Toon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⡄⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⢄⣀⠔⠂⠁⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡠⠐⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡄⢴⠃⠋⣠⣾⠁⠀⠀⠀⠀⠀⠀⠢⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⠀⠀⢄⠀⢨⠀⠠⠀⢀⠃⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠄⢘⣤⣀⣰⣦⣄⣀⠠⠄⠀⠀⠀⠀⠀⠴⠁⠖⠈⣀⣴⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠱⠤⢘⣤⠤⡀⠀⠀⠀⠀⠀⢠⣴⡦⣄⡀⠀⠀⠁⠀⠘⠦⠄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢃⣼⣿⠀⠀⠀⠀⠀⣿⣿⣴⠸⠁⢰⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡘⠈⠛⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠈⠀⠀⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠄⠀⠀⠀⠀⠀⠘⢄⣥⡀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⣴⣄⣠⡀⠘⡆
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣞⠂⠀⠀⣀⣀⡤⠔⢯⠁⠀⣦⣃⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠀⠀⠀⠈⠙⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢁⡰
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢦⡀⠀⠀⠀⢰⠀⠀⠀⠀⠠⡆⠀⢄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣿⡏⠀⠀⠀⣼⢨⠀⠀⠀⠀⠘⡎⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠊⠀⠀⠀⡯⠃⠀⠀⠀⡷⠊⠀⠀⠀⠀⠀⡸⠿⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⡰⢇⢀⠀⠀⢠⠳⠤⠠⠤⠤⠒⠊⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⢀⠀⠠⠀⠀⡅⠀⣸⣻⡇⠃⠀⢒⠐⠀⠀⢸⠀⢈⣉⠀⣃⠀⠘⠠⠠⠄⠤⢠⠠⠀⢸⡇⠸⠛⡧⢼⠤⠄⢀⣀⣀⢀⣀⣄⣀⡄⣀
⠀⠠⠀⠠⠈⠀⠁⠀⡋⢉⡃⠀⠀⠀⠡⠊⠀⢸⠀⠠⠴⠀⠦⠀⢸⠘⠀⠂⠒⠐⢠⡄⠼⠇⠰⠆⡃⢸⠒⠂⢰⠠⢀⡦⠤⠈⠟⠄⠠
⠀⠀⡀⢀⠐⠀⣲⠒⣀⣀⡀⢹⡆⠀⠀⠀⠀⠈⡤⡈⡛⣚⡓⡓⡛⡛⠛⡇⣉⢈⢸⣄⣀⡀⠰⠂⡅⢹⡁⡁⢰⢀⠀⡦⠦⠐⠖⠶⠶
⠀⠐⠒⠂⠀⠀⢬⠱⠶⠶⠆⢸⠇⠀⠀⠀⠂⠀⠱⠆⠠⣤⡀⡄⡤⠤⠄⠄⠤⠠⠠⠘⡇⠀⠐⠆⡆⢺⠀⠀⡌⠉⢉⠉⠡⠤⠠⢔⠢
⠀⠀⠀⠀⠀⠀⢉⠒⠓⠛⡃⠛⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠤⠦⠦⠤⠄⡃⠒⠐⠂⠀⣇⡇⠐⠖⠓⠚⠶⠦⠇⠀⠄⠀⠄⠀⢠⠀⢲
⢈⠁⡁⠈⠀⠀⣚⢉⣉⣉⣁⠀⠂⠀⠀⠀⠀⠀⠖⠻⠃⠒⠖⠖⠒⠲⠆⠁⠉⠈⠁⠀⡇⡇⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠈⠀⠈
⢀⠀⡀⢐⠐⢠⠼⠀⣀⣀⣀⡐⡲⠔⠀⠐⠓⠠⣄⠨⡅⠴⠤⠦⠰⠶⠆⠒⠴⠢⢀⡠⠴⠇⢘⠀⠠⠀⠀⣠⠠⠄⠀⠀⠀⠀⠂⠂
⠀⠀⣀⠀⣀⠈⢀⢨⡀⠄⠤⠥⠄⠀⠐⠐⠀⠀⠀⢀⡀⠚⠒⠒⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢻
⠀⢈⣎⣈⣉⠀⠠⠤⠆⠖⠐⠖⢀⠀⠠⠠⠠⠀⠀⠀⠁⠲⠰⠒⠐⠚⠀⠀⠆⠰⠠⠄⠤⠀⠸⠄⣄⣤⣤⡌
⠖⠛⠘⠐⠚⠛⠒⡂⡂⠃⠁⡃⠈⡡⠄⠀⠀⢠⠀⢤⡄⠚⠘⠘⠘⠛⠁⡃⠀⠀⢠⠀⡜⠛⠒⠚⠛⠛⠛⠛⣂⣀⡤⢀⡄⡀⢀⣀
⢸⢩⠉⡅⡍⡍⢸⠁⠩⠭⠤⠭⠄⠁⠀⠀⠀⠈⠀⠈⢹⠚⠘⠘⠘⠛⠁⠗⠒⠀⠘⠳⠇⠠⠀⠀⠀⠀⠀⠀⡖⢖⣥⣤⣆⠀⠤⠴⠦
⠐⠐⠀⠆⠂⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠤⢸⠒⠚⠸⠘⠛⠃⠀⡈⡀⠈⡊⡀⠈⠀⠀⠁⠀⠂⠀⠖⠚⠓⠐⠊⠙⢻⠿⠿
⢈⢈⠀⡁⡁⡁⠸⠒⠒⠒⠒⠚⢿⠀⠀⠀⠂⠀⠀⠀⠘⡋⠙⣘⢀⣉⡁⢀⡀⠀⠀⢀⡅⠄⠀⠁⠁⠀⠀⠀⠸⠩⠅⠅⠥⠅⢐⠀⢀
⠠⠠⠀⠄⠄⠄⢸⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⢈⠈⠀⡁⠀⢛⠀⠀⣂⠀⠬⢀⠀⠀⡇⠒⠐⠂⠀⡂⠂⠀⢐⡐⡂⡂⡂⠂⢀⡐⠃
⠒⢐⠀⡂⠂⠂⠀⡤⠤⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠈⢀⠃⢀⠀⠂⠈⠀⠃⠅⠠⠀⠀⠀⡄⠀⠠⠀⠄⠄⠄⠄⠸⠤⠤
⣁⣨⣀⣅⣁⣠⠀⢤⣄⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠃⠅⠭⠬⠭⠭⠭⠽⠀⡀⠠⠀⠍⠄⠁⠀⢐⠀⡂⡂⡀⠀⠀⠐⠒
⢀⣀⠀⠀⡀⠀⢠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠐⠃⠈⠃⠀⠀⡀⣀⣁⣅⣁⡈⢉⡉⠉⡁⠀⡂⢐⠀⠂⠂⠐⠀⠠⠠⠄⠄⠤⠤⠀⠐⠂
⠀⠤⠀⠶⠆⠀⠀⠀⠐⠄⠆⠀⠀⠀⣁⡁⣀⠁⢁⡠⠠⠼⠽⠿⠭⢭⠙⡃⣦⣀⣀⡄⠀⠃⠀⠀⠂⠀⠐⢠⠐⠀⠂⠂⠐⠐⠀⠐⠃
⢀⣉⠀⢉⡁⠀⢀⠀⢰⠀⣇⣀⡄⠁⠀⠀⣈⡁⢲⡇⠀⠀⠀⠄⠀⠨⡀⡀⠍⣀⠈⠅⠀⠀⢰⠂⠀⡆⠀⢸⠀⠀⠄⠖⠄⠀⠀⠐⠂
⠀⠴⠀⠦⠄⠀⠉⠉⠉⠁⠉⠉⠃⢚⣚⠀⣑⢉⢸⠓⡚⢒⠒⡒⢒⠚⠋⠀⠀⠀⠻⠶⠦⠠⠴⠠⠤⠇⠄⠸⠠⡚⠀⠐⢈⠂⠓⠐⠒
⠀⣉⡀⣉⡁⠨⢉⣉⢉⠉⣡⡔⠁⠠⠤⠀⠤⠤⢸⠐⠍⠩⠐⠜⠉⠀⢶⣆⢀⠑⡛⠒⠒⠒⠒⠓⠒⠒⠒⠒⠓⠆⠀⠀⠸⡆⡾
⠀⠄⠀⠀⠆⠠⠀⠀⠀⠀⠂⠀⢴⠶⠤⠶⠴⠤⢾⠰⠓⠦⠠⠼⠛⠀⣀⣀⣈⣈⡄⢰⣐⠀⣈⣁⣀⣘⠀⣂⡂⢘⠉⠀⠈⠉⠉⢉⠉
⠀⠉⠀⣉⡁⠀⠀⠉⠉⠁⣀⣀⠀⠀⢈⠀⠈⠀⠘⠒⠒⠀⠒⠒⠒⠒⠆⠈⣉⠈⢱⠀⠀⣠⠀⠀⠀⠀⠀⠀⠄⠐⢧⠁⠠⠈⠄⠨⠤
⠀⠀⠀⠠⠄⠀⢀⣀⣀⣀⠘⡇⠀⠟⠀⠀⠀⠈⠁⠀⠀⠠⠔⢴⠀⠀⠄⠇⣒⡙⠚⠉⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⡀
⢀⣀⡀⠐⠂⠀⠀⠀⠀⠁⡀⢀⠀⠀⣀⣀⣠⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠃⠀⠐⠂⠀⠀⠀⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡄⢠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⣷⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠉⠙⢓⣀⣠⡀⠀⠀⠀⠀⠀⠐⠲⣿⣿⣿⣶⡀⢀⣀⣀⠀⣰⣿⣿⣽⡷⠃
⠀⠀⠀⠀⠀⠀⡄⠁⢰⠘⡗⠈⢠⠆⠀⠀⠀⠀⠀⠐⢿⣿⠿⣿⣶⠖⣿⣿⣿⣿⣿⣿⣿⡟⠺⣿⣿⣿⣿⠆⠀⠀⠀⠙⠛⠿⢿⣇⠀⢈⣺⠿⠟⠋⠁
⠀⠀⠀⠀⠀⢰⡿⠀⡆⠑⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢻⣦⡈⠙⠇⣿⢟⣯⣿⣧⠀⠀⣠⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟
⠀⠀⠀⠀⠀⢨⣇⢰⡇⠙⣶⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡛⠀⠁⠈⠈⠉⠙⠓⠘⠛⠛⢻⡟⠁
⠀⠀⠀⠀⠀⡟⢧⠀⠱⠀⠏⢰⣃⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠅⢈⡧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠐⠀⠑⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣴⣿⣿⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣯⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⠟⣼⠇⣴⢻⣿⣿⣿⡿
⠀⠀⠀⠀⢀⣾⣿⣟⣿⣿⣿⣷⣄⡀⠀⠀⢠⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠸⣵⣿⣿⣧⠙⢿⡿⠃
⠀⠀⠀⣠⣤⡔⣾⣽⣾⣿⣿⣾⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢠⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⣿⣿⣿⣿⣇⠈⠁
⠀⠀⠀⠻⠋⠻⠿⠋⠀⠀⠙⠛⠛⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣮⡙⣷⡄⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⣿⣿⣿⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠈⠋⠀⠀⠀⠀⠀⣼⣿⠿⠿⠿⠟⠃⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡄⣀⡤⠔⠒⠲⠤⣄⢀⣤⡀
⠀⠀⠀⠀⠀⣤⣀⡀⢀⣀⣀⣀⡀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⣯⣾⡛⣀⠙⣳⣾⣿⣿⣵⡇
⠀⠀⠀⠀⠀⢷⣽⣿⠿⠿⣿⣿⡿⣿⣯⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⡩⠙⠙⣿⡟⠉⠉⣰⣿⣿⣧⡀
⠀⠀⠀⠀⠀⣾⢋⣭⠻⢿⣿⣿⠟⣫⡙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⢋⣉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⢹⣿⢁⣴⠛⠛⠛⢷⡄⢹⣿⠙⣿⣷
⠀⠀⠀⠀⢸⣷⣾⣟⢿⣶⣿⣷⡞⣟⣯⣾⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⣭⡤⠄⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⣿⣟⡀⢸⡇⠸⠿⠶⠀⠲⠾⠟⠀⡟⢀⣸⡿⡇
⠀⠀⠀⠀⠀⠛⠋⠙⣌⡿⣦⢾⣃⠝⠙⠛⠀⠀⠀⠀⠀⠀⣿⣿⠟⣩⣿⡿⠂⠀⠀⠈⠀⠐⠀⢀⡀⠀⠀⠀⠘⢿⣇⠀⠁⠀⠾⠋⠉⠉⢻⠂⠀⠀⢸⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣾⣆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢩⡿⠁⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⣶⣦⣶⡄⠀⢀⣾⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣁⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢸⣷⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷⢀⡹⠿⠟⡀⣰⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣾⣿⣤⣤⣼⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣛⠒⢚⣡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡉⢩⠌⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠂⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠃⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣠⣠⣀⣄⣠⣠⣀⣀⣀⣀⣀⣄⣄⣀⣠⣠⣀⣀⣀⣀⣀⣄⣠⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣬⠿⢦⠉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⢀⡀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣄⠀⠀⠀⣠⡶⠛⠉⠙⢷⣄⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⣤⣤⣈⠳⣄⡼⠋⢀⣤⠶⠶⣦⠹⣆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡞⠁⠀⠙⢧⠘⠁⢠⡟⠀⠀⠀⠘⣧⢻⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⠀⢀⣤⣄⠘⡇⠀⡿⠀⣼⠛⣆⠀⢻⠘⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡏⠀⣿⡇⠙⡇⣷⢸⡇⣼⣿⠀⢸⠀⢸⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣇⠀⣿⣇⠀⣿⢸⢸⡇⣿⣿⣀⡿⠀⡿⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡀⢿⣿⣶⣿⢸⢸⡇⣿⣿⣿⠇⣸⠃⣸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⠳⣌⢿⣿⡿⠛⠟⣛⣻⢿⣏⡼⢃⡴⠃⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠳⣌⢹⠏⠀⢀⣠⣾⡏⣁⡽⠰⣏⠀⠀⠀⠻⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡇⠟⠒⠛⣿⢻⡼⣸⠁⠀⠀⠙⣆⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⢶⣶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣸⠁⠀⠀⠀⠘⠳⠞⠁⠀⠀⠀⠀⠸⣆⢀⣀⠀⠀⠀⠀⠠⠶⠚⢋⣥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢹⡟⠻⡶⠶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠻⣟⢯⣄⡀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⠋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠟⠋⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡷⣦⣤⣄⣀⣤⣤⡴⠾⠛⠉⣉⣛⣓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡥⠖⢀⠀⢈⡿⠁⠈⢷⣄⠀⠒⢦⣄⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣴⠁⢠⡾⠃⠀⠀⠀⠙⠻⢶⣤⣼⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⣀⠤⠄⠒⢈⣉⠤⢼⡄⠠⠤⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣤⢖⡴⠊⠉⠒⠤⣀
⡠⠶⡉⣁⠠⣴⣲⠭⠓⠂⢉⣀⡤⠈⠀⠀⠀⠀⠀⣀⣀⠤⠤⠒⠊⠉⠀⠀⠙⢄⠀⠀⠀⠀⠀⠉⠢⢄⡀
⡇⠀⢨⠔⠻⣄⠠⠔⠒⠉⠁⣘⠰⡄⠀⡀⠀⠀⡜⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀
⡇⠀⣿⠀⠀⡇⠀⠀⢀⠔⣫⠥⣴⣤⠞⠐⡀⠄⡘⢆⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⣠⡼⠃
⡇⠀⣿⢠⠀⡇⠀⢀⡸⡞⡡⠤⢼⣾⣍⡁⠀⡀⢈⠨⠣⡀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⣀⡤⠖⢋⠤⣻⡆
⠧⢶⢿⢈⢠⡇⢘⣧⣄⡁⠀⠀⠀⠀⠀⠉⠳⢄⡘⣇⣠⠽⢄⠈⠣⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡽⢇⡠⣒⠕⠋⠀⠈⠓⢦
⠀⠈⠙⠼⢼⢶⡙⠯⡢⣉⠓⠤⣀⠀⠀⠀⣠⠔⢛⡏⠢⣀⠈⠳⡀⠙⡤⠴⠒⠚⠋⣉⡩⢤⣚⠷⢵⡊⠁⠀⠀⣠⠴⠺⡇
⠀⠀⠀⠀⠘⢟⢬⡑⠮⣗⣕⡠⠈⠑⣶⠉⣀⢴⡯⠓⢄⡈⠓⢤⡙⢾⡑⢁⣂⡠⠭⠒⠊⠉⢀⣠⢴⣋⡤⠖⠋⣁⠴⣫⠟
⠀⠀⠀⠀⠀⠀⠙⠪⣒⢄⠉⢛⢶⠤⠟⣊⠕⢏⠈⠢⣄⠈⠢⣄⠉⠲⢄⡁⠀⠀⠀⣀⡤⠚⢉⠤⣪⢿⣀⠤⣊⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⣸⠶⠊⠁⠀⠈⠓⢄⠈⠑⢦⣀⠑⢦⡀⠉⢢⢔⠋⢁⡠⣂⢕⣫⠔⣿⠵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠈⠓⢤⡈⠓⢼⣕⣠⣵⡾⠛⢉⡠⢖⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠈⠓⢤⢔⡋⠁⡠⢔⡩⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⣿⠅⢐⡩⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠂⠉⠉⠉⠉⠉⠉⠒⠢⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⠄⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⣾⠀⠀⠀⢀⡀⢤⡞⠛⠒⠒⠒⠒⠂⠠⠤⠤⠀⣀⠙⢆⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠰⠀⣸⠗⠊⠁⠀⢉⠤⠐⠒⠤⡀⠀⠀⠀⠀⡄⣒⡐⠪⣅⠒⠠⣀⠀⠀⠀⢰
⠀⢀⡴⠓⢠⡟⠀⠀⠀⠰⢁⣾⣿⣥⣦⣰⡀⠀⠀⣼⠴⠿⠷⠧⠬⡆⠀⠈⣿⠀⠀⢸
⠀⢸⡀⠀⢹⡇⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸
⠀⠀⢹⡋⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠷⢤⣘
⠀⠀⠈⣇⠀⠸⣆⠀⠀⠀⠀⠀⠀⢳⣄⡀⠀⠀⠀⢀⣀⢴⠆⠀⠀⠀⠀⢀⡿⠀⠀⠻
⠀⠀⠀⠘⢧⡀⠙⢦⡀⠀⠀⠀⠀⠀⠓⢄⡉⠉⠉⢀⣠⠞⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀⠄⢒⡆
⠀⠀⠀⠀⠀⠉⠓⠤⠽⣦⣄⡀⠀⠀⠀⠀⠉⠉⣉⠉⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠢⠀⠱⢀⠞⠀⠰⣫⠖⠉⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⢤⣤⣤⣤⣤⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠑⠆⠀⠀⣔⡊⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠀⠀⠨⣄⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠄⠀⠀⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠈⠫⣅⣀⠀⣀⣠⠟⠉⠉⠉⠙⠓⠒⣦⠠⠤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣠⠶⠶⠤⠤⠴⠋⠛⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡗⠒⠒⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⠿⠒⠒⠒⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠠⠋⠀⠀⠘⣀⣼⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠴⢴⠇
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠈⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠈⡄⠀⠀⠀⠀⣠⠲⣆⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠐⠧⣄⡀⣼⠀⣩⠦⠴⠀⠀⠀⢠⠁⠀⢻⡀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠉⢉⡏⠀⢀⣀⠀⠀⠀⡦⠀⠀⠘⡇⠀⠀⠀⢀⣀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⠀⠀⠀⠉⠁⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⢀⣀⠸⣇⣀⣀⣀⣀⣀⣀⣠⠇⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⡀⣾
⠀⡠⠒⠛⠒⠠⡀⠀⠀⠀⠀⠀⢠⠉⢹⡆⠀⠀⠀⠀⠀⡇⢀⡠⠤⠒⠒⠂⠀⠷⡀
⡜⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⣩⠗⢿⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠳⠶⠶⠦⠤⠤⠤⠼⠦⠤⠤⠤⢤⣥⡤⠾⠀⠀⠀⠀⠀⠳⢤⣄⣀⣀⣀⣀⣀⣀⣠⡴⠇
⣷⣿⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣀⣀⣠⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣦⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣤⣶⣿⣿⣿⣿⡿⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠈⢦⣠⠒⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠤⠀⠐⠀⠀⢟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⢳⠈⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠃⠀⠀⠈⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣼⣿⡿⠋⠉⠉⠙⢿⣿⠀⠀⠀⠀⢀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⢀⣶⣤⣀⠀⠀⢀⣸⣿⣆
⠀⠀⠀⠀⠀⠐⠄⡃⠀⠀⠸⠀⣿⣿⣿⣿⠀⠀⠀⢠⠄⠀⠙⠀⠀⠀⠀⠟⢠⡼⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠒⠂⢶⣿⣿⣿⣿⡟⠉⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⢀⢿⣿⠟⠈⠣⡀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠈⠉⢱⣿⣿⣿⡗⣠⣀⡀⠀⠀⠀⠀⠀⡿⢿⠀⠀⠀⠀⢻⣿⡿⠿⡃⠀⠀⠀⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⡀⠀⠀⠐⡆⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠟⠋⠀⠀⠀⠀⢙⠀⠀⠀⠀⣇⠈⠆⠀⠀⠀⠌⠀⠀⠀⠘⢄⠀⢀⣰⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠘⠢⡤⢿⣗⣤⣀⣀⣀⡀⣤⡔⢉⣀⡠⠖⠂⠈⠉⠁⠀⠀⠀⠀⠹⡄⠈⣶⣶⣶⡀⠀⠀⠀⠀⢸⣿⣿⣿⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠑⠈⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣿⣿⣿⣿⡤⠀⠀⠴⠿⣿⠟⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠊⠀⠀⢀⣀⡠⠤⠔⠒⢦⠈⡄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⢙⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠙⠮⣟⣿⣀⠀⣀⣀⣠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡛⣿⣧⡀⠀⠐⢤⡀⠉⠀⠀⠀⠀⠀⡠⠊⠀⠀⣠⣾⠟⠋⠉⠀⣠⣉⠱⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⣦⣤⣴⣾⣿⣤⣀⢀⣀⠜⠀⠀⢀⣾⠟⢡⣶⡆⠀⠀⠛⠛⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠺⣶⠟⠋⠉⠙⣿⣿⣿⠟⠁⠋⠀⠀⣰⣿⠋⠀⠀⠉⠁⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠄⠠⠊⣡⣌⢻⣿⣿⠀⠋⠀⠀⠀⢠⣾⣟⠁⠀⠀⠀⠀⠀⠀⠠⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠠⠀⠀⠀⠻⢿⣿⣿⣿⠇⠈⠣⢤⣰⡟⢡⣬⡓⠦⣀⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠰⣾⡾⢷⣦⡌⡀⠆⠉⠉⠉⠀⠀⠀⠀⠙⠀⢈⣉⡀⢾⡷⠈
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⣶⣄⠈⠑⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⣿⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠷⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣄⣄
⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠉
⠀⠀⠀⢿⠄⢰⣷⠀⠛⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣤⣄⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠻⢿⠀⠀⠀⠀⠀⠀⠀⢿⢀⠀⠀⠀⠐⠀⠉⠀⢠⡟⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠉⠁⢀⣴⣶⡏⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣀⣀⣈⣉⣀⡀⠀⠀⢀⡕⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠂⠀⢀⠀⠰⣾⣧⠀⠹⣿⡃⠀⠀⠀⠀⠀⢀⣠⣷⣤⣶⡶⠛⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣶⣿⣤⣀⡀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠐⢿⣿⣶⣿⣿⣷⡀⠘⠇⢀⣠⠰⣲⢾⣿⣿⡟⠉⠁⠀⢀⣴⡄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠈⠉⠉⠛⠛⠷⢦⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠋⢉⣟⠛⢿⣿⣶⣾⣿⠋⢀⠁⣠⣿⡿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠤⡀⠀⠀⠀⠀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢻⣿⡿⠿⣿⣿⠿⠇⠸⠟⠹⠟⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡴⠋⠀⠀⠀⠀⢠⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⢀⣶⣤⡀⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⢠⣾⣿⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠲⠆⠀⠀⠀⣀⠴⠛⠀⣦⠰
⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠸⣿⣿⣿⣿⣿⠆⠀⣸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⠶⠶⠎⠀⠙⠀⣟⠂
⠀⠀⠀⠀⣿⠋⢁⡀⠙⠛⠧⠀⠀⠐⣀⠀⣈⡉⠀⠀⢻⣿⣿⡿⠁⠀⠀⠛⠿⣿⣿⡿⠁⠀⠀⣤⠀⠀⠠⠂⠘⠀⠀⣹⣤⣦
⠀⠀⠀⠀⣿⣿⣿⡇⢻⣶⣄⡙⠓⢠⠤⠄⣹⡯⠁⠱⠜⡍⢿⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⡐⡏⠀⠰⠖⠊⠁⢈⣴⡆
⠀⠀⠀⠒⠉⣻⣿⣿⠀⣿⣿⣿⡆⠀⠀⠀⠀⠁⠀⠄⠀⠸⡇⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠾⠛⠃⠀⠀⠐⠋⠉
⢠⡀⠀⠀⠀⣿⣿⣟⠚⣽⣿⡿⠿⡄⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠞⠀⠈⠐⠀⠀⠂
⠈⠀⠀⠀⠻⠛⠙⣿⡷⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠀⣠⡀⠀⠀⠀⠄
⠀⠀⠀⢰⠐⣶⣾⣿⣿⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣿⡿⠃⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠙⠛⠋⠁⠀⠂
⠀⠀⠀⠀⠀⠉⠛⠁⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠭⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣎⢻⡇⠀⠀⠀⠀⠀⠀⠐⠿⣶⣤⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠰⡐⠿⠛⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⢰⣤⡀⠀⠀⠀⠀⠙⠛⣻⡿⠃⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣴
⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠈⠄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿
⠀⠀⠀⠈⡼⢢⡀⠀⠀⠀⢀⡔⢶⠂⠀⠀⢀⣄⣠⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⢐⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠋⠉⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⣴⡿⠛⠁⠀⣉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠥⠔⠂
⠀⠀⠀⠀⠀⣿⡟⠙⠻⣦⡘⠐⠠⠈⠀⠀⠀⢀⣿⡁⠀⠚⠁⠀⠀⠀⢸⠛⠄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠋⠈⠀⡁⠒⠁⠀⠀⠁
⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣰⣤⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠀⠘⠀⣿⣿⠀⠀⠀⢹⣿⠶⢶⣤⣤⣄⣀⣀⣀⣀⣀⣤⢶⠀⠠
⠾⣿⠀⠀⣿⣿⣿⣷⡆⠀⠀⠀⢿⡿⠟⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⠃⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠢⠤⠤⠤⢤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⠀⠁⠈⠁⠙⠀⠀⠀⠀⡀⠔⠢⡀⢀⡠⠐⢄⠀⡠⠔⠑⠄⢀⠠⠂⡀⠀⡠⠔⠉⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡗⡀⢀⠀⠘⢂⠰⠒⠁⠀⢀⡠⠘⠁⠀⠀⠔⠉⠀⢀⠠⠊⠁⠀⣀⠜⠋⠀⠀⢀⠔⠉
