Snowflake Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠈⠁⢀⠶⠂⠀⠀⠀⠀⠀⠀⠀⢸⣫⡆⢐⢮⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠺⠂⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣤⣄⠁⠀⣠⡄⠀⠀⠀⠀⠀⣀⣤⣠⡋⠈⢩⣤⣶⣦⠄⠀⠀⠀⠀⠀⠐⠛⠢⣤⡤⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠚⢈⡶⠭⢶⣁⠉⠀⠀⠀⠀⠀⠀⠀⣔⡶⠊⠉⠈⠐⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣠⡄⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢼⡝⠂⠙⠾⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣺⡃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣠⢀⡘⠓⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⠁⡀⠀⣤⠀⠀⠀⠀⠀⠀⠰⣖⡴⠈⠪⠞⢱⢰⣲⠂
⠀⠀⠀⠀⠀⠀⠐⠷⡵⠄⡦⢱⡎⣥⢀⡴⣠⡀⠀⠀⠀⠀⠀⠀⠬⣖⣭⡲⠅⠀⠀⠀⠀⠀⠀⠀⠀⣓⠊⢑⡊⢰⠉⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠇⠻⡂⠀⠘⠈⠀⠀⠀⠀⠀⡀⠶⠀⠔⠙⠂⠀⠶⠀⠀⠀⠀⠀⠀⣠⣖⢭⠃⣨⡁⢹⣱⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠑⠀⠠⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⡮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡡
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠇⡰⠲⠔⢦⢸⣷⠂⠀⠀⠀⠀⠀⠛⣨⣄⠀⠭⢀⣸⡀⠓⠀⠀⠀⠀⠀⠘⣂⣅⡀⠸⠇⣀⣦⡘⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⣁⠀⠀⣁⡶⠈⠁⠀⠀⠀⠀⠀⢈⡀⢈⡹⣿⢎⠀⣀⡁⠀⠀⠀⠀⠀⠀⡀⢈⣉⠾⠦⣉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⢿⡇⠳⢞⠦⠆⢰⠯⡄⠀⠀⠀⠀⠀⡤⢘⠇⢀⣖⠀⢸⠑⡴⠀⠀⠀⠀⠀⠠⠌⠋⠁⢸⡆⠉⠏⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠰⣦⠀⠀⢺⣇⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠛⣤⢘⣇⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⣆⠀⡐⡿⠁
⠀⠀⠀⠀⠰⠾⠾⠒⡒⣇⣪⡓⠓⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⣟⢆⢸⢃⣤⡼⠞⠃
⠀⠀⠀⠀⠀⠀⣐⡶⠋⢐⣇⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣈⣨⡭⠝⡿⡗⠤⣶⣴⡄
⠀⠀⠀⠀⠀⠐⠋⠂⠀⢐⡗⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠉⠁⣺⡇⠈⢶⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠈⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠜⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠
⠀⠀⠀⠀⠀⠀⢬⢵⠷⣛⠀⠀⠀⠀⠀⠀⠀⠠⡄⣆⡄⠀⠀⠀⠀⠀⠀⣀⡇⠀⢠⡥⠀⣀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⡺⡿⡖⠀⠀⠀⠀⢀⠀⠀⡘⠣⣀⣀⡔⠓⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠼⠉⠉⠉⢉⡽⠯⣉⠉⠋⠉⠙
⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠰⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠋⢀⡆⠘⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣥⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠑⠀⢨⣇⠀⠈
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠘⠉⡴⢰⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠌⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⣦⣄⠀⣿⠀⣠⣴⠞⠃⠀⠀⠀⣰⢤⡹⣽⢃⣤⡆⠈⠀⠀⠀⠀⠀⠀⠶⠀⠰⠇
⠀⠀⠀⠀⠀⠰⣶⠆⠀⠀⠀⠀⠀⠀⠂⠀⢉⣓⢾⣞⡉⠀⢐⠀⠀⠀⠀⢈⣛⣻⣿⣟⣋⡁⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠠⡷
⠀⠀⢂⠨⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⣤⠾⠋⠁⣾⠀⠙⠻⢦⡀⠀⠀⠀⠻⠞⢱⣻⡜⠾⠇⠀⠀⠀⠀⠀⠀⢐⡴⠀⠰⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠤⣤⢠⣬⣼⣥⡤⢤⡤⠀⠀⠀⠀⠠⠄⠈⠀⠉⠀⠄⠠⠀⠀⠀⢀⡀⢀⢀⠀⠄⠀⢀⠀⠀⠀⠀⢀⠀⠀⠻⡦⠀⣴⠦⠄
⠀⠀⠘⢣⣿⣯⣝⣿⣿⡜⠁⠀⠀⠀⠀⠂⠀⠀⣤⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡉⠀⢉⡤⠀⠀⠀⠀⠀⠘⠶⠖⠀⠀⠀⠉
⠀⠀⢰⣮⢟⣿⣽⣿⡿⢴⡆⠀⠀⠀⠀⠂⠀⠈⠉⠀⠀⠐⠀⠀⠀⠀⢠⡄⠡⢔⠀⠤⠀⢠⠀⠀⠀⠀⠀⠀⣰⠄⢀⡀⠘⠛⢧
⠀⠀⠉⠉⠀⠡⣭⡍⠀⠉⠉⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠃⠭⠘⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡄⢓⣿⢿⢠⡄⣠⡄
⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⠀⠀⠀⠀⢬⠑⢣⣄⣻⣠⡄⠪⡥⠀⠀⠀⠀⠀⠠⠠⠡⠀⠀⠀⠀⠀⠀⠀⢩⢻⡶⣍⣹⣩⡶⣟⣯⠁
⠀⠀⠀⠀⠠⠘⠛⠣⠀⠀⠀⠀⠀⠀⠴⢄⡠⠜⢻⠳⢆⡠⠦⠀⠀⠀⠀⠀⠀⠡⠡⠌⠀⠀⠀⠀⠀⠀⠰⣰⣥⠞⣿⠳⣮⣇⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠆⡀⢭⢀⠰⠮⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠫⠆⡹⣿⢾⠱⠏⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠍
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳
⠀⠰⣶⢫⠧⣩⠉⣏⠴⡜⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠢⣤⣾⢾⣆⣤⠴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢙⡛⢴⢽⣿⡯⡦⢚⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⣽⣻⣯⣿⠋⠀⠀⠀⠀⠀⡀
⠀⢀⣮⣱⡄⠾⠭⠗⣀⢟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⠷⢾⣹⡷⢿⣑⣄
⠀⠀⠉⠉⠁⢏⣒⡟⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⠁
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢹⣿⠁⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶⣄⢸⣿⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⣀⠀⠀⠀⠀⠰⣿⡀⠀⠀⣠⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⢸⣿⠀⠀⠀⢴⡆⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⣿⡇⠀⣸⣿⠁⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣨⣿⣆⡀⠀⣿⡇⠀⠀⠀⢠⣤⠀⠀⠀⢸⣿⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣸⣿⣴⡾⠟⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠙⠿⣷⣿⣧⠀⠀⠀⠀⠀⣤⡀⠀⢸⣿⠀⠀⣰⡶⠀⠀⠀⢀⣠⣶⡿⠿⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⠿⢿⣦⣄⡀⠀⠙⣿⣄⢸⣿⠀⣰⡿⠁⣀⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠉⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣜⣿⣾⣿⣴⣿⣷⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⢀⣀⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠶⠀⠰⠆⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠛⠃⠈⠉⠉⢉⣩⣿⢿⣿⣿⣿⡿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⢁⣾⠟⣿⡿⣿⡄⠉⠛⢿⣶⣄⡀⠀⠀⠀⠀⢀⣠⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣶⣶⣶⡿⠟⠉⠀⠀⢠⣾⠏⠀⣿⡇⠘⢿⣆⠀⠀⠈⠙⠻⢷⣶⣶⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣴⣾⠟⣿⡿⠁⠀⠀⠀⠀⠘⠋⠀⠀⣿⡇⠀⠈⠉⣀⠀⠀⠀⠀⠀⢹⣿⠿⣷⣦⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠉⣿⡏⠀⢠⣿⠃⠀⠀⠀⠀⠸⠃⠀⠀⠀⣿⡇⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⣿⡄⠀⠉⢿⣏⠉⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⡾⠟⠀⠀⢸⣿⠀⠀⠀⠀⠰⠆⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠺⠇⠀⠀⠀⠀⣿⡇⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⣿⡇⠈⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣿⣇⡀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⣿⣡⠄⢄⢸⣇⡤⠀⠀⠀⡆⣶⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠑⢄⠀⢹⡏⢀⡴⠃⢀⡿⠯⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡆⠀⢰⠈⠀⣤⠑⢼⡷⢋⣄⠀⠈⡆⠀⢰⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢤⣠⠀⡄⠠⠤⠷⢇⠀⢸⠀⠘⣿⠇⣸⣇⠸⡿⠀⠀⡇⢀⡼⠯⠤⠄
⠀⠀⠀⠀⠀⠀⢘⣛⣷⣇⢀⣀⣀⣠⣵⣾⠀⠀⡠⠊⢸⡏⠳⣄⠀⢀⣷⣋⣀⣀⣀⡀⠀⢀⡔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠀⡱⢎⠀⢠⢾⣧⡀⢈⡵⢏⠀⠀⠀⣀⠀⠐⠚⡻⣟⠻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠈⠳⣄⠺⠿⠗⣠⠞⠁⢀⡝⢇⢸⣇⡽⠫⡀⠀⠑⢄⠻⠿⠛⣠⠊⠀⡨
⠀⠀⠀⠀⠀⠰⠶⠾⡷⠶⠾⡷⠶⢾⠷⠶⢶⡷⠶⢶⣿⣿⠶⠶⣾⠷⠶⢾⡷⠶⢾⡶⠶⢾⡶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⡊⠀⡠⠋⣤⣶⣦⠑⢄⠀⢉⡶⣋⢸⡇⢱⣞⠁⢀⡴⠋⢴⣾⡦⠙⢦⡀⠙
⠀⠀⠀⠀⢀⣀⣦⣽⣮⡤⠀⠀⠉⠀⠀⢀⡵⢋⡀⠈⢻⡷⠃⠀⡱⢎⠀⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠋⠜⠁⠀⠈⠉⠉⢉⡽⣿⠀⠀⠙⢦⣸⣇⡠⠊⠀⠀⡟⢏⠉⠉⠉⠀⢹⢿⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡿⡏⠀⢹⠀⠀⣾⡆⢹⡏⢰⣿⡄⠀⡇⠀⣷⢖⠒⠂⠘⠀⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠇⠀⠘⡀⠀⠙⣡⢾⡗⣄⠛⠀⠀⠇⠀⠸⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣲⣾⠁⢠⠞⠁⣸⣇⠀⠑⢄⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⠸⠀⠀⠀⠚⢹⡇⠑⠐⢋⣿⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣿⡇⠀⠀⢸⣿⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠙⢿⡇⠀⠀⢸⡿⠋⠀⢘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⢻⣷⡄⠀⠈⠃⠀⠀⠘⠁⠀⢠⣾⠟⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⣿⠟⠉⠻⣿⡄⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⢠⣿⠟⠉⠻⣿⠀⣀⣤⣤⣀
⠀⠀⠀⠀⣼⡿⠋⠙⠻⢿⣿⣧⠀⠀⠹⣿⡄⠀⠀⠀⠈⢿⣧⡀⠀⠀⢀⣼⡿⠁⠀⠀⠀⢠⣿⠏⠀⠀⣼⣿⡿⠟⠋⠙⢿⣧
⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠈⠛⠦⠀⠀⠹⣷⡄⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⠏⠀⠀⠴⠛⠁⠀⠀⢀⣤⣾⠏
⠀⠀⠀⠀⠀⠈⣹⣿⣷⣦⣄⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀⣠⣴⣾⣿⣏⠁
⠀⠀⠀⠀⠀⣼⡿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣤⣿⡇⠀⠀⢸⣿⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢿⣇
⠀⠀⠀⠀⠀⠸⣿⣦⣤⣤⣤⣶⣶⣶⣶⣶⣦⣀⠀⠀⠈⠙⠻⡇⠀⠀⢸⠟⠋⠁⠀⠀⣀⣴⣶⣶⣶⣶⣶⣤⣤⣤⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠀⢠⣶⡿⠿⠿⠿⣶⣶⣶⣶⣶⡿⠛⠉⠀⠀⢀⣠⡆⠀⠀⢰⣄⡀⠀⠀⠉⠛⢿⣶⣶⣶⣶⣶⠿⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⢺⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⣿⡇⠀⠀⢸⣿⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡗
⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠟⠀⠀⠀⠀⠀⢰⣿⠟⠋⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠙⠻⣿⡄⠀⠀⠀⠀⠀⠻⢿⣿⣿⡟⠁
⠀⠀⠀⠀⢠⣾⠿⠋⠁⠀⠀⣀⡄⠀⠀⢠⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠸⣿⡄⠀⠀⢤⣀⠀⠀⠈⠙⠿⣷⡄
⠀⠀⠀⠀⢿⣇⡀⢀⣠⣴⣿⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⣴⡿⠃⠀⠀⠘⢿⣦⠀⠀⠀⠀⠹⣿⡄⠀⠀⢿⣷⣦⣄⡀⢀⣼⡿
⠀⠀⠀⠀⠈⠛⠿⠿⠛⠉⣿⣇⠀⣠⣿⠏⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠹⣿⣄⠀⣨⣿⠉⠛⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⣰⣿⠋⠀⠀⡀⠀⠀⢀⠀⠀⠹⣿⣆⠀⠀⠀⠙⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⢀⣼⡇⠀⠀⢸⣧⡀⠀⢘⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⡿⣿⡇⠀⠀⢸⣿⢿⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣾⠿⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⣀⣜⣿⣟⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢦⣿⡴⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡂
⠀⠀⠀⣽⢿⣿⡈⢹⠋⣸⣿⢿⡅⠀⠀⠀⢻⣿⣶⣨⣿⣅⣰⣿⣿⠂⠀⠀⠀⢳⣾⣄⠀⣿⢀⣠⣷⡚⠀⠀⠀⠈⡿⣷⣆⢉⣏⢁⣶⡿⡟
⠀⠀⠀⠰⣏⣁⣹⣿⣿⣁⣉⡷⠀⠀⠀⠀⠀⣈⣙⣿⣿⣿⣏⣉⠀⠀⠀⠀⠀⣍⠀⣈⣽⣿⣯⡁⢀⣉⠀⠀⠀⠀⠀⣍⣈⣿⣩⣏⣀⡅
⠀⠀⠀⠽⣿⣿⢁⣼⣄⢸⣿⡾⠅⠀⠀⠀⡼⣿⠿⢙⣿⣍⠹⢿⢿⠄⠀⠀⠀⠼⢿⠉⠀⣿⠀⢙⡿⠧⠀⠀⠀⠠⢿⡟⠏⣀⣇⡀⠿⣷⠧
⠀⠀⠀⠀⠁⠈⠩⢾⠮⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⣿⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠆

⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⢤⡀⣦⠙⢾⠞⢡⣆⣠⠄⠀⠀⠀⣴⡆⢿⠶⣿⡴⣿⢀⣦⠄⠀⠀⠠⣤⣴⠀⢙⣿⠋⢀⣆⣤⠀⠀⠀⠠⣤⣄⠀⣸⣿⡁⢀⣤⣤
⠀⠀⠀⢠⠽⠛⣦⠞⢦⡞⠻⢥⠀⠀⠀⠀⣉⡽⠿⢦⣿⡤⠿⢯⣉⠁⠀⠀⠀⠹⠛⣷⢯⣿⡽⡾⠛⠏⠀⠀⠀⠀⠙⠛⡿⣬⣯⡼⢿⠛⠁
⠀⠀⠀⠘⣳⣶⠛⢶⠞⢳⣶⡚⠀⠀⠀⠀⣍⣹⣶⠚⣿⠙⣶⣟⣉⡀⠀⠀⠀⣰⣤⡿⣟⣿⣻⢷⣴⣆⠀⠀⠀⠀⣠⣼⢷⢛⣟⢳⢿⣤⡄
⠀⠀⠀⠉⠁⠟⡤⢾⠶⡌⠇⠉⠁⠀⠀⠀⠛⠃⣾⠞⣿⠳⢿⠈⠟⠁⠀⠀⠈⠛⠛⠀⣠⣿⣄⠀⠋⠛⠀⠀⠀⠈⠉⠉⠀⢩⣿⡁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠶⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣙⠻⠀⠟⢋⡽⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢰⣋⠳⠿⠸⠷⠊⣹⢀⣤⡀
⠀⠀⠀⠀⣀⠀⡏⢹⢀⣠⡖⠮⣷⠀⣾⠵⢲⣄⡀⡏⢹⠀⣀⠀⠀⠀⠀⢠⠶⢤⡇⢸⢠⠬⣕⣦⢠⣖⡫⢤⢸⡀⣧⡴⢦
⠀⠀⠀⠘⢏⡙⠃⢸⣸⠀⡟⠲⣤⠀⣠⠖⢻⠀⣇⡇⠘⢋⡹⠇⠀⠀⠀⣈⡷⠄⠀⢿⡞⢠⣄⡉⠈⣉⣤⠘⣯⠇⠀⠴⣏⡀
⠀⠀⠀⣴⠚⣡⠴⣦⡉⠀⢧⣄⣸⠀⣇⣠⠼⠀⠉⣴⠦⣌⠓⣦⠀⠀⠘⠥⠴⣚⡽⠆⠀⠸⡤⠿⠘⢧⡼⠀⠀⠾⣝⡲⠤⠽
⠀⠀⠀⠈⠉⠱⣏⣡⠖⠛⠲⣌⡙⠀⢋⣡⠖⠛⠲⣌⣹⠎⠉⠁⠀⠀⣞⠳⣄⢧⡀⢾⣉⡗⠀⠀⠀⠀⠐⣏⣹⠆⣠⢇⡴⢛⡆
⠀⠀⠀⣠⢤⣘⢧⣉⠓⠶⠚⣉⣤⠀⣤⣉⠓⠶⠚⣉⡼⣃⡤⣄⠀⢀⡬⠷⠈⠛⣋⠀⢩⣤⠀⠀⠀⠀⢠⣬⠁⢈⠓⠋⠰⠯⣄
⠀⠀⠀⠙⢦⣌⠙⢋⣡⠀⡟⠁⢸⠀⡇⠈⢹⠀⣌⡙⠋⢡⡴⠋⠀⠘⠲⢲⠂⡾⡽⠀⠷⠼⠃⡴⠶⡄⠻⠤⠇⠸⡽⡆⢲⠲⠚
⠀⠀⠀⠰⣏⡤⡆⢸⢹⣀⡷⠞⣉⠀⣉⠓⢾⣀⡏⡇⢰⢦⣹⠆⠀⠀⠀⠻⠴⢃⣙⣒⣲⠂⣤⠙⠞⢡⡄⢲⣒⣚⣁⠳⡼⠃
⠀⠀⠀⠀⠀⠀⢧⡼⠀⠉⢓⣫⠽⠀⠿⣝⡚⠉⠀⢧⡼⠀⠀⠀⠀⠀⠀⠀⠀⢯⣥⣤⠀⡈⢯⡳⠴⣫⠏⠀⢠⣬⣭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡤⢶⠀⡶⢤⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡼⠳⣄⣳⢰⣃⡴⠳⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡶⢼⠉⣧⠶⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣙⠾⠹⢚⣩⠇
⠀⠀⠀⠀⠀⢠⡶⣴⢋⣇⣠⢽⣶⠀⣶⡯⣅⣸⡝⣧⢶⡄⠀⠀⠀⠀⠀⠀⡴⣄⢠⣄⠰⣟⠻⢿⢰⠿⢚⡽⠀⣀⢠⡤⡄
⠀⠀⠀⠀⢠⡴⢛⣀⡸⡿⣸⠓⢮⠀⡵⠚⣇⢻⠇⣀⡛⢦⡄⠀⠀⠀⠀⡴⠇⣿⣿⢸⣀⡬⠟⣂⢀⡚⠯⣄⣸⢹⣿⡆⠷⣄
⠀⠀⠀⠀⣀⠉⣹⣛⣋⣤⡻⣄⢸⠀⡇⣠⠞⣠⣘⣛⣯⠉⣁⠀⠀⢀⡴⢋⣤⣬⠋⠘⣩⡖⠋⢹⢸⡏⠓⣮⡙⠈⢫⣤⣌⡓⣦
⠀⠀⠀⣘⣏⢳⣧⡹⣄⣀⣙⣮⡻⠀⢟⣡⣊⣀⣠⠏⣼⡾⣹⣃⠀⠀⠉⢹⣋⡵⣶⢰⠦⣝⠲⢾⢸⠷⢚⡥⢶⢰⡶⢍⣳⡍⠁
⠀⠀⠘⠯⡭⢠⣭⢄⡬⠭⠭⣭⠅⠀⡨⣭⠭⠭⢥⡠⣭⡄⢭⠽⠃⠀⠀⣠⢤⣀⣿⢸⣀⡤⠟⣂⢀⡚⠯⣄⣸⢸⣇⣠⣥
⠀⠀⠀⠸⠥⠋⣯⠾⣤⣠⢞⡵⢻⠀⡟⢮⡳⣄⣤⠷⣽⠙⢮⠇⠀⢠⡶⢼⣶⣬⠋⠘⣭⡖⠋⢹⢸⡍⠓⣮⡝⠈⢫⣴⣾⠖⡦
⠀⠀⠀⠀⢠⣖⠾⠿⢖⡀⢿⠀⣸⠀⣇⠀⡿⢀⡲⡾⠷⢲⡄⠀⠀⠀⠉⣗⡈⣱⣶⢰⠦⣝⡲⢾⢸⠷⢚⡥⢶⢰⣶⡍⣐⡏⠁
⠀⠀⠀⠀⠀⢩⣟⣤⢸⡿⣼⣋⣥⠀⣬⣙⣧⢿⡇⣤⣻⡍⠀⠀⠀⠀⠀⠉⣇⣹⠻⠼⢀⡤⠟⣂⢀⡘⠧⣄⠸⣼⢿⣇⡏⠁
⠀⠀⠀⠀⠀⠀⠉⠘⠷⠇⢠⢟⣫⠀⣝⡻⡄⠸⠶⠃⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢒⡿⠟⠘⠻⣷⡋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠶⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠖⠛⠞⠛⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⡀⠀⠀⠀⠘⠀⠃⠀⠀⠀⢀⠀⢔⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⡛⠀⢀⠀⠀⠅⠀⠀⢚⣥⠒
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠊⡄
⠀⠀⠀⠀⠤⠀⢀⠄⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠁⠐⠀⠢⠄⡀⢁⣄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠈⠤⠛⠀⠀⠈⠀⠠⠔⠀⠳⠠⢁⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠜⠋⠡⠄⢀⠀⠀⠀⠀⠂
⠀⠀⢀⣢⣀⠀⠀⠀⢀⢰⡀⠀⠀⠀⣀⣐⠄⠂⠀⠀⠀⠀⠠⠠⢤⡂⠆⠂⠈⠁⢠⠀⠀⠀⠋⠐⠤⠤⢣⠄
⠀⠀⠀⠀⠉⠐⣰⠄⣀⠈⣀⠰⣂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠁⢠⡀⠀⢾⡀⣰⠶⠂⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠓⢒⣉⠡⢴⣄⠀⠰⠦⠄
⠀⠀⠀⠀⣀⠠⠻⠀⠉⡀⠁⠰⠏⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠂⠀⠠⠶⠋⠀⣷⠀⠈⠁⠀⣆
⠀⠀⠀⠍⠁⠀⠀⠀⠈⠏⠁⠀⠀⠀⠉⠹⠄⠀⠀⠀⠀⠀⠀⠀⢪⠔⠃⠆⢠⠀⠀⠀⠃⠀⣀⠰⠰⠎⣟⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢠⡔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⣦⣻⣟⣴⠟⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣦⡀⢀⡈⢻⡟⢁⡀⢀⣴⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢿⣿⣿⣧⢸⡇⢸⡇⢸⡇⣼⣿⣿⡿⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⢀⣈⣉⣻⣿⣇⢸⡇⣸⣿⣟⣉⣁⡀⠀⠀⠀⢀⣴⣿⣿
⠘⢿⣿⣿⣷⡄⢸⣆⠀⠀⢿⣿⣿⡇⣀⡀⣶⣤⡉⠉⠉⠉⠻⣿⣿⠟⠉⠉⠉⢉⣠⣶⢀⣀⠸⣿⣿⡿⠀⠀⣰⡇⢠⣾⣿⣿⡿
⠀⠈⠻⣿⣿⣿⣮⣿⡀⣴⣄⡻⣿⣰⡿⠁⢸⣿⣿⣶⠀⢀⠀⢸⡇⠀⡀⠀⣶⣿⣿⡇⠈⢿⣆⣿⢟⣠⣦⢀⣿⣵⣿⣿⣿⠟⠁
⠀⠀⠀⢠⣴⡶⠿⠛⠿⣦⣍⡛⢿⡟⠀⠀⠘⠻⣿⣿⣀⣿⠁⢸⡇⠈⣿⡀⣿⣿⠟⠃⠀⠀⢻⡿⢛⣩⣴⠿⠛⠿⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠛⠷⣦⣝⣻⣾⣿⣀⠀⠰⢶⣮⣿⣿⡏⠀⢸⡇⠀⢹⣿⣿⣵⡶⠆⠀⣀⣿⣷⣟⣫⣴⠾⠛
⠀⠀⠀⢀⣴⣾⣿⣿⣷⢿⣿⠟⠉⠉⠛⠷⣦⣄⡀⠈⠹⣷⡀⢸⡇⢀⣾⠏⠁⢀⣠⣴⠾⠛⠉⠉⠻⣿⡿⣾⣿⣿⣷⣦⡀
⠀⠀⠐⠛⠛⠻⠿⠟⢡⣾⠃⠀⠀⠀⢶⣄⠀⠙⠻⢶⣤⡘⣷⣼⣧⣾⢃⣤⡶⠟⠋⠁⣠⡶⠀⠀⠀⠘⣷⡌⠻⠿⠟⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣴⣾⣿⣷⣦⣽⣷⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣾⣯⣴⣾⣿⣷⣦⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠙⠻⠿⠟⢋⣽⠟⠉⠉⢉⣭⡿⣿⣿⣿⣿⢿⣭⡉⠉⠉⠻⣯⡙⠻⠿⠟⠋⣩⡀
⠀⠀⠐⢶⣶⣾⣿⣷⣌⢻⣆⠀⠀⠀⠛⠁⣀⣴⡾⠛⠉⣰⡟⢹⡏⢻⣆⠉⠛⢷⣦⣄⠈⠛⠀⠀⠀⣰⡟⣡⣾⣿⣷⣶⡶⠂
⠀⠀⠀⠀⠙⠻⠿⠿⠟⣿⣿⣷⣤⣤⣶⠟⠋⢁⣀⣠⣼⡟⠀⢸⡇⠀⢻⣧⣄⣀⡈⠙⠻⣶⣤⣤⣾⣿⣿⠻⠿⠿⠟⠋
⠀⠀⠀⢀⣀⡀⠀⠶⠟⣋⣵⡾⢻⡿⠀⠀⠘⠛⣫⣿⣿⣧⠀⢸⡇⠀⣼⣿⣿⣝⠛⠃⠀⠀⢿⡟⢷⣮⣙⠻⠦⠀⢀⣀⡀
⠀⠀⠀⢈⣙⣛⣿⣶⡿⣋⣥⡶⣿⣷⡀⠀⢰⣾⣿⣿⠀⢿⠄⢸⡇⠠⡿⠀⣿⣿⣷⡆⠀⢀⣾⣿⢶⣬⣙⢿⣶⣿⣛⣋⣁
⠀⢠⣾⣿⣿⡿⢫⣿⠀⠙⢁⣾⣿⠘⣷⡄⣸⣿⡿⠛⠀⠀⠀⣸⣇⠀⠀⠀⠛⢿⣿⣇⢠⣾⠃⣿⣷⡈⠋⠀⣿⡝⢿⣿⣿⣷⡄
⠰⠿⠿⠿⠟⠁⠸⠃⠀⠀⣿⣿⣿⡇⠀⠀⠛⢉⣤⣤⣤⣤⣾⢿⡿⣷⣤⣤⣤⣤⡉⠛⠀⠀⢸⣿⣿⣿⠀⠀⠘⠇⠈⠻⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⠀⠀⠀⢀⣠⣤⣾⢿⡗⢸⡇⢸⡿⣷⣤⣄⡀⠀⠀⠀⠀⠙⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣿⣿⣿⡟⢸⡏⢸⡇⢸⡇⢻⣿⣿⣿⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠛⠋⠀⠀⣠⣾⣷⣄⠀⠀⠙⠛⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢋⣾⣷⡙⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣌⢹⡆⣿⢩⣤⣀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢦⣄⠀⠀⠀⠻⣄⠈⠻⠇⠛⠋⣠⡟⠀⠀⠀⠀⡼⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠹⣆⠀⠀⠀⠈⠙⢦⠀⣴⠛⠁⠀⠀⠀⢀⡾⠁⣼⠃
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⣆⠀⢰⡖⢦⣽⠀⣿⡴⠲⣆⠀⢀⡾⠁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⣾⡛⠙⠛⢶⡄⢰⡟⢦⡀⠀⠀⠀⠘⣧⠀⠘⣆⠘⠳⣄⠉⠀⠋⢀⡴⠇⢀⡞⢁⡼⠁⠀⠀⠀⣠⢶⣄⠀⣴⠟⠉⠉⣿⡟
⠀⠙⢷⣄⣀⣈⡳⠾⡇⠸⡇⠀⣴⢦⡀⠘⢧⠀⠘⣦⠀⠈⢳⡄⣴⠋⠀⢀⡞⢀⡾⢁⡴⠶⡄⠀⡿⠀⣿⡶⢋⣠⣤⡾⠟
⠀⠀⠀⠙⢋⣭⠿⠶⠀⠀⠻⣄⣻⠀⢹⡆⠈⢧⣀⣸⡁⠀⢸⡇⣿⠀⠀⣸⢠⡞⠀⢸⡇⢠⣏⡴⠇⠀⠀⢾⣯⡀
⠀⠀⠀⠀⠾⢦⣤⡴⠞⠛⢳⣦⡉⠀⠘⣇⠀⠀⠉⢳⡳⡄⢸⡇⣿⠀⡼⣳⠋⠀⢀⣾⠀⠈⢩⡴⠛⠛⠲⠦⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢁⣠⡤⠶⢬⣛⠶⣤⡀⢳⡹⣼⡇⣿⣼⡷⢃⣤⠶⣋⡥⠦⣤⣈⠉⢻⡄
⠀⠀⠀⣀⣀⣀⣀⣀⣈⣙⣛⣋⣁⣀⣀⠀⠉⠛⠶⣝⡳⢷⣹⡇⠿⡽⠟⣩⠴⠚⠉⠀⢀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣄⣤⣄
⠀⠀⠺⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣛⣂⠉⠀⠀⢀⣻⣿⣿⣿⣭⣽⣭⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⠟
⠀⠀⠀⠈⠉⠉⠉⠉⠉⣉⣉⡉⠉⠉⠁⠀⠀⢀⣤⠖⣫⢵⡆⡀⣤⢤⣍⡳⢦⣄⡀⠀⠀⣀⣤⠦⢤⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠛⢶⣄⣠⡴⢞⡭⠖⠋⢁⣞⣼⡇⣿⣜⣦⠙⠳⢮⡉⠓⠛⠉⠀⣀⡼⠇⠀⣀⣀⡀
⠀⠀⠀⠀⠸⣟⠛⠳⢦⣈⣹⡶⠀⠈⣵⠞⠉⠀⠀⢠⢏⡞⢸⡇⣿⠘⣎⢧⠀⠀⢹⡆⠀⣘⣿⢥⡤⠖⠋⠉⢨⡟

⠀⠀⠀⠀⠀⠈⢙⣦⠀⠈⣠⠖⣷⠀⣿⠀⠀⠀⡴⠋⡞⠀⢸⡇⣿⠀⠘⣾⢧⡄⠀⣷⠀⣿⠙⣧⠀⣀⡲⣿⡉⣀
⠀⢀⣴⠞⠛⠚⢋⣥⡄⠀⡟⠀⢿⣀⣿⠀⢀⡼⠁⣼⠃⢀⡼⠇⢿⡀⠀⢿⡀⠹⣆⠸⣄⣸⡆⢹⡄⢹⡟⢻⣍⠉⠛⢶⣄
⠀⣸⣇⠀⢀⣸⠏⢸⡇⢠⡿⠀⠀⠉⠁⢀⡾⠁⡼⣡⠶⠋⢀⠀⢀⠙⠶⣄⠹⡄⠹⣆⠈⠉⠀⠘⢧⣰⡇⠀⠙⢶⣄⣠⣿
⠀⠉⠉⠛⠋⠁⠀⠀⠙⠟⠀⠀⠀⠀⢀⡞⢁⡾⣹⣃⣀⡴⢻⡇⣿⠳⣄⣸⣇⠹⡄⠙⣆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡞⠀⠈⠉⢉⡴⠟⠁⠙⢷⡈⠉⠉⠀⠹⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⠀⠀⢠⡶⠋⠀⣠⡄⣶⣄⠙⢳⣄⠀⠀⠹⢶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠋⣽⠇⢯⡈⠷⠾⠟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡾⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢬⡥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢬⣙⣋⡥⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠐⠠⠀⠑⠢⢬⡥⠔⠊⢀⠀⠂⠀⠀⠀⠀⠀⢀⢠⠊
⠀⠀⠀⠀⠀⠀⠂⠤⠜⡳⢄⡄⡆⢀⢀⠀⠀⠀⠀⠰⠀⢸⠁⠀⠆⠀⠀⠀⠀⠀⡀⢠⢠⡬⢞⠣⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡨⠜⣳⠶⣸⡀⠀⡐⠀⠀⠀⠈⠀⠀⠀⠀⢒⠀⢀⣧⠶⣎⠃⢍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠠⠒⠉⢉⠲⢄⡁⠄⢈⡢⠔⡀⠠⢈⡤⠒⡉⠉⠒⠄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠑⠂⠁⠂⠀⣊⠀⠁⠀⠁⠐⠀⠐⠈⠐⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⡀⠄⠀⢄⢀⠀⢀⠀⡩⠀⠠⢀⠠⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠐⠤⣀⣈⠤⠊⡁⠂⢈⠔⠪⡁⠐⢈⠑⠦⣁⣀⠤⠂⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢠⡹⠶⢻⠁⢀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⡏⠶⢏⡔⡊⠄
⠀⠀⠀⠀⠀⠀⠄⠒⢢⡴⡚⠃⠃⠀⠀⠀⠀⠀⠀⠰⠐⢀⡀⠂⠆⠀⠀⠀⠀⠁⠀⠸⠘⢑⢮⡔⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠁⠀⠀⠀⠀⠀⠰⠀⠁⡠⠔⢚⡓⠢⢄⠀⠂⠄⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢚⣩⣍⡓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢚⡓⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⣤⡀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣠⠴⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣏⠀⠀⠙⠳⣄⡀⡇⠀⠀⡇⣠⠴⠋⠁⠀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⢲⠀⠀⠀⠙⠦⣄⠀⠀⠙⠃⠀⠀⠋⠁⠀⣀⡴⠚⠁⠀⠀⢰⠚⠋⡏
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣰⠋⠈⠛⠦⣄⡀⠀⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⣀⡤⠞⠉⠈⢧⡀
⠀⠀⠀⠀⠘⠳⢤⡀⠀⠀⠈⠙⠲⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠷⠚⠉⠀⠀⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⠀⠀⢀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣀⡤⠞⠋⠀⠀⢀⠀⠀⠈⠛⠦⣄⡀
⠀⠀⠀⠀⠀⣴⠞⠋⠁⠀⢀⣠⠴⠚⠉⠛⠦⣄⡀⠀⠈⠙⠲⣄⣀⡇⠀⠀⡇⣠⡴⠚⠉⠀⠀⣀⡤⠞⠉⠙⠲⢤⣀⠀⠀⠉⠓⢦⡄
⠀⠀⠀⠀⠀⠈⢧⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠉⠃⠀⠀⠋⠁⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣦⠄⠀⠀⠀⠀⢤⣞⠉
⠀⠀⠀⠀⠀⠀⡴⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⡀⠀⠀⡀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⡄
⠀⠀⠀⠀⠀⢾⣁⠀⠀⠉⠛⠦⢄⡀⠀⢀⣠⠖⠋⠁⠀⢀⣠⠴⠛⡇⠀⠀⡟⠲⢤⡀⠀⠀⠉⠓⢦⣀⠀⢀⣠⠴⠞⠋⠁⠀⣀⣹⠆
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠉⠛⠉⠀⠀⢀⣤⠖⠋⠀⠀⠀⡇⠀⠀⡇⠀⠀⠉⠳⢦⣀⠀⠀⠈⠙⠉⠁⠀⣀⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⣠⡄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣤⡀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠈⢳⡀⠀⢀⡤⠖⠋⠁⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠉⠓⢦⣀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠹⠞⠉⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠞⠃⠀⠀⠳⢦⣀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇⠀⠀⠀⠈⠙⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⣸⠀⠀⠀⢀⣠⠖⠋⠀⠀⡀⠀⠀⡀⠀⠈⠓⢦⣀⠀⠀⠀⢹⣀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠠⡖⠋⠀⢀⣠⠴⠛⡇⠀⠀⡟⠳⢤⡀⠀⠈⠓⡦⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠶⠋⠁⠀⠐⡇⠀⠀⡇⠀⠀⠉⠳⢤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣠⡗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⢀⣸⣇⡀⣄⣤⠆⠀⠀⠠⣼⡆⢹⡟⢁⣿⡤⠀⠀⠰⣤⣆⢶⣼⣇⡶⢠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠋⠙⣿⡍⠀⠀⠀⠀⣛⡋⣙⣿⣿⣟⢉⣛⡀⠀⠀⠨⣭⣿⣿⣿⣿⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠻⠷⡾⠟⡶⣤⡀⠀⠀⠸⢿⡏⢹⣇⠉⣿⠏⠀⠀⢀⣴⡶⣻⡿⡿⣟⢲⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠏⠓⠈⠀⠀⠀⠀⠀⠀⠉⢼⡷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣀⠦⣽⠴⣀⣴⡶⠀⠀⠲⣤⣀⠀⣹⡁⠀⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣝⣳⣾⣞⣛⠌⠀⠀⠀⠀⠀⠉⣛⣾⣶⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⡇⣿⢬⡛⣶⣦⠀⠀⣠⡶⠞⠉⢺⠒⠉⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⠀⠘⡏⠀⣠⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⣷⡚⠉⠁
