⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⡛⠛⠿⣿⣿⣿⡇⠀⠀ ⡟⡩⢲⠎⠓⠒⠂⠐⢤⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢹⠿⠟⠛⠋⠉⠉⠉⠁⢠⣷⣾⣄⠀⡇⠀⠀⠀⠻⣿⡇⠀⠀ ⠀⣏⣷⡀⡀⣀⣀⣦⣤⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠀⠀⠀⡇⢠⡆⠀⠀⠀⠀⠀⠀⠀⡞⠙⣻⠃⣼⣧⡤⠀⠀⠀⡏⠹⣀⠀ ⡀⡽⣿⣗⠙⢿⢽⡋⣻⣾⣽⣿⡉⠉⠉⠀⠀⠀⠀⢳⢀⢸⣆⠀⢰⡆⣧⣼⡇⠀⠀⠀⠀⠀⠀⢠⠽⢀⣿⣾⠹⠁⢰⠀⠀⢠⣃⣀⢿⣷ ⣧⣻⣿⣿⣿⣾⣆⣿⠾⠋⢙⣻⡇⠀⢤⠤⡀⠀⠀⢸⣾⣾⣿⢆⣼⡹⡏⣽⣃⣀⡀⠀⠀⠀⠀⠠⠊⠉⠛⠤⣶⣣⣾⣷⡧⠓⠾⠇⠑⢿ ⣿⣿⣿⣿⡙⢻⣿⣿⣷⡤⢭⣿⢆⣐⣛⠀⢈⡆⣠⠔⠳⢷⣼⣦⣼⣿⣷⠋⠀⠀⠈⢆⠀⠀⢀⠃⠀⢀⣰⠀⠀⢹⣲⣿⠑⢌⡻⡀⠀⠘ ⠁⠉⢻⣿⣷⠛⠙⠛⠚⠋⠁⠀⠱⡀⠈⡴⢺⣴⠅⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⣼⠄⡔⡎⠀⢠⡻⡝⠀⠀⢸⢻⣿⠀⡎⢄⡇⠀⠀ ⠀⠀⠎⣿⣿⡷⠀⣰⠀⢠⣄⡀⠀⠔⡄⡤⢞⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⡜⠀⢠⡿⠋⠀⠀⠔⠉⢸⣿⣸⢃⠨⢣⠀⠀ ⠀⠀⣃⣿⣿⣗⣺⣗⣒⣺⢮⣪⣢⣨⠞⣇⠀⢹⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠏⡜⠀⡠⣿⠀⠀⠀⠀⠀⠀⣸⣿⠀⠣⡡⡀⢱⡄ ⠀⢳⢻⡿⣿⠻⡀⠘⠂⠀⠈⢻⡟⠻⡾⡁⠑⣼⠈⢷⣤⣀⣠⣤⠶⠓⠛⠿⠿⣿⣇⠊⠀⣔⠮⠼⡄⠀⠀⠀⠀⠀⡟⣯⠀⢀⠼⠮⠾⠤ ⠀⠄⠻⢇⠈⠂⢷⠀⠀⠀⠀⢘⠓⣠⡓⡌⠒⠟⡆⠈⡝⡿⠟⠥⣴⣶⡂⠀⣀⣈⣧⣀⢌⣮⣀⠀⢻⠀⠀⠀⠀⠀⡿⣿⡷⣀⠀⠀⠀⠀ ⠀⠀⡆⡼⡄⠀⠈⡇⠀⠀⠀⠈⣍⢨⠈⠁⠀⠀⠀⠀⡼⠟⣉⡥⠶⠶⠶⠾⠿⠟⠳⠭⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠘⠁⠀⠉⠒⢄⠀ ⠀⠉⠉⢉⠇⠀⠀⢻⠀⠀⠀⢀⣠⣝⠦⣶⡄⠀⠀⢸⠷⣋⣥⠴⠒⠒⡂⡉⠉⠉⠉⠛⢿⣿⢿⠏⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠁ ⠀⠀⡠⢿⣦⣤⣖⢦⣖⣚⣉⡙⣫⠖⠁⠀⠑⡄⢠⠗⢿⡟⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢱⠀⢃⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠉⢱⣬⣭⡽⠞⠁⠀⠀⠀⠀⠘⡆⠀⡎⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠆⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⠀⠀⠀⠀⠀⠀⣰⢛⢄⠀⠀⠀⠀⠀⣇⡜⢄⠀⠀⠀⠀⢀⠌⢠⢏⠑⠠⠤⣰⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⢠⡉⢦⣆⠀⠀⠀⣀⠔⡱⠼⠦⣍⣒⠀⣐⡺⠋⠈⢦⣕⡂⠄⢒⡡⢴⣏⣟⡤⣸⢿⣿⣿ ⠀⣀⠀⠀⠀⠀⠀⠀⢨⢳⢕⡢⠤⠀⠀⣤⡶⠁⢳⠁⠉⠚⠫⢥⢶⣾⣦⡄⠀⢸⣿⢟⠕⠁⠀⠀⠘⣿⣿⣿⣧⠰⢏⣯⣶⠟⡈⢱⠽⢿ ⠀⠘⣗⡢⠄⠀⠤⠔⣡⡞⣻⣹⣿⣿⡉⢰⠁⠀⠸⡆⠀⠀⠀⠀⠑⢝⢿⡇⠀⢸⡏⡌⠀⠀⠀⠀⠀⢸⢿⣿⣿⡀⠏⠉⣧⢰⠁⠀⠀⠀ ⠀⠘⠀⠙⢏⠀⡏⡩⠚⡘⠯⣛⣿⢿⢣⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡪⠃⠀⠀⠉⠛⠢⠄⣀⠀⠀⠀⣯⣿⣿⣇⢸⣰⠉⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⢰⢡⠃⠀⠈⠢⣸⢧⣎⣄⢃⡇⠀⠀⠸⡀⠀⠀⠀⠉⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⢠⣣⡼⣿⣿⣞⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢃⢣⠃⠀⠀⠀⠀⠈⢣⠀⠈⠻⣧⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡈⢢⠘⢿⣿⡙⠀⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⡌⣎⠇⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢳⢤⡆⡘⠀⣀⡤⠶⠶⠶⠦⢤⡤⢔⡶⠛⠉⠉⠉⠉⠉⠙⢇⠀⢸⡇⠀⠀⠸⠀⠀⠀⠀

⠀⠀⠀⠀⠸⠀⠀⡇⢸⠀⢇⠙⠉⠉⠉⠉⠉⠛⡶⢔⡤⢤⠦⠶⠶⠶⡤⣀⠀⡘⡆⢤⢳⠈⠀⡀⠣⠀⠀⠀⠀⠀⠀⠀⠇⣎⡌⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⡙⣿⢿⠘⢢⡈⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⣧⠻⠈⠀⢣⠈⠀⠀⠀⠀⠃⢣⢃⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⣞⣿⣿⡼⣣⢠⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠉⠀⠀⠀⡀⠸⠀⠀⡇⢃⣄⣎⢧⣸⠢⠈⠀⠃⢡⢰⡎⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⣰⢸⣇⣿⣿⣯⠀⠀⠀⣀⠄⠢⠛⠉⠀⠀⠃⡪⣠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⢣⢿⣿⣛⠯⡘⠚⡩⡏⠀⢏⠙⠀⠘⠀ ⠀⠀⠀⠁⢰⣧⠉⠏⡀⣿⣿⢿⢸⠀⠀⠀⠀⠀⡌⡏⢸⠀⡇⢿⢝⠑⠀⠀⠀⠀⡆⠸⠀⠁⢰⡉⣿⣿⣹⣻⡞⣡⠔⠤⠀⠄⡢⣗⠘⠀ ⢿⠽⢱⡈⠟⣶⣯⢏⠰⣧⣿⣿⣿⠘⠀⠀⠁⠕⢟⣿⢸⠀⡄⣦⣾⢶⢥⠫⠚⠉⠁⢳⠁⡶⣤⠀⠀⠤⡢⢕⢳⢨⠀⠀⠀⠀⠀⠀⣀⠀ ⣿⣿⢿⣸⡤⣟⣏⢴⡡⢒⠄⡂⣕⢦⠈⠋⡺⣐⠀⣒⣍⠦⠼⡱⠔⣀⠀⠀⠀⣆⢦⡉⢠⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣰⠤⠠⠑⢏⢠⠌⢀⠀⠀⠀⠀⢄⡜⣇⠀⠀⠀⠀⠀⢄⢛⣰⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠀⡆⠘⠀⠀⠀⠀⠁⠞⡽⣭⣬⢱⠉⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠀⠀⠀⠀⢃⠀⢱⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⡟⢿⠗⢠⡄⠑⠀⠁⠖⣫⡙⣉⣚⣖⢦⣖⣤⣦⢿⡠⠀⠀ ⠁⠀⠀⠀⠀⠀⠇⠙⠀⠀⠀⠀⠀⠀⠏⢿⣿⢿⠛⠉⠉⠉⡉⡂⠒⠒⠴⣥⣋⠷⢸⠀⠀⡄⣶⠦⣝⣠⢀⠀⠀⠀⢻⠀⠀⠇⢉⠉⠉⠀ ⠀⢄⠒⠉⠀⠁⠘⠁⠀⠀⠀⠀⠀⡇⣿⣿⣿⢿⠭⠳⠟⠿⠾⠶⠶⠶⡥⣉⠟⡼⠀⠀⠀⠀⠁⠈⢨⣍⠈⠀⠀⠀⡇⠈⠀⡄⡼⡆⠀⠀ ⠀⠀⠀⠀⣀⡷⣿⡿⠀⠀⠀⠀⠀⢻⠀⣀⣮⢌⣀⣧⣈⣀⠀⡂⣶⣴⠥⠟⡿⡝⠈⡆⠟⠒⡌⡓⣠⠓⢘⠀⠀⠀⠀⢷⠂⠈⢇⠻⠄⠀ ⠤⠾⠮⠼⢀⠀⣯⡟⠀⠀⠀⠀⠀⡄⠼⠮⣔⠀⠊⣇⣿⠿⠿⠛⠓⠶⣤⣠⣀⣤⢷⠈⣼⠑⡁⡾⠻⡟⢻⠈⠀⠂⠘⡀⠻⣿⡿⢻⢳⠀ ⡄⢱⡀⡡⠣⠀⣿⣸⠀⠀⠀⠀⠀⠀⣿⡠⠀⡜⠏⣨⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⢹⠀⣇⠞⣨⣢⣪⢮⣺⣒⣗⣺⣗⣿⣿⣃⠀⠀ ⠀⠀⢣⠨⢃⣸⣿⢸⠉⠔⠀⠀⠋⡿⢠⠀⡜⠋⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣽⢞⡤⡄⠔⠀⡀⣄⢠⠀⣰⠀⡷⣿⣿⠎⠀⠀ ⠀⠀⡇⢄⡎⠀⣿⢻⢸⠀⠀⡝⡻⢠⠀⡎⡔⠄⣼⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠅⣴⢺⡴⠈⡀⠱⠀⠁⠋⠚⠛⠙⠛⣷⣿⢻⠉⠁ ⠘⠀⡀⡻⢌⠑⣿⣲⢹⠀⠀⣰⢀⠀⠃⢀⠀⠀⢆⠈⠀⠀⠋⣷⣿⣼⣦⣼⢷⠳⠔⣠⡆⢈⠀⣛⣐⢆⣿⢭⡤⣷⣿⣿⢻⡙⣿⣿⣿⣿ ⢿⠑⠇⠾⠓⡧⣷⣾⣣⣶⠤⠛⠉⠊⠠⠀⠀⠀⠀⡀⣀⣃⣽⡏⡹⣼⢆⣿⣾⣾⢸⠀⠀⡀⠤⢤⠀⡇⣻⢙⠋⠾⣿⣆⣾⣿⣿⣿⣻⣧ ⣷⢿⣀⣃⢠⠀⠀⢰⠁⠹⣾⣿⢀⠽⢠⠀⠀⠀⠀⠀⠀⡇⣼⣧⡆⢰⠀⣆⢸⢀⢳⠀⠀⠀⠀⠉⠉⡉⣿⣽⣾⣻⡋⢽⢿⠙⣗⣿⡽⡀ ⠀⣀⠹⡏⠀⠀⠀⡤⣧⣼⠃⣻⠙⡞⠀⠀⠀⠀⠀⠀⠀⡆⢠⡇⠀⠀⠀⠀⢠⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣤⣦⣀⣀⡀⡀⣷⣏⠀ ⠀⠀⡇⣿⠻⠀⠀⠀⡇⠀⣄⣾⣷⢠⠁⠉⠉⠉⠋⠛⠟⠿⢹⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⢤⠐⠂⠒⠓⠎⢲⡩⡟ ⠀⠀⡇⣿⣿⣿⠿⠛⡛⠻⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠉⠉⠉⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