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010101 0101010 01010 0101 1010101 10 01010101 01010 1010 10101 1010 101010101 10 10 0101 0101 010 010 010 010101 101 101 101 1010 010 10 0101 10101 101 01010101 01010101010 01010 101 1010 101010 010101 01010 1010101010 010101 0101 01010101 10101010 01010 1010 010 101010101 0101010 01010101 010101010101 010 010101010 10101010101010101 01010 01 1010 01 101 010 10101010 101 10 1010101 010 10 0101010 0101 0101 010 10 10101010 010 10101 01 0101011101 10 01 010101010101010 0101010 10 010 10 0101 01 101010 10 1 01 0101 10101010️
⠀⠀⡠⠤⠤⢀⡠⢤⡒⠢⠄⠀⠤⠐⣒⡤⢄⣀⠤⠤⢤⡀ ⠀⢸⠀⡄⠚⠃⢀⡴⡃⠀⠀⠀⠀⠘⢱⡁⠀⠀⠐⠆⠀⡇ ⠀⠀⠱⢦⣴⣾⣿⣶⣤⡑⢄⠀⡠⣂⣥⣾⡷⣶⡤⢤⢺⠀ ⠀⢠⢡⡿⣽⣿⣿⣉⣿⣷⠈⡞⣰⢻⣾⣿⡏⢹⡽⣆⢹⠀ ⠀⢸⢸⡥⢿⣿⣿⣿⣿⣺⢀⡇⢿⣸⣿⣿⣿⣿⣧⡟⢰⠀ ⠀⠈⢆⠙⢯⣻⣛⣫⠷⣣⢾⢱⡌⠷⣟⣿⣛⣯⠾⢡⠎⠀ ⠀⠀⢸⠉⠒⠒⠒⠒⠊⠁⡈⢸⠈⠑⠢⠭⠭⠔⠊⣱⠁⠀ ⠀⠀⢸⠀⠰⠄⠀⠀⢀⠴⡇⢸⢄⠀⠀⡔⠳⡀⡀⡘⠀⠀ ⠀⠀⢈⢧⠀⢶⠄⢠⢎⠀⡆⢸⢀⣣⠸⡠⣤⠇⢱⢧⠀⠀ ⠀⠀⠠⣬⡆⠁⠒⠒⠍⡰⡇⢸⢖⡲⠖⠒⠒⠢⣎⠸⠀⠀ ⠀⠀⠠⢇⡟⠛⠛⠙⠛⠿⣇⣸⠿⠟⠹⠿⠿⢹⢻⠀⠀⠀ ⠀⠀⠀⣎⢙⠱⣖⣒⣒⡏⠙⠓⠒⣶⣖⣲⡖⠺⢡⠀⠀⠀ ⠀⠀⠀⢷⡟⠀⠀⣶⠀⠀⠀⠀⠀⠀⣷⠃⠀⢳⡞⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⢀⠉⡀⠀⠀⠀⠀⢀⢿⡀⠀⠀⠤⠀⠀⠀ ⣀⣀⣀⣀⣿⣾⠿⣿⣃⣀⣀⣀⡀⣺⣿⣷⣿⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣀⣤⡤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠉⠀⠈⣉⡓⠒⠚⠉⠴⢶⠀⠈⠉⠉⠂⠉⠉⠀⢠⡶⠶⣌⠙⠒⠒⠒⠋⠉⠉⠙⢷⣆⠀⠀⠀ ⠀⠀⠀⢿⠀⢀⡀⠘⠿⠃⠀⠀⣠⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣦⠀⠀⠀⠀⠀⠘⢿⡆⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠈⢣⡈⠁⠀⢀⣠⣴⣾⣏⣈⠉⠒⢄⡀⠀⠀⠀⠀⣀⡤⠖⠛⣳⣦⣄⣀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⢉⣿⣿⣿⣿⣿⣿⡿⢿⣦⡀⠱⣄⠀⢀⠜⢁⣠⣾⣿⣿⣿⠿⣿⣿⣏⠛⢻⡉⡇⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⢰⣿⢋⣿⣿⣿⣿⠋⠁⢾⣿⣿⡀⠸⣄⡎⣰⣿⢻⣿⣿⣿⣿⠛⠻⣿⢻⣷⡀⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣾⢀⣿⡇⣿⣿⣿⣿⣿⣦⣴⣿⣿⢻⡧⠀⡿⠀⣿⡇⣾⣿⣿⣿⣿⣄⣠⣿⡟⢻⡇⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⣿⠸⣿⣤⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⢀⣇⠀⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⡇⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠙⣿⣦⠿⣿⣿⣿⣿⡿⣏⣳⡟⢀⣼⢿⡀⠹⣿⣉⣿⣿⣿⣿⣿⣿⠟⣩⣿⠁⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⡈⠛⠷⣼⣯⣭⣥⣴⠟⠋⣠⠞⣿⢸⡷⣄⠘⠻⣷⣬⣟⣏⣹⣿⡷⠟⢁⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠙⠲⠤⣤⣤⣤⣤⣤⠴⠛⠁⠀⡟⢸⡇⠈⠓⠦⣤⣈⣉⣉⣉⣁⣤⠶⠋⣱⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⡇⠀⠀⠀⠀⠀⠉⣉⡍⠁⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢴⡄⠀⠀⠀⠀⠀⢀⡴⣿⡇⠀⡷⣄⠀⠀⠀⠀⡼⠙⢳⡀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⡀⠀⠀⠀⢠⠏⠀⢈⡇⠀⡇⠈⢧⠀⠀⡼⠁⠀⠈⡇⠸⠃⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⢻⠀⠘⢿⡿⠆⠀⢴⠛⡄⠀⢸⡇⠠⡇⢠⣈⡼⠀⢧⡘⢾⡷⠃⠀⢸⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⣈⡷⠖⠒⠲⠶⠤⢼⡛⠓⠶⣾⠃⠀⣷⡤⠭⢤⣶⠦⢬⣤⠤⢤⣀⡼⠀⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⡟⢻⣤⣤⣤⣤⣀⣀⣈⣓⣊⣽⠀⠀⣇⣙⣖⣋⣀⣀⣀⣀⣀⣀⣹⣿⠛⠉⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⢀⣀⣀⣇⢸⠙⠛⠛⠛⠁⠙⠿⠿⠿⣿⠀⠀⣿⠿⠿⠏⠉⠿⠿⠿⠿⠋⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠸⣦⢤⣄⣀⣀⣀⣀⣤⡤⣬⣿⣾⣁⣀⣀⣀⣀⣀⣀⣠⣤⣀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠣⡄⡇⠀⠿⢦⣄⣀⣀⣸⡆⠀⠀⠀⠀⠀⠸⣿⣿⣍⣿⣿⠈⢸⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⢻⠇⠀⠀⠀⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠀⢸⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦⣾⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣿⣇⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣘⣻⣿⣟⢛⣻⣟⣁⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣷⢤⣂⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⡀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⡿⠛⠻⠁⠿⠿⠿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⠃⣔⡒⢶⡄⠀⠀⠀⣀⣉⠙⠐⠿⣿⣿⣿⣿⣿⣿⣿⡷⠀ ⠘⢿⣿⣿⣿⣿⢸⠁⠀⠹⢿⡟⢛⠆⢠⠶⣶⣦⣤⡑⠀⢹⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠈⠻⣿⣿⣿⣄⡁⠀⠀⠀⡠⠈⠀⠘⢇⠈⠋⠉⠀⢀⢸⠋⢸⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠈⠻⣿⣿⣟⠲⢆⣀⣉⡓⠒⠒⠚⠑⠄⠀⢀⠌⣇⣀⣾⣿⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⠀⠈⠙⠻⣆⠀⠙⠬⢉⣁⣑⣲⡶⠚⢀⠃⣰⣾⣿⣿⣿⠿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⠀⠈⠉⢀⠐⢁⣤⠿⡛⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠋⠞⣦⣀⡀⠀⢀⣀⣤⠖⠉⢻⣳⡼⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣜⡀⣸⠜⠂⢹⡭⠿⢾⣄⠎⠀⠀⠀⡇⢻⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠉⠻⡄⠀⠀⠈⠙⠑⠂⣄⡇⠈⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢤⠀⠠⠤⠐⠊⠢⣀⠀⠀⢀⠔⢫⡄⠀⡿⠀⠀⠀⠀⠀⠀⠀
ദ്ദി(˵ •̀ ᴗ - ˵ )
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀⠀⣰⢿⡾⢧⣾⣷⠖⠀⠀⠀⠀⠀⢀⣤⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠀⠀⠀⣼⢧⣟⡴⣫⠟⠁⠀⠀⠀⠀⣠⢞⣫⠞⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⠀⣼⢣⣿⣟⡿⠋⠀⠀⠀⠀⣴⢟⣵⡿⢛⣯⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣧⣰⡏⣿⣟⡾⠁⠀⠀⠀⣠⢞⡵⣻⣵⣾⠭⢔⣒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⠛⣿⡟⠛⠛⢛⠷⠶⠚⠓⠛⠾⣅⠄⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⣤⡤⡤⣤⡄⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⣄⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⡟⠿⣽⣢⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⠧⢍⣻⣥⠀⢸⠋⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣘⠋⣿⢻⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⢈⠥⠈⣟⣿⠀⠀⢸⡵⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢳⣧⡤⠴⠒⠀⠘⣿⠀⠀⠀⠸⠛⠉⢩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⡾⠒⢋⣀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠛⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣀⣠⣴⣿⣿⣷⣄⠀⢀⣻⣦⣤⡤⢴⣦⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠻⢾⡿⣿⣿⣼⡝⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠛⠁⠒⠊⠉⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣀⣀⣠⣾⣧⣿⣥⡾⠃⠀⠙⠷⣄⠀⠀⠀⠀ ⢀⣤⠞⠋⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣛⠒⠧⠇⡛⣛⣯⡭⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⢀⣈⣻⣦⡀⠀ ⠛⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⠀⠀ ⡀⠀⠀⠀⠀⠀⣀⣀⣼⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀ ⠛⠛⠛⠛⠛⠛⠉⠁⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⢰⣟⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⢀⣼⠟⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠈⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
/)/) (\(\ ( . .) (. . ) ( づLove you forever⊂ )
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣴⣦⣶⣶⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻⠛⠛⠋⠉⠁⠀⠀⠀⠁⠉⠉⠻⣶⣺⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⢠⣤⣾⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣛⣛⣛⣛⣛⣳⣶⣤⠘⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢦⡿⢩⡁⠀⢶⣶⣾⣭⣭⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣾⢡⣼⣷⣿⣿⣿⣿⣿⣿⡟⢻⣯⡉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣾⠋⠹⣿⣿⣿⣿⣿⣿⣉⡿⣷⠀⣧⠀⠀⢀⣠⣀ ⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣤⣾⣿⠃⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣦⣌⡻⠿⣿⣿⣿⣿⠃⣾⠀⢹⡄⢈⣭⣾⣿ ⠀⣤⣤⣀⠸⡟⣿⢹⣿⣿⣿⣿⣿⣟⣁⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠶⠾⠃⠀⠀⠙⠃⠀⢨⡇ ⠠⣟⠒⢤⣘⡇⠹⣧⣭⣭⣽⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⠀⢻⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀ ⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⠸⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣧⠀⠀ ⠀⠀⠀⠀⢵⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⣀⣀⡀⢀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣤⡧⠚⢻⡆⠀ ⠀⠀⠀⢀⡼⣅⣳⠀⠀⠀⠀⠀⢠⣴⣶⣆⡀⢀⣠⡄⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣵⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⣸⣇⠀ ⠀⠀⠀⢸⡇⠀⠋⠛⣇⠀⠀⠀⠀⠀⠈⠙⠻⠿⢶⣶⣶⣤⣤⣴⣶⣶⣶⣶⣶⣶⠶⠿⠿⠟⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⡄⠀⠀⣹⡿⠀ ⠀⠀⠀⢹⡟⣄⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠧⠤⡾⠟⠁⠀ ⠀⠀⠀⠀⠹⣌⠙⢀⣻⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⣀⣀⠠⠤⣀⡤⠔⠒⠛⠛⠩⠛⠢⣤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠊⠉⠁⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⡖⠒⢃⣀⢈⣅⠂⠤⣀⡀⠀⠀ ⠀⠀⢠⠀⠀⢠⢎⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠒⠪⡤⠧⡀⢱⠀⠤⣨⡅⡂ ⠀⠹⣯⣇⣠⢣⠎⡄⢠⠁⠀⣄⠀⠀⠀⣀⠀⢻⡶⡺⢦⡰⢻⡇⠀⢰⢯⡼⠁ ⠀⠀⠹⣿⣿⣿⣼⢸⣻⣾⡀⣿⠄⠀⡄⢿⡿⢸⡇⣇⡏⠉⢻⣿⣴⢽⡞⠁⠀ ⠀⠀⠀⢹⣿⣿⣿⣼⢸⡇⢿⣻⢷⠀⠗⡽⣧⡿⣗⡿⡇⡏⣸⣿⣯⠟⠀⠀⠀ ⠀⠀⠀⣐⣿⣿⣷⣿⡞⢲⣶⣿⠜⣆⢸⠇⣿⣧⣿⣇⣧⣷⣿⣿⣱⣀⡀⠀⠀ ⠠⠔⡉⠀⣿⡟⠻⣿⣇⠘⠿⠏⠀⠀⠉⠀⢻⢿⡏⢸⣿⣿⢿⡏⠀⡠⢜⡫⠄ ⠈⠉⢢⣰⣿⣷⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠉⢠⣟⣸⡌⣴⡃⠀⠀ ⠀⠰⣯⣿⣿⣿⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢰⣿⣿⡼⣷⡼⠇⠀⠀ ⠀⠀⢨⣹⣿⣟⡒⡒⠉⠉⢽⠂⢄⣀⡀⠤⣶⣿⡿⣐⡾⣯⡋⠽⣿⡿⣦⡀⠀ ⠀⠀⢸⡿⠊⠀⣟⣇⠀⠀⠈⢄⠀⠀⠀⠀⠙⠛⢳⡖⢢⠀⡻⣦⣯⡛⢮⡻⣦ ⠀⢠⣿⡟⠂⠀⢿⣯⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣸⠀⡆⢱⣿⣿⣶⡝⣮ ⠀⠀⣿⡇⠀⠀⠈⢯⣇⢷⠀⠀⠀⠀⢀⠌⠀⠀⣼⣿⠇⠰⠀⠈⣿⣿⣿⡟⣾ ⠀⠀⠿⡇⠀⠀⠀⠨⠈⢿⠆⠀⠀⠀⠤⢀⠀⢀⣿⠎⠠⠁⠀⠀⣿⣯⢷⢻⡜
⠀⠀⠄⣀⣉⡩⠒⣪⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣀⡤⠀⠀⠀⡀ ⠀⠀⠀⡞⠙⠝⢿⡹⣠⠔⠂⠉⠀⠀⠀⠀⠀⠀⠈⠑⠀⣑⣫⠵⠒⠋⠉⠉⠁⠀ ⠀⠀⡞⠁⠀⠀⢰⡡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢜⢯⡀⠀⠀⠀⠀⠀⠀ ⠀⠠⡧⠀⣠⢣⠋⠁⠀⠀⡆⢿⣶⠌⡟⢏⢵⣷⠉⡢⠀⠀⢀⠱⡆⠀⠀⠀⠀⠀ ⠀⠀⣷⡇⢇⠃⠀⠀⠀⠀⠈⠂⣡⣞⡀⠈⢄⠁⠚⠁⠀⠀⠀⠁⡙⣖⠀⠀⠀⠀ ⠀⢤⡗⡑⠁⠀⠀⠀⠀⠀⠀⠾⢿⢿⣇⡭⡶⠷⠀⠀⠀⠀⠀⠀⠈⠊⠳⣀⠀⢀ ⣿⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠈ ⣿⢹⡀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿ ⣿⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠸⠿ ⡇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣰⣷⣿⠀⠀ ⠟⢸⡟⠅⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠀⣷⠃⠸ ⠀⡝⡧⠄⠀⠀⡶⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠋⠀⠀⠀⢃⠀⠀ ⢠⡇⠂⠀⠀⡠⠇⢸⡗⠉⠒⠀⠀⠀⠀⠀⠢⠤⠐⢺⢷⠏⡰⠀⠀⠀⠀⠸⠀⠀ ⠸⣑⡒⠒⠀⠘⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⡕⣱⣉⣉⣙⣠⡿⠀⠲⠖⠒⠒⠒⠠⠤⠤⠤⠤⢤⢸⡠⣀⣀⣀⣀⣀⠊⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢔⣖⣒⣒⡲⢶⡒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠔⠊⠉⠉⠙⢍⠀⠈⡻⠷⠖⠠⣑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⢡⢸⠀⠀⠀⠀⠀⢸⠀⡎⠀⠀⠀⠀⠀⢣⠈⢢⠀⠀⠀⠀ ⠀⠀⠀⢀⡰⠁⠈⠾⢆⡀⠀⠀⡠⠊⠀⢇⠀⠀⠀⠀⠀⡜⡇⠀⢣⠀⠀⠀ ⠀⢠⠞⠁⠀⠀⠀⠀⠀⡼⢍⣙⣻⣛⡋⢩⠷⡦⠤⠔⠪⠊⠀⠀⠘⠀⠀⠀ ⢀⠇⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠈⠒⠳⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀ ⢸⠒⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⡠⠔⠒⠠⢇⠀⠀⠀⡀⠈⡟⠀⠀⠀ ⠀⢧⣠⠄⠀⠀⠀⣇⠀⠀⠀⠀⢀⠎⠀⠀⠀⣀⣼⠀⢀⠀⠉⡲⠁⠀⠀⠀ ⠀⠀⠳⢄⡀⠀⠀⠈⠁⠂⠉⠁⢀⣉⠢⡤⢄⠠⠂⠀⠀⡹⠎⠀⠀⠀⠀⠀ ⢰⣿⣿⣶⣾⣿⣶⣶⠢⡼⠃⢲⠅⠀⢻⠀⠈⡤⠐⠂⠉⡷⣶⣶⣶⣶⣶⣦ ⢸⣿⣿⣿⣿⣿⣿⡿⡟⢹⣂⡞⠚⢞⠀⢳⣾⣇⣀⣠⣾⡇⣿⠏⢹⣿⣿⠺ ⢸⣿⣿⣿⣿⣿⣿⣇⠁⡰⠀⠀⠀⠀⣦⠀⢀⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⠁ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠈⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠷
⠛⠋⠁⢀⣿⣶⣽⣿⣿⣿⣿⣿⣷⣴⣶⣾⣋⣯⣥⣬⣭⣿⡓⠶⢤⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀ ⠄⠒⠉⠀⠈⠙⠛⠛⠻⣿⣿⠟⡟⠙⢻⣷⣦⡀⠀⠀⠈⠹⣷⠀⠀⠈⢩⣳⣦⣤⣤⣭⣵⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⡿⠃⢸⠀⠀⠘⣿⣿⣷⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠉⠓⠲⢤⡀⢀⡀⠈⠭⠟⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⡼⠁⠀⠘⣆⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠿⠿⠿⣷⣍⠳⢤⡀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⠋⠀⢸⠃⠀⠀⠀⠈⠳⢄⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⠁⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡀⠀⠀⠀⠀⢀⣤⡶⠾⢿⣿⣿⣿⣶⣦⣤⣀⠀⠈⠳⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⢈⡟⠀⠀⠀⠀⠉⢧⠀⣦⣀⠀⠀⢀⠞⢁⡜⠁⠀⠀⣠⡼⠛⢇⠀⠀⠀⠛⠿⢿⡿⠿⠛⠛⢷⣦⡀⢸⣦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⢿⠀⠈⠉⠒⠛⠊⠁⠀⠀⢀⡾⠋⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀ ⣀⣿⠀⠀⠀⠀⣾⣄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠤⠖⠚⠉⠀⢀⣾⡿⣿⣿⣶⣶⣤⣤⣤⣤⣤⡀ ⠉⣿⠀⠀⠀⢸⣿⣿⠗⢤⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣹⠃⣸⠛⢿⣯⣭⣉⠛⠛⠛⠃ ⢀⣿⠀⠀⠀⣿⣿⡃⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⠏⢀⡟⠀⠀⠙⠻⣿⣿⣶⡆⠀ ⠋⢻⠀⠀⠀⣿⣿⣿⣷⣤⣀⠀⠀⠉⠒⠦⢄⣀⠀⠀⠈⠑⠲⠤⣀⣀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⢠⡟⠀⣸⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀ ⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠈⠉⠑⠒⠤⠤⣤⣄⣀⣉⣭⡿⠟⠉⠀⠀⠀⠀⣠⠏⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠈⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢀⡴⠃⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡄⠀⢹⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣶⣦⣤⣤⠞⠁⠀⠀⠀⠀⣠⡶⠋⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣷⠀⠈⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡿⠋⠁⠀⠀⣀⣠⡴⠞⠉⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠘⣆⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣞⣁⣀⣤⠴⠖⠛⠉⠁⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢠⣾ ⠀⠀⠀⠀⠹⣆⠀⠀⠙⠲⢤⣀⣀⣀⣀⠤⠞⠛⠿⣭⣍⠡⠤⠤⠤⠤⠤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠀⠀⠀⠀⠀⣰⠟⣿ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠂⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⣿ ⠀⠀⠀⠀⠀⠀⠘⠦⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣩⣿⣿⣿⠛⠛⠉⠉⣁⣀⣀⣀⣤⡤⠤⠶⠚⠋⠁⠀⠀⢠⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠒⠒⠺⣿⠛⠋⠉⠉⠉⠈⣧⣾⣿⣿⡇⠀⠀⠀⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣀⣤⣴⣿⣿⣿⣿⣿⡷⠚⠶⢤⡀⠉⠛⠶⢤⣤⣄⣀⣀⠀⠀⠀⠀⠘⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠹⣦⣀⣤⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠞⣿⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⣴⠞⠁⠀⠀⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⡤⡤⣄⣤⣤⡤⡤⠤⠤⠤⠶⠶⠶⠦⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡭⣿⣛⡫⠭⠭⠉⣉⣉⡤⠤⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠉⠛⢝⢦⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠎⠉⠀⠀⠀⠦⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⣀⣀⡀⠳⣕⡌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡔⣿⡇⠀⠀⣀⡀⣐⡤⣤⡒⠂⠃⠉⠉⠉⠓⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣆⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⡿⡏⠉⠁⣀⣀⣀⣀⣀⠈⢇⠀⠀⡄⠀⠀⠀⠀⠀⠔⠀⠩⠶⢄⡂⠂⠂⠂⠐⠐⢀⣿⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢃⣼⡿⢀⡖⡩⠖⠫⣯⡿⣷⢷⡀⠀⠀⠸⠀⠀⠀⠔⠁⠀⠀⠀⣀⣀⣈⣉⠁⠁⠀⠀⠀⠙⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡯⠋⠀⠸⣎⣀⣀⣼⠿⠛⠛⠻⣟⡄⠀⠈⠂⠀⢰⠁⢀⢄⡲⣟⣾⣋⠉⠉⠉⢧⡀⠀⠀⠀⣏⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣶⡛⠁⣠⣿⣿⣒⡒⢤⣀⣼⠃⠀⠀⠀⠈⢣⡙⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⢯⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠀⠀⠀⠀⢠⠇⠀⠀⠀⠸⠝⠋⠉⠀⠀⣆⡈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠫⣿⣆⠀⠀⠀⠀ ⠀⢠⣇⠇⠀⠀⠀⣠⠤⠴⠖⠒⠒⠛⠁⠀⠀⡤⢤⣔⠋⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⡟⣷⠀⠀⠀ ⠀⠘⡞⠀⠀⠀⢐⠇⠀⣰⠀⠀⠀⠀⠀⠀⠀⠧⡇⠂⠀⠀⣞⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣸⡟⠀⠀⠀ ⠀⠀⠙⣦⡀⠀⡞⠀⠈⣿⡶⣤⠄⢄⣀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⢂⠯⠀⠀⠀⣠⡏⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⡄⠃⠀⠀⠨⡇⠀⡉⠓⠖⣟⠶⠦⡤⣄⣀⡀⣀⡀⣀⡀⠀⠀⠀⠀⡀⣀⣄⣔⠶⢵⡟⡝⠀⡏⠌⠀⣼⡟⡝⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣆⡀⠀⠘⣺⣗⣄⠄⣀⠈⠍⢑⠒⠂⠬⢝⣋⣁⣉⣧⠡⠍⠛⠁⠩⡱⢀⡠⣴⡻⡹⠁⠀⡌⢠⡞⡹⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⢆⣗⢕⢗⣄⠁⠳⣌⡆⠀⠀⢐⠇⠀⠀⢚⠄⡀⢀⢀⠔⣓⣥⣋⠶⢱⠉⠉⠈⣔⡩⡛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡓⣦⡪⣇⠑⣅⠋⠳⠦⠬⣅⣁⣁⣊⣂⡂⣒⡲⡥⠕⠒⡉⢇⡕⠁⢀⠃⠀⣰⡿⡊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⢦⣷⠹⣧⡀⠉⠒⠤⢄⡀⣀⣀⣀⠀⠀⠀⠀⠀⡠⡞⠖⠁⠀⡔⠃⣠⠞⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⡇⡇⠁⠿⡲⡤⣀⣁⡀⢀⠀⠀⠉⡩⡩⣝⡩⠊⠀⣀⠔⡊⣂⠟⠃⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠁⡇⠀⠀⠈⠊⠵⠤⠤⠭⠯⠧⠗⠭⠟⠤⢆⢊⠍⢂⢅⣞⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⡇⠉⠉⠑⠒⠢⠄⠤⠄⠤⠂⠂⠊⠀⠁⠡⢀⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⠃⠀⠀⠐⠤⡀⡀⡀⡀⡀⠄⠠⠐⢀⣡⣦⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⢫⣇⡃⠀⠀⠀⠀⠀⢀⣀⣀⠠⣄⡴⠖⠛⣉⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠿⣭⣷⣲⡶⡶⣒⢚⢛⢫⡥⡔⠖⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣤⠴⠾⠿⠟⠿⣛⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⠤⠤⠖⠒⠛⠉⢉⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣯⡽⠶⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠻⣅⠀⠀⠀⣯⠉⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣴⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣀⣀⡼⠙⠳⡎⠉⠙⢢⡀⠀⡈⠙⠛⠲⢤⢠⡀ ⠀⠀⠀⠀⣦⠀⠀⠀⢰⡟⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠙⡶⠟⠳⣄⠀⢀⡇⠀⠙⠢⣄⡿⠁⣠⠇ ⠀⠈⣶⣯⣻⣆⠀⢠⡟⢀⡞⢁⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠿⣶⣦⡤⣾⣄⠀⢀⡿⢷⣾⠀⠀⠀⣤⣿⣛⣴⠏⠀ ⠀⠀⠘⢷⣟⣷⣲⣿⣷⣿⠁⡾⢀⣰⡿⣠⠀⠀⣇⡆⠀⠀⠀⠀⠀⣾⣤⡆⠀⣿⠏⢱⠇⣈⣷⣏⣀⣼⣿⡀⠀⢀⣿⢹⣧⠏⠀⠀ ⠀⠀⠀⠈⣿⣽⣿⣿⡿⣿⣸⠃⣸⣻⡇⣿⡆⢰⣿⡗⡄⠀⠀⢠⠀⣿⣿⡇⢀⣿⠀⢸⣿⡏⠀⠉⠙⣏⣿⣧⣴⣿⣶⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣧⣿⣿⡄⢿⢿⣷⣿⢻⣼⣿⡇⣿⠀⠀⣿⡀⣿⣿⡇⣾⣿⠀⣸⣿⡇⠀⣶⠀⣿⣾⣿⣿⣷⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡼⣷⣸⣀⣿⡏⠘⠿⣼⡇⢿⡌⠀⢻⡁⡿⢹⣷⣿⢻⣤⣿⣿⡇⠀⡇⢠⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣼⣽⣿⣶⣶⣶⣿⣧⠸⣷⡀⠈⣿⠇⢿⣿⣏⣠⣿⡽⠁⣇⣸⢇⣿⣿⣿⣿⠛⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠴⣿⣿⡿⣿⣿⣿⣿⣿⠀⢙⣿⣿⣿⡟⠁⠹⠳⣤⣿⠀⢸⣿⣿⣿⣯⠙⢷⣿⣿⣿⣿⣿⣿⣧⠜⠓⠲⠤⣤⣄⠀⠀ ⠀⢤⡞⠁⠀⠀⢹⣿⣿⠛⠻⣿⣿⣇⠑⠘⢟⣛⡿⠀⠀⠀⠀⠈⠉⠀⠈⣿⣿⣿⡟⠀⢿⣿⣿⣿⡻⣿⣿⠁⠀⢀⣠⠄⠞⣋⡠⠂ ⢠⠖⠤⣝⠢⣄⣾⣿⣿⠀⠀⠈⢻⡉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⢠⣿⡿⠋⠉⣷⣿⢻⡆⢀⠎⣡⡶⠉⠁⠀⠀ ⠀⠀⠀⢈⣳⣸⣿⣿⣿⡇⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠀⠀⣰⣿⣯⡄⣿⡇⣸⣿⣄⠀⠀⠀⠀ ⠀⠀⣴⡿⣻⣿⣿⣿⣿⡇⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⣴⣿⣿⣿⡑⣿⣷⣅⣻⣷⠀⠀⠀⠀ ⠀⠀⠙⠻⣿⣧⣿⣿⣿⡇⠀⠠⠔⣻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⠀⢀⣿⡿⣿⡿⣧⣹⣿⣿⣏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⣹⣿⣿⣿⠛⠲⠞⠋⠉⠀⠀⠼⣿⠓⠤⣀⠀⠀⠀⣀⠤⢴⣾⣿⣿⣿⣀⣒⣾⣿⣧⣘⠇⠸⣿⣿⣿⢿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣯⡿⠛⢹⣷⣿⠀⠀⠀⠀⠀⢹⠂⠀⠀⠉⠈⠉⠀⠀⢸⣿⣿⣿⣥⣈⣉⣩⠘⠋⣻⣧⡠⣬⡿⣿⣷⡙⢿⣦⣀⠀ ⠀⠀⠀⢠⣿⣿⠋⠀⠀⢸⣏⣿⣇⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⠉⠹⡇⠀⢈⢻⣿⣎⣻⣮⡉⢻⣾⣙⣿⣗ ⠀⠀⢀⣾⣿⡿⠦⠀⠀⠈⣿⣿⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠀⠀⡇⠀⢨⠀⢹⣮⣿⣿⣿⣶⣍⠻⣯⡙ ⠀⠀⡸⢹⣿⠀⠀⠀⠀⠀⢻⣿⣿⡊⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢸⣿⢠⣾⠇⠀⡸⠀⠀⣿⣿⣿⣿⣿⣿⣷⡹⣿ ⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠻⣧⣷⡘⣿⠂⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠠⣿⣿⣼⡟⠀⢠⠃⠀⠀⢹⣿⣿⣿⡿⣿⡟⣿⡽ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠛⢿⣽⣇⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⢰⣿⢏⡾⠁⢀⠇⠀⠀⠀⢸⣿⣿⣿⣷⡹⣿⡟⣿ ⠀⠀⠀⠃⢻⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⣿⡿⠂⠀⠀⠀⠀⠐⠛⠢⢄⣀⠀⢀⣼⣿⠟⠁⠠⠋⠀⠀⠀⠀⢸⣿⣿⡇⢻⣷⡹⣿⠈
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⠀⠀⠀⡼⠋⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⢿⣷⠀⠀⠀⠀⠀ ⠀⣿⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣹⡄⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠛⠛⢳⣦⠀⠀⠀⠀⠀⠀⢷⠘⣇⠀⠀⠀⠀ ⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣂⠀⠀⠀⠀⠈⣇⢿⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⢀⠀⠀⠃⢀⣄⣀⣠⠀⠀⠀⠱⡕⠀⠀⠀⠀⢹⣾⡇⠀⠀⠀ ⢻⣷⣶⡄⠀⠀⠘⠀⢰⣾⣿⡿⠟⠉⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠹⡇⠀⠀⠀ ⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⡄⠀⠀⠀⠀⣷⠀⠀⠀ ⣀⢰⠰⣇⣀⣾⡦⠄⠀⠀⠁⠀⠤⠠⠽⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⠀⠀⠀ ⢟⣧⠁⠈⠹⡃⠠⠄⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⢸⠀⠀⠀ ⠀⢿⣶⣾⣾⣿⣷⣶⣧⣤⣤⣴⠾⢟⠋⠉⠉⠀⠀⢀⡼⠀⠀⠀⠀⢸⡆⠀⠀ ⠀⢸⣿⡟⠋⠁⠀⠈⠉⠉⢁⡀⣀⠬⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⢷⡽⠤⢄⣠⣀⠩⣶⣔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠻⣶⡀⠀⠐⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⣇⡃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠴⣇⠀⠀⠀ ⠀⢀⣠⢞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡈⠹⢶⣄
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⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠚⠉⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠋⢀⣠⡴⠞⠛⠋⠉⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⣡⡶⠋⢁⡴⢋⣷⡋⢳⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⣸⡿⠛⠉⢉⡿⠁⡼⠛⠒⢫⣧⣤⡔⠛⠀⠙⣦⠤⠤⠔⠒⠈⠉⠀⢘⡄ ⢀⠏⠀⠀⠀⣼⣷⣰⠃⢠⠊⠁⡟⠀⠈⠙⠢⢄⡘⡏⠉⠑⠢⣄⠀⢀⡜⠀ ⡼⠠⠤⣀⢰⣿⣿⠃⠀⣿⡀⡸⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠈⡗⠋⠀⠀ ⢣⠰⠤⠬⠛⠟⡃⠀⡸⣿⡿⢁⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⠈⣷⣄⠀⠀⠀⠙⠊⠀⠉⠐⢦⣀⡀⠀⠈⡣⣀⣀⣀⣀⡤⠊⠁⠀⠀⠀⠀ ⠀⢹⠙⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠉⠲⣄⠀⠀⠀⠀ ⠀⠈⣇⠀⠈⠉⠓⠻⠭⠶⣶⠶⠶⣶⣛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀ ⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠒⠢⠤⣄⣀⡀⠀⠀⠀⣹⠀⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀ ⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠉⠉⠉⠉⠉⠙⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⢀⣠⠴⠒⠒⠒⠒⠦⠤⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠸⣏⠀⠀⡀⠀⠀⠀⣤⢤⡀⠰⡄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⡽⠷⢯⣁⡀⠀⠀⠙⣦⣽⣄⣹⡄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠙⠏⠁⠀⠀⠀⠀⠀⠀⢹⣦⢤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣠⠾⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡤⠛⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣼⠃⠀⢠⣀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢀⡞⠀⢀⡴⠋⠀⠀⠀⠘⣇⠀⠀ ⠀⠀⣠⠶⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠿⢿⡇⠀⠀⠀⠀⠐⣿⡷⠀⠀⠀⢿⠀⠀⠀⣸⠁⢠⠏⠀⠀⠀⠀⠀⠀⢹⠀⠀ ⢀⡾⠁⢰⠃⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠳⠤⣄⣀⠀⠀⠀⠀⠀⠀⣤⠟⠀⠀⠀⠸⣦⡜⠀⢰⠀⠀⠀⠀⠀⡾⠀⠀ ⣼⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣲⡯⠤⣀⠀⠀⢠⠇⠀⠀ ⠸⣦⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠧⢤⡀⠈⣧⢀⡞⠀⠀⠀ ⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠶⠤⠄⠉⢀⢇⡞⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⣄⠀⠀⠈⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠶⠒⠲⠤⠤⢤⣀⣀⣀⣀⢀⡴⠚⠛⡷⠦⣄⢀⡴⢧⣀⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⡜⠁⠀⠋⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⣧⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠿⠶⠶⠶⠶⠿⢦⣸⡀⠀⠀⠀⣼⢃⣠⣾⣟⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠙⣄⠀⠀⠀⠀⣀⡤⠞⠋⣿⠒⣺⡯⠟⠋⠀⠈⠳⣄⠀⠀⠀⠀⠀⣼⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠀⣀⣸⡆⢀⡴⢞⣉⠀⠀⢀⡿⠋⢹⡄⢠⠞⠉⣽⠀⠈⠳⢤⡀⠀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠉⠁⡀⠘⠋⠀⠉⢈⡑⠦⠚⠀⠀⠀⢻⡟⠒⠋⣡⠴⠲⡆⠀⠈⢛⣿⠿⠿⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⣴⠿⠗⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣄⣀⣀⣀⣇⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⡀⠀⠀⣈⣹⣦⣤⣤⣶⣶⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣤⡶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀ ⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣇⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⠙⠉⠀⠀⠀⠀⠈⣿⠀⠀⠀ ⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣶⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢾⣯⣀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠉⠉⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢶⣦⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣾⠇⠀⠀⠀⠀⠀⠀⣠⡿⢀⠀⠀ ⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠊⠀⠀ ⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢡⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢠⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠚⠁⠀⣴⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠾⠿⣭⣄⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⢻⣿⣭⣍⣀⡀⠀⠀⠀⠀⢠⣍⢉⠙⠛⠒⠲⠦⠤⣤⣀⣀⡀
⠀⠀⠀⡔⠂⠁⠀⡀⡠⠁⠀⠀⡄⠀⡄⠀⢀⠀⠁⠒⢢⠙⣳⡄⠀⠀⠀ ⠀⠠⠊⢠⠂⢀⡎⢠⠇⠀⠀⠀⢇⠀⣿⡄⠀⢂⠀⠀⠀⢏⢉⠙⣆⠀⠀ ⠔⠀⠀⠇⢠⢿⠀⣲⠀⠀⡈⡰⢸⠂⡟⣻⡒⠤⣆⠀⢠⠀⠙⡀⢸⡆⠀ ⠀⠀⡘⠀⣦⠇⢰⢹⠀⠰⠡⠁⡇⣆⠁⠘⢷⠀⢹⡄⠀⡄⠀⡅⠘⢾⠀ ⠀⠘⠇⢰⠏⠄⡆⠈⡠⠟⠁⡜⠀⣟⣀⠀⠈⢃⠘⢷⠀⠇⠀⠙⠆⢸⠀ ⠀⡆⡇⢸⡾⠻⢷⣯⣆⠀⡰⠀⠸⠿⢿⣟⡛⠛⡦⢸⢇⠀⠀⠀⢸⢠⠀ ⠀⠃⢱⠈⠃⢾⣺⣽⠉⢢⠃⠀⠀⢼⣹⣯⣷⠀⠇⢸⠈⡇⠀⠂⡜⡇⠀ ⠀⠘⡸⢢⠀⠈⠣⠜⠀⠀⠀⠀⠀⠈⠓⠜⠁⠀⠀⡈⠀⠀⠀⣧⠏⣾⡀ ⠀⠀⠘⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⡏⡎⢸⠁ ⠀⠀⡀⠸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡬⠊⠀⢸⠀ ⠀⡄⠁⢀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⠀⢀⢿⠁⠀⠀⠘⠀ ⠠⢣⠀⢜⠠⠤⠂⠪⠐⣀⣤⠤⡤⠤⠐⠊⢁⠛⢄⠄⣜⢼⠩⡤⠀⠀⠀ ⠀⠀⣦⣸⡀⠤⠄⣀⡞⠁⣿⠀⢃⠀⡠⠀⢁⠄⣸⣇⡿⠁⣀⠀⠀⠀⠀ ⠀⢠⠁⠑⢷⠉⠉⢸⠀⠀⡇⣀⠶⠯⢆⠀⠀⣰⠃⢹⠇⠁⠈⠀⠀⠀⠀ ⠀⡈⠀⠀⢞⠀⠀⡇⠀⢰⠓⠀⠀⠀⡰⠱⠔⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡞⠀⠀⠀⠀⠀⡠⠈⠒⠻⠰⡤⡀⢣⢀⡏⣧⠈⢆⠃⠀⡠⠈⠂⠀⠀⠀⠀ ⢡⢳⠁⡠⢄⠀⢰⠏⠀⠀⠸⠀⡤⢠⠀⠀⠁⡷⡇⢣⡈⢆⠀⠀⡠⠜⠀⠀⠀⠀ ⠁⠸⠀⠡⡀⢀⣎⠤⠀⠤⠀⠀⠱⡀⠆⠀⠈⣩⠹⠁⠘⠪⠲⠊⠀⠀⠃⠀⠀⠀ ⠀⠀⠐⢲⠺⡟⠀⠉⠉⠉⠁⠀⠀⠁⠀⡀⠔⣪⡴⠤⣄⡀⢀⠴⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⣆⣰⠚⡿⢲⣅⠀⠀⠀⠀⠰⣻⡇⣰⣦⠈⡿⠅⠀⠀⠀⢀⠀⠀⠀ ⡈⠍⠁⡇⠀⠘⡃⢸⠿⠿⡇⠀⠀⠀⠀⠀⢹⠛⠛⠹⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀ ⠀⠉⠐⠁⠀⠀⡇⢔⠓⡖⠁⠀⠀⠀⠀⠀⠀⠉⠙⡵⢳⡄⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢫⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⡆⠐⢑⡤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠔⣿⣟⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⢰⡇⠀⢠⡇⢸⢸⠇⢘⡗⠢⣤⡤⣐⡂⠥⢐⡪⢻⣿⠀⠀⠀⠀⣸⡇⠀⠀ ⠀⠀⣿⡇⠀⠸⠶⠚⠚⠣⠴⣧⣠⣇⢀⡀⠀⡹⡏⣠⡼⡑⡄⠀⠀⢀⠛⠻⠀⠀ ⢾⠷⣿⢿⠀⠀⠀⠀⠀⡠⢊⣔⣏⠿⣇⣇⣴⠻⡘⠕⠀⣦⡇⠀⠀⠌⠀⠀⠀⠀ ⣿⡿⠻⠋⠆⠀⣆⠠⢊⣴⣿⠏⠨⠮⣀⠠⠔⠊⠐⠀⣸⣾⠀⠀⡰⢄⡀⠀⠀⠀ ⠟⠀⣀⠧⢘⡀⠇⣺⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⢠⠓⠢⠌⣁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣠⣤⣾⢿⣿⠿⠿⠿⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠚⠉⣉⣽⡿⠟⠋⠉⠉⠀⠁⠀⠀⠀⠀⠉⠋⠐⠁⠙⠛⢶⣶⡶⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠶⠶⠚⠛⠉⠉⠉⠁⠀⠀⠀⢀⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣙⣿⡞⠉⠉⠀⠉⢷⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠙⢧⡀⠀⠀⠀⢸⣆⡀⠉⠛⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣫⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⠀⣠⠏⠙⠳⣞⠉⠙⠛⢦⡀⠀⢀⠈⠙⠻⠓⠦⣤⡀⢠⠄ ⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢠⣴⡾⠋⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠑⠳⣤⣸⣦⣿⡄⠀⠀⠀⣷⠀⠀⢳⣤⡐⠂⡴⠎⠁⢸⡆ ⠀⠀⠀⡄⣠⢠⠿⡄⠀⠀⢀⣼⡟⠁⣴⠏⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣼⡇⠀⠀⠀⢀⡼⠉⠀⠀⢹⣦⡀⢀⡟⠀⠀⠀⠈⢹⡆⣇⠃⣰⡿⠀ ⠀⠀⠀⢻⣷⠦⣭⣷⡀⠀⣰⡟⢀⣸⠏⢠⡇⠀⢀⣾⠁⠀⠀⠀⢸⢀⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠛⢻⣿⣷⡶⠿⢿⣄⠀⢀⣼⠛⣿⣿⠁⠀⠀⠈⢲⣾⣋⣩⣴⡟⠁⠀ ⠀⠀⠀⠀⢻⣾⣙⣧⢖⣾⣿⢧⣿⡏⠀⣿⠁⡀⣸⣿⢠⢀⠀⠀⣏⢸⠀⠀⠀⠀⠀⠀⠀⣾⡇⣷⡆⠀⢸⣿⠘⢡⡟⠀⣙⣷⣿⠁⢀⣿⣿⡀⠀⠀⠀⣺⣧⢿⣤⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣽⠏⢿⣿⣟⣿⢻⡇⣸⠇⢰⡧⣿⡏⣼⣶⠀⢠⣿⣿⢠⡀⠀⠀⠀⠀⠀⣿⣧⣿⡇⠀⢸⣿⠀⢸⡇⣿⡟⠁⠛⠛⢿⡟⣿⣿⡄⣠⣾⣩⡭⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣿⣿⣻⣿⢸⡇⣿⠀⢺⡷⣼⠇⣯⡿⡆⢸⣯⡿⢸⡇⠀⠀⠀⣇⠀⢻⣿⣿⡇⣰⣼⣿⠀⢸⣇⣿⡇⠀⢀⠀⢸⣧⢻⣿⣿⢻⣚⣚⣷⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢸⡇⣿⡆⢸⡇⢻⣤⣿⠁⣷⣾⡿⡇⢸⣿⢀⠀⠀⣿⠀⢸⣿⣿⣇⣿⣿⣿⢠⣼⣿⣿⡇⠀⣿⠇⢸⣿⢸⣿⣿⡏⣯⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣎⣷⠻⣿⢸⡇⢸⣿⡟⠀⢹⣿⡟⣷⠸⣿⡈⠆⠀⣿⠀⣿⠇⣿⣸⣿⡟⣿⣄⣿⡿⣿⡇⠀⣿⠀⣸⣿⢸⣟⣿⢺⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣟⣄⣿⡘⣇⢻⣿⣥⣤⣤⣤⣻⣿⠀⢻⣷⠀⠀⠹⣶⡟⢰⢯⣿⣿⠁⢹⣿⢫⠏⢸⡇⢰⡟⢸⣿⣿⣿⣿⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⠛⢻⣿⣿⣿⣿⡿⣷⠈⢿⣧⠀⢀⣿⠇⠈⣿⣿⣷⣶⣿⡷⣾⣄⣸⣷⣿⣧⣿⣿⣿⣿⣿⡇⣠⣅⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⢻⣿⣿⣟⢻⣿⣿⣿⣿⣿⢹⡀⢠⣭⣿⣿⣿⡟⠁⠀⠈⠋⢷⣾⣿⠀⠀⣿⢿⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠋⠈⠉⠙⠒⢶⣶⡄⠀⠀ ⠀⣀⣤⡞⠉⠀⠀⠀⠈⣿⣿⣿⠋⠙⢿⣯⣿⣿⡇⠑⠈⢿⣛⣿⡿⠃⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⣾⣿⣿⣿⡇⠀⢾⣿⣿⣿⣿⡟⣿⣿⣿⡇⠀⠀⢀⢀⣴⠶⠞⢋⣁⣰⠀ ⢀⣀⡤⣄⡛⠦⢄⠀⢰⣿⣿⣿⡇⠀⠀⠉⢻⡏⠻⢤⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠮⠴⠋⠀⠀⣸⣿⣿⡟⠋⢻⣼⣿⢿⣇⠀⢀⡾⠋⣠⠴⠛⠋⠀⠀⠀ ⠀⠛⠁⠀⠉⠷⣄⢙⣾⡿⣿⣿⣧⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢻⡟⠁⠀⠀⣼⣿⡘⠀⣿⣦⠚⢀⡿⠗⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣿⣆⣿⢿⣿⣿⣿⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣼⣿⣿⣧⣷⢸⣿⠀⡾⢾⣷⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⠏⣹⣿⣏⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⣼⣿⣿⣿⣿⡁⢿⣿⣧⣇⠘⣿⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣝⣿⣿⣸⣿⣻⣿⣿⠀⠀⢀⣀⠼⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⢠⣿⣿⣿⣿⡿⣯⠸⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣻⢷⣿⡿⣿⣿⣿⣄⣀⣨⣶⠴⠟⠛⠛⠛⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡿⠁⢀⣀⣼⣿⣗⠙⢿⡧⢙⣷⣿⣿⡻⣿⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣸⣿⡇⣿⣿⣅⣈⠉⣉⠀⠀⠀⠀⠀⠐⠻⣿⠀⠉⠳⢤⣀⠀⣀⣠⠤⠒⠋⣿⣿⣿⣿⣿⠷⢤⣦⣥⣿⠿⣿⣦⣬⠃⠘⢿⣿⣟⢷⡝⢿⣟⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⣿⣿⣥⠟⠋⠉⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⢽⠂⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣤⣄⣠⣤⠐⠋⢉⣿⣦⡀⢠⣜⠿⣮⣻⣦⡙⢿⣷⣄⡀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⣿⡟⣿⣧⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠉⠙⠉⣿⣿⡏⠹⢻⡆⠀⢈⠻⣿⣻⣆⠹⢷⣌⠙⢛⣿⣾⠙⢷⣿⡦ ⠀⠀⠀⠀⢀⣞⣿⣿⣀⠀⠀⠀⠀⢿⣷⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⡇⠀⢸⡇⠀⠀⣧⠈⢿⡝⠿⣾⣿⣷⣤⡘⢿⣿⣎⠻⣿ ⠀⠀⠀⠀⡜⣸⣿⡟⠉⠉⠁⠀⠀⢸⣿⣿⣿⢘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⠀⠀⣸⡇⠀⠀⣇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⣌ ⠀⠀⠀⢠⠃⣿⣿⡇⠀⠀⠀⠀⠀⠈⣯⣿⡿⣯⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣸⣿⢀⣷⣿⠇⠀⢠⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣆⢹⣿ ⠀⠀⠀⠈⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢾⣯⢹⣧⠘⣷⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⢿⣿⣸⣿⡏⠀⢀⡞⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⡛⣿⣧⢻ ⠀⠀⠀⠀⢸⡿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠹⡼⣿⣧⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⣰⣿⡿⢻⡿⠀⠀⣼⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡌⢿⣿⡜⣿⣷ ⠀⠀⠀⠀⢸⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡈⢻⣿⣿⡆⡀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⠀⠀⠠⣷⡿⣡⡿⠁⠀⣰⠃⠀⠀⠀⠀⠘⣿⣿⣿⡏⢻⣿⣈⢿⣿⡌⢿ ⠀⠀⠀⠀⠘⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢻⣿⢇⠁⠀⠀⠀⠀⠀⠀⠛⠉⠓⠦⣄⣀⢀⢀⣰⣿⡿⠛⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⡈⢿⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠴⠋⢠⠔⠂⠀⠀⠒⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⠀⠀⠨⠶⠆⣀⣀⣫⢧⣱⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⠀⠀⠀⡠⠀⠀⢀⣀⡀⠀⠀⡁⠀⠀⠀⢠⠜⢀⠲⢄⠀⠀ ⠀⠀⢀⡜⠀⠀⠀⡞⠀⣤⡜⠁⠀⢀⣄⠀⠙⡀⠀⢠⠁⡔⠁⠀⠀⢣⠀ ⠀⡔⢡⠁⠀⠀⠀⠑⠀⠀⠳⠤⠀⠈⠁⠀⠠⠃⠀⠸⣼⢀⠀⠀⠀⡜⠀ ⠈⣅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡀⢢⢠⠃⠀ ⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡒⠒⠀⢬⠂⠀⠀ ⠀⠀⠀⢣⠀⠀⠀⠠⠒⠀⠤⠤⠤⢄⡠⠒⡒⢤⡠⠧⢀⠁⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠰⠀⡜⠀⠀⠀⠀⢸⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣄⣀⣀⣠⣰⠀⠀⢀⠄⣠⡎⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⢄⠀⠀⡀⠝⢲⣒⡾⠞⣉⡓⢄⠀⠀⢠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠛⠐⠈⠖⠙⠒⠄⠜⠀⠣⠮⠔⡡⢤⠑⠢⣧⠤⠤
