GIRL Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣒⣟⡻⢟⣿⣷⣶⣦⣿⣷⣦⣀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣄⠒⠚⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⢉⣿⣿⣿⢟⣫⣷⡿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠤⠤⠤⢶⣺⣿⣿⣿⠿⢋⡼⣫⠞⠁⣿⣦⣤⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠿⠛⠉⠀⣠⣾⠟⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠀⠉⠉
⠀⢀⠔⠒⠚⠛⠛⠛⠛⠋⠉⠉⣁⣤⡤⠴⠾⠟⢛⣰⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢿⣛⡥⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠛⠛⠋⠁⡠⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢉⠉⠭⠔⠈⠁⠀⠀⢀⣀⣠⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠿⠛⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣞⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠂⠾⣥⢸⡏⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣷⣄⠈⢿⢀⣷⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⣽⡿⣄⠀⠀⠀⠀⠀⠀⣠⠏⢹⠀⠀⢀⡟⠸⡆⢸⠛⢌⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠻⣧⠀⠀⠀⠀⣀⡠⠞⠁⢀⡾⣂⡼⠞⠁⢠⣇⡞⢳⡈⠀⠀⢰⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣼⠀⢠⡇⠀⠳⡴⢁⠀⠉⠁⢀⣤⡀⠈⠁⠀⢠⣴⠤⠏⢩⡗⡄⢹⡄⠀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡟⢧⡈⣇⠀⠀⠳⣙⠀⠀⠀⠀⠛⠁⠀⠀⣀⠈⠉⠀⠀⣸⡵⠃⠸⠧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠙⢦⡀⠀⠀⠀⠉⠁⠀⣀⡴⠋⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠆⢤⡀⠈⠁⠒⠒⠒⠂⠉⠁⠀⣀⣀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⢦⠀⠀⠀⠀⠀⢀⡼⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢦⡀⠈⠓⢤⡀⠀⣠⠊⠀⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠉⠓⠦⢄⠈⠉⢣⡠⠞⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⢷⣤⡠⠇⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢦⣀⣄⡀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠉⠉⣿⠚⢹⡇⠉⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠈⡇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡇⠀⢠⡧⠄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠺⣇⠀⢸⠃⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⢞⠱⣿⠞⠫⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠚⠁⢀⣾⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⣻⡿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡶⠛⢿⣿⣿⣿⣿⣿⣷⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡀⠀⠙⢿⣷⣿⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⠖⠀⠀⠛⠉⣁⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣻⣿⣿⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣟⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣿⡿⢿⣿⢟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠻⣿⠆⢉⡿⠟⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⢾⣽⠁⠀⠁⠀⠀⠀⢰⣦⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠀⠀⠀⠀⠀⠀⢈⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠀⢸⣧⠀⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣄⣠⣤⣄⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⡿⠟⠛⠛⠛⠛⠛⠛⣿⣿⡿⠿⠿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣽⢿⣿⣿⣿⠿⣿⣻⡟⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣼⣿⣿⣾⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠿⡿⣿⣿⣿⣿⣿⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣗⣿⣷⡦⠤⣤⣾⣿⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣿⣿⣿⣬⣤⣻⣿⣿⣿⣿⡇⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣷⣍⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢘⡛⢋⠛⠉⠀⠀⠀⠉⠉⠉⣠⣯⣒⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣧⠀⠀⠀⠘⠷⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣍
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣆⠀⠀⠀⠀⣠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣷⣤⣀⣰⣿⣄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣠⣌⡻⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣽⣿⣯⣵⣾⣿⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣤⣶⣾⣿⣿⣋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣯⣉⠉⠉⡿⢖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⢦⠀⠀⠾⠿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⡌⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣧⠀⣵⣀⣀⠀⠀⠀⠻⢼⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣵⣿⣿⣿⣿⣧⠻⠭⠉⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⡶⠿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⢿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢃⣼⡿⢟⣵⣿⠟⠓⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠟⢡⣿⡿⠏⠀⠀⠀⢰⠂⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⢿⣿⣯⠀⠀⠀⠀⠸⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢋⣼⣿⡾⣿⣿⣧⠀⠀⠀⠀⠀⢀⢴⣿⣿⣿⣿⣿⣿⣿⡿⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣡⣾⣿⣿⣼⣿⣿⣿⣧⡂⣄⣤⣴⣵⣿⣿⣿⢰⣿⢿⣿⣿⡗⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢛⣿⣾⣿⣾⡟⢿⣿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠁⠀⠈⠁⠀⠈⠋⠡⠀⠀⠀⢸⡿⢿⣿⣿⡟⠀⠹⡎⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣱⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣺⣿⣯⣽⣽⣿⣿⣶⣿⣿⣦⡀⠀⡀⠀⠠⠤⣤⣦⣤⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⣾⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⣿⠷⣻⢟⠕⢻⣯⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠿⠟⠋⢁⣴⠟⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠛⠋
⠀⠠⠒⠀⠛⠛⠛⠛⠉⠉⠉⠤⠤⠶⠟⣛⣣⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠯⠥⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠿⠛⠉⠁⠀⠔⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⣀⣶⣿⣿⣷⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⡈⠭⢕⡤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢀⠊⡰⢊⡕⡇⠠⡀⢬⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⢠⠃⡜⠉⠉⠉⢡⡀⠀⡈⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⢂⠂⡌⠀⠀⠀⠀⠀⡇⢄⠱⡀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠆⢼⣿⡇⠀⠀⠈⣿⣿⢄⠑⠑⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣌⡌⠀⠉⠁⠀⠈⠀⠉⠁⢠⠷⠆⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⢦⠀⢀⣀⣐⣀⠀⢀⠎⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠓⢄⠑⠒⢁⠴⠁⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠁⠈⢡⠸⠀⠀⠐⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣀⣠⠤⠶⢶⡋⠁⠀⡠⡳⠒⠢⠤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠁⠀⠀⠀⠀⠑⠁⠈⠊⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠐⡆⢁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠑⡎⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣸⢠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡂⣇⣀⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠂⠀⠀⠁⢀⣴⣶⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⠈⠉⠁⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠀⠠⡏⢿⣷⣦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣵⣾⢿⣶⣷⡿⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⠀⡇⢸⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⡇⠲⠦⣉⡛⢊⠟⡇⠀⠀⠀⠀⠀⠀⡾⡿⣿⣿⠛⢿⣿⡷⠸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃⣿⣿⡿⡇⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠧⠶⠛⢉⡇⠀⣿⡇⣿⣿⣧
⠀⠀⠀⠄⢀⡼⠋⣐⠉⠀⠀⣿⣿⠅⠙⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⠃⢸⣿⡇⣿⣿⣿⣇
⠀⠀⠀⠀⠞⠀⡘⠏⠀⠀⢰⢿⣿⡇⠰⣁⡀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠃⡟⡆⢸⡟⠠⣿⣿⣿⣻⡆⠠
⠀⠀⠀⠀⠇⢸⠂⠀⠀⠀⣿⠐⣿⣇⠀⢛⣄⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠄⠰⢰⣇⣼⠃⠀⣿⡇⢹⡇⢷
⠀⠀⠀⠀⢸⡏⠀⠀⠀⢠⣿⠀⣿⣿⠀⠀⢺⣷⣄⠀⠀⠀⠙⢻⡗⠀⠚⠀⠀⠀⢀⣴⠀⣥⣿⣿⡟⠀⠀⣿⠇⠀⣿⢸⡄
⠀⠀⠀⠘⡈⠇⠀⠀⠀⢾⣿⠀⢹⣿⠀⠀⠈⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢀⡠⠖⣻⡇⢸⣾⣿⡟⠀⡆⢠⠈⠀⠀⣿⣸⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠐⣾⣿⡀⠘⢿⠀⠀⠀⢸⣿⣿⠃⠈⠳⢤⣠⠤⠖⠉⠀⠀⣿⡀⡏⣿⡿⡄⢰⢀⡆⠀⣠⢀⣿⠁
⠀⠀⠀⠀⠀⣰⡆⠀⠀⣿⣿⡇⢸⢿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣷⠀⠘⣼⠁⣰⡇⣼⣿
⠀⠀⠀⠀⣠⡀⢀⠀⡀⣿⣿⡇⢸⠈⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡃⣰⡏⢰⡿⣵⣿⠇
⠀⢀⠴⠚⠉⢘⣿⡄⢣⣿⣿⠀⣸⠀⠀⠠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⣿⣿⣿⢳⡿⢠⣏⣼⣿⡟
⠠⠏⠀⠀⠀⡸⠘⣿⣬⣿⡟⠀⡏⠰⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⣿⣿⠇⣾⣼⣿⡟⠛⢦⡀
⠀⠀⠀⠀⠆⠀⠀⢸⣿⡿⠁⣸⢠⢀⣾⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠋⣹⢲⣿⣿⣿⡇⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢠⣟⣠⠞⠋⠀⠈⠒⠤⣄⡀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠄⠊⠀⠀⠈⣿⣸⣿⣿⣿⠇⡠⠊⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠼⠁⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠐⠈⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⠀⣧⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⣧⢀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣾⡿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢰⣿⠘⣿⣿⣿⠿⠞⠁⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⣠⣤⡆⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⣿⣿⣿⣦⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡾⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⢔⡟⢿⣿⡿⣿⣿⠟⣿⣿⣛⣟⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣷⣿⣷⣼⣿⣿⣯⣾⣿⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣿⣿⣿⣿⡿⠿⠿⠿⠻⢿⣿⣿⠿⣿⣿⣿⣿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣆⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡄⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⣷⣻⣿⣿⣧⠤⢤⣴⣾⣿⣿⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣬⣭⣿⣿⣿⢇⣃⡀⢿⣿⣿⣿⣿⣿⣿⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣏⠻⠟⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠟⠛⠛⠿⠏⠉⠉⠉⠁⠈⠙⠛⠛⠃⣈⣟⠲⢤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡄⠀⠀⠀⠀⠀⣾⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣤⣍⣁⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣄⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣷⣄⡀⠀⣠⣿⣣⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠛⠛⠛⠛⠛⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⢀⡞⠁⢀⠄⢀⠆⠀⠀⠀⠀⠀⠀⢠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣠⡴⠶⠶⠶⠶⠶⣤⣀
