Mango Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⣿⣿⠃⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⢿⣿⠟⣎⡼⣿⣚⣿⣰⣺⣻⢇⣧⣫⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠂⠈⠉⠠⠈⠁⠀⠈⠉⠉⠓⠢⢤⡀
⠀⠀⠀⠀⠸⣿⣾⣿⣷⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⠖⠔⠓⠒⠲⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⡼⠓⠛⠓⠲⢤⡄⠀⠀⠀⠀⠈⠉⠑⣢⣦⡀⠀⠃⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣛⣤⡄⠀⠀⠀⠀⠀⠀⠐⠛⠀⣀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⢂⣉⣅⣬⣭⣵⠵⠇⢙⣶⣦⣀⠂⠀⠀⠀⠀⠈⠉⠀⣀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡩⠴⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⢯⣤⣄⠀⠀⠀⠀⠩⣤⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠻⠶⡦⣄⡐⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠀⠈⢳⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⣿⢈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣿⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠘⡀⡠⢤⣄⠀⠀⡄⠀⠂⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣶⡈⠃⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠗⠉⠀⠀⣿⣧⣠⣀⣀⣀⣼⣧⣿⣿⢀⠄⠀⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠛⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠛⢀⣶⣤⣾⣀⡀⠈⣻⣿⣿⡋⠉⠉⠙⣺⣿⣿⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⡟⣇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣿⡗⠒⠀⠉⠙⣿⣇⠈⠉⠀⠈⣿⣿⠓⠓⠄⣀⣼⣿⣿⢏⠀⠉⢻⣿⣯⠓⢄⠀⠀⠀⠀⣠⠞⣁⣼⠇⡿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠙⢿⣆⠀⠀⢄⡸⣿⠀⠀⠀⠀⣹⣿⠀⠀⠀⢸⣿⡟⠛⠛⢄⣠⣿⣿⡿⢿⡈⣧⣠⡴⢋⠴⢈⡼⠏⠐⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣛⣷⣄⣀⣤⠽⠦⣤⣾⣷⠿⠇⠠⣬⣶⣹⣿⠀⠀⢰⢸⡿⠁⠀⠀⣰⣿⡿⢿⡟⠓⢹⣿⣷⣀⠠⠐⠋⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠉⡏⠉⠉⢻⠉⠉⠉⢹⣿⠉⠀⠒⢢⣿⡿⠋⣁⡀⢹⣿⣾⠧⢠⣞⣴⡿⠋⠀⠀⠑⢠⣿⣿⣿⢻⡀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠈⡄⠀⠀⠸⣿⣀⠀⠀⢀⣿⡇⠀⠚⢿⣿⣿⠉⠐⢦⣽⣿⣶⣤⣄⣰⣶⢿⠛⠎⠙⢦⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠒⢲⡄⠀⠠⣿⡗⢲⢶⣿⡿⠛⠶⠾⢟⣷⠦⠤⣤⣿⣏⡀⢀⣸⣿⠃⠀⠉⢿⡿⠿⣷⠄⢈⣆⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠘⡇⠀⠀⢹⠀⠀⠀⢻⡋⠉⠉⣁⣿⡏⠀⠒⢦⣼⡿⠽⣿⣻⣯⣤⣀⣠⣾⠃⠀⠢⢕⣦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢅⠀⠀⠘⠃⠀⠀⠘⡇⠀⠀⠈⠘⡇⠀⠀⢈⣹⠇⠀⠀⢿⠉⠉⠉⠿⡟⠲⡄⠀⠄⣙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠀⠤⣀⣀⣁⣀⠀⠀⣀⠠⠄⠀⠤⠤⠤⠤⠤⠀⠀⠐⠒⠂⠐⠀⠒⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⠿⣿⢿⣿⣷⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⣀⣤⣴⣶⠾⠟⠛⠉⠉⠁⠀⠀⠀⣠⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⣀⣴⣶⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⢀⣿⣿⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⢸⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⢾⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠈⠛⠻⠿⣿⣷⣶⣶⣾⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣄
⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄
⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄
⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿
⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏
⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⢀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁
⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏
⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠁
⠈⢿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠛⠁
⠀⠀⠉⠻⠿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⠿⠛⠉
⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠛⠛⠛⠿⢶⣤⣄⣠⣤⣤⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⣀⣀⣠⣼⣿⣿⡿⠛⢋⣿⡿⠻⢷⣶⣤⡤⣤⣶⡶⠶⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣀⣀⣀⣀⣀⣤⡾⠛⠛⠉⣡⡿⠁⠀⠀⣾⡟⠁⠀⠀⠉⠻⣷⣤⣀⣀⣠⣤⣤⣽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠉⠉⠉⣩⣿⢿⣉⣀⣤⣶⣿⣋⣀⣀⠀⢸⣟⣀⣠⣤⣤⣤⣀⡀⠙⢿⣍⠛⠻⠉⠉⠀⠙⠻⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣤⢤⣴⣾⠟⣡⣾⣿⠿⠛⣋⠉⠉⠉⠙⠿⠸⠿⠛⠉⠉⠉⠉⠛⠛⠿⣦⣝⠿⣶⠀⢦⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢰⣿⢡⣾⡿⠋⣠⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣜⢷⣾⣧⣀⣀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢈⣿⣿⠏⢠⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡙⢿⣟⣟⠛⠋⠁⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣰⣷⣶⠟⣽⡏⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⢻⣿⣦⣀⡀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⠁⣾⠇⢸⡿⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠙⢿⣿⠟⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⠇⣴⣦⣼⡏⠀⣾⡇⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⣿⣧⣤⣤⣹⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠟⠀⠀⣿⡇⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢸⣿⠁⠀⣻⣿
⠀⠀⠀⠀⠀⠀⣿⣷⣾⡏⠀⠀⠀⢻⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠸⣿⡀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⣷⡦⣿⡇
⠀⠀⠀⠀⠀⠀⠹⣿⡏⠀⠀⠀⠀⠀⢻⣇⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠘⣿⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠙⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠙⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣴⣶⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⣤⣤⣀⡀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣴⢏⣼⣟⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⡟⠳⣌⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠹⡀⠈⠻⣆⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢡⠀⠀⠹⡆⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠃⠀⠀⣿⢦⡀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⣿⠀⠙⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡆⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠈⡇⠀⣰⠇
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⢿⣠⠏
⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠲⠶⠶⠶⠒⠒⠛⠛⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢚⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⠀⢷⠀⠀⠘⠛⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⣿⠇⡀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠟⠃⠀⠑⠸⡄⠀⠀⡀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠐⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⣴⣤⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠙⠿⠧⠂⠀⠀⠈⠀⠂⠀⠀⠀⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣤⣤⡄⠂
⠀⠀⠀⠈⢷⡠⢄⠀⠀⠀⠀⠀⠀⢾⢿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⢣⡀⠙⢄⠀⠑⠀⡀⠀⠀⠉⠉⠉⠈⠁⠀⠠⠠⠖⠀⠀⠒⠂⠀⠐⠦⠀⠠⠄⡀⡙⠃⠀⢄
⠀⠀⠀⠀⠀⠀⠙⢖⠀⠑⢀⡀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣤⠀⠀⠀⣀⠀⡀⠀⠀⠈⠗⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠙⢦⡈⠢⡀⠀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠳⡄⠠⣀⡀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡙⠳⣝⣄⠀⠀⠀⠀⢤⠄⠠⢤⠄⠤⢤⣼⣀⣀⡀⠀⣀⠁⠀⠀⠉⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠚⠛⠦⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⢹⠒⠲⢤⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⠀⢈⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢾⣿⡿⠁⠀⠀⣾⡏⢸⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢶⣿⠋⠀⠀⠀⢈⣿⠁⠻⣆⣀⣤⣴⣮⣵⣤⣤⣤⣤⠄⣀⣅⣀⡘⢛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡾⠃⠀⠀⠀⠀⣸⡟⠀⢀⣿⠈⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⢻⡏⠙⣿⣷⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⣰⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣁⠀⡀⠀⠀⢈⣿⣤⡶⠋⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⣸⣿⣿⣏⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⡇⠀⢸⡏⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠁⣠⣴⣿⡇⠀⠀⢀⡴⠋⠀⣿⣿⡾⠁⠀⣾⡇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠁⠀⠀⠈⠻⣿⡁⢀⠔⠋⠀⢰⣾⣿⣿⠁⠀⠀⢸⡟⢦⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠠⠀⠀⠀⠀⠀⢀⣴⣣⠎⠀⠰⣿⣿⣿⣿⠀⠀⣄⠈⣧⠸⡄⠀⠈⢿⣦⣤⡄
⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠁⠀⠀⠀⢸⣿⣟⣿⣦⠀⣿⡆⣿⠀⠻⡄⠀⠀⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣸⣿⣿⡿⢁⠎⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣸⣿⣿⣿⡄⠀⢹⡀⠀⠀⠈⠛⠛⠻⣶⠆
⠀⠀⠀⠀⠀⣿⣿⣿⣡⠏⠀⠀⠀⠀⠀⠰⠁⢀⡄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⢻⡀⠀⠀⠀⠱⡀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠈⠀⠀⠀⠀⠀⡀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠛⠀⠀⠀⠀⢱⣿⡟
⠀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⠀⡰⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠈⠉⠙⢷⣦⣄⠀⢿⣟⠿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣿⣾⣿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢷⣼⣿⣿⣿⣿⣯⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣠⣲⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠟⠈⠛⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣠⣠⣼⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⠋


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣉⣤⣹⣇⣠⣏⣈⣷⣉⣼⣞⣡⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣉⣠⣤⣤⣌⡁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣾⠿⠿⠛⠃⠈⠑⠛⠿⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠎⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠪⢻⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠚⠉⠀⠂⢀⣀⢠⣤⣀⠶⣤⣤⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠶⣭⣭⣻⣮⡝⠳⠭⠙⠽⠆⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢬⣭⣏⣻⣿⠖⠋⠉⠀⠀⢀⣀⠤⠊⠀⠀⠀⠙⢧⣁⢀⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⢐⡴⣿⣶⠟⠛⠀⠀⠐⠓⠒⠯⣽⣏⡡⠥⠤⠤⠭⠭⠭⢤⣶⣿⣧⠽⠳⡥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡾⣻⣿⠋⠁⠀⠁⠀⠀⠀⠀⠀⡰⢃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠂⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣰⣟⢿⡏⡫⠈⠁⠀⠀⠀⠀⠀⠀⢰⣇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡛⡃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣾⣿⣿⣬⡃⠁⠀⠀⠀⣀⠤⠤⠖⠒⠞⢸⠦⠤⢤⣀⠀⠀⠀⠀⠀⢰⠀⢸⣛⠁⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣀⣼⡿⢿⡧⠊⠀⠀⢀⠴⣫⣄⠚⠛⢿⣋⢧⣄⣿⢒⣀⣄⣍⡢⣄⠀⠀⠈⠄⢨⣅⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠋⠁⠀⠀⢀⡔⣱⣾⣿⣿⡿⠀⣀⣙⡋⠉⡁⡉⣩⣼⣿⣷⣌⣳⡀⠀⡖⢸⡧⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡜⣠⣿⣿⣿⣿⣇⣀⣹⣿⣿⣿⡿⠟⠛⠛⢿⣿⣿⣷⣷⡀⡄⠀⣿⣣⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠣⠀⠀⠀⠀⠀⢸⣿⣿⡏⡇⢡⠀⡙⢿⣵⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣿⣿⣿⣿⣿⡟⠻⠫⠍⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⡇⠀⠁⢄⠈⢻⣶⣀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠙⠢⡙⢯⡤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢘⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠘⠸⣷⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢠⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡍⠻⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠷⠀⡀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠿⢿⡤⠴⠾⠛⠁

⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠶⢶⡦⣄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⣻⣾⣧⠀⠀⡔⠈⠀⣠⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡼⣦⣤⡤⡄
⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢸⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣲⣾⣿⣤⣿⡞⠀⣿⠶⡄
⠀⠀⠀⣸⣿⠀⠀⠀⣀⣠⣾⣿⡿⠋⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠀⠀⠠⣾⠟⢿⣀⣸⣇⣷⣤⣿⢶⡿
⠀⠀⠀⠼⣿⣿⠿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣟⣛⣛⡽⠋⠀⠀⠀⢸⡭⡶⠟⣿⠛⣻⣍⣬⣿⡟⠁
⠀⠀⠀⠀⠀⠉⠉⠉⢁⣀⢤⡔⢊⡅⠀⠀⠀⠀⠀⠀⠀⠉⣉⣁⡤⣤⣤⠄⠃⠀⠀⠙⠿⢝⣻⣉⡽⠷⠚⠉
⠀⠀⠀⣀⣤⣤⣶⣾⣭⣖⣚⣛⡿⣤⠤⠤⠀⠀⢀⠴⣚⣭⠿⠶⢻⠿⠃⠠⠂⠀⠀⠀⠀⠀⣀⠤⣤⡀⠀⠀⡄
⠀⠀⠀⠙⠛⢍⠉⠉⠙⠠⠀⠀⠀⠀⢀⡞⢀⣴⣯⠟⣋⠤⢒⣩⣤⣤⡀⠀⠗⠀⠀⠀⠀⡼⣱⢿⣫⣤⣤⣜
⠀⠀⡀⠀⠀⠀⠉⠢⠄⣀⢀⣀⡠⠔⠀⢀⣾⠞⢁⠘⢁⣴⣿⣿⣯⣉⣿⣧⡞⣶⣤⡀⠀⣗⣿⣸⡟⠁⠀⠉⢷⡀
⠀⠀⠈⢙⡿⣿⣿⡲⣄⠀⠀⠀⠀⠀⠀⣼⡏⠄⠁⢠⣿⣿⣿⡿⠟⢿⣿⣿⠟⠉⠈⢳⠀⢻⡇⣿⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠈⢷⣅⢡⢋⠟⣷⣦⣄⡀⠀⠀⠛⠁⠀⠀⣼⣿⡟⠁⠀⠀⠈⢹⣿⠀⠀⠀⠘⡇⢸⣿⣿⡅⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⠻⢮⣴⣰⠉⠻⣿⣦⡀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢠⡇⠀⠸⣿⣿⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⢈⠛⡿⣆⠀⠀⢸⣿⣏⠀⠀⠀⠀⣼⣿⣷⡀⠀⢀⡼⠀⠀⠀⠈⠻⣿⣷⣶⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠛⠛⠂⠈⠿⣿⣦⣤⠴⠊⠈⠳⢿⣷⡶⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠉⠒⠤⠄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⢤⣄⣀⠠⣄⡠⠴⠶⠂⣈⠶⠤⣤⣀⣤⠤⠒⢈⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⢉⡩⠖⠚⠉⠉⠑⠢⣄⠙⠦⣄⡀⠀⠈⠁⣀⣠⠴⠛⠁⠀⢀⡠⠔⠉⣰⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣠⡤⠶⠷⠶⠷⠦⢼⣦⡀⠠⡈⢳⡀⠀⠈⠉⢉⠩⠥⡴⠶⠶⡶⠞⢃⡰⠔⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⣀⡇⢀⠤⢊⣠⠂⠀⡗⣒⣊⣴⡖⠋⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠈⢉⣉⡁⠒⣦⣄⡀⠀⠀⠀⠀⣀⣀⡀⠤⠤⢹⠋⢀⠜⠸⠀⢰⠏⠁⡈⣾⣠⣤⣤⣀⡞⢉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⣁⣤⠔⠋⠁⠃⠀⡰⠃⠀⢉⣛⠿⠛⣠⠬⠤⢶⠞⢛⠇⠐⠟⡆⠀⣰⢏⡴⠋⠉⠉⠀⠀⠀⡿⠁⡜⠗⢜⠄
⠀⠀⠀⠀⠀⠀⡠⠁⣠⠊⠈⠀⢀⣠⡤⠊⣴⢾⢁⠔⠋⠉⠉⠁⣀⠴⢯⠀⢸⠀⣸⠀⠀⡴⢣⠏⠀⠀⠀⠀⠀⠀⢀⡇⠀⠃⡸⣄⢰
⠀⠀⠀⠀⠀⢠⠁⠸⠃⢀⡴⠞⠋⠁⡠⠺⣇⣨⣿⠴⠖⠒⠤⣎⠁⡄⠈⣧⢘⠀⢙⠀⣼⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁⡏
⠀⠀⠀⠀⠀⠈⠀⢀⡴⠋⠀⠀⢀⠎⣠⠀⠸⡏⠀⠀⠀⠀⠀⠈⠹⡿⠀⢻⠀⢆⠈⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠞⢧⢸
⠀⠀⠀⠀⠀⠇⢠⠞⠀⠀⠀⠀⡌⠘⡉⠄⠀⢣⠀⠀⠀⠀⠀⠀⢠⢳⢀⡟⠀⠈⠄⠈⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡜⣆⠀⠀⠀⡌
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⡇⠀⢧⡀⠀⢸⠀⠀⠀⠀⠀⠀⢸⢸⡞⠀⠀⠀⠈⢦⡇⠀⠸⡀⠀⠀⠀⠀⠀⠀⠐⣻⠟⣆⠀⠰⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⢰⠁⠀⡾⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠉⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢺⠀⢰⠇⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⡾⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⢀⣞⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡠⠾⡌⠂⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠤⠊⠁⠀⠙⢦⣀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢷⠀⢸⠃⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡀⢘⡦⠶⠒⠺⢄⠊⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⡄⠀⠀⠀⣀⣠⠄⠾⠀⠀⠀⠀⠈⠇⢡⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠁⢀⣀⡿⠀⠀⠀⣀⠀⢀⢀⣶⠀⣀⠀⢀⢀⣤
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠁⠀⠀⣷⢰⣿⠀⣾⡾⢸⠌⣿⢠⣿⡟⣾⢔⡿⢀⣶⠷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⠛⠶⣌⠙⠃⠘⠛⠉⢁⠀⠀⠙⠋⠈⠀⠀⠘⠷⠻⣇⣠⡾⠋⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⡿⠀⠀⣆⢰⡇⣴⠀⣿⣽⠀⣾⡒⢠⡞⠦⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢻⣼⠀⣿⠀⣿⢸⢷⡇⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠙⠂⠛⠋⠈⠓⠂⠘⠾⠃


