Turbine Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠱⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠘⢄⢈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠈⢢⠡⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⢄⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠠⠤⠀⠒⠒⢂⣉⡭⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠑⠀⡈⠳⢄⠀⠀⣀⡀⠀⠀⣠⠊⡡⠄⠀⠀⢀⣠⡠⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠤⣌⢳⠬⢤⣿⠤⠊⣀⣠⠤⠖⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣮⣿⣙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠠⠀⠀⢀⠂⠀⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢋⠈⣉⣇⡔⢄⣫⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢐⢸⡐⡇⠀⠀⠀⠀⠀⢀⡤⠤⠀⠀⠀⠀⢠⠒⠙⠀⠀⠀⠀⠀⠀⠐⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠃⢸⡡⡇⠀⠀⠀⠀⠀⢈⠀⠀⠉⠉⠒⠀⠃⠀⠀⠀⠀⡠⠠⠀⢀⠀⠀⠸⠢⢄
⠀⠀⠀⣀⠔⢄⣀⢀⡀⡼⠂⠀⠀⠀⠉⠒⠚⢆⡀⠀⠀⠀⠀⠠⢁⡊⢠⡏⢀⡇⠀⠀⠀⠀⠐⡈⠀⠀⠀⠠⠠⠀⠠⠤⠅⠄⠐⠐⠡⠠⠀⠂⠀⠄⡀⠈
⠀⠀⠘⣀⣴⡦⠤⠥⠬⠤⠠⠎⠈⠀⠄⠰⠴⢠⡅⠀⠀⠀⠀⠂⡔⢡⠟⠀⠐⢿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠐⠒⠒⠲⠶⣀⠐⠒⠒⠊
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡰⢩⡇⠀⢐⢹
⠀⠀⠀⠀⠀⠀⢀⠁⠱⢠⡀⣘⡀⠀⢣⠀⠀⠀⠀⠀⠀⠠⢁⠔⠀⢸⠀⠀⠠⢸
⠀⠀⠀⠀⠀⠀⠍⠀⠄⠀⠂⠉⠂⠞⠉⠵⠀⠀⠀⠀⠀⢦⠋⠀⠀⠸⠀⠀⢈⠰⡀⠀⠀⠀⠀⠀⣀⡠⢀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠱⢖⣶⠠⠀⢐⡨⡇⠀⠐⣒⠈⠭⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⣀⣠⡄⠀⠀⠈⠅⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⡒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢀⠐⢆⠀⠀⠀⠠⠊⠄⠔⠠⠰⠂⠀⠀⠠⠀⣺⡌⠡⠤⣄⠀⠀⠀⠀⠀⠀⢠⠁⠔⡡⠊⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠕⠁⢊⡘⠉⠙⠂⠛⢎⣨⣡⡴⣼⠀⠀⠀⠀⢁⢸⡧⣄⣄⣬⣉⡒⡐⠒⡊⡁⡳⠊⢀⢄⠔⡡⠨⡀⠒⢄
⠀⠀⠀⠀⣀⠀⢀⡀⣀⠠⡤⡠⣂⣦⠬⠶⠐⠚⠛⠉⠉⠀⠀⠀⠘⠦⢀⡀⠀⢒⣘⣇⠀⠀⠀⠀⠈⠉⠉⠙⠚⠓⠷⠵⣥⣌⡢⡊⡈⠁⠸⢤⡜⡍
⠀⠀⠀⠈⢠⠀⢀⣠⡤⠖⠂⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢶⣀⣀⣠⣷⣴⡿⠶⡴⠦⠄⠠⢄⡠⢄⡀⢀⠀⠀⠀⠀⠉⠙⠲⢶⣕⡠⣪⠂
⠀⠀⠀⠀⠀⠖⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠁⠀⠁⠀⠁⠈⠁⠂⠙⠁⠈⠁⠂⠄⡨⣀⠀⠀⡈⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⡀⢀⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⢿⡿⣭⣟⣛⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⠞⢱⡆⠙⠓⠒⠒⠒⠛⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣣⢟⣵⡟⢹⣾⣭⣭⣭⣽⣦⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣫⠞⠁⠀⢸⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢝⣵⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠟⠛⢷⡄⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⠛⠙⠛⠷⣶⣶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠈⠁⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⢀⣀⣀⣿⠀⢀⣤⣴⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣾⠟⠉⠙⠻⣶⠟⠁⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁⠘⢷⣄⣀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠉⢹⣿⣏⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃⢹⡇⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣾⣿⠇⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣤⣤⣤⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠋⠉⠀⠀⠈⠙⠻⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠿⠟⠿⠷⢶⣤⡀⠀⠀⠀⠀⠀⠘⣿⣷⠶⠶⠶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠠⡾⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⡶⠾⠿⠟⠛⠛⠋⠉⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⠈⠙⠓⠢⠀⠀⠀⠀⠀⠠⠃⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠐⠲⠤⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⡀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⢀⠀⠄⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⢠⡘⠣⣀⡷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠙⢿⣶⡋⠢⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⢁⡼⢂⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠢⣀⡱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⡼⠛⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡛⠣⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢁⡴⠋⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠢⡀⣱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⡼⢣⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡞⠣⣀⠱⠀⣠⡀⠀⠀⠀⣠⣾⡟⢁⡴⠋⡠⠎⠀⠀⠀⠀⠀⣀⢀⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡉⠀⢈⠁⠁⢀⢠⣾⠟⢁⡽⢯⡠⠊⠀⠀⠀⠀⠀⡔⢘⠀⠘⠀⡙⠀⠗⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠙⢧⡄⠀⠈⣤⠟⠁⠈⠋⡤⠊⠁⠀⠀⠀⠀⠀⡖⠊⠀⣑⡤⠷⠧⣃⠴⠈⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠠⠙⣖⡞⠑⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠒⡟⠐⣶⣄⢹⡎⠁⠈⡹⠴⠖⠒⠒⠚⢻⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡤⢤⣴⣧⡾⠉⠙⢶⣗⣠⣤⣴⡄⠀⠀⠀⠀⠀⠀⠰⣁⠀⠩⢻⣼⣿⣷⣼⡓⠄⡠⡽⠈⠙⠛⠛⠓⠚⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡁⡨⠃⣠⣾⠉⠟⠃⢰⡤⠹⢿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠔⠁⡾⢹⡟⡃⠙⠦⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠛⣦⣾⠟⠩⢐⡦⠀⠨⣄⠸⣇⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⣇⣸⣇⡜⠐⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⡠⠊⣠⣾⡿⠁⠀⠀⢰⣦⣤⣴⡛⢢⣨⠿⣅⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⢀⠔⠁⡨⠛⣤⣾⠟⠁⡆⠀⠀⢠⣌⣿⣾⣾⡟⢺⠘⢦⡈⠳⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⢠⢻⢿⢿⣧
⠀⠀⠀⢀⡔⠁⡠⠊⣠⣾⠟⠁⠀⢀⠁⠀⠀⠘⣉⠉⣻⢿⡁⠈⢠⣬⣍⣦⣈⠷⣏⠙⢿⣦⡀⠀⠀⠀⢸⣾⢾⢾⣾
⠀⠀⢴⠁⡸⠿⣠⣾⠟⠁⠀⠀⠀⢸⡆⠀⠀⠀⣚⠉⠀⠐⠋⠁⠘⣉⠁⠁⠈⠢⡈⠳⣄⠙⢿⣦⡀⠀⡇⣽⢸⢸⡏⡆
⠀⠀⠀⠙⢤⣾⠟⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠚⠁⠀⠽⠖⠀⡔⠛⣧⣤⠀⠀⠈⠢⣈⡳⣎⠙⢿⢂⡅⣏⢸⠈⡇⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⣶⡄⠀⠯⠿⣧⣸⠀⠀⠀⠀⠈⠢⣈⠓⠀⢸⠋⣟⠹⢉⡏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢐⡦⠄⠁⢀⡀⠁⢬⣁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡯⠭⠭⣭⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢐⡦⠀⠀⠐⠋⢰⣻⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⡇⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠷⠂⠨⠗⠈⣰⣦⡀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠃⢸⡟⠒⠓⣿⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⠀⣤⡀⠀⠽⠖⠀⠀⢤⣔⠋⠃⠀⠀⠀⠀⠀⠀⠀⢸⠋⢻⠛⢻⠛⢻⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠛⠡⣄⡀⠸⠷⠂⢩⣭⠗⠂⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⠀⢸⠀⢸⡆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡀⠀⠀⠀⠋⠀⠀⠀⢀⡚⢫⡷⢆⠀⠀⠀⠀⠀⠀⠀⠁⠀⡟⠀⢸⠀⠸⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠇⠀⠘⠀⠀⠇⠀⠺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⠀⠀⣰⠀⠀⠀⠀⢤⠄⠠⡀⠀⡇⣀⢀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠠⢰⣄⠄⠀⠀⣨⠄⠀⠀⢤⣤⡀⠀⣡⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠐⠀⠀⠸⠖⠖⠒⠂⠀⠀⠀⠀⠀⣷⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠶⠗⠒⠒⠒⢂⠀⠀⠒⠒⠶⠂⠂⠀⣶⠖⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⡈⠀⣭⠨⢏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠆⡇⠀⠰⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢍⢈⢀⠅⠀⠂⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⢀⠄⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠠⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀

⠀⠀⠀⠀⠀⢀⡤⢖⢒⣞⢒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣀⠠⣤⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢖⡒⢒⡶⣤⡀
⠀⠀⠀⠀⢠⢯⣜⠻⡌⠟⢸⠏⣬⣳⡀⠀⠀⠀⠀⠀⠀⠀⡜⣵⢟⣵⣮⢧⠙⣦⣤⢉⣙⡓⢆⢀⠀⠀⠀⠀⠀⠀⡼⠃⢦⡈⣃⡸⢁⡴⠙⣆
⠀⠀⠀⠀⡏⣭⣍⠁⣴⠲⡄⢊⣩⡆⣧⠀⠀⠀⠀⠀⠀⢸⢹⡏⣼⢫⣶⡎⡇⣿⣿⣾⣿⣿⣿⡎⣷⠀⠀⠀⠀⢸⠇⠓⠢⡞⠋⢻⣧⠐⠖⢹⡀
⠀⠀⠀⠀⢷⢩⣴⢂⠘⠛⡁⠠⣤⢥⡇⠀⠀⠀⠀⠀⠀⠸⡎⣦⡸⣷⣭⢱⠇⣿⣿⢹⣿⣿⣿⢇⡿⠀⠀⠀⠀⠸⡗⠋⣉⠻⡦⠾⢏⠐⠒⣼
⠀⠀⠀⠀⠈⢳⣅⠾⢀⣷⡸⢗⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣳⣎⡽⢋⣼⣿⣯⣿⣿⡿⠋⠈⠀⠀⠀⠀⠀⠀⠙⢮⡃⢰⠀⢲⠄⣻⡼⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠚⠋⠁

⠀⠀⠀⢀⡤⣤⡰⣶⡶⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⢻⡏⢩⡟⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠛⠛⡛⠛⢶⣄
⠀⠀⢠⠏⣾⠿⡟⠜⣷⣶⣶⣏⣿⣿⣿⣦⠤⣄⡀⠀⠀⠀⠀⢠⣞⡈⠳⢌⠳⠸⣠⠞⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠁⠀⠁⠀⠀⠽⢷
