Rabbit Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢾⣿⡄⠀⠀⠀⠀⢀⣀⣠⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠚⠁⠀⠀⢀⡤⡺⠛⠀⠨⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠢⠁⢂⣼⡍⡞⠀⠀⢀⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠉⠄⠄⠀⣾⣿⢀⣿⣆⣀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠤⣴⣹⣿⡈⢿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣦⠬⣅⠽⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣛⣋⠔⠋⢬⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢨⢁⢌⣁⣴⠮⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⠀⠀⠀⠀⠀⢸⣏⠃⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠑⠀⠀⠀⠀⠀⠀⡠⡿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠡⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⢀⣠⣾⠛⠓⢀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⠀⠀⢀⣿⡋⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⡠⠀⠀⠀⠸⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠺⠖⠂⠂⠀⠻⠦⠴⠤⠆⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡟⡛⢻⡛⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠹⣆⠀⠀⠀⠀⠀⣰⡏⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⡿⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣷⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⠤⣤⠀⠀⠀⠀⠀⢀⢤⣄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⡿⠀⢀⠀⢀⠀⠸⣿⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⢀⡄⠀⢙⣿⣏⠁⢀⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠛⣟⣹⣙⡟⠛⠁⠀⠀⠀⠸⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠈⢀⢄⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠔⢡⠋⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡎⠀⡆⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⠀⠁⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠠⡀⠀⠆⠀⠠⠃
⠀⠀⠀⠀⢀⠔⠋⠁⡠⠴⠄⠀⠠⡀⠀⡄
⠀⠀⠀⢠⠎⠀⠀⠀⠸⣭⠄⠈⠀⠐⠆⠀⠄⠀⠀⠀⠀⡀⠀⠤⠄⠀⣄⠀⣀
⠀⠀⣠⠟⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠅⠀⠨⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⡗⠒⠁⠀⠀⠐⡀⠀⠀⠀⠀⠈⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠘⠔⠒⠤⣀⡼⠀⠄⠀⠈⠁⡠⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠉⠀⠀⠈⠀⠉⠁⢆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠕⣠⠤⣀⠀⠀⠀⠀⣆⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣂⠀⠀⠀⢀⠌⠌⠀⠀⢀⠙⢆⣀⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⢀⣁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠥⠬⠤⠄⠀⠀⠀⠀⠀⠀⠸⠴⠂⠈⠐⠤⠤⠎⢀⣤⠄⠠⠤⠴⠒⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⢐⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠎⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠸⡇⢀⠀⠀⠀⠀⠠⢲⠀⡄⢠⣿
⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠍⠀⠀⠀⡁⠈⣄⠀⠀⠀⢰⡿⠰⡁⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠘⣇⢡⠀⠐⡆⠀⣿⠀⠀⣥⣾⠀⢸⡞⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡿⣾⠁⣠⠿⠃⠸⠿⠟⣄⠘⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠏⡌⠁⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣻⣿⡄⢀⣤⠀⠄⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠄⡴⠛⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⡔⠁⠀⠀⡸⠀⠈⠛⠀⠀⣰⡿⢷⣀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠈⠀⠀⠀⢰⡅⠀⢠⠇⠀⡠⠂⠀⠀⠛⡄⢰⡜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢹⡃⢀⡄⠀⠀⠀⠘⣷⣆⡈⠄⠀⠀⠘⢶⠷⠂⡠⢀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠿⣿⣄⡀⠀⠀⠸⠀⠀⢀⡾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢵⣠⣤⣶⢤⡴⠎⠁⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠤⠤⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠀⠀⠀⠀⢇⠀⠀⠀⠀⢰⣴⣤⣾⡆⠀⠀⢠⣿⡅⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⣤⣀⣄⣼⠀⠀⠀⠠⣿⠋⢻⣿⡿⠀⠀⠘⠿⠛⠓⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠷⠄⠀⠠⣄⣸⠀⠈⠉⠙⠺⠷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡠⣀⡀⠀⠀⠀⣀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⣀⠀⠀⣠⡄
⠀⠀⠀⠀⠱⠕⠃⠀⠀⠀⢆⡼⠁⠃⠀⠀⠀⠠⠡⠁⠐⢀⣀⠤⡠⠀⠀⢬⡳⣀⢇⠇⠀⠀⣖⢆⣸⣿
⠀⠀⠠⠤⡄⠠⠒⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠙⠟⠂⠈⠀⡈⠜⠀⠈⠙⠄⠀⢀⠜⠛⠓⠇
⠀⠀⠈⠲⣈⡶⡤⡁⠀⠀⡀⢸⢓⠀⠀⠀⠀⠀⠔⠀⠠⡄⠀⠀⠀⠀⢀⠆⠀⠀⠠⡂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠤⠀⢸⣄⠀⠀⠂⠶⠄⠁⠀⠀⠀⠀⠸⢄⣀⠀⠘⠀⠀⠘⡀⠀⠀⠎
⠀⠀⠀⠈⠀⠀⠖⠀⡀⠀⠀⠀⠘⣧⠀⣟⠀⠀⠀⡀⢤⢀⢠⡀⣀⡄⢀⠀⢀⠀⠀⠀⠀⠀⠢⠤⠦⠞
⠀⠀⠀⠈⠂⠀⠰⠀⠈⠀⠀⠀⠀⣿⠀⠀⣷⠿⠷⠁⡸⠈⠸⠏⠡⡇⠘⠚⠿⠃⠀⡀⠀⠀⢠⣄⠀⡔⡢
⠀⠐⣄⡀⡤⠀⡀⠀⠀⠀⠀⠀⠀⣿⣄⣰⠟⣼⠃⢸⠁⠀⢠⡐⠘⠁⠀⣼⠀⠀⠀⠌⠔⠀⠹⡨⠷⠤⡅
⠀⢠⢎⣹⠀⠀⠐⠂⠀⠀⠀⢤⡄⠀⠈⡁⠀⢿⠀⢿⡘⠗⡗⠃⠿⢆⡆⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠈⣴⣂⣴⢛⡞⠀⠈⠁⠀⠀⠀⠁⠄⠀⠀⠁⠈⠀⢦⠲⣼⣩⠀⠐⢤⡶⠄⢲⡀
⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠰⠁⠁⠈⠫⠠⢶⠀⠀⢀⠀⠀⢀⡔⢅⠀⠀⠀⠀⠀⠕⠋⠋⢂⠀⠘⠀⠂⠀⠁
⠀⠀⠀⡎⠲⣲⠀⠀⠀⠀⡥⠀⠀⠀⢠⠀⠀⠀⠀⠛⠿⠂⠙⠰⠁⡀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⠁⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠁⠸⠴⠀⠀⠀⢔⣁⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠁⠀⠀⠀⠀⠀⠀⠁⠓⠀⠀⠈⠀⠀⠀⠀⠈⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⢀⡠⠄⡀⠀⠀⢰⠀⢀⡀⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⡔⠁⠀⠀⢰⠀⢀⠜⠊⠁⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠎⠀⠀⠀⠀⡸⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⠎⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡄⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢰⠁⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⡄⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠒⠀⠈⠉⠉⠉⠉⠐⠒⠇⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉
⠀⠀⠀⠀⣃⣀⡀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢢⡀
⠀⠀⠀⠰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⠁⠒⠂⠤⢀⣀
⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠲⠀⠀⠀⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠊⠁⢀⡨⠃⠀⠀⠀⠀⠀⡌⠀⠀⠀⣀⠀⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⡠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡐⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠈⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠤⠀⠤⠔⠊⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠒⠈
⣿⣿⡿⠿⣿⡿⢿⢿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣦⡙⣿⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡌⣷⣴⣷⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⢿⣿⡿⣾⡆⠀⠙⢷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠈⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣧⣀⣀⡀⠀⠀⠸⠿⠯⡃⠈⠉⠛⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⡿⠉⠀⢈⡁⠀⠀⠈⠛⠦⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡂⠀⠀⠀⢙⡋⠀⠀⠀⢰⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⠷⢶⣤⣾⣷⣤⡦⢄⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢿⡿⢿⣿⠿⣿⢿⠟⠋⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⠉⠀⣠⢡⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣇⢀⠀⠀⠀⠀⠋⠺⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⢠⠀⣤⠇⠀⠈⠀⠀⠀⠀⠀⠆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠙⢿⣿⣿⣽⣴⡏⠀⠀⠀⠀⠀⢀⣴⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⣦⣠⣼⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⠈⢹⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⢿⢿⣄⣀⡀⠠⠼⠿⠛⠛⠲⠔⠂⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣿⠃
⠀⠀⠀⢠⡶⠶⢤⣀⠀⠀⠹⣆⠙⣆⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣼⡿⠁⠀⠀⢀⣠⣴⣶⡄
⠀⠀⠀⠸⣆⠀⢤⡈⠳⣄⠀⠸⣆⢸⡄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣸⡿⠁⠀⢠⣶⣿⢟⣿⡿⠃
