Possum Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⡀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⡶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠂⣈⡀⠀⢀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⣯⣈⠁⣈⡁⠐⢘⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠁⣸⡀⠉⢀⡈⢻⣷⠀⣀⣀⡠⠄⠊
⠀⠀⠀⠀⠄⢀⣠⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⡀⠀⠘⠉⢸⡿⠀⢀⠀⠰⣿⠏⠁
⠀⠄⠀⠀⠀⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣉⡉⠀⠀⠀⣁⢸⡇⠀⢺⠀⢠⡟
⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⡀⠀⠰⠴⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣝⣅⣀⣠⡴⣿⡇⢠⠿⠶⠟
⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠄⠬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠐⠿⠿⠄

⠀⠀⠀⠀⠀⠀⠀⢀⢴⡊⠉⣁⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⢛⣷⢶⣦⣄
⠀⠀⠀⠀⠀⠀⣴⣶⣈⣡⣤⣤⠐⢀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣴⣯⣉⣡⣬⣅⠒⣈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⡿⢄⠀⠠⡄⠀⢳⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⣿⣿⣿⡄⠁⣠⡌⢻⣷⣀⣀⡤⠤⠐⠉
⠀⠀⠀⠀⠀⢀⣤⡄⠀⠈⠁⠀⠈⠀⠂⡀⠐⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣤⡄⠀⠈⠁⢸⡿⠐⢂⡀⠲⣿⠏
⠀⠆⠀⠀⢀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠠⠁⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣀⣀⣉⣀⠀⠀⠀⣍⣸⡇⠀⣿⠁⣠⠟
⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠠⡆⢀⠘⠶⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣾⣅⣀⠤⠴⢿⡇⣰⠟⠾⠏
⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠯⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠐⠿⠿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠴⠂⠀⠈⠉⠉⠉⠋⠐⠀⠆⠐⠖⠢⠖⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣐⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠈⡙⢤⠤⢄
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠠⡁
⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠁⠀⢀⣤⣄⠀⠀⠀⠀⠐⠣⣄⣀⠴
⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠿⡃⠀⢀⣴⡔⡆⠀⡇
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⡉⠀⠀⠈⠭⠕⢁⡴⠁
⠀⠀⠀⠀⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⢀⠀⢀⠀⠀⠀⠀⠈⢶⠀⠀⠀⠀⠀⢠⠴⡉
⠀⠀⠠⠀⠀⠀⠀⠄⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⡀⠀⠈⠈⠀⠱⡀⠀⠀⠀⠠⡞⠦⡄⠀⠐⣤⠏⢸
⠀⠀⠜⠁⣈⠀⠁⠀⠀⠀⠐⢄⠄⢀⠀⠀⢀⠀⠤⣀⡄⠀⠁⡐⡀⠀⠀⠣⣀⠀⠀⠀⣁⠀⠙⠒⡖⠁⠀⠈
⠀⡜⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⡄⣪⠀⠀⠘⠀⠐⠋⠀⠀⠀⣀⠑⣄⠁⠀⠑⠀⠆⢈⠠⡃⠓
⣰⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⢸⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⡀
⢣⡀⠘⠦⣀⣀⣀⡠⠚⢁⣠⠤⠤⠤⡀⠑⠠⢀⡀
⠀⠙⠦⣄⣀⣀⣀⠤⠖⠉⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠐⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⡀
⠀⠀⠠⠀⣀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠂⠀⠙⠉⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠈
⠀⠀⠑⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡒⠀⡀⠐⠀⠀⠇⠀⡀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠘⠈⠘⠈⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣬⣢⣤⡳⣵⡄⡤⣰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⢿⣾⣿⢿⣿⣾⣷⣷⣿⢻⣿⣧⣾⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡮⣿⣿⣯⣛⠿⠍⣡⣽⣿⣏⢹⣿⣿⣿⣿⣿⣷⣿⣱⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣻⣿⣿⣿⣿⣷⣇⠀⠘⣿⣿⣿⣿⡇⠈⠙⢿⣿⣿⠟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⡾⠭⡽⣯⡄⠁⠀⠈⠟⠋⠀⠀⠀⠀⠘⣿⠃⠀⠈⠹⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠷⣿⣏⣽⣗⡿⠍⣶⣷⡦⣴⣬⡀⠀⠀⠀⢠⠀⠀⠀⠀⡟⠀⠀⣐⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣙⠛⣹⣿⣷⡆⢒⣿⣿⣿⣿⣿⣿⣧⡀⣤⠀⢸⢸⣄⠀⠸⠃⢀⣴⠃⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣽⣿⡿⠿⣋⠽⠛⣩⣽⢿⣿⣿⢿⣿⣿⣷⣻⡆⠀⠻⣿⡆⠀⠀⣿⠏⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠉⠀⠙⣿⡣⠼⣷⣾⣖⣽⣿⣿⣿⣦⣾⣿⣿⣧⣈⣿⣄⠀⠹⡇⠀⢀⢫⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠈⠓⣷⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⣀⠻⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢸⠁⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠁⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠏⠀⠀⠀⣿⣿⡇⠈⠻⣿⣿⣿⡏⠘⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣩⡇⠀⠀⠀⠀⠀⢠⢾⣾⡺⡀⠀⠀⠀⣶⣨⢑⠀⠀⢸⣿⣿⣧⡀⠀⢘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠸⠟⠃⠤⢒⣊⠝⠹⠏⠺⠯⠄⢹⢨⣥⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⢀⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠵⠊⠘⠁⠀⠀⠀⠋⠞⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣳⠖⡲⠟⠋





⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠃⡀⢠⣀⢀⠀⣀⡤⠀⠤⣻⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠤⠒⠮⠇⢠⣅⣀⣤⡴⠻⠦⠠⠼⠃⠀⠴⠃⠠⠺⣿⣄
⠀⠀⢨⣷⢀⣴⣿⣄⣠⣾⣾⡿⠋⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧
⠀⠀⠈⠿⠋⠉⠻⢿⠇⠀⠈⠁⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⣥⡽⠟⠃⠀⠀⣤⡴⣍⠁⠀⠀⠀⠀⢀⠘⣦⣴⣤⡈⣤⣦⣄⡀
⠀⢀⣀⣀⠔⠋⠩⠷⣶⣤⣤⣴⣤⣴⣶⣶⣥⣤⣠⣤⣤⡀⣠⣿⡿⠃⠉⠁⠉⠉⠉⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣈⡿⠟⠛⠉⠉⡽⡏⠫⠉⠙⠻⠿⠿⢿⣧⣷⣯⣤⣠⣄⠀⠀⠀⠀⠀⠙⢿⡀
⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣾⣿⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⡯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣤⠀⠀⠀⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠻⣯⠋⠀⠀⠀⠸⣿⣟⡟⠛⠉⠉⠉⠉⠉⠉⢙⣍⣻⡿⠁⠀⠀⠀⣫⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠁⠀⠀⠀⠀⠀⠙⡻⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠐⠀⠀⠈⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⣼⣿⣷⠀⠆⠀⠀⠀⡸⡅⠀⠀⠿⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⡖⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢤⣼⡋⢁⠂⠀⠀⠀⣰⣿⣇⠠⠀⠀⠀⠀⡀⠀⠀⣀⠀⠨⠀⠀⠀⠀⠀⠐⣿⣿⡆⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠛⠿⢇⠁⠀⠀⠀⠀⣿⢻⡏⠹⣦⠀⢾⣿⠗⢀⣴⡟⣠⣤⠈⣧⠀⠀⠀⠥⡍⢩⣧⣷⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⢨⣖⠾⡀⠀⠀⠀⠀⣿⣿⢷⠄⠙⢷⣶⣤⣶⣯⡝⠿⠃⠀⢰⣶⠃⠀⠀⠀⣱⣨⣏⡥⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣿⡟⠁⡀⠀⠀⠀⢿⣿⣇⠈⢢⣈⠉⠉⠸⡄⣠⡄⢶⣾⣿⣌⠂⠀⠀⠀⢿⡿⠟⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⢤⠁⠀⠀⠈⠂⣽⣿⣧⠰⠂⠀⢰⢖⣟⣛⣻⣶⣶⣿⡿⠀⠀⠀⢀⡃⠰⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍⣛⡅⡘⠀⢌⠀⠀⠀⠈⠛⣿⣷⣤⣴⣾⣿⣽⣽⣿⣿⡿⠋⠀⠀⣾⣿⣿⠁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣍⣈⠁⢳⣿⣿⣤⣤⣤⣀⣀⣈⣻⣿⣿⡿⣿⣿⣿⡿⠉⠀⢤⠄⢠⠿⡋⣡⠰⡆⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡄⢂⠀⢀⣀⠈⠉⠉⠉⠉⠛⠛⠟⠛⠱⠶⣶⣶⣶⣦⣤⣍⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠃⠏⢹⣿⣯⡇⢀⣀⠀⣼⣭⣿⡄⣴⣶⣦⡘⢿⡿⠣⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠘⠂⠆⠘⠛⢋⢠⣿⣿⡧⢸⣿⣿⣈⠹⣿⠿⡡⢀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠙⠀⠉⠉⠉⠁⢿⣟⡽⠃⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣇⢀⠀⡀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠿⣿⣾⡾⠿⠟⡭⢶⣿⣿⣷⣤⡠⠤⠤⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠶⡌⠻⢿⣿⣷⡚⢯⣤⣄⡀⠬⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⡉⠋⣯⣿⣴⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣟⣟⡂⣒⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣉⣾⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⣾⣿⠦⠐⠀⠀⠀⠀⠰⠢⣤⡶⣰⣿⡛⢿⣆⠀⠀⠀⠀⢿⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⡿⠓⠄⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠙⣶⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣘⡟⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⡭
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠱⢒⣠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⣿⡻⣿⣤⣬⡙⠂
⠀⠀⠀⠀⠀⠀⣠⣴⠽⣠⣴⢟⣻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣿⣿⡻⡟⣿⣷⡍⠀⡀
⠀⠀⠀⠀⠀⢮⢏⠔⢋⣯⡞⣻⠟⢻⡿⠛⢛⣡⠔⢊⢁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡼⣿⡹⣷⢞⣎⠓⠀⠐⠌
⠀⠀⠀⠀⠀⣐⣈⣳⠀⠿⠋⠉⠈⢂⣉⣉⣀⣤⣂⣵⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣔⣼⢳⢹⣇⢿⢮⠊⠁⠂⠁
⠀⠀⠀⠀⠀⠐⠫⠛⢞⣛⣛⣛⣋⣉⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣤⣾⣼⣿⣿⣿⡟⡋⣿⠞⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠓⠒⠒⣒⠋⢵⠚⢻⢹⣿⡏⠿⢞⠺⠿⢻⣍⡇⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠘⠀⠀⠈⠀⠀⠰⠸⠘⠀⠯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡏⠉⠛⠳⢦⠴⠛⠻⣆⠀⣠⡶⢻⡆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠘⠷⠶⠋⠻⣤⣤⠖⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣼⣿⣍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢶⣼⡿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠛⠉⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣦⣄⠀⠀⠈⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡇⠀⠀⠐⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠄⠀⠈⠁⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣶⡄⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠘⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠛⣶⣆⣠⣤⡀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠙⢦⣄
⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣇⠀⣠⣴⡄⠀⠀⣀⡀⠀⠀⠀⢀⣠⣿⣿⠷⠲⣆⠀⢀⣄⠀⠀⣰⡿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⢰⡿⠋⠙⠀⠀⠀⠀⠀⣠⣿⠟⠁⠙⠛⠉⢸⣧⣴⣿⣿⣿⢀⣠⣾⣿⣿⣿⣷⣶⣤⡙⣦⣿⣿⣷⣦⣿⡇⠈⠉⠻⢿⣿⣿⣿⣿⣦⣀⣀⡀⠀⠀⠀⠀⢀⣼⠇
⠀⠸⣷⣄⣀⠀⠀⣀⣠⣾⠟⠁⠀⠀⠀⠀⢀⣤⣿⣿⡿⠛⠛⠛⠁⠀⠀⠈⠉⣿⡿⣯⡉⠈⠁⠈⣿⣿⣿⣷⣤⣤⡀⠀⠀⠈⠹⣿⣿⡿⠿⢿⣿⡛⠛⠛⠉⠁
⠀⠀⠈⠉⠛⠛⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⣿⣷⣶⣶⣶⣶⣤⡄⠙⠁⠈⠁⠀⢠⣾⠋⢿⣏⠻⣷⡄⠉⠀⠀⠀⠀⠻⠈⠛⠷⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠉⠛⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠀⠈⠁

⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠼⠁⠈⠀⠰⠄⠔⠄⠀⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠚⠴⢃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠡⠚⠭⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣡⠤⠔⠾⢥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠈⢣⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣄⠀⠀⠀⠀⠈⠀⡞⠁⠀⠀⠀⠀⠀⠈⠓⠲⠦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣞⠃⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠦⢤⣀⣀⣀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡷⠦⣤⣥⣤⣤⡤⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡴⢖⣠⠴⠋⠀⢀⡤⠂⡉⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠚⠁⠀⠀⣠⡐⠏⠈⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⠑⠂⠋⠤⠥⠤⣤⣄⡠⠴⣋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⣀⡀⠠⠔⠲⠤⠀⠀⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠓⠒⠒⠒⠂⠀⠀⠀⠛⠃⠀⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⣁⣤⠤⠶⣶⣦⣤⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣴⠞⠉⢠⡶⣫⠵⠶⢾⢹⣦⡔⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⣰⠟⢁⡀⠀⡏⣼⠁⠀⠰⡯⢞⡽⠭⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢳⡏⢠⣾⣿⠀⢷⡙⠲⠦⠶⠒⣋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠒⢾⠀⢸⣿⣿⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⢰⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣤⣼⡀⣼⣿⣇⣀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⢙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢈⣿⣿⣿⡃⠉⠛⢦⡀⠀⠀⠙⠛⢻⣿⡆⠀⣠⢿⣿⠇
⠀⠀⠀⠐⣶⣶⣦⡀⠀⠘⣆⡤⠞⠛⠋⠉⠉⠙⠲⢾⠛⠖⠶⣤⣼⠟⠿⠾⣅⠀⢽
⠀⠀⠀⠀⠙⠻⣿⣿⣧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢅⠀⠀⠀⠈⠳⣼⣤⣤⣄⣀⣀⣀⠤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⡾⠟⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡔⠀⡀⠀⣈⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤⠤⠤⠴⠖⠒⠒⠒⠋⠁⠸⣵⠁⣠⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠙⠓⠲⠤⣄⡀
⡴⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠙⠢⡀
⢧⠀⠀⢌⠑⠢⢤⣀⠔⠚⠙⠉⠀⠀⠉⠉⠙⢲⠦⣄⠀⠀⣠⠔⢋⡡⠒⠂⢉⡇⠀⠀⠀⠘⣖⠢⢤⣀
⠈⡇⠀⠈⠢⡄⢠⡰⠀⠀⢣⠀⠀⠀⠀⢀⠠⠃⠀⢈⠳⠚⠁⡠⠃⠀⠀⡴⠋⠀⠀⠀⠀⠀⠘⡆⠀⠈⠑⢦⡀
⠀⢣⡀⠀⠀⣸⠇⠀⠤⡀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠠⡀⠀⠜⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣷⢄⡀⠀⠀⠈⢢⡀
⠀⠀⠉⢱⣠⠃⣠⣤⣄⡈⠄⠈⡐⠁⡠⠔⠒⠒⠢⡀⢆⢸⣀⠀⠀⢀⡼⢠⠂⠀⠀⠀⠀⠀⠀⣿⠀⠈⠳⢄⡀⠀⠹⣄
⠀⠀⠀⠀⡟⢘⢿⣁⣹⣳⠀⠀⠀⡜⢀⣶⠿⢗⣆⠘⡌⠉⡧⣠⠖⠉⢠⠃⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⢣⠀⠀⠙⡆
⠀⠀⠀⢰⡧⠈⠻⠿⠗⡡⠂⠀⠀⡀⠸⣿⣶⣾⡿⢠⠃⠀⢺⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠈⡇⠀⠀⢹
⠀⠀⠀⠀⢧⠈⠒⠐⠊⠀⠀⠀⠀⠱⢄⡈⢉⣉⠔⠃⠀⠀⡾⠀⡆⠀⠸⣄⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈
⠀⠀⠀⠀⠈⢳⢤⡀⠀⡎⠉⠲⡀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠀⢰⡤⠔⢋⣨⠓⠒⠒⠉⠳⠤⣀⣀⡀⠀⠀⠀⢰⠃⠀⠀⢀
⠀⠀⠀⠀⠀⣾⡀⠙⢆⠭⣖⡪⢄⡤⠖⠒⢛⡏⠉⠁⠀⠀⢠⠏⠀⠺⠗⠒⠒⠢⠤⣀⡀⠠⢔⣪⣻⡆⠀⢠⠏⠀⠀⠀⡼
⠀⠀⠀⣰⢊⡥⢑⠒⠂⠻⣖⠚⠉⠀⠀⣀⡎⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠟⠛⢀⡴⠃⠀⠀⢀⡼⠁
⠀⠀⠀⠙⠁⣷⢿⡴⣦⡏⠉⠀⢠⣚⡍⣁⠈⠉⠉⣲⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠹⡽⢧⣴⣇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠁⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠒⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⣙⣌⡦⣿⣿⣇
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣀⠅⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⢄⠀⢠⣃⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣴⡟⢠⣿⠋⠁⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⡿⠀⣾⣇⣄⠀⠈⠉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⣡⢸⣁⠀⠀⠀⠀⠀⠐⢰⡇⠀⠀⠀⠀⠠⠇⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣿⣶⡿⣾⣿⣀⡀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⣳⣶⣸⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⣠⣿⡿⠃⣼⣀⡀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⠈⠁⠀⣿⣿⣷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠠⣼⠟⠀⢸⢿⣛⠛⢿⡄⠀⠀⠀⡘⠀⠀⣤⣾⣿⢆⡄⣉⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠸⠃⠀⣰⣿⣿⣿⣟⣿⣿⡆⠀⠀⠀⠀⣼⣿⠿⢿⣷⣿⡄⠀⠸⣿⡛⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢘⣿⣃⣾⡟⢻⣿⣿⣿⡿⢻⡇⠀⠀⠀⢰⣿⣿⣿⣿⡿⠻⣇⠀⠘⢿⡇⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⡇⢻⡟⠀⠈⠙⠛⢻⣿⠞⠁⠀⠀⠀⠘⣿⣿⡿⠿⠚⠀⠻⣷⠀⣾⡆⠀⠐⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⡀⠀⠀⣿⣧⠀⠀⠀⠀⠀⢈⣏⣀⠀⠀⠀⠰⣤⡠⡇⠀⠀⠀⠀⠀⣿⠰⠛⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⡇⠀⢠⣿⣿⣧⣄⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠹⣷⡅⠀⠀⠈⠁⢐⣤⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠿⠅⢸⠀⢹⡀⠀⠀⠈⠛⠿⡶⠄⠀⠈⢿⠀⢺⣾⣷⡦⢀⡿⠃⠀⠀⠀⣠⣾⣿⣿⠗⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠡⠆⠀⠀⣿⣧⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠈⠢⢤⣼⣧⣤⠼⠖⠈⠡⠴⣻⠿⢿⣿⡇⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⠠⣀⣴⡿⠉⠀⠀⠀⠀⠐⢿⣿⣆⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠉⣁⣴⠇
⠀⠀⠀⠀⠀⠀⣼⠾⠋⠁⠀⠀⠀⠀⢐⡿⣟⣿⣿⣷⣴⣿⡇⠀⠐⣶⡾⠿⠯⠠⣀⢺⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡿⠏
⠀⠀⠀⠀⡴⡿⠉⠀⠀⠀⠀⠀⠒⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⠋⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⣄⡀⠁
⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⣤⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⣼⣦⣤⣦⣤⣴⣿⣿⣿⡿⣏⣃⠀⠀⠀⠀⢉⣰⣶⣟⢁⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⣿⠁⣹⣿⡇⢠⣌⡇⡔⠒⢲⣏⣴⣿⣿⣷⣶⠶⠿⣿⣿⣿⣿⠈⠉⠻⠟⠀⠈⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠋⠛⠙⠛⠛⠓⠂⠀⠉⢹⣿⢠⢿⡿⠂⠀⠀⠙⠻⣿⢠⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣏⢨⡇⠀⠀⠀⠒⢟⣫⡜⣑⡞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠛⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⢸⣷⠀⠀⣿⠉⠀⠀⠀⣿⣧⠄⠀⠀⢸⣧⠀⢸⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⣾⣿⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⣷⣄⡆⠀⢸⣿
⠀⢸⡇⠀⠀⣿⣆⠀⠀⠀⣿⣿⡆⡀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⣿⣿⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⣿⣋⠃⠀⢸⣇
⠀⢸⣿⠀⠀⣿⣍⠀⠀⠀⣿⣿⡟⠁⠀⣼⣿⠀⢠⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠇⠀⢀⣿⢀⣿⠀⠀⠀⠀⢸⣏⢹⠀⠀⢸⣧
⠀⢸⣧⠀⠀⣿⡉⠀⠀⠀⣿⡿⡇⠀⠀⣿⡟⠀⢸⡇⠀⠀⠀⠀⠀⢸⡁⠀⠀⣿⣿⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⣹⣿⣻⠀⠀⢼⣿
⠀⢸⡗⠀⠀⢿⣧⠀⠀⠀⣿⡿⡇⠀⠀⣿⣷⠀⢸⠃⠀⠀⠀⠀⠀⢾⡇⠀⠀⡿⣿⠀⠀⢸⣿⠀⠻⠀⠀⠀⠀⣹⣿⣿⠀⠀⢸⣯
⠀⠈⠓⠀⠀⠙⠋⠀⠀⠀⠛⡂⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⢼⣿⣽⠀⠀⠀⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⡇⠀⠀⣿⣻⠂⠀⠀⠀⠀⠀⠀⠀⢸⣟⢀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⡋⡉
⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⣿⣯⣄⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢺⡏⣿
⣾⣿⣿⣿⣿⣯⣍⣑⣚⣣⣴⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢾⠆
⣠⣤⣶⣶⢉⣉⡉⠩⡉⠍⠉⠙⠛⠀⢶⠀⠀⡶⣖⡒⠂⠀⠀⠀⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢸⡇⠀⠂⠀⠄
⣙⡛⠛⠿⠿⠿⠿⣿⣿⣿⣶⣦⠀⠀⠘⠂⣤⡀⢸⣧⣠⠄⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠈⡁⠀⠀⠀⠀⢀
⠛⡛⠿⠷⢦⣤⣭⣅⣠⣄⣀⣀⠁⠀⠁⠀⠸⠿⡁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⡄⠀⠀⠈⠘⠋
⠻⢾⠶⢶⣶⣴⣤⣶⡖⠉⢹⣿⡀⠀⠘⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠃
⠈⠀⠂⠀⠒⠈⠉⠉⠁⢠⣀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠁
⣄⣀⣤⣄⣤⡄⠀⠀⠀⠸⠿⠄
⠈⠉⠉⠛⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⡖⣶⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⢻⡍⢧⡘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⣠⣴⣾⡿⣿⠹⣄⢳⡄⢷⠈⢧⠘⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣴⣿⢿⠻⡍⢷⠘⢧⠘⣆⢻⣨⣷⡾⠟⠋⠉⠛⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠘⣆⢻⡌⣧⣼⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⢀⣤⣾⣻⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣸⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⣶⣶⡦
⠀⠀⠀⠀⠀⠈⠳⠺⠿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⡇⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣏⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠳⣌⠳⣄⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⡈⣳⡾⠋⠙⣿⣆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠰⡄⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠈⣿⣇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢠⣿⡁⠉⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣧⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠆⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣥⢤⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⢿⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⢸⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣰⣿⠃⠀⠀⢸⣿⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠈⠁⠀⢸⣿
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⣿⣇⣤⡶⠶⠶⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢸⣿
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⢸⣿⡏⠥⠀⠋⠀⠒⠀⠯⢉⡻⣦⡀⠠⠏⠀⠀⠀⣠⣿⡏⠀⠰⠆⠀⠀⢸⣿
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡌⢿⡄⠀⠀⠀⣰⣿⢿⡟⢿⠻⢶⣤⡀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣀⣠⣾⡿⠃⠈⠀⠀⠀⠓⣘⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣤⣄⣀⣀⣤⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠻⣿⣅⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣶⣶⡿⠿⠛⠋⠁

