⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢻⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡟⣧⢟⡼⣝⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⡿⢿⡹⣞⡽⣺⡝⣮⢷⡹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⡿⣿⢻⣏⢷⣫⢏⡷⣝⢾⣱⢏⡷⣫⢷⡹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⡿⣏⡾⣱⠿⣿⣿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⣟⢿⡹⣏⢷⣹⢎⡷⣭⢷⣚⣧⢏⡿⣜⢯⡞⣧⡻⣵⣛⢮⡗⣯⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣟⡳⣝⠾⣭⣻⣜⣳⢻⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣷⣶⣦⣤⣀⣼⣿⣿⣛⢧⡟⣼⣳⢻⡼⣫⡞⣽⢺⡵⣫⢾⡜⣯⢞⡽⢮⡽⣖⡻⣵⢫⣗⣻⠼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⢮⡽⣭⡻⣵⢳⢮⡝⣧⢟⣮⣛⢶⡹⣶⡹⢶⣹⢶⡹⢶⣹⢎⡿⣹⢟⣿⣿⣶⣾⣿⡿⣟⢿⡹⢯⡝⣯⣛⢿⣻⣿⣿⣟⡶⣭⢗⣯⢳⡭⣷⡹⢧⣻⢵⡻⣼⡝⣮⡽⣾⣝⡞⣯⢞⣵⢻⡼⣳⡝⣮⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡽⣺⢵⡳⣽⢺⡭⣗⢯⡽⣚⣶⢫⣏⢷⣣⢿⡹⣎⡷⣻⡝⣮⢻⡼⣏⢾⣣⣿⣿⢿⣭⢳⣏⡾⣝⣳⣏⣷⣹⣞⣵⣫⢟⣿⣷⢯⡞⣮⢟⣼⢣⢿⣹⢎⡷⣛⡶⣽⢣⣿⣿⡻⡼⢧⣻⢎⣷⢫⢷⡹⢧⣏⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣯⡗⣯⢞⡽⣎⡷⣻⢼⣫⢞⡽⣎⣷⡹⣮⢳⣏⢷⡻⣜⣧⢻⡵⣏⢷⡭⣗⣿⣿⣻⣾⣾⣿⠾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣮⣿⣜⣯⢳⡽⣺⡝⣧⣻⡜⣯⣿⣷⢫⣽⢻⡜⣯⢞⡽⣺⡝⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢾⣱⡻⣞⡵⣫⢗⡯⣞⡽⣺⢿⣶⣏⢷⣫⢞⡧⣟⡵⣞⢯⡞⡽⣎⣷⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣾⣵⢻⣜⢧⡻⡵⣿⣯⣟⡼⢧⣻⢎⡿⡼⢧⣻⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣟⡶⣻⣜⣳⢽⣫⢞⣵⣫⢗⡯⣿⣿⢧⣛⣮⠽⣎⡷⡽⣮⣽⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠻⢿⣾⣭⡗⣯⠽⣿⣷⣯⣻⡜⣯⢞⣽⣯⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣷⢳⢮⡽⣎⢷⣫⠶⣏⡾⣳⠽⣿⣯⡗⣞⢯⣳⣽⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠉⠻⣿⣾⡝⣧⢟⡿⣿⢿⣿⡿⣿⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣯⢷⣹⢞⡧⣏⢿⣜⣳⡭⣿⣿⣳⢽⡺⣽⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠻⣿⣽⡞⣵⣫⢟⡼⣝⣮⣛⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣧⡿⣜⢯⡞⣮⣳⣽⣿⢯⡳⢯⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠈⠻⣿⣧⣛⡮⣟⡼⣖⢯⣏⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣿⣿⢿⠿⣭⡳⢿⣿⠏⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠙⢿⣷⣝⢮⢷⡹⣞⡼⣎⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣟⣧⣛⢾⡹⢮⡟⣵⣻⡿⠃⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠈⢿⣾⣯⣾⣽⣧⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡽⣲⢏⡷⣻⡝⡾⣵⡿⠁⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣨⣶⣾⣿⣿⣿⣿⣿⣋⣭⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣯⢷⡹⣞⡳⢧⣻⢽⣿⠃⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠒⠈⣨⣿⣿⡟⣯⢻⣜⢯⡟⣿⣿⣿⢻⡽⣭⢏⡟⣿⢿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣯⣞⣽⣺⣝⣻⣼⣿⡇⠀⡀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠈⠁⣿⣿⣆⢠⣿⣿⢏⡾⠋⠉⠉⠺⣝⣮⢻⡼⣳⣝⢮⢯⡽⣎⡟⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠟⣻⣿⡟⠀⢀⠀⣾⡏⠀⠀⢒⣶⡀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⣿⣿⣿⣛⣞⡇⠀⠀⠀⠀⣹⡜⣷⣹⢳⢮⣛⡮⢷⣹⢞⡵⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠏⠀⠀⠀⠀⣿⡇⠀⠀