The smiley company Emojis & Symbols

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


⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣛⣛⣛⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡳⠚⠁⠀⠀⠀⠀⠀⠀⢠⠀⠁⠉⡓⢄⠀⠀⠀⡰⠊⠀⠀⠀⠒⡀⠀⠀⠀⠄⠈⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⡠⠂⡀⠀⠀⠐⠂
⠀⠘⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⢌⠀⠀⡁⠈⠀⠀⠠⠁⠀⢁⢀⡃⠀⠸⠀⠀⠀⠀⠃⠀⢒⣄⡃⠀⠀⠀⢠⡄⠀⠀⣥⢈⠀⠀⠀⠀⡄⣀⣀⢀⠌⠁
⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠢⡀⠐⠂⣀⠄⠀⠀⠀⠢⡐⠃⠀⠛⠠⠀⠀⠀⠈⢦⡀⠘⢈⡿⠃⠀⠀⠀⠪⣁⠀⠀⠈⠀⠀⠀⠀⠣⡐
⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⠀⠀⡀⠘⠂⠓⠢⡀⠀⠀⠀⠠⠐⠀⢀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠃⠀⠂⠘⠀⠀⠀⠀⠀⢸⠁⠒⠀⠂⠀⠀⠀⠀⠀⠁⣡⠒⣀⡄⠀⠀⠀⠀⠀⣾⣿⠛⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡠⠂⠀⠀⠘⣀⠈⠀⠁⢀⠆⠀⠀⠀⠄⠙⠋⠙⠁⠀⠀⠀⠀⢠⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠈⠉⠓⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠉⠁⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠉⠑⢂⠀⠀⠀⢠⠖⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠒⠀⠒⠀⡇⠀⠀⠈⠀⠉⢀⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⢈⠀⠀⠀⡇⠀⠃⠀⠈⠁
⠀⠀⢄⣀⠀⠀⡠⠀⠀⠀⠈⠆⠀⠀⢀⡀⠌⠀⠀⠀⠙⢄⣀⢀⣀⡴⠃⠀⠀⠀⠂⠀⠙⢁⡠⠀⠀⠀⠀⠂⠈⠐⠂⡠⠊⠀⠀⠀⠁⠀⠀⠀⠀⠠⠃
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⠈⣁⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢀⣈⣀⣀
⠀⠀⠊⠁⠀⠀⠘⠆⠀⠀⠀⠐⢉⡀⢀⡈⠣⠀⠀⠀⡰⢉⠀⠀⡄⠐⡄⠀⠀⠀⠀⣀⠀⢠⠀⣄⠀⠀⢀⣘⣥⡀⣤⣽⢷⡀⠀⠀⣰⢋⡀⠀⣈⠑⡄
⠀⢀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠁⠀⣁⣀⠀⢠⠀⠀⠀⢇⠀⢀⠄⠀⠀⡇⠀⠀⠀⠀⠀⢠⣤⠄⠠⠀⠀⢠⠀⢭⣀⣠⡅⢠⠄⠀⠀⡄⠠⠉⣄⣉⠀⡗
⠀⠈⠣⠄⠀⠀⠔⠁⠀⠀⠀⠑⠄⣀⡀⠀⠁⠀⠀⠀⠈⠢⢄⣀⠠⠊⠀⠀⠀⠈⠢⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠤⠊⠀⠀⠀⠈
⠀⠀⢀⡀⠤⠀⡀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠤⡀
⠀⢠⠋⣀⠀⡠⠌⠂⠀⠀⠀⠊⠀⠀⠀⠀⠹⠀⠀⠀⠰⠁⡀⠀⣠⠘⡆⠀⠀⢠⠊⢀⠀⢀⡘⠆⠀⠀⠠⠃⠀⠀⠀⠀⠁⠀⠀⠀⡜⠁⢀⠀⡀⠀⡆
⠀⠨⠀⠀⠠⠀⠀⡀⠀⠀⠰⡀⠠⠤⠀⠀⢸⠀⠀⠀⠃⠀⠠⠀⠀⠀⠇⠀⠀⠸⡀⠈⢠⡀⠁⡄⠀⠀⠠⡀⠀⠀⠀⠀⠠⠀⠀⠀⢇⠀⠊⠈⠁⠀⡆
⠀⠀⠙⠦⠀⠠⠈⠀⠀⠀⠀⠑⠤⠤⠀⠐⠋⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠚⠁⠀⠀⠀⠑⠀⠠⠤⠔⠀⠀⠀⠀⠈⠢⠄⠀⠀⠈

⠀⡠⠂⠈⠉⠓⢄⠀⠀⠀⢀⠔⠀⠈⠉⠢⡀⠀⠀⠀⡠⠂⠀⠉⠑⢦⠀⠀⠀⠀⡴⠂⠈⢉⠒⡄⠀⠀⠀⢀⠔⠀⠈⠉⠢⡀⠀⠀⠀⡠⠂⠀⠉⠑⢄
⠘⠀⠈⠁⠈⠁⠸⠀⠀⠀⡆⠀⠁⠀⠋⠀⢱⠀⠀⢠⠁⠘⠃⠘⠃⠀⡇⠀⠀⡘⢀⠛⠀⠘⠃⢸⠀⠀⠀⡎⠠⠄⠀⠤⠀⢡⠀⠀⢰⠁⠘⠃⠘⠓
⠰⣌⠒⠤⠴⢂⡜⠀⠀⠀⢣⡀⠀⠀⠀⣠⠆⠀⠀⠘⢆⠐⠂⠉⠁⡰⠁⠀⠀⠰⡈⠙⠙⠋⢋⠟⠀⠀⠀⢣⡀⠀⠀⠀⣠⠇⠀⠀⠘⢄⠀⠰⠂⢀⡴
⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠀⠈⠒⠒⠈⠁⠀⠀⠀⠀⠀⠁⠒⠒⠉⠀⠀⠀⠀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠀⠈⠒⠒⠈⠁⠀⠀⠀⠀⠀⠁⠒⠂⠉
⠃⢀⠄⠀⠀⢤⡀⠃⠀⠀⠀⡠⠀⠀⠠⢄⠀⠀⠀⠀⠀⡠⠀⠀⠤⡀⠀⠀⠀⠀⢀⠄⠀⠠⢄⡀⠀⠀⠀⠀⡀⠄⠀⠠⢄⠀⠀⠀⠀⢀⠠⠀⠀⠤⡀
⠠⢁⠲⠄⢴⠂⠹⠀⠀⠀⡜⠀⣤⢠⡄⠀⢣⠀⠀⠀⠎⠠⠆⠠⡤⠈⡆⠀⠀⢰⠁⠰⠆⠤⠀⢱⠀⠀⠀⡜⠩⠄⠠⡌⠀⢃⠀⠀⢠⠃⠰⠀⣶⡷⠘
⢠⠘⠢⢄⡀⠀⣠⠀⠀⠀⢇⢶⡶⠆⣆⡶⡜⠀⠀⠘⡀⢀⡀⠀⠀⢀⠇⠀⠀⢠⠀⠀⣀⠀⠀⡸⠀⠀⠀⢇⠀⠐⠢⠀⠀⡌⠀⠀⠸⡀⠀⠐⠭⡁⢀
⠀⠑⠤⠤⠤⠒⠁⠀⠀⠀⠈⠒⠤⠤⠔⠊⠀⠀⠀⠀⠘⠢⠤⠤⠖⠁⠀⠀⠀⠀⠑⠤⠤⠤⠚⠁⠀⠀⠀⠈⠓⠥⠬⠔⠊⠀⠀⠀⠀⠙⠢⠤⠤⠒⠁
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠰⢤⣤⣤⡴⠆⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⢀⠞⠁⠀⠀⠈⢢⠀⠀⠀⢠⠊⣄⠀⣄⠙⠄⠀⠀⠀⡔⢅⡀⢀⡈⠳⡀⠀⠀⢀⠞⢁⠀⣀⠉⢦⠀⠀⠀⢠⠊⡀⠀⣀⠙⡄⠀⠀⠀⠔⣉⠅⢈⡽⠣
⢈⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠋⠀⠛⠀⠸⠀⠀⢰⠀⢈⣁⣈⡠⠀⡇⠀⠀⠈⠀⡀⠀⢈⡠⢸⠀⠀⠀⡇⠒⠡⠤⠥⠄⠸⠀⠀⢸⢘⣛⣋⣙⣓
⠈⢦⡀⠠⢘⣡⡞⠀⠀⠀⠑⢄⡊⠉⣃⠴⠃⠀⠀⠀⠣⣀⠀⠀⣠⠜⠀⠀⠀⠘⢦⡀⠉⢙⡲⠊⠀⠀⠀⠑⢄⡀⠀⣀⠴⠃⠀⠀⠈⠪⣓⠼⠴⡪⠜
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⡠⠐⠀⢐⠢⡄⠀⠀⠀⠀⡠⠂⠀⢒⢦⡀⠀⠀⠀⢀⠔⠀⠐⡲⢄⠀⠀⠀⠀⡠⡂⠀⠒⠂⠀⠀⠀⠀⢀⣴⣒⠒⣲⣦⡀⠀⠀⠀⣠⠖⠒⠒⠲⣄
⠰⣁⠈⠀⠙⠁⠘⠀⠀⠀⡎⠐⠃⠰⠀⠇⢡⠀⠀⢀⠃⠘⠃⠘⠃⠈⡆⠀⠀⠰⠀⠘⠀⠸⠃⢘⠀⠀⠀⡚⠘⠋⠀⠛⠀⢳⠀⠀⢰⣓⣋⣁⣉⣙⠸
⠰⡐⢄⠀⠀⠀⡸⠀⠀⠀⢇⠰⠴⠴⠶⢀⠌⠀⠀⠘⣄⠀⠐⠀⠄⣠⠃⠀⠀⠰⡉⠢⠄⠠⠜⡟⠀⠀⠀⢇⠐⠉⣀⡠⢀⠏⠀⠀⠘⡙⢛⣛⣛⠟⡩
⠀⠈⠒⠠⠐⠊⠀⠀⠀⠀⠀⠑⠢⠀⠒⠁⠀⠀⠀⠀⠈⠒⠀⠐⠊⠁⠀⠀⠀⠀⠉⠒⠄⠒⠉⠀⠀⠀⠀⠀⠑⠢⠀⠒⠁⠀⠀⠀⠀⠈⠒⠈⠐⠊
⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢀⠜⠁⡀⠀⠈⢢⠀⠀⠀⠠⠊⣤⠀⣬⠙⠄⠀⠀⠀⣴⣥⣤⣠⣤⣵⡀⠀⠀⢀⠎⢠⣤⣀⠈⢢⠀⠀⠀⢠⠊⡀⠀⣀⠙⠄⠀⠀⠀⡔⢃⡄⢀⡈⠳
⢘⢀⣉⠀⢀⣠⢀⠀⠀⠀⡇⣆⢐⡒⡒⡶⠸⠀⠀⢰⣄⠉⠁⠈⢉⣡⡇⠀⠀⢈⢀⣘⢂⢛⡀⢸⠀⠀⠀⡇⢖⣠⣤⣀⠁⠸⠀⠀⢸⠀⠠⣀⣀
⠈⠊⣓⡒⣐⡡⠊⠀⠀⠀⠑⢌⡓⠂⢒⠕⠁⠀⠀⠀⠣⣉⠉⠉⣡⠜⠀⠀⠀⠈⢮⡁⠀⢀⡡⠊⠀⠀⠀⠑⢌⡉⠀⣀⠴⠁⠀⠀⠈⠢⣀⠉⢑⡠⠞

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⣛⡫⠭⠶⠶⠿⣿⣿⣿⣿⣿⣶⣶⣮⣽⣿⣿⡿⠛⠉⠉⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣙⠛⣝⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⣹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿
⣉⣭⣤⣤⣤⣤⣤⣤⣤⣬⣭⣍⣉⣩⣭⣥⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡞⣭⣿⣿⣷⢻⣿⣿⣿⣿
⠉⠉⠛⠛⠛⠉⠉⠻⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡃⠀⣥⣿⡏⣿⣿⣟⣿⣿⣿⣿
⠐⠒⠒⠂⠀⠀⠀⠀⠀⣶⣶⣷⣿⣿⠁⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⡖⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣙⣋⣙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣭⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⣶⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡆⠙⠛⠁⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠩⠽⠿⠻⠋⠙⠛⠛⠛⠛⠋⠛⠇⠀⠀⣤⠀⠀⠀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⣤⣄⣐⣒⣲⣶⣖⠀⣰⣦⠀⣼⣿⡄⠀⠀⠁⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣽⡽⢩⣉⡹⠟⠛⢏⠰⣿⣿⣇⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠿⠛⠋⠉⠙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⣿⣿⣿⡄⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣠⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⠴⠒⠀⠀⠀⠀⠀⠐⠒⢿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣤⡵⣻⢏⣿⣻⣿⣿⣿⣿⣿⣿
⠄⠀⠄⡤⣤⡜⠀⠛⠀⠀⠀⠁⠀⠀⢰⠼⣿⣻⣿⣇⠀⠀⠀⠀⠀⠙⢷⣤⣀⣘⣰⣵⡿⣷⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⡠⠾⠉⡀⣶⡜⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠛⢛⣻⣥⣾⡟⣽⣿⣿⣿⣿⣿⣿
⣿⣷⣦⣀⠀⠀⠀⠀⠈⠉⠉⠷⣶⢄⠀⠀⢈⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠛⣻⣧⣋⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⣌⣉⡓⠿⠶⢤⣽⣿⡴⣿⢿⡇⠿⠊⣛⣿⣿⣷⣤⣀⡀⠀⢐⣛⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣇⠀⠀⠰⣿⠆⠀⠀⠀⠘⠟
⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠰⣿⡧⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⡏⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠈⠓⠶⠤⠤⠤⠶⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣶⡆⠀⠀⠑⣄⠱⡀⠀⠀⣧⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡄
⢀⡤⠶⠒⠒⠶⢤⡀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡇⠀⠀⠸⡄⠘⣆⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⢸⠇
⢁⡤⠒⠂⠀⠀⠀⠈⠃⡀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠃⠀⠀⠀⠙⢦⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠁⠀⠀⠀⠀⣴⣦⠀⠀⢣⠀⠀⠀⡆⠀⠀⠿⠇⠀⠀⢀⡴⢁⡞⠀⠀⠀⠀⠀⠈⠛⢦⣀⠙⠓⠲⠶⠆⠀⠀⢀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣠
⠀⠀⠀⠀⠀⠈⠁⠀⠀⣸⠀⠀⠀⠈⠦⡀⠀⠀⠀⠐⢉⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠉⠉⠓⠶⣄⠀⠀⠀⠀⡇⢸⡄
⠀⠀⢺⡿⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢱⡀⠙
⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠂⠀⠀⠀⠹⡄⠀⠀⠱⣄
⠙⠒⠒⠒⠋⠁⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠉⠉⠉⠓⠲⣤⡀⠉⠳⣄⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⢧⡀⠀⠀⠀⠀⡿⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⢷⠀⠀⠀⠀⣷⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⡞⠁
⡤⠤⠤⠤⢤⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿⠀⠀⠀⠀⠘⢦⣀⠀⠈⠓⠦⠤⠤⠶⠚⠉⣠⠶⠋⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⠟⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⣠⠖⠉
⠀⠸⡿⠀⠀⠀⠀⠘⡄⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⢣⠀⡇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢀⣠⡤⠤⠶⠖⠒⠒⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⡎⢠⠇⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠀⠀⠀⡇⠀⠀⣴⡆
⠀⠀⠀⠀⡠⠞⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⣴⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢧⠀⠀⠈⠁
⠀⠐⠒⢉⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⢷⠀⠀⠀⠀⠈⠳⣄
⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠖⠛⠉⣉⡉⠙⠓⠲⢄⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⠚⠉⠉⠉⠉⠉⠒⠀⠀⠹⣄⠀⠀⠀⠈⣇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠘⢦⡀⠘⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠦⣄⡈⠉⠓⠒⠶⠶⠒⠋⠁⣠⠴⠋⠀⠀⢀⣠⠤⠔⠒⠒⠢⠤⣄
⠑⢄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠈⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⠶⠶⠒⠛⠋⠁⠀⠀⢀⡴⠋⡠⠖⠋⠉⠉⠓⠲⢄
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠜
⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣈⣳⣄⣀⣀⣀⣀⣀⣀⣠⣴⣚⣁⣀⣀⣀⣀⣀⣀⣠⣴⣛⣉⣉⣉⣉⣉⣛⣦⣄⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣷⡄⠀⠀⢠⠚⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⢰⡏⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⡇⠀⠀⢻⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠶⠦⡄⠀⢹⡆
⠀⣼⠃⠀⠚⢹⡍⠁⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠁⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⣧
⠀⣿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣿
⠀⢻⡄⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢠⡟
⠀⠸⣇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣼⠇
⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣀⣀⣀⣀⣀⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣉⣩⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⢉⣷⠴⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠒⠒⠲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠯⣶⠖⢰⡋⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠹⡄⠀⢸⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⡾⢀⡀⠀⠹⡄⠸⡆⠀⠀⠖⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⠃⠈⢦⣀⣷⠀⠹⡴⣶⡉⢩⠏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡄⠀⠓⠿⣥⡾⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⡇⠀⠀⢠⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠘⠿⠛⠀⠀⠀⠀⠀⢠⠆⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢚⡳⡟⠃⠀⠀⠀⠀⡇⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠘⠉⣠⡆⠀⠀⠀⠀⢣⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊⠀⡇⠀⠀⠀⠀⠘⡆⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠉⠛⠲⠶⠤⠤⠴⠶⠞⠋⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⠤⢤⣤⣤⠤⠤⢴⡖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡒⢒⡒⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⡇⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡮⠓⠺⢧⣀⡀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⢸⢻⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣤⣀⠀⠉⠑⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣇⣠⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠑⠢⢄⡀⠀⠀⠉⠑⠒⠤⢤⣀⡀⣠⠼⠶⠟⠀⢹⡀⣿⣤⠤⠒⣾⠷⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠈⢙⡦⠀⠀⠀⠀⠉⢛⣛⠛⡛⢛⢉⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠃⢰⠀⠀⠀⢹⣆⠀⠀⠀⠀⠉⠑⠢⢄⣀⠀⢱⣆⣀⣀⣾⣿⡏⠉⣟⠩⣯⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣆⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠉⡏⠉⢸⣿⢧⣤⠼⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠉⢹⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡏⠴⡿⠟⣠⣝⢅⡈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠓⠲⠦⢼⡄⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⢀⣽⡋⣾⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⠀⠀⣇⢷⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡿⢿⣷⢈⣿⣥⣈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠧⠉⠚⠉⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡿⡟⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠲⡤⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣞⣀⣾⡦⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⣹⣿⠶⠢⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠛⣻⠋⠉⢉⣛⣧⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⠿⠥⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⣛⡛⠉⠉⠉⣡⣶⣿⡿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣾⣿⡿⠿⣷⡌⢰⣿⣿⡏⠁⣸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣿⣿⣯⣁⣠⣿⣿⠘⢿⣿⣿⣿⣿⣿⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣆⠻⣿⣿⣿⣿⣿⠏⣴⣬⣙⠛⠛⣋⣥⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣷⣬⣉⣉⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣿⣿⣿⣿⣿⣿⣿⡉⠻⠿⣿⣿⡿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡤⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⠉⠛⠛⠛⠛⠛⠋⣁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⢿⣿⡿⠿⠿⠿⠛⠛⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⣿⠁⣿⠤⣾⣿⠭⠥
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣛⡀⢛⡀⠘⣛⢓⢒⠀⠀⣀⣀⡀⡀⠀⣀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⢭⣍⣿⣧⣸⣿⣿⣿⠀⠀⣿⠭⠅⠹⣶⠋
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠛⠶⠛⠛⠘⠃⠛⠛⠛⠒⠒⠛⠒⠒⠀⠛
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⠉⠙⢲⠏⠙⣧⣿⣇⣸⣿⣿⣉⡷⣼⢷⡀⣿⣆⣿⠙⣦⡞
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⠶⠞⠙⠷⠶⠋⠿⠹⠇⠿⠿⠀⠰⠋⠙⠧⠟⠘⠿⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⠿

