠉⣿⣿⣿ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⣿⣿⡿⠋⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠙⠻⣿⣿⣿⣿⡿⠁⠀⢸⠃⠀⠀⢸⣿⣿ ⠀⠈⠁⠈⠉⠉⠛⠿⠿⠿⣿⠁⠀⠀⡹⠋⠀⡼⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢱⠀⠀⠙⣄⠀⠈⣻⠟⠋⠀⠀⠀⢸⣇⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢠⡞⠀⢀⣾⠋⠉⠀⠀⡆⢸⡏⠉⠁⢹⠀⠀⠀⢸⠀⠀⠀⠘⡶⠋⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡴⡿⠀⠀⡜⡏⠀⠀⠀⢠⠁⡜⡇⠀⠀⢸⡇⠀⢸⠀⡆⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠇⠀⣸⢹⠁⡄⠀⠀⢸⠀⡇⢹⠀⠀⠈⣿⠀⢸⠀⡇⠀⠀⠀⠘⣷⠘⠉⢀⣠⣴⡟⠁⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⡸⡄⢀⡇⣸⢴⡇⠀⠀⣾⡄⡇⢼⣦⢤⡄⡏⣇⠸⡄⡃⠀⠀⠀⠀⠻⡍⠉⠁⠀⠹⣇⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⣠⠤⢿⠀⣇⣧⣿⡿⢿⣿⣿⠤⠤⠿⠷⠇⣼⠿⣿⣿⣿⣿⣶⣷⡇⠀⠀⠀⠀⡆⢳⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠙⢳⡏⠈⠹⡿⠁⣷⣿⣿⡟⠀⠀⠀⠀⠀⣸⣶⣿⣿⣿⡇⢸⠏⡇⠀⠀⠠⠀⡇⠸⣍⠆⠀⠀⠘⣷⠄⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⢘⡇⠀⢿⣿⡿⠁⠀⠀⠀⠀⠀⠸⣿⠛⣋⡿⠁⠀⠀⠀⠀⠀⢰⠀⡇⠀⢻⠓⢤⣄⣀⣈⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡇⣸⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠄⠀⠀⢸⠀⣷⡀⢸⡀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢧⠀⠀⠀⠀⣼⣿⣿⣿⠟⠛⠓⢄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢸⢀⡇⠀⢀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠁⠘⣆⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⡇⠀⠀⣸⣸⡞⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⠈⢳⡀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⡇⠀⠀⣿⠟⡆⠀⠀⠀⡄⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⠀⠸⣿⡓⠬⣿⣄⠀⠀⠀⠀⢀⡼⠃⠀⣀⡤⠺⣿⡇⠀⣸⢏⠀⡇⠀⠀⣼⢃⣾⣿⠃⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀⣿⣷⣄⠠⣈⣉⡿⡗⠒⠚⣗⠿⠋⠁⢀⡴⢻⠀⢠⣿⣀⣿⣁⣤⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡄⣿⣿⣿⣿⡾⠯⣄⣳⡀⠐⣂⣄⣀⡴⠋⠀⢸⠀⡞⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⣷⣼⣿⠻⡏⠀⠀⠘⣯⣿⡻⠇⠀⠉⢦⠀⣀⣿⣼⠁⠀⠀⠈⢻⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⢁⠞⠃⡇⠀⠀⢠⣧⡈⢏⠀⠀⠀⠀⣻⠉⡏⠉⠙⢳⡒⡶⢤⣻⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠗⠈⠓⠤⠼⢦⣤⣞⣹⣷⡾⢦⣀⣀⡞⠹⠀⠁⠐⠂⣄⠙⣿⣷⣿⣿⣿⣿⣿⡿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠁⠀⠀⠈⡀⠉⣿⣟⣷⣤⡻⢤⡀⠀⠀⠀⠀⠀⠀⠙⠛⣿⡻⡷⠟⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠁⠀⠀⠀⠀⠉⠑⠒⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⢀⣤⣶⣶⡶⠶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠎⠀⣠⠞⠉⠘⠋⠁⠀⠀⠀⠉⠛⠀⠀⠙⠲⢄⠀⠀⠀⠱⡀⠀⠀⠀ ⠀⠀⢰⠁⣠⠊⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⡄⠀⠑⡄⠀⠀⠱⡄⠀⠀ ⠀⢰⠇⡔⠡⠀⠐⠀⠀⡘⠠⠀⠀⠀⠀⠠⠀⠀⡄⠀⠰⠀⠀⠠⡀⠀⠀⡇⠀⠀ ⠀⣿⢰⢀⡇⠀⡄⠀⢰⡇⡀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠃⠀⠀⢃⠀⠀⢸⠀⠀ ⠀⡫⠂⢸⡄⠀⡇⠀⢸⡇⡇⠀⠀⠀⠀⠠⡆⠀⠈⡆⠀⢸⠀⠀⠸⡀⠀⠘⠀⠀ ⠀⠁⠀⢸⡃⢰⠀⠀⢸⡇⠁⠀⠀⠀⠀⡀⣧⠀⠀⢻⠠⠈⡆⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⢸⢠⢸⡀⠀⢸⠇⢸⠘⠀⠀⠀⡇⢿⡄⠀⢸⣇⡃⠃⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⡀⠈⣿⣾⣏⡁⠉⠈⠈⠛⠃⠐⠒⠉⠈⠁⢀⣬⡿⢱⠃⠀⠀⣇⠀⠀⠀⣦ ⠀⠀⢃⠀⠸⡇⠉⠙⠳⢷⣴⠀⠀⠀⠀⠀⣿⣚⣋⠁⠀⢸⠀⠀⢸⢿⠀⠀⡀⢱ ⣼⠠⠸⠀⠀⣇⠙⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⢸⠀⠀⣠⢾⠀⢀⠇⡾ ⠿⡄⢇⣷⡄⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣴⠏⠘⣠⢪⠜⠀ ⠀⠈⠺⣿⣷⠀⢻⡆⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⡭⢠⣿⣤⢼⣯⠁⠀⠀ ⠀⠀⠀⢾⣿⣷⣾⠀⠐⠛⠷⡂⠤⠒⠒⠀⠶⢏⠙⢏⠐⣿⣿⢹⣿⣿⣏⠀⠀⠀ ⠀⠀⢀⣶⣿⠿⢇⠀⠀⠀⠀⠈⠒⠦⠀⢔⠢⠀⠑⠀⠁⡏⢉⣚⣿⣿⣹⡇⠀⠀ ⠀⠀⢀⣿⣿⠆⠤⣶⡄⣀⣀⠤⢿⡂⠀⣆⠥⢄⣀⣠⠚⠙⢅⠘⣾⣿⣿⠿⣦⢀ ⠀⠀⣾⣿⠛⠀⠀⠁⣆⣠⠲⠤⣼⠉⠢⠈⣲⡖⠀⡼⠁⠒⢺⠀⡆⠈⣻⣿⡿⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠨⠁⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⡇⢸⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡅⢸⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⡄⠀⠀⠀⣿⠀⢠⡄⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⣿⣿⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠒⠒⢿⡄⠉⠑⢦⡤⠤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⣤⡆⠀⠀⠀⢸⣃⠀⠀⠀⣿⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⣿⣿⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠋⡇⠀⣼⣷⣿⣿⣶⣶⣤⣿⣶⣾⣷⣶⣾⣷⡀⠀⠀⠀⠀⠀⠀⡇⢨⠀⠀⠀⣿⣿⠶⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠶⠟⠋⣩⣿⣾⡿⢿⣿⣿⣿⠟⠋⠉⠙⠿⣿⣿⡿⠷⢦⣄⡀⠀⠀⡇⢸⠀⠀⢀⣿⠃⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⣀⡴⠚⠉⠀⣠⣼⡿⠛⠉⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠙⠳⢤⡇⢸⠀⠀⣾⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠙⠲⠤⣦⣞⠁⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠙⠻⣄⢀⡿⠁⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⣶⠏⠁⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠙⢯⡁⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⣰⠀⠀⢸⠀⠀⠀⠀⣀⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⢤⣀⡀⠀⠰⡄⠀⠀⠱⡄⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⢰⡏⠀⠀⡎⣀⠴⠚⠋⠀⠀⢸⡇⠠⡄⠀⠀⠀⠀⠀⠀⠘⣇⠀⠉⠳⢤⣹⡀⠀⠀⠸⣆⠀⠃⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠲⣄⠀⠀⠀⠀⠐⣶⣿⠃⠀⠀⢠⣯⠃⠀⠀⡟⠁⢀⡏⠀⠀⠀⡻⡇⠀⡇⠀⠀⠀⠀⠀⡇⠀⣟⣦⠀⠀⠀⠙⣧⡀⠀⠀⠹⣆⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠓⠦⣄⣀⠀⣠⠇⠀⠀⠀⣼⢻⠀⠀⢱⠇⠀⢸⡇⠀⠀⠀⡇⡇⠀⡇⠀⠀⠀⠀⠀⢧⠀⢸⠹⡄⠘⡆⠀⢸⣷⠀⠀⠀⣿⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠈⢉⡿⠀⠀⠀⠀⢻⡜⠀⠀⣿⠀⠀⣼⡇⠀⠀⠰⡷⡇⠀⡇⢠⡄⠀⠀⠀⣾⠀⢸⠆⢳⠀⢹⡀⠀⢏⡆⡆⠀⣯⢧⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⢠⣤⣮⠇⠀⠀⠀⠀⣼⡇⠀⠀⣿⠀⠀⣿⠀⠀⠀⢀⡏⣧⢸⣇⢸⡇⠀⠀⠀⣿⠀⠘⡄⠈⢇⠘⡇⠀⢸⡇⢕⠀⣿⡸⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠴⠖⠛⠁⠀⠀⠀⡰⢛⡿⢸⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⡄⠀⣿⠀⠀⠀⣼⠡⣿⣸⣿⢸⡧⠀⠀⢀⣿⡆⣀⣇⠀⠘⡄⢹⡀⠀⣇⢸⠀⣿⡇⡿⢧⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠳⠤⠤⣠⡤⠤⠴⢲⣿⠃⡜⠀⠀⠀⠀⠀⣿⡇⠀⢸⠏⣇⣠⣷⣦⣶⣿⣿⣯⠉⠉⠉⠉⠉⠉⠉⠛⢿⣿⣍⣉⣙⡒⠳⠼⢷⣀⣷⡞⠀⣇⡇⢷⡤⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡿⠁⠀⢠⢯⡏⠀⡇⠀⠀⠀⠀⠈⣿⣧⠴⣾⣤⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⣿⣿⣿⣷⣶⡖⠈⣿⡇⠀⢻⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠞⠁⠀⠀⠀⡞⠁⢀⡇⠀⠀⠀⠀⠀⡇⠀⣠⡿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠂⠘⣧⠀⠐⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⢲⢾⡁⠀⠀⠀⠀⢀⡼⠁⢀⡞⡇⢀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⡀⠀⠹⡄⠠⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⣝⣆⠀⠀⠀⠞⠀⠀⣸⠀⡇⠸⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣲⠄⢿⡀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⣦⠀⠀⣀⣤⡞⢛⣆⣧⡞⠃⡀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣠⠞⠛⢋⡴⠞⣹⠏⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⣆⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣗⠒⠚⢉⣠⠞⠁⣀⡤⠀⣿⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠲⢬⣷⣄⠈⠳⣦⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠛⢳⡾⠋⢰⣦⣶⠋⢀⣰⠏⠀⠀⢠⣷⣭⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣁⣀⣀⣀⣰⣯⣽⡟⢿⣿⡿⠀⠀⠀ ⠀⠀⢀⣴⠟⠀⠀⢻⣀⣠⡼⢿⣿⣽⡿⠤⠤⠤⠶⠛⠁⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠛⠻⠿⠷⠞⠃⠀⠀⠀⠀ ⣤⣶⣏⣁⠀⠀⠀⠈⠙⢿⣧⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⢡⡀⠀⣴⣶⣶⣶⣶⣶⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢢⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⡴⢶⡄⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣾⠋⠀⣼⡇⠀⠘⣿⣿⣿⣿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⣿⣿⣿⣿⣿⣿⡿⢛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣍⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣇⣾⠃⠀⢠⣯⠀⠀⠀⢻⣿⣿⣿ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢿⣿⣿⠟⠁⣠⠏⠀⠀⠀⠀⢠⠆⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠙⢷⣄⠀⠉⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⡇⠀⠀⠀⠈⣿⣿⣿ ⠀⠀⠋⠁⠈⠉⠙⠛⠛⢿⣿⡿⢿⣿⡏⠀⠀⠀⢸⡟⠁⠀⣰⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⠀⠀⠀⠀⢹⠀⠀⠀⠙⣆⠀⠀⠈⢻⣿⠿⠋⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⠋⠀⠀⣴⡷⠒⠒⠀⠀⢠⠀⢸⡗⠒⠒⠤⢿⠀⠀⠀⠀⠈⡇⠀⠀⠀⠘⣇⣠⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⣠⣾⠃⠀⠀⣰⣿⠁⠀⠀⠀⠀⡼⠀⡞⡇⠀⠀⠀⢸⡆⠀⠀⢢⠀⡇⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⢯⡏⠀⠀⣰⢇⡏⠀⠀⠀⠀⢀⡇⢰⡇⣿⠀⠀⠀⢸⢷⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⣀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣸⠁⠀⢠⡏⢸⠀⡀⠀⠀⠀⢸⡇⢸⠁⣹⠀⠀⠀⠀⡿⡇⠀⢸⠀⢹⠀⠀⠀⠀⠀⢸⡷⠘⠋⠁⠀⣀⣠⣾⠛⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⡇⠀⠀⡼⠀⣏⣀⡇⠀⠀⠀⣸⡇⢸⠀⣘⣇⠀⣀⠀⣇⢹⠀⢸⡀⢸⠀⠀⠀⠀⠀⢸⣿⡖⠖⠒⠛⠉⠻⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠇⢰⢳⡇⣼⣧⣤⣿⣽⣧⡀⠀⠀⣿⣷⢸⠀⢹⣿⣯⣽⣦⣼⣈⣇⠈⣇⢸⠀⠀⠀⠀⠀⠀⡏⣧⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠛⣿⢀⣾⣸⣵⡿⣟⠛⣿⣿⣿⠓⠒⠒⠛⠛⠾⠰⣾⠛⢻⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠐⠂⠀⡇⢸⣦⡀⠀⠀⠀⠀⣿⡆⠁⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⡏⢸⠉⢿⡿⠁⢸⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣷⣾⣹⣿⣿⣿⠀⢸⠏⢻⠀⠀⠀⠀⡇⠀⡇⠀⢯⠹⠆⠀⠀⠀⠸⣿⡤⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠀⢾⠇⠀⢸⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠋⣿⡿⠀⠋⠀⢸⠀⠀⠀⢠⡄⠀⡇⠀⢸⣷⢤⣀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⡞⠀⠀⠈⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠤⠞⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⣇⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⠃⠀⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢠⠇⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢸⠟⡄⠀⢿⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⢸⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠛⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⡇⡸⠀⡇⠀⠀⢀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢇⠀⢷⡀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⡇⣼⠃⠀⠀⠈⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢸⠀⡈⠻⣄⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣸⢹⢟⡁⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠀⠇⠀⢹⣶⣀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⣿⡟⢸⡇⠀⠀⠀⢀⡶⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠘⣿⣿⠓⠦⣿⣧⡀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⢀⣠⠶⠻⣥⡇⠀⠀⣸⡏⡄⢸⡇⠀⠀⢀⣾⢁⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣇⠀⣿⣿⣆⠀⢀⡈⠉⠛⣲⣶⠶⠶⠾⡷⢖⣺⠟⠉⠀⠀⣰⠋⡇⠀⢀⣿⡀⢹⡼⠁⢀⣤⣾⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⣿⠀⢸⣿⣿⣷⣦⣝⣳⡾⠃⢸⡀⠀⣀⣛⠉⠀⠀⠀⣠⠟⠁⢀⡇⠀⡼⠉⠻⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢹⡆⢸⣿⣿⣿⣿⡿⠛⠛⢳⡤⣧⣀⣀⣠⠖⠲⣤⠞⠁⠀⠀⣸⠃⣰⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⣿⣼⣿⣏⠹⡟⠀⠀⠀⠈⢣⡼⡟⣹⠓⠀⠀⠈⠳⡄⢀⣀⣿⣴⡋⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠋⣡⡽⠆⡇⠀⠀⠀⠀⣽⡀⠙⣿⠀⠀⠀⠀⠀⠹⡏⠉⣟⠉⠉⠓⢶⠲⢤⣤⣀⢻⣿⣿⣿⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣃⠀⢧⣀⠀⢹⣄⡀⠀⢸⡿⣽⢆⣸⣆⠀⠀⠀⢠⡾⣇⠀⠛⠀⢤⡀⠈⠳⡜⡆⣎⣻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠁⠀⢀⡈⠉⠉⠁⡿⠞⣿⣴⠟⢾⡛⠛⣦⠤⠴⠏⠀⠙⠀⠀⠀⠀⠘⠳⣄⠹⣷⡸⣿⣏⢿⣿⣿⣿⣿⣋⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⢸⣿⣟⣿⢦⣌⡳⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⡚⣿⡛⢾⠖⠛⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⣠⢔⢏⢆⡬⢀⢢⠃⡆⠑⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⢺⢃⢮⣇⣾⠁⡎⣾⢠⡄⣆⠀⢗⡰⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⢗⢏⣏⠜⢀⣩⠉⠉⠉⣀⡉⠑⢿⠀⠸⡄⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢸⡏⢺⠋⠉⠀⠀⠀⠉⠉⢓⣮⠀⠀⡏⠻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸⠁⠀⠐⠚⠻⣿⣷⣄⠀⠀⢸⠀⢰⡁⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠄⠀⠀⠀⠀⠈⣯⠽⡇⠀⠈⣰⡾⠹⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠴⢼⣟⣀⣀⣀⣄⠀⢀⣸⣿⣃⠴⣧⡿⠃⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣺⣿⠛⠋⠡⣪⣿⠟⠛⡯⢽⣟⠻⢁⠿⣼⡿⢁⣴⡴⠓⠚⠛⡏⢹ ⠀⠀⠀⠀⡸⠛⠛⠃⠀⠀⠙⠫⡄⠀⢨⡷⣲⠊⠁⠀⠉⠻⣍⣿⠷⠶⠒⠒⡇⠀ ⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⢸⣦⣮⠶⣯⣤⣤⣶⣾⣿⣷⣷⡆⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⣀⣀⣀⠀⠀⢀⣀⣀⣸⣿⣇⣛⣿⢿⣾⣿⣟⢉⡁⢻⣳⠀⠀⠀⡇⠀ ⠀⠀⢀⠤⠃⠏⡄⢸⠈⠀⡸⠷⠚⢸⢧⣴⣲⢧⣽⣶⣞⣛⣫⡾⣿⠇⠀⠀⠀⠀ ⢀⠀⠙⣴⡋⠘⢵⣬⣤⣠⣶⡅⣀⣨⣾⣿⣭⣕⣻⣟⣿⣯⠟⠉⠈⠉⠁⠈⠁⠀ ⠀⠓⠀⠉⠄⠀⠀⠈⠉⠉⠀⠈⠙⠋⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢹⠀⠈⢣⠀⢀⣆⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡸⠀⠀⠘⣤⠞⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡷⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⢠⡇⠀⠀⢠⢢⠀⠀⠀⣸⠀⠀⠀⠀⢀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢧⠖⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠁⢸⡇⣀⣰⠃⡎⢀⡇⢠⠏⠀⠀⠀⠀⠈⡆⢸⡆⠀⠀⢣⠀⠁⠀⢸⡀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠐⠀⠀⠀⢸⡀⠀⠱⣈⡇⢸⠀⣼⠁⣾⣦⡄⠀⠀⢠⠀⡇⢸⣿⡦⢄⡈⡄⠸⠀⠀⣷⠄⠀⣀⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣸⠀⡏⠀⡟⠀⣯⢹⢀⠀⠀⢸⠀⣿⠈⣟⣇⠀⢠⣇⠀⠇⠀⢿⠊⠉⠀⣿⡧⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠶⣶⣶⣤⡀⠀⠀⣾⠀⠀⠀⡟⣸⣷⢸⡇⢸⣹⣼⣈⡄⠀⢸⠀⣿⠀⣿⣼⡀⢸⣿⠀⡆⠀⢸⠃⠀⠀⠹⢿⣇⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣾⠉⠙⣧⠀⠀⣿⠀⢀⡼⣇⣿⣿⡸⣿⣾⡿⢿⣿⣿⠓⠉⠉⠉⠛⢿⣻⣿⣿⣿⣿⠇⠀⢸⡖⠂⠤⠠⣴⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣿⠀⠀⡇⠀⠀⣿⠂⠈⠳⡇⣿⠉⣿⡇⠁⢻⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⠿⢻⠇⣿⠀⡄⢸⢷⠀⠀⠀⡇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⣻⠀⠀⠈⡇⣿⠀⢿⣷⠀⠘⠙⠚⠁⠀⠀⠀⠀⠀⠀⠈⢩⣁⡠⡟⢀⠇⡞⢸⠀⠀⠸⡇⢀⣾⣿⣇⠀⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⢻⣿⠀⢸⣿⣇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣸⠀⣿⠻⡆⠀⠀⢳⣸⣽⣇⡿⣀⡠⣤⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⡿⢧⣆⢻⡟⣦⡀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠤⠤⢾⣤⡇⣼⡟⠀⠃⠀⠀⠀⢳⡠⠀⠐⠚⠂⠀⢸⣿⠁ ⠀⠀⠀⠀⡄⠀⢀⣿⣀⣠⠤⠞⠓⠛⠛⠛⠛⠛⡿⠷⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⣷⣶⣶⣶⣶⣶⣾⣿⠀ ⠀⠀⠀⠀⣧⠎⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠻⣧⡄⠀⡇⠀⠰⣤⣿⣿⣿⣿⣿⣿⣿⠻⠀ ⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠘⡇⢠⡇⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⡇⣼⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡔⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⢀⠘⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢉⡦⢤⣀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⢀⡨⠟⠉⠙⠲⣄⣀⣠⡇⠀⡆⠀⠀⠀⠈⡦⢹⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠈⠳⣀⢀⡟⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢀⡟⣹⣿⠁⢰⡇⠀⠀⠀⠀⢹⣸⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢣⡀⠀⠀⠀⠀⠙⠚⠛⠒⠢⢄⣀⠔⠁⠀⠀⠀⠀⠀⣠⠎⢠⢿⣿⡀⣼⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⡰⠃⠈⠒⠤⢀⣶⣎⠉⠉⠒⠒⠊⠁⠀⠀⠀⠀⣀⠤⠚⠙⣄⡆⠸⣿⣷⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢸⡗ ⠀⠀⠀⠀⡏⠉⠀⠀⡽⠁⠀⠀⠀⠐⡯⠉⠅⠀⠀⠀⠀⠀⣀⣠⠤⠒⠛⢄⠀⠀⠀⢹⠁⠀⠘⣿⣿⡀⠀⠂⠀⠀⠀⡀⠙⣿⣿⣿⢸⡇ ⠀⠀⠀⠀⡇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠘⠫⢭⡤⠤⠔⠊⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡆⠀⠀⢹⣿⡇⠀⢸⡀⠀⠀⠘⢦⠈⢿⣿⢸⣧ ⠀⠀⠀⠀⡇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⢿⣿⡀⢸⣧⠀⠀⣆⣺⡷⢼⣿⢸⡏

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⣤⣀⣉⣉⣙⢒⣢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠒⠊⠉⠁⣿⠃⢠⠀⠀⠀⠈⡆⠀⢿⡄⠀⠀⠀⠈⠉⡛⠒⠤⢄⣀⠀⠀⠀⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠔⠉⢰⡟⠀⠀⠀⢠⢰⢿⠀⢸⠀⠀⠀⠀⢿⡀⠘⣷⡀⠀⠀⠀⠀⠘⡄⠀⠀⠠⡉⠒⠢⣄⣀⠀⠈⠑⠤⠀⠀⠀⠀ ⠀⠀⠀⣠⢶⣿⢃⠀⠀⡎⠀⠀⢀⣀⣼⡔⢸⠀⢸⣷⠀⠀⠀⠘⣧⠀⠱⠳⡀⠀⢆⠀⠀⠸⡆⠀⠠⠱⡀⠀⣿⡄⠉⠁⠒⠢⠠⠄⠀⠀ ⠀⠀⢀⡇⡼⡞⣸⠀⠀⣇⣸⣬⣥⣤⣿⣧⠀⠓⠚⠛⠓⠒⠒⠒⠻⠳⣤⣯⣽⣆⣘⣆⠀⠀⢻⡄⠀⢳⣳⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠰ ⣀⣀⣾⠁⡇⡆⣧⣠⣾⡿⡛⢿⣿⣯⣍⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢻⣿⣿⠿⣷⣶⣬⣷⡀⢈⣧⡇⠀⢿⡿⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⠇⢰⠀⡇⣯⣹⠋⣰⣧⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣿⣿⣿⣄⠈⠙⣿⠷⠤⠿⠷⠀⢹⡇⢳⡀⠀⠀⠀⠀⠀ ⣿⣄⣀⣸⠀⠿⢿⠁⠀⢿⣿⢿⣷⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣇⣿⣿⣿⠀⠀⠀⡇⠀⠀⠀⠀⠘⣷⠀⢿⡢⢄⠀⠀⠀ ⡀⠻⠉⡏⠀⠀⢸⠀⠀⠈⠳⣄⣀⣀⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣈⡉⠉⢨⡟⠀⠀⠀⢰⠀⠀⠀⠀⠀⢹⡆⠈⢷⣄⠀⠀⠄ ⠤⠀⠀⣇⠀⠀⡟⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠸⣿⠀⠀⠻⠦⠀⢀ ⠀⠀⠀⣿⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⣶⣶⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡆⡌⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠻⣦⡾⠁⡿⠶⠤⣤⣍⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡇⢱⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⠀⠀⢹⣃⡼⠀⠀⠀⠀⠈⠙⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠱⣄⠀⠀⠀⠀⠀⡿⠁⠘⢇⣰⡭⢻⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⢀⡼⣇⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⢢⠈⢳⣄⠀⠀⠀⢳⣀⣀⡼⠋⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡠⢊⠀⢸⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⢆⠈⣏⢿⡶⢤⡤⠛⠉⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⠤⠒⠉⢳⠀⡑⣾⠸⡇⠀⠈⣿⠀⠀⠀⠀⢀⣴ ⠀⠀⠀⠀⠀⠀⣵⡈⡟⠹⣌⡷⠊⠀⠀⠒⠊⠙⣶⠤⢤⣤⣤⡤⠤⠤⠴⠒⣻⠿⠋⠀⠀⠀⡀⢸⡓⢬⣹⣰⣇⠀⠀⣿⣄⣴⣶⣾⡟⠛ ⠀⠀⠀⠀⠀⣰⠁⣿⠁⢠⠟⠀⠀⠀⠀⠀⠠⠖⢙⡆⠀⠘⢆⠀⠀⢀⡴⠊⠁⠀⠀⠀⣀⠞⢀⡜⠁⠀⠙⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿ ⠀⣠⠖⠋⠉⣿⢠⣿⢠⠎⠀⠀⠀⠀⠀⠀⠀⢀⠞⡇⠀⠀⠀⢱⡞⠉⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⣿⠸⠖⣿⣿⣿⣿⣿⣿⣿⣿ ⡸⢁⠔⠋⠁⢸⡼⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢇⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿ ⣧⠎⠀⠀⠀⠀⣇⠀⢱⡀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠈⠳⢤⣀⡀⠀⣀⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠁⠀⠀⢠⠞⠁⠘⣦⡀⣧⣀⣀⡀⠀⣠⠞⢉⣹⣧⠀⠀⢸⡟⠫⣉⡠⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻⣏⣻⣿⣿ ⠀⠀⠀⠁⠀⠀⠀⠈⢿⣟⢘⡂⠺⠿⣯⣉⣛⢤⡿⣷⡀⢸⣧⠖⠉⠳⢄⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡐⠉⢮⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⠉⠉⠙⣿⣟⠖⡻⢹⢿⣾⣇⠀⠀⠀⢀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⢇⠠⡘⡄⠈⠃⠙⠻ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⢠⡿⣯⡰⢡⢃⠏⢻⡇⠑⠦⡚⠁⠈⣿⠀⠀⠀⠀⠐⠒⠒⢊⠉⣁⡤⠒⢳⠈⠆⠱⠀⣠⡃⠀⠸

⠀⠀⠀⠀⠖⢆⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠔⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⠀⢆⠀⡀⠔⠈⡛⠉⠉⡉⠩⡝⠪⡕⠠⡀⠌⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠈⢞⠎⠀⢀⠁⠀⠀⢰⠀⠘⡀⠈⢒⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣔⡞⡌⠀⠀⡺⠁⠀⠀⢘⠀⠂⢡⠀⢈⡦⢂⢜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢠⢡⢸⠀⡀⡇⢠⠀⢠⢀⡇⠀⡜⠀⠈⣯⡀⢸⠀⠀⠀⡰⠀⢀ ⠀⠀⠀⠸⢥⢣⠿⣸⠶⣟⣿⡛⠒⠚⠚⡛⣶⡿⡇⠀⢳⠤⡀⠵⠂⠠⠁⢀⠎ ⠀⠀⠀⠀⠈⢹⠀⢸⠀⠿⠻⠇⠀⠀⠈⢟⡻⠇⢰⠀⢸⠀⢠⠀⢀⠃⢀⡞⠀ ⠀⠀⠀⠀⠀⡇⠀⡈⡆⠀⠀⠈⠀⣀⠀⠀⠀⠀⢸⠀⢸⡸⠀⠀⡎⠀⣼⠁⠀ ⢀⣀⣀⣀⣀⣇⠀⣧⡑⡤⢀⣰⡉⠉⢙⣆⢤⣶⣹⠀⣼⡥⠊⠰⠀⢰⡇⠀⠀ ⠀⠀⠀⠀⠀⢿⡄⢸⣿⣿⠟⠄⣈⣉⣁⠀⠜⢄⢸⠰⣸⡿⠀⡆⢠⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣼⡟⠁⠀⠀⣿⣄⢧⠀⠀⠀⠙⣷⣿⣿⣷⠀⢸⡿⠀⢀⣼ ⠠⠇⠈⠉⠉⣩⣿⡿⡦⣰⣎⢭⠪⡠⣾⣭⣴⣰⢖⣾⣿⣿⣿⡄⡏⣇⢀⣾⣿ ⠀⠀⠀⠀⠀⢸⣷⣝⣈⣊⣒⣻⢍⡈⣿⣉⣁⣫⣯⣥⣾⣿⡿⣯⠇⢻⣾⣿⣿ ⠀⠀⠀⠀⡠⡏⠀⠀⠀⠀⠀⠀⡏⠑⡏⠀⠀⠀⠀⠀⠀⠈⡜⡌⢢⣾⣿⣿⣿ ⠀⠀⠀⡰⡡⠄⠀⠀⠀⠀⢀⣄⠟⠣⡄⡀⠀⠀⠀⠀⠀⠀⠘⣳⡄⠻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡤⢶⣷⣿⣭⠟⠉⠉⠉⢩⢭⢭⠷⠖⠦⢄⣀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⣞⡡⠀⠀⠀⠛⢻⣤⣀⣀⣀⣠⣶⣶⣄⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⣧⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⠗⠉⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⠿⠿⣿⠛⠛⠛⢷⡶⣤⣀⠀⠑⢄⣀⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⢀⡀⠀⠀⢀⣤⠞⠋⠉⠛⠋⠀⠀⠀⠀⠀⠀⢄⠀⢞⠉⠀⠈⣷⣦⣬⣿⣿⣶⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⠶⠋⠀⢀⡴⠟⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢣⠈⢇⣠⠤⠋⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠀⢀⠀⢀⠇⠀⠀⡀⠀⠀⠀⠀⢈⠀⠀⠐⢷⠒⠓⠂⣧⠀⠀⠈⣿⣿⣿⡿⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣷⡾⠃⠀⢠⡇⠀⢸⣠⠤⠺⡗⠀⢰⡇⠀⠀⡆⠀⠀⠘⡀⠀⠀⠈⡆⠀⠀⣯⢿⣿⣷⡟⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠁⠀⠀⣿⠃⠀⢺⠀⠀⠀⡇⠀⠐⡃⠀⠀⢂⠀⠀⠀⡇⠀⠀⠀⢳⠀⠀⠸⣏⠹⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣯⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⢸⡀⠀⡇⠀⠀⢸⠀⠀⠀⣧⠀⠀⠀⢸⣇⠀⠀⣿⡀⣿⢳⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⢸⣿⢠⠀⣸⡀⠀⠀⠈⣧⠀⠃⠀⠀⢸⡆⠀⢀⣿⣦⣤⣤⣼⣿⡀⡄⣿⡇⢸⠀⠀⠹⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⣿⢸⠀⢿⣧⣀⣠⣴⣿⣷⣀⠀⢰⣸⣇⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡧⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⡄⠀⢿⣸⣤⣾⣿⣿⣿⣿⣿⣟⠙⢦⠼⠿⠉⠀⢸⡋⠹⣍⡏⠈⢙⡿⣿⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⡏⠀⠀⢸⣿⠿⣿⠛⠋⢯⡍⠁⢹⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⠀⢀⠜⠀⣿⠁⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠛⣧⠀⠀⠘⣿⡆⠸⣆⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠁⠀⢸⡏⠀⠀⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⢠⢿⡆⠀⠀⢹⠀⠀⠈⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢀⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠈⣏⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⣼⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠘⣄⡸⣶⣆⠀⢹⡦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⣥⣿⡿⠁⡰⠋⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⣽⣿⣦⣘⣿⣦⠀⢳⡀⢻⡉⠛⠲⠶⠶⠶⢶⢶⡶⠖⠋⠉⠀⣈⡿⢛⣿⣷⣾⣷⠋⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⠻⣷⣄⠱⡀⠹⢦⣀⠀⠀⢀⣼⣿⣦⣀⠀⢠⡴⠁⠀⣼⣿⡟⣻⡿⠁⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⠀⢙⣿⣿⣽⣦⣈⠈⠉⠉⠀⠀⠈⠉⠉⠁⣿⢿⣿⠉⠉⣉⣀⣤⣾⣿⣿⣟⣿⣿⣦⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣋⣿⣿⣿⣿⣏⡇⣼⣏⡗⢲⠒⣶⣶⣶⣶⣶⣿⢶⣿⣿⣿⣿⣿⣛⣿⣿⠉⣿⠿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀ ⡿⡟⠹⠛⠛⢭⣽⣟⣛⣛⠛⢻⡿⠿⣿⣿⣿⡿⢿⣿⢿⣟⣿⠭⠽⠋⠁⠘⡗⢲⡚⣿⣖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠀⠀⠀ ⣧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠉⠠⣿⠛⣿⠷⠀⠀⠀⠀⠀⠀⡤⠜⠁⢻⣿⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄ ⣿⡟⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⢻⣤⣄⣀⡀⠀⣸⣾⠧⡀⠀⠀⠙⠢⡖⢇⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⣁⣴⣿⣿⣻⣶⣶⣤⣀⣤⣤⣠⣶⠛⡟⠁⠀⡟⢠⠀⡏⠈⣿⡉⣏⢃⠙⣦⣀⠀⠀⢳⠈⠓⠤⡀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡏⠹⣿⣏⣹⡿⡏⣼⣅⣰⡏⠀⠘⣆⢹⣠⠎⠀⡞⠢⡿⠖⠚⡇⢸⠧⢌⡿⠀⠉⢲⣼⡀⠘⣆⠈⠳⡀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⢀⣠⡤⠶⢶⣿⣶⣤⣥⣆⡄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⢀⣠⠞⠋⠁⠀⠀⢠⠉⠉⠀⠈⠻⠿⢮⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠌⠀⠀⣠⠊⠁⢀⠂⠀⠠⢠⡇⠀⠀⠀⠀⠀⠁⠀⠙⢷⠀⠀ ⠀⠀⠀⠀⠀⣘⠀⠀⠰⠁⠀⢀⢂⠀⣠⠧⢦⢀⠀⠀⠀⠸⠀⢸⠀⠀⠈⠇⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠆⠀⠀⣆⠂⣼⠙⡸⠈⠘⠀⠀⡀⡇⢠⢸⠀⠀⢸⢸⠀ ⠀⠀⠀⢀⠊⡄⠀⣼⠀⠀⢰⣾⢾⢶⣶⣗⡂⡇⠀⢀⣷⠃⡎⣼⠀⠠⢸⠀⡀ ⠀⠀⡠⠂⠰⠀⡜⣻⠀⠀⢸⠣⣿⣾⣿⡏⠉⠑⠂⠘⣹⣰⣣⠟⠀⡄⡈⠸⡆ ⠀⠀⡇⠀⡆⡸⡇⢻⠀⠀⢸⠀⠙⠤⠘⠀⠀⠀⠀⢀⣮⣿⣿⢳⢤⢁⡏⡆⠇ ⠀⠀⠐⠄⢣⠃⡼⠾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⡻⠏⠠⡟⢢⣀⠱⡇ ⠀⠀⣴⣺⣮⣎⡠⠤⡄⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⠁⡄⠉⠀⠀ ⠀⠸⣿⣿⣿⣿⠆⠓⢃⣇⠐⡗⠄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠆⢢⠀⠀⠀⠀ ⣾⣻⣿⣟⠟⠁⠀⠀⠘⡟⡄⣇⠀⠀⠁⢐⢲⡒⢶⢊⢿⡇⡸⣸⡌⠀⠀⠀⠀ ⣿⣿⡿⣃⣀⣀⣀⠀⠀⢻⣡⣸⡹⡲⠚⠉⠁⠙⣿⣿⢹⡇⢣⢹⠃⠀⠀⠀⠀ ⣿⡿⣏⢣⡰⠒⠲⡌⣍⠔⡢⡟⡠⠚⡀⣦⠄⠀⢹⡃⢸⢻⢸⢸⠀⠀⠀⠀⠀ ⡿⠑⡬⢤⠤⡶⠧⢐⣀⠤⠆⡟⢄⢽⡌⢧⠈⡧⣈⡃⠈⠘⠛⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀⠈⠉⠑⠒⠒⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠔⠒⠒⣻⡟⠉⡉⠉⠉⠉⠉⢻⡉⠉⢻⣏⠉⠉⠉⠑⠒⠚⠫⢶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣾⠟⠁⠀⠀⠀⠀⢰⣿⠁⠀⡇⠀⠀⠀⠀⠈⣷⠀⠀⣟⣆⠀⠀⠀⠀⠀⠀⠀⢆⠈⠉⠙⠲⠦⣄⣀⠀⠀⠀⠈⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⣸⣻⠀⠀⠀⠀⢀⡇⢸⢻⠀⠀⣧⠀⠀⠀⠀⠀⢿⣇⠀⢸⡻⡄⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠘⡄⠀⠉⢓⣦⢤⣀⡀⠀⠈⠙⠢⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⡿⢹⠁⠀⠀⠀⡏⢸⠀⠀⠀⠀⢸⡆⡇⢸⠀⠀⣽⣿⠀⠀⠀⠀⠈⣿⡀⠀⢧⠹⡄⠀⠀⢆⠀⠀⠀⠘⣆⠀⠀⢠⠸⡄⠀⠈⣟⣆⠈⠉⠓⠲⠤⠤⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⡟⢀⣇⡏⢸⠃⠀⢸⠃⢸⡀⠒⠋⠉⣹⣷⡇⠀⢧⣠⡯⢿⣦⣤⣤⣄⣀⣸⡷⣄⠈⡦⠙⡦⠤⠈⣆⠀⠀⠀⢻⣆⠀⠀⢧⢹⡀⠀⠸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤ ⠀⠀⠀⢰⡇⣼⢸⠇⡿⠀⢀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣷⣶⣿⣤⣀⠀⠘⣿⡄⠀⠸⣇⢷⠀⠀⢿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⣀⣀⣻⣿⠀⡏⢸⠀⣿⣴⣿⣿⠛⡍⠙⢿⣿⣷⣦⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠉⢿⣿⣭⣛⠿⣿⣿⣶⣾⣳⡀⠀⣾⡌⡇⠀⢸⣿⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠃⢰⠃⢸⠀⣏⢙⡟⠃⣼⣧⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣼⣿⣿⣿⣷⡄⠈⠙⢿⣿⠧⢤⣹⣻⣷⠀⠈⣿⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⠋⠀⠀⢸⠀⢸⣶⢿⠋⠃⠀⣿⣿⣿⣿⣟⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⠀⠘⠸⡆⠀⠀⠀⠀⠀⠀⢹⡇⠀⢿⢤⡀⠀⠀⠀⠀⠀ ⠽⢻⣶⠶⣾⠀⠈⠙⣸⠀⠀⠀⢻⡿⠉⠛⠛⠛⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠉⢿⣿⡿⠛⢿⣿⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⣿⠀⠘⢷⡉⠓⠂⠀⠀⠀ ⣄⠈⠟⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠙⠦⣤⡤⠤⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠦⢤⣀⣀⣀⣾⠋⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠈⣿⢧⠀⠀⠀⡆ ⣀⠀⠀⠀⡇⡀⠀⠀⡿⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠈⢻⡳⡀⠀⠀ ⠀⠀⠀⢀⡇⡀⠀⢠⠇⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠈⠀⠘ ⠀⠀⠀⠀⢻⡇⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣿⣏⠉⣰⡟⢹⣟⠉⠉⠉⠻⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠰⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠘⢿⣾⡟⠀⡼⠛⠛⠛⠷⣶⣤⡘⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⡇⠀⠀⠈⢻⠀⡼⠃⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡆⠈⢧⡀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⢹⡂⢀⠞⡫⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢹⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⡀⡆⠙⢦⡀⠀⠀⠀⠀⠈⣏⠀⠀⠀⢻⣾⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡰⠋⠘⡆⢸⠀⠀⠀⢰⡌⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠱⡀⠘⣿⢦⣀⠀⠀⠀⠹⣦⣤⣴⠞⠁⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⣴⠊⠱⣄⠀⡇⢸⡀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⢱⠀⠸⣆⢻⣿⠶⣤⡤⠞⠁⠀⠀⢀⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⣠⠴⠚⠉⠈⣧⢀⡈⠳⣷⢸⣷⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⣠⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⢷⡞⢻⡘⢻⣠⠞⠀⠀⠠⠤⠖⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⢿⣖⣿⠉⠀⠀⠀⠀⠀⢿⢧⣉⠙⣿⢸⣿⠀⠀⢸⣿⡇⠀⣎⣤⣴⣾⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⢰⠛⣧⡞⠀⠈⣿⠞⠁⠀⠀⠀⠀⠀⠀⢀⡼⢏⠉⠉⠻⣏⠙⠉⠉⠉⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⣠⠏⠀⣸⠇⠈⠛⣿⣸⣽⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣦⣤ ⠀⠀⠀⠀⣀⣀⣤⡟⠀⣿⠃⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⣸⡀⠀⠀⠘⢣⡀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⢀⠔⠁⠀⡾⠁⠀⠀⠀⢸⣿⣾⡆⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⡴⠚⠉⠉⢸⡇⢠⣿⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⡇⠀⠀⠀⠀⠉⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⣿⠀⡷⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢰⠏⢠⠴⠖⠒⠀⣧⣸⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⡞⢠⠏⠀⠀⠀⠀⢹⡁⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠹⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿ ⡷⠋⠀⠀⠀⠀⣀⡤⢧⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⠀⠀⠈⠙⡶⣲⣄⣀⡠⠤⠤⣶⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⠞⠁⠀⠈⢷⣄⠘⣧⣄⣀⣀⠀⠀⣀⡴⠋⢀⣸⣿⣆⠀⠀⠀⣧⡏⠳⣄⣠⠔⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⡻⣇⢹⣯⣿⣿ ⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⢻⣷⡷⠒⠦⠩⣭⣻⣯⠛⠒⠿⣅⣸⢿⣧⠀⠀⣿⣁⡴⠊⠓⢤⡀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡎⠹⡝⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡔⠓⠶⠶⠶⠽⣿⣿⠯⣬⣻⡾⢿⣷⣄⣿⠋⠀⠀⠀⠀⠉⢲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⠸⣄⠀⠙⣆⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢹⣿⢶⠇⣰⢃⡾⢩⣝⣿⠦⣀⠀⠀⣀⡴⠉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⣁⠘⢧⡘⣦⠘⠆⠀⡼⠰⠁⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⣼⠏⣧⡰⠃⡜⢀⠏⠘⣿⡆⠈⠳⢞⡋⠀⠀⢸⣳⠂⠀⠀⠀⠐⠚⠛⢛⠋⢁⡀⣀⣠⠴⠛⠙⡇⠈⢧⡈⢣⠀⣰⣡⠃⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠒⢋⡽⠋⠉⠉⡙⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣠⡾⡿⢂⡞⢡⣾⠀⢀⠆⣼⠀⢰⠀⠈⠑⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⣶⡿⠋⡴⢡⡏⢠⣿⠃⠀⡞⢰⣇⠀⡎⠀⡀⠀⠀⢷⣄⠀⢠⠞⢹⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠷⠋⣼⠁⣰⢛⡿⢡⣯⡿⠀⢸⡃⡞⣏⠙⣷⠀⢡⡀⠀⠸⣝⣦⠇⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢵⡞⣸⠇⢠⠿⠚⠓⠛⠛⠉⠈⠉⠉⠁⠸⠉⠙⢄⣸⡇⠀⠀⢻⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣥⡾⠀⣿⡶⢋⣀⣤⣶⣯⡀⠀⠀⠀⠀⣰⣶⣖⣀⠀⠙⣷⠀⠀⢸⣧⣄⡄⡰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢠⣿⡇⢘⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⠻⢶⣿⠀⠀⢸⡟⠻⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⢸⣿⠀⠈⠉⠀⣠⣤⣶⣶⣶⣤⣀⠀⠀⠀⠀⠙⠋⡏⠀⠀⢸⡷⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣸⡇⠀⠀⠀⠈⠉⠉⠉⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⡇⠀⠀⣸⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠻⣿⡄⠀⠀⢰⠃⢰⣧⣿⠉⡗⠚⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢈⣸⡇⠀⠀⣼⠀⣿⣽⡏⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡼⣦⣿⣿⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣽⣿⡿⠀⣀⠴⣯⣼⣷⠟⠇⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣷⣶⠶⢋⡽⣿⡿⣿⣿⣿⣿⠟⠢⣶⣾⣿⣿⠛⠻⣿⡁⢰⣿⣿⠏⠀⢰⢛⣰⣧⣤⣤⣤⣤⣤⠤⣤ ⠀⠀⠀⠀⠀⠀⢰⣫⣿⣿⡏⠀⠀⠀⠀⢋⣴⣿⣷⠞⠉⠀⢟⠓⠦⣾⣉⡤⠒⠀⡸⠛⢳⣿⣿⠋⢀⣴⣿⣿⠏⡉⠀⠀⠀⠀⡇⠀⡿ ⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠆⠀⠀⠀⠘⠻⢿⣹⡀⠀⠀⠀⢹⣷⣦⣴⡴⠒⠉⠀⠀⠘⠙⢿⣿⠛⢻⣿⣿⣤⣠⣤⣤⣤⣴⣇⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡀⠀⠀⣿⠞⠛⣾⠀⠀⠀⠀⠀⠀⢀⣠⣽⡿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀ ⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣼⣇⠷⢯⣿⣤⣤⣤⣶⣶⣿⣿⣿⣻⣿⣿⣷⡟⠈⠉⠉⠉⠉⠈⡏⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⠛⣤⡜⣿⣿⣟⣹⣟⣻⣿⣿⠿⠿⠛⢻⣿⣿⡄⠀⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⠀⢠⡤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢠⣿⣿⣿⣊⡀⠩⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⣿⣿⣷⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠘⡇⢹⣹⡇⠀⢸⠉⢹⠀⠀⢽⣿⣇⡸⠟⠻⣿⡁⢀⣶⣤⣸⣜⡋⢷⣤⢤⡽⠿⠿⣏⣢⣽⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡰⠋⢡⣀⠈⣇⢇⠀⢸⡀⢸⠀⢰⠛⣛⡛⠉⠀⢰⡉⢻⡻⣿⣿⣥⡸⣿⣿⣿⣧⣷⣾⣃⣾⣿⣇⡛⣇⣱⣀⡀⠀⣠⠀⠀⠀ ⠀⠀⠀⠉⣠⣛⠉⠁⠸⢾⣧⡀⢧⣼⠄⢌⣷⣂⠀⠀⠀⢠⡿⣿⣿⣭⣿⠽⠗⣛⣿⣟⣹⣭⣭⣿⡿⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⣆⠀⠈⠻⠟⠀⠀⠀⠀⠙⠛⠻⠿⠿⠟⠛⠙⠳⢿⣿⣿⠾⠿⣿⣿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⡴⠁⠀⣯⠆⠀⠀⠀⣀⣤⡤⢐⣶⣐⣒⣀⡤⠤⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠕⠉⠀⠀⣸⡏⢀⠴⣺⠿⠛⠉⠁⣀⣀⣤⣤⣤⣴⣶⣿⣽⣛⡯⣶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢡⠋⠀⠀⠀⠀⢻⣉⠴⠋⠀⣀⠴⠚⠉⢁⠀⠀⠀⠀⠻⢿⠟⠛⣿⣿⣶⣕⠯⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠙⢄⣀⠞⠁⠀⣠⠊⠀⠀⡰⠃⠀⠀⠎⠀⠀⠈⡟⠋⠙⠳⣌⠻⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣠⡔⠁⠀⠀⡔⠁⠀⠀⣰⠃⠀⠀⡞⠀⠀⠀⠀⣇⠀⠀⠀⠈⢦⠙⡝⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠸⡀⠀⠀⠀⠀⣼⠏⠀⠀⢀⡞⣀⣠⣤⣼⣇⡀⠀⣼⠁⡄⡆⠀⠀⠁⠀⠀⢆⠀⠀⠳⡘⣟⡄⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠒⠁⢀⠞⢄⠐⣤⣿⠏⠀⠀⠀⡞⠀⠀⡜⢰⡿⠀⠀⢰⡟⢰⠁⡇⠀⠀⣧⠀⠀⢸⠀⠀⢆⠱⣽⣁⡤⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⣾⡟⠀⠀⠀⢸⠁⠀⢠⢣⠃⡇⠀⢀⢇⠅⣾⢀⡇⠀⠀⣿⠢⣀⢸⡇⠀⠸⡀⢻⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠠⠼⠀⠀⠀⣻⠃⠀⠀⣀⣏⣀⣀⣾⣜⢰⠃⠀⡼⢸⢀⣿⢸⠇⠀⢰⣿⠀⠈⢻⣆⠀⠀⡇⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠂⠤⣤⠤⢶⡟⠀⠀⢰⣿⢛⣟⣿⣿⣿⣿⣿⣦⠃⢸⣸⢸⣿⠀⠀⠸⢹⠀⠀⢸⣿⠀⠀⠇⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣠⠃⠀⠘⣇⠀⠀⢸⠉⢹⡿⣿⣿⣿⣿⠉⠀⠀⠈⠛⠸⢿⣠⣦⣇⡘⠀⠀⣾⣿⠀⡀⠀⠀⢹⠄⢀⣠⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⣜⡕⠁⠀⠀⣼⡏⢠⠁⡎⠀⠈⠣⣬⡹⠿⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣦⣰⡏⣿⠀⡇⠀⠀⣿⢹⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢴⢹⡀⠀⠀⢸⣿⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⢻⢷⡟⢸⡇⡇⠀⣿⣿⡁⠀⠀⠀⠤ ⠀⠀⠀⠀⠀⠀⠳⡱⣄⡄⢸⢸⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⣹⣽⠏⠈⣸⣇⣾⡇⡇⢀⣯⣑⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⡎⢳⣈⣮⡇⢸⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⣿⣿⡟⢹⡇⣿⣿⡆⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⣴⣟⣻⣿⣷⠀⡁⣇⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢟⣿⣿⡇⠀⢸⢹⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠰⣿⣿⣿⣿⣿⠀⣧⣟⢉⣩⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠒⠋⠀⣿⠀⣂⣿⠈⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢊⣥⣤⣿⣿⣿⣿⣿⡄⣿⣟⠀⢧⠐⠄⠙⠯⣍⣒⡶⠖⠢⢤⣴⠒⠊⠉⣇⢻⠀⠀⠸⡟⢠⣾⡟⣠⠟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣶⣿⣿⣿⣯⠟⢷⡏⢿⠀⠀⠓⢤⡀⠢⣼⠁⠀⠀⣠⠼⠉⠳⣶⠤⠬⣿⣷⣶⣶⡇⢸⠧⠼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠁⠀⠀⠀⠀⣼⠯⡓⠛⣳⣶⠿⠥⠐⠂⠁⠈⢣⢠⣿⣿⣿⣾⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣶⢶⣾⣿⣿⣿⣿⣿⠳⣄⠀⠀⠀⠀⠀⠀⢠⣿⣠⠜⠻⣨⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⣾⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣷⣾⣿⣿⣿⣬⣿⢟⣾⠟⠙⠒⣤⣀⣀⠀⣸⡟⢄⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣭⠹⣤⠞⡏⠰⢻⢦⢣⠂⣀⠈⣿⣃⠴⠛⢅⣼⣗⠒⠒⠒⡖⢊⢉⣀⣹⣿⣴⣿⣿⣿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⡿⠙⠲⣌⣷⣬⣑⢛⠎⣎⠘⣹⢰⣿⠦⡀⢀⡤⣿⣿⠀⡖⣶⡇⠸⡘⣇⡇⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⢀⠀⠀⠀⠀⠀⠈⠒⢺⣯⡗⠢⠤⠤⣼⡧⠔⠛⠣⣀⣿⠛⠶⠷⠟⣧⠀⢋⣉⠤⠚⢉⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠻⡇⠀⠘⣇⠀⠀⢠⣆⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⠀⠀⣸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⢸⡆⢀⡿⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡼⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢀⣠⠞⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡇⠀⠀⠀⣰⠃⡞⠀⣀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⠀⠀⢄⠀⠀⣿⠛⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢘⡇⠀⠀⣰⠃⡸⠁⢠⡟⢀⣿⠃⠀⠀⠀⠀⠀⠀⡇⠀⢻⡀⠀⠀⠈⢆⠀⢸⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⡇⠀⠈⢧⡈⢻⡏⢰⠇⠀⣾⠁⢸⣼⢠⠀⠀⠀⠀⢠⠀⢸⠀⢸⣧⡄⠀⠀⢸⠀⠀⣇⠀⠀⣧⡀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠈⠳⡾⠀⡼⠀⢸⡏⠀⡾⡿⢺⠃⠀⠀⠀⢸⠀⢸⠀⢹⡻⡏⠉⠓⠆⣇⠀⢻⠀⠀⢹⣋⣁⣤⠶⢺⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡇⠀⡇⠀⢸⡇⠀⡇⡇⢸⢠⠀⠀⠀⢸⠀⢸⡆⢸⣇⢳⡀⠀⢰⣿⠀⢸⠀⠀⢸⣍⠀⠀⠀⢸⠘⡿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣤⣶⣬⣀⠀⠀⠀⢸⡗⠀⠀⠀⣾⠇⡾⣷⡀⣿⡇⢠⡇⣇⣼⣘⡆⠀⠀⣼⠀⣼⣇⢸⣿⣼⣇⠀⢸⣿⡀⢸⠀⠀⢸⠿⠄⠀⠀⠘⢶⣻⣧⢀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀ ⠶⣬⡟⠛⠿⣿⡄⠀⠀⢸⡂⠀⠀⢠⣿⢰⣿⢹⡇⣿⣧⣼⣷⣿⣿⣯⣧⣶⡤⠿⠶⠋⠿⣼⣿⠿⣿⣶⣾⣿⣧⣼⠀⠀⢸⣧⣤⣀⡀⠀⢀⣀⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⠀⢸⡇⠀⠀⣿⠁⠀⠀⣸⣈⠀⠴⣏⣹⢸⣼⠸⣧⣽⠛⡟⢻⣉⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⢱⣶⣿⣿⣿⣯⢻⣿⠀⠀⢸⣿⡆⠈⠉⠉⢹⡗⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀ ⠷⢾⣅⠀⠀⣿⠀⠀⠀⢾⡝⠀⠀⠈⣿⢸⣿⠀⣿⣿⡄⠉⠸⣿⠿⠿⣻⠇⠀⠀⠀⠀⠀⠀⠘⣯⡙⢋⣽⠃⢸⡏⠀⡆⢸⡝⣷⠀⠀⠀⢸⠁⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⡅⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⢸⣿⠀⢹⣿⣧⠀⠘⠊⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣀⣠⢸⠃⢸⠁⢸⠃⣽⠀⠀⠈⣿⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠻⣾⣿⠀⠸⣿⣿⡀⠐⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣸⠀⣟⣴⢿⡀⠀⠀⠘⣇⠀⡟⣹⠁⣻⠀⠀⠀⣀⣠⣿⣿⣤ ⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⡀⡀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡇⢀⣿⡇⢸⡇⠀⠀⠀⠘⣦⠛⠛⠛⠋⣰⣏⡙⠛⠛⣿⣿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠇⢧⣿⣈⢻⣏⣷⣤⡀⠀⠀⠀⢀⣠⣤⠤⠖⠒⠒⠒⠒⠒⠒⠻⣶⣼⢁⣿⡿⠀⠈⠁⠀⠀⠀⠀⠈⣆⠒⠉⠉⠁⠀⠀⠀⠀⣿⣿⠀ ⠀⠀⠀⠀⠀⣆⠀⠀⢀⣸⣇⣀⣠⡤⠶⠟⠊⠉⠉⠉⠉⠙⠛⢾⡿⠷⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣷⡇⠀⠀⠀⠀⠀⠀⢰⠀⢹⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠀ ⠀⠀⠀⠀⠀⣿⣤⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⢿⡇⢀⠀⠀⣷⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⠀ ⠀⠀⠀⠀⠀⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⣿⠀⠀⣿⠀⠀⠈⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠨⠀ ⠀⠀⠀⠀⠀⣿⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠀⢰⡏⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠖⠀⠀⠀⠀⢸⠀⣼⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢸⣸⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⣀⡀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣉⣁⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠰⡄⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢉⡗⠤⣄⣀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠋⠉⠙⠓⢶⠀⣤⣠⣼⠁⠀⣶⠀⠀⠀⠀⠀⢜⠆⠸⣿⣿⣿⣿⣿⠀⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢺⠀⠀⠀⠈⠉⠳⣄⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡿⢻⣿⡟⠀⢠⡇⠀⠀⠀⠀⠀⠈⣧⠀⣿⣿⣿⣿⣿⡀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠆⠘⣇⠀⠀⠀⠀⠀⠈⠳⣴⣃⣴⣆⣀⡀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⣼⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠉⢓⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠀⡼⢹⣿⣧⢀⣾⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡼⠁⠀⠈⠙⠢⢤⣘⡫⣥⡄⠀⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⢧⢠⠇⣿⢿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇⢼⠉ ⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⢉⡟⠀⠀⠀⠀⠀⠰⣶⡚⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠻⣅⠀⠀⠀⠀⠘⣿⠀⠀⠘⢿⣿⣿⡀⠀⠀⡆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⣼⡄ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠙⣶⡶⢶⠆⠀⠀⣀⡠⠶⠒⠊⠉⠁⠀⠀⠀⠈⠓⠄⠀⠀⠀⣿⠀⠀⠀⠘⣿⣿⣇⠀⠀⣷⠀⠀⠀⠈⠳⣄⠈⠻⣿⣿⡇⢿⡇ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⣿⣿⠀⠀⢸⡆⠀⠀⠀⠀⠙⣦⠀⢻⣿⡇⢸⣷ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⢿⣿⣇⠀⣸⣿⡀⠀⢸⣇⣸⣿⡳⢾⣿⡇⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣰⠃⢰⠃⠀⢀⣿⠁⠀⠀⠀⠀⢠⡆⠀⡇⠀⠀⠀⢧⠀⠙⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢰⠇⠀⡇⠀⠀⢸⡏⡇⠀⠀⠀⠀⠸⠃⠀⢱⠀⡄⠀⠘⡆⠀⠹⡄⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡟⠀⢸⠁⠀⠀⣸⠇⠇⠀⠀⠀⠀⠀⠁⠀⠘⡆⢰⠀⠀⢳⠀⠀⢻⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠀⠀⠀⠠⡼⠀⠀⠀⢸⡇⠀⣾⠀⠀⠀⣿⠀⡆⠀⠀⠀⠀⠀⣷⠀⠀⣷⠀⡄⠀⠘⡇⠀⠘⡇⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠲⠤⢠⡇⠀⠀⠀⣿⠁⢠⡇⢠⠀⣀⣿⣤⣇⠀⠀⠀⠀⢤⣏⠀⢀⣿⣤⣇⠀⠘⣷⠠⠀⢷⠀⠀⠀⠀⡷⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠁⣼⡇⢸⠁⠀⡿⠄⣧⠀⠀⠀⠀⠘⣿⠀⠀⡷⡇⡇⠀⠈⣿⡆⡇⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣿⠀⢹⢣⢼⠀⠀⡇⠎⣿⡀⠀⠀⠀⣀⣿⠀⠀⠇⠀⠳⠀⠀⣼⡇⣧⣼⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⠚⡃⠀⠀⠀⣿⡇⣸⣤⣼⣤⣤⣷⣾⣿⠷⣄⢀⠀⣿⠿⡦⣼⣷⣾⣾⣤⣴⣧⣿⣭⡌⠀⠀⠀⠀⡍⠳⠄⠀⠀⠀⠀⠀ ⠑⠲⠦⠤⣤⠴⠚⣧⠀⠀⠀⣿⡟⢻⢛⣋⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣯⣹⣟⣿⣿⣿⢻⠟⣏⠀⠀⠀⠀⡍⠒⠒⢦⡤⠀⠀⠀ ⠀⠀⠀⢠⠇⢰⠀⣿⠀⠀⠀⢸⡇⠀⠚⣿⢿⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⢹⡟⠉⠀⣿⠀⠀⠀⢠⣿⠀⠀⠀⢳⠀⠀⠀ ⠀⠀⠀⢸⢀⡏⠀⣿⡆⠀⠀⠘⣿⠀⠀⠈⠻⠤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠀⡏⠀⡀⠀⣸⣿⠀⢸⠇⢨⠇⠀⠀ ⠀⠀⠀⠈⢿⡇⠀⣿⣷⠀⠀⡆⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢀⠇⠀⣿⡿⢠⠏⣠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⣹⡜⡆⠀⢹⠸⡿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢹⠇⢸⠀⢸⣿⣡⡿⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⠀⠘⡆⢱⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠊⠀⡼⠀⡎⠀⣿⣿⡿⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⢳⠈⡆⠀⠘⡌⠑⠲⠤⣀⡀⠀⠀⠀⠀⣀⣠⠤⠖⡿⢩⠏⠀⠀⡇⢰⠃⣼⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠉⢧⠈⣧⢸⡀⠀⠘⢄⠢⢄⡀⠈⠉⠻⡽⠋⠁⠀⡠⢞⣰⠃⠀⠀⢸⢁⡟⢠⠉⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⡛⢆⠈⢧⠘⡆⢧⠀⠀⠈⠳⣤⣈⣐⣒⣀⣀⣀⠐⣋⣴⡿⠃⠀⠀⢀⣇⣼⢁⡏⢀⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⡿⣿⠑⣎⣧⡈⢧⣹⣼⣆⠀⠀⠀⠈⢢⠁⢈⡰⠴⢏⣿⣿⠋⠀⠀⠀⠀⣼⡿⣿⡞⢠⠎⠉⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣧⢻⣦⣿⢳⠈⠺⣿⣏⠻⣆⠀⠀⠀⢸⠸⢧⡀⢀⡠⠇⢠⠀⠀⠀⠀⣰⠟⠁⣻⢗⣉⢻⣧⣾⣃⣽⣿⡟⠀⠀⠀⠀ ⠀⠀⢀⣶⣿⣿⣿⠿⢄⣻⡇⡆⢸⠛⢢⠙⡖⠤⣄⡀⠀⠈⢈⡠⠜⠛⠠⣀⢸⠀⠀⠀⣀⡠⠴⡏⠁⢸⠈⣆⣻⣏⡽⣿⣿⣿⢦⡀⠀⠀ ⠀⠀⢸⣿⣿⣿⡏⠀⠠⣇⣙⣟⢦⣀⡞⣸⢡⠁⡤⢬⣉⡗⡟⠦⣀⡠⠚⠁⠸⠏⡉⢩⠤⢶⠀⢣⢸⣠⢞⡿⢻⠃⠀⢹⣿⣿⣿⣧⠀⠀ ⠀⠀⠸⣿⣿⠿⠁⠀⠀⠀⠀⢹⣑⣮⣀⡇⢸⣀⠁⢠⠃⠁⣇⠔⠋⠓⢤⣀⠸⠀⡇⠘⠇⣀⠇⢘⣦⠕⣿⠒⠉⠀⠀⠀⡟⠛⢿⡏⠀⠀ ⠀⠀⠀⠈⡇⠀⢇⠀⠀⠀⠀⠀⠀⠉⠻⣍⣶⣦⣭⣙⣸⠀⠛⠦⣀⢀⡤⠻⠀⣄⣸⣞⣭⡔⢒⡿⠛⠛⠁⠀⠀⠀⠀⠀⠇⠤⣞⠀⠀⠀ ⣶⣶⣶⣶⠃⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢻⢸⣀⠤⠚⠑⠢⣤⠀⡟⠓⠋⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⣷⣶⣶ ⣿⣿⣿⠁⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠸⠓⢄⣀⣀⠴⠚⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿

⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⠀⠀⠀⠀⠀⡐⠀⢀⠊⡌⠀⣼⡀⠀⠀⢸⠈⡀⠀⢡⠈⠄⠀⠈⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠁⠀⡞⢠⠀⠀⡏⠇⠀⠀⢐⠀⢃⠆⠀⡆⠘⡀⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠤⢀⡇⠀⢠⡇⡸⠀⢸⣇⡃⠀⠀⢸⠀⣸⣸⣀⢥⠀⢧⠀⠀⠧⠀⠀⡀⠀ ⠀⠀⠀⠀⡇⠀⢸⠁⣿⡄⢸⢣⡇⠀⠀⢸⡀⠘⢸⠀⢹⣼⢸⠀⠀⠀⠀⠀⠁⠀ ⡀⠀⠀⠔⡃⠀⢸⣇⣯⣤⣼⣾⡿⠄⠀⠿⠧⣶⣶⣤⣮⣿⡍⠀⠀⣔⠠⠀⠀⠀ ⠀⠉⡙⡁⣀⠀⠈⡇⠃⡾⣿⠿⠇⠀⠀⠀⠀⢸⡾⠿⡿⠊⣣⠀⠀⣇⠀⠹⡀⠀ ⠀⠀⢇⠃⢹⡀⢀⢷⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡇⠘⢠⡏⠰⢀⠇⠀ ⠀⠀⠀⠓⢼⣃⠈⡸⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠇⡇⣼⣷⠗⠁⠀⠀ ⠀⠀⠀⢰⣿⣿⡄⢃⢃⠈⡆⠤⢀⡀⠀⠀⢀⡀⢤⢒⠁⢰⢠⢠⣿⣯⣧⠀⠀⠀ ⠀⠀⢀⣨⣿⡿⠘⡌⡎⡄⠘⢄⠢⢀⡙⠋⢀⢔⡥⠃⠀⣆⡆⠆⣿⣿⣏⠀⠀⠀ ⠀⠀⣾⣿⡿⡗⣵⢜⣼⣴⡀⠀⠙⢏⠹⠽⡩⠟⠀⠀⢰⢿⣞⣔⠻⣿⣿⡇⠀⠀ ⠀⢀⣼⣿⡿⣻⢦⠠⠝⢣⢁⡀⠀⢈⡱⠄⣁⡇⠀⢀⡫⠜⢱⢊⣿⣳⣿⣧⡀⠀ ⠀⢸⣿⡿⠀⠂⠹⢗⠌⡌⠳⠒⠽⡏⡢⢂⠁⡏⡍⡖⠇⢃⣶⡕⠏⠀⢿⢿⡇⠀ ⠀⠀⢋⠐⡀⠀⠀⠉⠻⠷⢭⡖⡄⠓⢄⡠⠹⢀⢳⡦⣑⠞⠒⠁⠀⠀⡘⠴⡁⠀ ⣿⣿⠃⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠢⣁⣈⢵⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣻⣿

⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣴⣮⡾⠛⠉⠉⠙⠿⠛⠉⠀⠈⠙⠿⠿⠋⠉⠉⠛⢿⣦⡀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠟⠁⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢁⠞⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢃⠀⡀⠀⠀⠻⣧⠀⠀⠀⠀⠈⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠏⠀⠀⠀⡀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠘⡄⢡⠀⠀⠀⢹⡆⠀⠀⠀⠀⠈⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡜⢠⠀⠀⣸⣁⣀⣾⠀⡸⠀⠀⢀⠀⠀⡦⠠⢄⣥⠀⠁⠸⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡎⠀⠐⡿⠁⠀⡯⠀⡇⠀⠀⠐⠀⠀⡇⠀⠀⢉⠙⢷⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⠀⢰⣧⡇⠀⢰⡇⠀⢠⡇⢰⠃⠀⠀⢦⠀⠀⣧⠀⠀⢸⠀⢸⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢿⡀⠀⡏⡇⠀⠘⣇⠀⣸⣷⢸⡄⠀⠀⢸⡀⠀⣿⣀⡀⢸⡀⠀⡆⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼⢱⠀⣧⣧⣤⣼⣿⣿⣿⣽⣾⠛⠒⠒⠚⠳⣶⣿⣷⣶⣾⣷⣦⣧⡇⠀⠀⠀⡘⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⢸⣸⠀⠈⣿⡘⡟⣭⣽⣿⣿⡏⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠛⠏⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠹⣯⡛⣿⠇⠀⠀⠀⠀⠀⠀⠘⢿⣛⣿⠟⠀⢀⠃⠀⠀⢸⢣⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢈⠀⢸⡇⠀⣀⣄⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⡆⣸⡄⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠠⠄⢸⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡔⢠⣷⠋⢣⠀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⢸⠁⠀⠈⠆⠀⣿⡇⢰⡖⠀ ⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂⠠⢾⠀⡇⠀⢹⡏⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⢸⠀⣇⠀⠀⠀⠘⠄⣻⡇⣾⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢷⠀⠀⣿⣀⢦⣈⠻⣗⠒⠶⡤⠀⣤⠤⠐⠒⠊⢉⣿⣿⠀⡌⢸⠉⠢⣀⠀⠀⢠⣇⣼⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⣆⠀⢱⠈⠙⠻⢥⣈⣳⠤⢷⡞⣿⠀⢀⣀⡤⠞⢩⡏⢠⡇⣾⡒⠲⠤⣿⣿⣾⣿⣿⣻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⣆⠘⡄⢀⡴⠊⠁⠀⠲⣿⣀⣈⣉⣉⣠⢴⣾⠝⢻⢸⡇⡇⠉⠑⠢⠿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣲⣿⣇⣀⣤⣂⡀⠀⠈⠣⢉⠩⠤⠒⠉⠀⠀⢸⣾⡿⠃⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣾⠿⠃⠀⠀⠀⠀⣇⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⠂⠀⠀⠀⠀⠸⣿⣿⣧⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⣠⠖⠒⠒⠦⢿⣀⠀⠀⢠⠟⢦⡀⠀⠀⢠⡤⠤⣀⣸⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢠⠎⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠙⠲⢼⡀⠈⢿⡄⠀⠘⠋⠭⠽⢸⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠃⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣼⣿⡄⠀⠀⠀⠀⢸⣧⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⢀⣀⠘⣿⣷⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣿⣮⠻⣿⣿⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡤⠶⠶⠶⠶⠶⠶⠶⠶⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⣴⡶⣿⣿⣿⣿⠟⠙⠛⠿⢿⣿⣿⣿⡟⠿⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⣴⡾⠛⠉⠀⠟⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠃⠀⠀⠈⠙⠳⢶⣀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠃⠀⢀⣴⠟⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⣠⡟⠁⠀⠀⡞⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢢⠀⠀⠈⢷⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢱⡆⠀⠀⠀⠀ ⠀⠀⢀⣼⠃⠀⡞⢁⠇⠀⠀⣼⠀⠀⠀⢀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⡇⠀⠀⠈⣧⠀⠀⠀⠈⣧⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⣰⡇⠀⡞⠁⡞⠀⠀⢠⠇⠀⠀⠀⣾⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢱⠀⠀⠀⠘⡄⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⡄⠀⠀⠀ ⠀⠀⣿⠇⣸⠁⢰⠃⠀⠀⣾⠀⠀⠀⢰⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⡇⠀⠀⠀⢿⠀⠀⠀⠀⢻⠀⠀⠀⠀⠸⡇⠀⠀⠀ ⠀⠀⣿⢠⡇⠀⣿⢀⠀⠀⡇⠀⠀⠀⣼⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣠⠀⢷⠀⠀⠀⠘⡆⠀⠀⠀⠀⣧⠀⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⣽⠸⠁⠀⣿⣼⠀⠀⠇⠀⠀⠀⣿⡏⠚⡧⠀⠀⠀⠀⠀⠀⢈⡇⢺⡏⠁⠀⠀⢸⣆⠀⠀⠀⣷⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠇⠀⠀⠀⡿⣿⠀⢸⠀⠀⠀⠀⣿⡇⠀⣧⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⠀⠀⠀⠈⡿⡀⢠⠀⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⣿⠀⣿⠀⠀⠀⠀⣿⡇⠀⣿⡀⢠⠀⠀⠀⠀⢘⡇⢸⣿⡇⠀⠀⠀⣷⣧⠘⡄⠘⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢿⠀⣿⡀⠀⠀⠀⣿⢽⠀⢿⡄⢸⡄⠀⠀⠀⢸⡏⢸⢿⢧⠀⠀⠀⢹⢹⡀⣷⠀⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡄⠀⠀⠀⣿⠸⣆⣏⡷⠶⠦⠤⠟⠀⢆⡸⢻⣲⢧⣀⣀⣀⣠⠷⠼⠜⠿⠤⠤⠤⠞⢛⣗⠿⣀⠟⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣆⡐ ⠀⢸⠀⢠⠀⠀⠸⡄⣿⢿⣷⣄⣀⠀⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣴⣶⡿⠿⠀⣿⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢸⡄ ⠀⠘⠀⢸⡆⠀⠀⠳⣾⠄⠉⠉⠛⠿⣶⣯⣕⡲⠄⠀⠀⠀⠀⠀⠀⠀⢸⣭⣶⠿⠟⠋⠉⠀⠀⠀⣿⠀⠀⠀⠀⣿⣯⡆⠀⠀⠠⠀⠈⡇ ⢠⡆⠀⠀⡇⠀⠀⠀⢹⠀⣤⣀⣀⣀⣀⣩⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⢶⣶⣶⣦⣤⣄⠀⡿⠀⠀⠀⢠⠃⣽⡇⠀⠀⢰⡆⠀⡏ ⣿⡇⠀⡆⢸⡀⣀⡀⣈⡇⠘⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⡇⠀⠀⡖⣸⣠⠿⡇⠀⠀⣸⠃⣸⠗ ⣿⢧⠀⢣⠘⡇⡄⠀⠨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡇⣿⠃⢠⠃⢀⡴⠃⡰⠃⠠ ⠛⢸⢦⡘⢧⣹⡟⡆⠐⢽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠂⠀⣸⣷⠇⠀⢈⣠⢞⣡⠞⠁⠀⠀ ⠀⠀⠀⠑⢦⣿⣿⣿⡀⠀⢷⣿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣼⡁⠀⣿⣿⡀⣀⣼⣷⡍⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣿⢻⣧⣀⣸⣿⠁⠀⠉⡷⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⣯⣤⣄⠀⣿⣀⣼⣿⢿⣿⣿⣴⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⢸⣿⣧⣿⡿⠀⠉⠉⠉⡓⠻⣄⠀⠠⠭⣍⠉⠩⠉⠀⠾⠧⣄⠈⠙⢦⡀⠙⣿⣿⣿⠃⢸⣿⣿⣿⣿⣅⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣧⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⣀⣀⣀⣠⡔⡇⠀⠈⠳⡀⠀⠙⠐⣿⠛⠛⠲⣶⢿⣿⣿⡿⢻⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⣿⣿⠟⠛⠃⢧⠀⠀⠀⠀⠀⠀⠀⠀⣨⣈⠑⢤⠀⠳⢇⠈⠂⠀⠀⠀⠀⠀⢀⣟⣀⡠⠴⣥⡟⣿⣿⣷⣾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⡷⠶⢄⣈⣳⣤⣀⠀⠀⠀⣀⡴⣽⣮⠃⠀⠙⠂⢈⡳⣄⣀⣀⣀⣀⡴⠋⠈⠳⣄⠀⠘⣷⣿⣿⣿⣿⣿⢿⣦⡀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣇⠀⠀⢠⠛⡏⠈⠙⠉⣍⠁⠀⠈⣽⠢⣄⡄⠳⣎⣀⣀⣍⠉⠉⢹⠿⢄⣀⣀⡼⠀⠀⢹⠉⠻⣿⣿⣷⣾⣿⡇⣾ ⠀⠀⠀⢹⣿⣿⡏⠀⠳⠀⠀⠁⠀⣻⣅⣠⠞⠀⠛⠶⢦⣞⡀⠈⠱⢄⢰⣼⣷⢨⠀⢀⡿⠁⠀⠀⢈⢺⠀⠀⣟⠀⠀⢈⡛⣿⣿⡟⡃⢹

⠀⠀⠀⠀⢸⠁⠁⠈⡆⡴⠂⢁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡄⠐⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⢸⠀⠃⠀⢌⢀⢀⡆⠀⠀⡀⠂⠀⠀⢀⠈⡔⠊⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⠄⠀⢸⠀⢖⡞⡄⡜⣸⣀⠀⢀⢀⢸⡄⡘⠀⡄⢡⠀⢀⡔⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⢸⠀⢠⢠⡀⡇⢿⡇⠀⢸⢸⢸⢁⠐⡇⡃⢸⡉⠀⣷⡆⠀⠀⠀⠀⠀ ⢺⠉⢣⠀⢸⢀⣼⣾⣇⣷⢿⣿⡗⠚⠊⠺⣻⣾⣷⡇⢸⡆⠠⢤⠏⠀⠀⠀⠀⠀ ⠉⠀⢸⠀⢹⠀⢸⣷⢸⡆⠘⠿⠃⠀⠀⠀⠛⣙⣸⢀⢸⡃⠀⡌⢠⣶⡀⠀⢰⡄ ⠀⠀⠈⠀⢸⠀⠈⣿⡘⣿⡈⠁⠀⠀⠀⠀⠀⠀⡘⡈⣼⢱⠀⠘⡜⢓⡃⠒⢾⡷ ⠀⠀⠀⣀⡼⠠⠔⠓⠛⠚⠛⠖⠒⠈⠁⠀⠀⠀⢸⣷⡇⠀⡀⠀⢸⣶⣶⣶⣾⡇ ⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⠀⡇⠀⣾⣿⣿⣿⣿⠁ ⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⣷⠁⠀⠘⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⢱⢄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣇⡀⠀⠀⡏⠀⠀⠀⠸⣿⣿⡇⠀ ⠀⠀⠀⠀⣸⠰⠉⠐⠢⡀⡜⠀⠀⠀⠀⡠⠊⠀⠈⡱⣶⠁⡇⠀⠀⢃⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⢀⠆⢀⠀⣈⠭⠅⡐⠔⠁⠀⠀⡀⠔⠐⣿⣰⠁⠀⠀⢸⣿⣿⣿⣄ ⠀⠀⠐⠈⢉⠋⠀⠀⢸⣫⡁⠀⢀⠀⠤⠐⠍⠀⠈⡇⠘⣿⡄⢰⠀⠀⡙⢿⣿⡇ ⠀⠀⠀⠀⢈⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣧⢸⡄⢠⢸⣌⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⡦⠄⠀⠀⠀⠤⠤⠤⠤⢀⣀⡀⠀⠀⠀⠀⣶⠒⢲⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢁⣈⡇⠀⠀⠀⠀⠀⣤⡤⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣜⣏⣉⣳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠸⡏⢀⣱⠀⠀⠰⣖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⣨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⢨⠷⣷⠋⢀⠷⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⡝⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣠⠋⢳⣇⠀⡸⠓⢦⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣄⠘⠿⠿⢇⣬⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⢚⡟⠧⠤⠎⠀⠀⠀⠀⠈⢿⣿⠿⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠟⠛⠛⠀⠀⣀⣘⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⣴⢺⣵⠄⠀⠀⠀⠀⣀⡀⣤⡤⠤⠒⠒⠐⠂⢲⠂⠉⡟⣇⡹⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⡠⠖⢯⣉⡋⢸⣇⣸⡇⢸⠀⠀⢠⣴⣼⣧⣤⣷⡿⡤⠇⠀ ⠀⠀⠀⢀⠴⡺⠁⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠻⣄⣀⣴⣿⣷⣿⣿⡟⠉⠉⠉⠉⢉⣽⣿⣿⣿⢸⠃⡇⠀⠀ ⠀⠀⡰⠋⢠⠃⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⡏⠈⣷⢿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣻⣿⠏⠘⡆⢀⠀⠀ ⠀⡜⠀⠀⣿⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⢹⠀⠈⠓⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢸⠀⠀ ⢸⠁⠀⠀⠘⣄⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣿⠼⢤⠀ ⢸⣆⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⠉⠓⠲⢏⣧⠤⠤⠤⠼⠔⠒⠒⠊⠉⠉⠉⠀⢀⡜⠀ ⠈⢿⣦⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠦⣄⠀⠀⣇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⡿⠀⠀ ⠀⠈⠣⣼⠓⡾⡄⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⢣⠀⠘⢆⡿⢶⣖⠒⣦⠤⡤⢤⠖⠒⢶⣲⠏⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠓⠚⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⠉⠋⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣠⣬⣴⣦⣤⣄⣀⣀⣀⣀⣄⠀⠀⠀⢀⣹⡤⠤⠤⠤⠤⠄⣀⡀⠀⠩⠶⠴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢲⢄⠀⠀⠀⠀⣀⣠⡤⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⡄⣤⡞⢉⢀⠀⠀⠀⠀⡌⠐⢄⠀⡐⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⣾⡀⠈⡹⠀⡆⢼⠄⡆⠀⠀⢥⢈⠀⢪⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⢷⣾⡇⠀⠀⣼⢰⣇⠀⢀⠸⡄⡆⠇⡗⠁⠀⠀ ⠀⠀⠀⠀⠀⢀⣘⠄⡺⡇⢸⢻⣿⣿⠋⠀⢸⣿⣓⢧⡄⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⡏⠷⡇⢠⠈⠛⠋⠀⠀⠘⠻⠋⢰⢹⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡇⠰⢷⢸⢆⠀⠀⠀⠀⠀⠀⢀⡼⡀⠀⠀⠀⠀ ⠀⠀⠠⡟⢴⠋⠀⢻⣥⣼⣶⣽⠳⡤⢄⡠⣤⠒⣏⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⣿⣿⢏⠉⠉⠑⢝⢚⠔⠙⢿⣷⠿⡁⠀⠀⠀⠀ ⢀⠀⠀⠰⡌⠁⢼⣿⠃⢀⠡⡘⢷⣌⣿⠀⠈⡄⢻⣄⠀⠀⠀⠀⠀ ⣨⡄⢄⣀⠁⢰⣾⡟⣉⡀⠣⡗⠎⠡⣿⠀⠀⡧⠬⣯⡀⠀⢀⠀⠀ ⠀⠁⠈⠁⠂⠈⣏⢀⢀⣀⠱⠋⢀⠔⠉⠳⡀⠓⠀⠉⡃⢤⠊⠀⠀ ⠠⠠⠒⠒⠂⡼⡕⣺⠁⠀⢀⠔⠁⠀⠀⠀⢨⣴⠶⣶⣃⡴⠉⢀⠀ ⠀⠀⠀⠠⢴⢙⠏⠛⣦⠐⢁⠀⠀⠀⠀⠀⠸⠃⠀⣿⢩⠋⠐⠂⠀ ⢀⠀⠀⢰⣿⠸⠀⡰⠟⠄⣈⠃⢤⣀⣀⣀⡜⠀⡸⢸⣸⢆⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠀⠀⠀⠀⠄⢀⣀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⣡⣴⣶⣤⣀⣀⣀⣠⣤⣶⣦⡉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⣴⣾⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣶⣤⡀⠈⠳⢤⠀⠀⠀⠀⠀⠀⢠⠀⠀ ⠀⠀⠀⠀⠈⡆⠀⠀⠀⡴⠁⢀⣤⠾⠋⠁⠀⠉⠉⢀⡄⠀⠀⠀⠀⠀⢄⠀⠀⠈⠙⠻⣶⣄⠀⠑⣄⠀⠀⠀⠀⡆⠀⠀ ⠀⠀⠀⠀⠀⠱⡀⢀⠞⠀⣰⠟⠁⢀⠎⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠹⣷⡄⠈⢳⡀⢀⡰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⢤⡾⠁⠀⢠⠃⠀⠀⢀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡀⠀⢈⢻⣦⠤⠗⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡠⢀⠇⠀⠀⢀⡞⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠘⡄⠈⡄⠹⡄⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠃⢸⠀⠀⠀⣼⠋⢹⡟⠀⡀⠀⠀⠀⠀⡏⠁⢺⣷⠀⢠⠀⠀⢹⠀⢱⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠢⣀⠀⠀⠑⣾⠃⠀⡸⠀⡏⠀⠀⢰⡏⠀⡞⠇⠀⡇⠀⠀⠀⠀⡇⠀⣼⠠⡇⠈⡆⠀⠈⡇⠸⡀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠨⠓⠢⠤⣼⠀⠀⡇⢠⡇⠀⠀⣿⡇⢀⠇⢣⠀⣧⠀⠀⠀⠀⡇⠀⣿⠀⢸⠀⣿⡀⠀⢣⠀⡇⠀⢿⣇⣀⠠⡄⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠰⠃⢸⡇⠀⣸⣿⣷⣾⣶⣾⡄⣿⡄⠀⠀⢠⣷⣴⣿⣀⣈⣆⣏⣇⠀⢸⠀⡇⠀⢸⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇⢸⡿⠿⢿⠛⣿⣿⣿⠛⠓⠊⠙⠒⠢⠜⠛⠻⡛⢻⣿⣿⣿⠿⢦⣸⢀⠇⠀⣾⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⢀⣿⠀⠀⢇⠘⡄⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⠀⠘⡟⢸⠀⢀⡿⠄⠀⠀⢠⠁ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢶⠃⠀⠻⣿⡟⢋⣹⠃⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⣩⡟⠀⠰⣧⠇⠀⡸⠀⠀⠀⠀⠘⠂ ⠤⠀⠀⣀⡠⠤⢚⣿⠀⠀⠘⡄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢠⠋⠀⢠⡗⠤⣄⣀⠀⠀⠀ ⠀⠀⠀⡼⠀⠀⢸⠈⡆⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⢀⡞⢧⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⣧⢠⡆⠸⠀⣿⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⠀⡼⠀⢸⢸⠀⣀⣼⡄⠀ ⠀⠀⠀⠻⣄⢹⡆⠀⠀⢧⠀⠀⢸⣷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡎⢠⠃⢰⠃⠀⡇⠀⠈⠀⡼⠁⠀ ⠀⠀⠀⠀⠈⠓⢻⣄⣤⠈⡆⢰⠀⣿⡀⣹⠓⠢⠤⣀⣀⣀⣀⣀⣀⣀⠤⠴⠚⣹⣯⠃⡞⢀⠏⠀⡼⣁⣴⠶⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⣿⣿⣷⣇⢸⠀⣿⣿⣿⠀⠲⢄⡀⠀⠉⢧⠟⠁⠀⠀⢀⡴⢻⣿⠀⡇⣼⣤⣾⣿⣏⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢾⡇⢻⡃⠈⠢⡀⠀⠉⠐⠂⠀⠒⠐⠂⠉⠁⢀⣾⡇⣸⣷⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⠟⣧⢸⠁⠀⠀⠈⠢⢄⣀⣀⣀⠀⠀⢀⣠⠞⠁⠘⣧⡟⠿⠀⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠃⠀⠿⣿⠀⠀⠀⠀⠀⠀⣸⠯⣀⡩⢿⡏⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢻⣿⣿⣿⠿⣦⡀⠀ ⠀⠀⠀⣾⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⠉⠢⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣾⣿⣧⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⡿⠌⠳⠦⢄⣀⡀⠀⠀⠀⠀⠀⣿⠑⣄⣀⢼⡇⠀⠀⠀⠀⠀⠀⣀⣀⠤⢺⣁⡼⣿⣿⣿⣿⡟⠀

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⠀⠀⠀⠀⠀⠀⣸⣒⠀⠉⠉⠉⠀⠀⠀⠀⠉⣁⣀⣒⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢩⠀⣀⣤⣴⠶⠾⠟⠛⠛⠛⠛⠛⠻⠿⢶⣤⣉⠂⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡻⠛⠉⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣦⠀⠀ ⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡠⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠙⢦⣄ ⠀⠀⠀⠠⠂⠀⠀⢀⠀⣰⠁⢀⣾⠁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈ ⠀⠀⠰⠁⠀⠀⠀⡄⢀⡇⠀⣼⠇⠀⠀⠀⡀⠀⠸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⢀⠇⠀⠀⠀⠀⡇⢸⠇⣰⡋⠀⠀⠀⠀⠀⡗⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⡇⢸⣿⡿⢷⣶⣶⡦⢤⣨⢷⡁⠀⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⡽⡀⣼⣿⣿⣿⣷⣦⡀⠉⠲⢦⣄⡀⡌⡌⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠸⠁⠀⠀⠈⠉⠛⠷⠚⠀⠀⠀⠀⠈⠉⠛⢣⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠷⣴⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣗⡹⢻⡆ ⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣾⠘ ⠀⠀⠀⠀⠀⠈⡀⠸⡀⠀⠀⠀⠀⠀⠈⠛⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢸⠸ ⡆⢠⠀⠀⠀⠀⡇⠀⡷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣀⣀⣀⣀⣀⣀⢰⠁⢸⠀ ⢧⠘⡄⠀⠀⠀⢰⠀⠃⠈⠀⢄⠀⠀⠀⠀⠀⠀⠠⡓⠤⠈⣉⡉⠀⠂⠄⡁⠢⢆ ⢸⡀⢁⠀⠀⠀⠀⠇⢸⠦⡀⡀⠁⢢⣀⠀⠀⠀⣀⠉⠦⢀⡀⠈⠑⠠⢀⡀⠉⠀ ⢨⢧⠈⡄⠀⠀⠀⠸⡘⡀⠀⠈⠢⣜⠙⠳⡎⡇⠀⠀⠀⢸⠈⠑⠤⡀⠀⠀⠀⠀ ⣪⡿⡆⠰⡀⠀⠀⠀⠱⡃⠀⠀⠀⠈⠆⠀⠉⣇⠀⠀⠀⠸⡆⠤⠀⠛⠒⠀⠀⠀ ⠀⠀⢻⡀⢱⠀⠀⠀⠀⢱⠠⠤⢀⣀⢀⣴⠤⠿⠦⠤⢬⣶⣤⣴⢖⣒⣢⣤⣀⡀ ⠀⠀⠀⢣⡀⢣⠀⠀⠀⠠⢂⠀⣼⠀⠀⠉⠁⠒⠚⠖⢒⠂⠀⣉⣭⣉⡒⠤⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢳⠀⠀⠀⠀⢀⣠⣤⠴⠒⠛⠛⠋⠙⠻⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡇⠀⣠⣾⡟⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠈⠑⢄⠀⠀⠀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⠇⠀⠈⠺⣯⠏⠀⢸⠃⢀⠀⠀⡈⠀⠀⠀⠀⢸⠀⠠⠀⠑⣤⠊⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⣿⣇⠀⠀⠀⣼⠀⠀⡌⠠⢺⡗⠀⡇⢠⠀⠀⢠⠶⡧⠤⡇⠀⡏⢆⠀⠀⡸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⣾⡇⠀⢠⠃⠀⣾⠀⢰⡇⢸⠀⠀⢸⡀⣷⠀⢡⠀⠀⢸⣦⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡟⢻⣿⠃⠀⢸⣰⣀⣿⣤⣾⡇⣼⠀⠀⢸⣦⣽⡄⢸⠀⠀⢨⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣠⠃⢺⣿⡆⠀⢸⠿⣿⣿⣿⣽⠉⠉⠉⠉⢹⣿⣿⣻⠾⣆⣀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠯⢥⡴⡿⣸⡇⠀⠈⠀⢿⡛⣿⡟⠀⠀⠀⠀⢻⣿⣿⣿⠃⢸⡿⣤⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⢻⠻⣧⠀⢠⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⣼⢹⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⣆⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠆⠀⣀⣀⠸⣿⡄⢸⠁⢹⡇⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇⡘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣟⣡⣼⠒⠀⠀⠈⢻⣾⣤⣸⣿⣾⣶⣿⠿⣶⠤⣄⣀⣀⣠⡤⠖⢋⠇⣾⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⢰⣿⣿⣿⣿⠿⢿⠿⠿⣦⠘⢦⣠⡟⢉⣿⣷⣤⣾⣞⣿⣠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢘⣿⣿⡟⢏⡀⠀⠀⠀⠀⠳⣼⢸⡥⠋⠀⠈⠻⣿⣿⡿⠿⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣄⠘⠃⠀⣼⣿⣿⡟⠀⠀⠑⣄⠀⢾⣷⡀⠘⡶⡇⠀⠀⠐⡄⠸⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⣿⠀⠀⠀⣻⣿⣿⣀⣀⠀⣆⠘⡇⠀⢹⣿⠶⣿⡇⠀⠀⠀⣧⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⢐⣀⠀⢴⣀⠀⠀⠀⢠⣾⣿⣾⠃⠀⠀⠉⠙⢦⣇⢣⠏⠀⢍⣾⡇⠀⠀⠀⣿⡤⠤⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀ ⠙⠿⠤⠘⠿⠋⠁⡠⠈⢿⣿⠋⠁⠉⠉⠑⠦⣀⣣⠎⠀⠀⢀⡼⢿⣄⠀⠀⣇⣀⡀⠽⢿⡟⠀⠀⢀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣧⡤⣤⢤⣀⣀⠤⠚⠁⠀⢠⠞⠁⠀⠀⠙⢦⡰⡏⠀⠀⠀⠀⡇⠠⢚⡁⠀⠀⠀⠀ ⢀⣀⣀⡤⢶⠤⠤⠐⢲⡟⠿⢤⡾⠋⠁⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢹⣀⡤⠴⢶⣶⡇⠀⢠⠏⠁⠀⠀⠀ ⠉⠀⠈⠀⠀⠀⠀⠐⣾⣰⣧⣤⣧⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠉⢸⣿⣧⣾⣟⡀⠀⠠⠖⠀ ⠀⠀⠀⠀⠀⠀⠤⣼⠡⢻⠏⠙⠛⣳⡤⠚⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣸⣿⡙⣽⠋⠀⠐⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⠃⡟⠀⠀⢠⡟⣇⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠟⣿⣷⣯⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⣸⣿⡿⢠⠇⠀⢠⠏⠹⠈⠲⣤⣀⡈⠙⠲⣦⢤⣀⣀⡤⢴⡏⠀⠀⡞⠂⢹⣿⡏⢧⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠲⠿⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠙⠛⠒⠤⢤⣀⣀⠀⠀⠀⢻⣁⡠⢽⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⣀⡤⣷⠀⠀⠀⠀⠀⠀⠀⣶⡶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢴⣦⣳⣀⣀⣹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⠃⠀⠸⡄⠀⠀⠀⣶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣀⢈⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠉⣳⣼⣧⠞⠉⠹⣄⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣈⠻⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⠁⢨⡿⣆⣰⠋⠉⢳⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣦⣤⣄⡀⠀⢸⣿⣿⣿⡇⠘⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣏⠀⢸⠧⣀⢀⡾⠈⠉⣷⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠛⠛⠛⢡⣶⣺⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⣺⠛⠦⣤⡼⠃⠀⠀⠀⠀⠀⠈⠿⣿⣿⠿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⠾⠿⠛⠛⠛⠛⠋⠀⠀⠀⠀⠈⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⣠⡴⣒⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠤⠤⠴⠲⣶⠒⠒⣶⢻⡉⢹⢯⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⡗⠛⠛⠁⠀⣠⡴⠒⢶⠒⢺⡏⠉⣟⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣘⡗⠋⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⡦⣼⠀⣾⣧⣴⣿⣄⣸⣀⣀⣀⣸⣿⣷⣿⣷⣶⠿⣿⠛⡏⠉⠀⠀ ⠀⠀⠀⠀⣠⠞⡹⠁⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠹⠦⢤⣤⣶⡿⢿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⢰⣦⣿⣿⣿⣿⠀⡏⠀⡇⠀⠀⠀ ⠀⠀⣠⠞⠁⣸⠁⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡇⠀⠀⠈⡇⠉⣷⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⣷⡿⠀⢷⡀⣧⠀⠀⠀ ⠀⡴⠃⠀⢰⡇⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣇⠀⠀⠀⡇⠀⠙⠷⣍⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢈⡇⢸⠀⠀⠀ ⣸⠃⠀⠀⠸⡇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡗⢸⡆⠀⠀ ⡏⠀⠀⠀⠀⠹⣄⡀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢿⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣹⡿⠚⠓⣶⠀ ⣿⡀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣼⠉⠛⠲⢼⣁⣷⠤⠤⠤⠤⠬⠥⠤⠔⠒⠚⠋⠉⠀⠀⠀⠀⠀⣰⠃⠀ ⢿⣷⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⡀⠀⠀⠈⣧⠀⢸⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇⠀⠀ ⠈⢿⡟⠳⣤⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠙⢦⡀⠀⠹⣆⠘⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠚⠉⠁⠈⠉⠀⠀⠀ ⠀⠀⠙⠾⣇⡈⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠙⠦⠏⠙⠽⣏⣉⡿⢋⡩⠟⠻⡍⠉⠉⢿⢥⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠚⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣢⣤⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠛⣦⣄⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠋⠉⠉⠉⠉⠙⠓⠒⠒⠒⠒⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡂⠀⠀⠀⠀⠀⠀⠉⠐⠲⢦⣤⣀⠀⠀⠀⠀⠀⠌⢡⠇⠀⠀ ⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⣀⡴⠺⣿⡿⠟⠛⢿⣷⣶⠦⢤⣀⠀⠀⠈⠳⣝⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠁⠀⠸⡀⠀⠀⢀⡴⠊⡁⠀⠀⠀⡄⠀⠀⠀⠉⠁⠀⠀⠈⠙⢦⣄⠀⠈⢷⣌⠳⡆⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠈⠢⣴⢋⠄⡜⠀⠀⠀⡰⠀⠀⠀⠀⢠⠀⠀⠀⠀⡄⠈⠛⢿⣶⣾⣿⠟⠀⠀⠀⡆⠀⡆ ⠀⡇⠀⠀⠀⠀⡰⠁⡌⢰⠁⠀⠀⢀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡀⠀⠀⢻⠉⠀⠀⠀⠀⢀⠇⠀⡇ ⠀⠙⡄⠀⠀⢠⠁⠸⠀⡏⡠⠄⠒⢾⢠⠀⠀⠀⠀⠀⡇⠀⠤⣀⠀⠇⠀⠀⠈⡆⠀⠀⠀⢀⠎⠀⡰⠁ ⠀⠀⠘⠢⢀⡏⢀⡇⢰⠇⠀⢠⠂⡇⠘⠀⠀⠀⠀⡀⣧⠀⠀⡏⠁⢸⠀⠀⠀⢱⣀⣀⠤⠚⠀⠀⡀⠀ ⠀⡀⠀⠀⢨⢁⠚⠀⢸⠀⠀⡸⢀⡇⡆⠀⠀⠀⠀⡂⢻⡀⠀⡇⠀⠸⠀⠀⠀⠸⡅⠀⠀⠀⠓⠚⡅⠀ ⠀⠘⠢⣤⡾⢸⢸⠀⣸⠀⠀⡇⢸⡇⡇⠀⠀⠀⠀⡇⢸⣇⠀⢳⢠⠀⡇⠀⠀⡀⣷⣄⠀⣀⡠⠚⢀⡀ ⠀⠀⠀⠀⡇⣿⢸⡀⣿⣤⣤⣷⣼⣇⣣⣀⣀⢀⣤⣿⣼⣹⣄⣘⣯⡆⡇⠀⠀⣧⣇⡼⢭⡅⠀⢰⠉⠀ ⠀⠀⠀⠀⠇⣿⡀⢷⡟⢿⣽⣿⣿⣿⠁⠀⠀⠀⠀⠈⢿⣽⣿⣿⣿⣿⡇⠀⢠⣿⡟⠀⠀⠙⡄⠀⡆⠀ ⠀⠀⠀⠀⠸⡟⣇⠀⡇⠀⠹⠯⠿⠟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⠟⠁⡇⠀⢸⣿⢿⠀⢸⡀⢱⠀⢹⠀ ⠀⠀⠀⠀⢠⠇⣿⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠇⡜⠀⣸⠇⢸⡀⠘⡄ ⠀⠀⠀⠀⢸⠀⢸⣼⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡿⢺⡇⡰⠋⠀⣼⠃⠀⡇ ⠀⠀⠀⠀⠈⠳⣦⣿⣦⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡆⣴⡇⣾⠟⠀⣀⠜⠁⣠⠞⠀ ⠀⠀⠀⠀⠀⢀⡾⣧⣸⣏⣻⢿⡿⠲⡆⠤⠤⣠⡤⠤⠔⣒⡋⢻⡛⣿⣴⣿⣿⣿⣿⣍⠀⠀⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣁⣁⠤⠛⠀⠈⠉⢙⣷⣤⡀⠈⣀⡤⠖⠁⣸⣇⢸⣿⠁⠿⣿⣿⣿⣿⡇⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⡳⢮⣷⣤⣖⣨⡵⢾⠃⢑⢦⣅⣠⣤⡴⠞⠉⡼⣉⢿⢣⠀⠙⢿⣿⣿⣅⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⢠⣎⠵⣏⡈⠋⠁⣸⣯⠹⣄⣾⣏⠹⣼⠟⠁⠀⣰⠁⠀⠙⢆⠱⢀⣾⣿⣿⣿⣿⠀⠑⠀⠀ ⠀⠀⢀⢠⡏⠀⣩⡿⠀⠀⠀⣳⡳⠀⠘⡇⢸⣾⣿⡀⣀⣰⣧⣴⢆⡀⠈⢧⡇⠻⢿⣿⣿⣟⡀⠀⠀⠀ ⠀⠀⣼⠸⡇⠀⣼⠁⠀⠀⠀⢲⣄⠀⢠⠇⠚⠁⠀⠈⠢⣀⠹⣦⢄⣹⢄⡈⣿⠀⢠⣿⣿⣿⣿⣧⠀⢢ ⠀⢸⠀⠦⠉⢺⣿⠤⠤⠤⠤⢼⡟⢷⠋⠀⠀⠀⠉⠑⠢⡹⣷⠸⣷⡝⢦⡈⣿⡇⠘⣿⣿⣿⣿⠟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠂⠀⠀⠀⠀⠀⠈⠈⠉⠐⠢⠴⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠⠄⠀⠀⠀ ⠀⠀⠀⡴⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣶⣶⣶⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠙⠪⣝⠶⣄⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠀ ⠀⢀⡜⠁⠀⡌⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠹⠛⠋⠁⠀⠈⠛⠿⣿⠏⠈⠉⠓⠦⣤⡀⠀⠀⠈⠳⣌⠙⢦⡀⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠘⣄⠀⠀⠀⣠⡼⠋⢠⠄⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢻⢦⣀⡀⠀⢹⣗⣄⢹⡇⠀⠀⠀⡄⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠈⠳⢦⡾⢋⡄⢠⠏⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢰⡀⠈⠛⢝⢿⣷⠾⣿⡾⠋⠀⠀⠀⠀⡇⠀⠀⡇ ⢸⡀⠀⠀⠀⠀⠀⢀⡞⠉⡼⢀⡞⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⢿⠊⠁⠀⠀⠀⠀⠀⢀⡇⠀⢀⡇ ⠀⢧⠀⠀⠀⠀⠀⡞⠀⣸⠁⣸⠃⠀⢀⣀⣀⡏⢀⠀⠀⠀⠀⠀⠀⢣⣀⣀⠀⠀⠀⠈⡆⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡼⠀⠀⡾⠀ ⠀⠈⢣⡀⠀⠀⣸⠁⢀⡇⠀⣿⠴⠚⠉⠀⢸⠃⣾⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⡶⣄⠀⢳⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡞⠀⠀⡰⠁⠀ ⠀⠀⠀⠉⠲⢤⡏⠀⣼⠀⢸⠇⠀⠀⢸⠃⣼⠀⡏⠀⠀⠀⠀⠀⡄⢸⡇⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⢸⣇⣀⡤⠖⠋⢀⠀⠀⡇⠀⠀ ⠀⡀⠀⠀⠀⢸⠁⡜⣿⠀⢸⠀⠀⠀⡎⠀⣿⢰⡇⠀⠀⠀⠀⠀⡇⠸⣷⠀⠀⢳⠀⠀⠈⡇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⠒⠒⣱⠀⠀ ⠀⠻⣄⠀⢀⡿⢸⠀⡇⠀⣸⠀⠀⢀⡇⠀⣿⢸⡇⠀⠀⠀⠀⠀⡇⠀⡿⡄⠀⢸⡄⡀⠀⡇⠀⠀⠀⡀⢹⣆⡀⠀⠀⠀⢀⡴⠁⠀⡀ ⠀⠀⠀⠙⢻⡇⣾⠀⡇⠀⣿⠀⠀⠸⡇⠀⣿⢸⡇⠀⠀⠀⠀⠀⣷⡀⢣⢷⠀⠀⣷⣹⡀⢹⠀⠀⠀⡇⢸⠒⠭⠴⠖⠚⠉⢀⡤⠞⠁ ⠀⠀⠀⠀⢸⡇⣿⠀⣧⡀⣿⣷⣶⣶⣿⣶⣿⣆⡷⠦⠤⠤⠤⠿⠿⣿⣿⣾⣷⣤⣼⣷⡇⢸⠀⠀⠀⡇⣟⣸⠋⠛⢾⡀⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⠈⡇⣿⡆⠙⢿⠉⠿⣧⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣯⣼⣿⣿⣿⣿⡟⣿⠀⠀⢠⣧⣿⡃⠀⢄⠀⢱⡀⠀⢧⠀⠀ ⠀⠀⠀⠀⠀⢷⣻⢻⠀⠘⡇⠀⠘⢿⣟⣻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⢿⣽⠟⠃⣿⠀⠀⢸⣿⡟⡇⠀⠘⡆⠀⣇⠀⠸⡄⠀ ⠀⠀⠀⠀⠀⢀⡇⢸⣧⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⡏⠀⠀⢸⣟⠁⡇⠀⢀⣿⠀⢿⠀⠀⣧⠀ ⠀⠀⠀⠀⠀⣼⠀⢸⡝⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣈⣼⠁⢀⣼⠏⠀⡇⡆⠀⢹⠀ ⠀⠀⠀⠀⠀⢿⡀⠀⣿⣷⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⡟⢉⡿⢠⠞⠁⠀⢠⡿⠁⠀⣼⠀ ⠀⠀⠀⠀⠀⠈⠻⢷⣾⣿⣆⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡼⢀⣾⠁⣼⡷⠋⠀⣀⡴⠋⠀⣠⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⢹⡟⢿⣿⣿⣿⠶⣦⢄⣀⣀⡀⠀⣀⣀⣀⡠⠴⠒⠻⣿⢿⣷⣇⣿⣿⣼⣿⣷⣞⡉⠁⠀⡠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠩⠏⠑⣻⠎⠁⠘⠛⠲⣾⣄⠀⠀⠉⠒⠉⠀⢀⡤⠛⢳⣴⠛⢠⣿⡏⣿⣿⣿⣿⣿⣿⣿⡆⠀⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣖⠦⢖⡋⠁⠀⢀⣂⡠⠄⣼⡿⣕⠢⠤⠤⠔⠒⠋⠀⣀⣼⠿⡤⣿⣿⣀⠈⠹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣍⣛⠷⣝⡶⣚⣥⠶⠞⢛⡟⠀⢨⡓⣶⣤⠴⣶⣶⠟⠋⠀⣸⠧⣄⡻⠘⣆⠀⠉⢛⣿⣿⣿⣦⣄⠀⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣎⣥⣖⣃⠨⠛⠁⠀⣸⣯⡉⢧⡀⣶⣗⠉⢧⣸⡿⠃⠀⠀⢠⠇⠀⠀⠙⢦⡈⢆⠀⣾⣿⣿⣿⣿⣿⡇⠀⠙⡄⠀⠀ ⠀⠀⠀⠀⣠⠟⠉⠒⣲⡏⠀⠀⠀⠸⣕⢯⡁⠈⢻⡙⠈⣧⢔⣿⠁⠀⠀⢠⣏⣀⣠⠀⠀⠀⢳⡘⡌⢻⣿⣿⣿⣿⣿⠇⠀⠀⠁⠀⠀ ⠀⠀⢸⡆⣿⠀⠀⢚⡽⠃⠀⠀⠀⢐⣚⠳⠁⠀⠀⣇⢠⡿⠟⠛⠳⣔⠛⠛⢿⣖⠊⠹⢦⡀⠀⢳⢳⠀⠉⢛⣿⣿⣿⣷⣦⡄⠀⢄⠀ ⠀⢠⠿⠃⢹⡄⠀⣼⠁⠀⠀⠀⠀⠀⢸⣿⣄⠀⡖⠉⠈⠀⢀⣀⣀⠈⠳⣤⡈⢿⣯⠲⣄⠟⠦⣘⣎⡆⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠇ ⠀⢘⠈⠓⡄⠉⢻⣽⡗⠲⠤⠤⠤⠤⢿⡯⢻⡟⠁⠀⠀⠀⠀⠀⠈⠙⠦⡹⣿⠄⡿⣷⣬⠳⣔⠈⡟⣿⠀⠘⣿⣿⣿⣿⣿⠟⠀⠀⠀

