⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡳⠃⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣿⠀⠀⠀⢀⣤⠀⠀⢀⡴⠀⠀⢀⣴⡿⢾⡟⠀⠀⢠⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠏⠀⠀⣇⣤⡦⠚⢻⠃⣠⠴⢋⣀⠤⠖⠛⠁⠀⡼⠁⠀⢀⡞⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⡇⢀⡟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣤⣥⣤⣠⣤⣼⡋⢉⣉⣭⣤⡀⠀⠀⠀⣰⣃⡄⣠⠞⠀⠀⢸⠀⣰⡇⠀⠀⣸⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⢧⠏⠈⢹⡇⠀⠀⠀⠀⠠⠔⠒⠉⡏⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠻⠿⠓⠀⠀⠐⠻⣡⡴⠃⣀⡀⠀⢸⣴⠋⡇⠀⡼⢹⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣴⠛⣾⣿⠏⠀⣠⢞⡇⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣼⡿⠿⠿⠟⣷⣤⣿⡞⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠞⣿⡿⠛⣟⠙⢶⣞⢿⣉⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠳⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⢀⡟⠁⢸⢻⣷⡀⠙⠳⡌⡇⠀⢄⣀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠃⡾⠀⠀⠘⠳⢿⣷⠀⠀⠈⡇⠀⠀⣟⣟⣶⣶⣤⣥⣄⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡀⡇⢠⣶⣶⣦⣤⣸⠀⠀⠀⡇⠀⠀⠈⣭⠙⠛⢿⡟⢿⣿⣿⣿⣶⣦⣝⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣧⣷⠘⢯⠉⠉⠉⣁⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⢸⢿⣿⣿⣿⣿⣹⣿⣿⣿⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶⣶⣶⣶⣾⣀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠙⢷⣤⡙⢿⣿⠟⠀⠀⠀⡇⠀⠠⡇⠀⠀⠀⢸⠀⠀⠉⠉⠉⠙⠛⠻⠦⠄⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢿⣿⣿⡟⠉⠈⠹⣿⡟⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣧⠀⠉⠻⢦⣷⡀⠀⠀⠀⡇⠀⠀⢹⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⠿⠿⠳⠦⢀⣠⠄⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⡿⢦⡀⠀⠀⠹⣧⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⣀⣿⡿⢲⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⡿⠈⡳⣄⣀⣠⣼⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣾⣋⠙⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠋⢸⡏⠉⢁⠀⣠⠬⠱⣦⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠉⠀⠈⢆⠈⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