Hearing Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⢶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣀⣴⡿⠟⠉⠁⠀⠀⠀⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠿⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠈⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⣰⡟⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠟⠁⠀⠀⢀⣼⠏⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠋⠀⣠⣴⠶⠶⠿⠿⠟⠛⠋⠁⠀⠀⠀⣠⠞⠁⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⢻⣷⣦⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁
⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟
⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣶⣦⣤⣤⣤⣤⣤⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣤⣴⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡕
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢴⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⣻⡿⠿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣶⣿⣿⣿⠿⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠁⠀⠀⢸⣿⣿⣿⣧⣤⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢀⣶⣿⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣴⣶⣿⣷⣶⣤⣀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣾⣿⣿⣻⡿⢋⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣾⣿⡿⠟⡱⠋⠁⢋⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣉⣉⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣴⣾⣿⡿⠁⠀⠀⣽⣿⣦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⡿⠁⠀⠀⠀⣀⣠⣄⣠⣵⣶⣶⣶⣾⡿⠿⠟⠋⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣏⠁⠀⠀⢀⣦⡽⠛⠛⣩⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣬⠋⠀⠀⣸⣿⣿⣿⡿⠀⠀⠀⢀⡴⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠃⠀⠀⢰⡇⠀⠀⢰⣿⡿⠛⠋⠀⠀⣀⠤⢘⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢹⠀⠀⠀⢈⠄⠀⠐⠛⠁⡀⠀⢀⣀⣠⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹⡂⠀⠀⠀⠘⣰⣿⠿⠉⠉⠉⠛⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠸⡆⠀⠀⠈⣷⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢻⡀⠀⠀⠈⢧⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⣿⣀⡀⠀⠀⠉⠠⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠘⢿⣿⣦⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠈⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⠀⠀⠙⢿⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠂⠐⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢤⠤⢤⣤⡤⠴⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠦⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠶⣤⣤⣀
⠀⠀⠀⠀⢀⠴⠋⠁⠀⣀⣀⣀⡀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⣀⣀⣀⡀⠀⠉⠻⣦⡀
⠀⠀⠀⠔⠁⠀⢠⡶⠋⠉⠁⠈⠉⠳⣆⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⢠⡶⠛⠉⠉⠉⠙⠳⣦⠀⠈⢻⡄
⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⢀⠈⢧⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⢀⠘⣷⠀⠀⢻⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⡆⠘⣇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⣇⠀⠸⣇
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢹⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢻⡀⠈⣿
⠀⠀⠀⠀⠀⠹⡛⠲⠤⡤⠤⠤⣄⠀⠀⠹⣌⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠲⠦⠤⠤⠤⣄⠀⠀⠹⣾⡇⠨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢹⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⣧⠀⠀⢹⡇⢸⡇
⠀⠀⠀⠀⢰⣷⡄⠀⠀⠀⠀⠀⠀⢸⠄⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣠⡀⠀⠀⠀⠀⠀⢸⠆⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠇⠀⠀⠀⠀⣠⠟⠀⠀⣸⠁⣼⠁
⠀⠀⠀⠀⢰⡿⠀⠀⣀⣤⠴⠋⠀⠀⠀⠀⠃⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⣀⣤⠶⠋⠁⠀⠀⠀⠃⢰⡟
⠀⠀⠀⠀⠸⣇⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣄⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⠛⠋⠉⠙⠿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷
⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠏⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠋⠀⠀⠀⠀⢠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣠⣿⣿⡟⠁
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⣴⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣰⣿⣿⡟
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁
⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇
⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿
⠀⠀⠈⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣦⣤⣄⣀⣀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⢀⣠⣴⣶⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡿⠋⠁⢸⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠛⠁⠀⠀⠀⠀⠈⠉⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⡿⠋⢈⡇⣸⠇⣿⣿⣿⡿⠛⠿⠀⠀⠀⠀⠀⠠⠶⠛⠉⠉⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⣠⢎⡴⣡⠞⢁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⣶⠦⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠀⢀⠙⠫⣼⡵⣛⣙⠻⠿⠿⠦⠀⠀⠀⠀⠀⠀⠉⢿⣛⠟⠀⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠈⢧⡀⣸⡄⡇⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠄⠀⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢻⢧⣷⡬⠶⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠀⢀⠤⢖⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡧⠀⠀⠀⠈⠁⣀⢾⡄⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣰⠃⠀⠀⠀⡰⠛⠻⣆⠻⣆⠀⠀⠀⠀⠈⢹⠖⠶⠤⣄⣀⣀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢠⠏⠀⠀⠀⠀⡇⠀⠀⠹⣦⠙⢷⣄⠀⠀⢠⣷⣄⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⣀⣼⣧⣤⡴⠃⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⠳⣦⣉⡛⠛⠛⣡⡿⠳⣄
⠀⠀⠀⠀⠀⢰⣏⣴⠶⡞⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠻⣏⠎⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠹⣷⡀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠙⢻⣧⡀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⢹⣷⡀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢀⣴⣾⠟⠛⠉⠉⠙⠛⠿⣷⣄⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⢻⣧⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠹⣿⡀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠘⣿⡄⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠐⠿⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢹⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣸⡏⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢰⣿⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠋⠀⠀⠀⢀⣤⣾⠏⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⢀⣾⡟⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⠿⠿⠟⠋⠁⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⢀⣤⣥⠀⠀⠀⠀⣼⡿⠁⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⢀⣤⡿⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⣀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡉⠙⣦⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣠⠏⠐⠀⢀⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⢱⡄⠀⣴⠃⠀⠂⢀⠌⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⣴⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢀⡇⠠⠀⠀⡌⠀⢠⡴⠋⠩⠙⠛⢿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⡇⡼⠐⠀⠀⠀⠀⠀⡞⠰⠀⠂⠘⢷⡀⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⡅⠀⠀⠈⣿⠁⠀⠀⠀⡘⠀⢀⡇⢶⠀⠀⠀⠀⠂⠀⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡆⠀⠀⡇⡀⠀⠀⡏⢀⠀⠀⢠⢁⠀⢸⡇⠀⣠⠴⡄⠀⣸⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⡇⢰⣧⠟⠀⢀⠛⡄⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⣿⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⢆⠀⠀⠈⠀⣹⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢸⡀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⠇⠀⠀⠀⢳⡈⠳⠦⣄⢰⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⢧⠀⡇⠀⠀⠀⠀⠀⢀⠀⠠⠴⠀⠀⠂⠂⢻⣄⠀⠀⠁⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠘⡄⡇⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⣷⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⢹⠛⢷⣀⣀⣲⠡⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡀⠄⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠈⠁⠀⠀⠈⠉⠉⡇⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠈⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡃⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⡗⠀⠄⠀⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃⠀⠀⠀⠠⠀⠤⠄⠀⠀⠠⡄⠀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠉⠀⠁⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⢀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣴⡟⠛⠛⠛⠛⠛⠛⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⢀⣾⢋⠀⠀⠀⠀⠀⠀⠀⠠⠛⡿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡯⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣴⣿⣟⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣿⠿⠿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⣿⠏⠉⠐⠃⠀⠀⠀⠀⠀⠀⠻⠇⢋⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣧⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡃⢿⣷⣤⣤⣤⣄⣀⣤⣀⠀⠀⠀⠈⠑⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣄⠈⠉⣉⡙⠋⠻⣿⣿⣿⡇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢿⣷⣌⡉⢠⡍⡻⢧⣿⣿⣿⡇⠀⠀⢠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⠀⢻⣿⣿⣷⡔⢳⣼⣜⣿⣿⠃⠀⠀⢼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⢀⠼⠀⠀⡿⠛⠠⠹⣟⣳⣽⡿⠁⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⡡⢂⡄⣠⠇⠀⢠⡾⠛⠛⠉⠀⠀⠀⢰⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠃⣴⠋⠀⢰⡏⠀⠀⠀⠀⣀⣤⣴⣿⠿⠃⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢀⡼⠃⠀⠀⠀⠀⠙⣩⣯⠏⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣄⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠻⠿⠷⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⣠⣾⣿⠿⠛⠛⠛⠛⠻⠿⣿⣿⣦⣄⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠀⠀⠀⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⣿⣿⣍⠛⠿⢿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄⡀⠈⠻⣿⣿⣦⣀⠈⠻⣿⣷⡄⠀⠀⠀⠀⣾⣿⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣄⠈⢿⣿⣿⣷⠀⢹⣿⣧⠀⠀⠀⢰⣿⠇⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⣿⣿⡆⠈⢿⡿⠏⠀⢸⣿⡿⠀⠀⢀⣿⡏⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠻⠟⢁⣀⣀⣀⣀⣤⣿⣿⠇⠀⢀⣾⠟⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠀⢀⣼⣿⡿⠿⣿⣿⠿⠟⠋⠀⢀⣾⠏⠀⠀⢀⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠉⠛⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣀⠀⠀⠀⣀⣤⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠶⠶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣴⣤⣷⣾⣿⣾⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠿⠿⠯⠭⠭⠿⠿⠿⠿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡋⠁⠈⠉⠁⠀⠀⠀⠀⠀⠐⠂⠀⢀⠬⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡷⢉⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠐⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣴⠏⠀⡴⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠥⠒⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣧⣿⡼⢡⡏⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠭⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣻⡿⣻⠇⣾⠀⠏⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠁⠐⠨⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡣⠞⡫⠔⢋⠴⢃⡼⠀⠀⠸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠄⡙⢷⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠠⡋⠀⠀⠀⠀⠈⠀⠞⠀⠃⠴⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⡀⢹⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⢉⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠠⠑⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⡈⠢⣀⢻⡆⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢌⠣⡈⢺⣧⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⣛⣽⢿⣿⢟⡿⣿⣷⣦⣀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⡌⠢⣿
⠀⠀⠀⠀⠄⠇⢰⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠯⠵⠛⠑⠋⡸⢣⠞⣿⢿⣦⡀⢸⠀⠸⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⠢⣽⠂
⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⠀⠀⠀⠀⠀⠙⣿⣿⣇⠠⠄⠀⠀⠀⠁⠼⢡⠿⣹⢿⣾⠀⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠢⣿⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣩⡀⠀⠀⠀⠀⠀⠐⢁⠞⣹⣿⡇⠏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢦⣿⠀⠀⠀⠀⢀⠀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⢿⣭⣍⡀⠀⠀⠀⠀⠀⠐⢃⡟⢻⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢢⣿⠀⠀⠀⠀⠀⠀⠠⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⢿⣭⣀⠀⠀⠀⠀⠀⠈⠰⠇⣹⣧⡄⠀⠀⠀⠀⠀⠀⠈⠲⡘⢠⡿⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠛⢄⠀⠀⠀⠀⠀⠀⠐⠩⢿⣿⡄⠀⠀⠀⠀⠀⠉⠀⠱⣸⡇⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠠⡘⢀⢠⣿⠁⠀⠀⠀⠀⡄⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣟⢎⠻⣷⡉⠖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠀⠀⠀⠀⠀⠁⠌⣼⡏⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠹⡄⡀⢉⢢⠄⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠳⣠⡿⠀⠀⠀⠀⠀⠀⢰⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠂⢀⣰⣿⣿⣿⠿⡱⢀⣀⣦⣼⣼⣷⣷⣾⣶⣦⣵⣄⣀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠠⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⣏⣲⣿⠟⠉⠁⠀⠀⠀⠀⠀⢄⠀⡉⠻⠿⠷⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⡆⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⠄⣸⠀⡁⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⡆⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠃⡜⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡆⠀⠀⡆⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⣄⣼⠏
⠀⠀⠈⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠿⢀⠁⣠⡴⠟⠁⠀⠀⠀⠀⡇⠀⠀⡀⢀⡿⠃
⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡼⠞⠋⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⣼⠟⠁
⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣤⡾⠃
⢀⡾⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠀⣬⡾⠋
⡸⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⢀⠀⠀⠀⠀⡄⠀⡄⠀⣤⡾⠋
⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸⠀⠀⢸⠀⡇⠀⢰⠀⣰⣴⠞⠁
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⡇⢸⢠⡆⡀⢂⣡⣤⡾⠟⠋⠁
⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⡿⢠⠁⠈⣬⣴⠷⠛⠋⠁
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⣼⢰⣀⣤⡾⠟⠉
⠀⠻⣴⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠅⡆⠸⢀⣼⡾⠛⠁
⠀⠀⠹⣦⡄⠀⠃⠀⠀⠀⠀⡄⠀⠀⢠⠀⡄⠖⢰⣤⡿⠛⠁
⠀⠀⠀⠈⠙⠷⣤⣄⣀⡇⠀⠁⠔⢀⣂⣠⣴⠾⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢠⣿⠂⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⢀⣠⡶⠿⠻⢷⣦⡀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢠⣾⠋⠀⠀⠀⠀⠹⣷⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⢀⣴⠄⠀⢸⡟⢀⣿⠃⢀⣤⣶⣶⡶⣶⣿⠀⠸⠇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢀⣾⠏⠀⠀⢸⡇⣸⡏⢠⣿⠋⠀⢀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⣿⡇⢸⡇⠀⠀⠈⠋⠁⣠⣄
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣧⢻⣇⠘⣿⣄⡀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⣿⡆⠀⠀⠈⣿⡌⢿⣄⠈⠙⠻⣷⣄⢸⣧
⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠸⣿⡀⠀⠀⠹⣷⡀⠙⠿⠆⠀⠈⢿⡆⠹⠗
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠈⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠉⠁⠀⠀⠉⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⣠⣶⡶⠶⢤⣄⡀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⡴⠉⠈⠉⠀⣠⣾⠏⢙⣷⣄⠀⠀⠉⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣼⠁⠀⠀⢠⡞⠁⠀⢀⡌⠁⠙⣆⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢰⡋⢀⠀⡰⠛⠁⠀⠀⠈⠀⠀⠈⠉⣧⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣼⠑⢋⡞⠁⠀⠀⠀⠀⠀⣀⣀⣰⣶⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣷⢀⡟⠀⠀⠀⣠⡴⠶⠟⠛⠉⡹⠋⡟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠱⣯⣼⠁⠀⣠⣟⣡⠀⠀⠘⠀⠀⠀⡠⠃⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⡇⠀⢰⡏⠙⠧⠀⠀⡀⣠⠶⠋⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢹⣿⠀⢸⣇⣤⠀⢠⠟⠋⠁⢤⣤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⣿⣆⠘⢿⠿⠂⠀⠀⠀⠀⢸⠟⠗⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⣍⢦⡈⠳⣭⣦⣄⠀⠀⢺⣧⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠻⣧⡙⢄⠈⠛⠧⠀⠀⠈⠙⠻⣿⣷⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢿⡀⠙⢦⠀⠀⣶⠲⢦⣄⡉⢁⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠳⢾⣦⣅⣤⠏⠀⠀⠉⠻⠛⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠉⠁⠀⠀⠀⠠⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣤⣤⡶⠟⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣉⣀⠀⠠⠀⠈⠉⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠉⠉⣻⣵⣤⣤⣤⣤⣤⣄⣀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠟⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣯⣄⠉⠑⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠁⢀⣴⣾⣿⣿⣿⡿⠉⠀⠀⠙⣿⣿⣿⣧⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡽⠀⢠⣾⣿⡿⣟⠳⠊⠉⠀⠀⠀⠀⠀⣾⣿⣿⣿⢂⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⣿⡿⠁⢱⠳⠐⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡇⢾⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⡟⡇⠀⠠⠋⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⣿⡇⡇⠙⠰⠂⠀⢀⣼⣿⣿⣿⣿⡿⢿⣽⣿⣿⣿⠿⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⣾⣿⠁⠇⣇⠘⠀⢠⣿⣿⠿⠛⠋⠁⣀⣼⣿⣿⣿⡿⠃⠈⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⠀⠀⣿⠀⢠⣿⡿⠃⠀⣠⣶⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢠⣿⣿⢀⠀⠃⠀⣾⡟⣠⣦⣾⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡜⢿⣿⣿⠀⠀⢰⣿⣿⡟⠛⡻⢛⣿⡿⣿⣷⣶⣿⣷⠿⢺⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⣿⣿⠀⠀⢸⣿⣿⣧⣶⣶⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠐⡂⢻⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠁⠈⢿⣇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⢶⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⢿⡄⠀⠀⠀⠉⣛⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⠀⠈⢧⠀⠀⠀⠈⢉⣠⡌⢻⣿⣿⣿⣿⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⣧⠀⠀⠀⠀⠙⠂⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠁⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⣄⣀⣀⠤⡢⢄⣴⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡷⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁


⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⢶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠁⠀⠀⠀⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠈⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⣰⡟⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⢀⣼⠏⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠋⠀⣠⣴⠶⠶⠿⠿⠿⠛⠋⠁⠀⠀⠀⣠⠟⠁⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⢻⣷⣦⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣶⣦⣤⣤⣤⣤⣤⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣄⣠⣴⣾⣆⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠿⠋⠀⠀⠉⠛⠛⠛⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢁⡅⡸⢃⢿⣿⣿⠙⠛⠀⠀⠀⠀⠰⠛⠉⠉⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠠⣎⢞⣵⣣⣼⣿⣿⡀⠀⠀⠀⠀⠀⢤⣶⣽⠑⠂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⢠⡈⠹⡏⡖⢲⠉⠉⠉⠀⠀⠀⠀⠀⠀⠳⠊⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠱⣾⣣⣡⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⡦⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠇⢀⠤⢖⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢻⠀⠀⠀⢁⣠⡿⣄⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⡖⠉
⠀⠀⠀⠀⠀⠀⢀⡴⠁⢠⠃⠀⠀⢀⠉⠈⢷⡙⣦⡀⠀⠀⢀⡏⠉⠓⠒⠦⠤⠜⠁
⠀⠀⠀⠀⠀⢀⣞⣀⣠⠃⠀⠀⠀⢸⠀⠀⠈⠻⣄⡛⠶⣤⡾⢻⡶⡄
⠀⠀⠀⠀⢸⣫⡭⡝⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⠙⠛⠶⠶⠛⠀⠹⡆
⠀⠀⠀⠀⠘⢿⠜⠀⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠻⡄
⠀⠀⠀⠀⠀⠙⡄⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⠾⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠉⠙⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠿⢿⣶⣄⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⢠⣤⣄⠈⠻⣷⡀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠈⠉⠻⣷⡀⠘⢧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣄⣀⡀⠀⠀⠀⠘⣷⠀⠈⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡉⠙⠛⢶⣄⠀⠀⢹⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠳⣄⠀⠀⠙⢆⠀⡼⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⡈⠀⠀⠀⠈⠀⠁⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠉⠉⠛⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⣠⠴⠦⢤⣀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡴⠞⠁⠀⠀⠀⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⡾⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⣀⣠⣤⣤⣤⣄⡀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢠⣾⣿⡿⢿⣿⢿⡿⣻⢿⣷⣦⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⢰⣿⣿⣷⣿⣥⣂⢕⢌⠪⡫⠙⢻⣷⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⣿⣿⣿⣿⠟⠙⠻⢷⣕⠀⠀⠀⠀⣸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⣿⡟⠁⠀⠀⠂⠀⠈⠂⠀⠀⠀⣻⡇⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠐⣿⣿⣿⣄⠀⡈⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⣿⣿⣿⡏⠳⡄⠀⠀⠀⠀⠀⠀⢻⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡅⠀⢹⡄⠀⠀⠰⡄⠀⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠈⡇⠀⠀⠀⡇⠀⡿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣟⠁⠀⠀⠠⡇⠀⠀⢠⡇⠀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⣿⡟⠣⢀⣠⣴⠾⠁⠀⢀⠞⠀⡀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⣿⠿⠷⠗⠛⠉⠁⠀⠀⠊⢀⡤⠂⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢿⣷⡀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⢧⣉⠀⣀⡤⠞⠉⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⠉⠁⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⢀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⠿⠿⠛⠉

⠀⠀⢀⡤⠖⣛⣋⣛⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣛⣙⣛⠲⢤⡀
⠀⣰⢋⡴⠋⠉⠀⠈⢻⡄⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢠⡟⠁⠈⠉⠛⢦⡙⣆
⢰⠃⡾⠀⠀⠀⠀⠀⠀⣷⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⣿⠀⠀⠀⠀⠀⠀⢷⠸
⣿⢸⡇⠀⠀⠀⠀⣀⣠⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣄⣀⠀⠀⠀⠀⢸⡇
⣏⢸⠀⠀⢀⡴⢛⣩⠞⣃⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣘⠷⣍⡛⢦⡀⠀⠈⡇
⣿⢸⡆⠀⢸⠀⠠⠖⠋⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠙⠲⠄⠀⡇⠀⢰⡇
⠹⡄⢷⡀⠈⠳⣤⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⡤⠞⠁⢀⡾⢠
⠀⠹⣆⠻⣦⡀⠈⢧⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⡾⠁⢀⣴⠏⣰⠏
⠀⠀⠈⢷⡀⠙⢦⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⡴⠋⢡⡾⠁
⠀⠀⠀⠀⠙⣦⡀⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⢀⣴⠋
⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⣤⡴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⣻⢛⣿⣿⣷⣄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡕⣄
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣆⠩⠞⢻⢿⣿⣿⣶⣿⣿⣿⠟⠉⠐⠈⠙⠓⢀⣿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣟⠃⠈⠀⠀⠉⠿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣾⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⠊⠀⠀⠀⠀⠀⠀⠘⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣾⡇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⣿⣿⣽
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⣵⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⡀⢠⣆⡐⢠⣤⣰⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣆⢳⡄⢠⣤⣶⡟⣿⣷⣶⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠉⠀⠀⠀⠀⠀⠈⠙⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⠀⠀⠀⠀⢠⣶⣿⣿⣯⣭⣻⣷⣤⣄⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣰⣿⠿⠋⠉⠛⠟⠗⢱⣾⣿⣷⣄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠃⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⡆⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠀⠀⠀⠀⠀⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⢿⣷⡄⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠈⢿⣿⡄⠀⠀⠀⣸⣿⡿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⢸⣿⣷⠀⠀⢰⣿⣿⠃⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣀⠄⠈⣿⣿⠀⠀⣸⣿⠃⠀⠀⣼⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⡰⡸⣻⡏⠀⢀⣿⠃⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠻⠿⢋⡖⠀⣰⡛⠁⠀⣼⠃⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⢀⣬⡽⠾⠟⠋⠀⠀⣼⠃⠀⣠⣿⡿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⢠⡟⠋⠀⠀⠀⠀⠀⠐⠃⠀⣴⣿⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣶⣦⣤⣤⣴⣶⣿⠧
⠀⠀⠀⠀⠀⠀⠀⢜⡟⡿⢫⠟⠁⠩⢛⡻⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠴⣣⠞⠁⠁

⡀⣀⢀⣀⢀⡀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⡀⢀⢀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⣠⡾⠋⢁⣀⣀⣀⣀⠉⠻⣦⡀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠈⣿⠀⠀⠀⠀⢠⡟⢀⣴⠛⠉⠉⠉⠙⢳⣄⠘⣧⠀⠀⠀⠀⢸⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣷⠀⢹⡆⠀⠀⣤⣼⣷⢸⡇⠀⠀⠀⠀⠀⠀⣿⢰⣿⣤⡄⠀⠀⣾⠁⢰⡟