⠀⠚⠒⠂⠒⠂⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠉⡇⠉⢻⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣹⣫⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠘⢦⣸⣇⡴⠁⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣰⡀⡄⢠⠀⠘⠻⡇⠀⠀⢹⡏⠀⠀⣸⠟⠃⠀⡄⢠⢀⣆⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣱⠿⣌⣇⠀⠀⢸⣦⣦⢼⣧⡤⣴⡃⠀⠀⣸⣡⠾⣎⣙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠚⠛⠲⣴⡟⠛⢇⢸⡇⡼⠓⢿⡤⠖⠛⠓⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⡴⣻⠈⠓⢮⣿⣾⡵⠚⢉⡟⣆⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠉⠉⢯⣹⢉⡩⢟⣿⣿⡻⢍⣉⣏⠟⠉⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⢤⣤⠴⢻⡧⣤⡎⢸⡇⢳⡤⢾⠟⠦⣤⡤⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⡻⣶⢋⡟⠀⠀⢱⠯⠽⢾⡿⠭⠵⡏⠀⠀⢻⠙⣶⢞⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠹⠡⠇⠘⠀⢠⣴⡇⠀⠀⣸⣇⠀⠀⢹⣦⡄⠀⠃⠸⠌⠏⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⢀⠞⢹⡍⢣⡀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⡝⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣏⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠛⢿⣠⠟⢠⠀⠀⢠⠏⠹⣄⠀⠀⡀⠻⣄⡿⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠛⢯⣠⠏⠀⣰⠏⢰⡆⠙⣆⠀⠹⣄⡽⠛⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣀⣀⠀⠈⠉⠛⣇⠀⣰⠃⠀⢸⡇⠀⠘⣆⠀⣸⠛⠉⠉⠀⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣤⡉⠙⠓⠶⠦⣼⣶⣧⠀⡀⣾⣷⢀⠀⣼⣶⣧⠴⠶⠚⠋⢉⣤⢀⡟
⠀⠀⠀⠀⡄⢠⡀⢀⠀⠈⣇⠈⠻⣦⣄⠀⣀⡙⠻⣇⡼⠁⡏⢹⠈⢧⣸⠟⢛⣀⠀⣀⣴⠟⠁⣸⠁⠀⡀⢀⡄⢠
⠀⠀⠀⢲⣿⣄⣧⠘⡇⠀⢹⡄⠀⠘⢯⡳⣌⡉⢛⢻⣡⠆⡇⢸⠰⣌⡟⠛⢉⣡⢞⡽⠁⠀⢠⡏⠀⢸⠃⣼⣠⣿⡖
⠀⠀⠀⠉⡤⠞⠋⣻⠿⢤⣀⣧⣤⠘⡆⠙⢆⠙⢮⡙⢻⢸⡇⢸⡇⡿⢋⡵⠋⡰⠋⢰⠃⣤⣼⣀⡤⠿⣟⠙⠳⢤⠉⠁
⠀⠀⠀⠀⠀⠐⠉⠀⢀⣠⠾⣿⠟⢶⣿⣀⣎⠳⣄⠉⠻⣿⢡⡌⣿⠟⠉⣠⠞⣱⣀⣿⡶⠻⣿⠷⣄⡀⠀⠉⠂
⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠠⠖⠋⠁⣞⣋⣓⣾⣦⣙⣾⣿⣿⣷⣋⣴⣷⣚⣙⣳⠈⠙⠲⠄⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠶⣏⡁⠰⠶⠶⠶⠿⢿⣭⣭⣉⣉⣉⣀⣀⠶⣺⣿⣿⣿⣿⣷⠲⣀⣈⣉⣉⣉⣭⣭⠿⠿⠶⠶⠶⠆⢈⣹⠶
⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠐⠶⣄⡀⣲⣬⠽⣻⠟⡵⢻⢿⡿⡟⢮⠻⣿⠯⣥⣖⢀⣠⠶⠂⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠠⣄⡀⠈⠙⢲⣽⣶⠖⣿⠉⢏⡴⠃⣠⢶⣿⡘⢃⣿⡶⣄⠘⢧⡹⠉⣿⠲⣶⣯⡖⠋⠁⢀⣠⠄
⠀⠀⠀⣄⡙⢲⣤⡽⣷⠛⠉⡟⠋⢰⠇⡰⢋⡤⢞⣥⣾⢸⡇⢸⡇⣷⣬⡳⢤⡙⣆⠸⠆⠛⢻⠉⠛⣾⢯⣤⡖⢋⣠⠄
⠀⠀⠀⠞⣿⢉⡟⢠⠇⠀⣸⠃⠀⣠⣾⡵⣋⣠⡤⣾⡉⠃⡇⢸⠘⢉⣷⢤⣄⣙⢮⣳⡄⠀⠘⣇⠀⠸⡄⢻⠉⣿⠳
⠀⠀⠀⠀⠁⠈⠁⠈⠀⢠⡏⢀⣴⠟⠁⠀⠈⣤⣼⡇⢳⡀⣇⣼⢀⡞⢸⣧⢤⠉⠀⠈⠻⣦⡀⢸⡄⠀⠁⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢉⣀⣤⠴⠖⠚⢻⠿⡝⠀⠁⢿⡿⠈⠀⢫⠿⡟⠓⠲⠦⣤⣀⡉⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⢀⣀⣠⣤⣏⠀⠹⣄⠀⢸⡇⠀⣰⠏⠀⣹⣤⣄⣀⡀⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣡⣤⣞⠘⣆⠀⠙⣆⠸⠇⣰⠋⠀⣰⠃⣻⣤⣌⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠈⢧⠈⠀⠀⠘⣆⣰⠃⠀⠀⠁⡼⢁⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠓⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠚⠉⠃

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢶⣧⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⣾⡴⢀⡀
⠀⠀⠀⠀⠀⢿⣾⣄⡽⣅⣼⣞⠇⠀⠀⠀⠀⠀⢸⡿⣤⣀⣇⣠⠿⣟⠀⠀⠀⠀⠀⠀⣿⠇⣄⡶⣄⡜⢿⡃
⠀⠀⠀⠀⠀⣰⣤⠾⣤⠼⣤⣤⡀⠀⠀⠀⠀⠀⠠⣤⡤⠿⡿⢧⣤⡤⠀⠀⠀⠀⠀⠀⣤⡠⠾⣤⠼⠄⣠⠄
⠀⠀⠀⠀⠀⠛⠙⠠⣾⠦⠘⠙⠃⠀⠀⠀⠀⠀⠘⠹⢀⣤⣧⡀⠻⠙⠀⠀⠀⠀⠀⠀⠋⠇⣠⣬⣄⠸⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⢀⣾⣤⠘⢿⠋⣠⣼⡄⠀⠀⠀⠀⠀⢠⣼⡀⢙⡏⠁⣶⡤⠀⠀⠀⠀⠀⠠⣤⡇⠈⣩⠉⠰⣦⠄
⠀⠀⠀⠀⠈⢐⡋⣻⣾⣞⡋⣓⠉⠀⠀⠀⠀⠀⢘⠉⢙⡏⢙⣟⠉⣙⠀⠀⠀⠀⠀⠀⡋⠈⣳⣿⣞⡃⢉⡃
⠀⠀⠀⠀⠘⢾⠻⢁⣼⣈⠹⢷⠏⠀⠀⠀⠀⠀⠸⢿⠋⢉⡏⠉⣿⠯⠀⠀⠀⠀⠀⠀⠿⡎⠁⠻⠈⢱⡿⠅
⠀⠀⠀⠀⠀⠈⠀⠨⠿⠯⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣀⡦⠙⢺⠚⢱⣄⡀⠀⠀⠀⠀⠀⢀⣄⠀⢸⡟⠀⣀⣄⠀⠀⠀⠀⠀⠀⣠⡆⠙⢻⠛⠱⣤⡀
⠀⠀⠀⠀⠀⠞⠛⢶⠚⢶⠞⠻⠆⠀⠀⠀⠀⠀⠈⠛⠳⢤⣧⠶⠛⠉⠀⠀⠀⠀⠀⠀⠟⠓⢶⠛⢶⠚⠹⠇
⠀⠀⠀⠀⠀⣻⡶⠛⢲⠛⢳⣾⡁⠀⠀⠀⠀⠀⢠⡴⠟⢩⡏⠛⢶⣤⠀⠀⠀⠀⠀⠀⣷⡖⠛⢲⠛⠲⣼⡇
⠀⠀⠀⠀⠀⠀⠋⠶⢺⠲⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠶⣾⠶⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⣿⡇⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⣿⡇⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠙⣿⣿⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⣿⠋⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠈⣿⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⡟⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣽⣧⠀⢸⡇⠀⠀⠀⠀⠀⠸⣷⣤⣿⣠⣶⠇⠀⠀⠀⠀⠀⢀⣿⠃⣰⡟⢀⣠⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣶⠶⠾⠿⠿⣦⣼⣇⠀⣿⡀⢠⣶⣦⠈⢻⣿⠋⢀⣤⣄⠀⢠⡄⠀⣾⣇⣰⣿⣿⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⡶⠾⠿⠿⣶⣿⡇⠈⠛⢿⡀⢸⣿⠀⣸⡿⠛⠀⣿⣧⣼⣿⣿⣋⠉⠛⠛⠻⠷⢶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠛⠻⢷⣤⡈⢷⣸⣿⣼⠏⣀⣤⣾⠿⢿⣥⣄⠉⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⣍⣻⣿⣿⣿⣿⣾⣛⣉⣀⣤⣄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠛⠁⣈⣭⣿⣿⣿⣿⣿⣯⣉⠉⠙⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣀⠙⢛⣷⣶⡾⠛⠉⣰⠟⣿⡏⢿⡍⠛⢷⣦⣤⣴⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⢶⣦⣤⣤⣀⣩⣿⣿⡟⢹⡿⠀⣴⣾⡏⠀⣿⡇⠈⣿⣦⡄⢸⣿⠿⣶⣶⡶⠾⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⠏⢹⡿⠀⠘⠃⠀⠙⠛⠁⣠⣿⣧⡀⠛⠟⠁⠘⣿⠀⢹⡟⠻⣶⣶⣶⠶⠿⠿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⣾⠏⢠⣿⠃⠀⠀⠀⠀⠀⢰⠿⠋⣿⠛⢿⡆⠀⠀⠀⠀⠀⢸⡇⠀⢻⣟⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⣼⠏⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣿⡀⠀⠉⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⣠⣿⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣿⣿⣄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⢸⣿⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⢸⣿⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡌⢸⡷⢁⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠄⢸⡧⠠⠶⠃
⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⠀⠀⡀⢀⠀⠀⢀⠀⣦⠀⠀⣴⢸⡇⣦⠀⠀⣴⠀⠀⠀⠀⡀⢀⡀⠀⡀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣐⠶⣌⡄⠃⢸⠇⠀⠈⢻⡙⣦⣄⠻⡿⢿⠿⣡⣴⢋⡞⠁⠀⠸⡇⠸⢁⣃⡶⢎⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣈⠚⢿⣦⣔⡷⣦⠘⣟⣿⣿⡏⣴⣦⢹⣿⣿⣿⡃⣴⢾⣦⣴⡾⠛⣋⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⡴⠂⣸⣝⣿⡟⢚⣉⠣⡁⢠⢻⡟⡄⢈⠜⣉⡓⢻⣿⣫⣅⠐⢦⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣉⣩⣷⣘⠿⢿⣮⠿⠟⠻⢿⣵⡿⠿⢃⣾⣍⣋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⢮⣽⣿⣿⡃⣈⡵⣿⠀⠰⠖⠀⣿⢞⡉⢘⣿⣾⣟⣱⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣩⣙⡿⢡⣶⣾⢟⣶⣦⣴⣶⡻⣷⣦⡍⢿⣋⣉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠳⠄⢙⣫⣿⣧⢬⣉⡔⡁⠘⣼⣧⠃⢈⢢⣉⡥⣼⣿⣝⡋⠠⠞⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣩⣤⡾⠟⠹⡷⠟⢠⣯⣿⣿⣇⠻⠟⣸⣿⣿⣽⡄⠿⢾⠝⢿⣷⣤⣭⡥⢀
⠀⠀⠀⠀⠀⠀⠀⣬⡱⠞⢩⢁⡄⢸⡆⠀⢀⡼⣡⠟⢋⣴⣷⣾⣦⠙⠻⣼⣇⡀⠀⠰⡇⢘⠙⡟⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠿⠀⠀⠻⢸⡯⠟⠀⠀⠻⠉⠉⠀⠀⠁⠈⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠂⢺⡗⠐⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢃⢾⡇⡘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇

⠀⠀⠀⠀⠀⠀⠀⣀⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀
⠀⠀⠀⢀⡀⡄⢀⡈⢻⡟⣁⠀⣤⢀⠀⠀⠀⠀⠠⣼⣿⣧⠀⣴⣿⣿⡤⠀⠀⠀⠀⠀⠶⣾⣺⣭⣭⣄⣷⠶
⠀⠀⠀⢨⡿⠿⣬⣿⣼⣷⣯⡴⠿⣯⠀⠀⠀⡀⢀⡘⢿⣿⣶⣿⣿⠛⣀⢀⡀⠀⢠⡎⣴⣻⣿⣿⣿⣿⢿⣮⢱
⠀⠀⠀⠀⠰⠷⢶⣿⣿⣿⣿⠶⠷⠀⠀⠀⠠⢿⣿⣿⣿⡇⠀⢈⣿⣿⣿⣿⠥⠀⢦⣬⣷⣽⣿⠋⠙⣿⣿⣿⣧⣴⠂
⠀⠀⠀⢈⣿⣿⢋⡿⢻⡿⣯⠻⣿⣏⠁⠀⠀⠋⠉⢉⣽⣿⣶⣾⣿⣍⠉⠙⠃⠐⢛⡽⣿⣿⣿⣷⣾⣿⣯⣟⢿⠛⠂
⠀⠀⠀⠀⠀⠃⠈⣡⣾⣧⡉⠀⠛⠀⠀⠀⠀⠀⠠⢾⣿⡿⠁⠿⣿⣿⠦⠀⠀⠀⠀⠳⠘⣾⣿⣿⣿⣿⣿⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⠋⠙⠀⠀⠀⠀⠀⠀⠛⢻⠈⠷⠽⠁⡿⠙⠂



⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⡀⠲⣶⠖⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣷⠞
⠀⠀⠀⠀⠀⢽⣿⣷⣀⣶⣿⣿⠀⠀⠀⠀⠀⣰⡀⣾⠛⠷⣿⠾⠛⣿⠀⣦⠀⠀⢠⣿⡤⣿⣇⣸⣇⣻⠿⠂⣿⣤
⠀⠀⠀⢀⢠⣹⣿⣿⣿⣿⣿⣏⣡⢀⠀⠀⠐⢋⣿⣿⣴⡿⠟⠿⣦⣿⣿⡛⠣⠰⠞⡛⠛⣶⣿⠟⠛⢿⣶⠞⣛⠳⠆
⠀⠰⠿⢾⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠾⠆⠰⣿⣍⠰⣿⠀⠿⠇⣽⠇⣉⣿⠆⠀⠐⣿⠗⣿⣧⠀⠀⢸⣿⠛⠿⠃
⠀⠀⠀⠀⠘⣩⢿⣿⣿⣿⣿⣏⡙⠀⠀⠀⠠⣤⡽⣿⠻⡷⣶⢾⠟⣿⣿⣥⡆⠈⢻⣷⡞⠙⣿⢿⣿⢿⣋⠻⣶⣟⠃
⠀⠀⠀⠀⠀⣺⣿⡿⠋⠿⣿⣿⠀⠀⠀⠀⠀⠙⠂⢿⣦⡶⣿⠷⣦⣿⠀⠋⠀⠀⠀⠿⠀⠻⠿⣸⣇⠸⠻⠁⠿
⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢹⡏⠓


⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⢰⠀⣤⢸⣶⣆⠀⠀⠀⠀⠀⠀⢀⡤⢄⢰⡆⡠⢤⡀
⠀⠀⣶⣷⣦⣰⡶⠟⠻⠶⣦⣰⣾⣷⡆⠀⠀⠰⣽⣻⣼⣿⣿⣽⣫⡵⠀⠀⠀⠀⠀⣤⣹⡆⠙⣻⣟⠋⢰⣅⣄
⠀⠀⠉⠛⣿⠋⣴⣿⣿⣶⡈⣿⠛⠋⠁⢠⣜⡶⣿⣿⡿⣟⡿⣿⣿⡧⢖⣢⠄⠀⢠⢬⠿⢿⣶⣾⣷⣶⡿⠿⡵⡄
⠀⠀⠀⣘⣿⡀⢿⣿⣿⣿⠇⣼⣃⡀⠀⢻⠿⣻⣿⣿⣯⡿⣯⣿⣿⣿⡻⢿⡓⠀⠱⠰⣦⣤⣿⣿⣿⢿⣤⣴⢦⠇
⠀⠀⣿⣿⣿⢷⣦⣉⣉⣡⡾⢿⣿⣷⡇⠀⠈⢁⣽⢿⣿⣿⣿⣿⢿⣅⠉⠁⠀⠀⠀⠚⢻⡏⢁⣿⣯⡈⢹⠛⠃
⠀⠀⠈⠃⠀⠈⠁⣿⣿⡏⠁⠀⠈⠃⠀⠀⠀⠨⣶⣿⢹⡏⢻⢹⣿⡮⠁⠀⠀⠀⠀⠀⠙⠦⠍⠹⠏⠫⠔⠃
⠀⠀⠀⠀⠀⠀⠐⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠀⠈⠘⠉⠁

⠀⠂⠀⠀⢠⠂⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢈⡲⢍⠴⣈⠀⠀⠀⢀⠀⠀⠀⠀⠺⣦⣀⠞
⠤⠄⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠾⠃⠀⠠⠹⣆⠀⠀⠀⠀⠀⠤⢶⣯⣵⡮⡯
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠄⠀⠀⢠⡀⠀⠀⣀⠀⠀⠐⠂⠀⠀⠋⠀⠀⢀⡀⠀⠘⠃⠀⠀⠀⠀⠀⢠⡯⠒⢿⡃
⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⣈⠃⠘⡐⢃⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠆
⠀⠰⠀⠀⠈⠀⠁⠀⠀⠀⠠⠴⠆⡵⣿⠧⠁⠴⠦⠀⠀⠀⠀⠀⠀⠹⣆⡰⠀⡄⣠⡖
⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡌⠁⠡⡈⠀⠀⠀⡀⠀⠀⠀⠀⠒⢻⡇⢀⣼⠟⠒⠀⠀⠀⠛⠀⠀⠀⢀
⠀⠀⢱⣜⣁⠀⠀⠀⠀⣀⠀⠀⠈⠀⠈⠀⠙⠀⠀⠀⠀⠀⣀⣈⣦⣀⣄⣻⣼⣁⣀⣠⣎⣀⣀⠀⠀⠀⠀⣈⣣
⠃⠐⡮⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠩⠏⠈⢁⡌⠱⣌⠁⠈⠯⠁⠈⠀⠀⠀⡀⠀⠠
⣿⣿⡦⣼⢴⡧⢦⠄⠀⠀⠀⠀⡗⢦⠀⣀⠀⢀⠤⡆⠀⠀⠀⠀⠐⢒⢾⠁⠀⡹⣶⠤⠀⠀⠀⠀⠀⣤⢸⡄⡦
⡛⢻⣀⡈⠀⠉⠢⠀⠀⠁⠀⣀⠡⡀⢣⠿⢠⠁⡠⠃⠀⠀⠀⠀⠠⠟⠀⠃⠐⠁⠙⠇⠀⠀⠠⠀⠀⠀⠌⠐⡠
⠑⠈⡵⡒⠒⠀⠀⠀⢀⡀⠤⠝⡓⢪⠛⠛⠺⡬⢞⣋⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣲
⠁⠘⠀⠻⠀⠀⠀⠀⠉⠒⠦⠔⢒⡻⣄⠀⣠⢟⣫⠤⠬⠽⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠞⢫⠖⡉⣭⢫⠲⡍⠃⠀⠀⠀⠀⢄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⣀⠀⡀⠀⠐⠀⠀⡇⡴⠃⠿⠈⠢⣘⠀⠀⠀⠀⠀⠈⢂⡀⣀⠓⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠂⠀⠀⠀⠠⠈⣤⠁⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠤⠄⠬⠁⠩⠤⠠⠠⠤⠀⠀⠐⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠔⠀⠆⠀⠀⢠⡄⠀⠀⣄⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⡜⠃⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⣘⣧⢂⡞