⡜⢠⡇⠀⢀⡴⠋⠙⢧⣀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠋⠉⠙⢦⡀⠘⢆⠘⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠃⡜⠀⠀⡜⠀⠀⣠⠀⢳⡏⡷⡀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣴⡄⠀⠀⠳⡀⠘⡄⢧⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢸⢻⣸⢁⠇⠀⠼⠁⠀⠀⢿⠤⠤⠿⢤⣷⠬⠭⣶⣄⠀⠀⠀⠀⢾⡛⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢾⡟⠀⢸⣿⣽⣦⠀⠀⠹⣄⢻⢸⠃
⠀⠀⠀⠀⠀⠀⡇⢰⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⡀⠀⠀⠈⠙⠲⣄⡀⠀⠙⠲⠶⠶⠷⠚⠛⠉⠉⠋⠀⠀⣀⣠⠴⠋⠀⠘⢿⠖⠉⠀⠀⠉⠀⠀⠀⠈⢧⣟⠟⠀
⠀⠀⠀⠀⣱⣶⠖⡟⣸⡷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠃⠀⠘⣄⠀⠀⠐⢄⠀⠉⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠠⣠⠷⡄⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀
⠀⠀⠀⣰⣿⡟⢸⡇⣯⢇⣸⠧⡀⠀⠀⠀⠀⢠⡞⠀⢀⠀⠀⠈⢣⠀⠀⠀⠳⢄⠀⠨⡳⡄⠀⠀⠀⠀⢀⡟⢀⡤⠊⠀⠀⠀⠀⡠⠖⠉⠀⠘⠦⣀⠀⠀⢀⣴⣿⡇⠀⠀⠀
⠀⠀⣰⡟⣸⣧⣿⣤⣾⠟⠁⠀⣈⢳⣄⣀⣴⠋⠀⠀⠈⢳⡀⠀⠀⠱⡄⠀⠀⠈⠧⠀⢙⠞⣶⢦⡄⢠⣾⡶⠋⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡼⢟⣉⣉⣏⢸⠃⠀⠀
⣠⣴⠗⢚⣯⣿⣿⠟⢇⠀⢀⡴⣿⣿⠿⠫⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠁⠀⠀⠀⢀⡴⠃⢀⡾⠈⢿⣾⡟⣦⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⡉⠉⣼⠚⠀⠀⠀⠀
⢿⡃⢀⣽⠟⠋⠀⠀⣠⠿⠉⠀⣿⠛⠦⡲⣄⡲⢤⣑⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⡞⠁⠀⢸⢹⡇⠈⢧⣠⠎⠀⠀⠀⢀⣠⠖⠋⠀⢀⣠⠖⠉⢠⡞⠁⠀⠀⠀⠀
⣸⡇⢻⣤⡀⠀⠀⠛⠶⢤⣀⠰⡇⡇⠀⠨⡷⣕⢦⡈⠛⢦⡀⠀⠀⢀⣠⠾⠋⢀⣠⢿⠟⠀⠀⠀⣿⢸⣧⠀⠀⠈⠳⣤⣀⡴⠋⠁⠀⣠⢴⣿⣁⣀⣴⣿⡇⠀⠀⠀⠀⠀
⣿⠇⠈⠹⠿⣷⣤⡀⠀⠀⠈⠛⡷⣼⣀⠀⣇⠈⢦⡳⣄⠁⢸⣠⠔⠋⠀⢀⠔⠃⣴⠏⠀⠀⠀⢰⣿⠈⣿⢦⡀⠀⠀⠈⠻⠯⠿⠟⠛⠋⠉⠀⠀⠘⣿⢹⣿⡄⠀⠀⠀⠀
⡾⠀⠀⢀⡅⣨⠝⣿⣶⣄⠀⠀⠛⠈⠙⠳⡟⠐⠀⡿⠚⠛⠉⠀⠀⠀⠈⣡⡴⠛⠁⢘⠁⠀⠀⢸⣿⡄⠘⣎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠘⢹⡇⠀⠀⠀⠀⠀
⠃⠀⣤⢶⡯⢓⣠⣴⣿⣿⣿⡄⠀⠀⠀⢰⡇⠀⠀⢻⡄⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⢸⡆⠀⠀⣾⣿⡇⠀⠘⢦⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⢔⣿⠁⠀⢠⠞⠀⠘⡄⠀⠀⠀
⠀⢶⣶⠽⣿⠿⢞⡿⣾⡾⠋⠀⣀⣠⠤⢿⠁⢀⣰⣾⣇⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⣿⣷⣅⠀⠈⢳⡀⠀⠀⠈⠁⠀⠀⠀⢀⡾⠀⠀⢘⣿⠀⠀⠀⣿⠀⠀⠀
⠀⠈⠙⠛⠁⣻⡿⠋⠁⠠⣶⡛⠁⠀⠈⢠⣴⠿⠿⠟⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣽⣷⠀⠀⣿⣿⣿⡘⠄⡀⠀⠹⣄⠀⠀⠀⠀⠀⣰⠯⠀⠀⢠⡾⠘⢆⠀⠀⣿⠀⠀⠀
⢶⣤⡤⠤⢬⣍⣙⠳⢤⣄⠈⣛⢶⠎⠀⠘⢾⡆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠠⣾⣇⣿⠀⠀⣿⣹⣿⣇⠲⣇⠄⠀⠙⢦⣄⣀⣤⠞⡁⠀⠠⠀⠀⣇⠀⢸⠀⠀⠏⡆⠀⠀⠀