⠀⡠⠒⠉⠉⠉⠓⢤⡀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠓⢦⡀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠙⠢⣄⠀⠀⠀⠀⢀⡤⠚⠉⠉⠉⠲⢄
⡜⠀⣠⣄⠀⣀⣄⠀⢱⠀⠀⠀⡸⠁⢀⣄⠀⢀⣄⠀⠹⡀⠀⠀⢠⠋⠀⣠⠀⠀⣠⡀⠈⡆⠀⠀⠀⡎⠀⢠⡄⠀⢠⡄
⡇⠀⢁⠈⠀⠁⡀⠀⢸⠇⠀⠀⢇⠀⠈⡁⠀⠀⣉⠀⢀⡇⠀⠀⢸⠀⠀⠉⣀⣀⡉⠀⠀⡖⠀⠀⠸⡇⠀⣠⠤⠤⢤⡀
⠙⣄⠀⠉⠒⠋⠁⣠⠎⠀⠀⠀⠘⢆⠀⠉⠓⠊⠁⢀⠜⠀⠀⠀⠀⢣⡀⠉⠀⠀⠉⢀⡰⠁⠀⠀⠀⠱⣄⠘⠦⠤⠔⠁⣠
⠀⠈⠑⠒⠶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠙⠒⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠉⠒⠲⠶⠒⠉⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠒⠊⠁

⠀⣠⠔⠒⠉⠓⠲⢄⠀⠀⠀⠀⠀⢀⠴⠒⠊⠒⠲⢄⠀⠀⠀⠀⠀⢀⡤⠒⠊⠑⠒⠦⡀⠀⠀⠀⠀⠀⡠⠖⠒⠉⠒⠢⣄
⡼⠁⢀⡀⠀⢀⡀⠀⢣⠀⠀⠀⢰⠃⡀⢀⠀⢀⠀⡀⢱⡀⠀⠀⢠⠏⠀⣰⡄⠀⣖⠀⠘⡆⠀⠀⠀⡜⠀⢄⡀⠀⢀⡤⠈
⡇⠀⠈⠃⢀⠈⠋⠀⢸⠇⠀⠀⡇⠀⠈⠋⣀⡈⠋⠁⠀⡇⠀⠀⢸⠀⡖⠒⠒⠒⠒⢲⠄⡕⠀⠀⠸⡇⠀⠚⢁⣀⠉⠒
⠱⡄⠈⠉⠉⠉⠁⢀⡜⠀⠀⠀⠘⣄⠐⠋⠁⠉⠓⢀⡼⠀⠀⠀⠈⢦⠙⢤⣀⣀⡠⠎⣰⠃⠀⠀⠀⢣⡀⠐⠉⠀⠉⠂⢠
⠀⠈⠓⠤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠚⠁

⠀⢀⡤⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⢤⡀
⡰⠁⢐⡋⠀⢉⡂⠈⢣⠀⠀⠀⢠⠋⢀⡀⠀⠀⣀⠈⢳⠀⠀⠀⢀⠞⢀⣀⡀⢀⡀⡀⠹⡄⠀⠀⠀⡜⠁⣀⠀⠀⠀⠀⠘
⡇⠀⠘⠃⠀⠘⠏⠀⢸⡆⠀⠀⡇⠀⠰⠛⠀⠘⠳⠀⠀⡇⠀⠀⢸⠀⠰⠛⠆⠀⠛⠂⠀⡳⠀⠀⢰⡇⠀⠴⠋⠀⠘⠋
⠳⡀⠰⠊⠉⠙⠂⠀⡜⠀⠀⠀⠸⡄⠀⠓⠤⠔⠋⠀⡰⠁⠀⠀⠘⣆⠀⠒⠒⠒⠒⠀⢠⠇⠀⠀⠀⢣⠀⠘⠢⠤⠖⠁⢀
⠀⠙⠢⠤⣀⠤⠴⠊⠀⠀⠀⠀⠀⠈⠲⠤⢄⡤⠴⠊⠀⠀⠀⠀⠀⠈⠓⠤⢄⡠⠤⠖⠁⠀⠀⠀⠀⠀⠑⠦⠤⣀⠤⠔⠋

⠀⢀⡠⠤⠶⠦⢄⡀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠶⠤⣀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠤⢄⡀
⣠⠋⠀⠴⠀⠠⠄⠙⢆⠀⠀⠀⢠⠋⠀⠴⠀⠰⠄⠈⢣⠀⠀⠀⠀⡜⠁⠠⡀⠀⠤⠈⠱⡄⠀⠀⠀⡰⠋⠠⣀⠀⣠⠀⠙
⡇⠀⠦⠴⠀⠢⠴⠂⢸⡆⠀⠀⡏⠀⢠⠎⠉⠉⢦⠀⠀⡇⠀⠀⢸⠀⠀⠶⠀⠀⢶⠄⠀⡣⠀⠀⢰⡇⠀⠺⠃⠀⠸⠃
⢣⠀⠐⠦⠤⠴⠂⠀⡸⠀⠀⠀⠹⡀⠘⢶⣋⣳⠞⠀⡰⠁⠀⠀⠘⣄⠀⠴⠚⠓⠢⠀⢀⠇⠀⠀⠀⢇⠀⠐⠒⠒⠒⠂
⠀⠑⠤⣄⣀⣀⠤⠚⠁⠀⠀⠀⠀⠙⠢⢤⣀⣠⠤⠚⠁⠀⠀⠀⠀⠈⠢⢄⣀⣀⣠⠔⠋⠀⠀⠀⠀⠈⠓⢤⣀⣀⣀⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡤⠤⠦⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢠⡾⠁⠀⠀⠀⢀⠔⠊⠉⢁⠜⠋⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⡠⠊⠁⠉⠳⣄⠀⠀⠀⢻⡄
⠀⠀⢀⡿⠁⠀⠀⠀⡴⠁⠀⠀⡰⠁⠀⠀⠀⠀⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⡜⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⢻⡀
⠀⠀⣾⠃⠀⠀⠀⢰⠃⠀⠀⢠⠇⠀⠀⠀⠀⢠⠋⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⠃⠀⠀⠀⠀⢠⠃⢸⠀⠀⠀⠈⣇
⠀⢸⡏⠀⠀⠀⠀⠘⡀⠀⠀⠘⡄⠀⠀⠀⠀⠘⢆⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡄⠀⠀⠀⠀⠈⢄⡸⠀⠀⠀⠀⢹
⠀⣿⠁⠀⠀⠀⠀⠀⠳⡀⠀⠀⢳⡀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠑⣄⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠙⢦⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣈⣳⡤⠴⠋
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠸⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠈⣇⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠇⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠘⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⠎⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠈⢦⡀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⣠⠎⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠙⠒⠒⠤⠤⠤⠤⠒⠒⠋⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣤⣄⣀⣀⡀⠀⠀⣀⣀⣀⣀⣤⡴⠶⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⠉⠀⠀⠀⢸⠀⠀⠀⠀⡟⠀⠀⠀⠻⠿⠁⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢸⡆⠀⠀⠀⠈⠓⢤⣈⡑⠒⣂⣉⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⣶⡆
⠖⠲⠦⢄⠀⡘⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡠
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠈⢦⠀⢀⣀⣀⣀⣀⣠⠤⠤⠤⠤⠒⠒⠂⣠⠏⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠉⠉⠉⠓⠢⣄⠀⠀⠀⠀⠀⠘⣄⠀⠀⡴⠋
⡠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠉⠓⠢⢄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠑⠢⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠤⠤⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⠀⠀⠀⠀⠉⠓⢤⡀⠘⣆
⢀⡠⠔⠒⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠈⠁⢸
⠊⠀⠀⠀⠈⠢⡀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠉⠉⠛⠲⢤⣀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⡼
⠀⠠⣶⠄⠀⠀⠈⢢⠀⠀⢳⠀⠀⠀⠀⠀⢀⡴⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠳⣄⠀⠀⠓⢤⡀⠀⠀⠀⠀⠈⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠈⡇⠀⠀⠀⢀⡞⠀⠀⠙⠳⣤⣀⡀⠀⠀⢀⣀⡴⠞⠁⠀⠘⣆⠀⠀⠀⠉⠑⠒⠤⠤⠤⠤⠒⠉
⢦⠀⠀⠀⠀⣴⡄⠀⠀⠈⢰⠃⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠚⠒⠲⠦⣤⣀
⠀⠓⢄⡀⠀⠈⠀⠀⢀⡠⠋⠀⠀⠀⠀⣿⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⡄⠀⠀⠉⠑⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠁
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣄⣀⣀⣀⣀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⡧
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⠉⠉⠉⠉⠉⠓⢦⡀⠀⠀⠈
⣸⠃⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠲⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠙⢦
⠁⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⣰⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠈⠧⠀⠀⣠
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠤⠤⠤⠴⠖⠋⠁
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢢⠀⢸⡆⠀⠀⢰⠇⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⣶⣦⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⣄⡀
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡇⠀⠀⡾⢀⣀⣠⡤⠴⠚⠁⠀⠀⠀⠀⠙⠃⠀⠀⢀⡇⠀⠀⠀⡴⠋⠀⠀⠐⠒⠢⠤⣈⠑⢦⡀
⠀⢸⠁⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⠁⠀⠀⣧⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡜⠀⠀⣀⡀⠀⠀⠀⠀⠈⠑⣄⠱⡄
⠀⢸⡆⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠏⠀⠀⠀⠸⡆⠀⠀⠀⠀⠺⣿⠃⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⡇⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠈⡆⢹⡀
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣰⠏⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⠇
⠀⠀⠀⠹⣤⡀⠀⠀⠀⠓⠒⠚⠋⢁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢾⡷⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠉⠓⠶⠦⠤⠴⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠚⠃⠒⠢⣄⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⣤⡄⠀⠀⠱⡄⠀⠀⠉⠑⠒⠒⠚⠉
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠉⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠉⠙⠢⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢸⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⣸⠀⡏⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠉⠁
⢠⣤⠀⠀⠈⢆⠀⠀⠀⠀⢰⠃⠀⠀⣀⣄⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠈⢷⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣀⠴⢃⠜⠀⠀⠀⠀⠀⠀⢠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠒⠒⠒⠒⠒⠒⠲⠦⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠤⣤⣤⣄⣀⣀⣀⣠⣤⡤⠤⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⢠⡾⢋⣭⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣴⠟⣩⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⡏⠀⠈⣿⠀⠀⠀⠀⠀⢸⡇⣼⣿⣿⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣼⣿⣿⣿⣶⣾⠏⠀⠀⠀⠀⠀⠘⢧⣻⣿⣿⣷⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣤⣄⣀⣀⣀⣀⣤⣴⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠟⠛⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠛⠻⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠋⠀⠀⠀⠀⠐⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢹⣿⡆⠀⠀⢰⠉⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⢠⡟⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠶⡀⠀⢻⡄
⠀⣸⡇⠀⠐⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣇
⠀⣿⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⣿
⠀⣿⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣿
⠀⢹⡇⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⢸⡏
⠀⠘⣧⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠶⠶⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣦⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣤⣴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠁
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⣟⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠻⣷⡀⠀⠀⡴⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⢰⡏⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡇⠀⠀⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⢦⡀⠈⣷
⠀⣾⠁⠀⠚⢹⡉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢹⡆
⠀⣿⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⡇
⠀⢻⡄⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣼⠃
⠀⠸⣧⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢠⡿

⠀⢀⠔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠉⠉⠙⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠤⡀
⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹
⠀⢱⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⣰⠋⠀⠀⠀⠙⣆⠀⢀⡔⠋⠉⠓⢤⡀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡜
⠀⠀⠙⢦⡀⠀⠈⠂⠄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠇⢀⣔⣷⣦⠀⠘⡆⡜⠀⣴⣶⡆⠀⢳⠀⠀⠘⣆⠀⠀⠀⠀⡀⠔⠋⠀⠀⡰⠊
⠀⠀⢀⡠⠗⠀⠀⠀⠀⠈⠢⡀⢠⠃⠀⠀⠀⠀⡆⠈⠻⠿⠟⠀⢀⡇⡄⠀⠙⠛⠃⠀⢸⠀⠀⠀⠘⡄⢀⡔⠃⠀⠀⠀⠀⢼⣀⡀
⡠⠊⠁⠀⡤⠀⠤⡀⠀⠀⠀⢳⣼⠀⣀⡀⠀⠀⠙⠦⣀⣀⣀⣠⠞⠀⠈⠢⣀⣀⣀⠴⠃⢐⣦⡀⠀⣧⡜⠀⠀⠀⢀⡠⠤⢄⠀⠉⠒
⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣸⣇⠈⠙⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢶⠋⠀⠁⠀⣿⣇⠀⠀⠀⢸
⠈⡲⠤⣄⣠⠤⠞⠉⣳⡀⠀⠉⢹⠀⠀⠀⠀⠙⢍⡙⠒⠶⠶⠶⠶⠶⠶⠖⠛⠉⣀⣴⠃⠀⠀⠀⠀⡏⠋⠀⠠⣜⠉⠳⢄⣀⣀⡠⢴
⠀⠑⢄⡀⠀⢀⣀⠴⠃⡷⣄⠆⠈⣆⠀⠀⠀⠀⠈⠻⣿⣶⣶⠤⠤⠤⠤⠤⣶⣿⣿⠇⠀⠀⠀⠀⣸⠁⠠⣀⢼⠙⢦⣀⠀⠀⠀⣠⠎
⠀⠀⠸⣈⠉⠁⣀⡠⠞⢡⠇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢀⣹⠏⠀⠀⠀⠀⣰⠃⠀⠀⠸⡈⠣⣄⡈⠉⠉⢉⠇
⠀⠀⠀⠀⠙⠫⠥⠔⠚⠁⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠙⢯⣀⣀⣈⣩⠟⠁⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠈⠒⠤⠭⠽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⡠⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣒⣦⣤⣤⣤⣤⣴⣒⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠙⠉⠉⠉⠙⠋⠋⠉⠙⠛⠟⠋⠛⡛⠋⠉⠙⠛⠿⠛⠻⢿⡿⠿⣿⡋⠛⠻⠟⠋⠉⠉⠛⠛⠛⠻⠿⠛⣛⠻⣟
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢻
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⣿⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠁⡀⠀⢰⣿
⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⣀⠀⠀⠀⠸⠿
⡇
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡇⠀⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠑⡦⠀⠤⢥⠞⡅⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇
⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠐⠁
⣿⡟
⡿⠁
⣷⠀⠀⠀⠀⠀⠄⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⣿⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⣿⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣶⣶⣶⣶⣆⣴⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣆⠀⠀⠀⣀⡀
⢀⣾⣿⣷⣾⣷⣜⣿⣿⣿⣿⣧⢴⣿⠿⠟
⠀⣻⣿⣿⠛⠻⣿⣾⡿⠉⣿⣏⡼⠳⣀⣀⣤⣤⣤⣶⣶⣤⣤⣤⣤⣀⡀
⠀⢿⣿⣿⣷⣄⡘⣿⢇⣼⣿⣾⣶⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣶⣤⣀
⢀⣤⣴⣾⣿⠿⠗⠰⢿⣛⣭⣍⣙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⡀
⢿⣿⣿⡏⠀⣠⣾⣿⣎⠻⣯⣛⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⣼⣿⣿⣿⣿⣿⡟⣿⣿⣄⣿⣿⡆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠙⠿⢛⣿⣿⠏⢸⣿⣿⣿⣿⡿⠇⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧
⠀⠀⣾⣿⠃⠀⠸⢿⠿⣿⠿⠁⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠈⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣿⠀⠀⠀⠀⢀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣄⠀⠀⠀⠀⠀⢰⣿
⠀⢻⣿⡆⠀⠀⠀⠉⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠃⠀⠀⠀⠀⣼⣿
⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁
⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣶⣶⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠐⠂⠐⠀⠀⠠⠤⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢀⠤⠤⡀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⢀⠤⠠⣀⠀⠀⡠⠄⠤⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠃⠀⠄⠈⠱⠁⠠⡂⠐⠈⡆⠀⠀⠀⠠⠃⠀⠀⠈⢣⡌⠀⠢⢂⠈⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠣⠀⠑⠡⡂⢐⠠⠂⠁⠂⠁⠀⠀⠀⠸⠀⠕⠀⠢⡀⢐⠅⠨⠂⢀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠀⢄⠄⠂⡠⠁⠀⠀⠀⠀⠀⠡⡀⠁⡨⡂⢐⠁⡊⠠⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢊⢔⣁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⢀⡀⢀⣀⡀⢀⡀⠠⠄⠒⠈⠁⠀⠀⠀⠠⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣁⣈⡐⡁⣀⣀⡀⢈⢀⣀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⡠⠀⡀⠄⡠⢀⠠⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡀⠄⢂⠠⠐⡀⠀⢂⠡⢀⠠⠐⡈⠔⡈⠄⠂⠠⠂⠁⢂⠡⢂⠠⢀⠠⠂⡠⠐⡡⠀⠡⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠈⠁⠐⠁⠐⠉⠀⠈⠀⠈⠀⠈⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⣠⣾⣿⠟⣉⣥⣤⣤⣤⣤⣤⣤⣬⣉⠻⣿⣷⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣆
⠀⢰⣿⣿⠁⣼⣿⣿⣿⠿⠛⠛⠿⣿⡉⣹⣧⠘⣿⣿⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⣆
⠀⣿⣿⣿⠀⣿⣿⡟⣠⣾⣿⣿⣶⡌⢻⣿⣿⠀⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠃⠀⠀⠛⠛⠛⣿⣿⣿⣿
⠀⣿⣿⣿⠀⣿⣿⣧⡘⠿⣿⣿⠿⢃⣼⣿⣿⠀⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠘⣿⣿⡄⢻⣿⣿⣿⣶⣤⣴⣶⣿⣿⣿⠟⢠⣿⣿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠘⢿⣿⣦⣌⣙⣛⣛⣛⣛⣛⣛⣋⣡⣴⣿⡿⠃⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠃⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⢠⣾⣿⣿⣿⠿⠛⣉⣉⣉⣉⠛⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⢠⣿⣿⣿⡟⢁⣴⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⣿⣿⡄⠀⠀⢀⣾⣿⣿⣿⡟⠻⣿⣿⣿⣿⠏⠉⠀⠉⠛⢽⣿⣿⣆
⠀⣿⣿⣿⡟⢠⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣷⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠉⠛⠛⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⣿⣿⣿⡇⢸⣿⣷⡀⠸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⣿⣿⣿⣧⠘⣿⣿⣿⣦⣀⠉⠁⠈⣹⣿⠃⣼⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠟⢁⣼⣿⣿⣿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣍⣉⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠏
⠀⠀⢸⣿⣿⣃⣤⣴⣤⣉⣉⣉⣉⣤⣶⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠛⠉⠁⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢦⡀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠊⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠙⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢠⣾⠋⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠉⢿⡄⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⢀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⢀⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠑⠒⢒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠚⠉⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢻⡿⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠃⣀⠴⠋⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⢤⡤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠂⠐⠀⠀⠠⠀⠀⠀⠀⠀⠐⠿⠐⠗⠀⠀⢠⡤⢠⡄⠀⣀⣄⠀⠈⠉⠀⠀⠂⢀⠂⠀⠀⠐⠂⢐⣀
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠿⠗⠀⠰⠉⠩⠐⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⠤⠤⢄⡄⢀⣀⣀⣀⣀⠀⠀⠀⠀⠄⠆⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤
⠀⠀⠀⠐⠛⠀⠃⠀⠀⡀⠀⢀⠀⠀⠉⢐⣀⠈⠁⠈⠛⠃⠙⠛⠀⠀⠀⠀⠀⠆⠀⢀⠁⠈⢀⠂⢠⣾⠽⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⠋⡁
⠀⠀⠀⠀⡀⢀⡀⠀⠀⣂⡖⣆⠂⠀⡠⠐⡄⠒⠄⠀⠀⡀⠀⠃⠀⠀⠄⠀⠀⠀⠀⡀⠐⠃⠀⡀⠀⢽⢀⢟⠩
⠀⠀⠀⠀⡁⢊⠀⠀⠘⠈⠐⠀⠘⠀⠐⠁⠛⠔⠀⠀⠈⠏⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠠⣤⣀⣠⣤
⠀⠀⠰⠏⠀⢀⠸⠆⠀⠀⡰⠬⠀⠀⢀⡈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑
⠀⠀⠀⣰⣶⣷⣦⠀⠀⣶⡾⢷⡄⠀⠀⣶⣾⢷⡄⢀⢂⣀⣀⢀⠆⠀⠐⠀⠀⡆⠀⢀⡀⠀⠀⠄⠀⣴⡶⠷⡄
⠀⠀⠀⠿⠁⠀⠻⠀⠈⢧⣦⡶⠇⠀⠀⣇⠁⠀⠇⠀⠀⠀⠀⠉⠀⠘⡃⠀⢈⠃⠀⠀⠁⠀⠄⠀⠀⠃⠠⠀⠃
⠀⠀⠀⢀⠀⠀⢀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⢸⡿⡀⢠⣿⡇⢠⡏⢛⠉⡇⠀⠀⠘⢫⡄⠀⠀⠘⠋⢾⣦⠀⠀⠚⢐⠈⣤⠀⠶⠛⡛⠷⡄⡰⠿⢿⣿⣷⡄
⠀⠀⠀⠁⠐⠎⠉⠀⠀⠳⣬⠾⠃⠀⠀⠃⣘⠷⠀⠀⠀⠀⠈⠻⠀⠀⠠⠈⠀⠀⠀⠐⠲⠖⠂⠁⠁⡤⠈⠙⠿⠁
⠀⠀⠀⢠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠠⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠾⠟⠁⠀⠀⠀⠤⢆⠌⡄⠀⠸⠟⢣⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⢀⣀⡄⠀⠋⠀⠀⠀⠀⠀⠠⢉⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠛⠁⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠃
⠀⠀⠀⡴⢂⣴⡀⡀⠀⢀⠰⠦⠀⠀⠀⠀⢀⠀⠀⠀⠒⡒⠐⣤⠀⢠⣦⣶⣴⡆⠀⣿⣟⠻⣿⡆
⠀⠀⠀⣶⡌⢉⣠⠃⠂⠀⠀⠀⢀⠂⠀⢎⠠⠀⠀⠀⠀⣽⣾⡁⠀⢸⣥⣤⣤⡟⠀⣿⠷⣆⣽⡇
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠈⠉⠁⠁⠀⠉⠉⠉⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⢈⣢⡀⠀⠀⠈⠐⠒⠊⢁⡠⠤⠴⠶⡇⠀⠀⠀⠘⠻⠖⠁⠀⠀⠀⠈⠛⠉⠀⠀⠀⡇⠀⠀⠀⠉⠁
⠒⠒⠒⠢⣀⡇⠀⠀⠀⢸⣿⠛⣻⠀⠀⠀⢰⡿⢿⣿⠑⠢⠤⣀⡴⠊⠁⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⣀⣀⠀⣀⣀⣸⡀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠘⢦⣼⠟⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢘⡿⠛⠉⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠈
⠒⠒⠒⠲⠮⢧⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⣢⣀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣤⡤
⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠈⠦⡀⠀⠀⠀⣠⠖⠀⠀⢰⠃⠀⠀⠀⣰⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⡍⡞⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠈⠉⢉⣉⠤⠤⠤⢄⣸⠀⠀⠀⠀⠹⣿⣀⡿⠀⠀⠀⠘⣇⣨⣿⠃⠂⠀⠀⠠⣿⠿⢿⠀⠀⠀⠰⢛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠔⠊⠁⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠹⠶⠊⠀⠀⠀⠀⡞
⡄⠀⠀⣾⣿⢿⣿⣿⡇⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⡀⠀⠀⠀⢇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠘⢧⣤⣿⡿⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣶⣷⣦⠳⡀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠙⠆⠀⠀⠈⣦⣀⣀⣀⣘⣤⣀⣀⣀⣼⠀⠀⠀⠻⣿⣧⣤
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⢃⣶⣷⣆⠀⠀⠈⢯⣉⡿⢀⣈⠦⠤⠴⠠⠤⠤⣀⡀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠈⠉⠲⢄⢸⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡞⠘⢿⣅⡽⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠠⡀
⢄⣀⣀⠤⠞⠁⠀⠀⠀⢀⠞⠐⠂⠤⣉⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠈⠑⢄⢀⠏⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⠦⣀
⢤⣤⣤⠤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣿⡿⢿⡇⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠲⢶⠶⠀⠀⠀⢸⣀⠀⠈⠑⢲
⠚⠁⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠙⠷⠞⠁⠀⠀⠀⢧⣨⣿⠃⠀⠀⠀⢸⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⡇⠀⠀⠈
⠀⠀⡅⠀⠀⠀⠛⠒⠀⠀⠀⠀⠐⠚⠃⠀⠀⢸⠀⢀⡠⠤⠒⠒⠒⠒⠒⠢⢄⡀⠉⠀⠀⠀⠀⠀⡎⠀⠀⠀⠉⠙⠒⠀⠀⠀⠀⢀⠞⢛⣚⠁
⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⣼⣅⣀⣀⡀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠀⠀⠈⠉⠓⠢
⠙⢦⣸⢆⠀⠀⠀⠢⣀⠀⠀⢀⠴⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣠⠞⠀⠀⠀⠀⠀⠉⠒⢶⡊⠁
⢀⡜⠁⠈⠳⢄⠀⠀⠀⠈⠉⠀⠀⠀⢀⢴⠃⠀⢠⣶⣦⣶⣦⠀⠀⢠⣶⣦⣴⣦⡀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⡞⠀⠀⠀⠀⣀⡉⠒⠂⠤⠤⢠⣶⣮⡁⢸⠀⠀⠘⢿⣿⣩⡿⠀⠀⠈⢿⣉⣿⡿⠁⠀⠀⡇⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠈⢧⣤⣄⠀⠀⠀⢀⣾⣿⣷
⠀⠀⠀⠀⣾⣻⢿⣆⠀⠀⠀⣾⠟⢿⣷⠸⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣷⣦⡀⠀⠀⠸⣏⣹⡇⠀⠀⠀⠘⡟⢻⡆⠀⠀⠘⢏⣈⣿
⠀⠀⠀⠀⠹⣧⣤⠏⠀⠀⠀⠘⠶⠾⠋⠀⢣⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡼⣿⣉⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠷⠚⠀⠀⠀⠀⠀⠉
⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠑⠲⠶⠖⠊⠀⠀⠀⣀⠞⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣀⣀⡀⠤⠤⠤⣴⡆
⠵⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⡔⠉⠑⠤⢀⡀⠀⠀⠀⢀⣀⠤⠚⠉⢢⠀⠀⠀⠀⣀⠠⠤⠴⠶⠤⠤⢄⡰⠁⠀⠛⢷⣶⣶⣿⡿⣋⠤
⠀⠙⢆⡀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⣶⣄⠉⠉⠉⢀⣤⣀⠀⠀⠀⢃⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⢀⡠⠴⠛⡇⠀⠀⠀⢿⣏⣹⠀⠀⠀⠈⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠞
⠀⠀⠀⢀⡄⠀⠀⣩⠟⠉⠉⠉⠀⠀⠀⠀⢡⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⣠⣄⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⡝
⠀⠀⠒⠛⠃⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠢⡀⠀⠀⠀⢀⠄⠀⠀⠀⡇⠀⠀⠀⢾⡿⠿⡇⠀⠀⠀⡟⠛⣿⠀⠀⠀⠃⠀⠀⠠⣄⣀

