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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠽⠿⡛⢿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⢀⠀⢿⣯⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠛⠁⠀⣼⣿⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠭⣄⠀⠀⣰⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠠⠴⡞⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠾⢡⠄⢠⢃⠞⣷⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠊⡉⠀⠀⠀⠈⢂⡑⣃⠅⠊⠀⠀⠉⠛⠲⢤⠀ ⠀⠀⠀⠀⢰⢇⠀⡎⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⢸⣸⠀⢸⡇ ⠀⠀⠀⢠⠃⠻⣟⢧⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⡼⠁⠀⢸⡇ ⠀⠀⠀⢸⠀⢀⡻⠦⠵⠤⢄⣀⣀⡠⠄⢤⣀⣰⣿⠁⠀⠀⠘⡅ ⠀⠀⠀⢸⡀⠋⠀⠀⠀⠀⠀⠈⠀⠈⣅⣸⠀⠤⢾⣄⠀⠀⡰⡇ ⠀⠀⠀⠘⢧⣀⠀⠀⢀⣀⣠⣴⣞⡉⠁⠀⠀⠀⠈⠉⠀⠐⣿⠀ ⠀⠀⠀⠀⠀⠈⢹⣿⡏⠀⣩⠉⠉⠙⠓⠻⠵⢾⣶⣶⣶⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠚⠛⠿⠅⠒⢊⣽⣛⡩⠤⠖⠒⠚⠋⠀⠀⠀ ⠠⠀⠠⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣀⡀⠀⠄⢐⡒⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠺⡕⣾⡺⡄⠘⠼⠦⠃⠀⡟⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡮⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⣇⠀⠀⠀⢉⣁⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣀⣀⡔⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣾⡿⠻⠿⠏⠀⣩⠳⡒⠀⠤⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣶⣿⡟⡳⣧⠎⠀⢰⣾⠉⠙⣧⠼⣿⠶⡢⠞⠑⠄⠀⠀ ⠀⠀⠀⠀⣰⡟⠷⢽⠟⠔⠃⠁⠉⢲⠾⡮⠆⠈⠀⠈⠉⠉⠀⠀⠀⠘⡀⠀ ⠀⠀⠀⣰⢯⣛⠀⢀⠀⠀⠀⠀⠀⢸⠀⣿⠸⠀⠀⠀⠀⠀⢡⣤⠀⠀⡇⠀ ⠀⠀⣰⣿⠈⡅⠀⣾⠂⠀⠀⠀⠀⠘⠚⣉⣀⠀⠀⠀⠀⠀⢨⡇⠀⢰⢹⠀ ⠀⠰⢿⡿⠊⠀⠀⡟⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡀ ⠀⢇⢰⣇⡇⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡇ ⠈⠉⠈⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⢿⣿⡙⢻⣿⣿⣿⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠋⠀⠀⠈⠉⠁⠈⢿⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⣀⣤⢤⣄⠀⠸⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠃⠹⡿⠻⠀⠀⠀⣹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⡀⠀⠀⠀⠀⢸⡿⢋⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣄⣀⠀⠀⠀⠀⣶⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠒⠚⠉⠀⢀⣠⠜⢻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⠤⠾⠿⡟⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡇⡆⠀⠀⢨⠇⢀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠒⠉⠉⠹⡁⠘⡜⠀⢠⠎⡠⠊⢀⡟⠟⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠉⠀⠀⠀⠀⠀⠀⠱⣄⠈⠾⠟⠉⣠⠔⠉⠀⠀⠀⠀⠉⢿⠿⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣌⡠⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⡠⠈⣄⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢰⡟⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠙⣦⣟⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡟⠀⠀⠀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⠈⢫⡹⣌⢟⣦⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠏⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⢠⡤⢿⣶⣤⣽⣦⣀⣀⠀⠀⠀⠁⠀⠀⣀⣀⣀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⢀⡞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠉⠛⠾⡏⠛⠻⢥⣀⠀⢹⠒⠒⠒⠻⣿⠁⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⣄⣠⠤⠴⢿⣷⡀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡤⠖⠛⠋⠉⠀⠀⠀⠀⢸⠟⠿⠀⠀⢀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠷⣦⣄⠀⠀⣀⣀⣀⣀⣤⣶⠿⢿⡥⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣟⡋⠁⠀⠉⠙⠛⠛⠛⠛⠛⠷⢾⣭⣗⡲⢮⣗⣶⣦⣴⣤⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣸⣿⣀⣤⣶⠟⠀⠀⢀⣀⣤⣤⣤⣠⠍⠉⠉⠛⠛⠛⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠯⠴⠖⠛⢉⣥⡿⠟⢉⣀⣤⠴⠶⠒⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⡀⠀⠛⠛⣛⢛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠁⠁⠉⠉⠉⠉⠉⠉⣉⣁⣀⠀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⡺⢻⣴⢶⣦⡤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⢁⣀⡀⠀⣒⡒⠲⢯⠄⣙⠥⢒⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣠⣤⣾⢥⣧⣀⣩⡋⠉⠛⠛⠶⣤⣈⠐⠢⠈⡆⠀⠀⠀ ⠀⠰⣿⡽⠟⡙⣬⣼⣲⣤⣯⣭⡟⣿⣤⣲⠄⣈⠈⠉⠢⣰⠀⠀⠀⠀ ⠀⠀⠈⠑⠦⣂⢠⠁⠀⠀⠀⠀⠈⠉⠘⠫⠝⣦⣭⣐⢤⣘⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⣾⣷⣤⡀⣠⣄⣀⡀⠀⠀⠀⠀⠀⣉⡐⢭⠛⠧⢦⣀⠀ ⠀⠀⠀⠀⢳⣩⠏⢻⠟⣇⠀⢻⠟⢷⢴⠖⠒⠲⠋⠉⠉⣧⠨⠺⠈⢦ ⠀⠀⠀⠀⠀⠹⡓⠙⠀⠘⣦⠀⣀⠜⠀⠀⠀⠀⠀⢁⢸⠋⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⢇⠣⠔⠒⠚⠄⠀⡀⠀⠀⠀⡠⠊⣱⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠾⠲⢷⠷⠤⠘⡀⠀⢀⠀⣰⠛⠒⠸⢯⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⢀⡬⠒⠁⠈⠠⠊⢈⡀⠁⠲⠤⢀ ⠀⠀⠀⠀⡀⠤⠚⠢⢤⢀⡠⢤⠔⠈⠀⠀⢀⡔⠁⠀⡘⠀⠀⠀⡆⠀ ⢀⠤⠂⠁⠀⠀⠀⡰⢁⠒⠥⢢⣁⢂⡀⠔⠉⠀⠀⡔⠀⠀⠀⠀⡁⠀ ⢸⠀⠀⠀⠀⠀⡔⠁⢸⠐⠠⣤⣯⣯⠭⠥⠀⡇⡰⠀⠀⠀⠀⠀⡇⠀ ⠘⠀⠀⠀⢀⠌⠀⠀⠀⡄⢀⣠⠏⠙⢅⠢⠀⣧⠁⠀⠀⠀⠀⢸⠁⠀ ⠀⢁⠀⠀⠈⠐⢄⠀⠀⡍⠉⠿⠀⠀⠆⠑⠤⠃⠀⠀⠀⠀⠀⠸⠀⠀
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⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⠀⠀⠀⠀⠀⣠⣶⣟⢑⣲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡏⣸⣿⠋⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⡏⠉⢧⣀⣸⠇⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠴⠚⣉⣍⠉⠓⠦⣄⠀⠀⠀⠀ ⠀⢀⡾⠛⠉⢿⡟⠁⣤⠞⢿⣻⡞⢋⣉⡍⠓⠛⠉⠙⢻⡏⠀⠀⢀⣠⠶⠋⠈⠙⠾⠗⠟⠀⠀⠀⠀ ⠀⢸⢀⠀⠀⠀⠙⠓⠃⠀⠀⠉⠀⣠⣟⣀⣀⣀⣀⡤⠾⣧⠶⠚⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⡟⢧⠀⠀⠀⠀⡀⠀⠀⠀⢈⡿⡿⠀⠀⠀⣠⠴⠚⠉⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡇⠘⡷⠦⠤⠾⠃⠀⠀⠰⠋⠰⡇⠀⢀⡾⠁⠀⢠⠟⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠛⠓⣦⣧⡀⠀⠀⠀⣀⡤⠴⠤⠴⠛⣶⠚⠀⠀⠀⡏⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⣴⣋⣽⠻⣏⠓⢾⣁⠀⠀⠀⠀⣰⠘⣆⠀⠀⢀⡇⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠷⣤⠜⠓⠒⠒⠚⠉⠛⠛⠒⢴⣿⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⠤⣤⣀⣀⣤⣄⡀⠀⠀⠙⠓⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠉⠳⠶⠶⠤⢠⠤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠲⠦⠤⣄⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⢀⣠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣡⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣷⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⡀⢿⣿⡿⣿⣥⣤⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⣿⠟⠛⠛⣻⣿⣿⣏⠁⠀⠹⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⠟⠁⢀⣠⣾⣿⡿⣿⣿⣄⠀⠀⠉⠙⠛⠿⠿⠿⠟⠙⠹⠿⠿⠿⢿⣿⣿⣿⣶⣄⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠁⠀⢸⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠉⠚⠋⠀⠀⢀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀ ⠀⠀⢀⣠⣴⣶⣶⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠋⠓ ⠀⣴⣿⠇⠉⠉⠛⠛⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀ ⣴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡏⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⠀⠀ ⠀⠀⠀⢀⡿⠁⠀⠀⠀⡀⠤⣤⡤⠲⠤⠉⣉⠉⠉⠉⠓⢶⣄⠀⠀⡺⠋⠀⠑⠄ ⠀⠀⢀⣼⠁⠀⢀⣴⡾⠗⠐⠁⠀⠀⠀⠀⡖⠚⠳⡒⠨⢁⢹⣧⠀⠀⢂⠂⢀⠜ ⢀⡴⠋⠙⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠹⡄⣀⡼⢃⢔⠕⠁⠉⠁⠀ ⢸⡃⠀⢀⣾⠟⠀⠠⠒⠉⠙⠒⠤⣀⠀⠀⠀⠀⢶⡄⠻⣁⠠⢦⡥⠤⣤⣀⠀⠀ ⠘⢧⡀⢺⡏⠀⢌⠢⢀⠀⠀⠀⠀⣈⣙⡢⠤⠂⠈⢁⠌⠀⠀⠀⠘⡄⠀⠙⣷⡀ ⠀⠀⠉⢳⡇⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠄⠁⠀⠀⠀⠀⢀⠃⠀⠀⢸⡇ ⠀⠀⠀⠈⢿⡀⠀⠀⠀⢠⠪⡭⢐⣒⣂⣒⣚⢄⠀⠀⠀⠀⢀⠠⠊⡀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⡻⠤⠤⠀⠈⠀⢷⣦⣤⣤⣶⣶⣾⠋⠀⠀⠉⠀⠀⠀⢡⠀⣰⡿⠀ ⠀⠀⠀⠀⢸⡇⠐⡖⠄⢠⠀⢈⢏⠉⠙⠍⠙⡏⡄⠀⠀⠀⠀⠀⠀⢸⠞⠋⠀⠀ ⠀⠀⠀⠀⠀⠹⢦⣬⣈⡼⣦⡀⠁⢑⠀⠀⢊⠜⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠈⠉⠀⠀⠀⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣦⣶⣶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠚⡄⢫⠉⢩⠃⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⡞⠳⡜⠦⠚⠘⠒⠋⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠉⠉⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡇⠀⡰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⢰⡆⢻⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⢰⠁⡰⠁⠀⠀ ⠀⠀⠀⠀⣶⣦⣤⠘⣿⣿⣆⠀⠀⢿⠇⣼⣿⣿⣿⣿⠛⢸⡇⠀⠀⠙⣿⣿⣿⣇⠀⠀⠀⠈⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣁⠀⠻⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣇⡀⣾⠃⠀⠀⢠⣿⣿⣿⡇⠀⡔⠒⠲⡄⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⠋⠉⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⠟⠀⠀⠱⠤⣀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⡀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⡗⡤⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣫⢸⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⡿⠿⠿⣷⣦⣠⣤⣾⠟⠛⠳⣦ ⡏⢀⢀⣠⣶⠟⣹⣿⠷⣦⡀⢀⢘⡇ ⢣⣤⣴⠿⠃⢀⡿⢿⡆⠈⠻⠿⠟⠁ ⠀⠀ ⠀⠀ ⣠⠃⠈⠳⡄ ⠀⠀ ⣰⡟⠁ ⠀⠀ ⣸ ⠀⠀⢰⡏ ⠀⠀⠀ ⢠⡟ ⠀⠀⠘⣇ ⠀⠀⠀ ⢸⡇ ⠀⠀ ⢿ ⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠉⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠊⡀⠀⠀⠀⠀⠀⠀⠀⡀⠼⢟⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣜⣆⠪⢓⣦⢄⠠⠤⠒⠣⠘⢡⣷⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢽⡄⠀⠀⠸⠀⠀⠀⠀⠀⡮⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠐⠒⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠳⡄⠀⠒⠀⢀⠞⢸⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⠁⣸⢈⠢⠤⠴⠁⠀⢾⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡠⠚⢁⠃⢠⢹⠈⡌⢄⠀⡌⠀⠈⠱⡀⢻⠻⡓⠤⢄⡀⠀⠀ ⠀⣀⡔⠃⠖⠉⡙⢠⢇⣘⣀⢱⠀⡰⢀⡀⣀⠄⠑⣄⢳⠒⠢⡀⠘⠢⡀ ⡸⢀⣈⡙⠢⠔⢁⠮⢀⠉⠒⢢⠘⠕⠒⣈⠡⠔⠁⠀⠣⡑⠤⠼⠤⠴⠯ ⡏⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⢂⡇⣧⠁⠀⠀⠀⠀⠀⠻⠛⠛⠻⡗⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠤⠤⠤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⢻⠹⣿⢨⣹⣶⣾⡿⠿⠿⠿⡶⠶⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡎⠈⠉⠍⠨⣩⡍⢭⠉⣉⣿⡉⠙⠒⠲⠶⢭⣍⣙⠛⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⡀⠀⠀⠒⠀⠈⠚⠗⠊⠋⠻⠿⢷⣶⣤⣄⠉⢛⠲⢤⣍⡛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡦⠶⢿⣶⠷⠿⠮⠭⠭⢽⣛⣛⣶⣶⠤⣷⣒⡲⠀⠈⠙⠛⠲⢦⣄⡉⠒⠦⣈⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⠶⠯⠤⠤⣾⣇⣀⣀⣀⠀⢠⡎⠀⠈⠉⠉⠉⠛⠻⠿⠭⣲⣶⣅⡀⠀⠈⠉⠳⠦⣄⠉⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⡶⣖⣿⣿⣿⠿⣷⠲⣖⣓⣺⣃⣚⠒⠒⢂⡿⠿⣿⣟⣳⠶⣦⣄⡀⠀⡀⠀⠀⠀⠀⠿⢽⡛⠿⣶⣦⡄⠀⠀⠈⢱⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣮⢿⣥⢶⡞⣻⣋⠏⣩⣩⣤⣴⠤⠼⠧⢤⣤⣦⣭⣭⣽⣛⡂⠳⣶⣭⣹⡛⠶⢥⣄⡀⠀⠤⣀⠀⠀⠉⠛⢯⣄⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⢿⣌⣧⠀⠀⠰⠞⠡⠚⠛⣶⠾⠷⠿⠛⠛⠻⠿⠶⠶⠿⠿⢬⣽⣛⠳⠮⣝⣻⡶⢤⡙⠛⠶⢤⣀⠀⠀⠀⠀⠈⢳⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢷⣦⣈⠲⠀⡀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠶⠬⣍⣙⠻⢶⣒⣄⢈⡉⠳⠦⣄⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢦⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠾⣭⣛⡻⢤⣄⡲⣭⣻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣾⣧⣦⣄⡀⠀⠀⢠⢢⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠛⠲⢤⣈⡛⠪⣿⡢⣝⠢⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣿⣿⢿⣶⣬⣸⣿⡽⣿⣿⣆⡀⣼⠿⣿⠿⢿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢵⢤⣄⡄⢸⣷⡀⠈⠳⣄⠑⣦⡹⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠙⣍⣹⠏⢻⣟⣵⡽⣿⣯⠀⠀⠠⢾⣿⡶⢿⣻⣦⣀⣠⣤⣤⣴⠶⠶⠶⣾⡿⠓⠛⠛⠋⠉⢹⢧⡀⠀⢙⡆⢹⠌⠈⢿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣼⡟⠀⠀⣽⡟⠀⠈⣿⣦⠀⠀⠸⣿⡟⠂⠙⣿⡟⢽⣿⠃⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⢸⢸⣏⠀⠻⠃⠹⠆⠇⡼⢸⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡷⠦⠞⢻⠇⠀⠀⠈⢿⣤⠀⠳⠒⠂⠀⠀⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠳⡀⢰⣿⡟⠉⠛⠛⠛⠛⠉⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⠀⢀⡏⠀⠀⠀⠀⠀⢹⡻⠶⠶⠷⠶⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⡅⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠸⣄⠀⠀⣴⡶⣶⣠⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠿⠟⠉⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡄⠈⠛⢉⠁⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣇⣦⣤⣿⣤⣖⠀⠀⠀⠀⢳⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣄⣼⢷⣀⣠⠞⠈⣿⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡿⠏⠻⠯⢍⣓⠚⠿⠷⠦⠄⢸⣧⠀⠀⠀⠀⠀⡄⠀⠀⣰⡿⠁⢀⠉⠁⠀⠈⡿⠹⡆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢣⠀⠀⠀⣰⠃⢀⣼⠟⠁⠀⡾⠀⠀⢀⡴⠃⠀⢧⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⡇⠀⣴⣯⠞⠉⠁⠀⠀⠀⡇⠀⣤⠏⠀⠀⠀⣼⠀⠀⠀⠀⠉⢿⡓⠲⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⢑⡼⠁⠀⠀⠀⢀⡟⠃⠀⠀⠀⠀⠀⢧⠀⠀⠈⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠉⠉⠈⠙⠶⢦⣤⣄⣀⣀⠤⠤⣶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⣠⠟⢁⡀⠙⠷⣄⠀⠉⠳⣄⡀⠀⠀⢲⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀ ⠀⣠⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣼⠉⠛⠦⣬⡓⢦⡀⠀⠙⢦⡀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀ ⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢸⠇⠀⠀⠀⠀⠈⠛⢿⣿⣶⣾⣿⡭⠤⠶⠶⠶⠶⢦⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀ ⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⢸⣧⠀⠒⠲⠦⠤⠤⡾⢡⣿⣉⣁⣀⣀⠠⠄⠀⠀⢸⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀ ⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠘⢹⠀⠀⠀⠉⠉⠙⢳⣾⣿⡶⢦⣀⠀⠀⠀⠀⠀⢸⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀ ⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⢀⣤⡾⠁⠀⠉⠳⣄⠙⢦⣄⡀⠀⢸⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⢺⣧⣠⣴⡾⢻⣿⠃⠀⠀⠀⠀⣈⢦⡀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⢸⡁⠀⠉⠀⢸⣿⠀⠀⠀⠀⢀⡏⠀⠙⠦⣄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀ ⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⣸⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⣛⣏⠉⣉⣛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠁⣿⡟⡟⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⢸⠏⠋⣦⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠛⠛⠓⠲⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣄⣤⡴⣤⣬⡿⠀⠀⢙⣷⣦⡿⣠⣤⡴⠦⣤⣀⣀⣠⣤⣤⣄⣠⠶⠞⠛⠋⠉⠁⠀⣸⠞⠻⣦⡀⣤⣙⣷⡆⠀⠀⠀⠀⠀ ⠀⢰⡟⠁⠀⠀⠿⣿⡀⠀⡶⠟⠙⣿⣹⡟⠀⣤⣴⠦⠈⠉⠀⠀⠀⠈⢻⠄⠀⠀⢀⣠⡴⠟⠁⠀⠀⠈⠙⠿⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⢸⣀⡀⠀⠀⠀⠈⠙⠆⠃⠀⠀⠀⠁⠀⢀⣼⢩⣂⣀⣀⣀⣀⣤⠶⢿⣦⠶⠛⠻⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⢟⡟⠁⠀⠀⠀⢀⣠⡴⠟⠱⡦⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⠈⢷⣄⡀⠀⢀⣰⡇⠀⠀⠀⣠⡾⠋⣼⠃⠀⠀⠀⣴⠛⠉⠀⢀⣴⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣼⣗⠀⢸⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⢻⣄⣀⣀⡿⠁⠀⠀⢀⡿⠁⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠈⠉⢻⣾⣷⡀⠀⠀⠀⠀⣠⣴⠖⠛⠒⠚⠋⠙⣿⡉⠁⠀⠀⠀⢸⠁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⣨⡞⢁⣽⠻⣿⠙⠶⣼⡋⠀⠀⠀⠀⠀⠀⣲⠈⣧⠀⠀⠀⠀⣸⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⠀⠈⢷⣄⢀⣙⣷⣦⣄⣠⡴⠞⠳⠶⠾⠧⣄⣠⣶⡟⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢦⣴⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠤⠤⣤⣤⣀⣠⣤⣤⣀⡀⠀⠀⠀⠉⠛⠛⠛⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠉⠳⠤⠤⠦⣄⣀⣀⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⣀⣠⣤⣄⣀⣈⠉⠉⢀⣹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣞⡁⠒⠻⣟⣟⠛⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⡼⣂⣤⣽⣾⣴⣧⣬⣧⣦⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⢿⣿⣾⣿⣿⣿⡻⠿⢿⡙⣿⣿⣿⣿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡏⠓⣪⣿⣿⣿⡀⠨⠿⣿⣿⣇ ⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠤⠀⣾⣿⣿⣿⣷⡁⠰⣻⣿⣿ ⠀⠀⠀⢰⠀⠴⠶⠦⢤⡀⠀⠀⠀⠀⠳⣿⣿⣿⣶⠀⢤⣿⣶⣿⡿⠓⠒⢺⣿⣿ ⠀⠀⠀⡸⠀⠑⢴⣢⢀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣶⣲⣾⣿⣿⣿⣿⣟⡉⣽⣿⣿ ⠀⠠⠊⠀⠀⠀⠞⠒⠛⠋⠀⠀⠀⠀⠀⣼⣿⡿⢉⢝⠫⡙⠿⣿⣿⡇⣈⣽⣿⡿ ⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠦⡃⢘⠔⢹⣿⣿⣿⣿⣿⠇ ⠁⢢⠑⠲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⣊⠆⣸⣿⣿⣿⣿⡏⠀ ⠀⡎⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠃⢈⠔⠁⠠⣿⣿⣿⣿⠟⠀⠀ ⠀⢫⠈⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀ ⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠂⠛⡟⠁⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠒⠒⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣀⠠⠔⠀⠁⣀⠤⠊⠁⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣧⢀⠤⠒⠈⠀⢀⡠⠖⠉⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠖⢩⠋⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⢀⠤⠚⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠃⣀⡄⢀⠠⠚⠁⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠈⢢⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠑⡄⡂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀ ⠀⠀⠀⡠⠁⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⣾⡉⣩⣲⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠘⠂⠂⣒⡒⣒⢒⣖⠚⠯⠭⠽⣛⣒⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⢀⠄⠀⠀⠁⠕⡘⠛⠿⠷⠦⢤⣉⡑⠢⢍⡛⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠚⣹⡏⠉⠑⠒⢒⠟⠫⠭⠷⣾⣯⡥⣀⣨⠉⠑⠲⢬⣑⠢⠍⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣤⣴⣖⣲⡖⣿⠭⡭⠉⠿⠷⢒⣒⣦⡾⣄⣀⠀⠀⠀⠈⠉⠙⣛⡶⢤⣀⣀⠉⠓⠠⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣇⢿⡭⢾⢓⡺⢏⣉⣭⡩⠭⠯⢅⣭⣉⣉⣛⡣⠶⣿⣙⡲⠧⣄⣀⠀⢀⠀⠈⠙⠯⣀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢮⣆⡀⠐⡊⠂⠉⣶⠛⠚⠋⠉⠛⠓⠚⠓⠣⠭⢝⣒⠯⠵⣒⣌⣙⠒⠤⣀⡀⠀⠈⢹⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠦⣍⡂⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠭⣟⡷⢦⣤⡉⢒⡤⣼⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣤⣯⣿⣄⡀⠀⠀⠀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢬⡑⠻⢷⡯⡲⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⢿⡷⣿⣥⣿⣽⣿⣦⣀⣼⠿⠶⢶⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣤⣠⣬⣷⠀⠙⢎⠑⣝⢢⡄⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠘⣬⠋⠹⣵⡏⢻⣇⠀⠐⢻⣿⣛⢽⣷⡤⣶⡶⠖⠚⠛⡿⠋⠉⠉⠉⢹⣧⡀⢨⡇⣗⠀⢻⡆ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣀⣰⣿⠀⠀⢻⣆⠀⢌⠉⠀⠀⣿⡈⠉⠀⠀⠀⠀⠀⠀⠰⡇⠀⣼⡿⠦⠬⠶⠿⠶⠿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⠆⠀⠀⠀⠹⡷⠦⠤⠤⠾⠃⠁⠀⠀⠀⠀⠀⠀⠀⡇⣨⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⣄⣀⡴⠶⠦⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠺⠋⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⡀⢠⠀⡀⠀⠀⠸⡄⠀⠰⠀⠀⠀⠀⠀⠀⣸⡁⠀⡰⢻⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⢿⣛⣯⣵⣦⣄⡀⢳⠀⠀⠀⠀⡀⠀⢀⣬⠃⡑⠊⠁⢸⡿⡌⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠉⠀⠀⠀⣀⡈⠳⡀⠀⢀⠇⣀⡾⠃⠀⠇⠀⢀⠜⠀⢧⠀⠙⢦⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⣠⠿⠊⠀⠀⠀⠠⠀⡰⠃⠀⠀⣼⠀⠀⠀⠈⢯⠙⠦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠳⢄⣀⣀⠀⠀⣀⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢠⠇⠀⠀⠀⠀⢸⡆⠀⠀ ⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⡼⠋⡉⠫⣉⠉⠲⢄⡀⠀⠠⡀⠀⢀⡴⠋⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⣇⠀⠀ ⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡼⠉⠳⠮⣕⢄⡀⠙⣆⣀⡴⠞⠁⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢰⡇⢀⣀⡀⠀⢉⡿⣿⠿⠓⠒⠉⠉⠉⢳⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀ ⠸⡇⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠨⢿⠀⠈⠩⠭⠽⣀⣿⣒⡒⠒⠉⠁⠀⢸⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀ ⠈⡇⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢸⡄⠀⠀⢀⣴⠏⠈⠑⢌⠑⢦⣀⠀⢨⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀ ⠀⣧⠀⠀⠀⠀⠀⠺⣅⠀⠀⠀⠀⠀⢸⠧⢴⠞⣽⡞⠀⠀⠀⢠⠳⣄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⠀ ⠀⠈⡆⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⢸⠄⠀⠀⢿⡇⠀⠀⠀⠞⠀⠈⠓⢚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