⠀⠀⠀⠀⣰⠋⠀⢠⠏⢀⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⡾⠅⠒⠂⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⢰⠇⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⣦⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⣿⡤⣴⠋⣠⠤⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠿⠴⠶⢶⠾⣶⣾⣤⡤⣤⣄⣀⣀⣀⣀⣀⣷⣴⡾⣿⡦⡀⠀⠉⠙⠒⠶⠦⠤⣿⣤⣘⡟⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠸⣆⠹⢿⣿⡶⢿⠏⢸⡅⠉⠹⣿⣿⣿⣧⣾⢃⠗⠀⠀⠀⠀⠀⠀⢠⠁⠀⣽⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡝⠲⠤⡤⠖⠏⠀⠠⠻⣄⡀⠙⠻⠿⠟⣫⡛⠀⠀⠀⠀⠀⠀⠀⠘⣷⠛⠁⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡖⠀⠀⠀⠈⠉⠓⡶⠒⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⡄⠀⡇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢠⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⡇⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢰⠁⢀⠇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡌⠀⡼⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣈⣉⡻⠟⡟⣻⠛⠻⠭⣥⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠀⠰⠁⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⢈⡁⠀⡠⣀⣴⠢⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡄⢠⠁⢀⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠉⢸⠁⠑⠒⠁⠈⠋⠀⢨⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢣⢸⠀⠸⡀⢳
⠀⠀⠀⡆⢀⠀⠀⢀⠠⢔⡪⠷⢤⡏⠀⠀⠀⠀⠀⠀⠀⠸⣦⡤⢞⢣⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⣆⠀⠙⢦⣵⣤⣄
⠔⢀⠍⠑⠀⢑⠨⠐⠊⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⠓⢬⣒⠤⣀⣀⡤⠂⠴⣀⠖⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠚⠛⠉
⠐⢔⠠⡂⠀⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⠙⠒⠺⡀⠈⠀⠩⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠁⠂⠥⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠰⠯⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⣤⣤⣤⠦⣤⣄⣀⣀⣠⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠨⣀⡇⡿⠠⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⢀⠛⠂⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡎⠀⠀⣰⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⡀⠁⠒⠺⠓⢲⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣖⠑⣿⠟⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣄⠀⠹⡖⠙⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⢀⢽⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡄⠀⠀⢸⡏⣧⡀⢻⣴⠓⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣼⣿⠙⠂⠀⠀⠀⠀⠀⣀⠞⠁⢸⣇⠃⣄⡼⠁⢸⡇⣸⡌⠳⠀⠀⢀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢠⠀⠀⣸⠃⢻⡂⢀⡀⢀⡀⠤⠚⠁⠀⠠⠟⠡⠞⠋⠀⢀⡾⠷⣇⠙⣦⠀⠀⠀⣷⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⣾⡄⠀⣿⠀⠀⢻⠃⡄⠀⠀⠀⠴⣶⡆⠀⠀⠀⠀⣾⡏⠛⠀⢸⠉⡇⢸⡇⢀⡴⠋⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠇⠙⠦⣹⡄⠀⠈⠳⢍⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡿⠞⠁⠘⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠖⢦⠀⠈⠉⠒⠒⠒⠒⠈⠁⠀⢀⣀⣀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⢠⠟⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠈⠳⣄⠀⠀⢀⡴⠋⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠓⠦⣄⡀⠉⠓⠮⡀⣠⠜⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⣦⡄⡀⣻⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⠗⠦⠤⣤⣄⡤⣤⠠⠖⢢⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⠀⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⡟⠀⠀⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢀⡇⠀⠀⡟⠒⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠋⢧⡀⢰⡇⡀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⡴⣛⠩⢿⡏⠩⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠚⠁⢀⣼⣅⣀⣀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⣿⣿⡿⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠤⠖⠂⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠦⣀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⢀⣀⠴⠖⠙⠉⠉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠈⠁⠀⠀⠀⠀⠀⣠⡴⠟⠻⢦⠄⠀⠀⠀⠀⠀⠀⣠⣤⣤⢤⡄⠀⠐⡦⣤⣄⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣠⣶⣛⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⡹⠻⣿⣿⡻⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣠⡇⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣿⣿⣿⠀⠉⠓⣶⣭⡥⠉⠻⠀⠀⠀⠀⠀⠀⣸⠻⣿⣿⡯⠈⣿⡟⡏⠈⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣠⡾⢻⡿⠋⢀⣿⣿⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢠⡇⠀⣿⡇⢻⣿⣿⡆
⠀⠀⠀⠀⢀⡾⠋⣠⡅⠀⠀⢸⣿⣿⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣼⠁⢸⣿⠇⢾⣿⣿⣿⡄
⠀⠀⠀⠀⡚⠀⡤⡛⠁⠀⠀⡿⢻⣯⡇⠰⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢠⠏⡇⢸⡟⠸⢾⣿⣿⣏⣷
⠀⠀⠀⠀⠇⢸⡗⠀⠀⠀⢸⡇⢸⣿⣇⠀⠉⣄⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⢀⠆⡘⣸⣧⣾⠃⠀⣿⡿⠈⣿⠸⡆
⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⣼⡇⠸⣿⣿⠀⠀⢻⣷⣄⠀⠀⠀⠈⠙⡟⠂⠐⠋⠀⠀⠀⣠⡞⢠⢷⣿⣿⠏⠀⠀⣿⡇⠀⢻⡀⣇
⠀⠀⠀⠐⣁⢻⠀⠀⠀⠰⣿⡇⠀⢿⡏⠀⠀⠈⣿⣿⣿⡦⣀⠀⠀⠀⠀⠀⠀⣀⠴⠛⣽⠃⣿⣿⣿⡏⠀⡆⢠⠈⠀⠀⢸⣇⠇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⢲⣿⣧⠀⠸⣷⠀⠀⠀⢸⣿⣿⡇⠈⠑⢦⣄⡤⠴⠋⠁⠀⢠⣿⢸⣛⣿⡟⡄⢰⠀⡎⠀⢠⠀⣾⡇
⠀⠀⠀⠀⠀⢀⡦⠀⠀⢸⣿⣿⠀⢸⡏⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⣿⣷⠀⠸⣸⠇⣠⡏⢸⣿
⠀⠀⠀⠀⢀⡈⠀⠀⢘⢸⣷⣿⠀⢨⠃⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣯⠃⢰⡟⢀⡿⣻⣾⡿
⠀⠀⡠⠖⠛⠙⢷⣇⠸⣸⣿⡿⠀⡇⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⢶⣿⢁⡾⣡⣿⣿⠃
⢀⡞⠀⠀⠀⢀⠟⣿⣆⣻⣿⠇⢠⡇⣰⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣾⡇⣸⣱⣿⣿⠿⢦⡀
⠐⠀⠀⠀⡤⠀⠀⠘⣿⣿⡟⠀⣼⢠⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠟⢿⢤⣿⣿⣿⣧⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣰⡷⣩⡾⠛⠀⠒⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⡁⠔⠀⠀⠰⣿⢨⣿⣿⣿⣿⠀⡠⠒⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣰⣿⠟⠋⠀⠀⠀⠀⠀⠈⠉⠑⠒⠀⠤⠴⠖⠒⡉⠁⠂⠀⠀⠀⠀⠀⢀⣿⣾⣿⣿⡟⡁⢻⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⣸⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⢹⣿⣿⣿⣿⣠⠇⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢻⣼⣿⣿⣿⠉⠁⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣴⣿⣟⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠩⠁⠀⠀⠀⠀⠀⠀⠀⡰⢸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠰⢋⣵⣶⣶⣄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣶⣶⣦⡀⠀⣿⣿⣿⣿⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠈⠻⠿⠟⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠤⠚⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢰⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣥⣴⣶⣶⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣰⣦⣭⣛⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⣿⣦⡀⠀⠀⠀⢀⣾⣿⣿⡆⣠⣾⣿⡿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⢋⣥⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣴⣾⣿⣿⠟⣵⣿⣿⡟⣡⣾⣿⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⢋⣥⣶⣯⣾⣿⣿⡟⢠⣿⣿⣿⣿⣠⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⣌⠻⣿⣿⡿⢏⣉⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡛⠻⢿⣿⣿⣿⣿⣷⣌⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣉⣭⣥⣤⣴⣶⣾⠻⠿⠿⡿⢿⠟⣩⣤⣌⡀
⠀⠀⠀⠀⠀⣠⣿⣿⣷⣦⣉⠻⣿⣿⣿⣿⣦⣹⣿⣉⣍⣉⣩⣭⣭⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⢂⣠⣾⠿⣿⣿⣿⠆⡀
⠀⠀⠀⠀⠐⠻⠿⣿⣿⣿⣿⣷⣌⡙⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣛⣉⣉⣉⣥⣤⣘⣻⣵⣾⣿⣿⡏⣸⣿⣿⡿⢠⣿⣆
⠀⠀⢠⣾⣿⣶⣤⣄⡉⠻⢿⣿⣿⣿⣦⡙⣿⠿⣯⣉⣉⣙⣛⣛⣋⣭⣴⣾⣿⣿⣿⣿⡿⠿⠿⣟⣻⣿⣿⡿⠛⢁⣿⣿⣿⠃⣾⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⠻⡿⢋⢿⣿⣿⠟⠻⣿⣿⣿⣿⣟⢿⣿⣿⣟⠋⢭⣷⣶⣶⣶⣿⣿⣯⣡⣤⣶⣿⣿⣿⠏⣸⣿⣿⠇
⢀⣩⣍⣉⣉⣉⣛⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣷⢿⣿⣿⠙⣿⣿⣿⣦⠻⣿⣿⣧⡀⠀⠀⠀⠈⠉⠉⠙⠻⣿⣿⣿⠟⢁⣼⣿⣿⡿
⣿⣿⠿⠛⣛⣋⣩⠟⣹⠃⣾⣿⣿⣿⠈⣿⣿⣿⣇⣿⣿⡆⢻⣿⣿⣿⣧⠙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣝⠻⠦⢿⣿⠿⠟⠁
⢉⣠⣶⣿⣿⣿⢋⣾⣿⠀⣿⣿⣿⣿⠀⣿⣿⠛⣿⣿⣿⣷⠈⢿⣿⣿⣿⣧⠹⣿⡿⠷⠀⠀⠀⠀⠐⠦⠀⠉⠁
⣿⣿⣿⣿⠟⣱⣿⣿⡿⢰⣿⣿⣿⡟⣰⣿⣿⡄⢹⣿⣿⣿⣧⠈⣿⡿⠿⠛
⣿⣿⠟⢡⣾⣿⣿⣿⢃⣾⣿⣿⠟⣶⣿⣿⣿⣧⠈⠿⠿⠛⠋
⠟⢀⣴⣿⣿⣿⠟⣡⣾⣿⣿⡿⠀⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⣿⣿⣾⣿⣿⢋⣹⣿⣛⣛⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡾⠛⢿⣿⣿⣿⣿⣿⣭⣽⣷⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣸⣿⡉⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠈⠛⣿⣿⣿⣷⣞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠃⠀⠀⠉⠉⣀⣀⡄⠀⠀⠀⣼⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢀⣿⣿⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡝⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣙⣿⡟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡼⣿⣿⣄⠙⠿⣾⣷⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⣄⠀⠀⠀⠀⠀⢡⠛⣿⡏⢀⣶⠟⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢈⢳⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠸⣧⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⡄⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⢻⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠁⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⣄⣀⣤⣤⣀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠛⠻⠿⠛⠛⠉⠉⠛⠋⠉⠉⠙⣿⣿⣿⠿⠿⠿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠖⠛⠛⠛⠛⠛⠛⠛⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢀⡿⠊⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⣰⠋⠀⢀⠎⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⡴⣛⠉⠁⠀⠀⠀⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⣼⠁⠀⠀⣾⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⣧⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠟⠋⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⢸⠇⣀⣀⣀⣷⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢈⣷⣤⡀⠉⠓⠦⣤⣀⣀⠀⠀⢸⡟⠉⢯⣴⣞⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠉⠉⠉⠉⣿⠙⣿⣿⣿⠛⣶⣶⢶⡶⠶⠶⣶⣾⣿⣿⠛⣿⠹⡄⠀⠀⠀⠈⠉⠉⠛⠻⠟⠳⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠙⠿⠿⢟⣽⠃⠸⣇⠀⠀⢻⣿⣿⣿⣿⡿⡴⠃⠀⠀⠀⠀⠀⠀⠰⣆⣀⣴⠏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢰⠉⠓⠒⠞⠋⠃⠀⠐⠉⠳⣄⣀⠉⠙⢛⣩⠾⠍⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠁⠀⠀⠙⠷⣄⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠸⣏⠀⠀⠀⠐⠀⠉⠹⠛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢡⠀⢸⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢠⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⢸⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⣸⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢠⠁⢠⠇⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⠛⢳⡶⠶⢶⡶⠾⣟⣛⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠆⠀⡞⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡍⠉⠉⠀⠘⠚⠀⠀⡀⠀⡭⣅⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠸⠀⡘⠀⠰⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢙⠒⠲⣄⠔⠑⠦⠚⠉⡏⠱⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢰⠀⡇⠀⡇⠸⡇
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣀⢽⣄⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢀⣨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣆⣇⠀⠘⣄⠱⣄⡀