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢸⠀⢰⠇⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⢀⡵⠒⠋⠓⠢⡉⡠⠤⠖
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢶⡄⠀⠀⠠⠴⠖⠘⠁⠀⠀⠀⠀⠛⠐⠶⠆
⠀⠀⠀⠀⠀⠀⢰⠋⠀⠠⠼⠃⢀⡀⣠⡀⢠⣆⣾⣇⣤⠀⢠⣤⢾⢂⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⡀⠼⣧⠿⣇⡼⣿⠘⠋⢾⣰⠿⠏⠻⢫⡏⣰⠟⠋⣠⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⠉⢻⡆⠀⠀⠈⣀⠀⠆⣠⢤⡀⣀⣀⠀⣈⡉⠙⠲⠺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣤⠴⠁⠀⢸⣤⡇⢸⡇⣿⠛⡄⡿⠀⠸⣇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⡇⢿⡴⠃⣷⣀⢠⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠔⠓⢆⡀⢐⣦⣠⠼⠷⡖⠀⠀⢀⠠⡾⠀⣤⣤⣤⣭⣥⣀⣀⡀⠀⠀⠘⠿⠃
⠶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⢶⣮⣷⢶⡚⠙⢯⣀⣈⣶⣤⠀⠀⠀⠀⠀⢱⠀⢒⣒⣒⣿⣿⣿⠿⠇
⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣧⠟⢾⡉⠉⢳⣄⡈⠀⠀⠠⠄⠀⠀⠀⢴⠚⠛⠩⠉
⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠺⠗⠀⠀⠀⠀⠀⣿⠶⠖⠛⠛⠩⡈⠀⠐⡀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣶⢆⣶⠁⢀⣀⠄
⠀⠀⠀⠀⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠰⠷⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⢸⣿⡆⢰⣿⢸⠇⣴⣿⣿⣿⣦⢠⡀
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡭⠋⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⣾⡄⢿⣿⣿⣿⡿⢰⡿
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣾⢿⣁⠀⠀⠙⠿⢦⣽⡿⣿⡁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠈⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⣤⣤⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⡏⠐⢁⢀⣰⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⣠⠀⢀⣰⣇⣴⣽⣦⣌⡖
⠀⠀⠀⠀⠀⠀⠀⣀⠙⢠⠻⠿⠋⣿⠀⢰⡇⠀⠀⠀⠀⣀⣰⣇⠱⡀⢀⡖⣯⣸⣷⣄⡠⢻⡄⠀⠀⠀⠀⠹⢄⡹⣧⣾⠏⢿⢋⢹⡁⡙⠁
⠀⠀⠀⠀⠀⠀⠀⣏⢀⠀⢠⠤⣖⢤⣠⢾⠁⠀⠀⠀⠘⠉⠀⠙⢆⠓⡏⠃⣹⠁⢹⡉⠃⡸⢁⠒⠖⠁⠀⠀⠀⠓⠀⣥⠘⣏⢾⢀⡜⣧
⠀⠀⠀⠀⠀⠀⠀⣿⢯⢸⡌⢳⡘⡏⠈⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠆⠈⣦⠙⠛⠾⠀⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠘⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡂⢀⠀⢰⡄⡆⣆⠰⢠⡆⠀⠀⠀⠀⠀⠀⠀⢁⠶⠙⢒⠸⠚⠆⠁⡀⠀⠀⠀⠀⢠⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⢠⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⢐⢸⠀⠀⢱⡇⡈⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⡌⡈⠀⠀⢀⠰⡄⡈⠀⠀⠀⠀⠀⠀⢣⢨⢸⢸⢰⠀⢡⠐⢰⠀⠈⣦⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠄⣤⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠏⠒⠀⡀⠮⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁⢀⡀⢀⡁⣀⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡿⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠁⠠⠀⢀⠅⣠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⠂⠘⡅⡷⠁⡗
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠚⠃⠁⠙⠂⠈⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠃⣘⠀⢰⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠋⠁⠓⠁⠃⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣿⠄⢈⡀⠀⠀⠀⠀⠀⢀⡴⢢⡄⠀⠀⣈⣉⣉⣉⣉⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣦⣤⢦⠂⡀⢀⠀⠀⠀⠀⠸⣧⡜⠁⣀⢀⣤⣤⣠⣤⣤⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠯⢅⣿⣴⣟⠛⣇
⠀⠀⠀⠀⠀⠀⠀⡠⡀⡀⠀⠁⣡⣌⠀⠁⣸⠀⠀⠀⠀⠀⠀⠙⣷⠯⠻⠿⠘⠙⠋⠘⠹⠛⠄⢿⡹⠃⠀⠀⠀⠀⠛⠋⠈⠃⠈⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠃⣿⠁⡜⠧⠻⡌⠟⠿⢯⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣒⣒⣒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⢻⠀⣯⠁⣯⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠓⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠓⠀⠛⠙⠂

⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⢀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⢀⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠢⢤⠀⢠⡠⠀⠀⣠⢀⡲⠶⠔⡉⢅⠉⠀⠀⢭⡉⠐⠦⡀⠀⠀⠀⠀⠨⠤⢉⡀⠄⠠
⠀⠀⠀⠀⠀⠠⠔⠀⠐⠀⠼⡋⠉⢹⠈⠑⠐⣀⠤⣶⣧⠴⠄⠊⢠⡦⢆⡷⠀⠽⠀⠀⡔⣩⣉⢀⡀⠴⣾⠇⣐⠀⠀⠀⠀⠤⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢄⠙⠟⠛⣆⣉⡔⣀⡠⣔⣎⠰⠤⠚⠁⠀⠀⠀⡂⠉⣁⠉⣠⣤⣀⠅⠉⣠⠒⠷⠦⠊⡶⠀⠒⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⢆⠤⣄⡀⢌⡨⢵⠀⠌⢰⡀⢠⠰⠞⠁⠠⢁⣄⡘⠿⠈⡃⣠⠈⡛⢲⣋⡴⢣⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⠈⠔⠂⡀⠰⣄⣈⠐⠀⡤⠃⠤⣈⣧⡀⠧⠭⠀⣀⣤⠃⠀⠉⠉⢉⠔⠁⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠢⢄⡄⠀⠐⠃⠀⠎⠙⠛⠛⣛⠉⡑⣲⠐⢀⣣⠀⠀⠀⡀⡄⡀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠐⢠⡠⠖⠀⠴⠆⣤⣤⣠⣤⠅⡥⢨⠟⠀⠀⠀⡆⣆⡗⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⠒⠒⠂⡠⢀⣐⡐⠲⠔⠒⠚⢖⠦⠚⠃⠀⠀⠀⠃⠓⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢀⠀⠀⠀⠀⠀⠈⠒⠀⠄⠀⠀⠀⠀⠀⠐⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠍⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡀⠀⠀⠀⠀⠈⣀⠤⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠐⢉⠁⠀⠀⠀⠈⡒⠰⢂⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠁⠀⠀⠂⠄⢀⠀⠀⠀⡀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠉⢷
⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣱⣄⣤⣤⣤
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢀⣤⠀⠀⣀⠀⢀⡄⠀⢀⢴⡄⠀⢀⣴⠶⣆⠀⠀⡇⠀⣰⡟
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢀⣤⡄⠀⠀⣤⠀⠀⣼⡇⡴⢹⣇⠔⢡⡟⠀⢰⡏⡰⣹⢇⡜⢡⡿⠀⢰⡟⢁⠠⠃⠀⡴⠁⣼⠏
⠀⠀⠀⠀⠀⠙⣷⡄⢀⠔⢉⣿⠁⣠⢺⡏⠀⠀⣾⡟⠀⣿⠏⢠⡿⠀⠀⣼⡟⠀⠿⠋⢀⣾⠁⠀⣿⡇⠀⠀⣠⠎⠀⣸⡏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⢸⣿⣴⢃⣿⠀⠌⠀⠛⠁⠀⠋⢀⣾⠁⡔⠀⠿⠁⠀⠀⠀⣸⠇⢀⠂⠹⣧⡴⠚⠁⠀⠀⠹⢧⠤⠚⠁
⠀⠀⠀⠀⠀⢀⠎⠘⣿⠀⠈⠛⠁⢸⡇⡸⠀⠀⠀⠀⠀⠀⣸⢇⡜⠀⠀⠀⠀⢀⣀⠀⣟⡠⠃
⠀⠀⠀⠀⢠⠃⠀⠀⣿⠇⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⣼⠋⢹⠀⠉⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⡇⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠴⠀⢀⣾⠃⢠⠋⠀⢀⣠⡤⣄⢀⣾⠋⣀⠟
⠀⠀⠀⠀⢧⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢏⣸⠁⢰⡖⠀⣼⣇⠔⠁⠀⢠⡿⠁⢀⠜⢸⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠇⢀⣿⠁⢰⡿⢁⠖⢄⢀⣿⠃⠉⠁⣠⠃⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⡞⠀⣸⡇⠀⣼⡇⠀⠓⣺⠁⢿⣄⣀⡴⢁⣀⡘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⡟⠀⠀⢹⣇⡴⢻⡇⠀⣠⠃⠀⠀⠉⠁⠀⡎⠀⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠀⠀⠀⠀⠳⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣤⣄⠀⠀⢠⣶⠂⠀⢲⣦⠀⠀⢀⣤⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⣖⠀⠉⣧⠀⠈⡟⢧⣀⡿⢹⠀⠀⢸⠻⣇⣠⠟⡿⠀⠀⣿⠛⢻⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣙⣃⡀⢻⡄⠀⢸⠆⢀⣿⡄⠻⠁⠼⠷⠠⠾⠄⠹⠋⣰⣇⠀⣰⠏⠻⠁⠀⢠⡟⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠉⢈⡷⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢀⡔⣹⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠃⣠⡿⢦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠁⠀⠀⠀⠀⠀⠀⣀⡤⣴⣯⡿⠱⢿⣷⠶⢢⡄⣂⣁⠀⠠⣤⣄⡀⠈⠁⠸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⢶⠋⣽⢣⡇⣼⢡⡾⢰⠇⣸⠿⢤⠍⠱⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⢠⣾⣿⡇⠀⠀⢰⢀⡡⠻⢈⢡⣬⣴⣿⠦⠔⢚⣒⣮⣅⣤⣄⣀⣹⣿⣿⣆⠀⣀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⢀⣾⣿⣿⣠⣤⣤⣤⣤⣤⡀⠀⠀⠈⠉⠀⠀⠘⠋⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠋⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠠⠃⡨⠋⠉⠱⠦⢀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠄⠀⡀⠇⠈⠀⢀⠀⡆⠀⠀⠀⢈⣡⣿⣿⡿⠛⣿⡿⠙⢻⡿⣿⣿⣷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⣿⣿⠟⠹⠃⠘⢿⠋⠙⠛⠿⡷⣄⠀⠙⠊⠐⠊⠁⠀⠐⠐⠃⠀⠛⠉⠁⠀⠀⠀⠛⠀⠀⢡⠀⠈⠋⠻⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠐⠂⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡟⠛⠻⠿⠿⢿⣿⣿⣿⣿⡿⠿⢶⣶⠶⠂⠀⠉⠁⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠂⡆⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠠⠒⠒⠣⠤⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠧⠤⠚⠒⠒⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠁⠀⢰⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡉⠐⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠦⣙⣤⠀⠀⠀⠀⠀⠀⠀⢮⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⣦⣫⡶⠋⠀⠀⠀⠀⠈⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠿⣷⣋⡦⠀⠀⠈⢻⢲⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡲⠆⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⡾⠀⠑⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡔⠁⠀⢀⠄⣢⡆⠀⠀⠀⠀⠀⠀⠘⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣻⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⢀⡈⢧⠀⠀⠀⡇
⠀⠀⠀⢀⠊⢠⠃⠰⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣾⡇⠀⠀⠀⢠⣿⡟⠀⢳⠀⠀⡇
⠀⠀⠀⠊⠀⠁⠀⠀⠀⢠⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠘⠛⢁⠀⠀⡇⠀⡇
⠀⠀⠶⢀⡵⠀⠀⠀⠀⢨⣼⠁⠀⠀⠀⠀⠀⠀⢀⣠⣖⣮⣽⣦⣤⣴⣦⣤⣇⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⢄⡀⠸⡄⡇
⠀⢘⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠛⠷⠟⠀⢻⡇
⠀⢨⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠻⣅⣀⠤⢊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠁⠀⠀⠀⠰⠀⣠⡇⣸⡃
⠀⣈⡀⠠⠀⠀⠀⣸⡿⢳⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠒⠈⠙⠲⠤⠤⠤⡤⠤⠤⠔⠒⠚⡉⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⣶⣤⣾⣿⡷⠀⢀⡴⠏⢀⣼⣿⢠⠟⡇
⠀⡍⡄⠰⣴⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠐⠀⠀⠉⠀⠀⠀⠀⠂⠀⢀⣀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡤⠖⠋⢀⣤⣿⣿⢿⣿⢘⡇
⠀⠳⡙⡄⠈⢿⣷⣤⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠤⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣠⣒⠋⠀⢀⣠⣴⣿⣿⣟⣵⣿⡇⢨⡇
⠀⠀⢹⣿⣷⣦⡙⢿⣿⣷⣤⣘⢮⣭⡹⠳⠂⠀⢀⢾⣷⠀⠀⠀⠀⠀⠀⠸⠶⠾⠿⠋⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠚⠀⢀⣴⣦⣴⣿⣿⣿⡅⣴⣿⣿⣿⠇⠰⡇
⠀⠀⠈⡄⠙⠿⣿⣜⠿⠿⠀⠙⢻⢞⡂⢀⡀⠀⠻⠞⣡⣶⡦⠀⠀⠀⠀⠀⠄⠀⣀⠠⠤⠤⠀⠀⠀⠀⠀⣀⣀⣠⣤⢰⣿⣿⣿⣿⡿⠟⠃⣼⣿⣿⣿⠏⠀⢸⡇
⠀⠀⠀⠱⡀⠀⠈⠿⢿⣶⣦⡀⠈⠛⢿⡿⣷⠿⠷⣾⣿⣯⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣯⣤⣴⣾⣿⣿⣿⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠛⠿⣿⣦⣤⣤⣤⣤⣀⣀⡀⠈⠛⢿⣿⣿⣿⣿⣿⠿⠟⠻⠛⢛⣿⣋⣽⣷⣶⣬⣟⣛⣉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠈⠉⠉⠛⠟⠿⢿⣿⣿⣦⣄⡀⠉⠛⠛⢉⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣴⠀⠀⠀⠀⠉⠈⠛⠿⣿⣷⣦⣤⣶⣿⠿⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⣤⣤⣀⠀⠀⠑⠛⠛⢿⣯⣶⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠾⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣀⡤⠤⠤⠤⠤⠤⣄⣀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠄⠀⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠖⠉⡉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⠶⠶⠶⠶⠶⠶⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⢡⠖⠛⢛⢲⣞⠒⢇⠁⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠋⠉⠉⠓⢦⠤⠤⣤⠶⠤⣤⠤⠖⢉⣨⠽⠛⣿⣆⠀⠀⠇⢴⠊⢱⠛⠉⠁⠀⢓⠩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⢀⣀⣈⣷⢖⣚⡷⢀⡔⠒⠛⠉⠀⢀⣴⡿⠋⠀⠀⠀⠘⠑⠎⡳⠖⢟⡠⠳⡄
⠀⠀⠀⠀⣠⣶⠿⠷⠈⠙⢷⣦⣀⡏⠉⠉⠁⠀⠀⠛⠉⠳⣄⣀⣤⡶⠛⢁⠀⣀⠤⠤⢤⡀⠀⠀⠁⢴⠈⢱⡆⣿⠐
⠀⠀⠀⠀⠛⣿⣄⠀⠀⠁⠀⡀⠉⠛⠷⠶⠶⢤⠶⠶⠶⠛⠋⢉⣀⣤⠖⠃⠰⢑⡄⠆⣤⢹⣄⡤⠦⠉⠙⠈⠡⠃
⠀⠀⠀⠀⠐⠈⠛⢷⣤⡀⣎⠉⠉⠀⠀⠀⠠⠀⠠⣄⢀⣠⣴⠿⠋⠁⠈⠀⠀⣈⠃⣄⠿⣸⠃⣠⠰⢤⡘⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣤⣤⣤⠴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⠟⠉⢿⢦⡀⠗⣤⡺⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣴⣻⡌⡇⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠉⠂⠚⢉⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡞⢹⠧⣄⠀⠀⠀⢀⡤⠼⡎⢳⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠗⠀⠀⠀⠺⣍⠀⣠⣄⠈⡽⠗⠀⠀⠀⠲⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢺⢃⡞⢳⡹⡟⣸⠁⠘⡞⣻⢋⡞⢳⡘⡗⢮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⣇⠸⡇⢰⠀⣿⠃⡼⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⣤⡴⣄⣤⣄⣠⡶⢻⣄⣧⣸⣠⠟⢶⣧⣄⣠⡴⠦⣴⢖⢶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡁⢺⣧⣾⠀⣿⣧⢸⠙⢠⠀⠋⠀⡟⠛⣄⠘⠃⢸⡇⢐⣓⣸⣮⢁⡍⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢲⡌⢻⡀⣿⡇⣼⠀⣾⡆⣸⠀⣷⠀⣿⢀⣿⢸⡇⠸⡿⢻⣿⣼⡇⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠛⢳⡬⢶⣻⡇⣿⣿⠟⠀⠿⣴⡿⠛⠿⣼⠟⣓⢶⡏⠀⠈⠳⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⢹⡇⣾⡂⣿⠇⣿⠀⣻⣥⣇⠘⢯⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢁⣿⡇⡿⠁⣤⡘⣿⡀⠿⢏⣿⡟⠶⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠓⠚⠷⠶⠞⠋⠙⠛⠋⠀⠙⠒⠋

⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢴⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡴
⠀⠀⠀⠀⠀⡴⢋⣀⠄⢀⡞⣷⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⡼⠁
⠀⠀⠀⠀⠈⠀⠉⣀⡴⠟⠁⣿⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠀⠤⠒⠋⠉⠀⠀⠀⣿⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢳⣶⠟⠛⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠉⠙⠋⠉⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣸⠃⠀⠀⠀⡔⠘⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠉⠉⠙⢻⡄⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣸⠇⠘⠢⢤⣠⠤⠞⠁⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⡽⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠷⢂⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣰⢟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡆⠀⢀⣴⠶⠾⠲⠶⣤⡀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⢀⣱⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠈⠻⠿⣶⣶⡶⠿⠋
⠀⠀⠀⠀⠀⠀⢠⠖⣦⡰⠀⢤⢀⣤⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠘⢆⠸⣷⢁⣾⣥⣾⣤⣀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⢴⡚⢲⡤⣄
⠀⠀⠀⠀⣠⠖⠒⠚⢂⣽⠾⠋⠁⠀⠉⠻⣧⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⢘⡥⢤⡿⠛⠦⣤⠷⢤
⠀⠀⠀⠀⠈⠓⣶⡾⠋⠁⡀⠀⠀⠆⠀⠀⢹⣇⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣧⣸⠀⢀⣧⡀⠀⠘⠣⠚⢷⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠁⠀⠀⡄⠀⠠⠈⣿⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⣰⢸⡏⠙⣇⠀⠈⡷⠒⢺⠙⢻⡅
⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠰⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠹⣮⡳⠶⢾⡓⠛⢷⣤⡴⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠠⠀⠰⠀⣿⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣤⣤⣤⣤⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⣤⣬⣿⠶⠚⣹⠶⠋
⠀⠀⣀⡀⠀⠀⠀⠀⠉⠲⢤⡁⠀⠠⡀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⠶⠟⠶⠶⠋
⣴⠋⢹⣷⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠘⢆⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢻⣿⣿⠆⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠐⠶⣤⣄⡀
⠀⠈⠂⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠈⢀⡟⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⣀⠀⠉⠻⣦⡀
⠀⠀⠀⢀⠘⠛⠙⠛⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣰⡟⠁⠀⢀⠀⠀⠀⠀⢀⡟⠲⣄⠈⢻⣆
⠀⠀⠀⣿⡇⠀⢄⡀⠀⠀⠀⠈⠙⠛⠷⠶⢶⣤⣤⣤⣤⣤⡤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⣿⠀⢀⠀⠀⠑⢄⠀⠀⠌⠀⠀⠘⣆⠀⢿
⠀⠀⠀⠸⣷⡀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⢀⣾⠏⠀⠀⠀⠀⢸⣿⠀⣼⠀⢀⣀⡤⢽⡿⠂⠐⠒⠒⢻⠀⢸
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠈⠙⠛⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠟⠋⠁⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠘⣿⡀⠸⡏⠉⠀⣠⠏⢠⠈⠢⣄⠀⣼⠀⢸
⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠹⣄⡰⠃⠀⠀⣇⠀⠈⣻⠃⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡈⠛⠶⠦⠤⠾⠶⠛⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣤⣤⣶⠾⠟⠁

