⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣿⣿⡿⠏⢰⣿⣿⣿⡏⠸⣿⣿⣿⣿⣿⠟⢡⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⠀⠿⢛⣩⡄⠀⠀⢀⡀⠉⠙⣁⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⣀⣀⡋⠉⠀⠃⠼⣿⣿⢃⣴⣶⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⢃⣴⢸⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⠟⠁⢀⣠⡄⢠⠀⠀⢺⣿⡟⠀⠘⡟⣿⣿⣿⣿⣿⣿⡏⢠⡹⠃⣾⣿⣈⠻⠃⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⠀⠀⠀⣴⣿⣿⣷⠈⢀⣶⡀⠙⠇⠀⠰⠀⠙⠻⠃⠛⢋⡉⠀⠀⠀⣓⣂⣀⠈⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡏⣿⠰⣷⠀⣿⣿⣿⡿⠖⣊⢛⠇⠀⠀⡇⢰⢠⣤⡄⣠⣾⡟⢀⠟⣠⣾⣿⣿⣿⡄⠀⡐⢌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⠸⠀⠛⣀⢻⣿⣇⣰⡆⢀⠈⠓⣦⣤⣇⠀⣿⣿⡇⣿⡟⠀⢈⡼⠿⠿⠿⢿⣿⠇⠈⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⠀⠀⠀⠿⠾⢿⣿⡌⢿⣬⣴⠃⡘⣿⣿⠀⢻⣿⠁⡿⢀⡴⠟⠛⠉⠉⠓⠒⠆⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣿⡆⠀⠀⠀⠈⠀⣙⠻⠶⣶⣶⣾⣿⣿⣿⣧⡘⠇⣧⢠⣿⣿⡿⠟⣛⡛⢶⣦⠀⠀⠘⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣘⠁⠀⠀⠀⠀⠀⠀⠈⠓⠘⠉⢻⣿⣿⢸⣿⣷⠀⣿⣾⣍⠉⣴⡅⠉⡉⢠⣉⣴⣷⠀⠰⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠑⠀⢀⣀⣀⣤⣀⠀⠀⠀⠀⢰⣿⡇⢿⡿⣿⣿⣿⣿⠇⠿⣧⣈⣄⠦⠙⢿⢃⣦⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣶⠀⣾⣿⣿⠿⣿⣿⣤⣧⣤⡌⢿⡄⠈⣧⢻⣇⢷⣌⡛⢷⣮⣭⣥⣾⣶⣤⣾⠟⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣇⢻⣶⣿⣿⡟⠀⡙⢿⣿⣿⣿⡷⢀⣷⣴⡘⠀⠁⠈⡁⢻⣶⣌⠛⡻⢿⣿⣭⣤⠆⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢻⡌⢿⣿⣿⡇⠀⠛⢶⣍⡛⢿⣇⢸⣿⣿⣿⣦⣇⡀⠿⠘⣿⢻⣤⠙⠂⢸⡿⠟⣰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⡆⠀⠀⠈⢿⣿⣿⡶⠆⢦⣍⠻⢷⣉⣭⣭⣭⣯⣭⣭⣁⠸⣆⠁⠈⠻⣶⡾⠋⠀⣰⣿⣿⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠁⣦⣀⠈⣄⠻⡇⣰⣿⠷⢨⣙⠳⢶⣭⣭⡛⠟⣛⠛⠋⢰⣿⣦⣀⠀⢤⠤⠀⣠⡾⢛⣡⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⢻⣿⣶⣤⠀⣿⣿⠇⢀⣿⣿⣷⡦⢠⣭⡧⠩⠄⣰⣿⣿⣿⡿⠛⠂⣠⡤⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣇⣿⣿⣿⡆⠘⢿⣄⣿⣿⣿⣿⣷⣼⡿⢃⣴⠀⣿⠿⠖⣋⣤⣶⣿⠟⠁⢈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠹⣿⡿⠟⣡⣤⣌⣁⣬⣭⣭⣛⣏⠉⢀⣬⣵⣶⠆⠸⠿⠿⠿⠛⡁⠀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠁⣄⣿⠀⠸⣤⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⢷⡄⠀⠙⢿⣯⡻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣉⣐⡒⠲⣿⣿⡍⠛⠷⣦⣄⠘⣷⡀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠠⠀⠌ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⢸⣿⡿⠀⠀⠟⠀⠀⠀⠀⠀⠀⣤⡠⢿⣇⠀⠀⠀⠀⠀⠀⢻⣟⣧⡈⢿⡀⠀⠀⠙⢿⣿⣿⡹⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠞⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠀⠙⢿⣧⠀⠀⠈⠻⣷⣽⣇⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⣸⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⣿⡄⠀⠀⠀⠀⠀⠈⢿⡌⢻⣌⢷⡄⠀⠀⠀⠈⠻⢿⣦⣈⠿⣦⣄⡀⢀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠈⣿⣿⡀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⢸⣷⡀⠀⠀⠀⠀⠀⠘⣷⡀⠙⣾⣷⡀⠀⠀⠀⠀⠀⠉⠛⢿⡆⠉⡟⠛⠉⢐⣤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⠤⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢰⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄ ⠀⠀⠀⡀⠀⠀⣿⡟⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠐⣿⣧⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠈⢹⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⢘⣷⡀⠀⣿⣧⡀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠙⡷⠀⠀⠀⣀⣤⠼⠋⠻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⣿⡟⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡇⠀⣿⡟⡅⠀⠀⠀⢿⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⣧⢿⡄⠀⢀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠸⣿⡄⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣷⠀⣻⡟⡇⠀⠀⠀⢸⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠹⡎⢿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⢀⠸⠟⠁⠀⠀⠀⠀⢰⣾⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⣇⠀⠀⢀⣠⣿⣩⣄⣠⣴⣤⣴⠶⠂⠀⢿⣆⠀⠀⠀⠀⠀⠀⢿⣷⠀⢹⡿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣇⣿⡇⠁⠀⠀⠀⠈⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢻⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⢈⣿⡏⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⢀⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠛⣿⡆⠸⣷⠈⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡈⢷⠀⠻⣆⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⣠⣶⣿⣿⣿⣿⣵⣿⣿⡿⡿⠿⠿⠻⠛⠟⠻⠿⢶⡤⠀⢿⣧⠀⠀⠀⠀⠀⠀⣻⣧⢀⡇⠀⠀⠙⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣷⢀⡇⠀⠀⠀⣸⡇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠹⣯⢷⡘⣇⠀⠙⢷⡀⠀⢠⡾⠋⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠐⣠⣾⣿⣿⣿⣷⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⢿⣿⣸⣧⠀⠀⠀⠀⠁⠄⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⠸⡇⠀⠀⠀⠉⣿⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢻⡎⢻⣽⣦⡀⠈⠻⣦⡿⠁⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⠀⠀⠀⠀⠀⠙⠢⠌⣽⣦⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠀⠈⢢⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⡆⣷⠀⠀⠀⠀⢿⡆⠈⢷⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢿⡄⠉⠻⣷⡀⠀⠉⠀⣀⣤⠞⠋⠀⣀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⣦⣤⣉⡉⠀⠀⠤⣄⡀⠀⠀⠀⠹⣧⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠸⣿⣷⢿⡄⠀⠀⠀⠘⣷⠀⠈⠂⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠙⣷⡀⣤⣶⠟⠁⠀⠀⠛⠉⠋⠙⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⣀⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠤⣄⣈⠙⠛⠻⢷⣦⣄⠀⠀⠀⠀⠀⠹⣧⠀⠀⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⡌⢷⡀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢿⣧⠘⣇⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣛⡀⡀⣀⣀⣀⣠⣴⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⠹⠿⣿⣿⣶⣄⡀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣶⣄⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠸⣧⠀⢀⣠⣤⣤⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣷⣄⠀⠝⢿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢹⣷⠿⠁⠀⠈⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠹⢿⣿⣿⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠸⣷⠀⠀⣄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠹⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⢻⡇⠀⠘⢧⡀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⣿⡀⠀⠘⣷⡀