Cute Christmas Emojis & Text

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠰⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠉⠉⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⣿⣿⣿⣠⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡎⠀⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡼⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠁⠀⢸⡇⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⡜⡗⠀⠀⣿⠀⢠⠇⠤⠤⠤⡤⠀⠀⠀⠀⠀⠠⠴⠶⠖⠒⠀⠀⠈⣷⠀⠀⠀⠀⠀⢀⡀⠀⠙⢿⣿⡇⠀⠀ ⠀⠀⠀⠀⡸⢰⡇⠀⢸⡟⠀⣸⣆⣀⣠⢤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⢀⣿⠀⠀⠀⢶⡆⠊⠀⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⡇⡇⠹⡀⣼⡇⠀⢹⣿⠻⣟⣻⣷⡄⠀⠀⠀⠀⠘⠿⠿⣿⣻⢿⣶⢿⡇⠀⠀⠀⡾⣇⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠁⢀⠟⢿⣿⠀⠈⣿⠇⠈⠇⠘⠃⠀⠀⠀⠀⠀⠐⠢⠿⢷⠾⠟⣸⠁⠀⠀⢠⣧⣯⠈⠣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⣴⣧⡖⢸⣿⣆⠀⠹⣧⠀⢀⣀⡤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣾⡯⡞⠀⠀⠀⠀⣶⣶⠀⠀⠀ ⠀⠀⠀⠀⡼⡿⣍⠁⠀⢿⣙⣤⠔⠚⠉⠁⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⡾⠀⠀⠀⣼⢣⢃⡇⠀⠀⠀⠀⢹⡈⢳⡀⠀ ⠀⠀⠀⡼⢹⡴⢩⣆⡴⠋⠉⡇⢶⣾⢾⣿⣛⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢸⠇⠀⠀⣰⠇⠀⣼⠀⠀⠀⠀⠀⣼⠃⠀⠳⡀ ⠀⠀⠀⣇⡞⡰⢩⡏⠀⠀⢨⡇⠘⣿⣷⢾⣿⠀⠀⠀⠀⡔⠊⠉⠉⢳⣶⢿⠀⠀⢠⡏⠀⣼⠇⠀⠀⠀⠀⣴⡏⠀⠀⠀⠉ ⠀⠀⢰⢃⡞⠀⢨⣇⠀⠀⠀⢧⠀⣻⡷⠾⠿⠇⠀⠀⠀⢻⣧⣠⣽⡍⠈⢻⡄⠀⠸⠀⢰⡟⡆⠀⠀⢀⣜⢿⡇⠀⠀⠀⠀ ⠀⢠⢃⠎⢣⠀⡟⢈⣦⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠭⠜⠁⠀⠀⣹⣆⣠⡀⢸⡿⠀⠀⢀⡾⠃⠈⣏⠀⠀⠀⠀ ⠀⡎⡞⠀⠀⢹⡇⢀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⣿⣷⡸⠃⠀⢀⡾⠄⠀⠀⣿⠀⠀⠀⠀ ⠀⡁⡇⠀⣰⠋⣇⠈⠢⠀⠑⣄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⢧⠹⠿⣻⣷⠇⠀⡸⠀⠀⠀⢠⣿⠀⠀⠀⠀ ⠀⠇⠃⡴⠁⠀⣾⡄⡀⠈⠀⠨⣕⢤⣈⣦⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠓⠋⠁⠘⢆⠀⢣⠀⠀⠀⣼⡇⠀⠀⠀⠀ ⠀⢈⡞⠁⠀⣾⠀⡇⠈⢶⡒⠒⠒⠒⠙⠇⠋⢳⣤⡀⠀⠀⠰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣌⣳⠤⠞⢁⡇⠀⠀⠀⠀ ⢀⡎⠀⠀⢰⢹⠀⡇⠀⠀⠉⠒⠤⠤⠔⠒⣋⠁⣳⠈⠱⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣆⠀⠀⣀⣴⡇⠀⠀⠀⠀ ⡜⠀⠀⠀⠘⠸⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣼⡄⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣆⠀⣱⣼⠃⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠿⠟⠞⠉⣸⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⠉⠒⣦⣀⠀⠀⠀⠀⡙⡄⠘⠄⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⣠⠎⠁⢀⡤⠒⠊⢉⠀⠀⠀⠑⢄⠀⡇⢹⠀⠈⡄⠀⠀⠀ ⡃⠹⣦⠀⡰⢁⡠⠊⠁⠀⠙⣶⠹⢲⠶⠴⡒⠀⡇⠇⢀⠇⢀⡇⠀⠀⠀ ⠑⡄⠇⠱⡵⠋⠀⠀⣠⠔⠉⠀⠀⠀⢀⢖⣉⡛⣼⠀⡜⢰⠁⠀⠀⠀⠀ ⢴⠀⢰⠀⠑⣄⢀⠞⣓⡢⡀⠠⣄⣀⣸⣿⣿⡗⡀⢋⢀⠴⠁⢀⣀⠀⠀ ⠈⢂⠀⠣⣄⠈⡿⠸⣿⣾⣮⡟⠛⠛⣸⠊⠉⠊⣱⠞⢳⡊⠽⠅⠰⣾⡆ ⠀⠀⠁⠢⣤⣉⣣⠑⠨⠭⠐⢉⡹⡶⣳⣒⣶⡿⠛⠈⠁⠀⠀⢀⡠⣃⠄ ⠀⠀⠀⠀⣧⠵⡶⡻⣋⡴⣾⣛⠚⠉⡁⡎⠁⢂⠀⠀⠀⠀⠮⠍⠛⠁⠀ ⡶⣢⣯⢟⡕⠚⡽⢁⡠⡜⠀⠀⡇⠀⡹⢧⠀⠈⢆⣀⣀⣠⣄⣤⠀⠀⠀ ⠀⡎⠀⢙⢳⠟⠤⠚⢣⠃⠀⠈⢣⠤⢁⠎⢀⡀⢈⣆⣞⠙⢈⡈⡟⠀⠀ ⠀⠈⠀⢴⣚⠀⣴⡷⢸⠀⠀⠀⣀⡇⠘⣶⢞⣩⣿⡻⣇⠀⠿⡳⠁⠀⠀ ⠀⠀⠀⠀⠸⠖⠀⠔⠺⣟⣠⣀⡀⠗⠂⠉⠙⠛⠋⠀⠈⠁⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣶⣶⣄⡀⠀⠀ ⠀⠀⠀⠀⢀⠖⠉⠉⠈⠉⠉⠙⠛⢿⠋⠉⢑⠀ ⠀⠀⠀⢶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⡈⠁⠀ ⠀⠀⠀⠏⣴⣿⣶⠀⢠⣶⣶⣦⠀⠀⢻⠃⠀⠀ ⠀⠀⢸⠀⠻⠿⠋⢶⠞⠿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⣆⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⣾⠂⠀⠀ ⠀⠈⣿⣿⣿⣷⣶⣤⣴⣶⣶⣿⣿⣿⣿⠆⠀⠀ ⠀⢄⠙⠇⠀⠉⠙⠛⠛⠛⠛⠉⠿⠿⠿⠀⠀⠀ ⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠀⠀⠀ ⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢉⡕⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣷⣶⠖⢶⣶⣶⣾⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⠿⠟⠀⠸⠿⠿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠴⠦⠄⠦⠤⠆⠤⠴⡄⠴⠦⠶⠶⡶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⡟⠁⠈⠀⠑⡄⠀ ⠀⠀⠀⠀⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⡄⠐⠢⠔⠁⠀ ⠀⠀⠀⠀⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣄⢹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⡛⢁⣴⣾⣷⣶⣄⠀⠀⢠⣴⣶⣶⣦⡀⠀⠀⠀⠙⠟⠛⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⢸⣿⣿⣿⣿⠏⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠛⠿⠟⠋⠰⢿⡿⠈⠻⣿⣿⣿⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⣠⣶⣿⣆⠀⠀⠀⠀⠀⠀⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡆⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⡀⠘⢿⣿⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀ ⠀⠳⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠹⠛⠋⡉⠻⠀⠀⠀⠀⠀ ⠀⠀⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⢃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠀⢹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠁⠀⠈⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⡀⠀⣀⣀⠀ ⠛⡛⠳⠿⠝⠻⠋⠟⠟⠛⠟⠓⠚⢻⠻⠛⡀⠐⠻⠻⠚⠟⠛⠿⠿⠿⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣃⣀⣠⡤⠤⠤⠤⠤⠤⠤⣤⣀⣀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⠉⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣲⡦⠤⠟⢦⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⢿⡶⠒⠛⣿⠉⠉⠉⠉⠉⢽⣟⠓⠒⢶⣿⠃⠀⠀⠈⣙⡆⠀⠀⠀⠀⠀ ⢀⡞⢀⣼⠁⠀⠀⠟⠀⢴⣿⣷⡆⠀⠻⠀⠀⢸⣿⠶⣦⣤⠴⠋⠀⠀⠀⠀⠀⠀ ⣼⠃⢸⡁⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⣹⠆⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣆⢨⣷⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣠⣿⣀⠀⣹⠀⠀⠀⣀⣀⡀⠀⠀ ⠀⠙⠻⢤⣽⣷⣦⣴⣶⣾⣯⣷⣶⣤⣤⣶⣾⣿⢥⣨⣿⣧⠒⠶⠞⠋⠁⠉⢳⡀ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣤⠼⠿⣿⠀⠀⠀⠀⠀⢠⣼⠃ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢿⡷⠚⠃⠀⠀⠀⠀⠀⠈⢷⠀ ⠀⠀⠀⣼⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣷⠀⠀⠀⠀⠠⠖⣠⡶⠋⠀ ⠀⠀⠀⢿⠀⢀⡇⠀⠀⠀⢸⠀⡆⠀⠀⠀⣇⠀⠀⠹⡄⠀⢲⡾⠤⠶⠋⠀⠀⠀ ⠀⠀⠰⡟⠀⢼⡇⠀⠀⠀⢸⡀⡇⠀⠀⠀⢿⠀⠀⠀⡷⠖⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠦⣸⡇⠀⠀⠀⢸⣇⣇⠀⠀⠀⢸⡧⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠲⠤⠶⠞⠉⠙⠢⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠉⠉⠙⠒⢦⣀⠀⠀⠀⢰⠁⠀⠀⡂ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠊⢢⠤⠐⠁ ⠀⠀⠀⠀⠀⢰⠏⠀⠀⣀⣀⠤⠤⠔⠖⠖⠚⠚⣵⣒⣀⠐⠂⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣸⡟⠋⠁⠀⠀⠀⠀⠀⣀⠀⠄⠘⢿⣿⣿⣿⣶⣦⠀⠀⠀ ⠀⠀⣠⣾⣿⡯⠀⠀⣀⡤⠔⠀⢊⠀⠙⠀⠑⠠⡀⠘⣿⣿⣿⠏⠀⠀⠀ ⢀⣼⣿⣿⣿⠃⡁⠭⠁⠀⠒⠠⠊⡎⠀⣀⣤⣥⠬⣄⣻⣿⣏⠀⠀⠀⠀ ⠘⠿⣿⣿⣿⣄⡴⠚⠛⢭⡙⡆⠢⠃⠘⣿⡞⢠⣖⡆⢻⣹⠋⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⡀⠿⠼⢀⣿⣥⣶⣶⣶⡮⣷⣄⣉⣡⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠹⠷⠶⢖⣿⠟⠬⡛⢿⢩⡬⡟⡛⠣⡀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⡼⠹⠠⠅⣣⣾⠿⠫⣄⠀⠀⡷⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢆⠀⠸⣄⠀⡴⠁⠀⠀⠀⠈⣳⠞⡡⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠈⠽⠷⠦⠄⠐⠒⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣻⣏⠂⣀⣀⠀⢰⠛⠰⠀⡀⡰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠁⠒⠁⠀⠏⠉⠀⠉⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣤⣠⣤⣵⡀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠖⠊⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⣦⢶⡶⢶⣾⢲⠤⠤⣀⣀⣤⠤⠖⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣀⣀⣠⠤⠴⠒⠒⠋⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⣰⣻⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠠⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⠖⠒⢹⡟⠀⢡⡀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣟⢃⠀⣀⢀⣀⣴⠶⠖⠉