Gotobun No Hanayome Emoji Combos

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⠀⠀⢀⣴⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⡏⣇⢹⠳⡘⢿⣿⣿⣧⡙⢷⣤⠄⢀⣴⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢳⠸⡄⢣⠙⣌⢺⡿⠳⣽⣮⣿⣷⣜⢁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⣷⡀⠀⠘⣆⠀⠀⠀⠀⠹⡄⠀⠀⢠⢸⠀⢱⣈⣧⣸⣿⣷⣼⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣳⠀⡀⠀⠀⢹⢳⡀⠀⠸⣆⠀⠀⠀⠀⠹⡀⢠⣼⣼⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡇⡇⢣⠀⠀⢸⡆⢳⡀⠀⢻⢦⠀⠀⠀⠀⢡⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠀⢀⡀⢀⠀⡀⢀⣀⣀⣀⠀⠀⠀⣀ ⣴⠿⢿⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⢷⠸⡘⣆⠀⠈⢿⡀⢳⡀⠸⡄⢣⡀⢳⡀⢠⡈⠙⠛⠛⠛⠛⠻⣿⣿⡄⠀⠀⠀⠈⣿⣷⠃⠀⠀⠀⠀⠀⣼⠁⣿⣾⣧⢿⡿⢯⡿⣦⡏⣹⠁ ⡏⠀⠘⡆⠀⠀⠀⠀⠀⢈⢸⡀⠀⢸⠀⢳⢘⣆⠀⠘⣧⠀⢳⣄⣱⠖⢳⣄⣷⣀⣧⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠋⠀⠛⠹⠋⠘⠓⠚⠃⠙⠁⠛⠀ ⣸⠀⡄⣇⠀⠀⠀⠀⠀⢸⡀⣇⠀⠀⡇⠈⣧⠏⠳⠤⠚⠛⠉⢀⣤⣾⠿⠋⠁⠀⠈⣇⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⢰⣇⣶⣰⢢⣾⢷⣴⠖⠀⠀ ⣿⣴⣷⣿⡀⠀⠀⢀⠀⠀⣇⠸⡤⠤⠴⠚⠁⠰⠂⠀⠀⠀⠰⠿⠿⠷⠶⠶⠶⠶⠶⢻⡀⠀⠀⠀⠀⠘⢻⣿⣿⠙⣄⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⢸⠟⠿⠧⠏⠹⠾⠃⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⠀⠸⣆⣄⣼⣶⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢻⣿⣇⠘⣦⠀⠀⠀⢹⡟⢿⣿⣆⠀⠀⠀⣤⡴⢦⡴⡄⣠⢤⡄⠀⠀ ⡉⢿⠙⣿⣿⠀⠀⠀⢸⡉⠉⠉⢁⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠘⣷⡀⠀⠀⢳⠀⠙⢿⣷⣄⠀⣼⢠⡏⣰⣿⠃⣼⠃⠀⠀ ⣿⡼⣸⣿⢻⣷⠀⠀⠀⣇⢠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠙⢷⡀⢹⣿⣦⡀⠈⣇⠀⠀⠙⢿⣷⣧⣀⢉⠁⣈⣉⣀⣀⠀⠀ ⡿⣡⡿⣿⠘⡇⢇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⠀⠀⠀⡄⠈⢻⣌⣿⣏⡿⣆⠸⡄⠀⠀⠀⣼⠷⣿⣿⢀⣿⡟⣿⡏⠀⠀ ⠀⣩⣷⣿⠀⢳⠘⡄⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠸⠀⠀⠀⢧⠀⠀⣿⣿⣿⡧⠈⠣⣹⡀⠀⠀⠃⠐⢻⣿⣿⡈⠛⠛⠃⠀⠀ ⠀⢩⣿⣿⠀⠈⡄⢱⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢀⣀⠠⠖⠀⠀⠀⠀⣠⣾⣇⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⡹⣿⣿⡇⠀⠙⢷⡀⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀ ⣴⡿⠉⣿⠀⠀⡇⠀⢇⠀⠀⡎⢧⡀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⢿⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⣇⢹⣿⣿⡀⠀⠈⢷⡀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀ ⠋⠀⣸⣿⡀⠀⢸⠀⡜⡆⠀⢱⠸⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⡼⡇⠀⢸⡆⠀⠀⢸⡆⠀⡆⢻⣷⣿⣿⣷⡂⠀⠈⢷⠀⠀⠀⠀⠈⣿⣿⠟⠃⠀⠀ ⠀⠊⢹⣿⡇⠀⢸⠀⣧⠸⡄⠈⠀⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⡜⠁⢳⠀⡸⢻⠀⠀⢸⣷⠀⢿⡄⠈⠿⣿⣿⣷⣆⠀⢸⡇⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀ ⠀⠀⣼⣿⡇⠀⢸⡆⢹⣆⢱⠀⠀⢹⣿⣿⣿⣿⣯⣿⠟⠁⢸⠘⡆⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢸⡄⡅⠈⡇⢀⢸⢻⣦⠁⢻⡀⠰⣿⣿⣿⡏⠙⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⣿⣿⡇⠀⣼⡧⢸⡿⣆⢃⠀⢸⠿⣿⣿⣟⢡⠀⠀⠀⢸⠘⣿⡄⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠁⠁⠀⠀⠸⡞⠈⣟⠀⠀⠁⠀⣿⠿⠛⠁⠀⢀⡿⣷⡆⠀⠀⢀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠤⠤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢓⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡙⠶⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡘⣿⣖⠲⢤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣦⡀⠀⠙⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⢳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢀⣴⡟⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⡄⠀⢸⣿⣿⣿⣿⣧⡀⠀⠈⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⣧⠆⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣇⠀⠸⡀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⢻⠀⠀⢰⢹⠀⢸⢰⠀⠀⠀⠀⢇⠀⠐⠀⠀⠀⢻⠀⠀⠠⡌⠛⣿⢻⢿⢿⠛⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡼⡏⠀⠀⣾⠸⠀⠸⡇⡆⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⢻⠸⣼⡟⠀⠙⠻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⣡⠟⣼⠻⢻⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠁⠀⠀⡏⠀⠀⠠⢧⡁⠀⠀⡆⢸⣧⠀⠀⠀⠀⠀⠹⠀⠀⡇⡄⢸⠀⡇⢧⠀⣄⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡞⣱⠃⢠⠃⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⠀⠀⣰⡇⠀⡀⠀⢸⣷⠀⠀⢇⠘⡞⡄⠀⠀⢰⠀⠀⠀⢠⡇⡇⠀⡇⡇⠸⡆⠙⡄⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣾⡽⢳⠂⡿⠀⣸⡇⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣾⡇⠀⢰⢿⠁⠀⡇⠀⠘⡿⡀⠀⢸⡀⡇⢹⡀⠀⠘⡇⠀⠀⢸⣇⣷⣀⣿⣇⢸⣷⣀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣯⣴⡇⣰⣧⡇⠀⠀⠀⠀⠀⠀⣷⡀⠀⢰⣿⠀⠀⡼⡌⠀⠀⣇⠈⠀⢷⣇⠀⢸⡇⣗⠋⢧⠀⠀⢿⢆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⠿⠛⠛⠋⠉⠛⠛⠛⠿⢥⣀⠀⠀⠀⠀⠀⣧⠃⠀⡼⣹⠀⢰⣷⡧⣀⠀⣿⢠⠀⠸⡽⡄⠈⣿⢹⣀⣸⡇⠀⢸⣆⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⣿⠀⢠⣇⣿⣀⣛⠛⠁⠈⠉⠉⠉⠀⠀⠉⠁⠤⢟⣾⣿⣿⣿⣷⠾⠿⣿⡌⠉⠀⠀⠀⠛⢻⣿⡇⣿⡀ ⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⣐⣿⢯⣗⣒⣾⡿⣭⡆⠀⠀⠀⢹⡄⠀⠀⠧⣶⣿⣿⣿⣟⠻⢿⣖⠂⠀⠀⠀⠀⠀⠀⠐⢺⣿⣿⣿⣿⣯⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠻⡾⢋⡟⠙⠷⣟⠻⠇⠀⠀⠀⠈⡇⠀⠀⣷⣿⣿⣿⣿⣷⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣛⣋⣸⠇⠀⢀⡤⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣯⣸⡇⠀⢸⡭⠄⠀⠀⠀⠀⠀⡇⠀⠀⡈⠻⢧⣈⣁⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠚⠉⠁⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣁⣸⣃⠀⠘⠛⠂⠀⠀⠀⠀⠀⢹⠀⠀⡇⠉⠛⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀ ⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢹⠏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⡦ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠛⣵⣛⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧ ⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣶⡛⠏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⠆⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿ ⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠈⠩⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘ ⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⢚⡃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠛⣳⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⠀⠓⢦⣄⡉⠁⠀⠀⠀⠀⠀⢀⣠⠞⠁⢸⡀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠛⠀⠀⡴⠋⠉⠙⠒⢲⣶⣶⠚⢹⠁⡄⠀⠘⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⣿⣿⣿⣿⠇⠀⠀⠀⣾⡇⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⣼⣿⡟⡄⠀⡼⠃⠀⠀⠀⢰⣿⣿⡿⠀⢸⠀⣧⠀⠀⣷⠀⠀⠀⢿⣿⣿⡟⡏⣿⣿⣿⡇⠀⠈⠛⢦⣤⣤⡤⠖⠋⠁⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⡇⡁⣼⠁⠀⠀⠀⢠⣿⣿⣿⠃⠀⢸⡄⣿⠀⠀⢹⡇⠀⠀⢸⣿⣿⣇⡷⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⣿⠀⠀⢀⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⠀⣧⠃⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠸⡇⡿⡆⠀⢸⣧⠀⠀⣾⣿⣿⡟⠀⢈⡂⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢋⠉⠉⣿⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⡀⡿⠀⠀⠀⣠⣿⣿⣿⡿⠁⠀⠀⠀⡇⡇⢻⠀⠸⣿⣆⠀⢻⣻⡏⠀⠀⠈⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⢸⣾⡁⠀⡏⢀⣼⡟⣿⢿⢻⡆⠀⠀⠀⠀ ⠂⠀⢸⣿⣿⣿⡇⡇⠀⠀⣴⣿⣿⣿⣿⣇⣀⣀⣀⣠⣿⣧⣨⡆⢠⣽⣿⠀⢸⣿⡀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠙⣿⢰⢀⡞⠁⢧⣟⡾⠈⡇⡀⠀⠀⠀ ⠀⠀⠀⠉⠛⠛⠿⣷⡀⢠⡽⢿⣿⣿⡟⠀⠀⠈⠙⠻⣿⣿⣿⣷⢸⣿⣿⣷⢈⡟⢧⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠟⠀⠀⠈⢿⣿⣶⣷⣧⣤⣶⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⠏⠀⠀⢙⣿⡃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡁⠈⣧⠀⠀⠀⠀⠈⠷⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⣩⡏⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠠⡤⠤⠤⠤⢀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠕⠊⠀⠀⠀⠀⠒⡀⠈⠑⣿⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⣩⣿⠇⠀⢠⠂⢀⠀⠀⠀⠀⠈⡄⠀⠘⣷⣌⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⠆⠀⡈⠀⠀⠀⠄⠀⢠⠀⠰⢿⣿⣟⠦⡀⠀⠀⠀ ⠀⠀⣠⣮⢑⠽⡿⡇⠀⠸⠀⠀⠃⠰⢀⠀⢸⠀⠀⡆⠀⢻⡉⠀⣺⣼⣦⠀⠀ ⠀⠀⠛⢿⣿⣀⢢⠁⠀⡆⡆⢸⢰⢈⢎⡄⢜⢃⠀⠁⠀⠘⢣⣾⣿⢯⡀⠀⠀ ⠀⠀⠀⡜⢺⣿⠛⠀⠀⣹⣇⣆⣴⠸⠸⢧⣸⣜⣇⢀⠀⠀⠘⢻⣏⠈⣷⡀⠀ ⠀⠀⣰⠁⣼⡇⠠⠂⠀⡧⣰⣛⡍⠀⠀⠀⢉⣿⣆⢼⠀⠀⠀⢸⣿⠀⢹⡇⠀ ⠀⣴⡇⢠⡿⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⢈⣿⢦⠘⣿⣀ ⡰⠡⠀⡜⣧⢀⠸⡀⠀⣷⣄⠠⠄⢀⣀⣀⠀⠀⣠⣾⠀⢣⡄⢰⢿⣸⠴⠋⠀ ⡇⢸⠸⠀⣟⢸⡀⣷⠀⣿⣿⣷⣦⠄⣀⣀⢤⣾⣿⣿⠀⡼⢀⡿⠊⠁⠀⠀⠀ ⡇⠸⡇⠀⣻⠾⠗⠸⡆⡟⣻⠋⡞⠀⠀⠀⡸⠏⢿⣿⢸⣿⠟⠁⠀⠀⠀⠀⠀ ⠈⠀⠡⡜⠁⠀⠀⠀⠘⣷⡏⠀⢣⠀⠀⠀⡐⠀⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⡖⠀⢀⣴⣽⠁⡠⠊⠑⡄⡎⠈⠂⢄⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⢀⣾⣿⡿⠋⠉⠢⠀⡇⢠⠜⡁⠊⠙⢿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⣿⣸⣿⠋⠀⠀⠀⠀⠀⠈⢉⠔⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢃⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡌⠀⢶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡷⢾⣷⣾⣦⣄⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠛⣲⣤⣤⠄⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⡀⠈⠹⣷⣦⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⡟⠀⠀⣾⠟⠁⢸⡀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⢦⠻⣿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢠⣾⠃⠀⠀⠸⣇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠈⢧⠹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⢀⡿⠁⠀⠀⠀⠀⡟⢁⡿⠛⢳⣦⣼⣄⣀⣀⣀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⣧⣤⠤⠼⣆⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢠⡿⠁⠀⠀⠀⠀⠀⡇⡜⠀⠀⡞⢠⠟⠃⠉⠙⠉⣿⢻⢀⡦⠤⠤⣤⠤⢤⣴⠤⡤⣶⡿⠒⠛⠛⠙⢻⡝⠀⠀⢹⡀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢠⡿⠁⠀⠀⠀⠀⠀⠀⡇⠁⠀⢸⠁⡼⢰⠀⠀⠀⠀⣿⢸⠘⠀⠀⠀⡇⠀⠀⠻⠀⣇⠘⠀⠀⠀⠘⠀⠀⢧⣧⠀⠀⡇⠘⣯⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠊⠀⠀⢸⡏⢠⣿⣁⣀⠀⣠⣤⠀⡀⢸⡇⠰⠤⢿⠶⠃⣾⠒⠶⠶⠼⢸⡸⠘⠒⠖⠞⡇⠐⠒⠒⡉⣿⠉⠉⠉⠉⠙⠓⠲⠞⢻⠲⠶⢿⡄⣿⡌⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡶⢃⣤⠆⣰⡿⣠⡏⣿⠃⢹⣾⠃⢻⣿⣿⣾⡇⠀⠀⡏⠀⠀⣿⡀⢸⡀⠀⢸⡇⣦⡇⠀⢰⣇⠀⠀⠀⡇⢹⡄⠀⠸⡆⠀⠀⢸⡄⠸⡄⠀⠈⡇⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⢠⡿⠃⣴⣟⣁⡏⢸⡇⢀⣾⣿⠀⣾⡇⢸⣿⡇⠀⠀⡇⠀⡀⣿⣇⡌⣇⠀⢸⡇⣿⡇⠀⢸⣿⠀⠀⠀⡇⢰⣻⡄⠀⢳⠀⠀⠀⡇⠀⡇⠀⠀⠁⣷⠘⣿⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⡾⠁⣴⡟⣸⣿⣠⣾⡇⣸⡏⣿⡀⣿⡇⢸⣿⡁⠀⠀⡇⠀⡇⣿⢹⣷⢿⡆⢸⡇⢻⣧⠀⠸⣿⡀⠀⠀⡧⢸⡅⢿⡀⢸⡆⠀⠀⢸⠀⣧⠀⠀⠀⢻⡄⢻⡄⠀⡀⠀⠀⠀⠀ ⠀⠀⠓⠚⢛⣴⠃⣸⠋⠽⢷⣿⣥⡿⠛⠹⢷⣼⣿⡇⠀⠀⡇⠀⣧⣿⣈⣿⠸⡇⠈⡗⠺⣿⡄⠀⡏⡇⠀⠀⠀⢸⡣⠤⢧⡀⣿⡀⠀⢸⠀⢻⠀⠀⠀⢸⡇⠘⣷⣠⡟⠀⠀⠀⠀ ⠀⠘⠀⠀⣸⡟⠀⢿⣷⣄⠀⠙⣿⣶⣶⣶⣶⠐⢿⣿⡄⠀⠇⠀⣿⣿⠀⢹⣇⢹⠀⢇⠀⢧⢷⠀⢇⢳⡀⠀⠀⢸⠁⠀⠈⢳⣾⣇⠀⠀⠀⢸⠀⠀⠀⠈⣷⣼⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠀⣽⣿⣷⣄⡙⣿⣿⣿⣿⣤⣾⡿⡇⠀⠀⠀⣿⣿⣿⣿⣿⠿⣆⣼⣷⢼⡀⢇⢸⠘⣧⠀⠀⣸⢶⣶⣾⣾⣿⣿⣆⠀⡄⠀⡆⠀⠀⠀⢹⣯⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⣸⣟⢻⣿⣿⣿⣦⡀⡄⠛⠇⠓⠈⠛⠃⠘⠛⠃⠓⢛⣿⣿⣿⡄⢰⠾⢧⡇⠀⠁⠀⠀⠀⢼⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡌⠀⢸⠀⠀⣿⡏⠘⢿⣟⠍⢙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣛⣿⡞⢀⣼⣧⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⣸⣿⣿⠀⠀⣸⣿⣿⣿⣿⣷⠀⢹⢠⡀⣇⠀⢻⡇⠈⠚⠯⠋⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠫⠴⠚⠘⣿⠀⠀⠀⠀⠀⣿⢹⡏⠙⡇⣠⣴⣿⣿ ⠀⠀⠀⠀⠁⠀⣿⣿⣿⠀⠀⣿⡟⣿⣿⣿⣿⡆⢸⡇⢧⢹⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⡇⠀⠀⠀⣿⠘⣿⠀⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⠁⣿⣿⣿⣿⣿⣎⣿⣞⣆⢳⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⣧⠀⠀⣄⣿⣧⢹⡄⣿⣿⡿⠂⠀ ⠀⠤⠄⠀⡇⠀⡿⣿⣿⡀⣾⡿⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⡞⠧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠇⠀⢸⠋⣿⡇⢸⡇⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⡇⢠⣿⣿⢹⣥⣿⡇⠀⢹⣿⣿⣿⡿⠻⠋⠻⢮⣿⣄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣀⠀⠀⠀⣸⢀⣿⣿⣸⡄⡉⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡈⣿⡁⠘⣿⣿⡇⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠙⢦⡀⠘⡆⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠶⠖⠋⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡏⠀⠀⠀⣿⢸⣿⣿⣿⣧⠃⠀⠀⠀⠀ ⡀⠀⠀⠀⠈⣧⣿⡇⠀⣿⡿⡇⠘⣾⡿⢯⡿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡟⣧⠀⠀⢸⣿⢸⣿⣽⡏⣿⡀⠀⠀⠀⠀ ⣿⣆⠀⠀⠀⠸⣿⣷⢰⣿⡇⢿⠀⢹⣷⠀⠁⢠⠟⠀⠀⠀⠀⠀⠀⠘⢆⠘⡟⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⢇⡇⠀⠀⣼⣿⣾⠏⠸⡇⣿⡇⠀⠀⠀⠀ ⢻⣿⣷⡄⠀⠀⣯⣿⢸⣿⡇⢸⣧⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢹⡄⠀⠉⠓⠲⠤⣄⣠⡤⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⠃⠀⢠⣿⣟⣿⠀⠀⣧⣿⡇⡄⠀⠀⠀ ⠀⠙⢿⣿⣶⡄⠉⠙⣼⣿⣧⡀⢿⣷⣄⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣿⣿⣿⣿⣽⣿⠀⢀⣿⣿⣿⠇⠀⢠⣹⠁⣷⠁⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣦⡀⠙⢇⣻⡿⠶⠛⠛⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⡟⠀⣼⣿⣿⡿⠀⡄⣸⠏⠀⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣷⣾⡟⠁⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⣰⣿⣟⣬⣷⠀⠰⠋⠀⠀⢸⠷⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⣹⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⠿⠋⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣤⣤⣤⣄⣀⡀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⠋⠉⠉⠹⣯⠙⣧⡀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⣶⣆⡀⠀⢠⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣷⣤⣀⣀⣀⡀⡀⡀⢀⣀⣿⠀⠀⠀⠀⠸⣧⠘⣿⣆⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢸⡇⠀⠀⠀⠀⣿⣿⣿⡀⠘⣧⡃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣧⠘⣷⡀⠀⠉⠉⠉⠉⠉⠉⢻⡆⠀⠀⠀⠀⠹⣧⠉⠻⠗⠀⠀⠀⢀⣿⣿⠸⡇⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⣿⣿⣿⣿⣄⣹⣟⣠⡴⡛⠛⠛⠛⠛⠻⠷⣶⣤⣼⡇⢤⣄⣿⣆⣀⡀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⢸⣿⣿⢀⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣚⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣤⡀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢿⢻⡇⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠈⠙⣦⡀⠀⠀⠀⠀⠀⡿⠋⠛⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⣿⠏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⣈⣻⣦⡀⠀⠀⠀⣇⠀⠀⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠴⠛⣡⣾⣿⡵⠃⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢻⣷⣍⠙⠲⢤⣸⡄⢸⡥⠤⠤⠦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠌⠢⣴⠋⣠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣿⣿⣷⡀⠀⠹⣷⠋⠰⣤⡀⠀⠈⠳⢄ ⠀⠀⠀⠀⠀⠀⢠⣼⢁⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⠀⠘⣄⠀⠈⠁⠀⠠⣄⠀ ⠀⠀⠀⠀⢀⣴⣿⣷⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀⠹⣆⠀⠀⠀⣀⠁⠘ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⢹⣧⠀⠀⠀⣀⣀ ⠀⣠⣾⡿⡻⢋⡟⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⡠⠜⠉⠀ ⣴⣿⠏⡴⠃⡾⣼⡿⢹⢻⠟⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡇⢿⡀⢻⢹⡌⠻⣎⠛⣿⣿⣄⠀⠀ ⣿⢃⡔⢁⡜⠀⡞⠀⡇⡞⢰⡇⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡄⡇⠈⡏⢧⠀⡘⣆⠈⢿⣿⣦⠀ ⣥⣾⣡⣾⠅⣼⠁⣸⢸⠇⢸⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⡇⡇⢹⡀⢳⠘⡄⢹⡘⡆⢀⢿⣿⣧ ⠿⢿⣿⣟⣰⠃⢰⠇⡸⠀⡏⠘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠾⢠⡇⡇⠘⡇⢸⡄⢧⣀⣷⣹⣬⣎⣻⣿ ⠀⠀⣼⣿⣿⣦⣿⢀⡇⢸⡇⠀⣶⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢻⠀⠀⠀⠀⣯⣿⣿⣿⣠⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⡿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢷⠀⠀⠀⢸⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣏⠉⠉ ⠀⠈⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⡤⢀⣈⣦⣀⡷⠚⠙⠘⡆⠀⠀⣬⣇⡀⠀⠀⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡉⢻⠉⠀⠀⠀⣀⡶⠿⢿⣿⣿⣿⣿⣶⣔⡚⠻⢦⣀⠀⠀⠀⠀⠈⠉⠉⠀⣀⣴⣶⣿⣶⣾⣿⢿⣦⠀⠀⠀⠀⠀⠛⡟⢿⡟⠋⠉⠉⢧⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⢀⡟⣿⠋⣿⡁⢸⠀⠀⠀⠀⠙⡇⠀⢸⣟⠿⣿⣯⡿⡟⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⣿⣿⣿⣟⣿⡟⠁⢸⠀⠀⠀⠀⠀⠀⡇⢘⣷⡄⠀⠀⠈⢧⠀⠀⢰⡀ ⠀⠀⠀⠀⢀⡞⢀⡿⣸⡏⡇⢸⠀⠀⠀⠀⠀⡟⣦⠈⢿⡛⠃⢀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡋⠉⠭⢽⣿⠃⣼⠄⠀⠀⠀⠀⢀⠃⠈⢹⠹⣄⠀⠀⠈⢷⡀⠈⡇ ⠀⠀⠀⠀⡜⠀⢸⣧⠏⠀⡇⠸⡄⠀⠀⠀⠀⡇⠘⠷⢤⡭⠭⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣒⣛⣥⡴⠥⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠘⢳⡀⠀⠀⢳⡀⠃ ⠀⠀⠀⡼⠁⠀⣿⠏⠀⠀⡇⠀⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣿⣦⣀⠀⠙⣦ ⠀⠀⠀⠀⠀⣼⠇⠀⠀⣼⡇⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⡿⣷⣤⡀ ⠀⠀⠀⠀⣸⠋⠀⢀⣾⣿⠃⠀⠸⡀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣿⣿⡇⡈⠻⣿ ⠀⠀⢀⡾⠃⠀⣠⣿⡟⠃⠀⠀⠀⠁⠀⠀⠀⢺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⣿⣿⡇⠀⠀⠙ ⠀⣰⠟⠀⠀⣴⢡⡟⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣒⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀ ⡾⠁⠀⢀⣾⠇⢸⡇⠀⢸⠀⠀⠀⢰⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢿⠿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠀⠀⠀⠀⡾⡌⠀⠀⡄⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⠀⢸⡇⠀⢸⠀⠀⠀⠸⡄⠀⠀⠀⠈⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠶⠃⠀⠀⠀⢀⣠⣾⣿⣿⣿⡇⠀⠀⠀⢰⠃⠇⠀⢠⡇⠀⡄⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⣴⣿⣿⡇⠀⡘⡇⠀⠈⡆⢠⠀⠀⣷⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣿⣿⠛⣿⣿⣿⠃⠀⠀⠀⡾⠸⠀⠀⢸⡇⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀ ⢾⣿⣿⣿⡇⠀⠁⡇⠀⠀⡇⠈⠀⠀⢸⡀⠀⠀⣆⠀⢿⣿⣿⣿⣧⠀⠀⠈⠙⠒⢤⣄⣀⣠⡤⠒⠋⠁⢸⣿⣿⠀⣿⣿⡏⠀⠀⠀⢸⡇⠀⠀⠀⡼⠇⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⠃⠀⠀⢻⠀⠀⢣⠀⠀⠀⠈⢧⠀⠀⢸⡆⠘⣿⠏⣰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠛⢿⣿⠃⠀⠀⠀⣿⡇⣠⠀⠀⡇⡔⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⢸⡆⠀⠀⠀⠘⡆⠀⢸⠇⢦⠻⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣻⣰⠀⠀⣼⣿⠀⡟⠀⣼⣼⣷⠀⣿⡿⢁⡩⠞⠀⠀⠀⠀ ⣿⣿⣿⣿⡄⣀⣀⣈⣇⣆⣀⣧⠐⡄⠀⠠⢿⡀⠸⣧⠎⠘⢦⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣠⡯⡇⠀⣸⣿⣿⢰⠃⠀⡟⠿⢿⢰⡿⠑⣛⠛⠛⠋⠉⠀⠀ ⢹⣿⣿⣿⣇⠀⠀⠀⢹⡇⠀⠘⣦⠹⡀⣀⡠⡇⠀⣧⡀⠀⠀⠳⣝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣴⠋⢠⠁⠰⢻⣟⡇⠚⠀⠸⠀⠀⠀⣿⠟⠋⠈⣧⠀⠀⠀⠀⠀
‧₊˚🖇️✩ ₊˚🎧⊹♡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠁⣴⣫⠖⢋⣿⡝⢻⡿⣽⠛⢿⣽⣠⣿⣿⠛⢲⣶⡿⢾⣿⣯⣴⡊⠈⣡⠄⣠⠖⢶⣄⣀⣀⠀⠀⠀⠉⠉⢻⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⡆⣠⣾⠏⠁⣴⣿⣿⣶⡟⣿⡏⠀⣴⡿⢿⣿⠃⢠⡿⠁⣰⠏⠀⠀⠀⠉⣹⠟⠾⠧⣄⣴⣻⢋⣿⠓⢶⡆⠀⠀⠀⡇⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣏⠀⣠⣾⣿⣿⣿⠏⣸⡿⢀⣾⣽⠇⣸⡏⢀⡾⠁⡼⠋⠀⠀⠀⠀⡾⠋⠀⠀⠀⢰⠋⣹⣿⣇⡀⡼⡿⣦⣄⠀⡇⠀⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢰⣿⣵⣯⢟⣿⢀⡟⠀⣼⠁⡾⠁⠀⡼⠀⣠⡾⠁⠀⠀⠀⢠⣏⣴⠏⠀⠈⠙⠳⣦⡟⠈⣷⡇⠀⠀⢨⣿⣹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡾⣿⣿⠃⣼⣟⣾⠁⢠⢃⡼⠁⠀⣼⠁⡴⣻⡇⠀⠀⠀⢠⣿⢯⣟⠀⠀⠀⢸⠀⠈⠙⢦⡉⡇⢳⡀⠀⣿⣿⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠻⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣅⢀⣿⣿⣿⠀⡜⡾⠁⠀⢰⠃⡼⢡⢿⠇⠀⢠⢀⡾⢃⡞⡞⠀⡼⢠⣾⠀⠀⠀⠀⢸⣇⢨⣧⠀⢻⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⣰⡟⢀⣼⠿⢿⣿⣿⣿⣭⣿⣿⣿⣿⣿⡏⢰⣿⠁⠀⢠⡏⣾⢛⡏⡏⠀⢀⣾⡞⠁⣼⡷⡇⢰⡇⣸⢹⠀⠀⠀⠀⢀⡏⠉⣽⠀⡟⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⢻⡟⠀⣰⡟⢠⡾⠃⠀⢈⣿⣿⣿⡟⠉⠿⣾⣿⣿⣷⣺⠟⣦⣴⣿⠿⢿⡿⣾⠇⠀⣸⡿⠀⢰⣿⣷⣇⣾⣧⠇⣸⠀⠀⠀⠀⣼⠀⠀⠘⢧⠋⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⣀⣾⣿⠟⠀⣼⡏⣵⠟⠀⠀⢀⣾⣿⣿⣿⡧⡆⠀⠀⠀⠀⢹⣧⣜⣿⠿⣿⣿⣌⡝⢿⣤⠴⣿⠃⠀⣼⣿⢸⣿⣸⡿⠀⡟⠀⠀⢀⢜⡟⠀⠀⠀⢸⢸⣿⣟⠻⡄⠀⠀⠀ ⠀⠀⣴⡿⣫⠏⢠⣾⣿⣿⡋⠀⠀⢠⣾⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⣾⠁⠓⠷⣄⣀⣭⡿⠁⠈⠉⠀⠀⠀⠀⠻⠇⣌⡏⣿⠇⢰⡇⠀⠀⣾⣼⠁⠀⠀⢀⡞⠀⣿⣿⡄⣧⠀⠀⠀ ⢀⡾⠋⣴⠋⣠⣿⣵⢟⡝⠀⠀⣴⠟⣿⢻⣿⡏⢸⡇⡇⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠲⣼⡁⠀⣰⢿⡏⠀⠀⠀⣼⠃⣸⡿⢹⡇⢹⠀⠀⠀ ⠟⢀⡾⠁⣴⣿⡿⢋⡞⠁⠀⣼⣷⣶⣽⣿⡟⠀⠘⡗⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠙⢶⡇⢟⠇⠀⣠⢠⠇⢸⣾⡇⠀⣿⡸⠀⠀⠀ ⣠⠟⢀⣼⣿⠟⢁⡾⠀⢀⣾⣷⣿⡿⣷⠏⠀⠀⠀⣧⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⣀⠀⠀⠀⠙⣾⠀⣴⢃⡾⢠⣷⣿⡇⠀⠸⠹⠀⠀⠀ ⠉⣠⣾⡿⠃⢀⡞⠀⣠⣟⣻⣿⠟⣼⠋⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⢀⣴⣿⡾⠃⠘⠁⣾⣿⣿⣇⣍⣓⣹⡄⠀⠀ ⣴⣿⠟⠀⢠⡟⢀⣼⡯⣹⡿⢃⣾⠃⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢹⡇⠀⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⡿⠁⠀⢀⣞⣴⣿⣷⡿⠛⢀⣾⠁⠀⠀⠀⠰⠀⠀⠀⢿⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣟⠀⣼⡇⠀⠀⣿⣷⣿⣿⣿⠿⠛⠛⠋⠁⠀ ⠀⠀⢀⣿⣿⣿⣽⠏⠁⢠⡟⠁⠀⠀⠀⣼⠃⠀⠀⠀⢸⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠃⣷⠀⣿⠁⠀⠀⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⢀⣴⣟⣉⡽⠟⠁⠀⣴⠟⠀⠀⠀⢀⠜⠄⠀⠀⠀⡀⢸⣿⡀⠀⠀⠹⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡇⠀⢸⣿⠀⣿⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠋⠀⠀⢠⡾⠃⠀⠀⠀⣠⠆⠀⠀⠀⠀⠘⢀⡾⠑⣇⠀⠀⠸⡇⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠛⠁⢸⠀⠀⢸⣿⣄⣿⠀⠀⢸⣿⢹⣿⣳⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠈⣾⠃⠀⢹⡀⠀⠀⡇⠀⠀⠉⠒⠢⣶⠒⠲⣾⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⠀⠀⣸⣿⠈⢻⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠈⣧⠀⠀⢻⡀⠀⠀⠀⠀⠙⢦⡀⠈⠙⢷⣄⠀⠀⠀⠀⠀⢰⠀⠀⢸⢸⣷⡿⠀⠀⢿⣿⠀⢨⢿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⣰⡿⠁⠀⠀⢀⠆⣀⣀⣴⡴⠶⢾⣿⠟⠉⠃⡇⠀⠀⠀⠹⡄⠀⢸⣷⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⠘⣿⣶⣦⣤⣀⣈⣀⣀⣼⠀⢿⡇⠀⠀⢸⣿⠀⠈⡟⢿⣿⡀⠀⠀⠀⠀ ⠀⣼⠋⠀⠀⣀⣀⣨⣾⡛⠁⠀⠀⠀⠀⢳⠀⠀⠀⢻⠀⠀⠀⢀⣧⠀⠀⢯⡆⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠘⣿⡿⠈⠉⠋⠉⢻⡟⠛⢻⡇⠀⠀⣾⣿⡇⠀⢸⡈⢿⣷⠀⠀⠀⠀ ⠘⠁⠀⣠⡶⠛⠋⠉⠉⠙⢳⡄⠀⠀⠀⠸⣇⠀⠀⢸⡆⠀⣰⠏⠹⡆⠀⢸⡹⠦⢄⣀⡀⠀⠀⡇⠀⠀⣀⢀⡨⠿⠶⠖⡒⠚⠛⠓⠒⣾⠷⠶⠴⠿⠯⠷⠤⢬⣇⠀⢻⣷⡀⠀⠀ ⠀⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣿⠀⠀⠘⣧⡾⢻⡀⠀⠹⡄⠈⣇⠱⣄⠀⠉⡆⣀⣷⠤⠂⡩⢋⣠⠴⠒⠈⢁⣠⣤⡄⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠻⣧⡀⠀ ⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿⣇⠀⠀⠈⢳⡞⠑⢦⣀⢳⡀⢹⠳⢾⣦⡀⠱⡄⠀⢀⣮⠗⠉⢀⣠⠴⠚⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠙⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣿⡏⠀⠀⠀⠘⡇⠀⠀⠀⠉⢳⠈⡷⢤⣀⠙⠲⣝⡞⠋⢀⡴⠚⠁⠀⣀⣠⡤⠖⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⣷⠀⠈⠷ ⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠁⠀⠀⠀⠀⣿⠙⠛⠋⠉⠉⢳⣸⡀⠀⠉⠛⠳⣤⠞⠉⣀⡤⠞⠋⣡⠞⠁⠀⣀⣤⣇⠀⠀⣀⣀⣀⣤⣾⣟⡃⠀⠀⠀⢸⡄⠀⠀ ⠂⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠘⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢳⣷⠒⠲⢤⣌⡄⠐⠚⢥⡄⢀⡞⠁⣀⣴⣺⠥⠀⠋⠉⠉⣭⡿⠩⠿⣽⡛⠛⠳⠀⠀⠸⡇⠀⠀ ⢠⠖⠀⠀⠀⠀⠈⢿⣤⡀⠀⠀⠀⣷⠀⢸⠃⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠈⠙⠒⢤⣤⡶⠋⣠⠞⢉⠍⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⣶⣶⣾⠇⠀⡇⠀⠀ ⠀⠆⠂⠀⠀⠀⠀⠀⠻⣿⣦⣄⠀⠸⡆⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠻⠶⢯⣍⢏⠁⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠈⠙⣿⡀⠀⢷⡀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠳⡈⠳⡀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢻⣧⠀ ⠀⠄⠊⠂⣀⠀⠀⠀⠀⠀⠀⠙⢿⣇⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢹⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡸⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⠉⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣧⠀⠀⠀⠀⢢⡀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⢀⡞⠁⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⠀⠀⢠⠇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⢀⣠⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⣸⣥⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⠀⢠⡏⡇⠀⣇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⠛⢿⣿⢿⣿⣿⡟⢿⣷⡄⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠀⠀⠀⢸⠀⡇⠀⣿⠀⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⠀⠀⡏⢸⡏⣆⢣⠀⠱⡿⡄ ⠀⣠⣾⠟⢁⣾⢿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡏⠀⠀⠀⡞⠀⡇⠀⡟⡄⠁⠀⠀⠰⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⢹⠀⡇⢻⠈⠀⠀⢉⠙ ⡴⢫⡞⢠⠞⢀⡞⠁⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠀⠀⠀⢠⡇⠀⡇⠀⡇⣧⠀⠀⠀⠀⡇⠀⣏⣇⠀⠀⠀⠀⡀⠀⠀⣇⠀⠀⡟⢸⠀⢸⠀⡇⠀⡇⠈⢆⠈⡧ ⢠⠏⢠⠏⠀⣼⠁⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡠⠀⠀⢀⢸⠁⠀⡇⠀⡇⢸⣸⡄⠀⠀⢿⠀⢿⠸⡄⠀⠀⠀⢳⠀⠀⢹⠀⠀⡇⢸⠀⠘⡆⢣⠀⢸⠀⠈⣧⢠ ⣟⣴⢋⡖⢠⡏⠀⢸⢻⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣿⠃⠀⠀⣸⡞⠀⠀⣇⠀⡇⠀⡇⡇⠀⠀⢸⡄⢸⠀⢿⠀⠀⠀⠸⡄⠀⠀⠀⠀⣇⢸⣆⠀⣧⣾⠀⣸⣧⠀⣸⣷ ⣿⣇⡜⢀⣼⠀⢀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⡼⣿⠀⠀⢠⡇⡇⠀⠀⢸⠀⡇⠀⢳⣸⠀⠀⠀⡇⠀⣧⣬⣇⠀⠀⠀⣷⢣⠀⠀⠀⣿⣾⣿⣿⣿⣿⣶⣿⣿⣷⣿⣿ ⣿⣿⣿⣿⣿⣠⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⣤⡷⣿⠀⠀⣸⢻⠃⠀⠀⢸⠀⡇⠀⢸⡏⡆⠀⠀⣿⠀⡇⠀⠸⡆⠀⠀⢸⠟⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠉⠛⠛⠶⢤⡀⠀⠀⠀⠀⠀⠀⡿⡼⠀⢰⣿⠀⡇⠀⢠⡏⡼⠲⣄⠀⢸⠀⡇⠀⠀⢳⢳⣀⠀⢻⣧⢳⣀⣲⣿⡀⠀⠸⣽⢿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢳⠇⢀⣎⣟⣸⣇⣠⠟⠓⠃⠀⠈⠙⠚⠃⠁⠀⠀⠈⠋⢁⡤⠬⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣧⠀⠉⠀⠀⠀⠀⠛⠋⣿⣿⡇⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣾⣠⣼⣿⣿⣿⣿⣿⣿⣶⡶⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣿⣿⣛⡇⠀⠀⠀⢽⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣯⢹⣿⣿⣿⣿⣿⡆⠀⠉⠉⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠹⣿⡏⢻⣿⠟⣿⡇⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿⡿⣿⡿⠿⡿⠻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠤⣤⣤⠟⠀⢀⣠⢾⡹⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡷⠝⢿⣷⣀⣀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠈⠉⠛⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⡴⠒⠈⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣖⣢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠸⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣅⣀⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠞ ⠀⠀⠀⠀⠀⠀⣀⣀⠴⠚⠁⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⡇ ⠉⠉⣻⣿⣿⣿⠁⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⡇ ⠀⣸⣿⣿⣿⡏⠀⢸⡀⠀⡇⠀⠀⢸⣇⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠈⠙⠲⢤⣄⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⢸⣿⣿⢻⣿⣿⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⡇ ⣰⣿⣿⣿⣿⠀⠀⠀⡇⠀⡇⠀⠀⠸⣿⠀⠀⠀⠀⣿⣿⣿⡏⢸⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⡇⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⡅ ⣿⣿⣿⣿⠇⠀⠀⠀⡇⠀⣿⡀⠀⠀⣿⡇⠀⠀⢰⢹⣿⣿⣇⡞⠁⠀⡄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠿⠾⠿⡇⠀⠀⢀⣾⣿⣿⡟⡇⠀⠀⠀⡀⡇ ⣿⣿⣿⡟⠀⠀⠀⠀⣇⠀⠟⡇⠀⠀⣿⣷⡀⠀⠸⡞⣿⣿⡟⠀⠀⠀⣄⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⡀⠀⢀⡇⠀⠀⣼⡿⣿⣿⡇⣧⠀⠀⠀⠀⠀ ⣿⣿⡿⠀⠀⠀⠀⠀⣿⢀⠃⢹⡀⠰⢻⣿⣧⠀⠀⣧⣻⡿⠀⠀⠀⠀⣻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣉⡆⠀⣼⠀⠀⣼⣿⢃⣿⢻⠇⣿⠀⠀⠀⠀⠀