⠀⠀⠀⠀⠀⠀⣸⡿⠉⣿⣿⣿⣿⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⠁⠀⠈⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣏⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣟⣻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠹⣮⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⠈⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⠀⠄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠂⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡷⠀⠀⠐⠒⠒⠀⠐⠂⢀⣤⣐⣀⣀⣀⣀⣀⡤⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣝⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢻⡾⣆⡀⠀⠀⠀⠀⠀⠀⠀⢻⡈⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⠀⢀⠀⠐⠈⡀⠀⠀⠀⠀⠀⠙⣮⠳⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⢠⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⣾⣿⠰⠀⠀⠀⠀⠀⠘⢧⡐⠀⠀⠀⠀⠀⠀⠌⢻⣧⣿⡇⠀⠀⠀⠀⠀ ⠘⢻⣿⣿⣷⣷⡄⠀⠀⠀⠀⠈⠁⢘⢠⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠩⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠹⠿⠻⠛⠁⠀⠀⠀⠀⠀⠀⡘⠻⠋⠉⠙⠉⠛⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠀⣴⠏⠀⠀⠼⣧⡀⣀⡀⠀⠀⠐⠋⠀⠀⣀⣀⡀⢐⣉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀ ⢠⣷⢰⢹⡄⠙⠿⣶⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠅⠉⠀⠀⠀⠀⠀⠀⢀⠀⢀⣻⣇⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀ ⠘⡟⣾⣬⠀⣤⠀⠈⠿⠇⢠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀ ⠀⠙⣯⣿⠀⣈⣠⣤⣴⣷⣼⣆⣀⠠⠤⠀⠐⠚⠉⠁⢀⣠⣧⣤⣤⣤⠤⢤⣤⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣿⠟⠻⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⡿⣿⡿⠿⠿⠋⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠰⠀⡞⠀⠀⠀⠀⠀⠀⠀⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⢸⣇⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⣤⠖⢀⣴⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⠻⣦⣀⣀⠀⢀⡀⠀⢉⣹⣬⣤⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣷⡀⠈⠉⠉⠉⠉⢉⣭⣭⣷⣾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣾⡅⠀⠀⠀⠘⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡇⡷⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡧⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⠀⣀⡤⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⢶⣤⣀⠀⠀ ⠀⠀⢀⣀⣴⢟⢁⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⢠⣤⠀⠴⠛⣛⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⠀⢀⣤⡴⠶⠶⠶⠺⠷⡷⠶⠶⠤⣤⣬⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⠽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠯⡉⠉⠀⠀⠀⠀ ⠀⢀⡼⠋⠀⠀⢀⣔⠤⠤⠄⣀⢀⠀⠀⠀⣀⠤⠄⠀⣀⠀⠀⠀⠈⠲⢄⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⣾⠁⠀⢠⣤⡀⠙⢧⡶⠛⠉⣉⣉⠉⠻⡆⠀⠀⠀⠀⠈⠣⡀⠀ ⢰⣿⡀⠀⢀⠾⣿⢠⠀⠘⠻⠛⠀⢀⡅⠀⠘⠿⠿⠂⠀⡿⠀⠀⠀⠀⠀⠀⢣⠀ ⢺⠀⠀⢢⣆⡀⢘⢷⡥⣀⣀⣠⠖⠚⠓⢄⠀⠀⢀⣠⢜⠄⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡆⠀⠈⣿⣿⣦⡀⠈⠁⡾⣿⠀⠀⠀⠀⢹⣛⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠘⡀⠀⢸⣿⣿⣿⣀⣀⢳⣹⢦⣄⢀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀ ⠀⠀⠑⣄⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣴⣶⣿⣿⠟⠀⠑⢄ ⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠋⠁⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠤⣄⣀⣀⠀⠉⢻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠄⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⠆⠀⠀⢀⣴⠏⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⣿⣆⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⢸⣧⠤⠶⠼⢿⣿⣖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠁⠀⠀⣸⠃⠀⠀⢀⣾⠟⠀⢠⢿⠇⠀⠀⠀⠀⠀⠀⠀⣼⠀⡄⠀⠀⣿⡹⣦⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⡀⠉⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⣸⠃⠀⠀⢠⣿⡟⠀⠀⡞⣸⠀⠀⠀⠀⠀⡄⠀⢀⠇⢀⣇⣀⣠⣿⣿⣾⣦⡀⠀⠀⠙⡄⠀⠀⠀⠀⣄⠀⠀⠙⠦⡾⡇⠀⠈⣿⣇⠀⠀⠀⠀ ⠀⣤⠞⠁⠀⠀⠀⢰⡇⠀⠀⢠⣯⣾⠗⠒⢛⣾⡟⠀⠀⠀⠀⢰⡇⠀⣾⠀⢞⣿⠁⠀⡟⢣⡹⣆⠉⠛⠦⣄⢻⡄⠀⠀⠀⢸⡄⠀⠀⠀⠙⡇⠀⠀⣻⣿⣆⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⢀⡎⠀⠀⢠⡟⢡⡟⠀⠀⣾⡟⡟⠀⠀⠀⠀⡜⠀⢰⠇⠀⣾⢹⠀⠀⡇⠀⢻⡜⣧⠀⠀⠀⠻⣿⡀⠀⠀⠀⢧⠀⠀⠀⠀⣹⠤⠤⢿⣟⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⢇⡞⡇⠀⢀⡿⠀⡇⠀⠀⠀⢸⠃⢠⠏⠀⣸⠇⢸⠀⢸⠁⠀⠀⠹⡞⣧⠀⠀⠀⣿⣷⠀⠀⠀⢸⡄⠀⠀⠀⣧⠀⠀⠚⢿⣬⣇⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠀⠀⢠⣇⡾⠁⡇⠀⣼⠀⠀⣷⠀⠀⢰⠇⣰⠃⠀⢠⣿⠀⢸⠀⡿⠀⠀⠀⠀⠘⢞⣇⠀⠀⣿⠎⣦⠀⠀⠈⡇⠀⠀⠀⢹⡀⠀⠀⠀⢻⣿⠀⠀ ⢠⠀⠀⠀⢠⠛⣿⠀⠀⢸⣿⠃⢀⡇⢀⡏⠀⠀⢿⠀⢰⣿⡞⠁⠀⢀⣿⠁⠀⣸⢰⠃⠀⠀⠀⠀⠀⠈⢿⡆⠀⣿⢧⢻⡄⠀⠀⢱⠀⠀⠀⠀⠛⣶⡀⠀⢤⣿⠀⠀ ⠞⠀⠀⠀⡄⠀⡏⠀⠀⣷⡇⠀⠈⡇⣸⠀⠀⠀⢘⡴⠛⠁⠀⠀⠀⣸⠃⠀⠀⣿⣿⣠⣤⡤⠄⠀⠀⠀⠀⣷⠀⡿⠈⢷⢷⠀⠀⢸⡄⠀⠀⠀⠀⠈⣷⠀⢀⣿⠀⠀ ⠁⠀⠀⠀⡇⠀⣗⠀⢸⣿⣅⣰⣦⣿⣿⣼⣛⡛⠛⣄⠀⠀⠀⠀⣸⠇⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣷⣶⣿⣧⡷⠀⢸⣿⣇⠀⢸⠂⠀⠀⠀⠀⠀⢹⠂⠈⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⣿⠀⠈⡟⣿⠛⠋⠹⡛⢿⣿⣿⣷⣾⡄⠀⠀⢠⡏⠀⠀⠀⢰⠿⠛⠛⠳⣷⣶⣦⣀⠀⠀⠀⢻⣟⠂⠀⣿⢿⡀⠸⠀⠀⠀⠀⠀⠀⠈⡇⢐⡏⠀⠀ ⠀⠀⠀⠀⡇⠀⢻⠀⢠⡇⢿⠀⠀⣶⣄⣼⣿⢿⣮⠻⢳⡀⠀⡾⠀⠀⠀⠀⠀⠀⣴⣷⢶⣿⡿⢿⣿⣧⠀⠀⠼⡿⠀⠀⡏⠈⢧⡐⠀⠀⠀⢀⡀⠀⠀⣷⡿⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢸⡇⢸⠁⠘⠂⢸⣿⢁⣴⣿⣴⣿⠀⠀⢱⣼⡇⠀⠀⠀⠀⠀⠀⣿⡿⣸⣿⣷⣨⣿⣿⠆⠀⠴⠃⠀⢠⠃⠀⠘⡇⠀⠀⠀⠀⠇⢰⡀⢿⣁⣠⠄⠀ ⠀⠀⠀⠀⢹⡄⢸⣻⣸⡇⠀⠀⠀⢿⣿⠟⠛⣯⣽⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠙⣿⡿⢉⡙⣧⣸⡏⠀⠀⠀⠀⠀⣸⠀⠀⠈⠁⠀⠀⠀⢰⡄⣼⠷⡀⢿⣠⠀⠀ ⠀⠀⠀⠀⠀⢷⣸⡇⢻⡇⠀⠀⠀⠀⠙⠦⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠾⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷⠻⡄⠹⣜⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡁⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⣷⡴⣿⣾⣦⠀ ⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⣿⡋⢀⠿⠁⣿⣿⠙⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣼⡿⠃⣾⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⠀⢸⣏⣡⠞⠁⠀⠀⠘⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⠀⢠⡇⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣧⣼⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⣤⠀⠋⠀⢸⡇⢸⠋⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⠀⢸⣧⡏⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⣯⣺⣿⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⣼⣷⠀⠀⠀⢸⣿⠁⠀⠀⠀⣀⣤⣙⠳⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠛⣟⣶⡀⠀⣿⠀⠀⢠⡏⢸⣧⡤⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⢻⡄⠀⠃⢸⡇⣀⠤⠤⣼⠁⠀⠀⠛⢤⡀⢹⡝⠓⠂⠤⡤⢤⣤⠤⠤⠖⠒⠛⠉⠀⠀⠀⣠⡟⠁⢿⣀⣿⠀⠀⣼⢁⡜⣇⣀⡤⣾⣶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⠀⠀⢸⣏⠀⠀⠀⡇⠀⠀⠀⠀⠀⢩⣾⡟⠛⣿⣿⠁⠀⡝⣆⠀⠀⠀⠀⠀⠀⢠⡼⠋⠀⠀⢀⢻⣿⠀⠀⣿⣿⡤⠛⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⡀⠀⢹⡀⠀⢠⣧⣤⣀⠀⠀⢠⣿⠇⠀⠀⢻⡟⠀⠀⠙⣏⠀⠀⠀⠀⣠⠜⠁⠀⠀⢀⡤⠁⣿⣿⡆⢰⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⢀⡿⠳⣔⠸⣇⠀⢧⣀⣀⣀⡙⠛⣿⠃⠀⠀⠀⢸⡇⠀⠀⠀⠘⢦⣠⡴⠋⠁⠀⠀⠤⠚⠁⠀⣼⡿⠈⣿⣿⣿⠀⣠⠴⠚⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠈⠳⣿⣶⠃⠀⠀⠉⠉⢱⣿⠀⠀⠀⠀⢸⡇⠀⠀⣴⣋⣿⣭⣙⣦⠒⠀⠀⠀⠀⠀⣼⡿⠀⠀⠉⣿⡟⠉⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣼⠉⠀⠀⠀⢀⣿⠀⣠⢾⡏⠙⠚⠋⠉⠙⢧⡀⠀⠀⠀⣸⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢰⣞⡁⠀⢀⣀⣀⣿⠀⠀⠀⠀⣸⣏⡔⠁⠀⡇⠀⠀⠀⠀⠀⡾⠱⢆⠀⡸⢻⣟⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣰⠃⠀⠀⠀⣸⡟⠀⠀⠀⢈⡿⠁⠀⠀⠀⣧⠀⠀⠀⠀⣼⠁⠀⠈⠛⠁⣼⣏⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⣴⣿⣵⠶⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⣿⡾⠋⠀⠀⡴⣮⢯⡒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠿⢼⣿⠿⢥⣀⣠⣮⡿⢿⡷⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠉⠐⢚⣤⣤⣄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠋⠀⣠⡶⠂⠀⠀⠀⠀⡞⣫⡉⢱⠂⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠀⠀⡿⠁⠀⠀⠀⠀⢰⠁⠤⢹⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠈⠁⠀⠀⠀⠀⣠⡿⡤⠓⠈⢿⠀⠉⠛⢉⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠰⢉⣉⣴⣦⡀⠘⣄⣀⣠⣈⣿⡀⠀⠀⠀⠀ ⠀⠀⢀⡤⡊⠀⢤⠄⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⡟⠉⠉⢙⣟⡿⡿⠳⣄⠀⠀⠀ ⣠⠔⠉⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠙⠽⣛⣉⣓⡦⠝⠛⠋⠉⠁⠀⠀⣵⣦⠀ ⠁⠀⠀⠀⣀⣦⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠉⠉⠉⠉⠁⠐⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫ ⠀⠀⠀⠀⣀⡤⠝⠧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢀⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣠⣿⣝⣳⣤⣀⣀⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣴⣶⡿⠿⠿⠿⠛⠛⠛⠉⠛⠻⠿⠿⠛⠛⠛⠛⠿⢶⣶⣶⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⣉⣽⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠹⣿⣿⣯⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⢀⡴⣂⡤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠉⠛⢦⣽⡄⠀⣠⣴⣾⡿⠶⠶⠒⠲⠶⣮⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀ ⠀⢰⣿⡇⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⢠⣶⣶⣦⡀⠀⠈⠻⣿⠟⠉⠁⠀⢀⣤⣤⡀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀ ⠀⣾⣿⡇⠀⠀⠀⠀⢠⣿⣿⡇⢀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⣏⠀⠀⠀⠰⣿⣿⣿⣿⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⣿⠻⡗⠀⠀⠀⣰⠏⠈⢿⣷⡜⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀ ⠒⣿⠀⠀⠀⠸⣦⣓⣒⠀⠀⢻⣝⢦⣦⡀⠀⠀⢀⣤⡶⠛⠋⠙⠳⣤⡀⠀⠀⠀⠀⠀⢀⣴⠟⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⢹⠀⠀⠀⠀⢿⣿⣿⣦⡀⠙⠈⠙⠲⢽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠹⣶⣖⣒⣒⣛⣩⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠨⣇⠀⠀⠀⠸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠰⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⣸⣯⣭⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀ ⠀⠀⠹⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠐⢿⡘⣿⣦⡀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣿⣶⣘⣧⣼⢉⣿⣷⣄⣒⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⠀⠀⠀⠹⣆⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣏⣁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣽⠿⣽⣟⣻⠿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⣾⣿⣿⠋⠑⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣛⣯⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿ ⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠃⠀⠀⠀⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠈⠻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⣠⣤⣤⣄⢀⣤⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⡗⢹⣉⣉⣉⣽⣏⢫⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣥⣤⣤⣤⣤⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠠⠟⣇⡜⠀⠀⣴⣩⣿⠶⢄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⢯⣭⣭⡭⠍⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡲⢿⣧⡈⣿⣿⣿⡭⢽⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡏⡾⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠇⢼⣧⣵⠘⢔⡀⠉⠉⢰⣷⠾⣷⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⢠⢇⡇⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠟⠛⠉⠀⠀⠀⠻⣿⣆⣀⠙⠓⠶⢊⣼⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢀⡇⢸⢸⠃⠀⠘⣆⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠷⠟⠛⠁⠀⠀⠠⡀⠀⠀⠀⠈⢧⠀⠀⠀⢸⠃⡏⡿⠀⠀⠀⣸⢻⡭ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡠⡨⠀⠀⠀⠀⠀⠐⠢⡄⣄⢰⡀⠀⠀⠳⡄⠀⡸⢠⣟⡇⠀⠀⠀⡟⢸⠁ ⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠛⠀⠀⠀⠀⠘⡇⠀⠀⣀⠀⡀⢁⠄⠀⠄⠈⠄⢰⠀⢳⡈⠈⠲⣧⡄⠀⠀⠹⣄⡇⣸⢸⠁⠀⠀⢀⡇⢸⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢱⣠⣿⠏⠀⠉⠛⠁⠠⡅⠀⠈⡽⠀⠀⠑⢤⣀⡀⠈⠓⣄⠀⢘⠇⡇⡿⠀⠀⣠⠞⠓⠺⢶ ⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠏⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠒⠊⠁⠉⠙⠷⣦⣼⠂⢸⢰⢇⡇⣠⠞⠁⠀⠀⠀⢸ ⡄⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⣸⠈⣇⢾⡶⣀⡀⠀⠀⣀⠤⠚⠋⠀⠀⠀⠀⠀⠠⠒⠀⠀⠙⢤⣇⣸⣈⣻⣓⣒⣂⣀⣀⣀⣿ ⣧⣄⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠤⠒⠊⠉⠟⠉⠩⠟⠉⠛⠉⠙⠓⡂⠀⠒⠒⠶⣲⣤⣤⣀⣤⣤⣶⣦⣤⣽⠿⠤⠤⠤⠽⠟⠒⠂⠐⣿ ⣧⣽⣆⡀⣦⣀⣀⣘⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣘⠷⠦⡀⠙⣔⠺⣦⡙⣿⣤⣤⣤⣤⠴⢶⣶⡶⠶⠾⠿⣟⣻⣻⢿⡏ ⣿⣿⣏⠉⠉⠉⠉⠠⢄⡈⠘⠛⠛⠛⠛⠖⠒⠒⠒⠒⠚⠛⠛⠉⠉⠉⠋⠩⠷⠼⣟⡿⢯⣿⣻⡎⠉⠉⠒⠒⠓⠒⠋⠉⠉⠀⡀⠀⢀⢇ ⣿⣿⣿⣧⡀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢷⡄⢀⠀⠤⠤⢤⣴⣺⣭⡝⣫⣾ ⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠃⠀⠀⠀⠀⠀⠈⣉⠉⠉⠉⠉
⣥⣿⢀⡜⠁⣾⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀ ⣽⣏⡞⣠⠾⣿⣯⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀ ⣿⡟⡴⠃⠀⣿⡞⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢻⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⠀⠀⠀⠀⡄⠀ ⣿⡽⠁⠀⠀⣿⣿⢸⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣄⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⣸⣀⣀⣙⣷⣀⣀⣀⣀⣤⣤⣼⣿⣿⠯⠛⢷⠀⠀⠀⠀⢳⣠ ⣿⠁⠀⠀⠀⡟⢿⢸⣧⡄⠙⡟⠿⣶⣦⣤⣀⣀⣰⣃⣹⡄⠀⠀⠀⠀⠀⠘⣇⢹⡇⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⢿⣟⣿⣻⡿⠿⣿⡿⠛⠋⠉⢨⡇⢹⣦⠀⠘⣆⠀⠀⠀⢸⡿ ⠟⠀⠀⡄⠀⠀⢸⢸⢏⣇⠀⡇⢠⢸⡏⠛⠿⣿⣿⣦⣬⣿⡿⣿⣿⣾⡖⠀⢻⡸⣧⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠉⣁⡀⡆⠘⢿⡄⠀⠀⢸⡇⢀⣻⣧⠀⣿⣀⣀⠀⠈⣿ ⠂⠀⢸⠁⠀⠀⢸⢸⢸⠈⠀⡇⢸⢸⠀⠀⢠⢿⠁⠘⠉⠉⢿⡉⠉⠙⠂⠀⠈⣇⢻⡇⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠚⠉⠉⠓⠃⠀⠈⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣟⡀⢰⠀⢻ ⠀⠀⡼⠀⠀⣼⣿⢸⠘⠀⠀⡇⠈⣸⠀⠀⡾⡏⢀⣀⣀⠀⠈⣧⠀⢦⠀⠀⠀⠸⡌⢿⡄⠃⠀⠀⠀⣿⡀⠀⠀⠀⢸⢀⣠⠀⢀⣤⣶⢾⣿⣿⣻⡿⠉⠙⢿⣿⣿⢿⡟⠛⠃⡇⢸ ⠀⠀⡇⠀⠀⠸⡟⠲⢦⠀⠀⣧⣿⣿⣿⣽⣿⣷⣶⣄⣉⠳⢦⣈⣷⣨⢧⡀⠀⠀⢱⡘⣿⡄⠀⠀⠀⣿⡇⠀⠀⠀⢸⢋⣤⣾⣟⣿⣿⣿⣿⣿⣿⠀⠀⠀⣶⣼⣿⡿⡇⠀⠘⢣⠀ ⠀⢰⡇⠀⠀⠰⣿⣄⡈⢙⣶⣿⣿⠻⠉⢻⣿⣿⣿⣿⣿⣿⣶⣄⡀⠹⣷⣆⠀⠀⠀⢷⡙⠀⠀⠀⢰⡏⣷⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇⠀⠰⣼⠀ ⠀⢸⠇⠀⠀⢠⡇⠙⢿⣍⣿⣿⠃⠀⡇⣿⣿⢿⣿⣿⣿⣻⡻⣟⣿⣶⣬⡻⣧⡀⠀⢼⣷⣄⠀⠀⣾⠇⢹⣠⣴⣿⠟⣿⣿⡏⠛⠻⠃⠀⣼⣿⣿⡇⠀⢠⣿⣿⠟⢠⡇⠀⢀⡏⣆ ⠀⣾⠀⠀⠀⡞⡇⠀⠓⠿⣿⣿⡆⠀⡇⡏⣿⣿⣻⡉⠙⣿⠟⠁⣿⣿⣟⡟⠿⠻⢦⡌⠻⣿⡄⢀⣿⠀⢹⡇⢀⡿⠀⣿⣿⣿⣦⣀⣀⣸⣿⣿⣿⡏⠀⠜⠛⠋⣀⢸⡇⠀⢸⢱⡏ ⢰⡟⠀⣠⡾⠁⡇⠀⠀⢀⣿⠹⣿⡄⣿⡇⢿⣿⣿⣷⡄⠀⠀⣸⣿⣿⣾⡇⠀⠀⠀⢹⣦⡹⣷⣼⠏⠀⢀⣇⡞⠁⠀⢻⣿⣿⣿⣿⣿⣿⣯⢛⡿⠁⠀⠀⠀⣤⡇⢸⡇⠀⡏⣼⢇ ⣿⣡⣾⣿⠃⢸⡇⠀⠀⣼⠻⡄⠘⣿⣽⡇⠈⣿⣾⣿⣿⣦⣾⣿⣿⣿⣏⡇⠀⠀⠀⢸⠏⢻⣾⣿⣶⣤⣾⡞⢀⡞⠀⢈⣿⣿⣿⣿⢿⣿⡿⠏⠀⠀⠠⣴⠸⣧⡇⢸⠁⠈⠁⢸⢸ ⣿⣿⢿⡏⠀⣼⡇⢀⣼⠇⠀⣷⡀⠈⢿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣠⣾⣰⣿⡏⣿⣿⣿⠿⣤⠏⠀⣰⠋⣴⢋⡛⣛⣋⣝⣁⣤⣴⡞⠙⠓⠀⠀⡄⢸⠀⠀⠀⠸⣼ ⣾⡿⣾⠁⢠⣿⠀⣼⣿⡀⠀⢸⣧⠀⠈⣠⢆⠀⠈⠙⠻⢿⣷⡾⠏⠀⢀⡠⣾⣿⣿⡿⣻⢟⣾⣿⣿⠃⣰⠃⢀⡾⢁⡾⢩⠿⠛⣳⢿⢟⡿⠋⡽⢃⡀⠀⢀⡼⡇⣿⠀⠀⠀⠀⣿ ⣽⣽⠇⠀⣼⣟⣞⣋⣼⣇⠀⠀⢿⡀⠈⠱⠟⠒⣦⣄⡀⠀⢀⣀⣠⣴⡏⣰⢋⣾⡏⣴⢻⣿⣟⠛⠃⣰⠃⢠⠟⢠⠞⣰⠋⡼⡿⣱⣯⠞⢠⡟⣡⣾⢦⠞⡾⣹⠀⡿⠀⠀⠀⠠⢻ ⣿⡏⠀⢸⣿⣿⢟⣽⣿⣿⠀⠀⢸⣇⡸⠀⣠⡴⠋⣿⡿⣛⠛⣽⡿⠋⣰⢣⠏⡞⣼⣱⠿⠃⠙⠧⠘⠁⠀⠏⣰⠏⡰⠃⢼⡟⠱⣻⠃⢠⠟⡴⣿⢣⢋⠞⢀⣵⣾⡇⠀⠀⠀⠀⢺ ⡿⠀⠀⠏⢹⣃⣿⣿⣿⣿⡆⠀⠀⣿⣇⣾⠟⢁⡞⣟⡵⢃⣼⡟⠁⡼⣱⢃⡞⢘⡟⠁⠀⠀⠀⠀⠀⠀⠀⡴⠁⠐⠃⢀⣾⣤⡼⠁⢠⣏⡜⣽⠁⢠⠏⣠⠾⢃⣿⠃⠀⠀⢠⠃⠘ ⢁⣤⡶⢾⣿⣏⢻⣟⣿⣿⡇⠀⠀⣿⣿⠏⣠⢏⣾⠟⢠⣞⡞⢀⡞⢱⢃⡞⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣈⣠⠤⠖⠊⠉⢻⣿⠃⠀⠉⠉⠈⠹⠞⣡⣾⡷⣁⣼⣿⠀⠀⣠⠆⠀⠀ ⣋⣥⣾⣿⣿⣻⠈⢿⣿⢿⡇⠀⢠⣾⡏⡰⢃⣾⠏⢠⢿⠞⠀⠎⣀⠐⢦⣤⣤⠤⠖⢲⡖⢲⠒⠋⠉⠁⠀⡀⠀⠀⠒⢋⡿⠃⠀⠀⠀⠀⣀⢸⣾⣿⣿⣷⣿⣿⡜⠀⢀⣾⣏⠀⠀ ⣯⣼⡟⢻⣻⣿⣦⠈⠛⢛⣿⠀⣹⡟⡿⣥⣿⠏⣠⢿⠏⢀⡀⣄⣸⠀⠀⠻⣿⣗⣒⣒⣧⣶⠒⠚⠉⢉⣀⣀⣠⣄⡀⢻⠀⠀⠀⠀⢀⣠⣿⣼⣿⠋⢹⢹⣿⣿⡇⠀⣼⣿⣝⣆⠀ ⣿⠉⠀⠈⢿⣏⣿⣾⣿⠿⣿⢰⡿⠄⠀⠻⠛⣶⣧⣀⢰⡄⢻⡄⠀⠀⠀⠀⠈⣀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⢷⢸⠀⠀⣠⣴⣿⣿⣿⡟⠁⠀⠸⣾⣿⢸⡀⢠⣿⡏⠀⢈⣷ ⢿⣆⠀⠀⠈⣿⣽⣷⡀⠀⣿⡿⠁⠀⠀⠀⠀⠁⠈⠛⢿⣿⣴⣧⣤⣤⣀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣷⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣿⣿⡌⡇⣾⡏⠀⠀⣼⠟ ⠈⢻⣧⠀⠀⠸⣿⡿⣷⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢿⣿⣿⣿⣿⣶⣤⣄⡏⣾⠁⠀⠐⠄⢢⠀⠀⢀⣠⣾⣇⣽⣿⣿⣽⠋⠀⠀⠀⠀⠀⣼⣿⢹⣇⢹⣸⠃⠀⣸⠏⣼ ⠀⠀⠻⣷⡄⠀⠻⣿⡞⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⣿⣿⣶⡦⣼⣼⣤⣾⣿⣿⣿⣿⣿⣿⢟⣿⣦⡀⠀⠀⠀⢰⡿⢸⠈⣿⠀⢿⡆⢰⡟⣰⠏ ⠀⠀⠀⠘⢿⢀⠀⠈⢷⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⣯⣿⡿⣿⣿⣧⢻⣿⣿⣿⣿⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠻⣦⡀⢰⡿⡇⢸⡆⢸⡇⠀⢡⡟⢰⡏⠀ ⠀⠀⠀⠀⠘⣆⠀⠀⠈⣳⣷⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠸⣷⠙⢷⣌⢹⠻⢼⣿⣿⣿⣿⣿⡿⢛⣿⣿⢟⣽⡿⡟⠁⠀⠀⠀⠙⢷⣄⣀⡀⢸⣧⠘⡇⢀⡿⢡⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠖⠒⠒⠒⠲⠶⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⢀⣠⡶⠞⠋⠉⠉⠉⠉⠛⠲⠶⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠰⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠐⣤⡀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢷⣤⡶⠛⠀⠀⠀⠀⠘⢧⡈⢻⡄⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠈⠙⠓⠶⢤⣤⣤⣤⡴⠿⠻⢿⣦⡾⠟⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠶⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⠞⠛⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠉⠁⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⡴⠋⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⣠⡟⠐⠀⠀⣼⣿⣷⡟⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⡿⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⣠⡶⠋⡟⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠙⠟⣿⡃⠀⠀⠀⠀⠀⠀⢻⡿⠗⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⡇⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⢀⣼⠋⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠀⠘⠷⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⠀⠛⢷⡀⡟⠀⢀⡆⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀ ⣸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠷⠤⣼⠃⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⢿⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠉⠉⠻⣦⠀⠀⣼⠃⠀⠀⠀ ⠘⠿⢦⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠛⢶⡄⠀⢸⠆⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠶⠶⣤⠀⠁⠀⡞⢰⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣀⣀⠀⠀⠀⠀⠀⣷⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⣿⠁⠀⠈⠙⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠉⠉⠛⠛⠒⠶⠤⠴⠶⠦⣤⣴⠋⠀⠀⣠⠏⠙⢳⣄⡤⠞⠛⠦⢤⡄⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⢸⡆⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠛⠿⠿⠿⠶⠾⠿⠿⢦⣼⡀⠀⠀⠀⠀⣼⠋⣀⣴⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠂⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠟⢳⡖⠒⢾⣟⣻⡽⠛⠁⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠈⢷⡀⠀⠀⣀⣴⠾⠋⠁⠀⠀⢸⣧⡴⢿⡏⠁⢀⣤⠶⠶⣦⠈⠙⢦⣀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣧⣀⡤⠖⠚⢷⣠⠾⢋⣦⠶⣤⡀⠀⢠⡞⠁⠀⠘⣇⣀⡞⠁⣀⡼⠋⠀⠀⡀⠙⠳⢦⣀⣰⣏⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⣀⢀⠀⢘⠛⠀⠀⢀⢀⣈⠛⠒⠋⡀⠀⠀⠀⠘⣿⠛⠛⠋⣀⡴⠞⠛⣿⠀⠀⢀⠈⣙⣿⠿⠛⢛⣛⠛
⠀⠀⠐⢰⠀⡶⢰⠀⠀⠐⢆⢂⠀⢆⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⡇⡌⢰⡿⡎⡀⠀⠀⠀⠑⡵⣜⡆⠈⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀ ⠀⠀⣱⡇⢸⡇⢇⢡⠀⠀⠀⠀⢡⠈⡿⡄⢸⡘⢄⠀⠀⡀⢃⠀⠀⠀ ⠀⢰⣿⣴⢼⣀⣘⣄⣧⡀⢢⠀⠀⠦⢴⠽⡄⠿⣌⠻⡅⠀⠈⡆⠀⠀ ⠀⠈⣿⠉⣼⡀⠤⠶⣭⠻⣦⡳⣄⠸⣄⠗⠛⢜⡊⠢⣹⢦⡀⡇⠀⠀ ⠀⠀⣇⣤⣼⣤⣄⣀⣌⣆⠈⠫⠺⠷⠇⣶⣤⣴⣷⣶⣾⣦⣽⣇⢀⠀ ⠀⠉⡟⢅⣀⣯⣿⣽⣿⠃⠀⠀⠀⠀⠘⢭⡀⢰⠾⠣⠿⠇⠈⠉⣸⠀ ⠠⠀⢁⠀⠀⠀⠀⠀⠀⠀⠐⢋⠂⠉⠑⠀⡀⠂⠀⠀⠀⠂⡘⢰⢻⠀ ⠀⢧⡈⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡕⢹⠸⠀ ⢀⢸⣱⣜⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢸⡇⠀ ⠀⡆⢯⡎⣏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀ ⠀⡘⡜⣵⡇⠑⢄⠀⠀⠀⠀⠘⠳⠅⠀⠀⠀⠀⠀⠀⡠⠞⣹⠃⢀⠀ ⠀⢱⡈⢜⢷⡀⠘⣿⠲⢄⡀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⢠⠏⢠⡞⠀ ⠀⠀⢷⡀⠑⣟⣤⡈⠢⢼⣿⠑⢢⠤⠔⠂⠉⠀⠀⢀⡴⢃⣴⡿⠁⡀ ⠀⡀⠈⢮⢢⣌⡢⣍⣀⣿⣿⣷⡤⠇⠀⠀⢠⣴⣿⣯⣶⣿⣛⣤⡾⠁
⠀⠀⠀⠀⢠⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡌⢂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⡆⠀⠀ ⠀⠀⠀⠀⡇⠈⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⢇⠔⣿⣧⣌⠙⣧⡀⠀⠀⠀⡠⣶⣖⠺⢅⠀⠀⠀⠀⠀⡸⠀⠀⠀ ⠀⠀⠀⠀⢸⠌⠩⠭⠬⠤⠼⠛⠒⠒⢾⣘⣛⣛⣓⣀⣧⣀⡀⠀⢰⠁⠀⠀⠀ ⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢇⠀⠀⠀⠀ ⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀ ⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢣⠀⠀ ⢠⢧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢣⠀⠘⡆⠀ ⡜⢸⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠉⠒⢤⣇⠀⢰⠀ ⣇⠈⠂⠙⢄⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠃ ⠈⢷⠀⠀⠀⠙⣦⠤⠤⠔⠒⣉⡠⠄⠊⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢻⠀ ⠀⠀⠉⠒⡤⠤⢬⡉⠈⠉⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡠⠖⠞⢺⠁⠀⠘⡀ ⠀⠀⠀⠀⠹⡀⠀⠀⠀⠐⠒⠀⠀⠀⡠⠃⠀⠀⠀⢠⠊⠀⣸⠀⢸⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠶⠦⢤⣤⡴⠟⠁⠀⠀⠀⠀⡠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣶⣶⣶⣶⠖⠒⠒⠒⠒⠒⠶⠦⠤⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠻⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣼⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣷⡀⠂⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡄⠀⠀⠀⠀⠀⠘⡿⠋⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣿⢰⣦⣴⠆⠀⠀⠀⠀⠀⠀⢉⣿⣯⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⢠⡿⢿⡄⠀⠀⠀⠀⠀⠀⠙⠁⠈⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠃⠀⠀⠀⠀⣴⡶⠶⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⣦⡀⠀⣾⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣀⠀⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢧⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣾⢁⠀⠀⠌⣿⠀⢸⠀⠀⠀⠀⠘⣇⠀⢀⣠⡶⠟⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠆⠀⠀⠀⢠⣾⣿⠟⢲⡄⠀⠀⠀⢿⣌⠀⠀⣡⡿⠀⣸⠀⠀⠀⠀⠀⢿⠶⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⡿⠀⠀⠀⠀⢸⡿⠁⠀⠀⢹⡀⠀⠀⠀⠉⠛⠋⠉⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠤⠀⠀⠀⠠⠤⠴⣿⠶⣤⣀⠀⠀⣷⡀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠉⠁⠀⠈⠛⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠀⠀⠀⠀⠈⢯⠉⠉⠋⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣀⣤⡴⠶⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢻⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠈⢻⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣤⣴⡶⠛⠋⠉⢀⣼⣿⠟⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⣼⠁⣰⠏⠁⣴⡿⠉⠀⠀⠀⠀⣼⡏⢿⡄⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⢚⠛⠉⠁⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⢰⣇⣾⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⣿⠀⠈⢿⡄⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠹⡆⠀⣷⡄⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⣼⠟⢁⣠⡿⠋⠀⠀⠀⠀⠀⡄⢠⡟⠀⠀⠈⣿⡄⠀⡄⠀⢹⣧⠆⠀⠀⠀⠀⠸⣄⠸⣷⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⣠⡿⢋⣴⣾⠏⠀⠀⠀⠀⠀⠀⢠⠁⣼⡇⠀⠀⠀⠈⢻⣆⢹⡀⠈⢿⡎⢦⠀⠀⠀⠀⠹⡄⠹⡄ ⠀⠀⢸⡷⠀⠀⠀⣠⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣿⠉⠀⠀⠀⢀⣤⣞⣯⣶⠛⢡⡟⠀⠀⠀⠀⠀⠀⢀⣾⢀⡿⠀⠀⠀⠀⢀⡀⣻⣦⣁⣀⢘⣿⡞⢦⡀⠀⠀⠀⠹⣆⠳ ⠀⠀⢸⠇⢀⣤⢞⣡⣴⣶⠶⠶⠚⢛⣛⣽⡿⠟⠛⠷⠶⣿⣦⣤⣠⣴⡿⠛⠉⢰⡏⢀⡿⠁⠀⠀⠀⠀⠀⠀⣸⣁⣸⣧⡶⠞⠛⠛⠛⠛⠛⠻⣿⡟⠛⠻⣿⡞⢷⣦⡄⠀⠀⠘⣦ ⣀⣠⣾⠿⠋⠉⠉⠁⠀⣀⣤⣶⢿⡿⠋⠁⠀⠀⠀⠀⠀⣿⠀⠉⠉⠁⠀⠀⢀⡿⠀⣼⠃⠀⠀⠀⠀⠀⠀⢠⡿⢛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣄⠀⠘⣿⡄⠳⠄⠀⠀⠀⠈ ⠛⠉⠀⠀⢀⣀⣠⣴⠿⠋⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠃⣴⡏⠀⠀⠀⠀⠀⠀⢀⣾⠇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⢿⣄⠀⠀⠀⠀⠀ ⠿⠻⢿⠛⠛⢉⡼⠋⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⢠⠏⣰⡿⠀⠀⠀⠀⣰⠏⢠⣼⣿⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢿⣆⠀⠀⠀⠀ ⡄⠀⣿⠀⣰⡟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠇⠀⠀⢠⣾⢠⣿⠁⠀⠀⢀⣾⠏⢀⡞⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠻⣦⠹⣦⠀ ⡇⠀⢹⣾⣯⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣼⠀⠀⠀⣼⣿⣿⠏⠀⠀⣠⣾⠏⣰⠟⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢷⡈⢷ ⣇⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⣰⡿⢋⡟⠀⢠⡾⣿⣥⠞⠁⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣿⣦ ⢻⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⡇⠀⣰⡿⢁⡾⢁⡴⣫⣾⠟⠁⠀⣠⡿⠁⠀⠀⠀⠀⣀⠀⠠⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿ ⠸⣇⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠶⠞⠛⠋⠉⣀⣴⡇⣴⠟⢀⣾⡷⠿⠞⠛⠁⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠹⣷⣦⣤⣀⡀⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⡿⠀ ⠀⢻⣮⣿⠙⢿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣼⡿⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠟⢹⠇⠀ ⠀⠈⢻⣿⡀⢠⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠻⠷⣦⡏⠀⢠ ⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢠⠜ ⡄⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣰⠏⠀ ⣷⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣾⡟⠀⠀ ⠹⣷⡄⠀⠀⠈⣿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢠⡞⣿⠁⠀⡞ ⠀⡾⠻⣶⡀⠀⠈⢷⡈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⣴⠏⢰⡟⠀⢠⡇ ⡄⢳⠀⠈⣿⣦⣀⠈⢻⣆⠀⠈⠙⠷⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⠟⠁⠀⡾⠀⠀⣼⠀ ⢳⡸⡇⠀⢸⣏⠻⣷⣄⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⣼⡇⠀⣸⡇⠀ ⠈⣿⣿⠀⠈⣿⡀⠹⣎⠙⠻⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠛⠉⠀⠀⠀⠀⣸⢿⠁⠀⣿⠀⠀ ⠀⠘⢿⣷⠀⠸⡇⠀⠹⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⡏⠀⣾⠇⠀⠀ ⠀⠀⠈⢿⣇⠀⣿⣤⠶⠼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⣿⠁⢰⡟⠀⠀⠀ ⡄⠀⠀⢀⣿⣦⠺⣿⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣼⠇⢠⡟⠀⠀⠀⣸ ⣧⠀⠀⠀⠻⣟⣷⣿⣷⠀⠀⠈⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⢰⡏⢀⡿⠀⠀⠀⣠⣏ ⢻⣇⠀⠀⠀⠙⣿⣿⣿⣷⠀⢶⡀⠈⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢠⡿⢁⡼⠁⠀⠀⣰⣿⡏ ⣆⢻⣧⠀⠀⠀⠙⣿⣿⣿⣦⡈⢻⡄⠀⠀⠉⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⢀⣾⢃⡾⠃⠀⠀⣴⣟⡿⣠ ⣿⣆⢻⣧⡀⠀⠀⠘⣯⣿⣿⣿⣦⣿⡄⠀⠀⠀⠀⠉⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣯⣤⣄⣀⣀⣀⣀⣾⢡⡾⠁⠀⢠⣾⠟⣿⠃⠙ ⣿⣿⣦⠹⣷⡀⠀⠀⠘⣿⣿⣿⡉⢻⣿⣆⣠⣶⣶⣿⣿⣿⣿⣿⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠏⠀⠀⣰⣿⣁⣾⡏⠀⠀ ⣿⣿⣿⣷⡜⢿⣆⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠈⠙⠛⠷⢤⣄⣀⡀⣀⣠⣤⠴⢞⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⣠⣾⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠛⠛⠓⠒⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣡⣼⡆⠀⠀ ⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠘⢸⡁⢿⡇⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⠞⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣶⠇⠀⠀⠀⠀ ⠀⠀⠀⢷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⢀⠏⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢀⡼⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⠈⠑⠂⠤⠤⠤⠀⠒⠉⠀⠀⠀⠀⣠⠎⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⡠⢸⡧⠤⠒⠤⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⠤⠀⠤⠔⠁⠀⠀⠀⠀⠀⢀⠔⠀⠘⣧⠀⠀⠀⠈⠑ ⠀⠀⣠⠔⠚⠉⠉⠉⠙⣻⡆⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠘⢦⠀⠀⠀⠠ ⣠⠾⠥⠤⣀⠀⠀⠀⣸⠟⡇⢄⣀⠀⣀⠠⠄⠊⡐⢀⡄⠀⠀⠀⠀⠀⠙⠢⣄⠀ ⠁⠀⠀⠀⠈⢧⡠⠚⠁⠀⢧⠀⠀⠀⠀⠀⠀⡰⢀⠎⠀⠀⠀⠀⠀⠀⣀⠤⠜⠃ ⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⡀⠀⠀⠀⠀⡔⢠⠊⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⢣⠀⠀⠀⣜⡠⠁⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡒⠠⢄⣀⡀⠀⠀⠈⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠈⣇⠁⠒⠠⠤⠤⠤⠤⡲⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⡄⠀⠀⠀⠀⠀⠀⢹⡆⠄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠙⢦⣀⠀⠀⠀⠀⠀⣷⠀⠀⢠⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⠀⠀⣀⣤⣴⡧⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠋⠀⣠⣴⠟⠋⣉⣅⢀⣠⡀⠀⠀⠉⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢃⣴⡿⠋⠀⣠⡞⠁⣼⣯⣉⠹⡆⠀⠀⠀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⢰⣷⡿⠟⠚⠛⢻⡟⠀⢸⠷⠦⠬⢭⣿⣀⣠⡤⠿⠃⠀⠹⣄⣀⣀⡠⠤⠤⠖⠚⠉⠁⠈⢳ ⠀⡿⠋⠀⠀⠀⢠⣿⡅⢀⡏⠀⢠⡴⠚⢻⡏⠙⠓⠦⣄⡀⠀⠹⡶⠶⠤⠤⣀⠀⠀⠀⠀⠀⡾ ⣸⠃⠀⠀⠀⠀⣾⣿⣷⡾⠀⢠⡏⠀⠀⡞⠀⠀⠀⠀⠀⠙⠳⣤⣻⠀⠀⠀⠈⠙⢦⠀⢀⡼⠁ ⡧⠤⠤⢤⣄⢸⣿⣿⡿⠁⠀⣸⣷⡀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈⡟⠉⠀⠀ ⡇⢠⣄⣀⣨⠛⣿⠟⠁⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀ ⢹⣆⠀⠀⠀⠀⠀⠸⣆⡴⠃⠻⠟⢁⡐⠊⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀ ⠀⣿⣷⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠲⠤⠤⠄⠠⠴⠃⣲⡤⠤⠶⠶⢯⡁⠀⠀⠀⠀⠀⠀ ⠀⢹⡈⠛⢯⣗⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀ ⠀⠈⣧⠀⠀⠈⠙⠓⠺⠭⣽⣶⣒⣲⠶⢶⣶⣶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀ ⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⡀⠀ ⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠤⣤⣀⣀⣀⣁⣼⠇⠀ ⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠛⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⣉⡤⠴⢞⠋⠉⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀ ⠀⠀⠀⠈⠙⠒⣲⣤⣾⣯⣤⣄⣿⠗⠀⢄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡤⠧⠾⣿⠀⣀⣤⠴⠶⠛⣛⣀⣀⣀⣀⡀⠲⠦ ⠀⠀⠀⠀⠀⣾⠋⠼⢫⠟⢿⣿⠙⣆⣀⡼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡄⢀⣻⣁⣤⠶⠿⠛⠋⠁⠀⠀⠈⠁⠀⠠ ⠀⠀⠀⠀⣾⠗⠀⠀⠀⠀⠀⣻⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⡀⠠⡏⡔⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠢⡈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⢀⠀⠀⢀⡴⠁⡼⠛⠀⠀⠀⠀⢀⡔⢻⣿⣷⣌⠉⢻⣷⡖⠋⣡⣿⣯⡙⠳⣄⠀⠀⠀⠘⠆⠙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠈⢸⠀⡞⢣⠸⠁⠀⠀⠀⠀⠀⠈⢧⠈⠻⣿⠟⢁⡼⠀⠹⣄⠹⢿⡿⠃⣠⡟⠀⠀⠀⠀⠘⢆⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡆⢸⠀⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢀⣴⣞⠁⠀⠀⠘⡄⠐⠲⠞⠋⠀⠀⠀⠀⠀⠀⠈⠣⡈⢻⡏⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣇⡾⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠒⡶⢦⡈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⢲⠿⠏⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⣀⡷⠾⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⣦⡀⠀⠀⢀ ⣿⣶⡿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠈ ⣿⣿⠃⡎⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣧⣀⣀ ⣿⣿⢸⣇⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⡿⢸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⢿⣿⣿ ⢿⡇⡾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⡇⠀⠘⠟⠋ ⡾⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠀⠀⠀⠀⠀⠒⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣥⣿⡆⠀⠀⠀ ⡇⣼⢺⣏⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠛⣿⢧⠀⠀⣄ ⡇⠛⣾⢹⠻⢭⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠉⠀⠀⣧⡾⠃⠀⢸ ⠀⠀⣿⢸⠀⠀⠀⠄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠋⠀⠀⠀⠀⢻⠃⠀⠀⠀ ⠀⠀⡿⢸⠒⠂⠀⠀⠀⠀⡏⢻⡀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠟⠁⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀ ⠀⣰⡇⠨⠀⠀⠀⠀⠀⢘⡇⠀⢸⣿⡗⠙⠓⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⢾⢻⣷⡿⠋⢰⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⣿⠇⠀⠀⠀⠀⠀⠐⣾⠇⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⣿⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⢿⠈⠈⠒⠒⠒⠒⠒⠞⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠘⣆⢻⡖⠒⠶⠶⠶⢦⠔⢠⣿⣇⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀ ⠀⠐⠌⢂⢹⣦⣀⣀⣀⣠⣰⣾⣿⠀⠀⠀⠛⠋⠉⠉⠉⠉⠉⠉⠙⠋⠛⠛⠛⠳⠶⠶⢶⡆⣿⡔⠦⣤⣤⣤⣄⣠⣤⣀⣀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⣿⣿⣿⠿⠿ ⠟⠹⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍⠁⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⣿⣼⣿⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢿⣿⠇⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⣾⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠃⠂⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⡠⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣧⣤⣄⣤⣴⠶⠟⠛⠛⠛⠛⠛⠛⠶⢦⣤⣀⠘⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⣀⣀⣻⣧⡀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠉⠍⢉⣉⣉⣽⣿⣥⠀⠀⠀⠀⠉⣽⣿⠯⢻⣦⡀⣀⣴⠞⠃ ⠀⠀⠀⠀⠀⣀⣀⣀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠙⢿⣏⠁⠀⠀ ⠀⠀⠀⣰⡟⠋⠉⠉⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⣼⠿⣷⡄⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠀⢸⡏⠈⠘⣿⠀ ⠀⠀⢻⣆⠀⠀⠀⠀⠀⢰⡟⢠⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠸⣿⠀⠀⣿⠀ ⠀⠀⠈⠻⣶⣄⣀⣠⣴⠿⠁⠊⠀⠀⠀⠀⢸⣏⣬⡿⠁⠀⠀⠀⠀⠸⣧⣴⠇⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠹⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣆⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⢀⣤⡾⠃ ⡆⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⣇⣠⡾⠟⠋⠀⠀ ⣷⣀⣀⣀⣠⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣆⣀⣀⣀⣼⣟⣁⣀⣀⣀⣀⣀