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠸⣧⠀⠀⠛⠻⡿⢸⡇⠀⠀⠀⠀⠀⠀⣿⠸⡿⠛⠃⠀⢀⡿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠛⢷⣄⠀⠀⠈⠻⣦⣀⣀⣀⣠⡾⠃⠀⠀⢀⣴⠟⢻⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠙⢷⡀⠙⢷⣄⠀⠀⠈⠉⠉⠉⠉⠀⠀⢀⣴⠟⠁⣠⡟⠁⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⠻⣦⠀⠉⠳⣆⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡾⠋⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠀⠀⠀⠙⣷⡀⠀⠀⢠⡟⠁⠀⠀⠈⠁⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠸⣇⠀⢀⣿⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⠀⠸⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣤⣄⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣿⣿⡿⣻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⡽⠋⠐⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⢿⣿⣿⡇⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⡇⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠤⢄⣀⣀⣠⣴⣾⣿⠟⠁⠀⢀⣾⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⣲⡷⠷⢿⣿⣿⣿⠟⠋⠉⠀⠀⠀⣠⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⢰⠟⠁⠀⣼⣿⣿⣿⠃⠀⠀⠀⣤⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡎⠀⠀⣼⣿⠿⠟⠁⠀⢀⡄⢞⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡃⠀⠐⠛⠁⠀⠀⣀⣀⣤⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠸⡆⠀⠀⠀⣠⣾⠿⠋⠉⠉⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡄⠀⠀⢿⡀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢹⣀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢧⡀⠀⠀⠻⢄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⣷⣤⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠻⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡠⠐⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠛⠒⠉⠉

⡀⣀⢀⣀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠦⠖⠹⣉⠛⠛⢋⣉⣉⣁⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠛⠉⠡⣀⡀⠀⠠⠤⣶⣷⣿⣿⣿⠟⠛⣛⠛⠻⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⡁⠀⠁⠤⠀⣈⣀⣐⡶⣶⠿⠟⠙⠛⠛⣛⠋⢭⡙⠢⡈⠙⣿⠿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠏⠂⠀⠈⠂⣤⠀⠀⠉⢩⣭⣴⡖⠲⠾⠋⠙⠋⠹⠛⢶⣵⣄⠑⢄⡘⠳⣌⣿⣦
⠀⠀⠀⠀⣠⡿⢣⠚⡄⠰⢄⡀⠀⠀⠀⣠⣤⡶⣾⣭⡉⢠⣤⣬⣠⣴⣄⠀⠘⢻⠳⣬⣿⣶⣬⣼⣻⣷
⠀⠀⠀⢰⣿⠣⣌⠳⢀⡀⠀⢙⣶⡾⠿⢟⣋⣁⠀⠀⠐⠒⠀⢉⡙⢶⡉⠳⣆⡀⠳⠆⣩⣽⣿⣿⣿⣿⣇
⠀⠀⠀⣿⡿⢦⠈⠑⠦⠙⣛⣩⣉⣙⣿⣿⣦⣤⣁⣠⠀⠴⠆⡀⠐⢈⡹⠆⣈⣹⣷⣦⣍⠡⠬⣛⣷⣾⣿⡄
⠚⠦⢀⡿⠤⠈⠓⠶⣤⣤⣬⣬⣽⣿⣿⣟⠛⢛⠛⠉⠐⠒⢦⡄⠒⢄⠙⢶⣄⣀⣁⣀⣀⠠⣤⢤⣜⣻⣿⣇⠴
⡇⠀⠈⣿⣧⣄⣂⣤⣤⣤⣤⣿⠿⠿⠛⠛⠛⠛⠻⠷⣶⣦⣤⣈⠣⣄⣱⣤⣬⣭⣭⡽⠿⠟⠓⠲⠈⣹⣿⡏
⡇⠀⠀⣿⠿⡟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣾⡿⠛⠛⠛⠛⠂⠚⠚⠉⠱⣤⠛⣿⡇
⡇⢠⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠟⢛⣛⣛⣋⣉⣉⡹⣿⣾⣿⠁⡄
⡇⠸⠃⢸⡆⠀⠀⠀⠀⢰⠞⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⠣⠀⠀⠈⢻⣿⡿⠲⡇
⠀⣆⠀⠈⣧⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⣰⣿⠇⠀⡰
⠀⠈⠳⠤⢸⣧⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣿⡏⣤⡶⠁
⠀⠀⠀⠀⢹⣽⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⣹⡟⠁
⠀⠀⠀⠀⢸⠏⠈⡿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⡰⡿
⠀⠀⠀⠀⣿⡀⠣⠈⠆⠉⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣟⠏⠀⠀⣸⠁
⠀⠀⠀⠀⢿⣧⠀⠀⠀⠸⠀⡌⠙⠷⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⢿⣏⠓⠤⠀⠀⡀⣿
⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⡀⠀⠌⢠⡾⠉⠉⢿⡟⠛⠓⠚⠛⠛⢻⡿⠉⠉⢳⡤⢤⡀⠐⠢⠈⢠⡝
⠀⠀⠀⠀⠀⣼⢀⠁⠀⢀⠁⠰⣤⡟⠁⠀⠀⠾⢧⠀⠀⠀⢀⡼⠉⣡⡀⠀⠀⢷⠀⠀⠀⠐⢲⡿⠁
⠀⠀⠀⣠⡾⠅⠊⠀⠁⠈⠂⠱⣈⠃⠀⢀⡼⣦⠘⢧⡀⠀⢸⠃⣰⠏⢱⡀⠀⠀⣟⠁⣠⡴⠋
⠀⠀⣼⠟⢁⠀⠁⠀⣰⠶⠖⠻⠏⠀⠀⡘⠀⠘⢧⡈⠳⠶⠋⢠⡟⠀⣸⠇⠀⠀⢸⡟⠁
⠀⠀⢿⣄⣠⣃⣠⠞⠁⠀⠀⠸⠀⠀⣰⠻⡄⠀⠈⠳⢄⣀⡰⠏⠀⢠⡏⠀⢇⠀⠀⢤
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢰⠇⠀⢰⡄⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡾⡇⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⡎⢿⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣇⣸⡇⠹⠀⠀⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣠⡷⠋⠉⢙⠿⠒⠶⠒⠒⠒⠲⠖⠒⠛⣏⠑⢲⣧⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⠋⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠸⣆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⢠⡎⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠘⣀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⣰⣟⠁⢀⣦⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⢣⡄⠀⣻⡆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⢿⣮⡽⣿
⠀⠀⠀⠀⣠⠞⠉⠻⡟⠉⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢻⠀⠉⠒⣆
⠀⠀⠀⠀⢻⣤⠀⣶⠘⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠻⢆⣀⣤⡍
⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢣⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠛⠛⠓⢲⡶⢶⣶⣶⠚⠛⠛⠉⠀⠀⠹⣥⠤⠴⣿⠁⠈⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⣤⠇⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⡤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣀⣀⣽⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣴⠋⠀⠈⠁⠈⣷⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠈⢳⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢐⡋⠉⠀⠀⠀⠀⠀⣠⠞⣻⠀⠀⠀⠀⠀⠀⢸⡛⢶⠀⠀⠀⠀⠀⠀⠉⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣵⣶⣶⣶⣶⣶⣶⣿⣶⣯⣤⣤⣤⣤⣤⣤⣤⣿⣾⣷⣶⣶⣶⣶⣶⣶⣥⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⠛⠛⠿⠛⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣠⣤⣤⣤⣤⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠟⠛⠛⠛⠛⠛⠻⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⣠⣴⣶⣿⠿⠿⠿⢿⣶⣦⣀⠀⠀⠈⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⢠⣾⣿⠟⠁⣀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⢠⣿⢫⡟⣠⣾⠃⠀⠀⠀⠀⠀⠀⢀⠙⣿⣦⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⠟⣻⣧⢴⡇⠀⠀⠀⠀⠀⠀⢧⠈⣿⡆⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠛⠁⠾⠄⠒⠀⠀⠀⠀⠀⠸⣇⠘⣿⡀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠀⠀⠻⣄⠀⠈⠉⠻⣿⣦⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⡀⠀⠈⠳⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⢸⢁⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠷⢤⣀⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⡎⢸⡇⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠉⠀⠀⠀⠀⢻⡄⠀⠀⠀⠁⣿⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣸⠃⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⡼⠀⠀⠀⣰⠋⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠁⠀⢀⣀⣀⣀⣠⣤⠴⠚⠁⠈⠀⠀⠀⡴⠃⠀⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⡾⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⠀⠀⢀⣀⣠⣤⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⡿⢿⣿⠿⢿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣦⣽⣤⣶⣤⣼⣦⣴⣿⣵⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⣀⣴⣶⣄⡈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠿⠟⠉⢹⣦⡘⢦⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣦⣄⡀⠈⣿⣷⠘⣇⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⣿⣿⣿⡟⠛⢷⡄⢹⣿⢀⣿⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣝⣿⣿⣿⠀⠀⠁⢸⡟⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⠿⠓⠙⠀⠀⠀⡼⣱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠖⠒⠂⠀⠀⢀⠠⢊⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠶⠂⠀⠀⠀⣡⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣴⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⣀⣤⣴⡆⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡿⠛⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠷⠋⠀⠀⠛⠛⠛⠛⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⡍⣸⢃⢿⣿⣿⠛⠻⠀⠀⠀⠀⠰⠚⠉⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠠⢞⡝⣵⣋⣼⣿⣿⡀⠀⠀⠀⠀⠀⢤⣶⣽⠑⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠰⡀⠙⡏⡐⢲⠉⠉⠉⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⣾⣷⣱⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠇⢀⠤⢖⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢛⠂⠀⠀⢈⣠⡾⣆⠀⠀⠀⠓⢤⣀⠀⠀⠀⠀⠀⢀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⠏⠀⠀⠀⠏⠀⢻⡜⢧⡀⠀⠀⢀⡏⠉⠉⠒⠲⠤⠞
⠀⠀⠀⠀⠀⢀⣼⣁⣠⠏⠀⠀⠀⢸⠀⠀⠀⠙⢦⣙⠷⠶⠾⣻⡷⣄
⠀⠀⠀⠀⢰⣯⡶⡾⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠘⣆
⠀⠀⠀⠀⠈⢻⡕⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠹⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢹⡄
⣀⣀⣀⣀⣀⣈⣣⣀⣀⣠⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣷⣤⣛⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣻⣻⣟⣙⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣟

⠀⠀⠀⠀⢀⣠⠴⠶⠛⠛⠛⠛⠛⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠛⠛⠲⠶⢤⣀
⠀⠀⢀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤
⠀⣠⠋⠀⠀⠀⢀⣠⡴⠶⠶⢦⣤⣀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⣤⣀⠀⠀⠀⠈⢳⡀
⢰⡏⠀⠀⢀⣴⠋⠀⢀⣠⡤⠶⠶⠿⠷⣆⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢀⡴⠿⠶⠶⠦⣤⣀⠀⠉⠳⣄⠀⠀⠈⣷
⣾⠀⠀⠀⣼⠃⠀⣰⠏⠁⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠉⢷⡄⠀⢹⡄⠀⠀⢸
⣿⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠘⢦⡤⠴⠀⠀⠀⠀⠰⠦⣤⣤⠞⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸
⢻⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣸
⠘⣇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢨⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⡟
⠀⠹⣆⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⡾⠁
⠀⠀⠙⣦⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠙⠀⠀⠈⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠀⠀⠉⠁⠀⠀⠀⠀⢀⡴⠟⠁⠀⢠⡞⠁
⠀⠀⠀⠈⠳⣄⠀⠀⠈⢳⡀⠀⠀⠀⣠⣤⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⣤⡀⠀⠀⠀⡰⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠛⣦⠀⠀⢷⡀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣰⠇⠀⢠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠋⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠶⠚⠋⠁







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡛⠋⠀⣰⠿⡆⠀⢸⠛⢻⡄⢸⡋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡋⠁⢠⡿⠶⢿⡀⢸⠛⢯⡀⣀⠙⣷
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣾⣷⣶⣾⣷⣾⣶⣾⣷⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⠶⠶⠶⢤⣤⣄⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣀⣤⡴⠶⠶⠖⠒⠒⠒⠚⠛⠛⠋⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢸⡏⠀⠀⠀⣀⣀⡀⠀⠀⠀⣠⣤⣤⡀⢸⡇
⠀⠀⠀⠀⠐⠒⠒⠲⠦⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠘⣧⠀⢠⡞⠉⠉⠻⣦⠀⢰⡏⠀⠈⢻⡜⣿
⠀⠀⠀⢀⡔⠀⠢⣀⡀⠰⢆⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠃⠀⢸⡇⣴⣶⡀⢹⡆⠸⣧⣾⣿⡌⣇⢿⡟⢷⣄
⠀⠀⠀⠀⡗⡶⠚⠤⠈⢹⣿⣷⣉⠑⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠿⣤⣶⡛⢶⣄⣿⠀⠀⠘⣷⣻⣿⡇⢸⡇⠀⠻⠟⠟⠁⠟⠘⣷⠀⠹⣇
⠀⠀⠀⠴⡷⠚⢻⣷⠶⠾⡿⢿⣏⣘⠻⣦⢻⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡴⠶⢦⣌⠙⠷⠙⣿⡇⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⢶⣦⡀⠀⠸⣧⠀⣿
⠀⠀⠀⠀⣇⣀⣀⣉⣤⣤⣁⣸⡀⠈⢷⡼⢾⣧⠀⠀⠀⠀⠀⠀⣼⠁⡿⠀⠀⠀⣿⠀⣠⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⢻⡆⣿
⠀⠀⠈⠉⣏⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣠⢯⣧⡱⣤⣀⠀⠀⣀⠿⡄⠀⡀⠀⢀⢍⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⣿⠇
⠀⠀⢀⣠⠭⠖⠒⠊⠉⠉⠉⠉⠙⠒⢤⡙⢾⡳⣅⠴⠜⠛⣃⣲⡿⣶⣦⠜⣖⢹⣾⣿⣿⡷⠤⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⡟⣑⠿⡿⠤⣿⡇⣺⡟⣲⡿⣸⡻⠿⠛⠛⢒⠀⠀⠀⠀⢀⡾⠛⠛⠶⠶⠶⠶⠶⠞⠋⠁⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠙⠭⣟⣟⠒⣛⣓⣩⠿⣶⣊⠁⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠊⠉⠀⠀⠀⠀⠈⠙⠻⠶⠶⠶⠞⠋⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠙⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣴⣞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠙⠻⢦⣄⡀⠈⠉⠉⠉⠉⠉⣽⠛⢷⣽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣤⣄⣾⠁⠀⠀⠙⢿⠏⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠒⠶⠶⣤⣀
⠀⠀⠀⣠⠞⠉⠀⠀⢀⣀⡀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⢀⣀⡤⢄⣀⡀⠀⠙⢳⣄
⠀⢀⡾⠁⠀⡠⠒⠉⠁⠀⠈⠙⢢⡀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡴⠉⠀⠀⠀⠀⠉⠳⡄⠀⠹⣆
⠀⣸⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢻⡀
⠀⣿⠀⢰⠁⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⠀⡷⠀⢸⠇
⠀⢻⡀⠈⡆⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⡇⠀⣾
⠀⠘⣧⠀⢱⠀⠀⠀⡰⠁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢹⡀⠀⠀⡼⠀⢰⠇
⠀⠀⠹⣆⠀⢣⠀⠀⢣⡀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⠀⠀⢀⡼⠀⠀⠴⠁⢠⡟
⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⠒⠒⠉⠒⠦⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠉⠉⠉⠉⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣤⣀⣀⣤⠾⠁⠀⠀⠀⠀⠀⠀⠙⠷⢤⣤⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠋⠉⠛⠒⠲⢤⡀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣠⣴⣶⣶⣤⣀⠀⠀⠉⠢⡀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣴⣿⣿⣿⣿⣿⡿⠛⠷⣦⡀⠀⠈⢢⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠳⣄⠀⠀⠱⡀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠱⡀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⡟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠱⡀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢼⣀⣠⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣶⣿⣿⣿⠿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⠛⠉⢻⡀⢈⣳⣤⠟⠒⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠋⠲⠀⠘⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠑⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠑⢄⢀⣤⣶⣾⡿⠟⣛⠷⠒⢛⡇⣀⣢⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣟⡆⠀⢀⢊⣾⣿⠃⠀⠀⠠⢤⣤⡀⠀⠀⣴⣿⣿⡿⢋⣴⣘⣄⠴⠊⠋⠉⢡⡀⠉⣷⡈⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⣼⣿⡇⠀⠀⠎⠀⠀⠙⣿⣄⣼⣿⣿⢋⠴⡻⡿⠁⠁⠀⠀⠀⠀⠀⢏⠾⠹⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡰⠀⢀⣿⣿⠀⠀⠰⠀⠀⠀⠀⢸⣿⣿⣿⠣⢂⣴⠍⢀⣀⣀⣀⠀⠀⣀⠤⠚⡁⢻⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠘⡷⢶⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣥⡞⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢬⡏⢹⣿⠀⠀⢰⠀⠀⠀⠀⣸⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⢿⣿⡇⠀⠈⢧⠀⢀⣴⣿⢿⣟⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣀⠀⣀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⣿⣿⡄⠀⠈⠛⠛⠋⠁⠀⢿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣆⡀⠀⠀⠀⠀⢀⡼⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠖⠒⠚⠉⠀⠀⠻⢧⣀⡀⠀⠀⠀⠀⢀⣠⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠉⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣠⣾⠯⠀⢀⣠⣤⣶⣶⣶⣾⣿⣿⣿⣛⢦⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⢀⣴⣿⡿⢿⣽⠉⠉⠛⠻⣿⣿⣿⣷⡙⢦⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⡟⠉⠩⢷⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡞⡄⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⣾⠃⠀⣶⣎⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢸⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠰⣿⠀⣾⣿⡧⠀⠀⠀⠀⠀⠀⢐⣿⣻⣿⣿⣿⡿⡧⠀⠀⠀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣸⡿⠂⣿⣿⠃⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⡟⣿⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡗⢐⣿⡟⠀⠀⠀⠀⠀⠀⠈⢈⠉⠲⣾⣿⣿⣿⣿⠀⠀⠀⢘⣿⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⡻⠀⣸⡟⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⣿⣿⣿⣿⠂⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣄⠀⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⢠⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣿⠀⠀⢻⡅⢸⣿⠀⠀⠀⠀⢀⣤⣶⡄⢠⢠⣄⣴⣴⣿⣿⣿⡟⠀⠀⠀⢪⠟⠁
