Fatty acid Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠋⠀⠑⢲⣦⣤
⠀⠀⠀⠀⢀⠀⠀⢀⣾⣅⠀⠀⠀⣰⣿⠋⠀⠀⠀⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⢺⣷⣶⣿⣿⣿⣶⣴⣾⣿⣿⣄⠀⠀⣰⣿⠁⠀⠀⠙⣿⣷
⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠙⣿⣿⠋⠉⠛⢿⣿⣿⣿⡀⠀⣀⣴⣿⣿⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠴⠟⠉⢦⣀⣠⡾⣿⡿⠿⢿⣿⣿⠟⠉⠉⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣀⣼⣿⣯⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢡⠹⣷⣶⣾⡿⠿⠳⢾⣦⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⠁⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⣤⣴⣿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠿⣿⣿⠛⠉⠉⠙⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣿⣿⣶⣶⣿⣿⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢽⣿⠋⠀⠀⠈⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣀⣀⣤⣾⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣿⣿⠋⠀⠀⠙⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠷⠞

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

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

⠀⠀⠀⠀⡀
⠀⠀⢰⣿⣿⣷⠀⠀⣠⠤⡄⢀⣀⡀⢠⠤⣄⢀⣀⡀⢠⠤⣄⠀⣀⡀⢀⠤⣄⠀⣀⡀⢀⠤⢤⠀⣀⣀
⠀⠀⠈⠛⢿⣟⣻⣷⣟⣻⣿⣾⣀⣿⣞⣻⣿⣾⣀⣿⣾⣻⣿⣾⣄⣽⣾⣻⣿⣾⣄⣽⣾⣻⣿⣾⣅⣼⡶⠒⣆
⠀⠀⢠⣞⣿⣿⠿⠟⣿⠉⡿⢻⣿⡟⢿⠉⣿⢻⣿⡿⢻⡉⣻⠻⣿⡿⢻⡉⣻⠻⣿⡿⢻⡉⣹⠻⣿⡿⠛⠚⠃
⠀⠀⠈⣿⣿⡟⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠧⣤⠇

⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⢼⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⣸⠀⢠⠀⠀⠀⠀⣠⣇⣰⠆⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⢸⣿⣶⡃⠀⠀⠀⣠⣿⣿⣇⡀⠀⠀⣠⣿⡿⣷⣤⣀⣀⣴⡿⠿⠛⠿⣿⣿⡟⠁
⠀⠀⠠⣷⣤⣤⣴⡿⠿⢿⣦⣄⣤⣴⠿⠛⠛⠿⣶⣶⣾⠟⠉⠉⠙⢿⣿⣿⠋⠁⠀⠀⠙⣿⣿⠏⠀⠀⠀⠀⠈⣿⡅⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠉⣿⠿⠇⠀⠀⠀⠀⣻⡟⠋⠀⠀⠀⠀⢸⡏⠉⡄⠀⠀⠀⠰⠟⢀⣠⠀⠀⠀⠀⢀⣿⣧⣀⣀⣀⣤⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢀⡰⠀⠀⠀⠀⠉⠀⠴⠃⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⡾⠉⡟⠛⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠫⠤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⠼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢑⠀⣄⢀⣀⣠⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠛⠛⠿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠠⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠗⢀⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡿⠿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠛⠛⣛⣛⠛⣿⣿⡟⢻⣿⣿⠟⢛⡛⠛⣛⠛⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⣧⣿⡿⣡⠀⢿⣿⣤⣿⡇⠀⣿⣧⣼⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣽⡄⣿⣿⠇⠿⠇⠘⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⠏⢾⣿⡿⠄⠸⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡀
⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣦⣶⣦⣶⣴⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⡶
⠀⠀⠀⠀⠈⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠆⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆
⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⣶⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡃⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉
⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒
⠀⠀⠀⠀⠈⠁⠈⠁⢉⠈⠁⠉⠀⠉⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⢀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠸⠒⠚⠛⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣷⠄⠀⠀⠀⠀⠹⠿⠿⠿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠈⣽⣿⣷⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠁⠀⣰⣿⣿⠛⠀⠀⠀⠀⠀⢠⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢴⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠉⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢀⣠⣤⠄⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠻⣄⠀⠀⠀⠀⠀⣿⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠈⢷⣄⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢀⡴⠛⣩⣍⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡃⣾⠁⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠘⣧⡀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⠛⠳⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠈⠛⠷⠆⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣄⣀⣀⣀⣠⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠪⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡫⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠑⡘⠠⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⠳⡘⠦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⡤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⠀⠀⠀⢸⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⠀⠀⠌⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡳⠄⣠⠞⠀⠑
⣾⣾⠿⠷⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⠾⠿⣛⠛⠛⢿⣿⣿⣟⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⣯⡡⠥⠀⠀⠀⠈⠉⢀⣀⣈⣩⠭⠭⠭⠭⣉⣿⡿⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠋⠁⠀⣠⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⢈⡐⠒⠒⣿⣿⣇⣨⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣯⠿⠋⠁⠀⠀⠀⠈⠀⠀⠀⠀⡀⠠⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠩⠟⢓⣿⢷⡮⠿⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣲⣿⢫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠀⢾⣿⣷⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣀⠠⣰⢏⠕⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠚⠁⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠙⡿⣷⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⠉⢵⠟⣥⠋⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠎⣿⢃⢏⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⢏⡾⠁⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠠⠄⢰⡟⡟⠘⣽⡏⡉⣿⢿⡇
⠀⠀⠀⠀⢀⣾⡟⠁⠌⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡟⡜⣴⠃⢻⠃⡁⣽⣾⣿
⠀⠀⠀⠀⢰⢿⡧⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣹⡏⡌⡾⣸⣧⣿⣿⣿
⠀⠀⠀⢐⣿⢸⣃⡀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣹⠟⡰⡿⢠⣿⢇⡟⢿⣻⣿⣿⡆
⠀⠀⠀⢸⣷⢸⢹⠁⠀⠀⠠⠁⠀⠀⠀⡀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣮⣾⡃⣰⣿⣿⢏⡟⣼⢠⣾⠻⣼⣿⠇
⠀⠀⠀⢸⡧⣾⢸⠀⠐⠀⠀⠀⡠⠅⡰⢁⡾⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠘⠀⠀⢀⠰⠋⠐⠉⠀⣸⢟⡿⣿⣾⠁⡣⢋⡞⣷⠇⣼⣧⡿⢹⣿
⠀⠀⠀⢸⢠⡿⢺⠀⠀⢀⠀⠀⠃⠘⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠊⠀⠓⣀⠔⡹⣫⢞⠟⠛⢹⣿⢯⡞⣹⡟⣼⣻⣿⠃⣿⡇
⠀⠀⠀⢸⣦⡇⢹⠀⡄⢸⠀⡌⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⡠⠀⠀⢐⡠⠂⡡⣪⠞⣡⣫⠆⣠⣿⢫⠞⣱⣿⡿⢡⡟⢩⣾⣿⠁
⠀⠀⠀⢀⣿⣧⠸⡆⠧⢼⠀⢃⡞⢀⠄⠀⠀⠀⢀⠔⠀⢄⠔⠀⣠⡮⠊⠀⠀⠀⠈⣠⢞⢐⡷⢫⡟⡡⣪⠟⣡⢋⣴⡟⣱⣧⡿⣀⣮⡿⠁
⠀⠀⠀⠄⢹⣿⡶⡇⠆⢸⢠⢿⡄⡈⠀⠜⠀⢀⡠⠂⠀⠀⠀⣴⠏⠀⠂⠀⣀⡴⠃⢐⡷⢃⣶⡿⠳⣾⢣⠞⣱⠟⣉⣴⢣⣿⢓⣼⡿⢁
⠀⠀⠀⠀⠘⣿⡇⢷⡅⢸⣼⢸⡇⢀⠌⡀⠀⢁⠔⠁⣀⣴⠟⠁⠊⢀⠄⠨⢋⣠⠞⢉⣤⠜⢋⣠⠞⣉⡽⠟⣋⣴⠻⣫⣿⠱⣡⡟⠁
⠀⠀⠀⠀⠀⢻⣧⢸⣇⣨⡏⣼⠃⡮⢂⠈⠀⢀⠔⣪⠞⠁⢀⡠⠞⠉⢀⡾⠋⢀⠀⠉⠴⣺⢟⣡⠾⠯⠒⣊⡼⡣⣨⣟⡵⡿⠛
⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣈⠕⣩⠀⢒⡵⢚⢡⠤⠚⢉⣠⡤⣖⠫⠖⠊⠡⠀⠂⠌⠒⠋⣁⢠⡶⠚⠩⣪⠞⣽⣫⠞⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⢕⣩⡶⠿⠿⠦⢴⣶⠶⠿⣛⡶⠿⠃⠉⢑⣈⣁⡔⠀⢀⣤⢒⡥⣊⣴⠶⣻⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⣿⣭⣾⣿⣿⠿⢿⣛⠉⢥⣤⡤⠶⠒⣋⣉⠭⠙⣁⡤⢌⣚⣭⠾⣻⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣻⣿⣿⣾⡧⠴⠶⠷⠶⠆⣲⣾⡿⢯⣽⠶⠿⠻⢓⣩⣽⡫⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⣩⠝⠛⠛⠻⠶⣶⠼⠏⣵⡤⠿⢯⠤⠶⠓⢚⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠐⠀⠀⠀⠀⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣤⣀⠀⣠⣤⠒⠘⠚⠋⠛⠻⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⠁⢀⣀⣀⠈⠙⢿⣿⣒⣩⣶⣟⠉⠁⠉⠉⠻⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠟⢀⢷⡀⠀⠀⠀⠁⠤⣀⠉⢻⣿⣿⣿⣦⠀⠀⠀⢨⣷
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠆⠳⢤⡐⢄⣀⡄⠜⣷⠀⠹⣿⣿⣿⣦⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⢀⣤⣽⣮⣙⢻⣿⡼⣦⠀⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢻⠄⢀⡠⣾⣿⣿⣿⣿⣧⣉⡉⠉⣠⣟⣩⣵⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢇⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⠿⠉⡁⠤⠀⢒⡠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⣿⣿⣿⣿⣿⡿⣔⠎⠻⣿⢥⡲⣄⡤⣴⣀⠀⢐⣒⠑⢀⡠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠳⣄⢬⡓⢍⠳⣕⠢⣍⠛⠙⠫⢶⣒⠋⠭⠭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉⠢⠙⠦⡑⠬⡑⠦⢍⠒⠮⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣿⡏⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋⠉⠉⠩⠟⠛⠻⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠂⢠⠂⠀⢀⡀⠀⠀⠀⣀⣈⣏⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⢰⣿⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡌⢅⠷⠀⠀⠀⠀⣀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠁⠀⠀⠀⠀⢽⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣞⣲⣲⣾⣿⣿⣿⣿⠲⠶⠦⠤⠤⠤⠖⠒⠒⠊⠉⣳⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠾⣥⣔⡀⠀⠀⠀⠀⠀⠀⣠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠰⠶⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠶⠶⢦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⢀⡠⠤⠴⠦⢤⡈⠙⢻⣝⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠉⠁⢩⢾⠿⣧
⠀⠀⠀⠀⠀⠀⢀⡔⠁⣠⠖⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⡆⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣁⣱⠊⠀⠹⣇
⠀⠀⠀⠀⠀⣰⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣇⠀⠀⢼⡆⣠⣤⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠦⣤⣼⡟⠛⠶⠾⣴⣿⡆
⠀⠀⠀⠀⣴⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢸⡇⠀⢲⣿⣿⣿⣤⣶⣟⣛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡿⢧
⠀⠀⠀⢰⡷⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇⠀⣬⣽⣿⠀⠓⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣯⣦⠀⠸⡇
⠀⠀⠀⣼⡇⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠋⢀⣾⠃⠀⣸⣿⡏⢀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠠⠄⠒⠂⠀⣿⣿⣄⠀⡇
⠀⠀⠀⢿⣇⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⡤⣠⠞⠁⢠⡾⠃⠀⠀⡸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⡿⢸⢀⡇
⠀⠀⠐⣿⠻⣦⡀⠹⢦⣄⣀⣀⣀⣦⡄⠈⢁⣤⠾⠋⠀⠀⢀⡀⢻⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡼⢸⠃
⠀⠀⠀⠈⢣⠀⡙⠷⣦⣄⣈⣀⣠⣤⣴⠾⠛⠁⢀⠀⢠⣶⣾⣿⣿⡿⢷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⢇⡟