⣿⢎⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⢠⠀⠀⠀⠁⠀ ⡿⠁⣾⢧⢀⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣙⣆⣀⣀⣸⢧⠲⡀⠀⢆ ⠇⡀⠁⢸⠇⣯⡛⢳⡾⣼⣶⣦⠀⡾⡄⠀⠀⡄⠀⢹⣛⣩⠹⡄⢰⣈⣆⣡⠀⢸ ⠀⠇⢰⣈⠀⣛⣆⣸⡁⢄⡰⡠⡀⠐⣱⠂⠀⡇⠀⢸⢄⣠⣴⣿⡟⠙⢿⣿⠒⡎ ⢰⠀⢸⢤⣵⡿⠋⣿⣿⣿⣮⣝⣧⡀⢱⡁⢀⢿⢀⣼⣿⠿⡟⣻⡇⠀⣿⢿⠀⣆ ⣸⢀⢼⠀⢻⢧⢠⢹⣿⡙⢋⣿⣿⠛⢪⣳⡸⠈⡠⠃⣿⣦⣴⡿⡏⠘⢉⢸⠀⡿ ⣷⡟⢸⢀⠎⡎⢻⡌⢿⣿⣾⣿⠟⠀⣸⣽⣷⣾⡱⢁⢻⠿⢿⣋⡠⠔⠛⢸⠀⢹ ⣿⠃⣯⣾⡄⢸⠀⠶⢄⣉⣛⣁⢖⣿⢫⣿⡟⡑⡰⡑⢝⣭⡯⡫⣳⣠⠾⡄⠀⢸ ⠇⢘⣏⣿⣧⠀⣿⡞⣵⡛⡵⠣⣗⢟⠋⠁⠁⠀⠌⢈⣸⡘⢱⢽⢓⣢⢮⡇⠀⠈ ⣪⣿⣣⢻⣿⢀⣟⢬⢎⡼⠁⠉⢤⣤⣠⡐⣒⡀⠉⠀⡞⠀⠀⣀⣶⣿⣾⠀⣼⠀ ⡏⠈⣿⡶⢺⡜⠈⠛⠮⣥⣪⠁⠀⢩⠈⠁⠀⠀⠉⠡⣇⣤⣾⡟⠁⢻⣿⢰⠋⣱ ⠙⣆⠸⣟⣜⠁⠀⠀⠀⢸⠙⢿⣷⣶⡗⣄⣀⣆⣠⣾⣼⣿⡋⠀⢀⣿⢇⢿⢠⢻ ⠀⠈⡆⠘⣿⣆⠀⠀⠀⢸⠆⠸⡿⡟⣯⣿⣿⣽⣿⣿⣿⠏⠈⢦⡚⢸⣸⢈⢣⠃
⠀⠀⠀⠀⠀⠀⢀⠂⡠⡌⠀⠀⠘⠒⠀⠀⠀⢈⣤⣀⡉⠄⠀⠀⠀⠀⣠⠴⠁⠀ ⠀⠀⠀⠀⠠⢴⠅⠊⢉⣵⡆⠀⠀⠀⠀⠀⢸⣿⡛⠛⠛⠓⠦⣦⡴⠋⠀⡸⡀⠀ ⠀⠀⠀⠀⠀⠈⠠⠶⠿⡟⣇⣀⣀⣀⢔⣾⣿⣿⢏⡁⠀⠀⠈⠈⢫⡀⠀⢯⠎⡀ ⠀⠀⠀⠀⠀⢀⢀⣠⣤⣼⣿⢻⡿⣿⡿⢻⡙⣻⣿⣏⢀⠀⡤⠂⡎⢻⣆⢆⠘⠃ ⠀⠀⢀⠤⠊⢠⣿⣿⣿⢫⣧⣼⣷⣜⠉⣿⣿⣄⣿⣿⣿⣞⣁⡼⡠⣾⣿⣄⠀⠁ ⠀⠠⠀⢤⡔⢿⡿⣿⡿⣏⠃⠀⣠⢽⣥⠸⡏⡿⣷⡾⠻⣿⣿⣿⣷⣿⡿⠋⠀⠀ ⡄⠀⠀⢼⣇⡸⢃⠃⠙⢷⠲⣦⠙⠋⠟⠀⢹⢔⢟⡿⣿⣀⠈⣻⣿⣷⡏⠀⠀⠀ ⡇⠀⠀⢸⣿⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⢘⢛⣿⢿⣿⠀⢹⠁⠀⠀⠀ ⠀⠀⠀⢈⣿⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⣾⢵⣫⣼⣿⣿⣧⡃⠀⠀⠀⠀ ⡆⠀⠀⠈⣿⣧⠀⠀⡔⠛⠛⢿⣗⡀⠀⠈⢺⡼⡛⠀⢹⢟⣿⠀⠀⠄⠀⠀⠀⠀ ⠻⡀⠀⡜⠀⢿⣆⠀⡇⠀⠀⠀⡟⠀⠀⠀⠀⡆⡇⢲⡟⣻⣿⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⡿⢧⣄⣸⣿⣦⡀⠂⠐⠉⠀⠀⠀⠀⠈⣳⣖⣻⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀ ⠈⢙⣿⣿⡿⢿⡁⠈⢉⡿⠶⢾⠄⠠⢤⣶⣾⠟⢿⠿⣛⠝⡡⠊⠈⠐⠠⠄⠀⠀ ⠺⠭⠁⣶⣶⡸⣯⠴⠈⠀⠑⣄⠀⠀⠈⠁⠈⠑⠖⡊⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡟⠻⣿⠋⡗⢶⣤⣤⣄⣑⡄⠀⠠⠄⠒⠈⠁⠀⠜⠜⡕⠅⠒⠀⠄⠀⠀
⣷⣇⡴⢡⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀ ⣿⣟⡴⠋⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠁⠀ ⣿⠏⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⢎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢘⡀⠙⣷⣀⠀⣀⣀⣀⣽⣷⠖⠿⡅⠀⠀⠸⣄ ⡟⠀⠀⠸⠟⣿⣷⡀⢻⠛⢿⣦⣤⣤⣼⠬⣆⣀⣀⢀⠀⢸⢸⡇⠀⠀⠀⠀⠈⠀⠀⠀⠻⡿⣿⠿⠻⢿⡛⠉⠁⣼⠘⣦⠀⢳⠀⠀⠀⣿ ⠁⠀⡖⠀⠀⣿⣧⠇⢸⢸⢸⠀⠉⣿⠛⠳⠿⡿⠿⠿⠅⠀⣇⢷⠀⠀⠀⠀⢸⠀⠀⠀⠀⡤⠔⢦⡇⠈⢷⡀⣀⣿⣴⣾⣷⣼⡷⠂⡀⢻ ⠀⢠⠇⠀⣴⣿⠛⠀⢸⢘⣼⠀⢸⡏⠀⣀⠀⠹⡄⢀⠀⠀⠸⡜⣧⠑⠀⠀⢸⡀⠀⠀⠀⣀⡀⠀⣠⣴⣾⣿⣿⠟⠛⢿⣿⣿⡿⠒⢱⠸ ⠀⢸⠀⠀⢻⡛⢦⣀⣸⣾⣿⣿⣿⣷⣦⣬⣑⠦⠽⣮⡧⠀⠀⠱⣹⡧⠀⠀⢸⡇⠀⠀⢸⣭⣴⣿⣿⣿⣿⣿⣯⠀⠀⣶⣿⣿⡇⠀⠘⠀ ⠀⣿⠀⠀⢸⠳⣦⣼⣿⡟⢹⢠⣿⣿⣿⣿⣿⣿⣦⣌⡻⣦⠀⠀⣳⡁⠀⠀⡟⢹⠀⣠⣾⣿⣿⠿⢿⠟⢙⣿⣿⠀⠀⣿⣿⠟⡇⠀⢹⡇ ⠀⡇⠀⢀⣾⠀⠨⢿⣿⡆⢸⣸⢿⣿⣟⠛⣿⠞⢹⣿⣿⡿⠷⢦⡙⣿⡄⢠⡇⢸⡏⣹⠇⣿⣿⣦⣀⣀⣾⣿⣿⠇⠰⠟⢃⢠⡇⠀⣿⣿ ⣸⠃⣠⡎⢸⠀⠀⢰⡏⢿⣌⣿⢸⣿⣿⣦⠀⣠⣾⣿⡿⡇⠀⠀⢿⣮⣷⣼⠁⢀⣧⠃⡀⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⢸⡇⠨⢸⢻ ⣿⣾⣿⠀⣾⠀⣠⡏⢱⠈⢻⣿⡄⢻⣿⣿⣿⣿⣿⣿⡷⠃⠀⠀⡞⣸⡿⣿⣷⣿⢃⠎⢀⡴⣻⢿⣿⣿⡟⠁⢀⡤⠼⠘⢛⢸⡇⠀⠀⢻ ⣽⣿⠏⢠⡟⢠⣿⠀⠈⣇⠀⢉⡅⠀⠙⠿⣿⣿⠿⠋⢀⣠⣶⣿⡿⣿⣿⣿⡟⢠⠏⣠⠎⡴⡳⠶⢾⡿⣻⠛⡻⢀⠀⠀⣾⢸⠁⠀⠀⣸ ⣿⡟⠀⣾⣷⣯⣿⡇⠀⢹⡀⠈⠛⠒⣦⣄⣀⣠⣤⣴⢋⣼⢾⢏⣞⣿⢿⡙⣠⠃⡰⢁⠞⡔⢡⡿⣱⡿⢡⡞⣴⣷⢞⡟⢇⣼⠀⠀⠀⢻ ⡿⠀⢰⢿⢟⣿⣿⣷⠀⠘⣧⣇⣴⠊⣼⣟⡍⣱⡟⢡⢮⢎⠎⣾⠋⠁⠈⠁⠀⠀⢡⠋⠜⠀⣝⣀⠟⢠⢏⢾⠏⢪⠋⣴⢻⡟⠀⠀⠀⠸ ⢃⣠⢴⣾⡟⣿⣿⣿⠀⠀⣿⣿⢃⢞⣿⢋⣼⠏⣠⢣⢫⠎⠘⠁⠀⠀⠀⠀⢀⣀⡡⠤⠔⠒⣿⠏⠀⠘⠋⢺⠔⣡⣾⣁⣾⡇⠀⣠⠁⠀ ⣩⣶⣿⣯⣇⠸⣿⣿⡀⢠⣿⣡⢫⡿⢁⣾⠏⠐⠁⠐⠲⣦⣴⣒⣲⢲⠊⣉⣁⠀⠀⠀⠐⣩⠋⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠁⢠⣿⡅⠀ ⣿⠟⠘⣿⢿⣆⣤⣼⡇⣼⠙⢻⣿⣡⡞⢃⡀⣜⠒⠁⠀⠙⠛⠒⠚⠾⠭⠤⠤⠐⠒⠒⢆⢹⠀⠀⣀⣴⣿⣿⠏⠀⣾⣿⠛⠀⣼⡟⠚⣄ ⣷⡀⠀⠸⣿⣿⡉⢀⣿⠃⠀⠀⠀⠋⠙⢿⣷⣼⣄⣀⣀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⣴⣾⣿⣿⡿⠃⠀⠀⣿⣿⢸⢰⡏⠀⢠⡿ ⠈⢿⣄⠀⢻⣿⢷⡜⠁⠀⠀⠀⠀⠀⠀⠀⣿⠙⢿⣿⣿⣿⣶⣼⠹⣇⠀⠀⣰⡄⢀⣤⣾⣧⣿⣿⣿⠋⠀⠀⠀⢰⣿⣹⡎⣿⡇⢀⡟⣼ ⠀⠀⠻⡆⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⣿⣿⣿⣿⡷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠳⣄⠀⢠⣿⢸⡄⣧⠘⠧⡾⣱⠃ ⠀⠀⠀⢸⡀⠀⠘⣿⣿⣦⠀⠀⠀⠀⠀⠀⣿⠂⠀⠸⣟⠻⣍⢻⠧⣿⣿⣿⣿⡿⢿⣿⡿⣿⣿⠏⠀⠀⠙⢷⣌⠉⠀⣧⢹⠀⡼⣱⠃⠀
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⢉⠡⠸⢾⣿⣿⣿⣷⣾⣏⠛⠒⠿⡍⠒⠤⢄⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⡠⡺⠁⡃⠀⢿⣧⠀⠀⠋⠀⠀⠉⠙⣫⣍⢍⠉⠒⠢⢄⡀⠀⠀⠀⠀ ⠀⠀⣠⠊⢰⠁⠀⠱⢄⣀⡽⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⢍⠢⡀⠀⠀⠀⠀⠀⠀ ⠄⡴⠁⠀⠸⠀⡀⠀⠀⡰⠡⠀⠀⣀⢴⠚⠹⣿⣿⣶⢦⣀⠑⣌⢢⠀⠀⠀⠀⠀ ⢀⠃⠀⠀⠀⢱⠉⠐⠚⠒⠁⢀⠜⠁⠈⠢⡀⠀⠉⠀⠀⡨⠷⣿⣾⡶⠶⠶⠄⠀ ⢺⠀⠀⣸⣷⢄⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠉⠀⠉⠁⢀⡼⡏⡻⣿⣛⠳⠶⠦ ⢼⠀⠀⣿⣧⡀⠉⠢⢄⡀⠀⠑⠠⣀⠀⠀⠀⠀⠀⢀⡴⠋⡰⢀⠃⠀⠙⠻⠷⠀ ⠀⡆⠀⣿⣿⣿⣷⣦⣀⠀⠁⠒⠂⠤⠬⠡⢤⠖⠈⠁⠀⡴⢁⠌⠀⠀⠀⠀⠀⠀ ⠀⢳⠀⢿⣿⡿⠿⠿⠿⠿⣷⣶⣤⣄⣀⠔⠁⠀⢀⡠⠊⢠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡆⠘⡅⠀⠀⠀⠀⠀⠀⠈⡹⠛⢁⣀⠤⠖⠉⣀⠔⠁⠀⠀⠀⢀⠀⠀⠀⢠ ⠀⠀⠘⡄⠈⠒⠤⠀⠠⠔⠒⠯⣍⠭⠥⠤⠄⠒⠉⠀⠀⠀⠀⠤⠒⠁⠀⠀⡰⢻ ⠀⠀⠀⠘⢄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢒⣢⣤⡤⠴⠒⣒⣉⣀⣀⠤⠴⠊⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢏⠉⠉⣀⣷⣿⣿⣀⡀⠱⢄⣀⠀⠀⠀⠀⠀⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣶⣿⣿⣿⣿⠏⠀⠈⠣⡤⠬⠝⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠝⠉⠻⣿⣿⣿⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠦⠀⠀⢄⣂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢉⣻⣆⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠉⣠⣤⣶⣾⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣟⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⣠⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⢻⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⠇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⣿⣿⣿⣶⣶⣶⣶⡄⠀⠀⠀⣤⣤⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⢀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠉⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡟⢠⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⣾⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠋⠁⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠋⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠿⠋⠁⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⢿⣿⢿⣶⣶⣦⣤⣤⣤⣶⣶⣶⣾⡿⠿⠟⠛⠋⠛⠛⠻⠶⠶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠈⣿⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡀⠉⠉⠛⠛⠛⠶⠶⠤⢤⣤⣀⣀⡀
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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⢿⡿⣿⢿⣿⣻⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⣿⣟⡿⣟⣿⢷⣿⣦⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⡿⣿⢯⣷⢯⣿⣻⣽⣟⡾⣷⣻⣞⡷⣿⣻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣟⣯⣷⢯⣿⣳⡿⣽⡿⣽⣻⣞⣷⢯⣟⡿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣟⡷⣿⢯⣿⣽⣻⢷⣯⣷⣻⢿⡽⣷⣻⣟⡷⣿⢾⣽⣻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣯⣷⣻⣽⡾⣟⣷⢿⣽⡷⣟⣯⡿⣽⡾⣟⣯⡿⣷⣻⢿⣦⡀⠀⠀ ⠀⢀⣼⣟⡷⣯⡿⣯⣿⣞⡷⣿⣻⢾⣳⡿⣯⢿⣯⡷⣟⣿⡽⣯⣷⢿⣽⣻⣤⡀⠀⠀⠀⠀⠀⠀⠐⣿⢯⣟⣷⣯⣟⣾⣽⢿⡾⣯⣷⢿⣻⣽⣻⣽⢿⡽⣷⢿⣽⢯⣿⢾⣧⡄⠀ ⠀⣾⣟⣾⢿⣽⣻⢷⣻⡾⣟⣷⢿⣻⢯⣿⡽⣿⢾⣽⢿⣞⣿⣽⢾⣯⡷⣿⡽⣧⣄⠀⠀⠀⠀⠀⠀⠘⣿⣻⣞⣷⣯⣟⣾⢿⣽⡷⣯⡿⣯⣷⢿⡽⣯⡿⣯⣿⢾⡿⣽⣻⣞⣿⡄ ⣸⡿⣞⣯⣿⣳⣿⣻⡽⣿⡽⣯⡿⣯⣿⣳⡿⣯⣿⢾⣻⣽⡾⣯⢿⣞⣿⣳⡿⣯⢿⣤⡀⠀⠀⠀⠀⠀⠘⣿⡽⣾⣳⣯⣟⡿⣾⡽⣿⡽⣷⢯⣿⣻⣽⣟⣷⢯⣿⡽⣟⣷⣻⢷⣷ ⣿⡿⣿⣿⡿⣿⣿⣿⢿⣿⡿⣿⣿⢿⣿⣿⣿⢿⣿⢿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢷⡄⠀⠀⠀⠀⠀⠹⣿⢿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⢿⡿⣿⢿⣿⡿⣿⣿⢿⣿⣿⣿⣿ ⣿⣽⢷⣟⣿⣳⣯⣟⡿⣾⣽⢿⣾⣻⢯⣟⣾⣟⣾⢿⣽⣾⣻⢷⣻⣾⣻⢯⣟⣷⢯⣟⣿⣻⣄⠀⠀⠀⠀⠀⠹⡿⣽⣯⡷⣟⣷⢯⣿⣳⣯⣟⡿⣽⣟⣯⣷⣟⡿⣞⣿⣽⢾⣻⣾ ⣿⢾⣻⣽⡾⣯⣷⣻⣟⣷⣯⢿⣞⡿⣯⣟⣷⢯⣟⡿⣞⣷⢿⣻⣽⣾⣻⢯⣿⢾⣻⣟⣾⣽⣻⣤⡀⠀⠀⠀⠀⠹⣟⣾⣽⢿⣾⣻⢷⣻⢷⣻⢿⣽⣾⣻⢾⣽⣻⢯⣷⣟⡿⣽⣾ ⢿⣟⣯⡷⣿⣳⣯⣷⢿⡾⣽⣯⢿⣽⣟⣾⢯⡿⣯⣟⡿⣽⣻⣽⢷⣯⣟⣯⣟⡿⣽⣾⣻⢾⣽⢯⠗⠀⠀⠀⠀⠀⠹⣟⣾⣟⣾⢯⣿⣻⣟⣯⣿⣞⡷⣿⢯⡿⣽⣻⢷⣯⢿⣻⡞ ⠸⣿⣳⡿⣯⣷⣟⡾⣿⡽⣟⣾⣟⡷⣯⣟⡿⣽⣷⣻⢿⣽⣻⡾⣟⣾⣽⣻⢾⣟⡿⣾⡽⡿⡙⠁⠀⠀⠀⣀⣠⣶⡿⣯⣷⣻⡽⣟⣷⣟⣾⣻⢾⣽⣻⣽⢿⣽⢿⡽⣟⣾⣟⣯⡏ ⠀⢻⡷⣿⣽⡾⣽⣻⢷⣟⣿⣳⣯⢿⣻⡾⣟⡿⣾⣽⣯⡷⣿⣽⣻⣽⢾⣻⣟⣾⣟⡗⠉⠀⠀⢀⣀⣶⣾⣟⣿⣳⡿⣽⡾⣯⣟⣿⢾⣽⣳⡿⣯⢿⣽⣾⣻⣽⣯⢿⣻⢷⣯⡿⠀ ⠀⠈⢿⡷⣯⣟⡿⣽⢿⣞⣯⣷⣟⡿⣽⣻⣽⣟⣷⣻⣾⡽⣷⣻⣽⡾⣟⡿⠾⠇⣃⢀⣠⣴⡾⣟⣿⣽⡾⣽⡾⣯⣟⣯⢿⣷⣻⣽⣯⣟⡷⣿⣻⢯⣷⢯⣟⣾⡽⣟⣯⣿⣞⠃⠀ ⠀⠀⠈⢿⣽⡾⣟⣯⡿⣯⡷⣟⣾⣟⣯⣟⣷⣻⡾⣟⣾⣽⢿⣽⣞⣿⣝⠁⠁⠀⠈⠻⣟⡷⣿⣻⢾⣳⡿⣯⣟⣷⢿⡽⣟⣾⣽⣳⣟⣾⣟⡷⣿⣻⡽⣟⣯⣷⢿⣻⣽⣞⠃⠀⠀ ⠀⠀⠀⠈⢫⣿⣻⣽⣻⢷⣟⣿⣳⣯⣟⣾⢯⣷⢿⣻⢷⣯⡿⣞⣿⣞⡿⣧⣄⡀⠀⠀⠙⢿⢷⣻⣟⣯⢿⣳⡿⣽⣯⢿⣻⣽⢾⣯⣟⣾⣽⣻⢷⣟⡿⣯⣟⣾⣟⣯⡷⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⣯⣟⡿⣾⢯⣷⣟⣾⢯⣿⣽⣻⢯⣿⢾⣽⣟⡷⣯⣿⡽⣯⣿⣦⣀⠀⠀⠹⣿⣞⣯⡿⣯⢿⣳⣿⣻⣽⢯⣿⢾⣽⣳⣯⢿⣻⡾⣿⣽⣻⡾⣽⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⡿⣽⣻⣟⣾⣽⡾⣟⣷⢯⣟⡿⣽⣻⣾⣽⣻⣽⣾⣻⢷⣻⣞⡿⣷⣀⠀⠈⠹⣷⣟⣿⣻⣽⢾⣻⡾⣿⡽⣯⣟⣷⣻⢿⣽⣻⢷⣯⡷⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⡷⣯⣟⣾⣽⢿⣾⣻⢯⣿⣻⢷⣻⣾⣽⣳⣯⣟⡿⣽⣯⢿⣳⡿⣿⣆⡑⠜⢾⣷⣻⡽⣟⣷⢿⣳⡿⣯⣟⣾⣟⣯⣷⢿⣻⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢿⣽⡾⣯⢿⣞⡿⣯⣷⢿⣻⣽⣾⣳⣟⣷⣻⢿⣽⡾⣟⣯⢿⣳⣯⢿⠃⠉⡱⣿⣻⢯⣟⡿⣽⣻⢷⣻⡷⣯⣟⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⣽⣿⣷⣯⣿⣯⣷⣯⣿⣾⣯⣿⣿⣾⣽⣿⣽⣿⣯⣿⡏⠁⠀⣸⣷⣿⣿⣽⣿⣯⣿⣿⣽⣿⣽⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⢿⣟⣯⣿⢯⣟⣿⣟⡿⣟⣿⣻⣯⣟⣿⡽⣿⣟⣿⠃⠀⢠⣿⣻⡿⣯⣟⡿⣿⣻⣽⢯⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⣯⣷⣟⣯⣿⣳⣯⢿⣻⢷⣻⢷⣻⣽⣻⢷⣻⡞⠀⢠⣿⣳⡿⣽⣷⣻⣟⡷⣿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⣽⡾⣷⣻⣟⣯⣿⣻⢿⣽⣳⣿⣻⣯⠁⢠⣿⣳⡿⣽⣟⡾⣷⡻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡿⣽⣾⣳⡿⣯⣟⣷⢯⣷⡏⢠⣿⣳⡿⣽⣟⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠻⣾⣽⣻⢷⣻⡾⣿⣽⢠⣟⡷⣿⣽⠟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠫⣿⢯⣟⣷⣏⡾⣽⠻⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢿⣾⡾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣳⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⡴⠁⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠏⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢁⣬⣉⣉⣙⣻⣶⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⠃⠀⠀⢻⣿⣿⣿⠟⣿⢷⡆⠀⢀⣴⣶⣦⣤⣄⡀⠀⠳⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣏⠀⢿⠀⠀⠀⠀⠉⠛⠛⠁⢀⣾⠁⠀⢸⡍⠙⣉⢿⣿⣿⡷⠂⠀⠀⠸⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣄⣸⠀⠀⠀⠀⠀⠀⢀⡴⠈⠁⠀⠀⠘⣟⠂⠈⠉⠉⠉⠀⠀⠀⠀⢀⣾⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⣀⠀⣀⠀⠀⠹⢧⣤⣀⡀⣀⣀⡈⡷⢤⡀⠀⠀⠀⠀⠀⡧⣼⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣋⡀⠘⠿⣤⣄⣀⣀⣀⡉⠉⠉⠉⠉⠁⠀⠳⠀⠀⠀⢀⡔⠁⣿⣀⣀⣾⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣷⡀⠀⠀⠻⣍⠋⠛⠛⠓⠚⠲⢶⣶⣤⡤⣷⠄⢠⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⢍⠓⠲⠤⠤⢶⣶⡿⠋⠀⠀⢠⠏⠀⣴⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠢⠄⠉⠉⠁⠀⠀⠀⠐⠁⢀⣼⣿⣟⡛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣿⣦⣌⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⠇⢹⠿⣦⣄⣀⣀⡀⣀⣀⣠⡴⢶⠟⠉⠀⠀⠹⣯⣽⣧⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢸⢀⡿⠒⠚⣿⡟⣻⣿⣿⣸⡁⢀⡎⠀⠀⠀⠀⠀⢻⠁⢻⣏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠒⠒⢾⣍⣀⣀⣠⣿⡟⠋⠁⠉⠓⠧⣞⣀⣀⠀⠀⠀⠀⢸⠀⠀⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⠀⠀⠀⠀⠀⠀⠈⠓⠉⠑⢦⣄⣸⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡏⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠖⠒⠉⠁⠉⠉⠑⢦⣀⡀⠀⠀⢀⣠⠞⠁⢳⣷⠀⠀⢠⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢼⢿⠀⣶⡀⠀⠀⢇⠀⠀⣿⠌⣧⠀⠈⢣⠀⢡⠀⠀⠀⣀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⡴⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃⠀⠀⠀⡄⢨⠀⠈⡏⠑⠃⠀⢣⡀⣿⡄⢿⢣⠀⠀⢧⠘⠀⠀⠰⠉⠁⠁⢀⠀⠀⠀⠀⠀⠀⠀ ⠃⡼⠁⡇⠀⢀⣀⣀⠀⠀⠀⣾⠋⠀⠀⠀⠀⢰⠃⠘⡆⠄⢸⠀⠀⠀⠀⠁⢸⠱⣼⠈⣳⡀⠀⢧⡀⠈⠀⠀⣀⣴⠤⠇⠀⠀⠀⠀⠀⠀ ⠞⠁⢸⠀⠀⢸⠀⠀⠁⠀⢰⢿⠀⠀⠀⠀⠀⢸⠀⠀⢳⢀⠀⠇⠀⠀⠀⠤⠼⡷⢿⡦⠤⠝⣦⡀⢳⣄⢀⠜⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⠀⠀⠳⣄⠀⢠⣏⢼⠒⠊⠉⠒⠂⣼⠀⠀⠀⢿⠀⠸⡄⠀⠀⣀⢀⣧⠀⠃⠀⠀⠀⠉⠣⠈⠋⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠤⡤⢬⣷⣹⠇⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠈⠉⠀⣀⠤⢒⣀⣤⣀⡀⠀⠀⢸⠀⠀⣢⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⡟⠀⠀⠀⣀⣀⣀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠴⠋⣠⣶⡿⠛⠉⠙⠻⢿⣦⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠁⠀⣸⡀⣠⡾⠛⢉⡿⠿⣷⣌⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⠀⢈⣿⣦⡀⠀⢻⣿⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠠⠤⠤⠤⠀⢾⠀⠀⠈⢿⣿⠁⢰⣿⣆⣴⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⣾⡿⢿⡇⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⢡⠄⠀⠀⠀⠀ ⢄⡀⠂⠀⠀⡘⠀⠀⠀⠘⡏⠀⠸⡿⠛⠻⠏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣁⠉⠉⠀⠴⠃⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⢶⡇⠀⠀⠀⠀⠀⠀⣠⣵⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠏⢰⡿⣦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⡇⠈⣵⢧⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠳⢻⠇⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠀⠀⠀⠀⠘⣇⠘⢉⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⡇⠀⠀⡝⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢺⣿⡇⢾⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⡎⠀⠀⠀⠀⡇⠀⢀⡇⢸⡏⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢀⣸⣿⡇⡞⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⡇⠀⠀⠀⢠⡷⠀⢸⠇⢸⡇⠀⠀⣿⠛⠲⢤⣀⣀⠤⠔⠒⢉⣁⡤⠴⠚⣉⡴⢿⣧⡇⢠⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣷⠀⠀⠀⢸⣇⡀⢸⣦⣸⡇⠀⠀⣿⡀⠀⢸⡟⠛⠒⠉⠉⠁⠠⠴⣶⠏⠁⠀⣸⣿⡃⠈⠀⠀⠀⠀⠀⢼⡿⣿⡆⠀⠀⠀ ⠄⠀⠀⢾⣿⣿⠀⠀⠀⠸⡟⠛⠉⠉⠉⠉⠛⠒⢿⡷⣤⣾⣿⠀⣬⡍⠁⠀⢠⢟⡝⢀⣠⡾⢋⣴⢀⡇⠀⠀⠀⠀⢀⣯⠉⠙⠛⠀⠀⠀ ⡦⣿⣤⣾⣿⣿⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠞⢁⠴⡏⢹⣿⣶⠁⡹⠀⣠⣿⡿⡶⠟⣩⠔⠁⢘⣸⡇⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀ ⣃⣿⣍⣸⣿⣋⣧⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⣠⣯⡴⠚⣄⠩⠛⠷⠧⠾⠯⠑⣉⠔⠊⠁⠀⢀⣿⣿⠃⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⢋⢿⡏⠘⡄⠀⠀⡆⢀⡠⠖⠁⣠⣾⣿⣿⠁⣀⣈⣦⡀⠀⣀⡤⠴⠟⠒⠒⠒⠀⠀⣾⣿⡿⠀⠀⠀⢠⠧⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠁⠀⠈⡇⠀⢹⡀⠀⢝⢉⣠⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⣿⡀⠈⠙⠒⠤⣀⠀⠀⠀ ⠋⠀⠀⣀⡤⠜⠊⢉⣧⡀⢸⢉⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠁⠀⠀⡼⠀⠈⠉⠒⠤⣄⡀⠈⠑⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣩⡤⠤⠆⠀⢻⠃⣿⡏⠀⠘⠀⠈⣿⡟⣿⡇⠉⢹⣿⣿⣿⠾⢇⣉⡛⠻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⠁⠀⠀⠀⠀⠀⣾⣀⣿⠁⠀⠀⠀⣸⡿⠋⢿⡇⠀⢸⣿⣿⣿⣷⣦⣈⠻⣿ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣼⡟⣾⡇⠈⠁⠀⠀⠀⢀⣀⣴⣿⣛⣿⠿⠛⠛⠛⠛⠛⠛⠒⢷⣄⣈⣿⠀⣿⣿⣿⣿⣷⣬ ⢠⡿⢹⠉⢻⣿⣿⣿⣿⣿⠿⠏⠁⣀⣠⣴⣿⣧⣟⣷⡶⠶⠞⠛⠛⠋⠉⣻⡿⠋⠁⠀⠀⠀⠀⠀⢀⣀⣠⣿⠀⠀⡿⣇⢹⣿⣿⣿⣿⣿ ⣼⡇⣼⠀⢸⣧⣷⠀⢸⢻⣧⣴⣿⠿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⠄⣀⣤⣶⣾⠿⠿⣿⡿⢻⠀⢀⡇⢻⡄⢿⣿⣿⣿⣿ ⣿⡇⡿⣧⣼⣿⠿⠛⠛⠈⠉⠁⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣾⡟⡟⠀⠀⢀⣸⣿⣷⣾⠀⢸⣧⠈⢿⣌⢿⣿⣿⣿ ⣿⣷⠇⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣿⣶⡷⣺⠟⠉⠁⣸⣾⣿⠀⢸⣿⡆⢸⣿⣆⠻⣿⣿ ⡗⠿⠀⠀⠀⣱⣶⣶⣶⣿⠿⠿⡿⣿⣿⣿⠛⠳⠦⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⠾⠟⠋⠀⠀⢀⢿⣿⣿⠀⣼⣿⣧⢸⣿⣿⣷⣝⣿ ⠛⣦⡠⢽⣿⠛⠋⠉⠀⠀⢀⣀⣤⣼⣿⣿⣶⠒⠂⠀⠀⠀⠀⠀⠠⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⢨⠀⠀⠻⠷⠤⠴⠶⠿⠟⠛⠛⠛⠹⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⡷⠖⣄⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣁⣀⠔⢻⣅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⡟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣾⣿⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣾⣿⠳⣼⣿⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠟⠁⠀⠀⠀⢀⣾⣿⠇⡜⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠈⠻⣷⡶⠻⣷⡀⠀⠀⠀⠻⣶⠶⣤⣶⣒⣲⣶⡿⠿⢟⣻⢟⡷⠃⠀⠀⠀⠀⣰⣿⣿⢏⣼⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⠀⠈⠳⣄⠾⣿⠀⠀⠀⠀⠀⠑⠚⠭⠭⠭⠽⠶⠯⠽⠚⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣾⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⢻⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⣿⡿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠙⠛⠛⢻⡿⠿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⡎⢀⣿⠁⠻⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣠⠔⠋⠀⠀⠀⠀⠀⠰⠋⠀⠀⢸⡏⡸⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⠀⠀⠀⠀⠀⢠⠇⢸⣿⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⠃⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡄⠀⠀⠀⠀⣸⠀⣼⣿⡀⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢰⣧⠏⠀⠀⠀⢠⠄⠀⠈⠻⣿⣿⣿⣿⣿ ⠻⣿⣷⡀⠀⠀⢀⡇⢰⡿⠀⠉⠲⠤⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⣾⡟⠀⠀⠀⠀⡜⠀⠀⠀⠀⠘⢿⣿⣿⣿ ⠀⠹⣿⣷⡀⠀⢸⢀⣾⠃⠀⠀⠀⠀⠀⡸⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣸⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿ ⠀⠀⢹⣿⣷⣀⢇⣾⠏⠀⠀⠀⠀⠀⠰⠁⠀⠘⡄⠀⠀⠀⢀⣠⣤⣀⣀⣀⣀⡀⠀⠀⣸⣿⣄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢣⠀⠀⠀⠞⠀⠠⠤⠄⠒⠊⠛⠉⢩⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿
⣿⣷⣷⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢂⡴⠋⢻⣿⣿⡿⢿⠀⠈⠉⢻⡿⣷⣄⣀⡷⠀⢧⠀⢱⠀⠸⡄⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⡎⠀⠀⢸⡿⠋⠀⠈⡆⠀⠀⠈⡇⠀⠈⣇⠀⠀⢸⡄⠘⡇⠀⢷⢹⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣠⣾⣿⠀⢀⡴⠻⠀⠀⠀⠀⠃⠀⠀⠀⢻⠀⠀⠸⡄⠀⠈⣇⠀⢷⠀⠸⣾⡿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠊⣠⣾⣿⣿⣿⠴⠋⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠸⡄⠀⠀⢧⠀⠀⣹⣤⠼⠶⣀⠉⠙⠢⣍⡻⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡤⠔⠯⣼⣿⣿⣿⣿⡀⠀⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⣀⣷⣤⠴⠚⠺⣉⠀⠙⠢⣄⡈⠑⠤⣀⠀⠉⠲⢌ ⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠁⠀⣠⣾⣿⡿⢋⡼⠋⠉⠁⢉⡿⠛⠒⣶⠚⠙⠻⣍⠁⠀⠀⠈⠳⢤⡀⠈⠑⠦⣀⠀⠙⠲⢤⡈⠙⠢⢄⡀ ⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⣾⡿⠟⢁⡴⠋⠀⠀⠀⣠⠞⠁⢀⡜⠁⠱⣄⠀⠈⠳⣄⠀⠀⠀⠀⠉⠳⢄⡀⠈⠓⢦⣀⠀⠉⠓⠦⣄⣉ ⠀⠀⢈⣠⡾⠋⠀⠀⣠⣴⠟⠋⢀⡴⠋⠀⠀⠀⢀⡜⠁⠀⢀⠞⠀⠀⠀⠈⠣⣀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢉⣲⣤⣀⣈⣷⣦⡒⣂⣩⣿ ⢀⣴⡿⢍⡀⠀⣠⡾⠛⠁⠀⣠⠋⠀⠀⠀⠀⣠⠋⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⣸⣷⣶⡾⢿⣿⣦⣤⡍⢥⠤⠤⡾⢿⡛⠛⡏⠙⣿⣿⣿ ⣿⣿⣷⣶⡤⡽⢿⣶⣦⣤⣾⣁⡀⠀⠀⢀⡜⠁⠀⠀⢠⠎⠀⠀⣀⡠⢔⡺⢷⣷⣿⣥⣀⣘⣛⣩⣽⡇⢀⠀⠀⠁⠀⡇⠀⡇⠀⠹⣿⣿ ⣿⣿⣿⣯⡴⠃⠀⢸⠉⠉⠓⠲⣬⣭⣉⣿⣷⣶⣶⣶⣟⢒⣊⣩⣵⠚⠉⠠⡌⢟⠛⢿⣿⣿⣿⣿⣿⢷⣜⠀⠀⡄⠀⡇⢰⠃⡄⢆⠹⣿ ⣿⣿⡿⠋⠀⠀⡀⢸⠀⢣⢠⡄⢇⠈⠉⠛⠛⠛⠿⠿⢛⡟⣻⠟⡿⠳⣄⠀⣿⡾⣆⠀⠀⠉⠉⠁⠀⢸⡟⢠⠀⣧⠀⣇⢸⠀⠘⣜⣷⣿ ⣿⡏⠀⠀⠀⡰⠁⠃⢣⡀⠈⢿⣜⡄⠀⠀⠀⠀⠑⠦⣀⠘⠁⠀⡅⠀⠈⠣⡘⡇⠈⠓⠀⠀⠀⠀⠀⠀⣇⡌⣰⠋⢧⣏⠻⡄⠀⠈⠻⢿ ⣿⢀⣤⣶⡞⠁⠀⠀⢠⠙⢷⡈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠙⠢⢤⡇⢸⠀⠀⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠹⡄⠈⠀⠀⠀⣠ ⣿⣿⣟⣁⣀⣀⣀⣠⡟⠀⡄⠑⢬⣻⣮⡑⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⢀⣀⡁⠈⠑⠲⣿⣿ ⣿⠉⠉⠉⠉⠉⠉⡿⢁⣴⡇⠀⢠⠌⣿⣍⠀⠀⠀⣀⠀⠀⠀⠀⣀⣉⣁⣀⣀⣀⣀⣀⡠⠄⠀⢀⣾⠏⠀⠠⣤⣀⣀⣀⣨⣷⣶⣦⣼⣿ ⡏⠀⠀⠀⠀⣰⣾⣵⣿⣿⡇⣠⡏⢠⣿⠈⠓⢄⠀⠀⠉⠻⠿⣉⣉⣉⣋⣉⣉⠩⠝⠋⠀⢀⡴⠋⣸⢮⢣⣄⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⠀⠀⠀⠈⠉⠉⠀⣿⣿⡾⠛⣇⡿⢻⣇⡄⠀⠑⢄⠀⠀⠐⠤⠤⠤⠤⠤⠤⠐⠂⠀⣠⠊⠀⢀⡇⡾⣦⡇⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⣷⣼⣧⣴⠶⣦⣄⣿⡿⠀⣀⣼⣷⣤⣿⣿⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠠⡀⠀⢀⠞⠁⠀⠀⢸⣼⠇⠹⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⣸⡿⠛⠁⠀⣨⣿⣿⡿⠛⢹⡟⣼⣿⣿⣧⢣⠀⠀⠀⠈⠳⣄⠀⠀⠀⡐⢁⡔⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠰⠋⠀⠀⠀⣰⣿⣿⠇⠀⠀⢸⡇⢻⣿⠟⠻⡈⢇⠀⠀⠀⠀⠈⠓⠲⠗⠚⠉⠀⠀⠀⠀⠀⢰⣿⣦⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠈⡇⠘⣿⡀⠀⡇⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⢿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⣧⠀⢻⣧⠀⠹⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⠻⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠘⣿⡆⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟⢻⣿⣿⣎⢿⡈⠙⠿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⢸⣇⠀⢹⣿⡄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢸⣿⣿⣿⡜⣧⠀⠀⠀⠈⠙⠛⠿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠻⣿⣿⣿⡟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠛⠻⠿⠿⠟⠛⠛⠛⠛⠛ ⠿⠉⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢨⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠆⠦⠦⠀⠀⠠⠰⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⢸⣿⣿⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⡀⢸⣿⣿⠙⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀ ⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⠀⠂⠀⣿⣿⢘⣿⣿⠇⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠂⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠖⢀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⢀⢄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠈⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠋⠁⣈⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣭⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⠋⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢠⠀⠀⠀⠀⠀⠄⢹⣿⣿⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⠈⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⣈⣿⣿⣆⠑⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣇⣀⣀⡀⠀⣀⣀⣤⣶⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⢷⣶⣤⣄⣀⡀⠀⠀⠈⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢻⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣠⣤⡆⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡛⠉⠛⠋⠉⠉⠉⢙⣿⣿⣋⣀⡀⠀⠀⠀⠀⠀⠀⠈⢠⣼⣿⣿⣯⠻⣿⣦⡀⠀⠀⢀⣠⣴⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⣶⣶⡶⠾⠿⠿⠿⠛⠿⠏⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉⠉⠉⠀⠀⠙⢿⣿⣦⣴⣿⠿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠛⠛⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡿⠋⠀⠁⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢉⠻⣿⣦⠀⠀ ⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠰⢀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠀⢻⣿⡇⠀ ⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢀⣻⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⣽⣿⡄⠀⠀⢰⣿⠇⠀ ⠀⠀⠀⠀⠈⢿⣷⣦⣤⡀⠀⠀⠀⠀⣠⣾⡿⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⣹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⢀⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠿⡷⠶⠶⢾⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠿⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠀⣠⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠙⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠘⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠙⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠘⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣽⡿⠀⠀⠀⠀⣠⣼⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⠀⠀⣀⣴⣾⣿⠟⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢀⣴⣾⡿⠟⠋⠁⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⣸⣿⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⣽⣷⣤⣤⣼⣯⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣭⣿⣷⣦⣤⣤⣤⣤⣴⣿⣿⣥⣤⣤⣤⣤⣤⣴⣤⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠁⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⠀⠀⢹⠀⠀⠀⠀⠀⠉⠙⠲⠦⠤⣄⠈⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠁⢀⠀⠀⠀⣰⠇⢀⡾⠀⠀⠀⠀⠀⢸⠀⠀⠘⣧⠀⠀⠀⢦⠀⠀⠀⠀⠀⠘⣧⣀⣞⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠁⠀⢰⠏⠀⢀⣼⠏⠀⣾⠇⠀⠀⠀⠀⠀⣸⢸⠀⠀⣿⣧⡀⠀⠈⢧⠀⠀⠀⠀⠀⢻⡉⠉⢉⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⣠⠎⠀⠀⢰⠏⠀⢀⣾⡟⢀⣼⣽⠀⠀⠀⢠⡆⢀⡇⣸⣠⢤⣿⣿⣷⣀⡀⠘⣆⠀⠀⠀⡄⠀⠙⠲⣿⠀⠘⣿⡄⠀⠀⠀⠀ ⠠⠞⠁⠀⠀⢀⡟⠀⢀⡾⣺⠋⢉⣽⣯⠀⠀⠀⣼⠀⡼⠀⡿⡇⢸⡏⢣⣳⡀⠉⠳⢽⣆⠀⠀⢹⡀⠀⠀⢸⣀⢀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⣼⢠⡟⠀⢸⠏⡇⠀⠀⢰⠇⣰⠃⣸⠇⡇⢸⠃⠀⠳⣽⡄⠀⠘⣿⡄⠀⠀⣇⠀⠀⢸⡁⠉⢿⣎⣇⠀⠀⠀ ⠀⠀⠀⠀⣴⡟⠀⢠⣧⡏⡇⠀⡟⠀⣷⠀⢀⣏⡼⠁⢠⡿⠀⡇⡿⠀⠀⠀⠙⣿⡀⠀⣿⣳⠀⠀⢹⠀⠀⠘⣇⠀⠀⠹⣿⠀⠀⠀ ⢰⠁⠀⠐⠋⡇⠀⣸⡟⠀⣧⢸⠃⠀⢹⢠⡿⠋⠀⢀⡿⠁⢠⣷⠃⠀⠀⠀⠀⠈⢧⠀⡟⣿⣇⠀⢸⡇⠀⠀⠈⠻⡄⠐⣿⠀⠀⠀ ⠊⠀⠀⣼⠀⡇⠀⣿⣃⣤⣿⣾⣰⡶⠾⡁⠀⠀⠀⡼⠁⠀⢸⣿⣯⣿⣷⣶⣶⣤⣼⣦⡇⢘⣿⡄⠀⡇⠀⠀⠀⠀⣷⠴⠋⠀⠀⠀ ⠀⠀⠀⣿⠀⡇⠀⣿⣿⠛⠹⡿⣿⣿⣷⣷⠀⠀⣸⠃⠀⠀⡾⠟⡛⢻⣷⣦⣄⠀⠈⢻⡗⠀⣿⢷⠀⠇⠀⠀⠀⠀⢹⢀⡏⠀⠀⠀ ⠀⠀⠀⢿⠀⣿⠀⡏⢿⠀⣾⠶⣿⡟⣷⠉⢣⢀⡏⠀⠀⠀⠀⣸⣿⢻⣿⠻⣿⣆⠀⢸⠇⠀⡇⠈⣿⠀⠀⠀⡦⠀⢸⡿⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⢸⡆⡇⠀⠀⢿⣷⠿⢿⣻⠀⠀⢻⠅⠀⠀⠀⠀⠸⣧⡟⠿⣟⣻⠏⠀⠉⠀⢸⡇⠀⠘⠀⠀⠀⡅⣸⣆⢻⣛⠁⠀⠀ ⠀⠀⠀⠀⢳⣸⠹⣇⠀⠀⠀⠙⢤⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠷⠟⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣧⢿⡌⣮⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿⢢⡷⢻⣿⢧⠀⠀ ⠀⠀⠈⠀⠀⠈⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⣿⡇⣸⠁⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡄⢸⣋⠔⠁⠀⠘⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⡏⢸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢸⣷⡟⠁⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⡇⡟⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠇⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⢠⣿⠀⠀⢀⣿⠁⠀⠀⣀⣝⡲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢻⣾⡍⢹⡇⠀⢸⠇⣿⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠙⣇⠈⡰⣯⠤⠒⣺⠁⠀⠈⠲⡄⣯⣹⣷⡶⠲⢶⠒⠚⠋⠉⠀⠀⢀⡼⠁⠻⣼⡇⠀⣿⡔⣿⠤⢺⠿⠦⠤⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠹⡄⠁⢻⠀⠀⣿⡀⠀⠀⢀⣾⠋⠉⣿⡇⠀⢻⡇⠀⠀⠀⣀⠔⠋⠀⢀⠔⣿⣇⢰⣿⠟⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⠀⢠⡟⢶⡸⣇⢸⣉⣉⣙⠒⣾⠃⠀⠀⣿⠇⠀⠀⠳⣄⡴⠚⠁⢀⠠⠚⠁⣼⠟⣿⣾⡟⢀⠤⢲⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠙⠿⡎⠀⠀⠉⢱⡿⠀⠀⠀⣿⠀⢀⣴⣽⣿⣭⣦⠂⠀⠀⠀⣼⡟⠀⠈⣿⠏⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⠀⠀⣤⡿⠀⠀⠀⣼⠃⠀⠀⢰⡟⡴⠛⡇⠈⠁⠀⢈⡷⡀⠀⡼⣿⠀⠀⢀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⢻⡝⠀⠈⢉⣿⠀⠀⠀⣿⠋⠀⠀⣇⠀⠀⠀⡼⠁⠘⠞⢱⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠔⡢⠊⢹⡿⠛⡇⠈⢛⠳⢤⠃⢡⠸⠀⡞⣿⣿⣿⣿ ⠉⠀⠀⠀⠀⠀⠀⠀⡠⢊⣼⡇⡠⢺⠀⠀⠃⠀⠘⡀⠘⡀⠘⡀⠇⠸⣽⢿⣿⣿ ⠀⠀⠀⠀⠀⢀⣀⠨⢒⣿⣿⡏⠀⠘⠀⠀⢀⠀⠀⣣⡀⠥⡀⠓⢌⠒⠄⡁⠪⢟ ⠀⠀⠀⢀⡾⠋⢀⣴⠿⢫⠊⠁⢈⠟⢉⠯⡉⠣⡀⠀⠉⠢⣈⠑⠤⡈⠒⠬⡐⠠ ⠠⢀⡴⠋⢀⡴⠟⢁⠔⠁⠀⡔⠁⢠⠃⠀⠑⢄⠈⢑⣄⠀⣀⠑⠢⣈⣵⣄⣚⣿ ⣾⣯⣄⣲⣯⣀⡔⠁⠀⢀⠊⠀⢠⠃⠀⣀⣤⣦⣟⡉⠿⣛⡇⡋⠙⢙⠀⡇⢻⣿ ⣿⣿⠗⠁⢸⢈⢁⠖⠯⢿⣶⣶⣧⢬⢷⡉⢰⣼⠙⠻⠿⠟⢳⣅⢰⢸⠀⠑⣢⣻ ⡿⠁⢀⠌⡈⢌⡸⣶⡀⠀⠀⠢⢌⠊⠈⠈⠢⢣⠑⠀⠀⠀⠈⣸⡘⢢⡓⡄⠘⠿ ⣧⡾⠋⠀⣠⠇⡑⢝⣗⠄⠀⠀⠀⠉⢂⢠⠀⠁⠀⠀⠀⠀⣰⠏⠀⢀⡁⠀⢤⣴ ⡏⠉⠉⣉⣝⣴⡇⡐⣹⠡⡀⠠⢀⡠⠤⠬⠤⠤⡤⠔⢀⠔⡏⡐⢦⣤⣴⣿⣶⣿ ⣇⢀⠀⠉⠉⣿⠞⢧⠿⣦⠈⠢⡀⠀⠉⠉⡉⠁⠂⡠⠃⠸⡼⡍⠑⣾⣿⣿⣿⣿ ⢛⡿⠞⢉⣷⣿⠔⡞⣿⣿⢆⠀⠀⢄⠀⠀⠨⡠⠊⠀⠀⣾⠁⠁⠀⣿⣿⣿⣿⣿ ⠈⠀⢀⣾⣿⠀⠀⡇⣿⠋⡎⠄⠀⠀⠉⠙⠈⠀⠀⠀⢰⣷⣦⠀⠀⣿⣿⣿⣿⣿ ⠀⢀⣾⣿⡇⠀⠀⢧⠸⡇⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣷⢤⢿⣿⣿⣿⣿ ⠀⠀⢹⣿⡇⠀⠀⢸⡀⢿⡄⠀⠈⡄⠀⠀⠀⠀⠀⠀⣼⠋⢸⣿⣏⡆⠈⠙⠻⠿
⠀⠀⠀⢰⠒⢲⠒⠒⣶⠖⠖⠒⠒⠒⠒⠲⣖⠲⡒⠒⠒⣶⠐⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⡌⠀⢰⢇⡇⢠⠀⠀⠀⠀⠀⠈⠢⡘⢆⠀⠸⣆⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠇⢰⠇⠀⡾⣿⢳⠘⡄⠀⠀⠀⠀⠀⠀⠈⢪⣷⣄⣻⡄⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⢀⣿⠀⢠⣿⡇⢸⡀⢣⠀⠀⠀⠀⠀⠀⠀⠘⡀⠙⢻⣷⡀⠀⠘⡄⢰⡀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀ ⠀⠀⢸⣼⣿⡆⢸⣿⠇⠸⣇⠈⢇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡿⣷⡀⠀⢿⡄⠹⣦⡀⠀⠀⢀⡀⠸⣼⠀⠀⠀⠀ ⠀⠀⣾⣿⣇⣇⢸⣿⠀⠀⢹⡀⢸⣆⡀⠀⢤⠀⠀⠀⢈⣇⠀⢣⡘⣷⡀⣸⣿⣆⠚⢿⣎⠉⠀⠀⠀⢻⡀⠀⠀⠀ ⠀⠀⣿⣿⣿⢻⠹⡟⠒⠒⠒⢷⠚⣿⣷⣄⠈⢳⡀⠀⠀⢸⡍⠹⣏⠉⣿⡀⢧⠙⢧⡀⠻⣦⡀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⢸⣿⡇⠈⣆⣇⣀⣤⣴⣾⣧⣽⠙⢿⡦⡀⠻⣦⡀⠀⣿⣄⢿⠚⠛⠻⡌⡗⠒⠿⣄⣻⡿⣦⠀⠀⡇⠀⠀⠀ ⠀⠀⢸⣿⠁⠀⠺⣿⠁⠀⠀⠀⠈⠻⣇⠈⠙⢿⣷⣜⣿⣦⣸⠙⢆⣇⠀⠀⠘⢿⣀⠀⣈⡙⣧⠘⢷⣤⠇⠀⠀⠀ ⠀⠀⢸⣷⣴⣶⣶⣿⣶⣶⣦⣤⣴⣤⣼⡆⠀⠀⠙⠈⠛⠛⠻⠇⢴⣿⣷⣷⣾⣿⣿⣿⣿⣷⣿⣷⣾⣿⣇⣀⢠⠀ ⠀⠘⢻⣿⣟⠁⠀⠀⣏⣭⡟⠻⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠰⣟⡉⠀⠀⠀⣤⣽⡏⢉⣿⣿⡇⡸⢻⠉⠁⣿⠀ ⠀⠀⠀⡇⠈⠑⠂⠀⠛⠛⠛⠛⠛⠛⠓⠁⠀⢀⣀⠄⠀⣤⣤⡄⡨⠹⠓⠒⡚⠛⠛⠛⠛⠛⠉⠁⠀⣼⠀⢰⣿⠀ ⢣⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠃⡼⠱⠉⡉⠀⠁⠀⢀⠀⠁⠀⠀⠀⠀⠀⠙⠀⢰⠇⢠⡟⢹⠀ ⠈⢧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⢿⠃⡾⠀ ⠀⢸⣧⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡾⠁⢸⠀⡇⠀ ⠀⠘⣟⢳⣄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⣿⣼⠃⠀ ⢸⡀⢿⠈⡟⢳⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀ ⠀⢧⠸⣇⣿⠈⣷⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀ ⠀⠸⡄⢻⡜⣧⣿⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣖⣂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⡟⠀⠀⠀ ⠀⢠⠹⡄⢻⣿⣿⠀⠈⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⣰⡿⠀⠀⡠⠀ ⠀⠸⡄⠙⣆⠻⣿⡄⠀⠀⢸⡟⡷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⣠⡿⠁⠀⣰⡇⠀ ⠀⠀⢷⡀⠈⠳⣝⢿⣄⠀⠀⠻⣷⠈⠉⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⢠⡿⠁⠀⣴⣿⠁⠀ ⠀⠀⠘⣿⣄⠀⠈⢻⣝⠷⣄⠀⠘⠲⢤⣾⣿⣏⠈⠑⢦⠤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣠⣾⣿⠃⠀⣠ ⡀⠀⠀⠹⣟⢶⣄⠀⠻⣏⠈⢷⣤⠀⢰⣿⣿⣿⣄⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡟⣁⣴⣾⣿⡿⠃⢀⣴⠏ ⠘⣄⠀⠀⠘⢦⢙⣷⣦⣌⡳⢦⣤⣤⣾⣿⣿⣿⣿⣿⡆⢹⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣩⣴⣶⣿⠋⠀
