Citric acid Emojis & Symbols

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢋⡉⠉⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣯⠀⣿⡇⠘⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣶⣶⣿⡀⢹⣇⠀⣿⡿⠃⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣧⠘⣿⣿⡿⣇⢸⣿⣀⣤⣤⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⢶⡌⠻⣦⣈⣉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⡿⢛⣿⣿⣷⠀⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣿⠀⠀⠠⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⡇⢿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣀⠙⣷⣤⣴⠇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⡟⠳⣌⣙⣡⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣀⡀⠙⢷⣄⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⠀⠀⢿⣿⣿⡿⡛⢷⣬⣻⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⣟⠿⢶⣿⡷⠀⠀⠀⠀⠀⠐⢰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠉⠀⠀⢸⣿⣿⣧⣛⠰⣦⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣆⠹⣷⡀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⣿⣟⠉⠀⠀⠀⠀⠀⠀⢿⣿⡇⠿⢷⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢹⣿⠀⠘⣿⣄⠘⠛⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠿⣷⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⡘⠟⠀⠀⠀⠀⠀⠀⢀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠊⢠⣼⣿⣿⣿⣿⣿⣿⣿
⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣋⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠿⠿⣿
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⣿⣿⣿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⠿⠿⠟⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠛⡶⠦⣤⠄⠀⠀⠀⠀⠀⠈⠓⠠⣤⡉⠛⠦⣄⡀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⡠⠂⢰⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⠂⠀⠀⠉⠁⠀⠀⠀⡼⠀⠀⢀⡠⠖⠁
⠀⠀⢀⣴⡟⠋⠘⠀⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠉⠛⣲⣄⣣⢁⠾⠂
⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⢈⡉⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⡀⠈⠉⠌⠐⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠈⠉⠉⣽⡭⠮⠒⢀⡝⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⠟⠁⠀⠉⠉⠛⠲⣄⠀⠀⠐⠉⠁⠀⠀⠂⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠲⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠖⠛⠉⠉⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠈⠑⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⠤⠤⠄⢰⠒⡩
⠀⠀⢠⣦⠀⠀⠀⠀⠐⠟⠀⢲⠤⠀⠀⢠⠟⠁⣀⠤⠒⠉⡐⠁
⠀⠀⠀⠈⠙⢖⣤⡀⠀⡠⠂⠀⠀⠀⡴⣣⡴⠋⠉⠁⡠⠞
⠀⠀⠀⠀⠀⠈⣇⡉⠙⠳⣦⣤⣤⡴⠾⣿⣛⣈⣉⣁⣀⣤⣖⣚⡉⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠘⣿⠉⢦⡀⠀⠙⢦⠀⠀⠀⠉⠑⢤⣀⠀⣸⡀⠁⠙⠲⢄⡈⠉⠓⣤⣄⡀
⠀⠀⠀⠀⠀⢰⠁⢷⡈⠳⣀⡴⠾⡶⠦⣄⠀⢀⠞⠾⠋⠀⠉⠛⠦⣄⠀⠈⠙⠺⠠⠤⠍⠕⡚
⠀⠀⠀⠀⠀⠀⡄⠀⠹⡄⢸⡇⠀⠀⠁⠪⡹⣎⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠁⠀⣇⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠢⣠⠇⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠋⠀⠀⠀⠀⠀⠀⠀⡿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⢠⠞⠀⠈⠳⢄⣀⣀⣀⣠⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⢀⡀⠨⠭⠭⠍⢀⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡈⠄⠲⠋⠉⠀⠑⠀⠀⢀⠂⠀⠛⠲⡤⣑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊⠀⠐⡀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠈⠆⠑⢌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⣌⠔⠂⢄⠀⠘⡄⠀⠀⠀⠸⢠⠁⠀⠀⠀⢠⠊⠀⠀⣀⠡⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡼⠁⠀⠀⠀⠈⠢⢌⠄⠀⠀⠀⡆⠀⠀⠀⠔⣁⠄⠂⠁⠀⠑⣥⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡈⢃⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⡇⠀⣠⠞⠈⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡅⠄⠀⠈⠁⠁⠒⢀⣀⣀⣀⣀⡹⠈⠁⢚⡁⠀⢀⣀⠀⠀⠀⠠⠄⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⢈⠠⠄⠐⠀⠀⠀⠀⠀⠀⠄⣉⠐⠠⢄⡴⢠⠤⣎⠉⠉⠉⠁⠀⠀⠤⢀⡀⠀⠈
⠀⠀⠀⠀⠀⢀⠔⢈⠠⢒⠅⠊⠀⠀⠀⠈⠄⠀⠀⠰⠀⠀⠀⠚⠔⠠⡈⠺⢄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠃⠃
⠀⠀⠀⢀⠀⢀⠐⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⠈⠑⢄⠑⡀⠑⡍⠢⣀⠀⠀⠀⢀⡝⠠
⠀⠀⠠⠂⡐⡁⠀⡀⠀⠀⠡⠀⠀⠀⠀⠀⢠⠀⡈⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠢⡈⢂⠘⠄⠀⠑⠢⢐⠍⡠⠁
⠀⠠⠁⡌⠊⠀⠀⠈⠐⠄⠀⠱⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠁⠀⣀⠄⠂⠂⡐⡀⢣⠈⡄⢀⠄⢁⠔
⠠⠁⠈⡀⠀⠀⠀⠀⠀⠀⠈⠂⢔⡄⠀⠀⠀⣧⠀⠀⠀⢀⢄⠠⠒⠁⠀⠀⠀⠀⠀⡔⠀⠯⢒⡡⠂⠁
⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⡇⠀⢀⡴⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⡇⢸⠀⠀⠀⠈⠁⠒⠀⠀⠄⣀⣀⠀⠀⡹⠈⠈⠒⠋⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠠⠂⢠
⡇⢸⠀⡠⠄⠐⠂⠀⠀⠀⠀⠈⠉⠉⠉⣱⠀⢀⣠⠉⠛⠛⠓⠂⠨⠄⠀⣀⠀⠀⠀⠀⠸⠀⠁
⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⢸⠃⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢂⠄⠀⠀⠀⠀⠀⣀⠤⢂⠍⠀⠀⠀⢸⠀⠀⠀⠘⠗⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠡⠀⠔⠄⣀⠠⠐⠈⠀⡠⠁⠀⠀⠀⠀⡈⡀⠀⠀⠀⠈⢂⠈⠢⢄⠀⠀⠀⢀⢄⠃⡐
⠀⠀⠡⡈⢂⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⢠⠁⠁⠀⠀⠀⠀⠀⢢⠀⠀⠉⠂⠐⡠⠃⡔
⠀⠀⠀⠐⢄⠑⢄⠀⠆⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡀⠌⠠⠊
⠀⠀⠀⠀⠀⠑⠄⡑⠢⢂⠄⡀⠀⠀⡰⠀⠀⠈⡄⠀⠀⠀⠀⡠⢊⠤⠊⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣈⠀⠈⠭⠀⣀⣀⣀⣈⠐⠲⠈⠑⢈⡠⠐⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣽⡾⠃⠀⠀⠀⠀⠀⠹⣞⣻⣿⣿⣿⡃⠀⠀⠀⠀⢀⣾⡿⢁⣤⠞⢋⣡⢰⡆⢠⣍⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣅⠀⠀⠀⠀⣾⣿⣥⡞⣡⡞⢷⣨⣼⠇⣽⢛⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣀⣀⣸⣿⣿⡟⠸⢀⣀⣀⡑⣾⣾⣉⡦⢖⠠⠆⠀⠀⠀⡀
⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⣬⡹⣿⣿⣿⠿⣿⣿⡇⣗⣿⣿⢷⣿⣿⣟⠲⣾⠍⡸⠀⠀⠀⠀⠙
⠑⢀⣀⠀⠀⠀⣾⣏⡿⣾⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣭⡵⠿⠛⠛⠛⠛⠙⢧⠘⠐⢠⣿⣿⣿⢻⣧⠟⡰⠁
⣤⣴⠉⠓⢄⡴⠿⠧⠿⠛⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣁⠻⠿⠿⠋⣛⠅⠊⠀⠀⠀⠀⣀⣠⣤
⣽⣿⡆⠀⠈⡏⠳⣤⡀⣠⣶⣟⣻⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣄⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣠⡾⠿⠥⢤
⣷⣿⡷⠶⠾⣧⡀⠈⢦⠀⠈⠉⠛⢿⣯⡭⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢾⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠀⠀⢠⣴
⡟⠁⠀⠀⠀⠈⢿⣦⠀⠱⠀⠀⠀⠀⠈⠛⢷⣟⡀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠳⡟⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠓⢒⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⡇⠀⢡⡀⠀⠀⠀⠀⠀⠙⠯⡀⠀⠀⠀⠀⠀⠀⢈⣻⣷⡷⠋⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣾⣿⠿⠛⠛⠲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣶⠿⠛⠋⠙⠛⠻⢶⣄⠀⠀⠀⢸⣯⡼⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠈⠀⠀⠰⣿⣿⣿
⣶⣀⢀⣀⣀⣠⣴⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀⠀⠀⢿⣯⣿
⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢽⡿⠀⠀⠀⠀⠀⠈⢿⣿
⣠⡶⠿⠿⠟⠋⠁⠹⣿⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣶⣤⣤⣤⣄⣾⠿⡇⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣝⠻⣿⣷⣶⣄⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠿⠧⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢶⣿⣿⣿⡂⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⡿⠿⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡿⣯⣻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿
⠿⠁⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⠟⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣠⡶⠁⠀⠀⠀⠀⠀⢠⣿⣯⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣿⣿⣿
⣿⣷⣾⣶⣶⡿⠋⠀⠀⠀⠀⣴⣿⠽⣷⠀⠀⠀⠀⠀⠀⢸⣟⠻⣤⣿⣷⣠⣤⠤⠀⠠⠤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⣈⣷⣿
⠛⠛⠛⠛⠉⠀⠀⠀⠀⢀⣾⢵⡟⣧⡟⠀⠀⠀⢀⣠⣤⣼⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣗⣿⣱⣾⣁⣀⣀⣀⣘⣷⣽⣼⣿⣿⣿⣟⣁⣀⣀⣀⣀⣀⣴⣶⣛⣻⣷⣶⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⣿⣯⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⡿⠿⠟⠛⠛⠿⠿⢿⣷⣦⣀⠀⠀⠀⠀⣿⡏⠀⠈⢿⣆⠀⣼⠟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠓⢦⡄⠀⣿⡇⣀⡀⠈⢻⣾⠃⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⢻⣧⡉⠉⠉⠙⠻⣦⣴⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠙⣧⣰⣿⠁⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣦⣬⣝⣛⡿⠿⠶⠿⣿⡁⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣹⣿⠿⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠋⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢁⣠⠖⣠⣾⣿⠏⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣠⣶⡿⢃⣼⣿⣿⣫⡇⡗⠀⣆⠀⢻⣿⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⡿⠋⣴⣿⣿⡿⡳⣹⢰⡇⠀⣿⡆⠈⣿⣷
⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⡿⠋⣠⣾⣿⣿⡟⡽⢡⡇⣼⡇⢰⣿⣿⠀⢸⣿
⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⣿⠟⢁⣾⣿⣿⣿⢟⡼⢡⣿⢀⣿⡇⢸⣿⣿⠀⢸⣿
⠀⠀⠀⣸⣿⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⣿⠟⢁⣴⣿⣿⣿⣿⢋⡞⢡⣿⠇⣸⣿⠀⢸⣿⣿⠀⢸⣿
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣠⣿⣿⡿⢁⣴⣿⣿⣿⣿⡿⢡⠟⢠⣿⡟⢀⣿⡿⠀⣿⣿⣿⠀⢸⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣴⣿⣿⠋⣰⠟⣽⣿⣿⣿⠟⣰⠋⣠⣿⣿⠁⣸⣿⡇⢠⣿⣿⡇⠀⣾⣿
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣼⣿⡿⣡⠞⣡⣾⣿⣿⡿⢋⡼⠁⣰⣿⣿⠇⢠⣿⣿⠀⣸⣿⡿⠀⣰⣿⠇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⣿⣿⡾⢫⣾⣿⣿⣿⡟⢡⡞⠁⣴⣿⣿⡟⠀⣾⣿⡏⠀⣿⡟⠀⣰⣿⡟
⠀⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣿⡿⢋⣴⣿⣿⣿⡿⠋⣴⠏⢀⣼⣿⣿⡿⠁⣸⣿⣿⠁⠸⠋⠀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠀⠸⠟⣰⣿⣿⣿⣿⠟⢡⡾⠁⢠⣾⣿⣿⣿⠃⢰⣿⣿⠇⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡀⠀⣨⣿⣿⣿⠟⠁⣰⠟⢀⣴⣿⣿⣿⣿⠇⢠⠿⠋⠁⣀⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣯⡀⠀⠁⠐⠛⠛⠛⠛⠉⠁⠀⣀⣠⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⡀⠉⠷⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣠⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠘⡈⠳⣌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⢚⣄
⠀⠀⠀⠀⠀⡏⢀⠂⠆⠐⠀⠠⠘⠲⢒⠀⠀⠀⠀⢿⡄⢱⠈⠢⡈⠛⠶⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⢿⣩⡛⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⡵⠄⢈⠑⠢⠤⠬⠝⠳⠆⠀⠀⠀⠀⠀⠄⠉⠴⠥⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠃⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠔⢂⣀⠀⠀⣀⠠⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢹⣤⠍⡠⣌⠂⡛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⣉⣿⣎⡩⢍⣅⣀⢁⠇
⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢳⠫⡴⠩⠙⣫⡽⠠⠊⠀⡘
⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⣀⠄⠁⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠠⣅⡓⠒⠀⠀⠊⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠈

⠀⠀⠀⠀⠀⠀⠀⣰⡏⠉⠉⠉⠉⢉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠁⠉⠁⠀⠀⢉⣀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠠⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠠⠄⠤⠀⠒⠐⠀⠠⠄⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠊⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠌⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⢄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠡⠄⢀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠒⠂⠀⡇
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠐⠀⡇
⠀⠀⠀⠀⠺⠿⠿⠿⣧⢤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣏⡁⠀⣆⠰⡀⡐⢳⠀⡆⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⣇⡄⢈⣀⠠⠰⠇⠇⠡⡰⠀⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠸⣆⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢠⣵⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⡌⠀⠀⠀⡀⠀⠀⠀⡴⠓⡀⡀⡀⠨⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡂⠀⡀⠀⢂⠀⠇⠀⠀⠀⠀⢠⣎⣩⢙⣦
⠀⡈⠈⠀⠠⡦⡄⢀⠀⡄⠀⣰⡙⠂⣼⣯⣵⠀⡏⢹⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⠁⡀⡗⢦⡀⠀⠀⠂⠰⠀⠀⠀⠀⢸⠼⢿⢻⢃
⠀⠡⡀⠳⣤⣤⣴⣧⠰⠓⠂⢹⡀⠛⡭⠱⠁⣼⢃⡎⠀⠀⠀⠊⠀⠀⢀⣀⡀⠀⠀⢄⣀⠀⠀⢀⣠⠑⣏⢀⣿⣧⠈⢷⠀⠀⠀⠘⠃⠀⠀⠀⠈⠐⠒⠛⠁
⠀⠀⠘⠜⠫⠈⠉⡟⠛⠁⠀⠀⠑⠄⣶⣴⣽⠵⠊⠀⠀⠀⠘⠄⡆⠀⠉⠡⠀⢠⣄⢀⠀⠀⠀⠀⠈⡀⠘⢄⡈⠀⠀⡾⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠄⢀
⠀⠀⠸⡀⠀⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠌⠁⠀⠀⠀⠑⠢⠤⠽⠷⠚⠁⠀⠀⠀⠀⠀⢁⠀⠔⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠁⠉⠀⠀⠀⠀⣠⠀⣀⠀⠀⠀⡤⠒⠒⢀⠝⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠆⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⢀⣸⠲⡀
⠀⠀⠀⠀⠘⠳⢄⡀⠀⠈⡄⠋⠁⢠⢞⡥⠖⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢎⠀⠰⡄⠁⡹⠀⢠⠛⠀⠦⠠⡀⠀⠀⠀⠀⠀⠀⠰⡜⠟⠁⡅
⠀⠀⠀⠀⠀⠀⠈⣏⠑⠛⢤⡄⠤⠶⣟⣒⠂⠈⠀⣤⣒⡒⠒⠦⣄⠀⠀⠀⠀⠀⠀⢰⣧⣄⣠⠒⠇⠀⠡⢄⡀⣑⠀⡱⢤⡿⠀⠀⠀⠀⠀⠘⠠⠝⠶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢷⡘⣆⠀⠙⣆⠀⠀⠈⠐⣤⡀⠧⣀⠈⠒⠤⣈⡱⠦⢤⡀⡀⠀⠀⢻⣾⡶⣤⣭⣤⣧⣤⣤⣴⡶⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠳⡌⢲⠋⠙⠉⠶⢄⠌⠈⠀⠀⠈⠙⠢⣤⠀⠡⠁⠉⠀⠀⠀⠀⠸⣿⣇⣿⣿⣇⣾⣿⣿⣿⣧⣿⡿⠀⠀⠀⠀⠀⠀⠀⠨⠶⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⡆⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣼⢽⣧⣽⢪⣿⣿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣴⠃⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣼⡟⣿⣽⣟⣿⣻⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡜⠲⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣿⣿⣻⣷⣿⣾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⡀⠀⡰⠋⠀⠀⠀⠈⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣽⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠠⠀⠄⣆⠀⡀⠀⠀⢠⣼⣷⣆⠀⠀⣘⣶⣧⣼⣿⣿⣶⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⡀⢠⣤⡀⠀⣜⠿⣇⠀⣨⢡⠑⡆⠀⠀⢈⣿⣿⣦⣾⣻⣿⣹⣿⣿⣽⠟⣡⡆⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠷⢄⣽⣧⣦⣹⣿⣤⠹⡷⣬⣤⣇⢰⣆⠀⢿⣿⣿⣿⣿⣿⣿⣟⠋⠀⣺⢟⡟⣠⡞⢋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣉⡿⣿⣿⣝⣿⣧⣹⣿⣿⡛⠾⣿⣼⣿⡿⢿⣿⡿⠾⠿⢛⣲⠟⡇⢁⠶⣷⣴⣟⠛⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣡⠰⠇⣤⣤⣿⡿⢛⣿⣿⣷⣄⣀⠻⣏⠀⠀⣨⠿⣛⡛⢿⣿⣻⣥⣼⠂⠁⠰⣙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⣴⣿⠟⢋⡣⠭⠟⠠⠄⠈⣿⣧⡿⣿⡟⠛⠲⣿⣷⣼⠿⣿⣯⡭⠾⣆⡀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣡⠊⠁⠀⠀⠀⠀⠀⠈⠙⠻⢿⣯⣴⣶⡶⠛⠻⠿⠷⣌⢁⣁⣀⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠾⢶⠲⢤⣀⢯⠻⡀⣴⣤⣏⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⡅⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠑⠤⡈⢻⡁⠇⣹⠌⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⡜⣿⢢⠑⠀⣤⡈⠈
⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠹⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⣌⠀⠀⡀
⠀⠀⠀⠀⠐⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⠀⠀⠀⣀⠀⠐⠆⠀⠀⠀⠀⠄⠀⠀⠀⣀⡀⠠⢀⢿⣷⡌⣿⣿⡁
⠀⠀⢀⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠡⡰⠄⠀⠠⠤⠄⠀⠀⠘⣀⠀⠀⠀⣿⠅⢀⠈⡔⠁⠀⠀⠳⠀⢻⣿⠙
⠀⠈⠁⠀⠈⠙⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠊⠀⠈⠃⠀⠀⠀⠀⠀⣄⠀⣀⠀⠀⠀⠈⠀⠈⠠⣄⠀⣋⠼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠠⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠓⣷⡴⠶⠂⠶⠤⠤⠀⠛⠁
⠀⠀⠀⠠⡐⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⠀⠀⠀⣐⠀⢧⠤⠀⠀⣴⠀⠀⠐⠀⠀⠼⠋
⠀⠀⠀⠀⠈⠑⢆⣈⠒⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⠀⠀⠤⣤⣼⣗⣶⡆⠤⠐⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠔⠛⠋⢈⠽⠋⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠀⠁⠐⠀⠀⠀⠀⠠⠂⡇⠀⢀⡴⠛⡄⠀⠀⠒⠁⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡀⡁⠐⠀⠀⠦⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⢘⠤⠀⠀⢠⠀⠀⠀⠀⠀⠀⠑⠶⢀
⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠇⠀⠐⠁⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠒⠄⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠶⠛⠛⠻⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠠⣄⡉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⡀⠐⣦⠀⠉⠓⢦⣙⠶⣌⠛⠛⠛⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⣀⠀⠀⠀⠀⢀⣀⣤⣤⣍⣉⡉⠐⠦⣤⣄⠈⠳⣤⠈⣧⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠚⠉⠉⠻⠶⠶⠟⠋⠁⠀⠀⠀⠈⠉⠓⠶⠀⠈⠻⣆⠈⠁⠸⣇⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢻⡀⠀⣠⠎⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣘⣛⡛⠓⠲⠶⠶⠶⠂⠀⠀⠀⠀⢀⣴⠶⠶⢶⣤⡈⠓⠀⠘⠃⠴⢫⡞⠁⣿⡇
⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠐⠋⠉⠉⠀⠀⠀⠀⠀⠀⣠⠀⣼⠀⠀⣀⣤⠤⢤⡄⠈⠻⡦⠀⠀⠀⠀⠋⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⡇⠀⡾⠉⢠⡶⠖⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠳⢦⣄⠀⠀⠀⠀⠀⢸⡇⠘⣇⠸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢸⣧
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣉⣙⣛⣛⣩⡄⠈⢧⠀⠹⣆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⢻⣇
⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠒⠖⠦⣭⡉⠉⠉⠀⠀⠀⠀⠀⠀⠹⠊⠓⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⣼⢋⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠈⠉⣀⠀⠀⠀⠁⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠾⠙⣎⠧⠀⢤⡀⠀⠀⠀⠀⠀⠐⠋⠁⢀⣀⠀⠀⠀⠙⣦⠀⠀⡼⠁⣠⣶⣿⣿⣷⣦⡀⢸⣾⠃
⠀⠀⠀⠀⠀⠀⢻⡀⢏⡈⠃⠀⠠⣍⠓⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣦⣄⣀⣸⡆⠘⢡⣾⣿⣿⣋⣀⣠⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠸⣇⣾⣰⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣀⣠⣿⠟⠿⠟⣻⡟⠉⢻⣿⣈⠛⠛⠋⢁⡀⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣎⠻⣧⡄⠀⠀⠀⠀⠠⢤⣄⣀⠛⠛⢋⣉⣡⣤⠤⠞⠁⣿⠀⠈⣿⠉⠙⠛⠋⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⢀⡀⠘⠂⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣠⣿⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⠲⠂⠀⠀⠉⢙⣇⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣷⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢧⣀⣤⣀⡀⢀⣰⡟⠛⣇⠀⠀⠺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣴⠃⠀⡼⠃⠀⠀⠀⠈⠉⠉⠋⠉⠀⠀⠹⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢿⠀⠸⠃⠀⠀⠀⣀⣴⣶⣶⣖⣒⣦⣀⡀⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠸⣆⠀⠀⠶⠟⢻⣍⠉⠉⠛⠟⠉⢩⡍⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠙⢳⣦⣤⣤⡴⢟⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠼⠋⠁⠀⠀⠀⠈⠳⠄⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⡶⠶⠾⠛⠛⠙⠛⠛⠉

⠀⠀⠀⢀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⡷⣧⣤⣝⣶⠃⠀⠀⠀⠀⠀⠀⠀⣀⠛⠇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠰⠀⣰⣁
⢀⡜⠁⢰⣿⣞⠈⢦⡀⠀⠀⠀⠀⢐⣶⡿⠁⠀⠀⠀⠀⠈⠉⠙⢿⣷⣼⣿⡆⠀⠀⠀⠀⠀⠀⡼⡿⢿⠃⠀⠆
⠮⢴⣎⣀⣉⣀⣱⣆⣳⠀⠀⠀⢦⣾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢴⠦⠄
⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⡀⠀⠀⢆⠀⠀⠀⣄⠀⠀⠀⡠⠋⢹⣿⡟⠑⢄⠀⠀⠀⠀⠀⢀
⠘⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠁⠀⠀⡇⠀⡱⠀⠀⣀⠀⠀⠀⢁⣤⣄⣽⣡⣤⣌⡀⠀⠀⠀⠀⠸⣷⠆
⠀⠈⠻⣿⣿⣿⣿⡏⠀⠀⠀⠈⠑⠁⠈⠲⠀⠀⠁⠉⠀⠀⠀⠺⡿⠋⠀⠙⠿⡟⠀⠀⠀⠀⢀⣤⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠐⠊⠁⠀⠀⠀⠀⠸⠿⣿⡿⠗
⠀⠀⠀⠀⡄
⠀⠀⣶⠀⡄⠀⠔⡀⠀⠀⠀⢀⣘⠁⣤⠀⠀⠀⠴⠀⠀⠀⠀⠀⠐⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣷⠀⡇⠀⠰⠇⠀⠀⠀⠘⠛⢄⣀⠶⠀⡶⠀⡀⠀⠀⠀⠀⠰⠿⠿⢆⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣶⠦
⠀⠐⠛⠂⡃⠀⢰⡆⠀⠀⠀⢀⣤⠜⢻⠂⠘⠛⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣰⣄⣀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠉⢀⡘⠗⠀⠀⠁⠀⠀⠀⠀⢄⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⡆
⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢶⣤⣴⣧⣄⠀⠀⠀⠀⠀⠀⢀⠉⢁⡘⠙⣀⠛⢃⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣆⠀⠀⠀⢀⢞⡟⠉⠉⢙⠲
⠀⢰⣏⣠⣟⣀⡀⠀⠀⠀⠀⠸⠉⠉⠉⠈⠉⠁⠘⡃⠀⠀⠀⠠⣾⣷⡇⠀⣸⣿⠀⠀⠀⣤⠞⠳⠄⠰⠚⠳⡇
⠀⠀⢉⣿⡋⢉⢹⠆⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠂⠂⢿⣿⣿⠿⠃⠀⠀⠀⠠⡀⡀⢸⡀⣠⠀⠄
⠀⠀⠀⠙⠛⢻⡟⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣠⣶⣾⣿⣿⣶⣶⠀⠀⠀⠀⠈⠛⠋⠉⠑⠈

