⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠈⠀⡁⠌⠠⠁⠌⠠⠁⠌⠠⢁⠂⡔⠰⠰⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠷⠼⠤⣧⣘⡆⢳⡘⢆⠳⡘⣌⠧⡹⣌⢧⡙⢮⡱⢫⣜⢣⢯⣹⡹⢮⡝⣭⢏⡽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠄⠂⡁⠌⠠⠁⠌⡠⢁⠂⡡⠄⢃⡆⡄⣱⡠⠔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢾⣌⢣⢓⢬⢲⠱⢎⡲⣙⣦⣝⣣⢎⠷⣪⢵⡹⢶⡹⢎⡾⣱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠂⢀⠂⠠⢀⠡⢈⠐⡀⠂⢌⠐⡈⢆⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⡶⠓⠛⠉⠉⠉⠉⠉⠉⠉⠙⣉⣚⣉⣳⣏⡻⣴⢫ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠠⠀⠂⠄⠂⠄⢂⠐⡁⠂⡌⣰⠎⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⢀⣄⡠⠤⠖⠓⠚⠉⢀⣴⡾⣝⡲⣝⡲⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠈⢀⠐⠈⠠⠈⡴⣤⠦⠔⠛⢩⠃⠀⠀⡀⠄⠒⠉⠉⠀⠒⢉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡙⠃⠀⠄⣰⠜⣫⢼⣿⢫⢳⠮⣵⢣⢟⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢤⣌⡤⣅⣳⣄⡠⠤⠖⠃⠀⠀⡔⠀⠀⠠⠀⠤⠄⢀⡀⠈⠒⢄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢳⡀⢀⡴⢊⡵⣾⢟⡽⣒⡏⣧⢻⡜⣽⢪⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⡐⠈⣗⠠⢀⠉⠀⠀⠀⠀⠀⠀⢠⠁⢠⢲⠒⢲⠦⢤⣀⠈⠐⡄⠀⢇⠀⠀⠀⠀⠈⠑⠒⠤⣀⠀⠀⠀⣧⢷⢺⣽⠻⣍⠾⣜⡵⢺⣥⠳⣽⡸⢧⣛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠠⠐⠀⠄⠓⢦⡠⠤⠀⠀⠀⠀⠀⠀⡄⠈⠌⢂⠘⠁⠀⠈⠳⡦⠁⠀⠸⡄⡠⠒⠉⠁⠈⠉⠁⠘⢷⡄⠀⢹⡾⣿⢬⣛⡼⣙⠶⣭⠳⣎⠟⣶⡹⢧⣛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠈⠀⠄⠡⢈⠐⣸⠕⠒⠩⢄⡶⠒⠀⠀⢡⠀⠀⠁⠈⠔⢀⡠⢤⠗⠀⠀⠀⠁⠀⢀⡒⠉⠉⠒⠤⡀⠀⠳⡀⢸⡀⢿⡖⡧⢞⡭⣳⢎⢿⣸⢛⡶⡹⢧⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⡄⠂⠘⠓⢲⣶⡆⠐⠒⠒⢲⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡔⢫⡍⠛⢲⣤⠈⡆⠀⡇⢸⠀⡌⣿⢹⣮⣵⢣⡟⡎⣷⢫⡞⣽⢣⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠂⡐⢀⠂⢔⡞⡌⠀⠀⠀⠂⠘⣆⠠⢈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡐⢇⣌⠁⠀⠀⠉⣳⡄⢀⣇⡞⡜⠁⠘⣷⢺⣬⢳⢳⡝⣶⢫⡞⣵⢫⣞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠠⠐⠠⠈⣎⣴⠬⠔⣲⠆⣠⢖⠸⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠊⠔⢂⡪⠜⢀⣼⣾⣥⠀⠀⢈⢹⡷⣎⣏⢧⡻⣜⢧⣛⡮⢷⣺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠠⠁⠌⠠⠁⠌⣀⠂⠔⠹⢋⠔⣸⡄⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡿⢿⡏⠏⠀⠀⠀⢧⠹⣞⡼⣣⢟⡼⣫⢞⡽⣣⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠐⠈⠠⠁⠌⡐⠠⠈⢌⠢⡁⢮⢏⠇⠐⢻⢆⠀⠀⠀⢴⡖⠢⠤⣀⡀⠀⠀⠀⠀⣀⡠⠔⢊⡵⢯⢏⣿⡽⣦⡀⠀⠄⠀⢣⡘⣷⣽⢎⡷⣝⡾⣹⢧⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠠⠁⢂⠁⠂⠄⡁⠎⡐⠤⢱⢯⡿⣦⢨⣽⠳⡃⠀⠀⠈⢯⡉⠅⢢⠉⠶⡄⢀⠀⠀⠈⣷⢿⣙⢮⢯⡟⣷⡹⣟⣶⡞⢀⠂⠌⡙⡮⢿⣺⢵⣫⢗⡯⣞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠒⠈⠉⠉⢰⡖⠒⠒⠤⠄⣀⡀⠀⠀⠀⠀⠀⠠⠀⢀⠁⠂⠄⡈⠄⡡⠐⠌⡐⣸⣻⠋⠀⢻⣴⠷⡀⡙⢾⣥⣂⠀⠙⠚⠒⠛⠋⠁⣘⣠⣶⣺⣿⣷⢪⣽⣾⣈⡼⣿⢼⣹⢷⣤⠘⡐⠄⡚⣄⠻⣞⡵⢯⣞⡽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠉⠉⠐⠒⠲⠬⢄⣀⣀⣌⡐⠠⠐⢠⣄⣥⠞⠉⠑⠧⡀⢀⠘⣏⠀⠁⠱⢾⡤⣈⠉⠐⠦⣤⣀⢀⢰⡏⡖⢾⢫⢿⣯⢻⡽⣗⣯⢳⣽⢺⡽⣺⣟⣦⠘⠤⠡⢌⠳⡌⢻⣳⢾⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠂⠀⠀⠀⠈⠘⠌⠉⠀⠀⠀⠀⠉⠂⠛⠑⣶⣶⣯⣟⡛⣬⡙⣎⢳⢎⡽⣫⡝⣾⠻⣟⠾⣟⣷⣻⡼⣿⡱⣈⠱⢌⢒⡘⠦⡙⢯⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⠀⠀⠀⠐⠠⡀⢰⣶⠀⠀⣠⠟⣹⢇⡎⢵⢢⡝⣬⢓⡮⣕⣣⠞⣖⢻⡬⣛⡭⢷⣟⣷⣻⢿⡄⢣⠎⢦⢉⠖⡙⣆⡹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢰⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