Player character Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢰⣶⣿⣿⣆⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡳⣽⢿⡟⣻⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣾⢹⡟⠻⠹⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⠚⢃⡀⡼⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣼⠗⣹⠝⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⡋⡀⠃⠀⠀⣸⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠰⠀⠙⠛⠃⢴⣞⣹⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⢟⣆⠀⢀⡀⠀⠨⠛⠷⣾⣭⡕⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡏⠀⠀⠙⢳⣌⣵⣶⣶⠀⠀⠞⠃
⠀⠀⠀⠒⠀⠀⠀⠠⠀⠀⠶⠂⠀⠀⢀⡤⠜⠃⠐⠀⠀⠈⠀⢻⣿⣿⠋⣀
⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⡌⠓⠀⠀⠀⢀⠙⠓⠀⠀⠙⢿⡌⣧⡀
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣀⢍⠈⠆⠑⠲⠀⢀⠒⠀⠀⠀⢀⠁⠘⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⣬⣓⠈⠀⠀⠀⠈⠙⢘⣷⣤⣀⠀⠀⠳⢶⣶⡆⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠋⠀⠉⠓⢠⣤⣶⣆⣤⣈⠛⠁⠈⠀⠀⠀⣠⡇⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠛⢷⣦⡙⠻⢿⢻⣿⣦⠒⣠⣦⣿⣦⣬⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⣁⣢⣹⡿⠗⡸⠀⢙⣿⣷⢿⠿⠟⠓⣛⣻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣏⣿⣿⡿⠀⠁⣄⣸⠿⣿⠷⠶⠾⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣧⠟⠿⣿⠣⠀⢀⣏⢿⡄⠙⠢⠉⠀⠶⠨⣽⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠐⡟⢀⠔⢋⡿⠇⠙⠀⢠⡛⠃⣙⣟⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠆⣺⡛⠀⣰⠏⣰⢂⡥⠾⡭⠿⡇⢈⣉⠙⠻⣿⣿⣷⣶⠶⠤⣤⠐⠛⠂⡄
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢿⡜⢻⡇⡼⣶⣾⡥⠿⢀⠀⠛⡀⢻⠷⢮⡱⢺⣿⣿⣿⡇⠶⡒⢿⡿⠀⣶⣬⢣⠀⡄⠤⣄
⠀⠀⠀⠀⠀⠀⣝⠀⣀⠀⠀⠀⣸⡐⠻⣿⣛⠋⠀⠀⠀⠀⠀⠠⡀⠀⢷⡆⠉⠀⢯⣽⣧⠁⠀⠉⠁⠀⠀⠀⠁⠀⠀⠉⠀⠛⠢⠟⠮⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⣤⣔⣿⠋⠀⠀⠀⠀⠀⠀⠘⠀⠀⠧⡿⣦⠀⠀⠈⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣋⢹⡇⠀⠀⠀⠀⠀⠀⣾⠀⠀⢤⡿⠋⢦⠀⠀⠀⠀⠀⠀⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡌⠻⢿⠁⠀⠀⠀⡠⠀⠠⣿⡀⠀⠈⡇⡀⠙⣣⣀⠀⠀⠐⠂⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣠⡀⠀⠀⠀⣀⠙⠛⠀⠀⠄⢠⢺⣿⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢻⣿⣆⠀⠀⣼⣷⡄⠀⢀⣸⣿⣼⣿⣿⣿⣷⣰⣆⠀⠀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⢺⣿⣷⣤⣿⣿⣿⣶⣿⣻⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢷⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣟⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⡄⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠁⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠃⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣼⣿⣧⣤⣴⣶⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠈⣹⡆⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⢉⣿⣿⣿⣿⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⢻⣿⣀⣤⡄⠸⣷⡄
⠀⠀⠀⢀⡀⠠⡶⠟⠉⠀⠀⠘⠃⠀⠀⠀⠀⠤⠶⣿⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣮⠉⢩⡀⠀⠈⠁
⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠀⠙⢿⣷⣿⣷⡆⢠⣽⡇⠀⠀⠀⠀⠀⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠈⣭⣿⣿⡛⠛⠳⣄
⠀⠀⠀⠀⠀⠤⣄⣠⣤⠟⢹⣿⣿⡿⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣿⣿⣷⡄⠀⠙⠃
⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣿⣿⣿⠇⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠶⠚⠋⠀⠘⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣧⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⣴⣿⡿⠿⣿⣧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠉⠀⠀⠙⠻⠿⠟⠃⠀⣿⡇
⠀⠀⠀⠀⢀⡄⠀⠛⠋⠀⢠⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣁⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⡄
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠟⠛⠀⠀⠀⣈⣛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢋⡤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⣿⣿⣟⣡⡟⠀⠀⣤⡄⠀⠀⢴⣦⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠃⠀⠀⠉⠁⠀⠀⠈⠁⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⣌⠂⠀⠀⢀⢀⣀⠀⠀⣠⡍⠘⠢⢉⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢈⠑⡚⠉⣍⣩⣤⡀⠀⠀⠀⠀⠤⠼⠛⠃⠸⠈⠀⠀⠀⠈⢃
⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠁⠀⠀⠀⠘⢠⣶⣿⣿⣿⣿⣿⣄⡀⣀⣴⣶⣾⣿⣿⡎⠣⠀⠀⠀⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡟⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠛⠛⡀⣿⣿⣿⣿⣾⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⠀⠀⣿⣿⣛⠛⠛⠛⠛⠛⠛⠋⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢿⡄⠀⠻⣿⣿⠂⣦⣶⣤⣤⣶⣶⡖⠈⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠘⠛⠚⠛⠛⠛⠛⠛⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣀⡀⣀⣀⢐⣀⣀⣀⣀⡀⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⣿⣿⣿⣿⡠⢸⣿⣿⣿⡇⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣴⡾⠈⣿⣿⣿⣯⣽⣿⣿⣭⣿⣿⣷⡏⠹⣿⣿⣷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠻⢿⣿⣶⣶⣤⣶⣶⣶⣿⣷⣶⣶⣦⣤⣶⣾⣿⡿⠿⠟⠋⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬
⡀⠀⠀⣈⢒⢃⣐⣒⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣒⣂⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣒⣀⡀⢀⣈⢀⡀⠀⠀⣘⣃⣀⣀⣀⣈⡁⠛⢁⣀
⡿⢿⠿⠿⠿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠉⠀⠀⣄⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠑⠂⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠄⠉⡅⠀⠀⠀⠀⠀⠠⠴⠀⠈⡄⠀⠀⠀⢀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⣀⡀⠀⠀⠡⣀⠀⠀⠀⣀⠀⠀⠀⢀⠆⠀⠀⢠⠁⢠⠠⠀⢡⠈
⠀⠀⠀⠀⠀⢀⠀⠣⡀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠁⣀⠀⢙⠂⠁
⠀⠀⢀⡆⠀⢈⠦⠔⠁⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⣀⡔⠒⠈⠀⠁⠁
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤
⠀⠀⠀⠀⠐⢠⢄⢠⠠⠄⠔⠀⠄⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢂
⠀⠀⠄⠀⠸⢀⣀⠀⡄⠀⠀⠀⠀⠀⢀⣀⢐⣂⣒⣈⣉⡉⠉⠉⠉⠉
⠀⠁⠂⠀⠀⠀⠀⠀⠑⠤⠤⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⣠⡄⠀⠀⠁⠀⡀⢀⠀⠀⠑⢄⠀⠀⠂⠀⠠⠈
⠀⠀⠐⢄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠀⣐⡀⠠⠀⠀⡁⠁⠀⡇
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠁⢀⢀⡤⠔⠈⣀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣂⣩⡤⠐⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⠳⣄
⠀⠀⠀⠀⠀⢼⣿⣿⣿⡇⠀⠀⡀⠀⠀⣴⣿⣿⣷⣦⡀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠘⠿⢿⣿⡄⠀⠀⠉⠀⠀⠿⣿⣿⣹⠋⠁⠀⠀⠙⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣮⢻⣿⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⢀⡈⣿⣿⢱⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟
⢰⠀⠀⠀⠀⣰⠟⠃⣾⣿⠀⠀⠀⠀⢠⣾⠛⠿⣦⡀⠀⠀⢘⡴⠋⠻⣆⠃⠀⠰⡶⠶⠶⣶⣿⣿⠶
⢸⠀⠀⣠⣾⡁⠀⠀⣽⣿⣆⠀⠀⣰⡿⠃⠀⠀⢸⡇⠀⠀⢸⠇⠀⠀⢻⡄⠀⠈⠃⠀⣸⡿⠛⠛⣿⡄
⠸⠀⠀⠀⠀⠀⠀⣀⣿⠁⠩⠇⢾⡇⠀⠀⠀⠀⠸⣷⣤⢤⣿⠀⠀⠀⢨⣧⢰⡟⠛⠛⠛⠀⠀⠀⠘⣷⣤
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠈⢉⠉⠉⠑⠃⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢠⣠⡀⠀⠀⠀⠀⠀⠀⢄⣀⣀⡤⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠈⠒⠂⣀⢀⡇⣦⡀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠈⠁⠀⠀⠀⠀⣀⡀⠀⢬⣴⡫⠀⡇⠈⠑⠒⠒⠒⠉
⠀⠀⠠⠀⠀⠀⠀⠁⠐⢀⠀⠢⠤⠔⠉⠑⠒⠒⠒⠚⠋⠉⠁⠀⠒⢄⠀⠀⠀⡇
⠀⠈⠁⠀⠀⠀⠁⡀⠠⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⠃
⠀⡀⠀⠀⠀⠀⠈⠀⠀⠈⠃⠀⡀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣀⢀⢼⡄
⠀⠐⣀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠡⠐⠣⠆⣀⣀⣀⣀⠠⢤⠔⠁⠀⠀⠀⠀⠀⡇⠢⢄
⠀⠀⠈⠀⠀⠤⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⢄⣀⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⡀⣀⣠⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠓⠂⠤⠬⢥⠀⠀⠀⠀⢀⠤⢀⣉⡁⠀⠀⠀⠖⠲⢴⡀⠀⠀⠀⠀⠀⠠⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠒⠈⠀⠀⠀⠀⢠⠀⠀⠀⣨⠀⠀⠉⠒⠤⠤⠠⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉⠩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠔⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠒⠀⠀⢀⣀⣌⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠲⠗⠚⠋⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⡀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠉⠋⠀⠁⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣤⠶⠶⠄⣼⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⡀⠀⠾⠋⠀⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡾⣿⣿⣷⣾⡿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠐⢤⠋⠻⠕⠠⠄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠳⠆⠀⡦⣀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣻⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠻⡿⣿⣿⣾⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠉⠻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀⠀⠀⣤⣶⡶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣁⣬⣽⣿⣿⣦⣾⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠁⠀⠈⡉⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⣶⣽⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡇⠀⠀⠀⠀⠀⢾⣿⣏⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⣀⣤⡶⣮⣡⠴⢾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣇⢸⣿⠰⡟⠀⠀⠘⠿⠛⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣷⣦⣀⢀⣤⣄⢈⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⣧⣴⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⡀⠸⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⠷⡀⢹⣿⣿⣿⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⠀⢖⣼⣿⡏⠙⠷⣑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⣿⣿⣆⠀⠀⠀⢀⠀⡀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣀⠿⠿⢿⣿⠀⠀⠀⢻⣿⣿⣦⣀⣴⣶⣼⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠇⠀⢘⣿⠀⠀⠀⢸⣿⣿⡿⠟⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠘⣶⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣶⣶⣶⣦⣤⡄⢠⣤⣤⣤⣽⣯⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠹⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣏⣠⣼⠿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠉⠉⠛⠋⠛⠛⠛⠙⠋⠙⠁










⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀
⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀
⠀⠀⢀⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄
⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠙⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇⢿⣿⣿⣶⠘⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣳⠟⣿⣹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣂⠿⡙⠉⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⣇⢁⣤⣼⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⠟⣴⠂⠙⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢬⣤⣀⠀⢀⡼⡿⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡁⠀⠉⠀⠘⠻⣼⣇⣀⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠉⠸⣤⡀⠤⣀⡀⠈⠉⢻⡟⠂⠁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⣯⠙⠀⠀⠀⠈⢿⣾⣿⣿⠃⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢾⡁⠀⠀⠀⠠⣤⠀⠀⠻⣿⠃⡄
⠀⠀⠀⠀⠐⡃⠀⠀⠀⠀⠀⠀⠀⠸⠄⢀⠠⣄⡀⠂⠀⠀⠀⠀⠈⠃⠘⣧⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠀⠰⠁⠃⠈⠀⠀⠡⠄⣦⡀⠀⠀⠀⢦⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⢶⡄⢀⣀⣤⠀⠀⢾⡟⠙⠂⠀⠀⠉⡿⠃⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣶⣶⣶⣤⡙⢿⣿⡿⣿⣦⢠⠀⣀⣠⣄⡚⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡖⠠⠙⣿⣶⠌⡇⠛⣿⣧⣼⣿⣷⠿⠿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣥⣶⠻⣿⣿⡆⠘⢁⠀⣿⣿⣞⣥⣴⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠟⣿⡿⠀⠀⢘⢻⣄⠘⠦⠐⠀⠠⠉⡻⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢰⠇⢀⠴⣻⣷⠙⠂⠠⠒⠆⠐⡶⣾⡿⣿⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡮⠀⣞⠂⢀⡔⢉⠄⢀⡰⢆⡵⣦⠈⣙⠙⠾⣿⣷⣶⣴⡤⠄⣤⠠⠿⢀⡀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠰⣇⠘⣽⢀⢯⣴⣋⣭⡅⡀⠸⣂⢹⡶⢯⡱⢶⣿⣿⣿⡏⢤⠴⢿⡶⠀⣦⣝⢢⠡⠠⢄⡀
⠀⠀⠀⠀⠀⢈⡛⢀⡀⠀⠀⠀⣯⠒⢿⣞⠛⠉⠀⠀⠀⠀⠀⡁⠀⢹⣆⠉⠀⢯⣿⣧⠁⠀⠙⠂⠀⠀⠀⠁⠀⠈⠑⠚⠓⠬⠷⢴
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⣧⣥⣺⡛⠃⠀⠀⠀⠀⠀⠀⠂⠀⠦⡹⣦⠀⠀⠈⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⡉⣻⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⡾⠋⢦⠀⠀⠀⠀⠀⠀⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠍⠿⡏⠀⠀⠀⣠⠄⠀⣼⢂⠀⠈⠇⠄⠘⢣⣠⡀⠀⠐⠂⠀⠐⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⣄⠀⠀⠀⢀⡨⠛⠀⠀⠠⢀⠘⣿⣿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠛⠿⣷⣀⠀⢴⣿⣦⠀⢈⣠⣿⣾⣿⣿⣿⣿⣴⣦⠀⠀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣐⣾⣿⣶⣾⣿⣿⣷⢿⣿⣿⣿⣿⡿⢿⣿⡏⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠷⢋⣯⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠋⠉⠉⠉⠑⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢀⠤⠴⠖⠒⠒⠒⠒⠒⠒⠲⠦⠤⣄⣀⡇⠀⠀⠀⠀⠀⠀⠄⠄⠄⠄⠀⠀⠀⠀⠀⠀⣇⣀⡤⠤⠶⠒⠒⠒⠒⠒⠒⠒⠶⠠⢄
⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣀⣠⠤⠴⠦⠤⠤⠤⠤⠶⠤⢤⣀⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⢸⣿⡇⠀⠀⠒⠀⠀⠀⠐⠂⠀⠀⣿⣿⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡇⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⡿⠓⢶⣤⣤⣤⣤⣤⣤⣤⣴⠖⠻⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⣠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⣼⣷⡀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣰⣿⣴⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡀
⢀⡾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⣇⠙⠶⠾⠷⠶⢶⡶⠶⠿⠶⠞⢁⡾⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣆
⡞⠀⠈⠑⠂⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠳⣶⣤⣴⠉⠉⠉⢱⣤⢴⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⠉⠀⠘
⢳⠀⠀⠀⠀⠀⠀⠉⢐⠆⠠⢀⡀⠀⢴⠛⠁⠀⠀⠀⠀⠀⠀⠈⠐⠠⠍⣹⣉⠥⠐⠈⠀⠀⠀⠀⠀⠀⠀⠙⢳⠄⠀⣀⠠⠀⢒⠈⠁⠀⠀⠀⠀⠀⢰
⡞⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⡤⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢀
⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠲⢄⡀⠀⠀⠀⠀⠀⣀⡤⠞⠁⣤⡄⠙⠦⣀⡀⠀⠀⠀⠀⢀⣀⠴⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⣀⣀⠈⠉⠉⠉⠉⠉⠀⠀⠀⣼⣿⣷⣅⠀⠀⠈⠉⠉⠉⠉⠉⢀⣀⣀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠓⢦⠀⠀⠀⠀⠀⠰⣿⣯⣾⡟⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣇⡀⠀⠀⠀⠈⠈⠉⠉⠀⠀⠀⠀⠀⣀⡧⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠉⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠠⠤⠀⠠⠤⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣤⣀⠀⠀⡱⠚⠁⠀⠀⠀⠀⢀⡟⠀⠘⣆⠀⠀⠀⠀⠈⠑⠲⡁⠀⢀⣠⣴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠉⠙⠓⠤⢄⡤⠤⠤⠴⠋⠀⠀⠀⠈⠳⠤⠤⠤⣠⠤⠔⠛⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⣯⠽⠻⠛⠲⠶⢶⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣶⠶⠶⠚⠻⠻⢭⡿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⣀⣁⣀⣀⣁⣀⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣃⣀⣀⣁⣀⣨⠇
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣿⠟⠛⠀⠀⠀⠀⠀⣠⣴⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⡄⢀⣀⡀⠀⠆⠀⣀⠉⠉⠛⣿⠿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⣀⠀⢰⠛⣾⣖⠥⠄⠀⠀⠹⠗⡄⣀⣀⣄⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠿⠤⠖⠊⢉⣡⠶⣁⢿⣭⡟⣿⣭⣭⠁⠄⠀⡀⠈⠉⠁⢀⠂⠒⣄⠲⣔⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣾⡿⢿⣾⣾⣿⣿⡽⣡⡞⠀⢟⠀⢤⣁⢀⢠⠘⠀⠀⠙⢘⡴⢋⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⢠⣟⣷⣦⣤⠠⣌⣿⡾⢷⡯⡞⣿⡉⣿⠀⠈⢰⠣⣌⡙⢿⠦⠀⠓⣴⠮⠄⠔⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢏⣟⣻⣿⣰⣿⡾⡲⢾⠎⠿⡿⠗⢂⣼⣷⠘⢦⡄⠁⠀⠘⣀⠔⠁⠀⠐⠂⣰⡾⠛⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡻⣯⡿⣟⣿⣟⡇⢼⣻⢁⠊⢸⣷⣚⡁⠘⢌⠁⢀⠿⣉⡷⡽⣯⡀⠀⢀⠘⣷⣉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣾⢸⣿⣾⣷⣏⣼⠟⣉⠔⠛⠃⣠⣤⣀⣈⠳⣬⠃⢡⢐⠦⣿⣧⣗⠀⢧⣾⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡯⢽⣙⡾⣾⣿⣭⣿⣣⡞⣁⣴⠊⠉⠀⠀⠀⠈⠻⣯⡀⣰⢚⢷⡾⢋⡨⣑⣾⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣫⠷⣧⢿⣼⢻⣿⣼⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⢻⡿⢟⠧⣀⡿⢛⣴⣼⠷⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣻⣿⣯⣹⣮⣝⣽⣞⢽⣿⠿⠋⠀⠄⠀⠀⠀⠀⠀⣸⠁⣆⢦⣉⣧⢭⣤⣏⡱⠊⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣿⣿⣿⡝⣿⣻⣭⠏⠃⠀⠀⠀⠀⠀⠀⠠⣴⡿⣧⡈⠳⡏⠙⣯⡠⠤⢰⣦⠔⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠛⠲⣾⡏⢾⣿⡆⠀⠀⠀⠀⠀⠀⢴⣾⠟⢀⡜⢡⣼⠸⢷⣾⠀⠆⠈⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⢠⠈⠉⡍⣿⡇⠀⠀⠀⠀⠀⠢⡀⠀⢀⣠⣾⣧⡹⣿⣳⢾⠿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠾⣝⠲⣧⣿⣇⠀⠀⠀⠀⢀⠈⠁⠀⠀⠉⣛⢿⣿⣷⡱⠁⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣆⡜⡉⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢻⣿⠟⡩⢛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣣⣸⣤⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⢠⣧⡾⠤⠶⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡝⡍⢳⣦⢤⣀⣀⡀⣠⣿⣦⣤⠎⢠⢳⠶⠚⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣌⣮⣷⡤⡭⣿⣬⢟⢩⢭⣿⠒⠓⢺⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⡏⢁⡴⠚⢻⠧⣤⣈⠈⢷⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡾⠀⣂⠷⡀⠀⠙⢆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉⠁⠀⠉⠈⠃⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠂⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣬⡓⢤⡀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡛⢿⣶⣌⡳⢤⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⣠⠞⣡⣄⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣍⡻⢿⣦⣍⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⡿⢋⡴⠀⠀⠀⠀⠀⠀⠛⠛⢀⠀⠀⠀⠨⠀⠀⢀⠔⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣍⠻⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠳⠄⠀⠀⠀⠀⡎⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢀⡤⠀⠀⢀⠖⠋⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢩⠛⠉⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀⢂⠘⢆⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⣀⠔⠓⠢⠀⠀⠀⡄⠀⠀⢠⠔⠈⠀⠉⠃⡀⠀⠁⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⡀⢀⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢣⠀⠀⠀⠀⠈⡆⠰⡇⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠁⠀⠀⠀⢀⠀⠀⣀⡀⠀⠾⢥⡤⠚⠀⢴⡇⢤⠀⠀⠀⢀⠇⠀⠙⠂⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⢀⣀⡀⠀⠀⠈⠀⠀⢀⡇⠀⠁⢀⡴⠟⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠚⠉⠉⠁⠀⠀⠀⠀⠀⠄⠊⢣⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡂⣒⣾⠟⠀⠀⢤⣄⣀⠀⣀⣠⠴⠿⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢠⡐⢄⠂⠭⣛⡭⡭⣒⠵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠓⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣤⣰⣷⣿⣿⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠐⢶⣦⣴⣶⣶⣦⣄⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡄⠀⣰⠆⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠛⠀⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣬⣀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠘⢿⡿⣿⣿⣿⣿⣿⣿⣋⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⡿⣿⣟⣛⣙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠟⠛⠉⢻⣿⢿⡇⢸⣿⣿⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠡⠜⠟⠻⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣟⠿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢠⡄⠀⠀⠀⠀⠈⢀⣿⣿⣿⣿⡟⠁⠀⢶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠃⠀⠸⣿⣶⣧⣀⣀⣴⣿⣿⣿⣿⣿⣴⣿⣦⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⠀⠘⠄⠀⠀⠀⠈⠻⠋⠻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⡀⠀⠀⣠⣴⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣷⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⠟⣼⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⡀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣽⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⣿⣿⡿⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠈⣯⣩⣬⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⡶⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠄⢰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣾⣿⣇⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠟⣉⣿⣽⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠁⠀⠀⡿⠿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⣯⣻⡙⠿⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣶⣯⡿⡟⠿⢿⣿⣿⣯⠙⡏⠻⡙⣏⠐⠀⠡⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣼⣿⣿⣿⣿⣿⣿⡔⣆⠀⡘⠛⣿⠀⠀⢀⡗⢨⠀⠀⡀⠀⠒⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠰⣿⣟⣿⢿⣿⣿⣿⣿⣿⣾⣷⣠⣿⣃⣤⣴⠇⣎⣄⣠⣁⡤⠀⠘⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣿⣿⣿⡿⣫⡄⠳⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⡿⠟⢹⣧⡝⠀⠀⠀⢻⣿⡿⢿⣟⡛⠻⠿⠿⣿⣿⣿⣿⣯⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠘⠾⣻⡿⣟⢳⣤⣀⠀⠂⠈⢻⡟⢷⣤⣄⡀⠀⠀⠀⠀⠉⠛⢿⣷⣕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠈⠀⢴⣤⣬⣉⣉⠓⢉⠳⣄⠨⢀⣿⣦⣉⠉⠓⡀⠀⠀⠀⠀⠀⠀⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠄⣴⣶⣦⡍⠙⢷⡀⠀⢘⣧⣼⣿⠻⣆⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠈⠻⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠦⠞⣷⠀⠀⠘⣿⣇⠈⣻⣿⣷⣿⣶⡐⢺⣿⡗⠀⠈⠳⣄⠀⠠⠀⠀⠀⠈⠛⠶⠄⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣛⠳⠀⠐⠈⣧⡀⠀⠈⠛⠷⠿⠿⠾⢻⠎⠀⢷⡇⠀⠀⡀⠀⡀⠀⠳⣦⡀⠀⠀⠀⠀⠀⠘⢦⡿
⠀⠀⠀⠀⠀⠀⢀⣾⣦⠀⢄⡀⠒⢠⡇⡛⠀⠀⣠⣤⣤⡀⠀⢠⣤⣾⣷⠀⠀⠙⣆⠀⠀⠀⢮⣿⣦⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣥⣙⢷⡌⠱⠆⢳⣠⡇⠀⠘⣿⣿⣿⣿⣖⣻⡍⠉⢻⡀⠄⠀⠈⠣⡄⠀⠈⢻⣿⣿⣷⣄⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢠⣞⣿⠉⠀⠀⠀⠀⠈⠛⡄⠲⠆⠹⠻⠿⠛⠉⣻⣷⣄⡀⠻⣄⠀⠀⠀⠈⠀⠀⠈⣿⠹⣿⠎⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠘⢧⡏⠀⠀⠀⣬⣾⣷⣶⣤⠠⠔⠀⠀⠄⢴⣆⣦⡉⢛⣣⣤⣬⡢⡄⠀⠀⠀⠀⡄⣿⡇⠛⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⢲⣦⣴⣿⣿⣿⣿⣿⠇⡀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⡝⢧⡀⢄⢶⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡟⢮⣻⠟⢻⡟⠟⠿⡿⢿⣿⣿⣿⣿⡿⣿⣿⣭⣌⣿⣛⣿⢻⣎⢿⡎⡞⣿⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠛⣋⡀⠀⠈⣿⠀⡀⢀⠐⢂⠈⣽⣿⣷⡿⣿⣷⣿⣿⢱⡏⠀⠋⠘⠟⣿⡏⢠⠃⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣷⣷⢸⣿⣧⣕⠠⡍⣬⣹⡷⠋⠀⣀⠞⣹⢯⡟⢸⠇⠀⠀⠀⣠⡟⠀⠘⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⢿⣿⣿⣿⡞⡽⣣⢫⡟⡠⡀⠁⠀⠹⠏⢠⡿⢠⠀⠀⢰⣿⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⡄⠀⠀⠀⠀⢹⠋⠁⢸⡟⢿⠻⣾⡵⣣⢏⡼⡃⠂⠀⠀⣰⣶⡿⠁⠃⣄⡴⣿⠇⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠧⠀⠀⠀⣀⢿⡄⠀⢸⣷⡀⠀⢻⣷⣇⣾⢸⣿⣤⠀⢠⣿⡟⣡⢏⣾⠋⢠⡟⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢦⣰⣿⣿⡿⣧⠀⢸⣧⢡⠀⠀⠙⢙⣿⣛⣿⣿⡄⠷⢟⠰⣱⣿⣿⠀⣼⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠈⢠⣾⣇⢸⠀⠀⠀⣸⢿⣏⣿⣿⣷⠀⡌⠀⣽⣿⣿⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡞⡜⠀⠀⠀⢼⣷⣿⠻⣽⣿⡀⠁⢰⡏⢻⢿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠠⣀⡄⢠⠉⡴⣭⢱⣾⣿⣿⡀⠀⠀⠀⠈⣧⡇⠀⠀⠀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣠⣄⣠⡁⠀⠤⠀⢐⣊⣶⣻⣿⣿⣅⠀⠀⠀⠀⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⢖⡨⢃⡤⢀⠀⠀⢀⠀⠀⢀⣼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⠠⠤⢦⠆⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⡿⠰⣣⡞⠀⢀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡛⠠⣤⣿⠁⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡶⠷⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠛⠻⣶⡄
⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡟
⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡶⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣠⡿⠁
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⡈⠇⠀⣠⢟⡻⣿⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡿⠃
⠘⠛⠛⢿⣷⣦⣤⣀⡀⠀⣠⡴⢻⣧⣾⡇⠀⠀⢠⠟⢻⡿⡇⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠘⣿⣇
⢀⣠⣤⣤⣿⣿⣦⣉⣹⡿⠷⣤⡀⣿⣿⣤⣄⣀⡏⣴⣿⡁⠀⠀⠀⠈⢿⣦⣤⣶⣾⡿⠿⢶⣿⣿⣆
⠀⠀⠀⠀⠀⠈⠻⢿⣿⡋⠛⠛⢿⡻⣦⣬⡿⠉⣽⣛⣛⣛⠛⠛⠂⠀⠾⢋⡵⠋⠁⠀⠀⢠⡇⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠈⢷⣄⣀⢀⣠⣿⣿⢿⣿⣟⡛⠛⠛⠲⠾⣧⣄⡀⠀⣠⡿⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⣩⣿⣿⠿⠁⠈⠁⠀⠉⠛⠻⢶⣾⣤⣭⣥⣶⠿⠋⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠛⢻⣿⠷⣤⣶⣤⣤⣤⣤⣴⣶⡾⠟⠉⠙⠿⣧⣄⠀⠀⠀⠀⠀⢀⣠⣴⡾⠇
⠀⠀⢴⣦⡀⠀⣀⣤⣾⡿⠋⠘⢛⣹⣿⣤⣾⡿⣍⠙⢿⣌⠙⢷⣤⣤⣤⣤⣤⣤⣥⣴⣶⣶⡾⠿⠟⠋⠁
⠀⠀⠈⢳⣌⠻⣍⣈⣻⣿⣿⡟⠉⠀⠀⠀⠙⠻⢶⣤⣤⣿⣷⡄⠈⠛⢯⣍⠉⢉⣵⣿
⠀⠀⢠⡟⣠⠞⠛⠋⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⣦⣤⣀⡀⢈⣿⠟⢿⠁
⠀⠀⣿⠞⠁⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠈⠉⠛⠻⢿⣄⢬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣴⣶⣶⣶⣦⣤⣀⣀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠙⢦⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⣍⠛⠛⣿⣿⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣤⣽⣆⣰⡟⠀⠙⠻⢿⣶⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡏⢹⠁⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣿⠀⣷⠸⣷⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⣰⡾⠋⠉⠉⠉⠉⢉⣛⣁⣀⣏⣀⣀⣀⣀⣀⣀⡀⠀⠈⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⣼⣿⣴⣶⠶⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⢀⡠⠀⢀⠄⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣋⠉⠳⣄⠑⢤⠀⢶⣈⣉⢡⣻⣿⣿⣷⣀⣾⣏⣴⠊⢀⡔⢁⣴⣉⣉⣵⠖⣊⣭⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣥⢹⣶⣾⣿⣯⣼⣧⢸⣧⡼⠯⠉⠀⠈⠛⠁⠀⠉⢻⡿⣿⣇⣟⢠⣿⣭⣭⣽⡿⢟⠋⡉⠅⠠⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠀⠀⠍⠿⣿⣿⣿⣿⣿⣿⡂⠀⠐⠀⠈⡏⠀⠀⠤⠀⣆⢻⣿⣿⣼⣿⣤⣿⣿⠘⡨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣁⣀⣐⢻⣿⣿⡟⣷⣿⠃⡀⣁⡶⢿⣿⡷⣤⡠⠎⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⢛⣡⡴⠟⣉⣤⣿⠆
⠀⠀⠀⠀⠀⢠⣏⣈⠹⠷⠓⢙⢙⢻⣻⣿⣿⡵⠟⠡⠜⠛⠁⣀⣀⣀⣀⡈⠙⠾⣡⠟⢿⣿⣿⣿⣿⣿⠯⠉⠆⠰⠀⠆⢠⠄⢠⠈⡁⠐⠃
⠀⠀⠀⠀⢠⡶⠈⢁⠰⠄⢃⠉⠄⠒⣃⣽⣿⣡⠝⣀⢴⡂⣀⣀⣩⣍⣁⣉⡓⣲⣬⣿⣷⣏⣿⣿⣿⣿⣄⣨⣅⠈⠀⠀⠀⠀⠈⠀⠁⠘⠂⡄
