Fnaf Purple Guy Emojis & Text

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⠀⠀⠀⢀⠤⢤⠤⠐⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠃⢀⣞⢉⣫⣀⣀⡀⢙⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⣳⣴⠛⢚⣿⣷⣶⡶⠿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡏⠉⠙⣟⣿⠁⢀⣠⡾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣧⣄⣴⠏⠈⢋⡩⢫⣼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢯⡱⠄⠲⠊⣙⣠⣾⠟⠀⠀⠀⢀⣀⡀⠀ ⠀⠀⠀⣤⣝⡯⠭⣭⡥⠟⡷⣾⠒⠂⠉⠹⠏⢷⠀ ⠀⠀⣸⠿⠇⠁⠀⠹⡸⣿⣷⠏⠃⠀⣀⣴⠀⠈⢣ ⠀⠀⡜⠃⢦⠀⠀⠀⠈⢻⠋⠰⡍⠍⠒⣿⠀⠀⠀ ⠀⢰⠃⠀⠀⢧⠀⠀⠀⣿⠀⠀⢡⡀⢠⢿⠀⠀⢀ ⠀⢻⣶⣄⡀⠘⡆⠀⠀⢸⠀⢀⠒⠭⢍⡈⡖⡎⠁ ⢠⣼⣷⣈⡇⡀⢳⣀⠀⠈⣷⣉⠈⠉⠀⣧⡇⣸⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣚⣋⣉⡻⠶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠞⠁⠀⠀⠛⡆⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⡶⠁⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠁⢠⡀⠀⠀⠀⠀⡸⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⠫⢟⣮⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡦⢌⣓⡤⣹⡆⠀⠀⣰⢣⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠛⠛⠲⣄⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⠔⠒⠒⠮⡹⠚⢯⣉⣵⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠁⢀⡤⠚⠉⠙⡍⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡰⠁⠀⠀⠀⠀⠈⢆⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣤⢀⠀⢹⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣲⠁⠀⠀⠀⠀⢀⣀⣸⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡔⠀⠀⢀⣽⣿⠁⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⣸⣅⡇⡏⠑⠄⠀⠀⠀⠀⣸⢣⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠸⡿⠛⠀⣾⣉⣶⣃⠀⠀⠀⠀⠀⠀⡿⣿⠿⣆⡼⡄⠀⠀⠀⠀⡴⠁⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⣀⡤⠋⠀⣁⣨⣇⠤⠤⠤⠤⠤⣾⣿⣭⣀⠈⠉⠢⢄⣀⡞⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢉⣉⣥⣔⠾⠛⠉⠁⠀⠀⠀⠀⠀⠰⣿⣟⡏⠻⣕⠢⢤⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠙⢶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⡜⠀⠀⡴⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣠⡼⣤⡤⣞⠀⠀⠀⠀⠀⠘⣆⣀⣀⡇⠀⣸⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢰⣞⡕⠉⠁⠈⠙⢷⡤⠃⠐⢤⣠⠾⠓⠒⠫⣝⢅⠀⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⡜⢀⡴⠚⠉⠒⢜⣆⡀⠀⢠⢇⡠⠤⠤⣀⠈⢟⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡈⠉⢿⣃⣜⠰⣶⣰⠀⡸⠯⠕⠒⠿⡏⠀⡄⠠⠈⣆⢸⡏⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠉⠻⣺⣄⣈⡠⠞⠃⢀⣀⠀⠀⠙⢦⡙⠞⠀⣾⣿⠁⠀⢰⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⠆⠀⣡⠂⣀⠴⠊⠁⠀⠉⠙⢲⠠⣍⠑⠚⠊⠉⠉⠀⡏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⢀⠇⠀⡞⠁⠀⣹⠂⠀⠀⠀⠀⢀⡞⠀⠈⢳⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢤⢻⠁⠀⡀⡝⠋⠉⠉⠓⠢⡎⠀⢀⠀⠀⠇⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⣞⠲⠼⢻⣀⣀⠀⠀⢀⡼⠁⠀⣼⣆⠀⠐⢠⡶⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢌⠪⣝⡒⠼⣀⣉⣹⡳⠿⠒⢓⡖⠉⣓⡶⣗⣟⣷⡟⢀⡤⠤⢤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⠉⠷⢬⣵⡞⠛⠒⡟⠛⠛⣯⠟⠛⣷⣯⢠⠿⢷⡿⠋⠀⠀⠀⠈⠛⣶⣤⡈⡹⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠛⠛⠒⢾⡿⠦⣀⠀⠀⠹⠤⣨⠧⠒⠟⢧⣀⠞⠁⠘⠃⣠⢿⡁⠀⠀⠀⠀⠀⠀⠈⢳⡈⠳⡄⠙⣆⠀⠀ ⠀⠀⠀⠀⣀⣠⣴⡏⠀⢷⡄⠀⠀⠀⠀⣿⠦⠈⠓⡤⢄⣀⣄⣀⣀⣀⣀⣀⣠⠤⠴⡞⠓⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠘⡄⢸⡄⠀ ⠀⢀⡴⢛⡽⠚⡿⢷⣀⡼⠃⢠⡦⠀⠀⡿⠒⠁⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠇⢰⠷⡀ ⠀⡾⢡⡏⠀⣠⣷⡀⡞⠀⠀⢯⠉⢦⣴⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠳⣄⡀⠀⠀⠀⢠⠏⣠⠾⢚⡟⠀⢧ ⢸⠁⡏⡇⠀⢧⣈⢻⣇⠀⠀⠀⢷⡽⠁⠀⠀⠀⣠⢧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⣠⣼⠛⠒⠶⣾⠛⠚⣡⡴⠋⠀⠀⢸ ⡾⠀⠣⠽⡦⠒⠁⠀⢈⡷⠦⢤⡞⠀⠀⠀⣀⠔⠁⣸⠀⠀⠀⣠⢴⡏⠳⢄⡀⠀⣀⣠⠗⠀⠠⣶⣾⠍⢠⠒⡆⢹⠎⠉⠁⠀⠀⡇⠀⢸ ⢷⠀⠀⠀⠘⠦⠟⠉⠉⠀⠀⡼⠀⠀⠀⠈⠁⠀⠀⠘⠉⠉⠉⠁⠀⠀⠀⠀⠹⢏⠀⠀⠐⠁⠀⠁⠺⠶⢋⣀⠓⠻⡄⠀⠀⠀⠈⠀⠀⡎ ⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢳⡀⠀⠀⠀⢀⠼⠀

⠀⠀⠀⢀⠠⠀⡀⠀⠀⠀⢠⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡐⢱⠈⡗⡜⡀⠀⢀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣜⠂⢚⣡⠠⣴⣿⡏⠙⠛⣿⡂⠀⡔⡨⡭⡑⠄ ⠀⠀⠀⠀⠉⡝⠁⣤⣿⢦⡁⠀⢘⣛⠻⢢⡄⢆⣈⡿⠸ ⠀⠀⠀⠀⣰⠃⡼⠿⠏⠀⡇⢰⣿⠉⠳⡄⣿⠒⠀⠂⠁ ⠀⠀⠀⣴⠋⣢⣑⣤⣠⣴⣇⣿⡉⠀⢀⡇⡿⠀⠀⠀⠀ ⠀⠀⢸⠹⠶⡟⠁⠀⠀⠉⠒⠛⠙⠻⣍⠔⢺⠀⠀⠀⠀ ⠀⠀⠸⡆⢰⡟⠷⣤⣀⠀⠀⠀⠀⠀⣸⢦⢾⠀⠀⠀⠀ ⢀⢔⢢⠙⢾⣹⣦⣀⣉⠈⡛⠛⠛⢫⠇⢀⡞⠀⠀⠀⠀ ⢸⠁⡠⠥⣆⠈⣹⣿⠿⢿⣿⣷⡿⠷⠖⠋⠀⠀⠀⠀⠀ ⢸⣿⣁⣠⡞⡏⣾⣿⣷⣿⣿⣿⣿⡇⠂⢄⠀⠀⠀⠀⠀ ⠀⠙⠛⣿⠋⢠⠿⠟⠋⡉⡈⠓⠛⡌⡄⠀⢆⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠏⠀⠀⠘⠿⠟⠀⠀⠸⣸⢀⣀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⡆⠀⠀⢰⣿⣷⠀⠀⢠⡏⠉⣻⣷⠀⠀⠀ ⠀⠀⠈⢻⣧⡘⠦⣀⣀⠉⣁⣠⠴⣫⢷⡾⠉⢹⠀⠀⠀ ⠀⠀⠀⢰⠉⠛⠷⣶⠼⢭⡥⠖⠋⠀⡌⢧⣠⠏⠀⠀⠀ ⠀⠀⠀⡸⠤⠤⠤⠬⡄⢸⠤⠤⠤⠤⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣅⡀⠀⠀⢀⡷⣇⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⠉⠉⠉⠉⠉⠉⠉⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠒⠒⠒⠒⠒⠒⠒⠒⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⠀⢠⡤⢄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⢤⡄⠀⣀⣀⣀⡀⠀ ⡰⠕⠀⠐⠂⠍⡆⠙⣭⣛⡀⠤⠤⠤⠤⠤⠤⠤⠄⢐⣛⣭⠋⢰⡩⠐⠂⠐⠫⢆ ⢣⢄⠀⠀⢀⢠⢛⠞⠁⠀⠉⠉⠁⠒⠒⠒⠒⠈⠉⠉⠀⠈⠳⡛⡄⡀⠀⠀⡠⡜ ⠈⠳⣕⠀⣰⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⣆⠀⣪⠞⠀ ⠀⠀⠀⠉⢠⠇⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠸⡄⠉⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢠⡾⠿⠿⠿⣿⣄⠀⠀⣠⣿⠿⠿⠿⢷⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠈⢀⣶⠛⠛⢦⠙⠀⠐⠋⡶⠛⠛⣷⡀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠃⠀⠀⠸⣷⡈⡃⣸⠇⠀⠀⠸⣇⢹⠁⣾⠇⠀⠀⠘⢇⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⢀⣩⠿⢿⡭⠤⢶⣶⣤⣭⡿⠿⣉⣀⠀⠀⠀⠈⡆⠀⠀⠀ ⠀⠀⠀⠘⢆⡀⢀⡞⠁⠀⠀⠀⠙⠛⠿⠿⠛⠋⠀⠀⠀⠈⢳⡀⠀⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⢷⣀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⡾⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠈⠫⣹⡒⠚⢉⠉⢉⡉⠉⣉⠓⢒⣏⠝⠁⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠒⠛⠤⠼⠧⠤⠛⠒⠋⠁⣀⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣤⣀⣠⣄⣀⣠⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠒⠒⠒⠢⢤⡀⠈⢷⣍⡓⠲⢤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⡤⠔⢊⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠋⡤⠒⠉⠉⠓⠢⢄⠈⢳⡌⠳⣌⡓⠲⠼⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡸⠧⠔⢊⡵⠏⠀⠀⠀⠀⡴⣧⠀⠀⠀ ⡞⢸⠁⠀⠀⠀⠀⠀⢀⠇⣸⣄⠀⣨⠟⠲⢤⣀⡀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⢀⣠⡤⠞⠿⣤⠤⠤⠶⠶⠴⠿⡇⠀⠀⠀ ⢸⡈⢇⠀⠀⠀⠀⢠⠊⢠⠏⣨⠟⠁⠀⠀⠀⠈⠉⠙⠓⠒⠲⠶⠦⠤⠤⠤⠴⠶⠒⠒⠛⠉⠉⠀⠀⠀⠀⠈⢻⣍⡩⠭⣍⢫⡁⠀⠀⠀ ⠀⠳⣄⠳⢄⡀⡴⠁⡴⢃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠂⠚⡆⡟⡄⠀⠀ ⠀⠀⠈⠓⠦⣉⣠⠮⣄⣾⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⣼⣹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠙⠶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠴⠀⠀⠀⠸⣇⡸⣧⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⣿⠷⢹⠸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡆⡿⡄ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣈⡻⣿⣆⠀⠀⠀⠀⠀⣴⡿⣋⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⡇⡜ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⡹⡆⠀⠀⠀⣸⢋⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣾⠃⢰⡥⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⡟⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⠀⠀⠀⢸⡿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⣀⠔⡿⠭⢗⣲⣺⢗⣽⣿⣿⣿⣿⣿⡟⠀⣀⣀⣀⣀⡀⠈⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⣶⠮⠿⣿⣾⠷⠿⠛⠛⠉⣿⣿⡟⠋⠉⢙⣿⣿⣿⣿⣿⣿⣯⠙⠛⠛⠷⠦⣤⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⠀⠀⠋⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣸⡀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣧⡴⡟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⣷⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁⠀⢀⡾⠉⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡴⢿⠇⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢠⠞⢿⣄⣹⡶⢤⣤⣤⣤⠶⠶⢲⣿⡟⠉⢻⣷⡖⠶⢦⣤⣤⣤⡴⣾⣏⣠⡿⢲⡄⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠣⣬⣿⣿⣿⣦⣤⣼⣿⣦⣤⣿⣿⣿⣷⣿⣿⣷⣤⣼⣿⣧⣤⣶⣿⣿⣿⠥⠞⣸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢹⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣉⠇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠈⢩⠞⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢳⡍⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⠒⠋⢰⣉⠉⣻⠛⠻⡟⠛⢻⠛⠛⡏⠉⢹⡄⠑⠒⠋⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠈⠉⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠁⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠓⠶⠤⣤⣤⣤⣄⣀⣀⣤⣤⡤⠴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠿⠿⠿⠿⠿⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⣶⣶⣤⡀⠀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣄⠀⢀⣤⣶⣶⣤⣀⠀ ⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣇ ⢸⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠙⠿⢿⠿⣿⣿⣿⣶⣿⣿⣷⣾⣿⣿⣷⣾⣿⣿⣶⣿⣿⣿⠿⡿⠿⠋⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⡟⠋⣭⠙⢿⣿⣿⡿⠋⣭⠙⢻⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣄⣀⣾⡟⠋⠙⢻⣷⣀⣠⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⡿⠛⠉⠉⠙⠛⢿⡿⠛⠛⠉⠉⠛⠻⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣷⣤⣤⣤⣤⣤⣾⣷⣤⣄⣀⣀⣤⣴⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣉⣿⡇⣸⣇⢸⣿⣉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢡⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⢆⣀⠜⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⢦⠤⣤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠩⢋⠩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡀⠅⡪⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡢⠅⡪⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠚⠛⠚⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀ ⠀⠀⣠⢋⡴⢂⢩⠭⣑⢦⠀⠀⠀⠀⠀⡴⣚⠉⣑⠢⣄⠙⣆⠀⠀ ⠀⡼⢣⡿⢠⠁⣸⣷⠈⣾⠆⠀⠀⠀⢸⢸⢠⣶⡀⠱⡘⣧⡈⢧⠀ ⢰⠃⣿⣧⠸⣄⣉⣉⢜⡞⠀⠀⠀⠀⠈⢾⢌⡛⠋⣠⢃⣿⡇⠸⡆ ⢸⠀⠹⣿⣷⣶⣴⠾⠋⠀⠀⠀⠀⠀⠀⠈⠳⣮⣭⣴⣾⣿⠇⠀⡇ ⠸⡄⠀⠀⠉⢉⣠⡤⣄⡀⠀⠀⠀⠀⢀⣀⡤⢤⣍⡉⠉⠀⠀⣼⠁ ⠀⠉⢳⠖⢚⠉⠀⡇⠀⠉⡗⠒⠒⠚⠹⠀⠀⢸⠀⠉⡟⢲⡏⠁⠀ ⠀⠀⠈⡇⢸⠀⠀⠇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⢸⠀⠀⠀ ⠀⠀⠀⡇⠈⡀⠀⢰⠀⠀⢀⠀⠀⠀⡇⠀⠀⡇⠀⢠⠀⣸⠀⠀⠀ ⠀⠀⠀⢷⠀⡇⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠇⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠸⣄⣰⠀⠀⡆⠀⢸⠀⠀⠀⠃⠀⢸⠀⠀⣇⣰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠓⠒⠧⠤⠬⠤⠤⠤⠤⠤⠼⠒⠚⠉⠀⠀⠀⠀⠀

