⢯⡝⣿⣿⢯⡝⣯⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣤⡶⢦⣤⣤⣠⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⢧⣛⢾⣽⣿⣦⣀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣳⡽⣾⣽⡿⠿⠖⠛⠛⠓⠺⠿⣭⣛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⢧⣛⡾⣽⣿⣿⣿⣷⣦⣄⣄⡀⠀⠀⢻⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⣹⣿⣿⢮⢵⣻⡟⠉⠀⠈⠙⣿⣿⣿⣿⣷⡎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡳⣝⣿⡿⠎⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⠀⠀⠀⠀⠀⠀⢀⢀⣀⣂⣐⣀⣀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣴⣾⣿⣿⠿⠿⡿⢿⣿⣶⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⢿⣿⡿⠂⠠⣿⣿⣟⣻⣿⣷⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⣀⠀⠀⠀⠙⠉⠉⠉⢹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⢰⣟⡃⢲⣤⣤⣿⣄⠀⠀⢸⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡀⠀⠉⠳⠌⣛⠿⠿⠛⠈⣥⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡗⠀⠀⠀⠛⠂⠀⠀⠀⣴⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⠿⢧⣀⠀⠀⠀⢐⠲⢀⣼⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢳⣦⣶⣤⡀⠀⠀⠀⠀⣠⠶⠛⠉⠻⣿⠟⠉⠈⠀⠀⠀⠈⠉⠛⠻⠷⠷⠿⠛⠁⠀⠀⠉⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠿⠉⠛⢿⣦⣄⣀⣀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⡿⠁⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢆⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠲⣯⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠈⠹⡄⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⣀⣤⣴⣿⣆⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⣴⢿⣹⣓⡞⣶⡹⣷⣄⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣴⡾⣟⣯⢷⣳⡽⣞⣳⡽⣏⡿⣷⣶⣦⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⡽⣿⣶⣄⣀⣠⣤⣴⣿⣤⣴⣿⠿⣽⣻⣞⣯⢷⣻⣽⣳⣿⣟⡿⣛⣿⣿⣿⡟⠉⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣯⣿⣷⣿⣾⣿⣿⣿⡿⣟⣯⢿⡽⣽⣾⣿⡇⠃⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡟⣻⣿⢿⣿⣇⠀⠀⠀⣸⣿⣿⢿⣛⣿⣛⡿⣛⣯⣟⡽⣞⣯⡟⣷⣿⣿⠃⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡿⣾⢿⣷⣶⣾⣿⡿⣾⣏⡿⣶⣏⣿⣹⡾⣾⣹⢿⣾⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠸⣿⣿⡽⣾⣽⣯⣽⣧⣿⣷⣾⣽⣳⣟⣾⣳⣿⣷⣿⠿⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⢻⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠸⣇⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣠⣄⣄⣤⣤⣤⣶⣶⣶⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⢠⣿⣾⣷⣿⢺⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣽⣯⣛⣿⣷⣜⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⣰⣿⢿⡽⣿⢷⡿⣿⣯⣽⢧⣿⡻⣾⡷⣿⡿⣽⡿⣿⣞⣿⡿⡼⣿⣿⣶⢻⣿⣻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠘⢰⣿⡿⣯⣻⡽⣯⢷⢯⡷⣿⣳⢯⢷⣻⣿⣿⣟⣳⣟⣿⡿⣾⣿⣟⣽⣿⣻⣟⣾⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⡷⣯⢿⡽⣯⣟⢾⣿⢧⣻⣏⣿⣷⣻⣯⢷⡾⣽⣿⣳⣿⣿⣺⣿⡽⣿⣞⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⡄⣼⣿⣿⢯⡿⣽⣏⡿⢾⣹⣿⣟⢮⡷⢯⣿⣞⣽⣿⣛⡾⣿⢷⣫⣿⣿⡳⣿⣿⣽⡾⣿⢾⣇⠀⠀⠀⠀ ⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠰⢳⣿⢯⣿⢿⣽⣳⣿⣽⣻⢷⣿⣞⡧⣟⣯⣷⣻⣾⣯⢿⡽⣿⣯⢷⣻⢾⣿⣹⣿⡞⣿⣽⣞⣿⡄⠀⠀⠀ ⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡆⣾⣟⣯⢿⣻⣾⣳⣿⡷⢯⣿⠷⡾⣝⡾⣽⣟⣳⣿⣯⢿⡽⣟⡾⣏⡿⣯⣷⢯⣿⡿⣽⣿⡞⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⣿⣻⢞⣿⢷⣿⣟⣿⣻⢯⣿⢻⡽⣏⣷⣻⡽⣳⣿⢯⡿⣽⢯⡽⣯⣟⣷⣻⣟⡾⣿⡷⣿⣟⡷⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣯⣟⣻⢾⣻⢾⣿⣿⡽⣿⢫⣿⡿⣝⣶⣻⡗⣿⣿⢯⡿⣽⣏⣿⣳⣻⢮⣟⣿⡽⣿⣿⣽⣯⣿⡿⠲⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⣷⣫⣟⣯⢯⣟⣿⡯⣟⡱⣿⡿⣽⡳⣞⣿⡽⣻⢯⡿⣽⣳⡞⣷⢯⢷⣻⣾⣹⣷⣯⣿⠿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⣿⣞⡷⢯⣞⡿⣞⣿⣿⣼⠿⠿⠿⢷⣽⣾⣼⣿⣽⣯⣿⣵⣯⠾⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⣀⣀⣤⣤⣶⠶⣖⣶⣿⣛⣿⡿⢿⡿⣟⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡽⢯⣙⠳⣭⡽⢾⣹⢶⣛⣯⠷⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣵⢟⣿⣟⣷⣿⣿⣿⣿⣿⣿⠻⠴⣋⣭⠓⣥⠖⢫⡽⢺⡝⢾⣻⣟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡿⣳⢟⡿⢿⣿⣿⣿⣿⡧⠄⠺⢉⠴⢋⠴⢉⡣⢞⣫⣝⣯⣷⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡾⣱⢾⣵⢿⣽⣿⣿⣿⣿⠊⠐⢋⡔⢩⡔