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠘⣿⣿⡽⢮⡽⣢⣄⣠⣴⢻⡼⣣⣏⢯⡳⢯⣝⢯⡞⣽⢺⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⣴⣶⣶⣶⣶⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠇⠀⠀⠘⣿⣿⢧⡻⣵⢫⣞⡼⣳⣝⡳⢾⣭⣛⢷⡺⣝⠾⣭⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⣿⣷⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢻⣷⣶⣾⠿⠀⠈⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠹⣿⣯⡷⣭⢷⡹⣞⡵⣞⡽⣳⢮⡽⣺⡝⣞⣻⣼⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⡆⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠁⠀⠀⠀⢸⣿⠀⠀⠀⠈⠛⠻⠷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣮⣽⢺⡵⣫⢞⡧⣟⡼⢧⣿⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣄⠀⠀⣴⡿⠛⠁⣰⡿⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣤⣄⠀⠀⠉⠙⠛⠿⠷⣶⣤⣤⣀⡀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⢿⡇⠈⠙⠿⣿⣷⣿⣵⣏⣷⣿⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣦⣾⡟⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢿⣿⣿⣿⣦⣶⣾⣿⣿⣶⣦⣌⡉⠛⠛⠿⢷⣾⠟⠋⠁⠀⢀⣤⣶⣿⣿⣿⣶⣿⣿⣿⣷⣶⠀⠀⠀⠀⢹⡇⣀⣀⣀⡀⠉⠙⠛⠛⢻⣏⢡⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠉⠀⠉⠙⢿⣿⣿⠛⠁⠀⠀⠀⢀⣼⣿⣿⢿⡿⣿⣷⣦⡀⠀⠸⣿⣿⣿⡿⣿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⡿⠇⠀⠀⠀⢀⣿⣿⣻⢞⣯⣽⡳⣟⡿⣿⣷⣤⣿⣿⢯⣽⡳⣟⣾⣻⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣺⣿⣷⣫⣟⢾⢶⣻⡽⢾⣝⣻⢿⣿⣿⣯⢶⣻⡽⢶⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣯⢳⢮⣽⣿⣷⡿⣼⢯⣻⡞⣽⡻⣞⣭⣟⢾⣻⢿⣿⣷⣻⣻⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡴⣶⢲⢦⣤⣀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣺⣭⠷⠛⢻⣿⣿⣿⣯⣗⡿⣳⡟⣽⣞⢾⣫⣽⣯⣟⡿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⡭⣟⡞⣶⣹⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⣿⣿⣿⣗⣻⠷⣾⣿⣿⡟⣿⡽⣽⣫⢿⡿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⠓⠛⠮⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⢀⣤⣶⣶⣤⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡏⠀⠈⣻⣿⣿⢯⢯⡿⣽⣿⣳⣻⢧⣟⣧⣟⣳⠿⣽⣻⣿⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⢀⣴⣿⡿⣽⡞⣿⣼⣿⣿⢯⢷⣛⡾⣞⡼⣯⢟⣳⡽⣞⢿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⢠⣾⣿⢯⣟⣶⢻⣷⣿⣟⣧⣟⢯⣯⠷⣏⡿⣞⣯⢷⣻⡽⣞⣳⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠋⢰⣿⠇⣿⣿⣏⡿⣼⣾⣿⣿⣻⡼⣞⡾⣻⣼⣻⢽⣳⠿⣼⣛⣶⣻⣭⢷⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠟⠉⠀⠀⣿⡿⠀⣿⣿⣞⡽⣷⣿⣟⡾⣵⣻⣭⢷⣻⠶⣏⡿⣞⣻⣳⠿⣼⢧⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⣸⣿⠃⠀⣿⣿⣾⣽⢯⢷⡾⣝⣳⢧⡿⣹⣞⢿⣹⢷⣫⢷⣏⡿⣽⣾⣿⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠘⣿⣿⣿⣿⣿⡼⣏⣯⣟⢾⣳⢯⡯⣟⡾⡽⣧⢿⣹⣿⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣞⣾⢫⡷⢯⡷⢯⣽⣳⢯⣿⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⢀⣤⣾⣿⣿⣿⠋⠛⢿⣿⣿⣿⣯⣟⣯⣽⢻⣮⣽⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⣠⣴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣶⣤⣀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣶⣤⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