Planeta Emojis & Symbols

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠖⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢀⡿⠟⣛⠛⠋⢁⠰⡄⠀⠀⠀⣼⡋⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠠⠶⣤⠤⢶⡆⡀
⠀⠀⠀⠀⣴⢶⣾⣿⠀⠀⠀⠸⠂⠀⠀⠀⠀⢿⣟⡃⢀⠀⠀⠐⠀⠀⠀⠀⠸⣿⣿⣿⣷⠞⠀⠀⠀⠀⠀⠀⠸⢒⣖⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠉⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⡀
⠀⠀⠀⠀⠀⢠⣶⣿⠋⠁⠲⠀⠀⠀⠀⠀⠀⣴⣾⣿⠋⠁⠠⡀⠀⠀⠀⠀⠀⣴⡿⢋⣉⣉⣤⣤⡀⠀⠀⠀⢠⣾⡿⠁⠀⢀
⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⢀⡇⠀⠀⠀⠀⢸⣿⠿⠏⠀⠀⠀⠗⠀⠀⠀⠀⣠⣿⣿⠉⠁⠀⠀⡾⠁⠀⠀⠀⠸⣿⣿⡐⠙⡁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⠟⠁⠀⠀⠀⠀⠀⠻⣥⣾⣤⣀⠀⠁⠀⠀⠀⠘⠷⠿⠿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⢶⣿⡶⠂⣀⠀⠀⠀⠀⠠⠦⣶⠀⣴⣶⣶⠆⠀⠀⠀⠀⠀⠀⢀⡾⠛⣉⣝⢿⠇⠀⠀⠀⢀⣴⡾⠏⠐
⠀⠀⠀⠀⠀⢠⣛⣻⡟⠐⠈⡁⠀⠀⠀⠀⠀⣶⠂⠀⡈⢠⣤⡀⠀⠀⠀⠀⠀⠀⠋⢠⡞⢁⣽⠏⠀⠀⠀⠀⢾⣿⡟⢁⠈⠀⠂
⠀⠀⠀⠀⠀⠈⠿⣿⡝⣛⡉⠀⠀⠀⠀⠀⢠⡿⠄⠠⠏⡀⠉⢿⡄⠀⠀⠀⠀⠀⣠⣟⣻⡯⠴⠃⠀⠀⠀⠀⠘⢿⣿⣶⣧⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠛⠛⠛⠛⢻⡿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⠁⠀⢀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣜⣿⠿⠟⠋⠁⠀⢀⣠⣴⠶⢋⣁⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢺⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠿⠛⠉⠁⠀⢀⣠⣴⠖⠛⣉⣤⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣾⣦⣤⡴⠷⠛⠉⠁⠀⠀⢀⣠⡴⠞⠛⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⢹⣿⠿⠟⠛⠉⠀⠀⠀⣀⣠⣤⠖⠚⢉⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠒⠋⢉⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣁⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠋⠑⣶⣶⠀⠀⠈⠀⠀⣀⣴⣆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡽⠃⠀⡼⠛⠃⠀⠀⠀⢀⣬⣽⣿⣍⣉⣀⠛⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⣾⠇⣶⠃⠀⠀⠀⠀⠀⢸⣮⣿⣿⡿⢾⣿⣿⣿⣿⣿⣦⣌⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣯⣿⡷⠃⠀⠀⠀⢀⣀⣴⣿⡟⢻⢝⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣨⣼⣿⣿⡟⠃⠀⠀⠀⠀⣰⣾⣿⣿⡏⢻⣠⣈⠾⠂⠄⣸⣿⣿⣿⣿⣿⣿⡟⠶
⠀⠀⠀⠀⠀⠀⣸⡿⠛⢻⠇⠀⠀⠀⠀⠀⡾⠿⣟⣻⣏⠡⠄⠠⠍⠀⠀⢤⣸⣿⣿⣿⣿⣿⣿⣿⣦⡁
⠀⠀⠀⠀⠀⢠⣿⡤⠄⠂⠀⠀⠀⠀⠀⠀⠳⣤⣤⣌⣈⡁⣀⣈⣀⡄⣁⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢘⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡴⡇⢨⠕⠂⢻⣿⣿⣿⢿⣿⣿⢃⡆
⠀⠀⠀⠀⠀⢰⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣿⠄⠀⠀⢹⡷⠀⢸⣿⠇⠈⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣟⢷⠆⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⠻⣅⠀⠀⠀⢸⠇⠀⠀⣿⡇⢠
⠀⠀⠀⠀⠀⠀⢿⣿⡯⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡟⡳⠃⠀⠀⣀⠀⠀⠀⠀⠈⢀⡌
⠀⠀⠀⠀⠀⠀⠈⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡞⠁⠀⠀⠀⠏⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢂⠈⠍⠉⠒⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣉⠀⠀⠀⠈⠀⠀⠈⠉⢀⠀⠀⠈⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠠⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠒⠆⠀⠀⠑⡄
⠀⢀⣀⠠⠤⠤⠤⠤⠀⢀⣀⣀⣀⠎⠀⠀⠀⠀⢀⣀⡀⠀⣀⡀⠀⠀⠀⠄⠀⠀⠐⠂⠀⠁⠘⡄
⠀⢇⠀⠀⣎⠉⠉⠉⠁⠈⠐⠒⡎⢀⡀⠁⠀⠀⠀⢰⢪⣶⠄⠠⠤⠄⢴⣮⢲⠄⠐⠀⠀⠁⠀⢘⡀
⠀⠈⠓⢄⠈⠑⠤⣀⠀⠀⠀⢰⠃⠐⠀⠄⠀⠀⢀⡈⠓⠋⠀⢀⢀⠀⠈⠓⠋⢀⠀⠠⠐⢀⡁⠀⣇
⠀⠀⠀⠀⠉⠒⠤⣀⠉⠒⠤⣸⠁⠈⠀⠐⠀⠀⠀⠐⠈⠀⠀⠀⠁⠀⠉⠀⠀⠂⠀⠁⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠈⠑⠲⠦⣄⡀⠀⠀⠀⢀⠤⠄⠀⠀⠀⡀⠄⠀⠐⢀⣁⠀⠀⢀⡷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠑⠢⠤⣀⡈⠉⠛⠠⠤⣀⡀⠀⠀⠈⠀⠀⠁⡀⠀⠀⠀⠀⠰⠉⠑⠪⢕⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠐⠒⠀⠈⠙⠒⠠⢤⣀⡈⠉⠙⠚⠥⠄⣀⡀⠀⠈⠁⡰⠁⠀⠀⠀⠀⠈⠑⠪⣑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⣀⠈⠁⡀⠀⠤⠉⠒⠒⠠⠤⢄⣀⡉⠉⠛⠓⠠⠤⠤⠄⣀⣀⣀⣀⣈⠇⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠠⠀⣉⡁⠉⠀⢀⡠⠛⠉⠉⠒⠒⠒⠠⠤⠤⠤⠤⠠⠤⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠀⠤⠤⠄⠐⠒⠉⠁

⠀⠀⡠⠒⠈⠉⠉⠀⠐⠄⡀⠀⠀⠀⠀⠀⢀⠄⠂⠊⠉⠉⠐⠒⢄⠀⠀⠀⠀⠀⠀⡠⠔⠀⠈⠉⠁⠀⠠⢀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠉⠉⠁⠐⠤⡀
⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⣠⠃⠀⠀⠐⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁
⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢐⠜⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠐⠂⠤⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠤⠤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠤⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠤⠤⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⠤⠐⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠐⠦⣔⡬⠔⠒⢳⢀⠀⠀⠀⠠⠀⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⢀
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠠⠁⠀⠀⡠⣐⠵⠋⠁⠓⡀⣠⠯⠂⢀⠔⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⡐⠊⠀⠀⠀⠀⠀⠀⠈⠢
⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠁⢀⢔⡡⠚⠁⠀⠀⠀⠀⢸⠕⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣖⡵⠋⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀
⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⡡⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠂⠄⣀⡀⣀⠠⠔⠊⠀⠀⠈⡞⠁⠀⣰⠦⣀⡀⠀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⢀⡠⠐⠁⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠠⢄⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡤⠀⠤⠉⠠⠀⠀⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⡁⠀⠀⠀⢻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣴⣶⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠙⠀⠀⠸⠆⠰⠀⠀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠐⠀⢠⣶
⠀⠀⣴⣶⣲⣦⠀⠀⠀⠂⠀⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠓⠂
⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠴⠒⠒⠀⠀⠀⢰⠛⠋⢲⠄
⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠂⠀⠀⢀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢿⠀⠀⠛
⠀⠀⢰⣦⣙⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀
⠀⠀⠳⠭⣭⣭⠇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠽⠃
⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⡇⠀⠀⢀⠴⣿⣛⣹⣬⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠉⠉⠁⠈⠉⠉
⠀⠀⢠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣺⡿⢶⣄
⠀⠀⠙⠉⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣡⣴⠿⢻⡇
⠀⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣥⣼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠤⢄⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⡓⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢰⠀⠀⡀⢤⠀⠀⢈⣿⣠⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⠴⠊⠠⠐⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⡞⢀⠈⠀⢀⠄⡠⢪⠃⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠀⠀⠀⠀⠀⠀⠐⢺⡏⠙⠓
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⠂⠃⠀⠀⣀⣴⣪⡾⠃⣼⡟⠀⠀⠀⠀⠀⠤⠂⢹⡥⠴⢂⣠⠔⠀⠀⠀⠡⠀⠋⠀⡐
⠀⠀⠀⠀⠀⠀⢸⡀⠨⠦⡤⠴⢖⡛⣉⣵⠞⠀⣼⠟⢁⠀⠀⠀⠀⠀⠄⢀⡀⠛⣀⣠⣄⠄⠠⠄⠐⣠⠏
⠀⠀⠀⠀⠀⢘⠎⠑⢦⣰⠔⣚⣿⣽⠟⠁⢀⠞⡥⣦⣍⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠛⠲⠶⠶⠖⠛⠅
⠀⠀⠀⠀⠀⢼⠀⡤⡀⠀⢉⠙⠋⠀⠀⡠⠃⠐⡀⣹⡽⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠅
⠀⠀⠀⠀⠀⠈⠂⠈⠓⠈⠀⠀⠀⣠⠎⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠈⠑⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣀⣄⠠⢀⠀⠌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡤⠀⠀⠀⠀⠅⠀⠈⠆⠈⠅
⠀⠀⠀⠀⠀⠀⠀⢀⣆⣹⡀⠀⠀⠀⠾⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢰⠄⠀⢀⡄⣀⡀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠰⠄⠘⡛⣖⠃⠀⣀⠈⢀⣀⠀⠰⣉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠇⠘⠛⢩⡁⠀⣠⢴⣸⣽⠃
⠀⠀⠀⠀⠀⢠⡀⠈⠉⡉⠙⠛⣩⠁⢠⣀⠂⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡉⠀⠘⠂⠐⠀⢈⠞⠁
⠀⠀⠀⠀⠀⠀⢠⡔⠈⠀⠀⠀⢘⡄⠄⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣦⣀⠀⢀⣤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠒⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣆⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢄⠀⠀⠈⠂⠀⠀⢠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠀⠀⠂⠀⠂⠁⠘⠀⠀⠀⠀⠀⠀⣀⠘⠂⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢐⠀⠀⡂⠀⠹⠂⢄⠌⠀⠄⡀⡀⢼⠀⠀⠀⠀⠀⠀⢵⣀⣣⣀⣠⣒⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠃⡀⠀⠐⢸⠁⠀⠃⠀⠀⠈⣡⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠑⠤⣤⡚⠀⠂⠒⣄⡴⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠶⠞⠛⠛⠛⠛⠛⢛⣷⣶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⣈⣽⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣠⡶⠛⢉⣠⣤⠶⠿⠻⣦⣄
⠀⠀⠀⠀⢀⣴⢟⡁⣤⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⠞⢉⣴⠞⠋⠁⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⣰⡟⠁⣿⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⣠⡾⢃⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣆
⠀⠀⣰⠏⠀⠀⠁⠀⠀⣀⣤⡴⠶⠞⠛⠛⠋⠉⠀⣠⡾⠋⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠹⣦
⠀⣰⠏⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⢀⣴⠟⠀⠀⠀⠀⣀⣤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠸⣆
⢀⡟⠀⣠⡾⠋⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⣛⣡⣤⠶⠛⠁⠀⠀⢀⡴⠛⠉⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⢀⡾⢻
⣸⣡⡾⠁⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⣴⠟⠉⠁⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢀⣤⠾⠋⠁⢈⡿⠀⠀⢠⡿⠁
⣿⠋⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣠⠟⠁⠀⠀⣠⡞⠁⠀⣠⠟⠀⠀⣠
⡇⠀⠀⢀⣀⣠⣤⣤⠾⠋⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢰⡏⠀⢀⣤⠾⠋⠀⢀⣴⠋⠀⠀⣴⠏
⣷⣠⡾⠋⢉⣠⣤⣤⣄⣀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠘⠓⠛⠋⠁⠀⠀⣠⠞⠁⠀⢀⡾⠃⢀
⢻⠋⠀⣰⠟⠁⠀⠀⠈⠉⠛⠷⠶⠋⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣴⠏⠀⢠⡟
⠘⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⢀⣴⠟⠁⢀⣴⠏⢰
⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⣠⡶⠋⠁⢀⣴⠟⠁⢠⡟
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠉⢀⣠⡴⠟⠉⢀⣠⡶⠛⠁⠀⢠⡾
⠀⠀⠀⠻⣆⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠛⠉⣀⣤⠶⠞⠋⢁⣠⣤⠾⠛⠁⢀⠀⠀⣠⡟
⠀⠀⠀⠀⠙⢷⣄⠀⣰⠏⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⢀⣴⠟⠉⠀⣠⡴⠾⠛⠉⢀⡄⣰⠇⡾⢁⣾⠋