⠀⠀⠀⠄⠀⠀⠈⠀⠀⠈⠑⢂⡄⠀⠘⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⢀⣼⣿⣿⣿⣿⣿⡟⢉⡩⠚⠡⠊⠁⠀⠠⠤⢄⠀⠼⢠⠞⠀⠀⠀⠀⠊⣁⣀⡈⠒⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⡀⠠⠖⠉⢁⣀⣤⣤⣄⡀⠀⢳⠀⢸⠀⠀⣠⣶⡾⣿⠿⠛⠛⠛⠳⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠘⠻⣿⣿⣿⣿⣿⣿⡇⢠⣴⠟⠛⠛⠳⣤⡀⠙⣷⠈⠦⠜⠀⠀⢻⣿⣷⡏⠀⣴⣏⣳⠀⢹⣷⠹⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠻⣿⣿⣿⣿⡿⠁⢠⣶⠒⡄⠈⣿⣴⠇⠀⣀⣀⣄⣀⣀⡙⢿⣇⠀⠻⠿⠟⠀⢸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⠀⠘⠿⠿⠃⢀⣿⣧⣶⣿⣿⣛⣛⣿⣿⠟⣿⣿⣷⣤⣤⣤⣶⣿⡿⠃⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢻⠹⣏⣷⣤⣤⣤⣴⣾⣿⠟⢙⡻⠿⢿⡿⠟⠋⣐⢺⡏⢿⠿⢦⡉⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠛⠛⠋⠁⣾⣿⠉⡀⣘⠙⠃⠈⣷⣘⣻⣏⠙⠇⠲⠀⠈⢳⡀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⠃⠹⠎⢡⡍⠈⣣⣾⣿⣿⠿⢷⣤⡀⠀⠀⠀⢸⡇⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠀⠀⠀⢸⣄⠀⠀⠀⠀⣰⠟⠈⠉⠀⠀⠀⠈⠻⣦⣄⣠⡿⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠻⣦⡀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣨⡿⢋⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠄⣈⣙⣻⣧⣤⣄⣄⣀⣀⣤⡴⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⢹⢸⠀⠀⠀⠀⠀⠀⠀⢸⠏⠃⣼⠃⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿⢹⠀⠻⠛⠛⠃⢲⠶⠸⣄⡠⡿⠴⢶⡿⠾⢯⡴⣶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⡄⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢧⠀⠀⢙⡾⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⠣⣀⠞⢣⠈⡇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣼⠟⠃⠀⠀⠀⠀⠁⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣇⢹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣆⠀ ⠀⠀⠀⠀⠀⢀⡟⠁⠈⠹⣄⢠⣤⡀⠀⢀⠘⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⠏⠈⣹⠀⠘⢿⣛⡀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀ ⠀⠀⠀⠀⠀⠘⠧⢤⣀⡀⠀⣠⡾⠋⠀⠀⠀⣿⣟⡠⠖⠋⠉⠉⠓⢤⠀⠀⠀⠀⣀⡠⠤⠒⠒⠛⡲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣄⡙⠿⠋⠀⠀⠀⢀⡼⠛⠁⣠⣶⣟⢲⡀⠀⠀⠑⠦⠖⠉⠀⠀⢀⣠⣤⣄⠈⢆⠹⣅⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀ ⠀⠀⠀⠀⠠⣾⠛⠋⢸⠇⠀⠀⠀⠀⢀⡞⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⢠⣿⣿⡁⢙⣧⠀⢳⡹⣧⠀⠀⠀⠀⣰⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠙⠓⠒⠛⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⣇⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠉⠛⢿⠆⠀⢿⣿⡆⠀⠀⢰⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠤⠂⠀⠈⠁⠀⠀⢢⣴⣾⡶⠤⣤⠀⠀⠙⠦⠤⠶⠋⠀⠀⢸⡟⣧⠀⠀⠀⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣠⣶⡿⠀⠀⠀⠀⠀⠀⠻⢅⣀⡴⠃⠀⠀⠀⠀⠀⠐⠀⠀⢀⡞⢠⡟⢀⠀⠀⠹⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡆⠈⢳⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣤⠀⣸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠋⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⢦⣺⡿⢺⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢻⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡯⠟⠋⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⠧⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⢈⡟⠲⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⣠⠾⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠹⢄⡀⠀⣠⠞⠉⠁⠀⣿⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢻⡄⠰⠁⠈⣏⢷⡄⠀⠀⠀ ⣀⣀⣀⣀⣼⣇⣤⣄⣀⣍⣽⣇⣀⣤⣀⣸⣿⣦⣤⣬⣽⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣉⣀⣄⣤⣄⣙⣦⣄⣄⣼⣤⣿⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣯⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⡟⣻⣻⣿⣏⣹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠈⢦⠊⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡘⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣰⠄⢀⠸⣆⠄⠀⠀⠀⠀⠀⠀⠰⡄⠈⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⣺⢴⢦⣠⢳⠈⡐⢦⠘⡤⠓⢤⠀⠒⣤⠤⡉⡤⣄⠀⢤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢸⠁⡘⢀⣀⢸⠀⢁⠜⠀⠧⡐⢨⡇⠈⢩⢀⠙⡀⣿⠀⢸⢆⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠢⣤⠃⠂⠘⠈⠀⠀⠳⡄⠑⠤⠊⠱⠇⠈⠀⠁⠓⠷⠋⠀⠓⠤⡞⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⣿⠀⢰⢲⡶⢦⠀⢰⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⡟⢦⣠⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⡤⣼⡤⠷⣈⣆⣼⣿⡯⠀⠀⠀⠀⠀⠀⣀⠴⠿⠄⢷⣿⣏⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⡋⠁⢠⣿⣷⡀⠀⠈⠛⢦⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡀⠀⠉⠛⠛⠛⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠈⠛⢠⠃⣿⡿⠨⠀⠛⠀⠀⢳⡀⠀⠀⣰⠃⠘⠃⠀⢺⣿⠀⠀⠛⠁⠀⠀⣱⣦⣤⣄⠀⠀⠀ ⡖⠲⠃⠀⠀⡎⠀⠈⠀⠀⡆⠀⠀⠀⠀⢧⠀⢀⡟⢦⣀⠀⠀⠀⠁⠀⢀⣀⡤⠖⣋⡴⢻⣜⡟⠀⠀⠀ ⠳⣄⠀⠀⡸⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠙⣷⢿⡟⠲⠦⠭⠭⣭⣭⡭⠤⠴⠖⠋⠁⠀⢻⡏⠀⠀⠀⠀ ⠀⡇⠀⢠⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⢺⡽⣼⡇⠀⠀⠀⠀⢿⣽⠃⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⡇⠀⢸⡀⠀⠀⢀⣀⠀⢸⠀⠀⠀⠀⣸⠀⠸⡷⣤⣀⡀⠀⣾⣹⣇⣀⣀⣀⡤⠴⣛⣽⠃⠀⠀⠀⠀ ⠀⠹⡄⠀⠑⠦⡀⢯⣉⠑⠀⠀⠀⠀⣰⠃⠀⠀⠙⢗⠛⠫⠭⠿⠿⡏⠉⠻⠒⠈⢉⡴⠁⣠⣄⡀⢀⡄ ⠀⠀⠈⠓⠦⢄⣀⣀⠈⢀⣀⣠⠴⠊⠁⠀⠀⠀⠀⠈⠑⠢⠤⣀⣀⣈⣁⣀⡤⠖⠋⠀⣸⠁⣿⣷⣼⣧ ⠀⠀⠀⠀⠀⠀⠻⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⠀⠀⠀⠘⠀⠉⠋⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠂⠁⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢸⠀⠀⠀⢠⠶⠚⢲⢦⢄⡀⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣇⠀⠀⠑⢄⠀⢀⠀⠰⠁⠀⢣⡘⠛⠉⢢ ⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠙⣦⡀⠀⠀⠁⠚⢂⠀⠀⠒⡅⠡⡀⢀⠜ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡟⢉⣂⣤⢀⡀⠀⠈⠀⠀⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣧⣼⠀⢸⠇⠀⡀⠀⠀⠀⠀⣀⠉⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠐⢸⡄⢸⡆⠸⠿⠂⠀⠀⠀⠿⠃⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣷⣌⣷⣾⣷⡤⣴⡖⡖⠒⢲⢲⣀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⠈⢿⢻⠻⣿⢿⣿⠋⠛⣷⣷⡶⣾⣾⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⡒⠡⠼⠅⣼⢠⠻⠀⣸⣀⡙⣷⡿⢾⣂⣹⠀⡇⠀⠀⠀⠀⠀ ⢀⠔⠁⠀⠀⠀⠀⠀⠙⢇⣰⣁⣀⣣⠉⡆⠈⠌⠑⠢⣇⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠑⢌⣍⣤⠤⠤⣡⡁⠀⠘⡀⠀⠤⠑⢄⠀⠀⠀ ⢇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠇⠯⠓⢤⠄⠂⠀⠀⣀⣀⠀⠠⠄⠃⠀⠀ ⠈⠂⠄⠀⠀⠀⠀⠠⠆⠁⠀⠀⠤⠘⠀⠀⠈⢙⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢖⣈⠉⠀⠀⠀⡠⠔⢀⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⡼⡁⠀⠉⣆⣀⠀⠉⠉⠀⠀⠀⠑⢄⠀⠀⠀⠀ ⠸⣀⡸⢀⡸⠒⠦⠂⠲⠶⠀⠲⠖⠀⠢⢥⡀⡀⠀ ⠀⠀⠀⢢⠀⠀⠀⠀⣀⣀⣀⣀⣄⡀⠀⠀⠀⠈⠆ ⠀⠀⠀⢈⡞⠕⣿⣿⣿⢀⡤⣡⠀⠀⠓⠦⢦⠔⠁ ⠀⠀⠀⢸⡇⣀⣿⣿⡏⣿⡿⢸⠀⠀⣷⡷⣾⠀⠀ ⠀⠀⠀⢸⣿⣤⣿⣿⡇⠈⠀⠈⠀⠒⠙⠂⣿⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⢨⣟⡲⠀⣠⡿⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡇⠉⠐⢢⡭⠶⡾⢿⡇⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡧⠀⠔⠉⠀⢀⠎⠀⠱⠀⠀ ⠀⠀⠀⣼⣿⠃⣿⣿⡧⠄⠠⠤⠤⡁⠀⠀⢠⠀⠀ ⠀⠀⢀⣿⡿⡰⠹⣿⣿⡁⠀⠀⢰⠀⠀⠀⡼⠀⠀ ⠀⠀⣾⣿⡇⢣⠀⠹⣿⣧⡀⠀⡆⠀⠀⠀⠅⠀⠀ ⠀⠀⠘⢿⠀⠘⣧⣄⡀⢉⣉⣠⠁⠀⠀⠀⢰⠀⠀

