Woman Dot Art

⠀⠀⠀⢿⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠘⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⡄⠸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠛⣇⠈⠀⠀⠀⡇⠚⠐⠀⠁⠀⠀⠀⠁⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⣼⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⡎⣿⢿⣷⣿⢿⠈⠀⠏⣿⠀⠀⠀⡟⣾⣴⠀⠁⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢿⢠⠀⠀⠀⠀⠀⠀⠀⠋⠾⣤⣠⣀⠀⣀⣀⣤⠦⠓⠉⠀⣷⣷⢿⡎⣽⣷⣿⠿⢿⣿⠻⠝⡿⣴⢈⠀⠏⣠⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢾⠐⠀⠀⠀⠀⠀⠃⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠽⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣰⡏⠀⠀⢹⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⡉⢻⠛⠈⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⣇⠀⢸⠀⠁⠸ ⠀⠀⠁⠟⡶⢠⠀⣀⣆⠻⠀⠀⠇⢀⠀⠀⠀⠁⠛⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠻⡘⢹⠀⡀⢹⢸⠙⡎⠀ ⠀⠃⡴⢀⠀⠀⠀⠀⠀⡀⢷⠀⣃⠀⠀⠀⠀⣷⣿⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣆⠘⠀⣧⢇⣿⢸⠀ ⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⡀⢠⠀⠀⠀⡀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠃⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⠃⢸⠀⡇⡇⣿⢠⠀ ⡇⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⣶⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⢿⠘⠄⠀⣼⡇⣇⢀⠀ ⡇⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⠳⠀⢸⡟⣿⠘⠀ ⡀⣤⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⡿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣸⢸⡇⣿⢠⣇⣿⢸⠀ ⠀⠀⠀⡀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡇⣿⢠⡇⣿⠀⠀ ⠀⠀⠀⠀⠀⣿⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣧⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⣿⠀⡿⢸⠀⠀ ⠀⠀⠀⠀⠀⣇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣰⢸⠇⣏⠃⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⡐⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⢸⡇⣿⡟⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⠳⠨⠄⠤⠶⡷⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⣆⠁⠉⠉⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠛⠁⠈⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣶⣬⣿⡿⠉⠄⠄⠄⢠⠂⣶⠞⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣶⣾⡿⠁⠄⠄⡀⠄⠄⠄⡈⠐⢻⡆⢹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣶⣶⣿⡇⠄⠄⢤⣁⣤⣀⣀⠃⢐⠈⢣⠈⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⢹⣿⣿⣿⣿⣿⡞⠄⠸⠄⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢃⠄⠄⠻⣿⣟⣿⣿⣟⠅⠄⠄⠄⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⢿⣿⠄⠄⠄⢨⣛⣛⡭⠄⠄⠄⠄⠄⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠏⣵⣾⣷⠤⠄⡀⠄⣸⣿⣿⣧⡀⠄⠄⣾⣿⣦⡙⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⣸⣿⣿⢖⣠⣄⣀⡐⣰⣿⣿⣦⣵⠄⣦⡙⢿⣿⣿⠸⣿⣿⣿⣿ ⣿⣿⣿⠇⣛⣡⣶⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣼⣬⣯⡠⢍⣛⠄⠨⡛⢿⣿ ⣿⡿⣡⠪⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣦⡙⠄⠄⢀⠄⠹ ⣿⢱⣷⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⢸⣿⣿⣿⣿⣿⣿⣿⣥⠝⡀⠄⠈⣷⢱ ⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠄⠄⡿⢀ ⣿⣷⣙⠿⣿⣿⣿⣿⡿⠋⣼⣿⣿⣷⣜⢿⣿⣿⣿⣿⣿⣿⠟⠄⠄⠄⣿⣿ ⣿⣿⡿⢰⣶⣶⠩⡴⢖⣵⣿⣿⢻⣿⡻⠷⣮⣍⡛⢋⣩⣵⡆⠄⠄⠸⣿⣿ ⣿⣿⢇⣿⣿⣿⡄⢿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⢃⣽⣿⣿⣇⠄⠄⠄⢿

⠀⠏⠴⠤⠤⠤⠤⡤⣀⣀⣀⢤⠯⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠵⠤⠤⠤⡤⣀⣀⣀⣀⠤⠳⠈⠀ ⠀⣸⠀⠀⠀⠞⠀⠀⠀⠀⠀⠇⢲⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣻⠀⠀⠀⡀⢤⠹⠀⠀⠀⠀⢧⠀ ⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⡀⠀⠀⠈⠀⡇⠀ ⠀⢹⠀⠀⠀⠀⠀⠁⠀⠁⡼⠀⠉⠚⠴⠤⣠⣀⢤⠲⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⣀⣦⣶⠛⠈⠀⠀⠀⠀⠀⢿⠰⡼⠀ ⠀⡇⠙⠀⠀⠀⠀⡀⠁⡟⣿⣻⢘⠀⠀⠀⠀⠀⠀⠀⠒⡌⠸⠀⠀⠀⠀⠀⠀⠀⠁⣿⢠⠀⠀⡄⣏⢹⠀⠀⠀⠀⠀⡄⠻⢰⠀ ⠀⡏⣔⠀⠀⠀⡄⠀⡇⣷⣿⣮⣿⠻⠀⠀⠀⠀⠀⠀⠁⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠃⡽⣿⣿⠈⠀⠀⠀⠀⠀⡄⠸⠀ ⠃⣼⠀⠀⠀⠀⠀⢰⡇⠀⣧⢧⣿⣾⠀⠀⠀⠀⠀⠃⡴⠀⢱⠀⠀⠀⠀⠀⠀⠀⡿⢷⠀⠁⣿⣿⣾⢧⣄⠀⠀⠀⠀⠀⠀⣆⠘ ⡟⢀⠀⠀⠀⠀⠀⠀⡆⠀⡇⣧⣳⢰⠀⠀⠀⠁⠋⣰⠀⠀⡆⠘⠀⠀⠀⠀⠀⡏⣸⡀⢹⡇⣏⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠋⣳⣻⣴⠤⠤⠤⡤⣀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢿⢠⠀⡀⢦⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢧⠀⠀⠀⠀⠀⠀⡿⣶⢷⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠇⣿⠀⠀⠀⠀⡀⣷⣽⠳⠙⠀⠀⠀⠀⠀⠀⠀⡞ ⡀⢦⠈⠀⠁⠊⡴⢀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠔⢀⡇⠈⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⡀⢤⣶⠹⠀⠀⠀⠀⠀⠞⢠ ⠀⠀⡀⣀⣀⠀⠀⠀⡞⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠙⠈⣇⡿⡿⣿⣢⢁⠚⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠲⠒⠖⡷⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡟⣿⣿⣿⡾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣷⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⠈ ⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣷⠈ ⠀⠀⠀⠀⠀⠀⠀⡇⣗⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⡴⢠ ⠀⠀⠀⠀⠀⠀⠀⡀⢄⡤⢻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣯⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣌⠳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⠀⠀⠊⣷⢋⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⠢⠓⠙⠈⠀⠀⠀⠀⠀⠑⡿⣿⣿⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⡤⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢷⠬⠤⠥⡤⣀⣀⡀⣳⣄⢤⣶⠒⠛⠛⠒⠒⠧⡿⣼⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡓⠀⠀⠀⠀⡇⠺⠙⠉⠀⠀⣇⠘⠉⡟⣿⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⢹⠈⠀⠀⠀⠀⡁⢹⡄⣿⠸⠀⡟⢿⣿⣾⣇⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣶⣶⣷⣾⣶⣶⣾⣶⣿⢿⠿⣿⣿⣿⣷⣾⣾⠀⠀⡄⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⣼⠀⠀⠆⠓⠁⠛⢿⠿⣟⣿⣿⣿⣿⣿⣿⢠⣿⠘⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⠀⠀⠀⠁⣿⣷⣜⣿⣿⣿⣿⣿⣿⣿⣰⠀⡆⠘⠀⠀⣿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢠⠀⠀⠀⡏⣿⠀⣧⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⢠⠀⠯⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠀⠀⠁⣿⢿⠀⡆⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠁⠟⣿⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠦⡶⣴⢿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠤⡤⣃⣟⣿⣿⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⣇⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⠟⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣿⣿⣿⣿⣿⣿⣶⣤⣀ ⠀

