⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣠⣤⢶⡶⣿⡿⣟⣿⣻⢿⡿⣿⢿⡿⣿⣿⣿⣶⡲⢦⣄⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣤⢶⣟⡿⣯⣟⣯⣟⣷⣻⡝⣷⡿⣯⣟⣯⣿⣻⢷⣻⣾⠋⠀⠀⠈⠙⠛⢶⣤⣀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⣤⢾⡿⣽⣻⢾⡽⣟⣾⢷⣻⣞⡷⣿⢯⣟⣷⢿⣽⡞⠋⠉⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣦⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣴⢿⣽⡳⣻⢯⡿⣼⣟⡿⣞⣯⣻⢾⡿⣽⣻⣟⣾⣯⣬⣁⣀⣀⠀⠀⠀⠀⠀⠀⣴⣽⣟⣿⣿⡿⠿⡻⣧⣄⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣶⢿⡝⣿⢾⡽⣽⣻⣽⣟⣾⡽⣟⡷⣏⣾⣟⣯⣷⢿⠗⠛⠳⠋⠛⠁⠀⠀⠀⠀⢀⡴⠿⠟⠚⠉⠀⣀⣸⡿⣯⣿⣷⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⠀⠀⠀⣴⢿⣯⢿⡽⣯⢿⡽⢿⣽⡾⣽⣚⢿⣯⣟⣷⡛⣾⠙⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣻⣿⣿⣽⣿⣦⡀⠀⠀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⣼⣟⡿⣼⠻⣿⣻⢿⡼⡜⣿⣻⣟⡿⣿⣼⡻⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⢿⡼⣧⣟⣿⣿⣟⣿⣧⡀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⢀⣞⡛⢾⡽⣯⣇⣽⣻⢯⡿⣽⠼⣿⣽⣻⢫⣥⣤⣤⣤⣤⣤⣀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⢯⣼⢯⡿⣿⣿⣿⣷⣿⡜⣿⣷⡀⠀⠀⠁⠀⠀⠀ ⠀⠐⠀⠀⠀⣾⣽⣻⣆⠻⣷⣻⣯⣟⡿⣽⢯⣿⣳⣯⣟⣯⢿⡽⣾⣽⣳⡟⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣿⣯⣟⣾⢿⣽⣷⣿⣿⣟⣯⢿⣾⣿⣷⠀⠀⠀⢂⠀⠀ ⠀⠀⠀⠀⣼⣟⣾⣳⢯⣆⡿⣷⣻⢾⡿⣽⣳⡜⣷⣻⢾⡽⡯⠿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠛⠛⠋⠉⠉⠉⢉⡽⣟⣿⣳⣿⣾⣿⣷⢻⣿⣧⠀⠀⠀⡀⠀ ⠎⠀⠀⢰⣟⣞⢷⣯⣟⡾⣽⢿⡽⣯⢿⣽⣳⢯⣿⣽⠯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣾⣿⣿⣿⢿⣿⡽⣯⣿⣿⣿⣷⡅⠀⠀⢰⠀ ⠀⠀⠀⣼⣟⣾⣣⣟⣾⡽⣯⡟⣽⢯⣏⡛⣽⠟⠉⠁⠀⠀⠀⠀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⣿⣻⣽⣿⣞⣿⣿⣿⣯⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⢠⣿⣻⣞⡷⣯⢷⣿⣳⣟⡾⣯⢿⣭⡤⢰⣶⢶⣶⡶⣿⢿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣽⣷⣿⣿⣾⣿⣿⣿⣿⣿⡿⣞⡿⣿⣿⣿⣾⣿⣿⡆⠀⠀⠀ ⠀⠀⢸⡷⣏⡿⣽⢯⣟⣾⢷⣯⢿⡽⣟⣷⣻⢷⣟⡿⣾⣽⣹⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠼⠿⠛⠚⠛⠛⠛⠛⢋⣽⣿⡿⣣⣾⣿⣽⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⢸⡿⣽⣻⢮⣟⡿⣾⣭⣞⣯⡿⣽⢾⣽⣻⠞⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢲⣶⣿⣿⣿⣟⣷⣿⣿⢿⣿⣿⣿⢿⣿⣿⠄⠀⠀⠀ ⠀⠀⢸⣻⣽⣟⡿⣾⡽⣷⣻⢾⣽⣻⣽⣻⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣳⣿⣿⣿⢋⣾⣿⣾⡿⣴⣿⣿⣿⣿⣹⣿⣟⠁⠀⠀⠀ ⠀⠀⠘⣧⢿⡾⣽⣳⢻⡷⣯⣿⣼⡫⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⣷⣾⣳⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠛⣿⣽⢷⣯⢷⡚⣽⣾⣉⢀⡀⣀⣀⣀⣠⡤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣫⣿⣿⣿⣿⡿⣯⣿⣯⣿⣿⣿⡿⠟⢛⣻⢿⣻⣽⣿⣿⠁⠀⠀⠀⠄ ⢃⠀⠀⠸⣿⡽⣟⡾⣯⢷⣼⣟⣯⡿⣽⣻⢿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⣉⣠⣤⣾⡿⣿⣿⣿⣿⡿⠋⢀⣴⣿⣯⣿⡿⣼⣿⡟⠀⠀⠀⠰⠀ ⠈⠄⠀⠀⢳⡿⣌⣿⣽⣻⢾⣽⡾⣽⣳⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⠱⣷⣿⣿⣿⣿⡿⣻⣿⣿⠃⠀⠀⠀⠁⠀ ⠀⠠⠀⠀⠀⢍⠻⢞⡷⡯⢟⣾⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣼⣿⢋⣽⣿⢿⣿⡿⠋⣠⣶⣻⣾⣽⣿⣿⣿⣳⣿⣿⠏⠀⠀⠀⠌⠀⠀ ⠀⠀⢀⠀⠀⠈⢳⣎⢻⣽⣆⣁⣠⣤⣤⣤⢲⣶⣶⠛⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⣠⣴⣿⣿⣯⣟⣿⠷⣿⣿⣿⣿⡟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠃⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡎⣷⢻⣯⡟⢳⡟⣾⡝⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣤⣿⡏⣼⣿⣿⢹⣾⣿⣧⣿⡟⣭⣿⣽⣿⣿⣽⢺⣿⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠫⣽⣟⣾⡽⣯⣟⣷⣻⠏⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣴⣷⣾⣿⣿⣿⣽⣿⠿⠟⣿⣿⣷⣿⣷⣿⣿⣿⣿⣷⢫⣿⣿⠗⠁⠀⠀⡐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠻⣾⡽⣓⡙⡾⠻⠆⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣻⢧⣻⣼⣻⢿⣿⣿⡿⢭⣀⣦⣿⣾⣾⣽⠋⣱⣼⣶⣿⣿⣧⣿⡿⠋⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠈⠻⣽⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣴⣮⣿⣿⡿⣿⢿⣻⠬⢷⡿⠫⣽⢯⠧⢞⣳⣿⣿⣟⣵⡿⠋⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⢟⣫⣳⣽⣿⠏⣱⣾⣿⡟⣠⣿⣿⠁⣶⣿⣿⣯⣻⣿⠿⡫⠞⠁⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠤⣟⣾⣷⣋⡼⣷⣿⣿⣿⣶⡿⠿⠿⣷⣿⣽⣿⡞⣻⣟⣿⣿⠿⠋⠈⠀⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠙⠹⠾⠿⣧⡝⣻⣿⣿⠿⡁⡴⣴⣻⣶⣯⣽⠿⠾⠛⠋⠉⠀⠀⠀⢀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