Extinguisher Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣼⡿⠛⠛⠛⠛⠛⠛⠛⠛⡿⠁⠀⠀⠈⠛⠛⠛⣷⠶⠶⠶⣤⣄⡀
⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⢀⡀⣀⢈⣧⠀⠀⠀⠀⣴⢀⣸⣿⣤⣤⣄⣀⠀⠉⠳⣦⡀
⠀⠀⠀⢀⣿⠃⢠⣿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡿⠉⠉⠙⠻⣿⣦⡀⠈⠻⣦⡀
⠀⠀⠀⣼⡏⢀⡾⠁⢀⣼⠟⠀⣴⣿⠟⠉⠀⠀⠀⠀⠈⠙⠻⢷⣦⡀⠀⠀⠀⠹⣿⣦⡀⠘⣷⡀
⠀⠀⢰⡿⠀⣾⠃⢠⣾⠋⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠈⢿⣷⡀⠸⣧
⠀⢀⣿⠁⣼⠃⣰⡿⠁⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠈⢿⣷⠀⢻⡆
⠀⢸⣯⣼⠃⢰⣿⣀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⡆⠈⣿
⠀⠘⠛⠁⠀⠈⠻⠟⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣷⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡆⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢹⣧⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⡆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡗⠓⠲⠶⠶⠤⠤⠴⠶⠖⠛⠉⢹⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣈⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣤⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠙⠛⠿⠶⠶⣶⣶⣶⠶⠶⠿⠛⠛⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁

⠀⠈

⠀⠐

⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣶⣿⢶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠉⠁⢈⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣼⣿⣦⣄⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠴⠛⠀⠘⠻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⠀⠀⠙⠛⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡿⠿⢿⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠄⠐⠒⠂⠈⢉⣉⣁⠲⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠋⣉⣁⠤⠤⠄⢐⡒⠈⠭⠅⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠞⠋⢉⡀⠤⠔⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⣀⠀⡸⠋⠀⢀⡴⠟⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⢉⣁⠠⡧⢀⣀⣈⣿⠉⠲⡶⢍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡠⠞⠉⢀⡤⠒⠋⠉⣡⠟⠤⢾⡀⣠⠟⢒⠳⠆⠐⠂⠀⠀⠀⠓⡄⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⠋⠀⠀⡰⠋⠀⠀⠀⠀⠙⠦⡀⠀⠀⠁⢀⡼⠀⠀⠱⣄⠀⠀⠀⠀⠈⠣⡌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣸⠃⠀⠀⢀⠇⠀⠀⠐⢄⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢩⡄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠋⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⠄⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⡌⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⡀⢦⡀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠇⠀⠀⠉⣀⣤⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⡟⠀⡞⠁⠀⡇
⠀⠀⠀⠀⠀⢀⡔⣡⡶⠏⠀⠀⠱⣄⠀⠀⠀⠀⠀⢰⠀⠸⡀⠀⢸⠀⠀⢠⠞⠁⡀⢤⠀⠀⢀⡨⠶⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡚⠋⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⢦⠀⢳⡀⡌⠀⠀⡇⠀⠸⢏⡷⠀⢠⠎⢀⣄⠘⠀⠀⠀⠀⠀⡌⠀⠀⡇⠀⠀⣧⠴⢄
⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⢆⠀⢙⠃⠀⠀⠑⠂⠶⠋⠀⠀⠀⠀⠘⠋⣰⠀⠀⠀⠀⢀⠁⠀⣠⠷⠐⠰⠷⠖⢙⠗⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⢨⠋⠑⡄⠀⢈⣦⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠁⠀⠀⠀⢀⡚⠀⢰⡇⠀⠀⢀⡠⣤⠊⣀⡴⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⢸⠀⠀⡃⣴⠋⢠⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠎⠉⠓⡄⠀⣡⠀⠀⢀⡇⠀⠘⣋⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⡄⢀⠙⠘⠙⣇⢀⣼⠁⠀⠀⠀⠀⠀⠘⢳⣦⣶⣶⠞⠋⠀⠀⠀⠀⡄⠀⠀⠐⡀⢹⠀⠀⠈⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡴⢀⠀⠘⢣⡇⠀⠀⠀⠄⠀⢦⣴⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠡⣌⠒⠀⠆⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠠⠞⣀⡼⢀⠀⠸⠀⠀⠀⠀⠐⠤⣀⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⡀⠀⠠⠏⠑⠂⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⣉⠰⠾⢻⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⢄⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠈⠑⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠈⠢⡉⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠒⠤⢌⣉⠓⠒⠂⠤⠤⠤⠤⠄⠒⣒⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⢲⠤⠤⣀⣀⣀⣀⣀⡠⠤⢖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⣇⠀⠀⠀⠀⠈⢀⣈⣡⡄⠀⢂⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⠴⠖⠛⢻⣀⡸⠇⡀⠀⠀⠀⠀⠀⢀⡠⣤⠞⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⠀⠀⠀⠀⢠⡏⠀⠳⠶⠞⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⢀⣠⠴⢒⡽⠋⠐⠚⠁⠀⠀⠀⠀⠸⡁⠄⡀⠀⠀⠀⠀⠉⠉⠉⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠴⠒⣒⡒⠮⠕⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠻⡖⢀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣤⣤⣤⣴⠾⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⡀⡄⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣼⣿⣿⣷⡷⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⣦⠔⠂⠀⠛⣿⣿⡔⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡫⠀⢉⢺⡇⠀⠀⠀⣼⠃⠐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠈⠀⢀⣾⣿⡇⢀⡴⠞⠁⠀⠀⢹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁⠀⠀⠀⠀⣠⣩⣿⠟⡴⠋⠀⠀⠀⠀⠀⠈⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⢼⣿⣿⠋⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⠀⠀⠀⠀⠀⣴⣾⣿⡿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣄⣘⣃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠀⠀⠀⣿⢁⡁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣄⠀⠀⣠⣷⣿⣿⠋⠀⠀⠀⠀⣿⠸⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣦⣿⣿⡿⠁⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠈⣿⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⢠⡶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠂⠀⠀⠀⠀⠀⠀⢸⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⢈⣱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠤⠤⠤⠴⠚⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠙⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣴⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠲⣦⡄⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢻⣿⣆⢻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⣿⡇⠀⠀⠀⠀⢀⠈⣿⣿⣎⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⣷⣌⠻⣿⣦⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣷⣤⣍⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢴⣶⣦⣌⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢻⣿⣷⣄⡉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⣙⠛⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠤⠤⠤⠄⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⣉⠁⠀⣀⠠⠀⣀⣀⣄⣤⣀⡀⠀⠀⠀⠈⠈⠛⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡉⢸⣥⣍⣀⣴⣞⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⡈⡉⣉⣹⠉⣹⣤⡿⠋⡠⢌⡈⠻⣌⢻⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠠⣀⡶⠟⠛⠉⠙⠋⠻⠿⢷⣄⡙⠚⢁⡴⠛⠿⣾⠞⡍⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠠⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢿⢻⢻⡅⠀⠀⠀⠓⠶⠦⡈⠀⢈⠑⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢲⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠎⠀⠀⢹⡿⣧⠀⠀⠀⠀⠀⠀⠘⠂⠠⢤⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠸⡇⠀⠀⠀⣠⠴⣛⠉⠉⠀⠀⠀⠀⠀⠘⠠⠛⡲⠶⡤⢄⣀⠀⠀⠀⠈⠑⠶⠶⠶⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⢿⡀⠀⢰⠁⣍⠀⠀⠀⢀⡀⣀⠀⠀⡀⠀⢈⡰⢊⣰⢊⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⣇⠀⢸⠀⠆⠀⠀⠀⢸⠁⢈⡉⢉⡉⠉⠉⠙⡉⠝⢋⡩⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢹⡄⢸⠀⡄⠀⠀⠀⢸⠀⠈⠳⠿⠿⠄⢸⠾⠿⠾⢿⡷⢺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⢸⠀⠀⠀⠀⠀⢸⠀⠐⣒⠲⠶⠒⠂⠀⠰⢾⡷⠶⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠨⡇⢨⠀⠀⠀⠀⠀⢸⠀⠈⣉⣙⣀⡀⣓⠚⠒⣈⠔⢊⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢐⡇⢸⠀⠀⠀⠀⠀⢸⠀⠠⢁⣀⣉⣉⣉⣀⣀⣡⣴⣁⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⠀⠀⠀⠀⠀⢸⠀⠀⣶⡴⠊⣷⣰⣦⢈⣠⡶⣏⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⠀⠀⠀⠀⠀⢸⠀⢀⣈⢁⠀⢃⡉⠋⠈⣤⠛⢋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡇⢸⠀⠀⠀⠀⠀⢸⠀⢨⣭⣉⡀⢈⣩⣍⣠⣹⣟⡡⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠸⣇⠘⠀⠀⠀⠀⠀⢸⡀⠐⠶⠰⢶⠖⠰⢶⣁⣟⣁⡔⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣈⣿⣴⠀⣀⣀⣀⣀⣈⣉⣉⣉⣙⣋⣭⣍⣉⣩⣝⣉⡍⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣠⣬⣭⡇⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠄⠠⠉⡇⠊⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣴⡏⢹⠋⠉⠉⠉⠉⠉⠉⠱⠞⢋⡉⠋⠉⠩⠛⣋⠟⢋⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⣹⠇⢸⠀⠀⠀⠀⠀⠀⠀⢒⡀⠥⠐⢀⠀⠀⢚⡡⠔⢋⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠴⣿⠀⢸⠀⡀⠀⠀⠀⠀⢉⡀⠤⠐⣁⠄⠀⠖⣉⡤⠞⢁⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢘⢹⡆⢸⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠠⠀⠀⢉⣡⠴⢊⡵⢺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠤⠌⠃⢸⠀⡀⠀⠀⠀⠀⠐⢂⣉⠤⠒⠀⠀⣉⠤⠒⣉⠴⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠐⠒⢸⡇⢸⠀⠀⠀⠀⠀⠀⣉⡀⠠⠄⢊⠀⣈⠡⠔⢋⡠⠔⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣉⠉⡜⠀⢸⠀⠁⠀⠀⠀⠀⡤⠀⠒⢈⠁⠀⠤⠖⠈⢁⡠⠔⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠠⠖⢢⠃⠀⢸⠀⡀⠀⠀⠀⠠⠔⠒⣈⡡⠄⠀⠤⠐⠊⣉⡴⠊⣡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣀⣀⣠⡽⠀⠀⢸⠀⠄⠀⠀⠴⠀⠐⣉⡀⠔⠀⢀⡠⠶⠛⣁⡴⢊⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⣉⡡⠀⠦⣉⠀⢠⡤⠖⢉⣡⠖⣡⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢌⣀⠐⠠⠄⡠⠈⠄⡄⢀⡀⠤⢒⡫⠕⣊⣥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠄⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⡡⠔⣉⠔⢊⠤⠒⣀⠔⢂⠠⠐⣁⠔⢂⡤⠒⡁⠔⢋⠄⠂⡠⠐⣡⠔⣀⠄⢂⠄⠀⡠⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠊⠀⠖⠁⠤⠊⠠⠖⠁⠴⠊⠠⠚⠁⠐⠋⠰⠊⠠⠞⢁⠔⠃⡴⠊⠠⠊⠠⠚⠠⠋⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡶⠶⠶⢛⣛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⣀⣤⡴⠶⠟⠛⠉⣉⣡⣤⠶⠾⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣈⣧⠶⠛⠉⠀⣀⣤⡴⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⣋⣭⣭⣍⣙⠻⢦⣴⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢋⣴⠟⠉⠁⠉⠈⠉⢻⣦⡙⢷⡀⠀⢀⣀⣀⣤⣤⣤⠶⠶⠿⠿⠟⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⣾⠃⠀⠀⠀⣀⡀⠀⠀⠈⣿⡈⣿⠛⠉⢉⣁⣠⣤⣤⡶⠶⠶⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣸⡇⣿⡤⠀⠀⠈⠿⠿⣤⡀⠀⣼⡇⣿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣩⠷⠛⠿⣷⡸⣧⡀⠀⡀⠀⠀⢀⠉⢠⣾⣣⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣩⠾⠋⠁⠀⠀⠀⠈⣷⣌⠛⢾⣧⣤⣤⣼⣾⣿⣿⣏
⠀⠀⠀⠀⠀⢀⡴⢋⣴⠛⠁⠀⠀⠀⠀⠀⣠⠾⠋⠉⠻⠶⠶⠶⠾⠟⠛⠉⠀⠈⠳⢦⡀
⠀⠀⠀⠀⢠⡾⣱⡟⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⢀⡿⢰⡏⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⣸⠇⡿⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⣿⢰⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣿⡄
⠀⠀⠀⢿⠸⡇⠀⠀⠀⢰⡇⠀⠀⠓⠶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⢸⡇⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⢿⠹⣆⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣧⢹⡆⠀⢸⡏⠳⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⡇
⠀⠀⠀⠀⠀⠘⣧⣿⣄⠈⡧⠀⠀⠀⠉⠑⠒⠢⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠖⠒⠋⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⡀⠈⣿⡿⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢀⣷⣀⣹⡇⠀⠉⠓⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠖⠊⢻⡇
⠀⠀⠀⠀⠀⠀⣿⣶⢶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉⠉⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⣀⣀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠋⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⢰⠏⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢀⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇
⠀⠀⠀⣸⠇⠀⠀⠀⠀⣿⡇⠀⠉⠓⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠋⣿⡆
⠀⠀⢠⡿⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠀⠀⠀⠀⣿⡇
⠀⠀⣾⠃⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⢰⡟⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣾⠃⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⢸⠁⠀⠀⠀⠀⠀⠀⢀⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣾⠀⠀⠀⠀⠀⠀⠀⢸⡿⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⣿⠀⠀⣀⣀⣀⠀⠀⢸⡇⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⢿⡟⠋⠉⠉⠉⠛⢷⣿⠁⠀⠀⠀⠀⠙⠻⠶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣭⣭⣉⣉⣉⣉⣭⣭⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡟⠉⠉⢻⣿⠿⣯⣭⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠹⣷⣄⣀⣼⣿⣤⣄⣉⣙⠛⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⢀⣿⠉⠉⣿⣇⠈⠉⠉⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢠⣾⠟⠉⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣷⣶⠶⠶⠶⠶⠶⠶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣿⡀⢸⣷⣶⣶⣦⣤⣤⣤⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣼⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣀⣀⣀⣀⣀⣀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣤⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢠⡾⣿⠿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⣼⣦⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⣼⣿⣯⣿⣯⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⠿⠿⠿⠛⠛⠛⠋⠉⠉⠙⣿
⠀⠀⢀⣴⣾⠿⠛⠛⠉⠉⠙⠻⠿⣷⣤⣀⡀⣿⡏⠀⠀⢻⣷⣶⣶⣿⡿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⡇⠀⠀⠈⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢰⣿⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣀⣴⠾⠛⠋⣉⣽⣿⣷⣶⣶⣿⣿⣷⡶⠶⣦⣴⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⢠⣾⣿⠇⢀⣴⡾⠟⠉⣡⣴⡾⠟⠋⠉⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⠿⠶⣶⣶⣶⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⣿