⣿⠿⣻⣿⢏⠃⣹⣾⠖⠒⣲⠟⢶⠚⠻⢻⡿⠛⠛⡿⠛⡟⠙⡎⡆⢹⣿⣿⣿⣿ ⢏⣴⣿⣿⠈⣠⢻⠼⠤⠤⣿⠀⡟⢲⠒⢾⡟⠀⠀⠻⡤⠿⢀⣇⣷⢸⣿⣿⣿⣿ ⠋⣽⣿⠇⠨⠀⢘⠀⢰⠀⡟⠀⠇⢸⡀⠈⠇⠀⠀⠐⡇⠀⠀⠃⠀⢹⢻⡟⣿⣿ ⣾⢻⡏⡇⢸⠀⠀⠀⢸⠀⠃⠀⠀⠈⡇⠀⢠⠀⢀⠀⢲⠀⠀⠀⢀⡏⢸⣧⢿⣿ ⠇⣿⡀⣧⢸⠀⡀⠀⠐⢸⠀⠀⣇⢠⠃⠀⠸⠀⢸⠀⢘⠀⠀⠀⣸⠃⣼⣿⡎⡇ ⣶⣿⣷⣿⢸⠀⣦⢈⣸⢸⣤⡆⣸⢸⢠⢰⢀⡆⢸⠀⣴⡆⡀⠠⣿⠷⢿⣿⡇⢣ ⢸⠛⠛⣿⣞⣦⡛⠛⣋⣾⣿⡿⠀⠉⠈⠉⠀⢲⣊⣵⣿⡗⢻⡄⠀⠀⠐⠿⢷⣿ ⡜⠀⢸⡿⢉⠀⠇⠐⠼⠾⠟⠁⠀⠀⠀⠀⠀⠀⠻⠥⢼⠡⠂⠀⠀⠀⠀⠀⠘⣿ ⠃⢀⣿⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⣼⣿⡇⣿⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢹ ⡰⢹⠇⣧⠏⡆⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡇⠀⠀⠀⡘⠀⢸ ⢁⡟⢀⣽⡀⣇⠀⠀⠇⡿⠖⠄⡀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⡇⠀⠀⢰⠓⡞⡶ ⣼⠁⡸⠛⠉⠸⠀⠀⠈⡀⠀⠀⡜⠐⠀⠤⠐⠈⠁⠀⠀⠀⠀⠃⠀⠀⡟⠀⢻⠀ ⡏⡜⠀⢀⠀⠠⡆⠀⢰⢡⠀⣜⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀ ⠸⠀⠀⣾⢠⣣⡇⠀⠸⠈⡔⠀⠁⠂⢄⠀⠀⠀⢀⠠⠄⠂⠉⠀⠀⡎⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢿⡿⢋⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣷⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⣱⡿⠁⠎⣽⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢼⣿⡯⠾⣧⡀⠀⠀⠈⢹⣏⢻⣿⣿ ⢳⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠁⠀⣰⡿⠁⣴⡞⠛⠶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢳⣤⡀⠀⠀⠀⢸⣿⣷⣰⢹⣷⡄⠀⠀⠀⢿⡆⠋⠿ ⢸⠀⠀⠀⣀⣴⡿⢛⣿⣿⣿⡏⢰⢰⣿⠃⠰⡟⠁⠀⢸⡟⠀⣴⡖⢶⢶⡄⢠⡤⠤⣤⣤⣤⣀⠀⢀⡤⠤⢤⣤⠤⢤⣖⢷⢻⠈⢻⡀⡄⠀⢸⣿⣿⣯⣬⣿⣿⣦⡀⠀⠘⣿⣾⠧ ⢸⣦⣞⣡⡾⠋⢠⣾⠋⢠⣿⠃⠈⠏⡟⠀⠀⠳⠦⠴⠏⠀⠀⢹⣀⡀⣸⠗⠋⠀⠀⢙⡿⠀⣻⠃⠘⡇⠀⠈⣿⡀⠘⢻⡼⡿⡆⢸⡇⡇⠀⣸⣿⣿⡏⢿⡟⣿⣻⣿⣄⠀⢹⣿⣆ ⠈⣿⣿⡿⢁⣴⣿⠋⢠⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠉⡟⢻⡆⠙⠒⠒⠒⡷⠶⠷⠒⠒⣦⣄⡀⣱⣇⠀⡟⠇⢹⡇⢸⡧⠀⠀⢠⣿⣿⣇⢸⣧⠘⣷⡻⣿⣧⠀⠉⢻ ⠀⡇⣿⣶⣯⣿⢃⣴⣿⢻⡇⠀⠀⡸⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⠀⢸⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠉⠉⠳⢦⠘⡷⠾⠓⠀⠀⠈⣿⠀⣿⣸⣿⡄⢸⣿⣎⠻⣷⣌⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⢃⣾⠇⠀⠀⡇⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⡾⠀⣸⡄⠀⡀⠀⢧⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢃⣇⠀⠀⠀⠀⢲⣿⠀⣿⣯⣿⣿⣾⣿⣿⣆⠘⣿⣷ ⠀⠸⣿⣿⣿⣿⣟⣼⣿⣿⢀⠀⠀⠀⠀⠀⡀⠀⢠⡏⢠⠀⢀⣼⢷⠀⡟⣇⠀⣇⠀⢸⣦⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢸⡈⠀⠀⠀⠀⢸⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿ ⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⡇⠀⣸⡇⣸⠀⢸⠏⢸⠀⡇⢸⡀⠟⣆⠈⢿⡄⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠀⠀⢸⠀⠀⢸⠃⢀⡟⣰⡇⢀⡏⠀⢸⠀⡇⠀⣧⢸⢻⡀⡎⣿⡀⢰⡄⠀⢸⣿⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⡿⠛⠙⢚⣿⣿ ⣀⣀⣀⣠⡿⠻⣿⣿⣿⡇⠀⠀⢸⠀⠀⣸⠀⢸⣷⣿⣇⣾⡀⠀⢸⣠⡇⠀⠸⣾⡀⣿⣿⠸⣷⠀⢷⠀⢰⢿⣧⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠈⢿⠿⢿⣿⣿⣷⡀⣈⣁⣤⣬⣿⠉ ⠿⠿⠷⡿⠁⠀⢈⣿⣿⡇⠀⠀⢸⢀⣤⣿⣿⠛⠻⠿⢛⣿⣾⣛⠛⠉⠁⠀⠀⠙⠓⠸⠿⠆⣙⣆⢸⣆⣸⣆⣿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⣿⣿⡟⠋⠉⠀⠀⠀⠀ ⣛⣛⣻⠃⠀⢀⣾⣿⣿⡇⠀⠀⠀⣿⣿⠛⠛⠀⢰⣤⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢿⣿⠟⢛⣿⣿⡄⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀ ⠤⢴⡏⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡆⠀⠹⣄⠻⣯⣭⣽⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣥⣴⣿⣿⣿⣿⠇⣹⡂⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀ ⣩⡟⠁⢰⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣇⠀⠀⠈⠉⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣥⣬⣿⢿⡄⠉⠙⠲⣶⡆⠀⠀⠀⠀⠀⡇⢰⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀ ⢶⠇⠀⠿⢷⣿⢿⣿⣿⡇⠀⠀⢰⣿⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⢨⢿⣷⡀⠀⠀⠀ ⣿⠀⢸⣻⣿⣟⣿⣿⣿⡇⠀⠀⢸⣿⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⡀⢼⡀⠀⠀⠈⢿⣻⣷⡄⠀⠀ ⠆⢀⣿⣾⡿⠶⣿⣿⣿⡇⠀⠀⢸⣿⠐⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠳⡿⣿⣆⠀ ⠀⣸⣿⣯⣭⣽⣿⣿⣿⡇⠀⠀⢸⣿⡀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⠀⠀⠀⠀⠀⠋⣿⡀⠀⠀⠀⠀⢠⡹⣿⣧ ⠐⣿⡿⠶⠶⣾⣿⣿⣾⣇⠀⠀⢸⣿⡇⠀⢰⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⢿⣇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠙⠘⣿ ⠀⣿⣍⣉⣉⣿⣿⣿⣿⣿⠀⠀⢸⣯⠃⠀⠀⠈⢈⣹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢻⡿⠁⠁⢈⣿⠀⠀⠀⠀⢠⠀⣿⣿⠀⢀⣤⡀⠀⠀⠀⠘ ⣸⠷⠶⠶⠶⣿⣿⡿⣿⣿⠀⠀⢸⣿⠀⠀⠀⠀⠐⡙⢨⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠟⠁⠀⢸⣟⠀⢸⣿⣿⡆⠀⠀⠀⠘⣾⣿⣿⡄⡸⠁⢻⡀⠀⠀⠀ ⡟⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠘⣿⠀⠀⠀⠀⢺⣷⣀⠀⠫⣿⡿⣶⣄⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠋⠁⠀⠀⠀⠀⢸⣟⠀⣻⣿⣿⣇⠀⠀⠀⠀⣿⢹⣿⣧⡇⠀⠀⣷⠀⠀⠀ ⡃⠀⠀⠀⠀⢿⣿⣧⣿⣿⣇⠀⠀⣿⡄⣆⠀⠀⢸⣼⣿⠀⠀⣾⣷⡉⠛⣿⣶⣶⡖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⡗⣿⣿⡀⠀⠀⠀⢿⡏⣿⣿⡇⠀⠀⣏⠀⠀⡀ ⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣷⣿⡆⠀⢸⣿⣯⠀⠀⣿⣿⡁⠀⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⡇⢸⡿⠁⠀⢸⣿⡄⣠⠁ ⣿⡿⠿⠿⡿⢿⡿⡿⣿⣿⣿⣧⠀⢸⣿⣿⣿⡘⠘⡟⡿⣷⡀⣿⣿⣷⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣷⢐⠃⠀⠀⠀⠿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⣟⣿⣿⡄⠈⣿⣿⣿⣿⣤⣏⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⡿⢿⣿⡀⠀⠀⢿⡀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠈⢿⡹⠀⠁⠹⣿⣯⣿⣿⣿⡻⠏⣺⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⢋⣽⠃⠀⠀⠉⠁⠀⢸⡟⠳⣯⣿⡀⠀⠘⡇⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⢳⣀⣠⡿⠟⠛⢈⣠⡤⡖⠋⠈⠻⣿⣿⣇⣀⡃⠀⣀⣤⠴⠒⠋⠁⠀⣠⡞⠓⠒⠀⢀⡀⠀⠀⢘⡷⣄⡀⠉⢳⡄⠀⢿⣲⠀⠀⠀⠀⠀⠀⠀ ⠀⠲⠆⠀⠀⠐⠂⢲⠂⣀⠴⠖⢊⣉⣽⡴⠶⠞⠋⠉⠁⠈⠀⠀⠀⠀⠀⠉⣿⡿⠉⠉⠉⠀⠀⠀⠀⢀⣴⠫⠤⣤⣀⠀⠈⠛⣦⠀⢸⠁⠀⠉⠓⠶⣥⡀⠈⠙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣻⡵⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⣰⠟⡁⠀⠀⠀⠉⠛⠧⡀⠀⢄⡟⠀⠀⠀⠀⠀⠈⢳⣄⢳⣾⡷⣄⠀⠀⠀⠀ ⠀⠲⣆⠀⠀⢀⡟⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀⣸⣿⠀⠀⠀⢀⣠⣤⠞⠛⠀⠀⠀⠀⠀⣀⡀⠀⠀⠂⠸⠃⠀⠀⠀⠀⠀⠀⠀⠙⢯⣻⣿⣟⠗⢦⡀⠀
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡰⢋⡠⠊⠁⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⣀⣀⣾⣷⠟⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⢽⣿⣿⠃⢀⡀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⡄⠀⢂⠙⣿⣦⣄⠀⠀⠀ ⠀⠀⠀⣀⡴⠋⣠⣾⡿⠁⠀⠃⢠⠏⠀⣠⠒⠀⢀⠀⡄⠤⡄⠀⡤⠀⠀⠀⠀⠀⢄⡤⠤⡀⡤⠔⠚⠹⡅⠀⠹⡄⠀⠑⣼⣿⣿⣿⣦⣀ ⣠⣴⣾⢟⣴⣿⣿⡿⠁⠂⠀⢀⡏⢠⠎⠁⠀⠀⡜⢠⠇⠀⠂⠘⠀⠸⠀⠀⠸⠀⠘⠀⠀⠃⢻⡀⠀⠀⠙⣄⣀⣿⡄⠀⠘⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⣸⢀⠏⡀⠐⠒⢰⣧⡞⠀⠴⡇⡀⣀⠀⢄⣀⢰⠀⠀⠀⠀⠀⢸⡏⠓⠊⠀⠀⠀⠈⣇⠀⠀⠀⣿⣿⣿⣿ ⣻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡟⡾⣼⠃⠀⠀⣼⣿⡇⠀⠀⡇⡇⠀⠀⠀⠀⢸⡄⠀⣆⠀⠀⢸⢿⠠⡀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠠⢷⣳⠇⠀⠀⢰⣿⢻⡇⠀⢀⡇⣿⠀⠀⠀⠀⢸⡁⠀⣿⠀⠀⢸⢸⡆⢷⠀⠀⠀⠀⣸⡆⠀⠀⠈⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⡏⠀⠀⣀⣿⠁⢸⠁⣀⣸⣇⢺⡧⢠⣄⢠⡸⡇⢠⢽⢠⡄⣾⠀⣷⣼⡆⢸⡆⠀⣿⡇⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⢸⣿⣰⡶⢣⣿⣇⣀⣸⠀⣾⢘⣿⢸⡇⠘⠿⣼⢀⡇⣼⣸⠀⢷⣯⠤⣿⣿⣿⡄⣧⣸⣿⡇⠀⠀⠀⢿⢿⡏ ⣡⠟⣿⣿⡇⡿⠀⠀⠀⠀⢸⣿⡏⠀⣾⠇⠀⠀⣹⣿⣿⢻⡿⢾⣗⣀⣀⣿⢸⣧⣾⣿⣦⣸⣇⣤⣿⣧⣸⣷⣽⣿⣿⡇⠀⠀⠀⠈⠈⠀ ⣽⡿⣿⡾⢀⡇⠀⠀⠀⠀⣸⣿⡷⣿⣿⣶⣿⣿⠻⣿⣯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⣿⣿⣿⡉⢌⠉⠻⠿⡟⣿⠃⠀⠀⠀⠀⠀⢠ ⣿⣷⡿⠀⣼⡇⠀⠀⠀⠀⠀⠹⡇⠉⣉⣹⣿⣟⣷⣼⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⣻⣿⣿⣿⣾⠀⢀⠀⡇⡞⠀⠀⠀⠀⢰⣶⣿ ⣹⠟⠁⣸⠇⡇⠀⠀⠀⠀⢸⠀⡇⠐⢿⣟⠛⠛⢛⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠯⠉⠁⠹⠿⠔⠋⠀⡇⠇⠀⠀⠀⠀⠘⠉⢻ ⠃⠀⢠⡏⢸⡇⠀⠀⠀⠀⢸⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠈ ⠀⢀⡿⢀⣿⡇⠀⠀⠀⠀⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡇⠀⠀⠀⠀⢠⠀⠀ ⢀⣾⠃⣼⢿⡇⠀⠀⠀⠀⢸⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠈⢧⠀ ⣾⠏⣸⡟⠀⣷⠀⠀⠀⠀⢸⡀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⢧ ⡏⣰⡿⠁⠀⣿⡀⠀⠀⠀⠀⡇⠸⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢹⣧⢀⠀⠀⠀⠀⢰⡀⠈ ⣰⣿⣇⠀⣰⣿⣧⣀⣀⠀⠀⢱⢀⣿⣿⣟⣶⣄⣀⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢻⣯⢸⡏⣿⠘⡆⠀⠀⠀⠘⣧⠀ ⣿⠿⣿⠚⠛⠋⠉⠀⠉⣉⡉⠉⠉⠉⠀⠉⠉⣁⣉⣡⣼⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣿⣿⡂⢸⣿⠀⡷⢻⡇⠀⠀⠀⠀⠀⣿⣆ ⠉⠀⢻⡀⠀⠀⠀⠀⠀⢀⠉⠒⠶⢶⣾⡛⠙⢿⠉⢘⣿⠉⠑⠢⢄⣀⡀⢀⣠⠴⠚⠁⢸⠃⣿⣹⡇⠸⣿⣧⣷⣾⣿⡀⠀⠀⠀⠀⣿⠘ ⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⠀⠉⠛⠻⠾⠟⣉⣆⣀⣀⠀⠀⠉⠉⠀⠀⠀⢀⣿⠛⠻⣿⡇⠀⢹⣿⣿⣏⣿⣿⡄⠀⠀⡀⢸⣧ ⠀⠀⠀⡇⠀⠀⢀⡀⠸⣧⡀⠙⢒⠿⢿⣶⣶⣤⠤⠤⠤⣬⢤⡘⠁⠀⠀⠀⠀⢀⡤⠋⣿⢸⠀⠘⣷⡄⢸⣷⣿⣿⣿⣿⣷⠀⠀⢸⣸⣿ ⣦⠀⢸⣧⣤⣾⣿⣥⡄⢹⡿⣣⢼⠶⣾⣿⣿⠇⠀⠀⠀⠈⢦⠈⠲⢤⢤⡤⠒⠉⠀⠀⢸⠹⣠⣄⡈⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣭⠿⠛⠛⢉⣴⣾⠟⣿⡭⢯⡙⣿⣶⣝⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⡿⠃⠀⠀⣠⢿⠟⠁⡼⠁⠀⠀⠹⣾⡈⢯⠳⣄⠈⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⡍⣡⠟⠀⠀⢀⡜⣡⠃⠀⢸⠁⠀⠀⠀⠀⠘⣇⠀⢳⡈⢦⡀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣱⣿⣿⣿⣷⠃⠀⠀⠀⡾⠀⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱⡀⢣⠀⠀⠘⡽⣆⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⣿⣿⣿⣿⡅⠀⠀⠀⢰⠃⠀⡰⠁⣸⠇⠀⠘⠖⠒⠂⠰⠈⡗⠒⠒⠁⠘⡇⠀⠀⢱⠘⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣻⣿⣿⠏⢹⣿⣿⣿⠀⠀⠀⢀⡏⢀⣴⣧⠘⣿⣠⡄⢰⡦⠤⣤⣴⠀⣧⠀⠀⢰⡀⢷⠀⠀⠈⣇⢻⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡴⡟⣹⣿⢓⣿⣿⡟⡇⠀⠀⠀⢸⠃⠈⢡⠇⣰⢿⡇⠂⣼⣷⠀⠀⣿⠀⣇⠀⢤⠘⡇⢸⠀⠀⠀⢸⣾⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣱⢣⠃⡟⡟⣽⢸⡁⠀⠀⠀⡟⠀⢀⡟⢰⠃⣾⠃⢨⣿⣿⠀⠀⣽⠀⢿⠀⠈⣇⣧⣬⡇⠀⠀⢠⢻⣿⡟⣟⣿⣦⠀⠀ ⠀⠀⠀⠸⣿⣿⣷⠏⡀⢠⠇⡇⡘⢻⡀⠀⢰⡇⢀⡞⣰⠃⢀⡟⠀⡾⢹⡏⠀⠀⡟⡇⡞⣇⠀⢻⣿⣽⡇⠀⠀⠈⢿⣷⢳⢸⣽⡿⠀⠀ ⠀⠀⠀⠀⠈⣻⣿⣶⣃⣾⢸⠀⡇⠀⣷⢀⣾⠀⡸⠷⠗⠒⢾⣇⣰⠁⣞⡇⠠⢀⠇⠇⢁⢹⡄⠈⣿⣿⠇⢀⡞⡀⢸⣯⢸⣮⣿⡄⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⣗⠀⢸⣼⣿⣾⣧⣤⣄⣀⠺⢴⠋⢹⣿⡇⠀⡸⠤⠬⠬⢤⣧⠤⣼⣿⡀⡼⠃⣷⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠀⢀⣴⣿⣿⡇⠉⠙⣿⡇⢰⣿⠀⣿⢻⣿⠛⣿⠟⠛⣿⣿⣶⠀⠉⠙⠓⠒⠁⠤⢴⣆⣠⣹⣧⡀⣿⡇⠀⠀⣿⣿⣿⣿⠛⣿⡄⠀⠀ ⠀⣠⠞⣿⢻⣿⠃⠀⣰⣿⠁⢸⣿⡇⠘⣆⢸⢧⣹⣀⠒⢷⠏⠀⠁⠀⠀⠀⠀⠀⢼⣿⠟⠻⣿⡿⣿⣿⣿⠀⠀⣿⣿⡇⢿⡆⢹⣷⠀⠀ ⡾⢁⡴⢁⣿⣿⠀⠀⣿⡏⠀⣿⣿⣿⠀⢹⣈⠀⠈⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣒⣸⣞⡠⢿⡏⡾⠀⢰⣟⣿⣧⢸⣇⠀⣿⣇⠀ ⣴⠋⢀⡞⣼⡏⠀⢰⣿⠁⣸⣿⣿⣿⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣸⣷⠃⠐⢸⣿⣿⣿⢸⣿⠀⢹⢿⡀ ⠁⢀⡞⢰⣿⠀⢠⢿⡏⢠⣿⣿⣿⣿⠀⠀⡾⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠀⡄⣾⣯⣿⣿⢸⢿⡆⠸⡌⡇ ⣠⢏⡠⠿⠧⣤⣮⡞⢀⣾⣿⣿⣿⣿⡀⠀⣿⣿⣿⣦⣄⠀⠀⠀⠀⠠⡶⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⢠⣿⣿⡏⢻⢻⠘⣆⡇⠀⣷⡇ ⠟⠁⠀⠀⠀⣼⡿⢠⣿⣿⡗⠛⢹⠛⣇⠀⢸⣿⣿⣿⠈⠑⠦⣀⠀⠀⢱⣜⢦⡤⠴⠾⣯⣴⣿⣿⡏⠀⣼⣿⢿⡇⣿⣼⠀⡇⣧⠘⠋⠀ ⠀⠀⠀⣠⠞⣽⡷⠃⠈⠟⠃⠀⢺⡄⣿⡄⢸⠙⣿⠙⢦⣀⠀⠀⠉⠉⠉⢹⣦⠙⢦⠀⠋⠈⢹⠟⣿⢷⢿⣿⠿⣷⣿⣿⠀⡇⣿⡀⠀⠀ ⠉⠉⠉⢡⣾⠟⠁⡄⠀⠀⠀⠀⠀⢷⣸⣷⣸⡆⠘⢆⠀⠈⠱⡄⠀⢀⠖⢁⡼⠷⠄⠱⣦⣴⠃⢸⣿⠏⢸⠇⠀⢻⢿⡟⠀⣧⢸⡇⠀⠀ ⣦⣤⣴⠟⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠻⣷⣿⣇⠀⠀⠙⠦⣀⡇⠀⡞⢀⡼⠓⠒⠂⠀⠀⠘⣄⣾⠋⢀⡏⠀⠀⠀⠀⠱⡀⣿⠈⣷⠀⠀ ⠉⠀⠀⠀⠠⠃⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠈⠙⢾⠓⠙⣟⠒⠒⠀⠀⠀⠀⠘⡇⢀⠞⠀⠀⠀⠀⠀⠀⢣⣿⠀⢻⠀⠀ ⣤⣴⣾⣁⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⣧⠀⠀⠀⠀⠀⠀⠘⢇⠀⣀⣄⠀⠀⠀⠀⢺⣿⡆⠘⠀⠀ ⣱⣿⡛⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣓⢶⣦⣤⣀⣀⣀⣨⠟⠛⢻⡀⠀⠀⠀⠀⣿⡃⠀⠀⠀ ⠯⠿⠃⠀⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣀⣈⢻⣦⠞⡋⠀⠀⠀⠀⢳⡀⠀⠀⠀⢹⠅⠀⠀⠀
⠀⠀⢰⡴⠀⠀⠀⣿⣿⠃⠀⠀⠀⠋⠉⠿⠒⠤⠤⣄⣀⣠⣤⢤⣤⠴⠿⠖⡞⢳⣼⡉⠻⡉⠑⢹⣧⠀⠀⠀⢠⠀⠀⠀⠀⣿⠀ ⠀⠀⣿⡇⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠹⠀⠀⠀⠰⠈⣿⣧⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠘⢿⣇⢀⡀⢸⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⣦⣇⠀⠀⠀⠆⠸⣿⡄⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⡟⠀ ⠀⠀⡾⠀⠉⠉⢹⡏⠑⠒⠒⠒⠓⠒⠎⠐⠒⠖⣺⠁⣿⠒⠦⠐⢿⣿⣄⣀⣀⣼⡤⢿⡗⠠⠷⠒⢺⠙⠛⠈⠙⣷⠀⠀⢸⡇⠀ ⠀⠀⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡆⠀⠀⠀⢠⣇⠀⣿⠀⢱⠀⢸⡽⡄⠁⠀⠀⠀⠸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⠀⢠⠀⠀⣼⡇⠀⢠⠄⣼⢻⠀⠉⡆⢸⡄⠘⡇⢹⡀⠀⠀⠀⠀⣇⠀⠀⢰⠀⠃⠀⠀⠀⠙⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠀⢸⣿⡇⠀⡸⢠⠇⢸⠀⡇⢧⠸⣇⠀⣇⠀⣷⣆⠀⠰⡄⢸⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⢀⡇⠀⢸⠁⡇⢠⡇⡞⠀⠸⣤⡇⠘⡄⢿⡄⢸⠀⠈⢿⡄⠀⡇⢸⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⠀⣷⣤⡇⣾⣿⡀⠀⡄⣿⡇⠀⢳⣸⢳⠘⡀⢀⣈⣇⠀⣧⣴⣼⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣝⠛⢿⣷⣤⡅⠘⠃⠀⠀⠛⠃⠻⣧⠿⣿⣿⣄⡿⠻⣿⢻⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⡀⢿⡿⠿⠿⢷⣬⠅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⠿⢦⡬⢀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⠛⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠛⠋⠁⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡿⠀⣸⠀⠀⠀ ⠸⡀⢸⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢀⡇⠀⣿⢀⠀⠀ ⠀⢧⢸⡆⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⢸⡇⢀⣿⢸⠀⠀ ⠀⠘⣆⡇⠀⠀⠀⠀⢸⡏⠙⠦⣀⠀⠀⠀⠀⠀⠈⠛⠯⠭⠭⠭⠟⠋⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠀⠀⠀⢀⣼⡇⢸⡇⢸⠀⠀ ⠀⠀⠘⢳⠀⠀⠀⠀⠈⣇⠀⠀⢼⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣧⣿⡇⡼⠀⠀ ⠀⠀⠀⠈⡆⢠⠀⠀⠀⢻⡄⠀⢸⠇⢀⣨⠟⠒⠤⣀⠀⠀⠀⠀⣀⡤⠖⠻⢿⣿⣿⣾⣿⣿⣿⠁⠀⠀⢠⣼⣿⣿⣯⠇⡇⠀⠀ ⠀⠀⠀⠀⠸⡄⢇⠀⠀⢸⣿⡤⠼⠛⠉⠀⠀⠀⠀⠀⠉⠑⠒⠉⠁⠀⠀⠀⠀⠉⠛⠻⢿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣼⠁⠀⠀ ⠀⠀⠀⠀⢀⣹⣾⣆⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠇⠀⢠⣿⣿⣿⠋⠉⣿⣿⣿⣶⣶ ⠀⠔⠒⠉⠁⠀⠀⠙⢦⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⡌⠀⡰⠋⠀⠀⠈⠉⠓⠲⠯⣍⡉⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠂⠵⢄⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⣼⡠⠮⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡞⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠐⡄⠀⠳⡀⠀⠈⠋⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢳⣦⠞⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢱⡀⠀⠀⢆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⣸⣿⣗⠦⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢱⡀⠀⠈⡆⢱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⠀⠀⣿⣿⣿⠳⡏⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⢳⠀⠀⠸⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⡟⢰⡇⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢧⠀⢸⠀⠀⠀⢨⢇⠀⠀⠇⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣾⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢇⠀⠀⠈⡄⠈⡇⠀⠀⠘⡌⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀ ⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠀⢀⠀⠀⠀⡄⠸⡆⠀⠘⡆⠀⠀⢳⠀⢱⠀⠀⠀⢣⠀⠀⠀⡟⢷⠀⠀⠀⠀⠀⠀ ⡩⣿⡿⠛⢹⢿⣷⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣧⡀⠀⢸⠀⠀⠀⣦⠀⡇⠀⠀⢿⡀⢀⠀⡇⠀⠆⡄⠀⠸⡄⠀⠀⢿⣸⡀⠀⠀⠀⠀⠀ ⡾⠋⢀⠔⠁⣾⢿⣿⡏⠀⢸⣿⣿⡿⣿⣿⢻⣿⣧⠀⢸⣾⠀⠀⣿⠤⢾⡀⠀⣼⢱⡀⢣⡘⡄⢰⣿⡄⠀⠁⠀⠀⠸⠛⡃⠀⠀⠀⠀⠀ ⠀⡰⠃⢀⣶⠋⢸⣿⠀⠀⠟⢻⢹⡆⢽⡄⠑⠤⣏⣇⢮⣁⡇⠀⠹⣤⠀⣿⡄⠸⡆⢳⣦⣳⡔⠈⣿⣷⣣⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀ ⡴⠁⢀⣾⠃⠀⣿⣿⠀⣰⡀⣀⣿⣿⣾⣿⣦⡀⠈⠻⡿⢿⣿⣶⣶⠿⠛⠉⠙⠒⠛⠀⠈⠉⣿⣦⣼⣿⠙⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠁⠀⡞⡟⠀⢰⣿⡇⠀⠛⣷⣤⣀⡀⠈⠛⠿⡿⢦⠀⢱⡜⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢯⣷⠰⡆⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀ ⠀⢸⠀⠁⠀⡇⣿⡇⠀⠸⣟⠒⠿⢿⡓⢄⠀⠘⢾⣆⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⡟⣿⡗⠀⠀⠘⢳⣤⡀⠉⠢⣷⡀⠈⢻⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡁⠀⠀⠀⡀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⣿⣿⠀⠀⠀⠀⢽⣿⠢⡀⠈⠻⣆⠀⠙⢄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⢿⣀⠀⣀⠬⠖⠚⠒⠐⠒⠠ ⠀⠀⠀⠀⢸⢰⣿⢽⣀⣀⡇⣠⢺⣿⠀⠑⣄⠀⠈⢤⠀⠀⠱⢻⠀⠀⠀⢠⡔⠚⢲⡖⠀⠀⠀⢠⠞⢸⡀⢀⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⢸⡇⣸⠓⠤⣈⡉⠉⠛⠢⠤⣸⡀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠁⠈⠀⠀⢀⠴⡇⠈⣿⣥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠀⣿⠁⣿⠀⠀⣶⠏⢱⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⡀⠀⠀⢀⡠⢾⣿⠀⣇⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⢰⡏⠀⣿⠀⠀⣿⠀⢸⣿⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢹⡟⣇⠀⠘⣇⠀⢹⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⠀⣰⡿⡇⠀⡧⠔⢻⣿⠃⠸⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠞⢿⣽⡄⠸⣿⡆⠸⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢃⡿⠁⠀⠀⠀⡇⠀⠄⡀⠈⣧⡇⠀⢇⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⠉⠒⠛⠛⢒⣫⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢂⣾⠁⠀⠀⠀⠀⢿⠀⡀⠈⠂⣿⣇⠀⠈⡆⠀⠱⢤⡀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠴⠊⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⡇⢘⠉⠒⢾⡄⠘⣇⠈⢣⠀⠀⠀⠀⠀⠀⠀⠱⣄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡏⠀⠀⠀⠀⠀⠀⠸⢡⠀⠀⠀⣇⢸⠀⠀⠀⢳⠀⢹⡂⠀⢣⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣇⠀⠇⠀⠀⠀⠳⠄⢧⠀⠀⢣⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢻⢡⠹⡳⡹⣿⣯⣮⣹⣦⠀⣴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡮⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠠⡀⠀⠀⠀⡄⠀⠀⠀⡇⢇⢡⠙⣜⣗⣝⣷⣾⣿⣥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⡟⡄⠀⢳⡀⠀⠀⠘⡄⢠⣤⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⡁⠀⠀⠀⠀⢰⠀⠀⡇⡜⡀⠀⢼⠘⡄⠈⡷⡄⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⠻⠿⠛⢻⣿⢋⠀⠀⠀⠀⢠⢄⣄⡄⣄⣠⣄⢀⣀⡠ ⡞⠉⡇⠀⠀⠀⠀⠘⡆⠀⢣⠱⠱⡄⠈⣧⠘⢄⠡⣘⢄⢳⡀⡆⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⢻⡇⠀⠀⠀⠀⡏⢸⠿⡟⣼⣩⠟⠾⢰⠁ ⡁⢀⢰⠀⠀⠀⠀⢠⢡⠀⠘⡀⢣⠟⠤⠼⠒⠊⣉⣴⠾⠛⠉⠙⡄⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⣤⣄⡴⣰⣦⡤⠀⠀ ⣷⣾⣾⡄⠀⠀⡀⠘⡌⠧⠔⠒⠃⠒⠀⠀⠀⠘⠿⠿⠶⠖⠒⠚⢣⠀⠀⠀⠈⠻⣿⣏⢢⠀⠀⠈⣿⣿⣄⠀⠀⠀⠟⠛⠜⠉⠞⠀⠀⠀ ⢿⡿⣿⣇⠀⠀⢳⠶⠿⠟⣻⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠹⣿⡄⢳⡄⠀⠘⡎⠻⣷⣄⠀⢰⢋⠟⣻⡖⣹⠀⠀ ⣧⢧⣿⢿⣆⠀⠈⡆⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠉⢷⡀⢿⣦⡀⠹⡀⠈⠻⣷⣌⡈⡚⢉⣓⣁⡀⠀ ⢏⣼⢻⠘⡘⡀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠀⠹⣼⣿⡟⢄⢣⠀⠀⢰⠗⣿⣧⡼⣟⣿⠃⠀ ⠀⢾⣿⠀⢃⢱⠀⠀⣇⠀⠀⠀⠀⠀⢠⠔⠂⠀⠀⠀⢀⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠘⡄⠀⢿⣿⡧⡄⠱⣧⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀ ⣴⠟⢹⠀⢸⠀⢇⠀⢈⢢⡀⠀⠀⠀⠈⠦⠤⠐⠂⠉⠀⠀⠀⣠⠔⠉⢷⠀⠀⠀⠀⠀⡇⠀⢸⡘⣿⣇⠀⠘⢧⠀⠀⠀⠘⣿⣿⣆⠀⠀ ⠁⠠⣿⡄⠀⡄⡜⡄⠘⡌⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⢀⡼⡆⠀⣇⠀⠀⣇⠀⡎⠿⣿⣿⣆⠀⠈⣇⠀⠀⠀⢹⡿⠛⠀⠀ ⠀⠀⣿⡇⠀⣇⢱⡸⡄⠁⢿⣿⣿⣿⣿⣿⠟⡟⣟⠉⠀⠀⠀⠀⢀⠌⠀⢱⠠⠘⡀⠀⣿⣰⠹⡄⢩⣿⣿⡗⢤⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢸⣿⡇⢀⣿⢸⣧⣡⠀⢸⢿⣿⡟⡉⠁⠀⠇⢺⡄⠀⠀⢀⠴⠃⠀⠀⠘⠘⠀⠁⢶⠊⡟⠀⠁⠈⡿⠿⠃⠀⢸⢧⡄⠀⠀⠀⠀⠀⠀