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⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢖⣩⣾⠟⠛⠉⠉⠙⣿⡿⠛⠉⠁⠈⠉⠛⢿⣿⡿⠋⠉⠉⠛⠿⣷⣦⡄⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣹⣳⠿⠋⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢁⡤⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⠟⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⡄⠠⡄⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠏⠀⠀⠀⠀⡀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⢧⠀⢳⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡜⠀⡀⠀⠀⢰⠇⠀⢀⢼⠀⢀⡇⠀⠀⠠⠄⠀⠀⡄⠀⠀⠀⣇⠀⢸⠀⢸⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⡇⣼⠁⠀⢀⣿⠶⠒⠚⡏⠀⢸⠀⠀⠀⠐⡃⠀⠀⡏⠉⠉⠓⣿⢤⡀⡇⠈⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⡏⠀⠐⢱⡟⠀⠀⢸⡇⠀⡎⠀⠀⠀⠈⠁⠀⠀⣇⠀⠀⠀⣿⠀⠙⡇⠀⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⢸⢠⡇⠀⠀⢸⡇⠀⠀⣼⡇⠀⡇⠀⠀⠀⢰⡀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢹⠀⣿⠀⠀⠀⠀⠀⣿⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠛⢺⣿⠀⡀⢸⢸⡁⠀⠀⢸⠀⠀⠀⡿⡇⠀⡇⠀⠀⠀⠸⡇⠀⠀⣿⡀⠀⠀⢸⡀⠀⢸⡆⣿⠀⠀⠀⠀⠀⡿⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⢸⠃⢸⠀⡇⠀⠀⢸⣧⣤⢴⣷⣧⢀⣷⡀⠀⠀⢠⣷⠀⠀⣿⡷⠒⠂⢸⣇⠀⠘⡇⣹⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢰⣿⢸⠀⢸⣶⣿⢶⣶⣿⣿⣿⣿⣷⣾⣿⣍⠉⠉⠉⠉⠉⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⢸⠇⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠴⠃⣿⢸⠀⠀⠘⣿⡌⢿⠙⣤⣸⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣿⣿⣿⣿⡗⢹⡇⡿⠀⠀⠀⠀⣼⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢸⠀⠀⠀⣿⡇⠈⠃⢿⡿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠿⣿⣿⠇⠀⠀⡇⠀⠀⠀⠈⣿⡄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⡄⠀⣿⡇⠀⠀⠀⠙⠲⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁⠀⠀⢰⠁⠀⠀⠀⣸⠁⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⠀⡦⠀⢿⡇⠀⣠⣤⢶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠒⠀⡟⢠⣿⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢦⠀⢸⡇⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢰⠂⢠⣣⡞⠀⡇⠀⠀⠀⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠸⠀⣸⠋⠀⠀⢹⡄⠀⢰⣿⡇⠀⣇⡆⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⠀⢸⠀⠀⢻⣽⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢀⡄⠀⡏⠀⠀⠀⠀⢱⡀⢸⣿⡇⢠⢿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡄⢸⡇⠀⠘⣿⡀⠈⠓⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣻⠂⢸⡇⢰⣇⠀⠀⠀⠀⠀⠃⢨⡟⣅⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠸⣇⠀⠀⣿⢧⡀⢳⣄⠘⢿⡍⠙⠲⠶⡶⠤⠴⣶⠶⠖⠒⠋⠉⠁⣿⣿⡏⠀⣸⠀⣿⠈⠳⣄⡀⠀⠀⠀⣸⢀⣾⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡄⠀⠙⡇⠙⠾⢿⣝⡂⠙⢦⣄⣸⣧⣴⢾⡟⠀⠀⠀⠀⣀⣼⠟⣹⡇⢠⣿⣰⠷⠦⣤⣀⣉⣓⣶⣶⣷⣿⣿⢿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢾⢿⡀⠀⢧⠀⠀⠀⣀⡹⠗⠛⢫⣀⣾⠃⠘⠧⠤⠴⠞⠋⢁⣠⢼⡻⡇⢰⡇⣻⠓⠦⢤⣀⢸⣿⣿⣿⣿⣿⣿⣾⡷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣇⢳⡀⠸⡆⣠⠞⠉⠀⡀⠀⠀⠙⢿⡦⢤⣤⣤⠤⠴⢚⣫⠵⠊⠁⣇⢸⣇⣸⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣙⣲⣿⣧⣤⣤⣴⣁⡀⠀⠀⠈⠳⢤⣤⡤⠴⠚⠉⠁⠀⠀⠀⢻⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⣛⡛⡁⠀⠀⠀⠀⠀⣯⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠈⢿⣿⣿⣯⠉⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣡⠞⠋⠀⠀⢰⣀⣀⣀⣀⠀⣿⠀⠀⠀⠀⠈⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡞⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⣠⡞⠁⠀⠀⠀⢠⡟⠁⠀⠀⠉⠛⠛⠦⣤⣀⠀⠀⡏⠈⢻⣤⠀⠀⠀⢰⣟⣛⣓⣲⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣰⠏⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢮⣇⠀⠈⣿⣧⠀⠀⠈⠓⠒⠒⠜⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢰⠃⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣸⣿⣷⠀⠀⠀⠀⠀⠀⢸⣷⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠆⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠉⠐⠶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄⣀⠠⡾⢦⡀⣿⣹⣷⠀⠀⠀⠀⠀⠘⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡝⠻⣝⣦⠻⣿⣷⣟⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⡶⠟⠉⠉⢙⠉⠀⠈⠛⠉⠉⠙⢶⣄⠀⠈⠢⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠄⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⢀⠀⠙⡆⠀⠀⠰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡌⡌⠀⢠⢀⡸⢠⠀⢀⠀⠀⣀⡀⡄⡀⠀⢸⠀⠀⠀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢀⢳⠀⣹⠀⡆⡀⠀⠈⠀⡄⠀⡍⠃⡇⠀⠀⡇⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⢈⢿⠌⢻⠀⣣⣀⣇⣇⠀⢰⠀⣇⠀⡇⢰⡃⠀⠀⠁⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠮⢺⡇⢻⡾⢟⣻⣿⠃⠈⠁⠙⣿⣿⣿⠻⡇⠀⢰⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⡇⠈⠫⠟⠀⠀⠀⠀⠙⠉⠋⠀⡁⠀⡌⡄⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠝⢃⠀⣣⢀⠀ ⠀⠀⠀⠤⠤⠤⠤⠀⡇⡄⢻⠢⢀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢠⢘⠀⠈⠆⣿⣸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢡⢃⠸⡣⢦⠝⢅⢲⣀⡖⠀⢉⡽⡇⡄⣏⣂⣄⣀⣵⣅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢆⢃⡠⠚⠉⠲⡅⣁⠨⡕⠞⠇⣟⠁⠒⠻⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡶⠛⠓⠚⡒⠠⢀⠀⠁⠀⠀⠘⠋⢀⠀⠀⠈⢻⣿⣳ ⠀⠀⠀⠀⠀⠀⢀⢞⠕⠁⢀⠆⠁⠒⠣⢄⡸⠑⣄⠀⢶⣦⣼⠈⠀⠀⠀⠸⣿⣿ ⠀⠀⠀⠀⠀⢀⠃⠈⠀⢠⠃⠀⠀⢀⠀⠀⠈⠢⢿⡆⠀⠀⢸⡄⠀⠀⠀⠀⣿⣷ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠀⠀⠀⠀⠈⠰⡤⣖⢼⣷⠀⠀⢸⠃⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⣀⡤⢤⡄⠒⠲⠲⠖⠒⠂⠀⠀⠒⠲⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣉⡠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣬⣉⡛⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣤⣶⣾⣿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⣿⣷⣦⣄⣈⣑⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⡶⠃⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣠⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢀⠄⠀⢰⠇⠀⠀⢰⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⠀⠀⢀⢷⣿⠁⠀⢀⡀⠀⠀⠀⠀⠆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⡟⠀⠀⡼⡎⠀⠀⠀⠈⠉⠉⠒⠲⢼⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⡇⠀⣠⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡧⣼⣿⣿⣄⣀⣀⣀⣀⡀⠀⠀⠀⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⠿⠿⣷⣶⣿⣟⣛⢓⣶⠴⠟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡹⡏⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠐⠫⢟⣲⢤⣀⡀⠀⠀⢀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢻⣎⠙⠓⠚⠿⠿⣿⣿⡿⣽⣟⠛⢿⡷⠀⠀⠀⠀⠉⠒⠭⣗⠦⣼⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡌⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣾⣿⣷⣀⠀⣠⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣧⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⢿⣷⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡏⢣⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⢿⣥⣿⣿⣷⡶⠛⣿⢿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣇⡇⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢥⡜⠁⢠⢷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⢨⢯⢀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸⠈⢸ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢺⠀⢸ ⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠸⡄⠀ ⣧⠀⠸⡄⠀⠀⠀⠀⠀⠀⢳⠀⠀⢿⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠦⠶⣒⣤⣤⣤⣤⠤⠤⠤⠤⠯⣀⠀⠀⡇⠀ ⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡆⠀⠸⡄⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠷⢦⣀⡀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠈⠓⠤⣳⠀ ⠸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⣇⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠈⠉⠛⠒⠲⠤⣄⠀⠀⠀⠉⠓⠤⠤⣈⠑ ⠀⣷⠀⠈⡆⠀⠀⠀⠀⠀⠀⠸⣧⠀⣟⠳⣄⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⣀⣠⠽⠶⣄⣀⠀⠀⠀⠀⠙⠲⢄⣀⠀⠀⠀⠀⠀ ⠀⣿⣆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠹⡄⢸⠀⠈⠉⠉⠳⣄⠀⢨⠟⢿⣲⢦⠴⢶⠋⠉⠀⠀⠀⠀⠀⡎⠙⠳⣤⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀ ⠀⡟⣿⡀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢷⠸⡇⠀⠀⠀⠀⠉⠳⢿⠤⠀⠈⢻⡄⢸⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⢺⡙⣽⣧⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⣇⢳⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⠙⣞⡄⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⣤⣼⣮⡵⠶⠀⠀⠀⠀⠀ ⠶⠛⠩⢻⡄⠀⠸⡄⠀⠀⠀⠀⠀⠀⠘⣾⡀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⣹⢣⠀⠀⠀⠀⣆⡈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⣿⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠘⡗⠦⠤⣤⣀⠀⠀⠀⢐⣦⠶⢤⡿⠿⡗⠦⢤⣤⡬⠵⣶⡶⣶⣶⣶⣒⡒⠒⡿⢤⣤⣀⠀⠀ ⠀⠀⠀⠀⠘⣷⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢀⠈⡏⠉⠑⠛⠛⠷⠤⣄⣀⣘⣆⣀⣀⣉⣉⠭⠭⠽⠶⠶⠿⠟⣛⡛⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠘⣧⠀⢈⣷⡄⠀⠀⠀⠀⠀⢇⢷⠀⠘⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⢉⣁⠤⠔⢂⣀⣀⣒⣒⣂⣐⡛⠛⠖⣢⣄⣀

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⡀⠐⠲⡤⡀⠀⠐⠐⠀⠀ ⠠⠁⠠⡀⢀⠔⡊⠀⢉⠀⠀⠙⠁⠈⠑⣄⡈⢢⣑⠂⠀⠀⠀ ⢀⠀⠀⢨⢣⢲⠀⠀⡄⠀⠀⢰⠀⠀⢡⠀⠙⡛⠁⠀⢠⠀⡇ ⠈⠆⡀⠆⡆⡆⠂⢩⠰⠀⠀⠰⠀⢲⠄⡄⠀⠃⠀⡀⠂⠐⠀ ⠠⠀⢸⡜⠀⠃⢸⢸⡄⠀⠀⡂⡇⢸⠀⠇⠀⠸⡁⠀⠐⡀⠀ ⠀⠈⡇⡿⠰⣄⣸⣼⡃⢀⢀⣧⣟⣀⣦⢰⠀⣠⡸⢶⠈⡔⠁ ⠀⠀⢠⢇⢹⠙⢿⣿⠀⠀⠀⠈⢿⣿⡿⠻⠀⣿⡅⢄⠃⢠⠀ ⠀⠀⢰⢸⡆⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢠⣣⠃⡜⢸⠀⡄ ⠀⠀⠘⢦⣷⣷⣄⡀⠀⠀⠀⠀⠀⢀⣠⡇⣼⣸⢊⡠⢊⠔⠁ ⠀⠀⠀⣎⢗⠻⠋⠫⣏⡀⠒⣀⠝⣢⢫⡟⢿⣿⣷⡄⠅⠀⠀ ⠀⠀⠀⢵⡯⠶⠜⠷⡃⡴⡅⡶⠂⠱⠩⡓⡈⢻⣿⣤⠠⡀⠀ ⠀⠀⡌⠡⡏⠀⠸⡃⠹⢹⡾⢃⠠⣅⠄⠈⢴⠻⢿⣿⣁⠀⠀ ⠀⠣⠣⣼⠀⠀⢸⢧⠌⠁⠐⠠⢱⡜⣗⢇⢺⡆⢾⣿⣿⠆⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⣂⠇⠀⠀⠀⡤⠍⠁⠀⠀⠀⠀⠀⠉⠐⠂⠤⣕⡀⡀⠀ ⠀⠀⠀⠀⠰⣢⣧⠘⣄⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡇⠀ ⠀⠀⠀⠀⠀⠁⢉⡦⡠⠁⡆⠀⠀⢰⣶⠀⠀⢠⣶⡿⣿⣿⡶⠘⠛⣼⠄ ⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠀⢠⡶⠆⠁⣀⣀⠈⡭⠅⠀⠀⡆⠒⣠⡋⠀ ⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⢈⣾⣼⣶⠧⠧⠴⣾⣿⣞⠻⠀⠀ ⠠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⠻⠿⠟⠀⠀⠀⠛⠛⠁⡄⠀⠀ ⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⣄⡀⠀⠀⠀⠀⠀⠀⡀⠴⠇⢠⠀ ⢷⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠉⠀⠁⠁⠀⠈⠀⠀⠀⡀⠠⠆⠀ ⠈⠒⠍⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠤⠦⠐⡆⠀⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⠥⠦⠤⠤⠤⠤⠀⠀⠀⠧⠤⠤⠤⠤⠤⠵⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⡄⡀⠒⢢⠀⡍⠁⠶⠤⢄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠐⢨⡏⠀⢠⠘⠀⡇⠀⠀⣆⢹⡄⠀⠀⠐⡀⠉⠄⠂⡤⢈⠐⠠⠀⠀ ⠀⢠⢺⡇⠂⢈⣇⣐⣺⡇⠦⠿⠤⠤⠼⠄⣞⣄⣣⠀⢱⡀⢮⡄⢳⡄⠈⠁⠀⠠ ⣤⡞⡀⢸⢴⢟⣝⣿⣯⡁⠀⠀⠀⠀⠀⠈⡉⣻⣿⡛⢶⣧⣸⣦⠸⡷⡀⠀⠀⠀ ⢯⣀⡇⠾⠉⠸⡿⠿⠟⡇⠀⠀⠀⠀⠀⠀⡿⣯⡿⣿⠀⠰⠀⠀⠀⢧⠱⡠⠀⠀ ⡂⠉⡀⢠⠀⠀⢁⠂⠈⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠃⠀⠀⡆⠀⠀⢸⡄⠹⣄⠀ ⠀⠐⡇⡌⠀⠀⠁⠀⢀⡤⢶⣒⢾⣖⡒⠤⣀⠀⠀⠀⠀⠀⢡⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⢧⢃⠀⠀⠀⠀⡿⢇⢈⣏⠌⠀⠈⠙⠺⣦⠀⠀⠀⠀⢈⢸⠀⠀⡇⠀⠀⠀ ⠀⠀⠘⡤⠑⣄⠀⠈⣅⣈⠖⢡⠃⠀⠀⠀⠀⠈⡆⠀⠀⡠⡊⡾⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠱⠡⣵⢻⡲⠊⣀⢔⡁⠀⠀⠀⢀⣀⣜⡤⠒⠉⢣⡬⡇⡆⢸⡇⣀⣀⡴ ⠀⠀⣀⡜⡵⢀⠋⠀⠀⠀⠐⣃⠉⢏⠀⡠⠒⠁⠀⠠⢂⠌⠈⢳⠇⣸⣿⣿⣿⣶ ⡐⡡⠀⣇⢧⠂⠀⠀⠀⠀⠈⢌⠀⠀⡏⠀⠀⠀⠀⡠⠊⠀⠀⠘⠈⠙⢿⣿⣿⣿ ⠗⠀⠀⠜⡀⢂⠀⠀⠀⡠⢾⠀⠑⡤⡤⢤⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿ ⠀⠀⠁⠀⠘⢞⢉⣱⣮⣒⢭⣷⡀⡧⠊⠣⣸⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⠹⣺⣿ ⠀⠀⠀⠀⢀⣼⠀⠀⠀⣿⡡⡑⠿⡗⠄⠔⠹⡆⠀⠀⠤⠤⠐⡂⠭⠱⠡⠁⡤⠩

