⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢋⡙⢿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⡐⡐⢂⡙⢿⣿⣶⣶⣶⢿⡿⣿⢿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢀⡑⠤⢁⠢⢄⠙⢿⠇⢄⠢⡐⠄⡂⢄⢂⠡⡉⡙⠛⠿⢷⣤⣴⣾⠿⠟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⡠⠘⡄⠣⢌⠢⢘⠠⠌⢂⠥⡈⠔⡡⢌⡀⢃⠔⠡⢊⣴⣿⡿⠋⡅⢊⠔⡸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⡟⢛⢃⠡⡑⢠⢃⠢⡑⠌⡒⢌⠂⢆⠱⡈⠔⡂⠜⡠⠊⠥⡈⢛⡉⢄⠣⢈⠔⠢⠐⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠏⡰⢁⢂⠢⢑⠂⢆⠱⣀⠣⠌⡂⢍⡐⠢⡑⢌⠰⡁⢆⠩⡐⣁⠂⡌⢄⠢⡁⠎⣁⠃⢾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠇⡘⢄⠢⠌⢢⠁⢎⡐⠢⢐⠂⠥⢘⡀⢆⠱⢈⠢⢡⠘⡠⢃⠔⡠⢃⠌⢢⠑⢌⠒⡄⢣⢸⣿⡏⢿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣦⡁⢆⠡⢊⠤⢉⠄⢢⠑⠌⣌⣴⣦⡘⡀⠣⢌⠢⡁⢎⠰⣈⠢⠡⢌⡘⢄⠊⡔⠢⡘⢄⠸⡿⠃⡌⢿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡏⠛⠿⢷⣿⣤⣶⣬⣬⣴⣾⡾⠟⠋⢻⣷⣌⠡⢂⡑⠌⡄⢃⠔⡨⠑⡂⢌⠢⡑⢄⠣⡐⠌⡐⠠⡑⢄⢺⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⣿⣶⣁⠆⡘⠰⡈⠤⢁⠣⢘⠠⡑⠰⡈⠔⣁⠊⠔⡡⠘⣠⣿⢿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣕⡄⠣⢌⠂⡅⢒⡈⠥⡐⢡⠂⡜⣠⣱⣾⠿⠃⢨⣿⠀⠀⠀⠀⠀ ⡀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣾⣴⣧⣼⣶⣼⣶⣿⠿⠟⠋⠁⠀⠀⢰⡿⠀⠀⠀⠀⠀ ⠻⢷⣶⣤⣽⣿⣀⡀⣴⡿⠳⣦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣴⣦⣴⣤⡀ ⠀⢠⣾⣟⣉⡙⣿⣷⠿⣿⣷⣿⡷⠀⠀⠻⠺⠀⠀⠒⢂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⡉⠍⣹⣿ ⢀⣿⠋⣿⣿⣿⡝⢿⣷⣄⡉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⡋⠙⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⣿⣧⠘⡐⣼⣿ ⠘⣿⠀⠈⢻⣾⣿⠟⠋⠙⠿⣶⡄⠀⣠⡀⠀⠀⠀⠈⠻⢿⣿⣿⡿⢀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⢿⣿⣴⣿⡿⢣ ⡀⠙⠷⣶⣾⡿⠟⠀⠀⠀⠀⠹⣷⣴⣿⣇⠀⠀⣀⠀⠀⠀⠀⠠⣴⢻⠟⣴⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⣽⣿⢿⠝⠂⠁ ⣧⣴⡿⠋⠀⡧⠊⠀⠀⠀⠀⠀⠀⣠⡤⠿⢿⡟⠛⠻⠷⣶⣶⣤⣤⣶⣼⣷⣿⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀ ⣿⣅⠀⠀⠀⠓⠊⠑⢲⢀⡤⠀⢸⡇⣠⠟⡂⢸⠄⠀⢲⠀⠈⠍⢹⣿⣁⠀⠀⠀⢀⣀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀ ⣿⣿⣻⢶⣦⣄⣀⠀⠈⠉⠀⠀⢨⢷⡄⣈⣧⠞⢠⢊⠘⠀⠐⣀⠤⠉⣻⣿⠟⠟⠛⠛⠿⢿⣦⣄⣀⠀⠀⠀⠀⠀⢠⣿⡟⡴⠀⠀⠀⠀ ⣿⣏⠛⠷⣮⣍⡛⠻⠶⣦⣄⡀⠈⠛⠿⠽⠂⠀⠈⠁⣎⡴⠁⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣤⣀⣰⣿⠟⡰⠃⠀⠀⠀⠀ ⣿⠛⠻⢶⣤⣍⡛⠷⣦⣄⣉⠙⠳⢶⣤⣀⠀⠀⠀⠀⠈⢀⣴⠿⠋⠀⠀⠀⠀⠀⡀⢤⢠⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣮⣁⠀⠀⠀⠀⠀