⠀⠀⠀⠀⡠⠒⠁⡀⠀⢘⠀⠀⠀⠀⠀⠀⣠⠇⠈⠉⢡⠞⠑⡄⠀⢀⠔⠉⡀⠀⢀⠊⠣⡀⢀⠔⠣⡀⠀⢀⠈⠑⡄⠀⡠⠀⠁⠎
⠀⠀⠀⡜⠠⠖⠁⠀⠀⠈⠁⠐⠒⠂⠈⠁⠀⠀⠀⠐⠁⠀⠀⠈⠒⠃⠀⠀⠈⠒⠁⠀⠀⠑⠂⠀⠀⠘⠒⠂⠀⠀⠸⠊⡀⠐
⠀⠀⠀⠃⠀⠀⠉⠉⠉⠉⠉⠉⠁⠈⡇⢀⣀⣤⠀⠒⠐⠀⠀⠀⠀⢈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⢉⠀⠀⠁⠀⠀⠀⢀
⠀⠀⢸⠁⠈⠀⠄⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠁⠢⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠂⠂⠒⠆
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠂⠀⠀⠀⠔⢀⡄⢠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢂⢄⠀⢠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⢀⡀⡀⠀⠀⠀⠀⠃⠀⠈⡀⠀⡀⠀⠁⠀⡀⠀⡁⢀⣀⣀⣀⢠⠄⢠⠀⠀⡀⠇⣈⡙⠸
⠀⣀⠤⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⡐⠈⠀⠀⠀⠀⠑⢄⠀⠀⠀⡄⠇⢀⠠⡅⠀⠄⠄⠤⠀⠇⠄⠀⠀⠀⠀⠒⠁⠀⠀⢈⠂⠀⠐⠁
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡘⠀⠀⢀⠀⠀⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠸⣄⣀⣀⢠⡄⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠴⠒⠺⠀⠖⠒⠚⠤⠓⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢐⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡇⠀⠀⣤⡀⠄⣴⡄
⠀⠀⠀⠀⠀⠀⢠⡄⠀⣾⡟⢉⣭⣤⣾⣦⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠇⠀⠀⢿⠇⠀⠿⠇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣠⠀⠀⠀⢙⣡⣿⣿⠟⣛⣫⡄⠀⠀⠀⠀⠀⠄⠀⠀⠉⠁⠀⠀⠀⣀⠀⠀⠠⠄⠀⠀⠁⠐⠦⢤⡀⠀⠀⠀⠀⠄
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠟⣡⣿⣟⡛⠀⠀⠠⠀⠀⠀⠠⡀⠂⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⢀⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠄⠀⢃⠀⠂⠀⠀⢇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠡⠄⠀⠹⣄⠀⠂
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⢸⠀⡼⠷⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂
⠀⠀⠄⠀⠀⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠜⠀⢷⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠐⣿⣴⠤⣤⡄⢶⣯⣷
⠀⠀⡀⢡⣄⠀⡀⠀⣐⠀⠂⠀⠀⠀⣠⡤⠀⠀⠀⠈⣉⠉⠃⠈⢃⣽⣿⣿⣻⣿⣿⣿⣻⣻⣿⣿⡇⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂
⠀⣿⣇⣾⢏⣩⡄⠈⣿⡀⠀⠀⠁⠐⠃⢠⣤⢀⣤⡄⠻⠃⠀⠀⠉⣿⣿⣽⣿⣻⡿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣈⣛⡃⠙⠛⠃⠀⢸⣧⠀⢀⠤⢄⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡰⠄⡀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣾
⠀⢩⡉⠛⠀⠀⢀⠄⠐⠉⠑⠏⡀⠀⠑⢄⠂⠀⠀⠀⠂⡌⠈⠐⣄⣀⠈⠹⣿⡿⠋⠹⣿⣿⣛⠖⠈⠉⢉⡐⠎⠀⠀⠀⠁⠀⠀⣴⣿⣿⣿⠷
⠀⠀⣙⠛⠧⠔⠁⠀⠀⠀⡀⠀⠈⢆⠀⠈⠄⢘⠹⡢⡀⠇⣠⠂⠉⠀⠀⠀⠀⠉⢢⠀⣿⣿⣇⠂⠀⠁⠀⠈⠀⢰⠲⠤⠀⠒⠀⠄⡀⠹⠇
⠀⠀⠘⠛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠰⠢⠈⡥⢱⡘⠁⢀⡀⠀⠀⠀⢀⠀⠀⢱⠟⠛⠛⠄⠠⠀⠉⠄⡠⠋⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄
⠀⠀⠰⠀⠀⠠⠄⠘⠛⣄⠀⠀⠀⣀⣤⣤⣼⣟⢄⣘⣽⠁⠀⠘⠛⢀⣳⡂⠘⠋⠀⠈⠄⠀⠀⡀⠀⠀⠺⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠄⠀⣀⠄⠀⠀⠀⢥⣰⣿⣿⣿⡟⠛⢿⣷⡈⠉⠄⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣂⠀⠻⠃⠀⠀⣀⡘⣄⠀⠀⠀⠀⡛⠁⠀⠶⠀⠀⡁
⢀⡀⠀⠈⢢⢄⡀⢀⠀⠀⢨⣿⢀⡌⣿⡇⠚⢸⣿⣧⡀⠈⠇⢄⢀⡀⠀⠀⢀⣠⠖⠉⠙⠀⠀⠀⠀⠰⣿⣿⣯⡢⠀⢀⡀⠀⠀⠀⠀⢀⠐
⠀⠛⠦⡈⢇⡀⢈⠀⠀⢀⡀⢿⣆⣀⠁⠀⢂⣼⣿⡇⠕⠀⠈⡇⠀⢀⡠⠤⢤⠻⠴⠤⣐⠃⢀⣀⡀⢀⠿⠋⠁⠐⠀⠀⣈⠰⣶⣶⣶
⠀⠀⠀⠡⢀⡇⣠⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠁⠀⠃⠀⠀⡰⢏⡲⠁⠀⠀⠐⠀⠀⠀⠀⠉⢆⠀⢨⡁⠀⠀⠀⣀⡀⠀⠀⠁⢹⣿⠇
⠀⠀⠀⠀⣠⣿⣿⣿⠿⡟⠉⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡇⠀⠀⠀⠀⠀⢄⠀⢧⠓⠀⠀⠀⠠⣼⡋⠀⠀⠀⠘⠤⡀
⠀⠀⠀⣾⣿⣈⣼⠁⠈⠃⠀⢾⣿⡿⣷⡄⠀⢠⣄⠀⠀⢠⡤⠀⠀⠁⠒⢁⠀⠀⠀⠀⡀⠀⠀⡄⠑⣄⢠⡀⠀⠀⠁⠀⠀⠀⠀⢸⠶⠈⡆
⠀⠀⠀⢿⣿⣿⣿⣄⡀⢀⣠⣿⣷⣤⣿⡇⠀⠀⠉⠐⠖⠈⠀⠀⢀⠔⠀⠘⠃⠀⠀⠘⠁⠀⡠⣤⡚⠉⠉⠣⣤⣀⣰⡤⠴⠉⠐⢎⠀⠆⠈⠢
⠀⡐⣆⢤⡽⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣈⠐⢢⠄⠀⠀⠀⡤⠐⠉⠢⢀⡀⠀⠀⠀⢀⡠⠖⠀⢿⣿⠀⢰⣶⡁⢸⣿⡗⢲⣤⡞⢩⠃⠐⠠⠄⠧
⠀⣭⣈⣺⣀⠀⣤⠈⠉⠉⠉⠁⣤⠀⠘⠋⣿⡆⠀⠀⠀⠀⠐⠀⠀⠀⢀⡜⠉⠉⠉⢃⠀⠑⢀⢼⣿⠀⠊⠀⠈⠉⠀⠑⣾⣿⠁⡎⠀⠀⠀⢠⠒
⠀⠀⠆⠀⡨⠟⠻⣷⣷⣤⣸⣶⣿⣧⣤⣶⠟⡃⠀⠄⠐⠀⠀⠣⠀⢠⠋⠀⢠⢀⠀⠸⢄⠇⢀⢸⣿⡄⢢⡀⠀⠀⢀⠴⣿⡏⢰⢤⣀⠀⠀⠁
⠀⠀⠀⠸⡀⠀⠀⡿⠿⢿⠿⠿⣿⠀⠀⣸⠉⠟⠒⢆⠔⠠⡊⠑⣧⠚⡰⠂⢼⡴⠤⡞⠙⠤⠈⠺⣿⡇⢸⣿⠒⢴⣿⢸⣿⠇⡌⠀⠠⣖⢀
⠀⠀⠀⠀⠈⠑⠚⠒⠒⠚⠖⠐⠛⠢⠚⠁⠀⠓⠀⠉⠀⠐⠓⠴⠛⠄⠐⠦⠜⠓⠴⠛⠀⠃⠀⠀⠉⠉⠉⠉⠃⠛⠛⠘⠛⠐⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⠿⠿⢿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠈⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢀⣴⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣷⡈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⢻⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⢠⣿⠏⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠿⠷⠶⣤⡀⠀⠹⣿⡄⢻⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⢸⠃⠀⠀⢀⣴⡿⠟⠋⠉⠀⠀⠉⠙⠻⣶⡄⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠀⠀⠀⠀⠈⠙⣦⡀⠙⣧⠀⠹⣿⣧
⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠁⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⠀⠀⢹⣿⣧
⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀
⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠻⣿⡟⠻⠶⠶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇
⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣤⡤⠶⠋⠁⡾⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡞⠁⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣦⣄⡀⠀⢀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠙⠛⠛⠛⠋⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢷⣀⣰⣏⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠐⠛⠛⠛⢛⣛⣛⠛⠋⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⡀⣸⣇⣀⣀⣤⣤⣶⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⡈⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢈⣀⣀⡀⠀⠀⠀⠈⠷⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠁⠀⠀⡠⠤⣄⠀⠾⠾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⣠⠀⠀⠀⢀⠎⠀⠀⠀⠑⣄⠒⠺⣄⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⢊⠏⠁⠀⠠⠊⠁⠀⠀⠀⠀⠑⠈⢢⠀⢈⣧⠀⠀⠀⢀⠜⢁⡠⡙⢆⡠⢔⠂⠉⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡠⠀⡇⠀⠀⣀⣀⡀⣠⠒⠐⠀⢣⢀⠊⠀⠀⡠⠃⠴⠁⠁⣸⡤⠒⠁⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢘⠁⠀⢃⢰⠋⠀⠀⠈⠉⠁⠀⠀⠃⢺⣆⠀⡔⢡⠊⠀⣢⠴⡇⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠤⢄⣈⠉⠑⢄⡄⠄⠀⠀⠠⡶⠄⣀⠠⠃⠀⠓⠊⡔⡁⠖⠊⠁⠀⠈⢳⣈⣁⠀⠀⢀⡄⠈⠄
⠀⠀⠀⠀⠀⣀⣀⡀⡇⠀⠠⠒⠲⠤⣭⣐⡚⠷⠀⠀⠉⡉⠀⠀⠀⠈⠐⢄⣠⠊⠁⠀⠀⠀⠀⠀⠀⢀⡴⠁⢠⠊⠁⢁⠀⠠
⠀⠀⠀⠀⠘⠁⠀⠐⠛⠒⠲⢤⣤⣀⣆⣀⣸⣑⡒⢤⣔⠀⠀⠀⠀⠀⠀⣸⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⢱⠔⠋⠀⠀⠈⡆⠀⠇
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⣀⠕⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⣀⣀⣠⣴⡿⠿⢿⡃⠀⠀⠀⠀⠀⠀⡘⢈⡠⠒⠁⠈⢣⠜⠀⡰
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣹⠉⢆⠀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠛⠛⠛⠁⠀⠀⠀⠈⡆⠀⠀⠀⠀⢠⠃⠉⠀⠊⠉⢁⠆⢀⠜⠁
⠀⠀⠀⠀⠀⠈⡆⠠⡤⠭⡀⠉⢳⡳⡀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⢁⣀⡀⠀⣀⡔⢁⣀⣀⡀⣤⠎⣠⠣⢄⡠⠔⢋⡔⠁
⠀⠀⠀⠀⠀⠀⢡⠀⢇⠀⠘⠤⠜⠣⡈⠢⡀⠀⠀⠀⠑⣄⣀⣤⠚⠁⠀⠉⠙⠛⠡⠭⢀⡠⠖⠁⡰⣁⠔⠉⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠈⠆⠈⡆⢰⠚⢉⢑⣛⠂⠈⠲⢆⣛⣉⡱⠚⢀⡔⠀⠀⠀⠀⣀⠝⠓⠲⡤⠴⠚⢏⢀⡠⠚⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠙⢄⠘⠂⠀⠀⡝⠒⠤⠤⠥⠤⠒⠁⠈⠉⠉⢏⠁⠱⡤⠦⠴⠁⠀⠀⠀⢣⠀⠀⠀⠀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠅⢂⡀⠚⠢⠤⠤⣀⣀⣠⠒⠒⠢⠤⠖⠋⣄⠠⠋⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⡐⠁⠈⢢⣀⣀⡤⠒⠀⡖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠠⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⡰⠁⠀⠀⢠⡇⣇⢘⠒⢤⠆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢲⠃⠀⠀⠀⢸⡇⡏⠁⠀⡸⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠁⠀⠀⠀⠀⢸⢽⠁⠀⢠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⠀⠀⢀⠤⡀⣸⣿⡿⠀⢠⠃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⣀⣀⡤⠤⠔⠒⠊⢫⠀⢆⠀⠀⢀⠔⠁⠀⢳⡜⢿⠃⡠⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢣⣈⡦⠒⠁⠀⠀⠀⠈⠧⣏⠔⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠑⢄⠀⠀⠀⠀⠀⠐⠚⠉⠱⡀⠀⠀⠀⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⢔⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠻⢿⣟⣛⠿⢿⡿⣿⣭⣭⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⢘⡏⠒⠀⠈⡉⣉⣉⠛⠺⠿⠿⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠄⠀⠠⠤⠤⠄⠒⠒⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠠⢤⣀⠀⢤⣄⠀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠀⢀
⠀⠧⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠀⠀⠉⠐⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨
⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⣶⣂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⡒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⠀⠤⠐⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠲⢄⡒⠦⣌⣹
⠀⠁⢠⡁⠀⢁⢀⠀⠀⠀⡀⠀⢀⣀⡀⢀⣀⠀⣈⠀⣉⡉⣀⠀⢀⢀⡉⠀⣀⠈⢀⠀⠀⢀⡀⡀⣈⢉⡀⢀⣉
⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢐⢮⡢⡈⢦⡈⢿⡜⣆⠈⢸⡇⠀⡋⠀⡎⠀⢀⡞⢕⢕⠕⢋⡴⠋⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣕⡪⡪⠂⠑⠄⠻⡜⡄⠀⡇⠀⠀⠐⠀⠀⠊⠀⠀⣡⠖⢁⣠⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠲⢄⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⡶⢟⣫⡵⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⡫⠕⠚⠉⠁⠈⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠍⠒⠀⣀⠠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣚⣯⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⡀⠀⠒⠤⢍⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠋⣡⠔⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡽⣄⠀⠀⠀⠈⢓⢤⣀⠀⢬
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡴⠊⡠⡢⡀⡴⠁⠀⠀⠀⠀⠀⡇⡀⢹⡹⣦⠐⢄⠢⣔⢕⢯⡳⢶
⠀⠃⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⢈⡴⣫⢮⢎⡞⠀⠀⡄⠀⠀⠀⠀⣷⢣⠀⢳⡹⣧⡈⢳⣌⠳⣕⢮⡳
⠀⠓⠀⢂⠚⢀⡀⣈⠃⠀⠀⠈⠀⠈⠁⠈⠈⠁⠁⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠤⢤⣤⣶⣦⣤
⠀⣟⣋⣉⡑⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⢛⢩⣭⣭⣿⣾
⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⢿
⠀⣿⣿⣿⣿⣿⣶⠒⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢙⣿⣿
⠀⠋⠛⠟⠛⠛⠖⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⣰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢸⡇⢠⡇⠀⠀⠀⠀⠘⣇⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠶⢶⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢸⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢄⣠⠱⠀⠀⠀⠀⢻⡿⣿⣦⣀⠀⠀⢸⠀⠘⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⡇⠈⠻⢿⣷⣦⣬⣄⣥⣴⣿⣷⣄⣀⣀⣠⣴⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠉⠙⠛⠛⠛⠉⠈⠙⠛⠟⠛⠋⣿⣿⠁⠀⣤⠤⠴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣧⣀⠀⢻⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣆⣠⠞⠉⠀⠀⠀⠀⠉⢻⡿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⠀⢀⣿⣇⣀⣀⠀⢠⡶⢶⡀⠀⠀⠀⡏⠀⠘⣿⡅⣴⡾⢛⣻⣷⠶⠿⢶⣿⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣶⣶⡾⠛⠉⠁⠀⠉⠙⢾⣿⡧⠙⢦⡀⢰⡇⠀⠀⠹⣷⣏⠀⢿⠀⠀⠀⠀⢸⣿⣆⣀⣸⡓⠂
⠀⠀⠲⡶⠺⡄⠀⠀⠀⠀⠀⢹⣿⡠⢀⣤⣴⣦⣄⡀⠀⠙⣯⢂⠈⠳⣼⠀⠀⡀⠀⢻⣟⠦⣼⡷⠟⠁⠀⣼⠹⡏⠀⠈⣷⣤⣤⣀⡀
⠀⠀⠸⠓⢴⠆⠀⠀⠀⠀⠀⣾⣿⣏⣾⠋⠀⠀⠉⢷⠀⠀⢸⡷⣄⠀⠈⠀⢠⣧⠀⠀⢿⣄⠀⠀⣀⣤⡾⣣⠾⠷⠶⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣷⡀⠀⠀⠀⣸⠃⠀⢸⣯⣿⣷⡄⠀⢸⠙⣧⣠⣬⡿⠻⠛⠛⠉⠰⡏⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⣀⡤⠶⠾⠿⠿⠿⢿⣿⣿⣯⠻⠦⠤⠞⠁⠀⢀⣾⣿⣿⡈⠻⡶⠟⠀⠉⠉⠁⠀⢄⣑⣄⣀⣀⣹⣄⠀⠀⠀⠠⢎⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⡹⢿⣿⣧⣀⡀⢀⣀⣴⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠳⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣠⠞⠁⠀⢈⠿⠛⠛⠛⠋⠁⠈⠻⣧⠀⠀⠀⢀⡴⠞⠛⠓⠲⣄⡂⠀⠙⢦⠈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣰⠋⠀⣠⠴⠶⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠔⢃⡀⠀⠀⠀⠀⠀⣿⣰⠃⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣃⡀⢰⠊⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠛⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⡋⣶⣳⣦⣴⢤⣶⣤⣴⡒⣀⣤⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣾⣉⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣽⣴⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢄⣴⣶⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣆⣀
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡷⠄
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⣶⡀
⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣀⣤⣴⣶⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣭
⠀⠀⢰⣿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣴⣾⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⣿⡷
⠀⢀⣾⣷⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠁⠀⠀⠉⠙⢿⣆⣠⣄⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣇
⠀⣿⣾⣿⣿⣿⣿⠃⠀⠀⠀⣰⣿⡿⠋⢀⣠⣤⣶⣦⣤⣄⠀⠀⠀⣾⡏⠀⠀⢀⣄⡀⠀⠀⠈⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡀
⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⡿⠋⢀⣴⡿⠋⠉⠀⠀⠉⠻⣷⡄⠀⢻⣧⠀⠀⠘⠛⠃⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇
⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⠁⠀⣾⡟⠀⠀⠀⣠⣀⠀⠀⠸⣿⠀⠀⠙⢄⡀⠀⠀⠀⢀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠛⠛⠀⠀⢀⡏⠀⠀⠀⠀⠙⢛⠶⣾⣿⣿⣷⣶⣄⣀⣤⠶⠖⢦⠀⠀⠀⠀⠀⠀⠸⣿⣿
⢈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢒⣽⣿⣦⡀⠀⠀⠀⠀⣠⡾⣡⠀⠀⠀⠀⠀⠘⢷⣿⡟⢧⡀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠙⠻⠷⠶⣶⣟⡋⢰⣿⠀⠀⠀⠀⠀⠀⠈⢿⣄⢸⡇⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣿⣿
⠀⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡾⠋⣽⠟⢻⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠇⠀⠀⠀⠀⠀⠚⢡⡌⠁⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠛⠋⠉⠀⠀⠻⣦⡘⣿⣇⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⡤⠶⣤⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄⣀⣀⣠⣴⣿⣿⢿⠀⠀⠀⢀⣴⣶⣾⡿⠁⠀⠀⠀⠀⢰⣿⣿⠇
⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⢿⡿⠿⠿⠿⠟⠋⠁⢸⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⡀⢀⣠⣤⣤⣄⠀⠀⠀⠳⡄⠀⣀⣠⣤⣤⣼⣄⣀⣸⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠈⠙⣷⣄⠀⣀⣽⡿⠟⠋⠉⠉⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⣠⠶⠶⢶⣤⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⢀⠀⠙⣿⡄⠀⠀⣀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢨⠼⡀
⠀⠀⠀⠀⠀⠀⢸⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣀⣀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠩⠀⠀⠂⠀⠠⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣼⣤⡆⠀⠀⠀⠇⠀⠀⠀⠠⠀⠈⠋⠙⠀⠲⠂⠒⠐⠒⠀⠀⢤
⡐⠀⠆⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⡃⠀⡇⠀⠋
⠯⠀⡇⠀⠀⢸⠀⠽⢅⠀⠠⠀⠠⢸⡟⠛⠘⡟⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠐⢲
⠆⠀⡇⠀⠀⠠⢰⡆⠀⠀⢸⣏⠂⠈⠃⠀⠀⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣷⣬⣹
⢀⣸⣇⠀⠠⠌⠈⠀⠀⠀⢀⣯⣤⠄⡁⠀⠂⡇⠀⢀⣀⣻⠀⠈⠀⠀⠀⠀⠀⠀⢉⡀⠧⠄⠀⠠
⢉⠩⠀⠃⠇⠲⠀⠀⠀⣈⠈⠉⠀⠀⠀⠀⠁⠆⠀⠉⠁⠹⡶⢶⠀⡀⠀⠄⣀⠔⠂⠁⠉⠀⠀⠀⠀⢠
⢶⣐⢸⡆⣶⣰⣠⣤⣴⣾⡾⢦⠀⠄⢀⣌⢶⠃⠀⠀⠀⠚⠃⠻⠤⡅⠀⠀⣷⠆⣀⡄⠉⢃⣻⠀⠀⢸
⢎⣡⣈⣥⡟⢾⢿⣿⢙⣻⢿⠟⣿⣷⣭⣿⠿⠥⠬⠯⢏⡿⠿⠧⣿⠷⢌⣥⣥⣤⣶⣯⣵⠾⠶⠎⠖⠸⠖
⣉⠉⠉⠉⢠⠄⠤⠶⠶⠞⠒⢳⣤⣴⣠⣤⣮⡅⠁⠚⠛⠛⠛⠓⠛⠈⠈⠉⠉⠉⠉⠉⠉⠋⣻⣥⠿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠈⠀⠀⠀⠀⠀⢀⡀⢀⠀⠋⠈⣠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢰⡆⣠⣷⠦⠀⠀⠀⠀⠖⠀⠀⠀⠈⠠⣈⡟⠸⠀⠀⠂⣼⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⢾⡃⠘⠃⢀⠄⠀⠤⡀⢤⠀⠀⠀⠀⢄⡀⠖⠁⣀⠀⡈⠁⡀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⢸⡇⠀⠸⠃⠀⣀⠊⠀⠐⣶⣧⡆⠀⠀⠀⠀⠚⠋⣀⠒⠒⠒⠒⠒⠈⠁⢀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⢡⡄⣰⢦⣀⠀⣤⠓⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⢿⡆⠀⠀⠀⠐⠀⠐⠢⠀⢤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⢻⡇⠀⢠⡆⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⣠⣾⣧⣀⠀⣠⣶⣤⣄⠀⢤⠠⢀⠠⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣄⣹⡆⠘⠿⠃⠀⠀⠘⠃⠀⠀⣀⡀⣃⠀⠀⠀⣤⢨⡋⡾⠈⠁⠀⠀⣌⠀⣰⡤⠶⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠉⠓⠤⠀⠔⠀⠐⠶⠾⠃⠘⠋⠠⢿⡭⠟⣠⠞⠉⡙⢧⠤⠒⠒⢠⡟⠂⠁⠀⠀⠘⢷⣀⣀⣶⡖⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⡀⠀⢀⡿⣇⠀⣤⡀⢨⣤⡀⠘⠂⠊⡩⢀⠀⠄⢀⠈⠁⠈⠉⢻⡄⠀⠒⠀⠒⠋⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡄⠙⠻⣦⡈⠁⠈⣿⡋⢀⡄⢉⡝⢠⣧⣄⠴⣿⣆⣠⡀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠀⠀⡘⠁⠀⠀⠈⠁⠉⣐⣋⣈⠀⢉⣽⣿⣿⡿⢠⣿⣶⣂⠀⠠⠛⣦⡀⠘⠀⡀⠂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⡀⠙⡄⠀⠀⠁⠀⠀⠙⡛⠉⠀⣬⠵⠾⠥⠤⠄⠘⠛⠉⣤⠀⢀⡹⠋⠀⠀⠙⠀⠀⠀⠀⣩⠄
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠌⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠢⠀⠘⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⡄⠈⠛⠠⠐⠒⡈⠀⠀⡀⠀⣿⢁⠠
⠀⠀⠀⠀⠀⢀⡅⠀⠀⠁⢤⡀⢀⡀⠄⠄⡀⠀⢠⠀⡄⠀⠀⠀⠠⡀⠀⠀⢴⢟⠀⠀⠀⠀⠀⠀⠈⠥⠀⠈⠐⢂⢸⠇⣄⠠⡿⢠⡷⠚⠠
⠀⠀⠀⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠰⣆⠀⠐⠀⠀⠁⠀⠷⠂⠀⠀⠺⠃⢬⠽⠘⠂⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣸⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢤⡀⠉⠀⠀⠀⢀⡄⡤⠀⠸⠆⠀⠚⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉
⠠⠠⣎⠉⠀⠀⠈⠀⠀⠀⠀⠀⠂⠰⡄⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠂⣳⠀⠒⢋⠀⠈⠀⠉⠀⠠⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡟⠀⣀⣤⣄⣀⠀⠀⠀⠀⠛⢠⠀⠀⠆⠤⠀⠘⣿⣹⠟⠀⢸⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠐⠇⠚⠁⠀⣈⠉⣀⡀⠀⠀⢠⡇⠀⠄⢂⠀⠛⠀⠁⠀⢀⠀⣸⠀⠀⠀⠠⣅⡀
⠀⠀⠀⠀⠀⠀⡾⢻⠹⢰⣿⡟⠀⠀⠸⣇⠀⠀⠉⠀⠀⠰⢠⡄⠘⣄⠃⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣷⡄⠀⡀⠻⢄⢠⣶⣶⠀⣀⠰⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣈⢁⠀⠀⠈⠿⢋⠀⣌⣸⠓⠀⠀⠀⠐⠂⠀⠀⠈⠀⠀⠀⠀⠀⡀⣀⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢰⣟⡽⢫⣆⣀⠀⠀⢾⣿⣏⠄⠀⠀⠤⠀⡀⢀⣀⣀⠀⠀⢀⣀⠀⠈⠉⠁⠀⠀⠾⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⢀⣾⣿⣷⣿⠅⠀⠀⢈⠛⠁⣀⣴⣶⡶⠿⠛⢤⠈⠉⠻⡗⣠⣭⣯⣰⠃⠀⠀⢀⣘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢾⣷⢘⣿⣿⣿⡟⠢⣶⠗⣬⠹⠶⠛⠀⠀⠀⠀⠀⠀⠀⡄⠀⠟⣼⡿⢿⣿⠃⠀⡲⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠘⢛⡋⣿⢿⣍⢀⡷⠇⣈⡝⢳⡆⠀⢠⣶⡧⢠⣿⡆⠀⢰⢾⠓⠙⠳⠄⠀⢠⡄⡙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⡈⡁⠈⣛⠉⠁⠀⠀⠃⣀⣀⣳⡀⢸⣀⠇⢸⣄⡄⠀⠸⠇⣠⠟⠀⠀⣀⠀⠙⠛⠀⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢿⠁⡖⠛⡛⠂⢼⣿⡃⠈⣤⣀⠙⠀⠀⠉⠀⠀⢦⡀⣿⠀⠀⢀⣿⡄⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢭⣾⣿⢇⡤⠜⠓⢠⠇⠹⠀⢠⣶⠀⠀⠀⠘⢧⣼⠀⠀⠈⣻⣡⣿⠀⠇⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠈⢳⣿⡁⠀⠃⠀⠀⠘⠚⠀⠀⠀⠀⢸⣿⣧⠀⠈⠉⠉⠉⠀⠘⠛⣷⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠿⠄⠀⠘⡄⠀⡀⠁⠀⠀⠀⢀⣈⡘⢣⡀⠀⢷⣤⣀⣀⣀⡀⡟⠃⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣦⣴⣦⠀⠀⠀⠀⠠⠀⠀⠸⠀⣷⣦⠶⠀⠀⠀⠰⠀⠘⢿⡥⠤⠬⠤⠤⣼⠋⣼⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠩⡭⠉⠉⠉⠛⠛⡃⠀⡰⠀⢀⣧⣤⣴⠀⠀⠀⠀⠀⠠⠃⡄⠀⠀⠀⠀⢘⡛⢹⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠉⠉⡟⠋⠀⠰⠀⠀⢨⣉⣭⣏⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠤⠤⡌⠟⢈⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠤⠤⠤⠤⠀⠗⣦⠀⢢⡄⣀⣋⠋⢉⢻⠂⠀⣠⢀⠀⢹⣿⠀⠀⠀⠀⠰⠀⢰⠀⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠈⠉⠛⠃⠀⣤⡴⠛⠻⠿⠿⠛⠳⠤⠏⠀⠀⠈⠛⠒⠂⠀⠀⠀⠁⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⡦⢄⡀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡀⠀⠀⠀⢀⠔⠈⠀⠠⠈⠀⢀⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠸⠀⢆⠀⠄⠀⡀⠐⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠘⠻⠒⡽⠃⠈⠂
⠀⠀⠀⡠⠂⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠤⠤⠤⢄⣀⠈⠁⠀⠀⠀⠄⠦⠤⠤⠤⠀⠀⡀
⠀⠀⢀⡁⠀⠀⠀⠂⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠐⠠⡀⠀⠈⠑⠢⣄
⠀⠀⢼⠀⠀⠀⠂⠐⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠈⢦
⠀⠀⠘⡀⠀⠀⠀⠈⢼⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⡈⠍⠛⠀⠀⠈⠀⠁⠈⠉⡉⠉⢉⠉⠉⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠂
⠀⠀⠀⠳⠀⠀⠀⣀⠙⠀⠀⠀⠀⠀⠀⠄⠈⠢⠠⠤⠂⠡⠔⠠⠀⠠⠀⠀⢄⡀⠐⠢⠤⠀⡀⡀⢤⣶⠀⠀⠀⣀⠤⠄⠒⠈⢀
⠀⠀⠀⠀⠉⠂⠀⢀⠀⠀⠀⠀⠀⡃⠀⢀⢬⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠀⠀⠈⠁⠈
⠄⠀⠤⠁⠀⠐⠂⣁⣀⡀⠀⠀⠀⠁⠊⠁⠀⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠠⠄⠈⠍⠉⢀⡀⢀⣐⣒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⡠⠘⠣⣀⢀⣈⡍⠁⠈⠀⠀⠀⠀⠀⢰⠂⠐⠒⠒⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢷⠀⡀⠀⡔⠋⡀⢀⠀⡬⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠔⠂⠈⠒⠑⠊⠀⠀⠣⠘⠒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡨⠄
⠀⠀⢀⠂⠤⠀⣀⡀⠀⠘⠀⡠⠔⣊⠤⠊⠀⠀⠀⠀⡀⠀⡀⠀⠐⠉⠉⠉⢨⡂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠊⡠⠊
⠀⠀⠀⠈⠑⠒⠦⠬⣉⣹⣁⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠐⣐⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⠀⠜⠀⠰⠤⢀⣉⠐⠒⠠⠤⠤⣸⡄⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠢⠤⠆⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣥⣾⣿⣿⣥⣴⣶⡤⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠈⠐⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡿⠻⢿⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠈⢠⣶⣤⣀⣠⠀⠀⡀⠀⠀⣀⠀⠹⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠫⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠳⠛⠋⠁⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠠⠖⠀⣀⠀⠀⠀⢠⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⠅⠀⠀⠀⠀⠘⢄⠀⠀⠀⡀⠀⠀⡖⠀⠀⠁⠀⠀⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠀⠀⠐⢄⠀⠀⠐⠒⠿⠛⠀⠀⡀⠀⠀⠀⡀⠀⠀⠂⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠐⠈⠑⠲⠀⠤⠤⠄⠐⠈⠀⠀⠀⢐⠀⠀⠀⠄⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⠁⢀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠄⠁⠒⠂⠂⠗⠀⠰⠁⠀⠀⠈⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⡰⠊⠀⠀⠀⠀⣰⠃⠀⠉⠀⢀⠤⠀⠀⡀⠁⠄⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢀⡒⠢⠁⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠠⠆⡴⠂⠒⠀⠈⠉⠉⠁⠀⠀⠀⠐⠀⠀⠀⠀⠂⠁
⠀⠀⠀⡈⠀⠀⠠⠀⠀⠀⠀⠄⠐⠀⣠⠦⠐⠂⠈⡠⡄⠀⠀⠀⠀⠀⠀⣀⠤⠄⣀⠠⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠌⡄⠷⢤⠤⡤⠒⠂⠹⡁⠶⠷⡖⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⢸⠰⡁⠠⣀⠔⠀⣰⠁⠀⠀⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠠⠀⠀⠀⠀⠀⠘⠤⠉⠒⠀⢤⡭⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣶⣶⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⢣⢸⢇⠎⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⣿⣿⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣵⣿⣯⣽⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢧⣟⡿⡾⢾⠶⣟⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⡾⢽⣭⣟⣹⡏⢹⣅⡼⡆⠀⠀⣠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣏⣹⠓⡿⢤⣯⡼⣯⡽⢧⡤⢷⢀⡴⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢧⠀⠀⣸⠦⣯⣹⣿⣾⡟⠚⣟⠶⢻⠒⠛⡏⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣄⣟⢺⠧⢼⡇⠙⣏⢛⣏⠓⣻⡓⢚⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢹⣍⣽⠓⢺⡇⠀⢹⣏⣿⣙⣹⣏⣉⣼⢰⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢦⣻⡀⢼⠢⣿⣝⣽⠇⠀⠈⡯⢾⣍⣉⣿⣭⢼⣾⡏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠻⡇⣾⣉⡿⢤⡟⠀⠀⠀⡷⢺⡯⡭⢿⠦⠾⡿⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⡷⢭⣽⣾⠁⠀⠀⢰⣟⣹⡗⠶⣿⡓⣾⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡖⢿⡏⠀⠀⠀⢸⣧⣤⣏⣋⣹⣿⠏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⢿⣹⠇⠀⠀⠀⢸⠶⠾⣧⣉⡽⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢿⠀⠀⠀⠀⢸⣓⢚⣷⠏⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠸⡇⠀⠀⠀⠸⣯⡟⠁⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⢻⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⢳⣄⠀⠀⠘⡇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣍⣷⣤⣼⡧⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠘⠻⣿⣽⣼⡆⠀⠀⠀⠀⠀⠀⢺⣿⢃⠀⠀⠀⡘⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠹⠛⠉⢿⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠠⠀⢀⠀⡄⢸⣿⡄
⠀⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣀⠀⠀⠤⠀⠀⣈⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⠀⢠⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢦⣄⠀⢠⢴⣿⠿⠋
⠀⠀⠀⠀⠀⠘⣿⣿⠿⠃⠀⠘⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⢋⠀⠉⠉⣋⢻⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⠀⠉⠀⡀⢻⡇
⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣿⡇⠠⠀⠀⠀⠄⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠀⠀⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠠⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢀⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠛⠒⠒⠒⠒⠻⠷⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⠰⠝⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⡀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⣀⠌⢋⣉⣤⣉⣉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡏⣶⡿⠋⠛⠻⣿⣷⡼⣦⠀⠀⠀⠀⠀⠀⠀⣿⠟⡙⠉⠀⠁⢹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⠉⠁⠘⣿⣿⡏
⠀⠀⠀⠀⠀⣾⣿⡟⢀⡀⠀⠀⡀⢙⣿⣿⠄⠀⠀⠀⠀⠀⠀⢿⣶⣷⡆⢰⣾⣶⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⠀⠀⠀⡀⢸⣿⡇
⠀⠀⠀⠀⠀⠘⢿⡉⠀⠀⠀⠀⠀⠘⣻⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⢈⡽⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠦⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣷⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⢐⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣴⡄⠀⠀⠀⠀⠠⠮⣷⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠥⡀⠀⠄⠀⠀⠀⠉⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢒⡒⡠⣏⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠃⠀⠀⠈⠢⡀⢀⠀⠀⠄⠀⠀⠐⠒⠢⡀⠀⠹⣄⠀⠀⠀⣀⠀⠁⢀⠀⠒⣠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⠀⠘⠀⡓⠀⠀⠀⠄⠀⠌⠀⠀⠀⠠⢤⡀⠊⠀⠀⠈⠐⢀⡙⢀⠔⠁⠀⠙⠄⠀⠀⠂⠀⠐⢄
⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⡀⠠⢀⠀⢸⠀⠀⠀⠉⠘⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⠀⢈⡉⠒⢄⠀⠙⡄
⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣁⠒⠈⣀⠀⠁⠀⠀⠀⠀⡁⠀⠀⠠⠞⠀⠀⠘⠋⠀⠀⠀⡇⠀⠀⢀⠡⣥⢀⡀⠙⠀⠈⡀⠀⠆
⠤⢵⣷⡴⠂⠀⠀⠀⠀⠀⠋⠉⠁⠀⠉⠣⠀⠀⠀⠀⠀⡇⠀⠀⠐⠍⠀⠀⠩⠄⠀⠀⣰⠀⠀⠠⡀⠁⠀⠪⠓⠀⠀⡰⠀⠌
⠀⠈⠻⣄⣀⣈⡀⠀⠀⠀⠬⠟⠀⢌⡻⠀⠀⠀⠀⠀⣠⠀⠀⠀⠙⠀⠀⠀⠀⠒⠀⠀⢾⢹⣦⠀⢨⣐⠒⣒⠎⠀⠔⣤⠊
⠀⠀⠀⠀⠉⠉⠡⠀⠀⠀⠀⡀⠀⠀⣀⣴⠁⠀⠀⠀⠈⣧⠀⠀⢀⠀⠀⠀⠀⠀⠀⣴⢟⣻⡁⠀⡸⣛⡻⠋⠀⠊⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠈⢬⠭⢚⠏⠀⠀⠀⢀⡴⣼⠆⠀⠀⠁⠂⠒⠉⠀⠚⢻⠟⠛⠣⡀⠀⠀⠀⠀⣀⣰⠋
⠀⠀⠀⡀⠀⠀⢸⡛⠾⠿⣄⡀⠀⠀⣀⢴⠉⠓⠚⠙⢲⣿⣆⡀⠀⢀⠔⡤⣀⣀⠠⠊⣀⡴⠞⠋⠐⠀⠒⣞⠁⣇⣤⣄
⠀⠀⠀⠙⠓⠶⢼⡇⠀⠀⠀⠉⢉⣭⠀⢸⡇⠀⠀⠀⠉⠃⠀⠀⠉⢷⡼⠁⢀⣀⠀⠀⠉⠙⠛⠛⣿⠇⠀⠹⡄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠳⣼⠇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠉⣿⠀⠀⠀⠀⠴⠟⠋⠀⠀⠀⠙⠛⠛⢛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠷⠶⠦⠀⠰⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠛⠁

⠀⠀⠀⠀⠀⠀⣴⣦⡤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⣠⡤⠤⠤⠂
⠀⠀⠀⠀⢸⣿⣿⣽⣧⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠞⣡⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠘⢛⣭⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣾⠛⡩⠭⠭⣙⠻⣷⡄
⠀⠀⠀⠀⠀⠈⠙⢻⡏⠀⠀⠀⠀⠀⠀⠐⢷⣦⣀⠀⢿⣿⣧⣎⡤⠒⠢⣌⠳⣌⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣀⣤⣤⣤⣶⣶⣶⣾⣿⣿⣾⣿⣿⣷⣬⣁⣉⢎⠣⠈⢦⡙⢿⣦⡀
⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠛⠉⠉⠀⠀⠀⢠⡾⠋⠁⠀⣈⡙⢿⡉⠙⠛⠿⣷⣵⣄⠙⢦⠙⣿⣄
⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠿⠍⣼⠇⠀⠀⠀⠈⠙⣷⣗⡄⢳⢸⣿
⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⢿⣾⣸⢸⣿⡄⢀
⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡸⣧⠙⠛
⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⣦⣤⣀⠀⠀⠀⠀⢻⣿⣷⣽⣷⡄
⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣷⠉⠀⠀⠀⡾⠟⠻⣿⣿⠿⠊
⠀⠀⠀⠈⠙⠛⠿⠶⠶⣶⣶⣶⣶⣶⣶⡶⠶⠿⠆⠀⠀⠀⢀⣼⠋⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢀⣀⣀⣠⣤⠶⠛⠁⠀⢀⣼⡇⠀⠀⠀⢿⣦⣶⡿⠋⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠹⣯⠀⠀⠀⣠⣴⣿⣿⠃⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠹⣿⣿⡿⠛⠁⣰⠟⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢠⣶⣦⣤⣾⣧⣾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠈⠛⠶⠶⠞⠋⢀⣾⠀⠀⠀⢀⣿⠁⠀⠀⠀⠈⠉⢉⣿⣿⣿⡿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠁⠀⠀⠀⣸⡟⠀⠀⠀⠀⣀⣴⡿⠋⠉⠉⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣍⣉⣛⡓⠒⠒⠶⣆⠀⣠⠤⠦⠴⠶⠶⠶⠲⣿⡃⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠒⠒⠒⠶⠶⠶⢾⣿⠛⠋⠉
⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣸⡇⠀⣹⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⣿⠀⢀⡟⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⠿⠆⣼⠁⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠿⠴⠞⠛⠛⠿⢶⣦⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠷⠶⠶⢶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣄⣀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⠈⢿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⠐⡄
⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠥⢇⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣉⠉⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢈⢳⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠀⠄⠠⠤
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡄⠻⠿⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣤⡀⠀⠀⠀⠀⢠⣦⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⡀⠀⠀⠀⠈⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠐⠿⠇⠀⠺⠿⠀⠀⠿⠇⠀⠸⠿⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⣤⠀⠀⣤⡄⠀⢠⣤⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠉⠀⠀⠉⠁⠀⠈⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠁⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠉⠁⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀⣴⣷⡀⠀⣾⠆⠀⢰⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠸⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠂⠀⠀⡀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆⠰⡄⣶⣶⣦⣳⣾⣾⣇⣷⣤⣿⣾⣴⣷⣼⣰⣀⣷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⢍⢿⣳⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣾⣀⡆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣼⣿⣮⣿⣿⣿⠿⠛⠛⠉⠉⠀⠀⢀⣀⣠⣤⠤⠤⣄⡀⠉⠉⠛⠻⢿⣿⣿⣿⣣⣠
⠀⠀⠀⠀⠀⠀⠐⢦⡐⢦⣾⣽⣿⣿⠟⠋⣡⣶⣾⣿⣿⣶⣶⣶⣶⣿⣿⠋⠀⠀⠀⠈⠙⣷⣄⠀⠀⠀⠈⠙⠻⣿⣿⣧⡄⢠
⠀⠀⠀⠀⠀⠐⢆⠐⣿⣷⣿⠟⠋⠀⣠⣾⠟⠋⠉⠉⠉⠛⠛⠿⠟⠛⠁⢀⡤⠴⠶⠤⣄⡈⠛⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣀
⠀⠀⠀⣀⡀⣙⣿⣿⣿⠟⠁⠀⠀⣰⠟⠁⠀⣠⠤⠖⠒⠦⢤⡀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⣀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣆⣀
⠀⠀⢄⣤⣹⣿⣿⠟⠁⠀⠀⠀⠐⠁⠀⣠⠋⠀⠀⠀⠀⠀⠀⠈⠳⣼⠁⠀⠀⢀⣀⡀⠀⠀⠀⢿⣜⣵⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣣
⠀⢀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣠⣤⡀⠀⠀⠀⣹⠀⠀⠀⠸⢿⠟⠀⠀⠀⣼⡟⠉⠉⠀⠀⠀⠀⠀⠀⠐⠨⢿⣿
⠀⣀⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣤⣿⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⡿⣇⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿
⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣩⠽⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠉⠻⣶⣶⣴⣶⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠱⠀⠆⢻
⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⣤⡴⠛⠁⠀⠀⠀⠈⠻⣦⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠘⠀⢀⠂⢸
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⡀⢀⠀⠀⠀⠀⠀⠹⣿⠀⢹⠀⠀⠀⠀⠀⢐⠀⠀⠄⠀⠰⠄⢈⢈⣸
⣾⣿⠠⠀⠠⠂⢀⠀⠀⠀⠀⡄⢠⡨⠃⣀⠀⠀⠀⠀⠀⢰⡏⠉⠺⡀⠀⠀⠀⠀⠀⢹⣇⣼⠀⠀⠀⢀⡄⠢⡨⠆⠒⠂⢒⠒⠀⠃⢸
⣿⡧⠀⠀⠀⠂⠀⠀⢁⠂⠀⠀⠐⣦⠂⠀⠀⠀⣀⠀⠀⠄⠹⣄⡀⢳⡀⠀⠀⠀⠀⢸⣿⠋⠀⠀⢀⡀⢐⠀⠃⢶⠀⢠⠨⠉⡀⠂⣼
⣿⡇⠐⠀⠀⠀⠀⠄⡀⠀⠀⡄⠠⠋⠐⠀⠁⢀⠈⠁⠀⠨⠀⡘⠉⢟⠻⣦⣀⣀⣀⣼⠟⠀⠆⠀⣀⢀⢀⡁⢂⠈⡆⠁⠌⠠⢀⣠⣿
⢻⣿⢂⠂⠀⠀⠀⠀⠄⠃⠁⡇⠂⠂⠀⠁⠠⠀⠄⠁⠐⢢⠀⠰⠀⢸⡐⢾⡏⢉⠛⢁⠂⠤⠀⠁⠉⡀⢈⢘⠐⣠⡃⠠⠈⠀⠀⣼⡿
⠸⣿⡄⡠⠀⠈⠀⡀⠀⡅⠀⠙⢶⣄⣀⣈⣀⠀⠁⣀⣐⣤⣤⠶⠶⠟⠛⠛⠛⠓⠶⢧⣤⣁⡝⠠⢐⣀⣤⠴⠚⠁⡙⠂⢀⠀⣰⣿⠁
⠀⠹⣷⡀⠂⡀⠀⠠⠈⠀⢀⠀⠀⢀⠉⠉⠉⠛⢛⡋⠉⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⢳⣊⠉⠛⠛⠋⠉⠀⠄⠀⡂⠈⡀⠈⣰⣿⠃
⠀⠀⠹⣿⡁⠀⠀⢌⠘⢂⢀⠀⠄⢀⠀⡐⢀⠐⠀⠀⠀⠁⠀⡈⠀⠀⠀⣶⢦⣤⣤⠾⠣⠀⡀⠔⠨⢡⠄⠂⠑⠀⠠⢈⣼⡿⠁
⠀⠀⠀⠘⢿⣄⠠⠂⠀⠄⠀⠀⠀⠀⢀⣂⠀⠄⡠⠁⠐⠀⠀⢂⠀⠕⠆⠙⢘⠉⠓⢷⣠⠂⠀⠀⢀⡐⠈⠀⢠⠁⣠⣿⠟
⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠐⡈⠁⠀⠠⠀⠀⠁⠀⠀⠀⠤⠤⡀⢨⠤⠈⠀⣤⠄⠂⢧⠄⢈⢈⡀⠀⠁⣋⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⣀⣀⣀⡘⠀⠀⡰⢀⠀⠁⠠⠐⠠⠂⠀⠂⠌⢩⠀⡨⠠⢸⣈⠘⠀⣀⣬⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣷⣶⣦⣤⣤⣬⣄⣠⣠⣀⣀⣤⣦⣥⣦⣾⣶⣿⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡂⠀⡦⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠀⠂⠐⠲⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⢀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠁⠈⠉⠉⠐⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣄
⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠠⠀⠁⠀⡈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠇
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠀⠂⠅

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣴⠃⢀⡴⢖⣶
⠀⠀⠀⠀⠀⠀⣿⡀⢸⡅⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤
⠀⠀⠀⠀⢀⣠⣬⣿⣦⣝⣶⣦⣴⣶⣾⣿⣿⣶⣾⣿⣿⣿⣯⣤⣤⣤⣀⣀
⢀⠀⢀⡴⢋⣴⣶⣿⣿⣿⠿⠛⠉⠁⢠⡿⠋⠀⠀⠀⠈⠻⣧⠀⠈⠉⠉⠛⠛⠷⢶⣦⣤⣀⡀
⠙⠶⠋⣰⡿⣻⣿⣿⠟⠁⠀⠀⠀⠀⣿⡇⣾⡆⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄⡀
⣀⣀⣴⠟⣱⢿⣿⠋⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀
⠀⠀⣠⠼⠁⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢀⣤⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢰⣿⠏⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠰⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠃
⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠉⠉⠉⢻⡿⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉
⠀⠀⠻⣿⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠠⠤⠶⠾⠛⠋⠻⣦⣀⠀⠀⠀⣠⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠉⠉⠉⠛⢿⣦⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠋⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⡄⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⢈⣿⣴⣶⣶⣦⣤⣀
⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠻⣷
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡶⠾⠿⠛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⡠⢫⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⡐⡱⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⢴⣦⣈⠏⡴⣤⣤⣤⣤⣤⡶⠶⠞⠛⠉⠁
⠀⠀⠀⢰⣿⠁⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠹⢿⣦⡀⠀⠀⠀⣠⣿⠋⠊
⠀⠀⠀⣸⡟⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⠿⣷⣶⣿⡿⣷⣷⣤⡄
⠀⠀⠀⣿⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢿⣟⣾⣷⣯⣭⡶
⠀⠀⢠⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢠⢊⠟⠿⣾⠏⠉
⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠁
⠀⠀⢸⣿⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⠿
