Microbe Emojis & Symbols

⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢸⠇⠀⠀⠀⠓⡀⠀⠀⠀⡄⠴⠄⠄⠀⠐⢠⣔⠂⠀⠀⣀⠀⡀
⠀⠀⠘⠠⠐⢀⠀⢠⣧⠀⢸⠇⠀⠀⠀⣠⣾⠂⠀⢾⣤⣀⡀⠀⠈⣅⠀⠀⠒⠀⠀⠀⠐⠀⠈⢸⣅⡀⠀⠀⠁⠄⠎
⠀⠀⠀⠀⠁⠀⠀⠀⠛⠋⠐⠀⠀⠈⠀⠍⠁⠀⠀⠀⠀⠉⠻⠂⠀⠉⠐⠀⠀⠉⠱⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠒
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⠿⠶⢿⠣⠀⠀⠀⠀⠀⠄⠀⠀⡀⠐⠄⠀⠀⠔⣂⡔⠀⠀⢸⣿⡿⠀⠀⠠⠆⢀⠀⠂⠀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣤⠀⠀⠀⠠⢺⢏⠭⠀⣠⡌⠉⠀⠀⠀⠠⡁⠈⠀⠈⠄⠀⡶⠀⠀⠀⠂⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⣀⠀⠀⣀⣄⠄
⠀⠀⠠⢣⡁⠐⢂⡀⠀⣼⣷⡭⣣⡄⠀⣿⣅⣼⠂⢠⠃⠎⠤⠀⠀⠀⠀⠀⠠⠌⠀⣀⠑⡂⠀⠈⢿⠀⠀⢀
⠀⠀⠐⠋⠀⡍⠀⠀⠐⠹⢟⣘⠛⠁⠀⠿⠞⠋⠀⠀⠠⠏⠁⠀⠀⠀⠀⠀⠈⠹⠉⡖⡌⠂⠀⠳⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡱⠁⣀⢠⡦⣴⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣹⡃⢴⠆⠈⣻⣥⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠰⣈⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⠀⠀⣬⣿⣶⣷⡌⢃⢨⣥⡀⠀⠘⢠⠇⠀⠀⠀⣠⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⡁⠀⠀⠺⢛⡿⢿⡏⠛⠈⠀⠀⣧⡿⠀⠀⡔⢋⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⢘⠷⠻⣶⣷⣤⠆
⠀⠀⠀⠀⠀⣀⣤⣦⠀⠀⠠⠿⠃⠀⠀⢀⢤⣤⡀⠀⢀⠄⠠⡀⠀⠀⠀⠀⠀⠀⣸⣟⠃⠶⢰⣿⣿⠶
⠀⠀⠀⠐⠅⠁⠊⠁⠀⠀⠀⠀⠀⠀⠀⠠⣈⡩⠃⠀⠸⢷⡅⠀⠀⠀⠀⠀⢀⣀⡀⣹⣄⠺⠃⣸⣿⠛⠂⠀⣈⣷⠆
⠀⠀⠀⠀⠀⢀⣠⠿⢲⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⠀⣀⠀⠀⢨⡽⣧⠈⠈⠛⠹⠃⠀⠀⠀⠘⠴⠋
⠀⠀⠀⠀⠀⠒⡏⠑⢂⣿⣿⡁⠀⠀⠀⢰⣶⠀⠀⠀⢠⣜⡿⣿⣿⣿⣶⠂⠀⠑⠉⠀⠀⢠⣴⣂⣠⠶
⠀⠀⠀⠀⠀⠘⢻⣌⣁⢾⠿⠆⠀⢀⡀⢸⠏⡇⠀⠚⢟⣀⢤⠍⣉⠘⣟⠀⠀⢀⣄⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠉⠀⠀⠀⢌⡾⠃⢨⢀⠇⠀⠀⠾⣧⣤⣈⣉⣴⠛⠁⡰⣁⠇⠀⠀⠀⠀⠴⢶⣤
⠀⠀⠀⠀⠀⠀⠘⠛⠂⠚⠃⠀⠀⠀⠀⠀⠁⣀⡀⠀⠀⠉⠀⠙⠁⠀⠀⠰⠿⠏⠀⠀⠀⢀⡀⣀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠉⣁⡀⡀⠀⠀⠀⠀⠠⢶⢷⠀⠀⠀⢀⡙⢾⠿⢿⡆⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢀⣼⡉⠏⠹⣤⠀⠀⠀⠀⠐⠊⠀⠀⠀⢸⠟⢩⠻⡏⣻⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⢿⣿⣮⣨⡏⠀⠀⠠⠀⠀⠀⣶⢆⠀⠛⢱⣦⡤⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⢠⡴⠁⠀⠀⠀⠈⢣⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫

⠀⠀⠀⠀⠀⢀⠤⠀⠀⠐⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠐⢤
⠀⠀⠀⢔⠀⣀⠐⠁⠈⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢹⠄
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠱⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢔⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⡀⠔⠓⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠰⣁⠄⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢀⣀⡀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡠⠒⠘⠀⠓⠒⠜⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⢮⠤⣠⠂⡆⠀⠀⠀⠀⠀⢀⠀⠘⠀⠈⠐
⠀⠀⠨⢍⠁⠀⡴⠀⠀⠵⠄⠘⠢⠴⡀⠀⠀⠀⠀⠀⢞⠱⠎⢄⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡎⢖⠄⠀⠀⠀⠀⠀⡠⡄⠍⠀⠀⠀⠀⡤⢄⡠⠃⠀⠂⠀⠠⡠⠒⠃⠀⠀⠀⠀⠀⢄
⠀⠀⢠⣃⡀⠀⠀⠀⢀⠀⠀⠐⠂⡨⣸⠀⠀⠀⢨⠃⠀⠀⠀⠐⢠⠒⠽⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠁⠣⡀⡠⢜⠒⠁⠀⡔⠒⠁⠀⠀⠀⢀⠜⣈⠀⡐⢀⠤⣈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠘⠘⠈⠒⢲⣘⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠐⢦⠄⠀⠀⠘⠛⠁⠀⠀⣠⣤⡀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⠰⠖⠀⠀⠀⠀⡀⠀⠰⠂⣤⡀⠀⣀⡀⠀⠈⠁⠀⠀⠐⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠀⠀⢀⠀⠀⢐⡆⠀⡰⠋⠀⠠⠀⠀⠀⠀⠉⠀⣠⣶⡂⠠⡀⠀⠲⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠄⠊⠁⠀⠀⠈⠜⠀⠢⠌⠀⠀⢠⡄⠀⠀⣿⡄⠈⠓⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠊⢀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠠⡲⠄⠁⠀⠀⠀⠸⣳⡀⠀⠈⠳⢜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠂⢤⠀⢀⡀⠀⠀⠀⠐⠀⠀⢀⣄⠀⠀⢀⠀⡤⠀⠀⠀⠛⠦⡀⠀⢀⡁⠀⢤⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠌⠀⠀⠀⠀⠀⠀⠀⠉⢲⣤⣉⠀⠈⠲⡄⠀⢻
⠀⠀⠀⠀⠀⠀⡁⠀⠛⠀⠀⠀⠹⠀⠘⠁⠀⠠⠆⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠘⠃⢠⡀⣦⠀⠀⠀⠀⠀⠍⠁⠈⠷
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠙⠃⣀⢀⡀⠀⠀⠀⠐⠂⠀⠀⠒⠀⡌⠀⠀⠐⠴⠤⠃⠉⡀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠤⠑⠀⢄⠀⠠⡄⠀⠉⠀⡀⠄⢞⠀⠀⠘⠒⠂⠀⠀⠀⠀⠄⠐⠐⠠⠂⠈⠀⠀⢠⡉
⠀⠀⠀⠀⠀⠈⠇⠀⢠⠠⠄⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⢘⠀⢠⡤⠀⠑⣤⠀⠒⠃⠀⠀⠀⣠⠨⠀⠀⠀⡇⠤⠀⠀⠂⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠂⡀⠆⠁⠔⢰⢰⡈⠀⢀⡈⠃⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡍⠂⠀⠁⠀⠘⠃⠀⠠⠄⠀⠈⠁⠀⢀⠢⠐⠂⠂⠠⢀⢀⠀⠀⠀⠘⠀⠈⡀⢀⠀⠀⠀⠀⠰⠒
⠀⠀⠀⠀⠀⠀⢤⣄⣉⠀⠠⣀⠀⠀⠀⢖⠀⠈⢁⡌⠦⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⢀⠀⢀⡀⠀⠀⠀⡆⠒
⠀⠀⠀⠀⠀⠀⠀⠋⠁⢠⣀⡀⠀⠀⠀⠸⠀⠀⠀⣀⠄⠀⠐⠃⠀⠘⠊⠀⣀⡀⠄⠀⠀⠀⢂⠀⠐⡂⢠⠄⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠶⠛⠃⠀⠆⠀⢀⡁⠀⠀⠁⠖⡄⠤⠒⠈⠈⠢⢄⣀⣀⠶⠀⠀⠀⠈⢠⡈⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣄⠘⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠁⠀⠀⢀⠐⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣈⠁⠀⠀⣆⡀⠀⣀⠀⠀⠀⠰⠚⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠛⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⠇⠀⠛⠁⠀⠈⠂⣀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⡀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⢳⠀⠀⢤⢅⠄⡪⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠠⠀⠀⢀
⠀⡀⠀⠂⠀⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⢀⢶⡅⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡈⠂⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠘⢻⠃⠀⠀⠀⠀⠈⢶⣽⣦⣌⡁⢀⠀⠀⠀⠀⠀⠀⢀⠺⠁
⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠂⠀⠀⠀⢨⢢⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠋⠀⠀⠀⠀⠀⠈⠋⠁⠲
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣇⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠂
⠀⠘⠉⢠⠀⢰⠆⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⣐⣀⣀⠀⠀⠀⢀⡟⠈⣹⡆⠀⠀⠀⠀⢀⣀
⠀⠀⡀⡀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣯⣩⡄⠀⠀⢸⡅⢀⡆⡀⠀⠀⡀⠄⢠⢼⡇
⠀⠀⠉⠛⠡⠒⠒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠃⠀⠀⠈⢧⠾⠙⠀⠀⢴⣡⠄⣂⡿⠁
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠁
⠀⠀⡠⡄⠈⠉⠉⠙⠛⢦⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡠⠴⠆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⢀⡠
⠀⠀⠁⢰⠀⣠⡀⠀⠀⠀⠈⠀⠀⣒⡂⠀⠀⠀⠀⣀⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣨⣧⣴⣧⡽⠅⣤⡀
⢀⠤⢴⣼⣶⣡⠁⠀⠀⠀⠀⠀⣆⠇⣸⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⢸⢼⠿⣿⣻⡏⡡⠴⢴⡆
⠈⠓⠒⠻⡙⢾⢭⡑⣄⠀⠀⠸⢸⣼⡇⠀⠀⠀⠀⠈⠑⢍⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢱⡀⠟⠿⡛⢹⠎⡗
⠀⠀⠀⠀⠑⠚⢶⣻⡅⠀⠀⠀⠻⣟⣷⠀⠀⠀⠀⠀⠀⠋⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠥⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⢀⢠⠄⠖⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠠⠂⠀⠂⠈⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠄
⠀⠀⠤⠞⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠠⢀⠂⠈⠒⠀⠀⢸⢁⡎⠱⠀⠀⠀⠀⠀⠀⢄⡸⠖⠯⠈
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠐⠀⠒⠂⠰⠊⡜⠉⠣⠈⠀⠀⠀⠀⠀⠶⠇⢴⣿⠒⠂⣀
⠀⠀⣤⣔⠀⠀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠀⠀⠄⢢⠀⠀⠀⣀⡀⡀⠠⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈
⠀⠀⠀⠀⠶⠀⡄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢈⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣴⣶⣦⣄⠘⣿⣿⣿⡄⠀⠀⠀⠀⠐⠀⠀⠀⡠⢖⠛⢷⡄⠀⠀⡤⡤⡙⠆⢀⣇⡜⡠⢠⣆⡱
⠀⠀⢀⣀⠈⠉⠉⣁⠀⠹⣿⣿⣿⡀⠀⠀⢠⡜⠀⡰⠫⠄⣤⢀⡼⠁⠀⠀⡔⡄⢀⣠⠺⡶⣠⢌⠁
⠀⠀⢿⣿⣿⣦⣄⠈⠓⠀⠹⣿⡿⠃⠀⠀⠀⣠⠻⠐⢋⠂⡠⠋⠀⠀⠀⠀⢿⣷⠧⠜⠉⠀⠿⠲⣏⡢
⠀⠀⠀⠉⠻⢿⣿⠇⢠⣿⠀⠀⠀⠀⠀⠀⢰⣇⣙⣠⠴⠋⠀⠀⠀⠀⠀⠀⠈⠻⣑⠄⣮⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣦⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⡴⣫⠭⢭⣶⠀⠀⠀⢀⣼⣛⣯⣷⡎⠁⢰⠆⠀⠀⠀⣀⣄⠠⣿⣽⣻⣿⠀⣠⣶
⠀⠀⠀⠀⠴⠃⣀⣀⣀⢇⡇⠀⠀⠀⠀⠀⠀⢀⠿⣯⣿⡽⢇⡀⠀⠀⠀⠀⠈⠿⠏⠀⠉⠉⠁⢀⣀⡉⠉
⠀⠀⠀⡔⡫⠭⠿⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢩⡄⠀⢀⣠⣀⠀⠀⠀⠀⢰⡟⣾⣆⠀⢿⣽⣟⡷
⠀⠀⠀⢧⡧⠐⢗⣦⣴⡶⠶⠶⠆⠀⠀⠀⢺⣿⠇⠀⠀⠀⠀⢯⣿⣿⢁⠀⠀⠘⣿⣽⠛⣾⡀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠙⠋
⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠎⠀⠀⡸⠀⡞⠉⡉⠉⠳⣄⠀⠀⠀⣸⡏⠀⠙⠳⠶⠦⢀⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧
⠀⠀⠀⡄⠀⠘⡄⠀⢹⠀⠄⠀⠂⢻⠀⠀⠀⢙⣤⡶⠿⠛⣃⣴⠟⠁⠀⠀⣠⢴⣶⣶⣦⣤⡉⠉⠉
⠀⠀⠀⠈⠑⠊⢀⡴⠋⠀⠀⠂⠁⣾⠀⠀⠀⠛⠡⠶⠾⠛⠋⣥⣤⡄⠀⠐⣿⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢾⡀⠈⠡⠈⠈⣰⠏⠀⠀⠰⢿⣷⣦⣤⢤⣤⣤⣄⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠠⣀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⣿⣤⡠⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⢾⣿⣿⣿⡷⠶⠆⠀⣀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡁⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠰⠊⢻⠿⢟⠑⢠⣤⠀⠀⠀⠀⠀⠀⠈⠛⠟⠏⠁⠀⠀⠀⠀⠈⠻⠆
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⡾⠀⠀⡶⠀⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⣿⣿⠀⠰⠷⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠛⠃⠀⢠⣿⡿⠁⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠿⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⢿⡇⠀⠘⠀⠀⠀⠀⢶⡀⣤
⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠠⣷⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢠⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠈⡁
⠀⠀⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⢀⣼⠃⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠛⣶⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡟⠀⠀⠘⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠉⠉⣀⠀⠀⠀⠀⠀⢸⣿⡯⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⢠⡠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠺⠥⣠⠄⠀⠀⠀⠀⠰⠄⠀⠐⠁⡀⠀⠀⠀⠀⠀⠠⠔⠬⠁⢄⠀⠀⠀⠀⠀⠀⢐⡀⠆⠔⡀
⠀⠀⠀⠀⠠⠄⠨⠄⡀⠰⠀⠂⠀⠀⠀⠀⣾⠠⠹⠊⣩⣄⠀⠀⠀⠀⢂⣀⠀⠁⠀⢀⠂⠀⠀⠀⠀⢈⡂⣛⠀⠦⠀⠀⠀⠀⠀⢒⢬⠉⠈⠱⢁⡂
⠀⠀⠀⠀⠐⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠼⠅⠠⠯⠀⢼⠂⠀⠀⠀⠐⠂⡀⡐⠀⠁⠨⠀⠀⠀⠀⠀⠐⡀⠒⡀⢒⠀⠀⠀⠀⠀⠨⢧⣒⠠⣈⡌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠐⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠐⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠐⢆⡀⠁⡴⠂⠀⠀⠀⠀⠀⢀⠁⠄⠅⢁⠚⡁⠤⠀⠀⠀⠀⢄⠄⢠⠁⡀⡀⠀⠀⠀⠀⡤⠤⠀⠀⡊⠀⠀⠀⠀⠀⠂⠀⣀⢀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⡁⠀⠀⠀⠀⠠⠤⢬⠐⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠐⡃⣰⠊⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠈⣀⠠⠄⢠⠀⠀⠀⠀⠀⠀⠀⢁⠰⢠⠰⠐⠄⠁⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⢀⠒⡜⠒⠚⠀⢢⠀⠀⠀⠐⠀⠐⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙

⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢎⢿⠀⢟⣦⡀⠀⠀⠀⠀⠀⠀⡅⠀⡠⠀⠀⠀⠀⠀⠀⠀⠠⠓⡠⠉⠄⠀⠀⠀⠀⠀⢀⣔⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⢤⠘⠒
⠀⠀⠀⠀⠀⡎⣱⠀⢼⢸⡆⠀⠀⠀⠀⠊⡓⣩⠴⢯⠄⠀⠀⠀⠀⠀⠀⠁⠐⠀⠌⠀⠀⠀⠀⠀⠀⢰⠠⠀⠀⠠⣖⠀⠀⠀⠀⠀⠈⢀⣂⣘⠊