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⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡞⣶⣾⣴⣀⠄⠄ ⡿⣿⣿⡇⣿⣿⣿⣹⣿⣿⣿⣿⠻⠈⠄⠄⠄⠄ ⠋⠟⠿⠿⠿⠻⣌⣿⣿⡎⣿⣿⣿⣾⡵⣭⡭⣍⣭⢮⠄⠄⠄⠄ ⡟⣿⣿⣿⣿⣿⣿⣿⡹⣷⣿⣾⣫⢟⣿⣿⣿⣿⣿⣿⣿⢿⠻⠄⠄ ⣶⣶⣿⣿⣿⣿⣿⣿⣿⢿⣎⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠄ ⠁⠈⠄⣇⣿⣿⣿⣿⣿⣿⢿⡎⣿⣿⣿⣼⣀⣀⣀⣀⣧⣿⣿⢠⠄ ⡀⣤⠄⡆⣶⣶⣿⣿⣿⣿⣿⢻⣅⣷⣿⢻⠈⠖⠶⠙⡟⣾⢉⠄⠄ ⡀⣚⣦⣷⣿⣿⢿⣙⣷⣿⣿⣿⣾⣫⡅⣷⠸⠄ ⠉⠟⡿⡇⢿⣜⣿⣿⣿⡶⣭⣿⣿⢿⣿⡇⡻⢨⠄ ⠋⡿⣿⣿⣿⣿⣿⣾⣤⢀⡄⡆⡽⣓⣭⣷⣿⣿⣿⣿⠘ ⠋⡿⣿⣿⣿⣿⢡⣀⣀⠄⠄⠋⠿⣿⡻⣪⣿⡄⣸⣧⣿⣿⣿ ⡟⣿⣿⣿⣿⣴⢀⠄⣱⠑⠞⡿⣿⣓⣛⣿⣿⡹⢇⠹⡇⣿⣿⣿ ⡏⣿⣿⣾⣭⢛⠛⠛⠛⡇⡄⠉⠄⢁⢦⣤⣥⣿⣴⠘⢩⡇⣿⣿

) ๏ 人 ๏ (⠀⠀⠀⢿⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠘⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⡄⠸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠛⣇⠈⠀⠀⠀⡇⠚⠐⠀⠁⠀⠀⠀⠁⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⣼⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⡎⣿⢿⣷⣿⢿⠈⠀⠏⣿⠀⠀⠀⡟⣾⣴⠀⠁⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢿⢠⠀⠀⠀⠀⠀⠀⠀⠋⠾⣤⣠⣀⠀⣀⣀⣤⠦⠓⠉⠀⣷⣷⢿⡎⣽⣷⣿⠿⢿⣿⠻⠝⡿⣴⢈⠀⠏⣠⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢾⠐⠀⠀⠀⠀⠀⠃⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠽⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣰⡏⠀⠀⢹⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⡉⢻⠛⠈⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⣇⠀⢸⠀⠁⠸ ⠀⠀⠁⠟⡶⢠⠀⣀⣆⠻⠀⠀⠇⢀⠀⠀⠀⠁⠛⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠻⡘⢹⠀⡀⢹⢸⠙⡎⠀ ⠀⠃⡴⢀⠀⠀⠀⠀⠀⡀⢷⠀⣃⠀⠀⠀⠀⣷⣿⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣆⠘⠀⣧⢇⣿⢸⠀ ⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⡀⢠⠀⠀⠀⡀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠃⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⠃⢸⠀⡇⡇⣿⢠⠀ ⡇⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⣶⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⢿⠘⠄⠀⣼⡇⣇⢀⠀ ⡇⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⠳⠀⢸⡟⣿⠘⠀ ⡀⣤⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⡿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣸⢸⡇⣿⢠⣇⣿⢸⠀ ⠀⠀⠀⡀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡇⣿⢠⡇⣿⠀⠀ ⠀⠀⠀⠀⠀⣿⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣧⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⣿⠀⡿⢸⠀⠀ ⠀⠀⠀⠀⠀⣇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣰⢸⠇⣏⠃⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⡐⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⢸⡇⣿⡟⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⠳⠨⠄⠤⠶⡷⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⣆⠁⠉⠉⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⠀⠀⠀⠀

⣌⠢⡄⣀⣔⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠙⠀⡉⠛⣛⢷⣭⡶⢟⣫⣵⣮⣹⢶⡹⢳⣭⣛⣯⢎⣹⡿⣾⢀⣀⢀⠀⢦⢶⣶⡶⣤⣠⠀⠀⠀⠀⠀⠓⡿⢿⡻⢿⣛⣭⡽⣮⣛⣯⣛⡶⢶⢤⠀⠀⠂⠖⣷⣻⣝⢮⡹⣶⡝⢧⣎⡹⣷⣎⣹⠷⣭⢷⣫⢷⣦⣜⠷⢧⣥⠶⣙⣴⠹⣳⢬⣳⡖⣿⢧⢦⣭⣷⠻⢖⢣⣤⣶⣿⣳⢺⣞⣧⣿⣿⣾⢲⢆⡈⣷⣿ ⡀⢄⠦⢓⠭⠈⢀⠀⡠⣔⣧⣶⣿⣿⣿⣿⣿⣿⣾⣫⣱⣽⡳⣜⢳⣬⣱⠧⣞⡴⢤⣤⣤⡷⢿⡶⠷⢶⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣤⣥⣭⣉⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣟⣿⢿⣿⡿⣿⣿⣿⢿⣿⡟⢻⣹⢾⣍⠳⣛⣌⡱⢶⣻⣜⡻⣜⠳⡥⡛⢧⣇⣣⡱⢏⣋⢕⣪⣭⢓⣉⣾⣜⠣⢆⣃⣗⣿⣿⢿⡃⣄⡚⣃⣷ ⠀⠀⠀⠀⠀⡐⣄⠤⠓⠉⡀⣄⠢⣄⣧⣿⣿⣿⣿⢏⣩⡽⡱⣞⠧⣱⡹⢦⣽⠧⠾⠾⠷⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣉⣉⣋⣛⢛⠟⡾⠈⠒⠚⠁⠈⠉⠓⠚⠷⣤⣼⣣⡴⢏⣥⣮⡕⣾⣷⣿⣶⣿⣿⣿⣿⣿⡿⣿⣿⡻⣝⠎⣮⡑⣶⢻⢎⡣⣜⢲⣹⡎⢃⣱⢦⡙⣛⡟⣊⠭⣛⣟⣻⢽⡏⣿⣸⣦⢻⡌⠜⢢⡜ ⠀⠀⠀⠀⠀⠀⠉⠛⡿⣿⣿⢸⠀⠄⠀⡀⣅⣟⣽⠳⢯⡖⡴⡤⢷⡿⡛⣟⡛⢻⣞⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⠉⠉⠛⠒⠤⡀⢁⣾⣽⣦⣠⢂⢀⠀⠀⠐⠄⠂⠀⡐⠌⠃⠄⡈⠒⢃⡄⠘⢣⡔⠩⢢⣘⣧⣷⡜⡜⣳⣇⣿⣿⣿⣿⣿⣿⣿⢿⣛⡹⣌⢶⢻⡍⢆⠣⢆⣃⡓⢾⡷⣾⢿⣼⣿⣹⣿⠿⣶⢳⣿⢻⠄⡢⢌⡑⢢⡑ ⠙⠉⠊⠗⡦⣜⣩⣿⣿⣶⣶⣙⢭⠚⠞⣮⣵⢎⡳⣍⢻⠓⠛⠉⡔⡠⣀⠀⠀⠀⠁⠉⠉⠉⠋⠛⠚⠀⠀⠔⠢⠓⠞⡿⢈⠀⠀⠀⠀⠀⠀⠀⠋⠼⣧⢹⠉⠋⠞⣠⢈⠀⠀⠐⠁⠄⡈⠄⠘⣂⠄⡘⡌⠆⠉⢠⡜⠃⢠⡜⠃⢠⡜⠃⢠⡜⢃⠡⢤⡜⠣⣌⡜⡟⣿⣬⣿⣿⣿⣿⣿⣿⣿⢿⠻⣙⢩⢻⠠⡇⣹⣎⣻⣟⡼⣙⡦⣿⡿⣉⣿⣠⡜⣮⢻⢊⡄⡘⣛⠰ ⣿⡭⡛⢚⢶⣤⣁⢉⠛⠵⣿⣒⣹⡴⢏⣡⡷⣉⣉⣁⣏⠻⣟⢩⠀⠀⠀⠁⠉⠞⣴⣢⣄⣀⣠⣀⣄⢤⠲⠒⠶⣷⣿⣿⣿⠿⠛⠉⠉⠚⠴⣠⢃⡟⣿⣾⣠⢀⠀⠀⠀⠌⡈⠑⠣⡄⠑⢢⡑⢊⣡⠒⢉⢤⠊⢡⡔⠊⢡⡔⠊⢡⡐⠩⢆⡈⠰⡑⠣⣀⠱⡌⠇⣾⢢⡌⠱⣮⣿⣾⣿⣿⣿⣿⣿⣿⣿⢫⢸⣿⠹⢯⠍⢢⡔⡓⠥⢎⡓⣤⢛⣆⠎⢌⡿⢘⢣⡏⣿⣿ ⣰⢉⠋⠖⠮⣱⣮⣉⠶⡇⣹⠦⣩⡖⢉⣲⡍⣙⡿⣽⣟⣿⣾⣵⣦⣌⣄⣠⢀⠈⠐⠀⠈⠐⠀⠁⠀⠀⠀⠇⣧⠸⠆⢂⣱⣾⣟⣧⣷⣿⢿⣿⣿⣿⣤⠀⠀⠐⠌⠢⢆⠃⢄⠱⠪⣑⠰⢣⡠⠜⢃⠤⠂⢠⡐⠄⡠⠄⢀⡠⠄⢀⠤⠀⢠⠄⡠⠐⠤⡈⠰⡌⠂⡐⢌⡑⠤⠒⣌⣱⢎⣧⣷⣿⣿⣿⣿⣿⢻⣿⢻⣷⣿⣿⣿⠻⣛⠝⢩⢬⠲⣙⢖⢏⣼⠃⢿⣽⣿⣿ ⢮⣕⠫⣛⢟⡶⠷⣛⢲⣍⡳⢆⢉⡴⠏⡿⣿⣿⣿⣷⣼⣦⣺⠑⠡⠂⢃⠠⢒⠍⡀⠱⢈⠱⣈⠒⡈⠑⠠⡟⣿⠀⠁⠂⠁⠆⣀⣼⡿⢧⣿⣿⣾⢰⠀⠁⢂⠔⡙⢣⣄⠲⣌⠢⢌⡐⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⣁⠠⢑⡠⠜⢨⡴⣜⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿⡻⡿⢿⣿⣿⣻⣿⣻⣿ ⣌⠹⣦⣹⡟⣷⣭⢬⢫⣾⡡⢞⢋⡿⣿⣿⣿⣽⢠⡿⠅⢂⡈⠰⡘⠣⢐⡭⠆⠙⣡⠲⢌⠳⡌⠳⢆⡘⠟⣡⢦⡈⠱⠂⠈⠠⢉⠤⡜⣻⣿⣿⢨⡀⠘⠣⣑⠦⡘⠦⣈⠰⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠒⢌⡡⡔⠫⣅⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿ ⢎⡉⢦⡍⠏⣱⣾⢃⣾⢎⣉⠴⣫⡿⣿⣾⣬⠑⠢⢌⡑⠢⢌⡱⠌⢣⡄⠘⢢⡐⡐⠣⣄⠒⣈⠱⢦⡍⠦⣋⠥⢎⡣⠜⠣⢄⠚⡌⢓⣯⣿⢨⠑⢢⡜⢊⡱⢆⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢂⠡⢈⡱⢆⣣⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢆⡙⢇⢻⡽⣦⢊⣷⢖⢎⡑⡿⣿⣿⣼⠆⠈⡱⠆⢈⡱⠆⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⠢⣐⠜⢪⡕⢊⣰⠝⢪⢳⣏⣾⠆⡙⢦⡙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣉⠤⡙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢆⡘⡓⣌⠓⢣⣆⢍⡬⠟⣿⣿⣾⢠⠌⠢⢌⡒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠢⣍⡆⠓⢦⣙⡷⣼⢏⡡⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠃⢤⡙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠤⡜⠣⣑⢨⡰⢞⢃⡿⣿⣿⣼⢉⣂⠍⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡱⢎⡹⣿⣾⠍⣘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⣈⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢣⡀⢸⠰⡍⠟⡧⣿⣿⣿⣾⠠⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠟⣿⣾⢻⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢎⠡⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡋⠜⢃⡿⣻⣿⣿⣿⣿⣾⣐⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣭⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⡨⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣽⡟⣿⣿⣿⣿⣿⣿⣌⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣿⣿⣿⣿⣿⢷⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣰⣵⣤⣤⣿⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢉⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢲⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢀⠁⡟⠸⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣁⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⠀⡧⣿⢿⠘⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡷⣿⣿⣻⠀⠀⡇⣴⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢆⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠸⠀⡖⣿⣾⢠⠀⠀⡇⠸⠀⣀⢕⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣌⡗⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⣇⠈⠀⡖⢘⠁⠊⢀⡆⢈⠀⠀⢀⡐⡄⢷⠙⠈⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠩⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⢁⠐⠀⣿⣈⠁⠀⠀⢆⠈⠀⠀⠈⠀⠀⣀⣤⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡂⡝⣯⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⠀⠀⡃⠟⣿⣾⡔⣍⣭⣭⢻⢂⠙⠈⠢⢈⠢⠈⠀⣄⣷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠓⣧⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠃⢀⠀⠁⣿⣶⢤⠠⣏⣿⠙⣀⠀⠀⡀⣤⢦⡗⠹⠉⠀⠀⠀⡄⢳⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣈⠱⢦⣟⣿⣿⣿⣿⣿ ⣼⣿⣿⣳⣷⣤⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡇⠘⠀⠀⠀⡟⣬⠃⠿⡿⣿⣽⣿⢿⠯⠾⠿⠛⠀⠀⠀⣧⣷⠿⠈⠀⠀⢄⠐⢂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⢄⡂⠴⣎⣿⣿⣾⣟⣿ ⢀⡆⣼⡐⠀⢢⠄⣇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⡇⢠⠋⡿⣿⣪⠽⣪⣻⣶⣎⢇⣿⣾⢠⠛⠙⡟⠺⣐⢿⠙⠀⠀⡀⢄⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⢃⠄⡑⢎⡡⢜⣯⣿⣿⣻⣿ ⠂⠀⣀⠂⢀⠠⢀⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠙⡄⠿⣷⣴⣧⡟⣺⢜⡈⠆⢁⡶⣏⢰⠇⣿⣿⢳⣶⠹⡀⣦⠻⠉⠁⠉⠔⣤⢦⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⠁⡼⠀⠃⠄⡈⠱⡆⢸⡖⡍⣷⣿⡾⣟ ⠀⠀⠀⠀⠀⢈⠡⢀⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣹⣿⣿⣻⣻⠿⡴⠃⢷⢼⠀⣈⠐⣡⡼⠃⡝⣻⣶⡞⣙⣧⢿⠿⣹⠉⢀⠂⠐⠤⣀⠀⡀⢍⠺⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠋⡴⠀⠌⠁⠡⢌⡉⢧⣸⠔⣋⡵⣿⣾⣟ ⠀⠀⠉⠀⠀⠐⠡⡐⠀⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⣿⣴⣏⢰⠀⡽⣼⠀⠀⠀⡔⠈⣷⡇⢸⡄⢻⣆⠃⣧⣿⣿⣀⣀⢤⠲⠒⠈⠉⠀⡀⣇⠀⠀⡀⢄⠢⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡔⢁⡞⢀⠂⠄⠀⠠⠒⠌⢃⡿⢡⡠⠝⣣⡽⣿⣟ ⠀⢣⢌⣢⠹⡂⠐⡀⠂⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⡿⣰⠁⣾⠀⠇⣞⠀⠀⠀⠀⠠⠐⡄⠘⢷⠀⡀⢀⠠⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⢄⠀⡀⠡⠀⠀⠀⠀⠀⠁⡚⢤⠯⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡥⠋⡴⣀⠀⡀⠀⠄⠂⣀⠌⢃⡿⣿⠀⡌⠚⢥⡳⣯⣿ ⠀⠀⢄⠈⠁⠀⢢⠁⠀⠂⠀⣧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⢠⠂⡏⢸⠀⡟⢰⠀⠀⠀⠀⡀⠀⡆⢧⡀⢣⠉⠀⠋⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠢⠁⠀⠀⠀⢆⠰⡽⣹⡖⣀⣀⠤⠻⠛⠙⠉⠈⠀⠀⠀⠀⠀⠁⠊⠒⠔⠥⣉⢚⠴⣠⠀⠀⠀⠀⠀⠀⠄⠀⢉⠟⣿⣿⣿⠛⠌⠆⣉⡳⣎⣿ ⠃⡁⠐⠉⠠⠎⠁⠢⡑⠐⢢⠑⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣸⠃⠠⣾⢀⠃⣿⠀⠀⠀⠀⠹⠈⠀⠀⡀⢹⠀⣄⣴⣤⣏⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠉⠈⠤⡑⢀⠤⠢⠒⠒⠓⠛⠗⠦⣿⣿⣹⣠⣔⣮⣷⣽⠾⠳⡛⣉⣉⣌⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠞⡽⣟⣾⣯⣽⢫⣵⡮⢏⡐⠼⣎⡷ ⢃⡰⡕⠊⣍⠆⣉⠦⡉⡱⢎⡑⠨⣧⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣾⠃⢡⡏⢀⠀⡰⢀⠀⠀⠀⠀⣙⠳⠀⠀⠀⡇⠈⠃⠟⠨⡆⢈⣿⠑⠈⠀⠀⠀⠔⡤⣉⣉⠀⠖⣤⣙⣬⡼⢿⠌⠯⠿⡿⣓⠛⠛⠙⣯⣿⢻⡑⡌⠒⢩⣆⢭⠦⡈⡔⣊⣡⣶⣿⢯⠿⠽⠦⠷⠿⡽⣻⣟⡿⣶⣼⢳⣤⢖⡣⢆⡩⢖⢫⣥⠞⣋⢧ ⡣⡐⠲⢆⠐⢤⠠⢆⡀⡐⠌⠠⠐⡃⣸⢧⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⡫⣾⣫⣷⣟⢿⢩⡰⡞⠀⠀⠀⠀⠀⠀⠀⠅⡰⠠⢧⠈⠀⡇⠀⣸⠀⣤⠻⣆⣿⠀⠀⠁⠛⠿⡿⣿⣿⠿⠛⠘⡞⠿⣷⣸⣿⣿⣿⣞⣿⡭⢷⣿⣿⣿⣿⣿⣿⣿⢿⡛⢇⡘⢜⡈⢂⠔⡊⡑⣿⣿⡛⣧⠾⣿⣧⣼⣣⣄⠡⢢⡅⠂⣉⠢⢐⢣⡄⠬⢒⣩⠶⢏⡱ ⠀⠠⠀⠀⠀⠈⡐⠄⡈⠄⠈⢂⡁⠀⢷⡼⠀⡀⢆⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡻⣟⡷⣿⡥⢛⣧⢻⡀⢀⠋⢠⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠁⢣⠀⡎⠀⢸⠀⠀⣇⠹⣷⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢾⣷⠿⢿⡿⣷⣿⣿⢿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠫⢙⢫⢟⡿⣿⣿⢵⢣⣌⠜⢣⡄⠊⣀⠣⡄⠈⢒⠌⠢⣂⠑⣂⠆⣈⠱⣎⠱⣳ ⠈⠠⠐⠡⠠⠐⠌⠡⠄⠀⠂⢀⠐⠠⡆⡾⠀⠀⠀⣹⣤⠤⢂⠒⠒⠒⠒⠶⠶⠶⣾⣶⣥⣦⣾⡙⣦⢿⡛⢧⢸⠏⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢹⠀⠀⢣⣀⢀⠀⢹⠀⠀⡀⣐⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠋⣴⣋⣗⣿⠼⣩⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⡰⠒⢌⡐⠡⢃⠅⢀⠰⢉⡄⠊⢁⠤⢂⡐⠡⢌⡁⠰⢎⡡⡳ ⠁⢂⡀⠐⡀⠁⠀⠀⠀⠀⠀⠀⠁⠁⠀⣿⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⢀⣶⠐⣇⢻⣧⠟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⣣⠣⠀⡇⠀⠀⠀⣇⠘⠀⠀⡘⣯⣿⣿⣿⣿⣿⣿⣿⣶⣠⠀⠁⢸⡵⢾⠀⣧⣿⠘⢣⡔⠢⣜⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣈⠤⠌⡌⠂⠐⠠⡐⠌⠁⡠⠐⠢⢁⠤⡌⠃⡁⠠⡡⠔⢊⡱ ⠉⠊⢁⠋⠙⠋⡈⠓⢋⢋⣛⠒⢀⠰⠀⢺⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢂⠀⣿⣟⣼⠀⠃⠁⠞⣤⢀⠀⠀⠀⠀⠀⡀⠹⢀⢀⡇⠀⡀⢄⠓⣆⠙⠀⠛⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⡏⠻⡛⣿⢿⠿⣿⣿⢈⡱⢆⠆⢃⢢⡜⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡐⢌⠂⠔⢈⡐⡈⠄⠀⠡⡀⠐⢈⠠⠌⠁⠠⠒⡀⢒⡁⠔⡊ ⣿⢯⣱⣾⡟⢞⣮⣳⢛⠚⠐⠠⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠾⠀⢀⠈⠠⢐⡇⣿⢚⠴⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⡇⠇⠀⠀⠀⢧⣦⠶⡟⣇⣽⣿⣿⣷⣼⢀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣷⣂⠌⡰⢙⢣⢥⡎⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⢂⢈⠡⠄⠂⠁⠠⢀⠀⡁⠂⠀⢈⠐⠠⡐⠌⡁⠡⡐⠡⢌ ⢯⡿⣴⣀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⢈⠀⠠⡏⣨⣎⢀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⡆⠈⠀⠀⡀⢹⠜⠃⡶⣻⣽⣿⣿⢠⠀⠀⠀⠀⠀⡄⣻⣛⣿⣿⣴⠎⠡⢌⡱⢎⡑⠳⣩⠿⢟⡻⣟⣿⣿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣾⢻⠡⠄⠂⡀⠁⠠⠁⡀⠀⠀⠂⠄⠂⡀⠁⠠⠌⠀⠢⡁⠠⡘ ⢟⣱⠀⠁⠑⠃⠀⢩⠉⠃⠾⠛⠛⠛⠿⡿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣀⠀⠀⠀⠀⠐⢈⡇⣿⢠⠀⡱⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⡇⣿⣾⠀⣧⣟⣯⡿⠁⠉⠈⠀⠀⠀⠀⠁⠉⡿⢫⣘⠔⢫⡔⠻⣌⡹⡳⣎⣽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢠⣧⠛⡁⠀⠌⠀⠐⠠⠀⠠⠀⠀⠀⠐⠄⠀⠐⠂⢀⠡⢂⡐⠌ ⣸⣀⠘⠀⡀⠀⡖⣿⣋⡿⣿⣟⣿⣿⣷⣀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⠀⠀⠂⠀⢀⠌⠂⢁⡯⣰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠢⡌⠙⠀⡇⣿⢸⠀⡀⢿⣯⣿⣿⡤⢠⠀⠀⠀⠀⡶⡿⣿⣛⣿⣮⠓⣬⠳⣝⡳⢮⣓⠷⣎⣷⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣼⠀⠀⣧⠙⠠⠀⠂⠄⠀⢀⠈⠀⠀⠀⠀⠐⢀⡀⠐⡀⠐⠡⢂⡁ ⠂⠀⠀⠀⠀⠈⠀⡇⣾⣿⣿⣿⣿⢰⡀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠊⡤⠀⠀⠀⠀⠀⠈⠐⠂⢁⡠⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢎⠀⠀⠀⠀⡄⡘⠱⡄⣿⢺⠑⠾⣇⣽⣿⢸⠀⠀⠀⠀⠋⡻⠙⠋⣿⣳⡼⢟⣣⣟⣛⡿⢾⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠊⠓⠉⣿⠘⢀⠁⠀⢀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠌⠀⡐⠁⠤⠂ ⠃⠋⠘⠋⠁⠉⠁⡂⢿⣏⣿⣿⣿⠀⠌⠈⡉⢻⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠈⢀⠁⡐⠈⢢⡇⣸⠀⠘⠀⠇⠀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⡆⣿⠀⠀⠀⠀⠀⡄⡸⠦⣿⢹⡟⣿⣽⣿⣿⢿⡿⣤⣉⣖⣭⣭⣿⣻⣦⡽⣎⡱⢖⡿⣩⢛⠟⠉⠀⠁⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠽⠤⡤⢳⠸⠀⠀⠈⠀⠂⢀⠀⠀⠀⠀⠀⢈⠂⠄⡈⠁⠠⢂ ⠷⠦⣿⣿⣳⣤⠾⣏⣿⠗⣻⣿⣿⣧⣜⣷⣿⣆⠘⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠂⠁⠄⠈⠡⠊⢠⡗⢸⡎⠀⠀⡇⠀⠀⡜⠀⢸⠀⠀⠂⠈⠀⠀⠀⣄⢱⠀⠀⠀⠀⠀⣇⠈⡇⣿⣷⣯⣾⡿⣿⣿⣿⠛⢉⡿⣿⣿⣿⢻⢤⡛⢾⣣⠰⣟⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⠉⣍⢈⠀⡀⢷⠈⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠄⠀⠐⠂⡁⠄ ⢺⡝⣿⣿⠻⣍⠾⣏⣿⡳⢎⣿⣿⢩⣷⡏⣿⣩⢿⠀⠀⠏⢠⠀⠀⠀⠀⠀⢈⠁⠂⠁⠄⠂⠁⢢⡇⢹⢸⠀⠀⡅⠉⠚⣩⠛⣠⠀⠀⠂⡌⠘⠀⠆⠲⠙⢆⠀⠀⠀⠀⡅⢸⣿⣿⠿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⡟⣿⢻⣌⡜⡝⣿⣿⣽⣮⣦⣷⡬⢘⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠽⣏⣿⣭⢷⡿⢿⠈⢀⠀⠀⠄⠀⢀⠀⠈⠀⡀⠁⡀⠐⠄⠈⡐ ⢿⡿⣿⣿⣿⣽⣿⣿⣿⠿⢭⣿⣿⣿⣻⣾⣷⣞⡶⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⡈⠄⠈⢣⡄⣿⣴⠎⣀⣀⠁⠉⠬⠫⡖⢠⠀⠀⢆⡈⠱⠀⡂⣛⢯⠘⠀⠀⠁⡿⣷⣿⣟⣿⣿⡟⣿⣿⣿⢛⣥⣏⣿⣿⣿⣿⡟⣿⣿⣿⢻⣿⣾⣿⣭⣤⣴⣵⣬⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⢾⡏⣿⣟⡳⣿⣿⣿⠘⠀⠐⠀⠠⢀⠠⠁⠀⠀⠀⡀⠐⢈⠆⡀ ⣿⣿⣿⣿⣻⣷⣛⣧⣿⢿⣲⣿⣿⣽⠯⣍⡯⣇⢣⣞⠹⢱⠀⠀⠀⠀⠀⠀⠡⠀⠂⠀⠁⢂⠄⠡⡞⣫⡿⢾⣻⠵⣭⣂⣒⠂⠓⡉⢬⠳⠙⢆⡈⠹⠒⡉⣌⣦⠻⠛⡿⢻⣷⣿⣳⣿⣿⣿⣿⣿⣿⣿⣸⣧⣹⣠⠏⣷⣿⣿⣿⣿⣿⣿⢻⡌⢿⡘⠡⠰⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⢿⣿⣿⣿⣿⣿⣿⠙⠀⠁⠂⡀⠁⠠⠀⠈⠀⡀⠐⡈⠐⢀ ⣿⣿⣿⣿⣷⣾⡿⣟⣾⣿⣻⢿⣿⣿⣼⢪⢱⡹⢮⡝⣧⡘⠰⠀⠀⠀⠀⠀⠀⠉⠀⠁⠠⠂⣁⡂⣿⣴⢀⠀⣦⣐⠀⠀⡹⣔⠀⠀⣀⠤⣦⣽⢷⡇⠘⠀⣁⢾⣿⣻⢿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠈⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡘⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢿⣞⡿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠀⠐⠀⠠⠄⡈⠄⠀⠀⠠⠔⡈⠐ ⡱⣮⣿⣽⡺⢷⣽⣿⣿⡖⢾⡧⣿⢿⡣⢜⣹⡶⣜⡻⢭⣷⡞⠘⠀⠀⠀⠀⠀⡄⠹⠀⠀⢀⡀⠷⣾⢿⠙⠀⠃⢰⠀⠃⣀⠸⠀⠀⠁⠉⠉⡋⣾⠻⣿⡿⣥⡜⣛⣧⢿⣾⣿⣿⢯⡲⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⣿⣿⣹⠬⣔⣭⣷⣾⣷⣿⣯⢻⠈⠠⠐⠠⠐⢂⡁⠀⠀⢂⡄⠈ ⡡⠖⣉⣦⣿⢿⡻⢣⣿⣌⡳⢎⣷⣿⢣⣦⡝⡣⢆⠏⣡⠸⣄⡜⠑⠀⠀⠀⠀⠀⡀⠈⡀⢷⠀⡿⣼⠺⣜⢿⣿⠀⠀⡅⠫⠞⠵⣮⣙⢣⣜⡸⡽⣿⣿⣿⣣⡜⡳⣎⡽⣿⣿⣇⣳⣽⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣴⣿⣿⣿⣴⣦⡩⠖⡃⢿⣭⣿⣿⣿⢿⠘⠄⡀⠐⢈⠡⡈⠐⡀⢆⠀ ⡆⠌⡓⢆⡌⣔⣾⢿⣿⣼⢎⣿⣸⣿⢹⢦⠹⡄⢻⢡⡿⢀⠀⡔⡸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢮⣝⠧⣿⣿⢿⡼⣹⠷⢩⢲⢭⡓⢧⡎⣝⡞⣿⣿⣿⢾⡝⢫⣵⡞⣿⣿⣿⣭⡿⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣉⢂⡐⣎⡁⢦⡹⢎⡛⡟⠿⣿⣿⣿⣿⣿⣿⣿⠹⢀⠡⠄⠂⠡⢄⠈⡀⢘ ⢌⡘⠣⢄⡘⢣⢆⣉⣶⣿⢻⣿⣰⢳⣯⠹⠀⠋⣤⠻⣸⠀⠀⠀⡄⡜⠱⠀⠀⠀⠀⠀⠂⠀⠀⢿⣭⡳⣏⢾⣿⠟⣎⡘⣿⠖⣣⡜⡹⢳⢭⢳⣯⣿⣞⣿⣿⠼⢻⣮⡝⣿⣿⢻⣿⡟⣻⣿⣿⣾⣦⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⡆⠲⣙⠆⢁⢫⠞⣵⣠⣱⣀⣿⣿⣷⣷⣿⣿⣿⣿⠿⠈⡈⠒⡉⠆⡈⠑⠎ ⠔⡈⠱⢆⡈⠰⢎⡁⠰⢪⣕⣷⣿⣿⣤⣷⠈⢠⠀⣇⢰⠀⠀⠀⠀⡀⡱⠡⠀⠀⠀⠀⠀⢁⠈⣿⣱⢾⡏⣷⣿⡖⢿⢈⣷⣩⢶⡭⡖⠯⣎⡳⣿⣿⣟⣿⣿⣿⠿⣎⡽⣿⣿⣟⣳⣾⣿⣷⣿⠘⠀⠄⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⡀⢧⣿⢢⢍⡡⡜⠋⣄⠚⡱⡻⢛⣿⣿⣿⣿⣿⢿⡜⠎⢃⢣⣌⠴⢎ ⡂⠌⡐⠣⢄⡘⠆⢃⡄⠎⡁⠴⣋⣧⠻⡉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⠿⠿⠿⠿⠿⡿⡙⣿⣿⢎⡱⣿⣿⣭⣿⠘⣯⣛⢻⣛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣳⣿⣿⣞⣻⣿⣟⣿⣦⢠⠀⠀⠉⠀⡀⣤⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⢀⠀⠀⠁⠈⠀⠀⠀⠀⡇⣴⢀⣻⠶⣈⠱⣌⠖⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢏⣙⠻⣛⣛⢟ ⠡⢌⡑⠢⢁⠤⢊⠡⢆⠄⢊⡄⠘⢣⣆⣧⣿⠛⠈⠀⠀⠀⠁⠋⡿⣷⣩⣼⠟⢣⢹⣲⡼⣟⣧⣿⣿⣿⣿⣿⣿⢟⣻⠿⣿⣽⣿⣦⣝⣳⣬⣷⣎⣧⣾⣷⣿⣿⣿⣿⣿⣿⣻⣷⢯⣿⣾⣷⠀⠉⠔⡠⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣿⣾⣶⣶⣿⣿⣶⣷⣻⣉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⡄⢺⢄⡐⠩⢍⡫⣟⠻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿ ⠀⡐⠣⡅⠂⢡⠆⢁⠢⣁⠔⢊⡄⠐⡱⢂⣵⣷⣯⢾⠷⠟⣷⣏⡭⠻⢧⣎⡳⢧⡳⣝⢮⡳⣜⡻⣿⣿⣿⣿⣿⣿⣿⣫⢧⣚⠵⣮⡓⢱⣳⢣⣜⢫⡴⣛⡵⣞⣯⣷⣿⣿⣹⡷⢿⣿⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣴⢀⠀⠀⠀⠀⣧⢿⠻⠈⡀⣄⣦⠹⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠛⠟⠿⡿⣶⣿⣷⣮⣭⣶⣹⣶⣭⣳⣬⢿⣎⢳⣮⡟⣎⡽⢟⣣⡷ ⠀⠀⠀⡠⠎⢁⠢⢈⠡⡰⠄⠘⣈⡔⠂⢡⡐⡫⢏⣇⡿⣿⣾⣰⢤⡀⢀⣀⡀⢀⡠⣕⣮⢻⣿⣯⣟⣩⣋⣿⣮⣙⠾⣓⢮⡝⣪⡵⢳⣬⡳⢧⡭⢞⣭⠞⣩⠶⣘⢽⣯⣷⣿⡿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢾⠀⠀⠉⣭⠛⠛⠿⠷⣶⣽⣦⣜⣫⣵⣋⠧⣍⡱⢳⢬⡳⢎⣍⡳⣌⡺⣕⠮⣭⠞⣓⢬⢻⢧⣎⠵⡸⣽⡳ ⠀⠀⠀⠀⠀⢂⢄⡘⠒⡁⢂⠄⡐⠌⡡⠄⠣⠅⣊⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⣬⣶⢿⣿⣿⣹⢾⣜⡜⢣⣄⠒⣄⡐⠢⣄⡐⢢⡔⠎⣑⠶⣋⢧⣎⠵⡫⣔⣾⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢸⠀⠀⠀⠀⠁⠉⠋⠟⣿⣾⡿⣴⣾⣭⣢⣱⣚⢇⡩⢦⠜⣪⠵⢎⡱⠞⢣⡜⡹⠶⣍⠲⢧⢎⡱⢞⣍⡱⢞⢣⡴⢛⣥⠞⢣⣜⡳⣎⡝⡧ ⠀⠀⠀⠀⠀⠀⡀⠆⣁⠳⢎⠧⠳⠛⢋⡉⠛⠛⠿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⠐⡟⣿⣲⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢒⢢⣜⡳⢏⣡⢷⣎⢿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣯⠻⠿⠿⣷⣬⣳⣭⣦⡙⢦⡜⠧⢊⢱⣬⡙⠴⢫⡔⢫⢥⣓⠭⣒⡭⡘⢽⡎⠱⡼⢓⣩⢲⢭⣓⠦⣙⡴⡝⢣⣬⠝⣣⡖⢎⡜⢳⢬⡲⣝ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⣙⡶⡞⢷⣷⡶⣼⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠣⢡⣼⡛⢥⣷⣿⣟⣎⢿⠳⠛⠉⠉⠋⠛⠟⠿⣿⣾⣼⣣⣗⢬⠳⣌⠳⡌⣙⠦⣙⡤⢞⡎⡓⢌⡲⡜⢓⡴⢋⡴⠞⡡⢳⢎⡥⠚⢥⡲⡜⢚⡬⢛⢤⡹⢦⡙⣬⡓⢪⣕⡚⢣⡵⢎⣍⠳⣌⢳⣎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢳⣧⡜⠹⢷⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡖⢋⣱⡮⣿⢿⢭⡽⢯⡯⣟⣿⣿⣾⣾⣏⣣⢆⡜⢣⠱⣎⠓⣌⠳⢎⡑⢦⡙⢤⠼⢇⡡⡜⢣⣌⡱⡎⢊⡱⢎⣑⠲⢎⣡⠜⣢⡜⢏⡆⢎⡙⣤⡙⢦⡓⢎⢡⡼⢋⡵⢎⡡⢜⡹⠧⣌⠳⣎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣞⡝⣻⢳⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣫⠴⣟⣿⣿⣿⣽⣦⣜⣓⢩⢴⠮⢃⢣⢣⣆⡘⠳⢌⠳⣌⠳⢌⡱⢮⡐⣳⡌⢣⡴⡙⢣⡴⢋⢥⢎⢣⣌⡜⡱⢎⣡⡜⢣⣌⠱⢮⢇⡡⣖⡘⣱⠼⣋⢧⡆⢏⡡⢜⣩⠴⡚⢣⣌⠼⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡞⡽⡳⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼⡟⣿⡿⣻⣿⣿⡿⠿⡻⡛⢛⣩⠹⢩⢭⡌⠳⣌⠳⣌⠳⣌⠳⡌⣘⠳⣌⢓⡬⠓⢣⣆⠙⣢⠝⢢⡜⡘⢳⡌⢓⡬⢓⡣⢆⡘⢞⡣⡔⡚⢣⡔⢚⢣⣔⠚⢣⡔⢊⡱⢒⢫⢇⣍⠯ tra txet nrop emos si ereh hctib uoy ton looc dna toh era elpoep ynroh ufts oS smaerts evil nrop hctaw ew elihw seittit ym selkcus dna ssa ym ni kcid sih skcitS,em sregnif eh, taem sdneirf ym taeb i toh si nrop dna ogeha dna iatneh ti gniniur gnikcuf era uoy dna etaberutsam anyrt mi ufts nnaM:esnopser ym KCUS UOY .LOOC RON YNNUF T'NERA UOY .FFUTS ESEHT OT UOY ROF ENIF STI NAEM T'NSEOD NOITARENEG TSETHGIRB EHT T'NSI AHPLA NEG/Z NEG ESUACEB TSUJ .EFIL RUOY NIUR NAC TI .FO DUORP EB OT GNIHTON SI NROP OT DETCIDDA/LAUXESREPYH GNIEB .KCUF SA GNITSUGSID ERA LLA'Y .SOBMOC IJOME LARETIL ROF DEDNETNI ETIS NMADDOG A FO DAETSNI SETISBEW NROP/3OA OT OG DNA SESSA YNROH RUOY LORTNOC

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣮⣝⢽⢿⣯⡽⡾⣞⣺⣾⡽⢿⣻⣾⣻⢵⢽⢷⣕⡽⡳⢯⣪⡻⢵⢷⣗⡪⣫⢯⣗⡫⣵⡽⣞⢯⣗⡮⣝⡽⢗⣫⡮⡺⢯⣫⡵⣞⡯⡫⢵⢽⣞⡯⢗⢮⣞⣟⣗⢝⣽⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢯⣇⡯⡮⡽⣽⣷⣮⣾⣫⢵⢽⣞⢯⣗⡪⣻⢵⣗⢞⢯⣪⢽⣗⣗⣗⢯⢇⢯⣪⡽⢞⢯⣗⡫⢵⣺⡽⡳⢯⢮⣝⣳⡯⡪⣺⡽⢞⢯⣫⡵⡺⢽⣳⡳⣯⡳⢯⢯⢯⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⢜⢽⣞⡯⡫⣵⡺⣯⡫⢵⢽⣞⢝⣳⡯⢗⣪⣻⡮⢞⣝⢽⣗⣗⣝⡷⡇⡯⡵⢞⣫⢯⣕⡺⢽⣞⡯⢗⢮⣝⡽⢞⢯⣪⣻⡵⡽⢗⢮⣝⡺⢽⣗⢞⢯⢯⢯⢮⢽⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⢱⢵⣳⡵⡺⢽⣳⡯⡮⢝⣳⡮⡽⣗⡫⢵⣳⡯⡮⣝⡺⢯⣏⢮⣞⣞⢎⢯⣕⡽⡷⡪⣺⡽⢞⣫⢯⣏⡵⢞⢯⣗⢕⣺⡽⢞⣪⢽⣞⢝⣳⡳⣺⡯⡮⡽⡺⣻⢯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣝⣞⢮⣝⡺⢯⢯⣕⡽⣞⡯⡮⢝⢽⣞⣫⡵⡽⢗⣞⡯⡫⣳⣳⣳⣣⡵⣞⡫⣳⡵⣞⢝⣺⡽⡳⢯⣕⡽⢞⣞⣫⡵⢞⣞⣝⡽⡳⢵⣹⢾⣪⡽⣝⡽⡽⡽⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡣⡳⣳⢮⣞⡯⡫⣳⡮⡺⢯⣗⢕⢽⣳⢯⣗⡪⣻⡵⢞⢮⣞⣞⣟⢕⢽⣳⢮⣞⣝⡳⢯⣕⡽⢞⣫⢯⣣⡵⣞⡮⣝⡳⣳⡯⡪⣻⢮⣞⡫⣵⢞⢯⢯⢯⣗⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢎⣝⣞⡯⣕⡺⢯⣗⡫⣵⢞⣫⢵⢽⣳⡮⢞⣟⡪⣻⡵⣞⣞⣝⢿⢇⢯⣗⡮⣝⡳⢽⣗⢞⢯⣕⡽⡳⣺⣯⡪⣻⢮⣞⢝⢾⣫⡯⡵⣞⡯⣕⡽⡽⡽⡳⣳⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡪⡯⣕⡺⢽⣳⢯⣪⡻⢵⣺⢯⣪⡽⣝⡳⣳⡯⡮⢝⣺⡺⣽⡽⢞⣝⡳⢯⣗⡮⢝⢽⣳⡯⡵⣗⡫⢯⣗⡪⣻⡵⡽⣗⢝⣳⡯⡫⢯⣗⡮⢞⢯⢯⣪⣺⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡮⣝⡳⢵⣺⡯⡮⢝⢽⣳⢮⣝⡽⡳⣮⢝⢷⣕⡽⡳⣳⢯⢯⣫⡮⢝⢽⢷⣕⡽⡳⢯⢵⣞⣫⡵⡺⢽⣗⢕⣺⡽⢞⢯⣫⡵⡺⢯⣗⡫⣳⢯⢯⣗⣗⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⡽⠊⢥⣃⠍⡹⢐⢬⠚⡌⡒⡔⢜⡼⢀⠀⠀⠀⠀ ⠀⢄⢹⡭⡛⠲⣖⠶⡶⣔⡛⠭⣚⡰⠀⠀⠀⠀⠀⠀ ⠀⠉⡆⣹⣧⠀⡐⢃⣘⣘⣃⣠⡕⢀⠀⠀⠀⠁⠓⠈ ⠀⢡⡊⢹⡷⠃⠶⠁⡚⡀⢱⡍⡂⠏⠟⠈⠂⢄⡈⢗ ⠀⡝⠄⢸⡳⡑⠠⢌⢂⠩⣆⣁⠨⣟⣻⠈⠙⢂⠐⣘ ⠁⢰⠹⣮⡵⡀⢲⠑⢈⡨⠝⠡⢻⡿⣯⢻⢁⢠⠏⢀ ⡆⢳⣗⢯⢿⡷⣭⣧⢽⢟⣩⣠⠔⣁⣠⣿⠨⠓⣬⠀ ⣦⣻⣿⣯⡙⡏⢻⣹⡊⢱⣇⠦⠹⡋⣞⣭⡏⢤⢨⠀ ⡇⣤⣜⣿⣿⣿⣿⠌⡇⠻⢛⠛⡦⣆⣀⢁⡹⠡⢠⠀ ⡇⢶⡏⣿⣿⣿⣾⢡⣶⢊⠒⡟⢛⠿⣿⣾⣶⣤⠀⠀ ⡄⣇⣿⣿⣿⣿⠽⣈⠠⠔⣃⣿⣿⣿⢿⠼⠐⠀⠀⠀ ⠀⠀⣷⣿⣿⣿⣿⣾⣋⡼⡿⣿⣿⣟⣿⣆⠀⠀⠀⠀ ⡤⡁⠋⣿⣿⣿⣿⣤⢡⠛⡙⣌⣿⣟⣿⢻⠘⠀⠀⠀ ⠀⠇⣿⣿⣿⣿⢸⡱⠄⠬⠌⠋⡼⣿⣿⣿⢈⠀⠀⠀ ⠀⡆⣏⣟⣿⣿⡿⢶⠼⠃⣾⢾⡿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⣧⢿⣾⣿⣷⣿⣀⡏⣍⠾⢿⣿⣿⣻⡴⠀⠀⠀ ⠀⠀⡀⣧⣷⣾⣿⢷⠻⣽⡟⣻⣿⣿⣾⣴⢀⠀⠀⠀ ⠀⠀⠐⠄⣦⣷⣞⣿⣷⣾⣽⢿⣿⣴⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣄⣦⣤⣄⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⢿⣯⠶⣟ ⣿⣿⣿⣿⣿⣾⣟⣿⣽⣠⣧⣿⣿⠋⣿⣿⣿⢿⣪⡛⢾⣱⡮⡟ ⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⣶⣶⢲⣷⣿⣿⣿⢃⣽⢯⠿⣿⣿ ⣿⣿⣿⣿⣾⣤⢀⠀⠀⠀⠀⠀⠀⠁⠁⡀⣦⢿⣿⡿⣿⣿⣿⣿ ⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿ ⣿⣾⠀⠀⠀⠀⠀⠀⠀⠃⣠⢨⠀⢀⠐⠁⠀⠀⣌⣷⣿⣿⣿⣿ ⣰⠀⠀⠀⠀⠀⠀⠀⠍⢀⠠⠀⠀⠀⠂⢠⠀⠂⠁⡄⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⠀⠐⠀⠀⠀⠀⠀⠒⡎⠀⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⡻⠫⡍⡸⢾⣳⡄⡡⢋⣤⠀⡀⣷⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣾⢿⣿⣿⡿⢰⠀⠀⠀⣇⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⡌⢃⡠⠘⠀⠀⠀⣧⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⠀⡢⢔⠫⣆⠐⠀⠀⠀⡀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠈⠀⠀⠁⡘⠌⠀⠀⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⡅⢨⠈⠱⠘⠀⣢⡀⠀⠀⠀⠀⠀⠀⠀

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

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       ⣰⣿⣿⣿⣏⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣷⣾⢸⣿⣿⣿⣷⣿⡏⠁⣿⣿⡀⢸⣿⣿⣿⣿        ⣼⣿          ⣼⣿⣿⣿⡟⣼⣿⣿⡇⣿⣿⣿⣿⡿⣟⣽⣾⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣷⡴⠿⢟⣛⣭⣭⣭⣭⣝⣀      ⢠⣿⣿⡀        ⣸⣿⣿⣿⣿⢱⣿⣿⣿⡇⣿⣿⡿⣫⣾⣿⣿⡿⣻⣵⣶⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀   ⢸⣿⣿⡇       ⢰⣿⣿⣿⣿⡟⣾⣿⣿⣿⣧⠹⣫⣾⣿⣿⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆  ⢸⣿⣿⣿       ⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⢸⣿⣿⣿⡇     ⢸⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣦⡻⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿     ⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⠿⣿⡎⣿⣿⣿⣿⡇    ⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢻⣿⣿⣿⡿⠛⣡⣾⣿⣿⡜⣿⣿⣿⣇   ⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢟⣵⣟⣼⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⢁⢿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣎⢿⠿⢋⣴⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿   ⢸⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣟⣑⣚⢍⣾⣿⣿⣿⣷⣦⣙⠻⣿⣿⣿⢧⣿⡸⣿⣿⣿⣿⣿⣿⣿⢇⣿⠟⣀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠿⡟   ⢸⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⡿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⠣⣿⣿⣧⢻⣿⣿⣿⣿⣿⠏⠜⡡⠞⠛⠃⠙⠿⠿⣿⣿⣿⢿⣿⣿⠿⣫⠇   ⠈⣿⣿⣿⣿⣿⣿⡟⣷⢜⣫⣽⢞⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⠵⠷⢬⡙⢿⡜⣿⢹⣿⣿⢏⣴⠊⣠⠶⠿⢷⣦⣄⠈⢙⣛⡛⣃⣐⣶⣾⠏     ⣿⣿⣿⣿⣿⣿⣧⣿⣿⣔⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⣠⡤⠴⠦⢤⣙⣿⣧⠛⣼⠟⣡⣾⣿⣾⣿⡗  ⠹⣿⣆⠈⣙⡇⣿⣿⡿⠋      ⢸⣿⣿⣿⣿⣿⣿⢉⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⢠⣾⣿⡷   ⠻⣿⣿⣴⣷⣿⣿⣿⣿⡇⠉    ⢻⣿⡆⢿⣇⠛⠉        ⠘⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣤⣲⣶⣾⠿⢀⣿⣿⠙⠁   ⡀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠰⣄⣀⣠⡇⢸⣿⣧⢺⣿⡄          ⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⢸⣿⣷⠠⣄⡀⢀⣰⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠿⠿⣡⣿⢿⣿⡏⣿⣷⡀         ⢻⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⢏⣽⢸⣿⣿⣧⠘⣿⣿⣆⠙⠿⠿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢲⢮⡿⣽⣷⣿⣿⣷         ⣸⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⡏⣾⣯⡍⣿⣿⣿⡼⣯⣟⣛⣻⢶⢼⣟⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠿⣫⣏⣾⢳⢳⢇⣿⣿⡿⡇        ⣿⣟⣿⣿⣿⣿⣿⣿⣎⢿⣿⡇⣿⡿⡇⢻⣿⣿⣷⣝⠳⠷⢯⢏⣟⣾⡏⣙⣛⢛⣋⣥⣶⣶⣦⣄⡀⠐⠆⣿⣿⣿⣟⣫⢾⣿⣿⡇⠃       ⡸⠋⣼⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⡜⠋⢀⡌⣿⣿⣿⣮⡩⢾⣯⣾⣿⣿⡇⣧⣣⣾⣿⣿⣿⣿⣿⣿⣿⣦ ⣿⣿⣿⣿⢏⣿⣿⠟⠁         ⣸⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⠃ ⣾⣿⡘⢿⣿⣿⣿⣷⡮⣹⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣿⣿⣋⠚⣩⡵⣸         ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢦⣇ ⣿⣿⣿⣤⠓⠈⢽⣭⣾⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣿⣿⡿⢛⡁⠘⢛⣱⡇         ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡱⢿⣿⣦⡘⠿⠿⢟⣱⣶⣤⣽⡻⢿⣿⣿⣿⣿⣮⣙⠻⠿⠿⠟⣋⣡⣾⠿⢛⣥⣶⣿⣧⡀ ⠛         ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣻⣿⣿⡏⠛⠿⡟⣫⠁⠸⢭⣝⣛⣛⣛⠿⡟⠛⢋⣭⣥⣶⣾⡟⠛⠋⢉⣁   ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⠓⠉⠛⠇⣀⣤⠶⢎⠠⠇ ⣀⠈⢉⡉⠉⢀⡀⠰ ⠉⠉⠉⠉  ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡳⠂ ⣠⡾⣫⣶⣿⣿⣷⣦⣄⣉⣀⣈⣁⣀⣠⣤⣾⣶⣦⣄⡀   ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠋⡱⠁ ⡰⡟⠑⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦𝓐𝓷𝓲𝓶𝓮𝓐𝓷𝓲𝓶𝓮𝓐𝓷𝓲𝓶𝓮𝓐𝓷𝓲𝓶𝓮

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⢶⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⠰⢻⡿⣿⣿⣿⣿⣿⠿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⣼⣼⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢺⡟⠒⠛⠛⠛⠛⠛⢻⣷⡾⠶⠦⠔⠒⣀⠒⠚⠛⠋⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠠⠤⠤⢔⡺⠇⠀⣞⡫⢤⡤⠀⠀⠀⢀⣇⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠘⡀⠀⠀⠀⠀⠀⠋⣸⡖⡖⢏⢹⠀⠫⡀⠀⠊⡐⠇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠹⡁⠀⠀⠀⢀⣰⣼⠏⡇⣷⢸⣱⣄⡠⠀⠀⠐⢵⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠠⡗⠂⡤⠒⣩⠼⢸⠀⡇⡏⡄⢳⣎⢋⠛⠲⠠⢎⠀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⡄⠀⠁⠈⠘⠀⣸⠀⢧⢐⠀⠀⡹⡌⠘⠠⡀⠀⡂⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⢠⠃⠀⠀⢀⠃⠀⡇⠀⡎⠮⠂⠀⣇⡜⡄⠀⢱⠀⠰⡰⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠀⠀⡌⠀⠀⡇⠀⡇⠀⡀⠈⢻⢸⠰⠀⠀⠆⠀⠠⣩⠀⠀⠀⠀ ⠀⠀⢸⣰⠄⡄⠀⠀⠀⠀⠀⡇⠀⢰⠀⢀⠀⣸⢠⠣⠃⠀⠘⠒⠀⠘⠣⠀⠀⠀ ⠀⢠⡏⠈⢸⠇⠀⠰⠀⠀⠀⠁⠀⠀⠃⠀⢃⢻⠸⠈⢘⠀⡀⠀⠲⡄⠀⢣⠀⠀ ⠀⢠⡯⢣⡏⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠆⠀⠈⡆⢰⠈⡇⠀⠀⠀⢷⡀⢀⢷⠀ ⢀⡾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡵⠐⡙⡇⠀⠀⠠⠊⠙⡁⠀⢱ ⡎⠙⠏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠤⡇⢸⠀⠀⠀⠀⠀⠙⠂⠁ ⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⡀⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣑⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠪⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⡠⠀⠀ ⠀⠀⠀⠣⡤⠤⢄⡀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡂⠀⢰⣀⠔⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡻⠖⠆⠉⠁⠀⠀⠀⠀⠐⠛⢻⡏⢸⡄⠈⢩⠟⠛⠯⠉⠈⠉⠙⢯⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣿⠿⡿⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⢤⡇⣸⣷⡘⠁⠀⠀⠀⠀⠀⢠⣦⣟⡇⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠁⣠⣇⠃⠐⠀⠀⢣⡀⠄⢀⣟⣷⣤⡷⢿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⣽⡯⣷⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⣴⣫⠜⣶⡴⠋⠒⣾⣷⣿⣿⠛⠟⠋⠁⠈⠻⠻⣿⣿⣷⣄⠀⠀⠀⠀⢹⣧⣘⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢠⡗⠡⣤⣿⣹⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⡀⣠⠞⠋⠸⣿⡜⣘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢯⢆⡔⢰⣽⠹⣿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡝⢀⡰⣒⡆⣸⡿⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠘⠼⡇⡄⣨⣯⢮⢏⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢸⣧⡟⣇⢸⡇⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣰⣷⣳⠻⡄⡟⠟⠀⣤⡀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢏⠁⡹⣼⠘⣷⣸⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡴⠃⣿⣿⡆⢷⣿⣲⣦⣶⣷⣦⣄⠉⠁⠀⠀⠀⠀⠀⠢⠀⡈⢀⡈⢽⣿⡸⡶⠃⠘⣰⠘⡟⠀⢈⣽⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠇⢸⣟⢿⣷⣝⣿⠋⠹⣿⣽⣿⣟⢧⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣻⣏⣷⣇⢠⣾⣿⣾⠃⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⡇⣰⣿⣯⣽⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠛⠛⠛⠛⠿⠿⣿⣿⣿⡞⢹⣿⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠓⠦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣷⣿⢰⣿⣿⡿⣿⣷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢱⣼⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠊⢉⢵⡟⣽⣺⣿⡿⣣⢿⣿⣄⠀⠀⠐⠲⢤⠀⠀⠀⠀⠀⠀⠈⢦⡄⠀⠀⠀⠀⣿⢟⡟⣿⣎⣯⢻⣧⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠈⠉⣽⠀⠀⠀⠂⠀⢸⡆⣿⣿⣿⣇⢻⢼⣿⣷⠀⠢⣔⠀⠀⠑⠲⢷⣦⡤⠀⠀⠀⠙⣆⠀⢀⣾⣿⣸⣿⣿⡃⠉⣼⡿⣧⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠸⠀⠶⠃⠀⣇⣿⣿⣿⣿⣿⣫⣿⣿⣦⡀⢹⣿⡷⢌⣙⣒⣒⣾⣳⣶⣶⠊⢉⣿⣿⣿⣿⣿⣿⣿⣯⣆⢹⣱⢨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⣿⣿⣿⣻⣾⣿⣿⣷⡀⢹⡝⢦⡀⠀⠀⣀⠴⡿⠁⣠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣼⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣬⣿⣿⣿⣇⣀⠻⢾⡷⣮⣥⡤⠞⢡⣾⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣯⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠋⠀⠀⠀⠀⠀⠻⣿⣿⣟⢛⣻⡿⣷⠖⠉⠀⡀⠀⢀⣴⠟⣋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣧⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⢰⠀⠀⡀⠹⣿⡯⠿⠗⡚⠁⠀⢠⣦⠤⢶⣟⡥⠖⢒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⢄⡠⠴⣫⣿⡿⢿⣿⢷⡀⠀⢠⣇⣘⠹⡄⢇⢇⠀⣀⣘⡶⠔⠛⠛⠉⠉⠁⢀⣰⠏⣙⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠛⢀⣴⣿⡿⢹⣿⠿⣹⠆⠀⣸⡇⠀⠀⡧⠞⠙⠋⢩⣳⣄⣸⣀⣠⣤⡷⢶⡿⠇⡊⠉⠙⠋⠉⠉⠛⠛⢹⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢊⣿⡿⣼⣿⣿⣿⣇⠀⣠⠏⠀⠛⣻⣿⢟⣻⣿⡛⣛⣁⣠⠴⠾⢿⢷⠟⠅⠄⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡆ ⠀⠀⠀⠀⠀⢠⠃⣼⡿⢰⣟⣿⡇⣼⠉⢀⣽⡤⠀⣴⣿⣱⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣮⣾⢀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀ ⠀⠀⠀⠀⠀⠀⣼⡟⣡⣾⣿⣟⣀⣷⠆⣼⡵⡢⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧ ⠀⠀⠀⢀⡦⣾⢻⢱⠟⣿⡿⢋⡌⠋⠰⢋⣔⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡇⠀⠀⠀⠀⠀⠀⠄⢠⢀⠂⡀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣵⢧⣾⡟⣼⣿⠛⠋⠋⣀⠀⡀⠦⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣤⣖⣸⡦⠤⠭⠭⢭⣉⡉⠯⠊⢷⠹⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠃⣿⣿⣿⣿⡇⡀⠀⡀⢿⡷⢃⣴⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢶⣶⡜⢧⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⣿⣿⣿⣆⢹⠆⡜⣿⣅⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠹⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣯⢻⠀⠀⢡⡟⣿⡸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⢹⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⠛⢸⠹⣄⠡⢤⡿⣷⡿⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⡄⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡏⣼⡟⠁⢈⡵⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣷⠀⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡏⠀⠀⠉⣠⣿⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡗⣧⣀⢀⣴⡿⠁⠀⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢉⣉⠉⠉⠋⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠒⠒⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⠿⣶⣶⣥⣴⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡀⢤⣤⣤⣶⣶⣶⣖⠃⠀⠀⠀⠀⠀ ⠀⠀⠠⢴⣾⣿⡿⠋⠀⠀⠀⣴⣾⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣾⣿⣟⠉⠉⠙⠻⣿⣿⣦⣀⠀⠀⠀ ⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠠⣿⣜⢶⡗⣹⡯⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⢭⣛⢹⣧⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀ ⠲⠿⠿⠿⣿⡀⠀⠀⠀⠀⠀⠻⠿⣷⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣫⣼⡏⠀⠀⠀⠀⠀⣹⣿⠿⠷⠦ ⠀⠀⠀⠀⠈⠉⠒⠀⠀⡀⢀⣠⠶⠖⠒⠀⠀⠀⠀⠀ ⠀:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢭⢥⣄⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ .:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ : ..⣴⣾⣿:⣿⣿⣦.. ⢿⣯⣫⣼⡏⠟

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

⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⢤⠀ ⠀⣏⠀⠀⠀⠈⠳⡄⠀⠀⡰⠚⠁⠀⠀⠀⢘⡄ ⢸⠁⠀⠀⠤⣤⣤⡎⠉⠉⣱⣤⣴⡄⠀⠀⠀⡇ ⠘⡄⠀⠀⠀⠀⢈⣷⠤⠴⢺⣀⠀⠀⠀⠀⢀⡇ ⠀⠡⣀⣀⣤⠶⠻⡏⠀⠀⢸⡟⠙⣶⡤⠤⠼⠀ ⠀⠀⢠⡾⠉⠀⢠⡇⠀⠀⢸⠃⠀⠈⣿⣆⠀⠀ ⠀⠀⣿⣠⢶⣄⠀⡇⠀⠀⠘⣇⣀⡤⢌⣙⡲⠀ ⠀⠀⠀⠀⠀⠙⠼⠁⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀ xxoxoleahh on tiktok and instaaa

