Socks Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠶⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣤⣤⣤⣤⣤⣼⡀⠀⢀⣤⣾⡿⠋⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠉⠉⠉⠉⠉⠉⠉⢹⣇⣴⣿⠟⠁⢀⣤⣾⠟⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⠿⠿⠿⠿⠿⡿⣟⠁⣠⣴⡿⠋⠀⠀⣠⣴⡿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⢀⡀⣳⠈⢿⠟⠁⠀⢀⣴⣾⠿⠋⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⠛⠛⠛⠛⠛⣳⡄⢳⣠⣶⡿⠛⠁⠀⢀⣠⣶⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣀⣰⣿⣿⡄⢻⡋⢀⣠⣴⣾⠿⠛⠉⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⠃⠀⣿⠿⠛⠉⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣤⣤⣤⣀⣀⣀⣀⠀⣸⡿⠃⠀⠀⢹⡀⣀⣠⣤⣶⣾⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⠉⠉⠉⠛⠛⢻⡿⠛⠁⠀⠀⠀⠀⠘⡿⠟⠛⠉⠉⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣶⣶⣤⣤⣤⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣤⣤⣶⣶⡾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠉⠉⢉⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠉⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢷⣶⣶⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣶⣶⣶⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡀⠀⠀⠀⠉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠛⠻⠿⣶⣶⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣤⡀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣭⣤⣤⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉

⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠶⠾⠛⠛⠛⠛⠛⠛⠛⣛⡳⣦
⠀⠀⠀⠀⣠⡶⠶⠒⠒⠒⠿⠿⠿⠟⠛⠛⠛⢛⡛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢫⣷⠂⠀⠀⠂⠀⣀⣘⣀⣀⣠⣤⣿⠏⢸
⠀⠀⠀⠀⡏⢿⣤⣴⣤⣴⣦⣤⣤⣾⡶⠶⠾⠛⠁⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢉⠛⠛⠟⠉⠙⡏⠉⢤⠀⠀⣄⠀⠀⢸
⠀⠀⠀⠀⡇⢰⡀⠀⡀⠀⢠⠀⠀⠀⡄⠀⢀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢰⠀⠀⠀⠀⠸⡇⠀⢸⠀⠰⣾
⠀⠀⠀⠀⡇⠘⡇⠀⣧⠀⠀⡀⠀⠀⡇⠀⠘⡆⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡄⠀⠘⡆⠀⢰⠀⠀⠧⠀⠘⠇⠀⠹
⠀⠀⠀⢸⣷⠀⡅⠀⠸⡀⠀⣧⠀⠀⢿⠀⠀⠇⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴
⠀⠀⠀⢸⣿⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠈⠻⢷⣶⡾⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠸
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢠
⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⣠⡿
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋
⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⣾⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⣸⠃⠀⠀⠈⠉⠙⠲⠤⡀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠐⠲⢤⣀⠀⠀⠀⠀⠀⢀⡴⠁
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⠀⠀⣠⠞
⠻⣧⡀⠀⠀⠀⠀⠀⠀⣀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣴⠋
⠀⠙⠷⣦⣤⣤⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣤⣀⡀⠀⠀⠀⣀⣠⡴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠿⣿⣿⣿⣿⠿⠿⠟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡆⣤⢀⡄⣠⠀⣦⠰⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠃⠿⠸⡇⢹⠀⠻⠀⠇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⠶⠤⠤⠤⠤⠤⠴⠖⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠆⠀⠀⠀⠦⠀⠀⠶⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⠿⠛⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠛⠀⠀⢀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠋⡉⠠⡄⢸⡸⡆⠀⠀⠀⠀⠀⠀⢻⠀⠰⠀⠀⢠⡄⠈⠁⣀⠙⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠈⣇⢸⡀⣧⢸⡆⢻⠀⢻⠈⠇⣷⠀⠀⠀⠀⠀⠀⢸⡟⠛⠓⠲⢦⣄⠀⡀⠈⠀⠀⠓⠀⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⢻⡈⠃⠙⠀⠃⣈⣀⣤⠴⠚⢹⡄⠀⠀⠀⠀⠀⠸⡇⣀⠀⠀⠀⠘⡆⠉⠀⠀⠦⠀⠀⠘⠂⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠸⡏⠛⠋⠉⠉⠉⡅⠀⠀⠆⠀⣧⠀⠀⠀⠀⠀⠀⢻⡘⢦⠀⠀⠀⡇⠀⠠⠄⠀⠀⠠⡄⠀⠀⠓⣠⠞⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠃⠀⢠⠀⠁⠀⡀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⢰⡇⢀⠀⠀⢀⡀⠀⠀⢀⡀⢰⠏⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡀⠀⠀⢀⠀⠃⠀⡈⠉⠙⠓⠶⠦⣤⣀⡀⠀⠀⠈⠙⠻⢦⣌⡉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣙⣀⣀⣈⡀⠀⡀⠉⠀⠈⠁⠀⠀⢀⡈⠉⠛⠶⣤⣀⠀⠀⠀⠉⠛⠲⠶⢬⣍⣀⣀⣹⣄⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠁⠀⠀⠉⠙⣦⠙⠀⠀⠘⠂⠀⠀⠀⠀⢤⠀⣴⠃⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡔⣆⠀⠀⠀⢸⡆⠀⠲⠀⠀⠀⠉⠀⠀⠀⢸⠇⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣝⡀⠀⢸⡇⠀⣀⠀⠀⠦⠀⠀⠈⠁⢸⡄⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠧⣤⣍⣀⣀⡀⠀⠰⠆⠀⠈⣧⣀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠋⠉⡉⠉⠉⡇⠀⠀⠀⠀⢸⠉⠉⢉⠉⠙⠉⠉⠉⠉⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠂⠀⠀⠃⡠⢸⠀⠀⠀⠀⠀⠀⡇⢄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠘⠀⡇⡌⠀⠀⠀⠀⠀⠀⢡⢸⡀⠇⠀⠀⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣨⣀⣀⣀⣀⣀⣀⣀⣐⣀⡇⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠒⠀⠈⠩⠉⠩⠉⢩⠉⠉⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⡍⠉⠍⠉⠍⠉⠀⠂⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠄⠠⠄⠀⠀⠀⣤⠀⠁⢰⠀⠀⠀⠀⠀⠀⡆⠈⠀⣤⠀⠀⠀⠰⠀⠠⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠂⣀⠀⠀⠀⣠⠸⠀⠀⠀⠀⠀⠀⠇⣄⠀⠈⠀⣀⠐⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⡆⠀⠀⠀⠀⢰⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⠀⠀⠄⠀⠐⠀⠒⣀⣼⠀⠀⠀⠀⣧⣀⡒⠀⠂⠀⠠⠄⠀⠂⠀⠰⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢠⠀⠀⠀⣀⠤⠚⠉⠀⠈⠀⠀⠀⠀⠁⠀⠉⠓⠤⣄⠀⠀⠀⡄⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⠀⠀⠀⡄⠸⡅⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⢨⠇⢠⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⠃⢀⡀⠀⢀⡀⠈⠢⡀⠀⠀⢸⠃⠀⠀⠘⡆⠀⠀⢀⠔⠁⢀⠀⠀⢀⡀⠘⠃⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠠⠄⠀⠀⢀⠀⠁⠀⠂⢈⠲⣤⠎⠀⠀⠀⠀⠳⣤⠖⡁⠐⠀⠈⠀⡀⠀⠀⠠⠄⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠠⠆⠀⠀⠐⠀⠀⠀⠀⠤⠀⢈⠔⠁⠀⠀⠀⠀⠀⠀⠈⠢⡁⠀⠤⠀⠀⠀⠀⠂⠀⠀⠰⠄⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡀⠀⢀⠀⠦⠀⠂⠀⠐⠀⢀⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡀⠀⠆⠀⠐⠀⠴⠀⡀⠀⢀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠁⡀⠀⠀⢀⠀⠰⠆⠀⡤⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢤⠀⠰⠆⠀⡀⠀⠀⢀⠈⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⠒⠀⠒⠀⡀⠀⠀⠀⢀⢀⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⡀⡀⠀⠀⠀⠀⠀⠒⠀⠒⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠤⠥⠤⠭⠤⠤⣀⡀⠈⠀⠀⢀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠁⢀⣀⠤⠤⠭⠤⠬⠤⢧
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⡘⠂⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠐⢂⠔⠉⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠀⠀⠀⠀⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⢶⡀⠀⠀⠀⠀⠀⢀⡴⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⣉⣤⡤⠦⠼⡇⠀⠀⠀⣠⣔⠋⣡⡴⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠀⠀⢿⠀⠀⠘⢍⣢⠟⠁⠀⡀⢘⡷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣌⣔⣠⡤⢣⠷⠋⢧⠀⠀⠸⡅⠠⠄⢨⡌⠜⠁⠂⢙⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠑⠆⠉⠓⠀⠀⢀⣸⣆⠀⠀⣇⣤⢓⠛⠑⠀⢀⡴⠋⠀⡈⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⡤⠴⢶⠛⠉⠁⠈⣆⠀⠘⣇⠈⠁⣠⡴⠛⢧⠂⠁⠀⠐⢸⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢺⡀⠀⢸⠁⠀⠀⠀⢈⣆⠀⠈⢶⠋⠹⣆⠀⠈⢣⡀⠄⠂⢈⠷⡀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢉⡟⡀⠘⡤⠤⠤⠄⡞⠘⡄⠀⠀⢳⡔⠊⣛⠰⠀⠑⡄⠂⠀⠀⢙⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡬⡇⠀⠀⠧⠀⠀⠀⣻⠀⣧⠀⠀⠀⠙⣆⢈⢦⡀⠀⠘⢆⠀⢀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡟⡤⠀⢰⠀⠀⠀⠼⣷⠃⠀⠀⠀⠀⠘⡆⠀⢧⠉⠀⠘⣦⠂⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠃⣱⠀⠀⢸⡀⠐⢀⠜⠁⠀⠀⠀⠀⠀⠀⢹⡈⠀⣹⠵⠀⠸⡄⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⣨⠏⠁⠀⡟⠀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠰⢜⡀⠀⠀⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢠⡾⠀⠀⢀⣇⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣸⠣⠆⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣰⠃⢡⡇⠘⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢹⠄⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢠⡏⠑⡄⠆⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠲⣌⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣤⠽⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢤⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣶⣿⣿⣿⢸⣯⣿⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⡿⣿⣿⣷⢿⣿⣏⣿⢿⣿⢿⣿⢿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣼⣷⣿⣿⡟⢻⠋⠛⠉⠀⠁⠈⠀⠈⠀⠐⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠩⠭⠟⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠁⢀⠀⠀⠀⠨⠛⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠈⠀⠀⠀⠐⠀⠀⠺⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⡀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⣹⢷⠰⠄⠈⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⡸⠀⣰⠀⠀⠀⠀⠁⠀⠀⠀⢀⠁⢸⣶⣶⣶⣿⣶⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣶⣤⣧⣀⠀⠀⠀⠀⣀⠀⣀⠀⠀⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⠂⠀⠒⠺⠏⠈⠀⢣⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣼⠇
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠢⡄⠙⠀⠀⠀⠀⠀⢣⡀⠀⠙⠛⠿⠿⣿⣿⣿⣡⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣤⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡏⠠⢀⠀⠄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢦⣤⡀⠁⠀⢄⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣇⠈⢂⠈⢀⠀⠠⠀⠠⠀⠢⡀⠲⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠈⠁⡀⠐⡀⠀⢀⡀⢂⣀⠀⠈⡳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢼⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⡀⠤⡀⠒⣂⡈⠡⢀⣉⣦⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠈⠠⡈⠚⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠠⠄⠤⠴⠤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠒⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣀⠚⠠⡀⠀⠀⠀⠀⢰⠀⠘⠢⡀⠀⠀⠀⠀⡈⠀⠀⠀⠈⡰⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠚⡤⠊⢡⠀⠀⠑⠀⠀⠀⢠⠃⠀⠀⠀⠈⢦⠀⠀⡰⠀⠀⠀⠀⠘⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠤⠃⠀⠀⠄⠀⠀⢁⢀⡴⠁⠀⠀⠀⠀⠀⡠⠧⠼⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠋⠈⢣⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠒⠒⠀⠀⠀⠀⠀⢀⣀⡀⣀⠤⠄⠐⣶⠀⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠰⡆⠈⠉⠉⠷⠀⠀⢠⠙⡄⠀⠀⠁⢂⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢆⠀⠸⠀⠡⠀⠈⠀⠈⠆⠀⠀⠀⢂⡈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⢄⡆⠀⠀⢁⡄⠀⠀⣀⠷⠀⠤⠘⠓⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠘⠃⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠐⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠄⠀⠀⠐⠒⠀⠀⠉⠀⠀⠀⠄⠐⠂⠈⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⢁⠤⠐⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⡠⠊⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠤⠄⡀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠄⡜⠁⠑⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⠢⠔⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣄⣀⠠⠀⠂⠁
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠈
⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠄⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣧⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠓⡦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠲⢤⣆⡘⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⡊⡆⠀⢈⡙⠳⢦⠏⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⠤⡄⢀⡠⡀⠙⠚⢠⠏⠀⣟⣁⣈⢈⡁⡋⢉⣉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⢀⠀⢉⣀⠈⠓⠁⠀⣠⠏⠀⢠⠏⠉⣉⠉⠉⢉⢉⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⡕⡄⠀⠁⠉⠀⠘⠚⠀⠾⠗⣰⠃⠀⠀⡾⠀⠸⠤⠃⠀⠈⠈⠀⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⡖⢟⠉⠉⠞⡄⠈⢎⠄⠀⢎⠆⠀⠮⠅⠀⡰⠃⠀⠀⣸⠃⢠⠖⡄⠐⠥⠃⠀⢸⡇
⠀⠀⠀⠀⣴⡎⠙⡍⣆⠀⠸⡘⡀⠀⠸⠸⡀⠈⢆⢂⠀⠀⣠⡤⣶⡾⠁⠀⠀⢠⠇⠀⠀⠁⢠⢤⠀⢴⡲⢸⠁
⠀⠀⠀⣸⡗⣇⠀⡁⢸⠀⠀⡇⡇⠀⠀⡇⠃⠀⠈⣎⣆⣼⣣⠾⠋⠀⠀⠀⢀⡞⠀⠺⠝⠀⠀⠁⡠⢄⠀⣼
⠀⠀⠀⠹⣶⣏⣀⡇⡎⠀⢰⢀⠇⠀⣀⣧⡶⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⢠⡾⢕⠄⡀⠀⢴⡱⠀⠉⢁⡤⡏
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡢⡀⠉⠪⡀⢄⠀⠀⣰⢋⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⡀⠀⠈⢮⠢⡀⠈⠑⢝⢦⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠀⠑⣌⢆⠀⠀⠱⡘⡄⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠑⡌⢆⠀⠘⡌⠆⠀⠀⣱⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢷⡀⠘⡌⡆⠀⢱⣸⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣧⣤⠷⠗⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⠙⠛⠒⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠉⠉⠙⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢹⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢸⠇⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡾⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⣀⣠⠴⠋⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⣴⠋⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠛⠉⠉⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⣿