⠀⠀⠀⠀⠊⢀⠐⠈⠀⠈⢀⠐⢦⡼⢛⣻⣿⣷⣮⢕⣀⣿⠤⠤⠼⣶⠦⠭⣽⣟⠂⠙⣿⣿⣿⣿⣿⣿⠃⡍⢘⠛⠛⢋⣃⣀⣀⣀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢡⡶⢃⡐⠂⠼⣿⣷⣽⡯⠀⣸⣇⡒⢡⡘⣛⣒⡿⠄⣠⢾⣿⣼⣿⣿⣿⣌⠑⠀⠁⠚⣠⠄⠉⠋⢥⣭⣥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⡞⠀⠖⠀⠈⣴⣿⣿⣿⠇⢉⢨⡯⣠⣾⡵⣩⣽⣛⣣⣿⣿⣿⣿⣿⡿⢉⠷⠶⣤⠈⠀⠀⠈⢁⡄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠃⣾⣿⠱⣿⣿⡾⢋⠀⠳⠾⢁⣰⡷⠚⢠⣿⢿⡟⣿⣿⣿⣿⡩⠄⠳⡶⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡆⢩⣿⣻⣐⡧⠘⠃⠀⠀⠋⠑⠛⢦⣜⣯⡿⣎⣿⣿⣏⠣⠨⠄⠻⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣾⡟⣳⣎⡑⠀⠒⠀⠂⠴⠆⢴⣼⣿⣿⣿⣿⣿⣿⣿⣄⣥⣵⣞⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⣿⣿⣧⣶⢶⠰⠂⠆⢶⣾⣿⣿⣿⣿⣷⣿⣿⣿⡟⣿⠟⣉⣰⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠚⠁⢙⢁⠎⣟⢻⢺⣿⣿⣿⣿⣿⣿⣿⣷⢛⣌⣷⣶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣿⢧⣶⡖⡾⣮⡶⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣤⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢰⣿⠋⢸⡏⡇⢠⠉⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⣀⠐⣾⣿⣿⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣾⠃⠀⠀⠄⠀⠀⣀⣁⣈⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣏⡑⣿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠃⠀⠀⠀⣙⡀⠀⣤⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣏⠛⣿⣿⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⢠⡀⠈⠁⠳⣿⣿⣿⢿⣿⣿⣿⡟⠛⣿⠀⢨⣿⡡⣽⣟⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠂⠩⣱⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠛⢠⣿⣿⣷⠚⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⡄⠀⠑⢤⡀⠀⠀⣄⡳⢦⣻⣿⣿⣿⡿⢿⣿⣿⣿⣄⣀⣤⣿⣟⠉⢿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠷⠀⢀⡀⢉⣲⣅⡠⣸⣿⣿⣿⠿⣹⠿⣾⣿⣿⣯⡏⠉⢸⣛⡉⣸⣾⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⣴⣾⡏⣸⣿⣿⣿⣿⣿⠿⢿⣶⢿⣶⣞⣿⣿⣿⡇⠀⠐⣿⠞⣯⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⠿⠿⠿⠛⠁⠀⣹⣛⣿⡷⣶⣿⣿⣿⣿⠀⢠⣷⠞⣿⣾⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⠿⠟⣺⣿⣿⣿⢿⣇⠘⡿⣿⣿⣯⡷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣒⡈⠿⣛⣿⣿⣿⣿⠀⣧⣜⣓⡚⣺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣬⣬⡴⠾⠛⢻⣿⠿⢿⣧⣀⠋⢙⣛⣿⣟⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⡛⠀⢲⡖⠛⣶⡝⠓⠚⣿⣛⣿⣉⣀⣾⣉⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠉⠉⠁⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⡐⠠⡀⠀⠈⠉⠁⠀⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁⠀⠀⠀⠀⠀⢰⡇⠀⠑⠎⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⢱
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⢈⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁
⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⢀⡀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠁
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠃⠐⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡎⠀⢠
⠀⠀⢀⠂⠀⠀⣀⣀⣀⣀⠀⠀⠀⠰⠴⠶⠶⠤⡄⠛⠂⠀⠀⠀⠛⠀⠤⠶⠶⠶⣤⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠀⠀⠀⠃⠀⡈
⠀⢀⠋⠉⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⡆⠀⠀⡄⠀⡆⠀⠈⢀⡆⠀⠀⠀⠆⠀⢘⠀⠂⠀⠠⠉⢡⠀⠀⠀⠀⠈⠉⡀⠀⠀⠀⠀⢸⠀⠀⣶⠀⠀⠃
⠀⠘⠀⠀⠀⠀⠀⢀⠁⢰⠀⠀⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠘⠀⢸⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢀⠁
⠀⠁⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⢰⠀⠀⢠⡇⢀⡀⢀⣀⢠⡇⠀⣸⠀⢀⠀⠀⡀⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠸⠀⢠
⠷⠀⠀⠀⠀⠉⠉⢻⠉⢛⠀⠈⡃⠙⠀⠀⠈⠃⠈⠀⠀⠁⠈⡇⠀⠸⠀⠉⠀⢸⠉⢹⠃⠀⠛⠉⠛⠉⠉⠀⠀⠀⠀⢴⠀⠀⠀⠁⠀⡄⠀⡈
⠐⠆⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠁⠀⡇⠀⠀⠁⠀⠂⠀⠀⠀⡇⠀⠀⠀⡇⠀⠈⠀⡀⠀⢠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣤⠀⠀⠃⠀⠁
⠀⠘⠀⠀⠀⠀⠀⠀⢁⡀⠃⠀⠀⡄⠀⡀⠀⢠⠀⡁⠀⠀⠀⡇⠀⠄⠀⠇⠀⠂⠀⠃⠀⡄⠀⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⡆⠀⠆
⠀⠀⠃⠀⠀⠀⠀⠀⠀⢡⣤⣁⣀⠰⠦⠀⠀⠀⠚⠀⠤⠘⡶⠠⠤⠘⠃⠀⠀⠑⠃⢀⣀⣡⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⠀⢠⠀⠠
⠀⠀⠀⠲⠄⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠶⠃⠀⠀⠀⢸⠀⠘⠀⡄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⡄⠀⡆⢀⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢈⡇⣍⢁⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠄⢠⣄⢀⣀⣀⣀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠄⠀⠀⠉⠀⠀⢀⡞⠢⠀⠘⠳⢮⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠉⢹⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⡋⠁⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⣀⣠⠼⡇⠈⡆
⠀⠀⠀⠀⠀⠀⡠⠾⠁⢄⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⡴⡋⠣⡀⠀⢸⡟⡀⢀⠄
⠀⠀⠀⠀⠀⢰⠀⠀⠂⠈⢤⠠⠈⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡠⠓⠄⠰⠎⠀⠀⠉⢄⠈⢶⡿⣇⡿⠁
⠀⠀⠀⠀⠀⢸⢀⡘⣀⠀⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣀⠖⠀⢀⡀⠀⢈⣄⠀⢀⠰⠂
⠀⠀⠀⠀⠀⠈⡋⠁⠀⠀⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠰⢎⣀⣀⣀⠀⠟⠋
⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⣀⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠆⢉⠤⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡷⠤⠀⠀⣠⢆⠀⠀⠀⠀⡀⢠⠄⠤⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⣀⡰⠁⠀⠀⠀⣿⢸⠀⠀⠀⠀⡅⢸⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠤⠤⠀⠀⣀⣿⠘⠀⡀⢀⠀⠇⢸⡄⠀⠠⠤⠄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠉⠉⢙⠛⡉⠉⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢤⣤⣄⡀⣀⣀⡼⠀⢣⣤⢤⣤⣤⡄⢲⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠙⠛⡦⠴⠴⠦⠠⠞⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠓⢄⠀⡀⠀⠀⠀⠀⠀⠀⠠⠚⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⠒⠀⢋⡘⢇⠀⠀⠀⢀⠶⣈⠳⠒⢎⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠁⢾⡃⠀⠀⢸⠗⠉⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠃⠀⠀⡇⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠃⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⢀⣀⠀⢴⡇⠀⠀⣿⠄⢀⣀⠀⠀⠀⠀⠀⠀⢁⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣴⣶⣒⣶⣶⣤⣄⣉⣃⣀⣀⣀⣀⣀⣀⣋⣉⣤⣴⣶⣶⣲⣶⣬⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⢀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠉⠉⠉⠉⠛⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣤⡄⢤⡄⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡷⢂⣨⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⡄⠠⣀⣠⣶⣄⡀⠀⢰⣿⣿⣿⣿⡿⢟⡱⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣾⣠⠤⠀⠉⣤⣶⣿⡿⠛⢺⡇⠀⣿⠿⣿⠟⢥⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡯⠐⣿⢋⣹⣿⣿⣿⣿⣿⢆⣼⢻⣿⣿⣿⣿⣿⣿⡟⣣⣴⣿⡿⠟⠉⠀⠀⢠⡇⠀⣿⡄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣿⣿⣿⣿⣿⢿⣿⡿⡇⢼⢣⣾⡟⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢸⡇⢸⡟
⠀⠀⠀⠀⠀⠀⢀⠀⣿⣀⢀⣈⣵⣾⢿⣿⣿⣿⡷⠆⠄⠀⡾⠿⢉⣿⡿⠿⣿⣿⡟⠹⢷⡾⠃⠀⠀⠀⠀⡼⠁⠘⡇
⠀⠀⠀⠶⠶⠿⠿⠛⠻⡟⠛⣿⣿⣷⣾⣿⣷⣿⠟⠰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣦⡌⣷⣾⠞⠁⠀⠀⣠⠜⠁⠀⠀⢀
⠀⠀⢀⣠⣤⣴⠶⠶⠚⢻⠉⠙⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣯⠛⠶⠿⠛⠉⠀⠀⠀⠀⢈
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠳⡀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣛⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⣿⣿⠟⠻⠟⠻⣿⣿⣿⡟⢻⠂⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⢿⡍⣶⣿⣷⣾⣶⣿⣧⣬⣿⡟⣠⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⣼⣿⣻⣿⣶⣶⣽⣿⣿⣿⣿⣿⡿⣿⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣯⡉⠻⣿⣏⣴⡿⢋⣼⣿⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠉⠉⠀⣸⣿⣇⠀⠀⠉⠉⠉⠉⠋⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⢀⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⣿⣥⣶⣶⣶⣿⡿⢿⣿⣿⣄⡀⠀⡄
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣥⢿⣿⠿⣿⣿⣦⡀⠀⠁
⣻⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠈⠿⣿⣿⣦⡀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢡⣿⣿⣿⣿⡿⢻⣿⣿⣰⣿⡟⠀⠀⠀⠙⢿⣿⣿⣦⡀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⣿⣿⣿⡿⢱⢸⣿⣿⢻⢻⡇⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣜⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⡀
⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠴⢶⣶⡦⠄⢻⡄⢻⣧⣿⣷⠀⠸⣿⣿⣃⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣥⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣷⣦⡎⠱⠈⢿⣿⣿⣯⠺⣿⣟⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣤⣄⡁⠐⠂⠀⠀⠀⠀⢀⠀⣠⣿
⣿⣇⠀⠀⣀⣿⣿⣿⣟⣛⣿⣿⣇⣼⣿⣀⣤⡐⢠⣿⣿⣿⡆⢿⣿⣿⠋⣀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣶⣦⣤⣷⣶⣿⡿⠛
⣿⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣤⠋⢿⣿⣷⢼⣿⣯⣄⣈⡑⠂⢀⠀⠀⠀⠈⠀⠚⠁⠀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣋⣵⣶⣿⣿⣿⠺⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⢆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣯⠓
⣿⣿⣿⣿⣿⡿⣿⡝⢹⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡯⢭⠛⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⣿⣯⣁⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠈⠉⠻⣤⣀⡀⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣼⣿⣟⠟⣋⡀⢹⣦⢶⡆⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⣿⣽⣇⠀⣀⣸⠟⣸⠃⣿⢿⡿⢃⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣿⣿⣷⣍⣭⣅⣴⣾⠏⣸⡟⣾⡷⣾⡷⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⡿⣍⡛⠋⢁⣴⣟⡼⣳⡗⢻⣧⠳⡽⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⡺⣽⠿⡿⢿⣫⣾⢻⣷⡌⣿⡳⡽⣾⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⡿⡿⣎⡻⣿⣿⣿⣱⣿⢻⣿⠘⣷⡝⣾⢷⡙⢷⣤⣀⣀⣀⣀⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣣⣿⣏⡟⣧⢻⣌⠻⣦⣙⠛⠻⠋⢸⡟⣇⢽⣿⣌⢷⡻⣮⣿⣿⠷⣶⣦⣦⣤⣤⣤⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢸⡇⢿⡘⣯⢳⣄⠙⠿⣶⣤⣿⡇⢻⡾⣿⣿⣦⡹⣮⣻⢿⣟⣶⣭⣍⣙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⢸⣷⠸⣷⠸⣧⡻⣷⣤⣀⠉⠙⠁⢈⣿⣿⣿⣿⣝⠿⣿⣷⣬⣛⠿⣮⣭⣛⡛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣆⠹⣷⡙⢷⣌⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣦⣍⠻⢿⣷⣄⡉⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡄⣿⣿⣧⡈⠿⣮⡿⣶⣄⡉⠛⠻⠿⠿⣿⣿⣿⣯⡻⣿⣿⣷⣤⣀⠉⠙⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⢻⡟⣷⡄⠘⠿⣮⡙⠻⢷⣶⣦⣤⣀⣀⡈⠈⠁⠀⠈⠉⠛⠛⠿⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢊⣠⣴⣾⠥⠖⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⠃⠴⣦⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠉⠤⠀⠀⠀⠀⠀⠠⡔⢄⠀⢀⡴⠛⠉⠢⣀⣀⣠⣤⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡴⠀⠀⠀⣀⠈⠀⠙⠾⢤⣤⠶⢚⣻⣉⣀⣤⣤⣷⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⡴⠒⠒⠂⢀⡀⠀⠀⣠⠁⠀⠀⠀⠀⢂⠁⠀⠲⠿⠿⠿⢃⣴⠶⠎⠑⠙⡏⠉⣽⠁⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠁⠀⠀⠀⠀⠀⠉⢫⣀⠉⢁⠠⠀⠀⠘⠛⠀⠀⠀⠀⠀⡠⠜⠀⠀⠀⠀⢰⣇⠶⠃⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠊⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠟⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠤⠔⠚⠁⠀⠀⠈⠐⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠀⠀⢀⡀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣎⠉⢉⣀⣠⣼⢄⠀⠀⣿⠐⠉⠉⠙⠛⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠔⠊⢀⠴⠋⠛⠝⣡⠞⠉⠉⠈⠀⢢⡤⠤⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⢠⣞⣁⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠈⣷⠀⢨
⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣀⡜⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢉⣡⡜⠡⠄⠒⠒⠀⠀⠂⠀⠒⠂⢤⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠤⣀⣀⣀⣀⣀⣠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠇⠀⠀⢠⠤⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⠀⡰⠃⠀⠀⠀⢀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢛⠉⠉⠁⠀⠀⠈⠉⢋⠉⠠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⢈⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠤⠬⢍⣉⡙⠛⠻⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣬⣉⡛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠴⠀⠀⢀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠚⠉⠀⠀⡾⠀⠀⠈⢈⣀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠀⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⠀⢠⠔⠂⠀⠄⠀⠀⠀⡀⠀⢸⠀⡀⠈⠀⠤⠤⠄⠐⠒⠒⠒⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣿⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⡆
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠹⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⢯⣅⣀⣤⣤⣤⠀⢰⢿⡿⣟⠻⣿⣿⡿⠿⣿⣿⣿⣿⡇
⣿⣿⣿⣦⣬⣾⣿⠏⣉⣿⣶⣿⣯⣭⣠⣾⣿⣿⣦⣤⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣿⣿⠋⣙⣿⣬⣿⣽⡏⣉⢹⣿⣿⣿⡿⢷⣥⡈⢹⠿⢿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠛⠛⢿⣿⡿⠛⠓
⣿⣿⣿⣾⠿⣾⡍⠉⢞⣿⣿⣧⣴⣿⣮⣵⣾⣿⢿⢿⣶⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢿⠃⠀⠈
⣿⣿⣿⣦⢔⣾⣿⣦⣿⣿⡋⠉⠿⠛⣿⡿⠿⢷⣄⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆
⣿⣿⣿⣿⣿⣏⡑⠀⣩⡿⠿⢿⡾⠿⣿⣠⣴⢸⡟⠉⣿⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣤⠶⢆⣤⣤⣤⡿⠀⠀⠀⠀⠀⠸⡧
⣿⣿⣍⠀⢎⣻⡿⣿⣿⣇⢈⣷⣶⡀⣸⡿⢿⡟⡛⢶⣽⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣷⡀⢀⣤
⣿⣿⣿⣷⣿⣏⣈⣃⣼⡟⠹⡿⣿⣿⣿⣿⣴⣿⣿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀
⣿⣿⣁⠘⠛⢿⣿⠛⣿⣿⣶⠿⢿⣿⡿⠳⣠⣿⣇⡙⢠⣿⣿⣿⣯⠀⠀⠀⠀⣿⣿⠛⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣧⣿⠟⢻⣿⣯⣤⣿⣿⣬⣴⣾⣿⡟⠿⢿⡟⠻⣿⠙⣻⣿⣿⣿⠀⠀⠁⠹⣿⡿⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⠿⠿⢿⡗⠐⠒⠒
⣿⣿⣿⣷⣮⡿⠿⣿⣏⠉⡻⡿⠟⠉⠰⠶⣽⣷⣿⢷⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⢸⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⣁
⣿⣿⠏⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⢿⣿⣿⣿⡄⠀⠀⠈⠉⠱⠎⠉⠉⠆⢿⡏⠉⠉⠉⠁⠉⠈⠉⠁⠈⠀⠀⠈
⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿
⣿⣿⣿⣶⣦⣤⣤⣤⣤⣦⣤⣤⣤⣀⣀⣴⣶⣶⣶⣾⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠒⠒⠒⠒⠒⠒⠂⠄⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣤⣠⣾⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⣿⣿⣿⣿⣤⣀⡀⠀⠀⣀⣀⢀⣤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣿⣿⣇⣾⣿⣿⣿⣶⡞⡉⠀⠋⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢀⠐⠁