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠩⠀⣼⡗⠀⠀⠀⣶⣯⣿⣟⣼⣾⣿⣿⣿⣿⣿⣧⡏⠀⣀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢲⠆⣿⣇⠀⠀⠀⣿⣿⣿⣿⠋⡹⢿⣿⣿⣿⣿⣿⣷⣶⡯
⠀⠀⠀⠀⠀⠀⠹⣿⡀⠸⢣⣸⣿⠀⠀⠀⣿⣿⠏⠉⠀⣡⣾⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⢱⣿⢹⣇⠀⠀⠹⣷⣷⣧⠄⠉⢛⡍⣻⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠛⠏⡽⣦⠀⠀⣴⣿⣷⣠⣔⣶⣾⣿⣿⣿⣿⣿⣿⣿⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠐⠕⢙⢷⣀⠈⠿⣿⣿⣿⣽⣿⣿⣿⠿⣿⣿⣿⣿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠳⣝⣵⣳⣤⡈⠉⠉⠉⠁⠔⠀⠀⠀⠉⠻⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣤⡀⠙⠛⣿⣿⡶⡾⡿⠶⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦⣀⢀⠀⠀⠔⣀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⠀⠀⠀⠀⠄⠀⠀⠀⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⣤⣂⣀⡴⠞⠛⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⣀⣀
⠀⠀⠀⢀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢁⣠⠴⣒⡒⠶⣄⡉⠢⣄
⠀⠀⣠⠋⣠⣴⣶⣤⣤⣤⣤⣄⣀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣰⠋⢠⠎⠁⢄⠀⢈⢳⡄⠈⠣⡀
⠀⢠⠃⠈⠁⠀⠀⠀⠈⡉⠉⠙⠛⠿⣷⣄⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠇⢀⡵⠒⢲⡄⠁⠈⡎⡇⠀⠀⢱
⠀⡈⠀⣀⣲⣤⣷⡾⣷⡿⣷⣶⣤⡀⠀⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⣀⠀⠀⠳⠄⠀⢠⡇⠀⠀⠈⡆
⠀⢣⠀⠈⠙⠻⡅⠀⢷⣳⣿⡻⠃⠙⢦⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢨⠆⡴⢋⡀⡄⢠⠇⠀⠀⢀⠃
⠀⠘⡄⠀⠀⠀⠈⠲⠤⢬⣭⠤⠶⠀⠈⠃⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠈⠒⠁⠀⠀⢠⠏⠀⠀⠀⡜
⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⡤⠔⠊⠉⠉⠉⠉⠒⠤⣄⠑⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⠜
⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⢀⣀⠔⢋⠔⠁⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠑⢌⠑⠤⣀⠀⠐⠤⠚⠁⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠁⠀⢠⠏⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠈⢦⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⣄⣀⠈⢦⠀⠀⣞⠀⣀⡀⠀⠰⣃⡀⢸⠆⠀⢠⠎⢀⣀⡤⠤⠤⠤⠤⣀⡀
⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡑⢄⠈⠈⠉⠉⠀⠈⠉⠉⠉⢀⠴⣣⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠉⠒⠤⠤⠤⠤⠤⠔⠊⠁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⢰⠁⠀⠀⢀⣠⡤⠤⣤⣤⠤⢤⣄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⡆⢤⣤⢖⣋⣓⣠⣄⣀⣰⣧⣐⣋⣙⡲⣤⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢃⠀⠀⠳⡀⠀⠀⠨⠉⠍⠅⠀⠀⢠⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠘⡄⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠊⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⣀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⠀⠀⢀⣀⠤⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠾⠟⠛⠛⠛⠛⠿⠶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⡸⠛⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⡠⠋⠀⠀⠀⣀⡴⠓⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⡞⠁⠀⠀⢀⡜⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠹⣷
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⣠⠏⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢹⣇
⠀⢰⡿⠁⠀⠀⠀⠀⢀⣴⠏⠀⠀⣰⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⢿⡀
⠀⣿⠇⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡾⣿⣷⠀⠀⠀⠀⠀⢸⡇
⢸⡟⠀⠀⠀⢀⣾⠋⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠈⠠⠤⠤⠤⠖⠚⠛⠛⠉⠉⠉⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣧
⣿⡇⠀⠀⠀⣼⠇⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⠋⠄
⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣿⠇⠀⠀⠀⠀⠀⡼
⣿⡇⠀⠀⠀⡏⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠋⠉⠉⠉⠉⠛⠛⢻⣿⡟⠀⠀⠀⠀⠀⢰⠇
⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢠⡟
⢻⣇⠀⠀⠀⢿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⢀⡾
⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⢀⠞
⠘⣿⡄⠀⠀⠀⣧⠀⠀⠀⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⡴⠋
⠀⢻⣇⠀⠀⠀⠘⡄⠀⠀⢸⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⢀⣴⠎
⠀⠘⣿⡀⠀⠀⠀⢣⠀⠀⠈⡆⠀⠀⠀⢸⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢿⣷⣄
⠀⠀⢹⣧⠀⠀⠀⠘⣆⠀⠀⢳⡀⠀⠀⢸⡄⠀⠀⠘⠤⣀⣀⣀⣀⣤⣤⠶⠚⠋⠁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⢻⣆⠀⠀⠀⢹⡆⠀⠈⣧⠀⠀⠘⣇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⣿⡄⠀⠀⠀⢿⡀⠀⠸⡆⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠈⢷⡀⠀⠻⡀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢷⡀⠀⠱⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢷⡀⠀⠃⠀⠀⠀⠀⠈⠙⠻⠶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⡀⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣄⣀⣀⣀⣀⣠⣴⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⡆⠀⠨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡄⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡠⠀⡇⠀⡆⠀⠸⠃⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⡐⠁⠀⠀⠰⠀⠀⡇⠀⠀⠀⠀⢰⡟⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡅⠀⠀⣄⡀⠀⢘⠀⢀⡀⠀⠀⢿⣧⠄⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⡇⠉⡁⠉⠹⣶⣠⡿⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡾⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⡀⠊⠐⠀⠀⠈⠧⠘⠁⠘⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠊⠀⠁⠀⠀⠀⣀⡠⠀⠈⠁⠀⠀⠀⠰⠾⠳⠗⠀⠈⠐⠠⠄⣀⠀⠀⣠⠃⠀⠀⠀⣷
⠀⠀⠀⠀⠀⣠⠄⠀⠈⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⢀⣴⣻⠃⠀⢸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠶⠿⣦⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⡀⠀⣹⣿⣿⠀⠀⠜⢀⠀⠀⠀⢀⠄⠤⠀⠀⠀⠀⠀⠀⠀⢹⠈⠀⠀⠂⠀⠀⣼
⠀⠀⠀⠀⠚⠛⠓⠺⠶⠶⠾⠛⠋⠁⠀⠀⠁⡠⢸⣿⢻⡏⠀⢠⠾⠟⠛⠁⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣠⡴⠊⡡⠪⠂⠈⠙⠻⠇⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⢤⣤⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⣠⠆⠀⠀⠀⢀⡀⠀⠄⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢢⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⡞⠁⢠⠆⠀⠀⠀⠀⠈⣤⠤⢴⡄⠀⠀⠀⢀⡀⠀⡛⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡠⠈⢀⣼⠟⠁⠠⠃⠀⠀⠀⠀⠀⠀⢹⠀⠘⢼⡀⠐⠂⢸⡇⠀⠀⡇⠙⢦⡀⢀⣠⡶⠟⠙⢷⠀⠀⠀⠀⠀⠀⠁⠀⡇
⠀⠀⠀⠀⠀⢠⠈⠀⣴⣿⠋⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⣸⠇⠀⠀⢸⠇⠀⢠⠅⠀⠀⠈⠉⠉⠀⠀⠀⠸⡄⠀⠀⢰⠀⠀⠀⢠⡇
⠀⠀⠀⢀⡔⠀⣠⣾⡟⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⣾⢀⣼⡿⠃⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢀⡴⠃
⠀⠀⠀⠈⠉⠈⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠙⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠶⠶⣶⠶⠶⢤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⠶⠶⠶⢶⡶⠆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⣿⠉⠉⠛⠛⠶⣦⣄⠀⠀⠀⠀⠀⠙⢷⡞⠁⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠈⢳⡄⠀⠀⣠⡾⠋
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⢿⣤⡾⠋
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣷⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠸⣇⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠻⣾⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣿⠞⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⠞⠙⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠘⢷⡀⠀⢸⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠻⣄⣿⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⢸⠟⣦⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⡿⠀⠈⢷⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣾⠁⠀⠀⠀⠹⣦
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⢀⡼⢷⡀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣿⣀⣀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⣠⡞⠁⠀⠻⣆⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠉⠙⠛⠋⢻⡇⠀⠀⠀⠀⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠸⠧⠤⠤⠤⠤⠤⠤⠤⠴⠤⠾⠧⠤⠤⠤⠴⠿⠶⠶⠶⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠤⠤⠤⠦⠴⠼⠷

⠀⠀⠀⠀⡠⠖⢊⣉⣉⠙⠲⣄
⠀⠀⠀⠀⢀⡴⠋⠁⠈⠙⢆⠈⢦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣭⢭⣭⣀
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠘⡆⢸⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⠀⣿⡻⣿⣖⣿⠏⢙⣶⣄
⠀⠀⠀⠀⠸⠦⠤⠤⢄⡀⠑⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⠶⠿⠿⠞⠋⠁
⠀⠀⠀⠀⣠⡀⠀⠀⠀⢱⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⢻⡟⠀⢀⡠⠊⠀⠊⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂
⠀⠀⠀⠀⢿⡠⠊⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⡀⠀⠀⢀⡴⠶⡦⠀⢀⡰⠀⠀⡖⠙⢆⠀⢸⠀⠀⡇⠀⢠⠂⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠁⠀⠀⠐⠈⠁⠀⠀⠀⡇⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢠⠀⢇⠀⠸⠀⠘⠀⠀⡇⢠⠁⠀⡘
⠀⠀⠀⣠⠔⠒⠙⠒⠒⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⠀⡇⡆⠀⠀⡇⡘⠀⠀⡇
⠀⠀⣈⣀⣠⣤⣤⣤⣤⣤⣤⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⢸⠀⠀⡇⡇⠀⠀⡇⠇⠀⢀⠇
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣏⡆⠀⢡⡅⠀⠀⠿⠀⠀⢸
⠀⠀⠀⠈⠉⠐⠒⠀⠐⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡠⠒⠉⠉
⠀⠀⠀⡀⠔⠒⠒⠤⠤⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠎⠀⠀⡠⠊
⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⢀⠎
⠀⠀⢀⣴⠤⠦⠀⠨⠄⠀⠦⠴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⣤⢤⠀⠀⠀⢀⡤⣤⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠒⠚⠛⠙⠛⠛⠻⠶⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣶⠷⣒⣻⣿⣦⣲⣜⣷⢾⣶⣤⣀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣳⣦⣄⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠃⠀⠀⠛⠀⢿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⠈⠁⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⡋⠁⠀⠈⠂⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⡵⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠘⣿⠿⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⢿⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣧⠀⢠⣄⣠⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⣿⣌⢿⣿⣿⣿⣷⣿⣿⣿⣶⡄⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣎⠁⠀⠀⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡶⣙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣍⣿⣿⣿⣿⠸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠻⣿⣿⣿⣿⣿⣿⣾⣷⡀⠀⠀⢿⣿⣿⣿⣿⡇⠇⠀⢠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⡁⣻⣿⣻⢿⣿⣿⣿⣏⠄⠀⢈⡟⢿⣿⣿⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⣾⣿⣿⣿⣷⣯⣻⣿⣭⡻⣿⣿⣆⠀⠀⢣⠸⣿⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⠀⠀⠀⢘⣿⡿⢂⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢨⣿⠏⡈⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢹⣿⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣬⣿⣽⡿⠃⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠟⠋⠁⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡾⣛⠉⢉⡤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠰⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠠⡀⢢⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠦⠼⠄⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⢀⣴⣟⡕⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠸⠿⢿⣧⠞⠉⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⣴⢋⡀⠠⣴⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⡇⠈⠁⠐⠻⢦⡀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⡇⠀⠀⢢
⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⢠⠀⢀⣤⣶⠶⢤⡄⠀⠀⢇⠀⠀⠀⣿⣷⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠁⠀⠀⠈⠀⠀⣼⠀⠀⣼⣿⡏⠀⠀⠀⢸⡆
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⡿⣠⣾⣿⣿⠃⠀⠀⠀⢸⡇⠀⢐
⢀⠔⣃⣄⠀⠀⠀⠀⠀⠀⠀⠔⠉⢹⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣼⡇
⠇⡾⠁⠛⠀⠰⢷⡄⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⣠⣾⡟⠀⡄
⠀⣄⢀⠀⠀⠀⠐⠁⠀⠀⠀⢀⡼⠋⠀⣀⣀⣤⣴⣾⣿⡿⠿⠛⠋⠉⠀⠀⠀⣀⣠⣴⣾⠿⠋⠀⣴⠃
⠀⠈⠁⠀⠀⠀⠐⠂⠀⢀⣴⣯⣶⣾⣿⣿⣿⠿⠿⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠛⠛⠉⠀⢀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⢀⠴⠚⡉⠉⠉⠉⠉⠙⠛⠶⣦⣄⡀⠀⠐⠒⠶⠦⣤⣤⣤⣤⣤⣴⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⠀⠀⠀⠐⢤⡙⠻⣷⣶⣤⣀⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡀⢹⣆⠈⠻⣮⡙⠻⠿⣶⣶⣶⣤⣤⣴⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡈⠻⣿⠀⠀⠹⣿⣆⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⣀⣠⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠉⠀⠀⣠⣤⣶⣶⣦⣴⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣾⠛⠻⠛⠛⠛⠻⠟⢿⣿⡿⣦⢄⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠁⢉⢝⣿⣿⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢸⣿⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠃⢽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠆⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢂⣱⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢠⣿⣯⣷⠼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⣿⢿⣿⣿⢿⠆⠀⠀⠀⠀⠀⠀⢸⣿⡷⡛⣤⣿⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⢠⣿⠋⠉⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⠙⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠐⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡘⣿⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⠈⡠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⠀⡀⣈⣉⡙⢋⠛⣿⢿⣿⣿⡇⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠹⣿⣿⣄⣙⠡⣌⡩⠓⢽⡾⣿⣿⣿⡇⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣶⠈⢻⣿⣿⣶⣥⡴⣱⣀⢏⢿⣿⣿⡇⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠚⠀⣹⠀⠀⣿⣿⡿⠛⢷⣾⣿⡻⣾⣿⠏⠀⠀⠀⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⢡⣠⠖⡉⠀⠀⣿⠁⠀⠛⢫⣷⣿⡿⠿⠃⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠑⡡⠎⡱⠀⣰⠏⠀⢀⡴⠛⠉⠁⠀⠀⠀⠀⠀⣠⣿⣿⠟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢄⠖⠁⣼⠋⠀⠀⣾⠁⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠟⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢹⡀⠀⢀⠿⠀⠀⠀⠀⠀⠈⠛⣹⣯⡟⠁⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣦⡶⣶⣾⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⢋⠉⠛⠛⠛⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣿⣦⣤⣤⣤⡀⠘⠃⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠉⠃⠈⠚⣿⣴⣦⣄⣀⣀⣤⣤⣄⣤⣀⡀⠈⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣻⠏⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠙⠛⠳⠄⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠁⠀⣀⣤⣾⣿⣿⣿⣿⡿⠿⠻⠻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠏⠉⠀⣀⣴⣾⣿⣿⣿⣿⣿⣭⠟⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢹⡏⠀⠀⣠⣾⣿⣿⣿⢻⣇⡞⠙⠙⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡟⠀⠀⣼⣿⣿⠟⢿⡇⣎⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡟⢠⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⣼⣿⣿⢻⡄⢸⢣⡙⠎⠁⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠃⢺⡏⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⢰⣿⣿⠏⡇⠹⢈⠀⠟⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣷⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣿⣿⡏⢸⠃⣴⢸⢀⡄⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣿⠃⢸⡄⢸⢸⠈⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠟⠋⣹⣿⣿⣿⣿⣿⣏⠛⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⡇⠀⣼⣿⡇⠀⢸⡇⣿⢸⠘⠀⢀⣼⣿⣿⣿⠿⠛⠋⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿⣿⣧⠰⢸⡇⣿⠘⠀⢀⣾⣿⣿⡟⠁⠀⠀⣀⣰⣶⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⢀⢸⡇⡿⠀⠀⣼⣿⣿⠇⠀⣠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⢠⣿⣿⣿⣸⢸⠀⠃⠀⢰⣿⡿⢡⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⣀⠀⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⡈⣿⣿⣿⣿⠈⠀⠀⠀⣼⣿⡷⣿⣿⢿⣿⣿⣟⣿⣿⣿⢿⣿⣨⣤⣼⣿⡉⣯⣱⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⡃⢸⣿⣿⣿⡆⠀⠀⠀⣿⣿⣷⣿⡿⢼⣿⢿⣿⣿⣽⣯⣾⣿⣿⣿⣿⡿⠃⠉⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠁⠀⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⡆⠘⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⣧⠀⠹⣿⣷⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣌⠀⠐⣶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠹⣿⡆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⡇⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⠉⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠸⠿⠇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠰⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠶⣾⠇⠈⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠙⠐⠀⠀⢀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠃⢀⡈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠆⠀⠁⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠘⡁⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣔⣣⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠘⢌⣦⡀⠀⠀⠀⠀⠀⠀⠖⠀⢰⠂⣀⢰⡀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣻⣷⣙⣿⣷⣤⣀⣀⣀⣐⣈⠴⣂⠔⣡⣦⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣯⣭⣩⣵⣾⣵⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉

⠀⠀⠷⠶⠶⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣦⢀⣰⣶⣷⣄⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠷⠶⠶⡇⡇
⠀⠀⣤⣦⣦⣬⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⣙⣩⣭⡤⢤⡿⠀⣴⢏⣾⡿⣳⣦⠀⠀⠀⠀⠀⠀⠀⣇⣴⣦⣤⡄⡇
⠀⠰⢍⣻⢟⡫⠆⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⢸⣿⡿⠁⠚⠛⠻⠳⠻⡿⣵⣿⠃⠀⠀⠀⠀⠀⠀⠀⠦⣝⣻⣛⠥⠃
⠀⠀⣤⣬⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⠯⠀⠀⣠⣤⣤⣄⣀⣀⠈⢹⣷⡀⠀⠀⠀⠀⠀⠀⣦⣤⣭⣤⡄⡆
⠀⠀⠁⠀⣠⠘⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣫⠅⢠⠎⠁⠀⠈⠙⠛⠿⠷⣾⣿⣧⣄⠀⠀⠀⠀⠀⠁⠁⢨⠉⠃⠃
⠀⢀⡻⣿⣿⠟⡀⠀⠀⠀⠀⢀⣠⠶⠋⢾⣿⠒⢀⣿⣷⣦⣤⣤⣴⣶⣤⣤⣤⠎⣾⣿⡆⠀⠀⠀⠀⣅⢿⣿⡿⢇⡇
⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⣿⠀⠀⢻⣿⣿⣿⣿⣿⣏⠉⠉⠛⠦⣻⣿⡀⠀⠀⠀⠀⠀⠙⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣸⡼⣿⠓⠦⣀⡈⠁⠀⠈⣿⣿⠿⣶⣄⠑⣦⣬⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣾⣷⠁⠈⡆⠀⠀⢀⣀⡀⣀⣿⣿⡷⣌⠙⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⡿⣦⡀⠀⠀⠀⠤⠚⠋⠉⣿⡇⢻⡌⢦⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣿⡸⠳⡦⠀⠀⠀⠀⢀⡼⢹⠃⠸⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠑⠀⠀⠀⣠⠋⡇⢸⠀⠀⡏⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⢷⣄⠀⠀⠁⠀⢣⠀⠀⠰⠁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣯⣛⢦⡀⠀⠘⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⠞⠋

⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀⠀⢀⣠⣤⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⣷⣶⣦⣄⡀⠀⢀⣀⣤⣤⣤⣤⣤⣄⡀
⢀⣴⣿⣋⣉⣉⠉⠉⠉⠛⠻⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠟⠛⠉⠉⠉⣉⣉⣙⣿⣦
⢼⣿⣿⣟⡛⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⣻⣿⣿
⠀⠀⠉⠻⣿⡄⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢠⣾⠟⠉
⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⢀⣠⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣤⣄⢸
⢻⣷⡿⠛⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠉⠙⠻⣿
⠈⢻⣧⣀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣷⣤⣾⡿
⠀⠀⠻⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠉⠈⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠟
⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠋⠉⠙⠛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣀⣤⣤⣤⣀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⢀⡴⠋⠀⠀⠀⠀⠙⣷⡄⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⢀⡞⠀⠀⠀⠀⠀⣀⠼⠛⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣾⠀⠀⣠⠖⠊⠉⠀⠀⠀⠉⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⠀⡇⠀⠀⠀⢀⣴⣶⣶⣶⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢻⣇⢳⡀⠀⠀⢸⣿⣿⣿⡟⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠈⠿⠈⢷⡄⠀⠀⠻⣿⡿⠃⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠘⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠙⠳⠦⣤⠴⠚⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣤⣴⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣿⣿⣏⣩⣍⣿⡿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢃⣻⠟⢻⢏⡏⡾⣵⢻⠏⣽⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣽⣿⣷⣾⣿⣾⣷⣿⣿⣿⣿⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣻⣿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢀
⠀⠀⠀⠀⠀⠀⢰⡆⣨⡷⠋⡉⠃⠀⠐⠄⠊⠀⠀⠀⣀⣴⣦⠀⠀⠀⠀⠀⠀⣍⠙⢿⣄⢰
⠀⠀⠀⠀⠀⠀⣾⣾⠟⣡⣾⠁⣠⣶⣶⡶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣴⡄⢿⣷⣉⠻⣿⣧
⠀⠀⠀⠀⢲⣼⣿⣶⡿⠛⠛⠀⠛⢛⡟⠀⠘⢿⣉⠛⠟⢛⡿⠁⠀⠀⠀⣠⡀⠋⠛⠛⣿⣮⣿⣤⡆
⠀⠀⠀⠐⣿⣿⣿⣿⡃⠠⠁⠀⠐⠀⠄⠀⠤⠄⠀⠈⠉⠉⠀⠀⠀⢀⣴⣿⠀⠀⠠⠀⣻⣿⣿⣿⡷
⠀⠀⠀⠀⢸⣿⣟⣽⣿⡇⠀⠀⠀⡠⠒⠒⠒⠤⣀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡄⠀⠀⣿⣿⣯⣿⣿⡇
⠀⠀⠀⠀⠘⣿⣿⣿⡿⠇⠀⢸⣿⠅⠀⠀⠀⠀⠀⠉⣷⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⡀⠠⠀⢸⣿⣆⠀⠲⠂⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠠⠀⢹⣿⣿⠏
⠀⠀⠀⠀⠀⠶⠿⣿⣷⣶⣇⠰⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣤⣠⣿⣿⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣼⣿⣿⣿⣥⣬⣦⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣶⠶⢲⡾⢟⣿⣿⣿⠟⠉⢩⣬⣝⢿
⠀⠀⠀⠀⠀⢸⡴⠛⠛⠛⢻⣿⠟⠛⠀⢾⣿⠀⢸⡏⠀⢿⣿⣤⣿⠀⠉⠀⢿⣿⣿⣧⣶⡔⠈⢿⣿⡾
⠀⠀⠀⠀⠀⢊⣿⣿⡏⢀⣸⠃⠀⠻⠀⢈⣟⠀⠘⠷⣄⣈⣉⡩⣟⢀⣘⣦⠀⢙⣧⠈⠇⢀⣤⢸⡿⠃
⠀⠀⠀⠀⠀⠸⣿⡏⢠⡞⢹⡇⠀⠶⠀⣸⡏⠀⣶⡄⠈⢿⠉⠀⠦⣹⡏⠁⠰⣌⡿⠶⣶⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠈⠻⢾⣷⣤⠇⠀⢶⠀⠙⣃⠀⠰⠖⠀⣴⠲⠀⠀⠨⡟⠦⠄⠀⣿⣠⡟
⠀⠀⠀⠀⠁⠄⠀⠀⠀⢀⣉⠓⠶⠋⢳⣆⠛⠟⠀⣄⣄⣬⡅⠀⠶⢃⡟⠲⠴⢞⢉⡁⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⣓⣦⣠⡀⠀⢀⣤⣴⣆⣧⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⡄⠀⠀⠀⠀⢀⡠⠂⢠⡟⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣼⣿⣿⣿⣿⣿⣧⣄⢠⡟⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣿⣿⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣧⡍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠛⣻⡟⡀⠀⠘⢦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⣠⡞⣰⠟⠋⠀⠀⠀⠀⠉⠛⠶⣾⣭⣭⣭⣛⣛⣻⣿⣿⣿⡿⠿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⣾⡟⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⡏⠛⠻⠿⢷⣦⣄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⢠⡔⢠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠉⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⣼⠃⠈⢧⣀⢀⣠⣤⣤⣝⡄⠀⠀⠀⠀⠀⠀⠀⢤⣸⣷⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⢀⡀⠛⠀⠀⠀⢹⠒⢲⣶⡌⠹⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⣦⠻⠿⠿⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⠀⠀⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠸⡇
⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠸⡄⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠸⣷⡀⠀⠀⢻⡀
⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠹⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢇
⠀⠀⠀⢸⣿⡟⣿⡿⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠘⡄
⠀⠀⠀⣿⡿⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⢳⡀
⠀⠀⢠⣿⠇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣦⣤⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢀⠈⣧
⠀⠀⢸⡿⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢷⣿⣆
⠀⠀⣿⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣸⣿⣿⣷
⠀⠀⡿⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⠀⠀⠀⠈⢣⡀⠀⠀⠀⢀⣴⣶⠦⢌⢻⣿⣿⣿⡇
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣾⣿⠀⠀⠀⠀⠀⠹⡀⢶⡄⠻⣿⣿⣷⡄⠋⣿⣿⣯⠁
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢁⣿⣿⠀⠀⠀⠀⠀⠀⢰⡀⢻⣦⡈⠉⠉⣽⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣦⣹⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠈⣿⡏⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⣿⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⣴⣾⣿⠿⠿⠿⠿⢿⣿⣷⣦⡀⠀⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⡀⠈⠻⣿⣶⣄⠉⠛⢿⣷⡄⠀⠀⠀⠀⣿⡏⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠈⢿⣿⣿⣦⠈⣿⣿⠀⠀⠀⣸⣿⠁⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢻⣿⣇⠀⠻⠿⠃⠀⣿⣿⠀⠀⢠⣿⠃⠀⠀⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠘⠛⢁⣤⣤⣀⣠⣼⣿⡟⠀⢀⣾⠃⠀⠀⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⣴⣿⠟⠛⠿⠟⠛⠉⠀⢀⡾⠃⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⡾⠋⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⣀⣀⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⣀⣴⣶⣿⣿⡿⢛⠋⠛⢿⢿⣿⣶⣤⣀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠈⠂⢸⣿⣿⣿⣿⣧⡀⠀⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⡰⣫⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⣿⡏⠿⠁⠀⠀⠀⠀⠀⣠⢾⣹⣿⣿⣿⡿⠟⣿⡆⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡸⣿⠙⠀⠀⠀⠀⢀⣴⠎⣣⣽⣿⣿⡿⠟⠁⢠⣿⡇⠀⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠋⠀⠀⠀⠀⣰⠛⠮⣿⠿⠋⠉⠉⠀⢀⣴⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡧⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡟⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⢠⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⢟⡿⣻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣴⣿⢿⡻⡿⠋⣉⣴⡿⠋⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡟⡀⠀⠀⠀⢀⣾⡿⡟⡁⠈⠀⠀⠛⠁
