⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⡴⠶⠒⠚⠛⠋⠉⠉⠽⣛⡲⣒⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠦⠒⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠚⠭⣖⠢⡀⠀⠀⢠⡀⠈⠑⠫⠆⠀⣭⣟⠷⣤⡠⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣼⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠉⠁⠀⠀⣼⠹⣟⢆⠀⠀⠀⠀⠀⠉⢈⣻⣦⡈⠳⣄⠀⠀⠀⠀ ⠀⠀⢀⣴⠞⠃⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⠂⠀⢠⡞⠋⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⢳⣑⡤⣀⠀⠀⠀⠀⠑⢌⢿⡢⡈⢷⡀⠀⠀ ⠀⢠⢾⠃⢀⣴⡮⠇⠀⠀⢀⡴⢉⠎⡾⠉⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣔⣮⠷⠃⠀⠀⠀⠻⠾⢭⣕⡆⠀⠀⠀⠈⠫⣻⡜⡌⢳⡄⠀ ⢠⣿⠃⣴⣣⠋⣠⡄⠀⢠⠏⣀⡼⢸⠃⢀⠀⢸⡇⠀⠀⡆⠀⣀⠀⠐⢿⣷⢄⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠑⢻⣱⠀⢻⡄ ⢸⢏⡮⣺⢡⡊⠀⠀⠀⡞⡠⡋⠀⣾⢰⠏⣠⢸⠀⠀⠀⣧⠀⣇⠀⠀⢸⡍⠳⣿⠀⠀⠀⠀⢼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡇⠈⣷ ⣿⢬⢱⠃⡽⠀⠀⠀⢸⢳⢡⡇⠃⢻⢈⠀⣿⠸⡇⠀⠀⢹⡀⢳⢣⠀⠀⢳⡀⠘⣧⢠⣺⣷⡮⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⠀⠙ ⣿⠘⡞⡆⡇⠀⠀⠀⢸⠁⢸⡌⢀⢸⡞⡀⢸⠀⢷⠀⠀⠀⢻⣞⣧⢣⠀⠈⣿⡄⠘⣷⠏⠈⢟⠿⠀⠀⠀⠀⠀⣄⠀⠀⠀⢸⠈⡆⠀ ⢿⢸⣇⠀⡇⠀⠀⢨⣬⣧⣆⣇⡘⠄⢿⣣⠈⣟⡜⣆⠀⠀⠀⠻⣎⣧⢧⡶⠺⣷⠒⢻⡀⠀⢸⣄⠀⠀⠀⠀⠀⠈⢧⠀⠀⢸⠁⡇⢠ ⠸⣏⣼⡄⣷⠀⠀⠘⣏⠘⣆⠸⡍⠙⠺⢿⣄⠘⣞⣽⡄⢀⡴⠟⠛⢮⡳⡕⣄⢹⣃⠘⡇⠀⠈⡘⡦⠀⣀⣀⡀⢸⡜⣇⠀⣼⢰⠁⡜ ⠀⠘⢦⡳⡌⢧⠀⠳⢮⣷⣶⠛⢻⣶⣤⡀⠙⠟⢮⣧⡙⣎⠀⠀⠀⠀⠙⢟⣮⠀⢿⠀⡇⠀⠀⣧⢿⡛⠉⢫⡿⣿⡀⢸⠀⡿⡘⣾⠁ ⠀⠀⠀⠙⠿⣮⣷⣀⢱⣸⠁⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠉⠳⢬⣾⣇⠀⢰⡉⢇⡇⣠⣏⠱⡈⣧⢸⢠⡷⣽⠃⠀ ⠀⠀⠀⠀⣰⠟⠁⣨⠅⢀⢤⡀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣟⣿⣿⡿⠋⠀⣸⢱⠀⣷⠋⢘⡇⢡⣿⡾⢸⣟⡼⣄⠀ ⠀⠀⢀⢶⡏⠀⡼⠁⠀⢸⡿⢷⣌⡻⣿⣿⣿⡄⠀⠀⠀⠀⠾⠋⠉⠀⠀⠀⠈⢉⡿⠁⠀⢀⢷⡜⢼⢷⢠⠞⠀⢈⣿⠃⢘⣯⣱⠬⠷ ⠀⠀⡎⣿⠀⣾⠇⠀⣀⣿⣶⠶⠎⠙⠛⢛⣋⡀⠀⠀⠀⠀⠀⠀⢠⡤⣤⡄⢀⡞⠂⣠⢴⡟⣳⢁⡟⡜⠉⠀⢀⣾⡯⣗⣷⢿⣿⣿⠂ ⠀⠰⢠⡏⢰⣾⠀⣼⠋⣧⡁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⣱⠋⢁⡞⡰⣱⢟⣠⣃⡤⣾⠿⡼⣙⣮⣙⣦⣌⠓⠓ ⠀⠠⠸⣇⢘⣿⠀⡿⢀⣿⡷⡀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠋⠀⠀⠀⠀⠀⠀⣿⢁⢀⡞⣸⠟⢉⣟⣩⡶⣹⠿⣆⡟⠛⠚⠋⠉⠛⠃⠀ ⠀⠀⢇⢿⡜⢹⠀⣷⡟⠀⠻⣟⢦⡀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⢻⡘⣾⣾⡇⢾⣿⢫⡿⠞⠁⠀⠻⠧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⢿⣾⡆⣿⠀⠀⠀⠈⠻⢮⣶⣤⠀⠀⠀⠀⠀⠀⠀⣀⣤⣲⡿⢿⡌⢿⣏⠀⠻⢿⣷⢬⣤⣤⣴⣢⡤⣢⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⡟⣇⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠒⠒⠛⠛⢻⣉⠁⠀⠀⢷⣿⣉⣧⠶⣻⡾⠋⠁⠀⠀⠈⠙⣯⣣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣟⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣤⠶⣾⣿⢵⠞⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢷⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⡘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⡽⣷⠺⠯⠛⠉⠻⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣷⣣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠈⠀⠀⣀⢤⠤⣒⣊⣩⣭⡵⠞⠉⠀⠿⠄⠀⠀⠀⢰⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠘⣧⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⢕⡵⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢇⡇⢻⡎⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡟⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠠⠻⣿⠀⠘⣧⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡇⠀⠀⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣦⣴⣿⣿⣿⣶⣶⣤⡀⣰⣧⣶⣶⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⠀⠀⢠⡿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⡇⠀⠀⢸⣇⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⠁⠀⠀⡿⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣡⣟⠀⢀⣸⡷⠁⠀⠀⠀