⢀⠀⠤⠧⠀⠢⡀⠄⣂⡭⠖⠉⠈⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠱⣜⠢⣄⠀⠀⠀⠀⢀⠍⡀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢦⣤⣈⣉⣻⣿⠿
⢁⢐⡃⡀⠀⠠⠂⠉⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠙⠲⢭⣒⢦⠞⠁⠘⠱⠖⣡
⠈⠘⠂⠡⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠠⠌⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣤⣤⢶⡶⠶⠦⣤⣀⣀⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢇⡼⢸⠇⠀⠒⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠇⡘⠓⠀⢂⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠁⠀⠀⡌⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣘⠒⠲⠾⠶⢶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠛⢶⣤⡴⠚⠒⠛⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⢀⣀⡈⠀⠀⠀⠀⠀⠀⠈⠙⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢀⡴⣆⣠⠞⠃⠈⣇⠀⠀⠀⠀⠀⠀⠀⣠⡞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⠀⢰⠋⠀⠙⠁⠀⠀⠀⠘⠳⣄⣶⡀⠀⢿⣉⡿⠗⠋⠙⡀
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢘⣧⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢡⣿⠀⠉⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⡞⠀⠉⠀⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣴⣇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢘⠀⠀⣶⢸⠀⠀⠀⠀⠛⠋⠋⠀⠀⠀⠀⢀⣀⣀⠀⠈⠉⠟⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡆⠀⠘⢧⣷⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠻⠟⠀⠀⢀⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠉⢳⡆⠹⣆⠀⠀⠀⠐⠦⣄⣀⣤⡄⠀⠀⠀⠀⠶⣿⡖⠀⠀⠀⠀⠀⢷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⡀⠤⣄⣀⣭⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢬⡷⠦⢄⣀⠀⠀⠀⣀⣀⠤⠖⠻⣿⠀⠀⠹⣿⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⢈⣟⠋⠉⠉⠀⠀⠀⢀⠿⢦⡙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠛⠓⣶⠾⢿⡶⠶⠶⠶⠶⠊⠁⠀⣾⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣸⠏⠀⠀⠙⠶⠞⠁⠀⠀⠀⣠⠖⢦⣼⡏⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣴⢋⣤⣄⠀⠀⠀⣠⢤⠀⠀⠀⠙⠦⠚⣿⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠇⠸⢧⠾⠀⠀⠸⣇⡴⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢦⠀⠈⢳⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⡞⠉⣣⠀⠀⠀⠀⠀⠀⠸⣦⠾⠁⠀⠀⢻⡄⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⡀⠀⠀⠉⠚⠁⠀⠀⢠⠖⢲⡄⠀⠀⠀⠀⠀⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⣾⣇⣠⡟⠀⠀⠀⠀⠀⠀⠀⠘⠦⠜⠁⠀⠀⠀⢀⡤⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⠼⠀⠀⢠⠿⡄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⢠⡞⢛⡆⠀⠀⠀⠀⠀⠙⠶⢧
⠀⠀⠀⠀⠀⢠⠟⢠⣿⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠋⠁⠀⠀⠀⣀⣠⣴⣦⡹⡆
⠀⠀⠀⠀⢠⠏⠀⢀⣿⠋⡷⠐⠚⠛⠛⠛⣿⣿⡛⠛⠛⠛⠿⠿⢿⣿⡿⡟⢿⠉⢿⠀⠀⢿
⠀⠀⠀⠀⢿⡀⠀⢸⣇⠀⠃⠀⠀⠀⠀⠀⢿⡀⣿⠀⠀⠀⠀⠀⠀⣿⠀⢣⠘⡆⠸⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠙⠳⢦⣥⣀⡀⠀⠀⠀⠀⠀⠘⡇⡭⠀⠀⠀⠀⠀⠀⠟⡀⠈⠀⠁⠀⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠶⠶⠶⠶⠶⠶⡶⢶⣦⣤⣤⣤⣴⣶⣶⡶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣄⣠⠄⢹⣆⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⠁⠀⠀⣯⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⢙⣲⠾⣇⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣶⡋⠁⠀⠈⠉⠛⠛⢋⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠛⡿⠟⠿⠛⠟⢻⡙⠻⢻⡟⠛⠛⢻⣿⣿⣿⣟⣻⣛⣛⣋⣉⣉⣛⣙⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠛⠉⠉⠉⠉⠉⠻⢷⠞⠋⠉⠉⠉⠉⠛⠛⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⣀⣴⡆⢀⡴⠛⠁⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⡴⠋⠀⠿⠏⠀⠀⠀⠀⠙⢦⡀⢀⣄⠀⠀⢰⡾⠘⣿⣧⠴⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⢷⡀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠆⣠⣄⠛⠖⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⣼⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⡿⠏⢀⡀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣸⠇⠀⠀⠀⢸⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣴⣾⣇⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣶⠀⡇⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠉⠹⠿⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠹⣦⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠂⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠘⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⠀⢻⣦⠀⠀⠀⠀⠈⠻⢶⣄⡤⠶⠆⠀⠀⠀⠀⠀⠸⠿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣧⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢠⡄⠀⣤⣄⣀⣀⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⣙⣳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠶⣿⣧⠀⠀⠸⣿⣶⣤⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠉⠉⠙⠛⢦⣤⣤⣤⠖⠛⠛⠉⠀⠀⢸⣏⠀⢤⣤⡼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⡀⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠉⠉⣻⡿⠛⢻⡟⠛⠓⠛⠛⠛⠋⠀⠀⢰⣿⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢸⡿⠁⠀⠀⠙⠷⠴⠟⠁⠀⠀⠀⠀⣠⠶⠶⣤⣿⡉⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⡿⢁⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠻⣄⡴⢿⣿⠁⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣠⠟⢰⡟⠉⣷⠀⠀⢀⣾⠋⢉⡆⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢳⡟⠀⠈⠙⠛⠁⠀⠀⠀⠙⠶⠛⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠚⢳⡄⠀⠈⢷⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⡼⠋⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⡾⠃⠀⠀⠀⠻⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣁⡀⠀⠀⠀⠙⠓⠞⠃⠀⠀⠀⢠⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⢶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢠⡶⠛⣦⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡴⠛⠀⠀⠀⡾⠛⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⣾⠛⢛⡆⠀⠀⠀⠀⠀⠀⠀⠻⠶⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠿⣠⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠞⠃⠀⠀⠀⠀⠀⠀⢀⣤⣔⢻⡇
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⣿⡶⢾⣟⢋⣠⣤⣤⣤⣴⣦⢶⣤⣤⣤⣦⣴⣶⣶⣶⣶⣶⣶⣦⣶⣾⠿⢿⡏⠉⠉⢹⡄
⠀⠀⠀⠀⠀⢰⡏⠀⠀⢰⡿⠃⢸⡅⠀⠀⠀⠀⠀⠀⢿⡟⢿⡄⠀⠀⠀⠉⠙⠋⠛⢿⡟⠹⡇⠹⡄⠀⢷⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠻⣧⡀⠀⠸⣿⠀⠌⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢱⠀⡷⠀⠘⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢀⡇⠀⠀⠀⠀⠀⠀⠀⠻⢁⡄⠈⠀⠁⠀⠀⢀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣠⣤⣤⣤⣤⣤⣴⣶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠈⣭⠉⠛⠛⠛⠛⠛⠛⣿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⣤⣀⣤⠄⢹⣧⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠉⠀⠀⠀⢹⡋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠶⣶⣴⣾⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣁⣀⣤⠞⠋⠀⠙⠻⠷⢤⣤⡶⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠷⢤⣄⣀⣀⣠⣤⣠⣤⠴⠶⠏


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠿⠿⠿⠿⢿⠿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣧⣼⣥⣥⣬⣤⣬⣤⣼⣧⣤⣄⣽⣥⣤⣤⣤⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠚⣭⣶⣿⣷⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⣴⣾⣿⣷⡀⠈⣿⣿⣿⡇⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⣛⢉⣩⣭⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⢛⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣰⣿⣤⠀⢀⣠⣿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⠛⢛⣉⣉⣭⣬⣽⣿⣦⣀⣀⣀⣴⣿⣿⡿⣣⣾⣿⡿⢋⣿⣟⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣟⣵⣿⣿⡟⢠⣿⣿⣿⡏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣬⡙⢿⣿⣿⣿⣿⠿⠛⢛⣉⣉⣉⣩⣭⣥⣤⣶⣿⣿⣿⣿⣿⠟⢁⣿⣿⣿⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣦⡙⢿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢛⣉⣥⣴⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⢀⣶⣦⣬⡙⠿⣿⣿⣿⣿⣦⡹⣿⠿⠛⠻⠛⠛⠛⢛⣋⣥⣶⣿⣿⣿⣿⣿⣿⣷⣤⣬⣉⠁⣁⣴⣿⣿⣿⡆
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣌⠻⢿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⣛⣉⠽⣟⣫⣴⣾⣿⠋⣾⣿⣿⡇⣴⣄
⠀⠀⢀⣴⣦⣄⣈⡙⠻⢿⣿⣿⣿⣦⡙⢿⣿⣟⠻⠛⠻⠿⠿⠿⢛⣫⣴⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⢸⣿⣿⡟⢠⣿⣿
⠀⢠⣾⣿⣿⣿⣿⣿⣶⣤⡙⠿⣿⡿⢻⣾⣷⡾⢿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠟⣛⣯⣥⣤⣴⣷⣿⣟⣋⣠⣴⣿⣿⣿⢁⣿⣿⡿
⢀⣙⣙⠛⠛⠛⢿⣿⣿⣿⢿⣷⣾⡆⣷⣿⣿⣴⣷⣿⠛⣿⣿⣿⣎⢻⣿⣿⣦⠀⠉⠉⠉⠉⠛⠛⠻⣿⣿⣿⣿⠟⢡⣾⣿⣿⠇
⣿⣿⡿⠿⠛⢛⣛⠟⣽⢃⣿⣿⣿⡇⢹⣿⣿⣷⣹⣿⡇⢹⣿⣿⣿⣆⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣙⡻⢧⣴⣿⣿⡿⠋
⠋⣡⣴⣾⣿⣿⢋⣾⡇⢸⣿⣿⣿⡇⢸⣿⡟⢿⣿⣿⣿⡈⢿⣿⣿⣿⣇⢹⣿⣿⡇⠀⠀⠀⠀⠠⡄⠘⠛⠁
⣿⣿⣿⣿⠟⣵⣿⣿⡇⢸⣿⣿⣿⠇⣾⣿⣇⠸⣿⣿⣿⣷⠈⣿⣿⠿⠟⠀⠉
⣿⣿⠟⢡⣾⣿⣿⡿⢀⣿⣿⡿⢣⣾⣿⣿⣿⠀⠿⠿⠟⠛⠁
⠟⢁⣴⣿⣿⡿⠏⣴⣿⣿⣿⠇⠘⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠋⠉⠉⠉⠉⠉⠙⠓⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⠑⡄⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢠⠁⠀⠘⢄⠀⠀⠀⠈⢄⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠃⠀⠀⡁⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⢀⠀⠀⠀⠢⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⡀⠀⠁⠀⠀⢀⠀⢢⠀⠀⠀⠀⠀⠈⠉⣀⠀⠠⠐⢄⠀⡃⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠛⠰⠨⠀⣾⣿⢿⣄⠀⠀⠀⠀⠀⢀⣾⢿⣿⠄⠇⠘⡾⠠⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠢⠈⣆⢀⠁⠛⠳⠚⠁⠀⠀⠠⠀⠀⠈⠓⠾⠛⡀⠀⢠⠅⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⠢⣄⠈⠀⠀⠢⡀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠔⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡔⠋⠀⠉⠐⠂⢄⠀⠈⠀⠁⠀⠠⠀⡒⠈⠀⠈⠲⣄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠁⠒⣒⡀⠀⠠⠊⠀⠀⠀⠀⠀⠘⡆⠀⢣
⠀⠀⠀⠀⢀⣤⣎⠤⠔⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⣤⣵⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⣀⣀⣀⣀⣀⣀⣀⣠⠇⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡅⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⢀⣖⠒⠒⠀⠳⡀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢨⣯⠀⠀⠀⠀⠈⢆⠀⠄⠠⢄⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠁⠄
⠀⠀⠀⠀⠰⡗⠀⠀⠀⠀⠀⠀⠙⡖⠄⠀⠥⡼⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢀⢠⠰⠱⠄
⠀⠀⠀⠀⠒⡗⠀⠀⠀⠀⠀⠀⠀⠈⠄⣀⡀⡼⢂⢘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⢸⠈⡗⠄
⠀⠀⠀⠀⢈⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠁
⠀⠀⠀⠀⠠⡧
⠀⠀⠀⠀⠐⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠄⢠⣀
⠀⠀⠀⠀⢈⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⡀⠀⠤⠀⢀⣀⡈⡈
⠀⠀⠀⠀⠠⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠃⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⣏⣁⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣤⠀⢰⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠉⠁⠀⠈⠃⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣶⡤⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣤⠞⠋⠉⠉⠉⠉⠩⠙⢲⣕⢢⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠈⠉⢣⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢻⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢥⣄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢣⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢀⠴⠖⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⡴⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡄
⠀⠀⠀⠀⠐⠁⠀⡀⢳⢀⠆⠀⠀⠀⠠⠔⠀⠀⠀⢀⠀⠈⠙⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⡀⢃
⠀⠀⠀⠀⠀⠠⣧⡱⡄⢻⠀⠀⠈⠀⢀⠀⠐⢶⣶⣶⣿⣞⠦⡀⠀⠀⠉⠀⠀⠴⠶⠾⢶⡆⠈
⠀⠀⠀⠀⠀⠀⣨⠿⣶⣿⠀⡤⠂⢠⠈⠐⠃⢤⣄⣹⠛⠋⠉⢷⠤⠤⠀⠀⣀⣤⣤⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢸⢁⣎⠏⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣅⣈⣹⠛⠓⣽⣿⠃⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣾⢇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣠⠊⠀⠉⠇⠀⠀⠈⠶⡇
⠀⠀⠀⠀⠈⢆⠢⠀⠐⢄⣄⢿⠀⠀⠀⠀⠀⠀⠀⠈⢧⡠⠔⠋⠁⠁⠀⠀⠃⠀⠀⣠⠞⣅
⠀⠀⠀⠀⢀⠈⠟⠛⠶⣾⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣣⡀⠀⠀⠀⠀⠀⠀⢶⠀⠒⢤⠄⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣷⠏⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢼⠏⢀⢀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⣤⡡⠊⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣦⣼⠋⠀⠑⢄⠀⠀⠀⠀⠈⡌⠀⢯⡠⠚⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⡀⠀⠀⠀⠀⡟⠳⣦⣿⠀⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠐⢾⡧⡀⢸⡇⠀⠀⠀⠀⢻⣵⡏⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣺⣿⣁⣾⠁⠀⠀⠀⠀⢀⡉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣉⣛⡁⠃⡀⠀⠀⠠⠁⢨⠙⡽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠘⡧⡀⢹⡄⠀⣷⢆⣿⢀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⢠⠀⢻⠀⢟⣼⠃⣸⣱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⡠⣾⠀⢰⠀⠘⣿⢰⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠟⢇⡸⠀⠀⠹
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣀⣴⣶⣿⣿⣿⣿⣶⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠔⣋⡴⠾⠿⠿⣿⣿⣿⣿⣿⣿⣷⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣩⠤⠄⠀⠀⠈⠞⠻⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿⣿⣿⣴⡟⠛⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣗⠒⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⢀⡴⠖⣲⡄⠀⠀⣿⣿⣿⣿⣿⣎⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠸⣿⣿⣿⣿⣿⡄⠀⠘⠻⠻⠿⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢿⣿⣿⣿⣿⣦⣄⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠸⣿⣿⣿⣿⣿⣿⣏⠉⠉⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⢿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠢⠹⣀⣤⣽⣿⣭⣯⣍⣱⣦⠀⠘⢹⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣨⣿⣿⣿⣿⣿⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⠀⠹⣿⣿⣿⣿⣿⣿⠆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡝⣿⣿⣿⣿⣿⣷⣀⣙⣿⣿⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⡿⠛⡻⠚⠛⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠋⢞⠩⠀⠁⠀⠀⠰⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠻⠟⠑⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⣠⣴⣶⣿⣷⣶⡦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⢊⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣤⡶⢋⠁⠀⠉⠉⠋⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣿⣿⣏⣩⢾⡤⠀⠀⠀⠀⠈⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣤⠄⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⣀⣤⣀⠀⠀⠈⣿⣿⣿⣿⣿⡴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀⢼⣯⣴⣾⠃⠀⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣽⢿⣿⣿⣿⣿⣄⠀⠀⠉⠈⠉⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⣿⣿⣿⣿⣿⣿⣶⡦⠤⠤⠔⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⡄⠉⠿⠿⠿⠿⠿⣿⢟⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠱⣼⠾⠻⢿⣾⣿⣶⣾⣷⡀⠉⢸⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⣾⣿⣿⣿⣿⣿⣷⡀⠸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢆⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣷⡀⠸⣿⣿⣿⣿⣿⣿⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡜⣿⣿⣿⣿⣿⣿⣄⣨⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⡿⠾⠟⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠣⠞⠉⠀⠀⠀⠀⠠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡿⠟⠙⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢦⡀⠀⠀⠀⠀⣀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢰⣎⡇⢀⣴⣶⠏⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣇⣼⣿⣿⣫⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣾⢻⣿⣽⣿⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠋⠉⠉⠉⠻⣿⣿⣮⠻⣝⠷⡏⠻⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣧⠙⢷⡀⠀⠀⡙⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣘⠃⠀⣀⣤⣬⣷⡄⢐⠘⠿⣿⣆⠀⠀⠀⠀⠙⢷⣌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡷⠶⣿⣿⣿⡿⢁⠎⠑⠢⢌⡙⢧⠀⠀⢳⡔⣆⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⠁⠀⠻⠿⠋⠕⠁⠀⠀⠀⠀⠈⠙⢷⣄⠀⠻⣮⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠏⠂⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⣠⣘⣿⣧⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣩⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠁⢰⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣶⣶⣾⣏⠉⠁⠀⠀⠀⠀⡟⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠜⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣦⣄⡀⢀⣴⣿⣶⣦⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⣿⣿⣿⣿⣿⣿⣿⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠞⣴⣟⣿⣭⣻⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡷⠆
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣯⡾⠿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠈⠟⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⣦⣄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⡦⠀⢀⣠⡾⠛⠛⠒⠒⠒⠚⡛⣦⣄⠲⢄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠒⠿⢶⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣿⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⢠⠚⠁⡄⠸⣇⠀⡀⠀⠀⠀⠀⠀⡠⠀⠐⠋⠀⠘⠁⠚⠿⢿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡄
⠀⠀⠀⠀⠀⠈⠄⡄⠰⠀⢛⣼⠀⠀⠀⠤⠂⠉⠀⢀⡀⢀⣀⣐⣄⣠⠀⠀⠈⠉⠻⠷⠀⠀⠀⢀⣀⣀⣀⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠾⣦⡳⡀⡟⠀⠀⠀⠀⢀⢴⠀⡀⠙⠿⢿⣿⣿⣽⣝⣢⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠙⠿
⠀⠀⠀⠀⠀⠀⢀⠠⠟⠿⣿⣿⠀⣴⠋⠀⡂⠀⠈⠉⠲⣶⣤⡝⠋⠃⠀⠹⠗⠒⠢⡀⠀⣀⣤⡶⢦⣤⣞
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠹⣇⢸⠇⣴⡹⠁⠄⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣇⣀⣉⡿⠛⠐⣼⣿⠛⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣠⠎⠉⠉⢿⠀⠀⠀⠉⣤⣷⠀⠈
⠀⠀⠀⠀⠀⠰⡀⢆⠀⠀⢀⠀⡋⢸⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣀⡴⠞⠡⠄⠀⠀⠠⠀⠀⠀⠀⣠⢏
⠀⠀⠀⠀⠀⠀⠙⢦⣥⣄⣈⢳⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠞⠁⢸⠂
⠀⠀⠀⠀⠀⠰⠁⠈⠀⠈⠉⢿⡏⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢿⡆⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⠶⠐⠆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣿⡟⠀⢑⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⠀⡀⣿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡦⣤⣰⡿⠀⠀⠀⡀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⡀⢁⠬⠁⠌⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⣁⢰⣧⡞⠂⢤⠀⠈⠀⠀⠀⠀⠐⠖⠆⢸⡷⠋⣠⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢯⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢲⣄⡈⠳⣏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷⠀⠀⢰⡇⠀⠀⠀⠀⠀⣾⢉⢻⣶⠿⠀⣀⣷
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠲⢿⡇⡀⠘⡟⠀⠀⠀⠀⠀⢹⣧⣾⠁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⡒⣾⣿⣀⣶⡇⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠻⠿⠋⡕⠀⠀⠀⠀⢀⠐⠉⡒⠖⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⢲⣆⠁⠑⣄⠀⠀⣾⡠⢠⣇⠨⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠋⠆⠀⢻⡆⠀⣿⢃⣾⠃⢸⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠰⡸⡄⠈⠟⠀⢹⣾⡏⢠⡏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣀⢷⡁⠀⢸⠀⠈⣽⡁⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⠏⠿⡀⢸⠀⠀⠙⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣙⣛⣛⣹⣯⣩⣉⣿⣋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣽⣭⣽⣿⣯⣭⣭⣭⣭⣿⣭⣭⣯⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⢦⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡌⡇⠀⣠⣴⡾⠉⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⡇⢸⣿⣿⡶⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣠⣤⣴⡿⣿⣿⣿⣾⣋⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⡝⢿⡿⣯⡻⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠘⢿⣿⣿⣌⠻⣮⠋⠀⠉⠻⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⡀⠠⠀⠀⢈⢻⣿⣿⡄⠈⠃⠀⠀⠰⣄⡙⢻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣼⣶⣦⣅⡐⣠⣶⣾⣿⣿⡆⢠⣀⠙⠻⣿⡄⠀⠀⢀⡀⠈⠻⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠛⢹⣿⣿⣿⠟⡰⠁⠈⠙⠒⠤⣙⣄⠀⠈⢷⡜⣦⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣟⢁⡀⠈⠛⠛⠕⠊⠀⠀⠀⠀⡀⠀⠀⢛⣷⡄⠈⢻⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣛⣉⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣠⣎⣽⣿⣦⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣩⣵⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣤⡤⠖⠁⢀⡏⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣶⣴⣶⣶⡛⠋⠉⠀⠀⠀⠀⡸⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠁⠀⢈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢝⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⡀⠀⠀⢀⣴⣤⣤⡀⢨⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣻⣿⣷⣴⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⢋⣿⣿⠿⢿⣿⣿⣿⣧⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣥⣿⣿⣾⣿⣳⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⢟⣿⣿⡟⠋⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠟⠛⢻⣿⠏⢿⣾⣿⡶⠟⠋⠛⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠈⠻⣷⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣟⣶⡌⢹⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣾⡿⢧⣬⣽⣿⣿⣿⣿⣿⣷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣷⣶⣶⣶⣶⣿⣭⣭⣉⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣉⠉⠉⠛⣻⣥⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣭⣿⡄⠀⠈⢠⣾⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠟⠛⠹⠀⠀⠀⠉⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠠⡆⠰⠀⠀⠀⠀⠀⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣆⠀⣶⣥⣤⣀⠀⠀⠀⠙⠣⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡼⣿⣿⣿⣿⣿⣆⢻⣭⠅⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⣀⣀⣠⣤⣶⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠟⢀⣿⣿⣿⣿⣿⡇⠙⠆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⣠⡾⣿⡿⣿⣿⣿⠇⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⡟⢁⣼⣿⠞⣋⣾⣿⡟⠙⠂⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣾⡿⠏⣸⣿⣿⡏⠀⠀⠀⠀⢠⠄⠀⠀⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣡⣾⣿⣿⠒⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢟⣯⡿⢻⣿⢇⣿⣷⣿⣇⠀⠀⠀⠀⠈⠀⠀⠀⣠⣿⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⣰⢿⣿⠟⣽⣿⣿⣿⡆⠀⠀⠀⠀⠀⣠⢎⣿⣿⣾⠟⣿⣿⣿⣿⣿⡿⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣡⣾⣿⣾⡿⣷⣿⣿⣿⣿⣷⣌⡰⠤⣶⣾⣷⣿⣿⣿⣿⢀⣿⡿⣿⣿⣿⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢿⣿⣿⡟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣹⣿⣾⣿⣷⣸⡟⢿⣿⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠈⠋⠉⠉⠙⠉⠈⠉⠻⠛⣁⠈⠀⠈⠡⢸⣿⣿⣿⣿⣿⡷⠀⢹⣇⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠈⠟⣹⣿⠀⠀⠀⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠃⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣰⣿⣧⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠐⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠂⡡⠒⡉⢑⢼⠉⠉⠑⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⠞⢀⠎⣁⣲⢹⡇⠒⠄⠨⣮⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⢀⠎⢠⠋⠈⠉⠈⠉⢣⠀⠐⠄⠸⠷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⢃⠎⢠⠃⠀⠀⠀⠀⠀⠘⡁⣄⠈⡄⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠃⠎⢠⢧⣤⠄⠀⠀⠀⣤⣤⢷⡈⠣⡘⣥⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡜⢠⠻⣿⣿⠂⠀⠀⠄⢸⣿⣿⠳⣄⠁⠘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣐⣰⡃⠀⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⡼⡻⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠏⠙⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠘⢦⡀⠲⣛⣛⡳⠂⢀⠾⢰⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠙⣦⣀⢀⣠⡖⢁⢸⢸⠀⡀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣷⠀⠁⠀⡇⠸⢸⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⣠⡤⣦⡞⠁⠃⠀⠀⡱⣢⠤⠬⢀⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠋⠉⠁⠀⠀⠈⠪⢕⣂⣐⡪⠔⠁⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⡞⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢹⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢰⡟⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠃⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢸⡄⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠤⠴⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠚⠧⠤⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠖⠚⠋⠉⠉⠉⠉⠉⠙⠒⠲⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠋⢂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠃⠀⠀⠢⡀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⡎⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⠀⠁⠂⠀⠀⠀⠑⢤⣀⠀⠀⠀⠱⡄⠀⠀⢠⠁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢆⠀⠘⢀⠄⠀⣀⣀⡀⢱⠄⠀⠀⠀⠀⠀⠀⠎⢀⣀⣉⠀⠲⠘⢦⠀⡨⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠸⠃⠦⢨⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠇⠀⣧⠃⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢆⡀⢣⡀⠀⠑⠼⠿⣧⠾⠃⠀⠀⠀⣤⠀⠀⠀⠙⢧⣼⠿⠇⠂⠀⢀⡍⠀⠘⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠷⡈⠀⠂⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠘⠀⣀⠞⠁⠀⠠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⣬⠷⠦⡄⣀⠀⠈⠒⠀⠤⠀⠀⠀⠀⠀⠀⣀⠀⠴⠞⢅⡀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡴⠋⠀⠀⠀⠀⠈⠈⠳⣀⠀⠀⠀⠀⠀⠀⠚⢀⡝⠀⠀⠀⠀⠉⢧⡀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠤⠔⠋⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢀⡴⣋⣀⡠⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣀⡳⣄⡀
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⡇
⣤⠤⢤⣤⣤⣤⣤⠤⠤⢼⠁⠀⠀⠀⠀⠀⠀⠈⢦⠤⠤⠄⠀⠠⠤⠤⠄⠀⠀⠀⠀⠠⠤⠴⠀⠀⠀⠀⠀⠀⢹⣤⣠⣤⣤⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠒⠂⠀⠀⠀⠀⠀⠐⠀⠚⢃⠀⠀⠀⠀⠀⠀⠇⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠘⡟⠃⠀⠀⠀⠀⠈⢦⠀⠀⠀⠄⠀⠠⢜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣠⠀⠀⠐⢆⠁
⠀⠀⠀⠀⠀⠙⣟⡁⠀⠀⠀⠀⠀⠀⠳⣤⣁⡔⠉⠰⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⠐⠀⠀⢁⠾⡙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠀⡄⢰⡙⡄⠓
⠀⠀⠀⠀⠀⠙⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⡡⠶⠇⡀⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠈⡗⠆
⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠃
⠀⠀⠀⠀⠀⠈⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢈⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢈⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠒⠒⠒⠂⠚⠤⢄
⠀⠀⠀⠀⠀⢠⣧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣈⣄⠀⠓⠢⠤⠄⣀⣀⣀⡀⠕
⠀⠀⠀⠀⠀⠠⣧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠰⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠋⠛⠉⠛⠉⠁⠀⠤⠀⠀⠒⠚⠉⠛⠛⠯⠭⠭⠉⠙⠛⠋⠥⠀⠂⠤⠶⠒⠋⠻⡖⢀⠳⠲⠶⠶⠶⠶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠁⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⡟⢉⣤⡄⠀⠉⠈⠉⣵⣬⠉⢹⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⣹⡇⠈⠛⠃⠀⠀⠀⠀⠙⠋⠀⣸⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⡟⠿⣿⣿⣿⣶⣤⠤⣤⣴⣶⣿⣿⣿⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠉⠻⣄⠈⠟⠉⢫⡁⠀⢤⣤⠟⠉⠙⢶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⢷⣦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠤⢄⣀⢀⣀⣀⣀⣀⣀⣠⠤⠴⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡜⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣤⣤⣦⣤⣤⣤⣤⡴⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⢰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠀⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡀⡀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡇⣴⠴⠀⠗⡺⢠⠔⠁⢸⡆⠀⠀⠀⠀⠀⡆⢀⠔⠀⡰⠟⢿⢄⠀⢄⠀⢁
⠀⠀⠀⠀⠀⠀⠀⣷⡋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣇⣠⢒⡉⠀⠀⠀⠀⣓⠢⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠤⠀⠀⠀⠠⠆⠀⠆⠀⠀⠀⠰⠉⢆⠀⠈⠷⠀⠀⠀⠰⠎⠀⠀⡉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡱⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢠⠀⢀⠀⠀⠀⠀⠀⠀⠒⠅⠤⠚⠁⠑⠤⢀⣀⣀⡠⠔⠁⠈⠢⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠒⡎⠀⠀⢑⠒⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⣁⠀⠀⠀⠀⠀⠀⠇⠡⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠉⡇⠀⠀⠀⠀⠀⠀⢀⠀⠇⠀⠀⠀⠀⢰⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢠⠁⢸⠁⠀⠀⠀⠀⠀⠀⠸⡆⠈⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⡘⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠁⢠⢻⠄⠀⠀⠤⠀⠀⠀⢰⡧⠆⢨⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠈⠑⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠰⣁⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠪⠵⠀⠒⠐⠀⠪⠕⠂⠀⠀⠀⠀⠀⠀⠀⠒⠭⠂⠐⠐⠀⠲⠕⠂
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢤⠤⠄⠊⠉⠀⠤⣤⠀⠆⠀⠀⠀⠀⠀⠲⠠⡤⠄⠊⠈⠂⠤⣤⠠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠳⠄⠀⠀⣠⠄⢾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢊⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⣀⡀⠀⠀⠈⠉⠙⠆⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⠂
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠆⠀⠀⠀⢨⡏⠁⠀⠀⢀⣀⡀⠀⠀⠐⠀⢹⡷⠶⢦⡾⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⣿⣿⠇⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢀⡶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⡀⠄⠒⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⣞⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⢠⡀⠀⠀⠀⠘⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠋⠀⠀⠀⠀⠼⠁⠈⠙⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⢀⡱⠀⠀⠀⡄⠀⠀⠛⠋⠛⠻⢿⣿⣦⠀⠀⠀⢰⣿⠟⠋⠉⠉⠙⠁⠀⠀⠀⠀⠀⢀⠻⢤⣀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡶⠶⠶⠶⣤⠈⠉⠀⠀⠀⠈⠁⣤⠶⠶⠶⣦⡄⠀⡆⠀⢠⡄⢲⣶⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣠⡔⢢⣦⠀⠀⠁⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⣤⠀⢣⡄⢘⠇⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢐⡦⠤⠀⠁⡤⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢨⣶⣄⡀⠀⠀⠀⢀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⠀⠈⠀⠐⠢⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣺⠁⠀⠹⣶⣾⠟⠉⠀⠁⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⢤⡊⠀⠀⠀⠀⠀⢀⣤⡄⢀⡌⠁⣦⣔⡆⠀⠀⠀⠀⠀⠀⠀⠲⢤⡴⠂⠀⠀⠀⠀⠀⠀⡘⢯⠏⠰⠏⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣢⣄⣀⣠⠾⠟⢻⣏⠙⠦⢩⡍⠀⣀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣄⡀⠀⠀⠀⠀⣰⡟⠀⠀⠖⠂⠀⠀⠀⠀⢹⣆⣤⣠⣤
⠀⠀⠀⠀⠀⠀⢠⠜⠉⠉⠁⠈⠉⠀⠀⠀⠈⡼⠆⢠⠜⠁⠀⠙⣷⡄⠀⠀⠘⠿⣿⣿⣿⣿⠟⠀⠀⣀⢰⣦⠀⠀⢹⠄⠀⠀⠀⠀⠀⠠⡟⠉⠙⠉⠀⢀⡀⠂
⠀⠀⠀⠀⡠⠀⠀⣀⠰⠆⠀⠀⠀⢀⡄⠀⠀⠀⠉⣸⠀⠠⠲⠤⠛⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢺⣟⡀⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⢸⣦⡀⣀⢀⠀⠈
⠀⠀⠀⠈⣠⡜⠋⠀⠀⠀⠀⠀⠠⣿⣧⡀⠀⠀⠀⠘⢦⣤⡶⣧⢰⡟⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠛⠻⠃⠂⣠⣟⡀⠀⠀⠀⠀⠀⠀⣸⠇⢈⠋
⠀⠀⠀⠉⡴⣙⠦⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣀⣠⡾⠇⢠⠜⠓⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢤⠆⣝⠋⠀⠀⠀⠀⠀⠀⢰⣯⡔⠁
⠀⠀⠀⠀⠀⠛⢦⣤⣤⠀⠐⠒⠋⠁⠀⠀⠀⠀⠈⠻⠋⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢹⡆⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠉⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠦⠶⠆⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣼⣿⣿⠟⠁
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠁
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣶⣶⣶⣶⣿⣿⠿⠛⠉
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣾⣿⡏⠉⠉⠉⠉⠉⠉⠉⠙⠛⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣫⡵⠊⢻⠻⢹⣿⠛⠀⠀⠀⢐⣚⣿⣿⣶⣽⣷⣦⣍⡛⢿⣦⣀
⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣷⣾⣿⠏⠀⠆⠀⢧⡈⠿⢠⠀⠀⠀⠀⠈⠛⢿⣿⣿⠻⣿⣟⠻⣶⣝⣿⣷⡄
⠀⠀⠀⢀⡴⣻⡿⢛⣻⣿⣿⣿⣿⣟⠀⠘⠇⣇⠀⠙⢦⣘⣆⠀⠀⠀⠀⠀⠀⠙⣿⣧⡈⢿⣆⠈⠻⣿⣿⣿⣦
⠀⠀⠀⠏⣱⠋⣰⡿⠛⠟⠋⣩⣿⣿⡀⠀⠈⢺⣴⣰⡀⢈⠙⠻⢦⣄⠰⡀⢢⡀⠈⢿⣷⡀⠹⡆⠀⠈⢿⣿⣿⣷⡀
