⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢉⢝⡕⡩⠔⢉⡰⠋⢀⠼⠓⠂⢄⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⠎⠘⠊⢀⠔⠁⠀⡰⠁⠀⠀⠀⠀⡇ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢄⡀⠔⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⢣ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠟⣀⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⡘⠁⠀⢦⠀⢸ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠔⢁⣤⣤⣤⡑⠢⡀⠀⠀⢸⠀⠀⡇⠀⢀⠘⠀⢸ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢀⣿⡿⣛⠻⣿⣦⠘⠆⠀⢸⠀⠀⠰⡀⡸⠀⠀⡜ ⠀⠀⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⡈⣿⣌⠦⢘⣼⣿⠂⢸⠀⠈⡆⠀⠀⠀⠀⠀⠃⠃ ⠀⠀⠱⡘⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠉⠀⠀⠀⠀⠀⠑⢌⣿⢿⡿⠟⣃⣴⡿⠂⠀⠘⢄⠀⠀⠀⣸⡜⠀ ⠀⠀⠀⠑⢄⠀⠀⠸⣿⣿⣿⡿⢿⣿⠇⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢏⢹⠋⠉⠀⢸⠁⠀⠀⠀⠀⠑⢒⡶⠋⠀⠀ ⠀⠀⠀⠀⠀⠉⠒⠤⠽⣿⣟⣁⡀⠁⠀⠀⠮⠵⠮⠵⠦⠏⠖⠀⠀⠸⣸⡄⣀⣀⣎⣀⡀⠠⠤⠒⠂⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠉⠉⠉⠀⢀⠶⣀⠀⠀⠀⠀⡠⠞⠉⠩⢻⡍⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⠀⡇⠒⠒⡏⠀⠀⠀⢠⠀⡋⣆⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣦⣤⣤⣾⣇⠀⠀⠃⠀⠀⠀⣠⠞⡖⠀⢀⠷⢣⠀⠀⠣⠀⠀⠀⠸⠀⢸⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣈⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣤⣾⣿⠃⣠⣤⠎⠀⠂⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠘⠤⣀⣀⠀⠀⠀⢀⣀⡃⠀⢸⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⠏⠁⠀⠀⠀⠀⠀⠢⣀⣤⠤⢄⣸⣀⣀⡅⠀⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⡂⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⢁⠀⡇⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠁⡇⠸⠀⢰⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢃⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡃⠀⠸⠄⡀⠈⡙⢪⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⠘⡀⠀⡇⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠘⢄⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠐⠊⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⢷⡶⡿⣟⡿⣟⠛⠛⠒⠺⣿⣯⣭⣶⣖⣦⣄⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⣴⠒⣦⣴⣢⣤⣤⣶⡤⠤⣤⣤⣦⣤⡭⢥⣗⣒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⣿⡟⣯⢳⡝⣮⣳⡝⣮⡳⢯⡷⡄⠀⠀⠈⢷⣏⢷⣫⢟⡿⣏⠓⠻⣿⣧⣥⣤⣶⣌⣷⣶⣒⣒⣲⣾⣥⣀⣠⣽⣤⣤⠼⢭⣿⣿⢿⡻⣟⡿⣯⣅⡀⠉⠻⠿⠿⠀⢸