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⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⢮⠿⠃⣤⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⡑⣌⠳⣌⢣⠓⡌⠎⠀⠀⠀⠀⠀⠀⠀⠁⡠⠔⢀⣾⣿⣦⣀⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⡱⠰⡌⠓⠘⠂⠡⠈⠀⠁⣀⣀⡀⠀⢀⣴⣶⠏⠫⠙⠛⣛⠛⠿⣷⡆⢠⢀⡀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠡⠑⠆⠀⠙⢿⣿⣿⣿⣷⢿⡿⠃⣰⣿⡿⢟⣒⠡⢒⣤⣦⡤⡀⠀⢦⠘⣏⠿⢿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠐⢠⠀⢠⣿⣿⢛⡉⠁⠀⠀⡿⠋⡾⠋⢹⡋⠉⠀⠀⠠⢁⠃⠈⢁⠘⣐⠢⢤⡉⣉⠉⠉⢩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠃⣾⠀⠀⣴⠈⠁⡗⠁⠀⡎⡕⢠⣶⠀⠀⠁⠀⠀⠊⠀⡟⢰⡄⠁⡄⢠⡆⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⠇⠀⡔⢿⠂⠀⠘⠀⠀⠘⠀⠦⠌⠛⠣⠀⣀⠔⠀⠁⠂⢣⠱⠀⢁⡞⢀⣆⠹⣿⣇⢦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠘⠀⠸⣿⣿⠀⠀⢹⡘⣦⠀⡀⠈⠑⢄⡈⠈⠀⢄⢲⠳⡌⠆⠀⠠⠀⢂⠁⠀⣾⠅⢾⣿⣇⠈⢻⣿⢷⣌⠃⠀⠀⠀⠀ ⠀⠀⠀⠤⢈⠉⠌⠀⠰⠀⣸⣗⠀⠀⠀⠃⠿⣷⣄⡀⠀⠀⠉⣂⠀⠀⠊⡵⢉⠆⠀⠰⠀⠀⠀⠀⠙⠀⢸⣿⡏⢀⠀⠹⣯⡝⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠌⠠⠙⠹⠆⠀⢻⣯⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠈⠐⠳⠤⣀⠁⠀⠀⠀⠀⠀⠀⡐⠄⠃⣼⠏⠀⡻⠄⠀⠹⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠁⢃⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣄⡀⠀⠀⠁⠀⢂⠠⠂⠁⠐⠀⠬⠈⠁⡰⣰⠑⠆⠀⠀⠙⢿⡆⡀⠀⠀ ⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢕⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⡐⢤⣱⣸⢻⠒⢃⡤⣠⡖⠀⠉⠈⠀ ⠀⠀⠀⠴⠀⢶⣊⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠀⠠⠀⠀⢂⣉⡀⠵⠟⠆⣼⢋⣜⠉⠃⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠉⠻⢷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠲⡔⢲⣶⣶⡶⠶⠶⠶⠾⠛⠛⠛⠁⠂⠁⠀⠀⣰⡽⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢶⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠃⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⣦⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠱⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣋⣵⣶⣥⠢⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⠉⠉⠀⠀⠀⠉⠶⠆⠀⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠷⡞⠛⢳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⣷⠾⣻⢷⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠑⡆⢳⡆⠀⣿⠀⠀⠀⠀⠀⢭⢓⠿⠇⠀⠀⠀⠀⠀⣿⠀⢰⡟⠐⢃⡞⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⡹⡈⠿⡀⢹⡇⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⢹⠉⣀⠏⡽⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠐⡜⠣⠬⠙⠦⢄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠛⠶⡟⠐⠃⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⠛⠛⠛⠛⣤⣍⡏⠁⠀⠀⣀⣀⠈⢻⡄⠀⠀⠀⠀⢠⠟⠁⣀⣄⠀⠀⠈⣿⣩⣤⠛⠛⠛⠻⣤⣀⠀⠀⠀ ⠀⣠⡔⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠛⠀⢨⣿⠀⠀⠀⠀⣞⡇⠀⠛⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠹⢧⣀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡟⠀⠀⠀⠀⢣⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⣀⠀⣼⠇ ⠀⠻⢆⣴⣤⣤⣤⣯⣭⣵⣦⣤⣤⣼⣄⡸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣾⣧⣤⣴⣾⣿⣿⣿⣤⣤⣼⣤⡼⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖⣤⣶⣿⣿⣿⣿⣿⣭⡶⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠁⠒⠤⠀⡔⠄⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⣥⣾⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣠⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⢤⡀⠀⠀⢀⣀⠈⠂⠉⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⣿⣀⢻⡟⠉⣷⠀⠀⠀⠀⠀⠀⢀⡤⠎⠁⣀⣿⣿⣿⣿⣿⣿⣿⠟⢉⣠⣶⡾⠋⠀⠀⠀⠀⣀⣠⡤⢶⡾⠶⠀⠀⠀⠀⠀⠉⠶⣽⣾⣿⣷⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣬⣺⡟⠀⠀⠀⠀⢀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⡿⣣⣴⡿⠟⠁⠀⠀⣠⣤⣶⡿⠟⢉⣴⠋⠁⠀⠀⢀⡞⠀⠀⣦⠀⠙⢿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣴⣯⣶⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⢿⠋⡀⣀⣤⣾⠿⣿⡿⢋⣴⣾⠟⠀⠀⠀⠀⣴⠋⠀⠀⠀⢹⣦⠠⢪⣻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣻⢋⡞⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠟⠉⣱⡾⣯⡶⣿⡿⠃⠀⠀⠀⢀⡼⠃⢠⣆⠀⠀⣇⣿⡆⡜⡏⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠁⠀⠁⣰⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢠⣾⣿⠟⢡⣾⣿⠅⠀⠀⠀⣠⡿⠁⣰⣿⢸⢸⡆⣿⣿⣿⣼⣼⡈⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣹⣿⡏⠀⠀⠀⢰⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣰⣿⡿⠃⢠⣾⣿⠞⠀⠀⡴⣷⣿⠅⠀⣿⣿⢸⣾⡇⢻⣿⣿⣿⣿⣇⠸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡿⠁⣸⣿⡟⢠⢀⢠⢀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢰⣿⠟⠀⢠⣿⣿⡟⠀⢀⣼⣿⣿⡿⠀⢰⣿⣿⡟⣿⣇⢸⣿⣿⣿⣿⣿⠀⣿⣿ ⠀⠀⠀⠀⢰⡾⢶⣀⣥⣤⡀⠀⠀⠀⢰⡟⠁⣴⣿⣿⣧⡟⣾⢋⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⣼⣿⣿⠀⢀⣾⣿⣳⡿⠁⠀⡇⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⡀⢻⡏ ⠀⠀⠀⠀⢸⣇⠀⠻⣇⣸⡇⠀⠀⢀⡞⠀⣼⢿⣿⣿⣿⣹⡟⣾⡿⠋⠑⠦⠤⠤⣀⣀⣀⠤⣾⡿⠂⠀⢸⣿⣿⡇⢀⣾⡿⢱⡿⠁⠀⠐⠁⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡇⢸⡇ ⠀⠀⠀⠀⠀⠙⢷⣴⠟⠋⠀⠀⠀⡾⠀⢰⠃⢈⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡏⠀⠀⠀⢸⣿⡿⢀⣾⡿⣇⡾⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⠇⠀⠸⢸⣿⣿⣿⢋⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⢸⣿⡇⣾⡿⠁⡸⢣⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣠⠏⢀⡀⠀⣸⣿⣿⡏⢀⣹⣶⣶⣶⣿⣯⡒⢆⡀⠀⠀⠀⠀⠀⠀⢸⣿⢳⡿⠀⢰⠇⠀⠙⢦⡀⢀⠀⠀⠸⣿⣿⣿⡿⣿⣿⣿⣿⣿⡃⣼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⠞⠀⣼⢿⣿⣿⣱⡿⠋⠁⢠⣴⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢮⡄⠀⠀⢻⣿⣿⣿⢿⣿⣿⣿⣿⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣁⠞⠁⢀⣾⣿⢸⣿⡿⡿⠀⠀⣰⣿⣿⣿⣿⡟⢻⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣀⠈⢿⣿⣿⠈⣿⣿⣿⣿⢠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢀⣴⣿⣿⣿⣾⣿⣿⠃⠀⢠⡟⠉⠙⠛⢻⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢠⣤⣀⠀⡀⠀⠀⠀⠙⠚⢿⣿⣧⠸⣿⣿⣿⣾⣷⢰ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⢛⡥⢀⣴⣿⣿⣿⠟⠀⢹⣿⣧⠀⠀⠘⢇⠀⣀⡀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣿⣷⣿⣤⡀⠀⠀⠀⠈⢿⣿⣆⠸⣿⣿⣿⣿⣾ ⠀⠀⠀⢀⣠⠾⠋⢉⣴⣫⣶⣿⣿⡿⠋⠁⠀⠀⠀⣿⣿⡄⠀⠈⢿⡀⠈⠉⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣧⡀⠀⠈⢻⣿⣆⠹⣿⣿⣿⣿ ⠀⠀⠀⠈⢱⣄⣾⣯⣿⣿⠟⠋⠀⠀⠀⠀⠀⣠⣼⠃⠙⢷⠀⠐⠚⠿⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠿⢿⣿⡏⢙⡏⠻⣿⣆⠀⠀⠻⣿⣷⣿⣿⣿⣿ ⡀⠀⠀⣠⣿⣿⣿⠟⣹⣵⣤⣤⣤⣤⣤⣤⡼⢿⡏⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⢘⣿⣿⠇⠀⠹⣿⡆⠀⠀⢸⣏⣿⣿⣿⣿ ⣡⣴⣾⣻⣿⠟⣩⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣳⠀⢤⣀⣠⠞⢉⡿⠀⠀⠀⢹⣷⠀⢀⣾⣾⣿⣿⣿⣿ ⣿⣿⢣⣿⣗⣼⣿⣿⡿⠿⢿⡟⠛⠛⠛⣷⠞⠋⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣸⠇⢀⣾⣾⣿⢿⣿⣿⣿ ⣿⣿⠠⣿⠿⣿⡁⠈⠀⠀⠀⠑⣄⣠⠞⠁⠀⠀⠀⣀⡹⠶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣒⠖⠋⠁⠀⠀⠀⠀⠞⠁⣰⣿⣿⠟⢡⣿⡿⠋⠀ ⡋⠙⣸⠃⠀⠈⠻⣦⠀⢀⡴⣶⠟⠁⠀⠀⣀⡴⠚⠁⠀⠀⠀⠙⣆⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⢟⡥⣺⣿⠟⠀⠊⠀ ⠀⠀⠃⠀⠀⠀⠀⢈⡿⠋⣰⠇⠀⠀⠐⠚⠁⠀⠀⠀⠀⣠⠴⠛⠋⠓⣆⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣛⣻⠵⠚⢁⡴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⢸⣦⠀⠈⠳⠤⠴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠉⠀⢀⣤⠶⠭⠄⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠁⠀⠀⠀⠀⢀⣀⣀⠐⠃ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⡎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠀⢀⠀⠀⢸⠀⠀⠀⡤⠤⠤⣤⡴⠒⠒⠒⢦⡖⠒⠲⠤⣄⣀⡀⠀⣀⣤⣾⡋⠉⠓⠶⠖⠚⠛⠉⠁⠀⠀⠀⢀ ⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⡞⠀⢠⡞⠀⠀⠀⠈⡇⠀⠀⠀⢸⠇⠀⠀⠀⡇⠈⠉⠙⢿⣿⣿⣿⣆⠀⠀⠀⠀⢠⠀⠀⣠⣀⣠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⡇⠀⢸⡓⢤⡀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠉⢹⣿⠇⠀⠀⠀⠀⡇⠀⠀⠀⡸⠀⠀⠀⢰⡇⠀⠀⠀⢸⣿⣿⡿⠟⠳⠤⠖⠶⠤⣤⣴⣿⣌⢿⣿ ⠀⠀⠀⠀⠀⠀⢀⠴⠋⠉⠁⡇⠀⠀⠀⠀⠇⠀⠉⠑⠶⢤⡤⠴⠞⠉⠄⣼⣠⠾⠿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠸⠁⠀⠀⢰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡹ ⠠⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠓⠤⢤⣤⣀⣀⣀⣀⣀⣠⡤⢖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⢀⡔⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢶⣶⣶⣶⣶⣾⣿⣿⣿⣧⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⡿⠟⠉⠛⠻⣿⣿⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠂⢀⣾⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡶⣾⣿⢿⣱⣿⣿⣷⢶⣦⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⣹⣿⢿⣯⢻⣿⠿⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⣯⣗⣻⡞⣿⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡿⠟⠉⠛⠷⣿⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠋⠁⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⠶⠶⠶⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠶⠶⠶⢤⣄⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧ ⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿ ⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀ ⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⣄⠀⠀⠀⣀⣠⠴⠛⠉⠉⠓⠦⣄⣀⠀⠀⠀⣠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡦⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⣾⣿⣿⣿⣷⠄⠀⠰⠤⣀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⢺⣿⣿⣿⣿⡄⠀⠀⣿⣿⢿⣿⣿⣦⣦⣦⣶⣼⣭⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡆⠂⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⠀⢸⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡟⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠛⠋⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀ ⠀⠜⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⠄⣠⠀ ⠠⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⢨⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⡿⠿⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠉⠻⠿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣠⠴⠚⡙⠙⠲⣤ ⣠⠖⢋⡛⠙⠲⣄⠀⠀ ⣿⠃⣰⠟⠉⠙⢦ ⢦⡈⢁⣾ ⡟⠉⠳⣆ ⠸⠀ ⠙⣆⠙⢧⡀⢀⡴⠃ ⠛ ⢧⡀ ⢀⡴⠃ ⣰ ⠈⠓⢦⡈⢡⣰⠞ ⡈⠈⠓⢦⡈⢡⣰⠞⠁ ⠀⣰⠃⣰⡏⠀ ⠙⣆⠙⢧⡀⠀ ⢀⡴⠃ ⣰⠏⠀⠀ ⠈⠳⣄ ⠙⠶⣄ ⠈⠓⠲⠖⠚⠀⠀⠀⠀⠀ ⠈⠓⠲⠶⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠛⠉⠉⠉⠉⠉⠛⠻⠶⣤⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⠉⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠈⠙⠷⣦⣤⣄⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠻⣦⡀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡾⠂⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀ ⠀⠀⠀⢀⣴⠟⠁⠀⣀⣤⠶⠞⠛⠻⠶⣤⡀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢤⣶⢻⡟⣶⢠⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃ ⠀⠀⢠⡟⠁⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⢿⣌⣛⡋⠀⠀⠀⠸⢧⡴⠛⠓⠞⠁⠀⠀⠀⠈⠛⠛⢈⣥⠟⠁⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⣾⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡽⠟⠀⠀⠀⠀⠀⢀⣤⣤⣴⣤⣄⣀⣤⣤⠶⠞⠛⠁⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣤⣤⣤⣤⡶⠾⠋⠁⠀⠀ ⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⣀⣀⣀⣤⣤⣴⡟⠁⠘⣧⠀⠙⠻⠋⠛⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⢋⣩⣽⠿⣯⣽⡇⠸⠋⠀⠀⣸⡟⠷⣤⡀⠀⠀⠈⠻⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠚⠛⠋⠉⠀⣰⡟⠉⢀⡀⠀⣿⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠘⠷⣤⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⢈⣻⢦⣄⣀⣀⠀⢠⣴⣶⠞⠛⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠈⠛⢷⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢀⣾⡿⠋⠉⠁⢠⣿⠏⢁⣿⣿⣿⠏⠉⢸⣿⡏⠉⢻⣿⣿⡇⠈⠙⢿⣿⣿⣿⣷⡆⠀⠀⢇⠢⣈⡒⡤ ⣿⣿⣿⣿⣿⣏⣴⡇⠀⠀⠀⢠⡿⠋⠀⠀⠀⣰⣿⠋⠀⣼⣿⣿⠏⠀⠀⡾⣿⠁⠀⠀⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣄⢀⣿⣷⣿⣶⣶ ⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⡟⠁⠀⠀⠀⢰⣿⠇⠀⢰⣿⣿⡷⠀⣀⣜⣁⣻⣀⣀⣀⣸⢻⣿⡇⠀⠀⠀⠘⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣿⠀⠀⠀⠀⢠⣿⡏⠀⢀⣿⣿⡿⠛⣩⣿⠿⠛⢻⡏⠉⠉⢹⠉⢿⣿⡀⠀⠀⠀⠹⣿⣿⡆⠙⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠀⠀⣰⣿⡟⠀⠀⠀⢀⣾⣿⠀⠀⣸⣿⡿⢥⣶⠝⠁⠀⠀⠀⡇⠀⠀⡜⠰⡀⢻⡇⠀⠀⠀⠀⢿⣿⣿⠀⠸⣿⣿⣿⡿ ⣿⣿⢿⣿⣿⡃⠀⣼⣿⣿⡇⣀⣀⣤⣾⣿⡇⠀⠰⣼⡟⣠⠎⠁⠀⢀⣠⠔⠁⢹⣀⣠⣧⣶⣦⣤⣷⣤⣤⣠⣤⠼⣿⣿⡆⠀⢹⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣏⣁⣼⣿⣿⣿⠀⢠⣾⣟⡔⠁⠀⠀⠀⢸⠁⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⣿⣇⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣟⣹⣿⣿⣿⡿⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⢰⣾⢟⣻⡿⠛⢻⢋⣻⣏⣱⠞⠙⣄⡀⠀⣿⡽⣿⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢘⡅⠚⠋⠉⠁⠀⠀⠀⠀⣔⣾⢏⢦⢄⣿⣧⣿⡆⠀⠈⣿⣿ ⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⡿⢻⣿⣿⡿⠋⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⢂⢻⣿⣿⣿⡇⠀⠀⢽⣿ ⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣷⣿⣿⣿⣿⡷⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢀⣠⣾⣟⡖⢻⣿⣿⠃⠀⠀⣿⣿ ⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⠟⣻⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠿⠛⠉⠁⢰⢸⣿⡿⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠋⠰⢟⣿⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢠⡇⣿ ⣿⣿⣿⣿⣿⣿⣏⠓⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢾⣿⡟⠀⠀⠀⣼⠃⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⣰⠏⢰⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣡⣴⣾⣿⣿⣿⣿⡿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣰⠏⣠⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⣃⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣼⣿⣃⠤⠚⠚⠉⠉⠉⠙⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⢀⡄⠀⠀⠀⠀⠀⠀⠙⢽⣿⠿⠋⠉⠁⠀⢠⡆⢰⠃⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⢀⡞⢠⠋⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⢠⠃⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⢠⠉⢿⣿⣿⡟⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⡇⠇⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣼⠀⠈⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⡗⠤⣀⠀⠀⠀⠀⠀⠑⢄⣀⡞⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠹⢇⠀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠈⠻⣷⣦⣤⣀⡀⠀⠉⠀⠀⠀⣀⡴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠀⠀⠀⠈⠳⣄⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⢿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⣀⣀⠀⠀ ⠀⣾⠛⠛⠻⢶⣤⣤⣤⣤⣤⣴⠏⠀⠈⠻⣶⠞⠛⠉⠙⣷⠀ ⠀⣿⠀⠀⠀⠀⠈⠉⠀⠀⢠⡟⠀⢠⡖⣶⠿⢶⣄⣀⣤⣿⡄ ⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣈⣻⡇⠀⠀⢹⣯⠀⠈⣿ ⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠳⢤⣴⡿⠾⠀⢀⢿ ⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠿⣷ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to ＿ノヽ ノ＼＿ me or my son `/　`/ ⌒Ｙ⌒ Ｙ ヽ ever again. ( 　(三ヽ人　 /　 | |　ﾉ⌒＼ ￣￣ヽ ノ ヽ＿＿＿＞､＿_／ ｜( 王 ﾉ〈 (\__/) /ﾐ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣀⢈⣩⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⣒⣤⣀⡲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣯⡿⠟⠋⠈⠻⡛⠋⠹⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⢔⢉⢙⣹⡿⠳⣙⡊⣓⣉⣒⡤⡀⠀⠀⠀⠀⠀⣰⡟⣡⠟⠁⠀⠀⠀⠀⠀⠈⠑⠢⡍⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡇⠀⠻⣿⠟⠁⠀⠀⠀⠉⠉⠻⣟⠋⠙⠓⢤⣠⡴⣶⡿⣛⣉⣁⠒⠢⣄⣀⠀⣀⣤⡶⢺⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⡀⢾⠁⠀⠀⠀⣀⡠⠤⠶⠒⣺⠿⣟⢠⣯⣃⣳⡾⠲⠷⣮⣥⣴⣮⣤⣤⣬⣿⣟⣻⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⣷⣦⣤⣾⣿⣷⣶⡂⢉⡤⢊⣥⣿⡿⠿⠿⢿⣦⣤⣀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⢤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⡴⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⢽⣿⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣡⢁⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣠⣴⣿⣿⣿⠞⠁⠈⢿⢿⡷⠀⠀ ⠀⠀⣰⣾⣏⠩⡉⠰⣄⠀⠀⠀⠀⢠⢂⡴⢛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠃⠀⢀ ⠀⣰⡇⠈⠙⠤⣽⣧⣹⣷⣤⣀⣴⣡⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠋⠁⠀⠀⠀⣀⣴⣾⡿⠁⠀⠀⠘ ⢰⣟⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡖⠁⢸⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣰⡁⠀⠠⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⠀⠣⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠒⠤⡀⡜⠁⠀⠙⡆⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⡇⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠈⠺⢷⣿⣿⡶⠤⢕⡄⠀⠀⠀ ⠀⠀⠀⣠⠔⠂⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠤⣀⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀ ⠀⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⣤⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠀⠀⡀⡤⡀⠀⠀⣾⣟⠋⠀⠀⠀⠛⢗⡧⣀⡀⢀⡀⠀⣠⠲⡄⠀⠀⠀⠀⠀⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠜⢻⡆⢀⣇⣀ ⠀⡤⠜⢇⠀⠀⢹⡛⠙⣦⣤⣌⢭⣤⠆⣤⠀⢀⡀⠈⠚⠉⠉⠁⣠⠍⠀⠒⡿⠁⠀⠀⠾⡧⠄⠰⣗⠒⠤⣀⣀⡀⡾⠃⠀⢨⡇⠀⠃⠀ ⠀⠉⢢⡎⠁⠀⡼⡇⢠⡈⠉⠐⣽⡏⣠⣿⣗⠃⠀⠀⠀⠀⠀⠛⠒⡆⣠⣄⡽⢲⡆⠀⠘⠃⠀⠀⢱⡄⠲⣦⣌⠉⠁⡰⡇⠘⡆⠀⠀⠁ ⠀⠀⠞⠁⠀⡰⠏⣁⣤⣿⠻⠆⠙⢣⡈⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠧⠃⠀⠀⢿⣷⠄⠀⠀⠀⠀⠀⡛⡄⢇⠉⠁⠉⠀⢳⡀⠙⢗⡔⠀ ⠀⠀⠀⠠⣾⣃⣀⣩⡄⠏⣠⡿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣸⡏⡃⠀⠀⠀⠀⢀⡼⠧⠚⠀⠀⠀⠀⠀⣁⣢⣀⡫⡳ ⠀⠀⠀⠘⠋⠉⠱⡏⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⣣⡞⠁⠀⢀⠀⠈⠛⠊⠀⠀⠀⣠⠖⢃⡔⣓⣫⣡⣀⠤⣄⢐⠁⢸⢷⣖⣶ ⠀⠀⠀⠀⣆⣀⠘⣷⡟⢀⢄⠲⠡⣅⣍⡭⡢⡀⠀⠀⠀⠀⠀⠁⢀⣴⡿⣷⡀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠂⠛⠂⢷⡙⡾⢀⡏⠀⠁⠀ ⠀⠀⠀⠉⠹⠁⠀⢠⡪⣿⠃⠋⠉⠉⠉⠻⡆⣯⡆⠀⠀⠀⠀⡀⡖⣡⠿⠟⣧⠀⠀⠀⣠⣴⣦⡀⠀⠀⣀⡤⠞⠀⠀⠻⣆⡰⠁⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⢔⡯⠊⠀⣀⣆⠀⠀⠀⠀⠻⠑⠁⠀⠀⢀⣜⡿⠋⢀⣶⢠⢽⣇⠀⠀⣿⣇⠟⠛⠛⠛⠋⠀⠀⠀⠀⠀⠈⠁⢠⢸⠁⠀ ⠀⠀⠀⠀⠀⡬⣞⠀⠀⠀⠀⠇⠀⠀⠀⣀⣠⣄⡄⣤⡴⣯⠗⢁⡤⠃⢸⠀⠞⠻⢻⣧⡜⠋⠀⠀⣀⣆⡀⠀⢠⡄⠀⠀⠀⠀⠈⠓⠷⠶ ⠀⠀⠀⠀⠀⡇⣗⡀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣷⣖⠀⢬⡕⠒⠃⠀⠀⠈⠓⠤⣀⣀⠀⢛⠧⣤⡀⠀⡏⠁⠀⣾⡣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⡷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣂⠳⡀⠀⠀⠀⠀⠀⡤⠖⠚⡑⣲⡨⢡⣿⣶⢴⣚⣋⠁⢈⣹⢶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⡟⣸⡧⠖⠲⣄⠀⠀⡇⠐⣿⡿⠝⠩⠋⠛⠉⠀⠀⠈⣦⠏⠀⠀⠀⠀⢀⡄⠀⠀ ⠀⠀⣴⢽⠃⠀⠈⢏⢿⢂⠀⠀⠀⢸⠀⠀⠀⢠⠍⣾⡡⣕⣴⣏⣠⡌⠢⣄⢇⠀⡯⡇⠀⠀⣦⡀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠘⡺⠂⠀⠀ ⠀⠀⢯⡫⠀⠀⠀⣈⣆⢟⠀⠀⠙⡻⠉⠀⠀⣩⡾⡯⠟⠋⠁⠀⠈⠛⢷⣌⡛⠐⡻⣯⠀⠀⣀⠉⠳⡴⣴⡱⣦⠀⢀⡤⣄⠀⠁⠀⠀⠀ ⠀⠀⠐⢝⣧⣶⣶⣟⡯⠋⠀⠀⠀⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⠷⠾⠇⠀⠐⣎⡑⡄⠀⠁⠉⠁⠀⡼⢀⠘⣆⣰⡟⡇⠀ ⠀⠀⠀⠀⠀⠉⠉⡁⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣹⢯⠀⠀⠀⠀⢀⡇⣺⠀⠚⠃⠀⡃⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣄⠀⠀⠀⡏⠀⠀⠈⢳⡆⠀⠀⣚⠏⠀⠀⣀⠔⠊⠉⠳⡀⠀⢀⣤⣄⠀⣘⡜⠀⠀⢀⡴⠋⣠⣏⣿⣟⣀⢳⠁⠀ ⠀⠀⠀⠘⠟⡏⡁⠀⠀⣩⡍⠀⠑⠒⡆⠀⢀⡳⠀⣸⡗⠀⣄⣈⡀⠀⠐⡖⠋⠀⠀⣗⢧⣈⣶⡫⠂⠀⠠⣏⣀⣈⣉⡟⢉⣩⣍⣘⣄⠀ ⠀⠀⠀⠀⠀⠈⡊⣄⡊⠃⠀⠀⠀⠀⠳⠤⠏⠀⠀⡽⡇⠀⠶⢦⣌⠉⠉⠀⠀⠀⠀⠀⠉⢉⠁⠀⠀⠀⢀⣤⡄⠀⡏⢁⡾⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡗⠀⠀⠀⠀⠀⢰⠏⣆⠀⠀⠀⢹⣧⣀⣔⣺⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⡇⠀⠀⠣⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⠀⢀⣠⡇⠀⠘⠓⣲⡖⠀⠑⠛⠿⠟⠃⠀⠀⣠⣤⣄⠀⢀⣴⢟⣿⡶⡤⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣤⡀⠀⠀⠀⣇⢤⠢⣀⠀⠀⣀⣀⣴⠟⠋⢨⣿⡆⠀⠀⢱⡇⠀⠠⣷⣒⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⡶⠛⠫⢿⡀⠓⠿⠯⠏⠛⠊⠁⠀⠀⠈⠛⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⠙⣠⠇⠀⠀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⠀⢰⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⢀⣀⠤⠖⠒⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡮⠁⠉⠁⠒⠤⢀⡼⠖⠀⠐⣗⠢⡀⢸⣏⡁⠀⠀⢀⡠⠥⠒⠲⠤⢄ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣈⣍⣈⡿⡘⠁⣹⡚⠁⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣇⣠⡶⣍⣀⣠⠴⠛⠻⢇⣜⡁⠺⠽⠀⠀⠀⢠⡞⠁ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡉⢳⡄⣸⠁⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢻⡖⠒⠂ ⠈⠉⠸⡍⠈⠀⠀⠘⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣶⡄⠀⠀⠠⢸⠅⣀⠀ ⠀⠀⠔⢷⠈⠀⠀⠀⠘⠛⠁⠀⠀⠀⣤⢤⠀⠀⠀⠀⠸⠿⠁⠀⢀⣠⠟⠀⠀⠀ ⠀⠀⠀⣀⠷⢎⠁⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⠒⠀⠀ ⠀⠀⠀⠁⠀⠀⠉⡖⠀⠈⠑⡦⠤⠄⠄⠀⠤⠤⠤⡖⠉⠉⠹⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠞⠁⠀⠀⠀⠀⠀⠀

⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆ ⠀⠹⣟⠋⠙⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⢛⡿⠁ ⠀⠀⣌⢫⠉⠸⡝⢿⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣻⠇⠞⠉⣹⢋⡄⠀ ⠀⢠⢸⣾⡵⢶⣦⣀⠳⣄⢾⡓⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣿⢀⡜⠁⣴⣶⢮⣿⡟⠀⠀ ⠀⠀⢣⡙⠛⠀⠘⠿⠑⢮⣿⣷⡙⢆⠶⡄⠀⠀⢀⡴⢦⠎⣹⡷⣿⡼⠙⠏⠀⠚⢛⡵⠇⠀ ⠀⠀⠀⠹⠖⣦⡶⡄⠀⠀⠈⠓⣻⣌⢇⢸⠀⠀⡞⢰⣋⣞⠛⠋⠀⠀⢀⡴⣦⠖⠟⠁⠀⠀ ⠀⠀⠀⠀⣤⡿⢷⣾⣦⡄⠀⠰⣟⣙⣿⣆⢧⢠⢧⣿⣟⣹⡶⠀⢠⣴⢟⡾⣿⣥⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣶⣶⢨⠉⠛⢟⣀⡴⠞⡦⠅⢸⣿⠈⢬⠛⠧⣄⣘⠛⠉⠉⢰⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣯⡴⢤⣢⠏⣡⣤⢾⡇⡀⠈⣏⢠⡘⢗⢦⣄⡉⣶⣦⣼⣨⡏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⢰⣿⡟⢡⡿⡾⣯⠈⠿⠈⡿⡼⣆⠙⣿⣦⠀⠈⠁⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⡾⢻⣷⡟⣹⢿⠇⠀⠀⠀⢏⢧⢹⣷⣿⢿⣄⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢱⡟⠉⠀⠀⠀⠀⠘⠹⣧⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⡦⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡇⠀⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠁⣤⣤⠀⠉⠉⠛⠷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠋⢀⣴⣶⣾⣿⣿⣿⣿⣿⣶⣦⡀⠈⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⣾⢃⣠⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⣄⡀⢻⡆⠀⠀⠀ ⠀⠀⣸⡿⢋⡁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢈⡙⢾⣇⠀⠀⠀ ⢀⣾⠋⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠙⢷⡄⠀ ⣾⡇⠀⣼⠀⠀⠀⠛⠀⠀⡀⢲⡶⢀⡀⠀⠛⠀⠀⠀⢿⠀⢸⣷⠀ ⠸⣧⡀⢹⡄⢀⣀⠀⠀⠈⠧⠞⠑⠖⠃⠀⠀⢀⣀⢀⡿⢀⣼⠇⠀ ⠀⠈⠙⢻⡿⠉⠉⢳⣄⣀⡀⠀⠀⢀⣀⣀⡞⠉⠉⢻⡟⠛⠁⠀⠀ ⠀⠀⠀⠀⠻⠶⠶⠾⠉⠛⠛⠛⠛⠛⠛⠉⠻⠶⠶⠟⠁⠀⠀⠀⠀

⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⡿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⡟⠀⠀⢸⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀ ⣹⣿⣿⡃⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⠻⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠃⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠀⠀⠿⣿⣿⣷⠀⠀⠀⠀⠀ ⣼⣿⣥⠀⠀⠀⠀⠀⢸⣿⣧⡄⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠈⣿⣿⣶⣄⠀⠀⠀ ⢿⣿⣿⡇⠀⠀⠀⠀⠸⠿⣿⣿⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠈⠿⣿⣿⠀⠀⠀ ⢾⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⣿⣿⡇⣶⣦⡀⠀⠀⠀⠀⣿⣿⣶⡀⠀ ⠀⢾⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠰⣿⣿⡀⠿⣿⣧⣀⡀⠀⠀⠙⢻⣿⣇⡀ ⠀⢻⣿⣟⣀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣷⣄⠀⣀⣼⣿⣿⡇ ⠀⠘⠛⣿⣟⡀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⣿⣟⠁⠀⠀⠉⣿⣿⣿⣧⣽⣿⡿⠃⠀ ⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣿⣿⠀⠀⠀⢰⣿⣿⠿⢿⡿⠛⠃⠀⠀ ⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠈⠛⠉⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣴⣶⣿⣿⣶⣦⣤⣶⣾⣿⣿⣿⣶⣶⣤⣤⣶⣿⣿⣷⣦⣄⠀⠀⠀ ⠀⠀⢰⣿⣿⠟⢹⣿⣿⣿⡿⠟⠋⠉⠉⠉⠙⠛⢿⣿⣿⣯⡹⠛⣿⣿⣆⠀⠀ ⠀⠀⢿⣿⣇⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣿⣿⣿⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⡏⠁⠀⢀⣤⡀⠀⠀⠀⢀⣤⣄⠀⠀⠻⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠈⢹⣿⣿⣦⠀⠀⠸⠿⢿⣤⣤⣤⣘⠿⠟⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣠⣤⣶⣶⣦⣼⣿⣿⣿⣿⣴⣶⣶⣦⣄⣿⣿⠷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⡿⠛⠛⠻⢿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣿⣿⣶⡄⠀⠀⠀⠹⣿⡿⠁⠀⠀⢀⣴⣾⣿⣿⣷⣦⡀⠀⠀ ⠀⢠⣿⣿⡿⠉⠛⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠛⠉⠻⣿⣿⡆⠀ ⠀⠸⣿⣿⣄⣀⣀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⣀⣠⣿⣿⡷⠀ ⠀⠀⢙⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣏⠀⠀ ⠀⣰⣿⣿⠟⠉⠀⠘⠻⣿⣿⣷⣄⠀⠀⠀⣠⣾⣿⣿⡟⠉⠀⠉⠙⣿⣿⣦⠀ ⠀⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣤⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⣿⣿⡄ ⠠⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⡟⠿⢿⡿⠛⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⠃ ⠀⠹⣿⣿⣄⠀⠀⠀⣠⣾⣿⣿⣶⣦⣤⣷⣶⣿⣿⣿⣄⡀⠀⠀⣠⣿⣿⡟⠀ ⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠋⠙⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⡾⠁⢠⠖⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⠀⣾⠃⠀⠨⠄⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠁⠀⠉⠳⡀⠀⢀⣀⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⢠⠮⣉⡿⠀⠀⠀⠀⠀⠀⣽⠟⣋⠥⠒⠛⢶⣤⡽ ⠀⠀⠀⠀⠀⠸⡂⢰⣰⡂⠀⠀⠀⠀⠀⠀⢙⣧⣦⣔⡾⠟⠋⠀ ⠀⣀⡐⢢⠀⠀⠘⡬⠒⠂⡄⢿⡿⠀⠀⢀⡽⠃⠀⠀⠀⠀⠀⠀ ⠘⢦⣁⢸⠀⠀⢠⠞⠀⣄⣙⣒⣀⣤⡴⣿⡁⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⣻⣧⠀⢰⠃⠼⢄⠀⠀ ⠀⠀⠀⠀⠀⢀⡷⠠⠞⠃⠀⠀⠀⠐⠒⠦⢿⡀⠑⠒⠂⠋⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⢾⠟⠉⢷⡀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢸⡵⢀⣟⣸⣇⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠓⠒⠒⠒⠚⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠇⣷⢶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡝⢚⣷⢿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠁⠉⠈⠀⠀⡀⢦⠉⣄⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣼⣫⠛⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⣭⣯⣹⣉⣉⣤⠤⣖⠻⡈⢦⠘⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠇⣳⠴⢯⡴⢀⠀⠀⡄⠤⠢⠛⠈⠀⠀⠀⠀⡟⠚⠒⡀⣦⣷⠿⠤⣶⣛⢍⠤⠶⢰⠀⣆⠘⠋⣿⣴⠀ ⠀⠀⠀⠀⠀⣧⣸⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠣⠋⠴⣠⢀⠀⠀⠀⠀⠀⡀⢄⠶⠓⠉⣀⠀⠀⠀⠀⣄⢹⡇⢀⠀ ⠀⠀⠀⠀⠀⡏⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡄⣷⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⡄⢳⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡀⠹ ⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠑⠀⠀⠀⠃⣾ ⠀⠀⠀⠀⠇⢀⡇⢸⠀⠀⠀⠀⠀⠀⠃⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⣀⣳⣾⠓⣴⠀ ⠀⠀⠀⠀⡟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡏⢠⠀⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠁⡿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀ ⠀⠀⠇⢠⠀⠀⠀⠀⡇⣼⠹⠀⠀⠘⡿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⡇⡾⠀⠀⠀⠀⠀⡇⢹⡀⢳⠀⠳⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⢦⠛⣿⣿⣿⣿⣿⣿⢿⠻⠙⠉⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⠈⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣥⣼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⢷⠀⡶⣶⡠⣤⢦⡴⡷⣯⡿⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠋⢰⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠘⠀⠀⠀⠀⠀⡄⢹⠀⠞⢠⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡼⢀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠈⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢼⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡆⠘⠀⠀⠀⠇⡼⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠹⣧⡀⠀⠀⠀⡏⠉⠙⠋⢹⡆ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠛⠿⣦⡀⠀⠸⣷⡀⠀⠀⠹⣄⠀⠠⡹⠃ ⠀⢀⣿⠃⠀⠀⠀⠀⣠⣶⠾⠟⠛⠉⠉⠛⠿⣶⣄⠀⠀⠀⠀⣰⠃⢀⣠⣤⣄⠀⠈⢻⣦⠀⢻⣧⠀⠀⠀⠈⠓⠋⠀⠀ ⠀⢸⣿⠀⠀⠀⣠⣾⠋⠁⠀⠀⢀⣠⣤⣤⣤⣈⠙⣷⣄⠀⢠⣏⣶⣿⣿⣿⣿⣿⣦⠀⢻⣧⠘⣿⢀⢸⡛⠛⢲⠀⠀⠀ ⠀⣾⡇⠀⠀⢠⡿⠁⠀⠀⣠⣾⡿⢿⣿⣿⣿⣿⣷⣌⢿⣆⢸⣿⡋⠉⢉⣿⣿⣿⣿⣧⠈⣿⠀⣿⣿⠀⠹⠶⠋⠀⠀⠀ ⠈⡟⣿⠀⠀⢸⠇⠀⢀⣼⣄⠈⠀⣸⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣶⣿⣻⣿⣿⣿⣿⣤⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⢹⡆⠀⢸⡄⠀⣾⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏⣸⢧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⢳⡀⠈⢧⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢎⠃⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⡿⠟⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⡻⠿⢿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣀⡀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠬⣷⣄⡲⣤⣈⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢛⡵⠚⠁⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⢻⣿⠒⠭⣟⣷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣶⢾⣟⠯⠗⠊⠁⠀⠀⠀⣾⠟⠁⠀⢘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣧⠀⠀⠈⣿⡄⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠇⠀⠀⠙⠛⠛⠒⠒⠛⠛⠛⠻⠿⢷⡢⣤⣔⡶⠿⠟⠛⠛⠛⠻⠿⠽⠟⠁⠀⠀⢺⡿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⠒⠲⠛⠙⠲⠦⢼⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⠀⠀⠀ ⠀⠀⠹⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣴⢯⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⣖⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⠮⣷⣶⡤⡤⠴⠾⠟⠋⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣤⣴⠶⠶⣤⡤⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣼⠿⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⢻⠶⠴⡟⡛⠟⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠙⠉⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⣠⣾⡶⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡄⢸⣟⡈⠁⣹⣷⣤⣀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡐⣿⠁⠀⢸⡇⠀⠀⠉⠙⠉⣻⣆ ⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⣄⣀⣤⡶⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⡀⣴⢿⠉⠉⠉⠉⠛⢿⣆⠀⠈⣿⣤⣈⣡⣤⡶⠟⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⠠⠍⢹⡿⠅⠀⠀⠀⠀⠀⢿⠛⠀⠀⢠⣿⣷⡄⠀⠛⢛⣫⣿⡿⠇⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⠈⠁⠁⠀⠀⠀ ⠀⠀⠀⠀⣸⡟⠏⠻⣷⡄⢸⡷⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢠⡾⣿⠻⠷⠀⠀⣻⣧⠈⠻⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣧⡀⠀⠀⠀⢀⣿⠉⠀⠀⠈⢛⣷⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⠀⠀⢀⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⠀⠀⠀⢀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡶⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣀⣀⢀⡀⣀⣀⣴⡿⠟⠛⢷⣦⣄⣀⣤⣠⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡤⣄⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢆⠙⣡⠏⠀⠀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⠀⢰⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⢀⣀⠤⠖⠒⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡮⠁⠉⠁⠒⠤⢀⡼⠖⠀⠐⣗⠢⡀⢸⣏⡁⠀⠀⢀⡠⠥⠒⠲⠤⢄ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣈⣍⣈⡿⡘⠁⣹⡚⠁⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣇⣠⡶⣍⣀⣠⠴⠛⠻⢇⣜⡁⠺⠽⠀⠀⠀⢠⡞⠁ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡉⢳⡄⣸⠁⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢻⡖⠒⠂ ⠈⠉⠸⡍⠈⠀⠀⠘⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣶⡄⠀⠀⠠⢸⠅⣀⠀ ⠀⠀⠔⢷⠈⠀⠀⠀⠘⠛⠁⠀⠀⠀⣤⢤⠀⠀⠀⠀⠸⠿⠁⠀⢀⣠⠟⠀⠀⠀ ⠀⠀⠀⣀⠷⢎⠁⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⠒⠀⠀ ⠀⠀⠀⠁⠀⠀⠉⡖⠀⠈⠑⡦⠤⠄⠄⠀⠤⠤⠤⡖⠉⠉⠹⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠞⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠳⢶⣦⣴⡿⠋⢸⣇⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⡀⠈⢿⣧⣤⠾⠛⠋⠉⠉⠉⠉⠛⠛⢷⣶⣤⡀⢀⣴⡿⣿⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⠿⠋⠙⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠿⣿⣿⠋⠀⣿⡇⠀⠀⠀⠀ ⠀⢰⡿⠃⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⣿⠷⠶⢿⣧⡀⠀⠀⠀ ⠀⣾⡃⠀⣠⠏⠀⠀⡀⢀⣼⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠙⢿⣦⠀⠀ ⠀⣿⣷⣴⡏⠀⢠⣾⡇⣼⣯⠀⠀⠀⠀⠀⠀⠀⣷⡀⢀⠀⠀⠀⢻⡄⢀⠀⠀⠈⢿⡆⠀ ⣞⣻⠟⣿⠁⠀⣿⠃⣿⣇⣸⣗⠒⣀⠀⠀⢀⣼⠋⣇⣸⣤⠀⠀⠈⣧⠘⣧⠀⠀⢸⡇⠀ ⠈⢿⡇⣧⡆⠀⣿⣼⣿⣿⣿⡿⢦⣼⠀⢀⣼⣇⣄⣽⠏⢿⡇⠀⢠⡿⣆⠸⡄⠀⣼⡇⠀ ⠀⠘⢿⣿⣿⣄⣿⡟⢹⡾⢿⡗⢀⡧⠶⠋⣽⢿⣿⣿⣷⣸⡇⠀⢀⡗⠛⠓⠻⣼⣿⣷⡄ ⠀⠀⠀⠉⣻⣿⣿⣗⠈⠛⠛⠁⠀⠀⠀⠀⢹⡟⢿⡿⣸⡿⠀⣼⣿⠇⢠⡆⣠⣿⠟⠛⠁ ⠀⠀⢀⣤⣿⣿⠃⠙⢦⣀⠀⠀⢀⠀⠀⠀⠀⠉⠉⢴⣿⣷⣾⡿⠿⣶⣿⡿⠟⠁⠀⠀⠀ ⠀⠀⠘⠿⣿⣾⠀⠀⢀⣿⠛⢶⣶⣿⡷⢤⣤⣤⣶⠾⠛⡟⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⢿⠇⡄⣨⡿⣴⡿⣧⣿⣶⣞⣵⡿⢿⠀⣾⡇⠀⠀⠀⣦⡙⢿⣤⡀⠀⠀⠀ ⠀⠀⢠⣿⢟⡀⢰⠁⢻⡿⢃⣷⣾⣿⣿⣿⠙⣆⠈⢧⣹⣿⠀⠀⢰⡘⣿⡿⠿⠃⠀⠀⠀ ⠀⠀⠈⣿⣿⠁⣿⣠⠟⢄⣼⡛⠛⠋⠻⠿⠀⠘⣆⠈⢿⠛⠀⢰⠘⣇⠸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⡀⣿⣏⣹⡾⡿⠋⠀⣄⠀⠀⠰⠄⢹⣦⠈⢧⡀⢸⠀⣿⣄⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣷⣿⣧⠀⢰⣧⣄⣚⣿⡀⠐⠒⣀⣨⣿⣧⣸⡇⠀⣼⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⣷⣬⣷⣦⣭⣍⣙⣏⣉⣭⣴⡟⠁⣉⣰⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢿⣀⠀⣽⡇⠀⠀⣿⣧⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣁⣽⣿⠁⠘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⠴⠚⡙⠙⠲⣤⣠⠖⢋⡛⠙⠲⣄⠀⠀ ⣴⠃⣰⠟⠉⠙⢦⡈⢁⣾⡟⠉⠳⣆⠸⣇⠀ ⣿⠀⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿⠄⣿⠄ ⠸⡄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⡏⠀ ⠀⠙⣆⠙⢧⡀⠀⠀⠀⠀⢀⡴⠃⣰⠏⠀⠀ ⠀⠀⠈⠳⣄⠙⠶⣄⣀⠴⠋⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢦⡈⢡⣰⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⠀⠈⠙⠷⠤⠤⠤⡾⠋⠉⠳⣦⡤⠤⢤⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣸⠁⢰⣿⡷⠣⣄⣀⣈⡇⠀⠀ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠘⠲⠦⢿⡀⢀⣼⣧⠈⣽⡆⠀ ⣀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣙⣋⡴⡟⠀⠀ ⠉⣉⣏⠉⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠈⣀⣿⣀⡀ ⠐⠙⣻⣉⡀⠀⠀⠀⠀⠀⣖⡶⠀⠀⠀⠿⠀⠀⢈⣩⡏⡉⠛ ⠀⢾⡿⣿⢖⠊⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⠋⠛⠀ ⠀⣾⢱⠃⠀⢱⢓⡄⣠⠛⢦⡤⣀⣀⣀⣠⡴⠾⠋⠉⠋⠂⠀ ⠀⠙⢾⣦⣄⠈⠉⢸⠁⠀⢸⠀⠀⣷⠀⠹⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠹⢮⣍⣙⣫⠷⠒⠼⢲⣺⡥⢶⡄⠙⣆⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠸⣆⡀⣸⠁⠀⣈⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⣄⣀⣐⣀⣀⣀⣩⣥⠶⠛⢻⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠹⡀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠙⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⡀⠀⠀ ⠀⠀⣖⣇⣷⢿⣷⣦⢀⣎⣟⣽⣿⣿⣧⡄⠀ ⢠⣿⣗⣿⣽⣷⣿⣿⣯⣿⣿⣿⣿⣿⣷⡷⠂ ⢆⣿⣷⡷⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⡿⡇⠀ ⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡱⠁⠀ ⠀⠀⠈⠟⣿⡿⣿⣟⣷⣿⣿⣟⣻⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡫⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠒⠛⠉⠉⠉⠛⠻⢦⡀⠈⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣿⠀⡏⡬⣍⣲⡤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠖⠚⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡧⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀ ⠙⣷⠅⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⢄⣀ ⠀⠘⣦⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠋⠀⠠⡇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⡆⡟ ⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠠⣿⣷⠀⠰⡏⢻⠉⠀⢸⡀⠀⠀⡇⠀⢹⣿⢆⢀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠟⡼⠁ ⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠸⣸⡆⠀⠀⠁⠀⠀⡇⠀⢰⡇⠈⠉⠛⠂⠸⣿⠆⠈⠁⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢⠧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠿⣦⣀⣀⣠⣤⣤⠖⠀⠀⠀⠀⠀⠐⢦⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⡿⠃⠀⠀⠀⠀⠀⠀⢢⠀⠈⠉⢻⡗⠂⠀⠀⠀⠀⠀⠀⠙⠲⣶⠦⠤⠔⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⠁⠀⠀⠀⠀⠀⠀⠀⠈⣉⣙⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡟⠲⡴⠒⠲⠆⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⠻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⠚⠛⢳⡤⣦⣄⣰⣴⠶⠶⠴⠶⠼⠷⠶⠤⠤⠤⠤⠤⠦⢴⡋⠉⠁⣰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

░░░░░░░░░░░░░░░░░░░░░▄▀░░▌ ░░░░░░░░░░░░░░░░░░░▄▀▐░░░▌ ░░░░░░░░░░░░░░░░▄▀▀▒▐▒░░░▌ ░░░░░▄▀▀▄░░░▄▄▀▀▒▒▒▒▌▒▒░░▌ ░░░░▐▒░░░▀▄▀▒▒▒▒▒▒▒▒▒▒▒▒▒█ ░░░░▌▒░░░░▒▀▄▒▒▒▒▒▒▒▒▒▒▒▒▒▀▄ ░░░░▐▒░░░░░▒▒▒▒▒▒▒▒▒▌▒▐▒▒▒▒▒▀▄ ░░░░▌▀▄░░▒▒▒▒▒▒▒▒▐▒▒▒▌▒▌▒▄▄▒▒▐ ░░░▌▌▒▒▀▒▒▒▒▒▒▒▒▒▒▐▒▒▒▒▒█▄█▌▒▒▌ ░▄▀▒▐▒▒▒▒▒▒▒▒▒▒▒▄▀█▌▒▒▒▒▒▀▀▒▒▐░░░▄ ▀▒▒▒▒▌▒▒▒▒▒▒▒▄▒▐███▌▄▒▒▒▒▒▒▒▄▀▀▀▀ ▒▒▒▒▒▐▒▒▒▒▒▄▀▒▒▒▀▀▀▒▒▒▒▄█▀░░▒▌▀▀▄▄ ▒▒▒▒▒▒█▒▄▄▀▒▒▒▒▒▒▒▒▒▒▒░░▐▒▀▄▀▄░░░░▀ ▒▒▒▒▒▒▒█▒▒▒▒▒▒▒▒▒▄▒▒▒▒▄▀▒▒▒▌░░▀▄ ▒▒▒▒▒▒▒▒▀▄▒▒▒▒▒▒▒▒▀▀▀▀▒▒▒▄▀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢱⡄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡅⠀⠀⢳⡀⠀⠀⠀⠀⢀⣠⡞⢫⣿⢟⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⢳⠀⠀⠀⣰⠞⡡⢜⡿⢃⢼⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡍⣙⣯⣙⣛⡓⠶⣤⣈⡇⠀⣧⠀⠀⠀⠘⡇⢠⡞⡱⢊⣱⡾⢃⣍⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣍⢍⠛⡻⠷⡦⢙⢻⡄⢹⡆⠀⠀⢀⣷⠏⠴⣁⣷⠟⡡⢎⣞⣁⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⡿⣿⢿⡿⣿⢿⣿⣾⣶⣿⣦⣿⣀⠀⣸⠏⡜⢶⣛⣥⠾⠛⠋⠉⠀⠀⢀⣠⠩⣹⠇ ⠀⠀⠀⠀⢀⣴⣿⣿⠽⡫⣍⠹⣌⢣⠜⣬⣧⣍⡙⡛⢯⣿⣽⣻⢿⣿⣾⣴⡛⠉⠀⣠⣤⡤⠶⠖⠛⠉⣁⡴⠋⠀ ⠀⠀⠀⣰⣿⢿⣾⠟⣹⡗⣌⠳⡌⢶⡿⢋⣼⢇⡚⣱⢊⠼⣷⣟⡿⣾⣽⣻⢿⣿⣿⣛⠛⡛⠶⠶⣾⣍⡁⠀⠀⠀ ⠀⠀⣰⣿⢯⢿⣇⡼⣏⠲⣌⠳⣘⠻⡷⣞⢋⠦⡱⢢⣭⣾⠟⢹⣿⢷⣯⣟⣿⣽⣻⢿⣷⣝⠻⠷⣶⢮⡝⢳⣦⡄ ⠀⢀⣿⣽⡏⢎⡜⡱⢌⠳⣌⠳⣌⠳⣰⣡⣮⣵⡿⣿⣻⣧⣴⣿⢯⣟⡾⣽⢾⣿⢯⣿⣽⣻⣷⣵⣤⠶⠞⠋⠁⠀ ⠀⣸⣿⡾⡘⢆⢎⡱⢊⡵⣈⢳⣬⣷⣟⣯⣿⣳⣟⡷⣯⣟⣯⣟⣯⢿⡽⣯⣟⡿⢋⣿⣾⢯⣟⣿⡄⠀⠀⠀⠀⠀ ⠀⣿⣷⠣⣝⣾⢾⡥⢋⡴⣽⣿⣻⣾⠋⣰⣿⣻⢾⡽⣷⣻⢾⡽⣾⢯⣟⣷⣿⣀⣾⡿⣽⣯⢿⣞⣿⡆⠀⠀⠀⠀ ⢠⣿⣯⢱⡿⢷⡿⣑⢣⣾⣟⣾⣳⣿⣾⢿⣳⣯⢿⣽⣳⣟⣯⡿⣽⣟⣾⣳⣟⣿⡿⣽⣷⣻⣯⢿⣽⣿⠀⠀⠀⠀ ⢸⣯⡗⢎⠿⢫⠱⣌⣻⣟⣾⣳⣟⡾⣽⢯⣷⣻⣟⡾⣽⣾⠏⣰⣿⣟⣾⣳⣯⣿⢿⣽⡾⠟⣿⣟⡾⣿⡇⠀⠀⠀ ⢸⡿⣿⣈⠞⣡⠳⣰⣿⣻⣞⡷⣯⢿⣽⣻⠾⣷⣯⢿⡽⣿⣶⢿⣳⣟⣾⣳⣿⢯⣿⣿⣁⣼⣿⣽⣻⢿⠇⠀⠀⠀ ⢸⡿⣽⡷⣎⣥⣳⡿⢻⣷⢯⡿⣽⣻⣾⠋⣰⣿⢯⡿⣽⣳⣯⢿⡽⣞⣷⣻⣯⢿⣳⡿⣟⣯⣷⢯⣿⡿⠀⠀⠀⠀ ⠀⣿⣯⣟⡿⣿⣋⣠⣿⣯⢿⡽⣷⢯⡿⣿⢿⡽⣯⢿⣽⣳⣯⣿⠟⢻⣯⣷⣟⡿⣽⣻⣽⣻⢾⡿⣽⠃⠀⠀⠀⠀ ⠀⢿⣳⣯⢿⡽⣟⡿⣽⣞⣯⢿⡽⣯⢿⡽⣯⢿⣽⣻⣞⡷⣿⣇⣠⣿⣿⣳⣯⢿⣻⡽⣷⣻⣯⣿⠃⠀⠀⠀⠀⠀ ⠀⠸⣿⣞⣯⢿⣽⣻⢷⣯⣟⣯⡿⣽⢯⣿⠟⢩⣿⢷⣯⢿⣽⣻⣿⣟⡾⣷⣻⢿⣽⣻⣽⢷⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣽⡾⣯⢷⣻⣿⠋⣸⣿⡽⣯⢿⣯⣤⣿⢯⣟⡾⣿⣾⣟⡷⣯⣿⡽⣯⣿⣳⣿⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣽⢯⣟⣯⣷⣴⣿⢯⡿⣽⢯⡿⣽⢯⣿⣽⣿⡿⢾⣯⣿⣽⣞⣿⣳⣯⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣯⣟⣾⣽⣻⣞⣯⢿⡽⣯⣿⢿⣟⡿⣾⡏⢀⣾⣟⣷⣻⣾⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣞⣷⣻⡾⣽⣿⣻⢿⣽⣻⡾⣿⡽⣿⣿⠿⠽⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠿⠿⠾⠽⠿⠷⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⣴⣶⣶⣶⣶⣶⣦⣀⡀⠀⠀⠀ ⢰⣾⡿⠋⣩⣉⣭⣉⣍⠙⢿⣷⣦⡀⠀ ⠀⢉⣼⣿⡟⠻⠛⠿⢻⣶⡌⠙⢿⣥⡀ ⢠⣾⣿⠇⣾⣿⣿⣿⣤⠸⣿⡇⢾⣿⡁ ⠸⢿⣇⡙⣻⣶⣀⡛⣳⣼⠟⢁⣻⡏⠁ ⠀⠸⢿⣷⣍⠿⠿⠿⢟⣡⣰⣿⡏⠀⠀ ⠀⠀⠈⠹⠿⢿⣾⣷⣾⡿⠏⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠉⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠉⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣦⣤⣤⣄⡀⠀⢀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠞⣿⠟⠋⠉⠉⠙⣻⠿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢠⡞⠁⠀⠀⠀⢀⡴⠋⠀⢀⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⠏⠀⠀⠀⠀⣰⠏⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⠤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⣠⡏⠀⠀⠀⠀⣼⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣄⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠋⠀⠀⠀⠀⢸⣧⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣾⡿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳ ⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⢿⣿⣷⣄⡀⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣦⣼⣿⠀⠀⠀⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⡿⠋⠉⠉⠁⠀⠀⠀⠀⠉⢯⡙⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠃⢀⡤⠖⠋⣉⣉⣉⣉⠉⠉⠒⠦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣾⣿⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠻⢿⣿⣷⣦⡀⠀⠈⠙⠛⠛⠋⠀⢰⠟⡇⠀⠀⠈⠻⡿⠛⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⣴⠟⣫⣿⣿⣄⠀⠀⠀⠀⡶⢌⡙⠶⣤⡈⠛⠿⣿⣷⣦⣀⠀⠀⠀⠀⡇⠀⢻⣄⠀⠀⣠⢷⠀⠀⠀⠀⠀⡶⠀⠘⡆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⢸⣟⢸⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠈⠛⠦⣝⡳⢤⣈⠛⠻⣿⣷⣦⣀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠛⠦⠤⠤⠚⠁⠀⠀⢳⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠈⢿⣞⣿⣿⣿⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠳⢬⣛⠦⠀⠙⢻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣿⠉⢻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⣠⣄⠀⠀⢰⠶⠒⠒⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡟⢿⣷⣦⣴⣶⣶⣶⣶⣤⣔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⣤⠀⠀⠿⠿⠁⢀⡿⠀⠀⠀⡄⠈⠙⡷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠙⣿⣿⣉⠉⠙⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠙⠷⢤⣀⣠⠴⠛⠁⠀⠀⠀⠇⠀⠀⡇⢸⡏⢹⡷⢦⣄⡀⠀⠀⠀⣿⡀⢸⡇⢸⡇⠀⡟⠀⢸⠀⢹⡷⢦⣄⣘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠢⣤⡀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⡷⣤⣀⡇⠸⡇⢸⡇⢸⠉⠙⠳⢦⣄⡻⢿⣾⣧⣸⣧⠀⡇⠀⢸⠀⢸⡇⢤⣈⠙⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣷⣌⡉⠛⠲⢶⣶⠖⠛⠛⢶⣄⡉⠛⠿⣽⣿⣶⣧⣸⡇⢸⠀⠀⠀⠀⠈⠙⠲⢮⣝⠻⣿⣷⣷⣄⣸⠀⢸⡇⠀⠈⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠻⢿⣷⣶⣤⣉⡻⢶⣄⣀⠈⠙⠳⢦⣈⡉⠻⢿⣿⣷⣾⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢭⣛⠿⣿⣷⣼⡇⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣶⣽⣻⡦⠀⠀⠈⠙⠷⣦⣌⡙⠻⢿⣟⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢯⣻⡇⠀⠀⠀⠀⠀⢸⣿⠀⣀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡏⠙⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣶⣤⣤⣤⣀⣈⠛⠷⣤⣈⡛⠷⢽⡻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢤⣀⠀⠀⢸⣿⡀⠈⠳⢤⣀⣀⣰⠃⠈⠛⠶⠶⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠉⠙⠛⠛⠻⢷⣦⣄⣩⣿⠶⠖⠛⠛⠛⠛⠛⠛⠿⢷⣶⣦⣄⠀⠀⠀⠀⠉⢻⣶⣿⣿⠇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⣠⠖⠂⠀⠀⠀⠈⠙⠿⣿⣦⡄⠀⠀⣸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠙⢿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠦⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠄⠙⡿⠿⠦⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠂⠀⠀⠀⠀⢀⡀⣀⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢴⠶⡄⠀⠀⠀⢠⠋⠀⢸⠁⠈⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⡿⠁⠀⠀⠀⡎⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⠀⠀⢀⡼⠙⢦⠀⠀⠀⠀⠀⣀⡰⠇⠀⢰⠀⠀⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⠓⠒⠙⠀⠀⠀⠑⠤⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢠⣆⢀⠀⡀⠷⢦⣖⠆⠀⠙⢶⠄⠀⠀⣴⣀⡀⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠘⠛⠛⠁⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⢙⡖⠂⠈⠓⠛⠂⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢎⣁⡀⠀⠀⠀⠀⠀⢀⣀⠤⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⡦⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⢠⠉⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠶⣄⢀⣠⣤⠴⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠉⠉⠉⠛⠶⠶⠖⠒⠒⣾⠋⠀⢀⣀⣙⣯⡁⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢯⣼⠋⠉⠙⢶⠞⠛⠻⣆⠀⠀⠀ ⠀⠀⠀⢸⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡤⢿⡀⠀⢀⣼⣷⠀⠀⣽⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢏⡉⠁⣠⡾⣇⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⢻⡀⠀⠀ ⣀⣠⣼⣧⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠖⢻⡟⠓⠒ ⠀⠀⠈⣷⣀⡀⠀⠘⠿⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠲⣾⠦⢤⠀ ⠀⠀⠋⠙⣧⣀⡀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠃⠀⠀⠀⠀⠀⠀⠀⢤⣼⣏⠀⠀⠀ ⠀⠀⢀⠴⠚⠻⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠉⠓⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⣶⣤⣴⡶⠶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀★welcome chessecake★

⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣆⠀⠀ ⠀⢀⣾⣿⡟⠉⠻⣿⣿⣷⡄⠀⠀⣀⣀⣀⣀⣀⠀⢀⣠⣾⣿⡿⠛⣿⣿⡄⠀ ⠀⣼⣿⡟⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠹⣿⣿⡄ ⢀⣿⣿⣫⣾⣿⣿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣦⣼⣿⣿⠁ ⠘⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀ ⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⣼⣿⡇⠀ ⠀⠘⣿⣿⣆⠀⠀⠀⠀⣾⣶⣠⣴⣿⣿⣦⣤⣾⣿⡟⠁⠀⠀⠀⣰⣿⣿⠃⠀ ⠀⠀⠘⢿⣿⣦⡀⠀⠀⢻⣿⣿⡿⠟⠛⠻⠿⠛⠋⠀⠀⢀⣠⣾⣿⡿⠃⠀⠀ ⠀⠀⠀⠈⠻⢿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⢠⣤⠤⠶⠤⠤⠦⠦⠶⠶⠶⢶⣶⣶⡶⠶⠶⠶⠲⠶⠶⠶⠒⠒⠚⣿⣷⡶⠶⠖⠒⠚⠛⠛⠛⠚⠒⠒⠛⠛⠛⠛⠛⠛⠿⣶⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⢠⡶⠶⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢾⣷⣤⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃ ⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢸⡁⠀⠀⠀⠀⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣠⡶⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢸⠀⠀⠀⠀⠀⠀⣾⠁⠘⣷⡀⠀⣀⣀⠀⣀⣠⣷⡟⠋⢹⣿⠿⣦⣀⠀⣰⡏⠀⠀⢀⣴⢿⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢸⠀⠀⠀⠀⠀⢰⡇⠀⡏⣿⢿⣶⢿⣿⢿⣿⠿⣿⠀⠀⣿⣿⠀⢸⡟⢷⣿⠴⠖⠛⠋⠀⢼⣧⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢽⠀⠀⠀⠀⠀⣾⠁⢀⣼⠇⠉⠟⠉⣿⠌⠿⠀⠹⢷⣸⣏⡟⠀⣺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⣻⠀⠀⠀⠀⣰⡏⢰⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⢿⣿⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣰⣄⣈⣿⣤⣤⠄⠀⠀⠀⠀⣿⠀ ⣿⠀⠀⠀⠀⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⣿⡄⠀⠀⠀⢀⣠⡦⠤⢀⣀⠈⠉⠈⠙⣿⢧⡄⠀⠀⠀⠀⢀⣿⠀ ⣿⠀⠀⠀⢀⣸⣇⣀⡀⠀⠹⣶⡿⠷⠀⠀⠀⠸⠿⠱⣶⣶⣿⣷⡀⣀⠀⠈⠉⠀⠀⠀⠉⣀⣰⣶⡿⢿⣶⣶⣶⣶⠾⠿⠏⣿⠀ ⣿⠀⠰⡖⠛⢉⣿⣿⣇⢀⡀⠀⠀⢀⣸⣻⣀⠀⢀⣀⣷⣿⣿⣿⣿⣿⡃⠀⢀⣠⡴⠞⠛⠉⠁⢹⣆⠀⣹⡟⠛⠛⠛⠶⢦⣿⠀ ⣿⠀⠀⠀⢺⣫⣵⣿⡿⠛⠙⢳⡞⠛⠉⠉⠉⣿⠋⠉⢹⣿⠿⢤⣿⡟⠋⠛⣿⠁⠀⠀⠀⠀⠀⠀⠙⣿⡛⠇⠀⠀⠀⠀⠀⣿⠀ ⣿⣤⡴⠞⠋⠉⠉⠉⢷⣄⣠⠾⠃⠀⠀⠀⠀⠙⢻⡶⠿⠃⠀⠀⠘⠿⣤⣴⢏⡿⣦⡀⠀⠀⠀⠀⠀⢹⡟⠇⠀⠀⠀⠀⠀⣿⠀ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠰⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀ ⢻⣿⣶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⣶⠶⣤⣤⣤⣤⣤⣤⡦⢶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣤⣤⣾⣿⡿⠁ ⠀⠀⠀⠀⠀⣀⠀⠠⣤⡀⠀⠀⠠⣄⠀⢦⡄⠀⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⢤⣄⡀⠀⠀ ⠀⠀⠀⣤⣄⣿⣤⣠⣘⡿⠄⠀⠀⣹⣦⣼⣿⣤⡀⠀⠀⢀⣦⣴⣿⡷⠶⠂⠀⠀⢠⡶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣧⠀⠀ ⠀⠀⠀⠀⣤⣽⣯⣍⠀⠀⠀⠀⠘⠋⣿⡀⠿⠜⠇⠀⠀⠈⠉⣿⣿⣯⠄⠀⠀⠀⠀⢀⣠⣿⣝⣷⠀⠀⠀⣀⣿⣀⠈⠘⠁⠀⠀ ⠀⠀⠀⠐⠿⠿⠠⣿⠂⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠈⢽⡿⠀⠀⠀⠀⠀⢿⣿⣟⣽⡟⠓⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠙⢲⠋⠁⠀⠘⡷⡄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡴⠒⠢⡄⠀⠀ ⠀⠀⠀⠀⣠⠋⠁⠀⠙⢾⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⡰⠃⠀⠀⠀⠱⡜⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣀⡞⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠈⠀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠏⠀⠀⠀⠈⢣⠀⢀⠖⠉⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⣄⠀⠀⠀⠀⠈⠳⢄⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⡀⣀⡔⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⠖⠒⢼⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡼⠀⠀⠀⠀⡾⠋⠉⠛⠳⣄⣴⠃⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢾⠇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠳⣀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⢀⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⡠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣲⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⠦⣠⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢄⠀⠀⠀ ⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀ ⠀⠸⠀⠀⠀⣠⡤⣤⣄⠀⠀⠀⢀⣴⢶⣦⡄⠀⠀⢳⡀ ⠀⠀⠀⠀⠐⣿⣴⣿⣿⡇⠀⠀⢿⣷⣾⣿⡷⠀⠀⢸⠀ ⢰⣇⠀⠀⠀⠙⠛⣿⠛⠁⠀⠀⠈⠛⠛⠋⠁⠀⠀⣸⠀ ⠀⠙⣆⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣰⠟⠀ ⠀⠀⠈⠑⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣊⣁⡀⠀ ⠀⠀⠀⠀⠀⠈⠓⡶⠒⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠈⢇ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣿⠀⠀⢰⠉⢹⣳⠀⠀⡸ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡟⡆⠀⢸⣄⣜⢘⣄⣠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠚⠀⠘⠶⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠿⠿⠿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠀⠀⢠⣴⣶⣶⣤⡀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⢰⡿⠋⣠⣴⠿⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢻⣧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣶⣄⠀⠀⢀⣤⣤⣤⣶⣤⣤⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣶⣿⠿⠛⠋⠉⠛⠛⢿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠛⠻⣷⡄⠀⠈⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢹⣷⠀⠀⢸⣿⡇ ⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⣠⣾⠏⠁⠀⣼⣿⡇ ⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⢀⣵⣿⡿⠁ ⠀⠀⢀⣾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣾⣿⣿⠟⠁⠀ ⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣄⠀⠀⠀⠀⢀⡤⠄⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠉⠀⠀⠀⠀ ⠀⠀⣿⣿⠁⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠹⠀⠀⢀⠞⠁⣤⣤⣀⣀⡀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣤⣾⣿⣭⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠙⣿⠿⠛⠃⠀⢱⠀⠀⠀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⠟⠛⠉⠉⠙⠛⢻⣿⡶⢶⣶⣶⣶⣤⣤⣤⣤⣀⣀⣜⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢸⠀⠀⠀⠉⠙⠛⢻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠃⠀⠀⠀⠐⢿⣾⣿⠿⢷⣶⣶⣤⣤⣌⣉⣉⠉⢻⡟⠛⠿⠿⢷⣶⣿⣧⣤⣀⣀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⣿⡇⠀⠀⠀⠀⢰⡟⠉⠉⠛⠛⠿⢿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢀⣿⣯⣈⣉⠛⠛⠿⢿⣶⣶⣤⣤⣀⡀⣀⣈⣻⣾⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣄⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣄⣀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣼⡿⠛⠛⠿⠿⣿⣶⣶⣦⣬⣭⣙⣻⣿⡟⠛⡻⣿⣷⣄⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⠿⠶⡀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⣻⣿⠆⠀⠈⠻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠿⣿⣦⣄⣀⣀⣀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠨⢿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣀⣀⣀⣠⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⢀⣀⣤⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣿⡀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣂⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⣼⣷⠼⣞⣽⢏⣿⣆⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠛⠢⠐⡍⡉⣾⣾⣽⣟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣦⠀⠤⢶⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⡙⢻⣿⣿⣧⣽⣉⣁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡔⡉⣩⢋⡋⠩⠯⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣘⣶⣁⢙⢐⣄⡴⠪⠓⠁⠉⠃ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣿⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⢐⢝⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⢛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠿⠗⠿⠇⠀⠀⠀⠀Pls don’t put innapropriet things here we just want to find cute emojis and have a good time. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⣸⠁⠀⠀⠀⠀⠀Younger children just want to find cute emojis, not see other things. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⠀pls spread the word and have a good day. <3⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

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