Cute Cat💜💜💜 Hamster Copy and Paste (don't Search For Those Things) Emojis & Text

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⠀⠀⠀⠀⡀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠏⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡼⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠸⠀⠀⠃⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠁⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡆⣿⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⡜⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠁⢰⠀⠀⠀⣄⠙⠀⠀⠀⠀⡀⢠⠀⠀⡄⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢠⠀⠀⡇⠀⠀⠀⠀⠀⡀⢤⠑⠀⠀⠀⠀⠀⠐⠀⣾⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠀⡽⠉⠒⠒⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⢠⠀⠁⡴⣀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠋⠴⣠⢀⠀⠀⣀⢤⠑⠀⠀ ⠀⠀⠀⠀⣾⠀⠁⣰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢷⠀ ⠀⠀⠀⠇⢀⠀⡇⠀⠀⠵⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠄⠛⡀⢸ ⠀⠀⠀⡸⠀⠀⡄⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡂⣠⠇⢠ ⠀⠀⡎⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀ ⠀⠇⢠⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡤⠘⠀⠀ ⠃⡼⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⢸⠀⠀ ⡆⢹⠀⠀⠀⠀⠀⠀⠀⠧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⠀⠀ ⠀⡄⠑⠀⠀⠀⠀⠀⠀⡀⣧⠉⠉⠉⠉⠉⠐⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠀⠀ ⠀⠀⠀⣀⠯⠿⠛⡈⣀⣀⣀⢻⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⢞⠓⠔⠾⡠⢀⠀⠀⠀ ⠀⠀⠀⡞⢏⣎⣇⣀⢯⠑⠀⣿⠀⠀⠀⠀⠀⠟⠊⠟⡼⢀⠋⣠⠎⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣼⢰⡇⠀⢸⡞⢣⣼⠀⠀⠀⠀⡇⣹⠈⠷⢀⠟⢳⠏⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⣿⠀⡀⠸⢻⢸⡇⢀⠀⠁⠖⡠⢀⠀⡀⢄⡶⣟⡀⡼⠳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠸⠀⢇⡆⢘⡇⠀⡤⢀⠀⠀⠂⠒⠶⠰⠈⡀⢦⢻⠀⢦⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠈⡀⢹⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸⠀⠀⡄⠘⠀⢇⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢸⠀⣇⡽⣴⠘⠀⠐⠛⠛⠐⠀⠀⠀⣀⣻⢟⠉⣏⠹⠀⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠛⣹⡇⠀⢣⠋⠸⣷⢼⢱⠛⠀⠀⠀⡦⣶⡛⣾⡇⠸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⠈⣿⠀⡅⣹⣤⢿⣶⣤⢀⠙⠘⠀⠆⠓⡟⣾⣠⢳⡄⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢸⣄⣧⠈⠀⣆⣸⡿⠢⠶⣤⣠⠀⠀⠋⡳⣰⠀⠀⡎⠇⢾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⡄⣗⠘⠀⠀⠉⠚⡥⢚⣠⠀⠀⠁⢸⡞⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⡀⢦⠤⣠⢀⠴⣠⠀⠀⠀⠀⡥⡞⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠉⠈⠀⠀⠀⠀⠀⠁⠉⠚⠴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢹⠄⡀⢀⠀⠀⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⠰⢉⡧⣿⢺⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡑⢂⡱⡜⢿⡀⠀⠀⠀⠐⠀ ⣿⠘⠤⣲⣰⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⡘⠆⠃⣇⣿⢺⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⡌⠡⡼⣏⠸⣠⣄⢈⠀⠀ ⣿⢿⠀⢀⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠃⢀⢩⡧⣿⢻⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡈⢱⡖⡍⢻⢀⠀⠀⠀⠀ ⣽⣿⠸⠐⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠤⢋⡧⣿⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⡃⠤⢚⣯⠘⠀⠀⠀⠀ ⣾⣟⢻⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡰⠜⡯⣟⣼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠘⣩⠖⣍⢻⠀⠀⠀⠀ ⣽⢾⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⡨⠖⣏⡃⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔⡃⠤⢚⣯⠈⠀⠀⠀ ⣻⣽⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡒⢎⣏⡇⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠒⣎⠇⣎⢹⠀⠀⠀ ⢾⣳⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⠴⢛⣯⡁⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⠰⢍⢢⡜⣿⠀⠀⠀ ⣟⣯⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⡱⢎⣿⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡨⠕⣊⠭⣗⠸⠀⠀ ⢻⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⣁⡓⢧⢸⠔⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠣⢆⡙⡧⢸⠀⠀ ⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠥⡂⡱⣾⠀⠀⡦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⢢⡜⡎⢽⠀⠀ ⡽⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠜⠃⣡⡿⢻⠟⠹⠋⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡉⠦⢃⢰⣾⠀⠀ ⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢂⡁⠆⠡⣿⣤⣀⣀⣯⣹⣄⣷⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡱⢆⡡⢽⠀⠀ ⣷⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢡⠠⡘⠣⣾⢀⠀⠀⠀⠀⢀⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⡰⢓⢡⡷⠀⠀ ⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠂⡁⠟⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠡⡱⠢⣑⡷⠈⠀ ⡿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠏⡴⢆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡡⠒⣡⡜⡯⠀⠀ ⡷⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡾⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⣦⠙⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠒⠌⣃⠠⢳⡌⣟⠀⠀ ⣻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢈⢠⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⣄⠹⠀⠀⠀⠀⠀⡘⠁⠄⡃⠄⡑⠢⣌⠚⢡⣾⠀⠀ ⡵⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠂⡀⢶⠈⠀⠀⠠⠄⠂⡐⠎⡁⠰⢎⡃⡔⢏⢸⠀⠀ ⣳⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢂⠁⣆⠑⠀⡐⠎⢁⡰⠎⢃⡄⠘⢱⡬⡟⢀⠀⠀ ⡾⣟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠌⠂⠁⠠⡐⡌⠆⡈⠱⢌⠡⠴⡈⠴⡓⣸⠀⠀⠀ ⣟⢧⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⠀⡐⠂⢁⢢⡐⠱⡌⠆⡈⠖⣈⡿⢀⠀⠀⠀ ⡼⢿⣯⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⡐⠌⠁⠤⡈⠢⡐⢌⡑⠦⢏⣰⠀⠀⠀⠀ ⣽⡞⣿⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠌⠂⠄⠈⢂⠔⢂⡡⠟⣼⠀⠀⠀⠀⠀ ⡳⣽⣸⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠁⢂⠄⢈⡐⢋⡷⣼⠀⠀⠀⠀⠀⠀ ⣼⡟⢰⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⢡⡀⠞⣫⣼⠀⠀⠀⠀⠀⠀⠀ ⣜⡿⢀⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠐⠁⡼⢏⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⣞⢰⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠃⢥⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⢠⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡱⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠈⠀⠀⠀⠀⠀⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠋⡷⣎⡞⢿⠈⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢑⡦⡟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠟⣾⣡⣸⢍⠂⣄⢻⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢨⠱⢂⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⡇⣩⠴⢋⠤⠒⣈⠑⣇⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⠆⡉⠤⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⢃⢆⠡⢶⠻⢉⠠⡐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠉⢢⡜⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢈⡱⢂⠤⡘⣆⢿⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⢋⢠⢽⡎⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠈⡰⠁⢂⠄⠩⣄⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⠇⣡⠖⢩⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⢸⠌⡀⠀⠀⠀⠐⠠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢾⡉⡰⢜⡻⣇⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡃⢸⠀⠀⠀⠀⠀⡁⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢿⠠⡱⢆⠳⣇⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠂⠀⣿⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⢊⠀⣿⣉⠤⣣⡕⡪⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠁⣼⠁⠉⠛⠛⠛⠿⠿⠛⠛⠉⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠋⠟⡿⣾⣛⣳⠾⣟⢛⢩⣿⠒⣈⡔⢻⢰⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠁⡿⣴⣠⣀⠀⢀⠀⢀⡀⣀⣄⢦⣷⢽⠻⠙⠈⠀⢸⠀⠀⠁⠛⡿⣶⣤⣀⢀⠀⠀⠀⠀⠀⠀⣀⣦⠻⢌⡑⡎⡼⡗⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠏⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣆⡶⣟⢯⠙⠋⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠻⠄⣯⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢿⣋⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡆⡍⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢦⠰⣿⠛⠀⠀⠀⠀⠀ ⠞⡿⢤⡷⠀⠀⠀⠀⣿⠀⠀⠀⠁⠛⠿⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠽⠽⠬⠙⠀⠀⠀⠀⣿⠡⣌⡷⣟⢹⠦⠷⠹⠀ ⡟⢠⠁⡿⠀⠀⠀⠀⣧⠀⠀⠀⡷⡇⣾⣿⡌⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠄⢠⡗⣿⣿⡼⠀⠀⠀⠃⢼⠡⡌⡗⣹⣼⠀⡃⣿⠀ ⣧⠈⡇⣿⠀⠀⠀⠀⡀⢹⠀⠀⡀⣦⣖⣠⣀⢀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣠⠀⠀⠀⠀⡟⣠⠐⡌⠓⣯⢩⠟⣿⢰⠀ ⠁⢄⠟⣹⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢲⢁⡡⠄⠣⣕⢻⡴⢠⠀⠀ ⠀⠢⡀⢸⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⣿⣸⣀⣀⣀⣇⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠌⠂⡀⠐⢊⡱⣷⠀⠀⠀⠀ ⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⣅⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡾⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠐⢀⠀⠀⠀⠐⣈⡷⠘⠀⠀⠀ ⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣯⣭⣯⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢸⡀⠀⠀⠀⠀⠀⠀⡐⡇⢸⠀⠀⠀ ⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣼⣤⣦⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⠀⠀⠀⠀⠀⠀⠀⡐⢂⢿⠙⠀⠀ ⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠁⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⣦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⠀⠀⢁⢸⣀⢳⠀ ⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⢀⠀⠀⠀⠀⣷⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⢧ ⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⡆⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡾⠀⠀⠀⡀ ⠀⠀⠀⠀⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⡄⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢙⠀⠀⠀⠀ ⠀⠈⠀⠇⣱⢾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠁⠋⠘⠀⠑⠉⠉⡏⢻⠉⠉⠀⠀⠀⠀⠀⠀⢆⠘⠀⠀⠀⠀⠀⠉⠟⣾⣻⣧⠹⠀⠀⠀ ⡰⠀⠀⡇⡀⢸⡇⢌⠻⠛⠉⠉⠁⠄⠈⠀⠀⠀⠃⠒⠒⠞⠤⡿⣠⣀⣀⢁⠋⢠⠀⠀⣃⢀⠀⣇⣸⣄⣦⣒⣝⢬⠶⠒⠀⠀⠉⠉⠋⠟⡿⣇⣽⣿⣷⢲⣿⠘⠀⠀ ⠀⠀⠀⡇⠘⢹⡏⠰⣇⢾⢹⡀⣆⣿⣿⣇⣿⢿⠻⠙⠈⠀⠃⣼⠀⠀⠀⡏⣰⠀⠀⠀⡄⠸⠂⡀⢿⠘⠂⠍⠒⠤⣠⣀⣄⠘⢀⠀⣿⣿⣿⠀⡡⣿⡇⣼⡿⣿⠀⡏ ⠀⠀⠀⠀⢳⣇⣿⠰⡇⢸⣻⠀⠀⣇⣿⠈⣿⣷⣿⣿⣾⢧⡿⢘⠀⠀⠀⣰⠀⠀⠀⠀⠀⢧⠁⠄⣿⢴⣠⢀⠀⠀⠀⠀⡇⢿⠀⡇⢽⣰⣿⠀⠀⣿⡇⣼⡟⣿⠿⣸ ⠀⠀⠀⠃⡷⠘⣷⢹⡀⢠⣿⠀⠀⡀⣾⣧⣇⡀⣿⣿⢿⣏⢠⣇⠀⠀⠀⠀⠀⠁⠜⠀⠁⡏⠰⡯⢀⠀⠀⠀⠀⠀⠀⠃⣾⣀⠁⣼⠀⠇⣸⠀⠀⣿⡇⣸⣿⣯⣼⠀ ⢳⠈⠀⣸⡇⢿⡌⣧⠘⠀⣆⡌⠘⠀⢸⡇⡼⠀⣿⣿⣿⣸⠀⡇⠀⠀⠀⠀⠏⣾⣫⠷⠹⣈⠐⣿⠀⠀⠀⠀⠀⠀⠋⣿⢀⠃⣾⠄⠁⡞⠀⠀⡇⣸⣄⡏⣼⣿⠙⠀ ⠂⢟⠟⢿⡆⡽⢻⡄⣷⠸⠀⢀⢸⠀⢸⡇⣸⠁⣿⢳⣾⠀⠀⡇⠘⠈⠋⡿⣼⣞⢯⣳⣽⢿⣋⣿⠀⠀⠀⠀⠀⠏⣯⢠⠃⡼⢨⠁⡿⢠⠀⠀⡿⢀⠃⣾⠏⣰⣿⠸ ⠀⡎⣻⣬⠳⣌⣳⢿⡈⢳⠘⠀⢿⠀⢠⡿⠡⡟⣣⣿⢠⠀⠀⡇⠿⣿⣿⣿⣶⣴⣤⣷⡿⣿⣿⣿⠀⠤⠀⠈⠇⣸⣸⠁⣼⣇⠀⡟⣰⠀⠀⠏⣰⠁⡾⢥⡼⠁⢹⢸ ⠏⣭⢞⣭⠶⣟⠻⣍⢶⠙⡀⢤⡉⢨⠇⣻⡟⢿⣯⣼⠀⠁⠋⡶⣤⣠⢀⠀⠀⠀⠀⠀⡀⣦⣷⣿⠀⠀⠀⠀⡧⣀⢹⡏⣂⡙⠀⣼⠀⠀⠏⣰⠃⡵⠟⣾⢀⡞⡟⢀ ⢾⣍⠽⣣⣜⠳⣌⣇⣤⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⠟⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢳⠈⠀⠀⡀⢹⡆⢹⠀⠄⠂⢁⠠⠟⣰⠀⢋⡿⣴⠋⡵⡞⢀⢸ ⢞⢣⡹⢧⡌⠳⣀⠰⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣽⠛⠀⠀⠀⠀⠀⠀⠛⠞⠤⠠⠒⠑⠈⠀⠀⠀⠀⣤⠛⠉⠀⡀⢻⣿⠙⠀⠀⠻⡷⣠⠋⡽⣾⣩⠿⢞⣠⠁⡟⢠ ⡜⢮⡙⢢⡜⠣⣀⠀⠋⡿⣿⣿⣷⣿⣿⣿⣿⣿⣻⢞⠤⠀⠀⠀⠀⠀⠀⣀⣀⠄⠤⠤⣤⠠⠀⠀⠀⠀⡀⣷⢿⠿⣿⣿⣿⣿⢿⠻⠿⣿⣿⣿⣾⣴⣠⠉⠟⣴⢀⠀ ⡖⢌⡱⢎⡌⠀⠃⡿⣿⣿⣿⢧⡟⣿⣵⣟⢿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⠶⡴⣤⣀⠀⠀⠀⠀ ⢣⣌⡓⠌⢀⠀⣿⣧⣾⢠⣾⡟⣿⣰⡰⡟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⢀⢧⠀⠀⠀⠀⠀⠀⡀⣄⠳⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⡌⠒⢀⠀⡇⣼⡟⢠⡁⢿⣽⣾⡀⠇⣿⢁⠈⠀⣋⣛⣛⠤⠀⠀⠀⠀⢤⠒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣻⢿⣿⣿⣿⣿⡿⣿⣿⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡜⠀⠀⠀⡇⢸⣟⠀⣿⣾⣇⢨⠀⣧⣿⣿⠸⡍⣯⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠏⠭⠤⠑⠀⠀⣷⡸⣖⣿⣿⣿⢧⣿⣿⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡜⠈⠑⠢⡇⣽⣿⠀⣿⢠⡄⠀⠠⡿⣿⣤⣿⣿⣿⣿⡿⣾⣷⠻⠙⠙⠀⠀⠀⠀⠁⠋⡶⣾⣿⢿⠈⢧⠈⡇⣿⠄⣇⣿⣿⡔⣿⣿⡧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⡀⡄⠀⢠⡄⣿⣷⠀⣽⠀⡀⠀⠃⣿⢠⠀⣿⣀⣄⣿⣿⠈⡇⣄⣷⣿⢽⠢⠎⠈⡄⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⢘⡡⣿⣿⡚⣷⢸⡿⢸⠈⠠⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⡟⠈⢹⠀⠀⠀⡇⣼⠀⠀⡇⢸⠀⢹⡄⣷⡟⢻⠉⣧⣿⢻⣯⣿⠈⡀⣿⣬⣾⣷⣹⣇⣹⡆⣿⢾⠈⣿⣿⡐⣾⠇⣿⢀⠀⠁⠂⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⠀⠀⠰⡇⢺⠙⠈⣤⣻⣈⣾⣶⣽⣦⣿⣦⡻⣤⣿⣿⡆⢹⠀⣇⢿⢸⡀⣯⣿⢢⠀⣷⢿⠀⣏⣼⡏⢣⣿⢠⠄⠀⠈⠀⠐⠀⠀⠈⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⣿⡇⠸⠀⠀⡇⢈⠀⣀⠦⣷⢿⢸⠀⡀⢷⡈⢤⣇⠸⣷⣿⠀⣯⠀⡿⣿⠀⠀⣟⣿⠀⢁⡤⣹⢀⡿⢃⣿⣾⢨⡀⠁⠀⠀⠐⠀⠂⠄⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⣳⣿⠀⠀⡆⠘⠀⠀⠀⡆⣿⣟⠸⠀⡇⢦⠘⠀⣷⠃⣸⠀⣟⠋⣿⢻⠛⠓⣿⢾⡤⠀⠇⢸⠏⣱⣿⣾⢁⠀⠂⠀⠀⠠⠀⠈⢀⠁⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣀⢱⠀⠀⢸⠀⠀⠀⡇⣷⢸⣇⠈⡃⠀⢧⠀⣇⠃⢰⣀⣿⣿⣾⠀⠀⡞⣏⢀⠃⢀⡞⠃⣻⡿⣴⠀⠀⠂⠀⠀⢀⠀⠠⠀⠂⠀⠀⠐⠄ ⠀⠀⠀⠀⠀⠀⠉⠛⡴⣀⢳⡀⠱⠀⡇⠀⠀⠀⡄⡼⢸⠀⢳⠀⠀⡇⢸⡇⡄⠀⠇⣿⣾⢀⠀⡞⣏⣸⠃⢰⠖⢫⣽⡿⢠⠀⠠⢀⠀⠂⠄⡀⠀⠈⢀⠂⠀⡀⠀⠄ ⠒⠒⠄⠤⣤⣠⣀⠁⠀⠀⡀⠳⡈⢤⠑⢠⠃⠀⠀⢣⢸⠀⡇⠈⠀⡼⠀⣼⠀⡅⡾⣿⠀⠀⡀⠟⣼⠃⣠⡁⠏⣿⡼⢀⡀⠀⠈⠠⢀⠀⠂⠄⠀⠀⠄⠀⠈⢀⠂⡀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢆⠑⡀⠠⠈⢣⠀⡄⢸⠀⠀⢸⠃⢠⡇⢀⠁⡴⢁⠠⠀⠃⡿⣰⠀⠀⠟⡿⣾⣠⠁⡀⠀⠐⠀⠁⠄⡀⠀⠁⠄⡀⠀⠐⠀⠄⠀⡁ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⡀⢤⠓⠈⠀⢄⠑⡄⠑⠀⢠⠀⠃⢡⠞⣠⠜⢀⠁⠞⣴⢀⠀⠋⡿⣴⣠⠄⡀⠀⠀⠠⠀⠀⠠⠀⠂⡀⠀⠀⠐⠠⠀⠠⡀⠀⠐ ⠀⠀⠄⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⣀⢤⠒⠙⢈⡀⠠⠐⠁⢋⣤⠀⡠⠀⠀⣠⠁⠉⠛⠶⣤⢀⠈⢀⠀⠐⡀⠀⠀⠠⢀⠁⠄⠀⠈⢀⠁⠂⠀⠠⠀⢀⠈⠄ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⢤⠿⠬⠶⡶⢶⠶⠴⣤⣤⣠⣄⠀⠀⠂⠀⠀⠀⠠⠀⠈⢀⠀⠄⠀⠈⠁⠀⠈⠁⠀⠈⠄⠀⢀⠈⠁⠀ ⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⢀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠄⠀⠀⠄⠀⠀⠠⠀⠄⠀⠀⠐⠠⠀⠐⠀⠂⡀⠀⠐⠀⠐⠀⠈⠐⠀⠈⠐⡀⠁⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠁

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⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈ ⠀⠉⠉⠉⠛⠟⠿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀ ⡀⣄⣦⣿⣿⣴⣤⣧⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠛⠿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣼⠀⠀⠀⠀⣀⣦⣶⣷⣿⣿⢻⠈ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣶⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠟⠿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠿⠻⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣸⠀⠀⠀ ⠉⠉⠉⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⠀⠀⠀⠀ ⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣾⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣶⣿⣾⣠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠙⠉⠀⠀⠀⠀⠀⠉⠈⠀⢿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⣄⣤⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣷⣿⣿⣿⣿⣿⣿⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣶⣴⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⣿⢿⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣷⣾⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

SUCK IT UP LOSERS! THESE EMOTICONS R HOT AS FUCK!

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

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

⠀⠀⠀⠀⠀⣀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠈⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠀⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⣄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠃⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣧⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⡼⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⡿⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⢽⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⣿⠉⠋⠒⠒⠒⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢰⠀⠀⠁⠾⣠⢀⠀⠀⠀⠀⠀⠀⣀⠦⠙⠀⠀⠀⠀⠋⠖⡴⣀⣀⣀⣀⣀⢤⠳⠈⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠃⣸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀ ⠀⠀⠀⠀⡇⢰⠀⠀⡼⠀⠀⠈⠉⠀⣄⠀⠀⠀⠀⠀⠀⠀⡀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⡆⢹ ⠀⠀⠀⠀⣾⠀⠀⠀⢸⠀⠀⣶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⠈⣿ ⠀⠀⠀⠏⢠⠀⠀⠀⢳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⢃⣼ ⠀⠀⠃⣰⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠀ ⠀⠀⣼⠀⠀⠀⠀⠀⠀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⠀⠀ ⠀⡏⢀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⣇⠸⠀⠀ ⠛⣼⠀⠀⠀⠀⠀⠀⠀⡄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⢀⠀⠀⢸⠀⠀ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⢹⢸⠀ ⣄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀ ⠀⡀⢢⠙⠀⠀⠀⠀⠀⠀⠉⠉⡉⣿⠛⠛⠒⠚⠒⠒⠴⠀⠓⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀ ⠀⠀⠀⠀⣄⢾⠿⠛⠙⣀⢀⠀⡀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣟⢲⠚⠤⠿⡤⢀⠀⠀⠀⠀ ⠀⠀⠀⠉⡼⣟⣧⣧⣸⢄⠳⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠘⠁⠋⠟⡸⣀⢀⡞⢀⠏⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⣹⢸⡇⢸⠀⣼⣅⠻⠃⣿⠀⠀⠀⠀⠀⠀⡟⠴⣀⡇⣮⢀⠋⡼⢀⠇⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⣿⢀⡀⢸⠀⢸⡿⠀⣿⢰⠀⠀⠀⠀⠁⠛⣴⠤⠳⡍⢰⠇⣿⣧⠻⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣻⣹⠀⠀⡇⠈⢿⣟⠀⣿⠀⠀⠁⠚⡴⣀⠀⠀⠀⠀⡀⣄⡳⢹⠀⣷⣄⠱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⠸⠀⡄⢹⡇⣈⠀⣹⠀⠆⣠⢀⠀⠀⠁⠉⠋⠒⠒⠀⠀⣀⠦⡟⠘⡀⢷⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⢿⠈⠀⡇⠘⢰⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡷⠈⠀⠀⡄⢻⠀⠀⢧⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⢸⠀⡀⢿⠁⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⠉⠙⠀⡄⠙⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⡇⣱⣼⣆⠀⠀⠆⠇⠿⠿⠾⠀⠀⠀⠀⠀⡞⢿⡿⠳⠛⣏⠻⠀⡄⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢹⠛⣽⠇⢸⠀⢻⠀⠾⡇⣿⢾⣷⠉⠙⠀⠀⠀⠀⣷⣿⠩⣛⣿⡆⢸⠀⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡀⢻⢸⠀⡇⣼⢶⠟⡛⢿⠾⣶⣀⠀⠀⠀⠁⠉⠉⡉⣿⢿⡴⣇⠀⡇⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣶⠻⣿⢸⠀⣄⣷⠛⡉⣿⢀⠁⠉⠛⢾⢠⠀⠀⡀⣏⣿⣼⢠⠀⡇⢸⡇⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡀⣄⢻⠀⠀⡀⢧⡇⣿⣄⣤⣠⣀⠀⠀⠀⠃⠞⣣⣼⠀⠀⠀⡇⢠⡏⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⣇⠀⠀⠀⡀⣧⣿⠘⠀⠀⠀⠁⠋⡴⣡⠞⣠⠀⠀⠀⠁⡼⠃⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⡆⢷⠊⠶⡴⣀⠉⠖⣠⠀⠀⠀⠀⠀⡶⢣⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠚⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⠤⠤⠶⠶⠶⠤⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⠻⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⡀⣀⣀⣀⣄⣤⣤⣿⣿⣿⢀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⢠⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⣿⣿⣿⣿⢹⠀⡇⣿⣿⣿⣿⣼⣤⣤⣤⣤⣤⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠛⣿⣿⣿⣿⣿⠀⡇⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣾⣶⣶⣡⣛⣝⣧⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⢸⠀⠀⠁⠋⠛⠛⡙⣈⣀⢀⠀⠀⠀⠀⣦⣿⣿⢿⣜⣷⣿⣿⣾⢠⡏⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⢸⠀⠟⣿⣿⣿⣿⣿⣿⠹⠁⡿⣿⣿⣿⣿⣿⣷⣿⣿⠻⣈⣀⠀⠁⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡀⣷⣿⣿⣿⣶⢀⠀⣦⣿⣿⣿⠹⠀⡟⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⠀⣷⣿⣿⣿⣿⣿⣿⣼⠀⠀⡀⣀⠀⠀⠀⠀⠀⣄⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣸⠀⠀⣄⣶⣶⣶⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠟⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⣿⣿⢀⡟⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣍⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣉⣬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠟⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣤⣶⣶⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

�🢦🝆🍑�tew lla uoy teg dna flesym yojne ot teg I dna naom uoy fo lla erehw emosevif a otni snrut ,hcihw emosruof a ni yssup dna stit slrig rehtona gnikcuf ,dna stit 'slrig rehto eht gnikcus dna ,ssa ruoy gnikcams yojne I dna kcid eguh ym gnikcus yojne uoy elihw emoseerht a evah ew ,dna lrig rehtona kcip I nehw gninrom lit pots non niaga dna niaga taht od I nehT .gninaom ylsselpleh ereht dnats uoy sa stit ruoy gnikcuf ot kcab og I neht stit ruoy revo lla muc I neht dna muc dna muc uoy litnu taht od I oS "��HHHA !YDDAD YM FO EDISNI YAW EHT LLA KCID RUOY TUP !REDRAH" ;naom dna maercs ot trats uoy drah os stit ruoy ezeeuqs I nehT .niaga naom uoy gnikam toof ym htiw ti gnibbur erofeb semit wef a skeehc ssa ruoy pals I os gninaom no peek uoY .syawedis uoy fo tuo lleh eht gnikcuf trats dna deb eht otno uoy worht dna riah ruoy barg I .etatiseh neve tnod I ,muc htiw derevoc erew taht stit ruoy ees I sa noos sa dna pu teg htob eW .uoy revo lla muc em gnikam ecaf ym revo lla gnitriuqs trats uoy nehT .yssup ruoy fo tuo gnippird strats muc sa deye-ssorc og ot trats uoY .enoyreve pu ekaw tsomla uoy taht ylduol os naom uoy sa yssup ruoy pu yot xes eht evohs neht I .steehs deb eht pirg uoy sa htuom ruoy ni muc ot trats I ylnedduS .kcid ym detaorht peed tsuj dah ehs sa denaom I ,ti debbarg I sA .kcid ym gnikcus ysub llits saw ehs sa ti debbarg I .ot erapmoc dluoc kcid ym neve ton hcihw gnol sehcni 03 tsaelta saw tI .nirg I dna yot xes reh ees I nehT .yssup reh kcil I nehw ylduol snaom neht kcid ym no gnikcus strats ehS .em no gnittis ssa yxes reh htiw em revo syal ehs sa nwod yal I .pu sdnats ehs sa ssa reh pals I nehT .yssem steg ti sa ot snaom ehs hcihw yssup reh edisni muc ot trats I nehT .t'nac ti hguoht neve reh otni rehtruf teg ot kcid ym teg ot thgim ym lla htiw hsup I dna tseuqer reh wollof I "!REDRAH OG DNA EM KCUF !YSSUP YM NI MUC !YDDAD EM NI MUC" ;smaercs ehs hcihw ot ssa reh kcams I .lrigwoc esrever a no reh edir I sa em otno reh hsup I .muc ot tuoba flesym leef I dna spil ym tsniaga snaorg ehS .reh gnissik yb pu reh tuhs I hcihw ot sa ylduol niaga snaom ehS .stit reh ezeeuqs I sa nwod dna pu kcab lla ti hsup I .ssa reh ezeeuqs I dna yssup reh edisni kcab kcid em evohs I sa reve neht no denrut erom m'I .kcid ym fo mottob eht otno gnimmuc si ehs litnu stit reh kcuf I .talf t'nsaw yletinifed ehs ,kceh ,ekacnap talf a naht regral erew taht stit suomrone reh neewteb kcid ym evohs em gnikam ,ylpeed snaom ehs dna ssa taf gib reh kcams I .sehtolc reh nepo pir dna deb eht otni reh hsup I nehT .no erom neve em snrut ti taht ylduol os snaom ehs dna yssup reh edisni peed saw kcid eguh sehcni 8 elohw ym litnu redrah dna redrah og I ,dias taht htiw dna '��yddaD-D' ;tuo spils drow eno sa gnilbmert em ta pu skool neht pil reh setib dna reduol neve snaom ehS .yssup reh edisni peed yrev muc I dna no denrut m'i dna ��snaom ehs ,nwod repeed dna redrah og i sa llaw eht no em skcuf ehS ~�🨫🝆�tumS