⡿⣜⡳⣟⣦⠀⠈⠻⣷⣕⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⢟⣧⣿⣼⣧⣿⣵⣣⢿⡱⣏⡷⣹⢿⡄⠀⠀⢸⣟⢾⣱⢯⣞⡽⣳⣤⣈⠙⠛⠉⣠⣿⡹⣝⢿⣳⣍⡀⠀⠙⠛⠾⠟⠁⠀⣸⠿⣽⣷⢫⢷⣹⡖⣯⣻⡷⣦⣤⣤⡴⣟⣳⡭⢷⣭⢻⣷⡀⠀⣿⣻⢷⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣹⣾⡟⣧⢻⡜⣯⢿⣞⣧⢟⡵⣫⢗⣯⢻⣄⣀⣾⣛⢾⡱⣏⢾⣱⢿⣜⣯⢻⣛⢿⣹⣾⡟⣼⡳⣝⡾⡽⣦⣄⣀⣀⣀⣀⣴⡟⣯⢽⣻⣿⣎⣷⣹⣶⡿⣝⢶⣣⢟⡼⣳⢧⣛⢷⣚⢷⣚⠿⣞⠿⣜⢯⣿⡽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⡿⢶⡿⣧⢻⡼⣣⠿⣜⢯⣻⣷⢯⡞⣧⡻⣜⡯⣞⡽⣣⢟⡮⣝⢾⡹⣎⡟⣿⢾⣧⣿⣾⢿⡳⣝⢧⣻⣜⡳⡽⣎⢷⣫⢟⡭⣟⢶⡹⢧⣛⡶⣭⢻⣽⣫⡷⠿⠚⠓⠛⠾⢽⣧⣛⡮⢷⣹⢮⣝⡻⣼⢫⡟⡾⡼⣷⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡽⣿⣻⠼⣧⢻⣭⣟⢮⡳⢧⢿⣿⣜⢧⡟⣵⢻⣜⣳⡽⣺⡽⠟⠛⠛⠙⠛⠳⠿⣮⣷⡹⣞⡽⣎⡟⡶⣭⢻⡵⣛⢮⡳⢯⣝⡮⣗⢯⣏⠷⣝⣷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣾⡝⣧⡻⡼⣝⢮⢷⣹⢳⡽⣹⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡷⣽⣯⣳⢻⡼⣿⣟⢿⣯⣽⢫⡞⣿⣞⢧⡻⣎⡷⣭⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣼⣳⡝⣾⡹⣞⢧⡻⣭⢗⡻⣝⢮⣳⢽⡺⣼⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢖⣻⡝⣾⡹⢮⡳⣏⢾⡳⢿⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣏⣿⡷⣹⢧⣿⣿⡹⣎⢿⣯⢷⡹⣞⣯⠷⣝⢧⣛⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣟⠶⣝⡮⢷⣹⢎⣯⠽⣭⢷⡹⣮⡽⣳⠏⠀⠀⠀⣠⣴⣶⣿⣾⣿⣷⣄⠀⠀⠀⠀⠸⣯⣳⠽⣖⣻⢭⡗⣯⢳⡝⣯⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⣿⣎⣿⣳⢽⣚⣾⣷⢻⡜⣯⣿⣏⠷⡽⣿⣏⡟⣮⢽⡟⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⢿⣻⢵⣫⠷⣭⢻⡜⣯⢳⣏⢷⣣⢟⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⢧⣻⡝⣮⢳⡝⡾⣭⣛⠶⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡜⣿⣵⢫⣞⡽⢯⡳⣽⢲⣿⡞⣯⢽⣿⣎⡿⡼⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣟⣮⢳⣏⢷⣫⢞⡵⣏⡞⣧⣛⢾⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣻⢶⣹⢳⢯⣝⡳⢧⣏⡿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣝⣻⣯⣻⢼⣹⡳⣝⢮⣿⣿⡹⣎⢿⡿⣎⢷⡝⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⡿⣼⢳⡞⣧⣻⣾⢻⣼⣿⣶⡿⣎⢿⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣰⡿⡽⣎⡷⠻⣞⣮⢽⡳⣞⡵⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⡾⣹⣿⣇⠿⣶⣏⡹⣾⣿⣇⢿⣸⢿⣿⢹⡎⣿⢹⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣰⡿⢷⣉⢷⣿⢿⣹⣾⡿⣿⡾⣏⢷⣹⡎⣿⣷⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⡹⢷⡏⠁⠀⠈⢹⣷⢹⡎⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣷⢧⣻⢿⣟⣶⣭⣷⣿⢳⡞⣽⣺⣿⢞⣭⠿⠾⠉⢿⣧⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠿⠋⢀⣴⣿⡹⢯⣝⢮⣝⠾⣝⢧⡻⣭⢻⡜⣯⢖⡻⣶⡹⣟⣦⣀⠈⠙⠛⠛⠟⠛⠉⠀⢀⣴⣿⢿⡽⣿⣧⣠⣴⣶⣟⣮⡯⣝⢾⣿⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣷⡹⣞⡽⣫⢟⣵⢫⢷⣹⢶⣿⣛⡮⣿⣀⣤⣀⣼⠿⣿⣦⡀⠀⠉⠙⠛⠋⠉⣀⣠⣴⡿⣏⢶⡻⣝⢮⣳⢞⡯⣝⢾⡱⣏⢷⡻⣜⢯⡳⢧⣻⢼⣣⡟⣿⣳⢶⣤⣤⣴⢶⡾⡿⣏⣿⠛⢄⠨⢉⣿⣾⠉⠁⠘⣿⢎⣿⡏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡿⣽⣎⢿⣱⢟⣮⣛⣮⣳⣿⢿⡟⠛⠉⢹⣯⣯⣽⠿⠚⣷⣻⠿⣶⢶⡶⣶⡻⣟⢯⡟⣼⡹⣎⢷⣭⢳⣏⢾⣱⢯⡞⣽⣚⡧⣟⢮⡗⣯⢳⣝⣮⢳⡽⣖⢯⡻⣜⣳⢮⡻⣝⣳⡭⢿⡾⣆⣱⣦⣼⢿⣆⠀⢰⣿⢫⡿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢿⣮⣝⡞⣶⣽⣶⠿⣭⣻⡄⠀⣠⡿⣞⡧⢀⠆⡉⠿⣷⡻⣜⣧⢻⡵⣫⣝⣮⢽⡺⣽⠟⠉⠛⠳⠾⣯⣞⣧⣻⣶⣹⣞⣽⡾⠿⢾⡿⣜⢮⣻⢼⣹⣎⠷⣝⣮⢳⣏⢷⣣⢟⣧⢻⡝⣯⡳⣏⢾⡹⣷⣿⡷⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠚⢟⡿⣯⣻⣜⡻⢧⣏⡷⣾⢻⡵⣛⡷⣬⡔⢸⣶⢿⣹⢳⢮⡻⣜⡳⣞⡼⣳⡝⣿⣤⡀⠀⠀⡴⠁⠀⠈⠉⢉⡽⠉⠀⠀⣂⣼⠿⣭⡳⡽⣎⢷⣚⢯⡳⣞⡳⣞⢧⣛⠾⣜⡧⣟⣶⣽⣾⢿⣟⡻⠽⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠫⣳⡿⣷⣺⡵⣫⢷⣹⢳⡽⣹⢻⢿⡹⣮⢳⣏⢷⣹⢭⠷⣝⢾⣱⢻⡼⣹⢻⢷⡾⣦⣤⣤⣤⣤⣮⣤⣴⢶⡟⣯⣝⡻⢶⣹⢳⡽⢮⡽⣺⢵⣫⢷⣹⣮⣿⣿⣗⡿⣿⠿⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⠹⢟⣳⣯⣷⣽⣣⣟⡮⣝⡳⣏⢾⡹⣎⢯⡟⣮⢗⣯⢳⣝⣳⢻⢮⡳⣝⢮⡳⣝⢾⡹⣎⢷⣫⢞⣵⢺⣝⣧⣯⣷⣽⣷⡿⣷⣟⠻⠿⠟⠛⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⠛⠫⢻⣟⢻⣷⣿⣾⣷⣿⠾⠽⠮⢷⣮⣷⣯⣾⣵⠯⡷⠿⠾⠓⠛⠚⣿⣟⠿⣿⠿⠛⠛⠓⠒⠓⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⣟⢧⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⣼⣿⡽⣳⣝⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⢻⢯⣾⠇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡗⠀⠀⠀⣸⣿⡿⢻⣷⣫⢟⣶⣵⣂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⣾⣻⣼⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⢠⣿⡿⠀⠈⠮⢝⡿⣮⣝⢯⡷⣶⣵⣒⡠⢄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⣿⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡾⠀⣿⡳⢾⣇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠿⠀⠀⠘⢟⣷⡄⠀⠀⠀⠈⠻⠽⣳⢿⣶⣭⣛⡟⣿⢶⣾⣭⣲⣔⣢⣤⣿⣿⣷⣧⣤⣤⣼⣾⡻⣵⢫⣾⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⡇⠀⢿⡽⣫⢿⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣟⣶⠀⠀⠀⠀⠀⠀⠈⣱⠳⣯⣟⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣯⣿⣏⠉⠉⠙⢻⣿⣿⣿⣿⣷⣮⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢸⡷⣭⢟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣇⣀⣠⣤⣶⣯⣿⣾⣿⣿⣿⢿⣿⣽⠟⠁⠀⠀⠀⣀⣿⣿⢿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣷⣾⣥⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⢿⣧⣛⡞⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠿⠿⣯⣷⡿⣿⣯⣿⣤⣴⣦⣴⣾⣿⣿⣿⣿⣯⠿⠿⢯⣿⣷⣿⣿⣧⣀⣄⣂⣭⣿⣿⣿⣿⣿⣶⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠀⠀⠀⠈⣷⡯⣝⣮⢻⣷⣄⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣟⣿⡟⠉⢄⢂⠒⢤⣿⣿⣟⣷⡿⣿⣿⣿⣿⣿⢿⣿⠋⠀⠀⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⣿⣿⡿⣟⣷⣿⣽⡿⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡇⠀⠀⠀⠈⢿⣳⢮⣗⢮⡻⢷⣤⡀⢀⣴⣾⣿⣿⣿⢿⡹⣮⣿⣿⣿⣶⣍⠄⣊⣴⣴⣿⣿⣟⣯⠿⠟⠾⠷⢿⣾⣿⣿⣀⠀⢀⣀⡀⣠⣿⣿⣿⢿⣟⣷⣿⣷⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣀⣀⣀⣀⣈⣻⣷⢮⢯⣝⣧⢻⡽⣻⢯⣭⡿⣟⡽⣎⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣯⡟⠁⠀⠀⠀⠀⠀⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣻⣯⣿⡾⣿⣏⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡉⠉⡏⠉⠀⢻⠿⣾⣜⢮⢷⡹⢧⣻⣜⡳⣝⢾⣹⣿⣿⣽⣾⣷⣟⣯⣿⣟⣯⣿⣟⣿⣿⣻⣄⣀⣤⣤⣼⣿⣿⡿⣿⣽⡿⣽⣯⣷⣿⣿⣿⢿⣯⣷⡿⣯⣷⣿⡿⣟⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣷⣤⣴⠞⠓⣿⢿⢯⣞⡽⣫⢶⣭⢳⣏⢾⡱⣯⡝⣯⢻⡽⣻⣿⣿⣾⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣟⣷⣿⣿⣿⢿⣻⣽⣾⣿⣻⣷⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⡇⠀⢸⣼⣿⣹⠿⣷⣏⣞⡳⣞⡭⢷⣣⢟⡵⣏⡷⣝⡞⣿⣿⣻⡿⣿⢿⣿⣷⣿⣯⣷⣿⣽⣾⣿⣿⣿⢿⣟⣿⣾⣿⡿⢟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣇⠀⠈⡿⣼⣿⡇⠀⢹⣻⢛⡾⣽⣧⣛⣮⣷⣹⣞⣵⢿⣫⠟⠛⣿⡿⣿⣯⣟⣿⣻⣿⢿⣿⢿⣻⣽⣾⠿⡟⠋⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⠀⠀⣷⣾⢿⣿⠀⠈⣿⣧⠈⠙⠣⠽⠿⠽⠻⠿⠚⠉⠀⠀⠀⠀⠀⠁⠈⠉⠻⠿⢻⣿⢿⢿⡻⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⡄⢀⣼⣿⢸⣿⡄⢠⢻⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠆⣸⢹⡎⣿⡇⢆⢸⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢈⢼⣸⠁⢹⣿⠠⠌⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠁⢸⣿⠃⠸⣿⡀⠈⠸⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⢸⣿⠀⠀⢿⡇⠀⠀⢳⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⢸⣿⡄⠀⢺⣿⠀⠀⠈⣧⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡞⠈⠙⠸⣿⣷⠀⠈⣿⡆⠀⠀⠘⠯⣽⣒⣦⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⢳⣿⠀⠀⣷⡇⠀⠀⢀⠄⡀⠆⡉⢍⣻⠶⢭⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⠟⠁⢀⠀⠀⠀⢸⢼⠃⠀⣿⢷⡀⠠⢋⠤⠑⣨⡴⠛⠁⠀⠀⠙⢮⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣾⠞⡁⠎⡐⢢⠘⡙⢂⢼⢸⠀⠀⠈⠑⢽⡦⣦⣈⣱⠋⠀⠀⠀⠀⢀⣠⣞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢁⡂⢅⠊⠤⡁⠆⡡⢊⢸⣼⠀⠀⠀⠀⠀⠉⠓⠿⠯⠍⠛⠿⠿⠟⠽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇⠈⠉⠉⠙⠲⠦⣕⡐⢤⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⢦⣄⡀⠀⠀⢀⣠⢵⣻⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠚⠛⠙⡫⢹⢒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