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⠉⠁⠀⢀⠀⣶⠚⠚⠚⠉⠉⠻⢿⡟⠁⠘⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡜⣼⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡙⣲⣶⣤⣶⣤⣿⣧⡀⠑⢀⠄⠀⠀⠉⠒⠢⠾⢬⣌⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⣿⣿⣿⣿⣆⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠉⢳⣆⣐⣀⣐⣒⣦⣾⣭⣥⣶⡾⠁
⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂⠈⠉⠉⠉⠉⠁⠀⠉⡻⣝⠙⠳⢦⠄⠀⣀⣠⣤⣤⣴⣶⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⢠⠏⠙⠒⠂⠀⠄⠀⠠⠒⠒⠒⢊⣠⣼⣿⠆⠀⠀⠀⠀⠒⣺⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠸⣷⣦⣀⠀⢀⣀⣀⣀⡤⠞⣛⣽⣿⠟⠉⠑⠓⠾⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⠧⢄⠀⠀⠠⠤⠞⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢅⣢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠬⣓⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣩⠗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⠛⣵⣛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠉⠉⠉⠀⠀⠀⠠⠤⣌⠡⡈⠻⠑⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⣀⠄⠀⠀⠀⠉⢀⠠⠤⠰⠂⢰⠁⠀⠘⠄⠱⢄⠤⠈⠂⠒⠒⠒⠒⠒⠂⡖
⠀⠀⠀⢀⠀⣀⡀⠀⢀⠞⠁⡀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠤⠺⣄⠀⠹⣄⡀⢀⣠⠀⠀⢶⠈⠉⠙⠒⠒⠳
⠀⠀⠀⠘⠃⠀⣌⣙⢳⣤⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⢁⡀⠀⠉⠉⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⢉⠟⠌⣷⡀⣠⠊⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠉⡗⠒⡏⢹⡉⢠⠳⡄⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠀⢘⣄⠸⣟⠒⠘⠈⢁⠀⢤⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⢺
⠀⠀⠀⠀⠀⣠⡜⠁⡎⠉⠉⠉⢆⠹⡍⠉⠉⠲⡑⡀⢂⠁⠢⢤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⡤⠚⢁⡧⡀⠑⢤⡀⠀⠈⢧⠱⡀⠀⢀⡼⠋⡈⠆⢀⠀⠙⢦⡀⠀⠀⢠⠀⠀⠀⠀⠰⠀⠀⡾
⠐⠊⢁⡨⠖⠋⠀⠈⠑⢢⠬⠄⢀⣘⡓⠃⣈⡡⠔⠊⠀⠀⠀⠉⠒⢄⡈⢷⢀⠎⡀⠸⠀⠀⠀⠀⢀⠇
⢧⠀⠁⠐⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠺⣆⢰⠁⠀⠀⠀⡀⠀⡌
⠈⣆⠀⠀⠔⢀⡴⠁⠀⢠⠀⠀⠀⠐⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡈⢸⠐⠀⠀⠀⠁⡜
⠀⠈⣆⣀⠔⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⢸⠀⠀⠂⠀⠀⠀⠀⠀⠀⡰⠁⢸⠀⢠⠀⢀⠌
⠀⠀⡇⠉⠒⡦⢄⡀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⢀⡜⠀⠀⡼⠒⠁⠀⠁
⠀⢆⠁⠀⠀⢓⠀⠀⠉⠘⠃⠤⡤⠌⠀⠀⠠⠔⠤⣄⣀⣀⡀⠤⠀⠹⠀⠀⢠⠃
⠀⠈⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⡰⢠⠇
⠀⠀⠘⢷⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡡⠃
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠣⠀⠈⠁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠑⠴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣓⣀⣲⣄⣤⣤⣔⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢜⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⠀⠀⠤⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠿⢀
⠘⠁⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⢀⣤⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⣈⠁⢀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠠⠀⠀⠹⡀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⢷⡀⠀⠀⠀⠐⡄⠀⠀⠀⠢⡄
⠂⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⣦⠀⠸⠀⠀⡧⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢅
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣠⢞⡡⠂⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⠙⠷⣄⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠛⠀⠀⠀⠁⠉⠀⠀⠀⠉⠒⢤⠤⠠⠀⠀⠀⠈⠉⠀⠠⠀⠀⠘⠃⠖
⢀⣤⠒⠀⠠⣤⣀⠀⠀⠀⠈⠋⢀⣀⡤⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⠀⠀⠠⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠉⠀⡀
⡛⠀⠀⠀⠀⢈⣿⡇⠀⢠⡴⠛⠉⠀⠀⠀⡽⢡⠀⠐⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠱⠀⠀⠀⠈⠁
⣧⣀⣀⣀⣀⡿⠋⠀⣰⠋⠀⠀⠀⠀⠠⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠂⠀⠀⠀⠀⠄⢈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠰
⠈⠙⠛⠋⠁⢈⣠⡴⠗⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠈⠉⠀⢀⣠⣤⣤⢤⣄⡀⢀⠀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠤
⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⢠⠀⢰⠋⠀⠀⠀⡀⠀⣄⠀⠈⠋⠀⠀⠀⠀⠈⢀⣄⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠳
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⡀⠀⠀⠀⠀⠀⡹⠀⠀⢀⠀⠀⠈⠀⠐⣄⡀⠀⠁⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠳⠤⠖⠂⠁⠂⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⣫⠂⠀⠀⠀⠈⠐⠠⠤⠤⠊⠀⠀⠀⠀⠀⠁⠀⢀⠐⠀⠀⠀⠀⠀⡄⠀⠀⠁
⠤⠤⠀⠀⠰⠀⢈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣐⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠄⠀⠀⠀⠀⠈⠊⠁⠢⢀⠀⠀⢄⣵⠀⠀⢰⠏⠀⠀⠀⣠⢀⠆⠀⠀⠀⠠⠀⠀⢀⡤⠂⠀⠀⠂⠀⠀⠀⢀⡀⠀⠂⠀⢰⠋⠉⠓⠀⠠⡀⠸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠓⠠⠀⡿⣡⠄⠀⠀⠠⠤⠶⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⢻⣄⠀⠀⠀⠐
⠄⠀⠀⠠⢀⠤⠀⠀⠀⠀⠀⠠⠀⠐⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⢀⠀⠈⠹⡆⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣇
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡟⠀⠀⠀⠈⠙⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠘⢦⡀
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⢻⡄⠀⠀⠀⠐⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⠦⣄
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⣠⠀⢀⠓⠂⠀⠤⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠰⡄⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡠⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠍
⠀⠀⢱⡀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⡆⠀⠐⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⢃⠀⠀⢀⠞⠏⠀⠀⠀⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⡇⢸⠀⢀⠎⢰⠀⠀⡠⢚⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠂⠉⢉⣉⠉⠉⠑⠒⠤⣄⡇⠱⡀⡇⢸⡀⡜⢀⠇⣠⢞⠕⠁⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠐⠈⠁⠀⠀⠀⠀⠠⠤⠀⢀⠉⠳⣧⢻⠀⡆⡇⣸⣾⣗⠥⢒⠉⡩⠎⠁
⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⠬⢿⣆⡷⠛⠛⠛⠒⠦⣔⠋⣀
⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⠔⠀⠀⣀⠤⡲⠝⠛⠉⠀⠀⠀⠀⠀⠀⡰⢻⠀⠀⡴⠒⠢⠤⣀⠉⠳⢄
⠀⠀⠀⡜⢡⠁⠀⢀⠔⠁⢀⠔⠋⠀⠁⠀⠀⠀⠀⠀⠀⡠⠄⠀⡰⠁⠸⡀⠐⡆⠀⠀⠀⠈⠙⠢⡀⠙⠢⡀
⠀⠀⢠⠁⠂⠀⠀⠀⠠⣺⠕⠁⠀⢀⡠⠀⠀⠀⠀⠒⠉⠀⠀⢰⠃⠀⠀⢳⡀⠱⣄⠀⠀⠀⠀⠀⠈⠣⡀⠘⡄
⠀⠀⢸⠀⠀⠀⢀⢀⠄⠁⠀⠀⠀⠁⠀⣀⠤⠒⠊⠉⠉⠉⠉⠛⠒⠤⡀⠀⠱⣄⠈⠦⡀⠀⠀⠀⠀⠀⢳⠀⢰
⠀⠀⠘⠀⠀⡐⠁⠀⠀⠀⠤⠒⠈⡠⠊⠁⠀⣀⠴⠒⠂⠦⠀⡀⠀⠀⠈⢣⡀⠈⠑⠤⣈⠑⠒⠤⠤⠤⠞⠀⢸
⠀⠀⢠⠁⠌⠀⠀⠀⠀⠠⠐⣲⠋⠀⠀⡤⠚⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⡿⡦⠤⢤⡀⠉⠓⠒⠠⠤⠤⣴⠋
⠀⠀⠈⠒⠒⠦⡀⠀⠀⠀⣰⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣇⡀⠀⡿⠁⠀⠀⠈⠆⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠇⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠈⢹⠃⠀⠀⡀⠀⡜⣀⣤⡾⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⢨⣿⣿⣟⠉⠉⠉⠉⠉⡯⠶⠒⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠓⠤⢄⣀⡠⠤⠶⠒⠉⡱⠦⠤⠒⠛⡿⢻⠌⢦⡀⠀⠀⢠⠯⢭⣭⣍⣁⡲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠼⢤⣀⠀⢀⡠⢃⠎⠈⠀⠉⢶⣖⠛⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠭⣒⣒⠒⠊⠉⢁⣀⣀⡠⠼⠫⠥⢴⣎⠀⢀⣠⡤⢜⠌⢟⠢⣅⡈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢇⡏⠙⣇⢸⠈⢢⡀⢣⠀⠉⠉⠒⠳⠄
⡰⠀⢨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⣜⡀⠀⠙⠦⣧
⡇⠀⠀⣆⠳⣎⠠⡀⠲⡖⡆⣆⣄⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠁
⣼⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠠⠤⠤⠠
⠀⠀⠀⠘⢷⣛⠓⣂⠔⠀⠀⢀⡼⣿⠀⠀⢐⠀⠀⠔⠉⠛⠁⠀⠁⠀⡠⠀⠀⠀⢾⡀⠐⢀⢂⣀⡔⢰⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠟⠐⠁⠀⠀⠘⠦⠤⠂⠐⠢⠀⠀⠐⠊⠀⠀⠀⠀⠈⠉⠓⠊⠉
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢢⡑⠂⠀⠀⠧⠥⠤⢤⠂
⠀⠀⠀⠹⠶⠄⠀⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣨⠇⠀⡄⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠧⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⣨⣿⣀⠀⠀⠀⠈⠂⠄⢀⣈⠭⠋⠀⠀⠠⠤⣤⣤⣾⠟⠁⠀⠀⠀⠀⠀⠈⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠈⠑⡀⡀⣦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠠⣄⣀
⠀⠀⠀⢦⣤⠤⠴⠆⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠁⠀⠈⠀⠀⢸⠀⠀⠂⠀⠐⡊⠀⠔⠀⠈⠻⢦⡀⣀⣠⠾⠃⠀⠘⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠰⠀⠀⠀⢀⡠⠄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣴⠖⠁
⠀⠀⢠⠂⢠⣷⠤⣀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⢀⡤⠀⢤⠀⠁⡐⠒⠲⢦⠀⠀⠀⠀⠀⠙⠛⠀⠁
⠀⠀⠘⢶⣿⣁⣠⣻⠇⣄⢰⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⡀⠘⡀⠀⣀⡾⠀⠀⠤⣤⣴⣶⣶⣶⣶⣶⢀⣀
⠀⠀⠀⠀⠀⠙⠛⠋⠀⣈⡛⠋⠀⠀⠀⠈⠓⢄⣀⣀⠄⠀⠀⠀⠀⢙⠚⠋⠀⢀⠈⣈⠉⠁⠀⢶⣾⣿⣿⣼⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⣀⣀⣴⡇⠀⠒⠛⠃⠀⢧⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⣅⠀⢐⠀⠀⠀⡌⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠊⠀⠐⠒⠛⠁⠀⠀⠋⠉⠉⠉⠉⠉⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠖⣒⡒⠒⠊⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠀⣠⠔⠋⠉⢉⣧⡀⠠⢄⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⡠⠞⠁⠀⣠⣾⠟⠁⠻⡀⠀⢣⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⣠⠞⠁⠀⢀⢔⠟⠁⠀⠀⠀⡇⠀⠀⢧⠀⠀⠀⠙⣄⢀
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⡔⠁⠀⠀⠠⠢⠃⠀⠀⠀⠀⠀⠁⠀⠀⠈⠆⠀⠀⠄⠘⣇
⠀⠀⠀⡠⣶⠃⠀⠀⠀⠀⠈⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀
⠀⡠⢢⡏⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀
⣼⠁⣼⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠊⠉⠐⠂⠄⣀⠀⠀⢀⣀⣀⡀
⠁⠀⡿⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠣⡀⠀⠀⠀⠀⠀⠀⣆⠀⣐⡠⠥⠀⠀⢀⡤⡀⠀⠈⠁⠉⠁⠀⠈⠀⠀⠉⠒⢀⠠⢀
⡀⠀⣧⠂⠀⡀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⡠⢸⠀⡠⠂⠂⠁⠀⠀⢀⠠⠒⠁⠀⠀⠁⠈⠁⠀⠀⠀⠀⠒⠒⠂⠄⠀⠉⠲⠙⡆
⠀⡰⡇⠀⠀⡁⠀⠀⠀⠀⠀⠙⠀⡀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⢸⢋⠊⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⡰⢿
⠜⠀⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡰⠣⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠀⢀⣥⠋⣋⣍⣉⠤⠊⠀⢸⡄
⠀⠀⢸⡄⠘⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢀⡟⢠⠚⡉⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢷⡀⣗⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠈⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⡠⠋⡰⠃⠀⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⢳⣸⣧⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡎⠀⢰⢠⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⡠⢊⡠⠊⠀⠀⠀⠈⡀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⡇⠀⢠⠂⠀⠀⠀⡰⠁⠀⢸⣇⢂⠀⠀⠀⠀⠐⠀⠐⠀⠉⠀⠀⢀⡠⠔⡩⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⣷⢀⡞⠀⠀⢀⡴⠁⢀⡴⠋⣹⡳⢕⠀⢀⠀⠀⠀⢀⣀⠠⠤⢚⢡⠐⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⠿⠶⠟⠛⠛⠉⠁⠑⣄⠉⠐⠒⠉⠉⠒⠂⠀⠁⠀⠀⠳⡀⠀⠀⠀⠀⢀⠈⡀⡀⠀⠀⠀⣾⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⡟⠁⠀⢀⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⠦⣀⠀⠀⠀⠀⠀⠀⠐⠢⣀⠀⠀⠀⠀⠀⠘⣄⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠒⠤⢄⣀⣀⡁⠒⠦⠭⣷⣶⣶⡶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⣸⣿⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⣿⣿⡆⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢿⣿⡿⣄⣿⣿⣇⣾⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢿⣷⣌⣿⣿⣼⣿⣿⣿⡟⢉⣭⣭⣍⡉⠓⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⣁⡂⣀⡙⢿⣿⣿⣿⣿⣿⣿⡇⢸⡟⠁⠀⠀⠀⠀⠠⡈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣈⣀⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⡄⠻⠇⠀⠀⠀⠀⠀⠈⠶⣄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣼⣦⡀⠀⠀⢀⠀⢠⣀⠠⣻⣦⠈⢧
⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠙⢙⣿⣻⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣷⣦⣤⡈⠙⠻⠿⠿⠿⠃⢸⡆
⠀⠀⠀⠀⠀⠀⢸⣦⣬⣖⣂⣀⠠⠤⠞⠛⠿⢛⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡞
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣭⣭⣠⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣟⡘⢿⣿⣿⣿⣿⣿⣽⣿⣿⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣟⠛⠙⠀⢀⣹⡟⣿⣟⠙⠮⡻⠿⠿⠟⠛⢻⣿⠟⠋⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣅⡀⠁⣴⠶⣏⣾⠇⠈⠻⣷⣄⣼⣷⣶⡀⠀⠚⠁⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⡶⠟⠁⠀⠀⠀⠈⠛⠿⠿⣿⣶⣴⣶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠋⠉⠉⠓⢲⠏⠀⠀⠀⠀⢀⡴⠷⠿⠦⣤⠴⠃⠀⠙⣆⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣏⠀⠀⠀⠀⠉⠀⠈⡇⠀⢀⡴⠀⠀⢀⡴⠓⠒⠒⠠⠤⠄
⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⢀⠗⠂⠄⠀⣿⣆⢀⡆⠀⠀⠀⢀⣷⠞⠛⠉⢳⣖⡭⠠⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣼⣧⡀⠀⢀⣠⡏⠀⠀⠀⢠⡼⠛⠛⢧⡀⠀⠀⠈⢷⣀⣀⣀⣼⣧⣤⣀⢀⠀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠊⠉⠉⢢⣀⣘⣿⡷⠞⡽⠁⠀⠀⠀⣾⠀⠀⠀⠀⠙⣆⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⠷⠶⠶⠛⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⣄⣀⡠⠤⠒⠒⠒⠒⠒⠲⢾⡀⠀⠀⡴⠋⠉⠑⠄
⠀⠤⠤⠤⠤⣄⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢠⠁⠀⠀⠀⡄
⢣⡄⠀⠀⠀⠈⠙⢦⡀⠸⡄⠀⠀⠀⢰⠃⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⠀⠀⠀⠀⣸⡇⡆⠀⠀⠸⢧⣄⡀⠠⠄⣄
⠀⠉⠐⠢⣄⠀⠀⠀⠹⡄⠈⠢⣄⣀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⠉⠀⠀⠀⠈⠙⠶⢤⣤⡴⠛⠀⠙⣄⡀
⠀⠀⠀⣠⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠁⠄⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⣇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⣀⣀⣤⡴
⠀⢀⡎⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠁⠀⠘⢦⣀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠈⠣⣄⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠄⠀⠐⢀⠀⠀⡀⠄

⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢋⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣽⣽⡇⠂⠀⠀⠀⠀⠀⢠⡿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠤⠀⠀⠀⠠⣄⣀⠀⠀⡁⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢤⡀⠀⠀⠀⠄⠠⠀⠀⢠⠀⠀⠀⠀⠀⣀⠠⡶⠆⠀⢆⠿⡁⡅⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠠⠇⠀⠀⠀⠀⠀⡠⠆⠀⠈⠁⣀⠀⠀⠐⠒⠹⠁
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⡀⠀⠀⠀⣄⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡄⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢀⠶⣭⠙⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⠀⠀⠴







⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠶⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈
⠀⠀⠀⡠⡖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣖⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠
⠐⠀⠐⣴⠔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣮⣯⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠤⠼⠂⠀⠀⠀⢤⣤⠂⠀⠀⣰⡿⠀⠠⠼
⠀⠀⠀⠈⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⣀⣄⠀⠀⣀⠀⡀⠀⠀⣀⣀⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣴⡓⢀⣲⣀⣄⠀⠀⠀⠀⡀⠀⢀⣀
⣿⡯⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠠⢐⣀⣰⠆⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡤⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠄⠀⠀⠁⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠈⠉⠠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⢀⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⡀⡀⠈
⠈⠀⢈⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠁⠀⠀⠀⠀⠀⠀⠀⣉⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠠⠤⠀⠠⠀⠰⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡲⠀⠀⠀⢆⡀⣠⠄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⢠⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠠⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠐⠄⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣉⣀⣈⡉⠤⢴⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⢀⠀⠀⠀⠇⠀⠠⠄⠀⠀⠤⢀
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⢂⢀⡄⢲⠐⠀⢀⡇⠀⠀⠀⠀⠆⡐⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⡈⢀⢀⠈
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⠀⠀⡠
⠀⠀⠀⠁⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠉⠒⠒⠓⠒⠉⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⣠⠴⡒⠈⢛⡋⢐⠒⠦⢄⡀
⠀⠀⠀⠀⠀⢀⣠⠤⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠙⢦⠀⠀⠘⠁⠶⠶⠤⢤⡉⠁⠢⠈⣢⠍⠢⡀⠀⠀⠀⠠⠤⠄⢄⣀
⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠠⠑⠦⣀⠒⠈⠲⣄⠠⠘⠀⠀⠁⠀⡠⠐⠈⢉⢓⡲⣤⣍⡢⡀
⠀⠀⠀⡼⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠸⡄⢤⢦⡀⠳⢤⡈⠀⠑⠂⠀⠀⠀⠀⣷⠒⠋⠉⠉⠉⠉⠉⠙⠛⠦⣄⡀
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠋⠉⠀⠀⠀⠀⠈⢄⠣⢜⠃⢤⠚⠒⢤⣀⠀⠀⠀⠂⢀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠈⠙⠒⠶⠤⠤⠶⠒⠊⠉⠀⠀⢀⡀⠤⠤⠤⣄⡀⠀⠀⠀⠈⠣⡀⠳⢤⡉⠁⣠⠐⠀⠀⠀⣦⢌⠓⠶⠤⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠊⠉⠁⠀⠀⠁⠀⠐⠙⠆⠀⠀⠀⠀⠈⠢⣄⣉⠒⠦⠤⠌⣍⠢⣉⠒⢭⠒⢤⠬⠉⠳⣄⣀⣀⣀⡀⠤⠖⡫⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠶⠛⠋⠉⠓⢤⡈⠐⠤⠀⣀⡀⠀⠠⠀⠀⢀⠀⢒⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⡀⠀⠙⠁⠀⣩⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣤⣤⡤⠤⠒⠋⣁⣤⠖⠒⠒⠒⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠄⡠⠤⠴⢋⢁⡠⠤⠐⠊⠉⠙⠁⠀⠆⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣠⠖⠉⢁⣀⣀⠠⠀⠀⠀⠂⣀⣬⠵⠖⢒⠛⠿⠅⡈⠳⠤⠾⠀⠀⢳⡄⠀⠀⠀⢀⡔⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⢠⠋⠔⠚⢋⣁⡀⠤⠀⣤⠀⠀⢀⣀⡀⠠⣄⠀⣀⠆⠀⠥⠤⠀⢀⠀⠀⡜⠀⠀⠀⠀⡞⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⡏⠠⠖⢰⣊⣁⠩⠤⠴⠚⠊⣉⠃⠁⠐⠚⠁⠤⠠⠄⠀⠠⡐⠂⠣⢀⠞⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⢻⡉⠋⠈⣈⣀⣠⠴⠔⠊⠉⠀⠀⠀⠠⠄⠀⠀⠀⠃⠀⠐⠀⣣⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⡀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠑⢄⠀⣀⣀⣀⠤⢀⠈⠀⣀⡤⠚⠁⠀⠁⠒⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠼⠤⠖⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣉⣹⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⢲⣤⣶⣶⣶⣠⣶⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠆⡆⠀⠀⢴⡾⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡩⠀⠀⠀⠀⠀⠀⠁⠀⠠⠤⢿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢄⡟⠀⠀⣔⣀⠉⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⢀⡿⠁⠈⠀⠁⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠠⣤⣼⠄⠤⠴⠤⢄⡀⠀⠀⠀⠀⣴⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⢛⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠓⠛⠚⠛⠛⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⡇
⡖⠈⠭⠭⠭⠭⠭⠭⠥⠤⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⢀⣀⣀⣀⡀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⢀⡠⠄⠂⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡔⠀⠉⢀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠆⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⠀⠀⠀⠁⠀⠀⡄⠰⠀⠀⢃⠀⠀⢠⠀⢰⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢸⠸⠀⢸⠀⠀⠀⠸⠀⠀⡸⠃
⠀⢦⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠆⠀⠀⢀⠀⠀⠀⠀⠀⠘⠘⣾⣾⠾⠬⠽⠴⠄⠚⢊⣉⣀⣐⡀⢲
⠀⠸⣄⣀⣀⠀⢤⠏⠀⠀⠀⠀⠀⠸⡀⠀⠊⠀⠀⠀⠀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠠⡈⢉⣩⡋⢻⣽⣇⣳
⠀⠀⠀⠈⠉⠉⠍⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡷⠀⠀⠀⢀⡓⠠⡟⢙⣿⣀⣻⡭⠇
⠀⠀⠀⠀⠀⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠙⠂⠛⢯⢉⡤⠛
⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⡀⠀⠀⠈⢇⠀⣀⠤⠒⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣐⣒⣒⣂⣮⣁⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣣⣀⢄⣄⣠⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠈⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤⡤⠒⠉⡡⠀⣨⡟⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠉⠀⠀⠈⣠⣾⡿⣤⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⣠⡾⢿⣀⡈⢯⠘⡯⡌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⡴⣾⡷⡝⠘⡇⢣⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣀⠴⠻⡅⠙⢏⢻⠙⢷⡈⠀⠳⣄⢻⣇⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡜⢱⠶⠶⠒⠀⠀⡀⠄⠺⡅⠀⠃⠀⡜⣆⠀⠂⢠⠙⢬⠀⠹⡏⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⢀⣀⣤⡖⢻⠳⡆⢐⣦⣈⢧⢲⡀⢀⠀⡇⠈⢇⠈⡁⢰⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣟⢿⣿⣧⢠⣷⡕⢸⡇⣱⠙⣇⢡⣈⡲⠘⠀⡄⠀⡗⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣯⡙⣧⡉⠛⠊⠳⠸⡎⡻⣎⠻⣇⢢⢀⢳⡸⠇⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣭⣷⣌⠣⣳⡄⠀⣌⠂⠘⠎⠏⠢⣁⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣿⣿⣿⣌⣓⣬⣻⣎⡓⠀⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠒⠒⠠⠤⣀⡀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠳⠶⠂⠚⠚⠀⠀⠀⣨⡍⢐⢢⣤⠈⠓⠁⡔⠒⠒⠒⠒⠒⡄⠀⠰⡉⣁⠀⠀⢀⠸⠥⠤⠼⢇⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠊⠻⠜⠂⢦⠭⢛⡀⠀⣴⠂⡰⠂⠈⠀⠀⢸⠀⠀⣠⠋⡜⠻⣆⠀⣠⠛⡀⠀⠈⠁⣠⠔⠁⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⣀⢔⡎⢡⡤⠤⠐⢒⠶⠫⣁⣤⡀⠀⠀⠉⠀⠀⠺⠀⠀⢘⠀⢰⠧⠤⠼⠾⠧⢴⠧⠤⠶⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⢘⠉⠙⠶⠚⠙⡄⠀⠘⠤⠔⣇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠢⡀⠇
⠀⠀⠘⠘⡀⠘⠒⠊⠀⠀⠀⠀⠀⢥⡠⠇⡠⣠⢤⣄⣀⠤⠔⠒⠊⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠔⠓⠉⠈⠁⠀⡔⠒⠒⠢⡀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠸⣼⣀⠠⠄⠒⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⡴⠁⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣤⣄⠀⠒⠒⠒⠀⠀⠀⠐⠒⠒⠀⢀⣤⡀⠈⠉⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢀⡠⠃⡄