⠀⠀⠀⠀⠀⠀⣇⢸⠇⣾⣾⢞⠀⠃⣿⢠⡞⣀⠀⣁⢀⢠⠀⠀⠀⠀⢁⡋⠛⣒⢤⣭⣛⣛⠛⠙⠀⠀⡀⡀⣄⠠⡀⣷⣿⣿⣿⣿⣴⢠⠄⠠⠀⠀⡀⣷⡿⢳⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢫⣵⡴⢀⠀⠃⣿⣹⡼⢀⠀⠀⡄⣬⢤⡠⠁⣧⣤⣀⠁⠚⠴⣡⢞⣤⢀⡇⠰⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠉⡍⣼⣣⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣡⡼⠀⠀⠏⣾⣿⡼⢀⠀⠀⠁⠊⢲⠉⠃⠳⣼⠋⠴⣀⠋⠴⣀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⠒⠀⣄⢷⠈⠀⠀⠀⠀⠄⡿⣿⢀⢧⠁⣿⠹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢡⡼⠀⠀⠞⢠⠏⣾⠀⠃⡿⠀⡤⣤⣠⣀⣿⡿⣴⢀⠋⡴⢀⠀⠀⠀⠀⠀⡀⡄⠹⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣄⠿⠙⠋⠋⠿⠓⢹⠀⡇⠚⡗⣿⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⢹⡴⠀⠀⠀⢋⡿⣾⠃⠏⣨⢠⠀⠀⠀⠀⠁⡾⢀⠋⣴⢀⠀⠀⠀⠀⠀⠛⠟⡨⣖⣶⣲⣒⠽⠉⠀⠀⠏⡤⣀⢦⠙⡀⣧⣿⣿⣠⠀⢿⠀⡆⢸⠶⣷⣿⠘⠀⡇⠀ ⠀⠀⠀⠃⣰⣀⠀⠀⠋⡴⣁⣼⣠⠛⣨⢈⠉⠀⠀⠀⠀⣴⠋⡴⢀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠀⠀⠀⠀⠏⣿⠘⠀⣸⠀⠀⠀⡁⢸⠀⣄⢿⠀⠀⡇⠻⡟⡞⠀⡀⢻⢹⠀⡏⠀ ⠀⠀⠁⡼⠀⠀⠋⡽⢉⠒⡴⠀⠃⣛⣙⣽⢞⠠⠋⠰⠁⡾⢠⠀⠀⠀⠀⠀⠀⠀⡏⢿⠛⠛⠛⠛⠛⠛⡿⣿⣿⢸⠀⣄⠦⠖⡴⣀⠀⠀⠀⣄⠹⠀⡇⣿⣧⣾⠙⠀⣿⡇⠀⣿⠀ ⠀⠀⡞⠀⠀⠏⣿⣠⠀⠞⠀⠃⡰⠀⣶⣠⠁⡾⢀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡹⡇⣿⡻⢻⣾⠀⡄⡇⡟⣸⠀ ⠀⠀⢀⠀⠇⢠⠁⠊⡿⢀⠃⣰⠀⠀⠀⠏⣰⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣯⣷⣿⣿⣿⣿⣿⣿⣹⣀⣤⣿⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣧⣧⣯⣿⢸⢀⠀⠀⡟⣿⢀⠀ ⠀⠀⠀⠀⡇⠛⠈⠇⢰⠀⣰⠀⠀⠀⡾⢀⠃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⣉⣤⣶⣶⣶⣶⣷⠀⠏⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣯⣿⢸⠀⠀⠀⣹⣸⠀⠀ ⠀⠀⠀⠀⡆⣯⢞⣼⠀⡀⠀⠀⠁⡾⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠢⠓⠛⠛⠒⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⣿⣧⠀⠀⠀⠇⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣾⢀⠀⠀⠀⠁⡼⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡟⢠⣿⠀⠀⠀⡇⢰⠀⠀⠀ ⠃⠀⠀⠀⠀⡇⢠⠀⠀⠀⠁⡼⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠂⣿⣸⠃⣸⠀⠀⠀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡼⢀⠀⠇⢫⠛⠚⠐⡄⣭⠧⠈⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠉⠀⠀⠁⠉⠉⠒⠟⠒⠤⣤⣄⢁⠉⠀⠀⠀⠃⣿⢀⣾⠀⠀⠀⠁⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⡟⢀⠀⠀⡀⣼⣧⠻⠟⡷⣘⡀⣁⢯⠿⠒⠙⠉⠉⠀⠀⠀⠀⠀⠀⡀⠄⣀⢀⡀⣉⠟⣩⢉⠉⠉⠟⠷⣻⠺⢻⠈⠀⡇⣸⠇⢀⠀⠀⠀⡏⢀⠀⠀⠀⡸ ⠃⠀⠀⠀⡆⠀⠀⠀⠃⣠⠀⠀⡜⠀⢸⡟⣾⣿⣷⣻⣙⠀⠀⡀⢦⠓⣌⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢞⠤⣁⠛⢛⡙⠀⣅⠹⡋⣿⢿⡇⢠⠀⠀⠀⠀⠀⣼⠀⠀⠀⡟⢠ ⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⢸⠀⡇⢰⢹⡀⢳⡀⣄⣽⣾⣶⠿⡶⣶⣤⠀⠄⡩⢉⠉⠀⠀⠀⠀⠀⠟⡿⣙⠉⢉⣉⣉⡉⣛⣿⣶⣶⣙⣀⡼⠑⠈⠀⠀⠀⡏⢀⠀⠀⡟⣰⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠈⣆⠘⡆⢻⠀⠀⡀⣀⣤⠤⠒⠒⠀⠁⣿⡇⣰⣄⠣⠉⠈⡀⣄⢤⡤⣤⣤⣤⣀⣤⣤⢀⠀⠀⡇⢷⢠⡇⢿⠀⠀⠀⣼⠻⠀⠃⣽⡿⣼ ⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⢹⠀⡇⢸⠀⣧⠈⣧⢻⠀⠁⠉⠈⠉⠊⠀⠀⡏⣷⡞⠀⠀⠀⣄⣷⡘⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⡸⡇⠉⡼⣿⠀⠀⠀⢹⣸⠁⡿⣽⣴⠀ ⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⡏⠀⡆⢸⠀⣄⢿⡇⣯⠘⠀⡀⣀⣀⠀⠀⠀⣾⣾⢠⠀⠀⠀⠀⡀⣧⣌⠤⠤⠤⠀⢦⠾⠙⠀⠋⠐⡏⢠⠃⣾⢀⡞⠀⠀⡇⣼⠀⡾⣿⣰⠀⠀ ⠁⠀⠀⢣⡎⠸⠀⠀⠀⠀⠀⡇⣿⠸⠀⢻⠀⠀⡆⢸⣼⢿⠈⠀⠀⠀⠀⠀⡟⢃⢸⠀⠀⠀⠀⠀⠀⡀⢳⠀⠁⠉⠛⠗⢾⣧⣸⠒⠇⢰⠀⡟⠀⠇⢸⠀⠏⣼⢋⣿⣾⢀⠀⠀⠀ ⡀⠀⠀⡀⢧⢷⠀⠀⠀⠀⠀⠀⣷⢹⠀⡇⠘⠀⠀⣧⣿⣧⣄⢦⠓⠉⠉⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢶⣤⣀⢀⡟⢰⡇⢸⠃⣰⠀⠃⣸⠁⡼⠀⠟⣼⢀⢋⣴⢀⠀⠀⠀⠀ ⠑⠀⠀⠀⠀⣷⢨⠀⠀⠀⠀⠀⡇⣟⠘⠀⢻⠀⠀⡆⣿⡄⠸⠀⠀⠋⣾⣤⣄⠀⠀⠀⠀⠀⠀⠀⣤⣴⣀⢸⠀⠠⠏⢠⠀⡇⢻⣠⠀⠀⡾⠀⡏⢿⡵⣴⠁⡞⢀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⣯⠱⠌⠹⠀⠀⠀⣷⢡⠀⡀⠀⠀⠀⡾⠀⢸⠀⠟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠇⢰⠀⠀⡇⣰⠀⠀⡎⢠⠏⣴⢏⠡⠟⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⡸⠀⠀⠀⠀⠃⣿⡀⢳⡀⢳⠈⠀⡀⣹⠀⠀⠀⠀⠀⢻⠀⢹⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠋⢠⠃⠀⠁⣸⠀⠀⡞⢀⠟⢀⡄⢋⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⡄⡹⢀⠀⠀⡀⢦⠿⠈⡆⠸⠀⠀⠀⠀⣰⠁⣾⢀⠀⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠟⣠⠃⡸⠁⡜⠀⠀⠀⠁⡼⢀⠁⡾⣯⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣽⠻⠈⠀⠀⠀⡀⢦⠯⠘⠀⠀⠀⠀⠁⡴⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⢠⠃⡼⠀⡤⠀⠀⠁⠞⣠⠁⠞⣠⠀⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⠀⠀⠀⠀⠀⡉⣾⢰⠀⠀⠀⠀⠀⢀⣄⠻⠀⠀⠀⡁⠉⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡽⣼⢁⠞⣠⠀⠀⠀⠀⠄⣫⠴⠏⢱⠋⠐⡇⣯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⣷⢉⠉⠉⠉⠀⠀⠀⠀⠁⠞⣠⢡⠩⠉⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠟⣠⡀⣩⠀⠀⠀⠁⠉⠖⡠⢀⣀⣀⣋⣴⠀⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢻⠀⠀⠀⠀⠀⠀⠏⢠⠉⠞⠩⠟⣩⠛⡴⣠⠀⣀⣤⠲⠛⠛⠉⠈⠀⠀⠀⠀⠀⠉⠚⣴⣴⢠⠀⠀⡀⣷⠤⡤⣠⠀⠀⠀⠀⠭⣾⢠⠁⠟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣆⠘⠀⠀⠀⠆⡶⣤⣟⣿⡾⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⣤⣤⣤⠤⣠⣀⣀⣀⢦⠙⡀⢳⠈⠁⠉⠀⠀⣉⢉⠋⠶⣠⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣦⠘⠀⠀⠁⠞⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⢦⠙⣆⣙⣈⣀⣀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⠒⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡶⢿⡻⢶⠙⠛⠛⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠃⣿⣟⣯⣶⣶⠰⠀⠁⠋⠚⡶⢀⠀⠀⣀⣥⡈⣄⣦⣛⣖⣮⠶⠿⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠐⠄⠤⠤⠤⣨⣛⢉⠈⠀⠀⡀⣤⠦⠓⣛⣌⣦⣷⢴⢤⠤⠤ ⠀⠀⠀⠀⠀⠀⠁⡾⡀⣦⣶⣴⣤⣠⣧⣨⠀⠀⠀⠀⠉⠛⠿⣿⢿⠿⠿⠿⠙⠈⠀⡄⣿⣿⣿⣻⣛⣝⣩⣭⣿⣻⠉⠀⠀⠀⠀⢳⣆⣘⣀⣤⠷⠳⠙⠈⠀⠀⣀⣄⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⣿⣾⠮⠳⣌⠧⠙⠉⡟⠀⠀⠁⠏⡿⣿⣴⣀⣀⠀⠀⠀⠀⠀⡀⣄⠦⡓⣭⣿⢸⠀⡀⣀⣀⣄⣦⣿⣶⠳⠙⠈⡆⠘⢆⠙⠈⠀⢰⠀⣀⢦⠳⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⡞⣷⣿⢀⢳⠐⡀⢧⡙⣄⣷⠀⠏⡿⣝⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣵⠹⠀⡀⢹⠀⢧⠉⡄⣿⢿⠟⠻⠉⠀⠀⡀⢀⠀⠀⠂⠀⠀ ⠀⠋⡾⣤⠂⡟⣸⠀⡸⠀⠁⡽⣹⢤⠲⠗⣿⡿⣾⢢⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣌⠘⠀⡆⠸⠀⣧⣤⣦⣿⣿⣹⣷⢾⠻⠙⠀⠀⠀⠀⠀⠀ ⡀⡃⢿⠀⠆⢧⢠⠇⢀⠀⡻⡸⣿⠉⢸⡏⣿⣴⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⠸⠀⢧⠡⠀⢧⠈⠀⣄⣷⡜⣳⡝⣿⣿⠻⠙⠀⠀⠀ ⠐⡿⣸⠀⠃⣷⢿⣸⠀⡏⡼⠀⣧⣿⠠⣿⣰⠤⠲⠽⠤⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢦⠙⠀⠀⠀⠀⠀⠀⠀⡀⠸⡄⠘⡀⡽⠱⠀⢆⠙⠀⠀⢇⡘⣷⣠⣀⣄⣤⢶⠙⠀ ⡯⣿⢸⠀⠠⠀⣿⢀⠃⢹⢰⠀⡄⣿⠋⢰⠀⠀⠀⡀⢦⢧⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠟⣿⢳⠀⠀⠀⠀⠀⠀⠀⡆⠘⡄⠱⣇⡹⠀⠀⡄⠳⠀⠀⣆⡈⢳⠋⠜⣠⠀⠀⣀ ⣿⣿⢻⠠⠀⠀⣽⠀⡎⡇⠀⠘⠀⣿⣠⠀⠀⠀⠀⠀⠀⡏⣿⠘⠉⠀⠀⠀⠉⠉⠋⠘⣿⣿⣿⣿⡿⢿⠈⠀⠀⠀⠀⠀⠀⣆⠈⡁⣧⣿⠻⠀⠀⡀⣄⠙⠀⣧⠘⣧⢹⠀⠀⠀⡀ ⣿⣶⢠⠁⠀⠀⣾⠀⢸⠀⠀⢻⡏⣰⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣻⣾⣣⢻⠀⠀⠀⠀⠀⠀⠀⢧⡘⠀⣄⣷⢳⠀⠀⠀⡀⢤⠙⢇⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⣸⠇⠀⢠⠇⢀⢸⠁⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⢾⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠄⡙⣦⢿⠙⠀⠀⠄⡑⣯⣿⡜⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠀⡇⠁⢸⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⢀⣏⣷⣾⣿⣿⣿⣻⣶⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⡀⢦⣐⡄⢱⠀⠀⡀⣄⣦⢸⠀⠀⠀⠐ ⠀⠀⠀⠀⢀⠁⠀⡇⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢴⠶⠴⡤⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⠈⡄⠑⡄⠳⠈⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣵⠳⠈⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣼⠳⠉⠉⡉⢿⠙⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠘⠀⠀⢠⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠤⣤⠻⣏⣿⣿⣴⣀⠳⠀⠀⠀⠀ ⠀⣇⠙⠉⠀⠀⢸⠀⠀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠐⠋⠚⠽⠋⠟⡿⢶⣿⣿⢞⠐⠀⠀⢀⠀⠀⠀ ⠈⡄⣼⡶⠛⠉⢹⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⣤⣫⣿⣿⣾⣿⣯⣶⣤⣁⠋⡿⣴⣠⠀⠀⠁⠋⠒⠀⠀⠀ ⢳⠸⣇⠈⠀⣄⣧⠈⠀⠀⠀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⣿⣿⣻⣟⣶⣿⣉⠛⠾⣶⣤⣋⠔⠤⠤⡥⣭⣋⠒⠓⠘⠀⠀ ⡇⢯⠈⣷⠻⠙⡄⢸⠘⠀⡇⣇⣿⢻⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠄⠷⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⣶⣤⣤⣭⣤⣠⣀⠀⠀⠀⠀⢲⠛⠖⠤⣗⣘⣆⠘⠎⢀⠀⠀ ⠉⣹⢳⡀⣾⣿⢿⣟⢸⠀⡇⡀⣿⣿⠉⡿⠀⠀⣷⠛⠟⠿⠿⠻⠗⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⡄⢷⠈⡀⠹⠀⡈⢷⠈⣞⢀⠀⠉⠈ ⡀⣧⡜⠙⡆⢿⣷⣿⣏⠘⡇⢸⣆⣿⣿⣶⢿⠿⡿⣿⣾⣤⡤⣩⣏⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠹⡄⠸⠀⡄⣿⢠⠁⡼⢀⠀ ⠀⠀⢧⣆⠘⣆⡘⢻⣸⢳⡇⢸⠀⣧⣿⣦⣽⣤⣤⣤⣤⣤⣤⣀⡄⠻⠀⠀⠢⠙⠀⠀⠀⠀⠀⠀⠀⡄⢷⠙⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⣏⠀⠃⣰⠁⡼⡀⠐⠀ ⠘⠀⡀⢳⢧⠀⢃⡄⢻⡄⡜⣿⠀⠀⣧⠸⣄⠓⠀⠀⠀⠀⠀⠀⢱⡀⢳⠈⠈⡀⣄⠳⠛⠈⠀⠀⠀⠀⡀⣷⠫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣯⢿⣠⠀⡟⠀⠀⠀⠈ ⣿⠘⠀⡀⣳⢷⡄⠘⣇⠸⢆⣟⢹⠀⠀⣧⠘⡀⢦⠙⠀⠀⠁⠉⡏⠘⡀⣧⠈⠀⠀⠀⣄⣧⠾⠙⠀⠀⠀⠀⢧⢮⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠏⢠⠀⠀⠀⢁ ⣧⣿⠹⠀⡀⡹⢳⠁⠀⢧⠀⣆⡞⠘⣀⢤⢷⠙⠈⡀⣦⣙⢀⠀⠀⣦⠈⠀⢆⠘⠀⠀⠀⠀⣀⡳⢮⠙⠀⠀⠀⣦⡌⠳⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⣤⢾⢠⠃⡸⠀⠀⠀⠀⠀⡀ ⡄⣶⣿⢿⠙⡀⣱⣧⠘⡀⢸⠀⣆⢯⠀⠀⠀⢱⣄⡶⠽⡚⢯⠈⠀⠀⢧⠈⠀⡄⠳⠀⠀⠀⠀⠀⡀⡣⢮⠙⠀⠀⢇⡈⢳⠈⠖⠶⠴⡤⣠⣀⠀⠁⡼⠀⠏⣠⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣤⣷⢿⡙⢣⢯⠈⡆⠘⠀⢦⢿⠀⠀⡀⢱⠀⠀⣄⢦⣕⠺⠙⠈⢣⠀⠀⡀⢦⠙⠁⠀⠀⠀⠀⣄⡳⢮⠙⠀⢧⠈⢧⠈⠀⠀⠀⠀⠀⠋⣰⠀⠞⢀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣤⢷⣿⢫⠀⢆⠈⠀⣆⢻⠀⠀⡀⠱⠀⠀⠀⠀⣄⡳⣌⣦⠻⠀⠁⠋⡀⠳⣌⠓⠈⠀⠀⠀⢄⡙⠢⠈⢳⠀⢧⠈⠀⠀⠁⡴⢀⠀⡏⢀⠀⠀⡄⢸⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⡀⣄⠹⠀⣦⠈⠀⣄⢿⠈⠀⡄⠳⠀⠀⠒⠓⠛⡚⠲⡽⣷⣃⠈⠀⡀⣦⠻⢌⠑⠀⠀⠂⡈⠣⡌⣷⢹⠀⢧⠁⠞⣠⠀⠀⡎⢠⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠑⠀⠀⠀⠐⠈⠀⠀⡄⢱⠀⢇⠘⠀⡀⢷⠘⠀⡀⢣⠈⠀⠀⠀⠀⠀⡀⢤⢷⢎⠙⠀⠀⡄⣷⠻⢌⠐⠀⣄⠰⢦⡈⣧⠘⠋⣰⠀⠀⠁⠞⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⠑⠈⠀⡀⢦⠑⠈⡄⠻⠀⣄⠘⠀⠀⣆⠘⠀⠀⢆⠙⠀⠀⠀⠀⠀⠀⠀⣆⡝⠳⠀⠀⠀⣆⣿⠓⠈⠀⠀⠀⡆⠙⣼⢀⠀⠀⠋⡰⠀⠀⠀⠀⠋⠟⡿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠲⠉⠀⠀⣀⢤⡖⠻⠈⡄⠱⠀⠀⡀⠢⠈⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⡄⠱⢆⠙⠀⠀⡀⣶⣭⠷⠛⠞⡴⣠⠀⠁⠛⡼⢛⠛⠻⠾⠿⣷⣵⢸⣏⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡇⢸⡀⣷⣿⣯⣿⣿⣿⣲⣗⣿⣯⣿⣰⠃⣿⣿⡑⣣⢟⢺⣿⢹⠟⣹⣟⢴⣡⣿⣿⣿⢴⢄⣤⠥⣩⣜⢋⣠⠋⠒⠤⣀⠊ ⠀⠀⠋⠒⡟⣾⢸⠀⡇⣹⣦⣿⣽⣷⣿⣿⣿⣿⣠⠁⣽⣾⣷⠀⢠⣷⡿⣿⣿⣾⣶⢷⠮⣽⣞⣯⢙⠀⠀⠁⡔⢋⡾⢁⠞⢀⠀⠁⡉⠈ ⢹⠏⣿⢸⡃⢸⢸⠀⡀⣻⣀⣀⣤⢠⡀⣧⣀⣀⠛⡶⣶⢛⠛⣿⠙⠀⣧⣽⢀⠀⠀⠀⢾⠘⣄⡦⡬⣄⢇⣿⡿⣿⠿⣾⠀⠀⠀⠀⠃⠙ ⣿⣿⣿⣿⡞⡇⢸⠀⠀⡿⠙⠈⠁⠚⠊⢠⠀⡜⠓⠖⠠⠀⠀⣀⣀⢦⡟⣻⢝⠳⠟⠸⢹⣿⠘⠀⡀⠀⣤⣿⣿⣿⣾⢀⠀⠀⠀⠋⣿⣿ ⣧⣿⣰⣄⣿⣿⢀⠁⠋⣿⠟⣷⣺⡴⠋⠀⡎⢀⠀⠀⠀⠀⠀⠀⠃⠀⡄⣻⣄⢷⣜⣤⣶⣿⢾⠀⠀⠀⠀⡀⣧⣴⠀⠀⠀⠋⠞⢻⣌⣦ ⡀⢀⠀⠄⣻⣾⡴⣀⠀⠁⡞⣠⠀⠇⣱⠏⢸⠉⠉⠀⠁⠀⠁⠋⣿⠀⠀⡄⢷⠘⢶⠿⠻⡙⣮⠿⠙⠉⠉⠉⡀⢦⠿⣿⣿⣻⣮⣿⢿⠈ ⠀⠀⠀⠀⣀⠀⠛⠏⣴⣠⣀⠀⠞⢣⡿⣶⣷⢾⣶⣤⣤⣀⣆⣴⢀⠀⠀⠀⡆⢳⠈⣧⣈⣤⣦⢷⡻⢛⠉⡉⢭⠭⣭⣋⡟⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠃⡾⣤⢀⠀⠋⠴⣀⠉⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⣄⠙⠀⠀⠀⣀⢤⠳⠟⡈⡀⣷⣿⣿⣿⣿⣿⣿ ⠀⠀⠄⡤⣠⠁⠉⠀⡿⣾⡤⣃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡑⢦⠙⠀⠀⠀⣆⣙⢧⠙⡄⣿⣿⣿⣿⣿⣿ ⠀⠉⠟⣿⢿⣡⣿⠙⣰⠀⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡆⠘⠀⠀⠀⠀⠀⠀⠒⢗⠙⢌⠠⠒⠒⡙⠹⣷⣿⣄⣿⣿⣿⡿⣿ ⡿⣿⣿⣾⡇⣾⣅⣼⠀⡁⣸⠀⠀⠀⠀⠀⢄⠙⣀⢄⠤⠲⠛⣿⠈⠀⣸⠃⠘⠁⠙⠈⠓⠛⠀⡇⣾⠻⠉⠀⠀⣄⡴⣿⢹⡀⣿⣷⣿⣿ ⣿⣿⣾⠀⠀⠃⡼⠆⠻⡟⠈⠀⠀⠀⠀⠁⠊⠋⢷⠠⠀⠀⠀⣀⢦⠑⢉⠁⡋⡟⣿⣿⣰⡁⠟⣿⢸⡄⣸⣄⠦⠒⣿⣶⣴⠤⡤⣤⣡⣯ ⣀⣄⢠⠀⠀⡿⢀⠄⡤⣿⣿⢿⠿⠿⣶⣤⢀⢶⠀⢧⠈⠀⠀⠀⠀⠀⣧⣿⣿⣟⣿⣿⠿⣿⣾⢠⣇⠀⢷⠀⠀⠀⡇⣬⣀⣸⣀⣀⣤⣿ ⠀⠀⠀⠁⡾⢀⠀⠀⠀⢹⡄⣷⠮⠹⣈⢀⠀⠳⠈⠀⢷⠀⠀⠀⠀⠀⠀⣆⣿⣈⣀⣀⣇⣿⠛⠖⣿⣸⣇⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣿ ⠀⠀⠆⣷⢹⠀⠀⠀⠀⣿⢿⠙⢦⠘⣇⠿⠛⠀⣧⠙⡄⢻⡟⢰⠀⠀⠀⠀⢆⣎⠙⠀⡤⢸⢇⠀⣻⢸⡇⠀⠀⠀⡍⢻⠈⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⣇⠳⠙⠀⠀⣿⣄⣿⢮⣿⠘⡀⣦⢿⡙⡸⢧⣏⣿⠘⠀⠀⠀⠀⠋⣷⣦⠘⠇⢸⡀⢻⣾⢹⡿⠻⠉⣞⣀⣄⣿⢤⠷⠰⠇⢀ ⠀⠀⠀⠀⠀⠀⡀⢦⠈⡇⢼⡀⢷⡌⣿⠈⡄⠳⣄⢿⠀⣧⣽⢸⠀⠀⠅⡿⢀⠀⠠⣿⡇⢰⠀⣿⠇⣾⢏⣾⣥⢰⠉⠃⡟⠸⡄⢹⠉⡞ ⠀⠀⠃⠈⠀⠀⠀⠀⣏⣿⣿⠈⡀⢧⡌⢷⠀⠀⠀⣆⢸⡞⣧⢰⠃⠀⠃⣼⢿⠀⠀⡇⣿⠀⠇⢿⣿⡿⣶⠖⠠⠀⢰⠏⣠⣧⠀⡁⣿⢀ ⠀⣀⡀⠉⣠⠀⠉⠔⢁⢰⣧⢿⠈⠀⢧⡄⢹⠀⠀⠀⣿⢀⡟⢸⡄⠄⡠⣗⣷⢳⠈⡇⢸⠀⡏⢀⠃⣼⠀⠀⠀⠀⡇⣾⣦⣾⠀⡔⠀⠀ ⠋⡰⠂⠃⠁⣏⢛⢠⡇⠛⣼⣿⣿⠙⠄⠀⡄⣴⠠⠁⣸⠇⢰⠀⠀⠀⠀⡆⠀⠀⢧⡇⢀⠇⢸⠁⡾⠀⠀⠀⠀⠏⣿⢀⡏⢻⠐⠀⠀⠀ ⠀⠀⠂⡄⠰⣿⢠⠀⡇⣿⢻⣆⣿⣿⠙⠀⠀⠀⠁⡞⢁⣿⠴⠰⠀⠀⠀⠇⠞⠉⡏⣿⠀⣿⢹⡿⢠⠀⠀⠃⡿⣿⢠⠇⣾⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⣠⢳⠈⠀⣿⣿⢻⣧⣿⣿⠰⠀⠃⣰⠁⡼⣀⠀⠀⠀⠀⠃⣿⡾⢀⠀⣟⡿⣿⣶⢶⠒⠛⠷⣿⣿⢠⠋⡴⢀⠉⠉⠀⠀⠀ ⠉⠀⠀⠀⠀⠁⠋⣹⠈⢇⡈⣄⢢⣿⡈⠀⠁⣰⠁⡼⠀⡀⠀⠀⠀⠞⣩⣙⢻⠉⠏⣿⣴⢀⠀⠀⠀⠀⠀⠀⣀⣦⣷⣠⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢀⠄⢀⣀⢦⣟⢴⠀⣄⢷⠉⣋⠖⣠⠀⠀⠀⠀⠀⠂⠄⠀⡀⣦⣚⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢣⠀⠀⠀⡀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠋⠻⠀⠀⠀⠀⠂⣰⠀⠀⠀⠀⠀⠀