.  +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠉⠉⠉⠉⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣧⠁⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢛⡿⣅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢿⡆⢳⡚⠳⣦⣄⣀⡀⢀⠀⣀⡤⢶⡯⢒⡲⠋⠀⣷⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣬⣷⡀⠉⠒⠈⠓⠋⢱⠈⠉⠉⠑⠒⠒⠉⠀⠀⣼⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⣧⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⢰⠥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣄⠀⠈⠉⠥⠭⠉⠀⠀⣰⠏⢸⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⡛⢧⡀⠀⠀⠀⠀⢀⡾⠃⠀⣼⡇⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⡇⢀⠙⠶⢤⣠⡴⠋⠀⠀⢠⢻⡇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢲⡏⠀⢀⡏⡇⠈⡄⢣⡀⠀⠀⠀⡄⠀⣸⢸⣿⣄⠀⠘⣿⢦⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣦⡤⠋⠁⠀⣼⠀⠀⡼⠁⡇⠀⢱⠀⢳⡀⠀⣰⠁⠀⠀⠀⠀⠹⣆⠀⠹⣆⠹⡌⠙⠓⠶⢤⣄⡀⠀⠀⠀ ⠀⠀⠀⢀⣠⠟⢀⡴⠊⠉⢳⡇⠀⣰⠃⢀⠇⠀⠈⣆⠀⠀⢠⠇⠀⠀⠀⠀⠀⣠⠞⢦⠀⢹⡦⠤⢤⣄⠀⠀⢈⡿⣀⠀⠀ ⠀⣴⠒⠻⢤⡀⣼⠀⠀⠀⡼⠀⢠⠟⠳⢾⡤⠤⠤⠼⢄⣀⣯⠤⠄⢒⣲⠴⠚⠁⢀⠼⠳⣄⠻⣆⠀⠈⠳⣄⠘⠀⠈⢳⣤ ⢰⡇⠀⠀⠀⠉⠛⠦⠴⠚⠀⣠⠿⣄⠀⠀⠈⠉⠒⢲⠶⠿⣖⠒⠋⠉⢀⣠⠴⠚⠁⠀⠀⠈⠢⡈⠳⠦⣤⣿⣤⣤⣴⣭⣭ ⣸⠖⠋⠉⠉⠙⠒⠢⠤⠤⠚⠉⠀⠀⠉⠓⠲⠤⢄⠙⡄⠀⡎⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⣤⣤⣼⣶⣤⣤⣴⣶⣄⣤⣤⣶ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡇⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⠉⠉⠉⠉⠙⡛⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠟⠛⠉⠉⠉⠛⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡖⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡠⠤⠔⠒⠚⠉⠉⠉⠉⠉⠉⠛⠻⢶⣤⣄⠀⠀⠀⠀⢀⢞⡵⠏⠀⠀⠑⡄⠀ ⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⣠⣴⠋⠉⢻⠟⠓⠁⠉⠉⠉⠉⠐⠒⠤⣤⡤⠤⠤⠤⣀⡈⠻⣷⣆⠀⠀⠘⢌⠀⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⢀⣴⣾⣿⠿⠆⠒⠋⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠛⠽⣖⠒⠢⢤⣀⠀⢹⣿⡇⠀⠀⢈⡷⢉⠆⠀⠀⣠⠏ ⠀⠀⢀⣴⡾⠻⡇⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠘⣧⡀⠀⠀⠉⢺⣿⠇⠀⡠⢊⠔⠉⠢⠴⠚⠁⠀ ⠀⣰⡿⠁⠀⠈⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠘⣷⣀⣀⣴⠟⠁⢀⠞⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠁⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⣠⠴⠒⠛⠳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠸⣯⠉⠀⢀⡤⣁⣊⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠘⣿⡀⠀⠀⢀⣿⣿⠏⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠸⣿⣧⠀⢙⡷⠂⠉⠉⠛⢿⡍⠉⠛⠿⣶⣤⡀⠀⠀ ⠀⠹⣷⡀⠀⠸⣿⡏⠀⠀⣄⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⠔⠀⠀⠈⠁⡴⠋⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⢻⣿⡄⠀ ⠀⠀⠙⠿⣶⣤⣽⡇⠀⠀⠈⠓⠤⠠⠁⠀⠀⠀⠀⠀⢀⠖⠋⠉⠙⠓⠒⠂⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⡀ ⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⣿⡇ ⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⡠⠒⠛⠒⠒⠤⠤⢤⣄⣠⠤⠴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⡇⠈⢻⠉⠒⠒⠲⠶⠤⠴⠶⠖⠋⢳⣤⣀⠀⠀⠀⢀⣀⠤⠚⠁⠀⠐⡄⠀⠀⠀⢀⣾⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠦⠤⢄⡀⠀⠀⠀⠀⠸⣷⣶⣦⣤⣤⣶⣶⣶⣾⣿⣿⠇⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣾⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠿⠿⣿⡿⠿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠈⡏⠳⡄⠀⡆⠀⠀⢄⠳⡀⠀⠀⠀⠑⠄⠀⢹⠃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⠈⠂⠑⢀⣿⣄⠀⠈⠢⡈⠢⣀⣀⣀⡠⠔⠁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠷⠾⠋⠙⢿⣧⡀⠀⠈⠒⠤⣀⣀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣤⣀⣀⣀⠀⠀⣀⣀⣀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣲⣡⣼⠟⠒⠢⠴⣿⣿⡿⣿⡿⡿⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣫⣿⣥⣶⠋⢁⣀⠀⠉⠻⣷⣧⡀⡄⠀⣀⡇⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣿⣿⣿⣿⣿⣷⣗⣥⠖⣋⣠⣤⣌⣿⣷⣧⣼⣿⣠⣾⣸⣴⣰⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⢏⣴⣿⣿⣿⣿⡟⢿⣟⣿⣾⣷⡾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠛⠙⠙⠉⠛⠿⠿⠿⣿⣯⣾⣿⣿⣿⣿⣿⣈⠻⠿⠟⢣⣀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣟⣧⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⡷⣈⣉⣿⣿⣿⣿⣿⣿⡛⠛⠻⣟⡻⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣛⣿⡀⠙⡒⠶⢿⣶⣾⣿⣷⠀⠀⠰⠾⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣯⠉⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⡩⠥⠤⢄⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⢿⣿⣿⣿⣟⡍⠉⠭⠽⠿⣿⡿⠿⢿⣿⣿⣶⡀⠀⠓⢬⣽⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⡏⠀⢤⣤⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣶⡤⠠⠄⣐⣻⣿⣿⣿⣿⣿⣿⠷⠶⠶⠾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡇⠀⢠⠈⠩⣉⠁⠈⠙⠳⢄⡀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣗⣒⣀⣀⣬⣿⣿⣿⣿⣿⣿⣥⠴⠖⠤⢬⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⠙⢲⡯⣑⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣅⠐⢦⣿⣿⣿⣿ ⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⡾⣯⣀⣨⠵⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠛⣉⠽⠿⠿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢻⣿⣿⣿⡿ ⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡞⠁⠀⠊⣡⢞⠉⢦⡈⢮⢻⣿⣿⣿⣟⣒⣶⣿⣿⣿⣿⡇ ⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢠⢧⡈⠆⠀⢳⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠣⣀⠀⠤⣤⣀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢻⠀⢠⠇⡾⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⢙⡖⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠠⢟⠀⣡⡜⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⢀⣎⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠣⠐⠊⢁⡴⠉⠀⠀⣸⣻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⣧⠀⢍⣳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢧⣄⣠⠴⠋⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⢫⣀⣀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠠⡌⢹⣻⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠲⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠀⠀⢀⡤⠚⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⠀⠀⠀⣀⣠⠴⠊⠁⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣧⠀⠀⣀⠤⠖⠉⠁⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⡽⠗⡿⠔⠋⠁⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⢀⡞⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒⠉⠙⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⡸⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⢔⡇⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⢢⡤⠖⣊⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⣸⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀ ⠀⠀⠀⠀⠀⣠⠏⠀⢀⡤⠊⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⣽⡊⠉⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀ ⠀⡤⠐⡽⢁⡵⡾⡵⣒⠠⠄⠠⡔⠒⢈⡡⠒⠢⡭⠆⠀⠀ ⠀⣤⠀⠈⠋⠀⠈⢠⡧⠀⠀⢐⠷⡂⠓⡄⠀⠀⠀⠀⠀⠀ ⣠⡅⡗⠤⠚⠀⠐⠋⡇⢀⠞⠁⡔⠁⢰⠁⠀⠀⠀⠀⠀⠀ ⠣⣹⣳⢄⠤⡒⠉⠉⢩⢇⠀⢀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⡎⠁⠈⠉⠉⠐⠿⠤⣊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠄⠤⢀⡀⠑⠒⠠⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠤⠭⠍⣈⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢠⢀⣀⡤⠤⠤⠶⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡠⠔⠒⡟⣦⡀⠀⠁⡠⠴⡖⠦⡄⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠺⣶⠂⢻⣍⡿⢷⠀⠀⠣⠤⠿⠔⠁⠀⠀⢸⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢳⠀⠈⠉⠉⠁⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⡀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⡇⠀⠀⠀⠀⠀⠙⠛⡃⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠺⠗⠂⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣤⣦⣤⣶⡾⠉⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⣿⣿⣿⡟⠁⠀⢸⡝⢷⡒⠦⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣉⡿⠛⠧⣍⣉⣁⣀⣤⣄⠤⣿⣿⡄⠹⣦⣴⣄⣤⢉⠝⢹⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⡟⢈⡿⣷⡞⠂⠀⠀⢠⣿⣿⡇⠀⠈⢙⣿⡐⢿⣿⣿⠿⢋⡸⠟⠁⠈⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣤⣘⣿⠿⡏⢀⠾⠄⠉⠉⠓⠶⣄⣰⣃⣉⣳⢠⠔⠋⠀⠉⠒⠾⠟⠚⠉⠀⠀⠀⠀⠀⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣂⠙⠛⠛⠓⠚⠁⠀⠀⠀⠀⠀⠀⣿⠈⢻⣿⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⣠⣿⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠈⣿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠁⢰⣤⡄⠀⠀⠀⢳⠀⠀ ⠀⠀⠀⣰⣿⡇⡽⣿⠁⠀⠀⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡄⠿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢺⡄⠀ ⠀⠀⣰⣿⣿⠉⢐⡷⠀⠀⢻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⢉⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣸⡔⡇⠀ ⠀⢠⣿⣿⣿⡧⠞⠁⠀⠀⢸⡟⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢁⠀⠀⠀⠈⠁⢷⠀ ⠀⡏⢹⢿⡏⢀⠀⠀⠀⠀⢸⡇⠄⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⠀ ⣸⢀⠈⣿⢃⣼⠆⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡆ ⠷⠏⠐⠿⠿⠿⠆⠀⠀⠀⠸⠿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠆⠀⠀⠀⠀⠀⠀⠇