⢴⡦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣈⣦⣌⢀⣀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠘⠄⠀⠀⠀⠐⠲⠖⠖⡲⠀⠀⠸
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠑⢻⡌
⠀⠤⠀⠀⠐⣢⠂⠀⣔⠃⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⡀⠀⠀⠱⣆⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠚⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠂⠘⢀⢀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠘⢆⣠⣀⡾⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠁⠙⠉⢁⡀⢀⡉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⢵⢬⡌⣵⡎⣵⣤⣤⣤⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣖⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⣧⢄⠄⠀⠀⠀⠀⠀⠀⡀⠀⠓⣧⠛⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠾⣶⣆⢺⠗⣤⣶⠶⠁⠀⠀⠀⢒⣶⢘⠯⡥⣟⢼⣖⠀⠀⠀⠀⡴⢷⢔⡘⡷⢓⡢⡶⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⠿⠯⣭⣅⠀⠀⠀⠀⠐⢕⠲⢪⠑⡇⣭⢺⢪⠇⠀⠀⠀⡀⢨⢭⡭⡷⢭⡭⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠿⠛⠣⣺⣷⠉⠛⠿⠄⠀⠀⠀⠖⢛⣲⢎⡇⢷⠻⠓⠀⠀⠀⠀⠙⡟⠓⠴⣛⠜⠚⣛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠉⠏⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠖⠟⠦

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⡶⢤⡄⠀⠀⠀⠀⠀⠀⢀⠤⢀⣆⠤⢄⠀⠀⠀⠀⠀⠀⠀⡤⠀⣖⢀⣤
⠀⠀⠀⠀⠀⠀⢀⣾⣧⢳⢭⡵⠆⣽⣧⡀⠀⠀⠀⢲⣤⠴⢮⡯⠦⣼⡴⠀⠀⠀⠀⠰⣴⡌⣮⣭⣶⢩⣴⠂
⠀⠀⠀⠀⠀⠀⢸⡥⡷⣋⠶⢆⡱⠶⢸⠆⠀⠀⢐⡃⠰⢎⡱⡷⣙⢾⠈⡇⠀⠀⠀⢞⠦⢾⣿⣿⣿⠶⠰⡳
⠀⠀⠀⠀⠀⠀⠈⢿⡟⡽⣚⡲⠏⢻⡟⠀⠀⠀⠀⠼⠛⠹⢖⣗⠯⢻⠳⠄⠀⠀⠀⠠⠿⣃⢟⣛⢿⠘⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⠷⠚⠃⠀⠀⠀⠀⠀⠀⠘⠒⠈⠏⠲⠚⠀⠀⠀⠀⠀⠀⠀⠓⠈⠿⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢰⡂⣠⡄⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⢦⣦⢴⡭⢵⡄⣧⠴⠀⠀⠀⠀⢠⣿⠽⢞⡏⡾⣼⣆⠀⠀⠀⠀⠠⣄⡄⠬⣟⠥⢠⣤
⠀⠀⠀⠀⠀⠀⠤⡊⠥⣧⣿⣷⣽⠌⢑⠤⠀⠀⠠⡫⢼⢜⣲⣧⣛⢼⢜⡇⠀⠀⠀⠀⠈⢝⣓⡶⣚⡫⠁
⠀⠀⠀⠀⠀⠀⢀⡼⡷⢵⠫⢷⠯⡾⢥⠀⠀⠀⠀⠹⣿⢩⡖⡗⣯⢺⡞⠀⠀⠀⠀⡰⠞⠏⠧⣗⠬⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢻⡛⠲⠇⠀⠀⠀⠀⠀⠀⠙⠿⠞⠓⠾⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣌⢿⡿⣡⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣀⠀⠙⢿⡿⠋⠀⣀⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢻⣿⣿⡄⣿⢸⡇⣿⢠⣿⣿⡟⠀⠀⠀⠀⢠⡄
⣀⣀⡀⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⣬⣭⣿⣿⣸⣇⣿⣿⣭⣥⠀⠀⠀⠀⣴⣿⣇⠀⠀⠀⠀⠀⢀⣀
⠈⢿⣿⣿⣦⢹⡇⠀⠹⣿⣿⢠⡦⢸⣷⣄⡀⠀⠈⢻⡟⠁⠀⢀⣠⣶⡇⢴⡀⣿⣿⠏⠀⢸⡇⣴⣿⣿⡿
⠀⠀⠙⣛⣛⣿⣿⣜⡻⢾⣿⡿⠁⠘⣿⣿⣇⢠⡆⢸⡇⢰⡄⣸⣿⣿⠃⠈⢿⣿⡷⢟⣣⣿⣿⣛⣛⠉
⠀⠀⠀⠉⠉⠀⢶⣭⣛⢶⣽⣇⠀⠠⣬⣝⣿⣿⠁⢸⡇⠈⣿⣿⣫⣥⠄⠀⣸⣯⡶⣛⣭⠶⠀⠉⠉
⠀⠀⠀⣠⣾⣿⣶⡾⣿⠟⠛⠙⠻⣦⣄⡈⠉⢿⡄⢸⡇⢠⡿⠉⢉⣠⣴⠞⠋⠙⠻⣿⢷⣶⣿⣷⣄
⠀⠀⠉⠛⠛⠛⠋⢼⠏⢀⣀⠐⢶⣄⠉⠛⢶⣤⣻⣾⣷⣟⣤⡶⠛⠉⣠⡶⠂⣀⡀⠹⡧⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⡷⣿⡷⠶⠶⢾⣿⣿⣿⣿⡷⠶⠶⢾⣿⢾⣿⣿⣿⡷⠆
⠀⠀⣀⣤⣤⣤⣄⢺⣆⠈⠉⠡⠾⠋⣀⣤⡶⠛⣿⢿⡿⣯⠛⢶⣤⣀⠙⢷⠌⠉⠁⣰⡗⣠⣤⣤⣄⣀
⠀⠀⠈⠙⢿⣿⡿⢷⣿⣦⣄⣠⣴⠞⠋⢁⣀⣾⠃⢸⡇⠘⣷⣀⡈⠙⠳⣦⣄⣠⣴⣿⡾⢿⣿⡿⠋
⠀⠀⠀⣀⣀⠀⠶⢛⣭⡾⣿⡏⠀⠐⠛⣫⣿⣿⡀⢸⡇⢀⣿⣿⣝⠛⠂⠀⢹⣿⢷⣭⡛⠶⠀⣀⣀
⠀⠀⣀⣭⣽⣿⣿⢋⣵⢾⣿⣷⡀⢰⣿⣿⡟⠸⠇⢸⡇⠸⠇⢻⣿⣿⡄⢀⣾⣿⡷⣮⡙⣿⣿⣯⣭⣀
⢀⣼⣿⣿⠟⣹⡇⠀⣠⣿⣿⠘⠗⢸⡿⠋⠁⠀⢀⣼⣧⡀⠀⠈⠙⢿⡇⠺⠃⣿⣿⣄⠀⢸⣏⠻⣿⣿⣧
⠉⠉⠉⠁⠀⠈⠀⠀⢹⣿⠟⠁⠀⠀⠀⢛⣛⣿⣿⢹⡏⣿⣿⣛⡛⠀⠀⠀⠈⠻⣿⡏⠀⠀⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣼⣿⣿⠇⣿⢸⡇⣿⠸⣿⣿⣷⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠉⠀⣠⣾⣷⣄⠀⠉⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣾⣷⡙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⠔⠁
⠀⠀⢄⠀⠀⠃⠀⠄⠀⠑⠀⠐⠀⠀⠊⠀⡄⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡀⠀⠈⠰⠷⠊⠀⠀⠀⢠
⠀⠀⠈⠀⠓⣀⡀⠈⠀⠀⠀⠰⠀⠀⠀⠠⠀⠀⠊⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠖⡂⠀⠃⠠⠥⢀⠁⠀⠀⣃⠒
⠀⠀⠀⠀⣀⣀⡀⠀⠢⠀⡀⠐⠀⢠⡀⠄⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠹⢆⡀⠆⣀⠐⠆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⠅⡳⣅⠐⠀⠠⠂
⠀⠀⠀⠀⠐⠀⠀⠀⡠⠄⢃⠀⡤⠘⠀⠀⠄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠢⠔⠈⠐⢀⠁⠠⠘⠣⢀
⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⡂⠀⠀⠀⡀⠘⠕⢨⠉⠁⠀⠀⠀⠀⠐⠂⠀⠌⠀⠀⠀⢀⡂⠁⠀⠀⠁⠈⠠⡀
⠀⠀⠀⠄⠂⢁⠄⠀⠁⡠⠀⠀⡀⠀⢄⠀⠰⠀⠀⡄⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠊⠢
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡒⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠡⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠻⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢨⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠀⠘⠂⢀⡼⠀⠀⢰⠀⠀⠘⢁⠠
⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⣄⠈⠀⠀⡄⠀⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠀⠙⠶⠆⠃⠀⠃⠘⠠⢦⣤⠴⠊⠀⣀
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⡀⠰⠤⢀⠀⠠⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠚⠢⠀⠂⠂⠄⢀⠴⠁⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⡉⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⢀⣸⣥⣀⡀⠀⠀⠀⠐⡈⠈⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠉⡀⢄⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⡤⠒⠋⠁⡐⠀⠆⠀⠠⠀⠐⠣⠤⡀⠀⠚
⠀⠀⠀⠀⠠⠲⠀⠀⠀⠐⠂⠀⡄⠐⠆⠐⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⠁⠀⢆⠀⠠⠉⠀⠀⣿⠀⠈⠢⠀⢀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠂⠀⠀⠐⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢃⢐⠠⠀⠀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡢⢤⡤⣒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⢀⠀⠀⡠⣀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⠨⣘⡯⠀⠀⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⢇⡀⠁⣀⠔⠛⠭⠀⠀⠀⠀⠀⠀⠀⡲⢤⣄⡄⠀⡀⠇⢠⠀⣸⣴⠾⡓⢄⡀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠓⣄⣾⠕⣫⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠊⠔⠋⢑⣚⣿⣷⣊⣀⠀⠁⠈⠁⠈
⠀⠀⠀⠀⠀⠐⢻⠟⠉⠉⠩⣭⢛⠟⣍⠓⠬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠔⢹⠙⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠁⡜⠀⠘⠁⠀⠀⠉⠲⣶⡄⠀⠀⠀⠀⠀⠀⠤⣐⣒⠾⠻⠀⠈⠀⢋⢷⣒⡒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠄⠀⠀⠀⠀⠈⡌⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣙⣇⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⡀⠡⠀⣤⠀⣂⠗⠠⠀⠀⠀⠀⠀⠀⢴⡰⡀⠠⡀⡀⠀⣇⢘⠀⠀⢠⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠽⠓⠤⠬⣙⣬⣠⡧⠊⣩⡅⠀⠠⠤⠀⠀⠀⠀⠩⠭⠛⠢⢔⡳⣄⡿⢁⠤⠒⠛⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠓⣂⢟⠿⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⡻⡿⣓⠒⠣⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊⠠⠎⠰⠈⠖⠈⢹⠳⡶⠀⠀⠀⠀⠀⠀⠀⠉⠀⢁⡔⢡⢇⠈⠑⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠙⠀⠀⡀⠀⠀⣃⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠿⠀⠀⠄⠀⠀⠸⢱⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠐⡹⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶
⠀⠀⠀⠀⠀⠀⣿⣷⣦⢠⣶⣿⣇⠀⠀⠀⠀⠀⠀⢀⡀⣰⡄⠛⢿⡿⠛⢠⡄⢀⡀⠀⠀⠀⠀⡀⢠⡀⠀⠻⣿⠟⠀⢀⡄⢀
⠀⠀⠀⠀⠀⣀⠿⠋⣭⢈⣽⠻⢟⡀⠀⠀⠀⠀⠀⢈⣻⣿⣧⣴⢻⡟⣦⣼⣿⣟⠁⠀⠀⠀⠀⣙⣿⣷⣄⣤⣿⣤⣀⣾⣷⣏
⠀⠀⠀⢴⣿⣿⡣⣶⠽⣾⢵⡦⢻⣿⣷⡆⠀⠀⠀⢈⣉⠀⣯⣹⣿⣿⣏⣿⠀⣉⠁⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠛⣣⡀⠿⠘⢷⣠⡟⠛⠁⠀⠀⠀⠀⢀⣽⣿⡟⢯⣼⣧⠽⢻⣿⣯⡀⠀⠀⠀⠀⣛⣿⣿⠛⠻⣿⠟⠛⢿⣿⣛
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠙⠃⣴⣾⣷⣦⠘⠃⠈⠀⠀⠀⠀⠀⠉⠘⠃⠀⣰⣿⣦⠀⠘⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⣠
⠀⠀⠀⠀⠀⣠⡤⣄⢰⣯⣿⠀⣤⢦⡀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣿⣿⣯⣷⣴⣄⠀⠀⠀⠀⠀⠀⢀⠀⠈⣷⡄⢻⡏⢠⣾⠃⢀
⠀⠀⠀⠀⠀⠙⢷⣻⢾⡏⣿⠯⣷⠟⠁⠀⠀⠀⠀⠀⠀⣯⣽⣵⡏⠺⠗⢹⢸⠷⣷⠀⠀⠀⠀⠠⣬⣷⣀⡘⠿⣼⡇⡿⢃⣴⣯⡤
⠀⠀⠀⠀⣶⣳⣿⢿⡋⠀⠀⢹⣻⣻⣳⣗⠀⠀⠀⠀⣿⣿⡳⡄⠀⠀⠀⠈⢁⢿⣿⣷⠀⠀⠀⣤⣤⣠⣍⠛⢶⣿⡷⠞⣋⣅⣀⣀
⠀⠀⠀⠀⠉⠉⣹⡿⣷⡤⢴⣫⢿⣋⠉⠁⠀⠀⠀⠀⢿⣿⠟⡁⡀⠀⠀⢀⣈⣻⣿⡿⠀⠀⠀⠁⠉⣉⣩⠶⠛⣿⠛⠶⣌⡋⠙⠙
⠀⠀⠀⠀⠀⠸⣳⡟⢛⡯⣿⠋⢷⣫⠇⠀⠀⠀⠀⠀⠘⢿⣻⡇⣧⢾⡦⣼⡨⣭⡽⠀⠀⠀⠀⠈⢹⠏⣠⡿⠃⣹⠘⢷⡈⠹⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⡿⡿⠿⠓⠛⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢠⡿⣇⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠰⣿⣇⠀⣻⡟⠀⠀⣀⡀⠀⠀⠀⠀⠀⡄⠀⣤⣄⣙⣋⣠⣤⡀⢠⠀⠀⠀⠀⠀⠀⠀⠨⣷⡄⣺⣗⢀⣾⡇
⠀⠀⠀⢠⣶⣄⡴⠛⢿⠉⡟⢛⣦⠾⠿⠃⠀⠀⠀⠀⣠⣧⣸⣿⠛⢿⡿⠛⣿⣇⣼⣄⠀⠀⠀⠀⠸⢿⣶⣿⣿⣿⣿⣿⣿⣴⣿⠏
⠀⠀⠀⠀⠉⣿⠓⠒⣾⣿⣷⣉⡘⣧⠀⠀⠀⠀⠀⠈⣁⣴⡿⠿⣷⠞⠛⣾⠿⢿⣦⣀⠉⠀⠀⠲⣶⣶⣿⣟⠏⠀⠉⠙⣿⣿⣧⣶⠶
⠀⠀⠀⢀⣀⣹⣆⠋⢩⠛⣆⠈⣹⠿⣶⡆⠀⠀⠀⢀⡉⠻⣿⣶⡿⢦⣤⢿⣶⣾⠟⢉⣀⠀⠀⣠⣤⣿⣿⣿⡀⠀⠀⠀⣾⣿⣿⣤⣀
⠀⠀⠀⠸⠿⠇⠙⢦⣶⣤⣼⣴⠋⠀⠈⠁⠀⠀⠀⠀⠙⡟⢹⣿⣤⣾⣿⣤⣿⡏⢻⠋⠀⠀⠀⠉⢉⣼⣿⣿⣷⣴⣦⣾⣿⣿⣏⡉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠛⠋⣨⣅⠉⠛⠁⠘⠀⠀⠀⠀⠀⠚⠛⢠⣿⠟⢿⡿⢻⣿⡈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠹⠏⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢹⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠈⢺⠖⠁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠈⠣⣸⣀⠞⠀⠀⠀⢰⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣢⠀⡄⠀⢆⠀⠀⠀⠻⣀⠀⠀⠀⢸⠁⠀⠀⠀⣠⠟⠈⠀⠀⠰⠀⢠⠀⣔⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠒⣼⡀⠘⡀⠀⠀⠰⡿⡟⢦⣄⢸⡀⣠⡴⢻⢻⠆⠀⠀⢀⠃⢀⣧⠒⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣈⡱⠷⣀⠀⠀⣷⠘⣦⡈⢹⠋⣁⣴⠃⣾⠀⠀⣠⠾⢎⣁⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⣲⢯⣸⠏⢏⢻⠋⡽⢹⢀⡹⣖⠋⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣤⠖⣛⣁⡴⠚⡓⢬⣾⣾⡵⢚⠳⣤⣈⠛⠲⣤⡀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠛⠦⣥⡙⠳⣍⡡⢜⢿⢿⠣⢌⡠⠟⢉⣬⠴⠛⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠽⣞⢹⣀⠎⣸⣀⠳⣸⠉⣳⠯⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⢉⡰⡶⠋⠁⠀⡿⢸⠟⢋⣸⣍⡙⠻⡄⢿⠀⠀⠙⢶⢆⡉⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡬⢻⠁⢠⠁⠀⠀⠐⣷⣧⠞⠋⢸⠁⠙⠳⣽⣾⠆⠀⠀⠘⡄⠉⡟⠥⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠋⠝⠀⠇⠀⠎⠀⠀⡀⣴⠁⠀⠀⠀⢸⡀⠀⠀⠀⠙⣦⢀⠀⠀⠱⠀⠸⠀⠫⠑⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⡴⢹⠙⢆⠀⠀⠀⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⢼⢆⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣸⣄⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡙⢴⡧⢊⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⣸⣇⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣤⢸⡇⣤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠙⡇⣬⡀⠆⠸⠀⣷⠀⠀⠓⢦⢣⣄⠰⣿⣺⣷⣿⠆⣠⡜⡴⠞⠀⠀⣾⠀⠗⠰⢀⣭⠸⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠝⠿⣶⣦⡁⣤⣤⣄⢸⡯⣟⣷⡖⣡⣌⢲⣾⣻⢽⡇⢀⣤⣄⢈⣤⣴⠿⠫⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢁⡤⠉⣛⣿⣾⠯⠼⠻⡟⠉⡅⢿⣿⢸⠉⢻⠿⠧⢽⢷⣷⣛⠉⢤⡀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠙⠾⠛⡆⢿⣷⣮⣓⣼⡼⢧⣷⣒⣵⣾⡷⢠⠻⠷⠋⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⠴⠾⣟⣿⠂⠪⢭⣿⠉⢄⡠⠉⣿⡭⠕⠐⣿⣻⠷⠦⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠙⠻⢿⡿⢂⣚⣭⣿⣄⡈⢉⣠⣿⣭⣓⡐⢿⡿⠟⠋⠙⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⣴⣿⣶⠃⠿⠿⢋⠔⡻⢻⡟⡟⠢⡙⠿⠿⠘⣴⡿⣦⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠄⣉⣤⣵⢿⣿⣯⢱⡾⣧⣠⠇⣿⣿⢸⣀⣼⢷⡎⣽⣾⡿⣮⣤⡉⠡⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣈⣱⣾⠛⠋⣄⠙⠋⠁⢼⢟⣯⡿⠳⣌⣡⠞⢿⣽⡻⡇⠈⠙⠋⣠⠛⠛⣶⣆⡁⢄