⠀⠀⠀⠀⠀⢻⠇⠀⣏⢠⠃⠀⠀⠀⠀⠂⠠⠄⠀⠀⡐⠀⠀⠀⠀⠀⠀⠂⠂⠢⠂⠀⠀⠀⠀⠄⠀⠀⠑⠄⡐⢂⠂⠀⠀⠀⠠⢊⠩⢆⠀⡑⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠨⣫⠅⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠁⢃⠀⠀⠀⠀⠀⠀⠀⠀⠴⠘⠁⠀⠀⠀⠀⠀⠉⠆⠀⠘⢠⢁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⡐⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠠⢄⢄
⠀⠀⠀⠀⠀⠘⠘⠘⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠠⠐⠰⠙⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠈⡎⠀⢵
⠀⠀⠀⠀⠀⠠⡤⠶⠤⡆⠀⠀⠀⠀⠀⠀⠐⣧⣰⠆⠀⠀⠀⠀⠀⢐⡡⢈⠠⢀⠠⢀⠠⠀⠀⠀⠀⠈⡀⠀⠀⢈⠀⠸⠂⠀⠀⠀⠠⠇⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⢀⡀⠈⠁⠀⠀⠐⠁⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠨⡀⠀⢇
⠀⠀⠀⠀⠀⠀⢰⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠘⠁⠆⠀⠀⠀⠀⠀⠣⠀⠀⢒⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⡤⠂⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣠⠄
⠀⠀⠀⠠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⡆⠀⠀⠁⠆⡀⠀⠁
⠀⠀⢼⠈⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠇⢠⡇⠀⠀⠀⠀⠀⠠⠄⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠆⡀
⠀⠀⠀⠈⠀⡀⣀⠴⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠤⠖⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠄⠀⠀⠄⠀⠀⠉⠀⢠⣶
⠀⠀⠀⠐⠀⠤⠀⠄⠚⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⢻⡀⠀⠀⠀⠀⠀⢀⡤⠒⠀⡅⠉⠓⠂⠤⢄⠀⠈⠀⠀⠈⠱⠄⢀⣀⡀⠀⠘⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠼⠁⠀⠀⠀⢀⡔⠁⠀⡅⠀⠁⡄⠀⠀⠁⠪⠳⣄⠀⠀⠈⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⢀⡌⠁⠀⠀⠀⠄⠀⠐⠂⠀⠀⠂⠠⠈⡄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⢸⠁⠆⠀⢀⡀⠀⠀⠂⢈⠀⡐⠀⠀⠂⢒⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠐⠁⠐⢂⠀⠀⠀⠀⠈⠻⠶⠶⠼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠉⠀⠁⣠⠀⠈⠄⡸⠀⠀⠀⢘⠀⠀⠀⠠⠀⢀⠁
⠀⠀⠁⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠂⠀⡁⠀⠈⠀⢠⠄⢈⠀⢰⡠⠃⠀⠀⠀⠈⠀⠀⠐⠀⠂⠘⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠑⢄⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠠⠀⠀⢀⠀⠄⠈⣀⠔⠁⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠈⠉⠁⣀
⠀⠀⠀⠀⠀⠀⢩⠀⠀⠛⠂⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠐⠂⠀⠠⠔⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡆⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠀⠀⠀⠀⠀⠑⢖⠀⠀⠀⠀⠀⡠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠈⠀⠃⠀⠀⠘

⠀⠀⠀⢀⢀⡀⠀⠀⠊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⣀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⡀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢠⢀⠀⠁⠘⠀⠀⠀⠔⠀⠒⢠⡕⡀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠐⠉⣄⠈⠀⠀⠀⠀⠀⠀⠊⠨⠀⠁⠀⠀⢠⢗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠀⠀⠀⠈⢄⠀⠀⢀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠖⠀⢀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠈
⠀⠀⠀⠈⠓⠀⠘⠖⠉⠁⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⡛⠋⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠐⠐⠒⠒⠶⠖⠒⠀⠈⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠐⠆⠆⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⣀⣄⣀⣀⡈⠤⠶⠤⠤⣄⣀⣀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⠀⠀⠀⢸⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣒⣛⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠁⠁⠀⠐⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠀⠀⠀⠀⠀⢈⠂⠀⠂⠀⠢⡑⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢶⠀⠁⠢⢄⠀⠀⠀⠀⠈⠢⡀⠈⠢⠊⠃⢂⠤⠊⠁
⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠴⡄⢀⠇⠀⠉⠉⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠙⠦⣀⡠⠖⠁⠀⠀⠀⠠⠐
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠒⠈⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡐⠤⠚⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠇⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⢀⡰⠆⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⡤⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠉⠀⠀⠀⠀⠲⣂⠀⠀⠀⠀⠀⠠
⠀⢂⠀⠀⠀⠀⠀⠐⢄⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠁⠉⠉⢓⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠾⠒⠙⠐⣶⠀⠉⠶⠄⠀⠀⠀⠘⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠀⠀⢀⠬⢝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠣⠖⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠄⠀⡲⠆⠂⡁⠈⠣⡀⠀⠀⠀⠀⠩⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢄⡈⢒⠚⠠⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⣀⢠⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠲⠌⠐
⡴⠋⡀⢠⡄⠀⠉⢦⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⠆⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⣌⠀⠀⠀⠸
⠀⠀⠀⠀⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠐⢀⠒⠂
⡘⠃⠀⠐⠴⡥⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠁⠰⠠⡆⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠜⠡⠀⣠
⠙⢦⣀⡀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠘⡡⠂⠀⠢⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠄⠊
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⠾⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠈⠂⠄⢒⡡⡂⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡄⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠤
⠈⠁⠀⠀⠆⠐⢀⠈⠀⠈⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠂⠄⡈⢑⡴⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠏⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠱⠢⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠆⠀⠀⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠓⠀⡀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⡠⠊⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠸⠁⣀⡠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡈⠀⠗⠁⢀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⡀⠈⠷⠄⠀⢀⡠⠊⠀⠀⠀⢀⣤⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢃⠌⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠈⠀⢀⡠⠔⠉⠀⠀⠀⠀⡰⠏⠀⠲⠒⡄⠀⠀⠀⠀⠀⠒⠒⠀⢤⠄⠊⡀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⡁⠜⠁⠀⠀⠀⠀⠀⠁⠉⠔⠋⡶⠚⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄
⠀⠀⣖⢊⡙⢢⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠴⠁⠈⢁⡜⠀⠀⠀⠀⠅⠠⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⡀⠀⠱⡄
⠀⣀⢉⠤⠽⠎⠧⠀⠊⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠈⠁⠀⠀⠀⠀⠀⢄⠀⠂⠀⠀⠀⠑⠀⠀⠀⡀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠡⢀⠀⠌⠀⠀⣀⠈⠄⠀⠀⠀⢨
⠀⠀⠀⠠⠀⠀⠀⠀⠙⡀⠀⠀⠀⡭⠊⠀⠀⠀⠘⠂⠀⠘⡀⠊⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⢀⠀⠀⠀⠀⠀⠀⠐⡀⠉⠀⡀⠀⠀⠈⠀⡘⠀⢀⠤⠊

⠀⡀⠀⣄⠀⠆⢀⡄⠀⠀⠀⢀⡰⠆⠲⠤⣀⡀⠀⠀⠀⠀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠄⣠⡀⣄⡀⠀⠀⠀⠀⠀⠄⡠⡀⢁⢀⠀⠀⠀⠀⠀⠀⠲⠀⡀
⠀⠁⠄⠈⠀⠀⠈⠰⠘⠀⠀⢸⡀⢀⡀⠀⠀⠉⠁⠂⠒⠀⠁⠉⠀⠀⠉⢆⠀⠠⠠⠟⠉⠀⠈⢩⠆⠀⠀⠀⣒⠄⠋⠁⠈⠚⢂⡀⠀⠀⢘⢰⡀⢤⠑⠀⠂
⠈⠒⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠉⠉⠈⠉⠦⣀⡀⢀⡀⠤⠰⠆⡤⠤⠴⠂⠀⠀⢝⠆⠁⠈⠀⢠⡕⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⡂⠀⠀⠀⠎⠀⠈⠙
⠐⠊⢠⠀⡀⢀⣀⠈⠀⠃⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠙⠗⠰⠲⢘⠀⠀⠀⡨⠂⣠⡀⠀⠀⠀⠍⠄⠁⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠸⠀⠈⠃⠀⠀⠀⠁⠀⠍⢠⠒⡠⡀⠀⠀⠀⠀⢀⠀⠀⡉⠀⠠⠀⠀⠀⠀⠀⠀⢀⡀⣤⠀⠀⠀⠀⠐⡑⠈⠈⠁⠐⠀⠀⠐⠂⠀⠀⣸⡄
⠈⠁⠀⡀⡀⠀⠀⠀⠀⠐⠀⠒⠀⠂⠀⠈⠠⠀⠀⠀⢀⠈⠈⡀⠀⠁⠀⡀⠀⡀⠀⠄⠀⠰⠎⠈⠀⢘⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⢈⢈⠀⠄⠉⠀⠀⠠⠈⠈⠡⠈⠂⠀⠁⠀⠄⠁⠀⠀⠀⠀⠀⠚⢠⠄⠆⠀⠐⣦⡀⠈⠓⠤⡄⡀⠀⠀⠀⠁⠀⠀⠈⠄
⠀⢐⠀⠈⠀⠆⠀⠉⠀⠀⠂⠘⠐⠒⠈⠀⠀⠐⢐⢀⠀⠀⢠⡂⠈⠁⢀⠀⠀⠀⠀⠀⣀⠀⠄⡀⠀⠀⠀⠀⠈⠃⡆⠀⠀⠉⠙⡣⠀⠀⠀⢠⠄⠀⠀⡀
⠀⡄⠀⠄⡐⠀⠀⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠀⠚⠀⠉⠈⠀⠀⠀⠈⢆⠀⠀⢀⠰⠀⢣⡀⠀⠀⡂⠈⠁⠀⠀⠀⠀⠆
⠀⢇⢀⠰⠁⠀⡈⠀⠀⠨⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠠⡑⠁⠀⠘⠀⠀⢧⠁⠀⠀⠀⡀⠀⠀⠠⢀
⠀⢸⠁⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⡀⢀⣀⠄⠖⠂⠉⠀⠀⠀⠐⠉⠀⠀⡀⣀⡠⣴⠏⠀⡀⠀⠀⣄⣀⠀⠉⠒⠃
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠒⠠⠀⠀⠀⠈⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠉⠁⠀⠀⡀⠀⠀⠀⠀⡀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⡄⠈⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⢀⣤⣴⣶⣶⢶⣶⣶⣶⡶⠶⢾⣿⣿⠿⡛⢿⣿⣷⣄⠀⠀⠀⠀⢀⣀⡀⠐⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠄⠀⠀⠠⠂⢀⡀⠀⠀⣰⡟⣻⢁⠀⠀⠒⢠⡌⢦⡀⢤⣭⣍⠻⣷⡤⣋⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠐⠐⠀⠀⠀⠀⠉⠀⠀⢠⠃⠑⢠⠀⠀⠀⠀⢠⣿⡇⠃⢸⡆⢃⢀⣌⣙⣄⣁⣸⣧⣤⣤⡿⢿⡟⢿⠀⠘⣷⠀⠀⠀⠀⠤⠠⠀⡀⠀⡀⠂⢀⢁
⠀⠀⠀⠴⠀⠀⠀⠀⠀⠤⠀⠂⠉⠦⠤⠪⡀⠙⠃⠀⢸⣿⣷⣤⣿⠟⢿⣿⢉⣙⣯⡉⢹⡉⠤⠾⠄⠒⢠⠈⠀⣆⣿⡁⠀⠀⡈⠀⠁⠀⠌⠂⠜⠀⠀⠐
⠀⢀⡠⠤⢄⡀⠀⠀⠀⠀⠀⠠⠆⠀⢀⠀⠈⠂⠀⠀⠀⢿⡄⢂⠹⡄⢠⠙⠌⢿⠿⢿⡜⣧⠀⠶⠿⡀⡈⠃⢀⣿⣿⠁⠀⠀⠀⠀⠀⢃⠀⢄⠐⠍⡀⠀⡠
⢠⠏⠀⠀⠀⠙⡄⠀⠀⠀⢄⠀⠀⢀⠉⢀⠀⠀⠀⠀⠀⠀⠙⢮⣁⣠⣼⣷⣼⣦⣤⣾⣷⣼⣧⣤⣤⣷⣾⣾⣿⠿⠁⠀⠀⢀⠤⠀⠀⠀⠠⠄⠃
⠘⣆⠀⠀⠀⣨⠃⠀⠘⠀⠀⠀⠄⡈⣀⡘⠀⠘⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠀⠀⢀⣀⡀⡒⢢⣄⠇
⠀⠈⠙⠂⠋⠀⢀⣀⡀⠀⠠⠄⠀⠼⡉⠈⡇⠒⠃⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠐⠴⡉⠟⠀⠞⠁⠃⠀⡀⠠⠄⠀⠂
⢠⠀⠀⡄⢀⠞⠁⠀⠈⠳⡄⠀⠤⠀⠙⠈⢀⠀⠐⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠗⢨⡀⠀⠀⠀⢠⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠂⠀⢀
⠈⠢⠔⠁⢸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠈⢀⡔⠉⠑⡄⠀⠁⠄⠀⠧⣀⡰⠃⠀⠀⢀⣀⠈⠀⡠⢤⡔⢴⣶⠲⡀⠈⠀⠈⠀⠂⡀⢀⠐⠁
⠀⡀⠀⠀⠈⠦⣀⣀⡀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢣⣀⣠⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠘⢻⡏⢷⣼⡧⠚⠷⠀⠁⠀⠀⢀
⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠋⠀⠓⠀⠁⠀⠀⠀⠐⠀⠀⠀⢀⠤⠤⠄⡀
⠀⠀⠄⠠⡄⠃⡄⢂⠒⠒⣀⣰⡀⢃⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⢀⠠⢤⠀⡀⠀⠀⠀⢀⢊⠐⡀⠀⢀⡌⢂
⣄⠙⠠⠒⠃⠂⠒⠀⠈⠁⠀⠒⠈⢧⣐⠀⠀⠀⠀⣠⠔⠚⠋⢲⡀⠁⠤⠀⢀⠤⠤⣀⠠⠀⠀⠀⠐⠀⠀⠃⢔⠉⠀⠀⠀⠌⡢⠅⠀⠆⡄⢀⠀⢀
⣐⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢕⡚⠀⢀⡴⠋⠀⣈⣠⡠⠞⠀⠀⢀⡰⠁⠀⠀⡘⠀⠀⠠⠄⠀⠀⠀⠀⢊⡀⠀⠀⠀⢈⡢⠀⠀⠡⡰⢄⠀⠀⣀⢜⠔
⠉⠖⠱⠴⣀⢀⣀⠀⠱⡐⢀⠤⠑⡄⠁⠀⣎⣠⠖⠉⠀⠀⠀⢠⠒⠊⠁⢀⢀⠤⠊⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⡠⠾⠐⠁⠀⠀⠀⠀⠈⠂⠈⠁⠐⠁