⠀⠀⠀⠀⠀⠀⠙⢷⣏⠀⠀⠀⣴⠋⠀⠀⠀⠀⢀⣴⠋⠀⣀⡴⠟⠉⠀⠀⠀⠀⠾⠁⠈⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣼⡃⠀⠀⠀⠀⣠⡟⠁⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣴⣏⣀⣀⣸⣇⣀⣀⣠⣤⣤⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢀⡀
⠀⠀⠀⠀⠀⢀⠚⠀⠀⡉⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⠀⠉⣂
⠀⠀⠀⠀⠀⢘⠀⠀⠙⠇⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠁⢨
⠀⠀⠀⠀⠀⠀⠢⣀⠀⢀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠈⣀⡀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣤⣀⣤⡤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢
⠀⠀⠀⠀⠀⠀⡔⠊⠁⠈⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠃⠈⠁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠭⠀⠉⠲⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡤⠀⣀⣀⢸
⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣈⡂⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠁⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠗⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡠⢀⡂⢀⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⡀⢠⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠐⠽⠞⠀⠀⠀⠀⠱⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⡀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠸⢨⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⣇⡀⠀⡀⠄⠀⢨⡉⠆
⠀⠀⠀⠀⠀⠣⡳⡀⠀⠀⣰⣭⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠚⠉⠒⠈⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠄⠂⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⠄⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠒⠢⢄⠘⠚
⠀⠀⠀⠀⠀⢀⠃⠀⢀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡋⠀⠀⠀⠀⡸⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠒⢄⣠⠒⠉⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠘⠢⠀⠄⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠓⠎⣀⣀⡱⠚⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠈⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡰⠊⠁⠀⠈⠓⢄⡄
⠀⠀⠀⠀⠠⣲⣇⡀⠀⠀⠀⣀⣸⣖⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣰⣀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠱⡉⠈⠉⠉⢁⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⠑⠦⢤⢜⣢
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⡀⠀⠀⠀⠲⡂⠀⠀⠀⠀⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠃⠐⠀⠀⡀⢄⠀⢀⠫⠷⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡤⡊⡱⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠈⢱⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡴⠃⣽⢚⠕⠎⠁⠀⠂⠰⠂⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠈⠣⢑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⡄⠀⠘⠃⠀⠀⠀⢀⠀⠀⠀⠈⠌⠄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡴⣖⠵⠚⣦⠦⡄⠀⡄⠛⠻⡄⠈⠄⢢⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠘⡀
⠀⠀⠀⠀⠀⠀⠐⠀⢈⡟⡡⠠⡄⠈⠋⣾⠻⣉⣌⡉⠀⠀⠘⠤⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⢁
⠀⠀⠀⠀⠀⠃⠀⠰⠇⠀⠀⠈⠣⢄⣠⢀⠀⢀⢀⠇⠀⠀⠀⣀⢀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⠑⢦⡄⠁⢨
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⢦⡀⠀⠀⢀⣉⡛⠇⡉⠉⠙⠧⣆⠀⢀⠀⠀⠀⠘⡉⡀
⠀⠀⠀⠀⠀⠄⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠱⣄⠀⠀⠀⠀⢀⠃⠀⠀⠀⠈⢻⠈⠀⠀⠀⢀⣙⢹
⠀⠀⠀⠀⠀⢀⠹⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⢷⣀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠉⡏
⠀⠀⠀⠀⠀⠈⠀⠹⣷⣤⡤⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠩⠐⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠙⢻⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡈⠀⠀⠀⠀⠊⢁⠀⢁⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡱⣄⠈⠻⣆⣀⠀⠀⠀⠀⣤⠅⠀⡀⠁⠀⠀⠄⠀⠂⣉⠀⠐⠁⠀⠠⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣬⡢⠀⠹⣷⡆⠀⠀⠐⠄⣀⠸⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠂⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠻⣧⢄⠀⠀⠀⠘⢀⠜⠀⡄⠈⠀⠀⠀⠄⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠿⣷⣤⣤⣠⡇⠐⠀⠛⠀⣀⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠠⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠉⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⢀⡤⢀⠀⠀⠀⠀⠀⠀⠱⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠤⢀⠀⠀⠛⠁⠄⠀⠀⠀⠀⠸⠋⠠⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⡼⠁⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢇⠀⢀⠀⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠒⠁⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡇⢀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠉⠀⢀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⢀⠤⢇⠠⡀⡸⠀⠀⠀⠢⠂⠀⠀⠀⠀⣀⡠⠤⠒⠊⠉⠀⣀⡠⠤⠒⠉⡹
⠀⠀⠀⠀⢀⠴⠊⠁⠀⢠⠞⠁⠀⠘⡄⠀⠀⠀⣀⣀⡤⠤⠒⠒⠊⠉⠀⣀⣠⠤⠒⠒⠉⠀⠀⠀⠀⢠⠃
⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠑⠒⠒⠀⠉⠉⠉⠁⠀⢀⣀⠠⠤⠔⠒⢏⣉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠑⠤⢀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠄⠒⠲⡉⠉⠁⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⡀⡀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣐⠠⠤⠂⠀⠀⠁⠀⠀⠀⠀⣃⡤⠚⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠀⠤⠤⠀⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⣡⡿⠒⣩⠖⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠛⡛⠉⠙⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⠶⠛⣁⢴⡺⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⣤⠶⠶⠶⠖⠒⠲⠆
⠀⠀⠀⠀⠀⠀⢀⠔⢃⣠⣔⡯⠗⣫⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⡠⠁
⠀⠀⠀⠀⠀⠰⠗⠚⠉⠉⠓⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠷⡦⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢐⣶⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠊⠊⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⢰⣾⣹⣗⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠂⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢋⡀⠈⢻⠿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣠⣷⣤⣫⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⠀⠁⠀⠁⠉⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠩⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⡃⠀⠀⠀⠀⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠁⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠐⠀⠂⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠒⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠂⣄⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⣔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠈⠁⠀⠻⢿⣆⠀⠀⠀⠀⠀⠀⢻⠽⣷⡄⠀⠀⠀⡴⠿⠮⡈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠿⣿⣦
⠀⠰⠅⢀⡀⢀⡈⢸⣿⡆⠀⠀⠀⠀⢠⢸⢀⣽⣿⠀⠀⢸⣄⡀⠀⢈⣿⣿⣷⠀⠀⠀⠠⣄⣤⣤⣼⣿⡇
⠀⠀⠀⡀⠀⠀⢘⣾⡿⠀⠀⠀⠀⠀⠀⢴⣿⣿⡟⠀⠀⠀⠹⣿⠀⣾⣿⣿⠇⠀⠀⠀⠀⡒⠦⡿⣺⡿⠃
⠀⠀⠀⠐⠐⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠙⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠶⠦⣄⠀⠀⠀⠀⠀⡴⠖⡶⣦⣤⠴⣶⠀⠀⠀⠀⠂⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠒⣤⡀
⠀⠀⠀⢀⣤⣤⣬⣭⣷⡀⠀⠀⠀⠀⠀⢈⣴⣿⡷⠋⠀⠀⠀⠀⠀⠀⠠⣿⣆⠀⠀⠀⠀⠀⠀⢀⣨⣿⡄
⠀⠀⠀⠴⢶⣦⢶⣶⣾⠃⠀⡀⠀⠀⠀⠩⠞⣡⡾⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⢀⣀⣀⣿⡇
⠀⠀⠀⠀⢀⣠⣤⡼⠋⠀⠀⠀⠀⢀⣤⣶⣾⠟⠁⠀⠀⠀⠀⠀⢀⣠⣿⠟⠁⠀⠀⠀⠀⠀⢉⣽⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠔⠀⠀⠀⠒⠴⣂⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⢉⠩⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢈⠀⣰⠖⠆⠀⢀⣾⢱⠀⠀⠀⠀⠀⠀⠀⣼⠇⠠⠜⡡⠐⠈⠀⢈⣧⣄⣀
⠀⠀⠀⠀⠀⠀⡜⠀⢀⡆⡷⠖⠊⠀⢀⠕⣪⢂⣾⠀⠀⠀⠀⠀⠀⣀⣧⠀⣀⠀⢀⡀⠀⠠⠅⢹⡅⠀⠁
⠀⠀⠀⠀⠀⠀⡇⠠⠄⠀⣀⣀⣤⠖⢛⡞⠁⣾⠏⠀⠀⠀⠀⠀⠉⠀⢻⡍⠁⠒⠋⠀⠀⢁⢨⡤⠄⠐⠂
⠀⠀⠀⠀⠀⢤⠷⣌⣩⣙⡥⣼⣶⡾⠋⢀⠾⣉⡰⠆⠀⠀⠀⠀⠉⠑⠀⠐⠶⣭⣋⣬⣥⠴⡋
⠀⠀⠀⠀⠀⡇⢀⡈⠙⠓⠾⠟⠉⠀⠠⠋⠌⠹⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⢐⠰⠈⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠃⠈⠃⠀⠈⠀⠀⢠⠔⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠑⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠆⢤⣦⡅⠠⢀⠊⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠴⠒⠀⠀⠁⠚⠀⠐⠂⠀⠂
⠀⠀⠀⠀⠀⠀⢠⣿⣼⡗⠂⠀⣠⠛⠓⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⡆⢀⠗⣦⣠⡖⠠⠖⠂⣤⢴⡃
⠀⠀⠀⠀⠀⠉⠨⣯⠽⢅⣤⠴⠄⠒⢒⠨⠱⠆⠀⠀⠀⠀⠀⠀⠀⠘⡎⠠⠅⠙⡇⢀⠒⠋⣾⠏
⠀⠀⠀⠀⠀⢊⠀⢀⠒⠀⢀⡲⠀⠃⠂⠠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠱⢜⣀⡄⠑⢘⠉⣁⣄⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠠⠄⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠠⠀⠂⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡉⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠄⡀⠀⠘⠒⠀⠀⡜⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣧⠠⠔⠊
⠀⠀⠀⠀⠀⡂⠀⠀⠈⣀⡑⠀⠀⠃⠀⠁⠀⠃⠀⠀⠀⠀⠀⡤⠸⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢇⠠⠆⡀⢘⡇⠢⠈⠐⠄⣠⡐⠇⠀⠀⠀⠀⠈⠻⢤⣧⣤⣮⣽⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⢤⠁⠈⢸⠅⠀⡁⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠤⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠭⣠⣀⠩⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡟⠁⠘⠗⠐⣲⣧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠛⠙⠉⠀⠀⠀⠀⣴⠿⠁⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⣛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⡀⢴⠃⠀⠀⠀⠀⠀⠀⠈⠁⢠⡾⣡