⠀⠀⠀⠀⠀⠀⣀⠠⠐⢂⠎⠉⣉⣁⡂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⢀⠄⢺⠉⠀⢀⠀⠀⠁⠚⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠃⡐⠀⡠⠁⠀⡠⢃⠋⠀⠀⠩⠔⢆⢄⠈⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡌⠀⡇⠰⠁⢀⣾⣧⢘⢧⡀⠀⠀⠈⠥⢦⠡⠘⡀⠀⠀⠀⠀⠀⠀ ⢰⠈⠑⢀⡇⠃⠀⠆⢻⢠⠟⠐⠻⢢⣀⠐⠂⠅⢧⢳⠁⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⢸⣿⠀⣼⠀⢯⠠⠴⠶⠖⠀⠈⠽⠿⣧⠏⢫⡄⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠁⠘⡼⢹⠀⠘⡁⠀⠐⠂⠀⠀⠀⢸⠋⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠀⢸⡀⠀⢹⠢⣀⠀⠈⣉⡴⠁⢀⡄⠀⡇⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⡇⠀⠈⣳⡀⠸⠆⡙⠿⣿⡿⣁⣀⡾⡇⢠⠁⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠕⠫⡀⢠⠐⠄⢸⠀⠉⣩⡀⠀⢙⠊⢇⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⠀⠈⠢⡁⢺⠸⠠⣰⠧⡟⠛⡁⢸⠈⠘⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠀⠀⢀⠀⠢⣼⡣⢃⠀⠳⠠⠐⠒⢁⡈⣜⡄⠈⣆⡀⠀⠀⠀⠀ ⠀⠠⡇⠀⠀⠀⠁⠊⢉⠔⡂⠵⡄⠀⡠⡄⣿⠰⠡⠫⠱⠁⠈⡄⠀⠀⠀ ⠀⠃⠀⠉⠀⠂⠉⠉⠉⠄⠐⠕⢉⠀⠈⠁⠇⠁⢓⠖⢁⠀⡠⠁⠀⠀⠀ ⠀⠑⠤⣀⣀⣀⠀⠀⢤⠼⡀⠀⢘⠀⠀⡔⡄⠑⢠⠀⠈⢝⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣌⠐⢄⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠴⠭⢄⣛⣻⡟⠛⠀⠐⢄⠀ ⠀⢸⢠⣤⡄⢀⠤⠤⠤⠤⡤⠬⡀⣠⣄⡀⡀ ⠀⠈⠪⣢⢀⠂⢾⣿⢀⢰⣿⠆⢐⠠⡊⠔⠁ ⠸⠀⠀⠀⢈⠥⣈⠀⠀⠃⠀⡠⠜⠁⠀⠀⠀ ⠀⠄⠀⠀⠘⣄⢀⣿⣶⣞⣁⣀⡜⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⣷⢟⣟⣫⣸⣷⢾⠁⠀⠀⡰⠁ ⠀⠀⠀⠀⠀⠬⠥⠶⠤⠸⠤⠼⢇⠠⠊⠀⠀ ⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠘⠀⠂⠐⠒⠒⠒⠒⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠈⠑⠤⣽⣌⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠎⢑⣏⡠⠤⠄⠐⠒⠒⠒⠒⠸⠿⡄⢧⠙⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⠎⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⣧⢸⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠒⡄⠀⡜⡁⠀⢀⣀⡠⠔⠚⠒⠒⠒⠈⠉⠙⢧⣷⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠡⠀⡘⠀⠈⠉⠀⡔⢂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⣷⡀⠀⠀⠀⠀ ⠀⢀⠀⠄⢐⠨⠥⡢⢀⢀⣀⣈⠁⠀⠀⠀⠀⠀⢉⣀⣀⢀⣼⡋⠙⢖⠀⠤⠀ ⡀⠁⠂⠉⠀⢀⠔⠤⡈⣮⡉⠩⠅⠂⣶⣦⡄⠂⠽⠉⢩⠎⡹⠷⢎⠀⠈⠁⠂ ⠁⠀⠀⠀⡾⠀⠑⠠⠬⠕⠁⠀⣅⣀⠬⠫⠄⣀⡰⠀⠈⠃⠤⠀⠊⢈⠀⠀⠀ ⠀⠀⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠂⢀⠋⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀ ⠀⠐⠀⠀⠈⠉⠑⠒⢥⡖⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠒⣮⠅⠂⡏⠉⠀⠀⠀ ⠂⠀⣀⣀⣀⢀⠣⠒⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠉⠒⢡⠀⠀⠀⠀ ⢠⠊⠀⡠⠒⡚⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠘⡄⠀⠀⠀ ⡇⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⣷⠄⠸⠿⢽⣿⣿⣿⣿⣿⣿⣭⣝⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⣄⡌⠁⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⡄⠀ ⠀⠀⠀⠀⠀⢀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣇⡇⠀ ⠀⠀⠀⠀⢀⠊⡐⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⡇⠀ ⠀⠀⠀⢠⠂⢰⠇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⢸⣿⡇⠀ ⠀⠀⢠⣹⠀⣼⢀⣇⣉⣉⠀⠀⠀⠈⣉⡁⠀⠀⡇⠀⢠⡠⠂⠀⠙⠃⠀ ⠀⠀⡀⠉⣆⣿⠈⣯⡻⣟⡆⠀⠀⠘⣛⣯⣻⣟⠃⠀⠘⡗⠄⠀⠀⠀⠀ ⠀⠀⠐⣴⡅⢿⠄⠹⣄⡀⠤⠤⢄⠀⠀⠀⠁⡜⠀⢀⢿⡇⠀⠀⡶⡀⠀ ⠀⠀⢮⡙⣄⠬⢺⢩⣤⣤⠀⠀⠀⠑⢄⠀⢠⠁⠀⡎⢠⠁⠀⠀⡴⠐⡄ ⠀⢰⢌⠊⡇⠀⢸⠸⣿⣿⡄⠀⢰⠉⢉⠵⢿⠀⡘⢠⠿⠀⠀⣴⠇⠀⠈ ⠀⢮⠡⣰⠙⡄⠀⠆⠁⠀⠀⠀⠀⠙⠝⠀⠈⢦⣇⢸⠆⠀⠾⠁⡇⠀⠀ ⢘⡆⢀⢺⠀⡈⢆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⡸⢿⣮⠀⡈⠁⢀⡇⠀⠀ ⠘⢠⠃⡴⡆⢄⠀⠓⠦⡢⢄⠀⠀⢀⢀⠀⠀⠈⠁⠈⢄⠣⣀⠼⡇⠀⠀ ⠠⠁⠀⢀⡇⠀⠐⠀⠀⠲⡈⡇⠢⢆⠀⠀⠀⠀⠀⠠⣾⡍⠁⠤⠃⠀⠀ ⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⢃⠀⠈⠆⠀⠀⠀⠀⠀⣯⠿⠤⢛⠀⠀⠀

⠀⠀⠀⠀⠀⢀⢠⠀⠄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠁⡸⡄⠀⠀⠀⠀⠄⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠈⣓⢹⠀⡃⢅⢔⡀⢻⠐⢸⠂⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡂⢁⣈⠀⢑⠑⠊⠓⠀⠈⢙⣋⣀⢲⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡇⣧⠧⣡⣼⡇⠀⠀⠀⢀⠼⠌⢼⡊⣀⠀⠀⠀⠀⠀ ⠀⠀⡰⠇⠀⣿⢠⠠⠉⠄⠀⠀⡔⠄⢠⣤⠀⠤⠈⢢⣀⡀⠀⠀ ⢰⡐⠁⠀⠀⠉⠈⡀⠀⠈⣄⣸⡂⠄⠀⠁⠠⢄⡢⠕⣣⠏⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠁⠀⠂⡾⣻⠀⠉⠹⣻⠉⠁⠀⠀⣠⠀⠀⠀ ⠀⠸⠀⠁⠀⡤⠄⠀⠀⢠⠁⠸⣶⠤⠼⢽⠤⣤⠔⢯⠎⠀⠀⠀ ⠀⠀⠁⠀⢠⢄⠀⠤⠀⠁⠀⠀⠀⠀⠀⢤⢤⡄⠀⠀⡌⢽⣦⠆ ⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⢂⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠢⠜⡌⡆⠀⠀⣤⢶⣾⣿⣿⣷⣶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠋⠁⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣟⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣦⠀ ⠀⠀⠀⢰⠊⠰⣀⢄⠀⢈⡆⢠⠁⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇ ⠀⠀⠀⢸⣀⠀⠉⡠⠃⠈⢶⢄⠠⠀⠤⡀⠀⠀⢀⣈⠰⠥⣀⠀⠀⠀⠀⠈⣿⠃ ⠀⠀⠀⣀⡴⡍⠋⠀⠀⡰⠋⣠⣾⣴⠀⠈⠒⠈⠀⣠⡔⣄⠪⢢⡀⠀⠀⢠⣿⠀ ⠀⠀⠀⠳⠤⠃⠀⠀⢰⢁⠀⢯⣉⡽⠀⠀⠀⠀⠀⡟⠓⠺⠆⢱⣧⠀⠠⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣨⡄⠀⠀⠘⢿⠋⡲⠀⠈⠀⠉⠀⢠⢻⠀⠀⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⢱⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣞⣀⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠱⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡿⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠺⢫⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡁⠀⠀⠀⠀ ⠀⠀⠀⢀⡜⠁⠀⠀⣠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠨⣄⠀⠀⠀ ⠀⠀⢀⡎⠘⠢⡤⠊⠀⢸⡉⠢⣄⣀⠀⠀⠀⠀⠀⣀⣀⠄⠒⠉⢆⠁⢰⢳⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢻⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠸⡀⠀⠀⠀⠀⠀⣰⠿⠋⠁⠀⣹⠛⡷⠦⣄⡀⠘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⡇⠀⠀⢀⠜⠁⠀⠘⢆⠀⣽⠷⠟⠑⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠛⣿⣧⠀⠀⠀⠀⠀⠑⠦⣀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡼⢻⠁⠀⠀⠀⠀⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠉⢙⣷⡀⠀⠀⠀⠀⠀⠀⠉⠘⠒⠒⠤⠤⠖⠒⠻⡀⠈⢣⡀⠀⠀⢀⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⡶⣄⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⢀⠀⣇⠀⠀⠉⠐⠊⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⡀⠀⠀⢰⣿⠁⣀⠠⠭⠶⣦⠤⢀⣀⣀⠀⠀⠀⠀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⣀⢀⡷⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⢻⣿⠀⠀⣿⡇⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⢠⣤⣤⡀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡁⠈⠙⣿⠀⠀⣿⡇⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠹⠿⠿⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡀⠀⢿⣧⢀⣿⣿⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⡶⢾⣽⣷⢹⡇⠀⠀⠘⣿⠘⣇⣠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠿⠿⣿⣼⣧⣤⣤⣴⣿⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⡇⢰⡋⡹⠀⢹⠀⢸⣿⡋⠛⢻⡧⠄⣀⣤⡞⠻⣿⠛⣯⡿⢿⣿⡙⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠛⣁⣠⣼⣿⣅⣀⡿⢀⡞⢻⡇⠀⢀⡟⠀⠀⠹⣿⣿⡿⢿⣿⠂⠀⣹⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠈⠙⢾⣷⡏⠀⢠⠞⠉⠉⢻⠘⠟⢻⠓⠒⢻⡛⠻⣿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣞⣀⠀⠀⢀⣧⠀⠈⡆⠀⠀⠱⠀⠀⠉⠓⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡈⢟⠁⣀⣀⣀⣀⠀⠱⡀⡇⠀⠀⠀⢇⠀⠀⠀⠀⠈⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⠚⣿⣿⡛⠉⠙⠒⢧⠗⠀⠀⠀⠘⠒⠒⠉⠉⠉⠀⠈⠣⡀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡾⠒⢷⠔⠛⠦⣠⠴⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠃⠀⠀⠀⠀ ⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠀⠀⠀⠀⠀⠀⣸⠒⠒⠒⠒⠲⣶⡖⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠢⠤⠤⠤⠄⠀⠀⠠⠤⠴⠯⠤⠤⠤⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠙⠁⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⢳⡀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⢀⣠⡤⠶⠚⠛⠛⠒⠒⢤⡀⠀⠀⠀⡇⠈⣷⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢀⣤⠴⠛⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⣷⠀⠸⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀ ⡸⠉⠹⣷⡀⠀⠀⠀⡼⠃⠀⢀⣴⠟⠋⠀⠀⠲⣶⣤⡴⢿⣠⣤⣤⣄⣀⣀⣀⠀⢳⡀⡿⠀⠀⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⣧⠀⠀⢻⡛⡄⠀⡼⠁⣀⡴⠛⠁⠀⠀⠀⠀⠀⣈⡿⠃⠚⢡⡏⠉⠛⠳⢤⣀⠀⡸⢁⡇⠀⢀⡟⠀⢀⡼⠃⠀⠀⠀⠀⠀ ⠙⠳⣄⠈⡇⠘⣾⣃⣴⠋⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠈⠀⠀⣠⠖⠋⠙⠻⣧⡾⠀⠀⣼⠃⡰⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠏⠀⣧⠀⠈⢿⠁⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⡀⠀⠀⢰⢣⣾⣏⣿⣆⠹⡿⣆⡼⠃⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠠⣯⠀⠀⢸⡀⠀⠈⢷⡄⠀⢠⡾⠛⠛⠒⢦⡄⠀⢀⡼⢖⣒⣀⣿⢸⣿⣿⣿⣿⢀⡇⢹⡁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⠀⠀⢷⡀⠀⠀⠙⢶⡏⠀⣾⣿⡛⣷⣜⢦⣴⣿⣿⣿⡏⠹⣞⠛⠟⠛⣡⠞⢀⣀⡷⢊⣁⡤⢶⡶⠋⠉⢉⣲⣤⡀ ⠀⠀⠙⢄⠀⠀⠙⢦⣄⠀⢰⢿⡀⢿⣿⣿⣿⣿⠾⣇⡉⠉⠉⢁⣾⠏⠉⠉⠉⠁⣠⣾⡟⠉⣹⣯⠤⠞⠒⠈⠉⠙⢿⣿⣷ ⠀⠀⠀⠀⠑⠦⣀⡀⠈⠙⠻⡆⠹⢦⣙⣛⣋⣡⠞⠉⠛⠷⣶⣾⣧⣤⢤⣤⣶⣾⣿⠿⠒⠋⠁⠀⠀⠀⠀⠀⠀⢀⡜⠀⡸ ⠀⠀⠀⠀⠀⠀⠸⡏⢻⣒⠒⠿⣄⣤⣄⡈⠉⠀⣀⣤⡖⢋⣽⣣⣾⠷⢖⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣛⣷⠖⠁ ⠀⠀⠀⠀⠀⠀⠀⢻⣄⣹⣿⡿⢿⡟⠋⣹⣟⣯⣿⡿⠗⠛⠉⠁⠀⢰⠏⠉⠙⢆⠀⠀⠀⠀⠀⠀⠐⣯⣄⡠⠽⠛⠁⠀⠀ ⠀⠀⣀⡠⣤⡶⣲⡟⢉⣴⣯⣴⡿⠒⠉⠉⣠⠏⠉⠙⢧⠀⠀⠠⣷⢼⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⣁⣴⣯⠞⢻⡾⠋⠉⣠⡟⠁⢀⡤⢶⡏⠀⠀⠀⢸⡇⠀⠀⡿⠸⣦⠀⠀⠀⠹⣄⣀⣀⣀⣀⣼⣦⣤⣤⡄⠀⠀⠀⠀ ⠉⠉⣠⠋⠉⠙⢾⣷⣶⣾⡉⢀⣼⡿⣄⣼⠁⠀⠀⠀⢻⡇⠀⠈⠁⢠⠏⠀⠀⠀⠀⠹⣇⠀⣿⡿⢯⠰⠋⠹⣿⣷⠀⠀⠀ ⠀⠀⢧⡀⠀⠀⣸⠀⣿⠀⠉⠙⠃⠀⢿⠃⠀⠀⠀⠀⠀⢹⡟⠉⢀⡏⠀⠀⣤⣄⣀⣤⣿⣨⣯⠀⠀⢀⣤⡀⢹⠁⠀⠀⠀ ⠀⠀⠀⠉⠒⢊⣵⡖⠛⠀⢠⣾⣿⡆⢸⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⣷⡶⣾⠏⢉⣿⡼⢿⣿⡏⠀⠀⣾⡿⢁⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢳⣦⠀⠘⠿⠟⠁⢘⣆⣤⠀⠀⠀⠛⢲⣿⠀⠀⣹⣿⣨⣿⣿⣿⣿⠞⠙⠷⣄⣀⣈⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⠞⠓⠒⠖⠚⠿⣿⡗⠀⡄⠀⢀⣈⣿⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠾⠿⠯⣤⣀⠀⠀⢉⡛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣜⢷⡄⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢄⣼⠋⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⢉⣿⣿⡄⠈⢷⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢰⣇⡤⠤⠶⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⢷⠀⠸⡆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⢸⡄⢰⡇⠀⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢿⢀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⣀⣠⣾⣧⡀⢻⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠟⠢⣀⠀⢸⡴⣇⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠛⠓⠒⠒⠒⠉⠉⠉⠀⠀⠹⣿⣶⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢄⠜⠁⠀⡼⠁⠘⠦⠤⠒⠒⠛⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡼⠁⠀⠀⠀⠀⠀⠀⢾⡁⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⠤⠔⠚⡑⠢⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣼⢿⡟⠙⢷⠢⠄⣀⠀⠀⠀⠀⠀ ⠀⢀⠔⠒⠉⢁⡠⠔⠊⠁⠈⠑⠂⠭⣢⡀⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣶⢀⣾⣿⣶⡀⢀⡼⠓⠢⢄⡈⠁⠂⠀⠀ ⢀⠎⠀⠖⠉⠀⠀⠀⠀⢀⡤⠶⢤⡀⠈⢷⣤⠀⠉⠭⠥⠔⠋⢩⣷⣾⣮⡍⠉⠲⢬⡍⠉⠀⢠⡾⠁⢘⡿⠷⣏⡀⠀⠀⠀⠀⠉⠂⠀⠡ ⠎⠀⠀⠀⠀⠀⠀⣠⡒⠙⣄⠀⠀⠈⠒⠚⣿⠇⠀⠀⡄⠀⠀⠈⠻⣿⠟⠁⠀⠀⠀⡀⠀⠀⢻⡧⠚⠁⠀⠀⣀⠝⠲⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠉⠑⠒⠒⠚⠁⠀⠀⠘⢦⣄⣤⠴⠒⠉⠓⠂⢤⣀⡤⠃⠀⠀⠀⠉⠑⠒⠊⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠄⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣀⡠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⠀⠀⠀⠠⠤⠤⢤⣀⡙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠒⢉⣀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀ ⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠙⢲⣿⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣷⣖⠉⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣀⠤⠚⠁⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠈⠙⠢⢄⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠴⠒⠒⠒⠒⠤⣼⠀⠁⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠃⠀⠀⢀⠴⠊⠉⡇⠀⠀⠀⠀⠀⠀⠀⢹⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⣰⠃⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⢻⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢒⡞⠋⠉⠉⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⠀⠀⢀⣞⣀⡠⠤⠄⠒⠒⠠⢤⣉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣀⠴⠚⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⢀⠄⠀⠀⢠⠞⠁⠀⠀⠙⡤⢤⠖⠀⠁⠀⠐⠤⠤⣀⡀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⡎⠀⠀⣠⠋⠀⠀⠀⣴⠋⠀⡄⠀⠀⠀⠀⠀⠰⠞⠈⣏⠑⢦⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⡇⠀⢰⠃⠀⠀⢠⣾⣿⡀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠚⣁⣷⡀⠱⡀⠘⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣞⠀⠀⠀⡇⢀⠇⠀⠀⢠⢻⡿⠿⠋⣼⡏⢻⣦⡀⠀⠀⠀⠀⠀⠉⢩⡿⡄⢱⠀⣣⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⠉⠉⠑⢢⡀⡇⡜⠀⠀⢠⠇⠈⡇⢀⣼⠿⠒⠒⠛⢿⣦⣀⠀⠐⠒⠒⠦⠀⢰⡄⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⠀⣷⣷⠃⠀⢀⡎⠀⢐⡷⠊⠁⠀⣀⣀⠐⡄⠈⠛⠷⢶⣤⣤⣤⠀⣨⠿⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢆⠀⠀⠀⢀⠾⣿⠀⢀⣾⡇⠀⠘⣷⠀⢲⠟⠿⠟⠛⠁⠀⠀⠀⠸⠛⠛⣿⣴⠟⠀⢱⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠒⠒⠃⠀⠘⣀⡾⠻⡇⠀⠀⢹⠓⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⠀⠼⡿⢻⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⡇⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⡜⠁⠈⡆⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣣⠀⠀⠀⠸⡏⢢⣄⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⢠⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣧⣧⠀⠀⠀⣷⠀⠹⣿⣷⣦⣤⣾⣿⠟⠀⠀⢀⣼⡇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣉⣧⠀⠀⠟⢳⢄⡈⠻⢿⣿⣿⠙⢄⣀⣠⣾⡿⡇⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⠀⠀⠀⡷⢶⡉⠉⠀⢹⠀⠣⡀⢸⠸⠀⠈⠑⠒⠙⠃⠀⠀⠈⠛⣭⠛⡇⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⠲⣄⠈⢧⡀⠱⡀⠀⠀⠀⠀⢀⠾⣷⣄⣀⣀⡴⠃⢠⠇⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠳⣄⠉⠒⡿⢠⠦⠤⢴⡿⠧⢾⠷⠛⢧⠀⠀⣾⢰⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⠀⠈⢂⣴⢃⡞⠀⠀⢿⠁⠀⠈⢆⣀⣸⠂⠀⢿⠘⡄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⠀⠀⠙⢲⣿⡥⠊⣀⡀⠀⠘⠓⠔⠊⠉⠁⠀⢀⣤⠤⠧⢵⡄⠀⠀⣷⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠃⠀⠀⠀⠀⠈⠑⠢⠖⠛⠉⢠⣾⠔⠛⢄⠀⠀⠀⠀⣀⠀⢰⠚⡏⢠⠀⡨⠏⣑⣶⠏⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⠹⢤⣀⡀⠀⠀⠀⢀⣀⣀⣀⣴⠋⠠⠒⢊⡩⢷⡀⠀⠘⣏⣱⠨⡿⣀⡇⢠⢃⠜⢁⠘⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⣆⠀⠈⠡⠒⠉⣹⠀⠀⠀⠁⢰⣧⠀⠉⠉⣻⠒⠃⢰⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀ ⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠦⣀⠀⠻⠀⠀⢸⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠢⢄⣀⣀⣀⣀⡠⠤⠤⠔⣾⡏⢻⡄⠀⠀⠀⡵⠀⠀⠀⢮⣹⠆⠀⠈⢹⣆⠀⠀⠀⠣⣹⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠖⠒⠒⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⡉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠞⠉⠙⠲⠤⡄⠀⠀⠀⠘⠧⠴⠒⠚⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⠧⣄⠀⠀⠀⢰⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⢸⠀⠀⣀⡿⠤⢤⣀⡴⠲⢤⣤⡤⠒⠢⣤⢤⡴⠒⠲⢄⢑⣄⠀⠀⠀⠀⠀ ⠈⠓⠒⠚⠀⡼⠂⠁⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠈⠈⠁⠀⠀⠈⠉⠟⠛⠒⠢⡀⠀ ⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡆ ⠀⠀⠀⠀⠀⠸⣠⣤⢤⣤⣦⣴⣾⣿⡟⠋⠙⠛⠋⠈⠛⠉⠢⣄⣀⠀⡀⠀⠀⣠⠃ ⠀⠀⠀⠀⠀⢰⡟⠐⠂⢹⣿⣿⣿⣿⠁⣠⣶⠢⣴⠀⠀⠀⠀⢉⣙⠛⢿⣶⠉⠀⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⢺⣿⣿⣿⡿⣸⣿⣿⠧⢹⡅⠀⠀⢰⣿⣬⢧⣸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣷⡀⠖⣿⣿⣿⣿⡇⠻⢿⠟⠁⢸⠁⠀⠀⢸⣿⡾⢸⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣷⣤⣿⣿⣿⣿⡇⠀⠈⠉⠉⠁⠀⠀⠘⠋⠙⠒⠂⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⢀⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⢷⣶⢬⣩⠇⠀⣠⣾⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠓⠢⠤⣀⣉⣋⣥⣴⣾⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⡿⠋⠀⠙⣏⠉⠛⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡦⠔⠲⠤⠇⠀⠀⠀⠀⢠⠏⠀⠀⠈⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⡟⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⠀⢸⣿⣿⣿⣿⠒⠤⠴⠛⠚⠒⠊⡤⠀⠀⠀⠀⠀⡞⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⡏⢀⡞⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⠁⡞⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⡟⠀⢷⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⠃⠀⠈⣧⠀⠀⠀⠙⠿⠿⠷⠄⠀⡾⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠛⡏⠀⠀⠀⣹⣷⣶⣤⡤⠤⢤⣤⣤⣴⠇⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⢲⣤⣀⠈⠒⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠫⠴⣶⣿⣿⣷⠿⢷⣲⠀⠈⠢⡀⠀⠀⠀ ⠀⠀⡄⠀⠀⠀⠀⠀⠀⡞⠛⠒⠒⠒⠒⠺⠿⠷⡄⠀⠀⠀⠀⠀⠙⢆⠀⠀ ⠀⢸⣁⣀⣀⣀⣀⣀⢀⣱⠤⠤⠤⣄⢀⣠⣤⠴⣅⢀⣀⣀⣀⣀⣀⢈⠀⠀ ⠀⠸⣄⠻⡉⠉⠉⣻⠋⢠⣶⣶⡄⠀⠀⣴⣷⣄⠈⢻⠛⠋⠉⡹⠋⡸⠁⠀ ⠀⠀⠈⠑⠬⣓⣤⡇⠀⠸⡿⠿⠇⣀⡀⠿⠿⠟⠀⢀⣇⣔⣊⠴⠊⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠈⣷⣀⠀⠠⠀⠤⣤⡽⠀⠀⠄⢀⣼⠉⠀⠀⠀⠀⠀⠀⡄ ⢀⠀⠀⠀⠀⠀⢰⠃⠈⠑⠢⣄⣀⠀⢀⣠⠴⠊⠁⢸⠀⠀⠀⠀⠀⠀⠀⡇ ⠈⠀⠀⠀⠀⠀⠘⣦⣀⠀⣀⣯⣿⣿⣯⣽⢀⣀⣤⡞⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣾⣻⢹⣿⠿⣙⠾⣿⢿⣯⣿⠃⠀⠀⠀⠀⠀⡰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣍⠷⠷⣶⠛⢲⠟⠚⠁⢿⡀⠀⠀⠀⢀⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠄⠀⡾⠬⠥⠤⠶⠿⠀⠈⠧⠤⠤⠾⢧⠀⠀⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠀⣤⡄⠀⣀⠀⣀⣀⣠⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠒⠚⠉⠉⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠋⠉⢻⡿⣶⣤⣀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⢀⡾⠃⠈⢧⠉⠙⠷⣦⡀⢹⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⠁⠀⠀⠈⢷⡄⢀⡾⠟⠛⠁⠈⠻⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠹⢻⣿⣆⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⣿⠀⠀⠀⠀⠀⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠐⠀⠀⠊⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠭⢤⣄⣀⣀⣀⣀⣠⡴⢿⠁⠀⠻⡄⠀⠀⠀⠀⠀⣸⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠰⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡈⠉⠉⠁⠀⠀⠈⣇⠀⠀⠙⢦⣄⣀⣀⡴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡿⠿⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠄⣀⡀⢻⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⢀⣀⣈⣙⣲⡦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⠄⠀⢰⣷⠀⠀⠀⣼⡟⠐⠋⠁⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠛⠛⠛⠒⠒⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣶⣦⣼⣿⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠉⣉⣹⣿⠀⠀⢸⣿⡇⠀⠀⣴⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠈⠁⠹⣿⡆⠀⠘⣿⡇⠀⠀⢻⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠈⠿⣿⠿⠁⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⢠⣿⣧⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣄⡀⠹⣿⣦⣾⣿⣿⣧⣀⠀⣠⠴⣶⡒⣶⡖⠒⠒⠒⠲⣶⡒⢶⡄⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⡙⣻⣷⣽⡗⢸⣿⠀⠀⠀⠀⣿⡇⢸⣿⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠁⠀⠉⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⢷⣿⣧⣾⣯⣤⣤⣤⣤⣿⣷⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⡖⠋⣿⠀⢸⡇⠈⠹⣿⡟⠻⠿⣿⣟⣁⠀⠀⢀⣠⡿⣿⣿⡿⣿⣈⣿⣿⣿⣿⠿⢿⡿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠀⢨⣷⡼⠃⠀⣸⡇⠀⣰⣿⣿⡀⠀⠈⣻⡌⠉⠉⢻⣿⣧⣤⣿⣷⣼⣿⡁⠀⠙⣿⡆⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣁⡤⠤⠴⠶⠯⠿⠦⣴⣿⠁⣰⡏⢠⡟⠀⠀⢠⣿⣁⣀⣀⠈⢹⣿⣿⡇⠋⢻⣧⠁⣀⣀⣼⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡏⠀⠀⢠⡟⠀⠀⠉⢻⡉⠙⠛⢿⠉⠉⠉⢻⡉⠛⢷⣯⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⢀⡿⠀⠀⠀⠀⠀⢳⠀⠀⠈⡇⠀⠀⠀⢳⡀⠀⠈⠙⠲⢦⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠈⣿⢿⡟⠉⠉⠉⠉⠉⠙⠳⣄⠀⣇⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠈⡆⠠⣤⣶⣶⣶⢦⣄⡀⢸⠀⢹⠀⠀⠀⠀⠸⡆⠀⠀⣀⣀⣀⡠⠾⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡟⠋⣿⣿⣍⠉⠀⠈⠉⠻⣶⠞⠂⠀⠀⠀⠀⠛⠉⠉⠉⠉⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡷⢤⣷⣤⡽⠷⣤⠀⣀⣤⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠿⠀⠀⠀⠀⠀⠀ ⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠟⠀⠀⠘⠃⠀⠀⠀⠙⣧⣀⣀⣀⣀⣀⣠⣀⣠⡤⠴⠶⠶⠖⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠸⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠒⠄⠶⠦⠠⠀⠀⠐⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⣄⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠈⠀⠀⠁⠀⠉⠛⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡄⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⠉⠂⠀⠠⠀⠀⠀⣀⣤⣤⡶⠶⠚⠛⠛⠓⠒⠲⢤⡀⠀⠀⠀⠀⢸⡀⠀⣿⡄⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠐⠄⠀⠀⢀⢀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⡇⠀⠘⣷⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡖⠲⣶⣄⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢀⣤⣴⠟⠋⠁⠀⡀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢸⡇⠀⠀⢻⡄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⠀⠙⣿⣦⠀⠀⠀⢀⣼⠋⠀⠀⢐⣴⠟⠋⠀⠀⠀⠀⠉⠻⣿⣲⡟⢹⣦⢖⣿⣿⣶⣤⠤⠤⠤⠄⠀⠸⡇⢸⡇⠀⠀⢸⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⡀⠀⠀⢻⡅⢳⡀⠀⣾⠃⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠃⠘⠁⣸⠏⠈⠉⠙⠓⠶⣤⡀⠀⡼⠃⣼⠀⠀⠀⣸⠁⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠷⣄⠀⠘⣧⠀⠳⣼⠋⢠⣼⠟⠁⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠉⠀⠀⠀⣠⡶⠞⠛⠻⢿⣅⣰⡏⠀⠀⢸⡟⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⣿⠀⠀⠹⣿⡟⠁⠀⠀⠀⠀⠀⠀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⣴⡶⢶⣄⠀⢻⣿⣆⠀⢠⡿⠁⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⢻⡄⠀⠀⠻⣆⠀⠀⠀⠀⠀⣠⣾⣇⣀⠀⠀⠀⠀⠀⠀⢠⠴⠄⠀⠀⢰⠇⣾⣿⣧⣼⣿⣧⠈⣿⠹⣶⠟⠀⠀⠀⢨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡆⠀⠀⠘⣧⠀⠀⠀⠙⣷⡄⠀⢀⣾⠟⠉⢉⣉⠙⠷⣆⠀⠀⣠⠶⢛⣉⣭⣤⣼⡰⣿⣿⣿⣿⣿⡏⢀⡿⠀⢻⡀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣇⠀⠀⠀⢹⣦⠀⠀⠀⠈⠛⢦⣾⠁⢠⣾⣿⡟⠛⣷⣌⢳⣤⣶⣿⣿⣿⣿⡏⠙⣷⡻⠿⠿⠿⠛⣡⡾⠁⡀⢘⡷⠞⠉⣀⣤⠶⣶⡿⠋⠉⠉⠙⣶⣤⠀⠀ ⠀⠀⠀⠘⢧⠀⠀⠀⠙⢷⣄⠀⠀⠀⢠⡿⡆⠸⣿⣿⣿⣿⣿⣿⣦⣿⠁⠻⠿⠶⠾⠁⣠⣿⠛⠒⠶⠶⠛⠁⠀⣰⣿⡾⠗⢋⡿⠋⣀⣼⣯⠤⠶⠶⠾⢿⣍⣻⣷⠀ ⠀⠀⠀⠀⠀⠱⢆⡀⠀⠀⠉⠛⠶⣤⣸⡇⠻⣄⠙⢿⣿⣿⣿⠿⢋⣼⢷⣶⣦⣀⠀⣰⡿⠃⠀⠀⠀⠀⣀⣴⡾⣿⡟⣀⡠⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⡿⠛⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⣀⠀⠀⠈⣷⠀⠙⠳⢦⣤⣠⣤⡶⠟⠁⠀⠈⢉⣹⣿⡿⠶⣻⡾⠛⣿⣿⣿⣷⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⢹⣿⡛⠒⠾⢷⣀⣦⣄⡀⠀⠀⠀⢀⣀⣤⡞⠉⣡⣞⣡⣾⡿⠶⠞⣫⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣛⢩⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠈⣻⣿⣿⣿⣿⡿⠞⠋⣹⠿⣛⣻⣿⣿⠷⠾⠛⠉⠉⠀⠀⣶⠛⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣁⠀⣈⣩⠿⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡿⠛⢋⡽⠋⣠⣞⣁⡤⠾⠟⠛⣿⠿⠶⢶⡆⠀⠀⠀⠀⣤⢀⡿⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣤⠴⠚⣻⠟⣩⡾⢋⣀⣴⡿⠾⣿⣿⠋⠀⠀⠀⢀⡾⠁⠀⠀⠀⢻⡄⠀⠀⠘⢿⡟⣿⠀⠀⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠟⢁⣤⠾⠷⠾⠋⢹⡟⠉⠀⠀⣴⡿⠃⠀⣠⡴⠚⣻⠃⠀⠀⠀⠀⠀⣷⠀⠀⠀⣽⠃⢹⣼⠀⠀⠀⠀⠘⣧⣀⣠⣤⣤⣄⣠⣾⡷⣤⣶⣶⡇⠀⠀⠀⠀⠀⠀ ⠀⠙⠋⠁⣰⠟⠉⠙⠳⣿⣷⣤⣶⣿⠋⠀⢀⣿⣿⣄⢠⡟⠀⠀⠀⠀⠘⢿⡏⠀⠀⠘⠃⠀⣴⠏⠀⠀⠀⠀⠀⠈⣿⠀⠀⣽⣿⠿⣧⠠⠿⠃⣽⣿⣷⡆⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠁⣿⡟⠉⠳⠶⠿⠉⠀⣸⣾⠁⠀⠀⠀⠀⠀⠀⢻⣦⠴⠒⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⣸⣧⠀⣿⡋⠀⠈⠀⢀⡀⠀⢻⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⣀⣀⣠⠟⣀⣻⡇⠀⠀⢀⣠⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⢀⣀⣠⣾⣿⠿⣶⡟⢿⣿⣶⣿⠃⠀⠀⣰⣿⣿⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡏⠈⠁⠀⢰⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢿⣿⡏⢿⣟⣀⣠⣷⣧⡛⣿⣿⣿⠀⠀⠀⢿⡿⠃⣸⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡆⠀⠈⠻⠿⠛⠀⠈⣻⣄⣤⠄⠀⠀⠈⠙⠻⢶⡇⠀⠀⠈⣻⣿⣀⣿⣿⣿⣿⣿⡷⠋⠙⠿⣦⣄⡀⠈⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡶⠦⠤⢤⡤⠴⢺⣿⣿⡥⠄⢀⠀⠀⠀⠘⢛⡿⠒⠛⠉⠁⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⢿⣷⡤⣿⣤⣤⡼⠞⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠉⠉⠉⠉⠉⠙⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠄⠄⢤⢀⡀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣧⡴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠒⠶⣤⣄⡀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢈⣿⡿⠳⠟⠋⢻⣠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⢻⣶⡶⠛⠻⣹⡏⠉⠀⠀⠀⠉⠉⣙⣛⡛⠛⠓⠶⣾⡿⠷⠀⠀⠀⠈⠈⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡿⠁⢰⡟⠀⠀⠀⣿⡇⠀⢀⣶⣷⣤⡀⠀⢹⡗⠀⠀⠀⣿⣧⣄⣠⡀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠠⣾⠁⢸⡟⠃⠀⠀⠀⠈⠀⠀⠸⣿⣿⣿⡿⠀⠀⠁⠀⠀⠀⠛⣷⠈⠉⢻⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡏⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⣾⠇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⡄⢄⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡀⡀⠀⣿⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀ ⠀⠘⠿⣾⡇⢙⡻⢶⣄⣀⡤⠤⣴⡟⣻⠦⢤⣄⣀⣀⣤⣴⣿⡿⠉⠉⢻⣶⣇⡤⣤⣠⡾⠟⠉⠙⠻⣦⠀ ⠀⠀⠀⠀⠉⠛⢻⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏⠙⢻⣟⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⣶⡚⠋⢉⡿⠀⠀⠀⠀⠀⠀⠀⣶⡟⠁ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣾⡷⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀ ⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠⣶⠟⠀ ⠀⠀⠀⠠⣾⡇⠀⠀⣷⠀⠀⠀⠀⠀⡄⢠⡄⠀⠀⠀⠘⡆⠀⠀⠈⢿⡄⠀⠀⣀⣠⠄⠉⣁⣾⠋⠀⠀⠀ ⠀⠀⠀⠀⣙⡇⠀⣠⡇⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⢻⡄⠀⠀⠈⣿⠀⠀⣹⡟⠒⠚⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⠁⠀⣿⡇⠀⠀⠀⠀⠀⣧⠸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠗⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣧⣄⢘⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿⣄⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⢿⣄⠀⠀⣀⣠⡿⠶⢿⡄⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠀⠀⠀⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣠⡤⠶⠶⠚⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣧⠟⠉⠛⠲⠦⣄⡀⠀⠀⠀⠀⠘⢫⡥⠤⠤⠖⠚⠋⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠋⠉⠙⣦⠀⠀⠀⠀⣼⠋⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣟⠀⠀⠀⣿⠀⠀⣠⣴⡟⠒⠲⣶⣤⡞⠉⠓⢶⣶⣶⠟⠉⠛⢦⡶⣶⠞⠉⠉⠳⣆⣈⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⠓⠒⠦⠞⠀⣠⠿⠄⠀⠀⠀⠘⠈⠃⠀⠀⠀⠉⠉⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠈⠉⠸⠟⠛⠓⠶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⣴⣲⣤⣦⣤⣤⠴⢺⣀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⡶⠲⢦⣿⣷⣾⣿⣿⣿⡏⠁⠀⠀⠉⠁⠀⠈⠉⠀⠈⢳⣦⣄⡀⢀⡄⠀⢀⣠⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠰⠲⠀⣿⣿⣿⣿⢻⣿⠀⢠⣴⡷⠦⡘⠇⠀⠀⠀⢠⡌⠉⠙⠻⠿⢿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣆⠹⡗⠀⠀⠀⠀⣴⣯⡙⢧⠀⣾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⣾⣿⣿⣷⡬⠀⣿⠀⠀⠀⠀⣿⣿⢻⠸⡇⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠋⢹⣿⣿⣿⣿⣿⡇⠛⠻⣟⠁⠀⢠⡏⠀⠀⠀⠈⣿⣿⠟⠀⣧⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠘⠛⠈⠑⠒⠂⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣙⡓⠲⠬⣽⠆⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀⠸⣿⠟⣷⡴⠋⠀⢀⣴⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠓⠶⢤⣄⣈⠉⣩⣤⣶⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡿⠋⠉⠙⢿⠋⠛⠻⢿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢀⣀⠀⢀⡞⠉⠙⠀⠀⠀⠀⢨⡿⠀⠀⠀⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⡷⠶⣄⣀⡴⠿⠼⠷⠴⠞⣡⠀⠀⠀⠀⠀⠀⠠⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠇⢀⡾⠀⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣾⠁⠀⠘⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⡏⠀⢿⡀⠀⠀⠈⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃⠀⠈⣷⠀⠀⠀⠀⠙⢿⣿⣿⣿⣄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠉⠛⠛⠛⠓⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⣻⠀⠀⠀⠀⣀⣿⣿⣿⣶⣶⠒⠶⠶⣦⣤⣤⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡀⠀⠀⢠⣾⣟⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠃⠀⠀⠙⠛⠛⠲⠶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡳⣄⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠈⠑⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⡿⠙⣿⣿⣿⣿⣾⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢠⠏⠀⠀⢸⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⡞⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣯⡆⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⡁⠀⠀⢸⡼⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠒⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢹⣿⣿⡟⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⣰⠃⠀⢀⡏⡇⠀⠀⡇⠐⠒⠲⠷⠶⠶⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠋⠉⠁⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠉⠿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⢡⢿⠀⠀⢸⢳⠃⠀⣸⣇⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣷⡦⠸⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⡜⠘⡇⠀⡌⣿⠀⠀⢿⣿⡿⢿⡿⣷⣦⣅⠀⠀⠀⠀⠀⠀⠀⣮⣾⡿⣿⡷⣶⣶⣤⣴⣿⡇⠀⠀⠀⠀⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⡇⠀⠹⣆⡇⣿⡀⠀⠸⣿⣄⠉⢷⡞⠛⢻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢿⡞⠉⣹⣿⠭⣽⠀⠀⠀⠀⢰⠇⣿⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠇⢀⡼⠋⢇⢹⡇⠀⠀⣯⣏⠁⠀⠭⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠛⠿⠛⠛⢰⡇⠀⠀⠀⠀⣾⣼⢻⠀⠀⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣰⣏⣴⡟⢸⣸⣹⡄⠀⠸⡿⡄⠀⠀⣀⣀⡤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⣟⡵⣸⠀⠀⠀⠀⠀⢰⣶⢶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣳⣏⠻⠀⠈⢏⡏⢳⣀⣀⡴⠷⠚⠋⠁⠀⠀⠀⠀⠀⠈⠛⣄⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡿⢈⠇⣽⠀⠀⠀⠀⠀⠈⣧⡋⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⡼⣱⠃⡼⢳⠀⢀⣨⡧⢾⠟⢁⣀⣄⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⡟⠀⠀⠀⢀⣿⠁⠉⣸⠃⠀⠀⠀⠀⠀⠀⣿⡇⠈⢷⡀⠀ ⠀⠀⠀⠀⢸⠇⢟⡞⢀⣾⡶⠛⠁⠀⡸⡀⠘⣷⣾⠭⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⡀⠀⢀⣿⠀⠀⠀⠀⣼⡃⠀⢠⢻⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⡏⢠⠏⡰⠋⣸⠁⠀⠀⠀⢁⡇⠀⣿⣾⣍⠿⢿⡆⠀⠀⠀⠀⢰⠖⠋⠉⠁⠈⢙⣷⡿⢻⠀⠀⠀⣸⡇⠀⠠⡟⡎⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⡇⢉⡞⠁⠀⢻⡆⠀⠀⠀⠸⣧⠀⠻⣿⣧⣼⣿⣷⠀⠀⠀⠀⠘⣯⢦⡀⢀⣶⡛⠁⠹⣾⠀⠀⠀⡟⠀⠀⣿⢁⠇⠀⠀⠀⠀⡴⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡸⢁⣸⡀⠀⢠⡏⢻⡀⠀⠀⠀⠹⡄⠘⠛⠉⠀⠉⠀⠀⠀⠀⠀⠀⠘⢯⡳⠞⣻⠇⠀⠀⠺⢷⡀⠀⡇⠀⠀⡿⡾⠀⠀⠀⢀⣜⡽⠑⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⣸⢃⡞⠁⢳⣄⣾⠀⢰⢳⡄⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⣾⢻⣦⢧⡀⢀⣧⠃⠀⠀⢀⡾⠟⠁⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⡇⣸⠀⠀⠀⢹⣿⠀⡀⠐⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣾⣿⣮⣷⡀⡟⠀⠀⠀⡼⠳⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⢸⠁⡇⠀⠀⢠⠏⣿⠀⠘⢆⠀⠘⢧⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠹⣽⡿⠷⡿⣴⠀⠀⢰⠇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠸⡀⢣⠀⣰⠏⠀⢘⣇⠀⠈⠑⠦⡳⡙⢦⡀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠙⢧⣀⡴⠟⠹⡌⠀⠀⣾⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⢣⠈⣴⠃⠀⣀⡿⢹⠀⢤⡀⠀⠀⠙⠣⠙⣢⣤⠽⢦⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⣆⠀⠘⣆⠀⠀⢀⡼⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡵⠁⠀⠀⡧⡇⢸⡇⠀⠻⣍⠉⠉⠉⠉⠉⠉⠃⠁⠈⣑⣦⣄⠀⠀⠀⢠⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣤⣈⣷⡶⠛⠀⢼⠀⠀⠀⠀⠀⠀ ⠀⠀⡞⠁⠀⠀⢠⠇⡏⢸⡇⠀⠀⠉⠓⠦⣤⣤⣤⡤⠴⠒⠋⠉⢿⠈⠛⠢⣤⡞⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣺⣿⣆⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀ ⠀⡼⠀⠀⠀⠀⢸⠀⡇⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠛⡆⠀⠉⠉⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣆⠀⠘⢯⠉⣿⠀⠀⠀⠀⠀⠀ ⠸⠁⠀⠀⠀⠀⠸⡀⣇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⣿⣿⣆⣀⣾⠽⡏⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⡇⢹⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡿⠿⠛⠙⡏⠀⣤⡇⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢲⡾⠛⠛⠙⠙⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠚⠉⠁⠀⢠⡏⠀⠀⠀⠀⢀⣀⣀⡀⠈⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠁⠀⠀⠀⠀⠀⣀⣿⠴⠖⠚⠉⠉⠉⠀⠀⠈⠉⠓⠶⢦⣉⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠘⢧⣀⣤⣤⠖⠚⠛⠀⠀⠦⠤⣀⣀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⡟⠀⠀⠀⢠⡞⠁⠀⠀⠀⢀⣤⠊⠁⡍⠃⠀⠀⠀⠀⠀⠀⣤⣴⠉⢯⠒⢤⣄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⢸⡇⠀⠀⢠⡏⠀⠀⠀⠀⣠⣿⠁⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣴⠳⡄⠈⢧⡀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⠀⠀⢸⠃⠀⢠⠏⠀⠀⠀⠀⣼⣣⣿⣆⠀⢸⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⣿⣆⠀⢳⡀⠀⢳⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠀⠀⢸⠀⢀⡞⠀⠀⠀⢀⡾⢹⣿⡿⠛⢠⣇⡟⠹⡳⣄⠀⠀⠀⠀⠀⠀⠀⠘⠋⣉⣽⢦⠀⢳⠀⢸⡄⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠒⠛⠳⠤⣄⠀⢸⠀⣼⠁⠀⠀⠀⡼⠀⡸⡏⠀⢀⣾⣽⣀⡤⢽⣮⡳⣄⠀⠀⠀⢀⡤⠤⣄⡉⠁⠈⣇⠀⢧⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⠈⣷⢸⣄⡇⠀⠀⠀⣸⠃⠀⢃⡇⣠⡿⠋⠉⠀⠀⠀⠈⠙⠪⣗⢦⣀⠀⣀⠀⠀⠉⠀⠀⡟⣧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⢹⣾⣿⠀⠀⠀⢰⠏⠀⠀⣸⡋⠁⠀⠀⢀⣠⣄⣀⣙⣄⠀⠀⠉⠛⠿⣷⣶⣶⣺⠆⢠⢷⠟⣆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣄⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⣰⣿⠇⠀⠀⢹⣷⠀⠲⡾⠿⠿⠛⠿⠏⠀⠀⠀⠀⠀⠼⠟⠟⠟⣿⣤⣿⠏⠀⢹⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⠤⠤⠤⠞⠁⠈⢻⠀⣰⣻⢻⠀⠀⠀⠀⣿⢧⡀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⡇⠀⠀⠀⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡷⠁⢸⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⣧⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠘⡆⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡤⠂⢀⡴⠋⠀⠀⢸⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⠙⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⣼⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣏⣇⠀⠀⠀⠀⡾⡄⠀⢻⣿⣶⣤⣄⣀⣠⢶⣿⣿⠃⠀⠀⠀⢰⢿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⡟⣦⠀⠀⠀⢸⢳⡀⠀⠹⣿⣿⣏⣿⣿⠿⣟⠁⠀⠀⠀⣠⣻⣿⡁⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣠⣼⣦⡿⢆⠀⠀⠸⡈⣟⠒⢤⣈⠛⠛⣿⣿⡇⠈⠳⢤⣤⣾⣿⣟⢙⡇⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⣾⣍⠀⠀⠀⢸⡀⠈⢳⡀⠀⡇⢸⠀⠀⠈⠉⠓⠚⠋⠀⠀⠀⠀⠉⠳⣦⠏⢿⠇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⠳⣄⡀⠈⢷⡀⠀⢳⡀⡇⢸⠀⠀⠀⠀⠀⡸⣷⣄⠀⠀⠀⠀⣠⠏⠀⣸⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠻⣆⠀⠙⠦⣄⣳⡇⢸⠀⠀⠀⢀⣼⡇⠘⣿⣟⣲⣖⠛⠁⠀⠐⡏⢸⠇⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣸⠁⣸⠋⠙⠛⣩⡟⠋⠛⣟⠉⠉⠙⣧⠀⠀⣾⡇⢸⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢃⣴⠏⣰⠇⠀⠀⠀⣇⠀⠀⠀⠸⠄⠀⣠⡿⠀⠀⠛⣇⢸⡆⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⣶⣿⢃⡴⠃⠀⠀⠀⠀⠿⢦⡠⠴⠛⠉⠉⠁⠀⠀⣀⣀⣸⣆⢳⣄⠀⠀⠀⣻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⠷⣄⡀⢀⣤⡾⠗⠋⢀⡖⢛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⠁⣉⠍⠙⠯⢤⣄⠀⣿⠃⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣰⡿⠛⠁⣀⣹⣦⠀⠀⠀⠀⢠⣤⣄⠈⣿⢨⠃⢰⠇⠀⡔⠉⣠⠼⢿⠁⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠈⠳⢤⣄⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣾⠉⠐⠒⠋⢉⣠⠼⣷⡀⠀⠀⢹⡄⣘⡆⢼⡸⣄⡏⠀⡼⢁⠞⠁⡴⠘⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠇⠀⠀⠀⠈⠉⠉⠉⠛⠋⠉⠉⠉⠉⠉⠉⠉⣇⠀⠐⠚⢉⡤⠞⠉⢻⠀⠀⠀⠉⠉⠀⣶⡇⠀⠉⠑⠓⢺⡦⠜⠁⢸⠃⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠉⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⠙⢇⡀⠀⠀⠀⣾⠀⠀⠀⣼⠀⣠⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢠⡤⣄⠀⠙⠳⣄⣀⠘⠀⠀⠀⠹⡌⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠳⠤⣤⣀⣀⣀⣀⡠⠤⠤⠤⠐⠛⣿⡏⠀⢷⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢻⣀⡿⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠙⣌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⢛⣛⣷⣦⣄⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢋⢠⢾⣶⣿⣿⣿⣾⣿⣷⡒⣦⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠦⠤⢤⣤⣬⣭⣭⣽⣿⣇⠀⠀⠉⠁⠀⠀⠀⠙⢦⠀⠀⠀ ⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀ ⠀⠀⣿⣄⣠⡤⠤⠤⠤⢄⣀⣀⡼⠶⠒⠒⠲⠦⠤⠤⠤⡴⠶⠻⣄⣀⣀⣠⡤⠤⠤⣀⣀⣠⡄⠀ ⠀⠀⢻⡀⠸⣍⠉⠉⠉⠓⡾⠋⠀⣴⣿⣦⡀⠀⠀⠀⣴⣷⣦⡀⠈⢳⡒⠚⠉⠉⢉⡟⠁⣰⠇⠀ ⢀⠀⠀⠙⠦⣌⠳⢤⣀⣸⠁⠀⠸⣿⣽⣿⡇⠀⠀⢸⣯⣿⣿⡇⠀⠀⣷⢀⣠⠴⢋⣠⠞⠁⠀⠀ ⢸⠀⠀⠀⠀⠈⠉⠓⠺⣿⠀⠀⣀⠉⠉⠉⠀⠺⠲⡆⠉⠉⠉⢀⠀⠀⡿⠾⠖⠚⠉⠀⠀⠀⠀⢀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⢄⡀⠀⠂⠀⠒⠶⠶⠛⠀⠀⠒⢂⣠⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠸⡄⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠉⠳⠦⣄⡀⠀⠀⢀⣀⡤⠚⠉⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⢃⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢰⣛⣻⣿⣿⣏⣳⠀⠀⠀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡷⣦⣶⣾⢿⣛⡿⣟⣻⢿⣒⣶⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⡇⢿⡟⠙⣆⡟⠙⣷⠏⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣬⠽⠾⠷⣶⠛⠛⣶⠓⠚⠃⠀⣿⡀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣏⣹⣋⣀⣰⣦⣿⠀⠀⠸⣧⣀⣀⣀⣿⣧⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢨⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⣿⡇⠀⠰⠦⠀⠰⠶⣶⡶⠆⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⠀⠀⠀⠀⠀⡀⡀⣀⡀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣖⣮⠽⠿⠿⠛⠿⠿⠿⢭⣖⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠚⠉⠁⠈⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢿⡢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⣗⣢⡤⣀⣀⣀⣀⣀⣣⡀⠀⠀⠀⠀⠀⣰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠋⠉⠉⠉⠛⢦⣄⣤⠤⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣤⢶⡶⠶⣿⠾⣻⡿⢞⣿⡏⢹⠲⠶⠤⠤⠤⠴⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⡇⠀⠀⣀⣀⣠⠤⣤⠖⠛⠖⠛⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣚⣻⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣷⣟⢿⡏⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣶⣖⡒⢴⠳⠍⠁⠐⠙⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣀⡴⠋⠉⠉⢻⡋⠀⠀⢧⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⠛⡀⠀⣀⠀⢀⣀⡴⣾⠦⠞⠁⠀⠀⠀⢀⠔⠂⠀⠀⠈⠑⠂⠀⠈⠙⠲⠦⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣹⠓⠿⣚⠽⠓⣩⠞⠋⠀⠀⢀⣀⠈⠢⠀⡸⠀⣠⠆⠀⠀⠀⠀⠠⠄⠒⠋⠉⠓⢤⡀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠠⠒⣁⡤⠤⠁⠀⠀⠀⠀⠉⠉⠙⢦⠈⠁⠀⡇⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣅⡀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠞⠁⢀⣠⣤⣴⣶⣶⢶⣤⣄⠀⠈⡇⠀⢀⡇⠀⠀⣴⣿⣿⢛⣿⠟⠉⠀⠀⠈⠙⢿⣮⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣠⣾⠟⠋⠉⠙⠳⣶⣀⠈⠙⣷⡄⠹⣄⡼⠀⠀⠀⣿⣿⣿⣾⡇⠀⢰⣿⡋⣻⡄⠀⢻⣷⠘⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣼⡟⠁⢀⣤⣤⢤⡀⠈⢿⣧⣰⡟⠀⠀⠠⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⢸⣿⣿⣿⠇⠀⢸⣿⣇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡁⠀⢸⣿⣧⣤⡇⠀⢸⣿⡟⣁⣠⣴⣾⣿⣿⣿⣿⣶⣦⣬⣻⣷⣀⠀⠈⠉⠀⢀⣠⣿⣿⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠈⠛⠛⠋⠀⢀⣾⣯⣿⢿⣿⣿⣿⣥⣤⣴⣿⣿⠏⠩⣿⣿⣿⣗⠶⣶⣶⣿⣿⣿⠟⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠘⣿⡘⠿⣦⣤⣤⣤⣶⣿⣿⣿⠟⢈⡛⠿⠿⣿⣿⠿⠛⠉⣂⡓⣿⡏⢿⣿⠻⣦⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠛⠿⠿⠿⠛⠉⣼⣿⠟⠃⠀⠘⠟⢶⠆⠀⣿⡀⠿⢷⣟⠋⣶⡄⣴⡄⠀⠘⣷⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣸⡟⢻⣃⠶⠆⠿⠇⣶⠆⣠⣿⠿⣶⣾⣟⠂⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣿⠀⠘⠛⠀⠾⠇⠀⢠⣾⣿⣷⣿⠟⠋⠙⢿⣦⣄⠀⠀⠀⠀⣨⣿⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⡀⢠⣿⠋⠠⠀⠀⠀⠀⠀⠄⠈⠻⣷⣦⡀⢠⡿⠃⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⢿⣆⠀⠀⠀⣱⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠟⢁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠙⠿⣦⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣟⣫⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⠤⠭⠿⢿⠿⠶⠶⠶⠶⠶⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠁⣟⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠃⢰⣿⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢰⣿⢸⠀⣤⢶⡶⣶⢤⢀⣀⣠⡔⡅⠀⠀⣸⡃⢀⣀⣴⣆⣾⡏⠁⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠈⠋⠸⢄⡨⠏⠀⠀⠀⣠⡼⠋⠀⠙⠶⠚⠽⠙⠛⠛⠛⠻⠋⠓⠋⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠛⠛⠋⠙⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠳⠴⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡏⠀⠠⡄⠀⠀⢹⡄ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⣦⠀⠘⠲⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠉⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣼⠃⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠈⢻⣶⣾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⢠⣾⣿⣿⣿⣿⣿⡆⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⢩⡍⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠀⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠙⢿⣿⠿⠋⠀⣼⣿⣿⠁⠙⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡁⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠀⠀⠀⠀⠀ ⠀⠈⠿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀ ⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣻⣿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⠈⣿⡉⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠻⢦⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣀⣠⣤⣀⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⢁⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣿⣿⣯⣉⣉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣰⣄⡀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠀⢀⣀⣀⣀⣀⠀⠀⢠⣶⢤⣄⣤⣴⣦⣦⡴⣄⣤⣤⣄⣤ ⠘⢛⡛⠓⢛⠃⠚⡒⠓⡚⠛⢚⠛⡓⠛⠒⠛⢚⠚⡋⡗⣃⠉⠘⠚⠘⡛⠛⠘⠛⠛⠛⡚⠛⠛⢛⠛

⠀⠀⠀⠀⠀⠀⠀⣠⠰⢆⢀⡤⢒⡏⢉⠉⠙⠦⠀⠀⠁⠀⠀⠈⠙⢦⠐⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠟⠀⢸⣇⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣠⠷⠄⢢⣸⢻⡀⠇⠀⠠⠀⢀⠀⠀⠀⠀⠘⡆⠀⢸⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⢾⣥⠶⡄⢠⢷⡄⠛⠲⣆⡈⢃⡤⠷⣄⠤⠄⠺⣄⡠⣌⠉⣡⢤⢀⠠⣤⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⣰⠋⢸⠀⠓⠚⠀⡇⢸⠃⢸⡇⢸⡄⢠⡈⢧⠀⡤⢺⠀⠘⡾⠁⢸⡜⠀⢸⡇⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢳⠀⢸⠀⡆⢢⠀⡇⠀⠰⡆⡇⢸⡙⠆⢈⣾⠀⡇⠀⡇⢧⡀⣞⢸⠃⣤⠀⡟⠢⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⣶⠚⠐⠁⠘⠀⠁⠀⠀⠉⣧⠀⠑⠒⠋⠈⠒⠃⠀⠁⠀⠉⠘⠘⠺⠁⠁⠙⠒⢶⡏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣼⣿⠂⠀⡶⢲⣴⢶⡀⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡞⢳⡀⢠⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⣷⠀⣧⠀⢻⠀⢸⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣇⠈⣇⣤⣷⠟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢉⣿⠿⠛⢻⣿⡍⠙⠓⠺⢧⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠉⠉⠛⢿⣻⢦⣤⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡏⡅⠀⢠⢾⣿⣿⢄⠀⠀⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢠⡀⠀⠀⠉⣙⠛⠋⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠃⠹⠟⢀⡇⢸⣿⣷⠈⡆⠘⠿⠂⠀⠘⢧⠀⠀⠀⠀⢠⡏⠠⢿⠃⠀⠸⣾⣿⠂⠀⠘⠟⠁⠀⠀⠈⢷⣤⣄⣀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⡏⠀⠀⠀⡼⠀⠘⠛⠃⠀⣇⠀⠀⠀⠀⠀⠘⣇⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⢀⣤⠞⢋⣿⡈⣏⡇⠀⠀⠀⠀⠀ ⣿⠀⠉⠁⠀⠀⢰⠃⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢀⣹⡄⢀⣸⣄⡙⠲⠤⣄⣀⣀⣀⣀⣠⡤⠴⠖⠚⣉⣤⠾⠋⣉⣷⡼⠃⠀⠀⠀⠀⠀ ⠈⠳⣦⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⡀⠈⣹⡿⣿⡏⠙⠓⠶⠶⠦⠤⣤⣶⡶⠶⠶⠚⠛⠉⠀⠀⠀⢙⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⠛⠺⣧⣧⣿⠁⠀⠀⠀⠀⠀⢻⣏⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢰⠇⠈⣽⣆⠀⠀⠀⠀⠀⢠⡿⢿⡄⠀⠀⠀⠀⠀⢀⣠⡴⠟⡿⠀⠤⠤⠄⠀⠀⠀ ⠀⠈⣇⠀⠀⠳⡀⠀⠀⢀⣤⢤⣄⠀⠆⠀⠀⠀⠀⠀⡾⠀⠀⠹⣮⣻⠶⢤⣤⣤⣼⣷⣾⣧⢤⣤⡤⠶⢞⣫⡭⠴⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣆⠀⠀⠉⠲⢄⠸⣅⣀⡈⠃⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠘⢯⡙⠒⠒⠒⠒⠒⠾⣅⠀⠈⠷⠋⠉⠀⣀⡞⠁⣠⠤⣤⡀⠀⣴⡄⠀ ⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠉⠁⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠈⠓⠀⢀⣀⡤⠞⠋⠀⢰⠃⢠⡿⣷⣠⣿⡁⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢿⡙⠓⡖⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣍⣉⣿⠉⠀⠀⠀⠀⠀⢻⡄⠸⢧⡿⠿⠛⠓⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀

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