Kanna Kamui Text Art

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

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

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

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

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

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

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

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

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

⣴⣿⠟⠉⠀⠀⠀⠀⠀⡀⠀⡏⠀⣠⠤⠄⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⣿⣿⣿⣿⣷⡀⠀⠀⡠⠖⠛⢥⠖⢠⠀⠀ ⠟⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⣧⠊⠘⡀⠀⠀⠀⠘⡇⠀⠀⠀⢀⣤⠒⠒⠤⢄⡀⠀⢠⠎⠀⣈⡿⣿⣿⣿⣷⡄⠀⠀⢀⡠⠊⠀⠈⠡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⡀⠀⢁⠀⠀⠀⠀⠈⠒⠤⠤⣼⠋⠀⠀⠀⠀⢉⣶⠎⡤⠊⠁⠀⠈⠻⣿⣿⣷⡤⠔⠉⢀⠠⠄⠔⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠑⠤⣸⡄⠀⠀⠀⣀⠤⠒⠈⡁⠀⠀⠀⠀⠀⠛⢤⣸⡟⠑⢤⡀⠀⠀⠈⢻⣿⣷⡤⠂⠀⠀⠀⢸⡆⠀ ⠀⠀⠀⠀⠀⣀⠔⠊⠉⡇⠀⢀⡠⠔⠉⠀⢀⡠⠊⠀⣄⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠙⣆⣀⡀⠀⠻⣿⡆⠀⠀⣴⣿⣾⠏⠀ ⠀⠀⢀⡠⠚⡇⠀⠀⠀⠉⠉⠁⢠⡀⠀⡴⠋⠀⠀⠀⢸⠳⡀⠀⠘⣏⠢⡀⠀⠀⠀⠀⠈⢣⡀⠀⢇⠁⠀⠀⢀⢿⣧⠀⠚⣇⣰⣿⠀⠀ ⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠱⡚⡄⠀⢳⡀⠀⠈⣇⠘⢄⠀⠸⡆⠙⢦⡀⠀⠀⠀⠀⠱⡀⠀⠑⢄⣸⡵⢄⣿⡀⠀⠈⢿⣿⠀⠀ ⠀⠀⠀⠈⠒⡷⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⣆⢸⣧⠀⠀⢹⠀⠈⠣⡀⢳⠀⠀⠉⠢⣄⣤⣤⣤⡵⣄⢢⠀⠉⠀⠈⠿⢇⠀⡀⠈⢻⣀⣀ ⠄⠀⠀⡠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⢮⡟⢇⠀⠈⡇⠀⠀⠑⣌⣇⣠⣴⣿⣿⠿⢿⣻⡇⠈⠳⣇⠀⠀⠀⠀⢸⠀⢳⡀⠀⠱⡀ ⠀⠁⠈⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡇⠈⡆⠀⢣⠀⢀⣤⣿⣿⣿⣿⣿⣀⣤⡀⠈⠓⢤⣀⠈⠲⢄⠀⠀⢰⠀⠈⣿⡖⠤⢀ ⠀⠀⠀⠀⢸⣇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡈⠘⡄⢸⣰⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣧⢀⠘⣆⠉⠒⠒⡭⠒⢼⠤⠄⣿⡇⠀⠀ ⠀⠀⠀⠀⢸⡟⡆⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢱⣸⣿⣿⣿⣿⣿⠛⢅⢠⠀⠀⣿⡿⠋⠀⢼⡄⠀⢠⠁⠀⢸⠀⠀⣿⠃⠀⠀ ⠀⠀⠀⠀⢸⡇⠘⡄⢹⠳⡀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⣿⣿⡟⣿⣿⣏⠀⠀⢉⡴⠚⠁⠀⠀⠀⠀⢷⣤⡎⠀⠀⢸⠀⠀⣷⣤⡄⠀ ⠀⠀⠀⠀⠈⣧⠀⠘⣌⡇⠱⡀⠀⠀⠀⠀⠀⠀⢘⠈⡇⠀⠸⠟⠀⠘⠿⣿⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⡘⠀⠀⣿⣯⡀⠀ ⠀⠀⣄⠀⠀⣿⠀⠀⠈⣿⣄⢙⣄⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⠀⠀⢰⠃⠀⢀⣧⡈⠑⠀ ⠀⠀⠸⣧⠀⢿⣤⣶⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢸⡇⢀⠇⠀⠀⢸⠉⠩⣷⣶ ⠀⠀⠀⢻⣦⣾⣿⣿⣿⣿⣿⣿⡿⢿⠿⣷⣄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⢸⣧⡞⠀⠀⠀⡿⠁⡴⠟⠛ ⡀⠀⠀⢸⣿⣿⡟⠁⠀⢿⣿⠁⠈⠚⢀⡽⠟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠙⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠇⢰⣥⠀⠀ ⣷⡀⠀⠀⡿⢏⡓⠂⠀⠈⠻⠷⣶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⢸⠟⠉⠀⡇⠀ ⢹⣷⡀⠀⢰⠘⣿⣦⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠀⡇⠀⠀⣿⢴⡶⠶⠀⠀ ⠀⣟⣷⡀⠸⡀⠹⡄⠙⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣣⣿⡿⠁⠀⡇⠀⢸⡇⡸⠀⠀⠀⠀ ⠀⣿⡏⢣⠀⡇⠀⢻⡀⠀⠸⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⣴⠟⣹⡿⠋⠀⠀⠀⢃⠀⡂⠁⡇⠀⠀⠀⠀ ⠀⣿⠁⠘⡆⡇⠀⠈⣧⠀⠀⢿⡇⠉⠢⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠖⣶⣿⣿⣙⣰⣰⣿⣅⡀⠀⠀⠀⠸⡄⠇⡧⠟⢹⠀⠀⠀ ⣠⠋⠀⢠⢷⣷⠀⠀⢸⡀⠀⢸⣇⠀⣀⡿⡐⠛⠛⠛⠭⢽⣿⣿⣿⣿⣿⣏⠉⠀⠀⢩⣿⠟⠛⠛⣶⡟⣆⠀⠀⠀⢻⣶⡀⣀⣀⠀⠀⠀ ⠀⠀⣀⣮⢺⢻⡆⠀⠘⡇⠀⣸⢻⡴⠃⢠⠗⠒⠒⠀⠄⠈⣿⣿⣿⣿⡟⠉⠆⠀⢀⡿⠀⠀⠀⠀⠈⡟⠋⢳⣤⣤⣾⣿⠀⠐⠉⠀⠀⠀