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠃⠀⣠⢏⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠁⠀⠀⠐⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣶⠔⠀⢀⣴⣶⠖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢞⡼⠻⠋⣰⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢈⣀⣠⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠴⠋⠀⢀⣴⡷⠟⠀⢀⣹⡿⠟⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⢀⡴⣭⠟⠀⠀⢀⡜⠋⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠹⣿⢄⡀⠀⠀⢀⣤⣶⡟⢁⣀⡴⣫⡾⠁⠀⢀⡴⠏⠁⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠸⣿⣿⣶⣿⣿⣿⣃⣼⡿⣫⣾⠟⠀⢀⣤⠞⠁⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣾⠟⣫⣾⣿⣡⣴⣶⡟⠁⢀⣠⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠿⠿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠑⠂⠐⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠒⠸⢿⣷⣶⣦⣄⡀⠀⢀⣠⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠶⠋⠀⠀⠀⣺⠟⣩⣿⣿⣿⣿⣟⠛⠛⠻⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢁⣾⠋⠁⢘⣿⣿⣿⣧⡀⣰⢇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠋⠀⠐⠉⠁⠀⣰⣿⣿⣿⣿⣿⡷⣫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⣾⠿⣋⣿⣿⡿⢋⠜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⢁⣴⣿⡿⣋⠔⣡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠤⠊⠁⠀⠀⣾⡿⠟⡡⢊⣥⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⣡⠔⣉⣴⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢒⣩⣖⣤⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⢤⣀⣀⣠⡬⠥⠖⣚⣩⣴⣾⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠈⠀⠃⠈⠃⠈




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⡿⠿⢿⠛⠿⣿⣿⣷⡶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⢿⣃⡾⠀⡐⠌⠐⠋⠈⠀⠙⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⢛⡛⣉⣉⣁⣄⣀⣤⣀⣀⣀⣀⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⢻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣬⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠛⠛⠃⠒⠟⠛⠹⠟⠟⠻⠿⠟⠻⠟⠻⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠹⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡤⣤⣤⣤⣄⠀⠀⠀⠀⢀⢛⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠝⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⣿⣿⣿⣿⣷⣾⣿⣿⣧⡄⠀⠀⡤⢈⢩⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣉⠛⠂⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⢎⣉⣉⡿⠿⠷⠾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣘⣛⣿⣷⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡠⡀⣀⢀⣤⢀⣄⡄⣠⠾⠆⠤⠐⠐⠒⠊⠁⠆⠀⠀⠀⠉⠛⡿⠉⠋⢭⣿⣿⣧⣍⢋⡉⠹⣿⣿⣷⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⠟⠙⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠈⠙⠧⡄⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣾⣿⣿⣭⣤⣴⣤⣶⣶⣶⣶⣶⣾⣷⣶⣪⣴⣶⣶⣆⠴⣦⡶⣦⣤⣄⣀⣐⣠⣤⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠋⣨⣴⣿⣿⣿⣿⣿⣿⠿⡛⠛⠙⠉⠋⠉⠉⠉⠉⠛⠉⠀⠁⠀⠘⠻⠻⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣡⢀⣂⣤⣠⣤⣴⣶⣶⣶⣤⣤⣴⣤⣀⣀⠀⠀⠀⠀⣹⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣹⢻⣿⣿⣷⣾⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⠏⢛⣿⣛⡛⠻⠙⢟⢿⣿⣿⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣽⣀⡆⠠⠦⡌⠠⡝⢛⡚⢢⣮⣾⣿⣿⣟⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣶⣥⣶⣷⣿⣿⣷⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣠⡴⠶⣚⣛⠋⣁⠐⢢⢱⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠁⠲⣿⠿⠿⠛⠋⠁⢠⠈⣆⠀⣬⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⢜⡜⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⢿⣿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⡅
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠉⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠋⠁⠀⠐
⠀⠀⠀⠀⢀⡴⣫⣾⠟⠁⠀⠀⠈⢀⠀⠀⣀⣠⣴⣾⡿⠛⠉⠀⠀⠀⠀⠐⠁
⠀⠀⢀⡴⡁⠀⡍⠸⣀⣀⠀⣀⣤⣴⣷⣿⡿⠛⠉⠁⠀⠀⠀⠀⢀⠄⠊
⠀⠠⢱⠰⡀⠐⠀⠒⣒⣒⣭⠿⠟⠛⠉⠀⠀⠁⠀⠐⠒⠂⠀⠈
⠀⠐⠠⠅⠤⠉⠟⠛⠉⠉

⠀⠀⠀⢀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣀⡴⣔⡁⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⢃⠀⠀⠄⠀⢀⠠⠀⠀⠀⠀⠀⠀⠔⠖⠚⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⡀⠂⠃⠀⠀⠁⢢⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢐
⢀⠑⠚⠰⠦⠖⠁⠲⡤⢮⡆⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⢀⠰⣠⠃
⠘⠈⠰⠐⠠⢀⠠⢶⠄⠄⠋⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡉⠰⠂⠂⠈⠒⠀⡈
⠸⡷⠄⠄⠀⠀⢲⣦⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⠀⡄⠊⠠⠔⠁
⠀⠘⢤⡠⠔⠂⠀⢤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⡄⠒⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠖⠀⠀⠀⠂⡀⢀⠱⡄⠒⠄⠤⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⠀⠁⠀⡠⠏⠀⠒⠀⠈⡠⣜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡤⠔⠀⠡
⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠁⣐⢠⠀⠠⣅⣉⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀
⢀⠀⠀⠄⠀⠀⠀⠉⠉⠉⠀⠃⠀⠀⠀⠀⠉⠔⠆⠀⠘⠄⠀⠈⣁⠋⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠔⠃
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠴⢋⠁⣤⣤⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⣠⡖⢋⡧⢸⠁⠈⠙⠲⡄⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⢈⡠⢋⠝⢦⡀
⠀⠀⠀⠀⠀⢰⠏⢂⡈⠀⢨⠁⡀⠘⠃⡈⣧⠀⠀⠀⠀⢰⠇⠀⠂⠠⣄⠉⡉⢉⣉⡹⡆⠀⠀⠀⠀⡼⢃⠄⠂⡀⠤⠤⠊⡠⠊⢹⡄
⠀⠀⠀⠀⠀⢾⠀⢅⡨⠀⢀⠤⡄⠻⠃⠀⢸⠀⠀⠀⠀⣿⠤⠤⠄⠒⠃⠘⠋⠘⠒⠂⣻⠀⠀⠀⠀⣟⣁⠄⢊⡀⠄⢂⡡⠔⢊⢵⡇
⠀⠀⠀⠀⠀⠸⡆⡀⡄⠀⠘⠶⠋⠀⠤⢀⡞⠀⠀⠀⠀⠸⡦⠴⠀⠚⠀⠫⠭⠥⠤⢠⡏⠀⠀⠀⠀⢳⡦⢊⠅⠂⠉⠐⠒⡈⠐⣹⠇
⠀⠀⠀⠀⠀⠀⠙⢮⡁⠀⠁⠀⠤⢀⣠⠞⠀⠀⠀⠀⠀⠀⠙⢮⣭⠭⠥⠤⠶⢐⡶⠋⠀⠀⠀⠀⠀⠀⠻⢵⣨⠔⡂⠉⠍⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⢞⡉⠒⠀⠤⠤⠬⠓⢦⠀⠰⠁⠄⡐⢉⣻⣟⣉⠁⠀⠂⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⡴⠋⣡⠀⠄⣒⡢⠉⠳⣄
⠀⠀⠀⠀⠀⢰⡇⠀⠉⠒⠤⢀⣀⣐⠍⣈⣧⠈⢄⠡⠑⢄⠑⢬⣉⣉⣉⣉⣉⣉⠉⠼⣇⠀⠀⠀⠀⡼⢱⠄⠀⢀⠂⠁⠑⠈⠛⠹⡆
⠀⠀⠀⠀⠀⢸⠉⣑⡒⠀⠤⠤⠤⠤⠤⠀⢾⠀⠀⠑⢄⠙⠟⠢⣄⠀⠲⠄⡀⠰⠐⠒⣿⣷⣄⠀⠀⡇⠀⠠⡠⠌⠀⠀⠂⠘⢃⠀⡇
⠀⠀⠀⠀⠀⠘⣆⠓⡁⠄⠀⠀⠀⢀⡀⢰⡏⠀⠀⠀⠀⠹⡶⢌⡁⠸⠃⡀⠠⠉⡉⠀⠛⢀⠙⠱⡄⢱⡀⡑⠉⠂⠀⠰⣂⢠⠈⣰⠃
⠀⠀⠀⠀⠀⠀⠈⠣⣄⠐⠀⠀⠐⣢⡵⠋⠀⠀⠀⠀⠀⠀⠈⠶⣌⡳⠶⣤⣁⣀⠀⠛⠁⠀⠈⢀⠄⠀⠙⢦⣀⠐⠀⠈⢀⣨⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠁⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⢤⣤⣀
⠀⠀⠀⠀⠀⠀⣰⠊⠀⠈⠉⡝⠀⢀⡟⢦⡀⠀⠀⠀⠀⠀⡰⠛⠡⠡⠈⢈⡤⠸⢛⢦⠀⠀⠀⠀⠀⢀⡴⠯⠥⠬⠥⠤⠔⢋⠷⣄
⠀⠀⠀⠀⠀⢰⢣⠀⢤⠐⠁⠀⢀⡬⠛⠼⣷⠀⠀⠀⠀⢸⠃⡀⠰⡅⠴⢀⣀⢣⠱⠬⣇⠀⠀⠀⠀⡾⠬⣉⣑⠒⠀⠒⢊⣁⣠⢼⡆
⠀⠀⠀⠀⠀⢸⠀⠁⢰⠉⠉⠲⡌⠒⢦⠀⢸⠀⠀⠀⠀⢟⠢⡍⠀⡊⠉⠁⢎⠘⠲⢒⡿⠀⠀⠀⠀⡯⢑⣒⠂⢀⣩⡽⠴⢒⡪⠭⡟
⠀⠀⠀⠀⠀⠘⣆⠀⠀⢡⠀⡰⠁⠀⠘⣠⠏⠀⠀⠀⠀⠸⣆⠃⠈⢀⠆⢀⠀⠉⠉⣴⠃⠀⠀⠀⠀⠹⣆⢀⠀⠉⠁⣒⡒⠉⠀⣺⠃
⠀⠀⠀⠀⠀⠀⠈⠳⢤⣘⡘⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠈⠣⣤⣀⡠⣈⣳⡽⠞⠁⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⣠⡬⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣖⣯⣼⣟⢲⣦⣽⣤⡀⢠⠀⠀⠈⠀⣠⣦⡙⣅⠀⠙⠷⣦⡀⠀⠀⠀⠀⣠⡴⠖⣲⢤⡀
⠀⠀⠀⠀⣰⣶⣯⡿⣿⣿⣿⣿⣿⣿⣦⣼⣿⡌⠄⣄⠀⠐⢅⠀⠑⢤⡐⢄⡀⠈⢑⡀⠀⠀⠐⠋⡀⠈⢁⣼⣿⡀
⠀⠀⠀⠀⣿⢄⣽⣷⡌⠻⠿⢿⣿⠭⣭⣁⣿⣷⡠⠏⠀⠀⠀⠑⢄⠀⠉⠲⢌⡑⠺⡇⠀⠀⠘⣁⠀⣠⠔⡻⣿⠁
⠀⠀⢀⣈⡟⢻⡿⣛⣿⣿⣷⣾⣧⡴⣿⣿⡟⡿⠃⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⣨⡿⠀⠀⠀⠀⠈⠛⠿⠷⠚⠁
⠀⢠⡼⢃⣀⣘⣿⡏⠙⣋⠈⠛⢋⡄⠈⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠵⠈
⠀⠀⠈⠑⠻⢏⠙⣻⣿⣧⣦⣿⣼⡳⢾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠉⠉⢉⡿⠿⣿⠟⠋⠑⠁⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠂⣐⣦⣤⡀⠀⠀⣤⣄⡰⣧⢠⡇
⠀⠀⣤⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣚⣃⣀⡀⠐⣒⣀⡀⣘⣻⣦⠀⠀⠲⠥⠤⠚⠁
⠀⠸⣏⣉⠉⢉⠀⠀⠀⢀⣴⣯⣤⠀⡟⣳⣦⡀⠀⠀⠉⠉⠙⠇⠈⠈⠉⠉⠛⢨⠙⠩⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠛⠛⠋⠀⠀⠀⢶⣶⠿⣏⠛⣉⡿⢿⣷⠀⢰⣶⣦⣤⡤⣤⣶⣄⠠⢤⣤⣤⣼⡧⠀⠀⣤⡾⠿⠿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⣷⣾⣿⡀⣠⡟⠀⠈⠋⠛⡛⠿⠿⠓⠛⠛⠙⠉⠉⢿⠇⠀⢸⣏⠤⠴⠛⠿⠶⣿⡆
⠀⠀⠀⠀⣴⣞⢦⠀⠀⠀⠉⠉⣉⣿⣿⣿⠟⠀⠀⠀⠈⠺⣉⣛⡛⡛⢛⣛⣛⣿⡿⠋⠀⠀⠘⣷⣶⣶⣶⣖⣲⡾⠁
⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠖⠛⢋⣉⠙⠓⠦⣄⠀⠀⠀⢀⣆⠀⠀⠀⢀⡤⠶⡟⢹⠋⠛⠲⢤⡀⠀⠀⢤⡞⣦⠤⠀⠀⣠⡴⡺⢛⠟⢉⠗⢶⣄
⠀⠀⢠⠞⡁⠶⠀⠻⠞⠀⠀⣶⠈⢷⡀⠙⣯⣨⡟⠁⣰⢛⢒⢒⠁⠘⠤⠤⠤⠤⠽⢆⠀⣼⠛⠻⠀⢀⡾⠉⢁⠀⠄⠒⠁⡰⠁⣨⠷⡀
⠀⠀⡟⢠⠔⠦⠀⠘⠂⠆⢠⢤⠐⠀⣧⠘⠋⠈⠓⢰⠏⠉⠈⠀⢉⡇⢠⣦⠠⣖⣒⣛⡆⠀⠀⠀⠀⣾⡤⠊⢁⠔⠂⠈⢉⠤⠊⣀⠴⢻
⠀⠀⡇⠘⠲⠚⠀⢠⠚⢲⠈⠉⠀⠀⣿⠀⣀⣀⡀⢸⣋⣉⡉⠉⣉⠀⣀⠤⠤⠤⠤⢤⡇⢀⠤⢄⠀⣿⠔⣒⠥⠐⠒⠬⠅⢒⣊⢅⡮⣿
⠀⠀⢻⡄⣞⡆⠀⡈⠛⠋⠀⠰⠆⣰⠇⢰⠋⠬⢳⠀⢷⡐⠋⡈⠋⠀⠑⠒⠒⠒⢒⡾⠁⠺⣘⡺⠀⠘⣯⣊⠕⡀⠬⠄⠉⣀⠠⡀⢭⡟
⠀⠀⠀⠙⢦⣀⠀⠁⠀⠰⢂⣠⠾⠃⠠⡈⠓⠒⠋⠀⠀⠻⢭⣭⠭⠭⠭⠝⢀⣯⠟⠁⠀⠀⠀⠀⢄⠀⠈⠳⣏⡴⢊⠩⠤⠀⣂⡴⠋
⠀⠀⠀⡰⠀⠈⠙⠛⠚⠛⠋⠁⠐⠄⠀⠀⠄⢀⣤⢠⣄⠀⠀⢉⠙⠛⠛⠛⠉⠀⠜⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⠛⠛⢋⡁
⠀⠉⢊⠁⣉⠈⠀⠀⠀⠀⣴⢶⡄⠐⠉⠐⠀⣾⢤⣻⢾⠀⠢⠀⠀⠀⠀⠀⠳⡈⠀⠈⡀⠒⠂⠠⠀⡒⢀⠀⠠⢿⡿⠆⠀⠻⠟⠠⠶
⠀⠀⠄⠉⠑⠄⣀⣀⣀⣀⡈⠛⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⠐⠀⣀⣀⣀⡀⠀⠤⠒⠄⡇⠀⠐⠂⢿⡽⢀⠀⠀⢉⣋⣀⣀⡀
⠀⠀⠀⢀⡴⠾⢉⡐⠀⠈⠉⣳⣤⡀⠀⢠⠂⡡⠐⠶⢶⣶⡶⠛⠩⠭⠭⠟⠻⢶⣄⠀⠈⠀⠀⠘⠀⠂⢀⡴⠞⠉⠉⣉⠉⣉⠓⢦⡀
⠀⠀⣰⠋⠙⠢⢀⡀⠀⠀⠀⡔⡤⠳⡄⠸⡀⢆⠡⡀⠻⡛⠒⠒⠦⠤⠤⠤⠤⠖⠚⢧⠀⠀⠺⠒⠀⢠⣞⡀⡈⠁⠈⡐⠯⣊⠂⣶⠹⣆
⠀⠀⡿⠤⣀⡀⠀⠈⠉⠒⠒⠒⠒⠒⣷⠀⠑⢄⠑⢬⣦⣈⠙⠶⣒⣒⣒⣒⣒⣉⣉⣹⣧⡀⠀⠀⠀⣾⠘⠭⠀⠀⠶⠀⠀⡀⢀⣤⠀⢹
⠀⠀⣇⢠⣶⡄⠉⠉⠀⠒⢂⣀⡉⠉⡿⠀⠀⠀⠑⢤⡉⠋⠭⡦⢄⣉⠙⠲⢄⣈⡀⢠⣿⢿⣷⡄⠀⢿⠀⢠⠫⠕⡄⠀⠀⣁⠀⠠⠄⣸
⠀⠀⠹⣄⠉⠄⠒⠈⣀⠀⠀⣤⠄⣼⠃⠀⠀⠀⡀⠀⠻⡑⠦⣌⡙⠂⠌⠐⡢⠤⢀⣈⢁⡴⢈⠜⡆⠘⣧⠰⠉⠊⠁⠀⡎⠡⢱⠄⣰⠏
⠀⠀⠀⠈⠳⣆⣉⡀⠆⢀⣉⡶⠞⠁⠀⢋⠐⢨⠁⢠⠀⠙⠷⣤⣛⡓⠦⣤⣄⣈⡉⠁⠀⠀⢁⡠⠃⠀⠈⠳⢤⣀⣛⠀⢈⣁⣥⠞⠁
⠀⠘⠃⠠⠆⠀⠉⠉⠉⠉⣁⠔⢀⠀⠠⠆⠒⠲⠆⠀⠀⠄⠀⠀⢈⡉⠉⠉⠡⠄⠀⠈⠉⠉⢠⣲⡀⠺⡗⠀⠀⠈⠉⠉⠉⠁⠀⠀⣴⡄
⠀⠀⠀⡁⠈⠐⠀⠀⠀⠈⠂⢀⠠⠁⠀⠀⡜⢢⠀⠈⡀⠀⠀⠐⠄⡐⠀⠘⢄⡀⠓⠠⠄⡤⠒⠁⠓⠠⠠⠄⠐⣶⠆⠀⠀⠀⢠⠀⠉⠁
⠀⠀⠀⠘⠀⢀⣠⣤⣤⣤⣈⡀⠈⠠⡔⠊⠀⠀⠑⣠⠀⠀⠀⣀⣨⣤⣤⣄⣀⠠⢶⠀⠀⢀⠀⡀⠀⠐⠁⠀⢀⣠⣤⣤⣤⣀⡀⠀⠺⠂
⠀⠀⠀⣠⠞⠉⠓⠒⢱⠄⠀⢹⢦⡀⠀⠑⠄⠠⠋⠀⠀⣠⠞⡉⢃⠵⠸⣄⢉⠿⣦⡀⠀⠆⠁⠐⠢⠠⣠⣞⣛⣀⣀⣒⣊⣠⠝⢳⣄
⠀⠀⣰⡇⠀⣀⣠⠔⠚⠀⢀⣻⣂⣿⡄⠀⠘⠁⠀⢀⣾⡁⠀⢠⢖⢠⡐⠋⢼⢰⡉⢳⡀⠀⠀⠀⠀⣰⡇⠒⠤⣄⣀⣀⣀⠤⠒⠁⢘⣆
⠀⠀⡇⠑⠌⣓⠤⠤⣀⠀⣏⣀⠀⠈⣿⢀⡖⢦⠀⢸⣅⠸⠤⢌⡢⠥⠖⢲⠀⣇⢉⣹⡇⠀⠈⠀⠀⡿⢭⣙⡒⠒⠰⠶⠶⣒⣒⣿⣗⣻
⠀⠀⣧⠀⠀⠘⡄⠀⠀⡑⠀⠈⡇⠀⡟⠀⠙⡋⠀⢸⡄⢹⡆⢤⠃⡀⠀⠘⠤⠬⠅⢾⠇⠀⠀⠀⠀⢿⡒⠲⠮⢭⡽⢿⣛⣉⡭⠖⢋⣿
⠀⠀⠘⢦⡀⠀⢸⢀⡔⠁⠀⠀⢹⡜⠁⣴⢋⡍⣷⠀⠻⣬⠥⠤⠤⠃⠠⡄⢒⠴⣴⠏⠀⢠⣼⣧⡄⠈⢷⡩⠍⣂⠒⠤⠤⠤⢆⣈⡽⠃
⠀⠀⠀⠈⠙⠦⣬⣚⣀⣀⡤⠖⠋⠀⠀⠙⢶⡴⠟⠀⠀⠈⠲⢶⣄⣐⣤⣹⠾⠛⠁⠀⠀⠀⠙⠋⠀⠀⠀⠙⠷⢦⣐⣒⣂⣴⠶⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠈⠈⠉⠉⣻⣧⠀⣸⣿⣿⢿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⢢⣤⣘⣱⣾⠟⢿⣿⣽⣿⣿⣿⣾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢄⣲⡶⣤⠌⠉⠉⢩⣾⣶⣻⡟⢻⣿⣿⣿⣿⣯⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⣶⢒⡄⠀⣤⣝⣉⠁⣶⣦⣁⠗⠀⢽⢿⠩⣿⣿⠿⣿⣿⣿⣿⢧⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣠⣻⣿⡿⡉⠠⠈⠛⢫⣿⠀⠉⠙⠁⠀⠀⠀⠁⠀⠁⠉⠈⢉⡿⢿⡋⣺⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢤⣵⠯⡭⣤⣎⣡⣞⡴⣿⣟⣆⠀⠀⠄⠀⠀⠀⠘⢀⠁⢀⠀⠀⢀⣄⠁⢵⡿⣷⣤⣴⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣗⣼⣿⡿⢯⣿⣿⣿⣿⣷⣵⣿⡯⠵⡁⠉⢠⣾⡞⠥⠏⠸⠀⠀⠀⡈⡄⠀⠈⣯⣼⣿⣷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠡⣟⠀⣀⣿⣿⣿⢻⣽⣿⣿⣻⠁⠀⠀⠀⠘⢚⠨⠃⠀⠀⢀⡀⠚⠀⠀⠀⣀⣭⠉⡿⢟⣷⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠓⠿⢿⣿⣿⣷⣾⣿⡛⠁⠐⠐⠀⢀⣀⠈⠀⠀⣈⠀⠈⠁⢀⣀⠂⠀⢹⡇⠠⠀⡠⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢆⣸⣤⣰⡞⣿⣿⣿⣿⣿⢻⡄⠀⠀⡀⠼⢿⣷⣶⣿⠋⡄⢡⡜⠁⠀⠀⠀⢀⠁⠀⠈⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠸⣯⡇⠙⢿⡏⣥⢹⢟⡻⣾⣿⣿⣷⢺⣉⣿⣦⣾⣿⣿⡃⡘⠠⣙⠀⠀⠀⠀⠀⣂⠀⠀⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡟⠆⢸⢷⡌⣼⢊⣽⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⡗⣀⣾⣿⣧⣀⠀⠀⢑⣿⣴⡀⢡⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⠀⠈⠈⠘⠽⣿⣿⢿⣿⣿⣿⣷⣷⠿⣿⣿⣿⣿⣿⣿⢛⠿⠛⠉⠀⠀⠈⡟⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠔⠀⠀⢘⠻⢹⣟⣯⣿⣿⢣⡄⠀⠀⠈⠛⣿⣿⡔⠋⣀⠀⡉⠀⠐⠀⠀⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⢀⣀⠠⣷⡶⢨⣽⣧⠀⠀⠈⠀⠀⠀⣿⠿⠁⡀⠁⠈⠁⠐⠁⣀⣦⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠁⠁⠉⠛⢧⣤⣀⡀⣨⣿⣿⣿⣷⣥⣶⣄⣬⣤⣶⣿⣉⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣎⣷⣄⢤⣰⣷⣴⡦⢡⣼⣿⣿⡛⣿⡿⣿⣿⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠶⠼⣷⣛⡻⡿⣴⣿⠿⣡⣴⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠏⡆⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⢦⡀⠀⠀⠀⠀⠀⠀⡜⡎⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠙⢆⠳⡙⢆⠀⠀⢀⡤⡞⡜⠀⠚⠂⣿⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡜⠀⠀⢀⡱⠬⠖⠛⠉⠈⣻⣰⡥⠤⠖⠊⢫⢳⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠴⠗⠒⠉⠁⣀⡠⠤⠖⠒⠉⠉⠈⢷⡀⠀⠀⠀⢇⢇⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠒⠉⢁⣀⠤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⢀⣀⡬⣧⢀⣀⠤⢾⣿⣠⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡳⣤⡴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⡤⣖⡺⠯⠗⠓⡏⠀⠀⠀⢸⣼⣿⡿⠟⢡⡾⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠜⣧⠼⢄⡀⠳⠗⠀⠀⠀⠀⠀⣀⡤⡴⣖⡹⠷⠛⠋⠁⠀⠀⠀⠀⣇⣀⣠⣴⣾⠟⠋⢀⡴⠋⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⣠⣾⣷⡜⠌⠓⢖⣉⡹⠀⢀⣤⢴⣲⣹⠓⠛⠉⠀⠀⠀⠀⣀⡠⠤⠔⠒⠻⡍⠳⡜⢯⠁⣠⠴⠋⠀⠀⠀⠀⠀⢀⣴⣷⡄
⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⠚⠉⠁⠀⢀⣀⡤⠴⠒⢎⠉⠀⠀⠀⠀⠀⠀⠈⢦⡈⢢⡙⣅⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⣽⡄
⠀⠀⠀⠀⠻⢿⣿⣿⣿⠀⢀⠀⢀⣀⣀⡠⠤⠶⢶⣯⣭⣭⣭⣭⣭⡭⠭⠶⣒⡤⠄⣀⠀⠀⠀⠑⣄⠙⣌⣳⡀⠀⣀⣴⣿⣿⠟⣡⣾⡿⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠈⠁⠒⠫⠵⠶⠶⠮⠍⠚⢉⣤⣾⣿⡿⠋⣁⣾⠟⠁⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠟⠉⣠⡾⠋⠁⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠛⠉⣀⡴⠚⠁⠀⠀⠀⠀⢀⣴⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⠿⠟⠋⠁⣠⠴⠊⠁⠀⠀⠀⠀⠀⢀⣤⠿⠋⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣶⣶⣶⣿⣿⣿⣿⠿⠿⠛⠋⠉⢀⡠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⢀⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⠛⠛⠉⠉⢁⣀⣠⡤⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⣠⣶⡿⠋⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⣀⣴⡾⠛⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠋⠁⠀⢀⣠⣴⠾⠛⠁⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣤⣤⣶⡶⠶⠞⠛⠋⠁⠀⠀⣀⣠⣴⡾⠟⠋⠁⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢄⣀⣀⣀⣤⣴⣶⡾⠟⠛⠉⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠯⠥⠄⣀⣀⣀⣀⠠⠤⠴⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⡀⠈⠈⠙⠂⠀⠙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⠁⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠘⠳⡄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠰⠀⠉⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⣠⠀⠈⠏⠀⠀⠀⠀⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡀⠀⠄⠀⠄⠒⢁⠀⠀⠀⠐⠊⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄
⠀⠀⠀⠀⠀⠐⠔⠀⠤⠋⠀⠀⠊⠙⡇⠀⠐⠰⣦⠸⡄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢎⠀⠀⠀⠠⡄⣀⠀⠈⠃⠀⠜⠒⠃⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠱⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⣈⣁⠙⠃⠀⠀⠀⡠⠀⠀⠀⢤⡆⠀⠀⠀⡀⠒⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠘
⠀⠀⠀⠀⠀⠘⣦⠀⠐⠁⠈⢧⠀⠀⠀⢰⠇⠀⠀⠈⠁⢿⡄⠀⠀⠀⣀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢸⡇⠀⢻⣀⡀⠀⠀⢀⡴⢚⠁⠀⠔⠋⠀⠈⠉⠻⣻⣄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠈⡑⠂⡊⠀⠢⠟⠫⠉⠁⠊⠐⠻⠁⠀⠀⠀⠀⠀⠁⠀⠀⠻⣿⠇⠀⠀⠀⠀⠀⢀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⡀⠆⠀⠀⠉⠛⠃⠠⣤⡐⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⣁⠀⠈⣀⠀⠠⣀⠈⠂⠀⠀⠀⢀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⢸⡉⠙⢿⢥⡀⠀⢀⣀⣀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡉⠀⠀⢙⠟⠀⠐⠠⠉⠝⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⡄⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠑⠛⠃⠀⠀⠀⣀⠄⠃⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⡠⠔⠚⠭⢭⡉⠓⠦⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠁⠀⠀⠀⢀⠾⢷⣴⡤⣀⠐⠈⢑⠢⣌⢢⠀⠀⢳⡤⠚⢲⡀⠒⢄⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡀⠰⠁⠀⠁⠄⠀⣶⣦⣼⣿⣿⠂⢀⡵⠬⠍⠱⡀⢨⣀⠀⠀⠉⠓⠿⠷⣄⡁⠢⠙⡇⠀⠌⠀⠀⠀⠙⢦⢀⡣⠀⠰⠁⠀⢠⣭⣳⡀⢠⣏⣀⣋⣽⡄
⠀⠀⠤⠾⠁⡇⠴⢄⠀⡘⠀⣿⣿⣏⣽⣿⠇⠸⣄⠀⠀⡀⠀⢸⠿⣿⢿⣷⣶⣤⣀⠈⠙⠦⣌⡇⠀⢃⠀⠀⠀⠀⠈⡟⡞⠀⠸⣀⠀⣿⣿⣿⠃⠐⠈⠓⠊⣉⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠙⠛⠛⠉⠀⠀⠈⢡⡌⠀⠀⠈⢆⠀⠀⠛⠻⢿⣿⣷⣦⣀⡜⠀⠀⠀⠳⠄⣢⣀⣾⡛⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣦⣀⣀⣈⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠯
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢿⠿⠿⢿⢟⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣻⣛⣿⣟⣛⣿⣟⣛⣻⣿

⠈⠓⠂⠀⠀⠛⡯⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⢠⠈⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠀⣀⣀⡀⢠⡤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⡀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠀⠀⠈⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢢⠀⠀⠐⠂⠄
⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡀
⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⠤⠄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠒⠂⠀⠒⠀⠀⡀
⠀⡀⠀⣀⡀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⡡⣤⡀⠈⠉⠉⢠⠉⠳⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⢟
⣥⣰⣀⣉⣁⣀⣞⣋⣲⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣐⣁⣀⣀⣀⣀⣀⣀⣀⣿⣲⣐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⢶⣄⡒⠖⠒⣀⠶⠒⠒⠒⠦⠤⠤⢤⡤⣤⣀⡀
⠀⠀⠀⠀⢀⠄⠶⠥⠈⠀⢤⡀⢨⡄⠉⠁⡘⠒⠒⡀⣤⣀⡀⡰⠊⠉⠀⠀⠈⠈⠿⣆⡐
⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⢧⠈⡕⠀⠑⢲⠀⡸⠁⠈⠋⠙⠶⢐⡀⢀⠀⠀⠀⢈⠰
⠀⠀⠀⠀⠑⢦⣤⣀⣀⣄⠀⠀⠀⠙⠁⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠟⠻⣝⠿⡇⠛⠿⡟⠒⣲⠚⠛⠛⣻⢟⡋⣉⡱⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠧⣃⣤⡄⢃⣀⣤⣤⣴⣤⠷⠋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⢤⡀⠀⠀⠀⠄⠐⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣽⣿⠂⠀⠀⠀⣰⡄⠀⠀⢰⠁⠀⠀⠀⠀⢹⠀⠀⠀⡤⠀⢀⢠⡜
⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠉⠁⠀⠀⠘⡀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠃⠓⠋⠁
⠀⠀⢀⢀⡀⠀⠁⠀⠀⠀⠀⣀⢘⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠒⠲⠖⠊
⠀⠀⠼⣿⠷⠀⠀⠀⠀⠀⢨⡀⢰⠹⡄⠀⠀⠀⠃⢐⡄⠀⠀⢤⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢻⣖⠚⠖⠓⠉⠀⠀⠀⠸⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠈⠁⠄⠀⠀⢀⠀⠀⠀⠀⠈⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢽⡿⠄
⠀⠨⠄⠀⠀⠀⠀⠆⠀⠈⠛⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠐⢤⠀⠁⠀⠀⠰⠀⠀⠀⠀⠁
⠀⠀⠐⠀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄⡐⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⢹⠀⠀⠀⠀⠘⣄⠀⠀⠀⡀⠀⢀⣄⠀⠀⣿⡟⠡⣾⣿⣷
⠀⠀⠀⣼⣿⣅⠀⢀⠄⠀⠀⠀⠀⣀⡖⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠈⠙⠁⠀⠱⣦⣄⠀⡉⠁
⠀⠀⡜⠘⠁⠀⢰⠁⠐⣄⣀⡤⠚⡡⠀⠀⣤⡤⠀⠀⠀⠀⠀⡄⠀⢸⠉⠐⢢⣤⡀⠀⠀⠈⠀⠀⡀
⠀⠀⡂⠀⢂⠀⠈⠓⠒⠋⠉⠈⠁⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⢸⣠⠖⡋⢀⠙⢄⠀⠀⠀⠿⠃
⠀⠀⠠⠀⡂⠀⠀⠀⠀⠀⡔⠉⠈⡁⣐⡀⠀⠀⠀⠈⠀⠀⠀⣠⣀⠈⠣⡀⠀⠊⠀⡈⠢⣀⣀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠐⠀⡀⡀⠀⠀⠀⠰⠆⠀⠀⠛⠇⠀⠀⠙⢆⠈⠢⢃⣔⠁⠈⢢⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⡨⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠚⠹⡀⠙⣄⡠⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢶⣾⣄⠀⠀⢰⠉⠢⡀⢈⠦⠜⡆
⠀⠀⠀⠐⠦⣠⡠⠔⠁⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠃⠀⠀⠀⠑⠢⢬⣣

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠟⠻⢦⡄⠀⠹⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠀⠀⠁⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠉⠀⣺⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠠⠀⣧⠈⠛⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣦⡄⠀⠀⠀⠀⠛⠻⡆⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣤⡀⠌⠘⡯⠄⣀⠀⠸⠄⣈⠛⠀⡆⡀⠄⣀⣤⣴⣶⣤⡀⠀⠀⠀⢠⡏⠀⠘⡟⠀⠀⠀⠀⠈⠙⠊⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠲⣄⠛⠞⢉⡀⣀⡤⢀⣤⡬⠖⣤⠾⠛⠉⠋⡽⣿⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⣿⣮⣳⣿⣷⣶⣮⠻⣲⣭⣤⣶⣾⣧⠀⠀⠀⠁⠸⣿⠟⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⣿⣷⠸⣅⢻⣿⣜⠻⢄⣀⣀⣤⣤⠁⠁⠎⠀⠀⠀⠀⣠⡾⢿⣿⣦⠀⠀⠀⠀⣠⠀⠀⢿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣆⣙⣽⣿⣿⣿⣿⣿⣽⣻⣃⠚⠋⠀⡘⠉⠁⠀⢀⣀⠀⠀⢠⡇⠀⠀⠸⡿⢀⠀⡄⠀⠈⠢⡀⢠⠀⢦
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣶⡱⡝⢆⣠⡝⠿⠼⠃⠀⠀⠉⣤⡀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷⠐⣆⠀⢀⣀⣤⣄⢄⣀⢀⠀⠈⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⣏⠘⣿⣿⢿⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢤⡀⠀⢀⠊⢹⡿⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⣈⣙⣿⣿⣿⣿⣿⣿⣶⣍⣴⣾⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⠀⠀⢼⠢⠀⠁⣠⣤⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⡀⣀⡀⣀⣄⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣾⣿⣿⣿⣿⣯⠿⠿⣿⣿⣿⣿⣿⣿⣦⡉⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⡿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁⠉⠋⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⣿⣤⣶⣶⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣶⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠏⠀⠀⠀⠀⠀⠡⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀
⠀⠀⠀⢀⡴⠃⢀⣠⣤⢶⣿⠾⠋⠀⠀⠀⠀⠀⠠⣀⣀⣼⡏⣻⣷⣻⣿⣿⣄⣀⠄⠀⠀⠀⠀⠀⢀⠀⣜⣿⡁
⠀⠀⢰⣟⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⢿⣧⣼⣿⣯⡇⠀⠀⠀⠀⠀⢸⣽⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⣴⠘⠻⣯⣀⣸⡇⠀⠀⠀⠀⡄⠘⠵⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠶⢿⣦⠀⣭⣿⣿⡇⠀⠀⠀⣸⡁⠀⡆⠀⠀⠀⣹⡄
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⣇⣾⡟⠉⠀⠘⠿⢦⣤⣤⢻⡇⠀⠀⠀⢹⡷⣄⡂⡄⢀⣠⣿⠃
⠀⠀⠀⢸⣿⡀⠀⢰⣛⣿⣷⠀⠀⣸⣷⠀⠀⠀⢸⠿⣾⠃⠐⠦⠶⢶⡌⠿⣿⣿⡇⠀⠀⠀⠀⠳⢿⣍⣿⣯⠿⠃
⠀⠀⠀⠘⣿⣳⣄⠈⠻⠷⠋⢀⡴⣿⡏⠀⠀⠀⢸⣷⣿⣷⣬⢻⣿⡜⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠁⠇⢀
⠀⠀⠀⠀⠘⢧⣾⡟⠓⣶⣿⣛⣿⠟⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⢿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠈
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠂⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⠈⢲⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠔⠰⡆⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠂⢀
⠀⣰⡇⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⣷
⠀⠹⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⡏
⠀⠂⠺⠛⣿⣿⣿⣦⣴⣤⣤⣤⣄⣀⣀⣀⣀⢀⣀⠀⣀⠀⠀⢀⠀⠀⡀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣾⣟⣿⣏⣿⠃
⠀⠀⣦⣀⣸⣿⣛⡿⠝⠛⠉⠋⠛⠛⠛⠛⠛⠛⢿⡿⢿⣿⢾⣿⣷⣿⡿⢷⡿⣿⡿⣿⣿⣿⣿⡿⣿⡟⠛⠙⠉⠋⠉⠀⠹⢯⡝⢹⣇⠘⣿
⢀⣼⣿⢿⣿⢿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣙⢻⠛⠛⣻⣷⣎⣤⢹⣷⠟⠀⠀⢛⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⢸⣿⣼⣿⡀
⠈⢿⣿⣿⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠿⠿⣾⡿⠿⣿⡿⠋⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢼⣿⣿⣥⠂
⠀⢰⣿⡿⣿⡛⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⢃⣿⠇⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢀⠜⠀⠀⣠⣶⣾⣉⣉⠟
⠀⠀⠛⡗⠉⢵⣦⠐⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⠀⠀⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⠀⠁⠀⡀⣿⠀⣸⡯⠃
⠀⠀⠀⠀⠀⠀⠙⠀⠈⢠⢉⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠃⣿⣏⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⢡⠛⠳⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⢣⣿⡏⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠰⣦⠀⣠⣴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠐⢤⠿⠋⢑⣦⡀⠀⣤⣀⠀⢀⡈⣀⠁⠀⢀⡴⠋⠀⣀⡀⢀⠈⣁⠀⠙⠛⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡉⠛⢧⢈⣿⣧⣽⡅⣿⡇⣸⣧⡀⢀⣉⣻⡿⠟⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠹⢿⣯⣬⣱⠾⡇⠻⡿⢹⣟⣁⣿⣿⡏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣦⣈⢿⣯⠇⣶⣏⠀⣶⣤⣾⢹⢿⣿⡇⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡶⢏⡄⢀⣧⣬⣶⣤⣿⣿⣇⠈⣷⠤⣦⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣛⠛⠛⣉⣁⢾⣙⣉⠿⠸⠿⠟⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠙⠋⢹⡃⠀⠀⣦⣀⠀⠀⢀⣀⠀⠀⠀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡷⠦⠀⣤⡄⢠⡄⠀⠀⠀⠞⡇⠀⠈⢿⣤⣤⣬⣿⣷⣶⢿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣅⣠⣄⣉⣀⣸⠑⠀⠀⣾⡆⢹⠆⠀⠀⠙⣿⣏⣉⣀⣹⡿⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⢿⡏⢸⣿⠉⠛⢷⡶⢶⣿⠀⢿⣶⣶⣾⣿⣾⣿⣿⣯⠘⢁⣀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣧⣈⡗⠘⠟⠀⠀⣘⣧⣼⣿⣹⣿⣿⡿⠈⢻⡏⠘⠛⠋⠀⠀⠀⠚⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣿⣮⣽⡟⣧⠀⣠⣠⣤⣿⣭⢠⣮⠿⠮⣿⡠⠿⠟⠙⢷⣄⡀⠀⢀⠽⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡤⠿⣿⣉⣿⠀⣸⠿⠋⠁⠈⠀⣿⣦⢛⡄⠀⢾⣷⣦⠀⢀⡄⠈⠛⢀⡌⠰⡏⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⣿⣶⠾⢻⣿⣼⣏⠀⣠⡀⠀⠸⣿⠁⠘⢧⠀⠀⢻⡟⠀⠚⡁⠀⠀⠈⠁⠐⠿⣀⠀⠀⠀⡂⢀
⠀⠀⠀⢰⣶⣦⣠⡴⢿⣿⣿⣿⠷⠶⠰⠛⠟⢁⠀⠙⣿⠀⠀⠁⠀⠀⢸⠀⠀⣸⡆⠀⢀⣶⣤⣧⠀⠀⣠⡟⠻⣶⠾⠏⡃⣠⡶⠦⠀⢠⣄
⢀⣠⣆⣰⣿⣿⣿⣿⣿⣿⣿⣟⡉⠀⠀⠀⠘⠷⠀⠀⢠⡴⠶⣦⣤⠀⠐⠖⠀⣿⠿⠛⠉⠀⣀⣤⣼⡟⠛⠁⣈⣁⣀⣀⣀⣀⣀⣠⣶⡿⠀⠂
⠛⠻⣯⣀⡴⣟⠚⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠂⠈⠁⠀⠀⣠⣶⣿⣿⣿⠿⠛⠛⠀⠈⠉⠉⠁⠉⠀⠙⠁⢷⣦⣨⣿⠟
⠀⠀⠘⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⣀⡀⣀⣴⣦⣤⣶⣤⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣿⠤⣡⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣴⣷⣄⣥⣾⢋⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⣄⣿⣿⣿⣯⣤⣀⡀
⣿⣿⣿⣿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣍⠀⠁⠀⢂⠲⢀⡀⠀⠀⠐⡡⢂⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⢊⠈⠁⠀⠀⢠⡀⣋⠀⠈⠉⠚⠠⠅⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠐⠐⠀⠄⢀
⠀⠀⠀⠀⠀⡀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⠀⣼⢤⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⢀⡀⠉⠀⠂⠀⣀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⣀⣸⡀⠀⠀⠀⠈⠈⠐⠘⠀⢰⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⡐⠈
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢇⠀⠀⠀⣠⡿⢛⡿⠈⠐⡠⢄⣠⠀⠀⠀⠀⠀⠈⠉⠚⠃⢇⡖⡤⣀⠀⠀⠀⠀⠀⠑⠀⣀⠔⢢⠜⢠⡀
⠀⠀⠀⠀⡠⠸⣽⣿⠿⠗⢛⣴⣵⢄⢘⡶⣶⡇⢀⠄⡀⠀⠀⠉⠀⠀⠒⠠⠀⡀⠀⠀⠀⠀⠁⠙⠽⢃⢂⢤⠀⠀⠄⠠⠃⠀⠂⣴⣿⣦⡀
⠀⠀⠀⢠⠽⡺⢁⡰⣢⣿⡶⢣⡇⠘⡻⢀⣍⡗⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠀⠀⢄⣀⡀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡆
⠀⠀⠀⡾⠄⢡⣳⠉⠹⡿⠂⢴⡟⢲⠁⠀⢖⠅⢀⡐⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠠⠀⠀⠀⠀⠠⠿⠿⠿⠛⠁
⠀⠀⢰⣄⠀⣘⠉⢠⡔⠂⢹⣿⠰⠈⠓⠊⠀⠁⠀⠀⠐⠀⠀⠀⠉
⠀⠀⢸⠀⠩⡇⢐⡺⠋⠸⠃⢐⣤⡟⡄⠀⠀⠈
⠀⠀⠀⠀⠴⠇⢈⡟⢶⣤⠶⢦⣟⣴⠇
⠀⠀⠀⠈⠠⢺⡞⢛⠻⠮⡶⡾⢞⣁⠈
⠀⠀⠀⠀⠘⠿⠗⠀⠀⠒⢃⣍⣄⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠘⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡁⠄⠀⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣡⡀⢠⠴⠴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢠⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠄⠞⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠋⠙⢿⣏⣉⢛⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡅⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⣀⣤⣶⣶⠶⠶⠶⣶⣶⣤⣾⠋⠀⠈⠻⠷⠶⢶⣄⠀⢀⣶⠿⠻⠷⣶⣤⣀⣀⣼⣿⣦
⠀⠀⠀⠀⢸⣿⠁⣴⠒⠒⠒⠒⠒⢲⣿⠃⠀⠀⠀⢀⣀⠀⠀⢿⡄⠀⠁⢀⣀⠀⠀⠈⠉⠉⠁⠀⢹⣧
⠀⠀⠀⠀⠀⠙⢷⣬⡙⠦⣄⡀⠀⣾⠟⢷⣤⣤⡾⠛⠛⠿⠀⠈⠻⠶⠶⠿⠋⠀⣠⣴⣶⣤⣤⣴⠟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣍⣛⠻⢤⣀⡈⠉⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣤⡾⠋⠀⠀⠀⠉⠀⠀⠸⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠶⣦⣭⣙⠒⠶⢿⣟⣻⣦⡀⠉⠉⠉⠉⠀⠀⢰⡾⠛⠿⢶⣦⣴⣿⣍⡻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠉⠙⠛⠿⠶⣦⣭⣍⣛⠲⠦⠤⣄⣀⣀⠈⠻⢶⣦⣤⣤⣼⡟⠀⠉⠓⢮⣙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠛⠛⠛⠻⠿⣷⡄⠈⠉⠙⠛⠻⠶⢶⣤⣭⣍⣙⣓⠒⠶⠬⠿⢧⣤⣤⣤⣤⡼⠇⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⢠⡿⠁⠴⠾⠟⠛⠛⠿⣦⣄⠈⠉⠉⠛⠛⢻⣿⠷⠶⠶⠶⠶⠶⠶⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠸⣷⣀⣀⣠⣴⣶⣦⡀⠈⠛⢷⣦⣤⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣌⡉⠉⣉⣀⣀⡈⠁⠀⠀⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠶⠾⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⡶⠛⠛⠓⠲⠤⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⡇⠀⠰⠒⠀⢀⠀⠉⠓⠦⣄⡈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡗⠂
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⡞⠉⠉⠓⠲⠄⠀⠉⠲⢄⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢳⡀⢰⡟⠒⠦⣄⡀⠀⠀⠉⢲⣄⣤⠤⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠱⡀⢳⡄⠀⠀⠉⢓⡤⠞⠉⠀⠀⠀⣀⡀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢦⡀⣠⠏⠀⠀⠠⠖⠋⠉⠉⠉⠉⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⢷⡀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⡇⠀⠀⠀⠐⢿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⣦⡀⠀⠈⠳⣦⡈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠀⠈⣇⠙⢶⣌⠳⣄⠙⢦⣈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢠⡷⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠳⣌⠙⢦⡉⠳⣄⡑⠂⠀⠀⠀⠀⢀⡾⠀⠈⠳⡄⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠈⠛⢦⡈⠀⠈⠙⢦⣄⠀⠀⣠⠞⠑⣄⠀⠀⠘⢦⡀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠙⠳⣄⡀⠀⠈⠛⠾⣅⡀⠀⠈⢧⠀⢦⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠛⠦⣄⠀⠀⠈⠙⠲⠦⠼⠇⠈⢧⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠶⣄⡀⠐⠢⢤⣄⣀⡼⠀⣀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠙⠳⢤⣀⡀⠀⠀⠰⠛⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠤⠀⠀⠀⠀⠀⠈⠓⠀⠀⠈⠉⠓⠶⠤⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⢀⣔⠟⠀⠀⣴⡶⠋⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠑⠁⠀⠀⣀⠴⠋⠁⢀⡴⡻⠏⠀⠀⠀⠀⠀⢀⣟⠦⡀⠀⣀⣀⠤⠤⠒⠒⠒⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⣀⠴⠚⠁⢀⡤⣾⠯⠟⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠙⣯⠐⠒⠒⠂⠐⠒⢄⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣡⣤⡶⠚⠉⢀⣠⢴⣂⣿⠏⠋⠀⠀⠀⠀⡠⠀⠀⡰⠋⠀⠀⠀⣰⡜⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠓⢉⣀⣤⣴⣾⠩⠿⠛⠉⠀⠀⠀⢀⣠⠔⠋⢀⡤⠋⠀⠀⠀⢀⣜⡷⠀⠀⢃⠀⠀⠀⢠⠎⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣄⣴⡿⠟⠁⠀⠔⠁⠀⠀⠀⠀⣠⣟⠟⠀⠀⠀⢸⡄⢀⠔⠁⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣤⣶⣾⣹⡿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡻⠋⠀⠀⠀⠀⣨⠗⠁⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣠⢶⣺⣟⢾⠯⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠟⠋⠀⠀⠀⠀⣠⠞⠁⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡾⠟⠁⠀⠀⠀⣀⠴⠋⢀⡴⢚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠉⠀⡀⠀⣀⠴⠊⢁⡤⠊⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⡠⢚⠕⠋⠈⢇⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠿⠛⠁⠀⠠⢴⣪⠔⠊⢁⡤⠚⠁⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⡠⢊⡴⠃⠀⠀⠀⠈⢢⡀⢀⣀⡤⡶⠿⠛⠉⠀⠀⢀⣤⠴⠛⠉⣀⠴⠊⠁⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⣠⠊⢠⠎⠀⠀⠀⠀⠀⠀⠀⠙⢮⡋⠁⠀⠀⣀⣤⠴⠛⠋⣁⡤⠖⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⡴⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠶⠖⠛⠉⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⡸⠀⠀⠀⠑⠤⠤⣤⡤⠤⠤⠒⠒⠊⠉⣀⡠⠔⠒⠛⠳⠤⢤⣤⣤⣤⣁⡤⠤⠔⠒⠉
⠀⠱⣀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠊⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣦⣄⣹⣦⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠹⠻⠿⣽⣿⣿⣷⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡁⠀⣀⣤⣤⣤⣼⣿⣹⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⢁⣌⣴⣿⠟⠛⡉⠉⢽⠿⣿⣿⣿⣿⣿⠿⡶
⢹⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢻⣾⣿⢋⣀⡨⠟⡲⠶⠾⢿⣿⣿⣿⣿⡆
⣼⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠻⠛⠀⡀⠂⠀⠀⢀⠀⣀⣀⣴⣾⡟⣿⣄
⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣘⡁⠠⠖⣳⣶⣿⣿⣿⣿⣿⣿⣿⣆
⠙⠛⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠋⠀⠀⠀⠀⢸⠂⢼⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠃⠀⠀⢀⠀⣼⠁⠿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡀
⠀⠀⠀⠁⠀⠹⠿⣿⣿⣿⣿⣧⣿⣤⠀⠀⠀⣀⣨⣿⡟⢠⣖⡀⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠠⠿⠗⢻⣿⣯⠀⠀⠀⢬⣹⣿⠃⠀⣯⢽⠂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠠⠄
⠀⠀⠀⠀⠀⠄⠀⠔⠁⠀⠀⠀⠉⠁⠀⠀⢠⣾⣿⡟⣘⠀⣿⢠⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢰⣿⣶⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡇⣼⢁⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠐⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠁⠏⠉⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⢹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⡇⠀⠐⠀⢉⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠐⢦⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠘⠀⠀⣯⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⣼⣷⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⠸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⠀⠀⣽⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣽⣿⣿⡏⠀⠀⢻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣿⣿⡇⠀⠀⢸⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡇⠀⠀⠀⠀⠾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡀⠀⢀⣴⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡁⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡁⠀⠈⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠃⠀⠀⣘⣻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢰⣄⣻⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠉⠙⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠦⠔⠒⠒⠢⠴⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢀⣠⢤⣔⣒⣒⣈⣉⣭⣭⣭⣀⣒⣒⡢⠤⣄⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠛⠉⠙⢻⣿⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣻⣿⣿⡀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣧⠘⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣀⣥⣭⣭⣅⢉⣾⣥⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠟⣷⣄⠙⠻⢿⣿⣷⣶⣤⣤⣄⣀⣀⣠⣤⣤⣶⣿⣿⣷⡧⠄⣠⣴⠬⠶⣾⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣄⣀⣿⣿⣷⡄⣀⡉⠙⠿⢛⣻⣿⣿⣿⣿⣛⡛⠿⠛⢉⣀⣴⣾⣿⣿⣀⣠⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠿⡿⣿⣿⣿⣿⣗⡏⠉⠑⠒⠲⠶⠤⠤⠤⠤⠶⠒⠒⠊⠉⢹⣿⣿⣿⣿⣿⢿⠿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⢻⡆⠇⢱⠀⠀⠙⠿⢿⣴⣒⡠⠀⠀⠀⠤⠄⠀⠀⠀⢄⣒⣾⡿⠿⠋⠀⠀⡎⠸⢰⡟⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⢸⡇⢰⠈⡄⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⠀⡇⢸⡇⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠈⡇⢹⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⢸⠃⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠸⠀⠀⠀⡰⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⢦⠀⠀⠀⠇⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣥⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⠿⠀⠀⠀⠈⢉⣲⣤⡀
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⣤⡀⠀⠈⠛⠂⢱⣤⠔⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢰⣧⢀⠀⠒⠀⠈⠀⠀⠀⡔⣰⠄⠀⢱⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡠⢾⣿⡄⠉⠀⢰⠉⠙⣷⠀⠀⠀⠀⣆⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠁
⠀⠀⣴⠟⠁⠸⣿⣿⣂⣀⡈⠃⡚⢃⣤⣶⣤⣿⠿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢘⠉⢄⠀⠀⠛⢛⣛⣩⣭⡲⠖⠛⠋⠉⢱⡄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀
⠀⠀⠀⠋⠉⠉⠉⠛⠿⣿⣿⣿⣿⣤⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⣠⣤⠀⠰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⠿⠃⣀⣴⣿⠁⠲⣄⡀
⠀⠀⠀⠀⠀⠀⣀⠀⣠⠄⠀⠀⢀⣤⣶⣿⣿⣿⣿⣯⠓⡀⠉
⠀⠀⠀⠀⢃⡐⠙⠀⢿⣶⣿⣷⣿⣿⣿⣿⡉⠀⢉⣄⡀⠁⠀⠀⢠
⠀⠀⠀⢀⡄⠀⠀⠐⢿⣿⣿⣿⠹⢿⣿⠟⠛⠂⠈⠛⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣾⢠⣶⡀⠀⠈⠙⢻⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⣾⣿⣿⣷⣠⣤⢈⣿⠉⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠘⠀⢿⣿⣿⣿⣿⠙⠟⠹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠐⢀⡻⣿⡏⠀⠀⠀⠈⠀⠀⠒⠒⣻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⣾⣅⠀⢳⠤⠀⠀⠀⠀⠳⣾⠣⠟⣹⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⢿⣷⣤⣤⣤⣾⣶⡤⠖⢃⣄⠉⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⡿⠟⠓⠄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⡄⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⠾⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠠⡤⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠴⢀⣀
⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣤⠴⠾⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠀⠴⠀⣀⣢⣄⣄⡀⠀⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⢀⣽⡏⠉⡀⠀⢀⣨⢿⣶⣄⣤⡤⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠖⠒⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢈⡟⠙⢦⣤⡄⢻⠇⠡⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⠀⠀⠂⠀⠀⠀⠀⠘⢦⠀⡀
⠀⠀⠀⠀⠀⢠⣼⡃⠀⣿⠉⠀⠀⣷⣄⡀⠀⣨⣿⣷⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣚⡆⢉⠠⠤⣈⡳⠾⢧⡀⡀⠀⠘⢂⠀⠀⠀⠰⡃
⠀⠀⠀⠀⠀⠀⠈⢻⣦⣸⡶⡄⣤⣼⠁⠉⠻⣯⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠑⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠳⣤⡀⠻⢄⣀⣀⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡐⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⠉⣷⠀⠀⠘⡿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠁⠠⡀⠉⠿⣀⠀⠀⠀⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⢏⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⠆⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⡀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢀⡀⠂⠁⠈⠁⠀⠀⠀⠂⠀⠀⠀⢀⠠⠀⠛⢆⠠⣮⠄⡀⠸⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⡍⠐⣂⠀⠀⠀⠀⠀⣠⡄⠀⠄⠬⠓⢄⢀⣰⠀⠀⠚⠀⠀⠀⠉⠁⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠠⣿⣷⣀⠀⠀⠀⠀⠀⠀⠸⠃⠀⣠⣶⣶⣦⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠆⠀⠀⠀⢰⣻⣀⡙⣏⡤⣠⣄⣤⣄⡴⣄⡤⡤⢦⡄⢠⠀⠺⠓⠞⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠋⠂⠋⠈⠓⠋⠃⠃⠓⠋⠃⠋⠓⠋⠃⠃⠘⠑⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⡤⡆⠀⠲⠆⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⣀⠀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣤⠄⠀⠀⠠⠀⡀⠘⡣⠀⠀⠻⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⠟⠒⠀⣠⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⡋⢐⠡⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢆⣀⠀⡀⠀⠈⠻⣶⣤⢀⡾⠀⠐⣆⡀⠀⠀⠀⠀⠀⠀⠈⡑⠉⢠⡘⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣸⡟⣩⠟⠀⠀⠀⠛⡛⠩⢂⠀⠀⠘⣿⠆⠀⠀⠀⠀⠀⠘⢁⡄⢠⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠠⠉⠀⠀⠂⠁⠀⠁⠈⠡⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡈⠁⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠃⠀⠈⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠂⠀⢂⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠷⠶⠲⢒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⠤⣖⡶⠽⠽⠿⠷⣒⡤⢄⡀⠀⠀⠀⢼⠫⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡪⡒⠝⠂⠉⠉⢈⠈⠉⠁⠚⢕⡪⡳⣄⠀⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣠⣤⡴⣫⡪⠊⠀⠀⠀⠀⢼⡉⡻⠄⠀⠀⠀⠈⠪⡪⣣⣤⣤⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⣏⢿⣿⠻⢛⣋⣹⡱⡕⠁⠀⠐⠲⠤⣤⡌⠘⠈⣤⡤⠤⠂⠀⠀⠱⡱⣻⡙⠻⣿⠋⢻⣗⡦⢄⣀
⠀⠀⠀⠀⠀⠀⡠⢚⡵⠊⣡⠞⠉⢀⠔⠉⠋⣧⣷⠁⠀⠤⠦⢭⠵⢤⠹⠀⡌⣠⠦⢭⢥⠦⠄⠀⢁⣣⡇⠉⠲⣵⠛⠓⢌⠑⢮⡑⡶⠳⣆
⠀⠀⠀⢀⡶⠛⣷⡏⠀⠐⣅⡀⣄⣸⡀⠀⢸⣿⠸⠀⠀⠀⠈⡓⠂⠁⠀⡇⡇⠀⠀⠒⡋⠀⠀⠀⠸⢨⣷⠀⠀⡘⠀⠀⣨⣇⠀⢹⠉⣿⠁
⠀⠀⠀⠀⠛⡶⢧⡱⢄⡀⠽⣏⠎⡳⠌⠒⠬⢿⣾⡀⠀⠀⣏⣹⠀⠀⠠⣇⣧⠀⠀⢸⣩⠇⠀⠀⣸⣾⠧⠔⠉⠀⣀⠴⠋⢁⡠⠋⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢭⣚⠯⣯⣙⡓⠒⠤⢤⣀⣉⣉⠉⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠋⣉⣉⣀⡤⣤⢒⣟⣉⡤⠴⣚⡩⠔⠋
⠀⠀⠀⢀⢴⠖⠀⠀⠀⠀⠈⠉⠓⠒⠯⠭⣷⣶⠶⣶⠤⠭⠭⠭⢭⣭⣭⣭⣭⣭⡭⠭⠭⠭⠤⢖⣒⣶⣿⡋⠌⣻⠾⠉⠁
⠀⠀⠀⠀⢈⡀⣵⡋⠀⠀⠀⣀⡀⠀⠀⠀⠀⣻⣄⣼⠻⡻⣝⡿⣛⠛⠛⠻⠛⠛⢛⡹⢟⡽⡫⠏⠁⠀⠜⠛⡞⠛⠄
⠀⠀⠀⡎⠔⠉⠈⢷⣒⡲⣬⠐⠠⠠⡄⠀⠀⠀⠈⠀⠀⠈⠓⠯⢖⣢⣭⣡⣉⣯⣒⠮⠗⠋
⠀⠀⠀⠉⠀⠀⠀⠀⡰⢼⡞⡄⢀⠇⠐⠄⠀⠀⢠⣀⣠⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⡊⡈⠛⢶⣄⠀⢲⡟⣩⡝⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠲⠾⠛⠚⢷⣬⣵⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣲⣯⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠉⠀⠀⡈⠙⠀⠻⠤⠛⠀⠀⠀⠀⠀⠾⠂⠘⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⢀⠒⠒⠀⠉⠁
⠀⠀⠀⠀⠘⠀⠀⠀⠐⠀⠤⠀⡀⠀⠀⢠⠀⠀⠀⠓⠰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠺⠇⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣊⣁⠄
⠀⠀⠀⠀⠁⠀⠀⣤⠀⣤⠀⣠⠄⡀⠀⠤⠀⠚⠀⠀⠁⠀⠀⣠⡄⠀⠀⠸⠷⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⡠⢪⡁⠾⠂⠂⢛⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠰⠶⠀⠀⠀⠀⠈⠁⠰⠆⡈⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⣄⢡
⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣦⡐⠗⠀⠀⠀⠉⠋
⡀⠀⠀⠀⢄⠀⠈⠉⠀⠀⠀⣺⡟⣹⠟⠀⠀⠀⠀⠀⠶⠂⠀⠀⢀⠁⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠦
⠀⠀⢀⠀⠀⠑⠀⠀⠀⠀⠀⢨⣿⣿⣦⣾⡖⠀⠀⠀⠀⠀⠀⠀⠒⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⢡
⠀⠀⠦⠀⠀⣂⠀⠀⠀⠀⠀⠀⠁⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠈⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡄⢐⢚⡆⠀⠀⠘⠋⠀⠀⡀⠶⠀⠀⠀⠀⠒⠀⠀⠀⠀⢤
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠻⠗⠀⣤⡄⠚⠦⠀⠀⠀⠘⠛⠁⠾⢂⡄⠀⠀⠀⠀⢀
⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡲⢄⠀⠀⠀⠀⠐⠀⠂⠀⠀⢀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠁⠰⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢁⠀⠀⢐⠀⠀⠠⠄⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠈⢂⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠆⠀⠀⠰⠆⠀⠀⠀⠀⠛⠀⠀⣀⡘⢃⣬⠁⠸⠏⠈
⠰⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠨⠁⠈⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠛⡀⣀⠀⠰⠂
⠀⠀⠀⠂⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠃⠀⠀⠀⠀⠁⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠉⡀⠀⠀⠀⠁⢄⡀⠀⠁⠀⠀⠀⠀⠌⠀⠀⠈⠀⢤⠈⠡⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢀⠀⡃⠁⠀⠀⠀⠄⠁⠐⠀⠀⠀⠊⠀⠈⠐⢄⡀⠀⠠⠚⠲⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠤⠄⠐⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠂⠀⠀⠀⡁⢠⣉⠦⠐⠉⠀⠀⠀⣑⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⢂⢠⣌⠀⠀⠀⠀⠀⠀⠓⢤⡀⠀⣔⠐⠉⠁⢤⠀⠐⠂⢂⠤⡬⣁⠠⣰⠽⢁⡣⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠈⠀⠀⠀⠀⢀⠀⣀⣀⠉⠻⠧⣄⡀⠀⠀⠑⠤⡂⠈⠲⡈⢯⢂⣠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢀⡀⠀⠀⠀⠀⠙⠦⣄⠀⣠⠼⢆⡀⠀⠊⢊⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠨⠈⠀⠀⠀⠀⢀⠈⠓⠿⣄⠀⢙⢬⡀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣀⣄⠤⠚⢁⠀⠂⠀⠀⠁⣄⠐⠓⠃⠉⠀⠄⠈⠓⠖⣓⡈⠢⡀⠠⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡐⢀⣀⠀⢠⠂⢀⡀⠀⠄⢀⣠⡀⢀⠤⠂⠉⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⢼⡟⠆⢼⡢⠀⠀⠀⠀⠄⠀⠀⡀⢀