⠀⠀⠀⠀⠀⢸⣇⠀⠀⢸⣷⠃⠀⠀⠀⣼⡧⡘⠀⠀⠀⠰⢾⣷⣷⣶⣄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⣿⡼⠀⠀⠀⢿⡇⠀⠀⠀⢠⠎⠀⢿⢯⣿⣿⣧
⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⢻⣧⡁⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿⣸⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠻⣧⡫⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠈⢿⣯⣷⣄⠀⠀⢰⣆⣀⠰⣤⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠈⠻⣿⣇⡀⠀⢻⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠈⠻⣿⡄⠀⠙⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠈⠻⠀⠀⠀⠙⠿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣕⠦⣀⡀⠀⠀⠀⠀⢀⢄⣤⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣾⣭⣭⣭⣿⣶⣿⣿⡟⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⢻⣻⢹⣿⡌⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣳⢻⣿⡌⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠹⣿⡌⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢆⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠄⠒⠒⠒⠈⠉⠉⠉⠰⢒⠶⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⠀⢀⠀⣀⢀⢀⢀⢀⢀⠀⠀⠀⠀⠀⠐⠊⡠⠐⠀⣙⡛⢲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⡄⢀⡰⠜⣤⣠⣵⡶⢦⠶⠒⣦⣥⣁⡠⠀⠀⠀⠀⠀⠐⠈⣡⠀⠀⠄⠼⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⣀⠰⠌⣣⠾⠿⣉⠒⠀⠉⣁⠀⠤⣒⠦⠐⢂⡩⠝⠓⣤⡀⠀⠀⠀⠀⠀⠤⠚⢀⣐⣒⡛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡀⢲⡈⣢⡜⠫⠭⢠⡤⠀⠈⠁⠀⠀⠁⠀⠀⠉⠀⠄⢂⠭⠔⢛⣳⣄⠀⠀⠀⠀⢉⡀⠠⠤⢀⣉⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢢⠘⠀⣴⢛⠂⠩⠄⢒⣒⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡡⢄⣚⠷⡄⠀⠀⠀⠀⠤⠄⠀⠤⠭⣺⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠⡈⣄⢁⡾⠭⠐⡂⠀⠟⠐⠒⡂⠈⠭⠭⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠐⠛⣆⠀⠀⠀⠀⠀⠀⠒⠒⢤⣙⡆
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢄⠡⠑⢠⣋⣔⡺⠇⠀⡉⡁⠤⠀⠠⠀⠘⡁⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠨⢆⠀⠀⠀⢈⠉⣉⠁⠒⢬⣇
⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⡙⠌⠂⣰⡟⢜⡩⠑⡂⠠⠤⢀⡂⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢻⡄⠀⠀⠈⣄⡉⠉⠒⢄⣹
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠠⡱⡈⣴⣿⠀⠁⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠠⢧⠀⠀⠀⠠⠤⣉⡑⢦⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢔⣘⠎⠜⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⢚⡀⠀⠀⢈⠐⠢⡉⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⡈⡔⣡⠝⡦⣄⠰⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡩⠬⡇⠀⠀⠠⡙⢦⡈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡔⠡⠊⠔⡩⠚⢲⣤⣇⠇⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣂⡇⠀⠀⠀⡌⢂⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⣷⢰⡇⢊⡴⠚⣡⠄⣉⠱⢾⣴⢀⠀⠊⠠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢾⠃⠀⠀⠢⡘⣮⡟⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡱⡀⠈⡿⠈⠀⠈⠀⠊⡠⠊⣠⠖⢀⠄⢛⡤⣀⠀⠈⠰⢁⢆⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠀⠀⡄⠀⣴⡏⢚⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⡅⠀⠇⠀⠀⠀⠀⠀⠁⠘⠁⠔⣡⠚⢁⠴⢊⠽⠒⣦⢌⡘⠰⡰⢉⠄⠀⠀⠀⠀⠀⠀⠀⣤⠇⠀⢆⠘⣴⠟⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡁⡇⠀⠀⠂⡀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠁⠐⠋⠰⠋⠴⢊⠭⢓⣦⡣⢊⠄⠀⠀⠀⠀⠀⣠⡞⢀⠘⢬⡞⡡⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⣱⡔⠁⢀⠀⠁⠔⠠⠠⢰⠀⡇⠰⠀⡀⠀⠀⠀⠀⠀⠈⠐⢁⠴⢻⡁⡂⠀⠀⠀⠀⠀⡝⠀⢄⢣⡾⢈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡳⢸⡆⠀⠠⢊⠄⠀⡀⠀⠀⠀⠀⠃⠃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠚⡡⠷⠂⠀⠀⠀⠀⡸⠀⠐⣈⢏⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣁⣞⠁⢀⠔⠅⠀⢈⠔⡡⢂⠔⡀⢀⠈⠃⠈⠘⠃⠃⠀⠀⠀⠀⠀⠐⢚⠀⠀⠀⠀⢰⠁⢲⣷⠟⡡⢊⠄
⠤⡀⠀⠀⠀⠀⠀⠀⠰⣥⠞⠡⠊⠀⠀⠠⠀⠕⠪⠔⡡⢊⠔⡡⢊⠔⠢⠄⠀⠀⠀⠀⠀⠀⠀⢈⡝⠀⠀⠀⢠⠃⡘⢄⡧⢊⠔⠁
⠐⡩⢦⡀⠀⠀⠀⠠⣌⡿⡪⢂⠔⡀⠠⢊⠤⢂⠠⡊⠔⡡⢊⠔⣡⠖⡤⣢⢖⠄⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠠⡱⡼⡡⢃⠀⠁
⢨⠔⡉⠷⠀⠀⠀⠐⢬⣏⠔⡡⢊⠀⠀⢁⠔⠡⠊⠠⠎⠀⠀⡀⢠⠀⡀⠁⠁⠈⠐⠃⠀⡀⢠⠆⠀⠀⠀⠀⠀⠓⣹⡷⠔⠠
⠰⢋⠴⠘⡃⠀⠀⠀⠙⣷⢎⠀⢈⠔⠰⣀⠀⠀⡠⠶⠶⠷⣤⣔⣁⣊⡴⡡⠊⠔⢣⢞⡶⠵⠋⠀⠀⠀⠀⢦⡘⢦⡿⡵⢊
⠀⣁⠔⢁⡥⠀⠀⠀⠀⠉⠳⢎⣥⢊⣔⣥⠞⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢆⡹⣾⢟⣔⡅
⠀⡡⢚⡡⢐⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁⠓⢎⢳⡾⡿⢫
⠀⠒⡡⢔⡨⡅⠀⠀⠀⠀⠀⠄⠠⣠⠂⠀⠀⠠⢊⠄⡔⡡⠂⢂⠄⡀⢠⠀⠀⠀⠀⠀⠀⡄⡁⠃⠀⡀⠳⡄⣰⣏⢔⠄
⠀⣩⠔⣉⠔⢋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠑⠀⠀⠀⢀⠑⢄⠱⣞⡡⠂
⠀⠐⢊⡠⠊⡨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡀⢣⡈⢵⢋⠔⡁
⠀⠀⣨⠔⢉⡤⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠹⠀⢳⡾⢁⠞⠁
⠀⠀⠀⠒⡡⠔⡡⠚⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢂⠘⡀⢣⡞⡰⢃⠞⠁
⠀⠀⠀⠋⠐⢊⠤⢊⡹⢷⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⠰⠘⠀⢣⣪⢆⡄⡠⠁
⠀⠀⠀⠀⠀⠠⠖⢁⠤⠊⣱⣧⡀⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡀⠃⢸⠀⡆⣶⡝⠑⣋⢊⠄
⠀⠀⠀⠀⠀⠀⠀⠁⡠⠊⡠⠞⢑⠧⣄⡀⠀⠀⠀⠐⢰⠀⠆⢰⠀⡇⢸⠀⠀⠀⡃⡀⣸⡴⢋⠈⢀⠜⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠂⢁⠴⢊⣹⠷⢶⣤⣅⡄⢰⠀⡄⠀⠃⣈⣀⣥⡴⢶⡋⠉⠀⠱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠉⡠⠖⣁⠄⢉⠉⢋⠘⠋⠚⠙⢋⠝⠁⠠⠁⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠿⡿⠶⠄⣤⣀⣀⡄⠬⠃⠀⠀⣿⣾⣤⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠈⠾⣿⠋⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣾⣷⣤⣸⣷⣶⣾⢒⣤⠀⠀⠀⠀⠀⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⢿⣿⢫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡿⣛⣟⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⡉⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋⠙⠋⠈⠀⠈⠛⠁⡟⢋⣹⣿⣿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢿⠏⠉⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣤⣄⠀⠀⠀⢀⣤⠃⠀⠧⠈⠷⠤⢴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣠⣴⡟⠁⠀⠀⠠⡀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⠈⣠⠄⠀⠀⠀⠘⠰⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⢈⣴⣿⣥⣠⣤⡀⠀⠀⠀⠀⡈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣰⠿⡿⠿⠟⠉⠙⠃⠀⠀⠻⣦⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⣤⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢦⡄⠀⠸⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠚⠛⠛⠙⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⡀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢠⠟⠁⠀⠀⠀⣄⡈⡗⠀⠀⠀⠀⠀⠀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⢬⣶⣕⠀⠀⠻⠿⠛⠀⠀⠀⠀⢀⡄⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠘⠛⢡⠖⠚⠛⠲⣄⠀⠀⠀⠀⢸⠁⠀⠀⢻⡀
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣄⣀⣠⡿⠀⠀⠀⠀⣾⠀⠀⠀⠘⡇
⠀⠀⡠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣿
⠀⡼⣱⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⢰⡇⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢻
⣸⢡⡇⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠰⡄⠀⠀⠀⠀⢸⡷⣤⣀⣀⣴⠛⡇⠀⠀⠀⢸
⡏⢸⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠳⣄⡀⢀⣠⣾⣀⡼⠛⠙⡇⠀⡇⠀⠀⠀⢸
⡇⠸⡆⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠀⠀⠀⡇⠀⣿⠀⠀⠀⢸
⢻⠀⢳⡀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣿⠀⠀⠀⢸
⠈⢧⠀⣽⠃⠀⠀⢀⠴⠚⠋⠛⠳⣄⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢹⠀⠀⠀⢸
⠀⠈⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢸⠀⠀⠀⢸⡇⠀⠀⢸
⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⣿⠀⠀⠀⠀⠀⣾⡤⠤⣤⠀⠀⡤⠤⠤⠶⠖⠋⣿⠀⢸⠀⠀⠀⠘⣇⠀⠀⣼
⠀⢸⡁⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡶⠒⠚⢻⡆⠀⠀⠀⣰⡏⠀⠀⡇⠀⢠⡇⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⢻⣦⡾⠋
⠀⠈⠳⣇⣀⠀⠀⠀⠀⠈⣉⠉⠉⠉⠙⢦⠘⣷⣀⣀⣴⠟⠀⡠⠴⠇⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠘⣩⢦⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢧⣎⣀⣴⣀⡼⠣⣌⡿⠛⠁⠀⠸⣄⣄⠀⣄⣀⣹⠀⠀⠀⠀⠀⠿⣤⣀⣀⡴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⣤⣄⡀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉⠻⣦⡀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢦⡄⠀⠈⢿⡄⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠿⢷⣦⣄⡀⠀⠀⠈⢻⡆⠀⢸⣇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠈⠛⢿⣦⠀⠀⠈⠁⠀⠈⠋⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⢠⣿⡿⠛⠉⠙⢿⣄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠟⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁

⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⣛⣿⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠦⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠀⠀⠀⠀⠀⢀⣾⣿⣻⣻⣿⣿⣶⣮⢿⡿⣿⣦⣄⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⣾⡿⠁⠀⠀⠀⠀⢠⣿⣿⣏⣩⠭⢛⠹⢟⡵⠧⡻⣶⣿⣿⣷⣄⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⢻⣿⡆⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⠟⠁⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠚⢰⣿⣿⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠌⢿⣿⣧⠀⠀⠀⠀⠰⢀⣾⣿⣿⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⡜⣿⣿⣇⠀⠀⠀⢠⣾⣿⣿⠇⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⣀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⣸⡿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡶⡀⢻⣿⣿⠀⠀⠀⣼⣿⡟⠀⠀⠀⢠⣿⠃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⡿⢡⡇⡾⢻⣿⠀⠀⢀⣿⡟⠀⠀⠀⢠⣿⡿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣿⣿⣿⡿⣡⠔⠘⣱⣿⠇⠀⠀⣼⡟⠀⠀⠀⣠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠚⠉⣋⣴⠋⠀⣴⣋⠏⠀⠀⣰⡟⠀⠀⠀⣴⣿⣿⡇⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⢁⣬⣭⣷⠿⠟⠋⠀⠀⠀⢰⡟⠀⠀⢠⣾⣿⡿⢏⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⢠⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣠⣿⣿⢏⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠇⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡿⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⣿⣿⣿⣻⣿⣶⣶⣶⣶⣿⣿⣿⡿⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣻⠟⣷⠟⣿⠯⠀⡉⠽⢻⣿⣿⣿⣿⠛⠋⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣣⠞⠁⠞⠁⠀⠀⠀⠈⠁⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠴⠦⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣠⠖⠊⠉⠉⠀⠈⠉⠙⠒⢤⡀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⣒⣚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠈⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⠇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠉⠉⠓⠀⠀⢀⠀⠀⠀⠈⡆⠀⠀⠀⡼⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⡸⠁⠀⠀⣰⠁⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠒⠁⣀⠜⠁⠀⢀⡼⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⣀⠔⠋⠉⠉⠀⠀⠀⡠⠋⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠊⠉⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢤⣤⠤⠴⠚⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⢇⡀⠀⠈⣼⣉⣀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣾⣧⣴⣤⣿⣿⣿⣿⣿⠃⢙⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⣀⣄⣠⠘⢛⠚⠁⣾
⠀⠀⠀⠀⠀⠀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠸⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣛⣿⣿⣿⣿⡟⠃⢰⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⢫⣴⣋⣽⣿⣿⠿⣿⣿⣿⡟⠛⢿⣸⣿⣿⣯⣿⣿⣿⡀⠀⠈⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠛⠀⠛⠛⠉⠈⠁⠀⠉⠻⠿⠃⠐⣟⠿⠋⠙⣿⣿⣿⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣴⠾⣿⣿⣿⡟⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡇⠀⠈⣿⣿⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡤⠊⠙⢿⡄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣶⣶⠆⠀⠀⠀⠀⠀⣠⣶⡟⠀⠐⠔⢡⠖⠁⠚⠉⠉⠙⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡧⠀⠀⠀⢀⣴⣿⡿⠛⠠⠀⠀⠀⢸⣄⠀⠆⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⡾⠟⢻⠟⠁⠐⢄⠂⠀⠀⠀⠈⢶⡀⠀⢠⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢀⣴⠞⠀⠀⠘⠀⠀⠀⠈⠁⠺⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢺⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢻⣿
⠀⠀⠀⠀⠀⣾⣿⠟⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣾⣿⣿⣶⣭⣿⣿⡄⠀⠀⠀⣀⣀⠀⠀⠂⠺⣿
⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⣿⣿⡿⢿⡟⠀⠀⠘⢛⠁⠀⠀⠀⡯⠻⣦⡀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠀⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠿⠇⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣏⠉⠉⠉⠉⠛⠿⣶⣄⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠸⣿⡆⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⢻⣿⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡶⠾⠿⠿⠷⣶⣦⣄⡀⠀⢀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣟⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⠟⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⣼
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣼⡿⠁⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠋⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠉⠁⠀⠀⠀⠀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⣠⣿⠟⠁
⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣴⣿⠏
