⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⢲⡞⣽⢻⣝⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⡻⣭⢳⣭⢳⡝⣮⢳⣎⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⢧⣛⢮⡳⣭⢳⣎⢷⡹⣎⢷⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣤⢤⣠⢖⡶⣲⢖⡶⣖⢶⣲⢖⡶⣒⢦⡤⣴⢏⡷⣹⢮⡝⣮⢳⣭⢳⣎⢷⡹⣎⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡖⡾⣏⠿⣜⢧⡝⣮⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⣏⢾⡹⣎⢷⡹⣎⢷⡹⢮⡝⣮⢳⣎⠷⣎⢷⡹⣎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡺⣝⢮⡳⣝⡳⣭⢻⡜⣧⢻⡜⣧⢻⡜⣧⢻⣜⣧⣿⣜⡳⣎⣷⣹⢎⡷⣹⢎⡷⣹⢧⡻⣜⡳⣎⠿⣜⢧⡻⡼⣭⢳⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡻⣜⢧⡻⣜⢧⡻⣜⡳⣭⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⣎⣿⣿⣷⡝⣾⣿⣿⣮⢳⣽⣾⣵⢫⡞⣵⢫⠷⣭⢻⡜⣧⢻⡵⣋⢷⡹⢶⡹⣴⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣯⡝⣮⢳⡝⣮⢳⡝⣮⣷⣯⣷⣭⡷⣹⢎⡷⣹⣎⠷⡹⠮⠷⠾⠼⣿⣿⡿⠶⢿⣿⣷⣫⣞⣿⣿⣧⢻⡜⣯⢻⡜⣧⢻⡜⣧⢻⡹⢮⡝⣧⢻⡜⣯⢞⡵⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⢻⣭⣛⢶⡹⣎⢷⡹⣎⢷⡹⣾⣿⣿⣿⣿⣿⠓⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⣧⢻⡜⣧⢻⡜⣧⢻⡜⣧⢯⡝⣧⢻⡜⣧⢻⡜⣏⠾⣭⢧⣢⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⢻⣜⡳⢮⡝⣮⢳⡝⣮⢳⡝⣮⡳⠟⢿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⠀⣿⣿⠃⠀⣸⣿⡇⠀⠀⣿⣿⠹⣧⢻⡜⣧⢻⡜⣧⢻⡼⡍⠛⠚⠧⣟⡼⣣⢟⡼⣻⡜⣧⢳⢷⡀⠀⠀⠀ ⠀⠀⣰⠷⣭⢳⢮⡝⣧⢻⡜⣧⢻⡜⣧⠟⠉⠀⠀⠀⠈⠁⠀⠀⣀⣠⣄⣀⣤⣤⣾⣿⠿⠟⢺⣿⠏⠀⠀⠻⡿⠁⠀⠀⠉⠁⠀⠙⣧⢻⡜⣧⢻⡜⣧⢻⡽⡀⠀⠀⠀⠉⠳⢏⣾⣱⢻⡜⣯⢞⡽⡄⠀⠀ ⠀⠀⢻⡻⣜⢯⡞⡽⣎⢷⡹⣎⠗⠋⠀⠀⠀⠀⠀⠀⣀⣤⡀⣿⣿⣿⣿⠿⠛⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡞⣵⢫⡞⣵⢫⡞⣧⠀⠀⠀⠀⠀⠀⠑⢯⢧⡻⣜⣏⠾⣽⡀⠀ ⠀⠀⠈⢳⣏⠾⣜⡳⣝⡮⠋⠁⠀⠀⠀⠀⠀⠀⣰⡀⢹⣿⠛⢻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⡷⣹⢎⡷⣹⢞⡆⠀⠀⠀⠀⠀⠀⠈⢷⢻⡜⣮⢻⣜⣣⠀ ⠀⠀⠀⠀⠉⠻⢎⡷⠉⠀⠀⠀⠀⠀⠀⢀⠀⢻⣟⡿⠿⣽⡷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣏⡾⣱⢏⡞⣧⠀⠀⠀⠀⠀⠀⠀⠈⢷⡻⣜⡳⣎⢿⡀ ⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⣀⣀⣀⣠⣴⣿⣿⠾⣿⣻⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢯⡞⣽⢺⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⣭⢳⡝⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⣿⣿⣿⣿⣿⡦⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣧⣛⢾⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣾⡿⣟⣯⣿⠀⠁⠒⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡼⣣⢟⣾⠁ ⠀⣠⣤⣴⣿⣟⣿⣾⣟⣷⣻⣿⣭⢿⠝⠓⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠂⠐⠠⠤⠤⠤⠤⠤⠤⣤⣤⡤⣤⡤⣤⢤⣤⣤⠤⠤⠤⠤⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡱⣏⣞⡺⠀ ⢠⣿⣿⣿⣿⣽⣿⣿⣿⣽⣳⣯⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡝⣧⢻⣜⡳⣞⣼⡀⠀⠀⠀⠀⠀⠀⠉⠻⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⢳⡝⣮⠇⠀ ⠘⣿⣷⣿⣾⣿⣿⣿⣾⢷⣻⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢜⡷⣎⢷⡹⣎⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣎⢷⣹⡞⠀⠀ ⠀⠀⠻⣽⡿⣿⣿⣿⣿⣻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢧⣻⡜⡾⣆⠀⠀⠀⠀⠀⠀⠀⣸⣏⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣝⢮⣳⠝⠀⠀⠀ ⠀⠀⠀⠈⠿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⣰⡳⢾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⡝⣮⡷⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡴⣖⢶⣫⢟⡽⣛⢿⡹⣞⡻⣏⢿⡹⢦⡖⡶⢦⣠⢤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⣞⢧⡻⠁⠀⠀⠀⠀⠀⣀⣤⢾⣹⢳⢧⡻⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣞⢧⣏⢷⡹⣎⢷⡹⣎⢷⡹⣎⠷⣭⢳⡝⣮⡝⣧⢻⡝⣧⣛⢮⣛⢶⡹⡞⢶⣓⢶⡲⢧⣛⢶⡹⣎⣟⣁⣀⣠⢤⡴⣺⡝⣯⢞⣣⣏⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣻⡵⣛⡼⡳⣎⢷⡹⣎⢷⡹⣎⢷⡹⣎⠿⣜⢧⣛⢶⡹⣎⢷⡹⢶⡹⢮⡝⣮⢳⡝⣧⣛⢮⡝⣧⣛⢮⡳⣝⠾⣜⢧⣛⢮⣳⣧⠿⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠛⠺⠧⠿⠜⠧⣻⣜⣧⣻⣜⡻⣜⢧⣛⢮⡳⣝⢮⡝⣧⣛⢧⡻⣜⢧⣛⣶⣹⣮⠝⠶⠽⠮⠷⠛⠙⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠫⣞⡵⣫⢞⡽⣲⡝⣮⢳⣽⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣵⢫⡞⣵⢻⣜⣳⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣧⢻⣜⡳⣎⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣧⢻⣜⡳⣭⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣧⢻⣜⣳⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣜⢧⡻⣜⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⡝⣮⢳⡭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡻⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