⠀⠀⠀⠀⠀⢸⠀⠈⢉⢍⣑⣒⣒⣒⠒⠀⠈⠉⠉⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠸⢿⣃⣠⣮⢿⠀⠀⠀⠀⠀⠀⠀⡏⠲⢄⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⡇⢰⣦⣶⢰⢴⠀⣤⡴⠀⢽⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠈⠱⣄⠀⠀⠀⠀⠀⠀⣇⡰⠋⠉⡆⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢇⠈⠁⠉⠈⠙⠓⠉⠙⠀⣸⠀⡇
⠀⠀⠀⠀⢀⠎⠁⠒⠒⠀⢴⡦⠤⠤⠤⠷⢤⠀⠒⠂⠉⠏⠀⠀⡰⠁⢸⡀⠀⣀⠀⡀⣸⠀⢀⣀⠀⠈⠢⣈⡉⣉⣉⣉⣉⣉⣉⣉⢉⣁⠔⠁
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠑⢄⠀⣞⡂⢂⡴⠁⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠋⢃⠀⢠⠤⢄⠀⢙⣂⣀⣐⡃⠀⠀⠈⣇⣀⣀⣺⠁⠀⠀⢹⣂⣀⣐⡃
⠀⠀⢸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠑⠁⠀⣈⣉⣉⣉⡁⠀⠀⠀⣏⣉⣉⣹⠀⠀⠀⢨⣉⣉⣉⡇
⠀⠀⠀⠈⠑⠒⠠⢤⣇⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠒⠊⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⢡⠀⠀⡘⠀⠀⠀⠀⡆⠀⠀⡎⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠀⠀⠀⠀⠀⣆⣠⠇⠀⠀⠀⠀⢱⣀⡘⠀⠀⠀⠀⠀⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠃⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠊⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠐⠒⠚⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢠⡄⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠠⠠⣤⡄⠄⠀⠀⠀⠀⢠⠄⠇
⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⢀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣸⣀⡀
⠀⠀⠀⠀⠀⠉⠒⠒⠢⠤⠤⠀⠤⠤⠤⠠⠀⠤⠤⠐⠒⠉⠀⠀⠀⠀⠯⠠⠀⠄⠄⠀⠀⠀⠀⠠⠀⠀⠤⠀⠄⠄⠀⠠⠄⠠⠀⠀⠀⠀⠠⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠉⠀⠒⠒⠦⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⣠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸⠁⠀⢀⠤⠐⠒⠊⠁⠀⠀⠀⠀⡔⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠒⠁⠀⡰⠁⠀⠀⠀⢀⠀⠀⠀⠀⡴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢀⠎⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡄⠀⠀⠜⠀⠀⠀⠀⠈⠀⢀⠖⠉⢁⠀⠈⢀⠎⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠒⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠛⠤⠀⠀⠁⣠⠊⠐⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⣠⠤⠐⠒⠊⠀⠀⠀⡀⠀⠀⠀⠘⠁⠢⠀⠀⠀⠀⡠⠒⠈⠁⡀⠀⢀⡼⠀⠀⠀⠀⠐⠀⠀⠤⢀⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⠀⠀⡀⠀⠀⢈⡤⠀⠠⡄⠀⠀⡠⠄⠀⠈⠀⠀⠠⠀⠈⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⣀⠤⠒⠁⢀⠀⠀⠀⣀⠜⡀⠀⠀⠦⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⠀⠀⠀⠈⠢⡀
⠀⠀⢰⠁⠀⢀⡰⠃⠀⡠⠀⣠⠁⠀⠀⡔⠁⢀⡀⠀⠈⠁⠐⢊⠑⠄⠈⢀⣀⡠⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⠀⠱⡀
⠀⠀⡆⠀⠰⠁⠀⡠⠎⡰⠋⠀⡠⠶⡊⠀⠀⠀⡠⠄⠀⠀⠀⢀⠔⠂⠉⠁⠀⠀⠀⢃⣀⣀⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠃
⠀⢠⠁⢀⠆⠀⠘⠀⢀⡀⠤⠊⠀⠀⠀⡠⠔⠊⠀⠂⡰⠀⢡⠃⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠁
⠀⠸⡀⡜⠀⠀⠁⠀⡏⡀⠀⠐⠀⢀⢎⡀⠈⠂⡠⠊⠉⢠⠂⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⢤⣀⡀⠑⣄⠀⡀⠠⠄⢒⡡⠊
⠀⠀⢣⡱⡀⠀⡔⠋⠀⠈⠂⠀⣀⠜⠀⢀⣠⠎⠑⢀⡴⠁⡜⠁⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢮⡆⠀⠐⠈⠁
⠀⠀⠀⠱⣁⠘⠀⢀⣀⡀⣠⠎⠀⣀⠴⠁⢀⡠⠖⠁⢀⡞⠀⢀⡀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸
⠀⠀⠀⠀⠈⠓⠦⠥⢀⣈⣀⣒⡊⠤⠤⠒⠉⠀⠀⠀⣎⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⡀⠀⠈⠛⠋⣉⣁⡤⠤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⡒⠢⣤⡀⢀⣠⡮⣻⣶⣀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢫⡦⠐⠀⠀⢐⠶⢊⣛⠟⠀⣍⢟⠣⣄⡭⠍⠛⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⡏⠀⠀⠀⠀⣀⠴⠋⣁⣠⣇⠘⢮⡳⣽⡝⠢⢄⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡁⠀⠈⠉⠀⠴⣢⡴⡾⢋⡔⠈⠀⡀⢀⡑⢆⠱⡜⢧⠀⠀⠑⣦⡄⠀⠠⢝⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⡼⠋⠀⠀⠀⠠⠒⠉⡰⣡⠁⠀⠡⡼⠊⠀⠀⠀⡆⢱⠘⣆⠈⠀⠀⠈⠢⡀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢠⠊⠀⠀⢀⡔⠁⠀⠀⡼⡽⠁⠙⢆⣰⡇⢀⠤⠠⣌⠅⢹⡄⢹⠀⠀⠃⠰⠀⠈⢳⣖⠀⠼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠆⠀⢈⡴⣫⠀⠀⢀⡜⡝⠀⠢⡀⠈⢣⠚⠁⠀⠀⡘⠀⡿⠁⢸⡀⠀⠘⡀⠀⠀⠀⠋⠓⢄⠀⠱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠀⡴⢋⠔⠁⠀⢀⡞⣼⠤⣀⠀⠸⢃⡣⠐⠒⠰⡘⠁⣸⠃⠀⣼⢛⠶⣤⠐⣄⠀⠀⠀⢄⠀⠁⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠔⣁⣀⡀⠄⡜⡰⠃⠀⠈⢦⡀⣎⠀⠀⠀⡀⠀⡰⠁⠀⣼⠃⠈⠀⢸⣄⠀⢹⠚⠓⠒⠓⠂⠲⠤⠴⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠤⠤⠤⠵⣶⢁⡗⠒⢤⠀⢸⡏⠁⣀⠀⠀⠀⣠⠀⠀⢰⠟⠀⠀⠀⠼⡇⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢘⡱⣀⠀⠹⣡⠑⠈⡀⠸⠁⢠⡏⠡⢠⠋⠹⡀⠀⠀⠀⢻⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡉⠀⠀⠲⢘⠧⠐⠂⢴⠂⢠⠎⢆⢀⠃⠀⠀⠙⢦⣀⡀⠘⠃⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠹⠀⢄⣀⣏⢀⣀⠔⠁⡴⠁⠐⢣⠎⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⣄⢀⣏⠠⠚⣁⣴⡿⠶⢂⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢈⣩⡤⠶⠭⠥⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢀⡀⡄⣀⠀⢀⡄⣄⢠⠀⡀⢠⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡸⢻⠀⠁⠈⡧⠸⠀⡇⡼⢠⡇⣼⢸⠄⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣵⣿⣿⣿⣿⣿⣿⡿⢽⣿⡛⢿⡷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣷⣿⣿⣿⣿⠿⠿⢿⣷⣶⣤⡄⣀⣀⣻⣿⣿⣷⡒⢄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣟⣙⡻⢿⣿⠿⠶⠤⡤⠤⠀⠈⠉⠙⠋⠽⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣀⣴⠋⠠⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠶⢤⢤⣀⣀⠀⠁⠂⠌⠙⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⡀⠀⠤⠀⠀⠒⠒⠲⠦⣄⣀⠀⠀⠀⠀⠀⠲⠤⣤⣰⣶⣕⣾⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⢨⡻⣿⣿⣿⣿⣦⡀⠀⠒⢒⣂⣠⡀⠀⣀⡀⢀⣀⡀⠀⠈⠽⣷⣮⣽⣻⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣞⣿⣿⣿⣿⣷⣦⣄⣤⣀⡀⠙⠻⠶⠶⢤⣍⣙⡛⠫⣤⣴⣿⣿⣿⣿⣿⣿⡿⢟⣿⣭⣴⣶⣶⣾⣴⣉⢛⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣏⡭⣟⣻⠎⠭⢀⣀⠤⠤⣤⣄⣠⣤⣦⣠⣭⣹⣿⣿⡿⣀⡜⣋⣁⣠⣤⣀⣀⠀⠀⠙⠻⣶⣀⠙⢷⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡶⠺⠭⣗⣶⣦⣬⣽⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⠁⠰⠛⠉⠉⠉⠀⠀⠉⠙⣄⠀⠀⠈⣻⣖⠀⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⣭⣻⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣷⣦⣠⢿⣿⠟⣑⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠤⠂⠰⠀⠤⣉⣬⣻⣿⣿⣹⡿⠊⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⣽⣯⣗⡯⠝⠿⣿⣿⣿⣿⣿⡿⠿⢿⣯⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢸⣽⣿⣿⣿⣿⡇⣀⣹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣤⣾⣿⡷⣶⡶⠖⠛⠿⣿⣈⡀⠸⢆⠀⠠⠀⠀⢠⠡⠛⠈⠈⣷⣿⡏⣸⡟⠀⣙⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠁⠀⠀⠸⣿⢷⣄⠈⠷⣄⠀⠀⠀⠀⠀⠀⣰⣟⣻⣴⡿⡄⢺⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠙⢷⣦⣤⣄⣀⣤⣤⣶⣯⣿⣿⠟⠁⣠⣴⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣧⣈⠙⠛⠿⠿⠛⠉⠉⠉⣅⣠⣷⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣶⣤⣶⣶⣶⣾⣿⣿⣶⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠛⣿⠿⠟⠛⠋⠉

⠀⠀⠀⡶⠛⠛⠉⠉⠑⠢⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠒⠒⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠁⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⣛⣷⡆
⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⡁⠐⠶⣿⣧⣤⣤⣤⣤⣤⡤⠤⠤⠄⣿⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠛⠛⠛⠶⣄
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠑⢄⠈⢷
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡆⠘
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡇⢠
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⣼⢃⡞
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⣠⠀⡄⡄⡄⠀⣤⠀⣿⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣴⠟⢁⠎
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠊⠒⠑⠃⠁⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠷⣦⣤⣄⣀⣀⣠⣤⣴⠶⠛⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠛⠁
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠸⣧⣀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠘⢿⣷⣤⣤⣄⣀⣠⣤⣴⣾⡿⠃⠀⠀⠀⠈⠙⢷⣄⣀⢀⣀⣠⣤⣶⡶⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂⠐⠋⠉⠀⠉⠳⣦⣄⡀
⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁
⠀⠀⢀⣀⣤⣴⣶⣛⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿
⠀⣴⠟⠉⠉⠉⠉⠉⠉⠒⠂⠄⢸⣧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⣀⡤⣀⠀⠉⠙⠒⠶⣤⣀⠀⠀⣿⠀⠀⠙⠻⢶⣤⣀⣤⡴⠚⠋⠉⢹⡇
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠙⠛⠚⠀⣀⣠⠶⢢⠀⢹⡇⠀⢸⠀⠀⠀⠀⠀⠋⠉⠙⠀⠀⠀⠀⢸⠃
⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⢸⣿⠀⠀⠀⢀⡴⠋⠀⣀⣀⣤⣤⠶⠶⠛⠋⠉⠈⠙⠁⠀⢸⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢸⡇⠀⢰⠆⢠⠀⠀⠀⠀⡎⠀⢸⡟⠀⢀⣴⣿⠶⠿⠛⠋⠉⠁⠀⠀⠀⠀⣰⡏⣠⡇⠀⠀⣼⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠈⣿⡀⠈⠁⠀⠳⠂⠀⠀⢝⠂⠸⡇⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⣋⣰⠆⠘⠛⠋⠀⠀⠀⣿⠇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠞⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⡇⠀⠀⢻⣾⣛⠂⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠄⠀⠀⠀⠀⠈⠈⠉⢀⣀⣤⠞⠓⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡫⠉⠉⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡀⢀⡏⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠋⠀⠀⠀⠀⠀⡴⠚⠉⠓⠲⠶⠶⠛⠉⠀⠀⠉⢢⠀⣠⠞⠉⠙⣿⡇⠀⠀⠀⠈⠒⠒⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠛⣿⠁⠀⠀⠀⢠⠖⠛⣇⣀⣀⣀⣀⠀⣠⠔⠒⠲⠦⣤⣴⠾⠋⠀⠀⠀⣿⠣⡀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⣿⡀⠀⠀⠀⢸⣴⢞⠋⠉⠈⠉⣩⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠙⢗⠢⣠⠖⠋⢳⡀⠞⠉⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⠁⠀⠈⠈⠙⠒⣤⠟⠑⠁⠀⠀⢀⡞⠑⠀⢻⣀⠀⠀⠀⠀⠀⠀⣀⠔⢋⠐⡲⢤⣄⣠⠜⠁⠀⠀⢸⠃⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣯⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡾⠰⠀⠀⠀⠈⡙⠛⠒⠒⠚⠻⣤⣰⡇⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⠙⠻⠿⣿⣧⡀⠀⠀⢿⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⢀⣠⣯⡴⠞⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠈⠉⠛⠒⠾⠷⣤⣄⣤⣾⣷⡀⠀⠀⠀⢈⣇⣀⣤⡀⠀⠀⠀⢈⡃⣉⣓⣶⡶⠶⠞⠛⠉⠁⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠶⠾⠿⠷⠶⠚⠓⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣟⣛⡻⠿⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠖⠚⠛






⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣠⣶⡄⢀⠊⠩⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⡾⣟⣫⣽⣿⣿⣿⠛⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⢛⣛⣻⣿⡟⣺⠃⣿⣿⠃⡠⠔⢃⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⢂⠥⠒⢋⠫⣿⠁⡀⢸⣿⠛⡎⡦⢅⡐⠀⠠⠬⢿⣷⡾⠂
⠀⠀⠀⠀⠀⠀⠀⣷⣤⡀⢠⣾⣿⣿⠷⣗⢋⠁⠟⢀⣧⡜⡟⣾⢃⣯⣄⣀⣠⣤⡶⢟⡿
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⠛⠛⠛⢻⡭⢠⣤⣶⠾⢾⡿⠷⢿⣏⣼⣷⣄⠀⠤⡐⠊⠑⣲⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣀⣠⣼⢚⡻⠿⠷⠿⠷⠞⡋⠝⠭⣈⣠⣤⣍⣢⣌⠿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⠁⠀⢈⣿⡛⠍⠙⠻⣦⣀⡀⠈⠉⠉⠛⠛⠛