⠀⠀⠀⠀⢰⡶⠒⣶⠖⠒⢲⣶⠖⣶⠒⠒⠒⠒⠒⠒⢶⡖⠲⣦⠐⠒⠒⢲⡆⠒⠒⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⡿⠀⠀⣸⠿⡆⢸⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⢧⡀⠀⠀⣿⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⢰⠇⠀⢀⣯⣴⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠻⣄⠀⢸⣧⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⢀⣾⠀⠀⣸⢯⡿⢻⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣮⡳⣄⢿⡇⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⣸⣿⠀⠀⣿⣿⠇⢸⡆⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠛⢿⣿⣆⠀⠀⠘⣆⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢰⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢀⣿⣿⠀⠀⣿⣟⠄⢸⣧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⡿⣿⡄⠀⠀⢻⣆⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠸⡄⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⢺⣿⢿⠀⠀⣿⡟⠀⠈⢿⡄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣧⠹⣷⡄⠀⠘⣿⣆⠀⢻⣷⣀⣀⣠⠤⠶⠂⠀⢳⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣸⣇⠀⣿⡇⠀⠀⠈⣧⠀⠘⣷⣄⠀⠀⢳⡄⠀⠀⠀⠀⣸⣄⣀⢸⣆⣘⣿⡄⢀⣿⢿⣷⠉⠙⢿⣄⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣏⡿⣿⠙⣿⠓⠶⠤⠤⠾⣷⠚⡟⣿⣧⡀⠀⠹⣄⠀⠀⠀⠀⢷⡈⠉⢿⠉⠉⢿⡄⠈⣇⠹⢷⡄⠈⢻⣷⡄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⢻⠃⠸⡄⣿⠀⠀⠀⣀⣠⡼⣆⢹⠙⢿⣿⣆⠀⠹⣷⡀⠀⠀⢸⣷⡀⢸⣯⡭⠼⢿⡄⠹⣦⣄⣹⣦⡀⢻⣻⣦⡀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡜⠀⠀⢳⣸⡤⠖⠛⠛⠛⠛⠿⣯⣧⠈⠻⣮⡳⣄⡘⢿⣦⡀⠈⣿⢳⡎⢻⡀⠀⠀⠙⣦⣷⠀⠈⠉⠻⣮⣷⠙⢿⣆⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠁⠀⠀⠉⢿⡇⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠈⠻⣽⡿⢦⣝⢿⣦⣼⡄⠹⣎⣧⠀⠀⠀⣈⣛⣧⣀⣀⣀⣀⢹⣦⠈⠻⣷⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣤⣼⣿⣿⣿⣿⣷⣶⣖⣒⣲⣶⡦⣤⣹⡆⠀⠀⠈⠻⠄⠛⠻⠿⠿⠷⠠⢼⣻⣿⣭⣵⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣾⣿⣿⡂⠀⢀⣆⠀ ⠀⠀⠶⣿⣿⣿⠟⠋⠉⠉⢹⠟⠛⢿⠿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠛⠋⠉⠉⠉⣉⣙⣿⠟⠛⣿⣯⣿⡏⠙⣿⡿⠛⠛⢸⣿⠀ ⠀⠀⠀⠘⡏⠛⢷⣄⠀⠀⢸⣿⣿⣿⣤⣼⣿⣿⣟⣩⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣦⣄⣀⣀⣸⣿⣿⣟⣂⣒⣿⣿⡿⠡⠚⢁⡇⠀⠀⣿⣏⠀ ⡀⠀⠀⠀⣧⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢂⣦⡴⠂⡀⣠⢶⢶⡖⢠⠆⠞⠉⠂⢀⡜⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡇⠀⣰⣿⡇⠀ ⠹⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠁⣼⢣⠋⠈⡈⠀⠋⠀⠀⠀⡄⠘⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⡟⠀⢰⡟⢸⡇⠀ ⠀⢳⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠈⠀⠂⠀⠀⠀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⣿⠁⢸⡇⠀ ⠀⠈⣷⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡼⠃⣿⠀⢸⠁⠀ ⠀⠀⢹⣷⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠟⠁⢀⣿⠀⡿⠀⠀ ⠀⠀⢸⡏⠻⣦⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠘⣿⢰⡇⠀⠀ ⠀⡆⠀⣿⡄⣿⡿⣦⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀ ⠀⢳⡀⢹⣇⢻⡇⢹⣏⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀ ⠀⠘⣇⠈⣿⡸⣧⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⠀⠀ ⠀⠀⢻⡄⠘⣧⢹⣆⣿⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡒⣂⣭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣹⣿⠇⠀⠀⠀⠀ ⠀⠀⡀⢳⡄⠹⣏⣿⣿⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣿⡟⠀⠀⢀⡄⠀ ⠀⠀⣷⠀⠻⡄⠹⣿⣿⡀⠀⠀⠀⢸⡿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣾⡟⠁⠀⠀⣼⠀⠀ ⠀⠀⠸⣆⠀⠹⢦⠙⢿⣷⡀⠀⠀⠀⢿⡌⡛⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⣼⡿⠀⠀⢀⣼⡟⠀⠀ ⠀⠀⠀⢿⡆⠀⠈⠳⣌⠻⣿⣄⠀⠀⠈⠛⣿⠀⠀⠉⢻⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠠⣼⠟⠀⠀⢀⣾⣿⠁⠀⠀ ⠀⠀⠀⠸⣿⣆⠀⠀⠈⠳⣮⠻⣦⡀⠀⠀⠙⠣⣄⣀⣿⣿⣿⠉⠙⠲⢤⣀⣀⣠⣤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⢀⣴⣿⣿⠏⠀⠀⢀ ⠀⠀⠀⠀⢸⣿⢷⣀⠀⠀⠹⣿⡾⢙⢷⣄⠀⠀⠈⢹⣿⣿⣿⡄⠀⠀⠈⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⠟⠁⣀⣴⣿⣿⣿⠏⠀⠀⣰⠏ ⠡⡀⠀⠀⠀⢻⣆⠙⢷⣄⡀⠈⢷⣄⠉⠛⠛⠂⠀⣸⣿⣿⣿⣿⣦⣄⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣟⣫⣴⣾⣿⣿⣿⠟⠁⢀⣠⣾⡏⠀ ⠀⢳⡄⠀⠀⠀⠙⢷⠈⣻⣿⣦⣤⣉⠻⢦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⣷⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣡⣴⣾⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⢿⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠫⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠸⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠢⡝⢦⡀⠀⣦⣄⢀⢀⣀⠀⠀⠀⢀⣾⡿⠁⠀⠀⡀⠀⠀⠀⡇⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠹⣌⠳⣄⠀⠀⠀⠀⢀⣀⣤⠿⠷⣄⡀⠈⠷⣝⢶⣇⣹⡿⠿⠛⣆⠀⣰⣿⡿⠟⠛⠛⠛⠻⡆⠀⠀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⠈⢷⣌⣻⣆⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠛⠁⠀⠀⣼⣾⢿⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢸⡆⠀⠀⠀ ⠀⠀⠀⡀⠘⣇⠀⠀⣐⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣀⣠⣶⠀⠀⠀⠀⣿⠀⠀⡏⢸⠇⠀⠀⠀ ⠀⠀⠀⣟⠚⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠘⠏⠉⠀⢸⠀⠀⠀⣰⠏⠀⢀⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⢀⡾⠀⣀⣴⣿⣶⠶⣾⠃⣸⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣦⣀⠄⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣇⣴⠟⠁⠀⠀⠀⠀⠀⠠⢾⣩⠿⠋⠙⠛⣶⠀⡟⢰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⣷⣦⣤⡞⠀⠀⠀⠀⠀⠀⣀⠀⢀⣶⣶⠟⠁⣻⣧⣀⢀⡀⠀⠀⠀⠀⠀⠐⢻⣤⡀⠀⠀⢽⡿⢀⣯⣄⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠋⠀⣸⠁⠀⠀⠀⠀⣀⣾⣧⠶⠟⠋⠁⠀⠀⠟⠛⠋⠉⠉⠉⠙⠒⠶⣄⡀⠀⠉⠁⢀⡴⠿⠃⠈⠡⠀⢹⡆⠀⠀ ⠀⠀⠀⠀⢀⡿⠁⠀⢰⣿⠀⠀⢀⣴⣷⠿⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⣴⠆⣸⠃⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⣼⢻⠀⠀⣻⣿⡑⠃⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣸⣣⠤⠚⠀ ⠀⠀⠀⣸⡿⠀⠀⠐⢿⣿⡆⣰⢿⠟⠁⠀⠈⠓⠒⠦⣄⡀⣼⠃⢀⡀⣀⣀⡤⠤⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠘⠳⠦⢭⣁⠀⠀⠀ ⠀⣀⣴⠟⠀⠀⠀⠀⣸⢿⣷⠏⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡴⠟⠋⣹⣷⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄ ⢺⡏⠁⠀⠀⠀⠀⢠⡟⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠚⠋ ⠀⠙⣦⣄⣀⠀⢀⣾⠳⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣠⠓⠁⠀⠀⠀⢳⡦⢀⣠⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠉⢙⣿⠿⢿⣄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⡴⣫⣶⠯⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠟⠁⠀⠀⠉⠀⠀⠐⠶⣤⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠸⣿⠃⢀⣀⡰⠛⠀⠀⠀⠀⠀⠈⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡥⠤⠤⣴⠒⠛⣉⣅⡤⢘⠀⠀⠀⠀⣼⣧⠀⠀⡄⠑⠾⣷⣄⠀⠀⠀⠀⠀ ⢰⣿⠋⠉⣹⢻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠉⠁⢠⡞⣶⠟⠛⠁⠀⢸⠀⠀⠀⠀⠘⣷⡀⠀⢹⠀⠀⠀⠉⠁⠀⠀⠀⠀ ⢸⣯⣤⣰⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⢀⡎⠠⠤⠤⠖⠒⠿⠇⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣯⡉⣁⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⢀⣀⡤⢶⡿⠁⠀⠀⠀⠀⠀⢄⡟⠀⠀⣠⡤⠤⠶⠒⠛⠒⠲⠽⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⢿⡅⠀⠀⠀⢀⣽⣿⠋⠳⣤⡶⠚⠋⢉⡴⠋⠀⠀⢀⣠⠖⢊⣴⣯⣴⡶⣿⡿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⠃⠀⠀⣿⠛⠲⠞⠋⠀⣀⣤⠶⠗⠒⢛⡋⠉⣾⡿⠞⣋⣴⢞⡥⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡷⠶⠛⠁⢀⣠⣴⠞⠉⠁⠀⠀⠀⢠⠟⠀⣾⡟⠀⠈⠻⣛⣉⣴⣄⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠊⠈⠛⣷⣶⡶⢾⣿⣿⡇⠀⠀⠀⠀⠀⣀⣿⣤⠾⠋⠀⠀⠀⠈⠙⠛⠛⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣶⣟⠁⢰⣿⠟⠀⠉⠀⣠⡤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠋⠀⠀⠀⣀⣤⢿⠛⠁⠙⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠎⠁⠀⠀⢀⣾⠟⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⠊⣀⠴⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣐⣴⢋⡔⢹⡭⡆⠀⣈⢀⠀⠀⢀⡀⠤⡀ ⠐⠋⠀⣸⣇⢂⠐⡹⠉⠂⢄⢛⠃⠠⡀⢀⠃ ⠐⠀⠠⠿⠃⢸⡦⠁⣀⠀⠀⠈⠀⠀⠨⠀⠀ ⠸⢦⣀⠀⠃⠈⠑⠠⠄⠠⢤⠤⠤⣂⠀⠀⠀ ⠀⠂⠁⠋⠶⠆⡠⠤⣤⠒⠁⠀⠀⠀⠑⠀⠀ ⠀⠈⠄⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠀⠀⠔⠀ ⠀⠀⠈⢆⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⠔⠛⠀⠀⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⠀⠤⠤⠤⠤⢤⡀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⣂⡤⠶⠛⠚⠉⠉⠉⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⡾⠁⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⠀⠀⠌⠀⠀⢠⣴⣶⣶⣶⣦⣤⠀⢠⣤⣤⣤⡀⠀⠈⣇⠀⠀ ⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⣻⣿⣈⣉⠉⠀⠈⣿⣏⠛⠁⠀⠀⢹⠀⠀ ⠀⠀⡇⠀⠀⠀⠠⣜⠀⠀⠀⠀⠿⠿⠿⠿⠟⠃⠀⠛⠛⠿⠿⠀⠀⠀⢸⠀⠀ ⠀⠀⢧⠀⠀⠀⠀⠈⡛⠓⠶⠤⠤⣤⣤⣤⡤⠤⠤⠶⠶⠛⠀⠀⠀⢀⡾⡀⠀ ⠀⠀⠸⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠁⠀⠀⠀⠀⡠⢹⠃⠀⠀ ⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⣰⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⡡⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠒⠒⠒⢶⣒⣛⠉⠉⠐⢒⠂⠤⠤⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⠀⢀⡀⠀⠀⠀⠀⢀⠶⡄⠀⠀⠀⠀⠀⠀⡠⠊⠁⢻⠀⠀ ⠀⠀⢸⠻⡢⡀⠀⣀⠼⠄⠙⢦⣷⡶⢂⣠⡾⠒⠒⡄⢸⡇⠀ ⠀⠀⣘⣀⡘⠾⠊⠀⠀⠀⠀⠀⠀⠀⢈⣿⠤⡄⠀⡇⢸⡇⠀ ⠀⠀⢇⠀⠀⢀⠂⠀⠀⠀⠀⣠⢀⠔⠀⠀⢠⣡⢼⡖⡆⠃⠀ ⠀⠀⠀⢹⠖⡆⠀⠀⣠⡠⠖⢩⠧⠤⠀⣀⠈⠧⢀⡷⠸⢤⠀ ⠀⠀⢠⠃⢰⠀⣴⠿⠁⠀⠀⡠⠀⠀⠀⠀⠁⠀⠋⠀⡰⣜⡀ ⠀⣀⠎⠀⢹⣧⠋⠀⠈⠑⠢⡡⢤⡖⠒⠒⢢⠀⠀⠀⠁⠂⢄ ⠈⠣⣀⣀⣦⡇⠀⠀⠀⠀⠰⠀⢸⡇⠀⠀⡼⠀⢠⡄⡠⠒⠉ ⠀⢀⡜⠋⠛⠀⠤⠀⠀⠀⡇⠀⢸⣃⡠⠊⠀⡀⠚⢍⠀⠀⠀ ⠀⡟⢲⣦⠀⠀⠀⠀⠀⠄⠉⡩⠖⠚⠡⠀⠀⣇⠘⡈⠑⠀⠀ ⠀⠻⣩⠥⠤⢤⣄⢀⡀⢤⠞⠀⠀⢠⣂⣨⠄⠘⠂⠣⠀⠀⠀ ⠀⠀⠈⠀⢰⣿⣀⠟⢒⡡⠔⠚⡒⣹⠛⡵⢇⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠊⢹⠖⣾⠏⢀⣀⠤⠖⠁⠀⠈⣉⡆⠀⠀⠀⠀⠀ ⠀⡠⠊⢀⡴⡋⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⢹⣧⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠨⡳⣄⠀⣤⣀⣀⡀⠀⠀⢀⣾⠋⠀⢀⡀⠀⠸⣿⡀⠀⠀⠀ ⠀⠀⠀⡇⠈⢯⡳⣄⠀⠀⣀⡤⠾⠛⠢⠀⠈⠺⣿⣿⣿⠋⠙⣄⣴⣿⠛⠉⠉⠉⢳⠀⠀⡇⡇⠀⠀⠀ ⠀⠀⠀⣷⠀⠀⢻⣾⣷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢻⣿⠃⢀⡀⠀⠀⢸⠀⠀⡇⡇⠀⠀⠀ ⠀⠀⡶⠾⠖⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠟⠋⠉⡇⠀⠀⡼⠀⢠⢇⡇⠀⠀⠀ ⠀⠀⢿⡀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⣠⠖⠃⠀⠀⠀⣰⣃⣠⣾⡿⠶⣾⢸⠁⠀⠀⠀ ⠀⠀⠈⠻⣦⣄⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⣠⡿⢳⡞⠁⠀⠀⠀⠀⠐⢫⡟⠁⠉⢹⣤⠃⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠛⡏⠀⠀⠀⢀⣴⣣⡴⠟⠋⠀⡾⠿⠗⠦⠤⠤⢤⣀⠀⠛⠂⢀⣸⠏⠘⠛⠻⡄⠀⠀ ⠀⠀⠀⣸⠏⠀⣸⡇⠀⢠⣶⡿⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟⠀⠀⠀⡄⢰⠃⠀⠀ ⠀⠀⢠⡟⠀⢀⣿⡇⢀⣿⡏⠁⢀⣀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠠⠧⠒⠁⠀ ⠀⢀⡾⠁⠀⠀⣹⣧⡼⠙⠀⠀⠀⠀⠉⠲⣤⢇⣴⠤⣶⡒⠚⠛⠓⠒⣦⠀⠀⠀⠀⠀⠉⠙⠒⢤⡀⠀ ⣾⠋⠀⠀⠀⢀⠏⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢰⣿⡇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⣀⡤⠿⠂ ⠈⠷⣤⣀⣀⣾⢲⡟⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣼⣿⠇⠀⠀⠀⡰⠃⠀⠀⠘⡶⢀⡴⠋⠁⠀⠀⠀ ⠀⠀⣀⡽⠛⠻⠾⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢹⡿⠀⠀⢀⠜⠁⠀⠀⢠⣾⡟⠛⠀⠀⠀⠀⠀⠀ ⢀⣼⠏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣀⣀⣠⠼⠗⣂⡒⠃⠀⠀⠀⣆⠀⢀⠉⢷⣄⠀⠀⠀⠀⠀ ⣼⠟⠛⣒⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠃⢀⡼⡴⠛⠋⠀⠄⠀⠀⠈⢻⡀⠈⡆⠀⠉⠓⠀⠀⠀⠀ ⣿⣦⠼⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⣠⠀⠐⠒⠒⠛⣇⡀⢻⡀⠀⠀⠀⠀⠀⠀ ⠈⠻⣤⡖⠒⠛⠛⢲⣶⠤⣀⣀⣤⠴⢚⡿⠁⠀⠀⣀⠄⣴⣃⣠⣴⡖⠉⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⢰⣿⡏⠀⢹⡷⢤⠴⠋⢀⣠⡴⠯⠴⠚⢻⡿⠿⣋⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡷⠖⠋⢀⣤⡖⠋⠉⠀⠀⢠⠏⣰⡟⠀⠘⣿⣩⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⢈⣽⡟⢛⣿⠿⠀⠀⠀⣀⣤⠼⠞⠋⠀⠀⠀⠈⢉⣉⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⢀⣸⠿⠀⠿⠧⠤⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠁⠀⢀⣴⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡀⢀⣸⣏⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⢖⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣷⣿⣿⣿⡿⣿⣷⣶⣦⣤⣤⣤⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠣⢤⣤⣤⣤⣤⣤⣤⣼⡿⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣻⢿⣶⣦⣤⣀⣠⣤⣀⣤⣄⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠸⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⠖⠛⠉⠉⠙⠓⠶⣤⣀⠠⢤⡀⠀⠀⠀⠀⢀⣠⣤⠶⠚⠛⠉⠁⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣝⢀⢀⣠⣶⣿⣿⠿⠟⠛⠋⠉⠉⠛⠿⢿⣶⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⣰⣿⣿⣶⣄⠀⠀⠀⠙⣿⣿⡿⠛⠁⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⢸⣿⣷⣇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀ ⠀⣸⣿⣿⡇⡀⠀⠀⠀⠀⣰⡟⢻⣿⡿⡄⣧⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀ ⠀⢿⡇⠙⠟⠁⠀⠁⠀⣰⠟⠁⠀⠹⣷⣳⡌⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣍⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠲⢾⡇⠀⠀⠀⠈⢳⣶⠟⠒⡂⠀⠀⠙⢷⣝⢦⣱⣄⠀⠀⠀⠀⢀⣤⡶⠛⠛⠉⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀⠀⠸⡇⠙⠷⣤⣉⡻⠶⠶⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⡤⠤⢤⡤⠤⠶⠟⢛⣡⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⢿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⠛⢛⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠶⠶⠶⢶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠐⢸⣦⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠘⣾⠉⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠾⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⢿⡄⢸⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠁⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣤⠈⣿⡌⣿⠏⣻⢷⣄⠀⠰⢄⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣷⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣶⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣶⣴⡾⣿⣭⣽⣛⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣶⣶⣾⣿⣿⣿⡟⠀⠙⢶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣠⣶⣴⣶⣴⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⡽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡟⢹⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢿⠈⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠸⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢒⢲⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⢴⢿⣽⣉⠉⠙⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣴⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⣵⣿⣿⣿⠿⡶⠀⠙⣟⢷⡀⠀⠀⠀⠀⣴⢋⣼⣿⣷⣦⡀⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⣈⣀⣉⣥⣤⣤⣤⣤⡾⠋⠉⠙⠛⠲⢾⡇⠈⠉⠛⣛⠉⠛⠀⠀⢹⡄⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠶⢦⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀ ⠀⠀⢀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠸⡆⠀⠀⠀ ⠀⠀⣼⢁⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢷⡀⠀⠀ ⠀⢰⠏⢸⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠒⠒⠲⠶⠦⢤⣄⠀⠀⠘⣦⠀⠀⠘⣧⠀⠀ ⢀⡟⠀⣾⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣸⡇⠀⠀⢸⡄⠀ ⢸⠁⠀⢹⡀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠀⠀⠀⣧⠀ ⠸⣧⢀⠀⠉⠑⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀ ⠀⠘⢿⣠⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⢀⣀⣀⡤⠶⠛⠉⠀⢀⣀⡴⠛⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⠀⠀ ⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠈⢿⣭⡉⠉⣁⣠⣤⡤⠴⠒⠛⠉⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣶⠟⠁⠀⢸⡀⠀ ⠀⠀⠀⠀⠈⠉⠳⢦⣄⣀⣀⣠⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⡿⠋⠉⡅⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠈⠙⠂⠀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡾⡁⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⣸⠁⠀⢸⠃⠀⠀⠀⠀⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠐⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡀⡴⠋⠀⠀⣠⣏⠀⠀⢸⠀⠀⠀⠀⠀⠀⣧
⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿ ⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⣞⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⢀⣀⠀⣘⡄⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠙⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⢘⠭⠭⣯⠫⢇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⣤⠤⠔ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡭⡯⢠⢿⡿⡏⡚⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡍⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⣨⡿⠟⠃⢻⣇⠩⢤⣀⢿⠛⠒⠂⢄⡀⠀⠀⢠⢸⡄⠘⡄⠀ ⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠉⠓⡒⠒⠋⠀⠀⠀⠀⠑⡀⠀⡘⣆⠇⠀⢸⡯ ⠀⠀⠀⠀⣰⠃⠆⠀⠀⢢⠀⠀⢀⢆⠀⡀⠀⡀⢕⠡⣃⡀⠘⡄⡇⢻⠀⠀⡇⡇ ⠀⠀⠀⠀⡿⠀⠀⠀⠀⢈⢴⠋⠈⠉⠐⠁⠈⠃⣈⠢⢤⡉⢢⢈⢸⡆⢀⠔⠑⢳ ⡀⠀⠀⢠⣇⠀⠀⠀⠀⡌⣇⣦⣀⠀⣀⠤⠚⠁⠀⠀⠄⠈⠫⣘⣄⣳⣁⣀⣀⣸ ⡷⡄⢀⠀⠻⣤⣀⠂⠉⠀⠀⠊⠈⠀⡩⣀⠉⡝⣕⢶⣖⣚⣓⣚⣓⣒⣬⣭⠤⢽ ⣿⣏⠉⠉⠉⢍⠙⠓⠓⠒⠒⠒⠒⠂⠉⠐⠙⠪⠾⠫⢿⣉⡑⠒⠓⠂⠈⢉⣁⣤ ⣿⣿⣧⡀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠀⠀⠉⠙⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣰⠃⠀⠀⠀⠀⠏⠖⠂⠀⠀⠀⠀⠀⠙⣅⠈⠉⠉⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣠⣉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣶⣤⣀⠀⠀⠀⢀⡤⠀⣠⡴⠟⢡⣵⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠐⠤⣠⣾⣠⠔⠋⠀⠉⣨⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠻⠛⠛⠿⠿⠷⢦⣴⣯⣴⡿⠋⠀⢠⠈⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⣠⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣷⡤⠀⠀⠀⠀⠀⠐⠊⠹⣿⠂⠀⠀⠈⣧⠎⣠⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠻⡏⢉⣏⣤⣦⣤⣤⣀⠞⣩⣿⣿⣿⣿⣿⣷⣤⡀⢀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⡀⢸⠟⠁⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⠟⡿⢿⠿⣿⣿⣿⡟⠉⠀⠀⠀⣀⡤⠀⣰⠛⣿⣦⠘⡄⠀⠸⠹⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠤⠦⣤⣾⣿⣿⣿⣿⣿⡿⠃⣸⣿⠛⣿⣿⣋⢰⣷⣀⡴⠛⣿⣿⣷⣀⣤⠀⣴⡟⠀⢠⡟⠀⠘⣿⣧⠘⠂⠀⢀⠀ ⠀⠀⠀⠀⠀⠠⡔⠁⠀⣰⣿⣿⣿⣿⣿⠋⣸⣧⣀⣧⣿⣦⡟⠀⠈⣿⣿⣿⣧⡀⣹⣿⣿⣿⣿⣿⠏⠀⣠⡟⢠⠄⡆⣿⣿⡆⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣼⡏⡿⠉⠉⠉⠻⣿⣧⡀⠹⡟⡿⢿⣿⣏⢉⣻⣿⣿⣿⣿⣾⣿⣰⡟⣸⣷⣿⣿⣷⡿⠀⠀⠀ ⠀⠀⠐⠢⠄⢴⣶⡏⠟⣿⣇⢿⢿⣿⣹⣿⣄⡁⠀⠀⣠⣶⣮⣷⣵⡀⢻⡇⡼⠻⣿⣿⣟⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⢸⣿⡇⠀⢻⢿⠈⠆⠙⢿⣿⡬⢶⣤⡀⠘⠿⠟⢸⡿⠀⠘⢿⠁⣰⡿⢿⣿⣿⣿⠁⠀⠙⣿⣿⣿⣿⣷⣾⠃⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠘⣿⣷⣴⠃⠈⢆⢀⣄⠀⠈⠃⠀⠙⠛⠂⠀⠀⠈⠀⠀⠀⣸⠞⣸⣣⡾⢛⣿⣿⣷⣄⣠⣾⣿⠟⠛⣿⣿⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⢈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼⣛⡁⠀⠚⠩⢿⣿⣿⠟⣽⣏⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠸⢻⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣛⡳⢿⣥⠾⠛⣧⣾⣿⣿⣾⢀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⡰⣄⠈⣩⣿⡟⠷⣬⣲⣶⣿⣿⣿⣿⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠘⢹⣿⣿⡇⠀⠀⠀⢀⡴⠾⠿⠿⣿⣿⣗⢄⠀⠀⠀⠀⠁⢼⡆⢳⠽⠇⠀⠙⣿⣿⣿⣿⡏⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⣸⠛⣿⣿⡀⠀⠀⢺⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⠀⠀⡜⡎⢇⠀⠀⢀⣿⣩⣶⣿⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣧⠀⠀⠀⢠⠃⠀⢹⣿⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢒⣻⠟⠻⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣼⣷⣶⣤⣏⠀⠀⠀⢿⣿⣷⡀⠈⢡⣀⡀⣠⣤⠶⠃⠀⠀⠀⠀⠀⠀⠠⣾⣚⣁⣠⣾⣿⣶⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣽⣛⢿⣷⣦⣤⣼⣿⢿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣍⣙⣿⣿⣿⣿⣿⡟⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠙⠛⣿⣷⣶⣤⣬⣀⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⠿⢟⡿⠋⡠⠃⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀ ⠀⣠⣴⣾⠿⠿⠛⠛⠛⣿⣧⡀⠀⠀⣸⠿⠻⡍⠉⠟⠁⠀⠈⠙⣿⡿⠿⠿⣉⠀⠉⠯⢤⡤⠖⠋⠀⣏⠀⠀⠀⠀⠀⠀⠉⠛⠒⠀⠀⠀ ⠛⢯⠥⠒⠀⣹⣿⣿⡇⢹⣿⣥⠼⠏⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⡉⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⣿⣧⣄⣀⡀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠬⠂⠀⠀⠀⡄⢸⡿⡝⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢾⡿⠀⠉⣿⣿⠀⠀⡇⠹⣿⣿⣿⣶⣶⣤⣤⣽⡶⠤⠤⠐⠒⢎⡉⠀⠀⠀⠀⠀⢠⡞⢠⠋⢱⠈⢦⡀⠉⠉⠁⠂⠀⠀⠀⢀
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⣿⣿⡿⠿⠿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛ ⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⣀⣀⠀⣀⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⣤⠶⠶⠚⠛⠛⠛⠛⠻⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣀⣠⣤⣶⣶⣶⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿ ⣿⣿⣿⡿⠃⣀⣳⢯⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿ ⣿⣿⡟⠁⠀⠟⢳⣾⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢹⣿ ⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢀⡆⣀⣿ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⡿⠀⠀⠠⣄⠀⠀⠀⣸⠂⠀⠀⠉⠀⠟⡼⠃⢹ ⣿⣧⠀⠀⠀⠀⠀⠀⣴⢣⡞⠉⠁⠀⠀⠀⠈⠳⢦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⣿⣿⡀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿ ⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀ ⣿⣿⡿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⣼⠀⠀⠀⢀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⡿⠀⢀⣠⠴⢚⣩⠤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠦⢬⣉⡙⠧⣄⠾⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⣿⣿⣿⣿⣿⣿⣇⡤⠏⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⠛⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⠏⢡⠞⠁⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣮⣳⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⡏⢰⡟⠀⠀⠀⣾⠿⠿⠿⢿⡻⣷⠀⠀⠀⠀⣴⠞⣻⢿⣿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣍⢷⣄⢀⡖⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⠃⣿⠁⠀⢀⣼⣧⣴⣿⣿⣿⡷⠂⠐⠉⢱⠇⠀⢺⣿⠿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣦⠙⣿⡀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣸⣿⠀⠠⠟⠉⠁⠀⠿⠿⠋⠀⣰⡀⠀⣟⣷⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠷⡎⢳⡄⠀⠰⠿⠿ ⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢻⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⣾⣿⣶⢻⡇⠀⠀⠀ ⣿⣿⣿⣿⡿⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⠶⠶⠶⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢹⢏⣿⣄⣏⠀⠀⠀ ⣿⣿⣿⡟⠁⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠐⠲⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣼⡟⣿⣿⡄⠀⠀ ⣿⣿⠏⠀⡰⣱⢻⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣿⠋⠋⠳⣄ ⣿⡿⠀⣠⡷⠃⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⠀⠀⠀ ⣿⣧⡶⠋⠀⢀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣱⡃⠀⠀⠀ ⣿⠟⠀⠀⠀⢸⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣼⡟⠀⠀⠀⠀ ⢅⣀⣠⣼⠛⣽⠛⢿⠉⡷⢦⣄⣤⠤⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⣼⠏⠀⠀⠀⠀⠀ ⡀⢻⢁⡾⠀⢳⠀⣿⠀⡶⡆⢻⠁⣶⡆⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡿⠁⠀⠀⠀⠀⠀⠀ ⣹⠀⡞⠁⠀⠸⣄⣹⣤⣷⣧⡸⣦⣭⣥⡾⠃⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣴⠞⢁⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠮⣍⠛⠛⠻⠶⠶⠦⠤⠥⠤⠤⣷⣬⣤⣤⣤⣤⣤⣤⠤⠶⢶⡚⠫⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡗⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢠⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⠁⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣆⠀⢠⢀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⡠⢒⠅⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⣵⠪⡊⠀⠀⠀⠀⠀⣾ ⣿⣿⣿⡏⡰⠁⢀⣤⣤⣤⣄⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠈⠳⣿⢄⠀⢀⠀⠀⣿ ⣿⣿⣿⣱⠃⢀⣾⢴⣶⡿⠃⠂⣒⠁⢾⣿⣷⡦⠀⠀⠀⠀⠀⠸⣧⡙⡇⠀⢀⣿ ⣿⣿⣿⡿⠀⠈⠀⠀⠉⠀⠼⡤⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣩⣬⢦⠈⠉ ⣿⣿⡟⢹⠀⠀⠀⠀⠀⢠⠖⠛⠓⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣼⣾⡀⠀ ⣿⡏⢠⡟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⡟⠓⠄ ⣿⡠⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣷⠀⠀ ⠟⠁⣠⣴⣴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡹⠃⠀⠀ ⡐⢣⠃⠇⣾⢸⠘⡫⣮⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⡞⠁⠀⠀⠀ ⡦⠂⠀⠈⠚⠛⠓⢿⠺⠧⣤⣤⣀⣀⣠⣂⣀⣀⣀⣄⣤⠴⠊⠐⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⠂⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿ ⣿⡿⠿⠛⠋⠉⠉⠉⠉⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⣀⣠⣤⣴⣶⣾⣷⣶⠶⠶⢶⣶⣶⣾⣷⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢿⣶⣿⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠁⠀⣷⣦⣾⠋⢙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿ ⣿⣿⣿⣿⡟⠁⠀⠀⠾⠟⠛⣷⣿⣋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⠏⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⣀⠀⠀⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⣰⡿⢀⣤⢸⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠈⠉⠉⠁⣼⡟⣠⣾⠋⠈⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠌⢿⣿⣿⡿⠃⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠁⠀⠀⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣰⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠉ ⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀ ⣿⣿⣿⡿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡟⠁⠀⠀⠀⠀⠀
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⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣝⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠐⠂⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠤⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣀⣠⣄⠀⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡿⠿⠛⠛⣦⡟⠛⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡼⠀⠀⠀⠀⠸⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠇⠀⠀⠀⡇⠀⠀⢠⣤⣤⣇⣶⡄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡿⠀⠀⠀⠈⣇⠀⠀⠀⠛⢁⡏⠛⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠘⢆⠀⠀⢀⡼⢦⣀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢴⡀⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡛⠟⢁⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠽⠗⠀⢺⣋⡉⠒⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢧⣈⣼⢷⡀⡄⢸⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠉⠀⠀⣻⡦⠼⠖⠋⠉⠉⢿⡀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⠀⢇⠀⠀⢶⡄⣀⡬⠷⠶⢦⣤⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠾⠖⠒⠾⢄⣠⡶⡟⠁⠀⠀⠀⠀⠉⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⢠⠏⡿⢷⣤⡀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⡄⠳⣾⣍⡽⠙⢶⠄⠀⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡁⠀⢳⠀⢛⣋⠄⠀⣸⠀⠀⢠⣿⠀⠀⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣠⠖⠉⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀ ⢶⣶⣶⣆⠀⠀⠀⠒⠒⠊⠉⠀⠀⠀⠀⠁⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠻⢦⣀⢠⠃⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠘⡟⠓⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣈⣽⢹⢮⠀⠀⠀⠀⠚⠑⠂⠀⠀⠀⡇⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣳⡃⠀⠀⠐⠚⠀⠀⠀⠀⡴⠒⠲⡀⡇⠀⠀⢳⠀⠀⣀⠤⠈ ⠀⠀⠀⠀⠀⡏⢹⠀⠀⠠⣾⠗⢦⠀⠈⢏⣀⡠⠃⡇⠀⠀⠸⠖⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠻⡞⠀⠀⠀⡇⠀⠘⡆⠀⠀⠀⠀⠀⠇⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠒⠀⠀⠒⠺⡓⠧⠀⢧⣀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢲⣒⠒⠂⠀⠀⠀⠀⠀⠀⠀⣜⣠⠤⠖⠒⠉ ⠀⠀⠀⣠⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠭⠓⠒⠀⡇⡿⠀⠁⢸⡿⡇⠈⣿⣿⣛⠨⣝ ⢻⢿⣿⣿⣿⣿⣿⡿⠟⢩⣟⡟⠈⢀⣀⣀⣴⣷⠷⠒⠒⠛⠒⢻⠤⣿⢹⣿⣷⣮ ⣸⢸⢈⣻⠙⣿⣍⣴⠶⢿⣿⡟⠉⠉⠁⠀⠜⢁⠀⣀⣤⡴⣶⢿⠀⡟⣆⣿⣿⣿ ⣿⡜⠾⠛⠋⠉⠁⠀⣀⠀⠈⠃⠀⠀⠀⠀⠰⠷⣟⣇⣠⠤⢻⣾⠀⣧⢹⣞⢿⣿ ⡿⠆⣀⣲⣴⠶⠶⠶⣶⡖⠻⠄⠀⠀⠀⣀⠔⠚⠻⠗⠃⠀⢾⣿⢠⣿⣼⣿⣮⣻ ⠜⠎⠹⣅⠠⠤⠶⠾⠿⣯⠅⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⠀⠸⡿⢸⣿⣿⣿⣿⣿ ⠞⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⣿⣿⣿⣿⣿ ⠉⣡⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡿⡀⣿⣿⣿⣿⣿⣿ ⣿⡏⠙⢷⡽⢦⡀⠀⠠⡤⣀⡤⣤⣤⠴⡶⡯⠋⠀⠀⣴⣿⣱⢹⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⠑⡜⡇⠀⠀⠈⠁⠛⠚⠛⠓⠁⠀⠀⣠⣾⣿⣷⡇⣼⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⡇⢹⣦⣄⣀⠀⠀⠀⠀⠀⡀⠔⠛⠛⠻⠿⢿⢃⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⢰⢠⡇⠈⠻⣿⡿⡷⠒⠒⠪⢀⠀⠀⠀⠁⠀⡞⠌⠉⠛⢿⣿⣿⣿⣿ ⣿⣆⠀⠀⡘⣸⠣⢀⠀⢀⠝⠀⠀⠀⠀⠀⠑⢄⠀⠀⢰⡙⠀⠀⡐⠀⠙⢿⣿⣿ ⠘⢿⡄⢀⢣⡏⠀⠀⠈⠍⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⡞⠀⠀⠀⠃⠀⠀⠀⠙⣿ ⠀⠘⣿⠮⠋⠀⠀⠀⠈⠀⠘⡀⠀⡐⠀⠀⠶⠲⠒⡞⠓⠀⠀⠀⠀⠀⠀⢀⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢶⣚⠛⠉⢉⣛⣿⣿⣿⡖⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣡⠴⠒⠛⠿⢿⣿⡿⠟⠁⠀⢿⣿⣦⣤⣤⣌⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣠⠞⠁⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢀⡽⠟⠛⠛⠋⠙⠲⣄⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠈⠛⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠀⠀⠈⢷⠻⣆⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡿⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢲⡶⠶⢶⡿⠷⠶⣶⣦⠤⠽⣦⡀⠀⠀⠀⠀⢀⡴⢏⡼⠃⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠷⠤⢤⣭⣿⣭⠭⠤⠤⣶⠚⠻⡗⠒⠒⠋⠉⠐⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠸⢦⣄⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠦⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢉⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠳⣦⣀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣆⣴⠿⠃⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⣀⣰⡃⠀⠀⠀⡀⠀⢀⡠⢴⡞⠀⠀⢤⣄⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠖⠒⠛⠉⠉⠉⠉⠲⢄⡀⣉⡉⠉⢀⣠⠇⠀⠀⠈⠙⢷⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡉⠛⠦⣤⣀⠀⠀⠀⢀⠀⠀⣤⡀⠀⠀⣠⠶⠒⢦⣀⡟⠁⠈⣆⠉⠀⠀⠀⢀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⠷⣤⡾⠋⠉⢻⣧⠀⠀⠀⢻⠀⠀⠀⢸⡤⠴⠒⠋⠉⠀⣼⣿⣿⡿⣿⣿⣿⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⡇⢠⠀⣼⣇⣼⣠⡖⠀⢳⣀⣤⣼⡇⠀⠀⠀⠀⣰⣿⠀⣿⡇⡿⠿⣿⣿⣿⣿⣟⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡿⠀⢧⣼⣤⠟⠉⠉⠹⡄⠀⠈⢻⡿⢿⣧⣄⣀⣤⣶⣿⣿⣀⣿⡇⠇⠀⣿⣿⣿⣿⡇⡻ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⡼⠁⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⡗⠇ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣾⣿⣿⠇⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠛⠛⠉⠛⠛⠛⠛⠻⠿⠷⢦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⢄⡀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠚⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢀⣼⢷⣾⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⡞⠃⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠘⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⣾⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⢹⡟⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⢀⣾⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡆⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢐⣴⠟⠀⠀⠀⠀⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢸⣧⣤⠴⠶⠲⢶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⣿⠀⠀⠀⠀⠀⠈⠙⢷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡓⠶⠦⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠏⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⢀⣠⣴⠶⠒⠛⠛⠛⠛⠒⠶⠞⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠁⠀⠀⠀⠀⠀⠈⣿⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠉ ⣀⣴⢟⣁⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣸⡿⢻⡇⣀⣀⠀⠀⠀⠀⠀⣀⡠⠔⠚⠁⢠⠇⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀ ⠛⠁⠀⠀⠀⠀⠈⠛⢶⠀⠀⠀⣠⠞⠋⠀⢸⣧⠀⠉⠉⠒⠒⠒⠉⠉⠀⠀⠀⢠⠃⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡆ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷⡤⠞⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸⢷⠀⠀⠀⠀⠀⠀⠀⣠⠃⢠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢸⠘⢇⠀⠀⠀⠀⠀⣰⠋⣠⠊⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢤⣀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠛⠼⠁⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡈⠙⠒⠦⣤⣄⣀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⠙⠲⠤⣀⣀⡈⠉⠉⠉⢉⣉⣩⢤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢀⣴⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣔⠤⠤⠤⠤⠤⠄⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿ ⠀⠀⠀⠙⠷⠤⠤⠀⠀⠤⠀⠀⠀⠀⠠⢽⡧⠤⠤⠤⠤⠾⠧⡤⠤⠤⠤⠤⠤⠠⠄⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠋⠀
__♥__♥_____♥__♥___ Put This _♥_____♥_♥_____♥__ Heart _♥______♥______♥__ On Your __♥_____/______♥__ Page If ___♥____\_____♥___ You Had ____♥___/___♥_____ Your Heart ______♥_\_♥_______ Broken ________♥_________…………….
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