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣼⡿⠃
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢀⣴⣿⠟⠁
⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣰⣿⠟⠁
⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃
⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠂⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠉
⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠏
⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⡔⠐⠒⠀⠄⢤⣤⣤⡠⠀⡄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣯⡮⣌⣍⠉⠑⠲⣦⠶⣿⠛⢿⠂⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠯⠀⠁⠀⠀⠀⠀⠀⠀⢒⣿⣀⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣾⣏⠁⠀⠀⠀⠀⠐⢀⣡⣾⠟⣛⢉⢽⢿⣧⡀⢀⣀⣀⣤⣶⣶⣤⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣿⢻⡀⡀⠀⣀⣠⣤⣾⣿⣏⣀⣀⡀⠈⢙⡻⠿⠆⠀⠈⠳⠾⢎⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⣿⣿⣿⣿⢅⢈⣽⠿⢟⠻⣿⡯⠍⠉⣻⠿⣷⣄⡀⠀⠀⢂⣀⣬⠍⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣻⣅⡉⠁⠀⠀⠨⣿⠂⠀⠀⠛⠋⠉⠉⠀⠀⠁⢁⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣦⣄⣠⣼⡏⠀⠀⠀⢻⠖⠒⠄⠀⢠⣜⠋⠁⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠻⣏⣉⢻⡟⠉⠀⠙⠛⠀⠠⢀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣀
⠀⠀⠀⣠⣾⣿⡟⠉⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⣰⣿⡿⠋⠀⠀⠀⢀⣴⣾⣿⡿⠟⠛⠋⠉⠉⠉⠛⠛⠿⣿⣿⣶⣄⠀⠀⠀⠀⠻⣿⣷⡄
⠀⣼⣿⡿⠁⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠹⣿⣿⡄
⢰⣿⣿⠁⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠹⣿⣷
⣾⣿⡇⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⣿⣿⡇
⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣷
⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⢸⣿⣿
⢹⣿⡇⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⣾⣿⡏
⠸⣿⣿⠀⠀⠀⣸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⢠⣿⣿⠃
⠀⣿⣿⡆⠀⠰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⢀⣾⣿⡏
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣗⣀⣤⣾⣿⡿⠋⠀⠀⠀⢀⣾⣿⡟
⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⠛⠁⠀⣀⣀⢀⣴⣿⣿⠏
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⡀
⠀⢸⣿⣿⠀⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣷
⠀⢸⣿⣿⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢀⣤⣄⠀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠙⠻⣿⣿⣶⣄
⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠙⠿⣿⣷⣦⣄
⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣦⡀
⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠈⠻⢿⣿⠆
⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣶⣄
⠀⠀⠀⠈⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣦⣤⣤⣤⣤⣴⣶⣿⣿⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠈⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⣥⣤⡈⣧⠀⠀⠀⠀⡟⠀⠀⢀⡴⠃⣛⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣷⡀⠀⠀⢸⠃⠀⡴⢁⠐⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣹⡆⠀⣼⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⢰⣏⣧⣴⡟⠋⠉⠀⠀⠀⢲⣄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣹⣿⡟⠀⠀⠀⣠⠤⣴⣤⣾⣿⣦⣤⣴⠶⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⢰⣿⣿⠁⠀⣠⣟⠃⠒⠚⠋⠉⠉⠀⠀⢀⣀⣀⣼⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠿⠛⣿⣟⠀⠀⣿⣿⡗⠀⠀⠀⢠⡴⠾⣿⣿⣿⡟⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⢐⣀⣿⣦⡄⠀⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⠛⠿⢿⠄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⠀⣀⡌⣴⡿⣿⡶⢿⢉⡧⠀⠀⢀⡎⣀⣠⠖⠠⠀⠰
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣝⣷⡽⡟⠁⠀⠀⠓⠡⠏⠀⠀⠀⣼⣿⡛⠇⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣏⢃⣴⠃⢀⠀⠀⠀⠠⠁⠲⠀⠀⢻⣿⡁⠆⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠨⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠻⣴⣶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢇⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠚⠀⠀⠀⠀⢀⡠⠖⠉⡛⠁⠀⢃⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⠀⠀⠀⠀⠈⠀⠀⣠⠃⠀⠀⠠⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⡴⠁⢀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣏⣿⠃⠀⠀⠀⠀⣠⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⣛⣂⣀⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⡿⠋



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⣾⣿⣿⣿⡛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⣻⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢃⣾⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢃⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢸⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣄⢀⣠⣤⣶⣶⠶⠶⠶⠶⠶⠶⠶⣶⣤⣤⣀⣀⣼⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢁⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣯⠁⢹⣿⣏⣹⡟⢿⣿⡇⠀⠀⢰⣷⠀⠀⠀⣿⣿⠛⣿⣿⣹⣿⠁⢉⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣤⣍⣉⣁⣠⣴⣿⠁⠀⠀⣼⣿⡄⠀⠀⢸⣷⣤⣀⣉⣉⣡⣴⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣼⣿⣿⣿⣦⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠐⢿⣿⣿⣿⣏⢨⡁⠀⠀⠙⣿⣿⣿⣻⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⣿⣿⡏⠁⠀⠀⠀⠀⠈⠉⣿⣛⣛⣛⣛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⢀⣴⡶⠾⠿⠿⠿⠶⢶⣄⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⣀⣠⣽⣦⣀⡀⠀⠀⠀⠀⠀⣀⣠⣾⣥⣀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠈⠙⠛⠛⠻⠿⠟⠛⠋⠉⠀⠈⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠦⣄⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⠶⠶⠶⠶⠶⠦⢤⣀⠀⠈⠳⣄⠀⠀⡠⠚⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⡶⠋⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢀⡦⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣤⣤⣤⣤⣤⡤⠴⠚⠁⠀⣠⠞⠀⠈⠲⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠁⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠋⠙⠛⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⢤⣄⣀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠛⠉⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠠⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣤⣀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⢀⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⢹⡀⠀⠀⣸⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⡇⠀⢠⡏⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⢀⢰⡇⢀⡾⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢠⣿⣿⢠⡞⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢠⣿⣿⡷⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇⠀⢀⣠⣶⡾⠟⠋⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⠛⠉⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⣴⣶⠶⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⢋⡿⠉⠙⣯⢻⣿⣿⣿⡛⢟⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣵⣟⣵⣿⡛⣼⢣⡀⠀⢸⣆⢿⢹⢋⢷⢸⡇⠁⣿⠟⣦⡀⠀⠀⠀⠀⠀⡎⠓⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡟⠁⠀⠀⢹⠇⡱⣿⠀⠃⡄⣸⣿⢸⠾⠀⣾⡇⣷⡀⠟⢸⡏⢿⢦⡀⠀⠰⡆⢻⡴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣫⢃⢆⡀⠀⢀⡴⡜⠀⣿⠸⢀⢀⠛⣼⢸⣖⠀⢸⡿⣾⢃⣤⠞⠻⠋⠻⠛⣤⡀⠿⢰⡢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠫⢡⠃⠆⡎⣹⠏⢉⢰⡇⢰⢸⡇⠘⡘⢀⣿⢸⣿⠀⣿⡇⣿⡞⠁⠀⠀⠀⠀⠀⠈⢽⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠁⡁⡜⠰⢰⡟⠀⠀⠀⠉⢫⢸⡇⠀⣷⡾⡿⢸⣿⣸⣿⢱⣿⡀⣀⡤⠦⠦⣄⠀⠀⠀⢇⢖⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⢱⢠⠁⠀⠃⢹⢿⡆⠂⢰⠘⡀⣿⡇⢀⢻⣿⡇⢸⡇⣿⡿⣸⣿⣽⠁⠀⠀⠀⠨⣇⠀⠀⣿⠁
⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢸⡎⡀⠄⢀⢰⢸⠘⣇⢴⠈⢆⣸⣿⠷⠮⠞⠻⣧⡞⡇⡟⢁⣿⣼⣹⠀⠀⠀⠀⢀⡧⠤⢿⠋⡤⠄⠂
⠀⠀⠀⠠⣤⡀⠐⠄⠠⢀⡸⣷⡇⡆⡌⠘⠀⣶⢋⣻⣷⠚⠁⠀⠀⠀⠀⠀⠙⠳⠦⠷⠋⠀⣠⣭⣝⡖⠲⣞⠃⡇⡄⣿⣦⡴⣂⡀
⠑⠀⣀⣀⠌⠓⢴⣀⠁⡆⠌⠙⣧⣄⣣⣠⠟⡁⡋⣹⣯⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠵⠿⣭⠁⠀⠙⢧⣧⠞⢻⠒⠒⠤⡈
⠀⠀⠀⡄⠠⠐⢠⣼⡷⠗⢿⡆⠾⣯⣏⠁⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢹⣿⣀⣸⠂⠈⠂⠁⠂
⠀⠀⠀⠀⢺⠖⣠⣖⡈⣉⠤⠙⡒⠚⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣗⣺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⡽⣋⠈⠉⡀
⠀⠀⠀⠀⣏⢊⠔⠁⠀⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢸⡧⠀⠘⡀
⠀⠀⠀⠀⢹⣤⠄⠂⠁⢀⠤⢛⡛⣛⡓⠲⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢡⠃⢸⠇⠀⠘⠃
⠀⠀⠀⣠⣿⠃⠠⢀⠚⠁⣠⡏⠀⠀⡈⠗⠢⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⢡⢆⠎⢠⠏
⠀⢀⡞⠋⡄⠀⠠⠁⢠⠊⠀⢆⠈⠀⣀⠮⢀⣀⠀⣀⡠⠌⠛⡲⠖⢤⡤⢤⠤⢴⣶⠾⠟⡐⠀⠈⢁⣁⠴⠋
⠀⣾⢸⡄⠃⢀⠂⢀⠃⠀⡐⠁⠉⠁⠀⠀⢀⣀⠀⠀⣀⠠⠊⠀⢠⠞⡐⣡⢖⡩⢂⣨⠴⠒⠚⠋⠉
⠐⣿⢸⠀⡄⢸⠀⠘⠀⡈⠀⡠⠒⠉⠀⣀⣀⡀⠀⠀⠀⠀⢀⠔⢁⡼⠡⠡⠂⢠⠏
⠀⢿⡄⡀⠃⠸⠀⠀⠀⠀⠰⠁⣠⠂⡁⠀⠐⠒⠂⠠⠤⠥⠤⠒⢁⠄⡡⠁⢀⡞
⠀⠈⠿⣴⣜⡄⣃⣆⠀⢰⠀⡜⡡⠊⢀⠄⠂⣈⣉⣉⠁⠒⠒⠀⡡⠔⢁⣠⠞
⠀⠀⠀⠀⠉⠉⠉⠉⢷⡜⣜⢁⠁⠔⡠⢐⡭⠖⠒⠒⠒⠿⠾⠶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡤⠊⣊⠞⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠁
⣿⣿⠟⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠛⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠛⠛⠓⠦⣄
⠀⠀⠀⠀⠀⣴⠏⠁⢀⣤⣤⣤⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⣤⡤⣤⣄⠀⠈⢷⡀
⠀⠀⠀⠀⣸⠃⠀⣴⠏⠁⠀⠀⠉⢷⡀⠈⣧⠀⠀⠀⠀⠀⣸⠃⠀⣴⠋⠀⠀⠀⠈⢳⡄⠈⣷
⠀⠀⠀⠀⣿⠀⢰⡏⠀⢠⠞⠛⠛⢿⡇⠀⢹⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⢠⠞⠋⠙⢲⣧⠀⢸
⠀⠀⠀⠀⣿⠀⢸⡇⠀⠏⠀⠀⢀⣼⠇⠀⠸⠀⠀⠀⠀⠀⣿⠀⢸⡆⠀⠋⠀⠀⢀⣼⠇⠀⠸
⠀⠀⠀⠀⢹⡄⠀⢷⠀⠀⣠⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢷⠀⠀⢠⣶⣿⡁
⠀⠀⠀⠀⠀⢻⡄⠈⠳⠀⠹⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠳⠀⠘⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠲⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣭⣭⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⠶⠖⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⠞⢋⣭⣭⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡏⣼⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢀⡏⣰⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣠⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⠟⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⣆⠸⣇⠀⠀⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢳⡸⣿⡘⣿⣿⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⢆⠈⠓⠦⣌⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢳⣝⣿⣦⣝⡻⢦⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣥⣭⣿⣤⡉⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠛⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⡤⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⠿⢟⣵⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠁
⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⠙⠛⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠙⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣧⠞⢀⣥⣶⣷⠿⣯⡦⠀⠀⠀⠀⡀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⡿⠋⠈
⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢯⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⣿⣶⣤⣀⠈⠙⠒⠄⡀⢀⣿⣿⣿⣿⣿⣿⠇⠀⠻⣿⣿⡟⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣷⣦⣄⣀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠙⣿⣿⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠢⢌⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠱⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣤⣤⣀⣀⣀⣤⣶⣿⣿⡿⠛⣡⣴⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣽⣿⣿⣶⣤⣄⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠿⢿⣿⣿⣿⡿⢟⣭⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡲⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⣷⣾⣦⣄⣤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡋⠉⡿⠟⠛⠀⠀⠙⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣦⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣾⣀⣀⡀⠀⠀⠿⢿⠋⠙⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⣅⣀⠀⠉⠒⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣥⣀⠀⣨⣅⢀⠀⢰⣦⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⣿⡿⣿⠿⣿⣿⠟⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣀⠉⠠⠜⡄⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣤⢀⠀⠀⠈⡙⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣷⣇⣼⠁⠀⠀⠀⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⣿⣧⠀⠀⠀⣿⣿⣿⡿⠀⠀⢠⣄⣼⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠘⢿⣿⣷⡀⠀⠀⠙⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠤⠀⠀⠈⠉⠉⠉⠈⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⡀⡄⠠⠀⠁⠀⠛⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⠟⠀⠀⣀⣼⣿⣿⣿⣿⣿⣦⣤⣤⡀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢻⣿⣿⠃⠀⠀⣰⣿⣿⠷⠄⠜⠋⠀⣠⣿⣿⣿⡿⠛⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⡇⠀⠀⢰⣿⣿⠉⠀⠀⠀⠀⣸⣿⡿⠿⠋⠀⣡⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⣿⣧⡇⣠⣿⣿⣽⡇⡇⠀⠀⢸⡟⠁⠀⠀⢀⡤⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡶⠋⠁⠉⣿⣧⣿⣿⣿⡇⠀⠀⠀⣾⢇⣀⣤⣶⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⢹⣿⣾⣿⣿⣶⠀⠀⣰⢿⣿⡿⠋⠉⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⡀⣸⠏⠀⣿⣿⣷⣧⣤⡜⠃⡽⣧⣠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢤⣿⡟⠀⠀⠈⠻⢻⠋⠁⠉⠀⠂⠊⠙⠷⠷⠧⣾⠶⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣀⣾⣿⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣬⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣯⠁⠀⠀⠀⠐⠀⣒⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⢿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠊⠀⠂⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⣼⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣮⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣄⣀⣀⣤⣤⠀⣜⠀⣌⣸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡷⢊⣡⡞⣿⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢦⢠⣾⣿⣿⣿⣷⣦⡀⠶⠒⠖⢬⡑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠏⠈⠉⠻⡿⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⣸⣿⡿⠂⠀⠀⠀⣽⡍⠒⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠉⠟⡀⠀⢇⠉⠃⠀⠀⠀⠀⠁⡤⠀⢠⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠠⠚⠃⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⢊⠁⢻⡇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠚⡁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠻⠧⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠋⠲⣋⡟⠀⠀⠀⠀⠀⠀⠀⣈⣤⠴⣤⣤⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠃⠀⢈⡚⠀⠀⠀⠀⠀⠀⠀⠀⠙⡾⣻⢾⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣶⡾⠿⢶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠯⢭⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⢢⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠆⠀⠀⡤⠄⠀⠠⠀⠀⡴⣤⠐⠎⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣷⠦⠀⠀⡀⣠⠀⡀⠀⣈⠄⢠⣤⣼⡀⢠⠀⠴⣿⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣸⣀⣼⡀⡃⠈⣿⠇⢰⣻⡉⡇⢹⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣶⣶⣿⣿⣿⣛⣿⣒⠐⣿⠓⢘⠟⢿⣷⣾⣥⣦⡤⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠃⠈⠈⠙⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣠⣠⢀⡀⠀⠀⠰⠄⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠟⠋⠋⠉⠛⠓⠺⢿⣮⣶⣦⣀⠄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⣿⡿⠟⠯⠒⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⡄⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢨⣿⣠⠀⠠⠀⠀⠩⠒⣄⠀⠀⠀⠀⠈⢷⢻⣿⣦⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡽⣏⡠⠀⠀⠀⠀⠀⢉⡇⠀⠀⠀⠀⢸⣾⣣⢹⡇⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠱⣿⡇⠀⠈⠀⠀⠓⠉⠀⠀⠀⠀⠀⠀⡯⣡⣼⡇⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢿⡇⠀⢀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠙⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⡚⣇⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣷⣀⢄⠀⠀⠀⢟⣿⠐⣵⠀⠀⠀⣿
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣯⣍⠙⢿⣷⡀⠀⠸⣾⣇⡹⡆⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠈⠙⠻⢦⣹⣷⠀⠤⢻⣇⢲⡇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡋⠟⠹⣷⣄⠀⠀⠙⣿⠀⠀⠘⣿⣿⠁⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⠀⠀⠘⠿⣇⠀⣀⣿⠀⠀⠸⣿⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⢡⠀⠠⠈⢰⣿⣆⣸⡇⠀⠀⢰⣿⡿⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡿⣏⣤⣭⣴⣤⣶⣾⣿⣿⣏⠀⢀⣠⣼⣿⡃⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠈⠛⢿⠋⠉⠉⠉⠉⠉⠉⠁⠀⣈⣹⣿⠟⣴⣿⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠹⣿⣧⣾⠅⣙⡁⣉⠋⠉⡋⠉⣓⡛⠛⠿⣋⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠉⠉⡿⠛⠛⠉⠁⠀⣨⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠐⠂⠂⠀⠀⠀⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠈⠀⠁⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠿⠛⠛⠛⠋⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣄
⠀⠀⠀⠀⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣄
⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠙⢿⣿⣷⣄
⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⣠⣾⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣦⡀⠀⠀⠀⠈⠻⣿⣿⣦
⠀⣸⣿⣿⠃⠀⠀⠀⢀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦⡀⠀⠀⠀⠙⣿⣿⣧⡀
⢀⣿⣿⡏⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⠀⠀⠘⣿⣿⣷
⢸⣿⣿⠁⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠘⣿⣿⣇
⣾⣿⣿⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⢹⣿⣿
⣿⣿⡏⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⢻⣿
⣿⣿⣧⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⢸⣿
⠹⣿⡿⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠋⠉⠉⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠁⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣶⣶⣾⣿⣿⠟⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣦⣤⣀⣀⣀⣀⣠⣴⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣠⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠒⠒⠒⠒⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⣀⣀⣤⣤⣤⣀⣀⣀⡀⠀⠈⠋⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢀⣴⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢧
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⡟⣿⣿⣿⣿⣿⣷⡀⠀⢧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠈⠁⣹⣿⣿⣿⣿⣿⡇⠀⠈⠇
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠈⢿⣿⣿⣿⣯⣻⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠈⣿⣿⣿⣿⣯⡹⣀⢀⡀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢻⣿⣿⣿⣿⡁⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢯⡿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠰⣿⣿⣿⣿⣧⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠈⣙⠛⢿⣿⣿⣿⣿⣿⡆⠀⢻⣿⣿⣿⡜⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⣻⣿⡿⢀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠩⣿⡟⠃⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠰⣿⠻⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁⠀⠀⣸⣿⠁⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢿⠿⠿⠿⠟⠋⠞⠀⠀⢀⡿⠟⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠝⠊⠒⠏⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠋⠀⠀⠀⠀⣀⠀⠀⡀⡀⠔⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠋⠀⠰⠘⠁⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⡀⠀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠶⠏⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡤⣤⣀⠀⣠⢀⣴⠃⠀⠀⣴⠲⣦⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣤⡀⢠⢶
⠀⠀⠀⠀⢸⡇⠀⢹⡇⣿⣿⡁⠀⠀⠀⣿⣶⡋⢀⣄⢠⣆⢸⡇⣰⢞⣆⢰⡶⢶⡆⣠⠖⣺⣿⠀⠀⠀⠀⠈⢿⣿⣾⣼⣀⡀
⠀⠀⠀⠀⠸⠧⠴⠚⠁⠿⠈⠛⠃⠀⠀⠛⠙⠻⠊⠛⢛⣿⠸⠇⠛⠞⠻⠋⠁⠈⠃⠻⠶⠟⣿⡇⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⣰⣿⣿⠇⣽⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠈⠛⠻⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠛⠁⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠀⠀⢸⣿⡿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡻⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⣿⣿⣿⣿⡷⢶⣦⣤⡴⣶⣿⣁⣬⣷⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⢻⣧⣽⡇⣌⢿⠿⣷⡘⣃⣾⣷⠿⣿⣿⠼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⡙⣿⠹⠏⢻⡄⣦⣿⡏⣿⡀⢿⡆⣿⣩⣾⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⣿⣷⣶⣸⣏⣱⣟⣷⣽⣇⣸⣧⣿⣼⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡀⣿⣿⣿⣿⣿⡟⠻⠿⠿⠿⠿⠿⠟⢻⣿⡗⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⣿⣿⠟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠸⠿⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠢⠀⠀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⡇⠀⢀⠀⣠⠁⠀⠈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡶⠈⠦⢀⡠⠇⠀⠀⠉⠁⠀⠀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠙⢆⣠⠞⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠔⠋⣠⠤⠦⣤⡙⢢⡄⠘⠁⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣸⠃⠀⠀⠀⠆⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢤⠎⠀⡿⠀⠀⠀⠈⡆⠋⠀⠀⠀⠀⠀⠊⠀⣀⠄⠒⠒⠲⣬⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⡌⠀⠀⡇⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠘⡏⠁⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠇⢀⠄⢿⠀⠀⠈⠂⡀⠀⠉⠀⠀⠀⠀⠀⡠⠉⠈⣆⠀⠀⠀⠈⢦⠏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡘⠁⠀⠀⠀⠐⢖⢀⡴⢂⣄⠀⠞⠁⠈⠁⠀⠀⠀⠀⠰⡄⠤⠤⠈⢆⠀⢠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡎⠀⠀⠀⠀⠀⠀⠂⢁⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠘⣷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢫⠁⠄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠠⢁⡌⣰⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠎⠀⡐⣫⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠀⡅⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠐⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠎⠀⠀⠀⡃⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠠⠄⠀⡀⠀⠀⠂⣀⡀⠔⠒⠀⠈⠑⢦⡀⠀⠐⠆⢀⠁⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⢌⡃⢻⠐⠢⣀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠲⢆⠀⢘⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠁⡿⢶⣤⣘⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣠⢽⠇⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣳⡄⡇⠀⠈⠛⠭⠭⠭⠍⣙⡒⢤⡀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠭⢳⡤⢤⠠⠎





⣶⣶⣶⠶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⢷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠈⣷⡀⠀⣼⣿⣿⠰⣂
⠀⠀⠀⠀⠀⠀⠀⣼⡏⢡⠀⢹⣧⠀⢿⣿⣿⡆⣿⣆⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢡⡿⠀⢸⣇⠸⣿⡄⢸⣿⣿⡇⢸⣧⣅⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⡃⠀⠛⠻⡀⢸⣷⣼⣿⣿⣯⠠⠻⣿⣷⠈⣼⣿⣿⡿⢛⠲⡄
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⣷⠀⢻⣿⣿⣿⣿⠌⠢⠤⠘⠀⢹⡿⡡⡇⣿⡇⣧
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⣸⣿⣧⠀⢿⣿⣿⣿⣆⠀⠁⠀⡀⣹⠗⡷⠛⣎⣥⢉⣠⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⣿⣿⣷⠘⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣘⣧⣴⣮⣝⢾⣏⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣤⣿⣿⣿⣿⢿⠟⠿⠋⠋⠙⢮⡻⣿⣿⣿⣿⡿⣿⡄⠐⠂⣤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠹⣿⣿⣿⡿⠛⠉⠀⢀⠠⠄⠀⣐⣬⣽⣷⣿⣿⡏⠙⢿⣮⡙⢦⡙⠧⣍⣳⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⢸⣿⣏⠀⠄⣤⠚⠉⢄⣴⣾⣿⣿⣿⡿⢙⡿⣇⣀⣀⡙⢿⣦⡈⠒⢿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣿⡄⢾⡿⢹⣿⡟⢆⠀⠀⠈⠉⠻⠿⣭⡁⠀⠈⠀⠀⡟⢹⡇⠈⠈⢿⣦⣀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠈⢻⣧⠸⡆⠀⠀⠀⠀⠠⠹⣿⠀⠐⠀⠀⠧⠸⠇⠀⠀⠀⠻⣿⣷⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⣼⣿⡀⡇⠀⠀⠀⠀⠀⠡⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣴⣾⣿⠟⠃⠇⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣦⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣦⡀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⢟⣿⣿⣿⡿⠀⢿⣿⣿⣿⣆⠀⠉⠻⢿⣿⡿⠀⠘⢿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⢸⣿⣿⣿⠇⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠘⢿⡿⠏⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⣀⣠⣤⣾⡇⠀⠀⠀⠀⠀⠀⣠⣶⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠛⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣶⣶⣤
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⢡⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟
⠀⠉⠛⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣾⠟⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠁
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⢶⣤⣀⣀⣀⣴⡾⠋⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠉⠉⠛⠉⠉⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠙⠻⢶⣶⣤⣤⣤⣴⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠷⢶⣶⣶⣶⣶⣶⣶⠾⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⠿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⠀⠀⣀⣤⣤⣴⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⡄⠀⠀⠀⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⠻⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣤⣀⠀⠀⠙⢿⣿⣷⣤⡀⠉⠛⢿⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣦⣀⠀⠙⣿⣿⣿⣶⣄⠀⢻⣿⣿⡀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡀⠈⢿⣿⣿⣿⠀⠈⣿⣿⡇⠀⠀⠀⣸⣿⠏⠀⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⣿⣿⣷⠀⠈⠻⠟⠃⠀⢰⣿⣿⠇⠀⠀⢠⣿⡟⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⠁⠀⠀⠙⠛⢁⣠⣤⣀⣀⣀⣤⣿⣿⡟⠀⠀⢀⣿⡟⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⣴⣿⣿⢿⣿⣿⣿⡿⠿⠋⠀⠀⢠⣾⠏⠀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⣀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⠙⠿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣦⣤⣶⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉




⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣯⣭⣭⣤⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣷⣶⣾⣿⣷⣧⣴⣶⣾⣷⣶⣼

⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⡖⠀⠀⠒⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⣿⣿⣦⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⡟⠀⠀⠀⣰⣿⣿⣄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⡿⠁⠠⠀⢠⠏⠻⣿⣿⣆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣼⠃⠀⠀⠀⠟⠀⠀⠘⣿⣿⣧⡀
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⣿⣿
⣿⡯⣿⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