⠀⠀⠀⠉⠋⠛⠾⠿⣽⣯⣶⣻⣴⡴⡁⠿⣿⣿⣻⡝⣧⠿⠾⠹⠙⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠠⠀⠀⠀⠈⠋⠿⣿⣿⣟⣻⡞⣿⣽⣿⣷⠿⠿⡿⣶⣿⣿⣿⣷⡼⣋⣷⣾⣟⠤⣤⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠀⠀⠁⠞⡫⠿⣿⣻⣯⣿⣿⣶⠁⣿⣿⣠⡟⣿⣾⣱⠏⣿⣽⣳⣫⢟⣾⣀⣀⢀⠀⠀⠀⠀⠀⠀⠂⠛⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀⠋⡿⣵⣟⣿⣿⣳⢞⠧⢯⣽⠫⡿⢷⠬⣻⢿⣿⡿⣿⣿⣮⣴⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⠻⠈⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠋⡿⣿⣧⣿⣿⣶⣼⣱⠋⣽⣾⣾⣿⣦⣀⢭⡿⣿⣿⢿⣻⣼⣻⢧⣻⣾⣴⣀⢀⠀⠀⠀⠀⠀⠀⠆⠻⡾⡙⣓⡽⣾⠻⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⠀⠀⠁⠗⣿⣿⢫⣷⣿⣿⣿⣿⣷⣿⣷⣿⣿⠟⠿⣿⣽⣿⣿⣿⣾⣷⣴⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠏⣻⣷⣟⣯⡽⣾⣟⣽⠫⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡗⣿⣿⢺⣽⣿⣿⣽⣿⣭⡟⣿⣧⣿⣾⢹⣿⣿⣼⡏⣿⣤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣶⢻⡝⣾⡟⢳⡟⣯⢻⣷⡎⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠃⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣠⡟⣿⣿⣿⣿⠷⣿⣟⣯⣿⣿⣴⣠⣦⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠛⣶⣶⢲⣤⣤⣤⣠⣁⣆⣽⢻⣎⢳⠈⠀⠀⢀⠀⠀ ⠀⠀⠌⠀⠀⠀⠏⣿⣿⣳⣿⣿⣿⣽⣾⣻⣶⣠⠋⡿⣿⢿⣿⣽⢋⣿⣼⡟⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠽⣾⢟⡯⡷⢞⠻⢍⠀⠀⠀⠠⠀ ⠀⠁⠀⠀⠀⠃⣿⣿⣻⡿⣿⣿⣿⣿⣷⠱⣿⣿⣿⣯⣿⣿⣿⣿⣿⣾⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣳⣽⡾⣽⢾⣻⣽⣿⣌⡿⢳⠀⠀⠄⠈ ⠀⠰⠀⠀⠀⡟⣿⣼⡿⣿⣯⣿⣴⢀⠋⡿⣿⣿⣿⣿⡿⣾⣤⣠⣉⠉⠋⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣽⢿⣻⣽⡿⣯⣟⣼⢷⣯⡾⣟⡽⣿⠸⠀⠀⢃ ⠄⠀⠀⠀⠁⣿⣿⣽⣻⢿⣻⢛⠟⡿⣿⣿⣿⣯⣿⣯⡿⣿⣿⣿⣿⣫⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡤⣠⣀⣀⣀⡀⢀⣉⣾⣽⡚⢷⣯⢷⣽⣿⠛⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣳⣾⣷⣺⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠷⡫⣼⣿⣯⡷⢻⣳⣽⡾⢿⣧⠘⠀⠀ ⠀⠀⠀⠁⣟⣿⣹⣿⣿⣿⣿⣴⡿⣾⣿⣾⢋⣿⣿⣿⣳⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⣻⣽⣻⣽⢾⣻⣷⡽⣾⡿⣟⣽⣻⢸⠀⠀ ⠀⠀⠀⠄⣿⣿⢿⣿⣿⣿⢿⣿⣿⣷⣟⣿⣿⣿⣶⢲⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⠞⣻⣽⢾⣽⡿⣯⣞⣭⣾⡿⣟⢮⣻⣽⡿⢸⠀⠀ ⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣽⣿⣾⣣⡿⣿⣽⢋⠛⠛⠛⠛⠚⠛⠿⠼⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣹⣽⣾⡿⣟⢷⣻⣷⣟⡽⢿⣯⢷⣾⣟⢯⣽⡿⣏⡷⢸⠀⠀ ⠀⠀⠀⡆⣿⣿⣾⣿⣿⣿⡿⣞⡿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣽⣿⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⡿⢿⣿⡶⣶⢶⣶⢰⡤⣭⢿⣯⡾⣟⣳⣿⢷⣯⡷⣞⣻⣿⢠⠀⠀ ⠀⠀⠀⠀⡿⣿⣿⣯⣿⣿⣿⣞⣿⣽⣻⣿⣿⣿⣿⣿⣴⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⢀⠀⠀⠀⠀⠁⠉⠟⣽⡛⣏⢯⣽⡟⣯⡽⣾⣟⣣⣾⣟⣼⠀⠀⠀ ⠀⢰⠀⠀⡅⣷⣿⣿⣿⣯⡽⣿⢿⣿⣿⣿⣾⣦⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠯⣽⣿⢯⣳⣽⢿⣯⡽⢿⣽⡾⣟⣯⢷⣞⣟⢰⠀⠀⠎ ⠀⡀⠀⠀⠀⣧⣿⢻⣷⣿⣾⣿⣳⣿⣟⡽⢉⠉⠉⠉⠋⠛⠛⠉⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠿⡯⡽⢾⣻⣷⡜⣳⣽⡿⢾⣻⣷⡿⣆⢯⣳⣾⣟⣼⠀⠀⠀⠀ ⠀⠀⢂⠀⠀⠀⣷⣿⣾⢿⣯⣟⣿⣿⣷⣽⢿⣾⣟⣯⣿⣿⣿⣺⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⡟⣳⣽⣾⡽⢿⣯⣟⣯⣳⣿⢯⣽⡿⣟⣯⣻⣷⠻⣆⣻⣽⣾⠀⠀⠀⠐⠀ ⠀⠀⠀⠁⠀⠀⡀⣷⣿⡜⣿⣷⣿⣿⣿⡿⢯⣼⢯⣿⣿⣶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣤⣤⣤⣤⣤⣥⢫⣻⣽⣿⠼⣽⡿⢯⣻⣽⣇⣯⡽⢾⡛⣞⢀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⡀⣧⣿⣟⣿⣿⣟⣧⡼⢿⣿⣼⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠼⡻⣼⣿⡿⣟⣻⣿⡜⡼⢿⣻⣿⠻⣼⡿⣟⣼⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠀⡀⣦⣿⣽⣿⣿⣻⣽⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠚⠙⣾⡛⣷⣟⣯⢿⣚⣽⡾⣽⢿⡽⢿⣯⡽⢿⣯⢿⣴⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⣷⣿⣯⡿⣸⣀⠀⠉⠚⠟⠿⡴⢀⠀⠀⠀⠀⠁⠛⠋⠳⠛⠗⢿⣷⣯⣟⣾⣏⡷⣟⡽⣾⣟⣽⣻⣽⡽⢾⣿⡝⢿⣶⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⣄⣧⡻⠿⡿⣿⣿⣟⣽⣴⠀⠀⠀⠀⠀⠀⣀⣀⣁⣬⣯⣾⣟⣻⣽⡿⢾⣻⣯⣞⡿⣟⣼⡿⢯⣻⡳⣽⢿⣴⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⣦⣷⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠋⠉⠋⡞⣽⢿⣷⣟⢯⣿⡷⣞⣻⢷⣾⣟⡽⢾⣻⣽⡿⢾⣤⢀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⣀⣤⢶⠛⠙⠈⠀⠀⠋⣾⣻⢷⣻⣿⣯⣟⣯⡿⣷⡝⣻⣷⣟⣯⣟⣯⡿⣟⢶⣤⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⣄⢦⡲⣶⣿⣿⣿⡿⢿⣿⡿⢿⣻⣿⣟⡿⣿⡶⢶⣤⣠⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