⠀⣀⣨⡍⠉⠉⣿⠋⠉⠉⠉⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠁
⠀⠻⣿⣯⣤⣤⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠉⢉⣡⣤⣤⡤⠤⠤⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣧⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⢰⡏⠁⠀⡄⠀⢀⣀⡄⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⣤⣀⠀⠀⢰⠀⠈⣻⡆
⣀⣀⣀⣈⣻⣶⣶⣷⣚⣋⣉⣷⣶⣛⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣶⣏⣙⣛⣷⣾⣶⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⠿⠿⠳⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣿⡟⠉⢹⠟⣛⣥⣤⣤⣄⠀⠈⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⢿⣾⣿⣷⣿⣰⣾⣿⣿⣿⣿⣝⢻⡄⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣰⣴⣿⠏⠁⠉⠙⠻⠿⠿⠛⠛⢿⣷⣿⡄⢼⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣬⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠰⠛⣿⣷⣶⡀⢀⣶⣶⣿⡟⠣⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⣹⠀⠀⠙⠛⣯⡿⠃⠘⠿⣯⡟⠛⠀⠀⣟⡱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⡄⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⢀⠎⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣾⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⣼⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢀⡴⣾⣟⣛⣿⣦⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣤⣴⡄⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠳⣄⠀⠀⠀⠀⠀⠀⢀⡴⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠻⣄⠘⣷⣶⣶⣶⣶⡶⠟⠀⣸⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡀⠈⠙⢾⣿⣿⡿⠋⢀⡴⠞⠁⠸⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣙⣷⣞⡉⠀⠀⠀⢸⣿⣿⣷⡹⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣖⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣧⠀⠀⢀⣾⣿⣯⡹⣿⢆⠀⠀⢸⣿⣿⣿⣷⡝⣿⣿⣿⣷⡦⣄⣀
⠀⠀⠀⠀⢠⣖⣻⣭⣶⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⠀⢀⣾⠟⢿⣿⣿⣿⣿⣆⠀⣸⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣷⣯⣝⡲⡄
⠀⠀⠀⢀⡞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣙⠿⣿⣿⣿⣿⣧⠞⠁⠀⠈⣿⣿⣿⡿⠻⢧⣿⣿⣿⣿⡿⢛⣵⣿⣿⣿⣿⣿⣿⣿⣷⣻⡄
⠀⠀⠀⣼⣹⣿⣿⣿⣿⣿⣿⣯⢻⣿⡇⢶⣶⣶⣶⣿⣿⣿⣿⠀⠀⠀⢰⣿⣼⣿⠀⠀⢠⣿⣿⣿⣷⣶⣶⣶⢆⣿⣿⣿⣿⣿⣿⣿⣧⢷
⠀⠀⠰⠣⢿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⡜⣿⡿⢿⣿⣿⣿⣿⣆⠀⢀⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⡿⣿⡟⣼⡟⣿⣱⣿⣿⣿⣿⣿⠎⠇
⠀⠀⠀⠠⠤⣄⣈⠉⠛⠻⠿⣿⣿⣿⣿⣿⡜⣿⣷⣾⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣷⣾⡟⣼⣿⣸⡿⠿⠛⠋⠉⣀⣠⠤⠄
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⣤⣈⡙⠛⠿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠰⠛⢉⣁⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣁⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣁⣤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣈⠛⠿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡙⠻⠿⠋⣡⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⠤⠀⢤⣴⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠉⡀⠴⠿⠿⠇⣀⠀⠀⢂⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⣀⡀⠀⠀⠀⢹⣥
⠀⠀⠀⠀⠀⠀⣈⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢀⠀⢀⡀⠃⠚⢿⡇
⠀⠀⠀⠀⠀⠀⠉⠛⠃⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠠⠀⠀⠀⠀⠀⠓⠤⡀⠀⠉⠓⢛⠀⠀⠀⠘⠗
⠀⠀⠀⠀⠠⠄⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠠⠐⠠⣤⣶⣦⣌⠁⠀⠀⠐⠟⣵⡆
⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢙⣿⣿⣿⣿⣶⡀⠀⠀⠟
⠀⠀⠀⠀⠒⠄⠀⠐⠂⠀⠀⠂⠁⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣀⢲⡀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠋⠉⠙⠻⠿⠋⠉⠦
⠀⠀⠀⠠⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠋⠘⢃⠀⣀⠀⢀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣐⢀
⠀⠀⠀⠀⠀⢀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠓⡈⠀⠁⠀⢁⣀⣢⠀⣀⠀⠀⠀⢀⠟⣛⡯⡆
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠛⠋⠀⠀⠀⠀⡼⠀⠤⠤⠄⠠⣀⠀⠘⠗⠋⠸⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠌⠲⠀⠨⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠂

⠀⠀⠀⠀⠴⠿⠂⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⣴⠶⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀⠀⢀⣀⣴⣆⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠈⠙⠉⠁⠀⠈⢢⠊⠈⠉⠛
⠀⠀⠀⠀⠀⠠⠆⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⠀⢜⠃⠀⢀⠍⠀⠀⠀⠀⠀⡀⠀⠀⠲⠃⢘⠘⠃
⠀⠘⡀⠀⠀⠀⠀⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠑⠀⠀⠈
⠀⠀⠈⠢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠀⢀⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⣒⠒⠠⢀⢀
⠀⠀⠀⠈⢄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠊⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠢⠀⡁⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠀⠀⠀⠘⠻⠆
⠀⠀⠀⠈⠉⠓⡆⠀⠐⠲⡄⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⢀⣀⣤⣦⠄⠀⠀⠀⠀⠀⠀⣡⣤⣉⠢⢀⣴⣤⠤
⠀⠀⠄⠀⠀⠀⠐⠀⡀⠀⠐⡀⠀⠀⠀⠀⢠⠀⠙⠛⠛⡿⠛⠛⠁⠀⡰⠀⠀⠀⠀⠀⠠⢀⣹⣷⣯⢀⢈⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡠⠁⠀⠀⠚⡅⠀⠁⠂⠀⠊⠀⠈⠐⠒⠈⠀⢀⠂⠀⠈⠋⠀⠀⠈⠉⠁⠈⠑⠀⠑⠈⢀
⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠦⢀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⠀⣀⠠⠐
⠀⠀⢋⠂⠀⠄⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⠁⠀⠈⠁
⠀⠀⠀⠓⣆⠁⠂⠀⠂⠈⠆⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠂⠁⢶⡀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡆⡠
⠀⠀⠀⠀⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠠⠶⠶⣤⣄⣀⣀⣀⣠⡤⠶⠿⠂⠀⠀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠛⠂
⠀⠰⡀⠈⠉⢉⠋⢉⠉⠀⢀⠔⠀⠀⠀⡀⠀⠀⠀⠀⣤⠈⣤⠄⠀⠀⠀⣀⠀⠀⠀⠃⠀⠈⠉⠀⠾⠀⠉⠁⠀⠐
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⡀⠔⠢⠀⠠⠊
⠀⠀⠀⠀⣀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢀⠤⠄
⠀⠀⠐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⠀⠀⢀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠘⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⡿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⡇⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠃⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⢯⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠙⠷⣄⡀
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠟
⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⣠⡴⠋⠀⢸⡇⠀⠈⠳⢦⡀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠈⠙⠦⣄⠀⣠⠞⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⡴⠋⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⢸⡇⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⢘⣇⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⢀⣤⠴⠶⠶⣶⣤⣀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢄⠀⠀⠀⠀⣠⡤⠰⠋⠁⠀⢠⡀
⠀⡀⠁⠀⠈⠳⡀⠈⠻⣿⠂⠀⠀⢀⠎⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⡀⠤⢤⠀⠣
⠨⠭⠽⠉⠉⠭⠏⠀⠀⡿⡄⠀⡠⠂⠀⠀⠀⠀⠀⠁⠰⠀⠐⠀⠀⣀⠀⠀⠀⡤⡤⠀⠀⠀⠀⠀⠀⠈⡀⠀⠁⠈⠀⠀⠙⠂
⠈⠒⠶⠁⢀⠀⠀⢀⠢⠔⠁⢇⠀⠀⠀⠀⠀⡠⠂⠀⠰⠀⣠⣀⠀⠈⢁⠀⠄⠀⠀⠊⠀⠀⠀⠀⠀⠐⡀⠀⠈⠓⠀⠚⠘⡀
⠀⠀⠀⠀⢀⡰⠞⠁⠀⠀⠀⠀⠉⠐⠒⠂⠈⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠂⢀⠀⡄⠀⡅
⠀⠀⠁⠈⠀⢀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⡠⠀⠁⠀⠀⠀⠀⠉⢄⣀⠠⠊⠁
⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁
⠀⠀⠀⠀⡉⢀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠠⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⡠⠒⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⡩⠛⠏⠉⡿⠿⣆
⠀⠸⠁⠉⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⢠⠠⠇⠙⠀⠀⠀⡐⠁⠀⠀⠀⠈⣹⣋⣹⣥⠖⠀⢰⡜⠀⡸⠄⠓⠀⠀⠘
⡇⡠⠀⠈⢁⠀⡸⠀⠰⠀⠀⠀⠀⠀⡀⠄⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠚⠁⠀⠀⠈⡃⠀⠣⠠⠔⠀⡄
⢁⢡⡀⠀⠈⣠⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡀⠐⡄⢀⠁⠀⠈⢇⠀⠁⠀⣀⠀⠀⢠
⠀⣾⡉⠓⠚⠁⠃⠸⠃⠀⠀⠀⠀⠀⠀⠠⠚⠄⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠈⣤⣈⠤⠀⠀⠀⠈⠳⣄⣀⣠⡤⠶⡇
⠀⠻⠀⠉⠉⠘⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠜⠀⠀⠀⠀⠀⠀⠙⠒⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠤⠂⠀⡄⠠⠔⠋⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠀⠀⠀⠤⠀⠆⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠄⠀⠀⠀⠀⠀⠰⡉⣁⠀⡠⠀⠢⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡈⠒⠒⡉⠊⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠙⠡⡦⢉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠋
⠀⠀⠀⣀⠀⠀⣄⠀⠒⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⢒⡤⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢀⡀⢈⣑⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠂⣰⠀⠀⣇⣨⣉⠀⠀⠀⠀⠀⠀⠀⠈⠀⢌⣀⢀⡀⢨⠁⠀⠀⠀⠘⡛⠀⠀⢒⡀⠈
⠀⠀⠀⢀⣁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠀⠠⠠⠊⠉⠀⠠⠟⠁⡠
⠀⠈⠀⠀⠁⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠈⠰⡠⢀⣨⠙⠃⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠡
⠀⠀⠐⠀⢠⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠠⠤⠬⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠂⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣮⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠠⠄⣐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠁⠀⠀⠈⢣⢁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⢀⠔⠲⣀⠜
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢰⡇⠈⠲⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⢸⣿⠇⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠔⠁⣸⡀⢸⡇⠀⣗⠈⠳⣄
⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⣿⣿⣮⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡔⠁⠀⠀⣤⠠⠄⢀⣀⡀⢄⠀⠈⢳⡄
⣿⣿⣿⣿⣿⣷⣝⢿⣿⠴⣿⣿⣿⣟⣽⣿⣽⢟⣵⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢮⡁⡜⡟⡤⠀⠒⠶⠂⠘⣆⡰⠊
⣿⣿⣿⣿⣿⣿⣿⡷⡍⠀⣿⣿⣿⣿⠿⢿⣷⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡸⣾⣧⠰⠁⠀⢀⣀⠀⢩⡀
⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣍⢯⣭⢅⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠙⠉⢲⡓⢚⡿⠉⠉⠙⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⣉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠏⢹⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠋⢹⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠓⡂⠠⢄⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠚⠈⠰⠃⠀⠀⠀⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠲⠄⠀⠀⠀⠀⠴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣿⠀⠀⡷⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠐⠢⠀⠀⠀⡤⠔
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢺⠀⠀⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⣠⡞⢅⡀
⠀⠀⠀⠀⢀⠄⠒⢉⠀⠀⠚⠓⠒⠻⢦⠀⠀⠀⢦⡄⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⢩⢉⡏⢀⡇⠀⠙⢦⡀
⠀⠀⠀⠀⠠⠊⠀⠁⠀⢀⡀⠀⠀⠀⠀⠠⣄⡀⠤⣌⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠛⣄⡌⢠⠎⠀⠀⣄⠀⠑⢄
⠀⠀⠀⠀⠰⠀⡐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⡇⠀⠘⠗⠁⠀⠀⠀⢏⢱⡄
⠀⠀⠀⣂⡀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢘⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⣠
⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢺⠀⡀⡈⠀⠀⠈⠛⠄⠀⠀⠀⠀⠀⠀⠲⠾⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠇
⠀⠀⠀⠀⢢⠀⠀⢰⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢰⡄⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢺⡏⠁
⠀⠀⠀⠀⠠⠀⠀⠘⠀⠀⠀⢻⠉⡗⠐⠴⠀⠀⠀⠀⠀⠠⢫⡇⠀⠀⠀⠀⠀⠀⠀⢉⠉⠛⢛⡓⠒⠒⠒⢾⠁
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢳⡄⠀⠀⢸
⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡀⢸⡄⡏⠀⠀⢈⡇
⠀⠄⠈⠀⠀⠀⢀⠀⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠖⠀⠀⠀⠀⢀⠴⠒⠉⠉⢉⡙⣧⠷⠦⠴⠖⢋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⡿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡾⠃⢀⣷⠋⠀⠀⠀⠀⠀⠀⠙⠶⣼⣆⠀⠠⣶⡀⠙⢿⣧⢸⡿⠉⠻⣟⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢻⡟⣻⣿⠋⣿⢀⡞⠁⢀⡾⠁⠀⠀⠀⠀⠀⣀⣤⣤⣄⣠⣉⣷⣤⣴⣿⣿⣿⣿⡿⠁⠀⠀⠈⠻⣌⢻⢿⣿
⠿⠻⠛⢯⣝⠻⣿⡟⢹⣿⠃⠀⢸⡞⠂⣠⠏⠀⣀⣀⣄⡀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠈⢻⣆⡾
⡠⠀⠔⠂⠈⠙⢿⣯⡿⠿⢦⣀⠀⣷⡴⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣏
⠐⠂⠀⠀⠀⠀⠘⣿⡇⠀⠀⠈⠙⢻⣇⣀⣠⠤⠤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢿⣿⣿⣧⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣀⣀⣀⣸⣿⣦⠤⠤⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢘⣿⣿⣿⠀⠀⠀⠈⣿
⠀⠐⠚⠛⠉⠉⠉⠀⢿⣇⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⣿⠿⠛⣿⡅⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⣿⡀⣄
⠀⠀⠀⠀⣀⠀⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡀⠀⠀⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⢹⣧⣿⣷⣄⠈
⠀⠀⠀⠀⣼⣿⣷⡶⠆⠀⢿⣷⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⢿⣷⣌⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠘⣿⡇⠀⠀⠀⠀⠘⣿⠀⠀⠀⢀⣀⠀⣀⣀⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿
⠀⢠⡄⠀⠀⣿⠀⢉⣻⣄⣀⣿⣷⣤⣶⣶⡄⠈⢿⡇⠀⠀⢻⠏⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⠿⠛⠛⠋⠙⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠁⠀⠀⠀⠀⠐⢋⣿⣿⡉⠁⠀⠀⠀⠘⠛⠉⠁⠀⠀⠰⣦⣜⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠠⡄⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠺⠳⢾⡆⠰⠛⡠
⠀⠀⠀⠀⠲⡀⠘⡀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⣴⣀⢀⡀⠀⠰⠈
⠀⢰⠀⠀⡀⠑⠄⠀⠄⣀⠀⠀⠀⢀⠄⢀⠔⠀⠀⠈⠑⠒⠀⡀⠉⠉⠉⠆⠀⡀
⠀⠀⠑⢄⠈⠢⣈⡄⠘⠋⠀⢰⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠙⠶⠈⠀⢠⠄⠉⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⢦⡀⠂⡀
⠀⠀⠘⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⢀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢙⡷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠘⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠉⠀⠀⠊⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢂⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⠶⠀⠉⠉⠉⠛⠻⠶⣿⡄⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢠⠀⠀⢀⡠⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢦⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⡄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠔⠋⠀⣼⣷⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢰⠀⠘⢷⠒⠂⠐⠒⠒⠊⠉⠁⠀⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢻⠀⠀⠀⢧⣤⣄⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⡷⠀⣀⡀⠀⠀⣀⡀⠐⠈⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⡀⠠⠿⢻⡟⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠓⠴⠂⣀⣀⣀⠴⠋⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠐⣂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠷⣤⣤⣀⣀⣠⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⣤⣤⣤⣠⣤⣤⠴⡾⠋⣀⠀⠷⠈⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢻⡅⠀⠀⡇⠀⠈⠁⠶⠂⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢄⣀⣀⠀⠀⠀⠀⠀⢀⣀⠴⠛⠁⠀⠘⠀⢆⣤⠁⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠈⠁⠀⠀⠀⠀⠀⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠈⢛⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠘⠃⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡀⠀⠀⠀⠀⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠛⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠸⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣄⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⣤⡞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⠶⠞⠁⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⠴⠞⠉⠀⠻⣆⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡴⢾⠁⢠⣼⣁⣀⣀⣀⣀⠀⡴⢶⡞⠉⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢇⠀⠁⠀⠀⠀⠀⠀⠀⠄⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠡⣀⠀⠀⠀⠀⠀⢠⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⢦⣤⣤⡴⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⠁⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⠍⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠙⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠇⠀⠀⠐⠶⢤⡤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⢀⡰⠆⠀⠀⠀⠀⠙⠒⠀⠠⠀⠈⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⡆⠀⠀⠀⠀⠀⠀⣾⡏⣭⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣐⣤⡂⠀⠀⠀⠀⠀⠀⠀⠸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠈⢓⠄⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠊⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⢠⠸⠇⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨
⠀⠃⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡃⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠀⢸⣏
⠀⠄⠊⠀⠫⠵⠄⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⣀⣰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠏
⠀⠀⢀⠁⠀⠜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡏
⠀⡇⡀⠀⠀⠈⢰⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣿⡇
⠀⠁⡁⠀⠀⠀⣿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠇
⠀⠀⠛⢶⣦⣴⣿⣷⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡀
⠀⠀⠀⠀⠀⠈⠙⠻⠏⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠉⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠉⠉⠁⠀⣀⣀⠀⠈⠉⠉⠛⠻⢿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠙⠛⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⣉⣠⠤⠖⠚⠋⠉⠉⠉⠉⠉⠉⠙⠒⠄⠀⣼⠀⠀⠠⠤⠒⠚⠋⠉⠉⠉⠉⠉⠉⠙⠓⠢⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⠇⠈⠁⠀⠀⠀⢀⣀⣀⣠⡤⢤⣄⣀⣀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠤⠤⢤⣀⣀⡀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⡇⠀⠠⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⠁⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠤⢤⣄⣀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠘⣇⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢷⡏⠀⠠⠴⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⡿⠀⠀⠤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣿⢿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⡟⣼⠁⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠲⠤⢤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⣿⢸⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⢡⡏⠀⠠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⠃⠀⠠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠂⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⡏⣾⠁⠀⠀⠀⢀⣀⡤⠤⠴⠒⠒⠒⠒⠒⠲⠤⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⣾⣿⢰⡇⠀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⢰⣿⡏⣾⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠒⠒⠒⠒⠒⠦⢤⡵⠀⢸⡇⠀⠀⠀⣀⣀⣠⠤⠤⠤⠶⠶⠶⠶⠦⠤⣄⣀⣀⠀⠀⠀⢹⣿⣿⡆
⠀⠀⠀⠀⣼⣿⢱⡏⠀⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿⣿⣧
⠀⠀⠀⠀⣿⣿⣼⠁⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣲⣶⠶⠦⣤⣀⠀⠀⣿⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣦⣤⣄⣐⠓⠂⠸⣿⡟⣿
⠀⠀⠀⢸⣿⣿⡟⠀⣀⣴⣾⣿⣿⣿⣿⣟⣛⣛⣟⣻⣿⣿⣿⣶⣿⣿⣦⣿⣠⣶⣿⣿⣿⣽⣿⣿⣭⣭⣭⣭⣭⣭⣭⣿⣿⣷⣾⣿⣿⣷⣤⣿⡇⣿⡇
⠀⠅⠀⣸⣿⣿⣷⣾⣿⡿⠟⠛⣋⣉⣉⣁⣀⣀⣠⣤⣤⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣷⠾⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⠿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠁
⠀⠀⠀⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠟⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⡈⠁⠀⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣌⠉⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢀⣆⠈⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠛⠻⡀⠀⠀⠀⠐
⠀⠐⠺⡖⠀⠑⠀⠤⠐⠊⠀⠁⠐⠂⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠐⠀⠀⠁⠒⠊⠁⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠈⠦⢀⡀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠁⠈⠈⠁⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⢀⢀⠤⠊⠁
⠀⠀⠀⠀⠠⡄⠁⠀⡃⠀⠀⡃⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠘⠪⡁⠀⠃⠀⠉⠁⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠐⠀⠀⠂⠉⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⠒⠒⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⢀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠁⠈⠉⠈⠉⠉⠙


⠀⠀⠀⠀⠀⠀⣴⠶⠖⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠂⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠄⠀⠀⠀⠀⢴⣦⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠐⠀⠠⡀⠀⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠈⠁
⠀⠀⢀⡀⠀⠀⠉⠙⠀⠀⠀⠀⠐⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣠⣤⠑⣊⣤⣤⣌
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡈⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⣿⣿⡿⢃⠛⢿⡿⠟⠀⠀⠀⠤
⠀⠀⠀⠀⠑⠂⠄⠀⠀⠀⠀⠀⣀⠠⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠠⠊⠉⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠠⠈⠉⠄⠊⠁⠂⠀⠐⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠑⠀⡀⠂⠐⠀⡱⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠤⣠⠖⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⣀⠄⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠄⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⢃⡠⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠭⠤⢀⠀⠀⡀⠉⡓
⠀⠀⠀⠀⣉⠉⠙⠿⡷⠶⣶⡶⢶⢿⠛⠉⠁⠰⠀⠀⠀⠀⠀⠐⣊⠁⠠⣤⠄⠀⠇⠤⡤⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠘⠦⡀⠀⠀⡠⠂⠘⠄⡀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣠⠧⢀⡀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⢀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣀⡀⠠⠊⠓⠀⠤⠐
⠀⠀⠀⠀⠀⠀⣠⠔⠈⠉⠁⠀⠀⡇⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢶⣦⣀
⠀⠀⠀⠀⢠⡞⠐⠒⢲⠐⠀⠐⡎⠁⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠈⣁⠤⠄⠚⠒⠒⠀⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠧
⠀⠀⠀⠀⠑
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣯⣥⣬⣧⣴⣠⣽⣮⣼⣯⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⣛⣭⣿⣗⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠀⣴⣿⣿⣿⣧⣯⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⣿⣋⡉⢉⣀⣈⣩⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣛⢿⠏⠠⢽⣟⠉⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠶⢶⣶⣶⡺⠋⢸⣯⡈⠀⡀⠈⠉⠀⡇⡷⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢻⡟⠁⠀⠀⠀⠘⣿⡿⣅⠀⢸⠀⢿⡀⠃⠠⠤⠟⣻⡷⢤⣄⠀⢰⣯⡟⠦⢭⣗⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠞⠛⠛⠉⠡⠶⣿⠀⠀⠀⠀⠀⠀⣿⣷⠶⣶⢸⡄⠀⠙⣦⣄⡀⣁⣿⡇⠀⠈⢷⡀⢹⣍⣙⣛⠢⣇
⠀⠀⠀⠀⠀⠀⠀⣸⣟⣵⠏⠀⠀⡀⠀⠀⣿⢰⡀⠀⢄⠀⢸⣿⡏⠀⢸⣇⢧⠀⠠⢾⡟⣻⣽⣿⡇⠀⠀⠼⣧⡸⢦⣤⣌⣁⡿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠏⠀⠀⢰⣿⠶⠤⠾⣧⣳⣰⡌⢳⣿⡿⠀⠀⠀⠙⢾⣦⣠⢟⡟⠉⢸⣿⠗⣩⡴⠋⢉⣿⢿⣿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠰⣻⠏⠀⠀⠀⣼⡏⢻⣿⣿⣟⠀⠀⠀⠀⠀⠀⡿⠕⠉⠀⢀⡿⢷⣿⢧⣤⣶⡿⠁⠀⠽⠿⢻⣯
⠀⠀⠀⠀⠀⠀⣸⣧⠤⣤⣤⠞⠁⠀⠀⢠⣾⡟⡃⠀⢱⡀⢹⣄⠀⠀⠀⠀⣀⣤⣤⣤⡾⠋⠀⠀⠉⠳⢦⡘⡇⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⣾⣡⡿⠞⠻⠿⣤⣀⠀⠀⠀⣹⠿⣷⣄⠀⠳⣤⣈⣉⡛⠛⠛⠋⣩⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣤⣀⣼⠟
⠀⠀⠀⠀⠀⢹⡇⠀⢀⠀⢀⡶⢹⠀⠀⣼⠧⢶⣿⣿⣷⣤⣌⣉⣉⣉⣩⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⢸⣇⣰⢿⣷⣤⣹⡾⠃⠀⣿⠀⣿⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠛⠛⠁⠀⠀⣿⡰⣿⢿⣿⣿⣿⣟⣃⠈⠙⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢖⣶⣄⠀⠀⠈⢿⡄⢻⣿⣿⣿⣿⣿⣷⡀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡿⢰⢟⣩⠟⠛⠛⠿⢿⣧⠀⠛⢿⣿⣿⣿⣿⣿⣆⠀⠹⣇
⠀⠀⠀⠀⠀⣠⡶⣋⣵⣿⣾⣏⡴⣦⡄⣀⣀⣹⣧⠀⠘⣿⣿⣿⣿⣿⣿⡄⠀⢻⡀
⠀⠀⠀⠀⢰⡏⣾⡿⢿⣿⣿⣿⣷⣿⣷⣿⣿⡿⣿⣷⣄⢁⣾⣿⣿⣿⡿⣃⣀⣸⡇
⠀⠀⠀⠀⢸⣳⣟⣴⡿⠋⠉⢀⣉⣙⣿⣿⣿⣧⣿⣿⡙⠘⣿⣿⣿⡿⠛⠉⠉⣿⡇
⠀⠀⠀⠀⠘⠷⠿⠟⠁⠀⠀⣿⢹⠋⣸⣿⣷⣭⣭⣿⣷⣔⡿⣿⣟⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⣾⣿⣿⣿⣿⡿⠿⠛⠛⠛⠿⠿⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣾⣿⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⢷⣭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣅⣾⡟⠀⠘⠙⠿⣿⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠠⠠⢼⣦⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⢹⣿⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡿⠃⠈⠋⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⠞⠛⠇⠀⠛⠟⠛⢿⡿⠻⣿⠇⢠⠀⠀⠀⢀⠆⠀⠀⠀⣠⣦⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⣬⠀⠀⠀⠀⠀⣸⠀⢀⡀⠀⠀⢘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡼⢳⠋⠀⡀⠀⠀⠀⣹⣿⣿⠁⠀⢀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣿⣿⡀⠐⠀⠀⡀⢀⡀⠀⠀⢠⡄⣡⣤⣦⣾⣷⠆⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⢻⣿⣟⡁⠀⠀⣀⡓⠸⡿⠄⢥⣾⣧⣿⣿⣿⣿⠿⡆⠀⠀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠀⠉⠉⣳⠷⣶⣶⣾⣿⣿⣿⣿⣿⠀⠠⡆⠀⣿⡇⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⡿⠉⢀⠀⠰⠒⠲⠉⠘⠛⢉⠈⡉⢿⣿⣿⣿⠀⠀⠀⠀⣿⠁⠀⡀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⠷⣗⠀⠾⠀⠀⢠⠀⠀⠉⠀⠈⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠘⠀⠀⠁⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠁⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⡄⠀⠀⢸⡆⢀⣿⠀⠀⠀⠀⠀⢀⣀⣾⠁⠯⣉⣧⠀⠀⠀⠀⠀⠀⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣦⣼⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⣿⡇⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠃⠼⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠱⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⣸⣆⣰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣀⣼⣿⣿⢿⡿⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠘⠛⠛⠉⠉⠘⠁⠷⢦⣈⡇⢀⡄⠀⢀⣠⣞⣿⠄⠀⠀⠖⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⣠⠄⠀⠀⠁
⠀⠀⠀⡀⣀⠀⠀⠰⠁⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠍⣶⠐⠆⠀⠀⠘⡄
⡔⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡈⠁⠀⠀⠀⠀⡅
⠑⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⢿⠆⠂⠀⢴⠀⠃
⠀⠀⢆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⢈⠣⠀⢀⣀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠈⠤⡀⠀⠀⠀⡌⠀⠄
⠀⠀⠀⠄⠀⡀⠘⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠰⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⡄⠀⠀⠀⠢⠤⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠑⠒⠒⠀⠋⠭⠀⡁⢀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣔⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠒⠀⠀⢠⡄⠀⠀⠀⠀⣛⡅⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣴⣴⠶⠾⠩⢿⠷⠒⠻⠷⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠁⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⢷⠤⡃⢀⣰⣶⡾⠃⣦⢰⣄⣠⢀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠸⠧⠇⢂⠂⢀⡅⠀⣀⡖⠀⢀⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣆⠀⢤⠉⠙⠁⠈⢋⠁⠀⠀⢈⠁⠈⠀⠀⠀⠀⠀⠀⠆⠸⠄⡆⡤⠤⢸⢃⡼⢇⣛⠀⢀⡒⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠓⠺⠃⠀⠀⠀⠀⢿⡑⠗⠀⣩⣥⡶⠀⠀⠀⠀⠀⠀⢙⣟⠀⠀⠉⠉⢸⡎⡄⠋⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠄⠀⠑⠀⣠⣄⢀⣀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⢀⠀⠈⠂⠖⡤⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⠀⢠⣄⣼⣽⢹⣿⡴⠀⠀⠀⢩⣅⠉⡁⠀⠀⠀⠀⠀⠈⡀⠆⠈⣶⣤⠀⢠⣄⣀⠀⠀⢠⣤⢀⣄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢿⢃⣿⠛⢾⢡⢾⡏⢀⣔⣋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠐⢿⣽⠇⠁⠀⠐⠁⢠⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠼⠵⠿⠎⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠳⢀⠐⠄⢀⠀⣼⠇⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠠⠄⠐⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠒⠉⠉⠈⠉⠛⠈⠷⠀⠀⠀⠉⠁⠀⠀⢾⢏⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣤⡒⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣼⡦⠀⢠⡖⢲⠆⣠⢀⣀⡁⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠆⠀⠄⡠⠀⣈⠀⠹⠇⠀⠈⠃⠀⠂⠀⠀⠀⠘⠧⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⣿⠄⠀⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡀⠀⡀⠀⠈⢯⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢀⣰⣤⡄⠀⠀⠰⢉⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠁⠀⠀⠉⠀⠀⠰⠽⠟⠀⠀⠀⠀⠀⠀⡰⠀⡴⠃⠀⠈⠡⠈⠀⠀⠀⠒⠋⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⣀⢀⠄⠻⠄⠀⠐⠳⠒⠖⠂⠀⠀⠐⠚⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⡿⡷⠀⢀⠀⠀⠈⠋⢀⢀⠀⠀⢰⣻⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠥⠊⠀⠉⠀⠀⠁⠠⠒⠒⠉⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠉⠀⠀⠀⠀⠡⡇⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡨⠝⠛⠛⠂⠀⠀⠀⡀⠁⠀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠔⠁⠈⠑⢄⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠁⠀⠀⠄⠀⠀⠀⠀⠀⠤⠱⡀⠀⠳⡄⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⡀⠈⠏⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⢁⠨⠀⠀⠀⢀⣀⠀⠀⢀⠃⠀⢀⠀⠀⠀⠀⠀⠈⠈⠢⢤⠤⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢍⣁⡐⠀⠤⣧⡇⠁⠀⠀⠘⠁⠀⠀⠁⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠘⢳⠖⢀⠔⠚⡇⠀⠡
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠦⢀⣇⠀⠁⠈⠋⠒⠤⠤⢀⡀⠠⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⠀⠀⠀⠀⠀⠀⠐⢇⣀⠎⠀⠀⠰⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠐⠓⠒⠓⠒⠒⣾⣧⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⡄⠸⢀⡠⠔⠢⣄⡇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢺⡁⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⢾⠟⠋⠉⠉⠉⢀⠀⠀⠀⠀⠀⢀⠇⠖⠁⠤⠴⠀⡟⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠤⡕⡀⠀⠀⠀⠀⠀⠈⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⡜⢠⡄⠀⠀⢀⠔⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢆⠀⣸⡌⢢⡀⠀⠀⠀⠀⣅⠀⠀⠀⠠⠐⠐⠀⠤⠖⠑⠂⠒⢒⡉⠟⢠⠎⣈⠟⠋⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠩⠥⠼⣄⠙⠢⣀⠠⡤⠘⠟⠀⠂⠀⠀⠀⠀⠀⠀⠍⠀⡀⠈⠀⣤⡣⠊⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⠐⠂⠀⠀⠈⠁⠀⠀⠈⠀⠐⠀⠀⠀⡠⠔⠊⠀⠀⠀⠉⠀⠀⠁⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠘⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡆⡆⢣⣀⠀⠇⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣠⠆⠀⠀⠀⢸⢷⡷⠜⠀⠹⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠌⠀⠀⠀⠀⢸⠸⠁⠀⢀⠃⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣤⠀⠀⠌⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠺⠀⠀⠀⠀⢀⠄⠁⡆⢿⣿⡏⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠖⠀⠉⠁⠀⠀⠹⡀⠳⠀⢀⠔⠁⠀⠀⠹⠇⡟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⢱⠴⢇⠀⠀⠀⠀⠀⠀⠈⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣤⣀⣤⣴⣾⠥⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢫⣍⢳⠖⠯⠭⣽⣿⣛⣛⣻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡓⠀⠸⠆⠄⠀⠀⠀⠀⢐⠒⠊⠉⠉⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠂⠒⠂⠐⠀⠂⠆⠂⠒⠀⠀⠂⠀⠐⠐⠐⠐⠂⠀⠀⠀⠀⠐⠀⠃⠃⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠁⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠄⢀⡀⠀⠀⠀⠀⢀⠔⠈⠉⢀⣀⣀⡠⠤⢄⡀⠀⠀⠈⣆⡀
⠀⠀⠀⠀⠀⡀⠴⠒⠉⠙⠉⠉⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⠒⠃⣠⠶⠚⠁⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠉⢢
⠀⠀⠀⡠⠊⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢨
⠀⠀⡐⠀⡠⠊⠁⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠎⢠⢀⣀⡤⠤⠤⠤⠤⣄⡈⡆⠀⠀⠀⢃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠱
⠀⠀⠴⠊⠀⠀⠀⠀⠀⠈⠤⠤⠤⢄⣀⠀⠀⠀⠀⡇⡈⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢸⢄⡠
⠀⠀⠙⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠙⠢⣄⣠⠃⠃⠀⡇⠀⠀⠀⠂⠀⠂⠀⠀⠀⡞⠀⠀⠀⠀⠸⡄⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⡮⢎⠄
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠽⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢸⣹⣄⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⢀⠞⠁⠉
⢀⣄⠀⠀⠳⣀⠀⠐⢄⡀⠀⢀⡠⠀⠀⢀⡴⠁⡀⣀⢡⠀⠀⠣⡀⠐⠄⠀⠔⢠⡞⠁⠀⠀⠀⠀⠀⠀⡼⠉⠳⢤⣀⡀⠀⠒⢂⣀⡤⠞⠁
⠈⠉⠓⠦⡤⠬⢑⡢⢤⣤⣉⣡⣤⡤⠚⣁⣠⠔⠋⠉⠀⠑⠒⠊⠉⠢⣄⣀⣀⣀⣈⡽⠶⠦⠤⠤⠤⢚⠀⠀⢀⡀⢠⡍⡋⠉⠉⠱⣤⠤⣄
⠀⠀⠀⠀⠢⢤⠔⠁⠀⠐⠀⠈⠀⠙⣭⠀⠁⠀⠀⣼⠖⠒⠒⡎⠀⡘⠀⠀⠠⢋⠘⡃⠈⢢⠤⠒⣂⢛⠥⠖⠺⠀⡔⠀⠈⠒⠂⠀⠈⢆⡜⠛⠛⠒⢴
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⠁⠀⠀⠀⠀⠀⢳⠒⠁⠀⠀⠛⠀⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⡓⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⢶⡋⠉⠐⠠⢤⣀⡹⢫⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠛⡖⠂⠀⠀⠉⠈⠉⠉⠉⣉⡭⠶⡶
⠀⢠⡤⠷⠀⠀⠀⠀⠀⠀⠀⢁⡟⠁⠉⠉⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⣀⣠⠤⠬⠆⠀⠀⠀⠰⢦⡤⠤⠤⠤⠼⠖⠚⠉⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠋⠉⠉⠁⠀⠑⢄⢀⡖⢀⡀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡆⠀⠀⠀⠀⠀⠀⠋⠀⠀⠙⠳⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠃⠀⠀⠀⠠⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠈⠀⠐⠂⢄⡀⠄⠀⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠃
⠀⠀⠀⠀⠂⠀⠀⣀⡀⠈⢀⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣄⠈⠁⣠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣘⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⡰⢄⠁⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡰⢄⠈⠀⢀⠌⠀⠀⠀⠀⠀⢀⡀⠐⡀⠀⠀⠙⠻⠀⠀⠀⠠
⠀⠈⠙⣍⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠈⡗⢤⠀⢀⠀⡀⣀⠀⢠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠘⣆⢀⠨⢀⡀⠀⡀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠺⠄⢀⡀⠀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⢀⠈⠁⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣆⣀⣀⣀⡀⠆⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠁⠀⠀⠀⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠁⠀⠀⠀⠀⠛⠻⠄
⠀⠀⠀⠀⠀⠠⠶⠄⠀⠀⠀⠀⣤⡤⠄⠀⠀⠀⢀⠀⠀⠀⠀⠔⠋⠀⠀⠉⠢⡤⠂⠀⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠐⢄⠀⠀⠀⠠⡀
⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⠆⡷⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⢾⣿⣿⣿⠄⣷⣿⣿⡇⠀⠀⢀⡀
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢀⠔⠣⢀⣀⡀⠔⠀⠀⠀⠀⠀⠚⡇⠀⠡⠈⠛⠛⢋⠔⠢⢉⡉⠠⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠓⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⠀⠤⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢀⡰⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠀⡀⠀⠀⢈⣛⠃
⠀⠀⠀⠉⡏⠙⠻⢿⡶⢦⣶⣴⣶⡟⠋⠉⢩⠆⠀⠀⠀⠀⠀⡎⠉⣀⣠⠄⠸⠅⢤⡄⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠈⠀⠀⠈⠂
⠀⠀⠀⠀⠑⢄⠀⠀⢀⠐⠀⠢⢀⡀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡰⠆⢀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠟⠀⢀⠛⠃⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠠⠊⠂⠤⠠⠔⠁
⠀⠀⠀⠀⠀⢀⢤⠂⠀⢉⠀⠀⠈⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢶⣤⣀
⠀⠀⠀⠀⢠⠛⠚⠒⡆⠉⠀⢸⠉⠉⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⢀⠸⠵⠄⠂⠋⠈⠀⠉⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⢸⣿⣷⣄⡀⣀⣤⣤⣼⣿⠀⠂⢠⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣤⠄⢈⣹⣿⣿⣿⣿⣿⣿⣿⡿⣶⣿⣿⣿⣿⣿⣶⡄⢀⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣼⣿⠇⠀⠈⠈⣿⡟⣿⣿⣿⣿⣿⡇⠀⠙⣩⣈⠙⠛⠻⣿⣾⣿⣿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⠿⠿⢷⡄⠀⠉⠀⠘⢿⣿⣿⣿⣿⡀⢌⡛⣋⠸⣿⠆⡃⢻⡿⢻⣌⣡⡉
⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣷⣋⣤⡀⢴⡶⢿⣾⣿⣿⠓⠈⠀⠀⠉⠉⠃⠸⢿⣯⣷⣶⣾⣿⣿⣷⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⢿⣋⣠⣤⣾⣿⠉⢉⡴⢦⣠⠜⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠟⣀⠉⡛⢿⣴⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠈⠿⢟⣿⡍⢸⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⠀⠀⢂⣴⣶⣿⣷⣾⣿⣷⠀⠀⠀⢹⣿⡏⠁⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣻⡭⣵⣿⡿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⠛⠙⣿⡿⠙⢀⡀⠀⣿⡏⠑⠂⠀⠒⠁
⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣍⠀⠀⠈⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠠⠄⣹⣷⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠘⠟⠉⠙⢿⣿⡟⠀⢀⣀⣼⣿⣧⠀⠀⣾⣿⠿⢷⣀⡀⠉⠀⠀⠀⠈⡟⣀⠈⢉⢸⡿⣦⣀⣀⡤
⠀⠀⠀⠀⠀⠀⢠⠀⠉⠀⠻⠀⢰⣿⣿⣿⠋⠉⡲⠼⡏⠀⠀⠀⢹⣿⣶⣿⣿⣿⣷⣧⣠⢦⣈⡼⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠐⢾⣿⣿⡟⠐⠀⣙⣛⣉⣁⣀⠉⣈⣿⠀⠀⢹⣿⣿⣿⠟⠿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⣿⡏⠀⢠⣭⣭⣽⣿⣿⣿⣻⣿⣧⡀⠀⢻⡟⠉⠀⠀⠈⠁⠀⠀⠀⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣤⣴⡶⠆⠒⠂⣤⠄⠛⠛⠿⣿⣇⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⣽⡀⢠⣶⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠐⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢴⠖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠀⠁⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⣨⣠⣤⣾⠅
⠀⠀⠀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢋⠐⠂⣀⡀⠀⣀⣀⣀⡀⠠⠤⢿⡴⠋⠙⠉⠉⠀⠀⠀⠀⢀⡠⣴
⠀⠀⠀⢙⠉⠁⠀⠈⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⣇⢸⠀⡏⢀⣀⠤⠠⠄⠒⠂⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⢱
⠀⠀⠀⠐⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠉⠀⠀⢉⡉⠭⠙⠛⠉⣧⠂⡍⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠠⠤⠒⡚⡆⠀⠀⢸⢠⢾
⠀⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢨⠉⠀⠀⠀⠀⠀⠀⣿⠇⠅⠀⠀⠀⠀⢢⠉⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠁⣸
⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⡀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⣴⢛
⠀⠀⠀⠤⠠⣤⣠⣤⣤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡇⠀⠀⠀⠀⢘⠀⠀⠀⠊⠠⠀⠀⠀⠀⡇⢀⡀⣴⡷⡛⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⡏⠩⢇⠂⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⡴⠶⠚⠋⠁⠀⠀⠀⠈⠀⢄⠀⠸⠀⠀⣀⣀⣀⣠⠤⠴⠾⠓⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠙⠲⢤⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠁⠀⠈⣡⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠉⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⢰⠇⠀⣠⡀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢃⠀⠀⡑⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⡔⣦⠠⡀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠱⠀⡃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⣋⣸⢁⣤⡌⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠰⠞⠂⢀⡌⠳⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠐⠁⠀⢸⠆⠀⠀⠀⠀⠀⢀⡜⢣⡈⠉⠟⢻⡞⡁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡦⢉⣉⢣⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠈⠳⣄⣹⣾⣣⡄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠛⠃⠀⠙⠀⠀⠀⠀⢀⢒⡼⠀⠀⠠⠴⠖⠋⠀⠀⠀⠠⡀⣠⠏⢳⡄⠀⠀⠀⢀⠏⢰⢟⡥⠲⠌⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡔⠀⠀⠢⡀⠀⠀⠀⠀⢨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⣠⠋⠀⠀⠀⠀⢸⡀⠀⢸⣼⢧⢞⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⣀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢁⡼⠁⠀⠀⠀⠀⠀⠀⠉⠙⢦⠐⣨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢉⣉⣁⡀⠈⠑⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠱⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⢤⣤⠌⠀⢀⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⢋⡾⣡⢆⡀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⡀⠀⣧⠀⠙⠒⠤⠖⠚⠉⠀⡇⢸⠀⠀⠀⠀⠀⠀⡠⢡⠞⣴⢣⡞⠡⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡈⣏⠀⠀⣀⠀⠀⢀⡴⠀⢸⣀⠴⠚⠳⡄⠠⡁⠈⠘⢡⠏⡐⠉⡂⠆
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡘⣎⠓⠋⣙⠓⠊⠁⠀⢀⠜⠁⠀⠀⠀⠷⠀⠙⣦⣀⠀⡸⢧⡞⠉⡆⢄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢻⣦⠞⠉⠉⠙⢦⡔⡁⠀⠀⠀⠀⠀⡎⢈⢦⠷⣈⠉⠀⢰⢀⡼⢁⠎
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣠⠶⢿⡀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⡇⠀⠒⢂⢮⡉⣇⠈⠉⠓⠋⠛⢳⡆
⠀⠀⠀⠀⠀⠀⠈⠳⣄⣤⡶⢫⠁⠀⠈⠓⠦⡴⠾⠋⠲⡄⠀⠀⠀⠀⠀⡇⠀⢀⠃⠀⡗⠹⡄⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡂⠀⠀⢀⠹⣆⠀⠀⠀⢸⡇⠀⠘⡆⠀⡇⠀⠙⢦⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠘⠀⡈⠳⢦⣴⠟⠀⠀⠀⢱⠀⢣⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠁⠀⠀⠰⠠⡀⠀⠀⢸⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠰⡀⠀⡟⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢧⢀⡀⠀⠀⢧⠑⢤⡴⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠦⡇⠀⠀⠀⠀⢸⡇⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠸⣦⣄⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣇⢀⣀⣀⣀⣀⢸⠀⠆⠀⠀⠀⢧⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠤⠤⠤⠤⠤⠴⠒⠃⠀⠀⠀⠀⠛⠛⠛⠛⢛⠓⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠀⠀⠀⠀⣀⡤⣞⠁
⣠⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡾⠉⠛⠓⠒⠛⠋⠉⡇⠘⡆⠀⠀⠀⠀⠀⣠⠴⠒⠒⠲⢦⡀
⡇⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⣾⢰⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⢸⡇
⢹⡀⠀⠀⠀⠹⣆⡤⠶⠂⠀⠀⣛⠈⢃⡀⠀⠀⠀⠀⡴⠓⢧⠤⠷⠀⠑⢶⠁⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠳⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⡉⠉⠀⢧⠀⠀⢸⠀⠀⢀⣀⣀⡀⠀⠈⠀⠀⠢⣀⣀⡴⠛
⠀⠀⠙⠳⢶⣤⠾⠋⠉⠛⠲⠶⠾⣇⣀⣀⣼⠀⠀⠘⠦⠤⠤⠃⠈⠉⠙⠛⠛⠛⠛⠋⠉
⣿⣿⣿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⡄⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⠀⢀⠀⢄⠀⠀⠀⠀⠀⢀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨⢀⠌⠃⠀⠀⠀⠁⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⡀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢄⠁⠀⠠⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠐⠀⢀⠔⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠈⠀⠀⠀⠀⠉⠙⠀⠀⠀⠁⠀⠀⠂⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠢⠋⠀⡠⠊⠈⢐⡄⠀⢄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠰⡄⠀⠀⠀⠀⠀⠀⡀⠀⢸⠄⠈⠜⠀⠀⠀⠀⠀⠀⠉⠐⠠⠄⠀⠀⠠⠄⠀⠀⠀⠄⠿⢀⣆⢠⠎⠀⠀⠀⡜⠀⠀⠀⡅⡀
⠀⠐⠀⠀⢃⠀⠈⢆⠀⠀⢀⠀⠀⡟⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⡀⠀⢀⡌⠀⠀⢀⡜⠀⣸⠂⠐⠐⠒⠂
⠀⠀⠀⠀⠀⠐⠤⠸⠦⣀⠜⠁⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠉⠉⠁⠑⠤⠤⠋⠔⠚⢁⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣵⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣶⣶⣾⣿⣼⣿⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢰⡄⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⠗⠘⠓⠒⢦⡒⠒⠓⠀⠀⠀⠀⠀⣀⣤⢄⣀⠬⠷⠶⠶⠻⢄⣀⠞⠀⠀⠀⠀⠀⠒⠲⣄⣈⣇⣼⡀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⣠⠃⡋⣉⡧⢀⣤⡟⠛⠒⠂⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢠⣮⠉⣄⠀⠀⠉⢉⡽⣷⣮⢭⡉⠁
⠀⠀⠀⠀⠀⢳⠀⠙⠋⠁⢿⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠶⢤⡀⠀⡠⣄⠀⠸⡀⠀⠀⠀⠀⠘⣔⠤⠞⠰⠤⠆⠰⠬⢜⡷
⠀⠀⠀⠀⠀⠈⢣⡀⠚⠓⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠧⡘⠴⠃⠀⠵⠬⠃⢠⠇⠀⠀⠀⠀⠀⢦⡈⢩⠆⠀⠲⡂⢈⡡
⠀⠀⠀⠀⠀⣤⢾⠇⠀⠀⠀⠘⢯⡙⢢⠀⠀⠀⠀⠀⠀⠀⠈⠓⣶⠀⠰⠦⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⢉⡏⠀⠀⠀⣟⠉
⠀⠀⠀⠀⠸⠁⢸⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⡠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠳⠋⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠈⢢⡤⠀⠠⠤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠁⠒⣲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢱⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠂
⠀⠀⠀⠀⠀⡀⢀⡈⢱⣀⡠⠔⠛⠛⠛⢦⡀⠀⠀⠀⠀⠀⠠⣀⠐⣆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⢀⣠⠤⠴⠯⠤⣄⡤⠤⠄
⠀⠀⠀⠀⠠⠤⠤⣬⠞⣡⣖⠲⠐⣏⣿⠆⡇⠀⠀⠀⠀⠀⠀⣼⢷⡋⠈⣓⣲⣄⠀⠀⠀⠀⠀⢀⣞⡤⣄⢾⡅⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠳⠭⠞⣀⠴⢀⡞⠁⠀⠀⠀⠀⢰⠱⣟⡠⠇⠸⣛⣨⠻⡀⠀⠀⠀⠀⢸⡙⠓⢚⡴⣦⢰⠦⢄⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠓⣄⠀⠀⠀⠀⠘⠦⣄⠀⠠⠄⠀⠀⠀⣇⠀⠀⠀⠀⠀⡟⢲⡬⣿⠷⠋⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢦⠀⠀⢀⡎⠀⢸⠄⠀⠀⠀⠀⠀⢸⠀⢦⡀⠸⠀⠀⢸⡆⠀⠀⠀⠀⡄⢸⠀⠇⠀⠀⣰⠃⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠉⠃⠈⠀⢀⡜⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠃⠘⠂⠘⠀⢠⡇⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠹⢄⡀⠀⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡶⠖⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣀⡠⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠉⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢋⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⣉⣵⡤⠤⡧⠤⣖⠉⠉⠀⠀⠀⠀⠀⢀⡤⢴⢡⠤⡀⠀⣀⣙⢞⠓
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠛⠓⠲⣍⣁⡀⠀⠀⠀⠀⠀⠀⢀⣠⠏⣬⣸⡇⢞⢩⡆⠀⠙⣏⠉⠃⠀⠀⠀⠀⡔⣛⢷⠄⣻⢰⡁⠌⣮⡙
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠞⢩⡇⠰⠤⠴⠶⠶⠷⠶⠖⢀⡼⠀⠀⠀⠀⠀⠀⠀⢻⠀⠙⠁⠀⠉⠋⢸⡇⣠⠇
⠀⠀⠀⠀⠀⢠⡇⢀⡔⣻⢲⡀⢠⣖⢮⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡴⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⢼⠀⠀⠒⠒⠀⠀⠀⡏⠁
⠀⠄⠀⠀⢠⡟⡄⠀⠓⠒⣚⠀⠈⠛⠋⡜⢧⠀⠀⠀⠀⠀⠇⠱⣄⠀⠀⠀⠸⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠈⢲⡤⠤⣬⡭⠭⢴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠤⠤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣀⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡏⠉⣽⣷⣦⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣴⣿⣷⣄⠀⠀⠀⠀⢀⣿⣿⣿⣇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣿⣿⣿⣿⣿⢻⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠘⢿⣇⢹⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢸⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣣⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣥⡸⣿⡟⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠇⠉⣠⣶⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠛⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇⣰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⡟⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⡿⠋⠀⢿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠏⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⡇⠀⠸⠿⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠈⠁⠐⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡱⠾⢡⢈⠄⠁⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠈⡠⠀⠉⠰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠁⡦
⠀⠀⠀⠀⠀⠀⠀⡠⢀⠚⠀⢰⠶⠤⠄⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⢰⠉⢡⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢑⠈⠀⠀⠀⠉⠁⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠷⢲⠛⠇⠱⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠸⠄⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⢉⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡀
⠠⠁⠀⠀⠀⠀⠀⠀⠠⣤⡀⣈⣉⠉⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⡀⠁⣀⡠⠄⠊
⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⡄⣩⠄⠀⠀⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⡸⣴⡤⢄
⠀⠀⠀⠀⠈⣢⠂⠀⠀⠀⠘⠒⠟⠒⠒⢍⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⢃⠉⠴⣄⠁⠀⠀⠑⢤⡀
⡤⣔⣤⠗⠒⠇⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠻⣶⠀⠀⠀⠀⠑
⠑⠬⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡃⠀⠀⣀⠄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠻⢯⣴⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡤⠴⠀⠀⣀⢖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⢀⠀⠐⠛⠃⠀⠀⠛⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⡂⠠⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠛⠀⠀⠘⢧⣤⣀⠀⠋⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⣀⡀⠀⠐⢋⣴⠆⠂⣴⢗⠆⠀⠀⠀⠠⡤⠶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⢤⡄⠠⡍⢧⠀⠇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠔⠀⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠋⠀⠀⠀⠀⠉⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠘⠗⠀⠀⡌⠀⡃⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠆⠔⢢⠀⠑⠂⡀
⠀⣠⡀⠀⠀⠃⣈⠁⠐⠿⡾⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⢐⠦⡄⠀⠀⢈⠠⠁
⠀⠉⠀⡄⠀⠀⠀⣠⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⢴⡦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⢆⠉⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠟⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠡⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀
⣿⣿⡿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠀⣀⠉⠁⠠⠄⠀⠀⠀⠀⠀⣀⣠⠛⠋⠈⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⠀⠀⢀⣠⣤⣮⠀⠀⠀⠀⠀⠀⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡳⠆⠉⠀⠀⠈⠉⠲⣤⡀⠈⢢⣤⠖⠉⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⠠⠶⠶⢆⣀⢀⡀⠀⠈⢣⣰⠇⠀⠀⠀⠀⠀⠋⢦⡀⠀⠀⣤⠴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠈⠻⣟⠦⠀⠀⠙⢧⡤⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⢾⠃⠀⠀⠐⠒⢦⡀⠀⠀⠈⠒⠂⣄⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣸⣧⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠶⠂⣦⠀⠀⠀⠀⠀⠈⠉⠀⠤⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠖⠘⠛⠀⠀⠀⠀⠀⠀⠀⠰⣦⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠚⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢀⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⣸⣷⠛⠱⡎⠉⠁⠶⣤⣤⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣷⠀⠀⢸⡄⠀⠀⠈⠛⠛⠀⠀⠀⠀⡧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠸⣧⣤⣤⣤⣬⣍⡁⠀⢠⣶⡃⠀⠈⣦⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⡀⠹⣟⡁⠹⣧⡀⠶⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢻⣧⡼⠏⠀⠀⢹⡇⠀⠀⠈⠙⢦⡀
⠀⠀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠹⣄
⠀⡼⠃⠀⢠⡀⢀⡴⠛⠳⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⠀⠀⠀⠀⠸⣆
⢸⡇⠀⠀⠸⣦⠟⢰⡟⠛⠛⠋⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠤⠖⡿⠟⠛⠛⠛⠋⣤⠋⠀⠀⠀⢾⠀⠸⣆
⣿⠀⠀⠀⢰⡟⠀⠸⣦⣴⡖⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠇⢀⡴⠋⠀⠀⠀⢀⡴⠃⠀⠂⠀⠀⠀⡆⠀⢻⡀
⢻⡄⠀⠀⢸⠇⠀⠀⠀⠀⢰⠀⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⡿⠋⠀⠀⠀⢀⡾⠋⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⢿
⠘⢧⡀⢰⡟⠀⠀⠀⠀⠀⢸⠃⠀⢰⡿⡀⢀⣤⠀⠀⠀⠀⣠⠞⠃⠀⢰⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠸⡇
⠀⠈⠙⢾⠇⠀⠀⡀⠀⠀⢸⡀⠸⢧⡀⠙⡏⣰⠿⠶⠶⠎⠁⠀⠀⠀⢺⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⢱
⠀⢀⣠⡿⠀⠀⢠⡇⠀⡀⢸⡟⠃⠀⠘⢿⣠⠏⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⣀⣠⣶⣦⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠶⠀⠉⠀⠀⠀⢸⡇⠀⡇⢸⡇⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⢀⣤⡴⢻⡝⣿⣿⠋⢩⢷⡈⠀⠀⠀⠀⢹⡇⠀⠀⠀⢸⡏⠀⠀⢸⡇
⠀⠈⠳⣄⡀⠀⣼⠁⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠉⠲⠷⠶⠛⠉⠀⣸⠂⢼⡟⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣷⠀⠀⢸⡇
⠀⠀⠀⠈⢣⡀⣿⣀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢿⡄⠀⢸⠃
