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