⠀⠀⠀⣀⣄⡀
⠀⢠⣾⣿⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⢀⣀⣀⣴⣷⣦⣤⡀⠀⢠⣤⣆⣶⣿⡄⠀⠀⠀⣄⡀
⠀⣸⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⢃⣤⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⡧⠄
⠀⢻⣿⣿⠿⠋⠁⠀⠀⠀⠈⢿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠙⢿⣿⡿⠁⠀⠀⠀⢨⠁
⠀⠀⠈⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⢉
⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⢠⣾⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠸⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡶⠀⠀⠀⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠁⣀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⡀⢈⣀⣠⣤⣤⣀⠀⠀⢀⣠⣀⣾⣿⣿⣧⣠⣄⡀⠀⣾⣿⣿⣶⡀⠀⣴⠿⣿⣿⡃⠀⠰⣶⣾⣿⣿⠆
⠀⢸⣗⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠛⠛⠛⠛⠓⠀⢻⣶⣴⣿⠗⠀⠈⠉⠛
⠀⠈⠻⣿⣽⣿⣿⠿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⢠⣤⣤⡦⠀⠀⠈⠿⠿⠇
⠀⠀⢀⣠⣤⣆⣤⡀⠀⠀⠀⠀⢀⣀⢈⡙⠛⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣤⣤⣄⡀
⠀⠀⣽⣿⣿⣿⣿⣯⡀⠀⠀⣺⣿⣿⣿⣿⡀⠀⠀⣶⣦⣶⣶⣦⠀⢀⣾⡹⣼⣏⢿⣷⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠛⠉⠋⠋⠋⠛⠃⠀⠸⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⡇⠘⣿⣷⣽⠿⣸⣿
⠀⠀⢠⣤⣤⣤⣤⡤⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⠟⠁⠀⠈⠻⠿⣿⡿⠇
⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠙⠛⠋⠀⡀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⡤⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⣿⣿⣧⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⣁⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠉⠉⠁⠀⠀⠀⠈⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡴⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣄⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠉⠄⠛⠉⢉⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠤⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠
⠀⠀⠀⠀⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣀⠀⢀⡞⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⡀⠀⠘⠀⠙⠿⢷⣶⡶⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠂

⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢀⠀⢰⠂⣈⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡆⠈⠀⠈⢳⡞⢤⡴⠎⠀⠀⠹⣧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣫⡷⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠠⠆⠀⠐⣮⠛⢉⣁⡛⠞⠓⠧⠾⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠈⠢⡀⠀⠀⠀⠀⢘⡀⡄⢀⣄⢐⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⣀⣠⣤⣼⠁⠀⡈⠛⢿⢠⡎⠀⠀⠀⠀⣧⡔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⣰⣠⡿⢳⡀⠀⡁⡁⠈
⠀⠀⠀⠀⠀⠒⠒⢀⡌⠁⠀⠉⠓⡄⡌⠋⠀⠁⠀⠲⠐⠒⠂⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⢀⣀⡥⠞⠋⠉⠓⠋⠀⠀⣀⠇⢠
⠀⠀⠀⠀⠀⠀⠀⠼⠃⢄⣀⠀⠐⠻⢀⡇⠀⡀⠀⠀⠀⣀⠀⠀⢠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⡋⠀⠀⡀⠀⠀⡀⠤⡀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣠⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠤⣀⡉⠒⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠌⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠦⢞⠖⣲⣆⠁⡈⠴⠂⢒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢰⣃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠋⠙⠁⠀⠀⠀⠈⢿⣯⠦⣨⣿⡋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⢿⡂⠀⢠⠶⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⣈⠀⢘⣹⣷⢯⠁⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠐⣄⣀⣐⡦⢄⠞⠉⠀⡛⢢⣠⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⣤⠀⠀⡙⠉⣲⣉⠹⠞
⠀⠀⠀⠀⠀⠈⠀⠀⠶⡏⠀⠀⠙⡋⠙⣤⡄⠏⠉⠉⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⡡⠃⢤⡄⠀⡴⠿⠑⠋⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠲⠀⠀⢠⢤⠄⠞⠁⠀⠈⠉⠈⠀⠎⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠱⣆⠂⣽⢧⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⠁⠘⠛⠃⢄⣀⠀⠀⠀⣁⠜⠂⠀⠀⠁⠀⠀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢹⡇⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠘⡷⠀⠀⠀⢰⠇⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠸⣷⢀⣠⠤⠒⠂⠈⠉⠁⠒⠲⢤⡀⠰⠋⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⢲⠄⠀⠀⠀⠘⠀⠀⠀⠀⢀⣤⡀⣠⣄⠀⢀⠀⢀⡀⢀⣤⡀⠀⠀⢀⡀⠻⢼⢤⣄
⠀⠀⠀⠀⠀⡀⠀⢀⠽⣿⣇⣠⠞⣿⠀⢠⣶⠀⠀⣷⠎⢸⣷⢣⡿⠀⣿⡠⠋⣷⠎⣸⡇⠀⣼⣯⠇⢠⠏⣼⡟
⠀⠀⠀⣰⠁⠀⠀⠀⠀⣸⣿⡇⠀⣿⣀⠎⣿⠀⡘⣿⠀⢸⡇⣸⡇⡼⣿⠃⠀⠟⠀⣿⠃⣰⣿⠁⣠⠋⢸⣿⠀⣰⠂
⠀⠀⠀⠑⠀⠀⠀⢀⡾⢁⣿⡇⠀⠈⠋⠀⣿⡸⠀⠀⠀⠀⠀⣿⡿⠁⠈⠀⠀⠀⠀⢿⡴⠋⠙⠋⠁⠀⠘⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢧⠾⠟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠃⠀⣾⠀⡟⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢰⠗⢺⡇⢀⣧⣾⢤⣄⣴⣾⠹⠆⣰⣿⠘⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡼⠀⢸⡇⣸⡿⢁⣴⡏⢺⡇⠀⣠⠇⡼⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠈⠛⠋⠀⣎⠼⠁⠈⠛⠚⠁⠈⠓⠋

⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠒⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠑⠒⣤⡀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡰⣠⠄⠳⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣹⡿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⡠⣀⠀⢨⡿⠒⠛⠁
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⠙⠗⠃⠀⢱⠀⠀⠀⠀⠸⣅⠠⣙⠢⠄⠀⠠⠤⣒⠾⢁⡜⢉⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡩⠷⠤⡜⠓⢦⡗⠻⡅
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⢜⠷⢄⣉⡐⠒⢈⣉⡤⢖⠩⣢⢞⠏⢸⠀⠀⠀⠀⠀⠀⢀⢠⠎⢉⠖⠀⠲⣏⠟⠉⠉⡖⢧
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠫⣀⣒⡤⣭⣭⡥⢄⣒⠥⠚⡡⠋⢀⠆⠀⠀⠀⠀⡔⢊⣇⢈⠖⠳⣀⣀⣠⣏⣐⠤⠚⣷⠼⡀
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢿⠀⠭⠍⣉⣉⠡⠤⠖⠋⠀⢀⠎⠀⠀⠀⠀⠀⠓⠾⡀⢩⠣⢤⠼⠤⡆⠀⠈⡷⠚⣷⡴⠃
⠀⠀⠈⠲⢄⡀⠀⠀⠀⢂⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠓⠒⠋⠒⠊⠉⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠆⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡲⠖⢶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡈⣇⠙⠈⡞⡿⡆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠘⢦⡈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⡠⠊⢠⠌⢙⠳⣄⠋⠀⡗⢀⡢⠄⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⣠⢟⣀⡀⡀⠀⠀⠀⠀⠀⢠⠏⡄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠸⡄
⠀⢀⠜⠃⠠⠄⠀⢉⡁⠘⠳⡄⠉⣙⣆⠀⠀⠐⠥⡀⠀⠀⠀⠀⠀⠀⠀⠚⢡⣾⡷⡅⠀⠙⡮⠙⣦⡀⠀⠀⢸⡀⢇⣀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇
⢀⡾⠈⠃⢀⢄⠀⠑⠁⠦⠆⠹⡑⢿⡌⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⣀⡴⢻⠥⢷⡦⢵⡪⠔⢒⢼⠹⡄⠀⠀⠳⣄⠘⠦⠤⠀⠀⠀⣠⠏⠀⣀⡴⠃
⡸⠤⠰⠆⠀⠈⠀⠘⠀⠠⣢⢀⡇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⢹⡤⣚⢧⡦⣝⠲⠞⡼⠀⠙⡄⠀⠀⠀⠉⠓⠒⠒⠒⠉⠉⠉⠉⠁
⡷⠂⠰⠀⠀⠃⠀⠐⠓⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣸⢀⣀⢗⡔⢁⡴⠚⠁
⠙⢤⣷⣀⣛⣠⠴⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡆⣿⣶⣿⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⣠⠖⠒⣓⡲⢶⡶⠀⠀⠀⠀⠀⠀⠀⠛⠻⡗⠦⣿⢹⡟⡷⠟⢫⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡘⣾⠔⠂⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠳⡈⡧⠛⢈⣩⠽⠟⠒
⠀⠀⠀⠀⠀⢀⣤⢄⣀⢀⡦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⢷⡹⠲⠤⠤⠤⠾⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣯⠿⣰⣶⠗⠺⣿⢦⡌⠶⡄
⠀⠀⢀⡤⢚⡩⠝⠦⢠⣙⡦⠘⠖⠲⣌⠙⠢⡀⠀⠀⠀⠀⢰⢡⢊⠀⠀⠒⠾⠗⠂⠀⠀⠀⢀⢹⠀⠀⠀⠀⠀⢀⡤⢚⣩⣉⠉⣄⣚⡞⢿⠢⢸⠚⠇
⠀⢠⠏⠰⠟⠒⢸⡣⢶⢰⠦⢬⣯⠉⠉⠀⠀⢹⠀⠀⠀⠀⠘⣆⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⣰⠋⢉⠀⠀⢃⠀⢰⠀⠘⠉⡇⠸⠂
⠀⢼⢀⠀⠀⠀⠈⠀⠘⠇⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡟⠀⠀⠀⢰⢧⠀⠸⠒⠒⢺⠀⠘⠓⠒⣷⠇
⠀⠸⣜⢄⡠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠁⠀⠀⠀⣇⢠⣀⣀⣇⣀⣸⠀⢤⠆⢰⠏
⠀⠀⠈⠳⠤⣤⣅⣈⣉⣡⣠⣤⣤⡤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣠⠤⢄⣀⠀⢀⡴⠃⠀⠀⠀⠀⠸⡼⡄⣀⣇⠀⣘⣀⣸⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣇⣸⠥⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣰⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣐⠤⣀⠀⠀⠀⠘⠁⡤⠞⠓⠄⢀⠠⠂⠀⠀⢀⣘⣷⣻⢆
⠀⠈⠒⠦⠘⠄⠀⢀⡰⠀⠀⠘⡆⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣄⠀⠀⠀⠀⠀⠘⠛⠮⠻⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠈⠐⠃⠀⠡⠖⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢠⠀⢄⡀⠀⠀⠙⠄⠀⠀⠀⠀⠒⡵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠈⠈⡀⢁⠀⠑⠀⠀⠸⣄⠴⠋⠱⡀⠀⠀⠂⠀⠀⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠑⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢁⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠤⠙⠂
⠀⠉⠃⠀⠈⠉⠒⠠⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⣀⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠴⠒⠂⠀⠀⠀⠠⠀⡠⠃⠂

⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀⣀⡀⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠉⠁⢉⠀⠈⢸⢳⠂⠀⢀⠴⠋⢠⠄⠀⠀⠈
⠀⠀⠀⠘⠀⠀⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣃⠀⢀⡀
⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠏⠉⠉⠉⠉⢹⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⣿⠀⣀⡤⠤⠤⠶⠒⠒⠒⠒⠒⠲⣿⠟⠒⠒⠶⠦⠤⢤⣄⡀⢸⡇
⠀⠀⢠⡏⠀⡟⠓⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠚⢻⡇⠘⣇
⠀⠀⢸⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿
⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢻⡀
⠀⢀⡇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⢸⠇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣
⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸
⢀⡟⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⡇
⢸⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷
⢸⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢿
⡿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣆⣀⣀
⡷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠛⠛⠛⠛⠻⣷⣶⣤⣀
⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⠉⠻⣦⡀⠀⠀⠀⢹⣧⠈⠙⠷⣦⣀
⢧⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣼⣿⡇⠀⠀⠈⠻⣦⡀⠀⠀⢿⡆⠀⠀⠈⠙⢷⣄
⠸⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢸⣿⣷⠀⠀⠀⠀⠈⠻⣦⡀⠘⣿⡀⠀⠀⠀⠀⣸⣷⣄
⠀⢻⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠸⣿⣿⣿⢶⣦⣤⣀⠀⠈⠻⣦⣹⣧⠀⠀⣠⣾⡟⠁⠙⢷⣄
⠀⠀⠻⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢻⣿⣿⣄⠀⠉⠛⠻⠷⣶⣼⣿⣿⣦⣾⠟⠉⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠙⢷⣀⠉⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠉⠳⢦⣀⠉⠛⠳⠶⠤⠤⠤⠤⠴⠖⠛⢻⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⡀⠀⠀⣠⣾⡿⠋⢹⣿⢿⣮⡙⠛⠿⢷⣦⣤⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢲⡶⢤⣤⣤⣤⣤⣤⠶⣶⠛⣇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⣾⡿⠋⠀⠀⠀⢿⡆⠙⢿⣦⡀⠀⠀⠉⠙⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢰⡇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠘⣿⡄⠀⠙⢿⣦⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⢼⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣄⡀⠀⢸⣷⠀⠀⠀⠙⢷⣄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣤⣿⣇⠀⠀⠀⠀⠙⣷⣾
⠀⠀⠀⣀⡴⠶⠞⠛⠛⠋⣻⠇⠀⠀⠀⠀⠀⠀⠀⢿⠙⠛⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣶⣾⣿⣿⠋
⠀⠀⠀⠻⣤⣤⣀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⣀⣠⣬⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣉⡿⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠓⠚⠋⠉⠉⠉⠉⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣷⣶⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠉⠒⢦⣀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡤⢄⠐⠀⡀⠈⣆⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠖⠀⢀⡆⠀⠐⠒⠂⠰⠦⠂⠀⠀⢸⡶⣌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢺⣀⠐⣯⠂⠾⠋⠀⡀⠲⣀⣤⠀⠀⠀⠀⢀⣼⢡⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠈⢄⠉⢰⡞⠀⡾⢛⠛⠁⢀⣤⣤⣾⡿⠃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠰⠉⠀⠀⣷⣾⣶⣶⣿⣿⡿⠟⠁⠀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⡦⠒⡂⢶⢤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⠊⠢⡀⠀⠀⠀⠀⠀⠡⠀⢓⢈⠈⡆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠀⣀⠔⠉⠁⠂⠀⠀⠑⣀⡀⠰⠋⠢⡘⠀⠣⠁⠀⠀⡌⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠖⠘⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠅⠀⠢⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠚⡁⠀⠀⠀⢰⡆⠀⠀⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⡠⣴⣶⡶⠧⠶⠓⠒⠒⠛⠒⠒⠷⠴⠂⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠃⠀⡇⠀⠀⠀⠜⡄⠀⠀⡲⣤⡀⠀⠺⡄⠀⠈⠀⠀⠀⠀⠁⠒⠻⢧⡤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠤⣤⠶⠞⠃
⠀⠀⠀⠀⡰⠁⠀⠀⢡⠀⠀⡄⠀⢱⠀⠀⠙⣈⠻⣶⣄⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡷⡒⢲⠶⠒⠒⡒⠂⠢
⠀⠀⠀⡰⠁⠀⠀⠀⢸⠀⡐⠀⢰⠸⡄⠀⢄⠈⠓⠀⠙⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢱⠈⠢⠌⠀⣰⡇⠀⠀⢁
⠀⠀⠀⡇⠀⠀⠀⠀⠘⠴⠁⠀⠞⠀⠈⡲⢈⠏⢀⠀⠀⠀⠈⢃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢢⡀⠈⡁⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⢶⡖⠒⣋⡵⢲⠀⠀⠙⢶⣄⠀⠈⠓⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠐
⠀⢀⡜⣀⣀⣀⠤⣤⠒⠉⠀⠞⢁⡔⠁⠀⡎⠀⠸⡄⠀⠈⠻⢦⣀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠠⡄⠀⠀⠈⢠⡐⠂⠀⠀⠀⡀
⠀⠀⠀⠈⡁⠀⠀⠉⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠊⠈⠑⠒
⠀⠀⠀⠀⠑⠲⠄⠤⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡠⠤⡀⠀⡤⠤⣀
⠀⠀⠀⠀⠀⠀⡼⠀⡈⢢⢀⠎⠀⠀⠀⠈⢢⠀⣀⡀⠀⠀⠀⡤⠒⠦⡀⢰⠁⠀⠹⡄⠀⠑⠉⠁⠀⢨⡀⢠⠤⠤⠄⢀⡀
⠀⠀⠀⠀⡜⠉⠁⠀⠇⠀⠿⡀⠀⠀⠀⢀⠍⡜⠁⠈⠉⠐⢺⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠶⢅
⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠈⠒⢤⣰⠋⢚⠀⠀⠀⣴⠤⠏⠉⠉⠓⡦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣁⣀
⠀⠀⠀⠈⡙⠀⠀⠃⠀⠀⠀⠑⠀⠀⣹⣀⡂⠁⡐⠠⡇⠀⠀⠐⠀⠠⣇⢀⡴⠚⠙⠒⢅⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⢀⠇
⠀⠀⠀⠀⢣⡀⠀⠀⢀⢄⡀⠀⠀⠀⢹⠁⠐⠀⠉⢰⠁⢀⠀⠀⠀⡤⢨⣟⠂⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⢻⣇⠀⠒⠀⠀⠀⠘⡆
⠀⠀⠀⠀⡎⠁⠀⢈⠥⣤⡁⠀⠈⢻⠶⠗⠒⡲⠂⢸⢰⡯⢦⡀⠀⠩⢿⡃⠀⠀⠀⠀⢠⢷⣀⠆⠀⠀⠀⠢⠀⢣⠀⠀⠀⢰⠴⠃
⠀⠀⠀⠀⣇⠀⠀⡆⠀⠀⠉⠢⣄⡼⠀⣠⣞⠃⠀⢸⡾⠁⠀⠀⡰⠃⡿⡟⠒⠢⠤⣴⠣⣻⡎⠀⠀⠀⠀⢀⢀⡽⠀⠀⠀⠈⠑⡄
⠀⠀⣄⣀⡈⣒⠖⡹⢆⠀⠀⠀⠨⠷⢆⠁⠘⡧⠄⠘⠃⢄⢀⡜⠁⠀⢈⠞⣆⠀⠀⢀⣠⡟⠓⠜⠀⢀⠀⠘⠁⢀⠀⠀⠀⠀⠀⠽
⠀⠀⡼⠃⠀⠀⠉⠚⠈⠳⡄⠀⠀⠀⢀⠆⠀⢃⠀⠀⠀⡄⠊⠀⠀⠀⠊⡜⢨⡖⠈⣌⠀⣼⡀⠤⢱⠉⠐⠄⣀⢅⠀⠀⠀⠀⡤⠃
⠀⠀⠱⣄⠀⠀⠀⣐⠦⠀⠈⠢⣀⠤⡙⢄⠀⢸⠀⠀⢠⡁⠀⠙⠄⠰⢱⠀⡈⠁⡞⠔⢀⣽⠛⠢⣄⠓⠛⠒⢅⠀⠀⠀⠀⢴⠁
⠀⠀⡖⠒⠛⠀⠀⠈⠀⠀⠠⠀⠀⠀⠈⠊⠀⠘⠢⠤⠞⠀⠈⠀⢠⠘⣾⠮⠉⣴⡽⠀⠈⠀⠀⠀⠀⣣⢀⠈⠀⢳⠀⠀⠀⠀⢱
⠀⠀⠈⣢⡴⠆⠀⠀⠀⣀⠀⠀⠀⡰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠀⢠⣟⠀⠊⠀⡠⠀⠀⠴⠁⠀⠀⠈⡀⠇⠐⠠⣔⠁
⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡠⠒⠉⠁⠐⢦⣰⠉⠉⠁⠛⠀⢰⢄⠀⠀⣠⠊⠀⡀⠀⠀⠀⢀⡏⠀⠀⠀⠱
⠀⠀⠀⠳⡀⠈⡀⠀⠄⠀⠀⢬⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣸⠔⡡⠊⠉⠉⠄⠑⠦⣀⣀⣀⡠⠎⢡⢀⠀⠀⠈⠆
⠀⠀⠀⠀⢨⡖⠛⠁⠀⠀⠀⡀⢇⣀⢀⠠⢤⠞⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡧⠔⠁⠀⠀⠀⠀⠀⠘⠠⠀⠀⠐⠄⢩⠀⡀⠀⡠⠃
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⢘⡤⡄⠀⢀⣀⣀⢴⠋⠀⠀⣸⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⡈⠀⠘⢣⡀
⠀⠀⠀⢼⡄⠀⠄⠀⠀⢀⡘⠙⠦⣀⡠⢶⣯⣞⠏⠂⠁⠀⠀⠸⢤⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠑⠀⠈⠠⣀⠀⠑⡀
⠀⠀⠈⠓⣅⣐⡀⣀⣀⠜⠀⠀⠀⠀⢠⠟⢉⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠴⢄⡀⠀⠀⠐⣲⣄⡴⣤⠐⠺⡀⠁⠀⣀⣅⠢⠕
⠀⠀⠀⠀⠀⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠑⠒⠊⠀⠁⠀⠁⠀⠀⠉⠑⠀⠉⠘⠀⠙⠚⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡽⣛⣻⣮⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣽⡷⣿⣿⣿⣧⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠻⠿⠿⠿⡄⢠⠊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡎⠙⠶⠾⠿⠟⢣⣤⠄⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣦⣄⣀⣰⣾⡯⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡧⡄⣤⣶⣾⣧⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⡉⣠⡆⠀⠛⢻⣾⣾⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⣿⣿⣿⣿⣿⡝⠇⠃⠁⠀⠀⠀⠀⠈⠏⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⢴⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣮⣠⢀⣠⣀⣠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣛⣛⣛⣛⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠋⠙⠛⠙⠛⠋