⠀⠉⠀⠃⡄⢠⠘⠀⠒⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣤⣤⡶⠶⠶⠶⣶⡟⠙⡟⠳⣶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⢯⣿⣧⣀⠝⠀⠀⠀⠀⠀⠀⠉⠛⢳⠋⠑⣤⣿⠋⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⣨⠿⣤⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠛⢛⠉⠉⠛⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⡏⠙⢡⡌⢉⡅⠀⠀⠀⠀⠀⢶⡀⠀⢀⠀⠀⠉⠁⢀⣀⠀⠉⠀⠀⠀⠀⠈⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠷⠞⠁⠙⠋⠙⠛⠛⠛⠁⠀⣀⣄⠀⢹⡿⠏⣠⣴⡞⢠⡁⢈⡿⠃⡀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢻⠀⢀⣀⣴⡀⢀⡀⠀⠀⢶⣅⣈⣿⣷⡿⠤⣨⠁⠀⠢⠞⢟⢋⣠⠞⢁⣴⣃⣀⣀⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡇⡀⣣⠱⣤⣤⣉⢛⡇⣤⣤⣤⠟⢛⠁⢈⣦⣠⠟⠀⠀⠀⠀⠀⠀⠈⠛⠁⢰⣤⠌⠉⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⣸⠀⠉⠁⠀⣄⡈⠉⠉⠀⠀⠀⣨⠀⠀⠙⠛⡻⠗⢤⣼⣦⣤⡄⢀⠀⠀⠘⠲⠚⢿⠷⠲⠆⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡏⠀⠀⠶⠾⠛⠙⠚⠀⠀⠘⠛⠛⠀⢀⡄⠀⠳⢤⡴⠟⢁⣴⢣⡈⢣⠀⠄⣠⠀⣯⡄⣀⠀⠀⢠⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢾⣁⣸⣄⢀⣀⣀⣴⣶⣄⠀⠀⢀⠀⢸⠷⠿⡿⢿⣧⠀⢦⣤⡋⠁⢈⣷⠈⡧⠚⠿⠀⡏⠁⠀⠀⠀⠈⠳⢶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⣹⣯⣉⣉⡉⠛⣿⠶⠾⡇⢸⣄⣀⣾⠀⠈⢱⡈⠋⠓⠶⠚⠛⠲⣧⣀⡼⠊⢉⣀⣀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠯⣉⣤⣤⡟⠁⠉⣿⣆⡀⣨⡦⠟⠉⠈⠣⠤⠞⠋⠀⠀⠀⠀⠑⠄⠈⠃⠉⠉⠀⠀⠀⠀⠀⠀⢸⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣼⠏⠀⠑⠤⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠢⠤⠜⠀⠀⠀⠀⠀⢤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣴⣆⣀⣴⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⠀⠀⠀⠀⠀⢄⣠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⠞⠒⣶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣾⣦⡄⠀⠀⡉⠙⠓⠋⠀⠀⠀⡀⠀⠀⡀⠀⢨⣟⢉⣹⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠿⣤⣀⣀⣀⣀⣠⣷⣶⣾⠿⠐⠛⠛⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣄⡀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠈⠒⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠙⡭⠹⢿⣧⡀⠀⠀⢀⠂⠀⠈⠁⠁⢂
⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢆⡺⢀⢛⣘⣿⡃⠀⠀⠁
⠀⠀⠀⠁⠄⠠⠈⠦⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣥⣽⣮⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠹⠛⠋⠁⠀⠀⠀⠀⠀⠀⠐⠢
⠀⠀⠀⠀⣠⣤⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⣠⣿⣹⣾⣧⣿⣿⢧⡀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠀⠃⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠐⣛⣾⠾⣷⣿⣿⣿⣪⡅⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⠈⠀⠀⠀⠀⠆
⠀⠀⠩⣿⣿⣻⣿⣽⡿⡽⠀⠀⠀⠀⠁⠀⢀⣀⣠⠤⠤⢤⣀⣀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠉
⠀⠀⠀⠈⠉⠋⠛⠉⠓⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣄⡴⠉⠈⠁⠂⢤⣂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⣀
⠀⢠⠄⠀⠀⠀⠀⠀⠀⠲⠀⠀⢰⠔⠀⠀⠀⠀⠀⣐⣟⡀⠀⠀⠀⠐⢻⣶⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⡄⢀⠀⠀⣀⢴⣿⠂⠀⠀⠀⠙⠶⢴⣤⣤⣀⢀⣀⣀⣼⣿⠇
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡷⠂⠦⠙⢜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣴⣦⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠄⣀⡀
⠀⠀⠀⠀⠀⣠⣄⠈⠛⠄⡘⠡⠄⠛⠋⢠⣦⠀⠀⠀⠀⠰⠁⢶⣦⣶⣦⡀⢂⠀⠀⠀⠀⠄⡰⡔⠄⠢⣂⠄⢀
⠀⠀⠀⠀⣀⠙⢫⠠⣶⣤⣭⠰⠷⢀⣅⠌⠉⣀⠀⠀⠀⢃⢸⣾⣿⣻⣾⡇⠘⠀⠀⠀⡜⠉⠀⠀⠂⠔⠀⠈⠤⠂⠀⠀⠀⠀⠀⠀⠀⢠⠔
⠀⠀⠀⠀⠿⠳⠡⠾⢠⣬⡅⠿⠿⢈⣯⠈⠝⠛⠃⠀⠀⠀⢂⠘⠻⠟⡉⠔⠁⠀⠀⠬⠂⠒⠀⠖⠀⠀⠃⠐⠂⠥⡁⠀⠀⠀⠀⠀⣰⠏⠂
⠀⠀⠀⢠⣶⡌⠐⠶⢈⣭⡀⢶⡶⢈⡟⠀⠱⣿⠆⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠅⠄⡉⢠⠆⠈⠀⠀⢀⠁⡈⠂⠀⠀⠀⠀⣘⠔⠁
⠀⠀⠀⠀⢙⣠⡂⢘⠈⣽⡅⢴⡦⢙⠡⢷⣦⠀⠀⠀⠀⠀⠀⢀⠠⠂⠓⠁⢆⠀⠀⠃⠔⡀⠰⡀⠐⠀⠁⠌⡐⢂⠁⠀⠀⠀⣸⡃
⠀⠀⠀⠀⠈⠛⠃⢀⣇⠌⢒⠔⠁⢲⣤⠈⠁⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠀⡸⠀⠀⠀⠈⠠⠑⢠⢀⢃⡠⢶⠐⠂⠀⠀⠀⣮⠓
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠺⠿⠀⠈⠉⠀⠀⢀⡄⠂⠁⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠀⠀⠀⠈⠀⠃⠁⠈⠀⠀⠀⠀⠀⠰⢧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣀⡀⠠⠄⠄⠀⠁⠀⠀⠀⠀⠀⠀⣠⠰⠦⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⣘⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡡⠅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢞⣷⢯⡶⢟⡄⠀⠀⢠⠗⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⡄⠐⠂⠀⠀⡞⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⣣⡾⣡⡶⡆⠟⠀⠀⠀⣿⠐⠈⡆
⠀⠀⠀⠐⠋⠠⠖⠂⠈⣹⠋⠀⠠⣈⣦⣁⠆⠀⠀⠀⠀⠀⣠⣆⠶⠶⣈⢩⣶⡼⠂⠀⠀⠀⡀⠀⠉⠱⠒⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠠⡌⢒⣤⢑⣜⠉⠀⠀⠀⠀⢰⡍⣱⠞⠐⣿⠉⠃⠀⠀⠀⣆⠀⢴⠀⢄⡠⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠉⠀⠀⣈⣲⡟⠈⢅⠱⠀⠀⠀⠀⠀⠠⠀⠴⠎⠼⠗⠁⠀⠀⠀⠀⠀⡋⠀⣄⠀⠼⠴⠀⠆⠀⠀⠀⠀⠀⠀⠀⢚⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢓⢼⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⡀⠨⠄⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣌⡙⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠴⣢⢦⡀⠀⠀⠀⠀⠰⠆⢠⢄⠆⡌⡀⠀⢀⡄⠀⠀⢠⢖⠳⠶⡄⠀⠀⠀⠈⠑⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢨⡇⣧⠻⢲⡇⠀⠀⠀⣀⠀⠐⠥⡛⣡⢅⡈⡦⠀⠀⠀⠀⡞⢨⠀⠁⠘⡄⠀⠀⠀⣿⣷⣤⡄⠀⠀⠀⠀⠀⠈⠻⡍⢢⠃
⠀⠀⠀⠀⠀⠀⡹⢡⡅⣾⢨⡇⠀⠀⠀⠉⠀⢧⡀⠀⣃⠂⢋⢇⡀⠀⠀⠀⢳⠀⡀⠉⠀⡅⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣡⠋
⠀⠀⠀⠀⠀⠀⡼⠘⢣⡆⡟⠀⠀⠀⠀⠀⠀⠀⠙⠐⠈⠖⠉⠀⠁⠀⠀⠀⠈⣧⢀⠘⠀⢳⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⣇⣳⣤⣀
⠀⠀⠀⠀⠀⡼⢳⡿⢉⠎⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡈⠤⢁⠀⡄⠀⠀⠀⠀⠈⠛⠇⠀⠀⠀⠀⠀⠈⠒⠂⢠⢀⡆
⠀⠀⠀⠀⠸⣵⡇⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠐⣈⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡞
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⣀⠀⣰⢢⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠸⢌⣧⠼⠺⢤⣣⠝⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⢠⣈⣵⣤⣏⣀⡄
⠀⠀⠀⣎⣑⡞⠡⠄⣀⡀⢑⣖⣹⠆⠀⠀⠀⠀⡀⢐⠏⠀⠀⣻⠄⠀⠀⠀⠀⠀⠀⢠⣨⠋⠀⢉⣇⡀⠀⠀⠀⠀⠰⡄⢢⣼⣿⣿⣿⣁⡀
⠀⠀⠀⢀⠤⢾⣀⠘⠧⢽⣸⠤⢄⠀⠀⠀⢀⡶⢋⢩⡄⠀⣠⡟⠀⠀⠀⠀⠀⠠⡴⠏⠁⠀⢀⡸⠁⠀⠀⠀⠀⠴⠴⣿⣻⡽⣯⡿⢧⡈
⠀⠀⠀⠈⠒⢁⡜⣛⢻⠚⡄⠑⠋⠀⠀⠀⠐⢧⣀⢒⣠⢖⠏⠀⠀⠀⠀⠀⠀⠀⢷⣠⣄⠴⡎⠉⠀⠀⠀⠀⠀⠀⣴⠛⡶⢻⡉⠳
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⢀⡤⠖⠒⣒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠺⡄⠈⢳⡀⠀⠀⠀⠀⠀⡼⠁⣄⠐⣿⡧⠀⠈⢧⠀⠀⠀⠀⡼⠁⣠⣾⡆⠀⠛⠈⢳⠀⠀⠀⢠⠏⡴⠆⣶⠙⡓⢀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢼⣀⢠⡀⠀⠀⠀⠀⠰⡇⠺⠇⢀⠀⠀⠢⡆⢸⠆⠀⠀⠀⡇⠀⠙⠁⠀⠀⣀⠀⢸⡇⠀⠀⢿⠐⠂⠶⡧⠀⣦⣀⡀⡇
⠀⠀⠀⠀⠀⠀⠐⠸⡙⢹⠁⠀⠀⠀⠀⠀⢳⡀⢊⢈⡇⣤⠀⢀⡞⠀⠀⠀⠀⢳⡀⠚⠃⢰⣿⠿⢁⡾⠀⠀⠀⠸⣆⢤⣄⠒⢀⣀⠻⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠌⠑⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠬⣤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⠤⠖⠋⠀⠀⠀⠀⠀⠈⠓⠮⢤⡭⠵⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠑⡆⠀⠀⠀⠀⠀⠙⢧⣠⣿⣴⡋⣠⡄⠀⠀⠀⠀⠀⢰⣯⣉⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢄
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡇⠀⠀⠀⠐⠷⠦⣾⣿⣿⣿⣿⠶⠶⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⠠⢈⠆
⠀⠀⠀⠀⢰⡁⡀⣞⡷⠀⢱⠇⠀⠀⠀⠀⠰⠖⢻⣿⣗⣮⠿⢤⡄⠀⠀⠀⠀⠀⠀⠀⣀⡘⠛⢻⣄⠀⠀⠀⠀⠀⢠⠋⡁⠲⠒⢃⠞
⠀⠀⠀⠀⠀⠳⢄⣤⠤⠔⠃⠀⠀⠀⠀⠀⠀⠰⠏⠀⡯⠸⠆⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠘⠶⡾⠏⠀⠀⠀⠀⠀⠘⠦⣀⠤⠖⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠰⡁⠈⠻⣥⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡴⠃⣀⣀⠀⠀⠀⠀⠀⢢⠄⠄⢠⢀⣜⡤⠄⠀⠀⠀⠀⠀⣀⣀⢀⡀⢴⣤
⠀⠀⠀⠀⠀⠀⠀⠈⢳⠗⢸⠅⠀⠀⠀⠀⣈⡛⢳⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠂⢴⠆⢠⠋⠳⠄⠀⠀⠀⠀⠀⣙⣿⡍⢭⣦⢨⡇
⠀⠀⠀⠀⠀⣀⡤⠴⡋⢘⡟⠀⠀⠀⠀⠀⠃⣽⣻⠟⢋⡽⠛⠋⠀⠀⠀⠀⠀⠰⠷⣤⢺⡓⡴⠾⠆⠀⠀⠀⠀⠀⠐⢛⡻⣦⡼⢿⠈⠃
⠀⠀⠀⠀⠀⠿⣀⣤⠷⠏⠀⠀⠀⠀⠀⠀⠸⣍⡻⣶⡛⠓⠋⠁⠀⠀⠀⠀⠀⠀⢀⣼⠮⠾⣅⠀⠀⠀⠀⠀⠀⠀⢠⣿⢾⣿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠙⠁⠈⠉

⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠰⣿⣿⠀⠀⠀⣠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣴⣶⣿⣿⣶⣶⣴⣿⣿⠁⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠀⠀⠀⢀⣤⣀⠀⠀⠉⠻⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠈⢿⣿⣴⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⣿⣿⠛⠉⢀⡀
⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣇⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠸⣿⣧⣶⣿⣿⠆
⠀⠀⠀⠀⠀⠛⠛⠛⠉⣿⣿⠀⠀⠀⠀⠘⠿⠿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠹⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠘⢿⣿⣦⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢾⣿⣿⠿⣿⣷⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠛⠿⣷⣦⣄⣀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧⠀⠀⠀⢸⣿⣿⣿⡷⠀⠀⠀⠀⠸⣿⣿⡧⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣀⣠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣧⡀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⡀⠀⠀⠈⠙⢿⣿⣿⡟⠉⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣠⣾⣿⣿⣿⣷⡀⠀⠀⠀⠻⣿⣿⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣶⣄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣀⠀⠀⠀⠀⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠻⣿⣷⣄⡀⠀⠙⠻⢿⣿⣿⣿⠿⠟⠋⠀⠀⣾⣿⣿⡆⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣾⣿⡿⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⢀⣾⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠏⠀⢠⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⣹⣿⣿⣿⣿⣿⣶⣶⣦⣤⣶⣶⣿⣿⣿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣿⣿⠃⠀⣽⣿⡟⠛⠻⠿⠛⠛⠋⠉⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠜⠁⠀⣀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠁⠀⢴⡖⢋⣍⠛⠶⢾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣾⣆⡈⡃⠴⠐⠾⡏⠀⠀⢠⠊⡵⠀⠀⠀⠀⢀⣤⡀⠀⠈⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡸⡄⠀⠛⢻⣿⣽⣟⣤⢠⣜⠿⠀⠀⡌⢸⠃⠀⠀⣀⡴⢋⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⠂⠀⠀⠈⠁⣽⠉⠛⠈⠁⠀⠀⠀⢷⡿⠀⠀⠨⠥⠔⠁⠀⢠⡄⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠋⠙⠾⣿⣶⠛
⠀⠀⠀⠀⢀⣀⡤⢶⠆⠀⠀⠀⠛⠁⠀⠀⠀⠴⣶⣦⠀⠀⣰⠂⡐⠄⠀⠀⠀⠀⠀⠀⠀⣼⣍⠁⢓⡸⣻⣿⣟⠃⠀⠀⣀
⠀⠀⠀⠀⠂⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡁⠝⠀⠀⠻⠿⠤⠀⠀⠀⠀⠀⠀⣠⣄⠀⣵⣄⡛⢁⣐⠾⠟⠃⠀⡨⢸⡿
⠀⠀⠀⠀⠀⠀⣠⣬⠗⢶⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⠀⣀⠀⠀⠀⢬⠟⣦⠀⠘⠋⠙⠃⠀⠀⠀⠀⠢⠞⠁
⠀⠀⠀⠀⠀⠐⢾⠉⠲⠰⣾⣿⡉⠀⠀⠀⢠⣶⡄⠀⠀⠀⣤⣼⡿⣿⣿⣿⣴⠆⠀⠀⠒⠁⠀⠀⣠⣤⣒⢀⣶⡆
⠀⠀⠀⠀⠀⠀⠺⢦⡛⣀⣽⡿⡅⠀⢀⡀⠀⡏⢱⠀⠀⠾⡆⠁⣤⠙⣛⠡⢟⠃⠀⠀⣀⡀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠘⠋⠀⠀⠀⠐⣲⠟⠀⡃⢸⠀⠀⠠⡿⣏⣀⠀⠛⣠⠿⠇⠀⡜⢹⠃⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠾⠧⠀⠴⠆⠀⠈⠉⠀⠀⠑⠁⠀⠀⠀⠈⠛⠉⠻⠏⠙⠁⠀⣼⣼⠃⠀⠀⠀⠀⠀⠀⠒⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡉⠁⠀⠀⠀⢦⣰⣆⣶⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⡶⠞⠲⣆⠀⠀⠀⠀⠀⠅⠉⠁⠀⠀⠀⣸⣿⠿⠟⠙⢣⡄⠀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠂⠠⢾⣯⣌⠥⢨⡯⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣽⣁⡘⠀⢃⡼⠆⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⡽⢿⠶⠞⠆⠀⠄⡀⠀⠀⠀⠘⢯⠢⠀⠀⠘⠳⠏⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠀⠀⠀⠀⠀⠈⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


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

⠀⠀⠀⠀⠀⠀⢀⣤⡄⢴⡦⠠⣤⣄⠀⠀⠀⠀⠀⠀⢀⠠⠀⠠⠄
⠀⠀⠀⠀⢠⣶⠀⠉⠂⣬⢑⡂⠉⠁⢶⡆⠀⠀⠀⢀⢀⣺⣷⣷⣶⠈⠂⠀⠀⠀⣰⠘⠎⠂⠐⡄⡂⠄
⠀⠀⠀⢀⣄⠁⢆⡛⠳⠶⣘⣛⢰⡦⠀⢰⣦⠀⠀⠀⡸⢻⣿⣿⠿⠃⠈⠀⠀⡰⠁⠐⢀⠁⢉⡀⠀⠩⢀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠘⠋⠁⣙⡱⠿⠆⢙⣋⢰⣶⠰⢉⣅⠀⠀⠀⠀⠄⡉⠁⠂⠁⠀⠀⠐⠃⠨⠀⡉⠠⠈⠀⠁⠀⡑⠀⠀⠀⠀⢀⠺⠁