⠀⠀⢸⠐⡱⡶⠀⣷⣽⣿⣿⣿⣿⣿⣿⣿⠀⢈⣿⠀⠀⠀⠀⢸⣉⣉⣩⠂⢺⡶⢑⠚⡛⢻⡆⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⠀⡃⣷⠀⠀⠀⠄⡇
⠀⠀⠸⡆⢳⣦⣶⢇⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⠀⠘⣏⢉⣴⢣⡆⡔⢮⣍⠙⡾⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⠁⡀⠀⢀⡷⠁
⠀⠀⠀⠈⠲⠿⠫⠾⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣅⣼⠃⢽⣀⣽⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣅⣀⣀⣡⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⠖⣯⣯⣽⣽⣓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠶⠖⠶⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣚⣭⡿⢿⣿⣿⣦⡀
⠀⠀⠀⠀⣼⣳⣿⣿⢟⣻⣿⣿⣧⣽⡄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⠓⠀⠉⠙⠲⣄⣀⡀⠀⠀⠀⠀⠀⡞⣼⠟⠀⣀⣀⡀⠙⣿⣿⡄
⠀⠀⠀⠀⡇⣾⣿⣫⣹⣿⣿⣻⣿⡇⡇⠀⠀⠀⠀⠀⠀⢾⣿⣀⣠⣤⣤⣤⣤⣤⣤⣶⣦⣤⣿⣿⣿⡦⠀⠀⠀⢰⣧⣿⡄⢸⣿⣿⡷⠀⣾⣿⡇
⠀⠀⠀⠀⢻⡽⣿⣷⣿⣿⣵⣿⣿⣳⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣤⣉⢉⣡⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠻⢽⣻⠿⠿⣟⣫⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⣥⣶⣴⣦⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⢀⣴⠾⣛⡻⠯⡛⣒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢩⣴⣶⣶⣶⣮⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⣴⣶⣶⣶⣍⡻⣦
⠀⠀⠀⠀⢰⡿⣱⣿⢟⡟⢷⡌⠚⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢢⣟⣿⣟⣿⢿⣿⣿⡜⡄⠀⠀⠀⠀⠀⠀⠀⡞⢠⣿⡟⣫⠭⡝⢿⣷⠸⣇
⠀⠀⠀⠀⢸⡅⣿⡇⢿⣍⢢⡿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣿⣿⡿⣿⣿⣷⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⣄⠣⡤⠏⣼⣿⢠⡟
⠀⠀⠀⠀⠘⢷⣜⠻⢶⡶⠟⡡⣱⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡡⠻⢿⣿⣻⣿⣾⢟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠛⣿⣷⣷⣾⡿⣋⡾⠁
⠀⠀⠀⠀⠀⠀⠙⠿⠶⣶⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢥⣙⣉⡩⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠥⠵⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠶⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⣀⣤⠤⠶⠒⠚⠛⠛⠛⠛⠛⠛⠓⠒⠶⢤⣤⣀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⢀⡾⠋⠛⠛⠛⠒⢶⡄⠀⠀⠉⠙⠳⢦⣄⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⣠⡴⠛⢁⣤⠶⠛⣷⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠞⠁⢠⠞⠉⠀⠀⠀⣿⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢀⣤⠖⠛⠙⠳⣄⠈⠳⣄⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⡞⠁⠀⠀⣠⠞⠁⠀⠀⢸⡆⠀⠀⠀⠀⢿⠀⠀⠀⠀⡿⠀⠀⠀⠀⣼⠁⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⣄⠀⠀⠈⢳⡄
⠀⠀⠀⣰⠏⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡆⠀⠀⠀⡇⠀⠀⠀⢰⠇⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠀⠀⠙⣦⠀⠀⠀⠹⣆
⠀⠀⢰⠏⠀⠀⢀⡾⠁⣠⣄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢷⠀⠀⠀⡇⠀⠀⠀⡿⠀⠀⣠⠟⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠹⡆
⠀⢠⡏⠀⠀⠀⡾⠁⣴⠃⠈⢧⡀⠀⠀⠀⠘⣦⠀⠀⠀⠘⣧⠀⠀⣿⠀⠀⢀⡇⠀⣰⠏⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢹⡄
⠀⡾⠀⠀⠀⣼⠃⣸⠃⠀⠀⠈⠻⣄⠀⠀⠀⠈⢷⡀⠀⠀⠘⢧⡀⢹⡄⠀⢸⡇⢰⠏⠀⠀⣠⠟⠁⠀⣀⣠⡤⠶⠒⠛⠛⠛⠛⠛⠛⠲⣆⠘⣧⠀⠀⠀⢷
⢸⡇⠀⠀⢠⡏⠀⣯⡀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠙⢦⡀⠀⠈⢳⡄⢷⡀⠸⡇⡿⠀⢠⡾⢁⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⡄⠀⠀⢸
⣼⠀⠀⠀⣸⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠙⠶⣄⡀⠙⢮⣧⠀⣿⡇⣠⣏⡴⠋⠁⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠈⡇⠀⣇
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⠀⠀⠈⠉⠛⠲⠮⢽⣷⣦⡿⠛⠛⢷⡿⢋⣠⡤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠶⠏⠀⣿
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⣤⣤⣤⣤⣤⣤⣴⣿⠀⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⠛⠒⠶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⣿⠀⣰⠶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠋⣡⣾⢷⣤⣤⣾⠻⢿⣗⠲⠦⣤⣀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣄⠀⠀⠀⠀⠀⣿
⢻⠀⠀⠀⢹⠀⢸⡀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⢀⣠⠞⣹⠋⢸⣿⠈⢻⡷⣄⠈⠙⢦⣄⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⢀⡟
