⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡧⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⣠⡾⠉⠙⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⣀⣠⡼⠓⠛⠉⣩⣇⠀⠀⠀⠞⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣢⡴⠶⢸⡋⠁⢀⣤⣄⡈⠻⣇⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⣀⡀⠀⠀⣀⡬⢇⠀⠀⠀⠈⠉⠲⢌⠛⢦⣼⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠒⠋⠁⠀⣠⠞⢩⢣⠈⢧⡀⠀⠀⠀⡀⠈⠁⠀⠉⠙⠦⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⡴⢳⢡⡎⢸⢧⡀⠙⠦⣄⠀⠙⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⣄⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣪⣦⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⣸⠁⠀⡾⠁⠀⣇⠳⣄⣉⡀⠉⠀⢸⡀⠸⣄⢄⠸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠣⣠⣶⡿⠋⠁⣠⠴⠊⠀⠀⢀⣴⠖⠲⣾⠟⠛⠉⢻⣆⢣⠀⠀⠀⠀⠀ ⠀⠀⣴⠇⡏⠀⢸⡇⡆⠀⢹⠀⠘⡇⠈⠙⣆⠈⡇⠀⢸⣎⠀⣧⣦⠉⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⡶⣴⠛⡵⠃⠀⢀⡞⣡⠊⠀⠀⢠⡞⠁⠀⠸⣍⠀⠀⠀⢀⣏⠳⡇⠀⠀⠀⠀ ⠀⠀⣿⠀⡇⠀⢸⡇⢿⠀⢸⡇⡀⣿⣜⣄⡸⣦⣿⠀⢸⣿⡄⣿⣿⣾⣿⡆⠀⠀⠈⠀⠀⠀⠀⠀⢻⠃⢠⠇⠀⢀⡞⡴⠁⠀⠀⢠⣿⠃⢰⠀⠀⢩⡇⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⣿⡇⢻⣤⣾⣷⣎⣇⠘⣧⣿⣾⡟⠺⣿⣿⣿⠛⣾⣿⠃⢿⣿⣾⢻⡿⠚⢄⠀⠀⠀⠀⠀⠀⣤⣴⡏⡰⠀⣸⢱⢁⠀⠀⢀⢿⠃⠀⠘⠀⠀⠘⠳⢤⣰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⡜⣿⣯⣼⣟⠹⣄⣿⡇⢼⡷⢶⣿⣿⣿⣷⣿⠏⠀⣟⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢁⣇⣰⡟⡎⢸⠀⡀⢸⡞⠀⠀⠃⠀⠀⠀⣄⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠹⢿⣽⡧⣼⡿⠿⠈⣻⣿⠀⠐⠚⠒⠛⠙⠻⣿⡆⠘⡯⢹⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⡇⣸⣿⡿⡇⣧⠸⡄⡇⢸⣿⣄⡀⠀⠀⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣿⡆⠀⣠⠤⠤⠟⠀⠀⠀⠀⠀⠀⠠⢿⠇⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⡿⠁⣾⢻⣿⣿⣿⣷⣷⣿⡄⣇⣧⡸⠹⣧⠰⡞⠏⢁⣠⢾⣁⡀⠀⣠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠸⡄⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠀⠀⠀⠀⣀⣠⣿⣁⡀⢹⡄⢻⡿⠩⣿⣿⡿⣷⣿⡎⢻⣿⣯⣷⣿⡋⠉⠹⠞⠛⡇⠀⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣄⣀⣀⣀⠀⠀⠀⠀⣠⡾⠋⣹⣿⡿⣿⣧⣶⣾⣿⣿⣿⣿⣿⠀⢸⣷⣺⠁⠀⠒⠂⠀⠹⣿⡝⠉⡽⣿⣿⣿⣿⡎⠀⢰⠀⡇⢰⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠒⠀⠀⠀⢀⣠⡾⠋⠀⢀⡿⢹⠁⠉⡙⣿⣏⢻⣿⣿⣯⡻⣄⡸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠣⠬⠝⢻⡟⠀⢠⠏⣰⢡⡟⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡤⢶⣿⡁⠀⢀⡴⠋⠀⢸⠀⢀⡅⢸⣾⣿⣿⣿⣿⣿⣮⣳⣍⢿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⠶⣋⣠⠖⣿⣇⣇⣾⣷⠈⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣷⢧⠶⠋⠀⠀⠀⣺⣀⡞⠁⣼⢿⣿⣿⣿⣿⣿⣿⣿⣮⣯⣷⡀⠀⠃⠀⠀⠀⠀⠀⠘⣻⡿⠋⢁⣴⡟⣻⢟⣼⣹⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⡿⣿⠉⠀⢀⣠⣶⣿⣿⣿⡶⣶⣟⡿⣻⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⣄⣀⡀⠀⠀⣀⣠⡴⠋⠀⣠⣿⡟⣰⣿⢻⠁⢼⠀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢻⣿⣿⣿⣷⣌⣳⣴⠛⣿⣿⣿⣿⣿⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢷⣿⠟⠛⠻⣿⣿⣿⣿⠟⣡⣴⣿⡿⠻⠿⡿⣿⣸⡀⢸⠀⠀⠁⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠻⠷⣦⡀⠐⠪⢻⣿⣵⣿⣿⣿⡿⠀⠀⡆⠹⣿⢯⣧⠈⡇⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣥⣄⣾⣿⣿⣿⣿⡟⠛⠉⣰⠃⠀⠀⠀⠀⠙⠳⣄⠀⠙⣿⣻⠛⣽⠃⢀⣴⠃⠀⠸⢷⣝⣷⣷⠀⠀⢠⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣨⠟⣳⣿⣿⣿⡿⣿⣿⠿⢿⣿⣿⡿⢿⣴⣮⣿⣿⣿⣿⣿⣿⣷⡝⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⢷⣸⢃⡴⠋⣀⣤⠀⠀⠀⠈⠙⢿⡆⠀⠘⣷⠀⠀ ⠀⠀⠀⠀⠀⠞⠁⣼⣿⣿⣿⣿⣿⣿⡯⠷⠞⠻⠋⠙⠾⣿⣿⣿⣒⣶⣾⡿⠋⢉⣳⡤⢤⢏⠀⠀⠀⠸⡄⠐⢤⡀⠀⠀⠘⠂⠘⣿⣏⣤⡾⢻⡏⠉⠳⡄⠀⠀⠈⣧⠳⠀⣿⡇⠀ ⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⡄⠀⠀⠀⣽⣿⣿⠟⡋⠀⣠⣿⡏⢀⡟⢸⠀⠀⠀⠀⠘⣄⠀⠙⠦⣀⠀⠀⢀⡿⠋⠁⢀⡿⠀⡀⠀⠙⣆⠀⠀⠈⢧⠀⠘⣽⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣀⠀⣷⠀⠀⣼⣿⡿⣿⣿⣿⣿⡿⠁⠁⢚⡄⢰⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠳⢄⠈⣿⡀⠀⣼⠗⠋⠀⠀⢠⠸⡄⠀⠀⠈⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠇⠀⢰⣿⣿⣿⡿⠋⢸⣿⠃⠀⠀⢸⠀⢸⠀⠀⠀⠀⣀⡀⢀⡱⡄⠀⠀⠀⠁⢸⣷⣾⡁⠀⠀⠀⠀⠈⡆⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡏⠹⣿⣩⣿⣆⠀⠀⡞⣿⡿⠋⠀⢠⣿⡿⠀⢧⠀⢸⠀⠘⡆⠀⠀⠈⢙⣻⣿⣯⡘⢆⠀⠀⠀⠀⢿⡇⠉⠳⢦⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⣤⣀⡟⠙⡇⠀⢹⣿⢛⣚⡀⢸⢳⠟⠀⠀⠀⣼⣿⡇⠀⠘⣧⢸⠀⠀⢧⠀⢀⡴⠿⣿⣯⣿⠋⢠⠁⠀⠀⠀⠘⣿⠀⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠇⠈⠈⡃⠀⠀⠀⠀⢻⣿⣿⣇⢸⣿⣤⣤⣄⣰⣿⣿⠇⠀⠸⠾⠘⠄⠀⠸⡦⠞⠁⠀⣠⣿⠛⣷⠆⠱⡄⠀⠀⠀⢸⣿⡂⣄⣀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