⠀⠀⠀⣠⣶⡾⠿⠿⣷⣦⡀⠀⠀⠀⣠⡴⢞⣛⡉⣩⣛⡳⢦⣀⠀⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⠀⢰⡆⠀⣾⠟⠛⠛⠛⠶⣄
⠀⠀⢰⣿⡏⠀⠀⠀⠀⠛⠃⠀⢠⡞⣡⣦⣹⣿⡧⣿⣿⣿⣢⣍⢷⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⢠⡟⣨⣻⠿⣷⠹⣇⢿⢟⣽⣿⣿⡧⢷⡀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡆⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠙⠻⢷⣤⣄⡀⠀⢸⢧⣿⣿⣿⣶⠅⠉⠉⠫⢭⣭⣿⣶⢸⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⡇⠀⣿⡟⠛⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠸⡎⣋⣽⣶⣾⡟⣴⢠⡽⣿⣶⡙⡿⣸⠃⢹⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⢸⣧
⠀⠀⢀⣤⡀⠀⠀⠀⢀⣿⣿⠀⠻⡜⢿⣿⣿⢹⣿⢼⣷⢿⣿⡿⣰⠏⠀⠘⣿⣿⠀⠀⠀⠀⠀⣰⣿⠃⠀⣿⡇⠀⠀⠀⠘⣿⡀
⠀⠀⠘⢿⣿⣶⣤⣶⣿⡿⠏⠀⠀⠙⠮⣝⡱⠿⠿⠻⠿⢏⣡⠞⠁⠀⠀⠀⠘⠿⣿⣶⣶⣶⣾⠟⠁⠀⠀⣿⡇⠀⠀⠀⠀⠹⣷⣤
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠸⠟⠛⠓⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣽⣥⣍⣹⣍⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⢀⣞⢿⠀⠀⠀⠀⢀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢾⣽⣶⣶⢳⣶⣿⣿⡇⠀⡀⠀⠀⠀⠀⢀⣤⢾⠉⠁⣠⣄⣨⢽⡶⢄⠀⠀⠀⠀⠸⣟⣩⠇⠀⠀⠀⠀⠓⠈⢸⣀⣀⣀⣀⣀⣴⣭⠥⠚
⠀⠀⠀⢰⠀⠀⠀⣷⣭⠉⠉⠀⣘⣿⡇⠀⠉⠀⠀⠀⢠⢾⡵⡏⠀⠸⣿⣿⣿⢿⣧⡈⢳⠀⣄⡀⠀⠈⠁⠀⠀⠀⠀⣠⠶⠛⠋⠿⣌⠀⠀⡤⠀⣠⡀
⠀⠀⠀⠈⠀⠀⠀⡏⠙⠀⠀⠀⢸⣚⡇⠀⠀⠀⠀⠀⣞⣋⣤⡽⠀⠀⠿⢯⣔⣓⣠⠟⠀⡇⠈⠹⠀⠀⠀⢀⣀⡀⣀⠹⡀⠂⠈⠀⢈⠑⢄⠑⠀⠉⠰⠇
⠀⠀⠀⠀⠀⠀⡼⠉⢳⠀⠀⠀⠚⠃⣇⠀⠀⠀⠀⠀⢏⠁⢀⣴⡶⣤⡀⠀⠈⠉⢁⣴⣶⠇⠀⠀⠀⠀⠀⠘⠉⣁⣹⣅⣘⢦⡀⠀⡀⠠⡈⢧
⠀⠀⠀⠀⠀⢸⣡⣶⣷⣶⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⡜⢆⠻⣅⣴⣆⡇⠀⣠⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⡞⠁⠈⠀⣀⠭⠛⢷⣤⣤⡤⠎⠲⠄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠂⠈⠓⢬⣻⡛⣃⣀⣿⡿⠟⠁⠀⠀⠀⠀⣀⣠⢠⠄⣷⣄⡀⠉⠄⠀⠨⠀⢱
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢖⣛⡲⡄⠀⠀⣀⣀⠉⠉⠉⠀⢀⠔⢤⠀⠀⠀⠀⠉⠁⣨⠷⠛⡉⠍⡻⣍⠙⠛⠛⠉⠀⢀
⠀⠀⠀⠀⠀⠻⣿⣛⣛⣻⣿⣿⣿⡿⠿⠋⣾⢼⠦⢇⡇⠀⠘⢥⡾⠃⠀⠀⠀⠈⠲⠛⠀⢠⡚⣦⠀⠊⠁⠂⠁⠀⠀⠀⢈⡇⠀⠀⠀⠟⠻⠰⠆⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡀⢀⣀⡀⠃⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⡔⠉⠀⠀⣆⣀⡇⠀⣏⣉⠁⣰⡄⣴⡀⠀⡆⠀⢯⡉⠀⠉⣿⠉⢸⣠⠞⠀⠘⠞⠁⠀⠒⠒⢿⣷⣾⠆
⠀⠀⠀⠀⢠⣀⡄⢠⡀⣤⢀⠀⡀⢀⢉⠉⠀⠸⣀⢀⡀⠐⠇⠀⠸⠀⠻⠤⠀⠃⠛⠁⠃⠀⠇⠀⠰⠛⠀⠀⠙⠀⠘⠀⠉⠀⠀⠂⠀⠀⠀⠀⠈⠻⠃
⠀⠀⠀⠀⠸⠁⠇⠹⠀⠛⠘⠀⠉⣿⠻⠸⡇⣀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠐⠃⢠⡟⠛⡇⠀⠀⢸⠿⢷⠀⠃⠀⢸⠛⠛⡇⠙⠀⠀⠀⠀⠴⠀⣶⢻⡿⠿⠿⠟⠻⢷⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠁⠁⠭⢉⠳⣴⡒⢲⠄⠀⠀⠀⢸⡇⠀⡃⠀⠀⢸⠀⢸⠀⠀⠀⢸⣤⣤⡇⢀⠀⠀⠀⠀⠀⠀⡟⠉⡇⠀⠀⠠⡣⢼
⠀⠀⠀⠀⠀⢊⠘⢀⡎⠀⠀⠀⠀⠀⠀⣡⣴⣸⡖⠋⠀⠀⠀⡇⢰⣟⣿⡇⠀⠀⢸⣀⣸⠀⠀⠀⢨⣿⣿⡇⢸⡀⠀⢠⣄⡄⠀⣧⣄⡗⠀⠀⢀⡧⢸
⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⢀⠠⠄⣂⡥⢖⢛⠽⡇⠀⠀⠀⠛⡟⠛⣿⣿⡿⠛⠛⠛⣿⣿⠛⠛⠛⢻⣿⣿⡟⢻⠋⠀⠈⠿⠁⠀⣇⣤⣧⣤⣶⣾⣶⣾
⠀⠀⠀⠀⠀⣰⢯⢻⣄⡬⠴⠒⠉⠁⠀⢰⢎⡼⠁⠀⠀⠀⠀⡇⠀⣿⣷⣇⠀⠀⠀⣿⣿⠀⠀⣀⣨⣿⣿⣇⣼⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠋⠉⠙⠦⣄⣀⣀⣀⣀⠴⠋⣠⣤⣤⡀⠀⠤⣿⠽⠿⠛⠛⠒⠒⠒⠛⠋⠉⠉⠉⠉⠉⠀⠀⠙⠀⠀⣴⡄⠀⠀⠉⠛⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣉⣩⡀⠀⠀⣇⠻⣪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣹⠃⠀⢀⣀⡋⠉⣟⡆⠀⠀⡄⢀⡤⠴⠧⣄⣀⣀
⠀⠀⠀⠀⢀⡐⠀⠀⣤⠤⠶⣿⣛⣛⡟⠉⣻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⢹⠀⠀⠀⠈⢁⡴⠞⠋⠤⣹⢦⢸⠀⠀⠠⢰⠋⣀⠀⡈⠜⣿⠤
⠀⠀⠀⠀⠀⠀⣠⢴⠷⠾⢷⠖⢾⠉⠀⠄⢹⠀⠀⠀⣸⠀⡤⠖⢦⣀⣤⣤⣴⡁⠀⣹⠃⠀⠋⠊⡼⠛⢀⡴⠚⢹⠁⢊⡇⠀⠀⠤⢼⠀⣏⡉⣹⢆⣼⠧
⠀⠀⠀⠀⠀⠀⣧⠘⠒⠖⠋⠀⢸⠀⠄⠀⢸⠀⠀⠀⠘⠲⣇⠀⢠⠟⠉⠁⠀⠙⠋⠁⠀⠀⠀⡼⠁⡰⠃⠀⣀⡇⠠⣿⠀⠀⠀⠐⠘⣆⢹⢣⣽⣼⠟⠄
⠀⠀⠀⠀⠀⠀⡗⠐⠂⠀⠀⠀⢸⠀⠁⡂⢸⠀⠘⣤⡆⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡇⢸⠃⠀⠀⢿⡇⢸⡟⡿⠁⠀⠀⠁⠀⢻⣇⣿⠉⠂
⠀⠀⠀⠀⢀⠀⡇⠀⠒⠀⢀⡀⢸⡀⠀⠤⠈⡇⠀⠙⠀⢀⣴⣾⠇⠀⣠⣶⡆⠀⣀⣀⠀⠀⢸⡇⠈⢳⠤⣀⣀⣹⣋⠉⠀⠀⠀⠀⠀⠀⣼⣼⣿
⠀⠀⠀⠀⠚⠁⡇⠀⠀⠀⠀⠀⠸⡧⠴⠖⠚⠁⠀⢀⣤⣞⠛⠛⠒⠲⣿⡿⠤⠿⠾⠼⠁⠀⠘⣧⠸⣯⡇⠀⠀⠠⣭⢉⡇⠀⠀⠀⡀⣀⣿⣿⣿⠀⠄⠄
⠀⠀⠀⠀⠀⠀⣣⡤⠖⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀⠁⠹⣿⣷⡀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠷⢶⣦⣤⣤⣤⣼⠟⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠌⠀⠄⠈⠄⠀⢀⢠⣴⡾⠟⠛⠉⢾⣿⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢐⢀⡀⠛⡁⠠⠀⠀⠀⠘⢿⣇
⠀⠀⠀⠀⠀⠀⠈⠒⠂⡗⣿⢛⠖⠂⠀⠀⡀⠀⠀⠀⠀⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢁⠃⠀⠀⠀⠀⠀⠑⢤⣄⣡⣆⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢄⡀⠀⠀⣀⠔⠀⡤⠩⠲⠃⠈⠁⠀⢀
⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡠⠈⠀⠀⠀⠑⠲⠀⠛⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠁⠀⠀⠀⢀⣶⣿⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⢀⠄⣀⠤⠒⠐⠤⡀
⠀⠀⠀⠠⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠘⠈⣱⠀⠀⠠⢶⠄⣀⠀⡀⠀⠈⢣⡔⠁⠀⠀⠀⠀⠈⢢
⠀⠀⠈⠋⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠃⢾⣿⢆⡐⠀⠀⠣⡀⠀⠀⠀⠐⠀⢣⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⣀⠞⠀⡀⣀⢀⠁⠀⠀⠀⠑⢀⣀⣀⠠⠔⢀⠑⢲⠶⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉⠉⠀⠀⠈⠀⣁⠤⠂⠒⠒⢤⠀⠀⠀⣀⢠⠔⠁⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⣷⡄⠀⠐⢠⠊⠀⠀⠀⠀⠀⠀⣷⣈⠉⠀⡜⠀⠀⠀⣠⣤⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠙⣿⠀⠁⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⡷⠞⠀⠀⠀⠀⠈⠛⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⡄⠘⡈⠀⠐⡀⠀⠀⠀⠀⠀⣿⣿⠏⠀⢀⠀⠀⢿⣶⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠟⠛⠛⠛⢀⡧⢴⣿⣇⠀⠀⠀⠀⠀⠟⠏⠀⢀⣾⣷⣄⡀⠉⠙⡿
⠀⠀⠀⠀⠀⠀⡸⠉⠀⠀⠀⠐⣾⣿⡇⠀⠙⠿⠆⠀⠀⢀⠼⢄⠀⠀⠸⣿⣿⣯⣿⣷⠞
⠀⠀⠀⠀⠀⠀⠃⢴⣿⡇⠀⠀⠻⣿⣷⡀⠀⠀⠀⢀⡴⠃⠀⠀⠉⠒⠶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠙⠋⠀⣀⠔⠉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⣒⣚⣉⣉⣉⣍⣉⣉⣙⣒⣒⣶⡦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠰⢞⣉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣷⠌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠓⠶⠤⠭⠭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠤⠴⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⡶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⣴⡶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⡀⢠⠀⠀⠠⠄⠠⠀⠄⠠⠄⠠⠀⣉⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡾⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠎⠑⠠⢤⣤⣤⣤⣀⣀⣀⣀⣤⣤⡤⠤⠄⠀⠀⠈⢧⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠋⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡱⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡼⠁⠀⠀⠀⠀⢯⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡜⢦
⠀⠀⠀⠀⠀⠀⣠⢏⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢧⡀
⠀⠀⠀⠀⠀⡰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢳⡀
⠀⠀⠀⠀⡼⣱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡱⡄
⠀⠀⢀⠞⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡙⣄
⠀⢠⢎⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣆
⠠⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠃
⣦⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠
⢯⠳⢭⣓⠲⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠖⣋⡵⢫
⠀⠑⠦⣄⣉⠙⠒⠲⠮⠭⢭⣥⣒⣒⣒⣒⣒⣢⣤⠤⠤⠤⠤⠤⠤⠤⠒⠒⣒⣒⣒⣒⣒⣋⣩⣭⡭⠤⠶⠒⠚⣉⣠⠴⠋
⠀⠀⠀⠀⠉⠉⠛⠒⠲⠦⠤⠤⣤⣀⣀⣈⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣀⣠⡤⠤⠤⠶⠒⠚⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠾⣆⠐⠙⢷⠀⠀⠴⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⢠⡎⢁⡀⠉⡆⠀⠀⢸⡯⠑⢂⠈⠀⠀⡀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⢨⣁⣀⢀⠀⠀⠀⢘⢷⣺⣁⡰⠃⠀⠀⢸⣿⠴⢤⠠⠘⠇⠃⠀⠀⠀⠀⠀⠈⠻⣿⠆⢀⣤⠈⢈⠟
⠀⠀⠀⠀⠀⢸⣥⣌⠘⢃⠀⠀⠈⢰⡟⠁⠀⠀⠀⠀⠐⣿⠙⣄⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠌⡐⡲⠃
⠀⠀⠀⠀⠀⠈⣿⣻⡓⠓⠛⠳⠊⡈⡇⠀⠀⠀⠀⠀⢸⣷⣘⣿⢄⣶⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘
⠀⠀⠀⠀⠀⠀⢻⣯⠀⠀⢸⡆⠘⠘⠀⠀⠀⠀⠀⠀⢈⣿⣷⣄⢀⠩⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆
⠀⠀⠀⠀⠀⠀⢸⢻⠇⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢅⡈⠱⣂⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠰⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠢⢤⣀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⠒⠲⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀⠀⠀⠰⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣠⠐⠘⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠂⠂⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡁⢀⠀⢠⡈⢆⣂
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣻⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣼⣇⠹⠾⠿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠖⠚⠸⠇⠀⠀⠀⠀⢀⢰⡀⢀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣶⠖⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠖⣠⡀⠄⠀⠀⠀⠀⠀⠀⢸⣅⡰⠇⠁⠘⠅⡅⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣇⣀⠀⠂⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠈⠈⠛⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣀⠀⢰⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣀⣈⣀⡀⠰⠀⠀⠀⠀⠀⠸⠏⡍⠉⠁⠀⠀⠃

⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣾⣿⣶⡀
⠀⢰⠆⠀⠀⠀⠀⠀⠹⣿⠀⠀⠄⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠠⠀⢰⠆⠀⠀⠀⠀⠁⠠⣶⡿⠁
⠀⠘⣦⡀⠀⠀⠀⠀⣠⠟⠀⠀⠈⢃⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢀⠉⡼⠁⠀⠘⣦⡀⠀⠀⠀⠀⣠⠟
⠀⠀⠈⠙⠺⡤⡴⠚⠁⠀⠀⠀⠀⠈⢳⣴⡿⠁⠀⠀⠀⠠⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠘⢾⢿⡞⠀⠀⠀⠀⠈⠙⠺⠤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⡉⠁⣀⡀⢊⠀⠰⠉⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⢿⡟⠚⠖⠁⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠁⠘⠀⠀⡃
⠀⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣤⣾⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆
⠀⠀⠈⠐⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠈⠐⠒⠒⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⠇⢳⢀⡖⠀⡄⢀⢀⣖⡀⢀⡀⡀⠀⠀⠠⣔⣋⣉⠀⣀⠀⡀⠀⢀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⡴⠀⣀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠼⠋⠘⠦⠌⠘⠿⠸⠤⠿⠜⠯⠑⠿⠘⣿⠁⢀⣀⣨⠤⠋⠸⠉⠸⠻⠸⠏⠀⠀⠘⠧⠄⠀⠾⠣⡎⠸⢯⠱⡇⠶⠿⠼⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠘⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢐⢁⡀⢘⠓⢢⣀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠠⠘⠋⣈⣁⣉⣉⣁⣠⣤⡀⢄⠀⠀⠀⠀⠠⠀⠈⠉⢉⡉⠉⠁⢀⡀⠐⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡽⠜⠁⠋⠁⠼⠿⢲⡆⡄⠀⡀⠤⢤⢄⣠⡾⠁⠀⠀⠈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠂⠀⠁⠒⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣟⣤⠠⠤⢼⡁⠀⢀⣀⣀⣼⠋⡀⢀⣀⡀⠈⠓⡀⠀⠀⠀⠤⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⢲⡄⡐⣂⡂⠒⢤⣀⠄⠀⠀⠀⠠⠀⢀⣤⣍⠈⠁⠑⠂⢒⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡨⠒⠉⠀⠀⠀⠀⠈⢤⣀⠀⠀⠀⢀⡄⢨⡟⠀⢰⠀⠀⢨⠸⠀⠀⠀⠀⠀⠀⠀⡀⡀⠁⠀⠈⠉⠀⠉⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡈⠤⡀⠐⠀⠀⠀⢔⠈⠉⠉⠙⢷⣼⠶⠋⡠⣺⠉⠙⡄⠈⡆⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠀⠀⠀⠈⠈⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣾⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣾⠰⠷⠦⠀⠁⡜⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡘⢿⡄⠀⠀⠀⠀⠀⠂⠀⠈⠀⡸⠀⠀⠀⠸⠿⠦⣄⣠⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠿⣄⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠈⠙⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⣁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢨⠀⠈⠓⠀⠀⢈⠉⠀⠀⠀⠐⢀⠀⠀⠀⡀⠀⣸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠉⠈⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣷⡀⠀⠐⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢡⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡿⠶⠥⠀⢀⣹⣦⣀⠀⠄⠀⠀⠀⠀⣠⣿⠏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⢠⠀⣀⡀⠀⢠⢄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣖⣀⠀⠀⠉⠛⠛⠛⠛⠉⠛⠁⣀⠨⢴⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⣀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢚⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⢀⢋⠀⠰⠄
⠀⠀⠀⠀⠀⠀⢀⡀⢤⠐⢒⠊⠁⠀⢡⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠴⠒⠴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⢁⡈⡒⠀⠠
⠀⠀⠀⢠⠊⢹⠀⠀⣈⠠⠼⠐⠲⠄⠤⠆⠀⠀⠀⠀⠀⠑⠀⢀⠀⠂⠀⠀⡀⠀⠀⠀⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠛⠉⡟⠀⢀⠈
⠀⠀⠀⠈⠒⠊⠉⠁⠀⠀⠀⠀⠀⠧⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣖⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢤⠅⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣩⠀⠙⡤⠤⡤⠤⠤⡤⠤⠤⠄⢀⡀⣀⠀⠀⠠⠠⠤⠄⠐⠒⢌⡀⠀⠀⡀⠄⠀⠀⠠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠨⠏⠌⠙⠒⠏⠉⢳⠉⠁⠈⠁⠉⠁⠐⠒⠒⠘⠋⠥⠹⠗⡠⢄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⣧⢝⡐⠒⠒⠂⢀⠼⠦⠴⠦⡤⠤⠤⡤⠤⠤⠤⠶⡂⠐⠒⠒⣂⠯⡼⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠐⠢⣔⠁⠀⠀⠀⠀⣈⠗⢏⡀⠀⠀⠀⠀⠈⣢⠒⠉⠀⠀⠘⡇⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠄⡀⠀⠠⠊⠀⠉⠢⢄⡠⠊⠁⠀⠀⠉⠢⡀⡠⠔⠉⠀⠑⢄⠀⠀⣀⡆⠀⠀⠀⠀⢄⠀⠀⠀⡄⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡑⠣⣀⠀⠀⢀⠊⠑⠦⡀⠀⠀⢀⠴⠋⠢⡀⠀⠀⢀⡨⢶⠉⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⠀⠑⣔⠁⠀⠀⠀⠈⢢⣔⠁⠀⠀⠀⢙⣤⡔⠁⠀⠀⢣⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡶⢄⠀⠀⢀⠊⠀⠑⢄⡀⠀⡔⠁⠀⠱⡀⢀⠔⠁⠀⠑⡄⠀⠀⡠⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠉⢢⡃⠀⠀⠀⠀⡝⠪⡀⠀⠀⢀⠜⢣⠀⠀⠀⠀⢘⡔⠈⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠃⠈⠒⢄⢀⠌⠀⠀⠈⢢⡔⠁⠀⠀⠱⡀⣠⠞⠁⢡⢀⠜⢃⠀⡀⠀⠀⠀⠀⠀⠀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⡳⡀⠀⠀⠀⠜⠢⠀⠀⠀⢀⣽⠀⠀⣀⠔⠁⠀⠈⠅⠂⠅⠀⠀⠀⠨⠅⠂⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠀⠬⠦⢀⣎⣀⣀⣱⡀⠠⠎⠄⠓⠉⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⠁


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠘⠁⠀⢈⠂⠀⠀⠀⠀⠺⣿⣿⣿⡿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠿⠿⠇⡄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠐⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⠜⠀⠀⠀⠀⠣⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣷⣷⡄
⠀⠀⠀⣀⣀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⣧⣦⣤⣤⡄⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀
⠀⠀⠀⣿⣿⣿⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⣿⣿⣿⣿⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⠀⠀⠈⣿⣿⣼⣿⣾⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⡟⣾⣿⡇⠀⠠⣶⣶⣶⣶⣶⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⣠⣿⣿⣿⣄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⣿⣿⣧⣿⡿⠃⠀⠀⠙⠿⢿⠿⠟⠁⠀⠸⢿⣿⣿⣿⣿⣿⡿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠄⢤⣤⣤⠀⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢹⠀⠈⠉⢱⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣀⣸⣄⣼⣀⣸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⠀⢰⣤⣼⠀⢰⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢙⣉⣻⠋⢻⣉⣻⠋⡟⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⠿⢿⣿⣿⠿⢿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⠀⢸⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⠀⢸⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⡂⢸⣿⣿⠀⢸⣿⡿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣶⣾⣿⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣷⣶⣶⣿⣷⣶⣾⣿⣶⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⢀⡀⢀⣠⡀⠀⠀⠀⡄⠀⡀⢠⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠹⢀⡟⢸⡇⡏⠗⢰⣶⡞⠣⠋⠀⣾⢹⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠦⢼⠁⣴⢆⣧⡬⢨⡼⠧⠗⠚⠦⠿⠸⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⡀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⡀⣨⡛⡅⢨⠑⡎⣇⢈⡇⢛⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠬⠵⠛⠲⠞⠁⠬⠞⠑⠞⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠠⠠⠴⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣙⠉⠓⠖⢄⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣘⣀⣀⣧⣚⠁⠀⠎
⠀⠀⠀⠀⠀⣀⣀⡄⠀⠤⢄⠆⠀⠀⠀⠀⠀⠀⠀⢼⠉⠉⠉⡉⡿⠿⠛⣿⣿⠇⠀⠀⡄
⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠤⠀⠀⠠⠀⠀⠀⠀⢀⢸⠀⢀⢠⣄⡘⠢⠁⢘⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⢀⡉⢡⠆⠈⣿⠀⠀⠋⠀⠐⠐⠘⠀⠀⠀⠟⠋⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⠤⢞⠃⢀⠄⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠉⠁⠀⠀⠀⠀⢀⣀⡧⠀⠰⡇⠀⢀⣠⢏⣿⡠⠀⠀⠂⠖⠀⠀⠀⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣶⠖⠚⠒⠛⣱⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣋⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣍⣉⣉⣉⣉⣉⣉⣹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⠋⢹⠉⢹⡟⢾⣝⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣸⣇⣞⣠⠟⢉⣷⣻
⠀⠀⠀⠀⠀⠀⠀⠘⢯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣛⣉⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣠⣾⡿⣭⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠜⠁⠈⢿⢦⣈⡽⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡤⠉⠀⠀⠀⠈⠳⣟⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⠎⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⢻⣿⣿⣿⣿⣿⣿⣿⡿⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠙⢿⣿⣿⣿⡿⠋⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠛⠛⠛⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠂⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠀⢸⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⠋⠉⠉⠁⠀⢹⣀⣸⠀⠈⠉⠉⠉⠓⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠿⠃
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣊⡥⠐⢲⠄⠠⡐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠎⠀⢊⢂⡈⠀⡠⠊⠢⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠄⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⡇⣸⠀⢀⡀⠂⠁⠡⠎⠄⠀⣁⢰
⠀⠀⠀⠀⠀⠀⠀⡟⠢⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣁⣀⣠⣼⠵⢳⡜⢇⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠁⠀⠀⢸⠈⠢⣢⠔⡡⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠂⣀⠥⠊
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢸⢰⠋⠒⠒⠒⠈⢁⠩⠳⡦⢄⡀⠀⣀⡠⠔⠂⠉⠉⠉⠲⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡘⡀⠀⠀⠠⠂⠁⣠⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⡄⠀⠁⠀⠡⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺
⠀⠀⠀⠀⠀⠀⠀⠀⢁⢁⠀⠀⠠⠀⠀⠀⠀⢀⠸⠁⢀⠀⠀⠀⠀⠀⠀⠀⢘⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢘⠀⠀⠀⠁⠁⠄⠂⠁⢠⠀⢀⠁⠀⠁⠀⠀⠀⠀⡉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠠⢈⣀⠀⠀⠀⠀⢠⠀⠀⠀⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⡰⠀⢀⠆⠀⠈⠓⠀⠀⠀⠀⠂⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢁⠀⠀⠀⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠀⠀⠀⠰⡀⠀⠀⢀⢀⠂⠀⠀⠀⠀⠀⢀⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢬⡑⠒⠶⠤⠤⠄⠴⠂⢒⣩⠔⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡈⠉⠁⠒⠒⠒⠊⠉⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠒⠂⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⡀⠀⠀⠀⠀⠠⡆⠀⠚⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁
⠀⠀⠀⠀⠐⠁⣠⠀⠠⡌⠁⠀⠀⠀⠀⢀⣦⠈⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠠⠂⠄⠀⠠⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⡂⠉⢂⠤⢄⡀⠀⠀⠀⠀⠀⠀⠐⡐⢀⣀⡀
⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠸⠅⠀⢨⡀⠀⢠⠀⠀⠀⠀⠈⠉⡅⠒⢦
⠀⠀⢀⡄⠴⠥⠤⠤⠤⠤⠴⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⠶⠃⠀⠀⠀⠀⠀⠘⠀⠀⠸⢧⡆
⠀⠀⠂⢵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰
⠀⠀⠀⢸⡀⠀⠀⠀⣀⡴⠁⠀⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠈⠉⠀⠀⠀⠂⢀⡀
⠀⠀⠀⠨⠟⠀⠀⠈⠋⠀⠀⠀⠀⠴⠀⠀⠀⠀⠰⠀⢡⠀⠀⠀⠀⠀⠈⠁⠃⠙⠿⠶⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠘⠀⠀⠀⠀⠀⠀⠀⠰⢸⠀⠁⠀⠀⠰⢁
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣤⣤⡤⠀⠀⠀⠀⢰⠁⣇⠀⠄⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢧⠀⠀⠀⠀⠀⠁⠁⣆⡆⠀⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠀⠀⠀⢌⡁⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠲⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⢈⣉⡱⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⡇⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⢀⢃⠀⠀⠀⡠⠐⠉⠀⡀⠀⠀⢤⠀⠉⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢆⡔⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢀⠀⠠⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⢈⠀⠀⠘⡄⠁⠀⠒⠀⠀⠀⠀⠀⠆⠈⡂⡽⠒⢄⠐⠕⡠⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡸⢃⡀⠅⠹⣄⡔⣉⣂⣄⣢⣠⣠⣄⣱⣤⣇⣁⣀⢑⢿⣋⣡⣴
⠀⠀⠀⠀⠀⠀⡐⠠⠊⠬⠾⠤⠲⢵⢬⣔⠷⢦⢹⡉⠑⢁⡬⠆⠄⠀⠀⠸⡬⠐⠒⢔⠀⠀⣊⡴⠇⡆
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⠀⢀⡴⢻⠜⠣⡪⡧⢯⡁⢕⣙⠒⠲⣶⠀⢐⣌⡪⣐⣗⡡⠪⠂⢕⢇⠁
⠀⠀⠀⠀⡰⠀⠀⠀⠈⠂⠊⡤⣨⡂⢕⣕⣄⡪⢐⣎⡗⠻⣕⠀⠀⣀⠀⡋⠀⠉⠖⡡⢈⢔⢕⡽⠸
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⢍⠪⣺⣇⢠⡿⡊⣽⡿⣤⣷⡑⠉⢊⠤⡱⢂⢖⠭⡪⡱⢗⠵⡡⠁
⠀⠀⢠⠁⠀⠀⠀⠀⢅⠌⠀⠸⣋⣌⠞⡊⣕⠄⡪⢐⢡⣱⣹⡶⡋⢕⠅⡪⢚⢕⠈⣊⡔⢁⠔⠁
⠀⠀⠈⢔⠄⡀⠀⠀⠀⠀⠀⢨⠢⠐⠍⡪⠐⢅⢨⣲⡋⢇⡗⣬⣪⣕⡥⢪⠄⠵⠊⣉⠔⠁
⠀⠀⠀⠀⠈⠉⠀⠘⠁⠰⠶⠷⠾⠶⠿⠾⠿⠥⠉⠐⠊⠉⠉⠉⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠠⡀⢀⠄⡀⢄⢠⠠⢀⠀⡀⡀⠄⠠⡀⢀⢀⠀⠀⠄⡀⠄⠀⡀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⣀
⠀⠀⠀⠀⠁⠈⠀⠀⠁⠈⠐⠁⠊⠀⠑⠁⠊⠂⠅⠊⠐⠀⠐⠑⠨⠀⠅⠊⠔⡩⠂⠕⠨⢂⠕⠪⠐⠡⡪⠠⠃⠔⠔

⠀⠀⠀⠀⠀⠀⠀⢠⢏⣼⠈⡧⣰⡃⢠⢀⠀⣴⡀⠀⡀⡀⠀⠀⠀⣔⣉⣉⠀⣀⢀⣀⠀⣀⠀⠀⢀⠐⠒⠂⢀⠀⠀⢠⠆⢀⠀⢀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠟⠁⠙⠆⠁⠋⠇⠇⠼⠒⠻⠅⠺⠄⢻⠃⢀⣤⠤⠄⠋⠸⠉⠺⠛⠸⠋⠀⠀⠘⠢⠄⠰⠏⠾⠅⠻⠅⠿⠰⠻⠱⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⠀⠀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠁⠑⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⢰⡃⣤⠠⠤⠄⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⠖⢶⢂⡴⠶⣶⡐⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠒⠀⠠⠤⠤⡀⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⣿⡯⠛⠀⠀⢠⠐⠉⠉⠛⡑⣄⠄⠒⠒⠒⠲⣏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠛⣓⡈⠐⢓⠂⠀⡒⠂⠚⠓⠒⠀⠀⠀⠀⠀⠤⠠⠄⢀⣑⣢⢇⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠈⡈⠉⠉⢝⠰⠄⠒⠀⠀⠓⠎⠀⠀⠀⠈⠀⠀⠞⣶⠀⢀⠀⠀⠰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠄⠰⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄⠀⠀⡀⠀⠀⠀⢈⠶⠦⢤⣄⠰⣃⡴⠃⣀⠤⢤⠀⡀⠇⠀⠀⠀⠀⠀⠀⠴⠀⠤⠄⠄⠠⠀⢠⠤⠀⠤⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣶⠀⠉⠠⠀⠀⠀⠈⠀⠀⠀⠀⠈⢿⣯⣐⢎⣔⣁⠀⠃⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡆⠀⠀⠀⠀⠀⠡⠀⡀⠀⠀⡄⠈⠈⡉⣦⣉⠀⠀⡠⠁⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣻⣄⠀⠀⠀⠀⠀⠀⠁⡠⠂⠀⠀⠀⠀⠁⠨⠷⣾⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡟⠙⠦⠄⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠀⠆⠂⠀⠒⠁⠲⠀⠆⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢰⡄⠀⠀⡤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣿⢦⣀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠸⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣙⣢⠤⠀⠀⠙⠻⠿⠶⠦⠖⠶⠆⠀⢙⣋⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠁⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠯⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣠⠼⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠘⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠴⠦⠀⠀⠉⠒⠀⠁



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⡶⢶⡶⢶⣶⣶⡶⢶⡶⠶⠶⠶⣶

⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠻⠀⠀⠀⠀⠀⣀⡩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠉⠁⠟⠀⠀⠀⠘⠠⢤⣤⢤⠜⠃⠀⠀⠙⠃⠀⢠⠴⣯⠈
⠀⠀⠀⠀⠀⠈⢆⠀⡬⠁⠀⠀⠀⢰⡦⠤⠀⠀⠄⣴⠀⠀⢀⠀⠀⠀⠘⡆⠀⠀⠀⢻⡾⠿⣀⠀⠀⠀⠀⠀⠈⠂⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⠀⠀⠘⠇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠼⠀⠀⠀⠀⠐⠺⠉⠀⠀⠀⠀⠧⡀⣈
⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠖⠀⠀⠀⠀⠀⣓⡀⠀⠀⠀⠀⠷⠆⢀⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⢩⠙⢢
⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠊⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢏⡇
⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠶⠿⠶⠦⣴⡀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠀⠀⠈⢄⠀⠀⠀⢠⣴⠃
⠀⠀⠀⠀⠀⢀⣞⢑⡀⠀⠀⣈⣱⠀⠀⠀⠀⠀⠐⠧⠀⠀⠀⢻⠃⠀⠀⠈⠀⠄⢀⢠⠀⢸⠀⠀⠀⠀⠁⠲⡄⠊⠁
⠀⠀⠀⠀⠀⣨⡉⠲⠅⠠⠀⢨⣟⠀⠀⠆⠀⠀⠀⠐⣴⠀⡜⠀⠀⠀⠀⠈⠁⢰⡀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢹⣇⣀⣀⡀⠀⢸⣿⠀⠄⠘⠀⠀⠀⠀⠛⠀⠃⠀⠀⠀⠀⠀⠰⠐⠤⠚⠀⠊
⠀⠀⠀⠀⠀⠀⠙⠦⠧⠤⠤⠼⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠚⠀⠀⠀⠀⠀⠲⠤⠴

⠀⠀⠀⠀⢠⣶⣤⣤⣀
⠀⠀⠀⠀⢸⣝⣿⣧⡉⠙⢄⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⠂
⠀⠀⠀⠀⠈⢳⣒⣿⡻⣶⠘⡄⠀⣠⢾⣹⣿⠟⢹⣿⠁
⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣷⡇⠀⣿⣼⠿⢃⣠⠟⠁⠀⠀⠀⣀⣀⣀⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣷⣾⡇⠒⠚⠉⠁⠀⠀⢀⡴⡟⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢓⡶⢗⢄⣀⠀⠀⠀⢰⡿⣷⣿⡿⠀⣿⠏
⠀⠀⠀⠀⠀⣠⡶⢋⣩⣽⣿⠋⠀⠈⠺⢝⢧⠀⠀⢈⣷⣿⣋⣀⠟⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣼⣿⣶⣿⣿⠿⠃⠀⠀⠀⠀⠀⠳⣝⢲⡞⢓⣂⣉⣀⣀⡴⣟⣿⣻⡿⠟⢛⣷⣶⣤⡀
⠀⠀⠀⠀⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣝⣦⡈⠉⠙⠻⢿⣿⣾⣿⣿⣿⡳⣶⣖⣻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠻⣦⡀⠀⠀⠙⠛⣿⣷⣙⢁⣨⣈⠙⠻⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⠳⣄⠀⠀⠀⠀⠉⠉⠛⠛⠟⠛⠛⠚⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠙⣆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣘⣧⣴⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣀⣀⣀⢠⣾⣿⣫⣵⣿⡅⠀⠉⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡳⠿⢿⣛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣴⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢯⣜⣁⣛⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠾⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣫⠄⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⢛⡀⠀⠀⠀⢀⠀⣑⠠⠵⠕⠃⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠁⠁⠀⠀⠀⠀⠘⠘⢀⡀⠈⠁⠀⡄⠀⠈⠈⠀⠀⢸⠀⠀⠀⢠⢫
⠀⠀⠀⠀⠀⠀⠀⣰⣻⠀⡀⠀⡀⠀⠂⠀⠀⠀⠀⠈⠿⠢⠀⠀⡀⠀⠀⠀⣀⢼⣆⠉⠁⢸⡑
⠀⠀⠀⠀⠀⠀⣰⠿⢹⠉⣃⡁⠅⢀⡀⠈⠠⢠⣤⠄⠈⠈⠀⡴⠇⠀⠰⠊⠀⢸⠀⠀⢒⡞
⠀⠀⠀⠀⠀⣰⡝⠃⠀⠀⠀⠁⠀⠀⠉⢣⠀⠀⠀⠈⠂⠀⠀⢀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡴⠿⣶⣷⣴⣤⣤⡄⡆
⠀⠀⠀⣀⣀⡀⢀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠂⣖⠀⠐⠞⠁⠆⠀⠀⠀⠰⠀⠈⠃⠣⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠈⠁⠉⠀⠀⠘⠁⠉⠉⠉⢻⠆
⠀⠀⠠⠤⠜⠗⢠⣄⢠⣐⣛⠻⠅⠀⠀⢠⠀⠀⠀⠀⠠⠷⠆
⠀⠀⠀⠀⠈⠉⠛⠙⠻⠉⣹⣿⣯⢭⣿⠩⢥⡦⠄⢦⠽⠿⠶⠶⠮⠷⠖⠒⠺⠥⠟⠿⠷⠮⠥⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠆⠀⠀⠰⠀⠀⡌⠉⠉⠉⠉⠉⠉⠉⠉⣱⠀⠁⠀⠀⠀⠀⢗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠚⠴⠿
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢨⠁⠂⠀⢠⡇⠀⠀⠀⠀⠡⠀⠀⠲⢦⠄⠀⠀⠀⠀⠶⣾
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠎⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⠀⠀⠘⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠂⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠌⠀⠀⠀⠑⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠄⠄⠐⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄
⠀⠀⠀⠀⠰⠀⣀⣄⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡝⠃⠀⠀⡀⠰⠂⢀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠃⠄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠸⠁⠆⠀⠀⠠⠄⠟⠀⠀⠀⠀⠀⠀⠀⢩⠄⠀⠠⡝⠓⡐⠀⠀⠀⠀⠀⠀⠖⠄⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⡦⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉
⣿⣿⣿⠿⣿⠿⢿⣿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣮⣶⣷⣶⣿⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⢡⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠒⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡂⠀⢸
⠀⠀⠀⠀⠀⠀⠐⢖⠚⡞⡒⠒⠒⠒⠒⠒⠒⡶⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⠃⠀⠀⠀⠀⡂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⣸⣀⣀⣀⣙⣇⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡧⡤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⡏⡇⠀⠉⣉⡉⢹⡇⠀⠀⠀⠀⠀⠀⣠⠴⠃⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣤⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢱⢡⠀⠀⠀⠆⢸⡇⠀⠀⠀⠀⠀⡼⠁⠀⠀⣤⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠘⡄⠈⣁⡁⢸⡇⠀⠀⠀⠀⢰⣇⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠤⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠇⣇⠀⠀⡃⢸⡇⠀⠀⠀⠀⠀⢿⢆⠀⠘⠝⣀⠺⢠⣿⠇⠀⠀⠀⠀⠀⠀⣿⣇⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣣⣤⣼⣧⣬⣭⣴⣪⠇⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣯⣶⠵⠃⠀⠀⠀⠀⠀⢀⣴⣻⣧⣤⣼⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠛⠛⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣉⣉⣉⣉⣉⣉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠓⠒⠒⠒⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⠒⠒⢺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠠⠬⣏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠚⢻⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠐⠒⢷⣻⡇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠉⠩⣇⣿⡄⠀⠀⠀⠀⠀⠀⣿⡏⠉⢹⢿⡉⢩⣍⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢀⣺⡾⣷⠀⠀⠀⠀⠀⠀⠸⡿⡄⠈⠉⢀⣬⠁⣤⠀⠀⠀⠀⠀⢠⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡇⠀⠀⠀⠀⠀⠀⠹⣝⢄⣀⣀⣉⣀⣉⣀⣀⣀⣀⡴⣣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠄⠒⠒⠂⠀⠀⢀⡉⠀⠇⠀⠘⠀⠀⠀⠈⠉⠙⠁⠒⠒⠲⠤⠤⣤⣀⡀
⠀⠀⣀⡤⠖⠛⠋⠁⠀⢀⡤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠙⠒⠤⣄⠐⠒⠀⠀⠉⠻⡆
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠙⠳⢤⣤⣀⣀⣀⣀⣀⣙⣉⣀⣉⣁⣀⣀⣀⣀⣤⣤⡤⠞⠁⠀⠀⢀⣀⣴⠇
⠀⣘⠳⣦⣤⣄⣀⣀⣀⣀⡀⠀⠀⢀⡉⠉⠉⠉⠉⠉⠉⠉⠉⣀⣀⣀⣀⣠⣤⡤⠴⠶⢶⠿⠛⠉⠀⠈
⠀⠈⢩⠘⠓⠶⠬⠭⠍⣉⣭⣉⣉⣉⠉⠀⣈⣍⣛⠉⠛⠋⠉⣩⡍⠉⠀⠀⠔⠀⠀⠀⠀⢀⣀⣠⡄⠂
⠀⠀⠸⠂⠠⢤⣄⣀⣀⣀⡀⠀⠉⠀⠀⠐⠁⠀⠀⡀⠀⣀⣀⣀⣀⣠⣤⣤⡴⠶⠖⠛⠋⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠒⠂⠀⠃⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⠀⣹
⠀⠀⠀⠀⣷⠀⠈⠀⠀⠀⡠⠤⠤⠄⠀⠀⠀⢀⣠⣤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿
⠀⠀⠀⠀⢿⡑⠢⠄⢀⣐⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠈⠁⠂⠀⠆⠀⠀⠀⢀⡀⠀⠀⢈⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣨⠓⠚⠛⠶⢤⠠⠤⢤⣤⡤⠶⠦⢶⣶⣖⣉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡄⠀⠀⣠⠊⠀⠀⠀⠐⠶⠀⠀⠉⠙⠢⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⣿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢻⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⣧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣯⠀⡀⠀⢀⡀⠹⣆⠀⠀⠀⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠁⠀⠀⠇⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠄⠲⠀⢈⡓⣤⡤⣠⡤⠶⠀⠀⠀⠈⠀⠈⠁⠂⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠰⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⢠⡾⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣤⣀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠾⠋
⠀⠀⠀⠸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⠶⠶⠶⠦⠤⠴⠖⠒⠋⠉⠁
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠊⠉⡆⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠵⡒⠁⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢦⣀⡼⠀⠀⠸⡯⠀⠁⠀⠀⢀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠓⠀⠀⠠⠄⠀⠈⠛⢇⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⣼⠁⠀⠁⠀⠀⢸⠀⠀⠘⡏⡇⠀⢀⣤⡈⠀⠑⠀⠀⠀⡀⠀⠀⠀⢱⠀⣸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠘⠻⢤⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⢀⠊⠈⠁⠀⠀⠃⠀⠀⠙⠿⠿⠿⠋⠀⠛⠉
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡖⠀⠀⡀⠀⠹⡆⠀⠀⡇⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠠⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢣⠀⠀⠅⠀⣠⠇⠀⠀⡇⠀⠀⠀⠀⠀⣸⠘⣦⠀⠀⠀⠀⡄⠀⠈⢩⠉⠉⡇⠀⠀⢠⡮⡀⠀⠀⢘
⠀⠀⠀⠀⡆⠀⢠⠀⠀⠀⠈⠟⠛⠟⠛⠏⠀⠀⠀⡇⠀⠀⠀⠀⠉⢻⠀⠉⠻⠉⠉⠋⠁⠀⠀⢸⠀⣗⡇⠀⡖⠉⠀⠀⢀
⠀⠀⣠⣤⣿⣀⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣶⣶⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣷⣧⣤⣷⣤⣤⣤⣼⣤⣬⣤⣤⡀

⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠀⡤
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠒⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⠀⠀⣀⣀⡀⢀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⠇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠐⠂⠣⢄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠄⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⡇⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣀⣀⣀⣀⣀⡁
⠀⠀⠀⠀⠀⠐⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡷⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡧⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⣷⣿⡿⠫⠊
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢻⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠉⠉⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠀⠀⠀⠀⠀⠘⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣟⠉⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣿⣿⣿⣏⣿⣏⣿⣿⣿⣿⣿⣿⢯⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⡣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠰⠶⠀⠀⠔⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⢤⣀⣀⣀⣠⠤⠤⠚⠑⣲⡖⢶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠉⠉⠉⠉⠉⠉⠁⠶⡖⠺⡉⠠⢨⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢳⡅⠀⠁⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠾⣷⡄⠐⡄⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠶⠤⠤⣧⣼⠈⠢⡀⠆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣋⠀⡴⠊⠂⠢⠀⣀⣀⡈⠓⢄⠈⠢⢼⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⠊⢳⢸⠀⠢⡀⡴⢋⠀⠀⠉⠆⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⡄⠈⣋⣗⠀⣴⠄⠠⢀⢀⣠⢆⡀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡜⠁⠆⣝⠻⣼⣶⣷⣢⣊⡭⢌⣀⢠⣱⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠣⣄⡅⠂⠭⣴⡞⡙⣧⠨⡤⣭⣤⣤⠟⠀⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⢀⡂⢂⠎⡀⠳⠷⠴⠖⠤⠑⡆⠀⢰⠖⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⣀⣀⡀⢀⠀⣀⣈⣦⡈⠪⣤⡍⡠⠁⠂⢳⣄⡀⣀⠔⢁⡴⠉⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠪⠶⢾⣟⡀⠺⢛⣛⣛⣛⠻⠽⠢⣀⡈⠑⠂⠒⠁⠀⣁⣠⡴⣿⣃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠾⠿⠭⠽⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡄⠀⠞⠒⠤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣾⣿⣿⣶⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢁⡴⠛⠁⠀⣆⣇⡴⠋⠉⠉⠉⠁⠀⠀⠀⠀⡎⠉⠉⠉⠉⠉⠁⠀⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠃⢀⠴⠊⢁⡤⠛⠁⠀⠀⠀⠀⠈⠁⠀⢴⢿⠆⠀⠀⣠⠀⡀⠀⠱⡀⠀⠀⠀⠀⢀⠜⠀⠀⠠⣳
⠀⠀⠀⠐⠈⠀⢿⣅⣠⠖⠉⠀⠀⣤⡄⠀⢠⠆⠀⡇⠀⠈⠉⠉⠀⠀⠁⠀⠇⠀⠀⠈⠒⣤⣴⠶⠁⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢠⡄⠈⠀⠀⢺⣀⣞⣀⣀⠀⠀⡄⢀⡀⠀⢠⠀⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀
⠀⠀⠀⠀⠀⠘⠁⢰⣖⠤⣀⠀⢀⢀⠀⠀⠀⡟⢉⣁⣹⠃⠀⠈⠀⠀⢠⠃⠀⠀⠀⠀⠈⡕⠂⠉⠰⠦⠀⣀⢠⡯⠚
⠀⠀⠀⠀⠀⠀⢀⡮⠉⣻⠚⢁⠀⠂⠂⠀⠀⠙⠋⡼⢉⣹⠂⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⡎
⠀⠀⠀⢀⡤⠒⠊⠁⢠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡹⠋⠉⢱⠄⠀⠀⠑⢄⠀⠀⠀⣀⠇⠀⠀⠀⢠⠀⣽⢒⡲
⠀⠀⠀⣿⣿⣶⣦⣄⠘⡆⠀⢰⡠⡇⡀⢰⠆⠀⠀⠀⢧⠄⠀⠉⠀⠀⠀⠀⠀⡄⠈⠁⠀⠀⣀⡀⠀⠸⡟⠉⠁
⠀⠀⠀⠙⢿⣿⣿⣿⣷⠇⠀⠘⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠘⣄⡜⠀⠊⠀⢀⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⢀⠤⣶⣶⣶⣐⡦⠀⠟⠳⠄⠇⠀⠀⠀⢹⡀⠀⢀⣴⠷⣴⠁
⠀⠀⠀⢀⠠⡞⢶⠀⠀⠀⠀⢾⣁⣀⣀⡤⠆⠀⠀⠈⢺⢻⠟⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⣴⠛⠁⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠚⠋⠿⣅⠀⠀⠀⠀⠀⠀⠀⡞⣷⡏⢹⡄⠀⠀⠀⠀⠀⣤⠀⠀⠘⠂⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠠⠚⢧⠀⠀⠈⢛⣦⣄⣼⠆⠀⡀⠀⠀⠀⠀⢹⢻⣷⠘⣇⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⢾⣉⣁⣹⠀⠀⠘⠉⠈⠀⠀⠠⠈⡼⣿⡄⢿⠀⠋⠉⠹⡇⢱⠆⠀⠀⠀⠀⠀⠀⠘⠬⠜
⠀⠀⠀⢠⣄⠀⠀⢠⠖⠊⠛⢿⡉⠀⠀⠀⡤⠄⢤⠀⡀⠀⢣⢿⣷⣸⡇⠀⠀⠀⡸⢧⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠈⣁⠀⠀⠙⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠯⠚⠀⠀⠀⠘⠃⠀⢱⡄⠀⠰⣮⣭⣭⣵⠂
⠀⠀⠀⠘⠖⢃⣘⡛⠀⠀⠈⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠇⡇⣀⡤⠒⠁⣠⣀⠀⢸⠀⠉⡇
⠀⠀⠀⠀⢐⠛⠉⠉⢹⠛⠉⡇⠀⠀⠀⠀⠀⠀⣀⡀⠤⠶⠶⠤⠤⣀⣀⣀⣀⣩⣤⡄⠀⠑⠋⣠⠜⠀⠀⠡⡀
⠀⠀⠀⠀⠈⡄⠀⠀⢸⠇⠀⢰⠀⠀⠛⠋⠉⠉⠙⠓⠤⠤⠤⠤⠜⠋⠉⠁⠀⠀⠀⠠⣶⠀⠀⣷⣶⣿⣿⣿⡟⢄
⠀⠀⠀⠌⠀⠉⠉⠹⠥⠤⠔⠚⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠈⡴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠔⠒⠚⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣊⢋⠙⠁⢀⠙⠂⠀⢧⠀⠀⠰⡟⠩⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡩⠉⣉⠉⠀⠀⠀⠈⡁⠁⠀⣀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡇⠣⢠⣙⠖⣠⣸⢠⡇⢧⡶⠶⢼⠂⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢓⡀⢉⠩⡈⠉⣙⠀⡀⠊⢀⣀⡀⣬⠇⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⢶⡇⠀⠁⠈⠀⠰⠘⠀⠃⠂⢸⡜⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⡰⡄⠀⣀⢀⠀⠀⠀⠀⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢳⢳⣦⣌⣿⢴⠶⣴⠀⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠈⠁⠀⠈⠈⠁⠀⠈⠃⢼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣥⡒⠛⠓⠭⣒⣚⣒⣒⣂⣒⣊⠥⠞⠛⠂⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⣆⢹⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠨⠁⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣠⣎⢹⠒⡇⡤⢠⢰⡁⢾⡴⠂⣶⣦⣆⢶⢂⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⡾⠀⠟⠹⠛⠸⠃⠘⢑⠊⠉⠁⣡⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢁⣤⣤⣠⢙⢦⠀⠰⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢯⠛⠈⠉⠁⠸⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⡀
⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡁⢀⠀⣁⣠⢀⡅⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠤⠀⠤⠤⠤⠤⠜⡀⡀
⠀⠌⠀⡄⢠⠆⢀⡀⢠⠀⠀⢹⠁⠀⠉⠈⠀⠀⠀⠀⠈⡇⠀⠆⠰⠀⠠⠤⠄⠂⠁⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁
⠀⠉⠀⠁⠈⡏⢈⠀⠠⡀⠀⣸⠀⣀⠀⠀⡀⠀⠀⠤⠀⠇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⡀⠠⣈⠃⠀⠀⡐⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⢀⠀⠀⠠⠀⠂⣀⠐
⠀⠀⠀⠀⠠⠆⠀⠀⠀⢀⡀⠀⢁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠒⠂⡑⡄⡅⠀⠀⠀⠐⠠⡤⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⣁⡒⠀⠠⠀⠒⠈⣀⠀⠐⠀⠀⠀⠀⠈⠀⠐⠄⠀⠀⠠⠄⠀⠆⡄⢀⠀⡆⠀⠑⠁⠀⠀⠀⢎⠀⠀⠀⣀⠘⠀⢀⡂⠶⡅
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠐⡱⠦⠤⠔⠊⠀⠀⠀⣇⢀⠙⣠⠀⢀⠠⠦⠀⢰⠀⠭⠃⢠⠠⡄⠀⠁⠀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠔⠁⠀⠀⠐⠀⠀⠀⠀⠘⢦⡀⠈⠁⠉⠁⢂⡠⠬⠀⠀⠉⠀⠋⠀⠠⡀⠀⠀⠐⠈⠐⠉⠐
⠀⠂⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠂⠰⠀⠀⠀⠀⠀⠀⠉⡁⠒⠒⠊⠉⠀⢠⠀⠀⢰⠀⠑⠀⠠⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠔⠀⠈⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⡊⠐⠀⠄⠀⠘⠀⠑⠁⠦⠀⠀⢀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠂⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣄⡀⢀⣀⣀⡀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⠈⠉⠉⠁⠁⠀⠀⠀⠈⠁⠀⠀⠀⡀⢸⣿⠀⠀⢸⠟⠉⢻⡇⣿⡇⢹⡇⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠍⠀⠁
⠀⠀⠀⠀⢨⠈⡅⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠃⢸⣿⠀⠀⢸⣆⣀⣸⡇⢸⣧⣾⠇⠀⠀⢀⣀⣀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠆⠺⠀⠆⡀⠠⡄⠀⠀⠀⠀⠱⡀⢀⠔⠀⢸⣿⠀⠀⢸⡇⠀⢸⡇⢸⡏⣹⡇⠀⠀⢸⠉⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠘⠃⠀⠘⠁⠘⠛⠛⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠂
⢀⠀⠐⠉⠀⠀⠀⡆⠀⠂⠀⠀⠀⢠⢀⠀⠀⣀⠀⠀⢸⡛⡟⣻⠻⢿⠛⢟⣿⢻⡇⠀⠀⠀⡄⠀⠆⠐⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠈
⠀⠉⠀⠀⠒⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣷⣷⢾⡾⣾⡷⣷⡿⡾⡇⠀⠀⠀⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠑⠀⠀⢸⠀⠠⠀⠀⠀⣀⠀⠀⠠⠀⠀⠐⢀⠀⠌⠐⢆⡃⠂⠀⠡⠠⢀⡐⠀⠀⠀⠀⠀⠠⡀⠠⠂
⠀⢀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠵⠀⠀⠀⠀⠊⢔⠀⠀⠀⠀⠀⠙⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠀⠀⠁⠀⠂⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠂
⠀⠀⢰⡆⢰⡆⠀⠀⢠⡾⢷⡄⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠐⠁⠊⠁⡐⠀⠀⠀⠉
⠀⠀⢸⣧⣼⡇⡶⣦⠸⣧⢸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠈⠀⠀⠀⠀⠀⠈
⠀⠀⢸⣿⢸⡇⢀⡿⠀⣿⣸⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⡄⣡⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠈⠛⠘⠁⠙⠛⠀⠙⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠓⣴⠃⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠇⠀⠀⠻⠤⣤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠼⠆⠀⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠡⠒⠉⢇⣏⠉⠉⠑⢪⡙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⣀⠣⡀⠀⠀⠸⡟⠀⠀⢠⣪⠞⠑⣜⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡎⠀⠑⠺⣦⡀⠀⣷⠀⣰⠟⠁⠀⠀⠈⡎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠙⣲⠟⢾⣁⣠⣤⣴⣖⣒⣃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⢸⢈⠭⠭⠛⠛⠋⠉⡽⢦⡞⢤⡀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠈⡎⢆⠀⠀⠀⣠⡞⠁⢸⡇⠀⠙⢗⠀⡀⢀⢇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠘⢌⢦⡠⢊⠎⠀⠀⢸⢷⠀⠀⠀⠑⣬⢉⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡆⠀⠀⡴⠊⠳⢄⡣⢄⣀⠀⢈⠸⣀⣀⠤⣊⠕⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠔⠃⠀⠀⠀⠉⠓⠂⠭⠭⠤⠅⠒⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠋⠑⣤⠂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠀⠀⠉⠖⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠧⠤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⠋⠉⠀⢰⢯⡼⠛⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⢀⣠⣶⣟⢾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠔⠋⠀⠀⣀⠀⠤⣄⠀⠀⣀⠠⠄⣾⢇⠉⢿⡿⣾⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠙⠂⠺⠁⠀⡏⠀⠀⢸⠒⡉⠜⢆⣄⠙⠞⡾⡌⣵⢸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠶⣶⣿⠛⣇⠀⢁⠀⠀⣭⢁⠁⡸⣤⠯⡙⢶⠘⠀⣹⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣟⢳⡐⡿⡷⣄⡀⢰⠂⠃⠀⠱⠘⢆⡙⢦⢡⠇⢸⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢽⡢⠙⢦⠈⠈⠅⢫⠀⠠⠀⡧⣲⡌⢃⠀⠈⡞⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢔⠿⣿⠀⣧⠀⢲⡀⠣⠀⡀⠀⢌⢷⠈⢰⡇⣣⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣷⣝⠃⢤⡀⠲⣄⣈⢦⠺⠦⠁⡆⣯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣶⣭⣄⣴⣦⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣄⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠈⠟⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠟⠛⠋⠁


⡶⠶⢶⢶⢶⡶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⡶⣶⣶⣶⣶⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠂⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠒⠒⠒⠀⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠠⠀⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠒⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠤⠤⠤⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣄⡀
⠀⠀⠀⠀⡄⠁⢀⠄⢄⠀⠉⠀⠀⠈⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⠉
⠀⠀⠀⡗⡁⠀⢈⠀⢈⠀⠀⡁⢈⠀⠀⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣁⡌
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠐⠐⡁⢸⢀⢀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠐⣇⣂⠿⡀
⠀⠀⠀⡇⠐⠄⢠⠀⠀⠀⠀⡇⢰⠀⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣈⠛⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠃⠂⠘⠈
⠀⠀⠠⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠄⠘⠚⠀⠀⠒⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠠⠄⠈⠁⠠⠭⠬⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠆⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠀⠀⡀⢀⣤⠀⣠
⠀⠀⠀⠀⢰⠋⠙⠦⠤⠤⠤⠤⠜⠋⢱⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢸⠖⠶⣧⠀⢀⡇⠠⡟⣋⡛
⠀⠀⠀⠀⢸⠀⣀⣀⣀⣀⣀⣀⣀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡎⠑⠒⠢⠤⠄⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠨⢐⡂⢸⠁⢙⡀⢠⢣⣛⣸⠆
⠀⠀⠀⠀⢸⢀⣒⣒⣒⣒⣒⣒⣒⣒⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡁⢸⠀⠐⢅⢨⠀⡆⠒⡀
⠀⠀⠀⠀⢸⠀⠒⠒⠒⠒⠒⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⢘⢨⡅⢺⠀⠸⡤⠰⠀⠊⠯⠇
⠀⠀⠀⠀⢸⠀⠨⠭⠭⠭⠭⠍⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠄⢺⠀⠀⡇⢸⠀⢸⢻⡼
⠀⠀⠀⠀⢸⠀⠨⠭⠭⠭⠭⠍⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣴⣿⠀⢘⡇⢘⠀⢸⣶⣾⡆
⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠁⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⠉⠉⠿⠆⠾⠇⠠⠀⠀⠯⠤⠇

⡿⢿⠿⠿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣻⣿⣿⣿⣻⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡁⡜⣻
⠀⠀⠀⠀⢀⠤⠤⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⢧⡄
⠀⠀⠀⠀⠸⠄⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⡄⠈⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣂⣮⣿⣿⣏⣱⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣿⢷⡄⠤⠋⠀⠀⠛⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢨⣿⢗⠁⠻⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣀⣾⣁⠀⠀⢠⣷⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠸⣿⣷⣭⣤⣾⡿⢇⠀⠀⠀⠀⠀⠀⠀⠀⢉⣸⣧⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⣠⠏
⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠁⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡤⣄⣀⣸⡶⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⡟
⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⠀⣀⣀⡀⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰
⠀⠀⠀⠀⠀⢰⠂⢲⣶⣶⣶⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⡀⠀⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⠒⠒⠀⠀⠉⠆
⠀⠀⠀⠀⠀⢸⠀⠀⠛⠿⠁⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠛⠂⠶⢀⡻⠀⠀⠀⠀⠀⠀⡄⠀⢀⣀⣀⣀⣀⣀⢀⣀⣘⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣠⡃⠀⠀⠀⠀⠀⢸⣷⣀⣀⣀⣄⣀⣉⣀⣭⣭⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣻⣿⠔⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠨⢹⡏⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣇⢀⠀⡀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⢸⣨⡤⠈⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣼⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣷⡄⢠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠦⣀
⠀⠀⠀⠀⠀⠀⣿⣻⣗⣋⡈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠘⠒⠦⠭⠍⠛⠀⠠⠴⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉

⠀⠀⠀⠀⡞⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⢻
⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠛⠿⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⡴⠋⠀⢰⡆⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⣠⣾⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⢆
⠀⢸⣁⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢤⣀⣠⣤⣄⡀⢈⣧
⠀⢸⣿⣿⡛⢳⣶⣤⣤⣶⣿⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠀⠀⢀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡀⠈⠗⠀⢠⣬⡁⠈⢧
⠀⠈⢻⣿⣿⣟⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠙⠋⠀⠀⠀⠹⠿⠃⠀⢈
⠀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⢤⡄
⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆
⠀⠀⠀⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⢿⣿⠇⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣒⡂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣀⡀⡃
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢒⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠻⡇⠄
⠀⠀⠈⢩⣶⣁⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡾⠇⠅
⠀⠀⣴⣾⣿⣷⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠭⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠿⡿⢣⠆
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀
⡏⠉⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠲⣮⡀⣸⡖⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏⠀⢈⣆
⠈⠢⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢦⢴⡷⠛⠳⣷⢤⢮⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢈⣧⠤⢹⡇⠤
⠀⠀⠈⣇⢰⠁⠹⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠫⣀⣨⢻⡄⠚⠂⡼⢧⣀⡸⠗⠀⠀⠀⠀⠀⠀⠠⠤⡷⠤⢵⡁⠀⣠⡧
⠀⠀⠀⢡⢸⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠙⣏⠿⣏⡏⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⡵⠒⠛⠁
⠀⠀⠀⠸⠇⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠊⠱⡀⡰⠉⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢺

⠀⠀⠀⠀⠀⢀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⣶
⠀⠀⠀⢠⣴⣿⣿⠋⣀⣀⣾⠛⣷⠂⠀⠀⠀⠀⢰⣶⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⡼⢼⣿⣤
⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣤⠘⠏⠀⠀⠀⠀⠀⠘⡇⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⣿⠶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⡳⡄⠀⡜⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢽⠟⠀⠀⠀⠀⢠⠀⠀⢀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣶⣶⠛⠁⠀⠀⠀⠀⢰⣶⣲⣶⣾⣿⣆
⠀⠀⠀⠀⠀⡠⠤⠤⠄⠴⠠⠄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠉⠀⠀⠀⠀⠀⠀⢿⣍⠁⠉⠉⠉⡹
⠀⠀⠀⠀⠀⢸⣧⠴⢿⣦⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⠒⠉
⠀⠀⠀⠀⠀⢈⣧⣤⣼⣄⣨⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠠⠶⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⢀⠄⠀⢀⡀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢻⣷⢸⣿⡇⠀⠀⠁⠀⠀⠈⠀⠀⠀⠁⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⡀⠘⣿⣾⣿⡇⠀⠀⠠⠀⠈⠀⡀⠁⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡶⣿⣿⣿⡧⠴⡶⠶⠶⠶⠚⠋⠀⠀⣀⢀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠊⠙⠛⠓⠀⠀⠀⠀⢀⣀⠀⠀⡆⣿⣾⣠⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⠀⣠⡀⢁⠀⠰⢎⠁⣦⢸⣿⣿⣿⣿⣥⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⣤⣤⡀⠇⠃⠐⠀⠁⠀⠀⠜⠀⠸⡇⢿⣿⣿⡿⣿⣿⣖⠋
⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣏⢻⣿⣇⠹⣿⣿⠄⠀⠀⠐⠀⠐⠀⠀⠄⢠⡇⠈⠇⢃⣨⣿⣿⠅
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⣀⠂⠀⣄⠀⠀⠀⢀⣠⠏⠐⡄⢈⣴⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠈⠻⠿⢛⣻⣿⣿⣟⣿⣻⣤⡆⠀⢈⣭⠿⣿⣿⣯⣄⠰⠀⢈⣽⢿⣯⣷⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⢋⣿⣿⢻⣿⣷⡇⣀⠋⠀⠐⠀⠈⠛⣿⡆⠀⠸⢿⣟⡿⢿⣯⣥⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⢏⣼⣿⢩⣏⠉⠢⡀⠀⡳⠀⠂⢸⡇⢀⣿⠾⣿⡗⢶⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⡗⠤⢬⢅⣤⣽⡤⠤⠖⢻⠿⠷⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠴⠰⠄⠠⠦⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⣛⣛⡉⣭⣉⣙⡒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣡⠆⠢⠌⠿⠛⠀⠉⠈⠙⠁⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣄
⠀⠀⣀⣤⣶⡶⣶⢶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣞⣠⡵⠞⠛⣛⣛⣉⣙⣛⣛⡒⣒⣶⠦⠤⣤⣀⠀⠀⠈⢧
⣴⣿⣯⣍⣘⠁⠙⡟⢹⣇⢻⣿⣷⣤⡀⠀⠀⠀⠘⣿⣛⡉⠛⠛⠻⠶⣤⣀⣈⣀⣿⣁⣉⡙⢙⣲⣮⣝⣶⣄⠈⡇
⠻⣎⠙⢦⣉⡓⢦⡀⠀⠃⠎⢿⢻⣿⣿⣦⠀⠀⠀⠀⢸⣭⣍⡙⠒⠒⢻⡟⢟⡿⠁⠈⠉⠉⠉⣻⠋⠛⢻⠛⠳⠾⠤⢤⣤⣀⣀⡀
⠀⠈⢢⡀⢻⣏⠲⣝⢦⡀⠀⠈⠀⢟⣾⣿⣧⠀⠀⠀⣿⠘⣨⠟⠛⠲⢬⣷⣈⢇⠘⣃⡤⠴⠊⢉⠶⣶⢧⠀⠀⠀⠀⠀⠉⣧⠀⣹⢧
⠀⠀⠀⠙⢮⠹⡄⠈⠶⣝⢦⡀⠀⠈⠹⣿⠙⣇⠀⠀⣿⠐⡏⠸⠦⠀⠀⠈⣹⠟⠻⢥⣀⡀⣠⠏⠀⡏⠀⠑⢤⡂⣀⠀⢙⠏⢠⠇⠈
⠀⠀⠀⠀⠀⠑⣷⢤⣰⠟⠲⣝⢆⠀⠀⠁⠀⣿⠀⠀⣿⡀⡟⣛⠛⠋⠉⠉⡹⢦⣠⣞⣉⡙⠳⠦⣀⡷⠀⠀⠀⢝⣮⠑⠋⢠⡎⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠣⣷⡤⣀⠘⢮⢳⡀⠀⢴⣿⡇⠀⣿⠰⡇⢤⡄⢀⠴⠋⠀⡜⠋⢯⢧⣽⡄⠀⠈⢿⠒⢤⣌⣠⠏⠀⣴⣏⢴⣎⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡓⢾⣧⢳⠀⠀⣿⠁⠀⠸⣆⢽⢦⡞⢁⡄⠀⢠⠃⠀⠈⢧⠡⡃⠀⢒⡞⠀⡼⢻⢁⣠⣾⡿⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣍⠲⣌⣿⡇⠀⡟⠀⠀⠀⠹⣿⡟⣧⢫⠆⡀⣼⠀⠀⢀⠨⣷⠥⠖⠋⣠⠞⠀⡼⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⢻⣇⡼⠁⠀⠀⠀⠀⠘⠿⣾⣿⣶⣥⠧⣤⣸⡤⠖⠁⢀⣴⠞⣁⡀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣤⣀⣤⣴⣾⡿⢋⣴⣿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠐⢲⣖⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠮⠔⡶⠶⣶⠶⢶⣤⣤⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠛⣒⠶⣴⣶⣴⣖⡒⣋⠁⣩⠟⢛⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠁⠀⠀⠀⠒⠂⠈⠉⠘⢧⢰⢿⣏⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣿⡞⢻⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⢻⠳⣄⢻⡻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠐⠚⠛⠛⠧⣈⠲⣽⢧
⠀⠀⠀⠀⠀⠀⠀⢠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠒⠐⢤⡈⠉⠉⢢⠀⠑⢌⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠸⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⢈⡀⠀⠀⠀⠱⠡⠊⢸⢡⠊⢂⠱⡀
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⡌⠁⠈⣒⠢⡑⣐⡆⣰⢯⠅⢀⡜⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡇⠀⠇⣀⡀⣀⣱⢬⡮⣿⠷⣎⠥⠒⠈⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠂⠀⠀⠀⠀⠀⣸⠀⢣⠀⢀⠊⢀⠄⡅⢨⡤⠘⡟⠀⠀⣤⡤⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⠀⢀⠀⠄⠀⠘⡄⠀⢡⡀⠢⡀⠀⣀⠜⡀⠆⠡⠀⢄⠨⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⣀⣥⠂⢀⣀⣥⣥⢹⠦⣤⣟⣦⣀⠉⠉⠢⠀⠈⠜⠒⠊⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠩⠶⢶⠤⠤⠴⠒⠈



⡟⠉⣿⣛⢻⢛⣻⣛⣟⣛⡟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣟

⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣂⣠⣄⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⢀⣴⣀⡔⣄⣄⠀⠀⠀⠀⠀⠇⠀⠤⠄⢿⠀⠀⠀⠀⠀⠀⠉⠀⠻⠀⠀⠀⠀⢀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠘⠯⠝⠉⢹⣿⠀⠀⠀⠀⠀⡄⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠻⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡟⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⡆⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⡁⢠⣀⣸⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣁⠀⠄⣸⠃⠀⠀⠀⠀⠀⣄⠀⠀⢀⣸⠀⠀⠀⠀⣀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠁⠀⠀⠀⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠐⠛⠋⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠂⠉⠁

⠀⠀⠀⠀⢠⡄⠀⠀⣲⡕⣠⠀⠀⠀⠀⠔⠂⠀⠐⠂⠐⡆⠀⠀⢎⠁⠈⠉⠁⢹⡖⠀⠀⢰⠖⠂⣀⢐⡶⠶⡦
⠀⠀⠀⠀⠈⠳⠀⠀⠀⡿⠃⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠃⠀⠀⠀⢣⠀⠀⢠⠋⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢣⡀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠰⠆⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⣷⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣋⣀⠃
⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠢⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠌⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⠀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⢸⠚⠀⠀⠤⠤⢽⡆⠀⠀⠀⠠⠧⠴⠿⠷⣶⡄⠀⠀⠀⠄⠀⠂⠀⣤⠀⠀⠀⠀⢸⠋⠀⠀⢾⡇⠀⠀⠀⠀⣖⠀⣀⠨⡲⢶⡄
⠀⠀⠀⠀⠈⡄⠘⠀⠚⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⢸⡇⠀⠀⠀⠀⡍⠴⢻⡖⣵⠸⡇
⠀⠀⠀⠀⠀⢱⠄⠐⠂⠁⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠯⠂⣑⣁⠞⠐⠇
⠀⠀⠀⠀⠀⠈⣄⠀⠀⣠⠁⠀⠀⠀⠀⠀⢦⠀⢀⣠⡇⠀⠀⠀⠀⠦⠠⠀⣠⡆⠀⠀⠀⠀⠀⠃⠀⠀⣸⠀⠀⠀⠀⠀⣤⠀⠀⠀⣠⣬⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠒⡄⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣬⣅
⠀⠀⠀⣴⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢻⠿⠿⠿⠇
⠀⠀⠀⢿⣿⣿⣿⣥⣤⣤⣤⣤⣠⣄⣄⠀⠀⠀⠀⠀⣿⣾⣷⣿⣿⣿⡏⠛⠷⠀⠀⠀⠀⠀⢩⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣍⣉⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠤
⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⠤⠤⠤⠤⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠉⠟⠁⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣛⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠿⠷⠦
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⢄⠀⠀⠀⠀⠀⡔⠀⠀⢢
⠀⠀⡇⢠⠛⡄⠀⠠⢦⡀⡀⠀⠀⠃
⠞⢇⠀⢈⠀⠘⠄⡀⠁⢸⡟⢀⡠⠠⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠈⠀⠀⢳⡄⠁⠒⡺⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠔⣺⠇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠓⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⠀⠈⠆⠀⠀⠀⣀
⠀⠀⠀⢀⡀⡀⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⡨⠓⠀⠀⣤⠘⠆⠀⠀⠈
⠀⠀⠀⠸⡜⠁⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠃⠀⢸⠆⠀⠀⠉⠀⠙⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢡⣈⠐⠠⠀⠀⠀⠀⠀⠀⠈⠁⠱⡀⢂⠀⠀⠀⠖⠈⢉⣳⡄⢀⣀⣀⢤⣀⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⠘⠐⠠⠐⡡⠆⠀⢦⠠⠀⡈
⠀⠀⠀⢰⠀⠀⠀⣀⣀⡄⠉⠂⠄⠀⠈⠁⠒⠠⢀⠀⢀⣥⠟⢂⠀⢠⢛⠒⠈⠮⢇⣀⠳⡴⠦⠠⠤⠄⠀⠚⢤⡳⠆⢍⠒⠤⡀⠀⠀⠀⠀⠀⠀⠐⠚⠒⠉
⠀⠀⠀⠀⢫⠉⠉⠉⠉⠣⡀⠀⡆⠀⠀⠀⠀⡠⠂⠀⣿⡆⢀⠀⠉⠈⣠⡄⠀⡨⠃⠘⢰⠳⠤⠤⠄⠀⠠⠤⠤⢷⣮⠌⣸⠋⠀⠀⠀⢤⣴
⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠤⢀⠦⠂⠀⠀⠀⠀⠀⠀⠁⠀⠰⣶⠛⠢⠤⠒⡈⣑⠒⠶⢔⣀⠀⠀⠀⠀⠀⢀⠰⠋⠁⠀⠈⠁⠐⠒⠞⠁⢀⡀
⠀⠀⠀⠀⠈⠢⠀⠀⣀⢀⣀⠀⠈⠊⠀⠀⠀⣠⠄⢀⠠⠤⠒⢈⠛⠖⠠⠤⢀⡈⠓⠚⠛⠒⢾⡝⠋⠻⠤⠀⡌⠁⠀⠀⠀⠀⠀⢠⣤⢴⣶⡬⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠃⠒⠠⠄⢈⡁⠄⣤⣠⣠⣤⡠⢀⣄⢀⠿⠔⣂⣤⣐⡠⠄⠊⡉⠤⢾
⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠟⠚⠀⠉⠓⣄⠁⠀⠀⠀⠀⡀⠓⠚⠉⠋⠙⠛⠙⠛⠘⠂⠀⠤⢈⡅⠀⠀⠁⠀⠰⠃
⠀⠀⠀⠀⠀⢀⠀⢲⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠒⠚⠋⠐⠁⠀⠀⠀⠁⠀⢈⣟⠰⣯⠠⡀⠀⠒⠠⠄⡀⣨⡀⠔⢈⠔⠉⠉⠉⠒⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠬⠁⠀⠀⠀⠦⠄⡀⠀⣍⡠⠒⠉⠐⠠⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠠⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⢀
⠀⠖⠲⠀⢸⠀⠀⠀⠀⠀⢀⢀⣀⣄⣨⣀⣄⣸⣀⡇⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⢀⠤⠀⠀⠀⠀⠀⢛⡀⡀⠀⠀⡀⢀
⠀⣍⢈⡄⡜⣄⣸⠉⡄⠀⠈⠉⠉⠉⢉⠉⠉⢩⠀⠁⡇⠀⠖⠰⠠⠄⠐⠒⠈⠀⠀⠤⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈
⠀⠁⢀⠀⠸⠁⡜⠀⠣⠀⠠⠄⠠⠀⠈⠠⠀⠈⠤⠀⠇⠀⢀⠀⠠⠄⠀⠀⢀⠎⠀⠀⠀⠀⠀⠠⠠⠤⣏⡁⠀⠀⠌⠁⠐⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠈⠁⠀⢀⠈⠀⠀⠀⠀⠀⢀⡀⠂⢀⠀⠀⠈⠁⠸⠀⠀⡨⠀⠀⡆⠈⠣⠀⠁⠰
⠀⠀⠀⡀⠰⠈⠀⠂⠀⡤⠀⠠⠄⠀⠀⠀⠠⡀⠀⠀⠀⠂⠀⢁⠑⠘⠦⠀⠀⠀⠀⣠⠲⠆⠦⠀⡂⠀⠀⠀⠀⠀⠀⠊⢢
⠀⠀⢀⡉⡁⠒⠒⠂⠁⠠⠄⠈⠀⠀⠀⠀⠀⠀⠈⠡⠀⡀⠀⠂⠀⢠⠆⠀⢠⠐⢈⡅⠀⠀⠀⢘⠂⠀⡄⣤⣈⠀⠀⠗⠳⡆⠀⡀
⠀⠀⠀⠀⡆⢀⠤⡀⠀⠀⠀⠀⢠⠄⢐⠀⠀⠀⠂⠀⢈⡞⠓⠒⠈⠀⠀⠀⠘⡆⠈⠱⣦⢠⣄⠛⠁⢰⠃⠒⢇⡸⣐⠂⠀⠀⠀⠀⠀⢠⠰
⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⢀⣀⡒⠀⠀⠀⠀⠠⠋⠀⠀⡀⠀⠐⠀⠀⠀⠈⠢⣄⣐⠀⣀⣡⠔⠚⠀⠀⠀⣐⢁⠀⠐⡤⠀⠂⡀⠀⠁⠀⡁
⠀⠁⠀⠀⠀⠈⡆⠀⠂⢐⠀⠀⠠⠠⠀⠀⠀⠀⠀⠔⠈⠉⡉⠀⠜⠠⠀⠀⠀⠀⠀⠢⠉⠉⠁⠀⠀⠠⠀⠀⠘⠀⠈⠀⠐⢠⡀
⠀⠀⠀⠀⠀⠔⠀⠀⡀⠈⠠⠀⠠⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⢀⢀⠀⠀⡀⢦⠀⢄⠔⡙⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠔⡈⠁⠐⠀⠀⢀⡀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠄⠀⠀⠀⠀⠀⠘⠀⠀⠉⠉⠀⠙⠁⠀⢠⠀⠀⠀⠢⠒
⠀⠀⠂⠀⠀⣀⣀⣀⣈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⣰⣶⠶⣶⡆⣶⠶⣶⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠠⠁⠠
⠀⠀⡀⠀⠄⠳⠄⠀⢸⠀⠀⠀⠀⢐⠀⣀⣀⡢⢸⣿⠀⠀⢿⡅⠀⢻⡇⣿⡀⣼⠇⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡁
⠀⠀⢧⠀⡝⢻⠀⠀⢸⠀⠀⠀⠀⢠⡀⠀⢠⠅⢸⣿⠀⠀⢸⡗⠒⢻⡇⣿⠿⣿⡄⠀⠀⡶⠶⠒⠒⢶
⠀⠀⠚⠁⠍⠈⠀⠂⢘⠃⠒⠀⠀⢀⠑⠐⠁⠀⠸⣿⣶⡆⣽⠇⠀⠸⠇⠿⣴⠿⠁⠀⠀⠃⠀⠀⠀⢸⠀⠀⠰⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⢀
⠀⠀⢠⠀⠠⠀⠀⠃⠩⠁⠉⠀⠀⡂⠀⠀⢀⠀⠀⢠⡤⣤⣤⣶⣶⣶⣶⣶⣶⡄⠀⠀⢀⠀⢀⣐⡀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑
⠘⠒⠤⠠⠤⠔⠂⠁⠀⡀⠀⠀⠘⠉⠑⠒⠚⠀⠀⢸⣧⣧⣿⣦⣿⣤⣿⣧⣾⡇⠀⠀⠸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⠉⠉⢉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠁
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠐⠀⠘⢘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⢀⠃⠄⠀⠀⠀⢀⢂⠀⣠⠀⠀⠀⠀⠀⣁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠖⠀⠀⠀⠀⠀⠁⡌⠀⠀⣑⡄⠂⠀⠐⠜⡡⠀⠀⠀⠀⠀⠂⠁⠀⠐⠁
⠀⠈⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⡐⠀⠀⢀⠈⠀⠈⠀⠀⠀⠀⠂⠑⠢⠁⡀⠀⠀⠀⠜⠁⠁⠀⠈⠀⠀⠄
⠀⠈⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠃⠠⠄⠀⠀⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⠄⠠⠀⠠⠀⠀⠀⠘⠀⠀⠀⠀⠆⠀⠀⠡
⠀⠀⢠⡄⣴⠀⠀⠀⢠⡶⣦⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⡀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠆⠰⠀⢀⠠⢀⠒⠂⠐⠀⠀⠀⠉
⠀⠀⢸⣇⣿⢠⣶⡄⢸⡆⣿⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢂⠀⠱⠚⠀⠀⠁⠀⠀⡌⠀⠀⠘⠀⡀
⠀⠀⢸⡇⢹⠀⢰⡇⢸⣇⣿⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠂⠁⢁⢈⡀⡄⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠀⠂⠀⠐
⠀⠀⠘⠃⠘⠀⠛⠓⠈⠛⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠈
⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣛⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠤⠀⠀⠉⢉⠐⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡞⠉⠉⠭⣩⣤⠈⠘⢀⡉⠀⠈⠐⡄
⠀⠀⠀⠀⠂⠀⠀⠀⣀⠔⠃⠉⠉⡩⠭⠛⢂⣉⠀⠀⠤⠀⣇⣀⢀⡄⢀⠤⠌⠖⠁⢡⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⡠⠀⠀⠀⢀⡴⠎⠀⢱⡀⠀⠀⡟⠘⢤⠴⠞⠓⠼⣀⠡⠣⢤⠂⠀⡏
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠸⠁⠀⠀⠰⡋⠀⠀⠀⠀⡇⠀⠀⠘⠄⠈⡓⣒⠀⠴⠄⡤⠀⠂⢁⡠
⠀⠀⠐⠀⠀⢸⠀⠀⠐⠘⠶⣦⠴⠀⠀⠀⢀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⢸⡀⠘⠦⠁⠀⠚⠀⠀⠈⠁⠁⠀⢰⠃⠀⢀⡠⠔⠚⣩⠍⢉⠀⢉⡙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠱⣄⠐⠒⡖⡀⠀⠀⢄⠀⠀⣠⠋⢀⠔⢁⢄⠀⠈⠁⠀⠀⠉⠂⡀⠉⠀⠈⠑⢦⡀⠀⠀⠈
⠀⠀⠀⠁⠀⠀⠀⠈⠓⠤⣄⣀⠀⣀⣀⠀⠐⠁⡠⠋⣀⡡⠎⣠⠁⠄⠉⠁⠀⠀⠀⠸⡀⠀⠀⠀⠙⢦
⠀⠀⠀⠐⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⡏⠀⢠⡹⡀⠀⠀⠀⣠⡤⠂⠀⠐⡈⠂⠀⠣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣠⠐⢈⣭⣉⣁⡲⡄⠀⢰⠃⡤⠂⠀⠀⢀⠽⠦⠠⣤⠶⠷⢤⡀⠀⠀⠀⠀⠐⠂⠀⠈⡄
⠀⠀⠀⠀⠀⠀⡜⣡⣼⡿⣿⣿⣷⡿⠈⠄⢸⠈⢣⠀⠀⠀⢨⡀⠀⠀⢉⠀⠀⠈⣿⣆⢀⣠⠄⠄⠀⠀⡠⡧
⠀⠀⠀⠔⠃⠀⡁⠒⣻⣿⣿⣿⣽⠇⠀⡀⢸⠀⠀⠱⣄⠀⠀⠈⠂⣀⣈⠲⣀⢠⣟⡽⡅⡂⠀⠄⠀⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠱⣸⣿⣿⠿⢿⠟⠁⡔⠀⡈⢧⠀⢠⠈⢦⡀⠀⠀⠀⠈⡝⡁⠿⢅⠊⠉⠓⠀⠴⠈⠄⡼
⠀⠀⠀⠀⠀⠀⠀⠉⠊⠡⠤⠀⢂⢊⡀⠄⡀⠈⢦⡀⠃⡀⠉⠢⣀⠀⠘⢧⠀⠚⡋⡤⠟⠀⠐⠃⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⠠⠒⠑⠢⠱⠀⠱⣄⠀⠀⠀⠈⠓⠦⣌⠒⠈⢁⡤⠤⠆⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡧⠁⢰⠫⠹⢉⠀⠀⠀⠈⠙⠢⢤⣀⠀⠂⠈⠳⣄⣈⡠⠔⠊⠁⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣐⠀⠓⠀⠎⠀⠁⠀⠀⠀⠀⡀⢀⣉⣀⡀⠀⠉⢁⣀⣤⠔⠊⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠀⠀⠉⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢀⢀⣀⡀⠀⠀⠀⢀⣀⣀⡔⡵⠒⠛⡆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⢢⣠⣤⢄⡀⠀⠀⠀⠀⠀⣼⠀⢀⡐⠄⠀⠀⠰⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⣀⣤⣾⣿⠋⣠⣿⠻⣻⣿⡓⠢⣿⡄⠀⠈⢁⣤⠁⠀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡝⢻⣿⣿⣿⣿⡟⣠⣬⠔⠋⠉⠌⣿⣔⠰⢻⡇⡀⣠⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣥⡈⠛⠟⢩⠛⠛⠿⠟⠀⠈⠉⣽⡇⣹⣷⣾⠷⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡌⠛⠲⠢⠌⢀⣀⣀⣠⣤⣶⡿⠿⢾⡞⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⠶⣿⣇⢀⠀⠀⠀⢀⡀⣀⠈⠀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⠒⠂⠈⠉⠉⢀⣴⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠄⠀⠀⠀⢀⡤⢌⣺⡿⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡃⢤⣒⣒⠐⠂⣉⣙⣁⣉⣀⣀⡛⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠙⠻⠿⠿⣿⣷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⣀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⣿⣿⡿⠿⠟⠛⠋⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣛⣝⣛⣩⣋⣻⣙⣹⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠘⣦⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠌⠤⠀⢧⠼⡷⢧⡤⠁⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⣬⡘⣧⡼⣐⣫⣩⠽⢛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣶⣾⣤⠏⣼⠿⣟⣁⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⢸⣿⣿⣿⠿⠛⠀⠈⠉⠉⠀⠀⠀⠉⠉⠉⠐⢺⣿⡗⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣇⡾⠛⠋⠀⠀⠀⣀⠔⠊⠓⢤⣀⠀⠀⠀⣠⡿⢾⣿⠁⠀⢀⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣷⢶⣶⠶⣴⣾⣤⣤⣤⣤⣤⣽⣶⣤⣶⣴⣾⣾⣿⣾⠿⢿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢻⡀⠀⢀⠁⠀⠀⠉⣿⡯⣉⠉⢉⠀⠍⠤⣾⣿⠟⠃⠀⣾⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣇⡀⠀⠀⠀⠀⠀⠘⠷⠤⠛⠛⠋⣁⣉⣉⣥⣤⠄⢰⡟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠉⠉⠛⠛⠛⠉⠉⠉⣿⣿⠟⠛⠻⠟⢋⡉⠉⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠂⠀⠀⠀⠻⣿⣿⠆⠀⢀⢲⣿⣆⠀⠀⣸⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⢈⢹⡿⠋⠀⣿⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⢻⣿⠁⡀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⡹⠋⠀⢠⣾⣷⠀⡃⢀⣿⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⡆⠀⠄⠀⠀⠀⠀⠀⣌⠏⠀⠀⣠⣾⣿⢿⣴⠇⢸⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣇⠈⠀⠀⠀⠀⠀⢸⡏⠀⢀⣴⡟⠃⣼⠋⣿⠃⢸⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠠⡀⠀⠀⠀⢸⡧⠾⠋⠁⣠⣾⠿⣌⣽⠆⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣇⠀⠈⠳⣄⡀⠀⠀⢀⣠⡾⠻⠋⣸⣿⣿⣄⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢦⣄⣐⡮⠽⡶⢶⣿⡇⠀⢀⣴⣿⣿⣿⡿⢋⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠈⠉⠛⠛⠛⠛⠛⠓⠛⠛⠛⠋⢉⠀⠐⣩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣤⣤⣀⣀⣀⣀⣀⣤⣤⠴⠖⠋⠁



