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