⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡏⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣾⣽⣿⣳⣿⣟⣾⡷⣿⣟⣷⡿⣾⢿⣽⣿⣷⣿⣽⣿⡿⣿⡿⣿⣿⣦⣠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣆⠙⠻⣿⣿⣿⣿⣿⣿⣿⢯⣷⣿⣻⣿⡷⣟⣿⡾⣿⣻⣟⣿⣽⣿⣻⣿⣿⡞⣿⣿⣾⢯⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠠⢘⣿⣿⣿⣦⡀⠀⠙⣿⣿⣿⣿⣽⣿⣟⣾⣿⡿⢿⣿⡯⢿⡟⣟⡛⣏⢯⡹⣱⢎⣽⣿⣖⣿⣿⣿⣻⣿⣞⣿⣷⣯⣿⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠐⣂⠘⣿⣿⣿⣷⡄⢠⣿⣿⡿⣾⣿⣿⣯⣿⣿⣗⣻⣿⣿⣩⢳⣮⣵⣾⣶⣿⣿⣿⣻⣿⣿⣯⣿⣿⣿⣽⣿⣾⢿⣷⣿⣿⣿⡟⠛⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢢⠡⣘⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣾⣿⣿⣻⣿⣿⣷⣿⣿⣿⣻⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣯⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⠳⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢆⠱⠘⣿⣿⣿⣿⣿⣿⢾⣻⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⢿⣿⣿⣷⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⢄⣀⣀⠀⢈⡀⠉⠳⢦⡀⠀⠀⠀⠀⠀ ⢐⡈⢆⠡⠌⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢹⣿⣿⣿⣿⣿⣿⢿⣿⣾⡿⣿⣀⣀⣀⣀⡉⣿⣿⣿⣽⣿⣿⡄⠀⠀⢀⣀⠀⠀⠙⢯⠙⣉⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀ ⠠⠐⢂⣴⠛⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠁⣀⣀⣹⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⠛⠲⡤⠬⠍⢳⡒⠋⠀⠈⠛⢶⠦⣤⣀⣀⣈⡇⠀⠀ ⢠⡵⠋⠀⠀⠀⠀⠀⠸⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⠛⣿⠟⠋⠉⠉⠁⠐⢿⣶⡾⠟⠻⢿⣷⠘⣿⣿⣿⡷⣿⣿⣧⣀⣙⡷⢤⣀⣹⠛⠢⢤⣤⣨⡇⠀⠀⠉⠁⠀⠀⠀ ⠻⠁⠀⠀⢀⠀⠀⠀⠀⠉⠁⣰⣿⣿⣿⣿⣿⣿⠛⣿⣿⠟⠛⠻⣿⡄⠀⠀⠀⠀⠀⠙⣏⣀⣀⣀⣨⠟⠀⣿⣿⣿⣿⣻⣿⣿⡝⠻⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠊⠁⠀⢀⣤⠆⣠⠾⢋⣿⣿⣿⣾⣿⣿⡀⢻⣀⣰⣶⡤⠾⠃⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣯⣿⣿⣷⣄⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠄⠀⠐⢚⡏⠘⢉⡟⢀⣸⣿⣿⣿⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⢿⣿⣿⠈⠳⡀⠀⠀⠀⠙⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡺⠁⠀⢀⡴⠿⣤⠖⠋⣿⡿⠛⣿⣿⣷⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣤⠴⠶⠒⣶⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠈⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⠴⠞⠉⠀⠀⠀⠀⡴⠋⠀⣰⣿⣿⣿⣻⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠘⢧⡀⣠⠇⠀⢀⣠⠖⠋⠉⢙⣿⣿⣿⣿⢷⣯⣿⣿⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⠃⢹⣿⣿⣯⣿⣿⣿⣿⣿⡿⠛⠓⠒⠦⢤⣤⣄⣉⣁⡤⣾⣏⠀⠀⠀⠀⣼⣿⣿⣿⣟⣿⣯⣿⣿⠀⠀⠀⣠⣔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⠀⠀⠠⠃⠀⠨⣿⣿⣷⣟⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢿⠳⣅⠁⢠⠇⠻⠤⠤⣤⣤⣿⣿⣿⣿⡽⣷⣿⡿⣿⣤⠴⢿⣿⣟⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⣀⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣾⣟⣿⣿⣿⣿⣷⡀⢀⣀⡤⠞⠀⠈⠙⡏⠀⠀⠀⠀⠀⣸⣿⣿⣿⢯⣿⣟⣿⡿⠉⠙⢤⡈⠻⣿⣷⣿⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⢱⡦⠀⠀⠀⠀⠈⢯⣿⣿⣾⣟⣿⣿⣿⣿⣿⡉⠁⠀⠀⣠⣤⠴⠛⠒⠚⠛⠲⢤⣿⣿⣿⣟⣿⣷⣿⡿⠁⠀⠀⠀⠙⢦⡌⠿⣿⣿⣷⣭⣷⠦⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠓⠒⠦⠤⠾⢿⣿⣷⣿⢯⣿⣿⣿⣿⣿⣄⣤⠞⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢾⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡛⢿⣿⣿⣿⣷⣯⣽⣓⡦⢤ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⣠⠶⢷⡛⢻⣿⣷⣯⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣿⣿⣯⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷ ⠀⠀⠀⣠⢾⣿⣿⡿⠃⠀⠀⠀⣠⠞⠁⠀⢨⡙⢶⡿⣿⣿⣽⣿⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⠀⢠⠏⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿ ⠀⣠⣾⣿⣿⣿⡿⠁⠀⠀⣠⠾⡅⠀⠀⠀⣀⠙⢦⠇⠀⢙⣿⣿⣟⣿⣿⠢⡄⠀⠀⠀⠀⠀⡴⠁⠀⠘⢿⣿⣿⣷⠤⠀⠀⡀⠀⠀⠀⠀⠀⠈⠳⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣷⣿⣿⡿⠋⠀⠀⠀⡴⠁⠀⠱⢄⣀⣀⡀⣹⡟⠀⠀⡸⢸⣿⣿⣿⠇⠀⠸⡆⠀⠀⠀⢸⡁⠀⠀⠀⠀⠈⠙⢧⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠋⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡽⠋⠛⠉⠀⠀⢠⡇⠛⠫⠟⠁⠀⠀⢠⠇⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠉⠓⡶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⣀⣀⡀⠠⠔ ⡿⠋⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢣⡀⣀⣀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠰⠯⣄⠀⠀⠀⢰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣨⠗⠋⠉⠉⠁⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⢏⠀⠀⠉⠓⠦⢵⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢳⡀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣠⠔⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⢹⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠙⢄⠀⠀⢀⡟⠀⠀⠀⠀⣀⣴⡎⠀⠐⠤⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢀⡞⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠳⡀⡜⠀⠀⠀⠐⠉⠁⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⡾⢷⠀⠀⠀⠀⠀⠀⠻⣄⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢹⡀⠀⢸⠃⠘⡆⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⢸⠃⠀⢀⡜⠃⠀⠀⠀⠀⣀⡴⠋⠙⠦⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⠀⠀⠀⣽⠀⠀⡰⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⠆⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢲⡇⠀⣰⠃⠄⠀⠐⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⣠⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⣀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⣼⠀⢠⠟⠢⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠁⠀⡰⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢯⠁⠈⠳⣄⠀⠀⠀⠀⢷⣠⠏⠀⠀⠘⣄⢀⠀⡀⠀⠀ ⣿⢿⣟⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⣀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠙⠒⠒⠖⠒⠛⢣⡀⠀⠀⠈⠁⠀⠀⠐⠠ ⣯⣟⢾⣱⠿⣜⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⡟⠃⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢤⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⠀⠀⠀⠀⠀ ⠉⠙⣏⣞⡻⣜⢧⡿⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡵⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀ ⠀⣠⠗⣎⡳⣽⡾⠁⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⣀⢀⣀⠴⠊⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢟⡩⢞⣰⡿⠋⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⣸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⣱⠞⠉⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⡏⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣶⡒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠣⡀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣸⠦⠄⠂⠀ ⠀⠀⠀⠀⠀⣠⠴⣿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣾⣱⡤⠦⣀⠀ ⠀⠀⠀⠀⢸⠁⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⢹⠆⠀⡀⠀ ⣀⣀⡀⠀⠈⠳⣤⣤⡄⠀⡀⠈⠙⠒⠤⣄⡀⠀⠀⠀⠀⢀⡎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠁⠀⡀⠀⢀⣠⠟⠀⡐⠀⠁ ⠀⠀⠉⠉⠉⠉⠉⠉⠓⠺⣄⠀⠀⠀⠀⠀⠈⠙⠒⠦⣤⣼⡧⢤⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠋⠁⢀⣀⣀⢀⣰⢤⣿⣟⠉⠀⠀⠀⠀⠀⠀