⠀⠀⠀⠀⠀⠀⢀⡴⠦⠩⠁⠂⠼⠀⠟⠀⠀⠶⠋⡎⠁⠰⣿⢿⡿⣿⠆⠈⢱⠗⠦⠀⠀⠿⠀⡦⠐⠨⢍⠰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣈⡉⣹⡏⢉⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡁⢹⠏⢈⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⢹⡏⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢙⡣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣦⣀⠀⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⠀⣾⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠁⠄⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⣾⣿⢿⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠐⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠻⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⣠⣄⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣷⣶⣿⣦⡀⠈⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⢰⣶⣾⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⣸⣿⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠟⠀⠀⢴⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠛⠁⠀⠀⠀⠀⠉⠉⠉⠙⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⡉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⣿⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣿⣠⠞⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠙⢧⡘⣿⢋⣤⠄⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⢻⡄⢀⡄⠀⠀⠀⠀⣈⠻⣿⠛⡁⠀⠀⠀⠀⢀⡄⢀⡾⠁⢀⣠⣴⠆
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣻⣾⣷⣘⣧⢀⡄⠀⣀⡙⢷⣿⠞⢉⠀⠀⡀⠀⣾⢁⣾⣥⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣡⣤⣼⠿⠿⣤⣷⠘⠿⣇⢸⡇⢀⡿⠇⢰⣏⣼⣿⣟⠛⠳⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠛⠙⠳⣦⣹⣾⣧⣟⣠⡴⠟⠻⢧⡌⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠒⢲⣿⣿⣿⣿⠷⠶⢶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡘⢳⣦⣴⠞⢋⡽⢻⡟⣟⠻⢦⣤⣤⡴⠄
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⢦⣤⣽⣿⡟⣹⠇⢰⣾⠁⢸⡇⢸⣶⡄⢿⠛⣶⣶⡟⠛⣋⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢛⡿⢁⡿⠀⠈⠀⠀⣁⡴⣿⢷⣄⠉⠀⠘⠁⢻⡍⢿⡿⣯⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠰⠟⠉⠁⢀⡾⠁⠘⠁⠀⠀⠀⠀⢈⣤⣿⣦⡉⠀⠀⠀⠀⠘⠁⠘⣧⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠐⠋⣡⣿⡌⢻⣄⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⣿⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄
⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠰⠆⢴⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢤⣴⢀⢙⠢⠌⣿⣠⠔⠃⢀⣤⣠⡶⠂⠀⠀⠀⠀⠀⢰⠞⣡⡂⡀⠠⢍⡟⠂⠈⢀
⠀⠀⠀⠀⠀⠀⡂⠀⠈⠈⠈⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠟⢬⣻⠉⣿⡋⣇⣤⠾⠛⠇⠀⠀⠀⠀⠀⠀⠀⠘⠈⠪⠛⠀⠂⠈⠀⠀⡄⣆⢱⠆
⠀⠀⡀⠀⠁⠀⠰⠅⠀⠀⠀⠀⠀⡡⠁⠀⠀⠁⡀⠀⠀⠀⠰⠶⣈⣎⠉⠈⡾⠡⠉⡻⢑⠤⠄⠀⠀⠀⠀⠀⠀⢀⡇⢄⢂⡀⠀⠀⠀⠀⠈⠫⠹⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣴⣤⢟⢻⢀⣯⣀⣟⠶⣤⣤⡄⠀⠀⠀⠀⠀⠄⠈⣗⠹⠩⠁⠀⢁⠀⠀⣤⢄⠀⡀
⠀⠀⠀⠀⠀⠀⢈⠁⠊⠀⠀⠌⠀⢁⠀⠀⠀⠀⠀⠀⠀⠶⠛⠺⠁⣨⠌⢃⣷⠚⢭⡀⠹⠟⠳⠦⠀⠀⠀⠀⠀⠠⠀⠃⡀⠠⣡⠗⠄⠐⠴⢛⠤⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢶⣿⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢢⡭⠤⠀⠒⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢢⣀⠀⢠⠀⢀⠀⠀⡠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⡀⠸⢽⣥⠋⠀⠈⠅⣰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⠆⠀⠀⠈⠀⢰⠏
⠀⠀⠀⢀⡀⠉⠉⠃⡲⢀⠄⡤⢶⠆⠚⠚⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠄⠛⠀⠀⠀⠁⠃⠄⠀⠂
⠀⠀⢀⠀⠡⠄⣈⢵⠂⠀⠀⠀⠘⣡⠀⢀⡘⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⢠⠀⠐⡀⣀⠀⠀⠤
⠀⠛⠓⠘⢫⡌⠻⡄⠀⠀⠈⠀⢤⡀⠿⠀⠶⠆⠥⠶⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠂⠐⠚⠕⢐⠀⠀⢀⡀⠮⡗⣀⠀⠀⠓⠪⠓⠒⠂
⠀⠀⠀⠀⠟⠀⠀⠐⣏⣠⡀⣀⠘⠑⠀⠈⢥⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠈⠑⢒⡌⣋⠀⠀⠀⣉⣔⡲⠶⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣈⠆⡄⠀⠀⠉⢎⡈⠀⠂
⠀⠀⠀⠀⠀⢲⡨⠃⠘⠆⠀⡞⠐⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠠⠀⠠⠀⠘⢶
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡿⠏⠋⠻⣏⡀⠀⠀⠀⠀⠀⠀⢘⠿⢙⡙⢿⣁⠀⠀⠀⠀⠀⠀⠲⣾⣶⣿⣿⣮⠴⠀⠀⠀⠀⠀⠀⠑⠄⣒⠤⠁
⠀⠀⠀⠀⠀⠀⠙⣿⡄⡉⢠⡟⠉⠀⠀⠀⠀⠀⠈⢻⣧⢙⠃⣼⠋⠁⠀⠀⠀⠀⠀⠤⢽⣿⣿⣿⡿⡤⠀⠀⠀⠀⠀⠉⠀⡡⢛⠪⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠋⠝⠟⠈⠙⠀⠀⠀⠀⠀⠀⠀⠘⠩⠻⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠎⠋⠮⠑⠀⠀⠀⠀⠀⠀⠀⠚⠀⠰⠀⠈


⠀⠀⠀⠀⠀⠀⢀⡄⢐⢂⣔⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⡴⡴⡠⠀⠀⠀⠀⠀⠀⠀⣄⠦⣶⢖⡄
⠀⠀⠀⠀⠀⠀⣄⠐⣾⣿⣷⠢⠆⠀⠀⠀⠀⠀⢀⡀⠐⢬⡌⠄⠤⠀⠀⠀⠀⠀⠀⠈⣟⢲⣿⣷⢺⢒⠀⠀⠀⠀⠀⢘⡊⢡⣷⡎⠬⠅
⠀⠀⠀⠀⠀⠀⠀⣬⠹⠛⠏⡅⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠘⡹⣤⣉⣧⢟⠂⠀⠀⠀⠀⠀⠐⢢⢄⢸⢴⡎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠖⠞⢶⣀⠀⠀⠀⠀⠀⠀⠀⡰⢈⠬⢤⡔⠄⠀⠀⠀⠀⠀⠀⠀⠢⣴⠛⠶⠶⠂⠀⠀⠀⠀⠀⠐⢶⣶⣿⣶⣗⡄
⠀⠀⠀⠀⠀⠀⠂⣿⡸⠽⢀⡧⡂⠀⠀⠀⠀⠀⠐⠂⣗⡺⢇⡿⡘⠀⠀⠀⠀⠀⠀⠰⠈⣿⠶⡤⠤⠠⠀⠀⠀⠀⠀⠾⢿⠿⢿⠿⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠎⠳⡓⠋⠒⠀⠀⠀⠀⠀⠀⠀⠠⠊⠍⡍⠈⠂⠀⠀⠀⠀⠀⠀⠀⠰⠋⢢⡖⠲⠀⠀⠀⠀⠀⠀⠀⠴⠰⢰⠦⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⢪⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠲⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢱⡆⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⠀⣾⡹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣄⠀⠈⣿⡇⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠦⣄⣿⣷⠀⣿⠤⠃⠀⠀⠀⠀⡞⠓⡄⠀⠀⠀⠈⡷⠞⣀⣠⣤⠾⠓⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣴⠃⠀⠀⠀⠀⠀⠀⢸⡞⠁⠀⢀⣤⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣠⣴⣾⡿⢿⡋⣉⣀
⣞⣻⣦⣤⣤⣤⣄⣀⣀⠙⠳⡀⠀⠀⠱⣤⣇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣠⣾⡿⠿⠋⠁⠀⠀⠀⠻⠼⠂
⠈⠉⠀⠀⠉⠙⡛⢻⣿⣿⣿⣿⣶⣶⣶⣦⣬⣷⣄⣀⣀⠀⠀⢀⡿⣤⣀⣀⡴⠿⠋⠙⠒⠲⠟⣛⡆
⠀⠀⠀⠀⠀⢨⣩⠏⠀⠀⠀⠀⠀⠉⣹⠛⠛⠛⠛⠉⠉⠙⢲⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⢠⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⢤⣾⡏⠀⠀⠀⠀⠀⠀⣟⢿⣷⣶⠒⠛⠳⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⠿⢁⣾⣿⠁⠀⠀⠀⠀⠀⠀⡽⣄⠙⠿⣳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠙⣆⠀⠀⠀⠀⠀⠸⣦⠟⠀⠀⢹⢿⣿⣦⣀⣀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡤⢠⣾⡿⠁⠀⡼⠒⣤⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠙⢿⣿⡙⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢠⣾⣿⠃⠀⠀⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠷⠟⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠐⢇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣧⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⢄⢸⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡀⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠤⣯⡙⣇⡟⣩⡧⠄⠀⠀⠀⠀⠀⢀⠛⠺⡀⡵⠚⣃⠀⠀⠀⠀⠀⠀⢢⣇⡀⠍⢀⣸⡔⠀⠀⠀⠀⠀⠀⣖⢲⠘⡞⣰⠒⠆
⠀⠀⠀⠀⠐⢛⣭⠜⡿⡿⢥⣝⠓⠀⠀⠀⠀⠐⢫⠝⢒⡿⡖⠚⢽⠒⠀⠀⠀⠀⠀⢅⣀⠼⠿⠥⣀⡤⠀⠀⠀⠀⠀⠀⡨⢡⠝⡟⢥⠭⡀
⠀⠀⠀⠀⠀⢡⠾⡺⢇⠿⡺⢦⠁⠀⠀⠀⠀⠀⠀⢲⣽⡀⣼⡴⠂⠀⠀⠀⠀⠀⠀⠈⠇⣠⣦⡀⠸⠁⠀⠀⠀⠀⠀⠀⠉⠊⢰⣹⠈⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⢯⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⣤⠐⣶⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡯⠄
⠀⠀⠀⠀⠀⣾⢼⣄⠽⢅⣼⣴⠆⠀⠀⠀⠀⠀⠑⠛⠮⣭⡵⡞⠚⠀⠀⠀⠀⠀⠀⣤⣉⡗⠛⢾⣉⣄⠀⠀⠀⠀⠀⠘⣺⠧⡴⠳⡤⢶⡚
⠀⠀⠀⠀⠀⠀⠡⣼⠆⢮⡠⠁⠀⠀⠀⠀⠀⠀⣔⡶⠫⣽⠝⢳⣲⠀⠀⠀⠀⠀⠀⠉⣠⠗⣶⠻⣤⠁⠀⠀⠀⠀⠀⠀⠀⣀⡗⠒⣅⡀
⠀⠀⠀⠀⠀⠀⠹⠏⠃⠋⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠎⠃⠀⠋⠗


⠀⠀⠀⠀⠀⠀⠀⠠⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣗
⠀⠀⠀⠀⠀⣴⡀⢢⣸⣤⠂⣰⡄⠀⠀⠀⠀⠀⢚⡾⣀⣹⢀⡴⡞⠀⠀⠀⠀⠀⠀⠯⢧⡤⣓⢤⠼⠽⠀⠀⠀⠀⠀⠘⢳⢦⡔⡗⣤⢶⠓
⠀⠀⠀⠀⠀⠉⡨⢿⣁⣸⠯⠌⠁⠀⠀⠀⠀⠀⠠⣤⠜⢿⠣⣤⡄⠀⠀⠀⠀⠀⠀⡤⡤⢎⣚⡼⣤⢄⠀⠀⠀⠀⠀⢀⣠⡼⣞⣟⠾⣤⡀
⠀⠀⠀⠀⠀⠀⣤⡎⢹⠉⣶⡄⠀⠀⠀⠀⠀⠀⠉⠘⠠⢾⠦⠈⠘⠁⠀⠀⠀⠀⠀⠑⠁⢠⢷⠄⠈⠊⠀⠀⠀⠀⠀⠈⠉⠁⢐⣗⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠶⣴⣀⡹⣁⣰⡴⠆⠀⠀⠀⠀⢀⡴⣠⡐⣿⠕⣄⡰⡀⠀⠀⠀⠀⢀⣄⠐⣄⣉⡠⠀⣀⡀⠀⠀⠀⠀⠀⠰⠧⡈⡏⡰⠷
⠀⠀⠀⠀⠀⠈⣀⣗⡀⣐⣇⡈⠀⠀⠀⠀⠀⠘⠛⠝⢓⡾⣚⠫⠗⠃⠀⠀⠀⠀⠈⢉⣑⣎⢉⡷⣉⠙⠀⠀⠀⠀⠀⠀⠷⠒⣿⣩⡗⠲⠇
⠀⠀⠀⠀⠐⠿⠻⢀⣽⣅⠘⠛⠗⠀⠀⠀⠀⠀⢠⡽⡟⠁⢟⠟⡤⠀⠀⠀⠀⠀⠀⠀⣤⠊⡍⠱⣄⠀⠀⠀⠀⠀⠀⠀⠐⠞⢀⣇⠸⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠤⠒⠋⠉⠉⠉⠙⠲⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠳⠚⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣐⡍⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⡀⢀⣀⠔⠊⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠈⠉⠉⠁⠀⠀⠀⠀⣀⣔⣁⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡄⢀⢀⡀⠀⣀⣤⠤⠜⣯⠑⠀⠉⠳⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢸⡀⠉⠁⠈⠀⠀⠂⢹⡧⠀⠀⠀⠀⢸⠄⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠠⢧⠀⠀⠀⠀⠀⠠⣼⠁⠀⠀⠀⠐⣼⡇⠀⠀⢀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⡆⠀⠀⠀⠐⢀⡟⠀⠀⠀⠀⠀⢱⡃⠀⣀⣀⠤⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⢅⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢀⡎⠔⠊⠁⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⢻⠀⠄⠀⠩⠚⠁⠀⠀⠘⠀⠀⠀⠠⣀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⠚⣧⠀⣠⠖⣡⠬⣆⢰⢩⣡⣈⠒⠢⠌⠋⢀⡤⠾⠶⢦⡀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣀⠘⠯⡴⠋⠀⠀⢰⠆⠀⠀⠀⠉⠑⠒⡔⠁⠀⢀⠤⠚⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⣺⣆⠀⠀⠢⢀⡴⠊⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠘⠳⠶⠶⠒⠋⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣸⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⡿