⢹⣷⣠⣿⠹⣿⣀⣾⠋⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣄⠀⠀⠈⠉⠉⠛⠛⠻⠿⢿⣶⣶⣿
⠀⠻⣿⡏⠀⢿⣿⢇⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠈⠁⢸⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡀⢸⣷⡄⠀⣸⣷⡀⢠⣿⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡿⣼⡏⠛⠶⠟⠘⠿⠋⠘⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⡇⠈⠀⠀⢀⡀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡇⣾⢷⣤⠟⠻⣦⡾⣿⢠⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣧⣹⡀⠁⠀⠀⠈⢀⣿⣼⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣄⣀⣀⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣼⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣼⣷⠀⣾⣷⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀⠀⠀⠀⠀⠚⠻⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠐⣒⣒⣒⣒⣒⡂⠀⠀⠀⠻⣿⠿⢿⡿⠃⠀⠀⢀⣉⣉⣉⣉⡀⠀⠀⠀⠘⣿⠙⠛⢱⠏
⠀⠀⠀⠀⠘⠿⠿⠛⠿⠿⠇⠀⠀⠀⠀⠸⠿⠯⠀⠀⠀⠀⠾⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠿⠿⠅
⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⢘⣝⣀⣀⣀⣀⣀⣭⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣾⣷⡶⣶⣿⣶⡄⠀⠀⠀⣸⠿⢿⣿⡿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣟⡃⣛⣿⣿⡇⠀⠀⠀⠻⣶⣷⣯⣀⡼⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣷⣿⣿⣿⠇⠀⠀⠀⠀⠙⣿⠶⡛⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⡀⠀⠀⠀⢰⣿⣿⣇⣶⣿⣿⢃
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⡿⡛⣋⡿⣧⠀⠀⠀⠀⢿⣿⡟⢸⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢱⣶⣾⣿⣿⠁⠀⠀⠀⠀⢸⣿⡇⢸⣿⡏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠁⠀⠀⠀⠀⠸⠿⠗⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⠀⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⠀⣤⣾⣶⡄⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠺⡿⣷⠿⠿⣆⠀⠀⠀⠀⣾⡿⣿⣿⣿⡄⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⢀⣟⣿⣿⣿⣿⣞⣇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⣮⠀⠀⠀⠘⣿⣤⣿⣤⣿⠟⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠘⠻⣿⡿⢿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣶⠿⠋⠀⠀⠀⠘⣿⡿⠿⣶⡶⠀⠀⠀⠀⠙⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈
⠀⣤⡤⢤⣤⠤⣤⡤⢤⣤⠤⣤⡤⢤⣤⠤⣤⡤⢤⣤⠤⣤⡤⢤⣤⠤⣤⡤⢤⣤⠤⣤⡤⢤⣤⠤⣤⡤⢤⣤⠤
⢰⡟⢠⣾⠃⣰⡟⢠⣾⠃⣰⡟⢠⣾⠃⣰⡟⢀⣾⠁⣰⡟⢀⣾⠃⣴⡟⢠⣾⠃⣰⡟⢠⣾⠃⣰⡟⢀⣾⠃⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠉⠉⠉⠻⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠤⡤⠄⠠⢤⠤⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⣀⡀⠀⣀⣀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣈⠡⠔⠢⠬⣁⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠉⠀⠀⠈⣃⣠⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠒⠒⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⠂⠂⠲⠒⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢻⡃⠙⠒⠒⠊⢠⣻⡦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠏⠉⠉⠁⠳⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠁⢸⡏⣇⠀⠀⠀⠀⢿⡿⠀⠀⠈⠉⠒⠦⣄
⠀⠀⠀⠀⠀⡤⠒⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠛⠒⢄⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢸⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠀⠀⢸⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⢸⡀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⡎⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⡇⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠷⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠶⠾⠀⠀⠀⠀⠀⠷⠶⠶⠶⠟⠷⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠟⠷⠶⠶⠶⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⢸⣿⠿⠶⠶⣶⣶⣶⠶⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢶⡶⠶⠶⠶⠿⣿⡇
⠀⠀⠀⠀⢸⣿⢸⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠻⣿⣿⣿⣿⣿⠏⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠙⣿⣿⣿⠏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⢿⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣬⡻⢿⣿⣿⣿⣿⣿⣿⡿⢟⣥⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣝⡻⣿⣿⢟⣫⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣶⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⡟⠉⠉⠙⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢃⣀⠀⢀⣀⢸⡏
⠀⠀⠀⢀⣿⣿⣿⣿⡠⣤⠀⠠⡬⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣶⣶⣷⣾⠇
⠀⠀⠀⠀⢽⣿⣿⣿⣷⣶⣶⣶⣶⣯⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠯⠿⣿⡿
⠀⠀⠀⠀⠸⠿⠿⠿⠟⢿⣿⣿⠟⠛⠛⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠚⠛⠿⠿⠛⠢⣤⣀
⠀⠀⠀⠀⠀⢀⣀⣠⠤⠊⠀⠀⠣⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠹⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⠑⠢⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣄⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⡎⠀⠀⠀⣿⣿⣿⣦⣤⣠⣴⣿⣿⣿⠀⠀⠀⢳
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⢷⠀⠀⠀⢸⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⡀
⠀⠀⠀⠀⡇⢈⡟⣿⣿⣿⣿⣿⣿⣿⣿⠉⢣⡈⢣⠀⠀⡎⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢣
⠀⠀⠀⠀⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣱⢈⠇⢠⠃⠀⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢱⠀⠀⠘⡄
⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠀⠈⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠁

⠀⠀⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠠⡆⠀⠘⡄⠸⣆⠀⠰⡇
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢁⠀⠀⠹⡀⠹⣧⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡀⢷⡄⠀⠙⠦⣘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠃⠀⠀⠀⠈⢳⠀⡄⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠛⠛⠋⠉⠂⠀⠐⠶⠆
⠀⠰⠊⢀⡀⠄⠀⠉⠛⠍⠩⡙⠆⠀⠄⢀⣽⠷⢦⡁⠀⠓⠀⠀⠉⠉
⠀⠀⠀⠉⠙⠛⠛⠂
⣶⣶⣶⣶⢶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠙⠻⢷⣦⣤⣴⣶⣶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣤⣤⣤⣤⣿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣉⣉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠋⠉⠉⠉⠉⠉⠉⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠿⠿⣿⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⣤⣤⣤⣤⣀⣀⣙⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠶⠿⠿⠷⠶⣶⣤⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⣿⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣶⣶⣶⣦⣤⣄⣀⣈⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢠⣤⣄⣀⣀⣀⡀⠀⠀⠉⠙⠛⠻⠿⣿⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⠉⠉⢿⣏⡙⠛⠛⠿⠶⢶⣦⣤⣄⣨⡿
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⠀⠀⠙⠻⣶⡄⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⢹⣿⠻⢶⣤⣤⣬⣿
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡀⠀⠀⣿⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢠⣿⠀⢠⣿⠀⠀⣶⠀⠀⢀⡄⠀⠀⣿⠛⣷⡀⠀⢻⡇
