Frog With a Lily Pad Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣲⣒⠒⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⠍⣒⣒⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣴⣡⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣎⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠙⢿⣿⣿⣻⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣷⠟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠳⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢳⡺⠵⣶⣒⠢⠤⠤⠤⠤⠤⠤⣤⣤⡤⠤⡒⡦⠤⠤⣤⣶⣶⣾⣿⡊⠁⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢰⠃⢧⠀⠀⠈⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⡭⠛⠉⠁⠀⠀⡇⢿⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⠀⠈⢧⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠒⠉⠉⠉⢉⡶⠚⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢦⡈⡧⢤⣀⡀⠀⠀⠀⠀ ⢀⡾⠁⠀⠀⢀⡴⠊⠁⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠙⢧⠀⠀⠉⠑⠦⡀⠀ ⢸⠀⠀⠀⢰⠋⠀⠀⠀⠰⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡠⠊⠀⠀⡜⠀⠀⠀⠀⠀⠙⡄ ⠘⡆⠀⠀⢸⡀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢸ ⠀⠘⢦⡀⠈⢣⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠉⠒⠤⢳⡀⠀⠀⠀⠀⢽⡈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⠀⠀⠀⠀⢠⠟⠦⣄⣀⣀⣀⣀⣠⠔⠁ ⠀⠀⠀⣀⡤⠤⠴⣷⠀⠀⠀⠀⠀⣇⠀⠈⠑⠢⠤⣄⣀⣀⡀⠀⠀⢀⣀⣀⠤⠔⠚⢉⡜⠁⠀⠀⠀⠀⢠⠏⣠⡀⠐⡌⠙⢿⣉⠀⠀⠀ ⠀⠀⠀⢷⣷⣀⣴⣋⣧⠀⠀⠀⠀⠸⣲⡤⠤⣄⠀⠀⠀⠀⠀⠈⠀⣀⣀⠀⢀⣀⣠⠮⠄⠀⠀⠀⠀⢠⡯⠞⡗⠡⠤⢼⢄⣩⠼⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠘⠲⠼⢦⡀⠀⠀⠀⠀⠀⣄⠀⢉⠍⠱⠖⢲⠖⠙⢄⣀⡽⠟⠒⠒⠀⠀⠀⠀⠀⢰⠏⠀⠀⠛⠒⠒⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠤⢴⡆⢀⠀⠙⡧⠴⠊⠀⠀⠳⠤⠼⣇⠐⠲⡤⠤⠤⠤⠤⢤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠈⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠉⠓⠯⣍⠒⠦⣄⣀⣀⣀⡀⠀⠀ ⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠉⠉⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⣀⣠⠆⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠊⠉⠓⢶⠃⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢳⠳⣄⠀⠀⢀⡠⠮⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠈⣇⠈⠉⠉⠉⠀⠀⢠⣙⣢⣄⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⣀⣀⣀⣀⠵⠀⠀⠀⠀⠀⢰⣮⣭⣏⣽⣯⣄

⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠤⠤⠋⢁⠰⢼⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⠁⠀⠀⠀⣵⠋⠳⡜⡆⠀⠉⠓⠲⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠳⣒⢄⣀⠻⢻⣟⣵⢻⡿⣿⣦⣄⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⣖⠭⣑⠠⠰⢬⠜⠀⠈⠻⢷⣶⣤⡀⠀⠀⠈⠻⣟⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠉⠀⠀⠈⠁⠀⠀⠀⠈⠙⠻⢷⣆⡀⠀⠈⢯⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣦⣀⠀⠀⠀⠀⠐⢄⠀⠀⠁⠢⡈⠻⣦⢀⡀⢱⣀⣀⡀ ⠀⠀⠀⢀⣠⣼⣝⣿⣿⣷⣄⡘⢄⠀⠀⠢⡀⠀⠀⡰⠊⢀⡤⠞⠉⠀⠈⢳ ⠸⠿⠟⣛⡿⣿⠾⡿⣟⠿⢿⣻⢳⠃⠀⠀⢸⠀⣸⠁⠀⡌⠀⠀⠀⢀⠄⡞ ⠀⠀⠯⠵⠉⠀⣀⠸⡿⢧⢤⣀⠏⠀⠀⠀⡎⠉⢧⠀⠀⠀⠀⢀⡰⠃⡼⠃ ⠀⠀⠀⠀⠀⠘⢭⡭⢍⣉⠂⠉⠀⠀⣠⡾⠃⢀⣈⡢⠤⠄⢒⠁⢠⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠯⠬⠐⠒⠒⠒⠒⠒⠋⠀⠀⣹⣶⡿⢛⠔⣁⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢼⠍⣓⢵⠞⡡⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡲⠂⠈⠉⠉⠉⠉⠁⠖⣒⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣁⣻⣷⠀⠀⠀⠀⠀⠀⠀⢰⣇⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠿⠿⠏⠀⠀⠀⡀⠀⠀⠀⠈⠻⠿⠟⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠂⡼⠉⠛⠡⠶⠶⠶⠶⠶⠚⠙⡲⠖⠛⠻⠃⠈⢂⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⢰⣁⡘⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢄⠀⡆⠀⠀⠀⠀ ⢠⠊⠁⢀⠔⠉⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠑⢏⠁⠐⠄⠀ ⢃⠀⢰⠁⠀⠀⠢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠊⠀⠆⠀⠀⠀⢱ ⠈⠢⡀⢂⠀⠀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⡜⠀⠀⠀⠀⣸ ⠀⠀⡀⠭⢧⠀⠀⠸⡈⠐⠤⠀⣀⣀⠀⣀⡀⠠⠐⡘⠁⠀⠀⡔⣈⠡⠒⣖⠈⠀ ⠀⠀⠻⠔⣇⣆⠀⠀⠙⠒⠢⠤⢀⣀⡠⡀⢤⣤⡚⠂⠀⠀⡜⠋⢍⣀⠗⠒⠁⠀ ⠀⠀⠀⠀⠀⠈⢑⠠⣆⡀⢹⠃⠂⠈⠢⢻⣑⡢⠀⠠⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣲⣂

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟥🟥🟥🟥🟥🟥🟥⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🏽🟥🟥🟥🟥🟥🟥🟥🟥🟥🏽⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🏽🏽🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏽⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🌫️🌫️🌫️🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🌫️🌫️🏽⬛⬜⬜⬜ ⬜⬜⬜⬛🌫️🌫️🌫️🌫️🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🌫️🌫️🌫️🏽⬛⬜⬜ ⬜⬜⬛🌫️🌫️🌫️🌫️🌫️🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🌫️🌫️🌫️🏽⬛⬜⬜ ⬜⬛🟥🟥🏽🌫️🌫️🌫️🌫️🟥🟥🟥🟥🟥🟥🟥🟥🟥🌫️🌫️🌫️🏽🟥🟥⬛⬜ ⬜⬛🟥🟥🟥🌫️🌫️🌫️🌫️🌫️🟥🟥🟥🟥🟥🟥🟥🟥🌫️🌫️🌫️🏽🟥🟥🟥⬛ ⬛🟥🟥🟥🟥🌫️🌫️🌫️🌫️🌫️🌫️🟥🟥🟥🟥🟥🟥🌫️🌫️🌫️🌫️🏽🟥🟥🟥⬛ ⬛🟥🟥🟥🟥🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🏽🟥🟥🟥⬛ ⬛🟥🟥🟥🟥🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🏽🟥🟥🟥⬛ ⬛🟥🟥🟥🟥🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🏽🟥🟥🟥⬛ ⬛🟥🟥🟥🟥🌫️🌫️🌫️🌫️🌫️🏽⬛⬛⬛⬛⬛⬛🏽🌫️🌫️🌫️🏽🟥🟥🟥⬛ ⬜⬛🟥🟥🏽🌫️🌫️🌫️🌫️🏽⬛🟧🏻🏻🏻🟧🟧⬛🏽🌫️🌫️🏽🟥🟥⬛⬜ ⬜⬛🟥🏽🌫️🌫️🌫️🌫️🏽⬛🟧🏻🏻🏻🏻🏻🏻🟧⬛🏽🌫️🏽🏽🟥⬛⬜ ⬜⬜⬛🌫️🌫️🌫️🌫️🏽⬛🟧🏻🏻🏻⬛🏻🏻⬛🏻⬛🏽🏽🏽🏽⬛⬜⬜ ⬜⬜⬜⬛🏽🏽🏽🏽⬛🏻🏻🏻🏻⬛🏻🏻⬛🏻🟧⬛🏽🏽⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🏽⬛🟧🏻🏻🏻🏻⬛🏻🏻⬛🏻🟧⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟧🏻🏻🏻🏻🏻🏻🏻🏻🏻🟧⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟧🏻🏻🏻🏻🏻🏻🏻🏻🏻🟧⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🏻🏻🏻🏻⬛⬛🏻🏻⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🏻🏻🏻🏻🏻🏻🟧⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟦⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟧⬛🟦🟦⬛🟧🟧🟧⬛🟦⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛🏻🏻⬛🟦🟦⬛🟧🏻🏻⬛🟦⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🏻🏻🏻🟧⬛🟦🟦⬛🟧🟧🟧⬛🟦⬛🟧🏻⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🏻🏻🏻🟧⬛🟦🟦⬛⬛⬛⬛⬛⬛🟦⬛🟧🟧🏻⬛⬜⬜⬜ ⬜⬜⬜⬛🟧🏻🟧🟧⬛🟦🟦⬛🏽🌫️🌫️🌫️🌫️⬛⬛🟧🟧🟧⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛🏽🏽🌫️🌫️🌫️🌫️🌫️⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🏽🏽🏽🏽🌫️🌫️🌫️🌫️🌫️🌫️⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛🏽🏽🏽🏽🌫️🏽⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟫🟧🟧🏿⬛⬛⬛⬛⬛⬛🏿🟫🟧⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟫🟫🟫🟫🟫🏿🏿⬛🏿🏿🟫🟫🟫⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🏿🏿🏿🏿🏿⬛🏿🏿🏿🏿🏿🏿⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡟⠿⣿⣿⣿⣿⣿⣿⠿⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⢨⣿⠀⠀⠀⠉⠉⠁⠀⠀⣿⡁⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⡶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠿⠛⠛⠛⣿⡟⢀⣠⣤⡤⠴⠶⠶⠶⠶⠶⢤⣤⣄⣀⠙⣿⠛⠛⠛⠿⣿⣿ ⣿⡟⠀⠀⠀⠀⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⡇⠀⠀⠀⢹⣿ ⣿⣿⡀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⣿⣿ ⣿⣿⣷⡀⠀⢀⣿⠁⠠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠦⠀⢿⡆⠀⢀⣾⣿⣿ ⣿⣿⣿⣿⣆⠘⠳⣦⣄⠀⠙⢷⣄⠀⠀⠀⠀⢀⣾⠟⠁⢀⣴⠾⠋⣰⣿⣿⣿⣿ ⣿⣿⣿⡿⠟⠓⠀⠀⠹⣷⠀⠈⢻⣆⠀⠀⢠⣿⠃⠀⣰⡟⠁⠀⠚⠻⢿⣿⣿⣿ ⣿⣿⣥⣄⠀⠀⠀⠀⠀⣿⠀⠀⠈⢿⣤⣤⣾⠃⠀⠀⢿⡄⠀⠀⠀⠀⣠⣤⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣶⣾⣏⣀⠀⣀⣸⣿⣿⣟⣀⡀⣀⡘⣷⣶⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⣓⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠿⠞⠛⠉⠉⠉⠉⠉⠙⠛⠲⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡶⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⠿⠃⠀⢸⡇⠀⠀⠀⠀⣸⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⠀⠀⢀⣼⠃⠀⠀⠀⢰⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠛⠁⠀⠀⠀⣠⠟⠀⠀⠀ ⠀⠀⣠⣴⠖⠛⠉⠉⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀ ⠀⣾⠋⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⣿⡀⠀⠀⠀⣰⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢦⣀⢠⡟⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠉⠉⠓⠒⠒⠒⠲⠶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢠⡟⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠈⠙⠻⢦⣄⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⠦⠤⠼⠀⠙⠷⣄⡀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⣴⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠞⢻⡇⠀⠀⠀⠀⠀⠀⠙⠳⢤⣠⡤⠾⠞⠛⣿⣟⡀⠀⠀⠀⠀⠀ ⠘⢧⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡋⡉⡙⠛⠲⢦⣄ ⠀⠈⠻⣦⣀⠀⠈⠙⠳⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⣯⣤⣈⠙⠳⣍⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⠍⠉⠙⠛⠋ ⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⡀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠛⠛⠯⣝⣓⠛⠁⠀⠀⠉⠙⠓⠲⠶⠒⠛⠓⠒⠲⠶⠭⠿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠶⠶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⣴⠶⠦⣤⣀⡀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢦⣄⡀⠙⢦⡀⠀⠈⠉⠓⠲⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

₊ ⊹🦢₍ᐢ. .ᐢ₎🪷⊹ ࣪ ˖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠦⢤⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠖⠛⠉⠉⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡀⠀⠀⠈⠳⣄⠀⠀⠀ ⠀⣠⠋⠀⠀⢀⣤⣤⡀⠀⠀⠙⢦⠀⢀⣀⣀⣀⣀⣤⣤⣤⣄⣠⡏⠀⠀⢠⣾⣿⣿⣷⣄⠀⠀⠘⣆⠀⠀ ⢰⠃⠀⠀⣴⣿⣿⣿⣿⡆⠀⠀⠘⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⢸⠀⠀ ⢻⡀⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⢀⡟⠀⠀ ⠈⢳⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠁⠀⠀ ⠀⠀⠙⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⢿⣦⠀⠀⠀⠀⠀⢀⡤⠤⠦⢤⣀⠀⠀⠈⢣⡀⠀ ⠀⠀⣼⠁⠀⠀⢀⣠⠶⠒⠒⠶⡄⠀⠀⣼⡿⠁⠀⠀⠈⢻⣧⡀⠀⠀⢰⡇⠀⡀⠀⠀⠈⢳⡀⠀⠀⢳⡀ ⠀⢰⠇⠀⢀⠖⠉⠀⠀⠀⠀⠀⣿⠀⢠⣿⠇⠀⠀⠀⠀⠈⢿⣧⠀⠀⠈⠳⣀⠀⠀⠀⠀⢀⡷⠀⠀⠈⣧ ⠀⣾⠀⠀⡟⠀⠀⠀⠀⠀⢀⣴⠋⠀⢸⣿⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠈⠉⠓⠒⠒⠋⠁⠀⠀⠀⣿ ⠀⢹⡄⠀⠙⠲⠤⠤⠴⠖⠋⠁⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃ ⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀ ⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣀⣠⡤⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡛⠋⠙⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣤⡤⠶⠟⠃⠀⣀⣀⣤⣽⡦⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠟⠉⠀⠀⠀⠀⠀⢚⣽⡶⣶⣬⡹⣦⠀⠋⠙⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣄⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢹⣷⢸⣧⡀⠀⠀⠀⠁⠉⠉⠙⠛⠛⠳⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⣷⠦⣤⡀⠀⠀⠻⣿⣿⣿⠿⣋⣾⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠳⢦⣍⡛⠲⢦⣌⡙⠛⠛⢻⡃⠾⠽⣏⠛⠛⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⡗⠢⢤⡉⠓⠤⢼⣷⣤⡴⠋⠀⠀⠀⠈⠻⢿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠈⠑⠢⠤⠤⠌⠁⠐⠒⠤⠀⠀⠀⠀⠉⠛⠻⢿⣿⣶⣦⣄⠀⠀⠀⠀⠈⠻⣿⡟⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠙⠻⣿⣦⣄⠀⠀⠀⠀⠙⢿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠉⠒⢄⠀⠙⠻⣷⣄⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⣄⠀⠀⠘⡄⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠑⡄⣀⡴⠛⠉⠙⠒⣤⡼⠖⠛⠛⢷⣦⠀ ⠀⠀⠀⠀⠀⢀⣠⣶⣾⢻⣿⣽⣞⣯⣻⣿⢷⣄⣀⠙⢦⡀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢠⡞⠉⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⢹⡆ ⠀⣾⣟⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢶⣽⡆⠀⠀⠀⠈⢷⠀⠀⢠⡏⠀⠀⠀⡸⠋⠀⠀⠀⠀⠀⠀⢠⠄⣾⠀ ⠀⠛⠛⢋⣠⡴⣿⣯⡿⠛⠉⢿⣬⣷⣍⠙⠛⠻⣦⡟⣼⠋⠀⠀⠀⠀⠀⣞⣀⣠⣾⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡴⠃⣰⡟⠀ ⠀⠀⠰⣿⣹⣿⠏⠁⠀⠀⠀⠀⢿⣯⣿⣇⣤⣄⠀⢰⡏⠀⠀⠀⠀⠀⢸⠋⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⡿⠁⠀ ⠀⠀⠀⠈⠉⠀⠀⠀⠀⣶⠶⢦⣬⣭⣥⣿⣄⡙⠷⠟⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⣴⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣒⠶⠤⣤⣄⡠⠁⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⢀⣠⣄⣹⠷⠶⠶⠾⠉⣁⠃⠀⣠⣾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⣛⣉⣁⣀⣤⣤⣤⣤⣤⣤⣴⡿⠛⠀⠀⠀⢸⣯⣩⣷⣿⣿⠆⣀⠔⠁⣀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡴⠟⡻⠟⣉⣴⠞⢁⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣸⡷⠼⠒⣩⣴⡿⠓⢡⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⣩⡶⠶⠛⠉⠘⠷⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠺⡆⠀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⣤⣼⣿⣶⡏⠀⢀⣠⣾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡷⠦⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⢺⣦⣤⣞⠁⠀⠀ ⢶⣤⣼⣦⡟⢸⣿⣦⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠲⠷ ⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⣀⠀⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠋⠁⠀⠙⢿⣆⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⠈⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣴⣇⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠋⠉⠛⠒⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠋⠟⠉⠉⠉⠓⢤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠊⠁⠀⠀⠀⠀⢀⡀⠀⠀⠉⣶⠀⠀⣀⣀⣀⡀⢀⣀⣀⣴⠋⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠱⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣀⠈⠋⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣦⡄⠀⠈⢳⠀⠀⠀ ⠀⠀⠀⠰⡏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡄⠀⢺⡇⠀⠀ ⠀⠀⠀⠈⣧⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⠳⡶⢞⠫⣍⠹⠳⠶⣦⠶⠀⠈⢿⣿⣿⣿⣿⣿⡿⠀⠀⣼⠆⠀⠀ ⠀⠀⠀⠀⠘⢦⡴⠀⠀⣀⠉⠙⠛⠛⠛⠁⢠⡀⠀⠀⠀⣟⠤⡓⠬⡱⣉⠖⣿⠀⠀⠀⠀⠉⣛⠛⠛⣋⡀⠀⠀⣾⠂⠀⠀ ⠀⠀⠀⠀⣰⠏⠁⠀⠀⠘⣆⠘⢦⡀⠶⡄⢨⠹⡄⠀⠀⣿⠢⡝⢢⠱⣌⡚⣷⠀⠸⡏⢲⡀⢌⠳⣄⢠⠙⣄⠸⢿⠀⠀⠀ ⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠘⣆⡌⢳⣲⠙⢬⡅⢻⡀⠀⢻⡅⢇⣣⠟⣤⢛⡯⠀⠀⢳⠀⠹⣜⣆⠘⢦⣇⠈⢣⠘⣧⠀⠀ ⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠙⠀⠀⠀⠀⠉⠀⠘⢯⣎⣵⢫⣴⡿⠁⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⣦⠀ ⠀⢠⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡄ ⠰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯ ⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋ ⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀ ⠀⠀⠀⢳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⢧⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⠶⢤⣀⣤⣤⣀⣀⣀⡤⢀⣀⣠⣤⡤⠴⠖⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⢤⣙⠻⠶⣤⣤⣄⣒⣀⠀⠀⠉⠉⠒⠂⠰⠶⣽⠦⣤⣄⣀⠀⠀⠹⣷⠘⡆⠀⡇⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⡾⢠⡾⠛⢛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣤⣀⡉⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣈⠻⣿⣦⡀⠹⣇⢻⠀⢱⠸⣿⣷⠀⠀⠀⠀⠀⢀⡾⢠⡟⠀⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠉⠙⠓⠂⠒⠀⠰⠤⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠐⠒⠛⠋⣩⠿⠛⣋⡽⠳⣌⢟⢷⡄⢹⡼⣇⢿⣄⢻⣿⡆⠀⠀⢀⠀⣼⢣⡟⢀⡾⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠞⢡⣴⣾⣏⣁⣄⡘⠏⠃⡙⣦⣿⣿⣯⣿⣦⡿⣧⣇⢷⣸⣼⢃⣾⢞⣤⣾⣿⣯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⡤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⣫⣞⡽⠃⢠⡿⠃⠀⣀⣩⠿⠿⠿⠞⣿⣿⣮⣛⢿⡜⠹⣇⠻⣿⡟⣿⣣⠟⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣞⢋⣡⡾⣿⣿⠁⣰⣟⣷⠞⣛⡿⠃⠀⠀⠀⣰⣿⠀⠀⠀⠀⠃⠀⠀⠀⠈⠃⣿⣿⠿⠛⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡧⠄⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣻⡿⠋⢁⣾⠃⡿⢰⣿⡿⠵⠚⠉⠀⠀⠀⠀⢸⡏⢸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢻⠇⠐⠠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⣶⡴⠶⠛⠛⢉⣴⣿⣯⠀⠀⢸⠃⢰⡇⣼⢟⠓⠒⠤⠔⠒⠒⢦⡀⠘⢦⢸⣧⡀⠰⢤⣀⠀⠀⠀⣼⠀⣸⣿⣟⢦⢻⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⠀⠀⠀⢀⡴⠛⠉⠀⠀⣠⣶⣿⣿⠟⠋⠀⠀⣿⢰⣿⣱⠿⡟⣆⠀⠀⠀⠀⣾⣳⣧⠀⠈⢷⣿⢿⣦⡀⠉⢳⡄⢠⡇⠀⣿⣿⠸⢸⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠇⠀⠀⠀⠉⠀⢀⣠⣴⠿⢛⣽⡿⠗⠀⠀⠀⠀⣿⠸⣧⠏⠀⢳⡞⢧⡀⠀⢀⡇⠙⣿⠀⠀⠀⢻⣿⣿⣿⣦⢀⣿⡼⡇⠀⣿⣿⠀⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠃⠀⣀⣤⡶⠟⠋⠁⠀⢠⣿⠟⠀⠀⠀⠀⠀⢠⡇⢸⠝⠀⠀⠀⢹⣿⢁⣤⠞⠀⠀⠻⡀⠀⠀⠈⣿⣯⡈⣿⡿⣿⣇⡇⢀⣿⡏⢠⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣾⣯⣥⣄⠀⠀⢰⡾⠋⠀⠀⠀⠀⠀⠀⢠⡿⠀⣾⠀⠀⠀⠀⣼⡷⠋⠀⡠⠂⠀⠀⠱⣄⠀⠀⠸⣿⣿⡟⠳⡌⣻⣧⣿⣿⠃⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣿⡀⠀⠀⠀⠀⠀⠀⢀⡿⠁⣼⠃⠀⠀⠀⢰⡟⠁⢠⠎⠀⣰⠀⢰⠀⠘⢦⡀⠀⠈⠻⣧⠹⡏⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⢹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⢀⡾⠁⣼⠏⠀⠀⠀⠀⣿⣄⣴⠇⠀⡴⠃⠀⡮⠞⡄⢀⠙⣦⡀⠀⢸⠀⠀⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣼⠃⣼⠏⠀⠀⠀⠀⣼⠁⡸⠁⢳⠞⡇⢀⡞⠁⡰⠋⣸⡤⠘⣿⢦⣸⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⢿⣿⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣼⡏⠀⠀⢀⡤⠞⠃⣰⠃⢠⠏⠀⣩⠻⣄⣴⠃⢠⠋⢰⡀⣼⣀⡿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠧⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⢻⣧⠀⢰⡿⣄⠀⠜⠁⡰⠋⣠⡾⠁⠀⡼⠧⣤⠏⢀⡎⢡⡿⢋⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠰⣦⠹⣷⡾⠃⠈⡇⠀⠚⠡⠞⢡⠇⣠⡞⠁⣠⠟⠆⣞⢠⠞⠀⠀⠙⢦⡄⠀⢸⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣧⣿⣿⣶⣿⣿⡄⢀⡇⠀⠀⠀⠀⠾⠚⣹⡥⢚⠏⢠⠞⣹⡁⠀⠀⠀⣶⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡋⢿⣏⡀⠀⠀⠀⠀⠀⠀⠉⠀⣾⠀⡏⡴⣧⣹⡇⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡴⠿⠥⣬⣿⣷⠤⠤⠤⡄⠀⠀⠀⠀⠀⠘⢰⡇⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⢩⣶⢽⣗⣆⠀⢧⠀⠀⠀⠀⠀⢀⡼⢃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣆⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣷⢰⣿⣞⡆⠈⡇⠀⠀⠀⢰⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣶⣿⣿⣷⣶⣿⣿⠇⠀⠀⠈⠀ ⡇⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⣆⠀⡇⠀⠀⢠⠏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣆

⣿⣿⣱⣿⠁⣼⣿⣿⣿⣼⣿⣿⣿⣿⡇⢸⣿⣷⡀⠀⠙⢿⣿⣿⣿⣸⡟⠀⠙⣆⠹⣿⣿⣎⢷⣆⠀⠀⠀⠉⣻⣿⡿⠛⣿⣿⣿⣿⣿⣿⡿⢿⠻⢻⡐⢻⣿⣿⣿⡋⠘⣿⣿⣿⣿ ⣿⢇⡿⠁⣸⣿⣿⣿⢻⣿⣿⡿⠿⣿⣷⠀⣿⣿⣿⣦⡀⠀⠙⠻⣿⣷⡅⠀⠀⠈⢣⡙⢿⣿⣌⢿⣷⣤⡀⠀⠛⠛⠀⠺⣿⣿⣿⠟⠽⠋⠀⢈⣧⠘⣷⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣼⠃⢸⣿⣿⣿⣿⣸⣿⡇⠱⠀⢹⡿⠇⢻⣿⣿⣿⡏⠳⣄⠀⠈⠁⠸⣦⡀⠀⢰⡹⣄⠻⣿⣎⢿⣿⣿⣦⡀⠀⠀⣰⡿⠏⠁⠀⠀⠀⢀⣿⣿⣷⡈⢷⡄⠘⣿⣿⣿⣿⣿⣿⣿ ⣟⠏⢀⡟⠉⢻⣿⣿⣿⣿⣿⣆⠀⠀⢹⣆⠈⣿⣿⣿⠃⠀⠈⢷⣤⡀⠀⠹⣿⣦⣸⣧⠹⣷⣝⢻⣮⢻⣿⣿⣿⣦⣞⠉⠁⠀⠀⠀⠀⢀⣾⣿⠿⣫⣿⡌⢿⣄⠘⣿⣿⣿⣿⣿⣿ ⡇⠀⣾⠀⠀⢸⣿⠃⣿⣿⣿⣿⣷⡀⠀⢻⣆⠹⣿⣿⣧⠀⠀⠈⠸⣿⡄⠀⠈⠻⣿⣿⣆⢿⣿⣧⡙⢷⣻⣯⣻⣎⡙⠷⣄⡀⠀⠀⠀⠸⢟⣥⡿⠟⢿⣿⣆⢻⣦⠼⣿⣿⣿⣿⣿ ⠀⢰⠗⠶⠤⣼⣿⢸⠈⣿⠻⣿⣿⡳⡄⠀⢻⣦⢿⠻⢿⣧⠀⠀⠀⠙⡇⠀⠀⢦⣌⠻⣿⣾⣿⣿⣿⣦⡻⣿⣿⣿⣿⡦⣌⠙⠦⡄⠀⠀⠀⠁⠀⣲⣿⣿⣿⣿⢻⡆⠸⣿⣿⣿⣿ ⠀⣸⣤⡀⠀⢸⣿⣸⠲⣿⣤⡈⠛⢬⠀⠀⠀⢻⣎⠄⠈⢿⣧⠀⠀⠀⣧⠀⠀⢸⠀⢻⣮⡙⠿⣿⣿⣿⣿⣾⣻⣇⠀⠹⣎⠛⢦⣀⣀⣠⣤⠶⠚⠻⣿⣿⣿⣿⣷⣻⡆⢻⣟⣿⣿ ⡆⣿⣿⣿⣷⣸⣿⣿⠀⢸⡏⠻⢷⣦⣁⡀⠀⠀⢻⣆⠀⠈⢿⢷⡀⠀⠹⢄⣰⡇⠀⠈⣿⣿⣷⣬⣻⢿⣿⠋⠀⠙⢦⣀⣼⣷⣾⣿⣯⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡽⡄⢻⣿⡻ ⢁⣷⣌⠉⠋⠉⣿⢻⣄⠘⡇⠀⠀⠙⠻⣿⣶⣤⡀⢻⣆⠀⠈⢿⢿⡄⠀⣦⣿⠁⠀⠀⠹⣿⡿⠉⠿⣟⠛⢲⢦⣶⡿⠿⠛⠉⠙⢷⡁⢙⢶⣄⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⡄⢿⡷ ⡜⣿⣿⡶⠖⠒⢻⢺⠻⠿⢿⣦⣤⣀⠀⠀⠙⢿⣿⣷⣿⣆⠀⠈⠫⢻⣦⡀⡟⠀⠀⠀⠀⢿⡇⠀⢀⣽⣶⣿⡿⠋⠓⢤⣈⣿⣶⠶⠻⣟⠛⠛⠛⢛⠛⢳⡖⠂⠹⣿⣿⣿⣿⡈⢿ ⢳⣿⢻⣄⠀⠀⠘⣾⠀⢀⣴⠗⠾⢯⠻⢿⣶⢤⡈⠙⠿⣿⣶⣤⣀⠰⡄⢹⡇⠀⠀⣀⣀⣨⣿⣶⡿⠿⠛⢇⣀⣴⠶⠋⣩⠖⠉⠉⢲⡈⠳⣄⠀⠀⢠⣞⡟⠁⠀⠈⠻⣿⡿⣷⡈ ⢸⣯⢻⠻⣧⡀⠀⢿⡀⢸⡇⠀⠒⢸⡇⠀⠈⠓⢮⡷⢤⡀⠈⢿⠻⠟⣩⠿⠻⢦⡐⣛⣩⡽⠏⠉⣀⣠⢖⡿⢫⡀⠀⠀⢧⡀⠈⠀⣸⡇⠀⠈⠃⣴⡿⢿⣷⣤⣄⠀⠀⠈⠉⣩⣿ ⡎⣿⣎⢧⠈⠻⠶⣼⣇⣀⣙⠒⠒⡋⣀⣀⣀⣀⠀⠈⠧⠙⠷⠬⢷⡞⢁⠀⠀⠀⠙⢦⡉⠀⠀⠰⡟⡱⠋⠀⠀⠤⣄⣀⣀⣙⣛⣛⣋⣀⡤⠴⠛⠁⠀⠈⣿⣿⣿⣷⡄⠀⣰⡟⠁ ⡇⣿⣿⣞⡆⠀⠀⠀⢿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠙⢦⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠹⣿⣿⣶⣿⠀⠀ ⣧⣿⣿⣏⣟⣆⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠱⣄⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣼⡟⣿⡿⠀⠀ ⡸⣿⣿⣿⠈⢿⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢰⡿⠁⣿⡇⠀⠀ ⣧⢻⣿⣿⠄⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⣇⣀⣿⡇⠀⠀ ⣿⣧⣿⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣸⡿⣽⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⡿⠁⣼⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣧⣾⣀⣼⣿⣿⡇⠀⠀⢀ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⢿⣿⣿⣿⣿⡇⠀⠀⠸ ⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⡆⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠙⠿⠻⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⡤⠆⠀⠀⠀⠀⢠⡿⢿⣷⣶⣈⠉⢹⢿⠇⠀⠀⠀ ⡋⣿⣿⣿⣿⣯⠞⣷⡀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠉⠙⠻⠒⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠟⣿⢛⣿⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠟⢠⣿⣿⣿⣿⣳⡎⣸⠀⠀⠀⢰ ⠅⢹⠿⣿⣿⣿⣀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣧⣎⣷⣶⡦⣤⢤⣤⣠⣀⣀⣀⣀⣀⣀⣀⣠⣷⣦⡴⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣰⢿⡏⠁⣿⣟⣹⡿⣿⠀⠀⠀⠈ ⠀⠈⣀⣿⣿⣿⣿⣷⠀⢻⡄⠀⠀⠀⠀⠀⠀⢻⣹⣿⡿⠃⣾⣿⡿⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣧⠸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⡼⠃⣾⠁⠀⡿⣷⢸⠃⡏⠀⠀⠀⠀ ⣦⡾⣻⡿⠋⢿⣿⣿⣦⡀⠘⣦⠀⠀⠀⠀⠀⠈⣿⣿⠃⢰⠃⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⣴⠟⣠⠟⠁⢠⠏⠀⠀⡇⠸⣸⠀⡇⠀⠀⠀⠀ ⣫⠞⠉⡇⠀⣼⣿⣿⣿⣿⣦⡈⢷⡀⠀⠀⠀⠀⠹⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣿⠀⣼⠏⠀⠀⠀⠀⠀⢀⡾⣫⡾⠃⠀⠀⣾⠀⢀⡇⡇⠀⣿⠀⣷⠀⠀⠀⠀ ⠃⠀⠀⡇⢠⡿⢿⣿⣿⣿⣿⣿⣶⣽⣆⠀⠀⠀⠀⠹⡆⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢠⠏⠀⠀⠀⠀⠀⣰⣯⣾⠋⠀⠀⠀⣸⢿⠀⢸⢷⠇⠀⣿⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⡇⠨⢻⡜⢿⣿⣿⣿⣿⣟⠳⣄⠀⠀⠀⠹⣄⡀⠙⠦⢤⣀⣀⣀⣀⣀⣠⣤⠴⠿⠛⣴⠏⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⢸⡟⢸⡀⡞⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⡇⣼⢁⣤⣌⢻⡈⠻⣿⢿⣾⣿⣷⣝⣦⠀⠀⠀⠹⣿⣄⣀⡀⠈⠉⠉⠉⠉⠀⣀⣀⣠⣾⠋⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⢸⠃⠈⣧⡇⠀⠀⠀⠈⠁⢸⡄⠀⠀⠀ ⠀⠀⠀⠇⣿⣿⠁⠈⠻⣧⠀⠉⢾⣿⣿⣿⡿⢿⣷⣄⠀⠀⠛⠃⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠃⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⢠⡏⠀⠙⣿⠃⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀ ⢰⠇⠀⠀⣷⡇⠀⠀⠀⠘⣇⠀⠀⠙⠄⠏⠁⠀⠙⣿⣷⣄⠀⠀⠀⠀⠐⠲⠶⠒⠒⠋⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢿⠦⠀⠀⠀⢠⢟⣾⡇⠀⠀⠀ ⡟⠀⠀⠀⣿⠃⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢲⡾⠁⠀⠀⠀⣼⠀⠀⠀⣠⢯⡎⠘⡇⠀⠀⠀ ⠀⡀⠀⠸⣿⠀⠀⠀⣰⡿⠁⢹⡀⠀⠀⠀⠀⠀⠀⠰⠻⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡟⠀⠀⢀⣿⠏⠠⢄⣇⠀⠀⠀ ⠀⢹⠀⠀⡇⠀⠀⣸⣿⠷⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣤⣴⣾⠋⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢱⡀⠀⠀⡏⠀⢀⣿⠟⠀⠀⠈⢻⣦⡀⠀ ⠀⠀⢀⠀⢠⠀⢀⣿⡇⠞⣰⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢘⠀⠀⢱⡀⢠⠇⠀⢠⠟⠀⠀⠀⠀⠢⡙⣽⣦ ⠀⠀⠈⠀⠈⣧⣎⠈⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⡟⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢳⣸⠀⢀⣾⢦⠀⠄⠀⠀⠳⡝⠎⢣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣀⠀⠀⠀⠀⠀⠀⣀⡄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⣿⣿⣿⣶⣶⣾⣿⣿⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢉⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣤⣤⠀⢠⡿⠟⠛⢛⣋⣉⣉⣉⣉⣉⡛⠛⠻⠿⣦⠀⣤⣤⣤⣀⠀⠀ ⠀⢠⣿⣿⣿⣿⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⢸⣿⣿⣿⡆⠀ ⠀⠀⢿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡿⠀⠀ ⠀⠀⠈⢿⣿⡿⠀⣾⣟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣙⣿⡀⢹⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠹⣧⣌⠙⠻⣿⣦⡈⠻⣿⣿⣿⣿⡿⠁⣠⣾⡿⠋⣁⣴⠏⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣬⣿⣿⣆⠈⣿⣷⡄⠹⣿⣿⡟⠀⣼⣿⠏⢠⣾⣿⣥⣄⡀⠀⠀⠀ ⠀⠀⠚⠻⣿⣿⣿⣿⣿⠀⣿⣿⣷⡀⠛⠛⠁⣼⣿⣿⡀⢻⣿⣿⣿⣿⠟⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⠿⣿⠿⠇⠀⠀⠠⠿⢿⠿⢧⠈⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢠⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠉⢀⣀⠀⠀⠉⡀ ⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠒⠀⠉⠀⠀⠀⠀⠀⡻⠋⢱⠀⠀⠇ ⠀⠀⡀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⢀⠞⠀ ⢸⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠴⠃⠀⠀ ⠈⠑⠦⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⡠⠂⠀⢀⠖⠁⠀⠀⠀⠀ ⢀⠤⠒⠈⠉⠉⠀⠒⠂⠠⠌⠢⣀⣰⠀⠀⠀⡊⠀⢀⣀⡀⠀⠀ ⠣⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣸⠝⣤⡀⠀⠀⠉⠀⠈⣧⠒⣢ ⠀⠈⠒⠤⠬⣉⣀⠀⠀⠀⠉⢀⣙⠛⠾⡀⠉⠐⠒⠀⠐⠛⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢌⣀⠉⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣲⣒⠒⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⠍⣒⣒⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣴⣡⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣎⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠙⢿⣿⣿⣻⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣷⠟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠳⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢳⡺⠵⣶⣒⠢⠤⠤⠤⠤⠤⠤⣤⣤⡤⠤⡒⡦⠤⠤⣤⣶⣶⣾⣿⡊⠁⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢰⠃⢧⠀⠀⠈⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⡭⠛⠉⠁⠀⠀⡇⢿⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⠀⠈⢧⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠒⠉⠉⠉⢉⡶⠚⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢦⡈⡧⢤⣀⡀⠀⠀⠀⠀ ⢀⡾⠁⠀⠀⢀⡴⠊⠁⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠙⢧⠀⠀⠉⠑⠦⡀⠀ ⢸⠀⠀⠀⢰⠋⠀⠀⠀⠰⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡠⠊⠀⠀⡜⠀⠀⠀⠀⠀⠙⡄ ⠘⡆⠀⠀⢸⡀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢸ ⠀⠘⢦⡀⠈⢣⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠉⠒⠤⢳⡀⠀⠀⠀⠀⢽⡈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⠀⠀⠀⠀⢠⠟⠦⣄⣀⣀⣀⣀⣠⠔⠁ ⠀⠀⠀⣀⡤⠤⠴⣷⠀⠀⠀⠀⠀⣇⠀⠈⠑⠢⠤⣄⣀⣀⡀⠀⠀⢀⣀⣀⠤⠔⠚⢉⡜⠁⠀⠀⠀⠀⢠⠏⣠⡀⠐⡌⠙⢿⣉⠀⠀⠀ ⠀⠀⠀⢷⣷⣀⣴⣋⣧⠀⠀⠀⠀⠸⣲⡤⠤⣄⠀⠀⠀⠀⠀⠈⠀⣀⣀⠀⢀⣀⣠⠮⠄⠀⠀⠀⠀⢠⡯⠞⡗⠡⠤⢼⢄⣩⠼⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠘⠲⠼⢦⡀⠀⠀⠀⠀⠀⣄⠀⢉⠍⠱⠖⢲⠖⠙⢄⣀⡽⠟⠒⠒⠀⠀⠀⠀⠀⢰⠏⠀⠀⠛⠒⠒⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠤⢴⡆⢀⠀⠙⡧⠴⠊⠀⠀⠳⠤⠼⣇⠐⠲⡤⠤⠤⠤⠤⢤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠈⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⣭⣏⣽⣯⣄