⠀⠀⠀⠀⢨⠀⣿⢀⢀⣴⠞⠁⣿⢻⣷⡘⣄⠀⠉⠳⣿⣿⣄⠰⣤⡉⠳⣽⣆⢳⡄⠈⢿⣧⠀⠈⠀⠀⠈⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠈⠀⣿⣷⠟⠀⠀⠀⠘⠿⣿⠻⣿⣶⣄⠀⠀⠉⠻⢷⣝⣿⣦⡘⢿⡆⢿⡀⠘⣿⡆⢠⡀⠀⣷⠘⣿⢿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠻⠿⣶⣦⣄⣀⠈⠙⠻⣿⣞⣿⣸⣷⠀⢻⣷⠈⣷⡀⢸⣇⢹⡞⣿⣎⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣠⡴⠶⠒⠛⠛⠙⠛⠿⣦⣄⠈⠻⣿⣿⣿⡆⢸⣿⠀⣿⣧⠀⣿⣼⣇⣿⣿⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣍⡀⠀⠀⠀⠉⢁⡶⢾⣿⡶⣶⣶⠶⠀⠈⠻⣧⡀⢹⣿⣿⡇⠀⣿⡇⣿⣿⠀⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⠟⠀⠀⠀⠀⠈⠁⠈⠛⠁⠋⠁⠀⠀⠀⠀⢻⣧⠀⣿⣿⡇⠀⣿⣿⣿⣿⣴⡏⢻⡟⣾⣿⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⣿⣿⠇⢠⣿⢸⡏⢹⣿⠃⠸⠇⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣿⢰⣿⡿⠀⣸⡇⠘⠁⢸⡟⣠⠀⣸⣿⣿⣿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣀⣾⣿⣿⣿⠇⢠⣿⠀⠀⠀⠈⢀⡿⢠⡿⣿⣿⡟⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⡏⣿⢫⣿⡟⢀⣾⠇⢠⠀⢰⠀⣼⣧⡟⣹⣿⣿⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣷⣤⣤⡄⠀⠀⠀⡾⠀⣾⠀⢫⣿⣿⠁⣼⡟⢠⡏⢠⣿⣴⣿⠏⣴⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⠁⠀⠀⠀⢸⡇⠀⣿⠀⣼⣿⡇⣼⣿⢁⣿⢡⣾⣿⠟⢡⣾⠏⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⣿⡿⣰⣿⢣⣾⣣⣿⡿⢃⣰⠟⠁⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⣸⣿⣷⣿⣣⣿⣿⠟⠉⡰⠟⠁⢀⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠘⣸⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⢧⣿⣿⡟⠉⠀⠀⠀⠀⣠⠎⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⢻⡄⡜⣿⣿⠃⣠⠖⡀⢀⡾⢁⣼⢋⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⡾⣿⡘⣿⣿⣾⣯⢞⡴⠋⣰⠟⣡⡟⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⢿⣽⣿⣿⡿⠋⣠⡾⠋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡜⠻⣿⣿⣷⡾⠋⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⢡⣠⡌⣿⣿⣧⣴⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣾⣿⣿⢁⣼⣿⠃⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⣿⣿⣿⣸⣿⣿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢻⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠃⠉⠈⠁⠈⠀⠀⠈⠀⠀⠃⠈⠀⠀⠁⠈⠀⠁⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠀⣤⡄⠀⡆⠀⠀⠀⣾⣟⣿⣿⣶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⠏⠉⠉⠀⠄⠉⢹⡆⠁⠀⠀⢠⣿⣿⣉⠿⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢃⠀⠁⢠⠀⠀⠞⠋⣴⣶⣀⠀⣾⣟⣤⡟⣷⢿⣽⣿⣧⣄⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⠁⠄⠀⠻⣀⡀⠛⣤⣿⣿⣾⣿⣿⣤⣿⢣⣴⡟⣿⣿⠿⠦⠐⠛⠁⠀⣠⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⢃⡄⠉⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⠀⠀⠀⠀⢀⡿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣽⣿⣿⣿⣦⣀⣀⣠⣉⣡⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠟⠉⠉⠁⠀⠉⠉⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠘⠋⣀⠔⠂⡀⠐⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠛⡙⢫⣟⣛⠛⠿⢻⣿⣿⣿⣿⡏⠁⠒⠃⣀⠘⠁⠀⠂⠀⡀⠘⠃⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⡟⠉⣤⠌⠉⣴⣿⠃⠠⠀⠀⡌⠻⣿⣟⠡⠄⠠⠀⠀⠄⠉⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠚⣡⡄⠀⣿⡇⠀⢤⣶⣦⣀⠛⠿⠏⠠⠈⠡⠀⠀⠀⠋⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿⣿⣿⡿⠀⠂⢠⣿⠉⢀⣿⡇⠀⠰⢿⣿⣿⣿⠀⠈⠁⠄⠀⠀⢀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣮⣷⣿⠿⠋⠀⢀⣴⠟⠁⣠⣿⠟⠀⠀⠀⠀⠀⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠋⣉⣠⣤⣴⠟⠀⠀⠀⠐⠋⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⣻⣯⣤⣶⣾⣿⡿⠿⣻⣥⣶⡆⠀⠀⠀⠀⠀⢠⣴⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣁⣤⣾⡿⠛⠉⠀⠘⠋⣠⣾⣿⣿⣿⣿⣤⡀⠀⠀⠀⠈⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⢙⡧⠀⠇⠀⠀⠀⢹⣿⣿⣿⣿⠀⠉⠛⢶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠈⠙⠷⠀⠀⢲⡄⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠰⣿
⠀⠀⠀⠀⠀⢰⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢁⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣄⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⢠⣄⠀⠀⢨⠿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠠⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⡾⠃⠠⣴⣶⣦⣀
⠀⠀⠀⣀⢷⡄⢠⡜⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⣶⣶⣶⣶⣤⣼⣛⠡⠦
⠀⠀⣼⣿⣸⡇⠈⠀⠀⠀⢸⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣄
⠀⢰⣿⣿⣿⣾⣷⣄⡼⠂⠘⣩⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠻⠿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠙⢿⣿⣿⣿⣿⣅⣠⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠁⠀⢀⣴⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠉⠁⠀⠀⠀⠀⠀⠀⣹⠿⣿⣿⣿⡿⠋⠁⢠
⠀⢻⣿⣟⣡⣼⣿⣿⣿⡿⠋⠁⣀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠀⠈⠻⠿⠀⠀⠀⢀⡀
⠀⣾⣿⣿⠻⠟⣿⣿⣿⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠀⣀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⡸
⠀⠸⣿⣿⣄⠀⢻⣿⣿⣧⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠉⠀⠀⠀⠀⡏⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠃
⠀⠀⠈⠉⠉⠀⠀⠉⢿⡏⠁⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⢻⣤⡀⣀⠀⠀⠀⠀⠚⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⣀⡾⠀⣦⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠁⠀⣠⠟⠁⠀⡏⠀⠀⢠⠈⠁⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⢉⡴⠄⠀⣤⣿⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠛⠻⠿⣦⡀⠀⠀⠀⠀⣀⠴⠚⠉⢀⣴⠟⠁⠐⠀⣿⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⡀⠀⠀⠀⢠⣼⠟⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⠀⢸⡇⠀⠚⠀⠀⢠⣴⠟⠁⠀⠀⠀⠀⢰⡌⢿⣧⡀⠀⠀⠁⠀⠀⠀⣠⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡇⠀⡏⠀⠀⠀⢠⠜⠛⠁⠀⠀⠀⠀⠀⠀⣾⡇⠀⠻⣷⣆⡄⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠈⠟⠁⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⡇⠀⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣆⠀⠀⠀⠀⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠉⠹⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢹⣿⣿⣿⣿⣿⡌⠙⠿⠆⠀⠀⠀⠀⠛⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⣀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠙⠻⣷⡌⠻⣿⣿⣿⡄⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠈⠻⠆⠈⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡍⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠑⠛⡇⠀⠀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠐⠶⣦⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠈⣿⡤⠔⠀⣈⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠠⢶⣾⣯⠙⠿⠿⠒⠢⢤⣤⣽⣿⣿⣾⣛⣿⡦⢀⣼⣿⡆⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣂⠈⢀⣩⣿⣿⣿⣿⣿⡍⠙⢿⣿⣿⣿⣇⡔⠀⢀⠠⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⡟⢻⣿⣿⣿⠏⠀⢀⣾⣿⣿⣿⣿⣿⡟⢛⠤⣀⣄⣈⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣅⣈⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠻⠿⠟⠀⠀⠘⢿⣿⣿⣿⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠪⠻⣧⠠⠀⠀⠀⠠⢆⣈⣿⣿⣿⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⠄⠀⡜⢢⠀⠀⠀⠙⠻⢩⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠄⠀⠘⠁⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⡃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠠⠾⣿⣿⣿⣿⠀⠁⠘⣷⣶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣠⣿⣿⡿⠇⠀⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⣿⣿⣿⠿⠿⣿⣿⣿⣿⠁⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠙⡄⠀⠿⣷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⡏⡂⠀⠀⠈⠻⢇⡀⠘⢀⡿⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠢⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠑⢤⣼⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡳⣄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢊⣿⣿⣿⠷⢶⣦⣀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢱⡇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣇⣾⠟⠋⠁⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⢷⣄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⢷⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⢾⡿⠿⢿⣿⣟⢿⣿⣿⣿⡟⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⢍⠙⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢃⡶⠚⢋⡷⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⢁⠀⣾⣀⣀⣘⣦⢀⣿⠀⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⢬⣦⠌⣩⣤⣽⣛⠻⠯⡛⣦⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⣩⠋⠉⠉⠉⢩⣷⠀⢸⣾⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⢒⡖⢹⠀⠀⠄⡄⠀⣠⡟⠀⣸⡟⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠷⣴⡏⠉⣾⣧⡉⠉⠀⠀⣿⠀⣸⡿⣷⣑⠶⢶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢐⠉⣿⡇⠀⠀⣀⠙⡇⠹⠁⠀⠹⣷⡶⢤⡀
⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⣤⣤⠾⢿⡙⠂⠀⢁⣰⣿⣶⣦⣌⠙⢿⡟⠶⡝⠆
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠲⢦⣘⣇⠀⠀⣿⣿⣿⣿⣿⣿⠠⢠⡇⠀⣰⡄
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠀⣿⡟⢠⡟⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠘⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡀⠈⠀⠈⠻⢦⣄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣍⠂⠸⠀⠸⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣦⣄⡀⢸⡀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠛⠳⢤⡀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣼⠁⢀⡿⠓⠂⠀⠀⠀⠀⠀⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣽⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⡿⢿⣿⣿⡟⠿⣿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠞⠁⠀⠀⠙⠻⣿⣷⣦⣍⣙⡒⠾⢭⣤⣈⡙⠲⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣝⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠋⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣬⣍⣙⠓⠲⢮⣭⣳⢮⣷⣵⡝⣿⣿⣿⣿⣿⣿⣿⣿⣦⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠭⢷⣒⣶⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⠓⠂⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⠈⠀⠹⣿⣿⣿⣿⣿⢧⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠰⠿⠋⢁⠀⣀⣀⣀⡀⢀⡠⠤⠒⠉⠁⠙⣿⣿⣿⣿⣧⡐⢀⣿⣿⣿⣿⣿⣷⡁⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢰⡶⠿⠗⠀⣠⠊⠉⠀⠉⠻⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠸⡟⠘⣿⡞⣿⣾⣿⣿⣿⣿⣿⣿⣷⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣷⠬⢄⣀⢠⣀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣀⡼⡟⢺⢋⠳⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⢃⠀⡇⠀⠙⠢⢄⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣆⠀⠈⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⡇⡿⣸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢠⠉⠉⠑⡄⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣏⠄⠀⠀⠈⢆⢈⡤⠴⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡟⣦⠀⠀⠀⠀⠡⡄⠐⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡏⢿⣿⣿⣿⣿⡟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢱⠘⣷⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⢸⠻⣿⣿⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡇⠈⢿⣄⠀⠀⠀⠀⠈⠂⠀⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠈⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠿⠿⠿⠿⠿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣡⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣴⣿⣿⠿⠛⢉⣀⣤⣴⣶⣦⣄⡉⠻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣵⣿⡿⠋⢀⣠⣾⣿⣿⠿⠟⠛⠿⣿⣿⣦⡈⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