⣼⠁⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣿
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣠⠞⠁⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣰⠇
⠹⣄⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⢀⡴⠋⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣀⣠⠴⠋
⠀⠈⠙⠓⠒⠒⠒⠛⠋⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⣀⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣀⣀⣀⣀⣀⣠⡤⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣧⠀⠀⠀⢀⣤⣾⣿⡄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⠇⢹⣦⣴⠾⠛⡿⣸⢻⡇⠀⠀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡼⠀⠀⠉⠁⠀⣸⢣⡏⠀⣷⣴⠿⡿⣻⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⡇⠀⠀⠀⠀⠀⢃⡟⠀⠀⠈⢀⡾⣱⠃⠀⣿⠀⣀⣠⣴⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣸⠀⠀⠀⠀⠀⡜⣼⠃⠀⠀⢀⡾⣱⠃⠀⠀⠿⠛⢋⡽⢋⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡏⠀⠀⠀⠀⡸⣹⠃⠀⠀⢀⡞⣵⠃⠀⠀⠀⠀⣰⠏⣠⠟⢠⣿⣀⣠⣤⣶⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠃⠀⠀⠀⢰⢣⡏⠀⠀⢠⡟⣼⠃⠀⠀⠀⢀⡞⢁⡼⠃⠀⠸⠟⠛⣩⠟⣡⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡞⠀⠀⠀⢀⡏⡾⠀⠀⢠⡟⡼⠁⠀⠀⠀⣴⠋⣠⠟⠀⠀⠀⠀⣠⡞⣡⡾⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢠⠇⠀⠀⠀⡞⣼⠁⠀⣠⠏⡼⠁⠀⠀⣠⠞⢁⡴⠃⠀⠀⠀⣠⡾⢋⡼⠋⠀⠀⠿⠛⣻⡿⠟⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⡀⠀⢀⡼⢱⡏⠀⣰⠏⡼⠁⠀⢀⡴⠋⣠⠟⠀⠀⠀⣠⡾⢋⡴⠋⠀⠀⠀⢀⣠⠞⣩⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠉⠉⠉⠀⢾⣄⡴⠋⣼⠃⠀⣠⠟⢀⡼⠃⠀⠀⢀⡾⢋⡴⠋⠀⠀⠀⣀⡴⢛⣵⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢰⠟⠛⣦⢀⣤⣀⠀⠀⠸⣧⣠⡾⠃⣰⠟⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⣠⡾⣫⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⡿⠀⢠⢏⡾⠁⡽⢁⣀⣀⠈⠉⠀⢰⡏⠀⢀⡴⢋⣴⠟⠁⠀⢀⣴⠞⣡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢸⡇⢀⡞⡾⢁⡾⢡⡟⠁⣹⠇⣀⣄⠀⠛⠾⠋⢠⡞⠁⢀⣤⡾⢋⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⣀⡾⣸⢃⡞⢠⠟⢀⡼⠃⡴⠋⣨⠗⣀⡀⠀⠘⠿⠿⠛⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣀⠀⠈⠋⠐⢷⠟⢰⠏⣠⠟⣡⠞⣠⠞⣡⠞⢉⣹⡦⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⠻⠶⣤⣀⠀⠀⠻⠾⢋⡼⢫⡾⣣⠞⢁⣴⡾⠋⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠉⠳⢦⣄⠀⠘⠷⠋⣼⣣⣴⠟⠁⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠙⠋⣀⣴⠞⠁
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠙⠳⢦⣄⠀⠀⠀⠀⠈⠙⢿⣿⠟⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⣠⣾⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⢀⣤⠆⣠⣾⠟⣡⡾⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠛⣡⡾⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠶⠿⠞⠛⠁

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⠶⢶⡶⠶⣶⣶⠶⢶⡶⡶⢶⣶

⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⠤⠤⠴⠶⡇⠀⠀⢸⠶⠦⠤⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣄⠀⢀⣴⡇⠀⠀⢸⣦⡀⠀⣠⡅
⠀⠀⠀⠀⢸⣛⣛⣛⣛⡃⠀⠀⢘⣛⣛⣛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣀⡈⠛⠇⠀⠀⠸⠛⢁⣀⡻⠇
⠀⠀⠀⠀⢸⣭⣭⣭⣭⡅⠀⠀⢨⣭⣭⣭⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⣠⡄⠀⠀⢠⣄⠿⣿⠇
⠀⠀⠀⠀⢸⠤⠴⠶⠶⡇⠀⠀⢰⠶⠶⠦⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠻⡇⠀⠀⢸⠟⢀⣤⣄⡀
⠀⠀⠀⢀⣄⠀⠀⢠⣾⣷⠀⠀⣾⣷⡄⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⠿⢡⣾⣷⠀⠀⣾⣷⡌⠿⠟⢁
⠀⠀⢀⣮⡙⢷⡄⢺⣿⡿⠀⠀⢿⣿⡇⣠⡾⢋⣵⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⢸⣿⡿⠀⠀⢿⣿⡇⠀⠀⢿⣷⡀
⠀⣠⠻⣌⠻⣦⣙⠖⠋⠀⠀⠀⠀⠙⠶⢋⣴⢟⣵⢟⣄⠀⠀⠀⠀⠀⡀⣠⣄⡀⢾⣿⠖⠋⠀⠀⠀⠀⠙⠺⣿⡷⢀⣤⣄
⣴⣍⢳⣌⢳⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡞⣡⠞⣩⣆⠀⠀⠀⣴⣄⠻⠿⠃⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠘⠿⠟⣠⣆
⠻⣿⣷⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣾⣿⠟⠀⠀⠀⠻⣿⣷⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣾⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠠⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣒⢒⠒⠒⠒⠒⢒⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣑⣒⠒⠒⠒⠀⠤⠤⠤⠤⢤⠍⣉⣉⣉⣉⡉⠛⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠍⣉⣉⣉⣀⡒⠒⠒⠒⠒⠶⠦⠤⠤⠬⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⠒⠒⠒⠒⠀⠤⠤⠤⠤⢉⣉⣉⣉⣉⣁⣐⠒⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠭⠉⣉⣉⣉⣑⡒⠒⠒⠒⠠⠤⠤⠤⠤⠬⠍⢉⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠂⠀⠤⠤⢄⣉⣉⣉⣉⣀⣒⡒⠒⠒⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢍⣉⣉⣉⣉⣉⣉⣉⣀⣈⣉⣉⣉⣉⣉⣁⣀⣀⣀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠉⠉⠉⠉⠉⢉⣽⠿⠛⠛⠋⠉⠉⣉⣉⣉⣉⣉⠉⠉⠉⠛⠛⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡿⢶⣦⠀⠀⣀⣀⣀⣸⣿⣦⣀⣀⣀⡀⠀⠙⠛⠛⠛⠛⠀⠀⣀⣀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠉⠉⣉⣹⣿⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⢸⡇⠀⢠⡾⠟⠛⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣷⣦⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠛⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠸⠇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⣠⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠉⢁⣤⣤⣤⣤⠉⠉⠻⣷⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠉⠉⣉⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣦⣤⣈⣉⣉⣉⣉⣠⣤⣶⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠛⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠉⠉⠉⠙⠉⠉⠉⠁⣾⠇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⢶⠶⠶⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣟⠉⠉⠉⠉⠉⠙⣿⣄⡀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠶⠆⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⡄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣄⣀⣀⣀⣀⣀⣀⣤⣶⠟⠀⠈⠻⠷⠶⠾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠉



⣿⣿⠿⠿⡿⢻⠿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⣀⣴⣾⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢻⡶⠞⢋⣏⡟⣷⠀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠤⣀⡀⠀⡜⣼⡁⢻⡿⣿⢻⠋⣿⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡿⠶⠤⠄⢠⣱⠯⢅⣀⣸⣳⠏⠀⣿⡴⣶⡿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣁⣘⠒⢶⣿⡏⠐⠢⣼⣳⠃⣄⠀⢄⣰⢋⡴⢹⣿⠀⢀⣠⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠦⠈⠉⣟⣯⡉⠓⡾⣱⠛⠂⠈⢱⡞⢡⠾⠀⠸⢿⣿⡿⣫⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⡏⠉⣙⡾⡸⠦⢄⡼⡱⡁⠈⠓⡴⢋⣴⠃⠐⢤⣠⡾⣫⠞⠉⣿⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣼⡀⠒⣼⢳⠃⢦⡞⡼⢁⡈⢳⠞⣠⠞⠉⠳⣤⡴⢋⠜⢁⡀⠈⢉⡽⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠛⠛⠁⣿⣠⠞⣼⠁⢀⡼⢃⡴⢇⠐⢦⣴⢟⠔⢋⠳⣌⣿⣾⣫⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣰⠋⢳⢄⡤⣄⠀⠘⢧⣴⠏⣰⠟⠛⢂⡴⢛⡵⠃⠐⢆⣽⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡏⢀⣎⠞⣰⢃⡴⢦⡀⠀⠸⣯⣀⡴⢋⡴⢋⣀⣳⣴⣫⠟⠋
⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⠁⡞⡞⡰⢣⠎⢀⠞⣡⠞⣲⠀⠁⠰⣿⣤⡴⢛⡵⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣃⡀⠈⠛⠸⡾⢡⠏⡴⢋⡔⣡⢞⡥⠚⣳⡄⠀⣡⠶⠋
⠀⠀⠀⠀⠀⢀⡞⠉⠙⠳⢦⣄⠀⠛⠞⣱⣫⢞⡵⢋⣴⠞⢋⡤⠞⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠈⠙⠲⣄⡈⠡⣿⠶⠋⣡⡶⠋
⠀⠀⠀⠀⣰⠆⠀⠀⠉⠳⢤⣀⠀⠀⠀⠙⠲⣤⣴⠞⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⣸⠇
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠐⠃⣰⠞⣿⠟⠃
⠀⠀⠀⠀⠈⢷⣄⠀⠀⠠⢞⣴⠞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠤⠿⠵⠚⠁

⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣿⣟⣿⣻⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠧⡀⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡙⠳⠶⠤⠤⢧
⠀⠀⠀⠀⠀⠀⣀⠤⠐⢒⢖⠤⡀⠀⠀⠀⠀⢀⠴⢏⡑⠚⠥⠖⠶⠶⠶⡇
⠀⠀⠀⠀⠀⠊⠀⢀⢔⠗⠁⠀⠈⣆⠀⠀⠀⡎⠀⠎⠀⠹⠁⠒⠒⠒⢲⠓⠄
⠀⠀⠀⠀⠀⢆⣨⣿⡁⣀⡠⢔⡪⠝⡄⠀⠀⠈⠒⠤⠄⣅⣀⣀⡇⠀⢸⠀⡇⠀⡌⢰⠂⡦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠣⡀⣹⠒⠈⠁⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⡷⠼⣀⠃⡜⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⣤⣤⣤⣔⣾⠋⢳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡠⢄⣈⣉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡄⢠⠃⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⢄⡉⣈⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠒⠒⠐⠴⣟⠁⡠⢎⠂⠀⠀⠀⠀⠀⠀⣀⣀⢤⣴⢷⣤⢉⡙⢙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡀⠀⣀⣀⡏⠉⠒⠀⠀⠀⠀⠀⡐⠉⢃⠈⡼⡀⠏⡆⠈⣁⠲⢽
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⣀⡃⠀⠀⠀⠀⠀⠀⠀⠘⠦⣸⡀⣸⣁⣸⡇⡎⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠈⠅⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠊

⣿⡟⠛⣿⡀⠻⠏⠀⢘⠃⢨⣟⠁⠀⣿⣿⠃⠀⠻⠟⣅⠸⠿⡀⠀⠹⠿⠛⣁⣴⣿⡼⠇⠀⣼⡏⢡⡟⢹⠏⠀⣾⣁⣿⠋⢠⣿⣿⠟⠁⠁⠀⠀⠈⣁⣴⠀⠀⡀
⠀⠀⡄⣸⠇⠀⣿⣷⡾⢃⡼⠋⢠⣶⠈⢡⣤⢠⡄⠀⢹⣷⡿⠗⠀⠀⠀⣾⣿⠉⡿⠄⠆⠀⠸⠿⡀⠀⠀⠀⠀⠀⢀⡤⣀⡾⠏⠁⠀⠀⠀⠚⠀⠶⠟⠁⢀⣰⡇
⡇⠀⢰⣿⡀⠀⠈⣉⠀⣼⠃⠤⠛⢁⡐⠟⠁⠈⠁⣀⠀⠀⣠⡶⠶⠂⠀⣾⣿⡀⠀⠀⢾⡗⣠⡾⣋⡄⢠⡇⠀⠐⠉⠀⠉⠀⠀⣠⡶⠀⠀⠖⠀⠀⢀⣰⣿⠛⡇
⠁⠀⠾⠻⠃⢴⠄⡌⢀⡍⢠⡄⢠⡿⠁⠀⠀⠀⢈⣿⠀⠀⠋⣠⣶⠀⣠⡤⢉⡁⠀⠀⠘⠋⣡⡾⢩⠇⠈⠛⠀⠀⠀⠀⢀⣴⠞⢋⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠁
⠀⢀⣴⠀⠀⠀⠈⠳⠟⠁⣬⡀⠀⡶⢀⡀⠀⣀⠿⠏⢀⣶⡾⠋⣴⠿⠋⣡⡿⣡⣶⣾⡗⠸⠃⠒⡀⢚⡷⠀⠀⣈⣤⡄⣘⡥⠚⠋⠀⣠⡶⠃⢉⡄⢀⣤⠆
⣠⡟⣡⣦⣶⣴⣶⢀⡴⡦⢈⠁⢾⡀⣈⢁⣼⡟⠀⣀⠛⠁⢠⡦⠀⠀⠐⣋⠾⠋⠿⠋⠀⠀⠀⢠⡄⢛⡴⢻⡟⠁⣼⠀⢛⡷⠀⣠⡞⠁⣠⡶⣻⡿⢛⠁⠀⣰⠈
⠋⠀⠛⠉⠟⣡⢙⡈⠀⢠⡿⠃⠿⠃⠿⢀⣭⢀⡘⠋⠴⠖⠀⠠⠞⠃⠚⠁⠈⠀⠀⢀⣤⠄⣘⠿⠃⢸⡷⠀⠍⣈⣅⠀⠛⠃⠈⠈⠁⠰⠿⠟⠉⠀⠁⠀⠀⠉⠁
⡇⠀⠀⠤⠾⠃⠛⠁⠶⢂⣴⠟⠘⠃⣴⣼⠏⣾⣅⡀⢠⡶⣿⠖⠃⠀⠀⠀⠀⠀⠰⠛⠁⠀⠁⠀⠀⢀⣀⣠⡜⠋⢡⣠⢂⡴⠶⣢⢆⡀⠀⢀⠘⠳⠃⠀⢰⠘⠇
⠃⣠⡶⢣⡾⠀⣠⡾⣢⡈⠁⠀⣰⡿⠛⣻⣆⠈⠻⠇⢀⣤⣤⠄⣀⣠⡄⢠⣤⢀⣀⡀⠀⠀⠀⢠⡿⣋⣙⠁⠀⠶⠈⠵⢊⣴⢞⡱⠋⠚⠃⠀⠀⢐⡇⠀⢸⡇
⠘⣿⠀⠈⣡⠘⢋⡠⡍⢠⡶⢛⡉⣁⢀⣿⡿⠀⠚⢃⣈⠙⢃⣀⢛⡄⠀⠘⠿⢛⣡⣤⣴⠆⠚⠫⠀⠉⠀⢀⡀⣠⣤⠀⠀⠛⠋⣁⣼⡿⠇⣾⡇⠈⡇⢠⣸⡇⡇
⠘⠛⣴⣾⠋⣰⡟⠁⢀⣿⠷⠟⢹⠏⣤⠿⠛⢃⡤⠞⣉⠐⠛⠁⠀⢠⣶⠀⠀⠙⠛⠿⠿⠂⠀⠀⢀⣀⠠⣻⠅⢱⠏⣴⠗⣺⡟⠉⢀⣤⡄⣿⡇⠀⣿⠘⢋⡇⢁
⣄⡀⠀⠁⠀⣿⣶⠀⠈⢉⡀⠤⠖⢺⣶⡆⠠⠟⣰⣿⢋⡀⡀⢠⣤⠿⠃⣴⠿⠃⣰⣿⡇⣠⡄⠀⠀⡴⠾⣱⡷⠀⠸⣯⡄⠉⣸⡁⠟⢉⡅⠉⠁⠀⢿⠀⣸⣧
⢙⣿⠟⠀⠀⠈⣴⠶⠖⡻⠷⣀⣠⣤⡄⠀⠳⣤⣿⣩⠽⠛⠳⠟⠁⠴⠢⢖⣀⣰⠟⣁⡠⢞⣻⡴⠀⠀⠰⠋⠴⠀⠀⠹⠷⠆⠉⣤⠸⠋⠗⣶⡄⠀⣾⠀⠙⣿
⠋⣡⣾⣿⡇⢶⣇⠺⢢⣶⢈⣭⡴⠟⣡⠞⠻⡿⢫⡴⠺⣻⠿⠣⣿⣤⠀⢙⣙⠃⠰⢯⠶⣋⣾⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⣀⠁⠀⠀⣠⣿⡇⠀⢸⡇⠀⣿⡀
⣤⠍⠉⢉⣶⠟⢡⠀⣂⡿⠛⢩⠌⠵⢿⣴⠟⣵⡟⢡⠾⢻⣿⠆⠀⠻⠟⣋⣡⡄⠀⠠⢊⣍⠦⠀⠾⠶⣻⣴⣆⣠⡬⢄⠉⠁⢉⠀⠠⢔⣿⢸⣿⠀⢸⡇⢰⠻⡇
⢻⡶⠀⠘⢛⡓⢚⣫⡵⠶⣤⣤⣤⣤⡄⠀⠘⣻⡥⠶⠾⣯⠷⣫⣴⢶⢈⡉⠹⠃⠚⠀⠈⠋⣰⠆⣠⡴⢤⣤⠈⠴⠟⠋⠴⠓⠀⠀⠀⠿⠟⠀⠀⠀⠈⠁
⢋⡴⠟⣉⠟⣡⣿⡁⣫⡜⣋⠰⣿⣿⡾⢠⡾⠑⠃⠀⠀⠀⠈⠁⣸⠖⡩⠀⠀⠀⠀⢀⣴⠎⠥⠤⢧⣤⡾⢡⡆⠀⠀⠀⠀⢀⢀⡀⠀⣅⣀⠀⠀⠀⢠⣴⣆⣶
⠿⠶⣂⠐⠋⠰⠶⠟⢡⣾⣿⠆⠁⣿⣿⡋⠄⠀⠀⠀⣆⣤⣧⡴⠁⢺⠁⠀⠀⠀⣀⣼⠀⠿⢶⣦⡴⢞⣁⣀⠀⢴⣄⣀⣤⣽⡋⠀⠀⠛⣿⣴⡄⣦⠘⣿⣏⠉
⡃⢹⡟⠀⣧⠶⠀⢰⣼⣏⣿⢸⠀⣿⣿⡅⠀⠀⠀⠀⠿⣿⢺⡯⠀⠉⠀⠀⠀⡎⢽⣿⣧⠄⣤⣤⠘⢉⠹⢻⡤⣤⠀⠸⣧⢸⡇⠀⢸⠀⣿⣿⡇⣿⠀⣿⣿⡀
⡳⣼⠇⣴⣅⠂⢀⡘⢹⣿⣿⢸⡆⢸⣿⣇⣄⠀⠀⠀⢀⣤⠈⠀⠀⠀⠀⠀⢰⣟⠘⢋⡱⡋⠈⣶⠆⠀⠀⠀⠀⠁⠀⠘⢻⠸⡇⠀⢸⢰⢿⣿⡇⣿⠀⠙⠛
⠃⢠⣤⠓⡈⠂⢈⡇⢸⣏⣿⢸⡇⢸⣿⡏⣿⠀⠀⠀⢸⣿⣠⣿⡄⣤⢠⡦⢸⣿⡾⢯⣤⣿⡂⡅⠈⡇⣬⢀⡀⠀⠀⣤⢠⡤⡆⠀⢸⡎⢸⡟⠇⡿
⡲⣌⠇⠙⣈⠂⠸⡟⠾⣿⣿⢸⡇⠈⢿⣧⣿⠰⡇⡄⢸⣿⣿⣿⡇⣿⣼⣧⠈⣟⣇⠀⠠⡿⡇⠇⠀⡇⢻⠸⡇⠀⠀⣿⠸⡇⣇⠀⠸⡇⠘⡇⠀⣾⠀⠀⣄⣇⡀
⢠⡿⠀⣧⠟⠃⠀⡇⠀⡟⠛⢸⡇⠀⢸⣿⣿⠀⡇⠿⢸⣿⢿⣿⡇⣿⢿⡿⠀⡇⣿⣰⣦⡇⡷⢹⠀⡇⢸⠀⠀⡇⢰⣻⡄⣇⣿⠀⠀⡇⠀⠁⠀⠘⠀⠀⣿⣿⠏
⣘⣃⣴⣦⡳⡄⠀⡇⠀⡇⠀⢸⡇⠀⢸⣿⣿⠀⡇⠀⠈⣥⢈⡀⠀⠈⠈⠁⠀⡏⣿⣿⢸⣧⣿⢸⠀⠃⠘⠀⠀⣿⢸⢹⡇⣿⢸⣠⠀⠁⠀⠀⠀⢰⡆⣤⡈⠁
⢭⡽⡏⢣⣵⠀⠀⣿⠀⠀⠀⢸⡇⠀⠘⣿⣿⠀⡇⢲⠀⣿⢹⡇⣤⢰⡀⠀⠀⠀⣿⣿⢸⣿⣿⣏⠀⠀⠀⠀⠀⠁⠈⢸⡇⣿⢸⣼⠀⢰⠀⠀⢀⣾⠁⢻⡇⣴⡆
⠲⡶⡚⢷⢸⢠⠀⠁⠀⠀⠀⠈⡇⠀⠀⣿⣿⣆⡇⣿⠀⣿⠘⠃⠁⢸⡄⠀⠀⠀⡿⣿⢸⣿⣿⣿⠀⣶⢠⠀⠀⣄⠀⠀⠀⢹⢸⢹⠐⠾⠃⣿⡆⠁⠀⠸⠇⢹⡇
⠶⠶⡟⢸⢸⢸⠀⢸⠀⡆⠀⠀⡇⠀⠀⢸⢹⣿⡇⣿⠀⣿⠂⠀⢀⢸⡇⠀⠀⠀⣿⢻⢸⣿⣿⣿⠀⣿⢸⠀⠀⣥⠀⠀⠀⢸⢸⡼⠀⡆⠀⠈⠁⡿⠀⠷⠀⢻⡇
⠑⠾⠇⢸⢸⢸⠀⢸⠀⣷⡆⠀⡇⠀⠀⠈⢸⣿⡇⢻⠀⢿⡆⠄⣶⠘⠃⠀⠀⠀⣿⢹⢸⡟⠃⠀⠀⢹⢸⠀⠀⠁⠀⠀⠀⠈⠉⠀⢤⡀⠀⠀⠀⣤⠀⢴⠀⣉⠁
⠀⠁⠀⢸⢸⢸⡇⢸⡆⣿⡇⠀⡇⠀⠀⠀⠘⣿⠀⢸⠈⢸⡇⠀⣿⠀⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⢸⠘⡀⠀⣤⠀⠀⠀⠠⠀⢴⠘⠋⢰⡆⠉⢻⠀⠈⠀⠉
⠂⠀⠀⠘⠘⢸⡇⢸⡇⣿⣧⠀⠀⠀⡆⠀⠀⣿⡇⢸⡆⢸⡇⠀⠈⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣼⠁⢸⡇⠁⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠛⠻⠂⢠⣄⠀⠀⢠⡤

⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠛⠃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢤⠀⢠⣀⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠢⡤⠄⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡴⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠈⢱⡆⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠖⢶⡧⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣐⣠⠌⠸⡀⠀⠀⠀⠀⠀⠀⠐⣤⣰⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠿⠿⢿⣿⣿⣷⡤⢄⣀⣀⠀⠀⠀⠱⣴⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠐⠀⠀⠈⠀⠀⠀⠀⠀⠈⠛⠻⠆⢀⠈⢻⡆⠀⠀⠀⣿⡉⠭⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠



⠀⢀
⠀⢸⠀⠀⠀⠀⠀⠀⣴⣦⣤⣄⣀⣠⣤⣤⣤⣶⣦⣄⡀⠀⠀⠀⠀⣀
⠀⢸⡆⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣷⣶⣤⣤⠅
⠀⢸⡇⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⣿⣿⡿⢿⣿⣴⣿⣿⣿⣿⠿⠁⠀⠀⠀⣠⣠⠀⡄⡄⢸⢃⡄⡄⣤⣠
⠀⢸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠃⠋⠀⠳⠃⠉⠈⠈⠁⠋⠉
⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠁⠈⠉⠛⠛⠀⠛⢿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠖⠁⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠈⠆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⠤⢤⡤⢤⢤⣤⣤⡤⡤⡼⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢻⡄⠀⢀⣠⣤⣤⣄⣰⡇⠈⠙⠳⢦⣄⣀⠀⠈⠉⠛⠶⣤⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣾⡷⠞⠋⠁⠀⠀⠈⢹⡷⢦⣄⣀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠉⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⢀⣤⠆⣼⣁⠀⠈⠉⠛⠶⣤⣀⠀⠀⠉⠛⠳⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⣿⠙⠛⠶⣤⣀⡀⠀⠉⠛⣳⣦⡴⠞⠋⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⠞⠿⣄⠀⠀⣿⣤⣀⠀⠀⢉⣻⣷⠶⠛⠉⠀⠀⣀⣤⡴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⣴⠞⢿⣄⠀⠈⠓⢸⡇⣀⣭⡿⠟⠋⠁⠀⢀⣠⣤⠶⠛⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠁⠀⠀⠀⣴⠞⢿⣄⠀⠙⢷⣄⠀⢸⡟⠉⠀⠀⣀⣤⡴⠞⠋⠁⠀⢀⣠⣤⠶⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢷⣄⠀⠙⢷⣄⠀⠙⠃⣾⣁⣤⠶⠛⠉⠁⠀⣀⣠⡴⠞⠋⠉⠀⢀⣠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⢷⣄⠀⠙⢷⣄⠀⠙⢷⣄⠀⣿⠉⠀⢀⣀⣤⠶⠛⠉⠁⠀⣀⣠⣴⣞⡋⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠙⢷⣄⠀⠙⢷⣄⠀⡁⠀⣿⡴⠞⠛⠉⠀⢀⣀⣤⠶⣿⣉⡁⠀⠉⠙⠳⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⡶⠀⠀⠀⠀⠙⢷⣄⠀⣹⠏⠁⢸⡇⠀⢀⣠⡴⠾⠿⣯⣀⡀⠀⠉⠙⠳⢦⣄⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⣇⠀⠀⠀⠀⠀⢠⡟⠛⠉⠀⠀⢸⡷⠟⠛⠷⣤⣀⡀⠀⠉⠛⠳⢦⣄⡀⠀⠈⠙⠛⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠈⠃⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⣼⠷⣤⣀⡀⠀⠉⠛⠳⢦⣄⣀⠀⠈⠙⠛⠶⣤⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠙⠳⢦⣄⡀⠀⠈⠙⠛⠶⣤⣀⠀⠀⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣶⠶⠶⠶⠿⠿⠻⠶⠶⠶⠶⠾⠿⢻⡷⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡾⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢄⠃⡄⠄⣣⠄⡄⡄⡄⠀⣯⠉⢠⠰⠠⣠⠤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠜⠀⠉⠓⠁⠁⠁⠀⠁⠀⠈⠈⠊⠈⠚⠈

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⣹⣯⡳⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⢀⣟⣵⣽⣶⠟
⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢴⣚⡉⢧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠹⢽⠀⠀⠀⠀⠀⠀⠀⠀⢰⣺⡍⢱
⠀⠀⠀⠀⠀⠀⠀⠈⣟⡃⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⢛⢣⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣟⡃⢴⡎⡆⠀⠀⠀⠀⠀⠀⠀⡼⢂⠒⣘⢣⠀⠀⠀⠀⠀⠀⠀⡍⠄⠉⢀⢣
⠀⠀⠀⠀⠀⠀⢀⡼⠙⣋⠤⠒⠁⠀⠀⠀⠀⠀⢀⡰⠱⢎⡶⠓⠃⠀⠀⠀⠀⠀⢀⡴⠑⢃⡤⠒⠁
⠀⠀⠀⠀⠀⠪⣥⡤⠝⠁⠀⠀⠀⠀⠀⠀⠀⠰⢍⣤⠵⠋⠀⠀⠀⠀⠀⠀⠀⠰⢅⣂⠼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⡠⣇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠓⢖⠁⠀⠈⢦⠀⠀⠀⠀⠀⠀⠛⢟⠁⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⣴⣅⠀⠀⡠⠟⠁
⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠗⠊

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⠀⢾⣿⣿⣿⣿⣏⣉⣉⣉⣹⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣧⣤⣤⣄⢠⣦⣤⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣤⣴⡄⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣥⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣟⣛⣛⡋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣛⡋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡿⠿⠿⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣷⣶⠶⠖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣶⡦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣉⣥⣤⣤⣤⣤⣄⡀⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣧⣤⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⠿⣿⣤⣤⣤⣼⡿⠿⠃⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣥⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣷⣶⣤⣤⣤⣤⣤⣤⡶⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣟⣉⣉⡉⢸⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⡛⠋⢸⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠛⠛⠛⠛⠋⢸⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠶⠦⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠛⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣷⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⡿⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢀⡼⠃⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⡴⢯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡤⠶⠚⢉⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡇
⠀⢠⠟⠀⠀⠈⠙⠳⢤⡀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⡇
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣠⠞⠁⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢠⡇
⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠁⢀⡴⢾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣠⠞
⠀⠈⠛⠦⢤⣤⣤⣤⠴⠖⠋⠁⠀⣰⠏⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⡥⠤⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⠀⠀⠀⠀⠀⢀⣠⡼⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣶⣶⣶⣶⣶⣶⣤⠀⢀⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡄
⠛⠛⠛⠛⠛⠻⣿⣿⡇⣸⣿⡟⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡅⠀⢈⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣿⠃⠀⣿⣿⡇⠀⠀⢀⣀⣄⠀⠀⣠⣤⡄⠀⢹⣿⣷⠀⣾⣿⡟⠀⠀⢀⣤⣤⣤⣤⡀⠀⢀⣠⣤⣤⡀⣠⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⣿⣿⠛⠛⣿⣿⣾⣿⣿⣿⣿⣿⣿⠟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣸⣿⣿⠀⠀⣸⣿⡟⠀⠀⢀⣿⣿⣿⡄⠀⠀⣠⣿⣿⠀⠀⣿⣿⡏⠁⠀⣿⣿⡏⠁⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣶⣶⣿⣿⠿⣿⣿⣷⣿⣿⣿⣿⣶⣴⣿⣿⠃⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠙⠛⠛⠛⠛⠉⠙⠛⠛⠋⢹⣿⣿⠛⠛⠋⠁⠀⠈⠙⠛⠋⠁⠈⠛⠛⠛⠋⠁⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⠀⠁⠉⠈⡏⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⣀⣃⣤⣀⣅⣀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠠⠋⢹⠁⢙⠉⡉⢻⠀⠀⠀⣀⣠⢤⡖⠚⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡁⠈⡄⢸⠀⠂⡏⢰⡶⠉⠇⠈⠀⠁⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠠⠂⠀⡇⢰⠀⢰⡇⠈⢧⠑⠈⢄⠠⠀⠠⠈⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡔⠀⠀⡇⢸⠀⢹⡇⠀⠘⡆⢂⣈⣠⡷⠴⠟⢫⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠂⠀⡜⠀⠘⢠⢸⡇⠀⠀⢻⡏⢹⠁⢣⠀⠠⠈⠂⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡄⠀⢐⠁⠀⡄⠀⣾⠀⠀⠀⠘⣷⠀⢁⠀⠱⡀⢡⠈⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢰⠁⠀⡎⠀⡐⠁⠀⢹⠀⠀⠀⠀⢹⡆⠈⠆⠀⢣⠈⠃⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⡰⠁⠀⡜⠁⡔⠁⠀⡼⢻⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⡇⠘⡄⢆⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠜⠁⢀⠔⠁⡠⠀⠀⣼⠁⡾⠀⠀⠀⠀⠀⢹⡆⢨⠂⠀⡇⠀⠰⠀⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢁⡔⠃⢀⠔⠊⢀⠔⠁⠀⢰⣇⣼⠃⠀⠀⠀⠀⠀⠈⣇⠀⠆⠀⢰⠀⢈⠀⠘⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢀⠔⠋⢀⠤⠊⠀⡠⠋⠀⡴⢊⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⢰⠀⠸⠀⠀⡏⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⢠⠄⠋⢀⠔⠃⢀⠴⠊⢀⡤⢚⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⢸⠀⢠⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢦⠊⠁⡠⠀⠂⡠⠀⢁⡀⠴⣫⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⠁⠀⡎⠀⡎⠀⠀⢻⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⣧⡀⠠⢐⡩⠤⢐⣡⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡎⠀⡰⠁⢠⠃⢀⠜⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⠶⠿⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡜⠀⢈⠀⠀⡄⠀⣸⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⡐⠁⢠⠃⠀⡜⠀⡘⢡⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠠⠃⢠⠋⠀⠊⢀⡴⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⡰⠃⢀⠊⢀⠎⣀⢋⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠲⣄⠐⢁⠔⣡⢎⣥⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣈⣳⣧⣾⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢩⠀⣠⣿⡗⢾⣧⣾⣷⡐⣤⣼⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⣿⠞⠁⢙⡿⢷⣿⣿⣿⡄⣰⣿⣦⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⠘⣿⠂⠀⠈⠉⢹⣎⣿⣧⣹⣿⢛⡸⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣶⣏⡀⠿⢿⡿⢿⡦⠀⠸⣿⣿⣿⢹⣿⣾⡟⡠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠛⠿⠀⢀⣸⣿⣦⡀⠀⢴⣾⣿⡄⢺⣿⠋⠄⢷⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣂⡧⣼⣀⠀⠉⠀⢿⣿⣦⣘⣯⡹⠃⠀⣿⡟⡠⢹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠃⣼⣴⡿⣸⡦⠀⡀⠀⠛⠛⠛⠋⠀⠀⣰⣿⣿⠻⠾⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⢏⠞⢋⣀⠉⠁⠒⠀⠘⠀⠀⠀⠴⠿⠏⠛⣇⡶⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⡀⣠⣾⡿⠀⠉⠀⠁⣀⠰⣿⠀⠀⠀⠀⣆⠀⡀⢂⣠⣙⣿⣱⠼⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⢿⣿⣿⣿⣿⣧⠶⠛⠢⣷⣘⠇⠛⠛⡤⠚⠿⣿⡿⠷⠖⠛⢻⣤⣿⣿⣻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠗⠸⣿⣿⣿⣿⣯⡆⠁⠀⠈⠉⠁⠀⠀⡿⠀⠘⠸⠷⠚⠋⠉⢧⣴⣌⢹⡟⢻⣭⣛
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣶⣔⠾⠿⠛⠁⠛⠃⡀⠤⠆⠀⣂⠤⢸⣿⠀⠂⠀⠀⠀⠀⠀⠀⣌⣿⣽⣿⣟⢿⡇
⠀⠀⠀⠀⠀⠀⣠⣿⣿⡯⠄⣽⠿⢻⣿⢦⠿⠃⠀⢂⣁⡄⠀⠀⠈⠁⠞⠁⠀⠀⠀⣴⡖⢿⣷⣿⠙⢻⡟⢿⢻⢏⣻
⠀⠀⠀⠀⠀⠀⣶⣶⠆⢀⠶⣿⢿⠛⠛⠀⠀⠠⣄⠀⠋⠀⠀⣀⡀⢄⡀⠀⠀⠀⣿⣷⣶⣶⣟⣩⣀⣿⣷⡄⠀⣸⣿
⠀⠀⠀⠀⣀⣤⣦⣤⠄⢘⠠⠞⠂⠀⠀⡆⠠⠺⡿⠀⢀⣦⣼⣿⣷⣿⣿⣶⣼⢿⣿⣿⡏⠘⠟⡏⢹⣿⣿⡿⣤⣿⣿
⠀⠀⢀⡀⠠⣫⡏⠈⠀⡠⠤⠄⠐⠠⠐⢀⠃⠀⠀⣀⡀⢴⠏⠙⠟⠋⠀⠹⠿⠽⠟⣡⣮⣤⡞⣃⣾⠘⠉⠁⣬⡈⠙
⠀⠀⢠⢁⡰⠀⠐⢂⡤⣀⣲⠞⠰⠆⠦⢿⠠⡃⣉⠁⠂⢈⠀⠀⠀⠀⠀⢐⡀⢿⣿⣿⣯⣽⣽⣿⣿⣦⣤⢸⣿⣿⣆
⠀⣛⡆⠁⠀⠀⠦⠄⠐⣸⠃⠐⠀⢀⡄⠅⣂⠛⠀⣉⡩⣼⣦⡈⠛⠃⠈⠉⣀⢐⡿⡟⣿⣿⢻⣿⣿⣿⣿⣿⣷⣼⣿
⢦⣌⢧⣴⢸⡡⢍⠀⠂⢁⠒⣈⠀⢀⣤⡞⣷⠀⣠⣶⣿⣿⣿⣷⡄⠀⠛⠛⣛⡮⣓⣿⡿⢡⠌⣿⣿⣿⣿⣿⣿⠿⣿
⢿⣿⣟⣿⣥⣿⣿⣓⣠⡄⣈⡔⡭⣅⣠⣭⣭⣸⣿⣿⣿⣿⣟⣿⠀⠀⣷⠚⢁⣤⣿⡭⣧⣀⣶⣾⣿⣿⣿⣿⣯⠀⣿
⠀⠳⢿⣿⣿⣿⣿⠿⠿⣦⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⠠⢡⠉⠴⠆⠿⡿⣁⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸
⠀⠀⠀⠉⠛⠛⠿⠿⣿⠟⠛⢿⠿⢻⣿⣿⣿⣿⣿⠛⠋⠸⢿⣿⡄⢀⡄⠀⠠⣦⢐⡏⢐⣻⡿⢻⣿⣿⣿⣿⣧⣠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠉⠙⠛⠀⠀⣄⠹⣷⣾⣳⠶⢶⣿⣶⣾⠿⠿⠾⠿⣿⣿⣿⡿⢿⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⣴⣿⠀⠈⢿⣿⡾⣿⣿⣟⡁⣰⣶⣶⣶⣿⣿⣿⣷⡈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣽⡁⣺⠷⣯⠀⠉⡁⠄⠀⠘⣹⢇⣿⢙⣋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡶⠀⠉⢰⣟⣇⢀⠀⠀⠀⠳⣽⢾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡀⠐⠡⡀⢽⣿⣿⣿⣶⡄⢿⡸⣧⣐⠀⡈⠻⢿⣿⣿⣿⠿⢟⣿⣿⣧⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣇⠀⠁⢀⣤⣿⡹⣿⣿⣷⡈⢻⣿⣿⣧⡀⠠⢀⡈⠙⠻⣤⣾⣿⣿⣿⠋⣼