Rainy Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠙⠢⡄⢀⡤⠔⠒⠚⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⠀⡰⠒⠋⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⢀⣀
⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠓⢤
⠀⠀⠀⣀⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⠢⡀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⣄
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⢲
⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠫⠽⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠁
⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠈⠉⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠉⠢⣄⣀⡀⠀⠀⠀⣀⣠⠞⠁⠙⠲⢤⣤⣀⣀⣀⡤⠴⠊⠁⠀⠈⠉⠙⠛⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⡼⢧⠀⠀⠀⠀⠀⠀⠀⡸⢳⠀⠀⡀
⠀⠀⠀⠀⢀⣴⡀⠀⠀⢯⣸⠇⠀⠀⠀⠀⠀⠀⡏⠸⡆⠀⠀⠀⠀⠀⣇⢸⡆⠀⠀⠀⡀⠀⠀⢇⣸⠇⢰⠻⡄
⠀⠀⠀⠀⢸⠀⣷⠀⠀⠀⠁⠀⠀⠀⢰⢧⠀⠀⠳⠼⠁⠀⠀⣠⡀⠀⠘⠛⠀⠀⠀⢰⠻⡄⠀⠈⠉⠀⢸⣀⡇
⠀⠀⠀⠀⠀⠙⠋⠀⠀⢠⡄⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⢠⡇⢧⠀⠀⠀⠀⣤⠀⢸⡀⡇⠀⢀⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠀⠀⠀⠙⠚⠀⠀⣠⡀⠀⠀⠘⢇⡼⠀⠀⠀⢸⠀⡇⠀⠉⠁⠀⢸⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠀⠀⠀⠀⠀⠀⢠⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠏⠀⠀⠀⠀⠘⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼
⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣛⣛⣛⡛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣻⡿⣶⣿⣾⣿⣿⣿⣿⣆⢻⣷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣝⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣴⣦⣄⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣟⣯⣭⣶⣮⣭⣟⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⡝⣿⣆
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣸⡿
⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⢷⣝⢷⣭⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠈⠛⢷⣿⣿⣿⣿⠿⠋⠛⠿⢿⣿⣿⣿⠿⠛⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢆⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠢⠄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠡⠀⠄⠀⢄⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠠
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣈⢀⣀⠔⠒⢢⠖⠒⠴
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠘⠈⡩⠐⠩⢅⠁⠉⠈⠭⣐⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠈⠑⢄⠀⠀⠁⠂⢄⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠬⠦⡀⠀⠀⠀⠐⠂
⠀⠀⠄⠀⠀⠀⠀⣀⠀⠠⠀⠠⠀⠀⠂⡄⠀⠤⠀⠀⠈⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢻⠀⠀⡔⢀⠆⢀⠃⠀⢀⠂⠀⠄⠀⡐⠀⡐⢀⢀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠋⣐⠀⠈⠀⠠⠄⠈⢀⠄⡔⠀⠉⠀⠘⠄⢀⠄⠀⡅⠁⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢠⠀⠀⢸⠀⠊⠀⠀⠚⠀⠀⠀⠇⡀⠘⠀⢈⠄⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠐⠀⠃⢀⡔⠠⠂⠰⠀⡰⠀⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⣢⣴⣤⣶⣶⣾⣆⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠡⢚⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡛⣥⣤⣤⣤⣄⠙⣿⣿⣿⣿⣿⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⠃⠈⠻⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢄⣀⣿⣿⣿⣿⣿⡟⣿⣿⣿⣍⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡦⠿⠋⠉⣿⣿⣿⣿⠻⣿⡃⣿⠻⢛⣹⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣆⣨⢀⣀⣥⣿⣿⣮⣿⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⠟⠿⣿⣆⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣾⣿⣿⣿⡟⠱⢖⣞⣿⣿⣷⡀⠁⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠏⠀⠠⠤⢿⣿⣿⣿⣿⡄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠏⠈⠀⠘⠚⠛⢻⡿⣿⣿⣇⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣡⡀
⠀⠀⠀⠀⠀⠛⠛⠛⠿⠏⠿⢻⣿⣿⣿⠻⢻⢿⣿⣿⣿⡿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠀⢹⠁⠀⣿⠀⠈⠉⠙⠛⡿⠛⠉⠉⠋⠋⢃⠈⢻⢡⡄
⠀⠀⠀⠀⠀⠀⠄⠀⢸⠀⠀⠀⠀⠀⢘⠀⠀⠸⠀⠀⢻⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠂⠀⢀⡗⠀⠀⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⢠⡀⠀⣶⡀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆
⢹⡆⢀⠀⠰⠇⠀⠀⢿⡀⠀⠀⣧⠀⠈⠀⠀⡀⠀⠸⠇⠀⠈⠀⠀⢸⡃⠀⠹⠃⠀⠀⠀⣗⠀⠀⠀⠀⠘⡼⠀⠀⠀⠀⣷⠀⠀⠀⡜⡆
⠈⠀⣿⡄⠀⠀⣄⠀⠙⠁⠀⠀⠙⠀⠀⠀⢸⣣⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⢰⢆⠀⠋⠀⠀⢠⡀⠀⠀⠀⢠⣳⠀⠈⠀⠀⠀⠙⠁
⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⣎⡇⠀⠀⠀⠈⠛⠀⠀⠀⠀⢠⡄⠀⠀⢸⣃
⢠⡀⠀⠀⠀⠀⠉⠀⠀⠀⠠⡴⠀⠀⠀⣄⠀⠀⢰⡄⠀⠘⠃⠀⠀⡀⠀⠸⡇⠀⠀⠀⣀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣀⠀⢸⡃⠀⠠⡴⠀⠀⠘⠋
⢰⡇⠀⠠⣻⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⣽⠆⠀⠸⠃⠀⠀⠀⠀⢀⣿⠀⠈⠃⠀⠀⠀⣏⠀⠀⠀⠀⠀⡀⠀⠀⠘⣬⠄⠈⠁⠀⠀⠁⠀⠀⠀⣆
⠀⠀⠀⠀⠉⠀⠀⢸⣥⠀⠀⠸⡧⠀⠀⠀⠀⠀⠀⣀⡀⠤⢤⠤⠼⣿⣄⣀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠘⣵⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⡀⠀⠉
⠀⠀⢠⡄⠀⣴⡀⠀⠁⠀⠀⣀⡤⠴⣒⡾⣛⠯⣋⠤⣒⠭⠐⠊⠁⠈⣣⢰⠂⡉⠉⠙⠓⠶⢶⣤⡀⣤⣉⣀⠀⠀⠀⠀⠀⠀⢸⣱⡀⢠⢛
⠀⠀⠰⡿⠀⠙⠀⠀⡠⡴⠚⠁⣠⡮⠕⡩⡰⠝⣂⠥⠒⠊⠁⠀⠀⠀⠃⣂⢳⠄⣐⠂⠄⠀⠀⠀⠙⠳⢤⡩⢉⡑⠲⠤⣄⠀⠈⠛⠀⠀⠛
⢰⡄⠀⠀⠀⣠⠔⡭⠭⠁⢀⠞⡩⢒⠕⣊⠔⣊⠅⢂⡁⠀⠀⠀⠀⠀⠀⢸⡀⡡⠄⡒⠨⠥⠀⠀⠀⠈⠁⠙⢧⡊⠕⡂⠄⠉⠲⢄⡀⠀⠀⣿⡀
⠸⠇⠀⣠⢊⡑⠨⠅⠀⢀⡎⡨⢊⠵⣊⠕⡪⠔⣊⠅⠀⠀⠀⠀⠀⠀⠀⠈⡅⣈⠥⠐⡀⠉⠥⠀⠀⠀⠀⠈⠀⠳⣬⠔⡂⠥⢀⠀⠙⢦⡀⠉
⠀⢀⠎⣄⢀⡂⠀⠀⠀⡼⣡⢜⡥⡊⣕⠯⢒⠭⢒⠠⠀⠀⠀⠀⠀⠀⠀⠀⢾⡴⠎⢁⡒⠤⠀⠁⠀⠀⠀⠀⠀⢃⠙⡯⢒⠨⠁⣀⠀⠠⡱⡄
⢠⡯⠾⠼⠯⠤⣔⡠⠀⣏⢔⡁⡢⢛⣥⣊⡴⢪⣤⣊⣡⣐⡠⢀⠀⠀⠐⠀⠨⢒⡩⢔⡂⠬⣀⣒⠂⠲⢀⡀⠀⠀⣂⠹⡥⢒⡡⣔⡈⠥⠽⢼⡆
⠛⠀⠀⠀⠀⠀⠀⠈⢲⣧⠿⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢺⣴⣀⠀⢸⠄⣪⡵⠾⠛⠒⠚⠐⠒⠒⠒⠒⠪⠽⢆⣷⠟⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⠑⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⡎⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢿⡀⠀⢀⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡉⠛⢁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⣀⠀⠀⡀⢀⠠⢀⠤⢂⠤⢀⠠⢀⠤⢀⠄⡠⠀⡀⢀⢄⡀⢀⠀⢀⢀⡀⣀⠀⡀⠀⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠁⠚⠁⠂⠁⠒⠡⠊⠵⠊⠔⠥⠊⠕⢩⠔⡡⠒⠕⡡⢊⠕⢋⠔⣡⢚⠕⡫⢐⠅⡢⢖⠕⡢⢒⡡⣂⠔⣡⢂⠔⡠⢠⠄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠿⠛⠛⠻⠷⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⢤⣼⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠉⠉⠙⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿
⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣿
⠀⠀⠀⠀⢻⡏⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⣽⡟
⠀⠀⠀⠀⠈⢿⣄⢅⡂⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⡠⢐⠠⢐⣼⠟