⠀⠀⠀⠔⠈⣁⡉⠐⠄⠀⢀⠔⣈⠀⢉⠒⡀⠀⢀⠔⠈⣀⠉⠢⡀⠀⢀⠔⠉⠀⠁⠢⡀⠀⢀⠀⠉⠀⠁⠢⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠈⠀⢸⠀⠆⠀⠀⠉⠀⠀⠠⠀⡄⢀⠀⠁⠁⡄⢰⠀⡃⠀⠀⠛⠀⠀⠁
⠀⠀⠘⢄⠀⠀⠀⢀⠜⠀⠘⢄⠀⠀⠀⢀⠌⠀⠐⡀⠀⠀⠀⢀⠆⠀⠰⡈⠛⠉⠛⢁⠂⠀⠡⡀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⢀⠄⠒⠂⢄⠀⠀⠀⡀⠄⠒⠂⢄⠀⠀⠀⡠⠄⠒⠠⢄⠀⠀⠀⡠⠄⠒⠠⢄⠀⠀⠀⡠⠀⠒⠠⢀
⠀⠀⠐⠁⡀⠂⠂⡀⠱⠀⠐⠀⠰⠀⠤⠀⢡⠀⡘⢀⣀⣾⣄⣀⢁⠀⡈⠀⠀⠒⠀⠀⢃⠀⡌⠀⠀⠠⠀⠀⠂
⠀⠀⠠⡀⠻⠒⠺⠋⠠⠀⠠⠀⠀⠀⠀⠀⡸⠀⢁⠘⠿⣿⠿⠋⡘⠀⢁⠘⠒⠒⠂⠋⡌⠀⢃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠁⠂⠤⠄⠂⠁⠀⠀⠑⠂⠤⠄⠊⠀⠀⠀⠑⠀⠤⠄⠊⠀⠀⠀⠑⠠⠤⠀⠊⠀⠀⠀⠑⠠⠤⠐⠊
⠀⠀⠀⢀⠤⠀⠠⢄⠀⠀⠀⢀⠤⠀⠠⢀⠀⠀⠀⡀⠄⠀⠠⢀⠀⠀⠀⡀⠄⠀⠠⣀⠀⠀⠀⡀⠄⠀⠤⡀
⠀⠀⠰⠁⠀⠀⠀⠀⠱⠀⠰⠁⠀⣤⡄⠀⢡⠀⠐⠀⠀⣤⠀⠀⢣⠀⡘⠀⠀⣀⠀⠀⢂⠀⡌⠀⠀⣤⠀⠈⠂
⠀⠀⠠⠀⠀⠈⠁⠀⠠⠀⢠⠀⠾⠛⠻⠆⠸⠀⢃⠠⠆⠀⠀⠦⡘⠀⢃⠀⠀⠀⠀⠀⡘⠀⢆⠀⠀⠴⠀⠀⡄
⠀⠀⠀⠑⠠⠤⠤⠐⠁⠀⠀⠑⠠⠤⠤⠐⠁⠀⠀⠑⠤⠤⠤⠊⠀⠀⠀⠑⠤⠤⠤⠊⠀⠀⠀⠒⠤⠤⠄⠊
⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⢀⠊⠀⢀⡀⠈⢂⠀⢠⠊⠀⠀⠀⠈⢆⠀⠠⠊⠀⣄⠀⠑⠄⠀⠠⢊⠀⠠⠄⢑⡄⠀⡰⠉⠀⠤⠀⠑⡄
⠀⠀⢀⠀⣄⣀⣀⡴⢀⠀⢀⠀⠀⠚⠂⠀⢸⠀⠃⢠⣶⣾⣿⡷⠨⠀⠇⢸⣿⣿⣷⡮⠸⠀⡅
⠀⠀⠈⠢⣈⠁⢉⡠⠊⠀⠈⠢⡀⠀⢀⡠⠂⠀⠈⠈⡉⠉⢉⠡⠁⠀⠈⠄⡀⠈⢋⠕⠁⠀⠐⠄⡀⠀⢀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣷⣄
⠀⢠⣤⣤⣤⣠⣤⣄⠰⣿⣿⣿⣿⣿⣦⠀⢤⣶⣾⣿⠆
⠀⣿⣿⣿⣿⣿⣿⣿⣧⣹⣿⣿⢿⣿⣿⡟⣿⡟⠁⠋
⠀⣨⣿⣿⣿⡏⠉⠻⣿⣧⣿⠏⢀⣿⡟⣴⠋⢙⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣀
⠀⢻⣿⣿⣿⣿⣦⣀⠹⣿⡿⢀⣼⣿⣾⣷⣾⣿⣿⡿⠿⠟⠛⠛⠛⠋⠉⠛⠛⠛⠛⠿⢿⣿⣿⣿⣷⣦⣄
⠀⠀⣉⣉⣉⣙⣻⣿⣧⢩⣴⣿⠿⠟⠛⠛⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣶⣄
⣴⣿⣿⣿⣿⠋⠉⠁⣠⣦⡁⢶⣿⠿⣿⣷⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣦⡀
⠹⣿⣿⣿⣇⣀⣠⣾⣿⣿⣿⡄⠙⣿⣦⡙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄
⣼⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣧⣠⣿⣿⣿⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀
⠹⢿⡿⠿⣿⣿⡿⠋⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄
⠀⠀⠀⣼⣿⡿⠁⠀⢿⣿⣿⣿⣿⣿⡏⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⣸⣿⣿⠃⠀⠀⠈⠛⠋⠙⠛⠋⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀
⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⣿⣿⣷⠀⠀⠀⠀⠀⢀⣠⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⢸⣿⣿⡀⠀⠀⠀⠀⠛⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁
⠀⠀⠀⠀⠙⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣶⣶⣶⣶⣶⣶⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⠄
⠠⠠⢤⠀⠀⠠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡀⠀⢀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠆⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠄⠀⠀⠀⢡⡄
⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠈⠚⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠁⠈
⠠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⣀
⠀⠈⠐⠂⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢨⡝⠀⠀⢘⢩⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣁⡆⠀⠀⣊⣁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠂⠀⠀⠀⣀
⠐⣰⡶⠀⠘⠐⣖⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠊⠈
⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠤⠤⠒
⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣤⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠴⠂⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⢠⢤⡄
⢀⣦⡀⠀⠀⢈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠚⠁⠀⠠⠀⠃
⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣥⣤⣤⣤⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠁⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠱⠤⠋⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠤⠤⠶⠋



⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⡀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⣈⡀
⠀⢀⣔⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉
⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠘⢿⠛⠛⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣶⣶⣶⠿⡿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠐⠂⠀⠉⠉⠉⠉⠉⠁⠀⠒⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠿⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠿⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡠⠊⠑⢄⣀⣀⡀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢀⠤⢄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠤⢄
⠀⠀⠀⠀⠢⡀⠀⠙⢦⡀⠀⢠⠂⠐⢄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠄⠀⠀⠀⠀⠤⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢢⠀⠀⢠⠞⠁⠀⡠⠂
⢀⠀⠂⠀⠀⠈⠢⡀⠀⠈⠢⡈⠢⡀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡠⠊⡠⠊⠀⠀⡠⠊⢀⡀⠄⠒⢢
⠘⠄⣀⠀⠀⠉⠒⠬⢑⢄⠀⠈⠢⢌⣂⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣊⠤⠊⠀⢀⢔⡉⠔⠊⠁⠀⢀⡀⠜
⡤⠒⠠⠉⢐⡠⠀⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡀⠀⣐⠨⠁⠐⠢
⠑⠤⠄⣀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠈⠁⠀⢀⡀⠤⠔
⠀⠀⢀⡠⠬⠉⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣐⠈⠭⠤⣀
⠀⠀⠈⠢⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠉⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠁⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⢀⠠⠔⠊⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣅⣀⣀⣀⠀⠀⠀⠆⠀⠀⠆⠀⠀⠀⢠⡀⠀⡄
⠀⠀⠰⠤⠤⠆⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠦⠤⠶⠀⠀⠀⣘⠞⠋⠉⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠁
⠀⢀⣀⣀⣀⣀⡀
⠀⠧⠰⠜⠣⠆⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣛⣛⡡
⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁
⠀⠀⠐⡀⠐⠂⠀⢀⡥⠀⠄⠀⡄⢩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⢀⣀⣀⡆
⠀⠀⠀⣀⣀⠀⠀⠘⢧⠠⡀⠀⡠⠠⠟⠀⠀⢀⣄⠀⠀⠀⠀⠀⠈⠤⠌⠀⠀⠀⠀⠉⠀⠈⢀⠀⠀⢀⡒⢉⡉⢰⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⡀
⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠠⠀⠄⠀⠀⠀⠐⢶⠆⢶⠶⠀⠀⠀⠲⠂⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠐⠒⠚⠀⠀⠀⠀⠀⠒⠒⠢⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⡀⠀⠀⢀⡀⠤⠤⢀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣄⠀⠀⠘⠂⠀⠔⠊⠀⠀⠈⠂⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢘⠀⠐⡀⠀⠀⠀⠈⠇⠀⠇⠀⠀⠈⠙⠛⢉⠛⢋⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠐⢀⠐⠂⠀⠀⠀⢐⠂⠐⡃
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉
⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⡐⠀⠀⢡⡐⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣨⠒⠀⠀⠀⠈⢉⠻⠋⠉⠂⠀⠐⠡⠀⠀⠌⠒
⠀⠀⢟⡃⢘⡹⠁⠀⠀⠀⠀⠀⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢠⣭⣴⣦⣥⠄⠀⠰⡰⠄⠨⢆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠾⠛⠛⠛⠛⠛⠻⠷⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢦⣄⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⣠⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⣦⣄⠀⠀⠀⣀⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠉⠳⣀⣾⠟⠁⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⢰⣿⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⢹⣷
⣾⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⢀⡾⣆⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⡤⣶⡟⠁⠈⠳⢤⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠉⠉⠀⠀⠀⠀⢺⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣄⣀⣠⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⡠⠂⠀⠉⠑⢦⠀⠀⠀⠀⢠⠔⠈⠉⠉⠲⡀⠀⠀⠀⠀⡔⠂⠈⠉⠒⢄⠀⠀⠀⠀⡠⠢⠀⠉⠑⢦⠀⠀⠀⠀⢀⠔⠀⠉⠉⠲⡄⠀⠀⠀⢀⡴⠂⠈⠉⢒⣄
⢸⠁⠈⠃⠀⠃⠀⡇⠀⠀⢀⠃⠘⠃⠀⠛⠀⢹⠀⠀⠀⡎⠀⠚⠀⠺⠀⠈⡆⠀⠀⠰⠁⠘⠃⠐⠛⠀⡇⠀⠀⠀⡇⢤⠄⠀⣤⠀⢸⠀⠀⠀⡎⠀⠿⠀⠸⠆⠘
⠸⡀⠢⢄⡀⠴⢂⠆⠀⠀⠘⣄⠀⠀⠐⠀⢀⡜⠀⠀⠀⢧⠀⠄⠒⠒⠀⡰⠁⠀⠀⠰⡈⠑⠚⠒⠳⢲⠇⠀⠀⠀⢆⠀⠤⠀⠀⠀⡼⠀⠀⠀⢧⠀⠀⢰⠀⠀⡰
⠀⠈⠂⠤⠤⠒⠁⠀⠀⠀⠀⠈⠓⠤⠤⠐⠋⠀⠀⠀⠀⠀⠑⠢⠤⠔⠊⠀⠀⠀⠀⠀⠈⠢⠤⠤⠒⠁⠀⠀⠀⠀⠈⠑⠤⠤⠐⠊⠀⠀⠀⠀⠀⠑⠢⠤⠔⠊
⠶⠀⢀⠀⠀⣀⠀⠰⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⢐⠞⢁⡀⢀⡠⠑⡆⠀⠀⠀⡰⠁⣀⢀⠀⠉⢆⠀⠀⠀⢠⠊⣠⠀⢀⡈⠳⡀⠀⠀⢀⠔⠁⣀⢀⡐⠑⡄⠀⠀⠀⡰⢊⡀⠀⡂⠈⢢⠀⠀⠀⢠⠊⣀⠀⣤⣌⢳
⢈⢰⣌⠁⠈⠁⠀⡁⠀⠀⢰⠁⣤⡍⡜⡅⣤⢸⠀⠀⠀⡇⠀⠉⠁⠈⠁⠀⡇⠀⠀⢘⠀⠀⠁⠈⠁⠀⡇⠀⠀⠀⡃⠈⣁⣀⠉⠀⢨⠀⠀⠀⡇⠠⠦⢄⠻⠃⢀
⠘⢦⡀⠑⠒⢀⡴⠁⠀⠀⠀⠣⡙⠋⠃⠓⡫⠊⠀⠀⠀⠱⣄⠐⠀⠀⣀⠜⠀⠀⠀⠈⢆⡀⠐⠀⢀⡴⠁⠀⠀⠀⠣⡐⠄⡠⠇⣠⠎⠀⠀⠀⠱⣄⠀⠀⠙⣂⠜
⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⣁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⢀⠠⠀⠐⠤⣀⠀⠀⠀⠀⠀⡠⠄⠐⠢⢄⠀⠀⠀⠀⠈⢙⠗⠒⠒⢮⡁⠀⠀⠀⠀⢀⠠⠀⠒⠠⣀⠀⠀⠀⠀⠀⡠⠄⠐⠂⢄⠀⠀⠀⠀⠀⢀⣤⠐⢲⣤⡀
⢠⠋⠀⠀⠀⠀⠈⡆⠀⠀⠀⡎⠠⡏⠀⣭⠀⢳⠀⠀⠀⡰⠉⣤⠀⣤⠀⠙⡄⠀⠀⢠⠋⠠⠄⠰⠆⠈⡆⠀⠀⠀⡜⢡⡄⠀⠤⠀⢱⠀⠀⠀⡐⣱⣌⡆⣤⡓⠙
⢸⠀⠀⠀⠀⣀⠀⡄⠀⠀⠸⡀⠀⢁⣀⠉⠀⡸⠀⠀⠀⡇⠂⠤⠤⠤⠔⢀⠇⠀⠀⢨⠀⠤⣀⣀⡤⠆⡇⠀⠀⠀⡅⠁⠐⠓⠒⠂⢸⠀⠀⠀⡇⢨⠯⢤⠭⢭⢠
⠈⠳⢄⣐⣈⡡⠾⠃⠀⠀⠀⠑⢬⣁⣀⣡⠔⠁⠀⠀⠀⠈⠢⣀⣀⣀⠴⠋⠀⠀⠀⠀⠳⢄⣀⣀⡭⠋⠀⠀⠀⠀⠙⢤⣀⣀⣠⠔⠁⠀⠀⠀⠈⠮⣑⣒⣒⠵⠊