⠠⠀⢀
⢸⡀⠃⠀⠀⣀⠀⠀⠀⢰⢆⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⢀⠠⢀⣀⠀⠀⠀⠀⠀⣇⢠⠀⠀⠀⣠⣀⠀⢐⣦⡀⠐⠀⠀⠀⡀⢸⠄
⢠⡅⠀⢀⢟⣞⡼⠀⢀⡋⢎⢫⡽⢀⠀⠀⠀⠀⠠⢀⠆⠀⢨⣿⣶⣻⠏⢀⠀⠀⠀⢀⣼⡲⡇⠀⡄⡟⠿⢧⣸⣽⡄⡄⠀⠀⢸⣷⣟⣖⡆
⠰⣿⡟⠀⡘⢩⠋⢤⣼⡅⠃⢶⣧⠈⠀⠀⠀⠠⢓⣶⡀⣴⣶⣿⠿⣯⣤⣸⠈⠄⠦⡜⢻⡿⣾⡜⠁⣰⣏⣸⣿⣾⣿⠙⠰⢸⡇⣽⣿⣿⣧
⠀⣿⡇⢸⠃⢼⡖⢉⢻⡇⣃⢸⡇⡾⢣⠀⠀⠀⣼⡿⡟⠀⣽⢏⡖⡿⣟⡀⣦⡀⣾⠧⢺⡇⣿⣸⣒⢿⣟⢻⣷⢻⢱⡀⢰⡟⠘⣿⣿⣈⣿
⣴⣿⣈⡟⠀⣸⠘⠈⢸⡄⠙⢾⡇⢸⠏⠐⠀⠀⡼⠀⡇⠀⣿⠻⢀⡇⠛⢇⢸⣇⡇⣀⣸⣻⣿⣋⣣⣼⣦⣹⣣⣿⣟⣆⣸⠀⠀⣿⣿⠼⠾
⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣾⣷⣾⣶⣶⣶⣶⣷⣶⣾⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣧⠀⠀⠀⠀⠀⠀⠇⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⢸⣿⣿⣧⡀⠀⠈⠄⠀⠀⠀⠀⣹⣿⢀⣤⣶⣾⣿⣿⣷⣶⣤⣀⢸⣿
⠀⠀⠀⠀⠘⠀⠀⠀⡌⠀⠀⠀⠀⠀⣠⣾⣧⢠⣶⣶⣶⣷⣄⠀⠐⡀⠀⠀⠀⢿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⣴⣿⣿⣿⢸⣿⣿⣿⣿⣿⢰⣄⡀⠂⢠⣾⡛⠙⠻⣿⣿⣶⡄⠈⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⡔⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢸⠏⠠⠠⣿⠋⣡⡀⠀⠙⢿⣿⡄⠀⠀⠀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡀⢼⣩⡅⣩⣭⣭⣭⣭⢈⣭⣭⣭⣭⣭⡈⠀⢀⠀⠀⠀⠄⠀⠀⢆⢠⠋⠀⠀⠀⠀⠀⣴⣿⣿⡇
⠀⠀⠀⠀⠸⢀⣠⢠⠤⣬⣿⣇⡿⠿⠟⠛⠛⠚⢛⡟⠛⢿⡿⣁⣀⠄⠀⠐⠀⢀⠀⢀⠀⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⠀⠐⢀⠈⢰⡏⠁⠐⡄⠀⠀⢀⠔⡁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡡⠄⠀⠀⠀⠙⠄⠀⠀⢉⡀⠈⡷⢖⣶⣞⣻⣄⣁⠔⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⠉⠭⣽⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠀⠀⠀⠀⠀⢀⠓⢒⡄⠀⠒⠦⡤⠤⠤⠴⠒⠋⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠒⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠐⢃⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣀⠀⠤⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠴⠀⠀⠀⠀⠀⠀⣿⣿⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢒⡬⠤⠐⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠘⢄⡀⠀⠀⠀⠀⠀⠀⣠⠂⢠⠬⠭⠥⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠉⠢⡀⠀⠀⠀⠈⠐⠊⠭⢒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⢠⠄⡶⠓⠊⠀⠀⠀⠀⣀⠤⠀⢖⣊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣐⠑⠁⠀⠀⠀⠈⠀⠡⣒⢤⠀⠀⠀⠈⠢⢘⡥⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢉⠱⣈⠆⠀⠀⠀⠀⠀⢀⢀⡦⠃⠀⠀⠀⣀⠤⣘⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠣⠯⠀⠀⠀⠀⠀⠃⠏
⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⣤⣤⡀⢀⡤⠤⠤⠤⠤⡄⠀⠀⢀⡤⠤⡴⠦⠤⠤⠤⡤⠤⠤⠤⢤⣠⢤⡤⢤⠤⢤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⣀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠳⢤⡔⠋⣀⠔⠁⡤⡄⠀⠀⡇⢀⢔⠁⡠⢉⢍⡠⣪⠆⠘⡡⡢⢉⢸⠃
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠘⠬⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⡀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⡇⢐⠅⡨⢒⠕⢅⡞⣱⣟⡝⣾⠔⣡⣎⡳
⠀⠀⠀⠀⠀⠈⢻⡻⡄⠀⠀⠀⠀⠀⠫⠂⠀⣦⠶⠃⠁⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡲⠷⠦⣈⢔⠕⣡⣠⠆⢿⡉⣀⠼⢖⢕⠕⡇
⠀⠀⠀⠀⠀⠀⢀⠗⡇⠀⠀⢀⡀⠀⠀⠀⠀⠑⠤⢤⡴⠞⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠻⠇⣀⣠⡧⡢⢊⠝⡺⢊⠔⡡⢀⢔⢡⠗⢁⡇
⠀⠀⠀⠀⠀⣠⣮⠜⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⠀⠀⢠⢄⠀⠀⠀⡸⢊⢈⠔⡡⢊⡰⣡⢊⢔⠕⣱⣡⣾⠁
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠌⠊⠈⠈⢱⠀⠀⠁⠀⠀⠀⡇⠔⡡⢊⢰⡙⠝⠉⡇⡡⠪⣪⢜⢆⣳
⠀⠀⠀⠀⠘⢷⡄⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣢⠀⠀⢀⡠⡰⠀⠀⠀⢤⢶⢲⢷⣾⣴⡡⡠⠙⠒⡲⢋⢔⣟⢕⡑⡰⣹
⠀⠀⠀⠀⢠⠎⠀⠀⠻⣍⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠐⣉⠔⠁⠀⠀⢸⡦⠃⠁⠀⠀⠀⢹⡔⡡⠊⡠⣳⠛⡹⣏⡱⢈⢼
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠻⢇⣀⠐⠒⣊⢽⠖⡡⠪⣪⣪⡾⢊⢄⢔⡕⡏
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⡴⡖⡶⢦⡀⠀⢾⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡹⢝⠍⠐⢡⡊⢎⠝⡠⣫⣖⣻⡼⠿⠗⣧⣤⡶⠶⠶⠶⠶⠄⣀⣀⠐
⠀⠀⠀⠀⢸⠋⠀⠀⠀⢰⢏⢜⡞⢋⣉⣱⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⡗⡧⡯⠪⣪⣪⣎⠮⠴⠯⣐⡛⠻⠿⢿⡷⠖⣲⣖⣛⡛⠓⠋
⠤⠐⢒⣒⠸⠦⠤⠶⠶⠟⣛⣛⠋⠹⠿⠽⢒⣒⠶⢿⣶⡿⠶⠖⣛⢒⠒⠶⢶⡶⣶⡶⠾⣷⢿⣿⣿⣽⣿⣟⠛⢩⣯⣬⣷⠶⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠁⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⡤
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠉⠲⠶⢤⠄⠉
⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠒⠲⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠃⡀⠀⠀⠀⠀⢄⠀⠀⣠⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠐⠂⠒⠶⢤⣄
⠀⠀⠀⠀⠃⠀⠀⠀⡿⠳⠞⣿⠀⠘⡴⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡶⠖⠻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⢀⠀⠀⠀⠀⠀⡸⢷⣤⣤⠀⠀⡄⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⣶⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠰⣀⠀⠀⢰⣀⣀⢀⣼⣆⠀⠑⢄⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠟⠀⠈⡟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡀⠀⠀⠀⠈⠀⠀⠈⡟⠉⠹⣇⡁⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠒⠂⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠑⠀⠀⠀⠀⠀⢀⡀⠷⢠⣾⣿⡇⠀⡄⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠱⣆⠙⢦⠀⠀⣇⠀⠀⠒⠂⠀⠀⠀⠀⠀⠎
⡀⠀⠀⠀⠠⠘⢷⡀⠀⣼⣿⡇⢠⡄⠀⠀⠀⠘⠀⠈⢆⠀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠁⠈⠳⡄⠀⠀⠀⠀⠀⡠⠊
⠁⠀⠀⠀⠷⣦⣈⡻⠞⠁⢿⠃⣠⡼⢆⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠈⠑⠶⠤⣤⣈⠷⣄⠀⠒⠉
⠀⢀⢰⣿⣄⣀⡙⠁⠀⠀⠈⠻⣋⢀⣬⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠶⢀⣤⡀⠀⠀⠀⠀⠀⠀⡈⠳⣄
⠆⠈⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⡋⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠂⢤⣤⣇⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠙⠲⢤⣌⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠒⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠠⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣶⣶⣶
⣿⣿⣿⡿⠋⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣴⣦⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠈⢻⡀⠀⢀⠀⣻⣇⣸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠇⠀⠈⡇⢸⠈⣷⣿⣧⠏⠀⢸⡅
⠀⠀⡀⢨⠉⠒⢦⢰⢿⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢧⠸⠄⠘⣿⡇⠆⠀⣸
⠀⠀⠀⠰⡇⠀⢎⣻⣾⠁⢧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⢘⠀⠀⢸⡐⠀⠆⡻⣿⠀⠀⣿
⠀⠀⠀⣁⡇⠀⠀⣿⡻⠀⢸⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⢨⠄⠀⢸⡇⠀⠀⣿⣿⠀⠀⢹⡀
⠀⠀⠀⠸⡎⠀⣠⣿⡻⠂⣼⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⢰⡇⠀⠀⢹⣿⠀⠀⢸⡇
⠀⠀⠀⡀⣿⠀⢨⣿⠟⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⡇⠀⠀⠀⣿⡆⠀⢸⡇
⠀⠀⠀⠨⣻⠀⣴⠿⣦⠀⢰⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢘⡄⠀⠀⣇⠀⢠⢸⣿⡅⠀⢸⡇
⠀⠀⠀⠂⢹⠀⢹⢢⡄⠀⠈⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠁⣿⠀⢸⢸⣿⡇⠀⢸⡇
⠀⠀⠀⡇⢸⡇⢰⣼⡇⠀⠀⣿⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢠⡇⢸⢀⢹⡀⡌⣸⢸⣷⠀⢸⡇
⠀⠀⠀⡆⢸⡷⢸⡟⡇⠀⠀⣿⠀⢸⡄⠀⠀⠀⢣⠀⡆⠀⠀⠀⢸⠀⠀⢸⡇⢸⢸⢸⣷⢣⣿⢸⣿⡀⢸⡇
⠀⠀⡇⡇⢸⡇⢸⣭⣿⠀⠀⣿⡆⠀⣇⠀⠀⠀⠈⡇⠇⠀⠀⠀⢸⠀⠀⠘⠃⠀⠈⠈⣧⠈⠁⢸⣿⣇⠘⠋
⠀⠀⠀⠇⢸⡇⢼⢻⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⣦⡄⠸⠂⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠘⠁⠉⢹⣧⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⡀⠀⠀⠀⢀⠀⠀⣀⡀⠀⠀⢀⢀⠀⢀⢀⡤⠆⠀⠐⠒⠚⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⢠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣄⡅⠰⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠀⠀⠀⢱⠶⠒⠲⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⢀⣀⡴⠊⠉⠀⠀⠀⢠⠆⠀⣰⠃⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠐⢢⠀⠀⠀⠀⠀⠀⢠⠃⣀⣀⡇⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣀⠀⠀⠘⠐⣆⠀⠀⠀⠘⢡⠋⠉⠉⠳⡄⣀⠀⠀⠀⢘⣇⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⡀⠈⢦⡀⠀⠀⢸⡄⠀⠀⣴⣏⠉⠀⠀⣠⣾⡽⠋⠁⠀⠉⡆⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣑⣄⣱⠀⠀⠀⠙⠦⠤⣺⠏⠑⠒⠊⠉⠀⣄⣀⣀⠤⠚⠁⠀⠀⠀⠉⠐⢒⣶⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⣉⣉⡉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢰⣋⠉⣠⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠛⠚⠋⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣤⠼⠓⠙⠒⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠤⠴⠚⠉⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣸⠃⠀⠀⠀⠀⠘⢧⡀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢰⠚⠉⠉⠤⠛⠚⠙⠧⡄⠀⠀⠀⡸⢉⠂⠈⢲⡌⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢈⠇⠀⠀⠠⠀⠤⢤⡶⠃⢠⠒⠧⣍⡛⣄⠀⠘⠁⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⣯⠜⠉⠀⠉⠉⠀⠀⢸⠀⢦⣴⣿⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡹⡁⠀⠀⠀⠀⣀⡇⢸⣀⣀⣤⡀⠀⠀⢀⣀⠴⡠⣈⠀⡽⢏⠒⠄⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⡄⠀⣴⠛⢻⠀⡞⠁⠀⣶⠟⠒⣋⠭⠒⠉⠀⠈⡏⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢜⡦⠃⢠⡏⢠⡃⠀⠀⣟⡏⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢉⣶⢰⠃⡜⠉⠑⠒⠿⠀⠀⠀⠀⠀⠀⢠⠞⡇⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⢠⡿⠻⡜⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠇⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢿⠝⢦⡀⡸⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣬⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠔⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠒⠒⢻⠉⣩⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⠀⡏⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠰⢾⠶⠇⢀⣇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⢻⡟⢶⠶⣲⡾⣿⣽⠿⠫⢿⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⣷⣴⡶⠞⠋⠀⠈⠛⠷⠶⣴⣧⠾⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠙⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣀⣤⠴⠤⠞⠁⠀⠉⠉⠉⠙⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠹⣆⡾⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⡇⠀⠈⠀⠀⢀⣿⠤⠤⠖⠒⠦⠤⣤⡒⠁⠀⢀⣀⡴⠚⠋⠙⠳⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡞⠉⠁⠀⠀⢀⠀⠀⠀⠀⠈⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⠀⠀⠀⣀⠤⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⠆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⠤⠒⠈⠁⠀⠀⠀⢸⡆⡀⠄⠊⠁⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠰⠀⠀⢀⠔⠊⠀⣀⠀⠀⠀⠀⠀⠀⣼⣈⣀⣀⠀⠀⠤⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢀⠀⠀⢸⠁⠀⠀⡀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠈⠑⠲⢤⡀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢂⠀⢸⠀⠀⠀⠆⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠙⢲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘⡇⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⢀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⢀⣀⠀⠀⠁⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡴⠋⣡⠞⢁⡤⡶⠛⠓⠲⠦⠤⠤⠶⠶⠦⠶⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⡞⣡⠞⢁⡴⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢟⣱⠿⠋⣁⠴⢋⡤⠚⢁⡤⠶⢒⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠿⠖⠋⣁⣤⣚⡥⠚⢁⡤⠞⣉⡴⠞⠉⠀⠈⠙⠲⢦⣄⣀⠀⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢸⣅⣠⣤⡤⠶⠿⠛⣉⣥⣴⡾⠋⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣤⣤⣀⣀⣤⣤⡤⠤⣤⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⣿⣀⣀⣤⡤⠶⠚⣋⡭⠞⢉⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⣁⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠐⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡐⠒⢤⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠻⠿⠋⠀⠹⠋⠀⠉⠛⠙⠿⠋⠈⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠔⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⡐⠁⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡿⠁⠉⠻⡏
⠀⠀⠇⠀⣀⡀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠉⠀⠐⠀⠀⡁
⠀⢰⠀⠘⠄⠈⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⣿⡀⠀⠠⠈⠠⠀⣶⠆⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠁
⠀⠈⠢⡀⠀⡀⠃⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⢀⣼⣿⣧⡠⠃⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰⣤⣶⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⠟⠀⠀⠁⠂⢀⠀⢀⠎⠀⠁⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠸⠥⠄⠀⠤⠄⠠⠀⠘⠛⠿⣿⣿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠄⠀⠠⠀⠀⠀⠀⠀⠈⠣
⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠁⠈⠅⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢂
⡇⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠈⡂⠎⠱⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠂⠂⠀⠀⠀⠀⠀⠈⠁⠒⠀⠈⠁⠉⠐⠄⠀⠀⠀⠀⠀⠑⠠⠀⢀⠠⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠐

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠠⠤⠀⠀⠶⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠑⡀⠀⠠⠫⠹⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡎⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃⠀⡙⢿⣿⠀⠀⠀⢀⣀⠰⠄⠚⠻⡃⠀⠈⠁⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣀⠀⠀⡀⢀⠄⠀⢾⡿⠢⡟⠀⠐⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠚⠀⠀⠈⠀⢰⡇⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠣⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⠀⢀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠍⠁⠀⠀⠀⠀⠀⠐⠀⠀⢠⠀⢨⠓⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣃⠄⠁⠀⠀⠱⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⡠⢤⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠔⠀⠀⠀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡧

⠀⣼⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠄⠀⢀⡀⢀⠀⡀⠀⠐⠂⢀⢀⡀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠃⠐⠀⠀⠀⠀⠀⠙⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⡀⠀⠀⠂⠘⠂⠒⠒⠊⠓⠘⠀⠃⠚⠈⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣦⠀⠠⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⡃⠀⠀⠀⠀⠀⠿⠇⠠⠭⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⢶⢤⣤⣿⣼⠃⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠈⢀⠂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠠⣦⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠳⠆⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢶⠖⠒⠒⠂⠒⠆⠀⡀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠒⠠⠋⢻⠀⠀⠀⠀⠀⡒⠺⠋⠂⠰⣶⢤⣀⣶⣶⢚⣶⣛⣦⣤⣄⡄⠀⠙⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠓⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⣿⠒⠋⠉⣯⣉⣹⣷⠀⢀⠒⠈⠈⠁⠀⡀⡀⢠⡅⠄⣿⣿⣿⣿⣿
⠉⣉⣓⣟⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡀⠛⠁⠈⣁⡀⠻⠙⠗⣾⡟⠁⠀⠀⣀⡀⠀⢁⠀⠀⠉⠻⠛⠿⠛⠋
⠀⠈⠻⣿⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣅⣾⣟⠀⠀⠀⠁⣰⣾⣿⢤⡀⠀⠀⠉⠱⠴⠈⠓⠦⠀⢀⡀⠋⡋⠴
⠀⠀⠀⣯⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠄⢸⣿⡌⠀⢤⣖⠉⣛⣻⡧⡤⠀⠐⠎⣢⣶⣦⡸⢀⡀⠁⠀⠀⠁
⠀⠀⠀⣿⢤⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⢻⣿⣯⡀⢀⣉⣭⠀⠙⢿⡆⠀⠄⢀⠀⠁⠛⠛
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⢸⣿⠋⠹⣮⠽⡇⠀⠀⠀⢀⡀⠀⠀⠁
⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⢸⡿⠀⠠⢿⣴⣦⠀⠀⠉
⠀⠀⠀⡇⢐⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⡇⠀⠀⠈⢸⠈
⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⢸⡇
⠀⠀⢈⣇⡆⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄
⣧⣠⣾⣿⡇⠀⠀⡴⢀⠂⢘⣗⣠⡄⢀⣤⣿⣿⣿⡧⣄⢠⣶⡆⠀⠀⣀⡇
⣋⣤⣹⣿⣧⣀⡂⣾⢾⣃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⡿⣣⣾⠴⣿⡅⠠⣦⣤⣤⠀⠀⠀⠀⠀⢀⣠⣀⣀⣤⡀⠀⣀
⡿⢻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣯⣹⣃⣿⣷⣾⣿⣿⣿⡆⢴⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⣰
⣙⣺⣿⣿⣿⣽⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⠸⠿⢿⡿⠟⢹⢿⠁⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣤⣥⣤⣤⣀⡀⣸⣿⢣⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠴⠠⠒⠒⠉⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢄⣡⠀⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠋⠀⠀⠀⢙⡶⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢠⠏⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠁⢠⡀⠀⠀⠀⠀⠈⠀⠈⠑⣄⢀⠀⠀⠀⠀⢇⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣀⠀⢣⣄⠀⠀⠀⣄⠀⠀⠬⣿⠁⠀⠀⢀⠔⠀⠋⠀⠀⠈⡷⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣦⣘⡆⠀⠀⠈⠒⠒⣒⠏⠀⠀⠀⠀⠀⣄⣀⢠⡴⠚⠁⠀⠀⠀⠈⠁⢙⡳⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢉⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠰⣏⡁⣠⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠋⠘⠉⢀⡠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡤⠶⠛⠈⠓⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠶⠚⠉⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⡰⠃⠀⠀⠀⠀⣈⠳⣄⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡂⠀⠀⠐⠛⠋⣉⠗⣤⠀⠀⠀⣘⢉⠇⠈⠳⡄⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡶⠃⢠⠞⠓⠬⡙⣦⠀⠈⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠸⠂⢰⡴⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠄⢠⣇⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠉⢹⠃⡜⠀⠀⣴⡜⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⣵⠂⠀⡞⢀⣇⠀⠀⢏⡏⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⢀⡵⢆⠃⣸⠀⠈⠐⠚⠁⠀⠀⠀⠀⠀⢠⠞⠃⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣄⣾⠛⠾⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠹⠘⠓⠄⣠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢀⣀⣀⠠⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠂⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠹⡇⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡇⡜⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⠀⠀⠈⢛⣟⣋⣀⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⢹⠿⠽⢟⣭⠿⠿⣾⣿⠗⠻⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣿⡶⠾⠛⠁⠀⠀⠈⠙⠛⠶⠷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠠⠀⠀⠠⠀⠀⠀⠄⠄⠄⠄⠀⠀⠀⠀⠀⠆⠆⠀⠄⠀⠐

⠀⠀⠀⠀⠀⠀⣀⢠⣤⣴⣶⣶⣶⣦⣄⣀⣀⣀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡴⠊⣇⠑⢄
⠀⠀⢀⠤⠒⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢆⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⢣⢂⣀⣁
⠀⠎⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⡄⣀⢈⣄⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⠀⠀⠀⠠⠤⠤⠀⠀⢀
⢰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆⠀⠩⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠖⡀⠀⠠
⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠁⠀⢀⠔⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢈⡴⢨
⠀⡄⠀⠀⢹⣿⣿⣿⣿⣿⡈⠁⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣠⣶⠟⠃⠂
⠀⠘⡄⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢊⣴⣾⠟⠁
⠀⠀⠈⠢⡄⠀⠀⠹⣿⣿⣿⣆⠀⠀⠈⠀⠀⠀⠀⡠⠃⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣾⡿⠊
⠀⠀⠀⠀⠸⠒⠠⠀⠀⠉⢩⠍⠋⠖⡀⣶⡒⠒⡘⠁⠐⠀⠶⣓⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁
⠀⠀⠀⠀⠀⠀⢰⠀⢠⠄⡄⠀⠀⠀⡜⠀⠀⠩⠄⠀⢀⠀⠀⠀⠀⠉⠉⢀⠒⠄⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢰⠀⢸⣴⡾⡄⠀⠀⠹⣶⣦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠆⢁⡠⡆⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠻⡀⠀⠔⠛⢿⣿⣿⣿⣿⣿⣿⣿⡖⠒⢶⣻⣿⠿⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣈⠩⠀⠉⠉⠛⠛⠿⠿⡇⠀⡟⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢠⠴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠈⣇⠀⠀⠀⠙⠶⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⠀⢹⠆⠀⠀⠀⢀⣤⠶⠖⢶⠖⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠛⠋⠀⠀⠀⠀⢸⡁⣀⣤⣀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠙⢶⡟⠁⠀⠈⢧⣰⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢰⠋⠙⡦⢤⠀⠀⠀⠀⣠⠤⣤⠞⢛⣓⠒⠶⡶⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⣀⠈⡷⢠⠖⠋⠀⠀⠀⠀⠈⢻⠁⠈⠋⠉⣀⡴⠃⠀⣠⡤⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⣠⠔⠊⠙⣏⠈⠻⡇⡼⠀⠀⠀⠀⠀⠀⠀⣸⠀⣀⣀⣀⣧⣀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠓⠒⠛⠒⠒⠒⠛⠒⠚⠓⠛⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⢳⡜⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡶⠖⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⠓⣶⠚⠹⣄⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⣀⠀⠀⣠⢄⠀⠀⢀⡤⢤⡀⠀⢀⣀⡀⠀⢀⣀⠀⢠⡇⠀⠀⠈⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠘⡀⠰⡇⠈⡆⠀⡞⠀⠀⣧⠀⠏⠀⠃⢀⠋⢸⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⡄⢃⠀⡇⠀⢡⠀⠁⠀⠀⢸⢸⠀⠀⡀⠘⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⠸⠀⡁⠀⢸⠀⠀⠀⠀⠈⣸⠀⠀⡇⡄⠀⡼⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⡇⠃⠀⠈⡇⡀⠀⠀⠐⡿⠀⠀⡇⡇⠀⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡆⢰⢸⠀⠀⠃⠀⠀⠀⢀⠳⠀⠀⠃⡇⢰⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢡⠘⠀⡇⠀⠀⢰⡀⠀⣸⢸⠀⢰⠀⡇⠸⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⠶⠃⠱⠤⠃⠀⠑⠶⠃⠈⠳⠋⠀⠛⠃⢸⣧⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⠴⠃⠀⠀⠿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⢻⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⣾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡴⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛
⣤⠤⠦⠤⢤⡀⠸⡧⣾⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⢸⡇⠀⠸⡳⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢹⡄
⣿⠀⠀⠀⠀⠙⣦⡟⢳⣠⠞⠁⣤⡏⢀⡔⠋⠁⢸⣷⠶⣦⣰⠲⣆⣞⡉⢩⡿⢾⠈⣛⣷⣰⠋⢻⣤⠖⢶⠖⠒⢦⠀⣠⠴⠟⠉⢻⠀⡇⢰
⣿⠀⠸⠟⠀⢠⠙⠃⢸⠛⠦⠤⡄⠈⣾⡀⠻⠃⠀⣿⡀⠉⠁⠀⡏⡴⠚⠀⢙⠸⡄⠳⠶⣤⡀⠈⡇⡄⢰⢲⡀⠸⡏⢧⠀⠛⠀⢸⣠⣟⣿
⢿⣀⣀⣀⡤⢋⠀⠧⠼⢃⡏⠉⠁⣀⢇⠙⠚⡆⠀⡇⠙⠦⡤⠞⠀⠓⠒⠒⢋⡀⠙⠒⠚⠃⠙⠉⣀⠉⢉⣈⠙⢛⣁⣌⠉⡇⠀⠘⡏⢣⡼
⡼⠮⠭⠤⠔⠋⠲⠶⠞⠦⠭⠭⠭⠕⠋⠙⠒⣇⠀⢻⠓⠦⠤⠴⠋⠑⠒⠒⠋⠙⠒⠖⠊⠉⠙⠋⠉⠋⠋⠈⠉⠉⠀⢸⠀⡇⠀⠀⡟⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠤⣼⣁⡇⠀⢸⠃
⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠶⠋⠀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡾⣏⠀⠈⠉⠀⢀⣾⡀
⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⢠⠟⣗⠦⠤⠤⢞⣿⡀⣠⢄⠀⠈⢠⣄⠀⢀⠀⠀⢀⢦⣀⠀⡄⠉⢀⣀⣈⣃⣈⣉⣃⣒⣾⠿⢹⡇
⢸⡀⡠⣄⠀⢸⠁⡇⠀⢰⠻⡄⢸⠀⠀⠉⡟⠋⢉⡇⠓⠃⠸⡆⠄⡏⠈⠓⠋⠹⡆⢸⠀⠀⠀⣿⠀⢸⠉⠈⠉⢸⡇⠀⣿⢹⡀⢨⠇
⠀⠉⠀⢸⡀⣸⠀⢹⣀⡟⠀⠳⠎⠀⠀⠀⢳⠀⢰⠁⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⢸⠀⠀⠀⢸⡀⡸⠀⠀⠀⠘⣇⠀⡏⠀⠉⠉
⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠎⠀⠀⠀⠀⠳⡴⠁⠀⠀⠀⠀⠧⠏⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠺⣝⠛⠷⠤⢤⣈⠉⠉⠒⢤⡀⠀⠀⣠⠴⠒⠲⢤⡀⠀⠀⠀⢀⣠⠤⠤⠶⠒⠒⣒⣶⢶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠉⠲⢄⠀⢱⡤⠚⠛⠒⠦⣄⡀⠙⢦⡠⠚⠉⠀⣀⡤⠖⠋⠉⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠱⣾⠀⠀⠀⠀⠀⠀⠉⠢⡀⢳⣀⡤⠊⠁⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢦⣻⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠔⢻⣆⢙⣦⣄⣀⣀⣀⣀⣠⠤⢤⣝⡇⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠲⠤⣀⠀⠀⠀⠀⠈⣿⣾⠏⢀⡴⠛⠉⠉⣙⣦⣼⢦⣁⠀⠀⠀⢀⣠⠞
⠀⢀⣤⣾⠭⠤⠶⠶⠶⠤⢤⣀⡘⡆⠀⠀⠀⠀⣸⣿⣠⠋⢀⡤⠚⠉⠁⠀⠈⠳⡌⠉⠉⠉⠉
⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⣿⣿⢃⡔⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢰⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⢀⡼⣁⡤⣄⡀
⠀⠀⠀⠀⠀⠈⠳⢄⣀⡀⣀⣠⣴⣃⣴⣊⠉⠉⠛⢾⣿⡓⠒⢶⣤⠤⠴⢒⠟⠛⠓⠦⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡞⠁⠀⠈⠉⠓⢤⡀⠙⣇⠀⣸⡇⠀⠀⣼⠀⠀⠀⠀⠈⠳⣌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠉⠢⡈⢦⣿⠁⠀⣸⡟⢦⡀⠀⠀⠀⠀⠈⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠀⢀⣿⠀⠀⠉⠙⠓⠚⠋⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⢤⡤⠖⠒⣿⠲⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣗⠀⠀⣿⡇⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠋⠀⠀⣿⡇⠛⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠒⡄⠀⠀⠯⠭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣄⣀⡷⠀⠀⢀⡴⠒⠶⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢼⡦⠒⠢⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠇⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠚⠁⠀⢀⢄⠀⠀⠀⠀⠀⠀⢠⣶⣀⣀⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢰⢀⠭⠃⠀⠀⠘⡟⠁⠖⢂⡨⠁⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠐⣅⣀⡔⡊⢻⡉⣻⣸⣀⣀⣀⣀⣀⣇⣤⣤⣭⢄⡤⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣴⠒⠒⠒⠒⠶⠦⠤⠤⠤⠤⠄⠒⠒⠒⢲⠞⠳⣜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢔⠄⢠⠒⡄⢀⠖⠲⠀⡔⠢⠀⠔⡄⣸⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡭⠠⢀⠀⢀⠸⠀⠀⡆⠁⢀⠰⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⡀⡀⢸⠀⠀⠀⢣⠀⢀⡀⢸⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠁⠀⠀⠀⠀⠀⣾⠀⠈⠁⠘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⣀⠰⠀⡆⢆⢀⠙⣀⠆⣄⠇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣉⣀⠉⠀⠀⠁⣀⣀⣀⣀⣀⠟⠛⢲⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣭⣭⡭⠭⠭⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡬⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈⠢⠠⡁⠀⠀⠀⡠⠀⠒⠲⠶⢦⡄⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡈⠀⠀⠀⠀⠀⠈⠙⠱⡄⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠁⢈⠀⠄⣄⠠⠀⡐⠀⠀⡀⠈⡀⠃⠐⠠⡀⠀⢐⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠁⠴⢡⡄⣀⢠⡄⠲⠀⠀⠀⠀⠀⠄⡀⣀⣴⠇⢀⠀⠀⠉⠁⠐⠓⠄⡀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠃⠀⠘⢺⠟⠋⠙⠙⠿⡗⠃⠀⠀⠀⠀⠀⠀⠉⠁⢆⡭⠌⠀⠂⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠀⠂
⠀⠀⠂⠀⠀⠀⣎⠀⠀⠴⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⢎⡀⣀⠀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠿⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⡼⠷⡄
⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠎⠀⣠⣇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠞⢫⠟⠛⣦⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⠃⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⡏⠀⢀⡿⠒⢲⠀⠀⠀⠀⢀⡟⠀⠀⠀⠠⠎⠙⠓⣲⠖⠲⣶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠾⠀⠐⠋⢀⠴⠚⣓⣦⣀⣴⣯⢷⣦⠀⠀⠀⠀⠐⠚⠁⣀⡴⠋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠒⠒⠚⠒⠒⠒⠒⠂⠙⣋⣿⣠⣷⠖⠛⠂⠀⠀⣀⣤⣤⣭⡥⠴⠋⠁
⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠉⢻⣀⡼⠻⠄⠀⢀⡞⠁
⠀⠀⠀⢀⡞⠀⠀⣤⣄⣴⣶⠄⠀⠈⢷⣄⠀⢠⡀⠀⠈⠉⠛⠀⠀⠀⠀⣼
⠀⠀⠀⣼⠀⠀⠀⣸⣿⣿⣷⡄⠀⠀⠀⠻⣧⠈⢻⡄⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⡇⠀⠀⠀⠉⠉⠈⠉⠁⠀⠀⠀⠀⢻⠀⣸⠇⠀⢤⣄⣀⣤⣤⡟
⠀⠀⠀⣧⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣾⠀⠋⠀⠀⠀⠠⣤⣀⣤⣿
⠀⠀⠀⠹⣷⣞⣋⣀⡀⠈⢻⡀⠀⠀⢀⣼⠏⠀⠀⠀⠑⣦⡀⠠⢤⠤⣾
⠀⠀⠀⠀⠀⠉⠉⠉⠉⣧⣸⠇⠀⠀⠈⠀⠀⣀⣠⢤⡞⠁⠉⠛⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠖⠒⡟⢿⡁⠰⣄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡷⠶⠚⠋