⠀⠀⠀⠀⠁⡐⢗⡀⠀⠀⠉⠀⠀⠉⠁⠘⠀⢀⣤⣤⣐⡀⠀⠀⠁⠀⠠⡀⠀⠀⠐⠀⠠⠆⠀⠈⠀⠴⣾⣧⠀⠀⠉⢺⡴⠆⠀⠠⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠑⠒⠆⠉⠀⠀⠀⠀⠀⠀⢄⡄⡀⠀⠀⣚⠀⡈⢠⡿⢽⡧⠄⠀⠢⠀⠈⠒⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⠂⡀⡄⠀⠀⠀⠀⠐⠋⠀⠀⠑⠆⠀⡀⢀⠀⢸⣼⠧⠀⣳⢆⣁⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⠄⠀⠀⡀⠀⠀⠈⢃⠮⣀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠘⠤⢄⣈⣘⣄⠿⠓⠛⠃⡉⢀⡂⠀⠀⠀⢄⠀⠁⠰⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠘⠀⠀⠁⠀⣀⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠁⠄⡤⠔⠓⠋⠉⠋⠁⠉⠀⠀⠀⠉⢢⡂⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠔⠁⠀⠀⠑⠀⠐⠀⠀⠑⠓⠀⠉⠅⠓⠀⠀⠀⠒⠓⠤⠒⠀⠂⠨⠃⠓⠒⠒⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠁⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠤⠤⠀⠀⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠁⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠁⠲⠭⠝⣋⡑⠒⡢⠤⣄⠀⠀⠀⠀⠁⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠤⠀⠀⠼⠀⠀⠀⠀⠀⠉⠀⠙⠷⠒⠅⣤⣶⣶⢆⠠⣒⠌⠈⠀⠀⠀⠀⢀⣂⣀⣉⣁⣠⣤⢤⣬⣍⣁⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠒⠒⠒⠒⠂⠀⠀⠀⠛⠓⠓⠀⠀⠈⠐⠒⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣴⢂⣴⣾⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⣠⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⣠⣴⣾⡟⣼⡇⣾⣿⣿⣿⡇⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠚⢿⠟⠂⠀⠀⠀⠀⠀⣀⡤⣷⣿⣿⣿⣇⣿⣇⢿⣿⣿⣿⣿⣦⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢖⣵⣿⣷⣾⣿⣿⣿⣿⣿⡸⣿⡌⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⣠⣶⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣦⡙⠿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢠⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⠿⠶⣤⠄
⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠓
⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⢿⣿⣿⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣷⣿⣿⣿⣷⣌⠻⣿⣿⣿⡿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣾⣿⠀⠀⢀⣰⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⠀⣶⣿⣿⣿⣿⣿⣿⡿⠟⢩⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⡀⠙⠟⠉⠁⠈⠉⠁⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⣼
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⣼⣿⡟⠀⠈⠙⠉⠸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣀⣰⣦⣀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⢹⣿⣧⠹⣿⣆⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⣰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠹⣿⡆⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⢻⣦⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣷⣶⣶⣶⣾⣿⣶⡶⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠃⠀⠘⠀⠘⠃⠀⠛⠀⠀⠀⠸⠀⡂⠀⠀⢀⠀⠁⠘⢀⠀⠠⠀⠀⠐⠂⢐⠀⠀⠀⠐⠟⠀⠘⠃⠀⠃⠀⠐

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣬⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣯⣿⣽⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡂
⠀⠀⠀⠀⠀⠐⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠈
⠀⠀⠈⠀⠀⢠⡀⣠⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠁⠠⠖⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⡀⠐⠐⢲⢤⡀⠀⠀⠀⠀⠀⠔⠀⠀⠤⠒⠖⠉⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠚⠶⠆⠚⠛⠷⠛⡀⠀⠀⠀⢁⠄⠈⠀⠀⣠⢼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢿⣶⣾⠷⠹⠞⢻⠁⠀⠀⡠⠁⣀⡤⡲⠋⠁⡘
⠀⠈⠀⠈⢀⠄⠁⠈⠀⠀⠈⠫⠭⠭⠭⠟⠃⠀⠠⠊⠀⡢⠕⠂⠒⠐⠈⠀⠀⠀⠈⡌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⡀⢴⣒⣶⣤⣄⠀⠀⣀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⢀⡤⠖⠒⠂⢄
⠀⠀⠀⠀⢀⠉⠉⠉⢐⣓⣏⣉⡤⠂⠄⠀⠀⠀⠀⠀⠀⡀⠰⠓⠰⠂⠀⠀⠀⢀
⠀⣀⠤⢦⢂⣴⣾⣾⠭⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⡞⠉⠈⠈⠂⡀⠂
⠨⠗⠒⠛⠻⡏⠁⠀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠲⠀⢀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠣⣈⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⣀⠀⠈⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢈⡟⠋⠀⣄
⠀⠀⠀⠀⠐⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠹⡿⣷⣶⣦⣤⣄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⣀⣀⣀⣤⣠⣴⣾⣿⣿⠏
⠀⠀⠀⠀⠀⢀⠀⢹⣿⠿⡿⠿⠛⠛⠛⠛⠿⠿⠿⢷⡶⢷⣶⣶⣶⣶⡶⣶⣶⣶⡴⣾⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⠩⢟⠛⣿⠉⢿⡀
⠀⠀⠀⠀⣠⣾⢿⡿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⣾⢋⠟⠛⣻⣷⣌⡄⢿⡷⠃⠀⢻⡇⠀⠀⠀⠀⠀⠀⡜⠃⢽⣦⣿⠁
⠀⠀⠀⠀⢹⣿⣿⣦⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣳⡿⠻⣿⡟⠁⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡜⠀⠀⠠⣿⣿⣬⠂
⠀⠀⠀⠀⢰⣿⣏⢿⡉⠁⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣅⣀⣿⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠊⠀⣠⠾⣿⣯⠄⠋
⠀⠀⠀⠀⠀⠀⠃⠀⠩⡗⠈⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⢿⣿⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢀⠌⠵⢠⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡴⢢⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢾⡇⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠃⠀⢉⢛⡶⠤⣀⠀⢀⡀⠀⠘⢰⡟⠇⠀⠀⡠⠎⠀⠀⠀⠀⠀⠡⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣶⠛⠳⡄⢹⣷⣰⡇⢹⡆⢲⣎⠀⠔⠻⣶⠾⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠶⣾⣇⣽⣽⡇⠸⣿⢻⢻⢰⣿⡿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⣸⡿⣾⢡⣾⠀⢤⣤⡟⣹⢿⡯⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣣⣄⣴⣤⣼⣶⣶⣿⣇⣸⣆⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⣐⡒⢖⡰⠷⢞⠛⠛⢛⠋⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸⣄⠀⠘⢦⣄⡀⣠⠆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠉⡁⠚⠂⠘⠂⠀⢀⣌⢳⡀⠀⠹⣿⡿⠻⠟⢿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠙⣾⢉⣿⠶⠷⣤⣤⣼⠇⢾⣠⣀⣶⣬⣿⣾⣿⠘⠇⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠻⠈⠿⠁⢀⢼⣅⣿⢓⡾⣿⡻⠙⣿⠋⠿⠟⠀⠈⠉⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣷⣤⡟⠻⠀⣀⣀⣴⣿⡇⣏⡹⠿⣿⡀⠿⠟⠳⣦⡀⠀⠀⢹⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣦⠻⢿⣭⡇⢸⡟⠋⠀⠀⢰⡿⢞⡂⠀⢾⣷⡆⠀⣤⠀⠙⢠⠄⢰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⣽⡿⠛⢹⣷⣿⠄⢤⡄⠀⢺⡇⠀⢱⡀⠀⢹⠃⠈⠂⠀⠠⠀⠀⠈⣴⡀⢀⣀⡈⠠
⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⣿⣿⣿⣿⡛⠓⠉⠉⣡⠀⠀⠣⠀⢠⠀⠀⠈⡅⠀⣾⣦⣀⠼⠟⠓⢀⣠⣶⠉⠽⠛⠁⠀⠲⠛⠀⣠⠷⡀
⠀⠀⠀⠀⣴⣷⠚⢻⡿⢻⠿⠿⠿⠓⠀⠀⠀⠀⡈⠁⠀⠀⠋⠛⠑⠇⣀⠉⠠⠟⠁⢀⣠⣴⣾⣿⡍⠤⠤⠤⠤⠀⠂⠠⠶⠶⡋⠀⣤⣄
⠀⠀⠀⠀⠀⠙⣷⣯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣀⢀⣤⣀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣽⠋⠛⣹⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣼⣄⣭⣾⢋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠥⠤⠮⠿⠿⠧⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠖⠒⠒⠲⠶⠶⠶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢋⣉⣠⡤⠤⠴⠶⠖⠒⠒⠲⠶⠀⠀⣀⣉⠙⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀⢋⣉⠁⠔⠒⠚⢋⣉⣉⣉⣠⣤⣶⣦⠄⠈⠉⠛⠷⠤⠀⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⣠⣴⣾⡿⠀⠚⠋⠻⠿⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠉⠛⣷⣶⣦⣤⣈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠴⣾⣿⡿⢛⡭⠀⣀⣀⣠⡄⠀⠐⠒⠒⠛⠳⠿⠷⠤⣤⣾⣿⠖⠀⠒⠶⠬⢭⣉⣀⣈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⡰⠃⣰⠟⡹⣫⢖⣵⣾⣻⢟⣭⣭⡓⠒⢲⣶⣶⣤⣶⠖⢲⣶⣶⣶⣶⣶⣶⣶⣶⣄⣀⣤⣭⣍⣁⣻⣧
⠀⠀⠀⠀⠀⠀⣸⠧⠾⣗⣻⣭⣟⠉⢩⢿⠇⢀⢶⡲⣔⣆⠀⡶⠛⠿⠶⠬⠓⠒⠛⠛⠛⠀⠒⠒⠪⠭⢭⣙⣁⠰⣾⣿⣿⣧
⠀⠀⠀⠀⠀⢰⠗⠚⠋⠙⡛⠉⣉⣁⣘⠊⡃⠻⠬⠛⢸⣾⢣⠆⠀⢀⣀⣤⡤⣤⣤⣤⣤⣀⣀⠀⠀⠀⣀⣆⠏⠇⠿⠃⠹⡽⣧
⠀⠀⠀⠀⠀⣎⣸⣿⣿⣿⠧⠴⢿⣿⣿⠀⠙⣒⣖⣻⣽⠇⠈⢀⣠⡽⠛⠉⠀⠉⠉⠉⠉⠉⠉⠉⠙⠓⠻⠿⢽⡛⣶⢷⡶⣷⢿⡄
⠀⠀⠀⠀⢰⠏⠉⣁⣀⣠⣤⣤⣤⣤⣩⠑⠿⠋⠉⠀⠀⠀⠖⠋⠡⠤⠶⠶⠶⠿⣿⣿⣿⡿⠋⣳⣦⣤⣀⣀⣀⣉⠘⠘⠗⢻⣿⡇
⠀⠀⠀⠀⢸⡆⠻⠛⠛⢋⣉⡩⠴⢒⡀⣠⣤⣴⣶⣶⡿⠧⠶⢖⣒⠛⠉⠀⠀⠀⠻⢓⣶⣆⣀⡤⣤⠭⣭⣤⣽⢹⠟⣿⣿⡏⢩⡇
⠀⠀⠀⠀⢸⣿⣶⣤⣿⣿⣿⣆⡈⣽⣦⣤⣭⠥⢴⠒⠒⠋⣉⣁⣀⡤⠤⠀⠤⠖⠒⠒⠒⠶⠬⠟⠛⣛⣋⣉⣻⣹⣉⣿⣷⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⢿⡿⢿⢿⡿⢩⣭⣽⠶⠞⠋⠛⠛⠋⢉⣉⣡⡤⠶⠚⢀⣤⣶⠯⣭⣭⣽⣶⣤⣄⣩⣏⣩⣍⣧⣼⣿⣾⣿⢾⠇
⠀⠀⠀⠀⠘⣿⣿⣟⢓⠀⠤⠤⠌⠓⠓⣀⡤⠴⠶⠒⠋⠉⣁⡤⠴⢒⡿⣻⣿⣿⣿⡆⣸⠖⣻⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⡿⡞⣖⢦⠲⠘⠉⠁⢀⣀⣀⣠⣤⣤⣴⣶⣤⣽⠶⣿⣿⠷⣻⡿⣣⣼⢁⣰⣿⣭⡄⠛⠓⣲⣿⣿⣿⣽⠇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⠛⠛⣻⣿⣿⣿⣟⣿⣿⣿⡿⢗⣀⣤⠴⣻⠏⣀⣬⣾⣿⣤⡽⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⢿⣟⠻⡟⠩⠭⣭⣽⣿⠛⠛⠛⠛⣃⡀⠉⠉⠉⠁⢙⣻⣀⣼⣷⣿⡿⣿⠿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⣿⣿⣿⣿⣿⠿⢿⡿⢟⣽⡟⣿⣿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣛⡛⠻⣾⣛⡛⠾⣿⣿⣿⣿⣿⣟⣯⣭⣶⣾⣿⣾⣿⣿⣿⢟⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣛⣿⣽⣞⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣮⣭⣿⣿⣭⣽⣿⣿⣯⣿⣿⣽⣷⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠾⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠈⠉⠉⠉⠐⠒⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⢋⣷⢄⡀
⠀⠀⠀⠀⢀⣀⠠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠛⢁⣴⠟⠁⠀⠉⠢⡀
⠀⠀⠀⠻⣥⠄⠒⠒⣉⣱⢤⡀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠛⠉⢀⡴⠋⠀⠀⠀⠀⠀⣠⣿⣄
⠀⠀⠀⠀⠀⠑⢯⣁⡩⠶⣔⠛⢢⣀⠀⠀⠀⠀⡜⠀⠀⠀⣀⣠⣤⣶⣿⣿⡿⠟⠋⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⣠⣾⣿⡿⣩⣆
⠀⠀⠀⠀⠀⠀⠀⠉⠢⣖⠊⣛⣥⡨⠷⢄⠀⣼⣶⣶⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⢉⣼⡿⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⡤⠝⠶⣊⠙⣻⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⢁⣴⠟⠁⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠉⠙⠿⣖⣒⡭⢿⠤⠤⢐⣒⡺⡍⠑⡔⢢⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠋⣠⠶⠋⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠙⡹⣆⠈⠆⢿⠿⣿⠛⢸⠀⢱⠴⠁⢀⣠⣤⣶⣿⣿⠿⠛⠉⣀⠴⠊⠁⠀⠀⠀⠀⢀⣼⠟⢉
⠀⠀⠀⠀⠀⠀⢈⠀⣀⣀⠤⢄⠀⠀⢡⢻⠀⢸⠘⢃⣉⣶⣼⣤⣾⣶⣿⣿⡿⠟⠛⠉⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⣠⡶⠋⢁⣴⡿
⠀⠀⡠⢤⣤⡲⢯⠭⠔⠒⠊⠉⠀⠀⢸⡿⠄⢺⣿⣿⠿⣉⡩⠷⢤⡚⢫⣄⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⢀⣴⡿⢛⠇
⠀⠀⠑⠉⠀⠀⠀⠣⡀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢣⣤⣤⣼⠶⣖⠊⢙⣧⣤⠵⢤⡀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⣠⣶⠟⠋⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⠤⠖⠁⠀⠀⠀⠀⠀⠫⡀⠀⠀⠀⠙⢤⡤⠜⠳⣎⣉⡦⣤⠔⠚⠉⠀⢀⣠⣴⠟⠋⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⣤⣤⡼⠶⣉⣉⠹⠤⠘⠓⢤⣴⠾⠛⠉⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢍⣀⣀⣀⣬⣷⣤⠴⠖⠚⠉⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠫⠥⠀⣀⣀⣀⠠⠤⠔⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠛⠂⠀⠀⠀⠒⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢀⡀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠕⠈⠀⠈⠁⠂⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠠⠤⠤⠥