⠀⠀⠀⠀⢀⣀⣠⣀⠠⠂⠀⠐⣲⣿⠃⠀⠈⠷⠀⡀⣀⠈⠀⠹⣷⣆
⠀⠀⠀⠀⠀⠉⠉⠛⠐⠊⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠛⠛⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⣠⠴⠖⠚⢉⡟⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢀⡜⠁⠀⢀⡰⠋⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠤⠒⠉⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⡀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣯⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣹⣦
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢄⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠈⡆
⠀⠀⠀⠀⠈⢢⡁⠀⠀⠀⠀⠈⠳⢄⠀⠘⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢱
⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣀⣀⣠⣤⠽⠶⠟⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠀⠉⠙⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠈⠻⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢠⠞⠋⠀⠀⠀⠔⠂⠉⠉⠉⠉⠉⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠔⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠒⠒⠀⣷⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠠⠊⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⣄⣀⣀⣀⠀⠐⠀⠀⠀⠀⠀⠠⣤⠄⠀⠀⣀⣤⡴⠞⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⡉⠉⠙⠛⠶⠶⠶⠶⠶⠶⠶⠶⠞⠉⠀⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⢤⣀⡀⠢⠤⢤⡄⠠⠄⠒⠂⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡒⠚⠙⠶⡚⠛⠦⣄⠀⠀⠀⠀⠉⠓⠶⠤⠴⠶⠚⠋⠛⠋⠉⠀⠀⠐⠤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠁⠠⣇⣴⠶⣄⠙⢦⡄⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠀⠀⣀⣀⣀⠀⠀⠄⢠⠂
⠀⠀⠀⠀⠀⠀⢀⠴⢦⠙⢄⡤⢬⠁⠀⠉⡷⠀⠧⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⡄⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⠂⡎⠉⠀⠠⠎⢱⡟⠓⠚⢦⠣⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣻⡀
⠀⠀⠀⠀⠀⠀⢀⢤⡂⢠⠞⠁⠀⣈⠒⠦⣌⠳⡄⠀⠀⠀⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡴⡆⣸⣶⠇⡀⡀⢀⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠈⣦⠁⠀⠣⣠⠜⢀⣉⣀⡈⠲⢬⡁⠂⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣿⢻⠃⠀⠘⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠲⠤⠆⠰⡉⠀⠈⠙⣇⡀⠙⢲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠇⠈⠀⡠⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⠀⡌⠀⠒⠒⠉⢻⡆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠐⣊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠒⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠒⠛⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⣐⣢⣤⣈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠮⠭⣀⠑⠦⠐⠬⣑⢄⡀⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠂⠀⠚⠙⠿⣝⣳⠄⢘⠛⠃⣥⡞⠉⠉⠉⠛⠫⣉⠉⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⢀⣀⠠⣵⣿⡿⣰⡟⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢀⠤⠊⣡⣴⣶⠞⠛⠷⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⠿⠶⡿⠋⠀⠀⠀⠀⠀⢱⣼⣧⠀⠀⠢⡀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⡠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠁⡿⣧⠀⠀⠌⢀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠇⠀⠙⠒⠳⢶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⡠⠊⢁⠀⠀⠀⠀⢀⠀⣸⠇⠨⠀⠀⠇⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠠⢼⠿⠞⠉⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣲⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⠂⠀⠒⠒
⠀⠀⠸⣍⡴⠂⠀⠀⢀⠐⢚⠫⡍⢉⣤⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⣉⢁⡤⠐⠂⠉⡇⠀⠀⠀⠀⠀⠀⣠⣌⠿⣿⣿⣿⡄⠉⢀
⠀⠀⠀⣸⠂⡧⠀⢀⠟⠦⠄⠀⠛⢂⣉⠄⠀⠁⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⡍⢀⣤⣴⡴⠃⡇⠀⠀⠀⠀⠀⠀⠀⠹⢿⡄⠠⡴⠒⠾⠉
⠀⠀⠘⠯⠴⠇⠀⠠⠄⠰⠖⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣅⡌⠛⢃⣩⣴⠖⠃⠀⠀⠀⠀⠀⠀⠀⡄⠈⠥⠀⠀⠤⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢐⣊⣁⣋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⢶⠖⢦⢴⠈⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠴⠖⠒⡊⠉⠉⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡒⠶⠶⢒⣂⡴⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣉⠡⢤⡠⠀⠐⢒⣈⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⣠⡀⠀⠀⠤⠉⠭⠥⠴⠖⠚⠉⠁⠀⠀⠀⣀⠠⣠⡔⢒⠏⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⢤⠤⠤⠄⠀⠀⡀
⠀⠀⢈⡿⣆⡀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠚⣿⠋⠀⡰⢿⣠⠎⠀⠀⠀⠀⠀⢸⠀⠀⠢⢽⡿⠟⢁⣶⠆⠀⡀⠀⠀⡟⠛⢛⠛⣓⣒⣒⡒⢒⠀⠁
⠀⠀⠀⢇⣹⡙⠓⠚⢋⣿⠉⠀⡸⢯⠠⠎⠛⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠰⠋⣴⣸⠿⠋⠀⠀⡇⠀⠀⡿⠀⠸⠛⠙⠛⠋⠃⢀⠀⠸⡄
⠀⠀⠀⠀⠈⠳⠦⠴⠋⠙⠛⠋⠁⢀⣀⣠⡤⠤⠶⠶⠒⠒⠲⠤⣀⠀⠀⠀⢸⠇⠰⣤⡼⢓⣯⣚⣅⠀⢰⡇⠀⢰⠁⠀⣴⡏⠀⠒⠂⠒⠉⢧⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣄⡀⠀⠀⢀⣀⣀⣠⣤⡀⠀⠀⠀⠀⣿⡆⠘⢁⣾⣽⠿⠋⠉⠀⢸⡇⠀⣸⠀⢠⠀⠁⠀⠀⠀⠀⠀⠠⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠳⠯⠶⠾⠿⡿⠛⠛⠋⠡⠀⠀⠀⠀⣿⡅⢀⣉⣁⣀⣀⣀⣀⡀⢸⡇⠀⣿⠀⣇⠀⠠⣤⣤⣤⣤⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⠀⡄⢖⠉⢈⣓⣂⠀⠐⠀⠀⠀⠀⠈⠀⠚⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⢻⡆⢠⠄⢀⠀⡍⢉⠩⢠⠀⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢱⠈⠂⠀⡈⢈⡀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡸⠇⠸⠀⡇⠈⡶⠸⠎⠀⠇
⠀⠀⠀⢠⠖⣒⣂⠀⢰⣲⡄⠀⠀⠀⠱⠄⠀⠀⠆⠀⠐⣉⡙⠂⠁⠀⠀⠀⠀⠀⠀⢠⣩⣭⣭⡅⠀⠀⠀⠀⠀⣖⣿⣀⣀⣀⡀
⠀⠀⠀⢈⠉⠉⠉⠉⠉⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠿⢭⠍⠗⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⢠⡎⠤⠀⠀⠀⠄⣼⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⣾⢁⠀⣤⣤⣄⠀⣏⠄⡇⠀⠀⢰⣖⣋⡉⠉⠉⠉⠉⠉⠉⠑⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢠⡄⢻⠀⠀⢰⣿⡿⠿⠿⠿⠿⠯⠍⠽⡗
⠀⠀⡇⢀⠈⠭⠭⣭⣉⠉⠀⡏⠀⠀⢠⣯⡿⠛⢛⣛⣛⠉⠙⣛⠈⠀⠀⠀⠀⣿⠀⠀⠠⠴⠦⠤⡀⢻⢸⠘⡇⠀⢰⣌⣙⣛⠛⠛⠒⠚⠛⠃⢡
⠀⠀⣿⡅⠀⠄⠀⠀⢹⣷⠀⡇⠀⠀⢸⡟⠃⠰⠿⠧⡼⠇⠀⠀⢠⡇⠀⠀⠀⠉⠀⠐⠀⠘⠁⠀⠐⢸⡾⣰⠁⠀⣿⡏⢉⣡⣤⣤⣀⣁⣀⠀⠈⡇
⠀⠀⢻⠘⢷⡶⠶⣒⠋⣿⠀⡇⠀⠀⢸⡇⢉⠙⢛⠛⢛⠛⠉⠁⢸⡇⠀⠀⠀⢇⢠⠀⡧⠀⠶⣀⢀⠀⠻⠃⠀⠀⣿⣰⠋⠤⠤⠄⠠⠤⠄⠙⢦⡇
⠀⠀⢸⠀⢲⡿⠻⣀⡄⣿⠀⡀⠀⠀⠸⡇⠨⠴⠒⠆⠘⠀⠠⢀⢼⡇⠀⠀⠀⢸⣞⠋⠁⠀⠈⠁⢸⠀⢠⠀⠀⠀⣿⡧⠀⠂⠂⠀⠀⠀⢂⠠⢸⡇
⠀⠀⢸⣄⣁⣀⡐⣛⣁⣿⡶⠇⠀⠀⠈⡧⠙⢓⣒⡶⠶⠶⠖⢚⢹⡇⠀⠀⠀⢸⠙⠀⣁⠀⡀⢀⡞⢀⣿⠀⠀⠀⣿⠘⢦⣐⡲⠦⠰⠚⣉⠴⢚
⠀⠀⠀⢧⡈⠉⠉⠩⠉⠅⠠⠁⠀⠀⠐⣇⣀⠙⠻⢯⣭⡽⠂⠀⠸⠃⠀⠀⠀⠀⢷⣆⣀⣋⣉⡁⢀⣠⠏⠀⠀⠀⠈⢧⣄⣈⣉⣉⣉⣉⣠⢄⣻⠆
⠀⠀⠀⠀⠉⠙⠛⠓⠂⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠴⠛⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠁⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠
⠀⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠛⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⡀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠴⠀⠒⡁⠀⠀⠤⠤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠐⠒
⠀⡀⠀⠀⠀⠈⠤⠠⠴⠒⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠉⠁⠀⠀⠀⣤
⠀⢁⠀⠀⠀⠀⠀⢀⡀⠄⠠⠀⠀⢉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠈⢀⡂⠀⠀⠀⠀⡅⠀⢀⡀⢀⡤⢠⠠⠀⠁
⠀⠈⠀⠬⠀⠈⠀⠃⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠘⡀⠀⠁⠀⠀⠀⠇⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠛⠁⠀⠀⠄⠀⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⢛⠉⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⢀⡀⠀⣁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢨⢀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠁⠈⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠲⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⠆⠘⠃⠂⢂⠄⠀⠀⠀⠀⠀⠤⠄⢙⣐⣒⣉⠠⠤⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⡀⠀⠀⠀⠀⣀⠤⠀⠀⠠⠤⢀
⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠸⡀⢆⢀⣄⠲⠀⢂⠀⡇⠀⠀⠀⠀⠰⢠⠂⠈⠲⠂⠀⠀⠀⠀⠀⢀⠈⠀⣀⡀⠁⡁⣀⣀⢱
⠀⠀⠀⠀⠛⠄⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢀⠜
⠀⠀⠀⠀⠁⠀⠈⠠⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠒⠒⠒⠒⠁⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⣶⣶⣶⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠁⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢴⣿⣿⠿⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⣠⡿⠛⠿⠿⠿⠛⠻⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠁⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠈⢷⡀
⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠈⢷
⠀⠀⣰⡟⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠸
⠀⢰⡟⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⢀⣿⠁⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⢸⡇⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢠
⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡾
⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⢻⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⣿⠛⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋
⢸⣧⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⢿⡄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⢠⡿⠀⠉⠉⠛⠓⠶⠶⠤⠴⠶⠛⠁
⠀⠈⢻⣆⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⣰⡟⠁
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣻⣶⣶⣾⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡼⠦⣄⡤⠚⠉⠤⠖⣚⡿⡶⠖⠈⠀⠀⠀⡀⠀⠈⣢⠀⠉⢒⣤⣵⣦⣀⣀⣠⠴⠞⢓⡺⣿⣿⣚⣷⢦⡘⣏⠉⠂
⠈⢁⠖⠁⠀⠀⢀⠠⠐⠍⡯⠀⠀⠀⣠⡾⠉⠀⠀⠈⡣⠔⠋⠈⠉⢀⡴⠋⠉⠀⠀⠀⢠⠞⠁⠀⠀⠈⢹⡿⠃⠀⠀⠀⠀⡀⠄
⡰⠃⠀⠀⠀⠀⠀⠀⢄⣲⠶⠒⠊⠉⠉⠉⣓⣦⠀⠠⣤⡰⢶⣄⣀⡃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⡷⠆⠠⣤⡤⠊
⣧⡤⠒⠒⠐⢤⣠⠚⠉⠀⠀⠀⠀⠀⠀⢀⣬⣿⠈⠑⡜⠁⠀⠉⠉⠛⣷⠂⠐⠀⠀⠴⣆⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠲⡤⠤⣤
⠉⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡀⠠⠤⠾⣿⠛⠀⢘⡅⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠄⡂⢍⣶⡓⣲⣿⣥⣀⠀⠀⠀⠀⠙⠁
⢳⡀⠀⠀⠀⠀⠀⠀⠈⠖⠋⠁⠀⠀⠀⠀⡠⠑⠒⠒⣃⠀⠀⠀⠀⠀⢠⡇⠀⠀⠠⢀⠈⠀⠹⣿⢡⠞⠅⢹⡗⠢⣀⠀⠠⠁
⣄⠙⢦⣀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣘⣇⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠷⢤⡀⠀⣀⠉⠾⣖⡿⠀⠀⠀⡼⠁⠪⠈⠳⠶⠃⠒
⢸⣦⠶⠋⠉⠀⠘⠶⠖⠲⠤⢤⣴⣶⡿⠿⠚⠒⢲⢶⡀⠀⠀⡔⠁⠀⠀⠀⠀⢹⡶⣤⣭⠽⠿⠄⠐⠀⠾⠥⡀⠀⠀⠀⠡
⡾⠀⢳⡀⠀⠀⠀⢀⡤⠗⢋⠙⠀⠀⠀⠀⠀⠀⢀⡾⣤⣈⣸⠀⠀⠀⠀⠀⠀⣸⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣆⡀
⣥⣀⣀⠙⢦⡀⠀⣏⡀⠀⠈⠀⠀⢀⠉⠛⠒⠒⠿⣅⠀⠉⠙⣄⡀⠀⣄⣀⣴⠏⠀⠀⠀⠀⠁⣄⣤⣤⣤⠶⠞⠁⠉⢳⣆⡤⠴
⣡⠻⠉⣷⠀⣍⡈⠈⠛⠦⣤⣀⣠⡁⠀⠀⠀⠀⠀⠈⢳⡄⡊⠠⢀⠔⣫⣿⠛⣦⠀⠀⠀⠀⠀⢠⠀⢈⡇⠀⠀⠀⠀⢰⡯⠀⡠
⠁⣴⠟⠀⠀⠘⠦⣄⡀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠊⠀⠂⠐⠁⢰⠁⠙⠓⠛⠒⢤⣀⣤⡀⠀⢀⣾⣤⣤⣤⡄⢀⡾⠃
⣼⠁⡀⠀⠢⢀⠀⢈⡽⠗⠒⠀⠀⠀⠙⠒⠤⣤⠴⠆⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠙⣆⠉⣻⠟⠉⠉⠀⢲⠟⠛⠁
⠹⡀⠀⠀⡀⠀⠱⠈⢣⡀⠀⠀⠀⠀⠀⠐⠛⠶⡵⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣀⡽⠋⠁⠀⠀⠀⣰⠏⣀⠀⠀⠀⠀⠂
⠀⠙⢦⡈⠉⠀⠀⢀⢀⠹⣄⠀⠀⠀⠐⢸⠃⠀⠀⢮⣴⡶⣾⠁⡀⠈⠂⢀⡀⠀⠀⢛⠉⠀⠀⠀⠀⣠⠞⠁⢰⠊⠛⠶⠿⠄⣀
⣄⠀⠀⠉⠓⢦⣌⣣⣍⣷⣼⠷⢦⣀⠀⠤⣄⠀⠀⠀⠀⠀⢸⡄⠀⠀⡀⠀⡘⠀⠀⢢⣦⠄⠀⠰⠏⠁⢀⠢⠔⠀⠀⠀⠀⠀⠈
⣸⠎⠉⠉⢉⡽⠛⠉⠁⠀⠀⠈⠁⠉⡻⠶⢶⠦⡀⠀⠀⢠⡏⠙⢦⣈⠉⠀⠈⠢⡠⡈⢿⡊⠀⠄⠀⠀⠀⠀⢰⡀
⠉⠚⠳⢴⣭⣤⣀⠀⠀⠀⠀⠀⢀⡔⡁⠂⠄⢠⠈⠀⢐⣿⠁⠀⠀⠈⠙⠶⣬⣻⣬⣻⣮⣧⠄⠶⠂⠀⡀⢤⣸⡟⢦⣤⣀⣠⠴
⠀⡃⠀⠀⠀⠀⠉⠳⣄⠀⠀⣀⣤⠂⠀⠀⠀⠔⠒⠠⢼⣟⣦⣀⣀⣀⣠⠔⠁⠈⣋⡿⠋⠁⠀⠀⢨⣀⣽⣿⠿⠿⣶⣿⣿⠇