⡠⢲⡖⠢⢄⠀⠀⠀⠀⠠⡴⠒⣴⣖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣿⠟⠀⡇⠃⠉⠉⠉⠁⠀⠸⣿⣿⢊⣀⠀⠀⢀⡠⠐⠈⠉⠉⠉⠲ ⠘⠣⠄⠊⠀⠀⠀⠀⠀⠀⠑⠠⠬⠑⢉⠑⠉⠲⡁⠀⠀⢀⣠⠆⠀⢀ ⠀⢲⠤⠀⣀⣀⣀⣀⣀⣀⡀⢠⠄⠒⡙⠁⠠⡀⠈⠀⠔⡡⠒⠁⢀⠂ ⠀⠡⡑⠪⢀⣀⣀⣀⣀⣀⠀⠤⠚⠉⠀⠀⠀⠀⢡⠌⡐⠀⢀⡠⠁⠀ ⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⠀⢸⢰⠀⡐⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠂⢄⣀⠀⠀⠀⠀⠀⠀⠀⣀⢆⣬⠉⠹⣤⣴⡐⢆⠀ ⠀⠄⠒⠤⢐⠁⠀⢤⠴⠞⢛⡉⠠⣝⣉⡡⠃⠀⠈⠤⡐⠒⢖⡀⡠⠀ ⠀⠢⠀⠊⡡⠐⢢⠈⢄⠜⠁⠀⢈⠀⢀⠔⡆⠠⠢⡈⠪⣱⠀⢈⠀⠀ ⠀⠐⠤⠔⠀⠀⠨⣀⡸⠀⠀⠀⠀⠉⠁⠰⠀⢠⠀⢃⠀⢀⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠊⠀⠀⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⠀⠀⠈⢢⠹⣧⡀⠘⢆⢀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠀⠀⠀⠱⡈⢳⡀⠈⢆⠱⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡘⣆⠀⠀⠀⠙⣄⠳⠀⠈⢆⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠀⠀⣤⡤⠊⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡟⢳⡈⢆⠀⠀⠀⠈⢦⣧⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠅⠀⠀⢈⡇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣠⠴⡾⠶⠲⠷⣬⢧⣀⠀⠀⠈⢿⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⡏⠀⠀⠀⡆⠀⠀⠀⠀⢀⠏⠊⠁⡀⢠⠃⠀⠀⠀⠘⢆⠀⠉⠑⠂⠈⢿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⡌⠀⠀⠀⢸⠁⠀⢀⣸⠇⠀⠀⠀⢠⡏⠀⠀⢠⢃⣎⣀⣀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠘⡆⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⢸⠁⠇⠀⠀⠀⢀⠀⡴⢫⢟⢳⠀⠀⢠⡟⠀⠀⣤⠃⠜⢉⣿⣿⣿⣷⣶⣶⣤⣬⡧⣀⠀⠀⢸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⠀⡴⠿⣼⠀⠀⠀⠀⠘⠈⢀⠎⡜⢀⣳⣴⣿⠀⢀⡼⢃⠞⠀⠩⠟⠁⢠⣴⣦⣌⠙⠻⣿⣿⣷⣤⠼⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢾⠁⠀⢸⠀⠀⠀⠀⢸⠀⡜⣠⣿⣶⣾⣤⠇⢀⣼⡵⠋⠀⠀⠀⠀⢠⣿⣿⣿⣇⡄⠀⠈⢻⣿⣦⣙⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⡏⠀⠀⣿⡀⠀⠀⠀⠀⣷⢿⣿⡿⢩⣿⡟⢠⡾⠋⠀⠀⠀⠀⠀⠀⢸⣯⣬⡄⢉⣿⠀⠀⠀⢹⣿⣿⠷⠦⠄⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⣼⠀⢀⠆⣿⡇⠀⠀⠀⠀⢻⣿⣿⠁⢸⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠿⠋⠹⡏⠀⠀⠀⢸⡟⡟⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀ ⡇⠀⡜⠀⢹⢱⠀⠀⠀⠀⡘⡌⢻⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢘⠞⠁⠀⠀⠀⠈⢰⠁⠀⠀⠀⠀⠀⡽⣄⠀⠀⠀⠀⠀ ⠁⠀⣷⠀⠸⡀⡆⠀⠀⠀⠸⣿⠚⠃⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣠⠤⠀⢠⠃⠀⠀⠀⠀⠀⡴⠁⠈⠳⣄⠀⠀⠀ ⠀⢠⢹⡀⠀⢇⠹⡀⠸⡄⠀⠹⣆⠸⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠉⠁⠀⠀⡠⠃⠀⣠⠎⡰⢀⡜⠁⠀⠀⠀⢈⡷⢄⠀ ⡄⢸⠀⣇⠀⠀⠀⠳⡀⢹⣦⣤⡿⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣊⠡⠔⣺⣃⠞⠀⠉⠀⠀⠀⠀⢠⣾⠇⢀⣵ ⢇⢸⠀⠸⡀⠀⠀⠀⠙⣶⣧⣹⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠁⠀⠀⠀⠀⠀⢀⣴⣯⣯⠴⡟⠉ ⢸⡘⡀⠀⢳⠀⠀⠐⢄⠈⠻⣿⠀⠀⠀⠀⢠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣤⣖⣊⣀⣀⡀⠀⠀⣀⡠⠖⢹⢋⠃⣇⠇⠸⣄ ⠀⢻⣇⠀⢈⢣⡀⠀⠀⠑⢤⣙⢧⡀⠀⠀⠸⡀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠖⡶⠂⠉⠀⡼⢁⠇⡘⢸⡟⠀⠀⠏ ⠀⠘⢿⡔⢀⠀⠙⢤⡀⠀⢢⡈⠙⢿⠁⠀⠀⠙⠂⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⡜⢁⡎⢀⠁⡆⠁⣀⠀⠀ ⢀⠀⠀⠙⢓⠒⢀⠀⠈⠑⠢⢬⡷⣄⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠃⠀⠀⢠⠎⣀⡞⠀⠀⡸⠃⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⡙⢹⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⠟⠁⠀⢀⡔⢁⣼⡟⠀⠀⢀⣧⡜⠀⠀⠀⠀ ⢀⠐⠀⠐⢀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠇⡞⡀⠂⡙⢄⠀⠀⠀⠀⣀⣀⣤⣶⣿⡿⠋⡱⠃⠀⠀⠀⠀⣠⡾⡿⠀⠀⠀⡌⠐⣇⠀⠀⠀⡀ ⢀⠐⠀⠐⢀⠐⠆⠀⠀⠀⢸⡵⠁⡜⣸⠃⡀⠂⡀⠂⡑⠒⡚⠋⡙⣆⡿⣿⠋⠀⡰⠁⠀⠀⠀⢀⣴⠋⢠⠃⠀⠀⠰⠁⠀⣇⠀⠀⠀⡀ ⢀⠀⠀⠀⢀⠘⠃⠀⠀⠀⢻⠁⠀⡴⡁⠂⡀⠂⡀⠀⡀⢃⣀⢂⡀⢋⣐⠟⡄⡸⠁⠀⠀⠀⣠⡿⠁⠀⠆⠀⠀⣠⡷⠚⠉⠀⠀⠀⠀⡀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⣠⠴⡖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡴⠿⢏⣁⡀⠈⠉⠳⣄⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⡤⠞⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⣏⡙⢦⠞⠓⠒⠒⠢⠬⢵⣦⣄⢘⡦⠠⣄⣴⠧⠤⠤⠤⠴⠯⠤⢀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠉⡛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠒⠒⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⠉⠙⠒⢷⡤⠖⠒⠒⠐⠒⠲⢤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠙⡆⠀ ⠀⠀⠀⠀⠀⣠⠼⠳⢤⣀⣀⠟⠦⣤⣀⣀⣤⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠳⣇⠀ ⠀⠀⠀⣠⠞⢁⣠⠤⣶⠞⠁⣀⡤⣴⠞⢩⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠀⠰⡀⠀⠸⡆ ⢀⣠⠾⠛⠉⠁⢀⠴⠛⠊⠉⢀⡴⠃⠀⢸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠾⣿⠆⠀⠀⢱⡀⣰⠃ ⠋⠀⠀⠀⢀⡔⠁⠀⠀⠀⢀⣾⠁⠀⠀⠈⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⣧⠀⠀⢻⡀⠀⢹⠀⠀⠀⢰⡷⠃⠀ ⠀⢀⣠⡶⠋⠀⠀⠀⠀⣠⠋⢸⠀⠀⠀⠀⢳⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⢾⠈⠣⣄⣀⣳⠄⢸⠀⢀⡴⠋⠀⠀⠀ ⠖⢩⠟⠀⠀⠀⠀⢀⡼⣇⠀⢸⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠻⡙⠻⣦⣼⡄⠀⠀⠀⠀⠀⣼⠛⠉⠀⠀⠀⠀⠀ ⡴⠃⠀⠀⠀⢀⣴⠟⠁⠘⡄⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡲⠤⠤⠤⠟⠀⠀⠀⠈⠑⠒⠠⠞⠁⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⡻⠋⠀⠀⠀⠱⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣄⣀⣹⡶⠀⠀⠀⠒⠒⠒⠒⠒⢶⣶⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⢋⡜⠁⠀⠀⠀⠀⠀⠙⣄⠹⡀⠀⠀⠀⠀⠀⢰⠓⢺⢛⣿⠉⠁⠀⠀⠀⠀⠀⠀⠱⣄⢠⡈⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀ ⡴⠁⢠⠎⠀⠀⠀⠀⠀⢠⡀⠀⠈⢦⠱⡀⠀⠀⠀⠀⢾⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⡰⠃⠀⠀⠀⠀⠀⣀⡀⠀⣠⣾⣿⣿⣿⣦⣀⠀⣀⡼⠧⢤⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀ ⡜⢁⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⣷⡤⠖⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⠇⣰⠋⠱⡀⡀⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡱⠃⠀⢸⢠⠃⠀⠀⢣⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡜⠁⠀⠀⠸⠃⠀⠀⠀⠈⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢞⣏⣙⠳⢄⣀⣤⡤⠤⢤⣤⣀⡴⢾⣏⡙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⢟⣡⣌⣹⣆⠀⠀⠀⠀⠀⠀⠀⣾⣫⣅⣉⣳⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠸⣎⡉⠋⣡⠟⠀⠀⠷⠒⣷⠀⠀⢷⣈⠉⢋⣼⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⠉⠉⢁⣠⠴⠖⠲⠤⠞⠲⢤⣄⠉⠉⠉⡀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠓⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠛⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠲⣄⣀⠀⠀⢀⣀⡴⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀ ⠀⠀⢠⡞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢳⡀⠀⠀ ⠀⠀⣾⠀⢸⠀⠀⠀⢤⡀⡞⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⣇⣠⠀⠀⠀⢸⡄⠘⡇⠀⠀ ⠀⠀⢻⡀⠸⣆⠀⠀⠀⢳⡇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠏⠀⠀⠀⡸⠀⢸⠇⠀⠀ ⠀⠀⠈⢻⣄⠘⢦⡀⠀⠀⢱⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⡏⠀⠀⠀⡴⠃⣠⠏⠀⠀⠀ ⣤⠴⠒⠚⠛⠳⣄⣙⠲⠀⠈⣧⡀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⢀⡞⠀⠀⠐⣋⣤⠞⠛⠓⠲⢦⡀ ⠛⠓⢶⡖⠛⠁⠀⠉⠉⣛⣠⠌⡿⠂⣀⠀⠀⢮⣉⣳⣤⣶⣋⣩⠄⠀⡀⠐⢿⠤⣜⣋⠉⠉⠀⠘⠓⣺⣷⠛⠁ ⠀⠀⠈⠉⠙⠛⠋⠉⠉⠁⠀⢸⣇⡠⠟⠷⣄⣈⣿⠁⠀⠀⣟⣁⡤⠞⠛⠦⣬⠇⠀⠈⠉⠉⠙⠛⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⢞⣩⣿⡍⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡤⡾⠋⢉⣼⣯⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⣼⣶⣿⡷⠀⠘⡌⠳⠄⠒⠒⠀⠐⠒⠊⢰⠁⠀⣾⣷⣿⣿⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠀⠀⠐⠒⢤⠀ ⠸⣆⢻⣿⠟⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⢿⣿⡿⢁⣾⡦⢤⣀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⠈⢓⡦⠤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠀⠬⠔⠋⠀⠙⠄⠈⠑⠺⡁⠀⠀⠀⠀⠀⠀⣠⣴⠆⠀⠀⠀⡏ ⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡿⠆⠀⠀⠀⠀⠘⠂⠀⠀⢀⠔⠉⣘⠇⠀⠀⠀⡸⠁ ⠀⠀⠀⡏⢟⠒⠂⢤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢶⣂⠉⢁⡴⠃⠀⠀⠀⠢⣀⠀⠀⠀⡔⠁⡰⠊⠀⠀⠀⠀⡴⠁⠀ ⠀⠀⠀⠹⡌⠳⢖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠑⣄⡞⢀⠞⠀⠀⠀⠀⣠⠞⠀⠀⠀ ⠀⠀⠀⠀⠈⠲⣄⡈⠉⠑⠒⠒⠒⠒⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠀⠀⠛⠀⡎⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣇⠀⠀⡆⢰⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡀⢀⡟⠚⠒⡞⠀⠀⢀⠤⠤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠙⠉⡟⠒⠤⠤⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⠤⣾⠦⠵⠎⡇⠀⠀⠙⠛⠻⠥⠖⠊⠙⠲⡀⠀ ⠀⠀⢀⡴⠒⠒⠤⠤⠒⠋⠀⠀⠀⣧⣤⠖⠶⠖⠋⢁⣀⣈⣩⣝⡉⠀⣀⠴⠃⠀⠀⠀⠘⣤⣀⠈⠓⠲⣖⠲⣄⣀⡴⠃⠀ ⠀⠀⠸⡄⠀⣀⡠⠔⠊⠁⣀⡀⠀⢻⡀⠀⠀⡴⠊⠁⠀⢠⠊⠉⠉⠉⢀⣀⡀⠀⠀⣀⠀⠘⢎⠓⢄⠀⠀⠉⠳⡄⠀⠀⠀ ⠀⠀⠀⢸⠋⠀⠀⢠⠔⠉⠀⢙⡆⠀⠓⢤⠚⠁⠀⠀⠀⠸⣄⠀⢀⡼⠁⠀⡟⠀⣸⠁⠙⣄⠈⠓⠼⣧⡀⢀⡠⠃⠀⠀⠀ ⠀⠀⠀⠘⢄⣀⣠⠞⠀⠀⠀⠸⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢠⠞⠃⠀⢿⠀⠀⣏⠀⠀⠀⣹⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣸⠀⠀⠘⠂⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⢦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠓⠋⠉⠉⠉⠉⠑⠲⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠈⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⢳⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⢀⡾⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⢀⣀⡠⠤⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⡼⠃⠀⠀ ⠀⣴⠚⠉⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀ ⠀⣇⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠉⠳⢤⣼⠁⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⢀⣀⠀⠉⠉⠉⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠴⠟⠛⠉⠉⠉⠉⠉⠛⠒⠶⠤⢤⣀⡄⠙⢦⣄⠀⠀⡞⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠛⡇⠀⠀⠀⠀⠈⠓⠦⠤⠶⠒⠻⣿⣁⣀⠀⠀⠀ ⠈⢳⣀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠦⢽⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡭⣍⣛⡦ ⠀⠀⠉⠳⣤⣀⠀⠉⠙⠓⠒⠒⠲⠤⠤⠴⠒⠚⠋⠉⠀⠿⢷⡶⡬⠆⠈⠙⠲⠤⢤⡤⠤⠤⠤⣍⣓⡦⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠶⠤⢤⣄⣀⡀⠀⠀⠀⣰⠦⠤⣄⣈⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⡈⢲⡀⠀⠈⠉⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣂⣩⣶⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⢹⢟⣭⣵⣤⣀⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠤⠄⣪⠔⠈⣀⠤⠂⠺⣿⣯⣟⡍⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⠀⠐⠲⠒⠒⠒⠊⠀⢠⣾⠁⠀⠀⠀⢉⣹⣵⡾⠋⠁ ⠀⠀⠀⠀⣀⠄⠂⣹⡵⣷⣎⣀⣀⣀⡀⣀⣤⠾⣫⢿⣇⣤⣤⣴⣿⣻⠏⠀⠀⠀ ⠀⠀⢀⠄⠁⢀⣼⢅⠦⠸⣷⡿⠋⠋⠉⠉⠀⣜⣱⢏⣯⠿⣿⡍⢛⡏⠀⠀⠀⠀ ⠀⡰⠃⠀⢠⣵⡥⡔⠠⡪⠋⠀⠀⠀⠀⠀⠀⠉⠵⠋⣾⡟⡠⢲⡿⠀⠀⠀⠀⠀ ⡎⠀⣀⣬⢹⢛⠎⠀⠈⢀⣀⣀⣠⣀⠀⠀⠀⢀⢽⣞⣽⡿⠻⡿⠀⠀⠀⠀⠀⠀ ⠑⢻⣿⣿⡟⢒⢒⠐⠬⠀⠀⠀⠀⠀⠉⠒⢤⡩⠺⣽⠏⠀⢠⣇⡀⠀⣀⡄⠀⠀ ⠀⠘⠿⣿⡿⠟⠿⠍⠩⠍⠉⠉⠝⡒⠦⣀⠀⠙⠄⢻⣆⢐⣼⣿⣿⣷⣯⣤⡴⠄ ⠀⠀⠐⢼⣄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠀⢀⠖⣛⣯⡟⠻⢷⣿⠿⠿⠙⠒⠀ ⠀⠀⠀⠀⠙⠓⠬⠴⠤⠉⢁⣒⣒⣒⣒⣶⣾⡟⢿⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠞⠛⠉⠉⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⡶⣶⡶⠶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡿⠁⢶⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡈⠁⠉⠉⠛⠻⠿⢶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡉⢧⡀⠀⠀⣀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢿⣿⣿⣿⣿⢼⣿⠀⠀⠈⠉⠛⠲⠶⠦⠤⢄⣀⠀⠀⠀⠀⠉⠉⠛⠛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢿⣷⢶⣤⣀⡀⠀⠀⠀⠈⢻⣄⠀⠈⠁⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣆⠈⠉⠛⠷⢶⣤⣀⡀⠉⠙⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠈⠙⠛⠳⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⣉⣲⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⣿⣦⡀⠀⠀⠀⠀⠀ ⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡀⠀⠀⠀⠈⢿⣟⠉⠉⠩⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣄⠀⠀⠀⠀ ⣟⠛⠛⠳⠶⠤⢤⣤⣤⣄⣠⣴⡞⣱⠋⢉⣿⣷⣶⣦⣤⣄⣛⠷⣆⡀⠀⢀⡉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀ ⠈⠉⠉⠉⠓⢒⣶⣶⣤⡌⠉⠀⠀⠀⣴⠋⠀⠈⠙⠛⢿⣟⠙⠛⠟⠛⣻⣿⣿⣶⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀ ⠀⣠⣴⣾⣿⣿⡿⠷⠖⠛⠛⢻⡄⢸⠁⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⣰⡿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠖⠒⠂⠀⠀⠀⠀⣷⡿⠻ ⠀⠻⡧⠥⠞⠁⠀⠀⠀⠀⠀⢸⣧⣸⣷⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⡿⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠁⠀⠀⠀⠀⢀⣠⣴⣿⡿⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠓⢦⠀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣈⣉⠛⠲⠶⠤⠤⢴⣿⡇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⣿⡟⠁⠀⠀⢠⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠤⣤⡤⢴⠾⠛⠻⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⣴⡟⠳⠦⣄⡀⠀⢀⣀⣀⣀⣀⣤⡶⠾⠛⠉⠀⣼⠟⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟ ⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⠶⠶⠒⠛⢳⡄⠀⠀⢀⣀⣀⣠⣤⣀⣙⣓⣶⡾⠋⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠟⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠒⢛⣡⠶⠛⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⣷⠶⠴⠾⠿⣿⣷⣤⣄⣀⣀⣀⣠⣤⡶⢟⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⣿⣟⡟⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⢁⣴⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠗⠒⠛⠛⠋⠉⠉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠿⠓⠛⠋⠉⠉⠉⠉⣿⣿⣉⣥⣤⣤⡤⠴⠶⠾⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠒⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣋⣀⣀⣴⢶⣾⣿⣿⣗⡲⢶⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠙⠿⢿⣷⣾⠿⠛⠻⢤⡀⠀⠀⠈⠙⢲⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣾⢃⣨⣾⣿⣷⣦⢻⣧⢆⣶⢀⠀⠹⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⣠⠖⠃⠀⠀⠀⢀⣿⠇⢸⣿⣿⣿⣷⢛⡞⣿⡾⠟⠋⠙⠂⠙⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠴⠖⠚⠉⣀⣴⠞⠋⠀⠀⢀⣠⡴⠞⠛⠋⠀⠘⠲⣯⣿⣿⣿⡽⢃⣠⡾⠅⠀⠀⣠⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⡁⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠞⠻⠁⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠓⠿⠿⠟⠟⠕⣿⣚⣥⣴⣾⡿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⢣⡇⣇⠀⠀⠈⢿⠿⠛⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⢀⣠⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⣾⡟⡏⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⡿⢁⣼⡏⡇⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣰⣿⣟⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⢀⣼⣡⣿⢿⣿⣷⣇⢧⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣠⣦⣷⠟⢁⣴⠇⣿⣿⣿⣠⣶⣦⣀⣠⣴⣿⣿⡇⢻⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⣠⣾⠟⠽⡷⠋⣿⣳⣟⣾⣷⡝⣻⡿⣿⣿⣷⣶⡶⣿⠿⠟⡋⢁⣴⠟⠁⣠⢟⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⣇⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠔⠑⠀⠀⠀⢀⡴⣻⡋⠀⠊⢠⠄⠸⢷⣟⣿⣃⡿⠏⠁⠋⠉⠀⠁⠀⠀⠀⠀⡠⠟⢑⣡⣾⣳⢏⣸⣇⣼⣿⠿⣿⠿⡁⣾⠐⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⢞⠁⠀⠀⠀⠀⣠⣞⣼⠟⢁⡔⡵⠃⠀⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⡿⡽⢁⣾⡟⣻⣿⣤⡾⠉⠻⠟⣩⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⡿⠋⠀⠀⠀⢀⣼⢫⣾⣫⣲⢫⠞⠀⠠⠓⣇⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣝⢡⡞⠉⠀⣿⣿⠟⠁⢀⡶⠞⣹⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠉⠀⠀⠀⢀⡰⢫⡿⡳⣽⡝⣱⠟⠀⠀⣡⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡟⠀⢀⣼⠃⣿⣢⣴⢟⣠⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠃⠀⠀⠀⠀⣀⣼⡇⡸⣽⡟⠞⣴⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠀⠀⠀⣼⠉⣀⣾⠏⣤⡿⣿⣿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢀⣠⣤⣾⣿⣿⡇⢃⣾⠆⡜⠁⠀⠀⠀⠀⣀⣤⡤⠶⠖⠶⠖⠒⠒⠂⠶⠤⣄⣀⡀⠀⠈⠁⢀⢴⡆⠀⣾⣟⡿⣾⣟⡭⠟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠷⠯⣽⣿⣿⣿⡯⢿⣿⡿⠰⣶⠒⠲⠤⠔⠚⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣦⣄⠀⢉⣠⡾⠃⡼⣴⣿⡏⠁⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠠⣾⣿⣿⣿⣿⣼⣾⡄⣧⣿⣦⡶⠉⣉⣉⣭⣥⣭⣭⣅⣲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠈⣵⣿⡟⠀⠀⠀⠀⠀⣾⣷⣶⣤⣀⠀⠀⢠⣖⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⢿⣿⣿⣮⣽⣿⣟⡋⠿⢧⣄⡀⠠⢄⣀⡠⢬⣉⡙⠿⠷⣶⣤⣄⡀⠀⠀⠀⠀⠙⢷⡀⢠⠉⢿⣷⣀⠀⠀⢧⣰⡷⣻⣜⡿⡿⣿⣶⣷⣿⡀⣀⣀⡤⣤⡀⠀ ⠀⠀⠀⠀⠈⠙⠙⢿⣿⠛⠋⠁⠀⠉⠓⠋⠙⠒⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⠒⠄⠉⠋⠛⢶⡄⠀⠀⠀⠀⣧⢸⢀⣚⣿⣿⣤⣤⣽⣿⣵⣿⢟⣿⢷⣿⢹⣿⢧⣿⣷⣶⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⢷⣄⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣼⠜⣿⠿⠿⣿⣡⣿⣾⣿⣿⣯⣾⣯⣯⣿⢾⡿⣸⡟⣘⣧⣤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⣾⣿⣶⡀⠀⢀⣀⠀⠤⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⣀⣤⣾⣿⡿⠏⠀⠀⠙⠻⠿⠿⠿⠷⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣦⣄⡙⠲⢤⣀⠀⠈⠉⠛⠓⠲⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣽⣿⣿⣿⣛⣫⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣙⡛⠛⣛⠿⠷⠖⠶⠤⠤⠤⠤⢤⣶⣾⣥⣤⣤⣭⣭⣍⣉⡙⡛⠒⠚⡻⡟⡛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠟⣻⣿⡍⠉⠉⠀⠀⠀⠀⠀⠀⠈⠹⠶⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⠋⠀⠉⠁⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠒⣄⠀⠀⡀⠈⠉⠛⠛⠿⠷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠈⣟⠻⣿⣿⡷⢼⡇⠀⠉⠙⠒⠲⠤⠤⣄⠀⠀⠈⠉⠙⠛⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⢿⡓⠶⣤⣄⡀⠀⠘⢦⣤⣀⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⣄⠀⠈⠙⠳⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⠀⠀⠀⠀⠈⠉⣓⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣬⣧⡄⠀⠀⠀⠀ ⣠⣤⡀⠀⠀⠀⠀⠀⠀⢙⢿⢦⣄⡀⠀⠀⠹⣯⡀⠉⠷⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀⠀⠀ ⠣⠤⠭⢍⣉⣓⡚⠲⠞⠃⠚⣠⠞⠻⠿⣿⡶⠾⣽⣦⣤⣦⣄⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀ ⠀⣠⣴⣶⣾⡿⠭⠒⠶⡄⢰⠁⠀⠀⠀⠀⠻⣄⠀⢠⡿⠉⠉⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⠤⠀⠀⠀⢀⣽⠷ ⠀⠻⠽⠚⠁⠀⠀⠀⠀⢧⣼⠆⠀⠀⠀⠀⠀⠘⢧⡿⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⢀⣤⣴⡿⠷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠲⠤⣄⣀⡀⠀⢀⣾⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⣀⣤⡶⠛⠉⠀⠉⠂⣼ ⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣩⠽⢷⠂⠀⠉⠉⢹⡏⠀⠀⢀⣾⢧⣀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⢩⡿⠁⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⢀⡿ ⠀⠀⠀⠀⠀⠹⢦⡤⠤⠒⠚⣆⠀⢀⣀⣀⣠⣄⣉⣒⣤⠞⠁⠀⠀⠉⠑⠛⠛⠉⠉⠁⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣖⢙⡭⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄⣀⣽⠒⠚⠛⠻⠷⠶⢤⣤⣤⡶⠞⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠾⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⠶⠒⠒⠒⠀⠸⣿⣟⣉⣤⣤⠤⠤⠶⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⢷⣴⢶⣻⣿⣿⡟⠛⠛⠒⠦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢈⡟⣉⣷⣶⣬⢲⣤⣤⣀⠘⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢉⡠⠔⠀⠀⠀⣀⡿⢠⣿⣿⣿⣟⣿⡿⠟⠋⠁⠈⢛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⠶⠶⠖⠒⠚⠉⢉⣤⠞⠋⠀⢀⣴⠖⠉⠉⠀⠀⢙⣿⣿⣿⢟⣴⠞⢃⣀⣴⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣇⡀⠀⠙⣶⠶⠒⠒⠒⠒⠐⠃⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⣢⣴⣷⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⡟⣠⣏⣇⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⢟⣿⣿⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⢀⣾⣿⣿⣿⣿⣯⣇⣴⣴⣦⣤⣀⣀⣀⣶⣾⠾⢋⣴⠏⣹⣿⣷⣾⣷⣶⣶⣿⢿⢹⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⣿⠁⠜⢁⠸⣿⣿⣟⣳⠟⠹⠟⠛⠋⠉⠉⠀⡰⠏⢁⣼⡽⢻⣟⣿⣿⣿⡏⡟⠟⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⡎⠁⠀⠀⢀⣾⣿⠋⡴⡔⠁⢀⢾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⠏⣴⠟⣿⣧⡞⠙⠛⣣⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⠋⠀⠀⠀⣴⣯⣿⣿⢯⠎⠀⠎⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡼⠁⢠⣿⡏⠁⡴⠋⣹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠋⠀⠀⠀⢀⡎⣸⣿⠿⣱⠏⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣻⠀⢠⠟⣨⣿⣿⣷⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⢀⣀⣤⣾⣿⣇⢩⡟⠰⠁⠀⠀⢀⣠⡤⠴⠶⠶⠒⠒⠴⠤⢄⣀⠀⠈⠁⣠⡆⢀⣾⡿⣾⣿⠿⠁⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⢾⣿⣿⣿⢻⡿⠃⢿⠉⣱⡒⠉⡠⢤⣀⢀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⡠⠤⠟⠰⣷⣿⠁⠀⠀⠀⣏⡀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣜⣺⣿⡧⢶⣖⠒⠒⡛⠒⢛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠛⣆⠀⠘⢿⣇⠀⠀⢀⢸⣿⣿⣿⣶⣤⣼⡟⠁⠀⣀⡀⠀ ⠀⠀⠀⠉⠛⢿⣿⠟⠋⠉⠛⠋⠓⠈⠉⠂⠀⠉⠀⠈⠑⠂⠌⠙⠛⠦⡀⠀⠀⠈⣆⠃⣈⣿⣧⣀⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣽⠟⠋⠀ ⠀⠀⠀⠈⠶⣌⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣾⠛⠛⢛⣯⣾⠿⠿⣿⣾⣿⣿⣿⣿⡿⠩⠷⠶⠄⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠐⢤⡈⠉⠛⠢⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣾⣥⡶⣾⣿⠟⠁⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡲⠚⢷⠶⠤⠤⠤⠤⣭⣭⣭⣯⣭⣽⣛⣛⣛⡻⠯⠽⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⠒⠛⠯⣈⠛⠙⠿⢗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⡀⣠⢞⠱⠂⣀⣅⠢⠀⠉⢢⣄⡀⠡⠛⢦⠤⠴⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⢰⠡⣇⠑⠏⢽⠽⣮⡁⠋⠀⠀⠀⢁⣀⢩⢁⣾⢻⣷⠘⢿⡁⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⢻⣆⠈⡆⠰⣬⣭⣻⣭⢞⡾⣿⢝⣩⣿⣹⡟⠃⡣⣌⣣⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⠘⣌⠀⠀⢠⡟⠚⡏⠛⢭⣗⠷⠹⢻⣿⣿⠷⠟⠛⢛⠉⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⡄⢭⠓⣻⣿⠏⠀⢀⣼⣉⣀⣠⣥⣯⣁⣀⣀⠀⣀⡆⣃⠀⠀⠀⠀⠀⠀ ⠀⣰⠴⢢⠖⠓⠝⣝⢀⠀⠉⢏⠛⠛⠛⠉⠉⠉⠉⠉⠚⠛⠷⠾⠗⠲⠀⠤⠤⠤ ⠀⠁⠀⢾⠀⠀⠀⠈⠁⠀⢰⣼⣿⣿⣷⣶⣦⣤⠤⣤⣤⣤⣤⣤⡤⣀⣀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⢤⣤⡴⠶⡤⢾⣿⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠛⠁⠀⠉⠛⠲⢤⣀⠁⠀⠘⠋⡓⣽⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⠋⣴⣶⢠⠄⠙⡀⠲⣄⠀⠉⠓⠦⣄⠀⠀⠈⠁⡬⠛⢷⣄⡀⣀⣠⣤⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠟⡖⠦⣼⡛⣴⢦⣿⣤⡘⠒⢿⠿⣴⡌⠀⠀⠀⠀⠸⠟⠳⠦⠤⣍⣌⣁⣉⣭⣍⡿⠋⣠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⢰⡷⣄⠈⠳⣗⠳⣾⠺⣿⣶⣇⠀⡈⠀⠀⠀⠀⠀⠀⢠⣀⣀⠠⡄⢠⡬⣟⠉⣿⣿⡆⠉⢟⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⡀⢷⡿⣆⠀⠈⢆⠀⢳⡄⡙⠛⠛⠿⣞⠒⠒⠦⣤⣼⢿⠛⣻⡟⢛⣯⠻⢯⣷⣾⠏⣠⣀⠈⠊⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⣇⠹⡆⠀⢸⡄⠀⣿⣿⡿⣿⠦⢺⣋⣙⠻⡟⠁⡿⠛⣉⣰⣎⣵⣴⣶⡿⠁⠀⣢⢨⣷⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣇⠀⠹⣆⠁⠀⠀⠀⠀⣿⠘⠷⠼⣾⢿⠿⣿⢹⡛⣶⡷⡎⣽⠿⣻⣿⣿⣿⣽⣼⡿⠿⠿⢿⠏⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢧⡀⠘⠷⠤⣄⣀⣾⣿⣷⣤⣴⠋⠀⠀⠉⣱⡷⠟⠀⠀⠉⡼⢿⣿⡿⠋⠁⠀⠀⠀⠀⠈⢇⡀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⢰⠀⠷⡈⠙⣋⣿⣿⡟⠁⠀⠀⢠⣾⣯⣀⣀⣀⣤⣴⣶⣿⣧⣀⣀⣀⣀⣀⡀⠀⣀⣸⠷⢤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣏⣠⣇⢀⣤⣬⣥⡻⢿⠛⢧⠀⠀⠐⠛⣟⠻⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⢿⣶⣶⣾⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀ ⢠⡿⠋⠉⣧⡏⠁⠀⠀⠉⠓⢷⣌⠳⣄⠀⠀⢈⣦⣄⣀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⢲⡞⣩⣼⣿⣯⣿⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⠿⡿⠿⠿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠘⠿⠛⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⠠⠖⠉⠉⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣏⠉⠁⠀⠀⠀⣴⣾⣖⢂⠀⢉⡉⠛⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠓⣦⢤⣀⠀⠸⡍⢉⡜⠀⠀⠀⠉⠁⠂⠀⠀⠀⠉⠐⠠⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢦⡀⠈⠑⠒⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀ ⡤⣄⡀⠀⡀⡹⠲⢤⣀⣈⢯⡉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⠀ ⢀⣤⣼⠿⠀⡄⡐⠀⠈⠙⢌⢉⠟⠓⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⢩⠧ ⠈⠉⠀⠀⠀⢑⡞⡀⠀⠀⢈⡏⠀⠀⡌⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⣀⡤⠞⠫⢱ ⠀⠀⠀⣤⠆⣤⣐⠓⠀⠀⠸⢇⣀⠞⠢⠄⣠⠀⠤⠖⠋⠹⠁⠀⠈⠁⠀⠀⣀⠞ ⠀⠀⠀⠈⠉⢤⡚⠔⠊⠉⠉⠀⠁⠀⠀⠀⢠⢤⣀⡲⠀⠛⠂⠤⣤⠤⣲⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠭⠉⢡⣶⣂⣀⠠⠤⠶⠊⠁⠀⠀⠀

