Genus Rana Emojis & Text

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