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