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⢄⡀⠀⣠⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠣⣄⠀⠀⡠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣩⠿⢅⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣳⣞⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠞⠁⠀⠀⢙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡴⠁⠈⢳⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣲⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡛⠙⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⡟⠛⡇⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡇⠀⡇⠀⡇⠈⠿⠄⢹⠁⠈⡏⠉⡏⠀⡏⠀⢸⠀⢸⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡇⠀⡇⠀⡇⠀⢸⠀⠀⡇⠀⡇⠀⣇⠀⢸⠀⣸⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡇⠀⡇⠀⢸⠀⠀⡇⠀⡇⠀⢹⠀⢸⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣄⣿⠀⢸⠀⠀⡇⠀⡇⠀⣸⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣷⣼⣄⣤⣷⣴⣷⣾⣿⣿⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠐⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆ ⠀⢻⣿⡇⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣽⣿⡇ ⠀⢸⣿⡇⠀⢸⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⠃ ⠀⢸⣿⣧⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡟⠀ ⠀⠀⣿⣿⡀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⣼⣿⠇⠀ ⠀⠀⢹⣿⣧⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⢠⣿⣿⠀⠀ ⠀⠀⠈⢿⣿⡆⠀⠸⣿⣷⡀⠀⠀⣶⣶⣶⣶⣶⣦⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡟⠀⢀⣿⣿⠇⠀⠀ ⠀⠀⠀⠈⣿⣿⡄⠀⠹⣿⣷⡀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣿⡟⠀⠀⣾⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣄⠀⠸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⢀⣾⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠀⠙⣿⣿⣦⡀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠟⠁⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠻⣿⣿⣦⡀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⠟⠁⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣦⡀⠀⠙⢿⣿⣶⣄⠀⠀⠀⠀⣴⣿⣿⠟⠁⢀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⠀⠙⠻⣿⣷⣤⡀⠀⠙⠋⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄⡀⠈⠙⢿⣿⣷⣄⠀⠀⠘⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣦⣀⠀⠉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠙⢿⣿⣷⣄⡀⠈⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⢀⣤⣾⣿⠿⢿⣿⣦⣄⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⣀⣴⣿⡿⠛⠁⠀⠀⠙⠿⣿⣷⣄⡀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⣠⣾⣿⣿⣡⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠈⠻⢿⣿⣦⡀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⣠⣾⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠟⠁⠀⠀⠀⠙⣿⣿⣆⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠏⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠘⢿⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⠏⠀⣠⣿⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠈⢻⣿⣦⠀⠈⢿⣿⡆⠀⠀⠀ ⠀⠀⠀⣼⣿⠏⠀⢠⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⢻⣿⣇⠀⠘⣿⣿⡄⠀⠀ ⠀⠀⣸⣿⡿⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠸⣿⣿⠀⠀ ⠀⠀⣿⣿⠁⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⢿⣿⡆⠀ ⠀⢸⣿⡟⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⣿⣧⠀ ⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣷⠀⠈⣿⣿⡀ ⠀⣾⣿⠇⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡇ ⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠿⡄⢀⡄⠀⢀⠾⡟⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠉⠀⢳⡾⣿⣠⠋⢰⡿⠻⠇⠀⢀⣠⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡏⠀⠀⠀⠃⠸⠁⠀⠘⢁⡴⠗⠊⢹⣿⠏⠤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠠⣶⣤⣾⣀⠤⣤⡾⠁⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠋⠀⠀⠐⠓⠒⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⠉⠉⠁⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠⢀⡀⠈⠉⠉⠉⢐⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⡁⠀⠀⠀⠉⣑⠆⠀⠀⠀⣰⠀⠀⠀⢹⣷⠿⣄⠢⡔⠚⢋⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠁⠀⠠⠴⣎⠀⢠⠀⢀⣼⣿⡆⣧⠀⠸⣯⢑⣦⣤⣝⣦⣤⣙⣝⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⢀⣴⠿⣾⣇⣶⣾⣿⣿⣿⣿⣷⡀⣿⣿⡿⡿⣿⣿⣿⣏⢻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⣀⣴⣿⡿⠿⠿⠛⢿⣿⣟⣿⣿⣿⣏⣀⣤⣿⣿⡟⢿⣣⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣠⠟⠉⣽⣿⠿⠦⠤⠴⠖⠋⠀⠛⠀⠛⠃⠀⠀⠀⠀⠀⢷⣾⣿⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⡏⠀⠀⠙⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⢸⣏⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡟⠀⢸⣤⣼⡳⠀⠀⠀⠀⠀⢀⠤⠒⠉⣉⣙⣿⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⢻⣶⣾⣿⣿⠿⠀⠀⠀⠀⠰⣏⣀⣀⡀⠀⠐⠛⠀⠀⣰⣫⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢩⡿⢍⣿⣿⠀⣄⠀⠀⠀⠀⠀⠤⠂⠀⠐⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢻⣺⣿⠻⣦⣤⣀⠀⠀⠀⠀⣀⣴⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢻⣇⠹⡝⢿⣿⣿⣾⣿⣿⠻⢫⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣀⠘⣄⠉⢿⣿⣿⡏⠀⣸⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠈⠱⢌⠓⠦⢍⠀⣠⠞⠁⠸⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⢁⡇⠀⠀⠀⣱⡀⠀⣿⢷⡄⠀⠀⢹⠀⠹⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⡟⠀⢸⡇⠀⠀⣰⠻⡇⠀⠛⠇⠙⣆⠀⠘⡆⠀⠹⡟⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣾⠟⢋⠃⠀⠈⣷⠀⣴⡟⠀⣿⡀⠀⠃⠰⠿⠳⡀⣧⠀⠀⢹⡀⠀⠉⠛⠻⠶⣄⡀⠀⠀⠀ ⣾⠿⠛⠁⠀⢸⠀⢀⣠⣿⡾⡉⢇⠀⠹⣿⣾⠁⠀⠀⠀⠈⢻⣶⣤⣤⣇⠀⠀⠀⠀⠀⠀⠈⠑⣆⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡿⡏⠀⠑⠈⠁⢀⣿⠁⠀⠀⠀⠀⠀⢈⠙⣟⠻⢟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄

⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀ ⢠⣾⣿⣄⠀⠀⠀⣀⣠⣴⡶⠟⠛⠛⠷⣦⣤⣾⠿⠛⠛⠛⠻⢶⣾⣿⠻⣷⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠀⠀⠀⣠⣶⡿⠛⢻⣿⠁ ⢾⡇⠈⠛⠛⠛⠻⠛⠉⢁⠀⠀⠀⠀⢀⣿⡿⠓⣦⣀⠀⠀⠀⠀⢻⣿⣷⡟⠀⠀⠀⠀⢀⣀⣴⣿⠟⣿⠀⢀⣼⣿⡥⠀⠀⣸⡟⠀ ⠸⣿⣄⠀⣿⣿⣿⣿⣿⡍⠉⠉⠛⠙⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠋⣉⡉⠉⠙⠙⠋⠉⠀⠀⣿⣠⠾⠛⠉⠀⢀⣴⡿⠁⠀ ⠀⣨⣿⠟⠛⠛⣻⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⠿⡿⠿⣟⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣶⡀⠀⠀⣿⣧⡀⢀⢰⡞⡿⡷⣶⡄⠀ ⢰⣿⠁⠀⢠⡾⣿⢹⠈⣿⣿⡇⠀⠀⠀⢸⠀⢀⣾⣿⣻⡻⣷⡄⠀⠀⠀⠀⡇⠀⠀⢈⡽⠿⣿⣦⠀⢻⠈⣿⣻⣸⣇⡇⡇⡿⣿⡀ ⠈⠿⣶⣾⣿⡇⣿⢸⣾⣿⣿⡇⠀⠀⠀⢸⠀⢸⠟⠉⣹⣷⠁⢹⣄⡀⠀⢰⡇⢀⣶⣏⡀⠀⠘⣿⣧⣸⠀⠙⠿⠛⠛⠻⣧⡇⣿⣿ ⠀⠀⠀⣸⡇⣷⣿⡟⠁⣿⣿⡇⠀⠀⠀⢸⠀⠀⢀⡴⠟⠁⢠⡾⠋⢹⣄⣾⣠⣟⣩⡷⠿⠂⠀⠘⣿⣿⠀⠀⠀⠀⣀⢀⣸⣧⡿⠐ ⠀⠀⠀⣿⡇⣿⠋⠀⠀⣿⣿⡇⠀⠀⠀⢸⠀⣰⠋⠀⠀⠐⠋⠀⢀⣼⣿⣿⠟⠋⠀⠀⠀⠀⢰⠀⢻⣿⠀⠀⠀⠀⠙⠻⣟⠋⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⠀⣷⡄⠀⢀⣤⡴⢾⢻⡟⣿⡅⠀⠀⣸⣿⠃⠀⢸⡄⢸⣿⡀⠀⠀⣠⡤⠿⢿⣶⡄⠀ ⠀⣤⣤⣀⠹⢿⣷⣤⡴⣿⣿⡇⠀⠀⠀⢸⠿⠿⣿⣇⣾⣧⣧⠼⠼⠿⣿⠇⢀⣾⢟⡿⠀⠀⢸⣷⡀⠉⠀⠀⣼⠋⠈⣼⠛⠛⢿⣄ ⠀⠹⣿⢻⣧⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣆⣀⣀⣉⣉⣁⣀⣀⣠⡤⠬⠶⠛⠁⣸⠁⠀⠀⠀⢿⡻⣦⣀⠀⡇⠀⠀⢷⡀⠀⠾⢻ ⠀⠀⢸⠨⣿⡀⢀⡴⠛⣿⣿⡇⠀⠀⠀⢠⣴⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢻⣿⡉⠻⣷⠀⠀⠈⠻⣦⡀⠈ ⠀⢠⣿⠀⣿⣷⣫⣴⣿⣿⣿⡇⠀⠀⠀⢸⢻⣿⣿⡏⠋⠙⠛⠛⠻⣿⣷⡄⠀⣼⠁⠀⠀⣠⣴⢶⢺⠻⡗⡶⡼⣧⠀⠀⠀⠘⣷⠀ ⠀⣼⠏⢀⣿⡟⡇⣿⣿⣿⣿⡇⠀⠀⠀⢸⠛⠻⣼⣿⠀⠀⠀⠀⠀⠈⢿⣿⢠⡏⠀⢀⣾⣿⣸⣼⣸⠀⡇⡇⡇⣿⢹⣦⣀⣰⡿⠐ ⢠⡏⠀⣼⡏⣇⣿⡟⠉⣿⣿⡇⠀⠀⠀⢸⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡾⠁⠀⢼⡟⠉⠉⠉⠻⢼⣧⡇⡇⣿⢼⣸⣿⡇⠀⠀ ⢸⡇⣰⣿⣇⣿⠟⠀⠀⣿⣿⡇⠀⠀⠀⢸⠀⠰⠟⢁⡠⠶⠶⢦⣄⠀⢸⣿⠇⢶⣄⠘⣧⡀⠐⢶⣦⡀⠙⢻⣧⠿⠟⠃⠈⡇⠀⠀ ⠈⠻⣿⠟⠛⢁⣤⠾⠛⣿⣿⡇⠀⠀⠀⢸⣷⣤⢠⡟⠀⠀⠀⠀⠈⠳⢦⣄⣀⣼⢻⠀⠈⠉⠁⠀⣿⢳⡀⠀⡇⠀⣴⠓⢷⠇⠀⠀ ⠀⢸⣿⠀⣴⠏⢀⣠⣤⣿⣿⡇⠀⠀⠀⢸⠈⠱⣿⣷⡄⠀⠀⢠⣤⣀⣀⣀⣀⣴⠏⠀⠀⠀⠀⣠⠏⢨⡇⢠⠇⢸⡇⣠⡟⠀⠀⠀ ⠀⢸⣏⣸⣧⡾⡟⡿⠋⣿⣿⡇⠀⠀⠀⢸⠀⡸⠋⠉⠻⢷⣴⣄⡈⠉⠉⠙⠛⠷⠶⠶⠶⠶⠟⠉⢀⣾⢁⠟⣠⣿⡼⠋⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⢹⢿⡿⠀⣿⣿⠇⠀⠀⠀⢸⠀⠹⡄⠀⠀⠈⣷⣞⣿⣿⠶⠶⢦⡄⠀⢀⣀⣀⣀⣴⣾⠿⠿⢾⠿⣯⣀⠀⠀⠀⠀⠀ ⠀⢀⣽⣿⣿⢸⠀⡿⣴⣿⣿⠀⠀⠀⠀⠘⢷⡀⠙⠳⢤⣀⠀⠙⢿⣽⢻⠶⡞⣷⢠⢀⡍⡭⡹⣸⢠⣣⣾⣾⣴⣴⣮⣿⣆⠀⠀⠀ ⢰⣿⠛⢻⣿⣾⣶⣿⣿⣟⣁⣀⣀⣀⣀⣀⣀⣙⣳⣤⣤⣈⡻⢦⡀⢻⣿⣾⣱⢃⠏⣼⣺⣷⡷⠿⠿⠿⠿⢿⣟⠛⠓⢮⡙⣷⡀⠀ ⠈⣿⣦⣼⣿⣿⡿⡿⣿⡿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⠿⠿⠿⠈⡇⢸⡟⠛⠷⢿⣾⡿⠧⠿⠞⠛⡿⣿⠉⠛⡎⣧⠀⠀⡿⣸⡇⠀ ⢰⣿⣯⣤⣉⡻⢷⣧⣿⣷⣿⣇⣀⣠⣤⡞⠁⠀⠀⠹⣦⣤⣤⣾⣡⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡻⢤⣤⣣⢿⣛⣛⣡⣿⠇⠀ ⠘⠋⠉⠉⠛⠻⠿⠛⠛⠛⠉⠛⠛⡋⠉⠀⠀⠀⠀⠀⠈⡛⠿⢟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡻⠛⠋⠈⠛⠛⠋⠀⠀⠀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢰⡶⠶⣦⡀⠀⢀⣶⣦⠀⠀⢰⣶⡄⠀⣶⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠀⠀⢸⣧⣤⣿⡃⠀⣼⠇⢻⡆⠀⢸⡏⢿⡄⣿⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⢸⣇⣀⣹⡗⣰⡿⠶⠾⣿⡄⢸⡇⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠁⠀⠀⠈⠁⠈⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢸ ⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠ ⠉⠉⠉⠉⣽⠏⣽⡿⣻⣿⣯⡍⣉⠉⣉⣽⠿⠿⠿⡫⣷⣩⣭⣍⠺⣏⠉⠉⠉⠁ ⠀⠀⠀⠀⡟⢰⣿⠗⣉⠤⠄⠈⠽⢿⣩⠤⢒⡶⠖⣚⣛⣛⣟⣿⣆⢱⡄⠀⠀⠀ ⠀⠀⠀⠀⡇⢸⡇⠘⠁⢀⡤⡲⡿⣿⣖⠒⢥⠔⢫⣿⣟⣷⠈⢻⡾⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⠸⡇⠐⠒⢵⡊⠀⣷⣻⣾⣧⠾⠤⠬⠿⠛⢛⣿⣿⡇⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⣧⢠⠔⢒⣚⠛⠯⠭⠤⠤⠤⠤⠖⣒⣊⡭⢴⣿⠃⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⢿⡈⠑⠲⠭⠭⢭⣉⣉⣉⣉⡭⠭⠭⠴⢖⡟⠁⣀⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠈⢻⡶⢤⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠚⠋⣷⡞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣿⣦⣰⠇⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣂⠀⠀⠀⠀⠀

⠀⠀⠀⢠⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣤⣤⣶⣾⣿⣿⣿⡷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⡀⠁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢹⠉⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢃⠈⠢⡁⠒⠄⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⣠⡀⢀⣴⣾⡇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⣳⡾⢻⣷⠯⠽⠿⠯⣉⣩⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⡽⠷⠛⠀⠀⠀⠀⢤⡤⠟⠋⣜⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⣶⡌⠃⠀⠠⠞⣿⣍⡓⢦⡀⢣⣀⡰⣿⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣇⣇⡀⠀⠰⢋⣈⡏⠙⣧⠱⠀⠉⠛⡹⢸⡈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣖⠛⠋⠉⠉⠓⢧⡀⣿⣄⢀⡿⠀⠀⠀⠀⠀⢨⡿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⠀⠀⠰⠄⠀⠀⠈⠉⠉⠋⠀⠀⠀⠀⠀⠀⡸⠙⣎⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢏⠑⠢⡀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⣶⣧⣤⡿⢀⣀⣤⢿⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠦⠬⣑⣒⣒⡯⠴⠦⡤⠤⠤⠖⠀⠀⠏⠹⣾⣫⠭⠭⠴⠚⠙⣌⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⣿⠲⣄⣽⡉⣹⣷⡶⢦⣼⣀⡀⠘⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡖⠀⠀⣿⡀⡘⢯⠻⡟⠁⠙⢆⠉⠉⠉⢳⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊⠀⠀⠀⢸⢸⣿⣸⠀⢯⠉⠒⢌⣧⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢾⣾⠿⠃⠀⠈⣿⠟⠉⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⢦⡀⠀⠀⠀⢀⡴⠒⠋⠙⡿⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣏⡒⣄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡇⢀⠙⢦⠀⢰⠏⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⡟⠛⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⡏⢦⣈⣇⣟⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⢆⢸⡄⠀⠀⠀⠀⠀⠀⠀ ⠻⠞⣇⠈⠹⣄⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣷⠼⠃⠀⡼⣸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⢻⣮⡳⢿⣄⠀⠀⠀⠀⠀⠀⢀⣠⠔⠃⠀⠀⡖⠒⠲⡽⠁⠀⠀⢠⡧⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⡄⠉⢾⣴⢮⠉⠛⠒⠒⠒⣉⠉⠀⢸⡟⠲⡄⢸⠷⠞⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠉⠛⠰⢯⣙⡆⢰⣇⣙⡆⠸⠓⠊⠉⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⢤⣄⣀⣀⣀⣤⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠶⡶⡶⣶⣶⣷⢶⣷⣶⠞⣻⠶⢶⣶⡶⡠⡀⠀⡐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⣂⣭⣭⣀⣀⣥⣥⡐⠢⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⢀⠔⢁⡴⠚⠛⠛⡋⠉⠉⠙⠛⠛⠳⣤⡁⢂⠀⠀⠀⠂⠀ ⠀⠀⠀⠰⣠⠂⡔⠉⡔⠁⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠹⣄⠑⣀⠔⠀⠀ ⠀⠀⠀⠀⠀⠍⠀⡘⠀⢀⠃⡄⠀⠀⠀⡀⢸⡀⠀⠐⡀⡌⢏⠀⠀⠀⠀ ⠂⠀⠀⢄⡜⠀⠁⠇⠀⡞⢸⡏⡆⠀⠀⡏⢩⢣⢰⠀⢡⢰⠘⡄⠀⠀⠀ ⠀⠈⠒⠠⡇⢸⢰⠀⢸⡇⡄⠆⣇⠀⠀⡇⢸⠈⡀⡇⠘⠀⠀⠷⠤⢀⠀ ⠀⠀⠀⠀⡄⢠⢸⢤⡾⣿⣿⠷⠍⠤⠤⠿⠿⢶⣷⣾⣄⢀⠀⡆⠀⠀⡆ ⠀⠀⠀⠰⠃⠘⣘⠀⣿⣿⢿⠇⠀⠀⠀⠀⢿⣯⡿⡇⢸⡘⢀⠓⠀⠀⠀ ⠀⠀⡠⠤⣺⠀⠰⠀⠈⠑⠉⠀⠀⠀⠀⠀⠈⠑⠊⠀⡘⠁⣜⠤⢀⠀⠀ ⠀⠀⡇⡄⡇⡆⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠰⢸⠀⢀⡆⠀ ⠀⠀⠣⣱⡀⠘⡀⡘⡖⢄⡀⠀⠀⠀⠀⠀⠀⣀⣔⢡⢁⠃⡈⢀⡡⠃⠀ ⠀⠀⠀⢠⣻⣷⡇⡇⣷⣾⠠⢉⠀⠢⠖⠈⣁⠔⡿⠀⣬⣴⣗⣯⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣟⢇⠻⠈⠢⡀⠉⠀⠀⠉⡀⠐⡇⣿⠻⣿⣿⣿⠀⠀⠀ ⠀⠀⣰⣾⣿⣿⠃⠸⠇⠀⠀⠀⣹⢉⠕⡏⠀⠀⠻⠄⠀⠈⢿⣿⣳⣄⠀ ⠀⠀⢿⣿⣿⣟⠤⢀⣀⠀⠀⠀⣿⢅⣑⡅⠀⠀⠀⢀⣀⢤⣺⣿⣿⡿⠀