⠉⠀⡀⠀⠀⠀⠀⢀⣬⠷⠾⠟⠘⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠐⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⡰⠷⠛⠋⠁⠈⠁⠢⡨⣙⣶⠖
⠀⠀⠀⢀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⢀⣰⡟⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⣠⠏⠈⢻⣇
⣠⡤⠴⠞⠃⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⣄⣷⣄⡀⠀⠀⠀⠈⠙⣿⠛⠻⠭⢧⣀⣀⠠⣊⣁⣀⣀⣀⣀⣀⣤⠶⠛⡁⠱⠦⣖⣧
⠀⠀⠀⠀⠁⠀⠀⢷⣄⣀⣀⣀⠤⠃⢸⡋⠉⠀⠉⠓⠲⠞⡓⢖⡚⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠫⡉⠉⠉⡏⠓⠦⣬⣭⡽⠟⢳
⠟⢿⡆⠀⠀⠀⢀⣠⣼⣄⠀⠀⠀⠀⢀⠹⠤⠄⠠⡀⠀⢀⠈⡑⠡⡀⠀⠀⠀⠀⠳⣄⠀⠷⠀⠀⠀⠀⠈⣿⡀⢀⣀⣤⠤⠶⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢒⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠁⠞⠉⠙⣳
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠀⠀⠀⠀⠀⠀⠰⡾⠷⠀⠀⠀⠀⠀⠀⠀⣿⢧⡀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢧⠀⠀⠀⣠⡴⢦
⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠂⠀⠀⠀⠀⠀⠀⢷⣿⠀⠰⠐⠀⡁⠂⠀⠠⡀⠀⠀⠀⠀⠀⠠⢬⣁⠀⠀⠀⠀⠊⠀⣸
⠀⠀⠀⠀⠀⠿⡄⠀⠀⢀⠔⠀⠀⠀⢀⡰⣲⣿⠀⠀⠀⠀⠀⣠⡾⣯⣻⠂⠀⠈⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠏⠉⠙⠚⠃⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠈⠉⢉⢻⣿⠀⠀⠀⠀⢠⣿⣇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⠀⠈⠀⢀⣀
⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠀⠀⠀⢀⡎⣼⡿⠀⠀⠀⠀⢸⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠇⠀⠀⠀⣾⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠟⠁⠀⠀⠀⠀⠈⠻⣷⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠸⡀⠠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠘⠃

⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢼⡒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣍⡓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢥⣉⠓⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡼⠓⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠉⢻⣔⢛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠚⠛⠉⠉⠉⠉⠀⣀⣀⡉⢫⡀⠳⡒⠲⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠴⠒⠀⠀⢀⣀⣀⣀⣰⠋⠀⢱⡄⠙⣄⠉⡉⠙⣆⣀⣀⣤⣤⡤⠤⠤⢄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠐⠋⠁⠀⠀⡀⠀⠀⠂⠉⠉⠁⠀⠀⣇⠀⠀⢥⡇⠀⠈⠓⠉⠀⠀⢀⣀⣠⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⢰⠀⠢⠤⣀⣀⠜⠁⢀⡄⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠚⠉⢙⡦⡄⠈⠓⠤⣄⡠⠜⠁⠀⢈⡇⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠈⠐⠲⠤⣄⣉⣳⢶⣮⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠱⣀⠀⠀⠀⣀⠀⠀⣠⣞⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⢹⠟⠚⣱⡄⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠈⡻⠒⠉⡇⠹⡅⠠⡌⢣⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠤⠼⣇⠈⣾⡒⠒⠒⠒⠒⠀⢤⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⣧⠀⠙⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⠆⠛⠛⠛⢦⠘⣗⠒⠒⠒⢬⡳⣄⠹⡝⠲⢄⡀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣠⠞⡻⠀⠸⣀⠀⠀⠀⠈⢧⠘⡆⠀⠀⠀⠙⢎⡆⠹⡄⠐⠉⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸
⠀⢀⣠⠔⡋⠀⣠⠞⠲⣄⡈⠓⠤⠀⣀⡈⣣⡘⣄⢀⡠⠖⠉⣠⠔⠁⠀⠄⣀⠐⠻⠢⡀⠀⢀⡇⠀⢀⡀⠀⠀⠃⠀⠀⡜
⠊⠁⢀⡤⠖⠋⠀⠀⠀⠀⢉⡷⠂⠠⠤⠤⠭⠭⠥⢤⠤⠒⠉⠀⠀⠀⠀⠀⠈⠑⠦⣀⠹⡆⠼⢁⡆⠘⠁⠀⠀⠀⠀⢠⠃
⢷⠈⠀⠀⠐⠀⠀⠘⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠈⠓⢷⡀⡎⠀⠀⠀⠀⢀⠀⢀⡎
⠈⣇⠀⠀⢀⡤⠀⣠⠞⠀⠀⣠⠀⠀⠀⠀⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠀⠇⡆⠔⠀⠀⠀⠚⠀⡜
⠀⠘⣆⠀⠀⣠⠞⠁⢀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠄⠀⠘⡄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡇⠀⠀⡠⠀⢀⠌
⠘⠀⢫⠑⠮⣀⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡄⠀⢠⠞⠀⠀⡇⣠⠞
⠀⡇⠸⠀⠀⠈⣏⠓⠒⠤⢄⣠⡏⠀⠀⠀⠴⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⢸⠋
⠀⢹⡀⠃⠀⠀⠹⠀⠀⠀⠀⠀⠉⠒⢲⠒⠶⠶⠒⠂⠀⠑⠒⡶⠤⠤⠄⠒⠂⠁⡜⠀⡀⢀⡎
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⡞
⠀⠀⠀⠻⡇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠎
⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⢇⠀⠀⠲⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠑⢤⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⡠⠂⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢄⡀⣄⠠⢀⠀⠀⠀⠀⠀⠀⠀⡠⠊

⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⣹⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠉⣹⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠂
⠀⠀⠀⠀⠀⢀⡼⠁⠀⣺⣿⢃⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⣸⡿⢡⠞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⠃
⠀⠀⠀⠀⢀⣞⡄⠀⡠⣾⣧⡞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠠⣾⣥⠏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃
⠀⠀⠀⢀⡞⡌⠀⠀⣲⣿⡿⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣺⣿⠏⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠇
⠀⠀⠀⡼⡐⢠⠆⣪⣽⣽⡳⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢠⠀⣨⣿⡟⡄⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⠋
⠀⠀⢰⠃⢡⣟⣸⣼⣿⢯⠃⣰⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡇⣤⣿⡿⠜⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣰⣿⣿⡯⠁
⠀⠀⢸⡠⢱⣯⣿⣿⢯⠃⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣨⣥⣿⡷⢭⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣿⣿⣿⡏⡍
⠀⠀⢸⣿⣿⣾⣥⣟⢏⡔⠁⠀⠀⠀⣀⣤⣄⠀⠀⠀⠄⣧⣷⣿⣿⡙⢂⠌⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢸⣿⣿⣿⣟⠳
⠀⠀⠸⣮⣿⣿⣿⠾⠋⠀⡠⠞⠳⣟⣿⣿⡌⢷⡀⠀⠸⣽⣿⣿⣧⠟⠁⢀⠴⠚⢳⣟⣿⣧⠙⣆⠀⠀⢈⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⡀⣠
⠀⠀⠀⠈⠉⠉⠁⠀⠀⢸⠁⢐⠀⠘⣧⢻⣧⠘⡇⠀⠀⠀⠈⠁⠀⠀⠀⡎⠀⠀⠀⢹⡜⣿⡆⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢘⠀⠀⣿⣋⣯⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⢹⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢾⠀⠀⢸⣧⣿⠇⣻⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠃⠀⠀⢻⣾⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣎⣇⡇⠸⣿⡦⢀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⡰⠀⢸⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⢧⠀⣷⣶⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡾⡀⢸⣿⡏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣀⣿⣿⠁
⠀⠀⠀⠀⣠⠖⣏⣙⢦⡀⠀⠸⣿⠎⣴⣏⣧⣿⠁⠀⠀⢀⡔⢋⢙⢢⡀⠀⠀⠹⣷⢁⢼⣿⣰⡟⠀⠀⠀⢀⢔⣾⣶⣄⠀⠀⠈⢿⣿⣽⣿⣿⣴
⠀⠀⠀⢰⠣⣞⢽⣸⢻⢣⠀⠀⠈⠻⣴⣿⣯⠃⠀⠀⢀⡿⢔⠸⣄⠑⢻⡀⠀⠀⠙⢧⣼⣿⡿⠁⠀⠀⠀⠁⠈⠻⣿⣿⡆⠀⠀⠈⠻⣿⣿⣿⠃
⠀⠀⠀⡾⣻⠕⡩⠂⠈⢸⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⢑⠅⠈⠁⠀⠉⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣇⣿⢊⡀⠀⢀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣨⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⢻
⠀⠀⢠⣏⡼⣃⡄⠘⠈⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡰⢃⡄⠀⠀⢸⠃
⠀⠀⠈⣇⣟⣿⣦⣢⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣷⣦⣀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⠁
⠀⠀⠸⡷⢫⣼⣿⣱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠫⣴⣮⣥⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⠃
⠀⠀⠀⠱⣦⣉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⢀⡴⠚⠋⠉⢀⡼⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⠴⠂⠀⠀⠀⠀⢳
⠀⢠⠏⠀⠀⢠⡴⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡤⠖⠋⠁⠀⠐⢒⠀⠀⢠⡟
⠀⠁⣀⡰⠋⠁⠀⠀⠀⠀⠀⠀⢀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣧⣀⠈⠀⠠⠄⠂⣁⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⣈⣱⣄
⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠠⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⢹
⠀⠘⢌⠢⡀⠀⠀⠀⠀⠑⢄⡀⠀⠱⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠓⢤⣀⡀⠀⠀⠄⣀⣉⣶⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠀⠀⠉⠉⠉⠙⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⢰⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⢀⡀⠀⠀⠉⠉⠁⠀⠀⠀⠐⠄⠙⠷⣦⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡌⠰⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⠶⠋⠁⠀⠀⡠⠤⠶⠄⠒⠒⠒⠦⠄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠀⢹⡀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣁⣀⠀⠒⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠖⠂⣀⡴⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⠒⠶⢦⣤⣤⣌⣁⡀⠀⠀⠀⠀⠐⠛⢀⣁⡤⠴⠖⠛⠉⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠋⠉⠉⠀⠠⠄⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠉⠛⠲⠤⢤⣑⠒⠒⠶⠤⠔⢂⣉⣉⣠⣤⠾⠋
⠀⠀⠀⠀⠀⠀⣠⡔⠢⣍⠛⠉⠙⢛⡉⠉⠗⢦⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠛⠉⠉⠉⠉⠀⠀⠀⢀⡓⢦⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠰⣁⠁⠀⢿⣤⠟⢦⣄⠙⢶⠄⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡆⢀⣀⣀⠠⡄⠀⠀⠀⢠⠂⠁
⠀⠀⠀⢀⠖⢦⡈⢦⡤⠦⡄⠀⠀⢹⡇⠘⠆⢀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⡤⠘⠲⣄
⠀⠀⠀⠀⠀⢀⡽⠇⢴⠉⠁⠀⠴⠋⣼⠟⠓⠞⢤⠳⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⣼⠃⠀⠀⢸⣆
⠀⠀⠀⢀⣤⠆⠀⡴⠋⠀⢈⠓⠦⢄⡈⠳⡀⠀⠀⠀⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣦⡆⣸⣴⠏⡀⠀⠀⣾⠻⣆
⠀⠀⠀⠙⣎⠁⠀⠣⣀⣠⠋⢙⡂⠀⠱⢤⣑⠂⠠⡠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣷⢿⠋⠀⠑⣿⢸⣿⠀⠈⠁
⠀⠀⠀⠀⠫⡀⠤⣄⡀⢠⡒⠋⠈⠙⠳⡄⠈⠳⢤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡇⠉⠀⢀⠀⠘⢿
⠀⠀⠀⠀⠀⠈⠃⢀⢀⠀⢈⠂⠀⣤⡴⠻⣶⡄⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡀⠔⣉⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣈⣀⣠⣄⣀⣤⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠦⢤⣤⣤⠤⠶⠚⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠚⠉⠓⣲⣖⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠛⠁⣠⣶⠆⠀⠉⠀⠀⠀⠌⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⠐⡌⢧
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢳⡐⡈⣷⡄⢀⣠⣠⠤⠴⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⠀⠹⡀⠆⠁⣠⢞⢫⠍⠀⠀⢀⣉⣀⣈⣀⠒⠲⢭⣒⢤⡀
⠀⠀⠀⠀⠀⢸⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠁⢠⢞⠕⠁⠀⣀⠴⠚⠉⠈⠀⠁⠉⠙⠓⢦⠙⢳⣿⡄
⠀⠀⠀⠀⠀⢸⣇⣼⣿⠀⠰⠀⢀⢐⡆⠀⠁⠀⠀⠀⠀⠐⢠⣟⠊⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⢹⣿⡀
⠀⠀⠀⠀⠀⢈⣿⣼⣷⠀⠰⡄⢠⠈⡇⡀⡇⠇⣷⢠⡜⠄⡿⡼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⣩⣍⣁⣼⣿⣧
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⡁⢇⠈⡄⡇⣇⣷⣦⣿⢸⡇⡀⢰⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡎⣰⣾⡿⠟⡟⠋⠟⠿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡰⢸⣷⡀⣧⣹⠹⣿⢹⣼⡇⣴⡾⣿⡄⠀⠘⢇⠀⠀⠀⠀⠀⣸⠀⣿⡏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣧⣸⣿⣿⣽⣼⣿⣧⣿⣷⣿⣷⣀⠀⠈⠒⠒⠒⠒⠚⢁⣰⠏⠃⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋⢹⣿⢶⣤⣤⣶⣾⣷⡾⡿⡏⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⢝⣦⣙⢮⡛⠻⡛⠀⠀⠁⠀⠀⣠⡆⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣓⣬⣀⣀⠀⠀⣀⣄⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠵⠋⠁