⠀⠀⠀⠀⠀⠈⠻⣷⣬⣄⡂⠀⠀⠄⣀⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⢤⣄⣅⣂⣌⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠛⠉⠑⢦⣥⣅⣐⡐⡀⠀⢂⠄⢅⣐⣐⡽⢿⣦⣄⠄⡀⡀⡀⠀⠀⠄⣄⡶⠟⠁⠀⠈⠉⠉⠉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠈⠙⠛⠷⠾⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢤
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣰⡟⠁⢰⡄⠀⠀⠀⠀⠀⠀⣠⡾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⣾⠋⠀⢱⡀⠀⠀⠀⢿⡄⠀⣸⠇⠀⠀⠀⠀⠀⢰⡟⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠋⠀⠀⢀
⠀⠀⠀⢿⣄⣀⡼⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⢀⠀⠀⠘⢧⣀⣠⠟⠀⠀⢀⣴⠞⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡞⠋
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠉⠁⠀⢀⣼⠟⠁⠀⠀⠀⠙⠷⠴⠟⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡾⠋⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣄⠀⠀⠀⠀⣿⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠻⣄⣠⡾⠁⠀⠀⠀⢀⡀⠀⠀⠀⣿⠀⠀⣸⠀⠀⠀⠀⠙⢦⡴⠟
⠀⠀⠀⠀⠀⢠⡾⠋⡀⠀⠀⠀⠀⠀⠹⢦⡴⠟⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠙⠶⠾⠋
⠀⠀⠀⠀⠀⣿⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⠏⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠻⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠐⣄⠀⠀⠀⠀⠀⠀⢼⡇⠀⢈⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⠷⠤⠾⠁⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣤⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠰⡀⢤⣶⣾⣿⣿⣿⣿⣿⣶⣴⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠀⠂⠀⠀⠀⢀⡽⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⣿⣿⣿⣿⠃⠀⠀⠀⠠⣶⠋⠀⠀⠉⠉⠉⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⢕⢄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠛⠁⠀⡄⠀⠀⠀⠀⠀⡟⢻⠶⣄⡀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣃⣠⣾⣦⠀⡀⣻⡇⠀⠀⠀⢸⡇⣾⠀⠈⠻⠃
⠀⠀⠀⠀⣠⠀⠀⠀⣴⣿⠀⠀⠀⠀⣰⣀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⣿⡇⠀⠉⠛⠛⠋⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⢀⣠
⠀⠀⠀⣼⣿⡆⠀⢀⣿⣿⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠐⠻⢧
⠀⠀⢰⣿⣿⣷⠀⣸⣿⣿⡇⣠⡄⣿⣿⣿⠀⢠⣾⡅⠀⠀⠀⠀⣿⠋⠁⠉⠀⢀⠀⠤⠤⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⢀⣿⢽⣧⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣇⣼⣿⡃⠀⠀⠀⠀⠉
⠀⠀⡗⡐⠻⣿⠟⠉⠉⢉⣿⣿⣟⠁⠉⠉⣿⡿⣿⡇⢀⣤⣤⠠⠀⠰⡄⢶⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⢠⣀⡀
⠀⠈⠀⠀⠀⠀⠀⠄⠀⢼⡡⣿⣿⠀⠀⠀⠈⠀⠁⠀⠙⠚⢻⣿⣿⣿⣿⣿⣿⡟⠋⠋⠁⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠿⠻⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣽⡿⠁⠀⠀⠀⠠⠤
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣮⣵⣦⣤⣮⣴⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠙⠛⠿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠃
⡏
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠁⢀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠰⠿⠟⣻⣿⣿⣿⣶⡇⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣠⣿⣿⡿⠛⢹⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⣹⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣾⣿⠁⠀⠀⣰⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣄⢀⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣿⣿⣿⠋⠀⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠰⢿⣿⣿⣿⣶⣶⣿⣿⣿⡟⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣀⣰⣿⣿⣿⣿⠋⠀⣿⣿⣿⠇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⠋⠀⢻⣿⣿⣠⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⠓⢦⡤⠶⢤⣀⡀⠀⠀⠀⣠⠴⠖⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠀⡴⠋⠉⠉⠛⣦⣰⣏⠐⠀⠀⠀⠻⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠀⠀⠀⣠⠤⢼⠁⠀⠀⠀⠘⠁⠀⠈⠉⠀⠂⠀⠀⠀⣼⠶⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠛⡞⠁⠀⠀⣀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣠⠞⠉⠉⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡴⠋⠁⠹⣆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣂⣁⠀⠀⠀⠀⠠⠀⠀⢀⡼⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠐⠲⠤⠴⠒⠀⠀⠀⠲⠀⠀⠀⣠⠋⠉⠓⠤⠄⠀⠀⠀⠐⠒⣉⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠠⠀⠈⠑⠶⠖⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠖⠋⠡⡀⠀⠀⠀⠀⢠⠀⠀⢀⡼⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠲⣦⡀⠀⣀⡼⠻⣤⣙⠢⣌⣀⡥⠆⠀⠤⣁⢀⣀⠀⠀⠀⠀⠀⠈⠲⠤⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠉⣉⢠⢂⠀⠉⠉⠉⠙⠦⣤⡤⠞⠉⠉⠹⣄⠀⠀⠀⠀⠀⣀⣀⣠⠏⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⡟⢰⠇⡎⡞⠀⠀⣶⡇⠀⢀⡄⢠⠄⣾⡇⠀⠉⠳⠦⠤⠴⠚⠁⠈⢁⠀⠂⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⢁⡟⡘⠸⢀⠃⢰⡟⠀⠀⣼⢁⡟⣸⡾⠀⠁⣠⡄⠀⢀⡤⢰⡇⡜⡞⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠇⣼⢡⢁⠃⠌⠀⣽⠁⠀⢰⠇⣼⢡⢷⠃⠄⠠⣿⠁⠀⣼⠃⡞⢰⢱⠁⠄⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡟⢰⠃⡎⡎⡘⠀⣰⡟⠀⢀⡟⢰⡇⣾⡟⠀⠀⢰⡇⠀⢰⡏⣸⠃⡇⡆⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡾⢁⡏⡰⢸⢡⠃⢠⣿⠁⠀⣼⠁⡞⣸⣽⢁⠃⢰⣿⠁⠀⡾⢀⡏⡸⡸⢀⠁⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠇⡼⢠⢃⠇⠆⠀⣾⡇⠀⢰⡇⣸⢁⣿⡏⠄⠀⣼⠇⠀⣸⠇⣼⢠⢇⠇⠌⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⡏⢰⠃⡄⡘⠀⠀⡸⡟⠀⢀⡿⢀⠏⣸⡿⠰⠀⢰⡿⠀⢀⡟⢠⠇⡎⡼⠠⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡼⢁⡏⠸⢠⠁⠀⢠⣻⠁⠀⣼⠃⡜⢠⣻⠃⠀⢀⢿⠃⠀⣼⠁⡜⠐⢱⠃⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⠇⡼⢠⢃⠇⡀⠀⢾⠇⠀⢰⡏⢰⠃⣞⡟⠀⠀⡜⡎⠀⢰⡏⢠⠁⠄⡎⠀⠀⡘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡎⢐⠃⠎⡌⠀⠀⢈⡾⠀⠀⣾⢀⡇⡸⣼⠁⠀⠰⡽⠀⠀⡾⠀⠇⠰⢰⠁⠀⢀⠱⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠇⡼⠀⡎⠸⠠⠀⠀⠀⠾⠃⠀⢸⠃⡼⢠⢣⠇⠀⠀⢣⠇⠀⢸⠇⠸⠀⠀⠇⠀⠀⠀⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣴⡾⠟⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠛⠛⠻⠟⠀⠀⠀⠸⣿⠶⣶⣄⣀⣀⣀⢠⣶⠟⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠛⠿⠃⠀⠀⠀⠹⠷⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⡟⣿⡟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣀⣠⣾⠛⠉⠀⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢻⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢀⣤⣿⡇⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢀⣴⣿⡂
⠀⠀⠀⠀⢰⡿⠋⣿⡇⠀⠀⠘⠿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿⠃⠀⠀⠀⠀⢰⡿⠉⣿⡇
⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢀⣤⣾⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⠀⠀⠀⠀⠀⢀⣴⣾⣿⠀⠀⠀⠀⠀⢀⣴⣾⣟