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥⬜⬛🟥🟥🟥⬜🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥⬜⬛⬛🟥⬛⬜🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🏼🏼🏼🏼🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬛🏼⬛🟥🟥🟥🟥🟥🏼⬛⬛⬛⬛🏼🟥⬛⬛⬛⬜⬜⬜ ⬜⬜⬛🟥🏼🏼🏼⬛⬛🟥🟥🟥🟥🏼🏼🏼🏼🟥⬛🏼🏼🟥⬛⬜⬜ ⬜⬛🏼🟥🟥🏼🏼🟥🟥⬛⬛⬛⬛⬛⬛⬛⬛⬛🏼🏼🟥🟥🏼⬛⬜ ⬜⬛🏼🏼🟥🟥🏼🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏼🟥🟥🏼🏼⬛⬜ ⬛🟥🟥🏼🏼🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟥🏼🏼🟥🟥⬛ ⬛🟥🟥🟥🏼🏼⬛⬛🟥🟧🟥🟧🟥🟧🟥🟧🟥⬛⬛🏼🏼🟥🟥🟥⬛ ⬛🏼🏼🏼⬛⬛⬛⬛🟥🟧🟥🟧🟥🟧🟥🟧🟥⬛⬛⬛⬛🏼🏼🏼⬛ ⬛🟥🟥🟥🟥🟥⬛⬛🟥🟧🟥🟧🟥🟧🟥🟧🟥⬛⬛🟥🟥🟥🟥🟥⬛ ⬛🟥🟥🟥🟥🟥⬛⬛🟥🟧🟥🟧🟥🟧🟥🟧🟥⬛⬛🟥🟥🟥🟥🟥⬛ ⬛🏼🏼🏼🏼⬛⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬛🏼🏼🏼🏼⬛ ⬜⬛⬛⬛⬛⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬛⬛⬛⬛⬜ ⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥⬛🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥⬛⬜⬛🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬛⬛🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥⬛⬛⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜ ⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛
⬜⬜⬛⬜⬜⬜⬛⬜⬜ ⬜⬛🟥⬛⬜⬛🟥⬛⬜ ⬛🟥⬛⬜⬜⬜⬛🟥⬛ ⬛🟥⬛⬛⬛⬛⬛🟥⬛ ⬛⬛🟨🟨🟨🟨🟨⬛⬛ ⬛🟨⬛🟨🟨🟨⬛🟨⬛ ⬛🟨⬛⬛🟨⬛⬛🟨⬛ ⬛🟨🟨🟨🟨🟨🟨🟨⬛ ⬜⬛🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬛⬛⬛⬛⬛⬜⬜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠐⠒⠂⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠰⣶⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⢤⣤⣤⣴⣶⣎⠉⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠆⣤⣤⣤⣶⣾⡀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⣽⠋⠉⠀⠀⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠈⣿⠿⠿⠿⠟⠢⣴⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⢹⠿⠿⠿⠿⠳⡀⠀⠀⠀⠀ ⠀⠀⠘⡄⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠧⣤⣶⣾⣿⣿⣆⠀⠀⠀⠀⢱⠀⠀⠀⠀ ⠀⠀⠀⠘⡄⠀⠀⠀⢀⣸⠟⠉⠁⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⠘⣶⣶⣿⣿⣿⣧⠀⠀⠀⠀⢀⣈⡟⠛⠉⠉⠀⠹⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡧⢠⣴⣾⣿⣿⣷⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠹⡟⠛⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⡤⠤⠀⠒⠒⠚⠛⢻⠛⠿⠆ ⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀⡻⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠒⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⢿⠓⠀⢀⡴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡒⠤⣀⡀⠀⢀⡴⠋⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⠀⠉⠑⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠵⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⢀⡤⠋⣀⣀⣀⣤⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠈⠉⠁⠀⠀⠀⠀⢧⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢐⣶⣆⠀⠀⢠⠈⢇⢰⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠀⠀⠀⣏⣧⠈⠟⠀⠀⠀⠀⠀⠀⠽⡿⠆⠀⠀⠀⢀⣿⣿⣦⣶⣶⠟⠀⠀ ⠀⠀⠀⠀⣀⣸⣿⣯⢧⠤⢤⣤⣴⠦⠀⠀⠀⠁⠀⠀⠛⠿⣿⣿⣿⣿⣿⡁⠀⠀⠀ ⠀⠙⠯⡻⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠰⣄⣠⡇⠀⠀⠀⠀⢸⣿⡿⠛⠛⠿⣆⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⢿⣿⠟⠒⠀⠀⠀⠸⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⣿⠿⠺⢝⡯⢧⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠓⠁⠀⠀⠀⠉⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡒⠒⠛⠁⠀⠘⠒⠒⢲⡶⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠈⢢⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⢠⠇⢀⡤⣀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠊⠁⠀⠈⠳⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣀⠀⠀⢀⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣟⠁⠀⠀⠺⡟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢉⠓⠀⠀⠀⠀⠀
⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🏼🏼🏿🏾🏾🏾🏾🏾🏾🏾🏾🏿🏼🏼⬛ ⬛🏼🏿🏾🏾🏾🏾🏾🏾🏾🏾🏾🏾🏿🏼⬛ ⬛🏿🏾🏿🏿🏿🏿🏿🏿🏿🏿🏿🏿🏾🏿⬛ ⬛🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾⬛ ⬛🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾⬛ ⬛🏾🏾🏿🏿🏿🏿🏿🏿🏿🏿🏿🏿🏾🏾⬛ ⬛🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾⬛ ⬛🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾⬛ ⬛🏾🏾🏿🏿🏿🏿🏿🏿🏿🏿🏿🏿🏾🏾⬛ ⬛🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾⬛ ⬛🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾🏿🏾🏾⬛ ⬛🏿🏾🏿🏿🏿🏿🏿🏿🏿🏿🏿🏿🏾🏿⬛ ⬛🏼🏿🏾🏾🏾🏾🏾🏾🏾🏾🏾🏾🏿🏼⬛ ⬛🏼🏼🏿🏾🏾🏾🏾🏾🏾🏾🏾🏿🏼🏼⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛
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⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⬜⬜⬜⬜⬜⬛⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬛⬛⬛⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬜ ⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜ ⬜⬛🏻🏻⬛⬛🏻🏻⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬛🏻🏻🏻🏻🏻🏻🏻⬛🏻⬛⬛⬛⬛⬜ ⬛🏻⬛🏻🏻🏻🏻🏻⬛🏻🏻🏻⬛⬛⬜⬜ ⬛⬛⬜⬛🏻🏻🏻⬛⬜⬛🏻🏻⬛⬛⬜⬜ ⬛⬛⬜⬜⬛🏻⬛⬜⬜⬛🏻🏻⬛⬜⬜⬜ ⬛🏻⬛⬛🏻🏻🏻⬛⬛🏻⬛⬛⬜⬜⬜⬜ ⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜⬜⬜⬜ ⬜⬜⬛🏻🏻🏻🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟥⬛⬛⬛⬛🟥⬛⬛⬛⬜⬜⬜⬜ ⬜⬛🟩🟥🟥🟨🟨🟥🟥🟩⬛⬛⬛⬜⬜⬜ ⬛🟩🟩🟥🟥🟥🟥🟨🟥🟩🟩⬛🟨⬛⬜⬜ ⬛🟩🟩🟥🟥🟥🟥🟥🟥🟩🟩⬛🟨⬛⬜⬜ ⬛🏻⬛🟥🟥🟥🟥🟥🟥⬛🏻⬛🟨⬛⬜⬜ ⬛🏻⬛🟥🟥🟥🟥🟥🟥⬛🏻⬛🟨⬛⬜⬜ ⬛🟩⬛🟨🟨🟨🟨🟨🟨⬛🟩⬛🟨🟨⬛⬜ ⬛🟩⬛🟩🟩🟩🟩🟩🟩⬛🟩⬛🟨🟨⬛⬜ ⬛⬛⬛🟩🟩⬛⬛🟩🟩⬛⬛⬛🟨🟨🟨⬛ ⬜⬜⬛🟩⬛⬜⬜⬛🟩⬛⬜⬜⬛⬛⬛⬛ ⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🌫️⬛⬜⬜⬛🌫️⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣨⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣦⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡿⣏⡸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⡏⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⡾⢻⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠘⢁⢀⠹⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣻⣿⣛⣛⣿⣛⣛⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣼⣧⣼⣯⣍⣿⣉⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣴⠀⠈⠹⣯⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣸⡇⠀⠀⠀⣿⡄⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢀⣿⠁⠀⠀⠀⢹⣧⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣶⣶⣾⣷⣶⣶⢶⠶⠾⡿⠿⠷⣾⢷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⢿⡿⠷⠶⡾⠶⠶⢾⠶⠶⠷⠶⠶⠿⠾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣸⣧⣀⣀⣷⣀⣀⣀⡀⣷⠀⠀⠀⣶⠰⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠗⠈⠁⠀⠁⠀⢀⣈⣩⣭⣭⣭⣉⡉⠛⠛⠛⠛⠓⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⣠⣴⠾⠛⢋⠉⠻⠿⠯⣽⣛⡿⣦⣄⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⠃⠈⠙⣻⣿⠟⣣⡴⠟⠉⠀⠀⠀⠀⠀⠈⠙⢶⡙⢷⣖⠚⠛⠉⠙⢷⣄⠀⠀⠀⠀ ⠀⠀⢀⣴⡿⠃⣀⣀⢰⣿⠃⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠹⣧⡀⠀⠀⠈⠻⣷⣄⠀⠀ ⠀⢠⣾⡿⠁⠙⠛⠛⣿⣏⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣸⣷⠒⠚⠛⠛⠈⠻⣷⣄ ⣰⣿⣋⣠⣤⣤⣤⣤⣿⣿⢙⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣛⣃⣿⣤⣤⣴⣦⣤⣤⣬⡁
⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to _ノヽ ノ\_ me or my son `/ `/ ⌒Y⌒ Y ヽ ever again. (  (三ヽ人  /  | | ノ⌒\  ̄ ̄ヽ ノ ヽ___>、__/ |( 王 ノ〈 (\__/) /ミ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>
⡿⠉⠄⠄⠄⠄⠈⠙⠿⠟⠛⠉⠉⠉⠄⠄⠄⠈⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿ ⠁⠄⠄⠄⢀⡴⣋⣵⣮⠇⡀⠄⠄⠄⠄⠄⠄⢀⠄⠄⠄⡀⠄⠄⠄⠈⠛⠿⠋⠉ ⠄⠄⠄⢠⣯⣾⣿⡿⣳⡟⣰⣿⣠⣂⡀⢀⠄⢸⡄⠄⢀⣈⢆⣱⣤⡀⢄⠄⠄⠄ ⠄⠄⠄⣼⣿⣿⡟⣹⡿⣸⣿⢳⣿⣿⣿⣿⣴⣾⢻⣆⣿⣿⣯⢿⣿⣿⣷⣧⣀⣤ ⠄⠄⣼⡟⣿⠏⢀⣿⣇⣿⣏⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣟⣿⣿⣿⣿⣏⠋ ⡆⣸⡟⣼⣯⠏⣾⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⡟⠸⠁⢹⡿⣿⣿⢻⣿⣿⣿⣿⠄ ⡇⡟⣸⢟⣫⡅⣶⢆⡶⡆⣿⣿⣿⣿⣿⢿⣛⠃⠰⠆⠈⠁⠈⠙⠈⠻⣿⢹⡏⠄ ⣧⣱⡷⣱⠿⠟⠛⠼⣇⠇⣿⣿⣿⣿⣿⣿⠃⣰⣿⣿⡆⠄⠄⠄⠄⠄⠉⠈⠄⠄ ⡏⡟⢑⠃⡠⠂⠄⠄⠈⣾⢻⣿⣿⡿⡹⡳⠋⠉⠁⠉⠙⠄⢀⠄⠄⠄⠄⠄⠂⠄ ⡇⠁⢈⢰⡇⠄⠄⡙⠂⣿⣿⣿⣿⣱⣿⡗⠄⠄⠄⢀⡀⠄⠈⢰⠄⠄⠄⠐⠄⠄ ⠄⠄⠘⣿⣧⠴⣄⣡⢄⣿⣿⣿⣷⣿⣿⡇⢀⠄⠤⠈⠁⣠⣠⣸⢠⠄⠄⠄⠄⠄ ⢀⠄⠄⣿⣿⣷⣬⣵⣿⣿⣿⣿⣿⣿⣿⣷⣟⢷⡶⢗⡰⣿⣿⠇⠘⠄⠄⠄⠄⠄ ⣿⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡟⢀⠃⠄⢸⡄⠁⣸ ⣿⠄⠄⠘⢿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢄⡆⠄⢀⣪⡆⠄⣿ ⡟⠄⠄⠄⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣻⣩⣾⣃⣴⣿⣿⡇⠸⢾
