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