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

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

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⢰⠟⠀⢰⠋⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠸⡆⠀⠘⢧⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢠⡏⠀⢠⡏⠀⠀⠀⣼⡿⡀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠘⡆⢀⠀⠀⠀⢹⡀⠀⠈⣆⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣿⠀⠀⣸⠀⠀⠀⠀⣯⡇⡇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣇⠀⣧⠀⠀⠘⣧⠀⠀⠸⣇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡏⠀⢀⡇⠀⠀⠀⢠⢿⠀⡇⠀⠀⠀⠀⠀⢀⢨⡁⠀⠀⢸⡄⠸⡄⠀⠀⣿⡄⠀⠀⢻⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⣿⠇⠀⢸⡇⠀⠀⠀⣼⣼⠀⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢸⣇⠀⡇⠀⠀⠸⣇⠀⠀⠘⣧⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠠⣤⣀⠀⠀⣹⠀⠀⠀⠀⢰⡿⠀⢀⣾⠀⢰⠀⠀⣿⣿⠀⡇⠀⠀⠀⠀⠀⢐⢸⢿⠀⠀⢸⣿⠀⢸⠀⠀⠀⣿⡀⢀⠀⣿⡀⠀⠀⠀⠀⢸⣁⣀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠑⡇⠀⠀⠀⠀⢸⣷⠀⢸⣿⠀⢸⠤⠶⣿⣿⠛⡟⠀⠀⠀⠀⠀⠀⣿⣾⠀⠀⢺⣿⡙⢿⠁⠒⠢⣼⣇⢸⡄⢸⡇⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⡗⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⣾⣿⠀⡼⠀⠀⣿⠹⠀⣿⡀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡾⡇⢸⠀⠀⠀⣿⣿⠘⡇⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⢹⠿⡄⣇⠀⠀⣿⠀⡇⡿⡇⠀⠀⠀⠀⠀⢠⣿⡄⠀⢸⠃⣧⢸⡆⠀⠀⢸⣿⠀⣧⢸⠃⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣼⡷⠀⠀⠀⠀⢸⢻⠀⢸⡀⡇⢻⠀⠀⣿⣤⣷⣿⣱⡀⠀⠀⠀⢀⣿⣿⡇⠀⣼⡤⣼⣤⡇⠀⢀⣟⣘⡇⠛⢸⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠐⠚⠉⢀⣧⠀⠀⠀⠀⢸⣼⣆⣾⣷⣿⣿⣿⣿⣿⣷⣿⣿⡍⠛⠒⠒⠒⠒⠛⠉⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣄⣀⠉⠒⠀⠀⠀⠀⠀⠐ ⠀⠉⠙⠓⠒⣶⠖⠋⠉⢸⠀⠀⠀⠀⠸⣿⡇⢹⡇⣧⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣴⣿⣭⣿⣿⣿⡏⣸⠉⣿⡀⠀⠀⠀⠀⢸⡄⠈⠉⠙⢷⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⡾⠀⡼⡄⠀⠀⠀⠀⡏⡇⠀⠣⢻⡿⢿⣿⣿⡟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡿⠿⠟⠉⣿⠃⠃⠀⣼⡇⠀⠀⠀⠀⣼⣇⠀⠀⠀⠈⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡃⢸⡇⠀⢷⣧⠀⠀⠀⠀⢷⣧⠀⠀⠀⠻⢿⣀⣀⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⣤⣴⠛⠁⠀⠀⠀⣿⠁⠀⡇⠀⢀⣏⣿⠀⢀⣷⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⣅⡿⠀⠀⢸⣽⡄⠀⠀⢻⠸⣿⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⠇⠀⢸⣿⡇⠀⢸⠏⠀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡀⠀⢸⡟⣧⠀⠀⢸⡀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡟⠀⣼⠀⠀⣾⣿⠇⢠⠏⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⣧⢸⡀⠀⠀⡇⠹⣯⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢸⠇⠀⡟⠀⢠⣿⢟⣴⡿⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣧⠀⠀⢷⠀⢧⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⢸⠀⢰⠃⠀⣾⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⡆⠀⠸⡇⠸⡆⠀⠀⢹⡳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠻⣯⠀⠀⢀⡏⠀⣼⠀⢰⣿⣿⣿⡀⣻⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣄⠀⢿⡀⢳⠀⠀⠀⢳⠀⢌⠉⠓⠲⠤⣤⣀⠀⠀⢀⣀⣤⠤⠖⠚⠉⣵⢁⡼⠁⠀⠀⢸⡇⢸⡏⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⠹⡄⠈⣧⠘⣇⠀⠀⠈⢳⡈⠳⣤⡀⠀⠀⠀⠙⢯⡽⠋⠀⠀⠀⣠⠞⢁⡾⠁⠀⠀⠀⡾⠀⣿⠁⣾⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡿⠻⡄⠀⢹⡄⢸⣆⢹⡄⠀⠀⠀⠙⣦⣀⠈⠲⠠⠤⠀⠀⠀⠀⠠⠴⢋⣡⣾⡟⠀⠀⠀⠀⢰⡇⣼⠇⢸⠃⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡷⢠⡸⢦⠀⠻⡄⢹⡄⢳⡀⠀⠀⠀⠀⠻⣝⢻⠛⠻⢿⡛⣛⡿⢲⢶⣿⡵⠋⠀⠀⠀⠀⢀⡾⣸⢿⢠⡏⠀⡼⣽⢿⣿⣿⣿⣯⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⢛⣇⠈⡷⣸⠳⣄⠻⣶⣿⣾⣷⠀⠀⠀⠀⠀⠈⡇⢠⣠⠴⠚⠛⠦⣼⠛⡏⠀⠀⠀⠀⠀⠀⣼⣷⠋⣾⡿⢠⣾⣡⡀⠼⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡜⣟⣶⢧⠏⡆⠈⠳⣽⣿⣎⠻⣧⠀⠀⠀⠀⠀⡇⠘⢧⣄⠀⢀⡴⢻⠀⡇⠀⠀⠀⠀⠀⣰⡿⠃⠘⣻⠷⣫⡌⢳⣷⣼⣿⣠⣼⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣆⡸⣿⡟⢰⠃⣼⠓⢦⣉⢳⡦⣀⡀⠀⠀⠀⢀⠃⡇⢀⣨⠿⠯⣀⠀⠀⠇⠀⠀⠀⠀⠀⢉⣠⣴⠛⠁⢸⡇⠹⡌⢷⡿⠋⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⡿⠁⠀⢹⠞⢧⡸⣆⠉⠀⢠⠇⢸⠁⡆⠉⠙⠲⠦⣼⢰⣿⡉⠀⠀⠀⣠⠟⠃⢦⡤⠤⠴⠖⠛⣉⡀⢹⡀⢲⠈⢁⣴⢧⣾⣷⠊⠈⢿⣿⣿⣿⣽⣧⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠘⠶⠤⣿⣮⡛⢦⡞⢠⡏⢰⠃⣾⠉⠓⡦⡼⢸⠀⠙⣦⣴⠋⠁⠀⡄⢸⠀⣆⠀⣞⡋⠉⡇⠀⣇⠘⣶⢟⡵⢋⣸⠁⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠈⣇⣙⣲⣤⣼⠁⢸⣄⡁⠀⢠⠇⡄⢸⡠⠞⠉⠈⠙⢦⣜⡇⢣⠀⣿⠀⠛⠃⣀⡇⠀⢸⣧⠞⢫⡞⠉⠁⠀⠀⠀⠀⣟⠉⠙⢿⡿⠀⠀⠀ ⠀⠀⠀⠀⠈⣟⠀⠘⡆⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⣏⠓⠦⣬⣉⠓⠚⢀⡇⠘⠳⣄⠀⠀⠀⣠⠽⡇⢸⠀⢸⡶⠒⣋⣩⠴⢲⣿⠗⠒⠛⠀⠀⠀⠀⠀⠀⠀⡼⢠⣀⡞⠁⠀⠀⠀ ⣀⣀⣀⣀⣀⣿⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⣏⣹⣾⡇⡆⠀⠀⣙⠶⣏⡁⠀⠁⢸⡿⣏⣹⠿⠛⠒⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠙⣦⣀⣀⣀ ⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣧⠖⠋⠁⠀⠀⠉⢳⣦⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠐⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠋⠙⢤⣀⣀⡤⠞⠋⣹⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿

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

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

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

⠀⢰⢄⠀⠀⠀⠀⠀⢀⡀⣤⣀⠲⠒⠒⠒⣂⠤⠄⡀⠀⠀⠀⠈⡀⠀⠈⢂⠀⠀ ⠀⠈⠀⡀⠀⠀⣠⠲⠁⠀⠀⠙⣦⣤⣤⢴⣶⣤⣀⣀⠁⠢⢀⠀⠀⠀⠀⠀⠂⠀ ⢀⠁⠀⠇⢠⠞⠁⡀⠀⢀⠤⠒⠻⠋⠋⠉⠉⠀⠀⡝⠉⢂⡄⣱⣷⡀⠀⠀⠘⠀ ⠘⠀⠀⢰⡧⠒⠋⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢘⠔⢊⠀⠙⣿⣿⡆⠀⠀⠀ ⢀⠀⠀⠀⠑⣴⣤⠃⢀⠂⢰⡀⠤⠄⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⢊⢻⣿⠂⡜⠀ ⠘⡀⠀⠀⠀⣿⠁⠀⢸⠀⢸⠀⠀⡆⠀⠀⠀⡇⠀⢨⠀⠀⢰⠀⠘⡆⣿⠾⡇⠀ ⠀⠐⣄⣤⣾⣿⠁⠀⠀⠀⢸⠀⠀⢰⡀⠀⠀⢀⠀⢸⣤⣀⣈⡇⡄⣷⢸⠀⠐⠀ ⠀⢠⠋⠳⢯⣿⣄⠀⢠⠀⢨⣦⣤⣾⣷⠄⢰⠸⠀⢻⢿⢿⠿⣿⣾⡇⢸⡄⠀⠁ ⠀⠘⡀⠀⠈⢿⡟⠁⢸⡼⠻⠛⢛⡏⢳⠀⠉⠀⠀⢰⡀⠈⢀⠌⣾⠀⢸⡇⠀⠀ ⠀⡠⠃⣀⢴⡏⣧⠀⠀⡗⠘⠄⠀⠠⠊⠀⠀⠀⠀⠀⠈⠉⠀⠀⡿⠀⣸⡇⠀⠀ ⠀⢁⠔⠁⠼⠀⠙⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡄⢠⡷⠁⠀⠀ ⠀⠸⣸⠀⢣⠠⢦⠒⡠⡀⢗⢢⠄⣀⣀⣀⣀⣀⣀⠠⠄⢾⣷⣷⣡⡊⠄⠀⠀⠠ ⠐⢄⠈⠓⣿⣶⣿⣇⣞⠳⣌⢂⠡⣀⡀⢀⡹⠪⡀⠀⡤⠋⣰⣿⢻⠇⠈⠐⠄⠀ ⠒⠣⡁⠢⣙⣤⢬⣿⡺⠦⡄⣉⣀⣀⣈⣁⣘⣪⢤⢭⢔⢮⣿⢯⣽⢷⡄⠀⠀⠀ ⠀⠀⠹⡀⢾⢾⠻⠡⠗⢒⣛⡑⢾⡷⢼⣿⡷⢞⠛⣈⠭⠝⠊⢸⢠⣸⣤⡄⠀⠀

