⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣴⣄⠀⠀⣠⣶⣶⡎⢛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢛⣛⣿⣿⣕⣦⣀⣼⡿⣍⢦⣶⣿⣿⣿⣦⡉⢳⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢰⣿⣿⣿⣿⣶⣿⠑⣻⣤⡻⣙⢿⣟⣛⢛⣿⣧⡘⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣿⣿⣟⣴⣿⣿⠓⠲⢼⣿⣮⡿⣉⠩⣻⡗⢻⣿⣿⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡌⣿⣿⡏⠀⣽⣿⣐⣋⣼⠟⠷⣬⣭⣶⣿⡂⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢠⣿⣧⢠⣿⡷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⢻⣿⣿⣿⣉⠈⣡⣽⢿⣽⣿⠀⠸⣿⣈⠻⢄⣀⡀⠀⠀⠀⠀⠀⢸⣿⣷⢸⣿⣿⡄⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣏⢸⣿⣿⣾⣿⡟⠀⠀⠀⠀⠐⢷⣤⡤⠇⣰⣿⠇⣸⣿⣧⣌⡙⢁⢄⢈⣴⣿⡿⠷⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⡇⣼⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠛⢿⣿⠀⠀⠀⣠⣤⠀⠙⠻⠿⠿⠋⠀⠀⠈⢹⣿⣿⠩⣯⣍⠏⠙⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄⡀⠀⢏⣇⡀⠀⠉⠙⠻⢿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠟⠁⠀⢀⢠⣴⣟⡆⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣠⠀⠈⢡⠢⢞⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣸⣾⣿⣷⡒⢢⣤⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⣶⣍⢁⣿⣿⣿⡟⠿⢟⡟⠀⠀⢶⣶⣶⣤⣿⣷⣤⣼⣿⣇⠳⢸⠌⠈⢸⠛⣕⣿⡟⠻⡣⢶⣿⣏⣤⣤⣲⠠⠀⠙⣿⠿⢻⣿⣿⣿⡗⣾⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠚⣿⣿⡿⠃⣠⠋⢲⣶⣶⡜⠻⡉⠭⣭⣭⢛⡻⢟⢾⡥⢘⣸⣦⣍⣸⠿⢶⢟⡛⠛⠂⠴⣍⡍⣽⣂⣗⡀⠀⠈⠲⢬⡻⠿⠟⢑⠻⠗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡙⣍⢡⢀⡀⢀⠖⠉⠀⠀⣠⡿⡿⠷⠏⣠⣞⠤⠊⠁⠀⠀⠀⢜⠂⠝⣿⠯⠀⡠⡗⠁⠀⠀⠈⠉⠢⡀⠀⠀⠙⢿⣿⠀⠀⠀⠈⣦⣠⣶⣧⣾⣿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡧⣼⠀⢀⠴⠊⠁⠀⠀⢀⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠣⠈⣿⠁⠉⠞⠀⠀⠀⠀⠀⠀⠀⠈⢐⠈⠉⠁⠈⠓⢤⡀⠀⡟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⠉⡶⠁⠄⠀⠀⡀⣴⡋⠒⠉⠉⠀⠉⠉⠒⠀⢀⠀⠀⠘⣿⠀⠀⠀⢀⡤⠐⠒⠉⠉⠑⠒⠤⣑⣄⠀⠀⢀⠀⠈⡾⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡀⠘⣤⣀⣤⣾⡂⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠠⠀⠀⣿⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⣀⡰⢁⡴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠃⠱⡄⣹⣿⣿⡇⠀⠀⠀⡔⠀⣀⡀⠐⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠔⠊⠙⠲⣄⠀⠀⠀⢻⡀⣹⣇⡞⠁⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⡿⠃⠀⠀⠀⣽⣿⣿⡇⠀⠀⠀⠃⠸⡿⠃⠀⠃⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢾⠀⠰⣯⣶⠘⠀⠀⠀⠀⣾⠰⣚⠀⠀⠀⠈⢹⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⠇⠀⠀⠀⣸⡿⠿⢿⣿⡀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣇⠀⠀⠀⠀⠀⠀⠘⣄⢀⠀⠀⠀⠀⠀⠀⢰⡇⢨⡄⠀⠀⠀⢈⣿⣿⣿⡵⡻⠋⠀ ⠀⠀⠀⠀⠰⣿⣿⣿⣇⠀⠀⠀⠁⠀⢀⣤⠿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⡁⠋⠉⠀⠀⢠⣾⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣶⣤⠴⠚⢉⡤⡄⠀⠈⠓⠤⣀⡀⠀⠀⣀⣀⣤⠾⠛⠁⠀⠘⠀⠈⠿⣶⣄⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠈⠉⠓⠶⢤⣄⣶⣿⣿⡛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠹⠿⠃⢀⣄⡀⠹⣠⡿⠀⠀⠀⠀⠀⣸⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠷⣶⣶⣶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤⣾⠁⠈⢢⢹⡀⠀⠀⢀⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⡆⠀⣦⠀⡇⡏⠀⠈⢯⣤⣄⡏⠈⡇⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠈⠉⠓⠶⣤⣤⠴⠒⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠔⠉⣢⠀⡞⠛⠁⠀⠘⠁⠀⠀ ⠀⠀⢀⡟⠀⠘⣿⢧⠡⣄⣰⠟⠀⠀⠀⠀⣠⣶⣻⣿⣿⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠅⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣺⢷⣂⠀⠀⠀⠀⢀⠔⠊⠀⠓⠒⣆⠀⠀⠀⠀ ⠀⢀⡇⣠⡶⣶⢳⠈⢿⠀⠀⠀⠀⠀⣀⣼⣫⣿⣿⣿⣮⣎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⠿⣵⡄⠀⠈⠛⠛⠋⣀⡀⠀⣴⠇⠀⠀⠀ ⠀⠈⠉⠁⠀⢸⡇⠇⠀⠀⢀⡠⠖⣻⢉⣡⣝⡛⣻⣿⡿⢻⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢿⣿⠿⢿⣿⣿⣝⠿⡆⠀⠀⠈⠢⡀⠈⠉⠁⠁⠀⠀⠀⠀ ⠀⠀⠀⠏⠙⠛⠁⠀⣠⠖⠛⠀⠀⡁⠛⠉⠀⠙⠉⠀⠀⠀⠈⠻⡟⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠟⣥⠏⠀⠀⠀⠀⠙⠻⢣⢘⠄⠀⠀⠀⠀⠀⠃⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⡀⢀⢨⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⠙⠒⠶⠤⠤⠀⠠⠤⠤⠞⠛⠁⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠘⢄⡣⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡥⠤⠤⠾⣵⡿⠟⠁⢀⣠⠶⠒⠀⠈⠁⠒⠤⡀⠀⠺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠙⠽⡍⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡯⠥⠐⠒⠒⣯⠊⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⠴⠂⠀⠀⠀⠀⠈⠉⠳⣦⡀⠀⠛⡍⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⢀⡇⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡟⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⢡⡀⠀⠀⠈⠱⡀⠀⠀⠀ ⠀⢠⠃⠀⠀⠀⣄⣠⣾⠃⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢠⣿⡆⠀⠀⠀⢰⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⠷⣦⣤⣀⣻⡀⠀⠀ ⠀⠇⣀⠴⣚⡩⠟⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⣿⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⡄⠈⠉⠻⣟⡄⠀ ⢸⠨⠔⠋⠁⠤⣀⡀⠂⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⣿⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⠀⠹⡀⠀⠀⢸⠁⠀ ⠜⠀⠀⠀⠀⠀⢀⣧⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⣴⣿⣄⣄⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠃⠀⠑⢀⡀⠈⡇⠀ ⡄⠀⠀⢠⣦⣴⣾⡃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⠁⢸⣿⠀⢹⢟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢉⡢⡏⢆ ⡇⠀⣾⡿⠟⠋⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⡟⣀⡾⠻⣆⢸⡆⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⢠⣤⣀⠈⡗⠚ ⠃⠀⢀⣠⣤⣤⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⡿⠛⠁⠀⠀⠈⠛⢿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠀⠐⠻⣿⣷⣇⡀ ⢆⢰⣿⣿⣿⣿⠇⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣿⡾⠁⠀⠀⠀⠀⠀⠀⠘⣖⣯⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣾⣿⣂⢻⣧⠕ ⢸⠸⣿⣿⣿⣿⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⣪⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠘⢻⣿⢿⣿⢱⠃ ⠈⣧⣿⣿⣿⣿⣆⠄⠀⠀⠀⠀⠙⠢⠤⣀⣀⣀⣀⢤⡴⠟⠉⢀⡽⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠝⠢⢄⡀⠀⠀⠀⠀⢀⣠⠖⠁⠀⠀⣠⣿⣶⣾⣿⣷⡻⠀⠀ ⠀⣸⢻⡿⠟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣆⡀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⣠⣿⠛⠉⠙⠻⣿⡇⠀⠘ ⠀⡿⣟⠁⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠊⠁⠀⠀⣼⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣷⡄⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⢹⡇⠀⠀ ⡰⠁⡿⡿⠷⠀⠠⢿⣿⡗⠀⠀⠀⠀⢀⣠⢴⠚⠋⠁⠀⠀⠀⠀⠀⢹⣿⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢻⣷⣶⡺⠷⠀⠀⠀⣴⣿⣿⣿⣏⣀⣀⢀⠀⠀⡀⠀⠀

⠀⠀⡀⠀⠀⢀⣀⣀⣏⣿⣿⣿⣴⠀⠀⠀⠷⡺⣶⣷⢻⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⢹⠀⠀⠀⠀⠀⠁⠋⠚⢴⣠⢀⠀⠀⠀⠀⡗⣿⢿⠠⠀⠷⡿⡿⠁⡰ ⠀⠀⡇⢹⠀⠀⠀⠀⣷⣿⣾⢠⠀⠀⠀⠀⠀⠀⢀⡄⣷⢿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣼⠀⠀⠁⠊⠴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠈⠀⠀⠁⣟⡿⠀ ⠘⠀⡇⣿⠻⠙⠉⠛⣿⣠⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈⡀⣆⣷⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢘⠀⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠛⠟⡿⢻⣸⠀ ⠀⠀⡻⣷⣿⣾⣶⣿⣠⠀⠀⠁⠖⣠⢀⠀⠀⠀⠀⡀⢄⠢⠝⣆⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡽⢀⠉⠟⡴⢤⣀⣀⣀⣀⠤⠢⠙⠀⠀⠀⠀⠄⣆⣿⣿⣿⣿⣧⠈ ⠃⢱⣿⢿⣿⢻⠘⠀⠀⠁⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡘⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣪⡮⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠀⠀⠀⠀⣿⣿⣿⣿⠸⢸ ⠕⣧⢻⣂⣿⣾⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡜⣯⣖⠘⠀⠀⠀⠀⠀⠀⠁⡾⣿⣟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠇⣿⣿⣿⣿⢰⢆ ⡀⣇⣷⣿⠻⠐⠀⠂⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⢿⠛⠈⠀⠀⠁⠛⡿⠀⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡀⣤⣤⣠⢀⠀⠃ ⠚⡗⠈⣀⣤⢠⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⡆⢸⣆⠻⡾⣀⡟⢸⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠋⠟⡿⣾⠀⡇ ⢆⡏⡢⢉⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢟⢹⠀⣿⢸⠁⣿⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃⣾⣴⣦⢠⠀⠀⡄ ⠀⡇⠈⡀⢀⠑⠀⠃⢯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣴⣄⣄⣿⣴⣀⣦⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⣧⢀⠀⠀⠀⠀⠀⠜ ⠀⠁⢸⠀⠀⡀⠹⠀⡎⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠀⠀⠀⣿⠀⠀⠀⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⡀⣀⠤⠁⠋⠔⠨⢸ ⠀⡄⣟⠻⠉⠈⡄⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⡇⣿⢸⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠁⠟⡩⣚⠴⣀⠇⠀ ⠀⠀⡀⣻⣀⣤⣦⠷⠙⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡷⢰⠀⠀⠀⡆⣿⢠⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢨⠃⣾⣠⣄⠀⠀⠀⠃⢠⠀ ⠀⠀⠀⡀⠱⠈⠀⠀⡀⢡⠀⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡰⡟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡇⣼⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⡇⢀⠀⠀⠀⠀⠃⣰⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⡍⠛⠀⡀⣦⠳⠉⠈⠀⠀⠀⠀⠂⠴⢀⠁⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣽⡀⢢⠈⠀⠀⠀⠀⠀⠀⠀⠁⠊⡠⠀⠀⠊⣯⠒⠒⠐⠥⡯⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⡍⠽⠙⠀⠀⡀⣀⠠⠀⠀⠀⠀⠀⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠺⠀⡀⠤⠒⠁⠈⠀⠒⠶⣠⢀⠁⠟⡿⣵⠾⠤⠤⡥⣾⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⡣⢄⠘⠀⠀⠀⠀⠀⠀⠀⠃⣾⢀⠁⠛⠞⠤⠤⠠⠀⠤⠤⠶⠒⠙⠈⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢨⢀⡀⠀⠁⠚⡠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠃⠀⠀⠀⠀⠀⠄⢘⢣⠻⠙⠀⠀⠀⠀⠏⣥⠟⡤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠷⡟⠻⠈⠀⠀⠀⠉⠙⠀⠉⠛⡁⠀⠀⠛⠖⣠⠀⠁⠛⠙⠏⠀⠀⠀ ⠀⠀⠀⠀⠁⠁⠉⠈⡀⠢⠈⠀⠀⡆⠿⣝⣿⣿⢿⠿⣿⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⡻⢻⡿⣿⣻⡛⣝⣡⢉⣻⠖⡠⢀⠀⠀⠇⡇⢸⠀⠁⠉⠈⠀ ⠀⠀⠀⠇⣴⠀⡀⣀⠋⠛⠛⠈⠀⡄⣵⠿⣿⣿⣿⣿⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣎⣮⣿⣿⣿⣫⣼⣀⠀⠀⠀⠀⠀⢿⠈⢳⣶⡶⣠⡇⢀⠀ ⠀⠀⠀⠀⣆⠒⠓⠀⠊⠔⢀⠀⠀⠀⠀⣂⢷⣺⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠅⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢋⣿⣿⣻⣶⣠⠀⠀⠀⠀⠟⣰⣄⠡⢧⣿⠘⠀⡟⢀⠀⠀ ⠀⠀⠁⠘⠀⠁⠛⡞⠀⣢⠉⠔⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⢿⠀⠀⠀⠀⠀⠒⠴⣤⣤⠶⠓⠉⠈⠀⠀⠀⠁⠟⣿⣿⣿⣾⢀⠀⡇⠈⡏⣄⣤⢯⠈⠀⡏⡇⠀⣦⠀⡆⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣴⣧⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⣿⣴⢀⠀⠀⡀⢹⢢⠈⠁⣾⡤⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠧⠿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⣶⣶⣶⠷⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡟⣿⣿⣸⠀⠀⠀⠀⠀⡿⣠⠹⡀⣄⢀⠃⠿⠹⠉⠉⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠛⡛⣿⣿⣶⣄⢤⠶⠓⠉⠈⠁⠞⣠⢀⠀⠀⠀⠀⠀⠀⣄⣶⠿⠈⠀⠘⠀⠁⠛⠾⣤⣀⣀⠀⠀⡀⣀⠤⠓⠈⠀⡄⡤⢉⠚⠴⣤⣶⣿⣿⣿⣸⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⣿⣿⣾⢠⠀⠀⠉⠋⡁⣾⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠿⣤⢀⠀⠁⠀⠀⠀⣇⣿⣿⣿⠰⠀⠀⠀⠀ ⠀⠋⡻⡵⣿⣿⣿⢈⠀⠀⠀⡄⢨⡇⢰⠀⠀⠀⠀⠀⠀⢀⣄⠘⠀⠀⠀⠀⠀⠀⣇⣰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⡀⣿⢿⠿⡿⣸⠀⠀⠀⠇⣿⣿⣿⢹⠀⠀⠀⠀ ⠀⠀⠀⡟⣿⣿⣿⢹⠈⠀⠀⠀⣚⠰⣾⠀⠀⠀⠀⠘⣶⣯⠰⠀⢾⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠃⠀⠃⡿⠸⠃⠀⠀⠀⡇⣿⣿⣽⠀⠀⠀⠃⡿⣿⣿⣿⣿⠸⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⠻⠁⡞⣇⣹⡀⢻⠀⠀⠀⣄⠲⠙⠊⠔⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠐⡀⣀⠀⡔⠀⠀⠀⡇⣿⣿⣹⡄⠱⠃⡟⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⡴⢁⡰⣀⡄⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⣿⠀⠀⠠⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⡂⣾⣤⣀⣤⠘⡀⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⠀⡾⠈⠀⢀⠀⠀⣄⣑⠤⠒⠑⠉⠉⠒⠐⡤⢀⠀⠀⠀⣿⠘⠀⠀⢀⠀⠒⠉⠉⠀⠉⠉⠒⡋⣴⡀⠀⠀⠄⠁⡶⠉⣷⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⡟⠀⡀⢤⠓⠈⠁⠉⠈⢐⠈⠀⠀⠀⠀⠀⠀⠀⠞⠉⠁⣿⠈⠣⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⢀⠀⠀⠁⠊⠴⢀⠀⣼⡧⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣿⣾⣧⣶⣠⣦⠈⠀⠀⠀⣿⢿⠙⠀⠀⡀⠢⠉⠈⠀⠀⠁⡗⡠⠀⠯⣿⠝⠂⢜⠀⠀⠀⠁⠊⠤⣞⣠⠏⠷⡿⡿⣠⠀⠀⠉⠖⢀⡀⢀⢡⣍⡙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠗⠻⢑⠟⠿⡻⢬⠲⠈⠀⡀⣗⣂⣽⡍⣍⠴⠂⠛⡛⢟⢶⠿⣸⣍⣦⣸⢘⡥⢾⢟⡻⢛⣭⣭⠭⡉⠻⡜⣶⣶⢲⠋⣠⠃⡿⣿⣿⠚⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣾⡗⣿⣿⣿⢻⠿⣿⠙⠀⠠⣲⣤⣤⣏⣿⢶⡣⠻⡟⣿⣕⠛⢸⠈⠌⢸⠳⣇⣿⣼⣤⣷⣿⣤⣶⣶⢶⠀⠀⡟⢟⠿⡟⣿⣿⣿⢁⣍⣶⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣤⢢⡒⣷⣿⣾⣸⣦⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⡀⣃⣿⣿⢞⠢⢡⠈⠀⣠⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣾⣤⡆⣟⣴⢠⢀⠀⠁⠟⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⢿⠻⠙⠉⠀⡀⣇⢏⠀⡀⣄⢶⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣿⠙⠏⣍⣯⠩⣿⣿⢹⠈⠀⠀⠋⠿⠿⠻⠙⠀⣤⣠⠀⠀⠀⣿⢿⠛⠟⡿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⣼⡇⣿⣿⣾⣿⣿⢸⠀⠀⠀⠀⠀⠁⠛⠿⠿⠿⠙⠀⠀⠷⡿⣿⣴⢈⢄⢁⡙⣌⣧⣿⣸⠇⣿⣰⠇⡤⣤⢷⠐⠀⠀⠀⠀⡟⣿⣾⣿⣿⢸⣏⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠈⡄⣿⣿⢸⣷⣿⢸⠀⠀⠀⠀⠀⡀⣀⢄⠻⣈⣿⠸⠀⣿⣽⢿⣽⣡⠈⣉⣿⣿⣿⢻⠀⡇⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⡷⣿⢠⣧⣿⢠⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠈⡀⣷⠸⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⢸⡂⣿⣶⣭⣬⠷⠟⣼⣋⣐⣿⣽⠀⡏⣿⣿⡌⣿⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⡏⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢦⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⢻⡗⣻⠩⣉⡿⣮⣿⢼⠲⠓⣿⣿⣴⣟⣿⣿⡀⣿⠘⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡘⣧⣿⢛⣛⣟⢿⣙⡻⣤⣻⠑⣿⣶⣿⣿⣿⣿⢰⠃⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⢳⡉⣦⣿⣿⣿⣶⢦⣍⡿⣼⣀⣦⣕⣿⣿⣛⢛⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠷⢛⡎⣶⣶⣠⠀⠀⣄⣴⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