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