⣩⡕⣉⡷⣛⡿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣳⢟⣵⣿⣽⣿⣿⣿⣿⣇⠀⠊⠼⣠⢞⣡⢞⣭⢞⡵⢚⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⣫⡶⣻⡿⣿⣿⣿⣿⣿⠀⠀⠒⠁⢊⠵⣫⡶⣫⠶⣻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡵⢞⡽⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣡⠞⣣⢞⣷⢚⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣐⣿⣾⣿⣾⡿⢾⡷⣿⡿⠡⢂⣼⣿⡞⣷⢻⡕⠉⣽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣿⡯⢜⠫⣿⢶⣿⣷⣿⡷⢣⡾⣵⢋⡖⡴⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⢺⣿⣹⠆⣻⣽⣷⣿⣞⢛⡡⢫⡾⡷⢋⠈⠀⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⠲⣧⠜⡏⡻⠏⣿⣟⠵⣯⠛⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⠳⢑⢈⣳⡑⠌⡇⢸⡏⠐⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⡆⢈⠢⡑⢎⣯⡇⠃⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢬⣣⢐⡏⣺⠟⡄⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⡙⢮⡙⢾⡦⠁⠐⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠢⠑⢫⣵⢾⣎⡅⢨⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠈⠒⡀⠂⡳⢼⠎⢻⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠈⠀⡙⢢⢨⡟⠀⢸⡇⠀⠀⠀⠀⠀⠒⣜⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠐⠀⠄⣿⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠁⠐⢈⢨⢼⡏⠀⠀⢸⠆⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⢈⠢⣆⣾⠁⠀⠀⣿⠀⠀⠀⠀⠀⢄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⡧⡱⣿⡏⠀⠀⢠⡿⠀⠀⠀⠀⢂⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⢈⡰⢱⣿⠀⠀⠀⣾⠇⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣼⣿⣧⣿⣷⠀⠠⣤⣿⠀⢀⢀⢴⣈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⢿⣿⣿⣇⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠠⠀⢾⠿⢿⣿⣼⡟⠋⠉⠉⠉⠹⠟⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢀⣼⡀⢈⣿⣿⡁⠀⠀⣀⠄⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣰⡿⣿⣽⣾⣿⠧⠀⢀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠠⣀⠔⢨⣿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠠⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡎⣸⡇⢸⣿⣇⣀⣀⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⣀⡀⠉⡎⠀⠀⠀⢀ ⠒⡚⡐⠒⡈⠐⠠⠐⢀⠢⠄⡰⢄⢂⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣷⣤⣼⡟⠈⣿⣿⣿⣿⢠⡟⠿⡼⠁⠀⣀⣸⣷ ⠷⠵⠭⠓⠚⠓⠒⠓⠒⠂⠑⠀⠈⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⠡⠐⠄⠢⣀⠤⢭⡡⢎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣽⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⣸⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣯⣽⡟⠿⡟⣟⢛⡛⠟⡛⢛⣻⡤⠴⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠶⠶⠶⠖⠒⠒⠂⠸⣿⣿⡟⡟⢞⠞⣿⣓⣞⣻⣯⣭⣵⣶⣾⣿⣽⠿⠷⠶⠶⠶⠖⠛⠛⠛⠛ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣤⡤⠤⠴⠶⠶⠛⣻⣟⣭⢫⣭⡹⣭⢏⣌⡱⢂⡔⣠⢂⠥⣊⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠂⠂⠀⠀⠀⠀⠠⠄⠀⠒⠈⠉⠉⠁⠀⠀⣀⣀⣠⣤⣤⡴⢶⠾⠿⠳⠎⠓⠚⠙⠉⠉⠀⠉⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⠀⠈⠀⡀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠁⡀⠁⢀⠀⠂⠈⠀⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⠀⠂⢀⠐⠀⠀⠄⠐⠈⠀⣀⣀⣠⣤⣤⣤⣦⣴⣤⣶⣴⣶⣤⣦⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠂⠁⡀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⢁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⢿⡶⣤⡀⠀⠀⠀⠀⠀⠂ ⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⣟⡦⣤⠐⠈⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣟⡷⣯⣓⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⣀⣤⠀⠀⣷⡖⠲⠶⠶⠶⠶⢤⣤⣀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⢐⣩⣽⣿⠀⠀⢻⣿⣿⣿⣿⣶⣶⣤⣄⠉⠓⢦⣄⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣆⣠⣶⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠘⢷⠄⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⣿⣿⣿⣿⣿⠟⠀⢀⠜⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠋⠀⢰⢦⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