⠻⣿⣿⡄⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢠⣿⣿⡿⢁⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢿⣿⣧⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢀⣾⣿⣿⣁⣀⣀⣉⠁⠀⠀⠈⣉⣀⣄⣀⠀⠸⠿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⣼⣿⣿⠇⠛⠿⠛⠙⠆⠀⠀⠐⠛⠛⠿⠛⠀⠀⠀⣿⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⣿⣿⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡿⠀⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢸⣿⣿⣧⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢰⣿⣿⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣿⣿⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣿⣿⣿⡄⣿⣿⣿⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢸⣿⣿⡇⢸⣿⣿⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢿⣿⣷⢸⣿⣿⡇⢸⣿⡄⠀⢀⣄⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠘⣿⣿⡄⣿⣿⡇⢸⣿⠋⠀⠀⠀⠙⢻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⣿⡇⢿⣿⡇⢸⡟⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠘⣿⣿⢸⣿⣇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢻⣿⡆⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠸⣿⣇⢹⣿⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠘⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⢀⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⣤⣴⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣿⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⠋⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⢀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠋⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⣀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠉⠛⠿⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠇⠀⠀⣰⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣟⣿⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⢀⣴⠿⣿⢿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⢽⣿⣽⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⢀⣀⣄⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠙⠻⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠈⣁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠈⠛⠛⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣷⠤⠀⠀⠀⠀⠀⢠⠃⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣜⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⣿⣿⣿⣆⣀⣀⣀⣀⣤⠤⢰⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⠀⢿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢰⣧⠀⢸⣿⡏⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⣿⡀⠀⢿⣿⡄⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢹⣧⠀⠈⢿⣿⡄⠀⠙⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡏⢆⠀⠀⢻⣿⡄⠀⠀⠈⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢷⠘⡄⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⠀⢡⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃
⣿⣏⢹⣟⡻⣿⣛⢟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣃⣴⣶⣶⣶⣦⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣯⡿⠛⠃⠀⠀⠙⢿⣿⡿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣽⣿⣿⣿⣿⡟⠿⢇⣤⢒⣢⣄⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠛⠻⠛⢀⣤⣿⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⣄⠙⣿⣿⣾⣆⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠉⠋⠀⠀⠀⠀⠲⠿⣾⣿⢏⠇⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣫⣦⡀⠀⠀⠹⣯⣙⢶⣿⣿⣦⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡦⣄⡀⠀⢩⡿⠿⡿⡿⠇⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⡷⠊⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⠺⣿⣿⣿⣿⠟⠛⣾⣿⣿⡿⢡⡶⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⢢⡉⠙⡓⠒⠪⠽⠿⠄⠀⣿⣿⡟⢁⣾⢡
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠉⠲⣄⡀⠀⠀⠀⠙⣿⢠⣯⡟⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠻⣬⣿⠃⠘⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠇⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣶⣾⣟⠛⠲⠶⠶⠤⣤⣄⣀⡤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠉⠓⠆⠀⠀⠀⠀⠀⣠⠤⠶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⡶⢲⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣤⡾⠃⠀⠉⠻⠆⢠⡀⠀⠀⠀⠉⠉⠉⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⡜⣿⠀⠀⠀⡇⠀⠀⠀⢠⢶⣆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠛⠛⠀⢀⣼⠇⠀⠀⠀⢻⣾⠏⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⠳⣄⠀⠈⡆⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⠤⣤⣀⠀⠀⠀⠀⠀⢰⣿⣟⣷⠀⠘⢷⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⢷⣄⢀⣴⠏⠀⠀⠀⠀⡠⠘⣿⣌⡁⣀⣠⡾⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⠛⠛⠁⠀⢀⣠⡶⠋⠀⢸⡈⠙⠛⠛⠉⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⣤⣤⡶⠟⠉⠀⠀⠀⢸⣇⠀⠀⠀⣠⠃⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⠀⠀⠀⠀⠀⠈⢿⠀⣠⠞⣡⡾⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠞⢁⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠇⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣧⡀⠙⢷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠉⠙⣷⠄⠀⠀⠀⠀⠀⠀⠀⠷⠶⠋
⠀⠀⠀⠀⠀⠀⢀⣀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⡴⠞⠋
⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠘⢷⣄
⢀⣠⣀⠀⠙⢷⣄
⣿⡹⣿⠇⠀⢈⣿
⠘⠿⢦⣤⡶⠾⠋
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⡄⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣠⣴⠞⠋⠀⠀⠀⠀⣠⠊⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠞⠋⠀⠀⠀⠀⢀⡤⠞⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢿⠏⠀⠀⠀⠀⠀⣠⠴⠋⣠⡶⠋⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⣴⠃⠀⠀⢀⣠⠴⢛⣡⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⢀⣾⣯⣤⣶⣾⣿⠷⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⢀⣴⣾⣿⣋⣤⣤⣶⣶⣾⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⣠⣿⡟⠁⠀⠉⠉⢉⣤⣾⡿⢻⠇⠀⠀⠀⠠⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⢀⡀⠀⠈⠳⣤
⢰⣿⡏⠀⠀⠀⢀⣴⠟⠉⡼⢡⡿⠀⢀⡀⢀⠀⠀⠀⠉⠳⠶⠤⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⢁⣀⡀⠀⠀⠀⠀⠀⢘⢳⡀
⢸⣿⠀⠀⠀⣠⠏⠀⠀⣼⠃⢸⡇⠠⢬⣿⠟⠻⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⣴⢾⣿⡿⢦⣴⣂⡀⠀⢸⠀⠹⣆
⠘⣿⠀⠀⠀⠁⠀⠀⢰⡏⠀⣾⠀⠀⠐⠟⠓⡆⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⡵⠛⠗⠉⠀⠀⢸⠀⠀⠘⣆
⠀⠙⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠴⠫⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⡆⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠚⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠾⠷⠆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣠⠴⠆⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠀⢸⠁⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠤⠴⠖⠛⠉⠀⠀⠀⢸⡄⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣲⣶⡶⣠⢖⠴⣒⠢⢖⠀⣆⣴⣠⣴⣦⠐⢦⠐⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣽⣿⣫⡾⠃⣴⣿⡿⢿⣶⡄⠈⠀⠉⠉⠁⣀⣌⠳⣌⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢫⣟⣵⡿⠁⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⡙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡫⣻⡿⢁⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣝⡳⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣦⣳⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣽⢿⣿⣿⣿⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣣⣿⣳⣿⣿⣛⣻⣿⣶⣄⠀⠀⠀⢠⡶⠟⠋⠉⠀⠀⢠⡿⣿⣿⡿⣧
⠀⠀⠀⠀⠀⠀⢀⣼⢟⣵⡿⣵⣿⣿⣿⣿⢿⣿⠿⣿⡇⠀⠀⢀⡼⣾⢿⡖⠀⠀⠺⢠⡹⣿⣧⠹⡆
⠀⠀⠀⠀⠀⢀⡞⣥⠟⣫⣾⣿⣿⣿⣿⡿⠷⠃⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⢿⣿⠀⣿
⠀⠀⠀⠀⠠⠋⠞⢋⡼⣿⣿⣿⣿⣿⣿⣿⣄⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⢸⣿⠀⢸
⠀⠀⠀⠀⠀⣠⣾⠋⣠⣿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠠⠀⠀⠀⠀⠀⠀⣾⡟⣿⠉⢸⡏⠀⠈
⠀⠀⠀⠀⠊⢡⣇⣼⣿⡿⡽⣹⡟⢠⡻⣿⣿⣿⣿⣿⣋⣁⣀⣀⠀⠀⠀⠀⣰⣿⢇⢻⣇⢸⠇
⠀⠀⠀⠀⠀⠘⣿⣿⡿⣽⢱⡟⢠⢹⣷⣝⢿⣿⣿⣿⣯⣉⣉⠁⠀⠀⠀⢰⣿⣿⣸⠈⣿⢾⣀⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⢣⣿⠁⡌⢸⡏⣿⣿⣿⡻⣿⣏⠀⠀⠀⣀⠔⠁⢸⣿⠇⡏⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡏⣾⡇⡀⠃⠈⣧⣿⣿⣿⣿⣿⣿⣥⣶⣾⠏⠀⠀⢸⠏⣸⠁⠀⠸⡄⠑
⠀⠀⠀⠀⠀⠀⡟⡿⠰⢿⡇⣇⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣠⠏⣰⠃⠀⠀⡄⢻⣆
⠀⠀⠀⠀⠰⡄⠃⢀⠀⠸⣇⣿⡀⠰⡘⣟⣾⣿⣿⣿⣿⣿⠋⠀⠀⣰⠃⡴⠃⠀⡀⡄⢿⡄⠙⣷⡀
⠀⠀⠀⠀⠘⡇⠀⢸⣇⡀⠹⡌⠳⡄⠁⢈⣿⣿⣿⣿⢿⠃⠀⠀⠀⡇⢸⢱⡃⢸⡀⣷⡈⠻⡄⠄⠻⡄
⠀⠀⠀⠀⢰⣟⣧⣠⠻⣿⣶⣦⡀⠙⣷⣄⡹⣿⣿⣻⣆⠀⠀⠀⠀⢻⡸⣿⣧⠸⣷⡘⣷⣄⠀⡀⠀⠹
⠀⠀⠀⠀⠐⠿⣿⣿⣷⣌⠛⠿⣿⣦⡀⠉⠛⠿⣿⡏⣿⠀⠀⠀⠀⠀⠻⣽⣿⣷⡘⢿⣌⠻⣷⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠂⠀⠈⠁⠀⠀⠀⠈⠛⢿⡀⠀⠀⠀⠀⠀⠈⠻⠮⡻⢦⡙⠳⣌⠻⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣛⡻⣿⣭⣯⠻⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏⠁⠀⠀⠀⠈⠉⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣗⣿⠁⠀⠀⠀⠀⢀⡀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣿⣿⣿⢿⣟⣒⣂⠀⠀⣫⣭⣥⣄⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⢻⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⣿⡿⣹⣿⣿⠟⠀⠀⠙⠿⠿⠋⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⣰⣿⣟⣿⣧⡀⠀⠲⠶⠂⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⣾⣵⣟⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣤⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢳⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣶⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣾⢿⢻⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠸⡿⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠐⠃⠀⠀⠈⠉⠉⠉⠉⠋⠉⠙⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⠿⢶⢤⣦⣤⣄⣄⣀⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣴⡶⢤⣉⠉⢉⣓⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⣾⡿⠏⠉⠁⣽⣿⡿⡦⢝⠣⡈⢪⣷⣄⡄⠸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡾⣿⣽⡿⠃⣠⡜⣧⣻⣿⣧⡘⠁⠈⠁⠀⠉⠉⡿⡿⡎⠘⣿⠻⣗⡲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣻⣿⠟⡀⣰⣼⣿⣸⣷⣿⣎⠻⣄⠀⠀⠀⠀⠂⢿⡀⠹⡀⢹⡆⠘⠫⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⢁⣨⣿⣿⣿⣿⣷⣿⢿⣞⢷⡿⣄⠀⠠⠀⠀⠀⢣⡀⠀⡀⢻⡄⢃
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⢏⡴⠿⢿⣿⣿⣿⣿⡻⡻⢷⡙⢧⣹⠆⠑⠄⠀⠀⠀⠀⡙⠆⠀⠈⡿⡜⣆⠀⡄
⠀⠀⠀⠀⠀⣠⢞⣭⣿⣿⣿⣿⣿⠋⠀⠀⠀⠻⢿⣿⣿⣿⣷⣝⢄⠳⠀⠙⢷⡀⠀⠐⢄⠀⠀⢄⠀⣄⡀⠈⠾⣞⢧⣿⡄
⠀⠀⠀⠀⢀⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⣮⢷⣆⢪⣎⣷⣄⡀⣬⡷⣆⢬⣦⠈⢿⠀⠀⢸⣮⢿⡇
⠀⠀⠀⠀⠘⣿⡿⢫⣾⣿⣿⣿⡇⠀⢀⣴⠞⠋⢉⠀⠀⠀⠀⠹⣿⣿⢿⣮⣿⣿⣿⣿⣿⣿⢿⢸⣧⡀⠘⠇⣴⡆⢻⣾⣧
⠀⠀⠀⠀⠀⢿⣧⣿⣿⣿⣿⣿⣿⢠⣾⠃⠀⠀⣠⠀⠀⠀⠀⠀⢹⣿⣎⣿⣿⣿⣿⣿⣿⣿⣸⣸⢻⣿⡇⠀⣿⣷⢲⣻⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣎⠉⠈⣦⣾⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⣸⣿⡇⠀⣿⣿⣿⣷⡽