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

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

⡾⠋⠁⠀⠀⠀⢸⡠⠖⠂⠒⠄⠀⠀⠀⣀⡀⠀⠀⡨⠻⣿⣿⣦⠀⠐⠈⡒⠠⠀ ⠀⠀⠀⠀⠀⡀⠘⡄⠠⠀⠀⠈⠂⢀⠏⠀⠀⢁⠶⣄⠈⠈⠻⣿⣧⠐⠩⠀⢄⠀ ⠀⠀⠀⡀⠄⠃⠀⡈⠔⠀⡠⠐⡉⠀⢂⠀⠀⠈⠐⢇⠈⢠⣀⠘⢿⡎⠀⣠⣼⠂ ⠀⢠⠊⠀⠀⠈⠁⠐⣠⠊⠀⠀⢉⢂⠀⢏⢆⠀⠀⠀⢂⠘⢄⢀⣜⣗⠈⢣⣿⠀ ⠀⠀⢒⠇⠀⠀⠀⠀⠐⡥⢸⡄⠈⡄⠡⡘⡄⠑⣢⣤⣤⠦⡀⠉⠀⠻⡄⡀⠻⠀ ⠀⠐⢡⠀⠀⠀⠀⠀⠀⠈⢽⠈⡀⠃⠀⣰⣷⣿⣟⣉⠑⢇⡈⠢⡀⠀⡅⢱⡤⡑ ⠀⠀⢸⢆⢰⡀⠀⠀⠀⠀⠈⣇⠰⢰⣾⣿⣿⡿⠛⠻⣷⠄⢣⢱⠸⠁⡗⢺⡇⠀ ⠀⠀⠀⡎⢆⡷⡀⠀⠀⠀⠀⡟⠀⢻⡟⣿⣇⠈⡠⠚⠁⠀⠈⣾⠆⠀⡇⢸⡤⠀ ⠀⢀⠀⡇⠈⢲⡐⣄⠀⠀⠀⡆⠀⠈⠀⠈⠛⠁⠀⠀⠀⠀⢀⢿⠀⠠⠀⢸⡛⠄ ⠀⠘⣆⣷⣾⣿⣿⣿⣶⡄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢸⣆⠃⠀⡄⢸⣶ ⡀⠀⢿⣿⠋⢹⣏⠑⠃⠟⠂⠀⠀⠀⠀⠀⠀⢀⠠⠂⠃⠀⢀⣼⡏⠀⠀⣃⠧⠀ ⢷⡀⢸⢳⣅⡀⠉⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⢀⣾⣿⢡⠀⢰⢡⣴⠀ ⢸⡷⠀⠀⢇⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⣰⢯⡾⠃⠸⠀⠷⡄⠀⠀ ⢸⠃⠃⡆⠘⡄⠘⡎⠂⡄⣀⣀⣀⣀⣀⣤⣤⡰⢶⢋⣵⡯⣀⠀⠀⣴⠠⠓⡄⠀ ⠊⢀⣺⣧⠀⢇⢀⢧⡔⠱⠤⠌⠉⣿⣿⣿⠓⠀⢰⠏⠁⠈⡿⠢⣀⣸⡇⠐⠃⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣿⣿⡿⠿⠟⠛⠻⠿⢿⣿⣿⣿⣯⣓⠲⠦⣀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡆⠀⠀⠀⢀⡴⠞⠉⠀⠐⢋⡁⠀⠀⠀⠀⢤⡀⠀⠀⠢⡄⠈⠙⠳⣦⡈⠙⢦⡀⠀⢠⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠹⣄⢀⡴⢋⠄⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠹⣆⠀⠀⠈⠳⣄⠀⠙⣧⠏⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢩⠟⣰⠏⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⡄⠀⠀⠀⠘⣶⠛⠁⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡏⢰⠇⠀⠀⠀⠀⢀⣿⣀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢻⡀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠻⢶⣾⢠⡏⠀⠀⠀⠀⠐⢻⡟⠀⠀⠀⠀⠀⠀⠀⠈⣏⠉⠓⠦⢀⠀⣇⠀⠀⠀⠀⢻⢤⣄⡶⠂⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢦⣼⠇⡼⠀⡏⠀⠀⠀⠀⢸⠁⠀⡀⠀⠀⠀⠀⡄⠀⣿⠀⠀⠀⢸⠀⢸⠀⠀⠀⢳⡼⣆⣁⡴⠞⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⡏⠀⡇⢸⠇⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⡀⠀⡿⡆⠀⠀⠈⣆⢸⡀⠀⠀⠀⠁⣯⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡾⡀⣸⠁⢸⠀⠀⠀⣴⣀⣿⡀⢸⣿⠀⠀⠀⢀⡇⠀⣷⣇⣀⠀⠀⢻⡈⡇⠀⠀⠀⢘⣿⣷⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠛⠁⡼⠁⣷⣿⠀⢸⢀⣀⣴⣿⣿⣿⣿⣽⣿⣄⣀⣀⣸⣷⣀⣿⣿⣾⣦⣤⣼⣇⣿⠀⠀⠀⠈⣿⡀⠁⠀⠀⠈⠳⠤⣄⠀⠀⠀⣼⠁⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣾⢃⣼⡾⠹⢠⣾⡿⢿⢿⡍⢙⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⢈⡁⢈⣿⣿⣿⢻⣿⡄⠀⠀⠀⣿⡛⠶⠶⣤⠤⠶⠚⠁⠀⠀⣸⠃⠀⠀⠀⣬⡎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⠇⠀⠀⢸⡇⠀⣾⣿⣿⣿⡟⣿⡆⠀⠀⠀⠀⠀⠀⣿⡻⣿⣿⡟⢿⡇⠈⡇⠀⠀⠀⢸⡇⠀⠀⠸⡆⠀⠀⠀⠀⢠⠇⠀⠀⠀⣠⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣧⠀⠈⠻⣍⣡⣷⠟⠁⠀⠀⠀⠀⠀⠀⠙⣯⡈⠉⣽⡿⠁⠀⢻⠀⠀⠀⠘⡇⠀⡀⠀⣇⠀⠀⠀⢀⡞⠀⠀⠀⢰⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⡄⣰⠃⠀⠀⠐⠁⠀⠀⠀⠉⠉⠁⠀⠀⡀⢸⠀⠀⠀⠀⡇⠀⡇⠀⢸⠀⠀⠀⡾⠁⠀⠀⢠⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡟⢸⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⠀⢀⡀⡇⢸⡇⠀⠈⡇⠀⢰⠃⠀⠀⢀⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⢀⣀⣸⡆⠀⠈⠁⡟⣾⠁⠀⣰⠃⢀⡞⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⣇⠀⠙⣷⣄⡀⠀⠀⠀⢸⠋⠀⠀⠀⠈⠙⢿⡆⠀⢀⣠⣴⡛⠁⢹⠇⠀⠀⣸⣿⢁⣠⠞⠁⠀⣸⠃⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀ ⠠⠤⠤⢤⣤⣤⣤⣤⣤⠶⠶⠶⢶⣿⣠⡄⠀⢸⣿⣷⣤⣬⣿⣙⠓⣶⣤⣼⣷⡔⠒⠒⢀⣰⣾⡷⠖⠛⣷⠤⣽⣶⣾⠀⠀⣸⢻⣿⣯⡁⠀⠀⢀⡏⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⣿⣾⣿⣿⣿⣿⣿⠿⡄⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⢀⣿⣄⠀⠀⢸⠀⢠⡟⢾⣿⣿⡇⠀⠀⣼⠀⠀⠀⣼⣟⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⣿⣿⣿⣿⣿⡟⠁⠀⠉⠳⢦⣤⡶⢤⣀⡴⠶⠖⠞⠁⠀⠈⢦⡀⣾⠀⡾⠃⣿⣿⣿⠁⠀⢀⡟⠀⠀⢰⣿⢿⡇⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⣿⡀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⢿⡀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠉⣯⣾⣃⣾⣿⣿⣿⣿⣧⣼⠃⠀⠀⢸⣿⣸⠀⠀⠀⠀⠀⢀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢿⣿⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⡼⢸⣹⣾⢹⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⢠⣿⣿ ⠘⠓⠀⠀⢠⣤⠀⠒⠒⠚⠛⠓⠒⠛⠛⠛⣻⣿⣿⣏⣠⣤⣤⣤⣤⡤⠤⢤⣇⣸⠁⠈⢿⢸⡦⢤⣤⣤⣤⣤⣄⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣻⠀⠀⢸⡏⣿⡇⠀⠀⠀⣠⣿⣿⣿ ⠀⠀⠠⠤⠾⣯⣀⣀⣄⣀⣀⣀⣀⣀⣴⣿⣿⡿⣻⢻⣇⣄⡀⣾⣹⣠⣤⣸⠏⣷⣄⣠⢾⠹⡿⣴⡶⣦⣹⢠⣰⠶⣎⢿⢹⣿⣬⣿⣿⣿⣿⣿⣷⡀⢸⡇⢸⣇⠀⠀⣰⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⡼⢣⣟⣁⣼⢻⢧⡇⠋⣸⣿⢠⡷⠛⢧⣸⠀⡗⣿⣁⣿⢻⡎⣿⣷⣼⠘⡏⢯⠿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⣿⠀⣰⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡴⠧⠬⠥⠤⠴⠿⠬⠟⠛⠻⣿⢸⡇⠀⠀⣹⠄⣷⠤⠴⠦⠴⠷⠤⠮⢥⣄⣷⣘⣓⣿⣿⣿⣿⣿⣿⣯⣾⠀⠈⣿⣷⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠷⠛⠒⠒⠓⠒⠛⠒⠒⠒⠚⡏⢘⣑⣶⡋⠙⡇⣿⠒⠚⠒⠒⠒⠒⠒⠚⠛⠒⠛⠛⠛⢻⡟⢻⡍⠙⢿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠉⠀⠙⢦⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢻⡆⠈⢳⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⣄⠀⢀⠴⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣿⠂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣇⡨⠿⣅⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⢷⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣁⡴⠛⠟⠒⠒⠒⠶⠠⠀⠠⠄⠀⠀⠀⣀⣸⣀⡏⠀⠀⠈⠳⣇⣸⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⡀⠀⠀⢈⣧⢸⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿

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

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

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

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

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⠀⠀⠀⠀⠀⠀⠀⠀⣶⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⢆⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣤⣤⣶⣶⣶⣤⣤⢤⣀⠀⠀⠀⠀⠀⢠⠎⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣆⠀⠀⠀⣠⠖⠋⠉⢛⠉⠁⠀⠀⡀⠉⠩⣍⠙⠳⢤⡉⠢⣄⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⢄⡠⢪⠄⠀⠀⠀⡏⠀⠀⠀⠀⢹⡀⠀⠈⢦⠀⠀⠙⢄⢈⡳⠊⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⢡⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⢆⠀⠀⠈⢏⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠦⣴⢃⠇⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⣗⠒⠤⠀⠘⡀⠀⠀⠘⣄⣀⡤⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⢤⠇⡜⢰⠀⠀⠀⢰⡇⠀⠀⠀⠀⠰⠀⢾⠀⠀⠈⠀⡇⠀⠀⠣⣧⣡⠔⠋⢣⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡜⢀⠇⡘⠀⠀⡀⢸⡇⢰⡄⠀⠀⢰⠀⣸⡄⠀⠀⣇⢧⠀⠀⠀⣿⣄⠀⠀⢸⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⣤⠤⠇⡸⢱⣼⠀⡇⢀⣠⣿⣾⣷⣾⣇⠀⠀⣸⡄⣿⣿⣦⣀⣸⣾⠀⠀⠀⢾⠙⠂⠀⠘⢤⣀⡀⠀⢀⠎⠀⠀⠀⠜ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⣶⣡⣿⠛⠠⣿⠿⢻⣍⣿⣿⡏⠈⠉⠉⠉⠉⢉⣉⣹⣿⣿⢿⡇⠀⠀⢸⡗⠲⠤⡤⠒⠊⠀⠀⡞⠀⠀⢀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠀⠀⣸⠀⢸⣿⠿⢏⣿⠀⠀⠀⠀⠀⢻⡿⠿⣯⣽⠀⢱⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⡸⠁⠀⢀⣼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣿⡇⠀⠉⠓⠉⠁⡠⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⢸⡀⠀⠀⡇⢰⠀⢸⠀⠀⢠⠃⠀⠀⣼⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⡏⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⡇⢸⠀⠈⡆⢀⡎⠀⠀⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⢳⣀⠀⠀⠀⠀⣠⠶⠿⠟⢶⣄⠀⠀⠀⢀⡤⢴⡇⠀⠀⣿⠏⢀⡴⠁⣼⠀⠀⢰⣿⠁⠀⠀⠀ ⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣇⡀⠀⢸⣧⣀⣹⣗⠦⣤⣀⣿⣀⣀⡀⢀⣼⣧⠴⣾⣙⣦⣼⡇⠀⣼⣿⡖⠉⠀⢠⠇⠀⠀⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠈⣿⣿⣿⣿⣿⠿⡁⠉⠉⠛⠛⠉⠁⠀⢀⡼⡀⠀⢸⠁⢸⢿⣿⣿⠀⠀⡜⠀⠀⣸⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⣿⣿⣿⡿⠃⠀⠈⠑⣶⠖⠢⣶⠒⠉⠁⠀⠈⠢⣼⣠⠏⣼⣿⣯⣀⢠⡇⠀⢠⣿⡟⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣧⣿⣿⠏⠀⠀⠀⠀⠀⣿⢦⡜⡿⡆⠀⠀⠀⠀⠀⠻⢿⣾⣿⣿⣿⣿⣿⠀⠀⢰⣿⡇⠀⠀⠀⣠⣿ ⠐⠂⠀⢠⡄⠰⠶⠶⠶⠶⠶⠾⢿⣿⣿⣁⡀⢀⣠⡤⠤⢼⣻⠋⠹⡆⡧⠤⢄⣀⣀⣀⣀⣈⣿⣿⣿⣿⣿⣿⠀⠠⡿⣿⡇⠀⠀⣰⣿⣿ ⠀⠀⠐⠚⠧⠤⠤⠤⠤⠤⢴⣾⣿⢟⣿⡿⢦⣤⣿⣷⢦⡞⢹⣤⠔⡏⣿⣶⢲⣼⣤⣶⢦⢻⢹⣷⣿⣿⣿⣿⣷⢀⡇⢸⡇⠀⣴⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⣎⣘⣒⣛⣜⣻⣤⣾⡗⡟⠀⠱⡇⣿⣛⣛⣉⣏⣛⣟⠘⡏⠯⣿⣿⣿⣿⣿⣣⠇⠸⣧⣼⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠯⠟⠤⠒⠤⠲⠶⠤⢶⠃⣳⣤⠚⣇⣷⠶⠦⠴⠦⠴⠼⠻⠽⠻⠿⢿⠿⡏⠻⣿⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠑⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢹⡆⠘⢆⣼⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⢓⣤⠖⢡⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣿⡀⠈⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⡜⣠⠞⠖⠀⠤⠤⠤⠀⠀⠀⠀⣀⣸⣸⠋⠀⠑⢾⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣿⡄⠀⢻⣿⣿⣿⣿⣿

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

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

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

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

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

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

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

⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣸⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠂⠀⢸⠙⢦⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⣀⣤⠶⣶⣿⣭⣉⠉⠛⠉⠉⠁⠀⠀⠀⢀⣉⣩⡽⠗⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠉⠉⣧⣿⠅⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀ ⠀⠀⠀⠆⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⡴⣛⡡⠤⠒⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⣤⣤⣤⡴⢿⣿⣿⣷⣤⣤⣀⣀⣀⠀⠀⠀⠈⠛⠦⣀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⡸⠀⠀⠀⠈⡇⠀⠀⠀⢀⣴⡿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⣿⣿⣿⣿⢿⡿⠤⢽⣿⡏⠉⠉⠛⠻⣛⡿⠷⣤⣄⠀⠀⠈⠳⣄⠀⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⣧⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⢹⣿⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠉⠙⡦⡄⠀⢈⣳⣿⣏⠀⡤⠀⠀⠀⠀⠀⠀⢡⠀⠀ ⠀⡸⠀⠀⠀⠀⠀⢸⠀⣸⠃⠀⠀⢀⣤⠊⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠹⣄⠀⠀⠀⠀⣿⠳⢄⢢⡙⢯⢻⣿⢆⡀⠀⠀⠀⠀⠀⢸⡄⠀ ⠀⡇⠀⠀⠀⠀⠀⢸⣰⣧⣠⡴⠾⠛⠁⠀⠀⢀⣴⠏⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢸⣅⣠⠶⠞⠁⠀⠀⠙⢿⣮⣧⣫⣿⣿⡀⠀⠀⠀⠀⢸⡇⠀ ⢠⡇⠀⠀⠀⠀⠀⠀⢿⣹⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⠤⠤⠤⠤⡀⣆⠀⠀⠀⠀⠻⡿⣿⣿⣿⣁⡠⠀⠀⠀⢸⠇⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠼⠀⢀⡾⠃⠀⠀⢠⠟⠀⠀⣾⠀⠀⠀⢀⣅⣀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠸⡄⠀⠀⠀⢦⠹⡜⣿⣹⡻⢻⠀⠀⢀⡎⠀⠀ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⠿⠁⠀⠀⢠⣏⠀⠀⠀⣟⣤⠖⠊⠙⡏⠉⠁⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⣧⠘⠸⣿⡿⣮⠀⢠⡟⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡏⠀⠀⠀⠀⢸⡟⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⣇⠀⢻⢷⢉⣴⡿⡆⠀⠀⠀ ⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⢸⠃⠀⠀⠀⡇⠀⠀⠀⠀⢹⡄⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⣿⡄⠘⣿⡟⠋⠧⣿⠀⠀⠀ ⠀⠀⠘⣦⠀⠀⠀⠀⠀⢀⣿⣿⣿⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⣧⠀⠀⢸⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢹⣇⠀⣿⠅⠋⠀⢻⡀⠀⠀ ⠀⠀⠀⠈⢳⣠⣤⠶⣾⢿⣯⣿⡏⡇⠀⠀⠀⠀⢸⠀⢠⠀⠘⣿⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣤⣤⣀⣀⣀⣸⢿⠀⢶⠀⢸⢸⡀⢹⡄⠀⠀⠸⠑⠒⡄ ⠀⠀⠀⠀⣸⡿⣯⡋⢓⣯⣿⣿⡇⡇⠀⠀⠀⠀⢸⠀⢸⠀⢰⢿⡀⠀⠀⠀⠀⢘⣿⣆⠀⠀⠀⠀⡀⢸⣷⠀⠀⢠⣾⡿⣻⣿⣿⣿⣿⡿⣿⢦⡘⣇⢸⠈⠁⢸⡇⠀⠀⠀⠀⡴⠁ ⠀⠀⠀⢀⡏⠀⠹⢿⣿⣗⣾⣿⡇⣇⠀⠀⠀⠀⢸⠀⢰⠀⢸⡀⣇⣀⣤⣴⣿⣷⣿⣞⣦⡀⠀⠀⡗⢸⣿⠀⠀⠛⣿⣿⣿⣿⣿⡿⢿⣿⣟⣿⣿⢻⢸⠀⠀⢸⣿⠆⠒⠒⠉⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠼⢇⣿⣧⣟⣷⣀⠀⠀⢸⡀⢸⣠⣾⣿⣿⣿⣿⣷⣽⣿⣿⣟⠃⠳⣤⣀⣷⠬⠙⠀⠀⠀⠟⠉⠸⣇⢠⡇⠀⠈⢛⣿⠿⣿⡟⠀⠀⢸⢹⡀⠀⠀⠄⠀⠀ ⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢨⣿⣿⣾⠚⠋⠀⠀⠀⣧⣾⣿⢟⣿⢿⠟⢻⡟⢻⠛⠛⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠋⠀⠀⠀⣼⠁⢰⢻⠇⠀⠀⢸⡈⡇⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠑⣴⠀⠀⠀⠀⠀⢱⡿⣿⡀⠀⠀⠀⢠⣿⣿⠁⢸⡋⠀⠀⠈⠻⡾⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⠀⠀⣀⡤⠞⠁⠀⡿⡟⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣴⢿⠁⢹⣇⠀⠀⠀⠀⢸⡿⡄⠈⢿⡃⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⠀⠀⠀⢸⣇⡇⠀⠀⠀⣿⠁⡟⠀⠀⠀⠀⠀ ⠀⠀⣰⠋⢀⣀⣀⣠⠶⠊⣧⡏⠀⣸⡽⡄⠀⠀⠀⠘⡇⠀⠀⠀⠉⠒⠲⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⢀⡿⣄⡇⠀⠀⠀⠀⠀ ⠀⠸⠗⠋⠉⢀⡿⠁⠀⢸⡜⠀⠀⡇⢷⢳⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢃⡇⠀⠀⢸⢁⣿⠀⠀⠀⠠⠄⠀ ⠀⠀⠀⢀⡴⠋⣰⠀⠀⢿⠃⠀⢰⡇⠈⣇⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⡗⢸⠃⠀⢰⣿⡼⠃⠀⠀⢀⠀⠀⢄ ⠀⠀⠀⢸⡇⠀⡇⠀⠀⣿⠀⠀⠈⡇⠀⢘⣧⠰⡄⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡛⢱⣷⢣⡟⠀⢀⣾⠋⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣧⠀⣇⠀⠀⢸⣄⣀⣤⣼⣦⠎⠈⣦⠸⣄⠀⠀⢧⠈⠙⣲⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠶⠞⠛⠯⣤⣹⡿⣧⡞⡀⣠⣞⣁⡴⠃⠀⠀⠀⠀⠀⠤⢤ ⠀⠀⠀⠀⠘⠳⣿⡀⢠⣾⡍⠀⢰⣶⣭⣷⣄⣈⣧⡹⣆⠀⠈⢧⠀⠸⣆⡀⠈⠉⠙⠻⠿⠿⠿⠿⣟⢛⡿⠋⠁⠀⠀⠀⠀⣀⣠⠟⠁⢻⣿⡏⠷⣩⣿⡇⠘⠦⣄⠀⠀⠀⠀⠀⠘ ⠀⠳⢤⡀⠀⠀⠈⠳⢾⣿⣿⣿⣿⣿⣿⣿⡇⣼⡟⠻⢿⣷⡀⠈⢧⠀⠘⢧⡄⠀⠀⠀⠀⠀⠀⢠⣿⢿⣧⡀⠀⠀⠀⢀⣠⠟⠁⠀⢠⡿⣿⡿⠿⠿⣿⠇⠀⠀⠀⠙⠦⡄⠀⠀⠀ ⠀⠀⣠⠙⠢⣄⠀⠀⢸⣿⣿⠏⠙⠛⢿⣿⣷⡏⠳⣄⠀⠙⠟⠦⣄⣳⡄⠀⠙⠒⠲⢤⣤⡤⠖⢻⣽⢀⣨⡷⠤⣤⣠⡞⠁⠀⠀⣠⢾⣇⣿⣧⣦⡴⢯⡀⠀⠀⠀⠀⠀⠀⠁⠠⠄ ⠛⠚⠿⣄⠀⠈⠳⣤⠈⠛⣿⡀⠀⠀⢀⣽⣿⡶⢶⢻⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠻⣥⡀⠀⢀⣀⣠⡤⢶⣾⡙⣿⣿⣿⣧⡀⣿⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⡄⠀⠀⠑⢄⡶⠋⣯⣍⣿⣿⠻⣷⠊⢸⠀⣤⡍⠛⡶⠶⡶⠶⣶⠶⡶⢶⣶⡶⡶⢿⣷⣶⣺⠋⣏⠏⡶⣦⣇⡟⠓⣾⣿⡏⠀⣿⠿⠿⠟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡇⠀⠀⣾⣿⣶⣿⡿⣿⣏⣛⣺⠿⠾⠤⢽⣟⣛⣁⣼⡥⠼⣿⣷⣋⣸⣛⣷⣋⡿⣄⣤⡿⡯⢽⣒⡚⠛⠟⠛⣿⡥⣼⠃⣠⣟⣀⣀⣀⣼⣇⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⣄⠀⢿⣿⡃⣾⠀⠛⠀⠉⠉⠳⠤⢖⣦⣀⣠⣤⠈⠉⣉⣉⠙⠛⣻⣻⣛⣿⡛⠉⢹⡧⠴⠲⢤⣤⣞⠛⠚⠁⠀⠀⠀⠈⣇⠀⣼⣅⢐⣿⣶⣿⢦⠀⠀⠀⠀⠀

⠅⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⠏⠀⠀⢀⡘⠀⠀⠀⣀⣀⣸⣇⣀⣀⡀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢲⠀⠀⠀⠀⠈⣧⠀⠈⢧⡀⠀⠀⠀⠀ ⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡿⠀⠀⠀⣏⡇⠀⠚⠉⠉⠀⡟⡇⠀⠀⠀⡿⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢹⣆⣀⠀⠀⠈⡇⠀⠀⠀⠀⠸⡄⠀⠈⢷⡀⠀⠀⠀ ⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢸⡇⠀⠀⢰⢻⠀⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⡇⡇⠀⠀⡆⠀⠀⠀⠀⠀⡆⠀⢸⢻⠉⠉⠙⠒⢿⡄⠀⠀⠀⠀⢳⠀⠀⠀⢳⡀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢸⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⣧⠀⢸⡌⣇⠀⠀⠀⠘⣇⠀⠀⠀⠀⠸⡆⠀⠠⡀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡿⢸⠃⠀⠀⡾⢠⡇⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⣇⢹⠀⠀⠀⠀⣿⡀⠀⠀⡆⠀⣇⠀⠀⢹⡄⢳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡇⢸⠀⠀⢠⢇⢿⡇⠀⢀⣧⠀⠀⠀⠀⢀⣿⠀⠀⣿⡘⡇⠀⠀⠀⢿⣇⠀⠀⢹⡀⢹⠀⠀⠀⢷⡄⠳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣼⠁⠀⠀⠤⠴⢲⡗⢺⠒⠒⡾⡼⢸⠃⠀⢸⢻⠀⠀⠀⠀⢸⠹⡇⠀⡇⡇⢻⠀⠀⠀⢸⢹⠀⠀⠀⡇⢸⠀⠀⠀⠘⡟⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⣤⣤⣴⣶⣶⣾⣷⣾⣶⣶⣧⡇⢸⠀⠀⡿⢸⠀⠀⠀⠀⣼⢠⡗⢲⡗⢳⠾⡦⠄⠀⢸⠸⡇⠀⠀⢡⠈⡇⠀⠀⠀⢱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣠⣴⠇⠿⠤⠤⢄⣠⠇⢺⣿⣿⣿⣿⣿⣷⣶⣦⣼⣀⣧⠀⠀⢘⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡀⢀⣻⡿⠉⢉⣿⠀⢀⣽⣿⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⢀⡇⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠛⡏⡿⣇⠀⣼⣿⢟⣹⣿⣿⢸⣿⡟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣾⢻⣿⣿⣿⡀⠙⡿⠏⣿⢺⣸⠀⠀⠀⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠹⡄⢹⡵⠋⠁⢻⣿⣿⡟⠳⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⣿⣿⣸⣿⠙⢿⡇⢀⡇⢰⡇⠀⠉⢰⡀⠀⡟⡆⢀ ⠀⠀⠀⠀⠀⠀⠀⣸⣼⡇⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠳⡈⢷⡀⠒⢀⣈⠉⡙⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣁⡸⠻⢟⠛⢳⣼⠃⠼⠁⢸⡇⠀⠀⢸⡇⢸⠁⠉⠁ ⠀⠀⠀⠀⠀⣰⠏⣁⣄⡇⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠉⠢⣉⠳⡦⠤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣀⠶⢆⣗⣾⠏⣀⠀⠀⣿⡇⠀⠀⢠⡇⡞⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⢠⣯⣀⣧⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⡔⠒⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠯⠽⠇⠔⠊⠁⠀⠀⡏⡃⠀⠀⢸⣰⠃⡄⠀⠀ ⠀⠀⠀⠀⣹⠀⠀⠉⣩⣼⠀⠀⠀⠀⠀⠀⠀⣧⡇⠐⢤⡙⢯⡡⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣹⠀⠀⠀⡇⡇⠀⠀⢸⠃⠀⡇⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠠⡏⠸⡆⠀⠀⢸⠀⠀⠀⢹⡇⠀⠀⠙⠂⠙⠈⠛⠓⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢜⢶⣦⣢⡀⢸⡷⡇⠀⠀⢸⠀⠀⠇⠀⠀ ⠀⠀⠀⠀⠀⢳⣄⠀⠹⢦⣇⠀⠀⢸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣸⠛⡇⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠈⠳⢤⣀⢹⠀⠀⠀⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⠀⠀⢈⠹⡆⠀⠀⣿⡀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠀⠀⢀⡟⡴⣧⠀⠀⢻⣇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⢀⡇⠀⠀⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣞⡼⠁⣸⡄⠀⢸⣿⠀⠀⢸⡙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣿⣧⠀⠀⡀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⣨⡾⠚⠉⠁⢧⠀⠀⣿⡇⠀⠘⡇⠀⠀⠉⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢖⡿⠉⠀⣸⢹⠃⠀⠀⡃⢠⠀⠀⣾⠀⠀⠀⡇⠀⠀ ⡀⠘⢧⣀⠀⣠⠞⠁⠀⠀⠀⠀⠘⣦⠀⢸⣿⠠⡀⣗⠒⢄⠀⠀⠀⠀⠀⠉⠉⠒⢶⡶⠤⣤⠤⠤⠤⠴⠖⠒⣿⠉⠛⢦⡤⠞⠀⢀⡴⠃⢸⠄⠀⡀⡇⢸⠀⢀⣿⣤⣴⣶⣷⣿⣿ ⣿⣿⣶⣬⡽⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣿⣇⠀⢹⢳⡀⠳⣄⠀⠀⠀⠀⠀⠀⠈⠻⡏⠁⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠙⢦⠴⠋⣠⣶⣿⠁⢰⡇⡇⡞⠀⣸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⣿⡄⠈⡇⢹⡄⠀⠉⠁⠀⠀⠒⢄⣀⠀⢀⣀⣀⣀⣀⠴⠋⢠⠇⠀⠀⠀⠀⠈⢷⡊⢹⣿⡏⠀⣾⡇⡇⡇⠀⡿⢿⠛⠛⠙⡏⠁⠀ ⣿⣿⡟⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠘⡆⠀⣿⣷⠀⢻⠀⠳⣄⣀⣀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠈⢧⠀⢻⣿⢀⡏⣧⣷⠃⣸⠁⢸⠀⠀⠀⡇⠀⠀ ⣿⡿⣀⡤⠖⠛⢉⡇⠀⡇⠀⣠⣌⣉⡙⢿⡄⠸⣿⣇⠘⡇⠀⠀⠈⠉⠙⢷⣄⣀⡀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢸⡇⣸⠁⣿⡿⢀⡏⠀⢸⠀⠀⠀⡇⠀⠀ ⣿⢛⣁⠤⢶⠀⢸⠁⢰⠁⠀⠿⠀⠀⠉⠹⣿⡀⢿⡼⣆⢻⠀⠀⠀⠀⠀⡼⢸⣧⡉⠉⠉⣹⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣧⡟⠀⣿⠃⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀ ⡏⡞⠁⠀⣾⠀⢸⠀⢸⠀⢀⣀⣀⠀⠀⠀⡏⢻⠻⣿⡝⠛⠃⠀⠀⠀⠀⡇⢸⠀⠳⣤⠞⣿⣸⢀⡀⠀⣤⡀⠀⠀⠀⣀⣠⠤⡤⠤⡤⣽⡝⠃⠀⣟⣰⢷⡄⠀⢸⠀⠀⢀⣇⣀⣠ ⠁⠁⣀⡠⠟⠀⣾⠀⠈⢉⣉⣉⣉⣉⡻⣾⣇⣸⡄⢹⣹⡒⠒⠦⢄⣀⠀⡇⣾⡴⠋⠙⢦⡇⡏⣹⠋⠉⠙⣦⢶⠚⢉⡥⠤⡄⢳⠀⢳⠀⣿⣦⣀⣤⣭⣬⣷⣶⣾⣿⣿⣿⣿⣿⣿ ⠖⠋⣁⣀⣠⠴⢛⣾⣉⣹⢧⣀⣄⡼⢯⣉⣹⠿⣟⣳⣌⣳⣰⠤⢤⣄⢹⠃⡿⣆⠀⠀⢨⡇⣿⢿⠉⡏⠉⡟⡼⡄⠸⠆⠀⢹⡘⡇⠈⣇⣈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