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⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠭⠛⠩⢍⠉⠉⠉⠉⢉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣶⡶⠒⠀⣱⠀⠀⢞⠁⠠⣤⣈⠲⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡇⠘⠁⢀⠄⠊⠁⠀⠀⠈⠢⡀⠙⢿⡀⣁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢔⠈⢀⠜⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢈⣀⡋⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⡎⢾⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀
⡇⠀⠀⠀⣿⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣰⠀⠀⠀⠀
⡇⠀⠀⠀⢰⢃⠘⢇⠈⠒⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⡿⠀⠀⠀⠀
⡇⠀⢀⡠⠐⣋⠀⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀
⣇⣪⡥⡴⠊⠁⡇⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠺⠋⠔⢁⠀⠀⠀
⠇⠁⠀⠀⠀⠀⣿⠐⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⠀⢀⠠⠂⠁⠀⠀⠀
⠀⠀⢀⠀⠀⠠⢿⡆⠈⢎⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⠃⠀⢰⡅⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⠀⠀⠈⢷⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠁⢸⠀⠀⠀⠺⡀⠀⠀⠀⠀⠀
⠁⠀⠀⣀⠠⢤⠀⠀⠣⢄⣀⠀⠀⠀⠀⠀⠸⠁⠀⠆⡇⠀⠀⠀⢁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⡄⠀⠀⠀⠀
⠀⠀⠀⠀⡜⠀⠀⠀⡠⢤⠀⠀⠀⢀⠀⠀⠀⣿⣦⣀⠀⢣⠀⠀⠀⢠⠀⠀⠀⠀
⠀⠀⠀⡘⠀⠀⡠⠊⠀⢸⠀⠀⠀⡜⣇⠀⢰⢿⠁⠈⠉⠺⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⠁⡠⠊⠀⠀⠀⢸⠀⠀⢠⠁⢺⠀⡆⠈⢧⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢩⠊⠀⠀⠀⠀⠀⢸⠀⢀⠃⠀⢸⡆⣇⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠊⠀⠀⠘⢳⣿⠟⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣠⣴⣶⣏⣉⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠻⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⡆⠀⣼⢿⣿⠷⣦⣄⣀⣴⣶⣶⣬⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣧⣾⣿⡂⡍⠙⣸⣿⣟⡙⠄⠦⠈⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣶⣿⠿⣋⡙⢻⣿⠾⠟⢿⢿⣿⣿⣷⠀⠀⢹⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠏⠁⠀⠈⠉⠉⠛⠲⠦⣤⣀⡀⠀⢸⠀⠀⠀⠀⠀⢻⣿⠀⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⡇⠀⣤⣼⡏⠉⠛⠲⢤⣄⣀⡴⠾⠛⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣼⡄⠀⠀⠀⠀⠈⣿⣇⢿⣿⡿⣷⣄⡐⣲⣿⡟⠻⢶⣭⣷⡿⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢷⣄⠀⠀⣼⠋⠙⠷⣶⡶⠟⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣈⠳⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠉⢹⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⡇⠀⠀⠀⠀⡐⣠⣶⣶⣄⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣸⣄⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣼⡟⠁⢫⢿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢀⣀⠘⣏⠉⠉⣯⠉⠉⠀⠀⠀⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⠁⠀⠀⠈⢟⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠷⠞⠛⠉⠉⠉⠹⠿⠶⢿⣗⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