⠀⠀⠀⠀⠈⠹⡿⠈⢻⠃⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⡇⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢷⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⢂⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡉⠂⠾⠆⠀⢀⣀⣀⣀⣀⠸⣷⡀⠀⠀⠀⢀⣼⠷⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠛⠓⠂⠀⠀⠠⠍⠉⠉⠐⠛⢷⣄⣀⣤⣾⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣠⣤⡐⣦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣹⠟⠓⠶⠶⠶⠚⣿⠃⠀⠀⠀⣰⡄⢻⣀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⠞⢡⠟⠋⠁⠀⣏⠀⠀⠤⠄⣀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⣰⠇⠀⠀⢰⠏⠀⠀⢶⠀⠀⠀⠈⠉⠿⣤⠄⢿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠠⢾⡁⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢠⡏⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠻⠦⠾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠸⣿⡄⠀⠀⠀⠀⡼⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠘⢷⣤⣀⡀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠘⣧⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠶⠶⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⣦⡀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⡇⠀⠀⢸⠇⢄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⠛⠛⠛⠛⠓⠀⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢠⡇⠘⠛⠶⠾⠟⠂⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠚⠛⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣠⣴⠖⠛⠃⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠤⠤⠄⣀⣀⣀⣀⣀⣀⢠⣤⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢤⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠛⠛⢿⣄⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣞⠻⠷⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠛⠛⠛⠒⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⡀⠘⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠉⠠⠀⢠⠄⠀⠀⢀⡄⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠲⣄⣰⠠⠀⠀⠀⠄⠀⠁⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⢄⠀⠀⠀⠀⠀⣀⡌⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣐⠀⠂⠈⠀⣸⠀⠀⠀⠀⠑⠁⠀⠀⡀⢀⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⢀⠛⠃⠂⠀⠀⠉⠉⠁⠾⠛⠁⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⡀⠀⠀⠒⠂⠀⠀⠀⠒⡄⢀⣥⠆⠀⠛⠛⠂⠁⠀⠀⠀⡀⣀⠀⠀⢤⠀⠒⠀⣀⠀⠀⠂⢡⢠⣴
⠀⠀⣸⠁⠀⠘⠄⠄⠀⠀⠀⡤⠃⡜⠑⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠑⠤⢴⡀⣷⣀⡀⠀⠀⢀⠀⠀⠈⠁
⢀⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠀⠀⠀⠀⠃⠀⠈⠀⠀⠩⢤⡅
⠙⠟⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠐⠁⠀⠀⠀⠀⠐⠦⣧⣀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠐⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠙⡗⠀⠀⠀⠄⡅
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⡀⠀⠀⠀⠤⠃⢰⡀⠀⠀⠀⠈⠁⠀⠀⠰⠠⠈⠂⢠⠂⠀⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠀⠀⠐⡤⠤⠤⠤⠤⠢⣤⠀⠀⠀⠁⠀⠀⢀⣶⠒⣁⡀⣱⡇⠀⡁
⠀⣶⠀⠀⠀⠐⠀⠴⡶⠀⠀⣠⡄⠠⠐⠈⠐⠀⢲⡀⠀⠀⠉⠂⠖⠀⠀⠲⠀⠊⠉⠀⠧⠌⠀⡧⠞⠁
⣀⡘⣦⢊⣀⡀⣀⣀⣀⣀⣈⣙⣁⣀⣀⣀⣈⡓⠂⠓⣀⡐⠶⠶⠆⣀⣀⡐⠲⠶⠆⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠟⠲⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠆⢀⣀⡤⠴⠖⠻⢿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠀⢀⣠⠖⠛⡄⠀⠉⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠒⠄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠤⠄⣾⠀⢸⡄⠀⠀⠀⠀⠀⠀⠜⣿⣤
⠀⠠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠙⠙⠆⢠⠀⠀⠀⠀⣀⣀⣀⠙⢩⣿⡷⢏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠈⠿⢻⡇⣶⣶⡶⢶⣶⣶⠀⣠⡠⠄⣠⣷⣦⣦⢙⣭⢤⣟⣡⣄⣠⣾⡏⢉⢽⣗⠈⢍⣷⠸⠀⠀⣇⡄⠀⡀⡀⠀⠀⠀⣿⣿
⢠⡐⢻⠿⢧⠏⡍⣧⢘⣛⡿⢠⠌⠳⢢⣿⣿⡏⢹⡄⡿⠿⣂⠘⠷⠻⢁⠙⠛⠊⠻⠆⠀⡀⢱⣶⢤⣤⣤⣄⣠⣤⣤⣤⢤⣿⣿
⢸⣿⡿⠆⠀⠘⡇⠀⠀⡛⢁⣨⠘⠁⠊⠿⠈⠀⡌⠀⠀⠀⠀⠐⢤⣄⢰⣴⡷⠂⣤⣇⣛⣿⢾⠘⠙⢘⡇⢙⣿⣿⣿⣿⢸⣿⣿
⠀⢐⡹⢀⣠⣨⡓⠦⣤⢈⠘⠋⢸⡄⠀⠀⢸⡆⢈⠀⠀⠄⠀⢰⣾⣻⣽⣟⢳⢴⣼⣿⢩⣍⠁⢆⡀⠘⡃⠸⣿⣿⣿⣿⠐⣿⣿
⠀⠘⠀⣲⣶⣶⣿⠟⠿⠆⠀⠀⣸⡏⢠⡀⠉⣱⠛⠀⠀⣀⣿⣾⠇⠀⠀⢿⡀⢸⠗⢸⣧⡝⢿⠊⣡⢀⡄⠀⠿⣿⡿⠟⢈⣿⡋
⠀⠀⠀⣧⡿⠩⠉⠀⠀⠀⠀⢉⡁⣀⢸⠃⣸⡟⠖⠸⢱⠔⣟⠉⠀⠀⠀⠀⠙⢤⣀⠞⣿⠃⠺⢧⣤⣄⣰⣶⣶⣤⢽⣷⣻⣟⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⡏⠁⠀⠈⠘⠤⠀⠁⠀⠀⠀⠀⠀⢀⣈⣿⡀⣌⡀⣀⣨⠇⢀⠀⢀⣭⣅⠘⠯⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⠛⠋⢧⠀⠀⠈⠉⢀⣘⠛⠉⠉⠉⢏⢆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡏⠀⠀⠀⠀⢀⠈⠀⠀⠻⣯⣤⣀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡶⣠⣴⣯⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣘⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣾⣷⣦⡀⠀⢀⠄⣨⣶⣿⣿⣿⣿⣷⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⣵⣾⣿⣿⡿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣹⣏⣿⣿⣷⡀
⠀⠀⢠⣿⣻⣿⣿⣿⣿⣻⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣷⠘
⠀⠀⠸⠘⣿⣿⣿⣯⣿⣿⣿⣿⣿⣛⣻⢿⣿⣿⡿⠻⣍⠹⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⢿⡏
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣽⡟⢉⠉⡀⡴⠁⠑⠤⠨⡓⠾⣄⡈⠹⡿⣿⣿⣿⣿⡿⢼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢿⣏⣼⢿⠞⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠭⠥⣾⣿⣵⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠛⠁⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⢛⣁⣠⣤⣤⠄⠀⠀⠀⠀⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣻⣶⣆⠀⠀⠀⠀⠉⠀⠰⠋⢿⣿⠜⠁⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣛⡛⠶⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠋⠉⣷⠀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣒⡖⠚⢻⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣴⠊⢠⠚⡗⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⣶⠁⣸⠃⢸⠀⠉⠙⣻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣾⠉⠀⠟⣿⠑⡿⢠⡾⠀⠀⠐⠁⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣰⡏⡆⠀⠀⡇⠈⠃⢠⣿⢢⡇⢈⣧⠀⠀⣀⠀⠀⠀⣀⣈⣳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣍⢁⠟⠲⣴⡁⡇⣆⠘⣿⣾⠁⣼⢻⠀⠀⢸⣿⡦⢄⡀⠀⠉⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣀⠀⠈⢳⣿⢹⣆⢻⣿⢰⠏⠣⠇⠀⢸⢿⡇⠀⠉⠲⢄⡀⢦⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣿⡜⣿⣦⠛⡞⠀⠀⠀⠀⠘⠸⡇⠀⠀⠀⠀⠙⠻⣆⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⣸⣿⣿⡀⠀⠀⡀⠀⢀⡒⠶⣿⠀⠀⠀⠀⠀⠀⠈⢧⣴⣾⠽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⣿⣿⣿⣷⣰⡦⣌⠛⠲⢿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣾⣿⣿⣿⣿⣿⠿⢿⣌⢳⣄⠀⠀⠉⠛⢧⡀⠀⠀⠀⠀⠀⠀⠳⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠿⠿⣿⡿⠋⠁⠀⢸⣿⣧⠙⢷⣄⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠉⠀⢀⣤⠞⠉⠀⠀⠀⢀⣾⣿⣿⣷⡀⠉⠉⠛⠲⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⢰⡟⠁⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡄⣠⣴⣦⣤⣬⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣴⣝⣿⡿⠟⠛⠋⠁⠀⠻⡿⢿⣿⣿⣿⣿⡀⠀⠉⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣶⣶⣶⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠈⣡⣿⣿⣿⣿⣿⠿⠿⠛⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠉⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿
⠀⠀⠀⠀⠀⣶⣶⣤⣀⣬⣿⣿⣿⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠿⢠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⣆⣀⠀⠖⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⡜⠛⣉⣉⣬⢋⠉⡋⠆⠀⠀⠀⡀⡀⠀⠀⠀⠀⢩⣰⠀⣀⠀⡆⠀⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡍⠂⠒⠻⠿⠡⢾⠓⠟⠋⠰⠀⢺⠁⠁⠀⠀⠀⡀⢠⢨⢀⣒⡂⡇⣰⣶⡧⠀⠒⡳
⠀⠀⠀⠀⠀⠀⠀⠨⠿⠿⢶⠇⠀⠀⠀⢰⡇⡦⠀⣺⣀⡝⠂⠀⠀⢠⠀⢲⡦⠈⠐⠒⠀⡇⡳⠟⠃⠀⠓⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠈⠙⠀⣠⡉⣉⡉⠀⠀⠀⠠⠄⢸⠇⠀⢀⠀⠀⠇⠅⡤⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⣄⣬⡟⣿⣧⠀⠀⠀⢹⡉⢹⡁⠀⠀⠐⠀⠈⠰⠄⢰⣦⡄⠀⣄⣀⠀⠀⢤⡄⣀
⠀⠀⠀⠀⠀⠀⠐⠠⠟⠻⣡⡿⢛⠟⡺⣟⠁⣶⣫⠸⠹⠁⠀⠂⠀⠀⠀⠀⠀⢂⠙⡁⠺⠽⠇⠁⠀⢊⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠛⠞⠟⣽⠂⠈⢀⠃⠰⠐⠀⠀⠀⠀⠀⠀⠀⠼⠋⢹⠶⠐⠂⠠⠠⡿⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢀⣬⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠯⠮⠤⠖⠆⢼⡀⠀⠀⠢⠀⠀⢀⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡠⠴⢊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣥⠀⢀⡤⣤⠄⡀⠉⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠐⢰⡦⠀⠀⣨⡀⠀⠈⠻⠀⠈⠁⠸⠀⠁⠁⠁⢦⠀⠀⠀⢨⠀⠀⠀⠀⠀⡐⠀⣠⣏⣃⠄⠈
⠀⠀⠀⠀⠀⠀⢀⡉⠅⠀⠀⢱⡿⠁⠐⠂⠀⡳⠀⠀⠀⠀⠀⢀⠀⡄⡀⢀⢚⣶⣤⠀⠀⠸⣅⢠⣍⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠌⠉⢀⡀⠀⠀⢀⠹⣎⣶⠁⠀⢉⠄⠁⠀⢀⠉⠉⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⣾⡄⠀⢀⠀⢿⣷⠀⠀⠀⠐⢰⡇⠟⠛⠊⠁⠘⠛⠚⠊⠉⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠤⢛⡇⠀⢼⠀⠁⣉⡠⠀⠀⠀⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠰⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡿⠛⠿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⠁⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠀⣸⣿⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣇⣀⣏⣃⡇⠀⠀⠀⠀⠈⣿⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠉⠉⠙⠛⣿⠆⠀⠀⠀⣠⣽⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣠⣤⣼⣻⢸⠀⠀⠀⠀⠀⠀⠀⣏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⠏⠁⠘⠱⢸⣾⡇⠀⠀⢶⠒⡾⠗⠸⡞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡟⠀⠀⠀⢀⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠊⠀⠀⠀⣠⣾⠟⠁⠀⣀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣀⣤⡴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣄⠀⣠⡄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣘⣦⣾⣷⣾⣿⣿⣿⣿⣿⣿⣧⣾⣃⣼⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⣸⣖⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢬⣲⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣽⣶⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢻⣿⣿⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣾⣿⣿⡿⠁⠀⣀⣤⣤⣤⣄⣀⠀⠀⣀⣤⠖⠛⠉⠉⠉⠙⠻⣶⣄⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠁⣠⣾⣿⠟⠋⠁⠀⠀⠉⠉⠉⠀⠀⣀⣀⣀⣀⠀⠀⢹⣿⣧⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣿⣿⣿⠁⣼⣿⡿⠃⠀⣠⣴⠾⠛⠳⢶⣄⣠⠞⠉⠁⠀⠉⠻⣆⠀⠙⠛⠀⠀⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⡇⠀⠛⠋⠀⢠⡾⠋⠀⢀⣀⠀⠀⢻⡏⠀⠀⢠⣤⡀⠀⢻⡆⠀⠀⠀⠀⠀⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠿⠃⠀⠈⣿⡀⠀⠈⠉⠀⠀⢸⡷⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢀⣼⠛⢿⣦⣄⡀⢀⣠⣾⠃⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣴⣾⣿⠁⠀⠀⠹⣿⣿⣿⣏⣁⡀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠨⢾⡿⠋⣏⠀⠀⠀⠀⠹⣿⡙⠳⠦⠀⠀⠀⠀⠀⠀⠆⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⢀⣠⣿⠀⠀⠀⠀⠀⢻⣏⠳⣄⠀⠀⠀⠀⢀⠈⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⡀⠀⠀⠀⠀⣼⡿⠀⣿⠀⠀⢀⠂⠀⠐⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠾⢷⣤⣀⣤⣾⡿⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠠⠀⠀⠨⢙⣟⢻⠁⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣨⣷⣾⣧⠀⠀⠀⠐⠀⠂⠀⢀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠠⣿⣿⣿⣿⣧⠀⠀⠠⠀⠀⠀⠀⠀⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⠏⠂⠀⠀⠀⠀⠀⢀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⡄⠀⢀⠀⠂⠀⠀⠉⠀⠈⠙⠛⠳⣦⠀⠀⠀⠤⠄⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣥⣀⠁⠄⡀⠀⠀⠀⠀⠄⠀⠘⠄⠸⣷⢀⣠⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⠷⠶⠶⠾⠶⠿⠿⠟⠛⠋⠁


⠀⠀⡀
⠀⠁⠀⡁

⣟⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠎⠀⠀⠈⢀⠀⡀⠀⡀⠀⠀⣠⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡰⠁⠀⠀⡀⡀⠒⢀⡠⠀⠀⠀⠸⠀⠀⠀⠀⠰⠀⠀⠈⠘⠯⠄⠀⠿⠋⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐
⠀⠁⠀⡇⠘⠌⠛⠁⠃⠛⠟⠀⠀⠀⠀⢰⡆⠀⠀⠀⠈⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢀⣾
⠀⠈⠄⠲⠀⠀⠀⠀⠀⠄⠀⠐⢺⠀⠀⢘⡇⠀⠀⠀⠀⠈⠢⢀⠀⠉⠀⠁⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣠⡴⠀⡌⢀⠌
⠀⠀⠀⠀⠑⠠⠀⣀⣀⠠⠔⠊⠌⢀⢊⠜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⠈⠥⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡊⠔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣶⣶⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠁⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠟⠿⠟⠛⠛⠋⠉⢻⣿⡄⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⠇⢀⠀⠀⠀⠀⠀⠂⠀⢸⣿⡇⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠄⠀⠀⠀⠀⠀⠀⠀⣿⡄⡀⣠⣠⠀⢐⣱⣦⠀⢸⣿⠃⠀⠀⠀⠸⠉⠍⠀⠘⡿⠇⠈⢹⣿⠖⠐⠄
⠀⠀⠀⠀⠀⢧⡿⢃⠃⠀⠙⠿⠛⠀⠂⠀⠀⠀⠀⠠⢭⠀⠀⠈⠉⡀⠀⢉⡍⠀⠀⡐⠂⠀⠀⠀⣶⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠘⣤⢼⠇⠀⡐⠀⠀⠀⠀⠀⣇⠀⠀⠁⢀⠀⠀⠈⠒⢚⡔⠁
⠀⠀⠀⠑⢄⠀⠀⠒⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠀⠀⠤⠔⠊⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠉⠈⠁⠀⠈⠀⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠈⠁⠒⠂⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠂⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃⠀⡀⠀⠀⠀⠂⠀⠀⡰⠖⣤⠀⠀⡀⠄⣤⣹⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠄⠀⠀⠒⠀⠀⠀⠶⠀⠒⠲⠒⠈⠁⠀⠀⠀⠀⠠⡆⠈⠘⠋⠄⠀⠑⠒⠛⠁⠠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⡀⠀⠂⠀⠀⠀⠀⠠
⠀⠐⠂⠀⠀⠛⠂⠀⠸⠗⠀⠀⡸⠀⠀⠀⠀⠀⠀⠆⠀⠑⡀⠀⠀⣄⣀⡇⠀⠀⠀⡰⠄⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⢀⡅⠀⢠⠁
⠀⠀⠀⠂⢀⠀⠈⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠁⠈⠀⣀⡠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠛⠙⠀⡰⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠉

⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⢀⣠⣶⣤⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⣠⣶⣶⣶⣦
⠀⠀⣰⡿⠟⠛⢿⣿⠀⠀⠸⢛⠉⡙⠇⠀⠀⣾⢁⠀⡀⣿⠀⠀⣼⠟⠉⠉⢿⣇⠀⠀⣿⠟⠛⠛⢿⠇⠀⠀⠀⣀⣠⣀⡀
⠀⠀⢿⡆⠈⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⡟⠀⠀⣿⡀⠀⠀⣸⡿⠀⠀⠠⠀⠀⠀⡤⠀⠀⠀⢀⠐⠀⠂⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠞⠀⠀⠀⠸⠿⠀⠸⠷⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣴⡿⣻⣦⣄⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⣠⡶⠻⠿⣦⠀⠀⢀⠔⠋⠛⢦⡀⠀⠀⢠⣿⠿⣿⣦⠀⠀⠀⢠⡶⠶⠶⡄
⠀⠀⠙⠐⠋⠈⠉⠃⠀⠀⠐⠁⠀⠀⠂⠀⠀⣿⠀⠀⠂⣿⡀⠀⠘⠂⠀⠈⠀⠀⠀⠀⠻⠡⠀⠠⠻⠀⠀⠀⠈
⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢠⣿⠇

⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⢠⣴⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⢀⣠⣤⣶⣄
⠀⠀⢸⠟⡉⢉⢻⣧⠀⠀⢠⡿⠻⣿⠀⠀⠀⣴⢶⠿⠿⣷⠀⠀⣸⢟⠉⢛⢻⡇⠀⠀⢾⠉⠙⢉⠹⠀⠀⠀⠀⠤
⠀⠀⣿⣇⠀⠀⣼⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢀⣾⠇⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢰⣄⠒⣠⡆
⠀⠀⠈⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠙⠛⠀⠀⠀⠀⠐⠶⠖⠀⠀⠀⠀⠀⠛⠛⠋

⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣴⣶⣿⣶⣄⠀⠀⢀⣴⣾⣦⡄⠀⠀⣠⣶⣾⣿⣶⣄⠀⠀⣴⣿⠿⣿⣶⠀⠀⠀⠀⡀⠠⣀⠠⠄
⠀⠀⢰⠋⠋⠀⠋⣳⠀⠈⢿⠋⠈⢹⠉⠀⠀⠻⠛⠉⠙⠿⠀⢰⣿⠁⠀⠀⢹⣿⠀⠀⣿⠀⠀⠀⢹⡆⠀⠰⠇⠀⠀⠀⠻⠂
⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠯⠟⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⢀⡟⠋⠉⠙⡇⠀⢠⣿⠿⠻⢿⣧⠀⠀⢸⠋⠀⠉⠧⠀⠀⢠⡿⠛⠛⢷⡄⠀⠀⣿⠿⠿⢿⣿⠄⠀⢰⡿⠿⠿⠿⢿⡆
⠀⠀⠀⠀⠁⠀⠁⠁⠀⠸⠇⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠁⣿⡇⠀⠀⠉⠄⠀⠀⠌⠀⠀⠈⠇⠃⠀⠃⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠈⠙⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡎⠀⠀⠀⠀⠈⠙⢿⣦⣤⣤⡤⣶⠶⣶⡶⠶⡶⠶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠗⠒⡄⠀⠀⠀⠀⠀⢹⠉⠉⠉⠀⣫⠀⠀⡉⠹⠀⢸⠁⠉⠙⢻⠿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠉⠢⡀⢘⠁⠀⡙⠈⠉⠁⠈⠀⠀⢘⠀⠇⡔⡻⠤⠤⠤⠆⠀⢀⠍⢙⠿⢿⣦
⠀⠀⠀⠀⠀⠀⢰⣿⣍⣉⠉⢢⠀⠈⠁⠀⠀⠃⠀⠀⠀⠀⠀⢀⠎⣈⡉⢀⠃⠀⡠⠤⣀⠀⠈⠲⠬⢍⢁⡿
⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠑⠊⠀⡤⢄⠀⢸⠀⠀⠀⠀⠀⢎⠁⢎⠤⠃⠸⠀⡰⠁⠀⢸⠀⠀⠀⠀⠈⢹⠇
⠀⠀⠀⠀⠀⢠⣿⠇⢡⠀⠀⠀⡰⢀⡀⠣⡧⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⡇⢠⢃⡠⠤⠤⠇⠀⡀⣀⠀⣿
⠀⠀⠀⠀⠀⠸⣿⡤⡀⠃⠤⠔⠠⡮⠀⢀⠃⣄⠀⢀⠤⢄⠀⠀⢸⠀⢀⠁⠀⠀⢛⣃⠀⠀⠀⠑⡌⢹⡏
⠀⠀⠀⠀⠀⠀⠈⠛⠾⣷⣤⡀⠀⠀⠀⢸⠖⡎⠓⠁⠀⢠⠃⠀⠜⠀⢸⠀⠀⢎⠀⢸⠀⡠⠚⠁⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣖⣄⡀⡌⠉⠀⠀⠀⠀⠠⣀⠎⠀⠀⡆⠀⠀⠈⡆⠀⣉⢀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣶⣤⣬⣭⣭⡭⠽⠿⠿⣷⣖⣤⣎⣁⠀⠓⢒⠁⡠⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠻⠿⣶⣧⣤⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢉⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⡀⣀⠀⡄⡀⠀⠊⠀⢀⡀⠀⠰⠀⠀⠀⠀⡠⠄⠀⡀⠀⠀⠠⢄⠀⠀⠀⠐⠆⠀⢀⡀⠀⠃⠀⢠⣤⢀⣀⢀
⠀⠀⠀⠀⠀⠃⠈⠁⠒⣏⡅⡀⠉⠀⠴⠀⠰⠒⣀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢄⡀⠲⠆⠀⠤⠀⠁⣀⢎⣝⠚⠈⠀⠑
⠀⠀⠀⣠⠂⠀⠠⠌⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠋⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠥⠄⠀⢐⡀
⠀⠀⠀⠈⡰⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⢆⠁
⠀⠀⢠⠀⠉⠱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠅⠉⠈⡄
⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠐⠀⢀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⡀⠀⠃
⠀⠀⠀⠈⢳⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⠎⡀
⠀⠀⠀⠙⠄⠀⠐⢂⠄⣀⡀⡀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⢀⢀⣀⠠⡒⠂⠀⠨⠃
⠀⠀⠀⠀⠀⠄⢀⠀⡆⣏⡂⠁⡀⠀⠲⠀⠰⠤⠉⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠚⠁⠴⠆⠀⠖⠀⠀⠉⢌⣫⢄⢁⠀⠠
⠀⠀⠀⠀⠀⠁⠉⠀⠓⠉⠀⣄⠉⠀⠁⠀⡰⠀⠀⠀⠀⠒⠂⠀⠀⠀⠐⠒⠂⠀⠀⠀⠠⢆⠀⠈⠈⠁⡀⠀⠉⠛⠈⠉⠈

⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠠⡀⠀⡀
⠀⠀⠀⢸⡟⡠⠭⡀⢈⠉⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠐⠁⠀⠀⠖⠀⠈⠅⠀⠁
⠀⢠⠀⠛⠀⠴⠦⢵⡄⠃⠘⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠁⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠰⠶⠛
⠀⠈⠂⡆⡀⠀⠀⠀⠀⠀⢰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠈⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢶⠠⢀⡀⠀⠐⠘⡇
⠀⠀⠀⡇⠰⣄⠀⠀⢀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢄⡀⠠⠍⠀⢀⠃
