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