⠀⠀⠀⠀⠈⢧⡀⠙⣆⠈⢳⡀⢹⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣴⣿⠟⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠹⣦⠈⠃⠀⢳⣸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣼⣿⣯⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠈⣿⠁⠀⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣧⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠤⠄⠀⠀⠀⠈⠁⠀⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡁⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⠦⠤⠶⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡀⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠈⢳⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠘⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⢦⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠙⠓⠶⠶⠶⠶⠶⠶⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠶⠻⠷⣶⡦⣤⡴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡿⢛⠉⠛⡿⠛⠛⠳⢶⣤⣠⣤⠼⣷⠉⣻⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⢠⣾⡟⢀⣤⣴⣿⡗⢀⣀⣴⣏⣿⡈⢿⡄⠸⣷⣿⠋⠉
⠀⠀⠀⣀⣠⢔⡥⠾⣿⣏⣤⣿⡻⣿⡿⢏⠘⢿⣶⣿⣿⣿⣿⣿⣿⣾⣷⣷⢉⣿⣧⣀⣀⣀⡀
⠀⠀⢏⣤⢔⡵⠞⠉⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠉⠛⠛⠉⠉⠉⠉⠁⠀⠊⠯⣙⡉⠛⠻⠶⣤⣑⠒
⠀⠀⠛⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠋⠀⠀⠁⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣙⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣒⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣿⠟⠛⠿⣮⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⠟⢋⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣼⠏⠀⠀⠀⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⢸⡇⠀⠀⠀⠀⣘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠂⠸⣧⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣿⠇⠀⢠⡇⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢰⡟⠀⠀⢰⡏⠀⠀⣾⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⣰⣿⠃⠀⠀⢸⡏⢀⣾⠇⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣠⡴⠿⠿⠿⠷⡶⣿⣿⠀⠀⠀⠈⣶⣿⡏⣰⣿⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⣴⡟⠁⠀⠆⠠⠀⠄⠀⠙⢿⣆⠀⠀⠀⣿⣯⣼⡿⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⡃⠀⠀⠈⠀⠀⢀⣀⣀⣈⠉⠻⣾⡀⠀⣿⠟⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠉⠀⣄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠻⣷⠀⠀⣴⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⡀⡹⠆⠀⠀⢠⠀⡄⣠⠀⠀⠛⠃⠀⢻⣆⣼⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⠀⢹⣏⠁⠀⠀⠀⠈⠀⢿⣷⠃⣰⣮⡀⠀⠘⣿⣿⡀⢹⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⠀⠁⠘⢻⣿⡄⠸⡟⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠰⠀⠰⠀⠁⠄⠀⠀⠀⠐⠿⠿⠍⠀⠀⠀⢀⣽⣧⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⣠⣾⠏⠀⠀⠀⣠⡄⣤⣤⣀⣀⠀⠀⠀⠀⠀⠛⢲⣄⠀⠀⠀⣬⠻⣦⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡿⠀⠀⠀⠶⠟⠉⠉⠙⠛⠛⠁⠀⠀⠀⠐⠊⠛⣿⣦⡀⢀⠀⢀⢹⡆⠀⢀⠂⠀⠘⢿⡆
⠀⠀⠀⠀⠀⢀⣀⠀⠤⣿⣿⢻⡗⠀⢲⠀⠰⣄⡀⢀⣠⡶⠀⠀⣀⠀⠀⠀⠀⠀⢿⡁⠀⠀⣦⢸⣌⠁⠀⢈⠒⠀⠀⢺⣿⣷⡄
⠀⠀⠀⠈⠁⢀⡀⠤⠘⣿⡟⠙⣧⡀⠈⠧⡀⠈⢿⡿⠋⠀⠀⠰⠃⠀⢀⠀⡉⠁⠞⠦⣀⠀⣠⣼⠇⠀⠀⠈⠃⠀⠀⣄⢻⣿⣷⡆
⠀⠀⠀⠀⠈⠀⠀⡀⠀⣿⡏⠀⠈⠿⣆⣀⠀⠀⣀⣷⣄⡀⠀⠀⠀⠢⣄⠈⣳⠇⠀⠀⣘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⠈⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⡇⠀⠀⠀⠈⠙⠳⢿⣍⣉⣉⣻⣶⣦⣴⣶⣿⣿⣷⣾⣷⣾⡿⠛⠁⠀⠀⠀⠀⠀⣀⠀⢠⠘⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣠⠄⢠⠀⠀⠀⠈⠙⠛⠋⠉⠉⠈⠉⠉⠉⠉⠉⠀⠀⠢⠀⠀⠀⠀⢀⣤⢀⣿⡄⠌⠀⠀⣿⡟⢟⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⢿⣿⣇⢸⡄⠀⢀⠘⠳⡄⣄⣀⢠⠀⣀⠠⠘⠋⠀⠀⠀⠀⠀⠀⡄⣼⣾⣷⣿⡟⠁⠀⠀⠀⣿⣷⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠙⢿⣷⣴⡄⢷⡀⠀⠈⠉⠻⠀⠏⠁⠀⣰⢆⠀⣀⣠⢀⣼⣷⣿⣿⡿⠋⠀⠀⠀⠀⠠⣼⡏⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠈⠙⢿⢿⣬⣷⡀⢀⣀⣀⣀⠀⢀⣴⣿⢟⣴⣿⣧⣾⠟⠋⠛⠋⣀⠀⠀⢠⠀⢀⠀⣿⣷⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠠⠀⠁⢠⠂⠀⡀⠀⣧⣿⣿⠀⠀⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⣿⣿⣿⠻⠛⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⣿⣿⠇⠀⡀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠙⣷⣞⡀⠀⢸⡆⡄⠀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⢠⢀⡄⠌⠀⠀⣿⠟⠁⣀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠈⣿⣧⠀⠀⠃⠇⢸⡄⢶⡀⠲⡄⠘⠀⠀⠀⠰⠀⡤⢀⣶⣷⡿⣡⢏⡾⠀⠀⠀⣼⣟⣤⣾⣋⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⢻⣿⠀⡀⢀⠘⢷⠀⠙⢷⠀⠀⠈⠀⠀⣴⠞⢡⡾⠋⠉⠀⠁⠈⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠈⣿⣇⣷⢸⣀⣶⣀⠀⢀⠀⠀⣤⡄⢀⠉⠀⢛⡀⠀⠀⠀⠀⠀⠸⣷⣸⣿⠿⠛⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣷⣿⣿⣿⠟⠛⠛⠻⣷⣌⠙⢦⢈⣷⡸⣰⢃⡿⢁⡴⠞⠛⠛⢲⣦⣽⣿⡇⡄⢠⡆⣄⣿⣧
⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⢿⡏⠀⡾⠁⠀⠘⣿⣷⣸⣿⣿⣿⣿⣾⣷⡿⠁⠀⠈⣷⠀⣿⣻⣿⣷⣷⣾⣷⣿⣿⣿⣶⣶⣶
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣧⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣠⣽⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⠙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⣲⠖⠚⠉⠉⠁⠒⠒⠒⠒⠲⠶⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⢠⠞⠁⠀⡠⠴⠶⠤⣄⠀⠀⠀⠀⠀⠈⠓⢝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠁⠀⠀⢰⠋⠀⡠⠋⠀⠀⠀⠀⠈⢣⠀⠀⠀⡀⠀⠀⠀⠊⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢠⠃⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡆⠀⠰⠀⠀⠀⠐⡀⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⡘⠀⠀⢸⠀⠀⠀⠀⢠⡀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡆⢠⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⡴⠚⡇⠀⠀⠈⡆⠀⠀⣶⣾⡇⠀⢠⠇⠀⣧⣴⡇⠀⠀⡀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢠⠎⠀⢀⡇⠀⠀⠀⢳⡀⣀⣈⣉⠀⠀⡞⠀⠀⢀⠛⠁⠀⢀⠄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⣴⠥⠤⠤⠄⣿⡰⠖⠋⠀⠀⠀⠀⠉⠉⠛⠷⠒⠒⠚⢦⡀⠀⠮⣴⡃
⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠄⠀⠀⠀⠀⠈⢶⠀⡇
⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⣰⠃⠀⠀⠠⠄⠐⠂⢲⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⣇
⠀⡠⠊⠁⠀⠀⠀⠀⠀⢐⠏⠀⠀⠀⠀⠀⢰⡄⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿
⡸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠹⢦⠂⠀⠀⠀⠀⠀⠀⢀⡠⠮⡀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣯
⢧⡀⠀⠀⠀⢀⣀⣠⠤⢺⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣠⠀⢈⠛⠒⠒⠒⠒⣞⠁⠀⢀⡏⠑⠂⠒⠂⠳⠉⠀⠀⠀⡇
⠀⠉⠉⠉⠉⠉⠁⠀⠀⢸⡀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠉⠙⠶⣄⠀⠀⠀⠁⢉⠉⠀⣀⡀⠀⠀⢀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢣⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⠆⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡸⠂⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠑⠀⠤⠄⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⡌⠀⠀⠀⠀⠀⠀⠀⡖⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⢀⠀⠀⠀⢠⠁⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⠌⠀⢀⢀⡴⠁⠀⢱⡄⠀⠘⡀⠀⢠⠎⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠣⠤⠴⠚⠁⠀⠀⠀⠀⠉⠐⠀⠓⠚⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣀⡏
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢄⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠠⡀⠀⠀⡀⢣⠀⠀⠀⢸⠃⠀⡀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢁⠀⠀⢠⢸⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣨⣀⡀⠀⠀⢀⣀⣼⣄⣠⠼⠞⠒⠒⠒⠛⠦⠤⠦⣄⣠⡤⢆⣀⡤⠏
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣤⣄⣀
⣿⣿⣿⡿⣿⣶⣦⣤⣀⡀⠀⠀⠀⣀⣠⣤⢶⣶⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⣶⣿⣭⣿⠩⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣷⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⡏⢽⠮⢩⣴⣶⣶⣶⣶⣶⣿⡿⣿⣿⣶⣤⣀
⣍⣛⡛⣿⣿⠿⣻⢻⣿⣿⣿⣿⣿⠽⢿⣏⣫⣗⣤⢤⡾⠻⠾⣿⣿⣿⣿⣼⣿⣿⣷⠘⡿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⡾⣿⢻⣿⣿⣻⠧⢉⡥⢞⣝⣔⡿⣿⣶⣶⡜⢿⣯⣟⠿⠿⠛⠍⠛⠤⣼⣿⣿⣿⣿⣿⣷⣤⡀
⣩⡭⠶⠿⠒⢺⣵⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣻⣿⣿⣿⣿⣯⣐⣍⣉⣋⣇⣀⣴⣷⣿⣿⣻⣻⣻⡟⣻⡿⢟⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣾⡻⡿⢿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡗⢠⠙⠻⣿⡿
⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣏⠞⡠⠰⠀⠀⡸⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⣿⣿⣿⣻⡟⠉⢉⡁⣠⣴⡟⣿⣷⣉⡯⣴⣠⢃⣂⡌⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣋⣞⠀⠈⠁⠉⠛⠷⠒⣟⢰⠟⠚⠹⣻⣿⣿⣿⣿⣾⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⠺⢶⠄⡐⠁⠀⠀⠀⠀⠀⣠⡷⠏⠁⠁⡈⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣶⣳⢺⣶⢦⣴⣾⡷⠟⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠌⠿⣿⣿⣿⡿⡿⣣⠟⠛⠿⡏⣿
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢸⣅⣙⣮⠑⠒⠺⡁⠁⢀⡙⣏
⣭⣿⣿⣶⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠁⠈⠤⠄⠀⣀⣵⡇
⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⣳⠀⠀⠀⠀⠀⣌⡻⠁
⣿⣷⣿⢙⡟⣿⠿⠛⠻⠟⣿⢯⡻⣿⣿⣿⣟⡷⣮⢆⡀⠀⠀⣾⡿⠃
⣿⣿⣏⣞⣩⠿⢦⢭⡄⣡⠀⢀⣿⠑⢿⣿⣿⣧⠀⢦⠄⠆⣾⣿
⣿⣿⣿⢻⢜⢷⡄⠆⠂⢈⡘⣆⠉⠃⠸⣿⣿⡟⡛⠃⢀⣴⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣟⣑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⣿⠿⣿⣶⠪⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⣯⡳⣬⡁⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢻⣤⡙⠟⢿⣄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠑⠶⣭⣹⢄⡺⣿⣾⣳⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣁⠨⣷⣤⣿⣿⡿⢿⠿⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣧⣾⣿⡎⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⡻⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠀⡽⡾⢻⠃
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣖⣿⠟⠉⠹⢿⠿⣿⣿⣿⣿⣷⣶⣄⣳⡶⠷⠻⠛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⠐⠤⠄⠈⠀⠉⢏⠻⢽⡿⡿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣌⣷⣶⢲⡹⣦⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠛⠛⠛⠛⠛⠛⠿⣿⢟⠟⣽⣶⣞⠛⣏⣡⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣻⣿⣿⣅⢐⡤⠤⢤⣄⣀⣀⣀⠀⠘⡛⢲⣷⣍⢛⣷⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣛⣛⣁⣶⣧⣛⣋⣈⡿⢿⣿⡿⣿⣿⣿⣿⣆⠑⣜⢻⡿⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠓⠘⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣭⣿⣭⣿⣭

⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣟⣻⡿⠟⠛⣧
⠀⠀⠀⠀⠀⠀⠐⣿⠿⡎⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣫⠟⠋⠉⠁⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠛⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣰⣿⠘⠁⠀⠀⠀⠄⠀⠂⣽⠅
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡆⣿⣿⣧⡀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢘⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⣿⠋⣿⢃⠀⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣼⡻⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠁⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣁⣠⣠⣴⠖⠀⠸⣿⢿⡗⠀⠀⠀⢠⠄⠀⡀⠃
⠀⠀⠀⠀⠀⢀⡀⢤⣤⣿⠉⣿⣿⡟⢰⣦⣀⡂⢹⠿⠂⠲⠀⢀⡿⠀⣠⡄⣠⣤⣤⣠⣤⡄⣀
⠀⠀⠀⠀⢀⣞⣱⢼⣿⣿⣿⠿⠉⡄⣀⠀⠈⢿⡆⢶⠀⠀⢣⡌⢁⣾⣟⣧⠻⠿⣿⣶⣿⣷⣋⡻⠿⢄⣠⣆⠀⡀
⠀⠀⠀⠀⣸⣿⣡⣾⣿⡿⣳⣆⣁⣔⠉⢀⣀⣠⣿⣿⠃⠀⠀⢠⣿⣿⡟⣿⣯⠤⡿⢿⡯⢽⣻⣿⠟⢣⣬⣛⣿⣧⣤⣀
⠀⠀⠀⢰⠿⠻⡈⠃⢩⠀⣷⠈⠋⢀⡴⣿⣿⡏⢹⣿⣀⣼⣤⣿⣿⣿⣅⣾⣧⣐⣹⡟⢳⣾⣭⣼⣿⣿⢭⣿⣿⣳⣿⣯⣵⣄
⠀⠀⢀⡾⠀⠀⠳⠛⠂⡿⠉⠀⠀⣾⣿⣿⣿⠇⠘⣿⣿⢷⣿⣹⠛⡟⣿⣿⣿⠁⣹⡗⣠⠟⢿⣾⣧⠭⣾⣿⣿⣿⣿⣫⣼⣿⢷⣄⡀
⠀⠀⡛⢡⠿⢢⡴⠶⠀⠐⠀⠀⠋⣈⣉⠛⢛⣢⣾⣿⣿⣾⡇⠀⠚⣛⣿⣿⢿⣿⡟⣱⣯⣀⢺⣍⡋⠒⣿⣿⣶⣛⣂⣼⣿⣦⣿⣍⣿⣦⣀
⠀⣤⡀⠀⠀⠈⢠⣀⠀⠀⠀⡀⣦⠉⠽⢦⣬⣹⣿⣷⡜⣿⡿⣂⡛⠉⣩⣥⣤⣿⡷⠾⠃⣼⣿⠿⡇⢀⣙⠻⢋⣽⣿⣸⣯⣽⣿⣭⣿⣿⣿⣄
⠐⠂⣠⣴⣄⣠⠹⠟⠲⠂⠀⡀⢻⡟⢴⣎⣴⠊⢻⣿⣿⣿⣧⣼⡓⣶⣚⠻⣿⡿⢋⣽⣿⣗⣿⠆⠸⣿⣿⣾⣿⡟⢉⣿⣿⡽⠛⣱⣼⣿⣿⣿⣇
⠐⢰⣿⢿⣃⠉⠀⠀⠀⠤⣀⡀⠀⣛⡋⠙⠛⣡⣼⣿⣿⡏⠀⣿⡿⢏⣨⣀⣰⣆⣹⠁⠘⢿⠀⢀⠴⣾⠟⠠⢿⣿⣅⣴⣿⡧⣌⣿⣧⣷⠸⣿⣻⣇
⠀⡈⢙⡟⣩⣀⠀⠀⠀⠀⣽⣿⠳⣿⣿⣿⣿⣿⠟⠛⠊⢁⣾⣿⡿⣯⣽⣏⣹⣧⣝⠁⡴⣻⠢⣭⣾⡛⠳⣤⡿⢉⠀⣿⠤⠐⠀⣹⡭⠛⣯⣼⠿⣿⡀
⠀⣹⣿⣿⣟⣁⡀⠀⠀⢦⠒⢉⡙⠫⡈⠁⠀⠀⠀⠠⣤⣹⠏⣴⣄⣼⣿⣿⣿⣿⠋⡀⠀⠉⠠⠼⠟⠉⠀⣠⣼⡋⠁⢉⡰⠤⢉⣯⣄⣸⣿⡿⠄⢹⣿
⢰⣿⡛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣟⠣⣤⢤⡄⠶⢿⣋⣿⣿⠟⢫⣁⡀⢤⣄⣦⣤⣄⣠⣴⣾⣿⠿⠉⠲⡆⡙⢻⣿⠿⣿⣙⡿⣿⣿⢿⡿
⢹⣿⣿⣖⡴⢺⣿⠿⣿⣿⣿⠿⣷⣿⣿⣿⣦⡿⢷⣄⠻⣿⡶⣶⣿⠟⠇⠒⠛⠹⠟⢠⣭⣄⣉⠿⣏⢉⣴⣿⠦⡀⢰⣽⢡⣤⡙⠛⣭⣿⡿⣾⣿⣿⣇⡀
⠸⣿⡟⣿⢿⣿⠧⠆⢩⣼⠁⣶⢠⡌⠁⣻⠾⣇⠀⢽⠗⠌⠳⡘⢶⠑⣐⡗⠀⡀⠀⣴⠿⢀⠡⢦⡿⢻⣿⡍⠀⢠⣿⡷⣠⣞⣙⣎⠹⡽⣟⣻⣿⣿⣿⡇
⠀⣿⢛⣷⢼⠟⣀⡠⢸⣧⢰⣿⡷⠏⣦⢱⣠⡏⠰⣦⡀⠈⣷⣹⣾⣿⣿⣁⣈⣹⣧⡿⣧⠀⣷⣄⣼⣏⢻⣁⣐⣿⣿⣁⣠⣄⢠⣿⡷⣾⣿⣿⣿⣿⣿⡇
⠀⠙⢛⣩⣶⣎⣿⣇⣚⡥⠘⢻⡟⢞⣳⣞⣿⣿⠀⠈⢿⣤⡜⠛⣻⣯⣯⣉⠛⣿⣯⣶⣤⣮⣽⣿⣳⣴⣿⣿⣿⡧⠀⠙⠁⠉⠐⠙⠛⢿⣿⣻⣿⣿⣿⣿⡄
⠀⠀⠸⣿⡟⠋⣷⢿⣿⣴⣶⡿⠿⢾⣹⣿⣏⣻⠾⣶⣦⣿⣹⣟⡹⠟⠳⢌⢢⣽⡿⢿⣗⠣⡟⠣⢸⣿⣿⣿⠟⣠⡐⠀⠀⣘⣷⣀⣩⣴⣿⣷⣿⣿⣽⣿⣇
⠀⠀⠀⢻⣿⣿⣭⣠⣟⣰⣿⣷⣸⡰⣿⣇⢿⠋⣴⣿⣟⣿⣷⣼⣍⠳⢦⣨⣷⡽⠿⡆⢘⠃⠹⣶⣾⡿⣿⣿⣀⣦⣼⡷⠀⠀⣿⣿⣏⣿⣿⣿⣻⡟⢻⣿⣿
⠀⠀⠀⠀⠉⢻⣿⣿⣿⠻⣉⡟⠙⣷⣟⣿⣾⣷⣝⣿⣿⣫⣝⣿⣿⣿⣺⣿⣻⢷⡀⢦⣌⣲⣿⣿⣿⡷⣿⣉⣿⡛⠁⠀⡀⢾⣧⣿⣯⣏⠘⢇⣉⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⢻⣷⣶⣶⡤⣤⣿⢹⣯⡟⣻⣿⣿⣿⣿⣿⣿⡟⠿⠛⠋⢱⣶⣾⣼⣿⣿⣿⣹⣿⠀⣻⣿⣿⣧⠰⠆⠙⣦⣿⣿⣧⡄⠁⠈⠋⢱⣌⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⣿⣿⣦⣿⡿⡻⠟⠻⠋⡉⢻⣹⢿⣗⡀⣯⣼⣿⣿⣿⣿⣿⣷⣭⣷⢘⠿⣶⣧⠈⠻⣷⣼⣿⡟⣶⣿⣿⣦⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡍⢈⣿⠄⠰⠲⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣄⣵⣯⣸⣷⣄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣵⣾⠃⠀⠶⢈⣳⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣟⣯⣥⠤⠀⠀⠈⠀⠉⠈⠉⠙⠀⠀⢉⣩⣼⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠰⣬⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣾⠟⢡⡇⠠⣼⣶⣶⣶⢀⣀⣠⣶⣶⣿⣿⣉⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠘⢛⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣿⣷⣷⣿⣿⣿⣻⣾⣿⣿⠿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢢⡀⠀⠁⣀⣀⢱⠶⣾⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣈⡇⠀⢰⡿⠙⣷⣶⣼⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣴⣾⣷⣿⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡌⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠁⠀⠀⠈⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠁⠀⠀⠀⠀⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣾⡿⡇⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣾⣧⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⢸⣿⣿⣿⣇⢀⣄⢀⣠⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢻⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣞⣿⣿⣿⣿⣿⣷⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠉⠉⠛⠋⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⣿⣿⣷⡄⠀⠀⠀⠐⠿⢿⣿⣧⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡿⣰⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣹⣾⣷⣷⣷⣾⣿⣶⣶⣄⣽⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠟⠀⠀⠘⢿⣿⣿⠻⢿⠛⣿⣿⣿⠟⠁⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⣿⣿⣦⣄⣶⣿⣿⣷⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠻⢿⣾⣷⡿⠋⠉⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⣠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣤⣤⣶⣾⣿⣿⣷⣶⣴⣶⣾⣿⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠛⠃⠁⠀⠀⠀⠉⠛⠛⠿⠿⠿⠙⠃⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⢿⣿⣿⡄⠀⠀⠀⣠⣴⠟⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢸⣿⡏⠃⠀⠀⣴⣿⠇⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⣿⡇⣷⠀⣸⣿⣿⠘⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣾⣿⣤⡿⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠶⠒⣾⣷⡮⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣸⠎⢩⡇⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣇⣨⣴⣾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢯⡇⠁⢹⡆
⠀⠀⠀⠀⠀⠠⡬⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⣤⣾⠁
⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⢠⣾⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡟⠟⠛⠛⠛⢁
⠀⠀⠀⠈⢻⣿⡿⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠀⠀⠀⠀⠈⠀⢀⠁
⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣾⠟⣧⠂⡀⣀⡀⡀⠀⠀⠀⠟
⠀⠀⠀⠐⠨⣿⣿⣟⣂⣼⣿⣿⣿⣿⣿⣿⣿⣾⣵⣿⣷⣿⣿⣿⣿⠗⢿⡀⢀⡠
⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⢿⣿⣿⣟⣁⠀⣿⣿⣿⣿⣶⢿⠂
⠀⠀⠀⠀⠉⠙⠿⣿⣧⣈⣋⣿⣿⣿⣿⣿⣿⣿⣆⠀⡘⢿⣿⣿⣿⣤⣻⣿⣿⣿⣯⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠿⠟⠛⠉⠛⠛⠉⠀⠩⠙⠏⠛⠛⠛⠋⠋⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠑⡄⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣴⠀⡀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⢡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢿⣷⣶⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡉⢟⠟⣷⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣷⡦⠀⣀⡀