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⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛🟥🟥🟥🟥🟥⬛⬛⬛⬛⬛⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬛⬜ ⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬛⬜ ⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥⬛⬛⬛⬜⬜⬜⬛⬜ ⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥⬛⬛🟥🟥⬛⬜⬜⬛⬜ ⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛🟥🟥🟥⬛⬛⬛⬛⬜ ⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥⬛⬛🟥🟥🟥⬛ ⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛🟥🟥🟥🟥⬛ ⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥⬛ ⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥⬛⬜ ⬜⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥⬛⬜⬜ ⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜ ⬜⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜ ⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜ ⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜ ⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬛⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟦⬛⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟦🟦⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟦🟦🟦⬛⬜⬜⬜⬜⬜⬛🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟦🟦🟦🟦⬛⬛⬛⬛⬛⬛⬛🟦🟦⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟦🟦🟦🟦⬛🟨🟨🟨🟨🟨⬛🟦🟦⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦⬛🟨🟨🟨🟨🟨⬛🟦🟦⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦⬛🟨🟨🟨⬛🟦🟦🟦⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦⬛⬛⬛🟦🟦🟦🟦⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬛⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬛⬜⬜⬜⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⠀⠀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣸⣿⣿⣿⣿⣿⣶⣤⣀⠀⠙⠿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣇⠀⠀⠈⠻⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠉⠻⠋⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣤⣴⣾⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⢀⣠⣀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉⢠⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢀⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣾⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣾⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠘⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⢿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⢻⣿⣿⣿⣿⣿⡇ ⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣬⣭⣭⣉⣛⣛⠛⠿⠿⠿⠟⠉⠛⠿⣿⣿⣿⣿⣿⣿⡿⢁⣾⣿⣿⠏⠀⠀⢰⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠃⣼⣿⡿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿ ⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣍⣙⣛⠛⠿⠿⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇ ⠈⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣬⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠁ ⠀⢹⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣶⣶⣤⣭⣍⣉⣛⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣶⣶⣦⣬⣭⣉⣛⣛⡛⠿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣄⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣮⣉⣙⣛⠛⠛⠿⠿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⢰⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⡆ ⣾⣿⣿⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣿⣿⡿ ⠸⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⠇ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⠙⠻⢿⡏⠾⠿⢸⡿⠿⠛⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠠⠀⠀⠁⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠂⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⠭⠈⠰⣮⣭⠿⠿⣯⣥⠆⠀⠨⠙⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠩⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠌⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⢐⠀⠀⢀⠀⡈⢑⠀⠀⠀⠀⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣠⣼⣿⣧⣤⣾⣷⣄⣄⣁⣠⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠀ ⠀⠸⡏⠙⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠖⠋⣸⠃⠀ ⠀⠀⢻⠀⠀⠈⢳⡀⠀⠀⠀⢨⢢⠀⢠⠞⠁⠀⢠⡏⠀⠀ ⠀⠀⠈⣧⠀⠀⠀⢻⡀⡠⠔⠊⠀⢣⡏⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⠀⠈⠓⠦⣴⣼⡏⠀⠀⠀⢠⣾⣤⣤⠶⠛⠁⢀⣿⠀ ⠀⠀⠀⠀⠀⣶⠟⢻⣿⣦⣀⣤⣾⣿⡏⠙⢲⠀⠀⣾⣿⡇ ⠀⠀⠀⠀⣸⠃⠀⢀⠀⢹⣿⣿⠃⢀⡇⠀⠘⣶⣶⣿⣿⠇ ⠀⠀⠀⠀⢰⠀⠀⠈⠻⣿⣯⣿⡿⠟⠁⠀⠀⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣄⠀ ⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣦⣴⣴⣤⣶⣤⣾⣿⣿⣿⣿⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣿⠟⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠺⠿⢿⣿⠏⠻⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⣤⣶⣾⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⠿⠛⠛⠛⠿⣿⡿⠿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠼⣿⣿⣿⣿⠏⣠⣄⠀⠀⠀⠀⠉⠀⠀⡈⠻⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠈⠓⠤⡀⠀⠀⠀⠀⠸⠖⢻⣿⣿⣿⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠙⠛⠒⠂⠀⠀⠀⠀⠒⠒⢂⠀⢿⣿⣿⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣄⣿⣷⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣠⣤⣄⠀⠀⠀⠘⠏⠙⢶⡶⠋⠃⠀⣰⡄⢰⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⡌⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⢀⣴⣿⣿⣿⠟⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠈⣿⣿⠟⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋ ⠰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠜⣦⠘⢿⣿⡄⠈⣿⡇⢠⡀⠀ ⠀⠀⠸⠀⢀⢀⠀⠀⢀⢀⢀⠾⠀⠀⠹⡇⠀⣿⠇⣾⡗⠀ ⠀⠀⣀⠀⢺⠃⠀⠀⠁⢿⠀⠁⠀⠀⠀⡇⢀⠟⣼⠏⣠⡇ ⠀⠀⠘⢷⣦⣤⣤⣥⣤⣴⣾⠇⠀⠀⠀⠀⠀⠈⠤⠞⣫⡄ ⠀⠀⠀⠀⢈⠉⠉⠉⣭⣭⣤⠀⣀⡀⠀⠀⠀⠀⠒⠛⠛⠁ ⠀⠀⢠⣾⣿⣷⣀⠀⠘⠿⠟⠀⠻⠿⡇⢰⣶⡔⠾⠟⠁⠀ ⠀⣀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀ ⢸⣿⣿⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠛⠛⠋⣁⣼⣿⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠤⠀⠀⠀⢠⠠⠕⠢⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⡢⠀⠁⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⡀⠄⠢⠢⣀⠉⡄⠀⡀⠀⠀⠱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⢷⠀⡈⡏⠉⣑⠂⠀⢡⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠉⣉⡠⠀⡀⠀⠀⠰⠀⠉⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡛⠦⠄⢤⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣀⡈⣦⣤⡜⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠄⠨⠘⡆⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠆⠐⠃⠀⠀⢀⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⡠⠂⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠊⠐⢦⡀⠈⠑⠢⠤⣔⣁⣈⡀⠀⠀⣀⡀⠜⠂⠁⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⠜⢅⠀⡀⡀⠀⠀⠀⢠⢤⡤⠀ ⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢀⣀⣠⠂⠀⠤⠙⠷⡳⠧⡠⠔⠁⠀⠀⠀ ⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⣦⠀⠀⣿⣿ ⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠘⣿⣧⣀⣼⣿⠃⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⣿⣿ ⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⠿⣿⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⡏⡔⠊⠉⡉⠢⡀⠀⡔⢁⡈⢿⣟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⢤⡔⠊⠟⢢⠱⣠⣷⠁⠘⠛⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⢷⠀⡤⠤⠶⢺⠀⡇⠈⢲⠒⣲⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⡈⢆⠈⠒⠒⢁⡜⠀⠀⡰⢍⣁⠤⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠒⠒⠉⠀⢀⣸⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⢀⣾⣿⠇⠀⠀⣀⠀⢀⣠⣲ ⠘⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⡿⡀⠀⢀⣠⣾⡿⠋⠀⠀⢸⠀⢱⠻⣀⠎ ⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠈⡹⢳⣾⡟⢹⢿⠀⠀⠀⡠⠂⡤⠀⢠⠏⠀ ⠀⠀⢠⣿⣿⣿⣿⠏⡩⠛⠳⠤⠤⠖⠃⠈⠉⠀⠁⢼⡷⠊⠁⠀⠀⠀⢀⠎⠀⠀
⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀ ⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀ ⠀⢸⣦⡙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⣴⡇⠀ ⠀⠈⠻⣿⣦⡙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢋⣴⣿⠟⠁⠀ ⠀⢸⣷⣌⢿⣿⣦⡙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢋⣴⣿⡿⣡⣾⡇⠀ ⠀⠈⠻⣿⣷⡝⢿⣿⣎⢻⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⡟⣱⣿⡿⢫⣾⣿⠟⠁⠀ ⠀⢀⡤⣌⢻⣿⣦⢻⣿⡎⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⢱⣿⡟⣴⣿⠟⣡⢤⡀⠀ ⢀⠘⠶⠟⠀⢹⣿⡇⣿⣿⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⣿⣿⢸⣿⡏⠀⠻⠶⠃⡀ ⠘⠿⢿⠿⠷⢸⣿⣧⣿⣿⣸⣿⡇⣀⣀⣀⡀⢸⣿⣇⣿⣿⣼⣿⡇⠾⠿⣿⠿⠃ ⠹⣶⣶⣶⣦⢸⣿⣿⡿⠿⢿⣿⠁⢿⣾⣿⡄⠈⣿⡿⠿⢿⣿⣿⡇⣴⣶⣶⣶⠏ ⠀⠀⠀⣠⣤⡘⢿⣿⣧⣀⡀⠀⢀⣼⣿⣿⣧⡀⠀⢀⣀⣼⣿⡿⢃⣤⣄⠀⠀⠀ ⠀⠰⠿⠛⠉⣡⣦⠉⠻⠿⣿⣿⣿⣿⣿⡇⢙⣿⣿⣿⠿⠟⠉⣴⣄⠉⠛⠿⠆⠀ ⠀⠀⠀⠀⠐⠛⠁⠀⡿⠂⣤⡍⢻⣿⣿⣿⣿⡟⢩⣤⠐⢿⠀⠈⠛⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡄ ⢿⣟⠛⠛⠁⠀⠀⠀⠀⣠⣾⣿⠋⠁⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠈⠛⠛⣻⡿ ⢰⣿⣿⣷⣶⣶⡶⢀⣾⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⣷⡀⣶⣶⣶⣾⣿⣿⡄ ⠸⢿⣿⣿⣯⣀⠀⣾⣿⣿⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⣷⠀⣈⣽⣿⣿⡿⠇ ⠀⠀⠀⣸⣿⣿⣿⢶⣮⣭⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣤⣴⡶⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⡏⢸⣿⢉⣿⠛⠻⡟⢻⡟⠛⣛⢻⣿⠉⣴⡆⢻⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⠶⣦⣼⣿⣀⣦⡁⢸⡗⠒⣂⣈⣿⣧⣴⠶⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⣭⣝⣛⣛⣛⣛⣛⣛⣫⣭⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠔⢄⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠙⠷⠄⠀⠀⢸⢀⣴⢁⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠊⣦⢤⡀⠀⠂⠀⠀⠀⢸⣿⣿⣿⣃⣤⣖⡄⠂⠀⠀ ⠀⠀⠀⠠⠀⠹⣷⣄⡀⢀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣏⣀⣠⣤⠀ ⠀⠀⢀⠀⠀⠀⢻⣿⣿⣾⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⠛⠓⠀⢀⠻⠿⠿⠛⠓⠂⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⢶⠃⠁⠀⠀⢀⡀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠙⠂ ⠀⠀⠀⠀⣸⡄⠐⠲⠠⠈⠁⠀⠠⢺⣿⣿⡿⢿⣿⣿⣿⣿⡀⠀ ⠀⠀⢀⣾⡇⢝⡀⡐⠆⠀⠀⠀⠡⢸⡿⠉⠑⢄⢀⠙⠟⢿⡧⠀ ⠀⣸⣿⣿⣷⡀⢧⠻⡏⢻⡿⣕⠆⢸⡇⠇⠖⠯⠃⠃⡈⠘⣧⠀ ⢠⣿⣿⣿⣿⣿⣦⣀⣈⣉⠙⠋⠑⢸⠀⠘⠀⠀⠰⢡⡴⠂⢹⠀ ⠘⢿⣿⣿⣿⣿⣿⣿⡤⠖⡂⠀⠀⢸⠀⠀⠀⠀⢀⡟⠇⢸⡘⠀ ⠀⠀⠙⢿⣿⣿⣿⣿⣿⢏⠀⠀⠀⢸⠀⠀⠀⡠⠛⢈⣤⠀⣧⠀ ⠀⠀⠀⠀⠻⡟⠋⠛⣿⣧⡇⡠⡀⢸⢀⠀⠼⠔⢪⣽⠃⠓⠉⠀ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠻⠷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣴⢶⣾⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡀⠀⠀⣀⠀⢉⡶⠠⣤⣀⡀⠀⠉⠉⠛⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡇⠀⠘⢁⣴⣿⠀⠀⣠⣿⣿⣽⣦⣤⡀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀ ⠀⠀⢀⠞⠉⠙⢀⣤⣾⣿⣿⠀⣼⣿⡿⠛⠛⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀ ⠀⣠⠃⠀⠀⠀⠙⢟⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢳⡀ ⠀⠇⠀⠀⠀⠀⠀⠀⠈⠺⣷⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⣧ ⣸⠀⠀⡠⠀⠀⣰⢟⡛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿ ⡇⠀⠊⠀⠸⢿⠿⠆⠀⠌⣿⣿⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣿ ⣧⠁⠀⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⢀⠔⠀⣼⠇ ⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣧⣀⠚⠿⢯⣀⣀⠀⠤⠔⠉⢀⣾⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣯⣿⢿⣿⣿⢄⠀⠀⠀⠀⢀⣠⣴⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠿⣷⣶⣶⣶⣶⠾⠟⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⢿⣿⣿⣷⡄⠀⠀⢀⣴⡟⢩⡟⠀ ⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⡉⠙⠃⢀⡴⠋⠰⢿⡿⠀⠀ ⠈⢹⡌⠉⠓⢦⡀⠀⠀⠀⠀⠀⣠⣴⣶⣴⡾⠃⣤⡌⣄⢠⠊⠀⠀⠀⢸⠁⠀⠀ ⠀⠀⠹⢆⠀⢼⠏⠐⢄⠀⠀⢠⣿⠉⠀⢠⣴⣿⣿⣿⣿⡿⣶⣴⣄⢀⠇⠀⠀⠀ ⠀⠀⠀⠈⢦⢸⠀⣀⣠⣵⣦⣸⡇⠀⣼⣼⠃⠁⢔⣻⡿⡇⠀⠿⠛⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⡟⠻⠉⠋⠀⠈⣿⣶⡷⢺⡅⠀⠜⠉⣠⠀⠀⠀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠁⢹⠓⡌⢁⣀⠀⡀⢹⣦⠀⡰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢸⠇⠀⠜⠙⢿⠶⡏⠉⢿⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣿⡴⠚⡀⠀⢀⣠⡄⢠⢈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣤⣦⣣⠀⠈⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣺⠄⢁⠎⣆⠀⢸⡿⡏⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⡯⠖⢁⣼⣿⠀⠀⠅⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⢤⣄⡸⣈⣿⢿⠤⠒⢂⢴⣒⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⢸⡟⢙⣇⠸⣿⣀⣴⡛⢆⠻⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⣿⣿⠀⠀⠀⣸⠇⢸⡏⢩⠑⣤⡀⣽⡮⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⠻⠄⠀⠤⢘⣣⣼⡇⢸⣾⡇⣾⢩⣤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠋⠉⠉⠉⠉⠈⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣦⠀⠀⣠⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢟⣠⣴⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷ ⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⣼⣿⠇⠀⠙⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⢀⣾⣿⣋⠀⠀⠀⠈⠋⠁⢀⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠙⢻⣿⡇⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣧⣤⣤⡀⠀⠀⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⠟⢻⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣴⣿⡿⠃⠀⠘⢿⣷⣦⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠟⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⣿⣿⣿⣷⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⡿⠟⠛⠋⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣀⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀ ⠈⠻⣿⣿⠀⠄⠀⠶⠒⡄⠀⡀⠒⠒⠶⠶⢖⡂⠤⡀⠈⣿⣿⣿⣿⣿⣿⣿⡶⠂ ⠀⠀⡄⢉⡖⠉⠀⠈⢢⡧⠤⡇⢠⠊⠉⠉⠑⡄⠀⡇⠀⢿⣿⣿⣿⣿⣿⣿⣷⡆ ⠀⠀⠀⡠⢫⠀⠀⠀⡸⠁⠀⣇⢸⠁⠀⠉⠁⡗⠂⣇⣠⡟⢉⠛⣿⣿⣿⣿⠟⠁ ⠀⠀⠘⡇⠠⠭⠤⠼⢅⣀⡠⠤⠵⢑⣒⣐⣊⣀⢠⠋⠉⢠⠓⢢⣿⡟⠋⠁⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠈⢢⡭⠯⠭⠵⠶⣤⡀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠾⢄⠀⠀⠙⠒⠒⠒⠈⠁⠀⠀⠀⠀⢀⠜⠀⡹⠿⣛⠓⠂⠀⠀⠀⠀ ⠀⣠⠋⠀⠘⡀⠠⡀⠰⢄⣀⣀⠀⠀⣀⣀⡀⠔⠁⢀⠜⠁⠀⠀⠉⠲⢄⠀⠀⠀ ⠰⠃⠀⠀⠀⠐⠄⡠⠟⠒⢲⡄⠒⠉⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀
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⠀⠀⠀⢀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣆⣀⣬⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀ ⠀⠀⠀⠀⠘⣷⣿⡟⢻⣽⣿⡶⣞⠍⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⢹⣦ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⢑⣌⣦⡷⠂⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⠘⣧⠀⠈⠻ ⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡟⠉⠁⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⠻⠛⠀⠀ ⠀⠀⠀⣠⡀⠀⢸⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠹⣷⣮⡻⣿⣿⣿⣦⡀⠀⠀ ⡶⣶⡞⠻⠟⠿⢷⡻⡇⢿⣿⣯⣶⣽⣿⡿⠋⠀⠀⠀⠙⠿⢿⡄⠉⢩⣿⡗⠀⠀ ⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⢿⡿⠟⠛⠁⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⢸⣿⠁⠀⠀ ⠀⠀⠶⣾⣟⠉⠇⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⣼⡏⠀⣀⣀⣾⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⠛⠃⠀⠛⠟⠏⠙⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣴⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⡿⠛⠋⠉⠉⠛⠛⠉⠉⠙⠛⢿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀ ⠀⠀⢰⣿⡏⠀⠀⠀⣠⣴⣶⣤⣤⣶⣦⣄⠀⠀⠀⢹⣿⡄⠀⠀ ⠀⠀⣿⣿⠁⠀⠀⣼⣿⠋⠉⠛⠛⠉⠙⣿⣧⠀⠀⠈⣿⣿⠀⠀ ⠀⢰⣿⡇⠀⠀⣰⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⡆⠀⠀⢸⣿⡆⠀ ⠀⣾⣿⠁⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠘⣿⣷⠀ ⠀⣿⡿⠀⠀⢸⣿⠿⣿⣶⡄⠀⠀⢠⣶⣿⠿⣿⡇⠀⠀⢿⣿⠀ ⢰⣿⡇⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⢸⣿⡄ ⢸⣿⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣼⣿⡇ ⣿⣿⣿⣿⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣿⣿⣿⠷ ⠉⠉⣿⣿⢸⣿⣿⠀⠀⠶⠿⠛⠛⠿⠶⠀⠀⣿⣿⡇⣿⣿⠉⠀ ⠀⠀⣿⣿⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⣿⣿⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠈⠻⣷⣾⣿⣿⣷⡾⠟⠁⠀⠀⠀⣿⣿⠀⠀ ⠀⠀⠻⠟⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠻⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠤⠤⠤⠤⢀⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠂⠈⠉⠁⠒⠄⠠⡄⠐⠀⠁⠀⠀⠀⣔⢺⠂⠄⡂⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠃⢀⠀⠀⠀⠀⢀⠌⠀⠘⢄⡀⠀⠀⠀⠀⠀ ⠀⡀⠜⠀⠀⠠⠄⡀⠐⠔⠈⠄⠀⠀⢀⢠⠌⠀⠀⠙⠀⠱⡀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠈⠓⠄⢸⢀⠔⢀⢪⠹⠀⠀⠀⠀⠠⠤⠨⠅⠀⠀⠀ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠌⠰⠀⡅⠆⠀⠀⠀⠏⠑⠄⡀⠀⠀⠀⠀ ⠀⣱⡀⠀⠀⠀⠀⠀⠀⠂⢸⡀⣆⠴⠈⠀⠀⠀⠀⠰⠀⠀⠈⠄⠀⠀⠀ ⠘⠀⠐⢄⠀⠀⠀⠀⢇⡢⠚⠺⠊⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠈⠄⠀⠀ ⠘⡀⠀⠀⠑⠄⡀⠀⠈⢄⠀⠐⠇⣶⢺⠀⠀⠀⢀⣸⠀⠀⠈⢢⠀⠀⠀ ⠀⢐⢄⠀⠀⠀⠸⡲⡄⡀⠢⡀⢤⢼⠈⠉⢠⠶⢚⠇⠀⠀⠀⠀⢡⠀⠀ ⠀⠆⠀⠑⢄⠀⠀⠡⡇⠀⠉⡸⠚⡼⠀⡌⡇⠀⠆⠀⠀⠀⠀⠀⠀⡆⠀ ⠀⠐⠄⠀⠀⢳⠠⡀⠑⢤⡀⠤⢊⡇⠰⢀⠀⠘⠀⠀⠡⠠⡀⠀⠀⠇⠀ ⠀⠀⠀⠐⠤⣀⠣⡈⢱⠒⠱⢤⣠⠁⡇⠙⠀⠇⡀⠀⠀⠑⢄⠁⠂⠈⠠ ⠀⠀⠀⠀⠀⠀⠈⣟⡺⠂⠀⢠⠚⠒⡟⠀⠇⢈⠴⠀⠐⠀⠠⠤⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣴⣶⣾⣿⣿⣷⣶⣦⣀⠀⠀⠀ ⠀⢀⣼⣿⠛⠉⣀⣤⣤⣀⠉⠛⣿⣧⡀⠀ ⢀⣾⡿⠁⢠⣾⣿⡿⢿⣿⣷⡄⠈⢿⣷⡀ ⢸⣿⡇⠀⣾⣿⣯⠀⠀⣽⣿⣷⠀⢸⣿⡇ ⠸⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⠇ ⠀⠹⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠏⠀ ⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀ ⠀⢀⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⡀⠀ ⠀⢸⣿⡇⢸⣿⣿⡟⢻⣿⣿⡇⢸⣿⡇⠀ ⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀ ⠀⢸⣿⡇⠀⣀⣀⣀⣀⣀⣀⠀⢸⣿⡇⠀ ⠀⢸⣿⡇⠀⢿⣿⣿⣿⣿⡿⠀⢸⣿⡇⠀ ⠀⢸⣿⡇⠀⠘⣿⣿⣿⣿⠃⠀⢸⣿⡇⠀ ⠀⢸⣿⡇⠀⠀⠘⢿⡿⠃⠀⠀⢸⣿⡇⠀ ⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀
⠀⠀⠀⠀⣀⠠⢤⡄⠠⡄⠠⢤⣄⣀⡀⠀⠀⠀⠀ ⠀⠀⡖⠿⢸⠘⣻⡇⠃⡇⠘⣾⡟⡄⡿⢑⣦⢄⡀ ⠀⠀⢹⣴⡼⠦⢤⣧⠤⣥⣉⣿⣠⡄⠇⣾⡏⣰⡿ ⢀⣤⣶⣾⣿⣿⡏⣿⠀⢸⠃⢸⢉⢹⡖⢾⣌⣽⠃ ⠸⣏⡏⡽⣿⣿⣧⢻⠀⣄⠀⡎⠘⢸⢰⠆⣿⠃⠀ ⠀⢹⡞⡻⢻⡏⢿⣈⢀⢉⢐⡃⠧⢌⣈⣰⠃⠀⠀ ⠀⠀⢳⣾⣿⣷⣥⡏⣨⢸⢐⡆⢼⠐⢌⠋⠀⠀⠀ ⠀⠀⠀⣭⣷⣶⣶⣶⣯⣟⢌⢣⡾⢘⡟⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣟⠛⠛⠻⠿⣷⣝⠇⢻⢣⠤⣄⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠙⢷⣝⣾⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⡶⠛⠉⠁⠀⠉⠙⠳⣄⠀⠀⠀⠀⢠⡞⠁⠀⠀⠈⢿⣿⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠏⠀⠀⠀⢀⣴⣶⣄⠀⠈⢳⡀⠀⢀⡿⠀⣴⠞⠳⢦⣼⣿⣿⣇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣤⣤⠶⠛⠁⣾⠏⢳⡄⠀⢷⡀⢸⡇⣼⠃⠀⠀⠻⠛⢹⣿⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢻⡇⠀⠀⠀⠀⠀⠀⢿⡀⠸⣿⠙⠳⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠸⣧⣤⣤⠶⠶⠶⠶⣿⠇⠀⡿⠀⠀⠈⠻⣟⠛⠉⠙⣻⠏⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡀⠀⠹⣧⡀⠀⠀⢀⣴⠟⠀⣸⠇⠀⠀⠀⠀⢹⣦⣴⠾⠋⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠳⣄⠀⠈⠙⠛⠛⠋⠁⠀⣰⠟⠀⠀⠀⠀⣠⣾⣧⣀⣀⣀⣤⠾⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠳⣤⣀⣀⣀⣀⣴⠞⠋⠀⠀⠀⠀⣰⠟⠀⠀⠉⠉⠉⠁⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢛⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⣾⣉⢻ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢸⡇⠈⢳⣤⣴⣟⠭⢹⡆⡾ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⣦⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⢀⣾⠇⠀⢸⡟⠉⢻⡄⢸⡟⠁ ⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠘⠻⠶⣶⣟⣠⣤⣴⣾⣿⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠸⠃⠀⢀⣧⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣰⠏⠉⣿⣿⣿⡿⠁⢀⣿⠙⣧⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⡶⠞⠀⠀⠀⣸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⣷⣽⣷⣄⡀⠀⠀⢀⣀⣠⡿⠀⠀⠹⠿⠋⠀⠀⠾⠃⢀⣿⣷⣶⡶⠶⠛⠉⠀⠀⠀⠘⠁⠀⠀⠀⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠴⠟⠁⠀⠉⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠰⢰⠰⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣣⢎⠀⢠⡇⢸⡇⠂⢹⡔⡄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⢀⢄⣾⡿⣫⠇⣀⣾⡇⣿⣧⠰⡄⢳⣽⡄⢱⡀⢰⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢡⡏⣾⡟⢰⡿⢰⣸⣿⡷⢸⡟⡇⢻⡌⢻⣷⣸⣷⡈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⢸⣿⠁⢸⠇⣼⣿⡿⠀⠹⣷⢹⡸⣿⡆⡹⣿⣿⣇⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⡧⢐⢼⢀⣿⣿⡇⠀⠀⢿⣿⡇⢻⡇⣿⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡏⠃⠈⢻⠘⣿⡇⡏⠒⠲⢼⣿⣿⢸⣇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡇⠀⠀⠀⠂⠹⡇⠁⠀⠈⠈⣿⣿⣼⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⢸⢿⠹⣼⡟⡿⢹⣿⠇⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠘⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢈⣾⡟⣹⣣⣿⢻⣤⣰⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡗⠀⠀⠁⠀⠀⠀⠀⠀⠀⣡⣿⢿⣿⣿⣻⢷⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⡠⠤⠒⢉⣨⣷⠿⢿⡿⢓⣿⣉⣭⡿⢿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⡿⠶⠶⠚⠛⠋⠉⢀⣤⠞⢛⡩⢐⡏⣿⡿⣧⣦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⡴⠛⠁⠀⢀⡔⠋⣆⡹⣿⣯⡯⡙⠃⠀⠀ ⠀⠀⠀⠀⠀⠴⠶⠶⢶⣿⠏⠀⠀⣁⣠⡤⠴⠾⣛⣁⣴⡉⠛⢿⣿⣿⣿⣷⡆⠀ ⠀⠀⠀⢴⡇⠀⠠⠖⠋⠡⠴⠒⠉⠀⠀⣔⣬⣽⣿⣿⣿⣿⣦⣤⣌⠙⠻⣿⡿⠂ ⠀⠀⠀⠀⠉⠀⠀⠀⢠⣴⢂⡾⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⡇⠀ ⠀⠀⠀⠀⠀⡠⠀⢀⣼⡿⢋⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣏⠀ ⠀⢠⡇⠘⠋⠀⠀⣹⡟⣡⡿⢿⣿⣿⣿⣷⣻⣿⡘⣿⣏⠻⣿⣿⣽⡛⠇⠘⢣⠀ ⢠⣾⣧⣴⢶⣾⡿⢋⣼⣿⣿⣾⣿⣿⣿⣿⣟⢿⣇⢿⣿⣆⠈⠻⣿⣿⡇⠀⣿⡆ ⢸⣿⣿⣿⢸⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣾⣿⣿⣷⣤⣈⠻⣧⠀⣿⡇ ⢸⣿⡿⢇⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣿⣿⣿⣿⣿⡿⠟⠀⠉⠀ ⠀⠋⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣇⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⢋⡝⣿⣶⣶⣶⡶⠀⠀⠀⠀⠀⢠⢠⢀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠤⠤⠥⠤⠀⠀⠀⠀⠀⠘⣿⣿⡟⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠖⠚⠂⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣇⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣀⣴⣶⣶⣾⣿⣿⣿⡿⠋⠁⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀ ⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀ ⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠿⠋⠛⠀⠀⠀⠀⡀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣾⡄ ⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⠀⠀⠈⣿⣿⡗ ⠀⠰⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡟⠁ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⡿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠙⠀⠋⠘⠉⠉⠁⠈⠉⠛⠋⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠀⠀⢀⣴⣇⡀⠀⠀ ⠠⠾⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣾⣿⣿⠤⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀ ⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣇⠀⠀⣠⣾⣿⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣒⠉⠉⠑⠢⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠤⠴⢯⠔⢀⡠⠔⠓⠊⠉⠉⠉⠉⠒⠊⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⢋⠀⠀⠠⠃⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀ ⠀⠀⢀⠴⠓⡆⠀⡠⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠃⠀⠀⠡⠊⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠤⠐⠁⠀⠈⢀⠀⢸⠀⠀⠀ ⠀⡿⠖⡇⢠⠃⠀⠀⠀⠀⠀⢀⡴⠊⢀⠤⠒⠒⢄⠀⠀⠀⢀⠤⠘⠦⣸⠀⠀⠀ ⡼⠀⠀⠇⢸⠀⠀⠀⠀⠀⢀⠎⠀⠐⡏⠉⣉⠉⠉⢣⠀⠠⠓⠉⡉⠉⠙⡟⠀⠀ ⢇⣠⡆⠀⢸⠀⠀⠀⠀⠀⡌⠀⠀⠀⢃⡀⠀⠀⢀⠎⠀⠀⠱⡀⠀⠀⠠⡇⠀⠀ ⢸⠁⢣⠀⠸⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠘⠖⠈⠁⠈⠆⠀ ⢠⠀⡀⠁⢀⠧⣤⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⡆ ⠈⡆⢇⠀⢎⠀⠌⢄⡀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⢹ ⠀⡇⠈⠢⠈⠢⢤⠀⠈⠐⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢸ ⠀⠱⡀⠀⢄⠀⠀⢆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⡜ ⠀⠀⠈⠳⡈⠒⠤⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠁ ⠀⠀⠀⠀⠈⠂⠤⡄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠲⡶⠥⣈⣩⠭⠃⠀⠀⢀⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⢁⣢⣄⠀⠀⠀⠀⠈⠒⠒⠊⠀⠀⡠⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⢑⡄⠀⠀⠀⠀⢀⠔⠲⢍⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡇⠉⠒⠒⠀⡀⡜⠈⠀⠀⠈⠢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠊⠐⢄⡀⠘⠅⠂⠤⠤⠁⠡⠜⡄⠀⢀⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣌⠔⠒⠢⡀⠉⢢⠈⢆⠀⠀⠀⠀⠀⠘⡠⢻⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠘⡄⠀⠑⠌⠆⠀⠀⠀⠀⠀⠇⢸⠸⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣤⣄⣀⢀⣀⣤⣴⣶⣾⣿⣿⣗⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀ ⠀⠀⠀⠸⢿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⡷⠀ ⠀⠀⠀⠀⠜⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⠀⠀⠀⠸⣿⣿⣿⣿⣷⡀ ⢴⣤⣤⣼⣤⣤⣤⣤⣤⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⣿⣿⣿⣿⣿⣧ ⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀⡿⠀⠠⠤⠤⠤⠤⠤⢤⣿⠛⢷⣿⣿⣿⣿⡏⠀ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠟⠉⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿⣿⣿⣿⠃⠀ ⠀⠙⠛⠟⠛⠛⠛⠛⠃⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠲⠖⠋⠀⠀⠋⢁⡤⠙⡇⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀ ⠀⠀⠀⢁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡔⠊⠀⠀ ⠀⠀⠀⠈⠄⠀⠈⠁⢆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⡠⣀⣀⠀⠀⠀⠀⢰⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇⠀⠀⠀⣀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⢀⣰⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠀⠉⢠⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣰⡏⢸⡇⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣉⣉⣉⣉⣉⣉⣉⣀⡿⠀⠀⠀ ⠀⠀⠀⠰⣏⠁⠉⠉⠉⠙⣷⠀⠀⠀⠀⠈⠉⠉⢹⣏⣉⣉⣿⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢻⡟⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⣘⣧⣀⡀⠀⠀⠀⠀⠀⠀⢸⠇⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠉⠉⠛⠛⠛⠛⠓⠶⠿⠶⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠀⢠⡾⠛⠳⣄⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠙⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⢸⣇⣸⣦⡟⠀⠀⠀⠀⠀⠀⢿⣁⣨⡗⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣦⡀⠉⠉⠙⠷⠆⠀⠀⠀⠀⠀⠈⠉⠉⠀⣠⡟⠀⠀⠀⠀⠀ ⢰⡶⠶⠶⠶⠾⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠶⠶⠶⠶⢶⡆ ⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⢀⠠⠒⢀⣬⠏⠉⠁⢲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠊⠀⠀⠀⠘⠉⠀⠀⠀⢸⡏⠀⠈⠒⠒⠒⠀⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⢠⠁⠀⠀⠀⠘⡈⠀⠀⠀⢀⢀⠔⠈⢀⡀⠤⠒⣒⣒⡄⠀⠀⠟⠉⠉⠐⣄⡀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⡠⠊⠁⠀⠀⠀⠠⠠⡅⠀⠀⠀⠀⠀⠠⡾⣿⡆ ⡇⠀⠀⠀⠀⠈⠢⡀⠀⢀⠁⠀⠀⠀⠀⣠⣦⣴⠾⠋⡁⠀⢀⣴⣶⢠⢹⢗⣿⣿ ⢃⠀⠻⠂⠀⠀⠀⠈⠄⠸⠀⣸⠇⣀⣠⣿⣟⣀⠀⡇⠀⠀⠘⣿⡏⡄⢩⣏⢸⣿ ⠈⢷⣿⠀⠀⠀⢀⣀⠘⡄⠙⢿⣷⣿⡿⠋⢈⡟⠀⢘⠀⡠⢄⠏⠣⠢⢼⣿⣿⠏ ⣀⣼⣿⣇⣀⠀⠈⢿⠀⡁⠀⠀⢀⣀⣠⡶⠀⠃⠀⣀⣉⡀⠀⠀⣀⣀⣼⡿⠁⠀ ⣿⣿⣿⣿⣿⣧⣴⣆⣠⡇⣰⣦⣾⣿⣿⣧⡴⠿⠛⠋⠀⠀⣀⡀⣲⣂⢸⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣶⣆⣠⣷⣾⣯⣭⣻⣿⣿⠃⠀⠀ ⠀⠀⠉⠉⠉⠉⠁⠉⠛⠛⠉⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⣿⣿⠿⠿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⡇⠀⠀⠀⠀⠈⠛⢿⣿⣯⡛⠛⠉⠙⣿⣋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠀⣼⠃⠀⢀⣤⣤⣄⣀⣀⡈⠻⣿⣷⣤⣤⣤⣽⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠃⠀⢠⡟⠀⠀⠀⠈⢹⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⣻⣆⣿⠀⠀⠸⡇⠀⠀⠀⠀⣾⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠿⠉⢉⠀⠀⠀⠙⢦⣤⣤⡴⠟⠀⠀⠀⠀⢿⣿⣿⡿⠟⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠘⣧⡀⠀⠰⣤⣤⣤⠆⠀⠀⠀⠀⠀⢸⣧⣤⡶⠆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣼⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣄⡀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⡀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠉⠉⠉⠉⠉⠙⣷⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠋⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣾⠁⢿⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣷⣿⣤⣾⣇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠘⢷⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣧⡉⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣀⡀⠀⠀⠀⢀⣴⠋⠀⠀⠘⣧⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⢿⣿⣿⡿⠀⢹⣿⣿⣦⣄⠈⠉⠛⠷⠶⠤⠴⠶⠛⠁⠀⠈⠙⠛⠶⢶⣟⡁⠀⠀⠀⠀⢻⡄⠀⠀⠸⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠈⠹⡇⠀⠀⣻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢁⡴⠶⢦⣤⣘⡇⠀⠀⠀⣽⣿⣿⣆⠀⠀ ⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠛⠁⠈⠛⠿⡿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡴⠋⠀⠀⠀⠀⠉⣣⣶⣶⡈⢻⣿⣿⣿⡆⠀ ⠀⢠⣿⣶⣿⣆⠀⠀⠀⠀⠀⢀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠛⠋⠛⢦⣄⠀⠀⠀⢀⡴⠋⠐⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣿⣿⣿⣿⣿⡀ ⠀⣾⣿⣿⣿⣿⣇⣴⣾⣶⣤⣸⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣤⣄⡀⢀⣀⠀⠈⠛⢶⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣹⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⠀⢀⣤⣿⠉⣿⣿⣷⡀⣀⣀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⢻⣿⡿⠁⣷ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣏⣀⠀⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠉⠁⠀⢿
