⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣦⢳⡬⣟⢻⣦⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⠜⣧⣯⡽⢾⠳⣞⡻⣛⠟⡿⢿⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡯⡟⡝⣦⣙⡮⠛⣝⠲⣍⢞⣱⢍⡞⣥⣛⢻⣦⣄⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣋⠶⣹⢜⡱⡄⢆⣡⡝⠷⡼⠞⢹⡎⡖⢦⢻⠦⣭⠹⣷⡟⣻⢫⣽⠭⡧⣧⣍⣛⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡲⣍⢾⡱⢎⣽⠵⣋⠶⡽⡹⣜⡧⣞⡹⡜⣣⢻⡳⢬⡗⡭⢿⣶⡟⣖⣫⣶⡷⢣⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⢻⢱⡎⣵⡞⢣⡝⣮⢱⢫⡜⣽⢱⢳⡌⢳⣬⢳⠙⣦⣿⢹⡖⣽⢸⡍⣿⣯⢹⣽⣦⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⢿⣜⣺⢣⡝⣼⢣⢏⠶⣩⠞⣬⡷⣋⠗⣎⡝⣦⠟⣬⢓⢮⠋⢷⢯⣽⢣⣙⢻⣿⣾⢹⣿⣿⠏⠁⠀
⠀⠀⠀⠀⠀⠀⢀⣴⢞⠫⡝⣢⠝⣦⣿⢣⠳⣼⣏⣳⣮⡷⠵⣛⢟⡱⣍⠞⡴⣽⢏⡝⢦⣫⠃⠀⠘⡾⣼⢣⢎⣽⣿⣿⠛⣼⡅⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠃⣌⠳⡌⣥⢫⣷⡏⣧⢋⡿⠛⠉⠀⣤⣚⠵⣪⣕⡮⢝⡻⣋⢞⡼⠋⠉⠙⢆⠀⣟⡿⣘⠮⣼⣿⣿⣡⢴⣿⡀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠰⣀⠳⡘⢴⣿⣿⢫⢳⣍⢧⣶⣤⣄⣒⣚⠉⠁⠀⠀⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⣿⠳⣍⠞⣼⣿⢾⣯⣷⣾⡁⠀⠀
⠀⠀⠀⢀⣤⣼⣧⠑⡠⢃⠜⣸⡿⢾⡩⢎⡏⠉⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⢠⣭⣒⠄⠀⠀⠀⠀⢀⣏⢳⢬⢫⣟⣯⣿⢯⡟⣽⣷⡀⠀
⠀⠀⠀⣿⠋⢿⣿⠄⡱⢈⠜⣸⠀⠈⣷⢩⣧⠤⠤⣄⡀⠀⠀⠓⠶⠤⣀⠄⠀⠉⠛⡿⢿⠶⢆⣠⠻⣌⠳⣎⣽⣿⣻⣽⣿⠸⣌⢿⣷⠀
⠀⠀⠀⣿⣇⢂⡙⠒⠖⢃⡘⡼⡳⠶⠛⡏⠀⠀⠀⠀⣳⠶⠒⠶⠤⢤⣀⠀⢀⣀⣀⠀⠀⠘⠯⢼⡷⣋⠷⣼⡟⣷⣻⣷⠏⡵⣊⢖⣻⡇
⠀⠀⠀⠘⣧⣓⠦⣉⠘⣤⢼⡋⠤⠄⠂⢛⡶⣦⠶⠟⠃⠤⠤⢀⣀⠀⠈⢹⠉⠀⠈⠙⢦⣀⣤⢟⡲⣭⣾⢻⡼⣗⣿⠏⣜⠱⣘⠲⡰⡇
⠀⠀⠀⠀⠈⠙⢻⣿⠟⢡⠊⠀⢀⠤⠐⠊⠉⢀⠀⠀⡀⠀⠀⠀⠀⠈⠹⠿⢤⣤⣀⣀⣨⠿⢵⣮⢿⣻⡉⠁⢀⡿⢃⠞⣠⠋⡔⢣⣱⡃
⠀⠀⠀⠀⠀⣰⡟⠀⡠⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠄⠁⠀⠂⠐⠄⢀⠀⠄⠀⠈⠹⣫⢥⣋⠦⡙⠶⣤⡀⣠⠞⡰⢁⠎⡄⢣⠘⣴⠏⠀
⠀⠀⠀⠀⣴⠏⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠌⠐⠒⠤⣀⠱⣢⠏⠛⠍⡉⠑⣽⠃⠜⣄⢃⠒⣨⣴⣿⠉⠀⠀
⠀⠀⢀⣼⠏⠀⡰⠁⠀⡀⠢⠄⠀⢠⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠉⢳⠀⢆⡀⠈⠢⢻⡌⢂⠌⡓⠼⠿⠟⣻⡇⠀⠀
⠀⢀⣼⠋⠀⠰⠁⠀⠀⠄⠀⠀⠀⠀⠀⠈⡀⠐⠀⠠⠂⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠈⠊⢄⠇⢸⣷⣌⠲⣈⣔⡡⣶⠟⠀⠀⠀
⠀⣼⡟⠀⠀⡇⡀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⡀⠀⠀⠀⠀⢀⠧⠀⠀⠀⢸⠀⠀⣿⠿⣧⣤⣤⠿⠃⠀⠀⠀⠀
⢰⣟⠀⠀⠀⠉⠂⠴⣀⠆⣀⠀⡀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠐⢂⡤⠊⣀⠀⠀⢀⠇⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⢶⣄⡀⠀⠀⠀⠀⠉⠐⠊⠥⣀⡂⠤⢀⡀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣠⠖⣩⢇⠃⠉⠚⠤⡜⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠉⠐⠒⠩⠄⣂⣁⠠⢀⣠⢴⣋⠖⣩⠇⠂⠀⠀⠀⡰⠁⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠙⠋⠚⠒⠋⠭⠥⠤⣀⣀⣀⣠⠃⢠⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣣⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠳⠶⠶⢶⠴⣶⢾⡷⠛⠁⠀⠀⠀⠀⠀⠀




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