⠀⠀⠀⠘⡄⠱⣬⠍⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠈⠗⠀⣠⠎
⠀⠀⠀⠀⠙⢤⣀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠅⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣠⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⡐⠒⠲⣤⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠡⠃⠀⢀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠈⠈⠀⠐⠈⣺⠛
⠀⠀⠀⠀⠀⡘⢷⠂⠀⠀⠀⠀⠙⠋⠀⠐⠃⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠂⠀⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⡀⠀⡂⠀⠧
⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠒⠂⡀⠌⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠑⠄⠠⠂⠠
⠀⢀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠀⢠⠔⠁
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠁⠁⠀⡄⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣠⠤⠤⠤⠤⣄
⠀⠀⡎⠀⡆⠈⠉⠀⠀⢸⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠦⠀⡠⢆⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⣀⡀⠀⠙⢦⡀
⠀⡴⠛⢤⡇⠀⠀⠀⡄⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡗⠀⠌⠓⠀⠂⠹⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢏⣷⡛⠉⡇⠀⠀⢹
⠀⠘⠢⡆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⢃⠀⠀⠀⠔⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠌⠄⠈⠁⠠⠀⠀⠰⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠐⢄⠀⠀⢠⡀⠐⠀⡠⢁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠀⠀⠀⠂⠄⡤⠞
⠀⠀⠀⡇⠀⠀⠀⢀⣀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠉⠐⠚⠉⠂⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢤⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠳⢄⡀⠀⠈⠉⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠂⣀⡤⠖⠚⠚⠃
⠀⠀⠀⠀⠀⠈⠙⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠜⠁

⠀⠀⠀⠀⡿⠿⠆⠀⠰⡂⠀⠦⠀⢀
⠀⠀⠀⠀⡧⢄⣀⡀⠀⡟⠓⠚⢶⠦⢤⣐⣴⠿⠱⡖⠤⢤⣄⣀
⠀⠀⠀⢰⡇⠀⠀⠀⠉⠉⠛⠓⠒⠳⠤⣄⡙⢧⣠⣝⠄⠀⣈⠙⠛⠶⠦⡤⣀⣀
⠀⠀⠀⢸⠀⠀⠀⠀⡔⠀⠀⠀⠱⢄⠀⠀⠈⠳⣿⣟⠛⠛⠶⢦⣤⣤⣀⣀⣀⠈⠉⢲
⠀⠀⠀⣼⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠈⠻⡳⣾⠀⠀⠑⠤⣈⠉⠉⠛⠛⠚⠀⢴⣶⣦⡤⠭⠭⠭⠉⡽⠃⠠⣄⣀
⠀⠀⠀⡏⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⢱⠈⠳⣄⢀⠂⠀⡄⠈⠀⠀⠂⠀⠀⠈⠛⠻⡉⢐⣚⣛⣛⣉⣂⣘⡿⢷⣦⣶⣤⣀
⠀⠀⠀⡇⠀⡘⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣇⠀⠉⢯⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠀⠀⣠⠎⠉⣉⠽⠛⠛⣿⣽⣏⣹⡄⠄
⠀⠀⠸⣇⡘⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢹⢦⣤⡤⠹⣦⠀⠀⢩⠉⠐⠒⠒⠂⠀⠀⠀⠙⣿⠛⠓⢤⡺⠁⠀⠔⡡⠀⢈⠀⡦⢻⣦⡀
⠀⠀⠀⢸⡯⠤⠶⠦⠤⠤⠤⠤⠤⠤⠀⠀⠤⢷⠤⠤⠤⢰⡏⠉⠉⣹⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠹⠀⡇⢀⡇⠀⠈⢀⡇⢰⠈⠉⠁
⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣤⣤⣤⡧⡤⢤⠿⠒⠲⠶⠖⢷⠒⠒⠒⠒⢲⠀⠀⠀⠘⣦⣄⠀⡀⣦⠃⠐⣷⠢⠠⠘⡇⢸
⠀⠀⠀⠀⡏⠉⠉⡏⠉⡏⠉⠉⡛⠙⠉⡏⣿⠸⠦⢶⠶⠶⠶⠶⠶⠶⡦⠦⠦⠤⠾⠦⠤⠶⢲⢺⠓⠒⠒⢺⠁⢉⡉⠀⠈⡀⠀⡏⠀⢒⡤⣧⢸⠀⡁
⠀⠀⠀⠀⣇⠀⠀⡇⠀⡇⠀⠀⢽⣠⣀⡇⣿⠠⠄⢠⡇⠀⠀⠀⠀⣷⠇⠀⠀⣠⠀⠐⣦⣽⣆⣿⡄⠀⢰⠸⡗⠀⠇⣼⡉⠺⢠⠷⢾⠀⠦⠮⣸⢀⠀⠆
⠀⠀⠀⠀⣿⠀⠀⡷⠒⡇⠀⠀⠉⠈⠀⠀⢹⠁⢀⠈⠇⠀⠀⠀⠠⣿⡄⠀⠀⢹⣦⣆⣰⠠⣌⡁⠀⠀⠠⠄⣷⣀⡲⢯⠻⣇⠸⡀⡢⣆⡀⢰⣮⡈⠛⢁
⠀⠀⠀⠀⣿⠀⠀⡇⠀⡇⠀⠀⢰⡀⠉⡇⢸⡤⢠⡀⠀⢳⡄⠀⠀⣯⠆⠐⠫⠀⠀⠉⢣⠀⠀⠑⢄⠀⠀⠀⠈⠀⠀⠀⢣⠘⠂⠙⠁⢅⢀⠋⢁⠹⡞⠻
⠀⠀⠀⠀⣿⠀⠀⡇⠀⡇⠀⠀⠜⡿⠿⠇⣼⣀⣸⣧⡄⢈⡙⠳⡦⣿⡦⡄⡀⠀⠀⠀⠀⡇⠀⢀⣿⡀⠀⠃⠀⠀⠀⢀⢸⡔⠀⠀⠀⡈⠨⡄⢼⡤⠁⡀
⠀⠀⠀⠀⣿⠀⠀⡇⠀⡿⠀⠀⣿⠀⠀⢄⠈⠻⣷⠙⠋⠀⡀⠀⡟⠁⠈⠉⢃⠀⠀⣆⠀⢷⠀⢸⠇⢷⣸⡄⠀⠀⠀⢸⡆⠃⡄⠀⠀⠃⠀⠙⠉⠀⠀⠇
⠀⠀⠀⠀⣿⠀⠀⡇⠀⡷⠒⠂⣿⠀⠀⠀⠋⢀⣼⠀⢀⣉⠠⢰⢁⡶⠴⢦⡈⠛⠆⠈⢳⠈⢃⢸⡆⢸⣶⠃⠀⠀⠀⡀⣏⡛⢋⡐⠀⠀⢀⠀⣀⡴⠀⡓
⠀⠀⠀⠀⣿⠀⠀⡇⠀⣇⣀⣤⣿⣀⣀⡬⠞⠁⣟⠏⠉⠀⠀⢰⣟⠁⡀⠀⠹⣊⣀⣀⢀⠏⠉⢨⡏⠉⢉⠀⢀⠀⠈⣃⢯⡤⣾⣿⣠⣿⠿⠿⠷⠶⢾⡏
⠀⠀⠀⢀⡿⣤⠴⠷⠾⢿⢿⡍⠉⡀⠀⠀⡀⠀⢹⡄⠀⠀⠀⠈⡏⠉⠙⠛⠀⡏⠉⠉⠩⠀⡀⣼⣏⢍⣉⡀⢈⠀⣈⢉⣸⣇⣿⣿⣿⣿⣒⣲⣶⠤⡾⣇
⠀⠀⠀⡎⠀⠉⠈⠉⠉⠉⠂⢹⠀⣷⠀⠀⠇⠀⠸⣇⣤⠤⠖⠲⣦⠤⠔⠒⠒⡞⠀⠀⣤⣠⣧⠟⠋⡿⢻⡁⠈⠀⠈⠁⠀⠛⠃⠿⠚⠏⠀⠀⠀⠉⢷⣈
⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⢸⠀⠘⣇⠀⢱⠀⡇⠀⢡⠀⡆⠀⡧⠀⢠⠀⠀⡃⠀⢠⡇⠈⡆⠃⢐⠀⠀⠹⠆⠒⢣⠴⠉⠀⠀⠀⠀⠀⡀⠀⡆⡤⣬⠁
⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡆⠀⠀⡇⠀⠘⡆⣹⠀⠁⠀⡜⠃⠀⡇⠀⠈⠰⠀⡇⡄⠠⡄⠁⢀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⡇⢸⠃⡏
⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢸⠀⣀⣘⠷⠶⢿⠄⠀⣄⣩⣿⡏⢀⠌⠀⡇⢀⠇⠀⠀⠀⠍⠅⠄⠘⠳⣇⣿⣇⡐⠁⠀⠀⠀⠀⠀⠀⠀⢳⡼⡶
⠀⠀⠀⢸⢷⣀⣀⣀⣀⢀⠀⠸⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠰⢄⣈⠀⠀⣇⣀⠶⠿⣦⠶⠤⠚⠃⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠤⡴⠖
⠀⠀⠀⠘⢊⠉⠉⠉⠉⠑⡐⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⣬⠆⠀⢨⣤⣵⡶⠒⠁
⠀⠀⠀⠈⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠦⠄⠈⠉⠛⠛⠛⠛⠋⠉⠰⠶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢠⣤⢀⣀⣤⣴⠶⠛⠛⠛⠛⠛⢿⣿⠳⢦⣤⣀⣸⣇⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡀⠀⣀⣴⡿⠷⠛⠉⠀⠀⠀⠀⣠⡶⠶⠶⣆⡙⠀⠀⠀⠉⠻⠿⢧⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠏⠉⠈⠉⣠⠶⠛⠛⠷⣄⠀⣸⠃⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡟⠀⠀⠀⢠⠋⠀⢀⣤⣤⣿⠀⡇⠀⢀⣴⡟⠓⣿⡄⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢠⣬⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣿⠀⠀⠀⠀⢸⠀⠀⣿⣿⣠⣿⠀⣇⠀⢸⣿⣧⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠟⠃
⠀⠀⢀⡶⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠘⢷⣀⢻⣿⡿⠋⠀⠙⢧⣼⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠋⠻⣿
⢀⡞⠛⡆⠀⢻⠙⢣⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢉⣻⣯⣤⠾⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇
⣰⡇⠀⢷⠀⠀⡇⠀⣶⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡶⠟⠁
⡏⢸⡆⠘⣇⠀⠰⠀⢸⡆⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠻⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⢣⠀⢷⠀⠘⠀⠀⠀⠈⣧⡴⠶⠦⣀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠘⣇⠀⠀⠀⢀⣀⣀⣰⡏⠀⣀⠤⠿⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠸⣇⠀⠰⠋⠉⠉⠉⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢿⣅⡀
⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣶⣦⣤⣤⣤⣤⣤⣴⣶⠾⢻⣿⠁⠀⠀⠹⣿⠳⣦⡀
⠀⠀⠀⠀⠀⠙⠛⣷⡄⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⢋⠛⠀⠀⢫⡍⠉⠉⠁⠀⠀⢀⣼⠇⠀⠀⠀⠀⢹⣇⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣤⠞⠉⠀⠀⡿⠀⠀⠀⠀⠻⢦⣤⣤⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢱⡀⠀⠀⣀⣤⢶⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠈⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠈⣧⣤⠞⠋⠀⢸⡇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣦⡀⠀⣿⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠙⠁⠀⣠⡴⢿⣃⣠⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠈⠛⢶⣿⡄⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣤⠶⠟⠉⠀⠈⠋⠉⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢻⣄⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠹⣆⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡴⠋⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣠⠋⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⡜⠁⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣴⣶⡿⠀⠈⣦⢴⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⠶⠤⠤⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠈⣿⠀⠀⠀⠀⠿⠞⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⢤⣄⣀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢻⡇⠀⢀⣀⣀⣀⣀⣤⣤⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡿⠛⠛⠻⣷⡶⠶⠾⠇⠀⠀⠀⠘⠛⢻⡟⠛⠛⠉⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡾⠃⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣀⣀⣀⣼⠏⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡖⠒⠒⠀⠉⠉⠉⠉⢩⣭⣽⠿⣦⣄⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠉⠉⠉⠙⢦⠀⠀⠀⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠳⢦⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠙⣻⡆⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⣀⣀⣀⣠⣤⡤⠤⠶⠶⠶⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣉⠛⠛⠒⠠⠤⠤⠤⠴⠤⠶⠆⢘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⢿⣀⣀⣀⣀⠀⣀⣀⣀⣀⣠⣤⡶⠾⠃

⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠰⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠾⠿⠿⠄⠀⠀⠀⠀⠀⣠⣴⣦⣆⠀⠀⠀⠀⢠⣴⣶⣦⣄⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⢰⣿⣻⣿⣿⡗⠀⠀⠀⠶⢿⠉⠁⠉⢻⠿⠂⠀⠀⠀⡿⠉⠀⢿⠀⠀⠀⢠⣿⣋⠉⣉⣿⡆⠀⠀⠀⣬⠔⠿⢣⡄
⠀⠀⠀⠀⠀⠀⠑⠈⠀⠉⠃⠀⠀⠀⠀⠀⢀⠚⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡁⠀⠀⠘⣿⡇⠀⠀⣿⡇⠀⠀⠀⠛⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣈⣀⣁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⣛⣳⣮⣟⡇⠀⠀⠀⠈⠻⠀⠘⠋⠀⠀⠀⠀⠀⡐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠃⠀⠁⢰⠀⠀⠀⠃⠀⠀⠀⠁⠈⣦⢹⡀⠀⠀⠀⠔⠧⡀⢠⠗⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢰⠰⠀⠐⠁⠀⢠⠀⠀⠀⠀⠀⢠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠿⢬⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡄⠀⠀⠀⠀⢀⣤⠤⣤⡀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⣴⠿⠿⣿⡆⠀⠀⠀⠀⢠⣴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠸⠿⠟⠋⢿⠀⠀⠀⠀⡸⢏⠀⠙⠇⠀⠀⠀⠀⠿⠉⠉⢹⡄⠀⠀⠀⠀⢛⠀⠀⠈⡇⠀⠀⠀⠀⢸⠛⠉⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠱⣤⣦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡈⠁⠈⡀⠀⠀⠀⠀⠀⡈⠀⠹⣿⠃⠀⠀⠀⣀⠍⠉⠁⣀⠀⠀⠀⠀⠠⠆⣠⣰⠦⠀⠀⠀⠀⢰⠈⠀⠈⠴⡄
⠀⠀⠀⠀⠀⣴⣿⣿⣾⣾⣿⣶⡄⠀⠐⠀⠇⠤⠴⠀⠛⠁⠀⠀⡻⠄⢀⠰⠇⠀⠀⠀⠀⠘⠦⠠⠤⠇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣤⠀⠀⠀⣤⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⡇⢀⠀⢀⠀⡀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⣴⣿⡿⢿⣦⠀⠀⠀⠀⠠⠾⠟⠽⠦⠀⠀⠀⠀⢠⣶⣿⣷⣆⠀⠀⠀⠀⢀⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠘⠤⠄⠆⠛⠀⠀⠀⠀⡟⠛⠀⠚⢻⠄⠀⠀⠀⢰⠖⠛⠓⢶⠀⠀⠀⠀⢸⣿⣿⣯⣿⠀⠀⠀⠀⣿⣿⠉⡻⢿⡄
⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠈⠀⠀⠀⠀⣿⣄⠀⢠⣿⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠘⣧⣴⣤⡏⠀⠀⠀⠀⣿⡇⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠔⢀⠐⠄⠀⠀⠀⠀⣿⠋⠀⠈⠿⡀⠀⠀⠀⢀⠉⠐⠈⠁⠀⠀⠀⠀⠀⢙⠛⢛⠀⢀⠀⠀⠀⠙⡻⠀⠘⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣦⣄⡀⢀⣠⣾⡄⠀⡀⠀⢀⣄⣠⡀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⠓⢺⣿⣿⡇⠀⠀⠀⠀⠸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡶⠶⠶⠶⠶⠿⠛⠛⠛⠋⠉⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣬⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠘⣷⡀⠀⢀⣀⣀⣠⣤⣤⣴⠶⠶⠞⠛⠛⠛⢉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠘⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠐⠂⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣋⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⠤⠤⠴⠶⠶⠒⠒⠛⢻⠻⢭⣀⠀⠈⠙⠳⣦⣄⡀
⠀⠀⢠⣴⡶⠶⠶⠶⣿⡶⠒⠚⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠳⢤⣀⠀⠀⠉⠛⢶⣤⣀
⠀⠀⠀⠙⢷⣤⡀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠈⢙⣻⣦⡀
⠀⠀⠀⠀⠀⠈⢻⣦⣄⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣤⣤⣤⣴⠶⠾⠿⣿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠙⢷⣤⡀⠀⠀⠈⠙⢦⣄⣀⣀⣤⣤⣴⠶⠶⠶⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠛⠛⠛⠛⠛⢻⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⡶⠶⠶⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⣴⠶⠶⠾⠛⠛⠛⠋⠉⠉⠉⠁

⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣤⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⡀
⠀⣼⠳⡍⢳⣠⣆⠀⢠⠶⠋⠛⢀⣈⣡⡾⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⡰⠊⠳⡄
⣤⢽⠀⢿⠄⠁⠘⡆⠈⣇⣤⠶⢿⡛⠭⠠⢾⡴⠀⠀⠀⠀⠀⡴⠒⣲⠶⣶⣤⣀⠻⣷⣽⣿⣠⠶⠶⠴⠶⣤⠏⠀⠀⠀⠉⣷⠀⠀⢀⣀⣀
⠸⡄⠀⣼⡇⠀⢀⣇⡼⠋⠈⣀⢠⡬⣤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣝⠿⣷⣶⣤⣈⣻⠀⠀⠀⠀⠘⢷⣤⡀⠀⢀⣿⠊⠁⠉⠀⢸
⠀⣽⠂⠈⢽⠂⠈⣸⣡⢤⠴⠺⣏⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠈⠻⢿⣶⣶⣿⠟⠙⣄⢀⠀⣄⣾⣿⣿⣷⣾⣿⣧⡀⠀⠀⠀⢈
⠀⠘⠧⠨⣙⣋⡤⣚⠇⣠⢀⠈⣁⣠⠀⠀⣙⣶⣀⣶⣿⣿⣿⣿⣿⣿⡷⠄⠀⠀⠀⢠⠴⠒⠋⠉⠉⠛⢺⣿⣿⣿⣿⣧⣾⣿⣷⠶⢤⣴⠋
⠉⠛⠳⣦⣼⣿⡿⠟⢏⠻⠉⠛⣟⠻⡳⣦⣄⣉⠻⡿⣷⣯⣛⢿⣿⣷⣄⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣈⣼⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠈⠚
⠀⠀⠀⠀⠙⣿⣄⠀⠈⠲⢤⠶⣌⡀⠁⢶⢤⣬⡽⠟⠈⢻⣿⣷⣌⡻⣿⣷⡀⠀⠀⠀⠀⠢⢤⣀⣀⡴⠋⡝⢿⣿⡿⠿⢿⠁⢦⠀⠀⠀⢠
⣠⢄⡀⠀⠀⠘⣿⡄⠀⣀⣀⠀⠀⠉⠉⠛⢀⣀⠀⠀⢀⠄⣹⣍⠉⠽⣮⡻⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠀⠘⡙⣧⠀⠀⠀⠙⡷⠶⠒⢋
⠀⠀⣁⣤⠶⠖⢿⣇⠀⢹⣿⣿⣶⣦⣴⣶⣿⣿⠁⠠⣏⠀⢀⣗⠂⣀⡽⢿⣮⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠂⢐⡜⠹⣄⡀⠀⢠⠁⠀⣀⡼
⣴⠚⠃⢡⠀⠀⣿⡏⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠁⢘⢱⣿⠇⢸⡆⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠉⠈⢉⣁⠀⠀⠀⠈⠓⠊⢠⠋⠁⠰
⠃⢰⣤⠋⠀⣰⡟⢀⡼⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⡶⢀⡾⢁⡀⢸⢇⣀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⣸⠋⠈⠛⠒⢢⡄⠀⠰⠯⡖⢈⡽
⣠⠟⠀⢀⣴⡏⠔⠊⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢧⡸⣁⠼⠹⢃⣾⣿⣷⣦⣄⡀⠀⠉⠻⢶⣤⣞⢗⢺⢣⣆⠀⠺⢇⠀⠀⢸⡀⡟⢁
⢀⣠⠴⠋⠁⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠋⠁⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠈⠙⢻⣀⠀⡝⣯⡶⠈⢳⡀⠀⠓⠟⠁
⠈⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢿⣀⡑⣹⠇⠀⠘⡟⠛⠚⠛⠛
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡜⢠⠞⢀⣆⡼⠀⣴⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠠⠗⢫⡴⠊⠘⠃⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣶⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣄⣀⠜⠛⠋⠉⣉⣉⢑⣠⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠞⠋⣿⠟⠉⠀⠀⠀⣀⣤⣴⣖⣚⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⡷⣄⣀⣀⡼⠁⠀⠀⣰⠏⠀⠀⠈⠁⠀⠀⠀⠀⠊⠉⣽⠟⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠀⠀⠀⠀⣰⠇⠀⡀⠀⣀⣀⣠⣤⣤⣤⣤⣼⣧⣄⣀⠀⠀⠀⠀⡀
⠀⠀⣿⠙⠲⣤⡀⠀⠀⠀⣤⣄⠀⣀⣿⡤⣶⣿⡟⠉⠛⠁⠀⠀⠉⠀⠀⠈⠀⠉⢳⠀⠀⠀⢈
⠀⠀⢸⠀⠀⠠⡙⣦⠀⣰⠃⢀⣿⣿⣿⠀⠘⣿⡇⠀⣿⣿⣷⠀⠀⠈⠍⠒⣦⣴⠋⠳⡀⠀⠈⠓⡆
⠀⠀⠈⢧⡀⠀⢜⡾⢷⡗⢲⣿⠀⠻⡿⠀⠀⠀⠀⢰⣿⣷⣾⠀⠀⠀⠀⠈⠁⠀⠀⠀⠹⡄⠀⠀⢱
⠀⠀⠀⢀⡗⠀⢀⡇⠈⠁⠈⠋⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⣿⣓⣤⣀⣀⣀⣀⣀⣀⣠⡴⠃⠀⠀⢸⡄
⠀⠀⠀⣾⠀⢀⣡⠟⠛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⠛⠻⣿⢿⡤⠋⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⡿⠖⠋⠁⠀⠀⢷⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⢸⣾⢳⣤⠖⡆⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⢆⠀⠀⢯⣑⠢⢄⠀⠈⠑⠢⠤⣤⠜⠉⠁⠀⠀⡇⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⢧⡀⠹⡏⠁⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠐⠒⡅⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠢⠤⠀⠠⠄⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⢄⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠑⠄⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣠⡤⣶⠟⠉⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠘⣅⣤⣭⡅⢀⡴⠃⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣤⣀⣀⣀⣀⣈⣉⣯⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⣿⢹⡇⠀⠀⢿⠉⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠀⢀⣿⠀⣧⠀⠀⢸⡇⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢡⡏⠀⠀⠀⣿⠀⢻⠀⠀⠀⢿⡀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣼⠃⠀⠀⠀⣿⠀⢸⡇⠀⠀⠘⣧⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣰⠏⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⢻⡄⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣰⠏⠀⠀⠀⠀⢰⡏⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⠀⠀⠀⠀⢠⡿⠀⠀⢸⠇⠀⠀⠀⣼⠃⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣾⠃⠀⠀⣿⠀⠀⠀⢀⡿⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⢀⣠⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣀⡗⠀⠀⠀⢀⣿⠀⠀⢰⡇⠀⠀⠀⣼⠇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣶⣾⣿⣿⣯⣾⣿⣆⠀⠀⠀⠀⠀⢠⡿⢀⠹⢿⣷⣄⠀⠀⢸⣿⠀⠀⣸⣃⣀⠀⢠⡿⠀⠀⠀⠀⣿⠃
⠀⠀⠀⢸⣟⣿⣷⣸⣿⣿⣿⡿⠀⠀⠀⠀⢀⣼⠟⠉⡀⠀⠙⣿⡷⢠⣾⣿⣿⣿⣿⣿⣿⡿⣼⡇⠀⠀⠀⢰⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢠⡞⠁⣰⣿⡿⠷⢰⡏⠁⣴⠋⠁⠀⠀⠀⠈⢧⠀⣿⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠉⢙⣿⣿⠀⠀⠀⠀⠀⢀⡏⠀⢰⣿⣿⣀⣴⠟⠀⡾⠁⠀⠀⣰⣾⣷⠦⢸⡄⣿⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⢧⡀⠘⠿⣿⡿⠋⠀⢸⠃⠀⠀⢰⣿⣿⡃⠀⣸⢇⡿⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⢠⡿⢉⡸⢯⣽⡃⠀⠀⢸⠀⠀⠀⢸⣿⣿⣷⣶⠻⢸⡇⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⣰⡟⢡⠎⠀⣼⠃⠁⠀⠀⢸⡆⠀⠀⠘⠿⣿⠿⣣⢃⡿⠀⠀⢀⣾⠁⠀⠀⠀⠀⣠⣤⣤⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⢀⣼⠏⠀⠸⣄⡼⠃⣀⠀⠀⣰⡏⠐⠦⣀⣀⣀⣠⠞⢡⡾⠁⠀⠀⣼⠇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⠃⠀⠀⣠⠟⠛⠛⠉⠀⣰⡟⠀⠀⣴⠟⠉⠉⠀⣰⠟⠀⠀⠀⣰⡟⠀⠀⠀⠀⠘⣿⣿⣿⣟⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠘⠃⠄⣀⡀⠀⣰⠏⠀⢀⡾⠃⠀⠀⢀⡾⠃⠀⠀⠀⢠⡿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣺⡟
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⡆⠠⡀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠚⠓⠒⢚⣿⡟⠁⠀⠀⠀⢠⡿⠁⠀⣀⣤⣾⣿⠿⠋⠈⠻⠿⠷⠛⠁
⠀⠀⠀⠀⠀⣠⡾⠃⠀⣰⣷⡀⠈⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣿⡟⠀⠀⠀⢀⣠⣿⣷⣾⣿⡿⠟⠋⠁
⠀⠀⠀⢀⣼⠏⠀⠀⣼⠋⠀⠳⣄⠀⠀⠀⠈⠉⠁⠒⠒⠒⠉⠉⢀⣴⡿⠀⠀⠀⠀⢿⡿⠟⠛⠉
⠀⠀⢠⡾⠃⠀⠀⣼⠃⠀⠀⠀⠈⣷⣤⣀⠀⠀⠀⠀⠀⢀⣠⡴⢋⣿⠃⠀⠀⠀⣰⡟⠁
⠀⢠⡿⠁⠀⠀⣼⠃⠀⠀⠀⢠⡾⠃⠀⠉⠙⠛⣻⡿⠛⠋⠁⠀⣼⠇⠀⠀⢀⣴⠟
⢀⣿⠁⠀⢀⡾⠃⠀⠀⠀⢠⡟⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣼⠋⠀⠀⢠⡾⠃
⣸⡇⠀⣠⠟⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣴⠏⠀⠀⠀⢀⣠⡾⠁⠀⢀⣴⠟⠁
⣿⠀⢰⠏⠀⠀⠀⢀⣴⠟⠀⠀⠀⢠⡾⠃⠀⣀⣤⠾⠛⠁⠀⠀⣠⡾⠃
⣿⠀⡟⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠟⠁⣠⡾⠋⠀⠀⠀⠀⢠⣾⠏
⢹⣿⡇⠀⢀⡾⠁⠀⠀⣠⡴⠟⠁⢀⣾⠋⠀⠀⠀⠀⢀⣴⠟⠁
⠈⣿⡇⠀⣼⠃⢀⣴⠞⠉⠀⠀⣠⡿⠁⠀⠀⠀⢀⣴⠟⠁
⠀⠘⣿⣴⣯⡴⠋⠀⠀⠀⠀⣴⠟⠁⠀⠀⢀⣴⠟⠁
⠀⠀⠈⠻⣿⣀⠀⠀⢀⣠⡾⠋⠀⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠈⠙⠻⣶⣿⣿⣶⣾⠟⠛⠉
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣴⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