⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿⠀⢻⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣰⠃⠀⠈⣇⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢠⠇⠀⠀⠀⠸⡄⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⣸⠁⠀⠀⠀⠀⠀⠘⡆⠀⠀⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⡏⠀⠀⠀⠀⠀⠀⠀⢻⠖⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠶⡄⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⢸⣶⣿⣦⡀⠀⢀⣠⣤⣼⠁⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣡⠗⠒⣾⣿⣿⢹⡆⠀⠀⠀⠀⠀⣴⠉⡇ ⠀⠀⣇⠹⣄⠀⠀⠀⠀⠀⣸⠉⠉⠀⠀⠀⠈⠛⣷⠋⠀⠀⠀⠀⠀⢀⡏⡼⠁ ⠀⠀⠘⣦⠈⠳⠤⣤⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣠⠞⢠⠇⠀ ⠀⠀⠀⠈⠙⠲⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⢠⡗⠒⠶⠶⠖⠚⢁⡴⠋⠀⠀ ⠀⠀⢀⡴⠚⢉⣁⣀⡀⠀⠀⠀⠀⠀⡀⠀⡀⢸⠛⣖⠒⠒⠒⠚⠉⠀⠀⠀⠀ ⢴⣶⡯⠔⠚⠉⣠⠞⢁⣴⠂⣠⡏⢰⣇⠀⢿⠀⢧⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⢁⡴⣻⠃⡴⣿⠀⡏⣹⠀⢸⣧⠘⣷⣄⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡥⠖⠉⢰⢃⡞⢡⠇⣼⡇⡟⣇⠘⡏⢦⠸⡌⠓⠾⠶⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⢠⣷⠋⠀⡾⣰⠋⣇⣧⠸⡆⣷⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢚⡁⠀⢀⣷⠃⠀⠸⣿⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠠⠄⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠴⠛⠋⠀⠀⡎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⡎⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⡼⠒⠁⠀ ⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡓⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀ ⠀⠀⢠⣪⠖⠒⢮⣢⠀⠀⠀⠀⡠⢊⢕⣢⡌⢦⠀⢤⣠⠔⠁⠀⠀⠀⠀⠀ ⢳⣴⠷⠃⠔⣒⠚⠇⡢⠠⠤⠺⠃⠘⢞⣋⠅⢠⠧⠊⠁⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⣔⣕⣁⣤⣬⢦⣤⣭⠤⢂⡀⠀⣀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⢋⡿⢛⣭⣴⣶⡿⢉⣤⣴⣿⠀⠁⡇⠀⢀⠠⠤⠀⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⣮⠁⣾⠟⠉⠀⢰⡘⡿⠁⣿⣄⠣⡍⠉⠔⠊⠉⠉⢱⡼⠀⠀⠀⠀⠀⠀ ⠀⠿⠀⢹⠀⢀⣼⠟⠉⢊⠆⠻⣿⢓⠪⠥⡂⢄⠀⠀⢗⢅⣀⣀⡀⠀⠀⠀ ⠀⠘⡹⡉⠀⢸⣟⠀⢀⢜⠆⠀⠹⣻⢦⡀⠈⡄⡇⠀⠀⠉⠉⠉⠁⠀⠀⠀ ⠀⠀⠈⠺⢄⠀⠹⡆⠻⠁⠀⢀⡴⡹⠀⠻⣄⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⣜⣦⠀⠀⠀⢠⡗⠉⠀⠀⠀⢩⡌⠙⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢽⣿⠀⠀⠀⠈⠓⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠫⣛⡄⠀⢀⢴⣾⣗⡶⢠⡴⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠛⠒⠒⠢⠤⠐⠲⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⣾⣦⡶⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠴⠓⠉⠁⠀⠀⠀⢠⠄⢰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠀⠀⠀⠀⠀⠀⢠⡏⠀⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢁⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠺⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠖⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⣡⣿⠿⠛⠿⣦⡌⢦⠀⠀⠀⠀⠀⠀⠀⣠⠎⢁⡤⠒⢢⣄⠈⠳⡄⠀⢀⣤⠀⣦⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡀⢀⣼⣵⠟⠁⢀⣀⣀⣈⣿⠘⣆⠀⠀⠀⠀⣠⣴⡃⠀⢸⡄⣿⣿⠟⡇⠀⢻⡆⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⡿⠟⠉⡴⠊⣁⣤⣀⡀⠉⠳⢬⣓⠒⢊⡉⠀⠉⠁⠀⠈⠳⠼⠤⠞⠁⢀⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