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