⠀⠀⠀⠸⠿⠀⠩⡅⢾⠆⢙⡋⠴⠆⣂⡘⠋⠀⠀⠀⠀⠀⠀⡀⡤⢀⠀⠀⠠⢂⠐⢘⠁⢀⠐⠀⠂⣀⠪⠀⠀⠀⢀⡗⠁
⠀⠀⠀⠀⢾⡷⠀⠀⢘⢃⢙⠋⣄⠀⠻⠃⠀⠀⠀⠀⡠⠔⠈⠀⠀⠈⡆⠀⠀⠉⠦⢌⠂⠀⠄⢈⡄⢆⠁⠀⠀⣀⠮⠋
⠀⠀⠀⠀⠀⠀⠰⣿⠇⢰⣧⠀⠺⠛⠀⠀⠀⠠⠄⠂⠀⠀⠀⢀⡠⠆⠁⠀⠀⠀⠈⠐⠨⠌⠎⠂⠈⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⠀⡀⡀⡠⠀⠊⠀⠀⠀⠀⠀⠀⡠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢜⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡾⣷⠾⡡⠀⠀⢠⠖⠲⠀⠀⠀⠀⠀⠈⠁⠀⠸
⠀⠀⠀⠀⣠⠀⠀⠀⠀⣶⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢞⣵⠏⣴⠶⠘⠁⠀⠀⣧⠐⠈
⠀⠀⠀⠊⠡⠐⠋⠀⣨⠃⢀⠠⣼⡼⣔⠀⠀⠀⠀⠀⣠⡦⠻⠟⣌⣴⡦⠋⠀⠀⠀⠠⠀⠁⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⡠⠔⠁⡐⣆⢣⣶⡡⠎⠁⠀⠀⠀⢠⠇⢸⢋⡸⡏⠈⠀⠀⠀⢠⠄⠲⠀⢢⠔⠐⠀⠀⠀⠀⠀⠀⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠤⡽⢯⣐⠣⠉⠀⠀⠀⠀⠀⠀⠚⠃⠚⠉⠀⠀⠀⠀⠀⢠⡀⠢⠄⠘⠊⠈⠀⠀⠀⠀⠀⠀⠀⠸⠍⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠀⠃⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⡢⠤⡀
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢣⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⣠⠀⣀⢀⠐⠂⠀⠀⠀⠀⠀⣀⡤⢤⡀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⣆⣷⢻⣍⡇⠀⠀⠀⠀⠀⢴⡱⢆⠌⠑⢄⠈⠁⠀⢀⠏⡀⠐⠈⡆⠀⠀⠀⣾⣦⣀⠀⠀⠀⠀⠀⠐⢶⡶⣄
⠀⠀⠀⠀⠀⢐⢏⡍⢰⢎⡇⠀⠀⠀⠃⠀⡄⠀⠈⢢⢕⡌⡀⠀⠀⠈⡇⢁⠘⠀⢡⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⢠⢡⠋
⠀⠀⠀⠀⠀⢠⠞⢧⡬⡻⠁⠀⠀⠀⠀⠀⠈⠲⠨⠴⠈⠈⠁⠀⠀⠀⢸⡀⠀⠂⢾⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⣏⣣⣄⣀
⠀⠀⠀⠀⢠⠟⣾⢋⡿⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠡⢈⡀⡇⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠈⠀⠀⢀⢰
⠀⠀⠀⠀⠺⣾⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣐⣂⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠇
⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠊⠉⠁⠈⠐⠄⠀⠔⠀⠀⠀⠀⠠⡀⢀⠂⠈⠐⠀⠂⡀⠀⢀⠔⠠⡀⠀⠀⠀⠀⠀⠀⢀⠔⣉⠐⠀⠀⠀⠐⢄⡀
⠀⠀⢀⠔⡡⠀⠀⠐⠀⠀⢌⡉⠠⠀⠀⠂⠀⢂⠈⠁⠀⠀⠐⠀⠀⢌⠢⠄⠈⢣⠐⡀⠀⠀⠀⢀⠔⡁⠀⡆⠠⠀⠐⠂⠀⡆
⠀⡊⢤⠄⠠⠀⣀⠤⢄⡀⢀⣘⡄⠀⢀⠤⠤⠜⢚⠀⠀⢀⠤⢄⠀⠀⢡⠀⠀⠀⠣⠐⡀⠀⠔⠁⠀⠀⠀⠃⠀⢀⣀⠤⠤⠇⡄
⠠⢃⡄⠀⢀⠎⠀⠀⠄⠈⠁⠺⡀⠀⠘⠀⠑⡀⡉⠀⠀⠆⠀⠀⠁⠀⡸⠆⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⠄⠀⠀⠃⠀⠤⡀⠊⠄
⢠⠈⠀⠀⢸⠀⢀⣀⡀⠀⠀⢠⡇⠀⢀⡤⠔⢋⡅⠀⠀⡄⠀⠀⠀⡔⠑⠆⠀⢠⠀⠀⠐⠂⠀⠀⠀⠀⣟⣤⣀⣀⠀⠀⠈⢃⠨
⡎⠴⡀⠀⠈⠄⠀⠀⠁⠀⢀⣞⡀⠀⠘⠀⠀⠸⡁⠀⢸⠈⠶⡀⠀⠘⢾⠀⠀⡎⠱⡀⠀⢠⠞⠁⠀⢸⣅⢀⠀⠉⠙⠀⠀⡜⢁
⠈⠢⡑⣤⣀⡀⠀⢀⣀⠴⠛⢈⡅⠀⣀⣀⠤⠤⠒⠤⠞⠀⠀⠘⠢⡴⠛⠤⠤⠁⠀⠐⠔⠁⠐⠦⠤⠎⢀⠀⠀⠀⢀⣠⠞⠃⡐
⠀⠀⠑⠄⢀⠉⠉⠉⠀⢠⡄⠀⠉⠉⠀⢀⢄⠀⡔⠀⠢⠀⢀⠒⡄⠀⠠⠒⡄⠀⡊⢂⢀⠒⡀⢀⠔⡄⢈⡉⠉⢉⡉⠠⠀⠁
⠀⠀⠀⠀⠀⠢⠔⠙⡀⡀⠑⠐⠁⠈⠀⠁⠸⠠⠀⠀⠀⠁⠁⠀⠈⠈⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠈⠠⠄⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⡀⠧⠐⠂⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠠⠓⠐⠃⢴⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠤⠄⠀⠀⠀⠀⠡⠄⠀⠀⠀⠠⠀⣀⠀⠄⠀⠀⠀⠀⠓⠁⠀⠒⠂⠀⠀⠉⡤⠄⠀⠀⠀⠀⠔⠈⠀⠀⠀⠁⢂
⠀⠰⠓⣄⢀⡠⡔⠳⠀⠀⠀⠀⠀⡠⢼⠦⡄⠀⠀⠀⠀⠊⠑⠀⠨⠁⠀⠀⠠⣀⠀⠀⠀⠀⢨⠀⠈⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠐⠉⢰⠂⠰⡆⠸⠄⠀⠀⠀⠀⠀⢂⠀⠀⠈⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡃⠉
⠀⠀⠀⠄⠊⠀⠈⠀⠒⠀⠄⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠊⠀⢁⠀⠀⠀⠀⠀⠀⡧⠤⠞⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⣀
⠀⠀⠈⠢⠤⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠸⡤⠤⡬⠀⠀⠰⠀⠀⠀⢀⠈⢐⠀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⡌⠠⠁⠀⠀⠀⠠⠀⠈⠀⢄
⠀⠀⠀⠀⠠⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠨⢉⠀⠀⠀⡀⠢
⠀⠀⠀⢢⠐⠉⠉⠉⠈⢀⡠⠄⠀⠀⠀⠀⠀⡀⠒⠊⠠⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠨⠬⠢⢀⠁⠈⠀⡠⠈⠀⠃
⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠌⠄⠀⠀⢀⠀⠀⠀⠀⠈⠀⠣⠐⠠⠀⠄⠉
⠀⠀⠤⠒⢄⠀⣀⡐⢨⠔⢤⠀⠀⠀⠀⠀⠨⠀⡁⠀⠐⠀⠀⠀⠸⡊⠀⠈⠉
⠀⠀⠀⠀⠘⠀⠘⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⠏⠄⢠⠀⡀⡀⢄⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢀⡂
⠀⠀⠀⠀⢀⡀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⣀⣰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡀⢀⠁⠀⠠
⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⡱⠈⠀⠀⠀⠀⠉⢀⢠⠀⠀⠀⠀⠀⠀⠌⠀⠀⢁⠈⠀⠀⠀⠅
⠀⠀⠆⠀⠈⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠐⠴⠀⠀⠘⠂⣐⠃⠄⠀⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠤⠀⠀⢀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⠀⢀⠃⠀⠀⠁⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠐⠀⠀⠄⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠨⠒⠈⡤⠀⢰⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠐⠂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⢿⣷⣶⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡫⠖⣏⡟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣵⣆⢳⠟⣹⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠡⢅⠞⠁⢸⡿⢳⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⢦⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⠏⠀⠀⠘⢷⡠⡎⣿⠀⠀⠀⠀⠀⣠⣶⢴⣄⠀⠀⠘⠛⠏⠁
⠀⠀⠀⠀⠀⣀⠤⣤⡀⠀⠀⠀⠀⠀⠀⢹⣳⠆⢿⡗⠀⠀⠘⡟⠊⣁⢩⣿⠆⠀⠀⠀⠀⠀⠀⣠⣀⣰⣆⣀⡀
⠀⠀⠀⠀⣰⢋⠛⡚⣛⢳⣄⠀⠀⠀⠀⠘⠛⢼⠞⠃⠀⠀⠐⣿⣦⢹⡊⣿⡀⠀⠀⣠⣴⡖⠿⢩⣥⢉⡹⢻⡀
⠀⠀⠀⠈⠻⢜⡞⠀⠸⠈⠉⠳⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠇⡹⣯⠀⠀⢴⠿⢢⠰⠎⣃⣨⣍⣵⣾⡇
⠀⠀⠀⠀⠀⠀⠙⣧⡀⠴⠖⠒⢰⡎⢹⡶⣤⣀⠀⠀⠀⠀⠀⡼⣁⠟⣶⣿⡀⠀⠘⢻⠞⠛⠋⠙⠋⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣶⠀⡘⠁⠸⡇⠙⣻⡄⠀⠀⠀⣾⠇⠹⠆⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣽⠆⢰⠀⣈⡽⠁⠀⠀⣰⡦⠞⠠⣖⣸⡟⠀⣀⣶⣾⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠒⠺⠃⠀⠀⠀⠸⣧⣄⣴⡾⠉⠀⣴⢿⣷⣬⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡴⣶⢾⡗⢲⢖⣶⢤⣤⡀⠀⠀⠀⠀⠈⢀⣀⡶⠝⠓⣬⣽⠉⠀⠀⢀⣴⠷⢶
⠀⠀⠀⠀⠀⠀⠀⠰⣟⢣⠖⣠⡄⠃⣤⠰⢚⠊⠰⣷⠶⠀⠀⣠⡴⣿⠟⠐⢟⣉⣿⠍⠀⠀⢀⡼⣫⢖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠠⢻⣯⣬⣩⣤⢿⡬⠵⠾⠽⣧⠟⠀⠀⠐⢿⣰⢋⠀⣿⣨⠟⠃⠀⠀⠀⣸⡧⠡⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⣴⣦⣦⣀⣀⢀⠀⠀⠀⠈⠙⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢨⣥⡹⠟⢿⠧⣤⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣥⡐⠯⡄⠇⠞⠢⠏⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⠗⢾⡧⡾⢤⣿⡟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⠔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⢀⠄⠀⠀⡀
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⡄⠀⠀⠀⠆⠀⠀⠈
⠀⠀⢰⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗
⠀⠀⠞⢀⡖⠁⠈⠉⢀⠀⠀⣀⠠⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡀
⠀⠀⠂⠈⠁⠀⠀⢀⠌⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠
⠀⠀⠀⠀⠄⢁⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⣠⠆⠲⠒⢿⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠐⠦⠠⢤⣀⠀⠀⠀⠈⠀⠀⣤⡀⠀⠀⠀⠀⠠⠆⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⣹⠁⠀⠀⠀⠀⠠⠊⠁⠐⠀⠀⠀⠀⠀⠐⠠⠓⣄⠀⠀⠀⠠⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⡐⠇⠀⠀⠀⡀⠀⠈⡄⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣀⠖⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠐⠀⢈⠀⠠⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢻⣄⣀⡀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠄⠃⠀⢀⠂⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠅⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⢀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⢀⠀⠀⠀⠀⠀⠃⠀⠄⠀⡱⠊⠀⠀⠀⠀⠐⠀⠀⢀⠀⡀⠀⡀⠤⠄
⠀⠀⠀⠀⠑⠀⠠⠙⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠠⠂⠈⢂⠤⠊⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⣄⡀⠀⠀⠀⠐⠀⣀⢀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠘⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠐
⠀⠀⠀⣀⠀⠀⠘⠀⠀⠀⠐⠊⠈⡁⡠⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠀⠀⠀⠀⢀⠀⠀⠀⡂
⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠉⠀⠀⠓⠉⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠙⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠐⢒⠒⠶⠶⠂⠀⠈⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠐⠦⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⡀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⡀⢀⣀⡀⣠⡤⢀⡤⣀⣀⡀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣀⠁⠠⠖⣋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉
⣿⣿⡿⠿⣿⡿⢿⣿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣶⣿⣷⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⢀⡄⢀⠀⠀⠀⠀⣠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠘⠠⠈⠀⠀⠉⠄⠂⠀⢊⠀⠀⠀⠈⠑⠂⠀⠀⠀⠉⠉⠙⢢⠀⠀⣠⠎⠉⠘⢓⡄⠀⠀⠀⡄⠓⠃⠀⠂⡈⠀⠀⠀⣄⢠⡘⠀⠂
⠀⠃⠁⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠒⢄⣀⡠⠤⠒⠒⠂⠤⠚⠀⠀⢲⠀⠀⠀⢠⡍⠀⠀⢠⡀⠀⠀⠀⠀⠊⠀⠀⠰⠉⠀⠈⠀⡀
⠀⠉⠠⠆⢀⠀⢄⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠉⠒⠛⠈⠀⠀⠀⠈⠠⡀⢀⣄⠐⠃⠀⠀⠀⠀⢹⡁⠀⠈
⠀⠀⠀⠀⠈⠀⢀⠀⢀⠀⡀⠈⠐⠃⡔⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠦⠓⠤⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠀⠰⠗
⠀⠀⠠⠂⠢⠀⠀⠀⠀⠀⠂⠀⢁⠀⠀⠀⡀⠀⠆⠀⠀⠀⠀⢀⠀⠄⠀⠁⠀⠩⢄⣀⡜⠂⣤⠀⠠⣤⣀
⠀⠀⠂⠀⢀⠀⠀⠃⠐⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⣀⣀⡈⠀⠀⠀⠈⠓⣦⠀⠉⠙⣆
⠀⠠⠀⠀⡈⠀⢀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠉⠁⠀⠀⠈⡆⠀⠀⣠⡄⢸⡀⠀⡦⠈⠃⠀⠀⠀⠆
⠀⠰⡄⠔⠀⢀⠁⠀⠠⠀⠀⠀⠈⠀⠀⠄⠂⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⡀⡤⠁⢀⡺⠂⠀⠈⠁⢀⡇⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠃⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠠⠀⢀⠀⠃⠢⠠⠐⠊⠉⠀⠀⠀⠀⠈⠀⠀⠤⠠⠒⠛⠀⠠⠀⠠⡂⠀⠀⢣⠁
⠀⠀⠀⠀⠀⠘⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⣷⣶⣤⡀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠘⠀⠄⠀⡀⠀⢀⣶⢿⠋⠉⠩⠉⡙⣍⢉⣙⣛⠿⣄⡠⢻⣿⣿⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠓⠀⠀⡴⠚⢢⠀⠈⠁⠀⣾⡇⠋⣸⠀⡄⣌⣳⣌⣂⣿⣍⣡⣿⢿⠿⡏⠙⣷⠀⠀⠀⠠⠠⠀⠀⠀⠡⠁⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠰⠀⠀⠑⠲⠚⠀⠈⠀⠀⣿⡷⠴⣿⠛⢿⡋⣍⣯⡍⣏⠰⠾⠄⠂⣄⠁⢲⣿⡄⠀⠠⠀⠁⠀⠀⠒⢂⠀⠁
⠀⢀⠄⠒⠢⡄⠀⠀⠀⠀⠐⠁⠠⠄⠀⠁⠀⠀⠘⣧⢡⡛⠀⣄⠡⡻⠛⣷⡸⣆⠛⠛⡀⣌⣀⣼⡿⠀⠀⠀⠉⠀⠁⠀⢀⠐⠠⠡⠔
⠀⡎⠀⠀⠀⢸⠀⠀⠄⠐⠀⠀⠆⠠⠄⣠⠀⠀⠀⠈⠓⠶⠷⠿⠟⠛⠟⠛⠛⠿⠻⠿⠿⠟⠟⠋⠀⢠⢀⠔⢂⠀⠀⠀⠈
⠀⠈⠢⠤⠤⠊⠀⠀⠀⢀⠈⢁⡖⠒⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣱⢢⡮⢰⠆⠤⠀⠀⢀⠀⠄
⠀⡤⠂⡄⢠⠖⠁⠉⠂⡀⠀⡀⠉⠒⢁⠀⠂⠀⠂⠀⠂⠀⠈⠀⠀⠀⠀⡰⠤⡀⠀⠀⠀⣄⢹⡶⠋⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠓⠄⠃⡅⠀⠀⠀⠀⡑⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⡔⠈⠢⡀⠀⠀⠀⠢⡠⠖⠀⠀⣀⣀⣁⣀⢤⡔⣲⡖⣄⠀⠂⠀⠀⠀⠀⣀
⠀⠠⠀⠀⠈⠢⢄⠠⠔⠁⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠣⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢛⡏⣿⠼⠏⠑⠃
⠀⠀⠀⠃⠀⠄⢀⢀⣀⠰⢀⢠⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡠⡀
⠀⠠⢍⠨⠥⠤⠌⠌⠄⠐⠆⢤⣂⡄⠀⠀⠀⢀⡠⡤⢄⠀⠀⠀⠀⢀⡀⠠⢀⠀⠀⢀⠀⠠⠀⠤⠈⠊⠘⠤⠠⠀⠔⠊⠐⠀⠀⠃⠐
⠈⠅⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠁⠀⣠⠚⠉⢀⣀⡼⠁⠀⢀⠔⠁⠈⡇⠀⠀⡀⠀⠀⢀⠸⢂⠀⠀⠀⠺⠀⠀⠃⢀⠀⠀⠁⡀⡐
⠀⠡⠐⠴⢀⣀⠠⠀⡀⢒⡆⢡⠉⠀⢚⣠⠔⠉⠀⠀⢠⠐⠂⠁⣀⠤⠊⠀⠀⠀⠀⠀⠀⠈⠀⠙⠠⠢⠘⠁⠀⠀⠀⠁⠀⠀⠀⠊
⠀⠈⠁⠁⠄⠆⠃⠘⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⢀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠢⠀⡀⠀⠀⠀⢀⠇⠈⣆⠀⠀⠀⢀⠀⠔⠈⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⣡⠴⠖⠚⠩⠋⠀⠀⠈⠫⠓⠲⠦⣌⡀⠀⠀⠀⠀⠀⠈⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⡀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⢄⠀⠀⠀⠈⠳⡀⠀⠀⡠
⠀⠀⠀⠀⠀⡠⠀⠌⣀⡞⠀⠀⠀⠀⢀⠔⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡆⠀⠀⠀⠀⢹⡄⡈⠤⠠⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠇⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡴⠃⠀⠀⠀⠀⠀⢧
⠀⠀⡀⠀⠀⠀⠀⠀⣯⠄⠀⠀⠀⠀⢣⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⡠
⠀⡆⠘⠐⢒⣒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠅⠈⠅⡀⠸
⠀⠡⠌⠉⠀⠀⠈⠁⣦⢄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠘⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠘⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠤⠀⠠⠀⣳⡀⠀⠀⠀⠘⢄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡘⠀⠀⠀⠀⡼⣑⠠⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠳⣄⠀⠀⠀⠀⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠋⠀⠀⠀⢠⡞⠁⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡠⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠐⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⢀⠌⠝⠒⠲⠷⣄⠀⢀⡴⠥⠴⠒⠻⠡⡀⠀⠀⠀⠀⠀⢰⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠘⡄⡜⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡂⢲⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣧⣀⣼⣭⣯⣭⣭⣯⣽⣭⣭⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣿⣯⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⢘⣿⣿⠀⠀⣰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠉⠉⠀⠈⠉⠉⠛⢿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⣾⣿⣷⠀⠀⠀⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠘⣿⣧⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠸⣿⡟⠋⢁⣀
⠀⠀⠀⠀⣠⣶⣾⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡀⠀⠀⢹⣿⣶⣿⡿⠃
⠀⠀⠀⠀⠈⠉⠉⠈⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⢿⣿⠇⠀⠀⠀⠻⣿⣅
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣦⣄⠀⠀⢀⣴⣦
⠀⠀⠀⠀⠀⠘⠛⠋⠉⢿⣧⠀⠀⠀⢰⣿⣿⣶⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠙⠻⢿⣶⣾⣿⠋⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣧⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠉⢿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣤⣶⣾⣶⣄⠀⠀⠈⠻⣿⣦⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣦⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠟⠉⢻⣿⣶⣄⠀⠉⠛⠿⠿⠿⠟⠛⠁⠀⠰⣿⣿⡇⠀⠀⣸⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣰⣿⣿⠿⠿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣠⣿⡿⠻⢿⣿⣷⣦⣄⣀⣀⡀⢀⣀⣠⣴⣾⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⢀⣾⣿⠛⢻⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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

⠀⠀⠀⢰⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠸⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛
⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢤⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⢀⣬⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠰⠀⡀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠐⡛⢁⡜⢃⠀⠀⢘⠑⠆⠀⠀⠀⠐⢄
⠀⠀⠀⡐⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠺⠋
⠀⠀⠀⡇⠀⠚⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⡀⠀⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣔⡮⠀⣰⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠤⢤⡂⠳⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡄⠀⠐⢺
⠀⠀⠀⠨⠡⢾⠯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠄⢁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⡅⠠⢠⡼⠁
⠀⠀⠀⡞⢹⡧⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡀⢀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⡇
⠀⠀⠀⢻⠟⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢺⡇
⠀⠀⠀⠸⣦⣤⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⢸⣹⣭⠃
⠀⠀⠀⠀⠀⢀⣹⣄⣴⠄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⠻⠟
⠀⠀⠀⠀⠘⠛⠋⢿⡏⢠⠘⠀⠀⠀⠀⢠⡴⠓⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠃
⠀⠀⠀⠀⠈⠢⠴⠋⠐⠀⠀⠀⠀⠀⠀⠀⢡⠶⢛⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠊⣁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠀⠉⠠⠜⣀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠠⠂⠈⢀⡀⠀⡈⢣⠀⠀⠀⠀⠀⢀⠐⢂⠑⠂⠆⡀⠀⠀⠀⠀⢀⣆⣹⢤⡍⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⠀⡇
⠀⠀⠀⠾⠀⠆⠀⢀⠀⡀⠌⡆⠀⠀⠀⠠⠎⠄⢀⢀⡀⠀⠁⠀⠀⠀⠀⡾⣼⢙⠆⠃⡠⠉⣔⠀⠀⠀⠀⠀⠀⣄⢀⣂⠠⠷
⠀⠀⠀⢳⡘⡃⠄⢈⠄⠀⠺⠀⠀⠀⠀⠐⠊⠇⣀⣀⠠⡍⠀⠀⠀⠀⠀⠙⢫⣿⣶⣇⡵⢈⡟⠀⠀⠀⠀⠀⠀⢸⣉⡀⠀⠀⡷
⠀⠀⠀⠈⠉⠁⠄⠩⠐⠂⠁⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠉⠚⠿⠷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠲⠴⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⡟⣆⠀⠀⠀⠀⠀⠀⠰⠛⢦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣄⠀⢹⣾⣟⣿⡿⡄⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⣠⠶⠛⠛⢿⣦⠀⠀⠀⢀⠀⣀⣘⠺⡢⠀⢰⣇⣠⠃⡠⠤⣴⠉⣳
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠛⠀⠀⢻⣽⡿⣿⢿⡄⠀⠀⠀⠀⡆⢁⡇⠀⠀⣠⠞⠁⠘⠁⠀⢸⡟⠀⠀⠀⠈⣀⡛⠒⠁⠀⣠⣯⣉⡇⠀⠳⠒⠋⠉⠁
⠀⠀⠀⣠⣶⣦⣄⠀⠀⠀⢶⣦⡀⠈⢿⣻⣿⡿⣷⠀⠀⠀⠀⠙⠊⠀⣠⠞⢡⡘⠃⠸⠇⣰⠟⠀⠀⠀⠀⠈⣅⣽⢀⡤⢾⣍⡹⠏⣴⣞⠲⣄⡀
⠀⠀⠀⢿⣿⣷⢿⣷⣦⡀⠀⠙⠃⠀⠘⢿⣽⣷⠟⠀⠀⠀⠀⠀⢠⡞⠵⢀⢛⣁⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⣯⢿⡿⣤⠜⠁⠀⠀⠷⠟⠺⣏⢙⡆
⠀⠀⠀⠀⠙⠻⣿⣿⣻⣿⡆⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠐⠶⠀⢈⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠟⢦⠀⢰⠓⡆⠓⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⢸⢛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠶⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠝⠀⠀⢀⣠⠤⠶⠤⣤⡀⠀⠀⠈⠁⠀⠀⣱⣶⣾⢷⣤⣀⠶⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣯⣿⣻⣆⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣞⠞⠁⠀⠀⠀⡞⣰⠛⠛⠓⠶⠟⠀⠀⠀⠰⠀⢴⣯⣤⣿⢿⣿⣧⡀⠄⠘⠟⠀⠀⠀⠀⠀⣤⣶⡄⠠⢛⣷⣾⣧⢾⡯⠀⢠⣿⣽⡇
⠀⠀⠀⠀⠀⠀⣼⠎⠀⠀⠀⢀⣀⡇⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⣏⣿⣿⣽⠯⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉
⠀⠀⠀⠀⢀⡤⠶⢚⣛⣛⣛⣭⣥⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠛⠛⠟⠁⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⣶⣯⣷⡄⠀⢰⡿⢻⣭⢷⣗
⠀⠀⠀⠀⣿⢰⡟⠉⢉⡉⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠋⠀⠀⠸⠂⠀⠀⣶⣾⣷⣆⠠⠀⠀⠀⠀⣤⣿⣧⣼⡿⣶⠀⠈⢻⣿⣿⡾⠏
⠀⠀⠀⠀⠹⣮⡗⠀⠻⣝⣒⣒⣚⠯⠽⠯⠭⠷⠀⠀⠀⠀⠀⢿⣾⣿⠂⠀⠀⠀⠀⠁⠘⣧⣿⣻⡿⢀⡀⠀⠀⠰⣉⣿⣼⠋⢻⣿⡅⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠄⠀⠀⠀⠀⠀⠈⠁⠛⠟⣿⠭⠁

⠀⠀⠀⠀⠀⣀⣤⠤⣄⡀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⡼⠁⠀⠠⠀⡗⠀⣼⡏⠉⠀⠉⠉⠻⣦⠀⠀⠀⠀⠀⢸⣿⠃⠀⠉⠻⠷⡶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⡇⠀⠀⠀⡞⠀⠀⠻⣧⠀⡉⠀⠀⡀⠹⣧⠀⠀⠀⠀⢿⡿⢀⣠⣤⡴⣶⣦⠀⢀⣼⡿⠂⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠙⠻⠿⠿⠽⠃
⠀⠀⠀⠀⠻⣄⠀⠄⣹⠀⠀⢠⡿⠀⠋⠀⠀⠁⠀⣿⠀⠀⠀⠀⣠⣖⡿⠟⠛⢉⣉⣤⣶⡿⠋⠀⠀⠀⠀⢠⣾⠫⣿⣾⣯⢿⣟⢶⣤⡀
⠀⠀⠀⠀⠀⠈⠙⠋⠁⢀⣴⠟⠁⠆⠀⠙⠀⠀⢀⣿⠀⠀⠀⠀⠛⠋⢰⡿⠿⠿⠛⠋⢡⣤⣤⣤⠀⠀⠀⢹⣿⢿⡾⣾⠟⣾⣿⣻⣯⣿⡆⠐⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠴⢀⠀⠆⠚⠀⣼⠇⠀⠀⠀⢠⣖⡶⣤⣄⣀⠀⠀⡀⣀⣉⡉⠉⠀⠀⠀⠀⠙⢿⣿⣿⣿⣻⣻⣿⣾⣿⠷⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⠀⠈⠁⢀⣠⣼⠏⠀⠀⠀⠀⠈⠙⠛⠷⢽⣿⣿⣿⣽⣽⣽⣽⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⠀⠈⠢⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣿⣦⣰⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠻⣧⣹⣿⣸⠇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣀⣤⣧⣤⣀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⣼⣿⣿⣿⣿⣿⣆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠿⠛⣿⣿⣿⣿⣿⣿⣋⠛⠀⠀⠀⠀⠀⠀⠀⠛⠉⣿⣿⣿⣿⣿⣿⡟⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢾⡾⢛⣿⢿⡿⢿⣏⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠻⢿⣿⠿⠟⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⢻⡿⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠰⠿⠏⢼⠇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠷⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⣤⡟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣧⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⢠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠺⣿⣿⣿⣚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣧⣿⣾⣶⣧⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡋⣿⣿⣿⣏⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢾⣿⣿⣿⣿⣿⣞⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⣿⣿⣿⠧⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣹⢿⣿⣿⣿⡿⢯⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣩⣿⣿⣿⢓⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠞⢹⠏⣧⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣨⡟⠛⣧⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⢿⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⢈⠇⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⣿⣿⣷⡎⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠘⡿⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣷⣿⣿⣷⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠒⠒⢺⣿⣿⣿⡯⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣧⣶⣾⣿⣶⣶⡛⠃⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠋⢹⣿⣿⣿⡧⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣸⣿⣿⣿⣿⣿⣿⣿⣄⣴⣶⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣁⣄
⠀⠀⠀⠀⠀⠀⠀⠛⠁⣹⣿⣿⣿⡗⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢻⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠋⢁⣸⣿⣿⣿⣏⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡿⣿⣿⣿⣿⡿⠛⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⡜⠉⡏⠈⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢩⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠂
⠀⠂

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠈⣄⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣄⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠈⠑⠄
⠀⢠⡄⠀⠈⠀⠀⠉⠁⠐⠁⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣄⡀⠀⠀⠀⠀⠀⠀⢠⠋⣽⣄⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠔⠂⠀⠀⠀⠀⠠⠀⠸⠏⣮⠃⠀⠂⠀⠀⠀⠀⠘⢷⣆⣿⣷⣄⡉⠋⠀⢠⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠿⣏
⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⡀⠀⠀⠀⡀⠀⢸⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣤⡟⠀⠀⠀⠀⠀⠀⠈⠓⢶⠞⠖⢨⣍
⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⡾⢠⡃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⡄
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⠀⠀⠀⠀⠀⢰⣇⣠⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠈⠢⠄
⠀⠀⠶⠒⠃⢀⠀⠀⣠⡀⢀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠀⠀⢀⠀⡁⠐⢤⠀⢀⠀⠀⠀⠀⠀⠀⣰⡟⠑⣻⣦
⠀⠀⠀⠀⠀⠃⠀⢀⡏⠁⠈⠁⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣾⣷⣤⣶⣦⣶⡄⠠⠀⠀⠀⢀⣿⡅⠨⠼⠯⡇⠀⠀⠀⠀⠀⡀⠠⢶⢶⡄
⠀⠀⠀⣀⣀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣄⣜⠀⠀⠀⠀⠸⡿⡄⢀⣷⢁⡇⠀⠀⠀⡀⠤⠅⢀⢼⣿⡇
⠀⠀⠀⠑⠻⣮⢉⣤⣤⣤⣶⣄⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣿⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⢈⣸⠏⡽⠀⠀⠀⣤⠉⢐⠒⡌⢾⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠹⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢻⣕⣩⣴⡷⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣀⣀⠀⠈⠁⠉⠉⠉⠿⠿⣶⣀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀⠠⡄⢰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡴⠠⢀⡠⢀
⠀⠀⠀⣏⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠗⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠃⠉⡀⠀⠀⠁⠀⠁⠀⢀⠀⠀⠀⠀⢀⡞⠡⣖⢠⢙⡏⢤⢤⠆⢰⡀
⠀⠀⠀⢹⠀⣇⠀⣰⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⢨⡴⢤⡄⢀⠀⠀⠀⠀⠠⢤⣠⡉⢁⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡽⢯⣤⣟⣷⣿⣭⣳⡞⣱⠶⢿⡄
⠀⣤⠦⢼⣤⣹⣴⢃⡴⠁⠀⠀⠀⠀⠀⠀⠀⣸⡜⡇⢀⡟⠈⠀⠀⠀⠀⠐⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⢹⣇⡿⠯⣿⡿⠻⣿⢋⢳⣴⠥⣾⣇
⠀⠳⣄⣈⡿⣿⠿⣋⣖⠛⠦⣄⠀⠀⠀⠀⢰⠋⣧⢹⣾⠁⠀⠀⠀⠀⠀⠀⠰⠶⡤⠖⠀⠀⠀⢠⠄⠀⠀⠒⠐⠈⠀⠀⠀⠘⠖⣁⢀⣹⣾⣟⡿⠚⢥⣀⢶⣏⠁
⠀⠀⠀⠉⠀⠹⡄⠙⡍⠳⣦⣈⡧⠀⠀⠀⠀⢀⡿⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣆⡀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⣂⠁⡀⠙⡥⠈⠼⢡⡼⠂
⠀⠀⠀⠀⠀⠀⠙⠛⠳⣿⡙⣿⠁⠀⠀⠀⠀⠈⢼⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣨⠁⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠰⠶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠌⠛⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⡘⠐⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠂⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠤⡖⠐⡋⠉⠂⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡀⠐⢃⠀⠀⠉⠁⠀⡀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⢦⠀⠘⠀⠀⡔
⠀⠀⠀⣀⣼⠛⠄⠀⠀⠉⠀⠀⠀⠀⠙⡋⠀⠀⠀⠀⠀⠀⡀⠀⡐⠂⠈⠠⡔⠀⡀⠁⢙⠟⠀⡇⠱⡄⠀⠀⠀⠀⠠⠀⠀⠐⢆⠀⣘⡧⢸⢎⡔⠁⠔⠁
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠁⠀⠱⢨⡀⢀⣀⡀⠀⠀⣹⢀⡿⠳⣼⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣹⡆⢀⣤⣨⠀⣀
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣛⡚⠀⠀⠀⠀⡐⠀⠀⠈⡀⠤⠍⠁⡀⠛⠈⠰⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠠⠚⠙⠣⢪⢿⣿⡅⠈⠡⢄⡀⢀
⠀⠀⠄⢃⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠁⠀⠀⠀⠀⠐⢄⢂⡄⠱⡤⠂⠀⠄⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠀⠘⠀⠀⠀⢄
⠀⠀⠀⠈⠉⠋⣱⢀⠈⠀⠀⠀⠀⠄⢑⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢓⠄⠀⠀⠈⠹⠛⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡀⠀⠰⢇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠋⠉⠸⡒⠐⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢀⣀⠠⠐⠔⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠄⠤⠤⠤⠄⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣈⣥⠄⠖⠚⡘⣡⠷⢯⠋⡘⠰⢲⢂⠬⡍⣁⡒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣡⠄⢞⢀⠂⠊⠈⠀⢠⠃⠀⢈⡆⠀⠁⠀⠈⠈⠀⠀⠘⠙⠲⢍⡒⢄⡀
⠀⠀⠀⠀⠀⠀⡠⠊⣠⠎⢀⠢⠀⠀⠀⠀⠀⠀⠙⠖⠋⠁⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠁⠙⠢⣌⠢⡀
⠀⠀⠀⠀⠀⠔⠁⠰⠣⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⡀⣀⡀⠈⠈⠀⠘⠀⠀⣎⠈⡇⠀⠈⠳⡜⢦⡀
⠀⠀⠀⢀⠎⠠⡀⡑⡐⠀⠑⠊⠀⠉⠀⠀⡠⠒⢉⣠⣀⣀⣀⣀⡠⠓⠀⠀⢄⠈⡂⠀⢸⣀⡄⠀⢠⠀⠙⢆⠳⡀
⠀⠀⠀⡎⢠⠙⢌⠌⠀⠀⠀⠀⢀⡠⠐⠊⢀⡰⠊⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢄⠀⠈⢂⢳⡀
⠀⠀⠘⠠⠏⠢⠂⢀⠘⠃⠀⠀⠎⠀⡰⠋⠁⠀⠀⠘⠃⠀⠀⠘⠀⠀⡖⠄⠀⠀⠀⠰⠀⡀⠀⠸⡄⠈⣆⠀⠈⡄⣧⠂
⠀⠀⠆⡴⠑⠁⠀⠣⠤⠀⠀⢨⠁⠀⡃⠀⠆⠐⠂⢀⣄⣀⠐⠝⠀⢀⡇⠸⠀⠀⢀⣀⣜⠊⠀⠀⢸⠀⢹⠀⠀⢐⢹⢂
⠀⠀⠀⢎⠌⢀⢤⠀⠀⠀⠀⡾⠀⢀⠃⠀⠀⠀⡴⣡⠖⠦⡑⢤⡤⠊⡠⠃⢀⡞⠁⡤⠞⠀⢀⣀⡸⠀⢐⠁⠀⠀⢸⢆⠂
⠀⠀⠀⡃⠀⠀⠁⠘⠃⢠⠜⠀⢀⠚⠀⠀⠀⢰⠁⡇⢎⡑⠭⡒⠒⠊⠁⠀⠈⠦⠎⠀⠀⠀⡇⢠⡤⣤⠎⠠⡄⠐⢸⢃⢂
⠀⠀⡇⢇⠀⠀⢠⡀⠀⠹⡤⠔⠁⠀⠴⠀⠀⠘⣆⠧⣄⡨⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⡆⠀⠠⠄⢠⠀⡴⠡⠃
⠀⠀⢡⠹⡄⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠈⠓⠒⠒⠉⠀⠀⠀⠖⠐⡄⠀⠀⢤⠀⠀⡇⢰⠇⢀⠀⠠⠋⢠⡇⠡⠁
⠀⠀⠀⢣⠱⡀⠀⢪⣀⣠⠍⠀⣠⠞⢁⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢰⠃⠀⠐⠒⠀⠸⣄⢼⣤⢈⡥⣾⢁⡾⡴⣡⠃
⠀⠀⠀⠀⠣⡙⢄⠀⠀⠀⠀⢸⠁⣼⠁⠀⠀⠈⠀⡀⠀⡌⠁⠀⠀⠈⠉⠁⠀⠰⠀⠀⠀⠀⠛⠺⠛⢘⣶⢃⣾⡝⡽⡥
⠀⠀⠀⠀⠀⠙⢄⠑⢄⠒⠀⠀⢧⡈⠓⠤⢤⣀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠙⢁⢎⠌⠌⡘⠁
⠀⠀⠀⠀⠀⠀⠈⠑⣄⠑⠤⡂⠀⠙⠖⠤⠤⣄⡈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢂⡠⠁⡡⠊⣴⢋⢂⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣌⠓⠤⣀⠀⠀⠀⠉⠲⢄⣈⣉⡹⠀⠀⠠⢄⠀⠀⠔⠤⠃⡠⠊⡠⡺⡡⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⢒⠤⣉⠒⠢⢄⣀⡀⠀⠀⠀⠀⠀⠈⢁⡄⠐⠤⠒⡁⢰⢊⠜⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠒⢢⠤⣀⣉⢉⡉⣉⣉⢉⡁⣀⠤⠐⠞⡐⠁⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠐⠁⠊⠌⠐⠠⠁⠊⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠦⣤⣞⠁⠀⠀⣠⠶⠦⣄
⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠀⠀⠀⠀⠈⠙⠻⢿⣥⠤⠀⠀⣠⠤⠤
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢰⠷⠀⣀⡀⠀⠀⠀⠹⣶⡶⠚
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⢲⡄⠀⠻⠇⠀⡤⢤⠀⠈⠉⠛⢿⣍
⠀⠀⠀⠀⠐⣇⠀⠀⠀⠙⠛⠁⢀⣀⠀⠈⠷⠞⠁⠀⠀⡄⠀⠈⢻⡋⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠙⠶⣄⣁⠀⡄⠀⠈⠛⠀⠀⠀⢀⣤⠀⠀⠋⠀⠀⠈⢷⡶⠚⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⠶⣤⣀⣀⣀⠀⠀⠈⠉⠀⠀⣠⣤⠀⠀⣼⣛⠛⠲⠶⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢠⡏⠉⠻⣯⣷⢶⣦⣀⣶⡃⠀⠟⣁⣠⣿⣍⣉⣭⣄⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⡄⠀⠹⡄⢻⣹⡉⠙⢻⡛⠉⠻⠦⠬⣭⣀⠀⠙⠦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠙⣇⠀⠀⠙⢦⣀⡀⠀⠀⠈⠓⢄⠀⠈⠉⠉⠉⠉⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠓⠂

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣫⠏⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠖⠁⠀⣶⡜⢛⡙⠛⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠄⣜⠃⣤⠠⣿⠟⠀⠀⢀⠖⢲⠀⠀⠀⠀⠀⣀⡀⠀⠀⠑⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣆⠀⠰⠾⢿⣿⣿⡷⣀⣄⡲⣶⠀⠀⡘⢠⡇⠀⠀⠀⣀⡴⢻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡨⠀⠀⠀⠛⢉⣿⠻⡿⠘⠁⠀⠀⠀⣧⣾⠀⠀⢠⣊⣁⠔⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢈⠿⠺⢯⣿⣧⣴⠆
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠂⣹⠟⠀⠀⠀⢀⣠⣄⡀⠀⠀⢀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⣘⡟⠃⢴⠄⡶⣿⣷⡦
⠀⠀⠀⠀⢔⢈⠩⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⠛⡿⠀⠀⣿⣶⡂⡁⠀⠀⠀⠀⠀⠀⠀⠉⢹⣄⠰⡶⠈⣽⣿⠶⠀⠀⡔⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⣀⡀⠀⠀⠀⠀⡛⣿⣆⠙⠉⢶⠶⣶⠋⠉⠀⠀⠰⣉⣿⠁
⠀⠀⠀⠀⠀⠀⣸⠿⢂⡈⣺⣷⡴⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣴⣦⣿⣤⣾⢀⣀⠀⠘⢅⠿⠀⠀⠀⠀⣀⡀⠤⣄
⠀⠀⠀⠀⠀⠀⢨⣇⢠⡅⠻⣿⡗⠀⠀⠀⠀⢸⡿⡇⠀⢀⣄⡟⠞⠋⢿⣻⠟⣿⡍⠀⠀⠀⠀⠀⠀⠐⠿⠷⠖⠚⠛
⠀⠀⠀⠀⠀⠀⠈⠹⠖⣶⠛⠛⠙⠀⣀⣲⡄⢸⡇⡅⠀⠀⠉⣧⡤⠛⠃⣶⠈⣽⣄⠀⢀⢴⡶
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⡀⠀⠐⠴⠏⠀⠸⣀⠆⠀⠀⠈⢫⣶⠶⣤⡤⢶⠏⠁⢀⡜⣼⠃⠀⠀⠀⠀⠀⠟⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠚⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢾⠿⠃⠀⠀⢀⠀⣀⢀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠴⡿⣦⠀⠀⠀⢀⣘⣷⠿⡾⣷⡄⠀⢸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣠⡟⣩⠝⢧⡄⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⢨⡽⠛⡛⢩⡋⡿⠂⢨⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡍⠀⠘⣿⣿⣦⡓⢰⠟⠀⠀⢀⠀⠀⠀⢀⣤⡀⠀⠾⠣⣴⢁⣨⣴⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠻⠙⠋⠁⢠⢢⠎⠀⠀⠀⠀⠻⡍⢆⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠙⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢢⡀⠀⠀⠀⡐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠠⠀⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠱⠀⠃⠀⠀⠀⡇⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⠔⠃
⠀⠀⠀⠁⢰⠓⢢⠀⠓⠀⠀⠀⠀⠀⠀⠰⠀⡂⠀⠀⠈⠳⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣠⠀⢸
⠀⠀⠘⡶⠋⠀⠀⠑⢄⡀⠀⠀⠀⠀⠔⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⠠⠀⠊⠀⠀⠀⠀⡰⢄⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⣌⠀⠸⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠊⠀⠀⠀⠔⠀⠂⠀⠄⠀⠀⠄⢀⠀⠀⠀⠀⡃⢸⠀⠀⠀⠀⡁⠇⠀⠀⠀⠀⠀⢢⡼⢖⠣⠀⠀⠀⠠⠂⠂⠀⠄⠂
⠀⠰⠁⠀⠀⠀⠜⢀⠀⠀⠀⠀⠁⢸⠀⠸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠇⢸⠃⠀⠀⠀⠀⠀⠀⠈
⠠⠤⠄⠀⠀⠀⢀⠈⠂⠴⠀⠀⠀⠘⠀⡀⠀⠀⠀⠤⠇⢰⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠤
⠈⠁⠐⠀⠀⠤⠠⠂⠀⠀⠁⠊⠀⠸⠀⠁⠀⠀⠀⢲⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠘⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡇⠀⣾⠙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⣀⣀⣤⣤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠧⢤⣯⣤⣞⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣁⣹⡤⠖⠛⢉⣉⣡⡤⣤⠶⠶⠒⠒⠒⠒⠒⣲⠒⠒⠒⠒⠲⠶⠦⠤⢤⣌⣉⡙⠓⠶⢤⣀⠀⠀⣴⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⣡⡴⠖⠋⠉⠁⠀⠀⠘⢦⣀⠀⠀⠀⣀⡴⠃⠀⠀⢠⠞⠛⢦⠀⠀⠀⠀⠈⠉⠛⠲⢤⣈⠙⠶⣇⢠⠞
⠀⠀⠀⠀⠀⣴⢋⣷⠟⣁⠴⠋⣁⡤⠖⠒⠒⠒⠦⣄⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠘⢦⣤⠜⠀⢀⣠⠴⠒⠒⠒⠲⢤⡈⠛⢦⡈⠻⣄⣠⣄
⠀⠀⠀⠀⠀⢩⡟⢁⡴⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀⠙⢦⡈⢷⣬⠗
⠀⠀⠀⠀⣰⠏⢠⠏⠀⠀⡾⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⣷⠀⠀⢳⡄⢻⡄
⠀⠀⠀⢠⡏⢠⠏⠀⢠⠀⡇⠀⠀⠀⠈⢿⡗⠒⠶⠤⠤⣠⡇⠀⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⢸⡠⠤⠤⠖⠒⢾⡏⠁⠀⠀⠀⣸⠀⠀⠀⢻⡀⢻⡀
⠀⠀⠀⡾⠀⡿⢤⠀⠂⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠁⠀⢀⣧⠈⣧
⠀⠀⢰⡇⢸⠃⠈⢇⠀⠀⠀⠱⢤⡀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢀⠞⠉⢹⡄⢻⡀
⣠⣤⣼⠃⣾⠀⠀⡟⠀⠀⠀⠀⠀⠉⠙⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠚⠋⠁⠀⠀⠀⠀⠸⣆⠀⠀⡇⢸⡧⠴⠲
⠓⠒⣿⠀⣿⣠⠞⢡⠾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢷⡌⠓⠒⣷⠈⡷⠒⠚
⠀⠀⣿⠀⡏⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⣿⠀⡇
⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⠈⣏⠓⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⡼⠋⠉⠙⠓⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠚⠋⠉⠙⢦⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡏⢰⡇
⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠘⣇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⠀⠀⠀⠀⠀⠀⠀⠀⣏⢺⡧⢤⡀
⠀⠀⢸⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⠇⣼⠧⠼⠁
⠀⠀⠀⣿⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣹⠀⠀⡾⢀⡟
⠀⣖⠊⠙⡆⠸⡄⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣰⠃⣸⠃
⠀⠘⠶⠖⠻⡄⠹⣄⠀⠀⠀⠀⠀⠀⠳⣤⡤⠋⠀⠀⠀⠀⠐⠂⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠇
⠀⠀⠀⠀⠀⠙⣦⡘⠦⣀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠈⠻⢦⡈⠓⠦⣄⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣀⣠⠴⠛⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣤⣉⡙⠓⠶⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⠖⠚⢋⣁⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡿⠉⠛⠓⠶⠶⠦⠤⣤⣤⣤⣤⣤⣭⣭⣭⣤⣤⣤⣤⣤⣭⣥⠶⠶⠷⠖⠚⠛⠙⣧⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⡇
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠘⢧⡁⠀⠀⢀⣾⣿⣷⠀⢰⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠧⠀⠸⣧⡘⣿⣦⠀⠀⠀⠀⠀⠻⠿⠛⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠉⠻⢿⡿⠿⣁⣀⣀⡙⣿⣦⣬⣠⣞⠻⢿⣷⣄⠀⢠⣶⣾⣍⠁
⠀⠀⠀⠀⠀⢠⣴⣶⣦⠀⠀⠘⣿⣦⠻⡆⢠⡾⢛⣋⣉⢹⣿⡿⠀⢹⣿⣷⣄⠙⣿⡗⠻⣿⣿⣿⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠘⠿⡿⠟⠀⠀⢠⣼⣿⣷⣄⠈⠐⢛⠋⠁⢿⣿⠇⣀⣬⣿⣿⣿⡆⣹⣏⣄⠹⣿⡇⠀⣾⣿⣿
⠀⠀⠀⠀⣤⣦⡄⠀⠀⠀⠀⠀⠈⠉⢡⣥⣤⣶⣿⡟⠀⣀⠀⢸⣯⣿⣿⣿⣿⣿⣯⣾⣿⠀⣿⠇⠀⢿⣿⠟
⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁⢀⣮⡉⢻⣿⡿⣿⣿⣿⣿⣿⡟⢻⣧⠉⠉⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠙⠛⠁⣀⡀⣤⣄⣘⣓⡂⠀⠀⠀⣸⣿⠇⢼⣿⣿⣿⣿⣿⣿⣯⣶⢿⣧⣶⠶⠶⡌⠽⡻⠦
⠀⠀⠀⠀⠀⠀⢐⣦⣿⣿⣿⣶⣿⣛⡻⠟⢛⣡⡘⣿⣍⡾⣯⡿⣿⣿⠿⠿⠅⠀⠀⣾⡏⣰⣶⠞
⠀⠀⠀⠀⣠⣶⣦⣿⣿⣿⣿⣿⡿⣋⣴⣾⡿⠛⠁⠻⠿⠿⣛⣁⣀⠀⠀⠀⠀⠀⠘⢿⣯⠉⠁⠀⠀⠀⠀⠄⢰⣿⣷⠄
⠀⠀⠀⢸⡿⣛⣿⢿⣿⣿⣿⣿⣷⣍⣩⣥⣄⠀⠀⣠⣤⠘⠛⠛⠿⢿⣦⡀⠀⠀⠀⠈⠛⢺⣷⣄⢀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠈⠛⠛⠉⠞⠩⢻⠿⡟⢋⣤⣿⣿⣿⠇⢸⡿⢿⣷⣽⣿⣷⣦⠙⠇⠀⣠⣤⡀⠀⠈⢿⣿⣷⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠘⢿⣦⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣷⣀⣦⠀⠙⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⣄⢰⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠸⣧⠀⠀⠀⠀⠀⢠⡾⠛⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⢿⡄⢿⡀⠀⠀⠀⠀⠈⢻⡿⢠⡾⠋⠀⠀⠀⢀⡴⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠈⣿⠀⠀⠀⠀⠘⣧⠸⣧⣤⣤⣤⣤⣤⣾⠃⢸⡇⠀⠀⠀⠀⣾⡅⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣴⣦⡙⠻⣦⣀⣀⣤⠿⠂⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣄⣀⡴⠛⠁⢀⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⣠⠶⠋⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠀⢀⣤⠦⣄⠀⠀⠀⠀⠀⠀⠀⣾⠛⣦⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⠇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⢀⠂⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⣦⡀⠀⣰⡏⠠⡍⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠸⢷⣤⣤⣤⡞⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣙⣛⠛⠛⠁⠀⠀⢠⠾⠛⠻⣍⣹⣷⠲⢤⡴⠒⣻⣤⠾⠉⠙⣦⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⣻⡆⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠛⠋⠙⢛⡃⠀⠀⠀⠀⢸⡇⠀⠀⣾⠋⠉⢿⡀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⡄⠀⣇⠀⠀⢀⡤⠖⠒⠒⠶⠋⠉⠉⠓⣆⠀⠀⢸⡇⠀⢠⡟⠀⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠛⠷⠶⠾⠃⠀⠀⠀⢻⣄⡀⣸⠀⢀⡴⠚⠛⠒⠦⣄⡀⢸⣄⣴⠟⠀⠀⢾⣇
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⢰⡶⠖⠻⣷⡀⠀⠀⠉⠛⠛⠛⠁⠀⠀⢀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙⣧⣤⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠁⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⣠⠶⠛⢷⣄⡀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⣴⠷⣶⣤⣤⣤⡀⠀⠹⣟⣉⠀⠀⠀⠀⣽⡏⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃⠀⢠⡾⠁⠀⠀⠀⠀⣨⡷⠀⠀⠈⣿⠀⠀⠀⠀⠈⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢿⡅⠀⠀⠀⠀⠀⠹⣦⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣶⠀⢠⡴⢃⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⠲⣦⡀⠀⢹⣦⣤⣿⣶⣿⣴⣏
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠠⣄⠀⠀⠀⠀⠈⠋⠀⢸⣧⣴⠟⠉⠀⠀⠀⠀⠉⠙⢷⣦⣴⠂
⠀⠀⠀⠀⠀⠀⠈⠟⢹⡆⠀⢠⣇⠀⣠⡈⣧⠀⠀⢸⣆⣀⣴⠿⠋⡄⠀⠀⠀⣦⠀⣀⠠⠀⠀⠹⣧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠿⠛⠛⠛⠻⠿⠷⠶⠿⠛⠋⠁⠀⠀⠀⠀⢠⡄⠉⠀⠘⠀⠀⠀⢠⣿⣉⡀
⠀⠀⠀⠀⠀⡤⠴⢦⣾⠋⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⠂⢰⡆⠀⠀⠁⠀⠀⠀⠀⠘⣢⣾⠋⠉⠉
⠀⠀⠀⠀⠈⠳⢦⣼⡇⠀⠀⣴⠀⠀⠀⠀⠀⠀⠾⠀⣀⠀⠀⠀⠈⠀⠀⠠⠴⠄⠀⢀⣠⣾⠟⠛⠻⠶⠒
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⠀⠀⠀⢀⣴⡿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠲⠾⠛⠻⣦⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⣠⣾⡟⢿⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣻⡷⢶⣤⣤⣤⣈⣀⣀⣀⣀⣠⣤⣤⣶⠾⠛⣿⠘⢷⣌⡛⠶⠂
⠀⠀⠀⠀⠀⠀⠀⣤⡴⠾⠋⠀⠸⠛⣯⠈⠉⡉⣹⠏⢻⡉⠀⢸⣇⠀⠀⠈⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿⠀⠰⢣⡟⠀⠘⣧⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⡧⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⢿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡫⠶⣏⡟⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣵⣆⢷⢟⣹⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠡⢅⠿⠁⢸⡿⢳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⢦⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⠏⠀⠀⠘⢷⡠⡎⣿⠀⠀⠀⠀⠀⣠⣶⢴⣄⠀⠀⠘⠛⠏⠁
⠀⠀⠀⠀⠀⣀⠤⣤⡀⠀⠀⠀⠀⠀⠀⢹⣳⠆⢿⡗⠀⠀⠘⡿⠊⣁⢩⣿⠆⠀⠀⠀⠀⠀⠀⣠⣀⣰⣆⣀⡀
⠀⠀⠀⠀⣰⢋⠚⡚⢛⢳⣄⠀⠀⠀⠀⠘⠛⢾⠞⠃⠀⠀⠐⣿⣦⢹⡊⣿⡀⠀⠀⣠⣴⡖⠿⢩⣥⢉⡹⢻⡀
⠀⠀⠀⠈⠻⢜⡞⠁⠸⠌⠉⠳⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠇⡹⣯⠀⠀⢴⠿⢢⠰⠎⣃⣨⣍⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠙⣧⡄⠶⠶⠒⢰⡎⢹⡶⣤⣀⠀⠀⠀⠀⠀⡼⣁⠟⣲⣿⡀⠀⠘⢻⠞⠛⠋⠙⠋⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣶⠀⡘⠁⠸⡇⠙⣻⡄⠀⠀⠀⣾⠇⠹⠆⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣽⠆⢰⠀⣈⡿⠁⠀⠀⣸⡧⠞⠠⣖⣸⡟⠀⣀⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠒⠺⠃⠀⠀⠀⠸⣧⣆⣴⡾⠉⠀⣴⢿⣷⣮⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡶⣴⢾⡗⢲⢖⣶⢤⣤⡀⠀⠀⠀⠀⠈⢀⣀⡶⠝⠓⣬⣽⠉⠀⠀⢀⣴⠷⢶
⠀⠀⠀⠀⠀⠀⠀⠰⣿⢣⠗⣠⡄⠃⣤⠰⢞⠊⡰⣷⠶⠀⠀⣠⡴⣿⠟⡐⢟⣋⣿⠍⠀⠀⢀⡼⣫⢖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠠⢻⣯⣬⣩⣦⢿⡬⠵⠾⠿⣧⠏⠀⠀⠐⢿⣰⣋⠀⣿⣬⠟⠃⠀⠀⠀⣸⣧⠡⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⣴⣦⣦⣀⣀⢀⡀⠀⠀⠈⠙⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢨⣭⣹⠟⢿⠧⢴⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣥⡐⠿⡄⠇⠟⠢⠏⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⠗⢾⡧⡾⢤⣿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠄⡀⠀⠀⠀⣤⡀⠀⠀⠀⣠⠴⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⠜⣲⣬⠽⢢⡶⡍⠁⠄⠀⠐⠧⡊⠙⠲⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢞⠄⠀⠀⠀⡈⠀⠀⠀⠀⠀⣸⠀⠀⠈⠢⡔⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡰⢡⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⣤⠖⠁⢀⣤⡀⢀⠃⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠔⠁⠆⠂⠁⠀⠀⠀⣀⣤⠖⣨⠞⠁⢀⡴⠋⠀⠙⢧⠌⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠪⣀⠜⢲⠒⠀⠀⠀⠀⠐⠖⠊⣠⠞⠁⢀⡰⠛⠓⠒⠒⢢⠸⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠂⠀⠀⣰⠞⠁⢀⣠⠚⣠⣤⠶⠢⠤⠊⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡔⠡⣀⠀⣠⠞⠁⠀⡰⠊⣰⣾⠗⠊⠀⠁⠀⠁⣠⡊⠺⡀
⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⠘⢱⡀⠀⠙⠁⠀⡠⠊⢄⡰⠛⠁⢀⠀⠀⠀⣸⠉⠀⡹⣄⠉⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠣⢀⡨⠓⠀⠙⢆⠀⡠⢪⡀⠐⠀⠀⡀⢄⠀⢀⡀⠚⠁⢀⠜⠑⠥⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠛⡠⣌⡁⠀⠒⠀⠤⠸⡀⠁⣀⡤⡞⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡇⠀⠉⠉⠒⠒⢲⠋⠀⡊⠁⠀⢋⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁⠀⠀⠈⠒⠊



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠐⣯⡿⠀⠀⠀⠀⢀⠄⠀⠀⠄⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⡐⢲⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠤⠀⠀⠀⠀⢜⠠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠄
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡐⠀⠀⠀⣮⠆
⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⢀⢀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢄⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠩⡀⠃⠀⠀⠀⠘⠀⠀⠀⠀⢉⠳⠀⠑⠢⠁⠀⠀⠠⠁⠀⠀⠀⡌⠱⡀⠀⠂
⠀⠀⠀⠀⠀⢘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠒⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠤⠀⠄⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠗
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠲⠦⣄⡀⠀⠀⢀⣠⠴⠛⠉⠙⠲⢤⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠞⠁⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⢴⣦
⠀⠀⠀⠀⠀⡖⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡞⠍⢢⠀⠀⠀⢳⣈⡼⠣⠀⠀⠀⠛⠲⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⠀⠀⠀⠈⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⠏⠀⢠⣞⣳
⠀⢀⣠⠴⠚⠁⠀⠀⠀⠰⡳⠀⠀⠀⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢦⣀⡏⠈⠳⠞⠀⠀⠀⠀⠀⠉⠁⠀⣠
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡁⠀⠀⠁⣀⣤⣄⣤⠶⠲⣄⠀⠀⠀⠀⠀⠳
⠀⠹⣆⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⠗⠀⠀⠀⠀⠸⣄⡀⠀⠙⠲⠶⠚⠁⠀⠀⠀⠀⣰⠇
⢀⡴⠃⠀⠀⠈⠛⠁⠀⠀⠀⠰⣁⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉
⢳⡀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠙⠓⠒⠛⠁⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠉⠛⠦⣄⣀⡀⠀⠀⠀⣀⣠⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠝⠁⠀⣀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠁⠀⢸⡶⢋⣍⠉⠳⢾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣾⣆⣈⡁⢴⠐⠾⠏⠀⠀⢠⠋⡹⠀⠀⠀⠀⢀⣤⡀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⡼⡄⠀⠛⢻⣿⣽⣟⣤⢶⣼⠻⠀⠀⡌⢴⠁⠀⠀⣠⡴⢋⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠂⠀⠀⠈⠁⣼⠉⠛⠉⠁⠀⠀⠀⢷⡿⠀⠀⠸⠥⠔⠁⠀⣠⡄⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠋⠙⢞⣿⣶⠛
⠀⠀⠀⠀⢀⣀⠤⣾⠆⠀⠀⠐⠛⠁⠀⠀⠀⠔⣶⣦⠀⠀⣰⠂⡐⠄⠀⠀⠀⠀⠀⠀⠀⣼⣍⠁⢛⡸⣻⣿⣟⠃⠀⠀⢀
⠀⠀⠀⠀⠃⠐⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣁⠞⠀⠀⠻⠿⠤⠀⠀⠀⠀⠀⠀⣤⣤⠀⣽⣆⣛⢁⣰⠿⠛⠃⠀⡨⣼⡿
⠀⠀⠀⠀⠀⠀⣠⣬⠓⢿⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⠀⣀⠀⠀⠐⢤⠟⣦⠀⠈⠋⠙⠃⠀⠀⠀⠀⠃⠞⠁
⠀⠀⠀⠀⠀⠐⢺⠈⠲⢰⣾⣿⡁⠀⠀⠀⢠⣶⡄⠀⠀⠀⣤⣚⡿⣿⣿⣿⣴⠆⠀⠈⠀⠁⠀⠀⣠⣴⣂⣀⣿⠆