⣿⡿⠛⣻⡿⣿⣿⣿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣥⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠄⠐⠂⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⠀⣀⡀⠒⠂⣸⠃⠀⠀⠀⢀⡤⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⣶⠊⣥⡀⠙⣧⢹⠀⠀⠀⠀⡉⡀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣧⡽⠈⠉⠙⠳⣮⡈⠣⠀⠀⣈⡽⣧⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⠉⠒⠒⠒⠀⢈⠁⢒⣾⡷⠂⠀⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⣀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⡅⡐⢦⠀⠀⣰⣿⣿⡟⣴⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠳⣦⢸⣾⡟⡿⣛⡃⠿⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣷⡿⢘⣵⡷⠟⠛⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣅⢸⣿⢨⣽⡇⢰⣿⠀⣠⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡿⢾⢑⡻⢮⣭⣥⣬⣍⡈⣿⢼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⢶⣿⣿⣿⣿⣿⣿⡵⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⢒⣀⠑⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣖⡊⠉⠀⣠⡶⠞⠋⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⢸⣿⣿⣯⣭⣥⣵⣚⣃⡢⠤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⡴⣖⡿⠟⠛⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⢸⣾⣿⠟⠉⠀⠀⠀⠀⠉⠉⠀⠒⠒⠒⠶⢤⣭⣶⢶⣾⢿⣿⡶⠋⠀⠀⠀⠀⠀⠀⠀⢠⡎⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠈⢿⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠶⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠈⠛⢦⣄⣀⠀⢠⠟⠉⢻⣦⠀⠀⠀⠀⠀⠀⣾⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⢀⣼⣿⣶⣷⠿⣧⡀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠈⠻⣦⣀⣀⣀⣠⡾⠛⠁⠀⠀⠀⡴⠒⢶⣄⣀⣀⡎⠉⠙⣇
⠀⠀⠀⣠⣶⠟⠱⠁⠘⣧⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢧⣀⡨⠋⠀⠈⢳⣦⠼⠿⠄⠴⠲⣦
⠀⠀⢀⣿⣏⣿⡓⣲⣶⡾⠂⠒⠛⣻⣿⠀⠀⠀⠀⠀⠀⠰⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢾⡁⠀⠀⠘⣧⣀⣼⠇
⠀⠀⠘⣿⣾⣿⣏⣿⣿⣹⣟⠀⣉⣿⡾⠃⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣼⡇⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠈⠛⠻⠿⠷⠾⠷⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⢶⣦⡄
⠀⠀⠀⠀⠀⣠⢤⣤⢤⡄⣠⠦⢤⣤⠀⣤⠤⡤⢤⠀⣤⠤⢤⣄⢠⡤⢴⣦⡄⠀⠀⠀⠀⠈⠐⠌⢰⡄⠀⠀⠀⠀⠀⠀⡿⠉⠉⢹⠁
⠀⠀⠀⠀⠀⢘⠟⠉⢻⠀⢸⠋⠙⢻⠀⢹⣉⣻⡏⠀⡙⠉⠉⡇⠀⣏⣯⣩⡅⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⠶⣤⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⣀⣼⢸⣿⣶⣿⠀⢸⡀⠀⣼⠀⢸⣿⡇⡇⠀⣷⢤⢠⡇⠀⡇⠀⠁⠀⣷⣄⠀⠀⠀⠀⠀⢹⠟⠟⠛⡏⠀⠀⠀⡇⠀⠀⠸⡀
⠀⠀⠀⣭⡿⡿⣿⠿⠿⠁⣸⣦⣠⡿⠀⢽⣿⣧⠧⠀⣿⣤⣵⠧⠀⣧⣤⣴⠇⢿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢰⠁⠀⠀⠀⢁
⠀⠀⠀⣈⣿⢡⣽⣽⣯⠭⢭⣯⣥⣽⠻⢭⣥⡴⠤⠤⣤⣼⢤⡷⠤⣼⡿⢿⡿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⢠⠇⠀⠀⠀⠀⠘⡀
⠀⠀⠀⣁⣿⢸⡟⠃⣿⠀⢸⠋⠉⢹⠀⢸⣿⠃⠀⠀⣿⠁⠀⡇⠀⡇⠀⠈⠁⣿⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⣘⣀⣀⣀⣀⣀⣀⣱
⠀⠀⠀⠀⣿⢸⡇⠀⣹⠀⢸⠀⠀⢸⠀⢸⣿⡀⠀⠀⡿⠀⠀⡇⠀⡇⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⣸⠀⠀⠀⢿⣰⣿⠻⠿⠧⠤⠶⠾⠛⣇
⠀⠀⠀⠀⣯⠘⠁⠀⣿⠀⢸⠀⠀⢸⠀⢸⣿⠁⠀⠀⣿⠀⠀⡇⠀⡇⠀⠀⡄⣿⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠄⣿⠐⡆⠀⣿⠀⢸⠀⠀⣸⠀⢸⣿⠀⠀⠀⣿⠀⠀⡇⠀⡇⠀⢸⠇⣿⠆⠀⠀⣾⣖⣒⠒⠒⠀⠀⠀⠐⢒⣶⡄⠀⠀⠀⠀⣠⣿⣇
⠀⠀⠀⠖⣿⢸⡇⣠⣿⠀⢸⣀⣠⣿⡀⣸⣉⠀⣄⣀⣿⠀⣠⣇⢀⣇⠀⣰⣄⣿⠂⠀⠀⣿⣿⡏⢉⠉⠉⠉⠉⠉⢿⣿⣧⣶⣶⣴⣊⣻⣿⠟
⠀⠀⠀⡤⣟⠘⡿⠿⣿⣈⣈⡛⠛⠛⢓⡈⠻⣿⣁⣀⡘⠷⠿⣓⡒⢛⣿⣿⣆⣻⣆⠀⠀⢻⣿⣇⠀⡀⠀⠀⠀⣆⣼⡿⠉⠉⠉⠉⠉
⠀⠀⠀⡄⡿⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠛⠛⠙⠒⠛⠛⠛⠛⠛⠛⠛⢿⡷⠀⠀⠀⠙⠿⣿⣷⣦⣴⣾⡿⠋
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⡀⢀⡔⡩⠰⠖⠎⣴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⣌⣠⣤⡀⠀⠀⠀⠀⠀⠀⣿⡄⢀⠢⡄⠀⠊⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⣀⣰⣿⡿⠃⣈⣶⠶⢶⣶⠶⢄⣷⠀⠈⠉⢁⣈⠁⠀⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣚⢿⣿⣿⣿⣾⣿⡟⣈⣉⡭⠓⠚⡹⣯⡄⠠⢿⡏⠀⠠⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡀⠻⢿⡿⣫⠿⠶⣿⠷⠀⠒⠒⣺⡏⢿⣆⣼⣥⡧⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠻⠦⣤⠀⠛⠀⠀⠀⢀⣠⣤⣾⣿⣵⡿⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣠⣤⣶⡀⠉⠉⠉⠙⠉⠉⠉⠘⠘⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠉⠉⠁⠧⡤⠤⠤⠚⠒⠉⣀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⣿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⠠⣀⣀⡀⠤⠤⠾⠥⠔⠛⠃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣖⣿⠈⢿⣶⣶⣶⣶⣒⣲⣶⣶⣿⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣧⠀⠈⠈⠉⠛⠛⠛⠛⠛⠛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠊⠉⠉⠉⠉⠐⠢⣀
⠀⠀⠀⠀⠀⢀⠴⠊⢀⡀⠤⠄⠒⠂⠀⠐⠒⠠⢄⠀⠑⣄
⠀⠀⠀⠀⣠⠋⣠⠖⠉⠀⢀⠤⠀⠐⠀⠤⡀⠀⠀⠑⢄⠈⢆
⠀⠀⠀⢐⠃⡰⠁⠀⢠⠊⢀⡤⠒⠒⠒⢤⠈⠳⡀⠀⠀⠂⠈⡆
⠀⠀⠀⠘⠀⠃⠀⢠⠃⠀⡎⠀⠀⠀⠀⠀⢡⠀⢱⠀⠀⢀⠀⢰
⠀⠀⠀⢠⠀⢃⠀⠘⡄⠀⢇⠀⠀⠀⠀⠀⠎⠀⡘⠀⠀⠀⠀⠸
⠀⠀⠀⠘⡄⠈⠂⠀⠘⣄⠈⢢⣀⣠⠔⠋⢀⠔⠁⠀⠀⠀⠂⠀⡄
⠀⠀⠀⠀⠈⠢⡀⠈⠒⠚⢦⠀⠹⣀⠤⠒⠁⠀⠀⠀⠀⠀⡆⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠘⡄⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⢆⡀⢀⣼⠛⠛⠛⢻⣀⠀⠀⠀⠀⣼⠛⠛⠛⢻⣄⠀⠀⠀⢀⣼⠛⠛⠛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠉⢸⠀⠀⠀⠈⠌⠉⠉⠉⠉⠀⠀⠀⠀⠀⡇⠉⠉⠉⠁⢀⠀⠀⠀⠀⡇
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠔⠃⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠺⠶⠶⠤⠼⠓⠀⠀⠀⠘⠺⠷⠶⠤⢼⠓⠀⠀⠀⠘⠻⠶⠶⠦⢼⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠣⡄⠒⠂⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣴⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠈⢧
⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⢿⠀⠀⠀⠀⠀⠀⠇⠀⠀⣄⠀⠀⠀⠀⠀⠀⡄⠀⠀⡼
⠀⡇⠀⠀⢀⡁⠀⠠⠄⣟⡁⠀⡀⣹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⠀⠀⠀⠀⠀⠀⠐⣄
⠸⠉⣀⠤⡄⠿⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢂⠀⠄⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠤⠀⠝⢆
⠀⠀⠀⠀⠀⢀⠌⠀⢀⡀⠠⠀⠀⣀⠀⠀⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⢔⠀⠀⡀⠀⠄⠀⡀⠀⠂⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⡃⠀⠀⠀⠀⠈⢁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠓⠶⣡⠀⣀⣀⠡⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⠚⠀⠀⠀⠃⠀⠀⠀⠀⠀⠚⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⠉⠁⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣭⡉⠉⠉⡏⠉⠉⢹⢉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡁⠀⠀⠀⠀⠀⠁⠁⠀⠀⠇⠀⠀⠈⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⣏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠒⠒⠂⡇⠀⠀⠀⠀⠀⢸⠒⠒⢲⡇⠀⠀⠀⠀⠀⢸⡖⠒⠒⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠔⣖⣮⡂⢄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡄⠀⣀⠇⠀⠀⠀⠀⠀⠈⡆⠀⡸⡇⠀⠀⠀⠀⠀⠸⡇⠀⢠⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣶⢣⡗⠉⠀⠳⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⢸⣧⡝⠀⠀⡠⠈⠁⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⣆⣀⣉⣀⣉⣉⣉⣉⡇⠸⣀⣀⣈⣉⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣆⣐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠤⣀
⠀⠀⠀⠀⣰⠀⠀⠀⠀⢀⡤⢄⡀⣀⡴⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⡩⠾⠖⠒⠒⠀⢴⠄⡤⡄⠠⠶⠶⠆⠀⠷⠇⠤⠼⠃⠐⠂⠸⠥⠿⠢⠆
⠀⠀⢠⣎⣿⡄⠀⢀⠂⢇⠀⠀⠈⡿⠧⡀⠀⢣⠀⠀⠀⠀⢠⣦⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⣠⣤⣤⣄
⠀⠀⠈⠉⠸⣽⠀⠈⠀⠈⣆⡤⢴⠗⠒⠛⠳⣻⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢠⡀⠸⠾⠿⠟⠁⠀⢹⠛⠷⡞⠀⣄
⠀⠀⠀⢠⢿⠀⠀⠀⡰⠊⠈⠣⣼⠀⠠⡶⠀⢸⢦⠀⠀⡇⠀⠀⢂⢀⠀⠀⣯⡤⠴⣿⠀⠀⠈⠁⠀⡶⠀⢸⠀⠀⢸⠀⠠⡇⠀⠈⠀⠀⠘⡷⠋
⠀⠀⠀⠳⢟⡀⠀⠀⢧⣀⡀⠀⠙⠢⣀⠀⠀⣜⡠⢷⠋⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⡇⠀⠀⠀⠀⠀⣷⠀⢸⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⣿⣢⠀⠀⠘⠋⠐⢻⠒⠋⠛⢯⣇⣀⡸⠀⠛⠀⠀⠀⠀⠀⠀⣠⠁⡀⢇⠀⠀⠀⠀⠀⣿⣤⣸⠀⠀⢸⣠⣼⡅⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢱⠉⠀⠀⠀⠀⢀⠸⡄⠀⢠⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠆⠀⠘⢦⡀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣚⣧⠀⠀⠀⠀⠚⠁⠙⠒⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣰⠃⠀⠁⠀⠀⠀⠱⡀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠘⠛⢸⣿⠁
⠀⠀⠀⠀⠀⠉⠈⡷⡀⠀⠀⠀⠀⣀⣤⡴⠼⠞⠚⠉⠀⢃⠀⠀⠀⠀⢧⣀⣀⣂⣀⣀⠠⠴⠁⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠽⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠀⠀⠸⣿⡿⠃⠀⠸⠔⢻⢽⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⠶⠖⠛⢇⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹
⠀⠀⠀⠀⠀⠐⠁⠄⠠⡞⠋⠉⠉⠀⠀⢀⠀⠘⡀⠀⠈⠀⠈⡆⠀⠀⡀⢀⢀⠀⠀⢀⠀⣦⣀⠀⠠⠶⠀⢦⡀⡶⡇⣤⠐⠷⠀⠀⠀⢺⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⠈⠀⠀⠀⠀⢡⠀⠀⠀⠀⢱⠀⠀⠓⠚⠙⠐⠆⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠁
⠀⠀⠀⢠⣦⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠘⡆⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠭⢠⠀⠀⠀⠀⠀⣇⠟⠧⠀⡋
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢱⠀⠀⠈⡀⠀⠀⠀⠀⢳⠀⢀⡠⠔⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀⣀⢧⡀⠀⠀⠉
⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠔⠋⠀⠉⠢⣀⠀⣠⠜⠁⠀⠙⠢⡀
⠀⠀⢀⡠⡼⠶⠀⢣⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⣸⠄⠀⠀⠀⠀⡠⠠⠀⠀⠀⠤⠤⡔⠁⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠁⢸⠀⠀⠈⢦⠀⠀⠀⢣⢀⡤⠖⠊⠉⠉⠁⠀⠀⢀⡁⠉⠲⠀⠀⣇⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠏⢇⠀⠀⠀⠀⠀⠀⢀⠁⠄
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠑⢄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠴⠃⠈⢣⠉⢈⠆⠀⠀⠀⠱⡀⠀⠀⠀⠀⡴⠀⠘⡄⠀⢀⣀⣀
⠀⠀⠠⠖⢸⠒⠂⠀⠀⠀⠀⠉⠓⠒⠶⠤⣴⠄⠀⠀⠀⢀⠊⠀⢆⠀⠃⣸⠦⠂⠀⠀⠀⠀⢀⠗⠒⢒⡒⠒⠃⠀⢠⠋⠉⠁⢠⡶⣦⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡌⠒⠆⢚⠓⣍⠁⠀⠀⢀⢀⠀⠠⠋⠀⢰⢵⣌⡇⠀⠐⠃⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⢸⠀⡀⡀⣀⣀⠀⣇⡀⢀⣘⠁⠀⠀⠀⠀⠄⠉⠁⠀⠀⠀⠂⠀⠀⠀⠘⠽⣛⠁⠀⠀⠀⠘⠃
⠀⠀⠀⢉⠽⠉⠉⠉⠉⠉⣩⡍⠉⠉⠉⠉⢩⢡⡄⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠒⠶⠶⠖⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠲⠶⠒⠒⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣠⣞⠰⠰⣧⠉⠅⠢⡀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣗⣂⡐⡒⠒⠚⢵⡫⣤⡈⢋⡀⠀⠀⠙⡖⠂⣀⣀⣠⣶⣶⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡟⢘⣿⡛⠿⢚⣿⣷⣯⠽⠟⣿⣻⣿⣟⡗⢀⠀⠀⢸⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣿⣷⢈⡟⠀⠀⠀⣾⡁⠀⠀⢰⠘⠀⠁⠀⠀⢸⡀⠀⠽⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣿⣿⣿⡇⠀⠀⠀⢹⣧⡁⠀⣸⠀⣄⠀⠀⠀⢃⣧⣘⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣿⣯⣿⣿⣷⣾⣿⣿⣿⠀⠀⠛⢀⣸⡆⢠⠆⠜⣸⣻⣿⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣛⠻⠿⠿⣿⣿⣿⣿⣿⣆⣠⣬⣤⣾⣷⣾⣟⣛⡿⠭⠵⡚⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡍⠓⢘⣿⣶⠾⠾⠟⠋⠹⠭⠉⠁⠂⠘⠒⠒⠈⠁⢰⣇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⢿⣷⣤⣤⣄⣤⣦⣄⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣤⣼⡿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠿⠿⠿⣿⣛⣻⣿⣿⠿⢿⣿⣿⣛⣛⣛⠛⠭⠽⠓⠊⠁