⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣿⣤⣨⣿⡀⠀⠀⠉⠙⠷⣤⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠋⠉⠉⠉⠉⠉⠛⠒⠦⣤⡀⠀⠈⢻⣆⠀⠹
⠀⠀⠀⣴⢶⣶⡶⠖⢋⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣾⣿⣠⡤
⠀⠀⠀⣻⠦⢀⣠⣴⡿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀
⠀⠀⠉⠀⢰⣿⣿⣿⣇⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠘⣷
⢧⣀⠀⠀⢸⣿⡿⠟⢋⣴⠋⣸⠁⠀⠀⠀⠀⠀⠀⣴⢻⡶⡄⠀⠀⠀⠀⠀⠀⠘
⠀⢨⠃⠀⡿⠋⢀⡴⠋⠀⢀⡟⠀⡀⠀⠀⠀⣹⣾⣅⠈⣇⡇⠀⠀⠀⠀⠀⠀⠀
⣾⠃⠀⠀⠀⣰⠏⣀⡀⠀⢸⢷⡾⠁⣀⣤⠾⠋⠀⠀⠀⢹⣇⠀⠀⠀⠀⠁⠀⠀
⡇⠀⠀⠀⣰⠏⣾⣿⣿⠀⠀⠘⠓⠛⠉⠁⢀⣴⣶⣄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡟⠀⠙⠛⠋⠀⠀⠀⠀⠀⢀⠀⠺⣿⣿⡿⠂⠀⡟⠁⠀⠀⠀⠀⢠⠀
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠸⠶⠶⡶⣾⠋⠀⠀⠈⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⣍⣻⣶⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⡇
⠀⢰⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣿⠏⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠈⢿⣷⣦⣿⣿⣿⣿⣿⣿⣿⠟⠙⠿⠋⠈⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⡞⠀
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⣿⣿⡿⠟⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠙⠻⠷⣦⣤⣀⠀⠀
⣿⠏⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓
⣿⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣆⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⢾⣿⣿⣿⣿⣿⡟⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⣿⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⠇⠀⠀⢹⣿⣯⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⠀⠀⠀⠀⠹⣿⣆⣠⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⣿⣿⣄⢸⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⡿⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠛⠛⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣇⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⠀⠀⠀⢻⣿⣿⣰⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠇⠀⠀⠀
⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠛⠉⠀⠀⠀⠀⢰
⣿⡿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣧⡀⠙⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣀⣹⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⣿⣿⣧⡀⢀⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠛⠋⠉⠛⠛⣿⣿⡋⣀⠀⠀⠀⠀⠘⠋⣩⣿⣿⡿⣿⣤⡀⠀⢀⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠿⠿⠿⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⢻⣿⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⢘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣾⡿⠉⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣾⡿⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⢀⠀⣿⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠉⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⣰⣿⠛⢿⣿⡃⠀⠀⠀⠀⠀⢸⣷⡀⣰⣿⠁⠀⠀⣀⣤⣶⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠶⠶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣃⣠⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠛⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠁⢀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣿⣁⣠⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⢦⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢠⣿⡟⠛⠁⠀⢀⢀⢀⣀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢀⢀⣀⣀⡀⣀⠀
ඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞඞ ඞ ඞ
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠤⠤⠤⠔⠒⠢⣄⡀⠀⠀⠀⠀
⠀⣠⣤⠤⠐⠒⠒⠂⠒⠊⠉⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⡀⠀⠀
⠀⡇⠈⠁⠉⠙⠢⠄⠠⣄⡀⠀⢀⡀⠤⠒⠒⠤⠔⠋⠉⠑⠚⠉⠈⡉⠉⢀⠝⠀⠀
⠀⡼⠀⠀⠀⠀⠀⣀⡀⠘⡀⢦⠀⠀⡀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠼⠇⢀⠇⠀⠀⠀
⠀⡇⠀⠀⠀⠠⣾⠿⠃⡜⠀⠀⡳⠔⠋⠉⠓⢤⡴⠚⠙⠓⢶⠀⠀⡠⠞⠀⠀⠀⠀
⢀⠇⢀⣤⠀⠀⠀⠀⠀⢱⠀⢸⠁⠀⣰⣿⣿⡆⢱⢀⣶⣿⡆⣧⢸⠀⠀⠀⠀⠀⠀
⢸⠀⠘⠁⠀⠀⠀⠀⢰⠉⠇⢸⡀⠀⠻⣿⡿⠃⣸⠘⣿⡿⢃⣇⠜⠀⠀⠀⠀⠀⠀
⢨⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠑⠤⣀⣀⡠⢞⣩⣗⠒⠚⠁⣇⠀⠀⠀⠀⠀⠀⠀
⢎⠀⠀⠀⣠⣾⡿⢠⡋⠀⠀⠈⠀⠀⡀⠀⠀⠀⠙⢦⣀⣀⣸⠟⠀⠀⠀⠀⠀⠀⠀
⣸⠀⠀⠀⠛⠋⠁⠀⡗⠀⠀⠐⠊⢩⡏⠉⠙⣷⣒⣋⣏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⢣⠀⠀⠀⠀⠀⠀⢸⠀⠤⠀⠀⠀⠨⣍⣉⠽⠁⠀⠤⢿⡀⣜⠀⠀⠀⠀⠀⠀⠀⠀
⣸⠐⠛⢀⣀⣀⣀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠿⢶⣾⡍⢲⠀⠀⠀⠀⠀⠀
⠱⢤⣀⢸⠀⠀⠈⠙⢲⣄⡤⢴⢠⣤⣴⣾⡟⣻⣏⣀⣤⣼⣿⣽⢏⠀⠀⠀⠀⠀⠀
⠀⢸⠤⣝⣆⠀⠀⡴⣍⣉⣑⣺⢛⡚⠻⠿⠿⠿⢿⣿⣿⣿⣁⣨⠟⠙⣦⣄⣀⡀⠀
⠀⠸⣦⣿⣿⣷⣶⣦⣿⣿⢿⡍⠛⣛⣿⣿⣷⣶⣿⡿⠂⠠⠤⢅⠀⣐⢮⡳⢾⠃⠀
⠀⠀⠈⠙⠛⢷⣼⣇⣠⠤⢾⠛⠋⠉⠈⠛⡟⡟⠋⠀⠀⠀⠀⠀⠑⢌⡢⣝⠢⣵⡆
⠀⠀⠀⠀⠀⠘⠻⠿⡿⡷⠛⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣤⣇⣇⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣟⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣷⣷⣤⡾⣿⣷⣄⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