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣻⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣼⢠⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀�😤😠🕵🨳😨�⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣽⣿⣷⢿⣿⣳⣿⣽⣿⣻⣿⢿⣾⣿⣟⣿⢯⣿⣿⣳⢿⣿⣷⢯⣿⣾⣻⣿⣷⣿⣟⣾⣿⣽⣿⢯⣿⣿⣯⣟⡿⣷⣽⣿⣟⣿⣟⡿⣾⢿⣿⣯⣻⣿⣻⣿⣷⣿⣯⣿⣷⡿⣾⣽⣻⣿⢿⣿⣷⣯⣻⣿⣿⣿⣿⣿⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣾⣻⣿⣾⣽⣿⣻⣿⢿⣾⣿⣽⣿⣟⣿⣽⡿⣿⣽⣻⣿⣾⣻⣿⣿⣯⣿⣻⣿⣿⣷⣯⣽⣿⣽⡿⣿⣯⣟⣿⣯⣻⣿⣟⣻⣿⣟⣿⣟⣿⣟⣻⣿⣟⣿⣯⣿⣳⣿⣿⣟⣿⣷⣟⡿⣿⣿⣾⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣧⣿⣿⣿⣿⣿⣟⣿⣾⣻⣿⢿⣾⣿⣽⣿⣻⣿⡿⣷⣽⢿⣿⣯⣻⣿⣿⣟⢿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⣷⣯⣟⢿⣾⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡃⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣍⣿⣿⣿⣿⣿⢿⣿⣾⢿⣿⣷⣽⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⣇⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣻⣿⣷⣽⣿⣯⡿⣳⣾⣟⣷⣯⡽⣿⣯⡽⣿⢯⣽⡿⣟⣯⢷⣽⣻⣷⣞⡿⣞⡿⣟⢾⣿⢯⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣞⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣻⣿⣟⣻⢿⣻⣿⣟⣻⣿⡿⣻⢿⣻⣿⣟⣻⣽⢿⣯⡽⢿⣯⡿⣞⣻⢷⣻⣽⣾⡿⣟⣳⣽⣾⣟⣳⢿⣯⢷⣻⣽⢾⣿⢯⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿ 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⣮⣿⢰⣿⣿⣾⣿⣿⡾⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣶⢿⡱⢮⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣢⣰⣆⣐⣶⣶⣿⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠐⠃⠟⡿⣿⣿⣿⣿⣿⣟⢯⣜⡻⣍⠳⢣⣥⡞⢏⡱⡾⣟⣯⡽⢿⣿⣿⣿⣿⣿⣠⠀⠀⠈⠀⠀⣇⣿⣿⣿⣿⣾⣟⣷⣿⣿⣿⠈⠀⡇⣿⣿ ⢏⣿⣿⣿⣿⣿⡿⣾⣟⣿⣿⣿⣿⠰⠀⠈⠡⠀⠀⠀⠀⠀⠀⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠢⢀⠀⠣⣟⠸⢀⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣟⣿⣿⣯⣿⣿⣻⣽⠿⣏⡳⢧⣹⡼⢻⣳⡽⢿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⡅⣿⣿⣿⣿⣾⣟⣳⣿⣿⣿⢿⠀⡇⣿⣿ ⣆⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣜⠠⠀⠁⠛⣿⣿⣹⠈⡀⣔⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⢿⣯⣻⣿⡷⣞⣻⣽⡾⣟⢯⣽⡿⣿⣿⣿⣿⣿⣿⣶⢀⠀⠀⠀⠀⠀⠀⠀⡃⣿⣿⣿⣿⣿⣽⣻⣷⣿⣿⣿⠁⡇⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠈⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⡹⢮⡑⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⣿⣿⣿⣿⣯⣿⣿⣟⡿⣿⣷⢿⣿⣿⣿⣿⣟⢾⣻⢾⣽⡾⣻⣷⢯⣳⣽⢿⣯⡿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⢿⣯⡽⣿⣿⣿⣿⠉⡿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⣀⣧⣿⣿⣿⣿⣿⣿⠹⠎⣍⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣻⢿⣯⢿⣷⣯⣟⣾⣻⣷⣯⣟⡿⣿⣿⣿⣿⣿⣬⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣿⣿⣿⣿⢿⣻⣽⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⣟⣯⣟⣿⣿⣿⣿⣿⠻⠉⠛⠟⠛⠛⠛⠉⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡿⢿⣿⡿⣿⣽⣿⣯⣟⣿⣿⣿⣿⣿⣿⣽⢬⢯⡐⠌⠁⠉⠉⠁⠈⠉⠁⠈⠉⠁⠈⠉⠋⣿⣿⣿⣿⣿⢾⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣾⣽⣾⣖⣦⣷⣾⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣷⣶⣶⣴⣾⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣦⣰⣶⣦⣖⣠⣴⣦⣆⣤⣄⣤⣴⣦⣄⣲⣦⣄⣰⣦⣆⣰⣴⣦⣶⣶⣶⣶⣿⣾⣷⣶⣷⣾⣶⣶⣶⣶⣶⣆⣴⣿⣶⣶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣦⣶⣶⣴⣄⣤⣶⣾⣞⣧⣷⣿⣿ ⣿⣿⣿⣝⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿ ⣿⣿⣿⣹⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿ ⣿⣿⣿⣹⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿ ⣿⣿⣿⡾⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡅⣿⣿⣿ ⣿⣿⣿⢘⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿ ⣿⣿⣿⢻⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⣿⣿⣿ ⣿⣿⣿⢸⠀⠀⠀⠄⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿ 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⣿⣿⢻⢀⠀⠀⠀⠀⠠⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿ ⣿⣿⢹⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⣿⣿⣩⠰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⣿⣿⣿⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡕⣿⣿ ⣿⣿⡾⢎⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠠⠀⢢⡁⣿⣿ ⣿⣾⢼⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡁⠆⠀⠀⠂⠀⠀⠀⠀⡀⠄⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⣿ ⣿⣾⣜⠲⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠠⢀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿ ⣿⣿⢿⡿⢿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⠿⢿⡿⣿⣿ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⠿⣿⣿⣿⣼⢠⠀⠀⠀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠟⠟⠿⠟⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣆⣷⣿⣿⠙⠀⠀⠀⠀⠀⡀⣁⣭⣿⣿⣿⣾⣴⢀⠀⠀⠀⠀⠿⠾⣄⣤⣤⣤⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣋⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⣿⣿⠸⠀⠀⠀⠀⠀⡆⣷⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣏⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⣿⢰⡿⣿⢿⡿⣿⣿⣿⣿⣼⠀⠀⠉⠉⠈⠀⠀⠁⠀⠀⠀⠀⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡿⣿⣿⣿⠟⣿⣿⣿⡆⣿⣿⣿⣿⠉⠛⡿⣿⣿⣿⠿⠉⡉⠈⠀⠶⠠⠀⡆⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣿ ⠀⠀⠀⠀⠀⠀⠃⠛⠛⠛⠙⠀⠀⠀⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣥⣿⣿⣾⣷⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠂⠛⠀⠀⡀⣿ ⠀⠀⠀⠁⠉⠉⡟⣿⣿⣿⣿⣿⠿⠛⡿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⢻⣿⣿⣵⢿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣥⣭⣤⣤⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠟⠸⠀⠀⠀⠀⠀⣷⢿ ⠀⠀⠀⡄⣶⣶⣤⣤⣧⣿⣿⣸⣀⣦⣿⣿⣿⣿⣧⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣀⠀⠆⠿⣿⣿⣶⣷⣿⢸⠀⠀⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣤⢠⠀⠀⠀⠀⠇⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⠀⠇⣿⣿⣿⣿⠙⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠃⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠉⠈⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢠⡿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⢀⠀⠀⣀⣷⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⣿⣿⣿⠻⣿⠻⡌⣤⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠈⣤⢠⠀⠀⣀⣤⣤⣦⣶⣴⣤⣤⣀⠀⠉⠉⠉⠉⠈⠀⠀⡀⣄⣦⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠀⠁⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⢸⡄⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡿⣿⣿⣿⣿⣿⣿⢿⠻⠈⠀⡀⣶⣿⢿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⢿⠀⣇⣿⣿⣠⣷⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⣿⣿⣿⣿⣻⠿⡿⣿⣿⣿⣿⣿⠈⠀⠀⣄⣷⣿⣿⣿⠿⠙⠀⠀⠀⠀⠀⠀⠀ ⣿⢰⣿⣿⣿⣿⣿⣿⣿⣴⣿⣾⡇⣿⣿⣿⠸⡀⣿⣿⠀⡀⣷⣿⣿⣿⠸⠀⠀⠀⠁⠉⠛⠿⣿⣿⣿⣿⣾⣠⣄⣤⣶⣶⣿⣿⣿⣿⢿⠛⠙⠉⠉⣏⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀ ⠀⠀⡄⣿⣿⣿⣿⣿⣼⠀⣤⢠⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣶⣶⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢿⠛⠉⠈ ⠀⠀⠀⣷⣿⣼⣿⣿⣿⠈⠀⡇⣿⣿⣿⣿⣿⣿⣿⣽⠀⠛⠘⠀⡆⣧⣿⣿⣿⣿⣿⣶⣿⣾⣶⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣷⣿⣼⣤⣄⣷⣿⣿⣿⣿⣿⣾⣿⣿ ⠀⠀⠀⡇⣾⠀⣿⣿⣿⢻⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⢀⠀⠀⠀⣄⣿⣿⣿⣰⠀⠀⠀⠀⡿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣶⣠⢀⠀⣥ ⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⡀⣧⣿⢿⠈⠀⠀⡏⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⢰⠀⠀⠀⠃⣿ ⠀⡇⢿⠙⠀⠀⡇⣿⣿⣿⢹⡇⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⠿⠟⣿⣿⣿⣾⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⠹⠀⠀⠉⣿⣿⣿⣶⣠⣀⠀⠀⠀⠀⠀⣶⣰ ⠀⠀⣇⣷⢿⠈⡆⣿⣿⣿⣿⡿⣿⣿⣿⣾⣠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⠸⠀⣦⣶⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠸ ⠀⠀⠀⡀⣿⢸⠀⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣤⠀⠀⠀⠉⠈⠀⠀⠀⠀⠉⠉⡏⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⠙⠀⠇⠸⠀⠀⠀⠀⠁⠟⠸⠀⠀⠀⠀ ⠀⠀⠀⠇⣿⢰⠀⡆⣿⣿⣿⣿⣿⣤⣤⠀⠀⠀⠁⠟⡿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⢩⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡿⣿⣿⠻⠉⠉⠀⠁⠿⠿⠉⠉⠉⠉⠉⠋⠛ ⠀⠀⠀⡿⣿⢸⠀⠀⣷⣿⣿⣿⣿⢿⠀⠀⠃⠟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶ ⠀⠀⠿⣿⣿⣿⠿⠀⡿⣿⣿⣿⣿⢛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣽⢉⠀⠀⠀⠉⠛⠟⠸⠋⠿⠸⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⠻ ⠀⠀⡀⣧⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠇⡿⣿⣼⣟⣿⣾⢀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⡿⣬⣷⣿⣿⣿⣿⣿ ⠀⠀⠀⡇⣿⣿⣿⣿⡻⣷⣿⣿⣿⣿⣰⣿⣿⢿⣿⣾⣶⣶⣶⣤⣡⢋⡿⣿⣿⣿⣿⣿⣴⣀⠀⠀⠀⠀⡄⣧⣻⡿⣿⣼⠀⠀⠀⠀⠀⡀⣄⣦⣿⣿⣿⣿⣿⣿⣿⠻⠉⣈⣀⣀⣀ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⢻⣄⣷⣿⣸⠃⣿⣿⣿⣿⣿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⣶⣿⣿⣶⣿⣿⣿⠿⠿ ⠀⠀⠀⡇⣿⣿⣿⣾⣿⣿⢿⡟⣿⢹⡀⣀⣀⠉⠛⣟⣿⣿⣿⣿⣿⣿⣴⣤⣠⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡄⣷⣿⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣀⣤⣶ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣯⣿⣿⣿⣴⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠛⡟⣿⣴⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⣀⣤⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠛⡙⣯⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⣶⠀⠀⡄⣿⣿⡜⣿⣿⡘⣧⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣶⣿⣽⣷⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠿⠀⠀⠀⠀⣧⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣷⢿⡿⣿⠛⡈⣦⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⡿⠸⠀⠀⠀⠀⣿⣿⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠈⠀⠉⠈⠀⠉⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⢿⠻⡛⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀ ⣶⢷⠀⠀⠀⠀⠀⡀⣿⣿⢻⣧⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡙⣈⣀⣄⣦⣿⣿⣻⢙⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢻⣤⢀⣧⣿⣿⣿⣿⣿⣿⣾⣶⣷⣿⣻⢀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣷⠿⠸⠀⠀⣄⣤⣶⣶⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢸⠀⠀⡄⣿⣿⣿⠸⠀⡆⣿⣿⣾⢀⣇⣿⣿⣿⣿⣿⣼⠀⠀⣤⣦⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⣶⠿⠻⠛⠘⠀⠀⠀⠃⠟⠘⠀⠀

⠀⠏⠴⠤⠤⠤⠤⡤⣀⣀⢤⠯⠻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠵⠤⠤⠤⡤⣀⣀⣀⣀⠤⠳⠈⠀ ⠀⣸ ⠀⠀⠀⠞⠀⠀⠀⠀⠇⢲⡴⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣻⠀⠀⠀⡀⢤⠹⠀⠀⠀⠀⢧⠀ ⠀⢸ ⠀⠀⠀⢠⠀⠀ ⠀⠁⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⡀⠀⠀⠈⠀⡇⠀ ⠀⢹⠀⠀⠀⠀⠁⠀⠁⡼⠀⠉⠚⠴⠤⣠⣀⢤⠲⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⣀⣦⣶⠛⠈⠀⠀⠀⠀⠀⢿⠰⡼⠀ ⠀⡇⠙⠀⠀⠀⠀⡀⠁⡟⣿⣻⢘⠀⠀⠀⠀⠀⠀⠀⠒⡌⠸⠀⠀⠀⠀⠀⠀⠀⠁⣿⢠⠀⠀⡄⣏⢹⠀⠀⠀⠀⠀⡄⠻⢰⠀ ⠀⡏⣔⠀⠀⠀⡄⠀⡇⣷⣿⣮⣿⠻⠀⠀⠀⠀⠀⠀⠁⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠃⡽⣿⣿⠈⠀⠀⠀⠀⠀⡄⠸⠀ ⠃⣼⠀⠀⠀⠀⠀⢰⡇⠀⣧⢧⣿⣾⠀⠀⠀⠀⠀⠃⡴⠀⢱⠀⠀⠀⠀⠀⠀⠀⡿⢷⠀⠁⣿⣿⣾⢧⣄⠀⠀⠀⠀⠀⠀⣆⠘ ⡟⢀⠀⠀⠀⠀⠀⠀⡆⠀⡇⣧⣳⢰⠀⠀⠀⠁⠋⣰⠀⠀⡆⠘⠀⠀⠀⠀⠀⡏⣸⡀⢹⡇⣏⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠋⣳⣻⣴⠤⠤⠤⡤⣀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢿⢠⠀⡀⢦⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢧⠀⠀ ⠀⠀⠀⠀⡿⣶⢷⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠇⣿⠀⠀⠀⠀⡀⣷⣽⠳⠙⠀⠀⠀⠀⠀⠀⠀⡞ ⡀⢦⠈⠀⠁⠊⡴⢀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠔⢀⡇⠈⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⡀⢤⣶⠹⠀⠀⠀⠀⠀⠞⢠ ⠀⠀⡀⣀⢀⠀⠀ ⠀⡞ ⠒⠙⣇⠀⠀⠀⣢⢁⠚ ⢄⠲⠒⠖⡷⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡟ ⠀⡟⡾ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⢿⡿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⢿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⠈ ⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣷⠈ ⠀⠀⠀⠀⠀⠀⠀⡇⣗⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⡴⢠ ⠀⠀⠀⠀⠀⠀⠀⡀⢄⡤⢻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣯⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣌⠳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⣷⢰ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⠢⠓⠙⠈ ⠀⠀⠀⠀⠀⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⡤⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢷⠬⠤⠥⡤⣀⣀⡀⣳⣄⢤⣶⠒⠛⠛⠒⠒⠧⡿⣼⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⡏ ⠀⠀⠀⠀ ⠀⠈⣇⠘⠉⡟⣿⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⢹⠀⡁⢹⡄⣿⠸⠀⡟⢿⣿⣾⣇⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢸ ⣇⣿⣿ ⣾⣶⣿⢿⠿⣿⣿⣿⣷⣾⣾⠀⠀⡄⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⡇ ⠀⠀ ⣇⣿⣿⢿⠿⣟⣿⣿⣿⣿⣿⣿⢠⣿⠘⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⢸⠀⠀⠁⣿⣿⣷⣜⣿⣿⣿⣿⣿⣿⣿⣰⠀⡆⠘⠀⠀⣿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧ ⢠⠀⠀⠀⡏⣿⠀⣧⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⢠⠀⠯⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈ ⠀⠀⠁⣿⢿⠀⡆⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠁⠟⣿⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠦⡶⣴⢿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠤⡤⣃⣟⣿⣿⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⣇⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⠟⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