Thorny people, get out of here ! There could be little kids just trying to find cute kaomoji's, then see your horrible stuff ! Copy & Paste this, and Submit it to spread the message #bekind #stopthethornys !! ⸜(。˃ ᵕ ˂ )⸝ 💕
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🤪 𝐚𝐥𝐨𝐡𝐚𝐚 𝐢𝐭𝐬 𝐚𝐛𝐛𝐲!!🌺🐬 ─.⋅ ꒰ 🧁⚡️ ꒱ ⋅. ─ 🌤️🌈𝐬𝐡𝐞/𝐡𝐞𝐫✰🍍 🛍️🌟🏝️𝐁𝐝𝐚𝐲 𝐢𝐧 𝐣𝐮𝐥𝐲!! ☆ ⌇🍋𝐣𝐨𝐢𝐧 𝐦𝐲 𝐠𝐫𝐨𝐮𝐩!-𝐚𝐛𝐛𝐲’𝐬 𝐧𝐚𝐭𝐢𝐨𝐧(𝐩𝐢𝐧𝐧𝐞𝐝)!!♾️🐬💗 👛🐬𝐧𝐞𝐭𝐟𝐥𝐢𝐱+𝐬𝐡𝐨𝐰!! 🌟🐬 🍋⚡️𝐕𝐢𝐜𝐭𝐨𝐫𝐢𝐨𝐮𝐬 𝐢𝐬 𝐦𝐲 𝐟𝐚𝐯 𝐟𝐚𝐯 𝐟𝐚𝐯 𝐬𝐡𝐨𝐰 𝐨𝐧 𝐧𝐞𝐭𝐟𝐥𝐢𝐱!!🌤🌸 ☆ 💗🏝️𝐭𝐭: 𝐚𝐛𝐛𝐲𝐬𝐚𝐯𝐚𝐭𝐢𝐨𝐫!! 🍋☆🐠☆⚡️☆🛍️☆🌊 💖🐬𝐌𝐲 𝐛𝐟𝐟𝐬 𝐚𝐫𝐞 𝐦𝐲 𝐟𝐚𝐯𝐬 𝐨𝐟𝐜 𝐨𝐟𝐜 𝐝𝐨𝐧𝐭 𝐬𝐭𝐞𝐚𝐥 𝐭𝐡𝐞𝐦 𝐚𝐰𝐚𝐲𝐲 𝐟𝐫𝐨𝐦 𝐦𝐞𝐞!!😜🌟🌈 🛍️🌺🐠𝐎𝐁𝐕𝐈𝐎𝐔𝐒𝐋𝐘𝐀𝐁𝐘𝐘 𝐦𝐚𝐝𝐞 𝐭𝐡𝐢𝐬 🫧🚦✈️𝐬𝐨 𝐝𝐨𝐧𝐭 𝐬𝐭𝐞𝐚𝐥 𝐢𝐭 𝐰 𝐨𝐮𝐭 𝐦𝐲 𝐩𝐞𝐫𝐦𝐢𝐬𝐬𝐢𝐨𝐧!!🌺✈️💗 🍋🥥🌊𝐉𝐨𝐢𝐧𝐬 𝐨𝐧 𝐟𝐨𝐫 𝐟𝐨𝐥𝐥𝐨𝐰𝐞𝐫𝐬 𝐬𝐨𝐦𝐞𝐭𝐢𝐦𝐞𝐬!!🚦🌤 𝐗𝐨𝐱𝐨 𝐚𝐛𝐛𝐲!!✈️🧸🐻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠤⠤⢤⣤⣤⣤⣤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⣒⠯⠽⠃⣠⠯⣟⠟⠙⢯⡉⢃⡀⠀⠀⠀⠀⠀⠉⠉⠒⠤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣠⡶⠊⡡⠔⠋⠀⠀⣠⠞⢁⡴⠁⠀⠀⠀⠱⣄⠙⣄⠑⢤⡀⠀⠀⠀⠀⠀⠀⣈⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣱⠞⢁⡴⠚⠀⠀⠀⢀⠖⠁⢀⡞⠀⠀⠀⠀⠀⠀⠘⣆⠈⢦⠀⠙⢦⡀⠀⠀⠀⢰⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣠⣾⠋⡴⠋⠀⠀⠀⠀⣰⠋⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⢧⠀⠀⠙⢦⡀⠀⢸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⠃⡼⠁⠀⠀⠀⠀⣰⠃⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⢧⠀⠀⠀⠻⣄⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣹⠏⢰⣣⢤⣀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⣧⠀⠀⢀⣽⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣽⣻⡿⠀⣿⠃⠀⢨⡦⢤⣼⣁⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠀⠸⣖⠒⠋⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣮⣮⣿⠇⢸⠃⠀⢀⡏⠀⡞⠀⠀⠋⢹⢦⠖⠒⠋⢻⠀⢸⠛⣿⠲⣞⡏⠁⠉⠈⣇⠀⢿⡄⠀⢸⠀⠀⡄⠀⠀⠀⠀ ⠀⢀⡴⣿⢧⣿⣿⣿⣿⣿⠀⡟⠀⢀⡜⠀⠀⢧⣤⣤⣀⣧⢿⣀⣀⣀⣸⠂⠘⣄⡷⠤⠧⠷⣄⣀⣠⣿⠀⢸⠳⢤⣼⠀⠀⡇⠀⠀⠀⠀ ⠀⣯⣼⣯⣿⣿⣿⣿⣿⡿⠀⡏⠉⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⡏⠀⠀⣧⠀⠀⠀⠐⣆⠀⠀⠀⠀⠈⠁⠀⢸⡄⠀⢹⠀⠀⡇⠀⠀⠀⠀ ⢐⣿⣿⣿⢿⡟⢛⣿⣿⡇⢰⠃⠀⠀⠀⠀⠀⡏⠀⠀⠀⢰⠀⡇⠀⠀⢸⡄⠀⠀⠀⢸⡄⠰⡀⠀⠀⠀⠀⠈⣧⠀⠘⡇⠀⢱⠀⠀⠀⠀ ⡎⢻⡿⢁⣿⢁⣾⢿⣿⡇⢸⠀⠠⡄⠀⠀⠀⡇⠀⠀⠀⣾⢸⣇⢰⡀⢸⣹⡀⠀⠀⠀⢷⡀⢧⠀⠀⢀⡀⠀⢸⠀⠀⢳⡀⢸⠀⠀⠀⠀ ⠁⣾⣧⣼⣿⣾⠏⢸⣿⡇⢸⠀⠀⣧⠀⠀⠀⡇⠀⠀⢾⢹⢸⢸⠸⣇⠈⡇⢧⠀⡇⠀⢸⡳⡘⡆⠀⢸⡇⠀⢸⠀⠀⢸⣷⡀⡇⠀⠀⠀ ⠀⠉⠻⣿⣿⣷⣶⣾⣿⡇⠘⡆⠠⣿⠀⠀⠀⡇⠈⠀⣸⣸⢸⠈⡇⡿⡄⡇⠘⡆⢹⠀⠈⣧⠹⣷⠀⠀⡇⠀⢸⠀⠀⠀⢧⠱⣵⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⣿⣿⣿⡇⠀⡇⠀⣿⡀⠀⠀⡁⠀⠀⡏⠀⣿⡀⢱⣼⢳⢸⠀⠹⡌⣧⡀⢸⠉⠹⡇⠀⣧⠀⠘⡄⠀⠀⠘⡆⠙⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⣿⡇⠀⢷⠀⡇⣇⣀⢀⣰⣶⣠⣖⣠⠼⠇⠀⠻⠯⣯⠇⠀⠱⡷⠧⣀⣆⣀⣽⠀⣹⡀⠀⡇⠀⠀⠀⢹⡤⣹⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⣿⡇⠀⠸⠆⣧⠘⢿⠉⣿⣯⣿⣿⡟⠿⣷⠆⠀⠀⠀⠀⠀⠠⣾⠿⢻⣿⣿⣿⣿⡿⠾⣤⡇⠀⠀⠀⠈⢷⢳⣇⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⣿⣿⠀⠀⠀⠹⡇⠀⢦⣘⠿⣟⡻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠻⣿⣿⢃⠉⡇⠀⠀⠀⠀⣼⡌⣿⡀ ⠀⠀⠀⠀⠀⢀⡏⢠⣿⣿⠀⠀⠀⠀⢻⡀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠉⠛⠒⠋⠀⡇⠀⠀⠀⠀⣿⣿⢻⣷ ⠀⠀⠀⠀⠀⢸⠁⢸⣿⣿⡇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⣿⢸⣿ ⠀⠀⠀⠀⠀⡞⠀⢸⣿⣿⣧⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡷⣿⣿⣿ ⠀⠀⠀⠀⢠⠇⠀⣿⣿⣿⣿⡀⠀⠀⠀⣇⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⣸⣿⣏⣿⣿ ⠀⠀⠀⠀⣼⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⣿⣹⣿⣹⣿ ⠀⠀⠀⢀⡇⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⢸⡀⣿⣟⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢹⣿⣿⣿⠇⠀⠀⢸⡿⣿⣿⣿⣿ ⠀⠀⠀⣸⠀⡼⢹⣿⣿⣷⣟⣻⡆⠀⠀⠀⡇⣿⢿⣷⢿⣿⣿⣿⣷⣦⣀⡀⠀⠀⣀⡤⠔⠚⠁⠀⠀⠈⣧⠙⣿⠀⠀⢠⣾⣁⣿⣟⣿⣿ ⠀⠀⢀⡇⢰⠃⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢷⣿⣾⣿⣸⡿⣿⣿⣟⢿⣿⢏⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⢠⣿⣨⣿⣿⣼⣇ ⠀⠀⣼⢀⡏⠀⣿⣿⡿⣿⣶⣷⣹⣇⠀⠀⢸⢻⣿⣿⣿⣷⣻⣽⣾⣿⠃⠈⡼⡄⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢸⠀⠀⣸⠙⠻⢿⣏⢿⣿ ⠀⢠⡇⡼⠀⢠⣿⣿⢧⣿⣿⣿⣙⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡸⠀⠀⡟⠀⠀⠀⠈⡛⣿ ⠀⣼⢰⠃⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⡠⠄⠀⡇⠀⠀⠀⠀⠀⠀⡼⡵⠀⠀⠀⡇⠀⢸⠃⠀⠀⠀⠀⣃⠗ ⣸⢁⡏⠀⠀⣾⣿⡇⣾⣷⣿⣿⣿⠟⠙⡆⠀⠘⡏⠛⢿⣿⣿⣿⠋⠁⠀⡂⢹⠀⠀⠀⠀⣠⠎⢀⠀⠀⠘⠢⡇⢀⡏⠀⠀⠀⠀⠀⠁⠀ ⢋⡜⠀⠀⢀⣿⣿⢡⣿⣿⣿⡿⠁⠀⠀⠽⡄⠀⢷⡀⠀⠈⡽⠃⠲⢤⡜⠁⢸⠀⠠⠤⡖⠃⠉⠁⠀⠀⠀⢸⡀⣼⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠍⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⢤⡤⢄⣀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡌⢹⣶⣶⢬⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠐⢿⠀⢈⠣⡈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⣠⠞⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡀⠀⠘⠣⣾⣇⠸⣆⠱⠈⢧⣽⡦⡀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⢀⡴⠁⠀⡜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢡⠀⠀⢀⡏⣽⢠⣿⣦⣇⠈⢿⣷⣌⠳⣄⠀⠀⠀⠀ ⡇⠀⠀⢀⣴⣿⠁⠀⡞⠰⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆⠈⣿⣿⣷⡌⠓⢄⡀⠀ ⣁⣠⣾⣿⣿⠇⠀⡜⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢰⠀⠀⠀⢰⠐⡄⠀⠀⠀⠀⡆⠀⢀⣾⣿⣿⣿⢿⣿⣿⣿⡿⡄⠘⣿⣿⣿⣦⠀⠑⢤ ⣿⣿⣿⣿⡿⠀⢰⠁⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠻⡄⠀⠀⠘⡄⠛⡄⠀⠠⠀⠱⢀⠞⣿⣿⡟⠈⢸⣿⣿⣿⡇⢳⠀⠸⣿⣿⣿⣧⠀⠀ ⣿⣿⣿⣿⠇⠀⡞⠀⠀⠈⠀⠀⠸⠇⠀⠀⢀⠀⠀⡆⠀⠈⣄⢷⠀⢺⡀⠀⠀⣤⠎⡜⠘⣸⣡⣧⢡⢹⣟⣿⠁⠈⡇⠀⢻⡿⡞⡎⢧⠀ ⣿⡿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣇⠀⡗⠀⠀⢹⡄⢧⠠⣇⠀⣰⣧⣾⢠⢠⣿⣿⣿⣿⣯⠏⣹⠀⠀⢸⠀⠈⢇⢹⣌⣾⠀ ⠁⣠⡴⡟⠀⢰⠃⠀⢀⠀⠀⠀⣔⣀⡄⠀⠀⢿⡆⢹⡄⠀⠘⣷⣨⣇⣻⣿⣿⣿⣿⣿⣿⣻⡇⠈⣿⣿⣯⣇⣀⡀⢸⡀⠀⠈⢾⣿⣧⣴ ⣿⣏⣴⡇⠀⢸⡆⠀⢸⡄⠀⢠⣿⠀⢱⠀⣀⠾⠿⠀⠓⠀⠀⣾⠿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣾⠃⠀⠀⠘⣿⣿⣿ ⡸⢿⣿⠀⠀⠸⠃⠀⢸⣷⡆⠀⣻⣴⣈⠉⠀⠀⠀⠀⠀⠀⠐⠃⣿⣿⣿⡿⢿⠀⡀⠉⠉⠀⠀⠀⠀⠙⡿⢿⣿⣿⣿⡆⠀⠀⠀⢹⣿⠋ ⣠⠈⡿⠀⠀⠀⠀⠀⠸⠿⣴⠚⢻⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠶⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡇⢱⠐⡄⠐⠀⢿⡃ ⢿⡇⡇⠀⠀⠀⠀⠀⠸⡋⠁⠈⣿⠽⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠈⣿⣿⣧⠀⢇⠘⢆⠀⠘⡌ ⢨⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⢠⣙⡷⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⣿⣿⡄⠘⡄⢋⢧⠀⠘ ⠘⣰⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⢰⠛⣿⣿⣇⠀⠸⡌⣾⠳⡀ ⣼⣿⠀⠀⠀⠀⠀⢀⠀⠘⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡎⠀⢻⣿⣿⠀⠀⢻⣾⡄⠙ ⣿⡟⠀⠀⠀⠀⠀⡜⢀⠇⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣀⣒⠶⠖⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡰⢀⠀⠈⢿⣿⡇⠀⠘⠙⣷⠀ ⣿⠇⠀⠀⠀⠀⣰⠃⡼⣸⣿⡿⢙⣦⡀⠀⠀⠀⠀⠀⠘⢿⣀⠀⠠⠒⠀⠀⠀⣸⡗⠀⠀⠀⠐⠁⠀⢠⠃⡀⠀⠀⠘⣿⣿⠀⠀⠀⠸⣇ ⠁⠀⠀⠀⠀⢀⡏⣰⣱⣿⣿⡇⠘⣼⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠀⠀⠀⠀⠀⢠⡏⢀⡇⠀⠀⡀⠘⣿⣧⠀⠀⠀⢇ ⠀⠀⠀⠀⠀⣸⢠⡿⣿⣧⣿⠀⢰⠇⠀⠀⠙⢿⣶⣤⣀⠀⠀⠀⠀⠀⢀⣤⡞⣠⠃⠀⠀⡄⠀⢠⡟⠁⡸⠁⠀⠀⣇⠀⠘⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⡎⢸⡿⢿⡏⢀⡏⠀⠀⠀⣠⠀⢹⣿⣿⠟⠒⠶⢶⡟⠋⢸⡟⠁⠀⢠⡼⠁⣰⢿⡇⢀⠇⠀⠀⢠⠁⠀⠀⠛⢿⡄⠀⠀ ⠀⠀⠀⠀⢀⡞⢀⣿⣁⣼⣇⣞⠀⠀⢀⣼⣁⢠⣿⠟⠁⠀⠀⠀⠀⠀⢩⠏⠀⠀⣰⢋⢃⡴⢿⡀⠑⡎⠀⠀⠀⠈⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⣠⠟⠋⠁⠀⠀⠀⠀⠀⢀⠉⠉⢁⣀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢀⡴⠁⣸⠿⣿⠛⠻⣄⠘⡧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡝⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣿⣯⠉⠒⢤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⣩⡿⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠱⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⡄⠀⣿⣿⣿⣧⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴⣿⡿⠀⠀⠀⠀⠀⡜⠀⠀⣸⠂⠀⢸⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢣⠀⠀⠰⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⢠⠁⠀⠀⣿⠀⠀⡞⠀⢸⡀⠀⠀⠈⡄⠀⠀⠀⠈⡆⠀⢱⠈⠏⣹⡿⠘⠷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢃⠞⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠁⠀⢸⡇⠀⠀⠀⢷⠀⠀⠀⠀⠱⠀⢸⠀⠇⠀⢇⢠⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⡔⣡⣣⠇⢰⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣼⠀⠀⠈⣿⠀⠀⡆⠋⣆⠀⠀⡄⠀⠀⣸⡀⢰⣆⢘⡀⢣⣦ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⣇⡇⢰⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠆⠀⢸⡇⠀⢧⢠⡼⡄⠀⢣⠀⠀⣿⣿⣾⣿⣾⣷⣾⣿ ⠀⠀⠀⠀⠀⢛⣿⠿⠿⠛⠻⠷⠿⣏⡀⠀⠀⠀⠀⡁⠀⡸⡏⠀⣾⣃⠀⢸⠀⠈⣷⡀⢸⣾⠀⢱⠀⢸⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⠖⠉⠀⢀⡀⠀⠀⣀⠀⠀⠉⢢⡀⠀⢠⠇⢠⣧⣇⣘⡛⠀⠙⠛⠋⠀⠉⠁⢬⣿⣿⣿⣷⠾⠿⣧⠉⠉⠉⠙⢻⣿⢹⡄ ⠀⠀⣰⠃⠀⠀⢨⣿⣿⡭⣽⣿⣯⠀⠀⠀⢣⠀⠘⣲⣿⣿⣿⠟⠻⠯⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣦⠀⠀⠛⠀⠀⠀⠀⢸⣿⣿⠻ ⠀⠀⡇⠀⠀⠀⠈⣭⢸⠁⢉⡇⠉⠀⠀⠀⢸⠀⠀⠻⣟⠻⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠃⡤⠔⠉⠀⠀⠀⠀⢸⣿⣿⠀ ⠀⠀⡇⠀⠀⠀⠀⢋⣿⡀⠘⠿⠀⠀⠀⠀⢸⠀⢰⠐⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⣿⣿⡀ ⠀⠀⢃⠀⠀⠀⢘⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣿⡧ ⠀⠀⢸⠀⠀⠀⢀⣽⡵⠇⠀⠀⠀⠀⠀⠀⢸⠁⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⠀⠀⠀⢧⠀⠀⠘⠳⠴⠂⠀⠀⠀⠀⠀⠀⡸⠋⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⢨⣦⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠘⣿⠟⣧⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⣰⣿⠃⠙⣦⢄⣀⣀⠀⢀⣀⡤⠊⠀⢀⠀⠀⢸⣿⣿⣿⣷⣦⣀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣠⢴⣿⣿⣿⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⣰⣿⡏⠀⡰⠃⠀⠀⢸⣿⡿⠀⡇⠀⠀⢸⠀⠀⢸⣿⣿⢿⣿⣿⣿⠙⠢⢄⡀⠀⣀⡠⠔⠋⠀⣸⣿⣿⡏⠀⠀⢸⣇⠀⠀⠀⠁ ⢠⣿⣿⠁⢰⠁⠀⠀⢠⣿⣿⠇⠀⠁⢸⠀⢸⡇⠀⠈⣿⣿⢸⠼⠿⣿⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣿⣿⣿⡇⠀⢀⣿⣿⠀⠀⠀⠀ ⣾⣿⡇⢸⡇⠀⠀⢠⣿⣿⡿⠀⠀⢧⢸⡆⠸⣷⠀⢰⣿⣿⠋⠀⣁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡉⠉⡇⠀⣾⣿⣿⠀⠀⠀⠀ ⣿⣿⣷⣸⠀⠀⢠⣿⣿⣿⠁⠀⠀⢸⡌⢱⠀⢿⡆⠈⣿⠇⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣿⣇⢐⠁⡼⣿⣿⠿⠆⠀⠀⠀ ⠻⠿⣿⣿⠀⢐⣿⣿⣿⡟⠒⠒⠾⣿⣿⣿⣴⣿⣿⡀⠿⡆⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⣾⡎⠀⠸⣿⣤⣶⣀⣀⣀ ⠀⠀⠀⠈⣳⠋⠈⢻⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⡃⠘⡄⠀⠀⠀⠱⠤⠄⠀⠀⠀⠀⠀⠀⠀⠐⢚⡏⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⠝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠙⠢⣀⠀⠀⠀⠀⠀⢸⣿⡟⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠳⣄⠀⠀⠀⢺⠁⢙⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⢚⣿⣿⠞⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡒⣿⣗⠢⢄⣸⡀⣼⠤⠤⣄⡀⠀ ⠀⠀⠀⠀⠀⠐⡶⢁⣴⣿⣿⡏⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣧⡀⠈⢿⠁⠲⠄⠀⠙⠢ ⠀⠀⠀⠀⣠⣾⣵⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠈⣆⠀⠀⠀⠒⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡘⣧⠀⠀⠀⠀ ⢀⣴⡿⡿⣹⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣷⣽⣷⡤⠋⠁ ⣾⠏⡜⢰⢳⡟⣙⡟⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠇⢻⠈⣏⡆⠹⡍⠻⣿⣄⠀ ⣣⣞⣰⠃⡜⢀⢻⠁⡎⡇⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡎⡆⢸⠸⠘⡜⡄⠹⣿⣆ ⠻⢿⣿⣴⠁⡌⡐⢠⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⣇⣮⡁⢸⢸⡄⣇⣽⣼⣼⣽⣿ ⠀⢸⣿⣿⣾⣧⣇⣾⣀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⣇⠀⠀⢸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠧⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄⢠⠤⠾⢃⠀⠀⣸⡀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⠃⠘⠆⠀ ⠀⠀⠀⠀⠀⣽⣿⣿⢻⠋⠀⠀⢀⡶⠿⣷⣶⣿⣶⣴⡖⠲⢄⠀⠀⠀⠉⠉⠁⣠⣴⣾⣶⣼⣿⢷⠀⠀⠀⠀⢻⠻⣟⠛⠉⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⡜⢹⢋⣿⠈⡄⠀⠀⠈⣧⠀⣿⣽⡿⠿⡏⠑⠂⠀⠀⠀⠀⠀⠀⠘⠋⣿⡿⠯⢿⣏⢰⠀⠀⠀⠀⢸⠀⣿⣆⠀⠀⠱⡀⠀⡆ ⠀⠀⠀⡸⠁⣾⡞⠸⡀⡇⠀⠀⠀⠆⠣⣜⣳⣴⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠬⠽⣃⣜⠁⠀⠀⠀⠸⠀⢸⠈⠣⡀⠀⠹⡄⠃ ⠀⠀⠰⠁⢰⡟⠀⢠⠇⢃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢻⣦⣀⠘⢦ ⠀⠀⠀⢀⡞⠀⢠⣾⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣷⣄ ⠀⠀⢠⠎⠀⣰⣿⠏⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⠻ ⢀⡴⠃⢀⡞⣽⠁⢀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣦⡄⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢠⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀ ⠎⠀⢠⣾⠁⡇⠀⣼⠀⠀⢠⠀⠀⠀⢻⣿⣦⣀⠀⠀⠀⠀⠀⣾⠛⠟⢿⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⢰⠇⠀⠰⠀⠀⣾⣿⡿⠀⠀⠀ ⠀⣰⣿⡟⠀⢧⠀⢿⠀⠀⠘⡄⠀⠀⠘⣿⣿⣿⣷⠦⣀⠀⠀⠈⠉⠀⠉⠀⠀⣠⣴⣿⣿⣿⣿⠀⠀⢀⡇⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀ ⢼⣿⣿⡇⠀⢹⠀⠘⡀⠀⠀⣇⠀⠀⡄⢹⣿⣿⣿⠀⠈⠑⠢⠄⣀⣀⡠⠔⠋⢸⣿⡇⣿⣿⡇⠀⠀⣸⠀⠀⠀⣿⠀⢸⣿⡟⠀⠀⠀⠀ ⣾⣿⣿⠁⠀⢸⠀⠀⡇⠀⠀⠹⡀⠀⢻⠈⢿⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠉⠻⣿⠀⠀⢀⡿⢀⠀⢸⣰⠀⣼⡿⠁⢀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⣇⠀⢱⠀⠀⠀⢱⠀⢨⡸⢸⡈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⢀⣼⡇⢀⣾⡇⢸⠀⣿⣿⡀⣿⠃⠲⠥⠀⠄⠀ ⣿⣿⣿⡇⠉⠉⢻⠀⠉⢇⢃⣀⣈⡇⢸⡁⠀⠙⢿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⠞⢩⠁⠼⣿⡇⠃⠐⠀⠀⣽⠗⠊⢢⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠒⢒⡒⠒⠶⡦⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠋⠁⠀⣠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠢⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢛⡽⢛⡏⡰⡷⠓⣦⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⡼⠰⠿⣁⣰⣿⣃⣽⠟⣶⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡴⢿⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⢰⠇⠀⠀⠀⠉⠀⠉⠈⠙⠛⠚⠁⢋⡁⡀⠀⠀⠉⠑⠮⠹⣆⣻⣇⠻⡈⣇⢻⣍⢢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣟⡁⣨⡴⣄⣠⡟⠀⠀⠀⠀⢀⣦⠀⠀⠚⠀⠀⢀⡞⣿⢻⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠈⣿⣆⢣⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡿⣿⢫⣿⢻⢠⡿⡇⡇⠀⠀⠀⠀⢨⡆⠀⠀⠀⠀⠀⣼⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⡎⠷⡄⠀⠀⠀ ⠀⠀⠀⣾⣟⣴⣧⠋⣇⣸⣟⢀⣷⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⠀⠃⠸⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⡄⠙⡄⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣾⣇⠀⠈⠉⠻⡇⠀⠀⠀⠀⠀⠐⠀⢸⠐⠀⢀⡇⢰⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⢸⡽⡄⠹⡀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡶⣶⠃⠀⠀⢀⡤⣾⣾⣤⣼⣽⠒⠺⠇⠸⡇⠀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⡿⠇⢳⡀⠹⡄ ⠀⠀⠀⠀⠙⢻⡿⣿⢻⠟⣻⠇⡟⠀⠀⠀⣷⡠⣿⡿⠿⣧⡍⠂⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣦⣄⣀⠀⠀⠀⠀⠀⢿⣿⣷⣀⣀⣱⠀⠀ ⠀⠀⠀⠀⢀⡟⣰⠇⡿⢰⡏⠀⡇⠀⠀⠀⡇⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡿⢿⣧⡍⢹⣷⠀⠀⡄⠀⣼⣿⣿⣿⡿⢛⣀⣀ ⠀⠀⠀⠀⣼⢣⠟⢰⢣⣿⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠒⠉⡇⠀⠀⢹⡆⠈⠙⣿⣿⣿⣿⠀⠈ ⠀⠀⠀⢰⣿⠏⢀⣿⡟⡟⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣾⡇⠀⠀⢻⣿⣏⢿⡇⠀ ⠒⠢⠤⣿⣋⣠⣿⡟⢸⠇⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢨⡿⡇⠀⣇⠈⣷⢻⠸⣷⠀ ⠠⠔⣶⠟⢡⣾⣿⠀⡿⠀⡆⠀⠘⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⡾⠛⠓⠻⣧⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⣾⠀⡇⠀⢏⠆⠸⣿⡆⢿⡀ ⠀⢠⡟⠀⣼⡟⡀⢠⡇⣶⣇⠀⠐⣷⠀⠀⢸⣧⡀⠀⠀⠀⠀⠣⣀⣀⣠⠇⠀⠀⠀⠀⠀⢀⣴⡿⠀⠀⢸⣟⠀⣷⠀⢸⠸⡀⢻⣷⠸⡇ ⠀⣾⠁⢰⣿⠀⡇⢸⡇⣿⣯⠀⠀⢻⡀⠀⢸⡇⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⢹⡇⠀⠀⣼⢻⠀⢻⠀⢸⡄⢧⠀⢿⡆⣏ ⣼⡏⠀⣾⡇⢀⠇⢸⠇⣿⣿⠀⠀⠘⡇⠀⠸⣷⠀⠘⣿⠉⠲⢄⣀⣀⣠⠤⠖⢻⣿⠁⠀⠀⣼⠃⠀⢠⡇⢸⡀⢸⡄⢸⣇⠘⡆⠈⣿⡈ ⣿⠀⢸⣿⠁⢸⣀⡼⠶⠿⠿⠷⣄⣀⣿⠀⠀⣿⣤⡷⠛⠙⣄⠀⠀⠀⠀⠀⢀⠀⠹⣧⡀⢠⡿⠀⠀⣿⣷⠈⣿⣾⣧⣘⣿⠀⠹⡀⡎⢧ ⡇⠀⣿⡇⣠⠞⠋⠀⠀⠀⠀⠀⠈⠙⢿⣇⠀⣿⠋⠀⠀⠀⠈⢦⡀⠀⣠⠚⠁⠀⠀⠙⣿⣿⠇⠀⣸⡿⠋⠉⠁⠀⠉⠉⠙⣇⠀⢣⢰⠀ ⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢱⠀⡌⠀⠀⠀⠀⠙⢶⠁⠀⠀⠀⠀⢠⣿⡿⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡞⠂ ⠀⣾⣿⠀⠀⣶⣿⠂⠀⠀⠀⠀⠀⠀⢀⡞⠹⣤⣰⠃⠀⠀⠀⠀⣠⣎⣀⣀⣀⡀⠀⠘⣻⠇⢀⡞⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢱⡀ ⢠⣿⣿⠀⢰⣿⡏⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⢹⣿⠀⠀⢠⣤⣾⣥⣤⣤⣤⣤⢸⠆⢠⡟⢀⣾⠁⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣷ ⣸⣿⣿⠀⢸⡟⠀⣀⣀⣠⠴⠋⠁⠀⠀⠀⠀⢺⣿⠀⠀⢀⣀⡀⢀⣀⠀⠀⠀⠀⣀⡿⢁⣾⡁⢀⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡰⠋⠁⠀⠀⠀⣀⣀⣠⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠎⢀⡠⠔⠒⠉⣩⠔⠋⠀⠀⠀⠀⠀⠈⠉⠓⠢⣄⣀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡤⠚⢁⠄⠀⢠⠞⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⠁⠀⡰⠋⢀⡔⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⢀⠞⠀⢀⠞⠀⠀⠀⠀⢠⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⢠⠏⠀⠀⡞⠀⢠⠃⠀⠀⢸⠀⠀⠀⠀⢻⠀⠀⠀⢄⠀⠀⠀⢻⣿⣿⣿⣷⣬⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠃⠀⢀⠎⠀⠀⡸⠀⢀⡾⠀⠀⠀⣾⠀⠀⠀⠀⢸⡄⠀⠀⠘⡀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⢟⣿⣿⡟⠀⠀⠜⠀⠀⢀⠇⠀⣸⡇⠀⠀⣄⣿⠀⠀⠀⠰⢸⣧⠀⠀⠀⡇⢠⠀⢸⣿⣿⢿⢣⠙⣌⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⣠⡞⢁⢞⡟⠟⡇⠀⠀⠀⡇⠀⡘⠀⢰⡇⡇⠀⠀⢱⠂⣄⠀⠀⠀⡍⢽⠱⠀⠀⢃⠀⢇⠀⢧⠝⡎⡆⢳⣌⣦⣤⡀⠙⢿⣿⣶⣄⡀⠀ ⣏⣾⠏⡼⢠⠀⡇⠀⠀⢸⠁⠀⡇⠀⣾⠀⣷⠀⠀⢺⠀⣿⠀⠀⠀⣇⡄⡆⡇⠀⠘⡀⠈⡄⢸⣶⣹⣼⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣇⠀ ⣿⣿⣴⣁⡎⢸⠃⠀⠀⣿⠀⢠⠃⢰⡟⠀⣿⠀⠀⣿⠀⢿⡀⠀⠀⢻⡇⢱⠸⡀⠀⢇⠰⡐⡀⢿⣿⣿⣿⣿⣿⣏⣿⣻⣼⣿⣿⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⠆⠀⠀⢹⠀⠸⠀⢸⣇⣀⠹⠀⠀⠿⠄⠸⢧⣀⠀⠘⣿⣿⣧⣳⡀⢸⡀⠳⣴⡸⠿⠿⠿⣿⣿⣿⣿⣿⠿⣿⣿⡿⡟⠁ ⠈⠻⢿⣿⣿⣿⠀⠀⠀⠈⠀⠀⣠⣤⣾⣯⣽⣝⠒⠒⠀⠀⠀⠠⠶⠛⠛⣿⣿⣿⣿⣏⣱⠀⠈⠙⡄⠀⠀⠸⣿⣿⣇⢹⣆⠈⠁⠀⠀⠀ ⠀⠀⡌⣰⣿⡏⡄⠀⠀⠀⢸⡀⠰⣻⠻⢿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣗⣛⣠⠾⢹⡄⠀⠀⠈⠀⠀⠀⠻⣿⣿⡆⢿⡄⠀⠀⠀⣀ ⠀⢀⣿⣿⠟⠀⡁⠀⠀⠀⠈⠙⡦⠟⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠒⠩⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣸⣿⡞⠉⠭⣂ ⢠⣾⣿⠋⠀⣰⠇⠠⠀⠀⢸⠟⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣹⣿⣶⣿⠍ ⣿⡿⠃⠀⢰⡇⢸⣧⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⠀⠀⠀⠀⢹⣿⣷⣻⣿⡄⠀ ⡿⠁⠀⢀⡏⡇⢸⢀⠀⠀⢨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡇⠀⠀⢠⠀⣿⣿⣯⣿⣿⡀ ⠇⠀⠀⡼⠀⡇⠈⠾⠀⠀⠀⡏⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⣿⠀⠀⠈⠆⠸⡹⣿⣿⣿⣿ ⠀⠀⢠⣇⢀⡇⠀⣆⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⠀⠀⠀⠀⣿⡇⠀⠀⢰⠀⢣⠹⣿⣿⣿ ⠀⠀⣾⠀⢸⡇⠈⢹⡀⠀⠀⠀⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⡟⢿⡄⠀⠀⠄⠘⡆⠹⣿⣿ ⠀⣸⡟⠀⢸⡇⠈⠘⡇⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣷⣦⡤⣄⡠⠤⠖⠋⠀⠀⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⢇⠈⣷⠀⠀⠐⡄⢹⡄⠘⣿ ⢠⣿⡇⠀⢸⡇⠀⠆⡇⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⡿⠻⡀⠀⠀⣀⡠⠤⠒⠒⠉⠀⣿⣿⣿⣿⣇⠀⠀⠀⢾⡆⠘⣇⠀⠀⠹⠿⣿⡀⠈ ⢾⣿⠃⠀⢸⠀⠠⠀⣳⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⠀⠀⠀⢸⡻⡄⠘⡆⠀⠀⠁⢸⠷⡀ ⣸⣿⠀⠀⢸⠀⠀⠞⢸⡆⠀⠀⢸⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⢸⣻⣿⣦⡀⠀⠀⠀⠈⣀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⣱⡶⡤⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠹⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢀⡼⠋⠀⢻⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠘⣟⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠋⢀⡾⠁⠀⠀⢸⠇⣴⠶⣤⣴⣀⣀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⣀⣸⡌⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠇⢀⡾⠁⠀⠀⠀⢸⡼⠁⢠⠃⡛⠁⠉⠉⡟⠳⡴⠒⢠⠤⠤⣴⠶⢶⠞⠚⢉⠉⢻⠁⠀⢱⠘⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠀⠀⡟⢀⡾⠁⠀⠀⠀⠀⢸⠀⠀⣼⡰⢸⢀⣀⠀⠇⡇⣄⠀⣰⠀⣀⡩⢼⠤⠤⠤⢤⣄⣈⣷⣄⣘⡇⢿⠿⡄⠀⠀⠀⠀⠀ ⠀⢀⠎⣠⠀⣼⢣⢿⡗⢳⡴⠻⣷⣶⣿⠀⠁⡏⠀⢸⠀⣇⠀⢸⢠⡀⠀⢸⠀⠀⢰⠘⡆⠀⢠⠀⠀⢠⠀⡆⠀⢹⣸⢷⡀⠀⠀⠀⠀⠀ ⢀⠂⡼⢁⣾⣋⡏⣸⠃⣼⣧⢰⡏⢸⣿⠀⠀⡇⠀⣾⣧⣹⡀⢸⣬⣷⠀⢸⡇⠀⠀⡅⡻⡄⠘⡆⠀⠘⡀⠃⠀⠈⢸⠘⡇⠀⠀⠀⠀⠀ ⠙⢸⣡⡾⣳⢿⡶⣿⣰⡿⣿⣾⣇⢸⣿⠀⠀⡇⢸⣿⢸⡏⡇⢸⣇⣿⡀⢸⣧⠀⠀⠁⣇⢹⡄⢷⠀⠀⠇⢸⠀⠀⢸⡇⢳⠀⣠⠀⠀⠀ ⠀⠂⠀⢸⡇⢸⣧⡈⠙⣿⣥⣤⣭⠫⣿⡄⠀⡇⢸⣿⠚⣿⢹⠈⡇⢻⢣⠸⠹⡀⠀⠀⣿⠉⠹⣼⣆⠀⠀⢸⠀⠀⠈⢇⣼⣿⠃⠀⠀⠀ ⠀⠀⠀⢹⠀⠀⣽⣿⣦⣘⣿⣿⣿⣦⣾⡷⠀⠀⢸⣿⣶⣿⠿⠦⢷⡶⡌⣆⡇⢧⡀⢠⢿⣶⣶⡿⠿⣄⢠⠀⠄⠀⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⡿⠻⠿⠳⠀⠀⡿⢹⣿⡿⢿⣴⡎⠁⠀⠈⠉⠈⠉⠉⠩⣿⣿⣷⡼⠙⣷⠀⠀⠀⠀⢺⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⡏⠀⣾⡟⠛⢻⣿⣿⣿⣧⠀⣆⡀⡇⠀⣿⠀⠿⠷⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠟⠣⠜⢿⠀⠀⠀⠀⢿⣿⠛⡇⢀⣤⣶ ⠀⠀⠀⠁⢰⣿⡇⠀⢸⡿⣿⣿⣿⣆⢻⣳⡹⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡄⠀⠀⣸⢻⡆⣿⣿⣿⠿ ⠀⠀⠀⠀⢸⣿⣇⠀⣿⠇⣿⣿⣿⣿⣿⣿⣧⢣⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠇⠀⣶⣿⡟⣧⣿⡿⠃⠀ ⠀⠁⠀⡀⢸⣿⢿⣸⣿⠀⢿⣿⣿⣿⠿⠿⣝⣯⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⢀⡇⣿⣷⡏⠛⠀⠀⠀ ⠀⠀⠀⢷⢸⣏⠘⣿⣇⠀⣸⣿⣿⠇⠀⠀⠈⠻⢅⠘⡄⠀⠀⠀⠀⠐⠲⠦⠤⠐⠂⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⢸⡇⣿⣿⣷⠁⠀⠀⠀ ⣄⠀⠀⠈⣿⣿⢠⣿⢻⠀⣿⡛⠞⠀⡀⠀⠀⠀⠈⢣⡘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⢧⠀⠀⣾⣿⡿⢿⣻⡄⠀⠀⠀ ⢿⣧⡀⠀⢸⣿⢸⣿⠘⣇⠸⣇⠀⠈⠁⠀⠀⠀⠀⠀⠳⡘⡌⠑⠢⢄⣀⡀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡾⠀⢰⣿⣿⠁⢸⣸⣇⠀⠀⠀ ⠈⠻⣿⣦⡈⠉⣾⣿⣄⢻⣦⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠉⠁⢸⣿⣿⣿⡟⣿⣿⣿⣽⡇⢀⣾⣿⡟⠀⢈⡏⣿⠁⠀⠀ ⠀⠀⠘⢿⣷⣄⢈⣭⠿⠛⠛⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⣿⣿⣿⣿⠃⣼⣿⣿⠁⢀⡞⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⠿⢧⣌⠀⠀⠘⠁⠀⠀ ⠀⠀⠀⠀⢸⢻⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⡀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⠿⠋⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⢯⡙⣦⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠇⣿⠀⠀⠀⣿⣷⡄⠘⣆⠂⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢿⠒⠲⠦⠦⠤⠴⢿⡀⠀⠀⠈⢷⡸⢷⡄⠀⠀⢠⣿⡿⡇⠀⠀⠠ ⠀⠀⠀⠀⠀⢻⠀⠀⠀⢾⣿⣿⣄⣹⣆⣠⡶⠖⠒⠲⠶⣦⣤⣼⠇⣌⣷⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣷⡀⠀⠀⠀⢸⣿⡇⢷⠀⠀⠀
⠀⠠⡀⠠⣄⠀⢀⠀⢀⣠⠴⡶⠛⠛⠛⢿⠥⢶⣤⣀⣀⡐⡤⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠑⣄⡀⣨⣧⣴⠟⢁⠊⠀⠀⠀⠀⠀⠁⡀⢈⠙⢿⠿⡳⢦⡀⠑⠀⠀⠀⠀ ⠀⠀⠈⡠⢺⣿⣿⠁⢠⠂⡀⠀⠃⠐⠀⢣⠠⠘⢦⡑⢌⣇⠈⠺⣷⡄⠀⠀⠀⠀ ⠀⠀⣰⣵⠅⢀⡇⠀⢺⢈⠊⠁⢀⡟⡀⠸⣖⢀⠈⠆⠀⠹⣶⣵⢾⠛⠳⣄⠀⠀ ⠀⣰⣿⣭⣤⣿⡀⠀⠀⢸⠀⢰⢼⢸⠃⠀⡧⠀⠀⠘⣆⠀⡵⠘⡊⢢⣵⣬⣿⣶ ⡼⢻⠏⡛⠌⡄⡇⠀⠀⡤⠀⠘⣸⠸⠘⡀⠀⠱⠀⢃⢣⠀⢣⡿⢶⣵⣿⣿⣯⣿ ⣰⣿⡷⢿⣤⢧⣇⠀⠀⠈⠀⡄⢹⠀⠃⠱⠀⣤⣵⠈⡸⢂⠘⢻⣿⣿⣻⠹⣯⠉ ⣿⣿⣿⣿⣿⡷⠟⠀⡆⢻⣶⣿⡇⠀⠀⠀⠀⠿⠿⣷⠜⡌⠀⢸⣿⡿⣧⡇⢸⡀ ⣿⠟⣽⣿⣽⣿⠀⠀⠇⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣷⣧⠘⢧⠸⣷ ⠇⢰⣿⣿⣿⢸⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⣿⣻⠙⢾⢀⢻ ⠀⠋⡏⢻⡇⢸⡇⠀⢿⣆⠀⠀⠀⢀⠠⠀⠀⠀⠀⡔⢱⡇⠀⡆⡿⣟⡆⠐⣾⠘ ⠀⢀⠇⢸⡇⢸⣷⠀⢸⣿⣷⣤⣀⠀⠀⠀⠀⣀⣴⣀⣿⡇⠀⡇⣷⡿⣧⠀⠹⢐ ⠀⣀⠃⠈⣷⠈⡏⡆⠀⡿⣿⣿⡇⠈⠀⠒⣞⡡⡔⡢⢛⠫⠖⢲⣿⠏⣇⠣⡂⠸ ⠀⠄⢼⠀⣿⡀⢻⠸⡀⠇⣿⣿⠇⠀⠢⡁⠢⣀⡁⠁⠀⠠⠒⠀⢛⡞⢸⡄⣸⠃ ⠀⢄⡘⢣⠏⢧⢸⣷⡱⡸⠊⠁⠒⠠⢀⠈⠢⠀⠀⠃⡠⠃⠀⠀⠀⢫⠏⠙⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢒⣀⠔⠀⠐⠁⠀⠀⠤⡀⠀⠀⠉⠛⠻⣶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢂⣶⠖⠒⢐⣶⡶⠖⣲⣶⠖⣡⢀⠝⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠈⢧⣈⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣾⣿⡯⠔⢺⠉⣴⣾⣿⡿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠈⢿⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠲⢿⣋⣩⣶⡇⠀⠸⠀⢿⣿⡿⠁⠀⠀⠀⠀⠀⣰⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⣿⣧⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣷⠀⢸⠀⢸⣿⠁⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⡆⠰⣠⠀⠀⠰⡀⠀⠈⠆⠀⠀⠈⣿⣿⣷⡀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⡇⠼⠐⢻⡏⠀⢸⠀⠰⠀⠀⣿⠛⠀⠀⢀⣽⠀⢫⣇⠀⠀⢳⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣏⡀⢀⣀⡤⣾⡇⠀⠀⠀⢰⠀⠀⣿⠘⣦⠀⠈⣿⣆⠈⢏⢧⡀⠀⢣⡀⠈⠀⠀⢠⣿⣿⣿⣿⣷⡈⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⠛⠉⠈⢀⣿⠀⠀⠀⠀⢸⠀⠀⢻⡇⡿⡆⠀⣻⣽⣦⠈⢾⠓⢄⡀⢻⣶⡄⠀⠀⣿⣟⣏⣘⣿⣷⣼⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⡄⠸⣄⠀⢸⡼⡄⠘⠛⠛⠋⠀⠀⠀⠈⣶⡾⢿⣿⣷⣶⡽⢧⠀⠀⣿⣿⣿⣿⣿⣿⣧⡘⠿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢀⣿⣿⡇⠀⣿⠀⣼⣶⢿⣶⣦⣤⠀⠀⠀⠀⠀⠁⠀⠿⠿⠿⠟⠃⢸⠀⠀⠈⠉⢹⡅⢹⡟⠛⢿⣷⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢸⣿⣻⣇⠀⠘⣧⠜⠁⣾⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⣧⠀⣿⣦⡀⠹⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⣼⣿⣿⡟⠀⠀⠙⡄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠸⣷⡳⣄⠘⣿⡁⠀⠀⠀ ⠀⠀⢀⡜⠀⠀⣠⣿⣟⣿⣿⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣸⡀⠀⠀⢧⢳⡙⢧⣙⣷⡀⠀⠀ ⠀⡠⠚⠛⠉⠉⠀⢸⠛⠛⢻⡆⠀⠀⠸⢣⡀⠀⠀⠀⠀⠀⣶⡾⣾⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢠⢸⡏⠱⣦⠀⠈⢀⢳⡀⠙⢿⣿⣄⠀ ⠋⠀⠀⠀⠀⣀⣠⣾⢰⠆⠀⣳⠀⠀⢸⡀⠑⢄⠀⠀⠀⠀⠘⠻⠋⠉⠁⠀⠀⠀⠀⣀⣾⡃⠀⠈⢸⡷⡄⢹⣧⠀⠘⠆⢹⣄⠀⠟⢿⣧ ⠄⠒⠒⠉⠉⠁⠀⣿⡇⠀⠀⢸⡀⠀⢸⡇⠀⡘⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⢸⠀⠀⡄⣸⣧⣿⡄⠻⣆⠀⢇⠘⢻⣆⠘⢆⠙ ⠀⠀⠀⠀⣀⣠⣤⣿⡇⠄⠀⣸⣧⠀⠀⡇⠀⢿⣇⠹⣎⠻⡳⢦⣤⣤⡔⠊⠁⠀⠀⠀⢸⠀⠀⣷⡯⢿⣽⣿⣦⡈⢳⣨⣦⣤⣿⠧⣬⣦ ⢒⣶⣿⣿⣽⣿⢀⣿⡇⡇⠀⣿⡏⣆⠀⠇⠀⢸⣿⣿⣾⣷⣿⣾⣿⡛⣿⡆⠀⠀⠀⠀⢨⠀⢰⢿⣿⡿⣿⣿⣿⣿⣿⣿⠏⠉⣀⠀⠀⠈ ⣿⣿⣿⡿⠿⠟⢸⣿⠐⠇⠀⢹⣿⣿⠀⡀⠀⠈⣿⣿⣿⣿⣾⣽⣿⣿⠁⠀⠀⠀⠀⠀⡞⠀⣼⣿⣝⣷⣿⣿⡿⢿⡿⢃⣴⠿⠃⠀⠀⠀ ⣉⣀⣀⠀⠀⠀⢸⣟⣀⣃⡼⠋⠸⣿⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣾⡤⠀⠀⢀⣤⣾⡇⢰⣿⣿⣿⣿⣿⣿⣾⣿⣼⣿⣷⣷⣴⣚⠓⠆ ⠀⠀⠀⠀⠀⠀⢸⣇⣴⣯⣶⣿⣿⣿⣷⠀⠀⠀⢸⣿⣻⣿⣿⣿⢿⣿⠇⠀⠀⣠⣿⣿⠁⢠⣿⣿⣿⣿⣯⣿⣿⣿⠿⠋⠉⠁⠀⠀⠉⠙ ⠉⠉⠉⠀⠀⢈⣿⡿⠋⠁⠀⠀⠈⠙⢿⠀⡀⠀⣼⣿⣯⣽⣿⣿⣶⣿⠀⠀⣴⣿⣿⡏⢀⣾⣿⣿⣽⠾⠋⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⠁⡇⠀⣿⣿⣿⣟⣿⣿⣿⡟⢀⣾⢿⣿⡿⢁⣾⣿⣿⠷⠶⠶⠿⠥⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠤⢼⣿⢽⢠⠿⢯⣭⣿⣿⣿⣿⣿⣾⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣻⠃⣸⣏⠠⠤⠄⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⠟⠉⡡⠞⡻⠛⢪⡟⡯⡙⠷⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢤⣶⡏⡑⠁⢀⢎⠊⢰⠁⠀⠀⠻⠈⠌⢆⠈⢳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣮⢾⣿⡟⠀⠀⡜⠀⠄⡆⠀⡤⠤⠀⡧⠬⠀⡆⠀⠞⣦⡀⠀⠀⠀ ⠀⠀⣠⣪⢿⡏⣿⣿⠇⠀⢰⠁⢾⢨⡧⠂⣗⠒⡆⡄⠀⢠⢱⠀⠘⣸⣷⡀⠀⠀ ⠀⠀⣹⣎⠢⠙⣿⢻⡀⠀⡌⢀⢆⠂⡇⢸⣿⠀⣇⢠⠈⣾⣼⠀⠀⣹⢟⣿⣢⠀ ⠀⠀⠙⣿⣧⣰⡘⡄⢣⢠⠇⢮⠦⢼⣀⢣⡇⡀⠸⠀⡆⢹⣿⠀⡄⢸⡛⣼⡇⠀ ⠀⠀⣰⣿⠻⢿⡇⣇⢸⣾⢾⣶⣤⣜⡊⠽⢇⡘⢒⡒⠺⡒⣿⠘⢹⣿⣿⣿⠁⠀ ⢀⢞⢿⡟⠀⣾⢀⣿⡈⡎⠢⣇⣺⠏⠁⠀⠀⠀⢴⠟⣻⢿⡿⡆⢸⣿⢹⡈⣧⠀ ⡣⢊⢾⠇⢸⡇⣸⣿⡇⠐⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⢊⣧⢡⣸⣿⡿⡆⢹⡆ ⢀⠊⡾⢀⢾⢡⣿⣿⡇⢰⣗⣄⠀⠀⠀⢀⡀⠀⠀⠀⣠⣿⠇⠨⣿⣿⡇⢳⢸⡁ ⠃⠁⢀⢿⡣⣿⠛⢻⢳⠈⣿⣿⠑⠢⢀⣘⢕⢤⠰⠪⣿⣿⣀⣯⢿⣬⡇⣹⠘⠃ ⠀⠐⣨⠟⠁⠈⠁⠘⣼⢆⡎⢇⠑⢠⠀⠠⢘⣦⣑⣄⡜⢹⡟⡟⠹⣿⠇⡏⡇⠀ ⠶⠞⠁⠀⢠⠀⠀⠀⠘⠛⢇⠀⠑⠠⣄⡦⡎⠀⠀⠀⠡⠏⡰⠁⠀⠀⢂⡇⢧⠀ ⣤⣶⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⡄⠀⠀⠀⠑⣀⣠⠀⠀⠘⣷⠸⠀ ⠮⠏⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⢙⢷⡲⠖⠁⠈⢄⠀⠀⠟⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠐⣸⠀⠀⠀⣰⠟⡿⠁⠉⠀⠀⡽⣻⣦⡾⠛⢻⢻⣦⡿⠒⠗⠶⣶⣯⣤⡶⠶⢤⣤⡴⠺⣷⡛⢺⠀⠀⠀⠀⠀⠸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠄⠇⠀⠀⢀⡇⢸⠇⠀⠀⠀⠀⣷⡿⣼⠃⠀⠀⡼⠹⠀⠀⠀⠀⠈⢿⠙⠀⠀⠀⢹⡇⠀⢸⡇⠀⠄⠀⠀⠀⠀⠀⣿⣿ ⣿⡇⠀⠀⣿⢿⣿⡄⠀⠀⣹⣿⣿⣿⠀⠓⠶⢦⣤⣄⣿⣰⣀⣀⣰⣾⢇⢸⠀⢠⡀⠀⢰⣿⣷⣧⢀⡀⣀⡇⢀⡀⠀⠀⠀⠀⢸⣤⣆⠀⠀⢀⢳⠀⠈⣇⠀⡄⠀⠀⠀⠀⠀⠈⣿ ⣿⠁⠀⣸⡿⠐⣿⡇⠀⠀⣿⡇⢹⣿⡀⠀⠀⠀⠀⠈⠙⠛⠙⠉⠈⠋⣼⠟⠛⠛⠉⠉⠋⣹⣇⡟⢫⡟⠛⠀⢸⠏⠉⣿⠉⠙⡇⡇⠉⠛⠻⡍⠙⠓⠛⠛⠲⢶⠤⠤⠀⠀⠀⢠⠘ ⣿⠀⢀⣿⡇⠀⣿⣇⠀⢸⣿⡇⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⡿⢸⠁⡞⡇⠀⠀⡟⡇⠀⡟⠀⢠⠇⡇⠀⠀⠀⣇⠀⠀⢀⠀⠀⢸⠀⠀⡀⣀⠀⣿⠀ ⡇⠀⣼⣿⠀⠀⣿⣿⢀⣿⣿⡇⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠀⡇⠀⠀⣸⠃⣼⢠⣇⡇⠀⢠⠇⡇⢀⣧⠀⢸⠀⡇⠀⠀⠀⢹⡄⠀⢈⠀⠀⢸⠀⠀⠀⢹⠀⢸⠀ ⡇⢰⣿⠇⠀⣀⣿⣿⣸⣿⣿⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⡇⠀⢰⡇⠀⠀⡟⠀⡏⢸⢻⠀⠀⣾⢠⡇⠘⣿⠀⡼⠀⡇⠀⡇⠀⢸⡿⠀⢸⠀⠀⢸⡄⠀⠀⢸⠀⢸⠀ ⡇⣾⣿⠀⠀⣿⣿⣿⣿⣿⣿⣆⡀⠀⣿⣧⠀⠀⠀⠀⠀⠀⡇⠀⢸⢁⡇⠀⢸⠃⠀⢸⠁⢠⡧⡎⢸⠀⢠⠇⢸⢁⡆⡟⢀⡇⠀⡇⠰⢹⢀⠸⣿⠀⢸⠀⠀⣯⡇⠀⠀⢸⠀⢸⣿ ⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡄⠀⠀⠀⠀⢰⠇⠀⡸⢹⡇⠀⣼⠀⠀⣏⡀⢸⣴⠇⡸⠀⡸⠀⢸⣾⡇⡇⢸⠃⢠⡇⣸⡀⢸⣴⣿⠀⢸⠀⠀⠃⡇⠀⠀⢸⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠻⠿⣿⣿⡧⠀⠀⠀⠀⣼⠀⠀⡇⣸⡇⠀⠇⢀⣸⣉⣉⣹⣿⢙⣇⣰⠇⠀⢸⣿⢳⣇⡏⠠⢼⣣⠟⠗⣛⣸⣿⠀⠀⠀⠀⢰⡇⠀⠀⣾⠀⢸⣿ ⠀⠉⣽⣿⣿⣿⣿⠙⠛⣿⣧⣀⣀⣤⣿⣇⠀⠀⠀⢀⣶⣿⣅⣴⣿⣿⣥⣤⣿⣷⣾⣶⣤⠉⠁⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠐⣋⣤⣥⣭⣿⣷⣴⣿⣦⣴⣾⡇⠀⠀⣿⠀⢸⣿ ⠀⢸⣿⣿⣿⣿⣿⠀⠀⢻⣿⡏⠛⠿⣿⣿⡄⠀⠀⢸⠛⣧⠉⣴⣿⣿⣾⣷⣶⣌⡉⠹⠯⡛⢿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⢛⣿⣿⣿⡍⠛⠋⠽⠋⢣⣿⣷⣶⣾⣿⠀⠀⣿ ⡆⣾⣿⣿⣿⣿⣿⡆⠀⢸⡏⠀⠀⠀⠀⠈⠃⠆⠀⣾⠀⠈⠳⢴⣿⣋⣉⣙⣋⣙⣻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⡟⠻⠛⣻⣿⠟⠀⠀⣼⣿⣿⡿⠟⠛⠀⠀⠀ ⣸⣿⣿⣿⣿⠇⢸⡇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠁⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠇⣿⣿⣷⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀ ⣿⣿⣿⣿⢆⣿⣿⣿⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⠀⠀⠀⠀⡇⠀ ⣿⣿⣿⠃⠀⣿⣿⣹⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⢸⣇⠀ ⣿⣿⡏⠀⠀⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⠀ ⣿⣿⠀⣾⣇⣸⣿⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⡀ ⣿⡏⠀⣿⣇⣿⣿⣿⣿⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⡇ ⡟⠒⠀⣿⣿⣽⣿⣿⣻⡆⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⡇ ⠀⢀⣳⣿⣿⣷⣿⣿⣿⣇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⡟⡇ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠈⠉⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⠀⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣤⣀⡤⠖⠋⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠇⠀⠀⠀⠀⢀⣿⣿⠀⣧ ⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣇⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠇⣿⠀⠀⠀⠀⠀⢸⠏⡏⠀⢹ ⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡄⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠻⢿⣼⣿⡿⣾⣿⡟⢠⡇⠀⠀⠀⠀⠀⡿⢀⡇⠀⢸ ⣿⣿⣿⣿⡀⠙⣿⣿⣿⣿⣿⣷⣿⣿⣿⡄⢀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣿⡿⠠⡞⠀⠀⠀⠀⠀⡾⠇⠼⠁⠀⠸ ⢻⣿⣿⣿⡇⠀⠙⢿⣿⣯⣿⣿⣟⠉⠉⢧⠀⢣⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⣰⠃⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠹⣿⣿⠀⣧⠘⣇⠘⢧⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⡤⠤⠤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⢠⠏⠀⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠸⣿⡆⠘⡆⠙⡄⠈⢷⡀⠀⠀⠈⡇⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⠉⣉⠉⠉⠳⡄⠀⠀⠀⣀⡾⠋⠀⠀⡞⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠹⣧⠀⠸⣆⢽⣄⠀⠳⣄⠀⠀⢹⡀⠀⣰⠃⢀⣤⣾⣷⠶⡤⡤⣄⡞⠁⠀⠀⠀⠹⣄⡀⠈⣁⣀⠤⠴⣾⠁⢀⡴⢯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⣄⢘⣯⠐⠛⢦⣀⡀⣷⡾⢁⠀⣸⣻⢛⣷⡿⠿⠛⠁⠀⠀⠀⣀⠀⠀⠀⢙⠉⠁⢀⣀⣼⣁⡴⢋⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣴⣤⣶⡶⠿⠿⠿⣯⣿⣟⣒⣲⣤⣄⡀⠀⠀⠀⠐⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢱⠂⠀⠘⠓⠤⢤⡤⠖⠀⣠⣴⡿⠟⢉⡼⠋⠀⠀⠀⠀⠀⠉⠳⣌⠉⠛⠿⣿⣶⣦⣶⣶⣤⣞⠁⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⣆⡀⠀⢀⣠⣶⣶⣾⡿⠋⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⢿⣿⡿⢏⡛⠷⣄⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠜⠀⢈⣽⣿⣿⣿⡿⠋⠀⢀⡴⠁⠀⠀⠀⡄⢠⠀⠀⠀⢦⠀⠀⠈⢳⡄⠙⢦⠀⠹⡆⠈⠹⣦⣘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⡴⠋⣼⠿⠟⣿⠇⠀⠀⣼⠃⣠⠀⢀⣀⡆⢸⠀⠀⠀⠀⣧⠈⠀⠀⠙⡶⠄⠑⢦⣻⣆⠀⢀⡙⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣼⣥⣾⡁⠀⢠⡟⠀⠀⠘⠹⠀⣱⠋⠁⠈⡀⠀⡆⣆⠀⠀⢿⡶⡄⡀⠀⠸⡄⠀⠀⠙⣿⣶⣦⣵⡶⡿⠛⠻⣧⣄⢀⠀⠀⠀ ⠀⠀⠀⣸⣿⡟⣶⠀⢠⣿⡇⠀⠀⠀⡇⠀⣿⠀⠀⢰⠇⡆⢷⣿⠆⠀⠸⡝⠀⠘⠀⠀⠹⡄⠀⠀⢸⢏⠉⢯⣔⢕⠐⢦⡀⠙⢿⣦⣀⠀ ⠀⢀⣾⣿⣿⢷⣶⢶⣾⡟⡇⠀⠀⠈⠀⠐⡇⠀⠀⣼⠇⡇⢸⡈⡆⠀⠸⡿⣄⠀⠀⠀⠀⢿⡄⠀⢸⡌⡄⡌⢏⢄⠳⣷⣿⣿⣶⣿⡿⣧ ⣠⣿⢿⣯⠇⢾⠃⡜⠁⠁⡇⠀⠀⠀⠀⢰⡀⠀⠀⡄⢀⡇⠘⡇⢹⠀⠀⠃⠘⢆⠀⠀⢇⠸⡅⠀⠈⣇⢱⣸⣼⣌⣦⣿⣿⣿⣿⣿⣱⣾ ⠋⢀⣾⢏⠀⡜⡜⢸⢸⠀⣿⠀⠀⠀⠀⢘⡁⠀⠀⡧⠜⡇⠀⣇⠈⣇⠀⠀⠉⠉⢆⠀⠸⡀⣷⡀⠀⢸⣿⣍⣽⣿⣟⣽⣿⣿⣿⣿⣿⣿ ⣠⣿⣿⣾⡿⣿⣇⣧⣼⣶⣿⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇⠀⠙⠀⠘⣧⠀⣰⣤⣾⣆⠀⢇⢹⢳⡀⠘⠛⢻⣿⣿⣿⣏⢹⠈⢿⣿⠀⠀ ⣿⣿⣿⣿⣿⣶⣿⣿⣷⣼⣿⡇⠀⢀⠀⣶⣆⣆⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣳⠀⣸⡄⢻⠀⠀⣸⣿⣿⣿⣿⡌⡇⠀⢻⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠉⠀⠀⢸⠀⠉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠒⠀⡇⠀⠀⠀⣿⣿⣿⣇⢻⣷⣷⠀⠈⣧⠀ ⣿⣿⠟⢁⣿⣿⣏⣿⣼⡇⠀⠀⠀⢸⠀⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⠀⠀⣿⣿⣾⣿⠀⠻⣿⡀⠀⣿⣷ ⣿⠋⠀⣾⣿⣿⡏⣿⡟⣷⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⠀⣿⣽⣿⣿⡤⣤⡼⡇⠀⣿⣿ ⠇⠀⣼⢻⣯⣹⣧⣿⠀⣿⡀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠸⠀⠀⡇⣿⣿⢹⡇⠈⠳⣧⠀⡇⢿ ⠀⢸⠛⢻⡯⢿⣷⡿⠀⣿⡇⠀⠀⢸⣯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣼⡇⠀⠀⢰⡇⣿⣿⡏⣧⠀⠀⢾⣤⡇⠸ ⠀⠈⠀⢸⡇⠸⣿⣿⠀⢿⣿⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⣿⡇⠀⠀⣸⠀⣿⢹⣷⣿⠀⠀⠸⣿⠇⠀ ⠀⠀⠀⠨⠀⠀⣿⣿⠀⢸⣿⣇⠀⠀⣾⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠀⣸⣿⡇⠀⠀⣼⠀⣿⣿⠸⣿⣦⠀⠀⢹⠀⠸ ⠀⠀⠀⢸⠀⠀⢻⣿⠀⠸⣿⢻⡄⠀⠘⣿⣿⣾⣿⣿⣿⠉⠓⠢⠤⣤⠤⣴⠟⠉⠀⣀⣀⣙⣿⠿⢦⣀⣧⣰⣿⣿⠀⣿⠘⢦⡀⡎⠀⣼ ⠀⠠⠤⠄⡆⠀⠘⣿⡄⠀⢿⡌⣧⠀⠀⣿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⠥⡤⠖⢻⠀⡟⠁⡠⠒⠉⠉⠈⣻⣿⣿⠀⡿⣇⠀⠻⣤⢀⡟ ⠀⢰⠤⣤⣾⠀⠀⣧⡇⠀⢻⣧⠸⡆⠀⢸⢸⣿⣿⣿⡿⠀⠀⠰⣏⠉⠉⠲⣄⠀⢸⣠⠁⠀⠀⢀⡔⠒⠊⠁⠹⣻⣾⠃⣿⡄⠀⣸⡿⠀ ⠀⠀⠀⠀⢻⣇⠀⡟⣿⠀⠈⣿⣄⠹⡄⠘⣄⡿⢿⣋⣀⡀⠀⠀⠀⠙⢦⡀⠈⠓⠚⢸⠀⠀⠀⡞⠀⠀⠀⠀⠀⢻⡧⠤⡿⣷⣞⣽⣁⠄ ⠀⠀⢦⣠⡎⠈⣆⠇⠘⣧⢸⣏⣿⣦⠿⠦⢇⠀⠀⠀⠀⠈⠑⠦⢤⡀⠀⠹⣄⠀⠀⠈⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢳⡘⠁⠀⠉⠉⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢛⠵⠂⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⡾⢛⡻⠶⡛⠢⠤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⢀⡤⢚⡽⡾⠛⠂⠢⡀⠉⠲⣄⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡞⠁⠀⠀⡴⠁⠀⠀⡜⠀⠀⡄⠀⠑⡄⠀⠻⡡⡀⠈⠻⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⡾⠆⡐⠒⣞⠀⠀⠀⡜⠀⠀⠀⠹⠀⠀⠘⠀⠀⢹⣹⣀⠀⠻⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⢁⣴⡟⠀⣸⠁⢰⠉⠹⠉⢻⠋⠹⠐⠀⣶⠂⠰⣶⠆⠏⠈⢧⠃⠀⠀⢹⣦⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣿⣿⠃⠒⠃⠀⡼⠒⠒⠚⠉⠉⠉⡛⠉⢹⠁⡈⠉⠑⠛⠒⠚⠓⠂⠑⢺⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣞⣹⡿⢿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⢰⠀⠀⠀⡇⠀⠸⠀⢧⠀⠀⡆⠀⠀⢰⠀⠀⠀⣿⣿⣿⣿⠻⣶⣄⠂⠀⣀⣀ ⠛⠛⠛⠛⠛⢻⣿⡋⢰⢇⡼⣿⢿⣿⠀⠀⠀⠀⢳⢸⢀⠏⡀⠀⡜⠀⡦⠀⡆⢸⡄⠀⠸⡜⡀⠘⡄⠀⠀⣾⡿⣌⣯⣳⣽⣹⡟⠻⠿⠿ ⠀⠀⠀⠀⠐⢿⣿⣿⣿⣟⢠⣇⡼⢻⠀⠀⠀⠀⣰⠇⡼⢶⠁⢰⣁⢠⠁⢀⣧⡌⢱⢀⠀⣿⣧⡄⠀⠀⠀⣧⣷⣬⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⢿⣿⣿⣿⣅⣿⠀⠀⠀⠀⡿⣲⣁⡟⠀⣏⣼⡜⠀⣿⢿⡧⢈⣾⡄⣡⣹⣧⠀⠀⠀⣷⣿⡿⢿⣿⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠛⠺⢿⡿⢻⣿⣿⠀⠀⠀⢀⣷⢿⣿⣷⣞⣛⠋⠁⠀⠀⠀⠀⠸⣿⣿⡛⠛⠿⡆⠀⠀⣿⣿⡿⠋⠙⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠇⠀⣠⣿⠃⣼⣿⢿⡀⠀⠀⢸⡇⢌⣿⣟⣻⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⢀⡇⠀⠀⣿⣿⣿⣄⠀⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⡼⣿⡏⣰⣿⣿⢸⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣧⠻⡆⠀⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⡜⢰⡟⢠⣿⠏⢹⠀⣇⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⣿⡟⣿⣧⠘⢆⠸⡀⠀⠀⠀ ⠀⠀⠀⠀⣾⡼⠀⡞⢠⣿⢿⠀⢸⠀⣿⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣼⡟⡇⢸⣿⣧⠈⢣⣇⠀⠀⠀ ⠀⠀⠀⠀⣿⢁⡼⢡⣿⡟⢸⠀⢸⣤⣿⣧⠀⠀⠸⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⢠⣿⡇⡇⢸⠈⣿⣆⠀⢿⣆⠀⠀ ⠀⠀⠀⢀⣷⡟⠁⣾⡿⠀⢸⢠⣿⣿⣿⣿⣆⠀⠀⣿⣿⣿⡖⠤⣀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠃⠀⣼⣿⣿⣇⣸⠀⢸⣿⡄⠈⢿⡆⠀ ⠀⠀⢀⣾⡟⠀⢰⣿⡇⠀⠸⣾⠸⣿⢿⣿⠛⡆⠀⢸⣿⣿⡇⠀⠀⠉⠒⠒⠒⠁⣾⣿⣿⣿⣿⠀⢰⣿⡿⣿⣿⡟⠀⠀⣿⣧⠀⠘⡷⠀ ⠀⠀⠈⠻⠀⠀⣼⣿⠀⠀⠀⠹⠆⠹⡇⢻⡀⠘⡀⠈⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⡿⠉⣿⣿⡏⢀⠇⢸⠃⡿⠸⠁⠀⠀⢹⣿⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⣀⡤⠤⠼⣷⢿⡿⢳⡀⢻⡷⣿⣿⣦⡀⠀⠀⢀⣾⠇⢄⡙⣿⡇⣸⣦⣤⣀⡁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠳⠀⠠⢠⡯⣼⠓⠂⠣⡘⡿⣞⠻⣿⣿⣶⣤⣾⣿⣿⣾⠁⠋⡱⢏⣿⡈⣿⠉⠳⣄⠀⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠦⠶⠀⠀⢸⣴⡏⠀⠀⠀⢻⠇⠈⢳⡾⣿⣿⣿⣿⣿⣿⡅⠀⡶⠁⠈⣛⣷⣿⡆⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠁⠘⠀⠀⣿⡿⠁⠀⠀⠀⣼⣦⡶⠁⠀⠘⣟⠋⠉⡏⠈⠑⣶⡁⠀⠀⢹⣿⣿⣷⡀⣄⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠓⢓⣿⠋⠉⠋⠉⠉⠟⠙⠟⠚⠉⠙⣿⠦⠄⣟⣨⠟⠉⠉⠁⠀⠈⢿⣿⣿⡿⠹⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡜⣿⣆⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠛⠒⢦⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⡿⣧⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢴⠏⢴⣶⣲⣄⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⠘⣦⢤⣦⣖⣹⣦⠀⠀⠀⠀ ⠀⠀⠀⡈⡙⢎⠀⠻⡿⠿⡟⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⢿⠀⠑⠹⠁⠙⡷⣄⠀⠀ ⠀⠀⠀⣾⣻⡀⠛⠢⢤⢼⢥⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⢸⠈⡗⣄⢠⣠⣀⣌⣮⣷⠀ ⠀⠀⠀⣿⣿⣷⣆⠈⢎⣼⡜⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠰⠀⠀⠀⠉⢿⣿⣿⣿⣿⣭⣿⣟⠋⠀ ⠀⠀⠀⢈⣽⡿⣿⡄⠈⢿⣿⡏⠀⠀⠀⣀⠤⣶⠞⠋⠙⠛⠆⠀⠀⠀⠀⠀⠀⠚⠋⠉⠙⠷⡦⠠⣇⠀⠀⠀⠘⠿⢷⣾⣿⣿⣿⣿⡆⠀ ⠀⠀⣀⣼⡿⢸⣿⣿⠄⠀⠉⠑⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠙⡌⠹⡿⠇⠀⠀ ⠀⠀⠙⢿⣷⠘⢿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⢇⢱⡀⢷⡀⠀⠀ ⠀⠀⠀⣈⣉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⣆⢣⠈⣷⠀⠀ ⠀⠀⣾⠟⢠⠆⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⡆⠸⣷⡀ ⢀⣾⠋⠀⡼⢀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠢⡀⠑⠂⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⢣⠀⠀⠈⠹⡄⢻⣷ ⡿⠁⠀⢀⠃⣆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣄⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⢀⣤⣾⣟⠀⠁⢠⠀⢆⠀⠀⠈⢻⡆⢿ ⠁⢠⠃⡸⢸⠃⠀⠀⠀⠀⢀⠀⠀⣠⣿⠛⢿⣿⠆⠀⠀⠀⠀⢠⠆⠤⠤⠔⣺⠀⠀⠀⠀⠀⢲⣿⣏⢈⣿⡄⠀⠸⡄⠈⢣⠀⠀⠈⢿⠀ ⡄⠃⢰⡇⣏⡤⠄⠒⠲⡀⠺⠀⢸⣿⣏⣴⣾⡟⠀⠀⠀⠀⠀⡎⣩⢟⣔⣎⠈⡄⠀⠀⠀⠀⠈⣿⣿⣶⣽⠿⠀⠸⠟⠒⠂⠧⣀⠀⠘⡇ ⠃⢠⣿⣿⠁⠀⠀⠀⠀⢃⢠⠄⢠⡀⠒⠢⠬⡀⠀⠀⠀⠀⣰⠗⠁⠀⠁⠈⢆⢱⢄⠀⢀⠀⠁⠈⠓⢄⠀⠀⠰⡀⡄⠀⠀⠀⠀⠁⠀⢿ ⠀⠈⣼⡿⠀⠀⠀⠀⠀⠀⣋⡠⠚⠃⠀⠀⠀⠈⠲⠞⠀⠀⠉⠀⠀⠀⠀⠲⠞⠁⠀⠉⠁⠀⠀⠀⠀⠀⢹⡦⡴⠒⢓⣀⡀⠀⠀⠀⠀⢸ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⢀
⠀⠀⠀⠀⠀⡴⢉⡵⢲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⠶⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⢁⠎⠀⢸⢢⠠⢤⣀⣀⣀⠀⠀⠀⠀⠀⡀⣈⣦⠬⡹⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⢃⠎⠀⠀⢸⠀⣘⣄⡀⠀⢉⡉⣹⢉⣋⡝⡁⣀⣸⣄⢡⢻⠄⠀⠀⠀ ⢀⢢⢢⢮⢺⢹⡎⡷⣾⠀⡇⢸⡸⡀⡷⡄⢸⠀⠠⣃⠰⠀⢠⢀⠈⢘⣦⠀⠀⠀ ⠂⠣⣯⢯⢾⣾⡷⢇⣿⠀⡇⣾⣹⡇⡏⣇⢸⡄⠘⣇⣆⠇⠀⠸⠀⢸⠸⣠⠀⠀ ⠈⠀⡇⢙⣦⣙⣿⣿⣹⡆⠁⣿⣼⡾⣠⣍⠞⢡⠀⣧⣬⣿⡄⡀⠀⠈⣾⡇⠀⠀ ⠀⠀⠇⣸⠿⣿⣿⡟⠛⢁⢰⡋⣟⣓⠆⠁⠈⠀⠉⠹⣟⡷⢩⡆⠀⠀⣿⣧⠀⢀ ⠀⠀⠀⣿⠀⡿⣿⣿⣸⣋⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡄⠀⡟⣸⣾⠿ ⠀⠀⢠⣿⣴⡇⣿⣿⡿⢟⣖⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠃⡞⣯⡿⠋⠀ ⠀⠀⢾⡇⣿⡄⣿⡿⠀⠀⠙⢌⢆⠀⠀⠁⠒⠂⠁⠀⣀⣾⣿⡁⢀⣿⣿⣏⠀⠀ ⢷⣄⠸⡇⣿⢣⠹⠀⠀⠀⠀⠀⢊⡅⠂⠄⢀⠠⣴⣾⣿⣿⣿⠇⣸⣿⠘⣹⡀⠀ ⠀⠻⣧⡈⣻⠮⠗⢷⠀⠀⠀⠀⠀⢺⡀⠀⠀⢸⣿⣿⢹⣿⣿⢠⣿⠇⠰⠹⡄⠀ ⠀⠀⢘⣿⠁⠀⠀⠀⠣⣄⠀⠀⠀⢸⡇⠀⠀⠈⠹⣿⣿⣿⣯⡾⠛⠓⢅⠀⠁⠀ ⠀⠀⠸⡇⠀⢀⡀⠀⠀⠈⠉⠉⠉⠺⣧⡀⠀⠀⠀⢻⠉⠹⡽⣄⠀⠀⢸⣧⠀⠀ ⠀⠀⠀⡇⠀⢸⣷⣌⣆⣠⠤⠤⢤⣀⡆⣳⡉⠉⠉⢹⠀⠀⠹⡍⠀⠀⣾⢹⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣫⠍⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠤⣄⣤⣄⣀⠀⠉⠙⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠋⠽⣦⣄⣇⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠒⠺⣿⡍⠻⢯⡓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠙⢆⠀⢻⣇⠀⢠⠙⢆⠈⢿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠨⢧⣸⣿⡆⠸⣧⠘⣆⠘⣧⣙⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⡰⢫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣆⠀⠀⠀⠀⣹⠋⡇⠀⣿⣧⠸⡄⠈⢿⣿⣮⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⣨⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⡼⢁⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠸⠀⠀⠀⣠⣯⣼⡏⢸⣿⣿⣧⣳⡀⠘⢿⣿⣷⣄⠙⢦⣀⠀⠀⠀⠀ ⣼⠀⠀⠀⣠⣴⣿⡟⠀⠀⡼⠁⡞⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠀⢠⣿⣿⣿⣷⣾⣿⣿⣿⣯⣷⠀⠘⣿⣿⣿⣷⡀⠉⠳⣄⠀⠀ ⢻⢀⣠⣾⣿⣿⣿⠁⠀⢰⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠈⣆⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⡇⠀⢹⣿⣿⣿⣿⣆⠀⠈⠳⣄ ⣿⣿⣿⣿⣿⣿⡇⠀⢀⡏⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⢣⠀⠀⠀⠀⢻⠀⢸⣦⠀⠀⠰⡘⠀⢇⠀⢠⡿⣿⣿⣿⡇⡏⢠⣿⣿⣿⣿⡇⢻⡄⠀⢻⣿⣿⣿⣿⣆⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⠀⠀⣸⠁⠀⠀⡾⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⠘⡀⠀⠀⡆⠈⣧⠀⠊⡆⠀⠀⠁⠀⠈⣠⠏⡼⢻⢋⡟⢠⢁⡜⡞⣿⣿⣿⡇⠀⢷⠀⠀⢿⣿⣿⢿⠻⣆⠀⠀ ⣿⣿⣿⣿⣿⡏⠀⠀⡏⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⣦⡄⠀⠰⡇⠀⠀⢸⣸⠺⡆⠈⢷⠀⠀⠀⠈⡾⠉⡼⠁⠈⣼⣶⣿⣾⢠⢠⣿⣹⣿⠀⠀⠸⡆⠀⠘⣿⠟⡌⢧⠙⣷⠀ ⣿⣿⡿⠛⣿⠀⠀⢀⡇⠀⠀⠀⠃⠀⠀⠀⠘⢸⡀⠀⠀⠀⢧⢆⠀⡿⠀⠀⠈⠏⡆⢹⡀⢌⣇⠀⢀⣾⣡⣿⠃⣴⢰⣋⣿⣿⣿⣞⡞⡞⠃⣿⠀⠀⠀⢧⠀⠀⠸⡄⢹⡄⢳⡏⠀ ⠋⠀⣀⣠⣿⠀⠀⠠⡇⠀⠀⠀⠃⠀⠀⢠⢰⠘⡇⠀⠀⠀⢸⡸⡐⢷⡀⠀⠀⢾⢷⠀⢳⡈⣾⣶⣿⣿⣿⣿⣼⣷⣿⢿⡟⠀⠹⣿⣿⣿⠸⡇⠀⠀⠀⢸⠀⠀⠀⢻⣴⣿⣿⢃⣠ ⣤⢾⡝⢁⡇⠀⠀⣦⠁⠀⠀⢸⠀⠀⠀⢾⣾⠒⢧⡀⠀⠀⣸⣧⣇⠘⣇⣀⠀⠈⢻⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⣿⡇⣷⣶⣶⣦⢸⡆⠀⢀⠀⢻⣿⣿⣿⣿ ⣿⣿⣴⢻⡇⠀⠀⣿⠀⠀⠀⢸⠰⠀⠀⣏⣯⠂⠘⣇⣀⡤⠝⠛⠚⠈⠁⠀⠀⠀⡿⠋⢻⣿⣿⣿⣿⡏⠛⢿⣿⣿⣿⡿⠀⠀⠀⠸⣿⣿⣶⣿⣿⣿⣿⣿⠁⠀⠈⠀⠈⣿⣿⣿⣿ ⣨⢿⣿⣾⠀⠀⠀⢿⠀⠀⠀⢸⡇⣇⠀⢸⢹⣔⣂⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢸⣿⣿⣿⣷⠺⠷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣿⣿⣿⣿⣿⡆⠀⠀⠐⠀⠸⣿⣿⠁ ⢁⠈⢻⣿⠀⠀⠀⠈⠀⠀⠀⣸⣳⣘⡴⠾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣎⠉⣡⣴⡧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⣿⣿⣿⠀⢳⠀⢄⠀⢡⠀⢻⣟⠦ ⣿⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⢤⡴⠿⠁⢤⣼⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⢸⣿⣿⣿⡆⠈⡆⠘⢦⠀⠀⠈⢿⠧ ⢻⣿⠂⠇⠀⠀⠀⠀⠀⠰⠀⢸⡀⠀⠀⢸⣷⢚⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣿⣿⣿⣇⠀⠸⡄⠈⢣⡀⠀⠈⣆ ⢐⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠰⣦⣙⣷⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣻⣿⣿⣿⡄⠀⢱⠀⠏⢳⡀⠀⠈ ⢸⢁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢠⠟⣿⣿⣿⡇⠀⠀⢷⠸⡌⡿⣄⠀ ⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⡾⠀⢹⣿⣿⣿⠀⠀⠈⣧⢻⡇⠘⣆ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠆⠀⡇⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡏⠀⠀⣰⠃⠀⠈⢿⣿⣿⡆⠀⠀⢫⢧⢻⡀⠈ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⣸⠀⢸⠁⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣒⣪⡭⠟⠛⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢠⠏⢰⠀⠀⠘⣿⣿⣷⠀⠀⠘⠈⢯⣇⠀ ⣿⡿⠀⠀⠀⠀⠀⠀⢠⡇⢀⡎⣼⣿⣿⡏⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠏⠀⠀⣀⣠⠆⠀⠀⠀⠀⣸⡼⠀⠀⠀⠀⠀⠞⠁⠀⠀⡼⠀⡎⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠈⢿⡆ ⡿⠁⠀⠀⠀⠀⠀⢠⣿⠁⡼⣱⣿⣿⣿⠃⣼⢹⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⠇⠀⠀⠀⡀⠹⣿⣿⡀⠀⠀⠀⠘⡗ ⠀⠀⠀⠀⠀⠀⠀⢸⠇⣰⣳⣿⠋⣿⡟⠀⠁⡟⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣰⠃⠀⠀⠀⠀⠀⠀⣰⡟⠀⣼⠀⠀⠀⠀⡇⠀⢻⣿⣧⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⢀⡿⢰⡷⢻⣿⢰⣿⠃⠀⣼⠃⠀⠀⠀⠈⠻⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠃⣴⠃⠀⠀⢀⡖⠀⠀⣰⡟⠁⢠⠧⠀⠀⠀⢸⡇⠀⠀⢻⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠁⡞⠁⣿⣿⢸⣿⠀⢱⡏⠀⠀⠀⠀⢀⠀⠙⣻⣿⣿⣿⠷⠶⣤⣤⣶⡾⠋⢁⣾⡾⠁⠀⠀⣠⠸⠀⢀⣴⣿⡇⠀⡼⠀⠀⠀⠀⡸⠁⠀⠀⠰⠻⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢄⡼⠀⢸⡿⠄⣿⡇⢀⡟⠀⠀⠀⠀⡴⠟⠀⣠⣿⣿⠟⠁⠀⠀⠀⠙⠛⠒⠲⣾⠋⠀⠀⠀⣴⢃⠇⢀⣾⠇⠉⢧⣰⠃⠀⠀⠀⢠⡇⠀⠀⠀⠀⡄⠹⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⣀⣾⣃⠤⠿⠷⠦⠿⠧⠾⠤⠤⣄⣀⣾⠥⠤⠖⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⡞⠅⣾⣠⣛⢸⠶⡄⠀⢻⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠀⠙⢷⡄⠀ ⠀⠀⠀⠀⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣠⣀⢀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣠⡞⡁⣠⢫⢻⣿⢛⠋⢻⣆⠀⣻⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⣿⣿⣿⡿⣿⣿⣿⡟⡷⠒⠲⣷⡾⣷⠦⠤⠶⣤⣼⠷⣤⣤⠽⡿⣿⠿⣿⡿⠿⠿⠿⢿⣿⡿⢿⣿⠟⠻⣧⢰⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣟⠉⣹⣿⣿⣿⢰⠃⠀⣸⣿⢳⡏⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠈⠀⣿⣿⠀⠀⠀⢸⠈⡇⠀⣿⡄⠀⢿⡄⣻⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⡿⢁⣼⣿⣿⣿⡇⡟⠀⢠⠏⣿⡾⠥⠤⠤⢼⢏⡖⠒⣿⠛⢲⡖⠚⢲⣿⠛⠢⠤⠤⠼⢿⣷⢤⠿⢇⡀⣼⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿ ⣵⠿⣿⣿⣿⣿⠁⠒⡟⠁⢀⡇⠀⠀⢀⠀⢸⣿⡇⠀⢿⠀⠀⡇⠀⢸⠛⡄⠀⠀⠀⠀⢀⣿⠀⠀⠀⠉⢻⠉⠉⠑⢺⣿⣿⣿⣿⣿⣿⡟ ⠋⢀⣿⣿⣿⢿⠀⠀⠃⠀⢸⠄⠀⠀⡞⠀⢸⡏⡇⠀⢻⠀⠀⣧⠀⢸⠀⡇⠀⠀⠀⠀⠀⡿⡆⠀⠀⠀⠈⠀⠀⠀⣼⡏⣿⣿⠉⣿⣿⣿ ⣰⣿⢿⣿⡏⢸⠀⢸⠀⠀⠸⠀⠀⠀⡇⠀⢸⠃⠃⢀⠸⠀⠀⢿⡀⢘⠀⢇⠀⠀⠀⠀⠀⡧⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⠀⣿⣿⣿ ⣿⠃⣿⡿⠀⢸⠀⢸⠀⠀⢐⠀⠀⠀⠳⠀⡸⠀⡆⠘⣠⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⡆⠀⡇⢳⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⡇⠻⣿⢹ ⡇⢰⣿⡇⠀⢸⡄⢸⠀⠀⢸⠀⠀⠀⠦⠀⡇⠀⡇⠀⢿⠀⠀⠈⡄⢸⠀⠈⡇⠀⠀⡇⠀⡇⢸⠀⠀⠀⠀⠀⢠⣿⠁⢀⣿⣿⡇⡆⣿⡀ ⡀⣸⣿⣿⡀⣸⡇⢸⡄⠀⢸⠀⠐⡆⣰⠀⡏⠀⢇⠀⡎⡇⠀⠀⡇⠘⡀⠀⢧⠀⠀⣇⠀⡇⢸⡇⠀⠀⠀⡆⣿⣿⡀⣸⣿⣿⣇⡇⢸⡇ ⣷⣿⣿⣿⣿⣿⣇⢸⡇⠀⣿⡆⢠⣇⣽⡀⣿⣖⡿⠀⡇⣇⢠⡄⣧⠀⡇⠀⣸⠀⠀⣟⠀⣿⣾⡇⢀⣦⠀⡟⠿⠿⠿⠿⢿⣿⣿⡇⠈⣷ ⠀⣿⠿⣿⢯⣿⣿⠀⣧⢀⡿⠿⠞⠿⠋⣱⣾⣿⣿⣯⠁⠈⠉⠁⠉⠉⠁⠀⠠⣷⡾⠛⣧⣿⣿⣷⣼⣿⡀⠇⠀⠀⠀⠀⢸⣿⣿⣷⣼⣿ ⠀⡟⠀⠀⢸⣿⣿⣷⡿⠿⡇⠀⢄⠰⣶⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣾⡿⠿⣿⣿⠀⠈⠻⡆⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿ ⢸⠃⠀⠀⣸⣿⡏⢀⠀⠀⢱⠀⠈⠢⣝⡳⠶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⣤⣤⠾⣃⡴⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⡟⠀⠀⢠⣿⣿⠀⢸⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠃⠀⢀⣿⣿⣿⠀⣿⡄⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⣼⣿⣿⣿⢀⣿⡇⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⠀⢰⣿⣿⡿⡿⢸⠉⡇⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿ ⢠⡟⢸⣿⠃⡇⣼⠀⣷⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢹ ⡿⠀⣿⠇⢸⡗⡏⠀⢸⡄⠀⠀⠀⢰⠀⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⢹⠀⠀⠀⠀⠀⢀⣿⣀⣐⣀⢘ ⠀⣼⡏⠀⢸⣷⣇⣀⣸⡇⠀⠀⠀⠸⣦⡿⠛⠛⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠸⣿⢹⠛ ⣰⣿⠁⠀⢸⡿⠟⠋⠉⢹⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⢀⠏⠢⢄⣀⢀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡏⠀⠀⣿⠈⠀ ⣿⡇⠀⡰⠋⠀⠀⠀⠀⢸⡀⠀⠀⠀⢳⣧⠀⠀⠀⢠⠏⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢿⡀⠆ ⡟⢀⡞⠁⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿⠹⡀⠀⢀⠏⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀ ⠇⡼⠁⠀⠀⢰⡇⠀⢠⠃⡇⠀⠀⠀⢸⡀⢧⢀⡎⠑⠢⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡇⠀⠀⠀⣾⠁⠀⠀⠀⢸⡇⠀ ⠰⠃⠀⠀⠀⣸⡇⣠⢃⣼⡧⠀⠀⠀⢸⡇⠈⣟⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⡠⠤⡒⠉⢁⡀⠀⡇⠀⠀⣰⡏⠀⠀⠀⠀⠸⣷⠀
⡀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠻⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⢀⣾⣿⣴⡟⠀⣸⡟⢀⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢸⣿⡌⡿⣆⠀⠀⠘⣏⠻⣿ ⠃⠀⠀⢀⣴⡿⣿⣿⣿⠁⣴⡟⠠⡿⠀⢀⡿⠀⡤⢤⢤⠀⣀⣀⣀⣀⣀⠀⣀⣤⣤⣤⣤⣤⣴⡟⢧⠀⠀⢸⣿⣷⣆⣿⣧⡀⠀⢹⣶⣦ ⢸⣶⣴⡟⢁⣼⠏⣸⡏⠀⠛⠁⠀⠓⠒⠚⠀⠈⢧⣄⣼⢙⡁⠀⢿⠁⠹⠀⠻⠀⠘⣇⠈⣻⣸⡇⢸⡇⠀⠸⣿⣿⠹⡿⣿⣿⣦⡀⢿⣧ ⠘⢿⣏⣴⣿⢃⣴⣿⠇⠀⠐⠀⠀⠀⠀⣰⠀⠀⠀⡉⢹⠀⠉⢉⠙⠉⠉⠉⠙⠒⠤⠿⠤⣇⡁⣿⣸⡇⠀⠰⣿⢻⡄⣧⠸⣿⡻⣧⡀⠙ ⠀⣿⣿⣿⣿⣿⢏⣿⠀⠀⡆⠀⠀⠀⢀⡇⠀⠀⢰⠁⣸⠀⠀⠘⡄⠀⠀⠀⠰⡀⠀⠀⠀⠈⠁⣿⠀⠀⠀⢸⡏⢸⣷⣿⣷⣿⣿⡌⢿⣦ ⠀⢻⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⡀⠀⣸⢠⠀⢠⡿⠀⡟⡄⢰⠀⢻⡄⠀⠀⠀⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿ ⠀⠀⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⡇⠀⡟⣸⠀⡞⢰⠀⡇⢱⠘⣇⢘⢷⡀⠀⠀⢹⣇⠀⠀⠀⠀⢹⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿ ⠀⠀⢀⣴⢿⣿⣿⡇⠀⠸⠀⢀⡇⢰⣷⣇⣸⠀⠈⣤⡇⠈⣷⡹⣾⡞⣇⠸⡀⢨⣿⡄⢰⠀⠀⠘⠀⠀⠀⠙⣿⢿⣿⣿⡟⢉⣀⣀⣿⡛ ⣿⣿⡿⠁⠀⣽⣿⡇⠀⠀⣠⣼⣷⠛⠻⢛⣿⣿⡚⠉⠀⠀⠘⠃⠛⠧⠼⣄⣧⣸⣿⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠛⠉⠉⠉⠀ ⠿⢿⠃⠀⣼⣿⣿⠀⠀⠀⣿⣏⠉⢀⢰⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠞⠻⠋⣩⣿⣷⡼⢷⠀⠀⠀⠀⠀⠀⢠⠀⠀⢻⣿⡄⠀⠀⠀⠀ ⣩⡟⢀⣾⣿⣿⣿⠀⠀⢠⣿⣿⠀⠈⠓⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣛⣻⣿⡃⠚⠦⣤⡀⠀⠀⠀⢸⠀⠀⠀⢿⣷⠀⠀⠀⠀ ⢿⠁⢸⣿⣿⣿⣿⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⠀⢸⡇⠀⠀⠀⠘⠀⡇⠀⠀⣿⣷⡀⠀⠀ ⡏⢠⣿⣿⣻⣿⣿⡆⠀⢸⣿⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠰⣇⠀⠀⠘⢿⣷⡀⠀ ⠀⣼⣿⣿⣿⣿⣿⡇⠀⢸⣿⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠰⣿⠀⠀⠀⠈⢙⣿⣆ ⢰⣿⣯⣭⣿⣿⣿⡇⠀⢸⣿⠀⠨⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠙⢿ ⢰⣿⣿⣿⣿⣿⣿⣇⠀⢸⣏⠀⠀⠀⢾⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢹⡏⢀⣨⣇⠀⠀⠀⠀⣿⣷⠀⡴⣆⠀⠀⠈ ⡟⠉⠉⠉⣿⣿⣿⣿⠀⠸⣟⠀⠀⠀⣤⡄⠛⢿⣶⣄⡀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠉⠀⠀⢸⡇⢸⣿⣿⡀⠀⠀⢸⣿⣿⣶⠀⠈⡆⠀⠀ ⡃⢀⣀⣀⣿⣿⣿⣿⡆⠀⣿⣤⡀⠀⣿⣿⠀⠨⣿⡟⠻⢶⣤⡴⠒⠋⠉⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣇⠀⠀⢸⡷⣿⣿⠀⠀⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣧⠀⢸⣿⡀⠀⣿⣇⣠⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠀⠀⣷⢸⡏⠀⠘⣷⡤⠁ ⠋⠉⠉⠉⠙⠙⢻⣿⣿⡆⢸⣿⣿⣦⣸⠛⣿⣶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⠀⠀⢻⠀⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⡏⠻⣟⠈⠙⢿⣿⣿⣿⠿⠻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⡠⠴⢺⠏⠉⠉⠉⠉⢹⠻⢿⣧⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⣉⣣⡤⠞⣛⣩⠤⢖⠊⠁⠙⠻⣿⣤⣤⣠⠤⠒⠋⠁⠀⡴⠋⠁⠀⢠⡀⠀⢸⠲⢄⡈⢣⠀⢻⣆⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⢨⣧⣖⡭⠤⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣠⠞⠁⠙⠶⢤⡀⠙⠀⡆⠀⠀⠈⠙⢦⡀⣸⣆⡀⠀⠀⠀ ⠄⢠⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢀⣼⠇⠀⠀⣀⣠⠾⠃⠀⠀⠀⣀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠳⣾⣿⣟⠦⣀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⢡⣾⠟⣫⣿⣹⣿⡿⠛⣿⣴⣿⠛⣲⠿⢷⠿⠿⢮⣀⣠⣠⠖⢲⣤⣤⣀⠀⠀⠈⢻⢢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣻⡴⠋⢀⣾⣿⣿⢏⣿⢁⣴⡏⢻⠏⢰⠏⡰⠋⠀⠀⢀⡾⠉⠉⠓⡾⢿⡾⠉⣿⣄⠀⠸⡀⠙⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣿⣿⣿⠃⣼⣧⣾⢿⣇⡟⢀⡏⡼⠁⢠⠀⣠⠞⠀⠀⠀⣼⣡⠋⠉⠒⢧⣽⠛⣾⠀⠀⢸⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣶⣿⡿⠁⣿⣿⠁⡼⡴⠁⢠⠇⣴⣿⠀⠀⠀⣼⢿⢇⠀⠀⢸⠀⠉⠲⢼⡞⣆⠘⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠟⣹⠟⣿⣿⣿⣿⣿⣿⣧⣼⣿⡿⢠⣿⠁⢀⠏⣼⣽⡟⠀⢰⡰⠃⣿⡇⢰⢁⣾⠀⠀⠀⢸⠧⢿⠀⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⡴⣿⠃⣰⠏⣴⠋⠈⣿⣿⣿⠟⠿⣿⣿⣧⣼⢧⣠⣾⡾⣷⣿⠃⢀⣿⠃⣸⣿⣇⣼⡼⢻⠀⠀⠀⡼⠀⠘⣦⢺⣿⣧⠀⠀⠀ ⠀⠀⢠⣾⡿⠁⣼⣫⡾⠁⠀⣴⣿⣿⣿⡆⠀⠈⠀⢹⣧⣺⠿⢿⣧⡭⢻⡶⠾⠇⢀⣿⢻⡿⣿⠃⡟⠀⠀⣴⡇⠀⠀⢸⢸⣿⠛⡄⠀⠀ ⠀⣴⢟⡟⢁⣾⣿⡿⠀⢀⣼⣿⣿⣿⢿⡇⠀⠀⠀⢸⠀⠙⠓⠴⠞⠁⠀⠀⠀⠀⠈⠉⠘⠧⣏⣀⠇⠀⣸⣿⠀⠀⢀⡇⢸⣿⡇⠃⠀⠀ ⠞⢡⠎⣠⣿⡟⡹⠁⢀⣾⣌⣿⡿⠃⢺⡇⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠳⣴⢻⡇⠀⡀⡼⢠⣿⠀⣷⡰⠀⠀ ⣰⠃⣴⣿⠋⡰⠁⣠⣿⣿⣿⡿⠁⠀⢸⡅⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠈⢻⠁⡜⣱⢃⣾⣿⠀⠙⡁⠀⠀ ⢀⣾⠟⠁⡼⢁⣴⣯⡿⢋⡟⠁⠀⠀⠈⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣰⠿⡟⠀⠁⣾⣿⣿⣶⣬⣽⣄⠀ ⡿⠋⠀⣼⣡⣾⣿⠟⣡⠟⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⢀⡇⠀⢸⣿⣿⣿⣿⠿⠿⠛⠀ ⠀⠀⣼⣿⣯⠟⠁⣴⠋⠀⠀⠠⠇⠀⠀⢸⣇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢛⡇⢸⡇⠀⢸⣿⣿⠛⠁⠀⠀⠀⠀ ⣤⣾⡥⠞⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢠⢿⡄⠀⢘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⡿⠀⢸⡇⢸⡇⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀ ⠿⠋⠀⠀⣠⠟⠀⠀⠀⠚⠀⠀⠀⠀⢠⡟⠀⢇⠀⠀⡇⠈⠒⠤⣀⡤⢤⣤⠴⠖⠋⠉⠀⠀⠀⠀⢸⣿⣺⠀⠀⣿⠀⢿⣷⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⠁⠀⠘⡄⠀⢷⠀⠀⠀⠈⣧⡀⠉⠳⣄⠀⠀⠀⠀⠀⠀⢸⢹⣿⠀⠀⣿⡄⢸⣿⣇⠀⠀⠀⠀ ⠀⣠⠟⠁⠀⠀⣂⡤⠶⠒⠛⢿⠋⠉⢹⡀⠀⠀⢣⠀⢸⣇⠀⠀⠀⠉⢱⠀⠀⠈⢿⣶⠶⢤⡤⣤⣾⣘⣿⠀⠀⣿⡇⠈⡟⣿⡄⠀⠀⠀ ⠰⠃⠀⣠⠶⠖⠛⠦⡄⠀⠀⠈⣇⠀⠀⡇⠀⣠⠾⡄⠀⣿⣄⡀⠀⠀⠈⡄⠀⠀⠈⣻⣤⡤⠤⠴⠧⢤⣿⣄⣠⣿⣷⣀⣱⠈⢿⡄⠀⠀ ⠀⢀⠈⠁⠀⠀⠀⠀⠸⡆⠀⠀⢹⠀⠀⢷⡼⢫⠀⠱⡀⢹⡀⡄⠉⢦⢀⣧⠔⡨⢋⡤⠔⠂⣀⡀⠀⡼⠁⠀⠀⠀⠀⠀⠉⠳⣌⢻⡄⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⡇⠀⠀⢱⠋⠐⠤⢷⠀⣏⠺⠦⡈⢆⣀⡴⠛⣁⠠⠖⠋⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠻⣄ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡆⠀⢸⠃⠀⠀⠈⡧⠤⠤⠤⠷⣸⠁⠒⠬⢅⣁⠴⠊⢀⡤⠔⡺⠋⠀⢀⡇⠀⠀⠀⢀⣠⣾⠆⠀⠀⢧⠀⠈ ⠄⠀⠀⠀⠸⣆⠀⠀⠀⠘⡇⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⣧⠤⠤⣄⠁⠴⢎⠁⡠⠊⣀⣤⠾⠉⠗⠒⣺⡿⠿⢿⡛⠲⠆⠀⢸⠀⠀ ⠰⠁⠀⠀⠀⠙⣦⣀⠀⠀⢧⢠⠇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠙⢆⠀⠀⠉⠒⣤⢞⣡⣚⡡⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢶⣾⠇⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠸⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠈⠉⢳⠓⢄⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠙⢇⠀⣧⠀ ⠀⠀⠂⡀⠀⠀⠀⠀⠘⢿⣆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢂⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠈⢧⡏⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢘⡿⣸⠛⠛⠓⣦⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣠⠴⠦⡆⠣⠘⣿⡀⠰ ⠿⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⢼⣧⡏⠀⠀⢸⣿⠋⠁⠀⠉⢉⡇⣠⠶⣦⡤⠤⠤⣤⣴⣤⠤⣶⣶⠒⠛⣿⠀⠀⠀⢱⠸⠀⣿⣷⡀ ⠀⣸⣿⡇⠀⢠⣿⣿⣷⠀⣀⣀⠀⣿⣾⠀⠀⢠⠟⠃⠀⠀⠀⣀⡜⢠⡟⢸⡏⠀⠀⠀⠈⠙⠋⠀⠈⡟⠀⠀⢣⢀⠀⠀⢸⡄⡆⣿⠹⣧ ⢠⠇⣿⡇⢀⣾⡏⢸⣿⡀⠀⠈⠉⣿⡎⠈⠉⠉⢰⠋⠉⠉⠉⢹⠃⣿⠃⣿⠇⢸⡀⢀⠀⢧⡀⠈⢹⣿⠀⠀⢹⠀⢹⡀⠀⡇⡇⢺⠀⠙ ⡿⠀⣿⡇⣼⣿⠃⠀⣿⣇⠀⠀⠈⡿⠃⠀⠀⠀⡎⠀⠀⠀⠀⣾⡼⡟⢀⣿⠀⡾⡇⢼⠀⠇⡇⠀⢸⠻⡄⠀⢸⠀⠘⡇⠀⡇⡇⢸⠀⠀ ⡇⠀⣿⣿⣿⣟⠀⠀⢹⣿⠀⠀⠀⡇⠀⡇⠀⢰⡇⠀⢀⠇⢀⣿⠁⠇⣸⢻⢠⠇⡇⣸⢀⡇⡇⢸⠈⡆⣿⠀⢸⠀⠀⡇⠀⡇⣇⣼⣄⣠ ⣷⣾⣿⣿⣿⣿⣷⣦⣼⣿⡇⠀⠀⡇⢰⠃⠀⣾⣷⠀⢸⠀⢸⠇⢸⢀⡇⣎⣸⢸⣧⣿⣿⠃⡇⢸⣠⠁⣿⡆⢸⠀⠀⣷⠀⡇⡟⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⠉⠙⠻⣿⠗⠀⠀⡇⢸⠀⢠⠷⣿⠀⣻⠀⣏⣀⡞⣸⠀⣿⠇⢸⣿⢿⡽⠀⡇⢸⣿⠋⣿⠇⣸⡇⠸⣿⠀⡇⡇⣿⣿⣿ ⢠⣿⣿⣿⣿⣿⠦⣄⣀⢹⡄⠀⠀⡇⣸⠀⣾⣰⣿⠀⡏⢸⣀⢀⣷⠃⠀⡿⠀⠸⠿⠸⠇⠀⢉⣘⣿⣼⣷⣶⣾⣆⢰⣿⠀⢓⡇⣿⡿⠿ ⣼⣿⣿⣿⢻⣿⠁⠀⠈⠙⠃⠀⢀⡷⠟⠒⣻⣿⣿⣾⡛⠿⠿⠿⢷⠀⠀⠀⠀⠀⠀⠀⠠⡾⢻⣿⣿⣯⡉⣋⠉⠉⢱⣿⡿⠿⣧⣿⠀⠀ ⣿⣿⣿⠏⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢄⢻⣿⠛⠛⠛⣶⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣭⡽⠿⠋⠀⢀⣿⣻⠀⠀⢸⣿⡆⠀ ⣿⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣼⠀⠀⣸⣿⢇⠀ ⣿⣿⣿⣇⠰⣿⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⢆⡉⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⡇⠀⠀⢻⢸⠸⠀ ⣿⠋⣿⣿⠀⢿⡄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠈⠁⠒⠂⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸⠃⠀⠀⣼⢀⠀⡄ ⡏⠀⢿⣻⡄⢺⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⣀⠀⠀⠀⠈⠓⠤⡀⠀⠀⠀⢀⣾⣿⡇⡾⠀⠀⠰⡇⢸⠀⢣ ⠇⠀⢸⡟⣇⢸⣇⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠈⠑⠲⣤⠞⢻⣿⢸⡇⠀⠀⢸⡇⡄⠀⠘ ⢸⡄⠸⡇⢹⠈⣿⠀⠀⠀⠀⠀⠀⠸⡿⠳⣄⠀⠀⠀⠀⠀⣀⠤⠍⢈⡩⠤⠤⠤⠤⠬⠦⠤⠤⠄⠀⠸⣷⣾⣿⣼⠁⠀⠀⢸⠀⡄⠀⢸ ⣿⡇⠀⣿⠸⡆⣿⠀⠀⠀⠀⠀⠀⠀⢿⡄⢸⡗⠢⣀⠀⢀⡣⠤⠚⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⣿⢠⠃⠀⢸ ⣿⣇⠀⣿⡄⢷⣻⡇⠀⠀⠀⠀⠀⠀⢹⡅⡘⣇⢀⡠⠛⠁⢀⡠⠤⠒⠊⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⢸⣿⣸⠀⠀⢰ ⣿⣿⡄⢸⣷⠘⣿⣿⠀⠀⠀⠀⠀⠀⠘⣷⠀⣿⣡⠴⠔⠊⠁⠀⠀⣀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⡿⣿⡟⠀⠀⠀⣼⣧⡇⠀⠀⠏ ⡌⡇⠹⣌⢿⡆⠙⣿⣇⠀⠀⠀⠀⠀⠀⣿⠶⠛⣦⣶⠠⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⠏⢣⠀⠀⢀⡿⠿⠠⠤⠤⠤ ⣦⣿⠤⠜⠷⢿⣤⣿⠿⡆⠀⡀⠀⠀⠀⢻⠀⠀⠳⠶⠾⠤⠤⠤⠒⠒⢋⡿⣻⢶⣆⠀⠀⠀⠀⠀⠀⣸⠏⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀ ⠘⢿⡄⠀⠀⠀⢻⣿⡀⠹⡀⢹⡄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠰⡅⡞⠁⠀⠀⠀⣀⠔⠊⠀⠀⠀⣾⠀⢠⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠀⠀⠀⠈⢻⣇⠀⢳⡘⡽⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠉⠒⠤⠄⠒⠉⠀⠀⠀⠀⠀⢠⠙⣧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠑⣷⡙⢆⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⢠⡾⠁⣠⠞⠉⠁⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⢦⡀⠀⠈⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⡴⢋⣴⡞⠁⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣾⡿⣿⠋⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠂⠙⢷⡲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣿⣏⡾⠁⠀⣠⠔⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠹⣦⠀⠈⢄⠈⢷⣝⢷⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡞⠉⣠⣼⣿⡟⠁⠀⡞⠀⢠⡏⠀⠀⣠⠞⠐⠠⢀⠀⡀⣤⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⡀⣠⠶⠟⠛⣏⠀⠀⠹⣆⠀⠈⠓⣌⢻⣷⣻⣿⣶⣄⠀ ⠀⢀⣤⣶⣿⢋⣠⣾⣿⣿⡟⢡⡄⠈⠀⢠⡟⠀⣰⠸⠃⠀⠀⢀⡟⠀⡇⠀⢠⡇⢸⠋⠀⡆⠀⠀⠀⡆⠀⢸⠉⠁⠈⣇⢻⡄⠀⠀⠀⠘⣆⠀⠀⢹⣆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣟⣵⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⠁⣼⠃⠀⢀⣀⠀⣼⠁⣼⠃⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠉⠘⣷⢠⡀⣀⡄⠸⠛⠓⠚⢿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⣿⣿⡿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⢠⡇⢰⠃⡄⠈⠉⠉⢁⣿⣰⡏⠀⠘⢹⠀⣦⢤⡀⠘⠦⢤⡀⣧⠀⠀⠀⠀⠄⠀⠂⣿⡆⠉⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠛⣿⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⢃⡿⣼⠇⠀⠀⠀⣸⢇⣿⠁⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡀⠀⠀⠀⡏⣧⠠⡀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣼⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣟⡿⠀⠀⠀⠀⠀⣿⣸⢣⡏⠀⠀⠀⢀⣟⡾⢹⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⡇⢹⡄⢿⡀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣡⣯⡿⠀⠀⠀⢀⣺⡟⠁⢸⠀⠀⠀⣿⠀⣿⡆⠀⠀⠀⠀⠀⣿⡄⠀⢸⣷⠀⠀⢰⡇⢸⡇⢸⡇⠀⢠⡀⠀⢸⢹⡇⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⢀⣎⣿⠁⠀⣼⠀⢠⡄⣿⣠⠉⡇⠂⢿⣶⢰⣷⢹⡇⢸⠾⣿⢰⡄⣸⡇⠈⣿⣾⢿⡀⠎⣇⢀⡘⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿ ⣻⣿⣿⣿⣿⣿⠇⡾⠀⠀⠀⠀⠀⢸⣿⡇⣴⣾⠏⣼⣿⣋⣀⠀⣿⠀⣼⡇⣻⣿⠀⡗⠀⢸⡿⣸⡇⢸⡇⣸⡀⣿⠘⣷⣿⣁⣠⣿⣿⢻⣷⡀⣿⠀⣿⣿⡇⠀⠀⠀⠀⢽⡿⣿⡌ ⠋⣹⠟⣿⣿⣿⢰⡇⠀⠀⠀⠀⠀⢸⣿⣻⠏⠁⢰⣿⠏⠀⠉⠙⣿⣴⣿⡷⣿⣿⣴⣿⠈⠀⠀⢿⡇⣾⢇⣸⡿⣿⡀⢹⡏⠁⢀⣿⣿⡈⣿⣇⢻⣿⣿⢸⡇⠀⠀⠀⠀⠘⠃⠘⠐ ⠞⣍⣼⣿⢻⠏⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣠⣤⣿⣏⣀⣤⣤⣼⣿⣿⠿⠦⠿⠋⠘⠓⠒⠒⠛⠛⠃⠛⠛⠛⠷⠛⣻⣿⣿⣿⣿⣿⠻⠷⣿⣿⢾⣿⣿⣾⡇⠀⠀⠀⠀⠀⠐⠀⠂ ⣾⣽⢣⣯⡟⠀⣼⡇⠀⠀⠀⠀⠀⣸⣿⣿⠟⣯⣿⣿⣿⣿⣿⡉⠙⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀⢳⡄⠀⠙⠛⣿⠉⡏⠁⠀⠀⠀⠀⠀⠀⠀⣰ ⣿⣧⣾⡿⠀⣰⢿⡇⠀⠀⠀⠀⠀⠀⠈⢿⠀⠉⣈⠉⣻⣿⣿⣻⣦⣽⠈⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡉⣻⣿⣿⣷⣿⣾⡇⠀⣀⡀⣿⠀⡇⠀⠀⠀⠀⠀⢠⣶⣾⣿ ⠛⣿⡿⠁⢠⡿⢸⡇⠀⠀⠀⠀⠀⢰⡂⢸⠀⠠⣿⡿⠿⠿⠿⠿⢿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣝⡛⠋⠉⢻⣿⣇⣴⠟⠀⣿⠀⡇⠀⠀⠀⠀⠀⠘⠟⠛⣿ ⡾⠉⠀⢀⣾⠁⣾⡇⠀⠀⠀⠀⠀⢸⠁⢸⡀⠀⠈⠛⠷⢤⡤⠀⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⣼⡇⢠⣿⠁⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡿⠀⣿⣿⡆⠀⠀⠀⠀⠀⢸⡄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀ ⠀⣸⣿⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⢸⡷⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀ ⣰⣿⠇⢰⣿⠃⢻⡇⠀⠀⠀⠀⠀⠘⡇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄ ⣿⡏⢠⣿⡟⠀⢹⣇⠀⠀⠀⠀⠀⠀⣧⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⡟⢠⣾⡿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡀⣿⡇⢀⠀⠀⠀⠀⠀⠀⣇⠀⠀ ⢀⣾⣿⠁⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠘⡆⠀⡿⠶⣿⠻⣦⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣿⡁⢻⣇⢿⡇⢸⡆⠀⠀⠀⠀⠀⣿⡄⠀ ⣾⣿⣿⣟⣐⣾⣷⡾⠿⠛⠳⠶⠶⠶⠶⠶⠶⠿⠟⠻⠿⠾⠛⠷⠶⠚⠻⢟⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠀⠸⣿⡇⠸⣿⢸⣿⠈⠇⠀⠀⠀⠀⠀⣿⣷⡀ ⣿⠍⠹⣯⠁⠀⠀⠀⠀⠀⠀⠐⠲⣄⡀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡴⢾⣿⡥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢿⡟⣿⡿⣿⡄⠐⣿⣿⠀⢿⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⡯⢇ ⠉⠉⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠛⠿⢿⣿⣟⡋⠉⢿⡇⠀⢨⣿⡇⠈⠙⠒⠦⣄⣀⡀⢀⣀⣤⠖⠋⠁⠀⣾⠀⣿⡇⣿⡇⠀⣿⣿⣧⢿⣼⣿⣷⡀⠀⠀⠀⠀⠀⢸⣇⠈ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢯⣶⡀⠀⠀⠀⠉⠙⠻⢿⣧⣾⡾⠛⣧⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⠷⠿⣧⣿⡇⠀⠘⣿⢿⣜⣷⢹⣻⣇⡆⠀⠀⠀⣄⠈⣿⣤ ⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢠⡶⡄⠀⠻⣯⣟⡷⢦⣄⣀⣀⡀⠀⠉⠀⠉⠙⠟⠉⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡇⢰⡀⠘⢿⣧⠀⠀⣿⣌⣿⣿⣯⢿⣿⣷⡀⠀⠀⠹⡄⣿⣿ ⠀⠀⠀⢸⡇⠀⠀⣀⣤⢤⠀⠻⣿⣦⣀⠀⢠⠉⠙⣻⣿⣿⣿⠋⠛⠛⠛⠻⡟⠛⢦⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⣧⣸⠃⠀⠈⢿⣧⣀⣛⣯⣿⣿⣿⣾⣿⣿⣧⠀⠀⠀⣧⢸⣿ ⣷⠀⠁⢸⣧⣴⢶⣿⣾⢶⣦⡀⣹⡿⢛⡴⢞⡒⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⣆⠀⠙⠲⠤⠤⡶⠚⠉⠀⠀⠀⠀⡱⠹⣠⣶⣄⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠉⠀⠀⣠⡤⢤⣖⣲⣾⡿⠿⢿⣿⣽⣛⣒⡒⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠲⢦⣤⠈⠙⢳⣆⣀⡀⠀⠄⣀⠄⠀⠀⢀⣤⣶⡿⠟⠋⣹⠟⠉⠀⠀⠀⠀⠈⠙⠿⣝⠛⠛⠿⢷⣯⣷⣦⣠⣀⣤⣄⣀⣉⣩⠟⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣄⡀⠀⠉⠀⠉⠉⠓⢛⢉⠀⣠⡾⣫⡿⠋⠁⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠉⠛⠻⣿⣿⣿⣯⣽⣿⣲⣦⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢙⣦⣀⡀⠀⣠⣴⣻⣿⣾⣿⠿⠉⠀⢀⡞⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣄⠀⠈⠻⣿⡿⠛⢦⡍⠙⠻⢦⡀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠋⠀⢈⣩⣿⣿⣿⢿⣿⠟⠁⠀⠀⣠⡞⠁⠀⠀⠀⠀⣶⠀⡄⢀⠀⠀⠰⣆⠀⠀⠀⠘⢷⡄⠉⠻⣄⠀⠘⣷⡐⠀⠙⢷⣄⡰⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⡐⠀⠀⣴⠟⢉⣽⢻⣿⢸⣿⠀⠀⠀⢀⣿⠀⢀⡄⠀⢀⠀⡇⠀⡇⢸⠀⠢⠀⠘⣆⠈⠂⠀⠈⠻⣦⣄⠈⠳⣄⠸⣷⡄⠀⠀⠝⠻⣿⣮⣧⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢀⡼⠃⣰⡟⠡⠈⠁⣿⠇⠀⠀⢠⡿⡇⠠⢎⡰⠦⠚⠸⡇⠀⢷⢸⠀⠀⠀⠰⣿⡄⡀⠀⠀⠀⠸⡆⠀⠀⠈⠻⣿⣿⠀⠀⠻⠇⠉⣻⣿⣿⣶⡖⠀⠤⠀⠀⠀⢀⠤ ⠀⠀⠀⠀⠇⣾⣧⣾⠿⠦⠀⡠⢰⡏⠀⠀⠀⠈⢰⠃⠀⣼⠁⠀⠀⢀⡇⢰⢸⡈⣷⡄⠀⠀⣿⣳⠻⡄⣄⠀⠀⠹⡄⠀⠀⠀⠈⣿⣿⣿⢾⢿⡝⢯⡊⠉⠙⠻⣗⣦⣤⠄⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⠃⣿⠀⠀⣶⣾⡇⠀⠀⠀⠀⡿⠀⠀⣿⠀⠀⠀⢸⠇⢸⠀⣿⠸⡇⠀⠀⢹⣧⠃⠁⠉⠀⠀⠀⢻⡄⠀⠀⠀⢸⢸⡌⡘⢯⣎⢢⡕⠈⢦⡀⠀⠙⢯⡳⣤⣀⠀ ⠀⠀⢀⣾⣿⣿⣷⣶⣤⣴⣶⣾⡿⡇⠀⠀⠀⠐⠃⠀⢴⡇⠀⠀⠀⣾⢲⢸⠀⣿⠀⣇⠀⠀⠰⡟⣦⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⢸⡄⢧⢰⡘⡞⢧⠙⢮⢦⡹⣷⣶⣮⣿⣿⣷⣌ ⠀⣰⣿⣿⡿⡿⢃⣿⡟⢰⠟⢹⠃⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⡏⠨⢸⠀⢸⡇⢸⡀⠀⠀⢣⠘⢧⡀⠀⠀⢰⡀⢸⡟⠂⠀⠸⣧⠘⡄⢣⢸⡆⢳⡈⣷⣟⣿⣿⣿⣿⠿⣅⣹ ⣾⡟⠋⣼⣷⠃⠈⡾⢁⡎⡄⡎⠀⣧⠀⠀⠀⠀⠀⠠⣏⡆⠀⠀⢰⡇⢠⣾⠀⢸⣧⠀⣧⠀⠀⠈⣀⣈⣷⡀⠀⠈⣧⠈⣿⠀⠀⠀⢻⣄⣿⣾⣷⣿⣌⣿⣿⣿⣿⣿⣿⡟⣶⣼⣿ ⠉⠀⣰⢳⢃⡆⣰⢇⡞⢸⠇⡇⠀⣿⠁⠀⠀⠀⠀⠀⣡⡇⠀⠀⢸⠷⢞⢹⠀⠀⣿⠀⠘⣆⠀⠀⠀⠀⠀⢳⡀⠀⢻⡀⢸⢧⠀⠀⢸⣿⣯⣤⣼⣿⣿⣏⣾⣿⡿⣿⣿⣿⣿⡿⠿ ⣠⣾⣿⣿⣾⠿⢿⣾⣇⣾⣠⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⠈⣾⠀⠀⢛⠀⠀⢹⣦⠀⠀⣖⣠⣴⣿⠀⠀⣧⠈⡏⣧⠀⠀⠿⠋⣿⣿⣿⣿⢿⡏⠘⡇⠙⣿⣿⡅⠀⠀ ⣟⢿⣿⣿⣿⣷⣬⣈⣟⡿⣏⡂⢩⣿⣧⠀⠀⠀⠀⢠⣄⣁⣀⠀⣿⣲⣶⡟⠀⠀⠀⠀⠀⠀⠈⠁⢺⣿⣿⣿⣿⡷⡤⠈⠀⣇⠈⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⢿⠀⠈⢻⡇⠀⠀ ⣿⣿⣾⣿⣽⣿⣿⣿⣿⣯⣽⣿⡷⢿⠟⠀⠀⢸⠀⠸⢛⣷⣿⣾⣿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⢷⣿⣀⠐⢻⠀⠘⠀⠀⠀⣿⣿⣿⣿⡿⣿⣷⣸⡇⠀⠀⣷⡀⠀ ⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡏⣿⡇⠀⠀⠀⠀⢸⠇⣀⠸⡿⣿⢿⣿⡻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢸⡀⠀⠀⠀⢰⣿⣿⡻⣿⡇⠸⣟⣿⣇⠀⠀⣿⣧⡀ ⣿⣿⣿⠛⢁⣾⣿⣿⣏⣽⣧⣿⡇⠀⠀⠀⠀⢸⠀⠈⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⠀⠀⢸⣿⣿⣇⢻⣷⠀⠹⢿⣿⠀⠀⢿⣿⣷ ⣿⡿⠃⠀⣼⣿⣿⣿⡇⣿⣿⢹⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢸⠀⠀⢸⡿⣻⣿⡸⣿⢀⣀⣀⢹⡆⠀⢸⢹⣿ ⡿⠀⠀⣸⡟⣿⠿⣿⡇⣿⡏⢸⣿⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢸⠀⠀⢸⡇⣯⢿⡟⢿⡏⠘⢿⣏⡇⠀⢸⠸⣿ ⠁⠀⣠⣟⣐⣿⡧⣿⡇⣿⡇⠀⣿⡆⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⡏⢸⠀⠀⢸⡇⣿⢸⣧⢸⡇⠀⠀⠙⢷⠀⣾⠀⣧ ⠀⢰⡟⠈⢹⡇⠖⣿⣇⣿⠁⠀⣿⣇⠀⠀⠀⢸⣿⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⣰⣿⡇⠨⠀⠀⣾⠀⣿⡞⣿⡾⣿⠀⠀⠀⢿⣇⣿⠀⡟ ⠀⢸⠁⠀⢸⡇⠀⢼⣟⣿⠀⠀⣿⣿⡆⠀⠀⠈⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣿⣿⡇⠀⠀⢀⣿⠀⣿⡇⣿⣧⣿⠀⠀⠀⢸⣿⡿⠀⠀ ⠀⠀⠀⠀⠘⡇⠀⢸⣿⣿⠂⠀⢹⡟⣷⠀⠀⠀⣀⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⢸⣿⣿⡇⠀⠀⠈⡏⠀⣿⡇⣿⢻⣻⣆⠀⠀⠀⢸⡇⠀⢸ ⠀⠀⠀⠱⠄⠃⠀⠈⣿⣿⡆⠀⢸⣿⢹⡆⠀⠀⠘⣿⣿⣯⡛⣿⣽⣿⣷⡦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠿⠛⠃⠄⢾⣿⣿⡇⠀⠀⢼⡇⢠⣿⣷⣿⢘⣿⠹⡄⠀⠀⢸⠁⠀⡆ ⠀⠀⠀⠀⠸⡀⠀⠀⢻⣿⡇⠀⠘⣿⡎⣷⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣿⡇⠀⠈⠙⠒⠲⠶⠖⣻⠟⠁⠀⣀⣠⢤⣄⣠⠽⠿⠛⢳⣤⡼⣧⣸⣿⢸⡿⠈⣿⡆⠘⢷⣀⡞⠀⠀⡷ ⠀⢰⠦⠤⠆⢧⠀⠀⠈⡏⣧⠀⠠⢻⣇⢸⣧⠀⠀⢸⣿⢹⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠺⢥⣤⡴⠚⢹⠁⢠⠏⠀⣠⠔⠋⠉⠀⠀⠈⣻⣿⣿⡇⠀⡿⣿⡀⠀⠻⣵⠀⢰⠟ ⠀⠸⣆⣀⣀⣸⡆⠀⠀⣇⢻⠀⠀⢸⣿⠀⢿⡄⠀⠀⣏⢨⣿⣹⣎⣿⣿⠇⠀⠀⣠⡖⠛⠛⠓⢦⡀⠀⠀⠸⡄⠸⠀⢀⠏⠀⠀⡴⠤⠤⠚⠁⢻⡿⣧⣼⠇⣿⣇⠀⠀⠈⣗⡞⠀ ⠀⡀⠹⠉⠙⢿⣧⠀⠀⡿⣼⡆⠀⢸⢻⡇⠈⢷⡀⠀⣿⠈⣿⣿⣿⠿⠋⠀⠀⠀⠀⠙⠲⢄⡀⠀⠙⢦⣄⣰⠃⣇⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⢳⣿⡏⠀⣿⣿⣆⣠⢞⡿⠁⠀ ⠀⠐⠀⢃⠀⢸⡏⢧⠀⡇⠹⣷⡀⢠⣼⣿⣦⠘⣿⡀⢸⡦⠜⠛⠓⠒⠦⢤⣀⡀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠉⠀⣼⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢿⠋⢉⡿⠛⠟⣧⣾⣡⡖⠃ ⠐⠂⠘⢦⡰⡎⠀⠘⣇⠇⠀⢻⣷⢸⣿⣹⣿⢷⡾⠹⡎⣣⠀⢀⠀⠀⠀⠀⠈⠙⠲⠦⣄⠀⠀⠈⢷⣀⠀⠀⠀⡹⢀⢤⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡘⠀⠀⠈⠀⠀⠙⢂⠚
⠀⣶⠀⠀⣿⠃⠀⠈⠉⠃⠒⠢⡄⠒⢖⠚⠛⠱⣏⠡⠉⢳⠀⠀⠆⠀⠀⡇ ⠀⡿⣀⣰⣏⠀⠀⡀⢀⠀⠀⡄⡆⠀⣨⡀⠀⢁⢿⡀⡀⠘⣇⣀⣀⠀⢈⠃ ⠀⠃⠀⠸⡇⠁⠉⢩⠁⠈⢹⠀⡏⠇⢹⠗⠒⠘⠙⡍⠉⠉⠀⠀⢸⠀⢸⠀ ⠀⠀⠀⠀⡇⠰⠀⢾⠀⡆⡏⠸⢁⢰⠈⠘⣀⠀⡀⠇⠀⡆⠀⠀⠈⠀⢸⠀ ⠀⠀⠀⠀⠆⡄⢸⢹⢰⡰⠀⣾⠘⡜⡆⡇⠹⡆⢠⠸⡀⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⣷⣾⣞⠿⣧⣘⠹⠀⠰⠟⢅⣶⣧⣸⢿⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠎⠠⠿⠛⠳⠇⠀⠀⠀⠀⠀⠀⠸⠿⠋⠶⠄⠁⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀ ⡄⠇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⣸⢰⢇⠀ ⠰⢰⠀⠀⠘⡷⢄⠀⠀⠀⠀⢤⠤⠤⣤⠄⠀⠀⠀⣠⣾⡇⠀⠀⣿⢸⢸⠀ ⠀⠛⡄⠀⠀⣇⠀⢕⠤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠀⠀⢸⣧⣿⡈⠀ ⠀⠀⢡⢂⠀⢸⣄⠨⠐⠉⠈⠐⠠⠄⠒⠉⠉⠛⠿⣿⡟⠀⢠⣿⣿⣏⠇⠀ ⢀⠠⠤⠛⣆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠃⡠⠛⠻⠅⣻⠿⠗ ⠀⠀⠀⠀⠂⠵⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⡬⠾⠐⠀⠀⠀⠀⠈⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣰⣿⣿⠀⢀⠔⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢝⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⣰⣿⣿⣿⠀⠈⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡑⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⣰⠋⢿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⡴⠁⢀⡜⠁⠀⢸⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠄⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⡉⡀⢀⡞⠀⢀⣞⣠⢤⣤⣼⣿⣿⡄⠉⠫⡑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⡠⢺⢏⠜⢉⣵⡟⠀⣰⠛⣸⠃⡌⠃⡁⣿⡟⣆⠐⢄⣙⢉⣡⠼⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ ⠀⠀⢠⣾⣶⣿⣟⣠⣿⡟⠀⣼⠃⢀⢋⣰⠁⣀⠧⣧⢷⠘⣇⡠⠚⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠙⢦⡉⠙⣿⡿⢁⣠⣧⣴⣋⣉⠽⣷⣿⣦⠩⣘⣦⣽⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣷⣶⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⠳⠮⣍⣉⣿⠟⢋⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⡿⠛⢁⣿⡟⠀⠉⢻⣿⣿⡟⠻⡟⠋⠀⠀⠀⠀⠀⠀⢸⠀⢸⣇⠀⣀⠀⠀⣄⠀⡂⠀⡄⢸⡆⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⠟⠀⠀⡜⢹⠁⠀⢀⠇⢺⣿⡇⠀⠁⠀⠀⡀⠀⠀⠀⠀⠞⠀⠈⠙⠛⠿⠶⣶⣧⠑⠷⢰⣷⠀⣧⢰⣿⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⣥⠏⠀⠀⡰⠁⡎⠀⠀⡼⠀⣿⣿⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⣶⣶⣼⣯⣀⠀⠀⠀⠀⠀ ⠃⠀⠀⢠⠃⠀⠀⠀⠀⢁⠒⢹⣿⡀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠸ ⠀⠀⠀⠎⠀⠀⠀⠀⠀⣸⡁⢸⣿⡇⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⡀⠀⣿⠀⠀⣿⡇⠀⠀⠀⢆⠀⢹⡄⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠇⠀⠛⠀⠀⢿⣷⠀⠀⠀⠈⡆⠀⢷⠀⠈⡄⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠻⣆⠀⢣⠀⠘⣄⠘⡄⠀⠀⠀⠀⠀⠈⠛⢌⣉⢀⡆⠀⠀⠀⡠⢫⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⡄⠀⠀⠀⣻⣷⣄⢣⣀⣈⣀⣱⣤⣄⣀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⠞⡁⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢀⣿⣿⡿⠋⠁⠉⠉⠙⠛⠷⢌⠻⣶⣦⡀⠀⣀⣤⣶⣿⡟⠀⠃⠀⠀⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣼⣏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⣇⠹⣿⡏⣿⣿⡟⠃⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣣⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⣿⠀⢿⡅⣿⣿⡁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣷⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⠀⢿⡇⢸⣿⣿⣿⣧⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⣪⢸⡙⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢸⡇⢸⣿⣿⣿⡟⠂⢠⠸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢿⣼⣧⠈⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢸⡇⢸⣿⣝⢿⠃⠈⡄⢧⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⣿⣿⣇⠈⢿⡇⠀⠀⠘⠉⠉⠳⣦⣄⣀⠁⢸⡇⠸⣿⣿⣿⣦⣄⡘⣌⢿⡄⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠒⠂⠀⠀⠀⠂⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠦⣄⠀⠀⠀⠀⠀⠀⣠⢀⣶⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢓⡤⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠋⠹⡄⠀⢧⡴⠃⠀⠀⣀⣀⣤⢞⣿⠋⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢼⢦⡀⡔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠉⠁⠀⣿⠀⠀⠁⠀⣼⠽⡿⣫⣴⡿⠁⠀⠀⠀⢀⠆⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠲⢤⣀⣘⣆⡀⠀⠀⣗⡫⢾⡿⡟⠀⠀⠀⠀⠀⡞⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠸⡀⢸⣟⡍⠑⢦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣿⣋⡴⢫⠞⠀⠀⢠⠀⠀⣸⢀⢳⠁⡼⠀⠀⠀⢰⠀⠀⠀⠀⠀⠸⠀⠀⠀⢧⠚⣿⣿⠀⠈⣿⣷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⢃⠀⠀⡆⣾⠀⢠⡇⣸⣬⣠⡇⡀⢠⣰⡜⠀⠀⠀⡄⠀⡀⠀⠀⠀⢸⢳⣿⣿⣧⡀⢸⣿⣷⣑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⢰⠁⡿⠀⣸⠃⠇⡇⢸⡇⡇⢸⣿⢷⠈⠓⠒⡧⣄⡀⠄⠀⠀⣸⣿⣧⣿⣿⣷⣼⣿⣿⡻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠹⣷⠀⡾⠀⣧⣧⠷⣷⣶⣽⣟⢱⣧⣸⣿⣸⠀⢀⢀⡇⠈⢹⠆⠀⢀⡿⡿⣿⠸⣟⡞⢎⢷⠳⡑ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⢰⡏⠀⡇⠀⣿⠙⢆⣇⢿⣟⡟⠂⠀⠀⠈⠀⡽⣿⣶⣷⣦⣸⠀⠀⢸⢸⠀⡟⡇⢸⠸⣼⠞⠳⠿ ⠀⠀⠀⠀⠀⠀⠠⣺⡿⠟⠁⠀⠀⠀⣼⢇⡀⡇⠘⢻⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠷⣿⣿⡿⣽⠿⠄⢿⣼⢰⡇⣇⣾⣤⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢠⡿⣸⠀⠂⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡹⠀⠀⠘⢻⡿⢿⣿⢋⠁⠀⣿⣆⠀ ⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⣼⢴⣿⠁⣿⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⣼⡇⠈⣿⠘⡄⠀⠘⣿⣧ ⠀⠀⠀⡾⠋⠀⠀⠀⠀⢀⡼⢫⣿⠇⢀⡿⡀⠀⠀⣿⣿⣆⠀⠀⠘⢧⡀⠉⠉⣳⠆⠀⠀⠀⠀⣸⠁⠀⡜⢠⡏⡇⢀⣿⡄⠹⣄⢠⠘⣿ ⠀⢀⡞⠁⠀⠀⠀⠀⣠⡾⢡⡿⠃⠀⣸⡇⣷⠀⠀⢻⣿⣿⣦⡀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣀⣼⡏⠀⢀⠃⣼⢳⡇⢸⣿⣧⡆⠙⣿⡄⠈ ⠀⢸⠀⠀⠀⠀⢀⣴⠋⣠⡿⠃⠀⢠⡟⢣⠛⡄⠀⢸⣿⣿⣿⡟⡶⣄⠀⠀⢀⣀⡤⠶⢿⣿⣿⠁⠀⡞⢰⡿⡜⡇⢸⣿⡟⣾⡄⠘⢷⡄ ⠀⡇⠀⠀⠀⣴⠟⢁⣴⠟⠀⠀⢀⠾⠁⠸⡄⣿⡀⠈⣿⣿⡿⠀⠣⡈⠫⠉⠁⠀⠀⠀⠁⠻⡏⠀⡜⢀⣿⢣⡇⢧⠼⢹⣿⠹⣵⡀⠀⠓ ⠀⣧⠀⡠⢚⠏⣠⡾⠃⠀⠀⢠⢋⡠⠤⠴⢿⡉⣇⠀⣿⠏⠁⠀⣠⠞⣒⡲⡀⠀⠀⠀⠀⠠⠀⡰⢡⣿⢏⣾⠁⢸⢀⠸⣿⡇⠹⡷⡄⠀ ⠀⣿⠆⠀⣨⣾⠏⠀⠀⢀⣴⣳⠋⠀⠀⠀⠀⣿⣿⡀⡏⠀⠀⣠⣇⣉⠉⢹⢃⠀⠀⠀⠀⠁⠀⣱⣿⣿⡾⠿⡄⠘⢼⠀⢻⣿⡄⠹⡞⠆ ⠀⠈⣠⣾⡿⠁⠀⢀⣴⠟⢱⠃⠀⠀⠀⠀⣸⠋⢮⠃⢸⠤⠞⠙⠀⢐⠤⠄⠙⣇⠀⠀⠀⢠⠜⣹⡿⢻⡇⠀⠈⠑⠮⣄⠈⢿⣷⡀⠘⠆ ⣠⣾⣿⣿⣶⣀⢐⠟⠁⠀⡎⠀⠀⠀⠀⣰⠃⢀⡏⢚⢸⠀⠀⠀⠀⠘⠓⠂⢀⡏⠲⠃⡴⣡⠞⡟⠀⣸⠁⠀⠀⠈⢀⠬⡣⣠⠻⣧⡀⠀ ⣿⡿⠁⠈⠛⣱⣇⣄⠄⠀⡇⠀⠀⠀⢰⠏⢀⡞⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⢸⠣⢡⣾⠟⠁⠀⡇⠀⣿⠀⠀⢀⡔⠁⠀⠙⣿⣇⠙⣷⡄ ⡟⠀⠀⠀⠀⠉⣛⡎⠀⠀⡇⠀⣠⣶⠃⢠⡞⠁⠀⠀⡜⠀⠀⠀⠚⠓⠂⠀⣃⣰⠟⠁⠀⠀⢸⠁⠀⡏⠀⢠⠎⠀⠀⠀⠀⢹⡏⡆⠈⠻ ⠀⡀⠀⠀⠀⢠⡟⠀⠀⢰⢃⣼⠟⠁⣠⠏⠀⠀⠀⡰⢻⡁⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⡟⠀⢸⠁⠀⠌⢀⡔⠁⠀⠀⠀⢣⠘⡄⠀ ⠞⠀⢀⣄⣀⡼⠀⠀⢠⣷⠋⠉⠀⠠⠃⠴⢴⣶⠞⢁⡰⢧⢰⡶⡄⠀⢰⡟⠀⠀⠀⠀⠀⢀⡇⠀⢸⠀⡔⡠⠏⠀⠀⠀⠀⠀⢸⠀⠸⡀ ⠠⠐⠀⠘⡶⠟⠒⠒⠛⠶⣤⣄⣠⣅⣤⡚⠉⠈⡉⠑⢶⡿⠋⡉⠁⣀⣿⠀⠀⠀⠀⠀⠀⢸⠇⠀⡎⠀⢯⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁ ⠀⡄⣴⡟⠀⠀⠀⠀⠀⠀⠛⠉⢶⡍⠉⠛⠒⠤⢝⣒⣾⡇⢀⣯⣉⠙⡏⠉⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠ ⠄⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢄⠀⠀⠀⣀⡶⠛⠋⠋⠀⠀⠙⠿⣤⣄⣒⣁⣀⣱⣯⣀⣀⣧⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⣏⠐⢦⢤⠤⠀⠀⠀⠀⣀⣴⣟⠻⣿⠇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡈⠉⠛⠒⠒⠦⠬⣉⣻⡎⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄ ⠃⣼⠦⢼⡶⣤⣤⡤⣶⣏⠉⢿⣿⢀⡇⠀⣠⣞⣳⣤⠤⣄⠠⡀⠀⠀⠀⠤⢦⣽⠀⠀⠀⠀⡠⠂⠈⠙⠿⡧⢄⡀⣠⠞⠀⢀⢸⡄⠀⢱ ⠀⢿⠀⣿⣿⠈⠻⠦⣿⣿⣿⣾⡠⢾⡇⠀⡜⢿⠟⠁⣤⣼⡄⠈⠳⠄⠀⠀⢀⣼⡇⠀⠀⡔⠁⠀⠀⠀⠀⠹⡄⡟⠁⠀⠀⠀⢸⢱⠀⠈ ⠀⠘⢷⣌⠳⡦⠤⠤⠝⠛⠋⣁⣴⠟⠁⢸⡳⠄⢷⣿⣿⣿⡏⡭⣷⡚⠛⢺⣟⢯⠀⣀⠜⠀⢀⡤⠚⠁⢀⠆⡷⣹⣄⠄⣀⠀⢸⡏⡇⠀ ⠀⠀⠀⠉⠛⠿⠷⠧⠴⠶⠟⠋⠁⠀⠀⠀⢳⣀⠈⠻⣛⠿⠸⣿⣿⣗⣀⣘⣻⡏⠈⠁⣀⠴⣻⡀⠀⠀⡼⠀⣸⡜⡎⠳⡀⠀⠘⣷⢻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠘⠂⠀⠒⠒⢰⣾⠟⠓⠚⠉⠀⢠⡧⠤⡀⣰⠃⢀⣏⡆⢡⠀⢻⢆⢀⣿⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⡀⡀⠀⠀⠀⠉⡉⠛⠚⠛⠛⢛⣋⢡⠄⠀⠀⠀⢀⡟⠀⣠⡴⢻⢟⠛⠉⠀⠀⠀⠈⢞⣿⣿⡇⡗
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