⠀⠀⠘⢦⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢀⣀⣴⡒⠛⠭⣑⣒⠊⠷⢖⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⢦⡀⠀⢠⡶⢫⢋⢯⢿⠻⡉⠓⠲⣛⣲⡖⠮⣷⣝⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡤⣺⡟⡵⢻⢸⢸⠀⢇⠹⡉⢑⡢⠸⣍⠒⠤⣙⣆⠳⣿⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⡄⣠⢋⣜⡟⡼⣱⢻⢸⢸⠀⠘⡄⡯⠗⠺⠥⡀⠙⡢⣄⡙⠦⡙⢟⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⢃⡾⡼⢰⢣⠇⡞⢸⠸⡄⠀⣇⠇⠐⠤⠤⣀⡀⠙⢮⡙⠷⣾⣎⠻⡒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⣧⠇⡏⡼⢠⠇⢸⢰⡇⢀⣿⣲⡼⢭⡉⠑⢯⡲⡄⠱⡀⠘⢮⠳⣾⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠻⢽⣲⢤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⡼⡟⣻⢸⠀⡇⡞⢀⡷⢳⣇⣸⣳⡒⠧⣄⡈⢢⡀⠙⢮⣆⠱⡀⠈⢧⠹⣧⠩⣛⠷⣤⡀⠀⠀⠀⠀⠀⣀⣤⠤⢤⣠⠋⠑⠦⠤⣅⡀⠀⠀⠉⠛⠿⣶⣤⣀ ⠀⠀⠀⠀⠀⠀⢰⢣⠃⡇⣿⡎⠀⣷⠃⢀⣤⠻⣟⠛⠁⠉⢢⣦⡙⢦⡙⡄⠀⢻⣆⢳⡀⡞⢀⢿⠀⠈⢻⣮⡻⡿⠶⣽⡟⠉⠁⣀⡀⠀⣸⠀⠀⠀⠀⠀⠙⠢⣤⣀⡀⠀⠀⠉⠛ ⠀⠀⠀⠀⠀⠀⢸⢼⠀⢹⣜⣧⡀⣾⠿⠃⢠⣤⣽⣆⠀⠀⠀⢱⣹⢄⠙⡼⣇⠀⣏⣆⠱⣝⢦⣀⠀⢰⡀⢳⣿⣼⠓⢦⣍⢆⠀⠸⡷⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠒⠭⢝⡒⠒⠢ ⠀⠀⠀⠀⠀⠀⠸⣿⠠⡈⡎⣏⡏⠉⠻⢦⣻⣿⡯⣹⡶⢃⣴⣟⣧⢤⣷⡼⣿⣦⡘⣌⢦⡈⠓⢬⠏⠁⠑⢤⡹⣌⠀⢸⠈⢾⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠦⠀⢠⠟⣦⢷⠃⡘⢿⠀⠀⣰⠿⡟⣵⢙⣿⠟⢝⣵⣿⣿⢃⣽⣿⡳⡑⢬⡣⣝⡦⢌⣓⡦⠤⢄⣉⣛⡷⠺⡏⠈⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⠶⣷⠾⢻⢸⡇⡇⡎⢯⠛⣛⣿⣮⣹⡿⣻⣇⠈⢹⣿⢿⠊⡀⠹⡷⡝⢄⠈⠱⡝⢷⣄⢦⢄⣀⣤⠞⣀⠀⣷⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢱⢳⢳⠘⢿⣛⣿⣿⡯⣷⠿⠿⣄⠟⠙⠛⢇⢧⡄⠹⣼⢾⣷⣤⣌⠈⢿⡈⠢⣄⣸⣤⡟⠀⠸⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠄⠀⠀⠀⢠⡇⠈⢿⡎⢇⢮⣷⡉⢋⠔⠿⠀⠀⠙⠳⠴⠀⣨⣾⣿⣆⠘⢆⠙⢦⡘⢗⠦⣌⡓⠦⣔⡿⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⡿⡇⣇⠀⢹⡌⠱⡻⣿⣦⣀⠒⠒⢦⣀⣠⣴⠿⠛⠈⣻⠷⢵⣦⡽⠂⠱⡜⡆⣠⢟⠽⠋⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣭⠭⠷⢾⡶⠶⠲⠶⢤⣀ ⠀⠀⠀⠀⠀⢀⡼⠋⠀⡇⢻⣦⠘⣿⣄⠑⣽⣻⣌⢙⡶⣦⣍⣉⡁⠀⢀⣤⣷⠀⠀⠀⠀⠀⠀⠹⡧⠟⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠰⡇⢳⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠒⠋⠀⣀⣀⠘⠮⠏⢧⠘⣮⡳⣈⣻⡈⠫⣧⡿⠿⡟⣽⣿⡅⢸⠈⠙⠒⠒⢤⡀⠀⢰⠂⢠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡜⣧⠈⣷⠀⠀ ⠀⠀⠀⠀⢀⠔⠋⠁⠈⢣⠀⠀⠈⣿⠚⠻⢚⢧⢳⣀⢸⡇⠀⢿⡟⠻⡟⠺⢤⣀⡀⠀⣀⣀⣐⡣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⢳⠹⣷⣻⣇⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⠀⠚⢲⠀⢀⡇⠀⠀⢸⠈⠛⠛⡏⠃⠀⠉⠁⠀⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢰⣶⠉⠀⢀⡠⣦⣀⣤⣿⡋⢿⡄ ⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⣸⠀⢸⠃⠀⠀⠸⡄⠀⠀⠹⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣼⡿⠾⠻⣿⠉⠹⡇⠘⣷ ⠀⠀⠀⠀⢧⡀⠀⠀⠀⡠⠃⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠳⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠐⠐⠀⠀⠀⢸⡟⠿⠇⠀⠀⠀⢻⡆⠀⢳⡀⠹ ⠗⠀⠀⠀⠀⠈⠙⠒⠊⠁⠀⠀⢺⠀⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⠀⢳⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⠀⠀⢀⣠⣼⡷⠚⠻⠿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠘⡆⠀⠀⠀⡇⠀⠀⣼⠙⣦⣌⠲⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢧⠀⠸⢿⣧⡾⢣⣤⣀⣤⡾ ⣠⣴⢶⡄⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢳⠀⠀⠀⠁⠀⢰⠇⠀⠈⠙⢷⣌⠓⢤⣀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⠀⠀⢠⢀⣤⡾⠟⠉⠀⠀

⠀⠀⠉⠟⡾⣤⢀⢠⠀⠀⢸⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠦⠓⠉⠀⣀⢤⠓⣌⢷⠙⠈⠀⠇⢰⠀⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⡄⢶⣴⣠ ⡾⣤⣀⣤⢣⡾⣧⢿⠸⠀⢧⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣄⠲⣌⣦⠙⣼⠀⠀⡇⠀⠀⠀⡆⠘⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠿⠻⠚⡷⣼⣠⢀⠀⠀⡇⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⢳⠀⠀⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⢺⠀⠀⠁⠊⠒⠙⠈⠀⠀⠀⠀⠗ ⠹⡀⢳⠀⡆⢻⠀⠀⠀⠇⠿⡟⢸⠀⠀⠀⠐⠐⠒⠒⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⡀⠳⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠃⡠⠀⠀⠀⡀⢧⠀⠀⠀⠀ ⣷⠘⡇⠹⠉⣿⠻⠾⡿⣼⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠹⠀⠀⡄⠸⠀⠀⠃⢸⠀⣸⠀⠀⠀⠀⠀⡃⠈⠀⠀⠀ ⡄⢿⡋⣿⣤⣀⣦⡠⢀⠀⠉⣶⢰⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠁⠀⠁⠉⠀⠃⡏⠛⠛⠈⢸⠀⠀⡇⢀⠀⢲⠚⠀⠀⠀⠀⠃⢰⠀⠀⠀ ⠀⣇⣻⣷⠹⢳⠀⠉⠞⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡣⣐⣀⣀⠀⡀⣀⢤⠺⡟⠻⡟⢿⠀⡇⢸⣀⢳⢧⢚⠻⠚⣿⠈⠀⠀⢣⠈⠁⠋⠔⢀⠀⠀⠀⠀ ⠀⠀⣷⠈⣧⡜⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡞⢠⠂⢰⠀⡀⢤⠒⠒⠙⠈⢸⡅⣿⣽⡟⠿⡿⣧⠫⡈⣻⣈⡳⣮⠘⢧⠏⠮⠘⣀⣀⠀⠋⠒⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⢳⡇⠰⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠁⠟⡧⠹⠀⠀⠀⠀⠀⠀⣷⣤⢀⠀⡁⣉⣍⣦⡶⢙⣌⣻⣽⠑⣄⣿⠘⣦⢻⡇⠀⠋⡼⢀⠀⠀⠀⠀⠀ ⣀⢤⠶⠲⠶⡶⢾⠷⠭⣭⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣧⠋⠽⢟⣠⡆⡜⠱⠂⡽⣦⢵⠷⣻⠈⠛⠿⣴⣠⣀⢦⠒⠒⣀⣦⣿⡻⠱⡌⢹⠀⣇⡇⡿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡴⢀⡿⣔⠦⡓⣌⠦⢗⡘⢦⠙⢆⠘⣆⣿⣾⣨⠀⠴⠳⠙⠀⠀⠿⠔⢋⡉⣷⢮⢇⡎⢿⠈⡇⢠⠀⠀⠀⠄⠀⠀⠀⠀ ⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣦⠸⠀⡟⣤⣸⣄⠢⡈⢿⠈⣌⣤⣷⢾⣼⠹⡄⢧⢇⠛⠙⠟⣄⠿⠿⣷⡯⣿⣿⣛⢿⠘⢳⢳⢱⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⠀⠀⣷⠀⣀⠞⣤⣀⢄⢦⣄⢷⡝⠱⠈⢄⡝⡷⠹⡀⠊⢿⣿⢹⠈⣇⣻⡿⣹⣮⣿⣛⠛⢯⡎⡇⡇⢸⢻⠾⣷⠶⠱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠈⡏⠺⡷⣛⣉⢄⠤⡦⣓⢌⡦⣝⡣⢬⡑⡳⣿⣽⢃⣿⣿⣵⢝⠟⣿⢙⣵⡟⠿⣰⠀⠀⢿⡘⠃⢷⣦⠟⢠⠀⠦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⢾⠈⢸⠀⣌⡹⢤⠑⠁⠏⢬⠓⡈⢦⣌⡘⣦⣿⡼⣷⢤⣧⣟⣴⢃⡶⣹⡯⣿⣻⢦⠻⠉⡏⣏⡎⡈⠠⣿⠸⠀⠀⠀⠀⠀⠀ ⠢⠒⡒⢝⠭⠒⠙⠈⠀⠀⠀⠀⠀⠀⡇⠀⡷⠸⠀⢆⣍⢦⠓⣼⣿⢳⡀⢰⠀⣀⢦⣝⠱⣆⣏⠀⣇⡼⠙⢄⣹⢱⠀⠀⠀⣆⣽⣤⢠⠃⠿⣾⡀⣧⣜⢹⠀⢼⢸⠀⠀⠀⠀⠀⠀ ⠛⠉⠀⠀⡀⣀⣤⠢⠙⠀⠀⠀⠀⠀⣸⠀⡀⣀⠁⠉⡟⣽⠶⡿⡻⣮⢻⠈⠀⢿⢀⡞⡀⢳⣆⢻⠀⡄⡙⢦⡙⣦⢢⠉⠁⠛⣟⠻⣤⢀⠃⣷⠀⡎⣿⡇⠃⢣⢰⠀⠀⠀⠀⠀⠀ ⣀⣤⣶⠿⠛⠉⠀⠀⡀⣅⠤⠦⠑⠋⣠⢤⠤⣤⣀⠀⠀⠀⠀⠀⡀⣤⠷⣛⠩⣧⠹⢧⠈⡀⠱⣆⢮⠙⡀⢢⡈⣄⠧⡒⣳⣸⣇⢳⡷⢀⡞⡇⠀⢸⣻⡟⡼⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢤⣲⢽⠻⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⣾⠳⢮⠘⡀⠱⡄⡲⢯⠑⡉⢭⡼⣲⣿⢀⡇⢰⢸⠇⢠⡼⡏⠇⣧⡜⠃⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠛⡒⠻⣎⣾⠷⡙⢮⠙⡀⣀⠤⠤⠐⠇⣇⠀⡄⠸⢸⡞⠇⢣⢰⡼⡾⢃⣹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠢⢟⡙⠦⡙⣄⡢⠙⡀⠥⠺⠗⡯⡄⠘⠀⢸⢸⢻⣱⡼⡟⣜⢋⣠⡄⠳⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡛⣿⠳⣆⣙⠤⠒⣍⠸⡢⢑⡉⠹⢇⠀⢸⢸⢻⡵⡟⣺⡤⢀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠢⣝⣷⠮⡖⣲⣛⠲⠓⡉⠻⢿⢯⢋⢫⡶⢠⠀⡀⢦⠈⠀⠀⠀⣄⠻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡦⢖⠷⠊⣒⣑⠭⠛⡒⣴⣀⢀⠀⠀⠀⠀⠀⣄⠹⠀⠀⠀⡀⢦⠘⠀⠀