⣶⣶⣶⢶⠾⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⣶⣶⣶⣶⣶⡶⣶⣾⢶⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠇⠀⠉⠁⠒⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠉⠑⠒⠤⠤⠀⡀⠎⠠⠚⢠⠐⠒⠒⠚⠛⠩⠭⠭⠼⠛⢲⠂
⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⢰⠀⠆⠀⠆⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠠⠀⠐⠀⠀⢸⠀⠀⠀⡇⠀⢀⠀⢺⡀⠐⠒⠒⠒⠂⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⢸⡇⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠓⠀⠁⢓⠲⠤⠤⠤⣤⣄⣤⠤⠤⠎
⠀⠀⠀⠀⠀⠀⢸⡇⠢⡠⠂⠀⠀⠀⢸⠀⠀⢠⡇⠀⠰⣿⣶⣼⠀⢠⠆⠀⠀⠀⠀⠄⢸⠀⠀⠀⢀⡄⠐⠒⠶⠶⠤⢤⣄⣀⡀
⢀⠀⠀⠀⠀⠒⠂⣇⠀⠀⠀⠀⠘⠀⢸⠀⠀⢸⠃⠐⠷⠿⠿⠇⡄⢮⢀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠸⠀⠀⠀⠀⠈⠀⠐⠂⠈⠉⠛⢲
⢛⠒⠒⠒⠂⠀⠀⣿⢠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠈⠀⠀⡤⠄⠞⢰⠃⣠⡶⣞⡓⠶⠞⠉⠙⢦⠀⠀⠀⠀⠀⢸⡄
⠀⠙⠒⠒⠀⠀⠀⢹⠀⠀⠉⠉⠉⠋⠀⢰⠀⠀⠀⠀⠀⠀⢀⡇⢰⠀⡴⠀⠈⠀⠀⢨⠾⡋⠀⠈⠻⣄⠀⢀⣀⠀⢳⠀⠀⠀⠀⣿⢇⣀
⠀⠈⡀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⡅⣸⠁⠀⡀⠢⠀⠀⠀⢀⡅⠀⠉⠀⠀⠀⢿⣀⠀⠁⠀⠐⠀⢀⣀⠀⠇⠨⠉⢙⠛⠛⠶⠦
⠀⠀⠑⠤⢤⡤⠤⠀⣀⠶⢠⠀⡄⢀⠀⠀⡎⠀⠀⠀⠀⢡⠇⠀⠀⠈⠒⣢⢀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠙⣧⠀⣄⡀⢳⠀⣀⠀⠉⠐⠒⠂⠼⢃⡴⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠐⠨⠀⠂⢱⠃⠀⠀⠀⡾⠀⠀⠀⠀⣎⠀⠀⠒⠶⢶⣤⣄⣉⡀⠀⠀⠀⠘⠇⠈⠁⣀⡇⢀⡉⠁⠀⠀⠀⢰⡯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠃⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠉⠙⠛⠷⢦⣤⡀⠐⡤⠊⠁⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣤⣤⣤⣀⣀⣉⣀⣀⣤⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠠⢰⡈⠍⠉⠻⠛⢉⣵⣂⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠉⠂⡀⢀⡕⣀⣉⣁⣭⠔⢒⠦⠬⣭⣙⣻⣤⡀
⠀⠀⠀⠀⠀⠀⠊⢤⡀⠀⠂⠉⣹⣭⣶⡿⠟⣛⣛⣻⣿⣿⣿⣿⣙⣓⠄
⠀⠀⠀⠀⠀⠶⠈⢀⠀⠀⢀⠨⢛⠫⠵⠶⡵⠘⠉⠉⠓⠐⣾⣿⣿⡿⡇
⠀⠀⠀⠀⠀⢈⢀⠀⡠⢀⣠⡴⠣⢻⢟⣇⠄⠀⢠⣴⣦⡴⣾⣵⣟⣽⠃
⠀⠀⠀⠀⠀⢸⡸⠩⠆⠑⠸⠒⠷⠎⢀⡠⠀⠀⢀⣷⣿⣟⣻⣽⣯⠉
⠀⠀⠀⠀⠀⠀⢧⣀⣤⡟⠀⠐⠂⠀⠈⠁⠐⠲⣿⣿⣯⣿⣿⣟⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⠀⠀⠔⢀⠐⠃⡒⣴⣿⣿⣿⠞⠋⠉⠀⠉⠑⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠗⠷⢾⣿⣶⠿⠼⠿⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⣦⣀⡀⠀⠀⠀⠀⢀⣠⣴⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⢹⠛⠟⠛⠋⠩⠯⣧⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠷⣦⣤⡬⠤⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡵⠋⠰⠸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠙⠻⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡱⣋⠀⠄⠀⠀⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠂⢀⠉⡪⢕⠦⡀⠀⠀⠀⠀⠀⠀⣠⢫⡞⠀⣡⠃⠀⠄⣿⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢁⣄⠀⠐⢬⡀⠹⣮⡳⣄⠀⠀⠀⡴⠱⠋⠁⠀⠃⠀⢠⠀⡇⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠾⡈⣀⠀⠉⠀⠀⡈⠐⢕⢤⡜⡝⡀⡰⠀⢠⠇⠀⠀⢠⣇⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠀⢣⠈⠀⠈⠂⠀⠈⠈⢢⡞⠀⡴⠁⠀⢀⠄⢀⢰⠃⢸⠘⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⠎⢇⠘⢆⠀⠐⢆⠀⡞⠘⡸⠇⡜⠀⣞⠀⠀⠘⠀⡼⠂⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⡄⠌⣆⠈⣀⠀⠸⣿⠀⠀⠁⠈⡀⡸⠉⠀⠀⠃⡄⡇⡆⣸⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡵⡐⡜⣶⠄⠀⢰⡋⢀⡏⢰⠂⠀⣁⠀⡆⢀⠀⢹⠀⠃⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡳⡙⠘⢆⢀⣯⠇⡸⠀⡀⡰⠰⠃⠈⠀⠀⠀⡎⠐⢸⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡱⡉⠈⢾⣹⠂⠁⡼⡰⠁⡀⠀⣠⢠⢳⠆⢁⠀⡎⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡑⡄⣟⠁⠘⠀⢱⢃⠀⠁⠀⠇⢸⢈⠀⡞⡸⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⡯⡗⢀⣧⢧⣇⠀⠀⠰⠀⡞⠈⡀⠠⢣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣁⢸⡟⠜⠀⠀⠀⠀⢤⢷⠐⡡⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⡗⠀⠀⠀⠃⡔⣾⢏⡤⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⡽⣤⣀⠼⣏⠭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣾⢳⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣽⡟⠛⠳⣦⢹⣀⡧⢀⣀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⢀⠀⠘⢄⠀⠚⠓⠦⠄⡠⢀⠀⠀⠀⠘⠷⠟⢸⡛⠢⢟⡀⠉⡠⠋⢉⡇⠀⠀⠁⢠⢂⠀⠀⠀⠀⠛⠀⠨⠀⠄⢀⠦⡄
⠀⠀⠀⠀⠀⠄⣀⠀⠀⠉⢳⡀⢀⣀⡀⠀⠑⠀⠀⠀⢠⠂⢈⣿⠶⠶⠃⠰⠥⠴⠟⠁⠀⠀⢠⡎⠀⠀⠀⠀⠘⠀⠋⡄⠀⡀⠀⠄⠦
⠀⠀⢣⡀⠀⠀⠈⢰⠳⠀⠀⡿⠉⠀⠀⠀⡰⠀⠀⠀⠈⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢤⣤⡘⢷⣦⡀⠀⠀⣀⣤⣢⠿⡀
⠀⠀⠀⠙⠲⠖⠚⢁⠀⢀⡼⠀⠁⠀⠐⠋⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡬⣍⣙⢉⣉⣈⣵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⡄⠈⠐⠢⠀⠀⠠⠀⠀⠀⠀⠭⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠃⠀⠀⠄⠁⠀⠀⠀⡁⠀⠀⠀⠀⠀⣠⠐⠄⠀⢀
⠀⠀⠀⠀⠀⢀⠴⠞⠋⠓⢦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⠞⠁⠀⠀⠀⣀⣀⣤⠤⠚⠀⠀⠀⠀⠈⢆⠀⢀⣀⣰⣄
⠀⠀⢀⡤⠚⠋⠁⣀⣤⡆⡈⠉⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠖⠛⠈⢀⠈⠁
⠀⠀⡃⣄⠀⢀⡞⠁⠉⠉⠛⢦⣤⣤⢄⠀⠀⠘⠀⠀⠰⢻⡇⡾⡀⣀⢰⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠂⢄⢰⡾⠿⠃
⠀⠀⠑⠦⠠⠶⢆⠰⡤⢤⣄⡀⠀⠈⢉⡷⠒⠁⠀⠀⠀⠿⠸⠗⠇⠏⠾⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠛⠶⢞⡉⠉⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⣠⢄⡤⣰⢆⣆⡤⣠⠄⡖⡌⣠⢄⡤⡄⠀⠀⠈⠓⠀⠀⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠓⠙⠚⠛⠃⠛⠚⠓⠓⠓⠙⠃⠓⠀⠀⠀⢤⠖⠀⡀
⠀⠀⠀⠀⣀⠄⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠦⡄⠀⢠⡇⡠⠊⢡⡀
⠀⠀⠀⢰⢇⠀⠀⠀⠀⢈⡶⠟⠛⠳⢤⡀⢀⡔⠃⠠⠞⠋⠐⠂⢸⠀⠀⠀⠀⠀⠀⢠⡾⠋⠈⠀⠘⠀⠀⡴⠋⠀⢠⠇
⠀⠀⠀⠘⠈⠓⠤⠶⢶⡏⠀⠀⠀⠀⢀⡏⠀⠳⠦⠀⠀⠀⠤⢖⠋⠀⠀⠀⠀⠀⠀⠈⠙⢀⣀⣀⣴⡀⡔⠀⢀⣤⠋⠀⠲⠖⢂⡁
⠀⠀⠀⠀⠐⢄⡀⠀⣠⡷⠄⠤⠐⠆⠻⢷⠀⠀⠀⠒⠒⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⠶⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡴⣾⡿⠇⢋⠁⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⣩⣥⣬⣍⡒⢴⡿⠞⠀⠀⠈⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⡟⠃⠉⠀⠉⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⢆⠘⠀⠀⠀⠀⠀⢠⠀⣿⣶⠆⠀⠀⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚⠿⠉⠉⠉⠙⣄⡀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠘⡆⠑⢤⡀⠀⠀⠒⢁⡰⠁⠉⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⣩⣖⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠤⠶⠶⠶⠖⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠶⠒⠒⠒⠛⠛⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠥⣀⣀⠀⠀⠳⡀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⡇⠀⠀⠀⠈⠁⠒⢻⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢯⣟⣯⡇⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⢀⡄⡇
⠀⠀⠀⠀⠀⢀⠔⠁⠈⠀⢜⠧⣄⠀⠀⠀⠀⠀⢸⢀⡄⢠⡤⡆⡖⠀⣹⣯⡀⡇
⠀⠀⠀⢀⠞⠁⡔⠀⢠⠀⠀⠑⡈⠙⢦⠀⠀⠀⢸⠀⣿⠛⠇⠇⠛⠛⠉⠁⠀⡇
⠀⠀⠀⡏⠀⠈⠀⠀⠈⠀⠀⠀⠈⠀⠈⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠣⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⡴⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡀
⠀⠀⠀⠀⢹⡌⠉⠉⠉⠉⠉⠉⠀⡼⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠻⠿⠓⠤⣀
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠰⠾⠿⣀⠀⢠⣶⣿⠒⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠋⠛⢒⣒⠒⠒⠚⠛⠳⠦⠤⠤⠤⠬⠯⠭⣷⡄
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢠⣇⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠙⠿⠷⠀⢰⣾⣷⡀⠀⠀⠀⠙⢷⡄⠀⡇
⠀⠀⠀⠀⠀⣠⣤⠟⠀⠀⠀⢸⣦⡍⠓⠦⣄⡀⢸⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠛⠿⠧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢿⣿⣶⣶⣶⣶⣿⣿⠏⠀⠀⠀⠉⠛⠶⠒⠚⠉⠉⢸⠀⠀⠀⠀⢰⣶⣶⠄⠠⣤⣄⠀⠘⠻⠟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠓⠶⠶⠦⠭⠿⠥⢤⣤⣀⣀⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢲⠛⢶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢟⠟⢡⠂⡰⢹⢻⠟⣦⡀⠀⣠⢞⠏⠍⠀⠀⠀⠈⠀⠁⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⢀⣾⠏⡌⡎⢀⠏⢰⠃⡎⣼⢀⢇⢻⣶⠣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠉⢉⡟⡏⡼⢸⢀⠞⠀⠀⡸⡐⡏⠸⡌⢠⢻⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠰⡄⣼⢡⡇⠇⣜⠂⠀⡆⢀⡟⢰⠃⣴⠁⡈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢨⡇⠘⢰⢠⢿⠀⡸⠃⡘⢀⠏⡸⢃⣴⢃⡿⡀⠂⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⠁⠀⡆⠌⡞⢠⢡⡶⠁⡞⠀⢀⠏⡈⣼⡇⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠒⠚⠋⣿⡸⠀⣤⠰⢡⠇⡞⠀⠸⢃⡴⢁⡜⣼⠓⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢸⡇
⠀⣀⣠⠤⠖⠚⠋⠉⠀⠀⠀⠀⠤⢀⡀⣿⡇⠀⠇⠀⡏⢰⠇⠠⢟⡽⡠⢊⡼⠃⠠⠀⠹⣆⠠⡐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠙⠳⢦⣀⠀⠀⠀⠀⠈⠦⠀⢀⡀⠙⣿⠇⡄⠀⡼⣡⠞⠀⡠⠂⣶⣡⢾⡀⠀⠀⠈⠦⢌⢧⡈⢦⡠⠀⠀⠀⠀⠆⠀⠀⠀⠁⣾
⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⠀⠐⠉⠀⠀⣿⠀⠇⠘⡰⠁⡠⠚⢁⣴⠿⠓⠒⠛⠶⣤⠤⠤⠤⠷⠽⣦⣙⠢⡀⠀⠀⠀⠀⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⢹⣄⠀⡰⢁⠜⢁⣤⠞⠁⠀⠀⣤⠔⠊⠁⠀⠀⠀⠐⠚⠃⠈⠳⢤⡀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣶⡵⢾⣞⣋⣀⣀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣀⣠⡤⠴⠒⠋⠉⠛⠲⠶⠤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠗⣒⢒⢈⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠁⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢆⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⠀⢀⠜⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠠⠄⡆⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡄⢀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠁⠘⠄⠁⠀⠀⠃⠄⠀⡀⠀⠀⠀⢀⡤⠂⠉⠀⠀⠀⠀⠀⠈⠁⠢
⠀⠀⠀⠀⠀⠃⠄⡀⠀⠀⠀⡀⠄⠈⠁⠀⠀⠀⡎⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠢⠁⠀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠂⠤⣀⣀⣀⡠⠄⠀⠀⠀⠐⢀⠀⡟⡉⠚⠀⠀⠈⠀⠀⠀⠀⠐⢈⠀⠀⠀⠸⡉⠒⠀⠀⠀⠀⠀⠂⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢀⡁⠀⠀⠀⠀⠀⠲⡢⠂⠀⠀⠀⠀⠑⢔⠀⠀⠀⠀⢀⣄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⡀⠁⠀⢀⡄⠀⠀⢤⠀⠀⠂⢒⠀⢀⠀⠀⠈⠉⠈⠀⠀⠀⢀⠀⠒⠂⢀⠄
⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠁⢀⠀⠀⠀⠀⠀⡏⣉⠁⠉⠹⠂⠀⠀⢸⠀⠀⠠⠈⠄⠀⠀⠀⡄⡀⠰⠪⠀⠀⠼⠆⠀⠀⠐⠅
⠀⠀⠀⠀⢀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢐⠄⢀⠤⠀⠀⠀⡀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠡⣀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠿⠀⠀⠀⢸⠀⢀⢀⢐⠂⠃⡃⠠⠀⠀⠈⠆⠯⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠉⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠂⠀⠀⠀⠂⠀⠀⠠⠄⠀⠀⠒⠒⠂⠂⠒⠒⠒⠒⠒⠀⠀⠀⠁

⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⠿⠿⠛⠛⠛⠛⢿⣶⣤⣄⡀
⠀⢸⣿⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⣤⡀
⠀⢸⣿⠀⠈⠛⢿⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⢸⣿⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠿⣷⣦⣀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢀⣠⣴⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾
⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣸⣿⠁⠀⠀⢀⣠⣴⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠋⠉
⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋
⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣄⣀⣀⠀⠀⠸⣿⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⣦⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⠁
⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣄⣀⣀⡀⢀⣀⣀⣀⣀⣤⣶⣶⣾⡆⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣶⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠛⠛⠋⠉⢸⣿⠃⠀⣼⣿⠿⠿⣿⣿⣿⡿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠘⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣿⣿⡿⠿⠿⠿⢿⣷⣶⣤⣿⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠛⠛⠉⠉⠙⠛⠛⠓⣤⣄⠀⠀⠉⠉⢻⡇⠀⠀⣸⣿⠁
⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⣰⡿⠁⠀⢠⡿⠿⣿⣦⡀
⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠙⢿⣇⠀⢰⡟⠁⠀⠈⠻⣿⣆
⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠛⠛⢿⣦⠀⠀⠹⣿⣏⠀⠀⠀⠀⠀⠈⠻⣷⣄
⣰⣿⠃⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣄⠀⠀⠀⢸⣿⠀⢰⣶⡄⠈⣿⡇⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠘⣿⣧
⣿⡿⠀⠀⠀⠀⢠⣾⠟⠋⠀⠀⠉⢻⣷⠀⠀⢸⣿⡀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠈⠻⣧⡄⠀⠀⠀⠀⠈⢿⣧⡀
⣿⡇⠀⠀⠀⠀⣾⡏⠀⠰⣿⡧⠀⢸⣿⡆⠀⠀⠙⢿⣷⣶⣾⠟⠃⢠⣦⠀⠀⠀⠀⠀⠘⢷⡆⠀⠀⠀⠀⠀⢻⣷⡀
⣿⣧⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠷⣄⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠻⣧⡀
⢹⣿⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠈⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢸⡟⠉⠛⢿⣿⡿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⣷⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⢹⣿⣿⠋⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠹⣧⡀⠀⠙⠿⣿⣶⣶⣾⡿⠿⠟⠛⠛⠛⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⢀⣼⡿⢿⣦⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⣸⡿⠀⠀⠙⠛⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠻⢿⣶⣄⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⣴⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⡿⠟⠛⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠛⠉⠉⠉⠙⠛⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣠⣤⠴⠶⢶⣤⣀⡀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠉⠉⠻⢷⣦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣽⣿⡄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠉⣻⣿⡀⠀⠘⣆
⠀⠀⠀⠀⣀⡤⣖⣻⣭⣭⠭⠭⠭⢭⣉⣉⡛⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣷⣄⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠠⢍⣸⣿⡇⠀⠀⢸
⠀⠀⣠⣾⠿⢛⣉⣁⣀⠀⠀⠀⠠⠤⢤⣀⣉⠙⠲⢬⣙⠳⣄⡀⠀⠀⠀⠸⣟⡆⡏⢙⣦⡀⠀⠈⠙⢷⣶⣀⠀⠀⢀⡀⣻⣾⠟⠁⠀⠀⢸
⢀⣾⡿⠗⠛⣉⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⢈⣉⠓⠢⠤⣝⡛⠿⣦⡀⠀⠀⢿⣧⢳⠸⡇⢻⣦⡀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⢀⣠⡟
⣾⣿⣤⣀⡈⠀⢀⣀⣈⣉⣉⠉⠉⠉⠛⠒⠦⠬⣍⡓⠲⢤⣉⠳⢿⣿⣄⠀⠈⢿⣏⢧⠁⢻⢨⡟⢳⡦⣤⣀⡀⠀⠀⢀⣀⣤⣴⣾⣿⠟
⣿⡿⢦⡈⠙⠛⠲⢤⣀⠀⠈⠉⠙⠒⠲⠦⢤⣀⠀⠉⠓⢦⣀⠙⠢⣽⣿⣆⠀⠈⠻⣮⣇⢸⢀⡴⢋⡴⢋⡽⢛⣻⣿⠿⣿⣿⣿⠟⠁
⢿⣿⣦⡙⢶⣄⠀⢀⡈⠙⠲⠤⣄⣀⠀⠀⠀⠈⠉⠑⠒⠦⣌⡙⢶⣬⣻⣿⡆⠀⠀⠈⠻⢿⣿⣴⣋⣤⣶⣚⣭⣤⣾⣿⡿⠟⠁
⠈⢿⣿⣍⠲⣈⠓⠦⣉⠓⠢⠤⣀⣈⣉⠉⠉⠙⠓⠲⠦⠤⠤⠌⠙⢻⣿⣿⣿⡀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠟⠛⠉⠁
⠀⠀⠹⣿⣿⣦⣉⠒⠬⣳⢤⣐⡢⠤⣈⣉⣉⣉⣉⣉⣑⣒⣛⣫⣭⣭⣾⣿⡿
⠀⠀⠀⠈⠻⣿⣿⣍⠓⠾⣷⠮⣭⣷⣶⠶⠲⠾⠿⣛⣛⣛⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⠿⣖⣾⠿⠿⠿⣿⣟⣛⣛⣫⣭⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣾⣿⣿⣿⣶⣾⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠋⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠏⠀⠀⣧⠘⣿⡅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⣇⠀⠙⠀⣿⡇⠐⣇⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢉⣉⣩⡉⠉⠛⠓⠮⣭⣓⠢
⠀⠀⠀⠀⢸⣿⣿⡹⣿⣿⣧⠀⢹⣆⠀⠀⠘⣿⡄⠘⠀⠀⠀⠀⠀⠀⣼⣿⡏⠸⣆⠀⠀⠀⠛⠲⠀⠀⠀⠈⠻⢿⣦⡀⡀
⠀⠀⠀⠀⠈⣿⣿⣇⠹⣿⣎⢷⣄⠙⠦⠀⠀⠈⠻⢦⣄⣀⣀⣰⣶⣾⣿⣿⡻⣄⣀⣉⠓⠀⠀⠀⠀⠀⠀⠀⠑⢦⠙⢿⣎⢦
⠀⠀⠀⠀⠀⢹⣿⣝⣦⠈⠪⡳⣮⣷⣦⣀⣀⣀⣀⣀⠀⠉⠉⣉⠉⢹⣿⣿⣿⣾⣿⣷⣭⣕⡂⠀⠀⠀⠀⠀⠀⠈⢳⡀⠻⣎⢷⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣮⣳⣤⣬⣿⣿⡿⠿⠟⢛⣛⠛⢿⣦⡀⠈⠁⠈⢿⣿⣿⣿⣿⣶⣾⣍⠛⢶⣄⠀⠀⠀⠀⠀⠀⢳⣰⠹⣎⢧
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⠛⣩⡴⣺⠾⠋⠉⠀⢸⣿⣷⣶⣤⣄⣀⠙⢻⣿⣿⣿⣷⣾⣭⣝⣿⣧⡀⠀⠀⠀⠀⢆⠁⡇⢻⣎
⠀⠀⠀⠀⢀⣠⣶⡿⢟⣭⣀⣴⣾⣽⣺⠗⢀⡔⢠⢇⣾⣿⡇⢀⡉⠙⠻⣿⣿⣏⡏⠀⠀⠀⠀⠉⠻⣿⣿⡄⢤⠀⠀⠘⡆⠹⠸⣿⡀
⠀⠀⠀⣠⣾⠟⣩⡶⣫⣾⣿⣿⡽⠋⠡⠖⠉⠀⠟⣼⣿⣿⡇⠀⠉⠳⣦⡈⠻⣷⡀⠀⠀⠀⠰⡌⠀⠈⣿⣿⠈⡆⠀⠀⡛⠀⠀⣿⡇
⠀⢀⣼⣿⣷⠾⣫⢾⣿⠟⠋⣡⠆⠀⠀⠀⢀⠀⣰⣿⣿⣿⡇⢰⡀⠀⠈⠁⢀⠹⣷⡀⠀⠀⠀⠸⠀⠀⣿⣿⡄⢿⣶⡞⣼⠀⠀⣿⡇
⢀⣾⣿⡿⣿⣿⣿⡯⡠⣢⡾⠃⢀⡄⠀⣰⠋⢰⣿⣿⣿⡟⢷⡄⢳⡄⠀⣴⠘⠇⢹⣷⠀⠀⠀⠀⠀⠀⣿⣿⣟⢤⣉⣛⣁⡴⢎⣿⡇
⢸⣿⣟⣼⣿⡿⢫⢞⡼⠋⠀⣰⠋⢀⣼⠃⣰⣿⣿⣿⣿⣷⡈⠻⣆⠻⣄⠈⢇⠀⠀⣿⣇⠀⠀⠀⠀⠀⠹⣷⣍⣛⣒⣚⣡⣤⣾⡿⠁
⠜⣿⣿⣿⡟⢱⡫⠋⣀⠀⠈⠁⣠⡿⠃⣴⣿⣿⣿⣿⢿⡿⣟⢦⡘⢷⡙⢧⡘⢧⡀⢸⣿⡀⠀⠀⠀⠀⠀⠈⠙⠻⠟⣛⣛⠛⠉
⠘⣿⣿⣿⡇⠟⢡⠞⠁⣀⣤⡾⠋⣠⣾⡟⠈⢻⣿⣿⡷⣝⣌⠳⣿⣆⢻⣦⠀⠈⢿⣼⣿⣧
⠀⠘⠻⢿⣷⣄⡓⠶⣾⣿⣯⣴⡾⠻⠋⠀⠀⠀⠙⠿⣿⣮⡻⣷⡈⠊⠳⡙⣷⣔⣌⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⢶⣤⣄⣀
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣲⣤⣐⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⣀⣴⡾⣟⡯⣿⠚⠋⠉⢁⣀⣤⣭⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣤⣄⠀⠀⠉⠛⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⣠⣾⢟⡽⡻⠵⠋⢀⣤⣶⢿⣿⣿⣟⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡽⠞⠋⠉⣿⡇⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⡥⠊⢀⣤⡶⣿⡿⠞⠋⢉⣠⣤⡿⠿⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠋⠀⣀⣼⡿⢡⣿⣿⠟⢿⣆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣫⢀⣴⣿⠟⢀⣿⣧⣶⠿⠛⣉⡠⢀⡀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠿⠿⠟⠉⠀⠘⣿⣿⣶⡈⣿⡐⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⣣⣶⠿⢛⡩⣀⡴⢚⠅⠀⢀⡴⣣⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠹⣯⢳⣷⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⢡⢖⣩⢞⡵⠊⠴⣞⡴⢋⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⣿⡆⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⣷⢑⡵⣫⠖⢋⡤⠴⣞⣯⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣏⣧⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠿⢼⣥⣤⣶⣶⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣌⡙⢠⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡇
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣴⠚⡩⢿⣿⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣾⢟⣟⣿⣄
⠀⠀⠀⠀⢸⡿⢛⡉⡤⠠⠄⠀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣾⣷⢛⣿⡙⡇⡃⣯⣧
⠀⠀⠀⠀⠸⣻⣟⣠⠠⠤⢄⡄⣀⡾⠏⠀⠀⡀⠀⠀⢠⡎⠐⠁⠀⠀⠀⢹⣿⢱⠗⣨⢇⢿⣿
⠀⠀⠀⠀⠀⠛⢿⣿⣯⣽⣵⣲⠞⠁⠀⠀⠀⢻⣿⣿⣿⡇⢀⠀⠀⠀⠀⢀⣧⡿⠚⣡⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢦⣁⣀⢀⣀⡾⣯⣴⣿⣽⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠔⠉⠳⠶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠔⠒⠲⣤⡀⠀⠀⠀⠰⣄⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣀⣀⣠⡴⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠹⣄⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⣀⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠸
⠀⠀⢠⠊⠀⡀⠈⠀⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⡰⠁⠀⠈⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠊⠉⠁⠈⠙⠳⡄
⢰⠃⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠇⠀⠀⠀⠈⠀⠀⠘⢦
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠂⠈⠆
⡇⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸
⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⢸
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣤⣤⣤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠳⡄⠀⠈⠒⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠈⠲⠤⣤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠄⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠛⠛⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠈⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢀⣀⣤⠶⠛⠋⠛⢄⠀⠀⠀⢀⣰⠆⠀⠀⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠑⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⣶⠄⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡈⢀⡀⠀⠧⢄⠸⡇⢹⢰⠧⠜⢨⢀⡆⢠⠀⠀⣷⠋⢣⢸⠀⣸⠀⢸⠀⣙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣠⠄⠱⠜⠑⠀⠐⠚⠀⠀⠈⠈⠙⠋⠈⠋⠙⠃⠀⠀⠙⠀⠈⠈⠙⠁⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠶⠶⠶⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣿⡿⠛⠛⠛⠿⠿⠷⢶⣦⣄⡀
⠀⠀⠀⠀⢀⡴⠋⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢸⡿⠀⢀⣤⣤⠤⢤⣤⣀⠈⠙⢿⣶⣄
⠀⠀⠀⢀⡾⠁⢰⣯⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣿⡇⠀⣾⠁⠀⠀⠀⠀⠉⢷⣄⠀⠈⠻⣧⡀
⠀⠀⠀⢸⣧⣦⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⠀⠙⢿⣆
⠀⠀⠀⢸⣷⠟⠘⢧⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣿⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠈⢻⣧
⠀⠀⠀⠸⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⣇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢻⣦
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⢿⡆
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⣿
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠉⠻⢦⣤⣀⣠⡼⠃⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣤⣀⡀⠀⠉⠁⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣷⣶⣶⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⣤⣤⣄⣄⣀⣀⣀⣤⡤⠶⠞⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠋⠉⠉




⣿⣿⣿⢿⣿⠿⢿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣷⣾⣾⣶⣶⣷⣾⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠶⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⣩⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⡋⠁⠀⠤⠤⢴⡯⠶⠤⠤⠉⠙⠻⢦⣄⡀⠀⢀⣤⠞⠉⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⡿⠁⠀⠀⢀⣠⣿⣤⣤⣤⣴⣦⣀⣀⡀⠈⠙⠿⣍⠀⠀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣀⣀⣀⣷⣤⡔⠚⠉⢸⠁⠀⠀⢨⡏⠀⠀⠀⠀⡄⠀⠀⠙⢧⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠿⢿⣿⣿⣿⣦⣜⢀⣠⠤⠾⢷⡶⠖⢦⣾⣇⣀⣠⡤⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣄⠀⠀⣼⠀⠀⠀⢹⠃⠀⢀⡇⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣈⣡⠤⠤⢤⣿⡤⠤⣾⡧⠤⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⣰⠋⠀⢀⡟⠀⢀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⢴⡥⠴⢶⣾⠗⢻⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⣰⠏⢠⠞⠀⢠⣿⠃
⠀⠀⠀⠀⠀⣴⡟⠁⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠠⠾⠥⣼⡿⠀⢀⣾⡟
⠀⠀⠀⠀⣼⡟⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠄⠀⠀⢠⠟⢀⣴⣿⠋
⠀⠀⠀⣸⡟⢀⡾⠁⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⣰⣫⣴⡿⠋⠁
⠀⠀⠀⣿⢃⡞⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣥⣤⡾⠿⠛⠉
⠀⠀⠀⣏⣼⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠀⠀⠀⢀⣠⣾⠿⠋⠁⠉
⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⢉⣠⡴⠋⠀⢀⣤⣶⡿⠛⠁
⠀⠀⢠⣾⣿⣿⣶⣶⡶⠶⠶⠶⣛⣛⣩⣥⠶⠞⠋⣁⣠⣴⣾⠿⠋⠁
⠀⠀⠛⠋⠉⠈⠙⠿⣭⣙⣛⣋⣉⣩⣤⣤⣶⣾⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