⡀⠀⠀⢀⣶⡟⠛⠛⠛⢻⣿⣯⣷⣿⠛⠛⠛⠛⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢠⣾⡟⠃⠁⠉⠠⠤⠜⠛⠛⠠⠄⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣺⣿⡇⠈⢺⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠈⠹⢿⣦⡀⠀⠀⠀⠀⠀ ⢻⣾⡿⠏⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠹⢿⣦⡀⠀⠀⠀ ⣻⣿⠃⠀⢱⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠈⢹⣿⡆⠀⠀ ⢸⣿⡀⠀⠘⢷⣆⡀⠀⠀⠀⠀⢀⢀⢠⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡄⢠ ⢼⣿⣧⡄⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠻⣷⣾ ⢿⣿⠛⣿⣦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣾⡿⠏⠀⠀⢰⡦⠀⠀⠀⣿⣿ ⢸⣿⡄⠀⠙⠛⣿⣭⣭⣭⣭⣭⣭⣭⣭⣽⠟⠛⣧⡄⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿ ⢿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣿⡇⠀⣀⣰⣿⠟⠀⠀⠀⠀⣿ ⡈⠻⣿⣦⣤⣄⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⠷⠟⠁⠀⠀⠀⠀⠀⣿ ⡇⠀⢽⣿⡏⠉⠹⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⣿ ⡇⠀⠈⢻⣿⣇⡀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⣿⣿ ⠇⠀⠀⠀⠘⠿⣷⣤⣴⣶⣦⡀⠀⢀⣀⣀⣀⣀⣀⣴⣞⠀⠀⠀⠀⢠⣼⡿⠋⠘ ⠀⠀⠀⠀⠀⠀⠉⠿⣷⣴⣶⣿⣿⡿⡏⠉⠉⠉⠉⢙⡿⢷⣶⣶⣦⣼⡿⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⢷⣄⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡤⠖⠋⠉⠀⢀⣌⠉⠉⠛⠒⠧⣄⡀⠀⠀⠀⣈⣡⣤⠶⠶⠾⠷⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢦⣀⡤⠟⠉⠀⠀⠀⠀⠀⣼⠉⠳⣄⠀⠀⠀⠀⠉⣷⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⡠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢛⡇⠈⢧⡀⠀⢀⡴⢋⣽⣿⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⡀⡄⣹⠞⠁⣴⠟⠁⠀⠀⠉⠹⣶⡄⠀⠀⠀⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣽⠟⠁⣠⠞⠁⠀⠀⠀⣀⣀⣠⣿⡇⠀⠀⠀⢀⡾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣼⡏⠀⠀⠀⠀⠀⠉⢿⡏⠉⠀⠀⠀⢀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⣠⠏⠀⠙⢦⣀⠀⠀⠀⠀⠀⣿⠄⠀⠀⣰⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⣠⠾⠥⡀⠀⠀⣠⠽⠛⠲⣶⣴⡶⠋⢀⣠⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡆⠀⠀⠀⢳⡀⠀⠀⢀⡠⠞⠉⠀⠀⠀⣠⠞⣁⣀⣀⡀⠀⠀⣀⠤⠤⠤⢤⣿⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢳⣤⡖⠋⠀⢀⣀⡤⠖⢋⡕⠉⠁⢀⣠⠈⠑⢎⠁⠀⣀⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⣀⡤⠖⠋⠉⠉⠉⢿⡍⠀⠀⠀⡎⠀⠀⠀⠘⠿⠃⠀⠈⡆⠈⠙⠉⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢲⣶⣶⠛⠙⠋⠉⠀⠀⠀⠀⠀⠀⠘⠻⡄⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣁⣀⡴⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀⡴⠗⠒⠒⢢⣀⠔⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣄⣀⠀⠀⠀⠀⣹⡟⠀⠀⠀⣠⠖⠛⠉⠙⣿⠘⣦⠀⣻⡇⠀⠐⠬⠑⠂⠤⠤⠒⠋⠠⣄⣀⣀⡰⠃⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣄⣀⢀⡟⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿⣴⣿⣿⣿⠇⠀⠀⠀⠀⣠⠤⠤⠤⠠⠤⠠⠬⢤⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾⢹⡇⠀⠀⠀⠀⠙⠛⠁⠉⠋⠀⠀⠀⠀⠀⢿⣷⠶⢶⣶⣤⡶⣶⣿⠏⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣧⠈⠻⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠿⠿⠛⠉⠀⠀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠓⠲⠖⠚⠉⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⣀⣴⡾⠿⣿⡿⠿⠻⠿⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣤⣽⡀⠀⢀⣤⠾⢿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⣿⣿⣿⡿⣦⣄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣧⣸⣿⣿⣷⣿⢿⣿⢿⡏⠑⠒⠒⠒⢻⣿⡿⠛⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶ ⣿⣿⣿⣿⣿⣿⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⠋⠈⢿⣾⠟⣾⣷⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⡟⢠⣿⣿⡤⣀⣠⣼⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣧⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⢹⣿⣿⠀⢀⣠⣿⣿⣿⠁⢸⣿⠻⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⡀⠀⠀⣸⣿⡆⣿⣿⠀⠀⠀⣿⢿⣿⣄⣼⣿⡗⢿⣿⣿⣿⣿⢠⠀⢻⣯⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠉⢹⡟⣿⣿⣿⠀⠀⠀⣿⣿⣿⡆⠘⣿⡷⠀⣿⣿⣿⣿⣷⡆⠀⠙⢻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣄⣠⣶⣦⣤⣴⣿⣟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠾⠛⠑⠻⠷⣭⣍⡉⠀⠐⠂⠈⠁⣻⡿⣿⡻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⣀⡀⠀⠀⠉⠛⢶⣤⡀⠀⠀⠈⠀⠄⠛⢦⡙⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⣾⣿⠆⡤⠄⠈⣁⠈⠟⣤⠀⠀⠈⠙⠷⢦⣀⠀⠀⠀⠀⠠⡤⠙⠻⣷⣄⣀⢀⣀⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠻⡶⢦⣄⣾⠯⣥⣤⣈⣽⣄⡀⠿⠲⣯⣿⢦⣤⡍⠀⠀⠀⠀⠀⠀⣏⡟⠲⣦⣄⣀⣋⣉⠉⠙⢚⣛⣉⠿⡯⠓⢠⣼⣟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠇⢀⣇⠀⠈⠻⣆⢼⡤⣍⣽⣽⣿⢧⣀⡮⠁⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠛⣞⣿⠿⢿⣯⣷⡄⠛⢝⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⢾⡙⣿⡄⠀⠈⠳⡄⠙⠳⣌⠛⠷⣯⣷⣤⣤⡄⢀⣀⠀⢀⠀⠀⠀⣀⢾⣦⡔⣦⣚⣧⣴⣿⢉⣧⡀⠛⣿⣯⠇⠀⠈⢧⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣠⠈⢿⣿⢿⡄⠀⠀⠹⡆⠀⠘⣦⢀⡈⠋⣉⠙⠿⣯⠉⣉⡹⠳⠶⣬⡟⢛⠋⣹⣿⠉⢩⣿⠊⠻⢷⣯⣿⡽⠃⣼⣄⣀⠈⠣⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⡇⠀⠀⣿⠈⣿⡀⠀⠀⣧⠀⠀⢹⣿⣿⣟⣿⣷⡤⡾⠛⠛⠛⢷⡶⠏⢘⣿⠿⠉⠁⣶⠬⣭⣤⣴⣶⣞⡋⠁⠀⢤⠤⡭⢔⣀⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣷⡀⠀⢻⣇⠘⠇⠀⠀⠙⠁⠀⢸⡏⢻⣇⠸⣯⣴⣾⣿⣿⡗⠮⣷⣄⣸⡇⡴⢚⣿⣿⣿⣿⣯⣭⣿⠷⠤⣴⣶⣿⣷⣛⣿⠟⠛⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣧⡀⠀⠻⣧⡀⠀⠀⠀⠀⠀⣼⣇⡀⠉⠉⢹⡟⠺⠋⢻⣧⡘⡆⢻⡽⠃⠇⢼⡟⣩⡶⣿⣿⣟⣿⡿⠿⠛⠛⠋⠉⠙⢿⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⣄⠀⠈⠻⠶⠦⣤⣠⣾⣿⣿⣿⠦⣴⠟⠀⠀⠀⠀⢀⣿⣷⠿⠃⠀⠀⠀⢰⠾⠯⣯⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⡦⠈⢷⡄⠉⠙⠛⢻⣿⣿⣿⠃⠀⠀⠀⠀⣤⣾⣏⡀⠀⢀⣀⣀⣤⣤⣶⣿⣯⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⠀⢠⡇⠀⠀⢙⣳⠀⣿⣿⣿⣷⡇⠀⠀⠀⢠⡴⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣶⣾⣿⢿⣣⡄⣩⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣧⣴⣿⡣⣤⡾⠿⠛⠷⢤⣙⢦⡈⠹⣆⠀⠀⠀⠀⠸⣆⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠈⠉⠉⠉⠀⠈⠉⠿⠗⢻⣿⠿⠿⠿⠿⠿⠿⠷⠶⠦⠶⠶⠶⠦⠤⠤⠤ ⠀⣾⡟⠉⠁⢹⣼⡇⠀⠀⠀⠀⠀⠈⠳⣽⣦⡘⢧⡀⠀⠀⠀⣬⣷⣤⣀⡤⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠈⡟⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠉⠳⠦⣤⠚⣉⣥⣟⣿⣛⣻⣥⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣋⣶⣿⣾⣻⡿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣴⣶⣷⠶⠶⠶⠶⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠓⠒⠛⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣠⡤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠤⢦⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢋⣡⣾⣷⡀⠉⢻⡳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡟⠉⠀⣰⢾⣷⣦⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠀⣾⣦⣿⣿⡇⠀⠀⢻⠈⣓⡦⠤⠖⠒⠒⠒⠒⠲⠚⠁⡞⠀⠀⢸⣿⣶⣿⣿⣷⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠒⠒⠒⠒⠲⣤⡀⠀ ⣧⠀⣿⣿⣿⣿⠃⠀⠀⣸⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠘⣿⣿⣿⣿⡿⢀⣿⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀ ⠙⢧⡘⠟⠋⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠈⠛⠿⠋⢠⡾⠙⢯⡙⠓⠦⣄⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⠇ ⠀⠀⢉⡗⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠶⠚⠉⠀⣀⠀⠳⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣺⠏⠀⠀⠀⠀⣸⠀ ⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⠇⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⢀⡴⠋⠁⢘⡧⠀⠀⠀⠀⢠⠇⠀ ⠀⠀⠀⡟⢳⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠴⠖⠋⠁⣴⠃⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠚⠁⠀⠀⠀⠀⣠⠏⠀⠀ ⠀⠀⠀⢷⠈⢧⡀⢀⣬⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠓⠲⣤⡤⠞⠁⠀⠀⠀⠀⠀⠈⠓⠦⡀⠀⢀⡾⠁⣠⠟⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀ ⠀⠀⠀⠈⢷⡀⠙⠻⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡞⠀⣰⠃⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀⠀⠀⠀⠀⡟⠀⢰⠃⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⡇⠀⠀⠀⡇⠀⡟⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⠀⠀⢠⣧⣀⣇⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣆⠀⣸⠁⠉⠁⢨⡃⠀⠀⢀⡴⠋⠉⠳⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠉⡽⠓⠲⠤⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⡟⠦⠼⠷⢙⡇⠀⠀⠈⠉⠛⠛⠻⠶⠖⠚⠉⠉⢳⡀⠀⠀ ⠀⠀⠀⣠⡤⠶⢤⣀⣀⡤⠴⠚⠁⠀⠀⠀⣇⣀⣠⠤⣤⣤⠴⠟⠉⠉⠉⠉⢉⣩⠟⠉⠉⠀⢀⡼⠃⠀⠀⠀⠀⢻⣄⠀⠀⠛⠲⠴⣖⠲⢦⡀⠀⠀⣴⠇⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⣀⡴⠄⠀⠀⠀⠀⢷⠞⠉⠉⠉⠀⣀⡤⠖⠚⠋⢉⡭⠖⠒⠦⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠹⡟⠲⣄⠀⠀⠈⠓⠦⣭⡓⠛⠁⠀⠀⠀ ⠀⠀⠘⢧⣀⣠⡤⠖⠋⠁⠀⣀⡤⠤⡄⠀⠘⣧⠀⠀⠀⣼⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⣠⠤⠶⡄⠀⠀⣠⢤⡀⠀⠙⢦⠈⠳⡄⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⠁⠀⠀⠀⣴⠛⠁⠀⠀⢹⡆⠀⠈⠳⣖⠚⠁⠀⠀⠀⠀⠀⢻⣄⠀⠀⢀⡼⠁⠀⢠⡇⠀⢸⠃⠀⠙⢦⡀⠈⠓⠲⣿⣄⡀⠀⣠⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⡀⠀⠀⣰⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⣴⠞⠀⠀⢸⡀⠀⠀⣿⠀⠀⠀⠀⠈⡇⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠓⠋⠁⠀⠀⠀⠀⠀⠈⠳⢤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⡇⠀⠀⠹⣆⡀⠀⢠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀⡴⠃⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣻⠉⣳⣽⣿⣶⣞⣿⣿⣷⣶⡆⢀⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠇⣠⣤⣀⣤⡌⣩⣷⣬⣁⢠⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣼⣿⣉⣽⣿⣿⣿⣏⠙⠏⢛⣿⣿⣿ ⠻⣾⣿⣧⣾⣿⣭⣉⣿⣿⣿⣿⣿⣿⣿⣄⣠⣤⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣠⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿ ⠈⠹⡿⡿⣿⠙⢿⠿⣿⣿⡿⢿⣿⣾⣷⣨⣿⣿⢿⣧⣴⡷⢪⣽⣷⣄⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠘⠃⢀⣷⣞⠂⣴⣿⣿⣷⣾⢟⢿⣿⣿⡿⣷⣀⡿⠿⢗⣚⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠉⠿⠟⣿⣷⠘⣽⣿⣿⡆⣿⠟⢋⣉⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⡋⠻⣿⣿⣿⣿⣿⣿⣅⣼⣯⣤⣼⡿⣿⣿⣟⣿⣿ ⠀⠀⠀⠀⠀⠃⠀⠉⠓⢺⢹⢟⣳⣻⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢳⡁⠀⠀⢳⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣷⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠿⠘⣶⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣁⡀⠀⠈⢷⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣼⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⢁⣀⠴⠒⠉⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣠⣴⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠠⠤⣐⠻⢁⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣡⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣿⣿⣿⠿⠿⠟⠛⠋⠉⠁⠠⠀⠒⠊⠉⣔⣲⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢯⡟⠋⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠉⠁⠀⠀⠀⠀⢀⣠⠤⣒⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠋⠉⠀⠀⠙⣆⠀⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣀⣐⣀⣤⣼⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⡉⠀⠀⠀⢹⡀⢀⡠⠖⠋⠈⣆⡇⠀⣿⣿⣿⣿⣿⡿⠿⣿⣿⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣻⠟⠋⠁⢻⡘⡆⠀⠘⣿⢰⠀⠀⢈⡷⠋⠀⠀⠀⠀⢻⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈ ⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢋⢉⡜⠁⢀⡴⠋⠙⠓⠦⣄⣳⣹⠀⠀⢿⢸⠀⡴⢻⡃⠀⠀⢀⣠⡴⡿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣿⣿⡿⡿⠛⠛⠋⡝⠉⠁⡼⠀⠀⠀⣸⣋⣀⣤⣋⣀⣀⣀⣀⣠⣲⣽⣯⡆⠀⠘⣾⠂⢠⣿⣴⣶⣾⡍⠁⠠⢧⡇⣸⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣼⢰⠃⠀⠀⣼⠁⠀⢠⡇⠀⠀⠀⣏⣱⠋⠀⠀⠀⢸⣿⣿⣿⡄⠉⠛⡇⠀⢀⣿⣠⠎⠈⣿⣿⣿⠇⠀⠀⢸⢳⡃⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣸⣿⠀⠀⢸⡇⠀⢀⠀⡏⠹⡀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⡇⠀⣸⡼⠃⠀⠀⠻⡿⠏⠀⠀⣠⣿⡇⠘⣆⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⣿⠀⠀⣿⡇⠀⢸⠀⡇⠀⠳⣄⡀⠀⠀⠈⠛⠁⠀⠀⣸⠁⣠⠟⠁⠀⠀⠀⠀⠀⠐⠒⠋⠁⢳⡇⠀⢹⡆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣧⣘⡄⠀⣿⡇⠀⠸⡆⢳⠀⠀⠀⠙⠀⠀⠀⠻⣦⣤⡴⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣸⠇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸⣿⠙⢦⡸⣷⠀⠀⢻⡈⢧⠀⠀⠀⠀⠀⡤⠐⠒⠛⠒⠒⠒⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠇⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠋⠀⠀⢑⣿⣆⠀⠀⢿⠺⢧⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡷⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠘⣟⣮⠳⠦⣈⣷⣤⣈⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⣀⡴⠞⠁⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⣺⣟⣠⣾⡏⢿⣦⣭⠿⠲⣤⢤⣀⣀⠀⠀⠀⠀⢀⣘⣭⣤⠤⢴⣺⢛⣁⡤⠤⠴⠚⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣫⣽⣿⣿⣿⣿⡇⠀⠀⢿⣷⣦⣄⣀⣀⣀⣽⡟⡅⠹⣿⡴⠛⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⢿⣿⣿⣾⣿⡿⠁⠹⡄⠉⠻⠦⠬⠭⠥⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠉⢳⢸⡏⠀⠀⠀⢹⣶⣶⡤⣤⢐⣦⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡄⠀⢀⣾⣁⣘⣞⣹⡄⠀⢀⣿⣿⣿⣿⣼⡄⠀⠘⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣴⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣷⢻⠀⣸⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⣾⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡸⣿⣿⣿⣿⣯⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⠤⠔⠒⠋⠁⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣯⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⢁⢀⣀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣼⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀ ⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⣶⣿⣿⣿⠃ ⠀⠀⠀⠹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⠛⠉⠁⠀⠀⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠤⢤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣴⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⣼⡏⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⣶⡄⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⢠⣴⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠈⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠉⠙⠻⣦⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠛⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀ ⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⡄ ⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇ ⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠀ ⠈⢷⡀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⣿⠀⣼⠃⠀ ⠀⠈⢷⣼⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡾⠃⠀⠀ ⠀⠀⠈⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⢠⠀⣄⠀⠀⠙⢿⣿⣿⣿⡿⠏⠀⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣴⣿⠀⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⠳⣦⡀⠀⠀⠀⠸⣿⡿⠀⢻⣿⡟⠀⠀⠀⠀⣤⡾⢻⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⢻⠻⣆⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⡾⢻⠁⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⢹⠒⡦⢤⠤⡤⢤⢤⡤⣤⠤⡔⡿⢁⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⢸⠦⣧⣼⣀⡇⢸⢀⣇⣸⣠⡷⢇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠺⣄⣇⢸⠉⡏⢹⠉⡏⢹⢀⣧⠾⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠉⠙⠓⠚⠚⠋⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠋⠁⡞⠀⠀⠀⠀⠀⠀⣰⠋⠀⡴⠃⠀⠀⠀⢠⡟⠀⣰⠫⠂⣠⢠⣿⠇⢰⠿⠶⠒⠒⠛⢯⣥⣤⠀⠀⠈⠉⠉⠒⠒⠒⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀ ⠀⠀⠀⠀⠀⠀⢹⡿⠉⠀⠀⠀⠀⠁⠀⠀⠀⠔⠀⡼⠃⢀⡞⠀⣠⠖⡄⠁⡞⠀⡴⠃⢀⣼⠃⣾⡞⢀⡞⠀⠲⠶⣦⣄⡉⠉⠉⠉⠉⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣠⠎⠀⡼⠁⣠⠏⢀⡾⢁⡼⠁⣼⢁⡼⠁⣠⢞⡟⣼⡝⢀⡞⠁⠀⠀⠀⠀⠀⢙⠿⣷⡶⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⢀⡴⠃⠀⡼⢁⡔⠁⣠⠟⢀⡾⠁⣸⠣⠋⣠⠞⠁⡾⡹⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢝⠦⣄⡠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⠛⠀⠀⣼⣡⠋⢀⡼⣣⡴⠋⣀⣰⣧⣤⣾⣿⣶⡾⣱⠁⡰⣼⣷⣤⣤⣴⣶⠾⠋⠀⠀⠀⠀⠀⠙⢮⡟⢦⣤⣘⡶⣶⣤⠤⠤⠤⠤⠄⠀⢀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⢰⠏⢀⣴⣫⠟⠉⢠⠾⣻⠟⠛⠿⢿⣿⣿⢃⠃⡰⣱⣿⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠙⣮⡙⠮⣍⠛⠛⠶⣤⡀⠐⠉⠒⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠁⠀⠀⣰⣯⠾⣋⡵⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⢈⣿⡎⣰⣵⣿⣿⣿⣿⣿⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡉⠲⠦⣄⡉⠙⣒⣚⡚⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⢀⣠⡾⢟⡥⠞⠁⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⡼⡞⣰⡿⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣶⣄⣉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡴⠛⠡⠊⣁⣤⣶⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⡻⢡⡟⠁⢳⠤⠄⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠙⢿⣒⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣴⡖⡞⢻⢩⣧⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢣⠞⠀⢀⣠⣤⣴⣖⣶⣶⣤⡶⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢦⡉⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢸⢸⠁⣎⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠗⢡⠟⢀⣶⣿⣿⡟⠙⠟⠉⠉⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⠙⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠏⢠⣿⣺⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡴⡗⣰⠏⠀⣸⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠄⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣾⢀⣟⡇⣿⠁⠀⠙⠲⢤⡀⠀⡼⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣿⡾⡿⠀⢹⡆⠀⠀⠀⢀⣙⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠀⠀⠀⠐⠠⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡈⢠⣿⢿⠁⠀⠘⢹⣶⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⣼⣟⠇⠀⡞⣠⠘⣿⡟⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⡼⢹⡞⠀⡼⡹⣣⠀⡙⢹⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠶⠖⢻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡜⣡⡞⢀⣾⡿⣡⡏⡸⠁⡿⣏⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠏⠁⠀⢀⡀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⢻⠉⠉⠁⠠⠀⣸⣿⢋⡴⠋⠀⢺⣯⣴⣿⢠⠃⣸⡇⢹⡀⠀⠀⠙⠀⠀⢀⣠⠔⠋⠁⠀⢀⣀⣤⣴⣾⣿⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘ ⢘⠀⠀⠀⢰⣤⠟⣵⠏⠀⢀⣤⡞⢻⠁⣧⠏⢰⠏⡇⢸⣷⠀⠀⢀⣠⠴⠋⠀⠀⢀⣤⡶⢟⡿⠟⠛⠉⣿⡤⠋⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀ ⠐⠀⠀⠠⡞⣡⣆⣥⣴⡖⠉⢀⡇⣸⣴⣃⡴⠃⠀⡇⣸⠈⣧⡀⠀⠻⢷⣄⠰⠾⣿⡟⢀⡞⠁⠀⢀⣠⣽⡇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⣠⡼⠀⠀⠀⠀⠀⢀ ⢶⠒⠊⣿⣿⣿⣿⣿⣿⡇⠀⣸⢷⣋⠘⠿⣷⠀⠀⡇⣿⢠⢹⡷⣄⠀⠀⠈⠙⢶⣾⢥⣾⢀⣠⠖⢉⣷⠏⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⡟⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⣼⣿⣿⣿⣿⡿⢸⡇⠀⢸⠈⢿⡀⢠⣿⢧⠀⡇⣿⢀⢸⣿⠈⠳⣄⠀⠀⠀⠙⢦⡘⠓⠛⠛⠉⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⢀⣠⠄⠀ ⢀⣼⣿⣿⣿⣿⡿⠃⢸⣷⠀⢘⣇⢈⣷⡀⣿⢸⣆⡇⣸⠈⢸⣿⣆⠀⡏⠓⣦⣀⠀⠀⠉⠲⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣼⣿⣿⠟⠁⠀⠀⠀⢀⣠⣾⡟⠀⠀ ⣼⣿⣿⣿⣿⣿⠃⠀⢸⡏⣇⠀⣿⠀⠈⢷⣿⠃⠙⢿⣿⠀⢸⣿⢹⡀⡇⠀⣷⡉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⣴⣿⣿⠟⠁⠀⠀⣠⣴⣶⣿⣿⡟⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⢀⣷⢸⡇⠸⣇⠟⡆⠀⠈⢿⠀⠀⠈⢻⡄⠸⣿⢀⢿⣧⠀⠙⣿⠀⡌⢻⢦⡀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣁⣤⣴⣾⣿⣿⠟⣁⣠⣴⣶⣿⡿⣻⣿⣿⡏⠀⠀⠀⠀ ⢛⣿⣿⠟⢻⠃⢸⣿⢸⡇⠀⠉⣧⢷⠀⠀⠀⢧⠀⠀⠀⢿⣀⣿⢸⠃⢿⡄⢀⣹⠀⠅⡿⢸⣿⠷⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⠏⠀⠀⠀⠀⣠ ⣦⣿⠁⠀⢸⠀⢸⣿⢸⡇⠀⠀⠘⡿⡄⠀⠀⠈⣇⠀⠀⠈⣯⣿⢸⡅⣸⠇⡸⢸⠀⢰⣷⢠⠿⡄⡏⡇⠀⠃⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣤⣾⡿ ⠉⠙⠒⢺⣾⠧⣼⣿⣠⣿⠀⠀⠀⢹⣷⠀⠀⠀⠸⡄⠀⠀⢸⣿⢸⣧⠏⠀⠃⠸⣠⢯⡏⣸⠀⢳⣱⡇⠀⢸⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣠⣶⣿⣿⣿⣁ ⠀⠀⠀⠀⣯⢷⡀⠀⠉⠙⡆⠀⠀⠀⢻⡀⠀⠀⠀⢳⡀⠀⠀⢻⣼⠃⠀⠀⠀⠀⢁⡟⣠⠃⠀⢸⣿⣷⣶⣾⣿⣏⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⢷⣷⣄⠀⠀⢹⡀⠀⠀⠀⣇⠀⠀⠀⠘⡇⠀⠀⠀⢣⡠⠀⠀⠀⡠⢋⡾⠁⠀⠀⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢻⢧⠀⠈⢧⡀⣿⡇⠀⠀⠀⢸⡄⠀⠀⠀⢸⡀⠀⠀⠀⠻⣿⡶⠒⠦⠯⢄⣀⣀⡤⢞⡹⡛⢻⢯⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠸⡎⢧⡀⠀⠳⣿⣳⠀⠀⠀⠀⢷⡀⠀⠀⠀⠻⡄⠀⠀⠀⢻⣤⠖⠃⠀⠀⠀⠀⠱⣄⣑⠀⠀⣀⢀⠀⠀⠀⠀⠹⠛⠛⠿⣻⡿⣿⡻⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣂⣉⣁⣒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⡚⠝⠛⠒⠢⡀⠀⢎⣒⣊⣒⣪⠇⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠊⠀⠀⠀⠀⠀⢈⡍⠀⠀⠀⠀⠀⠉⢇⡀⠀⠀⠑⢦⠀⠀⠀⠀ ⠀⠀⢀⡴⣇⣀⣀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢱⠀⠀⠀ ⠀⣤⣮⡄⠀⠀⠸⠉⢑⡞⠁⠀⠀⠀⣀⠔⠋⠉⠉⠉⢢⠀⠀⢸⠢⠄⠠⡄⠀⠀ ⡰⠈⣿⡇⢀⡠⠁⡠⠊⠑⣄⠀⢀⣜⣁⣀⣀⡉⠉⢉⣈⢣⢀⡎⠀⠀⠀⡷⣦⠀ ⠇⠀⠈⠉⠉⠑⡉⠀⠀⠀⠈⠑⣇⣀⡀⠀⠀⠀⠀⠀⠀⢸⡊⢉⠒⢖⠺⡬⠃⢃ ⢸⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⣸⠠⠉⠢⢄⠀⠉⠀⠈⢉⠏⡇⠘⣆⠀⢀⣀⠀⠘ ⢀⣀⢀⢀⡴⡏⠀⠀⠀⢀⠔⠉⠝⠒⢄⡀⠁⠢⠄⠒⠁⡠⠫⠑⢌⠲⣿⣽⡙⣦ ⠸⡅⠁⢹⣀⣬⠇⠀⠀⣼⠀⡌⠀⠀⠈⠝⢆⣀⣀⢴⢊⠂⠀⠀⠈⡶⣯⢓⢐⠋ ⠀⠹⠷⠯⠾⠃⠀⠀⠀⢸⡀⡇⠀⠀⠀⠰⢸⠸⡀⢸⡄⠀⠀⠀⡰⠁⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⣣⠤⡀⠀⡤⠊⠀⠱⡜⡄⠀⡠⢾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠓⠾⢷⠚⠀⠀⠀⠀⡎⠉⠉⠉⠉⠣⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⡴⠖⢢⣠⠔⠁⠀⠀⠀⠀⠀⠈⠲⢄⡆⠍⠫⡀⠀⠀⠀