⣿⣷⠿⠷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⢻
⣀⣠⣤⣤⣀⡀⠀⢸⣇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣷⠀⠀⢸⠧⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⡆⠀⢸
⢿⠀⠀⠀⠀⠉⢳⣈⣷⣾⡀⣠⠞⠋⠙⡗⠀⢀⠴⠞⠛⢳⣀⣤⣄⢠⣤⣤⢀⡖⠛⠛⣶⣸⠇⠻⢤⡄⢸⠷⢿⡀⣠⣤⣄⡤⢤⣀⠀⠀⢀⣠⡖⠚⣷⠈⡇⠀⣿
⢸⠀⠀⣖⡄⠀⠈⠿⡇⠈⡷⣇⠀⠘⠛⠳⣤⡏⢠⣤⠀⢸⣿⠈⠻⠼⠀⢸⠞⣓⣢⠈⠳⡸⡇⢴⣒⡓⠛⠀⠈⡏⡇⠈⢁⡀⠀⢹⡶⢾⠉⠡⡆⠀⢻⠀⣧⣤⡏
⢸⠀⠀⠉⠀⠀⡼⠀⡇⠀⡇⢈⣍⣩⠆⠀⡟⢧⣀⣁⠀⢸⡹⣆⠀⠀⠀⡜⢸⣁⡀⣀⡠⠃⢣⡀⠉⣹⠿⣄⣀⠇⠧⢤⠇⢹⣀⣈⡇⠘⠦⣤⠀⠀⢸⣶⡧⢾⡅
⢸⡤⣤⠤⠴⠋⣠⠀⠙⠛⡁⢾⣀⣀⣀⡴⢣⣄⠀⢹⠀⠈⣇⡈⠛⠛⠋⢀⣀⡈⠉⠉⣠⣄⠀⠉⠉⣩⣀⣀⣀⣤⣀⣀⡰⢦⣀⣠⠤⠶⡄⢸⠀⠀⢸⣇⣨⠟⠁
⡞⠓⠲⠶⠒⠋⠈⠓⠚⠛⠓⠶⠶⠶⠖⠚⠁⠈⠙⢻⡆⠀⣿⠙⠲⠶⠖⠋⠀⠉⠉⠉⠁⠈⠙⠓⠋⠁⠈⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⡏⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⡇⡼⠀⠀⢸⠁
⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠶⠾⠁⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⢠⢞⡏⠀⠀⠉⠀⠀⢀⣿
⢻⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⢠⠿⡷⢤⣀⣀⣠⢞⣏⠀⢀⣄⠀⠀⠃⢀⡀⠀⠀⠁⠀⠀⣠⡄⢠⢤⡀⠐⠀⡀⢀⡘⢦⣙⠒⠦⠤⠤⣒⡿⢹⡄
⢸⠀⠀⡀⠀⠀⢰⠛⡆⠀⠀⡴⣄⠀⢸⠀⠉⠒⣦⠥⠶⢻⠉⢧⡞⠈⡆⡀⢰⠏⠙⣤⡼⠶⡆⠀⡟⠈⠁⠀⢷⠀⠀⡟⠚⠙⠚⢹⡏⠛⢻⠻⡇⠀⢸⡇
⠘⠧⠞⠉⡆⠀⣟⠀⢧⠀⢸⠀⢸⣀⡿⠀⠀⠀⢹⠀⠀⢸⠀⠀⠀⠀⣧⠀⢸⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⠃⠙⠦⠼⠁
⠀⠀⠀⠀⢳⣀⡇⠀⠘⠳⠞⠀⠀⠉⠁⠀⠀⠀⠘⣇⠀⡾⠀⠀⠀⠀⢻⠀⢸⠀⠀⠀⠀⠀⣟⢀⡇⠀⠀⠀⠘⣦⡼⠁⠀⠀⠀⠀⠳⣤⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣄⣀⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠲⣤⣀⣤⠴⠂⠐⠦⣤⣠⣤⠖⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣧⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⣼⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣩⡄⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠛⠛⢻⠀⠉⠀⠀⠉⠀⡟⠛⠛⠛⠛⠛⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠀⠀⠀⠀⠀⠀⠍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠒⠚⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⣋⣭⣤⡀⠀⠀⠠⠾⣥⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠿⠶⠶⠾⠛⠛⡿⠀⣀⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠚⣛⠉⢉⠡⠄⠀⠀⢂⣰⠀⠀⠀⢰⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⢩⡅⠀⡒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣋⢅⠀⠹⢄⡀⠁⠈⠀⠀⠀⠤⠆⢀⣁⣁⣥⣤⡤⠶⠶⠿⠷⠶⠶⠶⠶⣶⣶⠾⠛⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⠄⢄⠏⠀⡂⠤⠂⣉⣠⣤⠴⠶⠖⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠠⠀⣀⣤⠶⠛⢉⠄⠀⢰⡇
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠙⡀⡘⠀⣉⡴⠞⠋⠉⠀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣠⣤⠴⠞⠛⢉⣠⣄⠒⠀⠚⢒⣾⠁
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠤⢋⡴⠞⣁⣤⡴⠖⠛⠋⠉⠉⣁⣠⡤⠴⠶⠛⠛⣩⠩⠀⠤⠀⠐⢱⡄⠁⢂⠀⠂⢠⡟⠁
⠀⠀⠀⠀⠀⢸⠀⠀⣠⣾⣿⠖⠋⠉⠀⣀⣤⠴⠖⣛⠉⡉⠀⠰⡂⢀⠛⠀⡄⡤⠆⠆⡃⠸⠬⠈⠀⣉⡤⠞⠉
⠀⠀⠀⠀⠀⢸⣧⡾⠟⠉⠀⠀⣠⡴⢚⠉⡔⠂⠰⠈⠤⠢⡀⠁⠓⣂⠠⡤⠠⠂⠀⠈⢉⣀⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⢞⠥⣰⠈⢂⣹⣄⣤⠶⣎⡴⠶⠞⠛⠛⠛⠛⠛⠓⠶⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⠰⡈⡄⣾⢁⡀⣉⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠴⣶⣚⠋⢹⠃⠀⣀⣽⠿⣇⢀⣽⡟⢧⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠈⠙⠓⠶⠦⢤⣤⣀⣀
⠀⠀⠀⠀⠀⢀⣤⣟⣁⣸⣧⣾⡿⠃⠀⠙⢶⠈⣙⠊⠁⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠦⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⣿⠃⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⠁
⠀⠀⠀⠈⣷⢤⣀⠀⠀⠀⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠞⠁
⠀⠀⠰⣦⣬⣧⠉⠳⢦⣀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⢖⣲⠾⠟⠛⠉⠙⠉⠣
⠀⠀⠀⠈⠳⣤⠀⢠⠶⣿⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⢦⣄⡴⠋⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⢳⡟⠠⠺⠝⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⠄⡀⢈⡳⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠸⣧⡡⠳⠂⠐⠬⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣅⡐⠈⠷⠈⠛⠲⠶⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠦⡊⠀⠀⠀⣙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠲⠶⢤⣬⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⢠⡢⠊⠣⢈⡙⢦⣀⠀⠀⠈⠳⠦⣤⣄⣀⣀⣤⠤⠶⠶⠶⠶⡶⠤⢤⠤⡶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣅⡒⢡⡰⢉⠆⣨⡓⢦⣄⠀⠀⠀⠀⠈⣷⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⢬⠃⢀⠔⡬⠙⡲⢤⣀⠀⢹⣧⡙⠲⣤⡀⠀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡒⠈⠃⡐⡙⢂⢨⠝⠲⠿⣽⣦⡀⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣕⡁⠀⠂⠀⠮⡁⢠⣿⣁⠀⢶⡶⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠮⣧⡴⠋⠀⠈⠙⠓⠿⢷⡄