⡀⠀⠀⠈⠑⠀⠀⣿⡼⡱⢎⡜⣣⠳⡜⢦⣋⠶⡳⣜⢫⡞⣥⢳⣝⢺⣣⢯⢿⣻⣯⣿⡆⡚⢤⢋⡜⡱⢌⢵ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⠀⠀⢻⡱⢣⡝⡼⣡⢛⡜⣣⢞⡱⢯⡜⣳⢺⡱⣏⡼⣣⢗⣫⢞⡿⣽⣞⣿⡕⣊⠖⡬⡑⡎⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠉⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⣗⡣⢞⡱⢣⢏⡼⡱⢮⡹⢶⣩⠗⣭⢳⣎⠷⣙⢮⡳⣏⠾⣽⡿⣯⣿⣦⠙⡴⣡⠝⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⢫⡜⣣⢮⡱⢏⡶⣹⢣⠞⣝⢮⣓⢮⣛⡽⣎⠷⣭⢻⡜⣿⣽⣟⣿⡗⣆⢓⠮⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠓⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢎⡵⢪⡕⣏⠶⣭⢳⢻⡜⣧⢛⣮⢳⡝⣮⢻⡵⣫⡽⢮⡽⡟⣿⣿⣮⢎⡵⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠺⠽⣲⣋⣧⢻⡜⢯⡲⣏⢾⡱⣟⡼⣳⢽⡳⣝⡿⣿⣿⣻⣧⢚⡥ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠓⠛⠋⠉⠉⠛⠚⠷⠯⣽⣞⣽⣿⡽⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠰⣤⣄⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢸⠃⠀⠀⢀⣶⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠦⡤⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢸⠀⠀⠀⣸⣿⠀⠀⣾⣷⠶⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⡖⠒⠒⠒⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠸⠶⠶⠶⢿⡟⠀⠀⣿⠋⠀⠀⠀⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢸⡟⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡏⠀⠀⠀⠀⣿⠉⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣿⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⢠⡟⠛⢦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡆⢐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡾⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠡⠐⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣲⠃⠀⠀⠀⠀⠀⠀⠀⠋⠛⠶⢦⣤⠀⠀⠀⢻⡀⣀⡴⠟⢡⣴⠶⣦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⢸⣛⠛⠋⠀⢸⣇⣦⠤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⢹⡏⠁⠀⠀⠘⢿⣄⣠⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⣀⣴⠟⠋⠀⢠⡿⠻⢦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣠⣤⣶⢶⡶⣶⢶⡶⣦⣀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠸⣆⣂⣸⡇⢀⣾⣤⣄⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⣶⢾⣟⣯⠷⣏⣯⡽⣯⣻⣽⣳⢿⣳⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣾⠇⠀⣿⣴⣟⣭⣉⣷⠀⠀⠀⠀⠀⠀⣰⣯⠷⣏⡷⣾⣭⢿⡽⣾⣽⣳⣟⡾⣽⢯⣷⣻⢟⡿⣿⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⣦⣈⢉⠀⠀⠀⠀⠀⢀⣴⣟⣞⠿⣭⠿⣵⣞⣯⣟⡷⣞⡷⣯⢿⣽⣻⢾⡽⣯⢿⣽⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣾⣅⣀⡀⠀⠀⣷⡞⠳⣦⠀⠰⠶⢦⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣠⡶⠃⠀⣰⣯⢷⢾⣹⠿⣽⣻⣳⣟⡾⣽⡽⣯⢿⣽⣻⢾⡽⣯⢿⣽⣻⢾⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡋⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⠁⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⣟⠀⠀⣸⠃⠀⢠⡿⠉⠉⣡⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣼⠿⣼⣫⢯⣯⣟⡷⣯⢷⢯⣻⢷⣻⣽⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢾ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