⠸⡇⠀⠀⠘⣇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⢁⡾⠃⠀⣾⢸⡆⠈⢷⠙⢦⡀⠀⠈⠳⣄⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠈⣳⠀⢸⠃⠀⠀⢸
⠀⢷⠀⠀⠀⢻⡄⠹⠦⣤⣤⣤⣤⣤⣤⠤⠶⠚⠋⠉⠀⢀⣴⠏⠀⠀⣰⠇⢸⡇⠀⠘⣇⠈⢳⡀⠀⠀⠘⢧⡀⠀⠀⠀⠙⣦⠀⠀⠀⢠⠏⢠⡟⠀⠀⠀⡾
⠀⠘⣇⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⣰⠏⠀⢸⠁⠀⠀⣿⠀⠀⢻⡀⠀⠀⠀⠻⡄⠀⠀⠀⠈⢳⡀⢠⠟⢀⡾⠀⠀⠀⣸⠃
⠀⠀⠹⣆⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⠀⠀⠀⠀⣰⠋⠀⠀⣾⠀⠀⠀⢸⠀⠀⠀⢷⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠙⠋⢀⡾⠁⠀⠀⣰⠏
⠀⠀⠀⠹⣆⠀⠀⠀⠳⣄⠀⠀⡴⠖⠛⠋⠁⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⢰⠇⠀⠀⠀⢸⠀⠀⠀⠸⡇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠙⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⢀⡟⠀⠀⠀⠀⣾⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠋⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⢦⡀⠙⢦⣄⣤⠴⠛⠁⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣿⠀⠀⠀⣠⡼⠃⢀⡴⠋⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢧⡤⠶⠛⢁⣠⠞⠋⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠘⠷⠤⣤⣤⣤⣤⡾⠁⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠈⠉⠛⠓⠶⠦⢤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠚⠛⠉⠀⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠖⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⡄⢀⡖⠀⣤⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡄⢸⡇⢸⡇⣼⠇⣠⣦⠱⡀
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⡈⣷⡸⣇⣿⢰⡟⠁⣀⠱
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⣆⠘⢷⣬⡿⣿⣿⣼⢰⡿⠟⠃⠇
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠹⣷⣶⡷⢉⣬⣭⣭⣙⣀⠶⣤⢰
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣶⣴⢿⠅⣿⣿⣿⣿⣿⣿⣿⣦⡸
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣉⣡⣿⠆⣿⣿⣿⣿⣿⣿⣿⠟⢱
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠿⠋⣾⣧⣈⡛⣛⢋⠭⢥⣄⠈⠸
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣴⣾⠃⡟⣿⣿⣿⡛⢷⡄⠻⠆⡇
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠉⢀⣼⠇⣿⢹⡎⢿⠈⣷⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠛⠋⣰⡟⢸⡇⢸⡇⠘⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠛⠀⠼⠁⠘⡡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢻⢹⢸⣡⢋⠖⣠
⠀⠀⠀⠀⠀⠀⠀⣠⠖⣫⡡⣶⣷⢺⣿⡇⣶⣶⣨⣝⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣛⢮⠧⠊⣨⣁⡕⠮⠥⢓
⠀⠀⠀⠀⠀⣠⢞⣷⣜⢿⣿⣝⣿⣯⣿⣧⣿⣇⣿⡿⣵⣦⡝⣆⠀⠀⠀⠀⠀⠀⠀⠰⠢⠵⢀⣼⡩⢹⡯⡔⡫⠭⡆
⠀⠀⠀⠀⡼⣱⣮⣛⡿⣿⣿⢿⡟⣿⢹⣇⡿⣻⡿⣷⣿⢯⣶⣮⢷⡀⠀⠀⠀⠀⠀⠘⡭⠍⣗⢜⢽⢙⢌⢜⢮⡓
⠀⠀⠀⣸⢡⣝⣛⣻⡿⣷⣝⢧⢻⣹⣼⣜⡵⣫⡾⣟⣵⣿⣟⣽⣌⣧⠀⠀⠀⠀⠀⠀⠐⠋⡔⡱⢳⢳⠘⣌⠖⠁
⠀⠀⠀⡏⣸⣿⣛⣿⣻⡷⢯⣳⡿⡫⢛⢭⢻⣖⣻⣭⣽⣾⡿⣛⣟⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠁
⠀⠀⠀⡇⢿⡿⣿⣿⣿⣯⣟⢺⡟⣄⠿⢃⢧⡿⣒⡲⠶⣿⡿⠿⡿⢼⠇
⠀⠀⠀⢷⢶⣿⡿⣻⣿⡶⣞⡯⢿⢶⣭⣷⡟⣝⢮⣝⣻⡿⠿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⢒⠖⣢⢄⡀
⠀⠀⠀⠘⣆⣽⣾⡿⣿⣾⣯⣾⣣⣏⣾⣾⢹⣜⣷⣽⣿⢿⣿⣿⢠⠇⠀⠀⠀⠀⠀⠀⠴⡉⢧⠹⠈⠠⢃⠖⣛⣆
⠀⠀⠀⠀⠘⢮⢩⣾⣿⢳⣿⣷⣿⣹⣿⣿⣯⢿⣿⣟⢿⣿⡎⣱⠋⠀⠀⠀⠀⠀⠀⢸⠦⠌⠐⣠⡶⢶⡄⠊⠥⢬⡆
⠀⠀⠀⠀⠀⠈⠳⢭⡩⣿⣿⣸⣿⣸⣿⡟⣿⣷⡹⣿⢇⣩⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡓⢂⠄⡙⠷⠾⠃⢀⡐⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣟⣛⣙⣟⣛⣘⣫⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣥⠞⣠⢠⠐⡌⢦⣹⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠥⠾⠤⠗⠊⠁

⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⢀⢴⡻⣜⣞⣷⣧⣞⡦⡀⠀⠀⠀⠀⠀⢠⠖⠿⣄⠹⡇⢸⡟⢢⡀
⠀⢀⣾⣿⣿⢿⣿⣯⣿⣿⣿⣿⡄⠀⠀⠀⢠⣝⣳⡯⣺⣿⣮⣯⢾⢿⣿⡄⠀⠀⠀⢠⠛⠳⠶⣌⣧⣇⡞⣠⠾⢻⡀
⠀⠠⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⡇⠀⠀⠀⢘⣾⣺⢎⣿⣯⣽⣿⣠⣽⡶⡇⠀⠀⠀⢸⠶⠛⣫⢿⡐⢊⡯⠥⠶⠾⡇
⠀⠀⢻⣿⣿⣿⣿⣻⣿⣿⣿⣿⠁⠀⠀⠀⠈⣭⢞⣕⣝⢻⣿⣷⣕⡿⡭⠁⠀⠀⠀⠘⣶⠟⢡⡏⣿⢻⡙⠲⠶⡾⠁
⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠈⠫⢽⣻⢿⡿⣟⡯⠝⠁⠀⠀⠀⠀⠀⠈⠢⣾⣀⣻⣄⣙⡷⠚⠁
⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣟⣻⡿⣿⡇
⠀⠀⠀⠀⠀⠠⠞⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⣹⣤⡤⠄⠀⠀⠀⠀⠀⢸⣇⣰⣶⣦⡀⠀⠀⠀⠀⠀⢸⢭⢭⠽⡄⠀⠀⠀⠀⢸⢷⠎⢀⠈⠱⢿⡇
⠀⠀⠀⠀⠀⠐⠄⣀⣒⡫⠴⠄⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢐⡖⠀⠰⠀⠀⠀⠀⠀⠀⠀⠛⠛⡿⠛⠃⠀⠀⠀⠀⢸⡿⢆⠈⠁⡼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣤⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠉⠙⠛⠿⠇

⠀⠀⠀⠀⠀⠀⡠⢀⡒⠀⠀⠀⠀⠀⠀⠀⣶⢠⣀⡀⣶⠀⠀⠀⠀⠀⢀⢠⠤⠶⢦⠀⠀⠀⠀⠀⠀⠐⢢⠭⡰⠀⠀⠀⠀⠀⠀⠐⠔⢊⠑⢄
⠀⠀⠀⠀⠀⢰⡇⠘⢭⡤⠤⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⢘⣶⣶⣶⣶⡃⠀⠀⠀⠀⠀⢉⡥⠤⢣⠉⠀⠀⠀⠀⠀⢘⠄⠻⠇⢀⠇
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠙⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠄⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠔⢢⠀⠀⠀⠀⠀⠀⠀⡀⡄⣴⢀⢀⠀⠀⠀⠀⠀⠀⡄⠠⢆⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠘⠃⠙⠄⠀⠀⠀⠀⠀⣟⡏⠉⡉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⣇⣙⣚⣒⡤⠀⠀⠀⠀⠀⠒⣷⣶⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠐⠶⠧⠴⠧⠴⠆⠀⠀⠀⠀⠀⠈⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⠀⠀⠀⠀⠀⠀⢀⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⣁⠘⣿⡆⠀⠀⠀⠀⠀⠀⢸⡓⡯⠀⠀⠀⠀⠀⠀⢠⠀⠈⣷⣷⡆⠀⠀⠀⠀⠀⠙⠓⢁⠢⠀⠀⠀⠀⠀⠀⢈⠁⣟⣳
⠀⠀⠀⠀⠀⠀⠙⠃⠾⠋⠀⠀⠀⠀⠀⠀⠀⠸⠤⠗⠀⠀⠀⠀⠀⠀⠶⠶⠶⠿⠿⠷⠀⠀⠀⠀⠀⠀⢵⡾⠗⠃⠀⠀⠀⠀⠀⠀⠁⠌⠡⠂


⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢈⣽⢿⣅⠀⠀⠀⠀⠀⠀⠀⣿⠾⣿⠁⠀⠀⠀⠀⠀⠀⣀⠀⢰⣤⡼⠀⠀⠀⠀⠈⢲⣿⣿⣿⠃⠀⠀⠀⠀⠀⣹⠟⢲⡤⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡿⠽⡀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⠆⠀⠀⠀⠀⠀⣼⣿⣾⣾⠷⣇⠀⠀⠀⠀⠀⣄⣽⣈⢇⣠⠀⠀⠀⠀⠀⠁⢀⠗⢳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⡨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢎⠀⠀⠗⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠘⡀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⣠⠊⠀⠀⠀⠀⠀⣀⡠⠄⠒⠉⠁⢀⡠⠊⡋⢹⠐⢄⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠔⢢⣒⣉⣀⣀⣉⣉⡒⠄
⠀⠀⠑⢌⡁⠒⠀⠤⢀⣀⢰⡁⠞⠁⠀⠀⠀⢤⣂⠁⠀⠀⢀⣀⡀⠔⠁⠀⠀⠀⢸⠀⠀⠈⠒⠄⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢀⡜⠲⠎
⠀⠀⠀⠀⠈⠒⠒⠒⠒⠣⣀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⠈⠑⠤⣈⡄⠀⠀⠀⠀⢠⠊⢀⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡄⠑⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⠠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠀⢰⠀⠀⠀⠎⠀⠉⠦⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠘⠂⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠡⢸⠀⠰⠈⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠁⠀⠀⠧⢄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠢⣀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠐⢣⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⡿⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢲⠤⠤⠐⠂⠀⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⣀⣀⠠⠤⠐⠒⠛⠁⠀⠈⠉⠀⠀⠐⠒⠂⠇⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⣀⣨⠄⠀⠤⠤⠤⠄⠨⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠓⠊⠁⠀⠀⠀⠀⠀⠀⢀⠤⠤⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⡅⠈⠁⡲⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢄⡀
⠀⠀⠀⠀⠀⣖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠑⠀⠀⠀⠀⡇⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⣀⠀⠴⠥⠀⠀⠒⠓⠒⠀⠣⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠄⠀⠠⠤⠤⠤⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⠀⠀⠀⠀⢀⡠⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢀⡀⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⠂⠀⠄⡀⠀⠀⢀⡠⠒⠒⠒⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⢠⡾⠛⣭⣥⣶⣭⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠻⠛⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣍⣦⣷⣶⣮⡝⢷⡄
⠀⠀⠀⠀⢠⡟⢰⣿⢯⡻⡻⣽⣿⣶⢹⣇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⢀⢀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⣼⢣⣿⣾⢛⣥⣝⢫⣾⣧⢻⡄
⠀⠀⠀⠀⢸⠀⢻⣿⣧⠻⡿⣊⢭⣿⢆⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢔⢂⠀⠀⠨⣿⣿⠀⠀⠀⠀⠀⠀⣿⠨⣽⣇⢻⣀⣸⢇⣟⣯⢼⡇
⠀⠀⠀⠀⠘⣧⠘⢿⣾⣵⣺⣿⡿⠟⣼⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠸⣏⠽⣫⣶⣌⣴⣮⡻⢏⡾⠃
⠀⠀⠀⠀⠀⠈⠳⣤⣉⡙⠋⣉⣵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣭⣏⣟⣛⣫⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠐⢤⣤⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣀⠀⠀⠀⠀⠀⢀⣾⠟⠳⡝⣿⣿⣿⣿⣿⣿⣦⢀⣀⠀⠀⠀⠀⠀⢠⣿⣿⢃⣾⣿⣷⢹⣿⣷⣄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣶⠀⠀⠀⢸⡏⢰⡦⡅⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣶⠀⠀⠀⢸⣿⣿⢸⣿⡛⢸⡇⣿⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠉⠀⠀⠀⠀⠘⣿⣄⣡⢃⣿⣿⣿⣿⣿⣿⡿⠸⠿⠉⠉⠀⠀⠀⠘⣿⣿⡜⢿⣿⡿⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⢭⣾⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⣴⠋⣰⣾⣾⣿⣾⣦⣙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠀⠀⠀⠈⠙⣷⡄⠀⠀⠀⠀⠀⠀⢀⡾⢩⣄⢿⣗⣿⣳⣮⠹⣦
⠀⠀⠀⠀⢸⡇⣸⣿⣿⢟⣟⢿⣿⣿⡈⣷⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢠⣾⣻⣦⡀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣾⢰⣮⣿⣿⡿⣿⣿⡶⠷⢸⡇
⠀⠀⠀⠀⢸⡄⢻⣿⣿⣜⣋⣾⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠸⣯⣿⡿⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⢿⠰⣶⢾⣿⣷⣿⣿⣻⠿⢸⡇
⠀⠀⠀⠀⠀⢳⡌⠻⣿⣿⣿⣿⡿⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠘⢦⡐⠿⣫⣿⢻⣎⠿⣡⡟
⠀⠀⠀⠀⠀⠀⠙⠳⠦⣬⣭⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣦⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢬⣥⣬⠴⠞⠋

⠀⠀⠀⠀⠀⠀⣀⣴⠶⠿⠿⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠷⠶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣶⣶⣦⣀
⠀⠀⠀⠀⠀⡴⠋⣠⣶⣿⣿⣷⣦⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⣴⡛⢱⣄⣿⣴⣟⣤⡝⢷⡄⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⣦⢸⢂⡼⠛⣿⣧
⠀⠀⠀⠀⢸⠃⢸⣿⣿⣷⢿⣿⣿⣿⠸⣷⠀⠀⠀⠀⠀⠀⢰⡇⠸⣾⣿⣿⣿⣿⣿⡶⠌⣿⠀⠀⠀⠀⠀⠀⣾⡿⣈⣛⣾⣿⣾⣷⣛⡘⣿⡇
⠀⠀⠀⠀⢸⡆⢸⣿⣿⣿⣾⣿⣿⣿⢠⡟⠀⠀⠀⠀⠀⠀⠸⡇⠲⠾⣿⣿⣿⣿⣿⠿⢄⣿⠀⠀⠀⠀⠀⠀⢿⣷⢨⡽⢿⣿⣿⡻⣍⢡⣿⡇
⠀⠀⠀⠀⠀⠳⡄⠙⠿⣿⣿⠿⠟⣡⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠛⢋⡿⢻⡿⠙⣡⡾⠃⠀⠀⠀⠀⠀⠀⠈⢿⣷⣔⠋⠸⠈⢗⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠴⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⠴⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡍⠀⠀⠈⠙⢻⣿⡟⠀⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⣿⣿⡄⠀⠀⠀⣿⡿⠁⠀⠀⠀⢻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠈⢻⣷⡀⠀⢠⣿⠃⠀⠀⣀⣴⣿⣿⠿⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⣀⡀⠀⠀⠀⠹⡷⢀⣘⣁⡀⢴⡾⠟⠋⠉⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⣷⣶⣤⣀⢰⣿⣿⣿⣿⡆⣀⣀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠉⠉⠸⣿⣿⣿⣿⠇⠈⠛⠿⢿⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⣀⣠⣴⡾⠗⠈⢩⡍⠁⢾⣆⠀⠀⠀⠈⠉⠛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣶⣿⣿⠟⠉⠀⠀⢠⣿⠃⠀⠈⢿⣧⡀⠀⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⠀⠀⠀⢀⣾⣿⠀⠀⠀⠘⣿⣿⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⣼⣿⣯⣄⡀⠀⠀⣘⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⢿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠘⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⠿⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⡀⠀⠹⣿⣿⣿⠀⢰⣿⣿⡿⠋⠁⠀⠀⣀⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄⡀⠹⣿⣿⣦⣿⣿⡟⢁⣠⣴⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠈⠛⠿⣿⣿⣿⣿⣶⠟⠁⣀⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣀⠀⠀⠀⠈⠉⢛⣿⠀⢸⣿⣿⡇⠀⣿⣥⣀⣀⠀⠀⠀⠉⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠉⢀⣴⠿⣿⣿⣿⣿⣶⣤⡀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠟⠋⢁⣼⣿⣿⠻⣿⣿⣆⠈⠙⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⠉⠀⠀⢀⣠⣾⣿⣿⠇⠀⣿⣿⣿⣆⠀⠈⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣶⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⡄⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠟⠀⠀⢠⣿⣿⣿⣿⣷⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣷⣿⡿⠿⠟⠛⠉

⠀⡀⠀⠀⢠⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣤⠠⡴⢦⣤⣴⣄⠀⣠
⠀⠛⠒⠓⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⢸⡷⠛⡄⠭⢢⠀⠉⠙⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⡼⠎⡥⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣼⡇⠈⠙
⠀⡀⠀⠀⢀⣀⣿⣶⠮⠶⠀⠀⠀⠀⡈⠁⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢤⠠⠄⠃⠈⠁
⠀⢄⣀⣤⡋⠁⠘⠻⡆⠚⠀⠀⢀⣘⠀⠀⢲⠀⢀⠠⠟⠃⠈⠀⠸⠀⠀⠠⡄⢅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⣧⠄
⠀⠠⠇⣈⢁⠀⡀⠔⠀⠀⠀⣦⠉⠙⠛⠶⣼⠠⣀⣀⣉⡉⠈⣁⠀⠀⠚⠀⡕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢑⠲⠸⢿⠁⡀⠀⠀⠀⠐⣿⡁⠀⣀⢀⣤⣄⣿⣿⣾⣿⡆⢙⣒⠋⠰⠀⠆⢠⣄⠀⠊⠀⠀⠀⠀⢀
⠀⠀⠓⣁⠈⠀⠀⠀⠀⢀⠴⠋⢓⣆⠀⠀⠈⠉⠉⣹⠃⠛⠃⠘⠛⠀⠶⠆⢷⣿⣾⣿⣦⠀⠀⠀⠂
⠀⠀⠀⠙⢿⣥⡠⠴⢈⠂⠀⢀⠸⣿⣷⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡇⣰⠂
⠀⡄⠘⠃⠀⠙⢫⣀⡀⣤⡄⠀⢠⡿⠋⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠁⠀⠀⠀⣤⠸⣿⣧⣼⣷⠕⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠢⠀⠀⠀⠂⠀⠀⠀⠠⠤⣶⠂⠀⠺⠟⠁⡶⠄
⠀⠀⠀⠀⠀⠁⣀⠈⠉⠁⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣠⠀⠛⠳⠢⠀⠉⠀⠀⠠
⠀⠀⡀⡴⠀⢀⡡⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠉⠳⡄⠀⠐
⠀⡀⠙⠖⢻⣿⣷⡄⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠘⠀⠀⢀⠀⠈
⠀⠸⢹⠚⠀⠤⡭⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠉⠀⠀⢠⣼⠁⣼⠇⠠⠀⠸⠲
⠀⡀⣌⠃⠀⡢⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⠈⠁
⠀⠛⠚⡁⠾⠗⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⢙⡟⠋⢡⣄
⠀⢠⡀⠀⠁⠀⠈⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠒
⠀⠈⢡⣶⣦⣀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠁⢀⡀
⠀⠀⠚⠁⠉⣹⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠘⠁⠀⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢐⣸⣿⡀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣂⡀⠀⢀⣀⡄⠂⠠⡀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠣
⠀⠀⠀⠐⡀⣀⠛⠉⠉⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠩⠄⠒⢛⣛⣉⣄⡢⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣠⠛⢋⣡⣾⣿⣶⣤⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣴⠀⠁⠀⠀⠀⠀⠀⠘⠋⠁⢠⡄⠈⡀
⠀⠀⠘⠋⠀⠙⠛⠗⠿⠁⠀⠈⠋⠙⠳⣶⠄⠀⠄⣰⠤⢤⣤⡔⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠓
⠀⠀⠀⠀⠀⠀⠒⣶⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⣟⠃⠀⠐⠓⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⢀⣼⠗⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠘⢀⡄
⠀⠀⠀⠀⣄⠘⠟⠋⠀⢈⠄⠀⠀⣴⡞⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⢀⠓⣯⠰⢈⠀⠀⠀⠀⠀⠑⠾⠇⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠐⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡆
⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠘⣆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡇
⠀⠀⠀⠘⢦⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹
⠀⠀⠀⠀⠀⠑⢦⡈⢧⠀⠀⢀⣀⡤⠤⠶⠶⠶⠦⣤⠀⠀⠀⢳⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠉⢾⢓⡾⣭⣀⣀⡤⠤⠴⠚⠉⠀⠀⢀⣀⣾⣁⣹⠶⠤⠤⠤⣄⣀⠀⠀⠀⠀⠈⣇⡏
⠀⠀⠀⠀⠀⠀⠀⢠⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⢠⠞⡏⡇⠙⠢⣄⡀⠀⠈⠉⠓⠦⣀⡤⣏⣵⠤⢀⣀
⠀⠀⠀⠀⠀⠀⣰⠃⢰⢣⡄⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⡴⠃⢸⡇⡇⠀⠀⠀⠉⠓⢲⡤⢤⣀⣈⣙⣿⡏⠑⢦⣀⠉⠲⢄
⠀⠀⠀⠀⠀⢠⠇⠀⣾⠸⡇⠀⠀⠀⢀⡴⠁⠀⣠⠴⠋⠀⠀⢸⠇⡇⠀⠀⠀⢀⣴⣋⡤⠖⠋⠀⠀⡅⠃⠀⠀⠈⠙⠒⠤⠽⠆
⠀⠀⠀⠀⠀⣸⢀⡜⢹⠀⡇⠀⠀⢠⣞⡤⠔⠋⠁⠀⠀⠀⠀⢸⠀⣥⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠻⠎⠀⣿⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⣀⣄⡀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠸
⠀⠀⠀⠙⠶⠒⢲⣤⡇⠀⢹⠒⠶⠦⣄⣠⠴⠛⠒⠢⠤⣄⢤⡏⠀⢸⠖⠒⠲⠶⢤⣠⡴⠚⠓⠦⣼⠀⠀⡗⠲⠴⠤⣄⣤⠖⠛⠦⠄
⠀⣀⣀⣀⣀⣀⣀⣠⠇⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⡇⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⣀⣠⠤⠶⣚⡭⢽⠀⠀⢸⡯⠕⣋⠵⣫⢟⡽⣋⠝⣩⠞⣹⠇⠀⠀⡇⡼⠀⡇⢸⡈⢇⠹⡄⠱⣄⠀⠀⣍⠳⣝⠣⣝⠦⣝⠢⣍⠃
⢀⡥⠴⢚⣉⠥⠖⣻⠀⠀⠀⡖⣫⢕⡫⠞⣡⠞⣡⠞⢡⠞⢸⠀⠀⠀⣷⠇⢀⡇⠈⡇⠸⡄⠹⡄⠏⠀⠀⢿⠳⣌⠳⣌⠳⢌⠓⢦⡁
⠀⠴⠚⣉⡤⠖⢉⡝⠀⠀⠀⣯⠔⢋⡠⠚⣡⠞⠁⡴⠋⢠⢾⠀⠀⠀⢿⠀⢸⡇⠀⡇⠀⢧⠀⣋⣉⣀⣀⣉⣳⡈⠳⣌⠳⣄⠙⢦⡀
⠀⠖⠋⣁⡤⢚⡋⠙⠋⠚⠊⠉⢲⠋⢀⠜⠁⢠⠞⠀⣰⠋⣾⠀⠀⠀⢸⠀⢸⠀⠀⣿⠀⠘⡄⠀⢻⡀⠈⢧⡀⠙⢦⠈⢦⡀⠑⢤⡀
⠀⠴⠊⣁⠴⢊⡩⠟⠉⣉⠝⠋⢉⡔⠁⠀⡴⠋⠀⡴⢁⣀⣿⣀⣀⣀⣸⣀⣸⠀⠀⢸⠀⠀⢳⠀⠀⢳⠀⠀⢳⡀⠀⠳⣄⠙⢦⡀⠁
⠀⡴⠊⣡⠔⠋⠀⣠⠞⠁⢀⡴⠋⠀⢠⠞⠁⢀⡜⠁⠸⣤⣠⣀⣤⣤⣤⣄⣿⠀⠀⢸⡀⠀⠘⡆⠀⠈⢧⠀⠀⠹⡄⠀⠈⢦⡀⠑⠆
⠀⡴⠊⠁⠀⡠⠚⠁⢀⡴⠋⠀⢀⡴⠃⠀⢀⠞⠀⠀⢰⠃⠀⠀⡼⠀⠀⠀⡿⠀⠀⠘⡇⠀⠀⢳⠀⠀⠈⢧⠀⠀⠘⣆⠀⠀⠙⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣻⣯⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣛⡵⠟⠉⠀⠀⣀⣀⡀⠰⣶⣿⣿⣟⡛⢶⣄⠀⣤⣀⠀⠀⠉⠻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣫⡾⠋⠀⢀⣠⣶⣯⣭⣍⡻⣧⠹⣿⣿⣿⣿⡎⣿⠄⣿⣿⣿⡲⣄⡀⠀⠙⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⢏⡼⠋⠀⠀⠐⠻⢿⣿⣿⣿⣿⣷⡼⣇⢻⣿⣿⣿⡇⣿⢰⣿⣿⣿⣿⡼⣷⠀⡀⠀⠙⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢠⣿⣿⢣⡞⠁⠀⣰⠾⣟⠿⣦⣝⠻⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⠇⣾⣿⣿⣿⡟⣼⠟⣰⣿⣆⠀⠈⢿⣿⣿⣿⡀
