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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣦⠹⠀⠀⠀⠀⠀⠀⠆⠛⠈⠀⠀⠀⠀⠀⠀⣄⢶⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⠳⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠘⠀⠀⠀⣄⢻⠈⠀⠀⠀⠀⣄⣄⣰⣄⣤⢶⠻⠈⠀⠀⠀⠀⣄⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠘⠀⠀⡇⢻⠛⣟⢻⠛⠛⠛⠛⠛⠈⠀⠀⠀⡀⠤⠀⠀⠁⠉⡉⢿⠙⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⣦⠹⠀⠀⠀⠀⡀⢷⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠠⣿⣾⣴⣠⣀⣀⣀⣀⣀⣈⣿⠀⠀⠀⠟⡿⣿⣶⣶⣶⣶⣶⣶⣶⢿⠘⢀⠀⠀⡄⠷⠈⠀⠀⣆⢹⠀⠀⠀⠀⡀⢿⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⣿⠹⠀⠀⠀⠀⠇⠻⠾⣴⢀⠀⠀⠀⡆⢹⠀⠀⠀⠀⠀⠉⠉⠛⣿⢀⠀⠀⠀⠀⡀⣧⠘⠀⠀⣧⢸⠀⠀⠀⠀⡄⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣦⠿⣰⣿⠙⠀⠀⠀⡀⣷⢷⠘⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⡀⣧⣘⠀⣇⠻⠀⠀⠀⠀⠀⠀⣷⠘⠀⡀⢿⠈⠀⠀⠀⠀⣇⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣾⣶⡴⢀⣧⠿⠾⠤⠷⡿⢸⣧⠻⠀⠀⠀⠀⠀⣷⠛⠛⠚⠓⡟⢹⠀⠀⣷⠘⠀⠁⠀⠀⠀⡄⢐⠀⠁⡟⢠⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⢿⠛⠏⠿⠋⠙⠙⠈⠀⠈⠁⠂⠀⠉⠆⠘⠍⠀⠈⣈⣿⠀⡇⣹⡉⠿⣽⢿⠙⠀⠁⡁⡋⣭⣿⠀⠀⣿⢻⠟⠛⡛⣿⠛⠛⠟⡟⠿⠟⠏⡟⣹⢛⢿⡟⠛⠛⠛⠽⣽⠉⠙⠙⠙⠻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡿⣿⡿⣿⣾⣶⣤⣤⣀⣀⣀⢀⣀⣄⣤⣤⣿⣿⣀⣀⣀⣄⣧⣤⣤⣦⡷⣾⣲⣙⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤ ⣇⣿⣤⣤⣆⣤⣍⣿⠛⣈⠉⡈⢀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⣦⠘⠀⠇⠴⣩⠀⠀⠀⠀⠀⠀⡇⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢰⠀⠋⠾⡷⣰⢀⡃⣼⣀⣿⠀⠀⠀⠀⠁⡏⢸⠛⠶⣤⣤⢦⠻⡿⣠⢀⠀⠀⣆⢸⣇⠉⣼⡆⣖⠠⠀⠀⠀⠀⠀⠀⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠇⣸⠠⣿⠀⠁⣾⠀⠀⣿⠛⠛⠛⠿⣤⣄⢿⢻⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⡇⢿⠾⣠⠀⡀⢀⠇⠻⡿⢦⣴⣀⣇⢸⠀⣷⣷⠉⠋⠛⠙⡟⣿⠉⠛⠛⠉⠏⣸⠀⠀⠀⠀⠀⠁⠛⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠻⡏⣹⢷⠞⠀⠀⠄⣶⡶⢲⠀⠉⠛⣾⢀⠉⡏⣸⣷⢿⠈⣹⣾⠋⠛⣿⣿⣿⠀⠀⠀⠀⠀⠏⣠⣻⣀⠀⠉⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠼⠶⣷⣿⢾⠴⣤⣤⣠⣀⣀⣤⣿⢶⡴⣤⣀⣀⠀⡀⣷⢿⣹⣾⣿⣿⣼⠇⣿⢿⠸⠀⠀⠀⢹⡞⢀⠁⠛⣴⢹⠉⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢠⠀⡇⣹⠉⠛⠾⠤⣤⣿⣬⣯⣿⠶⣤⣤⣤⠦⠻⠀⠀⣄⣀⠀⡋⣈⠀⡆⣿⣿⠀⠀⠀⠁⠚⠖⠤⡘⢧⠋⣶⢀⡿⠐⠀⠀⠁⠋⠾⠶⠤⠤⠶⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠸⠀⠀⣄⣶⣶⣷⠘⠀⣇⣿⣸⠅⠉⠈⠀⠀⠀⣇⠀⠀⠉⠛⡖⢒⡖⠒⠒⡒⢒⠒⠛⠙⡿⠉⠈⠀⢣⡬⣤⠁⠟⣾⠑⠛⠶⣤⣠⠀⠀⠉⠀⠀⡀⢷⠘⠁⠉⠉⠈⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⡀⣧⠘⠀⣧⣿⣨⣀⣆⠹⠀⠁⣾⠀⡟⢀⠀⠁⠉⠚⠖⠶⠤⠤⠤⠶⠒⠓⠙⣈⣄⣦⢸⠀⡟⣇⣶⣠⢀⠀⠀⠋⠾⣴⣀⣧⠻⠶⣤⣠⣀⣀⣀⣄⢷⠀⠀⠀ ⡇⢹⠁⠉⠉⠉⠉⠈⠀⣧⠻⠀⣦⢿⠙⠀⣇⠁⡞⢁⡟⢫⠞⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢯⠛⢸⠀⣼⡾⠀⠁⠋⠞⣴⢀⠀⠀⠇⣼⢁⠛⠶⣤⣠⣀⣀⣄⣧⠀⠀⠀ ⣭⣻⣛⣶⣶⣤⣤⢀⠀⠀⣄⢷⠙⡀⣀⠁⡟⣾⢴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣤⢷⢿⡾⣤⣀⠀⠀⠀⠀⠀⡀⢷⣼⢀⠀⠀⠀⠀⠀⠀⡆⠻⠈⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠾⠀⠷⠨⠀⠁⠋⠛⡟⢿⠈ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠻⠀⠀⠀⠀⠀⠀⠀⠃⣾⢀⠀⡄⣷⠉⡿⢠⢀⣄⣤⢻ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⠙⠀⠀⠀⠀⠀⡇⢸⠀⠀⠁⡟⣿⣦⢿⠙⠉⠋⣼ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠤⠳⠀⠄⠶⠙⠀⠀⠁⠉⠋⠛⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠓⠙⠉⠉⠀⠀⠀⠀⠀⡀⣷⠸⠀⠀⠀⠀⡇⢸⠀⠀⡗⢀⣧⠻⡈⣀⣀⣏⢰ ⠀⡇⠈⠀⠀⠀⠀⠀⠀⠉⡟⢹⠀⡇⠸⠀⠀⣇⢼⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢤⠶⠓⠉⠉⡾⢠⠀⠀⠀⠀⡇⢸⠀⠀⡇⢻⠈⡀⣤⢧⣾⣠⠀ ⠀⡄⢹⠀⠀⠀⠀⠀⠀⣷⡈⣷⠈⡏⢀⠀⠁⡾⢀⠀⠀⠋⠞⠥⡾⠶⠤⠤⠶⠓⠉⠀⠀⠁⠋⠛⠛⠛⠙⠉⠉⠀⠀⠀⡀⣤⣷⠻⠀⠀⠀⠀⡿⢀⠀⠀⡇⣸⣤⢦⡴⣤⢀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⡄⢻⡀⣷⢛⠙⠉⠉⠉⠈⠃⡼⢁⡾⣠⠀⠀⠀⠀⠀⠀⡀⢧⠞⣠⢟⡴⣀⠀⠀⠀⡀⣄⠶⠘⠀⠀⡀⣿⠀⠀⠀⠀⣿⠉⠁⠋⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡆⢿⠛⠛⠉⠉⣉⣉⣟⣿⢸⡼⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⣧⡞⢀⠀⠁⠀⠈⠃⠊⠈⠀⣆⠻⠛⡶⢠⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠸⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢿⠙⡀⣀⣸⡇⢸⠀⠀⠈⠉⠀⠀⠙⠀⠀⠀⡇⢰⠀⠀⠀⣄⣷⠪⣌⡢⠨⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⢸⠀⠋⠛⠛⠙⠁⠉⡈⢷⣿⣻⣿⣿⢿⠹⢷⠈⢳⠀⠀⣀⡢⢾⠀⡀⠀⠀⠁⡾⢹⠀⠦⢿⠙⠀⣄⣳⠪⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⢸⡇⢸⠀⠀⣆⣴⣀⣄⣤⣷⣿⣽⣾⣷⣟⠉⢮⡙⢾⠙⠀⠀⡀⠀⠀⠁⠋⡴⢳⡍⠳⠈⡀⠀⠀⠀⠀⠀⠋⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⣀⣄⣿⣧⣤⣤⠤⠶⠴⡤⣠⢋⠀⠀⣀⣤⣤⠦⠲⠒⠛⠿⣿⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⢸⡄⢿⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⣷⡎⢸⠀⠀⠀⠀⠁⡿⣠⠀⠀⠀⠀⠀⠀⠉⠟⣿⣿⣿⣿⣿⠿⠿⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⢀⠀⣇⠹⠀⠀⠙⠛⣿⢻⠛⡿⢸⠀⠀⠀⠀⠀⡄⢻⣧⠿⠟⠿⡿⣿⣿⢿⠿⠻⠛⠟⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⣄⢷⠛⠋⣿⣿⣿⣿⣿⣿⣿⣽⠀⠀⠀⠀⣆⠻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠋⣿⠀⠀⠀⠀⠀⡀⣇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠀⠀⠀⣆⠻⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣉⠟⣰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠉⠉⡀⣦⠻⣍⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⠏⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⣍⢮⡻⣙⣬⣦⣶⣶⣶⣶⣶⣶⣴⣡⢋⠞⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⠶⠶⠴⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣾⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣤⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢿⠿⠰⠀⠛⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⢿⠘⠟⣺⠓⠘⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠛⣀⣀⢀⠈⠂⠀⠠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⣿⠹⠉⠉⠉⠉⠉⠉⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