⠁⡟⣿⣿⣿⣿⣿⣶⣴⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿ ⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢷⠼⠾⠶⠶⠷⠿⠿⠤⣤⣯⣿⡋⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠙⣿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡿⣿ ⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⡟⣿⣠⢀ ⣶⣷⢿⠘⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⠿⣾⣶⣴⣤⣠⣤⣦⣿⣿⠙⠀ ⠀⠀⣿⣿⣿⣾⣶⣶⣿⣿⠿⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠻⠒⠀⠀⠉⠛⡿⣾⣴⣦⢸⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⠈ ⠀⡏⣿⣼⢀⠀⠀⠀⠀⠀⡀⣾⣤⣶⣿⠿⠛⠙⠈⠀⠀⠂⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣴⣠⢉⠋⠟⠿⣶⣤⣧⢻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸ ⠀⣿⣾⠀⠀⠀⠀⠀⠀⠼⡦⢸⠀⢹⠀⡀⣀⣤⣦⢷⠿⠛⠛⡉⣤⢳⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠛⠈⡁⢛⠿⣾⣴⣠⣇⠙⠀⠉⣿⢰⠀⠀⡟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸ ⡇⣿⢸⠀⠀⠀⠀⠀⠀⣧⠸⢧⠈⣆⢻⠈⠀⠀⠀⠀⠁⣏⣤⣧⣿⠿⠙⠟⣿⢸⠀⠀⠀⠀⠀⣄⣶⣿⣿⣴⣆⠻⠈⠀⠀⣀⣀⣀⠀⠀⠋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠃⡴⡏⣿⢀ ⠀⣿⢽⠳⠈⠀⠀⠀⠀⡇⢸⠀⣄⠳⡉⣤⠶⠲⠞⠶⣤⢁⠋⣴⠀⡄⣷⣿⣀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢰⠀⠀⣄⣦⠳⠙⠉⠉⠛⠖⡴⣠⠀⠀⠀⠀⠀⠀⠀⠁⠞⢠⠋⣿⣸⠋ ⠘⣇⣿⠘⢦⠘⡆⢶⠷⡾⢿⠾⠶⠰⡀⣄⢤⠶⠶⠴⡤⣠⢀⠀⠀⠀⡇⣿⠸⠀⠀⠀⠀⠀⠀⠀⡆⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⣀⠀⠟⣿⣽⠟⣿ ⢿⠈⣷⣿⠙⡀⠢⠀⡿⢀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠴⣠⠀⠀⠋⡿⣿⣿⣿⣿⣿ ⣿⣿⠻⣮⣿⠻⠈⠀⣄⢶⡗⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠐⢏⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⢻⠉⠀⠀⠀⠀⠀⠀⠀⠄⡠⣀⠀⠀⠀⠁⠛⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⡀⣀⢤⠤⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⣿⠿⠛⠙⠉⠉⠉⠉⠉⠋⠛⠿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠛⠉⠉⠀⠀⠀⠁⠉⠋⠛⠿⣿⣽⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠛⠾⣤⣤⣤⣤⣶⣶⣷⣭⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣀⠀⣀⣀⣤⢤⠤⠦⠴⠀⠀⠀⠀⠀⠀⡤⣤⣀⣀⠀⠀⠀⠀⠀⠉⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠉⠀⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢹⣀⠀⠀⠀⠁⠁⡁⣉⠀⠀⠀⠀⢀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⡰⠀⠀⠋⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠻⠀⠀⡇⠵⠤⡠⣀⢀⠁⡿⣿⢿⠼⠤⠤⠤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠁⠟⣰⠀⠀⠋⣸⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⠀⡀⡼⠀⠀⠀⠀⠀⣈⢀⡀⠉⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⡠⠀⠃⡴⡐⠀⠋⡴⣎⠀⠁⣴⠁⠉⠉⠉⠋⠙⠀⠀⠀⠀⠀⣦⠘⣄⠘⠀⣆⢹⠀⠹⠀⠃⢿⠈⠃⣿⠻⠛⢿⠐⠀ ⠀⠀⠀⠀⡀⢀⠀⠀⠃⣾⢠⠀⡴⢀⠎⢀⠁⡞⣠⣒⣄⣠⣀⣀⣄⣦⢷⠘⠀⠀⠀⣌⢷⠆⠈⡀⣏⠙⣿⠿⡿⣷⣿⣿⣴⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⠀⠀⠀⠀⠋⣠⠀⠀⠀⠀⠊⠤⣀⢄⠓⠀⢄⠑⠀⠀⠀⡀⡾⢿⣚⣖⢸⡇⢿⣿⡀⣿⣿⠀⣷⣿⢡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠃⠰⠀⠀⠀⠁⡜⢀⠀⠀⠀⠃⣹⠀⠀⠀⠀⠀⢇⠈⠀⢇⡄⠸⠀⢁⣧⠼⠀⢸⡀⣿⣸⠀⣷⣸⠁⡇⢸⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠟⣠⠀⠀⠀⠀⠀⡆⣿⢿⠛⠛⠉⠉⠛⠀⠀⠀⠀⢆⠈⡀⡄⢿⠄⢣⠘⣄⠀⠇⠸⠁⠸⠀⡿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠟⢫⠠⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣤⣶⣰⠀⠀⠀⠀⠀⣄⠈⠀⣿⠸⠀⠁⠋⠀⡷⢿⡿⣴⣣⣿⢹⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⢡⢿⢠⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⢎⡧⣾⣧⠀⡄⣿⣿⠀⡟⣸⣷⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⣱⡟⢰⠀⠀⠊⠒⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣸⣄⠇⠸⠀⠋⣿⣿⠮⣴⠀⡀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⣿⠈⠀⡆⣿⣿⢼⠀⠀⠘⠀⣇⠺⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⡟⣿⣿⢸⠂⡿⢿⡿⢿⣷⣿⠧⣿⢻⠈⡇⠘ ⠁⠀⠀⠀⠀⠀⠀⠀⡘⡀⣿⣿⠳⠉⡉⣉⠟⠸⡟⢻⢹⡿⠐⠸⠀⠃⠿⠽⠸⠀⠧⠟⣷⣼⣧⣿⠜⢠⡇⢿⣿⢀⡇⣿⠘⣿⣷⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⡆⠑⠉⣿⣿⠹⠈⠏⢿⣿⣾⣣⣿⣴⣷⠀⢸⢦⡙⣤⣤⢀⠁⡞⢁⡏⢀⡏⣿⣿⢀⡇⣿⢰⠀⡿⣾⢿⣿⠀⣆⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣽⣷⣿⢻⣿⣿⣿⢃⣿⣻⠀⡄⡿⢰⠁⡕⣏⠾⣡⣟⢠⡽⠊⠏⣷⣼⡄⠰⡆⣰⠁⡟⣿⢀⣧⣿⢸⠀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⣦⣿⣹⣿⠻⣮⢀⡿⣻⣿⣾⠃⣿⠛⣿⣹⡟⢟⣯⢡⡿⣟⠴⢁⡰⠀⠘⠀⠀⠁⡿⣤⢁⠉⠀⡇⠿⢉⡿⡟ ⠀⠀⠀⠀⠀⠀⠀⠆⢷⠘⠀⡀⢦⡿⣿⢿⡈⣦⣿⣧⢿⡿⣿⣿⠻⡉⣤⣿⣶⣴⣠⠁⠟⣷⣄⡥⣭⠀⠀⡟⣼⠀⡿⣿⠻⡯⣿⣀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣄⣶⣷⠻⣆⡻⣿⣿⣾⣶⣴⣤⣀⢀⠀⡀⣁⣛⣟⡶⣶⣤⣦⠀⠃⣿⢸⠀⣇⣸⣷⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⠉⠀⠀⠀⣄⣤⠶⠲⣇⠤⡒⠱⣉⣊⢀⠀⠀⠀⠀⠀⠀⠀⠤⣇⠹⠁⢌⠲⠛⢰⠀⡿⣿⢻⠀⣿⢸⡀⣿⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢄⠲⠙⠉⠀⠀⠀⠀⢱⠊⡴⢀⠀⠤⡤⣤⠀⠀⠀⠀⠀⠀⠀⢧⠒⠒⠂⡜⠀⡟⣿⣀⣿⠸⡇⢰⠀⣴⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠼⠢⠒⡒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁⣀⣀⣄⢀⠏⣿⢰⠀⣆⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠤⠤⡭⢤⠤⠠⣀⣀⣤⣀⣀⣀⣤⣠⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠣⠀⠀⠀⠀⠡⡱⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡏⢈⠀⠀⠀⠃⠇⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠁⡐⠀⠀⠀⠀⠀⢰⡰⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠁⠜⢀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠪⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⠠⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡎⠹⡑⠠⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀ ⣤⠀⠀⠀⠋⡴⢣⠑⠁⠊⠓⠘⠀⢀⣼⡗⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⢠⠀⡙⡰⢀⠀⠀⡀⠃⡌⠀⡀⠢⠒⠒⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⣸⠀⡎⡼⠀⠀⠀⠀⠀⡅⢰⢀⡤⠑⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⠀⠁⢆⠀⠀⠀⠀⠀⠊⡿⠀⠀⠀⠀⢣⠁⠊⡕⠘⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⣧⠀⡏⠹⠀⠀⠀⠀⢱⢹⢣⢠⠀⠀⠀⡏⡉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⡆⠙⣴⣞⠀⠀⠀⠀⡇⣾⢠⠀⠀⠀⠀⣹⣸⠀⠁⢴⠢⠈⠀⠀⠀⠀⠀ ⣿⠀⠀⣷⠀⢱⠀⠀⠀⠀⡎⢀⠀⠀⠀⠃⠟⡘⠀⠀⡈⠇⠁⡄⠠⠀⠀⠀⠀ ⣿⠀⠀⡀⢤⡐⠣⠀⠁⠗⢀⠀⠀⠀⠀⡏⣕⠈⠀⠟⢈⡇⠀⡀⣊⠛⠨⠀⠀ ⣿⠀⠀⠀⠀⠀⡁⡋⣠⣆⠙⠉⠁⠂⡤⢁⠋⢼⡗⣿⢠⡇⠀⠀⡀⡢⣸⠑⠀ ⣾⠀⠀⠀⠀⠀⡇⢹⠈⠀⣻⣧⡳⣈⢑⣄⢹⣧⡜⣾⠈⠀⠈⠈⠀⠀⡄⠤⢠ ⢸⠀⠀⠀⠀⠀⡄⣷⣹⣴⠀⢽⢳⣌⠱⠣⣧⡄⠻⣰⠀⠀⢹⠄⠐⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣥⠘⣆⣿⠎⣿⠉⠈⡔⢱⠏⠛⢃⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⡪⣏⠇⣿⣿⢻⢛⡄⣢⣞⣿⠐⠀⠀ ⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡱⡴⢳⣿⣟⡌⢦⢟⣕⣩⠐⠀⠀⠀

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⡇⠀⣄⢶⠻⠈⠁⣿⣻⠛⠛⠛⠛⠛⠿⠻⣘⢈⣀⣀⣀⣤⣴⣰⣄⠶⠶⢿⡶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣷⢿⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡄⣠⢰⠀ ⡟⠀⠀⠀⠁⣞⣴⣀⢀⠀⠀⠀⠀⠀⠀⡀⣀⣤⢶⠿⠛⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢹⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⡔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢶⠻⠈⠀⠑⢸⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠹⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⢳⠀⠀⠀⠀⠁⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⡇⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀ ⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡙⢦⠛⠛⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⣧⢸⠀⡆⠘⠀⠁⣯⡋⣿⣿⠈⠁⠀ ⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⢿⠀⠉⢿⡿⣿⣿⣽⣄⣤⣧⣾⣷ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣾⢣⢿⣿⣿⣿⣸⠀⠁⣏⠻⠞⣶⠙⠉ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⣀⢀⠀⣿⣿⣽⢀⠀⣏⢾⣠⢀⠀⠀⠁⣽⢉ ⣏⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣽⠩⠉⠉⡏⣼⣀⣀⣧⡴⣸⠀⠀⠁⠀⠀⡇⣹⡀ ⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡿⣿⣿⣿⢼⣿⣤⣤⠶⡿⣠⠀⢰⠀⠀⡆⠀⠀⣏⣿⢿ ⣵⣾⣷⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠀⠀⡀⣀⣄⣤⣧⠻⠓⡽⣿⠶⠤⣤⣤⣤⣤⠤⠦⢻⣿⢠ ⢖⣽⠉⣿⣾⣤⢦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⠀⠀⠀⠀⠀⠀⠀⡆⢻⠉⡞⣠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃ ⠀⠀⣀⣧⠈⠀⠀⠀⣀⢤⠲⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢧⣾ ⠀⠀⠀⡄⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⡿⢠⠀⠀⠀⠁⡟⣉⠈⠀⠀⠀⠀⡇⢙ ⠀⠀⠀⠀⡄⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠞⡤⢀⠀⣀⠦⠒⠖⠤⠤⠬⠯⠾⠓⠓⠛⠉⠀⠀⠀⠀⠀⠁⠋⡿⣴⢀⠀⠉⠛⡿⣇⣷⡾⢳⠀⠀⠀⠀⡇⣸ ⠙⠀⠀⠀⠀⡀⣦⢿⠁⠀⠀⠀⠀⠀⠀⠁⠋⠟⣿⡘⣄⠦⠑⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣿⠿⣿⣿⢿⣿⣿⣿⡿⣭⣿⣴⢀⠉⠞⣿⢂⡿⣿⠀⡇⢈⡄⠿⠷⠙⠀⡏⠀ ⡆⢿⠙⠀⠀⠈⠀⡀⣄⠦⠒⠓⠛⠟⡿⣿⣿⣿⣿⣿⠻⠈⡿⣻⠀⠀⠀⠀⠀⠀⠁⠞⡴⢀⠀⣀⣀⣀⣄⣤⣷⣿⣠⣇⣿⣦⣷⣿⣽⣟⡿⣿⠈⡄⣿⠘⡆⢸⠀⣆⡜⣠⠀⢻⠀ ⠙⡀⣦⠻⠈⣄⠳⠈⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣻⠈⣄⣷⣿⣟⢠⢷⠈⡀⢧⠈⣇⠉⠁⢸⠀⠀⣼⠉ ⣦⢻⠈⡀⣦⠻⠈⣄⠳⠈⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⣷⢿⠈⠀⣄⣿⠀⡁⣿⠙⡟⣼⣤⣿⣿⢰⠀⠏⣴⣠ ⠉⡄⢷⠙⠀⡀⣧⠻⠈⣄⠳⠈⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⡉⣬⡷⡿⣿⣿⠘⠀⡇⢼⡞⢀⠀⡾⢀⡏⣿⣸⠋⡴⢀⠀⠀ ⡁⢦⠙⣄⢷⠛⠀⣄⣶⠻⠈⣆⠹⠀⠀⠀⡀⣧⣿⣼⣿⡈⣿⣠⠀⣿⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣟⠻⣿⢹⣄⢷⠀⠀⣿⢠⠆⡾⢀⠇⣾⣼⠀⠀⠀⠀⠀⠀ ⡀⢦⣗⢿⡛⣮⢮⠙⠀⡀⣄⠳⡈⢣⠈⠀⠀⠃⣿⢸⡄⢹⣄⣧⠿⣼⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣷⣼⣤⣿⢻⠈⠀⠀⣄⢻⡾⢀⠃⣰⡇⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⣷⢿⣎⡻⢮⠙⠀⠀⣤⠻⣌⠹⠀⡇⣧⢸⠀⣆⠹⠏⣷⣿⡿⡆⠹⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⡟⢀⡄⣷⠛⣿⡇⢾⠙⢰⠇⣼⢀⠃⣼⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣦⡻⣿⡹⢄⠳⠈⠂⣧⡻⢮⣸⡇⢿⠀⠀⣆⣻⡂⢿⣄⠳⣿⠘⠀⠿⣸⣿⣙⢿⠋⡟⢻⠀⡟⢨⠀⠀⠆⣿⣿⠀⢻⣶⠞⣧⠀⠁⡾⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢿⠈⣄⠳⡉⣦⣿⣮⡖⣿⠹⠀⠀⣆⢿⣮⠹⠀⣄⢷⡟⣿⣿⣿⣿⣿⣷⣿⠠⡟⣱⢠⠀⠀⠀⡆⣿⠀⡁⡼⢀⡌⠋⡾⢀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣮⠻⠈⣄⢶⡙⢯⠙⡀⣄⢦⠙⠈⡀⣷⣿⢱⠀⠀⣄⣶⣿⣛⣉⠉⡟⣿⠿⣾⠀⠀⠀⠀⠀⠀⣽⠀⣠⠀⠁⡟⣼⢀⠁⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢳⣄⠻⠈⡀⣦⣹⢦⠙⠀⠀⣄⠲⠀⣄⣳⢪⠈⠀⠀⡀⣤⣳⣬⣷⠀⣿⢀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⡿⢀⢣⠟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⡀⢤⠁⠀⡄⠰⡀⢦⠙⠀⠀⠀⠀⠀⣤⢷⠘⠀⠀⠀⠀⣄⡶⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠐⠋⣷⢦⠃⣴⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⣿⡌⣥⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⡀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣀⣀⣀ ⠄⠀⠀⠀⠀⠇⣾⣦⠰⣀⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠞⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⣀ ⠈⠂⠀⠀⠀⡀⣤⣳⣿⣉⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣶⠿⢰⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣀⣸⢤ ⣀⠀⠀⠀⣾⣧⠰⡟⣾⣶⣷⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⡃⣿⣿⣿⣿⣿⣿⣶⣿⣿⢶⠶⠤⠥⠯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⢀⠀⠇⢠⡸⠀⣶⠽⠿⠟⡛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣯⣿⣿⣶⣿⣴⣡⠟⣾⣠⢀⠀⠃⢞⣠⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⡼⡏⢉⠞⡤⣉⠟⣭⣉⣏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⣠⢋⡴⢀⠃⡿⣴⠀⠀⠀⠄⣠⠀⠀⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏ ⠀⠀⠏⢰⣠⢉⠖⣥⢈⣧⣿⢀⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡴⢀⠀⡴⢀⠀⠃⣣⣰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣟⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀ ⠴⣀⠋⠖⣠⢀⠀⡼⣀⣇⢸⠀⠀⡅⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⣠⠀⠀⠀⠀⠀⠀⠀⣹⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣷⣹⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣀⠀⠀⠀⠀⡞⢀⠁⣿⣿⣶⣒⣒⣗⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢀⠀⡿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⣤⢶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢠⠀⡼⠀⣌⠉⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠸⠀⡆⠘⠀⢷⠀⠀⠀⠁⠀⠁⡟⣶⠤⣤⣤⣤⢤⠲⠀⠀⠀⠀⠀⠀⠁⠚⡴ ⠀⠀⠀⠀⠃⣰⠀⡞⢀⠀⢿⣴⣀⣿⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠘⠀⢡⠀⡀⢻⠉⠟⢼⡤⣀⣄⠤⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣡⠞⡴ ⡞⣄⠳⠙⡼⠀⠏⢠⠀⠁⣼⠀⡏⢠⠀⠀⠀⢦⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠻⠉⣟⠾⣠⢀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⠀⠀⠀⠀⠃⣰⠟⣠⡀⠀ ⠀⠁⡼⣞⠀⠀⢶⠓⠉⡼⠀⠃⣰⠀⠇⠾⠒⠙⣄⢹⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠾⡠⢇⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⡸⠇⢀⠀⠀⠀ ⠁⡿⡴⢿⠛⠉⠈⠀⠀⢀⠁⡿⠙⠚⠉⣈⠣⡌⣦⡞⡜⣷⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⣠⣀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⢠⠀⠀⠋⢰⠀⢹⠋⠙⠀⠁⠛ ⡃⣰⠎⢀⡼⠀⣀⣇⠠⠀⡟⣾⣐⢦⡑⣄⠳⣇⠀⣧⢈⡇⢻⢆⠙⠉⠉⠙⠉⠋⠖⡥⣬⢀⠀⠀⠀⠀⠀⡆⡞⠘⠀⠀⠀⠀⠃⣿⣸⠁⣼⠀⠀⠀⠋⡿⢲⠒⠒⡓⣿⣿⣯⣿⣽ ⢠⠄⢀⡜⠀⠀⠏⢰⠀⡟⢀⢸⠀⠉⡉⢣⠀⣄⠀⠀⠁⡟⣿⠾⣡⣼⢀⠋⣴⢁⠟⣴⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠻⠈⠀⠋⣽⣿⠉⡿⢻⠓⠶⣸⢀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣼ ⠉⠁⡼⠀⠀⠇⣹⠀⠟⢠⠀⡜⠀⢳⠙⣀⢀⠀⠀⠀⡟⣾⣠⠿⣠⠀⡞⢀⠄⣀⠀⠀⠀⠀⠁⠀⠋⠚⠓⠞⠴⠤⣠⣇⣈⣷⣼⠀⠀⠀⠀⡉⡏⢚⠛⠴⠦⠭⠛⡿⣿⣿⣿⣿⢀ ⣀⣄⠀⠀⠁⠉⡉⣍⢩⠉⠉⢻⠉⠉⡉⢻⠈⠃⠋⡼⢀⠀⡞⢀⠀⠃⢸⠀⠀⠀⠀⠁⠚⡴⣤⣀⢀⠋⣠⠀⠀⠀⠀⠀⢣⠀⢤⠀⠀⠛⡿⢀⡿⠉⢾⠶⣠⠀⡏⣿⣿⣿⣿⣿⠘ ⠀⠀⠁⠜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⠀⠀⡄⢀⠀⠀⡀⢹⠀⠁⠋⠔⣸⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠁⠋⡖⠹⠀⠀⠀⢆⣴⣠⣀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠃⡴⢀⠀⠀⠀⠇⢠⠀⠀⠀⠁⠞⣀⠀⠀⡀⢦⠙⠈⠀⠀⠁⠀⠁⠉⠉⠛⠟⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠟⠰⠀⠁⠛⢴⣠⠀⠀⠀⠀⠀⡼⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⠤⡤⣀⠉⣞⣴⣯⣿⢿⠿⡋⣟⢿⠛ ⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠉⠉⠛⠒⠴⠤⣠⣀⣄⣤⣷⣾⢶⠴⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⣠⠀⠀⠀⠀⠀⠀⠀⠉⠚⠶⣴⣀⢤⡶⣶⣴⣀⠀⡆⣿⣿⣿⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⡀⣎⣧⣠⣆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇⣠⠀⠀⠀⠀⠀⠀⠃⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⡆⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢡⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⠂⣿⣿ ⠀⠀⠀⠀⠀⠀⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠃⣰⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣟⣿

⠀⢇⡿⠀⠀⠂⠂⠓⠛⡶⢠⠀⠄⣀⣒⣍⢨⢺⡞⠘⠀⢳⣧⠀⠀⢃⠠⠀⠀⠀ ⠁⠔⢀⢄⢔⡬⡼⣠⠄⠐⠀⠀⠀⠀⠋⡂⣶⣤⢤⢤⡇⡀⣦⠸⠀⡇⠀⠀⠀⠀ ⣨⠀⠀⠁⠾⢤⠆⠀⠀⡀⠊⠔⠠⢀⠀⠋⢖⠹⠒⡦⡙⠢⠘⣬⠱⡰⠡⠀⠀⠀ ⢸⠁⠟⣿⠉⡸⠀⠉⠔⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⢹⠏⠀⠀⢄⠈⢤⠓⠁ ⠂⢿⣿⣾⣤⡀⣔⢀⠀⠀⠀⠀⠀⠀⠀⡄⢤⠤⠂⡐⠓⣿⣿⠈⠀⠀⡀⢡⠀⢄ ⡿⣤⢊⠜⠉⡱⠠⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠰⠀ ⢸⡤⢅⠏⢃⡧⠊⠉⢉⠀⢡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⢸⠀⠂⢿⢻⡿⣄⣷⢙⠀⠋⡛⠟⠹⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠋ ⢿⠛⠟⣿⣿⣶⠹⠀⣼⣶⣷⠿⠿⣟⠻⠛⠀⠀⠀⠀⠀⠀⠉⠿⠹⠒⠂⢁⡇⢸ ⣿⣿⣿⣿⡆⠻⣾⢻⡏⠈⠂⠄⠤⡀⣒⡐⠀⠀⠀⠀⠈⡀⣦⠿⡟⢻⠉⡉⣿⣿ ⣿⣿⣸⣷⠘⣧⢿⡄⣿⢣⠙⢸⠐⠉⠈⠀⠀⠀⠁⡴⠋⠻⡿⣼⣀⣅⣼⢁⡟⣿ ⡆⣮⢺⡀⢸⡀⣿⠀⡆⡈⣍⣶⠻⠉⠀⠀⠀⠋⣻⡿⣿⣴⣞⠀⠃⡿⠛⡴⣟⣿ ⢢⢨⣧⠃⢀⡄⡏⠀⠁⢰⢧⠀⡀⣄⣶⠿⠜⣟⣿⣴⢀⡟⢿⡿⣿⣿⢩⡿⣴⣟ ⢀⣄⠈⣷⠘⠃⣇⡇⡀⠰⠏⠘⠋⡼⠟⣼⡏⣰⢀⠀⡟⣫⡴⣏⣜⢕⣮⢑⠏⣿ ⠀⡀⢒⡆⢳⠀⢰⡄⡀⠁⣿⢿⢟⣿⣿⠟⢓⠿⠿⣿⣴⣀⣏⣴⡉⡻⣿⠻⡴⢀

⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⣇⣿⣽⣦⣿⣿⣿⣢⣛⣛⣟⢟⣥⣻⣿⢴⠀⣻⣿⣻⡙⣧⣫⢔⢋⡿⣞⣡⠟⣴⢋⣻⢾⣴⣟⣿⣣⣽⢞⣰⡖⣺⠖⡭⣡⣞⢣⡾⢀⠋⠛⠖⠤⣀⠋ ⠀⠀⠀⠀⠀⠀⠾⣾⢸⠀⡀⢿⣦⢿⣛⣮⣿⣿⠿⠿⣿⡿⣛⣿⣠⠀⡟⣿⣿⢸⡄⢳⢥⣻⢋⡿⢿⣿⢟⣿⣷⢉⠋⡿⣵⢟⣾⣠⠀⠀⠀⠀⡅⣾⣡⠟⣴⠁⡞⣀⠀⠀⠁⠔⢀ ⠙⠀⠃⡿⣨⣦⣿⢠⢸⠀⠀⣾⠺⡙⣯⣿⠻⣌⣶⣿⣿⣾⣿⢘⠀⠏⣿⡼⣠⢦⠉⠀⡀⣷⣫⣿⣟⢶⣠⣀⣤⠷⡌⢶⣵⢋⣷⢮⠛⠛⠁⠞⣩⠞⣿⢠⠏⣴⢀⠀⠀⠀⡶⠲⠴ ⣿⠏⣿⣿⢹⠀⣾⠁⢸⠀⠀⢀⢻⠀⠀⡀⣀⢠⠀⠀⢸⠀⡀⠋⡶⣶⣒⢒⠿⠿⡿⢿⠈⠀⣦⣹⢉⠀⠀⠀⠀⡁⣾⠹⠀⣄⣦⣙⣀⠀⡿⣽⣿⣿⣽⣯⣾⠀⠀⠀⠀⠀⠀⠟⠙ ⣧⣿⣿⣿⣿⠻⢰⡏⢸⠀⠀⠀⣿⠉⠀⠀⠁⠛⠁⡞⢠⠀⡎⢉⠋⠚⠢⠐⠀⡀⣀⣀⣦⠹⡿⠪⣝⢦⠙⠛⠽⡀⢹⣿⠘⠀⠀⡀⣀⡄⣷⣿⣯⣿⣿⣾⢠⠀⠀⠀⠀⠁⡟⣿⣿ ⡇⣿⣿⣼⣷⣿⠇⣿⢠⠀⠀⠇⣾⣃⢽⠿⣴⢏⣰⠎⠀⠃⢰⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣽⣦⢿⡹⣦⣷⢻⣿⣿⢻⠈⠀⠀⠀⠀⠀⣧⢫⣿⣴⢀⠀⠀⠀⠀⠋⡽⣤⣷⣿ ⡆⣶⣲⠀⠀⣿⣷⢸⢁⠛⠶⣴⣤⣯⠻⣶⣠⢀⠏⢰⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⣧⢻⠈⣄⢻⠀⠀⣀⣦⣿⢙⠀⠀⠀⠀⠀⠀⡄⢻⠉⠉⠉⠛⠞⣿⣙⣞⢿⠈⣀ ⠀⣀⢀⠀⠀⢱⡿⣼⣠⠀⠀⠉⠉⠾⢠⠀⠀⡎⣧⠉⡿⢉⠋⠙⠈⠀⠊⠒⠁⠉⠟⡟⣼⠀⠀⠀⣆⢿⠒⣴⡼⣷⢿⠻⡍⣶⣿⠻⠋⠚⠒⠙⠀⡀⣧⣿⣿⣿⣿⠻⣮⣿⣿⢿⠀ ⠐⠀⠀⠀⠀⡀⠀⢀⠙⠍⣿⣴⣰⣠⠀⠁⠞⢡⡟⡞⣶⣿⢿⡶⣶⣤⣤⣤⣤⣦⣶⣠⠀⠀⠀⠀⠂⡗⠻⠀⣦⣹⣄⣤⣦⣷⠿⠛⠙⠉⠉⡉⢬⠤⡤⣥⣉⠛⣽⣿⢿⣯⣿⣿⢻ ⠀⠀⠀⠀⠀⠀⠋⠿⣾⣠⢀⠀⠁⠋⠴⡠⠀⡤⣠⢀⠀⡀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⡀⠣⠀⠀⠀⡀⣀⣤⣶⣛⣉⣃⣌⣠⣆⣿⣿⣿⣿⣮⣽⣿⣿⣿ ⠀⠀⠀⠁⠉⠟⣾⣠⠀⠀⠀⠏⣾⢡⠋⠖⠿⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⡘⢷⠙⠀⠀⠀⠀⠀⡂⣭⢷⢻⠈⠀⣇⣿⣽⣿⢿⣎⣿⣿⣿ ⠀⠀⡀⣀⣁⢈⠁⠋⠛⠘⡇⣻⡴⣀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠣⡈⢦⠛⠈⠀⠀⠀⡄⠷⡈⣷⠻⠀⣿⣿⣿⣟⢿⣦⣿⣿ ⠀⠀⠋⠟⣿⢸⣼⢃⣿⢸⡞⢀⠀⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢧⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⣉⠻⠈⣄⠶⠲⠒⠉⠉⢧⡜⣿⢿⣌⣷⣿⣿⣿⢸⣷⣿ ⠟⡿⢻⣿⡏⢀⢹⡾⣂⢻⢰⠀⠔⣾⠀⠀⠀⠀⠀⠀⠀⠓⠈⠀⠦⠒⠓⠙⠈⠀⣾⢸⠀⡇⣼⠀⠁⠀⠀⠀⠀⠀⠉⠙⠀⡀⣷⢿⠙⠈⠀⠀⡀⣄⢻⣇⣿⢿⠀⣦⣿⣹⣿⡇⣿ ⣇⣿⡇⣿⣠⠀⣤⢠⠏⣰⠀⠀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⠉⠉⠀⡀⣀⣤⢶⢿⠈⡇⢼⡄⣤⠐⠇⣿⠿⠛⣞⣦⠀⠃⡿⣸⣆⣽⠶⠛⠈⠀⡃⣜⢿⣷⠹⠀⣯⠉⣿⣿⣿ ⡿⣿⡿⣴⠀⠀⠀⡟⢸⠀⣦⢿⣿⠉⠀⠀⠀⠀⠀⠁⠛⠼⠣⣵⢳⠀⠀⠀⠀⠀⠀⡀⢦⠛⠙⠂⠛⡿⣿⣿⣿⣾⢀⠁⠟⣿⣾⢻⠀⣇⠀⠀⣀⢤⠶⣛⣬⣭⣉⣉⣉⣉⣉⠛⣟ ⢀⡀⣦⠀⠀⠀⡇⣿⠀⠀⠤⣦⣽⣾⣷⣿⣿⣿⣿⣶⣠⢀⢾⢠⡀⢷⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⢿⣻⣛⣛⣟⢿⣿⣿⣿⣴⢀⡇⠀⡆⢸⠀⠀⠀⠀⡇⣌⣀⣇⢀⣀⣀⣄⢰⣿ ⠀⠀⠀⠀⠀⠏⣼⢀⠀⠀⠀⡇⢸⣄⣷⢮⠛⠈⠦⣤⠀⠀⠱⠀⠀⠀⢻⠈⠀⠀⠀⠀⠀⠀⠀⢧⣾⣼⣤⣤⣤⣥⣧⣿⢈⠁⠏⡟⢾⠤⣿⠀⠀⠀⠀⡇⢸⢀⠀⠀⡄⢠⠀⠁⣿ ⢀⠀⠀⠁⠟⣿⠀⠀⠀⠀⠀⡇⢿⠙⡀⢧⡘⣤⠲⠙⠈⠀⡀⢷⠙⠀⡆⢻⠀⠊⠘⠀⠀⠀⠀⠀⣆⣞⠹⠀⠀⢁⡇⡸⣷⣈⠀⣾⣿⠀⣿⠀⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⡇⣼ ⠀⠀⠀⣤⣦⣿⠘⠀⠀⠀⠀⡇⣾⣿⣿⠻⣌⠹⠂⣿⣿⣿⠈⡀⣽⢷⠈⣇⠸⢸⣧⠀⠀⠀⠀⠀⠀⢆⡌⠿⠴⣀⡇⢸⡄⢹⠃⢸⣸⠀⣿⠀⠀⠉⠛⡛⣯⠻⠈⠀⠀⠀⠀⡇⢀ ⠀⠀⠀⠀⠀⡀⢿⠻⠈⠀⠀⠀⢿⡄⣷⡹⣧⡿⢻⠀⠀⣦⣿⠻⡇⠈⢦⡜⣿⢸⡿⠀⠀⠀⠀⠀⠁⠞⣷⣄⢻⠀⡇⢸⠀⣇⡏⢸⢸⡏⣶⠽⠡⣟⠰⡀⣄⣿⣘⣦⠿⠶⠠⡇⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠘⠀⣧⠿⠀⣧⠻⣆⣿⠸⠀⠆⡻⡄⢷⢻⠀⣆⣿⢱⣸⠀⠀⠀⡆⡞⣸⠀⡄⠸⣧⠸⡇⢀⠀⡇⣿⠁⣿⣼⠟⣿⣶⣻⢀⣀⡁⡏⣿⠀⡇⢹⠀⠸⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠓⡟⣿⠈⠀⣆⠹⡄⣿⠘⠀⡀⢀⡄⣿⠘⠀⣻⡿⢸⠀⠀⠈⡆⢱⢳⠈⠀⢀⡆⣿⡟⠀⠀⡏⢡⡟⣫⡿⣼⢁⠏⢠⠁⣰⣀⣿⣶⠸⠀⣆⡿⢿⣠ ⠀⠉⠈⡇⠒⠁⠐⠀⠀⠀⠃⡴⣾⣿⢿⠀⠀⣆⠹⡄⣿⠀⠀⠀⠀⡄⢻⠏⣠⡏⢀⠀⡬⠀⢽⡟⡟⢣⠀⠀⠀⣿⣼⠀⠀⣿⣤⢾⣯⣼⣄⣠⢀⠀⡆⠁⡟⢩⠈⢸⠀⠁⡟⢲⠀ ⠈⡀⢀⠀⠙⡀⠀⠀⠁⠜⢀⡇⠀⣇⣿⢻⠀⠀⣇⠸⡄⢻⠀⠀⠀⠀⣧⢰⠃⣿⢸⠀⢰⠤⣀⣇⣸⣼⢷⠈⠀⣿⢠⠀⡇⣸⠀⠃⣾⠀⠀⠀⠀⠀⠀⡟⣾⣠⣷⢰⠀⡷⢀⠀⠀ ⠁⡏⢠⠋⡃⡀⣀⣯⣁⣞⠀⡇⠁⣾⣿⣿⢿⠀⡀⠸⠀⣆⡿⠤⠰⠀⡾⠀⡟⢠⢸⠀⠀⠀⠀⡀⢸⢸⡀⣷⠘⣿⠀⠃⣾⠀⠁⡿⢠⠀⠀⠀⠀⠁⡟⣿⢠⠁⣾⠉⠈⠀⠀⠀⠀ ⣄⠈⠀⢈⡅⠈⣇⣻⣼⢀⠀⣟⣿⢻⡆⣿⣿⣿⢈⠀⠀⠀⠀⠀⠀⡏⢰⠇⢱⢉⠀⠀⠀⠀⠀⠀⢸⢹⠈⡀⢸⣿⠁⡿⣾⠁⡿⣸⠀⠀⠀⠀⠉⡿⣿⢰⠀⡿⣿⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⢦⡀⣀⡏⣹⠀⠀⠀⡇⣿⣯⠙⣇⣿⣿⣿⠘⠀⠀⠀⠁⠞⣠⠃⡿⣸⣁⣠⠀⠀⠀⠀⠋⢾⣛⠴⠦⢸⣼⡃⣿⢻⡿⣰⠀⠀⠀⠁⡟⣿⣿⣰⠀⠇⣾⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⣠⣀⢳⠙⠀⡇⣿⢻⣿⠙⣷⣻⣿⣾⠀⠀⠃⡾⢀⠁⡼⣀⠀⠀⠀⠀⠀⠀⠏⣷⢿⢸⠀⠀⡏⢻⣿⣿⣾⣴⠤⠶⠿⠾⣿⣿⣿⣸⠁⠟⣴⢀⠉⠉⠉⠉⠀⠉⠈ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⡏⠀⠀⢻⡀⣄⣦⡙⢷⣈⢀⠀⠀⡜⠀⠁⡾⢀⠀⠠⠀⠀⠀⠀⠞⣠⡍⣧⠸⠀⠁⣿⣿⣴⢀⠀⠀⠀⠀⡀⢀⠀⣀⣀⣦⣿⢾⠴⣠⣀⣀⠀⠈⠀⠀⠀ ⣄⠀⠀⠀⠀⠄⠶⡠⣁⣼⣆⠶⡙⢢⠛⠈⡀⣷⢿⠀⠀⠶⢠⠋⡴⠀⠀⠀⠀⠀⠀⠀⡀⠎⣠⣄⠶⣾⠶⣿⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣄⡿⣄⠀⠀⠀⣄⢿⠼⣶⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡎⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⠒⠀⠃⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⣄⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠊⠟⢿⠙⠀⠉⠉⠀⠐⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀

⡉⣄⢦⠚⡿⢊⢲⠒⠉⠀⠀⠀⡀⠦⠑⡄⠾⠘⠀⠀⠀⠀⠋⠠⡞⠡⡎⠀⠀⠀ ⠀⡉⣓⣿⣩⣔⣤⠿⠾⠒⠙⠌⠑⠈⠀⣀⡦⢷⠉⠀⠀⠇⣤⡶⣹⠋⣿⣟⣤⠢ ⣁⢷⢺⠚⡟⠸⠀⡛⠿⣾⣶⡲⢖⡲⠲⠈⠀⠀⣀⣀⣀⣆⢲⠌⠦⣞⣾⣱⢋⠀ ⢧⢃⢩⣌⣤⣶⡞⣄⣿⢀⠋⠀⠀⠤⠑⡀⠢⠉⠈⠒⠔⡨⠶⡅⠢⢊⣏⣿⡈⢳ ⢪⠋⣌⠤⢹⠑⢁⠀⢸⠀⣇⠀⠀⠋⡖⢢⠀⠀⢀⠀⡄⡑⣄⢿⡻⢻⡀⣾⢸⡀ ⢝⢢⠯⡺⡘⠡⡄⠛⠀⠁⠁⢗⡴⢤⢀⠀⠀⠀⠀⠁⡞⣝⣿⣱⣧⣿⠀⢃⢃⢸ ⣇⠉⢌⢁⡯⠯⠡⡇⠂⢎⢀⠀⠀⠀⠀⠀⠀⠀⠄⠵⡢⣐⢡⠶⢃⣦⠀⡀⠀⢿ ⣿⠿⣧⠟⠢⡈⠻⠳⢰⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠄⡦⠋⠀⢰⠀⠀⢸⣷ ⡄⡕⣦⣿⠟⡆⠀⡷⠃⠆⠀⠀⠀⠀⠛⠵⣯⠰⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡾⣿ ⠀⡄⠸⡇⣧⠛⠈⡇⡀⠈⢂⠈⠀⡹⡋⣾⣡⠉⠰⠈⠐⠀⠀⠀⠀⡇⢸⠁⢠⣿ ⠒⠉⢆⠈⢢⢌⢦⠓⢡⡂⠢⡁⣉⣭⡂⠐⠒⢀⡴⠠⠒⠙⠉⠀⠀⠀⢠⡘⠇⣿ ⠀⠁⣿⢿⠈⣀⠢⠁⣎⠔⣁⣂⠖⠤⠤⠤⠀⠀⠒⠀⠉⠀⠀⣁⠤⢰⠜⠀⡟⣿ ⠏⡇⣿⣿⣿⠙⠀⠃⢊⡤⢘⠠⠑⡁⠠⠒⠁⠈⠀⠀⠀⡀⠄⠁⠈⣃⠟⡾⣴⣤ ⡿⣿⣿⣿⣿⣿⢿⡈⠲⠀⠀⣀⣀⠑⡫⣌⢐⡍⣛⢋⠛⡚⣶⠴⠤⣠⢈⠀⠀⠟ ⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠂⠄⡠⢀⠀⠁⡟⣿

⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡏⣿⣾⣦⣸⣯⣿⣝⣷⣿⣿⣴⢀⡀⠪⡈⣦⠻⠈⠀ ⠀⠀⡀⢦⠙⠈⠀⠀⠂⡘⣶⣿⢳⢸⠇⢠⠀⡀⢨⣄⣷⠸⠀⠀⡀⡢⠠⡀⣦⠻ ⠀⠀⠀⠀⣼⣠⠁⠒⣾⠓⠉⡀⠀⠀⡄⠀⠀⠀⢸⠀⢄⡀⠁⠣⠀⠀⢄⠂⠪⡌ ⠀⠀⠀⠀⢱⡔⣾⡠⠋⠩⠀⢄⠐⠀⠀⠀⠀⠂⣒⠉⠈⠂⠗⡿⣉⣦⠳⠟⡘⠀ ⠀⠀⠀⠆⠁⣼⣟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡒⣄⣦⣷⣿⢶⠈⣄⣿⡙ ⢄⠂⠁⠀⣇⠄⢢⢉⠛⠐⠀⠀⠀⠀⠀⠇⠷⠹⡦⣤⠀⠀⠀⠴⣾⢧⡆⡼⣄⣹ ⠽⠉⠈⡖⣯⠤⠃⣜⢀⠀⠀⠀⠀⠀⠁⣹⡏⣼⠸⠁⠋⠈⠞⠄⠎⢂⠀⢈⣿⡼ ⣦⢺⠰⠞⢀⠀⡇⣻⠀⠀⠤⠸⠀⠀⡀⡄⣿⠰⢔⠿⣀⡠⠼⠐⠀⠄⢀⢀⡇⢰ ⠀⢀⡆⠀⠀⠊⡸⣀⢤⠑⠀⢸⠀⠀⠀⠀⣏⠿⡀⣂⣡⢤⢤⠘⡈⠄⠁⠇⣿⢣ ⠀⠀⠀⠠⠀⡱⠀⠀⠀⠀⣀⠀⠀⠂⠄⠀⣅⣿⢿⣙⠬⠰⠓⡡⢋⠘⠊⣷⣪⡯ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣶⣭⣿⣿⢿⢛⡛⢋⠚⣤⢝⢴⣠

⠀⠀⠀⠀⠀⣤⡭⡿⢟⣟⣟⣿⣻⣉⣽⣄⠡⡟⣿⡟⢿⣿⣿⣽⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⣿⣶⣤⣤⣤⣤⣦⣷⣿⠹⡟⣿⣿⢿⡽⣿⣿⣿⢿⠘⠀⠀⠀ ⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣾⣠⣀⠀⣀⣀⣀⣦⣷⠈⠀⠀ ⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠀ ⠀⠀⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀ ⠀⠀⠀⣾⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀ ⠄⠿⢀⣲⠒⡃⣦⠻⠙⠉⠀⠀⠉⠋⡹⠉⢙⠈⠀⠀⠀⠁⠋⠴⢀⠀⠀⠀⠀ ⠖⢴⠇⠐⠐⣿⠈⡎⣧⣷⣿⣿⣽⣯⣿⣿⣾⣶⣴⣤⣬⣈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠑⡞⣴⣄⠃⣿⣿⣹⣾⣿⣿⣿⣿⠃⣨⠀⠀⠏⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡔⠀⠖⠀⡿⣿⣿⣿⢸⣿⣴⣿⣿⣿⠚⠀⠉⣀⢡⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠆⠀⠃⠘⡄⣿⣿⣿⠄⠀⢠⠀⣿⣏⣾⢇⡤⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⢀⠀⠀⣤⣶⠲⠉⠉⠖⣴⣤⢂⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠤⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡯⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⣿⠀⣳⠈⠀⠀⠀⠀⠀⡀⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠇⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠶⡭⣾⣴⣤⣀⣇⠸⠠⣇⠿⠿⠿⠿⠿⠻⠛⠉⢎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠻⠈⠂⡿⣿⢰⠀⠀⠀⠉⠉⠛⠛⠿⡿⣿⣛⠛⠞⡴⣀⠀⠀⠀⠁⡾⠀⠀⠀⡆⣾⣷⣿⣿⣿⣿⣿⣿⣾⣶⠻⠙⠀⠀⠀⠀⠀⠀⠀ ⠉⡈⣷⠏⣿⣼⠏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠁⠔⣠⠀⠁⠈⠀⠀⢇⠀⣀⣦⣷⣿⣿⣾⠀⠏⣿⣿⣿⠿⠙⠈⠀⠀⠀ ⣄⣷⡸⣧⣿⢠⣿⣿⣿⣿⣻⡟⣿⣿⣾⣴⢀⠀⠀⠀⠀⣽⣧⣰⠁⠀⠀⡀⣸⠀⠀⡄⠀⠀⠀⠀⣀⣦⢹⠀⣷⢹⣭⣽⣭⣽⣿⢾⠶⠛ ⠀⠀⢄⣻⣰⠧⣀⣧⡿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⡄⣿⠴⢠⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣠⠀⠃⣾ ⠹⠀⠀⣧⠀⡄⢿⡿⣿⣿⣾⣠⠀⠂⠓⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⡿⠈⠀⠀⡿⠹⠀⠀⠀⠀⠆⣩⣉⣀⣤⣻⣉⣤⢳⠈⠀⣿⢼ ⡀⠀⠀⡆⠀⠀⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠸⠀⠉⠛⡿⣿⢻⠙⠏⣿⣿⠹⠀⠀⠀⠀⢦⡀⠀⠀⡀⣷⢿⠘⣀⢦⣿⠀ ⠀⠀⠀⠀⠀⠀⣧⣇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⢻⠈⠀⠀⡀⠀⠉⠉⠀⡄⣿⣿⠹⠀⡄⠹ ⠀⠀⠀⠀⠀⠀⡇⡆⢸⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⡏⣿⣿⣿⣬⣶⣷⣾⣶⣶⣤⣩⠞⣠⠀⠀⠀⠀⠀⠁⠐⠀⡞⣄⠻⣟⣿⣿⠘⠀⣇ ⢻⠰⠀⠘⠀⠀⡇⠏⢰⠋⠗⡾⣠⢀⠀⠀⠀⠀⠏⣰⢀⠀⠀⣀⣄⠤⠒⠔⠤⣠⣀⠀⠀⠀⠀⠀⠀⠋⡡⠃⡴⠏⢠⠆⣷⣿⣿⢸⠀⡀ ⣷⠘⠀⠀⠀⠀⡇⣾⣠⠏⣠⠀⠈⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⢏⣩⠟⣼⡝⠀⡆⢿⣌⢻⠀⠀ ⡵⢹⠀⠀⠀⠀⡇⠀⠟⢠⠀⡇⣇⢘⠀⠋⡰⠀⠋⠠⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⡳⣹⡼⢃⣶⢋⡾⢃⠼⠀⣦⢹⣇⠀⠀ ⡀⣿⠈⡇⠀⠀⡄⠃⢷⠘⠀⠋⣫⡿⣽⢎⢋⡴⢀⠁⠞⡡⠛⠟⣾⠠⠀⠀⠀⠀⠀⠱⠁⠞⢀⠆⣲⠖⣶⡴⣤⢀⡦⣿⠙⠀⣿⡌⠀⠀ ⠀⡀⢷⡏⠀⠀⠀⡏⡄⢿⡟⣴⢞⣯⣣⡴⢆⡠⠒⣱⠟⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠃⠶⠤⠳⠈⠀⠀⠁⣿⣿⢿⣿⢠⠀⠀ ⠀⠀⡄⣿⠸⠀⠀⢸⠀⣿⣧⡄⠷⠕⢛⡷⠿⠿⠿⣶⣴⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡿⣿⣿⠿⣿⠛⠿⣿⣴⣧⣷⣿⠈⠁⠛ ⠀⠀⠀⣇⢹⠀⠀⢰⠀⣼⡇⠀⠇⣸⠀⠀⠀⠀⠀⠊⡤⠦⠳⠟⣿⠀⠀⠀⠀⠀⠀⡿⠈⠀⡀⣦⣾⣶⣶⣶⣤⣠⢀⠀⡇⣿⣘⣀⣀⠀ ⠀⠀⠀⠀⣷⠈⠀⠀⠀⢸⡇⠻⣿⠹⠀⠀⠀⠀⠇⢁⠟⠿⡿⣴⢟⢉⠀⠀⠀⠁⠈⣄⢿⠀⠀⠀⠻⠉⠉⠋⢿⠙⠀⠁⡛⢸⢸⠀⠀⠀ ⠀⠀⠀⠀⡄⢹⠀⠀⠀⢀⠀⢹⡤⣦⣶⠿⠿⠛⡿⣾⣶⣥⣛⡿⣤⣀⣠⣠⣠⢉⡜⢷⡟⠹⠀⠀⡇⡘⢀⠀⡆⣼⣿⣼⣀⢸⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⠀⠆⠹⠁⣧⠈⠀⠀⠀⡀⠿⠚⠖⡾⣴⣤⣀⡄⠻⠿⠶⡴⣀⢧⡟⣸⣷⡀⣤⣦⢸⠀⠀⠀⢸⣇⣿⣿⢸⠀⠀⠀⠀ ⠒⠰⠀⠀⠀⠀⢹⠀⠀⣷⡿⡙⢹⠃⠙⠀⡏⣀⣽⠻⠙⠉⠋⠟⡿⣿⣬⠀⠀⠀⡆⣿⢸⡀⢳⠀⠀⢸⠀⠀⠀⠇⠀⢿⣾⠀⠀⠀⠀⠀ ⠀⠆⠀⠀⠀⠀⡆⠘⠀⡄⣿⣸⣄⣠⣇⠾⢸⠀⣧⣿⠀⣀⣀⠀⣇⡏⢹⠀⠀⠀⠀⣿⢷⠀⡄⢻⠈⢸⠀⠀⠀⡀⠀⡇⢀⠀⠀⠀⠀⠀ ⠀⠀⢠⠀⠘⠀⠀⢧⠈⠀⣇⣿⠘⠀⠀⢣⢸⠀⡇⣾⢹⠀⠀⠀⡀⣿⣿⠀⠀⠀⠀⣆⡇⠸⠀⣇⣿⢀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢣⠀⠀⢳⣄⠀⠀⡀⢷⠀⡆⣧⣌⠰⠀⠀⠀⡆⣸⢸⠀⠀⠀⠀⡀⢸⠀⡇⣿⠀⠀⠀⠃⢰⠀⡏⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠈⡀⢳⠈⠀⠀⠀⠀⠀⢰⢦⠈⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⢸⠀⡇⣹⠉⠛⠚⠶⠴⣤⣠⢀⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⠤⡀⢈⠀⠀⠉⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠔⠡⠆⠤⢀⠀⠁⠔⡀⠀⠀⠀⠀⣀⠢⠈⠡⠀⠀⠀⠀⠀ ⠀⠂⠄⡀⠄⠀⠑⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⡄⡈⠘⠀⠀⠀⠀ ⠌⠀⠀⠀⠀⠀⠀⠀⣀⢆⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⢃⡄⠈⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⠀⠀ ⠡⠀⠈⠀⠀⠀⠀⠀⠀⠀⡧⠑⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⠘⠸⠀⠀ ⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠤⠮⡠⠀⠀⠀⡆⣾⡙⡐⡇⠀⠀ ⠀⡄⢤⠙⠀⠀⠀⠀⠀⢀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀⣆⣻⡪⠰⢸⠀ ⠀⠀⢄⣿⢿⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⣦⣷⡟⠀ ⠀⠀⠀⢸⣾⢀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠹⠀⠀⠀⠀⠀⠀⠀⣇⠰ ⠀⠀⠀⡇⢸⠀⠃⢰⠀⠈⠒⡠⠈⠀⠀⠱⣇⠼⠠⠐⠀⠀⠁⠊⡰⠀ ⠀⠀⠀⡀⢡⠀⡏⠐⡠⠀⠁⠈⢶⠷⠙⠀⡧⢻⠉⠛⠼⣡⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⢿⠞⠤⣀⠀⠀⠀⣄⠲⡌⣿⣿⣿⣟⡸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⣾⢀⠁⠈⠀⠈⠀⠀⠀⣄⣿⣿⣿⢻⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⢀⠂⠦⣀⣤⠤⠀⠊⠈⡇⣿⣿⣷⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡟⢹⡀⢤⡠⠀⠀⠀⡓⠛⡔⡇⣿⣿⠉⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣘⡟⣃⠿⠿⠐⠛⠻⡟⠘⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⢿⣿⡿⣶⣿⠁⣼⣦⣷⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣼⣤⠀⣀⣸⢀⠀⠎⣥⣾⣄⣿⣿⣿⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⠈⠀⠀⠀⠀⠀⠀⡎⢠⠀⣿⣿⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢄⠐⠈⠀⠀⠀⡀⠀⠀⡁⡖⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠄⠤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠀⠄⠀⠀⠀⠄⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⡉⢋⣿⠀⡇⢙⠀⠀⠀⠀⠀⢀⣀⠀⣄⣶⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀ ⠄⠀⠄⠁⠄⠁⡏⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⡾⣿⣛⡿⣶⣤⣧⠘⠉⣌⠳⠉⠋⠛⠙⠉⠛⠛⠉⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⠙⠄⠁⠄⡁⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠟⠶⡤⣤⣉⢟⡴⣠⢀⠀⠀⠀⡟⣸⠀⠀⡠⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡛⢯⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠿⠉⠆⣿⣿⣿⢠⠀⠀⠁⠉⠉⠛⠟⠿⡿⣿⣿⣿⢿⠿⠿⣿⣴⣠⢀⠀⠀⠀⠀⠀⡏⣴⠀⠀⠀⠀⠀⣳⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠈⣆⣻⠏⣿⣿⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠁⠞⣤⢀⠀⠀⠉⠀⠀⠀⡄⠹⠀⡀⣄⣶⣿⣿⣿⡿⣴⠀⠏⣿⣿⣿⣿⢿⠻⠙⠈⠀⠀⠀⠀ ⣦⣿⠻⣌⣷⣿⡾⠀⣿⣿⣿⣿⣿⣽⣀⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠟⣶⠳⣼⠀⠀⠀⠀⠀⣯⢠⠀⠀⠀⣷⠀⠀⠀⠀⡀⣤⣷⣿⠀⠀⣿⣽⣄⣶⣶⣶⣷⣶⣿⢿⠛⠙⠈ ⠀⡀⣦⢱⡾⣿⢣⠈⣶⣷⣹⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⡄⠻⡼⠉⠎⠀⠀⠀⠀⡟⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣄⢦⠓⡏⣻⣿⡿⣿⣿⣿⣿⡾⣠⠀⡁⣿ ⠀⠀⠀⡀⣿⣤⠀⣿⠈⡇⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⢈⢀⠀⠀⠀⡇⣾⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣟⣿⣶⣶⣿⣿⣿⣠⠀⠀⠁⣿⣥ ⢳⠀⠀⠀⣇⠀⠀⡇⣿⡿⣿⣿⣿⣾⣠⠀⠀⠆⠦⠘⠀⠀⠀⠀⠀⠀⠀⠀⢿⠰⠀⠀⠀⠀⠁⡿⢻⠀⠀⠀⡇⣿⠹⠀⠀⠀⠀⠀⡄⣣⢛⠙⠀⣀⣆⠻⡙⣀⢦⠓⠈⠀⡇⣿⣠ ⡀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⡿⢿⠈⠀⠀⠉⠟⣿⣿⣿⠻⠈⠋⡿⣿⣿⠹⠀⠀⠀⠀⠀⡄⠾⣄⠀⠀⠀⣄⣿⣿⠻⠀⣀⣤⡿⣿⠀ ⠀⠄⠀⠀⡆⠀⠀⠀⣿⡇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⣿⡻⢷⠈⠀⡀⣷⠈ ⠀⠀⠇⠀⡀⠀⠀⠀⣧⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢁⣾⣠⣄⣶⠀⠀⠀⠀⠀⡄⣤⢤⠿⠙⠈⣇⣿⣻⢿⠀⠀⡀⣿ ⠀⠁⠐⠁⠀⠀⠀⠀⡇⠀⢿⠰⠀⠀⠀⠉⠋⠛⠖⠰⠀⠀⠀⠀⠀⡿⣿⣶⣶⣷⢉⣌⣦⣶⣶⣤⣤⣠⣁⠋⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠁⡞⢠⡌⣶⠿⣟⣿⣿⢹⠀⠀⡇ ⢿⡸⠀⡀⠸⠀⠀⠀⡇⠡⣸⠁⠋⠵⣿⣴⣀⠀⠀⠀⠀⠀⠀⠁⡾⣠⠀⠀⠀⠀⠀⣀⣤⢤⠲⠴⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡽⢈⠃⡼⠃⡽⠀⠆⣧⣿⣷⣿⣿⠀⠀⡄ ⣿⢸⠀⠀⢀⠀⠀⠀⡇⡿⢾⣠⠋⣴⢀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣫⡴⠟⣰⠋⣿⣵⡼⠀⡄⣿⡹⢰⣿⠀⠀⠀ ⡜⢻⠀⠀⠀⠀⠀⠀⡏⣰⠀⠏⣠⠀⠀⠟⠷⠐⠀⠀⠁⠞⣠⠤⠁⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡴⢞⣡⡾⢥⡿⣤⢣⡾⢤⠩⠀⡇⣿⠸⣧⠘⠀⠀ ⣆⣇⠸⠀⡃⠀⠀⠀⡇⠀⡇⣰⠀⠀⠀⢰⡿⠡⠊⠛⣱⠘⠀⠞⣠⠀⠐⠁⠚⠀⠈⡋⠑⠜⢀⠀⠀⠀⠀⠂⠈⠀⠀⡤⢏⣠⡔⢞⣠⠃⡽⣉⠟⣿⢩⡯⢛⠀⡀⡆⢻⡀⢸⠀⠀ ⠀⣧⢿⠀⡇⠀⠀⠀⡄⠀⣼⢿⠈⠀⠋⡱⢞⣣⡼⢋⡰⠋⡴⢉⠀⠃⠞⣠⠋⡿⡵⢞⣠⠀⠀⠀⠀⠀⠀⠀⣆⠙⠋⡴⢀⠄⡤⢤⠤⣤⣤⣠⣀⠀⡀⣥⣿⢻⠘⠀⣿⠘⢰⠀⠀ ⠀⠀⡇⢻⡏⠀⠀⠀⠀⡇⢠⡇⢿⠏⣾⣡⠞⣯⣴⢋⡴⢂⡠⢃⠟⣠⢟⡶⣷⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢘⠀⠀⠀⠋⠶⠴⠷⠙⠀⠀⠀⠀⡅⣿⣿⣿⡿⣿⢰⠀⠀⠀ ⠀⠀⠀⣇⣿⢸⠀⠀⠀⡟⠀⡇⣟⣴⢸⡳⡘⢋⡵⢋⠟⠛⠟⠻⠖⣷⡿⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣟⠿⠿⠻⡛⢿⠉⠉⠟⣿⣿⣷⣿⣿⣿⠈⠀⠀⠉ ⠀⠀⠀⠀⣷⣿⠀⠀⠀⣻⠀⡀⣿⠀⢸⠀⣁⠞⣠⢄⠤⠤⠤⣤⣀⣀⠁⠘⠈⠀⠀⠟⠸⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⡄⢷⣿⣯⣶⣶⣶⣷⣿⣿⣾⣴⢀⠀⢿⣧⣶⠶⠶⡴⣄ ⠀⠀⠀⠀⡆⣿⠘⠀⠀⣤⠀⠀⢸⠀⢸⠁⡿⢠⠀⠀⠀⠀⠀⠀⠃⡴⣀⣀⣄⢷⡿⣾⢩⠀⠀⠀⠀⠀⠀⠀⡇⢻⠈⠀⠀⠀⣧⣴⣤⣤⣤⣤⣈⠀⠀⠀⠀⡀⣿⡆⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢹⠀⠀⠀⠀⡇⢀⠀⣿⡟⣿⠹⠀⠀⠀⠀⠀⠀⣼⠁⠟⡿⣿⣿⣴⢏⣹⠉⠀⠀⠀⠀⠋⠙⡀⣆⢿⠀⠀⠀⡀⢿⠉⠉⠉⠋⣷⠻⠉⠀⠁⠛⡿⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠘⠀⠀⠀⡄⠀⠀⣿⠀⣴⣶⣿⠿⠻⠛⠛⠛⣿⣿⣿⣶⣤⢋⡿⣴⣠⣆⣤⣤⠤⣤⢡⡌⢷⠛⣯⠘⠀⠀⠀⡇⡘⣀⣀⠀⡀⣸⣷⢷⣴⣠⡇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠃⠈⠀⡇⢸⠀⠀⠀⣀⣀⣄⣭⣬⣈⣁⠛⠿⡿⣲⢶⠠⠛⠉⠉⠉⠋⠞⣴⢿⡀⣿⢮⣿⠂⠗⠿⡿⢸⠀⠀⠀⠀⢧⡀⣽⢷⠻⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⡇⢻⠇⠈⣷⠈⠀⠀⠀⠀⠁⡼⣻⣽⣀⣰⣀⠀⠀⠀⠁⡏⣿⣿⣀⣀⠀⠀⡆⣿⣿⢀⣦⠹⠀⠀⡀⢻⠀⠀⠀⠀⡇⠸⡇⡸⣿⣼⠀⠀⠀⠀⠀⠀ ⠴⢠⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⣿⡜⢿⡝⢹⠇⠷⠀⠀⡿⢀⣷⡘⣿⠳⠛⠛⠟⡿⣿⣾⣷⣄⠀⠀⠀⠀⠀⣿⣼⢸⠀⣇⠸⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⢷⣟⢰⠀⠀⠀⠀⠀⠀ ⠀⡀⠸⠀⠀⠀⠀⠀⣇⠸⠀⠀⡆⣾⣿⡀⣄⣠⡄⣿⠶⣼⠀⡄⣿⣿⠀⠀⠀⠀⠀⡄⢻⡇⢹⠀⠀⠀⠀⠀⣇⢸⢻⠀⠀⣧⠹⠀⣼⠀⠀⠀⠀⡇⢠⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠙⠀⠀⠀⠀⠀⣧⠈⠀⠀⢧⣎⢹⠀⠀⠀⣧⠸⢸⠀⠀⢿⣷⢹⠀⠀⠀⠀⠀⣧⡟⣿⠀⠀⠀⠀⠀⡄⢹⡇⠀⠀⡄⣿⢿⢠⠀⠀⠀⠀⡇⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢷⠈⠀⡀⢿⣆⠹⠀⠀⠀⣇⢻⠀⠀⣼⢻⣧⠸⠀⠀⠀⠀⡀⣿⡆⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⢳⠈⠀⡀⢳⠀⠀⠀⠀⠀⣦⠐⠀⣇⡄⢹⣄⠀⠀⠀⠀⠀⣆⠘⢸⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣇⣿⠀⠀⠀⠀⠃⢰⠀⠉⡟⠉⠉⠋⠂⠒⠒⠄⠤ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⢷⠘⠀⡄⢻⠉⠀⠀⠀⠀⠀⠀⡄⢱⣆⠹⠈⠀⠀⠀⠀⠀⣀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢹⠉⠛⠛⠶⠶⠤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢁⠟⠛⠛⣈⣧⣿⢿⠶⣶⠶⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⢿⡘⣾⢀⡟⣿⠿⠈⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣷⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⢠⢘⡿⣿⣿⣿⢿⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢁⠟⡿⣶⣶⠶⠳⣍⣦⣿⣿⡘⣅⣶⣿⣶⣠⠁⢸⣇⣿⣿⣿⣿⢸⡀⠁⠍⠈⡑⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣶⣶⣴⣤⣠⣤⠃⣿⣴⣟⣿⣿⣿⢿⡙⢧⡘⣷⢿⡘⣷⠟⡿⢹⡀⣿⡘⣷⣿⣿⣿⢀⡇⣿⣿⣿⡘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣦⣷⣿⣿⢂⠛⠛⠛⠛⠀⠻⡟⠿⠘⡇⣿⡇⣿⣿⣿⣿⣿⣿⢻⢧⡄⣿⢿⠀⣿⣿⣿⠸⣷⢸⠷⡛⣙⠘⠃⡆⣿⣿⣿⢿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠟⠿⡿⠈⣆⣿⠀⣧⣿⣿⢹⡆⣿⣿⣿⢿⡆⣿⡜⣿⣿⣿⣿⣿⣿⣿⡘⢸⣿⣿⠀⣧⣿⣶⣶⡀⠄⣿⣿⣿⢳⡌⢸⡁⣭⣭⢃⠀⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿⠸⣧⢿⡘⣍⣥⣋⠙⣄⣿⣾⣤⠈⣤⢿⣎⣿⣿⣿⣿⣿⣿⢸⢠⣿⣿⠀⠋⠿⣿⣿⣿⣿⣿⢿⠻⣛⢿⠈⡆⣿⣿⣶⠁⠟⠙⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣴⣥⣬⣷⣿⡙⣄⣭⣩⠟⡄⣾⢁⣿⣿⣿⣾⢠⠻⢁⡛⣿⠉⣇⢿⣝⣷⣿⣿⣿⣾⠁⠀⣀⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⡛⣹⠈⡧⣿⣿⢿⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢠⠁⠋⠛⣟⠙⡀⣦⠀⣆⣴⣤⢩⠋⡓⣛⣿⣿⣿⠈⢰⡿⣿⣿⣿⠻⣀⣤⢶⣄⣤⢋⡴⢋⡿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣦⣻⣿⣴⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢹⡆⣿⣿⣶⣀⣫⠟⠿⣿⣿⣿⣿⢃⡿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⢿⠘⡧⣰⡡⠟⣿⣿⠿⣿⣿⣿⣿⢿⣛⣍⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣛⡛⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⠿⠿⠀⡟⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⢹⣧⣿⣿⣿⣿⣿⣿⠘⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣸⠃⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⣌⣷⣿⣿⣿⣿⢸⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⠸⣥⣭⣭⣬⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠦⣙⣬⣶⣶⣶⡆⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⢸⣿⣿⣿⣿⣿⠻⣙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣧⣿⣿⣸⣿⣿⣿⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⣸⢿⣿⠸⣧⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⢿⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⣧⣿⢿⢿⣿⣿⣿⡘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢰⡙⣧⢻⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡇⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⣆⣿⣿⣿⣿⣩⣿⡹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣼⡏⣿⠻⣌⢷⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣴⣩⣛⡛⣙⣬⣷⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣅⣟⣿⣿⣿⣿⣿⠻⣎⣿⣿⣿⣿⣿⣿⣿⣯⣾⢇⣼⠏⣿⣿⣿⣿⠻⣙⣤⣇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢃⡿⣿⣿⣿⣿⣿⠻⣌⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣭⣽⣾⣶⣿⡿⣷⣿⣿⣿⣽⢟⣿⢥⣴⠋⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⣄⣧⣿⣿⣿⣿⣿⣿⣶⣥⣪⠒⠒⡖⣿⣿⣿⣿⣿⣯⣿⣿⢸⠛⣄⣷⣿⣿⣿⣿⣿⣿⣿⢿⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢶⠿⣛⠭⣦⣶⣿⣾⣿⣹⣠⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⣀⣧⣮⣿⣾⢀⣋⠞⠶⣭⣩⣛⣛⣟⣿⣾⣷⣿⣿⣿⢸⠏⠿⠙⣇⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠿⡛⣌⣷⣿⣿⣿⣸⣸⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⣧⣰⠞⣥⢋⠽⣿⣿⣿⣿⣿⣿⣿⣿⡹⣦⣿⣿⢹⣇⣿⣿⡶⣿⣿⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⡑⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⣿⣿⡆⣿⣴⠇⣿⣿⣿⣿⣿⣿⣿⢡⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡇⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⠘⢉⠋⡿⣿⣿⣿⣿⣿⣤⢃⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠋⣙⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⢚⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⣿⣿⣾⣶⣥⢋⠟⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⢏⣿⣿⣿⠿⡛⣝⣬⣦⣶⣶⣶⣶⣤⣩⢛⠿⣿⢡⢻⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣤⣋⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣍⣶⣿⣿⣿⣿⣿⣼⢀⠉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡟⣿⠈⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢩⠛⡛⣛⣛⠛⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⣿⣿⢹⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣡⠟⡿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⠘⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢿⠈⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡆⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢋⡵⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⣿⣿⣿⣿⣿⢿⠙⡄⣷⣿⣿⣿⣿⣿⣿⣴⣫⣾⣡⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣼⢋⡴⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢿⠛⣍⣤⣶⣶⣶⣥⣩⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣧⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣰⡟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢡⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠄⠀⡀⣀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿ ⣿⣿⣿⣿⣼⢋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠋⠀⢠⠃⠙⠉⠀⡀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣿ ⣿⣿⣿⣰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣰⠀⠊⠃⠹⣼⠀⠀⠋⣿⣨⢉⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿ ⣿⣿⣰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣍⣶⣿⣿⣹⠀⠀⠃⡿⡟⢺⡇⠀⣿⣸⡏⣼⠻⠘⡀⣿⣿⣿⣿⣿⣿⣿⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿ ⣿⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣦⢠⠀⠆⣿⣿⣿⢸⡀⠀⣿⣿⣄⣿⢀⣠⠀⣇⣾⣴⣩⣟⢛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿ ⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⡟⣿⣿⣿⢸⠀⡇⣿⣰⡇⣾⠿⡠⠒⣡⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⡆⣿⢿⣿⢸⠀⣿⣹⠈⡿⢰⣸⠀⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⣆⣻⣿⢸⠀⣿⣿⢻⢠⣠⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠠⠁⣦⣰⠟⠠⡿⣾⢠⠀⠁⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⡏⣿⣿⣿⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢻⠟⣿⣻⣿⣽⣏⠟⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣀⣀⣷⣿⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣓⣌⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠀⠀⠀⡀⣷⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣼⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣾ ⡜⣿⣿⣿⣿⣿⣶⣿⣿⣿⣼⠀⠀⣀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣆⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠁⠉⠋⠹⢀⢷⠿⡿⢿⡙⣧⣿⣿⣿⢸⡍⢀⡀⣷⣿⣿⣿⣿⣿⣿⢸ ⢻⣧⣿⣿⣿⣴⢩⣆⣿⣼⠏⠿⡼⠏⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠘⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⢻⡀⣧⣿⣿⣿⢿⣙⣷⣿⢸⣷⢻⠉⠉⣦⣿⣿⣿⣿⣿⢇ ⣿⡘⣿⣿⣿⠸⡇⢻⣀⡟⣿⣿⢃⣿⣿⣿⣴⢀⠤⠙⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢃⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣷⣿⣿⣿⣿⡹⣷⣿⣿⢿⠈⣌⣷⣿⣿⣶⠹⣧⣿⡘⣷⣿⣿⢿⡙⣇⣿⣿⣼⡏ ⣿⢿⡌⣿⣿⢃⡿⣼⡇⣶⣶⢸⡿⣿⣾⢡⠘⠀⠀⡀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀⠀⠀⣄⣷⣿⣿⣿⠹⣧⣿⣿⢿⡌⠹⠧⣿⣿⣿⡘⣷⣿⠸⣁⣉⢁⢸⣿⣿⣿⢡⣿ ⣿⣿⢿⡜⣰⡆⣭⣸⡇⣧⣿⢸⣿⣴⢋⣿⣿⣾⢋⡿⣿⣿⣿⣿⣿⣾⣴⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠉⡟⡙⣦⣿⣿⣿⠹⣧⣓⣟⠘⡔⠸⡄⣿⣿⣿⡙⣶⢃⡿⣿⡧⠃⣿⣿⣰⡟⣿ ⣿⣿⣿⣿⠻⡀⣅⢸⡀⡟⣿⢸⢋⡿⣿⣿⣼⠏⣿⣿⣿⣿⣶⣥⣀⠗⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣆⣿⣿⢻⣌⣿⣿⣿⡘⢸⣿⣿⠘⡷⠀⣧⣿⣿⣿⠻⡝⣷⣹⡼⠀⣿⣰⡏⣿⣿ ⣿⣿⣿⣿⣿⢻⡀⢠⣷⣿⣿⢃⢳⣝⣭⣤⠏⣿⣿⣿⣴⢋⡿⣹⠀⡀⣉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢿⡙⣣⠟⢿⡙⣦⣿⢸⢈⣧⣿⣿⡻⢙⡁⣿⣿⣿⣿⣿⠻⣆⢠⠀⣰⡟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠘⠛⡆⣿⣿⡇⣿⣿⣿⡉⣦⣶⣩⠟⣦⣿⣿⣴⢋⡿⣿⣿⣿⣴⣯⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⡂⣍⣦⣿⣿⣿⣿⢿⣌⣷⣿⢿⡻⢛⢫⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣴⢉⡼⠀⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢻⡆⢿⡙⣦⣿⣿⣿⢺⢃⠿⣿⣿⣿⢿⡴⢋⡿⣾⣵⣩⣚⠒⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠂⣿⢿⡛⣭⣬⣶⣷⣿⡸⣄⣿⣿⣿⣿⣼⣿⣿⣿⣿⢸⣿⣿⣿⣴⢋⡰⠋⢿⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⣧⣿⢿⡙⣦⣷⢛⣿⣿⣿⣿⣵⢛⡋⣛⠟⠿⣿⣹⠀⠁⡉⡟⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣧⣼⣋⣛⣟⢭⠩⠉⡌⣷⣿⣿⣿⣿⡿⣿⣿⣿⢿⡾⣡⢟⡴⢋⡰⡟⣿⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣭⠢⣙⣭⣤⣶⢃⡿⣿⣿⣾⣴⣥⣫⢛⠿⣿⣿⣿⣿⣿⣿⠛⣿⣾⣴⣢⣿⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⣝⣮⣷⣿⣿⣿⣿⠹⣦⣷⣿⣿⣿⣿⣶⣥⢋⠾⣥⢊⡡⢛⡿⣿⣿⡇⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⣷⣿⣿⢿⠿⡛⣍⣭⠤⠿⠻⠚⠁⣍⣦⣶⣶⣶⣶⣶⣶⣶⣥⣩⣋⠛⠽⣤⢦⠶⠲⠓⣉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡀⣭⣦⣶⣶⣶⡶⣥⣩⣋⠖⡴⣩⢛⠿⣿⣿⣿⣿⣸⣿⣰⡟⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⡉⣬⣶⣷⣿⣿⣿⣿⣿⣿⣀⠋⣶⣶⣶⣶⣤⠠⠗⠿⠛⡛⣙⣭⣬⣶⣶⣷⣿⠿⠿⠿⣿⢿⡛⣍⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣍⣷⢿⠽⡭⣫⣛⣛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠨⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⡁⣾⣿⣿⠿⡿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⠿⠻⣛⣍⣬⣶⣶⣶⣶⣶⣶⣶⣶⣴⣤⣩⣛⠛⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣛⠟⡿⣿⣾⣴⣩⡙⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣋⢛⠿⣾⣴⣩⢋⡙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢸⣇⢻⣇⠘⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣧⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⢠⣾⣇⣿⣿⢸⡏⣿⠹⣧⠻⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢻⣆⣿⣿⣿⣿⣿⣾⣧⣿⣿⣴⠋⢠⡞⢣⡿⣿⣹⠏⣿⣿⣾⣶⣴⢡⣍⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣆⣿⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠹⣦⣿⣿⣿⣡⠋⣿⣾⢱⠔⢀⡉⠛⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⢿⠿⡻⣙⣀⣉⣭⣭⣭⣩⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⣿⠀⣿⢸⣷⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡛⣛⣛⢛⠟⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⣷⣿⣿⢿⡌⠹⣧⢻⡇⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠦⡛⣍⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⣿⢿⡙⡈⣷⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡌⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣧⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣆⢿⠻⣍⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⠹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡐⠠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⢀⠋⡟⠻⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣡⡟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣡⢋⠟⣿⣿⣿⣿⣿⠿⡛⣌⣶⣶⣿⣿⣾⣴⢁⠟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣛⣝⣭⣬⣶⣶⣶⣶⣶⣶⣶⣽⣭⣭⣋⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣛⠟⠿⣿⣿⣿⣿⣿

