⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣾⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⣿⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣯⣷⣿⣿⣿⣿⣿⣿⠏⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣯⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠁⠀⠋⠉⠉⣽⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⢿⣿⣯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⠤⣤⣤⣀⣀⡀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⣻⠻⠉⠙⢫⣵⠇⠙⣆⣀⡀⠀⠀⠀⠀⣀⣀⣀⣾⢉⡐⡴⣤⣴⣐⠈⠍⡙⠳⢤⡟⠉⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⣶⣛⣳⢓⣗⣯⡿⠗⠀⠘⠉⠙⡆⠀⠀⢰⣿⣇⣳⠹⡀⠛⡐⠠⡐⠌⡛⢶⠁⢆⠡⠙⡌⢂⠩⢛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⣿⣿⣿⠯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⠙⠉⠳⠟⠉⠀⠀⠀⢀⣀⣇⠀⠀⠘⣿⣿⡉⠙⠻⢦⣱⣄⠡⡘⢠⠌⢒⡨⢐⡁⢒⡈⠤⢉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢛⡏⠀⣠⣄⠙⠯⣷⣴⡄⠀⠈⠉⠉⠙⠒⠶⣄⡒⠠⡘⠤⡘⢄⠢⠌⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠻⢿⡟⡥⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣯⡷⢾⣷⣿⢲⣤⢄⣹⣿⣄⠀⠀⠀⠀⠀⠀⠢⡙⢻⣔⢢⠈⠄⢣⠘⡀⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠃⢰⡀⠀⠠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠳⡞⠉⠑⢦⣟⣼⠿⠁⡩⣦⠀⠀⢀⠀⠀⠀⠀⠀⠈⠳⢏⡐⠄⢣⠈⠄⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⣄⣀⣭⣭⡻⢫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⢀⣖⠛⠡⢂⠱⢄⠻⡳⣄⠘⣆⠁⠀⠀⠀⠀⠀⠈⠳⣭⡀⠎⡀⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠈⢉⡇⠣⢌⠒⡌⢠⢉⠞⢦⣟⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠡⠌⣽⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠏⠀⠀⠀⠀⣼⠑⠤⡘⠤⠑⡌⢌⠰⢈⢿⣻⡀⠀⠀⠀⠀⠀⢠⠀⢀⠙⢤⠠⣙⢣⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡀⢀⡿⠌⢢⠑⡌⠱⡈⢄⠣⢌⡀⢿⡇⠀⠀⠀⠀⠀⠀⠱⡈⢦⣬⣳⡠⡙⢳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⣼⠡⡘⢄⠣⢌⡑⠌⡄⢣⠐⠄⣸⣧⠀⠀⠀⠀⠀⠀⠀⠁⠈⢧⠘⢷⠈⡜⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⢁⠎⡐⢢⠘⡰⢈⠆⡉⢄⠸⣽⠀⢰⡀⠀⠀⠀⠀⠀⠀⠘⣧⠂⢣⠐⠌⢾⣆⠀ ⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡔⡈⢆⡑⢢⠑⡄⢣⠘⡰⢈⠔⣻⣆⢿⢀⠀⠀⠀⠀⠀⠀⠀⢹⡈⢅⠊⡜⢈⢿⠀ ⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢰⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡔⡐⢢⠐⡡⢒⡈⢆⠱⣀⠃⢆⠹⠻⢿⡀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠈⡒⢌⡐⠎⡇ ⠀⠀⢠⠞⠀⠀⠀⠀⠀⡀⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⡘⠄⢣⠐⡡⢒⡈⢒⠠⡉⢆⠢⣁⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⢠⠂⡄⢚⡇ ⠀⢠⠏⠂⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⡘⢌⢂⠱⣀⠣⠘⡄⢣⠘⡄⢣⠐⡌⡇⠀⠀⠀⠀⢀⠀⠀⠀⢸⡏⡄⠱⡐⢨⡇ ⣠⠎⠀⠀⠀⠀⠀⠀⠠⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠌⠢⠌⡒⠤⣁⠣⠘⡄⠣⢌⠢⢁⠆⡇⠀⠀⠀⣠⢿⡢⡀⠀⡾⠃⠤⡑⢌⢨⡇ ⣟⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡘⢣⠘⡠⢃⡀⢇⠣⡘⠣⢄⠣⡘⢀⡇⠀⠀⣠⢿⠀⢻⢧⢸⡇⠣⠄⡸⢀⠸⡇ ⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢀⠱⣀⠣⠐⡌⠒⡌⡑⢢⠑⡠⣱⠇⠀⡼⢉⠤⡉⢌⠫⣟⠠⡁⢎⠐⣢⡿⠁ ⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢁⠢⣁⠣⠌⡱⢠⠑⢢⠑⡠⢹⡴⠋⡌⢃⠆⡘⢄⠒⠤⣁⠒⣈⣴⡿⠁⠀ ⢦⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠡⡄⢣⠘⠤⡁⠎⡄⢣⠐⣁⠋⠤⡘⢄⠊⡔⢨⠘⡐⢠⢅⣮⠏⠀⠀⠀ ⠀⠈⠓⢴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡔⢂⠩⡐⢁⠎⢠⠁⠎⡀⠎⡐⣁⠊⠔⡈⠆⡱⢌⣾⠎⠁⠀⠀⠀⠀