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠇⠈⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⡀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣶⡃⠀⠀⠀⠀⠰⣀⣠⣤⠶⡿⠲⠶⣤⣴⡃⠀⠀⣨⡿⠧⠤⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⠶⠞⠛⠉⠁⠀⠀⡇⠀⠀⠀⠈⠙⢳⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⣆⢠⠁⠀⠀⠀⢳⡗⠃⠀⠀⢦⣴⠋⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣾⠁⠀⠼⠿⣄⢀⣀⣠⣼⣧⣤⣀⣴⠟⠉⠙⠀⢿⣤⡤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⡀⠀⠀⢀⡼⠻⣅⠀⢸⡇⣠⠟⢹⡀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⣀⣠⣏⣀⣘⣆⣀⣾⣁⣀⣈⣷⣼⣿⣋⣀⣈⣇⣀⣤⣞⣀⣿⣀⣀⣀⣤⣶⡚⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠼⠋⠉⠹⣏⠉⠽⠋⠉⠙⢯⡉⢉⣽⢿⡿⣍⡉⣹⠏⠉⠹⠍⢩⡟⠉⠉⠉⠙⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣷⣞⠁⢸⡇⢈⣻⣯⣀⣀⠀⢠⡿⣄⡀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢧⡀⠒⢒⣿⡇⠈⠓⢾⡷⠋⠁⠈⠿⣦⣀⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⠏⠀⠃⠀⠰⢺⡗⠄⠀⢀⣠⠴⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠛⠲⣦⣤⣄⣸⣧⡴⠞⠛⢇⠀⠀⠀⠙⢶⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⣿⠏⠀⠀⠀⠠⠇⠀⠀⢹⡇⠀⠀⠀⠈⠀⠀⠀⠀⢸⠙⢧⡍⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣿⠀⠀⠀⠀⠀⢀⡠⢾⡷⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠲⣄⡏⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠘⠇⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⡿⢿⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠸⠁⠀⠙



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣄⢸⡇⣀⡀⠀⠀⠀⠀⠀⢀⢀⠠⣷⠄⡀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠈⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡃⣻⢿⣿⣿⣿⣿
⠀⠀⠀⢀⣀⢰⣆⠀⠉⢻⡟⠋⠀⢰⡆⣀⡀⠀⠨⠛⢦⣿⡔⠻⠁⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⠉⣿⣷⣤⠀⣴⣾⡟⢹⡿⢿⣿⣿⣤⣝⠃⢋⣤⣾⣿⣿⣿
⠀⠀⠀⠀⣙⣿⣿⣄⣀⣼⣧⣀⣠⣾⣿⣋⠁⠀⠨⢿⢉⣿⡙⡿⠄⠀⠀⠀⢸⣿⣿⣿⣿⡶⠀⢀⠛⠿⠟⠀⢿⠿⠃⠀⠠⣾⣿⣟⣀⣴⠇⢷⣀⣸⣿⣿⣿
⠀⠀⠀⠀⠉⠀⠀⠉⣿⠁⠉⣿⠋⠀⠈⠉⠁⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣷⠀⢴⣷⡆⢰⣿⣿⣶⣾⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣶⣶⠟⠛⢷⡾⠛⠷⣦⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⠉⠉⣡⣤⣌⢉⣤⣄⡙⠋⢡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠛⢹⡇⠀⠀⣸⣇⠀⠀⢹⡏⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣶⠀⣿⣿⠟⠸⢿⣿⡇⢰⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠟⢻⡟⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣡⣤⢠⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣦⠀⠀⣿⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⣿⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣤⡈⢻⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢶⣄⡀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⣸⣇⠀⣶⠀⠀⠀⠀⠀⣤⣘⣿⣁⣤⠀⠀⠀⠀⠀⣴⠆⣰⡟⢀⣠⣴⠾⠛
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣾⠿⢿⣦⣿⡀⢴⡀⢠⣤⡈⢻⡿⠋⣡⣄⠀⣠⡀⢰⡟⣰⣿⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⠶⠿⠛⢷⣾⣇⠘⠻⣇⢸⡇⢀⡿⠛⢀⣿⣤⡿⣿⣉⡉⠛⠛⠳⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣉⠙⠳⣦⣽⣾⣷⣟⣠⡶⠟⠛⠿⢦⠄⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠗⠲⢶⣿⣿⣿⣿⠷⠶⠶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠐⠻⣶⣤⣴⠞⢋⣽⢿⡿⣟⠻⢦⣄⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠐⠷⠶⢦⣤⣤⣈⣉⣿⣾⠛⣿⠁⣴⣾⠁⢸⡇⢹⣦⡄⢹⡿⢷⣤⣶⠶⠾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⣿⠏⣼⠇⠈⠋⠀⠉⢉⣠⣾⣧⡈⠛⠃⠸⠷⠨⣿⠻⣷⣶⣿⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⣤⡶⠟⠋⠁⣼⠏⠰⠟⠀⠀⠀⠀⠀⠛⢉⣿⡍⠛⠀⠀⠀⠀⠀⠶⠀⢻⡏⠛⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠈⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣧⡈⠛⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⣿⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣿⠀⠀⠻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣴⣲⠭⠖⠛⠛⣛⣛⣲⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠒⡶⢒⣛⠭⠛⣛⠳⠶⣿⣟⣻⣿⣿⣿⣿⣿⣿⣶⣶⣖⣺⠯⠟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣾⣷⣾⣿⣿⣾⣟⣫⣤⠀⠀⠙⢛⣻⣿⣬⣙⣻⡿⢿⣿⣿⣿⠯⠭⣀⠂⠈⣷⣤
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠊⠉⡛⢙⣛⠿⣿⣿⣿⣿⣿⣯⣀⣀⡀⠀⠉⢭⣿⣿⣿⣭⣭⣝⡻⣯⡀⠀⠀⠀⠀⠻⣮⢣⡀
⠀⢠⣦⡆⠤⢰⣪⣵⣤⣶⠿⠿⢿⣿⣿⣄⠻⢿⣿⣿⣿⣿⣷⡦⠭⣀⠐⣮⣟⣻⡿⣶⣂⠀⠀⠑⠄⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠹⢿⣿⢿⣿⡿⠟⠿⣵⣿⣿⡎⣿⣿⣿⡋⢙⢻⣿⣿⣿⣿⣏⡓⠆⠸⣿⡷⢦⠁⠀⠨⣅⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣧
⠀⠀⢠⠃⢰⡟⠁⠀⠀⠀⠀⠉⢸⣿⣿⡿⣼⣿⠛⢻⣿⣿⣿⣿⢿⠑⠱⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣤⠀⢣⠀⢹⣿
⠀⢠⡇⢠⣼⣽⡟⠀⠀⠀⠀⠀⠀⠂⢽⣿⣿⣿⠠⣜⣿⣿⣿⣿⣷⡀⢀⠿⠀⠀⢀⠀⢀⠀⠀⠀⣰⣷⣆⣿⣠⠈⡤⣞⣿
⠀⠘⣿⠻⣿⣿⣿⣷⣶⣦⣤⣾⠐⠄⢺⣿⣿⡇⣀⣿⣿⣿⣿⣿⢷⡁⢮⠇⠀⠀⡘⣧⣂⣧⣶⣾⣿⣿⣿⣿⣸⠄⣷⣿⣼
⠀⡴⠃⣴⡏⠉⠉⠹⢟⣻⣿⣿⡧⣀⢻⠛⣿⣾⣿⣿⣿⣿⣿⣿⣤⢀⣄⠀⠀⠀⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣿
⣼⣁⣤⣿⡅⠀⣠⡜⢻⣿⣿⣿⣵⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣿⣾⣤⠀⠘⣌⣿⣿⣿⣿⡟⣿⣧⣿⣿⡿⠟⢸⣿
⠙⣾⡛⣿⣿⣿⠿⣿⡿⠟⢉⣿⣿⣾⣷⣺⣹⣟⣿⡏⣭⣽⣿⣿⣿⣿⣿⡿⠋⠀⠀⣿⣿⣿⣿⣟⣷⣿⣿⣿⡿⠁⠀⣼⠃
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⡟⣸⣶⡆⠀⢿⣿⣿⣧⢻⣿⣿⣿⠟⢁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣬⣿⣿⣿⣿⣿⣶⣽⣍⣿⣿⣶⣿⣧⠀⠀⠈⢿⣿⣿⣨⢿⡿⡋⢠⡞⡄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣿⣿⣿⣿⡿⠃⠘⣿⣿⣿⣿⣅⠀⠀⢸⣾⡿⠀⢿⣾⣽⣿⣯⡾⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⡿⠁⠀⠀⣿⣿⣿⣟⠁⠀⢸⣿⣿⣇⣠⣼⣿⣿⣿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢎⣄⡿⣿⣿⠁⠀⠀⣀⣿⣟⡋⠅⣀⢀⡾⠿⠛⢯⣏⣏⣭⣭⡭⠷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣⣯⣯⡦⠼⠟⠀⢠⡞⡟⣽⣹⡌⢀⣠⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣹⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠄⠀⢀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⣻⣤⡀⠀⡀⢀⢺⣗⠀⠀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠄⡄⠢⡝⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⡳⣦⢰⠟⠎⣀⣲⠵⣛⠫⠁⠀⠀⠀⠀⡀⡀⠠⣦⡀⢫⢛⠌⣠⡞⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣰⢒⢿⠐⣏⠂⠁⠀⠀⠀⠀⠀⠀⢐⠭⡻⠓⠂⠨⣷⣿⡯⠤⠄⢶⢶⠆
⠀⠀⠀⠀⠀⠀⢀⣠⡵⢿⠛⠸⠹⡾⠅⠋⠛⢥⡢⠄⠀⠀⠀⠀⠀⠀⠀⠐⠛⣡⢂⣝⡌⠱⠶⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⢭⠏⡂⠀⠀⠀⠸⠱⠆⠀⠀⠀⠀⠀⠠⢐⣸⡆⠀⠃⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠹⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⣟⡠⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠹⡅⠂⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⢤⠀⠀⠁⢀⠀⣨⠾⠡
⠀⠀⠀⠀⠀⠀⠠⣁⡀⠀⠀⠙⡇⢀⠀⣆⢠⠶⡀⠀⠀⠀⠀⠈⠟⡺⠤⢀⡀⠀⠣⣸⣀⡪⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠊⠔⠩⠛⠒⢴⣶⣅⣊⠉⠑⠉⠂⠁⠀⠀⠀⠐⠋⠀⠀⢀⣀⠉⢶⡉⢹⢐⠊⠛⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢉⠔⢹⠱⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠔⡱⢻⠙⢆⠈⠹⡳⡣
⠀⠀⠀⠀⠀⠀⠀⠤⢄⡶⠉⠀⠀⠐⡙⣦⠴⠤⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠘⢁⡌⠀⠀⠃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠁⠀⠀⠀⠱⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢱⢯⢢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⢼⣧⢊⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡁⣸⣇⢈⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⢸⡇⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠹⠇⣭⡀⠆⢸⠀⣷⠀⠀⠳⠦⢧⣄⠐⣿⣾⣷⣿⠆⣀⡼⡰⠖⠀⠀⣾⠀⡗⠰⢀⣬⠸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⠝⠟⣶⣤⡁⣠⣄⡀⢸⡦⣟⣷⡖⣡⣌⢢⣾⣻⢵⡇⢀⣠⣄⢘⣤⣴⠿⠏⡅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀⣬⠉⣻⢾⡾⣿⠼⠿⡟⠋⡃⣿⣿⢈⠙⢻⠿⠧⣿⢷⡷⢟⠛⣥⡐⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠻⠾⠟⡄⣾⣷⣬⡲⣼⡾⢷⣧⢔⣥⣾⣷⢠⠻⠷⠟⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⠴⣶⣟⣷⠂⠬⣝⣿⠉⢀⡀⠉⣿⣫⠥⠐⣾⣻⣶⠦⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠺⠿⣯⡿⠄⢒⣫⣿⣀⠈⠁⣀⣿⣝⡒⠠⢿⣽⠿⠖⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⣴⢶⣦⠃⢿⡿⢛⠕⢻⢿⡾⡟⠮⡛⢿⡿⠘⣴⡶⣦⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠈⢛⣄⣵⢿⢷⣟⢲⡶⣧⣄⡅⣿⣿⢘⣠⣼⣶⡖⣿⡾⡿⣮⣀⡛⢁⠴⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢘⣢⣾⠟⠛⡅⠙⠋⠁⢸⢗⣯⡿⠧⡙⢋⠼⢿⣽⠺⡇⠈⠙⠋⢈⠛⠿⣶⣔⡂⢄
⠀⠀⠀⠀⠀⠀⢀⣴⡆⡛⠅⠆⢼⠀⡿⠀⠀⠴⠎⡞⠉⠰⣿⢿⡿⣿⠆⠙⢣⠑⢦⠀⠀⢿⠀⡆⠰⢨⢛⢴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⢸⡇⠋⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⡁⢹⡇⢈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡠⢻⡗⠌⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠘⠃⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣠⠤⢠⢤⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣸⠤⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⣰⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠉⣿⠇⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠋⢴⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠂⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⢀⡄⠐⠀⣴⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠏⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣤⣠⣤⣠⣤⠞⠉⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠐⠀⠁⠀⠢⠄⣠⠀⠀⠀⢦⡆⠠⠠⠘⠂⠉⠃⠀⠙⠀⠸⣶⠆⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣻⣛⣿⣛⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣯⣭⣿⣿⣟⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣯⣿⢿⣮⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠄⠀⠀⠠
⡿⣻⡿⣿⣟⠿⣫⢿⠿⣛⠿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇
⣿⣾⣾⡿⣯⣺⣭⢿⣿⣶⣿⣿⣿⣿⣿⣷⣟⣧⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠄
⣿⣿⣿⣿⡿⣽⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⣿⣿⣿⢻⣿⣛⣿⡿⣻⣿⣿⣿⣯⣻⣷⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠇⠀⠀⠐⠀⠀⠀⡀⢀⠀⢨⠄⢀⠠
⣿⣿⣷⣿⣿⣿⣟⣷⣿⣿⣿⣿⣯⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠄⠁⣀⣀⠀⠀⠐⠃⠀⠐⠀⠈⠁⡀
⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣷⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠌⠈⠑⠚⠁⠂⠆⠀⠀⠀⠀⠀⠐⠆⠂
⣿⣿⡿⣿⣿⣿⣿⣯⡿⣿⣿⣿⣿⢛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠈⠡⣄⠀⠀⠀⠀⠠⠀⢀⠀⢀⠖
⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠎⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠆⡀⠁⠈⠀⠈⠀⠐⠀⠀⠀⠀⡀⠀⠅⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⡇⠀⠐⠀⠀⡴⠏⠉⢲⠀⠐⠂⠀⢀⠀⠈⠀⠀⠀⠁⠄
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣷⡇⠈⢀⠀⠈⢣⡀⢄⡸⠁⢀⡈⠉⠀⠁⠃⡁⠘⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⠀⠠⠀⠀⠉⠉⢀⠀⠄⠀⠀⠀⠀⠀⠀⢒⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠐⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠓⠲⣄⡀⢀⣠⠤⠶⠒⠒⠶⠦⣤⣄⡀
⠀⠀⠀⣬⢰⣷⢢⣦⣢⣄⠀⠀⠀⠀⠀⠀⢀⢀⡔⢁⠿⠇⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠿⢿⠀⣿⢸⡏⢛⢿⣆⡤⠒⠠⡦⠎⠉⠖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠈⢢⠙⠓⠀⠸⡈⠹⡇⣷⡄⠙⠞⠃⠀⠀⠀⠀⢀⡤⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠈⠦⣤⡀⠀⣷⠀⢹⡎⠀⠀⠀⠀⠀⠀⣀⠺⠋⣴⣶⣄⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠰⢭⣰⣿⡄⣟⠷⢀⠀⠀⠀⠀⠀⢸⣷⣤⣼⠟⠛⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣾⡟⡷⠠⡦⢇⡴⡾⣧⣈⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡋⠁⠀⠹⣈⠙⢻⠹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡙⠋⣹⠇⠈⣀⠚⣩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣼⣐⡉⢀⣼⣽⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢩⣯⣽⣯⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⢠⢠⠇⠀⠀⠀⠀⠀⠀⠀⡘⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡜⢀⡏⢀⣶⠋⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠞⠁⠀⢠⢴⢖⡤⢀⠀⠀⠀⣰⠃⡰⣡⣞⠔⠟⠛⢦⣀⠀⠀⠀⣀⣴⠋⠉⠉⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠰⢫⡟⢥⠏⣠⢀⣾⡣⡾⠓⠩⠃⠀⠀⠀⠀⠈⠛⠒⠛⠵⣭⠽⢦⣀⡤⠋⠁
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⠄⡀⠀⣤⡀⠀⣀⣠⡴⠟⠉⠉⠀⠉
⠀⠀⠀⣀⡪⠿⣉⡤⠒⢀⣀⠀⠀⠉⠴⠾⠻⡟⠁
⢠⣴⣯⡫⢲⢗⣭⣴⢞⡃⠀⠀⠀⡀⠀⠀⡼⡇
⠋⢠⠟⣩⠷⠛⣺⡵⠽⣿⣲⡤⠥⠬⠬⠭⠚
⣤⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢠⣾⣎⣻⣏⣿⣦⠀⠀⠀⠀⣴⣆⢹⡏⣰⣦⠀⠀⠀⠀⣴⣆⣙⡏⣠⣶⡄⠀⠀⠀⢠⣶⡙⣿⢡⣷⡄
⠀⠀⠀⢨⣭⣽⣿⣿⣭⣭⠀⠀⠀⠀⣥⣬⢿⡿⣥⣬⠀⠀⠀⠀⣭⣬⢿⡿⣯⣬⡀⠀⠀⠀⢭⣭⡽⣿⢯⣭⡅
⠀⠀⠀⠈⠛⢣⣾⣧⠟⠋⠀⠀⠀⠀⠙⠃⣼⣧⠘⠋⠀⠀⠀⠀⠙⠃⣴⣷⠈⠛⠀⠀⠀⠀⠈⠛⢴⣿⡌⠛⠁

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣶⣎⣻⣏⣴⣦⠀⠀⠀⠀⣴⣞⢻⡟⣷⣦⠀⠀⠀⠀⢤⣆⠙⡟⢡⣦⠀⠀⠀⠀⢠⣶⣿⣿⣿⣦⡄
⠀⠀⠀⢀⣍⣽⣿⣿⣍⣭⠀⠀⠀⠀⣯⣽⣿⣿⣯⣽⠀⠀⠀⠀⢍⣉⡽⡿⣍⣩⠁⠀⠀⠀⢼⣯⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠻⢃⣾⣧⠹⠛⠀⠀⠀⠀⠻⢯⣼⣷⡽⠟⠀⠀⠀⠀⠈⠏⡴⣧⡘⠏⠀⠀⠀⠀⠙⠻⣷⣿⡾⠟⠃
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣤⡾⢾⡗⣶⣤⠀⠀⠀⠀⣄⡖⢺⡗⢲⣀⠀⠀⠀⠀⢠⡄⠙⡟⢀⣤⠀⠀⠀⠀⢠⣦⠙⡟⠁⣦⡀
⠀⠀⠀⠀⣟⣹⣿⣿⣙⡷⠀⠀⠀⠀⢾⣉⣾⣷⣉⡷⠀⠀⠀⠀⣉⢉⣳⣷⣋⢉⠀⠀⠀⠀⣈⣉⣳⣿⣏⢉⡃
⠀⠀⠀⠀⠛⢯⣼⣧⡿⠓⠀⠀⠀⠀⠊⢧⢴⡧⡼⠑⠀⠀⠀⠀⠚⠏⢠⣇⠈⠟⠀⠀⠀⠀⠘⠿⣀⣧⡈⠟⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠲⠀⢠⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠐⠆⠀⡀⠀⠀⠀⠀⠀⡀⠀⠖⠀⢀
⠀⠀⠀⠀⠈⠁⢰⠄⠉⠀⠀⠀⠀⠀⠄⠁⠠⡄⠈⠠⠀⠀⠀⠀⠈⠁⡠⡦⠈⠁⠀⠀⠀⠀⠀⠉⠀⡤⠂⠉
⠀⠀⠀⠀⠈⠁⣠⡀⠹⠀⠀⠀⠀⠀⠀⢁⠠⠄⡈⠀⠀⠀⠀⠀⠈⠃⢀⡄⠈⠋⠀⠀⠀⠀⠀⠃⠀⣀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢰⣄⡀⠀⠈⠻⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣾⠋⠁⠀⢀⣠⠂⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠘⣿⣶⠆⠀⣰⣿⣿⠯⠉⠁⣀⣀⣀⣀⠹⣿⢿⡿⢃⣀⢀⡀⠈⠉⠙⢿⣿⣿⡀⠠⢤⣼⡿⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⣿⣿⣿⣿⠟⣉⣀⣰⠾⠛⠋⠉⠉⠉⠳⡝⠘⡵⠋⠉⠉⠙⠛⠷⢦⣀⣈⡛⢿⣶⣾⣿⡇⠐⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣴⣿⣿⠋⣴⡾⢿⣂⣀⠀⠀⠀⠀⢀⠀⡀⢷⠸⢧⡀⢀⠀⠀⠀⠀⠀⣀⡹⢷⣦⡝⢿⣿⣷⣄⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⣿⡟⠁⠈⢁⣴⠞⠛⣉⣁⣀⠘⢶⡌⣧⠀⠀⠀⠀⢠⡏⣴⠖⠀⣀⣙⠛⠻⢦⣌⠁⠀⠻⣿⡟⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⢫⣾⠃⠰⠋⠀⠀⠀⠀⠀⠉⠳⣮⣿⡏⠀⠀⠀⠀⠈⣿⣧⡴⠋⠁⠀⠀⠀⠀⠙⢧⠈⢷⣜⠇⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠿⠋⠀⠠⠟⡉⠀⠀⣾⡀⣀⣤⣶⢿⣷⣮⣿⡿⠷⠄⠀⠀⠀⠴⠿⣿⣯⣶⡿⢶⣤⣀⠀⢸⡀⠀⠘⠻⡆⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣇⡀⠀⠀⠀⠉⠀⢀⡀⠙⠟⠹⣯⡙⢛⣻⣿⠋⠀⠀⢀⠀⠀⢀⠀⠀⠉⣿⣟⡛⠚⣩⡟⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠰⣿⣿⠏⣰⡟⠀⠀⠀⢀⠎⠁⠀⢦⣄⣈⣹⣿⠋⠁⠀⠀⢀⣈⣁⣈⣁⡀⠀⠀⠈⠛⢿⣞⠉⣀⣤⠀⠀⠱⡄⠀⠀⠀⠹⣦⠹⣿⣿⡆
⠀⠀⠀⠀⢈⣿⡏⢠⣿⠃⠀⠀⠀⠁⣴⠀⠀⠈⣿⣿⢋⣷⠃⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢶⡝⢿⣿⠏⠀⠀⣤⠘⠀⠀⠀⠈⣿⡆⢹⣿⡃
⠀⠀⠀⠀⣼⣿⠀⢸⣿⠀⠀⠔⡀⠀⠹⣆⠀⠀⠸⠃⣾⣯⡀⣼⣹⣿⣛⠻⣿⣿⡟⣛⣿⣿⣷⠀⣸⣿⡘⠟⠀⠀⢠⡟⠀⠀⠀⠀⠀⣹⡇⠀⣿⣷
⠀⠀⠀⢠⣿⣿⡀⠘⣿⡇⠀⡾⠀⠀⠀⠙⣦⡀⠀⣼⣿⡿⠁⠘⠘⣿⠟⢡⣿⣿⣆⠻⣿⠏⠋⠀⢻⣿⣧⠀⠀⣰⠟⠀⠀⠀⢷⠀⢀⣿⡇⠀⣿⣿⡆
⠀⠀⠀⠀⣿⣿⠇⠀⢹⣇⠀⠁⢸⠀⣦⡀⠈⠛⠶⢿⣿⣧⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⢸⣿⡿⠶⠟⠁⠀⣰⡄⡆⠈⠀⢸⡟⠀⢸⣿⣿⠁
⠀⠀⠀⠀⢻⣿⡄⠀⠀⢿⣧⠀⠘⣷⣿⣿⣴⡆⠀⠸⣿⣿⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠰⣿⣿⡇⠀⢰⣄⣾⣿⣿⡇⠀⢰⣧⠁⠀⠀⣿⡿
⠀⠀⠀⠀⠘⣿⣧⣦⡀⠈⢿⡇⠀⠹⡏⠻⣿⣷⢰⡆⣿⣿⣀⡴⢎⣠⣴⣿⣿⣿⣿⣦⣀⠱⣤⣀⣿⣿⢠⡆⣾⣿⡿⢹⡟⠀⢰⣿⠏⠀⣀⣴⣿⠇
⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠸⣷⣷⣄⠀⠀⠈⠿⣿⣷⠸⣿⣿⣿⠋⢹⣏⣏⣏⣿⣿⣹⡏⠻⣾⣿⣿⡇⣼⣿⡿⠋⠀⠀⣠⣶⡾⡏⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⢸⣿⣿⣷⣄⡀⠀⠹⢿⡆⢿⣿⣿⡄⠈⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⡿⢰⣿⠏⠀⠀⣀⣶⣿⢿⠃⠁⣰⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣦⠀⢹⣿⣿⣿⣷⣆⡄⠘⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣿⠃⢀⣠⣼⣿⣿⣿⢸⠀⣰⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⡟⠟⡿⣿⣿⣿⣿⣿⣿⣽⠿⢻⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⢇⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⠀⢰⣿⣿⣿⣿⣿⣿⡆⢀⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⡿⠁⠀⠉⠻⢿⣿⣿⣿⣿⣿⠀⣈⠻⣿⡿⠏⣀⠀⣿⣿⣿⣿⣿⡿⠟⠉⠉⠙⡿⠟⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣾⡉⣃⡀⣀⡏⢉⣇⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣆⠙⢿⣿⣿⡟⠁⣼⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡈⠛⠋⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⣋⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⡛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⢿⣿⣿⣟
⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣏
⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⣀⣤⡎⠃⠀⠀⠀⠀⠐⢶⡄⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⣴⣿⣿⠀⠀⢀⣀⡸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡧⣀⣀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠸⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⢿⣿⣿⠿⠂⠀⠠⣬⣿⣿⣷⠀⠀⠀⠀⣄⢻⡇
⠀⠀⠀⢸⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣷⣂⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣦⠀⠀⠀⢹⡄⠁
⠀⠀⠀⢿⡏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⣿
⠀⠀⠀⢹⣏⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⡄
⠀⠀⠀⢸⣿⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣯⣭⣭⣭⣭⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣰⣿⡅
⠀⠀⠀⢸⣿⣷⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢴⣿⣿⠁
⠀⠀⠀⠀⣿⣿⣿⣦⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⡇
⠀⠀⠀⠀⢈⣿⣿⣿⣷⡀⠋⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠉⢿⣿⣿⣷⡆⢹⣿⣿⣿⣿⣿⣿⣿⣄⢀⣾⣶⣿⠿⠿⠿⠿⣷⣾⣷⡆⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣏⣿⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣯⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⢧⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠠⠟⠋⠉⠉
⣿⣄⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠛⣿⣿⠻⠛⠈
⣿⣽⣷⣄⠀⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢿⣿⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⠀⠙⢿⣦⣿⣿⣴⡿⠋⠀⢠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠙⣿⣿⠋⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣻⣿⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⣾⡇
⠀⠀⠀⠀⠀⠀⢰⣶⣤⣈⣿⡇⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⢸⣿⣁⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣄⡀⢿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⣠⣿⣿⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠉⠉⠛⣿⣿⣿⣾⠿⢿⣶⡄⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⢠⣶⡿⠿⣷⣿⣿⣿⠛⠉⠉⠛⠛⠿⠿
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⡿⠿⢻⣿⠁⠀⠀⢹⣿⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⣿⡏⠀⠀⠈⣿⡟⠿⢿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠁⠀⠀⠀⠈⠻⣷⣦⣶⡿⢿⣶⣤⣠⣴⣿⣿⣦⣄⣤⣶⡿⢿⣶⣤⣾⠿⠁⠀⠀⠀⠈⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⢹⣿⠋⠀⠀⠙⣿⡏⠁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣼⣿⣄⠀⠀⣠⣿⣧⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣶⣤⣄⣀⡀⠀⠀⠀⢀⣾⡿⠛⠻⣿⣾⠿⠛⠙⠻⣿⣿⠟⠋⠛⠿⣷⣿⠟⠛⢿⣷⡀⠀⠀⠀⢀⣀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣷⣶⣾⣿⡀⠀⠀⣸⡿⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⣿⣇⠀⠀⢀⣿⣷⣶⣾⠿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢶⣶⣦⣤⣄⣀⣴⣿⣿⣿⢿⣶⣾⠟⠁⠀⠀⢠⣴⣿⣿⣦⡄⠀⠀⠈⠻⣷⣶⡿⣿⣿⣿⣦⣀⣠⣤⣴⣶⡶
⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⣿⣿⠋⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠙⣿⣿⣿⣍⡀