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⠶⠶⢾⣿⠟⠛⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢸⣷⡀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⢀⣼⠏⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⢻⣿⡄⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⣟⣿⡈⣿⣷⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⡘⣷⠺⣿⣿⣷⣄⡙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⣾⡗⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⣆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢹⡇⠸⣿⡏⠉⠻⣿⣿⣶⣤⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣸⣷⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡄⠘⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢸⣧⠀⢹⣧⠀⠀⠀⠙⠿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣤⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⣿⣶⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢿⡄⠀⣿⠀⠈⣿⡆⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⡿⢻⣟⣟⣼⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⢻⣿⣹⣯⠛⠿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢸⣧⠀⢻⡄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡞⢡⣾⣧⣤⣴⣿⣝⣿⣯⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠙⣿⣿⣤⡆⠈⡙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣈⣿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢿⣿⣿⣿⣾⣏⣹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠹⢿⣄⣀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠀⠀⠌⣿⡀⠀⠀⠀⠀⠀⠀⢼⣷⡶⠀⠀⠈⣹⣇⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣯⣾⡿⠋⠙⠿⣿⣿⣷⣾⣿⣿⣿⣧⣾⠁⠀⠀⡀⢀⡀⠀⠀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣈⣻⣯⣄⡀⡀⠀⠀⠀⠀⠙⠻⢶⣦⣄⣄⣼⣧⡄⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⢈⣿⣘⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡀⢀⡀⢀⣀⠀⡀⠉⢹⡛⠋⠁⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡅⠀⠀⣾⣿⣿⣿⣿⣿⠿⠿⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠞⠀⠀⢀⣰⡏⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⣠⡞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢸⣿ ⡇⠀⠀⠉⠉⣿⣀⡤⠖⢻⣿⣿⡿⢿⣶⣦⠾⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢸⣿ ⡏⠀⠀⠀⢰⠿⠿⢴⣶⣿⣼⣃⠀⠀⡼⠋⠉⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡼⠋⡇⠀⠀⣼⢿ ⡇⠀⠀⠀⣿⠀⣠⣾⡿⠟⢻⡟⣿⣿⡅⠀⢠⣿⣧⢠⠀⠀⠀⠀⠀⠀⢰⡟⢆⣼⠁⠀⠷⣄⣼⠏⢸ ⡇⠀⠇⠀⣿⣿⣿⠋⠀⠀⠈⣷⡿⠉⢿⣦⣸⣿⣏⣿⣦⣄⣼⣤⡴⢶⣿⣿⣿⠬⠽⠿⣷⣿⡁⠀⢸ ⡇⢸⢰⠀⣏⠈⣿⠀⠀⠀⢀⣩⠵⡤⣸⣿⣿⢸⡏⡟⠛⢻⠟⠁⢠⡿⣠⠟⠁⠀⠀⠀⢻⣿⢯⡳⣾ ⡇⢸⣸⣇⣿⣤⠿⡄⠀⠸⠏⢹⡿⣷⣬⠙⠛⠸⣿⠀⠀⢸⠀⢠⣿⡷⢃⣀⣀⣀⡀⠀⣸⣷⠈⠙⣿ ⡇⢸⠟⣿⣿⣿⣀⣁⡀⠀⢳⡀⠓⠋⣼⢧⠀⠀⣿⡄⠀⣾⢀⡿⢋⣠⣤⣶⣶⣬⣭⣹⣿⣿⠁⠀⣿ ⡿⣼⠀⢹⣿⣿⣿⣷⣿⠦⣄⣉⠉⠉⠁⠀⠀⠀⠘⢧⣸⠘⡟⠀⠀⢀⣠⠤⢤⡉⠙⣿⣿⣧⣀⠐⣿ ⣇⠘⠧⣾⣿⣿⣿⣿⣿⣿⣷⣬⣧⣶⡄⠀⠀⡇⠀⠈⣿⠀⠁⠲⣶⠋⢺⣶⢶⡟⠶⠋⠈⣿⣏⣻⢿ ⡇⠘⣿⣿⣮⣿⡿⠿⠿⠛⠿⣿⣿⣿⣿⡏⠀⢸⡀⢀⠀⠀⠀⠀⣸⣀⠘⠷⠻⣙⣦⡀⡼⠙⣿⡇⢸ ⡇⠀⢹⣿⠉⣿⠁⠀⠀⣀⠀⠀⠛⠘⠛⢳⡀⢻⣷⠘⡄⠸⡈⠳⢤⡈⠑⠒⠚⠁⠉⠛⠁⣠⣾⣷⢸ ⡇⠀⡏⠸⡄⠉⠀⠀⢠⣿⢦⡀⠀⠀⠀⢈⡿⠈⠋⢧⣿⣾⣷⢾⡄⠉⠳⣤⢄⡀⠀⠒⠛⣹⣿⡏⢹ ⣧⠀⣿⡄⢳⡀⠀⠀⢸⣿⣤⡉⠲⢤⡀⠸⡇⠀⠀⠀⠙⠸⢿⣀⣧⠀⡄⠛⣦⣽⡇⢀⣠⠏⠀⠀⣾ ⡟⡆⢹⣿⣿⣷⡀⠀⠀⢉⣹⡙⠲⣄⡈⠶⠒⠒⠒⠐⠒⠒⠾⣇⠹⣾⣷⣄⠉⢁⣴⣿⠏⠀⠀⣰⢿ ⡇⠘⣾⠙⠿⣷⠻⣄⢸⠏⠀⣈⡗⠦⣌⡉⠒⠒⢤⣠⠤⣤⣴⡏⠀⠙⠿⣿⡛⣛⣿⠟⢁⡤⠞⠁⢸ ⡇⠀⠈⠃⡄⠀⠉⠛⣿⠀⠀⣸⡿⠀⠀⠈⢙⡟⠒⢘⣖⣻⠏⠀⠀⠀⢀⣤⣽⠟⢛⣿⠋⠀⠀⠀⢸ ⡇⠀⠀⢀⠸⠀⠀⠀⢹⣧⡀⠻⠀⠀⠀⠀⠈⠃⢀⡼⠋⣿⠀⣀⣩⠴⠛⠉⠀⣠⣾⡷⠀⠀⠀⠀⢸ ⠁⠀⠀⠘⣆⠀⢀⣠⠞⠛⠳⠾⠓⠒⠒⠤⠰⣶⡿⠓⠊⠉⣹⣇⣀⣀⣀⣤⢾⣿⠟⠀⠀⠀⠀⠀⢸
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