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