⠀⠀⡠⠖⢓⣫⣃⠹⡇⠀⠀⠀⠀⡰⢁⣦⣄⣀⣀⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀ ⡰⠋⣠⠖⠁⠀⣈⠵⠧⣄⠐⠒⠚⠓⠛⠒⠓⠿⢽⣧⣀⣠⠴⠋⣸⠀⠀⠀⠀⠀ ⢁⠞⠁⢀⡠⢴⠁⠀⠀⠀⠱⣄⣀⣀⣀⣬⣭⣶⣤⣈⡑⠒⠢⢴⣧⢤⡀⠤⢤⠀ ⢼⡒⣲⠊⠀⢸⣆⠀⠀⠀⠀⡈⠓⣾⠱⣖⡒⢺⠈⠳⣍⠑⢤⡀⠈⠙⢦⡴⠋⠀ ⠀⣹⠁⠀⠀⢸⢈⠷⣔⡒⢮⡤⠤⠬⠷⠒⠒⠉⠁⠀⠉⢣⠀⠙⠄⠀⠀⠱⡄⠀ ⠀⡇⠀⡀⢀⡏⡏⡶⡎⠉⠙⢚⠷⠒⢲⠦⢄⠀⠀⠀⠀⠈⡇⠀⠘⣆⡀⠀⢹⠀ ⢸⡀⠀⢰⡜⣇⣛⡵⠃⠀⢠⠃⠐⠚⠁⠀⠀⠱⡄⠀⠀⠀⡇⠀⠀⢸⠹⡄⡼⠀ ⡸⡇⠀⠈⢧⠀⠀⠌⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢰⠣⡀⢠⠎⠰⠟⠳⣄ ⠃⢣⠀⠀⠈⢷⡁⠀⠀⠀⠈⢇⠀⠀⢀⡠⠒⠒⠁⠀⣠⠋⠀⠈⡏⠀⣧⡀⠀⠘ ⠀⢼⡄⠀⠀⠀⠙⠦⣀⣀⠀⠀⡑⠒⠉⠀⠀⠀⣠⣴⣷⣶⣶⠒⡗⢠⣧⢼⡆⢀ ⢀⡎⠱⡀⠀⠀⠀⠀⠐⠶⣾⠭⣤⣤⣤⣴⣶⣿⣿⣿⣿⢿⡟⠚⠋⡡⢻⠈⠉⠁ ⠾⠤⡤⠛⣄⠀⠀⢠⢤⣀⣀⡩⠝⠛⡩⠿⣿⡿⣭⢁⣴⠋⠀⠐⢯⡀⣼⠦⣄⣀ ⠀⢠⡇⢿⣿⣿⡶⠾⢦⣀⣠⠀⣴⠊⣳⠚⠁⢀⣫⠏⠁⠀⠀⠀⢠⢃⠇⠀⠀⠀ ⠀⠘⣇⣆⢼⡟⠀⠀⣠⠚⠚⠀⠈⠉⡹⢶⡚⣿⠀⠀⠀⠠⡴⢚⡡⠋⠀⠀⠀⠀ ⠀⠀⠙⠚⠓⣇⠀⠀⠣⠤⢴⡿⠀⠘⠦⢞⣨⠟⠀⢀⣀⣴⠗⠋⠀⠀⠀⠀⠀⠀

⡟⠀⢠⡇⢀⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⣹⠞⠁⠀⠀⠸⣿⠀⢹⡀⠀⠈⠀⣾⡀⠘⡇⠀⠀⠀⠀⠱⠑⠸⡍⠙⠲⢤⣄⡀⠀⠀⠀⠀ ⠁⢰⣿⠂⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠣⢄⣀⠀⠀⠀⣿⠀⠀⢳⡀⠀⠀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠙⠒⠤⣀⡉⠓⠀⠀⠀ ⢀⣾⡇⢰⣿⣿⠀⢀⠀⠀⠀⠀⡀⢀⡿⠁⠀⠀⠀⠉⠑⠒⢿⠶⠦⠈⣧⡀⢀⡇⠘⣇⠱⡄⠀⠀⠀⢀⢰⠀⢸⠀⠀⠀⠀⠉⠑⠂⠄⠀ ⣼⣿⣇⣿⣿⡗⠀⣼⠀⠀⠀⠀⣧⣼⢡⠴⠒⠛⠛⠒⠲⣤⡀⠀⠀⠀⠸⣧⢹⢇⠀⠸⣦⢹⡄⠀⠀⢸⢸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⡇⢰⣿⠀⠀⠀⠀⢻⣿⡀⢠⣄⣀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠸⡟⠀⠙⠢⢿⡀⣇⠀⠀⡸⡸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢱⡇⢼⣿⠀⠀⠀⢸⠀⢹⡟⠚⠀⠀⠈⠫⢿⠶⠖⠀⠀⠀⠀⢰⠉⠉⠑⠢⡄⢸⣿⠀⢸⢇⣇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢸⡇⣸⣿⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠸⢿⣿⣧⡏⣼⡟⠳⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢷⣿⣿⠀⠀⠀⠈⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⣦⣀⣿⠋⠈⠁⣇⢀⡄⠀⠈⡇⠐⡟⠶⢶⣄⣀ ⣿⣿⣿⣿⣿⠘⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⠀⠀⣿⠉⠁⠀⠀⡇⠈⠁⠀⠀⠀⠉ ⣿⣿⣿⣿⣿⡆⣿⣿⠀⠀⠀⠀⣆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⣿⠀⠀⠀⠀⡇⢰⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⢻⣿⡄⠀⠀⠀⣼⡗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣷⠀⢠⣿⠀⠀⠀⠀⠃⢸⡇⠄⠀⠀⡄ ⣿⣿⣿⣿⣿⣿⣼⣿⡇⠀⠀⠀⣿⡁⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣇⢁⣰⣯⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣷⣄⢠⣄ ⠛⠉⠉⠉⠀⠈⣿⣿⣿⠀⠀⠀⢹⠳⣄⣀⣨⠗⠦⢄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡟⢻⣇⠀⣿⣿⠀⠀⠀⠀⠀⢸⣷⣾⣿⣭⣿ ⠀⠀⠀⠀⠀⠀⠘⠸⣿⡀⠀⠀⢸⡇⠀⠉⠀⠀⢒⡶⣾⣿⣿⣷⣶⣶⣿⡿⣼⣿⣿⣿⣿⠁⣸⣿⢰⡿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⢸⠁⠀⠀⠀⢀⣾⠀⠈⠫⠹⢿⣿⣿⡿⢃⣿⣿⣿⣿⠃⣰⣟⣿⣿⣇⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣴⠟⠁⠀⣰⣿⣯⣿⣿⣿⣿⡏⠉⢁⡜⠁⠀⢀⣴⠋⠀⣠⣿⠟⣷⢀⠀⢸⢳⡄⣧⡆⠀⠀⠀⠀⠈⣇⢰⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠹⣞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⢠⡿⠃⠀⣠⣼⠋⣹⢿⣿⠃⡼⠟⠳⣄⣸⡁⠀⠀⣾⠃⠀⣴⣿⠃⠀⡇⣄⠀⢸⡞⣠⢻⢣⠀⠀⠀⠀⠀⢹⡘⣆⢱⡀⠀⠀⠀⢳⠀⠀⠀⠀⠸⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣰⡿⠀⢀⣾⣿⠃⣰⣟⡎⣿⠀⡇⣆⠀⢈⣿⠁⠀⢰⠏⠀⣴⡿⠃⠀⠀⢧⢿⠀⠀⣿⡟⡎⡿⡇⠀⠀⠀⠀⠀⣇⢿⡄⢱⡀⠀⠀⢸⡄⠀⠀⠀⠀⢳⢇⠀⠀⠀⠀⠀⠄⠀⠀ ⣳⡟⠁⣰⣫⣿⠃⢠⡿⣼⡇⣿⠀⣇⢹⡀⣼⡇⠀⠀⡼⠀⢰⡿⠁⠀⠀⠀⢸⣾⠀⠀⣟⣾⢹⢻⣽⠀⠀⠀⠀⠀⢻⠸⣧⠀⢣⠀⠀⠈⡏⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠃⣰⣿⢻⠇⠀⣼⢿⡿⡇⢸⠀⣿⠀⢧⣷⠁⠀⢰⡇⢠⡿⠁⠀⠀⠀⠀⠈⣟⣇⠀⣿⢹⣧⢏⢿⡆⠀⠀⠀⠀⠸⡇⡻⣇⠘⣇⠀⠀⣷⡇⠀⠀⠀⡎⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⢰⣳⠃⢸⠀⢰⣿⡾⡇⡇⢸⡀⢹⡄⢸⡿⠀⠀⣼⢀⣿⠃⠀⠀⠀⠀⠀⠀⢸⣻⡀⢸⡀⢿⢿⠞⣿⡄⠀⠀⠀⠀⣿⡇⢹⡄⢸⡀⠀⣿⡇⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⡏⠀⣿⠀⢸⡏⡇⢱⢧⠸⣇⠸⣿⣸⡇⠀⢠⡇⣼⠏⠉⠉⠉⠉⠒⠦⣄⡀⣿⣇⠀⡇⠈⢿⠦⣹⣷⠀⠀⠀⠀⢿⡇⠀⢳⡀⣧⠀⣿⡇⠀⠀⠀⢹⣽⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⡟⠀⠀⣿⠀⢸⣇⠇⠀⢿⡇⣿⡀⣿⣿⠁⠀⢸⣷⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣾⡄⢱⠀⠈⠻⡅⣻⣷⡀⠀⠀⠸⣦⠀⠈⢧⢹⠀⣿⡇⠀⠀⢰⠸⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⢻⠀⢸⣿⠀⠀⠀⠹⣿⣱⣼⣏⠀⠀⣾⡿⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠘⣿⡌⣇⠀⠀⠹⣦⢻⣳⡄⠀⠀⣿⠤⠤⠼⣼⡆⣿⡇⠀⠀⢸⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⠀⠀⠘⡆⠘⣿⠀⠀⠀⠀⢹⡟⢁⡏⠀⠀⣿⣇⣐⣦⣼⡦⣴⣯⣷⣦⡀⠀⠀⠀⠈⠻⣞⣆⠀⠀⠈⠻⣿⡙⣦⠀⣿⠀⠀⠀⢻⣗⣿⡇⠀⠀⢸⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠆⠀⠀⢻⡀⢿⠀⠀⠀⠀⣼⢷⣿⡇⠀⢸⣿⣾⡟⠋⠁⠀⠀⠈⠙⠳⣯⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠈⠛⣮⣷⢿⡀⠀⠀⠘⣿⣿⡁⠀⠀⡏⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⣸⡇⠀⠀⠀⢻⢸⣿⡇⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⣞⣿⡿⠿⠾⠷⣮⣀⡀⢸⣷⠃⠀⢰⣧⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⣧⠀⠀⠀⠘⡇⢿⡇⠀⢸⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠈⠻⣶⠆⣿⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⢄⡀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⢻⢸⡇⠀⢸⣿⠉⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡟⣿⠀⠀⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠛⣆⠀⠀⠀⠀⠀⠈⠲⠄⠀⠈⢷⡇⠀⠈⣿⣤⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⠀⢠⢇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠒⠒⠢⣴⣿⠀⣾⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠺⣦⣀⠀⠻⣫⠙⣉⣉⣉⡁⠀⠀⠀⣿⡀⠀⡟⡀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⣀⣰⡟⣿⠀⡟⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⠻⢷⣽⣀⡉⠙⠉⠛⣦⠀⠀⢻⡇⠀⢻⣷⣄⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠉⢩⣿⡿⣿⢸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⡇⠀⠀⠀⠈⠀⠀⢸⣷⠀⢸⣷⡌⠳⣦⣀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢁⡟⡞⢠⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡀⢸⣽⣧⠀⢻⡉⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⠻⠃⠀⣼⢷⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣿⡇⠀⣿⡿⡀⢸⣇⢸⣿⠈⠙⠲⠦⣤⣀⣀⣀⣤⣤⣤⡴⠶⣶⣿⠋⣽⡿⠓⣿⠀⠀⣼⣿⣾⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⢀⣴⠿⠋⠉⠀⠀⠉⢻⣾⡀⢹⣧⡇⢨⢻⠀⣿⠁⠀⠀⠒⠠⠴⠚⠛⠉⠁⣼⣁⡼⠯⢿⣖⢿⣥⣬⣿⣿⣾⠟⣼⣻⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢿⣣⠈⣿⣇⡼⢸⢠⣿⠀⠀⠀⢀⣀⣠⠤⠔⣚⣻⡭⢤⣄⣀⡘⣿⠈⣿⣿⣿⣿⠇⣰⡟⠀⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠲⠮⠵⡒⠦⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡄⠘⣿⠇⣸⣿⡥⢤⣖⣪⡭⠵⠖⠛⠋⠉⠀⠀⠀⠉⠛⣧⢻⡆⠸⣿⣿⠏⢠⡿⠁⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣩⠤⣒⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⢾⣿⣯⠿⠗⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢻⠀⢻⡟⢠⡿⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠠ ⠐⣒⣒⣺⡭⣗⣾⡄⠀⠀⠀⠀⢀⣀⣤⢾⡏⢠⢴⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⣸⣧⢸⣇⣾⡥⣤⣀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠽⠿⠟⠋⠁⠸⡇⠀⠀⠀⠀⠈⡏⡛⠹⣇⢶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⣇⠽⠛⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢸⣱⡀⢿⡸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡞⠁⠀⠀⠀⠀⢀⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣧⣇⠘⣇⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡴⠋⠀⠀⢀⣤⣤⣴⣿⡁⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠘⡾⡆⢹⡎⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠈⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⠒⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢷⢻⠈⣷⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⡄⠀⣙⣿⣿⣿⣯⣿⣷⠀⡇⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⡤⣀⣄⠀⡀⣀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠘⡏⡆⢸⡈⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣓⢤⣄⣸⣛⠻⢿⣅⣸⣿⣿⣿⣿⣯⣽⣞⢸⠃⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣟⣟⣋⣁⣀⠠⠖⠘⡆⠀⠀⠀⠀⠀⢻⡸⠄⢧⢸⣿⠛⢶⡦⠤⠤⣤⣀⣀⠀⣠⣻⣿⣿⣿⣾⣿⣅⡀⠀⠈⣛⣿⣟⣻⣿⣿⡟⢃⢸⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⣉⣩⠵⠶⣖⡒⠒⠒⠊⣹⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀ ⠀⠀⠀⠀⠀⡤⠚⠑⢊⣉⠀⠀⣀⣀⣀⠉⠓⡦⠀⠑⡚⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠑⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠔⠁⠀⠀⠀⠀⠠⣎⠉⠉⠉⠉⠉⠐⠊⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠔⠀⠀⠀⠀⠀⠀⢀⣀⡀⠙⠢⣄⣀⣀⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⣸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣿ ⠀⠀⠀⢀⣀⠤⠊⠉⢛⠈⠳⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣅⣈⡉⢹⣿⣿⣿⣿⡿⢇⠈⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢻⣤⡀⢀⡀⠀⡤⣤⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣇⠋⠉⠉⠁⠈⠁⣾⣿⣿⣿⡿⣿⣿⣿⣿⡇⢘⢀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⠾⣇⡇⢃⣹⠔⠧⣽⣿⣿⣿⣿⣿⣿⣿⣾⣟⢧⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⢸⣿⣿⣿⡇⢣⣿⣿⣿⣿⣿⣿⣧⣏ ⠀⠒⣁⣴⣿⡇⠹⢿⣠⣮⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⣿⣿⣿⠳⣿⣿⣿⣿⡿⣿⣿⣿⣿ ⣶⣿⣿⣿⣿⣷⣄⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⣿⣿⣿⣯⡀⠹⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⠟ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣄⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡗⢂⣟⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⣇⡈⠓⡒⠒⢾⠿⢻⣿⣟⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣆ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⢀⣠⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠩⠻⢧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠆⠀⠀⠀⠀⠀⠀⠽⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢀⣤⡴⠚⣿⠀⠀⠀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⠞⠉⠓⠰⠦⢤⡀⢳⡀⠠⢶⡋⠀⠀⢠⠙⠦⣄⠀⠀⠀⠃⠈⠳⣤⠀⠀⠀⠀⢀⠹⣿⠀⠀⠀⠀⠀⠀ ⠒⠀⠀⠀⠀⠀⠀⠀⢴⠇⠀⢇⠀⠀⠀⠀⠀⠀⣳⠀⠳⣀⣠⠃⠀⠀⢸⠀⠀⠈⠙⠦⣴⠚⠁⠀⠈⣇⠀⣠⠖⠉⠀⠻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⢧⡀⠀⠀⢀⡴⡿⠀⠀⠉⣽⠀⠀⠀⢸⠀⢰⠀⠀⠀⠸⡆⠀⠀⠀⢸⡆⠈⣦⣀⣠⣤⣿⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⡧⡴⠚⠁⢀⡇⠀⠀⢀⣿⣀⡀⠀⢸⠀⢸⠀⠀⠀⣗⣷⣲⣀⡀⠸⣿⠀⢸⠉⠉⡇⠉⠉⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠃⠀⠀⠀⢸⠶⠒⠉⢹⢿⡀⠀⠀⣿⡇⢸⡄⠀⢀⣿⡟⡿⢇⠈⠙⣿⡇⢸⠖⠶⢾⣆⣴⡟⢹⣅⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⢀⠏⢸⠁⠀⢠⣷⣧⠨⡇⠀⢸⠀⣇⣧⢸⡀⠀⠋⢇⣸⡇⠀⢸⣽⡃⡀⢸⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⣰⡇⠀⠸⡀⠀⠀⢻⣼⠤⣤⣾⣶⣾⣷⣶⡚⠉⠛⠲⠧⠤⠾⠀⣰⣿⣿⣷⣖⠃⢸⣿⡇⠀⢸⣿⣿⣷⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣹⡇⣿⡇⠀⠀⣇⠀⠀⠈⣿⣿⣿⣿⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⣿⣿⣷⣀⡏⠉⣷⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⣇⡿⠀⠀⠀⠸⡀⠀⠀⠘⣿⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠩⠟⢹⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⣠⡆⢰⣷⡀⡄⠀⠈⢦⠙⠿⠽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠐⠀⣿⠀⢸⡏⠁⠉⠉⠉⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⣰⡿⣠⡿⠀⣿⠃⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣾⡟⠀⠀⣰⡟⢰⡟⠁⣠⡏⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⣻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡿⣿⡇⠀⢠⣿⣇⡾⠁⣼⡿⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⡴⠒⠒⣤⠀⠀⠀⠀⠀⠀⣰⡇⢹⣿⠀⠀⢹⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡇⢿⢻⡀⣸⢹⣿⠁⢀⣿⣧⠀⠀⠀⣼⣤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⢀⣠⡾⣿⣿⠈⣿⠀⠀⠞⣸⣿⣿⣿⣿⣿ ⣤⣤⣤⣤⡍⡘⣇⣽⠏⠈⣇⠀⠈⣿⠙⣦⡀⠀⣏⣴⡇⠉⠑⠲⠤⣀⡀⠀⠀⠀⢀⣠⣴⣾⡏⣿⠁⢉⣿⢰⣿⠀⣠⠟⠁⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⡄⣧⢸⡁⠀⣷⣿⣤⠀⢿⣀⣽⣧⣻⣿⣿⠇⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⠁⠟⣿⣇⣿⣀⣿⣃⣾⣿⢰⣿⣷⣶⣶⣶⣿⣿⣿ ⠉⠉⠙⠉⠁⣠⣿⣷⡀⣿⣟⠛⢿⣿⣿⡿⢃⣿⣿⣿⣷⠖⠀⠀⠀⠀⠀⠀⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣷⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠹⣿⠟⠛⠻⣷⣦⡙⢿⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢸⣿⠿⣿⣶⣾⣿⣷⣶⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⠻⣿⣆⠻⣿⣿⣿⣿⣿⣿⣷⠒⠒⠢⠤⠔⠒⠋⠹⣿⣿⣿⣿⣿⡟⢸⣿⠀⢻⣿⣿⣿⣿⠿⠿⣿⣿⣿ ⣀⡀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⢿⣧⡙⢿⣿⣿⣿⣿⣿⣷⣤⡶⠿⠛⠛⠳⢶⣿⣿⣿⣿⣿⠇⣿⡏⡃⠸⣧⣌⣉⣠⣀⣈⣉⠁⡀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠹⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡿⠠⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡠⠄⢒⣾⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠤⢤⣀⡀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠙⢎⠢⡀⢰⠀⡄⡀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⢁⣠⢞⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠈⠻⣄⠀⠀⠈⢧⠹⡄⢧⡇⡇⠀⠀⠀ ⠀⠀⣠⠞⠁⣴⠟⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠈⢆⠀⠀⠈⢇⢰⠸⣧⠇⠀⠀⠀ ⢀⠔⠁⣠⠞⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠑⡄⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠆⠀⠀⠘⡄⠀⢸⢸⠀⢀⣤ ⠈⠀⣼⠋⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠈⣦⡀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⢄⠈⠉⣯⡀⠀⠀⢱⡄⢸⠰⠀⠀⠀ ⠀⠘⠃⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠤⡙⠲⡄⠀⠀⠀⠉⠒⠤⣀⡀⠀⠈⢆⠀⠹⠷⡄⠀⠀⢧⠀⡆⡇⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⠺⢷⣤⣶⣤⣤⣄⣀⣀⡠⠖⠉⢃⠀⠀⠸⡄⠀⠈⢧⣇⡇⠀⠀ ⠀⠀⠀⣀⠴⠣⣀⠀⠀⠀⠀⠀⡠⠈⠢⡀⠀⠀⠀⠘⢑⡤⢊⣩⣶⣿⣟⠙⡟⠀⠙⢍⠀⠀⠀⠀⣤⣤⣤⣴⣅⣀⠀⠈⢧⠠⠀⠀ ⠀⣠⠞⠁⠀⠀⠈⠣⡀⠀⢠⠊⠀⠀⠀⠈⠢⡀⠀⠀⠈⢰⡿⡟⡟⢿⡈⣇⠀⠀⠀⠈⢆⠀⠀⠈⠉⠉⡽⣻⠙⠋⠀⠀⢸⠀⠀⠀ ⠸⠁⠀⡤⢄⠀⡠⢤⠈⢆⠈⢧⠀⠀⠀⣀⠀⠈⠲⢄⠀⠉⠀⢷⣿⣬⡷⠛⠀⠀⠀⠀⠘⡆⠀⠀⠀⠸⣶⣿⣧⣄⠀⠀⢸⡀⠀⠀ ⠆⠀⠀⡄⠈⠋⢀⡜⠀⡎⠀⠈⢂⡔⣊⣤⣤⠀⠀⠀⠑⢦⡀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⣿⣾⡟⠀⠀⠈⡇⡄⠀ ⠱⢄⠀⠘⠢⠴⠊⢀⠤⣷⡀⠀⣾⡿⣿⣿⣟⣦⠀⠀⠀⠀⠈⠢⣄⠈⠳⣄⠀⠀⠀⠀⠀⢀⡇⠀⠀⠐⠛⢻⣧⡄⠀⠀⠀⡇⠀⠀ ⠀⠀⠙⠢⣀⣠⠖⡅⠀⠀⠁⠀⠉⠉⡛⢿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠱⣄⠙⢧⣄⡀⠀⢀⠎⠱⡀⠀⠀⣠⣄⡟⣇⠀⠀⠀⢸⢰⣦ ⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⣷⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⢍⡰⠃⠀⠀⢣⢀⡀⣽⠛⢻⣾⣿⡆⠀⠸⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢠⠎⠉⡳⠀⠀⠀⠀⢱⣌⠱⣄⠻⣦⣼⡿⠃⢸⡇⢻⣯⠘⢿⡄⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⡴⠁⠀⣰⡁⠀⠀⢀⡴⠁⠈⠣⡈⠢⡀⠙⣿⡀⠀⣀⣀⣿⣧⡈⠹⣄⡄⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣹⠃⡇⠀⠀⡟⢿⢻⣷⣿⠃⠀⠀⠀⠈⢦⠈⠢⡼⠓⠀⠀⠚⠛⠛⠿⣆⠹⡇⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡼⠁⡸⠀⠀⠀⣆⠘⠋⠁⠈⠀⠀⠀⠀⢀⡠⠳⡄⢹⢻⣆⣐⣄⠀⢲⡀⠀⠑⢇⠰ ⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡰⠡⠞⠀⠘⠁⠀⠀⠀⣇⣭⣿⣶⣶⣄⠀⣠⣚⣁⡀⠀⠈⢾⣯⡿⠚⠁⠀⠈⣷⡀⠀⠠⠸ ⠀⠀⠀⠀⠐⠀⣸⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠋⠀⢀⡠⠃⠀⠀⠀⢣⠀⠀⠀⡐⠀⠘⣔⢀⣴⠀ ⠀⠀⠀⠀⢃⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⢀⠔⠁⠀⠀⣀⣀⠠⠤⢧⠀⠘⣿⣇⠀⠘⣎⢻⡆ ⠀⠀⠀⠀⢸⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⠤⠒⠊⠉⠀⠀⠀⣀⣴⣇⠀⢹⣿⣆⠀⠈⢿⡇ ⠀⠀⠀⢀⡞⢸⠇⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠢⣀⡀⠀⠀⠒⠤⡞⠋⠀⠀⠀⠀⠀⣀⣴⠾⠛⣼⣿⡄⠀⢻⡿⣧⡀⠈⢷ ⠀⠀⢀⠞⢀⡟⠀⠀⠀⠀⢸⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄⣀⣬⠟⠛⠛⠻⢿⡿⠟⠁⠀⢀⣿⠋⣧⠀⠘⣷⠛⢷⡀⠸ ⠀⢠⠊⠀⣼⠁⠀⠀⠀⢀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣴⣻⣕⣀⣀⣀⣤⠀⡀⠀⠀⠀⣿⡟⢀⣿⡀⠀⢿⣀⢈⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⣁⠤⠀⠤⢤⣤⡀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⡠⠊⠁⠀⣠⠔⠂⠉⠉⠐⢄⡀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⠞⠁⠀⡠⠊⠀⠀⠀⠀⣀⣤⠖⠤⡀⠀⠀⠀⠑⠻⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢸⢠⠎⠀⢠⠎⠀⠀⠀⢀⡴⠋⡠⠋⠀⣀⠘⡄⣀⣤⢔⡖⠒⠛⢢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣷⠋⠀⣶⠃⠀⠀⠀⢰⠋⢀⣾⠖⠚⠛⠛⠓⠛⠉⠛⠛⠻⣦⡀⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⢀⠄⢠⡏⠀⢸⠃⠀⠀⠀⠀⡎⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡆⢸⡄ ⠀⠀⠀⠀⠀⢀⡞⣠⠋⡀⢸⠁⠀⡼⠀⠀⠀⠀⢠⣡⠏⠀⠀⠤⠀⠀⠀⠀⠀⠐⠤⠄⠀⢸⡄⢸⠀⡇ ⠀⠀⠀⠀⠀⣼⡷⡿⢠⠃⡜⠀⠀⡇⠀⠀⢀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇ ⠀⠀⠀⠀⠀⣿⠁⡇⣸⣼⣷⣤⣰⡇⠀⠀⢸⠀⣿⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣼⠃⠀⢸⡇ ⠀⠀⠀⠀⠀⠙⠀⢳⣿⠹⡟⠽⢾⣇⠁⠀⣸⢠⡟⢛⣩⢭⡉⠉⠀⠀⠀⠀⠀⢉⡿⠻⡄⣸⠀⢸⣾⡇ ⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⢷⠀⠴⣿⠀⢸⡟⣾⣥⠋⠀⠀⣹⠀⠀⠀⠀⠀⢰⡏⠀⣠⣷⠏⠀⢸⣷⡇ ⠀⠀⠀⠀⠀⠀⣴⣋⣈⣀⣈⡧⣄⣻⠀⠈⡇⢿⠹⣄⣀⣠⡿⠀⠀⠀⠀⠀⠘⠷⠤⠿⣏⠀⠀⡎⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⠏⢀⣀⣸⡇⡀⣷⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⡰⠁⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⢿⣟⠋⣿⣷⣧⣏⢻⣷⣤⣖⡀⢀⡤⠶⠤⢤⣀⡀⢀⣠⠞⢹⠟⠁⠀⠁⠀ ⠀⠀⠀⠀⠀⢀⠞⠃⠀⠀⠀⠹⣿⡗⠹⣿⡿⠀⠹⣏⠛⣿⠋⠀⠀⠀⠀⠀⠹⡅⠘⣷⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠒⠳⡄⠀⠀⠀⢿⠷⣤⣾⣿⢀⣴⣿⠟⠁⠀⠀⠀⠀⢀⣀⢠⣻⠀⠈⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⢃⠀⠀⠙⢦⠀⠀⠸⣧⡞⠛⢹⣃⡿⣇⠀⠀⠀⠀⢀⡴⠋⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢿⡏⢸⠀⠀⠀⠈⠳⡄⠀⣿⡇⠀⣸⡟⠀⡇⠱⡄⠀⠀⠞⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⢸⠀⢸⡀⠀⠀⠀⠀⠙⢶⣟⣧⣰⠏⠀⠀⣿⡄⠙⢦⡄⠀⠀⠀⢀⣤⢶⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⣼⠀⠘⡇⠀⠀⠀⠀⠀⠀⣿⣾⠏⠀⠀⠀⠙⣷⣄⣀⣷⠀⢠⣶⣯⠼⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠛⣿⣧⠀⡇⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⢀⣼⡿⠻⢿⣶⣿⣿⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⣸⣋⣽⣷⣧⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⣴⣶⡟⠁⢀⡼⢻⣿⡏⢀⣴⡿⡶⠯⠭⢍⡉⠓⢲⡀ ⣸⡧⠛⢁⢤⣸⣿⣥⣄⣀⡾⠀⠀⠀⠀⠀⠀⣀⡼⠋⣠⠞⡏⢠⣿⣟⣿⣿⣿⠂⠀⠀⠀⠀⠉⠲⣄⣷

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠿⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⠉⠀⠀⠀⠀⠈⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⠋⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠃⠀⠐⢿⣿⣿⡟⠛⠁⠀⠀⠀⢀⣀⠘⣿⣄⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡟⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⣴⣿⡿⠁⠈⠋⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠁⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⢠⣾⣿⣷⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⢰⡿⠋⠀⠉⠁⠀⠀⠀⠀⢸⣿⠃⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣧⣤⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢽⣿⣄⠈⠉⠉⠛⠻⠿⠿⣶⣶⣶⡿⠟⠛⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⣄⣀⣀⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⣿⡟⠙⠿⠛⠉⠉⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠉⠀⠀⠀⠀⠉⠛⢿⣆⠀⠀⠀⠀⠀ ⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣷⣶⣦⣄⡀⠀⠀⠙⢿⣦⡀⠀⠀⢀⡄⠀⠀⠘⣿⣧⠀⠀⠀⠀ ⢰⣿⣷⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣆⠀⠀⠀⢿⣿⣄⠀⢸⣿⠀⠀⠀⢹⣿⣇⠀⠀⠀ ⢸⣿⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠹⣿⣧⡘⣿⡆⠀⠀⠀⣿⠉⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠘⢿⣷⣿⡇⠀⠀⠀⣿⡀⠀⠀⠀ ⢸⣿⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠈⢿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡂⠀⠀⠀⠻⣿⡛⠿⠿⣿⣷⣤⣄⠀ ⢹⣿⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣴⡶⠿⠿⠿⠻⣷⡀⠀⠀⠀⢹⣷⡀⠀⠀⠈⢻⣿⡄ ⠘⣿⡆⠀⠀⣠⣼⣿⣶⣶⣿⣿⣿⡟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠻⣿⣿⣿⣾⣿⠿⠃ ⠀⢿⣧⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣦⣀⣻⣷⡀⠀⠀⠀⠉⠀⢹⣿⠉⠀⠀ ⠀⠀⢿⣿⣦⣄⡀⠀⠀⠀⢠⣤⣄⣀⣀⣤⣴⣾⣿⣿⣿⣿⠿⠛⠋⠉⠙⠿⣶⡀⠀⠀⠀⣼⡇⠀⠀⠀ ⠀⠀⠀⠉⠈⠻⠿⠿⠶⠶⠾⠿⠿⠟⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣠⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⣉⣉⠉⠀⠀⠀⠀

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⡆⢀⣠⠤⠖⠒⠛⠉⠉⠉⠙⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⡼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠥⢄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠲⢤⣄⠀⠀⠀⠀⢀⣤⠖⠛⠉⠉⠛⢦⡘⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⢀⠀⢀⡞⢡⡶⠒⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠉⠀⠀⠀⠈⠲⡄⠀⠻⣾⠉⠲⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠉⡏⢀⡏⠀⠏⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⣽⠀⠀⢻⠳⡄⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡖⠒⡇⢸⠁⠀⠀⣼⠋⢹⣿⣮⢳⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣷⠈⡇⠀⢸⠀⠁⡌ ⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀⠀⠀⠀⠀⢸⡀⠣⠀⢻⣸⡄⠀⢸⣿⣿⣿⣿⣿⢸⠆⠀⠀⠀⠤⢄⠀⢸⣿⣿⣿⡟⢠⠇⠀⡞⠀⡰⠁ ⠀⠀⠀⣠⡴⠋⠁⠀⠀⠈⠙⣆⠀⠀⠀⠀⢳⣄⠀⠈⢿⣧⠀⠀⠻⣿⠿⠟⢁⡜⠀⠀⠀⠸⢦⡼⠁⠳⡝⠯⠭⠴⠋⠀⣼⣡⠞⠁⠀ ⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠉⠓⠲⠬⠿⢷⡀⠀⠀⠉⠉⠁⠀⠾⣤⢄⣀⡸⠥⠴⠋⡿⠀⠀⢀⣠⢞⣉⣀⡀⠀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣳⣦⣄⡀⠀⢀⡀⠙⣆⠒⣄⡠⠃⣴⡧⠴⠚⡹⠋⠁⠀⠀⠈⢙⡄ ⢀⡏⠀⠀⠀⠀⠀⠀⣤⠖⠋⠁⠀⠀⠀⠀⠀⢠⡞⢉⠄⠀⠈⠉⠣⡀⠈⠉⠉⠛⠛⠒⠤⣍⣉⡤⠞⢡⡀⠀⠀⢧⠀⠀⠀⡀⢨⣣⠀ ⢸⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠋⡀⠀⠀⠀⢀⠇⢀⣀⡠⠄⠀⠀⠀⣀⠤⠤⢄⠀⢻⠉⠉⠉⠳⣄⠀⠱⡀⢻⠀ ⠈⣇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠀⡜⠁⣰⠛⠋⠁⣸⠀⠀⠀⢀⡞⠁⠀⠀⠀⢳⠀⡆⠀⠀⠀⠈⠳⢄⣧⡜⠀ ⠀⢹⡄⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⣀⡴⠁⠀⣀⠴⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣄⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠒⠉⠀⣰⠁⠀⠀⣀⣈⣳⣤⡤⠴⠚⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⡠⠔⠒⠛⠒⠲⢄⣸⠁⣾⣁⣀⠤⠚⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡜⡽⠋⣠⠔⠂⠀⣀⠀⠙⣦⡇⠀⠀⣄⠀⠐⠲⣍⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⢤⣧⠤⠴⠚⠉⠁⠒⠁⠘⠒⠐⠋⠑⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣿⠟⢉⡽⠋⠀⡠⠒⡩⠛⠉⣀⡬⠭⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢾⠃⡞⡸⠀⡞⠀⠀⡸⡤⠋⢀⡴⠋⢁⠴⠒⠻⣿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡛⠣⡄⠀⠈⢸⠀⡇⡇⣸⠀⠀⣰⠁⢀⡴⠃⠀⠴⠁⠀⣠⠞⣁⠴⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠴⠾⢭⣓⠈⢢⠘⡄⣧⣸⠀⠀⠃⡇⡰⢀⠇⡰⠋⡀⠀⠈⠀⣠⣾⡷⠮⠗⠒⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣟⠛⠛⠂⠤⡈⠳⡄⠇⠀⣽⡇⠀⠀⣸⢀⠇⣸⠞⣡⠞⣡⣔⡵⠟⠉⠠⢤⣀⠈⠙⠆⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⡥⠶⠤⣀⠀⠐⡌⢆⢹⠀⡆⣿⣇⡜⢡⣣⣎⣴⣳⣾⣶⠿⠞⠉⠀⠀⠀⠀⠀⠀⢁⡀⠈⣣⡈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠟⠂⠐⠀⠈⢑⣤⡘⢾⣼⣼⣵⣿⣟⣴⠟⠛⠉⠉⠉⢯⠙⠦⣄⠀⠐⠤⣀⣀⠀⠀⠀⠀⠀⠈⣳⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠃⠐⠊⡉⠉⠉⠉⢹⠏⠚⠛⠉⠑⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⠤⢀⣄⡀⠀⠀⠀⠉⠒⢄⠀⣦⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⢠⣾⡿⠷⢶⡶⠤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢖⣦⡴⠶⠶⡓⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⡟⠁⡠⠒⢉⣠⡾⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⢸⣤⠀⢸⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢁⡜⢀⠖⣩⠎⠀⡞⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⢸⡄⣇⡼⣏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣸⠀⡎⢰⠃⣠⠎⡰⠡⣇⠀⠀⣤⣤⣤⠶⠒⠋⠉⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⢸⡴⠛⡝⠹⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⡀⠀⢸⡄⢁⡞⢁⣠⣾⣋⣲⣌⣁⣀⣠⣶⣶⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠀⠀⠉⠻⣄⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⢻⣷⡄⣼⣧⣸⠀⠿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠻⡿⣌⠻⣿⡄⠀⠈⠻⣿⣿⡇⠀⠙⢿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠉⠪⣶⣌⠻⣄⠀⠀⠈⠙⢣⡀⠀⡠⣬⠽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟⢦ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⠀⠀⠀⠀⠉⠛⣇⣀⣀⣀⣀⠄⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠹⣄⡠⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣀⠔⠙⢆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⠔⠊⠁⠀⠀⠈⢢⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⢀⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠙⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠛⢣⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠶⠶⠶⠛⠳⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⣶⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⠻⣿⣿⣿⣿⣦⡀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣃⠀⠀⠀⠀⠀⡈⣙⣳⣤⣀⠀⢀⣼⣦⣤⣀ ⠀⠀⠀⠘⣿⣴⣦⣻⣿⣿⣿⣿⣷⣴⡟⠁⠀⠀⠀⠀⠀⠀⣠⡶⢛⣉⣠⣤⣤⣉⡙⠻⠶⣶⣦⣶⣿⢿⣭⣙⣿⣴⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠛⠋⠉⠉⠉⠉⠉⠉⣹⡏⢁⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡿⠿⠿⣿⣿⣿⣾⡀⠀⠉⣻⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⡏⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠉⢀⣠⣤⣠⡈⠙⢿⣿⠀⠀⣿⡟⢋⣥⣹⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⡀⠀⠀⠀⠀⠀⢘⣿⡟⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⣿⡆⢠⡿⠀⣼⣿⣿⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠇⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢿⣿⣿⣿⣿⡿⠁⣀⣿⡇⢸⡇⠀⢿⣿⡿⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣆⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠉⠉⠉⠉⢁⣀⣿⣿⠁⠀⣿⣄⡜⢉⣤⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣅⠀⠀⠀⠀⠘⠙⢿⣿⣶⣶⣶⣶⣶⣾⣿⡿⠟⠀⠀⣻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠈⢻⣿⣷⣤⡀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠉⠉⢀⣴⣿⣿⣿⠋⠀⣹⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣤⣤⣶⣿⡿⠷⣿⣿⣷⣤⣀⣀⡞⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⢀⣴⣟⣷⡶⠶⢶⣒⠀⠀ ⢀⣀⣀⣀⣀⣤⣴⠿⠛⠙⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠠⠄⠀⠀⠀⠀⠀⠀⠈⠩⠀⠀⣸⠋⠉⠀⠀⠀⠀⠈⠁⠀ ⠈⠉⠉⠽⠛⣿⣿⣶⣶⣶⣶⣶⣤⣤⣠⣦⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠈⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⡇⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣤⣤⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠋⠉⠉⠙⢿⣿⣴⡾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⠶⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠒⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⡽⣹⣷⠆⣸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⠙⣿⡏⠀⠈⣿⡋⢾⣏⠰⢻⡃⠸⢻⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣠⣶⣿⠷⣶⣤⣄⣀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡶⠚⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣶⣿⣷⣦⡀⢀⣀⣾⠃⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠛⠋⢹⡏⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⠀⠀⣼⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣛⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣭⣽⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣠⣤⣤⡄⠉⠻⠿⠿⠿⠛⠘⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠛⠁⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀ ⠀⣠⣤⣤⣸⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣦⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡆⠀⠀⠀ ⠘⢿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠙⢾⠁⠀⠙⢳⡄⠀⠀⣠⡴⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠓⠀⠀⠀⢻⠀⡼⠃⠀⠀⢹⡈⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠙⠓⠦⣄⡀⢿⠀⠀⠀⠀⠀⠀⠀⠘⣶⠇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣸⣇⣀⠀⠀⠀⠀⠀⠙⢾⣆⠀⠀⠀⠀⢠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢆⠀⠀⠀⠈⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⣀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢦⠀⠀⢠⠃⢸⠃⠀⠀⢠⠀⠀⠀⣼⡥⠖⠋⠁⠀⠀⠀⢉⣣⣀⠀⠀⠀ ⠀⠀⠀⠀⣀⡠⠤⠬⠷⢦⣤⣀⠀⠀⠀⠀⠀⢣⠈⣦⠤⠛⠒⠚⠒⠤⣴⠃⠀⢀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡀ ⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡁⠀⡠⠤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣈⠑⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇ ⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡤⠤⠤⠶⠶⢤⣤⣤⢤⠶⠶⠊⠁⠀ ⢼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠄⠒⢒⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⠤⠤⣀⡀⠀⠀⠀⠉⠛⢶⡄⠀⠀⠀ ⠘⢷⣤⣤⡤⠴⠒⠊⢉⡴⠊⠁⢀⠴⠋⠉⠀⠙⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠔⠁⠀⠀⠀⠀⡼⠁⠈⠙⡖⠲⡖⠒⠒⠫⢄⡈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣧⠀⠙⣦⡀⠀⠀⠈⠢⡀⠈⠙⢦⡀⠀⠀⠀⠀⠀⡷⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⡇⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⣠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣤⠞⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡸⠀⠀⠀⠀⢹⢧⠀⠀⠀⠀⠀⠀⠠⡀⠘⡍⠙⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⢿⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠀⠳⡀⠀⠀⠀⠀⠀⢁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣦⣀⢀⣀⡴⠞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢦⡀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠘⣧⠀⠀⠀⢀⣤⠊⠀⠀⠀⣸⠇⠀⠀⠀⠙⠢⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠞⠋⠈⠙⠳⠶⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠉⠑⣶⣤⣄⣀⣠⣤⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⣀⠤⠒⠉⠈⢉⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣶⣿⣷⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⠏⠁⠀⢀⠄⠀⠀⠈⢀⠄⠀⢀⡖⠁⠀⢀⠀⠈⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⢀⡴⠁⠀⠀⣠⠖⠁⢀⠞⠋⠀⢠⡇⢸⡄⠀⠀⠈⢻⣿⣿⠁⠀⠀⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⢀⡞⠀⠀⢀⡴⠃⠀⣰⠋⠀⠀⣰⡿⠀⡜⢳⡀⠘⣦⠀⢿⡇⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢀⠆⡞⡄⠀⣠⡞⠁⣀⢾⠃⠀⣀⡜⢱⠇⣰⠁⠈⣷⠂⢸⡇⠸⣵⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⡜⣸⡟⢀⣴⡏⢠⣾⠋⡎⢀⣼⠋⢀⡎⡰⠃⠀⠀⣿⣓⢒⡇⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠴⢻⣟⢀⣀⢀⣧⡇⢨⠟⢾⣔⡿⠃⢸⢀⠞⠃⢀⣾⡜⠁⠀⠀⠀⡏⠁⢠⠃⠀⢹⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣼⢸⣿⡟⢻⣿⠿⣶⣿⣿⣿⣶⣾⣏⣀⣠⣾⣿⠔⠒⠉⠉⢠⠁⡆⡸⠀⡈⣸⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣸⣿⣇⢸⠃⡄⢻⠃⣾⣿⢋⠘⣿⣿⠏⣿⡟⣛⡛⢻⣿⢿⣶⣷⣿⣶⢃⣿⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣰⠃⣿⣿⣿⣿⠀⣸⣧⠈⣸⣿⠃⠘⠃⢹⣿⠀⣿⠃⠛⠛⣿⡇⢸⣿⡇⢸⣿⡿⣿⡀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣦⡀⠀⢀⡔⣹⣼⡟⡟⣿⣿⣿⠛⠻⠶⠿⠷⣾⣿⣿⣬⣿⣠⣿⣀⣿⣿⣿⡇⠸⡿⠀⣾⡏⢠⣿⣇⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣿⣷⡞⢠⣿⢿⡇⣿⡹⡝⢿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⣶⣶⣾⣿⣇⣾⠉⢯⠃⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⣿⣿⣿⠇⢸⠇⠘⣇⠸⡇⣿⣮⣳⡀⠉⠂⠀⠀⣀⣤⡤⢤⣀⠀⠀⠀⠀⠀⢈⣿⠟⣠⣾⠿⣿⡆⡄⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⡘⠾⣄⠀⠘⢦⣿⠃⠹⣿⣿⣶⠤⠀⠀⣿⠋⠉⠻⣿⠁⠀⠠⣀⣤⣾⣵⣾⡿⠃⣾⠏⣿⣧⠋⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⠳⣄⡈⠃⠀⠼⠋⠙⢷⣞⢻⣿⣿⣀⡀⠈⠤⣀⠬⠟⠀⢀⣠⣶⠿⢛⡽⠋⣠⣾⣏⣠⡿⣃⣞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠛⠓⠢⠶⣶⡤⠺⡟⢺⣿⠿⣿⣶⣤⣀⣠⣴⣾⡿⠿⢵⠋⠙⠲⣏⡝⠁⠀⣹⢿⡣⣌⠒⠄⠀ ⠀⠀⠀⠀⠀⠀⢸⠈⡄⠀⠇⠀⠀⡖⠁⢢⡞⠀⢰⠻⣆⡏⣇⠙⠻⣿⣿⣿⣿⠋⢀⡴⣪⢷⡀⠀⡘⠀⢀⠜⠁⢀⠟⢆⠑⢄⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠱⠀⠸⡀⠄⠳⡀⠀⢳⡀⢰⠀⢸⢇⡟⠑⠦⢈⡉⠁⢼⢠⡏⣴⠟⢙⠇⠀⡇⢠⠃⢀⡴⠁⠀⠘⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠇⠀⠣⠀⡗⢣⡀⠘⢄⠀⢧⠀⢳⡟⠛⠙⣧⣧⣠⣄⣀⣠⢿⣶⠁⠀⠸⡀⠀⠓⠚⢴⣋⣠⠔⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡤⠙⢤⡈⣦⡼⠀⠀⠧⢶⠚⡇⠈⠁⠈⠃⠀⡰⢿⣄⠀⠀⠑⢤⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠖⠊⠉⠁⠀⠀⠀⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⢧⣻⣆⠴⠯⣄⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⢠⠉⢁⡆⠈⠉⠸⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀ ⠸⣀⠾⢁⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠻⡄⠀⠀ ⠀⡿⠇⠺⠿⠿⡟⣲⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⡶⠿⢿⡀⠀ ⠀⣦⣦⢀⣀⣤⡞⠁⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⡴⠻⣏⣶⠞⠛⠷⠀ ⠀⠈⠉⠁⣧⠀⠙⡆⠀⠀⠀⠀⠀⠀⢸⠳⣄⡀⠀⠀⢣⠀⣻⣷⠖⠛⢷⡇ ⠀⠀⠀⠀⡟⠀⢀⡇⠀⠀⢀⢲⠛⢉⣥⠒⠁⠀⣀⡤⠋⣠⣿⡿⠿⢶⣸⠃ ⠀⣀⠤⡴⠁⣠⠎⡇⠀⣆⡼⠛⠀⠛⠷⢶⠴⠛⠁⠀⣴⠿⠿⢷⣦⣀⡟⠀ ⠀⠛⠿⠵⠷⣋⡴⠁⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣄⣀⠀⢸⡟⠀⠀ ⠀⠀⠀⠀⠰⣷⣄⡤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⠟⠉⠉⠙⠉⠙⢿⣽⠉⠉⣿⣿⠟⠉⢉⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠁⠀⣴⣟⠛⣶⠀⠀⢹⠀⠀⡿⠋⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⣼⡟⢿⡿⠂⠀⣸⠀⠀⣄⡀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣦⡀⠀⠙⠛⠁⠀⣸⣿⠀⠀⢻⣧⣀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠲⠦⠴⠶⠛⠋⠙⠓⠠⠜⠃⠙⠂⠤⠬⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣤⣄⠀⣠⣤⣤⣤⣄⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⢠⣤⣤⣄⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀ ⢸⠀⠀⠙⢧⣻⡇⠀⣾⣿⠏⠉⠀⢀⠀⠀⠙⣦⠀⠀⢀⡾⠋⠁⢀⡀⠀⠉⠻⣾⡆⠀⠙⢷⣽⠀⠀⢸⡧⠀⢰⣄⣰⣄⣸⡇⠀⠀⠀⠀ ⢸⠀⠀⣦⠐⢿⡇⠀⣿⡟⠀⢀⣾⣿⣿⠀⠀⠸⣧⠀⡜⠀⠀⢸⣯⣙⣷⠀⠀⢹⡇⠰⣆⠀⠻⣀⠀⢸⣟⠀⢸⣿⠷⠿⢿⡇⠀⠀⠀⠀ ⢸⠀⠀⢹⣆⠀⠻⡆⣿⣧⠀⠈⢿⣹⣧⠁⠀⢠⡿⠀⢣⡀⠀⠸⣝⣿⡿⠀⠀⣼⡇⠀⣿⣆⠀⠛⠆⢸⣿⠀⠸⣿⣿⣷⣾⡇⠀⠀⠀⠀ ⣸⡀⠀⣸⡟⢷⡀⠀⣿⡟⣦⡀⠀⠉⠉⢀⣠⡞⠁⠀⠘⠷⣄⠀⠉⠉⠀⢀⣴⣿⡇⠀⣿⠘⢷⣄⠀⢸⣯⠀⠈⠛⠩⠍⣽⡇⠀⠀⠀⠀ ⡞⠛⠷⠟⠀⠀⠙⠿⠇⠀⠀⠙⠛⠺⠟⠛⠉⠀⠀⠀⠀⠀⠈⠛⠺⠓⠛⠋⠁⠈⠛⠓⠚⠀⠀⠙⠳⠖⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢠⡶⢶⣶⣶⠀⠀⢀⣤⡶⠶⠶⠦⣄⣴⠶⠶⢶⣤⣠⡶⠶⣶⡶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⡶⢦⣀⠀⠀⠀⠀⣠⣴⠶⠶⢦⣄⠀ ⠀⠀⡼⠁⢠⡇⢻⣧⣰⡿⠁⢠⣤⡄⠀⠉⢿⠀⠀⣿⡿⠉⠀⣰⣿⠁⠀⢠⣤⣤⣀⣿⠀⠘⢦⣤⣀⠀⠈⢷⠀⠀⣾⠋⠀⣤⣄⠀⠙⡆ ⠀⣸⠇⠀⣼⡇⠀⢻⡜⣧⡀⠀⠈⠋⠻⠿⣿⠀⢰⠟⠀⢰⣞⠁⣿⠀⠀⠀⢉⡉⢙⣿⠀⠀⠀⣷⣿⠂⠀⠈⡆⠀⠙⣿⣽⠟⠁⢀⡴⠋ ⢠⡏⠀⢀⠋⣹⠀⠈⣿⠘⠙⢻⣲⣦⡄⠀⢸⠀⠘⣰⣆⠀⠘⢷⣿⡀⠀⢸⣿⣷⣿⣿⠀⠀⢀⣷⡿⠃⠀⢰⠇⠀⠀⢸⣄⣤⣴⡏⠀⠀ ⣼⠀⠀⣿⠏⢹⣇⠀⠉⢷⣄⣀⣉⣁⣀⣰⣿⡀⠀⣿⠜⣦⡀⠀⢻⡅⠀⠀⠀⠀⠀⣿⡀⠀⠈⠀⣀⣀⣴⠏⠀⠀⠀⢸⣏⠀⣀⡷⠀⠀ ⠋⠉⠛⠛⠀⠀⠙⠛⠛⠛⠈⠉⠉⠉⠉⠀⠈⠙⠛⠛⠃⠀⠙⠋⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠘⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⡄⢸⠀⠀⢢⠀⠉⠻⣦⠀⣿⣿ ⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⠔⠊⢀⠀⠀⠀⠀⢀⠔⠀⠀⠀⡴⡇⠀⠀⠀⢰⠁⡸⠀⠀⠀⣧⠀⠀⠘⢧⣿⣿ ⣷⡀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢠⠎⠀⠀⠀⢀⠔⠁⢀⠔⠁⠀⠀⢀⠴⠃⠀⠀⢀⡞⠀⠁⠀⠀⢠⠃⠀⡇⠘⡆⠀⠘⣧⠀⠀⠀⢻⣿ ⡿⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⡴⠁⠀⠀⢀⠔⠁⠀⡴⠁⠀⢀⣤⠞⠁⠀⠀⢀⡴⠋⠁⢰⠁⠀⢀⠎⠀⣸⠇⠀⢣⠀⠀⠘⡆⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⡜⠁⠀⠀⡠⠋⠀⢀⠎⣠⠴⢊⠝⠁⠀⠀⠀⡴⠋⠀⠀⠄⡞⠀⠀⡜⠀⢠⠇⢠⠀⠈⡆⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡔⠁⠀⣰⣿⣿⣤⠔⠁⠀⠀⢀⡴⠊⠉⠛⠉⠁⢰⠀⠀⡰⠁⢀⡞⠀⢸⡀⠀⠸⡀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠞⠀⠀⣼⠋⣹⠟⠁⠀⠀⢀⣴⣏⡀⠀⠀⠀⠀⠀⡎⠀⣰⠁⠀⡜⠀⠛⠉⡇⠀⠀⠃⠀⠀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠎⢀⠆⠀⢠⠎⠀⠀⡾⣿⠞⠁⠀⠀⢀⣴⣿⣿⣿⡙⢦⡀⠀⠀⠰⠀⡰⠁⠀⡜⠀⠀⠀⠀⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⣠⠎⢠⢧⠃⠀⠀⣼⡔⠁⠀⠀⣠⠞⠉⡏⠉⣙⣿⣿⡍⠻⠀⢠⠃⡰⠁⠀⡰⠁⠀⠀⠀⢀⣸⣇⠀⠀⡇⠀⠀⠀⠀⠀ ⡀⠔⠉⢀⡠⢾⡟⢀⡿⠃⠀⠀⡼⠋⠀⢀⣴⡊⠀⠀⠀⠙⠦⠤⠾⠻⠗⠀⢠⢇⡔⠀⠀⡴⠁⠀⠀⠀⠀⠀⠈⣿⣄⠀⢣⠀⡆⠀⠀⠀ ⡰⠂⠛⠛⠢⢸⢁⠜⠀⢀⡜⣸⢋⣠⣾⣿⡟⠉⠑⠦⣄⣀⡀⠀⡀⠀⠀⢠⠃⠋⠀⢀⡞⠀⠀⠀⣀⡀⠀⠀⠀⠈⢹⣇⢸⣤⠁⠀⠀⠀ ⠁⠊⠀⠀⠀⡾⠊⠀⡠⠊⢠⣷⢻⣿⡏⠁⠑⢶⡄⢀⠲⡀⠉⠑⣗⢄⣰⠃⠀⠀⣰⠟⠀⠀⢀⣀⣀⣉⣉⣒⠢⣀⠀⢣⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⢁⡠⠊⠀⠀⡸⠨⠟⠁⠙⠦⠳⡷⡵⣤⡱⣌⢞⠁⣸⡼⠁⠀⣠⣞⠁⠀⡄⠀⠘⡟⡿⢿⣿⣿⣿⣿⣥⠄⣧⡟⠀⠀⠀⠀ ⠖⠶⠏⣴⡞⠉⡇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠙⠋⣱⠋⠀⢀⣴⣿⢻⣤⡄⠛⣄⠀⠹⢿⠿⠟⠁⠀⠹⣿⣶⣿⠃⠀⠀⠀⠀ ⢧⠀⠀⢸⠇⠀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣠⠾⠟⠹⡰⣵⣝⣿⣶⣿⠳⡀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀ ⠈⣧⡀⢹⠀⢰⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣥⡖⠉⠀⠀⠀⠀⠀⠈⠈⢻⣻⣿⣷⡘⢶⡤⠤⡤⠞⣱⣿⣿⠇⠀⠀⠀⠀⠀ ⢀⡿⠉⡿⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠴⠟⣻⣅⡀⠈⠓⠢⠤⣀⡀⠀⠀⠀⠀⠙⠟⢿⣿⣦⠙⢶⠂⣰⣿⡿⢻⠀⠀⠀⠀⠀⠀ ⣼⠃⢀⠇⠀⣾⠀⠀⠀⡇⠀⠀⠀⠀⠒⠉⠀⠀⢰⣿⣷⢛⠋⠉⠋⠒⢦⣉⠓⣄⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⣏⡿⠁⡆⠀⠀⠀⠀⠀⠀ ⠋⠀⡼⠀⢠⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⣰⣿⡽⠭⠥⠬⣧⣈⣆⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⠃⢰⠁⢠⠀⠀⠀⠀⠀ ⠀⣰⡇⠀⣼⣥⡇⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⠀⠉⢻⡿⣏⣓⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⡎⠀⡈⠀⠀⠀⠀⠀ ⠐⠉⠀⢰⠏⠀⢣⠀⠀⣿⣿⣦⡀⠀⠀⣀⡴⠟⠉⢹⡀⠀⠀⢸⠇⠀⠘⣿⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢠⠃⠀⠃⠀⠀⠀⠀⠀ ⠰⠀⢀⠏⠀⠀⢸⠀⠀⡇⠉⠛⠻⣶⡞⠋⠀⠀⠀⠀⡇⠀⠀⠊⠀⠀⢸⡋⣷⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⠃⠀⡜⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢷⣽⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⡣⠠⡀⢇⠀⠀⠀⠀⢀⣴⢟⠇⡌⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⢸⡆⠻⣷⣄⡀⣠⣧⣄⣀⣤⢾⠟⠀⠀⢁⣸⣀⣠⡤⣶⡟⡸⠸⢰⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⠁⠀⠈⠹⣿⣯⣀⣠⣔⣁⡤⠔⠒⠊⠉⠁⠀⢰⠁⢹⡟⢳⡇⡜⠀⢸⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀

⢀⡄⢀⠃⢠⡟⠉⠀⠀⠀⠀⠀⣿⣴⠁⠘⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⢕ ⣿⢀⣾⢠⣿⡇⠀⠀⠀⠀⠀⠀⢿⠑⠀⠀⢻⡟⠿⡁⠀⠀⠀⠀⠀⣠⠞⢙⠢⠀ ⣿⣸⡏⣾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢆⣂⠀⠃⠀⠀⣜⣹⠀⢏⡇⠀ ⣿⣿⣄⠼⠒⠷⡀⣀⣀⣠⣤⠤⠀⠀⠀⠤⠤⡤⠭⢉⣛⡛⠶⠦⣤⣉⠙⠋⠀⠀ ⠿⡿⠡⠂⠉⠄⠸⡀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢈⡑⠠⣀⠈⠉⠑⠒⠭⢽⣷⣦⣄ ⢸⠡⠋⢀⠠⡼⠀⡇⢀⠎⠀⠀⠀⠀⠀⠈⠲⠒⢢⣌⣉⡍⢖⠖⠁⠀⢠⣈⣙⣽ ⠈⢇⠀⠃⠀⢅⠀⠸⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠙⠁⢄⠀⠀⣴⣿⡖⡼⠙ ⢀⣼⣆⠑⢄⡨⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⡸⡜⠀⠀⠀⠀⠀⠀⠀⡏⠛⡺⠁⠀ ⣾⣿⣿⣆⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢀⠔⠀⠀⠀⠇⠀⡇⠀⠀ ⣿⣿⣿⣿⡟⠉⠸⡄⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠸⡠⠤⠀⠀⡠⣰⠁⣠⣦ ⣿⣿⠻⣿⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠒⠂⠁⠠⠋⣈⠋⠠ ⠉⠙⠒⠃⠤⢀⣀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠒⠂⠤⡀⠀⡰⠁⠀⢀⡀⣠ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠄⣀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢀⠔⠀⠀⠀⠸⢧⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢀⡀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠣⢄⣀⠀⠀⠰⡇⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀

⠀⠀⠀⢀⡴⠋⠉⢉⠍⣉⡉⠉⠉⠉⠓⠲⠶⠤⣄⠀⠀⠀ ⠀⠀⢀⠎⠀⠪⠾⢊⣁⣀⡀⠄⠀⠀⡌⠉⠁⠄⠀⢳⠀⠀ ⠀⣰⠟⣢⣤⣐⠘⠛⣻⠻⠭⠇⠀⢤⡶⠟⠛⠂⠀⢌⢷⡀ ⢸⢈⢸⠠⡶⠬⣉⡉⠁⠀⣠⢄⡀⠀⠳⣄⠑⠚⣏⠁⣪⠇ ⠀⢯⡊⠀⠹⡦⣼⣍⠛⢲⠯⢭⣁⣲⣚⣁⣬⢾⢿⠈⡜⠀ ⠀⠀⠙⡄⠀⠘⢾⡉⠙⡟⠶⢶⣿⣶⣿⣶⣿⣾⣿⠀⡇⠀ ⠀⠀⠀⠙⢦⣤⡠⡙⠲⠧⠀⣠⣇⣨⣏⣽⡹⠽⠏⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⢕⡋⠶⠄⣤⠤⠤⠤⠤⠂⡠⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⣄⣀⣀⣀⣠⠔⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠛⠉⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠛⠲⢦⣤⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠹⣧⡀⠀⠀⠀ ⢀⣼⠟⠅⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠑⠿⠃⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠹⣧⠀⠀⠀ ⣾⠏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢽⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣿⣆⠀ ⣿⣆⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠠⠒⠠⡄⡀⢢⡀⡠⡈⠙⣦⠑⣍⢦⠙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⡅⡌⢸⣀⠙⡔⡀⠲⡄⠙⡄⠈⢦⡘⢦⣷⢈⠥⠒⠒⠠⢀⠀⠀ ⠀⠀⠀⠀⢰⣟⠁⣷⠸⠻⡆⢳⠰⠘⣹⡄⢸⣄⠘⡵⡌⡰⠁⠀⠀⠀⠀⠀⢂⠀ ⠀⠀⠀⠀⡿⢹⠀⣿⡄⢻⣿⣸⣦⣧⠂⣟⡀⣿⠹⣾⢱⠁⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⣿⢸⡄⠼⡼⣿⣿⡍⡏⢻⣠⡜⠣⠚⣄⡯⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣾⣯⡄⠀⠹⠬⠖⠁⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠟⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢳⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⢅⡀⠠⠀⠀⢀⡀⠀⠀⠀⠀⡐⠃⠙⢆⠀⠀⠀⠀⠀⡰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠢⣳⡾⣓⠅⠀⠀⠀⡠⠊⠃⠀⠀⠀⠐⡤⡀⢤⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⡠⠊⢠⠇⢠⣧⣶⠟⠛ ⠀⠀⠀⠀⠀⡠⢀⣀⡀⠀⠈⠒⠒⠉⠑⠄⠀⠀⢀⠤⠊⠀⣰⡏⠀⣼⠟⣡⣴⡟ ⠀⠀⡔⣉⡉⠂⣪⠂⡈⢫⠂⠀⠀⠀⡠⢺⠀⣴⠁⠀⣠⣾⣿⣷⣼⠏⣴⣿⡿⠁ ⠀⠀⡟⣥⠇⠀⠀⠀⠇⠀⠀⡱⣴⣾⣷⡼⣧⡏⣑⣾⣿⣿⣿⣿⡏⣼⣿⣿⠁⣠ ⠀⠀⠃⠡⡖⠀⠀⠀⠀⠀⠀⠀⣟⣿⣯⣸⢹⠁⣿⣯⣿⣿⣿⣿⣸⣿⣿⣇⣴⣿ ⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⠆⣼⣿⣟⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢰⠡⡀⠀⠀⣀⠀⣾⣿⡟⠀⠘⢸⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⡀⠀⢀⠞⣤⣧⣴⣿⣿⣷⡌⣿⡇⢠⠂⣿⣿⡿⣿⣿⠇⡇⠿⣻⣿⣿⣿⣿⢿

⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⡟⠁⠀⠀⠀⠀⠀⢀⣤⢀⣀⣄⣠⡀⢠⣿⣼⣄⣠⣢⣤⣦⣄⣰⣀⣀⣶⣷⣾⣿ ⣶⣂⠀⠀⠀⢀⣳⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿ ⣿⣿⣗⣀⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣟⣻⣽⡿⠇⠠⠿⢿⢿⣿⣿⠙⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠄⠉⠈⡄⠀⠀⠀⠈⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠛⠛⢻⠉⠡⡀⡌⠀⠀⡇⠀⠀⠀⠀⡟⡄⣿⣿⠻⣿⣿⠟⠻⣿ ⣿⣿⣿⣿⣿⡿⡄⠀⠛⠀⢰⡟⠉⣂⠘⠇⠀⠀⠀⠈⡅⣿⣿⠏⠀⠈⠃⢀⠀⠈ ⠛⠉⠉⠁⠲⠂⠀⠒⠒⠚⠛⠷⣼⣧⡀⢀⠀⢒⡈⠀⣽⣿⡟⠀⠀⠀⠀⢀⡵⠀ ⠀⠀⠀⠀⢀⠆⠀⠄⠀⣀⠀⠀⠀⢈⣑⢄⠉⠀⠀⣸⣿⣿⠇⠀⠀⣀⣴⠟⠁⠀ ⠶⣤⣄⡀⠉⣦⣀⣀⡀⠀⢀⣬⣶⣿⣿⣷⣦⣴⣾⣿⡿⠃⣀⣤⣾⠟⠁⠀⠀⠀ ⠖⠀⡺⢏⠃⣿⣿⣯⣉⡙⠛⢻⣿⡿⠛⢹⣿⣿⣿⡟⠁⣾⣿⣿⣿⠀⠀⠀⢀⣴ ⡴⠋⢰⠈⠀⢻⣿⣿⣿⣿⣿⣿⡏⣿⡃⠀⣹⣿⡿⠁⢀⡿⣿⡇⢻⡄⠀⠀⣾⣿ ⠁⠀⠈⢰⠈⠄⠻⣿⣿⣿⣿⣿⡟⠈⠻⣷⢪⣟⠔⣺⠋⠀⣿⢧⠘⣇⠀⠀⠈⠙ ⠀⠀⠀⠀⢧⣨⣦⣜⣿⣿⣿⣿⣽⠀⠀⠈⠃⠀⠘⠁⠀⡸⣻⡌⠑⢿⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢽⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣽⢿⡿⣶⠷⢤⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣾⡽⢛⣲⣎⠀⢀⢬⣷⣼⣷⣷⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⢿⣿⣿⣷⡀⠀⠀⢀⠖⠛⣷⠯⡏⠹⣿⣿⣿⣇⢢⢘⣵⣿⣿⣿⣿⣿⡄ ⢏⡇⡆⣸⣿⣿⣿⣧⣿⣷⢾⣷⠾⣿⢥⠇⢤⡿⢿⠿⣋⣿⢃⡍⠝⠹⢸⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⠟⢿⣿⣷⣾⣶⣿⣶⣶⣾⣧⣧⣶⣿⣿⣿⣧⣦⣴⣼⣿⣿⣿ ⠀⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⡸⣿⡙⣻⡿⠻⣿⣿⡇⠉⠋⢹⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠄⣾⢿⣿⣷⣯⠿⡿⡿⡄⠀⠀⠙⠛⠋⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡰⠈⣾⢼⣿⠀⠱⣹⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣒⠶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⣄⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⣈⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡍⠁⠀⠀⠀ ⠀⠐⣺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀ ⠀⠊⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢆⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠘⡟⠒⠐ ⠀⢰⡇⠀⠀⠀⠀⠀⣬⠀⡀⠀⡌⠈⢧⢰⡔⣷⣰⠀⠀⠀⠀⠀⢡⠸⣸⡄⠒ ⠀⣼⡁⡀⠀⠀⠰⢻⣯⣦⡙⣡⠋⠉⠈⢫⡏⢼⡟⣀⢀⠀⠀⢀⣸⣦⢱⣿⠦ ⠈⢸⣷⣄⣄⢸⡷⡃⢈⣿⣧⠇⢰⠞⣻⡉⠓⠀⠁⣿⣼⣦⣄⣌⢧⣿⡿⠁⠀ ⠀⠰⣻⢿⣾⣾⡟⣚⡛⢧⠁⠀⠀⠐⠛⠃⠙⠃⠀⠘⠇⢸⡯⣟⣪⣿⠃⠀⠀ ⠀⠀⠋⠘⣼⣿⣆⠙⠛⢉⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠃⠛⠛⡄⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢻⢿⣏⠉⠡⡀⠀ ⠀⠀⠀⠀⣠⠤⠄⠐⢀⠖⣦⣤⣤⣤⡤⠄⠀⠀⠀⣠⡖⠀⠀⠢⡀⠀⠀⠈⠒ ⠀⠀⡔⠊⠁⠀⠀⠀⠀⠁⠈⠉⠛⠥⢀⣀⣀⣠⡾⠋⠎⠀⠀⠀⠈⠂⠤⠤⣀ ⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠤⢠⡴⠂⠈⠉⠀⠀ ⠀⠀⢤⡂⠋⢩⠦⢄⡀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠠⠀ ⠀⠀⠀⠀⠉⠁⢀⡠⠂⠉⠐⠒⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠑⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⠀⠀⠄⠀⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠒⣠⣤⣐⠁⠀⠀⠀⠀⠀⠀ ⠀⡠⠖⠊⠉⠉⢹⠀⠈⠉⠉⠒⢦⡀⠀⠀ ⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀ ⠘⠈⠓⠒⠤⠤⠤⠤⠤⠤⠒⠋⠁⡇⠀⠀ ⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀ ⠰⣿⣚⣗⣦⣤⣤⣴⣒⣒⣒⣯⣽⣫⣿⠀ ⠀⢹⠁⠒⠚⠵⠶⠛⠿⠯⠭⠭⠕⠚⢱⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆ ⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇ ⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀ ⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣴⣶⣶⣶⣤⣀⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⠿⢿⣿⣿⣿⠟⠻⠿⠿⠛⠛⢿⡛⠋⠁⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠙⢻⣀⠀⣿⣿⠃⠀⣀⣀⣀⠀⠀⠀⠑⡄⢀⣜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⢹⣷⣿⣿⢠⠋⢹⢿⣿⡷⠂⠀⠀⠰⠯⣜⠀⠀⠀⠀ ⠀⠀⠀⠀⢴⡙⣲⣿⣿⡟⢠⣀⠘⣜⠿⠁⠀⠀⠀⠒⠒⠒⡻⠃⠀⠀ ⠀⠀⠀⢰⣏⣟⠛⠛⢻⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⡁⠑⡄⠀⠀ ⠀⠀⠀⠀⠑⠾⡗⡊⠀⠀⠀⡠⠊⠁⠀⢀⠼⡀⠀⢸⣄⠠⠔⠣⡄⠀ ⠀⠀⠀⠀⠀⠀⠘⢍⠁⠘⠅⢀⣠⠔⠊⠀⡠⠙⢦⣼⣿⠷⠀⢀⢼⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠉⣿⡏⠑⠹⠤⠄⠊⢝⡩⠔⠊⢀⡠⠒⠁⠀⣱ ⠀⠀⠀⠀⠀⠀⠀⠇⠰⡟⠉⠀⠀⢀⠔⠊⠁⣀⠤⠂⠁⠀⠀⢀⠔⠁ ⠀⠀⠀⠀⠀⠀⠀⠘⠄⢫⠀⢀⠔⠁⠀⠀⠈⠀⢀⡀⠤⠒⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣳⠃⠀⣀⡀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣴ ⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣇⣿⣿ ⣿⣽⣿⣿⣿⣿⣿⠿⣯⠼⠑⠋⠓⠓⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣧⡈ ⢷⣿⣿⣿⣿⣿⡏⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠻⣿⣷ ⣾⣿⣿⣿⣿⣿⡁⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⣿⣿⣿⢡⣿⣿ ⣿⣿⣿⣿⣿⢧⣷⣿⣦⣐⣷⣄⠀⢀⠀⠀⢀⠀⢀⣴⣗⣂⣴⣿⣳⢸⣿⣼⣿⣿ ⣿⣿⣿⣿⣿⣾⣇⠙⢏⢻⣿⡟⢷⣤⡱⠠⢥⣾⠟⣿⣿⠋⠛⣹⣷⣿⣿⣿⣿⣿ ⣋⡽⣻⣟⣿⣷⣌⠣⠀⠛⠲⠶⠶⡋⡇⠀⢀⣐⠒⠖⣒⣅⡰⢉⣾⣿⣿⣿⣿⣿ ⣿⣶⣿⣿⡿⣿⢿⣷⣆⠀⠀⠀⠀⠻⢧⠀⠈⠉⢺⣫⣷⣿⣷⣿⣿⣿⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⡀⠀⠁⠢⣀⣀⡠⠐⣡⣇⡼⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⢿⣿⣿⣿⡿⠀⠹⡒⢄⡀⠐⠒⠀⢘⠭⠪⠀⢸⣿⣿⣿⠇⢸⠂⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠱⡀⠙⢶⣴⠞⠁⡰⠁⠀⣐⣿⣿⣿⡖⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⠓⠵⡢⠤⠽⡄⠀⠁⠀⡰⠃⠀⢈⣀⣿⣿⣿⡇⠀⠀⠀⠀ ⢠⡀⠀⠀⢰⣿⣿⣿⠀⠀⠈⠑⢄⠘⢢⣠⠔⠁⡠⠊⠁⠀⣿⣿⣿⣷⠀⠀⠀⠀ ⠈⢷⡀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠑⠤⣤⠔⠋⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⢀⡼

⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡠⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⠠⢄⡠⠊⠉⠉⠉⠍⡉⠉⠚⠲⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⡀⠀⠀⠀⠀⡠⢁⡴⠫⠃⢀⠐⠆⠀⠀⠈⠒⡂⠕⢍⣳⡇⠀⠀⠀⠀⠀⠀⠀ ⢟⠛⢤⠀⠀⠀⠑⡞⡡⠁⠀⠀⠁⠢⢄⣀⡀⢀⣀⠔⠚⠡⠙⣦⠀⠀⠀⠀⢀⠁ ⠈⠫⣙⣧⡀⡀⢐⠡⢁⠀⢰⠀⠀⠀⠈⠄⠀⡺⣄⣁⠀⠀⢡⠑⡀⠀⠀⠀⠘⠀ ⠀⠀⠘⣠⣤⠀⢼⠀⢸⡀⠀⠡⡀⠀⠀⣼⣞⣤⡼⢼⠀⢸⠀⠢⠬⠂⠀⠀⢀⠀ ⠀⠀⠀⠟⠁⣰⢞⠠⠈⣴⣭⣵⣜⠢⡤⢘⣍⠛⠛⢰⢀⣿⣴⣂⠚⠀⠀⠀⠠⠀ ⠀⠀⠐⠠⠂⡜⢸⡈⣄⠹⣧⠛⠛⠀⠊⠀⠀⡀⠀⠒⠃⣩⠵⠏⠀⠀⠀⢀⠀⠀ ⠀⠀⡰⢁⡾⠁⠀⠟⠼⠢⣕⠤⠀⠀⡴⠘⠃⢉⠀⢀⣬⠂⠀⠀⠀⠀⠀⠁⠀⡀ ⠀⠐⢁⡞⠁⠀⠀⠀⠀⠀⠀⠑⢀⠀⠑⠀⠠⠊⣠⢎⣷⣄⠀⠀⢀⡀⣀⠀⠀⢰ ⢀⡦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣷⢂⠤⠊⣠⣿⣿⣿⠖⠊⠀⠀⡠⠁⠄⢡ ⡄⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣽⡇⢠⣼⣿⣿⠟⣏⠀⡀⠠⠎⠂⢰⣾⣧ ⢣⢸⣶⣾⣶⡀⠀⠀⠀⠀⢀⢻⣿⣿⠏⠀⣸⣿⣿⣿⣿⣍⣀⡇⢀⣔⣺⣿⡏⠁ ⠀⠀⠈⠻⣿⣿⠀⠐⠁⢠⠥⠞⠛⠻⡿⠼⠿⢁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡻⣡ ⠐⠂⠤⠴⠽⢣⠁⠀⢠⠏⠀⢀⠴⠃⠐⠨⢠⣬⣼⣦⣼⣿⣿⣿⣿⣿⣿⣯⣶⣾

⠀⣴⠒⢲⡒⠤⣖⠒⣒⠒⠄⢴⡒⠒⠤⣖⠒⣖⠒⢢⣔⠒⠢⠀ ⠀⣸⡇⢨⡅⠣⣿⠀⢹⠀⢆⢸⡇⠘⡀⣿⢸⣿⠀⢈⣍⠀⠇⠀ ⢠⡿⠀⠈⠁⢀⡟⠀⠸⡇⠀⢾⣇⠀⠀⠀⣸⡟⠀⠸⡿⠀⠰⡀ ⠈⠉⠀⣠⠼⢛⠑⢶⣶⠛⢲⣾⠈⢙⠲⢌⢨⡥⠒⢢⠉⠀⠈⠁ ⠀⠀⢰⡏⠀⣹⡵⠂⣿⠂⠀⣹⠀⠘⠁⢌⠀⣿⠀⡇⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⠀⡿⠀⠘⡿⠀⠘⣇⠀⢦⡟⠀⠑⠂⠂⠀⠀ ⠀⠀⠀⠈⠓⠒⠂⠉⠓⠒⠒⠓⠒⠒⠛⠒⠘⠓⠒⠒⠒⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣤⣴⣶⣶⣶⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣹⣟⢻⣿⣿⣿⠿⢿⢿⣿⡿⣿⣛⣿⣿⡿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡿⡿⣌⡾⢫⣿⣿⣷⡿⣘⣒⣿⣿⣿⣷⣿⡾⢿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣧⣿⣷⣥⣾⣛⣻⣥⣿⣿⣿⠋⠀⠀⠀⠀⢀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣟⠟⣿⣿⣿⡿⠁⠉⠉⠓⣲⡆⢾⡟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡿⣴⣿⣿⣿⠇⠀⢀⡔⠋⡟⠀⢏⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⢖⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⢡⠚⠝⠦⢰⢆⢑⡄ ⠀⠀⠀⠀⡖⡟⡕⣡⠔⠁⡈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠀⠀⠀⠈⢿⠋⠀ ⠀⠀⠀⣰⣿⣧⡘⢤⢣⢭⣾⢿⡛⢫⡻⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠐⡏⠀⠀ ⠀⠀⣸⣿⡟⢻⣿⣦⣵⣦⣿⣾⣧⡈⠈⢐⣙⣿⣿⣿⣿⣿⡦⣄⠀⠀⢰⠁⠀⠀ ⠀⠀⣿⡿⣆⠀⠈⠙⢿⣿⣿⣿⣿⣯⣿⣿⣿⣾⠇⠉⠈⠋⠁⠀⠉⠀⠁⠀⠀⠀ ⠀⠀⣿⣇⢃⠆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⢏⠪⡘⠄⠀⠀⠀⢸⡏⢿⣿⡆⢻⡇⡆⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡿⠀⢣⠙⠢⠀⠀⠤⠞⡟⠻⣧⢼⢸⡇⡗⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠁⢃⢢⠀⠳⡀⠀⠀⠀⢰⣷⠀⢸⣾⣿⡇⡇⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠃⣛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠻⠟⠋⠀⠀⠀⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿ ⠹⣿⣿⡟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⣒⡒⠂⠤⣀⠀⠀⠀⠀⢸⣿⣿⣿ ⠐⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠈⣉⣁⠂⢕⢦⡀⠀⠸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡎⠀⠀⠀⡠⠀⠀⢲⡽⡉⠙⢷⠃⠀⠀⠀⠉⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢋⠃⠀⠀⣠⡧⡂⠀⢸⡈⠻⣄⠀⢣⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⢂⣞⢀⡀⣿⣁⣀⣤⠃⠀⠀⠈⠳⠬⠇⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠹⡊⡁⢲⠯⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠘⢄⣀⣡⣆⣴⡔⠓⢖⣢⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠤⢽⠀⠀⠀⡴⠋⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴ ⣄⠀⠀⠀⠀⠀⣾⠀⠀⠐⠀⠀⠀⠑⠒⠂⠄⠸⢱⠩⠵⠶⠤⠄⠒⢤⠔⠉⠁⠈ ⣿⣷⡄⠀⠀⢠⣿⣄⡀⠘⣄⠀⠀⡀⠀⢀⠔⢣⢉⣷⠒⠒⠤⠄⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣦⣄⣈⣿⣿⣿⡟⠷⠶⠒⠂⠤⠤⠰⠞⠛⠉⠓⠛⠛⠛⠁⠀⠀⠀⠀⠀ ⣦⣬⠽⡉⠉⠛⢳⡿⣿⣷⣶⣞⠙⠣⠤⣀⡀⣀⣀⢲⣦⣤⣤⣬⡍⡀⢀⣀⡀⠀

⠐⢦⡲⡉⡑⠚⠉⢢⠀⢔⠕⢐⡕⢁⣩⣭⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿ ⠀⠀⠑⡑⣽⠷⠌⡤⡪⢂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣴⢻⠛⡟⠈ ⠀⠀⢈⡜⠀⠀⠀⠀⣵⣿⣿⣟⣉⡀⠙⣿⣏⣽⣿⣿⣿⣿⡆⠀⠀⠈⢸⡄⠀⠀ ⠀⠀⠀⣂⠠⢤⡀⣴⣿⣿⣿⣯⣮⣇⣠⣥⡶⡝⣿⣿⣿⣿⣷⠀⠀⠀⠀⠁⣠⣶ ⠀⠀⠀⢨⢘⣣⢍⣿⣿⣿⣿⠑⣻⠟⠛⡿⠿⠋⢸⣿⣿⣿⣿⡄⠀⠀⢰⣿⣿⣿ ⠄⠈⠑⠀⠰⢎⣰⡿⣿⡿⣏⣆⠀⢀⣾⣅⠀⣰⣿⣯⣿⣿⣿⠃⠀⠀⢙⣿⣿⣽ ⠀⠀⠀⡃⡠⣳⡎⠠⣡⠿⣾⠟⣷⠌⠁⡠⠼⣟⣻⢛⠉⠉⠀⠀⠀⠀⠀⠈⠛⢿ ⠀⠸⠹⣶⡘⢥⠼⢠⢐⣽⣪⠉⡍⠀⠀⠀⠀⠈⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⣐⣴ ⠀⠀⠈⡛⠿⠭⢭⣛⣉⡽⡟⣄⠁⠢⢄⣀⣀⣀⠠⠐⠁⠑⡄⠀⠀⢠⣴⠾⣻⣿

⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠙⢦⡀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠔⠁⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣓⣻⣞⡚⣿⡿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀ ⠀⡴⠛⢳⣾⣿⣿⣿⢿⣏⠿⠽⣓⣛⣓⣓⣚⣛⣚⠿⢦⣿⣿⣿⡿⠃⠀⢀⠄⠀ ⢰⢣⣤⡼⠃⠹⣶⣯⣵⣶⣿⣿⣛⣿⣿⣿⡿⡿⡿⠿⣷⣮⡟⣿⡆⠀⢠⠃⠀⠀ ⢹⡏⠉⠀⠀⣼⣿⣿⣿⡿⣿⣇⣤⣿⣷⣏⡇⣏⣫⡉⢻⣿⣟⢯⠢⡀⡆⠀⠀⠀ ⠞⡝⠓⠂⠀⠚⣿⣿⣹⣷⠏⡀⣒⢽⡿⣿⣿⣟⠩⢍⢺⣽⣧⣯⡧⢹⠀⠀⠀⠀ ⣴⠃⠀⠀⠀⠀⣻⡿⣿⡟⢄⣳⠽⠆⠉⠇⠘⠻⣛⣾⠀⣿⣿⠿⠃⣘⡄⠀⠀⠀ ⢽⡷⠀⠀⠀⠀⢻⣄⣶⣹⣿⣻⣿⣤⣤⠤⠄⠈⣀⠄⠁⡿⢛⡄⠀⠀⢃⠀⠀⠀ ⡟⠀⠂⠀⠀⠀⠀⠈⠲⣿⣿⣿⢻⠛⠛⠛⠿⣿⣿⡇⣰⡫⠋⠀⠀⠀⠈⢂⠀⠀ ⢀⡠⢀⣴⣶⣶⣦⣄⠀⢀⣽⣯⣙⢄⣀⠀⢀⠧⣫⠔⠉⠀⣀⡀⠀⠀⠮⠂⠈⠐ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣷⠶⠖⢲⣿⣿⣿⣷⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⣾⢿⣿⢿⢿⣿⣿⣿⣿⣿⣿⠧⡀⠈⡇⢀⡟⢉⠼⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⢛⢾⡯⣾⢦⣻⣿⣿⣿⣿⣇⡀⠻⠦⠳⢾⠖⢁⡀⣻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠘⠕⠈⠋⡠⣻⣿⣿⣿⣿⡇⠈⠁⠀⠀⠐⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⠀⠀⠀⠉⠉⠉⠁⠂⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⢼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀ ⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣄⠀⢀⣠⣧⠀⠀⠀ ⠀⠀⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠈⢢⡟⠿⠹⣶⣤⠀ ⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⡏⠁⠀ ⠀⢠⠯⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⢀⡆⣾⣏⣢⣄ ⣀⢟⣶⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠉⢰⡋⢹⡿⠟ ⢸⣿⣿⣿⡿⣻⣆⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⢿⣟⣫⠿⣾⢿⣷⡦ ⠀⣸⡿⣿⢧⣴⣿⣽⣾⢇⠀⣆⡀⠰⣄⡀⠀⣵⢀⣶⢾⣽⣿⣾⣿⣿⣭⣀ ⠀⠉⠋⢹⣿⣿⣯⣿⣿⣾⣽⣿⣧⡀⣙⣿⣿⡟⣿⣿⣗⣛⣼⣿⣽⣿⡿⠟ ⠀⠀⠀⢀⣬⣿⣿⣿⡟⣻⠛⠻⣿⣿⣤⣿⣧⣿⡟⠛⣿⣿⣿⣯⡆⠉⠁⠀ ⠀⠀⠀⠀⠉⠻⣿⣤⡛⣳⢦⣼⡿⡁⢈⢻⣧⣼⣷⣿⡟⡷⠻⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⠘⣦⡟⠛⠻⠏⠪⢵⣿⡽⠛⡅⢿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠶⢤⣤⣤⣄⣀⣀⣀⣀⣡⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡀⠀⠀⢱⣤⣄⡀⢀⣠⡤⢄⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢆⠀⠀⠀⠀ ⠐⠚⣻⣿⣿⠋⠙⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⢘⡆⠀⠀⠀ ⠀⢀⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣤⡐⠀⠀⠀⠀ ⠠⠞⢹⣿⢗⣠⡀⠀⣤⣐⣻⢹⣿⡿⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⣸⢏⠏⠉⡇⠀⠀⠉⢿⢸⠿⡟⣿⡟⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠈⠸⣴⠤⢤⡤⢀⡀⢌⣰⣞⢻⣻⣿⠛⠈⠻⢿⣿⣷⠀⠀ ⠀⠀⠀⠀⡴⠁⠰⡓⣕⣯⠔⢁⣞⠢⣽⢿⢏⠀⣸⡆⠌⢻⣿⠀⠀ ⠀⠀⠀⢘⡻⡭⡽⢾⣿⡗⠀⠈⢃⣴⣿⡏⠸⣵⠟⢻⠁⢠⡿⠀⠀ ⠀⠀⠀⣜⣎⠀⢿⠈⢻⣿⣿⣿⡿⠟⠉⠠⠀⢫⡔⡭⠃⠄⡇⠀⠂ ⠀⠀⠠⠀⡇⠘⣺⡀⢀⠼⠈⢏⠀⠀⠆⣈⠁⣤⣛⡖⣾⠂⡇⠀⠀ ⠀⠀⠀⠇⡇⡄⢻⡷⣿⠧⠞⣁⡗⠤⡼⢹⠀⡿⣟⡃⠋⢞⠃⠀⠀ ⠀⠀⠀⠀⠀⠁⠸⡇⢹⢻⡿⠋⢃⣀⡀⠃⠀⣽⡯⢰⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠀⠃⠠⢯⠄⠈⠘⠀⠀⠐⠰⠧⠔⠈⠠⠇⠀⠀⠀

⠆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠈⠀⠀⠀⢀⢔⠕ ⢠⣤⡄⠀⠀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠉⠉⠑⠢⣄⠀⠀⠀⠀⠀⢐⠕⠁⠀ ⣿⡿⠁⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢱⣄⠀⠀⠔⠁⠀⠀⠀ ⡿⠁⠀⠀⠀⠀⢠⠃⠔⠀⠀⢀⡜⠀⢰⠀⠀⡄⠀⠹⣠⠎⠿⡆⠀⠀⠀⠀⠠⠚ ⠁⠀⠀⠀⠀⢀⠇⡜⠀⣰⠀⡇⠃⠀⢸⠀⠀⣧⣾⣗⡇⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⡇⠀⡏⠀⣿⠀⠀⡾⡇⢀⣿⣋⠀⢸⠀⠸⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠨⢧⢯⣹⣷⣔⡟⠒⠂⠥⣶⣿⡟⣿⠀⢸⠀⡇⡘⡄⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⣠⡾⢨⣯⠸⣿⡃⠀⠀⠀⠘⠿⠆⢻⠀⢸⢡⡇⠱⣘⢦⣀⠀⣀⡠ ⠀⠀⠀⢀⣼⢿⢡⣿⢾⠀⠁⠀⠐⠀⠀⠀⠈⠁⣸⠀⣺⡾⠃⣀⠨⠿⠾⠛⣅⠀ ⠀⠀⣠⠟⢡⢣⢏⡼⠊⣇⠀⠀⠐⡗⡄⠀⠀⠀⡿⢀⡿⢄⠀⢿⠳⠶⠶⠚⠁⠀ ⣀⡰⠁⠀⡜⣏⢁⣠⢆⡎⡗⠢⣄⡀⢀⣀⣴⡾⢡⣾⣷⣦⡑⣤⣵⣦⣄⠀⠀⠀ ⠀⠇⠀⠀⢳⡙⠋⣒⢝⣸⢳⣴⠇⣨⠿⡿⢿⡵⠋⠙⣟⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⡠⠠⡀⠀⠈⠃⠀⠈⠀⣸⡈⢿⠟⡹⢰⣳⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠉⢉⣏⠇⠀⠀⡤⢤⣾⡇⢣⡘⢾⡇⢸⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⡁⣼⡏⠀⠀⠀⠙⣦⣌⣉⢒⠓⠀⠁⠀⠈⠒⡏⣿⣯⣿⣾⣿⣿⣿⣿⣿⠇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢉⢢⡌⠁⢸⠀⠀⠀⠀⠀⠀⠂⠀⠘⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣐⠃⢤⡢⠀⡃⢀⠠⠗⠀⢄⠀⢠⣄⣰⠦⡀⢈⠤⠂⢀⠀ ⠀⠀⠀⠐⡀⠀⠀⢔⠊⣐⢲⠓⠊⠁⠀⠀⢀⠔⠝⣠⡘⠣⠈⠑⢌⢀⢀⡠⡃⠀ ⠀⠀⢔⠁⠠⢭⠤⠽⡑⣾⠒⠀⠀⠀⢀⡤⠊⠉⠛⠏⣈⡁⠚⢧⡀⠡⡡⠀⠇⠀ ⠁⠀⢸⣉⠈⠀⢀⠘⣒⡆⠤⡤⣂⣻⣖⣀⠀⠀⢤⡔⠒⠓⠲⠄⠉⠀⠁⠡⡀⠀ ⠀⠀⢸⡀⡈⢱⠀⠀⠀⢡⠀⠁⢻⣻⣿⣿⡄⠀⠀⢀⣠⣿⣤⠀⠀⠀⠀⠀⢡⠀ ⠀⠀⠂⠉⠑⣼⣏⡀⠀⠀⢣⡄⠀⠈⠁⠈⠁⢀⢴⣿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⢀⠺⢡⠤⠅⣒⢼⡉⠂⠀⠀⠀⠀⡀⠀⠉⢈⣿⠟⠐⠄⠀⠀⡀⠀⠁ ⠀⠀⢀⠴⠅⠋⣪⣆⠀⠀⡛⢧⡀⠑⠆⣠⣁⡀⠀⡠⠎⡤⣤⡤⠤⣷⡎⠀⠀⠀ ⠀⠠⢺⠉⢋⠀⠀⠉⠀⣰⠃⢄⠷⢄⡀⢀⡀⠄⡾⢢⡚⠝⣁⡔⠈⢀⡈⠆⠀⠀ ⠀⠀⢸⠀⢸⠀⠀⢀⡔⠉⠙⢾⣀⢀⡏⠩⠤⡾⠃⡡⢴⢛⠊⡠⠋⢫⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⢀⠔⠁⢀⣴⠮⢝⠍⠉⠀⠀⠌⣠⠎⠀⣆⠧⢰⠁⠀⠀⠁⠀⠀⠀ ⠀⠀⡀⡠⠋⠀⠀⠀⣓⣧⣀⢜⡜⠀⠀⢸⠘⠁⠀⢸⢸⢄⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠞⠀⢀⡠⡖⠙⡘⠁⠲⢁⠨⣢⡀⢈⡇⠀⠀⢘⢼⢌⡇⠀⠀⠀⠀⠀⠀⠀ ⢀⠃⡠⠒⠁⠡⡈⠢⡈⠒⡈⠔⠈⡠⠑⢾⡇⠀⠀⢰⢺⠄⡇⠀⠀⠀⠀⠀⠀⠀ ⡦⠊⡀⠄⢂⠡⢈⢂⡈⣉⠤⡒⠣⡀⠀⠈⢥⠀⠀⣸⡋⠷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠤⠤⣐⡂⠠⢀⡀⣀⡀⠀⠀⠀⠀⠀⠉⠚⠛⢖⣋⠉⢑⣄⠀⠝ ⠀⠀⢀⡀⣀⡔⠝⠂⠐⢀⠊⠁⡀⠀⢳⠴⠶⣿⣶⠀⠀⠀⠀⠳⡃⠘⠂⠙⠀ ⠐⣯⡛⢛⠏⠀⠀⠀⠀⡌⠄⠀⠡⠀⠈⠮⢾⣿⡇⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀ ⠀⠘⢿⢃⠄⢀⠂⢀⢼⢀⢊⣦⣄⣱⡀⢩⠪⡟⠀⢀⠀⠀⠀⠀⠀⠀⠣⠀⠊ ⠀⠀⠼⡎⡠⣁⢴⡿⢗⣽⣿⠻⡹⡹⢦⢈⠳⣊⡩⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣜⣩⢿⣇⣐⠾⡪⠖⠓⠅⣒⣒⣿⠀⡞⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤ ⠀⠠⠮⠼⢀⢏⠒⠈⠀⡀⠠⠔⠀⠀⣸⠜⡏⠉⠁⠀⠀⠀⠀⠀⣠⣾⣻⣿⡿ ⠀⠀⠀⠀⠹⢋⠢⡀⠀⠀⠀⠀⠀⡰⢫⢣⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⣎⠣⣦⣤⣶⣿⡁⢁⣀⠤⢀⣠⡀⠀⠀⢰⣿⠏⠀⠀⠀⠀ ⠀⠀⢀⠴⠒⢲⣶⡶⢾⡿⠛⠛⢻⡿⡻⢁⡀⣢⣾⣿⡄⠀⠸⣿⠀⠀⠀⠀⠀ ⠀⠀⣎⠀⢁⣾⣠⣿⢾⣗⠀⠀⣠⡿⠰⣼⣿⣿⢿⣿⣿⡀⠀⠈⢷⣄⠀⠀⠀ ⠀⠀⣿⣶⣾⣿⣿⣿⣇⠻⣭⣭⣴⠇⢰⠏⠈⣿⣦⡹⣿⣷⡀⠀⢸⣿⠀⠀⠀ ⠀⠀⢿⣿⣇⢸⣿⣷⣿⣷⣶⣽⣇⣴⣾⣶⣴⣿⣿⣷⠘⢿⣷⣀⣿⡿⠀⠀⠀ ⠀⠀⠀⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣷⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢔⣩⣿⡿⢿⣿⣿⣄⠆⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢟⣮⣁⣾⠟⡩⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢟⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈ ⢿⣻⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⢀⣠⠴⣺⢷⡋ ⠀⠉⠛⠳⣯⣓⣦⣀⡀⠀⠀⠑⣦⠀⠀⠀⡌⠀⠀⠀⠀⣀⣴⣾⣿⢚⠋⢏⠁⠀ ⢐⣩⣥⣶⠶⢿⣿⣿⣿⣷⣦⡤⣼⡇⠀⢸⣥⣤⣴⣾⣿⣿⠿⠶⠶⢶⣮⣭⡂⠀ ⠛⢉⡀⠀⠀⠀⠀⠀⠉⠻⠄⠫⠟⠀⠀⠈⠉⠉⠰⠋⠁⠀⠀⠀⠀⢀⣠⡿⠻⠟ ⠀⠘⢿⣶⣤⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠄⣲⣾⣿⠟⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣷⣤⣈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣠⣴⣾⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣛⣋⣉⣛⣋⣉⣍⣉⣩⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢰ ⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣾ ⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⠬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠲ ⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀ ⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⢇⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣹⠃⠀⠀⠀⠀

⠀⠀⠀⠀⣠⣾⣿⡷⠶⣿⣷⡶⣶⣖⣿⣯⣿⣿⣿⣿⣿⣿⣯⣻⢽⡷⣄⠀ ⠀⠀⠀⣼⣿⣿⣥⣿⣶⣈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣆ ⠀⠀⢰⣿⣿⣿⣿⣛⣿⣿⠟⢻⣿⣿⣿⣿⡿⠿⠛⢛⠛⠻⠿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⡿⣋⣾⣿⣷⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠻ ⠀⠀⣿⣿⣯⠟⣛⠻⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⢠⣿⣿⠇⡂⣦⡆⠹⣿⡿⢫⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠶⣾⠤⠀⠀ ⠀⢸⣿⣿⡇⢠⢸⠀⠀⠀⠠⠁⠀⠀⠀⢀⣠⣀⣄⣩⡖⠤⠀⠐⠃⣠⣤⡆ ⣿⣿⣿⣿⢿⢌⡫⠁⠀⠀⠂⠀⠀⠀⠀⠈⠣⡸⣿⡟⠁⠀⠀⢠⣾⣿⠟⠀ ⠋⠎⡟⢩⢸⣂⠼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡏⠀⠀ ⠀⠀⠀⠈⠸⣿⣿⠇⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠛⡴⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠀⡨⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠢⡀⠀⠀⠀⠀⠀⢉⣉⡹⢉⠚⠀⠀⠀⠀⠀ ⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⡀⠀⠀⠀⠀⠀⣠⣿⡵⡆⠀⠀⠀⠀ ⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⣿⣷⣦⣤⣤⣶⣿⣷⣶⡇⠀⠀⠀⠀ ⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡀⠀⠀⠀