⣿⡋⢸⡿⠀⠀⠀⠀⠀⣿⡋⢸⡿⠀⠀⠀⠀⠀⣿⡋⢸⣿⠀⠀⠀⠀⠀⣿⡋⢸⣿⠀⠀⠀⠀⠀⣿⡋⢸⡿
⠈⠛⠛⠁⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⢀⣴⡾⣿⡇⠀⠀⠀⠀⢀⣴⡾⣿⡇⠀⠀⠀⠀⢀⣴⡾⣿⡅⠀⠀⠀⠀⢀⣴⡾⣿⡅
⠀⠀⠀⠀⢸⣯⣀⣿⠇⠀⠀⠀⠀⢸⣯⣀⣿⠇⠀⠀⠀⠀⢸⣯⣀⣿⠇⠀⠀⠀⠀⢸⣯⣀⣿⠇
⣶⣶⡶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠦⠤⣄⠀⢀⠤⠒⠊⠉⠉⠉⠙⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣠⠊⠁⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡤⠔⠒⠒⠒⠤⣄⡀
⠀⠀⠀⠀⣠⠔⠚⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡌⢱⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⡜⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢀⡬⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠉⠁⠀⡸⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣄⡀
⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⣀⣀⣀⣀⣤⡀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠷⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⣇
⠈⠲⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⠞
⠈⢧⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁
⠀⠀⠙⠒⠶⢶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⢠⣄⠀⠀⠙⠢⢤⣀⣀⣀⣀⣠⠤⠖⠊⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⠓⠶⠤⠤⠤⠤⠴⠒⠋⠀⡀
⠀⠀⠀⢿⡾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠙⠒⠒⠤⠤⠤⠐⠒⠋⠁⠀⠀⠀⢀⣄⠀⠀⠀⢰⢳⡀⠀⡟⢦
⠀⠀⠀⠀⠀⢀⡀⠀⠀⡼⢹⠀⠀⠀⠀⠀⠀⣼⢹⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠸⠸⡄⠀⠀⠸⣤⠇⠀⠙⠋
⠀⠀⠀⠀⠀⡏⡇⠀⠀⠳⠞⠀⠀⠀⢀⣄⠀⠘⠚⠀⠀⠀⠀⢰⠛⡄⠀⠀⠀⠀⢿⢸⠀⣀⠀⠸⣤⠇⢠⠻⡄
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢠⡄⠀⠀⡎⢸⠀⠀⠀⠀⢀⣄⠀⠘⠦⠇⠀⢀⣶⡀⠈⠉⠀⡟⡆⠀⠀⠀⠸⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣳⠀⠀⠣⠼⠀⠀⠀⠀⢸⠘⡆⠀⠀⠀⠀⢸⠀⢧⠀⠀⠀⠳⠃

⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⢀⡄⠀⠀⠀⠀⠀⠲⠁⢸⠀⠀⠀⢸⠈⢃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠀⡀⠀⠀⠀⢁⡀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠓⠤⠈⠉⠈⠁⠂⣀⠠⠄⠀⡀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⢰⠀⠀⠀⠀⠠⠅⠉⠈⠉⠉⢈⠝⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠀⠀⢈⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⡐⢩⠀⠀⠀⠀⠈⡁⠀⠄⠀⠀⠐⠈⠁⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠺⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⢠⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠁⠐⠒⠈⠀⠄⠀⠉⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠠⠀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠈⠀⠩⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠁⡖⢁⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠒⠆⠚⠉⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠚⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠀⡄⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠘⠀⠤⠀⠒⢀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀
⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀
⡎⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠂
⣡⣤⣀⣀⣀⣠⣀⣀⣀⣀⣀⣠⣤⣄⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⠶⠶⠦⣄⠀⡼⠁⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣟⣥⣤⣄⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠳⢤⡀
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢹
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠁⣠⠞
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠳⢦⠀⢀⢀⠀⠀⠐⠀⡷
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⢀⡴⠲⠶⠚⠁
⠀⠀⠀⢹⡀⠀⠄⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠆⡄⠀⠀⠀⠔⠐⠀⣠⣄⠀⠀⢸⡏⠉
⠀⠀⠀⠈⠳⣄⣀⣀⣀⣠⠴⠋⠓⢦⣀⣉⣈⣀⣠⡴⠚⠁⠈⠳⠦⣤⣄⣀⣀⣤⡤⠴⠚⠁⠈⠉⠉⠉⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣷⠀⠀⠀⠃⠀⠀⢸⠇⠀⠀⢸⡇⠀⠀⡀⠀⠘⠇⠀⠀⢾⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⡆⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡄⠀⠀⠀⢰⡆⠀⠘⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⡆⠀⠀⠀⠀⣀⠀⠀⠀⠋⠀⠀⠿⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠃⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣤⠀⠘⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣤⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀
⠀⠄⠀⠀⠀⠀⠀⠀⣀⣠⣤⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠃⢀⣀⣴⣾⣿⡿⠚⠋
⠀⠒⠛⠛⣿⣿⡿⢿⣿⣆
⠀⠀⠀⠀⢹⣿⣿⢠⣽⣿⣦⡀
⠀⠀⢠⡄⠀⣿⣿⣯⣼⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣶⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣙⣦
⠀⠀⢀⠀⠀⠈⠛⠉⡀⠙⢷⣀⡄⠀⠀⠀⠀⠰⣎⠁⠀⠀⠀⠐⢿⡿⡴⠀⠀⠀⠀⠠⢾⡇⠀⠀⠀⠘⢿⡏⠁
⠀⠀⠰⡆⠀⠀⠀⠀⠃⠀⠘⣿⠀⠀⠀⠀⠀⢰⠻⡀⠀⠀⠀⠀⠈⡏⢣⠀⠀⠀⠀⠀⢸⢧⠀⠀⠀⠸⣿⡇
⠀⠀⠼⠿⠆⠀⠀⠀⢸⠀⠀⢏⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠺⠄⠘⠶⠀⠀⠀⠀⠈⠈⠀⠀⠀⠴⠦⠷
⣤⣤⣤⡄⢠⣴⡖⠹⣾⡄⠹⣿⡄
⣿⣿⣿⣿⠿⠏⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⠛⠛⠋⠛⠛⠻⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠙⠻⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⡀
⠀⠀⣠⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣀
⠀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⣀
⣸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦
⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⠀⠈⠻⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⡿⠁
⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠀⠀⠀⠀⠀⣴⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⠀⠈⢿⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠀⠀⣠⣿⣧⡀⠀⠀⠀⠀⠀⣠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⢀⣤⣶⣿⠿⠿⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠛⠋⠉⠛⢻⣿⡿⠫⠚⠛⠛⠦⠈⢻⣿⣧⠀⠀⠀⠀⣠⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢰⣿⡟⢡⠞⠋⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣴⣿⡿⣛⣛⣛⢿⣿⣿⣆
⠀⠀⠀⣀⣤⣼⣿⣧⣈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠹⣿⠏⠚⠁⠀⠉⠓⠙⣿⣿⡆
⠀⣰⣾⡿⠟⠋⠉⠉⠙⠳⣆⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠶⠛⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣼⣿⡟⡴⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣇⢀⣼⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃
⣿⣿⡀⠧⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠉⠋⠁⠀⠀⠀⠀⢸⡇⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠠⠴⣿⣿⣯⡀
