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