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣈⣃⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⠶⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠉⠉⣿⡉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢰⣶⡆⢰⣶⣶⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣤⣤⣬⣥⣤⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠸⠿⠷⠾⠿⠿⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣟⠉⠘⠦⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣶⣷⣘⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣄⣴⠚⠛⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠻⠟⣩⣤⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡤⣄⢀⣿⠀⣼⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⢛⡛⣿⠃⣻⡟⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠘⣿⣿⠀⢻⢈⣭⡵⣠⢠⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡅⠀⣫⣿⣿⡀⠀⣟⣧⣷⠶⢛⡿⣿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣶⣿⡟⠀⠈⠳⣝⠱⠿⠆⢟⣣⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠘⠛⠋⠁⠀⣿⣿⣮⡳⢾⣁⣸⣤⠔⣩⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠙⠁⠀⠀⠀⠈⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣰⡦⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠁⠀⠏⢀⣴⠞⠋⠉⠁⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠲⠶⠦⣄⡉⠀⠀⠀⢛⠃⠠⠀⠀⠈⠀⠀⠀⠀⠀⣤⣶⣾⢿⣦⡀
⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⢵⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢿⣇
⠀⠀⣾⡏⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡆⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⢀⣄⣠⣀⣤⣶⣶⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⡟
⠀⠸⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⠟⠁
⠀⠀⢻⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠙⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⠏

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢨
⠀⠀⠀⠀⣠⠴⠖⠒⠲⠶⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⡼⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣄⠀⣀⣡⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠁
⠀⠀⡠⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠠
⠀⠀⠒⠚⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠤⡐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠐⠓⠉⠀⠀⠀⠀⠁⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠀⠀⠀⠀⠯⠤⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠑⢄
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠙⢲⠂⠀⠀⠀⠀⠀⠀⢂⠈⡀⢑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⣧⣀⣠⣴⡾⠃
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁
⠀⠀⠀⠀⠀⢸⢈⠀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡒⡢⢄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠐⠀⣁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠔⠂⠀⠀⠀⠀⠀⢀⠈⡀⡈⡀
⠀⠀⠀⠀⠀⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠑⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠉⠙⢒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⡇⡁⢈⠢⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⣼⡆
⣟⣿⣻⣻⣟⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⢉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⣀⡈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠀⠈⢳⣤⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⡟⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣄⠀⠀⣿⣿⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⡆⠀⢸⣺⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⢿⡀⢠⠏⢀⣾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠻⢦⠈⠇⢠⠟⠉⠉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠄⡀⠙⠀⠀⠋⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⠁⠀⠀⠀⠁⠐⠂⠺⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⢀⣤⠄⠀⠀⠀⠀⢈⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⡋⠀⢀⡄⢀⡠⠀⡀⠀⠲⣦⢀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠸⠁⠀⠰⣦⠈⢷⣌⢳⣶⣶⣾⣿⣿⣿⠛⢿⣿⣿⣿⡏⣰⡟⠁⣼⣧⡄⠀⢉⢸⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⣆⠀⢰⡇⣿⡄⠘⣿⣬⣿⣿⣿⣿⣿⣏⠀⢸⣿⣿⣿⣷⣿⠃⣰⣿⡟⣧⡀⢸⡸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣿⣴⣿⡇⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣴⣿⣿⡇⣿⣿⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢨⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠁⠌⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢄⠄⢈⣀⣾⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢐⡤⠀⣝⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠖⢠⢶⡟⡴⢴⣴⣦⡴⢢⡖⣀⡴⡾⣡⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣈⢄⣶⢻⣽⠟⢿⣻⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠈⠧⠁⠀⠉⠁⠙⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⣿⠟⢁⣬⠂⠅⣈⡛⢺⠻⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡳⣿⣀⠷⣤⡘⡙⢮⢀⠗⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠸⣿⣼⣿⣷⣿⣷⣿⣿⣒⣍⣞⣎⡓⠻⣿⢯⣟⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡤⠶⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣭⣭⣝⠳⡉⡰⣘⢣⣼⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣽⣞⡃⢧⣼⠏⣻⣏⣷⣿⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⢆⣻⣰⣿⣿⣿⣍⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠰⣿⣷⣦⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⡙⣷⣼⣟⣿⣻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣏⣤⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⢄⠀⠀⠀⠀⡀⠀⣤⢦⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⣿⡿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⣤⡀⠠⡙⣄⣜⢾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣯⣿⣻⢟⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⡿⢺⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⢿⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⡿⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⢦⣤⣤⣤⣤⣤⣤⣤⣴⣾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⣠⣤⣼⣿⣿⣿⠶⠀⠀⠀⠐⠁⠐⡄⠀⠀⠀⡠⠤⠶⢶⣦⣀⡀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠠⠞⠀⠠⠞⠁⠀⠴⠋⠀⠄
⠀⠀⠀⠉⠉⠋⡁⠰⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠄⠀⢾⣼⣿⡇⠀⠀⠀⠀⣿⠀⠀⢰⣦⣤⣴⣦⣀⣰⣤⣀⣠⣤⣄⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠃⠀⠀⠰⠀⡿⠀⠀⠘⠛⠈⠡⠜⠆⠛⠰⠼⠧⠴⠦⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⠀⠀⢀⡀⠀⣠⡆⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⠀⠀⠀⠈⠁⠀⠀⢀⣴⡿⠛⠛⠻⠛⠢⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣽⣶⣿⣿⠻⠿⠇⠀⠉⠉⠀⠁
⠀⠀⢀⠐⠄⠀⠀⠀⠀⠂⢈⠄⠀⠀⠀⢀⣽⠏⠁⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⡄⠀⡀⠀⠘
⠀⠀⣄⠀⠁⠒⠠⠁⠀⠖⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠷⠀⠀⠀⠀⠇⠀⠀⢰⠘⡆
⠀⠀⠓⠺⢿⣈⡢⠞⠁⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⡀⠀⠀⠔⠀⠀⠀⠀⠂⠀⠀⣠⠁⢀⠘⠞⢣⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⡷⠈⠀⠀⣤⣶⠆⠀⠀⠀⠀⠀⠀⡅⠀⢠⡇⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣟⣻⣿⣿⣟⣩⠁⠀⠀⠈⢂⠀⠀⠸⣿⣏⠰⡇⠀⠀⠀⠀⠀⢁⠀⠀⡇⡇⢸
⠀⠀⠀⠀⠀⡀⠀⠓⠂⠀⠀⠀⢀⡆⠀⠀⠀⠀⠿⠉⠉⠉⢙⠉⠹⠀⠀⠠⠀⠀⢻⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⡁⣹
⠀⠀⠀⠀⠈⢡⡆⢈⠜⢧⠠⠤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣄⣠⣄⠀⢀⠀⠀⣦⠀⠀⢆⠃⣿
⠀⠀⠀⠀⠀⠉⡤⠋⠀⠈⡆⠒⡀⠀⠀⠀⠀⢀⣠⠄⡐⢻⠷⠢⠀⠀⠀⠀⠀⠀⣸⠀⠀⡟⠛⠋⠉⠻⠀⠈⠙⠂⠀⠀⠀⢸⡃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢰⣮⣿⣷⣽⣭⣦⣴⣿⡤⠀⠆⠀⣠⠋⠀⠀⠷⠂⠀⠀⠀⠀⢀⡀⠀⠀⣀⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣐⠶⢿⣯⣝⡳⣆⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠰⠃⠀⠚⠀⠀⠘⠆⠀⠀⠀⠄⠀⣹⠀⢀⡳⢶⣶⡼⢷
⠀⠀⠀⠀⣀⠀⠀⠛⢷⣦⠋⠟⠁⠛⠁⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡜⠀⣴⠏⠀⠀⠉⠀⠋⠑⠚
⠀⠀⡆⠀⢹⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⢀⣤⢴⡶⠀⠀⠀⠀⠜⠀⣼⠇⠀⠀⠀⢀⡀
⠀⠀⡇⠀⠈⡱⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠜⠋⠀⠀⠀⠀⠀⠤⣴⠏⠀⠀⠀⠠⢸⢃⠐
⠀⢀⡇⠀⠀⡷⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⢀⡴⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⣀⣤⡀⡀⠀⠀⠀⡘⠘⠀⣇⡁⡐
⠀⠸⡇⠀⢀⡘⠂⡁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠁⠁⠈⢹⡷⠁
⠀⠀⡇⠀⢠⠟⠀⠀⠀⠀⣄⡀⣔⡾⢤⠗⣤⢠⣆⠤⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣶⡄⠄⠆⢂⢐⡐⡀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⣾⡾⠂⠀⠀⢃⣀⠐⣛⣂⢛⡚⣘⣋⢳⠞⠋⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸⡟⠒⠐⠂⠂⠃⠐⠀⠀⠀⠀⠀⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠙⠀⠀⡀⠀⢉⣵⣆⠀⠀⡀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠄⠀⠀⠀⠠⠀⠘⠋⠀⠐⢁⡴⠞⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣤⡔⠁⠀⠀⠀⢀⣴⠞⠉⢀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠛⠶⣄⠀⠈⠛⠷⣦⣴⡶⠓⠈⠁⣨⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢈⠂⠰⠦⢤⡙⣿⡄⠀⠀⠞⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣀⣷⡄⠀⠀⠀⠙⠧⠀⠔⠂⢋⡤⠦⠈⡣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⠉⠛⠻⡦⠐⠿⠿⠶⠁⠀⠀⠞⠁⠚⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⣶⣤⠾⠶⣶⠮⠐⢶⡾⠂⢠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢰⠆⣀⣁⣤⡶⠦⢶⣦⣾⡷⡄⠀⣄⡈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣇⣨⢉⢹⣿⣯⣀⣾⠋⠸⣿⡿⢶⣼⣿⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢻⣿⠃⣿⡟⢠⠀⠈⣿⡡⠄⠸⢧⠀⠙⡎⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠸⣷⢴⣿⡇⠉⠀⠀⣹⠀⠀⣄⠀⢃⡿⠀⠉⢠⡔⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⣤⡘⢷⠃⠙⣇⣠⠴⠚⠹⣆⠀⠉⠀⢈⢷⡶⢄⣤⠀⣄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢿⣷⠋⠀⠀⠈⠁⠐⠶⡄⠈⣷⣀⠔⠁⠀⠛⣄⢀⡄⠁⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠁⣄⡈⠻⡴⠚⡉⠙⢇⠀⠋⠀⢀⣼⠿⡠⠴⠶⠄⠘⡟⠀⠸⡇⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢠⠀⣀⣾⡅⢻⣓⡀⢘⣧⣠⠔⠉⠀⠀⠻⣆⢀⠤⠂⢻⡂⠀⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢾⡟⣉⠉⢏⠉⠀⢉⣠⠴⢏⡒⠶⠿⠦⠄⡟⠧⢤⣄⡀⣷⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⡇⠧⡄⠈⢣⡴⠋⢀⡀⠀⠹⣀⣀⠤⠐⢿⣄⠘⠩⠉⠈⠉⠒⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣤⣧⡀⣤⠖⠘⢧⠲⠟⠧⢄⠠⣿⠀⢠⣆⠀⢘⣇⠀⠀⣠⡸⡇⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢙⢻⡇⣴⠃⠀⢀⡘⢀⣤⠄⢾⣀⠤⠟⠉⣉⠸⢷⡴⠋⠁⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡈⠻⣦⠁⠀⠈⣿⠉⠀⣀⠀⠙⣆⢠⠞⠁⠀⠀⠻⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠈⢡⣼⣿⣶⠶⠾⠟⣢⡴⠿⡄⠀⠙⣟⠀⠠⠞⠣⠀⠧⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣇⣶⣄⠀⢱⡄⢠⡶⠒⠉⠉⠳⣀⡄⠀⠘⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣆⠛⠽⢡⡼⢉⡛⠀⠠⣄⡀⠠⠥⢄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠘⢄⡙⣦⠀⠀⠀⠀⠀⠀⠀⠓⣤⣇⠀⠀⠀⠀⠀⠀⠫⣉⣲⡴⢊⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠲⣄
⠀⠀⠀⠀⠀⢠⢖⠉⠛⠓⠂⠒⢄⠀⠀⠀⢀⡎⠀⠈⢇⠀⠀⠀⠀⢠⢋⠀⠌⡉⣉⡆⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢘⡄
⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⢸⠀⠀⢀⠞⠀⠀⠀⠘⢆⠀⠀⠀⠸⡠⠀⠄⠄⢠⠃⠀⠀⠀⠀⢀⡠⠞⠁⣠⠀⢨⠃
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡜⠀⠀⡎⢰⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢄⠂⣂⠎⠀⠀⡴⠖⠍⠡⠤⠴⠚⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠘⢆⣀⡤⡠⠞⠀⠀⠀⠘⢼⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠓⠒⠐⠒⡒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢹⡀⠀⠀⠀⠀⠀⡠⣒⠒⠚⢖⠳⢄
⠀⠀⠀⠀⠀⠀⣴⠿⠂⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⣠⠒⢾⡽⠓⠻⣼⠒⠒⢤⠀⠀⢸⢱⠁⠀⠀⠈⡇⠀⢳
⠀⠀⠀⠀⠀⢼⠉⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡞⡳⣤⠼⣇⠀⣠⡿⠷⢖⠉⠀⠀⠸⡘⠀⠀⠀⠐⠁⠀⡜
⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⣸⣛⠼⠣⡄⠀⡏⠉⣣⣀⠜⠀⠀⠀⠀⠑⠤⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⡠⠔⠃⠀⠀⠀⠐⢇⡸⠦⠤⠚⠒⠋⠚⠁⠀⠀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢇⠒⠀⠂⠀⡀⠁⠀⠁⠀⠢⠀⠂⡇⡬
⠀⠀⠀⠀⠀⠀⠀⣦⡀⡼⢳⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢦⡈⢠⠄⡀⠘⠀⠈⠠⡀⢉⡜⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡴⣌⢣⠔⢉⢼⡀⠀⠀⠀⠀⡠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⡲⠤⣁⣈⣀⣉⡠⠴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢱⡤⣿⡴⠥⣜⠀⠀⠀⠀⠮⣤⡤⢾⠟⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⢀⡜⢇⢀⡼⠳⣄⡏⢦⠀⠀⠀⠀⠀⢠⢣⠂⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⢸⣤⡴⠻⢄⣠⠊⠉⡿⠀⠀⠀⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡔⠉⠒⠊⠁⠒⠂⠉⢉⠆
⠀⠀⠀⠀⠀⢻⡀⢑⣤⣞⠉⢲⠾⣸⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣀⠴⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⢟⠻⢤⣈⡽⠛⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⡀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠫⠥⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢷⠀⠀⢿⠀⠀⡿⠀⢀⡎⠀⢠⠆⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠐⣄⠀⠈⢧⠀⠘⣇⠀⠸⠄⠠⠧⠀⣼⡀⣠⠏⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣾⡟⣿⡆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠈⢣⡠⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢎⠀⠀⠀⠀⠀⣀⣤⣤⡄⠙⣿⡿⢛⣿⠟
⠀⠀⠀⠀⣴⡟⠁⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣤⣤⣀⣴⣶⣦⠀⣴⣟⣽⠟⢀⣼⠟⢀⣾⠏
⠀⠀⠀⢸⣿⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⠀⢀⣤⣤⡀⣴⠾⣿⡆⢀⣿⣿⡟⠀⣿⣿⠃⣿⡇⢰⣿⡿⠋⢠⣾⠋⠀⣾⡏⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠘⢿⣆⡀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⢰⣶⠆⠀⣼⣿⣷⡟⠁⣿⣿⠏⢸⣿⠀⣼⣿⡟⠀⢰⣿⠇⢰⣿⣁⣾⣿⣤⡴⠟⠁⠀⠀⣿⣇⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⢀⣴⣿⣿⠀⢠⣿⣿⠀⣼⣿⣿⡟⠀⢸⣿⡏⠀⣿⣏⣼⣿⣿⠀⠀⠺⠛⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣶⠛⠁⣿⡇⢀⣾⣿⣟⣰⡟⢹⣿⠀⠀⠸⠟⠀⠀⠈⠉⠁⣠⡤⣤⡄⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⣿⣇⠀⠻⠷⠾⠋⠈⠛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢡⣿⠇⠀⠀⠀⠀⣾⡟⣽⡟
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣼⣟⣰⡿⠋⠀⠀⠀⠀⠀⢘⣿⣿⣅⡀
⠀⠀⠀⢰⣿⠁⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣾⡟⣿⡆⠈⠛⠀⢠⣿⣿⣋⠀⠀⣴⡟⣿⡇⢠⣾⠏⠀⠙⣷⡄
⠀⠀⠀⠈⢿⣦⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠻⣶⣿⠷⣿⡟⠀⣾⣿⢿⣽⣷⣼⣿⠟⠋⣰⣿⣷⡶⠷⢄⣿⠇
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢀⣿⡏⠀⣿⡇⣸⣿⡇⢀⣿⡏⠸⣿⣤⣾⠟⠘⠿⣤⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣾⡟⠀⠀⣿⣷⡟⠙⠻⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠾⠋








⣿⠛⠛⣿⢿⠿⢿⠿⠿⣿⡿⠿⠿⡿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠿⣿⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠳⣾⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⢤⣤⣤⣴⣶⡶⠾⠶⣶⣤⣀⠸⠃⠈⣷⡀⣀⣤⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠃⠀⠀⣀⣀⣀⣀⣀⣀⠈⠙⢷⡄⢠⣿⠟⠋⠀⠀⠀⠀⠈⢉⣷⣦⣀⣠
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠚⠉⠉⠉⠀⠀⠀⠀⠉⠙⢦⣼⠿⣿⠁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠨⠽⠧⠤⣴⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⢠⣤⡤⠖⣂⣤⠴⠖⣲⡿⣿⠇⣺⣿⠟⠉⠉⠉⠉⠉⠛⠳⠶⠤⠤⠴⠶⢺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣶⣛⣭⣶⣶⠟⢁⣴⠏⣼⣿⣿⢠⣤⣂⣤⡀⠀⠀⣤⣤⣤⡤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢉⡽⠋⢁⣴⠿⡟⢸⡏⠘⠻⣷⣭⣭⣭⣤⣤⣶⠶⠶⠾⠿⠆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⠟⠁⠀⢠⡟⢁⣴⠟⠁⢸⡇⢸⠁⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⣠⣶⠿⠛⡉⢉⡿⠿⠿⠷⣶⠏⢠⡞⠁⠀⠀⠸⡇⢸
⠀⢠⣾⠏⠀⠀⠀⠳⢮⡶⠂⠀⢀⡏⢠⣿⡄⠀⠀⢀⣠⣧⢸⣤⣤⣤⣤⣀
⠀⣾⡇⢠⡆⠀⠀⠀⠀⠀⠀⠀⣸⢠⡏⢸⣿⣀⣶⡿⠟⠻⡄⢫⣉⠉⠛⠛⠿⣦⡀
⠀⣿⡇⠸⣇⠀⠀⠀⣀⣠⣤⣤⡇⣼⣀⣼⣿⣿⠏⠀⠀⠀⠚⠾⠋⠀⠀⠀⠀⠈⠻⣦
⠀⠘⣿⣆⠉⢀⣴⡿⠟⠉⢁⠘⡇⡏⠉⠉⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠈⠻⣷⡿⠁⠀⠀⠀⠈⠻⣷⡷⠏⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⡇
⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣿⠇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⡴⠾⠋⣠⣾⠟
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⢰⣿⣤⣄⣀⣀⣀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠙⣷⣄⠀⠀⣀⣀⣀⣀⣤⡾⠏⢀⣴⣿⠋⠈⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠈⠙⢿⣶⣦⣭⣭⣭⣭⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠃⢀⣀⡀⡀⠀⠀⠀⠀⠈⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢀⣀⡀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢰⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⠁⠲⣄⠀⠀⠈⣄⠀⠀⠈⠁⠸⠄⠀⠀⠀⠀⠀⡈⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⣤⠀⠀⣠⣤⣤⣤⡉⠢⢀⠘⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⣼⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠍⢠⡄⠀⢈⣤⠀⠀⠉⠂⠀⢷⡄⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠁⠘⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠃⠀⠀⠉⠂⠀⠀⠀⠀⢸⣧⠀⠀⠀⠸⠐⠢⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠁⠈⠄⠁⠤⠀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢄⠀⠀⠀⢀⣠⣤⣴⣆⣀⡀⠀⠀⠀⠀⢸⣤⠀⣈⠆⠀⠀⠈⠂⠀⠀⠀⠆⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⠂⠠⠄⠀⡀⠂⠀⠈⠙⠻⠯⣭⠍⠿⠛⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠴⠋⠀⢰⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠦⠤⠶⠒⠁⠀⠀⡰⠋⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢲⣿⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠉⠓⠦⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠒⠁⢠⠋⠀⠈⠸⣖⣤⣤⣤⠠⠄⡐⡅⠀⢀⣠⠂⣠⡊⠀⠀⠈⡉⣲⠶⢄⠀⢰⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠞⡵⠃⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⢉⠀⠐⡎⠃⢰⡟⠀⣦⠀⡾⢰⠃⠀⠀⠑⢬⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠔⡀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠀⢰⠀⣤⣼⠁⠀⠁⢸⠃⢀⡔⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⠁⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣿⡏⡜⠀⡠⡿⢸⣿⡧⠊⠀⣀⣈⢢⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡟⢹⢹⡇⣼⢡⠇⡾⡏⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠶⠀⢸⠚⠀⠀⢸⣿⠃⠸⠈⢱⡇⠀⠁⡀⠀⡂⠀⠰⡀⠀⠀⡰⠀⠦
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠄⢰⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡏⠀⠆⠀⠀⢧⡀⠋⣀⣾⡗⠄⠀⢈⠉⠉⠀⢀⢰⠂
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠙⡀⣿⢣⠐⣄⠀⠻⣆⠀⠀⠈⠈
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡏⠀⡀⠀⠀⠀⠀⠀⠇⠹⡈⡄⠈⢗⠀⠙⠂⠀⠀⡐
⠀⠠⠇⠀⠀⠀⠀⠀⠀⢀⢮⠀⢈⡇⠘⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⡇⠀⠀⠈⠀⢰⠁⠀⠀⠀⠀⡞⠀⠀⠀⠛⠒⠠⠀⠀⠀⠐⠈
⠀⡧⠘⠀⠀⠀⠀⢀⡔⠁⠰⠰⠊⡅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡏⠀⠀⠀⠀⣽
⠀⠸⡀⠃⠀⠀⡠⠋⠀⠠⠃⡦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠃
⠀⠀⠑⣦⠤⠐⠁⢀⡴⠕⠊⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠒⠶⠒⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡿⣿⣇⣤⣄⠀⠀⢠⣦⣰⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢠⣤⡀⠀⣿⣿⡇⣿⣿⣿⣿⣧⠀⣿⣿⡇⣾⣿⣷⣷⡄⠀⠀⣀⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢻⣿⣆⠸⣿⣷⡀⢻⣿⣧⢹⣿⡇⣿⣿⢸⣿⣿⢰⣿⡟⣼⣿⡇⢠⣾⣿⠟⢡⣿⡇
⠀⠀⠀⠀⠀⢠⣾⡟⠻⣷⣄⠈⢿⣿⣄⢿⣿⣿⡎⠿⠿⠈⠛⠃⠙⢋⠈⠛⠃⠘⠿⠁⣿⡿⢠⣿⣿⣏⣴⣿⠟⠀⢀⣤⣦
⠀⠀⠀⠀⠀⠈⢿⣷⣤⣈⣛⠀⠀⠙⢿⣿⠃⠉⠁⠀⣠⡀⠀⠠⣴⣿⣦⡄⠀⢀⣀⠀⠀⠀⠘⣿⣇⣉⠛⠉⣠⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠾⠛⠇⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠁⢠⣾⣿⠟⠉⠀⢾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠛⠀⠀⣠⢖⣿⣿⣿⣿⣿⣶⣦⣤⠀⣤⣴⣶⣿⣿⣿⣿⣿⡲⣄⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣼⣿⣿⣿⣿⣿⣿⣿⠏⣀⡹⣿⣿⣿⣿⣿⣿⣿⣧⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⢡⡾⠉⡇⠈⠻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠶⠆⠀⠀⠉⠛⠋⠉⠀⠀⣾⠃⢰⠁⠀⠀⠀⠉⠙⠛⠉⠁⠀⠰⠾⠿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠀⠀⠀⠀⢀⡀⠀⠤⢸⣿⢠⢃⣀⡀⠀⠀⣀⠀⣠⣄⠀⠀⠀⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⠉⢀⠀⠀⣼⠀⢿⣆⣴⠆⢸⣿⣡⠋⢸⡇⣠⡾⠍⠀⣿⡘⢀⠀⠀⣀⠈⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⢻⡀⡜⠀⣿⠀⡜⣿⠷⢒⣿⠋⢸⡇⣠⠆⣨⢿⡁⠀⠀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠻⡴⢡⡏⣀⣾⠏⠀⠀⠉⠁⠀⠣⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⣀⣴⣞⣡⡄
⠀⠀⠀⠀⠀⠀⡔⣿⣿⣮⢞⡵⣫⠝⠁
⠀⠀⠀⠀⢠⢖⡣⣞⡿⠁⢀⣜⣡
⠀⠀⠀⠀⣎⣿⣿⣿⣷⣠⠜⠻⡀⠀⠀⢀⡀⠀⠀⠀⠈⠁⢀⣀⡀
⠀⠀⠀⠀⠙⠿⣿⣿⠿⣇⠀⠀⠱⣄⠀⢉⡤⢤⣀⠀⢀⠞⠁⠀⢸⠂
⠀⠀⠀⠀⠙⠓⣼⣅⠀⠀⠑⢢⡄⠀⠙⠺⣆⠀⠈⠳⣼⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢠⡎⢻⣷⣄⠀⢀⣭⡓⢤⡀⠈⢣⡀⠀⠈⢳⡭⠥⠤⠤⠤⠤⠔⠒⠚⠉⠁⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠳⢿⡈⢮⣑⢮⡀⠈⠙⢿⣦⡀⠙⠲⢤⠤⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⢀⡤⢔⡛⠿⠆⠀⠀⠀⠃⠀⠀⢹⡉⠁⠐⠒⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⠋⣉⠴⠚⢇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠻⠻⡖⠚⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢣⠀⠀⠙⠛⠓⠿⣶⡄⢀⣤⣶⠿⠛⣁⣸⠾⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠹⡭⠞⠋⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⣄⠀⠀⣾⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠷⢖⠤⣈⣋⢿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠸⡁⢠⡼⠂⠀⠙⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠔⣊⡥⠄⠒⠂⠀⠀⢲⡀⢱⠀⠁⠀⠱⢬⡑⢤⡀⠀⠀⠀⠀⠀⣈⡦⡇⠀⠀⠈⠳⡞⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣈⠳⢄⡠⢊⡵⠊⠁⠀⠀⠀⠀⠀⢰⡣⠷⠞⠀⠀⠀⠀⠈⢯⠓⢬⡒⠒⣒⡩⠥⠒⠊⠹⣤⣀⡀⠠⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠑⣒⣻⡀⠀⣀⠉⣉⣉⡹⠂⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠕⠊⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⣀⣀⣀⣀⣀⣀⢤⠤⣴⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⠧⡔⠈⢋⠫⠏⠉⢖⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣍⠋⢀⢿⣾⣿⡛⠺⣧⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⣶⠷⠞⠿⢳⣾⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⡴⢩⠃⠀⠀⣠⠎⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⡀⠈⣛⣦⣀⡀⣀⣨⠇⣴⡉⠀⠀⢉⣑⣾⣖⠒⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣏⡫⢟⣽⡩⠊⠀⠀⠉⠒⠭⣓⠿⣏⡩⣟⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠽⠷⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠄⠀⡀⠀⠌⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠡⡰⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⢀⣀⠀⠀⠠⠀⣒⠂⠒⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠉⠁⣵⠂⠻⡐⠂⠠⣀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠊⠉⠀⠆⠀⠀⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⡀⢸⠃⠀⠀⠈⢲⡄⠀⠀⠀⠀⠀⣠⣾⣿⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠭⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠘⠢⣤⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠉⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠂⠀⠀⠠⠞⠉⠀⠤⡀⠀⠀⢀⠤⠤⠤⠦⠸⢿⣿⣿⣿⡿⢀⠀⠀⠀⠀⢀⣤⣶⣦
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠓⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠯⠉⢉⠔⠉⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠤⠊⠀⠐⠆⠀⠀⠀⠀⠀⠈⠉⠀⠁⠑⠀⠀⠀⠀⠀⠴⠈⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄⣠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⡠⠊⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⠁⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠋⠀⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⣒⠂⣠⣐⣒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣠⢞⠵⠊⠁⠀⡇⡇⠀⠀⠉⡲⢉⠢⡀
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⡐⡡⢬⡢⡀⠀⠀⢹⡇⠀⢀⣜⠕⠁⠑⡜⢆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣰⢰⠁⠀⠉⠚⢦⣄⠸⡇⢠⡞⠁⠀⠀⠀⢘⡜⡄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣆⣀⣀⣀⣀⣀⣉⡟⠙⣯⠤⠶⠶⠦⠭⠭⡄⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣇⢰⠒⠒⠉⠉⠁⣠⠟⣶⠙⢦⣀⠀⠀⠀⠀⡇⡆
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⡜⡄⠀⠀⣠⡾⠃⠀⢹⡀⠀⠙⢷⡢⣀⡼⡰
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠘⢌⠢⢜⡕⠁⠀⠀⠈⠃⠀⠀⠀⣙⢆⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠑⠬⣓⠤⢄⣀⡸⠸⡤⠔⣊⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠊⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⣤⠀⠀⠀⠀⠀⣀⣄⠀⢀⣀⠀⢀⡀⠀⣀
⠀⠀⠀⠠⣦⠀⠀⣀⣄⡀⠀⠀⠀⣿⠀⣃⢤⡟⢀⣴⠂⢀⣾⡣⣻⡟⢡⡟⢠⣿⡐⣿⠖⢹⡇⣰⡿⠃⠀⣸⡧⠊⠙⠀⠀⣤⢤⣄⠀⠀⡤⢄⡀
⠀⠀⠀⠀⢻⣧⣼⣯⣹⡏⠀⠀⠀⣿⠊⠁⠸⡷⠋⣿⡴⠁⠿⠁⠛⠀⣼⢣⢿⠟⠰⠏⠀⣿⣠⠿⡤⠴⠊⡿⠁⠀⠀⠀⠘⡿⠛⠛⢠⡾⢁⠀⠁
⠀⠀⠀⢰⠛⠛⢛⡻⠻⡁⠀⠀⣮⡾⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣄⠘⠁⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⣠⠛⠒⠘
⠀⠀⠀⠈⠃⠈⠹⣧⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⢠⡄⢸⣿⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣠⣤⣄⡀⠀⠀⠀⠀⢀⠀⠐⠃⠀⠁
⠀⠀⠀⠀⠄⠀⠀⠹⣇⠀⢃⠀⠀⠀⠀⠀⣿⡆⠀⢠⣿⠃⣴⠄⢸⣿⣴⣶⣦⡄⢠⡿⠋⢹⣿⢸⣿⣉⡙⠃⠀⠀⠀⠀⠀⠢⢀⠀⠀⡠⠂
⠀⠀⠀⠀⠐⡀⠀⠀⠹⠆⠈⠀⠀⠀⠀⠀⢸⣧⠀⣾⠇⠀⣿⠀⢸⣿⠁⢀⣼⡏⢸⣟⠛⠛⠁⠀⠉⠛⠻⣷⡀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠐⠄⠀⠠⠐⠊⠀⠀⠀⠀⠀⠀⠻⡿⠋⠀⠀⣿⠀⢸⣿⠟⠛⠉⠀⠈⠻⣶⣶⠗⠈⠻⣶⣶⠟⠀⠀⠀⠀⠀⠔⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⡄⠀⢀⣀⠀⠀⣀⡀⠀⢀⡀⢪⣃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⢠⢶⣶⣇⢀⣿⣿⣤⢠⡏⠿⣶⡼⠗⠁⢸⡧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠁⠘⠋⠈⠉⠛⠀⠙⠁⠃⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⡿⡰⠃⣀⢀⡤⠀⠀⣀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⣀⠀⡀⡁⢠⡗⠁⣸⢋⢼⣤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⠀⠀⠀⣿⡘⠹⡷⢺⡇⢻⠉⢁⠜⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠹⡇⠀⠀⢸⣇⠇⠀⠎⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⢸⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣤⣤⣤⣶⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣻⣾⠿⠏⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣛⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠋⠁⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡛⠿⣦⣌⣉⣉⣉⡉⣻⠉⠉⠉⠉⠉⠁⠀⠀⠀⣉⣈⣀⣀⣠⡤⠤⠖⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣀⡍⠉⠉⠉⠉⠉⠀⠀⠉⠀⠀⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣀⡀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣿⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢷⣶⠿⠶⢷⢶⣶⠶⠾⣿⠿⠋⠉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣅⣀⠀⠈⠉⠀⠀⠁⠠⠴⠀⠈⠀⠰⠒⠀⠀⠳⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣾⣦⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⢻⡛⠭⠽⠋⠿⠿⣷⣦⣀⢀⡀⠀⣀⠀⢀⣀⣠⣤⡶⠖⠛⠛⠛⠉⠉⠁⡀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡶⣦⠄⣀⡀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣶⣾⡿⠛⠛⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⡿⢿⡟⠅⠁⠀⠀⠀⠀⠀⠀⣠⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣭⣟⠉⠉⠙⠙⠀⠀⠀⠀⠀⠛⠋⠉⠉⠀⠀⠀⣁⣤⣄⣤⣤⠶⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⡳⠦⢙⠻⢿⣿⣿⣿⣿⣾⣾⣶⣶⣶⣶⣦⣶⣶⣶⣾⣷⣾⣿⣿⠿⠛⠋⠡⠀⠐⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⣈⡙⠛⠲⠶⠍⢉⡛⠛⠛⠛⠉⠉⠋⠙⠛⠛⠛⠛⠛⠋⠀⠐⠊⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠁⠀⠀⠀⠛⠛⠉⠉⠉