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⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀ ⠀⣰⡿⢉⡇⠀⠀⠀⣠⣾⠟⢡⠞⠀⠀ ⣰⡿⢀⡼⠁⠀⠀⣰⣟⣡⠖⠁⠀⠀⠀ ⣿⡷⠟⣇⠀⠀⢰⣿⠀⣸⠀⠀⠀⠀⠀ ⢿⡇⠀⢸⢀⣀⡼⠿⠤⡃⠀⠀⠀⠀⠀ ⠘⢿⣄⡾⡟⠁⠀⠀⢀⣨⣦⠀⠀⠀⠀ ⠀⠀⢸⣿⠁⣾⡟⢃⣸⣿⣹⣦⠀⠀⠀ ⠀⠀⢸⡿⣄⠙⡳⠋⠛⠛⠃⠈⠢⠀⠀ ⠀⠀⠈⢿⠦⠭⢇⠀⠀⡀⠤⢤⡇⠀⠀ ⠀⠀⣠⢴⣻⣶⣾⣷⣤⣤⣴⢎⠀⠀⠀ ⠀⣼⠇⠀⢻⣿⣿⠿⠛⠙⠻⣦⣣⠀⠀ ⠀⣇⣆⣀⣸⡇⠀⠀⠀⠀⠀⠸⢃⢃⠀ ⢸⣄⡏⠁⢸⡇⠀⠀⠀⠀⠀⠀⢟⣬⡄ ⠈⠛⠓⠒⠚⠓⠒⠀⠒⠀⠀⠈⠉⠉⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣚⣋⣉⡻⠶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⠞⠁⠀⠀⠛⡆⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠑⡶⠁⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠁⢠⡀⠀⠀⠀⠀⡸⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⠫⢟⣮⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡦⢌⣓⡤⣹⡆⠀⠀⣰⢣⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠛⠛⠲⣄⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⠔⠒⠒⠬⡹⠚⢯⣉⣵⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⡤⠚⠉⠙⡍⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡰⠁⠀⠀⠀⠀⠈⢆⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣤⢀⠀⢹⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣲⠁⠀⠀⠀⠀⢀⣀⣸⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡔⠀⠀⢀⣽⣿⠃⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⣸⣅⡇⡟⠑⠀⠀⠀⠀⠀⣸⢣⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠸⡿⠛⠀⣾⣉⣶⣃⠀⠀⠀⠀⠀⠠⣿⣿⠿⣆⡼⡄⠀⠀⠀⠀⡴⠁⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⣀⡤⠋⠀⣁⣈⣇⠤⠤⠤⠤⠤⣾⣿⣭⣀⠈⠉⠢⢄⣀⡞⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢉⣉⣥⣔⠾⠛⠉⠁⠀⠀⠀⠀⠀⠰⣿⣟⡏⠻⣕⠢⢤⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠙⢶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⡜⠀⠀⡴⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣠⡼⣤⡤⣞⠀⠀⠀⠀⠀⠘⣆⣀⣀⡇⠀⣰⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢰⣞⡕⠉⠁⠉⠙⢷⡤⠂⠐⢤⣠⠿⠓⠒⠫⣝⣅⠀⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⡜⢀⡴⠚⠉⠒⢜⣆⡀⠀⢠⢇⡠⠤⠤⡀⠈⣟⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡞⠉⢿⣃⣜⠰⣶⣴⠀⡸⠿⠝⠒⠿⡏⠀⡄⠠⠈⣆⢸⡟⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠈⠻⣺⣄⣈⡠⠞⠃⢀⣀⠀⠀⠙⢦⡙⠚⠀⣾⣿⠁⠀⢰⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⠄⠀⣡⠂⣀⠴⠊⠁⠀⠉⠙⢲⠠⣍⠑⠚⠊⠉⠉⠀⡏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⢀⠇⠀⡞⠁⠀⣹⠂⠀⠀⠀⠀⢀⡞⠀⠈⢳⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢤⢻⠁⠀⡀⡙⠋⠉⠉⠒⠢⡎⠀⢀⠀⠀⠇⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⣞⠲⠼⢻⣀⣀⠀⠀⢀⡼⠁⠀⣼⣆⠀⠀⢠⡶⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢎⠪⣝⡒⠾⣀⣉⣹⡳⠿⠒⢓⡖⠉⣓⡶⣖⣟⣷⡟⢀⡤⠤⢤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⠉⠷⢬⣵⡞⠛⠒⡟⠛⠛⣯⠞⠛⣷⣯⢠⠿⢷⡿⠋⠀⠀⠀⠈⠛⣶⣤⡈⡹⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠛⠛⠒⢾⡿⠦⣀⠀⠀⠹⠤⣨⠧⠒⠟⢧⣀⠞⠁⠘⠃⣠⢿⡁⠀⠀⠀⠀⠀⠀⠈⢳⡈⠳⡄⠙⣆⠀⠀ ⠀⠀⠀⠀⣀⣠⣴⠏⠀⢷⡄⠀⠀⠀⠀⣿⠦⠈⠓⡤⢄⣀⣆⣀⣀⣀⣀⣀⣠⠤⠴⡞⠓⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠘⡄⢹⡄⠀ ⠀⢀⡴⢛⡽⠚⡿⢧⣀⡼⠃⢠⡆⠀⠀⡿⠒⠁⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠇⢸⠷⡀ ⠀⡾⢡⡏⠀⣠⢷⡀⡞⠀⠀⢯⠉⢦⣴⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠳⣄⡀⠀⠀⠀⢠⠏⣠⠾⢚⡟⠀⢧ ⢸⠁⡏⡇⠀⢧⣈⢻⣇⠀⠀⠀⢷⡽⠁⠀⠀⠀⣠⢧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⣠⣼⠛⠒⠲⣾⠛⠚⣡⡴⠋⠀⠀⢸ ⡾⠀⠣⠽⡦⠒⠁⠀⣈⡷⠦⢤⡞⠀⠀⠀⣀⠔⠁⣸⠀⠀⠀⣠⢴⡏⠳⢄⡀⢀⣀⣠⠗⠀⠠⣶⣾⠋⢠⠒⡆⢹⠎⠉⠁⠀⠀⡇⠀⢸ ⢷⠀⠀⠀⠘⠦⠟⠉⠉⠀⠀⡾⠁⠀⠀⠈⠁⠀⠀⠘⠉⠉⠉⠁⠀⠀⠀⠀⠻⢏⠀⠀⠐⠁⠀⠁⠺⠶⢋⣀⠓⠻⡄⠀⠀⠀⠀⠀⠀⡏ ⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢳⡀⠀⠀⠀⢀⠼⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⣁⣠⣤⣄⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠀⣴⠏⠁⠀⡏⠹⣆⠈⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⢿⡇⠀⠀⢸⣶⡏⠀⡜⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⣸⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠙⣄⠀⠛⠲⠴⠾⠋⠀⣰⢃⣠⣤⠶⡾⠿⣿⡍⠉⠉⠙⠻⠿⣿⣿⣿⠁⠀⠀⠀⣠⠞⠉⣠⣤⣤⡀⠙⢦⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⣴⣻⡟⠋⠁⢸⣿⠿⠿⢿⣿⠂⠀⠀⠀⢠⣼⡛⠷⣤⠀⠀⢰⠋⢠⡞⠉⠙⢏⣛⣧⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣠⣼⣾⣶⣶⣄⠀⠀⠀⠀⠀⠘⠛⠿⢿⣶⡟⣄⢺⠀⠸⣆⠀⠀⠈⣿⣿⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢠⣿⣿⡟⣿⠙⠛⣿⣷⠀⠀⠀⢀⣴⣾⣶⣤⡈⠁⠈⢿⣷⡀⠘⠣⣤⣼⠟⠁⢠⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⢠⣿⣻⣿⣿⡿⠀⠀⠀⣿⠀⠀⢰⣟⠻⡟⠛⠛⢿⣦⠀⠈⣿⠛⠲⣤⣄⣠⣤⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣸⠉⠛⠛⠛⠀⠀⠀⢀⣿⠀⢠⣿⣿⣿⠏⠀⠀⠀⢹⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠳⣦⡀⠻⣧⡄⠀⠀⠀⢀⣀⣿⡏⠀⡼⠿⠛⠋⠀⠀⠀⠀⢨⡷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡃⠀⠀⣨⣇⣠⣬⣽⣿⣦⣼⣿⣿⣿⣤⣤⣿⣶⡄⠀⠀⠀⠀⢀⣾⠇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⢿⣷⣀⣸⣿⡿⠛⠁⠀⠀⠀⠀⠙⠻⢿⣦⣠⣾⣿⠿⢿⣿⣷⡿⠾⠏⢀⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠈⠛⠛⢫⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠙⢷⣦⢰⡟⠹⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⣧⠀⠀⠀⣸⣿⣷⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⣇⠙⠻⣿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣷⣾⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠹⣿⣆⣀⡿⣿⡆⠀⠀⠉⠙⠯⣉⣓⣲⡶⠦⠤⢤⣀⣀⣀⣤⣴⣾⡿⠀⠈⠉⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠋⠉⠳⣄⠙⢿⣿⣿⡌⢿⣾⣥⣀⣀⠀⠀⠉⠉⠉⠒⠒⠒⠋⠉⠉⠉⢉⣿⠁⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢃⡴⠊⠀⠻⣀⠀⠈⠙⠿⢾⣝⣿⣿⣷⣷⣶⣶⣭⣑⣦⣆⣀⣀⣀⢀⣴⡿⠃⠀⣀⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡏⠀⠀⠀⣀⣿⣙⣆⠀⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣯⣶⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣧⢀⣰⠟⠁⠀⠉⢻⣄⢀⣴⢾⣿⣿⣿⣏⠉⠉⣉⣉⣹⣻⣿⣿⣯⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡿⣿⠏⠀⠀⠀⣀⣼⠟⣿⠃⢾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣷⣴⣴⣾⣿⣟⣴⠟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⡿⣟⣿⡿⠃⠀⢀⣿⣽⣧⣾⡿⠋⠉⠉⠉⠈⢛⢿⣦⣽⣿⡄⠙⣄⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣩⣿⠛⠀⠀⢀⣼⠏⠙⠛⠁⠀⠀⣠⠴⢶⣤⠀⠀⠉⠉⠀⢹⡄⠘⣆⠀⠀⠐⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⣿⣤⣶⣿⡇⠀⠀⠀⠀⠀⣿⡀⢿⡀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⢹⣧⠈⣇⢀⣀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣿⢰⠟⠒⠤⣿⢿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⡿⠟⠀⠀⠀⣸⡆⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣦⡇⣆⠀⢻⣧⡀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠁⠀⠀⠀⠀⣠⣿⢽⡀⠀⣠⣾⠿⠛⢾⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣼⣦⡄⠙⢷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⢡⣾⢛⣿⣿⠅⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⣦⣄⡈⠙⠛⠿⠶⣶⣦⣴⡶⠾⠟⠛⣩⣤⡾⠿⡁⠘⣿⠋⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠉⠛⠻⣿⣿⣷⣶⣤⣴⣦⣤⣤⣤⣴⡾⠟⠋⠁⠀⠀⣧⠀⠹⣧⣀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠙⠀⠀⠀⠀⠀⠉⠻⣿⡏⠉⠉⠙⣿⠟⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠉⠻⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣄⠀⣶⠟⠉⠉⠉⠉⠉⠉⠉⠉⠙⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⡟⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣾⠓⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠖⢻ ⣿⠀⢰⢤⡈⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⢉⣠⢤⠀⢸ ⢻⠀⢸⠀⠈⠓⠦⣀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⢀⡤⠒⠉⠀⡄⠀⣸ ⢸⡆⠈⡇⠀⠀⠀⠀⠙⠢⢄⡀⠈⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⠀⠀⣀⣤⡶⠀⠀⠀⢀⣴⠟⠉⠀⣀⠔⠊⠁⠀⠀⠀⠀⡀⠀⣿ ⠸⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⡏⣠⠞⣩⠟⠀⠀⠀⠀⢸⡇⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⡇ ⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡇⢸⡷⠃⣴⠏⠀⠀⠀⠀⠀⢸⠇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⠃ ⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡀⠀⠀⠀⠀⠀⠸⡇⢸⠁⡼⠃⠀⠀⠀⠀⠀⠀⣿⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀ ⠀⠀⣿⡀⢹⡀⠀⠀⠀⠀⠀⠀⢀⡽⠀⣸⠇⣀⣴⠶⠶⠦⢤⣷⠀⡼⠥⠤⣴⡶⠶⢶⣄⠀⣿⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣸⠃⠀ ⠀⠀⠘⣧⣀⡉⠓⠒⠦⠤⠤⠔⢉⣴⢾⣥⡾⠛⠁⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⠀⠀⣠⣿⣷⣮⡿⢦⣌⠳⠤⠤⠤⠖⠒⠉⣁⣰⡏⠀⠀ ⠀⠀⠀⠀⠉⠙⠛⠶⠦⣤⣤⣶⡏⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠙⢿⣄⣙⣷⣤⣤⡴⠶⠚⠛⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠙⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⡀⠀⣠⣶⣾⣿⣶⣶⣤⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀ ⠀⠘⣿⠶⣤⣉⠻⣍⠓⠶⣴⡏⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣋⣉⡈⠉⠻⢿⣿⣆⠀⠀⠀⠘⣧⠴⠞⣋⡽⢋⣠⠴⣾⠏⠀ ⠀⠀⠘⣷⡀⠉⠛⠺⢷⣤⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⣿⡄⠀⢨⡍⠉⠚⢻⣿⣧⠀⠀⠀⠀⣠⡾⠿⠚⠉⠁⣴⠏⠀⠀ ⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣶⣤⣤⣤⣤⣾⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⣻⣿⡿⠿⠖⠒⠒⠒⠒⠲⠾⢿⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⣰⣿⡟⢰⣏⡄⣆⠀⣖⣚⣫⣽⣿⣶⡄⢰⡶⡾⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠿⢿⣤⣼⣿⡾⠀⠀⠉⠻⠿⠿⠿⠋⠀⠉⢻⣷⣿⣤⣤⠴⠶⠶⠶⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣿⡟⢿⠶⣦⣤⣄⣐⣤⣤⡶⣿⠛⣿⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣽⠈⠛⠛⠦⠿⡼⠧⠞⠛⠁⣸⣽⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢻⡞⣧⣤⠀⠀⠀⠀⣤⣴⠻⡿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧⡟⢸⣧⣠⢄⣠⡇⢹⣴⠃⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢧⣸⣁⡇⠈⡇⣧⣸⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣬⣉⣉⣉⣉⣁⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠙⢷⡀⠀⠀⡀⣄⠄⠀⠀⣴⠋⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⣄⣀⢀⣼⠇⣤⣤⣼⣯⣤⣤⡸⣧⡀⢀⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠡⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⠉⠙⠻⠿⠛⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣄⣀⠴⠶⣀⡠⣼⣿⣧⣤⠀⠀⠀⠀⠀⡠ ⠀⢷⣄⠀⠀⠲⣶⣶⣿⣿⣿⣿⣯⣤⣤⣼⣿⣿⣿⣿⣶⣶⠶⠀⢀⣾⠃ ⠀⠈⢿⣷⣄⠀⠀⠀⠉⠉⡍⠈⠝⡟⢻⠻⠉⢩⠉⠉⠀⠀⢀⣴⣿⠃⠀ ⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⢿⢃⡀⠀⠀⢀⠀⡾⠀⠀⢀⣴⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣦⣀⠈⠷⢥⣧⣼⡬⠾⠁⣀⡴⣻⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⢦⣄⠀⠀⣀⡴⢞⣭⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⣆⠀⠈⢙⡿⣮⣝⣒⠦⣬⣉⡀⠀⠀⢠⡶⠂⠀⠀⠀ ⠀⠀⠀⣠⡀⣤⣤⣿⣦⢘⣭⠷⠒⠈⠙⠛⠶⢯⣭⣟⣵⡟⣥⣤⣔⣶⠀ ⠀⠀⠘⠭⠉⠉⠉⠘⢿⣄⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠃⠀⠀⠊⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠶⠖⠛⠓⠓⠶⠶⠶⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⣠⡶⢛⣉⣩⣉⣛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢛⣉⣍⣉⡛⢶⣄⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀ ⠀⠀⢠⡿⠀⠀⠀⢀⣤⡾⢫⠔⠉⠀⠀⠀⠈⠑⠮⣙⣓⣦⠀⠀⠀⠀⠀⠀⣴⣞⣋⡵⠊⠁⠀⠀⠀⠉⠢⡙⢷⣤⡀⠀⠀⠀⢻⡆⠀⠀ ⠀⠀⣾⠃⠀⠀⠀⠹⢷⣶⣁⠀⠀⠀⠀⠀⠀⣀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⣈⣳⡾⠟⠀⠀⠀⠘⣷⠀⠀ ⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⠓⠒⠛⠛⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⠛⠓⠒⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⢹⣇⠀ ⢀⣿⠁⠀⣠⠖⠋⠉⠙⢦⡀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢀⡴⠛⠉⠙⠲⣄⠀⠀⣿⡄ ⢸⡇⠀⡼⠁⠀⠀⠀⠀⠀⣷⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡇⠀⣼⠁⠀⠀⠀⠀⠈⢣⠀⢸⡇ ⣿⡇⠠⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⡆⠀⣷ ⢸⣇⠀⢧⡀⠀⠀⠀⢀⡼⠃⠀⠀⢷⠀⠀⠀⢸⠀⠀⣀⣠⡤⠤⠤⠤⠤⢤⣄⣀⠀⠀⡏⠀⠀⠀⡼⠀⠀⠘⢧⡀⠀⠀⠀⠀⡸⠁⢸⡇ ⠈⢿⡄⠈⠙⠒⠶⠒⠋⠀⠀⢀⣀⣸⣤⣤⡤⠬⠧⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠼⠧⢤⣤⣤⣇⣀⡀⠀⠀⠙⠓⠲⠖⠋⠁⢠⡿⠁ ⠀⠈⢿⣦⡀⠀⠀⠀⠀⢀⡾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢷⡄⠀⠀⠀⠀⢀⣴⡿⠁⠀ ⠀⠀⠀⠙⢿⣦⡀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⡇⠀⠀⠀⣰⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⢿⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣾⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠈⢷⡄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⡾⠃⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠻⣦⡈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⣴⠟⠁⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠈⠙⢶⣤⣈⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⢁⣤⡶⠛⠁⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠈⠙⠛⠶⢦⣬⣉⣉⣙⣛⣉⣩⣥⡤⠶⠛⠋⠁⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣀⡤⠤⠭⠭⠭⠭⠥⢤⣀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡀⠀⠙⢦⣀⠀⠀⠀⠀⣀⡤⠊⠀⢀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣌⣉⣉⣉⣉⣥⣤⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⣿⠆⠀⠀ ⠀⠀⢠⣾⣿⠋⢀⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋⢀⣾⠋⠀⠀⠀ ⠀⣠⣿⡿⠁⠀⣼⠇⠀⠀⠀⠀⠀⣴⣿⡿⠋⢀⣴⠟⠁⠀⠀⠀⠀ ⢠⣿⣿⠁⢀⣼⠏⠀⠀⠀⠀⠀⣴⣿⠯⠴⢿⡟⠁⠀⠀⠀⠀⠀⠀ ⢻⣿⣯⣼⡿⢿⡀⠀⠀⠀⠀⢸⣷⡏⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⢺⣿⡏⠁⠀⠸⣧⠀⠀⠀⠀⣾⣿⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⠀⠀⠀⣿⠀⢀⣀⣤⣽⠿⠧⣤⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣧⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣷⣿⠋⣿⠀⠀⢀⣀⡀⠀⣰⣶⣦⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⣿⣿⡏⢠⣿⣿⡿⢷⠀⢻⣿⣿⢹⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⡇⠘⣿⡿⢇⣼⡟⣾⣿⣷⣿⠟⠿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠹⣦⣀⠈⠉⡽⠋⠀⠛⠛⠋⠁⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣶⣄⠉⠛⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣍⡛⠛⠛⢶⣄⠤⡤⠤⠒⠃⠉⢙⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣦⣀⣀⣠⣴⣖⡋⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⡿⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢦⠀⠀⠀⠀ ⠀⠀⣼⣿⠃⠀⠀⢸⣷⣿⣿⣿⡟⠛⠉⠀⠀⠉⢻⣷⣬⣧⠀⠀⠀ ⠀⠀⡧⢸⡄⠀⠀⠀⣿⡇⠙⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⡉⢧⠀⠀ ⠀⢠⡿⠾⣷⣤⡴⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣧⠘⣆⠀ ⠀⣾⡇⢠⡟⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣆⣼⡀ ⠀⢿⣷⣾⡇⠀⠀⢀⣿⣷⢀⠀⠀⠀⠀⡀⠀⠀⣀⣤⠤⢿⡿⠟⠃ ⠀⠀⠈⠁⠉⠉⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⣡⠴⢦⣄⠑⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⢸⡅⠀⢸⣌⡧⢸⡄⠀⠀⣠⣤⣿⣿⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⡈⠳⢤⣤⠟⠁⡼⣀⣠⣤⣿⣿⡛⠛⠻⠿⣿⣿⣷⠀⠀⠀⣠⠖⢉⣉⣉⠓⢄⠀ ⠀⠀⠀⠀⠀⠙⠶⠤⠤⣶⡿⠛⠉⢸⣿⠿⠿⠷⠀⠀⠀⣤⣟⣳⢄⠀⢰⠃⡴⠉⠙⣽⣷⡈⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢠⣴⣿⡿⣿⣦⡀⠀⠀⠀⣉⣙⡛⠿⠳⣽⡄⠻⣄⡀⣸⡿⠁⡿ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢠⣿⣿⣷⡿⠀⢩⣧⠀⢠⡾⣿⠿⠿⣦⡀⢹⣿⠦⣈⣉⣉⡤⠞⠁ ⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⣿⠙⠛⠋⠀⠀⢸⡟⢀⣿⣿⡿⠀⠀⠈⣷⢸⣿⠀⠈⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠋⠙⣆⠙⢷⣤⣀⣠⣦⣿⡃⢸⣛⠉⠀⠀⠀⢀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣧⠀⣴⣿⠟⠛⠉⠉⠙⠿⣿⣉⣹⣿⣷⣶⣦⣶⣾⠃⢀⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠈⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠙⢷⣄⡾⠹⢙⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡆⠀⢠⣿⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣨⣼⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣄⢸⣿⡆⠈⠛⠿⣗⣶⠤⣤⣀⣀⣀⣀⣀⣠⣴⡟⠙⠛⢫⡇⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⢛⢢⡈⠿⣿⣏⢻⣮⣤⣀⡀⠉⢉⡙⠒⠒⠛⠛⠛⢉⡿⠁⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀ ⢀⣯⠞⠁⠈⢧⢄⠈⠙⠛⢿⣿⣿⣿⣿⣶⣾⣷⣶⣦⣤⣴⣟⣁⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡀⢠⡶⠛⠻⣧⠀⢀⣴⣾⣿⡟⠛⠛⣿⣿⣿⣿⣿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⠀⠀⣀⣿⢻⡏⢾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡗⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣶⣿⣿⣧⠟⠁⣿⣿⢿⣿⡿⣿⣿⢿⣿⡻⢿⡟⢧⡀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠻⣿⡿⠁⠀⣰⡟⠿⠟⠋⠀⣀⣄⡀⠋⠻⠟⢻⡄⢳⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠃⠀⢰⡟⠀⠀⠀⠀⢸⣧⣾⣿⠄⠀⠀⠀⢻⡌⣷⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⠀⡿⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠘⣷⢸⣄⠤⣄⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⣷⡀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⢀⣿⡏⠉⠉⣿⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⡆⡄⠹⣧⡀⠀⠀⠀⠘⢿⡿⠟⠀⠀⠀⢀⣾⢿⠀⢀⣶⠿⢾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣦⡈⠳⢦⣤⣀⣀⡀⠀⣀⣠⣴⡾⢟⣡⡞⣿⣿⠇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠛⠿⣿⣷⣦⣬⣉⣹⣛⣛⣉⣭⣥⠾⠛⠉⣇⠘⣧⠀⠀⣼⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠉⠛⢿⡟⠛⠛⣿⠟⠉⠀⠀⠀⠀⢻⠀⠙⠻⠾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⣄⣀⣀⣀⣀⣠⣧⠀⠀⣿⣀⣀⣀⣀⣀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⣆⣾⠃⠀⠀⠀⠀⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⣄⣀⠀⠀⠀⠀⣀⣸⡿⣿⡀⡀⠀⠀⠐⣘⣤⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣴⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⠟⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠋⣠⣾⠋⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⠃⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⣰⡿⠃⠀⠀⠀⠀ ⠀⢠⣾⣳⡿⠁⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⢀⣿⣷⣿⠁⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣥⣴⣶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⡏⠤⣶⣿⡏⠀⠀⠀⠀⠀⠀⢀⣾⢫⡿⠈⠉⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⡿⠿⠛⠁⣿⡄⠀⠀⠀⠀⠀⢸⣿⣼⠇⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⢿⡇⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣼⣧⠀⠀⠀⠘⣿⠀⠀⢀⣠⣤⣼⣿⠿⣦⣤⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣷⣿⣆⠀⠀⢀⣿⣶⣿⡿⠛⠉⠁⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣦⣠⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⣿⣿⣤⣽⠇⢀⣠⣴⣶⣦⡀⠀⢸⣿⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢠⣿⣿⣿⣿⠛⢷⠀⠸⣿⣿⡿⢀⣿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣷⣿⡇⠀⢻⡿⠿⠿⣀⣾⠘⣷⣿⣿⣾⣿⠿⠿⠾⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⢿⣆⠀⠀⠙⠙⢛⡽⠊⠀⠻⠿⠛⠛⠋⠀⠀⠀⠈⣶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣀⠙⠻⠶⣤⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣻⣶⣤⣤⣤⣿⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣈⠉⠉⠉⠻⣷⡄⠦⠤⠴⠞⠋⠁⠀⠀⣸⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣤⣶⣛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠟⠉⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⡟⠀⠀⠀⢹⣿⠻⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⣷⣄⠙⣦⠀⠀⠀⠀ ⠀⠀⢰⡏⣿⠃⠀⠀⠀⠀⣿⣿⠿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡿⣄⠀⠀⠀ ⠀⠀⢼⡇⢿⣇⠀⠀⠀⠀⣻⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⡆⠘⣇⠀⠀ ⠀⠀⣾⠿⣶⣿⣄⣤⣴⠾⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢿⡄⠸⡆⠀ ⠀⢸⣿⠀⢀⣼⠋⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⣧⠀⢹⠀ ⠀⢸⣿⣆⣾⡏⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣏⣿⡇ ⠀⠘⢿⣿⣿⣧⣄⣀⣀⣤⣼⣿⣧⣠⣤⣀⠠⠤⠤⠤⠄⠀⠀⠒⠒⠒⠒⠛⠾⠛⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣵⣿⣿⣿⣿⣿⣾⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡴⢖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⣦⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣷⣿⡿⠿⠿⠿⣿⡿⠟⠋⠉⠉⠙⠻⠤⣄⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠳⣄⠀⠀⠀ ⠀⠀⠀⣠⠔⠒⠒⠢⢄⠀⠀⠀⠚⣠⠜⠋⠀⢀⣀⣀⡀⠘⣇⠀⠀⣤⣴⣶⣶⣦⣤⣑⣦⣀⣸⠃⢠⠞⠉⠉⢻⣆⠈⢧⠀⠀ ⠀⢀⡾⠁⣤⠖⠒⢦⡀⠙⣦⢀⠞⢁⣴⣾⣿⠿⠿⠿⠇⠀⣿⠀⠀⢻⣟⣛⠉⠉⠛⠻⠋⢻⣽⠀⢸⣄⣀⣦⣾⡏⢀⣼⠀⠀ ⢀⣾⡇⢸⣯⠀⠀⠀⣿⠀⢻⡌⠀⠙⠋⢀⣤⣶⣶⣤⣄⠀⣿⠀⣠⣾⣿⣿⣿⣷⣦⠀⠀⠈⣿⣦⣀⡙⠛⢛⣋⣤⣾⠏⠀⠀ ⠈⠹⣿⣄⠻⠿⣶⠿⠋⢀⣾⠁⠀⠀⣰⣿⡿⠟⠛⠻⣿⣇⣸⡄⣿⠋⠁⠀⠈⠙⢿⣧⠀⠀⢹⣟⠛⣻⡿⠿⠛⠋⠁⠀⠀⠀ ⠀⠀⠈⠻⢷⣶⣶⣶⡾⢿⣿⠀⠀⢠⣿⠃⠀⢀⣀⠀⢀⣿⣿⣿⣷⣄⣀⣶⡄⣀⣼⣿⣀⠀⢘⡟⠃⠀⢲⣶⣀⠀⠀⠠⡄⠀ ⠀⠀⠀⠀⣄⠀⠀⢀⡀⢠⣼⣄⣀⣀⣿⣦⣤⡼⢿⣚⣿⣿⣿⣿⣿⡿⠈⠙⠩⠭⣟⣿⣿⢿⡿⠿⣄⠀⠀⠀⠀⣀⠀⠀⠈⠀ ⠀⠀⠀⠀⢿⣇⠀⢧⠉⢀⣼⣿⡿⢿⣿⡟⣡⠖⠁⠀⠈⠙⠻⣿⡏⠀⠀⠀⠀⠀⠀⠉⣿⣶⡹⣿⢿⣷⡄⠈⢁⡋⡀⠀⠈⠀ ⠀⣀⡀⠁⠐⣄⠉⢩⣀⡝⢡⡴⣷⣶⣿⡴⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣿⣿⡟⢧⢀⡏⠀⠙⣆⠀⠀ ⠀⢠⡁⢠⠀⠈⠓⠀⣸⡡⣟⣠⣼⣿⡏⣿⣄⡀⠀⠀⠀⣀⣤⣿⣷⣤⣤⣤⣴⣾⣿⣿⣿⣿⠙⠿⠟⠁⣸⠤⡟⠢⡤⠬⣁⠀ ⠀⠀⠉⠧⣠⡖⠀⢶⡻⣄⠻⣿⡿⢛⣿⣿⣿⡿⣿⡟⢛⣟⠉⣹⣯⣉⣹⣥⡼⢿⣴⠿⣤⡿⠷⠦⣴⣾⠛⠃⡿⢿⠁⠀⠈⡇ ⠀⠀⠀⠀⠈⠻⣄⠈⠳⡿⣷⣶⠶⠿⢿⠖⠛⠓⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣀⣩⣩⠀⡧⠀⢠⣀⡼⠋⠈⠓⠤⢞⡁ ⠀⠀⠀⢀⠀⠀⠛⣆⠸⡁⣩⡷⢀⠠⣀⣤⣤⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣤⡀⢸⡆⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⢸⣦⠀⢀⣠⣄⠀⠹⢂⣼⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣠⡿⡅⠈⡽⢇⠂⠀⠀⠔ ⠀⠀⠀⠀⠀⢉⠏⣁⡼⣄⢠⠋⢿⣄⣠⣿⣿⡿⢿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣛⣿⣯⡽⠷⠿⠛⠉⢁⣴⣿⠀⠀⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠝⠟⠀⠜⣯⣧⣀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠥⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠉⠐⢒⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⠤⠤⠜⣿⠀⠿⠹⣿⣷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣤⣤⣀⣠⣤⡴⢾⣿⡿⠛⠁⠀⠀⠀⢈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠖⢋⣤⣯⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣭⣷⣿⣿⠁⠀⢀⡆⠐⠦⠤⠚⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠚⢿⣿⣿⣿⠿⠛⠋⠉⠟⠉⠟⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠠⠤⠤⠊⠀⠈⠁⠀⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠉⠉⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⡀⠀⢰⡤⣀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⢴⠆⠀⠀⠀⠀ ⡐⡡⠐⠒⠠⡑⢢⠻⣒⠭⠆⢀⣀⣀⠀⠀⠀⠀⣀⣀⡀⠼⠅⡢⠋⠀⠀⣴⠀⠀ ⠇⡆⠀⠀⢀⠂⠖⡴⠊⠉⠒⠢⠤⠤⠀⠀⠀⠠⠤⠤⠔⠂⠉⠑⣌⣉⡩⢝⠀⠀ ⠈⠬⡢⠄⣡⢊⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠈⢞⣆⠀ ⠀⠀⠈⠉⠉⡏⠀⠡⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠈⢧⣼⣿⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⠀⠀⢠⣴⠟⠉⠀⠀⠀⠀⢸⠉⡎⡆ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⣤⣬⡷⡄⠀⠀⣰⣟⣥⣤⣄⡀⠀⠀⠀⢸⠀⡵⡘ ⠀⠀⠀⠀⠘⣆⠀⠀⢸⣿⣿⣿⣿⣿⠉⠀⠀⢱⣿⣿⣿⣿⣿⡆⠀⠀⡼⠀⠉⠀ ⠀⠀⠀⢀⡞⢁⣤⣄⣸⣻⣿⣿⣿⡿⠀⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⠀⠘⢦⠀⠀ ⠀⠀⠀⢸⠀⢹⠶⢚⠿⠛⠛⠋⢿⣟⣉⣹⣿⣿⣿⡯⠙⠛⠣⢤⡀⠀⠀⢸⡆⠀ ⠀⠀⠀⠘⢦⡀⠀⡇⠀⠀⠀⠀⠀⠈⠛⢻⠟⠋⠁⠀⠀⠀⠀⠀⢱⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⢹⠲⣇⠀⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡄⠀⡼⢺⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡆⢸⡦⣀⠀⠀⠀⠀⣀⣸⣀⣀⠀⠀⠀⠉⡠⢾⠁⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⢃⣷⣿⣭⣹⣯⣩⣿⣦⣼⣯⣩⣿⣍⣽⣷⡏⢝⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢆⠣⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡯⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠒⠩⢏⡻⠛⣟⡻⠛⣏⡹⠙⠒⢡⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⣀⣀⣀⣀⣀⢤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀

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.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⢹⣋⣀⣠⡀⠀⠈⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⢀⡟⢉⣉⢹⣆⣀⣀⣀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⣀⣴⣟⣻⣦⣧⣿⣋⣉⣙⣛⡿⣶⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣟⠉⣉⣉⣙⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠟⠛⠛⠻⢿⡿⢿⡟⠉⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⢸⡇⠸⣷⣀⣠⣴⣾⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣀⣴⣿⠁⠀⠙⠉⢉⡽⠛⣅⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡛⠉⠁⣀⣠⠤⢶⠋⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⢻⠋⠉⢹⡀⢀⣀⣧⣴⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⣤⡤⡀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠛⠛⠉⠉⣉⣨⡿⣿⣶⣾⡷⠶⠶⠒⠛⠋⣿⣿⠻⣗⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠟⠛⠛⢻⡟⢯⣁⣠⣿⢻⣿⣇⠀⠀⠀⠀⠀⠁⠀⠀⠹⣦⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⡟⠈⠀⠀⠀⠘⣧⠘⣿⣿⣧⣾⠇⠉⠀⠀⠀⠀⣴⣶⠀⠀⠀⠘⣧ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢠⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣿⣿⠏⢀⣤⠤⠶⢚⣋⣿⡇⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠈⣷⠂⠛⠉⠁⢸⣇⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠘⡇⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠻⢦⣀⣰⠏⢻⡄⠀⢀⣠⠾ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣳⣶⣆⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢿⠀⠀⠀⡛⠻⠶⣽⣁⡀⢸⣷⠺⡏⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣍⠉⠻⣟⠀⠀⢹⡇⠀⠀⠀⠀⢸⡇⡀⠾⢥⣤⡤⠄⠈⣿⠀⣿⠀⢻⠀⢀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⣧⣤⡿⠤⣄⠀⣿⢦⡄⠀⠀⢸⡿⢧⣤⠀⠀⠀⠀⠀⢹⣷⣿⣀⣼⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⢹⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⢧⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⡙⣼⣿⣧⡀⠀⠀⠀⠀⣸⠆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⢦⣄⣤⣴⣿⣟⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢌⢿⣻⣝⢒⣶⠖⠋⢁⡴⠛⠀⠀⣀⡠⠤⠤⠤⠐⠒⠒⠒⠢⢽⣿⣶⣤⣤⣤⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠈⢻⣮⣋⣀⣠⣴⣿⣇⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣶⣤⡀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣾⣿⣿⣿⡿⢿⣿⣿⣷⠀⢠⣿⡋⢹⠛⣿⣶⠈⣉⣿⣇⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢿⡇⠀⣿⣿⡯⠟⠁⢿⣶⣿⢿⣿⣿⣧⠀⠘⠿⠿⠛⠀⢀⣿⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢃⡿⠀⠀⣿⣿⡀⠀⠀⠀⠉⠁⣸⣟⣛⣿⣦⣄⣀⠀⢀⣴⣿⣿⠟⠀⠀⠈⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠛⢿⣿⣦⣄⣠⣴⣾⣿⣿⣿⣿⣿⡿⠻⠿⠿⣍⣁⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢉⡽⠟⠋⠁⠙⠛⠛⣿⠛⠋⠁⠀⠀⠀⠀⠈⠙⣦⠴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⢀⣀⡤⢞⣿⠙⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠞⢻⣿⠘⣷⣤⣤⣀⣀⣠⣤⣖⣫⣥⠾⢿⠿⣿⣿⡿⠶⠞⠋⠀⣷⣟⣠⢤⣤⡤⠤⠤⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⡴⣾⡋⠀⠀⠈⣿⣧⡉⠻⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡁⠙⣷⣿⣿⡄⠀⠀⠈⢧⡀⠀ ⠀⠀⣀⡼⢠⣿⠀⠀⠀⣰⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣟⣛⡛⠻⣿⣿⣿⣿⡆⠀⠀⠀⢇⠀ ⣠⢞⠿⣷⡘⠁⠀⠀⣰⣿⣿⣿⡿⣿⡿⠿⠷⢶⣶⣶⡶⠿⢿⣿⠟⠛⣉⣿⠿⠛⠋⠉⢹⣿⠛⣯⠻⣿⣿⣿⠀⠀⠀⠈⠆ ⠁⠋⠸⣿⣷⣄⣀⣴⣿⣿⣿⢏⣰⣿⠀⠀⠀⠀⢀⢉⣻⣿⠛⠙⢳⣾⣿⡧⠀⠀⢠⡀⣼⠇⠀⢹⣧⣿⣿⡿⠀⠀⠀⡰⠃ ⠀⠀⠀⢿⣿⣿⣿⣿⠿⣿⢧⡞⠘⢿⣄⢀⠀⠀⢻⣿⣿⣿⣇⣠⣾⠛⠛⠃⠀⠀⢀⣿⡏⠀⠀⠀⠘⣿⣿⡇⣠⠔⠋⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣶⡟⢸⠁⠀⠀⠙⣿⡶⠀⠀⢉⣼⡟⠉⠉⠹⣷⡆⠀⠀⠀⣸⡿⠀⠀⠀⠀⢀⣿⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠈⠉⠀⠀⠛⣏⠛⣛⡿⠋⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣖⡒⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣲⠶⠒⣀⣠⡍⠓⠀⠉⠲⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠞⣡⠎⢠⡴⠋⠁⠀⣀⣀⣀⠀⠀⠘⣎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠤⠤⠤⠚⣁⡾⠁⢠⣿⠁⠀⣴⣿⣿⣦⡈⠃⠀⠀⡘⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⠶⠶⠿⢿⡇⠀⢠⣿⠀⡸⣿⢿⣿⠻⢷⡀⣰⣾⣷⣾⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⣰⢷⠀⠘⣿⡄⠀⣿⣼⣿⠖⠾⢿⣿⣿⣿⣋⠁⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣤⡆⣬⣥⠾⠀⠀⡇⣻⢦⡉⠉⢿⡇⣠⣴⢿⡿⣿⣿⡛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡉⠲⠖⠀⢀⡼⣱⠏⠀⠈⠀⠘⣿⣯⢠⣿⠁⠀⠙⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣴⣺⠯⠞⠁⠀⠀⠀⠀⠀⢟⣿⠟⠁⠀⠀⠀⢀⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣴⣶⠛⠙⠛⠷⣦⣤⣄⣀⣀⠀⠀⢰⡟⣅⣤⣴⡞⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣷⣽⣿⣿⣿⣿⣶⣍⠙⢯⡁⠀⠀⠈⢠⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣈⣻⣿⡟⣿⣿⣿⢿⣿⣆⠈⣷⣀⠀⢀⣿⣿⣯⡇⢘⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣀⠙⠒⠛⠿⣧⣽⣟⣿⡿⠃⢹⡿⠁⣨⠿⣿⡿⢭⡽⠷⣛⡉⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⣆⠀⠀⠈⠉⠛⠛⠛⠓⢛⣧⠟⠁⠀⠘⢿⣦⡀⠀⡙⢿⣿⣄⠀⢀⣤⠶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⢸⢹⡄⠀⠀⠀⠀⠙⢦⡴⠋⠁⠀⠀⠀⠀⠀⢻⣿⡄⣸⣦⠋⣯⢷⣿⡁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⡇⠘⡎⢷⠀⠀⠀⠀⠀⠘⢿⣶⣄⣀⣀⡀⢀⣤⣾⡿⠷⣿⣿⣠⣿⠄⠈⣿⡆⠀⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⡙⠻⢷⡇⠸⡗⠦⣀⡀⠀⠀⠈⢿⣮⡉⠙⠻⢿⣿⣿⡥⠎⢹⠹⣿⠟⣠⡾⠃⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠀⠠⣶⣶⠦⠤⣄⣀⠀⠀⠙⠳⢤⣀⢀⡿⠀⠀⠙⠓⢦⣤⣀⣙⣛⣿⣛⣞⣻⡟⠀⢠⣼⣿⡷⠿⠉⠀⠀⠀⠀⢰⣿⠀⠀⠀⣀⠤⢀⣾⣿⣿⠿⢿⣿⡟⠀⠀⠀ ⠀⠀⠀⣿⢿⣶⣦⡀⠉⠙⠲⢦⣄⠀⠉⠉⠀⠀⠀⠀⠀⠈⢷⠀⠈⠉⠛⣿⢹⣿⠃⣀⣾⣟⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠸⣅⣰⣿⣿⣿⣿⣦⡀⢉⣄⠀⠀⠀ ⠀⠀⠀⣿⠈⢻⣿⡿⣦⣄⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⣠⠞⠷⣤⣄⣀⣼⡇⠀⠀⠀⢸⡿⣧⣱⣄⠀⠀⠀⠀⢘⣹⡇⠀⠀⢀⣴⣿⣿⡇⠈⠻⣿⢛⡏⠀⡆⠀⠀ ⠀⠀⠀⢿⡆⢸⠏⠿⣦⡙⢷⣄⠀⠀⠀⠀⠙⣦⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣷⠈⢿⣄⠂⠀⠀⠀⢈⡿⠀⠀⢠⣾⠟⠉⣙⣿⣦⡞⠉⠉⢳⣶⠁⠀⠀ ⠀⠀⠀⠘⣿⠄⠠⠞⢻⣷⣌⢿⣷⣄⠀⠀⠀⢹⣻⡗⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢢⠈⠻⡄⠈⠻⣧⡀⠀⢠⣾⠃⠀⣠⣿⣿⣷⣼⡃⠀⢙⣿⡧⠤⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⣤⠄⢀⣴⡿⢿⣦⠻⡟⠋⠀⠀⠀⢹⡇⠀⠀⠈⠉⠓⠒⠲⠤⢤⣄⣀⣈⡀⣀⣿⠀⠀⠈⠛⢶⡿⠛⢦⣼⣿⣿⣿⣿⣿⣿⡒⠋⣹⣷⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣞⣾⠋⠄⠀⠈⢷⡘⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣁⠀⠀⠀⠀⠀⠙⣶⣿⣿⣿⣿⣿⣿⡿⣿⠉⠛⠁⢸⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠃⠁⠀⠀⠀⠈⢻⡄⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠸⣷⣦⣄⣠⡴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡏⠐⠀⡀⠀⠀⠀⠀⢻⣦⣶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣠⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠁⠀⢰⠀⠀⢀⡿⠁⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣀⣠⠾⣥⡤⢤⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⠀⣄⣄⣐⠃⠀⣸⠀⢀⡏⢻⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣠⣶⠟⣻⣭⡙⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠴⠖⢾⣿⣿⣷⡄⠈⣿⣬⠇⠀⠀⠀⠀ ⠀⠀⢠⠟⠀⠈⣿⢿⠁⠀⣴⠃⢀⡞⠀⠀⢿⡄⠀⠀⠀⠉⠓⢠⣀⣄⣴⡿⢁⣼⠟⠉⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⠀⠀⠀⠙⣿⣿⣿⣾⣼⠟⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠈⠀⣴⠁⢀⡞⠁⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢉⣿⣿⣴⣟⡷⣄⠀⢦⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣄⠀⢶⡀⠈⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⢸⠁⢠⡞⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⣰⣿⡏⠸⣿⡉⠁⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⣿⣧⡝⣿⡄⠀⢿⣦⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣟⢻⢶⣤⣀⠀⡀⠁⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣼⡿⢯⣿⡄⠙⢿⣶⣵⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠸⣷⣀⣼⣿⣄⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠛⠉⠉⠛⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀ ⠀⢠⡇⠀⠀⢀⡴⡫⠭⠭⢓⢤⣀⠀⠀⠀⠀⢀⡤⡚⠭⠭⢝⢦⡀⠀⠀⢸⡄⠀ ⠀⣼⠀⠀⠸⢭⣊⡀⠀⢀⣀⠽⠊⠀⠀⠀⠀⠓⠯⣀⡀⠀⠀⣑⡯⠇⠀⠀⣧⠀ ⢰⠇⢀⡤⠤⢄⠀⢹⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡏⠀⡠⠤⢤⡀⠘⡆ ⣾⢠⠃⠀⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠘⡄⢷ ⢿⠘⡄⠀⠀⡠⠃⠈⡄⠀⢠⠀⣀⠠⠤⠤⠄⣀⠀⡄⠀⢀⠃⠘⢄⠀⠀⢀⠇⡼ ⠘⣦⠈⠉⠉⠀⣠⠔⠓⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠚⠲⣤⠀⠉⠉⠁⣴⠃ ⠀⠈⠳⢦⠀⠀⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⠀⡠⠞⠁⠀ ⠀⠀⠀⠈⢳⡄⠱⡜⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⠎⢀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣆⠘⠦⣑⠢⣀⡀⠀⠀⠀⠀⢀⣀⠄⣊⠴⠃⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠉⠒⠮⠭⣤⣦⠭⠵⠒⠋⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠪⣉⠉⠉⢉⠕⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠦⠭⠭⠶⢶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⠈⡖⠒⢲⡞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣄⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⡜⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠈⠳⡀⠀ ⠀⠀⠀⣧⠀⢀⡇⣠⣏⣀⣀⣀⣀⣀⠀⠀⠀⠀⡠⠊⣠⠴⡇⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⢹⡀⢸⣷⠏⠀⠀⠀⠀⠀⠀⠉⠳⢦⣎⣠⠞⣵⣴⡇⠀⠀⠀⠀⠸⡆ ⠀⠀⢠⢞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠈⢻⡟⠋⠁⠙⣄⠀⠀⠀⢰⡇ ⠀⢠⠏⢸⣄⡴⢲⣤⡀⠀⠀⠀⢀⠂⢀⡴⢲⣤⡔⢳⠀⠀⠀⠀⠉⠒⠊⠉⠀ ⢀⡞⠀⢘⠏⠀⢰⡇⢹⡄⠀⠀⡌⠀⡎⠀⢀⡏⢯⠉⣇⠀⠀⠀⢠⡀⠀⠀⠀ ⢸⡇⠀⢸⡦⢤⣾⣧⢸⣿⠀⠀⠆⢰⣷⣦⣾⡀⣸⡄⢸⠀⠀⢠⣿⣷⡀⠀⠀ ⠀⢃⠀⠸⣧⣀⣿⢉⣽⠿⠂⢶⡶⠺⢿⣿⡏⣹⣿⡇⢸⠀⢠⣿⣿⠏⡇⠀⠀ ⠀⠘⣆⠀⠀⠈⠉⠉⠀⢤⣤⠼⢷⡤⠃⠈⠉⠉⢁⡴⠃⢠⣿⣿⠃⢀⠇⠀⠀ ⠀⠀⠈⠑⠦⢄⣀⠀⠀⠀⠙⢶⡞⠁⠀⣀⣠⣴⡋⠀⣠⣿⡿⠁⡰⠃⠀⠀⠀ ⢀⣀⠤⢴⠖⠊⠉⠉⣑⣤⣶⣿⣿⡟⠛⠋⢹⣿⣿⣶⣿⠋⠑⠊⠀⠀⠀⠀⠀ ⢸⠀⠀⠸⡄⠀⠀⡄⠹⣿⣿⢻⣾⣿⡄⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣧⠀⠀⢧⣠⠞⣷⠀⠀⠀⠀⠉⡇⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣇⢱⣖⠉⠀⢰⡏⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣹⠈⠑⠶⣉⣀⣀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⢹⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⣀⠀⠀⣈⣆⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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😠💧🗯️🚫