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠁⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⣿⢏⣁⣁⣿⣾⣡⣼⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣼⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⣤⡄⠐⠀⠀⠀⠀⠀⠈⠛⠩⠾⠛⠛⠛⢿⠏⠀⠈⠘⠋⠉⠉⠙⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣴⠛⠓⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠟⡇⠻⣿⣿⣿⠻⣄⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠝⡌⠀⠇⠀⠈⠻⠿⣇⠘⡀⠀⠀⠀⣀⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠉⠁⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠃⠀⠀⠀⠀⠉⠀⠀⠀⢢⢬⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⠄⢀⠔⠙⢌⠢⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠳⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⡡⠖⠁⠀⠀⠀⠑⢬⡀⢄⡄⠀⠀⠀⠀⢄⡢⠀⢈⢄⠀⠘⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢬⣐⠄⡀⠉⠢⠀⠀⠀⡠⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠅⠶⠊⠀⠀⡤⠄⠤⠄⠀⠀⠀⢠⠄⠄⠠⠤⡄⠉⠒⠬⠴⠀⢒⡆⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢀⡄⢀⠀⠀⠀⠘⡄⢀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠄⠀⠄⠀⠄⠀⠀⠀⠐⡤⠠⠤⠤⢔⠀⠀⠂⠀⠀⡰⠆⠀⠀⡀⠂⢀⠢⣼⡔⠀⠐
⠀⠀⠀⠀⠀⡄⠀⡄⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠠⠂⣱⠀⠀⠘⠃⠘⠁⠀⢿⠀⠘⠁
⠀⠀⠀⠀⠀⣄⠀⣦⠠⡄⠀⠀⠀⡇⠀⠀⠀⠸⠀⠈⠉⠉⠉⠉⠀⠀⢰⠀⢠⠄⢸⡾⠀⣤⠀⠂
⠀⠀⠀⠠⠤⠥⠤⠴⠬⠾⠤⠤⠥⠧⠤⠤⠤⣼⣄⣄⣀⢀⠀⡀⣀⢀⠧⣄⡤⣤⣼⠭⣤⣭⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣒⣒⠒⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⣿⣿⣿⣿⣽⣛⠯⣍⢒⠮⣝⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⣿⣿⣿⣷⣯⡻⣝⠮⣑⠭⣒⠭⢄⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣥⣄⠀⠀⠀⠀⣰⣿⣿⣿⡿⣿⣮⡢⢝⡪⠙⠂⠍⠒⠮⣮⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠁⠀⠈⠂⠀⠀⠀⢸⣿⣿⣿⢿⣾⣝⠯⣲⢍⡙⠲⠤⣄⡁⠪⣻⣷⣾⣟⠯⠉⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠈⠓⠒⠀⠀⠀⠀⠀⠀⢿⣿⣿⡷⣭⡓⢝⠢⣕⠪⣀⠀⡢⣝⢷⣌⢿⣿⢗⡫⠭⠩⠍⠲⣵⡀
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣮⣝⢦⠱⡌⢳⣌⢦⠘⢮⣷⣽⣿⣿⠏⣠⢽⡿⣿⣶⣸⡇
⠀⠀⠀⠀⠀⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡳⡹⣄⠙⣦⡀⢮⡻⣿⣿⣟⡘⡵⠋⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⢀⠀⠀⠈⣷⡑⡑⡜⢆⢪⡻⣦⣙⢿⣿⣿⠀⡄⡄⢠⣿⡟⡇
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄⠘⣮⡳⣝⣮⣝⣿⣿⣿⡄⡇⣸⢸⢸⢱⠇
⠀⠀⠀⠀⠘⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣞⢞⢦⡘⢿⣮⣟⣿⣿⣿⣿⣷⣿⡧⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⢀⢮⣿⣿⣿⣞⢎⢦⣙⠦⠭⠽⢟⣭⣿⣿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⢿⡝⣮⡳⢬⣛⣛⠛⣋⡴⢻⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣟⢮⡻⣮⣙⡒⠒⢒⠚⢉⣴⢋⡇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣝⠲⠭⠭⠭⠴⢚⠋⣡⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⠭⠍⠒⣊⠭⢴⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠑⠲⠤⣀⣠⠤⠖⠘⠉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠲⣤⠶⣇⠀⠀⠀⢠⠖⠂⠒⠒⠋⠀⠀⠀⠀⠙⠂⠒⠒⠢⡄⠀⠀⠀⡸⠶⣤⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠘⡄⠘⣆⠀⣠⠋⠀⡤⠖⠂⢤⠀⠀⠀⢀⠤⠒⠲⣄⠀⠹⣄⠀⡰⠁⢠⠃⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⣄⣼⠁⠀⠀⢸⠁⢰⣿⡆⠁⠀⠀⠀⢰⣿⡆⢘⡇⠀⠀⠈⣧⡠⠃⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢸⠈⡆⠀⠀⠈⠳⠤⠠⠔⢁⣠⣄⠈⠦⢤⡤⠞⠁⠀⠀⢰⠁⡇⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⣤⠶⠚⠉⠀⠀⠀⠀⠀⢀⡰⠃⠀⠘⣄⠀⠀⠀⠀⠀⣀⡈⣁⠈⠁⢀⠀⠀⠀⠀⠀⣠⠃⠀⠘⣄⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤
⠀⠀⠀⠀⠙⠲⠤⣀⣀⣀⠠⠔⠋⠀⠀⠀⠀⠈⠣⣀⠀⠀⠈⢯⡉⠉⠉⢉⡝⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⠢⠄⣀⣀⣀⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠓⠢⠤⣀⣉⡒⣒⣉⣀⠠⠔⠚⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠦⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⠓⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠚⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠈⠙⠛⠒⠒⠶⠶⠒⠂⠛⠋⠉⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⢤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡤⠰⠶⢇⠀⠀⠀⡙⠋⠙⢋⠁⠀⠀⡸⠒⠢⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⢀⡤⢦⡶⢿⠀⠀⠀⣇⠀⠀⣸⠀⠀⠀⡿⢶⡤⢤⡀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⡜⠁⠠⡋⠀⠈⠀⠀⢀⠟⡃⢸⢿⡀⠀⠀⠀⠀⢹⠄⠈⢢⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣄⠀⠀⠉⠒⠒⠒⠊⣡⠜⠁⠈⠣⣉⠒⠒⠒⠒⠉⠀⠀⣰⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠙⠲⠶⠲⠶⠒⠋⠁⠀⠀⠀⠀⠈⠙⠒⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠒⠒⠒⠀⠈⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣻⣛⣛⣫⣘⡛⣿⣛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣏⣿⣭⣉⣹⣿⣿⣍⣛⣛⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢟⡽⠃⠀⠀⠹⠉⠹⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢃⠎⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠌⠀⠀⠀⠀⠀⠀⠀⢰⠇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡵⣴⣤⣤⡀⠀⠀⠀⠀⢠⣮⣤⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢁⣀⣀⡀⠀⠀⠀⠀⢀⠞⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⡿⢻⠋⠛⠛⠂⠀⠀⡠⠃⠐⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢛⡄⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡾⠁⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠠⠤⠄⠀⠠⣄⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠠⠤⠴⠘⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡉⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠒⠤⠔⠒⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⢼⢏⣞⡝⡱⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⣿⢋⠞⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠈⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡼⠁⠁⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⣾⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡠⢞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡿⣡⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣈⣴⠿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡻⣿⣿⣿⣿⣿⡟⠁⠀⠠⠐⠚⠉⣁⣤⣾⣿⠟⣡⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢡⢻⠟⡽⣹⠋⠀⠀⠀⠀⢀⠠⢒⣽⡿⢋⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠸⠁⠉⠀⠀⠀⠀⠀⠠⠐⠋⠊⠀⠝⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⣿⣿⣿⣿⣷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢻⣿⣿⣿⣿⣷⡐
⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠹⣿⠉⢳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡰⠒⠀⢿⣷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⢠⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡠⠀⢀⠀⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠘⠁⠑
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⢀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡁⡀
⠁⠐⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣀
⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣖⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣻⣛⣙⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡐⠐⢶⠄⠦⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⠈⠡⡗⢤⢳⠄⣤⣱⠉⢨⠕⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⢹⣲⠇⠊⠀⠀⣼⣷⣦⣚⣙⡁⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⡖⣸⣤⡾⠎⠀⠀⠀⠙⢯⣟⡟⣷⣿⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠝⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠀⠨⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢺⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠈⠉⠁⣶⠆⠀⠀⣶⡆⠁⢸⣼⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠠⢀⠄⠛⠳⣤⠴⡋⠗⢀⣼⡿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠗⡄⠇⠀⠀⠘⠀⠀⠁⠀⠘⢿⣷⣜⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠁⡄⢸⠀⠀⠀⠀⠀⢰⠀⡄⣎⣿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣏⠀⢄⠀⣸⠀⠀⠀⠀⠀⠸⡁⠀⠏⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠎⢈⠁⠀⠄⠀⠀⢀⠀⠉⠀⢲⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⠛⠃⠀⠂⠀⠀⠐⠀⠄⠀⠀⠘⣯⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠣⢀⣀⣀⣀⠀⠠⠤⠔⠓⠒⠒⠐⠒⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣿⢻⣿⣿⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠘⣴⢿⣹⡆⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⣤⠈⠻⢿⡿⢾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣾⣿⣇⠀⣀⠀⠀⠀⢰⣿⣿⣿⢷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣷⣸⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣟⣿⡿⠀⠀⠀⠀⠈⢿⣹⣿⣿⣿⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣟⠿⡿⣿⣿⣿⣿⣿⣿⣿⠁⢈⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣏⠀⠈⠟⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣡⠄⣠⣼⣿⣿⣿⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣹⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⢻⣬⣿⣿⣿⣿⡿⠁⠀⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠉⠉⠉⠉⠑⠪⢧⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡠⠀⠀⢀⠠⠔⠂⢩⣿⡧⢦⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⢸⠁⡠⠊⠁⠀⠀⠀⠉⠁⠀⣴⡯⢲⠂⠀⠀⡖⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⢸⡐⠁⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⡇⢀⡄⢸⠇⡀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠂⣒⣒⢄⠀⠀⠀⠸⠘⡿⠁⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⢴⠓⠀⡒⢄⠸⣱⣎⠇⠑⡄⠀⢠⠃⣃⠞⢉⣳⡄⠀⠀⠀⠀⠀⠀⠀⠛⣷⣸⡇⠘⠆⣧⠀⠀⠀⠀⢠⠀⠀⢠
⠀⠀⠀⡎⢧⠐⡺⡢⣸⣀⠬⠐⠊⢉⠝⠀⡆⢸⠀⢰⣾⣿⡇⠠⡄⠀⠀⠀⢀⣀⣀⠸⠉⣿⡀⠀⢿⡀⠀⠀⠀⢸⠀⠀⠸
⠀⠀⠠⢀⠏⠑⠒⡶⢋⣀⡤⠔⠚⠓⡆⠀⢰⠆⠀⠘⠛⠛⠁⠘⠁⠀⠀⠀⢉⣩⣿⣷⡵⡈⢷⡀⠘⣇⠀⠀⠀⡟⢠⢃⠇
⠀⠀⢸⠉⠀⠀⠘⠞⣭⡤⠧⣤⠴⠊⠀⠀⠘⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠘⢌⠳⠀⠘⠂⠀⠘⣠⠋⠎
⠀⠀⠀⡀⠀⠀⣀⣀⣀⠠⠏⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⣤⢀⡉⢀⠀⠀⠈⠙⢋⠁⠀⠀⠀⡱⠀⢀⡀⠤⠤⠥⡎
⠀⠀⠀⣏⠉⣁⣀⡀⠤⠐⢺⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠘⢟⡒⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⡜⠀⡔⢁⣴⡛⠙⠲⠱
⠀⠀⠀⢱⠤⠀⠒⠒⠈⢉⡠⢇⠀⠀⠀⣀⣀⡠⠤⠬⠷⣄⡀⠬⠬⠅⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⡀⠈⠀⠟⢀⡴⠃
⠀⠀⠀⠘⠂⠒⠂⠈⠉⠀⣀⣼⣤⢊⣥⡈⠉⠀⠸⣿⠞⢩⢟⠑⠲⠤⢄⣀⣀⣀⡀⣤⠤⢒⡚⠉⠀⠉⣡⠍⢹
⠀⠀⠀⠀⢷⣲⣲⣲⣺⠽⠜⠺⣹⠈⠛⠁⠺⣿⠞⠁⠀⠘⢌⡒⠤⠤⠔⡫⠔⠁⣩⣮⣦⡈⠉⠻⣦⣼⠃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠈⡤⣿⠆⣰⠋⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⣔⠉⠛⠉⢻⣖⢤⠈⠃⣀⠧
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠱⡀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠃⢠⣤⠘⠛⠳⣌⠻⡏⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣀⡀⠘⠛⠀⣴⣄⢹⣇⠀⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢲⠇⠀⠀⠀⠀⠀⡤⢄⡀⠀⠀⠀⠀⢸⠀⠻⠃⠀⣠⡀⠉⢁⡸⠫⣝⡧⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣠⠤⣙⢦⠙⠶⣄⠀⠀⢸⣰⣶⡄⠀⣛⠧⠞⡏⠀⠀⠈⠻⠑⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢉⣒⣤⡉⠁⠸⡤⣠⣤⠴⠛⠛⠛⠛⠶⠀⠀⡇⠀⠀⠀⠐⢆⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠓⠠⢤⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠤⠤⠤⠒⠤⠤⠤⠤⠤⠤⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣦⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠈⠁