Pelvic girdle Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⡖⠲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⣤⢄⠀⠀⠀⡀
⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣟⡀⠀⢼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⣿⢵⡖⠄⠀⠀⠀⠈⠁⠂⢤⡀
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠘⣿⡿⠃⠐⠆⠀⠀⣦⠀⠀⠀⠀⠀⠲⡆⠀⠀⢰⣯⠀⠀⢟⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣸⠋⠖⠃⠀⠀⠀⠀⡂⠐⠃⠀⠀⠀⠀⢄⠀⠀⠋⠉⢳⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⡗⡀⠀⠀⠀⢰⢻⡼⠀⠀⢀⣀⣀⣈⡀⠀⠀⠀⠀⢀⣤⣿⡀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠹⣿⣿⣿⣿⡟⡛⠉⠀⠀⠀⠀⠀⠸⣤⣴⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣶⣦⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⣿
⠀⠀⠰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣤⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⣀⣿⡿⣿⣿⣿⣿⣿⣷⡂⠀⠀⢰⡿⠁⠀⠀⠻⠛⠿⣟⣻⠙⠿⠟⠋⣿⡹⠿⣿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣾⡿⠁
⠀⠀⠀⠁⠀⠀⠈⠀⢻⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣼⠋⠀⠀⠀⠀⡈⠰⣰⠇⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⢀⣾⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡿⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠙⠛⠿⢶⠒⠒⢚⡭⠞⠋⠀⠀⠀⠀⣠⣾⠇⠀⣰⡏⢴⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠺⣿⣍⡀⠀⠀⠀⠀⠈⠻⣿⠆⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢻⠟⠀⠀⢻⣷⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⢠⡀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣤⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⢿⣿⣷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢻⡄⠀⠑⢂⣤⣤⣤⣀⢼⠰⠀⣠⣤⣤⣐⡟⠉⠀⠀⢨⣿⡏⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠹⠆⠀⠀⠉⢤⡤⠈⢿⣿⣾⣿⣿⣿⣿⣦⣤⣤⣤⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠖⠉⠀⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣲⣒⣃⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣻⣿⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠌⠀⢀⣦⠁⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⡎⠁⠀⠻⠄⠀⠀⠸⠋⠀⠉⠆⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⡇⠀⣠⠚⡏⠁⠉⣿⢲⡄⠀⡨⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠊⠉⠀⠈⢆⢥⠀⢀⣅⡜⠀⠈⠉⠂⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣕⠀⢀⡀⠀⠀⠘⠴⡂⣰⠖⠀⠀⠀⠀⠁⢠⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠋⡀⠐⠀⠀⠀⠀⠃⡋⠀⠀⠀⠐⠀⡀⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢰⠀⠀⠠⠀⠀⠘⠁⢀⠠⠂⠀⢸⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣯⣽⣯⣿⣽⣿⣽⣿⣿⣯⣽⣿⣿

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡤⣠⢤⣄⡀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⡟⠋⠉⠙⠂⠈⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠞⠉⠁⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀
⠀⠀⠸⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⢠⡇⢠⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡟⠁⠙⠦⠀⠀⠠⠀⠠⢤⣄⠳⠠⠊⠑⢦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣆
⠘⣇⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠀⠀⢸⣚⡄⠀⡄⣠⣨⣵⣦⡀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢹
⠀⠈⡄⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣤⣴⢶⠃⠉⠛⠟⠿⣿⣿⣿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣿
⠀⠐⡇⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⡇⢐⣿⣿⣿⣿⣷⣦⣀⣀⣀⣻⣿⣿⣿⣿⡛⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⡿
⠀⠀⠙⢦⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣤⠈⠿⣻⣿⣭⣍⠉⠉⠀⠀⠉⣻⣿⣯⣟⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠟⠁
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⣼⣿⣧⣼⣿⠿⠿⠟⠻⣿⠆⢠⣶⣿⠿⢿⡟⠃⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣧⠀⠀⠀⠀⢹⠀⠈⠙⠿⣿⣿⣤⡎⠉⠀⠀⠋⣵⣼⣿⠇⠀⠘⠛⠁⢠⠀⠀⠀⠀⠀⢀⣤⡿⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⡄⠀⠀⠸⡄⠀⠀⠀⠉⣽⣻⡷⡶⢶⡺⠿⢟⣻⠷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⠃⡎
⠀⠀⠀⠀⠀⠀⣄⣺⣶⣿⣿⠀⠈⢷⣆⠀⠻⣦⡀⠀⠀⠸⣭⣽⣃⡀⠀⠚⠷⠍⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢸⣛⣿⣧
⠀⠀⠀⠀⠀⠈⢿⣿⣿⡛⠇⠠⣄⣜⣿⣧⠀⠘⢿⡆⠀⠀⠻⣿⠩⠛⠀⠰⢡⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⣶⠀⢀⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠻⢷⣼⡇⠙⠋⠓⠈⢨⣷⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠠⣿⢀⣿⣿⢟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣻⣿⣀⣀⣠⣢⠤⠈⠙⢦⣀⣀⢀⡀⠀⡀⠀⣀⡠⠔⠉⠀⠀⣀⣀⣠⠾⢋⣼⡿⠣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣿⣿⠉⢻⠏⠀⠀⠈⠙⠲⣯⣅⡀⠙⠃⢀⣤⣿⣷⠖⠀⠉⠀⠸⡿⢥⡶⣿⣿⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢹⡇⠀⠀⠀⠀⠀⢠⠙⣷⠀⡇⢸⣿⣿⠋⠀⠀⠀⠀⠀⡇⠉⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⣼⠀⠀⣀⠆⣼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠐⠠⠤⠔⠊⠀⢀⠞⠁⠀⠈⠻⣿⣿⣶⡄⠀⠀⠀⠀⠀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠘⠟⣿⠁⠀⠀⠀⠀⡨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠊⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⡤⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡟⠟⢿⠛⢟⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⣿⣷⣶⣶⣶⣶⣿⠀⠀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠉⡛⠛⣿⠛⠛⠏⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⣿⣧⣾⣿⣿⣿⡿⣿⢷⣤⣿⠁⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠰⠀⠙⠓⠋⢥⡁⣈⠈⠄⠉⠓⠋⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⣄⠀⠀⠀⠀⠀⠀⠸⣋⡿⠀⠀⠀⠀⠀⠀⣀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠁⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠓⠂⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠚⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡇⡇⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠁


⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠂⢢⡲⠒⠀⠀⠀⠐⠂
⠀⠀⡄⢀⣾⡏⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀
⠀⠀⠄⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢈⣢⠀⠀⣀⣀⣠⡤⠺⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⠉⠴⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠆⢰⠻⣿⣿⣟⡀⠀⠀⢀⢀⣠⣴⣦⣄⡀⠀⠀⢀⣤⣤⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠳⡍⢻⣿⠁⠀⠀⡟⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠀⠀⠱⡘⣿⡆⠀⢰⠋⠀⠀⠮⣿⡟⠳⡾⡲⡟⠻⣿⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠈⠝⠉⠢⠚⠐⠙⢻⠃⠀⠀⠀⠐⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⢠⠾⠀⠀⠀⢢⠘⢄⠀⠀⠀⠀⠘⠠⠶⠞⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⢀⣶⣟⠁⠀⠀⠀⡸⠃⠂⠀⠀⠀⠀⠀⠒⠀⠚⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠂⢀
⠀⠀⢸⠟⢣⠀⠀⠀⣠⢃⡘⢦⠤⠦⢄⣀⠀⠀⠑⠐⠀⢀⣴⡆⠤⢴⣎⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣨⡄
⠀⠀⢸⣾⠈⠀⠀⣼⣿⣯⠾⠋⠀⠀⠀⡈⠳⠌⠦⠀⠠⣾⣟⡾⠒⠖⢸⣿⠷⠤⠀⠀⠀⠀⠠⠀⠀⠀⠑
⠀⠀⠈⣿⡆⠀⣾⡏⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣅⠈⠀⢀⡴⠋⢰⡇⠀⠀⠀⠀⠃⠀⠀⢀⡞
⠀⠀⠀⢸⡏⣀⣿⠃⠀⠘⣿⡄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠻⣧⣰⠞⣿⠆⡸⠀⠀⠀⣾⡀⠀⠀⠀⡼
⠀⠀⠀⢸⡇⣽⡟⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠓⠊⠀⠀⠀⠀⠈⠃⠂⠀⢐⡇
⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠘⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡐⠄⠀⠀⠀⠀⢇⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠁⠈⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠉⠁⠀⠢⡀⠀⠆⢐⠠⠀⠀⠤⡤⠄⠜⡂⠱⠀⠀⠔⠀⠈⠉⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠇⠀⠀⠀⠀⠀⢀⢀⠠⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⡁⠲⠂⠭⠀⠐⠀⠬⠐⠡⠊⡐⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⢀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠠⠂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠢⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠳⠄⠀⠀⠀⠀⠆⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠐
⠀⠀⠀⠔⠁⢁⡠⠂⠀⠀⢸⠄⠀⠀⠀⠐⡀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢀⠄⠀⠀⠀⠀⣾⠀⠀⠀⠢⡠⠁⠑⡄
⠀⠠⠊⠀⠀⠀⠀⢀⠠⠀⠌⠂⢢⠀⠀⠀⠈⠢⡀⠀⠈⠐⢀⠀⡠⠒⠁⠀⢀⠀⠀⠀⠀⠀⡐⠒⠃⢀⡀⡀⠀⠀⠀⠀⠈⢢
⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⠈⠀⡀⠤⠂⠁⠀⠀⠂⠀⠀⠇⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⢠
⠀⠀⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠂
⠀⠀⠐⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠉⠐⠤⡀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠐
⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰
⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠘⢿⣦⠀⠐⠀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⣀⢠⣤⡄⠀⠀⠀⢼⠟⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢡⠐⡀⠡⣤⡤⡘⠷⠀⠁⠀⢰⡾⠀⢴⡶⠎⣑⣾⣦⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠐⣿⠈⠠⣀⣀⡀⠠⣤⡵⠀⠐⣦⡤⠀⢀⣤⡤⠈⠡⡿⠁⠀⠀⠀⠀⠶⣚⡚⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠘⠛⡀⢈⡙⠁⣠⠄⡀⠀⠀⠀⠁⠀⢈⣉⡀⠈⠛⠢⠀⠀⠀⠀⢀⣀⠉⡀⠉⡀
⠀⠀⢠⡤⠄⡉⠛⠋⢁⠀⢀⡁⠀⠀⠀⠁⣉⠉⠛⠛⠁⠴⢤⠀⠀⠀⠀⠈⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠠
⠀⠀⠀⣀⠐⠾⠟⠒⠀⠀⢀⡅⠀⠀⡥⠤⣄⣐⠒⠻⠗⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠘⠉⣠⣴⡦⠄⠀⠀⢸⣇⠀⢀⣿⡀⢀⠀⠤⢴⣦⡄⢹⠀⠀⠀⠀⠸⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡀
⠀⠀⢰⠂⢀⡁⠐⢊⣡⠴⠐⠻⠀⠙⠷⠰⣦⣉⡓⠂⣀⡀⢻⠀⠀⠀⠀⠀⠘⠴⡦⠸⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑
⠀⠀⠀⠌⢉⡑⠛⠋⠀⠀⣀⡈⠂⠊⢤⣤⠀⢀⡙⠳⣉⡉⢯⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠘
⠀⠀⠀⠠⠙⣀⠀⡀⠀⠈⠀⠀⠒⠒⠀⠀⠀⠀⠀⢀⡈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁⡀⠐⠃⠛⢀⠆⣀
⠀⠀⠀⠀⠞⠉⠠⠀⠀⠀⠀⢀⠤⠤⠁⠀⠀⠀⡀⠈⠩⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠈⢠⡄⠀⠀⢠⡄⠉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡊⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠰⠚⠻⠶⢂⠓⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⢀⡀⠀⠚⠻⡆⠀⠀⠀⡶⠂⣄⠀⣀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣶⡈⠀⠀⠀⠀⠄⠀⠀⠠⠄⠀⠀⠀⠈⠘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢷⡀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⢀⠄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠑⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠋⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠩⡄⢉⡀⢀⠾⠡⡤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠑⠅⠲⠤

⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠂⠲⠶⢶⣄⡀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⠛⠉⠉⠉⠑⠈⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦
⠀⢀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⢠⡎⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠙⠿⢀⢈⣦⠤⢤⣬⣤⡛⠀⠀⠈⠳⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧
⢸⡇⠸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⣼⣛⣤⠄⡤⢀⣨⣿⣶⡀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸
⠀⠙⠆⠹⣿⣿⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀⣀⣤⣶⣾⠏⠙⢿⡛⣿⣿⣿⣿⠻⣿⣆⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸
⠀⠀⡄⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⣿
⠀⠀⠳⣤⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣯⣟⡻⡏⠀⢂⣿⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⢀⣴⠿⠃
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⡷⣴⣿⣿⣿⣿⣿⡿⠻⢆⣼⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣄⠀⠀⠀⠸⡟⠙⠛⢻⣿⣿⣶⣠⣿⣿⡿⣿⣿⣿⣵⣾⣿⣿⡿⢿⠟⠙⣷⠀⠀⠀⠀⠀⠀⣠⣶⢿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⣴⠆⠀⠀⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿⡇⡾
⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⣿⣿⢻⣷⣄⠀⠸⣧⡀⠀⠀⠀⢻⣿⣯⣿⢙⣿⣻⣿⣿⠟⢠⠃⠀⠀⠀⣼⡏⠀⢀⠀⠀⠀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣏⣼⠿⣿⣷⡀⠘⣿⣦⠀⠀⠘⢿⣿⢿⣿⣿⣿⣿⣏⡀⠃⠀⠀⠀⣾⠟⣠⣾⣿⣶⡆⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣭⣿⣙⣿⠿⣿⣿⣄⣼⣿⡇⠀⠀⠈⠙⠶⠡⠀⢀⠙⠋⠁⠀⠀⢀⣴⡿⠾⠋⠉⢸⣿⠁⣾⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⠙⢿⣿⣿⣿⣡⡈⠛⠟⢿⣦⡀⠀⠀⠒⠀⠐⠋⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⣀⣿⡿⣸⣿⡿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣠⣿⣿⢿⣿⡿⠳⠶⠶⣼⣿⡶⠦⠐⠻⡾⠃⠀⣶⣾⣏⣁⠠⠤⠤⣾⣿⣿⣿⣴⣿⣟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⠈⣿⠀⠀⠀⠀⠀⠙⢿⣿⣦⠀⡇⢠⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠘⣿⠄⠀⠀⠀⠀⠀⢸⣿⠿⠆⡇⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠛⣷⡀⠀⠀⠀⢠⠾⠟⢀⡼⠃⠾⣿⣿⣧⣄⠀⠀⠀⢀⣰⡀⠀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠉⠒⠖⠊⠁⠀⣠⡞⠀⠀⠀⠈⢿⣿⣿⣿⡿⠖⠛⠁⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⡀⠀⠀⣀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣩⣤⣀⡬⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⡟⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠈⠉⠉⠉⠉⠉⠛⠓⠦⣄
⠀⠀⠀⣠⣖⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⢄⠀⡀⣠⣤⠀⠀⢐⣦⠀⠀⠀⢀⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⡴⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢀⡿⠟⠋⢠⣤⡉⠈⠛⠻⠿⠛⢾⡃⠋⠉⠀⠀⢀⡸⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⢸⢁⣿⣿⣿⣿⣿⡿⢀⡀⠀⠀⠀⠀⠀⠁⣸⠟⠀⠉⢉⠀⠀⣠⣄⠀⠀⠀⢙⡄⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣾⡟⠉⠀⠀⠀⠀⢠⠀⠃⠀⠀⣠⣾⣷⣤⣽⣷⣾⣧⣤⣾⣷⣆⣀⠀⠀⠀⠀⡶⠄⠀⠀⠀⠀⠀⠀⠀⣦⣿⣷⠀⠀⠀⣿
⠀⠃⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⡔⠃⢀⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⢶⣯⣠⣏
⠀⠘⡀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢠⣿⡿⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣦⠊⢹⡁⠀⢀⡀⠀⠀⢀⣖⡀⠸⣍⣿⡇
⠀⠀⠇⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⠏⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⢿⣷⠀⢁⠶⡈⠉⣉⣷⠋⠻⠃⢀⣴⡿
⠀⠀⠈⠳⢿⣿⣿⣿⣿⣿⡄⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⡦⠈⣶⢇⣴⡿⣯⡴⠿⠶⠟⠋
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡟⡄⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠛⢻⣿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡷⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠈⢿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠿⢛⠿⠛⠉⠀⠀⠀⡟⡀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⢠⣿⡟⠻⠀⠀⠀⣠⣶⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡻⠟⠓⡀⠀⠀⠂⢙⣴⡃⠄⡀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⢀⣤⠿⠋⠀⠀⢹⣴⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣤⣀⣀⣋⣈⠁⠀⠁⠐⠦⣤⣤⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣅⣀⣀⡀⠀⠘⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⣿⡏⠉⠀⠈⠉⠉⠻⣿⣦⣤⣄⠐⠂⢀⣤⣼⣿⡿⠛⠉⠉⠙⠋⢻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢧⡀⠀⠀⠀⠀⣴⣿⣿⣿⡤⠀⠀⠾⢿⣿⡿⠷⢄⡀⠀⠀⠀⠈⣹⡟⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⣩⠋⡀⠀⠀⠀⠀⠙⢦⠀⢀⣿⣦⠀⠀⠀⠈⠁⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠘⠻⢿⣿⠆⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡤⠞⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠈⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣠⣶⠛⠉⠉⠁⠐⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠂⠀⠈
⢀⢴⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓⠀⠀⠀⣤⣀⣀⡠⠠⠀⠠⠀⢺⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠
⣿⣼⠿⣟⣸⠀⠀⠀⠀⠀⠀⠀⢸⣳⠄⠀⢀⣰⣦⣭⣤⣤⣤⠀⠀⠀⢤⠽⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿
⠐⢿⡀⠹⣿⣄⠀⠀⠀⠀⠀⢀⣾⡁⣠⡾⠟⢛⣹⣿⣿⠧⠾⠟⠲⠀⠀⣀⠀⠀⠀⠀⠀⣠⠌⠀⠀⠀⣰
⠀⠀⠉⠢⡙⣿⡇⠀⠀⠀⢰⣿⣿⣿⢋⠴⠛⡛⠋⢿⠍⠀⠛⠁⢢⣰⣿⣿⣇⢀⠀⠀⠀⠑⠂⠀⠐⠉⠁
⠀⠀⠀⠀⢹⢼⣇⠀⠀⠴⢼⣏⠉⠛⢇⡈⢹⠿⠦⢤⡤⠘⠟⠓⠘⠛⠛⠉⠛⠁⠀⠀⠀⣶
⠀⠀⠀⠀⢀⣾⣥⣀⣠⣄⠀⠈⠑⠠⣤⡹⠟⠚⠓⠐⠀⠐⠲⠸⠇⠀⠔⠋⠀⢀⡴⣀⣀⣰⡇
⠀⠀⠀⠀⠸⢿⡿⠿⣿⣿⠧⠀⣠⠤⠀⢽⡶⠃⠀⠀⠀⣠⣶⣾⡿⠷⠄⠀⡰⢻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠈⢀⡀⠈⣿⣷⢾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠾⣿⠟⠀⠀⣾⢦⣿⣿⠿⠋⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣾⣿⡆⢼⠟⠁⠀⠀⠀⢠⠖⠀⠸⡯⡀⠀⠀⠳⠻⣿⣷⡄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠈⡀⠀⠠⠂⡴⠁⠀⠀⠀⠟⣿⠀⠀⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠁⠀⢠⠞⠁⠀⠀⠀⠀⠈⢮⡀⠀⠀⠀⢸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣄⣀⣀⣠⣥⡤⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀⠈⠉⣺⡿⣿⣿⣿⣿⠛⠋⠁⠀⢀⣀⡤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢿⠖⢀⡻⢷⣿⢻⡟⢳⣶⠶⠀⠒⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⣤⣿⣾⣄⣀⣀⣠⠴⣾⣶⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣴⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣭⣛⠛⠉⠋⠑⣚⣿⣶⣼⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢇⡀⠀⠀⠀⠀⠀⠰⠋⠉⠉⢻⣿⣿⣿⣿⡟⠻⣿⠍⠛⠋⣿⠋⠉⠈⢻⡄⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡙⣸⡻⣵⣦⡶⠞⡉⠀⣇⠀⠀⠀⠸⠃⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⢀⠈⠀⣸⣿⡳⡅⠀⣷⣿⡷⠀⠁⠀⣸⡄⠀⣀⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣷⠀⠄⡁⠄⠀⠙⠲⣿⠋⠉⠙⢷⠼⣩⠴⠿⠃⠈⢿⡿⠞⠁⠀⢀⣴⣶⡿⠷⠷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⢤⢀⣼⣿⡇⣿⣆⠀⠈⣠⡄⠀⢀⣀⣄⡀⠀⠀⢷⢦⡎⠀⠀⠀⠈⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⠁⣿⣿⢾⣴⣷⣾⣿⡿⠿⣏⠛⠒⠒⢚⣼⡖⠒⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⠤⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣿⣿⡿⢿⡏⠉⠉⢿⣿⣶⠏⠋⠀⠀⠀⡘⡉⣇⠀⠀⠸⣿⣀⣠⣀⣡⣿⣿⣧⣄⣀⣀⡤⠈⠋⢸⡷
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢿⠋⠀⠘⡧⠀⠀⠀⠈⠉⠀⠀⠀⡠⠊⠀⠀⠈⠣⡀⠀⠃⠤⢭⠄⠌⠀⠉⣩⠍⣿⣿⠇⢀⠐⢹⣅
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⡆⠀⠀⠙⠤⣀⣀⠀⠀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠀⠀⠀⢀⡠⠃⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⣠⣄⡀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⠟⠉⠉⠑⠂⠀⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⠟⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠸⣾⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⢠⡆⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⠟⠁⠙⠦⠄⠀⠠⠀⠠⢤⣄⠰⠀⠊⠑⢤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣆
⠘⡇⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠀⠀⢸⣊⠀⠀⠀⢀⣀⣵⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸
⠀⠈⡀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣤⣤⢆⠃⠉⠛⠛⠟⣿⣿⡿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣿
⠀⠀⡇⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⣿⣿⣿⣗⣀⣀⣀⡀⠛⣻⣿⣿⡟⡓⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣺⡿
⠀⠀⠙⢦⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢰⣄⠈⠿⣺⣯⣭⣍⠉⠉⠀⠀⠉⢻⣿⣯⣛⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠟⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣧⣼⠿⠿⠿⠛⠿⣿⠆⠠⣶⣟⠿⠿⠛⠁⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⠀⠀⠀⠀⢹⠀⠈⠙⠟⡿⣿⣤⡊⠀⠀⠀⠋⣵⣼⡿⠇⠀⠘⠘⠁⢰⠀⠀⠀⠀⠀⢀⢄⡾⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠗⠄⠀⠀⠸⡄⠀⠀⠀⠀⣽⣛⡒⠶⠲⠲⡿⢛⣛⠗⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⠃⡄
⠀⠀⠀⠀⠀⠀⣄⣸⣶⣿⣿⠀⠀⢶⣄⠀⠹⣦⡀⠀⠀⠨⣉⣵⣃⢀⠀⠈⠳⠍⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⣛⣿⣧
⠀⠀⠀⠀⠀⠈⢿⣿⣮⡛⠏⠀⠄⢈⣿⢢⠀⠘⢿⡆⠀⠀⠱⢯⠉⠙⠀⠠⢁⠀⠀⠀⠀⠀⢠⠊⠀⠀⠐⡦⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠛⢶⣼⡄⠈⠈⠓⠈⢈⣷⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠠⣭⢀⣾⣿⢟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢻⣷⣀⣀⢠⣀⠀⠈⠁⢄⣀⣀⢀⡀⠀⠀⠀⣀⡠⠔⠁⠀⠀⢀⣀⣀⠼⠋⣼⡿⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣿⣿⠉⢻⠏⠀⠀⠀⠐⠲⢯⣍⡀⠘⠃⢀⣤⣿⣷⠖⠀⠉⠀⠘⡟⢥⡶⣿⣿⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠸⡇⠀⠀⠀⠀⠀⢀⠙⢷⠀⠄⢸⣿⣿⠋⠀⠀⠀⠀⠀⠃⠁⠀⣸⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⡼⠀⠀⡀⠀⣸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠐⠀⠤⠔⠊⠀⠀⠞⠁⠀⠈⠻⣿⣷⣤⡄⠀⠀⠀⠀⠀⡀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠈⠛⣋⠀⠀⠀⠀⠀⡈⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡯⠿⠛⠛⠻⠿⠟⠽⣿⣿⣿⣿⣿⣿⣷⣦⣄⡈⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣀⣴⡿⠿⠟⠉⠋⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣖
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠎⢠⣿⡷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠘⠀⠳⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠛⢹⣷⡆⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠉⠀⠀⣿⣿⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⡿⠉⢆⢣⠀⠀⢶⣿⣿⠀⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⠁⠂⣤⡽⣿⡷⡄⠀⠀⣀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡀⠃⠀⠀⠈⡰⣆⠰⣾⣿⣶⣄⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⡆⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⠀⠈⣷⠄⠀⠀⠄⠉⠛⠿⣿⣿⡿⠿⠞⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣧⠄⢀⣄⠚⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠈⠑⠓⠄⢁⣤⣸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠳⠀⠀⠀⠀⠀⣀⣄⣠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢠⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⡧⢀⣠⣾⣿⣿⣿⣿⣿⡿⣇⣸⣻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣠⢟⣴⣿⣿⣿⣿⣿⡿⣿⡏⠀⡟⠉⠉⠉⠛⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢟⡵⢿⣿⣿⣿⣿⣿⣿⣿⡜⠁⠈⠋⡀⠉⣁⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣵⡟⠰⣿⡏⠉⠉⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢻⣻⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠾⠃⠀⠙⡿⠁⠀⠀⠀⠀⠀⠙⢿⣿⣦⣤⡄⣠⡀⣠⣿⣿⣿⠁⠀⣀
⠀⠀⠀⠀⠠⠆⠆⢰⡆⠀⠀⠛⠋⠀⠀⠀⠇⠀⠀⠀⠶⠆⠀⠀⠀⠻⣿⣿⣍⠹⢿⣿⠿⢿⣿⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⡷⡄⠸⠐⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣦⣄⡀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠈⣿⠀⠁⠀⠀⠀⠀⣻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠉⠛⠒⠦⠄⠂⠐⠛⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠈⠙⠛⠿⠿⣿⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠋⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢦⣤⣀⣠⣤⣶⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⠸⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⣴⣺⣛⣲⢭⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡫⣰⡿⣿⠿⣿⣿⣿⣯⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣹⢡⡏⠉⣨⣶⣿⣿⡿⣿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠊⠉⠉⠙⠻⢦⣠⣿⣿⣿⣿⡟⣿⣿⣿⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⢸⣟⣯⣽⣿⣷⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠲⡄⠀⠀⣠⠞⠁⠙⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⣷⠃
⠀⠀⠀⠀⠀⠀⣾⣗⠀⠀⢴⣿⣿⡏⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⣼⣿⣿⣿⣟⡯⣫⡾⠋
⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠘⣻⣿⠻⣄⣀⡄⠀⢀⣼⣷⣄⢀⣼⣿⣿⣿⣯⣵⠞⠉
⠀⠀⠀⠀⣰⣿⣿⡅⠀⠀⠀⢳⡄⠀⠈⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⣼⣿⣿⣿⣗⠀⠀⠀⠐⣧⣤⣶⡿⠿⠋⠀⠀⠀⠀⠀⠀⢻⣿⡧⠃⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⣿⣿⡿⣿⣯⡇⠀⠀⠀⠙⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠻⣿⣷⣤⣰⠉⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠸⣿⣿⣏⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠑⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⢹⣿⣷⠛⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠒⠀⠒⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠟⠿⠀⠀⠀⠀⠈


⣶⣶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡤⠖⢛⣛⣛⣛⣓⠒⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢚⣛⣛⣛⣛⠓⠦⣄
⠀⠀⣴⠋⣠⠞⠋⠉⠉⠉⠉⠉⠙⠒⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠔⠚⠉⠉⠉⠉⠉⠉⠛⢦⡈⢳⡄
⠀⣼⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢻
⢰⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⣸⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⡌⢷⡀⠀⣏⠙⠷⣄⠀⣀⣀⠀⡠⠊⠉⡇⠀⣰⠏⡼⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠈⠺⢷⣄⡿⠀⣧⡈⠋⠀⠈⠉⢀⡀⠸⣇⣴⠿⠊⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠉⠀⡏⠀⠁⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠐⠛⢶⣄⣀⠀⠀⣀⠤⠞⠛⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⢻⣄⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡠⢴⠦⣀⠀⠀⠀⢀⡀⢲⠤⣀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮
⠀⠙⠻⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠠⠾⡏⢀⠀⠀⠀⢀⠈⡽⠦⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠛
⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣥⠴⠾⡅⠀⠀⠈⢀⢠⡀⠀⠀⣠⣲⠆⠀⠀⠀⡽⠶⢤⣵⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⢳⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⢸⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠘⡄⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⡀⠀⠀⠭⠐⠂⠠⠤⠚⠨⠅⠀⠀⢸⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⡇⡜⠀⡿
⠀⠀⠀⠀⠀⠀⠘⢧⣀⣿⣇⠀⠀⠀⠀⠀⠀⢻⡓⢤⡀⠀⠑⠲⠤⢤⣀⠀⠀⠀⢀⣠⠤⠤⠒⠁⠀⣠⠔⣻⠁⠀⠀⠀⠀⠀⢀⣿⣇⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠀⠀⠀⠀⠀⠳⣴⠃⠀⠀⠀⠀⢀⡽⠗⠒⠒⠿⣄⠀⠀⠀⠀⠀⢳⡴⠃⠀⠀⠀⠀⢀⣴⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣧⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠸⣦⣀⣀⣀⣠⡾⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣆⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣀⣾⣅⣈⣀⣽⣆⣤⣤⣴⠞⠁⠀⠀⠀⠀⠀⢀⡾⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠙⠳⣶⣶⡶⠶⠦⢤⣄⡉⠓⠄⠈⠏⠁⠉⡏⠀⠔⠋⢁⣤⡤⠤⠶⣶⣶⡶⠛⠁⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠶⠾⡏⠉⠱⡀⠀⠀⠈⠙⣦⠀⠼⡇⠀⠀⡿⠆⠀⡞⠁⠀⠀⠀⣰⠃⠉⡿⠶⢶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠹⠀⠀⢳⡄⠀⢀⡴⠃⠀⡰⣧⠀⢠⣷⡀⠀⠳⣄⠀⠀⡰⠃⠀⠸⠃⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠐⠛⠒⠉⠀⢀⢄⡤⠛⠓⠛⠳⣕⣄⠀⠈⠛⠛⠃⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⣐⡵⠋⠀⠀⠀⠀⠀⠈⠳⣕⡄⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⠶⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠂⠀⠀⠂⠀⠐⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠃⠋⠀⠂⠀⠘

⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀
⠀⠀⠀⢀⡄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠸⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠆⠀⠀⠀⠀⢀⢀⣄⣰⣿⠃⠀⠈⠿⢿⣿⣿⣿⣿⠇⡀
⠀⠀⠀⠀⠹⣜⠇⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢉⣼⣿⣿⣿⣿⡆⠈⠀⠙⠀⠂⠀⠀⢸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⣈⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⣙⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠠⠻⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠟⢧⠀⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣼⣄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣿⣿⣿⡿⠋⠀⠀⡠⠊⠀⠈⢉⣠
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⣀⡀⠈⠻⢿⣿⣿⣿⣿⠟⠁⠤⠄⠀⠀⠀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⣿⣿⣶⡞⠉⠙⢦⣤⣤⣭⣿⣭⣥⡤⠴⠋⠉⢹⣟⣟⣛⣿⠏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣿⣿⠀⠀⠀⢈⣿⣿⣿⠿⢏⠀⠀⠀⠀⠀⢀⠛⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⣠⣼⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡠⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⡠⡠⠒⣀⣡⣠⡄⢈⠑⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠿⡛⣿⣷⠝⣷⡄
⠀⠀⠀⠀⠀⠀⣰⣿⠟⡿⠋⠉⠀⠀⠀⠀⠀⠘⣿⣤⣀⠀⢠⣤⣄⠀⠀⠀⠀⠀⣀⣤⡀⠀⢀⡀⢠⣾⠟⠁⠁⠀⠀⠀⠀⠀⠈⠛⣷⠘⣿⡄
⠀⠀⠀⢸⡆⠐⣿⣵⢟⠆⠀⠀⠀⢀⠀⢀⡠⢶⠏⠙⠛⣷⣾⠿⠿⠇⠀⠀⠂⠸⠿⠿⣷⣤⠾⠿⠧⢹⣦⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⢸⡷⢰⣿⢿⡿⣆⠀⠀⠀⠈⠀⠀⠀⡟⠀⠀⠀⠈⢓⣜⣓⣛⣒⣒⣀⣀⣠⣴⡋⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⠀⣿⣇⠂
⠀⠀⠀⠀⣿⡌⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣄⣀⡀⢀⢸⠆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⡿⠋
⠀⠀⠀⠀⠈⠛⢿⡿⣿⣿⣿⢄⠢⠀⠀⠀⣿⡞⣧⣤⣾⣿⣿⣭⣝⣽⣛⣏⣿⣛⣷⣶⣿⣿⣿⣿⣇⣸⡀⠀⠀⠀⠀⠀⠀⢰⠟⣸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢮⡛⣹⣆⡹⣦⣤⣼⣿⣿⣿⣿⣿⣿⣾⣿⡿⡿⣿⣿⣿⣿⣿⡿⣿⣿⠾⣿⣷⣿⣧⡄⠀⠀⠀⠀⠀⡼⢤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢹⡿⡿⢶⣷⣾⣿⡟⠿⣿⣾⣝⣿⡿⢶⣶⣼⣾⣶⣾⣶⣼⣯⣥⣶⡿⠟⠋⢉⣧⠀⠀⠀⠀⠀⠈⣿⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⣬⣇⠀⠀⠻⣾⣿⣇⠀⢠⡘⢿⣿⣿⡞⢺⣛⡋⣻⣿⣟⣛⠟⣿⡟⠀⠆⠀⡼⠁⠀⠀⠀⠀⢀⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⡄⠀⠀⠀⠈⠛⢦⡈⠀⠈⢛⡛⣷⠤⣨⣿⣿⣿⣿⣻⣿⡟⠀⢀⣠⠞⠁⠀⠀⠀⢀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣀⡀⣀⣀⠀⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠤⣺⠛⠑⠐⢒⣳⠶⠄⣻⣿⣿⡿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡻⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣾⣤⣤⣄⢨⠋⡁⣠⣬⣼⣿⣿⠋⠙⢛⣻⣛⣛⣚⣻⣿⣿⠁⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢾⢿⡽⣿⣿⣯⠁⠀⠙⠻⣿⣿⣿⣿⢸⣬⡁⣿⣿⣿⡿⠁⠀⠀⠈⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣿⣿⣿⠀⠠⠀⢀⣿⣿⣿⣿⣠⣿⡅⣿⣿⣿⣷⣄⡀⠀⢀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣠⣶⡿⣳⣿⠟⠋⠁⠰⠀⠈⠙⢿⣿⡿⣿⣷⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢟⡴⢛⠁⠀⠀⠀⠀⠀⠀⠀⢠⡙⢿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠛⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⣤⡀
⠀⠀⠀⡠⢊⣤⠖⠀⠙⠛⠒⠲⠭⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠐⠀⠀⠘⠓⠦⡍⠢⡄
⠀⠀⡰⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢹⡄
⠀⢠⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⢠⡀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧
⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⢤⣦⠀⡇⢠⠱⣤⠖⢦⡴⢣⠀⡇⢠⣏⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠛⠃⡞⠓⠂⠤⠄⠒⠛⡆⠛⠋⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⣿⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠐⠳⣤⣀⣀⣀⣠⡴⠛⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢸⡇
⠀⠸⣄⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠤⢶⢢⣌⣉⣉⣠⣲⠦⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣀⡼
⠀⠀⠈⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⡀⠀⠘⠻⠓⠂⠀⠐⢶⡝⠛⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉
⠀⠀⠀⠀⠀⠙⣦⢆⠀⠀⠀⠀⠀⠀⢸⡟⠊⠉⢳⡀⠀⠁⠶⠓⠀⠀⠳⠇⠀⠀⣼⠋⠁⠚⡿⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠘⠀⢢⢰⠀⠀⠀⠀⠀⡇⠀⠀⠈⡀⠀⠀⠐⠦⠀⠀⢔⡂⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠐⢀⠀⣾
⠀⠀⠀⠀⠀⠀⠘⢧⣸⣿⡀⠀⠀⠀⠀⠹⡲⣤⠀⠛⠶⠤⣄⡀⠀⠀⣠⡤⠴⠞⠃⢠⡴⣾⠃⠀⠀⠀⠀⣸⣿⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣦⡀⠀⠀⠀⠻⣞⠀⠀⠀⠀⡴⠛⠑⠙⠳⡄⠀⠀⠀⢘⡾⠃⠀⠀⠀⣠⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⣧⠀⠀⠀⠀⠘⢦⣀⠀⠀⢹⡆⠤⠄⣾⠁⠀⢀⣠⠞⠀⠀⠀⠀⢠⡟⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠙⢦⣤⣤⣤⣀⣀⡉⠻⢟⠛⢿⠛⢺⠛⢛⠿⠋⣁⣀⡀⣠⣤⣤⠟⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠤⣟⠉⢣⠀⠀⠉⠳⡄⢠⣆⠀⠀⣧⠀⡰⠊⠉⠀⢠⠊⢙⡧⢤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠸⠀⠈⢧⡀⢀⠼⠁⢀⢿⡀⣰⢧⠀⠑⣦⡀⣠⠆⠀⠸⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠉⠉⠀⢀⣤⡴⠋⠁⠈⠳⣇⣀⠀⠉⠉⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣴⡬⠷⠋⠀⠀⠀⠀⠀⠈⠳⠧⣤⣄⣀⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣦⡙⣦⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣈⠳⣌⠳⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠳⣌⠳⣌⠳⣌⡓⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⢲⣬⡓⢮⡛⠦⣝⣓⠶⠾⢽⣗⣲⣲⢿⣯⣙⣿⣿⣿⡟⢃⣿⠝⣳⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⡿⣿⢠⣝⡲⢭⣓⠦⠭⡭⠭⢽⣛⡶⢽⣛⠓⣶⢃⡴⢋⡴⢋⣥⠞⣋⣤⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢹⢣⡏⡇⣍⣓⠮⣝⣓⣒⡯⢽⣲⡭⢡⢏⡞⣱⢏⡴⢋⡴⢋⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⡾⡼⡼⡽⡬⣝⣒⠶⢖⣪⡭⣰⢳⢏⡞⡼⢡⠟⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡇⡇⣇⢳⢳⢱⡹⡨⣭⣵⢰⢣⡇⡏⡾⢸⢣⡏⡾⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡾⣸⢃⡇⡾⣸⢸⢣⠇⢟⣛⡊⣎⢇⢧⢧⢹⢸⢸⢇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞⣴⢣⡞⡼⣱⢣⠏⣚⡫⠵⠶⠭⣝⣘⣞⡞⡞⡼⡾⣾⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣡⠞⣡⠞⣱⢏⡼⣱⣃⣚⠯⣗⣺⠭⢭⣝⡲⢮⣙⢸⣱⢳⣇⡏⡇
⠀⠀⠀⠀⣤⠶⠛⣩⡴⢛⣡⠞⣡⠞⢡⠯⢤⣍⣓⠮⢭⣗⣒⣒⣒⠲⢭⣓⠮⣝⠃⡿⣾⠿⡇
⠀⠀⠀⠀⠈⠐⠻⢯⣔⣻⣡⣼⣿⣿⣿⣍⣻⣷⠼⠯⣽⣗⡲⠶⢭⣝⠲⣍⡳⢬⡛⠧⣧⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⢮⡙⢦⡙⢦⡙⢦⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢦⡙⢦⡉⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠻⣌⠻⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠌

⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠢⡀
⠀⠀⠀⠀⣽⣿⣿⡿⠉⠉⠉⠛⢹⡿⣿⣿⠛⢣⡀⢰⣄⠀⣰⡄⠀⠰⣦⡘⢃⣴⡙⡆⠄⠀⠀⠀⠀⠀⠀⠀⠊⣳⢹⣆
⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⣿⣷⡿⢡⣤⠾⠁⢦⡏⢨⡁⢀⢀⠰⣽⠶⠛⠚⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⣼⡟⣼⡿
⠀⠀⠀⠈⣿⣿⣿⣿⣶⡀⠀⣴⣿⣿⣿⣏⢁⣤⣤⣦⣀⡛⠛⣙⣩⣴⣿⣦⠀⢠⣼⣿⡗⠀⠀⠀⠀⠀⢀⡀⣹⣿⡟
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣿⣿⡟⠸⣼⠿⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣦⣐⠈⢷⡃⠀⠀⠀⠀⡀⣸⣋⣿⠏
⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⠋⠻⠋⠙⠻⡿⣶⡆⠀⠉⢿⢿⣿⡿⠛⠋⠙⠛⠂⣷⣄⡀⡀⠀⢄⡽⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⠶⠀⠠⡴⠟⠋⠁⠀⠀⠀⠀⢠⢇⠪⠁⡄⣰⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣟⢿⢻⠉⠛⣿⣄⠀⠀⠀⠈⢻⠠⠀⣴⣯⠀⠃⠀⠀⠀⠀⣰⡷⠁⣶⣟⢠⣾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⢇⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠘⠍⠀⠀⠀⠀⢠⣾⠟⠀⣠⣿⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⣬⣁⡿⠟⢧⡀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⢀⡴⢋⣀⣴⣿⡿⠛⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢈⣿⣿⠂⠀⠙⢷⣦⠄⢀⠀⣀⠀⢀⢄⣾⡿⠛⠛⢻⣿⡟⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⡆⠀⠀⠀⢻⢿⣶⡆⢰⣶⣶⠟⡏⠀⠀⠀⣸⣏⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠹⡿⠤⣤⣴⣤⣠⠟⠁⠈⠻⣳⣾⣷⣄⣀⣀⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⠀⠀⠀⣠⠆⠁⠀⠀⠀⠀⠈⠙⢧⡴⣈⢹⡿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠭⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⢀⡴⡂⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⢺⣷⣾⣿⣿⣿⣶⣤⣤⣤⣼⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⣀⣹⣛⣿⣿⣿⣿⣿⣄⣀⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⡴⢿⠟⠛⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⢀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠙⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠋⠈⠛⢿⣄⣤⣤⣀⠀⣨⢶⣀⠀⠠⣤⠄⠀⠀⠀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠙⣿⣿⣿⡏⠠⠘⠋⠀⠀⠀⠀⠀⠀⢠⠏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⢀⣀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠠⣤⣀⠀⠀⠃⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉

⠀⠀⠀⠀⠀⠀⣠⣴⣚⣽⣵⣶⣶⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠐⠒⠒⠒⠲⠤⣀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠋⠀⠀⠈⠁⠈⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠸⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠈⡾⣿⡆⠤⣀⠀⢠⠀⠀⠀⠀⢢⡀⠀⢤⣁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣
⠀⠀⢶⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠈⢱⢄⠉⠉⠉⠙⢆⡄⠀⠀⠙⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢣
⠀⠀⠈⠂⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⣀⣀⡞⠳⣾⣾⣷⣿⣿⣿⣷⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸
⠀⠀⠀⢰⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⣶⣿⣿⣶⣧⣂⡠⠎⣽⣿⣿⣶⣿⣿⣶⠄⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡿
⠀⠀⠀⠈⢦⣠⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⡀⣿⠿⣟⣯⣛⣿⣿⡏⠹⢿⣿⣿⣛⠻⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡁⠀⠀⠀⠀⢠⣿⣿⣴⡿⠿⠿⠟⢿⣿⡤⣤⣶⡿⠿⡟⠛⠁⣠⣯⢠⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠈⡏⠈⠉⢷⣞⣿⣤⡎⠉⠂⢾⢫⣤⣿⠟⠀⠘⠛⠋⢹⠀⠀⠀⠀⠀⠀⣰⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢫⠘⣿⣿⠂⠁⠀⠀⢳⠀⠀⠀⠉⢞⣋⡟⠛⠿⠛⠟⢉⣛⠒⠂⠀⠀⠀⣸⠀⠀⠀⠀⠀⣟⢏⣸
⠀⠀⠀⠀⠀⠀⠀⣠⣚⢷⣿⡿⢀⠙⢷⣄⠈⢳⣄⠀⠀⠸⣭⠾⣧⢠⣆⢈⡳⠀⠸⠀⠀⢀⣰⠏⠀⢀⠀⠀⠀⢫⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣍⣃⠈⠁⠨⡟⢦⠀⠙⣇⠀⠀⠘⠣⠘⠋⠉⠉⠷⠐⠀⠀⠀⢸⠋⠠⠀⠈⡇⠀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠉⠑⠀⠀⠀⠀⠑⠈⠻⢆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⡆⢰⣿⢟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠠⡠⢤⣤⠤⠀⠠⢀⣁⡠⠤⠐⢀⠀⠀⢠⣶⣋⣁⠤⠤⠴⣶⢿⣉⣴⣿⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠒⡅⠀⣋⠀⠀⠀⠀⠈⠉⠱⡆⠈⠀⣼⣿⣿⠋⠀⠀⠀⠀⢏⡿⢋⣹⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠈⠛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⢀⣀⡴⠊⠀⠰⠂⠈⠱⢶⣶⣤⣀⠀⢀⠔⠀⠀⣠⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠀⠀⠀⠀⠈⠀⠀⢀⠔⠀⠀⠀⠀⠈⠻⡿⡖⠀⠀⠀⠀⢞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⠤⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⢀⡞⠀⠂⠄⠀⠀⠀⠀⠀⠓⢸⢃⠘⣿⠁⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠏⡜⣀⢣⢣⠰⣿⣟⣞⣷⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢸⡇⠠⢸⡄⠀⠀⠂⠀⠐⣡⢎⠈⠐⢿⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⡘⣡⢫⡌⣎⢦⠹⡜⣞⢦⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠀⠀⠀⠐⢨⠀⠄⠃⠜⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠡⠙⢯⡜⡌⢆⠳⡝⢎⠳⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠑⡈⢞⣜⢦⡑⣜⠦⣑⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⢈⣽⣿⣶⣶⣦⣤⡕⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡘⢆⠻⢷⣝⣮⡓⢬⡓
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰⠐⠂⠀⢉⠀⡀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⢄⡙⢿⣟⣲⢬
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠰⠀⠀⠀⡀⠀⠢⠀⠈⠄⢀⢈⣅⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣦⣍⠢⢍⡑⠻
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⢀⠣⣄⠀⠈⠀⢀⠀⠀⢀⣴⡾⠋⢀⡀⢴⡆⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡎⣿⢻⡟⣶⣬⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠐⠈⠑⠂⠀⠀⠀⣠⣿⣿⠃⠀⠁⠀⣼⡀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⢸⠃⡇⣽⡈⡇⣏⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⣠⣿⣿⣿⡁⣀⠲⣈⠰⣿⠀⠠⣤⣔⠶⣯⠀⠀⠀⠀⡀⠐⣒⣤⢌⡓⠤⣙⠳⣄⡀⠀⠀⠀⢸⠀⡅⣿⣧⡄⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣶⣶⠏⠸⢻⣝⢚⣤⣍⠀⢸⡟⠒⠂⠒⠉⠄⣐⠀⠀⠀⠀⠀⠀⠉⡛⠿⣟⣷⣄⡑⠆⡙⢦⠀⠀⢸⡄⡇⢻⣿⡇⡏⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⠍⠀⡀⠡⠈⠠⠉⠉⠀⡀⢾⠇⠀⠠⠤⠀⣀⠉⠀⠀⠀⠀⢀⡐⠂⠤⣓⠤⡙⠿⡻⣦⡙⢆⠳⣄⠈⣇⢣⠘⣿⣧⢱⢳⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠘⢿⣥⠀⠀⠀⠀⠀⠀⠐⠮⠕⡂⢽⣆⠀⠤⠈⠁⣂⠨⠭⠥⠬⠭⢔⣒⠩⣐⢄⡑⢎⡲⡙⢿⣫⡤⠱⠘⢆⠸⡌⣆⠹⣷⢇⠳⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠜⢳⡚⠐⠀⠀⠀⠀⢤⣒⣮⣽⣿⠁⣐⣓⣂⡀⠤⠐⣛⣛⣛⣓⡢⠭⣛⠮⡓⢝⠢⡑⡜⢆⠙⡵⢃⠀⠈⢆⠹⡌⢆⠻⣯⣷⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⠹⣢⠔⣀⣴⣞⣿⣟⠓⣽⣿⣧⠶⠶⠶⢶⣞⡛⣯⣭⣭⣿⣻⢷⣮⡳⣌⢦⠓⡱⡘⡆⢀⢱⢫⡆⠠⠸⡀⠙⣌⠳⡜⠷⣮
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠄⠉⠀⠀⣙⡳⠮⣛⣿⣟⠻⠿⠿⠿⠷⠾⣙⣻⠿⢿⣛⢿⣿⣟⢷⡜⣆⢡⢱⢣⠀⠄⡄⡞⣱⠀⡆⢇⠀⠈⠳⢌⠲⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡶⣼⡻⢯⣿⣇⣬⠉⠉⠉⠉⢭⣄⠒⢾⡖⢬⠳⣹⣿⡼⣷⠸⡇⡇⡎⠀⢸⢠⠀⡟⡀⢠⢸⠀⠀⠀⣼⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠠⠤⢬⡛⠦⠝⠛⠻⡛⠶⢛⣛⣛⣛⠶⠮⣹⣿⢿⡇⡆⣿⢸⡃⣿⠀⠇⡇⡇⡄⢸⢸⢰⡇⡇⢸⢸⠀⠀⢸⠃⠂⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡠⠬⠛⡳⠒⠒⠚⠛⠋⣅⠪⢒⠕⣠⣻⣼⢇⢿⢀⡆⡇⡇⠁⢨⢸⠸⡇⡇⢸⢸⠃⠀⢸⢀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡩⢔⠲⢬⣭⣉⡉⠉⠛⠓⠮⢑⣡⢞⣵⡿⣫⣾⢃⡞⡴⠱⠸⠀⡌⡆⣦⢿⠀⡄⡼⠀⠀⢸⠘⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢲⣸⡕⢊⡥⣒⢲⣶⣦⣤⣭⣽⣻⡾⡿⢫⣾⠟⣡⢚⠞⡡⣣⢃⡆⡔⢰⡝⡎⣰⢡⠇⠀⠀⠘⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢔⣒⡲⠶⣶⣶⣦⣤⣿⣿⣃⡔⣡⣶⢿⣛⣿⣿⣯⣽⣭⣭⡷⠶⢛⣡⢞⡵⡡⢊⠔⣡⢎⠌⣰⡷⡝⣠⢀⡎⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⠔⠉⡳⠭⢛⣒⣶⣿⣿⣿⣿⣿⣷⣿⣎⣿⠿⢋⣭⣔⡲⠶⠶⠶⠶⢯⡝⠒⠥⠂⠄⣡⠊⠕⣣⣾⣿⠟⡱⢣⡞⠀⠀⠀⠀⠀⠀⢣⡘
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠁⠀⢀⣡⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⡽⠓⠈⢉⡉⠉⠐⠒⠒⠂⠉⢂⡠⢀⠁⠀⢄⢙⠿⣩⠞⣵⠋⠀⠀⣀⣀⣠⢴⣓⡈⠿
⠀⠀⠀⠀⠀⢀⠀⠈⡄⠀⢀⢮⢾⠟⣿⣿⢟⣻⣭⣭⣭⣿⣿⣿⣿⣧⣿⡐⡴⢉⠄⠒⠤⠤⠤⢤⣬⠍⠐⠂⣀⠠⢀⠼⣡⠈⡥⠛⠀⣠⠔⣭⡔⠂⠲⣝⢶⣭⣙
⠀⠀⠀⠀⠀⠈⠀⡇⢘⠀⡞⣇⢣⡸⢏⡴⡫⠛⠂⢉⠉⠉⠛⣿⢿⣿⣷⣿⡐⡑⢊⢤⡐⠶⠶⡶⢶⢶⣬⡙⠢⢘⠠⢀⡠⠊⢀⡠⢖⣵⣮⢖⡮⣝⡛⣿⣛⡢⠬
⠀⠀⠀⠀⠀⠀⢠⢁⡄⠀⠇⣽⢈⡇⢸⢱⠁⡀⠊⡴⢮⢙⣻⣿⣿⣿⣿⣿⣿⡀⣾⡷⣪⠍⢒⣒⣒⣒⣀⣀⣭⡥⠖⠉⠀⡴⢫⢞⢡⠾⣿⡗⣩⠖⠒⣿⣗⣈⣭
⠀⠀⠀⠀⢀⠴⡻⣿⣿⡧⣼⣧⣾⣧⡾⣸⢀⡇⢸⢸⠰⣾⣟⢿⣿⣿⣿⣿⣿⣿⣿⠐⣡⠚⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⣕⣇⢯⣻⢝⣻⣿⡕⣨⣤⣾⣿⣟⣛
⠀⠀⠀⢀⢇⢺⡁⡔⣰⣿⣿⢿⣿⣿⣿⣷⣮⣷⣄⣿⣸⣿⣥⡆⡞⠋⠛⠿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣱⣋⠖⣩⣿⣟⣽⣲⣿⣷⠺
⠀⠀⠀⢸⢸⡇⡇⠀⢻⣿⡟⣿⢣⡿⡟⠙⡁⣰⢟⢿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠙⠿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⢋⠼⣻⣿⣿⣧⣾⡟⣹⣿⣟⣭⣿⣟⣛
⠀⠀⠀⠀⢯⣾⣵⣆⢿⣼⣧⣿⡸⣿⢇⢷⡁⣵⢀⠜⣷⢻⠉⡽⠛⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡤⢺⡝⢾⣿⣿⣮⣵⣮⣿⡝⡿⣿⣿⣿⣟⣽⣿⣯⣾⣷⣶
⠀⠀⠀⠀⠀⠉⠛⢿⢿⣿⣿⣿⣿⣿⣿⣞⣷⣜⢧⣜⣿⣾⣷⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣱⢫⣾⢿⠿⣿⣿⣿⣿⡧⢞⠝⣹⣿⣿⣿⣿⣜⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣸⡄⣅⢸⣿⡟⡻⢿⣿⡟⠳⢻⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣻⡜⣧⢣⡞⡱⢫⣽⣿⣿⣶⣾⣽⣿⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣼⣥⣹⡙⢁⣾⢯⣿⣽⡟⣼⣄⠂⠸⢸⠁⠁⡿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡴⡻⢿⣿⣿⣿⣼⣏⣠⣷⢫⣿⡿⣿⣿⣿⣟⣫⣾⢟⣿⣿⣿⣿⡏
⠀⠀⠀⡰⣺⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣼⣽⣅⣀⢀⣞⠄⣠⣳⡜⡾⢩⠇⠀⠀⠀⠀⠀⢸⡀⣇⢻⡹⢏⡟⡿⢿⣿⣿⣿⣏⣿⡟⡽⣻⣿⣿⣱⣫⣿⡟⣼⣿⣧
⠀⠀⣼⢱⡹⡝⢁⣾⢿⣿⣿⢟⣿⠿⠛⡩⣹⡿⢿⣿⣿⣿⣿⣿⣽⣷⠏⠀⠀⠀⠀⠀⠀⢸⣧⡏⣼⣇⡾⣸⢰⣿⣯⣿⢿⣿⣿⣿⣾⣿⣫⢿⣿⣿⣯⣼⣟⣿⣻
⠀⠀⣷⢸⠇⡇⢸⣼⡏⡟⣿⢸⢌⠀⡄⠰⢹⠀⣞⣷⢳⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣽⣿⢻⣿⣿⣧⡝⠻⠿⣯⠞⠁
⠀⠀⠹⣎⡾⣵⣄⢯⡾⣷⣿⣎⢾⡶⡷⢦⢻⢶⠼⡿⣿⣷⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣧⣻⣿⣿⣯⡟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⢸⢠⡇⣿⢸⣷⣇⣿⣿⢸⡇⡆⢹⢘⠰⠀⡇⣿⠰⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢯⣿⣿⣿⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣛⠁
⠀⠀⠀⣷⡇⣿⡿⢸⡇⣿⢿⡏⣸⡇⢉⢸⢸⣶⠀⣷⢸⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡏⣿⢻⢻⡏⡟⣿⣿⢻⡟⣿⣿⠛⢻⡟⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⡈⡟⠁⠀⠈⠉⢩⣟⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢰⣾⡿⠛⢉⠀⠈⢳
⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⡋⠁⣬⠐⠻⣆⣤⠄⢠⡖⠀⢀⡌⣤⢠⣼⡄⠀⠁⠂⠠
⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠠⠁⡾⠁⠀⠀⠈⠀⠉⠀⣀⠀⠀⠙⢧⠈⠻⠇⠀⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠸⣳⣤⠤⣂⣀⣿⣤⠀⠄⣦⠛⠚⠊⣹⣧⡄⢠⣷⣄⠈⠆⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣶⢿⡛⣿⠉⠈⢳⠰⣿⠀⠀⠀⣾⠟⣱⠁⠈⡟⠀⣠⢾⣿⡀
⠀⠀⠀⠀⢀⠀⢠⠞⠉⠹⠄⢻⡈⠳⢤⣤⣯⠙⠀⣀⠀⢛⣃⣇⣤⡞⢰⣾⠃⠴⠁⠙⠂⣀⣠⠒⢢⡀
⠀⣰⠃⢀⠈⢻⡦⢀⠀⠤⢇⡼⠡⡖⠈⠓⣂⠀⠀⣉⠒⠀⠁⠉⠉⠉⢲⣧⡀⢤⣤⡀⠂⠀⢖⠀⠀⣷⡀
⠀⣯⡀⠉⠃⠸⡷⠋⠀⠀⠀⠀⠀⣯⠀⠀⠋⠁⣠⠜⠠⡄⠀⢄⡀⡀⢈⣻⡇⠀⠀⠙⠆⠀⠀⠀⠀⣹⠃
⠀⠘⢿⠀⠠⡄⣇⠀⠀⠀⠀⢳⡀⠈⢁⣠⠶⠂⠀⠀⠀⠈⠨⢟⡿⡿⠠⡡⠁⠀⠀⠀⢰⣄⠀⠀⢼⠃
⠀⠀⠈⡇⠰⡇⠇⠀⠀⠀⠀⠀⠑⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸
⠀⠀⠀⡧⠐⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡏
⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⡆
⠀⠀⠀⢿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⣄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢀⡇
⠀⠀⠀⠸⢬⣤⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡤⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⢀⣀⣀⣀⣤⡶⠆⠀⠀⠀⣀⠤⠖⠒⢢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢖⡒⠚⠓⠒⣤⢄⢣⣀⣀⢀⣈⣰⠘⢴⡦⠆⠞⠀⠀⠀⠀⠀⠙⠎⣆
⠀⠀⠀⠀⠀⢀⠔⠁⠐⠈⠁⠀⠀⠀⢳⠃⠀⠈⠐⠴⠴⠿⠃⣔⠉⠀⣦⡀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠎⡀⠀⠀⠀⠀⠀⠀⠘⢻⠀⠀⠘⠲⡤⠤⡤⣖⡇⠀⠀⢣⠇⠀⠀⠀⠀⠀⢰⢁⡇
⠀⠀⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠙⢷⠎⠋⠁⠤⠁⠀⡘⢤⡄⠀⠀⠀⠀⠁⡼
⠀⠀⠀⠀⠈⢮⣦⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠁⢢⡀⠰⠂⠀⢒⠀⢸⠃⠀⡁⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠙⢦⠰⡀⠀⠀⠀⠀⠣⡀⠀⠀⠘⣄⢁⠀⠉⢰⠃⢀⠜⠁⠀⠃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣀⠀⠀⠀⠀⠈⢢⠀⠀⠈⠓⣀⣰⠋⠀⠋⠀⠀⣀⣠⡖⠫⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⡀⠱⠀⠀⠀⠑⠮⣀⠀⢀⣀⡨⠗⠊⠀⠀⢀⡞⢅⠀⢹⠖⠠⣓⡓⢒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠖⡈⠀⠉⢁⠄⢰⠚⠓⠢⣄⠸⣄⡀⠠⢒⡒⠛⠂⢾⣐⢬⣭⡃⠀⠀⡔⡡⠃⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠉⠀⠐⢹⡀⠀⠣⡀⠘⠚⢀⡤⠉⠓⠢⣉⠒⠒⠈⠪⣕⣂⣬⣱⠀⠀⠁⢱⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣹⠀⠀⠈⠑⠚⠉⠀⠀⠀⠀⠈⠑⠒⠒⠊⠀⠀⠀⠙⢀⠀⡇⠞⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡒⠚⠓⠾⠃⠶⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⣒⠿⣛⣀⠀⢶⣀⣤⣵⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠏⣉⣀⣀⣀⣈⠉⣯⡉⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠛⠻⢿⠉⠛⠿⠷⣄⠀⠀⠀⠀⣡⡶⡞⡛⠋⠉⢿⣿⣿⣿⣿⣿⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡾⡷⠈⠀⠀⠀⠂⠈⣽⡳⣤⡈⠀⢉⡡⠤⠄⡠⢮⣿⣿⣯⡙⢁⡄⠾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⢸⡄
⠀⠀⠀⠀⠀⠈⢀⠱⣿⣿⣿⣿⡆⠤⠀⠀⠀⢀⠀⠘⣋⣾⣿⣿⣶⡾⣙⠓⠒⠐⠛⠀⠓⣹⣿⣿⣿⣷⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡞⠡⢿⠇
⠀⠀⠀⠀⠀⠀⠈⢦⠈⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠨⠉⢛⣾⣯⣤⣤⣤⣶⣿⡟⠛⠿⠿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⢠⣥⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠐⣿⢄⣡⣴⣾⣿⣿⣼⣯⣿⣿⣿⣿⣏⣷⣤⣤⡀⠱⢤⡀⠀⠀⠀⠀⠀⠂⠀⠀⢰⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣿⡿⣿⠄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢂⡸⠩⡁⠀⠀⠈⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢸⣿⣿⡤⠀⢀⣼⣷⣽⣿⣿⣿⣿⣿⣾⣿⠿⠋⠻⠷⢿⠳⣦⣴⡿⢃⠭⣶⡆⢹⠀⠀⠀⠀⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣜⣷⣿⣣⠀⢸⡟⠉⠙⠛⠺⣿⣿⢿⠶⠿⠤⠓⠲⠚⠻⠾⢟⣛⡵⠶⠞⠉⢷⣟⡁⠀⠀⠀⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠁⠀⠸⣧⡀⠀⠀⠀⠻⣵⡾⢿⡡⠠⠀⢤⠀⣬⠿⠿⡿⠁⠀⠀⢀⡾⣣⢤⠖⠻⠟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡀⠀⠀⠁⠛⠦⣀⠀⠀⠈⣊⢉⣀⠃⠈⡀⠘⢠⣍⡞⠁⢀⣠⠔⠃⡀⠀⠀⢀⣴⣿⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⣦⠀⠈⢷⠐⣀⣑⣦⣖⠶⠤⠄⠀⢀⠀⠠⠝⠻⢓⣤⣾⣥⠶⣿⣷⡆⣰⣿⣿⣧⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⣿⣶⣶⡿⠛⠉⠀⠙⢻⡟⠛⠲⡋⠀⠀⢰⣾⣿⢿⡏⠁⠀⠀⢈⢻⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣣⣿⠰⣿⡆⠒⠀⠀⢀⠗⠀⠀⢡⣴⠄⢸⣣⣿⠿⣄⠀⠀⠉⢻⣸⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠁⢻⡇⠀⠀⠀⠀⢀⡤⠂⠁⠘⠂⠀⠉⠺⣕⣿⣷⣄⠀⠀⠹⠿⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠁⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⠷⠃⣸⢎⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⡀⢄⣀⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣇⣾⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⢀⣠⣄⠤⠤⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡤⣀
⠀⠀⠀⠀⠀⢀⣏⣾⠃⠀⠀⠀⠈⠋⠉⠙⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣲⣮⠟⠛⠘⠛⡿⠀⠀⢨⢧
⠀⠀⠀⠀⠀⢸⡘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢿⣀⠤⣄⢠⡄⠀⠀⠀⠀⣤⣀⠀⠀⡜⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠈⠻⣍⠳⡀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡿⠁⠀⠈⢳⣿⣿⣒⡲⠿⠀⠁⠀⠘⣇⠘⠆⣤⠤⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⢰⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢱⡜⢀⢠⠴⠄⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣄⠀⠀⣠⠀⣸⣿⣄⠀⠀⠀⢀⡀⠳⠆⠀⠐⠒⠻⠇⠀⠀⢀⣼⣁⠀⠉⢣⡀⠀⠀⢐⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡻⢛⣩⣤⣶⣼⣿⠿⠷⡄⠈⠁⠽⠇⠀⠀⠀⠀⠿⠿⠿⢀⡸⠿⢿⣷⠀⠈⠀⣀⣶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠶⢮⡁⢙⣿⠁⠀⠀⠹⡖⠻⣿⠄⠀⠀⠀⠀⢴⠟⠀⡟⠀⠀⢀⡇⠀⢀⣠⠶⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠉⢿⡀⠹⣆⠘⢷⣄⣀⠀⢹⡚⠛⠃⠀⠀⠀⠰⠾⠂⣸⠁⣀⣴⠫⢠⢢⡞⠁⢠⠏⠉⢹⢄⡀⠀⠀⡠⠤⢤⡀
⠀⣠⠖⠈⠉⠓⠰⠊⠉⠀⠀⠀⢈⡇⠀⣻⠀⣀⣈⣉⣛⣉⠉⠀⠀⠀⣶⢀⡀⢐⣃⠩⣿⠿⠶⣤⣲⣾⠁⠀⢈⠀⠀⠀⠀⠉⠂⠊⠁⠀⠀⢳⡄
⣸⡧⡎⡀⠀⠀⠁⡖⠀⢠⠴⠒⠺⢧⡴⠋⢻⣿⠀⠀⠈⢡⠀⠀⠀⠀⣈⠈⠀⠀⠀⠀⠁⠀⠀⡏⣿⣯⣦⣤⠿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⢹⣷
⣟⣰⡷⠋⠀⠀⠀⣧⡔⠁⠀⠀⠀⢸⠁⠀⢨⣿⡀⠀⢀⠜⠀⠀⠀⣀⠾⢴⡤⠀⠀⠀⡀⠀⠀⣤⠉⠱⣿⡇⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠁⠈⣹
⠹⣿⣆⠀⠀⣄⠀⢹⠁⠀⠀⠀⠀⠀⢣⠀⠀⠙⠧⠐⠃⠀⣀⡴⠊⠀⠀⠀⠀⠰⡐⠤⣬⡒⠢⠇⢘⠿⠉⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡼⠃
⠀⠘⣿⡀⠀⢘⡀⣮⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⢠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡉⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢹⣠⠂⠀⠀⢸⠃
⠀⠀⢸⡇⠀⠺⠇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⢸
⠀⠀⠘⣧⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⣾
⠀⠀⠀⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⡆⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠁⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡅⠀⠀⢠⡏
⠀⠀⠀⣿⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⢸⡇
⠀⠀⠀⣿⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⢸⡇
⠀⠀⠀⠸⣄⣢⣀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣠⠼⠃
⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠝⠛⠟⠆⡰⠀⢂⢀⣶⠄⢠⡼⢄⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠀⠀⢸⣷⡄⠀⣿⡤⠚⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠀⣸⣠⡀⠀⣹⡅⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠄⣠⣤⠞⠉⠀⢸⠻⢮⣜⢿⣿⡆⠀⠀⣀⣠⡤⣶⠞⣡⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡦⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠋⢀⠀⢀⣀⣤⡈⠀⠒⠀⠀⢹⣶⡶⠂⢺⣿⣷⣶⣿⣏⣿⣷⠃⣼⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢶⣾⡿⠟⠁⠀⣠⡄⠀⢸⣝⠯⠂⠿⢿⣿⣿⣷⡉⠉⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠈⠉⢹⢻⣿⣿⣿⣿⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡲⢿⡁⡀⢀⣼⠻⠁⠀⣿⣿⣷⠀⢀⠛⣹⣿⣿⡞⠀⣰⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡅⡀⠙⠛⠋⠉⠀⠀⠀⣿⡿⠏⡷⠻⣼⣿⡟⠙⠀⣠⣿⣿⣿⣿⣿⣿⠿⣆⠀⠀⠀⣀⣤⣄⢸⣿⣿⣿⣯⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢣⣱⡆⠀⠀⠀⠈⠀⢨⣿⡇⠀⠀⡄⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⡅⠙⣆⢀⠀⠻⣿⣿⣿⣿⣯⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⣷⠀⠀⠀⠀⠀⠀⢸⣿⠓⠀⠀⠁⠀⠀⠈⢀⣼⣿⡹⢯⣿⣿⣿⣿⣿⣶⢁⣿⣦⡀⣡⣍⢏⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢸⡇⠀⠰⢀⠀⠀⢹⡇⠀⠠⠀⠀⠠⠈⢀⣾⡇⣨⠥⣿⣎⡷⣿⣿⣿⣿⣺⣿⣿⣸⣿⢿⣿⣿⠟⠛⠉
⠀⠀⠀⠀⠀⣀⣤⠶⠄⢻⡀⠘⣷⡀⢀⣈⠀⠈⢸⡇⠀⢂⡀⠐⠂⠀⣿⣿⣿⣿⣷⣷⣮⡿⣿⣿⣿⡏⢀⣸⣿⣿⣿⡿⠋
⠀⠀⠀⠀⣰⠏⠀⠀⠁⠘⠷⠀⠻⣷⡌⠁⠀⣠⣿⡧⡀⠋⠴⠂⠁⣴⣿⣿⣿⠇⠀⠈⠙⠻⣿⣿⣿⣿⠀⢿⣿⠟⠏
⠀⠀⠀⣰⣏⠀⠀⠀⠀⠀⠀⠑⠀⢻⡳⣦⣼⠸⠛⣿⣾⣶⠀⢀⣼⢿⣿⣿⣿⠀⠄⠀⡀⠀⠹⣿⡇⠛⠀⠸⣿⡇
⠀⠀⠀⣿⣧⠀⠀⢀⠀⠀⠀⠀⠀⡤⣟⣤⡏⣰⡆⢸⣏⠁⢀⢼⣯⠓⣿⣿⡿⠀⠀⠀⠀⡂⠀⣿⣧⡀⠀⠀⢻⣿⣴
⠀⠀⠀⣿⣿⠀⠀⡄⠀⠀⠀⠀⡀⠀⠁⢹⠁⡿⡷⢺⠏⣰⣋⠶⡌⠋⠘⣿⣿⠀⠀⠀⡌⠀⠀⣿⣇⠀⠀⠀⢠⣿⣯⣧
⠀⠀⠀⢿⡯⠀⠐⠀⢀⠔⠀⠀⠀⠀⠀⡀⢜⣠⡄⣨⣠⣉⡑⢄⡀⠀⠀⢼⣿⣦⡀⠀⠀⠀⣰⡏⠀⠀⠀⢀⣼⠿⣿⣿⣧
⠀⠀⠀⠈⢁⣴⠀⠈⢀⡀⠐⠈⠀⠀⠀⠀⠢⠤⣼⠟⢁⠀⠉⠁⠊⠀⠀⠛⢻⣿⡗⢠⡤⢠⣿⣿⡄⠀⠀⣾⠁⠀⢹⣿⠹⣇
⠀⠀⠀⣰⡟⠃⠀⣴⣾⣷⡀⣄⠀⠀⠀⠀⠀⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠛⢿⡎⠙⠇⠸⣿⣿⣿⣾⣿⠁⠀⠀⠀⣿⠀⢻⣄⠀⣀⣀
⠀⠀⠀⡿⠁⠀⠀⠈⢿⠟⣿⣿⣾⠀⠀⠀⠀⣶⣶⠒⠀⠀⠀⢀⡴⠒⠀⠀⠐⣤⠱⣄⠀⠀⠹⣿⣿⣿⣿⣿⡆⣠⢀⣿⠀⠨⠿⠋⡈⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢉⣿⣯⡁⠀⠀⠀⣿⡯⠀⠀⠀⠀⡏⠀⠀⠀⠈⠀⠀⢳⠙⢆⠀⠀⠈⣿⣿⣿⣿⣿⣬⠿⠁⠈⣴⣇⣀⢩⢿⣿⣧
⠀⠀⠀⠀⠈⠀⠀⠀⢠⣀⣼⣿⠿⠁⠀⠀⢀⣿⡇⠀⠀⠀⠀⠘⠦⣄⣀⢀⠀⠀⠀⢣⠉⢳⣄⡀⢸⡇⠈⠻⠟⢉⣀⠄⣴⢻⣿⠈⠛⠿⣿⣿
⠀⠀⠀⠀⠁⠀⠂⠉⠛⠃⠀⢀⠠⠤⠒⠛⠛⠛⠛⠛⠲⢤⣀⠀⠀⠤⠀⠈⠀⠙⠂⠀⣶⣥⣿⠁⢸⠃⠀⠀⠀⢛⣮⡵⣯⣿⠏⢰⣵⣼⣷⡿⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⣀⠀⠀⠠⠏⠁⢙⠴⠋⠀⠀⠀⠀⣿⠄⢀⠾⠃⠰⣿⣿⣿⠟⠁
⠀⠀⠀⠐⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠦⠤⠖⠁⠀⠀⠀⠀⠀⢠⡟⠀⡀⣰⠾⢳⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⢳⣿⣯⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠉⠀⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⣰⢷⡟

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣇⣅⡀⣃⣤⣇⠀⣁⠖⣁⡅⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠂⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠉⠐⠀⠠⠈⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢨⠀⢨⠄⠀⠀⣁⠐⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠢⠂⠀⠀⠉⠁⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠑⣀⠀⢠⠁⠀⠈⢈⠁⢀⠀⠉⠀⠁⠀⠈⠀⠀⡐⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠐⢸⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠁
⠀⠀⠀⠀⠀⠘⡄⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠉⠛⠲⣄
⠀⠀⣠⢖⣭⠖⠒⠒⠒⠒⠈⠙⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠚⠉⠉⠑⢦⡈⠳⡄
⠀⡼⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⡄
⢸⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢻
⢸⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡀⠀⣯⠉⠳⣄⠀⠀⠀⠀⢀⡴⠖⣦⠀⠀⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸
⢸⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠻⣄⣘⡇⠀⠈⠷⠒⠒⠶⠋⠀⠀⣿⣀⡼⠃⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸
⣼⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⠉⠁⢠⡶⠲⠦⠤⠤⠶⠟⢶⡀⠉⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸
⣿⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⢀⣠⡤⠞⠁⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠙⠳⠚⠉⢻⡅⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠿⢤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠧⢤⣤⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠟⠛
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⢀⣾⠀⠀⠀⢠⡏⡀⠀⠀⠀⣿⠀⠀⠀⠀⣰⢋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠒⠉⠘⣷⠀⠀⠈⡿⠋⠉⠓⠚⢿⠀⠀⠀⠀⣯⠀⠀⠙⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣿⠀⠀⠘⣷⣦⣀⣀⣀⣸⡇⠀⠀⢠⡟⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢀⡄⢰⡇
⠀⠀⠀⠀⠀⢀⡇⠀⢲⠀⠆⠀⠀⠀⠀⢻⡄⠀⠀⠙⠷⠤⠤⣧⡀⠀⠉⠉⣨⣿⠤⠴⠞⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢾⣥⡼⠃
⠀⠀⠀⠀⠀⠀⠙⠒⠾⣄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⣿⠶⠲⠾⣥⡀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢯⡀⠀⠀⠀⣨⠗⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⣀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢢⡀⠀⠀⠀⠀⠀⠙⢳⡖⠚⠛⣻⠦⠤⣼⣧⣤⣤⣠⠴⠋⠀⠀⠀⠀⠀⣀⠴⠋⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠓⠦⣤⠤⠤⠤⣤⣀⠉⠀⠀⣇⠀⠀⣸⢇⡴⠛⢁⡤⠶⠒⠒⠚⢳⡏⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⡤⠾⢏⠈⢧⡀⠀⠀⠈⢻⡆⢀⣿⠀⠀⣯⠈⠀⣰⠏⠀⠀⠀⣠⠂⢀⡿⠶⢺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠂⠘⣇⠀⢀⣠⠾⠃⠀⢹⡇⠀⢹⡆⠀⠙⢦⡀⠀⣰⠇⠀⠘⠁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⠶⠏⠁⠀⢀⡴⠋⠙⠓⠛⣧⠀⠀⠀⠙⠒⠋⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣤⠼⠃
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣷⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⢀⣉⣿⣿⣏⡁⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣾⣿⣿⡃
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⡉⣿⣿⡏⣡⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠀⠹⣿⣿⡟⠀⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣄⠀⠙⠟⠁⣀⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⣾⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠉⢿⡄⠈⣻⢿⡁⢀⣿⠏⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠙⠋⠁⠀⠙⠛⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣽⣫⣍⣉⣟⣻⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣐⣒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠦⣄
⠀⠀⠀⡀⢠⣿⣿⠛⠀⠀⠀⠀⠘⣧⠀⠠⡀⢠⢀⣄⠀⢀⠀⠀⠀⣄⠀⠀⣀⣀⡔⠀⠀⠀⠀⠀⠀⠘⢧⢹⣇
⠀⠀⠀⡁⠜⣿⡅⠀⠀⠀⠀⠀⠐⠏⠀⠀⠈⣻⡟⠛⣀⣀⠀⢸⠂⠙⢶⠚⠉⠈⠷⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿
⠀⠀⠀⢱⠀⠻⢇⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣶⣶⣶⣶⣟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡿⠀⠘
⠀⠀⠀⠈⠳⢦⣿⣄⠀⠀⠀⠀⠀⠠⣄⣴⣿⣿⣯⣽⣿⣿⣿⣿⣿⣽⣿⣿⣿⢁⠀⠀⠀⠀⠀⠀⡠⢀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⢉⠣⡀⠀⠀⠀⣸⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀⡞⢡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠻⡄⠀⠘⢿⣿⣾⣿⣿⣿⣿⣯⣿⣿⠟⠋⠀⡟⠀⠀⠀⠀⠳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠈⠢⠀⠘⠻⣟⣿⣿⣿⣿⣻⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⡙⠻⠿⠿⠿⠿⠃⠀⣀⣀⣀⠀⢀⠀⣴⣿⠟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣷⣿⣿⠋⠉⢿⣿⣿⣷⢀⠀⣴⣾⣿⡿⠋⠀⠸⣿⣦⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢸⡇⠀⠀⠀⡙⢿⣿⠸⢿⣿⣿⣿⡅⠀⠁⠀⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣧⣤⣴⣏⡴⠊⠀⠀⡀⠈⠻⣿⣩⣷⣶⣿⣃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠟⠉⠀⠀⠀⠀⠁⠀⠀⠈⠛⠋⠩⠤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠈⢻⣆⣀⣤⣴⣶⣶⣶⣤⣀⣸⡟⠁⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⠀⠀⠀⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⡀⠀⠀⠻⣿⣿⡀⠀⠀⢀⣿⣿⠟⠀⠀⣠⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⣤⣌⡛⠛⠓⠚⠛⢛⣡⣄⢠⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⢿⣿⡷⠀⠀⠀⠀⢾⣿⡿⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠉⣠⣾⠛⠛⣷⣄⠉⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠈⠙⠻⠛⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠒⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⢈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢸⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻
⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠙⠧⠀⠀⠀⠀⠀⠀⠀⠠⠟⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠉⠉⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠐⡂⠀⠀⠐⠂⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⠖⠒⠒⠦⣄⣀⢈⠁⢉⢀⣀⡤⠴⠒⠒⠢⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⡄⡌⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⠀⠀⣠⠞⠁⠙⢦⡀⠀⠈⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠋⠁⠀⠀⠀⠀⠉⠓⠒⠚⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣺⡇⠀⠆⠀⢸⢣⣿⣧⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⢶⣛⠛⠿⣳⣶⡤⢀⠀⠀⠀⠈⠉⠉⠙⡇⠀⠀⠀⢀⣀⣠⡟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠀⠉⠀⠀⠉⠻⣿⣶⣄⠀⢀⣀⡀⠀⣼⣷⡠⠀⠀⠾⠿⣿⣷⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣿⣄⣉⣲⣷⠶⢄⣀⢀⣀⣀⣬⣿⣶⣯⣭⣿⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⢩⣿⣿⠁⠀⠀⠀⠉⣿⣿⣿⣿⣿⡟⠿⠅
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⣤⣿⣿⡙⠀⠤⠀⠀⣼⡿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢹⣆⢔⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣦⣀⣀⣖⣶⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠴⢿⣿⣿⣿⣿⡿⢿⣻⠀⢀⣸⡻⢿⠿⢯⠛⢹⠿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣿⢛⣾⣷⣿⣄⣀⠸⣧⣤⡄⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡆⠀⣄⠀⠀⠀⢸⣿⣆⢻⠿⢈⡋⠉⡁⢉⡉⢠⣾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠙⠻⢿⣧⣀⠐⣿⡀⠀⠀⢸⡟⢹⣞⣟⣿⡇⠒⣝⠋⠀⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢵⣾⣮⡏⠁⢽⣷⣄⣠⣺⣑⣠⣾⣿⣶⣇⢛⣷⣡⣶⣾⣅⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⢘⠿⠅⠀⠈⠉⠻⣿⡗⠈⠁⠚⠙⠓⢀⠚⠉⠉⠙⠻⡿⠃
⠀⠀⠀⠀⠀⠀⠔⢰⠟⠀⠀⠀⣿⡄⡒⣲⣮⣶⣖⣀⣀⣀⠑⠢⣄⣀⠀⠘⡞⠀⢀⡀⠄⢀⣤⣴⣞⡻
⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⢠⣿⣿⣿⣿⣫⡗⠈⠉⠀⠀⠈⢣⠤⡌⢫⡙⣿⡟⣡⣤⣾⣿⣮⠙
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣼⠋⢹⡗⠈⢻⡄⠀⠀⠀⠠⡤⠚⠀⠹⠀⢽⣿⣀⣿⣿⣿⠀⠍⡈⣀
⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠰⠁⠀⠘⡉⢀⠐⠙⠂⠀⠀⠀⠀⠀⠠⠐⠊⠉⠉⠓⠻⢿⣿⣿⣷⣾⣷⣉
⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⣆⠀⠀⠀⠁⠀⣀⣀⣠⡤⠔⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡆
⠀⠀⠀⠀⠀⡌⠀⠀⢸⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