💢🙄😳

(´・ω・`)🤕<💢<🐈💕

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🙅‍♀️💢/🙅‍♂️💢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠷⣶⡶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⣚⠉⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢉⡤⠖⠊⠉⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⣤⠶⣒⠒⠒⠒⠲⠦⠤⠤⢤⣀⣀⠀⢀⣀⣀⣈⣷⣄⠙⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⠴⠊⠁⠀⠀⠀⠀⠀⠇⠘⡇⠀⠀⠀⠀⠀⠀ ⣇⠀⡏⠉⠉⠉⠉⠒⠂⠤⣀⣠⣾⣯⣭⡤⠤⣄⣀⠉⠳⡄⢳⠶⠒⠋⠉⠉⠻⡇⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⢸⠀⠸⡀⠀⠀⠀⠀⠀⠀⠋⠉⠳⡄⢸⠀⠀⣠⡼⠛⣳⡇⠈⠀⠀⠀⠀⠀⠀⢻⡈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣼⣠⣾⢃⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡈⢆⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡄⠈⡄⠀⠀⠀⠀⠀⠀⠀⠸⢀⡿⠁⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠳⡌⠣⡀⠀⠀⠀⠀⣠⠇⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⠹⡀⠀⠀⠀⠀⠀⢠⠇⡼⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠀⠈⠦⣙⣦⡈⠉⠉⠉⠉⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡀⠱⣄⠀⠤⠤⠔⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⣄⣀⣀⣀⡤⠴⠚⡟⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⣆⠀⠀⠀⠀⢠⠞⣀⠤⣴⡶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⢞⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⢀⡀⠈⢇⠀⠀⠀⠏⡴⢁⣔⡥⠒⠉⠉⠉⢳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢀⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⣧⣼⠉⠉⠙⠪⡀⠀⠀⠀⡇⢸⡎⠀⠀⠀⢾⣧⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠙⢶⣏⠛⠀⠀⠀⠀⠈⢆⠀⠀⢧⠘⡄⠀⠀⠀⠈⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠴⠯⠤⠒⣺⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠹⣄⠀⠀⠀⠀⠀⠈⢧⠀⠈⢧⡹⣄⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠦⣈⠱⣄⠀⠀⠀⣠⣼⣷⣶⣾⠛⢺⠷⣦⣤⣴⠞⠁⠀⠀⠀⠀⠀⣀⣤⣶⡋⠀⠀⡴⢎⣓⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣁⠈⠑⠲⣾⣿⣿⣿⣿⠏⠀⠀⠀⣸⣿⢧⣄⣀⣠⠤⢴⡖⠻⣿⣿⣿⠛⣦⣼⣧⣾⣡⣴⠒⡗⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡗⠒⠴⣿⣶⣧⣭⣷⣤⡤⣴⢾⣿⣿⠀⡇⠀⠀⠀⠀⢣⠀⢻⠀⠁⣰⢹⢧⣍⢳⣤⡚⣓⡶⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠓⠛⠀⠀⠈⢣⣿⣷⡘⣄⢳⣼⣾⡿⠋⠂⡇⠀⠀⠀⠀⢸⠀⣸⠀⠀⣏⢸⣀⡈⠟⢧⣄⠀⠈⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡤⠒⠒⠒⠒⢤⡀⡼⠛⡿⣿⣟⠉⠁⠁⣀⣤⣧⡇⠀⠀⠀⢀⡜⢠⣟⠳⠤⣸⣦⣹⠶⢳⡂⢻⠑⣄⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣷⣤⠤⠤⢤⣀⠀⣿⠇⢀⣻⡈⢻⡷⣶⣟⣯⣿⣿⡇⠀⠀⢠⣾⣵⢯⠬⢻⣦⣀⠀⠀⠀⢸⠶⠋⠀⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡏⡞⠀⠀⠀⡄⠈⠻⣿⠔⢋⣠⠿⣦⣙⢮⣿⣯⣶⣋⣀⣤⣺⣿⡟⠻⠾⠯⣄⣻⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⡀⠀⠀⡧⠀⠀⢻⣴⣋⣉⡑⠲⡏⠛⣷⠛⠛⠓⠛⠉⠁⣸⠛⢄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠃⠀⣰⠃⠀⢀⡾⠥⢄⣀⠀⣹⢃⣼⠃⠀⠀⠀⢀⣤⠞⠁⠀⠀⠑⠦⣄⣀⣀⠤⣾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⣴⣇⣠⠴⠯⣀⣀⠀⠤⠟⠋⢡⡏⠀⠀⢀⣴⣏⡀⠀⠀⠀⠀⠀⣠⠆⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠳⠦⢭⣽⣶⣶⡒⠒⠓⠲⣏⠑⣯⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠷⡶⠒⠒⣲⠖⠦⠤⢄⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣜⡀⢀⡜⠁⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⠴⠶⠒⠚⠛⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠁⢸⣏⣀⣀⡰⠤⡀⠀⠀⠈⠉⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⣿⠟⠉⠉⠻⣧⠀⠀⠀⠀⠀⠂⠀⠀⢹⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⣠⡾⢿⣦⠸⣍⣿⡿⠛⠛⠿⣿⣿⣦⣤⣲⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣴⣿⣿⠶⠶⠿⣿⢿⣿⣷⣶⣶⣾⣶⣶⣮⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣯⣅⣀⣠⣠⣤⣴⣾⣿⣷⣿⣿⠿⠟⠉⠉⠉⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠛⠛⠛⠿⣿⡿⢿⣟⠋⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣿⡇⢼⣿⡆⠀⢀⣠⣤⣾⣿⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⣴⣿⠃⠀⠹⠿⠿⠟⠟⣫⣿⠋⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⣶⣾⡿⠏⠀⠀⠀⠀⣀⣤⠾⠋⠈⣧⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣏⠻⣯⣉⠀⠀⣀⣤⣤⠶⠚⢻⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡈⢿⠛⠉⠉⢱⠀⠀⠀⢈⣧⣴⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⡀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣼⡶⠶⠶⠾⠿⠿⠛⠋⠙⣷⣾⣟⣁⣴⣶⣤⣤⣀⣠⣴⣶⡟⣿⣿⣿⢷⡛⡄⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣌⣿⣦⣤⣤⣤⣤⣤⣶⡶⠟⠋⢉⣿⣯⣿⣿⠉⠉⠁⠀⠀⠀⠀⡿⠛⠏⠀⠻⣆⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡶⢸⠃⠀⠀⠀⢸⣧⠙⣷⣦⣠⣾⡏⢸⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠿⢿⠃⠈⠀⠀⠀⠀⠈⢿⣆⠘⣿⣿⣿⣶⣿⠏⠀⠁⠀⠀⠀⠀⢀⣾⣾⡇⠀⠀⠀⠀⢸⣷ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⣿⣿⣿⡏⠀⣀⣀⣤⣤⠶⠞⠛⣿⣿⠀⠀⠀⠀⠀⠀⠹ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠇⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠏⠀⠘⣿⣉⠡⠤⠴⠚⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠻⣦⣀⢀⣾⠏⢹⣧⠀⠀⠀⢀⣴⠿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢿⣦⣤⡀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠶⢶⣶⣄⣙⡟⠁⠀⠈⣿⣤⢶⡿⠋⠁⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⠿⠻⣶⣤⣤⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢠⡾⠀⠀⠈⠉⠛⠻⣷⠀⢻⣿⠀⣿⡄⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣦⡀⠀⠻⣦⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣿⢠⣄⠛⠛⠾⠿⠛⠛⠀⠀⣿⡄⢸⣿⠀⠘⣇⣀⣤ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣛⣿⣽⣧⣴⣶⠿⠴⣦⡄⢸⣿⢷⣤⠄⠀⠀⠀⣿⠸⢧⠤⡤⠀⠀⠀⠀⠀⠀⢾⣷⣸⣟⣀⣤⣿⣿⣝

⡏⢓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⢹ ⠇⢰⠁⠂⢌⠙⠲⢄⡀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⣠⠔⠊⡁⠔⠈⠁⢸ ⢸⠘⡀⠀⠀⠈⠒⢄⠙⡆⠀⠀⠀⠀⡎⡇⡠⡺⠃⠀⢠⠋⢠⠐⠉⠀⠀⠀⠆⡘ ⠸⡄⠇⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⢸⢰⠏⡜⠁⠀⠀⢸⠀⡆⠀⠀⠀⠀⠐⠀⡇ ⠀⢧⠸⡀⠀⠀⠀⢀⢆⡿⣠⠤⠤⠬⡌⠬⢤⡤⠤⣄⢸⡀⣅⠀⠀⠀⠀⡄⢸⠀ ⠀⠘⠒⠤⢭⣀⣊⡕⣫⠞⠁⠀⠀⠀⠈⠉⠀⢀⣴⠞⠳⣏⢲⣅⣀⣩⠤⠖⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⣤⣀⠲⡤⢄⣸⠀⠀⣠⣶⣿⣿⣿⣧⢰⠾⠛⠿⣶⣄⠀⠀⢧⣀⢤⡴⢀⣠⠆ ⠀⠘⣆⠉⠚⠦⠀⠀⢰⣿⣿⣿⣿⣿⡟⠸⣄⠹⠍⠘⣿⡆⠀⠀⠴⠓⠉⣡⠏⠀ ⠀⠀⠈⢧⡀⠀⠀⠀⠀⣻⡿⣿⠿⠯⠤⠤⠬⢿⣿⡿⠛⠁⠀⠀⠀⠀⡰⠃⠀⠀ ⠀⠀⠀⠀⠙⠦⣄⣀⣰⣟⣸⣦⠃⠺⣵⣿⠿⠠⣿⣗⣀⣀⣀⣀⠤⠚⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣟⢗⣦⢤⢤⢴⡲⠻⠍⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡿⠀⠈⠉⠉⠁⠀⣾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢱⣣⢀⠀⠀⢀⡰⡟⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢾⢹⢤⢤⡏⢧⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⣚⣒⣚⣒⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠀⠉⠉⠀⠈⠉⠉⠉⠛⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢾⣤⣤⣄⣀⣀⣀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠏⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡚⢫⣛⡉⠙⠷⣤⠀⠀⣼⡿⠛⠛⠛⣻⣷⣶⣶⣶⣦⣤⣤⣤⣤⣴⣧⣤⣤⡀⣠⣴⠾⠛⠛⠛⠛⠷⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡏⠻⢯⣍⣙⠶⠄⠘⣧⣀⣿⡷⢶⣟⣛⣿⣿⣿⣭⣉⠉⠉⠙⠛⠿⣯⣅⣽⣿⣿⡏⠁⢀⡤⠶⠒⠶⣤⡈⢻⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡞⣿⠀⠀⠉⠉⠛⠛⠛⠙⠉⠋⠙⠋⠉⠁⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⠈⠙⠿⣿⡏⢀⡴⠋⠀⠀⢰⡖⠚⠓⢲⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⡇⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⠀⣸⠁⠀⠀⠀⢸⣇⣀⣀⣰⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢃⣴⠾⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⣆⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⠉⣹⢹⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢿⡿⠃⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠻⣦⣀⡀⠀⣠⡼⢋⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠛⢠⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠲⠯⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠁⢠⠈⠲⢦⣄⣀⡀⣼⠃⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣦⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠳⠁⣰⡟⠀⠀⠀⠈⠉⠉⣿⠀⠲⠒⠦⢿⠃⢿⡄⠀⠀⠀⠈⠁⠀⢀⣠⠤⠊⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⢻⣟⠉⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⢁⡀⢠⡿⡀⠀⠀⠀⠐⣠⠾⢹⡆⠀⠀⠀⣾⠀⠀⠻⣦⣀⣠⣴⠶⠛⠉⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⠀⠀ ⠀⠀⠀⢀⣠⣾⣯⡶⠂⠀⣾⠇⠀⠀⡚⣻⡾⠃⠀⠀⣿⡄⠠⣶⡿⠀⠀⠀⠈⠛⠿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀ ⠠⣴⣶⡟⡫⠀⠉⠀⠀⢀⡿⠀⠀⢀⣽⡟⠀⠀⠀⠀⠘⣷⡦⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣶⣤⣀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢰⢿⡀⠀⠀ ⠀⠉⠿⣿⣧⣄⡀⠀⠀⢸⡇⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠘⢿⣏⣇⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣶⣾⣧⠀⠀⠀⠀⠀⠀⠈⣸⣇⠀⠀ ⠀⠀⠀⠈⠻⢾⣅⡰⢤⣸⡇⠀⣸⣿⡇⠀⠀⠀⣿⣿⣷⠀⠀⠙⢿⠀⠀⠺⣿⣿⠿⠀⠤⢄⡀⠀⣿⠷⣿⣿⣽⡿⠟⣹⡇⠀⠀⠀⠀⠀⠀⢡⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠈⢙⣿⠛⣷⣰⣿⣿⣿⠀⠉⠙⠿⡋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡶⠊⠀⠀⠀⠀⣸⡟⠀⢀⣼⠟⣡⢾⡟⠀⠀⠀⠀⠀⠀⠀⠘⢹⣧⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⢁⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⡀⠀⠀⣄⡀⢀⡤⠀⡟⠀⠀⠀⠀⢀⣴⣟⣤⡾⠛⠁⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄ ⠀⠀⠀⠀⠀⠀⣸⣷⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢸⠃⠀⠀⠈⠉⠉⠀⠀⢡⠀⠀⢠⣶⢟⠛⠉⠁⣀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢘⣼⡇ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⣩⣿⣿⣿⣿⣦⣄⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠃⢀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣴⣶⣶⣶⡾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣧⣴⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣏⣩⣿⣿⠿⠛⠻⢤⣄⣠⡴⠛⠉⠀⢀⣀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣨⡴⠿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠛⠛⠒⠦⢤⣤⡟⠃⠀⠐⠒⠚⠋⣥⠀⠀⠀⠀⠉⠉⠙⠓⢦⣴⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡾⡿⡄⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣰⡟⣸⢷⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⠏⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⠙⠿⠋⢸⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⢠⠇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢣⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⡀⠀⠘⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢻⣆⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣤⣄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠖⠉⢀⡇⣠⠖⠢⣄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣠⠊⠀⢧⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠉⡆⠀⣀⣉⣽⣦⣤⣽⣆⣀⡎⠉⠉⠙⠻⣿⠟⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠈⡆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢀⡅⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣼⣿⢟⣯⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⡻⣿⣿⣮⡀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⣾⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣮⣿⣿⣿⣦⣤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣳⣿⣿⡿⢻⣿⣿⣿⠋⣿⣿⣿⣽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢸⣿⡿⠁⣰⣿⣿⣿⣿⣿⣿⠏⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⡿⠉⠉⠀⠼⣿⣿⣿⣿⣿⣿⡌⠉⠀⠰⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀ ⣷⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⠇⠀⠀⠀⣠⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⢻⣿⣷⣄⠀⠙⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⣀⢀⣿⣿⣿⣿⣿⣤⣤⣶⡿⠀ ⠈⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠋⠉⠀⠀⣀⣀⣉⡋⠉⠁⠠⣶⣿⣿⠇⠀⠈⢉⣭⣥⣤⡀⠀⠀⠈⠹⣿⣿⣿⣿⣿⡿⣿⣿⠃⠀ ⢶⣼⡿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⢉⣠⣤⣿⣦⠀⠀⠀⠀⡠⣔⡄⢰⣿⣿⣧⡈⢻⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⢀⢴⠒⡞⠳⡌⢳⢸⣿⣿⣿⣷⣾⡇⠀⣠⣾⣿⣿⣿⣽⠛⠛⠉⠁⠀⠀ ⠀⠀⠈⠙⠿⣟⣿⣿⣿⣿⣿⣿⠦⡀⠙⠻⠿⠿⠛⠁⢸⣸⠀⢹⠀⢈⡞⠀⠙⠿⠿⠿⠋⣠⠞⢁⠀⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠴⠿⠿⠿⢿⣽⠟⠛⠁⠀⠈⠒⢤⡀⠀⠀⠀⠀⠉⠓⠚⠓⠊⠀⠀⠀⠀⢀⠴⠊⠀⣠⣾⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⣠⣾⣿⣿⣧⠀⠀⢀⣀⣀⡀⠀⣀⠀⠀ ⠀⠀⣠⢲⠃⣍⣏⠉⣹⣿⣿⣷⣤⣀⠀⠀⠀⠀⣰⠁⠈⠉⠓⠒⠤⠔⠊⣇⠀⠀⣠⣾⣿⣿⣿⣿⠗⠒⢺⠁⠀⠀⢸⠀⠉⡇⠀ ⠀⠀⣇⣸⣀⡟⢼⣀⡁⠘⣿⣿⣿⣿⣿⣶⡴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑⣾⣿⣿⣿⣿⡿⠛⠀⢠⡞⠐⡇⠀⣼⠀⢀⠀⠀ ⢀⡞⠋⢉⣀⣀⣀⣀⡉⣶⣿⣿⣿⣿⣿⣿⣧⠈⠳⢄⠀⠀⠀⠀⠀⠀⢀⡴⠃⣿⣿⣿⣿⣿⣆⠀⢀⣰⠧⠤⠖⠤⠭⣀⡘⠀⠀ ⠈⣠⠊⠁⠀⠀⠀⠀⡏⠀⢻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⠢⣄⣀⡠⠒⠁⠀⣼⣿⣿⣿⣿⣿⡿⣿⡟⠒⠊⠉⠉⠉⠑⠢⣱⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⡇⡰⠋⠹⣿⣿⣳⣿⣿⣿⣦⣄⠀⠀⠀⠁⠀⢀⣤⣾⣿⣿⡽⣿⣿⠟⢦⡈⢇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠙⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣹⠋⠀⠀⠙⢾⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢹⠛⠻⠿⠿⠟⠛⠁⠀⠀⠙⠛⠛⠛⢻⡅⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⡈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣮⣷⣄⡈⠑⣄⠀⠀⠀⠀⠀⠀ ⢀⣤⣀⣀⡀⠀⠀⢀⣀⠤⠤⠒⠒⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡻⢿⣦⡈⢳⡄⠀⠀⠀⠀ ⠸⣷⣤⣀⠈⠉⠉⠁⠀⠐⠀⣀⣤⣀⢀⡞⠲⡀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⣿⣷⣈⣵⠀⠀⠀⠀ ⠀⠘⠿⣏⣛⢿⣷⠦⠤⠿⠿⣿⣽⣿⡟⢦⠀⠘⡄⠀⠀⠀⠀⠀⠀⣿⠾⠟⠋⠙⢧⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠚⢿⣿⣿⠁⠀⠳⡀⢹⠀⢀⣀⣀⣀⣀⣿⡀⠀⠀⢀⠏⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⠀⣠⠗⠊⠉⠀⠀⠀⠀⠀⠉⠙⠲⢶⣋⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⢤⡀⠹⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠉⠳⣄⠀⠀⠀⢠⡞⠁⠀⠀⠀⠈⠢⠈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡤⠤⣄⠘⠆⠀⠰⠋⣠⠖⠒⡖⢦⣀⠀⠀⢸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⣆⡀⢨⣳⡀⠀⠀⢰⣧⠀⠀⣇⣠⣿⣧⠀⢸⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⠻⣷⣶⣿⣇⠀⠀⢹⠻⣿⢿⣿⡿⣻⣹⣤⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣛⠂⠽⣮⠟⠋⠉⠑⠚⠷⠌⠷⢶⣾⢿⣋⠉⢹⣿⠒⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢠⡯⠷⢤⣤⡤⠀⠀⠀⠀⠰⠶⣏⣤⠞⠓⢤⣾⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠬⠷⢯⣙⠢⠄⣀⣤⣤⣤⣤⣤⡤⠔⢊⣁⡤⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷⣾⣿⣭⣴⣶⣶⡿⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣝⣡⣿⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠟⠉⠀⠀⠘⢿⣯⢹⣇⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⣀⡠⠴⠒⢿⠏⠀⠀⠀⠀⠀⣀⡼⠭⠿⣿⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⣿⣿⣏⠀⠀⠀⡼⠉⠙⣷⣄⣤⠔⠉⠀⠀⠀⠀⠈⣇⣀⡤⢼⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⢸⣿⣿⣀⠠⠔⣿⡄⠀⠈⢿⣮⣙⠂⠀⠀⠀⢀⣼⣿⡁⢴⣀⣀⣻⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠓⠿⠛⠛⠒⠚⠛⠛⣆⠀⠈⣿⣿⣷⡦⠴⠞⠛⠋⠉⠉⠉⠁⠀⠀⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⠏⠀⢀⡤⣄⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠋⠉⠉⣿⠀⠀⠀⣿⠀⠀⢸⠀⠀⠈⠳⡀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠛⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠈⡆⠀⠀⠀⢱⡀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⠦⠤⣀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢹⠀⠀⠀⢣⠀⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⢠⠏⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⢷⡆⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⡆⠀⠀⠘⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⡜⠙⢦⡀⠀⠀⠑⢄⠀⠀⠀⠙⢷⡀⠀⠀⣀⣼⣧⣤⣤⠀⠀⢳⠀⠀⠀⢣⠀⠀⠀⡞⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⡇⠀⢳⠀⠀⠙⣄⠀⠀⠈⠳⡀⠀⠀⣈⣿⣿⡟⠋⣽⢁⣿⣿⣶⣿⡈⢇⠀⠀⠘⡆⢀⡾⣷⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀ ⢧⠀⠘⣆⠀⠀⠈⢣⡀⠀⠀⠙⣄⠀⡿⠛⠛⠿⠗⠚⠋⠉⠉⠀⠉⠛⠺⠦⣀⠀⣷⣤⡞⠁⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀ ⠘⡄⠀⠘⢦⠀⠀⠀⠱⣄⠀⠀⠈⢦⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⠉⠉⠋⠉⠙⢲⡄⠀⠀⠀⠀⠀ ⠀⠹⣄⠀⠀⠙⠢⠤⣤⠌⢳⣄⣀⠜⠉⠓⠤⢤⡖⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠑⢄⠐⢦⠒⡾⠒⠒⠢⣄⠀⠀ ⠀⠀⠈⠲⠤⣀⣀⡘⠛⠛⣿⣾⠋⠀⡠⠒⣶⢬⣧⣄⡠⢃⡔⠉⠸⡍⢻⣷⣦⣄⠀⠀⠀⠈⢫⠉⠞⠀⠀⠀⠀⠈⢦⠀ ⠀⠀⠀⠀⠀⠚⠥⠒⣎⣀⢴⠇⠀⢸⠁⠀⢹⣼⣿⣷⣄⢸⠀⠀⠀⠙⢿⠛⠿⠋⠳⢄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⣇ ⠀⠀⠀⠀⠀⠀⡠⠊⠙⢢⡼⠀⠀⡇⠀⠀⠀⠻⣌⠟⠛⢺⡄⠀⠀⠀⠀⠙⠦⠤⠏⠈⡆⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢧⠀⠀⢻⠀⠀⠀⠀⠈⠓⠒⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⢀⣠⡾⠒⠢⡀⠀⡇⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢰⢣⠖⠉⠚⢷⣄⡀⠀⠀⠀⢀⡼⠁⠑⠤⠠⠄⠒⣉⢽⠀⠀⠀⣽⠀⠇⠀⠀⠀⣠⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠑⠦⣄⡤⡇⠸⣀⠀⠀⢠⡇⠈⠑⢒⣒⣭⣤⣒⣒⣒⠒⠢⢤⣿⠊⠑⠒⠋⠁⡸⠀⠀⠉⠛⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⣧⠀⠈⠙⠋⠉⣀⡠⢲⣿⣿⣿⣿⣿⣿⠿⠛⠀⢠⡟⠀⠀⠀⠀⡴⢁⠀⠀⠀⠀⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠯⢧⠀⠀⠀⠀⠻⣆⠀⠉⠉⠉⢻⡁⠀⠀⢀⡠⠞⠀⠀⢀⡠⠊⣑⣾⠓⠦⣀⣀⣀⠜⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠈⠓⠤⣀⣀⣠⣿⡿⠟⠉⠀⠀⣀⣴⣿⡟⠛⠋⠙⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠓⠲⠾⣷⣤⣄⣀⡀⠀⢀⣀⣀⣀⣀⣴⡖⠉⠙⠻⣿⣿⠃⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠛⠳⠦⣤⣭⣿⣿⠋⠉⠀⠉⣿⣿⡄⠀⠀⠀⠈⢿⡦⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢀⣠⡶⠛⣻⡿⠻⢶⣦⣤⣿⠿⠛⠛⢦⡤⠤⠤⣌⣷⠶⢶⡟⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠒⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣤⠀⠀⠀⠀⠀ ⠀⣸⣿⡄⠀⠀⠀⠎⡆⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⣼⡟⠀⠀⠀⠀⠀ ⠀⠐⠽⡿⡢⣤⠄⢊⠇⠀⣀⠀⠀⠠⠤⠤⣣⣥⣚⣻⡵⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠮⡤⣶⣿⠖⠉⠀⠀⠀⠀⠀⠀⠀⠙⢏⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⣤⣴⣶⣦⡄⠀⣴⣾⣿⣿⣷⡄⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⢸⣿⣿⢻⣻⣷⣤⡏⢹⣽⡆⢸⣿⠘⢣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⠁⢸⣏⠀⠈⠉⣹⣿⣷⣄⣀⣠⡾⠟⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⠈⠙⡻⠖⠛⠿⢿⠿⠋⠉⠁⠒⢄⣤⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢳⣶⠎⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⢼⢿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠴⢻⡟⣦⣤⣀⣤⣴⡮⠟⠶⠶⠾⠗⠉⣾⣡⢤⡄⠤⢄⠀⠀ ⠀⢀⢺⡇⠀⢸⣿⣦⡉⠉⠉⠀⠀⠀⠀⠀⢀⣠⣾⡷⢮⣿⣿⡄⠀⢱⠀ ⠪⢻⣌⠀⣠⣿⡿⢻⠟⠛⠒⠶⣟⡿⣏⣩⡟⠉⡉⣹⠙⣞⣿⡇⠀⠀⡃ ⠀⠸⣿⣿⡿⣿⡝⠸⣄⡄⠐⣾⣿⣦⣾⠛⠁⠀⣱⠇⠀⠙⣿⣇⠔⠊⠀ ⠐⠠⠼⠿⠿⠧⠇⠀⠈⢏⠬⡴⠋⠀⠈⠳⠤⠤⠏⠠⠤⠔⠋⠁⠀⠀⠀

⠰⣶⣶⣶⣄⠀⠀⠀⢀⣀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⡀⠀⠀⣿⠿⠷⢾⡏⠉⣿⣄⢀⣿⣷⡆⠀⠀ ⢀⣠⣬⡁⢸⣿⣶⣿⣿⡇⠀⣾⡇⠀⣿⡏⠛⢻⣿⢧⣤⠀ ⢸⣿⡿⡿⢻⠇⠀⢿⣿⡇⣠⣿⡇⣼⡿⠀⠀⣼⡏⢠⣾⠀ ⢸⣿⡀⢀⣿⠀⣴⠈⣿⣿⣿⣿⣿⣿⠃⣾⣤⣿⠀⣼⣿⠀ ⢸⣿⣧⢸⣿⣧⣿⣇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣏⣼⣿⣿⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⢹⣿⣿⣿⣿⣿⠉⠙⣿⣿⣿⣿⣿⡯⠉⢻⣿⣿⣿⣿⠀ ⠀⠸⣿⣿⣿⣧⡀⠀⣠⣿⣿⣿⣿⣄⠀⢀⣼⣿⣿⣿⠇⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣷⣄⣀⣀⣠⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠍⠩⡗⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡔⠁⠀⠀⢸⢸⠀⠀ ⠀⠀⠀⠀⠀⠤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⣦⣰⠀⠀⣼⠆⠀⠀ ⠀⠀⠀⠀⠀⠠⠞⠉⠑⡤⠷⢄⠀⠀⠀⠀⠀⠀⠀⡰⡡⠂⠐⠻⠙⠬⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠀⠀⣀⡈⠎⡆⠀⠀⠀⠀⠀⣰⣱⠁⠀⠀⢀⡇⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠠⡿⢁⡔⡼⠀⠀⠀⢀⣾⣖⣠⠀⠀⠀⡐⡱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠄⠠⢜⣁⡭⠇⠐⠒⠒⣿⣧⣄⠑⠠⠌⡔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⡸⠋⠁⠀⠀⠀⠀⠈⠙⠂⠁⠫⡃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣌⣀⠂⠀⠀⠣⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡘⠀⢰⠟⢉⣉⢳⠂⠐⡴⠛⠛⢛⣄⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣃⠒⣿⡈⢤⡄⡹⠲⠴⡗⠉⠉⢂⡷⠂⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡅⠀⠈⠓⡀⢊⠠⠀⠤⣈⡢⠥⠾⠧⢠⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣠⢁⡄⠁⣇⣀⣀⢀⠌⠈⢂⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⠦⢶⣀⠀⠀⠍⠀⣇⠈⢠⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢫⠪⢎⢜⡢⢼⢽⢭⡯⢼⡾⣿⣿⠔⠒⠒⣖⡂⢤⡀⠀⠀ ⠀⠀⠀⠀⣠⢴⠒⠒⠲⡗⢄⠈⠡⠼⠐⠚⠤⠊⢛⡰⡏⠀⠀⠀⠀⢫⠑⠌⢆⠀ ⠀⡠⡲⢿⢇⣈⠃⡄⠀⡯⠀⢎⠁⠃⠀⠀⠀⠉⢹⠀⠘⡀⠀⠀⠀⠀⡇⢸⢸⠆ ⠸⣱⠁⡜⢦⠁⠈⠌⡶⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣢⢄⣀⡴⠵⣣⠏⢸ ⡆⠣⢦⢊⣈⡵⠂⡜⠀⢀⠔⢩⣀⣀⠤⠓⠤⣀⠤⠅⠀⡶⠏⠔⣈⡗⠈⠀⠀⢸ ⠣⠀⠀⠉⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠉⠒⠀⢃⠀⠀⢀⠆

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⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡟⠉⡉⠻⣿⣷⣮⣿⣿⣿⣿⣿⣿⡿⠿⢷⣦⠀ ⠀⢠⣾⣿⣿⣿⣷⡀⣿⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣧ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢰⣿⣿⣿⣿⣿⣿⣍⠉⠿⠋⠹⠟⠛⢿⡿⢿⣿⠿⢿⡿⠻⠟⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⠁⠀⡿⠀⠘⠁⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣠⡄⠀⠀⠀ ⠀⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀ ⠀⠘⣿⣿⣿⣿⣶⣶⣦⣤⣶⣶⣶⣆⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠈⠁⠂⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀ ⠀⠀⡘⠀⠀⠠⠂⠁⠀⠀⠑⠄⠀⠀⠀⠔⠁⠀⠀⠉⠂⠀⠀⠘⡀⠀ ⠀⠀⠇⢀⣾⠖⠀⡨⠍⠓⠠⡸⠀⠀⠘⡠⠀⠊⠩⡀⠐⢾⣆⠀⡇⠀ ⠀⠠⠀⢸⡏⠀⡜⡄⠀⣹⣷⡈⡇⠀⡏⡀⠀⣿⣷⡈⡄⠈⣿⠀⠠⠀ ⢠⠁⠀⠘⣇⠀⢇⠹⣿⣿⡿⢃⣇⣀⣇⠻⣿⣿⡿⢁⠇⢀⡟⠀⠀⢡ ⢸⠀⠀⠀⠈⠒⢠⠗⠈⠉⠀⠈⠛⡟⠋⠀⠀⠉⠐⢦⠐⠊⠀⠀⠀⢸ ⠀⢣⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢠⠃ ⠀⠸⠈⠒⠠⡼⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⡤⠐⠊⢸⠀ ⠀⠀⠱⡀⠀⠈⠪⢟⡛⢿⡿⠛⠿⡿⠟⠻⢿⠟⢛⠯⠊⠀⠀⡰⠁⠀ ⠀⠀⠀⠈⠐⠄⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⡀⠔⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣭⣷⣶⣤⣼⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡡⢀⣽⠟⠋⡹⠇⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣿⡷⠋⠀⠀⢠⠡⠄⠛⢿⠉⠒⢶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣾⣿⠟⠁⠀⢳⠀⠀⠈⠲⡀⡄⢸⣇⠀⠀⢻⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢠⠞⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠸⠋⠀⡀⠀⠀⠘⠀⣴⣶⠈⠀⠀⣠⣿⠀⠀⢸⡏⣿⣿⣷⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢹⡿⢿⣿⡿⠛⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣤⣤⡊⠀⠀⠀⠀⠀⠀⡠⠀⠀⣠⣦⣥⠀⠀⢸⣷⣧⣦⣿⣿⠿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣴⣧⠈⠱⠀⠈⠛⢦⣰⣦⣹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢉⠝⠛⢿⣶⡄⠀⠀⡠⠊⢀⣤⣾⠟⠁⢹⡄⠀⠈⣿⣿⣿⣿⣿⣾⠋ ⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⢠⡟⠀⠀⢁⠆⠀⠀⣠⠙⠻⣿⣿⣟⢄⠀⠀⠀⠀⠀⠀⠀⡜⡠⠊⠀⠀⠀⠉⢿⣦⣌⣤⣾⠟⠋⠀⠀⠀⢸⠇⠀⠀⠈⠙⢿⣿⣿⠁⠀ ⠀⠀⢀⣠⣶⣿⣿⡏⠀⠀⣼⠃⠐⠀⡅⢠⡄⠀⡇⠀⠀⠈⠛⢿⡄⠱⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⢸⣄⣼⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣛⢻⢸⡇⠀⠀⢹⢓⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠄⠀⠁⠎⠀⠀⠀⡔⠁⠀⠈⢤⣄⠰⠀⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣏⣽⣿⣿⣿⣿⠇⠀⠀⣾⠛⢷⣄⠀⠑⢄⠀⠀⠀⠀⢀⣴⣿⡿⠿⣶⡀⠀⡇⠀⠀⠠⡿⣿⠠⠁⠀⠀⠀⢀⣿⣿⣀⣀⣀⣤⣾⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⣿⠟⠀⠀⢰⡇⠀⠈⠙⢿⣦⣌⠑⠄⢀⣴⡿⠋⠀⠈⢆⠘⡇⠀⠱⡄⠀⠀⠀⠁⡠⡢⠒⠊⠉⠉⠉⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⠛⠋⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠉⠛⢿⡶⠛⡏⠀⠀⠀⠀⠀⠑⠘⢄⠀⠈⠂⠠⢤⣂⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢨⣿⡶⠃⠀⠀⠀⡀⠀⠀⠄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⡁⣾⣯⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠒⠂⠀⠚⠿⠦⠤⢄⡀⢀⠁⠿⠙⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠑⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠉⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⠐⠠⢀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠳⠦⢶⣤⡤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢤⡀⠀⠑⡀⢀ ⠀⠀⠀⠀⠀⠀⠀⣔⠐⠃⠈⠨⡁⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠌⠈⠘⢢⠥⡆ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢡⢸⡠⠤⠤⠤⢄⣀⠀⢀⣮⠂⠀⠀⠀⡸⢠⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢄⣀⠼⠃⠢⠝⢃⣀⠀⠤⡍⠇⠃⠀⠀⠀⠐⢉⠎⠀ ⠀⠀⠀⠀⠀⠐⠶⠔⡾⢁⠠⠑⡄⠫⠀⠐⢁⠤⢒⠦⠁⠀⠆⢀⡀⢈⠔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠩⡡⠊⡀⡈⠀⣱⠔⣈⠭⠉⠶⡀⠰⢊⡡⠔⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⡇⠁⢸⡱⠡⢴⠁⠌⠀⢠⣴⠀⡗⠐⠈⠉⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⣀⢹⡱⡷⢎⣁⠨⠛⣼⡀⠀⢈⣡⠊⠃⠀⠀⣠⠎⠀⠀⠀⠀⠀ ⠀⡠⠏⡩⣭⠑⠒⢩⣷⡧⠤⣤⣶⣾⡯⡏⠉⠁⠈⡀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀ ⠸⠁⣎⡉⡺⢦⣼⠀⢡⢈⢲⠤⡤⠄⠚⠓⠒⠒⠖⠙⠇⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⢙⣿⠄⢼⠳⠒⠽⠂⡾⢷⠇⢎⠊⢉⠕⡲⠊⡌⠙⣷⡿⣍⠻⠀⠀⠀⠀⠀⠀⠀ ⠀⠡⠤⠂⠃⠄⠊⠒⠁⣸⡄⠌⠣⣨⣘⣄⣠⠧⠶⠁⢊⣼⠠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⢾⢿⠘⢌⠂⠔⠁⠀⢇⠀⣠⣷⡓⣿⣎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠴⡟⣓⣩⠄⠓⠎⠉⠐⠒⠒⠚⢿⢮⣤⠬⠼⢴⢳⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⢇⠀⠳⠤⠤⡤⠊⠀⠀⠀⠀⠀⣔⠛⠠⠤⢔⡑⠇⢿⠇⠀⠀⠀⠀⠀ ⠀⠀⣴⣛⣭⣕⣲⣐⢲⠃⠀⠀⠀⠀⡠⠚⢉⢩⠭⠬⠭⠭⣶⠗⠀⠀⠀⠀⠀⠀ ⠀⠮⠈⣈⣀⣉⣉⡈⠏⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣴⣌⠐⣄⠀⠀ ⠠⣖⡒⠂⠐⠂⠌⣉⡀⡱⢄⠀⠀⠀⠀⢹⢯⣷⣜⡆⠀ ⠀⠙⠋⠽⢟⣛⣛⣿⣿⠑⡄⢂⠀⠀⠀⢸⠚⠉⠱⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡸⠚⠈⠉⠉⠉⠒⠤⡑⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠢⡀⠀⠀⡴⠋⠉⠢⡑⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⡔⠒⢌⠀⠈⡔⠈⡐⣠⠀⢱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⡾⡶⣿⣄⡀⡻⡶⠿⣻⣧⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠛⣪⠝⣉⡀⠀⠉⠬⣙⡹⢆⣼⠁ ⠀⠀⠀⠀⠀⠀⠐⠒⠛⠪⠔⣼⣶⠶⣒⣒⣥⠒⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⣿⣻⡇⠀⠆⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⢀⡀⠤⡴⠊⠀⠀⢈⠷⣷⠀⠹⡀⠀⠀ ⠀⠀⠀⠘⡸⣿⡅⢀⣊⠉⢷⡰⠈⠀⠀⢀⡦⠐⠗⣄⠀ ⠀⠀⠀⠀⠐⠛⠛⠒⠛⠢⣀⡿⠷⠤⠖⠛⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠈⣏⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡀⠀⠀⠸⡄⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡸⡇⠀⠀⣰⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⡇⠙⠒⠚⠁⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠓⣶⠒⢶⡶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠟⠛⡻⠟⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⢉⡠⠔⢉⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⣁⠤⠒⣁⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣉⡠⠔⢊⡡⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠠⠔⠚⣉⠤⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠿⠶⠶⠿⠶⠾⠿⢷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⢁⣠⠴⠖⠒⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⢤⣀⠀⠉⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⣠⡿⢁⣴⠋⢀⡠⠖⣖⠓⠲⣄⠹⣆⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⡴⠖⠒⠦⣄⡈⠻⣦⡀⠘⣷⣄⠀⠀ ⠀⠀⣰⠟⣠⣿⠇⢀⡞⠁⠀⣿⣿⣄⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⣾⢱⡏⢀⣾⣿⠀⠈⠳⡄⠸⣿⣄⠈⢿⣆⠀ ⠀⣴⡏⢠⣿⣿⠀⣾⠀⠰⣿⣿⡿⠃⢠⢇⡟⠀⠀⠀⠀⠀⠀⠀⢻⡼⣇⠘⣿⣿⣷⡶⠀⢻⠀⣿⣿⡆⠈⢿⡄ ⢰⣿⠀⢸⣿⣿⣆⠘⢧⣀⣀⣀⣤⠶⣫⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⢦⣀⡉⠉⢀⣠⡟⢀⣿⣿⡧⠀⠸⣧ ⢸⡇⠀⠘⣿⣿⣿⣷⣤⣤⣉⣥⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣬⣉⣉⣉⣁⣴⣾⣿⣿⡇⠀⠀⣿ ⢸⣇⠀⠀⠈⠛⢿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠋⠀⠀⢠⡿ ⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠉⠁⠀⠀⠀⠀⢠⣾⠃ ⠀⠈⠻⣦⣄⣀⣤⣴⠾⠛⠉⢹⡀⠈⠉⠛⠷⣦⣤⣀⣀⣠⣤⡶⡟⠋⠉⠀⠀⡼⠉⠛⠷⢶⣤⣤⣤⡶⠟⠁⠀ ⠀⠀⠀⠀⢹⡍⠁⢿⠀⠀⠀⠈⡇⠀⠀⠀⠀⡇⠈⠉⠉⠁⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠈⡇⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢠⡇⠀⠀⠀⡾⠀⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⣇⠀⠀⠀⢻⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⠀⠀⠀⢰⠇⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⢸⡄⠀⠀⠘⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⣾⠀⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣀⠀⣇⠀⠀⠀⣷⠀⠀⠀⢸⡄⠀⠀⠀⠀⡟⠀⠀⠀⠀⡇⠀⠀⢀⡏⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠳⢾⣤⣄⡀⢻⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁⣀⣠⣼⠶⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠒⠓⠒⠶⠖⠒⠓⠒⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠛⠛⠉⠉⠉⠉⠙⠛⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣰⠦⡤⢲⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⢸⠁⢸⡤⠖⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣾⣿⣿⣿⣷⡄⠀⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⠀⢻⡙⢦⣀⡧⠼⣤⡟⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡷⣴⠋⠀⠀⠈⢳⣤⠾⠥⡄ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠀⠀⠹⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⡇⢻⡴⠶⣄⠀⣸⣀⣠⠶⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⡴⣿⣹⠟⠀⠀⠘⣏⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣏⠻⢿⣻⣶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⢶⣟⣻⠟⢋⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡈⠉⠓⠚⠯⠭⣿⣏⣹⣿⣙⣿⡭⠽⠗⠒⠉⢁⣀⣴⣿⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣶⠤⠤⠤⠤⠤⠤⠤⠤⠴⠦⢴⣶⠾⠟⠛⠋⠉⠉⢳⠀⢀⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢀⡾⠖⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠙⢦⠀⠀⠀⢀⡤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠙⠒⢺⡍⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢈⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡀⠀⠀⠀⠀⠀⣴⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⢷⣀⣀⣠⡴⠊⠁⠀⢀⡾⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠋⠀⠀⠀⠀⠀⡿⠲⣄⣀⡞⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠤⠐⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢀⣞⢉⣫⣀⣀⡀⢙⡆⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣴⠛⢚⣿⣷⣶⡶⠿⣿⡇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠙⣟⣿⠁⢀⣠⡾⡇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣴⠏⠈⢋⡩⢫⣼⠇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡱⠄⠲⠊⣙⣠⣾⠟⠀⠀⠀⢀⣀⡀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣝⡯⠭⣭⡥⠟⡷⣾⠒⠂⠉⠹⠏⢷⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠇⠁⠀⠹⡸⣿⣷⠏⠃⠀⣀⣴⠀⠈⢣ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⢦⠀⠀⠀⠈⢻⠋⠰⡍⠍⠒⣿⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢧⠀⠀⠀⣿⠀⠀⢡⡀⢠⢿⠀⠀⢀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣄⡀⠘⡆⠀⠀⢸⠀⢀⠒⠭⢍⡈⡖⡎⠁ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⣈⡇⡀⢳⣀⠀⠈⣷⣉⠈⠉⠀⣧⡇⣸⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣿⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⡤⠤⣤⣤⣀⡀⠀⠀⢿⣍⡛⠶⣤⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣤⠶⢛⣩⡿⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⣴⠟⡩⠤⠔⠦⠤⢄⣈⠙⠳⣤⠈⠻⣬⡛⠲⠽⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠯⠖⣛⣽⠟⠁⣴⠞⠋⣁⡠⠤⠴⠦⠤⢍⠻⣦⠀ ⣸⢇⡎⠀⠀⠀⠀⠀⠀⠈⠱⡆⣹⠀⠀⠀⣹⣷⢦⣤⣀⡉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⢉⣀⣤⡴⣾⣏⠀⠀⠀⡇⢰⠊⠁⠀⠀⠀⠀⠀⠀⢱⡘⣇ ⢻⡘⡆⠀⠀⠀⠀⠀⠀⠀⢰⢁⣿⢷⣤⣾⠟⠁⠀⠈⠉⠙⠛⠳⠶⠶⠶⠶⠤⠤⠤⠴⠶⠶⠶⠶⠚⠛⠋⠉⠁⠀⠈⠻⣷⣤⡾⣿⡘⡆⠀⠀⠀⠀⠀⠀⠀⢰⢃⡟ ⠘⣧⠙⣄⠀⠀⠀⠀⠀⢠⢃⣼⢃⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡘⣧⡘⡄⠀⠀⠀⠀⠀⣠⠋⣼⠃ ⠀⠘⢷⣌⠳⢄⡀⢀⠔⢡⡾⢣⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡜⢷⡌⠢⡀⢀⡠⠞⣡⡾⠃⠀ ⠀⠀⠀⠙⠷⣤⣉⢁⣴⢿⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⡿⣦⡈⣉⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠋⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠙⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⡄⠀⠀⠀⠀⣰⣿⣿⡿⠿⠛⠛⠛⠛⠛⠿⢿⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠀⠀⣤⣶⣾⣿⣿⣷⣦⡈⠙⢿⡄⠀⠀⢰⡿⠋⢡⣴⣾⣿⣿⣿⣶⣄⠀⠀⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠈⠹⣿⡄⠀⠁⠀⠀⠈⠀⢠⣿⠏⠁⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢿⣿⡗⢲⠒⣶⡒⡖⣿⣧⠀⠀⠀⠀⠀⠀⣾⣿⢲⢒⣖⠒⡖⢺⣿⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣈⠢⠭⢔⣡⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣌⡢⠭⠔⣁⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⠿⠟⠋⢀⣀⣀⣀⣀⣀⣀⡀⠙⠻⠿⢿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠟⠛⢻⣿⡟⠋⠉⠉⣻⣿⣿⣿⣿⣿⣿⡟⠛⠻⠶⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠈⠻⠷⣶⣶⣾⣿⣿⣿⣭⣶⠿⠛⠁⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢹⡻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⠏⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠻⣯⠙⠿⣶⣦⣤⣴⠶⠾⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠷⠶⣶⣶⣶⣶⠿⠋⣽⠏⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⠳⣤⣻⣰⠒⠒⠲⡄⡠⠖⠒⠲⡄⢠⠖⠒⠲⢄⢠⠖⠒⠒⢆⣏⣠⠞⠁⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠈⠙⠛⠶⣤⣤⣷⣧⣀⣀⣀⣇⣼⢀⣀⣀⣼⣾⣤⣴⠶⠛⠋⠁⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠶⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⠶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣽⣯⣿⣟⣻⣿⣿⣿⣿⣿⢿⣻⡋⢉⢹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣤⣿⣿⣅⣀⣠⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢛⠻⣿⠿⠛⢉⡉⠉⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠃⠘⣀⣀⠭⠒⠊⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣭⠽⣿⣿⣿⣷⣎⣍⣹⣀⣨⣤⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠯⣍⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠉⠒⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣯⡀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⢸⣽⣿⣿⣿⠇

⠀⠀⠀⠀⢀⠠⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠊⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⢀⠇⡸⠉⠀⠀⠀⠀⠀⢀⠔⠒⢄⠀ ⠀⢸⠀⣌⡐⠠⠤⠄⣀⠀⡠⢊⠤⠂⠀⠀⠇ ⠀⠠⠂⠛⠁⠀⠀⠀⡐⠉⠲⡯⠛⢃⠀⠀⢸ ⢠⠁⡦⠒⠢⡀⠀⠌⠠⠒⢶⠵⠀⠀⠉⠉⠁ ⢏⠀⡧⢴⣆⣧⠀⠅⣷⣴⣀⡆⡇⢀⣾⡆⠀ ⠘⡀⠑⠛⠒⢉⡹⢏⠕⠓⠚⡣⢃⣾⠏⡰⠀ ⠀⠈⣐⠤⠄⣀⣱⣏⣠⢴⣮⣀⡾⢏⠔⠀⠀ ⡏⠀⡇⠀⡌⠿⠿⣿⢆⡘⣿⣿⠁⠀⠀⠀⠀ ⢛⢠⠐⢉⡇⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⠁⠋⠤⠰⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠰⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⢠⠃⡠⠤⡀⠈⠂⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠔⠊⠉⠀⠀⡇⠀⡇⠀⢣⠀⠈⠆⠀⠈⠄⠀⠀⠀ ⠠⠒⠒⢄⠀⠀⠻⣄⠀⠀⠀⢸⠁⠀⢰⠀⠈⡄⠀⠘⡀⠀⠸⠀⠀⠀ ⠃⡖⠢⡀⠀⢄⠀⠘⢧⣀⣀⣼⢤⡄⡀⡆⠀⢡⠀⢠⠀⠀⢠⠀⠀⠀ ⡀⢣⠀⠑⠄⠀⠑⡀⡶⠿⠧⠼⠚⠋⠻⠼⣀⠈⣔⡝⠁⢀⠂⠀⠀⠀ ⢡⠀⠡⢀⠈⠢⡀⢐⠧⣀⢀⠀⠀⠀⠀⠀⠀⠉⠋⠉⢉⣉⢐⣀⡀⠀ ⠀⠑⠤⡀⠜⠓⢿⠃⡠⢲⢼⡄⠄⠔⠹⣱⣶⣄⠀⠀⢃⠑⠁⠀⠈⢆ ⠀⠀⠈⢉⠝⢆⠇⢰⠀⠈⢟⠿⢾⡀⠀⠙⠭⠁⠑⡀⠀⡄⠀⠀⠀⠈ ⠀⠀⠀⠃⠀⠀⡆⠈⠄⠀⠀⠉⠉⢣⠀⠀⠀⠀⢠⣃⠀⠃⠀⠀⠀⢠ ⠀⠀⠀⢄⠀⠀⢥⠒⠚⢦⣀⠀⢀⠌⠑⠤⠐⢪⣇⢀⡕⡀⢀⡀⠔⠁ ⠀⠀⠀⠀⡕⠈⡈⠂⠄⠋⡠⣴⣿⣷⣶⠦⠉⡿⠀⠀⡠⡁⠀⠈⠢⠀ ⠀⠀⠀⠀⠉⠘⠒⢄⠀⠘⠆⡈⠉⢡⣀⡤⠚⠀⣠⡮⠥⣮⠂⠠⠘⠀ ⠀⠀⠀⠀⠀⣴⠖⠒⣱⠦⢤⣀⣉⡉⢁⣤⠒⠛⢿⡖⠀⢸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡀⠀⢀⣩⠷⡾⢧⣀⣼⠿⠦⣀⠀⣹⡤⡼⠀⠀⠀⠀

⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠆ ⠀⠀⠀⠇⢆⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⡠⢺⠈ ⠀⠀⢸⠀⠀⠣⡀⠀⠑⢄⠀⠀⠀⢀⢼⠀⠀⢠⡊⠁⠀⢀⠄⠀⡈⠀ ⠀⠀⠸⠀⡄⠀⢸⡦⡀⠀⠑⣀⡔⢁⠖⠈⠉⠉⠊⠴⣤⣹⡀⠀⠇⡆ ⠀⠀⠀⠆⢰⠀⡌⠣⢱⠀⠀⢹⠐⠁⠀⠀⠀⠀⠀⣀⠠⠖⣅⠜⢀⠃ ⠀⠀⠀⠐⠄⠲⣧⠀⠋⠀⣠⣋⠀⠀⠀⠀⠀⡀⡀⠉⢆⡘⢅⠠⠊⠀ ⠀⠀⠀⠀⠰⠖⠈⡠⣤⣾⣧⣤⣬⣦⡀⠀⣸⡯⠉⢻⡷⡏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⡇⡇⣿⣿⢻⣿⡧⠠⣿⢷⠀⢈⣦⡦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣋⡜⠝⡿⠿⣿⠿⠃⠀⠉⠘⣢⣾⣨⠗⡂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡈⠻⣅⡀⠘⠲⢤⣄⣀⣀⣹⣽⣫⠔⠁⠀⠀⠀ ⠀⠀⢀⠒⣴⠁⡆⠀⠈⠉⢉⣿⣿⡍⠑⠒⠙⠛⠉⡉⡁⢀⣠⣆⠀⠀ ⢸⠁⢌⡶⢻⡉⣇⠀⠀⠀⣤⣿⡟⠁⠀⢀⡀⡀⠀⣿⣯⣁⠘⢿⡆⠀ ⠀⠙⢉⣱⡚⠭⠛⠂⣰⠉⣿⣿⠏⠀⢠⡿⠋⢱⡄⣿⠧⠌⣣⣼⣿⠀ ⠀⠀⠀⠡⡀⠀⠀⠈⡨⠋⠙⣣⣵⣶⣿⣇⣃⣤⠗⠘⣿⣾⣛⣻⣿⡇ ⠀⠀⠀⠀⠈⠢⣶⣾⣦⢸⣟⡛⠉⣻⣿⣹⣿⠏⠀⠀⠹⣿⣿⣟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠉⠀⠈⠉⠉⠉⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠙⠛⠓⠲⠶⠦⠤⢴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢾⣟⠓⠶⣄⠀⢀⣿⠷⠾⢶⣤⣤⣤⣤⣤⣤⣀⣰⣇⣀⡀⣀⡤⠶⠒⠲⢦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡟⠻⢭⣑⣂⣈⣧⣸⣿⣾⣿⠿⠿⠿⣭⡉⠉⠙⠻⢿⣭⣿⣿⠋⢀⠴⠒⠒⣦⡌⢷⡄ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⡏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠈⠻⠃⠰⠃⠀⠀⣾⠉⠉⣹⡷ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⢃⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣆⠀⠀⠀⠀⢇⠀⠀⠀⠙⠛⣻⢿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠈⠳⣄⣀⣀⡴⣻⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠁⢀⣀⠀⠀⢀⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠹⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀ ⠀⠀⠀⠀⠀⢀⡾⠇⢀⡞⠀⠈⠙⠒⢾⡇⠤⢀⣼⠟⣆⠀⠀⠀⠒⠀⠀⣀⠙⢦⣿⡀⠀⠀⠀⠀⠀⠰⣶⠒⠞⠃ ⠀⠀⠀⠀⣠⡾⠁⠀⡾⠀⠀⢀⢐⡴⠛⡇⠀⠀⢸⠀⠘⢷⣄⣤⠴⠒⠉⠁⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀ ⠀⣀⣤⡾⠿⠟⠀⢸⡇⠀⠠⣽⠟⠀⠀⢹⣆⢸⣿⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢈⣧⠀⠀ ⠘⢿⣷⣅⡀⠀⠀⣾⠀⠀⣾⠃⠀⠀⠀⠀⠻⣿⣿⠀⠀⢀⣀⡀⠀⠀⠉⢻⣷⣶⣤⣤⣿⡆⠀⠀⠀⠀⠀⢻⡄⠀ ⠀⠀⠉⠻⣯⣠⣤⣿⠀⣸⣿⠀⢀⣰⣿⡷⠀⠈⢻⠀⠀⢿⡿⡇⠠⠤⠀⢸⠿⠿⣿⣿⠟⣿⠀⠀⠀⠀⠀⢸⣧⠀ ⠀⠀⠀⠀⠀⣨⠏⢹⣶⣿⣿⠃⠀⠉⢫⡀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⡟⣀⣴⠟⣱⣿⠃⠀⠀⠀⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⢠⣯⣴⣿⣿⣿⣿⡀⠀⠀⠀⡇⠀⠈⠲⠞⠁⠸⠀⠀⣠⣴⠿⠛⠋⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡷ ⠀⠀⠀⠀⠈⠉⠉⠉⣉⣿⣿⣿⣦⣀⡘⠁⠀⠀⠀⠀⠀⠀⠡⠀⣁⣠⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⢿⡿⢿⣷⣶⣶⡶⠶⠶⣶⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣺⡶⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⠿⢍⣈⣙⡶⠚⠁⠠⠤⢖⠒⠒⠒⠒⠲⠤⣄⣠⠤⠖⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣠⣿⡅⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣼⣣⠟⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⡼⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⡀⠰⠃⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⣷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢹⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⣁⣈⣉⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣲⡒⢤⠀⡶⣚⣠⣤⣤⣤⣤⣭⣄⣠⠔⠒⠢⣄⠀ ⠀⠀⠀⠀⢀⠊⢣⠉⠚⠒⠓⠛⠋⠉⠉⠒⢄⠈⠑⠿⠡⠊⢡⠛⢺⡆ ⠀⠀⠀⠀⠀⢢⡴⠃⠀⠀⡄⠀⠀⠀⠀⠀⠘⢣⠀⠀⠣⡀⠈⢉⡿⠁ ⠀⠀⠀⠀⢠⠏⡡⣀⠀⡼⠀⢀⡀⠀⠀⠀⠀⢄⢧⠀⠀⠈⠉⠑⠣⡀ ⠀⠀⠀⣰⠋⡸⠁⠀⡨⢇⠁⢸⠑⢄⣀⠤⠒⠈⢻⡄⠀⠀⠀⣻⠉⠀ ⠠⣴⡞⠋⢀⡇⢠⠟⠀⠘⣤⡏⠀⠀⠙⠒⢤⣀⣀⠹⡀⠀⠀⠸⡆⠀ ⠀⠈⠻⢦⣼⣀⣾⠀⣰⡶⠈⠳⠀⠾⡇⠠⢀⡿⢿⣟⡳⠀⠀⠀⢷⠀ ⠀⠀⠀⣰⣥⣿⣿⠀⠀⠠⠀⠤⠔⠈⠀⣠⠾⠖⣩⠟⠁⠀⠀⠀⠈⡆ ⠀⠀⠀⠉⠀⣽⣿⣷⣦⣅⣀⣀⣀⣀⣨⠤⠒⠉⠀⠀⠀⠀⣀⡠⠚⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠿⠭⣱⠖⠩⠄⡒⠒⠒⠠⢤⡤⠒⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⡰⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠈⢸⠀⠀⠀⠘⠀⠀⠜⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⠀⢸⠀⠀⠀⠀⡀⠊⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠁⢱⡀⠀⢸⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡂⠰⠢⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠤⢔⡕⢱⠋⣴⣦⠂⢈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣔⠉⠉⢇⢸⡄⠿⡏⢳⣿⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⣙⣀⡼⠋⠁⢻⡵⠋⠙⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⡘⣀⠤⢤⣀⡀⠀⢠⣞⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢀⣄⣷⣿⣿⣷⣑⡀⢠⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⢳⢦⠈⠛⢛⠧⡫⠊⠙⣍⢙⢶⡀⡠⢤⠀⠀⠀⠀⠀⢀⣾⣿ ⠀⠀⠀⠀⠀⢻⣘⢣⡀⠀⠹⡤⢀⣠⡼⢻⣧⡏⡳⠀⡆⠀⠀⠀⣠⣿⣿⠏ ⠀⢰⣖⡠⠄⣁⠪⠼⠈⠐⢢⠽⢶⣾⡇⣸⠞⠊⠀⠀⡇⠀⢄⣼⣿⠻⠏⠀ ⠀⠸⡌⢿⡢⡀⠉⠢⣀⡠⠊⠒⠐⠃⠀⣹⢶⡀⠀⢨⠃⢠⠿⣯⡹⠿⡁⠀ ⠀⠀⢣⠈⡿⣾⠦⠀⠙⡇⠒⠠⠤⢀⣈⣈⡆⠑⢤⠮⣰⣿⣿⡤⣻⠒⠇⠀ ⠀⠀⠀⡛⠀⠀⢣⠀⡸⠁⠀⠀⠀⠀⠀⠀⠢⡀⢀⣿⣿⣿⠏⠧⣄⠼⠀⠀ ⠀⠀⡰⠀⠀⢀⠀⡝⠐⢄⠀⠀⠀⢀⣀⢤⣤⣼⣿⣿⡿⢃⣀⡤⢮⣤⠀⠀ ⠀⡐⠁⠿⢀⠊⠌⠘⢄⠀⠑⠤⣴⣫⡋⣃⣿⣿⣿⣿⣿⡀⡙⢿⣶⠋⠀⠀ ⢰⣤⣀⠀⢂⠌⠀⠀⠈⠢⣀⣾⡝⢯⣱⣿⣿⣿⡟⠘⣗⣳⣸⡞⠁⠀⠀⠀

⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿ ⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿ ⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⣶⣿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⣻⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡳⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡆⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣯⣽⣟⣲⠶⢤⣤⣀⣀⣀⠀⢉⣿⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣴⣾⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⡏⢻⣍⣻⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠛⠻⠿⢿⣿⣿⣿⣿⣄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣬⣙⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠈⣧⣀⠀⠉⠉⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠷⠾⠋⠉⠛⠓⠶⢤⣾⠋⠙⠛⢻⡿⠋⠉⠉⠛⠛⠛⠀⠀⠈⠛⠿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡃⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠙⠿⣿⡿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣷⣤⡄⠻⣿⣿⠗⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⣿⣿⣿⣿⣿⣷⣦⣴⣤⣤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡟⠙⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⣠⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣴⣿⣿⣿⣷⣄⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣇ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣹⣿⣿⡿ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⠃ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⡿⠁⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢿⣿⣷⣤⠆ ⠀⠀⠉⠉⠉⠉⢻⣿⣿⣯⠀⠀⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⣀⣤⠒⢲⠀⠀⠀⠀⢰⢠⣿⢹⠶⠀⠀⠀ ⢀⠞⢁⣾⣴⣏⡠⡆⡷⢶⡯⣤⣖⣕⡖⢠⠀⠀ ⠈⠒⣀⣇⠤⢺⠟⠧⠇⠿⠚⠙⠊⠛⠒⠁⠀⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⠞⠛⠛⠶⠶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠛⠛⠛⠛⠷⢶⣦⣄⡀⠀⠙⣷⡀⠀⠀⠀⠀⢨⡟⠀⠀⠀⢀⣀⣤⣤⡴⠶⠶⠶⢶⣤⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡘⢿⡄⠀⠀⠀⢸⡇⢀⣤⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⡄⠀ ⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣿⡄⠀⠀⣾⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠘⢿⣷⠀⣼⠟⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠘⣷⣄⣀⣀⣀⣤⣴⠶⠾⠛⠛⠋⠉⠉⠉⠉⠛⠛⠷⣦⣄⠈⢿⣴⠏⢀⣠⣴⠾⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠶⢶⣤⣤⣴⠟ ⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣷⣾⣿⣶⣿⣭⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⠀⠀⠰⠿⠿⠿⠟⠛⠿⠿⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠿⠛⠛⠿⠿⠿⠷⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠈⠙⠛⠃⠀⠀⣀⡀⠀⠛⠛⠉⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀ ⠀⢀⣿⠃⠁⠀⠀⠀⠀⡠⠚⣩⠖⠋⠉⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⠉⠓⢯⡙⢦⡀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀ ⠀⣸⡇⠀⠀⠀⠀⢀⠞⠀⡼⠁⠀⢀⣀⣀⣀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣀⣀⣀⠀⠀⠹⡀⠙⢆⠀⠀⠀⠀⠈⣿⡀⠀⠀ ⢀⣿⠀⠀⠀⠀⠀⢸⠀⢀⡗⣊⣉⣥⣤⣤⣄⣉⣙⣺⡀⠀⠀⠀⠀⠀⠀⠀⣾⣚⣉⣁⣠⣤⣤⣍⣉⡒⡇⠀⢸⠀⠀⠀⠀⠀⢸⣇⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⡟⠋⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠛⣿⣿⣷⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠈⢇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⠏⠀⠀⠀⠀⠀⠀⣿⠆⠀ ⢹⡇⠀⠀⠀⠀⣀⣤⣤⣙⠚⠻⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠛⢚⣡⣤⣀⡀⠀⠀⠀⠀⣿⠀⠀ ⢸⡇⠀⠀⣠⠞⠁⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠉⢦⠀⠀⠀⣿⠀⠀ ⠈⣿⡀⢠⠇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⣇⠀⣸⡏⠀⠀ ⠀⠸⣧⢸⡄⠀⠀⠀⠀⠀⢠⠇⣴⣤⣤⣤⣤⣤⡤⠶⠶⠞⠛⠛⠛⠛⠻⠶⠶⣶⣤⣤⣤⣤⣤⣴⡌⣧⠀⠀⠀⠀⠀⠀⡼⢠⡿⠀⠀⠀ ⠀⠀⠻⣧⢳⡀⠀⠀⢀⡠⠋⠀⢿⣿⣿⣿⣏⣿⢹⣷⠒⣶⠖⢶⡶⠶⢶⡖⢲⡟⢹⣏⣿⣿⣿⣿⠁⠈⠧⣀⠀⠀⢀⣼⢣⡿⠁⠀⠀⠀ ⠀⠀⠀⠙⣷⡍⠉⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣿⣦⣼⣷⣤⣾⣿⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠉⠉⠉⣴⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀⠀⠀⠈⠳⣿⣏⢹⣿⡏⢻⡟⢹⣿⠉⣿⣟⢹⣿⠷⠋⠀⠀⠀⠀⠀⢀⣤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠛⠚⠛⠓⠛⠛⠉⠁⠀⠀⠀⢀⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠛⠷⢶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⠾⠟⢛⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠰⢿⣿⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣿⡿⠆ ⠀⠀⢻⣿⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⣿⡟⠀⠀ ⠀⠀⠠⣻⡆⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⢰⣟⠄⠀⠀ ⠀⠀⠀⢼⣷⠀⠀⠀⠀⠀⠙⠛⠶⣶⣶⣶⣶⠶⠛⠋⠀⠀⠀⠀⠀⣾⡧⠀⠀⠀ ⠀⠀⢀⣾⠃⢳⣧⡀⠀⠠⡀⢀⠀⠀⠉⠉⠀⠀⡀⢀⠄⠀⢀⣼⡞⠘⣷⡀⠀⠀ ⠀⠀⡾⠃⠀⠲⡾⢿⣓⣢⡀⠻⢷⣄⡀⢀⣠⡾⠟⢀⣔⣚⡿⢷⠖⠀⠘⢷⠀⠀ ⠀⢠⠃⣰⠁⠀⠐⣿⢫⣿⣿⣆⠀⢈⡻⢟⣉⠀⣰⣿⣿⡝⣿⠂⠀⠈⣆⠘⡄⠀ ⠀⠀⠀⣽⠀⠀⠀⠘⣄⠙⣋⣼⠆⠈⢛⡛⠁⠰⣧⣙⠋⣠⠃⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣾⢱⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀ ⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⢀⡀⠀⠀⢿⡸⠀⠀⢀⡀⠀⠀⠀⢀⣰⠟⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⠉⠛⢦⡀⠸⠇⢀⡴⠛⠉⠀⠀⠐⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣠⡤⢤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠸⠀⠉⠓⢶⣄⠈⠻⣄⠀⠀ ⠀⠀⠀⢀⣴⣋⠀⠉⠳⢤⡀⠀⠀⠀⠀⣸⢃⣿⡄⢣⠀⠀⠀⠀⠀⠀⠈⢷⡀ ⠀⢀⣠⠟⠋⠁⠀⠀⠀⠀⠙⢧⠀⠀⢀⡇⣾⣿⣿⣦⡤⣀⡀⠀⠀⠀⠀⠀⣧ ⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⠃⣸⣿⣿⣿⣿⡾⢽⡲⢄⠀⠀⠀⣿ ⠈⣷⠲⣭⣥⣐⠦⣀⠀⠀⠀⠀⠘⡆⢸⡀⣇⠹⣿⣿⡟⠁⠀⠉⠳⣆⠀⠀⣿ ⠀⠙⢷⣿⢻⣿⣿⣾⣧⣄⠀⠀⠀⡏⡍⠉⠉⠙⢻⣿⡀⠀⠀⠀⠀⠘⢦⣴⠇ ⠀⠀⠀⠈⠻⠶⣿⣿⣿⣿⣷⣶⣤⠇⡇⠀⠀⠀⡴⢿⡿⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠟⠙⠿⣿⣿⣿⣿⠄⢿⠀⠀⠀⠉⠛⢻⣬⣧⣀⡶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⢀⡀⠘⣯⠉⠁⠀⠈⢧⠀⠀⠀⢠⡿⣻⣿⣯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⣏⣀⡀⢹⣶⡽⠟⠻⣶⣄⡈⢳⣄⠀⣾⡷⠿⣿⡿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⠀⠉⢻⡏⢀⣠⡼⣿⣿⣷⡀⠙⢦⣹⣷⣾⢿⣠⢷⠲⢦⡀⠀ ⠀⠀⠀⠀⠀⢻⡀⠀⠈⢿⣾⡿⣦⣾⣿⣿⣇⠀⠀⠈⣿⠗⠭⢒⣷⡀⠈⠉⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠛⠛⣻⠟⢛⠭⣄⣀⡤⢤⡼⣤⡾⠋⠀⠻⠶⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⣩⠷⣶⣤⣴⣇⣰⡏⣀⣈⣙⣤⣾⢹⡍⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⡀⠀⡰⠋⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⡟⠙⠛⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣧⡼⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⢠⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠛⠁⠀⢧⣠⣴⣟⠨⣿⣿⣿⣿⣿⣿⣿⡇⠈⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣻⠀⠀⠀⣸⣿⣧⠏⠀⠛⠛⠛⣿⡿⠻⠿⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠳⣶⣿⣿⠃⠀⠠⣄⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⣿⣿⣿⡇⠀⠀⢈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⢸⣿⣿⣷⠶⠛⠉⠘⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣸⣿⣿⣿⠀⠀⠀⠀⢹⡿⠿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣷⢿⣿⣿⡀⠀⠀⠀⠈⣷⣴⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⡟⠘⣧⠖⠋⣏⠑⠛⣯⣿⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣶⣦⡀ ⠀⣤⡀⢀⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠈⢩⣿⣿⣿⣿⣿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⣿⡋⠀ ⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀ ⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣤⡄⠀⠈⠻⣷ ⠀⢿⣿⣿⣿⣿⣿⠀⢴⣾⠿⢿⠿⠿⣿⠏⠀⠸⣿⡿⠿⢿⡟ ⠀⠘⣿⡿⠿⢿⣏⠀⠀⠻⢷⣤⣤⡾⠟⠀⠀⠀⢻⣷⠶⢿⡇ ⠀⢰⣿⠀⣤⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄⢸⡇ ⠀⠀⢿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣶⠾⠛⠀⠘⣿ ⠀⠀⠀⢸⣯⠀⠀⠀⠀⣾⠛⢿⡷⣶⣤⣤⣤⣤⣤⣤⣶⠾⠋ ⠀⠀⠀⠘⣿⠀⠀⠀⠀⠻⢷⣾⣇⣀⣿⡇⠈⣿⣇⣸⣇⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⢛⣿⠇⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀ ⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣆⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠛⠛⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⣼⡿⠁⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠛⢁⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡙⠛⠀ ⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣄⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡷

⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥⬛⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥⬛⬜⬛⬛⬛⬜⬛🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥⬛⬛🏻🏻🏻⬛🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥⬛🏻🏻🏻⬛🟥🟥🏻⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥⬛🏻🏻⬛🟥🟥🟫🏻🏻⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥🟥🏻⬛🟥🟥🟫🏻🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥🟥⬛🟥🟥🟫🏻🟫🟫🟫🏻🏻⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟥🟥🟥🟫🟥🟥🟥🟥🟫🏻🏻🏻⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟥🟥🟥🟥🟦🟨🟥🟫🏻🏻🏻🏻🏻⬛⬜⬜⬜ ⬜⬜⬜⬜⬛🟫🟥🟥🟨⬛🟨🟥🟥🟫🏻🏻🏻🏻🏻⬛⬜⬜ ⬜⬛⬛⬛🟫⬛🟥🟥🟥🟨🟫🏽🏻🏻⬛🏽🏻🏻⬛🏻⬛⬜ ⬛⬛⬛🏽🏽🟫⬛🟥⬛⬛🏻🏻🏻🟫🟥⬛🏽🏻🏻⬛⬛⬜ ⬛⬛⬛⬛⬛⬛⬜⬛⬛🏻🏻🏻🏻🟫🟥🟥🟥⬛🏻🏻⬛⬜ ⬛🏽⬛⬛⬜⬜⬜⬛🏻🟨🟥🏻🏻🏻🟫🟥🟥🟥⬛⬛⬜⬜ ⬜⬛⬛⬜⬜⬜⬛🏻🟥🟨🟥🏻🏻🏻⬛⬛🏽⬛🏽⬛⬛⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟥🟥🟥🟥🏻🟥🏻🟫⬛🏽⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬛🟫🟫🟫🟥🟥🟥🟥🟥🟥🟥⬛⬛⬛⬛⬛⬛ ⬜⬜⬜⬜⬜⬛🟫🟫🟥🟫⬛🟫🟥🟥🟥🟥⬛⬛⬛⬛🏽⬛ ⬜⬜⬜⬜⬛🟥🟨🟥🟥⬛🏻⬛🟫🟥🟥🟥🟥⬛⬜⬛⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟥⬛⬛⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬛⬜⬛🟥🟥🟨🟥🟨⬛⬜⬜⬜ ⬜⬜⬜⬛⬛🟨⬛🟨⬛⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬜⬛⬛⬜⬛⬛⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟨⬛🟨⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬛⬛⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⢄⡀⠀⠀⢀⣀⣀⣤⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⢀⡏⠉⠉⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⡾⠁⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠈⢧⡀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢸⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣴⠂⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢸⣄⣴⠗⠒⠒⠒⠓⠒⠒⠲⢤⣄⡀⠀⣠⡞⠁⣠⠶⠋⣹⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⠀⢸⣆⡀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠿⠻⢯⣠⡞⠑⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⣠⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠀⠀⠀⢙⣿⠟⠋⠀⠀⢳⣄⠀⠀⠀⠀⢀⣇⡄ ⠀⠀⣰⠏⢺⡄⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⢠⡄⠈⢀⣠⣄⡀⢀⡽⡆⠀⠀⠀⠀⠉⠓⠦⠤⠴⠛⠉⠀ ⠀⢀⡏⠀⢿⣷⠞⠁⠘⡏⢷⡄⠀⠀⠀⠀⡶⠀⢠⠟⠀⠘⡟⢯⠤⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠀⠀⢀⡇⠀⠀⢸⡇⠀⣿⡆⠀⠀⠰⡆⠀⣏⠀⠀⢠⡇⠘⣆⠀⣷⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀ ⢐⣿⠀⠀⢸⡷⢤⣼⣿⣿⠀⣿⢳⠀⠀⢰⠆⢰⣿⣷⣶⡟⠀⢐⣿⠀⢸⠀⠀⠀⢠⣿⣾⣧⠀⠀⠀⠀ ⠀⢿⠀⠀⢸⣧⠀⣠⣿⠟⠻⡟⣸⠆⣠⣤⣤⣸⣯⢹⣿⠟⠻⣾⢸⠀⢸⠀⠀⢠⣟⣽⣿⠛⡆⠀⠀⠀ ⠀⠘⣆⠀⠀⠙⠓⠷⠿⠤⠞⠋⠁⠀⠸⣿⡁⠀⣹⠛⠿⠦⠾⠷⠛⢀⡾⠀⢠⡟⣽⣿⠃⠀⡇⠀⠀⠀ ⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠐⠲⣖⠚⠋⣹⡗⠁⠀⠀⠀⠀⢀⣠⠞⠀⢠⣿⣿⡿⠁⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠈⠙⠶⢤⣀⠀⠀⠀⠀⠀⠙⢲⣾⡋⠀⠀⠀⣀⣤⣶⣏⠀⠀⣠⣿⣿⡟⠁⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⡤⠴⠞⠛⠉⠳⢆⣠⣴⣾⣿⣷⠶⠿⠿⠗⢺⣿⡿⣷⣴⣿⡏⠙⠦⠼⠁⠀⠀⠀⠀⠀⠀ ⢰⠟⠉⠁⠀⡇⠀⠀⠀⠀⢸⣿⣿⣾⣿⣯⢻⣷⡀⠀⠀⢸⣿⣷⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡆⠀⠀⠀⡇⠀⠀⢀⡞⠀⠻⢿⡿⠃⣿⣛⡿⣧⣀⣀⠘⣿⣷⣿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣷⡄⠀⠀⢹⣀⡴⠛⣷⡆⠀⠀⠀⠀⠀⢸⢀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣇⠙⢶⡶⠚⠉⠀⢠⡿⠁⠀⠀⠀⠀⠀⡼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠷⢾⠻⢦⣀⣠⠾⠁⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠀⠀⠈⠓⠤⢤⠤⠤⠶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠒⠒⠒⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡠⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢣⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠖⢁⡌⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠠⢄⣀⠄⠀⠀⠀⠑⠒⠒⠁⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠚⠁⠀⠀⠀⡇⠀⡠⠀⠀⠀⢀⠈⠢⣀⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡃⡀⠌⣐⠒⠒⢊⣴⠞⠒⠚⠂⢴⡣⠂⠀⠈⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⠲⡖⠉⠈⡙⢀⢰⠁⠐⡆⡄⠀⠀⠑⡀⠀⠀⠀⠣⡀⠀⠀⠀⠀ ⠀⠀⢠⠇⠠⡁⠀⢸⣿⢦⢹⡀⡏⣷⢸⠀⠀⠀⢡⠀⢸⡇⠀⠀⠑⢄⠀⠀ ⠀⢀⠃⡾⠀⢣⠀⠘⢼⣿⢸⢣⠐⢌⡿⠀⠀⢠⠋⠀⡆⠘⢄⠀⠀⠀⠑⢄ ⢀⠆⢠⡑⠁⠙⡧⢀⠀⢀⠜⠀⠁⠤⢤⠤⠾⠤⡀⠸⠀⠸⠀⣨⠐⠂⠠⠄ ⠘⠀⢸⠑⠤⢠⣃⣀⣀⣤⣤⠖⢄⠀⡆⠀⠀⢀⠇⢘⡀⠀⠃⠈⢆⠀⢸⠀ ⢠⠀⠀⠣⡐⠀⠈⠙⠻⡉⠀⣀⣀⢆⠈⠒⠒⣉⠴⠁⠱⡀⠀⠀⠀⠀⠁⠀ ⠈⢆⠀⠀⠈⠓⠊⠭⡅⠀⠀⠀⠤⠤⣥⠶⠛⠁⣀⣣⢀⢀⡦⠂⠉⠱⡄⠀ ⠀⠀⠑⠤⠀⣀⠠⠔⠁⢠⠒⠒⠒⠒⠂⠵⣴⠁⠀⠈⣿⣭⠖⠊⠉⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠉⢉⡔⠋⡹⠒⠐⠊⠑⠢⠭⣉⣀⣀⡜⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠀⠒⠒⠒⠒⠒⠲⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⡠⠤⠄⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠠⠤⣄⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⢠⡇⠀⠀⢠⣯⣤⠤⠤⠤⠔⢒⣲⣤⠤⠤⢽⡀⠀⠀⠀⢠⡧⠤⢤⣤⣔⠒⠢⠤⠤⠤⣤⣵⡄⠀⠀⢸⠀⠀⠀ ⠀⠀⢸⠀⠀⢠⣿⡿⠁⠀⢀⡴⠊⠁⣀⡀⠉⠓⢤⡇⠀⠀⠀⣞⡴⠊⠉⣀⣀⠉⠑⢦⡀⠀⠘⣿⣿⡄⠀⠸⡆⠀⠀ ⠀⠀⡼⠀⠀⣿⣿⠁⠀⢠⠟⡀⠀⠀⠘⣿⣷⣦⠀⢻⠀⠀⠀⡟⡆⠀⠀⠈⣿⣿⣦⡀⢱⡀⠀⠸⣿⣇⠀⠀⢇⠀⠀ ⠀⡼⠀⠀⠀⣿⣿⠀⠀⢺⠀⢷⣤⣤⣾⣿⣿⣿⡆⢸⠀⠀⢸⡁⢹⣤⣤⣾⣿⣿⣿⡇⠀⡇⠀⠀⣿⡟⠀⠀⠈⢆⠀ ⢸⠁⠀⠀⠀⠘⣿⡄⠀⠘⡄⠘⢿⣿⣿⣿⣿⠟⠀⣼⢀⣀⡀⣇⠈⢿⣿⣿⣿⣿⡿⠃⣰⠁⠀⢰⣿⠃⠀⠀⠀⢘⡄ ⠈⠀⠀⠀⠀⠀⠘⠳⢄⣀⣘⣦⡠⠿⠛⠋⠉⠉⠙⠿⣿⣿⣿⠿⠋⠉⠉⠙⠛⠯⣠⣴⣁⣀⡠⠟⠁⠀⠀⠀⠀⠀⡇ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠳⡀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢠⠏⠀ ⠀⠀⡟⠦⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⣀⠔⢳⠀⠀ ⠀⠀⢇⠀⠀⠉⠑⠲⡲⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢲⠖⠊⠉⠀⠀⡼⠀⠀ ⠀⠀⠈⢧⡀⠀⠀⠀⠙⢦⣹⣿⠿⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠶⠿⣿⣋⠔⠁⠀⠀⠀⢀⡜⠁⠀⠀ ⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠑⠢⠤⢌⣿⣋⣁⣀⣈⣙⣿⣋⣁⣀⣉⣻⣟⣁⠤⠔⠋⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠋⠉⠙⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠚⠋⠉⠉⠉⠙⠒⢦⣄⠳⡄⠀⠀⡾⢀⣠⠴⠒⠚⠛⠛⠒⠲⢤⣄⠀ ⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⢠⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⠀⠸⣄⣀⣀⡤⠤⠖⠒⠒⠒⠒⠲⢤⡈⣧⠎⣀⡤⠖⠚⠛⠛⠛⠒⠒⠦⠤⠤⠼ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠛⠛⠛⠛⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⣰⠋⠀⠀⠴⠶⠶⠶⢶⣤⡀⠀⠀⠀⢀⣤⣶⠶⠶⠶⢦⠄⠀⠙⣆⠀⠀⠀ ⠀⣰⠃⠀⠀⠀⡠⣤⠤⠤⢄⠈⠉⠀⠀⠀⠈⠁⡠⠤⠤⢤⢄⠀⠀⠀⠘⣆⠀⠀ ⢠⡏⠀⠀⠠⠊⣌⡀⠀⠀⢀⣱⠀⠀⠀⠀⠀⣜⡀⠀⠀⢀⣱⠀⠄⠀⠀⠸⡄⠀ ⣸⠀⠀⠀⠇⠀⣷⡶⢻⣿⣶⣾⠀⠀⠀⠀⠀⣷⣶⣾⡟⢶⣶⡄⠀⠀⠀⠀⣧⠀ ⡟⠀⠀⠀⢰⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⡆⠀⠀⠀⢸⠀ ⣿⠀⠀⡠⠤⠥⡚⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⢛⡬⠤⢄⠀⠀⣸⠀ ⢸⡀⡜⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢣⢀⡏⠀ ⠀⢳⣣⠀⠀⢀⠌⢾⣶⣶⣲⣯⢍⡉⣉⢉⡭⣽⢶⣶⣶⡷⠱⡀⠀⠀⣜⡾⠀⠀ ⠀⠀⠻⣍⠉⠁⠀⠈⢿⣿⣿⣿⣾⣷⣿⣶⣷⣿⣿⣿⡿⠁⠀⠈⠉⣩⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⡀⠀⠀⠙⢽⣻⣿⢻⣟⣟⣿⣛⡿⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠓⠦⢤⣄⣀⣀⣈⣉⣁⣀⣀⣠⡤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣀⡤⠤⠶⠶⠦⠤⣄⣀⠀⠀⢸⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣸⣿⡆⠀⠀⠀⠀ ⠀⠀⣶⠤⢄⣤⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀ ⠀⠀⠈⠓⢤⣤⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠒⢤⠀⠀ ⠀⠀⠀⡰⠋⠀⠸⣿⣿⡗⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠐⣿⣿⣿⠀⠀⠀⢳⠀ ⠀⠀⢰⠃⠀⠀⠀⠙⣋⡀⠀⢠⣀⡀⠀⢀⠀⠀⢸⣀⠀⠀⢘⣛⠁⠀⠀⠀⠀⢇ ⠀⠀⡞⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠈⠢⢼⡄⠔⠉⢇⠀⠀⠀⠀⠉⢢⠀⠀⠀⢸ ⠀⢰⠃⢀⠀⢸⣄⠃⠀⠀⠀⠀⠘⣄⠀⠘⡝⢄⡀⠘⣆⠀⠀⠀⠀⢘⣸⠀⠀⢸ ⠴⠋⠀⣠⠉⢺⠺⡷⠶⠤⠴⠶⠒⠚⠲⣶⢱⡖⠛⠲⠾⠶⠶⠤⠶⢿⠺⡆⠀⠸ ⣙⣲⠞⠁⠀⢸⠀⣟⢦⣀⠀⠀⠀⢀⡴⠉⠓⠿⢆⡀⠀⠀⠀⣀⠔⣻⠀⢣⠀⢠ ⠛⠦⢤⣤⣴⢇⠀⢿⢦⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⣉⣉⠭⠋⠁⡰⢻⠀⢠⣓⣤ ⢀⠀⠠⢾⠕⡇⠀⠸⡄⠑⢄⡀⠀⠈⠉⠀⠀⠉⠉⠀⠀⠀⣠⠞⠁⡼⠀⡀⢳⠀ ⠋⢀⡴⠋⠀⡇⢠⠀⠙⢤⣀⣩⢓⣦⣤⣤⡤⢤⣤⣴⣶⣏⠀⣀⡰⠃⢀⠇⡸⠀ ⠒⠋⠀⣀⠆⠳⣜⣦⠤⠤⠔⠁⢸⣿⣿⣿⣃⣸⣿⣿⣽⣿⠇⠙⠒⣲⣋⠴⠃⠀

⠀⠀⠀⠀⠀⠀⠉⠛⠲⢖⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣒⠦⢉⢱⠀⠀⠀⠀ ⡄⣄⣀⣀⠀⠠⠤⢀⣀⠠⠵⣮⡳⡄⠀⢀⣀⡠⠊⡡⠐⠉⠀⠀⠸⠸⠀⠀⠀⠀ ⠇⢁⠀⠀⠈⠉⠖⢟⠐⠀⢒⡢⢵⠸⠁⠀⠀⠱⢸⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀ ⠸⠈⠄⠀⠀⠀⠀⢰⢸⢴⡣⠊⠀⠀⠀⠀⠀⠀⣧⠡⠀⠀⠀⠀⡇⡜⠀⠀⠀⠀ ⠀⢣⠘⡀⠀⠀⢀⢆⠏⠸⠀⠀⠀⠀⠀⢀⠤⠀⠡⠕⣕⠒⠒⣈⡠⠁⠀⠀⠀⠀ ⠀⠀⢣⡑⢂⣀⡡⡜⢄⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠱⡀⠀⢀⢎⢔⢶⡲⢤⡀⠀⠀⠀⠀⢰⡠⢺⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠀⣇⡖⠒⠴⡀⠈⡆⡖⠁⠀⣦⠸⡀⠀⠀⠀⠉⠠⠃⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⡌⢣⠁⠀⠀⠐⡀⠰⡡⡀⠀⠀⢀⠇⠀⠀⠀⠀⠁⡩⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⡢⠕⢄⡀⣠⣴⣶⡟⠛⢲⡴⠊⠀⠀⣀⣠⣴⣇⢠⢲⠴⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⢈⣵⡦⠬⡯⣝⢫⡀⡤⣺⡏⡏⠉⠉⡄⢫⠙⡘⣟⣻⣩⣢⡌ ⠀⠀⠀⠀⠀⠀⡴⢋⡉⠁⡀⢰⢿⣮⠼⠻⠋⣁⡇⠀⠀⡄⡼⣀⢃⢄⣊⠲⢄⢠ ⠀⠀⠀⠀⠀⢰⡿⠥⠀⠤⣈⡆⡸⢎⢷⣶⣿⣿⠇⢀⣴⣽⡉⢶⣌⠉⠸⠑⠀⠁ ⠀⠀⠀⠀⠀⢰⢸⡀⠀⡆⠈⣯⣒⡋⠵⢻⠿⠧⠞⢋⡷⡈⠉⠀⠈⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡈⠁⡰⢁⡐⠓⠒⡤⠧⡎⠀⢀⠴⠋⠀⠈⢐⠒⢒⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠊⡹⠁⠀⠉⠀⠀⢸⠀⠀⠛⠩⠴⢤⣀⣋⣒⣫⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢔⣩⠋⡀⠁⠉⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⢄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢩⠁⠀⠀⠀⠀⠀⠑⣄⠀ ⠀⢠⠞⠉⠙⢶⢤⡀⠀⠀⢀⣛⣭⣑⣲⢤⠔⠁⠀⠀⢘⣤⢤⡀⠀⠀⠀⠀⠈⢆ ⢀⡏⠀⠀⡀⢀⡆⠈⠳⣾⡷⠂⡠⠊⠀⠈⠦⡀⠀⠂⢁⡼⡍⠱⡄⠀⠀⣀⠴⠁ ⢸⠀⢀⠌⠀⠀⠟⠢⠀⣮⣮⡰⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠹⡄⠘⠶⠊⠁⠀⠀ ⢸⠀⡌⠀⠀⡸⠦⠤⣽⠀⠁⡁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠠⢳⠀⠀⠀⠀⠀⠀ ⠘⣆⣡⠴⠋⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡔⠉⢀⠹⠀⠀⡠⠃⠈⡇⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⣷⠀⠀⠃⠀⠀⡜⠀⠀⢗⣷⠰⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⣄⠘⡀⡠⠥⠤⢤⡔⢫⠃⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣺⡔⠌⢵⢯⡝⠀⠀⣠⣵⠃⣀⣠⠤⠒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣵⣧⠷⠯⠷⢬⣛⢯⡿⠟⢋⣡⢟⣋⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⣺⠋⠀⠀⠀⠀⠀⠀⠉⢹⠛⠛⠊⠁⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠚⡽⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⣠⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠞⢚⢝⣹⣦⣤⣤⡴⡲⠒⠒⠚⠒⠒⠊⠹⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠈⣨⢾⠏⢠⠁⠀⠀⠀⠀⠀⢠⠃⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⢾⠅⢀⣡⣘⣀⣀⠀⠀⠀⡠⠃⠀⢘⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠉⠙⠺⢤⣀⠠⠂⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠥⢩⠷⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⠔⢉⢂⠄⠀⣠⣶⣿⣿⣿⣿⣿⣷⣦⡀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠛⡁⢀⣣⣌⣢⣀⠝⠛⠿⡿⠟⠛⢿⣿⣿⣿⣄ ⠀⢠⣿⣿⣿⡏⠁⠀⠀⢃⣴⢾⣿⣿⣿⣿⣿⣷⣦⣀⠃⢀⣠⣾⣿⣿⣿⣿ ⠀⢸⣿⣿⣿⣿⣶⠆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⡿ ⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢩⣿⠏⣼⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⠇ ⠀⠘⣿⣿⣿⣿⣾⠋⠉⠸⢿⣿⣿⣇⠁⠘⠿⣿⣿⣿⠀⠀⢻⣿⣿⣿⡟⠀ ⣦⡀⠘⣿⣿⣿⣿⠀⠀⢀⣤⣿⣿⡏⠀⢀⣤⣾⣿⡿⠀⠀⢸⣿⣿⡟⠀⠀ ⠸⣿⣦⣬⣿⣿⣿⠆⠀⠈⠛⠿⠛⢠⣤⡄⠙⢻⣛⡁⠀⠂⣾⣿⣿⣷⣾⠏ ⢰⣿⣿⣿⣿⣿⣇⠀⢰⣫⣴⣷⡄⠀⣠⠶⢰⣿⣧⣹⡆⠀⣾⣿⣿⣿⡿⠗ ⠀⠙⠻⣿⣿⣿⣿⡦⡘⠿⠿⠟⢸⡇⠃⢱⠋⠻⠿⠟⡡⢊⠙⢿⡿⠀⠀⠀ ⠀⠀⠘⠛⠛⣿⡁⠀⠈⠒⠠⣀⠀⠈⠉⠁⠀⣀⠔⠀⣤⣿⡀⠀⠀⠀⠀⠀ ⠀⠠⠚⡹⡍⠽⣿⣦⣄⡀⢀⡜⠈⠀⠂⠒⢹⣀⣠⣾⣿⡿⠒⡎⡀⢘⠉⠃ ⢀⠖⣃⣁⣁⢢⣿⣿⣿⣿⡍⠀⡀⠀⠀⠀⡠⢺⣿⣿⣿⠀⡀⠧⠧⠜⣀⠀ ⠐⠎⠀⠀⠀⡇⡼⣿⣿⣿⣷⡀⠈⠂⠔⠀⣠⣾⣿⣿⣿⠹⠉⠈⠉⠉⠰⠀ ⠀⠀⠀⠀⠀⠏⠀⢘⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡟⠀⠑⡇⠀⠀⠀⠀⠆ ⠀⠀⠀⠀⠠⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠁⠈⠛⠛⠛⠛⠁⠉⠛⠛⢻⠁⠀⠑⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠶⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⣠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⣼⣷⣶⡟⠋⠉⠉⠉⢉⣩⡭⠭⢭⣍⡙⠒⢺⡄⠀⠀⠀⠀⢀⡗⠒⢋⣩⣭⠭⢭⣭⡉⠉⠉⠉⠉⠳⣶⣾⣧⠀⠀⠀⢸⡆⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⣤⠞⠋⠠⣤⣄⡀⠀⠉⠳⣄⣧⠀⠀⠀⠀⢸⣠⠖⠉⠀⢠⣀⡀⠀⠈⠓⢦⡀⠀⠀⠹⣿⣿⣇⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⣿⣿⡏⠀⠀⢀⡾⢱⠀⠀⠀⠀⢻⣿⣷⣦⡀⠈⢿⠀⠀⠀⠀⡿⢳⠀⠀⠀⠀⢻⣿⣿⣶⡄⠀⢳⡀⠀⠀⢸⣿⣿⠀⠀⠀⣧⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⢳⣿⣿⠃⠀⠀⢸⠁⢸⣄⠀⠀⢀⣼⣿⣿⣿⣷⠀⢸⡄⠀⠀⢰⡇⠸⣆⠀⠀⢀⣼⣿⣿⣿⣷⠀⠈⣷⠀⠀⠀⣿⣿⡇⠀⠀⠈⢧⠀⠀ ⠀⣼⠃⠀⠀⠀⠀⢿⣿⡆⠀⠀⢸⠀⠈⣿⣿⣾⣿⣿⣿⣿⣿⡿⠀⢸⠃⠀⠀⠸⡇⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⠁⠀⡿⠀⠀⢀⣿⣿⠀⠀⠀⠀⠈⢇⠀ ⢀⡇⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠘⢧⠀⠹⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⣀⣀⣀⣀⣳⡀⠈⢿⣿⣿⣿⣿⣿⣿⠏⠀⣸⠁⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣀⠀⠈⠳⣄⣀⡽⠿⠛⠛⠉⠉⠉⠻⢿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠛⠛⠿⢯⣀⣠⠾⠁⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡍⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀ ⠀⠀⢠⠟⠢⣄⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⣠⠴⢻⡆⠀⠀ ⠀⠀⠘⡆⠀⠀⠉⠓⠶⢤⣤⣘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⡤⠶⠚⠉⠀⠀⢰⡇⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠙⢄⠙⢶⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠋⣡⠏⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠑⢤⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⡤⠞⠁⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣤⣜⣿⣋⠁⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠈⢙⣿⣃⣤⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠋⠉⠙⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⠀⠀⠀⠀⠹⢤⣀⠔⠒⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠉⠉⠑⠢⣄⠀⠈⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⣿⣿⢿⡛⢋⡽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⣷⡄⠀⠀⠀⠱⡄⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠳⠟⠀⠈⠓⣝⠋⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⡴⠁⠉⠓⠮⣧⣀⣷⣠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠈⢦⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡞⠁⠀⠀⠀⠀⠀⡿⠈⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠘⡆⢸⣧⡤⠤⠶⠶⠶⠤⣤⣄⣀⠀⠀⠀⣰⣯⠎⠀⠀⠀⠀⠀⠀⢰⢇⢠⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢠⣧⠏⣤⠴⢒⣒⡦⠀⠀⠀⠀⠈⡙⠳⣾⢵⡏⠀⠀⠀⠀⠀⠀⣠⠟⠛⣽⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⠳⣦⠴⠟⠁⣀⡀⠙⠉⠀⣠⠤⠶⠖⠚⠉⢹⡆⢻⢸⠀⠀⠀⠀⠀⢀⠔⠁⢐⡽⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣶⣶⠴⢾⡽⠋⠀⣀⡬⠦⡀⠀⢿⠀⠀⠀⢎⠀⣀⡤⠖⢚⣓⡟⠁⢸⠸⡆⠀⣆⢀⠴⠉⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡾⢧⡤⠊⡡⠖⠒⢺⡄⠈⢧⡀⠀⢀⣭⠥⠶⠶⢯⡀⠀⠀⢸⡀⢹⠤⠟⠁⣠⡞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⡞⣡⠊⠀⣠⡀⣼⠀⠀⢀⡽⠛⠁⣠⠴⠒⠛⠛⠺⣦⠀⠀⠻⣥⣤⠴⠚⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⢡⡇⠀⣼⡿⣱⠇⠀⢠⡾⠁⣠⠎⠀⠀⠀⣠⣄⠀⣻⠶⠶⠶⠖⠒⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡸⡇⠀⢛⣷⣧⣤⣉⣹⡇⢰⠃⠀⠀⠀⣾⡿⠋⢠⣿⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢻⡄⣱⣿⠿⣍⠀⢀⣠⠜⠙⢳⣸⡀⠀⠀⠀⠀⢀⡴⠋⠘⠄⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠻⠿⠭⠽⣏⣉⣛⠶⣿⡅⣿⠀⠈⠉⢉⣀⣀⣴⣾⠿⡗⠶⠶⠖⠚⠛⢧⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠛⢉⡭⠟⣿⠋⠁⠀⢈⣙⣾⡿⣿⠓⠾⠿⣿⣿⣿⣿⠾⠽⡿⠀⠀⠀⠀⠀⢸⠄⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠓⣤⠛⠛⠓⢾⣶⣄⣠⡇⠀⠙⣇⠘⠳⢤⣤⣀⣀⣀⣤⡤⠾⠧⠤⠤⠤⢶⡶⠞⠛⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣹⣄⡿⠛⠢⣰⡏⠉⡙⢾⣇⠀⠀⣹⣹⢧⡴⠋⡠⢚⣡⣄⣀⡀⠀⠀⣀⡤⢦⣝⣤⢄⣈⣤⣍⣲⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣹⣿⠷⠒⢦⡿⣻⠋⠉⢮⡏⠓⢺⡯⠽⣽⠃⡼⢡⠏⠀⠀⡠⠛⣻⠟⠛⢢⠀⠀⠙⡷⣿⠷⡦⡉⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⠀⠀⣸⠁⣇⠀⢀⡼⢦⣤⠾⠁⠀⣿⠀⡇⠘⢦⠀⣼⠀⢰⠃⠀⠀⣼⠧⣤⡴⠯⣉⢳⡹⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠋⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⣴⡿⣇⠹⣄⠀⠑⣼⣶⠼⣧⣴⣮⠝⠛⠙⢲⡀⢈⣦⣷⡇⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣿⣿⡇⠙⢆⠈⠳⢬⣓⡋⠀⠀⣀⡏⠀⠀⠀⣼⣷⠟⠚⣾⣷⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣡⠾⠁⢳⡀⠀⣹⠦⣄⣈⠉⠉⠉⢉⣹⣶⣶⣫⠞⠛⠓⣦⢃⣿⠙⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⠾⠻⡇⠉⣉⣠⣒⠇⠀⠉⣿⠁⠀⠀⠉⠉⠉⠉⠉⠉⠻⣿⣯⣶⣤⣶⣵⣮⢿⢾⡉⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢡⡏⠀⠀⢿⣦⣀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣟⣀⣀⡀⠀⢴⣒⣌⣆⣱⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⣀⠳⣄⠀⠀⠉⠉⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⣤⣀⣈⣭⣭⣍⣗⣦⣌⠁⢉⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⢛⣋⣉⣋⣛⠻⢇⡸⠽⢲⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⢉⣀⣤⣤⡶⣶⣬⣭⣙⣻⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⢟⠿⢋⠝⢋⡽⣻⢝⠟⠻⣦⡾⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⣶⣒⣋⣉⣉⣁⣀⣁⣠⣤⣬⠬⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⠦⠤⣤⣤⣤⣦⣤⣤⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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