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠿⠿⠿⠿⠷⢶⣦⣄⡀
⠀⠀⠀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣉⠛⢷⣤⡀
⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠙⢷⣆
⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠳⡄⠻⣧⡀
⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⣦⣄⡀⠀⠀⠀⠀⢀⢻⣇
⠀⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣀⠀⠈⠀⣿⡄
⠀⠀⠀⠀⠀⠉⠛⠿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⣶⣦⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⠶⠶⠶⠶⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣰⡿⠁⠀⠀⠀⣠⣾⠟⠉⠀⠀⣴⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢰⡿⠀⠀⠀⣠⡾⠋⠁⠀⢀⠀⡐⠁⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣿⠃⠀⣠⣾⠟⠁⠀⠀⢀⣠⠞⠁⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡿⠀⣴⡟⠁⠀⠀⠀⠒⠉⣀⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⣼⠏⣀⣤⣤⣶⡶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠾⠿⠿⠷⢶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠛⠉⠁
⠀⠀⢀⣠⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢤⣈⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋
⠀⠠⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣌⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠰⢶⣦⣤⣀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣦⡀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄⡀⠀⠀⠈⠀⠹⣷⡀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢶⣦
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀⠀⠀⠙⣇⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⢸⣦⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡈⣿⡄⢠⣿⠁⠀⠀⠀⢀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣹⣷⣾⣇⣸⡏⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⠃⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⡸⠂⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⣰⡿⠁⠀⠀⠀⠀⠀⢠⣼⠟⠁⠀⠀⠀⡴⠃⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣰⡟⠁⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⣠⠞⢁⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⡿⠁⠀⠀⣠⣴⠿⠋⠀⠀⠀⢀⠀⠀⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⢁⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣴⡟⠁⠀⠀⢀⣀⣠⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣤⣶⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠾⠿⠿⠿⠷⣶⣦⣄⡀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣠⠞⠁⠀⣀⣤⣴⡶⠿⠿⠷⢶⣦⣤⣀⠙⢿⣾⣿
⠀⠀⠀⠀⠀⠀⣠⣾⠋⢠⠞⠁⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣹⣿⡀
⠀⠀⠀⠀⠀⣰⡟⠁⠴⠃⠀⠰⠟⠁⠀⠀⠀⠀⠀⣠⣴⠶⠿⠛⠛⠿⠾⣿⣿⣿⡇
⠀⠀⠀⢀⣾⠟⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿
⠀⠀⣠⣾⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⣴⣿⣁⣤⣤⣤⣤⣤⣤⣴⣶⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠁⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣾⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠉⠓⠢⠤⠏⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡖⠒⠒⠋⠀⣀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢳⠀⠀⢀⡎⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠠⠒⠋⠀⠀⢈⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠤⡄⢠⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⡄⠀⢰⣀⡀⠀⠀⢏⠴⠛⠐⠒⠒⠂⠀⠀⠀⠀⠢⠀⠀⠀⠀⣠⠄⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⣆⠀⢣⡀⠀⠀⡛⠐⠶⠄⠀⠀⢤⠠⠐⠀⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠨⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣞⡄⠀⠉⠒⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠐⠲⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡃⠀⠀⢧⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⣉⡀⠀⢣⠀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⢭⣳⡀⢳⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⡀⠙⣆⠀⢳⠃⢹⠉⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⢸⠦⣼⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢳⠼⣦⡇⠀⠀⠌⠀⠀⠀⠤⣆⠀⠀⢐⡲⠶⠾⠛⠛⢾⣋⣼⢣⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠓⠨⠄⢀⠈⢁⡐⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⡟⡀⠱⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠃⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡈⠠⠤⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠰⠖⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣄⡤⠇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡇⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣇⣠⠁⢀⡀⠀⢀⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢒⣛⠀⠀⣏⣸⡏⠀⠀⢰⡛⠭⢀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⣉⡁⠁⠈⠁⠀⡐⠂⠢⠴⠀⠀⠐⠭⢓⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠼⠭⠯⣿⣑⣐⠇⠀⢀⡰⠶⡞⠉⡇⠀⠉⠐⠮⢑⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣚⣹⡛⠤⠤⠀⠠⠴⢦⣚⣻⣉⣲⠄⠀⠀⠈⠒⢬⡷⠦⣄⠀⣀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠂⠈⠋⢀⣀⣤⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⢉⡠⠔⡒⠟⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠀⠀⠠⠠⠀⠠⠰⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠠⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣴⣿⡧⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣼⣶⡄⢠⣿⣿⣤⣿⣿⣶⣶⣿⣿
⠀⣀⡆⢠⣾⣆⠀⠸⣿⣧⣼⣿⣿⣷⢆⣴⣧⡀⠀⣼⠀⠀⢀⣿⡀⠀⣸⣿⡗⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣷⣼⣿⡟⢺⣿⣿⣿⣸⣿⣯⡷⢲⣿⣷⣀⣴⣿⣿⣀⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣅⣼⣿⣿⣅⣽⣿⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢲⠀⠀⠸⠭⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣄⣈⠇⠀⠀⢠⠖⠒⠖⠒⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⣽⠖⠒⢢⢀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢼⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠦⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠙⠁⠀⢠⢄⡀⠀⠀⠀⠀⠀⣰⣧⣀⣀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⡀⠣⢨⠝⠀⠀⠀⠻⡏⠐⠒⣀⠜⠀⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⣖⣉⣻⣈⣳⣎⣀⣀⣀⣀⡠⠤⠤⢤⡧⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠙⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣲⠊⠣⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠄⢰⠓⡄⢠⠊⢣⠀⠖⠆⠠⢲⠀⡏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠸⠀⠃⠘⠀⠈⢰⠀⠀⠀⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡈⠀⠀⢰⠀⠀⠀⡄⠀⡆⡅⡘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠆⠆⠀⢀⠀⠀⡇⠀⠃⠇⠇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⣠⢠⢀⠈⢄⡠⠰⣠⠀⣤⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⡼⠉⠉⢷⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⠶⠦⠴⠶⠲⣶⣀⣀⣀⣀⣀⣤⣤⠤⠤⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣻⣄⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠝⢽⠭⡢⣱⠑⠀⢤⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠒⠒⢄⠴⠊⠁⢱⠊⠀⢈⣳⣄⠔⢭⠎⣰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠭⠽⢷⡾⠦⢤⣠⠎⠀⠀⠸⢋⣉⢳⢄⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠉⠉⠉⣡⠙⠶⠊⠀⢠⣶⠆⠀⣤⣴⠿⠋⠉⢉⠐⠢⡄⠀⠀⠀⠰⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⡀⠀⠀⠀⣀⠔⠁⠀⠀⢀⣔⡧⢁⣠⠴⠿⣀⠀⠀⢀⠆⠀⢀⠇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠈⠉⠉⠉⠀⠀⢀⣠⠶⣉⢎⡔⠁⠀⠀⠀⠈⠳⡄⠘⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢩⠼⠊⢁⡎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢺⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠶⠒⢤⣈⡬⠄⠉⠁⢇⠉⠀⠀⠀⠀⢀⣀⡠⠔⠊⠁⠀⠸⣄⣂⠀⠀⠀⠀⠀⢸⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡜⠁⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⠿⠆⠀⠀⠀⠀⣇⢀⠎
⡠⢮⠿⣳⢊⡱⠀⠀⣃⣤⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠄⠐⠒⠚⠀⠀⠀⣸⠁⠈⡻
⢩⠁⠀⢠⢃⡠⠐⠊⠁⠀⠈⢉⣗⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠒⡶⠀⠒⠈⠁⡃⠀⢀⢃⠀⢰⡁
⢈⠃⠀⡜⠇⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠉⠙⠓⠶⠖⠠⠤⣄⣿⠀⠀⠀⡘⠀⠀⠀⠘⠅⠲⠀⢰⣺⠁⡜⠁
⠸⠀⡠⠤⣞⣀⠔⠊⠉⠚⣄⠀⠀⠉⢐⣒⣶⡖⠛⠛⠛⠛⠛⢋⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠈⣉⣀⣤⠇
⠈⠊⠁⠀⠉⠀⠀⠀⢠⢤⣌⡩⠍⠬⠷⠌⠙⠓⣶⠠⠤⣄⣀⠀⠀⠀⠨⠀⠀⣀⡠⠤⠐⠊⢯⣸⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣡⠤⠦⠴⠖⠒⠂⠈⠀⠀⠀⠀⠀⢉⠃⠒⠖⡚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⣠⣠⣠⣀⡤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠛⠛⠛⠛⠛⠩⢥⣋⠹⢿⣿⣷⣖⢂⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢥⡄⠩⠽⠿⣧⠛⣿⣷⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠦⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢤⣿⣿⠏⣍⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣷⣿⣶⣶⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⠠⠀⠀⠀⠀⡀⣀⣠⢀⣶⠿⣶⡀⠀⠀⠀⠰⣆⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠟⠫⡀⠀⠀⠀⠀⠀⠀⠈⠉⠸⣿⣷⣾⡿⠦⠀⠀⠀⠉⢁⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠂⣶⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡘⡟⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠡⢂⣠⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣽⣿⡛⣿⣤⣬⠁
⠀⠀⠀⠀⠀⣀⣤⠞⣡⢴⣟⣽⣿⣿⣿⣿⡿⠿⣿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢼⣿⣿⡿⡟⢿⠷
⠀⠀⠀⠀⠸⠽⣕⠉⢽⡞⣙⢈⠹⣟⡙⠭⠔⢊⢅⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡜⣿⢾⢆⠁⢀⠐
⠀⠀⠀⠀⠐⢤⣬⣃⣘⣁⣀⣀⣥⣤⣤⣴⡶⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣠⣧⣯⡼⡼⣧⢿⠫⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠁⠛⠓⠀⠠⠤⠤⠤⠤⠤⣤⣀⣀⡀⣀⣀⠄⣀⣤⢤⢶⢾⣿⣿⣿⣿⡿⣧⡅⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⢸⠄⠙⠸⠘⠈⡉⡆⡍⡁⣷⠞⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣧⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣬⣶⣦⣿⣵⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢀⣠⣀⡤⠤⡀⠀⡀
⠀⠀⠀⠀⣀⠀⠀⠀⣠⡖⠂⠀⡀⣀⣤⣤⣦⣶⡯⠋⠐⠟⠉⠉⠉⠉⠛⠛⠁⠂⢀⠠
⠀⠀⠀⠀⣿⣇⣠⣶⣿⣇⣠⣶⣿⣿⣿⡏⣟⣭⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢙⡿⠛⠛⠻⢿⡿⠀⠈⠙⠧⡥⠟⠛⠌⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠻⠂⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⡀⢠⣀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈⢀⡀
⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠠⣠⣦⣤⣾⡶⠀⠀⠀⢀⣴⣶⠶⠀⠀⠀⠀⠀⠀⢺⣌⢷⣎⡀⡦⢬⣣⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⢖⡛⢻⣻⠛⢋⠁⠀⢀⣀⣼⡿⢿⠳⠂⠆⠀⡀⢠⣬⣶⣄⠽⣿⠿⡿⢾⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠤⠴⠋⠀⠐⠓⣺⣭⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣾⡾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠟⠈⠁⠀⠀⠸⠹⠈⠂⠀⠈⠙⠛⠛⠿⠿⠾⢿⣿⣲⣄⠤⠄⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⡈⣿⡉⠉⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢻⣿⣿⣿⡿⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⣤⣻⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢤⣼⣾⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠀⣴⡎⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⡙⢷⡀⠀⠀⠀⠀⣀⠔⢺⣿⣤⣴⠀⠀⠉⠋⠁⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⢸⡇⠀⢀⠄⠊⠀⠀⣷⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠀⣠⢞⣵⠖⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⠀⠠⠐⠮⢀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠀⠀⠀⠀⠀⢿⡟⣿⣧⠞⣱⠟⠁⠀⠀⠠⠀⠈⢉⠉⠛⠛⠻⠗⡒⠤⣀⠀⠀⢴⣿⣴⣿⣿⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⡿⠀⠀⠀⠀⠀⠀⣰⢃⡾⢁⡴⠋⠀⠀⣀⡄⠈⠟⠀⠀⠀⠀⠀⠈⠑⠦⡙⠲⣌⠙⠻⠃⠉⠉
⠀⠀⠀⠀⠀⠀⢠⣄⣀⡀⠈⠀⠀⠀⠤⣶⣄⣠⢇⡞⣴⢋⣀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠈⠱⢄
⠀⠀⠀⢠⣔⣒⠐⠀⠰⠁⠀⠀⠀⠀⠀⠺⡛⠛⢿⣡⠟⠁⠀⢀⠀⠈⢢⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢇
⠀⠀⠀⠙⠈⠁⠐⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡎⠀⠀⢰⠿⣻⣶⣿⠗⠤⠀⠀⠀⠀⠀⠀⢰⠂⠡⠘⡠⠎⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⢀⣀⣴⡾⡄⢀⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠻⠿⠟⣿⣗⣾⡆⠀⠀⠀⠀⠀⠀⢡⡀⢌⣶⠀⠀⠀⠀⠀⢠⠠⢘⠿⣿⣿⠂
⠀⠈⠛⠻⡿⢿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠉⢻⣿⡀⠀⠀⢤⣄⠂⠀⠈⠶⠞⠀⢀⠀⠀⠀⠀⠀⠃⢿⣷⡿⣿⣿⡆
⠀⠀⠀⠀⠀⣼⣶⣲⣖⢀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡇⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠽
⠀⠀⠀⠀⠀⠀⠋⢍⣧⡀⠀⠐⠦⠀⣠⣿⣿⠿⠿⠟⠻⠿⢿⣿⣷⣤⡀⠀⢀⣀⠐⣿⣟⣻⣿⡇
⠀⠀⠀⠀⢨⠀⢀⣠⡀⠀⠀⠀⢀⣤⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⢫⣭⡅⢐⠋⠉⠑⢄⣈⡝⠋⠉⠉⠙⢶⡀⠀⠀⢴⣿⢧⠐
⠀⠀⠀⠀⠈⠧⣈⣛⠝⠀⠀⠀⢸⡇⠀⠀⣀⢴⣿⣶⣦⠀⠀⠀⠀⠙⣧⡀⠙⠋⢀⡾⠋⠀⠀⣠⢰⣦⠀⣣⠀⠰⡿⠿⠟⡏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣾⡿⠿⣻⣧⠀⠀⠀⠀⢻⡭⢿⣿⡟⠀⠀⠀⠀⢷⣸⠿⣠⠟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⡗⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⠀⢇⠀⠀⠉⠉⠁⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠈⠓⠤⣤⣤⡤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⠻⠟⣿⡋⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⡴⠦⠀⠈⠛⠁⠛⠿⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡆⠀⠀⢠⠞⠀⠀⠚⠂⠀⠀⠀⠒⢤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⠀⣤⣶⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣄⡀⣠⡀⠀⠀⠀⣿⠟⠀⠀⣾⣿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣆⣾⣶⣄⠘⠃⠼⠧⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⣠⣎⣁⣀⠀⠈⡃⠀⠠⠤⠛⠀⣀
⠀⠀⠀⢸⡆⠀⣴⠀⠀⠀⢻⣏⠉⠉⠐⣾⠀⢀⣀⠠⠶⣄⠉⣀⠀⠀⠀⠀⠀⢀⣀⣀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡆⠀⠀⠈⠓⠀⠈⠛⠛⠶⠿⣿⡷⣤⣴⣿⡖⠃⣀⠀⠀⠋⠀⡈⠘⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡛⠉⠋⠀⢋⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⣯⣄⠀⠀⡹⠇⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⣹⣶⡄⢀⣀⠀⠀⢀⣉⡹⠷⢦⣤⣄⡀⠀⠀⠀⠀⣀⣤⡄⠲⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡏⠀⡆⢸⣆⠀⢠⡌⠃⠀⠀⠀⠈⠈⠿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠿⣆⠘⢿⡀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠈⠲⠟⠁⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣿⡟⠛⠘⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⢻⣶⡞⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣽
⠀⠀⠀⢠⡄⠀⢾⣀⣉⣁⣤⣤⣿⠀⢸⡇⢠⡆⠀⠀⠀⠀⠀⠀⠠⣆⠹⠀⢸
⠀⠀⠀⠈⠁⠀⠀⠉⠉⠉⡘⢻⠟⣦⣼⡇⠘⡇⠀⠀⠀⠀⠀⠠⠆⢸⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡴⠃⠀⠙⢹⣿⠆⢣⡀⠀⠀⠀⢀⠇⢀⡌⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⡏⠀⢸⡇⠀⠀⢀⠟⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣀⠁⠀⠸⡇⠀⠀⠿⠀⠀⡈⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⢸⠀⠀⢰⡇⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠼⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠶⠶⠶⠖⢀⣼⡇⠀⠀⠀⠀⠀⠈⣧⣤⣤⠄⠒⠒⠒⠂⣠⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣶⣶⣶⣶⣶⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣶⣶⣶⣶⣶⣿⣤
⣿⣿⣿⣿⣿⠿⠛⢿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⡿⢿⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⣰⣿⠇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢿⣷⡀
⢠⣿⡏⠀⠀⠀⠀⠀⠀⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠃⠀⠀⠀⠀⠀⠈⣿⣧
⣸⣿⠁⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⢹⣿
⣿⣿⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠙⠛⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⢀⣤⣄⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠻⣿⣶⣿⠟⢿⣷⣾⡿⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁
⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⡿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣲⣯⠤⠶⠒⣒⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠊⠉⠀⠀⠘⠉⠉⠉⣉⣩⡭⠽⠶⠦
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⠭⠝⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠉⢷⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣞⣀⣀⠀⠀⢀⣀⣀⣀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣞⣉⣡⡤⠤⠤⠭⢽⡯⠤⠤⠤⠤⢵⠄
⠀⠀⠀⢀⡤⠒⠒⠢⣄⡇⠀⠀⠐⠓⡒⠒⠠⠤⠄⠒⠊⠙⠒⠒⠲⣖⡭⠖⠲⣄
⠀⠀⢀⡏⠰⠞⠓⠆⠈⡁⠀⠙⣆⢙⠦⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠀⠠⠾⣁
⠀⠀⠘⢄⠠⠤⠒⠈⠀⠈⠲⣄⠈⢿⡀⢰⠁⢠⠏⠉⡽⠉⠉⠀⠀⠀⠀⠀⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠉⠳⠤⠮⠤⠴⠛⠇⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⡀⠤⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠇⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⡾⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠲⢍⡑⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠳⠴⠋⠽⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠦⡀⣱⠚⠀⠰⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⡄⠉⠀⠀⡿⠧⠤⢄⣀⣀⣀⣀⣀⠀⠤⠇⠰⠋⣿⢄⠀⠀⡜⢰⠂⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡿⠂⠀⢸⠲⢄⣀⣿⠒⠒⠒⠒⠒⠂⠀⠀⠈⢉⠁⢄⡴⡇⠀⢑⡄⢙⠎⢆⠀⠀⠠⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⣳⠀⠀⠈⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠀⠀⡇⠀⢸⠀⡎⠀⠎⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠉⣿⣟⠁⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠪⡀⠀⡇⠀⡼⠀⡇⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⡇⢻⣤⢄⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣴⠇⠀⠇⠈⠁⠀⠀⠀⠀⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡨⠝⠧⠼⠍⠉⡗⡶⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠂⠀⠘⡄⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢰⢣⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠎⡞⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢻⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠇⠀⠶⠶⢾⠾⡃⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠺⡄⠀⠀⠀⠀⠀⠑⢢
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⡇⠀⠀⣮⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢠⣰⠇⠀⠀⠀⠀⠀⣴⢶⡢
⠀⠀⡖⠋⠉⠉⢹⣟⡟⢛⣛⡿⠿⢿⣿⣛⣛⣫⣋⠉⠉⣙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠛⠿⠶⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠓⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠆⠀⠀⠀⠀⠀⠀⠤⠶⠶

⢦⣼⠀⡌⣿⣿⡆⢻⡰⣴⣃⡶⠋⠹⢲⡼⠀⢠⡸⠀⠀⢸⡄⢴⠥⣰⣷⡞⢻⡈⢸⣿⣿⣧⢸⣿⣀⢼⢿
⣛⣿⣇⡿⣿⣿⣷⠋⣷⠋⢸⠀⣥⠟⡼⠓⠂⢩⡤⣰⠀⠈⢷⡘⠮⢼⡞⣷⠀⢻⣾⣿⣿⣿⣾⣿⣸⣽⣿
⠘⢧⣸⣧⣿⣿⣿⣼⠉⣧⡯⣂⡴⠚⠁⠀⢐⠘⠆⣬⡳⢦⡈⢷⡤⣉⣿⡜⣄⡄⠹⣿⣿⣿⣿⣿⢉⣿⣿
⡦⣹⡟⠈⣿⣿⣿⣇⣾⣿⡞⠉⠀⢬⠌⣠⠀⠤⠄⠰⠭⠵⢿⣿⣷⣌⣐⠿⣎⠻⣄⣿⣿⣿⣿⣿⣼⣿⡷
⣷⣼⣷⣞⣿⣿⣿⠞⢡⡿⢀⣤⣉⣤⣞⠚⠯⠀⠀⠉⠊⠀⠀⠀⠉⠻⢾⣝⠾⣿⡟⣿⣿⣿⣿⣿⣿⣯⣏
⠸⣏⣿⣿⣿⣿⣿⢸⡿⣷⣩⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣿⣿⣿⣿⣿⣿⣦⣾
⠀⢹⣏⣸⣿⣿⣿⣿⣋⡽⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢹
⢀⡾⠙⣿⣿⣿⣿⣏⠿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢸
⣼⠁⢰⣿⣿⣿⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⡇⢸
⣏⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⣿⣿⣿⣿⣿⣧⢠
⣿⡟⢰⣿⣿⣿⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠤⢻⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⡏
⣿⣇⢸⣿⣿⣿⣿⣧⡀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡇⠉⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣾⣿⣿⣿⣿⣿⡘⣌⠂⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⣴⣿⣿⣿⣿⣿⣿⣇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⡿⣝⡞⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⢸⡷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢹⣸⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿
⢋⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡕⠀⠀⡀⢀⣀⣀⣠⣤⣤⡤⣶⣷⣿⣿⡟⢻⣿⣿⣆⣿⣿⣧⢻⣿
⣾⠃⣸⣾⢻⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣦⣴⡷⠛⢋⣭⢿⣉⣴⢿⣿⣿⣿⡿⣠⣾⣧⢻⣇⠟⣿⣞⣷⣻
⡟⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣷⡟⢣⣾⣱⣷⣟⣿⣿⣿⢇⣿⣿⣿⣾⣿⣷⣻⣿⡟⣿
⣷⠀⣿⡟⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣷⣿⣿⣿⣿⡏⣽⣿⣿⠸⣿⣿⣿⢣⣿⢹⣿⣿⣿⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠒⠒⠂⠀⠀⠐⠒⠒⠒⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠶⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠶⠶⢦⣤⡀⠀⠀⠀⠀⣾
⠘⣇⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣅⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⢠⡟
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠶⠶⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠶⠶⠶⠞⠋⠁⠀⠀⠀⣸⠃
⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠶⢶⣤⣤⣀⣀⣀⣀⣀⣤⡴⠶⠶⠖⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⣧⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⠇⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⣠⣴⠶⠶⠚⠛⠛⠛⠛⠛⠛⠶⢶⣤⡀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣾⣋⣁⣀⣀⣤⣤⣴⠶⠶⠶⣤⣤⣀⣀⡀⠙⣷⣄⣤⡾⠋⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣓⣒⣦⣔⣶⣤⣴⣶⣞⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣓⡦⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡴⠖⠚⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⠁⣠⡶⠉⠀⠙⠳⣝⡆⠀⠀⣠⡴⠋⠉⠙⠋
⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡟⠀⠀⣦⠀⠀⠀⠉⠲⣴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⠁⠀⠚⠁⠀⠀⠀⠀⠀⠘⣾⡄⠀⢸⠁⠀⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣟⠛⠃⢀⣴⠀⠲⠦⣀⠀⠀⠀⠀⣸⠀⠀⢹⣷⡀⠘⣇⠀⠳⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⠃⣀⡼⠀⠈⠓⠀⠀⣠⠏⠞⠀⢀⡇⠱⡄⠈⠳⢦⡙⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⢀⣀⣀⡀⠔⠁⠀⠀⢀⡼⣧⠀⠙⣆⠀⠀⠙⠲⣝⣦⡙⠦⣄⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣝⣒⣾⠋⠉⠛⠲⢾⣉⡁⠈⠳⢄⡈⠳⢤⡄⠀⢀⣹⣿⣷⣄⣙⣦⣤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣒⣒⣒⣒⣀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠷⠶⠶⢄⠁⠉⢙⡛⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⠀⠀⢀⣀⣀⣀⠹⣎⢻⡄⠈⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠙⠇⠹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠂⡀⠤⠀⠚⠛⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣧⡀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣧⣿⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢰⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠆⠀⢀⠄⠀⠀⠀⠿⠃⠀⣀⠤⠙⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⠏⠈⠀⢀⡴⠋⠀⠀⠀⣀⣤⠖⠋⠁⠀⠀⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⢱⠀⠀⠀⠀⢀⣤⣿⠋⠀⣀⡴⠋⢀⣠⣴⠞⠋⠁⠀⢰⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⣀⣴⣿⠟⣡⣴⣾⡥⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠿⠛⠛⠋⠀⠉⠛⠉⠉⠀⠒⠒⠂⠠⢄⣀⣀⣠⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⢰⡇⢀⣴⣶⡿⠿⠛⠉⠤⠀⠒⠒⠒⠲⠦⠤⣄⣀⡀⠀⠀⠈⠛⠀⠀⠀⠈⢻⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠇⠀⠀⠀⠀⣠⣾⡿⠛⣁⣤⣶⣶⣾⣷⣾⣿⣿⣿⣶⣶⣦⣤⣉⠛⠧⣄⡀⠀⠀⠀⠀⠀⠘⢻⡿⠹⠿⢿⣷⡄
⠀⠐⠲⣄⡀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⣠⣾⠟⣩⣴⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉⠉⠉⠛⠿⢿⡻⢦⣌⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⡀
⠀⠀⠀⠙⣿⣦⣄⠀⣀⠀⠀⠙⠋⠀⠀⣴⡿⢋⣼⣿⣿⠟⠛⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣝⢷⣄⠁⠀⠐⠷⠆
⠀⠀⠀⠀⠙⣿⣿⣾⣿⠀⠀⠀⠀⢀⣼⡟⣳⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡹⣆
⠀⠀⠀⠀⠻⣿⣿⣿⡟⠁⠀⠀⠀⣾⣿⣿⣿⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣇⠀⢠⣶⡆
⠀⠀⠀⠀⠀⠈⠈⠙⣇⠀⠀⠀⣸⣿⣿⡿⠁⢰⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠲⠄⠀⠀⠀⠀⠀⠀⢡⢹⡆⠈⠉⠳⡄
⠀⠀⠀⠀⢤⣀⣀⠀⠀⠀⠀⢇⣿⣿⣿⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠛⠁⠀⠃⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣆⢸⣿⣿⠀⠀⠀⢠⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠘⡈⣿⣿⡀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢡⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡆⠀⠈⢣⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣒⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⢿⣿⠟⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠹⣿⣿⣿⣭⢴⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡯⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣿⣿⣿⣖
⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣗⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢤⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣉⣤⡄
⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣭⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⣬⡛⢶⣿⣿⣿⣿⣿⡟⢋⣀
⠀⠀⠀⠀⠀⢤⣽⣿⣿⣿⡯⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣻⣟⡍⠻⣾⣿⣿⣿⣿⣿⢿⣛⣩⡀
⠀⠀⠀⠀⠐⢶⣾⣿⣿⣿⣿⣶⡶⢊⣀⢀⡀⠀⠀⠀⠀⣀⡠⠀⠀⠀⡐⢿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇
⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⠈⠈⠉⠉⠉⠄⠄⠴⠤⢯⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣼⣿⡗
⠀⠀⠀⠀⣤⣈⣿⣿⣿⣿⣿⣿⢚⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡥
⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣛⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡀
⠀⠀⠀⠀⠉⠉⠉⠻⣿⣿⣿⣿⣟⠟⠀⠀⢀⣿⠀⡇⠀⡆⢠⡆⣹⣖⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⣽⣹⡆⢰⣤⣿⣞⣧⣴⣧⣸⣷⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣽⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⡀⡀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠉⠻⢿⣿⣿⠻⢻⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⢯⡙⣠⣤⣄⡀⠀⠀⠉⠉⠀⠀⣉⣻⣍⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣶⣿⣿⣿⠟⠛⠙⠁⠸⣿⣷⣾⣿⡆⠀⠀⠀⠀⠘⢿⣿⡼⣇⢀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⠛⠻⠉⠀⠀⠀⠀⠀⡀⠀⠘⠁⢿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠁⢄⡀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣿⡄⠀⠀⣠⣤⣤⣤⣀⡀⠀⠑⠳⣼⡁⠷⠀⠀⠀⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀⢠⣿⠋⣸⠟⣿⣿⣿⣷⣶⣶⣷⣤⣤⣤⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣌⣿⠈⢻⣤⣿⡿⠛⠛⢻⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⠀⠈⣇⢽⠀⠀⠀⢹⣳⣿⢇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠈⢫⣸⠀⠀⠀⢸⣹⠏⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢸⣉⡆⠀⠀⢈⡸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢳⣭⠀⠀⣸⣱⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣧⠓⠊⠑⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣀⣼⡿
⠀⠀⢠⣶⣤⣤⣤⣠⣤⣶⠦⣤⠠⢤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⢸⡆⡇⡛⢿⢸⣿⡇⠶⡎⢰⣦⡿⢻⡇⣿⠉⣇⠃⡏⣿⠙⡏⢠⠶⢿⣷⣿⠐⡉⢴⢸⣔⢾⡐⡇⡇⡇⠃
⠀⠀⠸⣷⣷⣿⣾⣿⢿⠿⠆⢠⡘⣉⡷⠼⣿⡿⢿⡿⠿⡷⠿⠿⣧⣈⣃⣼⣿⣿⣾⣿⢶⠾⡷⢾⠷⠷⠶⠿⠿⠇
⠀⠀⠀⠀⠘⠛⠓⠋⠀⠳⠶⠿⠿⠿⠃⠀⠈⠁⠀⠀⠈⠉⠉⠉⠉⠋⠉⠁⠀⠈⠉⠉⠙⠋