⠀⠀⠀⠀⠀⢸⡇⠀⣾⡟⠀⢸⣿⠀⠀⣾⣿⠀⢀⣿⠀⢹⣧⠀⣸⡇
⠀⠀⠀⠀⠀⣿⡇⢸⣿⡇⠀⣿⣿⠀⠀⣿⣿⠀⢸⣿⠀⠀⠙⠿⠟⠁
⠀⠀⠀⠀⠀⢻⣧⣿⣿⡇⢀⣿⣿⠀⢸⣿⣿⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠉⠁⢻⣇⢸⣿⣿⠀⢸⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⢿⣄⣸⡟⢿⣦⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣻⠿⠋⠉⣿⠉⠙⠻⣿⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⢀⡾⠋⠀⠀⠀⣿⠀⠀⠀⠈⢷⡄⠀⠙⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠙⠷⣤⣾⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣻⣤⡶⠛⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣼⠋⠛⠶⠶⢤⣤⣿⣤⣤⠶⠶⠛⠋⣿⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠉⠉⠉⢻⠋⠉⠉⠉⠉⠉⠉⣿⠋⠉⠉⠉⠉⠉⠙⣿⠋⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢿⡀⣀⣤⣤⡴⠶⠿⠶⠶⢤⣤⣀⣀⣾⠁⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⢀⣤⠾⣿⠉⠀⠀⠀⠀⣾⠀⠀⠀⠀⠉⣹⠿⣦⣀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡁⠀⠘⣧⡀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠏⠀⢀⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣈⣻⣦⡀⠀⣿⠀⢀⣠⣾⣃⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠑⠌⠢⢄⡒⠤⠀⢀⣀⣀⣠⣤⣤⠶⠛⠉⠁⠀⠀⠀⠈⠉⠂⠀⠀⠀⡄⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⡀⠀⠀⢀⡴⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡘⠦⠤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⠇⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⡤⠞⢃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢞⡿⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⡇⠀⠀⠀⠀⠀⠀⠀⣰⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠻⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣠⠞⠉⢸⠀⢠⡦⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⡀⠀⠀⠀⣀⡤⣿⠀⠀⠀⣴⣸⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠇⠀⠀⠀⠀⡼⠁⠀⠀⣞⣠⢾⡇⠀⠀⠀⡞⢩⡇⠀⣠⠞⣿⠁⠀⠀⠸⠿⠚⠁⠀⠀⡾⠉⣽⢃⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠷⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨⠟⠉⠀⠀⢀⣀⠛⠋⠀⣸⠃⠀⢹⡆⠀⣠⡶⠀⠀⠀⢀⡾⠁⠘⠷⢞⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣶⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣏⠀⠀⠀⢠⡞⢧⡀⠀⣠⠏⠀⢠⠞⠁⠘⡇⢷⡖⠀⣴⠋⠀⢀⣤⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢧⣠⣄⣠⠴⠞⠁⠀⣠⠀⠈⠓⠶⠖⠋⠀⠘⠓⠋⠁⠀⠀⢸⣀⣠⠞⢁⡾⠁⠀⣿⠀⠀⣾⠁⠀⢀⣾⡷
⠀⠀⠀⠀⠀⠀⢠⣆⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢀⣴⡷⠀⠀⣀⠀⠀⠀⠀⠀⣟⠀⠀⣰⠏⠀⠀⠻⣤⡴⠋⢸⠇
⠀⠀⠀⠀⠀⢀⡞⠿⠃⠀⠀⢀⡄⠀⠀⠀⠀⠀⡼⠻⣄⠀⠀⣠⠖⠛⠋⠸⠧⠴⠚⢻⡄⠀⠀⠀⠀⠉⠙⠛⠁⠀⣰⡷⠀⠀⠀⠀⢿⡀
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢠⣿⡇⢀⠀⠀⣀⡞⠁⠀⠺⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⢤⣀⣀⣀⡴⠟⠉⠉⠷⣄⡀⠀⠀⠀⠙⠦⣄
⠀⠀⣠⠏⠀⠀⠀⠀⢀⡴⠋⠈⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠈⠳⠶⢷⠀⠀⠀⠈⠙⣆
⠀⢰⠃⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠸⡆
⠀⣿⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠟⠿⠿⣷⡄⠀⠀⠀⢰⣿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠘⢷⡄⠀⢠⡇
⠀⣿⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣀⣀⣤⣿⠇⠀⠀⠀⢸⣿⣧⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠸⡇
⠀⢹⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠉⠙⣿⣦⠀⠀⠀⠀⢸⣿⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⢷⡀⠀⠘⣧⡀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠸⡿⠀⠀⠈⢿⡇⠀⠀⠀⠘⠿⠷⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿
⠀⠀⠈⠳⡄⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡇
⠀⠀⠀⠀⠙⢶⣄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠉⠛⠦⣄⣀⣀⣤⡤⠶⠚⠉⠁⠀⠀⠀⠀⠉⠛⠲⠤⣤⣀⣀⣀⣀⣤⣤⡤⠶⠖⠒⠒⠶⢤⣤⡤⠴⠞⠋⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⣀⣠⡤⠶⠶⠶⠶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⠶⠶⠦⠤⠤⠶⠶⠖⠒⠛⠋⠉⠉⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠄⣀⣀⣤⣤⣤⣄⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠉⠉⢀⣠⠔⠒⠈⠉⠀⢀⠂⣒⠥⠒⠉⡌⠻⡓⠶⣶⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢀⠀⡠⠒⠉⠀⠀⠀⠀⡂⠌⡠⠊⠁⠀⠀⠀⠒⠒⠙⢆⠠⣉⠓⢮⡙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠤⣠⠀⡰⠊⠀⠀⠀⢀⣐⠂⠄⣠⠊⠀⠀⠀⠀⠀⠀⠀⠍⠁⠈⡆⠐⠨⢐⡈⠓⢥⡨⡙⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠻⠿⠿⡲⠦⢅⡰⢁⣠⣤⣤⡤⣤⣤⣄⣀⠐⢒⡀⢰⠀⠈⠄⡒⠨⠀⠙⢆⠥⡂⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡉⠁⢄⠉⢻⠮⢺⡿⠎⣻⠯⢶⣄⠀⠀⠀⠡⠒⠨⠔⠢⠄⢳⡂⠕⡂⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣑⢄⣣⣾⣃⢞⡠⠔⠈⠀⠙⣋⣉⠿⠯⣿⠷⠶⠬⡀⢗⠡⣒⢥⠌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⣿⠷⠅⠒⠒⠈⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢱⠇⠀⠀⢠⡇⠀⠀⡎⠵⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣜⠤⣚⠤⣀⠀⣼⠃⠀⠀⢣⣀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣷⡀⠬⠒⢡⢈⣋⢦⡻⢀⠤⣎⢿⣋⡂⢆⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⢄⡸⠳⡏⠇⢀⡀⢒⢸⠙⡟⡆⣞⡣⠹⠟⢯⡉⢻⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⢢⡍⠣⢡⡄⢀⡐⠂⠬⡴⢷⠆⠈⢚⣑⣟⠤⢽⠫⣼⠀⠰⠆⢲⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡬⠷⣾⡇⡀⠦⠷⣤⣀⣭⠝⡟⣾⡆⠀⢠⠀⠑⠥⡾⡀⡿⡥⡅⢲⠞⠢⢀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣹⠊⠈⢳⣦⢸⠀⠛⣹⣣⢎⣿⠀⠀⠀⢸⠀⠀⠀⠈⠀⢣⢱⠅⠀⠀⡇⠈⢌⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠳⣿⣇⣤⡼⠀⠰⠹⣟⡝⢻⠄⠀⠀⢸⣄⠀⠀⣀⡀⠜⠈⡶⢶⣖⢣⡀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡍⠛⢛⡈⡌⢇⡔⡧⠀⣳⠃⡼⠀⠀⠀⠀⢲⣤⡤⠤⣤⠒⠊⡀⡞⠙⠀⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣧⣶⣂⣀⣞⣡⢥⠶⡄⠳⠶⠊⢰⡧⣄⡀⠀⣀⣴⣀⣷⠴⣇⡶⢂⡧⢰⣶⡺⡶⠆⠀⠂⠠⠤⢀⣀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠛⠉⠒⠛⠶⠖⠾⠛⠻⠧⠊⢱⠾⠛⠉⠚⠧⠌⠑⠂⠛⠋⠒⠩⠁⠐⠂⠨⠓⠓⠈⠐⠊⠉⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠻⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠀⠀⠀⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠂⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠰⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢠⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⡇⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣎⣤⠀⠀⢾⣿⢿⣿⣿⣿⡟⣩⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⣿⡷⠆⠁⠀⣼⣿⣿⠉⡁⢩⣿⣿⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠈⠂⠓⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣄⡀⣿⠙⠛⠀⠀⣾⡿⠉⠂
⠀⠀⠀⠀⠀⠀⠰⠆⠶⠴⠰⠲⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣻⣤⣤⡀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢻⣿⢿⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⢿⠏⠓

⠀⠀⠀⠀⡠⠔⠒⠉⠉⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠉⠑⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠉⠒⠢⣄
⠀⠀⢀⠎⢁⣴⣾⣿⣷⣦⣄⠀⠈⢦⠀⠀⠀⠀⠀⢠⠋⣶⣾⣿⣿⣿⣷⣶⣀⠙⡄⠀⠀⠀⠀⠀⡔⠁⠀⠀⢀⠀⢀⣀⣀⠀⠣⡀
⠀⠀⡜⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⡇⠀⠀⠀⠀⡇⠀⣿⣯⣍⣀⣬⣽⡿⠉⣷⠸⠀⠀⠀⠀⢸⠁⡴⣒⣏⣥⣭⣥⣤⣶⣭⡆⢱
⠀⠀⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡇⠀⠀⠀⠈⡄⠀⠀⠉⠉⢋⣥⠤⠶⠖⠃⢠⠀⠀⠀⠀⢸⠘⢾⣿⣿⣿⣿⡿⣿⣿⡿⠀⢸
⠀⠀⠘⡄⠀⠈⠉⠛⠿⣿⣿⡿⠟⡱⠁⠀⠀⠀⠀⢳⡐⠀⣠⣄⣀⡉⠉⢛⣻⢆⡞⠀⠀⠀⠀⠈⢆⠀⠉⠛⠛⠛⠀⠉⠉⠀⢠⠃
⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠙⠦⣀⠈⠉⠉⠉⣉⠥⠊⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⠀⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣀⠤⠄⠀⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠐⠠⠤⣀
⠀⠀⠀⡰⠋⠀⢀⢀⣴⣼⣴⠌⠳⡄⠀⠀⠀⠀⠀⢀⠔⢁⣶⣿⣿⣿⣷⡄⠈⠢⡀⠀⠀⠀⠀⠀⢠⠞⠁⣤⣤⣤⣤⠀⠀⠙⢆
⠀⠀⡸⠁⢰⣿⣿⣾⣿⣿⣿⢠⡄⠘⡄⠀⠀⠀⠀⡎⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⢱⠀⠀⠀⠀⢠⠃⣶⣦⣿⣿⣿⣿⣄⠀⠀⠀⢇
⠀⠀⡇⠀⠳⣿⣿⣿⣿⣿⣿⣾⠇⠀⡇⠀⠀⠀⠀⡁⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⢈⠀⠀⠀⠀⢸⢀⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⢸
⠀⠀⢱⡀⠀⠘⢿⣿⣿⣿⣿⠋⠀⢠⠃⠀⠀⠀⠀⢇⠀⠀⠘⠿⣿⣿⣿⡿⠀⠀⡸⠀⠀⠀⠀⠘⡌⠿⢿⣿⣿⣿⣿⣿⡿⠿⢃⡎
⠀⠀⠀⠱⣄⠀⠀⠉⢿⡿⠛⢀⡰⠃⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠧⢀⠔⠁⠀⠀⠀⠀⠀⠘⢦⡀⠉⠛⠛⠟⠛⠃⣠⠎
⠀⠀⠀⠀⠀⠉⠒⠂⠄⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠒⠒⠉

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⢀⠔⠋⢁⣴⣶⡄⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⣠⢖⣍⣤⣀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⣀⣀⣀⡈⠙⠢⡀
⠀⠀⢠⠃⠀⢠⣾⣿⣿⣿⡄⣀⠀⠱⡀⠀⠀⠀⠀⡼⠁⣾⣿⣿⣿⢸⣿⡇⠀⠈⢧⠀⠀⠀⠀⢀⠎⠀⡴⠋⠁⠀⠈⠉⠳⡄⠘⡄
⠀⠀⡇⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡆⡇⠀⠀⠀⠀⠃⠀⡿⠿⠿⢿⣿⣿⡗⠀⠀⠘⡀⠀⠀⠀⢸⠀⣘⣴⣄⠀⠀⠀⢀⣤⡹⡀⢸
⠀⠀⢇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢰⠀⠀⠀⠀⢸⡀⣹⣿⣿⣆⠀⢀⣾⣿⣿⠇⡼
⠀⠀⠈⢮⠿⣿⣿⡿⠛⠋⠉⠙⢉⠞⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⢸⣿⡇⠀⣠⠃⠀⠀⠀⠀⠀⠳⡈⠛⠿⠟⠀⠸⡿⠿⠋⡴⠁
⠀⠀⠀⠀⠑⠢⠤⣀⣀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⣀⣈⡩⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⣀⣀⡤⠔⠋

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀
⠀⠀⠰⡔⣀⣠⢲⣀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢦⣬⠆⡀⠀⠦⡄
⢀⣀⠠⡏⡀⠘⢦⡅⣤⠀⠀⠀⢀⠰⡅⢰⡞⡉⢠⠃⡤⠀⠀⠀⣠⣼⡆⠀⢶⡁⣾⡃⡠⠘⡀⠀⠀⠀⢠⣆⡀⢹⠀⣬⡀⡀⠀⠀⠀⣄⣿⠀⠀⠹⣦⠟⡀⡄
⠈⢻⡆⣩⣝⣰⣸⠁⣤⣄⠀⠀⣶⡴⠏⠀⣸⡅⠀⠀⢳⡀⠀⢀⢸⡟⠑⣀⣼⠻⠛⡿⣅⢰⡗⡀⠀⠀⢘⢷⡗⢇⢀⡾⢿⠁⠀⠀⣀⢈⣿⠟⠀⣠⣇⠀⢱⡇⣡
⣴⣾⣷⣿⡟⢈⣷⣶⢲⢯⡀⠀⢸⡟⢁⠐⣿⠀⠀⣽⠋⠁⠀⢮⣬⡿⠺⣿⢻⣆⣀⣧⡌⠛⣻⠇⠀⣦⢿⣬⣧⣿⣄⢹⣾⣱⠂⠀⠀⣦⣿⡄⡸⣿⡨⠀⢀⠻⣿
⠻⣿⣷⣜⣿⣾⣯⣼⣿⣧⡟⠀⠈⠳⣿⣤⢻⣴⣿⣥⣼⠇⠀⠀⠺⣿⣦⣼⣬⣭⣽⣇⣈⣼⠿⠀⠀⠸⣿⣿⣿⣷⣿⣿⣋⣿⡿⠀⠀⠛⢻⣷⣬⡹⣇⣸⣬⣶⡼
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣾⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶
⣿⣿⣧⣦⣭⣦⣦⣤⣷⣥⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⢤⡼⢤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠩⠀⣠⢴⠔⠃⠈⠀⠀⢀⠂⠉⠁⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠠⠊⠁⠠⠭⠡⠀⠈⠀⠀⠀⠀⠀⠡⠀⠁⠀⠀⠀⠉⠂⢄⠂⢄
⠀⠀⠀⠀⠀⡔⠁⢀⠐⠁⠀⠀⠔⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠰⠂⠂⠀⠀⠀⠉⢂⡀⠀⠒⠒⢂⣶⣀⠒⠦⠠⠀⠀⡠⠄⠂⠀⠈⠉⠁⠒⠰⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣭⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⡀⠐⠠⠠⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢞⢋⡿⡋⠝⠉⠐⠷⠛⠇⠘⢫⣶⣱⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠀⠈⠀⠰⠵⠂⢀⣠⢊⡌⢑⡢⠈⠙⠛⠠⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠄⢣⣅⠇⠰⠆⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠓⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠔⠹⡧⠬⣝⢭⡉⢀⠀⣥⣤⡄⢺⣇⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡂⠀⠀⠀⠀⢀⠱⢚⣥⣶⣼⣶⢿⣾⢿⢉⣉⠃⠜⡿⠀⠀⠀⠼⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠩⠄⠀⠀⢀⠁⠀⠀⠀⠀⠙⠾⠴⠗⠦⠯⣬⡀⠀⣈⠓⠲⠃⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠉⠁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⢻⠿⡗⠨⠙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡐⠀⡀⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⢀⢻⣦⣄⣔⠉⡠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠊⠉⠓⡄⠀⠀⠀⠀⠀⠐⡖⠂⣋⣤⠾⢂⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠌⡀⢣⠀⠀⠀⠁⠀⠨⢰⡞⠳⢠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠲⠤⠵⠤⠏⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐

⠀⠀⠀⢠⣿⣷⣶⣿⣿⣿⣿⣷⣦⣄⡉⠛⠋⠐⢇⣦⢹⡆⠀⢀
⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠲⠐⠚⠿⣿⣿⠰⣴⣆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⡍⠁⠀⣶⣾⠢⠀⠙⣧⣻⣇⠀⠀⠀⠶⠲⣾⣶⡆⠀⠀⠀⠀⠀⠂
⠀⢸⣿⣿⣿⣿⣿⣿⣷⣒⣂⡠⠞⠁⡄⠁⠀⠻⠟⠁⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣾⣷⣄⠀⠀⣀⣀⡴⢄
⠀⠘⠛⠛⠛⠛⠛⠛⣻⡿⠉⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠳⠤⠤⡀⠀⠁⢹⣿⣿⣿⣧⣤⣾⣿⣿⣿⣦⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣥⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠙⢦⠀⢠⡿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢹⡆⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠠⢾⠇⠀⠀⠀⠀⠀⠙⢶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⣶⣾⠀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠐⢧
⠀⠀⠀⠀⢤⣀⣀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠈⢲⠀⠀⠀⣼⢡⡇⠀⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤
⠀⠀⠀⠀⠀⠈⠙⠲⠿⣯⣍⣉⣘⣓⡦⣄⣤⣤⠀⠠⠜⠁⠊⠀⠸⡆⠀⠀⠀⠀⠀⣷⣤⣿⣿⣿⣿⣿⣿⣿⣙⡿⢠⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠩⠅⢵⣭⣤⣤⡀⠀⠀⠀⠀⠇⠀⠀⡄⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠿⢥⠶⠈⠛⣁
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢲⡇⠉⠙⠃⠀⠀⣤⡄⢠⣴⣶⣟⠂⠀⠐⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠻⢄⠀⠐⣦⠄⠀⠀⠀⠏⣀⠀⠀⠀⠀⢰⠈⠃⠸⠇⠿⣩⡝⡉⠋⠉⠁⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⢀⡐⠻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⢠⠀⠀⠀⠀⠀⠀⢹⣟⢻⣿⣿⠫⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⡀⣠⣌⠉⢻⠇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠉⠘⠉⠓⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣽⠉⠙⣙⠷⢀⣹⡿⣭⣤⣶⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⢈⣿⣧⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠈⠩⠿⢏⢤⠄⠀⠀⠀⠦⣀⠁⠈⢀⡰⢤⣴⣶⠾⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⠁⠀⡴⠀⠈⣿⡄⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣾⣿⠀⢸⡇⠀⠀⢸⣷⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣸⡇⠀⢰⣿⣿⡀⢸⣇⠀⠀⣾⣿⠀⠀⠀⢠⡿⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢰⣿⠀⠀⢸⣿⣿⣧⠈⢿⣷⣾⣿⠃⠀⠀⠀⢸⣷⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢸⡯⢠⡀⢀⣿⠇⠀⠀⠸⣿⣿⣿⡇⠀⢿⡿⢁⡀⠀⠀⠀⢸⣿⡄⠀⠀⣿
⠀⠀⠀⠀⠀⣾⣿⣾⠇⣼⣿⠀⠀⣶⠀⢻⣿⣿⣧⠀⠸⢁⣾⠁⢀⡄⠀⠘⣿⣧⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢹⣿⣿⠀⣿⣿⠀⠀⣿⠀⠀⣿⣿⡟⠀⠃⣼⣿⠀⣼⡁⠀⠀⣿⣿⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⣼⣿⣿⣶⣿⣿⣤⣼⡟⠀⠀⢸⣿⠇⠀⠀⣿⣿⠀⢿⡇⠀⠀⣿⣿⡇⠀⠀⢹⣿⡆
⠀⠀⠀⠀⣼⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⡟⠀⠀⠸⣿⣿⡆⠘⣿⣦⣴⣿⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⣸⣿⡟⠀⠸⣿⣿⣿⣿⣿⡇⠀⠠⠏⣸⠂⠀⠀⣿⣿⣿⡄⠈⢿⣿⣿⣿⣿⠀⠀⢸⣿⣿
⠀⠀⢀⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⡄⠀⠀⢹⣿⣿⣿⣆⠀⢻⣿⣿⣿⣶⣶⣿⣿⣿
⠀⠀⢸⣿⣿⡄⠀⠀⣿⣿⡿⣿⣿⣿⣷⡀⠀⠸⣷⡀⢸⡄⢻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡏
⠀⠀⠸⣿⣿⣧⣀⣰⣿⣿⡇⠘⢿⣿⣿⣷⣄⠀⢹⡇⢸⡇⠈⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⡿⠁
⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⠀⠈⢿⣿⣿⣿⣆⠸⡇⣿⡇⠀⢸⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⢁⡶
⠀⠀⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⢸⣧⡀⣸⣿⣿⣿⣿⣿⣿⠋⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⠀⢀⣿⠿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⣾⣿⣿⠃⢀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣆⠀⢸⡇⠀⠘⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⡟⠀⢸
⠀⠀⠀⠀⢰⡀⢸⣿⣿⣿⠟⠿⣇⠀⠑⠀⠀⣿⣷⣄⣀⣼⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣧⠀⢸⡀
⠀⠀⠀⠀⠈⣷⠀⣿⣿⡇⠀⠀⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢈⣷⡀
⠀⠀⠀⠀⢠⡏⠀⣿⣿⣇⠀⠀⣿⠀⠀⢠⡿⠋⠉⢻⣿⣿⣇⠀⠀⣸⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣨⠀⠀⣿⣿⣿⠇⢸⡇⠀⠀⣼⠃⠀⠀⣼⣿⠛⢿⣦⠀⡿⠛⣿⡿⠁⣀⣾⡿⠛⠻⣿⣿⣿
⠀⠀⠀⢀⣿⠀⢀⣿⡟⠁⠀⠘⠃⠀⠀⠉⠀⠀⠀⣿⡇⠀⠀⣿⠀⠁⢠⡿⠁⠈⠉⠁⠀⠀⢠⡌⢻⣿
⠀⠀⠀⢸⣿⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⣿⠂
⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣼⡟
⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⢠⣿⠋⠹⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⡇
⠀⠀⠀⠀⢿⡀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠸⠁
⠀⠀⠀⠀⠀⢁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡀
⠀⠀⠀⠀⠀⣼⡀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣸⠇
⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠻⣷⣤⣼⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⢀⡾⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡄⠀⢸⣧⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⣿⠀⠀⣠⡾⠁⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣾⣿⡀⠀⠀⢠⣿⡇⠀⠀⠀⣼⣿⠀⢸⣿⠁⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⣄⣀⣼⣿⣷⣦⣴⣾⠿⠃⠀⠘⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠾⠛⠋⠁⠀⠀⠀⠀⠀⣠⣤⠶⠛⠁⠙⠻⢦⣄⣀⠀⠀⠀⠀⠀⠉⠛⠓⠶⣤⣤⣀⡀
⠀⠀⣀⣀⣀⣤⣤⡶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⣦⣤⣄⣀⣀
⣴⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢷
⣿⠀⠀⠀⠀⢀⣀⣠⣤⣴⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢶⣤⣤⣀⣀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⢰⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣷⠀⠀⠀⢸
⢻⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾
⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿
⠘⣷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡟
⠀⢿⡄⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣼⠇
⠀⠸⣇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⡿
⠀⠀⢿⡄⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣼⠇
⠀⠀⠘⣧⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢠⡟
⠀⠀⠀⢻⡆⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢀⣾⠁
⠀⠀⠀⠀⢿⡄⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠙⢷⣄⠀⣠⣴⠟⠁⠀⠀⠀⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠉⠛⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣠⡴⠟⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡆⢠⡀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢰⣿⣄⡤⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣴⡇⡄⢻⣾⣿⡄⢀⡀⠀⢀⣼⡇⢀⢀⣇⢸⣿⣿⠇⣸⡄⣷⡀⢀⠀⠀⠀⠀⣰⣿⣾⣿⡏⣧⣠⣦
⠀⠀⠀⢀⠀⢀⣼⡇⣿⣿⣿⣼⣇⣼⣿⢿⣧⣿⣷⣠⣿⣿⣄⣾⠻⣿⣿⣿⣿⣶⣿⣷⣿⣷⣾⡀⢤⡰⣄⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀
⠀⠀⠀⣼⣧⣿⢿⣧⡟⢿⢿⣿⣿⣿⢃⣿⣿⣿⣿⣹⣿⠹⣿⢿⣾⣿⢿⡟⢻⠿⣿⡟⢱⣿⡿⣿⣾⣷⣿⢿⣿⡏⢼⣿⣿⠏⡿⢿⣿⣷
⠀⠀⠀⠈⠉⠛⠀⠙⠋⠀⠀⠉⠉⠉⠀⠙⠉⠀⠉⠉⠉⠀⠈⠈⠉⠉⠈⠀⠀⠀⠈⠁⠈⠉⠁⠋⠁⠉⠁⠀⠉⠁⠈⠉⠁⠀⠀⠘⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⣆⠀⠉⠓⠪⡑⢤⡀⠀⠀⣠⠔⡉⠖⠋⠁⢀⣾⡿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠲⣌⠁⠀⠰⣄⠙⡄⢱⠀⢰⠁⠜⢁⣴⠀⠀⢉⡴⠂⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣷⣤⡈⠲⢬⡂⠀⠀⢫⠀⠀⢹⠀⢸⠁⠀⢸⠃⠀⠀⣪⠴⠊⣠⣴⡿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠘⠻⠟⠆⠀⠙⠄⠀⠀⠀⢤⡞⠀⠘⡦⠄⠁⠀⠀⠜⠁⠀⠞⠿⠛⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡦⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠱⣄⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⢠⠏⠐⠋⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠁⢀⡴⠁⠈⢆
⠀⠀⠀⠲⡀⠐⠀⠀⢤⣮⣤⠶⢷⣾⣷⣄⠀⠈⠙⠶⣷⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢰⡷⠞⠉⠀⢀⣴⣿⣶⠷⠦⣬⣦⠠⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠈⢲⡴⠞⠋⠁⠀⠀⢸⠿⠛⠉⠀⠀⠀⣠⣼⡟⠁⡜⠀⠀⠀⠀⡀⠀⣠⡾⢿⣤⡀⠀⠀⠈⠙⠻⢿⠀⠀⠀⠉⠛⠶⣴⠊
⠀⠀⠀⠀⢒⠁⠀⣠⣤⣤⣤⣤⣼⡆⠀⢀⣠⠖⠋⢻⡟⠀⠘⠀⠀⢀⠤⠊⢀⣼⡟⠁⠘⣿⠛⠓⢦⣀⠀⠀⣾⣦⣤⣤⣤⣤⡀⠀⢑⠂
⠀⠀⠀⠀⠘⣤⡾⠋⠙⢿⣿⣿⠟⢁⡴⠋⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⠀⢀⣾⡟⠀⠀⠀⠙⢆⠀⠀⠈⠳⣄⠙⢿⣿⣿⠟⠉⠻⣦⡜
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠻⣁⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⡹⠃⠀⠀⠀⠈⢣
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠣⣀⢀⣠⠄⠀⠀⠀⠀⡠⠀⢀⣴⣿⣿⣿⣷⣄⠀⠠⡀⠀⠀⠀⠢⢄⡀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣤⡀⠀⠀⣠⣾⣇⠀⢿⠿⡛⠀⠘⡻⢿⠇⢠⣿⣦⡀⠀⠀⣠⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠈⠢⡀⢠⣤⣤⣤⣶⣶⣶⣶⣿⣿⣇⣴⣿⡿⠟⠁⠀⡔⠀⠀⠀⠐⡄⠀⠙⢿⣿⣷⣄⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠈⢻⠏⠙⠛⠿⢿⣿⣿⣿⣿⡿⠛⠉⠀⠀⣠⠊⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠙⠻⣿⣿⣿⣿⣿⡿⠿⠛⠉⢿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⡀⠀⠉⠉⠛⠓⠀⠠⠤⠾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠽⠦⠤⠀⠐⠛⠋⠉⠉⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⢸⣽⣶⠳⣶⣤⣆⣤⣤⣤⣄⠀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⢀⣤⣤⣤⣄⡶⣦⣶⣼⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⠹⠶⠋⣿⢿⢻⣗⣺⣿⠃⣿⠿⣿⡿⣟⢹⡏⡏⢹⠤⣏⠀⢸⢸⡿⣤⡿⠯⠹⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠠⠄⣀⡀⠀⠀⠀⠉⠉⠈⠁⠉⠀⠋⠙⠙⠋⠀⠃⠙⠉⠉⠉⠈⠀⠁⣀⡀⠠⠄⠂⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠈⠉⠁



⡿⢿⠿⠿⡿⢻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠆⠲⠤⡀⠐⠐⠉⡀⢀⠄⢀⢄⠀⠠⠆⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠄⠒⢀⠒⠤⡘⠀⡇⠈⠇⠀⠱⡙⠠⡑⠆⠈⡆⠁⠠⢆⠊⠀⠰⠙⢆
⠀⠀⠀⠀⠀⡄⠀⡀⡠⢀⠀⠄⠀⠠⠈⢢⠘⠢⠁⠖⡄⠀⠀⠸⠃⡰⠀⡔⠧⠃⢸⠈⠩⡀⠀⢰⢈⠐⡄⠀⠠⠀⠲⠆
⠀⠀⠀⠀⠀⠔⢠⠐⠁⠨⢒⠨⣀⠂⠀⠔⡒⢂⠄⠀⠰⠀⠀⠀⠎⠀⠄⠀⠓⠀⠈⠣⡀⠀⠀⢆⠀⠐⡘⠀⡚⡀
⠀⠀⠀⠒⢠⡐⠂⠇⠈⠁⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⢄⠎⢈⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡁⠖⠂⠀⣠
⠀⠀⠀⠀⡗⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠳⡄⠄⢊⡄⠁
⠀⢀⡄⠤⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⠔⠀⠁
⠀⢀⠄⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣈⠡⡀
⠀⠸⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢣
⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠠⠀⢐⣲⡦⠶⠶⠶⡶⠀⣠⢶⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⢀⡠⠖⠊⠁⠀⠠⠐⢊⡥⠚⠉⠀⡒⠙⢍⠙⠯⣶⡦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⣁⠀⠀⠀⣀⠔⠁⠀⠀⠀⡀⡐⢊⠔⠁⠀⠀⠀⠀⠀⠶⠌⢂⠁⠢⢍⠳⢬⣝⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠴⠥⢤⣦⣤⣤⣒⠂⢠⠊⠀⣀⣀⡀⠀⠀⠀⠀⠐⠀⡄⠨⢐⡈⠀⠉⠳⡤⣈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠠⣉⠓⠊⠉⠻⣯⡩⣿⡟⢿⣶⣬⡀⠀⠀⠐⠨⠀⡐⢄⠹⡦⢑⠠⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠢⣡⣼⣏⠔⡁⠄⠊⠉⠒⢒⡲⢷⣶⣶⣤⣀⠸⣖⠠⠐⡌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡷⠬⠐⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⠓⠉⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⣦⠀⠀⠀⢸⠇⠀⢀⡀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢸⠀⠀⠀⡾⠀⠀⡗⠚⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠫⡛⠝⢰⣄⢰⡇⠀⠀⣰⡤⡋⡀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣮⣿⠆⠈⢁⡂⢰⢮⡿⢠⣎⢱⣼⡖⠧⡅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠨⣑⢣⠁⡀⠐⠤⠄⢙⢸⣌⠘⠦⠄⡥⣈⣦⢄⡐⠀⣠⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣤⣿⠀⢆⣡⣈⣉⣀⣾⣧⣧⠀⠀⡉⠫⣶⡿⢨⣗⣀⠻⡤⠃⡀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠷⠑⠙⣤⠀⠀⠛⣻⣫⢺⡟⠈⠀⠀⠇⠀⠀⠉⠀⡍⡍⠀⠁⡒⠘⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠾⣿⣩⣼⠀⠠⠹⣻⠟⣧⠀⠀⠀⣄⠀⢀⢀⡀⠃⢰⢤⣴⠣⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⠙⠋⣃⡅⠉⡔⡷⠀⣼⢀⡇⠀⠀⠀⠐⡦⡄⠠⡶⠒⢡⢸⠙⠀⠆⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⡷⠾⣄⣼⣥⣇⡖⣇⠙⠒⣁⣼⣲⠤⢀⠤⣶⣦⢿⠺⣶⠟⣼⣂⡾⣍⡖⢓⡀⢀⠀⡀⡤⢤⣠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠛⠉⠛⠉⠙⠊⠀⠛⠋⠁⠉⠁⠀⠀⠈⠁⠀⠐⠀⠈⠀⠈⠉⠀⠀⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣄⠐⣾⣷⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⢻⣿⣿⣷⡈⣿⡇⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠁⡀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠸⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣷⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡀⠈⢻⡿⣄⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⢀⣾⣿⣿⡏⠀⠰⣤⣀⠀⠀⠈⠻⣷⣦⣄⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠁⠙⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣷⣄⠀⠀⢹⣿⡻⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠘⣧⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣼⣿⣿⣿⡆⠀⠀⢿⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣄⣀⣠⣿⣿⡏⠀⢶⣄⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣌⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⣸⣿⣿⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣿⣤⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢀⡆⣴⣿⡄⠀⠀⠀⠀⠀⣠⣾⣿⢠⠀⠀⠀⠀⢰⣦⣿⣿⣴⡆⠀⠀⠀⠀⣰⣄⣿⣷⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⣿⣿⣤⠀⠀⠀⣸⣿⠏⣿⣿⣄⠀⠀⠀⣦⣿⡟⢻⣿⣴⠀⠀⠀⢠⣿⢿⠋⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠻⠈⠀⠁⠻⠏⠀⠀⠀⠹⠇⠀⠀⠼⠏⠀⠀⠀⠙⠇⠁⠈⠸⠋⠀⠀⠀⠈⢿⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⣰⣯⠀⠀⠀⠀⠀⢠⡙⢸⣷⡍⡀⠀⠀⠀⠀⠀⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⣰⢸⡿⣿⣄⠀⠀⠀⠀⢠⣠⣿⣿⡆⠀⠀⠀⠀⢠⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢻⣿⡇⠀⠀⠀⢸⡿⠁⢿⣿⡆⠀⠀⠀⠈⠘⣿⡿⣿⡇⠀⠀⠀⠀⢠⣿⡏⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠛⠁⠀⠀⠀⠈⠃⠀⠈⠛⠀⠀⠀⠀⠀⠘⠟⠁⠹⠃⠀⠀⠀⠀⠈⠻⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⡄⠀⠀⠀⠀⠀⢠⢷⣎⠂⠀⠀⠀⠀⠀⠀⡼⢧⠀⠀⠀⠀⠀⠀⠀⢀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⣾⣰⣿⣿⡇⠀⠀⠀⠀⡠⣫⣾⣿⣤⢢⠀⠀⠀⣼⡞⢀⡌⢳⣧⠀⠀⠀⠀⣠⠏⣠⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠰⣿⡿⠁⣿⣧⣆⠀⠀⢸⢰⣿⠃⠿⣿⡎⠄⠀⠀⣿⣴⠃⠐⣆⣿⠀⠀⠀⠀⡏⣤⣿⣧⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠈⠛⠁⠀⠀⠀⠛⠃⠀⠀⠛⠘⠀⠀⠀⠈⠳⠀⠀⠞⠁⠀⠀⠀⠀⠙⠻⠿⠟⠛




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣾⣷⣿⣿⣿⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⠉⠛⠉⠉⠉⢻⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠙⠉⠀⠀⠈⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣀⠀⠀⠀⣀⡀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⣀⡀⠀⠀⣀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢧⠉⠿⠁⠀⠈⠿⠉⡼⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃⣈⣿⣂⣀⣀⣿⣋⣸⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⡗⠚⠉⠉⠉⠙⢺⣇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣏⣁⣀⣀⣀⣀⣉⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢧⡤⢤⣄⣤⠤⢤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⢀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠙⣦⣀⣠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢹⡉⠒⠒⠒⠉⢸⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠃⠀⠀⠹⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣟⣤⣾⣧⡀⠀⠀⢀⣿⣶⣜⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⡀⣀⣤⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⢸⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡀⠸⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣀⣸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣇⣀⡇⠀⠀⢸⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣤⣤⣤⠀⣴⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⡿⣹⣿⡇⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣶⣤⣄⡈⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⢿⡿⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡏⢸⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⡇⢸⡇⠸⣿⡀⠀⠘⢿⣿⣿⣿⣿⣿⣷⡟⠀⣤⣾⣿⣷⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣿⣇⣿⠁⠀⢹⣧⠀⠀⠀⠙⠿⣿⣿⣿⠏⠀⠀⠀⠙⠻⠏
⠀⠀⠀⠀⠀⠰⡾⠛⠁⠀⠀⣿⣇⣉⣤⣤⣶⣟⠂⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠈⠻⣿⣆⠀⠀⠀⠀⣄⣤⢀⣀⢠⡀⡀⣀⡀⣄⣀⠀⡄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠤⠀⠤⠡⠄⠤⠤⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠱⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⡍⠑⠢⢄⠀⠀⠤⠷⡅⣀⡀⠀⠣⡀
⠀⠀⠀⠀⡠⠠⢀⡀⠀⡘⣅⠢⠀⠀⠑⢆⠀⠉⡟⠁⠀⠉⠢⡈⢦
⠀⠀⠀⠀⢣⠠⡀⠈⠢⡀⢈⠷⡑⠀⠀⠀⠳⡀⢳⡐⠄⠀⠀⠈⠢⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀
⠀⠄⠠⢄⠉⠳⣄⠠⠀⠈⠑⢖⠘⢦⡑⠀⠀⠘⢧⣝⣎⠀⠀⠀⠀⠘⢌⠢⡀⠀⠀⠀⠀⠀⣀⠤⠔⠊⡁⢀⣠⠴⠣
⠀⣶⢄⠀⠉⠫⢝⣲⡰⠀⠀⠀⠑⣤⠵⡄⠀⠀⠀⠉⢘⢣⡀⠂⠀⠀⠀⠳⡌⠓⢤⡐⠒⠉⠀⡀⣀⡴⠞⠉⠁⢀⡀⠀⠠⠄⠐⠀⠤⡀
⢈⡘⠷⡘⡄⠀⠀⠑⢽⢆⠰⡀⠀⠈⠑⠂⠀⠀⠀⣀⠠⣹⢷⡐⡁⠀⠀⠀⠘⢶⣢⠍⢢⡀⠀⠘⠓⠂⠀⠈⠁⢀⠀⠀⠀⡀⡀⠔⣲⡇
⠀⠓⣈⠉⢦⡰⠄⠀⠀⠉⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠈⠀⠡⡳⡰⡠⠀⠀⠀⠀⠈⠳⣆⡈⢣⠀⠀⠐⢀⣀⣈⡈⣤⣥⡤⠶⠖⠛⠉
⠀⠀⠀⠀⠠⠘⠢⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠐⠀⠀⠀⠀⠀⠀⠀⠙⢦⢻⡀⠰⢯⣄⣀⣀⣁⣀⣀⡀⠀⠤⠀⠂⠐⠀⠢⣄
⠀⠀⠀⠀⠀⢨⣿⢟⠦⡁⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⢀⠀⠊⠘⢶⡀⠀⠀⠀⠀⡀⠀⢀⢀⢀⢀⠀⢠⣤⠀⢐⡼
⠀⠀⠀⠀⠀⣹⡏⢷⡇⠙⢦⡉⠢⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠀⠀⠀⠀⠀⠙⠦⣄⠀⢈⡭⠤⠤⠤⠴⠴⠶⠶⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠈⢿⣎⢿⡄⠠⡝⣢⡐⠀⠀⠡⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⢍⡺⣍⡁⢉⠉⠉⢈⠁⢉⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠐⠀⠉⠦⡀⠇⢡⢂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢔⠄⡄⣄⡀⣀⡀⢀⠀⣠⣤⣿⣯⣽⣿⣿⣹⣿⣿⣾⣿⣿⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠒⢻⣟⣷⣄⠈⠠⢁⡙⢢⡐⢁⢊⢂⠄⡀⠀⠈⠠⠀⠀⠀⠀⠁⠪⢊⢜⢶⠄⣴⡾⣶⡦⡢⣴⢴⡶⣤⡶⠚⠛⠛⠙⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠚⠻⢷⣄⠀⠀⠠⢝⣦⡀⠆⠈⡔⡡⢀⠀⠀⠑⡀⣀⠀⠀⠀⠀⠡⡪⣿⡝⠕⠬⡛⣢⣵⡾⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⡌⢤⡦⡿⡆⡀⠀⠐⡐⠜⢦⣀⠰⡐⡅⡂⠀⠀⢈⢎⠪⣒⢭⢒⡀⣺⣯⡢⡴⡿⠞⣟⡁⢻⡔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠾⠿⣤⡤⠬⢬⡰⠴⠦⢚⡻⣄⠌⡔⠄⠀⢀⣣⣹⢯⡒⣝⣭⣵⣽⣊⣙⣶⠶⢬⣷⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠅⠔⣀⡩⠅⣀⠈⠉⠑⠦⢬⠦⣴⡭⣿⢻⣻⣥⣶⡿⠗⠋⣉⡀⠤⠤⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⢪⡍⢙⡻⠟⡛⠯⢷⠮⠄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠙⢦⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢳⣰⠃⠀⠀⠀⠀⠀⠀⠉⠸⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣀⠀⢸⠁⠀⠙⠀⠀⠀⡀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢀⡞⢹⡀⡾⠀⠀⠀⠀⠀⡼⣧⠀⠀⠀⠀⠀⠀⢧⢠⡄⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡜⠀⠀⠉⠃⠀⠀⠀⠀⢸⠁⢸⡀⠀⠀⠀⠀⠀⠘⠁⢧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⡀⠀⡇⠀⠀⠀⠀⠀⢀⡞⢦⠏⠀⠀⠧⠚⣆⠀⠀⠀⠀⠀⠸⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠉⠓⠃⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠳⠋⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠳⢤⣀⣀⠀⣀⣠⠴⠋⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣭⣶⣤⣀⡀⠀⠀⠀⢀⣉⠉⠉⠀⠀⢀⣀⡤⣴⣊⣙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⢦⣰⣷⠀⠀⠉⠙⣳⠊⡍⡩⠭⡷⡟⠉⠉⠀⢰⣿⠻⢌⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣞⡵⢻⣂⣀⠤⠶⡇⢸⠀⢧⡽⡿⢹⠒⠦⠤⠬⢯⣓⣪⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠁⠀⠀⠀⠘⢦⡓⠶⠚⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⢉⡉⠛⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣠⣮⣀⣀⣀⠀⠉⠲⡀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠲⣶⣶⣶⣤⣭⣙⠒⠶⣄⠀⢢⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⣿⣿⣿⣿⣶⣬⢷⠀⢧⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡼⠋⠉⠙⠛⠿⢿⡿⢟⢃⣼⣿⢸⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣷⢊⣉⣓⠒⠀⠀⣿⡟⣸⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠸⡯⠤⠄⠀⠀⠀⢿⢁⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠙⠯⢥⣤⣴⣶⢃⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢒⣶⢶⣬⣭⣭⣥⣾⣿⠟⢠⠟⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢩⠇⢸⣿⣿⣿⣿⣯⣡⡶⠃⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⡼⠀⠀⠉⣡⠞⠉⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣴⣧⠀⠀⡼⠁⠀⠀⣠⠎⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⣥⣄⣠⣞⣁⣀⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣿⡯⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⢰⠃⠀⢀⡠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠸⠀⢠⠎⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠏⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⠀⠀⡼
⠀⠀⢀⣀⣤⠶⠖⠲⠦⣏⠀⡐⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠑⡄⢧
⠀⠀⠀⠙⢧⡀⠀⠀⠀⣼⢷⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡨⠃⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠉⠐⠒⠊⢹⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⣀⡠⠤⠤⠤⠠⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⠤⣀⠀⠤⠤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⢰⡟⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢿⣿⣿⣿⣿⠀⠀⠀⠀⢠⢏⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠙⠻⠟⡿⠀⠀⠀⡴⠫⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠉⠀⠀⡠⢊⠔⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢱⠀⠀⠀⠀⠀⠀⠔⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠁⠠⢄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠑⠒⠊⠀⠀⡠⠐⠈⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠁⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⣠⡿⠤⠀⠀⠀⠉⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⡀⠀⠀⣧⣀⣀⣀⣤⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠯⠭⣍⣉⣀⣀⣀⣀⣀⡠⠤⠔⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⢀⡴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⣰⡟⢸⣷⠀⠸⣥⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⠀⠀⠀⠀⣼⠏⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠏⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣿⠀⠀⠀⠀⠸⣿⡀⠀⠘⣆⠘
⠀⠀⠀⠀⠀⢰⣄⠀⢰⡄⠀⢠⡟⠀⠀⢻⡀⠀⠀⠀⠀⠹⣷⡀⠀⢸⡆⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠉⠀⢸⣧⠀⢸⡇⠀⠀⠀⠣⠀⠀⠀⠀⠀⠘⢿⣄⣾⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢧⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⢀⡾⡇⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠉⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣠⠟⠀⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⢻⡁⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⣠⠀⠀⣀⢸⡟⡆⠠⡀⠀⢸⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡇⠀⢠⡇⣼⠁⣿⠀⣷⠀⢸⡇⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠣⠀⢸⣇⠁⢀⡿⠀⠏⠀⣸⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣄⠉⠛⠋⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠬⠿⠖⠒⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⡀⠀⠀⣸⡄⠀⠀⢷⡀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡆⠀⠀⣸⠀⠀⠀⠀⠱⣿⣿⣿⡇⠀⣄⣸⣿⠀⠐⠤⣤⣾⣧⣀⡀⢢
⠀⠀⠀⠀⠀⠀⠀⣤⢠⠀⠀⠀⢹⡄⠀⠘⣦⢠⣤⡷⢀⠀⠀⠻⣶⣴⣿⠀⠀⠀⡀⢀⡈⣿⡿⠀⣷⠉⠻⣿⠀⢸⣆⠘⣿⡏⣿⠁⣼⡆⠀⢠
⠀⠀⠀⠀⠀⠁⠀⣿⣿⡇⣄⠘⣾⣷⡐⣦⣾⡇⠙⣇⣀⣿⣦⡀⢸⣟⣿⣦⢆⣀⢸⡟⣡⣿⣷⣤⣿⣆⣠⣿⣷⣾⣿⣿⣿⣶⣿⣿⣷⠃⠘⡿
⠀⠀⠀⠀⢶⠦⠤⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠹⠿⠿⠿⠟⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⢏⣢⣴⠁
⠀⠀⠀⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⠃⣀
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣠⡟
⠀⠀⠘⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣣⠿⠁
⠀⠀⠠⢬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢟⣀
⠀⠀⢧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠶⠛⠁
⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣇⡀
⠀⠈⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟
⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠱
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠁
⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⡀⢀⣀⡀⠀⣀⡀⠀⣀⣀⣀⠀⢀⣀⣀⣀⣀⠀⠀⣀⣀⠀⣀⣀⣀⣀⡀⢀⣀⣀⡀⠀⣀⣀⣀⣀⣀⡀⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠁⠀⠈⠁⠀⠈⠉⠉⠀⠀⠁⠉⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢀⣿⣿⠁⠀⣠⡔⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⢸⣿⣿⠀⣾⣿⠀⢰⡄⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⣼⣿⣿⠀⣿⣿⡄⢸⣿⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣿⣿⠀⢸⣿⣇⣸⣿⡇⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⠀⠀⢹⣿⣿⡀⣾⣿⣿⣿⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣿⡆⠀⣼⣿⣿⣿⣿⡿⢹⣿⡿⢀⣿⣿⡇⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⣿⡇⠀⣿⣿⣿⣿⡏⠀⣸⣿⣧⣾⣿⣿⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣿⣷⡀⠀⢸⣇⢰⣿⣿⣿⣿⣷⠀⢻⣿⣿⡟⣿⡟⠀⣰⣿⡟⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠹⣿⣧⣀⣿⣏⢻⣿⡟⣿⠌⢻⡇⠈⣿⣿⠇⠸⣧⣴⣿⡿⠁⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢻⣿⣿⣿⣿⠀⣿⠀⠿⠀⢸⡇⠀⣻⣿⠀⣾⣿⡿⠋⠀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣌⣿⣿⢿⣿⠀⢻⡀⢀⠀⠘⠁⠀⣿⡏⢸⣿⡿⣧⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⡇⠸⣿⡀⠈⠃⢈⣿⠄⠀⠀⢹⡇⣼⣿⠃⣹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠘⢿⣄⢸⣿⠀⠀⣾⡏⢠⡆⢠⡈⠀⡽⠃⢠⡿⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⢙⠓⢹⡇⠀⣿⣧⣸⣿⣾⡟⣸⡇⠀⡟⠁⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⢻⣆⠀⣿⣴⣿⣿⣿⣿⣿⣾⣿⣃⣴⠟⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