⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢯⠥⣙⠿⣛⠛⡙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢿⣯⡙⣷⢊⡔⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⢿⡿⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣾⣱⣎⠹⢌⡂⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⣼⠦⣝⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢼⣿⣳⢿⣽⡇⣺⠆⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠜⢼⡓⢬⣏⣿⣇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⡈⣿⡆⣱⣾⣷⣀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⡀⠀⠀⠈⢆⠷⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡙⣧⡿⣟⠛⠻⢿⣿⣶⣖⠀⡌⠀⠀⠀⠀⣀⣤⣤⣤⣦⣌⣻⣯⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠀⠤⣴⣿⣿⣿⢶⡙⡟⣴⣷⣾⣷⣾⣿⣿⣗⣸⠀⠀⣶⣰⣿⣿⡿⣏⣁⣉⠿⣷⡷⣎⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠀⠐⡀⠀⠀⡴⣺⣿⣿⣿⣿⣿⣿⣿⣿⡈⢽⡟⣿⣳⠟⠻⢁⠽⣹⡿⠀⠘⣿⡟⡿⢻⣿⣿⢻⣷⣆⠹⣿⣝⣾⣿⣿⣿⣿⣷⣄⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⢁⡀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⢇⡈⠇⠈⠇⠀⠠⠝⠲⣿⡇⠀⢘⣿⢧⡙⢭⠉⠁⠾⣿⠻⠐⢿⣯⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣠⠀ ⠀⠀⠘⣿⣿⣧⣄⠀⣿⣿⣿⣿⣿⡟⠡⠬⢍⣿⡼⣦⠡⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⢺⣎⠁⠀⠀⠀⠀⢹⡀⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉ ⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡸⠀⣫⣿⣳⢃⠦⠁⠀⠀⠀⠀⢠⡾⡏⠀⢀⠀⠀⣿⡄⠈⠑⠀⠈⢠⣇⡚⣿⡏⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣇⡇⠀⢙⣿⣧⢺⠞⠀⢠⠀⠀⠠⣿⡴⣷⣠⠀⡀⢀⣽⣷⠀⠸⠀⠈⢷⡙⣼⡟⢳⡠⠀⡀⢀⣿⣿⣿⣿⡿⠃⠀⠀ ⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠻⣶⣶⣒⣿⣷⡎⢿⡀⠈⠂⠀⡀⠳⢭⠟⠛⠿⠶⡛⠙⠋⠀⠀⠆⠀⢺⡞⣼⠇⠀⠃⠀⣎⡞⡉⠈⠉⠉⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠀⢻⣿⣿⠟⠁⠀⠀⠀⠘⠲⠭⠴⣿⡗⠀⣿⡇⢀⢤⡷⣆⠉⠰⣟⠀⠀⠀⣀⢀⣧⠀⢀⢤⡿⢃⣿⠢⣅⣴⣠⠇⡴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢄⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠇⣺⡇⣏⠼⣷⣶⣶⣲⡮⡴⢲⣤⣌⣻⡗⢆⢸⣼⠃⣾⡷⠤⠌⠽⡻⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇⠸⠀⢹⣆⠹⡉⠉⠉⠹⣿⢿⡿⠁⡸⣸⡇⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⣿⣞⣿⠀⠁⠀⠙⠷⠤⣤⡀⣊⣼⠿⠁⠀⢠⣿⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠻⣿⣿⡆⠀⠀⠀⠀⠢⠤⠬⠁⠀⠀⢀⣤⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠙⠿⣟⣥⡑⠂⠄⠎⣉⣷⠿⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣛⡾⡟⢫⠝⠻⠿⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢛⡣⣕⣐⡒⠄⢃⡐⣬⣸⣟⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢯⣿⣶⡬⢃⡀⠋⠀⠁⠈⢰⣌⣾⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣐⣿⣿⣿⣯⣻⣷⣮⡿⣿⣶⠄⣦⣾⣿⣏⡛⣿⣿⣿⣿⣦⡀ ⠀⠀⠀⠀⣠⣾⣾⣿⣿⣿⣿⣧⣻⠷⠍⠷⣵⡟⢠⣿⡺⣙⠫⣿⡯⣿⣿⣿⣿⣿ ⠀⢀⣾⣆⣹⣿⣿⣿⢫⢽⣿⡽⢏⠄⠀⠀⣽⡇⠘⢿⡇⠙⡐⣿⣣⣿⡿⠿⣿⣿ ⢀⣾⣿⣿⣿⣿⢿⣿⡌⠐⣿⢷⡏⣂⠈⡴⣯⡈⠀⣸⣣⠀⠈⡼⣿⡿⣢⢌⢸⣿ ⠘⠻⢿⢿⣿⣿⢗⣊⣷⡛⣹⣿⢸⡝⢄⣾⠶⠉⠏⢝⣣⡂⢞⣜⣿⢁⢁⡸⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⢟⢬⣿⣮⡿⠘⣿⡶⢾⡷⣮⣽⢱⣿⢣⡿⠎⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣚⣿⣷⣟⠑⢈⠻⠺⡬⠟⠃⢰⣧⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡽⣙⡿⣿⣎⠠⠀⣀⠀⣄⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢟⠵⣹⣾⠿⠷⠿⢾⡶⣾⡿⢽⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢿⢷⠎⠑⠉⠩⠁⠶⣶⣹⠷⢝⢣⣽⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