⠀⠀⠀⠀⣾⣿⢣⡟⠀⠀⣼⣵⣿⣿⣿⣶⣽⣷⡌⢿⣿⣿⣿⡇⣿⣿⣿⡟⣰⣿⣿⣿⣿⡾⢋⣼⣿⣿⣿⢧⠀⠀⢻⣿⣿⣷⡀
⠀⠀⠀⣸⣿⡇⣾⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⣿⣿⣧⢹⣿⡿⢡⣿⣿⣿⠟⣁⣴⣿⣿⣿⣿⡿⢸⡇⠀⠈⣿⣿⣿⣇
⠀⠀⠀⣿⣿⢸⡇⠀⠀⣠⣤⣤⣤⣭⣙⡛⠻⢿⣿⣿⣿⡌⠛⢉⣀⣉⡁⠛⠿⢛⣥⣾⣿⣿⣿⣿⢿⣫⣵⠿⢁⡀⠀⢸⣿⣿⣿
⠀⠀⢸⣿⡏⣼⠀⠀⣼⢏⣴⣶⣶⣶⣿⣿⣿⣶⣦⣍⡛⢀⣾⣿⣿⣿⣿⣷⡀⢻⣿⠿⠿⠿⠛⣛⣋⣭⣴⣾⣿⣧⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⡇⣿⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⢸⣿⣿⣿⡿⣋⣿⡇⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⡇⢻⠀⠀⢻⣿⡿⠟⣛⣩⣭⣤⣶⣶⣶⣿⣧⠈⢿⣿⣿⣿⣿⡿⠁⣬⣙⠻⠿⣿⣿⣿⠿⠿⠿⢟⣱⡟⠀⠀⣿⣿⣿⡇
⠀⠀⠈⣿⣿⢸⡇⠀⠈⢁⣶⢟⣩⣷⣿⣿⣿⣿⡿⢛⣥⣶⣤⢈⣉⠉⣁⣤⡘⣿⣿⣿⣷⣦⣬⣍⣛⠛⠛⠛⠋⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⢹⣿⡆⢿⡀⠀⢸⡇⣾⣿⣿⣿⣿⠟⣋⣴⣿⣿⣿⢇⣾⣿⡇⢻⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣿⣿⣿⡏
⠀⠀⠀⠈⢿⣿⡌⣧⠀⠀⢳⣿⣿⣿⡿⣡⡾⣿⣿⣿⣿⠏⣼⣿⣿⣿⢸⣿⣿⣿⣷⡘⢿⣟⠿⣿⣿⣿⢟⡟⠀⠀⣼⣿⣿⡿
⠀⠀⠀⠀⠘⢿⣷⡜⢧⡀⠀⠹⣿⠏⣴⡏⣼⣿⣿⣿⡿⢰⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣦⣝⠻⣶⣭⡶⠏⠀⢀⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⢿⣿⣎⠻⣄⠀⠈⠀⢿⡟⣿⣿⣿⣿⠃⣿⢸⣿⣿⣿⣧⢹⡞⢿⣿⣿⣿⣿⣷⣦⠄⠀⠀⣠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣜⢷⣄⠀⠈⠙⠮⣿⣿⣿⠀⣿⠸⣿⣿⣿⣿⣆⢻⣮⣙⣛⣻⠿⠋⠁⠀⣠⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣌⡳⢦⣄⠀⠀⠉⠛⠀⠙⠷⣮⣽⣿⣿⠿⠆⠈⠉⠉⠀⠀⣠⣴⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣭⣛⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⢶⣛⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣶⣦⣭⣭⣍⣛⣛⣛⣛⣯⣭⣭⣷⣾⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠀⡦⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡶⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢀⣀⣀⣄⣽⣭⣀⣠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⠼⡿⠥⢤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠉⠈⠉⠁⢸⡃⣻⠁⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣉⣻⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡀⠀⠀⠀⠀⠀⠀⢸⡅⣽⡀⠀⢸⡇⠀⣠⡀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⢠⠄⣿⠇⠀⢸⡷⠟⠿⠃⠀⣠⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡃⠀⠀⠀⠀⠀⠀⢸⠂⣿⠀⠀⢸⡇⠀⠀⠀⠰⣿⣿⠀⣿⡰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡋⢹⣯⣹⣷⣄⣀⣄⣀⠀⢸⡃⣿⠀⠀⣸⣧⡀⣀⠀⠀⢠⣝⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠉⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣹⡟⠛⠛⠛⠛⠛⠛⠛⣿⢹⡏⠀⢹⡁⣿⠁⠀⢏⣿⡏⠛⠛⠀⠉⠉⠁⠀⠈⠋⠁⠀⠀⠀⠁⠀⠀⠀⠈⠁⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠋⠀⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⣴⡇⠀⠀⣠⠈⡆⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⡇⠀⢀⣀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠉⠀⠀⠀⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣷⣦⢤⣤⣤⣤⣶⡾⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠉⠙⠻⢾⡋⠉⢻⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⣩⡉⣿⣛⣿⣟⢙⣛⡉⠙⠋⠉⠉⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣘⣟⠃⠀⡝⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⣿⠟⣿⣿⣹⣿⡟⠻⡇⠀⠀⠓⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⠃⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢤⣾⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣰⣿⣿⣿⡟⢀⢀⠀⣿⣿⠇⠀⢀⣿⣦⡴⠗⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠉⢹⣿⣿⣿⣤⣶⡄⠰⠿⠒⠒⢺⣿⠉⠁⠀⠠⠀⠀⠀⠀⠙⠛⠛⢉⣵⣿⣶⣶⣤⣌⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠿⠿⢿⡇⠰⠷⠀⠀⠐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⡠⠀⠀⠀⠄⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⣿⣿⣿⣷⣾⡟⠐⠓⠂⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⣿⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠙⠿⠟⠿⠛⠿⠿⠿⠛⠿⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇



⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