⠙⣿⣿⣶⣶⠶⠶⠶⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢿⣿
⠀⠀⢹⡟⣤⠊⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣀⣀⣀⣀⣀⣤⡴⠖⠋⠀⠀⠀⠀⠀⠀⣄⠀⠀⣠⡞⣼⣿
⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣴⣾⣿⠟
⠀⠀⢸⣷⡙⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠉⠁
⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⢀⣠⣿⣿⣷⣤⣶⣾⠿⣿⣆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠛⢿⣿⣷⣶⣶⣶⣿⣿⠟⠃⠀⠉⠉⠁⠀⠙⣿⣮⣓⢦⣄⣀⡀⠀⣀⣠⣶⣿⡟⠀⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⢠⡆⠀⠀⠀⢀⡀⠈⠻⣿⣿⣿⣷⣾⣿⣿⣿⠿⠋⠀⢰⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢠⠞⠙⡄⠀⠀⣼⡀⠀⠀⠀⠉⠙⢛⠉⠉⠁⠀⠀⠀⠀⣇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡾⠉⣧⠀⠀⠀⠘⠒⠚⠁⠀⡞⠁⢹⡄⠀⠀⠀⢀⡾⡄⠀⠀⢀⣿⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠋⠀⠀⣀⠀⠀⠀⠀⠀⠙⠒⠋⠀⡀⠀⠀⡞⠀⢻⠀⠀⡜⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡀⠀⠀⢀⠀⠀⠀⠀⢀⣿⠀⠀⠙⠒⠋⠀⠀⠓⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⣱⠀⠀⢸⡄⠀⠀⠀⡜⠈⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⡴⠃⢳⠀⠀⠀⠓⠚⠁⠀⠀⠀⡞⢧⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣒⣋⣀⣀⣀⣀⣀⣀⣀⣀⣈⣧⣤⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠀⠀⠀⠀⠠⠄⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄⠀⠀⠀⠀⠀⠁⠙⠀⠀⠁⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠰⠆⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣶⣦⠀⠀⠀⠀⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣽⣿⣿⣿⡇⠀⠀⠀⠀⣀⣠⣤⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣤⣀⠀⣀⣄⣀⣀⣰⣶⣶⣶⣾⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠉⠙⣷⡀⠀⣀⣀⣀⣀⡀⢘⣭⣿⣿⣯
⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣷⣤⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠉⠉⠓⠦⡄⢀⣠⠤⠖⠒⠛⠓⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣠⠴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⣠⠚⠉⠁⠀⠈⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠛⠲⢄⡀
⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⣠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⣄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣉⣀⣀⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊
⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠳⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠈⠉⠉⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠉⠳⢤⣄⣀⣀⣀⣀⣀⣠⠴⠋⠀⠀⠉⠙⠒⠒⠒⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡏⢸⡆⠀⠀⠀⠀⠀⠀⢀⠏⢳⠀⠀⠀⠀⠀⠀⣼⠈⣇⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⡴⣆
⠀⠀⠀⠀⠀⡞⢹⡀⠀⠀⠙⠚⠁⠀⠀⠀⣤⠀⠀⢸⡄⣸⠀⠀⠀⠀⠀⠀⠸⣤⠟⠀⠀⠀⢠⣦⠀⠀⠙⠶⠃⢠⡇⢹
⠀⠀⠀⠀⠀⢧⣤⠇⠀⠀⠀⠀⠀⠀⠀⣸⠉⡆⠀⠀⠉⠁⠀⠀⠀⡼⣇⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⠀⠀⠀⠀⠳⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⢿⣀⡗⠀⠀⠀⠀⠀⠀⢰⡇⢸⠀⠀⠀⠀⡼⢳⠀⠸⣤⠇⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠉⠀⠀⢠⢶⡀⠀⠀⠀⠳⠞⠀⠀⠀⢠⡇⠘⡇⠀⠀⠀⠀⢸⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⣾⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠁⠀⠀⠀⠀⠀⠙⠃

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢾⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣶⣾⣿⣿⠏⠙⣛⣿⣷⣄⠱⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠑⣼⣿⣿⣿⣿⡿⠑⢂⡺⠭⢿⣿⣿⣧⡀⠈⠡⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠴⣿⠿⣿⣿⣿⣷⠀⠀⠀⢙⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠂⠠⠄⠲⠶⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣻⣿⣿⣿⣏⣀⣠⣤⣴⣶⣦⣤⣼⣿⣽⣿⣿⣿⠀⢀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠈⡏⠙⠉⠉⠛⠂⠛⠁⠿⠿⣿⣿⠙⢹⣿⡿⡟⣛⣿⠃⡿⣿⣿⢿⡇⣿⣿⣿⣿⢿⣿⣧⣿⢿⣿⣿⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⡀⠀⠀⠸⡇⠀⠀⣿⠀⠀⠁⠉⠘⠁⡟⡏⠉⢀⠈⠉⠃⠃⡄⠸⡇⢰
⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⡎⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⡷⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⣸⠀⠀⠸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠈⠀⠈⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠈⠱⡀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠦⠤⡀⡀⠄⠠⣀⢂⠀⢀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢀⣄⡀⠐⠃⢢⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠄⠈⠂⠀⠀⠈⠀⢀⠦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠚⠐⣄⡀⠀⠀⠀⠐⣀⠈⢀⠀⠀⠀⠀⠀⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠓⠠⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠐⠁⠀⠑⡄⡀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠺⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠁⠀⠀⠂⠒⠂⢋⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠈⠀⠀⠀⠀⠘⠄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠆⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠰⡄⠀⠐⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠐⠈⠀⠀⣄⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢤⠀⠀⠈⠓⠀⠀⠀⠈⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠈⠀⠀⠀⠀⠘⠄⠀⠀⠈⠣⠀⠀⠀⠀⠘⠆⠀⠀⠀⠈⠂⠀⠀⠀⢰⡀⠀⠀⠀⢈⠠⠀⠀⠀⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠘⠦⠃⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠇⠀⠀⠀⢤⠀⠀⠀⠀⠘⢀⠀⠀⠀⠈⠛⠈⠃⠓⠀⡀⠲⠀⠀⠀⠈⠀⠘⠀⣤⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠘⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⠀⠀⠀⠀⠸⡄⠄⠀⠐⠄⠷⠴⠀⠀⠀⠟⠦⠀⠀⢸⣧⡀⡀⣄⣿⢷⠈⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠺⠖⠐⠂⠸⣧⡇⠉⠀⠙⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠈⠀⠃⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠲⠀⠀⠀⠘⠦⠀⠀⠀⠘⢆⠀⠀⠀⠸⠄⠀⠀⡀⠈⠃⠀⠀⠀⠘⠆⠀⠀⠀⢇⡁⠀⠀⠳⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠃⠀⠀⠀⠀⠙⠀⠀⠀⢨⠀⠀⠀⠀⢠⠀⠀⠀⠈⠃⠀⠀⠀⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢑⠀⠀⠀⠀⠸⡈⠀⠀⠀⢇⠀⠀⠀⠀⠸⡈⠀⠀⠈⠇⠂⠀⠀⠈⠓⠀⠀⠀⢧⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠙⠲⣄⢀⡤⠴⠒⠚⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣤⣀⣠⠖⠛⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⡀
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠳⣄
⠀⠀⢀⣠⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑
⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣉⣀⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁
⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠙⠲⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⣄⡀⠀⠀⠀⠀⠀⢀⣠⠞⠙⠒⠦⠤⣤⣤⣤⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠤⠴⠖⠚⠁⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⣘⣇
⠀⠀⠀⠀⠀⣀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢰⠋⡇⠀⠀⠀⠀⠀⡏⢸⡄⠀⠀⠀⠀⠀⠀⡇⢸⠀⢰⢦
⠀⠀⠀⠀⢸⠙⡆⠀⠀⠙⠋⠀⠀⠀⣴⡀⠀⠸⣀⠇⠀⠀⠀⡀⠀⠹⠾⠃⠀⠀⢠⢷⡀⠀⠙⠊⠀⣏⢸⡄
⠀⠀⠀⠀⠘⠶⠃⠀⠀⢀⠀⠀⠀⢰⠁⣇⠀⠀⠀⠀⠀⠀⡞⢳⠀⠀⠀⠀⣀⠀⢸⠀⡇⠀⢀⡀⠀⠘⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡆⠀⠀⠘⠦⠏⠀⢀⡀⠀⠀⠀⣇⣸⠀⠀⠀⢰⠉⡇⠈⠛⠁⠀⣼⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠇⠀⠀⠀⠀⠀⠀⡜⢹⡀⠀⠀⠀⠁⠀⠀⠀⢸⣀⡏⠀⠀⠀⠀⠹⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣰⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠷⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠶⠶⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀
⠀⠀⠀⣀⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃
⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⡾⠳⠶⠚⢛⠉
⠀⠻⣦⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡴⠟⠁⠀⠀⣠⡾⠋⠛⠶⢦⣤⠶⠞⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠛⠛⠛⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠷⣦⣀⣀⣀⣀⣤⠾⠛⠻⠶⣤⣤⢤⡶⠾⠛⠁⣀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠻⢦⣄⣀⡀⠀⣀⣀⣠⡴⠟⠁⠀⠀⠉⠉⠉⠉⢁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⡿⢻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠚⠋⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠒⠚⠓⢦⣀⣼⠁⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢀⣠⠤⠤⠦⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠵⠶⠶⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠙⠲⡄
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⡽
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠠⢾⡁
⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡋⠀⠀⠀⠀⠀⡀⠹⡆
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠐⠐⢀⣀⣀⡴⠃
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠳⡤⠖⠁
⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⡱⢦⣄⠈⠦⠂⠂⠀⣀⡴⠋⠳⣄⣈⠘⠁⠀⠀⠈⣀⣤⠞⠙⠶⠶⠞⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠈⠙⡛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡆⠀⢠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠃⠀⠀⢰⡄⠀⠀⢸⠀⠀⠀⠀⠀⢲⠀⠀⢠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡆⠀⠀⠀⠀⠘⠃⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⡆⠀⠀⠀⢠⡄⠀⠸⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣦⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣦⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠤⠀⠠⢄⡠⠒⠒⡂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠈⠒⠒⠁
⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢠⠃⡀⠀⠂⠲
⠀⠀⠀⢀⠀⠀⠀⠈⠢⠄⢂⠤⢀⠄⢀⠄⢀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⡔⣠⠂⡰⠁⡔⠁⠈⠠⠡⠂⠆⡸
⠀⠀⠀⠈⠲⠖⠂⠑⠦⠄⠁⠀⣁⡀⢁⢀⡁⠐⠡⠒⠡⠖⠠⠂⡠⠂⡠⠊⡠⠊⠔⠡⠖⠠⠊⢀⠶⠄⠀⠄⠀⠊
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠠⠀⠠⠄⠉⠓⠲⠶⠶⠀⠒⢤⣄⠀⠀⣠⡁⠔⠒⠐⠴⠶⠀⢁⠀⠰⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠐⠀⢀⠀⠀⠀⢀⠔⠒⠄⠠⢉⡐⠒⠄⡀⠃⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⢀⡅⠀⠀⡀⡀⠀⠀⠀⢀⡈⠢⡀⠄⠠⠀⡄⠀⠄⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠚⠈⢁⡜⠀⠉⢲⡀⠀⠁⠈⢣⠈⠣⡀⠀⡀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⣇⠀⠀⠀⢣⡖⢢⠀⠞⠀⠀⠀⠀⠤⡀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣧⠀⠀⠉⠀⠀⠀⢽⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⢰⠦⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⡃⠀⠀⠀⠀⢸⢀⡤⠀⠄⠀⠀⠀⠀⠀⢡⠈⠑⢦⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⣛⠀⠀⠀⠀⢈⠙⡈⡐⢠⠘⠀⠀⠀⠀⠀⡄⢀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠄⠀⠈⢶⠠⢀⠂⠃⠀⠀⠀⠀⢸⠄⢁⠄⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⣅⠂⠄⠀⠈⢧⠂⢾⠀⠀⠀⠠⢀⠧⢊⡠⠔⡁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⡄⠠⠄⠀⠀⠱⠆⠀⠀⠐⢀⠜⢂⡡⠔⣊⠄⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠛⡄⠉⣀⠀⠀⠀⠀⠀⢀⣊⡉⠤⠒⣉⠄⡊⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠂⠘⡄⢀⡰⠓⢢⠜⢦⠐⢀⠀⠀⢀⡴⢋⠉⠐⠒⠃⠤⢩⡔⠢⠄⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢂⠡⢂⠹⢋⠥⢀⡌⠀⠠⢃⠴⢲⠖⠋⠔⠡⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠡⠒⡡⠖⡡⠊⢸⡇⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣊⠔⢉⠀⠰⢨⡇⠀⠀⠐⡡⢂⠀⠐⠊⡥⠂⣡⠖⣡⠔⡠⠊⠐⢀⡬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠡⠚⡡⠀⢰⠀⠁⠀⠀⡡⠔⣉⠀⣟⠳⠶⠶⢤⡬⣥⣬⣡⢤⡴⢊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢊⠤⠂⠀⡀⢸⠀⠀⠰⢊⡡⠄⠸⢊⠔⡃⢀⠖⡡⠊⡰⢊⠔⠡⢊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠠⠒⣡⠀⠁⠀⡀⠀⠐⡡⠄⠂⡀⢣⠜⣥⠀⠜⠁⠈⡰⠃⠔⠡⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠀⠐⠩⠄⠀⢸⠀⢃⠀⠀⠐⢂⠡⠀⠈⡯⢺⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠁⠀⠀⠀⠀⠀⠀⣈⢃⣹⠀⠀⠀⠄⣂⠁⠀⢰⠭⡀⠀⠀⠀⡠⢊⠔⡡⢀⠀⢰⡄⠄⢀⠠⠤
⠀⠀⠀⠀⠀⠀⠉⠀⠂⠉⠄⠋⠉⠱⠚⡃⠉⣉⠍⠋⠁⠀⠀⠀⠀⠀⢀⡤⠢⢦⣅⣀⡤⠤⢤⠤⠤⡤⠄⠠⠞⢈⠀⢂⠡⠀⡈⠔⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠲⠤⢤⡤⠤⢤⠶⠞⠋⠄⠂⠡⠐⠈⠐⠈⠁⠀⠁⠀⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⢛⡛⠛⠓⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⠶⣤⣄⣠⡶⢋⣥⣶⠿⠿⠿⠿⣿⣿⣶⣤⡉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣩⣴⣶⣿⢿⣿⣿⣶⣦⡌⢉⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⡈⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣴⠟⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⠀⠈⢻⣿⣤⣍⣉⡛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠛⠻⢿⣷⣄⡙⠛⠻⠿⣿⣷⣦⡈⠳⣦⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣠⡴⠟⢀⣠⣴⣾⠿⠿⠿⠿⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠈⠙⢿⣿⣶⣶⣮⣭⣍⡛⠶⣤⡀
⠀⠀⢀⣤⠞⣫⣵⠾⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⣿⣶⣌⠻⣦
⠀⢠⡞⡡⠚⠉⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡈⢷
⢠⡟⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠘
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣸
⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠙⠳⣦⣀⡀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠶⠶⠶⠶⠶⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⢦⣄⣀⡀⠀⠀⠀⣀⣠⣤⣤⣤⣤⡴⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⠶⠶⠛⠋⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣿⡇⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⢰⠏⠀⠀⣸⣷⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⢀⡟⠁⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠴⢞⣿⠇⠀⣠⡞⠁⣿⡀⠀⠀⠀⠀⠸⣇⡠⠾⣻⡟⠀⢀⡼⠋⢸⡇⠀⠀⠀⠀⠈⢷⣀⠴⣟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠉⠙⠉⠁⠀⣼⠋⠀⠀⣿⡇⠀⠀⠀⣠⣦⠈⠙⠋⠉⠀⢠⡟⠀⠀⢸⣿⠀⠀⠀⢀⣴⡀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣷⠀⠀⠀⠀⠀⢻⣄⠤⠾⣻⠇⠀⢀⡾⠋⢿⡄⠀⠀⠀⠀⠸⣇⠠⠴⢿⡿⠀⠀⣴⠏⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⡆⠀⠀⠀⣠⡄⠉⠛⠛⠉⠀⣰⠟⠀⠀⣸⣇⠀⠀⠀⢀⣤⠈⠛⠛⠋⠀⢀⡾⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⣤⡾⣿⠇⠀⣠⡾⠋⣿⠀⠀⠀⠀⠀⢻⡄⢠⡴⢿⡟⠀⢀⣴⠏⢻⡆⠀⠀⠀⠀⠸⣇⠀⣤⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠛⠓⠛⠁⠀⣰⠏⠀⠀⣿⡇⠀⠀⠀⢀⡄⠙⠓⠚⠋⠀⢠⡞⠁⠀⢸⣧⠀⠀⠀⢀⣤⠈⠛⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠹⣇⠀⠀⠀⠀⠀⢿⡀⣀⡴⣿⡇⠀⢀⡴⠋⣿⠀⠀⠀⠀⠀⢸⡇⢀⣤⢿⡿⠀⠀⣠⠟⢻⡆
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣿⡀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⣠⠟⠁⠀⣹⡇⠀⠀⠀⠀⠀⠙⠳⠶⠛⠁⢀⡾⠃⠀⢸⣷
⠀⠀⠀⠀⠀⠸⣇⠀⣀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠦⢤⣀⠀⢀⡤⠖⠋⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠈⠳⠏⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢴⣋⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⢀⣀⣙⣲⡀
⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠈⠳⣄⠔⠋⠉⠀⠀⠉⠙⢦⡀⠀⣠⠎⠁⠀⠀⠀⠀⠙⢦⣠⠞⠉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠤⢤⣀
⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠛⠁
⠀⠀⠀⠈⠉⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢯⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⣠⠶⣄⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠙⠦⢤⣄⣤⠤⠞⠁⠈⠙⠒⠒⠒⠚⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣤⠴⠞⠁⠀⠈⠉⠓⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠖⣆⠀⠀⠀⠀⢠⠞⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⡞⠉⢳⡀⠀⠀⠀⡏⠀⠘⡆⠀⠀⠀⡟⠀⠀⠸⡆
⠀⠀⠀⠀⢠⢶⡀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠈⢳⠀⠀⠀⠀⠀⠀⣏⢸⡆⠀⣼⠀⠀⠀⣷⠀⠀⠈⣇⠀⣠⠇⠀⠀⠘⣇⠀⠀⢀⡇
⠀⠀⠀⢠⠏⠀⢹⡀⠀⠀⡀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⢻⡀⠀⢀⡿⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠈⠓⠖⠋
⠀⠀⠀⢸⡀⠀⣸⠇⠀⡾⢹⡄⠀⠈⢧⣀⣀⡼⠁⡴⠛⣆⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⢠⡏⢷
⠀⠀⠀⠀⠉⠛⠁⠀⠀⠓⠞⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠞⠳⡄⠀⠈⠳⠚
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡴⢦⠀⠀⠀⠘⢦⣀⡼⠃⠀⣀⠀⠀⠀⢠⠏⢱⡀⠀⠀⡟⠀⠀⢹
⠀⠀⠀⠀⠀⢠⠞⠙⣆⠀⠀⠀⢸⡁⢈⡇⠀⠀⠀⠀⠀⠀⠀⡼⠉⢳⡀⠀⠸⣄⣸⠃⠀⠀⢧⡀⢀⡼
⠀⠀⠀⠀⠀⡟⠀⠀⢸⡄⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡶⣄
⠀⠀⠀⠀⠀⠳⣄⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸
⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣯⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⢛⣛⣛⡛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣚⣛⣛⡒⠶⢤⣀⡴⢋⣵⡾⠿⠿⠿⠿⠿⣿⣶⣤⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣵⡾⠿⠿⠿⠿⢿⣷⡦⠈⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡹⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠈⢿⣷⣶⣤⣍⡙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠰⠛⠉⠁⠀⠀⠀⠀⠉⠙⠻⢿⣦⡉⠉⠙⠻⢿⣷⣄⣙⡶⠶⠦⣤⣀
⠀⠀⠀⢀⣠⠶⣛⣯⣠⣶⠿⠛⠋⠉⠉⠉⠉⠛⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠙⠛⠿⠿⢿⣷⣦⣍⡛⢦⡀
⠀⢀⡴⢋⡴⠛⢋⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠹⣆
⢀⡾⠁⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠸
⣼⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢰
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠉⠳⢦⣄⣀⡀⠀⠀⣀⣠⡤⠞⠛⠒⠶⠶⠚⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠳⠦⣤⣀⣀⣀⣀⣠⡤⠶⠶⠶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠒⠚⠛⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠈⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡾⠃⠀⣿⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⣿⠀⠀⢀⡼⢿⡄⠀⠀⠀⠀⢾⡀⢀⣠⣿⡇⠀⢀⡴⢻⡆⠀⠀⠀⠀⢸⡇⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠳⠯⠷⠋⠀⣴⠏⠀⢸⣇⠀⠀⠀⢀⡈⠳⠯⠷⠋⠀⣠⠟⠁⢸⣿⠀⠀⠀⠀⣀⠛⠾⠽⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⣧⠀⠀⠀⠀⠸⣇⢀⣠⣾⣿⠀⠀⣠⠞⣷⠀⠀⠀⠀⠀⣯⠀⣀⣼⣿⠀⠀⣠⡞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣿⡀⠀⠀⠀⣀⠙⠳⠷⠞⠁⢀⡾⠃⠀⣿⡆⠀⠀⠀⢀⡈⠳⠷⠞⠋⠀⣴⠋⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣀⣴⣿⠇⠀⢠⡾⢻⡆⠀⠀⠀⠀⢸⡅⢀⣤⢿⡇⠀⢀⡴⠛⣇⠀⠀⠀⠀⠸⣇⢀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠛⠲⠞⠋⠀⣴⠋⠀⢸⣷⠀⠀⠀⢀⣀⠙⠲⠖⠋⠀⣠⠟⠀⠀⣿⡀⠀⠀⠀⣀⠙⠳⠖⠛⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣷⠀⠀⠀⠀⠀⣧⠀⣠⣾⣿⠀⠀⣰⠟⢻⡀⠀⠀⠀⠀⢿⡀⣠⡼⣿⠇⠀⣠⠞⢻⡆
⠀⠀⠀⠀⠀⢠⡞⠁⠀⣿⡇⠀⠀⠀⠀⠈⠛⠒⠛⠁⢀⡾⠁⠀⢸⣇⠀⠀⠀⠀⠈⠙⠓⠛⠁⠀⣴⠋⠀⢸⣷
⠀⠀⠀⠀⠀⢸⣄⢠⡴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⣴⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣤⢾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⢤⣄⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠙⢦⡴⢞⠋⠉⠀⠒⠀⠀⠈⢍⡓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣎⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠏
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢁⡴⠋
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠒⠤⢀⣀⠀⠀⢀⣀⠀⠠⠀⢀⣈⠴⠚⠉⠉⠓⠶⠶⠤⠴⠶⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⠤⠶⠒⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢳⡀⠀⠀⠀⠀⠀⠀⡏⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⡇⠀⠀⠀⠀⠀⠀⢧⣐⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠣⠀⣸⠀⠀⠀⠀⡀⠀⠀⠀⠙⠒⠋⠀⠀⠀⣠⠶⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⣾⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢚⣛⣛⣛⡛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣚⣛⣛⣛⡓⠶⢤⡴⣫⡴⠿⠛⠛⠛⠻⠿⣿⣶⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡶⠟⠛⠛⠛⠛⠿⠟⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡘⠦⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⠿⠿⠿⣶⣦⣄⠹⢿⣿⣶⣦⣍⠛⢦⡀
⠀⠀⠀⠀⠀⣀⣠⡏⢀⣠⣴⣶⠶⠶⢶⣶⣤⣀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠈⠙⠿⣿⣦⣭⣭⣛⡓⠦⣄
⠀⠀⢀⡴⣋⣽⢾⣶⠟⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠈⠉⠉⠛⠻⢿⣷⣌⠻⣄
⠀⣴⠋⠞⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡘⣧
⣸⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣸
⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠙⠶⣤⣀⣀⣀⣀⣀⣠⡴⠞⠓⠒⠖⠒⠛⠳⣄⣀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠶⣤⣄⣀⣀⣀⣤⠴⠶⠶⠶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⡇⠀⠀⠀⣠⠀⠀⠀⠀⠀⣴⠋⠀⢸⡇⠀⠀⠀⣤⠀⠀⠀⠀⠀⡼⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠴⣿⠇⠀⣠⠞⢹⡇⠀⠀⠀⠀⢧⡀⠴⣿⠇⠀⣠⠞⢹⡆⠀⠀⠀⠀⢧⡀⠴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠉⠋⠉⠀⣼⠃⠀⢸⣷⠀⠀⢀⣴⡄⠉⠋⠁⠀⣼⠃⠀⢸⣷⠀⠀⢀⣴⡄⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠈⣧⠀⠀⠀⠀⠹⣄⣒⣻⠟⠀⣠⠟⠈⣧⠀⠀⠀⠀⠻⣄⣒⣻⠏⠀⣰⠟⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⣿⠀⠀⢀⡴⣆⠀⠉⠀⠀⢸⠃⠀⢠⣿⠀⠀⢀⡴⣆⠀⠉⠀⠀⢸⠃⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣼⡽⠟⠀⣰⠏⠀⣿⠀⠀⠀⠀⠘⠷⣼⡽⠟⠀⣰⠏⠀⣿⠀⠀⠀⠀⠘⠷⣼⡽⠟
⠀⠀⠀⠀⠀⠀⢀⡼⢿⠀⠀⠀⠀⢸⡇⠀⣠⣿⡇⠀⢀⡾⣿⠀⠀⠀⠀⢸⡇⠀⣠⣿⡇⠀⢀⡾⣷
⠀⠀⠀⠀⠀⣰⠋⠀⢸⡇⠀⠀⠀⠀⠙⠾⠷⠋⠀⣰⠋⠀⢸⡇⠀⠀⠀⠀⠙⠾⠷⠋⠀⣴⠋⠀⢸⡇
⠀⠀⠀⠀⠀⣧⢀⣠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣤⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠎⠛⠅⠈⠑⠔⠒⢄⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠄⢠⠄⠀⠀⠀⠀⠀⣄⠈⡵⠤⠴⠒⠊⠀⠀⠖⠐⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣀⡴⠚⠄⠀⠀⠈⠀⠀⠀⠀⢀⡔⡲⠚⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡶⠚⠁⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⢳⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣩⠤⣀⠤⡤⠤⢄⠀⠀⠀⠀⠀⢰⡟⢡⣄⡀⠐⠁⠀⢀⡀⠀⠀⠀⠺⠀⠀⢈⠁⠀⠀⠀⠀⠈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠟⠚⠁⠀⠀⠀⠀⠀⠐⢳⡠⣋⠑⡖⠀⠀⠁⠈⠙⠔⠢⡤⡢⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⡂⡄
⠀⠀⠀⠀⠀⠀⡠⠤⢖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠈⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠭⠖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄
⠀⠀⠀⢀⣠⣼⡅⠀⠘⠀⠀⠀⠀⡠⠂⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⠿⢗⠂⣀⡀⢀⣀⢀⣀⣀⣀⣘⣳⣶⣶⣦⣠⣄⣀⣀⣀⣀⣀⡀⠂⢱
⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣅⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣉⢁⣉⣀⣈⣉⢀⣙⣛⡯⠛⠛⠛⠛⠛⠋⠉⠉⠉⠈⠉⠉⠉⠋⠉⠁
⠀⠀⠀⠈⠒⠢⠤⠶⠘⠳⠶⠖⠒⠛⠛⠛⠛⠛⠛⠉⠉⠛⠙⠛⠋⠉⠛⠋⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠈⠀⠀⢀⡏⠀⠀⡼
⠀⠀⠀⠀⠀⠠⡆⠀⠀⣼⠀⠀⡏⠀⢀⡇⠀⠀⠰⠀⠀⠀⠀⡾⠀⠀⠀⢠⠆⠀⠀⠀⠺⠂⠀⢠⡇⠀⠀⣼⠀⠀⡀⠀⠀⣸⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠃⠀⣸⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⠇⠀⢸⠁⠀⢀⡇⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠚⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢰⠃⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⡞⠀⢀⡏⠀⠀⠘⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⠀⠀⢸⠁⠀⠀⠀⣀⠀⠀⢰⠃⠀⠀⠀⡞⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣸⠁⠀⣸⠀⠀⢀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⠀⠀⡟⠀⢀⠀⠀⠉⠀⠀⡟⠀⡀⠀⢸⠁⠀⠀⠀⢸⠃⢰⡄⠀⠀⠀⠋⠀⢠⠇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠁⢰⠇⠀⠏⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠷⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣚⣛⣉⣛⣛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣚⣛⣩⣙⣛⡲⢦⡴⣫⠴⠟⠛⠛⠛⠛⠿⣿⣦⣍⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠟⠛⠋⠉⠛⠻⠿⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡙⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡾⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠛⠛⠛⠻⢷⣶⣄⠻⠿⢿⣷⣦⣌⠳⢦⣀⣀
⠀⠀⠀⠀⣀⣤⠼⠃⣠⣴⠾⠿⠿⠿⠿⢶⣦⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠙⢿⣷⣶⣯⣭⣝⡓⢦⣀
⠀⠀⡴⢞⡵⠞⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⡙⢧⡀
⢀⡞⠑⠉⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⢳
⣼⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠸
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼
⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡤⠞⠉
⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠒⠛⠁⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣤⣤⡤⠶⠚⠁⠀⠉⠛⠒⠒⠒⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢀⣼⣿⠀⠀⣰⢿⡆⠀⠀⠀⠀⣏⠀⣠⣿⡇⠀⣠⠾⣧⠀⠀⠀⠀⢾⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠛⠿⠞⠃⢠⡞⠁⢈⣷⠀⠀⠀⣀⠙⠻⠷⠋⠀⣴⠋⠀⣿⡄⠀⠀⢀⡈⠓⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⡀⠀⠀⠀⠸⣄⠠⢾⡿⠀⢀⡾⠹⣇⠀⠀⠀⠀⢧⡠⠴⣿⠇⠀⣴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣸⡇⠀⠀⣠⣦⠈⠉⠉⠀⢰⠏⠀⢠⣿⠀⠀⢀⣴⡌⠉⠋⠁⠀⡾⠁⠀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣚⡿⠃⢀⡴⠋⢸⡄⠀⠀⠀⠘⢦⣐⣻⠟⠀⣠⠟⠈⣧⠀⠀⠀⠀⠳⣔⣚⡿⠃
⠀⠀⠀⠀⠀⠀⢀⡾⣇⠀⠀⠀⠀⣾⠀⢀⣼⡇⠀⢀⡴⢷⠀⠀⠀⠀⢸⡃⠀⣠⣿⠀⠀⣠⢾⡆
⠀⠀⠀⠀⠀⣴⠋⠀⣿⠀⠀⠀⠀⠘⠶⠭⠟⠁⢠⠞⠁⢸⡇⠀⠀⠀⠈⠳⠮⠽⠋⢀⡼⠃⠀⣷
⠀⠀⠀⠀⠸⣇⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢀⡴⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠈⠙⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠟⠛⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠿⣿⣿⣿
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿
⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⠁
⣿⣿⡇
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠀⢻⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⣀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣽⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠿⠷⣦⣄⡀⠀⣰⡿⠋⠀⠀⠀⠀⠈⠙⢷⣄⠀⣀⣤⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠉⠛⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠁⠀⠀⠀⠙⢿⣦⡶⠶⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⣴⡿⠋⠁⠀⣀⣉⣀⣀⠀⠀⠀⢀⣴⠿⠛⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⣄⡀
⠀⠀⢸⡟⠀⠀⢠⡾⠛⠉⠉⠙⠛⢦⣴⠟⠁⠀⣀⣀⣀⠈⠳⣤⠶⠛⠛⠛⢷⣆⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣷
⠀⠀⣿⡇⠀⢠⡟⠁⣠⡶⠖⠒⠶⠀⠉⠀⠀⠀⠀⠀⠈⠓⢄⡠⠔⠚⠛⠒⠀⠛⠁⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⡇⠀⣼⠇⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣠⡿⠿⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋
⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠿⠿⠿⠿⠟⠛⠋⠁
⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠈⠻⢷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠂⠁⠂⢄⡀⠀⠀⠀⠀⠀⠀⡠⠄⠠⣀⠤⠤⠂⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠄⠒⠊⠈⠀⠀⠀⠀⠱⠐⠂⠥⣀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠰⠀⢠⠈⠆⠀⢄
⠀⠀⠄⠀⠀⠀⡀⠀⠀⢀⣠⠴⠲⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀⠐⠀⠀⠀⠀⢀⠠⠊⠀⠀⠠⢠⠀⢀⠄⡁
⠀⡔⠐⠉⠉⠉⠀⣄⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⢀⣀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠓⠐⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⡊
⠪⠀⠠⠀⠠⠠⠬⢥⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠉⠈⠳⠤⣀⠄⡀⢀⡴⠒⢦⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⣐⡒⣀⣁⣂⠄
⠀⠀⡀⠀⡼⡀⠴⠁⠀⠀⠀⠀⣀⡴⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠻⠃⠀⢴⡃⠁⠀⡀⠀⡀⠠⡐⡀⠀⠈⢃⠀⠀⠀⢠
⠀⠀⢃⠄⠚⠀⠀⠀⠀⢀⡤⠎⡁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠵⢴⡀⠀⠈⠁⡡⠁⠀⠀⠀⢀⠈⡄⠀⠉
⠀⠀⠄⢀⠂⠀⠀⢀⠀⠀⠀⠲⢲⡤⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⡈⠈⠈⢂⠔⠀⠄⢀⠠⠤⠹⢮⠀⠐⠐⠀⣂⣀⢂⣀⣂⠀⠇
⠀⢰⠀⢠⠌⠁⢐⠐⠀⠠⡅⠀⠈⠉⠃⠐⠒⠦⠬⠤⠦⠤⢰⢒⢲⠲⠲⡲⢈⡍⣉⢉⠉⢉⡍⠁⠉⠀⠘⠄⠀⠀⢀⠀⡤⠀⠆
⠀⠋⠀⠘⠀⡴⠚⠐⠁⠄⢀⠀⢐⣒⣃⠐⠄⠀⠀⠀⠂⠠⠀⠀⡠⠑⠑⠐⠉⠄⠠⠄⠂⠀⠠⠄⠀⠀⠉⠁⠀⠂⠀⣠⠄⠚
⠀⠀⢚⠀⣠⠆⠰⠂⠏⣠⢀⠀⡖⠀⠀⠈⠁⢂⠀⠐⠀⠀⠀⠠⠅⠤⠨⠥⠥⠭⠴⠤⠴⠅⠦⠠⠀⠸⠀⠀⢐⠃⢀⠀⠀⠀⠁
⠀⠘⠁⢀⠀⠀⠶⠀⢔⠁⠀⠘⢡⠇⢠⠀⠀⡞⠀⢀⡀⠠⠆⠀⠚⠀⠀⠠⠆⠀⡴⠀⡴⠐⠀⠀⢠⠂⡂⠀⠛⠀⠀⠀⠖
⠀⠐⠠⠛⠀⠀⣠⠘⠋⢠⠄⠠⠏⢀⠏⠀⠞⠀⠠⠊⠀⠂⠀⣡⠁⡤⠀⠞⠀⠐⠁⠸⠃⠀⡴⠀⠀⠀⢀⡆⠀⠜⠀⠴⠂
⠀⠀⠂⠃⠀⠀⡁⠀⢀⡀⠀⠀⠀⢛⠀⠄⠀⠀⡡⠂⢀⡀⠀⠁⠐⠃⡀⠀⠁⡏⢰⡆⠀⡶⠆⢠⠰⠤⣾⠂⠾⢇⠀⠀⡀⠞
⠀⠔⠀⠎⠀⠘⠁⡄⠘⠁⣰⠀⠀⠚⠀⠁⡖⠀⠀⠀⠸⠀⠀⠠⠟⠀⠀⢀⡵⠀⢉⡆⠀⠀⠠⡄⠀⠀⠀⢰⢤⡾⠀⠾⡇⢠
⠀⠀⠰⠂⠠⠀⢠⠄⠀⣠⠄⠀⠚⠁⢀⡤⠁⠀⠀⠴⠃⢠⠀⠀⠀⡔⠠⠀⠤⠠⡸⢃⡄⠰⠶⠀⡴⠀⣴⠀⠶⠆⠰⠖⠁⠺⠆
⠰⠃⠀⠀⡄⠀⢁⡆⠀⠈⠀⠀⡏⠠⠈⠀⠸⠀⠀⠀⠀⡙⠀⠀⠠⠂⠀⠆⠀⠙⠁⠘⢀⠆⠀⢈⠃⢀⠀⠀⡤⠀⠀⠀⢀⡄
⠟⠀⠀⣤⠀⠀⠈⠁⠆⠀⠀⡶⠀⠀⠀⠴⠂⢠⠄⠀⠙⠁⠀⣠⠀⢠⡥⠀⠀⠀⡤⠂⢈⠀⠐⢃⡀⢀⠀⢀⡀⠀⡖⠀⢀
⠀⠀⠀⠀⣠⠈⢀⡰⠀⠖⠀⠀⠼⠀⠂⠀⢀⡀⢀⡄⠠⠀⢀⠃⠀⢀⠀⠐⠃⠀⠀⠀⢈⠀⠀⡈⠀⠘⠀⠉⠀⡤⠂⠀⠉
⠀⠀⠀⣀⠄⠀⠀⠀⡤⠆⠀⠸⠂⠠⠇⠀⠉⠀⠨⠀⡀⠀⠋⠠⠋⠀⠠⠖⢠⠆⠀⠘⠁⡄⠈⠁⠀⠀⠃⠠⠀⠀⠀⡆⢨
⠀⠀⠀⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⠖⠀⠀⠀⠘⠁⢈⠁⡀⠀⠶⠁⡆⠀⢠⡄⠀⢀⠀⣈⠁⠀⠀⠀⠐⠁⠀⠀⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡎⠀⢠⡂⠉⠐⠠⠀⠀⠀⠀⠉⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠒⠀⡘⠃⠀⠙⠏⡁⡀⠀⠀⠀⠀⠀⠘⠿⠛⢡⡦⠴⡤⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀⠈⠉⠁⠀⠈⣿⡄⠀⠀⠀⠁⠓⠃⠀⠀⠀⠀⠀⠰⣀⠀⠠⠄⠸⢤⠀⡤
⠀⠀⠀⠀⠀⠠⢀⠄⠀⠈⠓⠀⠀⡀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠛⣷⣾⣦
⠀⠀⠀⠀⢀⣴⠛⡄⢰⣤⣿⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡄⠉⠙⣿
⠀⠀⠀⠀⠄⠀⠠⢆⡀⠉⠿⡇⠀⠀⠛⠂⠂⠀⠀⠀⠠⢷⠀⠁⠦⣀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⣣⠛⠛⢹⣦
⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⣥⡀⢹⣄⡀⠀⠀⡀⠀⠀⢾⣷⢀⣀⣀⣀⡀⠀⠀⢀⠹⣾⣦⣴⠞⠁⠀⠐⠀⣹⠃
⠀⠀⠀⠐⢴⣶⠆⠀⠰⠐⠈⢸⣿⣄⡐⠚⣃⠀⠀⠀⢀⣈⠛⠻⢿⢟⣉⡄⠀⠀⠀⠓⠎⠉⠘⠆
⠀⠀⠀⠀⠀⠁⣦⡲⣦⠀⡀⢾⣿⡽⣷⣼⡿⢯⣝⡛⠿⡉⠀⠠⠄⣄⢤⠀⠀⢀⠀⠠⠀⢤⣀⠀⡣⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠈⠋⠛⠂⢻⡀⢛⣆⡾⠂⢧⡀⠿⢿⠟⠁⡄⢨⡜⠈⠈⠇⠀⠈⡄⠀⠇⠈⠃⠀⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⢧⠀⠀⠘⡄⠀⠸⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠀⠀⠀⠈⠀⠀⠁⠀⠑⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⢿⣿⣿⢷⣿⣿⠿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣿⡿⣫⣿⣿⣽⣿⣿⣟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣫⣷⣷⣟⠽⢿⢿⣿⣿⢷⣿⣿⢿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣽⣿⡞⠿⠿⠿⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠰⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢠⡄⠀⠠⡄⠀⠠⡄⠀⠀⡄⠀⠠⡄⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢀⠀⠀⣀⠀⠀⢀⠀⠀⢀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠉⠀⠀⠉⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠐⠃⠀⠐⠃⠀⠐⠃⠀⠀⠃⠀⠐⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠴⠀⠀⠴⠀⠀⠴⠀⠀⠴⠀⠀⠴⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⡄⠀⢀⡄⠀⢀⡄⠀⢀⡄⠀⢀⡄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠻⣿⣆⠀⠀⠀⠀⠀⠀⣿⣏⠙⢿⣷⡄⠀⠀⠀⠀⠀⢸⣿⠙⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣠⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣀⣨⣿⡗⠀⠀⠀⠀⠀⠸⣿⣆⣀⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠋⠓⠲⣄⢀⡤⠔⠒⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⣠⠖⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⣀
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣠⠔⠚⠃⠀⠀⠀⠀⠀⢀⡠⢤⣀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⢣⠀⠀⠀⠀⠀⡌⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⡀
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⡨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁
⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠈⠓⠒⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⢀⡴⠋⠲⢤⣀⣀⣀⣀⣀⡤⠚⠈⠉⠒⠒⠶⠶⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⠀⠀⠀⠀⠀⠀⡰⣆⠀⠀⠀⠀⢀⡟⡄⠀⠀⠀⠀⠀⢠⠛⡄⠀⡀
⠀⠀⠀⠀⠀⢰⢳⠀⠀⠹⠼⠀⠀⠀⣀⠀⠀⡇⢸⠀⠀⠀⠀⠘⣆⡷⠀⠀⢀⣄⠀⠘⢤⠇⢸⠹
⠀⠀⠀⠀⠀⠸⣤⠇⠀⠀⠀⠀⠀⢰⠙⡄⠀⠉⠁⠀⠀⡴⡆⠀⠀⠀⢀⠀⢸⠙⡄⠀⠀⠀⠘⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠸⠤⠇⠀⢀⠀⠀⠀⡇⣸⠀⠀⠀⠞⣆⠘⠶⠁⠀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⠀⠀⠀⠀⠀⢠⠛⡆⠀⠀⠈⠁⠀⠀⠘⣄⡼⠀⠀⠀⠀⠧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠇

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠊⠉⢉⡩⠟⠒⠲⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠙⡄⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠱⣄⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠓⠒⣤⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⡰⠋⠀⠈⠳⣴⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣠⠏⠉⠉⡗⠒⠤⢄⡀⠀⡇⢀⣀⣀⣀⣀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡠⠞⢹⠀⠀⢠⠃⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⢀⠆
⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⡘⠓⢂⢾⡄⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠎
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣠⠭⢍⠥⡊⠀⡠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢇⠀⠀⠙⠓⠊⠑⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠈⠣⣄⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡠⡄⠉⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⢲⢄⣀⠀⠀⠺⠊⠀⠰⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡠⠔⠊⠉⢻⣿⠟⠉⢳⣶⣖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⡤⠴⠃⠀⠀⢠⠿⠟⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣸⠀⠀⠀⠀⠀⠈⡆⠀⠀⠣⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣠⠤⠔⠋