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠸⠏⢘⣿⣿⣿⣿⠟⠛⢿⣅⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠙⠿⣿⣦⡀⠀⠀⠀⠘⠿⣏⢻⣷⣶⣦⠝⠻⠃⠂⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣰⡤⠀⠀⠀⠀⠀⠈⣉⣀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⢀⠦⠼⡥⠬⠿⣶⣖⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡄⠀⠀⠠⠄⠀⠀⠄⠈⠂⠀⡐⠀⠀⠀⢀⠀⠐⠠⡀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠠⠄⠠⠀⡀⠁⡀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠤⠤⠤⠤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⡀⡈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠂⠙⠦⠛⠳⣦⣤⣶⣿⣿⣏⠹⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣷⣷⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠒⠈⠻⣿⠿⣿⣿⣿⣿⣿⠟⢺⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠊⠄⠀⠀⠀⠰⣿⠗⣀⣤⣹⣿⢿⣿⠆⡀⠁⠀⠀⣀⣴⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠁⠈⠁⠀⠀⢀⡀⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠤⢤⣠⣴⠚⠻⣆⣀⠀⠀⠀⠀⢹⡿⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⣀⠀⠀⢀⠀⠀⢀⣴⣿⠏⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠒⠂⠀⠐⠠⠂⠀⠀⠀⠐⠀⠄⠀⠀⠠⠀⠈⠋⢁⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⡿⠛⠉⠉
⠀⠀⠀⠂⠤⣤⠀⢠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⢦⡙⠷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⡿⣿⡶⢉⣽⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠙⠛⢤⡠⢄⣀⠀⠀⠀⠀⠘⣷⠀⠉⠁⡽⠉⢸⠉⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠛⣷⣋⣴⣯⠀⠀⠀⠀⠀⢸⣇⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⢰⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣼⣿⡇⢀⡎⠀⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣻⣿⠇⣀⣀⣠⢤⠐⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡠⠙⠋⣴⣿⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠌⠈⠁⠀⠀⣿⢷⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣤⣀⣀⣀⠰⡇⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢹⠉⣿⠏⢳⣌⠀⠀⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⣼⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠉⢉⠉⢩⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢠⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢤⡂⠀⠀⠀⠀⠈⠀⠀⣽⠀⢰⣿⠀⠀⠀⠛⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣟⣛⣛⣀⢒⣠⡼⣿⡦⢸⣼⡆⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠛⠛⠚⠛⠛⠛⠛⠉⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⣀⣴⣿⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠈⢿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣾⣿⣿⣿⣿⣷⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡄⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣆⡈⠻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⢿⣿⡆⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⡆⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠉⠸⣿⣿⣿⣿⠇⠸⢻⣿⣿⡟⠋⠘⣧⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⣿⣿⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢤⡤⠄⠀⠀⢀⣄⣠⣴⣾⣿⣿⣿⡿⠿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⡿⠷⠀⢀⣨⣿⣷⣤⣤⣤⣤⣄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠆⠀⠀⠨⠿⠿⠿⠟⠋⠉⠉⠉⣉⡉⠉⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠶⠶⣶⣶⣶⣶⣶⣶⣤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⢻⡟⠛⠷⣦⡀⠀⠀⠀⣠⡾⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠻⠂⠀⢀⡀⠀⠀⠟⠻⣦⠀⠀⣿⡁⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⢸⣇⣀⣀⠀⢀⣻⡆⠀⠘⢷⣤⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠀⠀⠀⠈⠛⠛⠛⠀⠙⣻⡇⠀⢀⣴⠾⠿⠿⢶⣄⠀⠀⠀⢠⣴⡶⠶⠿⠛⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⠀⠀⠀⠀⠀⠀⣤⣰⡟⠀⢰⡟⠁⠀⠀⠀⢀⢹⣟⠛⠿⢿⡇⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣰⣆⣀⣤⡾⠋⠀⠀⢸⡇⠀⠀⠀⠀⠛⠛⠛⠿⠶⠾⢿⣤⡀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘⣷⠀⠐⠻⠷⠶⠶⣦⣤⣤⣤⣀⣼⡇⠀⣀⣀⣠⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠘⣿⠀⠉⠹⠿⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⣦⣄⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⢀⣴⠟⠀⠀⣈⣽⠿⣦⣄⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⢀⣠⡾⠛⠁⠀⠈⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⣀⣠⣴⠟⠋⠀⠀⠀⠀⠀⢸⣇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⠁⢠⣴⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣬⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣴⡶⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣛⣿⣿⣛⣿⣿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠉⠉⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠈⠋⣻⠀⠀⠤⠤⠀⠀⣿⠉⠁⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⣿⠀⠀⠢⠤⠀⠀⡟⠀⠀⠀⠀⠀⠀⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡃⢐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠁⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⢄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤⣤⣄⡀⠷⠀⠀⡠⠠⠾⢄⣀⣤⣤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠶⠃⠀⠀⠉⠉⢉⠛⢁⠀⠀⠖⢰⠀⠀⠀⠎⢰⠀⠀⡆⠰⠀⠀⡄⠁⠀⠀⠠⠈⢡⠀⠀⡞⠻⠉⠉⠉⠀⠀⠘⠷
⠀⠸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠸⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠁⠀⣤⠀⠀⡄⠘⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠇
⠀⠂⠀⠀⠀⠀⠀⢰⠀⠰⠀⠀⠸⠀⠈⠀⠀⢀⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⡄⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠐
⣄⠀⠀⠀⠀⠴⠦⢶⠆⠶⠆⠀⢾⠀⠳⠀⠀⠻⠀⢿⠀⠀⡗⠘⠃⠀⠸⠀⣿⠀⠐⡷⠰⠷⠀⠰⠇⠴⠷⠤⠀⠀⠀⠀⡀
⠁⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⢰⠀⠀⠀⡀⠸⠀⠀⡇⠀⠀⠀⣆⠀⠀⠀⢀⠀⢰⠀⠀⡆⠀⠆⠀⠀⠀⠀⠀⠀⢀
⠀⢠⠀⠀⠀⠀⠀⠀⠘⡀⠸⠀⠀⡇⠀⡀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠋⠀⠀⠀⠛⠀⠀⠀⢰⠀⠸⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠆⠀⠀⠀⠀⠀⠀⢃⠀⡇⠀⠀⣀⡷⠀⠀⢡⣄⣁⣀⣡⣤⣀⣀⣡⣜⠀⠀⠤⠰⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⣆⡀⠀⠤⠤⠄⠀⠛⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠁⠀⠠⠤⠄⠀⢀⡐
⠀⠀⠀⠈⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠈⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡉⠛⠂⠲⠶⣶⣶⠶⠂⠀⠀⠘⠇⠀⠀⠰⣤⣤⡴⠶⠒⠲⠦⠄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠁⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⠑⢢⡄
⠀⠀⠀⠀⠀⠀⠤⠉⠀⠑⣄⠀⠀⣀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢀⡀⠀⣠⠖⠁⡘⠧
⠀⠀⠀⠀⠀⢰⠀⢀⠈⠀⢠⠞⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠈⠙⢆⠀⠀⠁⠀⣷
⠀⠀⠀⠀⠀⠸⣤⡾⠀⠆⠾⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⢃⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡘⠁⠀⠈⠙⠿
⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⡠⢼⣏⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡃⠦⣀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⠔⠂⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠂⣬⢛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠸⣯⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠀⠀⠀⢸⠒⠂⠀⠠⣾⠠⠦⠤⠤⠴⠄⣿⠒⠒⠀⣻⠀⠀⠀⣀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡤⠊⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠦⢠⡾⠻⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠀⠀⠤⠠⣿⢀⣀⣀⣀⣀⡀⣿⠄⠀⠐⠒⠒⠀⣿⡶⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠿⠉⠉⠁⠀⠀⠀⠀⢀⠀⡍⠻⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠶⣤⣤⣀⣀⣠⠆⠀⠷⠤⢦⣶⣴⠶⢰⣏⣱⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠹⠖⠒⠒⠒⠒⠋⠁⠀⠀⠀⡟⢁⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⡏⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⢀⠈⣧⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠚⠢⣀⠸⠀⠀⢀⠃⠘⡷⢀⠴⠚⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢙⠆⠲⣈⡻⢆⠀⠈⠒⢀⠿⣋⡳⠐⠖⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠈⠓⢿⠀⠘⢠⣿⠖⠉⠀⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠇⠀⠀⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⣤⠤⣤⣄⣀⠘⠛⠂⠈⠀⠀⠀⠈⠀⠚⠛⢀⣀⣤⡤⣤⣤⣤⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠩⠆⡀
⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠖⠛⠋⢉⣠⣤⣄⡀⢠⣤⡶⠶⠤⣤⣤⣄
⠀⠀⠀⠀⠀⢰⡋⠁⠀⢀⣀⣤⠞⠉⣁⣤⠿⢃⣎⣀⣀⣀⠀⠀⠁⠉⠜⣳⣄⡀
⠀⠀⠀⠀⠀⢘⠉⢰⣿⠋⠁⢀⡴⠟⠉⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠘⠀⣿⣿⣷⠞⠉⠀⠀⢠⣿⣿⣿⠿⠋⠉⠛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⢀⡴⠟⠿⢿⡄⠀⠀⠀⢸⣿⣹⡏⠐⢚⡦⡴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣀
⠀⠀⠀⢀⡴⠉⣀⠀⠀⠀⢣⠀⠀⣴⣯⣿⠏⣁⠀⣀⣁⣾⠋
⠀⠀⡀⠊⠀⠀⢻⣿⣿⡄⠈⢷⣦⣽⣿⣿⣦⣯⡈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠈⢙⠙⢡⠟⢿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠾⠹⠟⠦⣀⠈⠀⠀⠀⠸⠋⡿⢸⠛⠋⠀⠀⠈⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇⣤⡀⢀⣸⣄⣇⣸⠀⠀⣤⣀⡤⠈
⠀⠀⠀⠀⠀⠀⠀⢤⣀⣤⡜⠁⠀⠈⠃⠙⣿⡛⡇⠸⣄⣸⠛⠛⠿⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠨⣏⠉⠀⠀⠀⣤⣤⣼⣿⣿⠛⠉⠉⠃⣀⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡆⠀⠀⠀⠀⠘⣿⡏⠉⠶⠀⠤⠤⠤⠤⣤⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣄⠶⠀⠀⣰⡟⠟⠻⠻⢇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣡⣆⣀⣀⣀⡠⠀⠀⢠⡈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⣿⡿⠋⠡⠋⠀⠀⠀⠀⢀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡐⠉⠜⢱⠀⣤⠀⠀⣤⣴⣶⣶⣿⡀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⣮⢰⣿⠂⢠⣿⡿⠿⣿⡏⣇
⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⣿⣿⡏⠀⠎⠉⠀⠀⢹⢃⣿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⠆⣼⣿⣿⣧⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡗⠀⠀⠀⢀⠋⠀⠛⢿⣿⣿⡆⠀⡀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⡇⠀⠀⠀⡾⠀⠀⠀⠀⠙⣿⣿⣿⣇
⠁⠀⠀⠀⠀⠒⠂⠀⠐⠋⠀⣿⡇⠀⠀⠀⠁⠒⠈⠛⠁⠀⠈⠹⣿⣿⣿⡆⠀⠈
⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⠡⣤⣤⣶⣴⣷⣤⣤⣴⣿⣿⣿⡇⠀⢀⣄⠀⠀⠀⠈⠐⠒⠀⠐⠋⠉⠂
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠀⠀⣭⣤⣛⠋⢛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠁⠀⠈⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠒⠆⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠔⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣾⣿⡀⢰⢁⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡆⠀⣰⣾⣿⣳⣿⣿⣿⣿⣿⣿⣻⣿⣉⣻⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣚⡂⠠⠊⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠘⠉⢹⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠁⠀⣈⡉⠁⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⢡⡄⠀⢀⣀⣠⣤⣶⣾⣿⡿⢱⠄⢀⠀⣾⠠⠄⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡄⠀⠀⢀⡇⠀⠰⠀⣀⠀⠀⠒⣀⠲⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⡇⠀⢠⣿⡀⠚⡍⠛⠢
⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⣴⣷⠔⠉⢛⡥⡤⣀⠀⣛⠒⠋⠉⡜⠛⣒⠿⠛⠋⠉⠌⡁⠩⠩⣠⠄⡈⠉⡓⠴⠸⢿⡇⠛⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⣿⠧⠘⠉⠁⢀⠔⡅⢀⠈⠁⠀⠁⠀⠸⠓⠒⠉⠀⢀⠄⠘⠆⢀⣿⠀⠀⡀⠉⠈⠑⡷⢤⠀⠀⠈⡖⠉
⠀⠀⠀⠀⠀⠄⠀⠙⠤⠊⠁⠀⡀⠂⠀⣼⢰⡄⠘⠃⠀⠀⠀⢠⡀⠂⢀⠀⠀⣿⢸⣿⡄⣀⣀⠀⢀⠀⠂⠀⡆⠀⠀⠇
⠀⠀⡆⠀⠂⠀⠀⠠⢀⣀⠀⢀⣤⣤⡤⣭⡁⠀⠰⠆⠀⣠⡄⣾⡇⠲⠵⠄⠜⠛⠛⠉⠉⠀⠄⠈⠀⠀⠈⠀⡇
⠀⠀⠁⠨⠁⠠⢈⠀⢀⠀⣀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠀⠒⠠⠅⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⠿⡷⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠃⢂⡆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⣶⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣀⡀⠀⢀⢸⡇⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⣀⡀⠈⠻⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣿⣿⡟⠛⠿⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠰⣿⣿⡄⠀⠀⠀⠈⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠷⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⢛⢿⠛⡿⢿⡟⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⠶⠷⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡀⠀⠀⠀⠀⣰⣤⣿⠀⠀⠀⠀⣦⣶⣄⠀⡄⠀⣿⣿⣿⣿⣿⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠃⠊⢠⡾⢋⣿⣟⠀⡀⠀⣸⣿⣿⠿⣃⣀⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⣄⡠⠀⠈⠢⠀⠉⠉⠀⠘⠋⠉⣡⢔⣨⣿⡫⠌⢋⠉⠙⣻⣿⡇⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠰⠛⠱⢦⣄⠀⠒⢶⣄⠀⠀⠀⠀⢀⣵⣿⣿⣫⣴⣮⣴⣾⡿⠋⣉⡵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣿⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠑⢦⣄⡐⣻⣿⣿⣿⣿⡿⣿⠆⠀⢠⣤⣤⣤⣤⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⢳⣄⠙⠢⣀⠀⠈⢉⣩⣽⠿⠛⠉⠀⢀⣠⠞⠃⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⢈⣿⡿⡋⠉⠀⠀⠀⠰⠄⣨⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢇⢢⣻⢀⡄⠀⠀⠀⠀⠈⡛⠻⠿⠟⢋⣵⣿⣡⣄⠀⠀⢀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣥⣤⢄⣤⡆⢳⣤⣤⣶⣿⣿⡿⠋⣡⣿⡇⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢁⣾⣿⣿⣿⣿⣿⡿⠟⢉⣴⣾⣿⣿⣀⣀⣤⣀⡄⢀⣄⠀⢰⡄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⣾⠈⣿⣿⣿⠿⠋⢀⣤⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣤⣿⣴⣸⣷⡄⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢡⠀⢸⣿⣰⡌⠉⠁⣠⣾⣿⠿⠟⠋⢉⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡄⠀⠸⠟⠉⢀⣴⣿⡏⠀⠁⠀⠀⠀⠀⢈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⠄⠀⢀⣠⣾⣿⣿⣿⠟⠀⠀⠀⣀⡀⠀⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠈⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⣤⠞⣿⣿⣿⣿⣿⣿⣶⢿⣿⣿⣷⣦⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢙⠉⠀⠀⣿⣿⣿⣿⣿⠋⠑⠛⠻⠿⢿⣇⣿⠉⠩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣸⡆⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠐⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⡟⠉⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⡇⣿⠇⠀⣿⣿⣿⣆⠀⢸⣷⡆⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡿⠀⠀⠋⠛⢻⣿⣿⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠿⡏⢹⣿⣷⣿⢿⡟⣹⣿⡟⣿⡟⠈⠻⠀⡿⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⠁⠘⢠⣿⣿⡿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠞⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⢀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠲⡄
⠀⠀⠀⠀⠀⠀⢀⣜⢁⣴⣦⣿⣷⠀⠀⠀⠈⠻⣿⣿⠿⠿⠿⣿⡿⠿⢿⣿⣧⠀⠀⢹⡀
⠀⠀⠀⠀⠀⣴⠉⠉⠛⠿⣶⣭⡉⠀⠀⢀⡤⢚⠭⡅⠀⠀⣀⠭⢭⡓⠀⠀⠉⠳⣄⢸⠅
⠀⠀⠀⠀⠀⣿⣶⣦⢀⣾⣿⡟⠀⠀⡠⠋⢰⢁⣤⡇⠀⡔⢁⣄⢠⠇⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⣼⣿⡟⢿⣿⣿⠏⠀⠀⡴⠁⡀⠉⡾⠿⠀⢸⣀⣿⡿⠃⠀⠀⠀⠀⠀⢼⣿⣿⠖⠒⢦
⠀⠀⠀⠘⣽⣿⢧⣿⣿⠏⠀⠀⢰⠃⠚⡁⠀⠓⠄⠀⠀⠁⠀⠀⠀⠀⣠⢄⠀⠀⠀⠙⠁⠮⡀⢸
⠀⠀⠀⣰⣍⡉⡿⢿⡃⠀⠀⠀⢸⠀⠀⠐⠠⣀⠀⠀⠀⠀⢀⣀⠤⠊⣡⡎⠁⠀⠀⠀⠀⣨⡴⠋
⠀⠀⢠⠷⠦⣸⡀⡰⡇⠀⠀⠀⠘⣇⠀⠀⠀⠈⢫⣍⣉⣩⣤⣤⣶⣿⠟⠀⠀⠀⠀⢀⣼⣁
⠀⠀⢸⢷⣄⡼⠁⢼⡀⠀⠀⠀⣀⠼⠣⡀⠀⠐⠫⣉⣛⣛⣿⡿⠟⠁⠀⠀⠀⠀⣠⠊⠀⠈⠉⠓⠦⣄⡀
⠀⢰⢫⣷⡿⣷⡴⠃⢨⠛⠛⠉⠁⠀⠀⣿⢷⣤⣀⠀⠈⠉⠀⠀⠀⠀⢀⣠⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⢰⣿⣿⡟⠀⠙⢦⠔⠁⠀⠀⠀⠀⠀⠀⣿⢼⣧⣈⡉⠓⠒⠒⠒⠒⠋⢉⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦
⠈⠛⠋⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⢀⣀⣿⣤⣷⣿⣽⣿⣿⣿⣿⣿⣿⡯⣇⣸⣧⠀⠀⡴⠒⠒⠒⠶⠶⠤⣤⣄⠃⣠⠷⢤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠁⠸⣇⣷⣺⣿⢻⣿⣿⣛⣻⣿⡿⣽⣿⣙⣶⣾⠇⠀⠀⠀⠀⠀⠀⡸⢉⠉⠁⠀⢀⡇⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⠀⠀⠀⠀⠀⠀⠀⣳⣾⡇⢀⣤⠎⢠⡶⠃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⣯⣽⣿⣭⣯⣿⢷⣿⣿⣿⢧⡀⠀⠀⠀⠀⢠⣎⡀⠳⠟⠉⢀⡠⠚⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣽⢿⢻⣟⣻⣿⡾⣿⣿⣿⣻⣭⣿⣿⡷⠻⣄⠀⠀⠀⢸⣼⡿⣆⠀⢰⡿⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⣿⣿⣯⣿⣿⣮⣭⣿⣽⣽⣽⣿⣟⣲⠿⣮⣷⣽⡄⠀⠀⠸⣯⣻⢿⡖⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣟⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣞⣟⣿⡄⠀⠀⠈⠙⠾⣧⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣯⣭⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⣥⣧⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢻⠿⠻⣿⣿⣷⣶⣶⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠻⠿⠿⠿⠿⠛⠋⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⣟⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⢾⣛⣿⣭⠽⠿⡟⠚⢟⢷⣄⠄⠊⠁⠀⡀⠁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢽⡿⠛⣿⠉⣷⣿⣀⣁⢹⡤⠈⢧⢿⣧⠤⣤⡀⠀⣤⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⣁⢠⢿⢈⣿⣿⣧⡁⢣⣿⣰⣸⣬⣿⣄⣾⣧⠴⣆⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⢸⣇⢸⣙⣿⣿⡿⣿⡟⣿⣻⣯⣵⣶⣷⣿⠿⠘⡘⢸⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣾⣟⣿⣯⣽⣿⣶⣿⣿⢿⢿⣿⣿⡿⡟⣿⡀⡆⠃⢁⣗⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⡟⣿⣧⣘⢻⡏⣿⣿⣿⣾⣿⣿⡟⠁⢧⢹⣧⣰⡰⠐⢸⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢳⠈⢻⠿⣿⢿⠛⢿⣿⡏⢀⣀⣷⣤⣼⣼⢿⣿⡷⠷⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⡆⠘⣆⣠⣼⣦⣾⣿⡿⢿⣿⣛⣿⣿⡷⢿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⢻⣿⣛⣿⣩⣿⣤⠿⠳⢻⡟⠛⠛⠁⠀⢸⣧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣏⠙⠛⠛⠉⠈⢶⣶⣾⣿⣥⣀⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣽⣦⠀⠀⠀⣴⣾⣿⣿⣿⣿⡿⠿⠂⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠛⠛⠿⣿⣷⠟⠀⠀⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣠⣄⣤⣤⣴⣿⣿⣿⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠠⠤⠔⣒⣦⡤⠤⣀⣀
⠀⠀⠰⠒⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢤⣠⣄⡀⣴⣿⣷⣦⠀⣾⣣⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⡀⠀⠤⠀⠀⠀⠀⠐⢦⡄⠀⠲⣭⣻⣿⣿⣯⠉⣥⣿⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣿⣏⡑⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⢻⣿⣿⣿⣷⣿⡿⢤⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⡜⠻⣿⣿⠃⠀⠀⠀⠀⣴⣷⣴⡄⠀⢸⣏⢹⣷⣿⣿⣿⣿⣿⣿⡧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣆⠀⠁⠂⠀⠀⣠⠾⠟⠛⠿⠃⠀⠘⠉⠀⣿⣉⣻⣿⣿⣿⣿⣧⣼⠟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠙⣥⣶⣄⣀⠈⠁⠂⢀⠂⠀⠀⢠⡀⠀⢿⣶⣿⣯⣿⣿⣿⡟⠻⠛⠉
⠀⠀⠀⠀⠀⠀⠈⢹⠟⠀⠀⢸⣿⡏⠉⠉⠉⠁⠀⠀⠀⠈⠁⠙⠁⠈⠛⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠾⠂⠀⡀⠀⠀⢠⣼⣿⣿⣷⣴⣤⡴⠋⠀⠀⠀⠀⠚⣦⣤⣾⣸⣿⣿⠟⠁⠐⢆
⠀⠀⠀⢰⣴⣀⡩⠀⠀⠠⣾⣿⣽⠟⣿⣿⣟⠁⣼⠁⠀⠀⠀⠀⠙⢿⣿⣯⠈⠡⣾⡇
⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠳⠉⠀⠘⣿⡇⢠⣀⣀⠀⠀⠀⠀⠀⠀⣸⣿⣯⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠈⣿⣿⡅⠀⠀⠀⠀⠘⢃⣿⡷⠀⠀⠸⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⣴⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣁⣴⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡧⠀⠀⠹⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠇⠀⢄⣀⣤⡦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣄⠀⠄⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⣿⡟⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⣿⣿⣿⣤⠰⠁⠀⠀⠠⠄⠀⠄⠠⠤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⣤⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠹⢹⠟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣻⣭⣩⣿⠂⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢠⣡⣧⣏⠀⠀⣀⣤⣿⣿⣿⢟⣽⣿⣿⣿⣿⢟⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣟⣠⢾⣯⡿⣛⣋⣵⣾⣭⣿⣿⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣾⣯⣭⡵⣿⣝⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⢠⢋⣺⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣾⣏⠷⠾⠿⠿⠋⠀⠀⠉⠑⠒⠠⠤⣀⣀⣼⡿⠁
⠀⠀⠀⣾⣿⣿⣿⠏⢸⣿⡿⢽⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣶⣶⣤⣤⣤⣤⣤⣾⣷⣿⣿⠉⠙⠿⢷⣦⣤
⠀⠀⢰⣿⣿⣿⣿⡄⠘⣿⣿⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠃
⠀⠀⣿⣿⣿⢯⣿⣧⠀⠹⣿⣿⣿⣾⣿⣷⠏⠉⠹⠋⠛⠛⠛⠛⠛⠉⠁⠀⢠⣿⠟
⠀⠀⠻⣿⣯⣿⣿⣿⣷⣼⣮⣻⣿⣿⡿⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⢀⡞⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⢠⣿⣶⣤⣤⣀⣀⣸⣿⣿⣿⣿⣿⣆⣀⣀⠀⡌⠀⠀⠀⠀⠀⣠⠞⠋
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣠⡴⠛⠁
⣿⣿⣿⣿⢛⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡲⡀
⣿⣿⡿⢿⣸⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢳⣄⢿⣿⡇
⠙⠹⠖⠉⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣻⢻⣾⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⢟⣥⣾⣿⣿⣿⣿⣿⠏
⣠⣤⣤⣄⣀⣀⣀⣀⣤⢠⣦⣨⡝⣸⣿⣟⣹⣿⠿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⢇⣿⣟⣛⡿⢿⡿⣶⣶
⠸⣿⣿⣿⡍⠙⠛⠛⠿⠟⠿⢯⣿⣿⣿⣿⠿⠣⠾⠟⠁
⠀⢹⣿⣿⣿⣀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁
⠀⠈⠛⠻⠿⠿⠃⠀⠀⢸⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⣿⣿⣿⣷⣶⡄

⠀⠀⠠⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡴⠦⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⢤⡄⠀⠀⠀⠠⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡷⠈⠄
⠀⠀⠀⠁⠀⠀⠀⢮⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⣼⣯⣀
⠀⠀⢠⣄⠐⠀⠀⢶⢉⡀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⢀⡄⠀⡀⢀⡀⠀⠒⢠⠂⠂⠀⠀⠀⠘⢁⣽⣅
⠀⠀⠀⠙⠢⣀⠀⠈⢏⢧⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠉⠁⠀⠀⢀⠈⠁⠀⠀⠀⡤⠀⠈⡁⠰⠆
⠀⠀⠀⠀⠀⠈⠓⠀⠈⠯⠢⠀⠀⠀⠈⠋⠀⠀⠂⠀⠀⠀⣧⡆⠀⠂⢶⠀⠀⠀⠀⢀⡀⠀⠀⠙⠃⠶⣄⠀⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⡰⠂⢠⡄⠀⠀⠠⠰⣆⠀⠀⠀⡧⠀⠀⠈⣧⠀⠀⠀⠈⠡⠋⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠦⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⢆⣀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠙⢂⡀⠀⠀⠀⠀⠉
⠀⠀⢰⠃⠠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡂⠂⠀⢀⡤⠶⠟⢀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⣠⠀⠀⢀⡤⠖⠂
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⡄⣸⢃⣤⡦⠀⠀⠂⠀⠀⠀⠔⠀⠠⠄⠀⠀⠂⠀⠐⠠⢶⠀⠀⠀⡾⠀⠀⠀⠂⡀⣠⠄⠀⠀⠘⡆⢨⡤⠖⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⠙⠛⠙⡆⠐⠂⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠐⠳⠀⠓⠀⠀⠀⠑⠋⠁⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠁
⠀⠀⠢⢂⡀⠀⠠⠀⠀⠀⠈⢀⠀⠀⡀⠀⠠⠀⡀⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠁⠈⠋⠉⣉⣉⡓⠦
⠀⠀⠀⡈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣼⠁⢰⡇⢄⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠠⠀⠀⠀⠘⠇⠀⠈⠙⠻⢛⢫⡢⡀
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢠⠆⠐⠐⠈⠘⠃⠀⠾⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠑⠒⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠿⠗⠈⠢⢑⡇
⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⡟⠀⠀⠀⠀⠀⢰⠀⠀⢀⣀⠴⠒⢦⣀⡀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢢⡄⢀⣠⠴⠺⣁⠄⢈⢀⠄⠀⠀⣀⠀⠀⣠⠒⠁⠀⠀⠀⠀⠁⠈⠀⠀⠆⠀⠀⠀⠀⠈⠂⠀⠒⠒⠁⠀⠀⠸⠇⢸⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠸⠁⠌⠁⠀⠀⠘⠀⠘⡄⠀⣦⣠⣟⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠠⠀⠻⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠉⠁⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡀⠀⠀⠀⠀⣠⡶⢶⣦⣤⠖⠋⠉⠁⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢹⣿⣿⣿⣿⣿⣿⣶⣤⣤⣼⣿⣵⣿⣯⣥⣼⣷⣶⡶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠗⠀⠠⣁⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠟⠛⠛⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣦⡀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⡉⠋⠛⠆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡙⢛⣿⣿⣿⣿⣀⣤⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠄⠀⠀⠘⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⡆⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠷⠤⣀⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠈⠉⠈⠉⣽⣿⣿⣿⣿⠃⠀⠀⠼⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢻⣿⡀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧⣠⣄⠀⠀⠈⠛⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⡇⠀⠻⣷⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⡿⠟⣿⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⣤⣶⡡⠔⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢈⣴⡿⡄⢠⣾⢟⣼⣿⣀⡤⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠴⠾⠟⣡⣾⠁⣿⣿⠿⠟⠛⢩⢰⣟⡀⣀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡀⣠⠞⢀⣤⣸⣿⠀⠈⠓⡂⠤⠿⣿⣿⣶⣏⣥
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣴⣤⣧⠈⣟⢸⡾⣿⠏⡝⠁⠀⠀⠀⠀⠀⢙⠻⡅⠙⢿⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣶⣾⡟⠁⢿⣤⣾⣿⣿⣭⢹⣶⣤⡀⠀⠀⢀⣀⢨⠀⠘⠂⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠜⣿⣛⣭⣖⣯⣽⣇⢿⣿⣿⣶⡄⣾⠋⠸⠃⠀⠀⠀⣡⣀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡞⣷⣍⡻⣾⣿⣿⣿⡇⠹⠀⣎⠀⠠⠀⠈⠋⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣜⢿⣿⣿⡿⡿⣷⡇⠀⠸⣿⡢⣴⣶⣶⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣮⣿⣷⣽⢿⣿⡆⠀⠀⡀⠀⠉⠻⣿⣿⣯⣉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣍⡻⣿⡟⣷⠒⠈⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣧⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠃⠘⠙⠂⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢨⠗⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠎⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⠂⣀⠄⠀⠀⡀
⠀⠀⠀⡌⠁⠀⠀⡄⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠁⠀⠀⠀⠀⢠⠜⠋⠀⠐⠀⠀⠁
⠀⠀⠀⠀⡀⠄⠊⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠄⠀⠄⠌⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠲⣍⠳
⢀⠊⢉⠉⢳⡀⡤⡄⠀⠀⠀⢠⠊⠁⢉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⠀⠀⠀⠀⠊⠁⠔
⠸⣀⣈⠤⠈⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⢊⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⠀⠀⠀⠄
⠀⠀⠀⠀⠖⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⢀⣄⠀⠀⡀
⠀⠀⠀⠀⢄⠀⠀⠀⠀⢼⢀⠀⠀⠐⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠉⠂⠀⠰