⣿⣆⣀⣀⣀⣈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣛⣻⡦⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⣸⠟⠶⢶⣴⣿⠟⠋⠉⠛⠛⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣿⠿⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣤⣀⠀⠀⠀⠀⠀⣀⣤⡶⢿⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⣧⣴⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⠛⠛⠛⠟⠛⠉⠁⠠⠀⠀⠀⢀⣩⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠋⢁⣴⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠉⠀⠈⠙⣷⣈⡉⢙⠛⣿⠋⠉⠉⠉⠀⠀⠉⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠀⠀⠀⠀⠀⢐⣾⠏⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⣿⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⢿⣀⣀⣀⣀⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⣧⡀⠀⠀⠀⣠⡾⢋⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⠹⠷⠶⢤⣤⣤⣴⣟⡻⠶⠶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⣤⣤⠶⠞⠋⠉⣿⣷⣦⠀⠙⢢⡀⠀⢀⣠⣄⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⢶⣤⣴⡶⠞⢛⡟⠛⠳⢶⣤⣤⣸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡆⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
🤍ㅤ ᵕ̈♡︎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀
⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀
⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⡾⠿⠿⠟⠛⣛⣛⣻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⠿⠟⠛⠋⠉⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⠿⠿⠛⠛⠉⠁⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡿⠿⠛⠋⠉⠁⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⠿⢿⡟⠉⠉⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⣉⡀⠀⠀⠈⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡿⠿⠛⠋⠉⠁⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⣀⣀⣤⣤⣶⠟⠋⠁⢿⣦⡀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⠿⠛⠛⠉⣀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠀⣀⣤⣶⡾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⡿⠛⠋⢉⣀⣠⣤⣶⣾⣿⣿⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⢀⣀⣀⣴⣾⠿⠛⠉⠀⠀⠀⢠⣆⣤⣴⣶⠄⠀⠀⠀⠀⢹⣧⡀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠿⠟⠛⠉⢁⣀⣭⣵⣶⣿⡿⠟⠛⠉⢩⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⠿⠋⠉⠁⠀⢀⣠⣤⣶⣶⠿⠛⠛⠉⠉⠀⠀⠀⢀⣀⣀⣀⠸⣿⡟⠋⣉⡀⠀⠀⠀⠀⠀⢹⣧⡀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⡿⠿⠛⠉⠁⢀⣀⣤⣴⣾⢿⣿⣿⠉⢻⣿⢇⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⣀⣠⣴⣶⡿⠟⠋⠙⠁⠀⣀⠀⠀⠺⠀⣼⣧⢰⣿⡿⢿⠿⠀⣿⣷⣾⠿⠟⠀⠀⠀⠀⠀⠀⢹⣷⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠟⠋⠉⠁⢀⣀⣤⣤⣶⣿⣿⡟⣿⣯⢻⣮⣿⣿⡞⢿⣿⣿⣧⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⠿⠛⠋⠁⠀⠀⢀⠀⢀⣠⣤⡍⣾⣿⣤⡄⢻⣿⡼⣿⣦⣤⣀⣀⡘⣿⣧⣠⣾⣿⠀⠀⠀⠀⠀⠀⢿⣦⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣶⣿⠿⠛⠉⠀⢀⣠⣤⣶⣿⢿⣿⢻⣯⣈⣻⣿⣅⣿⡿⣷⠿⣏⣿⣥⣶⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡴⠿⠛⠛⠉⠁⠀⠀⢀⣀⣀⣀⡀⣿⣿⡿⠛⣋⡁⠘⣿⣿⣿⣶⣿⣷⢈⣉⣙⣻⣿⣿⠈⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⣿⡿⠋⠀⣀⣤⣴⣾⣿⣿⣏⢹⣇⣨⣿⡇⠉⢻⡇⠛⣛⣩⣥⣶⣿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠋⠀⠀⠀⠀⠀⠀⣤⡄⠀⢀⣼⣿⢿⣿⡷⢹⣿⣶⣿⠿⠃⠀⠸⣿⣎⠛⠿⠿⠘⠛⠛⠛⠋⠁⠀⠀⠀⠀⢀⡀⠀⢀⣤⣀⠀⠀⠘⣿⡄⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣰⣿⣿⠃⣿⣿⢿⣿⣿⣦⣸⣏⣹⣿⣿⡾⢇⣛⣠⣴⣿⡿⠿⢛⣉⣥⣶⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢿⣧⣀⣸⣿⡛⠀⠀⠀⠀⢻⣿⡀⣀⣶⣶⠀⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣄⣿⣿⣿⡆⠀⠀⠘⣿⡄⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣿⡿⡀⠸⣿⣾⣿⣄⣿⡏⠛⣛⣯⣶⣿⠿⠟⣛⣭⣵⣶⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠸⣿⡆⠀⠀⠀⠀⠸⣿⣇⠈⣿⣷⣆⠀⣠⣶⡌⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣾⣷⠀⠀⣿⣿⣋⣫⡿⣿⣇⠀⠀⠀⠸⣷⡀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣧⠁⠀⠹⣿⣯⣽⣿⣿⡿⢟⣛⣭⣴⣶⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢻⣿⣂⠀⠀⠀⠀⢻⣿⣤⠈⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣦⣹⣿⡟⣋⣦⡄⠀⠈⠙⠿⣿⣿⣿⠟⠀⠀⠀⠀⢻⣇⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀
⠀⢹⣿⣿⣄⠀⠀⠹⣿⣛⣭⣴⣾⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠈⢿⣿⠀⢀⣠⣦⡈⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⣿⣿⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣿⡆⠛⢿⣷⡀⠀⠀⠀⠀⠀
⠀⠸⣿⢿⣿⣀⡀⠉⢻⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣄⡀⠀⠀⠀⠀⠘⣿⡄⠀⠘⣿⣷⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣀⣍⣀⣀⡀⠀⠀⠀⠀⠈⢿⣷⣾⣿⢿⣿⣿⣿⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠘⣿⣇⠀⠀⠀⠀⠀
⠀⠀⣿⣷⣿⣏⣁⣀⡈⠻⢷⣆⢰⣦⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠙⣷⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠳⣾⡿⠛⢻⣿⣆⠀⠀⠀⠀⠀⢻⣿⣤⣼⣿⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣽⣿⡄⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣉⣝⡛⣷⡄⢻⣧⢹⣧⠀⣾⠟⠉⣥⣭⣛⣷⣄⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠄⠀⣠⣿⣧⠀⠀⠀⠀⠀⠀⣿⠀⠘⢷⡿⢿⣿⡅⠀⠰⣿⡇⠀⠀⣹⣿⠀⠀⠀⠀⠀⠈⢻⣿⠋⠁⠀⠀⠀⢀⣤⠀⠀⠀⠚⠃⢰⣆⠀⠀⠀⠀⠀⠀⠈⢻⣥⣬⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠹⣿⣿⣧⡝⢿⣎⢿⡄⢻⡇⣿⠸⣿⣸⣇⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⢰⡿⠁⢿⣇⠀⠀⠀⣠⠀⣹⣶⣦⡀⠀⠈⣿⣧⠀⠀⠻⣿⣦⣶⡿⠃⠀⠀⠀⠀⠀⠀⣀⠀⢴⡀⠀⠀⠀⣾⠇⠸⣇⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢹⣿⡆⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣷⣾⣿⠈⠁⢸⡇⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡶⠀⢸⣇⢸⣎⢿⡆⠀⣿⣿⣷⣿⠙⣿⡇⠀⠀⠈⣿⣷⡄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠈⣿⡄⠀⠈⢻⣿⡀⠙⠻⣿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡈⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣿⡿⣁⢀⣤⣾⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠸⣿⣶⣤⣾⣎⡙⢿⣿⣿⣿⣷⡄⠀⢻⣮⡻⣮⣿⡆⠻⢿⣾⣿⣦⣿⣷⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢋⣻⠀⠀⢿⣿⣤⣀⠀⢿⣿⡄⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢟⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣬⣍⣭⠄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏⢈⣿⡇⠰⣦⠰⣿⣭⣭⣾⡷⠀⢻⣿⣿⣿⣿⡄⠀⠙⠿⣶⣽⣷⠀⠀⠉⠛⠻⠛⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢿⣷⠀⠈⢿⣿⣿⣷⣮⣿⣷⡆⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⢀⣴⢶⣦⣀⣾⢿⣿⡀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣤⠉⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣠⣾⡟⣿⡟⢡⢶⣿⣯⡉⠁⠀⠀⠈⣿⣿⣿⣿⣷⡆⠀⠀⠀⠈⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣦⢠⡄⣶⣾⣿⣿⣶⣬⢽⣿⣿⣧⣤⣄⡈⢿⣷⣌⠙⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡎⣿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠉⣡⣾⡿⠃⣸⣾⠿⣻⣿⣷⣦⡀⢰⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⢠⣼⣿⠀⠀⠻⣿⣇⠀⢹⣿⠃⠈⠙⣿⡟⢹⣿⣿⠛⠻⠏⠈⠻⠟⠁⠀⠀⠀⣀⣀⣠⣴⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀⠉⠉⠀⢰⣿⣷⣿⣿⡿⠿⠿⢣⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠈⠙⣿⣷⣴⣿⣿⣿⣆⠛⢿⣦⣜⣠⣿⡇⠈⠛⠛⠀⠀⠀⠀⠀⠂⣀⣠⣴⣶⣿⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣄⠀⠀⢸⣿⣿⠟⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠙⣿⣿⡋⠀⢻⣿⣧⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⣀⣤⣶⢾⣿⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⢀⣤⣴⣿⣿⣿⣿⣶⣀⣀⣀⣰⣶⡈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠿⠛⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠿⠛⠉⢀⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣫⣿⣿⣿⣿⣿⠇⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⣀⢀⣰⣦⣾⣿⣿⣿⡇⠘⣿⣿⣟⣭⢹⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣿⡟⠿⣿⣏⣩⣦⣿⡍⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⣿⣩⡉⢸⣿⣿⣿⣿⣿⣿⠛⢻⣧⣶⣾⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣶⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⡞⠻⠿⣿⣯⡁⠀⣾⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⣿⣧⣴⣾⣿⣿⣧⠀⠙⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⠀⠀⠀⠀⠀⠻⡿⠉⠁⠀⠀⢸⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣧⣤⣤⣤⣴⣶⣶⣾⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣦⣤⣴⣖⣒⠶⢤⠀⣔⣒⣻⣭⣻⣻⣻⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣻⣻⣻⣻⠏⣩⣴⠟⢛⣻⣭⣻⣻⣻⣻⣻⣻⣻⣻⠛⠡⢐⣒⣻⣻⣻⣶⣦
⠀⢸⣻⣻⡿⠡⠞⢋⣤⣾⣻⣻⠟⣛⣻⣻⣻⡻⣻⠋⣰⣶⣻⡻⠁⣠⣠⣲⣻⣻
⠀⢸⣻⠋⣰⠃⠀⡨⡿⣻⡟⢫⣾⣻⣻⣻⣻⡃⣻⢰⣻⣻⣻⣲⡀⢹⣻⣻⣻⣻
⠀⢸⠃⣸⠃⣸⣻⣻⣶⠟⣰⣟⣻⡿⢻⣻⣻⠇⠹⢸⣻⢻⣻⣻⣻⡂⣹⣻⣻⡇
⠀⢀⣺⠃⣸⣻⣻⣻⡏⣼⣻⣻⣻⣷⠿⠟⠓⠒⠤⣻⣾⢸⢻⣻⣻⣻⣻⣻⡿⠀
⠀⣺⡏⣼⣻⣻⣻⣻⢸⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⢸⣻⢸⢸⣻⣻⣻⣻⡿⠁⠀
⠀⠇⢃⣻⣻⣏⣁⣋⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⡼⣾⣻⣻⣻⡟⡇⠀⠀
⠀⠀⠸⣻⣹⣻⠙⠉⠙⠳⠀⡠⠀⠀⠈⠴⠿⠷⣦⣤⢤⣳⣻⢻⣻⣻⡇⡇⠀⠀
⠀⠀⠀⣻⣻⣻⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣷⣻⠃⣺⣻⣻⣷⡇⠀⠀
⠀⠀⠀⣻⣻⣻⣧⠀⠀⠀⢱⡶⠶⠶⡶⠀⠀⠐⠻⢻⣻⢫⣺⠋⣸⣻⣻⣷⠀⠀
⠀⠀⢠⢣⣻⣪⡹⢻⣦⣀⠀⠈⠂⠒⠁⠀⣀⣤⣾⣻⢡⣻⣻⢸⣻⣻⣻⣼⡀⠀
⠀⢀⣏⣫⢹⣢⡻⣲⣩⡛⣻⣷⣶⣖⣫⣭⣶⣻⣻⣻⣢⡙⢻⣈⢻⣻⣻⣯⣧⠀
⠀⣼⣼⣻⣃⢻⣻⣈⢻⠧⠸⣻⣻⢿⢿⡿⠛⠋⠛⠛⠿⠿⣢⣻⣢⢹⣻⣻⣾⡆
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