⠀⣠⠔⠀⠈⡒⢤⠀⠀⠀⠀⢀⠔⠂⠈⢑⠢⡀⠀⠀⠀⠀⡠⠂⠀⢈⠲⣄⠀⠀⠀⠀⡠⠐⠀⠘⠓⠀⠀⠀⠀⠀⢀⣴⣚⠛⣻⡶⡄⠀⠀⠀⢀⡴⠒⠛⠛⠲⣄
⠰⢁⠈⠁⠘⠋⠀⠇⠀⠀⢀⠂⠰⠇⠠⠀⠇⢱⠀⠀⠀⡜⠀⠿⠀⠙⠂⠈⡆⠀⠀⢰⠁⠘⠃⠀⠗⠀⠓⠀⠀⠀⠋⠘⠋⠀⠛⠂⠙⠄⠀⠀⡞⣛⣉⡃⣋⣙⢸
⢰⡘⢄⡀⠀⠀⢀⠇⠀⠀⠘⡄⠤⠤⠤⠤⠄⡜⠀⠀⠀⢇⠠⠄⠂⠤⠀⣠⠃⠀⠀⠰⡘⠦⣀⢀⡠⢛⠏⠀⠀⠈⣇⠐⠛⡀⣀⠀⡸⠁⠀⠀⢏⢻⡛⠛⣛⡿⣹
⠀⠙⠦⠤⠤⠖⠉⠀⠀⠀⠀⠈⠲⠤⠤⠴⠊⠀⠀⠀⠀⠀⠑⠤⠤⠤⠚⠁⠀⠀⠀⠀⠙⠢⠤⠤⠖⠉⠀⠀⠀⠀⠈⠲⠤⠤⠴⠊⠀⠀⠀⠀⠀⠑⠭⠭⠥⠚⠁

⠀⡠⠎⠀⠀⠉⠢⡀⠀⠀⠀⢀⠖⡁⠀⠉⠲⡄⠀⠀⠀⢀⣔⣈⡀⢈⣑⣆⠀⠀⠀⠀⡠⢊⡀⠈⠉⢢⡀⠀⠀⠀⢀⠔⠁⠀⠉⠓⣄⠀⠀⠀⢀⠴⠎⠀⠈⠕⢄
⢸⠀⠢⠂⠀⠄⠀⠁⠀⠀⢀⠃⠄⣋⣀⣛⣀⣸⠀⠀⠀⡎⠻⠿⠋⠻⠿⠛⡆⠀⠀⠰⠀⠰⡯⢽⠏⠀⡇⠀⠀⠀⡇⡌⠁⠀⠙⠆⠘⠀⠀⠀⡎⠀⠙⠀⠘⠁⠈
⠸⡘⢗⣂⣒⠾⢣⠆⠀⠀⠈⢆⠣⣖⣒⣒⢞⠜⠀⠀⠀⢻⡢⠤⠤⠄⠒⡹⠁⠀⠀⠰⡘⠟⠈⠁⠻⢡⠇⠀⠀⠀⢇⠰⠏⠛⠓⢀⡼⠀⠀⠀⢣⡀⠬⠒⠎⠀⡰