⡰⠊⠀⢀⣀⣨⣷⣤⣄⣈⣉⣁⣀⠔⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⣤⣴⣫⣿⣶⣾⡿⢿⠛⢛⣩⣿⣿⠿⠛⠋⠀⣠⡞⠀⡠⠀⣼⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢁⣿⠟⠉⣠⣴⣞⣿⣿⣿⡟⢁⡤⣶⣲⣯⣿⡇⠀⡇⠀⡇⠀⠀⠀⣀⡤⠤⠒⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣏⠏⢀⣾⣿⡟⠋⠉⠁⠀⣇⠘⣶⣿⡿⢻⣿⣧⠀⠻⣄⠙⠒⠒⠋⣀⠤⠶⠛⠛⠛⠲⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⣠⣾⣦⡘⢿⡀⠈⣿⣿⣷⣄⡈⠳⣖⡒⠉⠀⠀⠀⠀⠀⠀⣰⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡿⡀⠀⣿⡇⠀⠀⢠⣾⣽⠟⠉⠑⢄⠱⡀⠙⣿⣿⡸⡏⠒⠤⠍⡑⠒⢄⠀⠀⠀⠀⣿⢻⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⢳⡴⠿⠃⠀⠀⣿⣿⠁⠀⠀⠀⢸⢂⡇⠀⠈⣿⣷⣽⣄⠀⠀⠈⠱⡄⢱⡀⠀⠀⠈⠓⠛⠻⠿⠛⠟⠓⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢦⠱⡄⠀⠀⠘⣿⣿⠀⠀⢀⡴⣫⠞⠁⠀⠀⠘⣇⢻⠫⡳⡀⠀⠀⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⣜⣆⠀⠀⠈⢻⣧⠀⢺⣿⠁⠀⠀⠀⠀⣰⠟⢸⠀⠘⢯⣢⡀⣅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡓⢤⣀⠀⠿⠀⠀⠉⠁⠀⠀⣠⢞⣣⠔⠋⠀⠀⠀⢻⣧⠘⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⣻⣦⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⢿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣷⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣚⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⠻⢆⠀⠀⠀⠀⣠⣶⣿⣿⣟⣷⣶⠤⢤⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢰⠧⠝⠛⠛⠻⠿⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⢸⠀⠘⢄⠙⠢⠀⠀⠀⠀⡐⡙⠊⠅⡧⠀⠀⠀ ⠀⢸⠀⠀⠀⠑⠪⢄⠀⠀⠀⠇⡀⠀⠒⠁⠀⠀⠀ ⠀⠸⠀⢠⠀⠀⠀⠀⢥⢀⠀⡄⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠌⡄⢠⣤⡀⢾⠃⡦⢡⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢜⣿⠟⢈⣰⠁⠆⠀⣀⠀⠀⠀⠀⠀ ⢀⢔⡎⠙⠀⠈⢄⡐⠙⢊⠀⢰⠒⢤⡉⠢⠤⣶⠆ ⢸⡇⠑⠈⠀⡠⢊⡄⠀⡈⡕⡄⢃⠀⠈⠉⠉⠀⠀ ⠘⢜⣂⣒⠬⠒⠁⢁⠀⣧⠘⡕⢆⣑⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢄⠣⡙⢬⠢⡈⢢⢡⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡜⡄⢡⢁⠀⢣⠡⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⡸⡀⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠑⠗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡼⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠃⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠀⠀⢄⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡿⠿⡝⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠈⢢⡀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⡜⢠⠊⠀⣠⠟⢘⡇⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠉⠳⢤⣞⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⠸⣤⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⣹⣄⡀⠀⠀⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⣼⠀⠀⠀⠀⠀⠀⢺⣬⣧⡙⡄⢠⠁⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⡜⠈⡇⠀⢰⠶⣦⡄⠈⢿⠏⠀⣿⠎⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠹⣄⢸⣴⣿⣿⡅⠈⠀⣴⠃⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⡀⠀⠈⠳⡞⠛⠁⢠⣠⠶⡿⠀⠘⠓⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣚⡇⠀⠹⡄⠀⠀⢣⣀⡀⠋⠉⠛⠁⠀⠀⢶⠒⠺⢦⣀⡈⠙⠦⠤⠶⣖⣾⠆ ⣸⡿⠉⣇⣀⠼⠁⠀⠀⢀⡜⠁⠀⠀⠀⢸⠢⡀⠈⣧⠀⠀⠉⠓⠢⠶⠤⠞⠋⠁⠀ ⡟⢇⠀⠀⠀⠀⠀⢀⡠⠊⣀⣶⠀⠀⣆⠈⢧⢹⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⡜⠦⣄⣠⠤⢒⣩⠴⠚⠁⢸⠀⠀⣿⡄⠈⢧⠷⣤⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠓⠦⠴⠚⠋⠀⠀⠀⠀⠸⡇⠀⢧⠳⣄⡈⢧⡈⠓⢶⡆⠙⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠘⢆⠙⠧⣬⡙⢦⠀⠉⢢⠈⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡙⡄⠈⠳⡌⢷⠀⠈⢷⠈⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠸⡀⠀⢱⢸⡄⠀⠈⢧⡈⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠈⡇⠀⠀⠀⠉⠙⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⠀⠈⢧⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⠇⠀⠀⠈⠳⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠁⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⢀⠀⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡰⡁⠀⠀⠀⠀⠈⢆⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⡡⠁⠀⠀⠀⠀⠀⠈⢏⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣡⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡠⠊⠉⠑⠴⠋⠉⠉⢆⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠘⠂⠀⠒⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠈⠢⠤⠔⠙⠢⠤⠐⠁⠀⣠⠃⠀⠀⠀⠀⠀ ⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⡠⠊⡝⠉⠀⢠⠆⠀⡖⡖⢲⠈⠁⠀⠀⠀⠀⠀⠀ ⡔⢁⣀⣀⡀⠀⠉⠒⠀⠒⠈⡠⠊⠀⠀⡠⡇⠀⠀⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠈⠲⢄⣀⡠⠔⠊⠀⠀⣀⠜⠁⡇⠀⠀⡇⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⡠⠔⡞⠁⠀⣰⡇⠀⢰⠀⡇⠀⠣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠃⢀⠔⠈⠁⢠⠎⠀⢀⠔⢱⠀⠀⡜⠀⠳⡀⠀⠈⠁⠐⠒⠒⠢⢄ ⠀⠀⠀⠀⢸⣠⠊⠀⠀⢀⠃⢀⡔⠁⢠⠃⠀⣰⠁⢸⠀⠈⠒⠒⠒⠂⠉⠁⠒⠊ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⢠⠊⠀⡔⠁⢀⠔⢡⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠆⡠⠊⢀⠔⠁⠀⠈⢆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡊⠁⠀⠀⠀⠀⠈⠣⣈⣆⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⡀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⣿⣿⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣦⣄⠀⠘⠿⠿⠋⠀⠀⠀⠙⠁⠴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢿⣿⣿⣿ ⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠳⣄⠀⠈⢻⣿⣿ ⣿⠁⠀⠀⠀⣀⣤⠞⠁⠀⢀⠀⠀⡄⠀⠀⡀⠀⢠⠀⠀⢷⡀⠀⠸⣧⠀⠀⢿⣿ ⣿⣶⣶⡾⠟⠋⠀⠀⢀⡴⠃⠀⣰⠃⠀⢠⡇⠀⢸⡄⠀⢸⣧⠀⠀⢻⡆⠀⠈⣿ ⣿⠉⠀⠀⠀⣀⣤⡾⠛⠀⠀⣴⠏⠀⠀⣼⠃⠀⢸⡇⠀⢀⣿⠀⠀⢸⣿⠀⠀⣿ ⣿⣶⣶⣿⡿⠛⠉⠀⢀⣤⣾⠋⠀⢀⣾⠏⠀⠀⣾⠃⠀⢸⣿⡆⠀⢸⣿⡇⠀⣿ ⣿⣿⣯⣥⣤⣤⣤⣾⣿⣿⣥⣤⣤⣿⣯⣤⣤⣼⣿⣤⣤⣼⣿⣧⣤⣼⣿⣿⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡏⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢃⡿⠁⠈⢿⡙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠛⠁⢀⣾⠃⠀⠀⠘⣷⠀⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⣼⡇⠀⠀⠀⠀⢹⣇⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣴⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠏⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢻⣦⠀⠀⠀⠀⣀⣤⣤⣤⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⠀⠀⠀⣿⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⣿⣤⣤⣄⣼⣿⣿⣿⣮⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⢻⡆ ⠀⠀⠀⣿⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣟⣭⣾⠏⠈⠉⠉⣿⣿⣿⣿⡿⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣸⡇ ⠀⠀⠀⢿⡆⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠈⠉⠉⠀⠀⠀⠀⠀⠈⠻⢿⣷⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡿⠁ ⠀⠀⠀⠘⣷⡀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣾⠁⠀ ⠀⠀⠀⠀⠘⣷⡄⠀⠙⠳⠶⣤⣤⣀⣀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⠀⠀⠉⠉⣉⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣄⣀⣀⣀⣀⣀⣤⣴⠟⠁⢀⣴⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣻⣿⡶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⠉⠉⠉⠉⠉⠉⠁⠀⣀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⡶⠶⠤⠤⠤⠴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣴⠟⠁⣀⣤⡴⠶⠖⢲⣶⠆⠀⢀⠀⠀⠀⣠⡄⠀⣰⠀⠀⠰⣧⠀⢹⣆⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣾⣛⣭⣥⡶⠚⠋⠁⠀⢀⣴⠟⠁⠀⣴⡿⠀⠀⣰⣿⠀⢰⣿⡆⠀⠀⣿⡄⠈⢿⡄⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⣰⣿⡿⠁⢀⣼⣿⠇⠀⣿⠛⣧⠀⠀⢸⣿⡀⠈⣿⣦⡀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣠⠾⢡⡿⠁⢠⡿⢡⡟⠀⣼⠇⢠⣿⡄⠀⠸⣿⣧⠀⠸⣯⢻⣆⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡟⢁⣤⡴⠛⠋⢀⡾⠁⣴⠟⢀⣾⠁⢠⣿⠀⢸⡿⣧⠀⠀⣿⠹⣧⡀⢹⡇⠙⠷⣦⣙⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡷⠟⠁⠀⠀⢀⣾⢣⣾⠋⠀⣸⡏⠀⣾⣿⡆⢸⡇⢹⡆⠀⣿⡆⠘⣷⡀⣿⡀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣼⣣⡿⠁⠀⠀⡿⠀⣾⠇⠸⣇⢸⡇⠈⢿⡆⢸⡇⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⢸⣇⣼⠏⠀⠀⢿⣾⡇⠀⠈⢿⣌⣧⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡤⠀⠀⠀⣸⣿⠏⠀⠀⠀⠘⢿⡿⠀⠀⢈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣿⡏⠀⠀⠘⣿⣿⣿⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⣀⣀⣴⣿⣿⣿⣦⣾⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣌⠻⣿⣷⡄⠀⠀ ⠀⣾⣿⣿⣿⠿⠛⣡⣾⣿⡿⣿⣿⢻⣿⣿⢿⣿⡟⣿⣿⡈⢿⣿⣇⠘⣿⣿⡀⠀ ⠀⠉⠉⢁⣠⣴⣿⣿⡿⢋⣼⣿⠏⣼⣿⡟⢸⣿⡇⢻⣿⡇⠘⣿⣿⡄⢹⣿⣷⠀ ⠀⣶⣿⣿⣿⠿⠛⢁⣤⣿⣿⠋⣰⣿⣿⠃⣼⣿⡇⢸⣿⡿⠀⣿⣿⡇⠀⣿⣿⠀ ⠀⠉⠉⠀⢀⣤⣶⣿⡿⠛⠁⣴⣿⡿⠁⣰⣿⣿⠁⣼⣿⡇⠀⢹⣿⡇⠀⢸⣿⠀ ⠀⠀⠐⠚⠛⠛⠛⠁⠀⠀⠚⠛⠛⠀⠐⠛⠛⠃⠀⠛⠛⠃⠀⠘⠛⠃⠀⠀⠛⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣰⢏⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣠⠊⠉⠀⠈⠙⢷⡾⠉⠀⠀⠀⠉⢷⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡇⠀⠀⠀⣴⡄⠀⠀⢠⣄⠀⠀⠀⠈⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣇⠀⠀⠀⠈⠀⢀⡀⠈⠁⠀⠀⠀⣰⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠘⠷⣄⣀⣠⠴⠋⠙⠦⣄⣀⡤⠞⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠴⠒⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠞⠀⠀⠀⠀⢀⡟⠀⠀⢸⡅⢹⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⣀⣀⣀⡤⠖⠉⢀⡴⠋⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣀⡠⠴⠒⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⡴⢻⡇⠀⠀⠀⢸⠃⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⣀⡤⠚⠉⠀⠀⠀⠀⢀⡴⠟⠀⢸⡇⠀⠀⠀⢸⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠖⠋⠁⠀⠀⠀⠀⢀⣠⣴⠋⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⢸⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣀⡤⠴⠚⢉⡽⠁⠀⠀⠀⣰⢿⠁⠀⠀⠀⡏⠀⢸⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⡠⠖⠋⠁⠀⠀⣰⠋⠀⠀⠀⢀⡼⠁⡞⠀⠀⠀⢰⠇⠀⣾⣧⠀⠀⠀⠀⠉⠓⠒⠒⠲⠶⠤⠤⢤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢠⠞⠁⠀⠀⠀⠀⡼⠁⠀⠀⢀⡴⠋⠀⣸⠃⠀⠀⢀⡟⠀⢀⡇⠈⠳⣄⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⠋⠀⠀⠀⠀⠀⣸⠁⠀⢀⡴⠋⠀⠀⣰⠃⠀⠀⢀⡾⠁⠀⢸⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢠⠇⠀⣠⠋⠀⠀⢀⡜⠁⠀⠀⢠⡾⡇⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠃⠀⢀⡰⠋⠀⠀⢀⡴⠋⠀⢻⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠏⠀⣠⠊⠀⠀⣠⠴⠋⠀⠀⠀⠈⢧⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠀⢠⠀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣛⣿⣭⡛⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠈⢧⡀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡞⠉⠀⢀⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡏⠀⠀⠸⡏⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠉⠲⢾⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠻⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⢳⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⣼⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠰⡖⠺⡓⢦⡀⠀⠀⡇⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⡆⠹⡀⣰⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣇⡼⠁⢻⡀⠀⢠⡾⡲⢦⡀⠀⢹⣿⡟⠀⠀⣷⠋⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠀⠀⠈⢧⡀⢸⣇⢸⣿⣿⣖⠀⠙⠀⣀⣸⠋⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣮⡛⣮⣿⠟⠛⠀⠀⢀⣼⠁⠀⣼⣅⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠤⢤⠀⠀⠁⠈⢿⠈⠁⠀⢠⣦⡼⠟⣹⠀⠀⠀⠈⠀⠀⠀⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⣹⡀⠀⠈⣧⠀⠀⠀⠘⣆⡀⠀⠈⠀⠉⠙⠋⠀⠀⠀⢾⡖⠒⠿⢦⣀⣀⠈⠙⠶⠶⡶⠶⠶⣛⣿⠂ ⠀⣼⢣⠟⢻⡇⠀⢀⡾⠀⠀⠀⠀⠈⣽⠃⠀⠀⠀⠀⠠⡷⣄⠀⠀⢻⡀⠀⠀⠙⠻⢦⣄⣤⣄⣠⣼⠿⠛⠁⠀ ⢀⡏⡟⠀⠘⠛⠛⠉⠀⠀⠀⠀⢀⠞⠁⢀⠀⠀⠀⣀⠀⣷⠘⣦⡄⠈⢷⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀ ⢸⡇⢻⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢠⡴⢻⡇⠀⠀⣿⠀⠘⣧⠹⣄⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⡄⠻⣤⣄⣠⣤⠶⢋⣡⡴⠟⠉⠀⢸⡇⠀⠘⣿⣇⠀⠘⣧⠻⣶⡆⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠶⣤⣀⣠⡴⠾⠋⠁⠀⠀⠀⠀⢸⣷⠀⠀⣿⠹⣄⠀⠘⣧⡀⠙⢶⣤⣄⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⠀⠹⡆⠙⢿⡒⢈⠷⣄⡀⠈⠻⣦⡀⠙⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣆⠀⠹⣦⡈⠙⢶⣦⠈⢷⡀⠀⠀⢳⡀⠹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣬⢻⡄⠀⠉⢷⡈⢻⡄⠀⠈⣿⡅⠹⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⢻⡀⠀⠈⢧⠀⡇⠀⠀⠈⢷⡀⠙⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠻⠶⣬⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢷⠀⠀⢸⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣼⠀⠀⠀⢷⡘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡏⠀⠀⠀⠈⠳⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