⣉⣉⣩⡤⠴⠖⣫⣾⠟⠁⠀⠀⡜⠁⠀⠀⢀⣿⣟⠂⠆⣉⡑⠂⠠⠀⢄⡠⠷⠀⢀⠀⠠⣄⢹⠀⠆⡈⢻⡄⠀⠀⠀⠀⠈⠙⠲⠤⢤⣀⣀⣤⣄
⡷⠀⣀⣠⣴⡾⠟⠁⠀⠀⢠⠞⠀⠀⠀⢀⣾⡏⠈⠷⢶⣦⣴⠶⠶⢲⡏⠡⠄⠀⠀⠑⠀⠞⠀⢰⠀⡍⢀⣽⣦⣤⣀⣀⡀⠀⠀⠀⠀⢀⣿⣯⡻
⡿⠛⠋⠉⠁⠀⠀⠀⣠⠖⠋⠀⠀⠀⢀⣾⣯⠷⢢⣤⣠⠭⠟⠛⢶⣿⣕⠂⠲⡀⠀⢠⣀⣨⠂⠁⡄⠁⠈⠀⠀⠀⠉⠙⠛⠻⠿⠶⢶⣿⢻⠟⣰
⣇⠀⠀⣀⣠⠤⠖⠋⠀⠀⠀⠀⠀⣠⣿⠃⠇⠀⠈⠀⢹⡆⠘⢦⠀⠈⠙⠿⣶⣍⡉⢦⣀⠴⠀⠚⠁⠀⡁⢰⣄⣀⠀⠀⠀⠀⠀⢰⠾⣿⠋⠀⠸
⢿⣟⠉⠡⠂⠀⠐⠂⠀⠀⢀⣤⣾⠏⠀⣠⠤⠈⠠⠀⠀⢿⡄⠈⢧⡀⠀⠀⠀⠙⠻⢷⣦⣤⣤⠔⠠⠴⢃⣌⠀⠉⠙⠒⠦⠤⠤⢬⣤⠃⠀⣼⡀
⠀⢻⡏⠘⠉⡵⠊⠳⠀⢻⢿⡋⠉⢻⢋⠀⠀⠀⣠⠴⠂⠪⣷⣄⠀⠙⢦⣀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣯⣽⣷⣦⣀⣀⣠⡤⠞⠉⣿⠀⠀⣿⣷
⠀⣾⣃⣘⠁⢁⡄⠒⠂⠀⠀⢿⡄⠋⡁⠀⡰⠀⣿⡄⠀⡀⠈⠙⠷⣦⣄⡈⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⢀⣀⣼⠿⡆⠀⠹⣿
⡎⠁⢃⠤⢌⠁⠱⠀⢊⣀⠼⠸⡏⣫⣀⣠⣁⠤⠿⠧⠀⠘⢦⣀⠀⠈⠙⠻⢶⣦⣄⣀⠉⠉⠓⠒⠒⠲⠶⠤⠤⢄⣠⣴⠞⣡⣿⠋⠀⢳⠀⠀⢹
⣷⠁⠠⡀⠀⠏⠠⠤⠎⣠⢂⡼⢍⠉⢳⣑⠢⠀⠀⢾⡆⠀⠀⠈⠓⢦⣀⠀⠀⠈⠉⠛⠿⢶⣦⣤⣤⣤⣤⣶⠾⠟⢋⡀⣴⡿⠃⠀⢀⡏
⣏⠓⢔⣉⡐⠒⢠⡀⢀⡠⠿⠄⠀⠐⠀⣄⢹⠒⡤⡈⢻⣄⠀⠀⠀⠀⠈⠙⠲⠦⢤⣄⣠⣤⣄⣈⣉⣩⣥⠤⠴⠒⣩⣾⠟⠁⠀⢀⡞⠀⠀⠀⢠
⣈⠳⢶⣦⣴⠶⠞⢲⡏⠀⠀⠀⠀⠁⠀⠞⠀⣰⠒⡌⢀⣩⣶⣤⣀⣀⡀⠀⠀⠀⠀⢀⣿⣯⡹⣿⡷⠀⣀⣠⣴⡾⠛⠁⠀⠀⢠⠊⠀⠀⠀⢀⣾
⢂⣤⣡⠬⠛⠛⢷⣿⣝⡒⠢⣀⢀⠤⣀⡨⠂⠁⡄⠁⡘⠂⠀⠀⠈⠉⠛⠛⠿⠷⢶⣿⢻⠏⣰⣿⡿⠛⠋⠉⠁⠀⠀⢀⣠⠖⠁⠀⠀⠀⢠⣾⣿
⠈⠀⢻⣆⠈⢦⠀⠈⠙⠻⣶⣭⡉⠦⣤⠴⠀⠊⠀⠀⠀⣸⢄⣀⠀⠀⠀⠀⠀⢰⠿⣿⠋⠀⠸⣿⣇⠀⢀⣀⡠⠤⠒⠉⠀⠀⠀⠀⠀⣠⣿⠁⠃
⠂⢀⠀⢿⡀⠈⢣⡀⠀⠀⠀⠙⠻⠷⣦⣴⣤⠚⠠⠴⢃⣅⠀⠈⠙⠒⠂⠠⠤⢼⣤⠃⠀⣾⡀⠈⢻⣏⠉⠁⢂⠂⠀⠀⢀⠀⢀⣴⣿⠋⠀⡠
⣠⠴⠒⠺⣷⣄⠀⠙⠦⣀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣯⣽⣷⣦⣄⣀⣠⡴⠞⠁⣿⠀⠀⣿⣷⡀⠀⢻⡏⠝⢉⡽⠚⠳⠈⠻⠿⣉⠁⢻⣋
⣿⡆⠀⡀⠀⠙⠷⣦⣄⡈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠁⣀⢠⣼⠿⡆⠀⠸⣿⣷⠀⣾⣉⢸⠁⢁⡄⠚⠂⠀⢀⢻⡄⠋⡀⠁⠰
⠿⢧⠆⠘⠢⣀⠀⠀⠙⠻⢷⣦⣤⣀⠈⠉⠓⠒⠒⠒⠶⠤⠤⢄⣤⣴⠞⣡⣿⠋⠀⣿⠀⠀⢹⣿⡎⠁⠁⠠⢬⠀⡕⠀⢊⢀⠜⠘⠏⣫⣄⡠⣆
⠀⢾⡆⠀⠀⠈⠓⢦⣀⡀⠀⠀⠉⠛⠻⢷⣶⣤⣤⣤⣤⣶⠿⠛⢉⡀⣴⡿⠁⠀⢀⡏⠀⠀⠀⣿⣿⠁⠠⣀⡀⠋⠠⠤⠎⡠⢀⠾⢍⠉⢳⢉⡢
⠄⠈⠻⡄⠀⠀⠀⠀⠀⠉⠓⠦⠤⣄⣠⣤⣄⣀⣉⣩⣥⠤⠖⠚⣩⣾⠟⠀⠀⢀⡞⠀⠀⠀⢠⣿⣏⠓⠐⠁⠈⠒⠠⠤⢄⡤⠒⠀⢀⡂⠀⢄⢹
⠐⡎⢀⢬⣶⣤⣄⣀⣀⠀⠀⠀⠀⣀⣿⣯⡹⣿⡷⢀⣀⣤⣴⠿⠋⠁⠀⠀⣠⠎⠀⠀⠀⢠⣾⣏⠈⡳⠶⣦⣴⠶⠞⣲⡏⠰⠄⠀⠀⠁⠀⢎
⡄⠁⡈⠂⠀⠀⠈⠉⠛⠛⠛⠿⢶⣿⣻⠏⣰⣿⡿⠛⠋⠉⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢠⣿⣿⠒⢢⢤⣠⠌⠛⠛⢷⣿⣝⡒⠰⣀⠀⠢⢄⠬⠃
⠀⠀⡀⣸⢄⣀⠀⠀⠀⠀⠀⢰⠛⣿⠋⢀⠸⢿⣧⠀⢀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⣰⣿⠁⠇⠀⠀⠀⢺⣆⠈⢦⠀⠀⠙⠻⢷⣬⣉⠢⠤⠔
⠀⠔⢁⣥⠀⠈⠙⠓⠲⠶⠦⢬⣴⠃⠀⣾⡀⠈⢻⣯⡉⠐⢂⠂⠐⠀⠀⠀⢀⣴⣿⠋⢀⡠⠀⠀⠱⠀⠀⢿⡄⠈⢳⡀⠀⠀⠀⠉⠛⠿⣶⣴⣤
⠿⣿⣧⣽⣿⣦⣄⣀⣤⡴⠚⠁⣿⠀⠀⣿⣷⡀⠀⢻⡏⠘⡁⡜⠊⠳⠀⢻⠿⣍⠄⢻⣃⠄⠀⠀⣠⠶⠂⠫⣿⣄⠀⠙⠦⣄⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠉⠉⠉⠙⠉⠁⣀⣠⣼⠟⡆⠀⠸⣿⣷⠀⣼⣁⠼⠀⣁⡄⠊⠀⠀⢀⢻⡄⢋⡀⠁⡔⠀⣿⡄⠀⡀⠀⠙⠳⣦⣄⡈⠙⠲⠤⣄⣀⡀
⠒⠒⠲⠦⠤⢤⣤⡶⠟⣱⣿⠋⠀⣿⠀⠀⠹⣿⡎⠀⠁⠤⠌⠀⠕⠐⢊⢀⠞⠘⡏⣫⣤⡤⣄⠤⠿⢇⠂⠈⠢⣄⠀⠀⠙⠻⠷⣦⣤⣀⡈⠉⠙
⣤⣤⣴⣶⡿⣛⣉⣀⣰⣟⣁⣀⣀⣏⣀⣀⣀⣿⣿⣁⣠⣀⣀⣋⣀⣤⣊⣠⣂⣾⣅⣉⣳⣈⣂⣀⣀⣾⣆⣀⣀⣈⣑⣦⣀⣀⣀⣀⣉⣛⡻⣷⣶
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⢀⣀⣛⣛⡛⠻⠿⢯⣛⠿⢦⠀⢦⣼
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⢁⣀⠀⠀⠚⠋⣉⣩⣭⣟⠛⠶⠀⠈⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢠⣿⣡⠴⠀⠀⠸⠟⣦⣀⣀⣠⣴⣶⡄⠀⠀⠀⠀⣠⡶⠶⣤⠀⣿
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⡟⣡⠾⠋⠀⠀⠀⠀⢉⣩⢴⣿⡽⠂⠀⠀⠠⡾⠋⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢸⠃⣠⠆⠀⠀⣀⣾⣯⣶⣯⡵⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢻⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣴⠶⣠⣾⠃⠀⠀⠀⣉⡵⢞⣽⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⡶⠿⠦⠀⠙⢷⣄⠀⠀⣠⣄
⠀⠀⠀⣀⡴⠿⠀⠀⣠⢴⡟⠀⢸⠇⡿⠀⠀⠀⠀⠉⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⡟⠉⠻⢶⣤⡶⢶⣄⣀
⠀⠀⣾⠋⣰⠟⢡⣾⡟⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⠀⠀⠀⠙⠷⢾⣧⣽⡿⣦⠀⠀⣠⠶⡆
⠀⠸⣏⠀⠿⠀⡿⠘⠇⠀⠀⠰⣄⡀⠀⠀⠀⠲⣦⣀⣀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣶⣞⣡⠞
⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣦⣤⣴⢿⣯⣩⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣙⠶⢤⣤⣤⠶⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢧⣤⣤⣤⡤⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡖⢀⡟
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠙⠻⠶⠖⠂⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠿⣤⡌⠻⠓⢶⣦⣤⣀⡀⠀⠀⠀⢠⡏⢀⡾
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣴⠏⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⠀⠀⠈⢻⡄⠀⠀⠓⠀⠈⣹⠟⠲⠦⣼⣁⡾⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⣶⣶⠶⠛⠁⠀⣀⣼⣄⣠⣄⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⣿⠆⠀⠀⢀⡾⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⠉⠛⠉⠈⠙⢷⣶⣶⣤⣴⣟⠉⠙⠛⠓⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠄⠶⢦⣤⣄⣀⠀⠀⠙⠿⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠉⠙⠻⠶⣤⡀⠀⠸⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠶⠛⠂⠀⠀⣀⠀⠀⠈⠙⢦⠀⣤⣿⣧⡀⠀⣀⡠⣄⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠴⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢶⣶⡉⣿⠟⢋⣡⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠗⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠈⢻⣽⡏⠀⡈⢻⡿⠳⠶⢦⣤⣤⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣿⠛⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠛⣅⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⣼⠂⠀⠀⠀⠀⢿⣿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣗⠀⠈⠙⠷⣦⡀⠀⠀⢀⣴⣿⠋⠀⠚⠁⠀⠀⠀⠀⠀⠈⢿⡉⠉⠛⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠛⣷⠀⠈⠙⠆⣴⡟⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⠳⢶⡶⣦⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⣰⠿⡅⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⣼⠃⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢿⣀⡞⠁⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⠤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠂⠀⠀⠂⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⢀⣀⣀⣐⣒⣒⣂⣀⣀⣠⣠⣤⣤⣤⣀⡄⡀⢠⣤⠤⠤⠤⠤⠐⠒⠉
⠀⠀⠀⠀⠠⠔⢶⠀⠀⠀⠈⠙⢲⣤⢀⣀⣀⣤⣤⠶⠛⠉⠉⠁⠀⣀⣴⡀⠀⠀⠀⠀⠐⠉⠈⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠶⢍⡉⠁⠀⠉⠉⠀⠀⢀⣀⣤⣤⣖⣋⣁⡀⡁⠂⢐⠀⣋⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡎⢭⠀⠀⠒⠬⠍⠉⠓⠒⠒⠊⢉⡀⠤⠛⠉⠉⠩⠉⠉⠻⠄⠀⡠⠂⠀⠹⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⢀⣠⣴⠶⡋⠉⠉⠉⢀⠀⢀⠀⠀⠀⢀⣀⣀⠰⠀⢠⠀⠀⢀⡀⠄⠁⢀⣀⣀
⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⠴⢋⠉⠙⠂⠈⠛⠛⠒⠀⠀⠘⠁⠤⠄⠈⠀⠀⠂⠀⠐⠶⠚⠉⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠔⠛⠇⠀⠀⢠⠶⠶⣿⡆⠀⠀⠀⢀⠴⠖⠶⠄⠀⢀⠞⠳⠄⠀⠟⡟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢾⠀⠀⠀⠐⠤⠐⠁⠀⠀⠈⠃⠐⠂⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⢀⣀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣤⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢿⣾⣿⣿⣿⣿⣿⠏⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⢿⣿⣿⣿⣿⣯⢰⣿⡿⢡⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⡻⣟⡛⠛⣷⣝⣿⡟⠅⠀⢿⢹⢰⡟⠁⢀⣼⢳⡾⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠻⠟⠻⣿⣜⣷⣎⠀⠈⠈⡿⠁⠀⣾⠟⠋⣴⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣧⣌⠻⣟⢿⡀⢄⠀⠁⠀⠀⠋⠀⢠⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠿⣿⣿⡻⡛⣦⠘⢾⣃⠀⡴⠉⠀⠀⠀⢀⣿⣿⣿⡿⢛⡿⢻⣿⣿⣭⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢉⣹⡿⢷⣾⣩⠻⠶⣍⣧⡀⠹⡄⠀⠐⠀⠀⠀⠀⠈⠛⣣⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣶⣍⡙⢿⣾⣆⠘⢷⠀⠘⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣬⡿⢷⣮⣙⢿⡆⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⣠⣿⡿⠿⠟⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣋⣉⠺⡉⠃⠹⣆⠀⠀⢀⠀⣀⠀⠉⠀⣉⣤⣆⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⡛⠻⣿⢐⣦⣙⡇⠀⠀⠀⢈⣤⠂⡼⠉⠛⢛⣁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡅⠐⠿⠿⣖⣊⣻⠷⠌⢭⡛⢷⣶⠷⠞⠁⠀⠠⣠⡶⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠒⢾⡷⢏⣙⠲⣇⠀⢙⡾⠧⠤⢀⣾⡷⠃⢴⣉⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡉⠀⣈⣿⡷⠠⣭⡿⠶⠶⢀⡼⠟⢠⣼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢏⣉⠩⣝⣦⣤⡯⠓⣣⠾⠦⢴⡟⣲⢏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠇⠐⢠⠶⡦⣾⣋⣉⣁⣄⣈⣃⣹⣦⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢿⠿⠋⠁⠐⠃⠀⠰⣿⠓⣼⣿⣿⣿⣏⡘⢿⣧⠀⠙⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⢀⠄⠐⠆⣀⠠⠛⡿⠁⠈⠹⣦⠉⠉⠛⣇⠀⠀⢃⠀⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⢻⡏⠀⠀⠀⠀⠁⠀⡃⠐⠢⣧⣤⡔⠂⠀⠠⣤⣰⠁⠀⠰⡾⠁⣰⣽⣷⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣲⣄⡜⠓⢶⡃⠀⠀⣏⣀⢀⡸⠃⠈⢣⣤⣤⡤⠀⡈⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠢⣴⠇⢬⣽⡋⠈⠉⣿⣂⣀⣼⠋⠀⢱⠖⠁⠀⠛⢼⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣭⠓⠐⣧⠀⣀⣹⣋⢀⣚⡟⠉⠉⢻⣄⣀⣼⠖⡇⠀⢖⠤⡀⠀⠀⠀⠀⠀⠈⠉⠚⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡀⢲⣿⣤⣵⣎⣁⠉⢹⣗⠚⣀⣿⢁⡍⣿⠊⢳⠶⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢛⣿⣿⣿⣿⣿⣿⣏⡉⠙⣿⣉⣤⣿⣂⣿⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣽⣿⣿⣿⣿⣿⣿⣹⣿⣿⣄⣨⣿⡧⢀⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⣉⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣠⣴⣾⢟⣻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⣰⣾⣤⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⣼⣿⡟⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠋⢙⣿⣿⣿⣿⡿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⠋
⠀⠀⠀⢿⣿⣿⣿⣿⣯⠀⠀⠈⠙⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⢁⡼⠃
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣤⣀⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣉⣁⣀⡀⢺⣇
⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⡿⠿⠷⢄⠀⠀⠀⠀⠀⢀⣶⣾⣿⣉⣙⠲⣇⣀⠉⠉⠛⣿⣳⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⢀⣾⣟⣉⡡⣤⢬⣹⠟⠛⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⣿⣿⣟⣻⠏⠀⠀⠠⠀⣱⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⣿⣧⣼⢿⣶⠖⢛⣾⣾⢁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣿⣿⣿⣿⡿⣿⣋⣿⡿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⢰⣦⠀⠀⢀⡀⠀⠀⢠⣤⡀⠀⠀⣀⠀⠀⣶⠶⠆⠀⢰⣶⣶⣦⡀
⠀⠀⠀⢾⣇⠀⠹⠃⠀⠀⠀⠀⣾⡿⣧⣰⣿⣿⠀⠀⢸⡿⣷⣀⣾⣿⡄⠀⣿⡦⠀⠀⢸⣿⣿⡿⠁
⠀⠀⠀⠈⣉⠻⣧⠀⢠⣶⣶⠀⣿⠃⠹⠏⠀⣿⡇⠀⢸⡇⠘⠟⠁⢹⣇⠀⣿⡀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠛⠛⠃⠀⠈⠻⠃⠀⠉⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠈⠛⠀⠉⠉⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣄⠀⢀⣤⣀⠀⢀⣀⣠⡀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⢸⡏⠀⣿⠀⢸⣿⡟⠀⢸⣏⡉⠀⣿⣁⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣼⠃⠀⣿⠀⢸⣿⣿⡄⢸⡏⠁⠀⢈⡙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠐⠿⠀⠸⠿⠟⠁⠸⠷⠶⠀⠈⠛⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢰⠿⢒⠐⠒⣒⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⡓⠁
⠀⠀⢀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⢽⡬⡇⠀⠄⢳⡄⠀⠀⠀⠀⠀⡔⠱⠀⠀⠀⡐⣄
⠀⠀⠄⠀⠘⠀⢠⠀⢠⠖⠀⡀⠀⠀⣀⠀⠀⠀⢰⠁⠼⡯⣼⣿⣶⡒⢉⡐⢨⣷⠀⠀⠀⠀⡌⠀⠀⠒⠀⠁⠈⢢⢢
⠀⠀⠀⢀⠁⠀⣘⡴⣁⢀⡀⠡⠀⠈⠁⠀⠀⠀⢻⠘⠎⡼⢁⠿⡆⢐⠢⢀⡞⡘⠀⠀⠀⢠⠀⡆⠀⠀⠀⣰⠀⠈⢀
⠀⠀⠀⠀⠀⠁⠎⢃⠀⠀⡄⠀⠈⠀⠀⠀⠀⠀⠘⡹⣄⡐⠁⠀⠃⣠⡶⠋⡠⠁⠀⠀⠀⠈⠂⠄⠀⡄⠀⡏⠀⡀
⠀⠀⠀⠀⢀⠂⠐⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠍⢉⣉⣋⠠⠜⠁⠀⠀⠀⠀⠀⠀⠱⣷⣀⠷⢰⠃⣟⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠁⠀⠀⡀
⠀⠀⠀⢠⡆⠂⢔⢿⢶⣶⡂⠀⡡⠌⣨⠽⠛⠀⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⡀⠘⠖⢢⠐⣶⣲⣦⣠⣴⣦⣏⠳⡽⣻⢧⡀
⠀⠀⠀⣘⣠⢃⠀⠌⡌⡄⡠⠈⣠⡾⠁⠀⠀⢸⣿⣿⣿⡇⣿⣻⣏⣿⢹⣿⣿⣷⠀⠈⠄⢢⡲⡿⡿⣨⠓⠿⣄⠖⡵⢃⠂⣼
⠀⠀⢆⠈⣀⠀⠁⠄⠀⠘⡠⡨⠉⠀⠀⠀⠀⠘⣿⣿⣿⢹⣿⣿⣿⣏⣿⣿⣿⠏⠀⠀⠈⢦⡙⠢⠈⠷⠟⢂⠤⢊⠕⢁⠼⠁
⠀⠀⠈⠳⢤⣈⣁⡥⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠉⠒⢒⠒⠊⡁⣀⣁⠪⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⡁
⠀⠀⠀⠀⠀⣀⠤⠊⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢗⣋⣲⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠞⡛⠍⠩⡭⠙⠦⡀
⠀⠀⠀⡠⡂⠀⠐⠁⠀⠈⢆⠈⢣⡀⠀⠀⠀⠀⢀⢔⣭⣶⣿⣿⡿⣏⣶⡄⠳⡀⠀⠀⠀⠠⡾⡱⢆⠲⣄⢲⠆⣉⣐⣜⠆
⠀⠀⠐⢰⠁⢠⠰⠀⠄⡇⠀⠇⠀⠁⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣷⣽⣿⣿⠄⢱⠀⠀⠀⣿⢱⢯⢨⢷⣾⣿⠮⣔⡀⣀⡈
⠀⠀⢀⠸⡀⠸⢰⠀⠀⣽⠀⠀⠀⣠⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣿⣺⡿⢀⠆⠀⠀⠀⢿⠘⢂⡤⣮⠘⠋⣱⠈⢟⠂
⠀⠀⠀⠐⢅⡀⠊⠂⠀⠀⠐⠀⠰⠃⠀⠀⠀⠀⠣⡈⠻⢿⣿⣿⡿⠞⢋⠠⠊⠀⠀⠀⠀⠈⠳⣝⠤⣄⠩⠆⢉⡐⠦⢋
⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠛⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠐⠚⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠿⠿⢟⣛⣛⣭⣭⣭⣭⣝⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢗⡲⣶⣿⣿⣿⣿⠫⣵⡤⣶⠝⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣵⣿⣿⡿⠿⢿⣿⣮⡃⠫⠾⠇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣛⣫⢍⢠⣚⠿⢸⣿⣿⣿⣮⡻⢏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝⡋⠾⠇⢟⣣⣿⣿⣿⠿⠿⣿⣿⣿⣀⠀⣤⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢟⣼⣿⣿⣿⡤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⢰⣭⡝⠻⠿⣿⣿⣿⣿⠛⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣣⣿⣿⣌⢵⡞⣴⡹⣶⢎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣥⣶⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⢤⡴⠦⣤⡴⡿⠃⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠛⠁⠀⢀⢔⣾⣿⠽⠛⠀⠀⠀⠘⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠉⠉⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⡄⠰⣄⠀⠀⠉⢫⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⣀⣤⡖⠲⠶⢿⣿⣆⣀⡰⠁⠀⢹⠆⠀⠀⢸⠀⣨⡟⢆
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⣰⠋⠁⠀⢀⣠⡤⠤⠌⠈⠉⢁⣠⣤⣤⠀⠤⢀⠜⠈⠛⠿⡄⢱⡀
⠀⠀⠀⠀⠀⠀⠀⣞⡤⠒⠀⠀⢀⠊⠀⠀⠘⠋⠁⠒⠦⠤⠀⠀⠠⠼⠿⠿⠀⠀⠈⠳⣄⠀⡀⢷⠠⣷⡀
⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠸⣖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⡔⠢⣤⣈⠀⠀⠀⢻⡌⣇
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⡔⠋⠀⠙⢮⣤⣑⣤⣦⣠⠕⠁⠀⠘⠀⠀⡞⠀⢹⡄⠀⠁⠀⠀⠀⠀⣷⢹
⠀⠀⠀⠀⠀⢠⡇⡀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠙⠛⠛⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢧⠀⠤⠄⣀⣀⣠⡟⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠤⣀⣠⠞⠀⠀⣼⡻⠛⠛⠋⠉⠉⣀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⢀⣠⣴⡿⠛⠁⠀⠀⠀⠀⣸⣍⡏
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⣠⣼⡼
⠀⠀⠀⠀⠀⠀⢷⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⡽⠁
⠀⠀⠀⠀⠀⠀⠘⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⢴⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⡴⠋⠉⠉⠛⠛⠛⠶⠤⠤⠤⠤⣀⣀⣀⣀⣀⣀⠤⠤⠴⠐⠒⠉⠁⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⣀⣀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢜⣶⣠⠾⣿⠃⣠⣤⣼⣾⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢤⣤⣬⣭⣭⠿⠛⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠛⠓⠚⠛⠋⠁⠀⣿⡆⢳⡀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠂⠑⢄⠀⠀⠀⠀⠈⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣦⡀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣔⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⡀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⢀⣨⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠈⠉⢀⡼⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠶⠶⠶⠾⠟⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⡞⠁⣠⢜⡁⢠⡀⢀⠀⢀⠆⠀⢀⠀⠀⢀⢀⠀⡀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⠞⠁⠀⢠⠏⠀⢠⢃⢈⣆⡎⣰⢣⠟⡼⣡⢏⡟⣸⢡⡎⡄⣰⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠁⠀⠀⠁⠁⠀⠀⠈⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⢄⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣀⠄⠀⠀⠍⠄⠠⣝⠅⠀⠀⣦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠷⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠠⠀⢀⡐⡁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⡏⣼⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢂⣄⠀⠀⠀⠀⠀⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠆⠀⠀⠋⡋⠉⣠⣤⣴⣿⠃⠸⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⢿⣷⣾⣿⠿⠟⠃⠀⢸⢇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⡔⠁⠀⠢⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠋⠀⠀⢠⠄⠀⠐⡂⡘⠀⠘⠧⠤⠤⣀⣰⡀⢀⠄⣠⠀⠀⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠴⠃⠀⠀⣠⢆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡀⠀⠜⠁⠀⠐⠀⠀⠀⠀⠰⠀⠁⣰⠇⠘⢰⠁⠀⠀⠀⠀⠙⠂⠠⢶⣎⡁⠀⣤⡶⠿⠿⠉
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⣠⡏⡄⠀⠀⠀⢰⣿⣦⣡⣾⢿⡇⠀⣸⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿⠀⠀⠀⠤⠀⠀⠀⠀⢠⠀⠰⠃⠉⣷⠁⠙⠁⠀⠀⠀⣿⢏⣿⣿⡿⠀⠙⠔⢁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⠀⠀⠸⢇⠀⠈⣿⣿⣿⣿⣧⢀⡄
⠀⠀⠀⠀⠀⢀⠔⠟⠁⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⠁⠀⠹⣿⡷⠿⠿⠞
⠀⠑⠄⣀⣤⣶⣊⡤⠖⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⡜⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠞⢉⣠⣴⣶⣦⣶⣶⢶⣶⣨⣭⣝⡒⠤⣄⡀
⠀⠀⠀⠀⠀⣴⠃⣴⣷⢿⣿⣯⣿⣿⣾⣻⣿⣿⣿⣟⣷⣞⢦⣭⡒⢤⡀
⠀⠀⠀⠀⢰⣿⡀⢿⣿⣿⣿⣿⣯⣿⣾⣿⡃⠉⢘⣻⡟⣻⣿⣿⣷⡶⡌⢢⡀
⠀⠀⠀⠀⣿⣿⣷⡄⠰⣾⣿⣷⣿⢿⣿⣿⣿⣶⣻⣿⣿⠾⢷⢾⣽⣟⣳⠆⢱
⠀⠀⠀⠀⣿⣿⣿⣿⣶⣌⠻⠿⠿⣫⣿⣿⣿⣟⡛⢃⢶⣷⡄⠂⠀⠝⠻⣗⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣷⣆⣰⣾⣿⣿⠁⠀⠀⠀⠈⢻⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⠀⠀⠀⠁⣠⣶⣾⣿⣿⣛⣉⡍⠛⢷⣦⣤
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣣⡄⠰⠀⢀⣾⣿⣿⣿⣿⣿⣿⣮⠀⢸⣶⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⢟⣔⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣝⠿⣿⣿⣿⣿⡟⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠦⠀⢴⣶⠆⠆⠹⣿⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡗⠀⠀⠀⠀⠆⡀⠸⠅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣶⣄⣤⡤⣾⢆⡄⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⡟⠙⠂⠈⠙⠻⣿⣿⣿⠇⡠⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⢻⣷⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⠁⢁⠐⠠⠀⠀⡉⠉⠻⣿⣿⣤⣠⣄⣤⡈⢻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠄⠄⠀⢀⣴⣦⠙⢿⣿⣿⣟⣤⣉⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣶⣿⣿⣧⣸⣗⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠉⠉⠉⢀⣀⣨⡭⠽⡶⣾⡇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠴⠚⠉⠁⠀⣠⠞⠁⡿⡷⠶⠦⣄⣠⣭⣍⣉⡉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⢰⠇⣇⠀⢰⡁⠀⠀⠀⠈⠉⠳⢦⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠶⠖⠚⠋⠁⠀⠀⠀⢀⡟⠀⢿⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⣞⡀⠀⣘⣠⣀⣄⣌⣙⠲⠦⣤⣀⡀⠀⠀⠳⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠉⠙⢦⣍⠓⢤⡈⠉⠓⠦⣄⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠙⢦⡀⠀⠈⠙⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⢧⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠳⢄⠀⠀⠀⢀⣠⠴⠋⠀⢀⡜⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⡓⠛⠛⠉⠁⢀⣠⠴⠋⠀⠀⠈⠳⣌⠳⠦⣄⣀⡀⠀⢠⠏⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣬⣭⡴⠿⠚⠉

⠀⠀⠀⠀⠀⢀⣤⣔⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⡀⡀⠛⠀⠠⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠒⠦
⠀⠀⠀⢠⡶⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⠀⠀⠀⠀⠀⠀⣠⠞⠂⠀⠐⠋⠀⠀⠀⠘⠋⠉⠀⡀⢀⠄⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡜⠁⠀⢀⣤⢀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⡀⠀⠀⢀⠀⠀⠘⡻⠋⠀⠀⡔⠁⠀⣾⠖⠀⠀⠀⠀⣀⡀⠉⠁
⠀⠀⢸⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣀⠴⠂⠀⠀⠀⠀⡛⠁⠀⣤⣄⣀⠤⠚⠁⠀⠀⢰⡗⠃⠀⠀⠀⠀⠀⠀⠀⠹⠏
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⡀⣠⣆⢒⣈⣀⣤⡤⠟⠉⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⡅⠀⠀⠀⠀⠀⠘⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢃⠀⠀⠀⠀⠚⠛⠃⠀⠀⠰⡿
⠀⠀⠘⠻⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠂⠀⠉⠁⠀⠀⠀⠀⠞⠀⠘⠟⠀⠀⠀⣠⣤⣄⠀⠀⣠⣤⣤⣤⣀⡀⢀⣾⢃⣼⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠘⠲⣿⠆⠀⠀⠈⡁⠀⠐⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⣠⣿⠃⠘⠟⠛⠙⠛⠛⠛⣿⡟⣛⡁⣘⠁⣤⢤⢿⣼⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢸⣿⠇⢀⣶⠲⡄⣼⡏⢹⢠⣿⣏⣼⢣⡿⢸⡧⢊⣔⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠛⢂⣾⣯⣠⣧⣿⠣⡼⢻⡟⢿⣄⠘⢓⣉⣙⡉⢸⣇⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⣠⠞⠻⣧⠟⠁⠙⠚⢁⣀⣥⣼⠿⢿⣍⣁⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠈⠿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠞⠃⠀⠈⠉⠁⢀⡀
⠀⠀⠀⠀⣴⠆⠀⠀⣤⠀⠀⠀⠈⠙⠁⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠒⠓⠚⠃⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⡾⠖⠋⠉⠁⠙⠒⠀⠀⠀⠰⠒
⠀⠀⠀⢠⠀⠘⠷⠀⠀⠀⠀⠀⣴⡶⠂⠀⠀⠉⠉⠀⠄⠀⠀⠀⡠⠂⠛⠁⠀⠐⠟⢃⡀⠀⢀⣤⡀⢀⣀⠀⠀⠀⠀⠘⢿⠁⣠⣤⠀⣀⣘⣀⣀⠠⣤⠀⠀⢤
⠀⠀⠀⣿⣧⠀⠀⣠⣄⢠⣴⣦⠀⠀⢠⣶⣤⠀⠔⢠⠆⠀⠀⣼⠃⠀⢛⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡄⢦⡤⠒⠉⠉⣉⠉⠉⠉⠓⢄⢀⡀⠁
⠀⠀⢰⣿⣿⣿⣧⣤⣤⣄⡀⢤⣄⣀⣀⣀⣀⣀⣴⡏⠀⠀⢀⡴⠀⠀⠙⠁⠀⠀⠀⠤⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⣀⠀⠀⠋⠀⠀⢀⡀⠀⠈⠡
⠀⠀⠘⢿⣽⣋⡉⣉⡉⠹⠿⠟⠛⠉⠉⢉⣽⡷⣀⣶⠀⠀⠈⠳⠀⠀⠦⢀⠐⠀⠈⠀⠁⠚⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⣏⠀⠀⠋⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃
⠀⠀⠀⢰⣿⣿⣿⣭⢤⣦⣦⣤⣤⣴⡷⠾⠿⠛⠙⠋⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠉⠀⣀⠀⠀⠤⠀⠀⣀⡀⠀⠀⢸⡇⣴⠄⠀⠀⠀⠀⢴⣆⠀⠀⠀⡀
⠀⠀⠀⢨⣥⣌⣉⠀⠀⣀⣀⣀⢠⠾⠆⠀⣀⣠⣤⣴⡛⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠉⠀⠀⠈⣿⠀⠀⣤⡀⠀⠀⠀⠀⠀⢠⡄⠛
⠀⠀⠀⢉⠾⠋⠉⢭⡉⠉⠋⢹⠟⢻⡏⠉⠉⠉⢈⣉⣤⠀⠀⠀⠀⠀⣀⣀⠀⠰⠖⠒⠒⠀⠉⠈⠁⠀⢠⡀⠀⠀⠀⠀⠘⣇⠀⠈⠁⠀⠶⠂
⠀⠀⢠⣿⡟⢛⡶⠶⣤⣤⣤⣤⡶⠶⠶⠞⠛⢋⡉⠡⢄⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢴⣦⡄⠀⠀⠀⠙⠁⢠⡆⠀⠀⠀⠈⠳⣄⣀⡀⠀⠀⢶⠆⣀⠤⠔⠁
⠀⠀⠀⠨⣷⣿⣿⣄⣀⠺⠷⠀⠀⠀⣀⡀⠀⣛⣣⠴⠊⠀⠀⠀⠀⠀⠀⠈⠁⣀⡀⠀⠀⠉⠁⠀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠃⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⢀⣴⠞⠛⢳⠀⠀⠀⠀⠀⣀⠀⣤⡄⢀⣄⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⣿⠃⠀⡠⠋⣠⡄⢰⣿⠀⣿⡾⢸⣿⢫⣿⠀⣾⣇⠎⣿⣧⢶⣦⠀⣀⡀⠐⣧⡇
⠀⠀⠀⠀⠀⢿⣦⣉⣀⠀⢿⣇⣸⣿⢀⢿⡇⠘⠃⣾⡏⢠⠿⠏⠸⠿⢡⣿⠃⣼⡿⠝⠀⡸⣳⣶
⠀⠀⠀⠀⠀⠀⠉⠙⠛⢷⣆⠉⠀⠙⠋⠀⢀⣀⡀⠙⠛⣡⣴⠶⡄⠀⣿⣃⡸⣿⣄⡠⠈⣾⠟⢡⡀
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡿⠀⠀⠀⠀⣰⠃⠠⣸⠆⢰⡿⠁⡰⠃⠀⠈⠁⠀⠀⠉⠀⢸⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠑⠶⠒⠋⣰⠋⠻⣷⡀⡇⠒⢚⡋⠀⣿⡗⣪⢤⣄⠀⠀⣤⣦⠀⣴⠟⢦⠙⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢹⣷⣧⠀⣿⡇⠀⣿⡷⠥⣼⣿⠤⣾⡟⠊⢀⢿⣆⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢿⣿⠀⢿⣧⠜⠘⢥⡴⠟⠁⠀⠻⠧⢖⡁⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⡴⠶⠶⠒⠒⠒⠒⠒⠒⠒⠚⠹⣆⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⣄⠀⡀⠀⣦⠀⣿⢹⡿⢹⡇⣼⠏⣽⠎⣿⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠻⠀⣿⡀⢿⡄⣿⢸⡇⠸⡧⠟⢰⠏⢸⣇⣾⢏⣠⡾⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣦⣽⠧⠜⠛⠁⠀⠀⠀⠀⠀⠀⠀⣈⣁⠙⠦⢤⡶⠟⠉⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⢀⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⣄⠄⠀⠀⠀⢀⠀⠀⣠⣴⣶⣶⣤⣘⣿⣷⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⡀⠀⢸⢀⡾⢿⠛⠋⢉⣩⣿⣿⣿⣥⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢄⠀⢱⡀⢸⡋⢠⠇⢀⣶⣿⡟⠁⢸⠹⣧⡙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠈⠣⠀⢃⣈⣁⠚⠠⠞⣿⣯⠆⠀⣿⠀⣿⡇⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣈⠓⣠⠞⠋⠉⠉⠙⠲⡄⢋⣻⠤⣼⡟⢸⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⢰⠃⠀⠀⠀⠀⠀⠀⠈⠀⢤⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠘⠀⠀⠀⢀⣀⣀⣀⣀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⣤⡀⢀⢾⡟⠛⢛⡉⠉⠙⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢠⡿⠀⢀⡾⠁⠆⣼⠇⠀⠀⠀⣀⡀⠈⣿⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⣿⠁⢠⡾⢁⡿⢠⣿⠋⢹⣦⡿⢁⡿⢠⡝⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⣴⠏⠀⢸⣇⠼⣇⢀⡿⠙⢯⣉⡤⠛⠧⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⢛⣛⡛⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠈⠿⣿⡶⠶⣤⣤⣤⣤⣤⣤⣤⡴⠶⠛⠋⠁⠐⢒⣤⣤⣾⠿⠛⠛⠛⠲⠿⣶⣄⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⣀⠀⠀⠀⠠⣀⢀⣈⣭⠿⢺⠏⠁⣰⠋⠀⢀⣠⡴⠚⠛⠚⠿⢷⣆⣰⠟⠂⠀⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣌⡉⠙⠛⠛⢋⠝⠋⠀⠰⠋⠀⠐⢁⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣀⣤⣤⣴⣾⣛⣥⣤⣤⣶⣶⣶⣶⣶⣤⣤⡿⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⣭⣶⣿⣿⠿⠿⠛⠛⠛⠋⠙⠛⠛⠛⣿⠃⢠⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠾⠿⠶⣿⣄⠉⠛⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⣤⣄⣀⣀⡀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⢀⣀⣀⣀⣠⣒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣭⣭⣭⡦
⠀⠀⠀⠀⢰⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣶⣖⢒⡇
⠀⠀⠀⠀⢸⠀⣴⡜⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠿⠯⢼
⠀⠀⠀⠀⠘⠒⠒⠂⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂


⠀⠀⠀⠀⠀⣀⣀⣀⣖⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⢠
⠀⠀⠀⠀⢰⠁⠀⠨⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠸⠘⠄
⠀⠀⠀⠀⢇⠀⠀⠇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡹⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⢹⠓⡆
⠀⠀⠀⠀⠀⠁⠒⡖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠂


⠀⠀⠀⠀⠀⣀⢠⡄⣀
⠀⠀⠀⠀⣰⣁⣰⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒⠄
⠀⠀⠀⠀⢸⠀⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⢫⠱⠋⠉⠉⠉⠉⠙⡗⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠘⡀⡄⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⣇⡇⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠞

⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⣠⣾⣿⠛⠉⠀⢸⡇⠀⠉⢛⣿⣷⣄
⢰⣿⡟⠈⠻⣆⠀⢸⡇⢀⣴⠟⠁⢻⣿⡆
⣿⣿⣀⣀⣀⣈⣻⣾⣷⣟⣁⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠉⠉⠉⢉⣽⢿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡽
⠸⣿⣧⠀⣴⠟⠁⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠙⢿⣿⣥⣀⠀⢸⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⣧
⠀⠀⠀⠀⠀⠀⢠⡞⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⢦⡀
⠀⠀⠀⠀⠀⢠⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⢳⡀⠀⠀⠀⠀⠀⣴⣿⣿⡦
⠀⠀⠀⠀⢰⠃⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢳⡀⠀⠀⠀⣼⣿⣿⡟
⠀⠀⠀⠀⡏⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣧⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠸⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡼⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠹⡄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣰⠃⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠙⣦⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⡾⢃⣤⠶⠞⠛⠛⢻⣿⡛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠙⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡴⠋⣴⠋⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠉⢀⡞⠁⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠙⠓⠒⠒⠒⠒⠒⠒⠒⠛⢁⡴⠛⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⣰⣦⠀⣰⠋⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢹⣿⣼⠃⠀⠀⠀⢀⣤⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢻⣿⣀⡠⠤⠖⠋⢀⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢀⡾⠋⠻⠆⠀⠀⠀⢿⡀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡤⠶⠛⠀⢀⡀⠀⢰⡶⠦⣄⡹⡄⠀⣤⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠓⡶⠒⠒⠋⣷⠀⡼⠀⠀⠀⠉⠛⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⠀⠀⣻⡼⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢧⠀⠁⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⢦⡀⠆⠀⠀⠂⠀⠀⠄⠀⠀⢠⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠀⠀⠀⠄⠀⠒⠀⢀⢀⡿⣦⠀⠀⠀⠀⠀⢀⡞⠻⣄⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢤⣤⣄⣀⣀⢀⣀⠀⠀⠀⠀⠀⣀⣀⣈⣹⣦⣄⡀⢠⠀⠀⠀⣨⠞⠀⠈⠳⢤⣤⣤⠶⠋⠀⠀⠘⠳⢤⣤⣤⠶⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣭⣿⣶⣶⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣠⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⣷⡀⠰⠟⠛⠉⢹⣿⡆⠀⣿⡇⢀⡀⢀⣀⠀⣠⣤⣄⠀⢀⣀⡀⢠⡶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠿⠁⣾⠀⣰⡆⢸⡿⣿⣸⣿⣇⢸⣧⡿⢻⣿⠋⢰⡟⣰⣟⣽⠗⢸⣇⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⣿⣀⣿⠁⢸⡧⠸⡿⠸⣿⠸⣿⠇⣿⠏⢀⣿⠁⣿⣉⣡⡶⢸⣿⠙⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠻⣦⠈⠛⢁⣀⣼⠇⠀⠀⠀⠿⠀⠀⣴⣦⡀⢸⡏⠀⠈⠛⠉⠀⠈⠉⠀⢿⣄⠙⣿
⠀⠀⠀⠀⠀⠀⢠⣿⠙⢻⡆⢹⣇⠀⣈⡉⠁⢠⣤⠀⠀⠰⠄⢸⡏⣼⠇⠘⠛⠀⢀⣶⠿⣶⠀⣿⣦⡀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⣸⡏⢀⣿⣧⠀⢸⡿⣧⣤⣶⠀⢸⣿⢏⣤⣦⣤⣤⣾⣧⡶⠟⢠⣿⠈⣻⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⣠⡾⠃⢻⡆⣿⠇⠀⠀⣿⠀⣾⣿⡿⢡⡾⢻⡇⠹⣧⡀⢀⣾⠃⣼⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠈⣿⣿⠀⠀⠀⠙⠿⠃⠙⠃⠸⣧⡿⠁⠀⠉⠛⠛⠁⠀⠘⠷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢦⣌⣿⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⢿⣯⡌⠈⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠋⠉⢠⣾⠟⢸⣿⠀⠈⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠉⡉⠙⠢⡐⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⢘⣿⣀⣀⠀⢀⣤⣤⠀⣀⣤⣀⠀⢀⣤⣄⢰⣿⢀⡀⠘⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢸⣿⠟⢻⡇⣾⣯⡿⠃⣋⣭⣿⣆⣿⠋⠿⢸⣿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠘⣿⣷⣿⠃⠻⣷⣾⠟⣿⣷⣿⡏⢿⣤⡶⢸⡿⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⣠⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢸⣷⠀⣴⡷⣚⠀⣿⡆⣀⠀⠀⣠⣄⠀⢀⣤⡔⠫⠿⠂
⠀⠀⠀⠀⠀⠀⠀⣼⢻⡄⠀⠘⣿⣷⣿⠃⣿⡇⣿⡿⢿⣧⣾⣯⣿⠇⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠙⣦⡑⡀⠀⢻⣿⡏⠀⣿⠇⣿⣷⣾⡏⢻⣿⣵⣶⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣄⠀⠉⡀⠀⠉⠀⠉⠈⠉⠀⠀⠈⠁⠀⠉⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣧⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣄⢠⣾⣶⡄⢀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠶⠾⣟⡛⣿⣿⣷⣿⣿⣿⣾⣿⣿⣷⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠡⠀⠠⢴⡾⢶⣿⣿⣿⠛⠡⠤⢤⣙⢿⣿⣿⣿⡆⣿⣿⠑⢦
⠀⠀⠀⠀⠀⠀⠠⠦⡌⡀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠒⠉⢀⡚⠒⠛⠳⢝⢿⣿⠰⠻⣡⡀⣘⡇
⠀⠀⠀⠀⠀⣰⠀⠘⣇⠹⣿⢿⢷⣶⣄⡀⢀⠀⠀⣰⡇⠰⠂⠈⠙⢦⣄⣀⣐⣄⣄⠀⢣⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⢷⣤⣌⣳⣶⣤⠦⣉⠻⣿⣮⡟⠛⠟⠀⠀⠀⠀⢶⣄⣬⠉⠉⣿⣿⡄⠞⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠢⠌⠳⣦⣴⠾⢃⡀⠀⠀⠀⠀⠛⠯⠀⡀⢀⣿⣿⣧⠈⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⡇⣠⣀⠀⠀⠀⠀⠁⠀⢤⡶⠟⠛⠶⠀⠀⠀⠤⠶⠾⠋⡼⢻⣿⣿⠀⣿⣿⡀⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⡞⠁⣼⢿⡏⢠⡘⠿⡿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⢳⡄⠀⠀⠀⠀⢠⠞⣷⣦⡀⠀⠀⠀⠀⠀⢡⡌⢻⣁⣾⠧⣄⣙⠳⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠿⣧⠀⠀⠀⠀⠀⢤⠿⠛⠁⠀⠀⠀⠀⠀⢲⡄⢸⣿⠏⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⡁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠙⠂⠉⠀⠁⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠒⢫⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⠠⣴⠶⠶⠦⠤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣦⣀⣠⣾⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⠛⠛⠁⠀⠀⠀⣴⣊⠉⠁⠀⠀⠀⣀⡨⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣽⠀⠉⠉⠉⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠾⣅⢘⠀⠀⠀⠀⠀⢀⡀⣀⠜⠚⢻⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠈⢿⡅⣀⣙⠀⠏⢉⡽⢁⠄⣠⠞⠉⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢩⡆⢀⣒⠚⠇⢹⣿⡗⠀⠉⢚⣿⠋⣠⠔⣡⠾⡄⠀⢀⡴⠞⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣠⡟⠀⠀⠈⠙⣿⣾⣿⣿⣧⠰⢻⣷⡞⣡⠞⢁⣴⡷⠖⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⢠⡟⢰⡟⠀⠀⠀⠀⠀⢈⣿⣿⣋⠁⢀⠈⠹⣿⢧⠾⠋⣡⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣦⡟⠠⣾⣃⠀⠀⠀⠀⠀⠘⡿⠿⠟⠃⠘⠳⠟⠛⠃⢰⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠏⠀⠀⣈⣛⡛⣦⠀⠀⠀⠐⣿⣿⣽⣧⣿⣴⣷⣿⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠈⣍⡉⠙⢧⠀⠀⠀⢻⣿⣄⣤⣤⣤⡶⠟
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⣄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣰⠟⠛⠿⢃⣠⠟
⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⣰⡟⠀⠀⠚⠋⠁
⠀⠀⢀⣀⣿⠃⠀⠀⣀⣤⡾⠋
⠀⠀⠛⣩⣿⣄⠀⠀⠈⣿
⠀⠀⠈⢧⠼⢿⣷⣤⣀⠁⣼⢿
⠀⠀⠀⠀⢶⣼⡟⢳⡇⢲⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠺⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⢀⣈⣀⣀⠀⠀⠀⠀⠙⠃⣬⡠⡘⡄⢃⡴⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⣛⣿⣿⣆⡀⣟⠲⢯⣍⠙⠶⣄⠀⠂⠀⠈⠃⠰⠠⠟⣡⡶⢡⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡾⠁⢠⣾⠟⠉⣰⡟⠀⢽⣿⡆⠻⣷⣄⠈⣳⡀⠈⠀⠀⣄⢀⣈⠡⢆⢐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣠⣾⡿⠂⢸⣿⠇⠀⣸⣿⡷⠀⠈⣿⣦⠈⢉⠢⠈⢀⠀⢈⠄⡀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣨⠃⢀⣿⣿⠁⢀⣾⣿⠀⠀⣉⣿⣿⡄⠀⠈⣿⡗⢫⡄⠛⠀⠂⣈⣬⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⠀⣸⣿⣇⠀⠸⣿⣿⠀⠀⢿⣿⣿⡿⠀⢀⣿⡷⠒⣐⡠⠁⠐⢉⣚⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡰⠒⠉⠁⠀⠀⠀⠀⠀⠀⠉⠒⠲⢿⣿⠆⠀⢹⢸⣿⣷⠀⠈⠟⢀⠀⠁⠀⠀⢠⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢾⣿⣿⠀⢘⢀⢧⠂⠀⠀⠀⠀⠀⠂⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⢀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⡀⡀⢸⡂⠀⢘⣿⡷⠀⠉⠀⠀⠃⠀⠄⠀⠀⠄⢀⠴⠂⠀⠃⠂⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⡋⠈⠉⢀⡀⢀⡌⠄⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⢠⠄⢀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠋⠉⠃⠄⣀⡀⠐⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢀⡀⠀⠀⠀⠀⠀⠀⠄⠓⠐⠲
⠀⠀⠀⠐⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠘⡄⠐⠂⠀⠀⠀⣀⠀⣴⠀⠀⠀⠀⠀⠀⠀⡧⠄⠄⢀⠀⠀⠀⣠⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠒⠒⠀⠒⠀⠄⠣⣄⣀⠀⢀⣠⠂⠀⠀⠀⠀⠀⢀⠇⢄⣀⠀⢀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠊⠀⠀⠉⠀⢈⠖⠉⠀⠐⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠐⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠⠓⠦⠤⠤⠞⠁⠄⠀⢀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣷⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⣀⠀⢇⢸
⠀⠀⠀⠀⠀⠀⠀⢠⣁⠀⠀⠈⢿⣆⠀⣀⠴⣿⠀⠀⣴⡀⠀⣴⣤⠏⢸⣧⠔⢻⡄⢀⣷⣰⠃⣿⣠⠞⣿⡆⠀⣼⠃⡼⠀⠀⡽⠃⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡠⠻⣿⡄⠀⣿⡆⣰⣿⡇⠀⣸⡏⠀⢸⡟⠀⣾⡇⢸⣿⠃⠀⣿⠏⠀⣿⡇⢰⣿⠁⠀⢀⡼⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢹⣿⠀⠙⠛⠁⠹⣧⡴⠛⠃⠀⠘⠃⠀⠹⣧⠜⠋⠀⠀⠀⠀⠀⠻⣧⠞⠿⣦⡴⠞⠀⠀⠘⢿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⢠⡏⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⣀⠀⠀⣼⡇⠜⠁⠀⠀⢠⡾⢹⠆⠀⢿⣧⡟⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢹⣷⠀⣸⠋⢩⣿⠀⠀⣿⡧⣆⠐⣆⡀⣿⡟⠁⠀⠀⢈⠟⢿⣦⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡿⠀⢸⣿⠀⢀⣿⡇⠀⢸⡏⠀⢿⡇⠀⢀⡴⠋⣠⠊⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃⠀⠀⠛⠒⠋⠘⠿⠶⠋⠀⠀⠈⠙⠚⠉⠀⠘⢧⣤⣾⠟





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠣⠈⠁⠁⠀⠀⠘⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠄⣀⠤⠶⠒⠀⠤⡀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠘⠁⠀⠀⠀⠀⠀⠢⢀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢶⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠈⠻⣿⣿⢦⡀⠀⠀⠀⠀⠀⠂⢠⠚⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠀⣿⠿⢿⠳⢄⠀⠀⣸⣿⣷⡄⠀⣠⠟⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠚⠁⣀⣠⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⢃⡄⣷⠚⢄⣀⣀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡀⠀⠔⠉⠀⢈⠀⠀⢲⣦⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠛⠔⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠃⠀⠀⢀⠂⠀⠉⠁⠙⠿⠷⣤⡄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠆⢀⡀⠀⠀⠀⠀⣬⡗⠠⠤⠤⠄⠒⠉⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢠⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢰⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⢀⣡⣄⢠⡤⠎⠁⠀⢣⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢈⠀⠀⠀⠀⢠⡂⠀⠁⠀⠀⠀⠀⠀⠀⠙⢦⣸⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠠⢚⠀⠀⠢⠄⠀⢠⣿⠁⡆⠘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⢩⡍⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱
⠀⠀⠀⠀⠀⠀⡐⠀⠸⠀⠀⠀⠀⠀⠈⠉⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠑⣄⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠀⠀⠀⡸⠀⠀⡄
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠉⠀⠈⠒⠂⣴⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣴⡾⠃⠀⠀⡇
⠀⠀⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠃⠀⢸⣿⠁⠀⠀⠀⢹
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⠁⠀⢀⡽⢰⠇⠀⠀⠀⠀⢸⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢸⡇
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⢈⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⡇
⠀⠀⣆⠀⠀⠀⠀⠠⠔⠊⣡⢀⡄⣸⠔⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⠀⠀⡇⡄
⠀⠀⠀⠙⠢⠤⠴⠶⣶⠾⠷⠛⠉⠀⠀⠀⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠁⢁⠀⠀⠀⠀⠀⢠⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⠀⠀⠀⠀⠈⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠀⠀⠀⠐⠋⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠑
⡿⢿⠿⠿⡿⣟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣻⣻⣿⣛⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⣤⣤⣤⣤⡶⠶⠒⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣠⠞⠋⠉⠁⣐⣒⡒⠾⠿⣟⡶⢦⠠⣤⡇
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣁⡄⠀⠚⢉⣩⣭⠭⠛⠒⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢠⡞⠁⠀⠀⣴⡋⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠘⣇
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢺⢗⣩⠄⠀⠁⠙⠲⢒⣯⣟⠇⠀⠀⣠⠞⠉⠙⠃⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⡞⢁⠄⠀⢀⣴⣾⣽⣫⠅⠀⠀⠀⠁⠀⠀⢶⠀⢻⡄
⠀⠀⠀⠀⣧⠀⠀⠀⣠⡶⢦⢶⠃⠀⠀⢈⡵⢫⡟⠁⠀⠀⠀⠀⠀⠳⠶⠾⠓⠀⠛⢦⡀⠀⣤⣄
⠀⠀⣠⠖⣻⢀⣠⢶⠏⠀⡏⠻⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃⠈⠛⢶⣛⣷⢶⣄⡀⠀⠀⢀⡀
⠀⢸⠇⢾⠁⡞⣿⠘⠀⣀⠀⠀⠀⠀⣄⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⠃⠀⠀⠀⠀⠉⠙⠻⣯⣷⣀⠔⡩⠃
⠀⠘⢧⡀⠈⠁⠀⠀⠀⠈⠛⠶⣤⣤⣬⣽⣟⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣤⡀
⠀⠀⠀⢻⠀⠀⠀⠀⣝⠶⠤⡤⠶⠋⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣤⣤⣤⠤⠤⠤⠤⠤⢀⣠⣀⣀⡴⢀⡟
⠀⠀⠀⠘⣇⠀⠀⠀⠈⠙⠛⠁⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠶⡎⠋⠛⣶⠶⢤⣄⣀⠀⢼⢁⡞
⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣤⠞⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢹⣦⠀⠀⢀⡴⠋⠉⠙⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣀⠙⠻⠛⠙⠳⣤⣤⣄⣰⡞⠒⠶⠦⢤⣤⣤⡶⠏⠀⠀⠀⠘⡇⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠰⠶⣤⣄⣀⠀⠙⠿⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⡀⠀⠀⠉⠛⠶⣄⠀⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡴⠛⠉⠀⠀⠐⢦⡀⠀⠈⠁⢐⣛⢿⣤⡴⠆⡶⠀⠀⠀⠀⣼⠄⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣨⡄⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠈⢿⣷⠇⠀⠶⡶⢤⣤⣤⣠⡷⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡟⠃⠀⠀⠀⠘⠃⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢠⣖⣒⡛⠡⣤⣀⠀⠀⠀⠀⢀⣠⠆⢀⠞⠀⠀⠀⠈⢿⣯⣤⣀⣀⣀⡀⠀⠀⠀⢀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡧⣤⣤⠙⠳⣄⢀⣴⠿⣧⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠙⢦⣤⣤⠘⢧⡀⠈⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣠⢿⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢰⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠸⠶⠃⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠁⢀⠂⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠄⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠤⠤⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⠈⡁⠞⢻⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣨⣄⣾⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠂⡂⢄⣐⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠓⠐⡀⠁⠄⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⡈⢃⡈⠤⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠤⠐⢂⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢀⡀⠠⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠤⠒⠀⠄
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠡⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠂⠀⠀⠊⠀⠀⠁⢀⠀⠀⠈⠆⠀⠂⠀⠀⠀⠁⢀⠂⠀⠀⠀⡔⠁⠀⠑⠄
⢀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢁⠀⠹⠐⠀⠀⠀⠀⠀⠀⠒⠈⢀⠁⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠢⣀⡠⠃⠀⠀⠁⠄⠈⠄⠈⢀⠀⠀⠸⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠑⠀⠑⢄⡀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⢀⠂⠐⡀⠀⠀⠈⠀⠈⠁⠀⢀⠀⠀⠀⠀⠃⠄⠀⣄⠡⡄⠀⠑⠤⠤⠐
⠀⡀⡀⠀⠀⠀⢌⠀⠀⠀⠀⠊⠀⠀⠀⠈⠁⠀⠈⠈⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠅⠀⠀⠀⠀⠈⠀⠠⠀⠐⠀⠁⠀⣀⠀⠠⡀
⠀⢸⡀⠈⠀⠀⠀⠈⠐⠠⡀⠀⠀⠒⠋⠑⠀⠀⢀⣤⣀⡀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡄⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⡌⢃⠀⠀⡀
⠀⠀⠣⡀⠀⠀⠀⠀⠀⢠⠌⠀⠀⠂⠀⠐⠀⠀⢹⣿⣿⣿⣷⣿⡄⠈⠢⠄⠀⠀⠀⠇⠀⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⣀⡩⠞⠁
⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⡀⠀⠀⠈⠐⠀⠐
⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⢢⡢⠀⢀⡀⠀⠀⡠⠀⠀⣀⣀⠠⠐⠁⠀⠀⠠⠀⠠⠄⠂⡀⠀⠀⡀⠤⠀⠀⠀⡠⠂⠁⠈⠉⠙⢂⠐⠒
⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡀⠐⢄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠐⠀⠐⠁⠀⢊⠠⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠠⠀⠀⠐⠀⠀⠉⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⡀⠀⠀⠀⠀⢀⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡂⡄⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠑⠄⡀⠀⠀⢀⠄⠁
⠀⠀⠀⠈⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠈⢉⡃⠀⠀⢠⠀⢂⠀⠀⠀⢨⠀⠀⠑⠠⠆⡀⠀⠀⠀⠀⠀⡠⠒⠂⠐⠠⡀⠀⠈⠁⠉
⠐⠂⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢘⠁⠀⠀⡅⠃⠀⠸⡄⠀⡄⠀⠀⠀⠁⠐⠃⣀⠠⠀⠀⠀⠄⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠁⠀⠉⠀⠀⠀⢁⠀⠀⠰⡀⠀⠆⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⡀⠀⠐⠌⠐⠡⠄
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠀⢈⣉⢐⠀⠀⠐
⠀⠀⠀⠐⡁⠉⠒⠄⠐⠀⠐⢄⠀⠀⢀⡀⡠⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣀⣴⣆⣀⡀⡀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠉⠉⠁⠢
⠀⠀⠀⡀⠀⠁⢂⡀⠊⢀⠀⢀⡁⠈⠁⠀⠀⢠⠊⠁⠀⠹⠓⠤⡀⠀⣠⣾⣿⣿⡟⣿⣿⣿⣿⡿⣿⢿⣟⠀⠀⠀⢇⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢘⡤⠤⢠⣀⠀⠀⠘⠄⡀⢈⡀⣀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡇⢸⣿⣿⣿⣿⡇⠉⠋⠁⠈⠁⠉⢉⠉⠀⠀⠀⠀⠁⠂⠀⠀⠀⡆
⠀⢀⣭⣦⣴⣿⣿⣿⣦⠀⠐⠀⠀⠀⠀⠀⠀⠱⡠⢄⣀⡀⠔⢋⠀⠀⠙⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠄⠐⠁
⠀⠙⣿⣿⣿⣿⣿⣯⡟⠀⠀⠀⡀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠠⠊⠀⠑⠆
⠀⠀⠀⠙⠛⠛⠛⠛⠁⠀⢀⠊⠀⠀⠳⢄⠀⠀⠉⠀⠀⡀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠐
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠂⠀⢀⠠⠀⠁⠀⠈⠀⠉⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠑⡀⠀⠀⠀⡠⠀⠐⠒⠂⠀⡀
⠀⢀⣴⠃⠀⠉⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠚⠈⠉⠁⠢⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⡈⠀⠀⠀⠀⠀⠀⠰
⠀⢸⣿⣆⠀⠀⠀⢠⠆⠸⠀⠀⠀⠀⠀⠘⠀⠀⠸⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠻⣿⣦⣄⣀⡥⠀⠀⠢⡀⠀⡀⠔⡡⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀⠀⢀⠠⠊
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