⠀⠀⠀⠀⠀⠀⠚⢧⣛⣀⣿⠿⠄⠀⢀⡀⠀⡏⢹⠀⠀⠿⣗⠁⣤⠍⣚⠱⢿⠃⠀⠀⣀⡀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠀⠀⠀⠔⣲⠟⠀⠃⢸⠀⠀⠠⠿⣏⣀⢀⠛⣠⠿⠇⠀⠜⢹⠃⠀⠀⠀⠀⢠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠻⠯⠭⠴⠆⠀⠈⠁⠀⠀⠙⠁⠀⠀⠀⠈⠋⠈⠻⠏⠉⠁⠀⣼⣴⠃⠀⠀⠀⠀⠀⠀⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡈⠁⠀⠀⠀⢶⣰⣦⣾⡀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡶⢚⡲⢆⡀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⣘⡿⠿⠟⡙⢣⡄⠀⣨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠐⢾⣷⣮⠥⠨⡷⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡽⣀⡘⠀⣋⡾⠂⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡽⠻⠷⠞⠂⢀⢀⡜⠀⠀⠀⠘⢯⠃⡀⠀⠘⠛⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠀⠐⠠⠀⠀⠀⠀⠉⠛⠚⠒⠒⠒⠂⠀⠄⢀⠄⢀⡀⡄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⢀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠉⠉⠐⣄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠂⢐⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠐⠂⠤⠀⠀⠀⠀⢂⠀⠑⢦⣄⣿⠀⢰⣾⠉⠈⠁⠀⠀⠀⢀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢖⠀⠀⠀⠀⠀⠀⠈⠀⠂⣀⣴⡇⠀⠀⠈⠁⠀⠈⠻⠖⠄⠀⢀⡀⠤⠚⠁⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢴⠀⠀⠀⠂⠀⢐⡟⠑⠲⣄⠀⠈⠉⠁⠀⠄⠈⠛⣧⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢀⣤⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠉⡀⠀⠀⠄⠀⠈⠲⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⡐⠂⣠⠐⠒⠀⠂⠀⠁⠀⠀⠀⢠⢟⠅⠀⠢⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⡀⠠⠀⠀⢺⡄⠀⠀⠁⡀⠀⠀⠡⠀⣡⡀⣰⠖⠁⠀⠻⢇⣤⣀⡀⠀⠀⠀⠀⠊⠀⠁⠀⠀⠀⢠⣦⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠑⢴⢾⡇⠀⠀⠀⠐⡀⠀⠀⡅⠈⠛⠋⠀⢀⣤⣄⠀⠀⠀⢀⠀⡀⠀⠀⢀⡔⠂⠐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⠀⠀⠄⠀⠀⠀⠀⢀⠑⠗⡾⠇⢀⠀⠀⠀⠋⠁⠘⠺⣄⠀⠃⠀⠀⢱⡀⠩⢣⠀⠄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠲⣶⠶⠃⠀⠀⠀⠀⢨⡅⠀⠀⠀⠁⠀⠆⠀⠀⠠⡀⠀⠈⠠⠀⠰⣀⣼⡇⠀⠀⠀⠀⠁⠀⠄⢠⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡄⠃⠀⡀⢠⠠⠂⠁⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈⠄⠀⠀⢠⡀⠀⠀⠠⠂⠩⣴⠀⠀⣀⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠌⠀⠈⠼⣲⠿⠉⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦⠀⢤⠀⣸⡇⠀⠀⠀⠀⠀⢛⠃⠀⠋⠁⠞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢠⠃⠀⢠⠀⢠⠀⠀⢺⠀⠀⠒⠛⠃⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢀⡤⠐⠂⠀⠀⠀⠀⠜⠋⠀⠸⡷⡶⠖⠀⢀⠀⢀⡚⠀⢀⡀⠀⢠⠀⠀⠠⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣵⣧⣀⣀⢀⠠⠂⠁⠀⠀⡀⠄⠀⠀⠒⢂⡀⠉⠉⠀⠌⠀⠛⡇⢈⢄⣤⠄⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡀⠈⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⡤⣿⠇⠀⠈⠀⢀⣀⠁⠈⠛⠉⠋⠀⠰⡵⢶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠇⣐⣁⠀⣀⣀⠀⠀⠈⠉⠉⠀⠀⠀⠪⣷⣶⠞⠁⠀⢀⠀⠂⠙⣇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠿⠿⠁⢀⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢼⣇⢀⡤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣄⠀⠀⠀⠀⠀⠀⢀⢴⡟⠀⠈⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠐⠀⠈⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣼⠁⠀⣤⣴⣦⡤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣴⣴⣆⡀⠀⢻⡄
⠀⠀⠀⠀⢀⣴⠏⠀⠰⣻⣿⢿⣿⠆⠀⣿⠀⢀⣶⣾⣶⠀⠀⠀⠀⢸⡇⠀⠸⣿⣿⡿⠄⠀⠈⢷⣄
⢀⣠⡴⠞⠋⠁⢲⠀⠀⠚⠫⠟⠛⠀⠀⣿⠀⠈⠿⣿⠿⠁⠀⠀⠀⢸⡇⠀⠀⠈⠀⠁⢠⠆⠀⠀⠉⠛⠶⣤⡀
⣿⣁⣀⣀⣀⡀⢼⣶⣶⠶⠤⣤⣤⣴⡄⠈⢷⣄⠀⠀⠀⠀⠀⠀⣴⠿⣤⣦⡴⠶⠶⠦⠼⡄⠀⠀⠀⠀⠀⠀⣹
⠈⠉⠉⠉⠉⣿⢾⣿⣿⠂⠀⢉⢿⣻⡿⠇⠀⠙⢷⡀⠀⠀⣠⠞⠉⣿⣿⣿⠄⠀⠀⠀⢀⣶⣶⣶⡟⠛⠛⠛⠉
⣐⣾⣿⡧⢸⡇⠈⠉⣸⡇⠀⠀⣵⠃⠉⢷⡶⢤⡴⠟⠀⣼⠋⣀⣠⣾⠏⠉⣠⡄⠀⠀⣿⡿⠿⠛⣷⠀⣠⣤⣀
⠈⠛⠞⠃⣿⠀⠀⣰⣿⡇⠀⠀⣿⣧⠀⠘⣧⠀⠀⠀⠀⢙⠛⡉⢡⡟⠀⢠⣿⡇⠀⠀⣿⣧⡀⠀⢸⡆⢻⢿⠗
⠀⠀⠀⠀⣿⣀⣴⠏⢸⡇⠀⣠⡟⠹⣆⠀⢹⡄⠀⠀⠰⣾⣿⣷⣾⠁⢀⡾⠘⣷⣾⣿⣿⠈⢷⣄⣸⡇
⠀⠀⠀⠀⠈⠉⠀⠀⠸⡧⢿⣿⡷⠀⠙⢦⣼⠃⠀⠀⠈⠻⠷⠟⢻⣤⠟⠁⠀⢿⡛⢻⡿⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢈⣿⠀⠀⣴⡟⠃⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣼⣿⣤⣴⣿⣀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⣠⡾⠟⢋⣉⣤⣤⣌⣉⡙⠻⢿⣄⣠⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠙⣷⡾⢋⣴⠾⠛⠉⠉⠉⠉⠙⠻⢷⣤⡙⢿⣄⠀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠙⣷⡾⢋⣴⠟⠱⠶⢂⣀⣀⣀⠀⠀⢶⣄⠙⢿⣄⠹⣷⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣠⡾⢋⣴⠟⠁⠀⠀⣴⠟⠋⠉⠛⢷⡄⠈⠋⠀⠈⢿⡆⢹⣧⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣄⠀⣠⡾⢋⣴⠟⠁⠀⠀⠀⢸⣟⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢸⣷⠈⣿⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⣻⡿⢋⣴⠟⠁⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣠⣾⠏⠀⠀⠀⠀⢸⡟⢠⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢻⣧⡾⢋⣴⠟⠁⠀⡀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣟⠋⠁⠀⠀⢀⠀⢠⣿⢃⣾⠇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢶⣤⡾⢋⣴⠟⠁⠀⠀⣾⠇⠀⠀⠀⠀⠀⣿⠁⠀⠀⢹⡇⠀⠘⠛⢛⣵⠟⣡⡾⠻⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣦⡾⢋⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣴⠿⠁⠀⢀⣴⠟⣡⣾⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣰⡟⢡⣿⠃⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣾⣏⠀⠉⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠁⣾⡇⠀⣴⡟⠛⠛⢷⡄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣾⠋⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣠⣿⠀⣿⡇⠀⣿⡀⠀⠀⢸⡿⠀⠀⠀⠉⠛⠀⠀⠀⢀⣴⠟⣡⡾⠋⠻⣦⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡇⢸⣧⠀⠘⠻⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⡾⣿⣄⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢿⣄⠹⣧⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣾⡏⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠁⠈⠻⣧⣈⠻⣶⣼⣇⣀⡀⣀⣀⣠⣶⠟⣡⣾⠋⠘⢿⣤⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠋⠻⣷⣤⣉⣙⠛⠛⠛⢋⣉⣤⡾⠋⠛⢿⣆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣼⠏⠈⠙⣿⠟⠛⣿⡟⠋⠻⣦⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⢠⣼⠟⠀⠀⣿⡁⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⡀⠀⠀⠀⢺⡑⢦⡀⠀⠀⠀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⣄⠙⣆⠀⠀⣀⡇⠀⢳⣀⣀⣸⠁⡏⣀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡽⠀⠘⠋⠉⡉⠀⠀⠀⠀⠀⠃⠀⠻⢅⣴⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣌⠙⠒⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠴⠚⢉⡹
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡉⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⠀⠀⠸⣄⢀⣀⡤⢤⡀
⠀⠀⠀⠀⠀⠰⢭⣭⣉⠀⠀⠀⠀⢠⠴⠛⠉⠉⠉⠛⢦⡀⠀⠀⡠⠞⠉⠉⠉⠉⠳⢄⠁⠀⠀⠈⠉⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢰⠃⠀⠀⢀⡤⠤⡀⠀⠱⠀⡼⠁⠀⠀⣠⡤⢄⠀⠀⢣⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠠⣖⡒⠦⡞⠀⠀⠀⡆⠀⠀⠀⡛⣷⣤⣿⠀⠀⡇⡃⠀⠀⢘⢛⣦⣼⡇⠀⠀⠀⠀⠀⢻⡤⣄⡀
⠀⠀⠀⠀⠀⠀⣈⣱⡄⠀⠀⠀⢣⠀⠀⠀⠙⠻⠟⠋⢀⢠⠃⢣⠀⠀⠈⠛⠿⠛⠁⡀⢰⠀⠀⠀⠸⠧⠤⠷⣄
⠀⠀⠀⠀⠀⢀⡵⠤⠇⠀⠀⠀⠈⢣⣀⠀⠀⠀⠀⠂⣡⠎⠀⠈⠳⣄⠀⠀⠀⠀⢈⡴⠃⠀⠀⠀⠀⢀⡴⡖⠚
⠀⠀⠀⠀⠀⠙⠒⠲⣄⠀⠀⠀⠀⠀⠈⠛⠲⠶⠒⠋⠁⠀⠀⠀⠀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⢀⣏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠒⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠙⡆⠈
⠀⠀⠀⠀⠀⠀⠐⠧⠖⠲⡄⠀⠀⠀⠀⠀⠠⠊⠉⡆⠀⡗⣇⠀⢸⢇⡸⠳⡀⠀⠀⠀⠀⠀⢠⡞⠙⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣦⡀⠀⠀⠀⠀⢸⣀⠟⠒⠁⠈⠑⠉⠀⠀⠀⠁⠀⠀⠀⢀⣴⡏⢸⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡽⢦⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠙⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠋⠀⠉⢳⠖⠦⣤⢤⣤⣤⣤⡤⠤⣶⠒⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠹⡄⠀⠀⠀⠀⢠⠇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠅⣠⠀⠀⠀⢱⠀⠀⠀⠀⡞⠀⠀⠀⡄⢩⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠷⠶⠖⠒⠋⠀⠀⠀⠀⠙⠒⠶⠦⠷⠴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⡀⡰⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠱⠲⠃⠀⠈⠀⠐⠁⠀⠀⠀⠀⢈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡀⠠⠀⡆⠀⡄⠀⠀⢀⠀⠀⠀⠀⠠⠹⠇⠀⠘⠀⠃⢀⡒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠈⠈⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠯⡬⠟⠀⠀⠀⠂⢀⠨⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⢂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠓⠀⠀⠀⠀⡔⡓⡄⠀⠀⠀⠀⠀⠀⠀⡀⢀⢄⠀⠀⠀⠀⠈⠒⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠄⠀⠀⠑⠚⠁⢀⡀⠀⠒⠁⠀⢠⠊⢀⢈⠀⠀⠀⠀⣅⡠⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠈⠉⠀⠀⠐⠥⠽⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠁⠀⠀⠐⠀⢠⠄⠀⠀⠠⡄⠀⠂
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠚⠀⢀⣤⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⡠⡄⡀⠀⠠⠀⠐⠂⠀⠈⠉⡀
⠀⠀⠀⣸⡦⠀⠀⠀⠀⠀⠀⢂⠀⠀⡆⠀⠀⢠⢎⣨⠃⠀⠀⠀⠀⢀⠀⠀⠀⠔⠂⠀⠀⡇⡄⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠖⠀⡀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠈⢄⠠⠃⠀⠂⢠⠀⠀⠀⢀⠐⠀⠀⠄
⠀⠀⠐⢄⡄⠀⠀⠀⠘⠁⠀⠈⣀⠀⠀⣠⠀⢀⠔⣡⠃⠀⠀⢴⣍⡇⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠲⠀⠀⠠
⠀⠀⠀⠈⠀⢀⡄⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠘⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠀⠢⠐⠁⠠
⠀⠀⠀⡀⠐⠂⠀⠀⠀⠐⠀⢠⠂⠐⠀⠀⠀⠀⠀⠀⡄⠠⠂⠀⠠⠂⠀⡼⢉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⢡⠰⠀⠈⠂⠀⠀⠀⠀⣧⠀⣰⠀⠈⠆⠁⢀⠀⢀⠄⠀⡀⠴⣤⠈⠣⣄⠀⡸⠀⠀⠒⠭⢗⠂⠀⠀⢀⠦⢄⠀⠀⣤
⠀⠀⠀⠀⠀⢀⢰⣄⠀⠈⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⢎⡀⠲⠨⣃⠀⠀⠉⠁⠀⠈⠠⣈⡀⠀⠀⠀⠸⠀⠈⡧
⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⢀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠰⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠨⣀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠈⠁⢀⠀⠆⠠⢀⡀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠠⠤⡀⢀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣐⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⣀⠀⠈⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠑⠀⠀⠀⠀⠀⠀⠂⠉⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠴⢶⢄⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠁⠀⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⢀⢠⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢷⡀⢀⡞⡇⠀⢀⡶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣄⠀⢀⣠⡼⠿⠓⠚⠛⠷⢦⣼⣹⠃⠀⠀⣀⡀⠀⠀⢴⢳⡀⠀⠀⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣷⠋⠁⢀⣠⣤⣤⣤⣀⠀⠈⢻⣴⣿⡆⣿⢿⠀⠀⢸⣿⣧⠶⠚⠛⠛⠲⢦⡀⣰⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⡀⢸⠃⠀⣴⠋⣵⠛⠛⠻⡏⢳⡄⠀⠈⠻⠧⣽⣼⡦⠶⠛⠉⠀⣠⡤⠤⣤⣀⠀⠹⣷⠋
⠀⠀⠀⠀⠀⣀⠀⠀⠉⢳⣽⠟⠀⢸⡇⠀⠈⠛⠒⠛⠁⠀⢿⣤⠶⢶⡄⠀⠀⣀⣀⡀⢀⡞⠁⣶⠲⢦⡙⢧⠀⢹⡆⢀⡀
⠀⠀⠀⠀⠸⣯⣳⣤⠶⠋⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⡿⠈⠛⠋⠁⠀⠸⣭⣬⡿⢸⡇⠀⠙⠓⠚⠁⣸⠇⠀⣿⣫⡿
⠀⠀⠀⠀⠀⠀⡿⠁⢀⡴⠶⣄⠀⠀⠙⢦⣀⠀⠀⠀⣠⡾⠁⠀⠀⠀⣠⡤⢤⣄⠀⠀⠀⠻⣄⠀⠀⢀⣴⠏⠀⠀⡟⠁
⠀⠀⢠⣶⠶⣼⠃⠀⠀⠙⠛⠁⠀⠀⠀⠀⠉⠛⠛⠛⠉⢰⣖⣲⡄⠀⠳⠦⠴⠟⠀⢀⣀⡀⠈⠛⠛⠋⠁⠀⠀⢰⡧⣤⡀
⠀⠀⠈⠉⠉⢻⡀⠀⠀⠀⢀⣤⠶⠶⣤⠀⠀⠀⠀⣀⣤⣤⣈⡉⠀⠀⠀⠀⠀⠀⠐⢯⣤⡽⠂⠀⢠⡖⢲⡆⢀⡾⠙⠛⠃
⠀⠀⠀⠀⣀⡼⣧⡀⠀⠀⠘⢧⣤⣤⡼⠃⣀⡴⠛⢹⣿⡇⠈⣹⢿⡶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣠⣞⢧⡀
⠀⠀⠀⠀⠻⠞⠉⠙⢶⣤⣤⣤⣤⣤⠶⠚⢻⡻⣆⠈⠙⠁⠀⠿⠞⠀⠀⢸⢿⡟⠳⢶⣦⡤⠤⠴⣶⢾⡏⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⢹⣾⡇⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⠀⠀⢸⣿⠇⠀⠀⠈⠳⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉





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