⢠⠂⠛⢦⠀⠉⠀⠀⠀⠈⠀⠉⠒⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠻⣄⣠⡾⡁⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⠀⠀⠐⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠙⣷⠀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⡽⠃⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡙⠂⠙⠢⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠁⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣯⡑⡄⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣷⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⡆⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣄⢠⣴⣦⣴⣶⣶⡤⠤⠄⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠉⠛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⢿⣿⣿⣿⣿⡟⣼⠋⠀⣿⣿⣿⣿⣿⣿⣿⣯⡚⣿⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠏⠀⠀⢠⣽⣶⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣾⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⢹⣧⡿⠇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⢀⣠⣿⣿⣿⣿⣿⣿⣿⣏⣴⣿⠇⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣾⡟⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣯⡿⠋⡀⠀⣿⣿⣿⣿⣿⣿⣟⡿⠛⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣭⣶⡿⠁⢠⢸⣿⡟⠻⣏⡁⠀⠀⢀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠟⠀⠀⠄⢸⣿⠁⠀⠈⢍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣠⠴⢾⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⠁⣸⣿⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⡘⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⠋⠀⠀⠀⠀⠀⠁⢀⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠂⠉⠉⠉⠉⠉⠉⠁⠐⡒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⡀⠠⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠤⠀⣤⠄⢠⠖⣀⠠⠤⠄⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⡀⢠⠆⢰⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠊⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⢀⠞⢁⠜⡷⠒⢎⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠀⠇⠄⠁⠤⣧⢀⣠⡆⠀⠒⠚⠓⠒⠠⡄⠀⠀⠀⠀⠀⠀⡘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡴⠀⠀⠀⠀⠤⠤⠚⠁⠀⠠⣄⠀⢰⡃⠀⢀⠴⠁⠀⠊⠀⠀⠀⠀⢀⡠⠔⠃⠀⠀⠀⠀⠀⢠⠃⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡠⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠀⠀⣴⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⢾⡄⠀⠨⠄⠒⠂⠀⠀⠀⢀⠈⠀⠠⠖⠻⠊⠀⠀⠀⠀⠀⠀⠀⡔⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠄⠀⠀⠳⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣀⠀⣷⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡇⠀⠀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡟⠀⣬⠟⢀⡵⣄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡠⠖⠲⢧⣠⡦⡀⠐⢸⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠲⣖⢟⣒⣓⣄⣽⣄⣎⣷⠦⣭⣭⣤⡀⠒⠒⠂⠀⠀⠉⠉⠀⠀⠀⠀⡇⢀⠀⠀⡃⢀⣸⠀⠉
⠀⠀⠀⡔⠚⠉⠉⠀⠉⠉⠁⠒⠢⠀⠜⠁⠀⠀⠉⠉⠙⡭⠋⠀⠟⠁⠙⠃⠈⠁⠀⢙⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃⠈⢳⠚⠉⠉⢈⠇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠓⢒⢊⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢂⠀⠀⠀⠀⠤⠤⢀⠀⠚⣄⠀⠀⢀⠀⣀⠠⠄⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠃⢰⡀⠈⠀⠐⠚
⠀⠀⠀⠀⠀⡄⠠⠱⡀⠀⢺⡗⠀⠀⠀⠀⢠⠌⠀⠀⠘⠀⠀⠈⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠇
⠀⠀⠀⠀⠳⣙⢦⡑⣌⢶⡥⠛⠀⢡⠀⠈⠀⠀⠀⠀⠀⢀⠤⣪⠔⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⡄
⠀⠀⠀⠀⠀⠈⠲⠛⢧⡋⠀⠀⠀⠀⣃⠀⠀⢀⡠⢔⡪⠖⠋⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⣯⣽⠿⠕⠛⠃⠀⠶⢰⠖⠒⠂⠻⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠻⠟⠋⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠈
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣠⠤⣆⡀⠀⠀⠀⠀⢀⠂⠀⠠⣧⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠚⠉⠁
⠀⠀⠀⠀⠛⠉⠂⠀⠤⠄⠨⠉⠙⠳⠶⠤⣤⣤⣤⡾⠶⠾⠛⠉⠡⠤⠤⠤⢤⠭⠴⠆⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠈⣨⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠁⣀⣀⣀⣽⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠋⠘⠛⠃⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡏⠁⠉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⣴⠄⠤⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠛⠉⠛⠋⣋⠁⠿⠉⠙⠻⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⡟⠈⠃⢿⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠡⣤⣦⡴⠀⠉⠀⠈⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣾⣿⣿⣿⠟⠀⠀⠀⠀⣰⣿⣾⠃⠀⠐⣦⣴⠶⠀⠰⠙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠴⡗⣈⣄⠖⠀⢰⣿⣿⣿⡟⠀⠀⢐⡦⠀⢩⡏⠁⠀⣀⣠⣿⡏⠀⠀⠘⣀⠜⠟⠉⠻⠃
⠀⠀⠀⠀⢀⠁⠀⡄⠀⠀⢸⣿⣿⣿⡇⠀⡀⣸⣧⣶⣾⣿⡶⢶⣼⠻⣿⣿⣶⣶⣶⣿⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⣿⣿⣿⣇⠌⣠⣿⣿⣿⣏⣥⣤⣴⡶⠶⠊⡿⢀⡈⢀⣼⡷⠀⣴⣀⣴⣿⣥⣴⠆
⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⢻⠿⢫⣼⡾⡋⠁⡀⢿⣿⣿⣿⣭⣀⠀⠰⢡⠞⣱⡿⠋⠀⢰⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣾⣿⣀⣰⣿⣿⣿⣿⣿⣿⡟⣀⢀⣠⣦⠤⠂⣀⣀⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣀⢀⡴⠿⣇⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣶⣾⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⢸⣏⣭⢃⠀⠘⣿⣦⡈⢻⣿⣏⣮⣹⣿⣿⣿⣿⣴⣷⡟⣿⣿⣿⣿⣿⠛⠉
⠀⠀⠀⣿⡆⠀⠀⠻⣿⣥⡲⡶⣀⣻⣷⣾⡟⡿⢿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣭⣥⣤⣄
⠀⠀⠀⡿⣿⠀⠀⠀⠀⠙⠡⣬⣿⣿⣾⡛⣡⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣏⠁⠀⠙⠃
⠀⠀⠀⢛⣿⡄⠀⠀⣄⠀⠀⠀⠉⠙⣻⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⡻⣿⣤⠀⠀⠀⢀⣀⡀⠀⠀⠀⣠⣾⠂
⠀⠀⠀⢸⣾⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣯⢻⣿⡉⠛⠻⠿⠿⠟⠛⠛⠋⠀⠀⢠⣿⠏
⠀⠀⣰⣾⣟⣿⠛⠓⠀⣤⠀⠀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿⠸⣿⣿⣿⣿⣶⣶⠒⣲⠲⠓⠁⢠⣿⡏
⠀⠀⠈⠉⢻⣿⡇⠀⠀⣷⠀⠀⠀⠀⡾⢰⣿⣿⣿⣿⠇⣸⣿⣿⡆⢸⣿⣧⣿⣏⠉⢿⣿⡿⣿⣁⡴⠤⢴⣾⣿⡀
⠀⠀⠀⠀⠸⣿⣇⠀⠀⣿⡀⠀⠀⣸⣇⣸⣿⣿⣿⠁⡐⣿⣿⣿⣦⠸⣿⣿⣿⣿⣷⡌⠛⣦⠈⢉⠀⠀⣰⣿⠋⠉
⠀⠀⠀⠀⠀⢿⣿⠀⠐⢿⡁⠀⢰⣿⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡀⠀⣾⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠸⣿⡇⠀⢸⡇⢀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⡇⣿⣿⣿⠻⣿⣿⣿⣻⣴⡏⠀⣼⣿⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢻⣿⡀⠈⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣇⠘⣿⣿⠋⣼⠁⢰⣿⠃⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⢻⠀⡏⠟⠉⠀⠈⣼⣿⣿⡟⠉⠿⠻⣿⡇⠈⣿⣿⣿⠚⠛⠡⠀⣿⠀⣼⠃⠀⠀⠁⡶
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣸⣇⢻⣀⣀⣀⣤⣿⣿⣿⣤⣤⣶⣶⣶⣷⣿⣿⣿⣿⡃⣀⣄⡀⣟⡰⣟⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⡶⠀⠀⠹⣿⡋⢻⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣛⣻⣿⣦⡀⠒
⠀⠀⠀⠀⣤⣦⣶⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣾⣿⠿⠟⠛⠛⢷⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠉⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢼⣯⣿⣶⣦⣄⣀⣀⣉⣉⣛⡓
⠀⠀⠀⠀⠀⠀⠀⠐⣙⢋⣭⣭⠉⠉⠉⠛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣭⣿⡯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⠛⠛⠛⠛⠋⠉⠛⠋⠑⠒⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢱⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢩⣿⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣾⣍⣩⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡭⣶⣦⣭⣽⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣰⣼⡇⠀⠈⣯⡿⢋⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⢠⣿⣿⣇⠀⠀⣻⣇⣸⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢻⡟⢻⡏⣿⡀⠀⣿⢩⡿⠹⣿⡾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠀⣸⣷⢿⣿⣾⣿⣿⡇⠀⠈⢻⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡏⢰⣯⢿⣻⠻⢾⣿⣿⣷⠀⠀⠀⠙⣿⣷⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣿⣿⣆⡟⣿⣚⠚⢢⢬⠿⣶⣿⡆⠀⠀⠶⠿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡟⠿⣧⣿⡛⣞⣿⣿⢻⢹⣿⡇⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⣸⣿⠿⣧⣏⣿⢸⢼⣿⣿⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⣿⣏⣃⣷⡇⣿⢻⣼⣿⣿⡀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⢠⡿⠳⠽⣿⣥⡿⠶⣧⢿⣿⡟⠳⢶⣤⣀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠈⠙⣶⣶⡟⠚⠛⠉⠹⣾⣿⡀⠀⠀⠀⠉⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⢻⢹⡇⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣾⡇⠀⠀⣠⣶⣾⣿⣿⣿⣷⣶⣤⣄⣀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣠⣴⡿⠋⠉⠿⢿⣻⣿⠿⠿⠿⠛⠀⠀⠘⣧⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄
⠀⠀⠀⠀⠁⠀⠀⠙⠋⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⡿⢋⣀⠇
⠀⠀⢀⣶⣿⣿⣦⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⡇⠀⠀⠀⠀⣄⣀⠘⠿⠿⠟⠁⠀⠀⢀⣤⡔⠁⠀⢀⡾⠁
⠀⠀⠘⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣤⣴⡄⠀⠀⠹⣻⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⢀⡴⣋⣴⡆
⠀⠀⠀⠀⠉⡙⠀⠀⠀⠀⠀⢠⣤⣤⡈⠍⠀⠸⠤⡄⠀⠀⡀⠑⢀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠙⢿⣿⠿⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡴⠶⢶⡄⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄
⠀⠀⠀⠀⣀⣠⣤⠶⠶⠦⣤⣄⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠟⠶⢤⣨⣽⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⢠⡶⠛⠉⠀⢀⣠⣤⣄⡀⠈⠙⣿⠒⠶⠖⢿⡀⠀⠀⠀⣸⡟⠙⠃⢰⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠈⢷⡄⠀⢠⣏⠀⠀⠈⠉⠲⢤⣈⠃⠀⠀⠘⠇⠀⠀⢀⣿⠀⠀⢐⣾⣿⠿⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠈⢿⣄⠀⠙⢷⡄⠀⠀⠀⠀⠈⣩⠶⠦⠤⠤⠤⠤⣼⠋⠳⣄⣈⡿⠁⠀⠀⣠⠟⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠹⢷⣤⣤⣹⣆⣀⣀⣀⣰⡃⠀⠀⠀⠀⠀⠦⣌⢳⡤⠤⢭⣥⣄⣠⣾⣁⣀⣀⣚⡛⢛⣛⣶⢦⣤⣀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡟⠛⣿⡟⠙⢦⣤⣀⠰⣌⣲⡼⠋⠀⠀⠀⠀⠀⠀⠈⢧⠈⠉⠉⠉⣏⠉⠉⠙⠛⠛⠛⢶⣶⡶⠶⣿⣷⡦⢴⣿⣲⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢰⡿⠁⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣄⣀⣘⣦⡀⠀⠀⠀⠀⣾⠃⢠⡀⣿⣠⣇⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⢻⡟⠉⠙⠛⠳⠶⢤⣿⠀⢸⠧⢉⠤⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠳⣤⡀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠈⠳⣾⣟⠒⢚⡇
⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢻⣦⡀⠀⢿⢸⡇⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠉
⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣜⣿⡇⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⢿⣏⠻⠇⠀⢀⣠⣴⠿⠋
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣤⣤⣦⣄⣀⣀⠀⠀⢻⣦⣤⡶⠟⠋⠁
⣸⣏⣀⣀⣀⣤⣤⣤⡴⠶⠾⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⠽⠿⠿⠿⣯⣿⡇
⣤⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⠉⠀⠀⠀⠀⠉⡆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠉⠀⠀⠘⠀⠀⢉⡈⠀⠀⡇⠀⠀⠉⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠤⠠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⠐⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢀⣄⣀⡀⠀⠀⠀⠤⠤⠀⢀⡀⠀⠀⠐⢂⠛⠛⠐⣒⠚⠋⡐⡂⠀⠀⠠⡄⠠⠤⣤⠄⠀⠀⣀⡀⣈⡀
⠀⠀⡌⠀⠀⠀⠀⠀⠂⢰⠀⠀⡆⠀⠀⠀⠸⠀⠀⠀⡇⠈⠀⠀⡇⠀⠀⠸⠀⢀⠀⠐⠀⢠⠀⠀⠀⠀⠀⢡
⠀⢠⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⡄
⢀⡀⠀⠀⠀⠀⠀⣤⢠⡆⠀⢼⠀⣦⠀⠀⠆⢸⠆⠀⡧⢰⠄⠠⡆⢰⡇⠀⡶⢠⡤⠄⣤⢠⡅⠀⠀⠀⠀⠀⢀
⠈⢁⠀⠀⠀⠀⠀⠰⠀⢠⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⢠⠀⠘⠀⢀⠃⠠⠀⠀⠀⠀⠀⠀⡈
⠀⠈⡄⠀⠀⠀⠀⠀⠂⠀⡄⠀⠃⠀⠆⠀⠈⠀⠀⠀⡇⠀⠀⠀⠁⡄⠀⡀⠀⠄⠀⠈⢀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠰⠀⠀⠀⠀⠀⠀⢂⡀⠀⠘⣠⣄⣀⡀⠀⢀⣀⢡⡌⣀⠀⡡⢁⣀⢡⡄⠁⠀⠂⠈⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠣⡄⠐⠂⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠐⠀⢠⠐
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⡤⠤⢤⣄⣀⣀⣀⠀⠀⢀⡄⡀⠀⣀⣀⣀⣀⠤⠤⣤⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠐⠙⠀⢢⠀⠀⡀⠰⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢀⡀⠀⠀⠈⠁⠷
⠀⠀⠀⠀⠀⠘⠀⢠⠀⠀⠓⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠙⠀⠀⠐⠀⡇
⠀⠀⠀⠀⠀⠘⡦⠃⠐⠊⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠄⣐⣀⠃
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡃⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠆⡉⠞⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠄⡑⢦⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣼⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠐⠆⠠⠤⣤⠒⠶⠶⠶⠶⠒⡦⠀⠐⠞⠀⠀⠀⢀⣻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⠂⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⡇⠀⠀⠘⠤⢤⡴⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠤⠄⢾⣀⣤⣤⣤⣤⢈⡧⠤⠤⠀⠐⠚⣷⠆⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⢀⣀⠟⢳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠶⢤⣤⡤⡂⣀⠃⣀⣭⠗⠛⠚⣯⣡⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠀⠉⡄⠀⠀⠀⡼⢂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡇⠀⠀⠀⣰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠘⡃⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠇⠀⢀⠆⠸⡇⢀⡤⢄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠢⠴⠌⡰⢆⠀⠸⠆⠘⢧⡡⠴⠴⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠑⢾⠀⠐⢼⡷⠊⠁⠀⠀⠙⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣤⣀⣀⣀⠀⠲⠦⠙⠁⠀⠀⠉⠠⠶⠀⣀⣀⣀⣄⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡜⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⡀
⠀⠀⠀⢰⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣼⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣀⡀
⠀⠀⠀⠠⣤⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣶⣶⣦⣤⣤⣤⣴⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⠛⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠤⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠈⠙⠻⢿⣿⣿⣿⣶⣦⣄⠦⢴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠉⢠⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⢀⣀⣄⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⠟⠀⠀⡼⠿⣿⢋⡠⠄⠀⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠙⢿⡏⠀⠀⠀⠀⠀⢰⣩⢆⠗⠚⠑⠒⢂⣀⠄⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣅⠤⣴⡎⡇⠀⠀⠀⠀⠀⠁⠀⣀⡀⠐⠒⠂⠣⠀⠀⠀⢀⠀⢸⣿⡇⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⠱⡌⠳⡸⣷⡟⠀⣇⠀⠀⠀⠢⣜⠀⣀⣀⠠⠎⠀⠀⣀⠐⢸⣇⠠⡟⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⣿⣿⣷⣤⡐⢌⢰⢠⡇⠀⠀⡐⠈⠀⠈⠀⠉⠀⠘⠁⠀⠀⠄⠈⣿⠀⢡⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠿⠿⠿⠷⠿⡈⢻⣿⣾⠀⠀⠀⠉⠢⠤⠀⢀⣀⣀⡠⠔⠂⠀⠸⡄⠹⣧⡾⠁⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⠹⣭⠀⠀⠀⠀⢀⠀⡜⠈⣿⣏⢄⠀⠀⠀⠠⣧⠀⡏⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢰⠃⠀⠀⠀⢹⡳⣦⣠⡄⣼⠀⡇⢰⡿⠋⠄⠀⢼⣆⠀⢿⣰⠟⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣣⠃⠀⠀⠀⠀⠘⣧⠀⠈⠑⠪⠒⠷⡾⠀⠀⡄⠀⠈⢿⡆⢘⣡⣤⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡀⠀⠀⠀⡀⢀⣿⣷⣄⡀⠀⠀⣸⠃⠀⢀⣿⡄⠀⠘⣿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡿⣄⠀⡀⠀⣸⣿⣿⣿⣿⣿⣶⣿⣶⣶⣿⣿⡗⠀⠀⠀⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⢀⣀⣌⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡸⢣⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠴⠛⠉⠈⠻⡿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣡⡆⠀⠀⠀⠉⢄⡰⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣴⡴⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢻⡿⠛⠻⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⡤⢤⠊⠀⠀⠀⠲⠰⢾⣧⣎⣶⣃⢀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⡇⠐⣤⠠⢠⠴⠆⢪⣧⠀⠠⠉⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⣰⡏⢸⡄⠸⠇⠀⠀⠰⠘⠇⣠⠂⣀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣁⡏⣧⠀⢿⡆⠀⠀⠀⠀⢧⢰⡿⠀⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠉⡐⣧⣿⠆⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢹⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢛⡉⡇⢼⡇⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣥⢜⡅⣿⢈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠏⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⡍⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢽⣯⣽⠀⠙⢦⣤⣤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⣠⣼⣄⣾⣾⣷⣤⡀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠿⠃⠀⠤⢀⡉⠓⠦⢄⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠛⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⣴⠀⠀⢀⢀⡍⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠺⢷⠀⢀⣈⠀⠓⣲⣶⣏⢠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⡟⢹⣥⣿⣿⣿⣿⡆⠀⢴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣤⣦⣿⠍⠉⠁⠀⠹⣦⡸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠏⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡐⣄⠀⠈⠓⢦⣀⠀⠀⠀⠋⠁⠀⢀⣉⣒⡆
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⢯⣳⣘⢷⣄⠀⠀⠈⠝⠓⠀⠀⠀⠀⢀⣀⡤⠉⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠛⢧⠀⠈⠉⠛⠛⢿⣶⣶⣶⣤⣶⣶⠶⠛⢋⡁⠀⠀⢀⠲⣤⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣭⣛⠀⠘⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⠀⠀⠈⠙⠲⠤⠬⠶⠆
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧
⠀⠀⠀⠀⠀⠀⣤⣾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⢛⡛⢿⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡡⠒⠁⠀⠀⠀⠈⢻⡝
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠉⠙⠻⢷⣄⡀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠛⠓⠾⣯⠔⣋⠀⠐⠂⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠐⡠⢀⡾⠋⠀⠀⠀⢀⢀⡀⠀⠑⢍⠛⠳⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠝⠃⠐⠆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠃⢡⠏⠀⠀⠀⠀⠀⠈⠑⠈⠢⣀⠈⢆⠜⠁⢀⠀⣀⠀⡀⠠⠐⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⡾⠀⡘⠀⠀⠈⠀⠀⠀⢀⣀⠤⠤⠐⠒⠈⠉⠉⠉⠙⢳⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠐⠉⠀⠀⠘⠀⢠⠁⠀⠀⣀⡤⠔⠊⠉⠀⠀⠀⠀⠀⣀⣁⠀⠀⠀⣸⢀⣴⠞⠁
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢾⠉⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠛⠲⢶⣟⠋⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠷⠦⣀⣀⣀⡤⠚⠁⠐⠀⠀⢀⠈⠁⠀⠈⠓⢦⣀⣠⣤⣬⡓
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⣤⣤⣤⣤⢤⡖⢹⡄⠀⡜⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⣴⣿⣿⡁⣹⣿⡶⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡇⠀⠀⠀⠀⢋⡠⠒⠢⣀⣀⠀⠀⠐⠒⠀⠀⣀⡿⢿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠠⡄⠀⠀⠀⠀⢸⣤⠤⠤⠌⢁⣈⡏⠀⣀⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣿⢦⡀⠀⠀⢸⡁⣠⠖⢁⣠⠄⣱⣦⣩⡏⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⢠⠇⣽⢛⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠛⠳⢦⡘⣇⢹⠈⠻⣦⠀⠢⠍⠁⠀⠀⠁⢰⢿⠈⢦⣄⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⢀⡞⢠⠇⡼⢫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢣⡾⠋⠉⠙⢶⡄⢻⣿⠈⡇⠀⠈⢷⡀⠢⠤⣠⡤⠴⠃⠈⠓⠦⣌⠙⢦⡀⠀⠀⠀⢠⡟⠀⢻⠋⠀⠁⠜⢡⣾
⠀⠀⠀⠀⢀⣤⣄⣤⠴⣋⡴⠋⠀⠀⠀⠀⠀⢻⣄⠏⢸⠃⠀⠀⠈⣷⠀⠀⡏⠀⠀⠀⠀⠀⠀⠸⣇⣀⡇⠀⠀⠀⢸⡇⠀⠀⠃⠀⠀⠐⢁⡟
⠀⠀⠀⠀⠈⠛⠒⠒⠛⠉⠀⠀⠀⠀⣀⣠⡤⠺⣧⡠⣿⠀⢀⡤⠖⢿⠀⠀⣟⡛⠒⠒⠄⠀⠀⢠⢟⣉⢳⠀⠀⠀⢸⡇⠀⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠺⠭⢣⡿⠀⣿⡴⠋⠀⠀⠙⠖⡖⠛⢄⠀⠒⢆⠀⠀⣾⡘⠸⠛⠀⠀⢀⡟⠀⢰⠶⠚⠉
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠘⠳⠞⣹⠃⣸⣿⡄⠀⠉⠉⠺⡄⢆⠀⡈⠀⠀⠈⢄⠀⠈⠃⠈⠀⠀⢀⡞⠀⣴⠇
⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠈⠉⠛⠲⢤⡾⠁⢾⠟⣹⠁⠀⡴⠂⠀⠈⠉⠉⠀⠀⢂⠀⡈⢦⠀⠀⡼⢻⢀⡞⠀⣸⠃
⠀⠀⣴⠋⢀⠄⠀⠒⠀⠐⠀⠤⣄⣀⣀⣀⠠⠔⠁⢠⠏⠀⠘⠀⠀⠀⠀⠀⠀⠀⡄⢸⡇⠈⠌⠳⣴⢃⣾⠋⠜⣰⠃
⠀⣼⠃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠓⠊⠀⢚⡡⠞⣹⠃
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢨⡇⠀⠀⠀⠀⠀⠋⢀⡖⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠚⠦⠤⠤⠄⠀⠀⣀⣀⣤⡤⠤⣤⠤⠤⠶⠞⠁
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⣆⡀⠀⢀⣀⡠⠴⠒⠋⠉⠀⠀⠀⠀⠙⡄
⠸⡆⠀⠀⠀⠀⠀⢀⣴⠞⠋⣹⠀⢾⠋⠛⠒⠒⠚⢋⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠙⢀⡀⢀⣀⠴⠋⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡄⢀⡾⠋⢇⠀⢿⣿⣿⣿⣿⣿⣿⡟⣻⡟⠿⡿⠁⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⠟⠡⠀⣾⠁⠀⠀⢠⠈⢿⣿⣿⣿⣿⢿⣽⢋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⣦⠀⠀⠐⢦⠀⡀⠐⠀⠑⣄⠀⠀⢀⡇⠀⣿⡷⣯⠗⢋⠄⠀⠀⣀⠠⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⡄⠀⠀⠐⠷⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣶⣬⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠸⡄⠀⠄⠀⡑⡤⠀⢶⠀⢀⣄⡘⠐⠚⠳⠶⣤⣀⠀⢼
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡤⢨⠀⠏⣠⠀⢧⠀⣆⠀⠐⣢⠶⣭⠋⠙⠛⠁⠉⢠⡆⣄⠀⠈⠙⢿⡄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣇⣺⠀⢀⡘⠇⠀⢇⢱⡉⠀⠀⠀⠉⠀⠀⣤⡀⠀⣶⢷⣿⠗⠆⠀⠐⡇
⠀⢀⣄⢺⠀⢀⠀⢀⠀⠹⢹⣷⡆⠈⠿⣀⣠⠘⣸⡆⠀⠀⠐⠃⠉⣈⣀⡈⠀⢃⠂⣿⡄⠙⠀⠀⠙⠲⠞⠀⠀⠐⠂
⢬⣦⣿⣿⣡⣤⡷⠖⣈⡤⣹⣿⠀⠀⡀⠸⡁⠀⠸⢻⡄⠀⣠⢶⡻⡖⠊⠉⢦⣀⠑⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀
⠈⠙⠛⠁⠋⣿⢾⡟⡏⠀⣿⠁⠀⠀⣇⠀⠀⣄⠀⠙⠁⠐⠣⣴⣶⣅⡀⣀⠀⠈⠉⣳⣦⡻⣦⣤⣄⣀⣀⠤⠤⣤⣤⣌⣂
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢹⡇⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠈⢻⣄⠉⠲⣍⠓⣄⠈⢻⣿⣿⣿⣿⣿⠿⢶⡄⠈⢋⠻⠿
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠃⠻⠎⠑⢄⠈⠣⠘⣷⣼⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⢸⡇⠀⡀⠀⠘⡄⠳⢄⣀⣰⣶⣦⣤⡀⠀⠀⠀⠀⠀⢀⡀⢀⢀⣀⢀⣼⡿⢿⣿⣿⣿⡿⣿⣷⡄
⠀⠀⠀⠀⡄⠳⠀⣷⠀⠀⢸⠖⣶⣶⣤⣍⡙⠛⠿⢶⣤⣤⣤⡶⢾⣰⢿⠟⠟⣉⡵⣶⠟⣻⣿⣿⡇⣿⣿⣯
⠀⠀⠘⡄⢷⡀⠀⠈⠀⠚⢡⢾⠃⠀⠉⢻⣿⣿⣷⣶⣶⣶⣲⣞⣛⣡⣴⣶⣿⣯⡤⠄⠞⣫⣿⡿⣸⣿⣿⡟⢀⢀⣮⠓⢀
⠀⠀⠀⠈⠈⢷⣄⣠⡤⣴⣶⠇⢀⣠⣤⠟⠉⠈⠉⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⠿⢒⣘⣿⡟⣰⣿⣿⣿⡧⢹⣾⠛⠄⢸⡆
⠀⠀⠀⠀⠀⠑⠊⠁⠈⠉⠙⡄⠀⣿⠋⠀⠈⠲⣄⠀⠀⠀⠲⣤⣀⣹⣿⣿⡟⠙⣿⣿⣿⣿⢠⣿⣿⡿⠏⢷⡀⢛⠳⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠙⢿⣿⣿⠀⠚⢩⣿⣿⡟⣸⣿⠟⢀⠶⠈⢧⣼⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢠⠀⡅⠀⠀⠀⠈⢷⡄⠀⠀⠀⠈⣿⡏⠀⠜⣁⢹⣿⣱⣿⠋⢠⣆⠀⠀⠀⠙⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠘⠀⡇⠀⠀⢸⡆⠘⣿⡀⠀⢶⡄⣿⠃⢠⢞⣥⡿⡟⣹⠇⢠⣸⣿⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡆⣷⠀⠀⣾⡇⠀⣿⣷⡀⢸⣿⣿⣰⣿⣿⣿⢃⠁⢹⣶⣿⠻⣿⣟⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⢻⡈⠀⢸⣿⠀⣠⣿⣿⣷⢀⣿⣿⣿⣿⡿⢋⠜⠀⠈⠻⣿⣆⠈⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠾⠿⠿⠿⣿⣿⣿⣿⠿⠿⢿⣿⠟⠁⠀⠀⠀⠀⠈⠙⠃
⣿⣿⠟⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡤⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡀⠀⠀⠀⠀⠠⠤⠀⠀⠄⠁⠀⡄⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠡⠀⠀⠀⠠⠀⡀⠀⠀⠀⢨⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠥⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠁⠀⠀⠈⡶⠀⠀⠀⠀⢀⣃⢴⠏⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠴⣰⡎⠉⠑⢤⠀⠀⠿⠋⠀⢀⣴⣶⠢⡀⠀⠰⢀⣤⡠⠖⢫⢆⠎⠾⠿⠋⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⢇⠀⠀⣀⠀⠈⠛⠁⠀⢸⠀⢠⠜⠉⠀⠀⢠⠎⢀⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡄⠀⠈⠢⣙⡀⠀⠀⠀⠀⣼⠴⠉⠀⠀⠀⣡⠟⠀⠀⢀⡈⠱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠈⠢⡀⠀⠀⠑⠲⣾⣿⡿⠃⠀⠀⠀⣠⠚⠁⠀⠤⠬⠊⢀⣀⡐⠒⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢁⠔⠈⠀⠀⠀⢀⣉⣛⣆⠀⠀⠀⠈⠋⠀⠀⠀⢠⠞⠁⠀⠠⠄⠀⣾⠟⠉⠉⠙⠳⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠄⢰⠃⢀⠤⠤⠤⠾⠋⢩⠉⠛⢳⡄⠀⠀⠀⠀⠀⣴⠠⠽⠀⠀⠀⠐⠀⠙⠀⠸⡞⠆⠀⢻⠀⠀⠀⠉
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢘⠀⠘⠀⠀⢠⡄⠀⠀⢰⠀⠘⡴⠋⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⡀⠀⠆⠀⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠰⠆⠀⠀⠄⡡⠋⠀⠀⠀⢀⡴⠙⢦⡀⠀⠀⠈⠢⣀⠀⠀⠊⠀⠱⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣵⢦⡀⠀⠀⠀⢠⡰⠊⠀⠀⠀⢀⡴⣿⣿⣄⢰⠟⠢⣄⠀⠀⠈⠳⡄⠀⠀⠀⠀⣿⡏⠁⠉⠉⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣦⣁⠿⣷⡤⣽⣡⠞⠁⠀⠀⢀⢴⡿⠀⠃⠀⠙⠳⠀⠀⢸⣳⣄⠀⠀⠈⠣⡀⠀⢀⠘⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠋⠰⢿⠁⠀⠀⢀⣴⠏⠈⠀⣀⠈⠀⠀⠀⠀⠀⠘⣽⢻⣷⢄⡀⠀⠘⠀⠀⠠⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⢠⣾⡏⠢⠤⠔⠈⠄⠀⢠⡀⠀⠀⣴⡀⠀⠀⠀⠀⣿⣷⡙⠆⢻⣷⣎⠐⢠⣀
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⢻⠿⠁⣼⡗⠀⠀⢠⣶⠁⠀⠀⠀⠁⠠⣄⠈⠡⣆⠀⠀⠰⠛⢿⣇⢦⠠⠛⢿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢾⡟⠀⠀⠀⠀⠀⠀⠁⠀⠠⢬⡶⠄⠁⠀⠈⡯⠀⢁⠀⠀⠀⠀⠀⠠⠀⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠌⠃⠘⠁⠀⠀⡀⠀⠀⠀⠀⠀⠐⠻⠁⠎⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⣦⡆⠀⠂⠀⠀⠈⢀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⠀⢤⣀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠒⠒⠒⠒⠲⠶⠤⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⣀⠀⠀⠀⠈⣁⠰⠖⠐⠚⠉⠉⠉⠈⠉⠀⠀⠒⠒⠒⠒⠀⠉⠛⣠⡶⠖⠛⠉⠉⠉⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣯⡥⠖⠀⡀⠀⠀⠀⣀⠰⠋⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠖⠚⠛⠉⠉⡀⠋⣀⠴⠒⠶⠃⢀⡄⢊⡁⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠐⣠⣄⣀⣀⡤⣄⠾⠋⠁⠀⠀⢰⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⡆⢸⡆⢀⠴⠂⠀⠀⢀⣠⠞⢀⣀⠀⠈⣉⣥⣆⣀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⣿⣄⢻⡾⠅⠈⣀⠤⠄⠀⠀⠀⠀⠀⣸⣴⣿⠿⢛⣿⣿⣿⣷⣥⣤⣴⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠻⣌⠹⣄⢈⠿⢏⠑⠆⣠⡟⡰⠲⡜⢶⡶⠋⠀⠘⣿⣿⣷⣉⣹⣯⣿⣿⡿⠿⢿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡈⢖⠉⠠⡀⠈⠳⣏⣾⡗⠀⠐⠉⡈⠁⠀⢀⣼⠂⠉⠛⠿⣿⠿⠟⠋⠀⠀⠈⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠣⡀⠉⣢⣴⠶⢶⣤⣥⠀⠲⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀⣤⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡟⠛⠉⠉⠉⠀⣸⠉⠉⠓⠛⠳⢶⣟⣈⠀⠲⠀⠀⢀⠀⠀⠀⠀⠀⠐⠺⡅
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠸⠃⠀⢠⠄⠐⠂⠐⠦⠄⠶⠄⠴⢾⣿⣶⣶⡶⠀⠲⠶⠶⣴⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⢶⠶⣦⠂⠄⠠⠄⠠
⠀⠒⠒⠒⠒⠦⠼⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⣀⠏⠉⠍⠉⠀⠀⠀⠀⠀⠀⠀⠸⢏⠀⠀⠀⠀⠀⠛⠂⠘⠃⠘⠳⠶⢶⡴⢶⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⠀⠈⠙⠉⠙⣏⠀⡀⠀⢱⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⢀⣀⣀⠴⣧⠀⠡⠀⠈⢡⡙⠲⣤⣦⣄⣀⡀⠀⠀⠀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⠤⠞⠀⠀⠀⠀⠀⢁⠀⠈⠉⠙⢛⣿⠛⠋⡃
⣀⣀⣀⣀⣠⡴⢦⣤⣀⣀⣀⣀⡀⠤⠛⠻⣿⣿⠀⠀⠀⠀⡀⠀⢆⠀⣆⠀⠀⠛⡿⠋⠀⠈⠣⠘⠛⢠⠶⠀⢀⣀⣀⣀⣀⡤⠤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⠑⠂⠐⠃⠀⠈⠀⠘⢳⣖⠊⣀⠀⠠⠌⠀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠤⠤⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠄⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠀⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠸⠃⡐⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⢀⠄⠀⣠⠊⠀⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⣠⠃⠀⡠⠃⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡖⠁⢀⠄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠤⠸⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠲⠃⠈⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠴⢧⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⡄⠂⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣠⣤⢃⠀⠰⢿⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠄⠀⣿⠀⢀⡀⠀⢤⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣷⡶
⠀⠀⢀⣠⡄⣤⣄⠀⣠⢶⣡⡖⠷⡏⠀⠈⠙⢶⡶⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⢦⣤⣡⡄⠐⠶⠆⠀⠉⠉⠉⠉⠁⠸⠋
⢠⠞⢁⣤⣤⣤⣼⣿⣥⣎⡉⢽⣦⣼⡷⠾⠷⠶⡶⢆⣉⣛⠃⢤⣤⡄⠤⣴⡶⠶⠂⢉⢉⡉⠉⢰⡄⠁⢒
⣇⢠⣀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⢈⣿⠿⢛⣒⣾⣿⣿⣿⡀⢠⡀⠂⠀⠶⡀⢔⣠⣿⡌⣧⣄⢈⣇⣀⡉
⠙⠷⣬⣅⣀⣀⣀⢁⡴⠦⠛⠲⠶⠞⠋⠂⠈⢹⠇⠹⣿⣻⣷⣭⣶⣎⣥⣼⣿⠾⠿⠟⠛⠉⠁⠈⠁⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠑⠁⠼⢷⣽⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠁⠰⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⠛⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠁⠰⠀⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣧⣄⡀⠀⠀⠂⠐⠂⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠦
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⠞⠀⠈⢙⠷⠦⣀⡐⢀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⣄⣠⣿⠀⠀⠀⠈⢻⠁⠀⢏⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⢠⣾⣿⣯⠟⠁⢸⣼⠟⠷⣦⠄⢀⣸⣁⣠⣾⢿⡻⣦⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⢠⡏⢑⣿⠈⠀⠀⠈⠇⠀⠀⠻⠀⠘⣽⠛⢋⢿⡌⣷⣙⢷⡀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⣿⠀⡟⠀⠀⡄⠀⠀⠀⢀⠀⠀⠘⡆⠙⠺⡂⠀⠀⠘⣥⡜⢷⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠛⣄⠀⠀⡀⣇⠀⡄⠀⣽⠀⢀⠀⡇⠀⠀⡇⠀⠀⣀⣿⣷⠂⠰⣀⡾⠁
⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠛⠿⠞⠛⡴⠾⣷⣥⣴⣶⣷⣶⣾⠏⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⢀⡀⠀⠶⠆⣰⣿⣿⣹⣿⣾⣭⣿⣄⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⢿⠉⠉⠙⠉⠋⢶⡾⣿⣿⡿⠟⠉⠁⢀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣀⣀⢈⣷⡴⠁⣍⡀⠀⠀⣀⣠⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠺⣿⠃⠀⠀⠙⢶⣿⣏⡿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠿⣿⠀⠀⠀⠀⠰⣿⣷⣭⣿⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡸⣿⠀⠀⠀⠀⠀⣿⣯⣛⣮⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠠⣻⡟⠀⠀⠀⠀⠀⢻⣿⣿⣷⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣑⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠢⡾⣇⠀⠀⠀⠀⠀⠀⠀⣿⢿⠏⠉⢣
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢠⣦⠶⠟⠀⠀⠀⠀⠀⠀⠀⠿⠶⣤⣄⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢦⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣲⣄
⠀⠀⠀⠀⠀⢠⡎⢲⡀⠀⠀⠀⠄⠀⠂⠀⠏⠋⠋⢉⠍⠁⠀⠀⠑⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⡀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠘⠁⠀⠋⣠
⠀⠀⠀⠀⠀⠁⠀⠀⣳⠀⠇⠀⠐⠆⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠃⠰⠄⠠⠶⠀⠐⠅⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠈⡀
⠀⠀⠀⠀⠀⠇⢃⠈⠁⠀⠈⠤⠠⡀⢃⠀⠬⠁⠀⠄⠐⠕⠀⠀⠄⢈⠁⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⡄⠓⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠉⠘⢁⣀
⠀⠀⠀⠀⢀⠀⠀⢄⣀⡀⠐⡄⠠⠁⠀⠌⠀⠀⢢⠴⠁⠓⠀⠀⠀⠀⠀⠀⠌⢠⡨⠀⠀⠀⠀⠀⠀⠀⡏⠳⠅⠠⠰⠆⠀⠀⠰⠂⠀⠀⠀⠀⠀⡀⠀⠠⠤
⠀⠀⠀⠀⠈⠀⢨⡞⠡⠰⠀⠭⠣⠞⠀⠀⠃⠀⠐⠤⠀⠀⠀⠂⠀⠂⠀⠑⠰⠂⠀⠐⠀⠀⠀⠒⠀⠀⡶⡆⠀⠀⡠⡠⠀⠀⠀⠂⠄⠀⠠⠀⠀⠈⢖⠒
⠀⠀⠀⠀⠀⢠⣀⣀⠀⠠⠈⠄⠀⠠⠀⠀⠤⠠⢠⠤⣄⠀⠀⡠⢂⠐⠀⠀⡐⠀⠀⢀⠀⠀⠀⠀⠢⠀⢁⡀⠀⠐⢠⠁
⠀⠀⠀⠀⡠⠠⣅⠄⠀⠀⠀⠀⠀⠀⠠⢸⠉⠁⠀⠈⢸⠀⠐⠀⠁⠀⢀⢀⠁⠀⠀⡄⠠⠄⠀⠠⠀⠀⠀⠀⠄⠠⠄⠐⠀⢸⠀⠀⠆
⠀⠀⠀⠀⡀⣆⠀⠘⢂⡦⠀⠀⠘⠉⠉⢉⠀⠀⠠⠄⠀⠀⠁⢠⡀⢂⠸⠁⠀⠐⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⢀⠂⠔⠀⠀⠈⠀⠐⠀⠀⠆⣠⠎⠁
⠀⠀⠀⠀⠔⢋⠑⢆⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠃⠂⠀⠁⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠐⠀⠀⡀⠠⠈⠛⣠⡀⠠⠂
⠀⠀⠀⠀⠀⢨⠒⠸⠂⠠⠀⠀⠀⠀⠼⠂⡄⠀⠐⠀⠀⠀⠄⠠⠀⠀⢞⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡄⠀⠂⠀⠀⠈⠀⠒⠀⠀⠀⠀⠊
⠀⠀⠀⠀⢸⢛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠊⠀⠀⠁⠄⡀⠀⠀⠁⠳⡌⠘⢦⢀⣀⣂⢀⠅⠀⠀⠀⠀⠀⠀⠀⠇⢠⠁⠀⠀⢡⠀⠀⠀⢀⢾⡷⠊⠀⠖
⠀⠀⠀⠀⠐⠈⠃⠐⠂⠂⠀⠀⠀⠀⡀⢁⡀⣀⡠⠀⠀⢤⠀⠀⠇⠀⠈⢢⡁⠳⡀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠄⡏⡁⠀⠀⠀⠃⠀⠀⠀⠀⠄⠠⠄⠂
⠀⠀⠀⠀⡇⠠⠀⠀⠀⠚⡆⠀⠂⢀⠀⠀⠁⠁⠀⡉⠀⠈⠖⠰⠀⠀⣠⠄⠑⡄⠹⡄⢀⠂⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⡐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠁⢰⠀⠀⠈⠂⠀⠙⠈⠉⠙⠁⠐⠀⠀⠀⠀⠀⢐⡀⠠⢸⠀⠈⠉⠄⠲⡁⠀⠀⠀⠀⣄⣀⠀⠐⠂⠾⢿⡄⠄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣤⡀⠀⠀⠀⠀⢠⡀⠀⠀⠄⠈⠀⠨⠀⡃⠀⠀⠀⠄⠀⠀⠈⠉⡀⣀⠼⠀⠀⠀⠀⠴⠘⡄⠀⠈⠀⡀⠈⠀⣦⡶⠸⡏⠀⠀⡄⢒⠂⠐⡆⠀⠰
⠀⠀⠀⠀⠠⢄⣀⡀⢄⠈⡻⠀⢀⠀⠄⠀⢳⠀⠃⡀⠀⠠⠀⡀⠀⠀⠀⠈⠀⠠⡞⢳⠀⡀⢐⡃⠀⠀⠀⠨⠠⠀⠀⠀⠀⢨⡗⠀⠀⠀⠉⠃⣠⠁⠀⢀
⠀⠀⠀⠀⠀⠘⡐⠢⡄⠀⠁⠀⠀⠐⠈⣠⢲⠀⠀⠀⠀⠠⡄⠀⠀⠄⠀⠀⢠⠀⠉⠉⠀⠀⠀⠵⠈⠀⠀⣀⣀⡇⠘⠀⠃⢸⡇⠀⠀⠀⠀⠀⠐⠀⠀⡀
⠀⠀⠀⠑⢀⠀⠀⡡⢇⠀⠀⠀⠀⠈⠁⠙⠿⠶⠤⠀⠀⠀⢀⣄⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⣀⡄⠤⠓⠂⠈⠉⠙⢳⠄⣐⣴⣀⣀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠪⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠀⠁⠀⠀⠀⠊⠀⠒⠈⠓⠘⠃⠛⠈⠒⠁⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠢⢄⣀⠉⢀⡐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣻⣛⣛⣿⣫⣝⣻⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣭⣽⣿⣯⣭⣭⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠚⠑⠖⠲⠄⡀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢈⣦⡀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⡖⠄⣡⡀⢡⠰⡄⢄⠳⡄⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠉⢠⡉⠐⠊⠲⠇⢀⠙⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⠃⠀⠀⡄⠀⠈⠻⠂⠀⠀⠀⡀⠰⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡆⢀⡷⠃⠀⠀⠀⠀⢀⡔⠙⣤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⠬⣦⣀⣠⣴⡾⡃⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⡏⠻⠓⢋⣨⠴⠁⠀⣠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⡪⠐⠉⠙⢲⡴⠯⠤⠤⣤⡞⠁⠠⡇
⠀⠀⠀⠀⠀⠀⠀⣼⡄⠏⠀⠀⠀⠀⡎⠀⠀⠀⢀⠀⠙⠉⠲⠓⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠔⠊⢁⠀⠀⠀⢘⣄⣀⠔⠁⠀⠀⠈⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠈⢦⠤⣊⠥⠋⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡁⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠮⠅⢀⣉⡒⣤⠌⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⢰⢄⠀⢀⠀⠀⠀⠈⠃⠲⠀⠀⠀⢀⠀⠀⣀⣠⡤⠴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠄⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠄⠀⠀⠠⠀⠀⠀⠂⠀⢠
⠀⠀⠀⠀⠀⠀⢳⡀⠀⢤⣀⠄⠠⠠⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠂⠀⠊⠉⠑⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⣀⡀⠀⢂⠀⠂⠈⠒⠀⠀⠀⠀⡀⠀⠀⠛⠛⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠀⠁⠀⠀⠀⠐⠴⢦⡄⠀⠀⠐⠉⠀⠀⠀⠔⠈⡀⠀⠀⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢸⡀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⡀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠇⠀⠀⢀⠀⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠃⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀⠀⠰⠀⠀⠀⠀⠀⠄⠀⡀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⡤⠀⠐⠶⣄⡲⣦⡀⠀⠀⠠⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠱⠀⠀⠠⠾⠋⠴⠋⠠⠀⠂⡁⠌⠀⠀⠀⠀⠈
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢷⣾⠠⠴⠛⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡤⠶⣄⣶⣦⡤⢤⡀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠁⢰⡞⠛⢄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠚⠉⣦⣾⣿⣗⣶⣿⣟⡓⠠⣀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠈⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠁⠙⠿⣿⣿⠉⠉⣀⣀⣑⣤⣀⠤⠤⢤⣿⣖⣂⠘⠚⢋⠻⠯⠟⢂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⡁⠀⠀⢀⢶⣾⣶⣤⡟⠉⠉⣤⣄⠄⠀⠒⢈⡤⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡄⠂⢄⣀⠀⣧⣿⣿⣿⣶⣶⣾⣿⣿⣿⡟⠀⠰⠋⢹⠁⠀⠀⠀⠀⡖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠉⢀⣞⣭⣩⣿⣿⣿⠟⣿⣿⣿⣿⠟⢹⠅⠀⣇⠀⠀⠂⠀⠀⠀⣠⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⡃⢠⣙⣦⣽⢻⣶⣿⣿⡟⠁⠀⢸⠀⠀⠉⡀⠁⢶⣤⣀⡀⠌⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢨⡿⠥⠞⣹⣿⠟⠀⠀⠀⢸⣇⠠⠞⠡⠀⣼⡏⠁⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⠋⠀⠀⣠⡿⠁⠀⠀⠀⠀⢸⣙⣆⠀⠀⣸⣛⠁⠀⠀⠀⠀⠀⠀⠙⢧⡈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣰⣿⠀⠀⠀⠀⠀⠀⢸⣈⡉⠓⢛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡟⢸⡀⠂⠀⠀⠀⠀⠸⠀⠭⠖⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⡇⠀⠀⠀⠀⠀⠀⡟⠩⢧⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣠⣷⡄⠀⠀⠀⠀⠀⡧⠰⠟⠀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⣿⣆⠀⠀⠀⠀⠫⡀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⠃⠀⠀⠀⠀⠈⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⣻⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣽⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⣤⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠘⢾⠋⠀⠀⠀⠀⠀⠉⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⢀⣄⣀⣴⣾⣿⣎⣵⣾⣿⣷⣄⠀⠠⣄⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢻⣧⡀⠀⣿⡟
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⣿⠀⣿⣿⠇⣤⣿⠇
⠀⠀⠀⠀⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣾⣿⣼⣿⣿⣾⣮⡟
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠈⠛⣽⣿⣿⣿⣿⣿⡿⢋⣙⡻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠟⣿⣿⠟⠁
⠀⠀⠀⠿⠇⠀⢿⣿⣿⣿⡇⠘⢿⣿⣿⣭⣙⣻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡟⢡⡿⠿⣦⢀⣃⣾⠛⢿⣄
⠀⠀⠀⢀⣀⣀⣀⡈⠹⣿⣧⠲⣄⣉⡉⠋⠉⡁⢠⣶⣿⣿⣷⣦⣄⢀⣴⣾⣿⣿⣿⢃⢸⡇⠀⠈⣿⣿⣿⣦⣾⣿⣓⣲⣶⣄⡀
⠀⢀⠔⠁⠀⠀⠀⠙⢦⡈⢿⣧⡽⠥⠉⠋⠁⠀⣿⠏⠀⠀⠉⠛⢿⣿⠟⠛⠛⠋⠻⢁⣶⣿⣦⠘⢿⠟⠋⣱⣿⣵⣿⢿⣿⣿⡇
⠀⡘⠀⠀⠀⠀⠀⠀⠈⢧⠈⢿⣿⣦⣄⡀⠀⠀⣿⠀⢀⣤⠒⠀⠂⣙⣦⣀⣐⣢⣴⣿⣿⡗⠀⢀⣶⣾⣿⣿⡿⠟⣡⣾⣿⠟
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣿⣿⣿⣿⡷⣦⣽⣷⠿⠿⢧⠀⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠿⡿⣿⠿⠛⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣿⣿⣿⣸⣿⣿⣿⡔⣦⣘⣛⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠘⢿⣧⣹⣟⣻⣿⣶⣿⣿⣿⡿⠀⠀⠀⠀⣿⠟⣛⣿⣿⣿⣿⣋⠉⣀⣿⣧⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠘⢷⣄⠙⠿⢿⣿⠉⠙⠉⠉⠉⠀⠀⠀⠀⡰⠴⠋⢀⣽⢿⡟⢻⣿⠆⠋⠛⠻⣥⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣤⣙⠛⣷⣶⢷⠀⠀⠀⡀⠀⠀⠀⠀⢠⣷⠶⡾⠟⠁⠸⣇⣠⠋⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⣿⣿⣿⣿⡿⠋⠀⠈⢣⡀⠀⠻⣶⣤⣤⣤⣾⠗⠋⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠋⠀⣀⣤⠤⠈⠛⠶⠦⠤⢬⣭⣿⡿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⡀⠀⣉⠀⠀⠀⠀⠀⣀⣤⡉⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡶⠀⠀⠘⢿⣿⣷⣦⣤⠶⠶⠶⠶⣶⣦⣤⡐⢢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡶⠶⠶⢞⣻⣿⣿⣧⣤⡀⠀⠀⠙⠻⢿⣿⣿⣷⣶⣶⣴⣿⡛⠁⠉⠐⠂⠠⠦⢦⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠿⣿⣯⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣠⣄⣀⡉⠽⣿⣿⣿⣿⣿⣿⡿⠶⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠿⠻⠿⣿⠿⠛⠿⠟⠁⠀⠀⠀⠀⠉⠉⠉⠉⠙⠁

⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⢀⣴⣶⣾⡆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠴⣿⣿⣿⣿
⠀⠀⣤⣤⣴⣶⣭⣍⠀⠀⠀⢀⡉⠙⣿⠀⣿⠿⠿⠟⠰⣆⠀⢸⣿⣿⣿⡇⠀⠀⠘⠿⠿⠓⠲⠶⠦⣤⣽⠛⣿⣏
⠀⠀⡏⠀⢠⣿⡟⠻⣦⡴⠖⠛⠋⠀⣿⠀⠀⠀⣿⡇⣠⡾⠃⠀⠉⠉⢿⣿⣄⠀⠀⠀⠀⠀⠰⣷⣤⣀⡀⣼⣿⣿⡀
⠀⢠⣧⠀⣾⣿⢁⣀⣀⡀⠀⢀⡄⠀⣿⠀⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⡶⠶⢶⡦⠀⠀⠀⠉⠙⠋⢿⣿⣇
⠀⠈⠉⠀⣿⠛⠛⠛⢻⣿⠀⠊⠀⠀⣿⢀⣴⡿⣿⡇⠀⠀⠀⣠⣶⣿⣷⡄⠙⢿⡷⠶⠿⠷⢦⣄⣀⣴⠀⠀⣸⡿⣷⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠰⣷⣄⠀⢀⣴⣿⡿⠋⠀⢻⡇⠀⠀⠈⠻⣿⣿⣿⠏⠀⠈⣿⡄⠀⠀⠀⠀⠉⠃⣠⣾⠏⠀⢹⣧
⠀⠀⠀⠀⣿⠀⠀⢀⣠⣤⣀⣴⣿⠟⠃⠀⠀⠀⢸⡇⠀⠀⣀⣀⠈⠉⣷⣶⡄⠀⠘⣷⡀⠀⢸⠀⠀⢸⣿⠁⠀⠀⠈⣿⡄
⠀⠀⠀⠀⣿⣄⠀⣾⣿⣿⣿⡟⢷⡀⠀⠀⠀⠀⢨⡇⠀⠰⣿⣿⣷⣤⣼⣿⣧⠀⠀⠘⣧⣀⣀⠀⠀⢸⡿⠀⠀⠀⠀⠸⣷
⠀⠀⣀⡀⠀⠀⠀⠘⠻⣿⠿⠀⠈⠛⠳⠶⠶⡈⠉⠁⣀⠀⠈⠉⠀⠀⠈⣿⣿⡄⠀⠀⣘⠋⠁⠀⠶⠾⠿⠀⠀⠀⠰⠶⠿
⠀⣾⣿⣿⣷⡄⠀⠀⠀⠘⢷⡀⠀⢀⣤⣤⡚⠁⠀⠀⠹⠶⠖⠛⠛⠛⠻⠿⢿⡇⢠⣾⣿⣿⣦⡀⠀⠀⠀⣰⣶⣦
⠀⠻⣿⣿⠟⠀⠀⠀⠀⠘⠞⠀⠶⣿⣿⣿⣿⠀⢠⠀⠀⠀⣠⣶⣶⣄⠀⠀⢸⡇⠘⢿⣿⡿⢋⣁⣤⡶⠚⠛⠿⠟
⠀⠀⣶⣾⣧⠀⢠⣶⣦⣀⣀⣀⣀⣙⣻⣟⡋⠀⠸⠛⠄⠀⣿⣿⣿⣿⠋⠀⢸⡇⠀⢸⣿⠖⠛⠉⠀⠀⠀⢀⣰⣿⣿⣷⡀
⠀⠀⣿⠻⣿⣷⡘⠿⠟⠋⠉⠉⠉⠉⠹⣿⣷⠀⠀⠀⣠⣤⣬⣭⣭⠁⠀⠀⢸⡇⠀⢸⣿⠀⠀⢀⣀⡀⠀⠈⠻⣿⣿⡿⠃
⠀⠀⣿⠀⠙⣿⣿⣤⡶⠟⢷⣤⡀⠀⢀⢻⣿⣧⠀⠀⣿⡇⠀⣿⣿⠀⠀⣀⣸⡇⠀⢸⣿⣶⠾⠟⠛⢷⡄⠀⠀⢸⣿⡆
⠀⠀⣿⠀⠀⠘⣿⡁⠀⡀⠀⠈⠱⣶⡟⠈⣿⣿⡆⠀⢹⠃⠀⣿⣿⠀⠀⠉⠉⠁⠀⢸⣿⠀⠀⣀⠀⠈⢻⣦⡴⢼⣿⡇
⠀⠀⠀⠀⠀⠀⠹⣧⠀⠇⠀⠀⠀⣈⣴⠟⠋⠹⣷⠀⠀⠀⠀⢸⣿⣶⣶⣶⠀⠀⠀⢸⣿⠀⠀⠈⠆⠀⠀⠁⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⣾⠛⣁⣀⣀⡀⢿⡆⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⣸⣋⡅⢠⣀⡀⣀⣤⣤⠶⠞⠋⢸⡇
⠀⠀⠀⠀⠀⣠⣏⡁⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⡌⠻⣦⠀⠀⢸⡇⠀⠀⠿⠶⠄⠛⠉⣠⡌⠛⠃⠉⠁⠀⠀⠀⠀⢸⡇
⠀⠀⢀⡀⠀⠉⣉⠉⠀⠀⢠⣴⡿⠀⠙⠿⠿⠟⠁⢀⣽⣷⡄⢸⡇⠀⠀⠀⠀⠀⠀⣼⠏⠀⣀⣴⠆⠀⠀⢸⠀⠀⢸⡇
⠀⠀⡀⢳⣄⣰⡿⢷⣦⣀⠀⠀⠀⣴⣿⡿⠛⣿⠀⠀⡀⠀⠀⠘⢛⣧⣤⡀⠀⢀⣾⢋⣴⠾⠋⠁⠀⠀⠀⠀⠀⣠⣼⡆
⠀⠀⣧⣀⣁⣈⣀⣀⣈⣻⣿⣶⣾⣿⡟⠀⠀⣿⠀⠀⠿⠀⠀⢠⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠃
⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣞⣛⣿⣿⣿⣿⣿⣛⣒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡇⠀⠙⢦
⠀⠀⠀⣶⢶⡶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠙⣮⣽⡖⠛⠛⢛⣿⣛⠛⠿⢧⣷⡀⠀⠈⡇
⠀⠀⢀⣿⣿⣿⣿⣷⣿⣿⣹⠇⠀⠀⢀⠔⡫⠖⢆⠀⠀⢀⡤⠶⢮⠁⠀⠀⠈⠙⢦⣀⡇
⠀⠀⢸⢹⣿⣿⣿⣿⣿⣿⠏⠀⠀⡴⠃⢰⢁⣤⡜⠀⡰⠃⣠⡀⡼⠀⠀⠀⠀⠀⢸⣿⣧
⠀⢀⣾⣬⣉⡙⠻⢟⡿⡏⠀⢀⡞⠀⠀⠉⡾⠿⠁⠠⡇⣸⣿⡟⠁⠀⠀⠀⠀⠀⢼⣿⣿⠷⠒⠲⡄
⠀⢸⣉⡉⠛⠛⠻⠷⣾⠀⠀⡼⠀⠚⠁⠀⠣⠄⠀⠀⠉⠀⠀⠀⠁⠀⣤⣄⠀⠀⠀⠙⠋⢰⣃⠀⣿
⠀⠙⢾⠺⠽⣶⣶⣤⡏⠀⠀⣇⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢁⡎⠁⠀⠀⠀⠀⠀⣊⡴⠃
⠀⠀⢸⡀⢀⡴⠚⠉⠀⠀⠀⢹⡀⠀⠀⠀⠉⢖⠒⠒⠒⢊⣉⣡⣴⣾⡟⠀⠀⠀⠀⠀⢠⠏⠁
⣴⢊⠛⡶⠚⢦⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⠀⣜⠛⠿⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⡴⠋⠙⠓⠦⣤⣀
⣏⣁⣉⣧⣠⢟⠆⠀⠀⠀⢀⡴⠁⢸⣶⣄⡀⠈⠉⠒⠒⠚⠋⠉⠀⠀⠀⠀⢀⣤⠊⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⢞⣠⣀⣹⠀⠘⡦⢤⡤⠖⠋⠀⠀⠘⣿⣸⡟⠲⠦⣤⣀⣀⣀⣀⣤⠤⠶⣾⢫⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢈⠇⠀⡽⣶⡼⠁⢠⠀⠀⠀⠀⠀⠀⣿⠙⣿⣶⢤⣤⣄⣀⣀⣀⣠⣤⣴⡟⢳⡇⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⡰⠙⣆
⢸⠀⢠⠇⠙⠳⣴⡃⠀⠀⠀⠀⠀⢀⣿⣷⣿⣾⣿⣿⣾⣷⣶⣾⣿⣿⡿⣷⣾⢿⡀⢀⣿⠉⠉⠉⠉⠉⠙⠛⢲⠮⣤⠴⠋⠙⡶⢦⣀
⠸⠤⠞⠀⠀⠀⠀⠉⠓⠲⠶⠶⠚⠋⠙⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⡯⣿⣿⣿⣽⣻⡇⠀⠀⠀⠀⠀⠀⠀⡞⢠⡀⠀⠀⢀⠇⠀⣙⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡻⢾⣻⣿⣿⣿⣯⡷⣿⣷⣿⢿⣟⣯⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣅⣀⡴⣾⣶⣿⡿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣾⢷⣾⣿⣿⡿⠶⣿⣟⣻⣽⡶⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣾⡿⣿⣭⣾⣿⡿⢩⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⡿⣿⣿⣿⣿⣿⣟⣟⣛⣻⣯⣿⣿⣿⣷⢚⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⢿⣿⣿⡾⠟⡠⠊⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣿⣿⢽⣻⣿⣽⣽⣿⣿⣯⣽⣿⣛⣿⢿⣿⣿⢞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡿⠛⢉⡄⠊⠀⠀⠀⣸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⢿⢏⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣝⡻⡞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠑⢆⠀⣀⠔⢡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⣟⣋⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣙⣋⣩⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣉⣥⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⣤⣶⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⣿⣿⣿⣇⠀⠠
⠀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣤⣤⣴⣷⣶⣷⣶⣤⣤⣄⣰⣶⣶⣷⣿⣿⣿⣿⣿⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠥⠟⠉⠉⠙⠿⠿⠿⣻⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⡻⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡻⠟⠋⣼⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⢸⣿⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡄⢘⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⣿⡿⢋⠀⠀⠀⠀⡞⢿⣿⣿⣿⣿⣿⣿⡇⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⠀⠈⠀⠀⠀⠀⠉⠈⠿⣿⣿⣿⣿⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢓⠂⠀⠀⠀⠀⠀⠀⠸⣿⣿⣃⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇

⣶⣶⠶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