⠀⠀⠀⠀⠀⠀⠺⠿⠛⢉⣿⡇⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢸⣿⡈⠛⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠃⣿⣿⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣠⣿⣿⣄⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⣠⣾⠟⣻⣿⠻⣷⣄⠀⠈⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⣿⣿⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠁⠀⠈⠂⠀⠀⣀⠤⠤⠠⠃⠈⠀⠊⠀⠄⣀⠀⢀⠔⠂⠁⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠲⡄⠀⠔⠉⠀⠀⠤⢀⠀⠔⠀⠀⠀⠀⠈⠑⠀⠀⢀⠀⠄⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠄⠈⠀⠀⠐⠛⠓⠀⠀⠁⠀⠀⠀⠐⠓⠆⠀⠀⠁⠃⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠲⠄⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⡃⠂⠀⣀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠊⠀⣀⢡⠀⠀⠀⠀⢰⠁⡀⠱⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⣷⣿⣏⡀⢀⡀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠈⠓⠒⢺⣷⣶⣶⣮⣷⠀⢑⠒⠉⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠚⠢⣀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⢘⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠀⠀⠀⢻⡶⢤⡴⢿⡏⠀⠀⠀⠀⣀⣀⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢠⡀⠂⠤⠠⠀⢀⠀⢀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠙⠢⠤⠤⠖⠋⠈⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠠⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡰⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠑⢤⣀⡀⠐⢄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡊⣀⡴⠖⠉⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠉⠒⠂⠁⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠢⠠⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠠⠤⠬⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠴⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠄⠀⡀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢀⠀⢠⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠓⠚⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠛⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢸⣿⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠈⠻⣿⣿⡿⠋⢠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢠⣦⠀⠀⠀⠀⠈⠻⣷⣄⢸⣿⢀⣴⡟⠁⠀⠀⠀⠀⢰⣦⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣄⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣠⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣬⣿⣿⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⣿⣥⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣉⣉⣿⣿⣿⠀⠀⠀⠀⣤⡀⣼⠇⢸⣿⢸⣆⢠⡤⠀⠀⠀⠀⣸⣿⣿⣉⣉⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠻⣷⣄⠿⢶⣼⣷⡟⠀⢸⣿⠀⢻⣿⣷⠾⠟⣠⣾⠟⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠻⣷⣄⠈⢹⣧⣤⣾⣿⣤⣼⣏⠀⣠⣾⠟⢡⡦
⠀⠀⠀⠀⠀⠀⣀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⣠⣘⣷⡀⠈⣻⣿⠟⠉⠀⠀⠀⠀⠉⠙⢿⣿⠁⢀⣾⣣⣤⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠻⣷⣄⠈⠻⣷⣄⠀⠀⠀⢀⣨⣽⡿⠷⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠟⠻⢿⣤⣄⠀⠀⠀⢀⣴⡿⠋⣠⣾⠟⠁
⠀⠀⠀⠀⠀⢀⣤⣌⣿⣷⣤⣌⣿⣷⣄⣤⣈⣉⣤⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣀⣤⣍⣤⣠⣴⣿⣯⣤⣾⣿⣡⣄⡀
⠀⠀⠀⠀⠀⠈⠉⢉⣽⡿⠋⢉⣿⠿⠋⠉⢉⡉⠉⠉⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠉⢉⣉⣭⠉⠉⠻⣿⣍⠉⠻⣿⣉⠉⠁
⠀⠀⠀⠀⠀⠀⣴⡿⠋⣀⣴⡟⠃⠀⠀⠀⠈⠛⣻⣶⣶⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠷⣾⣿⣉⠁⠀⠀⠀⠈⠻⣷⣄⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠉⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠛⢋⣿⠃⣠⣾⠿⣦⣄⡀⠀⠀⠀⣀⣤⡾⣿⣄⠀⢹⣏⠉⠁⠀⠀⠀⠀⠀⠈⠻⣷⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⣾⠟⠁⠀⣨⡿⠛⢻⣿⠛⠻⣯⣀⠈⠻⣷⣄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣾⠟⠁⢴⠶⢟⣿⣷⡀⢸⣿⠀⣰⡿⣿⠻⠶⠌⠻⣷⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣉⣩⣿⢿⣿⠀⠀⠀⠀⠘⠃⠘⡷⢸⣿⠠⠿⠀⠙⠀⠀⠀⠀⢸⣿⣿⣍⣉⣉⣉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣛⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠈⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠘⠛⠀⠀⠀⠀⢀⣴⡿⠋⣸⣿⠈⠻⣷⣄⠀⠀⠀⠀⠘⠋⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣠⣾⢿⣿⣷⣄⠈⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⢸⣿⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠃⠐⣂⡈⢀⠦⠌⠒⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡊⣂⠬⠤⠎⢔⠬⠓⠉⠉⠉⠉⠉⠓⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⣄⠉⠂⠤⠀⠀⠀⠀⠀⡌⠑⠤⣀⠀⠀⠀⠀⠀⠀⢀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠧⡈⠐⠀⠀⠀⢠⠀⠘⠓⠾⠤⣤⣭⣅⣠⠶⠶⡖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣇⠀⠒⠀⠀⠄⠀⠐⢂⣀⠭⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⢒⡜⠀⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣋⠀⠀⢃⣸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢡⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠒⠉⠈⢆⠀⠀⠀⠀⠀⠀⠈⠙⠲⡄⠀⠀⢸⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠑⢄⡀⠀⠀⠀⠀⠀⢠⡇⠀⣠⠃⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⠉⠉⠉⠉⠓⠋⠀⢰⠁⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⠖⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⡠⠊⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⠷⠄⠒⠚⠉⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢸⡀⠀⠀⠀⠰⣀⠀⠀⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠃⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣿⣇⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣠⣿⠀⢀⡀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⠀⢸⣧⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣀⣼⡇⠀⢀⠀⠈⠷⣦⣀⣿⣇⣠⡶⠃⠀⢀⠀⠀⣿⣄⣼⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣇⠀⣿⠃⢀⡀⠈⢻⣿⡿⠋⠀⣀⠀⢻⡇⢀⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⣿⣾⣿⠀⢸⣿⣷⣤⣿⣧⣴⣿⣿⠀⢸⣿⣿⡟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠿⠿⢿⣷⣾⡇⠈⠙⠿⠟⠉⠀⣿⣶⣿⠿⠿⠿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣤⡀⠀⢠⣶⣶⠶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⠷⢶⣶⣦⠀⠀⣠⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠈⢿⣄⠀⠘⢿⣄⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⢀⣼⠟⠀⢀⣼⠏⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠶⠶⣿⣿⡷⣾⣿⣿⠶⣿⣿⣿⣶⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣾⣿⣿⡷⢿⣿⣿⠷⣿⣿⡷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⢀⣾⠋⠀⢠⣾⠋⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠈⢻⣦⠀⠈⢻⣆⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠁⠀⠘⠿⠿⠶⣶⣦⡀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠾⠿⠟⠀⠀⠙⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣶⣶⣾⡟⢻⡇⢀⣤⣶⣦⣄⠀⣿⠟⣿⣶⣤⣴⣶⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣿⢿⣿⠀⢸⣿⡿⠛⣿⡟⠻⣿⣿⠀⢸⣿⢿⣧⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⠇⠀⣿⠀⠈⠁⢀⣼⣿⣷⣄⠈⠉⠀⢸⡇⠀⢿⣿⣿⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠉⢿⡆⠀⠈⠀⢀⡾⠟⠉⣿⡏⠙⠷⡄⠀⠈⠀⠀⣿⠋⢹⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⣿⠀⠈⠁⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠉⠀⢸⡟⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⣿⡏⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃



⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣻⣛⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠄⠶⠤⣤⡤⠒⠚⠒⠂⠉⠉⠉⠉⠉⠉⠐⠒⠒⠒⠤⣤⡤⠦⠤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡠⣒⣶⣦⡈⢆⠘⠦⢄⡑⠢⣴⣾⣧⣦⠔⢋⡠⠴⠇⡰⢁⣴⣶⣒⢄⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢨⣿⣿⣛⣽⠿⠠⠾⠰⠤⠀⡛⢻⣿⣿⡟⢛⠀⠤⠆⠲⠁⠿⣯⣛⣿⢿⡅⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢡⣿⠛⣡⣴⠶⠞⠛⠶⢤⣌⠘⠻⠟⠓⣡⡤⠶⠛⠳⠶⣦⣌⠛⣿⡌⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣧⣿⣉⡤⣖⡾⠶⢶⣄⣉⢻⣿⣿⡟⣉⣠⡶⠶⢗⣲⢤⣉⣿⣼⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⢀⣨⠙⢻⢾⡿⣟⣙⣳⣶⣿⣿⡿⢿⣿⣿⣶⣞⣋⣿⢿⠷⡟⠋⣁⡀⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣻⠃⠀⠸⣤⣤⡈⠉⢽⣿⢿⠉⠀⠀⠉⡿⣿⡏⠉⢁⣤⣤⠃⠀⢘⣟⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠘⠁⢷⡀⣰⣾⡏⠛⢻⣿⠃⠈⢀⣀⣀⡀⠁⠘⣿⡟⠻⢹⣷⣆⢀⡾⠈⠃⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣧⠆⠟⠀⠸⣷⠻⣿⡇⠀⢸⠃⠀⢠⣿⣽⣿⣿⡄⠀⠘⡇⠀⢸⣿⠟⣾⠇⠀⠳⠠⣼⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠶⠀⣴⣿⣤⡿⢡⡄⢸⡄⠀⠀⠙⢿⡿⠋⠀⠀⢠⡇⢠⡌⢿⣦⣿⣦⠀⠶⠀⡘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡀⢠⣴⠀⠙⣿⠁⠸⣷⠸⡇⠀⣀⡤⠼⠧⣤⣀⠀⢸⠇⣾⠇⠈⣻⠋⠀⣦⡄⢀⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⡀⠘⠲⣄⢹⡄⠀⢿⣷⣭⣻⣅⢀⡀⢀⠀⣨⣟⣭⣾⡿⠀⢠⡏⣠⠖⠃⢀⣼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣄⡈⠀⠻⣶⡀⠻⣿⢿⣿⣿⣿⣷⣿⣿⡿⣿⠟⢀⣶⠟⠀⢁⣠⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠻⢦⣄⣈⠛⣦⣿⣾⡿⣇⠻⣿⣿⣿⣶⣟⣴⠛⣁⣀⡴⠟⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣌⠙⢿⡷⣿⣿⣨⣿⣷⡿⠋⣡⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠦⣿⣦⣿⠏⣼⣿⣷⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢻⡟⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⢸⡇⣾⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡆⢀⠀⠹⣿⣿⠏⠀⡀⢰⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⢲⣶⡆⠀⠈⣿⣿⣿⣿⢁⡄⣿⣿⢠⡈⣿⣿⣿⣿⠁⠀⢰⣶⡖⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⢦⣙⣷⡀⠈⠛⠿⣿⣿⣾⡇⢸⡇⢸⣷⣿⣿⠿⠛⠁⢠⣾⣋⡴⠾⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣶⣿⣿⣿⣦⣌⠛⠿⣿⣿⣇⢸⡇⣸⣿⣿⠿⠛⣡⣴⣿⣿⣿⣶⣶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⢨⣉⠛⠿⣦⣌⣿⣿⣿⣿⣿⣿⣡⣴⠾⠛⣉⡅⢀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⣶⣿⣷⣶⣤⣽⣿⣿⣿⣿⣿⣿⣯⣤⣶⣾⣿⣶⣿⣿⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⠿⣿⣿⠿⠛⣻⣿⣿⣿⣿⣿⣿⣟⠛⠿⣿⣿⠿⣿⣿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠘⣉⣤⣶⠟⢋⣿⣿⣿⣿⣿⣿⡙⠻⣶⣤⣉⠃⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⣿⣿⣿⠟⢋⣤⣶⣿⣿⡏⢸⡇⢹⣿⣿⣶⣤⡙⠻⣿⣿⣿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⣤⣤⡴⠞⣩⣿⠁⢀⣤⣾⣿⣿⢿⡇⢸⡇⢸⡿⣿⣿⣷⣤⡀⠘⣿⣍⠳⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠛⠟⠁⠼⠿⠇⠀⢀⣿⣿⣿⣿⡈⠃⣿⣿⠘⢁⣿⣿⣿⣿⡀⠀⠸⠿⠧⠈⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠏⠉⠀⣰⣿⣿⣆⠀⠉⠹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡿⢹⡏⢿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣼⣧⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁


⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