⠀⠀⠀⠀⢂⠀⡄⠀⠀⠀⡆⠀⠀⢠⢎⣠⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣯⣤⣀⡸⠃
⠀⠀⠈⠀⠀⠀⠄⠀⡄⠀⠑⢀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⢿⡟⠛⠛⠿⢿⣿⣿⣿⠟⡟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⣠⣢⣴⠶⣶⣿⣿⣿⣿⠟⣫⣏⣁⠂⠙⣏⣿⣿⣶⡈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠀⠀⣀
⠀⠀⠁⠀⠀⠁⠰⡀⠀⢰⠁⠀⠀⣼⣿⣿⣿⣟⣯⣍⠁⢹⡿⠀⠀⢸⠛⠟⣿⡷⢸⠃⠀⡐⠸⢁⠄⠀⡀⠀⠀⣀⠥⣌⣉⡉
⠀⠀⠀⠀⠁⠨⠀⢣⡀⠸⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣾⡎⢀⡤⢺⣷⣼⢻⢃⡎⢀⠔⠁⠘⢁⣠⡠⠈⠙⠀⠃⢀⡠⢀⡠⠄
⠀⠀⠀⠀⠐⢤⠀⠀⢡⠀⢣⠀⣾⣿⣿⣿⠟⠋⣁⣀⠉⠻⣿⣿⠃⠓⠝⠿⠁⣸⡷⠃⠠⠂⠠⢉⠄⠀⢀⠔⠁⠀⡴⠀⠉
⠀⠀⠀⠀⠀⠀⠙⣀⣨⢀⠈⢠⣿⣿⢟⣡⣶⣾⣿⣿⣷⠀⣿⣷⣷⠞⠀⠀⢰⡏⠀⠰⢁⠴⢈⡡⠖⠋⠀⠀⠀⠀⠀⠶⠶⣄
⠀⠀⠀⠀⠈⠁⠈⠁⠸⣹⣿⣼⣿⢷⣾⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⡧⠀⠀⣾⡇⠀⠰⠀⠠⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠛⠉⢀⠀⢫⣿⠇⣼⣿⣿⡿⢳⠀⠀⣿⡇⠀⠀⡀⠠⣜⢁⡁⠈⠁⢌⡉⠒⢁⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠔⠀⠀⠒⠀⢰⣿⣿⠏⠀⠸⡀⠀⢛⠀⠀⠀⠀⠀⠙⠣⠙⠂⠤⠀⠐⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢛⢃⡰⣾⣤⣶⣾⠁⠀⢠⣿⣿⣵⠿⠷⠓⢷⠀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠾⠿⠿⠿⠟⠓⠛⠉⢦⠀⠀⢁⢣⣼⣾⣷⣦⣾⣿⣄⡄⣀
⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣏⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⠴⠛⠖⠊⠉⠛⠛⠋⠛⠋⠉⠈⠈⠙⠉⠊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢹⠀⠀⠀⣠⠖⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⡇⢀⡴⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣧⢞⣼⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣸⠏⣾⣿⡇⠀⠀⣾⡇⠀⠀⣠⣴⡶⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⣀⣀⠆⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡏⢸⣿⣿⡇⠀⢰⣿⣡⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⡴⠋⠁⠁⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡘⠀⢼⣿⡟⠀⣰⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡅⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠸⠋⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢚⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣰⣾⡇⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⣿⣦⡀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣸⣿⣿⡿⣖⠀⡀⠀⠀⠀⣵
⠀⠀⠀⠀⠀⠀⠑⢬⣄⣀⣀⣀⣀⡠⠶⠖⠊⣡⠖⠊⠉⠙⠛⣿⣿⣿⠿⠷⠖⠂⠀⠀⠀⢀⣼⣿⣟⣝⡹⠛⠫⡇⣼⡁⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢿⣧⣾⣤⣴⣾⣿⠋⣴⢀⡆⠀⠀⢀⣠⠖⠋⠀⠉⠉⠉⠁⠙⠻⠟⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁⠹⠿⢿⣾⣷⣶⠾⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢀⡄⠠⢰⠀⠲⠀⠀⠀⠂⠀⡀⡀⠰⠀⠠⠐⠀⡄⢂⠐⡀⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠂⠀⠒⠈⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠁⠈⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡄⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠙⣿⣄⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠈⠿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠟⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠐⢶⡶⠀⠆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢀⠀⣸⠿⠿⠻⡇⢀⣠⣆⣀⣨⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⣀⣀⣠⣄⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣿⣿⣟⡲⢤⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡳⣄
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣄
⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠈⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠂⠀⠈⡠⠔⠒⠶⠤⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠁⠂⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠠⠤⠴⠊⠉⠉⠉⠉⠉⠁⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⢿⣿⣟⣛⣻⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣴⠤⠉⣉⣸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢸⣆
⠀⠀⠀⢀⣴⠗⠋⠰⠷⠈⠙⡆⢰⣄⣀⣀⣀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧
⠀⠀⠀⠸⣉⣱⣦⣦⣠⣶⣸⠗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⠿⠦⡷
⠀⠀⠀⠀⠈⢩⣷⣶⣄⣤⣤⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣿⡏⣵⣿⣿⣿⣿⣻⣟⣊⠠⠰
⠀⠀⠀⠀⠀⠸⣏⣻⡿⣿⣵⢿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣋⠿⠛⠋⠛⣝⡿⣿⣿⣆⠂⠐⠘⣤⣤⡴⠤⠄
⠀⣠⣦⢄⣨⣿⣮⣿⡻⣩⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠟⡁⠁⠀⠀⠀⠀⠀⠁⠀⠛⢍⣷⠶⡾⢋⡽⠶⢦⣼⡆
⠀⠈⠉⠉⠀⠀⠀⢘⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣛⠓⠈⠥⠐⠂⠀⠀⠀⠀⠁⠁⠀⠀⢴⣠⠀⠀⠀⠀⠀⠀⠸⠇⠐
⠀⠀⠀⠰⣿⣍⡋⠥⠾⠦⠉⠉⠅⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠆

⠀⠀⠀⠀⠀⢰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⡀⠀⠀⡄⠐⣆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣷⣴⠀⠀⣼⣷⣶⣶⣯⣀⣄⣴⣦⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢦⡖⠋⠀⠀⠀⢈⡁⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠠⡎⠀⠀⠀⠀⣵⠄⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⣷⠀⠀⠀⠀⠀⠃⣿⠀⢇⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠉⠀⠈⠀⠀⠃⠀⠉⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⡰⠀⠀⠀⢼⡧⠀⠀⠀⡄⠀⣿⡂⠀⠀⠀⠀⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⣽⡄⢂⠀⢀⡐⣼⡷⣂⡀⢀⠃⣰⣿⣷⠀⠀⠀⠖⠀⠀⠀⠘⡉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠝⡶⢆⣀⡀⠉⠛⠛⠉⢀⣄⡴⣿⣿⡿⠀⠀⠀⠆⠀⠀⠀⠀⢣⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣳⡇⠀⠀⠀⠣⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⡃⠀⢀⣰⣴⡃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠁⠀⣾⣿⣷⡧⠄⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠿⣄⡀⠀⣀⣀⣠⠶⠟⢋⣶⣩⣧⣾⣿⡯⠬⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⠀⣼⡿⢻⠏⠉⠁⠀⣰⡿⠿⠿⠿⢏⠏⣰⠂⠰⢆⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠴⠤⠴⠋⠀⠦⠴⠤⠼⠴⠋⠀⠀⠀⠀⠛⠒⠛⠓⠒⠋⠉⠁

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠲⢤⣀
⠀⠀⢀⠈⠲⢤⣀⡀⠀⠀⠀⠀⢸⠀⠓⢄⠈⠳⣦
⠀⠀⠀⠁⢠⠀⠈⠉⠉⠒⠢⢄⡘⣆⠀⠈⢦⠀⠈⢧
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠂⢄⠀⠉⠛⢧⣄⠈⠃⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠙⢦⡈⠀⠀⠈⠢⣀⠀⠈⠳⣦⡀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠈⢢⡀⠀⠈⢳⡀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢍⣄⠀⠀⠑⢄⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠁⠀⠐⠒⠈⠉⠑⢦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠸⠣⠐⡄⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣄⠠⡀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠈⠐⠐⠀⠰⡈⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢄⠀⠀⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠳⡄⠀⠘⢆⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⢠⠀⠀⠀⠉⠂⠀⠀⠀⢹⡄⠀⠈⣧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣸⠃⠀⠀⣿
⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⡘⠀⠀⣀⠄⠊⠁⠀⣠⠏⠀⠀⣠⠏
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠤⠞⠁⠀⠀⠚⠁⠀⠂
⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣈⣁⡀⠀⠀⠀⠠⠤⠀⠀⠀⠀⢘⠀⢀
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠶⢦⣄⠀⠀⠀⡌⠿⣍⠁⠀⠀⠠⡀
⠀⢸⡄⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠈⠓⠦⣄⡁⠀⠈⠳⣄⠀⠀⠘⠆
⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⡇
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡜⠀⠀⠀⠀⢸⠇⠀⠀⡰⠃⠀⠀⠀⠑⢀⠄
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⣠⠋⠀⢀⠞⠁
⠀⢀⣠⠤⠬⠻⢶⣤⣤⣤⣤⣴⡾⠋⡄⠀⠀⠀⣴⠁⠀⣰⠏
⠀⠋⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⢰⡇⠀⠀⢸⠃⠀⠠⣯⡀
⠀⠀⠀⠀⠀⠀⣀⣀⡿⠀⠀⠀⠀⡞⠀⠀⠀⠘⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠄⠠⠤⠄⢈⠀⠀⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠢⠀⠌
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣀⣀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠊⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠡⡄⠀⡀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣀⠀⠀⢙⢶⣇⣾⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣠⡶⣫⣭⣍⢢⣼⣷⡙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡸⠿⣀⠿⣿⠏⣠⣿⣿⣧⠀⣸⡶⠂⠀⠀⠀⠀⠀⠀⢒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣈⠁⠀⢿⣿⡶⠺⠋⠛⢀⡅⠀⡉⡁⠀⢀⠀⠀⠄⠁⢀⡀⠸⠀⠠⡀⢠⡄⠀⢠⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠀⠀⠸⣿⣁⢰⡌⣰⡾⠂⣸⡇⣿⠀⢿⣢⣶⣀⣆⣸⠏⢰⣑⠠⢟⣠⡴⠃⢈⣼⠎⠓⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣉⣉⣵⣶⣿⡿⡧⠹⠆⣹⣿⣿⣿⣇⢰⣿⢯⣽⢧⣼⡾⡷⠄⠝⠈⠀⠄⠈⠉⠷⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡆⠁⠀⢠⣼⣩⣿⣿⣿⣿⣷⣿⣿⣿⣿⣏⣄⣶⣴⣶⢄⡀⢈⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣻⣯⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢦⠈⠉⠘⠋⠈⠀⣀⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢛⢣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⢧⣿⣿⣿⣿⣿⣿⢿⠛⢿⠿⠿⣿⣿⣿⠀⠀⣴⣂⠀⢠⣤⣀⡀⠀⠀⢈⠱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠟⠋⠉⠁⠀⠀⠀⠈⠀⠀⠀⠙⢻⡄⠀⣿⣿⣙⣴⡇⠀⠉⠀⠀⢠⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢿⣿⣿⣿⣷⣷⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣮⣽⣟⠈⠀⠀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡮⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣀⣴⣶⣷⣶⣶⣶⣤⣤⣼⣿⢿⠿⠏⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣄⡀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠈⠉⠙⢦⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣂⠀⠀⠀⠀⠙⢷⣿⣧⣠⡰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⣿⣷⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢶⣤⣼⣿⠿⠟⠉⠛⠿⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠀⣴⣩⣟⢦⢈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠒⠒⠒⠤⢤⣀⣀⣤⣄⣿⣿⣿⠃⠀⠙⠻⠟⠻⠘⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⢿⣿⣛⡓⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣆⣁⠀⡀⠀⣰⡦⠔⢀⠌⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠛⠒⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⢔⡮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠈⢻⣞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⡁⠢⣀⣀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣟⡅⠀⠀⠉⣶⣥⠃⠀⠀⢀⡴⠃⠀⠀⠀⠀⣰⣾⡄⠀⠀⠟⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⠀⠀⢹⢷⣶⡞⢺⠋⠀⠀⠀⠀⢀⣼⣭⣐⣟⣡⣴⣾⡇
⠀⠀⠀⠀⠀⢠⢴⡀⠀⠻⣿⡿⣡⠀⢀⣼⣾⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠙⠒⣁⣠⠵⠛⠀⠴⠾⠛⠛⢿⣿⣿⣷⡀⠀⠀⠠⣿⡿⠿⠋⠙⢿⣿⡿⠣
⠀⠀⠀⠀⠀⢅⠀⠃⠀⠄⠀⡀⢀⣀⡀⢰⡄⠦⠛⠿⠛⠃⠀⠀⠘⡄⢆⠀⠀⠀⠀⠉⡁⠀⡀⡴⣦⡀⠀⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁⠈⠈⠉⠁⠠⠠⠀⠁⠊⠑⠊⠀⠀⠀⣀



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡙⣾⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡌⣷⣴⣷⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠻⢻⣿⡿⣷⡆⠀⠙⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠈⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣧⣀⣀⡀⠀⠀⠸⠿⠯⡃⠈⠉⠛⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⡿⠋⠀⢈⡁⠀⠀⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡂⠀⠀⠀⢙⡋⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⠷⢶⣤⣾⣷⣤⡦⢄⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢿⡿⢿⣿⠿⢿⢿⠟⠋⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⠈⠀⣠⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣇⢀⠀⠀⠀⠀⠑⠺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⢀⠀⣤⠆⠀⠈⠀⠀⠀⠀⠀⠆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠙⢿⣿⣿⣵⣴⡏⠀⠀⠀⠀⠀⢀⣴⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⠀⣦⣠⣼⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⠈⢹⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⢿⣄⣀⡀⠠⠼⠟⠛⠛⠲⠔⠂⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⡈⠀⣤⡤⢤⣤⡀⠀⠰⠀⠀⠀⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡖⡠⠁⠀⠀⠀⢘⣛⠂⢀⢁⠔⡁⠔⠁⠀⠀⠀⣀⡀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣴⢷⡿⢃⣤⠞⣤⠤⠤⣿⣿⣟⠉⢛⣡⠞⣁⣀⠀⠀⠀⣴⠹⣼⡌⣡⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⣦⠟⡡⠊⡐⣀⢐⣡⡄⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⡼⠁⣾⢿⣶⠫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢉⡴⢃⠜⠁⡼⠁⠉⠙⢻⡧⠾⡁⠀⠂⠀⠀⠀⠀⢀⣼⣷⣾⢏⣼⣿⡜
⠀⠀⠀⠀⠀⠀⢠⡴⢾⡍⣠⡞⠁⣼⠀⣷⠟⠃⠀⢻⡟⠁⢀⠜⠃⠀⠀⠀⠀⢀⣼⣿⣿⣷⣿⣶⢾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠙⠉⠋⢠⡏⢀⣠⣯⡴⠋⠁⣠⣶⣋⡤⠒⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⠋⠀⣨⡋⠄⢀⣾⣿⠟⠁⢀⡌⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠨⣿⣿⠿⣿⣿⣿⠝⣄
⠀⠀⠀⢀⡴⣦⠼⠁⢰⣏⢶⣾⣯⣱⣾⣯⠟⠁⣠⠜⠀⠁⡄⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠀⡈⢢⣴⣼⢷⣿⣏⣿⣿⡿⢿⣷⢿⣤⣤⣂⣠⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢉⡟⠁⠀⠀⠀⠀⢀⠀⠀⠾⠉⢀
⠀⠀⣀⠐⢄⣴⡟⠉⣿⣽⣿⣿⣿⡿⢻⡏⢀⡠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣋⠋⠉⢻⣿⠁⠀⢀⣠⣄⡄⠀⠀⡀⠤⡀⡌
⠀⠀⠐⣈⣿⣡⣆⣺⣿⣿⣿⣿⡏⠠⣾⠖⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡟⢿⣿⣿⡟⠁⠀⠀⢸⣿⡻⢇⠄⠹⡼⠀⣄⠆⠓⢤⣇⢱
⠀⢀⡤⠛⠛⢳⣿⡏⢀⣿⡿⣽⠿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣻⣿⣿⣿⣧⣀⠀⠀⠈⣿⠓⠠⠆⠤⠄⡖⠁⡀⣠⠀⣽⣼⠇⠈
⠀⠀⠀⠀⠀⣸⡯⠈⣿⣿⣧⣿⡞⣣⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⡏⢿⣿⣿⣿⣿⣯⣹⠿⢦⣄⣌⣱⡀⠐⠀⠀⠀⠁⠋⠈⠀⠈⡟⠂
⠀⠀⠀⠀⣩⣟⣥⢸⣟⣽⣿⣼⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⣳⣆⣽⢻⣿⣿⣿⣿⣷⣶⣯⠉⠉⠉⠛⠯⣉⣉⠉⠉⠐⠒⠀⠛
⠀⠀⠀⡀⠹⢉⣿⣞⣿⣷⢾⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣥⣿⡟⠻⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠐⠤⣆⠀⠀⣤⠀⠀⠀⠀⠁
⠀⠀⠌⠁⠀⢴⣿⣿⣹⡇⣾⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⢻⡿⢿⣩⠤⠀⠁⡟⣽⡇⣻⣿⣇⠀⠀⠀⠀⠀⠄⠘⠀⠀⠈⠀⠀⠀⠀⠖⠀⠁
⠀⠀⠀⠒⠛⠸⣿⠻⠌⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣳⠶⢦⡤⢴⣦⢠⣿⣿⢧⡸⣽⣿⡀⠀⠀⠀⠀⠀⠉⢠⡜⡒⠂
⠀⠀⠀⠠⠂⠀⣿⡧⣾⢿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣦⣼⣿⣿⡗⠀⢻⣽⣿⣷⣀⠀⠀⠀⠀⠁⢸⡏⠁⠀⠐⣶⡀
⠀⠀⠀⠀⠀⠀⠏⠁⢸⣯⢟⣷⣿⣿⣿⣿⠏⠉⠻⣿⣿⣿⣿⣿⣿⣟⡟⣂⣸⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣾⣽⣿⠦⠤⠂⠘⢀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣽⣷⣾⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⢀⣰⣫⣾⢇⣧⢿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣩⣥⣽⡿⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠘⠛⠣⠿⣿⣿⣷⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣥⣴⠾⠿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠉⠉⠙⠻⠿⡟⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡘⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢸⠙⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠘⡀⢳⠀⠀⠀⠀⠀⠀⢀⡞⢰⠃⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡇⠘⡄⠀⠀⠀⠀⠀⡼⠁⣸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢳⠀⢳⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠀⠀⠀⠘⡇⢸⡀⠀⠀⠀⣸⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡇⠀⠀⠀⠀⠀⢻⢸⡇⠀⠀⠀⣟⠀⠀⣇⠀⠀⠀⠀⡔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠀⠀⠀⠀⠀⢸⠨⡇⠀⠀⠀⡟⠀⠀⢿⠀⠀⠀⢰⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣃⠀⠀⠀⠀⢸⠄⡇⠀⠀⠀⣿⡀⠂⢸⠀⠀⢠⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⣀⡀⢸⣆⣇⠀⠀⠀⣿⢧⣆⣼⢠⣦⢟⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣵⣮⣻⣻⣉⡉⠘⠳⠾⣏⣻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢛⠩⡑⠙⠫⠄⠀⠉⠁⠑⣌⠹⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⡜⠁⠀⠀⢡⠀⠀⠀⠀⠀⠀⠆⣱⣄⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣿⣿⠣⡀⠀⠀⠠⠀⠀⠀⠀⠀⡼⣿⣿⢹⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠻⣿⣿⠔⠉⠀⠀⠀⠶⠀⠀⠀⠀⠑⠿⢿⠿⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠓⠦⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡀⠀⠀⢀⡀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠾⠔⠀⠀⡬⢀⡀⠘⢿⣕⡒⣨⡴⠂⠀⠀⢱⠀⠀⢀⣈⣁⣦⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⢷⣶⣶⣐⣣⢷⠤⠤⣀⠀⠈⠹⠉⠀⠀⡀⡀⣼⡙⣃⠀⡐⣶⡗⠀⠤⠀⠤⠄⢀⡈⠉⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠤⠀⠒⠈⠻⣿⣷⣿⣿⣆⣀⠀⢀⡤⠚⠲⢤⣀⣠⠄⣠⢤⣀⣆⣥⠟⠉⠀⠂⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⢷⣍⣁⣀⣀⢀⣀⣠⣤⣾⠿⠷⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⢀⠄
⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⣿⢆⢠⣿⣶⣇⡀⠂⡀⢠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠃
⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣄⡀⢈⠐⢿⣿⣿⣿⣷⡀⠀⡀⢤⢄⠀⢀⣠⣾⣷⣄⠀⠀⠐⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃⠀⠀⡀⠀⠀⣎⣠⣤⣢⣽⣿⣿⣿⣿⣿⣼⣿⣞⣿⣰⣶⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⢀⠀⢢⠀⢀⡊
⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠐⠀⠀⠀⢳⣄⣸⣷⣻⣿⢋⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⡄⠀⡀⠀⣆⡘⠂⡆⣷⡾
⠀⠧⡞⠀⠀⠀⠀⠀⠀⢢⠈⢷⣅⠀⣛⢌⢢⣧⣌⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣷⣼⡇⣦⣸⣇⣰⣿⣿⣧⣶
⠀⠸⡧⠀⣄⠰⡀⠑⢠⢸⣾⣼⣿⣿⣿⡿⣿⡿⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⡟⣿⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⣿⣿⣿⢿⣏⡆
⠀⠀⠉⠀⠀⠀⠉⠀⠀⠙⠃⠋⠻⠛⠘⠙⠁⠉⠁⠃⠈⠙⠋⠃⠙⠛⠙⠛⡟⠏⠉⠁⢻⡟⠘⠛⠏⠙⠉⠙⠛⠈⠛⠋⠙⠁⠉⠉⠙⠁⠁⠈⠛⠈⠙⠋

⠀⠀⠀⣀⡀⠀⢠⣄⠀⢠⣤⠀⠀⣠⣠⡄⠀⠀⠀⢴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡠⠄⠲⣶⠄
⠀⠀⣰⣓⣲⠀⢻⠈⢧⣼⣿⠀⢸⣏⠀⣻⠂⣴⡖⠚⠛⣿⠟⠳⢶⣶⡀⠀⢸⢿⣿⡅⠀⠀⠂⢀⣴⢭⣲⡚⠛⢛⣶
⠀⡘⣿⠈⠀⠀⠈⢧⣼⠿⢿⣤⡈⠉⠛⠉⠀⠀⠉⠉⠙⡿⢸⣿⠯⠟⢋⠀⠈⠙⠂⠀⠀⡟⢂⠺⠿⠧⠇⡟⠉⠉⣁⣄
⠸⠎⢛⣾⠀⠀⠀⠸⢳⣿⡆⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣥⣀⣀⣀⣠⣬⣶⡆⠀⠀⠀⠀⠈⠀⢀⠀⠀⢔⠛⢟⠋⠙⠏⠄
⠀⠀⠈⠁⡶⣢⣤⣤⡀⠈⠁⠀⡸⠃⠀⠀⠀⠀⠀⠀⠸⠈⠻⠟⠋⠈⡿⢻⡶⠀⠀⠀⠀⣀⠀⠀⡀⠀⠘⠃⣇⢰⣿⡟
⠀⠀⠀⠸⣼⣿⡟⢿⣍⠛⠻⠇⠀⠀⠀⣴⢶⠀⣀⡀⢠⣀⡀⠀⣀⣀⣇⣸⠇⠀⠀⠀⠀⢿⣷⣔⠁⠺⠍⠶⠥⠭⠽⠁
⠀⠀⠀⠀⢻⣿⠇⢾⡿⢀⡀⢄⠀⠀⢸⠃⣸⣿⡿⠁⠘⠛⠋⠉⠛⠋⠙⠛⠀⣀⡀⠀⠀⢈⣹⣿⢦⣤⡶⠚⢋⣻⠃
⠀⠀⠀⠀⠈⠁⠈⠉⠁⠉⠁⠁⠀⢀⣦⣭⣍⠉⢀⠀⠀⣰⡾⣏⠷⣄⠀⢰⢤⡿⠁⡀⢀⣾⣿⢱⣶⡘⢿⠋⠉
⠀⠀⣠⡲⡶⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣫⢇⡀⠀⠀⢿⣭⢻⣹⡇⠀⠈⠡⣭⠆⠀⠈⢏⠩⠈⠉⢀⣐⣀⡀⢤
⠀⠘⠟⠋⢁⠀⠀⠀⠀⠀⢸⣷⡆⠔⣄⣀⣀⣘⠿⠋⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣞⢋⣿⢿⣿⣎⡀
⠀⠀⠀⠐⢫⣤⣺⡄⠀⠀⢶⣾⠑⣶⠈⠙⣿⣿⠄⠀⠀⠀⠀⠀⠀⢠⣦⢄⠀⠀⠀⠀⠀⠀⢣⠀⠛⣿⣧⢸⣿⡿
⠀⠀⠀⠸⠯⢀⡀⠀⠀⠀⠘⡷⠿⡛⣤⠔⣿⠟⡄⠀⠀⠀⡨⢭⡆⠀⠛⠿⡷⠀⠀⡀⠀⠀⠓⠘⠓⠘⠓⠂⠘⠃
⠀⢠⢶⠀⢐⣓⣺⡀⢫⣇⣤⠀⠀⠉⠁⠈⠁⠀⠀⠀⡴⣬⠙⠟⠉⣤⡄⠀⠀⠀⢈⣷⡄⣀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠢⡄
⠀⣤⡾⢦⣤⠈⠁⠀⣜⡍⠛⠀⠀⢰⣶⣄⡀⠀⠸⡷⣾⠀⠀⣆⠄⢑⣧⣲⡄⠀⢠⣛⣻⠻⣾⡟⠁⠀⠀⠑⠔⣿⣿⢌
⠀⠈⠁⠈⠁⠀⠀⠀⠈⠀⠀⢿⣉⠉⢓⡦⠘⠄⠀⠀⠛⠃⠠⠂⠀⠺⠷⠀⢠⣶⡄⠀⠀⠘⠇⠀⢀⣾⡆⠀⠐⠄⠄⠁
⠀⠀⠀⠀⣀⠀⠀⣴⡾⣿⠟⠀⠈⠙⠣⣟⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡴⠛⡟⠀⠀⢸⣿⡇⢀⡤⠶⣦
⠀⣠⣾⣿⣿⡿⣛⡛⣿⣤⠀⠀⠀⠀⡀⠈⠉⠩⢄⡨⠀⠀⠀⠀⠀⢀⣴⣶⠾⠿⣿⡤⠞⠁⢀⠄⣾⠿⢿⣯⡤⠖⠁
⠀⠀⠉⠁⢘⠉⠿⠧⠼⢿⡇⠀⠀⠀⠻⣷⣶⣶⢆⠀⠀⠀⠀⠀⠀⡾⠻⠧⣿⣇⠽⡆⠀⠀⡌⣼⣿⣿⡶⠛⠂
⠀⠸⣷⣶⣶⡦⣀⣀⣀⠐⠁⠀⠀⢸⣤⡙⡟⣡⣴⠆⠀⠀⢀⢿⣦⣼⣍⣀⠀⣀⣠⠁⠀⠀⠱⠄⡂⢀⣀⣴⣤⣤⣻⠂
⠀⢲⣿⣿⠹⣷⡄⠉⠉⠄⠀⠀⠀⡐⡙⠛⠗⠛⠋⣆⠀⠀⠸⣾⠛⡏⠀⠙⠛⠿⢿⡄⠀⠀⠀⢸⠛⠉⢡⣾⢫⣿⣿⡜
⠀⠈⡿⠛⣘⣿⢓⣤⢘⠄⠀⠀⠀⣧⣅⢀⣀⢀⣠⣏⠀⠀⠀⢻⣀⣇⣀⡀⠀⢀⣠⠃⠀⠀⠀⢠⠢⣤⢸⣿⡘⠿⡿
⣀⣀⣠⣀⣄⣀⢀⡀⣀⠀⢀⡀⢀⡉⢉⡀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠉⠛⠋⠉⠛⠛⠀⠀⠀⠀⠀⢀⣠⣄⣀⡁⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠊⠀⠀⠄⡀⠔⠈⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠠⠁⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠠⠄⣀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁
⣈⡀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡀
⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀
⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠈⠀⡖⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠄⠀⠀⠀⢠⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠌
⠀⠀⠀⠀⠀⡃⠀⠔⠈⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠑⠠⢄⠀⠀⠀⠀⡠⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠⣶⣶⣮⡤⠀⠀⠀⢰⠃⠀⠀⢀⠎⠀⠀⣀⡀⢀⠄⠀⠐⠂
⠀⣀⢀⡀⠀⠀⠀⠠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣤⣤⣾⣿⣿⡿⠟⠛⠹⠆⠀⠀⠀⣀⠀⠀⠀⠊⢀⠀⡀⠈⠀⠀⠀⡖⠀⠀⠀⠀⡀
⠀⠈⠛⠏⡜⠂⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⢀⡠⣀⣤⣾⣿⠟⠛⠛⢯⡀⡀⠀⣸⡄⠀⠀⣰⣿⢠⣤⣠
⠀⠀⠀⠀⠀⠥⠀⠀⠀⡀⠀⠀⠉⠁⠉⢹⣿⣾⠋⠈⠻⣿⠀⠀⠀⠀⠁⠁⢀⣿⣿⣦⣴⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠲⠀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⢻⠀⠀⠀⠀⡘⢀⣾⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣠⣴⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣼⣿⣿⠀⠀⡀⠀⣾⣧⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡄⢀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠛⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣾⡇
⠀⠀⠸⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣿⣿⣿⣿⡿⢛⠝⠊⠉⢀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢰⣄⣀⣀⣿⣿⣟⣡⠞⣁⡶⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡿⠟⠋⠈⠁⢾⢟⣤⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠄
⠀⠀⠀⠀⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣧
⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠻⠂⠀⠀⠀⣀⡶⠿⠿⠿⠿⡿⠻⠿⢛⡳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⠀⠀⠐⠠⡤⠀⡀⠀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠈⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠈⠁⠙⠙⠋⠉⠉⠉
⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⢀⡀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠎⡁⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡆⢀⠰⠐⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠷⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢓⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠄⠀⠀⠀⠆⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠁⠁⠀⠀⠀⠀⠁⠈⠈⠋⠈⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠉⠁⠐⠂⠀⠉⠂⠈⠈⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠐⠂⠐⠀⠂⠂⠂⠒⠀⠃⠂⠁⠀⠀⠐⠀⠐⠀⠀⠀⠀⠈⠀⠁⠀⠈⠃⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠞⠁⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢻⣇⣤⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⢿⠷⣤⣴⡞⢿⣿⣿⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⡿⢁⠀⣼⣿⣄⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⡿⢿⣿⣟⣿⠃⠁⣀⠙⣿⣿⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠙⠉⠁⠈⢹⣿⡏⢀⣾⣿⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠸⣿⣿⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄⠀⠀⠀⠀⠺⣿⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠘⣝⡈⠋⣾⣷⡆⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢶⡈⠻⠟⣁⣼⣿⡟⠶⢤⣤⣤⡁⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⢿⣿⣿⡿⠿⠓⠀⠀⠀⠺⡿⠟⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠍⠥⠀⠀⠂⠀⢀⣀⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠲⣆⣽⣿⣿⣿⣿⣧⠠⠈⠁⠀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⠀⠹⠛⢛⣙⣽⣧⣿⡽⣻⠿⠟⠂⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⠿⠻⣿⠛⠏⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⣿⣮⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠃⠀⠀⠀⠀⠘⢻⡏⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣴⠛⠚⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣆⠀⢻⡅⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⠀⠈⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡀⢸⡀⠁⠀⠀⡼⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠱⢸⡇⡀⠀⠀⣥⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⢼⠀⡁⠈⢿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣀⡀⠹⣆⠀⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⢻⣷⣦⣠⡌⢿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣴⡇⠿⣿⣟⠘⢓⣾⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠱⠟⠋⠛⠻⣏⠁⠀⠉⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣠⣠⠶⠀⠀⢰⡤⠿⠶⠤⢤⠤⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⣿⣯⣾⣿⠃⢘⣠⡶⣄⢀⠤⠖⠋⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⣥⣀⡛⠛⠋⠁⠀⢠⠀⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠋⣘⠯⠁⡰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢄⠀⠂⠠⠄⠘⠂⠲⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣸⣇⢈⠁⠀⠀⠰⡆⠀⠀⠀⠂⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢻⣿⡈⠀⠀⠁⠠⣿⠀⠀⢀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡼⣻⢷⡄⢿⡁⠀⠠⠀⠀⣿⣿⣁⠀⠀⠀⠘⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠈⣥⠋⠀⢷⡈⢷⠔⠀⠀⠀⣿⣿⡟⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⢈⣶⡀⠀⠁⠘⣤⠴⠂⠀⣿⡿⢳⢠⡜⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠹⢻⡄⠀⠀⢹⡁⠀⠀⡋⠀⠀⡇⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠉⣀⣤⠌⢀⡀⠀⠁⠀⠀⠀⠀⠀⢏⣄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡵⣶⠇⡠⡴⠞⠑⣰⠈⡀⢠⠀⠀⠀⠀⠀⠀⠀⣠⣾⡴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠃⠉⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢗⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠸⣦⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠙⠁⠹⢱⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⡥⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⡀⠀⠀⢠⠇⣧⠀⠀⠀⠀⠀⢀⡴⢋⡶⠋⠠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠁⠀⠀⢼⠃⣿⡆⠀⠀⢀⣴⠃⢃⣾⢐⡞⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣳⣤⣼⠀⣿⡇⠀⣰⣏⠁⠀⣼⣧⡾⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢈⡿⢁⣰⣿⡇⢠⣿⣻⣈⢠⣿⠏⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢁⡬⠉⠉⣉⠉⠙⠻⢿⡨⠋⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡤⠂⠀⠈⠁⠈⠁⠀⠀⠀⠃⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢒⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠀⠀⠀⠀⢃⠀⢀⠐⠃⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢥⣾⠜⢂⠃⢠⣾⠗⠀⣴⡎⠃⣀⠀⠃⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⣍⡠⠀⣷⣄⢙⠀⠘⠁⠀⠘⠋⠁⠀⠀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠐⠀⠀⠀⠛⠛⠻⠷⢦⣤⣤⣚⣃⣤⣤⠞⡻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢣⠀⠀⠀⠀⢶⣶⠀⠀⢀⠀⠀⠨⠛⠟⢙⠋⠄⠈⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠡⡀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢼⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡰⢀⣾⣿⡴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠀⢠⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⠁⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⣸⡟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠅⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⣿⡇⠀⠻⠀⠀⠸⠀⢀⢠⠀⠀⠀⡠⠈⠀⠠⣴⡟⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⡇⠀⠀⠀⠀⣶⣶⡛⣿⣄⠀⠀⠀⠀⠀⢨⣿⠂⠀⠀⠀⠘⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣸⣿⡗⠂⠀⠀⢸⣿⢃⣼⣿⣿⣇⡀⠀⠀⠀⣾⣟⡀⢠⣤⣤⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡰⠂⢨⣿⠁⠀⠰⠀⢸⣿⣤⣬⣤⡝⣿⠁⠀⠒⢴⣿⣿⡀⣀⣤⢄⠈⠉⢰⡄
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠼⠥⠶⢿⡷⣽⡿⠋⠚⠀⢀⡾⠛⠛⠛⠻⠿⣿⡆⠰⠆⢲⡿⡿⠿⢿⣁⣈⣇⣠⣄⣧⣄
⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠿⠾⠶⠶⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠓⠓⠀⠙⠛⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⡀⠀⠀⠠⡀
⠀⠙⠐⠀⠀⠀⢂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡭⠉⠉⣭⢩⠝⢁⡄
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⡇⠀⠀⢀⠤⢄
⠀⠀⠀⠀⢀⡔⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢱⡀⢀
⠀⠀⠀⠰⠡⡁⠀⠀⢂⠄⠁⠀⠀⠀⠀⠀⠀⠸⣷⣾⡄
⠀⠄⠀⠀⠀⡀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⠀⡀⠀⠁
⡇⠀⠀⠀⢘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⡿⠚
⡇⠠⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⡟⣉⠻⣿⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⠿⠟⣿⣧
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⡿⣿⣿⣿⣆⡾⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠐⠛⠉⢉⡉⠴⠿⠻⣿⢳⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣯⠉⠀⠀⠰⠁⠸⢶⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⢰⡄⠀⠀⠀⢼⣻⣿⣿⣽⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⠀⠀⠀⢸⣿⣻⢼⣿⣿⠿⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⠁⠀⠀⢸⣿⡇⢸⡿⠁⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⣼⠃⠀⠀⠈⠂⣰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠐⠀⠀⠀⠀⠀⠀⠀⢁⠖⠀⠀⠀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢀⣐⠆⠀⠀⠀⠊⠀⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠇⠘⠻⣧⢀⣠⠂⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣄⢠⣄⠀⢿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣀⣴⠀⠀⡀⠀⠀⣾⡿⠈⠋⠉⠋⠀⠈⡏⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⡇⠀⠀⡿⠀⠀⠀⢠⣤⡾⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠚⠛⢁⠀⢀⢙⠛⠋⠉⠛⡀⠄⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⣠⣶⡷⠀⠀⠀⠀⠀⠀⠀⣞⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⠈⣷⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣽⠟⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⡠⣿⣷⣻⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣶⡟⠁⠀⠀⣼⡏
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⣿⢧⠆⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢡⡿⠋⠀⠀⠀⢰⡟
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠻⣌⠢⠑⣌⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠉⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡘⢦⠀⠈⢧⡈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⢸⠀⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠙⣦⠈⣿⠀⠸⣿⣿⣷⣄⠀⠀⠀⣸⣿⣟⠀⠀⠀⠀⠀⠀⣿⠀⣿⣷
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠈⠀⢿⡇⠀⢹⣿⣿⣿⣆⠀⢀⣿⣿⣿⠂⠀⠀⠀⠀⣰⠏⢠⣿⡿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⢸⡇⠀⢸⣿⣿⣿⣿⡄⢸⣿⣿⡏⠀⠀⠀⠀⠘⢁⣴⢿⣿⠃
⠀⠀⠀⠀⠉⠛⠿⠿⠷⠙⣿⣿⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⢀⡼⢿⡿⠿⢿⣷⣼⣿⣿⣧⠀⠀⠀⢀⡴⠋⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⣧⣞⠤⠄⠀⠀⠀⠹⢿⣿⣿⣿⡀⠀⠰⠋⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣾⡄⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⢙⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⣸⡆⠀⠀⠀⠀⢀⠴⢦⡄⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠤⠴⢶⣾⡿⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⣼⣿⣍⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⡿⢃⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠺⠧⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⡋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣿⣦⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⢸⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⢠⣾⣿⠟⠋⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢸⡀⠀⢀⣰⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢠⡿⠸⣇
⠀⠀⠀⠀⢨⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠙⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠴⠛⠁⠀⣿⡄
⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣠⣶⣄⠀⠀⠀⠀⠀⠀⣀⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⣬⠻⠶⠶⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⣿⡇
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡄⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⡄⢷⡀⠀⠀⠀⠀⠀⠀⠀⠛⣇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠹⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣠⣶⣁⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢻⠇⠀⠐⠛⢛⡿⠋⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠹⣦⠀⠀⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠉
⠀⠀⠀⠀⠀⣠⣏⡀⠀⠀⠀⣿⡷⣶⠦⣀⡶⢾⣿⣿⣿⣷⣦⣤⣄⣀⣹⣧⡀⠈⠛⢻⣿⣿⣷⣦⣤⣄⣤⣄⣤⣤⣶⠾⠟⠋⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡙⠻⣿⣿⣿⣦⡀⠈⠁⠀⠙⠛⠉⠈⠁⠘⣿⡄⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠈⠉⠉⣷⡀⠀⠀⠀⠀⠀⣶⠀⠀⣿⡇⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡤⢀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣹⣧⠀⠀⠀⠀⠀⠟⠀⠀⣿⣧⡀⠀⠠⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠦⠔⠛⠋⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣶⠀⠀⣿⠛⠓⠂⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠰⠆⠈⡄⠀⠙⠦⣤⣴⣦⣴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⡄⠰⡇⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠔⠛⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣺⣆⢀⣤⣶⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣿⣿⢟⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣳⣧⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⣿⣿⣵⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⡿⣿⣿⣿⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣏⣳⣾⣷⣻⣿⡾⣽⣵⣾⣤⣀⡄⣀⣀⢤⣤⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟⠉⠀⠙⡷⢿⡿⡿⢻⣭⣶⣾⣿⣿⣚⢿⣎⣧⠂⠀⢹⣿⣽⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⣀⣰⡿⢿⢿⣻⣿⣿⡿⣿⣽⣯⣿⣿⣟⣻⣶⣿⣿⣾⣟⣏⣡⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣻⣟⣹⣯⢯⣿⣿⣿⣿⣿⣏⣶⣯⣿⣋⣿⣏⡹⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣫⣿⡻⣿⣟⡻⣿⠢⣽⣻⠛⢿⣿⣟⣿⣿⡟⣷⣽⢿⣿⣿⣬⣿⣦⡷⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⢿⣟⣭⣝⣿⡋⢐⣻⠛⠿⠂⣿⣿⣯⢯⣹⣇⣢⣾⠟⣿⣿⣿⣿⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠮⠉⠙⣿⣾⢿⣋⠟⢷⣦⠼⣿⡽⢟⣯⣷⣼⣟⣷⣶⣼⣿⣿⣇⣑⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣿⣛⣻⣿⣿⣿⣿⣷⣯⣉⡫⡿⢻⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣸⣿⡟⢣⣴⣶⣴⣛⣻⢟⣓⢉⣾⣿⡧⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⠀⢀⣀⣀⣀⡀⠀⢀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣠⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⣿⡴⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣴⣿⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣾⣿⠁⢠⣴⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⢀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣏⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠨⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⠻⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡠⠀⠂⠒⠒⠀⠀⠀⣀⡀⠀⠀⠀⠄⠀⠀⠀⠘⢿⠯⡿⠟⠋⡌⠀⠀⠈⠉
⠀⠀⠀⠀⠈⠳⡀⢀⢀⠠⠀⠐⠂⢾⠷⠒⠀⠀⠀⠐⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠲⠲⠴⠀⠀⠀⡔⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠄⠀⠀⠀⡀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠃

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⠷⠖⠒⠒⠒⠒⠒⠲⠼⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⠀⠀⠀⢀⡴⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⠙⢄
⠹⢄⣀⣀⣀⡠⠔⠋⠀⡇⠀⠀⠀⠀⣼⣏⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣹⣦⠀⠀⠀⠀⢧⠀⠀⠙⠦⣄⣀⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠆⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠉⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢢⠀⠀⠀⡔⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⡆⠀⢠⠃⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡼⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡤⠤⠤⡑⠤⣀⠀⣠⠃⠀⠘⣄⠀⣀⡠⢊⡤⠤⢤⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⠃⠀⠀⠀⠈⢦⠀⠈⠀⠀⠀⠀⠀⠉⠀⡴⠁⠀⠀⠀⠈⢆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡼⠁

⠀⠀⢀⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠥⢰
⠀⠀⠀⠁⢀⣝⠲⢤⡀⠀⠀⠀⠀⠀⢀⡴⢫⡞⠀⢀⡟
⠀⠀⠀⠀⠈⢯⢳⡄⠉⠳⡄⠀⠀⢠⠏⢠⣿⣁⠄⡼⠁
⠀⠀⠀⠀⠀⠈⢷⡑⡄⠀⠀⠦⠄⠀⠀⠸⠟⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⡇⡦⠀⠀⠀⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⢀⡰⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠑⠛⡀⠀⠀⠀⢠⡁⠈⣿⡿⠟⠛⠛⠋⠉⠉⠉⠉⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠃⢀⡅⡼⠁⠀⠀⠀⠀⠹⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⣼⠀⢸⠀⠇⠀⠈⠳⠜⠃⠀⢃⡀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⣧⠀⢹⣣⠄⢀⣀⣠⣀⣀⣰⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠙⠀⠉⠉⠀⠈⠉⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠠⡄⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠠⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣼⡿
⠀⠀⠀⠀⠀⠀⢀⣞⠉⠂⠙⣶⠄⠆⠀⡟⠃⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⢀⡖⠋⠁⠀⣠⡾⠃⠀⣀⣇⠀⠀⠀⣴⣿⣉⣀⡀⢀⡴⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⣿⣶⣀⡀
⠀⠀⠀⠀⠚⠷⠶⠖⠛⠛⠁⠀⢸⣭⣉⣀⣤⣾⡿⠋⠉⠉⠹⣿⣦⣤⣤⣤⣤⣤⡤⠤⠤⠠⠴⠾⡿⠿⠿⠿⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⡒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢀⡶⠈⠀⠀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⡏⣧⡼⠀⡼⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⡏⠀⠀⠐⣤⣼⣿⣿⡿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣻⣿⣷⠀⠀⣰⠉⠘⠋⠉⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣰⠋⠀⣠⣶⣲⣿⣿⣿⣿⣿⣾⠋⣿⠀⠀⡄⠃⠀⠀⠀⡄⠀⢀⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣷⣇⣼⣿⢀⣾⣿⣿⣿⡯⠿⣀⣨⣿⣧⣾⡿⡇⠘⡇⠀⣀⢢⡠⢀⣤⢿⣿⡹⡄
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠠⠀⠀⠉⠉⠁⠀⠀⡀⠀⠙⣄⠈⣆⠃⡾⠁⠀⠉⣷⠇
⠀⠀⠀⠀⣠⡾⣿⡿⢿⣿⣿⣿⣿⣴⣷⣾⣿⢻⣿⡗⣿⠀⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢶⣯⠴⠃⠀⠀⠀⣹
⠀⠀⠀⢰⣟⠀⠙⢿⣿⣿⣿⣿⠿⢿⠋⣴⠟⢸⣿⣿⠍⠳⡌⢦⣴⣤⣶⣤⣤⡀⠀⢨⠀⠀⢇⠀⠀⠖⠀⠁⢸
⠀⠀⠀⢸⣷⣀⣴⣾⣿⣿⣀⣀⣹⣾⠓⠀⢠⠃⢿⣿⡤⠶⠟⠘⠡⣀⡀⠸⡁⠀⠀⣸⡄⠤⠀⣷⣶⡇⠄⢀⣼
⠀⠀⠀⠀⡛⠛⣿⣿⣿⣉⣿⣭⣩⣤⣾⡜⠛⠷⠤⠼⠿⠿⠧⠤⠄⠉⠉⠉⠛⠒⠒⠛⠓⠂⠚⠋⠛⠓⠂⠚⠛⠁
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢛⡦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣠⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⣯⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣠⡇⣿⣷⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⠉⠉⠉⢉⢁⡿⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠠⢀⠀⠄⠀⠀⢀⠄⢹
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⣿⡿⠂⠀⠀⠂⠀⠈⢢
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣤⣤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠛⠋⠜⠉⠁⠀⠀⠀⠂⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠳⠤⣀⣀⡀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⡀⠀⢀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢀⠀⠀⠐⠀⠘⠀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣠⠀⡀⠀⢵⠆⠀⡀⠀⠐⠀⠀⠀⠐⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣺⠉⠈⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠠⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⡀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡟⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⣶⡄⢠⡀⢣⠀⠀⠀⠀⠀⠀⠠⠐⠀⢀⠀⠀⠀⠀⠀⠀⣾⣱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢕⢄⣌⣠⢪⣔⣻⣄⣧⣤⡅⢄⠀⠀⠀⢄⡤⠦⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇
⠀⣠⠆⠴⠄⠠⢦⣤⢾⠿⠿⡿⡿⣿⣿⡦⣤⡶⣢⣴⣧⣴⣋⣼⣟⣴⣿⣗⣦⣤⣴⢶⣿⣿⣾⣫⢞⣁⠔⠤⠦⠤⡎⠁⠠⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠐⠀⠀⠼⠉⠉⠋⠙⠛⠛⠉⠋⠁⠻⠉⠉⢀⡙⠈⠉⠁⠘⠀⠉⠉⠚⠉⠈⠁⠀⠀⠁⠀⠀⠀⠀⠁
⣿⣿⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡄⠀⠀⠀⠘⣽⣄⣤⣤⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣨⣼⠤⠀⠋⡟⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⢀⣄⣀⠀⠀⠀⢦⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⡿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠐⣴⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣆⢀⣰⣧⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠈⠁⠀⠤⠀⠄⠀⠀⠇⠀⢠⡄⠀⠂⠀⠀⠀⢀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠐⠀⠀⠀⠀⠀⠀⣠⠀⠈⠀⠄⠀⠠⠄⢠⠊⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⣦⣌⣀⣀⣀⣀⣥⢆⣷⡀⢀⣀⣀⣠⡇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢉⠂⣹⠋⠈⠁⠈⠻⢫⠉⠉⠉⠉⣽⢿⠟⠛⠂⠀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠁⢠⠋⣴⢀⢠⠀⠀⠀⠀⠀⠛⠣⠾⠤⠠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