⢰⣿⡆⢀⣤⣴⣶⣶⣤⣀⠀⣿⣇⠀ ⢸⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠇ ⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠀ ⠘⢿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡿⠋⠀ ⠀⠀⣽⣿⣿⣿⣶⣾⣿⣿⣿⡄⠀⠀ ⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀ ⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀ ⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⡇ ⣿⣿⠀⠸⣿⣿⣿⣿⣿⡿⠀⣼⣿⠇ ⢸⣿⠀⠀⠻⠿⠿⠿⠟⠃⠀⣿⣿⠀ ⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀ ⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀ ⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢾⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠁⠀⠀⢀⣀⠠⠬⢉⣸⡯⠁⠀⠀⠈⠁⠀⠢⡄⠀⠀⠀ ⠀⠀⠀⠀⡘⠀⠀⢀⡠⠔⡊⢅⡪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢀⠃⠀⠀⢈⡴⢊⠔⠁⠀⠀⣀⠠⠀⠀⠒⠫⠉⠃⠐⡘⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⢉⠔⠁⠀⠀⠀⠇⠀⡀⠀⠀⣤⠀⡀⢳⡊⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡀⢠⠋⠀⠀⠀⠑⡀⠀⠈⠋⠀⠀⠀⠀⠀⡨⡇⢀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠿⠀⠀⠀⠀⠀⡁⠀⠴⠀⠀⠀⠀⠈⡉⠜⠀⠀⢱⠀⠀ ⠀⢀⠔⠂⠉⠀⠀⠀⠀⠀⣠⠾⡥⠄⠤⠤⠤⠴⠢⢅⡀⠃⠀⠀⢼⠆⠀ ⣰⠁⠀⠀⠀⠀⠁⠀⠀⢸⠧⠊⠀⠀⠀⠀⠂⠤⠈⠢⡈⠒⢤⣈⠌⠀⠀ ⢃⠀⠄⠀⠂⡄⠀⠀⢰⠁⠀⠀⡠⢲⠥⠄⠀⠀⠀⠀⠐⢄⠀⡵⠀⠀⠀ ⠀⠑⠈⠦⣁⣃⠀⠀⠘⠦⠀⣀⣀⡘⠀⠀⠀⠀⠀⠀⠀⠈⢏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⢂⠩⠙⠁⠀⠀⠀⠀⡀⠀⠀⠀⠠⠉⢀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠠⠆⠀⢄⠘⠀⡠⠢⢄⠀⣠⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠖⠀⠰⠦⠳⠀⠉⠉⠙⡄⠀⠀⢱⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⠀⠀⠀⠀⠀⠒⠒⠎⠄⠒⠒⠋⢠⠱⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠈⣆⢀⡘⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠬⠆⠤⣀⠈⠀⠀⠀⠀⠈⣀⣟⢀⣀⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⣔⣊⣉⠀⠐⢶⠐⠒⠂⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢸⡥⠯⠵⠯⣄⣀⠀⠀⠀⠀⠉⠑⠢⣶⣾⣿⣿⣿⡷⠖ ⠀⢀⠀⠀⠠⠴⠃⠀⠀⠀⢀⡤⠀⠚⢟⡦⣄⠀⠉⠒⠀⠀⠙⠻⣇⠁⠀⠀ ⢀⣿⠀⠀⠄⠸⢀⠀⣠⣤⣂⣨⣦⣴⢋⠄⠈⣷⣦⡀⠀⠈⠂⢄⡈⠳⣄⠀ ⠘⣿⠷⠃⣠⡀⣼⡶⠒⠒⠀⣀⣠⡤⢤⠽⠮⠁⠁⠉⢢⡀⠀⠀⠹⠷⠾⠃ ⠘⣿⠀⡾⠟⠛⠙⠓⠌⠁⠈⢉⢭⣀⣠⣄⠀⠀⠀⠀⠀⢿⣆⠀⠀⠈⠄⠀ ⠨⢚⣆⠁⠀⠀⠀⠀⣀⠄⠂⡍⠀⠇⠀⠙⢀⠀⡀⠀⠀⠀⠙⣆⠀⠀⠘⠀ ⠀⠁⠈⠑⠂⠤⠤⡔⠁⠀⠀⢸⠎⠀⠀⠀⡈⠀⠀⠉⠒⢄⢠⠉⢆⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⣸⡀⠀⠀⠀⠀⢈⡿⢇⠈⡄⠀⡇ ⠀⠀⠀⠐⠠⣤⣬⣷⣀⠀⢠⠀⢀⡠⢜⢃⠷⠶⠶⠖⣺⠟⠀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠔⠁⠙⠉⢉⡝⠿⠄⠁⣒⣒⣶⠖⠚⠁⠀⠀⠀⠈⠶⠀⠀ ⠀⠀⠀⠀⠀⡌⠠⠀⠀⠀⣈⠀⠀⢀⠠⢣⠀⢀⣑⠄⠀⠀⠀⠀⠘⠃⠀⠀ ⠀⠀⠀⠀⠀⢧⢂⢀⢆⡀⠁⢀⠀⡙⠀⠀⠀⠎⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠋⠉⠀⠀⠉⢁⣁⠰⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⠿⠋⣁⣤⣿⣿⣤⣈⠙⠿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠋⣠⡾⠛⢉⣿⣿⡉⠛⢷⣄⠙⣿⣧⠀⠀⠀ ⠀⠀⢸⣿⡇⢰⣿⠁⣴⣿⠿⠿⣿⣦⠈⣿⡄⢸⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀ ⠀⢰⣿⡿⠛⠉⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠉⠛⢿⣿⡆⠀ ⠀⠀⢻⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⡟⠀⠀ ⢠⣤⡀⢻⣿⡄⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢠⣿⡟⢀⣤⡄ ⢸⣿⣇⣴⣿⣿⡄⠀⠀⢸⣿⣿⡇⠀⠀⢠⣿⣿⣦⣸⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⡿⠋⠙⠛⠛⠛⠻⠟⠛⠛⠛⠋⠙⢿⣿⣿⣿⡇ ⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇ ⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀ ⢀⣠⣴⣿⣿⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣿⣿⣦⣄⡀ ⠻⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣠⣾⣆⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠋⠉⣿⡏⠉⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣰⣿⣧⡀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡏⠀⢸⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⡄ ⠈⣿⣿⠉⠉⢹⣿⡏⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢹⣿⡏⠉⠉⣿⣿⠁ ⠀⠸⠿⢿⣿⣾⣿⣧⣄⣠⣾⣿⣿⡟⠉⢹⣿⣿⣿⣆⣀⣼⣿⣷⣿⡿⠿⠇⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠿⠀⠸⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣾⣯⣍⡒⠒⠒⠒⣒⣒⠒⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠑⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⣦⡀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣵⣶⣶⣶⣶⣶⣶⣶⣤⣽⡄⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉⠉⣉⣽⣿⣿⣏⡀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣴⣿⡿⢿⣿⣶⣄⣀⣠⣾⣿⣋⣉⣙⣻⣿⣄⠄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⠓⠒⠒⠺⠿⣿⡿⠿⣿⠁⠀⠀⠀⠉⢹⣿⠉⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡟⠀⠈⢣⠀⠀⠀⢀⣾⣿⡄⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣷⣄⣀⣀⣠⣾⡿⠃⠀⠀⠀⠳⣶⣾⡿⣿⣿⣝⡄ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⣸⠂⠀⢸⣿⣿⣷ ⣾⣿⣿⣿⣿⣿⣿⣿⢇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠚⠉⠀⠀⠀⢸⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠀⠀⠀⠀⣼⣿⣿⠃ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷⣄⠀⠀⠀⠲⣾⣿⣻⠛⣿⣹⠄⠀⣠⣾⣿⣿⠏⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣤⡀⠈⠛⠿⠟⢁⣠⣴⣿⣿⡿⠟⠁⠀⠀ ⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣤⣀⣀⢠⠜⢱⣿⣿⣷⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⡟⢻⣿⠀⢹⡟⠻⣿⣿⣆⠀⠀⠀ ⠀⢠⣿⣿⡟⢀⣼⣿⠀⣸⣿⡄⠙⣿⣿⡆⠀⠀ ⠀⣼⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⠀⠀ ⠀⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⠇⠀⠀ ⣀⡀⠈⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠃⢀⣀⠀ ⣿⣧⣀⣀⠻⣿⣿⣿⠀⢸⣿⣿⡿⢁⣀⣸⣿⡇ ⣿⡿⠿⠿⢿⣿⣿⣿⣀⣼⣿⣿⡿⠿⠿⢿⣿⡇ ⣿⣿⣶⣤⣄⣿⣿⣿⣿⣿⣿⣿⣠⣤⣶⣿⣿⡇ ⣿⡏⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⢸⣿⡇ ⠉⠁⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⡌⠉⠉⠉⠙⢶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⢻⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣀⣀⣀⡀⠀⠿⠿⢿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣉⡉⠡⠤⠄⠒⠒⠒⢲⣶⣶⣶⢂⣼⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣏⠁⠄⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢸⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⢀⠠⢀⡀⠀⠀⠀⢀⠔⠀⢰⡹⣿⣿⢸⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⣧⡇⠇⠀⠀⠘⠢⠀⢀⠃⠀⠀⢠⢳⣿⡏⣄⠀⠀⠀ ⠀⠀⢻⣿⣝⣿⣿⣿⣿⡇⣿⣿⣌⡂⢄⣀⣀⠃⠀⠢⠤⢐⣵⣿⡿⢠⠿⣿⣿⢢ ⠀⠀⠀⠹⣿⣿⣿⣟⠻⠷⠿⢿⣿⣿⣦⣀⣀⣀⣀⣀⣠⣿⣿⠿⠷⠷⠛⣋⠡⠊ ⠀⠀⠀⠀⠈⠛⢿⣿⣿⠗⠒⠒⠀⠀⢤⣤⣤⣤⣤⣤⣤⠄⠐⠒⠒⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣁⣀⠀⠀⠈⠂⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⠩⠤⠤⠭⠯⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣻⠀⠀⠈⣣⣤⣶⣶⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣥⣀⣀⣹⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡌⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣾⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⠀⠀⣠⣴⣾⣿⠿⣿⣿⠡⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀ ⠀⣼⣿⠟⠙⠄⠀⠸⡇⠀⠐⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠙⠀⠐⢀⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠙⠢⠄⠠⠠⠀⠀⠀⠀⢠⣤⠾⠄⠀⠂⢠⠓⠊⢀⠀⠀⠂ ⣿⣿⣿⡆⠀⠀⠘⡀⠀⢄⠀⠀⡄⠀⠄⠁⠀⠀⣿⣿⠌⠉⠀⢤⣄⡄⡌⠀⠀⠀ ⣿⣿⣿⣷⣶⠀⠀⠀⡨⠊⠀⡀⠂⠀⠀⠀⠀⠀⣿⣯⡐⣀⠀⠘⢂⠁⠀⠆⠀⠀ ⠸⣿⣿⣿⣿⣷⣶⣾⠁⠀⠀⠀⠘⠐⠀⡀⠀⠘⢿⣿⡿⠃⠀⠔⠀⠀⢸⠀⠀⢰ ⠀⠙⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⢀⠀⠀⠁⠠⢈⠟⠠⠀⠀⠀⠀⠀⡞⠀⠀⢸ ⠀⠀⠈⠻⣿⣿⣿⣿⣆⠈⠀⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠈⠿⣿⡿⠿⠿⢿⣿⠿⠁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⢀⣤⡄⠀⣀⣸⣿⣿⣿⣿⣷⣤⣿⡇⢠⡄⢸⣿⣤⣾⣿⣿⣿⣿⣇⣀⠀⢠⣤⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠸⣿⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣇⢰⡆⣸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⠇ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠀⣿⣿⡘⢃⣿⣿⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⡿⣿⠋⣹⣏⠙⣿⢿⣿⣦⡀⠀⠀⠀ ⠀⠀⢠⣿⡿⠁⣠⣿⣿⣿⣿⣿⣿⣄⠈⢿⣿⡄⠀⠀ ⠀⠀⣾⣿⠁⣼⣿⣿⣿⡿⢿⣿⣿⣿⣧⠈⣿⣷⠀⠀ ⠀⠀⣿⣇⠀⣿⣿⣿⣯⡀⢀⣽⣿⣿⣿⠀⣸⣿⠀⠀ ⠀⠀⢻⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⡟⠀⠀ ⠀⠀⠈⢿⣿⣄⠈⠻⠿⢿⡿⠿⠟⠁⣠⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣶⣦⣼⣧⣴⣶⣿⡿⠋⠀⠀⠀⠀ ⠀⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣀⠀ ⢸⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⡇ ⢸⣿⣷⣧⡀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣼⣾⣿⡇ ⢸⣿⣿⣿⣷⡀⠀⢿⣿⣿⣿⣿⡿⠁⢀⣾⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⡄⠀⠉⠉⠉⠉⠀⢀⣾⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⡇ ⠸⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠇
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⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⡿⠛⠋⠉⠉⠙⠛⢿⣿⣦⡀⠀⠀⠀ ⠀⠀⢠⣿⡿⠁⣠⣾⣿⣿⣿⣿⣷⣄⠈⢿⣿⡄⠀⠀ ⠀⠀⣾⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣷⠀⠀ ⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⠀⠀ ⠀⠀⢻⣿⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣿⡟⠀⠀ ⠀⠀⠈⢻⣿⣄⠈⠻⠿⢿⡿⠿⠟⠁⣠⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠙⠿⣿⣶⣦⣼⣧⣴⣶⣿⠿⠋⠀⠀⠀⠀ ⢀⣤⣤⣤⣤⡄⠀⢿⣿⣿⣿⣿⡿⠀⢠⣤⣤⣤⣤⡀ ⢸⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⡏⠉⠙⣿⣿⣿⣿⠋⠉⢹⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⡇⠀⠀⠈⠛⠛⠁⠀⠀⢸⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇ ⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀ ⠀⠘⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠃⠀
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣄⣠⣶⣶⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⣿⣿⠀⣿⡟⢻⣿⠀⣿⣿⣿⣿⣿⡇⠀ ⠀⠸⣿⣿⣿⣿⣿⣦⣿⡇⢸⣿⣴⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠹⣿⣿⣿⣿⠻⣿⣷⣾⣿⠟⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠙⠿⣿⣿⣄⣿⣿⣿⣿⣠⣿⣿⠿⠋⠀⠀⠀ ⣤⣄⠀⠀⠀⣿⣿⠛⠿⠿⠿⠿⠛⣿⣿⠀⠀⠀⣠⣤ ⣿⣿⠀⠀⠀⣿⣿⣤⣤⣴⣦⣤⣤⣿⣿⠀⠀⠀⣿⣿ ⣿⣿⣀⣴⣾⣿⣿⠿⠛⣿⣿⠛⠿⣿⣿⣷⣦⣀⣿⣿ ⣿⣿⣿⣿⠟⠉⠀⠀⠀⠈⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿ ⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟
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