⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⠙⠛⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠲⠿⣿⣿⡿⠱⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢡⡀⡀⠁⢏⣓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⡠⣢⣾⣟⡽⠁⣾⢣⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⡘⣿⡄⠽⣞⢦⡀⠛⠱⡝⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠁⠀⡐⢃⣾⣿⣿⣿⡇⡼⣱⣿⣿⣻⢟⣟⣿⣿⣿⣿⣿⣿⣷⠈⠳⡀⢨⣣⡁⡀⠀⡈⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⡴⣻⠏⢪⣿⣟⡼⢱⡟⢻⢓⡟⣹⣽⣿⣿⣿⢍⢻⣿⣻⣳⡀⠻⡄⠳⣳⡘⢆⠉⠀⠰⡈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⠎⠀⠀⠀⠃⢠⢎⠴⠃⢀⡟⢾⣿⠃⠘⠁⣾⢿⠀⢳⠇⡟⣿⣿⢘⠾⣾⣱⢳⢣⢢⢣⢰⢳⢳⡈⢣⡀⠀⠁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⠁⢀⡠⠄⠀⣠⠋⠂⠀⠀⠞⠀⠣⠃⠀⠀⢸⠇⡾⠀⠸⠔⢱⡍⡏⠼⡄⢳⣏⢫⢡⠏⣇⠐⠉⣇⢃⠀⠱⡀⠀⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡼⠁⠀⢢⠉⠀⡀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢸⠀⠁⢀⢧⠈⣾⠘⡆⢇⠘⡄⠃⡜⡜⡆⠀⢳⢇⠰⣠⠀⢳⡀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⡃⠀⠀⠀⢰⣸⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⡷⡑⠞⡄⣱⢢⢱⠁⢀⡄⠘⡞⡆⠁⡇⡄⢣⠀⠀⠀⠀⠀⠀
⠀⢀⣟⠁⠈⠀⢀⢧⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⠀⢱⢁⡟⣴⣰⠘⣽⡄⣵⢳⠀⣿⢳⠈⣆⠀⠀⠀⠀⠀
⠀⡾⠀⠀⠂⡇⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⢸⠘⣄⣇⠁⡇⡅⡏⢹⡀⣸⡟⢄⢹⡀⠀⠀⠀⠀
⣰⢳⡀⠀⢸⣇⢸⢸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⣆⢸⠘⠀⠡⠀⢹⡘⡆⣿⣧⠀⢸⠇⠀⠀⠀⠀
⢷⡇⡇⠀⠐⣿⡞⠈⡇⠐⠀⠘⠆⠀⠂⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠠⠃⣷⡀⢀⠂⠀⢀⢸⡧⢁⢹⣿⡄⢽⠀⠀⠀⠀⠀
⠀⢣⣭⣼⣴⣿⠃⣼⣶⡤⢠⡴⡆⢠⡄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡄⣿⢠⢩⣷⠌⠜⣾⣧⢸⣸⣿⠃⣼⠀⠀⠀⠀⠀
⠀⠀⢯⣿⣿⡇⠀⠀⡠⠖⠋⠉⠻⢼⡙⠃⢻⠰⢶⡀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣷⠶⠶⠲⠶⣤⣤⣬⣄⡀⠈⠳⣿⣿⣞⣸⣿⣹⣸⣿⣿⠃⡟⠀⠀⠀⠀⠀
⠀⠀⢸⠘⣍⡇⠀⢨⢆⣠⣤⣤⡤⣤⣙⢺⠤⣴⡎⠀⠀⠀⠀⠀⠀⡨⠃⣁⠥⠖⠒⠒⠲⢦⣀⢀⡉⠙⠛⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠰⡇⠀⠀⠀⠀⠀
⠀⠀⢼⡴⠀⠧⠀⢼⢯⢿⡿⣾⣺⠆⠈⠉⠯⢟⡆⠀⠀⠀⠀⠀⠀⣦⠀⣁⣀⣀⣤⣤⣄⣀⣙⢦⠩⢆⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⡼⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣦⠀⠀⠀⢑⡤⢽⣻⡭⠴⠒⣃⢯⣺⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⠧⡱⣿⣾⣿⡏⢻⣯⣇⠛⠃⠀⠀⠀⠈⣿⣿⣿⡛⠉⣿⡿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣧⠃⠀⠀⠀⠙⠷⣶⣶⣾⠟⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢮⣓⡬⠭⠭⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠻⠻⣿⡇⠀⣸⣷⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢷⣾⣷⡶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⢸⡽⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠴⠒⠩⢵⣂⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢾⣤⣀⣀⣠⣄⣄⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⠀⠀⣠⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⠅⠀⠀⠀⠀⡀⠠⢀⡠⠀⠍⣺⡖⠯⠛⢿⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⡿⠦⠶⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢯⢀⠀⠀⢰⣇⠸⣀⣁⣓⣐⡙⠃⠀⠂⠲⠟⠠⢀⡐⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⢤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠑⡿⡿⣿⣿⣾⣿⣯⣷⣽⣿⣿⣶⣦⣤⣀⡀⡄⡀⢀⠁⠀⠀⠀⠀⠀⠀⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠠⡀⡙⢿⣿⣾⣿⡖⠾⣯⡬⣵⣾⣟⣫⠍⠙⠳⣶⡾⠀⠀⠀⠀⠠⠈⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡁⣤⣀⣭⡿⣿⣿⣿⣿⣿⡿⢿⠟⠂⢀⠈⠉⢉⡥⠆⡀⢠⢕⣳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢉⠉⣀⡀⠈⠉⠏⠙⠤⠠⣄⠉⠓⠓⠄⣠⣄⣰⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣅⣷⠜⠶⡄⡠⡱⣦⣿⠗⡁⣀⣔⣾⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣶⣯⣿⣷⣦⣾⣶⣿⣿⠿⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