⡶⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠿⠀⠀⣾⠁⠀⠀⣿⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡿⣳⢯⣟⡶⣯⣟⡽⣯⢿⡽⣯⢷⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣸⠃⠀⠈⠉⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣠⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡾⣝⣯⣟⡾⣽⣳⢯⡿⣽⢯⡿⣽⣻⢾⡽⣞⡿⣾⣽⣻⢾⣽⣻⢾⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢬⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡟⠳⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣝⣻⡼⣯⣽⣳⢯⡿⣽⢯⡿⣽⣳⢯⡿⣽⢯⣟⡷⣯⣟⡿⣾⣽⣻⢾ ⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⡠⡺⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⠙⠁⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢯⣞⣷⣻⢷⣫⣟⣯⢿⡽⣯⣟⡷⣯⡿⣽⣯⢿⣞⣿⣳⣯⣟⡷⣯⣟⣿ ⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⣠⡷⠁⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⢰⣿⠀⠀⠀⣰⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣟⡾⣳⢯⣟⣷⣻⣞⣯⣟⡷⣯⣟⡷⣿⣽⢾⣻⣽⣾⢷⡿⣾⣟⣷⡿⣾ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⢀⣿⠃⠀⠀⢠⣿⠿⠛⠀⠀⢸⣧⣤⣄⡀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣸⢿⣻⢿⡼⣧⢿⡼⣧⣟⡿⣧⢿⡿⣧⣟⣿⢿⣻⣼⡿⣿⣻⣼⣟⣿⣿ ⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢠⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⠇⠀⠀⢠⡿⠁⠀⠀⠀⠀⣿⠋⠀⠈⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢯⣳⢯⢯⣟⣳⢯⡿⣽⣳⢯⣿⣽⣻⣽⣷⣻⣽⣟⣯⣷⡿⣿⣽⣟⣾⣟⣾ ⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⠀⢸⡇⠀⣼⠟⠋⠛⢳⡄⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⡿⣯⢽⡯⣟⡾⣽⢯⣟⡷⣯⣟⣾⣳⣯⡷⣯⣟⣷⢿⣯⣷⢿⣻⣷⢿⣻⣾⢿ ⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠁⠀⣷⠤⠴⠶⠾⠃⢰⣟⠉⠉⠉⠋⠀⠀⠀⠀⡿⣧⢿⣹⡽⣽⣫⣟⡾⣽⣳⣟⣾⣳⢯⣿⣽⢾⣯⡿⣷⣻⡿⣯⣿⣟⣯⣿⢿ ⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠿⠀⠀⠹⣦⡀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⣟⣧⡟⣧⣟⣷⢻⡾⣽⣳⣟⣾⣳⣟⡿⣾⣽⣻⡾⣟⣿⣽⢿⣽⣾⢿⣽⣾⣿ ⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠠⠠⠀⠀⠈⠉⢉⡩⠚⠉⠁⠩⠁⠶⠐⢒⣒⡂⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠀⠀⠀⠀⠀⣹⡧⠀⠀⠀⠀⣿⢮⣽⣳⢾⣭⢿⣽⣳⣟⣾⣳⣟⣾⡽⣷⢯⣷⢿⣻⣽⡾⣟⣿⡾⣿⣻⣾⣽ ⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠐⢁⠄⠂⠉⣁⡤⠞⠑⠂⠁⠀⠀⠀⠀⠀⠀⠄⠀⢀⠉⠑⠂⠤⢍⣒⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⣤⠴⠛⠉⠀⠀⠀⠀⠀⣿⣻⢶⣏⡿⣞⣻⣼⣳⣟⣮⢷⣻⢾⣽⢯⡿⣽⣻⣽⢷⣿⣻⣽⣟⣿⣽⡷⣿ ⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠐⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈⢙⠒⠭⢝⡒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⢟⡾⣽⣫⢷⣯⢷⡾⣽⢯⣟⡿⣞⡿⣽⣻⣽⢾⣟⣾⢯⣷⣟⡿⣾⣟⣿ ⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠐⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⠈⠉⠒⠤⣍⡡⢒⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢾⣹⢧⣟⣟⡾⣏⡿⣽⣻⢾⡽⣯⢿⣽⣳⣯⢿⡾⣯⢿⣳⣿⣻⣽⣾⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⢴⣂⢭⣗⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡽⣫⠾⣝⡾⣭⢿⣽⡻⣷⢯⡿⣽⢯⣟⣾⣳⢯⡿⣽⢯⣿⣻⢾⣽⡷⣯⣿