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠢⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⡀⠀⠀⠀⠀⣀⣴⣦⣴⣶⣦⣄⡀
⠀⠀⠀⠀⠀⢀⠖⠁⡄⡀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⡴⠂⢁⠈⠭⣍⠀⢀⠷⠆⠀⠘⣭⣭⣝⣛⣭⣽⣿⠁
⠀⠀⠀⡀⡆⡞⠀⢰⢧⡇⣞⡃⠰⣼⡤⠚⠁⢸⢸⠃⠀⣼⡕⠊⠀⠀⠀⠡⠛⠁⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠇⢹⡀⠋⠀⠁⢈⣤⣚⠟⠀⠀⡰⠃⠀⠀⠀⠛⠀⠀⣠⠤⠶⠦⢤⡀⠀⠀⢀⡀⠀⠨⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠓⠦⣄⣀⣀⣉⣁⡀⣀⣺⡀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠴⠆⢱⠀⠀⠀⡀⠀⢠⡆⢠⡆
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⢠⡇⠀⣾⢴⣀⢤⢀⠤⣰⣾⡇⠀⠀⠘⡄⡸⣁⢊⠅
⠀⠀⠀⠀⣿⣦⡀⠀⠀⠶⠦⠤⠤⠤⠒⣿⠲⢀⠀⢸⠁⠀⡏⠉⠛⠛⣛⣻⠭⠽⡇⠀⠀⠀⠘⠇⢋⣸⣄⣤⠄
⠀⠀⠀⠀⢸⡏⠻⣄⢠⡤⠼⠇⣼⣷⡀⣿⠀⣽⡤⢼⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠀⠈⠀⡀
⠀⠀⠀⠀⠘⣇⠀⢹⢼⡗⠒⣀⠋⠙⣯⢸⡄⢸⡇⠸⣇⠀⢹⡀⠀⠀⠀⠀⠀⣰⠇⠀⣄⢰⢓⡶⣒⡖⢲⢻⣲⣸⡀
⠀⠀⠀⠀⢤⣿⠀⠊⠘⠉⠙⠋⠀⠀⠻⠀⠀⠀⠀⠀⠉⠀⠀⠱⡇⠲⠒⠚⡆⢱⠀⠀⢸⣸⡿⣀⡽⢣⡼⢸⠹⠉⣧
⠀⠀⠀⠀⠀⣠⠤⢤⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠀⠀⠙⠚⠀⠔⠒⠒⠷
⠀⠀⠀⢠⡞⠀⠀⣾⠀⠀⠈⢧⠀⠀⠀⡠⠀⢠⠀⡀⢀⠈⡏⢁⡤⠂⠀⢀⢀⠀⠀⠀⡀⠄⢄⡀⠄⠠⠤⢀⠀⡠⢠
⠀⠀⠀⣾⠀⠀⣸⣷⡂⠀⠀⢸⡇⢀⡾⣷⠟⣼⠎⡴⢿⠂⠇⣨⣟⠤⠀⠈⠀⠇⠄⠀⡆⠀⠀⠃⠘⠦⠹⢀⠉
⠀⠀⠀⢻⣤⠾⢻⡏⠛⢦⣀⣸⠇⢀⡴⠋⢀⡏⠣⠀⠘⠀⢀⡁⠀⠀⠀⠀⠀⠰⢀⣷⢬⣀⣠⣆⣸⢄⣸⣡⠶⣌⣂
⠀⠀⠀⠈⠙⠶⢼⣧⣤⠴⠟⠁⠀⠞⠁⠀⠈⠀⠀⠀⠀⠀⡼⢳⣀⣀⣤⠀⠓⠋⠋⠀⠀⠉⠁⠀⠁⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠠⢤⡀⠰⡀⠀⠀⣤⡖⢺⠋⠉⣯⠟⠁⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠃
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⡆⠀⡄⢱⠀⡇⠀⠀⠀⠙⢾⣤⠞⠹⡄⠀⠀⢸⠀⢰⣶⣤⣓⢢⣶⡴⣶⢧⡏⣽
⠀⠀⠀⠀⠀⠈⠓⢑⡆⠰⢁⡂⠐⢃⣾⠀⢙⣉⡆⠀⠀⣵⠋⠳⢄⣳⠀⠀⢸⣄⣾⡳⠞⠯⠟⠳⢂⣋⠘⠙⠻⠄
⠀⠀⠀⠀⠁⠀⠀⠘⠁⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠇⠀⠀⠁⠀⠀⠀⠒⠚⠭⠿⠉

⠀⠀⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⢀⠄⠀⠈⠉⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠂⠈⠉⠁⠐⢄⠀⠀⠀⠀⠀⠀⠀⠈⠉
⡀⠀⣶⠄⠀⢴⡆⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠔⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄
⠃⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⠤⠤⢤⠀⡈⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⡀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠐⠌⠀⠀⠀⠐⠡⠂⠀⠀⠀⠀⠁⠀⠂⠀⠀⢂⠀⠀⠀⠀⠀⠀⠢⠈⠀⠀⠂⢀⠔⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀

⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠂
⡀⠀⣶⠄⠀⣴⡆⠀⠀⠀⠀⠀⠂⠠⣶⠀⠀⣶⠄⠐⠀⠀⠀⠠⠁⢰⡦⠀⠠⣶⠀⠡⠀⠀⠀⠀⠀⢴⡆⠀⢰⡦⠀⠂⠀⠀⠀⠀⠀⣶⠄⠀⢴⡆
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡈⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠉⠉⠉⠉⠁⠄⠀⠀⠀⠀⠐⢄⠁⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠁⠀⠀⠀⠀⠢⡈⠒⠀⠒⠁⠔⠀⠀⠀⠀⠀⠀⠙⠂⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⡀
⠀⠀⠀⠀⠈⠣⠀⠀⣀⠄⢀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢂⣀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠌⣠⠀⡀⠈⡄⠀⠀⣀⠀⠀⠀⢀⡀⠀⠁⠚⠐
⠀⢁⠀⠀⠀⢀⢁⠊⠀⠀⡀⠱⠀⠐⣀⣀⠀⠀⡈⠊⠂⠒⢁⠔⠉⠀⠈⠉⠒⢌⠢⣀⡈⠜⢀⠤⠀⠄⠄⡀⠄⠠⠠⠄⡰⠀⡴⠊⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠁⠀⠀⠀⢀⠀⠄⢀⠀⢀⠀⠀⢀⡀⠤⢤⠄⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⠔⠁⠀⠀⠀⠀⠈⠄⠁⠀⠉⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠔⠉⠉⠐⡄⠒⠤⠠⠄⠂⠀⠀⠀⣁⡀⠬⠚⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠈⠀⢀⡄⠀⠠⣂⠀⠨⠀⠀⠀⠀⡇⠀⠀⠊⠀⠀⠀⠈⠂⠀⠀⡇
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⣀⠀⠘⢄⠐⠄⠐⠀⠃⢀⠌⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⡜⡠⠔⠐⢄⢧⠀⠀⠀⠀⠤⠤⠄⠀⠀⡔
⠀⠈⠢⣀⣤⠤⢂⠔⠒⠉⠐⠀⠀⠀⠀⠊⠀⠀⠀⠀⢃⠀⠀⠑⠒⠀⠐⠊⠁⠔⠉⠉⠆⠠⠄⣀⡉⣀⠠⠊⠰⡃⠀⠀⠠⠈⠓⢄⡀⠀⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⢠⠃⠐⠕⠀⠐⠀⠃⠀⠀⢄⠈⣀⡈⠀⠄⠀⠀⠀⠀⠀⢀⡀⠀⠁⠄⠤⠂⠀⠀⠀⡀⠀⠀⠀⠀⢈⣐⠊⢁⣀⠀⠀⠀⠀⠀⠀⠄⠒⠐⠒⠢
⠀⠀⠀⠀⠀⠘⡄⠀⠊⠉⠉⢀⠆⠀⠀⠈⠐⠀⠒⠈⢀⠀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⡆⢀⠔⠉⠀⠀⠀⠀⠀⠉⠲⡄⠀⢀⠀⢤⠀⠀⡄⠀⠁
⠀⠀⠀⠀⠀⢀⡀⠑⠒⠐⠂⠡⠐⠒⠒⠄⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠑⠒⠉⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢰⠀⠡⡤⢤⠄⢀⠆
⠀⠀⠯⡷⠈⠁⠈⠑⡀⠀⡄⠒⠒⡄⡀⡀⢡⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⠀⠀⠢⠀⠀⢀⠁⠀⠁⠒⠬⠅⠒⠁
⠀⠀⢰⠀⠀⠀⠀⠀⡃⠀⠘⠒⠊⠀⠀⠁⡸⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠌⢠⠁⠀⠀⠔⠈⠁⠉⠢
⠀⠀⠀⠲⢆⣌⡠⠗⠁⠀⠐⠤⢀⣀⠠⠔⠁⠀⠘⡀⠀⠀⢀⢠⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⢀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡀⠀⠈⢰⣂⠀⢦⢠
⠀⠀⠀⠀⠀⢀⠤⠒⠈⠀⠈⠁⠲⡄⠀⠔⠉⠈⠱⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢆⠀⣁⠇⠀⠁⠒⠠⠤⠄⠂⠉⠀⠀⠀⣀⣀⡀⠈⠪⠴⠮⠑⠁
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⠆⢄⠀⠐⡰⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣄⠀⠀⢀⠠⠤⠤⢤⠀⠀⡞⢷⡏⠀⢀⠐⠈⠀⠀⠀⠁⠢⡀⠐⠍⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⢸⠀⠈⢁⣠⠤⢄⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠄⠀⡔⠁⠀⠀⠀⠀⠱⠀⠉⠉⠁⠠⠁⠀⠀⠀⠀⠀⠀⠀⠘⡈⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⠠⠠⡀⠀⡘⠀⠀⠈⠀⠀⢀⡀⠑⠄⠀⢀⠋⠀⠀⠀⠈⠢⡀⢐⠀⠊⠀⠀⠐⠀⠀⠆⠀⠀⠀⡂⠀⠊⠀⠀⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠤⠚⠓⠒⠒⠁⡰⠁⠀⠀⢺⡇⠀⠸⠗⠀⠐⠀⠇⠀⠄⠀⠠⠐⠀⡇⠘⢄⠀⠪⠝⠀⠀⡰⢀⡠⠄⡀⢡⠀⠀⠠⠤⠀⠤⠂⠀⢀⠇
⠀⠀⠀⠀⠐⠠⣀⡀⠀⠀⢀⡠⠜⠀⠀⠀⢄⠀⠀⠈⠀⢀⠔⠁⠀⠣⡀⠂⠀⠒⠁⡠⠁⠀⠀⠑⠂⠤⠐⠊⠀⢋⡀⠀⠈⠀⠑⢄⣀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠁⠀⠀⠀⠀⠈⠐⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊
⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠐⠀⠀⠠⢨⡀⢀⣀⠤⠄⠒⠊⠉⠉⠉⠀⠀⠀⠈⠉⠉⠑⠒⠤⠄⣀⠀⢀⡅⠄⠀⠀⠂
⠀⠠⢄⠀⢼⡄⠄⡠⠀⠻⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠟⠀⢄⠠⢤⡧⠀⡠⠄
⠀⠀⠚⠐⠊⠀⠀⠈⠑⠂⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⠊⠁⠀⠀⠑⠂⠓