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡀⠀⠀⠀⠑⢌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡁⠀⠡⠀⠀⠀⠀⢂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⡦⠀⢀⡉⠉⠐⠠⠄⢀⠀⠀⠀⠀⢳⠀⠀⠑⠄⠠⠀⠀⠀⠀⠀⡆⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠔⠂⠀⠁
⠀⠀⠀⠉⠢⡀⠀⠉⠀⠐⠂⠄⢈⡁⠒⠠⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠐⠂⠀⠀⡁⠠⠀⠤⠤⠤⠀⡄
⠀⠀⠀⢠⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⡄⡈⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⢀⡠⠔⡠⢁⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠉⠁⠀⠀⠀⠀⢀⡀⠄⠐⠂⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢊⡠⠐⠂⠉⠀⢈⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠒⠒⠊⠉⠀⡠⠔⠁⢀⠔⠁⠀⠀⢀⠠⠐⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠈⠂⠐⠒⠈⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⢔⠒⠠⠄⢀⣀⣀⣀⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠛⠛⠒⠲⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⢸⠃⠀⣠⣾⣻⣿⣛⣛⣓⣶⣦⣭⣙⡓⠦⣤⣀⣀⣠⡤⠤⢤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠸⡆⠀⢿⡟⡛⡿⠉⡭⠬⠭⢭⣛⣛⢿⣿⠖⠋⢁⠀⠀⠀⠀⠀⢄⣌⡉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⣿⣷⣿⡈⢇⠀⠀⠀⠀⣨⠏⡄⠀⠀⠀⠉⠣⠄⠀⠐⠀⡆⢻⣿⣦⣝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⢻⣽⣟⣌⠳⣄⠀⡼⠁⠈⠉⠳⣦⡄⠀⠀⠀⠀⠉⣵⣶⣶⣯⠝⠿⠧⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢷⣟⣳⣌⡻⢇⡀⠐⢲⣀⣈⡹⠺⣦⡀⡤⢀⡈⣛⢿⣿⣯⣿⢲⠆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡝⠳⣟⣿⠦⣙⠲⣄⣻⣛⣿⣿⣼⠧⣿⣟⣻⣿⣷⣿⣿⣗⡯⣐⢸⡗⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠳⢯⣼⢳⣬⡙⠻⣽⣿⣿⣿⣿⣿⣯⡿⢿⣿⣿⣯⣷⠎⢸⣿⣷⣌⡳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠛⢾⣯⣷⢦⣍⠛⠿⣿⣿⣿⣶⣿⣷⣭⢹⠏⠃⡼⠲⣝⢿⣿⣦⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⠳⢤⣈⠙⠾⣷⣫⡖⣦⣍⡛⠻⢿⣿⣿⣧⠈⡼⠁⠀⠈⠳⡜⢿⣿⣶⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠹⠻⢶⣄⣉⠛⠷⢾⣫⣻⢶⢤⣍⣙⡚⠳⠤⠤⠤⠤⠟⠀⣿⣿⣿⣦⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣈⠈⠙⠿⠶⢤⣌⣉⠛⠾⠯⣯⣯⣟⣟⣶⠶⣶⣶⣟⣿⣻⣿⣻⠇⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠉⠙⠓⠶⠤⣤⣉⣉⡛⠛⠛⠓⠛⠛⠛⠛⠉⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠒⠒⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡿⢉⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠰⠿⠋⣤⣤⣤⣤⣤⣌⠙⣧⡘⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠟⠁⠀⠀⠀⠀⠠⠾⠿⠿⠿⠟⢉⣉⣉⣉⣰⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠒⠒⠲⣶⣶⣶⣿⡿⠿⠏⣉⣉⣉⣉⣉⣉⣉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡶⢀⣿⣷⡆⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⣉⡉⢻⣿⠀⣶⣶⣿⣿⣿⣿⠟⠛⠛⠛
⠀⠀⠀⠀⠀⢀⣴⠚⣁⣾⠀⠿⠟⢋⣠⡿⠛⢋⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⣸⣿⣦⣤⣤⡤⠤⠤⠤⢴⣿⣿⣿⠃
⠀⠀⠀⠀⢠⣾⠃⣼⡿⢋⣁⡐⠻⣿⠋⣰⡞⢉⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣉⣉⣉⣉⠛⣿⡏⢰⣶⣶⣶⣆⣙⠛⠋
⠀⠀⠀⠀⣿⣿⡀⢻⣷⠈⠻⠿⠆⢘⡄⢻⣷⣌⡙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⢀⣿⣿⣦⣤⠈⠛⠛⠋
⠀⠀⠀⢸⣿⣿⡷⠀⣿⡿⠒⡀⢺⣿⣿⣄⠙⢿⣷⣄⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠸⣿⠟⣡⡾⢋⣴⣿⡇⠸⣿⣿⣿⣷⣄⠹⣿⣷⡆
⠀⠀⠀⠀⣠⣾⡏⢠⡏⢠⣤⡉⢢⣉⠻⢿⣿⠿⠃⣽⡿⠁⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠘⢿⣇⠘⢧⠘⢋⣤⡾⠛⣡⡾⢁⣴⣿⡟⠁⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠙⠷⣤⣉⡛⠋⣰⣿⡿⢁⡾⠟⠉⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣰⣿⡿⠋
⠀⠀⠀⠀⢀⣴⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣋⣡⣴⠾⠛⣉⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣷⣤⣤⣬⣉⣉⣭⣤⣤⠴⠶⠞⠛⣉⣥⣤⣶⣿⡿⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⣉⣩⣥⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠠⣼⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠏

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄⡀⠸⢀⣄⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⣀⣴⣾⡯⠤⠾⠛⠁⠀⠀⠀⢠⣿⣥⣿⣿⡷⠀⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠛⠛⠋⠂⠈⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⣿⣇⠄⠈⣾⠇⠀⢀⣀⡀⠀⠀⠀⠀⠀⣸⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠏⠈⡄⠀⡠⠔⢏⠉⢹⣇⣇⣦⠖⠁⠀⣴⣿⣿⣿⡆⠀⠀⠀⠤⣿⡀⠃⣼⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢵⣢⣇⣴⠿⣦⣤⣼⣿⠾⣷⣆⠀⠹⣿⣿⡿⠃⠀⠀⠀⡖⣿⣏⣹⣿⢸
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠄⠄⠀⠀⠈⠁⢻⣄⣽⣿⡿⠧⠤⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⡇⢸⣿⣹
⠀⠀⡤⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⢰⠀⠀⢻⣥⣽⣷⠀⣠⣴⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⡷⡿⡇⢸⢿⢾
⠀⠀⣤⣀⣴⡇⠀⠀⠈⠉⠛⠶⢶⣾⣄⣤⡀⠀⠈⢿⡏⠀⣿⡓⣶⣵⡀⠀⠀⠀⠀⠀⠀⣿⠃⡇⢸⡎⢿⡀
⠀⢾⣿⠋⠙⠳⣄⠀⠙⠓⠶⠟⠋⠀⠈⠉⠉⠀⠀⠈⢿⣤⣴⡝⢿⣟⠁⠀⠀⠀⠀⢀⣾⣹⡿⢹⣾⢹⣿⣷⡄
⠀⢠⣿⣦⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠁⠘⣉⠀⠀⠀⠀⠀⠀⠁⣟⣷⢿⣿⢾⣘⠆⠁
⠀⠉⠀⠀⠉⠳⢴⣄⣀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠻⢥⡑⣄⠀⠀⠀⠀⠘⠁⠈⠁⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣈⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢂⠀⠀⠉⠁⠀⠀⠀⠀⣠⡖⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠈⠙⠲⢕⢄⠀⠀⠀⠀⠀⠀⠀⢹⣤⡆⠀⠀⣰⠃⠀⠘⠋⠉⠠⠂⡀⠐⠀⣆
⠀⠀⠀⠠⠐⠄⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⢀⢈⠀⠀⠀⣄⠁⠰⠆⠀⡀⣐⣰⣿
⠀⠀⠀⠀⠘⢠⣤⡀⠀⣠⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⣤⠶⠷⠛⣨⠀⠀⠈⣶⣴⣰⣾⣥⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠛⠃⠀⠛⠏⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⡤⠚⠋⠀⣀⣴⣾⣯⣄⣀⠀⠈⠙⠛⠛⠛⠛⠁⠀⡀
⠀⠀⠀⡀⠀⠀⠀⢀⢀⠀⠀⠀⠠⠀⠀⠀⠀⣤⠚⠋⠀⢀⣤⡼⢟⣋⠥⠭⠯⠥⠭⠵⠖⠀⠈
⠀⠀⠈⡄⠀⠀⠀⠈⠁⠀⠀⢀⠐⠁⠀⣠⢾⠀⣀⣴⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠤⣶⣾⠛⠁
⠀⠀⠀⠀⠀⠔⠂⠄⠀⠄⠒⠐⠁⠀⠰⠿⠷⠛⠋⠉⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠂⠀⠀⠒⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⠀⠀⠀⠤⠤⠄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⠀⢀⡄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢡⠤⠤⢀⡀⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢇⡀⠔⠁⠀⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠉⢀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⣁⡆⡂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠈⠁⣀⠠⠐⡎⠁
⠀⠀⠀⢀⡠⠒⠁⠀⡔⠊⠀⠡⠀⠀⠀⣀⣀⠠⠤⠐⠒⠈⠉⣀⠠⠄⠒⠈⠁⠀⠀⠰⠁
⠀⠀⠔⠁⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠁⢀⣀⠠⠄⠐⠒⠋⠡⠁⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠑⠂⠠⠤⠤⠄⠀⠐⠒⠒⠈⠉⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⣀⡀⠀⠀⣀⡀⠤⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⢀⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠩⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡽
⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠸⣿⡉⠁⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣄⣠⣠⣠⣠⠀⠀⢠⡄⠀⠀⠀⠀⣾⠀⠆⠑⠍⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠘⢆⣐⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠒⢤⠀⠀⠀⠀⠀⠐⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠠⠾⣄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢒⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠳⣄⣀⣀⣀⣠⠴⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠈⠈⠈⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠒⢿⡄⠤⠤⠔⠠⢄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠤⠤⠔⠋⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠁⠀⠈⠙⠦⡀⠀⠀⠀⠀⢰⠩⠩⣦⠀⠀⠀⠀⠀⠀⠀⠸⣁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⠉⠉⠉⠙⠛⢳⠀⠀⠀⠀⠈⠒⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠠⠴⣶⠖⠢⠄⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠂⣠⠶⠛⠒⠆⡀⠐⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠒⠒⠁⡄⢠⡄⢠⠈⠒⠒⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢱⡦⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢴⡎⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠌⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢡⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠐⠀⢀⣀⣅⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⡀⠀⠆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠁⡌⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⢰⠀⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠄⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡄⠠⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠔⠁⠀⠸⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠃⠀⠈⠢⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢁⠔⠁⠀⠀⡠⠂⠀⠀⠋⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠀⠀⠘⢤⡀⠀⠈⠢⡈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢀⠔⠁⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠢⡄⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠂⠁⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠈⠐⢄⠈⠳⣄
⠀⠀⠀⠀⢀⡴⠊⠁⡠⠊⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠧⠤⠄⠠⠤⠤⠠⠤⠤⢸⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⢄⠈⠑⢦⡀
⠀⠀⠀⣰⠋⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠦⠀⠠⠠⡔⢢⠤⠄⠀⠸⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈⠢⡀⠙⣆
⠀⠀⠀⢹⠀⠃⠒⠀⠒⠒⠒⠀⠒⠂⠀⠒⠒⠒⠒⠒⠒⠂⠖⠁⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠈⠲⠐⠀⠒⠒⠒⠒⠀⠐⠂⠒⠂⠒⠒⠒⠂⠒⠘⠀⡏
⠀⠀⠀⠺⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠆⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠰⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⡇
⠀⠀⠀⠀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠠⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠄⠚⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠃⢤⣀⣀⡀⣴⢿⡿⢠⣀⣀⣀⠠⡞⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣅⣠⣀⣭⣹⣯⣨⣅⣀⣈⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⡿⠋⣍⣀⣀⣀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