⠀⠀⠄
⣆⡅⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣤⣶
⣿⣿⣿⣧⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣻⡄⣿⣿
⣿⣿⣿⣿⣿⣧⢀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⢀⠀⣀⣸⣿⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣧⣾⣇⣠⣸⣀⣆⢀⠀⣴⣆⣠⡄⠀⣄⢀⣴⣤⣶⡆⣀⠀⡧⣾⣦⣤⣿⣇⣼⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣷⣾⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎⠀⠀⠀⠉⠉⠉⠉⠙⠒⠲⠶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⣠⣶⣿⣿⣷⣈⣿⣝⢿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣀⣀⠀⠀⣠⣾⣿⣿⣟⠷⠞⠉⠉⠉⠀⠟⠿⢿⣿⣷⡄⠒⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢸⣿⣯⣹⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠐⢶⣷⣦⣿⣿⠀⠀⠉⠉⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⡜⠁⢀⢀⣿⣿⣿⣿⣿⣏⣻⠀⠀⠀⣀⠈⠑⡄⠀⠀⠀⠀⢙⣿⣻⣧⡤⠖⠚⠉⠁
⠀⠀⠀⣠⠴⠚⠛⢛⣷⣶⣾⣅⡀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡿⢿⠛⠉⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⣠⠟⠋⠁
⠀⠀⠀⢀⣐⠔⣀⠄⠉⠛⣿⣟⡿⣶⣄⠀⠀⠀⢸⠙⢿⡿⠻⠷⢋⠀⠀⠀⠀⠀⠀⠀⢀⠞⡀⠉⠣⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠉⢻⣷⣶⣤⣠⠄⠘⠿⣾⣿⣷⣄⢀⡼⡆⠠⢐⠀⠀⠸⡄⠀⠀⢸⣶⣄⠀⠆⠀⠙⢢⠖⡠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣁⠄⠈⠿⣭⡻⣿⣼⠃⠄⠨⠀⠀⠀⠙⣆⠀⠀⠙⠛⣀⠤⣢⠖⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠘⢶⣤⡤⢀⡀⠙⠿⣿⣦⡀⢀⠈⠹⣯⣿⣶⣂⠎⠀⠀⣀⣤⣾⡷⠒⠒⠉⠁⣘⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠙⢿⣿⣔⢀⡀⠀⠘⠿⣷⡴⠂⠀⠈⠉⠛⠦⣀⠹⠿⠛⠁⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⡤⠀⢀⠀⠀⠉⠑⠲⢶⣄⣀⠄⠈⠙⠲⢤⣤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠥⣖⠁⠀⠀⠀⠀⠉⢻⣿⣦⣴⠄⣀⠈⢙⣦⣀⠈⠑⠶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣭⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠮⣁⠤⠀⠀⠹⢿⣿⣯⡁⠀⣀⠘⢿⣷⣄⠀⠀⠉⠓⢦⡀⠀⠀⢴⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠀⠙⠻⠿⣌⠄⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠳⡐⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢭⣉⠛⠲⠦⣌⣢⡀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠈⠉⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠾⠳⢦⣀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⢚⣋⣉⣀⠀⠀⠀⠀⠀⢶⡬⣷⣄⠀⠀⠀⠀⠹⡄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⡡⠖⠉⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠙⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⢀⡞⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠒⠒⠒⠶⠤⠈⠳⢄⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢰⠋⡔⠒⢄⠈⢇⡀⠀⠀⠀⣿⠗⢃⠤⠒⠂⠈⠉⠁⠀⠀⠀⠀⢀⡽⠒⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠣⡀⠈⠃⠀⠉⠙⠛⠉⠁⠀⠉⠙⠒⠒⠤⠀⠀⠀⠀⠀⠴⣥⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⢤⠀⠀⠊⠁⢀⠔
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢀⡄⡘⠀⠀⠀⠀⡎⢃⣰⣁⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣠⠎⢻⢡⠀⠀⠀⠀⢈⠎⡠⢤⡧⢀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⢀⡖⠚⠛⠓⠲⢖⠒⠒⠒⢦⣀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠲⢞⠁⠀⢸⠉⠁⠀⠀⠈⠉⠐⠧⠒⡗⠠⡎
⣀⣐⣇⠱⣀⡠⠐⢈⣉⡇⠀⠀⠀⠀⢠⠙⠢⢄⡀⠀⠀⠘⠂⠀⠀⠀⠀⣀⡀⠈⠓⠹⠦⠀⢹⡀⢈⡉⠀⠀⠀⠀⠀⠑⡤⣚⣥⠵⢥
⠑⣤⡬⠀⢀⡐⠊⠥⡄⠙⣄⣀⡠⢤⠇⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠒⠉⠁⠈⢳⠶⠤⠤⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠣⣽⣡⣐⣚⣢
⠈⠃⠄⠊⠁⠈⠉⠉⠁⠀⠈⠁⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠣⡑⣤⠚⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⣢⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⡤⠠⣠⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡇⠸⡀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣼⠀⠀⠀⠀⠲⠓⠒⠳⠶⠆⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡹⢮⡧⡽⠒⠤⢄⣀⠄⠀⢸⡆⠀⠀⢀⣀⠴⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠭⢄⣐⣒⡒⠒⠀⢸⠄⠀⠀⢏⣉⠉⠉⠀⠀⠀⠈⢀⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢦⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠋⠉⠉⠁⠀⠀⠈⠀⠀⠉⠉⠓⠒⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠳⠎⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠙⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⣿⣀⣠⣄⡠⣤⣀⡴⠤⣤⢿⠒⢾⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⣰⠖⠶⠋⠈⠛⠋⠻⠿⣏⡷⠋⠈⠧⣤⠟⢹⡶⠾⠞⠋⠓⠊⠙⢦⣤⣀⣤⠶⠞⠁⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢀⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠖⢦⡀⢠⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢆⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣇⠀⣸⣿⢛⣷⠶⢆⣠⡄⣠⡀⢀⣀⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠓⠚⠒⠚⢷⣞⡛⠛⢻⡿⣷⣿⣄⡧⣿⡾⡟⢺⡾⠏⠈⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⣷⠹⣼⠻⠃⠀⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠿⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡏⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣧⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠁⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⣿⣝⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⡀⠀⠀⠀⣼⣿⣿⣌⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣩⠴⠋⡝⢁⡤⠚⠋⠛⠻⠿⣿⣿⣶⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠈⠛

⣷⣷⣾⣿⣶⣿⣿⣿⣷⣿⣶⣾⣿⣷⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾⣿⣶⣷⣾⣷⣾⣾⣿⣷⣾⣿⣷⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⣟⣿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡶⣦⠖⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⢿⡛⢯⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡟⢿⡉⢧⡈⣧⠈⣧⠹⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⣴⣾⡿⢿⠹⡆⢻⡄⢳⡈⣧⢘⣆⣼⣶⠿⠛⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⣿⡏⢳⡘⣇⠹⣆⣻⣤⣷⡾⠛⠋⠉⠀⠀⠀⠀⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡌⢷⣼⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⢀⣄⣠⡀
⠀⠀⠀⠀⠀⠘⢯⣻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠘⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⣿⣇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡛⢦⡈⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠙⢦⣙⣷⠿⣿⣧⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡿⠋⠀⠘⣿⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠸⣿⡆⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠙⠂⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣴⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⠇⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠈⣿⣇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣿⢷⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢸⡷⠆⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣼⣿⣿⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⡇⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⣿⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣿⡟⠀⠀⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣿⡟⢀⠀⠀⣿⣿⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠉⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣸⣿⣤⣴⡶⠾⠷⢶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢻⣿⠫⠄⠐⠋⠀⠓⠀⠿⢉⡻⣷⡄⠀⠟⠀⠀⠀⢀⣾⡿⠁⠀⠾⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠁⣌⢻⣆⠀⠀⠀⢠⣿⡿⡿⠿⡿⠷⣦⣀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⡄⣀⣴⣿⠋⠀⠁⠀⠁⠒⢊⡻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣄⣀⣀⣀⣀⣥⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣶⣦⣤⣴⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠄⠄⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠋⣍⠀⠀⠒⠂⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢊⠡⠐⠀⢋⠔⠁⠨⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠒⠈⠀⠀⡐⠡⠁⠀⠀⠀⠈⠢⡑⢄⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢣⢆⠜⣐⢠⠀⠀⠀⠀⠀⢶⡈⢆⡛⠊⡃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣀⡡⠶⡰⠂⡀⠀⠀⡠⠈⢻⣇⡠⠓⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠠⠀⠀⣳⢄⣀⣃⣠⡴⠒⣁⡠⠘⠉⡠⠉⡍⢀⠡⡀⠀⠻⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠄⢀⣀⠄⠈⢀⠊⠋⠹⠑⠤⢀⠀⠀⡠⠞⠀⣰⠁⠘⠀⢱⠀⠀⠀⠑⢌⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⠔⠀⠉⠀⠀⢠⠃⢰⠀⠀⠑⢄⠀⠉⠛⢄⡠⠊⠀⠀⡆⠀⠀⡆⠀⠀⠀⠀⠁⠀⠑⢄
⠀⠀⠀⠀⠀⢀⠤⠊⢁⡰⢊⠂⠀⠀⠀⠀⡎⠀⡆⠀⠀⠀⠠⣢⡀⡠⠊⠀⡆⠀⢰⠀⠀⠀⠹⡄⠀⠀⠀⠘⡀⠀⠀⠣
⠀⠀⠀⠀⢠⢃⠔⠈⠀⠀⡈⠀⠀⠀⠀⡐⠀⠀⡇⢀⠀⠀⠀⢻⡨⠁⠀⢠⡆⠀⠘⠀⠀⠀⠀⠙⣄⠀⠀⠀⠱⠄⡀⠀⠁
⠀⠀⠀⠀⠞⠀⠀⠀⠀⢠⠁⣀⠤⠒⢹⠀⠀⠀⠋⠢⡐⢀⠀⠈⠇⠀⠀⡞⡆⠀⢠⠐⡀⠀⠀⠀⠂⠈⠒⠤⡀⠑⣌⠢⣴⡀
⠀⠀⠀⠀⠘⣦⠀⠀⢀⢣⠊⠀⠀⠀⠈⡀⠀⠀⠀⠀⣈⠑⠳⡀⠀⠀⠰⠖⡸⡀⠘⡀⢱⡀⠀⠀⢀⠀⠀⠀⠈⢢⡈⠑⣤⣇⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠸⡆⠀⡞⠁⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠘⢇⡠⠰⡐⡀⠀⢋⠀⠐⡀⢡⡀⠁⠀⠀⠘⠀⠀⠀⢸⣧⡉⢳⡞⣽⣛⣒⣶⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⢀⣀⣀⠀⠀⠀⢄⠐⣀⡙⡄⠀⠈⠉⠙⢵⠀⠸⡀⢀⠸⠄⣳⡀⠙⡀⢸⠀⠀⠀⠀⠙⠙⠿⠞⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⡀⠀⠉⠁⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠈⢣⠀⢓⠀⠀⠀⠉⠻⢦⡙⡈⢄⠀⢙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠲⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡈⠀⠀⠀⠀⠀⠀⠹⠜⢦⣍⠡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠃⠠⠀⠐⠀⠀⠀⠀⠳⣆⠀⣠⠀⠀⠀⠀⠀⠀⠶⢀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣤⣴⢄⠀⠀⠀⢀⠀⠀⠠⣤⡠⠟⢀⠀⠀⠀⠀⠶⠀⢉⡁⠀⣄⠀⠉⠀⠀⠀⠀⠀⢿⣷⡄⠑⠀⠈⠠⡄⠓⠓⠂⠀⠀⠀⢈⡏⠁
⠀⠀⠐⢿⠿⠋⢠⣹⣶⣏⡀⠀⠀⠈⠓⠀⠇⠀⠀⠀⠠⠀⠀⠘⠁⠀⡀⠀⠙⠸⠃⠀⠀⠀⢦⣌⠻⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⡀⠀⠀⠀⠈⠛⣿⠅⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠈⠙⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⢹⣾⡷⡄⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⢀⣀⡀⠀⠐⢈⢨⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠂
⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣀⡀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡤⠀⠀⡀⠰⠐⠃⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⢀⢸⡗⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡀⢠⠀⠉⡞⢀⣀⠀⠀⠀⠈⣿⢀⡞⠀⢀⣀⠀⠀⠀⢸⡄⢀⡠
⠀⠀⠀⢼⡯⠁⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⠀⠀⣀⡬⠉⠁⠀⠀⠀⣿⡜⡇⣠⡟⠁⠀⠀⠲⣾⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠘⢇⡡⡿⠀⠀⠀⠀⠀⠉⠁
⠀⠄⠀⠀⠀⠐⠓⣾⠂⠸⢿⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢠⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⢠⣦⣤
⠀⠀⠀⠀⠚⠛⠡⣾⣟⡳⢄⣻⡼⣃⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠳⠊⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠘⠃⡴⠂⢀⡀
⠀⠀⢠⣄⠀⠀⠘⠉⠀⠉⣵⡾⠉⠉⠁⠀⠀⢾⣧⣷⡄⠀⠀⠚⠃⠠⠾⠲⡀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⢿⣿⣿⠃⠄
⠀⠀⠻⡿⠃⠀⠀⠀⠶⠀⠉⠀⠀⠀⠀⠀⠀⢿⡽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠗

⠀⡀

⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⣤⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠛⠓⣤⡀⠀⠀⠀⠹⢟⣹⣷⠖⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣓⠻⠶⠤⣄⣀⡤⠒⠛⣽⠛⢆⠶⣐⠛⢍⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⣻⣿⢿⢿⢷⡆⢸⠀⠀⠨⢸⡟⠳⣮⡹⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠉⠹⢺⣯⣶⣿⡳⠶⢰⣶⣅⣙⣟⠂⢿⣾⡁⠒⢤⡴⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣠⠛⢻⣾⣿⣦⣄⣩⣼⠿⢷⡿⠋⢿⣶⣿⡟⠻⠙⢿⣄⠉⠙⠃⠀⠈⠁⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠴⠴⣶⣦⢬⣝⣻⣷⣮⣄⠉⣨⡷⠋⣡⣴⣾⣷⠀⣈⣠⣿⣅⣰⡾⢊⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣷⣷⣦⣽⣟⣋⠉⣹⠷⠋⠀⠠⠏⢡⣴⣿⣧⢛⣿⢷⣿⡄⠀⢻⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠙⠛⠁⣽⣟⠋⠉⣹⠟⠁⠀⠀⠀⢀⡰⠿⢿⣿⠟⢩⠟⣻⠟⡿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠤⣿⠿⣟⣉⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⣿⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣶⣀⡤⠤⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠋⠉⠀⠐⠚⠛⠓⣒⣒⠶⠶⠤
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠭⠭⠷⠶⠄
⠀⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠠⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⣀⡠⠄⠀⠀⠀⢰⡒⠒⠒⠒⠺
⠀⠀⠀⠠⠀⠀⣀⠀⠺⠀⢀⡤⢠⡄⠀⠉⠊⠉⠀⠀⠀⠉⠉⠣⠂⠉⠀⠂
⠀⠀⠀⠃⠀⠀⠀⠀⠐⢤⡀⠙⣤⠋⢑⠒⢲⠦⠤⡤⠤⠄⠀⠀⠀⠀⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠲⣜⠀⡜⢀⣰⢥⠀⠀⠀⠀⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠉⠀⠀⣈⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣸⠀⠀⣠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢖⠓⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠳⠤⠎⠵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⡀⢱⠞⠀⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠄⠉⠈⠉⠇⠀⠀⠀⠀⣀⡀⠀⠀⠐⠀⠋⢻⢆⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠘⠀⠀⣨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢥⣀⣀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢻⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠌⠂⠀⣃⠀⡆⠠⠆⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⢤⢸⠸⡟⠰⣄⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡺⠋⠀⠃⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠈⠉⠁⠀⡇⠋⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣸⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⢠⣤⣤⣴⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⢼⠀⠀⠀⠀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⡜⠀⠀⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠠⢠⠇⠀⠀⠀⠀⢠⣤⣦
⠀⠀⣴⠊⠉⠉⢻⣿⢿⣓⣲⠿⠷⣶⣟⣛⣩⡋⠉⢉⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠉⠁⠁⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠀⠀⠒⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢭⡙⠲⣾⠀⠀⢸⡀⣧⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡘⠓⠶⣧⣦⠙⠆⢦⠈⢷⣌⠳⢾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⣁⠀⠀⠀⠀⠛⠂⠈⠳⢤⣈⡉⠀⠀⠙⠷⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⢀⡴⠋⠁⠠⠒⠉⠉⠉⠁⠀⣀⡤⠖⢒⣠⡤⠤⠄⠀⠀⠉⢙⡛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⣰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⠒⠒⠛⠛⠙⠛⠓⠂⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⡰⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠲⣄
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣆
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢻⡀
⠀⠀⠀⠀⠀⠀⡖⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡇
⠀⠀⠀⠀⠀⣸⠁⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢸⡇
⠀⠀⠀⠀⠀⣿⡄⠀⢸⠁⠀⠀⠀⠂⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⢀⡼⣡⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢢⡀⣀⢸⡇
⠀⠀⠀⠀⠀⣿⠃⠀⢸⡆⠀⠀⠀⢀⣤⣤⣤⣤⣤⠴⠖⠒⢾⡆⠉⠛⠋⠛⠁⠀⠀⣄⣀⣠⡴⢻⣿⣷⣦⣄⣀⠀⢹⡏⠘⡇
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠠⠟⠀⠀⠠⠤⠤⠔⡂⠔⠈⠁⠀⠀⡀⢠⡀⠀⠀⠈⣹⠟⠓⠾⠿⣿⣧⣄⣉⣷⠘⡇⢰⠇
⠀⣠⡴⠶⠶⣿⣤⣄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⠀⢠⠊⠀⠲⢤⣤⣤⣤⡄⠀⠀⠀⢸⣇⡾
⡾⠁⣀⣀⣀⠀⠈⣿⠟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⡴⠂⠀⠀⠠⠋⠀⠀⠀⠸⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠟⠛⠛⠳⢦
⠇⠚⠉⠉⠙⢷⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⡶⠶⣤
⠀⡀⠀⠀⠘⠻⣿⢀⠀⠀⢀⠄⠀⠀⠀⠀⣰⠟⠁⠸⣆⠘⠿⢷⡄⠀⠀⠀⠀⠀⣀⣀⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠂⠀⠀⢀
⠀⠹⣆⢀⠀⠀⢿⢸⡀⢠⡏⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⣀⠚⠋⠉⠉⠘⣿⠀⠀⠀⠀⠀⢸⠀⢀⡼⠀⠀⣀⠔⠁
⠀⠀⠈⠻⣆⠀⠼⢸⡇⣾⠀⠀⠀⠐⠁⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⡇⠀⠋⠀⠀⠉
⠀⠀⠀⠀⢹⡄⠀⠈⣿⡇⠀⠀⠀⠀⠀⢀⡴⠟⠛⠹⣄⣴⠉⠳⣄⡙⠒⠤⠤⡀⠀⠀⠀⠀⡟⠀⠀⠀⢸⣾⠃⢀⡤
⠀⠀⠀⠀⠀⠙⠶⠶⢻⡇⠀⠀⠀⣠⠞⠁⠀⠀⣀⣤⡴⠿⣄⠀⠸⡟⠒⠤⣤⣤⣀⠀⠀⢸⠇⠀⠀⠀⣾⡟⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢠⡞⠁⠀⠀⡴⠛⠉⠀⠀⠀⠀⠉⠀⠃⠀⠞⠙⢿⣿⡆⢀⡟⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢴⣻⠖⡼⠁⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠈⠁⢀⡼⠁⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠞⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣤⣤⣤⠶⠛⠉
⣿⣿⣿⣿⣷⡾⢿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣷⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⡿⡿⡿⠿⠿⣿⣷⠿⠿⣿⠿⢿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣠⣠⣤⣤⣤⣴⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿⣿⣿⡛⠛⠛⠿⠿⡿⣿⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⡌⣟⣿⣿⣿⣾⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡠⣄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⢀⣤⠿⠟⠿⠋⠉⠛⠒⠻⠿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠠⣔⣻⡟⠀⠀⠀⠀⠀⠀⣴⣷⣶⣶⣶⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣷⣄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⢻⣿⡇
⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠛⠛⣩⣰⣽⣿⣇
⢰⣿⣷⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠠⣶⣟⣷⡄⠀⠀⠀⠀⢄⡀⠀⠀⠀⣠⣻⣿⣿⣿⡟
⣿⠃⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠁⠀⢴⠞⠾⠶⣷⣿⣿⡅⣠⣶⣶⣿⡟
⢁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠂⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⡄⠀⠀⠀⢀⠀⠀⠀⠀⣈⣿⣿⣷⣿⣿⣿⡿⠁
⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢁⠤⠀⠀⠀⠀⡀⠀⢦⣽⣿⣿⣿⣿⣿⣏⣤⣄⡀
⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣧⡤⢀⣀⣀⠀⠻⣶⣬⣿⣿⣿⣿⣿⣿⣿⡶⠦⠙
⠐⠿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠿⢻⣿⡯⠶⠶⠖⠋
⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡶⠇
⠀⠀⣸⣻⡯⢿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣽⣿⣿⡟⢛⡛⢿⣿⣯⣻⣿⣿⣿⣿⣿⣿⢟⣿⡟⣻⠽⠍⠶⠃
⠀⠀⠀⠀⠀⠀⠸⣽⣿⠀⠀⢸⣿⣿⣿⣿⣿⣟⢿⣧⣿⣿⣿⣿⣷⣄⠛⠻⣿⣿⣯⣿⡟⠿⠿⠍⣿⣿⣩⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⠀⠸⡍⠙⠉⠻⠿⢿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠉⠙⠛⠛⠳⠒⠒⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡉⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⢬⣭⣙⡷⠾⠭⠝⠛

⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣣⠊⠀⠀⢀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢠⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠱
⠀⠀⠀⡀⠀⠀⠈⢇⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡌⠀⠀⢀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢱⡌⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢰⡴⠃⠀⡜⠀⠀⠀⠈⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠆⠔
⠀⠀⠀⠈⢣⡀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠁⠀⠀⠀⠀⠰⡆⢠⠏⠀⠀⠀⠀⢄⠀⠀⠀⠀⠸⣸⠂⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠙⢄⣼⠃⠀⢀⠀⠀⠀⢠⠂⠀⠘⠄⠁⠀⠀⠀⠀⠀⠀⢹⠏⠀⡄⠀⠂⠀⠘⠇⠀⠀⠃⠀⣷⠀⠀⠀⠀⠀⠆⠀⠙
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⣇⠁⠀⠸⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠧⠀⠀⠀⠀⠀⠀⠁
⠸⠇⠀⠀⠀⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⡻⣛⣛⢻⡛⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠴⠗⠒⠒⢲⣄⣤⣤⣀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢰⠙⠂⠀⢀⣀⠤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣤⠏⠸⡄⠀⠀⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠷⠲⠥⡀⠀⠁⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⡔⠅⠀⠐⠀⠘⢄⠀⠀⡠⠛⠉⠙⢋⠿⠛⠉⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢄⠂
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⡠⠊⠁⠀⠀⠀⢘⡤⠄⠀⠠⣇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢰⣁⣠⣄⣤⣤⣤⣤⣤⣤⣤⣱
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠀⢀⠴⠂⠉⠉⠀⠈⠛⠋⠉⠀⠀⢀⣠⣿⣿⣿⢃⠠⠔⠊⣩⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢀⠠⠐⠶⠾⠿⠿⠛⠋⠁⠀⢀⡠⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠒⠐⠒⠂⠒⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠶⢲⡆⠀⠘⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⣤⣀⣤⠴⠦⣄⡀⠀⠀⠀⠀⠀⢁⣴⠋⡀⠀⣴⣏⣤⡄⠀⣴⣋⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠙⠏⠁⠚⠉⠀⠀⠀⢸⡇⣀⡀⠀⠀⠀⠛⠛⠋⠁⠀⠉⠉⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣠⠶⠶⣄⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⣀⡀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠙⢳⡄⠀⠀⣠⡤⠴⠶⠶⢦
⠀⠀⠀⠀⠀⣽⠆⠀⠀⠈⢮⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡶⢿⣤⣤⣤⡄⠀⠀⠀⠘⢿⣦⣼⠃⠀⠀⠀⠀⢘⡷⠶⠤⣤⣀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⢸⡷⠶⠶⠞⠋⠁⢀⠀⠤⣄⡀⠈⠙⢦⡤⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⢷⣶⠒⠒⠦⢤⣀
⠀⢀⣠⣾⣅⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣾⠁⢠⠶⢦⣄⠀⢀⣀⣠⡾⠁⠀⠀⠀⢻⡄⢀⣴⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠸⡏⠳⡄⠀⠀⠈⠉⠓⠦⣄
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⣿⠀⠀⣹⡦⠈⠉⠁⠀⠀⢢⡶⠃⠘⣷⡾⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈
⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠛⠶⠚⢿⠃⠀⠀⣰⠀⠀⢸⡇⠀⢰⡿⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷
⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠘⠦⠤⠟⠁⠀⠀⣸⠇⢀⡾⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⡆
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣷⠀⠀⠀⢀⣀⡠⠋⠀⣾⠃⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡉⠂⠛⠋⠉⠀⠀⣸⠏⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⡳⣶⣶⣤⣤⣴⡿⠀⠀⠀⠀⠀⢀⡍
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣴⠾⠛⣃⠀⠉⠙⠛⣿⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣠⡶⠟⣉⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣋⣴⠿⣫⣾⡿⠛⢾⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠦⣤⣄⣀⣀⣀⣈⣿⣿⡿⠿⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠒⠒⠒⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠐⠚⠋⠁⠀⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⠠⠄⢀⡈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣰⠃⡖⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢱⢀⠞⠁⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠱⠒⠉⢱⡨⠀⠀⠀⠀⣠⡀⠀⠘⡆⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠰⠄⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠄⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠠⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⢀⠀⠂⠀⠤⢀⣀⡄⢄⣸⠛⣯⡲⢂
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠔⡁⠀⠉⠱⠇⠀⢀⣀⠈⠀⠀⠈⠓⠈⠁⠁⡀⠈⣀⠀⠈⡀⠠⠠⠀⡄
⠀⠀⠀⠀⠀⢸⠀⢠⡰⠀⠀⠀⠂⠄⠀⠀⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠙⢠⡄⠁⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠱⡌⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠔⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠂⢀⠒⠁⠀⠀⠀⠀⢠⠀⠀⢀⠀⢤⢀⢲⠀⠠⠀⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠰⢸⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⣀⡀⢙⢚⢀⣀⢘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢙⢛⡟⠛⠛⠿⣛⠛⠻⢿⣉⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣄⠀⠀⣀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⣴⣽⣤⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⢀⢴⣿⣿⣿⣀
⠀⠀⢀⣼⣿⣿⣷⣿⣤⢀⡀⢰⣿⢿⣾⣦⣬⣭⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣭⣿⣫⣍⠛⢿⣶⠄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢱⣿⣿⣿⢿⠉⠯⢠⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⡀⢀⣠⣶⡄⣘⣿⣿⣿⣟⠻⢿⣿⡿⠟⠿⠆
⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢛⡛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣼⣥⣶⠿⠓⠲⠶
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢬⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣷⣴⣾⡟⣰⣆
⠸⣿⣿⣿⣿⣽⣿⣼⠿⣿⣿⣿⣿⣿⣿⣤⡇⠺⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡛⠓⣿⣾⣿⣿⣿⣿⣿⡏⢹⣏⣿⢋⣹⣿⣿⡇
⣤⣿⣿⣿⣿⣽⣯⣾⣻⡟⢻⣿⣿⢿⢿⠉⡇⠀⣿⠉⢹⡟⣿⢹⣿⣿⣻⣿⣿⣿⠷⡿⢛⡃⣼⣿⣿⡿⠀⢸⡭⢽⣼⣿⣿⣿⣿
⠈⠙⢛⣿⣿⣿⡿⢼⢛⡇⢺⠻⢭⢴⢺⢹⠃⠘⢿⡇⢈⡟⢿⠙⢻⡟⣙⡏⣿⠁⠀⡇⢸⠀⢸⣟⣉⡟⠀⢸⡄⣼⣹⣿⣿⡟⣧
⠀⠀⠠⣿⡏⢙⡇⣻⢀⡇⢸⣾⠀⢸⢸⢸⠁⠀⢸⡇⢐⡇⢹⠀⢸⠀⠉⡇⣸⢰⡂⡇⢸⠀⢸⢨⠀⡇⠀⢸⠀⢸⢸⣿⣿⡗⡃
⠀⠀⠀⡋⣇⠈⡇⢹⠀⡇⢸⣿⣶⢸⢸⢈⠀⡇⢸⣷⣼⣇⢸⢸⣸⠀⠀⡇⣾⣿⣇⡇⢸⠀⢸⣤⠀⡇⠀⢸⠀⢸⠈⠹⠿⡇⠃
⠀⠀⠀⣇⡇⢠⡇⣼⣤⣷⣼⣿⣿⣼⣼⣷⣾⣿⣼⣿⣿⣷⣾⣼⣿⣿⣇⣷⣿⣿⣿⣷⣸⣇⣸⣿⡄⣷⣴⣸⠀⢸⠀⣀⡚⡇⠃
⣤⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⢿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠙⠛⠋⢻⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁⠈⠉⠉⠙⠋⠙⠀⠈⠻⡿⠛⠛⠉⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣶⠦⢤⣀⡀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢏⡀⠀⠀⠉⢡⣌⣍⠉⠿⣿⣿⣶⣦⡀⠀⠀⠀⣠⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄⠠⡀⢬⡭⠿⡷⠾⠿⠿⠿⣇⢠⣴⡾⠿⠟⠉⢩⣅⣠⣤⣤⣉⣉⣈⡻⠿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡜⣦⡾⣻⣿⣷⣉⡭⡻⣷⠀⣄⠐⠾⣿⣿⣿⣿⣿⠿⠟⣛⠛⠛⠻⠿⣶⣭⡙⢿⣝⠂
⠀⠀⠀⠀⠀⠀⣴⣶⣒⣛⡒⠻⠹⣧⣥⡟⣸⡗⠻⠾⢟⣼⣿⣿⣶⣌⠻⠟⠋⣠⡶⠛⣡⣶⣿⣿⣷⣶⣍⠻⣦⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣶⣾⡿⢣⣿⣾⠟⣡⣤⣬⡙⠿⢁⢠⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣧⠹⣧⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣦⠘⢿⡇⣼⣿⡟⠛⢿⡄⣆⢸⣿⡇⣼⣿⣿⡟⢁⣀⡀⠙⢿⣿⡄⣿⡄⢹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠈⠷⢸⡟⣴⣿⡌⣷⢸⣄⠻⠇⣿⣿⡟⢰⣿⡟⢙⡀⠘⣿⡇⣿⠃⣸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⡄⢸⡇⣿⠁⠟⢹⢨⣿⡓⠀⣿⣿⡇⣿⣿⣆⠿⠇⣼⣿⠇⡿⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠿⣿⣾⣧⠸⣧⣤⣿⢸⣿⠳⠀⣿⣿⣇⠘⢿⣿⣿⣿⣿⢯⡾⢃⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⠋⢻⣆⠙⠛⠁⣸⣿⢰⣇⠙⣿⣿⣦⣀⠉⠉⠉⠁⣋⡴⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣿⣿⠁⠀⠀⠙⣷⣶⣾⣿⡇⠺⠟⠃⢙⢿⣿⣿⣿⣿⣿⠿⠋⠀⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣼⠏⢷⠄⠺⢦⣿⣿⠉⠁⠀⠀⠀⢠⣭⣱⣮⣭⣭⠍⠀⠀⢀⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⡀⠀⠀⠰⠟⣿⠹⣦⠀⠀⠀⠀⠀⠉⣠⡟⢩⡏⠀⠀⣠⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⢿⣿⣿⣷⣤⡀⠘⠛⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠈⢁⣠⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⠛⢿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣶⠞⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠈⠙⢦⣀⡤⠖⢒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠀⠈⠈⣧⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠄⠀⠀⠈⠉⠀⠀⡠⠤⡴⠛⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡷
⠀⠀⠀⢀⣀⣀⣠⣤⠤⠤⠤⠤⠤⠤⢿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠐⠓⠢⣄
⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⢤⡀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠴⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠆⢸
⠀⠀⠀⡇⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⣤⠤⠤⠖⠋
⠀⠀⠀⡇⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⠤⠖⠋⢧⠀⠀⠀⠀⠀⣄⠀⠈⠀⣠⠇
⠀⠀⠀⣧⠀⠀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⢒⣊⣀⣙⣒⣛⣩⡆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠑⡖⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⡇
⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣇⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⠤⠤⠤⠴⠶⠶⠖⠒⠒⠒⠒⠒⠚⠉

⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣿⣿⡿⠿⠟⠛⠒⠒⠒⠀⠁⠁⠤⠸⠋⠁⠉⠐⠤⠀⠀⢀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠄⣴⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠤⠄⣀⠀⠀⠀⠈⠐
⡿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⣾⣿⣿⣦⡄⠀⢻⣿⣿⠾⢿⠿⠛⠟⠻⠶⢺⣷⠶⠂⠀⠀⠀⠀⡀⠔⢊⣀⡀
⡇⠀⠀⠀⡀⠀⢘⡫⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠫⠛⠀⠀⠀⠚⠙⠌⠉⠉⠀⢀⣀⣴⣵⣾⣿⣿⣷⣶⣶⣦⡕⡀
⢦⡤⢥⡾⡡⣶⢾⠷⠋⡉⢻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⠾⡁⡀⠀⣠⠎⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠁
⠀⠀⠀⢹⡀⢀⣴⡴⠊⠀⠀⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠠⠯⢚⡴⣡⣻⠃⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⢸⡁⠉⡎⠀⠀⣰⡁⢀⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠛⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠋
⠰⣀⣌⡡⠓⣤⠁⠀⠀⣸⢠⡟⠀⠀⠀⣠⡾⠿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠈⠛⠛⢫⡀
⠉⠾⠜⣛⣣⡟⢰⣤⡘⢁⡿⠀⠀⠀⠀⠸⣷⣴⠟⠀⠀⠀⠀⠀⠀⠀⣾⡁⢈⣿⡦⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠈⠀⠛⠁⠙⠁⠸⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⢘⣇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠧⣄⡐⢤⣄⡈⠁⠀⠀⠐⠋⠀⠀⢀⣴⡟⠋⠀⠀⢀⣤⠀⠀⠀⠀⣸⠷
⠀⠀⠀⠀⠀⢀⠂⠀⢰⠰⠂⡀⡄⠀⢱⣄⠈⢩⣦⣴⣦⣴⣶⣶⣸⣿⣿⣿⡟⣿⣿⠟⢁⣼⡟⢠⡷⠛⠂
⢀⠀⠀⠀⠀⢼⢐⣸⣝⠂⠌⠳⠸⢦⡀⠙⡆⢸⣿⡏⣿⠋⠉⠛⢻⡿⢿⣿⢣⣯⡴⣰⡿⢋⡴⠋
⣶⣖⣡⢂⣠⡸⣶⣽⠊⠁⡖⢢⠔⠚⢿⣧⣹⡊⣿⡧⣯⣤⣤⣄⣠⣏⣿⡿⡼⣹⡿⢋⡴⠋
⣯⣥⣦⡀⣹⣯⡿⠯⢡⣤⡤⠼⢦⢔⣶⣽⣿⣧⢻⡗⠚⠋⠉⢻⣿⢼⠇⣻⣗⣧⠟⠉
⣿⣿⣿⣿⣮⣿⡓⢾⣶⠀⡆⠠⡼⢹⣟⣿⣜⣿⡆⠇⠀⠀⠀⠀⡛⣾⠎⢸⠉
⣿⣿⣿⣿⣿⣷⣆⠈⢩⠶⠟⣿⣠⣨⣿⣿⣟⣿⣷⠰⠀⠀⠀⠀⢰⠃⣰⠃
⣿⣿⣿⣿⣿⣿⣿⠇⠉⣂⣿⢿⣿⣟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠒⢠⡶⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣯⠰⢻⠾⣿⢿⣿⣿⣿⣿⣿⠗⢆⠀⠄⣡⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣰⠓⣾⣾⣿⣿⣿⣿⣿⣄⡑⣀⠚⢁⣀⣀⡀⢀⠤⠤⠤⢀⣀⢀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠀⠀⢀⠀⡄⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⣆⢁⡇⠀⠀⠀⠀⠀⢸⣾⠃⠀⣄⢁⢿⠇⠀⠠⠀⠀⢀⠀⠀⡇
⢰⣿⠃⠀⠀⠐⢉⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡀⠀⠄⣠⣤⣤⡚⠃⠀⠀⢸⣿⣹⣷⠰⠀⠀⠀⠈⡄⠀⡷⠀⠄
⢼⣿⠀⠀⠀⠀⠉⠀⠄⠀⢀⠀⠀⠀⠠⢄⠐⢄⠀⠀⠨⢸⡧⣀⠘⢿⣶⡿⠃⠚⠠⣀⣈⠉⠟⠋⠀⠐⠀⠀⠀⠃⠀⠁
⢸⣿⡄⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⢀⡀⠀⢦⠀⢳⣄⠘⣾⡇⢠⠈⠀⢁⢷⡦⠴⢀⣸⡗⠁⠰⠀⠀⠀⠀⠱⠀⢺⠱⡟⡀⠠⣴⢾⣶⣦⠈
⠈⣿⣿⡄⠀⠀⠀⠀⢀⣀⡀⠀⠤⡴⡀⢰⣜⠆⠀⠙⠀⢿⠇⡌⠀⠀⠀⢰⣷⠖⠋⠉⠀⠀⠀⠀⢀⠀⠀⢦⡀⣸⣄⡄⣚⡋⠼⢯⣽⣿⡗⢄⠀⢀⡀
⠀⠘⣿⣿⣦⣀⠀⠀⠀⠀⢄⠀⠀⣀⣉⣠⣤⣴⣤⣴⣤⣼⣄⣻⡃⡸⠃⣘⡣⢀⢍⣅⠀⠈⡡⠀⠢⠄⠀⣈⠙⠵⣿⠀⠉⠄⠀⣜⣩⣿⡋⠱⣶⢋⡀
⠀⠀⠈⠻⣿⣿⣷⣦⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣔⠢⢍⡀⠀⠀⠀⠀⢀⡀⠈⢈⠀⢀⡽⠄⡠⠐⠒⣫⣾⣿⣿⣿⣯⡿⡀
⢐⣒⣀⣦⣈⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠞⣀⡵⠾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣒⡍⡀⠀⢀⣾⡥⠷⣶⣛⣉⣫⣥⣿⠛⠛⠩⠹⠿⠦
⢀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⢸⣿⣿⣯⣲⠀⡴⠋⠀⠀⠙⠿⣟⡿⣿⣿⣿⣦⣴⠀⠀⠠⣮⣤⣬⡿⢷⡐⣈⡿⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠
⢺⢠⡺⠿⠿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡥⠀⢰⠁⠀⠀⠀⠀⠀⠙⡃⣾⣿⢿⣿⣿⣷⣄⢔⠾⠿⠋⠀⢀⣈⠙⠁⠀⠀⠀⣀⣀⣠⣴⣿⡿⠁
⠀⠀⠻⣤⣨⣟⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⠀⠀⢠⣃⡀⠀⠀⠀⠈⠈⠝⠿⣿⣿⣿⣷⡀⠀⣁⠀⠂⠈⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠁
⠈⠀⠀⠹⣆⠀⠀⢠⠟⡿⣿⢿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣧⣄⣨⣿⡁⠀⠀⠀⠀⠰⡶⠖⠚⢻⣿⣿⣿⣄⡀⠀⠀⣀⣼⣿⣿⣿⣿⣋⣿⣿⡿⠁
⠀⢀⡓⡂⢷⡀⠀⠸⡀⠀⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠟⢀⣤⠄⠊⠡⠀⠀⠀⠀⠜⣻⡟⢻⠟⠟⠉⡟⠘⣱⣺⣽⣿⣿⣿⣿⡟⠀⠀⠀⡀
⠀⠀⠈⠁⣸⣷⠀⡿⠁⠀⢤⣀⡛⠃⠈⣿⣿⣿⣿⣿⣿⠞⣿⣿⣿⠛⢁⡆⠀⠀⠀⠀⠀⠀⢀⡍⠁⠘⠀⠂⠀⠁⠰⢬⣛⣿⣿⣿⣿⣿⠃⠀⢠⡴⠖
⢰⠶⣦⣄⣙⣻⠸⣯⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⣨⡿⡆⢻⡇⡧⢀⣼⣷⣶⣄⢀⠀⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⡀⠈⠙⣿⣷⣿⣿⡟⣰⣬⣾⣷⣶
⢨⣰⠏⠉⢳⣿⣞⣿⣿⢿⣧⣻⣿⣿⣟⢿⣿⣿⣿⣿⠟⢉⠈⣿⣷⣿⢹⣿⣿⣿⣧⠘⠃⠀⠀⠀⠋⠀⠄⠀⠣⣀⡀⠀⢘⣳⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠛⠛⠂⠈⢛⣿⣿⢯⠀⣸⡿⢿⣿⣹⣿⣾⣿⣿⣿⣶⣾⣾⣷⠸⣿⡟⣸⣿⣿⣿⣿⠀⠀⠀⠐⠀⠀⣀⠘⠀⠀⠈⠀⢀⢬⣛⣿⣿⣿⣿⣿⣿⣿⢿⡿
⢰⣶⢄⣖⣩⣭⡉⢠⠲⣿⣿⣾⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣧⣿⢿⣯⣿⣿⣿⡿⠟⢛⣾⣿⣿⣿⣼⣶⣶⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣘⡛⠟
⢸⢱⡎⣹⠳⣫⠟⣮⣁⠈⡿⣿⣿⣿⣿⢿⣿⣿⢿⣿⡿⣷⡿⣿⣿⣾⠇⣼⣿⣿⣶⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢟⣉⢉⡉⠉
⠀⠀⠀⠛⠶⣫⣽⣷⢏⣶⡈⢤⡎⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣮⣻⣯⣼⣿⣿⣿⣿⣿⣿⣧⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⢿⣿⠿⠁⠀⠀⠀⠉
⠀⠀⢰⡄⠘⠿⠿⣷⣿⣿⣾⣽⣷⡿⢿⣟⣽⣿⣿⡿⣼⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣌⠛⠟⠻⢹⣿⡿⣞⣫⡿⠖⠻
⠀⠀⠀⠀⠐⠀⠂⠠⠨⠁⠢⠘⠁⠰⡞⢩⣿⢿⡿⢾⣿⣿⡿⣿⣿⣆⢻⣿⡿⢿⠷⠿⢷⢄⣂⣴⡚⠛⠶⠿⠄⠌⠛⠚⠃⠐⠋⠒⠁⠀⠂⠀⠚

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⣀⡀⠀⠀⣁⠀⣊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣶⣶⣿⣿⡯⣶⡿⣿⠾⣶⣭⣻⣿⡿⠏⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣸⣿⣿⣿⠿⠛⠛⠛⠻⣿⠟⠋⣼⣿⣿⡅⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣔⡗⢛⠍⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡿⠋⠁⠀⠀⠀⢺⣿⣟⡷⠀⠀⠀⠿⣿⣿⣿⣿⣶⡿⡅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⢛⣛⣭⣾⣧⣿⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠶⣪⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣁⣙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⢸⣷⣿⣿⣿⣿⢻⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣉⠙⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣿⣿⣿⣿⣿⢻⠃⠃⣰⣿⣫⠇⠀⠀⠀⢀⣴⣾⣿⣿⣤⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠳⢿⣿⣿⣿⣧⣿⣠⣾⣯⡾⠋⠀⠀⠀⣀⣾⣿⣿⣿⣟⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡙⣿⣰⡚⠿⡛⠁⣻⡿⠙⢁⣠⣤⣆⡀⢸⣏⣹⣿⣻⢿⣿⣷⡿⣲⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠆⠀⠀⠓⠒⣭⣾⣿⣻⣿⣏⣁⣉⡘⢃⠘⠛⠿⠿⠙⠛⢋⠅⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠇⣠⢀⠀⠀⠈⠁⠈⣿⣿⣼⠿⣏⣿⠂⠸⣗⠀⠀⣤⣠⣠⡖⢶⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⣃⡎⢸⠀⡠⡀⣀⠘⡟⡋⣀⢘⡀⢀⠀⣉⠍⠀⣿⠸⡇⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠧⠇⣇⢸⣇⡇⣽⢸⠆⢸⠀⣸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠉⠈⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠙⠛⠿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠀⣀⣴⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣀⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⣿⡆⠀⠀⠀⠀⠐⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⡿⠋⠀⣠⣴⣆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠉⠛⠛⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢿⣿⣿⣷⣄⠈⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀
⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣾⣿⣯⡀⠀⠙⢿⣿⣿⡆⠀⠈⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦
⣾⡿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠻⣿⣿⣦⡀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⢀⣴⣿⣿⣿⣧
⠙⣿⣦⠀⠐⢶⣾⠂⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣦⣤⣴⡾⠟⠀⠀⠘⠛⠉⣀⣼⣿⡆
⠀⠈⠻⣷⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣧⣤⣤⣀⡀
⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠻⣿⣶⣤⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠘⡷⣤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⣿⣿⠿⣿⣦
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣶⣤⣤⣶⠟⠁⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠋⠀⠀⠸⠟⠁⢀⣾⣿⣷⡀
⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁⠀⠀⠀⠀⠀⠀⠠⡿⠿⠛⣿⣷
⠀⠀⠀⠀⠀⠹⣿⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠋⠁⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣏⠀⠈⠙⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⠿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠈⠁⠀⠀⠀⠀⠉⠉⠁⡀⠀⣿⣿⠃⠀⣠⡀⠀⠀⣠⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣾⣿⣿⣿⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⣷⣤⣶⣿⣤⣾⣷⣴⣿⣿⣷⣾⣿⣿⣶⣾⣿⣷⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⠿⠿⠿⢿⣿⣿⡟⠋⠀⢈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢿⣧⣤⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠙⠛⠛⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣄⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣦⣼
⣿⣿⣷⣷⣾⣦⣷⣿⣄⣠⣦⣴⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣤⣰⣴⣠⣷⣷⣾⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣶⣾⣼⣧⣀⣠⣠⡄⠀⢠⣆⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⢸⣿⣿⣦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⢀⡞⠀⠀⠀⠴⠖⠀⠀⢨⣿⠏⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠐⣻⠁⠀⠀⣤⣀⣄⠀⠀⠀⣄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡄⠀⠀⠈⠉⠁⠀⠀⢸⡟⠀⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⣿⣿⣆⡀⠀⠀⠀⡀⠀⠀⣾⠇⠀⠘⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⣼⣿⣿⣿⣿⡀⠀⢠⣥⠀⢸⠏⠀⠀⡜
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠉⠀⡀⢠⠀⠀⠈⢿⣿⠂⠀⣿⣿⣿⣿⣿⡇⠀⠈⠁⠀⢁⠶⣡⡞⠃⠀⠀⡰
⠀⠀⠀⡽⠞⢿⡧⣶⡤⠀⠉⢀⣿⣯⣤⡄⠀⣸⣿⣷⣿⣿⣿⣿⠏⠀⠑⠀⠀⠀⠀⢀⠔⠫⠈⠼⢀⡖
⠀⠀⢠⠾⠒⠘⠇⠉⠙⠂⢰⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡧⢤⣀⣦⡀⠀⡰⢋⠀⠐⣠⠔⠋
⠀⠀⢸⣧⢀⣀⣦⣾⣷⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠇⠈⠉⠁⣀⡥⠚⠉⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣿⢿⡻⠄⢀⣀⡤⠖⠊⠁
⠀⣀⢸⡿⠋⠑⠋⠉⠉⠀⠀⠈⠙⢦⠐⣚⣻⣻⠷⠊⠀⣠⣤⠶⠞⠛⠁
⠀⠀⠈⠀⠐⠀⢉⣀⠀⢀⣠⡤⠀⢸⡇⢉⣉⣀⣠⣤⠶⠿⠃
⠀⠀⠀⠀⠀⠈⠚⠉⣉⣭⣁⣤⣴⣾⠁⠘⠉⠉
⠀⠀⠀⠀⣠⣴⠶⢿⣛⠉⠉⠀⠈⠁
⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⢲⣴⡘⠗⢻⠾⠗⡖⡀⣿⡦⡆⠀⠀⠀⠀⣿⣿⣿⡏⡍⠋⢱⣄⣄⣈⢠⡅⢿⡇⢘⢹⣿⣿⣿
⠀⠀⣿⣴⡔⠋⡻⣶⡯⣗⣥⢸⢷⡮⠐⣾⡇⠀⠀⠀⣿⣿⡑⠛⠛⡤⡦⡉⢡⠪⠅⡏⢠⠁⣮⡍⠘⣿⣿
⠀⠀⠠⣯⣱⣬⣼⢼⠹⣉⡾⢽⣠⡶⢹⢳⡗⣤⡄⠀⣿⣿⣿⠐⠾⠛⠘⢃⣾⠰⢊⡀⠟⢃⡷⢈⢠⡹⢻
⠀⠸⣿⡙⠭⡧⡽⢤⣁⢻⣱⡏⢠⢏⡰⣦⣔⣎⠀⠀⣿⣿⠀⠙⣒⣀⢃⡙⠲⡅⠘⢱⡛⡀⢞⡁⠋⢡⣿
⠀⠀⠉⠱⣶⠦⠓⠒⠻⣿⣯⠤⠿⠟⠉⠉⠙⠁⠀⠀⣿⣿⣷⣮⡈⣙⣦⣭⣅⡀⠀⢛⣃⣨⣴⣶⣦⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠳⣔⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣉⠛⠒⠬⢷⣄⠈⠑⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠒⠚⠋⠉⠳⢤⡀⠀⠀⠀⠈⢧⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣚⠭⠕⠒⠒⢤⠀⠀⠀⠀⠙⢟⠛⠦⠀⠀⠀⠀⢳⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⡠⠊⠀⠀⠀⠀⠀⢸⠁⠀⢀⣀⣀⣀⠑⠦⡀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⡴⢋⢀⡀⠰⡇⠀⠀⠀⢠⣦⡴⢃⣀⠤⠤⠤⠀⠀⠁⠀⠈⠓⣄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⡐
⠀⠀⠀⠀⠀⠀⢰⠃⢫⠀⠘⠆⠙⠒⠤⠤⠚⠉⠐⠫⠤⢤⣀⠀⠀⠀⠀⠀⣴⡋⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⢀⡀⠀⠠⠃⠀⡠
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣠⢰⠀⠀⠀⢠⠐⡁⣑⠀⠀⠀⠈⢑
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⡴⢳⢣⠀⠀⠀⠀⢱⠋⡩⣱⣀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⡴⠚⠛⠒⠲⣖⠒⠒⠲⣄⣀⢤⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⢶⡋⠀⢸⠋⠀⠀⠀⠀⠁⠸⠴⢺⠠⣜⠁
⡀⠘⣅⢣⡀⠄⢀⣁⣁⠀⠀⠀⠀⡈⠑⠢⢄⡀⠀⠀⠃⠀⠀⠀⠀⣀⡀⠉⠋⠓⠆⠘⣆⢈⡹⠀⠀⠀⠀⠈⢢⢔⣯⡵⠧⡀
⢑⡦⠤⢀⣀⡚⠑⣤⠈⢆⣠⠤⢰⠃⠀⠀⠀⠈⠉⠑⠒⠒⠒⠈⠉⠀⠈⢷⠒⠒⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠈⢮⣇⠴⠮⣷
⠈⠑⠊⠁⠀⠈⠉⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠋⢪⠲⡊⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠼⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠒⠒⠒⠒⢠⠠⠄⠀⠀⠀⠀⠀⠒⢲⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⣸⣀⣣⣀⡀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢲⡔⣟⣤⣀⠀⠀⢁⠀⠀⡏⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣃⣒⡨⠭⠥⠤⠬⠉⣏⠀⠀⢳⠲⠖⠒⠋⠉⠉⠒⢂⡢