⠀⠀⠀⠁⠈⠀⠀⠀⡀⠦⠑⠉⣀⣦⠀⠀⠀⡏⣡⣯⠑⣀⠠⢕⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠺⠀⠐⠀⠀⠀⠀⢄⠸⠀⠀⠀⢀⣰⡀⣀⢄⠌⡘⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⠀⣸⠄⠠⠓⡄⠄⠂⠛⠠⠀⠀⡄⠀⠈⠀⠀⠀⢧⢀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⠀⠅⡀⣀⢸⠀⠁⠔⢰⠀⠀⠀⠀⠀⢂⠀⠀⡆⢨⠉⠊⠒⢑⠈⠀ ⠀⠀⠀⠁⠉⡇⠀⠃⠂⡠⢀⠀⠀⠀⠀⠀⡆⠈⠃⡎⢙⠋⣾⣠⠀⡘⠦⡘⠢ ⠀⠀⠀⠀⠁⣔⡠⠄⠐⠀⠀⠁⠀⠀⠀⠗⢥⠠⢣⠖⣷⣽⠉⠈⠁⢩⠈⡂⠻ ⠀⠀⠀⠂⢰⠀⠃⠀⡀⠬⠒⠂⡙⠤⠃⢠⠨⠂⠄⢰⢱⡉⣂⣆⣲⡏⡀⢻⡄ ⠀⠀⠀⠀⠀⠁⠪⡠⢀⠀⡀⢄⠊⣰⣿⠈⢆⠀⡏⠁⠓⢛⠈⠗⠟⢸⠀⡇⠀ ⠡⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⡞⢌⠀⣄⢌⠀⠇⠸⡷⠛⣾⢀⠀⣳⣿⠂⢠⠀ ⠀⢄⠢⣒⠚⠐⠠⢇⢉⠂⡰⡠⠀⠀⠀⠎⠤⠐⢠⠔⣶⠵⠲⠎⣺⢠⢸⠀⠀ ⠀⠀⠀⠃⣰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠦⠀⠀⠇⢠⠀⠀ ⠀⠀⠀⡆⢸⠐⠀⢆⠈⠀⠀⠀⠀⠀⠀⠁⢌⠃⠉⠀⠀⠊⠠⠁⠂⢃⠘⠀⠀ ⠀⠀⠀⠀⢂⠲⠙⠀⠀⠂⠁⠈⠀⠀⠀⡥⠲⠒⡐⣠⣦⡦⣧⠀⠇⠻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣀⠄⠤⠤⢀⠀⠀⠀⣀⢢⡹⠺⠁⠉⡉⡐⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⢸⠄⡄⣩⠛⠿⣿⣶⡐⣶⣶⣿⣿⣿⣽⣿⣿⣿⢿⣶⢶⡑⣷⠄⠇⣿⢠⠄⠳⠛ ⢋⠿⣿⣿⣾⣡⠟⡿⣿⣿⢿⠻⣌⣷⣿⣾⣥⢋⠿⡿⣿⠿⠙⠄⡇⣿⠄⢿⠈⡀ ⣿⣿⣿⣿⠃⣴⣈⣆⣿⣿⣿⣿⣿⠻⣄⠏⣿⣿⣿⣿⣿⣠⣈⢣⠈⣤⠄⡆⣿⠻ ⣿⣿⣿⢡⡆⠙⢁⡟⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⠹⡉⠋⢰⠄⠿⠛⣍⣭ ⣿⣿⣿⡎⠹⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠏⡇⣿⣿⣿⣿ ⣿⣿⣿⢿⡄⢰⣄⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣵⠟⣸⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⢻⠄⠃⢿⣟⣿⣿⣿⣿⣿⢫⣮⣿⣿⣿⣿⣿⢟⣿⣿⢃⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢸⡁⡽⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣾⢃⣿⣿⣿⣿⣿⣴⣄⡿⣿⣿⢴⠠⠄⣀⣄⣡⣛⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣾⢃⣿⣿⣿⣾⣤⢀⠄⠄⢀⠄⣄⠄⠄⠄⠄⠄⡟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢡⣿⣿⣿⣴⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣼⡏⣿⣿⣸⠄⠄⠄⡆⣿⠷⠙⠛⠕⠤⠸⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢸⣿⣿⣿⢡⠈⠄⠄⠄⣄⣦⣿⣿⢯⠼⠰⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢸⣿⣿⣿⡋⢙⠈⠄⠄⠄⠄⡀⣧⣰⠄⠄⠄⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢹⣬⣦⣶⣶⣿⣿⠹⠄⠄⠄⠄⠄⠄⠄⠄⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠿⠻⠙⠉⠋⠛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠁⠉⠉⠉⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠚⠒⠉⠉⠉⠀⠀ ⠆⡿⣿⣿⣽⣦⢿⠙⠀⡀⣿⢻⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⡿⣿⣿⠿⠿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⢋⠒⠒⠒⠒⠴⡤⣠⢀ ⠀⡀⣄⣦⣿⠀⡀⣦⣷⠻⡟⣿⢿⠙⠀⡄⢿⠀⠀⠀⠀⠀⠀⠀⠃⡿⣶⣠⢀⠀⠀⡀⣄⣶⣿⠻⠃⠿⠿⠿⠿⠛⠛⠀⠁⣼⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢧⠘⠀⠀⠀⣄⣦⣿⣾⢿⠻⣏⢿⠘⠀⠀⠀⠀⠃⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣸⣀⣀⠀⠀⡏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⠹⠀⠀⠀⠀⣿⠀⡀⣀⣀⣧⣿⠸⠀⠀⠁⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⢸⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢧⠘⠀⠀⣿⢿⠙⠀⠀⡅⣾⠀⠀⠀⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⠈⠀⠀⡇⢀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⡄⢻⡌⢳⠈⡄⢳⠈⠀⡏⣰⠀⠀⠀⠀⠀⠀⠀⠋⠙⠉⠈⠀⠀⠀⠀⠀⡀⣷⠘⠀⣾⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⡄⢷⡘⢷⠀⠀⢧⠛⣸⠀⠀⠀⠀⠀⠀⠁⡞⣧⣾⣷⣿⠘⠀⠀⠀⠀⠀⡄⣿⡟⢸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⣦⡹⢻⠀⡏⣾⠀⠀⠀⠀⠀⠀⠃⣼⠀⡇⢸⡄⣿⢿⠀⠀⠀⠀⠀⠀⣷⣴⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⡄⡿⢿⣿⢠⠀⠀⠀⠀⠀⠏⣼⠀⠀⣿⠀⠀⣧⣽⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡄⣿⣸⠀⠀⠀⠀⠀⡟⣰⠀⠀⠃⣼⠀⠀⡏⣿⠒⠐⠀⠀⠀⠀⣼⠀⠀⠀⢿⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⣼⠀⠀⠀⠀⠁⡾⢠⠀⠀⠀⡟⢠⠁⡟⣿⢠⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⣇⣿⣿⠉⠚⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠀⠀⠀⠀⠀⠀⠀⠋⣴⢀⠀⠀⠀⠇⣸⠀⣿⣿⣽⠰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢻⠀⠀⠀⠀⠀⠋⡾⣸⠀⠀⠀⠀⠀⡾⠀⠀⡀⣧⣿⢿⠿⠛⠉⠀⠀⢀⠀⠀⠀⠀⡇⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⠛⠛⠾⡴⣀⠀⣆⠙⠀⠀⠁⡞⢀⠀⠀⠀⠂⣿⣿⣿⣿⣿⢿⠛⠀⠀⠀⠀⠀⡟⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣶⣶⢸⠀⠀⠀⠏⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢿⡏⣿⣿⣿⣶⠒⠀⡀⠣⠿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣿⣿⣿⣿⢻⠀⠀⠀⠉⡟⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣸⢀⠇⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⢻⠛⡿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣴⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣻⣶⡿⣟⣯⡽⣾⡿⣞⡿⣟⣯⣟⢯⣳⣽⣾⣿⣷⣽⣻⣿⣾⣟⣶⣿⣿⣯⣿⣿ ⣻⣷⢯⣳⢷⣯⣞⢟⣯⢯⡷⢯⡾⣞⣯⡟⣧⣟⣽⡿⣽⡷⣞⣻⣯⣞⡽⢿⣿⣿ ⡵⣻⣳⣼⣻⢻⣶⣛⢷⣭⡾⢫⣷⣎⢻⣧⣜⡿⣻⢾⡽⣳⣝⣿⢿⣿⣿⣿⣿⣿ ⣼⡻⢧⣹⢶⡹⣶⡝⢻⣧⡝⢳⣳⢮⣜⢫⣵⡿⢯⢯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⣩⢽⣲⡹⣶⡝⣣⢞⡹⢶⡭⡴⡺⢗⣣⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢎⡱⢮⣙⢦⡹⢦⡜⡝⢣⣙⣬⡝⢣⣕⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡜⣊⠵⣋⢦⡙⢦⣉⠳⢢⡜⡜⡘⢱⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣼⣱ ⡜⡌⠳⢃⡤⠓⣦⣉⠱⢣⢆⡌⡐⡿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣼⣺⢌⡱⢆⣈⠱ ⠔⣊⠤⡘⣘⠣⢆⠌⡘⠣⢄⡘⢣⡄⣳⡟⣿⣿⣿⣷⣾⣘⢧⣸⠔⢊⡠⠜⢃⠠ ⡩⠞⢻⠔⡉⠰⢎⠄⡘⢃⡠⠜⢂⡡⠔⡋⣿⣽⣦⣬⢑⢠⡟⢤⡘⠆⢃⡄⠒⢈ ⣿⣟⣯⣷⠛⡙⠍⢋⡙⠛⢛⡙⢌⡂⠐⣌⢎⡀⠰⢂⡐⠏⢰⢢⡐⢌⠢⡐⠤⠐ ⢟⣻⣽⣻⣿⡯⣝⢯⣹⡾⣝⡷⣏⢮⠻⠍⠂⢄⡘⢈⠷⣠⠒⢄⠊⢁⠤⡐⢌⠠ ⠠⡐⣂⣀⠐⣈⣥⣂⣀⣤⣥⡼⢦⣿⡟⣎⣷⠹⠄⠈⠠⡐⠄⢂⠄⠃⡀⠔⠂⢂ ⠀⠡⢂⡁⠄⠈⠠⠃⠔⣠⠁⠉⠛⡷⡙⣬⢻⣿⠈⠂⢀⠡⢀⠠⢈⠠⡐⠂⢁⠠ ⠀⠀⠀⠀⠀⠀⠀⢀⠋⠿⣣⣝⠮⣹⡽⢮⠻⣌⢻⠀⡀⠀⠀⢀⠀⢀⠠⠄⠂⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⣀⣀⠀⠀⠀⣀⣀⠀⠤⠲⠒⠛⠛⠞⠶⠤⣀⣀⠀⠀⠀⡀⣀⢀⠤⠶⠓⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⢸⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⢸⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠁⡔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠊⢨⠁ ⠢⠈⠀⠀⠑⠑⠀⠀⠀⠀⠀⠀⠘⡇⣿⢸⠀⠀⠀⠀⠀⠊⠴⢀⠀⠃⡠⠀⠆⡀ ⠀⡀⠢⠑⠀⢢⠈⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⡄⠀⠁⠂⠄⢸⢁⡄⠘⠀ ⠃⠠⠈⠀⢄⠑⡀⠡⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⢊⡠⠀⠀⠀⢀⠀⠡⠀⠈ ⠂⠞⢀⠀⠀⠀⠄⠈⠄⠀⠀⠀⠀⠀⡇⠀⠐⠀⠊⡠⠀⠀⠁⠐⠀⡀⠐⠀⢂⡈ ⠀⢀⠆⠑⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⡇⠀⠀⡜⢀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠀⠀ ⠀⠀⠀⡀⢢⠈⠀⠀⡀⠡⠀⠀⠀⠀⠋⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠢

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⠀⠀⠀⠀⠿⢻⡞⢤⡭⠴⠀⠀⠀⠀⠀⠀⠀⢾⠠⠇⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⣼⣣⠜⣎⢀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢡⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠜⣄⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠘⠀⠄⠐⠀⠀⠀⠀⠁⡐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠣⠈⠀⠁⡘⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠙⠀⠐⡤⡔⠛⢠⠀⠠⠒⠄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠧⠙⠀⠁⡏⣽⠸⠈⠀⠀⠊⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠒⠠⣀⠀⠀⠀⡀⣌⢀⣀⢀⠀⠀⢢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠐⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠀⠀⠀⠒⠉⠍⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⡀⢹⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠸⠀⠀⠀⠀⠀ ⡅⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠀⠀⠀⠀⠀ ⡄⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀ ⠀⠄⠘⠀⠀⠀⠀⡀⡧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠢⠉⠀⠀⠀⠀⢆⠘⠀⠀⠀⠀⠀⠀⠁⠋⡨⢀⣧⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⠠⠀⠀⡤⠳⠓⠚⠒⠐⠽⣁⡵⣸⢢⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡘⠀⣀⠀⠀⠀⢀⠀⠁⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠓⠛⠛⠛⠞⠠⣀⣇⠹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣿⡿⣿⠹⠀⠋⡓⣟⣿⠿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣻⣿⣾⣿⡝⢭⡾⣰⡿⣿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢿⡿⣿⣿⣿⢿⣤⣶⡶⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣷⣙⣾⢠⠀⠀⡀⣀⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⢙⠉⣖⣷⣿⣿⣿⢐⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢄⠤⠤⠳⠀⠀⠀⠀⢹⡀⠰⡆⠘⢸⠁⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⣿⣿⠿⠀⠀⠃⣘⣀⣄⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⠈⠀⠀⢄⠻⠈⠀⡇⠻⠈⠀⢸⣇⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⡴⠀⠀⠁⠊⠀⠋⠒⡖⢶⠒⢲⡚⠑⠉⡈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⡀⣦⠘⠀⣆⢻⠀⣇⡏⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠊⣠⠋⡴⢀⠀⡇⢛⠀⠀⢣⠀⠀⣀⣄⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⣄⠳⠈⣏⠸⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⡰⠁⡴⢀⠂⠀⠀⡏⠀⢦⠑⡈⠱⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠮⠒⠉⠀⢄⡄⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠀⠀⠀⠁⡴⢀⠀⠀⠀⡀⡀⢦⠙⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡀⢇⠘⠀⡀⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⡟⢈⠀⠀⠀⠀⡙⠀⠀⠀⠀⠄⠙⠓⠈⡙⠸⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡁⣿⠸⠀⠀⠀⠀⠀⠀ ⣀⠤⠤⠤⠤⠦⠲⡟⢀⠀⠀⠀⠀⠀⣷⠹⠃⠀⠀⠀⡄⡏⣟⣿⢠⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣁⣿⠈⠀⠀⠀⠀⠀ ⢿⠙⠉⠉⠉⠉⠃⢰⠀⠀⠀⠀⠀⠀⡇⣿⠻⢿⠛⠙⠃⢻⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀ ⣿⣿⠻⠈⠀⣀⣇⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⠈⠀⠀⠀ ⣿⣿⣿⣿⠿⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⡄⣳⣈⣁⣊⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⠻⡿⣿⣿⣿⣿⢿⣉⠀⠀ ⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠿⣲⠛⠛⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢻⡟⣿⣿⢿⠀⠀⠀⡈⣀⣤⣶⠤⠦⠗⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⡋⣞⣶⣳⠙⠛⡿⣲⠀⡄⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢹⠋⠾⣤⢥⠿⠶⠿⠚⡝⣤⠀⠀⠀⠀⠀⠀⠙⠉⣟⢋⠛⠟⡿⣶⣪⢐⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣧⢾⣿⢻⠛⠟⣿⣴⠃⠛⠙⠉⠍⠉⠉⡃⣴⣧⣾⣴⣤⣠⢀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠃⠀⠀⠀⣀⣀⠀⠏⠀⡀⡁⣈⣀⣀⠀⠀⡄⠱⠈⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠀⠒⠑⠈⡀⣀⠀⠀⠀⡀⣢⠈⠀⠀⠀⠀⠀⡀⣀⣀⠁⠋⠔⠫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡿⣿⣿⣿⣿⣿⣿⣾⢀⡇⠻⠉⠉⡀⢄⠶⠛⠈⠀⠀⠀⢆⠀⠁⠈⠉⠉⠋⠟⡿⣼⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣹⠀⠁⡏⣿⣿⣿⢿⠿⠻⡛⣝⢨⠀⠀⠀⠀⣤⣤⣀⣄⣀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣧⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠯⠙⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣤ ⣄⠳⠈⣄⣶⣿⣿⣿⣿⣿⣼⣶⣿⣿⣻⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠁⠚ ⠀⠀⣀⠢⠑⡉⣍⣶⣶⣷⣿⠻⡉⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⣤⣤⣤⣀⠀⠀⠀⠀⠄⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢤⡲⠙⣈⣤⣤⣥⣾⣶⣶⣷⣿⣿⣿⣿⣿⣿⣾⣶⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠌⠐⠀⠀⠀⠀ ⠀⠈⠐⠦⠠⠤⠤⡤⣤⣠⠐⠉⠈⠔⢀⠀⠡⠀⠀⠀ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣘⠤⠂⠀⠀⠡⠀⠀ ⠀⠀⠤⠀⠀⠈⠄⠠⠀⠀⠀⠠⡄⢈⠀⠀⠢⡀⠐⠀ ⠀⠀⠀⠀⠁⢀⠀⢀⠀⠂⠀⠁⠛⠈⠀⠀⠀⢂⡄⠈ ⠀⠀⠀⠀⡘⡌⢀⠀⠀⠀⡰⠀⠄⢯⠀⠀⠀⠀⢡⠃ ⠀⠀⠀⠃⢠⢄⠀⡁⠀⠏⣿⠀⠀⣧⠀⠐⠀⠀⡀⡐ ⠀⠀⠀⣼⠠⠄⡠⣤⢤⠀⡿⠀⠀⠋⠀⠀⢄⠐⠈⠔ ⠀⠄⡄⢾⣿⣿⢶⠁⡿⢿⣿⠹⠀⢸⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⢋⣈⣀⣀⣀⢋⡖⢠⣾⠂⢀⠀⠀⠀⠀⠀⠀ ⡀⠀⢀⡀⡶⢩⠙⡭⠉⠋⠅⢰⠀⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠀⠀⠀⠂⠀⠀⠀⠀⠀

⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⢀⠞⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠏⣠⠀⡆⠟⡤⣸⣀⠧⠀⠀⠀⠢⠛⠈⢄⠽⠒⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠛⠚⠙⠉⠀⠀⠀⠀⡄⢘⠀⠀⠁⡔⡠⢀⠋⢠⠀⠀⠀⠀⡀⣷⠘⡀⠣⡀⢧⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠧⣼⢀⠞⣠⠋⣡⣼⢀⠀⠀⠀⠀⢳⠀⠃⣰⠀⠿⣴⢀⠀⠀⠀⠀⠀⠀⡀⡿⠘⠀⢸⠀⣧⠸ ⠀⠀⠀⠀⡁⢌⠨⡇⢚⠖⣲⠉⡝⠀⠋⢡⡰⣄⠘⠀⠀⠉⠊⡖⣀⡦⠘⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠁⡏⢸⠁⢰⠀⡇⢰ ⠋⠀⠓⠿⡿⣰⣦⠀⢱⠛⡷⣽⢀⠀⣊⣠⠃⠴⣤⣀⢀⠀⠀⠀⠀⠀⡀⠳⠈⠀⡀⢷⠙⠀⠀⠀⠀⡇⣠⢿⡠⠀⠃⣰⠀ ⡀⠀⠋⣶⠿⡿⠘⠳⡀⢺⠘⢰⣀⡼⠀⠎⣠⠀⠀⠁⠏⠿⠺⠀⠀⠀⠀⠀⣄⠱⠀⡀⣿⠸⠀⠁⠞⢀⠊⢠⠁⠞⢠⠀⠀ ⠀⠀⣴⢀⡄⣀⢀⠀⠀⣿⢶⠫⡠⠀⡟⢀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠗⠙⠀⠀⡄⠸⠀⡇⢡⠊⣠⠀⠄⢀⠊⣠⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠇⢠⢸⡀⠤⠓⣉⠀⠁⠛⠿⠿⠈⠀⠀⠀⠉⡉⣬⣤⢤⠦⢿⠀⡀⡇⢚⠀⠄⠁⡼⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢢⠙⠈⠀⣇⠊⣄⣿⣿⣾⢀⠀⠉⠉⣄⠀⣉⣁⣀⠀⣿⠀⠀⣼⢣⠀⢳⡰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⣀⠣⡇⢿⡿⣿⣿⢛⠟⣽⡀⣀⢄⠱⡄⣼⢤⠇⢸⠀⡞⠁⠀⢃⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠶⢹⠀⡞⣿⣟⣿⢳⠈⠀⡀⠀⢦⠀⠀⡆⠈⢸⠀⡀⢁⡜⠀⠀⢦⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢸⣆⣷⡀⠀⣀⠀⠀⠀⠀⢰⠀⠀⢹⢠⠀⠃⡠⢸⠀⠀⠀⢀⡀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⢻⠀⡀⢤⠑⠀⠀⠀⠀⠢⠈⠀⠀⣠⠀⠃⢀⠀⢆⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡛⠨⠀⠀⡀⠢⠈⠀⠀⠀⣄⠓⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡈⢤⠒⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⠮⠒⠑⠉⣉⠻⠙⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠁⠔⣁⢞⠤⠳⠚⠒⠔⡿⢶⡤⢀⠀⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠂⣫⠔⣀⠀⠀⠀⣤⠱⠀⠀⠓⠉⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠂⠀⠂⢳⡖⠔⠠⠀⠀⠐⠒⠒⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣦⣿⡹⣬⢻⣘⠀⠆⠂⠐⠇⠛⡿⣿ ⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣯⢹⠀⠀⠉⡿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣽⠉⣍⡤ ⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⢸ ⢻⢃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠯⣿⣿⣤⡄ ⣿⠘⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣻⡈⢋⢁⠈ ⣶⢸⠈⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣁⡮⣿ ⣀⢻⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡽⣿⣿ ⠀⡇⢳⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿ ⣿⣿⡞⠀⡏⣯⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢽⠀⣀⢻⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣙ ⢹⣏⢹⠘⢳⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⡆⠘⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣭ ⣠⣀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢹⠀⠀⢧⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀ ⠀⠃⡈⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠂⠘⣇⠀⢰⠘⣆⡙⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⠀⡀⣤⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡾⠀⢧⡁⡏⡇⢀⠀⡀⢦⡙⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣻ ⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢧⢰⠀⡀⠸⢱⣸⠀⠀⠀⠀⡀⢦⠳⢌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⢻ ⠀⠀⠀⠀⠀⡄⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢫⣰⠀⠀⠀⢁⡾⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠁⡿⣿⣷⣿ ⠀⠀⠀⠀⠀⠀⡀⣿⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡵⣞⢀⠀⠀⠀⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⠀⠁⡟⢿⠘⣿⢿ ⠀⠂⠐⠀⠀⠀⠦⣦⢧⡙⠦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣋⢴⣀⠀⠀⠀⠀⠀⠇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠁⠟⣼⣿⢶⠶⣰⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣄⠳⡉⣅⠤⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⡠⣀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡼⢀⠀⣰⢁⠀⠀⠀ ⠀⠀⠄⠦⠒⠒⠉⠈⠀⠀⠀⠀⡀⣤⣳⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⣶⢾⠐⡶⠼⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠢⠗⠩⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⡶⣼⠀⢐⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠤⠲⠒⠙⠉⠉⠉⠀⠀⠁⠈⠀⠀⠀⣄⠠⣀⠤⠤⠀⠀⠀⠀⠀⠂⠐⠤⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡿⡀⣤⠲⠉⡟⢲⠒⠒⠒⠖⠶⡻⠙⣈⣀⣄⣤⣀⢤⠥⢾⣠⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣷⠸⠀⡀⠸⠀⠀⠀⠀⠀⡄⣄⠀ ⣿⠀⠁⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⠙⠈⠀⠀⡼⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⡈⢹⠀⠀⠀⠁⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⡀⠘⠀⠀⠀⠀⠈⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡑⠯⠞⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠸⠀⢸⠁⡋⢛⣿⢻⠉⠉ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣽⢿⠟⣿⣾⣤⣧⠙⠋⣼⣄ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⣀⡏⣿⣸⣀⢯⠴⣤⣀⢀⣏⣩ ⣟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⠻⠛⠛⣽⣀⣁⡴⢸⠀⠃⠀⠀⣿⣈ ⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡤⣤⣶⣶⣶⣹⡉⣟⣹⠋⢒⠒⠒⠓⠋⣯⣼ ⡦⠹⣟⣾⢶⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠀⠀⠀⠀⠀⣷⣉⣾⣠⠀⠀⠀⠀⠀⡀⣿⠁ ⠀⠀⣆⠘⠀⠀⡀⢄⠤⠒⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠁⠐⠀⠀⠀⡄⣼ ⠀⠀⠀⢣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⠦⠑⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠁⠋⣾⢀⠀⠉⠟⡿⠿⠈⠀⠀⠀⢾ ⠙⠀⠀⠀⢄⢳⠀⠀⠀⠀⠀⠀⠉⠛⠻⣤⣲⣁⣸⠀⠀⠀⠀⠀⠀⠁⠿⣿⢿⣿⣿⠻⠿⠿⠾⠯⣴⣀⠋⠷⣂⣿⣸⣇⣀⢳⠛⠈⠁⢠ ⡆⠻⠈⠂⠈⠀⣀⠤⠦⠷⠿⣿⣿⣿⣿⢿⠙⣿⢸⠀⠀⠀⠀⠋⠴⣀⠀⣀⣀⣀⣄⣶⣹⣏⣿⣦⣿⣻⣿⣿⠘⣆⢹⡄⠘⡀⣸⢀⡇⠀ ⠻⡈⣦⠻⡈⠢⠈⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣥⣷⠻⠀⣦⣿⢠⢦⠙⡃⠻⢗⠛⢸⠀⡏⠖ ⡉⢦⠙⡀⣤⠻⡈⠢⠈⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⢿⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠾⢻⣿⢿⠈⡄⢻⡞⣀⣏⢠⡟⣾⢃⡴⢀⠀ ⡁⢻⡉⢷⠙⡀⣦⠳⡈⠣⠈⠀⠀⣧⣿⣧⡘⣿⢈⣿⢁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠿⡟⡿⣿⣌⢰⠀⣷⢈⠿⢠⡏⣷⢀⠀⠀⠀⠀ ⠀⣄⡶⢿⣜⢿⠑⠈⣄⠳⢌⠑⠀⡇⣿⠀⢧⠀⣯⣻⡟⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⣧⢹⡏⣧⠹⠈⠁⣾⢀⠏⢠⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⢿⣜⠳⠈⣄⡻⢪⣼⣧⠘⠀⣧⢸⣿⣦⡟⠘⠀⠟⣧⣽⠻⠋⠹⠁⡼⠀⠀⣗⣿⠀⣿⢹⡶⢀⠃⢠⠁⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⣿⠻⡈⠢⡙⣦⢬⡦⢻⠈⠀⣦⣿⠹⡀⣦⡿⣿⣿⣿⣶⣿⢨⡟⣐⠀⠀⠀⣷⠀⡎⢠⠃⠟⢰⠁⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣦⣽⠳⡀⢤⣷⠺⠈⣀⠦⠑⣄⣷⢻⠀⡀⣄⣶⠾⠿⣼⣿⢰⠀⠀⠀⠀⡇⠀⠀⠃⡼⢸⠋⡼⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⣄⠀⠀⢆⣄⠲⠈⠀⠀⠀⣄⢷⠈⠀⠀⡀⢦⢰⡆⠀⠀⠀⠀⠀⡄⠸⠏⣾⠁⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠇⠀⠀⡇⠀⠀⠉⠀⠁⢠⠙⠀⡇⠀⠈⠒⠒⠲⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠈⡆⠠⢀⠀⠀⡉⠔⣀⠁⡀⡞⠀⠀⡐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⡠⠀⠀⢄⠀⠀⡞⣠⠛⠹⡀⢄⣷⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠀ ⠀⢰⠀⠁⠉⠛⠟⡿⢿⣿⣿⣶⢿⠉⡁⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀ ⠀⠿⡿⣿⣿⣴⣠⣀⠀⠀⠀⠀⡄⣿⠸⣆⣹⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠇⣿⣿⣴⠀⠀⠉⠉⠉⠋⡜⣯⣿⣿⢀⠀⡇⢼⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣴⢀⠀⠀⡀⠀⠀⠗⡿⡶⣷⣾⢀⠀⠀⡇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠋⠀⠊⠶⣠⠒⠀⡀⢰⠁⠁⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⢩⡴⠒⠀⠈⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣸⢄⠑⠈⠀⠀⠀⠀⠀⠀⠁⠝⢀⠀⠀⠀⠀⠀⠀⠉⠟⣻⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⢼⠤⠤⠀⠿⡶⣤⣄⢤⠿⠘⠀⠤⠤⣹⢉⣿⣤⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⡆⢀⠀⠀⠁⣿⠖⠲⠒⠒⣶⢸⠀⠀⠀⣄⡄⣶⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡏⢹⠀⠀⠀⠀⠁⡽⠈⠀⠀⠀⠀⠀⡇⢠⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠟⣫⢿⠿⣸⠉⡖⣶⠴⡤⢣⠋⠓⠟⣴⠤⣤⣶⠱⠉⠯⠿⣻⢙⠉⠀⢄⠑⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⣿⣿⣶⣷⣿⣾⢀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣾⣷⣿⢿⠘⢄⠑⠀⠀⠀⠀ ⠀⠁⡏⣴⣀⠀⠀⡟⣿⢹⠉⠊⠒⠒⠒⠙⠛⠀⠀⠀⠳⠊⠒⠓⠒⠑⠉⡇⣿⢸⠀⠀⣄⢧⠉⠀⢄⠈⠀⠁ ⠀⣳⡾⠀⠀⠀⠋⣿⣼⣀⠋⠿⣿⣿⠶⡷⣸⠀⠀⠀⡇⢶⡶⣿⣿⠿⠘⣄⣷⢿⠈⠀⠀⠀⣿⠀⠀⢰⠀⠀ ⠀⠀⢹⠉⠛⠿⣿⣿⣠⣀⣀⢀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢳⠀⠀⠀⡀⣀⣀⣤⣿⢿⠻⠙⠉⣿⠈⠇⠀⠀⠀ ⠛⠈⣿⣿⣾⣴⣤⣿⠙⠀⠀⠀⠁⠋⡴⢀⠀⠁⡴⠘⠀⠀⢦⠙⠈⠀⠀⠀⠏⣿⣤⣦⣷⣿⣿⢠⡇⠉⠀⠉ ⣇⠀⡇⢀⠀⠀⠀⣿⣿⣟⣿⣬⣀⢿⠿⠿⠿⡼⠀⡆⠿⠿⠿⠿⣜⣤⣿⣿⣿⣿⠈⠀⠀⣀⣼⠀⡄⢠⠀⣤ ⠀⢧⡿⠿⠿⣿⣿⣿⣿⣿⣿⢻⠁⣿⣿⣩⣉⢠⠀⠀⣹⣍⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⠿⠿⢿⠚⠀⠀⠀⠀ ⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⣦⠈⠀⠀⣼⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠃⠀⠀⠀ ⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢹⠀⠉⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡀⣷⣾⣶⣡⣄⣿⣼⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿ ⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⡀⣦⠿⠛⡟⣴⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣠⠀⠀⠀⣄ ⠀⠀⡀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⢀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⡴⣬⣀⣄⢦⠷⠛⠉⠀⠀⠀⠀⠁⠉⠛⡾⣶⢹⠀⠀⡇⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣨⣤⢷⠙⠉⠀⠀⠀⠀⠀⠁⠋⠛⠾⣴⣠⠀⠎⢀⠀⠀⠀⠀⠆⣠⣄⣤⣤⣯⣴⣀⣧⠘⠀⣇⠸⠀⠀⣇⠸⠀⠀⠀⠀ ⠀⠀⠀⠆⠙⠁⢸⠀⠀⣁⣎⣶⣤⣦⣤⣤⣠⣀⠀⠀⠀⠉⠖⠲⠒⠓⠈⠈⠀⠀⠀⠀⠁⡞⣠⢄⠤⠤⣦⠹⡞⣠⣀⣧⣈⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣀⠀⠁⠜⣀⠀⠀⠀⠁⠋⠒⠒⠄⠤⡠⣀⠀⠀⠟⠶⠓⣿⡒⢶⠳⠚⡤⣠⠀⠀⠀⠀⠀⠀⣆⠳⠚⠖⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣁⢼⢠⠀⠃⡴⣠⣀⣤⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⠀⠀⢄⠑⠈⠀⠀⠀⠀⠀⠀⠀⢺⠒⠖⢸⠀⠁⣸⠉⠚⠑⠉⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠒⠑⡈⠤⠓⠈⠀⡀⢄⠢⠒⠙⠈⠀⠀⣧⣋⣰⢀⠀⡏⣤⣤⢷⡿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⣨⠀⠀⠀⡁⢾⠀⡀⢤⠒⠈⠀⠀⠀⡀⢦⠘⡇⢠⠀⠀⡄⢻⠀⠀⡶⢠⡀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⢀⡀⢤⠫⠔⢠⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠁⠰⡇⠀⠀⠀⠁⣾⢧⠘⠁⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢤⠢⠖⢰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠊⣠⠀⡀⢱⠀⠁⡟⢸⠀⡀⣁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⢄⠤⠶⠲⠒⠙⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠒⠒⠴⠤⠠⣀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⡀⣀⣀⣄⣤⣤⠤⠤⠤⠦⠶⠒⠺⠀⠒⠒⠿⠀⠀⠀⠀⠀⠃⠚⠖⠴⠥⠭⠭⡮⣶⣴⣒⣀⠁⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⢄⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⢻⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⠀⡄⢀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⡀⠳⠈⠀⠁⠞⡴⣀⠀⠀⠀⠀⠀⡀⣄⠶⣝⠻⠀⠀⠀⠀⠁⣼⠈⠈⠀⠀⠀⠀⠀⠉⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⣀⣀⠀⠀⠀⣀⣀⢤⠳⠉⠀⠀⠀⣀⠯⣰⠀⠀⠀⠀⠀⠉⠚⠒⠒⠐⠂⡙⣦⢿⠈⠋⠟⣶⣶⢶⡲⣓⠿⠻⠚⡴⢀⠀⠀⠀⠀⠀⠁⠉⠋⠒⠒⠒⠒⠛⠈⠀⠀ ⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢾⠒⠛⠋⣰⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣰⠀⠉⠚⠤⣠⡀⣀⣄⠢⠙⠀⠀⠀⠁⠚⡴⣀⠀⠀⠀⠋⡰⠀⠀⣆⠙⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⣧⢻⠉⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢾⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠃⡰⠀⠀⠀⠀⠁⡜⢀⠀⠀⠀⠀⣄⠘ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣆⠹⠀⠀⡀⢻⣀⢤⠶⠲⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⡼⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠦⠈⠀⠀⠀⠀⠀⠏⡻⣶⣸⠀⡀⣦⠳⠙⣯⠀⠀⠘⠀⠀⣀⣀⢤⠶⠶⠒⠛⠉⠉⡏⢸⠀⡄⠷⠙⠈⠀⠀⠀⠀⠀⠀⡿⣟⣾⠤⠷⠈⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⢀ ⠀⠀⠀⣄⠣⠙⠀⠀⠀⣿⢠⠀⣧⠈⠀⠀⠀⣥⣿⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣤⢤⠤⠤⠦⠒⠒⠒⡒⣿⣸⠀⠀⡇⢸⠄⢸⠀⠀⠀⠀⠀⠀⠟⣠⠀ ⠀⠀⠀⠀⠀⡆⣿⢤⠤⣧⠘⠀⡀⣄⠿⠤⡤⣀⠋⡴⢠⠀⠀⠀⠀⠁⠉⠛⠒⠒⠒⠒⠔⠿⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⠏⣰⡄⡿⢿⠙⠀⠀⠀⠋⡶⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣳⠈⠀⣄⠻⠉⠁⡾⠀⠋⡴⢀⠀⠀⠀⠀⠁⠟⣴⣀⢀⠀⠀⠀⠀⠁⢰⠀⠀⣀⢧⠳⠉⠀⠀⠀⠀⠀⡇⣷⠛⡴⢀⠀⠀⡏⣸⣄⠷⠛⠾⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⣇⣌⣴⢀⠟⣠⠀⠀⠀⠀⠀⠛⡴⢀⠀⠀⠀⠀⠀⠀⠃⡿⠀⠀⠋⠴⣀⠀⡀⣄⠳⠈⠀⠀⡀⣦⢙⠉⠀⠁⠋⣷⣸⠀⡇⣾⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⡆⢻⠀⡇⢸⠀⠀⠀⠁⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠟⣷⣸⠀⠇⢸⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⡀⣀⣃⣿⢀⠀⠏⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⣧⠘⡉⠙⠋⠖⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣰⠀⢿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⣄⠻⡿⣾⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣞⣹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣼⠀⠀⣿⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡀⢦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⢸⠀⠀⡀⢷⡎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⡀⣄⣤⣦⢿⣤⣤⣤⡀⣿⣸⣧⠸⠀⠀⠀⡀⣷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢦⠙⠈⠀⠀⠁⡍⢺⠒⠒⠒⣟⢻⡙⣄⠤⠤⠢⠒⠒⣿⢯⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⡵⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣋⣞⣶⢳⠙⠀⠀⠀⡏⣿⣿⢩⠉⠉⠉⠉⠏⣿⣿⢀⣆⣤⠷⠾⠻⠚⠗⠿⡿⣩⢖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠛⡽⢓⠀⠀⠀⣆⠛⠴⣠⣀⣦⣳⣭⣬⣤⣭⣿⣿⣼⢀⠀⠀⠀⠀⣄⣳⠈⠄⣻⢧⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢼⣤⢤⡀⣷⢻⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⣋⣴⣤⣏⣠⠀⠀⠉⠚⠐⠀⠀⠀⣎⠻⣿⣼⣒⣀⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡉⢿⠙⠀⠀⠀⣷⢹⠛⣿⠉⠉⠉⠉⠀⠀⡎⢠⠋⡶⢀⠁⠎⡴⣀⠀⠀⠀⠀⠀⠀⡀⣷⠺⠀⠀⡏⢹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠟⣿⣽⠋⠚⠖⠴⡤⣠⢦⠳⠛⢟⣶⣷⢿⠿⠯⠶⣛⣌⠷⠉⠞⣠⠋⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣤⣀⣁⣉⣙⣍⠯⠻⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠟⣿⢠⠁⡿⣿⣿⣿⢾⡤⢳⡏⣴⢋⡼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠗⠀⣀⠀⠀⠀⡀⣇⣿⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢦⠹⠀⠀⠀⠉⠛⣟⣿⡿⣿⣿⢙⡉⣿⣿⣿⣿⣿⢿⣼⢡⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠸⠀⠀⠀⠀⠀⠋⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠦⠿⢿⣒⣒⣟⣿⣿⣶⣶⣶⣶⣶⣷⣿⣾⢠⠃⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠉⠋⠚⠖⣤⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡴⣀⢀⠉⠞⣤⣀⠀⠀⠀⠀⠀⠁⡟⣴⢀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢘⡑⣄⠦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠏⣴⢀⠁⠞⡴⣀⠀⠀⠀⠀⠀⠀⠀⠋⣴⢀⠀⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢸⠀⣄⣤⡳⣿⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⢰⠀⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢠⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢠⠀⠀⠀⠀⣄⣿⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣱⢋⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⠸⠀⠀⠉⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣠⠀⠉⠖⣠⠀⠀⠀⠀⠁⠟⣼⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⢀⠀⠀⠀⡀⢦⠙⠀⡀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⢰⠀⡤⢀⠀⠈⠀⠁⠋⠴⣠⠀⣄⠳⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⣀⢦⠙⠀⠙⠀⠀⠀⡀⠣⠘⡇⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣤⠤⠶⠒⠒⠴⠤⣤⣀⠀⠀⠀⠀⠀⠀⣄⠦⠙⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⣠⠀⠀⠀⠀⡀⣄⢦⡒⢻⠛⠛⠛⠛⡾⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢤⠲⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⠂⠔⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣄⣦⣷⣿⠻⠈⠀⠀⡏⣿⢰⠃⡿⢈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⣈⣤⠢⠙⠀⠀⠀⣆⢿⣧⠘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣡⡘⠀⠄⣿⢃⠸⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠙⠉⠂⠀⡀⣦⣶⢾⣿⣿⢰⠇⣾⣤⣤⢦⠷⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠻⠈⠀⣀⣻⣧⡸⠀⠀⡀⠀⠀⠀⢀⠀⢀⡁⡿⣸⠀⢀⠟⣸⠈⢇⠋⣼⠀⠀⠀⠀⠐⠀⠐ ⠀⣠⣄⣤⠦⡶⣴⣷⡻⣿⣾⣷⠿⠻⠛⠙⠙⠋⣉⣀⢀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⣄⣷⠛⣟⢹⣷⠘⠀⡀⠀⠁⠀⠀⠀⠀⡟⡞⢹⠀⠟⣿⣼⢀⡀⣿⢿⠾⠴⡥⠭⠿⠙⠠ ⠐⢀⠀⠉⠊⠖⣶⣶⣹⠉⠁⡾⣤⢰⡀⣿⣼⣷⣿⢿⠻⠛⠉⠉⠀⣀⢦⠙⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣾⠙⠂⠀⠀⠀⠀⠀⠁⢸⡀⡦⣶⣷⣿⢸⠀⠋⣿⣿⢿⡿⣨⣀⣈⣄⢻ ⠋⠟⡷⣹⠛⡴⣰⣃⣀⢧⡽⢈⠀⠀⠀⣠⢮⣠⠁⠛⠟⠿⣿⣿⣬⠶⠓⡙⣌⠳⠈⠀⠀⠀⠀⠀⠀⠀⣄⣶⣶⠾⠟⠛⠛⠚⡶⢻⠉⠉⠈⠀⣀⣤⡷⣿⣾⣟⣿⣿⣧⠻⢀⠀⡘ ⠀⠀⡏⣋⣷⠙⠛⠞⠳⡿⣿⢿⠀⠀⠀⠎⢫⠿⣿⣿⣿⣿⣶⣷⢿⠻⠛⡛⣿⠻⣟⠻⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⡏⣳⢯⡘⣀⣀⣤⣷⠿⣇⢱⣿⣿⣿⠀⡀⠻⠀⠀ ⠏⣴⢃⣦⠗⣰⡇⢻⣿⣿⣿⣿⠹⠘⠀⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄⠳⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣇⠘⠀⣀⠢⠙⠀⠀⣧⣸⠀⣿⣛⣙⢤⠶⡟⢹⠠ ⣦⠟⢢⠙⡀⢻⠀⣦⣲⢖⡷⣙⣷⢸⡏⠀⣆⣿⣿⣸⠀⠀⠀⡟⣠⣀⣀⣀⢤⠲⠉⠀⠀⡀⣦⠻⠈⠀⠀⠀⠀⠀⠉⠛⠾⡴⣠⣀⠦⠓⠚⡖⢶⠙⠀⢱⠀⣄⣿⣾⢿⠀⡄⣷⠈ ⠁⣼⠠⡓⢻⣽⠦⠒⠑⠉⠀⡀⣠⢻⣸⠀⠀⣧⣿⢀⠀⠀⡞⣿⠀⠀⠀⠀⠀⠀⡀⢣⠈⠀⠀⠀⣄⢦⠶⠿⣤⣠⢀⡀⣄⠤⠓⡉⣉⣭⠬⠢⠒⡉⢫⡀⢢⣷⣿⠿⣿⠈⠀⡇⣿ ⣶⠸⠀⠀⡥⣾⢶⠲⠓⡙⢮⠘⠀⡇⢨⠀⠀⡇⣸⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠉⠟⣿⣹⠀⠀⠀⠀⠀⡀⢄⠤⠤⠤⡤⣳⣈⣀⣄⣷⣿⢿⠻⡈⣧⢸⠀⠀⣽⣷⣿⢸⠀⡇⢸ ⠛⣄⠳⣏⣺⠐⠤⠦⡒⢟⣈⣤⠙⠀⢻⠀⠀⡟⢀⠀⠀⠀⠀⣷⠀⠀⠀⠁⠿⡿⣾⣠⢞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠀⠀⣿⣿⣿⣿⡻⣷⠈⠀⡆⡘⣷⢸⠀⡇⠰ ⣀⢸⡇⣀⢦⠚⠛⠖⡤⣀⣄⠹⠀⢂⣏⠈⠀⢸⠀⠀⠀⠀⠀⡄⠳⠋⠗⣿⣿⣻⠶⣠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⣷⣿⣿⣿⢖⣀⣿⣿⣿⣿⢰⠀⠀⢿⡀⢳⠀⡇⠀ ⠟⢸⠀⢆⠛⣕⡯⣼⠶⠼⠤⡄⠻⠀⡀⢷⡿⠀⠀⠀⠁⠉⠓⠛⠶⣾⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣶⣵⢡⠟⣿⣼⢦⠙⡀⣳⣯⣿⠐⠀⠀⡆⠘⡀⢹⡿⠈ ⣰⢻⠈⠀⡄⠹⡀⢲⠉⣏⠲⠙⡀⢹⠀⡄⣿⠀⠀⠏⣠⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣹⣉⣯⣾⣶⣥⣾⢀⠙⡌⠳⡀⢣⣷⢸⠀⠀⠀⢸⠀⡄⣿⢸ ⠀⡆⢹⠙⠈⡀⠳⠈⠀⣀⢹⡀⣷⣄⠻⠀⣇⠈⠃⢠⠏⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣩⣀⢒⠖⡤⣀⠀⠃⣴⢸⡀⢳⡀⣾⢠⠀⠀⠀⣇⠀⡇⡿⣿ ⢻⣝⡬⣀⣍⢿⠶⣤⣀⣀⣀⢄⡷⠈⡄⠸⡀⢹⡼⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠲⠙⠈⠀⠀⡸⠀⢸⠀⡀⢳⢸⠀⠀⠀⠀⡇⠀⡇⣸⣿ ⣷⣿⣿⣿⣼⠁⣛⣛⣟⢮⠳⠈⠀⢇⠻⣏⠈⣿⢸⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⢳⠀⠸⠀⠀⡆⢸⠀⠀⠀⠀⡇⠀⡇⢸⣿ ⠦⣽⣶⣿⢻⣿⣿⣿⣸⠀⠀⣄⠙⡘⡄⡘⣿⣀⢸⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠦⢶⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⡏⢳⣿ ⠀⣦⠻⡨⣦⣷⣿⣿⢀⠋⠸⠁⡟⢸⠀⢧⡏⠀⢇⢸⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠾⣶⡷⣾⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠸⣼⡟⣿ ⠀⠀⡄⢻⠀⠀⣄⣷⠇⣿⢹⡇⣆⠀⠀⡀⣷⠀⡇⢸⠀⣧⠈⠀⠀⠀⠀⠀⠁⠋⡿⣷⣸⣇⠿⣿⢿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⠀⠀⠀⠀⣿⣇⣿⣿ ⠀⠀⠀⣎⣻⠀⠁⣧⣿⣿⣿⡞⠈⠸⠀⠀⡅⠸⠀⢸⠀⠀⢧⠘⠀⠀⠀⠀⠟⣼⢀⠀⣉⣿⣿⣼⢀⠀⠀⠟⢉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢸⠀⠀⠃⣰⡇⣿⣿ ⠀⠐⠀⠀⣧⠸⠂⡀⢻⣄⣷⢻⢷⢹⠀⠀⡾⢸⠀⢇⠘⠀⠀⣦⠻⠉⠀⠁⣿⢻⠟⡿⣾⣶⢀⠀⠒⠗⡾⣠⠀⠉⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⡞⠀⡇⣧⣿ ⠀⠄⠀⠀⡄⣷⠌⠀⡤⢻⠀⣄⡳⣯⠹⠀⢸⣇⠈⠀⣧⠲⠈⠀⡄⣳⣬⡦⣿⣿⢚⣖⢲⠒⠒⠒⠒⣶⠒⠒⡽⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠏⢠⠀⡟⡇⣿ ⣤⠲⠙⢉⠀⡀⣿⠈⠀⡀⢷⠈⠀⡀⣤⢷⣏⡈⢱⠀⡀⢳⡀⢤⠓⠉⣍⡩⢹⡉⣚⢶⠶⠲⠔⠤⠤⠠⠀⠠⠀⡒⣒⣄⠤⠷⠫⠛⠑⠉⠀⠀⠀⠀⠀⢸⡆⠀⠃⣰⠀⠀⣹⡿⣿ ⠀⠀⠀⣀⣇⠿⡿⢻⠈⠀⠀⣄⠳⠈⠀⠀⡀⢦⡌⠘⠀⠉⢻⠚⠷⣾⣓⣛⢛⠛⠙⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣤⢶⠿⠛⠈⠛⢰⠀⠃⡸⠀⠀⠏⣟⣿⣿ ⠀⠀⠀⠃⡿⣿⣿⣿⢿⠈⠀⠀⠀⣀⢦⠛⠈⠀⡇⣾⣠⢀⠀⠁⠉⠒⠶⠵⡤⣀⣀⣀⡀⣀⣀⣀⣀⠤⠦⠶⠒⠙⠉⠈⠀⠀⠀⠀⠀⠀⠁⠈⣀⣀⣦⠘⠁⣰⠀⠀⠁⣟⣿⣿⣿ ⠀⠀⠁⡛⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⣀⢯⣰⠀⠋⠿⣷⣉⠀⠀⠀⠀⣄⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠑⠉⠀⠀⡀⣄⠦⠲⠝⣹⠀⠀⠀⡿⣿⣿⣿⣿ ⠃⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠃⣸⠋⣴⣤⣧⠘⣄⢴⠲⠙⠉⠀⠀⡀⢤⠲⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠠⠀⠀⠀⠀⠉⠛⠞⡿⣿⣿⣶⣦⣤⣀ ⡤⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⡇⣾⢀⠀⠀⠐⣦⠛⠉⠉⡛⣻⣄⠤⠲⠛⠙⠋⣙⢌⠤⠢⠛⠛⠛⠙⠉⠉⠉⠋⠛⠛⠛⠒⠀⠤⠤⡠⣁⣯⣿⡾⣴⣠⢀⠠⠀⠀⠄ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⢷⠙⠀⠀⠠⠀⠠⡄⠀⡄⣄⠻⠀⠄⠾⡙⢤⠲⣙⣀⣀⣇⣘⠳⣄⠳⠓⠙⠉⠀⠀⣳⣝⠿⠾⠿⡶⣤⣠⢀⠀⠀⠀⠁⠉⠉⠉⠟ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⣄⢠⠐⠈⠀⢈⡀⠀⠁⠀⣌⢷⠶⡶⣶⠳⠉⡀⣄⠿⠟⣶⡶⢷⡶⠶⠶⡬⣤⣠⣀⣀⠀⠀⠀⠀⠉⠋⠞⡤⡀⣀⠀⠈⠁⡟⣿ ⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠀⠀⠐⠀⠐⠀⠀⠂⠀⠐⠂⠀⠐⠀⠀⣂⣤⣐⣀⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⡴⣠⢀⠀⠀⠀⠀⠀⠟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿

⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣫⣀⢄⠠⠀⠀⠀⠁⠈⠀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡞⢀⠀⠀⠀⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⣇⢳⠉⠉⠚⠒⠖⣠⡀⣃⡿⢿⠻⠉⠉⠉⠋⠙⠚⠴⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠀⠀⠋⡼⢀⠀⠀⠀⢿⣠⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⡆⢸⠀⠀⡀⢹⢱⠀⠀⠠⠀⠀⠀⣿⣿⣦⣷⣾⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠟⣠⠀⠀⠞⣾⢀⠀⠀⠁⡿⢰⠀⣇⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⣇⠈⠀⠀⣇⡎⠈⠀⠀⠀⠀⠀⠃⠀⠀⡀⡇⠈⠂⠀⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠁⡼⢏⢠⠀⠁⠞⣠⡞⠀⠀⡞⢤⠀⠀⠀⠀⠁⠉⠉⠀⠀⡀⠀⠀⠀⠀⡇⠘⠠⢧⠈⠀⠀⢻⢹⠀⠇⠈⠀⠁⡿⠹⠀⠀⣿⢿⠘⠉⣿⠚⠐⠀ ⠀⠂⠀⠀⠀⠀⠤⠀⡀⠀⠀⠃⡿⠔⠀⠁⠞⣠⠀⡞⢀⠀⠇⢾⡤⡥⣯⣶⣴⣤⣤⣦⢷⢿⠻⠈⠀⠀⠀⠀⣄⡱⠸⢧⠀⠀⡄⡧⠈⡆⢻⠋⡟⣿⣿⠿⡿⣾⣿⣾⣿⣿⠀⠀⠀ ⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠁⣶⢠⠀⠈⡠⠀⠀⡜⢀⠀⠟⣤⢂⡠⢀⠀⠀⠀⠉⠉⠉⠀⣀⣦⡳⠈⠀⠀⠀⡆⡀⣧⡁⢻⠁⠊⠕⣬⣤⣿⣬⣿⢸⣷⢹⣿⢸⡇⣿⣿⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡀⠀⠃⡾⢀⠀⠀⠀⠀⠀⠊⡴⢀⠀⠀⣄⠳⠈⡀⢦⠙⠀⠁⠀⠀⠀⡌⡞⢿⠶⡤⢿⠀⣷⣿⣿⠀⡇⣿⣿⢠⠀⣿⣿⢣⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⠃⣹⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡀⢧⡄⢻⠀⠀⢣⣇⢿⠜⢀⣿⠀⡇⣿⣼⠀⡄⣿⣸⠀⠀⣷⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠋⡼⢀⠀⠀⠀⠀⠀⠀⡇⣿⢻⠙⠈⠀⠀⠀⠀⠙⢸⠀⠀⡀⠀⣦⠘⠀⡄⠸⣿⠹⠋⣷⠁⠀⣶⢠⠀⠛⣄⢀⠃⢀⡀⠟⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠋⡥⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣾⣿⣿⣿⢿⠿⡿⣿⢀⠀⠀⠀⠀⠀⣆⠙⠀⢠⡇⣫⠀⡇⡆⠀⠀⠀⠐⣿⠹⢏⣻⢋⠛⣿⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡟⢃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⢠⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⡆⣸⠸⡇⠀⠛⠟⠀⣄⣿⣾⣿⣸⣀⡇⣿⣿⠈⠀⠀ ⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⣿⢰⣽⡾⢀⠀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⢸⢮⡤⡿⣴⣷⢰⠀⣧⣿⣿⢀⠃⣿⢸⣧⢿⠀⠀ ⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⣸⠃⣿⢀⠀⠀⠀⠀⢄⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠏⣾⣼⣧⢂⡏⡀⠀⠀⡇⣿⣿⠘⡿⣾⠀⡄⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡏⣿⢠⠀⠀⠃⡿⣛⣙⢱⠀⠀⠀⠀⠀⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣻⢠⠀⠀⣿⠸⠁⡟⡏⣿⣟⢸⡋⠛⠸⠀⠀⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠻⠀⠀⡄⡿⢿⡿⣰⠀⠀⠇⠸⡃⠁⣿⡰⠀⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠇⠏⠿⣿⣿⣿⠀⠋⣦⣿⣾⣿⣾⣿⣣⡿⢀⣿⣿⢿⠙⠀⣿⠀ ⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡇⣿⡿⢮⠻⠙⠉⡉⠋⠟⠿⠃⣿⢻⡽⡏⢻⠀⠙⠀⠀⠇⡻⣛⢯⠀⠀⠀⢻⡿⣧⣾⡇⣿⣯⠜⣜⠀⣿⢿⣿⢰⠀⡟⣿⠸⣧⣿⣧⣿⡿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⡀⣯⣿⢻⠀⡀⣀⣾⠏⣿⣿⣾⣣⣿⣛⢷⢸⠀⣿⡇⠈⡄⢶⣶⣴⠀⠀⠏⣴⣈⡏⢠⡇⣿⣿⣉⢰⠀⣿⣿⣼⠀⠁⣿⣿⢻⡿⣿⠀⣦⣿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣿⡿⣷⣯⢿⠸⡇⣿⣿⣯⣼⠃⣿⣼⢀⡄⢹⠇⣾⠀⣄⠯⠓⠙⠋⠒⡷⣼⠃⢸⣰⠀⡿⣿⣼⣇⠈⠀⣿⣼⢀⠀⡟⣿⢸⣷⣿⣿⠀⠀⣇⣾⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡌⣿⣿⢿⣿⣧⣻⣾⢃⣿⣿⠟⠁⠈⣇⣿⢠⠁⡾⢋⠟⣼⢁⠺⣾⢀⡟⠋⡴⡟⣴⣞⢀⡆⢠⠀⣴⢀⠃⣿⣿⣾⠀⡄⣶⣿⠂⠋⡇⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⡀⣦⣿⣿⢸⣿⢿⡙⣷⠀⡿⣿⢇⢿⣿⢀⡟⣿⠛⣿⡿⢙⡿⠟⣡⣞⢃⡾⢋⢾⣴⢁⡾⢀⠀⠸⠀⠀⠀⠃⡿⣸⣀⠁⠩⠀⠀⣿⡟⢉⠟⢿⡻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣞⠹⠀⠀⡀⣦⢻⣟⣿⣿⠸⡀⣷⢿⣿⡷⢿⠏⣿⣿⣿⠳⠈⣄⣶⢿⣿⢿⣾⣤⣀⠀⠋⡿⠯⡲⣒⢤⠈⠀⠁⡇⣿⢀⠀⣿⣿⠻⠊⡿⣿⣠⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢰⠀⠀⠀⡀⣄⣷⣿⣿⠻⠙⣆⢿⡌⢿⣿⣿⣿⢿⣭⣿⢾⠲⣲⣒⢒⠒⠖⠴⣤⣻⣟⠭⠭⠿⡿⢠⠀⡇⣿⣸⠀⠀⣿⣼⣿⢿⡿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠉⠀⠀⡁⣌⣦⣷⠸⣆⢿⣿⣾⣶⣤⣤⣀⢀⠀⠀⠀⠀⠀⠁⠋⠜⠤⡷⣭⣀⣀⣀⣜⠀⠀⡿⣿⢺⠀⠀⣿⢸⡆⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠈⠀⠀⠀⠀⣀⣤⣶⢶⠲⣳⣄⠦⡒⢙⣉⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⣠⣆⢻⠉⠉⣉⢦⠛⠗⢠⠀⡇⣿⣿⣿⠈⡇⣿⢸⠀⣄⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⠙⠉⠀⠀⠀⠀⠀⠀⡄⠸⠁⠋⡴⣀⠀⠆⠶⡶⣶⢠⠀⠀⠂⠀⠀⠀⠀⠀⣴⠹⠉⠈⠀⠋⡰⠀⠇⣿⣿⡄⣿⢻⠀⣿⢸⠀⡇⣶⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣢⣄⠦⠓⠉⠉⠀⠀⣦⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠶⠶⠴⡼⠀⠁⣿⣿⢠⠀⣧⣾⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢹⣀⣀⣄⠤⠤⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠒⠙⠈⠀⠀⠀⠀⠙⠀⠀⠀⠁⠋⡟⣷⣙⠉⠉⡉⢉⠋⣿⠛⠛⠛⠛⠛⠛⠛⠛⠚ ⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠁⠉⠀⣀⣄⠭⠬⡡⣈⣀⣀⣀⣀⣀⢄⡤⣀⠀⠀⠀⡆⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠛⠛⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⣿⣿⢿⠈⡇⣾⢠⠀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⣿⣼⢻⣶⢀⠀⠀⡄⠃⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⣿⢠⣆⠀⠀⠀⠀⠿⡇⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⢸⠠⠀⠀⠀⡄⣷⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣿⢸⠈⠀⠀⠀⠀⡀⣿⠈⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⢻⠀⠀⠉⠈⠀⠀⣧⢸⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⣿⢻⠀⡇⣿⣿⠻⡙⢰⠀ ⠀⠀⠀⠀⠀⠃⣿⣿⣿⣼⠀⡄⣠⣄⣷⣿⠻⠈ ⠀⠀⠀⠀⠃⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⣿⣶⢸ ⠀⠀⠀⠁⡏⣿⣿⣽⢿⠸⠀⠀⠀⠀⡀⢀⠈⢀ ⠈⡒⢤⡠⣇⣿⣿⣾⢨⠀⠀⠀⠲⡿⣿⠿⠸⠀ ⠀⠀⠀⠀⡀⣧⣿⢸⠀⠋⣶⣿⣿⣿⣿⣿⢼⠀ ⠀⠀⠄⠠⣀⢀⡀⡀⠀⠀⠀⣖⣶⣷⣴⣠⢀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠞⣠⢈⠀⠀⠀⠇⣿⣿⢿⣌⡼⡷⣷⡻⠣⡏⢳⠋⣏⢿⠈⡃⠈⣀⠳⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⣀⠀⠀⣄⠀⠀⠀⡿⣿⣿⣿⣿⡜⡻⣳⣯⢫⣦⡞⢼⣄⣿⣿⠨⢧⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⣥⢙⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠻⢯⣎⢞⠝⢿⡏⠘⡇⣿⢿⠘⢽⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠋⠴⠦⠓⠛⠟⠥⡴⣠⣀⠀⠀⠀⡀⣀⣤⠾⠓⠉⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⢿⣝⡹⣤⡱⣿⣯⠘⣿⣿⣿⡽⠻⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠋⡼⣋⡾⢠⠂⠐⡀⣱⣉⣉⣍⣭⢭⠯⠒⠒⠓⠉⡉⠉⠈⣀⣤⠢⠙⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⣄⣷⣿⡍⣿⣿⣿⣿⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠴⣀⠀⠀⠁⡟⣴⡿⣰⠀⠀⠋⠖⡤⣀⣀⣀⣀⣤⠦⣙⣌⠤⠓⠈⣀⣀⣄⣤⠦⠷⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡙⣾⣤⣦⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠁⠉⠞⡴⣠⠀⠀⠁⠉⠞⣠⣿⡿⣰⠃⡴⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠄⢻⣈⠣⠈⠀⠀⠀⠀⣄⠳⣈⣦⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠉⠋⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡤⣀⣉⠉⠚⠶⡤⣠⣀⠀⠀⡟⣿⣰⠀⡆⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣅⡷⢻⠀⠀⠀⠀⠀⠀⣄⠳⡙⣄⠷⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠒⠔⡤⣨⣀⣧⣿⢿⠿⠛⠙⠀⠃⣾⢠⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⡸⡟⣿⠀⠀⠀⠂⠿⠈⠀⡀⣤⢾⡓⣮⣿⣿⣿⣿⣿⣿⣿⣿⣬⣦⣶⣶⣿⣿ ⠄⡀⠀⠀⠀⠀⣆⠹⡀⣿⣿⣿⣿⣿⢿⣼⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠛⠛⠛⠛⠛⡿⢹⢺⣯⣟⠀⠀⠀⠀⣄⢳⠈⠀⠀⡆⡘⣦⡿⣿⣿⣿⣿⣽⣤⣀⣤⠻⠈⠀⡀⣦ ⠀⠀⠀⠀⠀⠀⠀⣧⠹⡇⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠁⠟⣻⣾⣴⣠⣀⣀⣀⣀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢆⠙⠀⠀⠀⢦⡌⣳⣯⣻⣿⣿⠻⠈⠉⣾⣿⠻⠈⡏ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⡿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⠛⠟⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠀⠀⠀⢧⡘⢧⣿⣿⣿⣿⣿⣿⣿⡙⣧⣾⢁ ⠀⠀⠀⠀⠀⠀⠃⣸⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢶⣶⢘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠉⠀⣄⠱⣇⡿⣿⣬⡿⣻⣌⣦⣷⣼⣿ ⠀⠀⠀⠀⠀⠁⡿⠀⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⢀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠞⡤⢁⠮⠒⠓⠙⢦⣦⣿⣿⡼⣷⢷⠙⠘⠒⡗ ⠻⠛⠈⠀⠀⡿⣸⠀⣿⣼⠀⠃⠙⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠶⣤⣤⢦⡙⣈⢀⠀⠋⣾⢿⠛⣞⣿⣿⡈⢰⣆⢸⠀⠀ ⡀⣦⣿⢿⡟⣿⢸⠀⣿⢠⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⣄⣷⣿⣿⣿⡙⠛⣟⠿⡶ ⠀⠀⡆⣿⣿⣿⣿⡿⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⢠⠀⡄⢿ ⠀⠀⠀⡟⣿⢹⣿⣿⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠊⠀⠉⠀⠀⠀⠋⣿⣿⣿⣿⣿⢻⠀⠀⡇ ⠀⠀⠀⣿⣿⣇⣻⣿⢣⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡼⣠⢀⣷⠉⠟⢻⠉⠛⡿⣿⣿⣿⣼⣤⣿⣿⡹⢻⡄ ⡇⠀⡇⣿⣿⡇⣿⣿⡟⠘⡇⢹⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⠈⠀⠀⠈⠀⣄⠦⠳⡟⣹⠈⠏⠿⡙⣉⠛⡿⣿⣿⣾⣥⣟⣿⢸⠀⣯⣿⣿⡿⠸ ⢩⠀⡇⣷⣿⡇⣿⣿⣿⢸⣿⠸⠀⢂⠈⠀⠀⠫⠴⡠⣄⢧⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠈⠀⢸⠀⠀⡀⣁⣯⣶⣷⣿⣾⣶⣶⣶⣤⣧⣿⢿⣠⠇⣿⢾⠠⣇⣿⣿⢿⣿ ⠨⠀⢿⠟⣿⡇⣿⣿⢿⢆⢸⠀⠀⡃⣎⠛⡴⢁⠞⣡⠞⣠⠀⠀⠀⠏⠠⠀⢀⠀⠀⠀⠀⠀⠀⠃⣘⡇⢻⠀⠀⠀⢸⠀⣏⣿⣿⢿⠒⠒⠖⠴⣿⣿⣿⡼⣄⣿⢸⠀⡇⣾⣿⣿⣿ ⢶⠀⣿⣿⣿⡆⣷⣿⣿⡟⢽⠀⠀⠁⣼⢁⠞⣫⡴⢀⠀⠀⠁⠼⠉⣿⢸⠀⠀⠀⠀⠁⠉⠟⡿⣿⢸⡇⣿⠀⢸⠀⢸⠃⣿⣿⣿⣿⠉⠋⠖⡧⣿⣿⣸⢸⠀⣿⢸⠹⡄⣺⣿⣿⣿ ⠛⠀⣿⣿⣿⠦⡿⣿⣿⣿⣿⢋⡀⣟⠈⣭⠞⢠⠀⠀⠁⠞⣠⠒⣧⣿⢁⠸⠀⠁⠟⣿⣿⣿⣿⣿⢹⡇⣿⢹⢱⠀⢸⡿⣿⣿⣿⡟⣹⠀⠿⡇⣿⣿⠀⣇⠘⣿⢿⣿⠀⣿⣇⣿⣿ ⣿⢹⣀⣯⣿⢸⣖⣿⣻⣿⣿⠺⡏⣿⣴⣀⠀⠀⠀⠀⡿⢀⠃⠿⡿⣼⡜⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⣿⣿⣿⣿⣠⡀⣿⠀⣧⡌⣿⢸⠀⡀⢻⣿⣿⣿⠈⣿⡗⣿⣿ ⡇⣿⣿⣿⣿⢿⠀⣧⣾⣷⣿⣻⣀⣿⠀⠀⠀⠀⠀⠇⣿⠀⠃⣿⣾⣾⢃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣸⠹⣿⣿⣿⣸⠀⠀⣧⢸⡇⢹⣿⢨⠀⠀⡆⡿⣿⣿⢸⣄⡧⣿⣿ ⡇⣿⣿⣿⣿⣿⠛⠀⣷⡿⣿⣇⡞⣿⠘⠀⠀⠀⠀⡇⣿⣿⣿⣴⣏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣏⡿⣿⣿⢀⠀⠀⡄⣿⠀⣿⣿⢸⠀⠀⠀⣷⣿⣿⣿⠈⡄⣿⣿ ⠀⣿⣿⣿⣿⣿⢹⠀⠀⣧⣿⡸⣿⣿⢿⠉⠛⠟⡿⣿⣿⣶⢫⡴⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⣧⣿⣿⣥⣿⣿⠘⠀⠀⠀⣇⢻⣧⣿⢿⠀⠀⠀⡆⣿⣿⣿⢻⠀⣿⣿ ⠀⣇⣿⣿⣿⣿⣿⠨⠀⠀⣦⢿⣧⣿⣿⣿⣿⣿⣿⣻⣟⣤⢹⠀⡇⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣼⣠⠈⠃⣠⣿⣿⠹⣧⣿⢻⠀⠀⠀⡛⣿⡿⣿⣿⢿⠈⠀⠗⣇⣿⣿⣿⢹⣇⣿ ⠈⡀⣷⣿⣿⣿⣿⢻⠀⠀⠀⣇⣾⣿⣾⣠⣀⣀⢀⡇⣿⠙⣏⠛⡟⣿⣿⣿⡟⣼⣿⣿⣿⣾⣠⠀⠀⠀⡄⠀⣇⣿⣿⡿⣿⣿⠘⢻⠀⣿⡿⣿⣿⣿⣿⢹⠀⣧⣹⣿⣿⣿⣿⡯⣿ ⢿⠀⡆⣿⣿⣿⣿⣿⠿⠘⠂⡰⠀⣇⣿⠈⠀⠃⠁⣿⣿⣿⡄⢻⡄⣿⣿⣿⢸⢷⣾⣴⣀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⢹⡇⡟⣿⣿⣿⣿⣿⣿⣿⠸⡇⣿⣟⣿⣿⣿⣾⣿ ⣧⠹⠀⣆⣿⣿⣿⣿⣾⣷⠈⠀⠀⠀⣷⢻⠉⡗⣸⣿⣿⣿⢸⣷⢈⣿⣿⣿⢿⡎⠘⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⢿⣷⣿⣿⣿⣿ ⡀⣷⠸⠀⣧⣿⣿⣿⢿⡿⢻⠘⠈⠁⡈⣿⢻⡀⢻⣇⣿⣿⣿⡈⢻⡇⣿⣿⡇⠸⢀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡜⠈⣆⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡼⣿⣿⣿⣿

⠀⣿⠬⠤⣸⠀⠀⠀⠀⠀⡏⣩⡚⢓⡿⣼⢁⡞⣠⠤⠁⡞⢏⣤⢧⣿⠛⡾⢀⠁⣿⠀⠀⢧⡄⠸⠀⣇⠘⠀⣷⠀⣧⠀⢸⡏⠀⠀⠀⠀ ⠀⡇⢹⡞⢀⠀⠀⠀⠀⠁⣹⣉⣋⠖⣼⠁⡾⢀⠀⠁⡽⡞⣀⣅⣸⣇⢸⢸⠀⡇⣿⠀⠀⡀⢻⣇⠈⠀⢷⠀⡆⠘⡇⠈⢸⣷⠀⠀⠀⠀ ⠀⡇⣿⢠⠀⠀⠀⠀⠀⡏⣦⢘⠀⡏⢁⡼⢀⠀⠃⡿⡜⠀⠋⡿⣿⣿⣿⢹⠉⡏⣿⠙⠀⠀⡇⠹⢳⠀⡇⣼⠤⣼⡷⢸⢹⡏⠀⠀⠀⠀ ⠀⡇⢰⠀⠀⠀⠀⠈⠃⣻⠀⢸⠇⢠⡞⢀⠀⠃⣿⣼⠀⠟⣿⣾⣷⣴⣀⣀⠀⠀⠀⡀⢆⠛⡇⣦⡽⢻⠀⣿⣷⣿⡷⢿⣿⣇⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⢁⡿⣧⠃⢻⢸⠇⢰⠀⠃⣿⣿⠚⠴⣠⢀⠀⠁⠘⠀⠁⠉⠉⠞⠤⠑⡀⣾⢹⣄⣿⢹⡄⡶⣷⡟⣿⣿⡟⢸⠀⠀⠀ ⠹⠀⠀⠀⠀⠀⠈⡏⢰⡿⡇⣾⠀⠀⠀⠁⡿⣼⢀⠀⠀⠀⠀⠀⡆⢰⠀⢋⡴⢀⠀⠀⡀⢳⠸⣀⢢⡝⣿⠸⠀⠀⣄⣿⣿⣸⣿⠀⠀⠀ ⣾⠀⠀⠁⢰⠇⢡⣾⠃⣼⣿⢀⠀⠀⠀⡿⣿⣴⣎⠀⠀⠀⠀⠀⠁⠛⡴⢀⠀⠀⠀⠀⠀⡇⢀⠀⠀⡀⣦⣿⠹⠀⠀⡆⣿⣿⣿⠀⠀⠀ ⢰⠀⠀⡜⠀⡷⡟⢰⡿⠇⢸⠀⠀⠀⠇⣿⢀⠎⢀⠀⠀⠀⠁⠟⣼⢀⠀⠀⠀⠀⠀⠀⠉⡿⠻⠘⠀⠀⠀⡀⣦⠻⠈⠀⣧⣿⡟⢸⠀⠀ ⠀⠀⠃⠀⠁⡿⣾⡏⢡⣾⠀⠀⠀⠁⡿⢰⡌⢀⠀⠀⠀⠁⡿⣿⣶⠴⢦⠴⠤⠤⠤⡠⣄⢦⡓⢿⠈⠀⠀⠀⠀⢆⢿⠀⠁⣿⣾⢸⠀⠀ ⠀⠀⡟⠀⡇⣿⣿⣿⡿⢠⠀⠀⠀⡏⣼⠀⠀⠀⠀⠀⠀⡶⣴⠤⠤⠤⠤⠤⠶⠤⠤⠤⠤⠤⠤⣤⣶⠠⠀⠀⠀⠀⡄⢳⡄⣽⢿⣿⠀⠀ ⠀⠀⢸⠀⡏⣿⡞⣻⣸⠀⠀⠀⠇⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⡆⣾⣿⠸⠀ ⠀⡇⢹⠉⣿⣟⣾⣶⢀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠐⣷⣿⢿⠀ ⠑⡞⣠⣇⣿⡀⢸⠀⠀⠀⠀⡇⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠀⠀⠿⠹⠀⣿⠹⡀⣿⣿⠀ ⣠⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠁⣨⣄⠀⢿⣿⠘⣇⣿⠘ ⡴⢃⠴⠁⠘⠃⢸⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡤⣋⠖⠴⠤⠥⣉⠩⠀⣷⣿⢻⡀⣾⢿ ⠀⡆⠈⡇⢹⡇⢀⠀⠀⠀⠀⡿⠀⠀⠋⠞⡴⣤⢤⠤⠤⠶⠲⠒⡖⠙⠀⠀⠀⠀⠀⠀⠀⣸⠀⣹⠋⠛⠛⠛⠀⣄⣿⠘⡄⣿⣿⠈⢧⣿ ⠂⠉⣉⣉⡞⡏⠀⠀⠀⠀⠀⣸⠁⠟⣰⠀⠀⠀⠀⠿⠼⠶⠛⠈⠀⡟⠻⠀⠀⠀⠉⠉⠉⢻⠛⣿⣿⣽⣉⣷⣿⠘⡏⣿⢾⣷⣿⢸⠀⡇ ⠀⠓⠚⡠⠋⣾⠀⠀⠀⠀⠇⢻⡿⣸⠀⠀⠃⡿⣿⣼⣀⢦⣿⣿⡿⣿⣿⢷⠈⣷⣀⢀⠀⣆⠻⡃⣿⣦⣿⣿⣿⣿⣾⣶⢠⡇⣏⢸⠀⡇ ⠀⢉⠞⡠⡏⢸⠀⠀⠀⠀⡇⣿⣿⣿⢿⠿⡿⣿⣿⠻⡿⣿⣿⣿⣿⣿⢿⠀⢷⡇⠘⠀⠀⠀⣆⠹⣄⢽⣧⣷⢚⠀⢀⠀⠀⡟⣄⢸⠀⡇ ⣠⢀⠀⠀⡇⣶⠲⠀⠏⡜⡇⣨⣄⡷⣛⣖⣶⣶⣶⣶⣤⣧⣿⣻⠛⣶⣠⠀⡄⣹⢸⠀⠀⠀⠀⡇⢺⣿⡟⡸⢸⠀⠀⠋⡿⣺⠀⢸⠀⠀ ⠸⠀⠀⠀⡟⠀⠀⠃⢸⢠⡇⣀⢦⠳⣍⠳⠈⠀⠀⠀⠀⡄⣿⣿⢀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀⣧⡍⣿⢿⣿⠿⣴⣠⡏⢸⠃⢸⠀⠀ ⢹⠀⠀⠀⣿⠀⠀⡾⠀⠀⡇⠰⠀⠀⣦⣿⣶⠿⠾⠿⠿⠿⣿⣿⣾⢷⢿⠘⠀⡄⣿⠀⠀⠀⠀⠀⡀⣿⣿⣼⣧⠀⠀⠃⣸⠀⡏⢸⠀⠀ ⣆⠀⠀⠀⣸⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⡀⢳⡈⢷⠈⠀⠀⣸⣆⣸⣦⣶⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⡇⢸⡇⠀⠁⡼⠀⠃⣿⠀⠀⠄ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢼⠲⠗⠘⠀⡀⢷⠈⢷⠈⠀⢸⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠁⡼⠀⠁⣼⣼⠀⠀⠀ ⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡇⣿⣗⠭⣦⠙⠀⠀⢧⡀⢻⠃⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⣴⠉⠋⣴⡆⠀⠀⠀⠠

⠀⠀⠀⠁⠓⠛⠛⠛⠖⠷⠓⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠚⠓⠿⣿⣿⣿⣴⠋⡿⢻⢈⠀⡚⠵⡟⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⡆⡀⢘⠀⠉⠒⡿⡶⣣⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣀⣀⢀⣇⣽⣿⢠⡟⣀⡀⣿⣸⠟⣿⣿⣿⣿⣰⣆⣿⣿⣿⣿⠘⠀⠀⠏ ⠀⠀⠀⠀⢣⢫⠉⢸⣼⢀⠏⣿⣿⣿⣾⣤⣠⣀⣀⣀⣀⣀⣀⣀⢀⠀⡤⣶⣶⠓⣸⠀⠁⣿⡼⣤⣤⣿⣾⣠⠀⠁⣿⣿⣿⣿⢿⠟⡿⣿ ⠀⠀⠀⠀⠀⣁⢯⡿⢿⠾⣹⠔⣣⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⠙⡾⣠⠀⠀⠛⣾⣷⠿⠻⡿⣷⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠜⣀⠀⡀⣄⠗⢹⠞⢀⠀⠀⠀⠀⡄⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣛⣿⠚⠉⠛⡴⣀⣀⠧⣾⣠⠀⠀⡏⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠃⢿⠻⠙⠉⠉⠏⣰⠀⠀⠀⠀⠀⠀⠋⠠⣀⣀⣀⠤⠤⠢⠓⠈⠀⠀⠀⠀⣷⢿⣾⢠⠀⠀⠇⣿⣷⠿⠶⣷⣿⣿⣽⢿⠙⡈⣀ ⠀⠀⠃⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠁⡴⢀⠀⠀⠀⠀⠀⠀⠀⠏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣻⡾⢀⠀⠀⣄⣶⣿⣿⣿⣿⠻ ⠀⠋⣽⣛⣼⣤⣤⣥⣰⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠉⠞⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠛⡙⣿⣿⣿⣿ ⠞⣦⢀⠀⢷⠈⠀⡸⠀⠀⠀⠀⠀⠀⡿⠙⠈⠀⠀⠉⠟⠿⣾⢲⠴⣧⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⡻⣄⠀⠀⣄⣷⣿⣿⣿ ⢤⠭⡭⣿⡿⢿⡟⠈⠀⠀⠀⠀⠀⠀⣆⣿⣻⣍⣿⣴⣠⠀⠀⠄⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⡟⢠⠀⠀⣦⡿⣿⣾⢳⣇ ⣿⣿⣿⣿⣿⣷⣿⣿⠸⠀⠀⠀⠀⠀⠀⣄⣶⣷⢚⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⣏⡿⣿⠹⠀⠀⣿⣿⢺⡤⣿ ⣿⣿⣿⣴⢁⠟⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣻⡴⣀⣄⣷⣿⠈⠇⣿⣿⠋⠟⣾ ⣶⣻⠋⠏⣿⣿⣿⠿⠿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⣿⣸⠀⠿⠟⣿⡾⢁⡿⣿⣹⣄⠿⣿ ⣿⠿⣾⣤⣠⣀⣉⣟⣿⣟⣿⢯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣟⠿⣿⣶⣶⢋⣿⣿⣴⡈⢧⡌⣿ ⣿⣿⣿⢿⡿⣬⣤⣤⣤⣤⣦⣶⣷⢿⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢁⠋⡿⣿⣾⣠⠏⣾⠱⣧⡜ ⣝⣿⣿⣿⣿⣿⢿⠴⠶⠽⠭⠭⠠⠓⠛⢹⠉⠉⠉⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⣾⣶⣿⣶⣡⠟⣿⣹⠀⡆⢻⣷ ⣿⢿⣎⣿⣿⣿⣿⢿⠲⡏⢚⣄⣤⣠⣉⣉⣞⠤⡤⣦⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢒⠔⣋⣷⢀⡄⢻⠈⣏⣿ ⣿⣮⣿⣿⣿⣿⣿⣿⢻⣇⢹⠀⠀⡇⣿⣿⢈⠀⠉⠋⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡄⠳⡈⣷⣼⢠⠀⠀⠀⡇⣿⣿⣿ ⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢹⠈⠀⡀⣦⣻⣿⡿⣾⣷⢼⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⣦⢿⡘⣷⣽⠹⠀⠀⠀⠁⡟⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣄⣧⣿⣿⢿⠛⠙⠉⣉⣈⢀⠀⠉⠏⣩⠀⠀⠀⠀⠀⠁⠊⠛⠜⡦⣌⢻⠀⠀⣀⣷⣿⣼⣷⠸⠁⠛⣿⣿⣿⣿⣿ ⡄⣷⣿⣿⣿⣿⣿⣹⠋⡯⣸⣧⣿⣶⣶⣿⣿⣿⣿⣿⣿⣴⢁⠉⠛⠹⠰⠀⡟⢻⡄⢹⠀⣆⡜⣿⠹⠱⡄⣆⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⢿⡆⣿⠹⠀⡧⢿⠚⠒⣷⣿⣏⣹⢻⡟⣿⡟⠉⣇⣿⠹⡆⠘⠀⢆⡌⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠻⠈⢳⢿⠈⡄⣹⢧⠀⣇⠸⣷⣹⣧⣌⣿⡞⠘⣇⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢰⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠐⠀⠀⠀⠀⠀⣄⠧⢿⠀⠀⠀⠀⠀⣀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⣦⡘⣀⣁⣀⢄⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠂⠽⠬⠤⠤⠤⡶⠘⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⣆⠸⠀⢄⠘⠀⡀⢦⠜⠳⠓⠈⠀⠀⠀ ⣷⢤⠒⠑⠉⠉⠈⠂⠒⠒⣖⢶⠲⠉⠀⣆⠘⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⣄⡹⢣⡀⠣⠈⠀ ⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⡆⡿⠸⠀⢳⠀ ⠀⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⠀⠃⠟⠴⣿⠙⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⡄⢸ ⡇⣿⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡋⣿⣰⣀⣀⣤⣿⣸⠷⠊⠈⠀⠀⠁⡼⠀⠀⠀⠀⠀⠰⠀⠀⡇⢸⠀⠀⢸ ⡇⡆⠀⢆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢁⡜⢀⠀⠀⠀⠄⡤⡵⠳⠈⠀⠁⠋⡶⠘⠀⠀⠀⠁⡜⠀⠀⠀⡇⠀⠀⠀⢸ ⡆⠸⠠⠀⡀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡷⠀⠃⠀⠀⠀⠀⠀⡀⢇⣟⠾⣶⠙⡷⢀⠀⠀⠚⣠⠀⠀⠀⠀⢰⠀⠀⠃⢰ ⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⣠⠀⡏⠹⠀⠀⠀⠀⠀⠀⠋⢠⣿⢿⠘⡀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⡀⠦⠙⠀⠀⠀⠀⠀⠀⠀⠼⢀⠉⠒⡦⣟⣿⠀⠀⠀⠀⠀⠀⣆⠛⣼⣷⣗⠿⠘⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⠀⠀⠁⠔⡁⣉⠿⠙⠈⠀⠀⠀⢧⠀⢢⠉⠀⡁⣴⣤⠢⠙⠋⠴⠠⠤⣷⠈⡀⢳⡆⣿⠸⡄⠹⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀ ⠀⠀⣿⠴⢀⠀⠀⠀⡀⢤⠑⠀⡀⢷⣦⡬⢰⡇⠈⠀⠀⡀⢸⠀⠀⠆⠀⢳⠀⡇⢶⣴⢀⠏⢠⠀⠀⠀⠀⠀⠁⡜⠀⠀⠀⠀ ⠀⡆⣸⠀⠀⠀⠀⠀⠀⠀⡀⢦⠘⡀⢄⣤⠀⠇⣌⠢⠈⠀⡄⠀⠀⠀⠀⡄⠀⡇⣿⢉⠎⢠⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⢄⠢⠖⠷⠈⢄⠣⠙⠀⠀⠁⣰⢀⠀⠀⠀⠀⠀⠁⠚⡠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⡇⢚⠶⡷⢉⡈⣏⢳⠀⢿⠷⠙⠉⠊⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠃⠼⠣⠚⡠⢀⠜⠁⠀⠀⣀⣦⡼⢧⣿⠀⡀⣧⠈⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠂⠟⡼⠀⠀⠀⡏⠾⡦⢷⣴⣿⢴⡇⠋⠔⣠⠀⠀⠀⡆⣿⢸⠀⠀⠀⢻⠀⠀⡆⢿⣶⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠟⣿⢛⠾⢀⡇⣹⠉⠉⠀⠈⠀⠃⠿⣿⣿⣿⢿⠀⠀⠀⣸⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣴⣟⢙⠀⡷⣿⣿⣿⣴⢀⠄⣿⡙⣀⣎⣿⣠⠀⠀⠇⢫⣿⠀⠃⢠⡈⢧⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡀⣦⠻⡟⡚⢩⠀⠀⠀⠀⡇⡀⣿⣾⢠⠀⠀⠂⣴⢃⢰⠀⡄⡤⣄⠤⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣃⣖⠻⣉⢄⠤⠯⣰⠀⡏⢠⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠀⡎⠰⡀⣤⣤⣷⢈⠀⠖⢀⠀⠋⠗⡽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡦⠓⣿⢿⠀⠛⠛⣼⢥⠯⠴⣠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⢧⡏⠀⠁⠉⠉⠀⠀⠀⠀⠁⠉⡉⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⡄⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠦⠑⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠣⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢀⠀⠀⠀⠁⠚⠐⠀⠀⠀⠀⠀⠀⠃⠉⠀⣀⢤⠑⠀⠀ ⠀⠀⠀⠀⠁⢙⡴⣅⢿⠲⠓⠙⠉⠈⠀⠀⠀⠀⠁⠋⠿⣧⣿⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⠓⠈⣆⠀ ⠀⠀⠀⠀⠞⣩⠞⣠⢀⠀⠀⠀⡀⠀⠀⠤⠦⣿⣶⣿⣾⣭⣿⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⠀ ⠀⠀⠁⡿⡞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡿⣻⣖⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠃⣼⠀⠀⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢠⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⡄⢳⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⢸⣀⢀⣄⠠⠠⠤⠒⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠇⣻⡖⠲⠉⠀⠀⠀⠀⠀⠁⢏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣤⠁⡿⠻⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⢀⠀⡀⣷⠀⠀⠄⠀⠉⠋⠀⠑⠉⠐⠉⠀⡋⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠀⠀⡀⢤⠶⠴⣤⣯⣟⢿⠙⠈⣀⠧⠳⠉⡉⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡿⣻⣀⣀⣄⣦⠻⡈⢸⠀⠀⡀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣹⢫⠀⠁⠀⠀⡀⣿⢹⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠊⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣼⠀⡇⣿⢿⠛⣽⣶⣷⠻⠈⠀⠀⡀⠳⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢓⠈⣦⣀⣀⣀⣀⣄⡳⠈⣈⠣⠈⠀⠀⣄⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣄⣦⢷⠻⠉⠀⠀⠀⣄⠻⠀⣆⠙⠀⠀⡀⢦⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⣄⣽⢄⠢⠑⠉⡀⢦⠙⡇⠸⠀⠀⠀⡀⠣⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⡾⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣄⠳

⡀⢳⠀⠀⠀⢦⠘⠀⠀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣳⠀⠀⠀⣆⠸⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠹⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⣀⢤⠲⠙⠉⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⠀⠀⡄⡹⢤⠳⠋⠚⠖⠤⣤⣤⣤⡤⣦⢷⠾⠧⠒⠒⠒⠔⠬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⠀⠀⠋⡖⢶⡘⣧⠘⠀⠀⠀⠀⠀⠁⠞⣠⠀⡸⢀⠀⠁⡟⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⡄⢸⠁⡾⢀⠀⠀⠀⠀⣠⠀⠀⠀⠉⠞⣠⠀⠀⡏⠿⠿⡿⣿⣽⣋⠚⠴⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠀ ⠀⠀⠀⠀⠀⣿⡟⢀⠀⠀⠀⠀⠀⠋⠔⠤⣀⢀⠀⠀⠀⠏⣷⣿⣿⣼⡉⣉⠈⠀⠀⠀⠀⡀⣄⠳⠈⠀⠀⠀⠀⠃⢠⠀⠀ ⠀⠀⠀⠀⠀⣧⢰⠀⠀⠀⠁⠋⡾⢀⠀⠀⠁⠈⠀⠀⠟⣾⣠⣟⣶⣠⣀⢀⣀⣀⢤⠲⠙⠈⠀⠀⣄⠳⠈⠀⠋⣰⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠉⠛⠟⡶⣤⣀⠁⠚⠖⡤⣠⠀⠀⡟⣼⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢾⠴⠤⣤⣤⣇⣰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠃⣼⠀⠀⠀⠁⠛⡾ ⠀⠀⠀⠀⠀⡿⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⡼⠀⠀⠋⠿⣠⣠⠀ ⠀⠀⠀⠀⠀⣿⠘⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⢀⠃⡾⣧⢠⠀⠁⠋ ⠀⠀⠀⠀⠇⣽⠋⠛⡔⠳⠛⠉⠉⠊⠒⠒⠀⠀⠀⠀⡀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠋⣴⠁⢹⠚⠴⣠⠀ ⠀⠀⠀⠀⡏⢤⣧⠘⠀⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢟⠙⠉⠀⠀⠀⠉⠉⠈⠀⠀⠀⠇⢱⠁⣿⠿⣩⢀⠁⠋⠖⠤ ⠀⠀⠀⠀⢼⠁⡿⢨⠀⠆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢀⡀⣀⣤⣤⣦⠶⠶⡶⢶⠻⠙⡿⡀⡇⣹⠀⡀⣀⣀⠀⠀⠀ ⠀⠀⠀⠃⢳⣰⣿⢠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣸⠃⢰⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢻⡀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⡿⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠤⠤⠲⠛⠖⠤⡠⣀⠃⣿⣿⣷⢿⡛⠻⠉⠋⠘⠀⠀⠀ ⠀⠀⡇⢀⡄⡀⢸⠀⠁⠉⠀⡄⠸⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠁⠚⠒⠑⠉⠉⠀⠃⣼⡇⣦⠸⡀⣀⢄⣤⣦⢛⠈⠀⠀ ⠀⠀⡾⣤⠤⠒⣗⠈⠀⡀⣄⣷⢹⢛⠘⠀⠀⠀⣿⢀⠀⠁⠁⠜⢀⠀⠉⠋⠐⡀⣀⢤⣲⣿⢳⢎⠈⠀⠀⠁⠖⣠⡆⠿⠾ ⢰⠏⢀⠀⠀⠀⠀⢦⠛⠀⠀⡀⠀⣀⣀⣀⣄⣤⣿⠈⠋⣻⣰⠂⠤⣀⢀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⠻⡾⢀⠀⠋⣴⢀⠀ ⠄⢹⠉⠉⠉⠉⠊⠒⣴⢦⠑⠈⠀⠀⠀⠀⠁⡟⣱⣷⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠑⣆⣿⣿⢿⠿⣦⣾⠙⠀⠀ ⡄⣤⣤⣦⠶⠓⢍⠲⠈⠀⡀⣤⣶⠽⠦⠓⡿⣿⠀⡇⣿⢋⣠⠀⠀⠀⠀⠀⠀⠎⠃⡏⣿⣿⢻⣴⣿⣏⣷⣿⢹⣼⠁⣿⠋ ⠀⠀⠀⠀⠀⠀⡀⣄⠦⠓⠉⠉⠜⠠⠉⣟⣾⢳⠃⣰⡏⣾⠞⡯⢻⠙⠙⠐⡇⢿⠉⠚⣒⣿⢿⠾⣿⢿⡀⣿⣿⢿⡼⢿⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣲⣟⣙⠈⠀⠀⣼⠿⣿⣿⣿⣿⣿⣿⣿⠖⣿⣿⢿⠛⠈⣿⣸⣿⣿⣴⠿⣘⣿⣿⠞⡇⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⠻⠈⢀⡟⣼⡇⣿⣿⣿⣿⣿⠙⣹⡀⣷⣿⣤⣿⢸⡀⣿⠸⣯⢿⣳⣯⢸⠇⣿ ⠀⠀⠀⠒⠚⠓⠓⠛⠙⠉⠉⠈⠀⠀⠀⠀⡀⣿⢿⣿⢸⡆⣿⣿⢀⣧⣹⣦⣿⠈⡏⣾⠘⡀⢿⠀⡇⢹⣿⣟⠘⣷⢸⡟⡇ ⠀⠂⠒⠶⠶⠤⣀⣀⠀⠀⠀⡀⣀⣀⣄⠷⡹⣇⣦⣿⣿⠈⣴⣸⠀⡀⣧⠘⡄⣿⣿⠀⣦⠀⣇⠀⠇⣿⣿⢠⣄⡿⢻⣸⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⡿⠹⣇⣿⢽⡀⣦⠘⠀⠀⣧⠙⣸⣿⠀⠀⠀⡀⠋⡿⣾⢒⠓⠉⡏⣰⠟⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⢽⣶⣿⢿⠿⣝⠿⠒⠒⡟⣀⣇⠛⠛⠛⠛⣒⢴⠤⣤⣤⣤⣿⡿⣼⢁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⢾⣕⣷⢽⠤⠤⠤⠤⡦⠓⠚⣴⣧⣿⣓⠉⠉⠉⠉⠋⡶⣶⢲⠶⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⣄⠳⢿⣧⣯⠻⠛⠉⠈⠀⠁⠉⡟⣴⣷⣙⣛⣶⣤⢀⠀⠀⠀⠀⠀

⠀⠀⣇⠀⣆⣿⣿⠈⠀⠀⡇⣿⢀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠛⡿⠀⠀⠀⠀⠀⣿⠒⠀⣄⣶⣿⣿⠈⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⣆⣿⢻⠀⠀⡇⣼⠀⠀⠀⠀⠀⠁⣼⠄⠶⡤⣤⢀⡇⠸⠀⠀⠀⠃⢸⠂⠀⠀⠀⠀⣄⢸⠀⠀⡇⢿⡛⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣿⠸⠀⣿⢸⠀⠀⠀⠀⠀⡟⢻⠛⠉⠛⠙⠉⡿⢸⠀⠀⠀⡇⠺⠴⠤⡀⢀⠄⡦⢲⠘⠀⡟⣿⣿⣾⢀⠀⠁⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⢿⠌⣿⢸⠀⠀⠀⠀⠇⣿⣼⣿⣿⣾⠀⣁⣿⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢰⠀⠀⡟⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢸⠀⠀⠀⠀⣿⣤⢀⡀⢀⠀⠁⡟⣴⣆⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⡄⣿⣼⠀⠀⠃⣾⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢿⠈⠀⠀⡇⢠⠀⠀⠀⠀⠁⡟⣴⠀⡇⢸⠀⠀⠀⠀⠀⠀⠏⣻⣉⣿⠀⠀⠀⠘⡞⢀⠀⠀⡿⢀⠋⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢹⠀⠀⡿⠀⠀⠐⠀⠃⡿⣴⠀⠀⡇⢠⠀⠀⠀⠀⠀⠇⣦⣿⣿⡿⠈⠀⠀⣏⢠⠀⠀⡇⣿⣿⣿⣴⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢻⠈⢸⠀⠀⠀⠀⡤⢀⠀⠀⠀⡇⠸⠀⠀⡇⠻⠈⡟⠀⣄⣤⣇⢸⠀⠏⢠⠀⠀⠃⣿⣿⣾⢠⡟⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⢸⠀⠀⠀⠀⠂⠙⠀⠀⠀⠀⢸⠀⠀⡄⠸⣄⣿⠘⠀⠀⡟⢀⠇⣰⠀⠀⠃⡿⣿⣴⠀⠃⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⠀⠀⠀⠀⠀⡀⠾⠒⠹⠀⣧⠀⠁⠉⢿⠙⣀⢀⠀⠀⣾⠃⣰⠀⠀⠃⣿⣿⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠿⣾⣀⣆⣿⣶⣧⠀⠃⣿⣰⠀⠀⠃⣿⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⠀⠀⠀⣷⠼⣶⠖⡿⢰⠀⠉⠟⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠉⠉⠉⠉⠀⠀⠁⡿⢠⠀⠀⠋⣴⣀⠤⣠⢀⠃⠛⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⣀⣀⣧⠚⠴⣠⣀⢤⠲⠋⠛⠶⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢻⠉⠉⠉⠉⠏⠼⣀⠀⠀⠀⠁⠋⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠲⠐⣄⢀⠀⠀⠀⠀⢱⠈⠀⠋⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠋⠰⠀⠀⠀⠀⠀⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡸⠈⠀⠀⠛⣴⢀⠀⠀⠀⠁⠊⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⡿⢠⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠁⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⣸⠀⠀⠀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡜⠁ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⡆⢰⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡎⠋⣿ ⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⠀⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠎⢏⣠⣿ ⠀⣄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠆⢏⢠⠀⠀ ⠀⠀⠀⢄⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠁⣼⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢤⠢⠓⠉⠉⠉⠉⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢡⠊⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⡏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡾⢴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢦⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠖⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⠚⣁⢫⠉⢿⡱⣈⣶⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡿⣿⢞⣤⣦⣷⣿⢰⣦⠷⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣰⠀⠀⠀⣸⡀⢤⢶⠙⣏⣹⣎⣷⣿⣿⣿⣿⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠋⠟⡿⣿⣿⣾⣠⠋⠔⠤⠤⠢⠙⠈⠀⠀⣀⣤⢶⡙⣦⣿⣿⣿⣿⢻⠀⠀⠀ ⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣠⠀⠃⢠⠁⠟⠩⠀⠉⡏⠻⠈⠀⠀⠀⡠⢦⣿⣿⣿⣿⣿⠺⠉⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⣾⣠⠀⠀⡟⠛⣿⣭⣊⣒⣄⣤⣀⣄⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⠈⠀⠀ ⠀⠀⠁⣿⣿⣿⣿⣿⣾⢀⠋⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠿⡿⣿⣿⣿⣿⣿⢻⠀⠀ ⠀⠀⡏⣿⣿⣿⣿⣻⠒⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢼⠀⡶⣶⣾⣤⣾⣤⣤⢀⣿⡿⣿⠀⠀ ⠀⠏⣿⣿⣿⣾⣿⣿⣻⣉⣉⢖⠶⠒⠈⠀⠀⠀⠁⠋⠑⢫⠟⠽⠺⡔⣤⣋⠏⠿⠻⣟⣿⣰⠀⠀ ⠀⣿⣿⣿⣿⠀⣆⣿⣿⣿⠻⠛⠌⠦⣾⢲⠈⠀⣟⢵⡿⣾⣷⢙⠍⠿⣯⣭⢻⡟⡟⣿⣶⣤⠦⠴ ⠃⣧⣿⣿⣸⠀⠀⡏⣶⣿⣿⣿⢿⠝⢉⠛⠒⡠⠀⣠⠀⠀⡀⠰⠀⡀⣀⣀⣀⣠⢀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⢹⠀⡜⣸⠉⣾⣷⢶⣎⣶⢸⢸⠁⠟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⣿⠘⢀⠯⣿⢉⡀⢄⡠⣏⡿⢾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⡞⣷⣶⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⣬⣿⢸⡀⣤⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢢⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠚⠒⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠽⠤⠤⠤⠶⠒⠛⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠁⠉⠟⠶⠴⡤⣀⣀⣀⣀⣀⣀⣀⣀⣀⢄⠤⠤⠦⠶⠒⠒⠓⠉⠉⠉⠉⠈⠉⠛⠿⠿⠭⠦⠶⠻⡈⣻⠈⠀ ⠀⠋⠟⠿⣷⣞⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠖⣤⣷⣏⣿⣥⣀⣷⣿⢿⣿⣿⣄⢻⠀ ⠏⢲⠑⣋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠚⠽⣿⣠⠀⠀⠀⠂⣍⣷⠈⠀⣇⣯⣿⣾⢀⠀⡇⠘ ⣦⣿⠽⠙⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡤⣠⣀⣀⠁⠚⡴⣤⣷⠀⠀⠁⡒⣖⡶⢶⢯⠀⠀⣄⣶⢀⠀⠀⡏⣾ ⠀⣄⣦⡿⣛⢮⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠿⡿⣉⠈⠀⠀⡇⠀⠃⣰⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠂⣾⣤⣀ ⠀⠀⠀⠀⣀⢤⡤⣦⠶⠷⠓⠛⠛⠛⠒⠗⠼⡤⣀⠀⠀⠀⠀⡀⣄⢷⠿⡬⠻⡟⠈⠀⠀⠀⠀⠀⠁⣟⢹⠀⠀⠀⣝⠹⠀ ⣀⣀⢤⠦⠲⠛⠛⠖⠴⡠⣀⣉⠚⠐⠁⡰⠀⠀⠀⠄⠤⠘⠀⠀⠀⠀⣧⡼⣀⢀⣦⠘⠀⠀⠀⠎⣿⣿⣿⠿⠙⠀⡄⣿⠀ ⠀⠀⠁⠚⡴⣀⠀⠀⠊⡠⣀⠀⠀⠀⡁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇⢰⠚⠷⠭⣎⢳⠈⡜⠀⡄⣿⣿⣶⡽⢾⡴⢀⠀ ⠞⡭⢀⠀⠀⠀⠀⠇⢀⠀⠀⠁⠊⡴⢀⠀⠀⠀⠀⢻⠉⠀⠀⠀⠀⠀⡜⠀⠀⠀⣄⠳⠈⣆⢸⠉⠋⣴⡤⣀⠀⠀⠀⠀⠀ ⠈⠒⣔⠲⠉⠀⠀⡀⠁⠊⠔⣠⠀⠀⠀⠀⠀⠀⠃⣾⢠⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⡇⢸⠀⣄⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢄⠑⡬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠃⣰⠀⠉⠉⠀⠀⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⢄⠱⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠁⡽⠋⠴⣀⢀⠀⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠱⠀⠀⠀⠀⠀⠀⢄⠙⠀⠀⠀⠀⠁⡟⠀⠀⠀⠀⠀⡞⣠⢀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢢⠈⠀⠀⠀⠀⠀⣄⢷⠿⠺⠶⡟⢰⠀⠀⠀⠀⠏⢠⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢆⠙⠉⠀⠀⠀⠀⠀⣄⠳⠏⢰⠀⠀⠀⠀⠇⣰⠁⠉⠉⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⡷⠸⠀⠀⠀⠀⠀⡀⣦⠸⠀⠀⠀⢿⣰⠀⣸⠀⡝⢹⠉⠒⣴⣧⢽⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⢰⠀⠀⠀⠀⠓⠈⠀⡇⠘⠀⠀⣼⠀⠏⢹⠉⡿⣴⠀⠀⠁⣾⣥⣊⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⡄⢸⠀⡇⢰⠀⡇⢘⠎⢀⡟⣿⣠⠀⠀⠀⡀⣋⣻⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠃⣲⣾⢀⠀⣿⣰⠀⠀⠀⠀⠓⣿⣟⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠃⣠⡞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣄⣷⣹⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠏⣨⡞⢀⠀⠀⠀⡇⠐⠋⠙⠈⠀⠁⢀⠀⣄⣦⢳⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠁⣹⡴⢀⢆⢳⠀⠗⠺⠀⠀⡃⣭⣷⣿⢿⣼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡿⣰⠀⠀⠀⡀⢦⠉⠊⠠⠰⡟⡀⣮⣿⣿⢠⠀⠀⠀⠀⠀⡇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⢠⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇⣿⡞⣶⣧⢰⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⢶⡷⢻⣾⢸⠀⠀⠀⠀⠀⠀⡀⢳⠏⠖⣠⠀⠀⠀⠀⠀⠀⡏⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠏⣰⣀⠀⡀⢿⢻⠛⠤⠤⠛⠉⠉⠉⠀⠁⠉⠈⠀⠀⠀⠀⠀⠞⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠇⣴⠸⠀⠀⠃⣰⡀⣇⣵⣠⠁⠞⣀⠀⡃⣻⢔⠠⠀⠀⠈⠋⡰⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠋⡾⢠⠀⠀⠃⢰⠇⢀⠀⠀⡼⠀⠀⡟⢠⠇⣴⠀⠀⠗⣸⠀⠀⠀⠀⠁⣾⢠⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⣀⠀⠀⠀⠁⡹⡼⢀⠀⠀⠏⢀⠀⠇⢸⠀⡘⠀⠀⠀⡼⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⡾⣧⢀⠀⠀⠀⣾⠀⠀⡇⢀⠀⢸⠀⠀⠁⢸⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⡆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠃⢰⡇⠀⠀⠀⡇⢀⠀⠀⡇⢸⠀⢇⠀⠀⡄⢸⠀⠀⠀⠏⣰⠤⠑⠉⠀⠀⠁⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⡗⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⣧⠈⡀⢲⠀⠀⢸⠀⠁⡞⢀⠀⠀⠀⡀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⣧⠃⢰⠀⠀⠀⢸⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⢸⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⡇⡸⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⢄⠙⠀⠁⢿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⡇⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠉⠘⠁⡏⢀⠁⠰⠋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⣵⠁⡹⣰⢿⡨⠏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⢀⠀⠀⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣄⠤⠲⠉⣧⢿⠃⢹⠰⠁⠛⠘⣻⠂⡶⢳⢳⠀⠀⠤⣠⣀⣄⠤⠢⠙⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣸⡇⡏⠀⡃⣽⣾⡆⠹⠀⠀⢦⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠇⠸⠀⠁⠟⢀⡷⣻⠞⡧⣿⢸⠆⡙⢄⠳⠈⣧⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠛⣿⠀⠀⡟⣿⠋⡶⣦⠈⡞⣹⢻⠑⡆⢿⣻⣼⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⢲⠗⣿⣴⢀⠋⠻⣶⢸⡍⣿⠻⢻⡀⣄⢷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⣾⢀⠁⡿⣴⣧⠛⣿⢿⣿⣟⣾⠷⠙⠀⢳⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠏⡿⣠⠃⣿⣿⣿⣿⣵⣿⢻⠈⣦⠻⡇⠈⠀⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠇⣾⢉⠞⣿⣟⣫⣴⣷⣿⣶⣼⣾⠘⣆⢸⢧⠁⠀⡀⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⡞⡆⠈⡇⠀⣿⣿⢹⠀⡏⣼⠀⣧⣆⢿⠀⢸⠁⢶⢜⠑⠀⡀⢦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⠀⠞⢦⠙⢳⡟⡧⣾⣶⣿⢿⣿⢸⠀⡟⣼⡇⠋⢺⡖⠠⡁⠻⢌⠓⠈⠀⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠈⠁⡖⠒⠙⡈⡀⣿⣴⢛⣿⣿⢷⣮⢹⡟⣿⢈⡇⠁⠋⠟⣸⢀⠀⡀⠦⡈⠢⠀⠀⣄⠱⠀⠀⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡴⢀⡠⠎⣠⠀⡏⣷⣿⣿⣿⠀⣿⣟⢠⠃⣿⣿⣿⣿⢈⡇⣿⣿⣶⠀⠀⠀⠁⠈⡀⢧⡘⠀⠀⠀⢦⠟⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠞⢠⠀⠋⡴⠺⠑⠉⣀⠘⣀⣇⣸⠇⣿⣿⠿⣾⣧⣿⣿⣿⢸⡇⣼⢀⠀⠒⠔⡤⣀⠀⠏⣸⡀⢣⣌⠳⠁⢰⠀⠀⠀⠀ ⢀⠀⠀⠀⠁⡴⠀⠁⡔⢀⠄⢸⠀⡼⣀⣤⠹⡟⠿⣿⣹⣿⣿⠀⣷⡁⣿⣿⢼⡷⢺⠛⠛⠛⠒⠔⡤⢧⡟⣿⣠⣧⡉⠫⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠀⠟⣻⠀⠀⠀⢣⡇⢹⠉⠉⣲⣼⡠⣸⣷⣿⣸⠀⡇⡼⣿⣄⢹⡀⢸⡀⣄⢠⠈⠃⠿⣿⣾⣤⠘⡇⣿⣿⢀⠀⠀⠀⠀⠀ ⠀⠀⢇⠀⠃⡶⣖⣿⠙⠀⠀⡆⣿⢻⠒⠀⠃⢸⠃⢰⠀⣆⢸⠀⠀⣷⢰⠀⣧⠀⢹⠉⠀⠁⢟⣿⣿⣿⣟⡟⣿⡈⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⢺⠑⠉⡄⣻⢠⠀⠀⣆⣿⠙⠁⠏⢻⢻⠉⠈⠀⢀⠀⠀⠀⠀⠉⡍⠚⡖⡷⣿⣿⣿⣦⣿⣷⣹⣟⣴⣠⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠀⢱⠀⠀⣀⣤⢦⠒⠛⠟⡾⣠⢀⠀⠀⣭⠈⣀⣤⠾⠛⠛⠼⣠⣉⣉⢈⠀⠀⠀⡀⣤⢷⣿⠖⣤⢀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢷⡄⠸⠀⠀⠀⠀⠁⡜⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡿⣽⣞⣠⣀⠈⠂⠒⠒⠒⢄⠀⠈⣄⠸⠀⠀⠀⡰⠀⠀⠘⠀⠀⠀⠀⠀

⠀⠀⠀⡄⠶⠙⠀⠀⠀⣿⣿⣿⣿⢀⠋⢾⢴⣥⣽⣾⣤⣀⠀⠟⡭⣉⠭⡛⣀⣦⢷⢬⠤⠤⣦⣿⣿⣿⣿⢻⠀⡀⢻⣷⠘⠀⠀⠀⠀⠀ ⢿⠙⠀⠀⠀⡀⢦⠙⠁⣿⣿⣿⣿⡼⣀⠀⠃⡾⣠⠀⠀⠀⠀⣄⣶⣤⣶⣴⢀⠀⠀⣦⠻⠉⠔⣦⣿⣿⣿⣿⢿⠈⣧⡾⢿⠃⠀⠀⠁⠟ ⣿⣿⢿⠙⠀⠀⠀⡀⣧⣯⣿⣿⣸⠀⠀⠏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠘⠀⣄⣿⣿⣿⣿⢿⡈⣿⣿⡿⠿⡿⣿⣿ ⣿⣿⣿⣿⣿⠾⠛⠋⣴⣟⣿⣼⠀⠀⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢛⡴⣁⠟⣿⣿⢹⠋⡿⡟⠞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠛⣏⠙⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣾⣤⣁⠛⡿⣿⣿⣿⣿⢹⡏⣿⣿⢹⠙⣋⡯⣿⠿⠟⠀⠀⠁⢿⠘⠀⠇⠛⡿⣽⣮⢙⣟⣿⣿⢻⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣤⣠⣤⣏⠁⠘⠁⡾⣇⣿⠹⠀⣇⣻⣖⣄⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣦⣿ ⣠⢀⢧⠈⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠺⠃⡿⢳⡿⢈⡟⣼⣿⣿⣿⢻⡏⣿⣿⠿⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⡀ ⠀⠀⠀⢧⠈⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢸⡟⣯⣇⣿⢿⣿⣿⣿⣿⡟⣿⣿⣿⢿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⡀⢦⠙ ⠉⠒⠴⡠⢇⠘⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡀⢦⠓⡈ ⣄⠲⠟⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠛⣿ ⠀⠀⠀⣇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣎⣿⣿⣿⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣠⣴⢀ ⠀⠀⠀⡆⠈⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣏⣼⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡞⢀⠀⠀⠀⠀⡆ ⠀⠀⠀⠁⢸⣁⣠⡇⢸⢸⢸⡄⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⢹⠉⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⡇⠀⡎⢸⠹⢂⠈⡄⣷⣪⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣸⡇⢠⣾⠀⡀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⢀⠀⢸⠃⢠⣆⡙⠢⡉⠢⠙⣌⣷⡻⣀⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢞⣡⠞⣡⠞⢸⠀⠀⡄⠹⠀⠀⠀⠀⡅ ⠀⠀⠰⠀⡏⠀⡼⠀⠈⠁⣜⠢⢝⠢⡑⠄⡢⣷⠺⠛⠉⠀⠀⡀⣴⢀⠀⠀⠉⠋⡛⣿⣪⣷⣫⠴⣩⠖⣠⠀⢇⠀⠀⠀⡆⠘⠀⠀⠀⡀ ⠀⠀⠀⠀⢰⠀⢸⠀⢻⣰⠀⠀⠀⣀⠢⣑⢌⠠⠒⠒⠀⣀⣉⣉⣉⣉⣉⣉⠉⠈⠒⠒⠤⣁⢿⡠⢦⠙⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠄⠀⠀⠀⠤⠦⠶⠶⠶⠴⡤⣠⣀⠣⠀⡀⠳⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢹⡞⢳⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⠈⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⣷⠘⠀⠀⠉⠉⠚⠖⠴⠤⠲⡟⢸⠀⡟⢸⠀⠀⠀⡇⠸⠀⠉⠞⠤⠤⣀⣀⣁⣠⢤⠤⠲⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡟⠚⠴⣠⣀⠀⠀⠀⠀⠀⠁⣼⢀⠏⣠⣧⠘⠀⠀⠀⢻⠇⣰⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣀⢤⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢐⠀⠀⠋⠖⣠⣇⠈⠀⠀⠀⠀⠀⠀⠀⠃⡼⠇⡾⢀⠀⠀⣇⠻⠈⠀⡇⡘⢸⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠏⣴⢀⠀⠀⠀⢳⠈⠀⠀⠀⠀⠀⠃⣹⠞⣷⠀⠁⠈⠀⡀⣸⣄⠳⠉⣿⣿⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⣴⢀⠀⠀⠀⠀⠀⠀⣀⢤⠳⠈⠀⠃⣿⣰⠀⡀⢻⡟⣿⠙⠀⢸⠀⠀⣄⣿⣨⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⢹⠋⠛⠛⣿⣿⣿⣿⣿⢸⠀⠀⠀⡀⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠙⠀⠀⠀⠀ ⠀⠀⠃⢰⠀⠀⠀⠀⠀⠉⠋⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⠻⠈⠋⠙⡟⣷⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠀⠀ ⠀⠀⡇⠀⠉⠛⠟⠿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣴⣤⣀⣀⣠⣀⢀⠀⠀⡀⣦⣿⣿⢻⡀⣦⡿⣿⣿⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈ ⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠀⠀⡄⣷⢿⠈⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄ ⠀⠀⡟⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠉⠉⠈⠏⣿⣿⠀⠀⠀⠀⣧⢿⠉⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⣤⣤⣿⣿⣿⣿⡿⣾⠀⠀⠀⠀⠀⣿⣸⢧⡈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠋⠞⠶⣤⣤⣤⣤⣤⣯⣿⣾⠉⡿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⣿⣿⠈⣄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣿⣾⣡⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⠿⣿⣿⠿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⣿⣼⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣸⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⣿⡾⣤⣀⠀⡀⣿⣯⣸⠀⠀⠀⠀⠀⠀⠀⠂⣼⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠟⡿⣶⣠⢂⠉⠀⠀⠀⠀⣄⣷⢸⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣰⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠁⠟⣶⣤⣀⢤⠦⠄⣤⢤⠢⠒⠒⠖⣤⢤⠢⠓⠉⠉⠊⠖⡠⢀⡀⢤⠤⠶⠤⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠁⣼⢀⠟⣽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⢤⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠁⠉⠉⡏⣿⢛⡶⣠⣀⣀⢤⠤⠲⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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