Honeycomb Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠻⠿⣈⠱⡀⠀⠀⠀⠀⠀⠀⢥⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠈⢣⡀⠀⠙⡰⠁⠀⠈⢣⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⢣⠀⠀⠀⣠⠋⠉⠉⢧⠀⠀⠀⡠⠋⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⢀⡶⡶⠶⢇⠀⠀⠀⢠⠗⠒⠒⢇⠀⠀⠀⢠⠗⠶⡚⢇⠀⠀⠀⢠⠓⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⢎⠛⠀⠠⢆⣷⠶⠶⢇⠀⠀⠀⢈⠖⠒⣶⡏⠃⠀⠁⢈⡶⢶⠶⡅⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠈⡦⠤⠤⡎⣤⠀⠀⠈⡦⠤⠤⡎⠀⠀⠙⢋⣦⠤⢤⡇⠿⠈⠀⢘⣤⣤⣤⡃
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠘⡤⠤⠤⡞⠀⠀⠀⠘⣤⣄⢤⡎⣰⠀⠾⠘⡄⠀⢠⡎⠀⢈⡁⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⡜⠀⠀⠀⠙⣄⣀⣀⡜⠈⠧⠀⠱⣌⣀⣀⡞⠀⠀⠀⠱⣀⣈⣁⠎
⠀⠀⠀⠀⠀⠀⠀⡰⠉⠈⠩⠵⡀⠀⠀⡰⢇⡍⢸⠳⡀⠀⢀⡜⠁⠀⠀⠣⡀⠀⢀⡜⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡠⠋⠉⠉⠣⡀⠁⠀⡰⠉⠉⠉⢣⠀⠀⠀⡰⣏⠉⠉⢣⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⢣⠀⠀⠀⢠⠋⠉⠉⢣⠀⠀⠀⡠⠋⠉⠉⢇⠈⠁⠀⡠⡛⠟⠛⣆
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡷⠶⠖⢇⠀⠀⠀⢀⡗⠒⠖⢇⠀⠀⠀⢠⠓⠒⠒⣅⠋⠀⠘⢪⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⢏⠡⠇⠁⢀⠗⠒⠒⣇⠋⠀⡧⢈⠖⢶⠶⡇⠀⠀⠀⢈⠖⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⡎⠀⠀⠀⠈⡦⠤⠤⡎⠀⠸⠀⢘⠤⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣠⡎⠀⠀⠀⠘⣄⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢀⠇⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⠱⠦⣀⣯⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠘⠉⠒⠤⣄⣀⠁⠀⠠⠘⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⢀⣻⡌⢯⡑⠂⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣈⢧⠀⠊⠁⠙⢆⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢸⠘⡀⠀⠠⠀⠘⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⢸⡀⠐⠄⢀⣀⠜⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⣄⠀⠀⠀⠀⠸⡄⢀⠄⠃⣤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡤⠋⠀⠀⠈⢡
⠀⠀⠀⠈⠒⠴⠤⢄⡀⠟⠀⠀⠀⠉⢀⣀⣤⠤⠲⠄⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⢶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠤⣼⠀⠐⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠃⣴⠂⠀⠄⠂⢀⠀⠀⠃⠀⠀⠀⠈⠒⠒⠆⠀⡠⠃⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠁⢃
⠀⠀⠀⠇⠀⠀⠁⠀⠀⠈⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠙⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠢⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⣨⠖⠐⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣀⠀⢀⣠⣄⣀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠁⠀⠀⢰⠏⠀⠀⠈⢱⡟⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣸⡀⠀⠀⢀⣸⡀⠀⠀⢀⠘⠃⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⢱⡞⠉⠀⠈⠁⡞⠁⠀⠀⣴⣾⣷⣤⢰⢾⢸⠟⠉⠉
⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⢸⡆⠀⠀⠀⢀⡇⠀⠀⠀⠉⡏⠋⠀⠀⠀⠉
⠀⠀⠀⠀⣶⠞⠉⠉⠐⢤⠞⠉⠉⠒⣠⡾⠋⠉⠒⢠⣴⠞⠙⠒⢠⣶⠟⠉⠒⠀⣴⠞⠛⠒⠄
⠀⠀⠀⠀⡇⠰⡇⣧⣄⣀⣤⣄⡀⠀⢿⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠃⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠿⠿⣿⡴⠛⠢⠄⣠⡴⠚⠢⠄⣀⣴⠞⠲⠤⣀⣴⠞⠳⠄⢀⣴⠞⠲⠤
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡏⠀⠀⠀⠀⡏⠀⠀⠀⠀⡟⠀⠀⠀⠀⡿⠁⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⠼⠧⣄⢀⣠⡴⠧⣄⠀⣀⣤⠧⣄⡀⣀⡤⠧⢄⡀⢀⣠⠾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⣸⠉⠀⠀⠀⢸⠏⠁⠀⣠⣼⡏⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣠⣿⣀⠀⠀⣀⠈⠀⠀⢠⠿⢿⣅⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⢁⡞⠁⠀⣄⢻⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠈⠆⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⢻⢽⡀⡯⠌⢸⠥⠁⠾⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠑⠈⠈⠁⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⢣⡁
⠀⠀⠀⠀⠀⢀⠀⠘⢧⡀
⠀⠀⠀⢃⣼⠋⣴⠗⢠⣌⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠸⢃⣾⠋⣰⣿⣿⣿⠀⣀⣰⠚⠋⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣷⡆
⠀⡀⣀⣤⣈⠁⢼⣿⣿⣿⣿⣿⣿⣿⢴⠀⠒⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠀⠀⠀⠀⠛⠉⠁⢿⣿⣿⣿⣶⣆⠀⠀⠀⢀⣘⠿⣿⣿⣿⣿⡿⢟⣻⢿⣿⣿⣿⣿⠿⣃⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠩⠇⠒⠛⠁⠀⣤⣶⣿⣿⣿⣾⣝⢛⣽⣾⣿⣿⣷⣮⣟⣫⣵⣿⣿⣿⣷⣤⡀⣠⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠳⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣦⣄⠀⢀⣠⣴⣿⣶⣽⡻⠿⢟⣭⣶⣿⣮⣝⡿⠿⣛⣵⣾⣷⣯⣛⠿⢟⣫⣷⣿⣶⣝⡻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⣻⣵⣯⣻⢿⣿⣿⢿⣫⣷⣝⡻⣿⣿⡿⣟⣭⣮⣟⠿⣿⣿⠿⣻⣵⣭⣻⢿⣿⡿⢟⣫⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⡎⣾⣿⣿⣿⣿⣿⣷⢵⣾⣿⣿⣿⣿⣿⣮⣴⣿⣿⣿⣿⣿⣷⡎⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢿⣃⡻⢿⣿⣿⣿⣿⢟⣙⡿⣿⣿⣿⣿⡿⣟⣛⢿⣿⣿⣿⣿⠿⠃⠻⢿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣯⣶⣿⣿⣿⣷⣯⢛⣽⣾⣿⣿⣿⣶⣝⢫⣵⣿⣿⣿⣿⣮⡝⠋⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠉⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠈⠙⠻⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣰⡶⣆⣎⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡘⠺⢧⣀⡀⠆⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠘⣤⣞⠻⠟⢡⡴⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠲⣾⣁⡀⢶⣌⣙⠷⠆⣣
⠀⠀⠀⠀⠀⠀⠀⠈⠓⡎⣿⡄⢠⣿⢱⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠈⠹⢶⣄⣙⠣⢤⡄⠙⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣹⢳⣾⣯⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠠⢶⡍⠉⢣⣬⡍⠛⠂
⠀⠀⠀⠀⠀⠀⣀⢨⣯⡆⣿⠛⢻⣿⣰⣅⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢧⣤⠽⠋⢀⣤⡛⢻⡆⣅
⠀⠀⠀⠀⠀⠀⠙⠀⢸⢯⣛⠻⢟⣣⣼⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠖⠀⢀⣈⠓⢶⡄⠉
⠀⠀⠀⠀⠀⠀⠠⢀⡾⠉⢍⣻⣟⡻⠋⢷⡔⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠉⠀⠀⠀⠙⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⡹⢧⡿⢇⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠲⠒⠀⢚⣥⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠤⡽⣿⡄⢠⣾⠿⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⢈⣁⣈⣉⣏⣭⣶⣾⣃⡄
⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⣹⠧⣼⣏⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡈⡀⠂⠀⢤⣮⣟⣉⣩⣿⣭⣶⠟⢿⣮⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠻⠿⠿⠟⣓⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⠒⠛⠻⣷⢤⡤⠽⠶⣿⣿⡟⣋⣽⣿⡄
⠀⠀⠀⠀⠂⠐⠀⠀⣴⢯⡛⠛⠛⣛⡿⣦⠀⠀⠂⠀⠀⠀⠀⠀⠄⡤⢄⣿⣙⣛⣛⡿⣦⡴⠞⠛⣻⣿⣿⣿⡟⣡
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⢉⣛⣛⡻⠁⢸⡆⠀⠀⠀⠀⠀⠀⠈⠀⣿⡶⠦⣾⣿⣿⣛⣉⣿⡿⣷⣿⣿⣿⣿⣿⢏⣱
⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠈⠉⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠈⠒⠦⠭⠀⠈⠻⠿⢿⣁⣝⣵⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠐⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⣼⣾⣿⣿⡧⠀⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡀⣽⣿⣿⣷⣄⣴⢂⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠚⠈⠉⢉⠉⠙⣛⠿⠿⠿⣷⣿⣿⣾⡷⠟⠛⠿⠉⠀⠐⠂⠀⠀⠀⠢⢄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣠⢤⡒⢻⣿⣿⣿⡖⣂⣤⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠒⠉⢀⠞⠉⣤⣉⡉⠁⠀⠈⢻⠩⢷⡀⠈⠁⠢⡄⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠖⠃⢀⡾⠁⣽⣉⣉⢻⣿⣿⣷⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣛⠛⠿⣿⣿⣿⣿⡃⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⢰⠏⠙⡅⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⢻⠿⠷⠿⢿⣿⣿⠁⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠘⢿⠿⠿⣿⣿⡟⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢤⡆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣲⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⠿⢿⣿⡟⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘⠓⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠼⠿⠿⠤⠤⠤⢤⣄⣀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⢉⣳⠶⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⣅⣀⠙⠶⣤⣀⠀⠀⢀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣿⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣴⣶⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠛⠉⠁
⠀⠀⠀⢠⣴⣮⣭⣉⡉⠉⠉⠉⠀⠈⢣⡀⠀⣠⠶⠛⢋⠁⠀⠀⠉⠳⠍⠡⠔⠉⠀⠀⠉⠹⠷⣦⣄⣀⠀⢰⣦⢄
⠀⠀⠀⠀⠀⠀⢀⡤⠈⠓⠀⠀⠀⠀⠀⠑⢬⣥⡴⠞⢉⡗⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠐⠛⠉⠙⠂
⠀⠀⠀⠀⠀⣴⡥⠴⠖⠒⠒⠲⠶⠤⠤⠭⠍⠀⠀⠚⣯⡄⠚⠶⠀⠀⠀⠀⢠⣼⠁⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠁⠀⠀⠀⠀⠀⠉⠘⠃


⣿⢿⢿⠿⣿⢟⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⢃⠀⠀⠀⢠⠣⠐⠒⠀⡀
⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢰⠃⠀⠀⠈⢣⢒⣒⣒⡃⡁⠀⠀⠀⢐⢀⣀⣀⣀
⠀⠀⠀⠀⡄⠀⠑⠄⡣⠀⢀⠀⠀⡼⠉⠉⠉⢯⢧⣀⣀⣰⣿⠋⠀⠈⠱⡔⠄⠤⠠⢢⠎⠀⠀⠈⢦
⠀⠀⠀⠀⠈⡁⢀⢰⣷⣾⣿⠄⠘⢇⠀⠀⠀⣼⡷⠛⠛⠳⡷⡀⠀⠀⣠⣿⠒⠒⠒⣜⣆⠀⠀⢀⣞⠞⠛⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠈⢰⣟⠷⣼⣶⠄⢈⣷⣶⣾⣻⡁⠀⠀⠀⡹⣹⠿⠿⣽⣇⠀⠀⠀⢸⣮⠿⠿⢯⣯⠀⠀⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⢠⡞⠀⠀⠀⢳⡱⣤⣤⡼⡽⠁⠀⠀⠘⣞⢦⣤⣴⢿⠃⠀⠀⠀⢳⢳⣶⣶⡎⠀⠀⠀⠀⠀⢀⠂⠀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⣀⣀⣾⠟⠉⠉⠙⣿⣆⣀⣀⣴⡿⠉⠉⠉⢯⢳⣀⣀⣠⣫⠋⠈⠉⠹⡄⠀⢀⣀⠰⠇⢂⠉⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠁⠙⣄⠀⠀⢀⣞⡜⠛⠛⢮⢧⠀⠀⠀⣼⡷⠛⠛⠳⣷⡄⠀⠀⢠⠏⠀⣘⣽⣷⣿⢄⠐⣈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣶⣦⢤⣶⡆⠀⢈⣿⣻⣏⢞⠀⠀⠀⢈⣿⣿⣾⣾⡹⡁⠀⠀⠀⡹⣹⠿⠿⣅⠀⢶⡿⠵⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡒⠢⣿⣿⣾⣃⠁⣠⠏⠀⠀⠈⢮⢧⣤⣤⢞⡞⠀⠀⠀⠱⡝⠦⠤⠞⣽⠁⠀⠀⠘⣦⢀⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠂⢹⠜⠛⠁⠀⠘⢆⠀⠀⢠⣯⠏⠉⠉⠻⣳⣀⣀⣀⣾⡟⠉⠉⠙⣜⣆⣀⣀⣴⡿⠉⠉⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠠⠋⠀⠀⡀⠀⠀⣨⠿⠿⢧⣳⡀⠀⠀⢠⢿⠞⠛⠻⡼⣄⠀⠀⠀⣼⡞⠛⠛⢾⣧⠀⠀⠀⣰⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⣳⣹⣶⣶⣻⡏⠀⠀⠀⢘⣟⣶⣶⣞⢿⠀⠀⠀⠀⣿⣹⠿⢿⡁⠠⢿⡷⣆⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⡴⡿⠃⠀⠀⠙⣿⢤⣤⡤⢿⠏⠀⠀⠈⢯⠳⣤⣤⢞⡟⠀⠀⠀⠹⡄⠀⣷⣾⣿⡔⢒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⣀⣰⠣⠂⠀⠀⢌⢦⡀⠀⣠⣾⠏⠉⠉⠹⣷⣄⣀⣀⡜⠁⠀⠉⠁⡆⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠅⠀⠀⠀⢀⠊⠍⠩⠥⡻⡀⠀⠀⢠⠏⠈⠉⠉⠀⠀⠀⠀⠀⠑⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢡⠂⠀⠀⠀⢱⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⣠⠂

⣿⣿⣿⠿⣿⠿⢿⣿⡿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣮⣶⣷⣶⣿⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⣶⠆⣠⡀⠛⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⣾⠟⢀⣾⣷⣷⠀⠀⠃⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣾⠋⣰⣿⣿⣿⣿⣁⣄⣴⠏⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣤⢄⡈⠰⢿⣿⣿⣿⣿⣿⣿⣿⡷⢋⠀⠙⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠀⣿⣿⣿⣿⣿⣾⡆⠠⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⡟⠉⡟⠓⠚⢻⠅⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⡀⠀⠊⠁⠀⠄⡀⠀⠀⠀⠐⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⠐⠈⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠿⢿⣿⣿⡟⠀⠹⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣄⠀⠈⢻⣦⣄⠜⠀⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡛⠟⠀⠒⠂⠘⠣⢴⡂⡀⠀⠠⣐⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠴⣿⣿⣿⠏⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⡿⠓⠲⠂⠀⠀⠀⠀⠤⠬⠓⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⣀⡎⠙⠋⠁⠒⢁⠤⠻⠛⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣤⣶⣿⣿⣇⠀⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠗⠀⣰⣾⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠟⠁⠀⠀⠀⠈⢹⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣶⣿⠀⠀⠀⣦⣄⣀⠀⠀⠀⠀⣆⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣄⠀⠀⢸⣿⣿⠀⠁⢠⣾⣉⣷⣼⣶⣯⣀⣠⣤⣤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣤⣼⣿⡟⠀⠀⠾⠿⡯⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠰⠂⡜⠛⠿⡛⡿⢿⡿⠛⣁⣴⠟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢠⠃⡇⠸⢱⠛⢉⣥⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢰⡘⡄⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠙⢆

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⣠⣝⣃⣀⡠⡀⠀⠀⠀⠀⠠⢤⡒⢦⠀⠀⠀⠀⠀⠀⠘⢾⣚⢀⡋⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤
⠀⠀⡀⠀⠸⣿⣏⠟⢿⣿⢹⡆⠐⠔⠀⠀⣀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⢀⠀⢰⣶⣶⠄⠫⢖⡟⠍
⠀⠀⠉⠷⣦⣼⣿⣶⣾⣟⣿⢿⣤⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣾⣷⠻⣋⡁⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠈⠙⠳⢤⢿⣷⢖⣽⢿⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣟⢷⣦⣿⢇⣩⠴⡶⠻⢧⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⣷⣿⡇⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡄⠀⠟⢨⠛⡹⠿⢀⣾⠁⠀⠀⣀⠙⠂
⠀⠀⠀⠀⠀⣄⡀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡏⣿⣶⡀⣀⣀⡧⣠⡿⠿⠻⢿⡰⡯
⠀⠀⠀⠀⠠⣯⡸⠋⠀⠀⠀⠀⠀⠀⢀⡍⢶⣶⣦⡙⠀⠀⢀⣿⣧⢰⣵⡿⠟⠙⣿⣿⣷⡽⣆⠄⢈⢙⢧⣥⣤⣤⡀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠿⢻⣷⣦⡇⣰⣿⣿⡿⣰⣴⣿⠛⠁⢨⣿⣿⣦⠀⣿⣿⠿⣳⡶⣶⣭⡱⡿⠏⢹⣭⣿⣷
⠀⠀⠀⠀⠀⠀⣤⣤⢤⣤⣄⡄⠀⢿⣿⡏⢛⣃⣉⢑⢉⣤⣿⣷⡼⠿⠿⠿⣫⣶⣶⣶⣄⢯⣐⠓⢺⣿⢘⡆⠄⠬⢊⠤⢶⣤⡤⡶
⠀⠀⠀⠀⠀⠀⣿⣛⠿⠛⠿⢿⠂⣄⡛⠀⠐⣿⣿⡟⠿⣿⡿⠟⡱⣶⣶⣦⡹⣿⡿⢹⡿⢊⣛⣻⠞⣷⣿⣿⣷⣆⢗⡰⣺⣿⣧⠃
⠀⠀⠀⠀⠀⠀⠘⢿⣿⢲⣴⣾⠙⠾⣿⡌⠢⠄⠹⠙⣏⣉⣿⣄⢺⣿⠛⣻⠓⢤⣤⣄⢺⣿⣿⣿⣷⢻⡛⢿⠿⡿⠘⠻⠿⢟⡣⢤⡀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣝⠑⣢⣛⡀⣴⣶⣦⡹⢛⣟⠿⠟⣠⣤⣤⡀⣴⣿⣿⣿⠎⠿⠮⠦⠋⢠⣬⣍⢡⣺⣿⣶⡀⣿⣶⣿⣿⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡾⠻⣿⠏⣉⠙⣿⠓⣶⣶⣦⢚⣸⣿⣿⣿⢈⣛⠛⢡⣊⣿⣷⡄⣓⡛⠛⣿⡏⢿⣿⡿⣃⣙⠿⠟⣫⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⣧⣶⡄⢀⣀⠄⠻⠹⣿⠇⠉⠙⠋⢡⣼⣿⣿⡜⠿⡻⠝⣣⣬⣍⡚⢩⣶⣶⣤⢸⣿⣿⣿⡆⣿⣿⣿⣇⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠐⠚⢀⢰⡄⠑⠆⠁⢻⣷⠘⡻⠿⠋⢤⡀⠼⠀⠟⠛⢿⡇⠸⠛⠻⠟⡘⠻⠿⢟⡃⠙⣛⣛⡻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣀⠀⡈⠋⢨⡹⢆⣉⠁⠄⣰⡆⠈⢉⠀⠿⢀⣀⠛⠁⠈⢿⡆⢀⣬⡕⡷⢠⡾⠿⣿⣦⠠⠿⠏⣰⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣏⡀⠤⢶⡄⢪⣼⠇⡀⣉⡀⢀⣼⠇⠀⠀⣿⡷⠀⠒⢛⠁⠓⢚⣁⣀⠀⠀⡉⠟⡃⢻⣷⡆⠻⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣾⣿⣟⣉⠁⠒⢶⡄⠠⣿⠇⠐⢶⣦⡀⠐⣭⡅⡼⢿⣿⣧⠐⠁⠙⠿⠀⣸⣟⠃⠻⠾⠟⡷⢺⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣯⣉⣿⣤⣼⣏⠀⢈⣿⠄⠀⢨⣿⠇⠂⠟⠃⠑⠄⠈⠿⣠⢲⣶⡄⢜⠉⣿⢧⣟⣿⣞⣧⣴⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⣿⣷⣶⣿⡴⣮⣭⡶⢿⣦⣴⠋⠈⣿⣷⣄⢶⣾⣷⡷⠼⠿⠛⠀⠉⠋⠚⠻⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣧⣿⠿⠿⠦⠞⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣁⣀⣈⣈⣉⣉⣀⣀⣁⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣼⣶⡄⢀⣤⣶⣦⣤⣄⣄⡀⠀⠀⠀⠀⣐⣺⣿⣷⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣿⣿⣿⣿⡇⢸⣿⣿⣽⣯⣿⣿⡇⠀⢤⢀⣀⠈⡳⠆⢹⣿⣿⣦⠀⠀⡌⠛⠓⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⠻⢯⣿⣿⠿⠟⠃⡙⢿⣿⣿⣿⣿⡿⢇⠀⠀⠀⠀⠐⠻⣦⣼⣿⣿⣿⡖⠊⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⠉⠀⣰⣿⣶⠿⣷⣮⡙⣩⣵⠶⠏⠀⠀⠀⠀⠀⠀⠈⢹⠧⠉⣩⣿⢾⣃⡈⠢⣆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⣿⣿⠀⣾⣯⣿⣿⣿⣯⣹⡇⠉⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⢣⠴⡾⠋⢴⡿⢿⣽⡄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣿⣿⠿⣃⠰⢿⣿⣿⣿⣯⣿⣿⠃⠀⢀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⢆⠱⣶⣁⣼⠟⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⣩⣴⠾⠛⠋⠂⢝⠫⠿⢚⣩⠴⢲⣦⣀⠀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠚⡆⠈⠙⠤⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢰⡯⣵⣾⣿⣷⣝⣓⠀⡶⣟⣿⣿⡿⠂⠀⠂⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⣿⣿⣷⣿⡏⣿⠀⣿⢿⣿⣿⣷⣶⣾⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣈⠻⣻⣿⣷⠛⠀⠛⠿⢿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠗⠛⠛⡁⡀⠺⢷⣦⡘⠾⠟⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠋⠀⡇⠀⠀⠉⠉⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⣨⣤⣈⡐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣶⣿⣦⣸⣷⣦⡄⢀⠀⢾⣷⣴⣶⡔⡀⡀⢱⣾⣛⣿⣿⣿⠋⠁⠀⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣿⣿⣻⣽⣟⢩⡁⢸⡷⢐⣨⣭⣥⡂⢾⡇⢈⡍⢻⣿⣿⣿⢿⣿⣷⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠧⠿⠿⢿⣿⣦⠝⢦⠁⢹⡒⢿⣿⣏⠈⡴⠪⣰⠾⠿⠿⠿⠿⠛⠃⠁⢸⡀
⠀⠀⠀⠀⡀⠄⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡏⠉⣰⣿⣿⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢬⣁⠂⢄⡀
⠀⠀⠀⠀⠀⠙⣧⡐⠄⡀⠀⠀⠀⠀⠀⢀⡀⠠⠀⢸⣷⣼⣿⣿⣿⣇⠀⠄⢀⣀⠀⠀⠀⠀⠀⢀⡠⢈⣜⠀⢀⢠⢰
⠀⠀⠐⠀⠀⣶⣾⣿⣷⣤⣤⡀⠀⢁⢀⣴⠆⣠⡀⣀⣿⠿⣿⣿⣿⣃⢀⣄⡠⢦⡀⠈⠀⠀⣀⣤⣾⣿⣟⣿⣿⡞⠈
⠀⠀⡃⠀⢀⣿⡿⣿⣿⣿⣿⡿⠀⢠⢞⣱⣷⠌⣫⣁⣊⣀⣤⣽⣗⣈⣝⠩⣶⣌⠳⡜⠀⠻⢛⢿⠿⣿⣿⣟⡉⠀⠀⠅
⠀⠀⠈⠢⣌⠙⠷⡾⠟⣫⣵⣾⠿⠒⢬⡑⠏⢰⠁⡿⠋⣉⣉⣙⣿⠻⠀⡆⠙⠋⠁⠒⠿⣿⣶⣤⡉⠻⠿⠋⢁⠔
⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠉⠀⠀⠀⠀⠈⠰⡾⣀⣿⠛⢊⣛⣻⣿⢿⢀⢷⠆⠀⠀⠀⠀⠀⠉⠛⠛⠂⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⡜⠁⣿⠸⡛⠛⠛⣿⣛⠋⣿⠈⢣⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠐⠋⢰⢀⣿⠤⠹⣶⣿⣿⠏⣤⢿⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠿⣦⣌⣹⣥⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣈⠙⠉⠁⣀⠄⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠓⢦⣄⡀⠀⠀⢀⡤⠞⠉⠀⠈⠙⠷⣄⡀⠀⢀⡴⠚⠁⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠈⠹⡆⡀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢻⣠⠏⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡳⣤⣀⠀⠀⠀⠀⣀⡴⢋⣠⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⡾⠹⣄⡀⠀⠀⠀⠀⠀⣀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠙⠳⣭⣛⠦⠴⠛⣥⠞⠋⠀⠈⠙⠿⣿⣦⣄⣀⡤⢞⡭⠂⠒⠾⣿⣷⢦⣤⢶⣻⠟⠂⠀⠈⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠉⢻⣰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⣡⡴⠋⠀⠀⠀⠀⠀⠉⢳⢀⡏⠁⠀⠀⠀⠀⠀⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢧⣄⠀⠀⠀⠀⠀⠀⢀⣠⠞⠹⣄⡀⠀⠀⠀⠀⠀⢀⣠⠞⠸⢦⡀⠀⠀⠀⠀⠀⠀⣠⠾⢀⢧⣀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠛⢮⣝⡲⣤⣀⡤⢞⣫⠖⠀⠀⢦⣝⠳⢤⣀⣤⢞⡫⠗⠛⠙⠲⣭⡳⢦⣄⣠⡴⣛⡵⠞⠉⠳⢯⣳⢦⣄⣤⠞⠋⠁
⠀⠀⠀⠀⢀⡞⠋⠀⠀⠀⠀⠀⠈⠙⡆⢠⠞⠋⠀⠀⠀⠀⠀⠈⠛⢦⣉⡖⠋⠀⠀⠀⠀⠀⠀⠙⠳⣌⢡⠞⠁⠀⠀⠀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠇⠹⣄⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⡴⠋⠸⣦⡀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⡴⢞⡥⠂⠀⢬⣝⡳⢦⣄⣠⠴⢋⡵⠞⠉⠛⢮⡙⢶⣄⣀⣠⠖⣫⠴⠛⠛⠶⣍⡓⠄⠀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠞⠋⠀⠀⠀⠀⠈⠙⠳⡌⢠⠞⠉⠀⠀⠀⠀⠀⠙⠆⠈⠉⡵⠋⠁⠀⠀⠀⠀⠈⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠘⣦⡀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠳⣤⡀⠀⠀⠀⢀⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⢀⣠⠖⠋⠀⠀⠀⠀⠙⠳⢦⣤⠴⠞⠉⠀⠀⠀⠀⠀⠙⠳⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠰⠃⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⡀⠈⠠⠀⠀⠀⢃⣂⣀⣀⠀⠃⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠟⢰⣶⣶⣆⣴⠋⠁⠈⠉⠙⠶⣶⣄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⡉⡀⠀⣢⣤⣄⡀⠰⠤⣿⠇⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢡⠈⢇⣼⢻⣃⡀⠘⠛⠋⠉⠉⠛⢲⡦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠻⣿⣿⣷⢃⣢⠀⣠⢤⡤⠏⢀⠉⠉⠷⣄⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⡙⠻⠿⠿⠋⣀⣵⣿⣅⠀⠀⠀⢰⡄⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠋⠐⢀⣠⢶⠿⠻⣿⣧⡀⠀⢐⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣖⠀⠂⠀⠀⠈⠁⠉⠋⢠⣞⠉⠉⢰⣾⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⠀⣴⣿⣧⡀⠀⠀⠀⢀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣤⠟⠋⣿⣿⣿⣆⠀⠸⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠈⠉⠋⢀⠑⢸⣿⣿⡉⣀⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠘⠣⠘⣿⣿⡉⠀⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢿⣿⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁

⠀⠀⠀⢀⡾⠉⠉⠉⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠉⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠉⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠉⠉⠉⢳⡄
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠻⣄
⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠛⠛⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠛⠛⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛
⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⡽⠛⠛⠛⠛⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⠛⠛⠛⣯
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠈⢷⡀
⠶⠶⢾⡁⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠶⠶⠶⢾⡁⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠶⠶⠶⢾⡁⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠶⠶⠶⢾⡁⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶
⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⣻⠦⠤⠤⠤⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⣻⠦⠤⠤⠤⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⣹⠦⠤⠤⠤⠴⣏⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⠤⠤⠤⠴⣟
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠙⣆
⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣤⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣤⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⣤⣤⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠈⢧⣀⣀⣀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣀⣀⣀⡾⠁
⠀⠀⠀⢠⡟⠁⠁⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⠻⡄
⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣀⣀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀
⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉
⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⢀⡼⠛⠛⠛⠛⠛⢧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠛⠛⠛⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠛⠛⢷⡀
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⢳⡄
⠚⠓⢿⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠒⠒⠒⠓⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠚⠓⠒⠚⢻⡅⠀⠀⠀⠀⠀⠀⠀⢠⡿⠒⠛⠛⠒⢻⡅⠀⠀⠀⠀⠀⠀⠀⢀⡿⠚
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⣻⠶⠶⠶⠶⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⠶⠶⠶⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⠶⠶⠶⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⠶⠶⠶⠶⣏
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠘⣧
⠤⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⢘⡧⠤⠤⠤⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⢘⣧⠤⠤⠤⠤⣼⡃⠀⠀⠀⠀⠀⠀⠀⠘⣷⠤⠤⠤⠤⢼⡃⠀⠀⠀⠀⠀⠀⠀⠈⣷⠤
⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠈⢷⣤⣤⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣤⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣤⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⡞⠁
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠹⣄
⣀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀
⠉⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠉⠁⠙⢦⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉
⠀⠀⠀⠘⣧⣀⣀⣀⣀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠘⢧⡀⣀⣀⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠈⢧⡀⣀⣀⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣀⣀⣀⣼⠃

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


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⢄⠀⠀⠀⢀⠤⠤⢤⣇⠀⠀⢨⡧⠶⠶⡄⠀⠀⠀⢠⠖⠒⢦
⠀⠀⠀⠑⠀⠂⣼⣴⡦⠀⢮⠀⠀⢀⣯⠿⠿⣿⡅⠀⠀⣸⡤⠤⢤⣯⠀⠀⢀⣷⠶⠶⣄
⠀⠀⠀⠀⠉⠁⣿⠿⣿⡦⠈⡷⠶⣞⣇⠀⠀⢨⣿⠶⠾⣿⠀⠀⠀⣿⡿⠿⢿⣇⠀⠀⢨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣞⠀⠀⠈⣿⡶⠶⣿⡃⠀⠀⢹⣷⠶⣞⢏⠀⠀⢈⣿⠶⠶⡏⠀⠀⠀⢀⠄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠾⡏⠀⠀⢘⣷⣶⣶⣿⠁⠀⠈⣻⣷⣶⣾⡏⠀⠀⢘⠆⢠⢶⣬⡄⠂⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣦⡀⠘⣦⣤⢾⡋⠀⠀⢻⣷⣤⣴⣟⠀⠀⠘⣿⣦⣴⡋⢠⣶⣯⣿⡏⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢼⣿⣾⡟⠁⡞⠁⠁⠹⡷⣤⣤⣿⠋⠀⠈⢿⢦⣤⡾⡟⠀⠀⠹⣄⣉⣁⠁⠁
⠀⠀⠀⠀⠀⠀⠐⠁⡀⢀⠆⠉⠀⠀⠱⣄⣀⣼⠏⠀⠈⢻⣦⣤⡴⡿⠁⠀⠙⡵⣤⣤⢾⠏⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⡴⠉⠉⢻⣣⣀⣠⣾⠋⠉⠙⢿⣄⣀⣴⡟⠉⠉⠹⡧⣤⣤⠎⢠⣤⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣴⡟⠉⠉⢿⣆⣀⣠⣾⠋⠉⠱⡷⣀⣀⣼⠟⠉⠉⢦⠈⣯⣽⣿⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⡜⠀⠀⠀⠳⣀⣀⣠⡿⠉⠉⢻⣦⣀⣀⡞⠀⠉⠩⡏⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠢⢧⣀⣀⡰⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡄⠀⡴⠺⠋⠷⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⢦⡟⠀⠀⠀⣿⣼⣋⢰⡋⣷⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⢀⣀⣀⣀⠀⠀⢯⣤⡉⣥⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⠃⠀⡴⠋⣴⠲⡌⠙⣆⠀⠺⠿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⢀⡽⠻⣧⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣶⠆⠈⢧⡈⠧⠤⠎⣠⣮⠤⣴⠋⠉⢹⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡉⠛⠛⠋⢹⡅⠀⣨⠤⠦⢬⡁⠀⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠞⡇⠀⠀⢸⠋⠉⣼⠁⠀⠀⠀⢹⡌⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⢦⡤⢻⡄⠀⠀⠀⣸⠣⣤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⠀⣩⠓⠒⢫⡁⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⢤⣤⠾⠉⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁⠘⠲⢄⡠⠂⠀⠈⠙⢢⢀⠀⠀⠈⠑⠢⢠⠐⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣷⣤⣀⣠⢔⠃⢷⣤⡀⣀⣴⡊⢸⣲⢄⣀⠤⠊⠘⣦⣄⣀⡠⢖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⢹⡞⠁⠀⠀⠈⢻⡟⠁⠀⠀⠈⢱⠰⠊⠀⠀⠈⠁⢱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⢰⡀⠀⠀⠀⢀⣾⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠐⠫⣖⠤⢔⡫⠀⠨⢷⣦⢀⡾⠗⠐⠶⡦⠤⡚⠅⠀⢭⡲⢴⠾⠑⠊⠛⢶⠤⠶⠟⠂
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠈⢰⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠂⣧⡀⠀⠀⣠⠼⠣⣀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠠⠨⡀⠀⠀⠀⣀⠇⣇
⠀⠀⠀⠀⠐⠉⠉⠳⣔⠟⠊⠀⠉⠛⠗⡫⠁⠀⠈⠛⢷⡋⠁⠀⠈⠒⢄⠀⠀⠀⠀⠈⠑⠖⡨⠒⠈⠐⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡤⠋⠢⢄⣀⣠⠴⡂⢳⣤⡀⢀⠤⡪⢗⠤⣀⢀⣠⢞⢍⡠⣀⠀⠀⢘⡈⠓⠄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠑⡎⡖⠉⠀⠀⠉⠊⡕⠉⠀⠀⠙⢦⠙⠊⠁⠀⠈⢳⠁⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⣀⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁⠈⠓⠤⠴⠊⠁⠀⠀⠀⡠⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠶⠚⠋⠉⠉⠀⠀⠉⠀⠀⠈⠉⠉⠒⠒⠶⠤⠤⠤⠤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⣰⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⣑⠁⠀⠀⡀⠀⠙⠲⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢇⠀⠀⠀⠀⠀⠀⠿⡠⢄⠀⠀⢀⣀⣀⣀⣈⣹⣷⣤⣼⡀⢀⣧⣀⣴⣧⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠰⡔⣃⣐⣀⣂⣐⣊⣐⣿⣬⣅⣉⣈⣡⣍⡤⣴⣶⡴⠶⡶⠋⣩⣴⣶⣶⣶⡚⠳⢯⣛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠉⡙⠉⠉⠉⠉⠀⠍⡸⠁⠈⠉⠉⠉⠅⠀⡢⢊⣩⠾⢻⠶⠛⣍⢣⠉⠀⠀⣿⠀⠀⠘⡆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⣀⣼⡀⢀⣴⡀⢀⡿⢤⣀⠀⠀⠀⣨⠀⢠⡚⠾⡏⡀⠀⠈⣳⣄⠈⣆⢱⠀⠀⠀⠃⠀⠀⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⢀⠈⠉⠀⠉⠉⠀⠀⠈⠉⠙⠉⢉⣟⣟⣣⡤⠾⢦⣤⠞⠙⠳⠶⢾⡄⢟⡲⠰⠧⠤⢂⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡞⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⣒⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢿⡘⣽⡗⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘⣦⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⡀⠠⡠⠒⠉⠀⠀⠀⠀⠀⠐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⢄⠅⠐⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⢀⡀⠞⠀⠀⠀⠀⠀⠖⠀⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⠈⢢⡀⠀⠀⣐⡀⠀⠈⠛⠀⠀⠂⠀⠀⠰⠀⡌⠀⠀⠀⢹⠐⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⠑⠤⠚⠓⠀⠀⠀⠤⠀⠀⡃⠀⠀⢀⡀⠈⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉


⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⡄⠀⠀⠀⠀⠀⣰⡶⠛⠀⣤⣤⣤⣤⣤⡄⠀⠀⠀⢀⣼⠋⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⢶⣤⠾⠋⠀⠀⠀⠈⠳⢦⣴⢶⣟⠁⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⠟⠁⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣷⠀⠀⢀⡴⠟⠉⠁⢴⠄⠉⠙⠷⣄⠀⠀⢰⡏⠀⠀⠀⢰⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⣤⡾⠇⠀⢠⡟⠁⠛⠀⠀⣴⠀⠀⠘⠃⠙⣧⠀⠀⠿⣦⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⣾⠁⣤⠀⠀⠀⢿⡀⠀⠀⢠⡄⢹⡆⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⣿⣀⠀⠀⢻⡄⠁⠀⠀⠀⠈⠛⠂⠀⠀⠀⣾⠁⠀⢀⣸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠹⣧⠀⠈⢿⣄⠺⠀⠀⢀⡀⠀⠸⢂⣼⠏⠀⢠⡿⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⢶⣟⠀⠀⠀⠙⠳⣦⣤⣍⣥⣤⡶⠛⠁⠀⠀⢘⣷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣴⠟⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⣧⣀⣀⣀⣠⡟⠉⠉⠛⣿⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⠀⠀⢀⠀⠀⢠⠀⠀⠀⢀⠀⣀⠠⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠊⠸⠁⣇⡱⢪⣸⠀⣄⡇⢇⡀⢇⠸⠸⡜⢸⠸⡀⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⠛⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠶⠶⠶⠶⠶⢶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⡼⡉⢉⡤⠈⠉⠹⣌⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢏⡔⡛⡛⠛⠛⠛⢦⡹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣾⢣⠞⠐⠀⠉⠀⠈⠀⠀⠘⣎⢿⣄⠀⠀⠀⠀⠀⠀⢠⡿⢣⢏⠐⠈⠀⠀⠀⠀⠀⢳⡹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣛⣛⣛⣛⣛⡛⢧⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢂⡿⠛⣛⠛⠛⠛⠛⢿⡅⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⡷
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢣⠎⠂⠀⠀⠀⠀⠙⣎⢧⡱⡄⣁⡀⠀⠀⠀⠀⡼⣡⡟⡴⠫⠀⠀⠀⠀⠉⢦⢻⡜⢆⠠⢀⠀⠀⠀⠀⢀⡼⣡⡿⠁
⠀⠀⠀⠀⠀⠀⣰⡟⣱⠃⠀⠁⠀⠀⠀⠀⠀⠘⢎⢳⡙⠤⠥⠤⠥⠤⠞⣴⢋⡜⡁⠁⠀⠀⠀⠀⠀⠈⢧⠻⣎⢧⣼⣤⣍⣤⣠⠞⣴⠟
⠀⠀⠀⠀⠀⠀⠹⣧⠳⡐⠀⠀⠀⠀⠀⠀⠀⢀⡜⣰⠟⣛⣛⣛⣛⣛⡛⢷⡸⡄⢄⠀⠀⠀⠀⠀⠀⠀⢠⢇⡿⠶⠶⠶⠶⠶⠶⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠙⣧⡹⡄⢰⠐⠀⠀⠀⢠⠞⣴⢫⠞⠐⠖⠒⠀⠀⠘⢎⢳⡘⣄⠐⡀⢀⠀⠀⠀⣰⢣⡞⣱⠋⣉⠉⠉⠉⠙⢎⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣘⣒⣒⣒⣒⣒⣋⡾⣡⠋⠀⠀⡀⠀⠀⠀⠀⠈⢧⢻⡜⠢⠤⠤⠤⠤⠞⣡⠟⡼⠁⠢⠀⠀⠀⠀⠀⠈⢧⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣭⡭⣭⡭⢭⡙⢧⡹⡄⠄⠀⠀⠀⠀⠀⠀⠀⡼⢡⠟⣛⣛⣛⣛⣛⡛⢯⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⣽⠇
⠀⠀⠀⠀⠀⠀⠀⣰⡟⡱⠋⠠⠂⠀⠀⠀⠘⣌⢷⡙⡄⠀⠂⠀⠀⠀⢀⡞⣰⢏⡜⠁⡂⠀⠀⠀⠙⣎⢷⡙⡌⢠⠠⣀⠀⢀⠀⣠⢋⣾⡏
⠀⠀⠀⠀⠀⠀⣼⠟⡼⠑⠀⠀⠀⠀⠀⠀⠀⠘⣎⢳⣜⣒⣒⣒⣒⣒⣋⡼⢣⠎⠄⠀⠀⠀⠀⠀⠀⠘⢦⢳⡜⠦⠤⠬⠥⠤⠴⣡⠞⠀⣿
⠀⠀⠀⠀⠀⠀⠹⣦⠳⡘⠀⠈⠀⠀⠀⠀⠀⢠⠞⣼⢋⡭⠭⠭⠭⠭⣍⢷⡹⡄⠀⠀⠂⠀⠀⠀⠀⠀⡸⢣⡟⠛⠛⠛⠛⠛⠛⠋⣀⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠱⡌⢰⠀⠄⠀⠀⣠⢋⡾⣡⢏⠀⠀⠀⠀⠀⠈⢯⢳⡙⡄⢁⣄⣀⠀⠀⢀⡼⣡⠏⠀⠀⠀⠀⠀⠀⣀⣀⡾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣘⣚⣓⣓⣚⣚⣡⡟⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⣻⣜⠶⠶⠶⠶⠶⢞⡴⣣⣤⡀⣰⣿⡆⠀⢼⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⢠⣤⡄⠈⢳⡘⣄⠂⡀⠀⠀⠀⠀⠀⢀⡞⣱⠟⣛⣛⣛⣛⣛⣛⢷⡏⠈⠛⠋⣾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⡇⠀⢸⣷⡜⢆⠁⠆⠆⠀⠀⢠⠟⣴⢋⠞⠠⠆⠀⠀⠀⠘⢆⢻⣆⠀⠀⣿⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⡆⠻⣤⣼⢿⠿⣌⣉⣉⣙⣛⣛⣫⡾⣡⠋⠈⠀⠀⠀⠀⠀⠀⠈⢧⢻⣦⠀⢿⣷⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⡿⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⣼⠆⠀⠀⠸⣯⣠⡀⠀⠀⠀⠀⠀⠀⢳⡘⣄⠆⠒⣤⡔⠄⢀⡞⣱⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣀⣴⠟⠀⠀⠀⠀⠈⢹⡇⠀⣀⠀⠀⣠⣄⠀⠻⣜⣒⣒⣒⣒⣒⣋⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠿⣤⣿⠀⠀⢿⠘⣇⠀⠈⠉⠉⠉⠉⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡆⠻⣷⣀⣴⠟⠳⠿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠀⠠⣿⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢂⡤⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⡟⣡⣿⣿⡇⣀⡴⠒
⠀⠀⠀⠀⠀⠀⠠⢠⠴⠈⢐⣿⣿⢿⣿⣿⣷⢃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⡿⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠘⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄
⠀⠀⠀⠀⠙⠿⣿⣿⠛⠿⣿⠋⢐⠀⠀⠀⢠⣶⣿⣿⣿⣿⠃⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠓⢀⣼⣷⡆⠐⠀⣰⣿⣿⣿⣿⡭⠥⠄⠀⠀⢀⠠⠤⠞⠋
⠀⠀⠀⠀⢀⣀⣠⡄⠀⣀⡌⠛⠁⠂⠤⠛⠋⠉⠉⠉⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⡀⢀⣰⣏⣤⡀
⠀⠀⠀⠀⠀⠈⠙⠿⣿⠋⠁⠀⠈⣻⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠈⣷⣄⠀⢀⡴⣄⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣤⣿⠏⠀⠾⢿⣿⣿⣿⣿⣿⡷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠛⠉⠀⠀⠈⠈⠉⠋⡟⠻⣩⠴⢋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⡄⡄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠶⠶⠶⠶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣤⣀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢀⣤⣶⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠈⠙⠿⣶⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣶⡾⠛⠉⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠶⠶⠶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠙⢷⣄⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡏⢙⣿⠀⠀⠀⠀⠻⣧⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠾⠃⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣱⡟⠛⠀⠀⠀⠀⠀⠹⣧⠀⠈⠿⢶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⢰⣿⠋⠉⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋⢀⣀⣀⡀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠉⠉⢻⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠰⠶⣶⣶⡾⠿⠟⢋⣁⣀⣀⢸⡏⢹⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⢸⡏⢹⣿⢸⡇⢸⡇⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠸⣿⣄⣀⡀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢠⣶⢶⣶⢸⡏⠉⣿⢸⡇⢸⣿⢸⡇⢸⡇⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢶⡄⠀⠸⣧⠀⠀⠀⢸⣿⠀⣿⢸⡇⠀⣿⢸⡇⢸⣿⢸⡇⢸⡇⠀⠀⠀⣰⡟⠀⢀⣶⠾⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄⠀⠹⣷⡀⠀⢸⣿⠀⣿⢸⡇⠀⣿⢸⡇⢸⣿⢸⡇⢸⣧⠀⢀⣴⡿⠀⠀⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠈⢿⣦⡘⠿⠶⠿⠿⠿⠾⠿⠿⠷⠾⠿⠿⠷⠾⠇⣠⡬⠉⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⠶⠶⠶⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⣠⣶⠿⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⠿⢷⣤⣀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠛⠉⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠈⠛⠿⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣝⡲⢄⣠⠴⣚⣓⠦⣄⡠⢖⣫⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⢸⡇⣿⣿⣿⣿⢸⡇⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣮⣝⢟⣫⡼⢷⣭⣛⣛⣥⡾⢧⣝⡻⣋⣵⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣵⣿⣶⡍⠛⠻⢶⣷⣮⠙⡿⠥⣺⣦⡍⣿⢫⣶⣿⣾⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢿⣿⡿⢃⠀⠀⠀⠉⠻⣾⣷⣿⣋⢉⣷⣿⡘⢿⣿⡿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⡤⣚⣭⣝⠳⣶⠾⣫⣤⣘⠛⢓⡆⠁⠈⠛⣉⣤⣝⣛⣽⡷⣶⠞⣫⣭⣳⢤
⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⡇⣿⢸⣿⣿⠟⢧⠀⢳⡀⠀⠀⢹⣿⣏⣀⣿⡇⣿⢸⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠓⢭⣛⣫⡴⠿⢶⣝⡻⣆⠈⢧⡀⠙⣰⠈⢻⡳⣉⣛⣉⡴⠿⢦⣝⣛⠭⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣾⣿⣷⡌⣿⢻⣶⣾⣯⢰⠏⠀⢸⣿⡎⣿⢡⣾⣿⣷⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡻⣿⠿⣣⣿⣘⠿⡿⢟⣀⠀⠀⢸⣿⣃⣿⣜⠿⣿⢟⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⢟⣩⣮⣝⢳⡾⣛⣥⣤⣴⣿⠟⣫⣵⣭⡻⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⢸⡇⢿⣿⣿⣿⢸⡇⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣫⠵⠊⠙⠲⢭⡭⠖⠋⠑⠮⣝⠵⠚⠁

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣾⣶⣶⣤⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⣀⣴⣾⣿⡛⣏⢻⣟⣿⣯⡻⣿⣿⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⡿⠉⡂⠤⠜⢛⡿⢿⣿⣿⣿⣿⣿⡒⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣤⠾⠻⠯⣷⣄⠀⠀⢠⠎⠔⠁⢰⣾⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠘⢿⣟⣻⠀⠈⣿⢀⢠⠃⣀⣰⡧⣀⣶⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠈⡟⠲⠶⠶⠊⢉⣿⣿⡄⠀⠀⠘⢿⣧⢷⡄⣸⣶⣽⣰⣿⣿⣿⣿⣷⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠘⡃⠀⠀⢀⠠⠀⠀⡀⠽⣩⡥⠀⠀⠀⠀⢹⠾⠥⠟⠿⣿⣶⣿⣿⣿⠟⠻⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢠⡇⠈⣹⡀⠀⢀⡠⠔⠀⡠⠀⠿⠾⢫⣤⠀⠀⠚⠡⠂⠀⢀⡼⠿⠛⠋⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢇⠀⢧⠀⠉⣧⠀⠄⠀⠄⠂⠀⢠⡄⡉⠋⠁⠀⠀⠀⠀⠀⠀⢾⣷⡀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⡼⣸⣿⡆⣆⠈⢄⠀⠀⠳⡀⠁⢄⠀⠀⠠⠛⠁⠀⠀⠀⠀⠀⠀⠂⠀⠈⣿⡇⠀⠀⠘⠃
⠀⠀⠀⠀⠀⢸⣧⠎⠹⣾⣎⢢⡀⢂⠀⠂⠈⠢⢄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣞⠋⠈⢢⠹⢛⣧⣕⣄⠁⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⣿⣆⠀⠀⠁⢎⡹⣿⣷⣵⣤⣘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠿⠿⠷⠶⠾⠷⠿⠾⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣶⣶⣶⣶⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣼⣿⣿⡿⠿⠛⠛⠋⠉⠉⠙⠛⠛⠿⢿⣿⣿⣧⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣿⡿⠃⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⠀⠀⠘⢿⣿⡄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠑⠿⠀⠀⠀⠈⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⢀⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡾⠋⠀⠙⢷⠟⠁⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⣠⡾⢋⣀⣀⣀⠀⠀⠀⠀⠀⣿⠉⣿⡇⠀⠀⠀⠀⠀⢸⣿⣧⣤⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⢠⡾⠋⠀⢸⡏⠉⣿⢀⣀⣀⣀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠋⠉⣿⣿⡄⠀⠀⠀⠀⣿⢰⣶⣶⣦⢸⡇⠀⣿⢸⣿⠉⣿⠀⣿⠀⣿⡇⠀⠀⠀⠀⢠⣿⣿⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡀⠀⠀⠀⣿⢸⡇⠀⣿⢸⡇⠀⣿⢸⣿⠀⣿⠀⣿⠀⣿⡇⠀⠀⠀⢀⣾⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣷⡄⠀⠀⣿⣸⣇⣀⣿⣸⣇⣀⣿⣸⣿⣀⣿⣀⣿⣀⣿⣇⠀⠀⢠⣾⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠛⢿⣿⣦⡀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠋⢀⣴⣿⡿⠛⠿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⡿⢿⣿⣷⣶⣤⣤⣄⣀⣀⣠⣤⣤⣶⣾⣿⡿⢿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⢹⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡏⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠁⠀⠀⠈⠿⠿⠛⠃

⠀⠀⠀⢀⡾⠉⠉⠉⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠉⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠉⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠉⠉⠉⢳⡄
⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠻⡄
⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠛⠛⠛⢻⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠛⠛⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠛⠛⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛
⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⡽⠓⠛⠓⠛⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⠛⠛⠛⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠛⠛⠛⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⠛⠛⠛⣯
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠈⢷⡀
⠶⠶⢾⡁⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠶⠶⠶⢾⡁⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠶⠶⠶⢾⡁⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠶⠶⠶⢾⡁⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶
⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⣻⠤⠤⠤⠤⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⣻⠦⠤⠤⠤⢴⣏⠀⠀⠀⠀⠀⠀⠀⠀⣻⠦⠤⠤⠤⠴⣏⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⠤⠤⠤⠴⣟
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠙⣆
⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣤⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⣤⣤⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⣤⣤⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤
⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠈⢧⣀⣀⣀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣀⣀⣀⡾⠁
⠀⠀⠀⢠⡟⠁⠀⠀⠈⠈⢳⡄⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⠻⡄
⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣀⣀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀
⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉
⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⢀⡼⠛⠛⠛⠛⠛⢧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠛⠛⠛⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠛⠛⢷⡀
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⢳⡄
⠛⠒⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠒⠒⠒⠒⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠒⠒⠒⠒⢻⡄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠒⠒⠒⠒⢻⡅⠀⠀⠀⠀⠀⠀⠀⢀⡿⠒
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⣻⠶⠶⠶⠶⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⠶⠶⠶⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⠶⠶⠶⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⠶⠶⠶⠶⣏
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠘⣧
⠤⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⢘⡧⠤⠤⠤⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⢘⣧⠤⠤⠤⠤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣷⠤⠤⠤⠤⣾⡃⠀⠀⠀⠀⠀⠀⠀⠈⣷⠤
⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠈⢷⣤⣤⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣤⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣤⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⡞⠁
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠹⣄
⣀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀
⠉⠁⠙⣆⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠉⠁⠙⢦⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉
⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠘⢧⡀⣀⣀⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠈⢧⡀⣀⣀⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣀⣀⣀⣼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣤⡀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣤⡀⠠⢇⠀⠀⠀⠀⠀⠤⢀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣾⣿⣿⡦⢠⣴⣾⣿⣷⣶⣦⣶⣤⠐⠀⠀⠀⠀⠉⣝⣻⡿⣿⢿⣶⣾⠂⠀⢀⡠⠐⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⣿⣿⣿⣿⣽⡇⢸⡿⣿⣯⣽⣿⣿⣿⣿⠃⠀⣤⣄⣀⣀⠈⣳⠾⠜⣿⠿⣿⣧⡄⠀⢀⡘⠋⠛⠶⠦
⠀⠀⠀⠀⢀⠠⠈⠈⠻⣿⣸⣿⣿⣿⣿⡿⠃⠸⣗⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠤⠿⣄⣐⣿⣿⣿⣿⣧⠤⠤⡃
⠀⡠⠂⠭⣶⣾⣶⣾⣷⣄⡙⠛⠛⠉⣠⣴⣌⣵⣮⣙⠿⣿⡿⠟⣋⣥⡶⠀⠀⠀⠀⠀⠀⡀⢙⠿⣿⡟⠻⠟⢿⣧⣴⡏⠑⢄⢀⡀
⢠⠀⠀⢠⣹⣿⣻⣽⣷⣏⣻⠀⢀⣸⣿⣿⣿⣯⣿⣿⣿⡄⣾⠿⠛⠉⠀⠀⠀⠀⠀⢀⠜⠀⢀⣠⡞⢉⢀⣼⠿⠋⣩⣤⣀⠈⠛⠦⢄⣄⣀
⡄⠀⠀⣿⣿⣽⣿⣿⣿⣿⡏⠀⣿⣿⣾⣿⣿⣿⣿⢶⣽⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⣸⠂⠛⠛⢲⠾⣿⠁⢰⡿⠟⣻⣷⣷
⢇⠀⠠⣿⣟⢿⣿⣿⣿⠿⢃⠐⢿⡯⣿⣿⣿⣿⣿⣿⣿⠀⡀⠘⠀⠀⠀⠀⠤⠀⠀⠊⢻⠀⠀⠀⠘⡄⠹⣶⡏⣠⣾⠿⢻⣶⡆
⠀⠙⠆⠈⠙⠿⢋⣩⣴⣾⠿⠓⠢⣑⠺⣝⣿⠽⠟⣋⣥⣶⣌⡂⢄⡀⠀⠀⢀⠠⠔⠂⠭⡀⠀⠀⠀⠾⡆⠈⠛⢯⣁⣠⣿⣿⡇
⠀⠀⠀⠀⠀⢀⠛⠛⠉⠀⠀⠀⠀⠀⠑⠆⢠⡶⣛⣩⣶⣿⣿⢻⣦⢌⠛⣩⣤⣶⣿⣷⣶⢬⡑⠤⡀⢀⡃⠀⠀⠀⠈⠉⠙⠋
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣇⣿⣟⣿⣿⣿⣿⣾⣶⢸⣿⣷⣾⣟⡿⣇⢀⡀⣠⠁⠀⠇
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇⡿⣿⡿⣿⣿⡿⢿⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⡿⢸
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⣷⣅⠉⢻⢿⣿⣿⠝⠛⠘⠇⡻⠿⣿⣿⣿⠟⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢌⠙⢿⡧⠿⠿⠋⢀⡠⢾⣷⣦⡙⠺⣿⡿⠟⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⢠⠖⠋⢼⠀⠀⠈⠛⠿⠆⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠢⢀⠀⡁⠀⡀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣻⣿⢷⡤⣀⠀⠀⠀⠀⠀⠐⢄⡀⢠⣹⣥⣔⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⡶⣦⢳⣱⣿⠿⠿⢯⡀⠀⠀⠀⠀⠀⠁⠀⠀⠏⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⣿⣮⡷⠉⠁⠐⢆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⡃⣿⢿⣿⡿⣃⡈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠛⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢀⡜⠀⡄⠐⢇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣄⢠⣤⡄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣠⣄⠀⣭⡈⠀⣰⡈⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠚⠛⠃
⠀⠀⠀⢀⣀⠀⢈⣀⠁⢉⡀⠉⣁⡉⢉⣩⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠚⠉⠁
⠀⠀⢠⡋⠉⠁⠁⢉⡀⠉⣹⠚⠉⢓⠋⢉⡋⠁⠀⠀⠀⣠⣼⠾⣏⠙⣧⠈⣧⢈⣠⠤⠔⠚⠉⠉
⠀⠀⠈⠇⠙⠈⡃⠉⠛⠐⠊⠑⠘⠛⠃⢘⠋⠀⠀⠀⠀⡏⢹⡆⢹⣆⢽⣶⣾⡿⠃
⠀⠀⠀⠘⠃⡈⠛⠆⠛⠛⠀⠞⠛⢆⠘⠀⠶⠀⠀⠀⠀⠸⣿⣿⣷⣿⣾⣿⠛⠁
⠀⠀⠀⠈⠳⠶⡄⠜⠶⠤⠋⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⠨⡝⠃⠀⣚⠠⠌⢹⡻⠦⣥⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⡀⠈⢘⠷⢤⣀⣈⣵⡒⠜⢃⡴⠋⣛⣻⣿⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡉⠀⠀⠈⠐⠯⢁⠵⠔⣩⡿⠙⠈⠉⠒⢊
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡟⢶⣴⠀⢳⢉⣶⢻⡇⢠⡴⠖⠚⠩
⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀⣀⠀⠀⠐⢀⣺⣖⢂⣸⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⣦⡙⠛⠟⠀⢸⡏⠀⠀⣠⢤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢉⠛⠳⠛⠛⢻⡯⡹⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡤⡼⠧⠤⠞⠛⠉⡇
⠀⠀⠀⠀⠀⠤⠀⠐⣷⠀⠁⠀⠒⢄⢚⡄⣿⡝⠯⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣤⣄⠠⢀⡀⠀⠀⠀⠀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠠⠝⠻⣦⡵⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡛⠊⠿⢶⣥⠴⡧⠤⠆⠂⠈⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠓⠀⠀⡠⠀⠳⡟⠃⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠅⠀⠀⠈⣀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣦⡇⢀⢓⣶⣾⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⡤⠀⡶⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣦⡀⠀⠀⠀⠀⠀⠀⢆⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣴⣾⣦⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠤⢤⣄⣀⡀⠀⠀⠙⢦⣴⣿⠿⡿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠈⠉⢉⣓⣶⣶⣶⣿⣿⣦⣿⣤⣹⣷⣦⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢛⣛⡉⠩⣽⣿⣿⣿⣿⣿⡿⠛⠛⠛⠇⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣿⣿⣿⣿⡿⠷⣦⣄⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣈⡙⢦⣀⠻⣿⣿⡟⣿⡿⢿⡇⠀⣠⠏⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⠛⠛⠻⣿⣧⣦⣝⣧⣹⣿⢧⣿⠁⣿⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣷⣦⣈⢻⣿⣿⣿⣿⠟⣾⡟⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⠉⠛⢿⣿⣿⣿⣿⣿⡿⢫⡼⠟⠀⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣦⣻⣿⣿⡿⠋⠀⣸⡇⠀⠀⠇⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣭⡝⣿⣿⣿⣿⣿⠋⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠘⠛⢹⣿⡟⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢈⡏⠀⠀⠀⢰⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⢀⡤⠦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣻⣛⣻⣋⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣯⣿⣿⣻

⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⢠⣤⡄⠀⢀⣤⡀
⠀⠀⣼⣿⣿⣿⣦⠀⠀⢀⣠⣾⣿⣿⡆⠀⢠⣾⣷⣆⠀⠀⠀⣼⣿⣿⡆⠀⣿⣿⣿⣷⠀⠀⢀⡀⠀⢸⣿⣿⣤⣾⣿⣧⢠⣶⣶⣤
⠀⣰⣿⣿⣿⣿⠋⠀⠀⣾⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣷⡀⢸⣿⣿⣿⣷⢀⣿⣿⣿⣿⠀⠀⣿⣿⣦⣼⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢛⠻⡛⡛⢻⡻⣿⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣾⡟⢻⣦⢰⣿⠛⣿⡆⢠⡾⠛⠻⣦⠀⣿⠛⠳⣦⡀⣿⡇⠀⣿⠀⣴⡞⠛⠳⠘⢻⣿⠛⠃⢻⣿⠃⢻⣆⠀⣾⠇⠹⣿⠃⠘⢻⣿⠛⠉⢿⣄⣼
⣿⡟⠛⠋⢸⣿⠻⣿⡁⢸⣧⡀⣠⡿⠀⣿⣀⣀⣿⠃⢿⣇⢀⣿⠀⢿⣆⠀⣀⠀⢸⣿⠀⠀⣸⣿⠀⠈⢿⣼⡏⠀⢀⣿⡀⠀⢸⣿⠀⠀⠈⣿⡇
⠉⠁⠀⠀⠈⠉⠀⠈⠉⠀⠉⠙⠉⠁⠀⠉⠉⠉⠁⠀⠈⠉⠋⠁⠀⠀⠉⠋⠉⠀⠈⠉⠀⠀⠉⠉⠁⠀⠈⠉⠀⠀⠉⠉⠉⠀⠈⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣄⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠙⢷⡀⠀⠀⠀⢠⡞⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠏⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢻⡀⠀⢰⣿⡄⠀⣼⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢧⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣀⠀⠀⠇⠀⠀⢹⣆⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⣾⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⠉⠀⢀⣶⣄⠀⠀⢙⣦⣄⣀⣠⣴⡟⠁⠀⠀⣰⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⢧⣙⣷⠟⠋⠙⠷⠿⠶⠛⠉⠛⢳⣾⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡞⠋⠻⢦⡽⢿⣄⣤⠶⢛⣋⣙⣛⠳⢶⡟⠁⠀⠀⣼⠻⣆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⣾⠀⠀⠀⠀⠀⣠⠟⣷⣞⣉⣭⣭⣍⠳⣦⠹⣆⢀⡾⠁⠀⢻⡈⠙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⢠⡏⠀⠀⣸⡇⠀⡟⢸⠇⣼⢻⡴⢦⡌⢷⡘⣧⢹⡏⠀⠀⠀⢸⡇⠀⠀⠀⠉⠳⢦⣄
⠀⠀⠀⠀⢠⡴⠞⠋⠀⠀⠀⠀⠀⠀⢸⠇⠈⠋⠉⠙⣻⡷⠾⠶⣿⡘⠷⠾⠃⣼⢁⡟⢸⠇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠒⠖⢋⣡⠞⣡⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠻⣤⣤⣤⣤⡤⠿⢦⣤⣤⣴⣏⣛⣛⣉⣥⠾⠋⠀⠀⣷⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⣀⣀⣀⡀⣀⡀⠹⣦⠀⠀⠀⢀⠀⠀⠀⠀⣈⣀⣀⣀⣀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⣠⡞⠁⠀⠀⢀
⠀⠀⣿⠉⠉⠉⢹⡇⠀⢰⡞⠛⠶⠟⢳⣦⠀⢸⡏⢉⣉⣉⣽⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠟⣦
⣤⠤⠿⠤⢤⡄⢸⡇⣴⠾⠁⢀⣤⡀⠈⠻⣶⢸⡇⢸⡏⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡈⠁⠀⠀⠀⣰⠏⠀⠘⢧⡀
⣿⠀⠀⠀⢸⡇⢸⡇⠻⢦⡀⠈⠻⠉⠀⣴⠿⢾⡇⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡼⠋⠻⡄⠀⢀⣼⣃⠀⠀⠀⢈⣷⡀
⣧⠀⠀⠀⢸⡟⠛⠃⠀⠸⣧⣤⡤⣤⣼⡗⠀⠈⠛⢻⣇⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⢠⡟⢷⡀⠀⠀⢀⡾⠁⠀⠀⠙⣆⠈⠉⣽⠀⠀⠀⣿⠉⠁
⣿⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠉⠀⠈⢸⣧⣤⣤⣤⣤⣭⡟⠉⠉⠉⠀⠀⠀⠀⠀⣰⠏⠀⠈⢳⡄⠠⠿⢶⠀⠀⠀⢰⠾⠧⠀⢺⠀⠀⠀⣿
⠀⠀⠀⠀⢀⣴⠖⠒⠒⠂⠀⢠⡶⠶⠶⠶⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⡀⠀⠀⢀⣹⣆⠀⢸⠀⠀⠀⢸⠀⠀⠀⢹⠀⠀⠀⣿
⠀⠀⠀⠀⢿⡁⠀⠀⠀⣴⠛⠋⠛⠳⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⢸⡏⠉⠀⢸⠀⠀⠀⢸⠀⠀⠀⣻⠀⠀⠀⣿
⠀⠀⠀⢀⡈⣷⡀⣀⢸⡇⠀⠀⠀⠀⣿⡛⠛⠛⣻⡆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⣠⡤⠶⠶⠦⣤⡀
⠀⠀⢸⣏⢉⣉⣉⣉⣹⡇⠀⠀⠀⠀⣿⣉⣉⣉⣉⣉⡉⢹⡇⢲⣄⠀⠀⠀⢀⡴⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠘⢠⡞⠉⠐⠀⠃⠀⠌⠙⣦
⠀⠀⠀⣿⢸⡏⠀⠀⣸⣧⣤⣤⣤⣤⣿⡅⠀⠀⠀⢸⡇⣾⠀⠀⠙⢧⡀⣰⠟⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⣾⢁⡄⠀⠀⣿⡄⠀⣅⢹
⠀⠀⠀⣿⢸⡇⠀⠀⠙⠶⠶⢶⡶⠶⠾⠃⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠛⠁⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⢻⡄⠤⠀⠀⠀⠀⠠⠀⣼
⠀⠀⠀⣿⠸⡇⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⢸⡇⣻⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⡀⠀⠂⠘⣡⡾⠃
⣦⣶⣦⣿⣿⣷⣴⣶⣶⣴⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣦⣴⣦⣧⣤⣦⣯⣦⣴⣼⣶⣤⣬⣦⣴⣼⣧⣦⣤⣤⣿⣿⣿⣿⣥⣶⣶
⣿⣿⣏⣀⣉⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠇⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⢀
⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⡆
⡄⠀⠀⠈⠁⠀⠀⠀⣤⠀⠀⠀⠉⠀⠀⠀⣠⡀⠀⠀⠈⠁⠀⠀⢀⣄⠀⠀⠀⠉⠀⠀⠀⣤⠀⠀⠀⠈⠁
⠇⠀⠀⠀⡀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⢀
⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⡆
⡄⠀⠀⠈⠁⠀⠀⠀⣤⠀⠀⠀⠉⠀⠀⠀⣠⡀⠀⠀⠈⠁⠀⠀⢀⣄⠀⠀⠀⠉⠀⠀⠀⣤⠀⠀⠀⠈⠁
⠇⠀⠀⠀⡀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⢀
⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⡆
⡄⠀⠀⠀⠁⠀⠀⠀⣤⠀⠀⠀⠉⠀⠀⠀⣠⡀⠀⠀⠈⠁⠀⠀⢀⣄⠀⠀⠀⠉⠀⠀⠀⣤⠀⠀⠀⠈⠁
⠇⠀⠀⠀⡀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⢀
⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⡆
⡄⠀⠀⠈⠁⠀⠀⠀⣤⠀⠀⠀⠉⠀⠀⠀⣠⡀⠀⠀⠈⠁⠀⠀⢀⣄⠀⠀⠀⠉⠀⠀⠀⣤⠀⠀⠀⠈⠁
⠇⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⢀
⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⡆
⡄⠀⠀⠈⠁⠀⠀⠀⣤⠀⠀⠀⠉⠀⠀⠀⣠⡀⠀⠀⠈⠁⠀⠀⢀⣄⠀⠀⠀⠉⠀⠀⠀⣤⠀⠀⠀⠈⠁
⠇⠀⠀⠀⡀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⢀
⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⡆
⡄⠀⠀⠈⠁⠀⠀⠀⣤⠀⠀⠀⠉⠀⠀⠀⣰⡀⠀⠀⠈⠁⠀⠀⢀⣄⠀⠀⠀⠉⠀⠀⠀⣤⠀⠀⠀⠈⠁
⠇⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⢀
⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⡆
⡄⠀⠀⠈⠁⠀⠀⠀⣤⠀⠀⠀⠉⠀⠀⠀⣠⡀⠀⠀⠈⠁⠀⠀⢀⣄⠀⠀⠀⠉⠀⠀⠀⣤⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠺⡉⠳⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⡾⠯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⠞⢉⠗
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⢸⠀⠀⠐⠊⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠽⠷⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢾⣄⣀⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⠂⠀⠀⡇⡿⢣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣤⣄⣠⡧⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⢲⢄⡀⠀⠀⠀⠀⢀⡴⠊⠓⢤⡀⠀⠀⠀⠀⢀⡴⠊⠩⣲⢄⡀
⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠈⠁⠍⠲⢄⣠⠞⠁⠀⠀⠈⠃⢉⠲⣄⣀⠔⠉⠀⠀⠀⠀⠲⠙⢦⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢀⡴⢧⣀⠀⠀⠀⠀⠀⠀⢀⡠⠧⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⢀⡠⠖⠉⠀⠐⠮⢓⢤⡀⢀⡠⠖⠉⠀⠐⠢⢙⡢⣄⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠈⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⣀⠴⠚⠁⠀⠉⠲⢤⣀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⣀⡀⢀⣀⠀⡀⡀⢀⣀⣀⣀⢀⡀⡀⢀⢀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⠸⠺⡝⢇⡽⢸⡼⠛⣇⠟⢯⡠⠸⠇⢸⡅⢳⠏⢸⠀⠿⠀⢻⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⢀⡔⠉⠙⢦⠀⣰⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⠸⡀⠀⠀⢸⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣶⣤⠽⢦⡶⠧⣤⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢰⠉⠛⢳⣾⣿⣿⢝⢅⡰⠙⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⡏⠐⢣⡷⢯⡻⢎⣿⣿⠀⠀⡇⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠧⢠⡼⠤⡤⣟⣟⠿⠋⠄⠀⢱⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⢲⢩⠖⠖⣤⢰⢒⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢹⣸⢫⡀⠃⣨⢿⣸⠀⢸⠀⠀⠀⢀⠀⠀⢠⠛⡄⢰⡃⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠼⣀⡀⠉⣉⣧⣤⠬⠟⠉⠀⠀⣠⠋⠳⡐⢧⠀⡼⠂⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠀⢰⠊⠳⣄⣨⡆⠀⠀⠀⠀⢹⠀⢸⠁⢸⠀⡇⠀⣇⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢩⠯⣯⣀⣀⡿⠯⢭⡽⠲⡀⣠⢺⠀⢸⠀⢸⠀⢡⠊⠀⡄⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⠀⠙⢲⠒⠁⠀⢸⡇⠀⠈⢁⣘⣀⣘⣀⣘⣀⣘⣄⠀⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⠀⠀⡠⢒⡉⠢⡀⠀⢀⣤⣶⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣠⢚⡥⠮⠵⢮⡑⡔⡨⠚⠓⠚⠳⢌⣲⣿⠭⠒⠨⢟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⢸⡏⠀⠂⡀⠀⢹⡇⡁⠀⠀⠁⡀⠐⣿⡇⠀⠘⠆⠀⢹⠋⠉⠉⠒⠦⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢰⠣⡀⠀⠁⠀⣸⠧⡗⢄⡀⠀⣠⠾⠛⢷⣤⡀⢀⣴⠿⡇⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢸⡏⠒⠵⣶⢟⡥⠎⠻⢿⣻⠟⡡⠶⠍⠶⣌⠻⡟⠁⠀⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⠀⠀⠀⠀⠸⢇⡀⠀⣺⠘⠀⠀⠱⠀⣻⠸⡀⠀⠀⠱⢘⠀⡇⠀⡔⠁⠀⠀⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢆⠀⠀⠀⠈⠒⢿⠪⣓⠤⡠⡾⠜⡗⠫⣒⠤⡲⠟⠋⣇⠎⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠸⣀⠀⢹⡎⠀⠀⡇⠀⠀⣿⠀⠀⢀⡇⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠑⠾⣷⠔⠊⠉⠑⠢⢿⠴⠊⠁⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⡀⠀⠀⠀⠀⣠⡖⠉⠉⠉⠉⠉⢲⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣠⠖⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡴⠒⠢⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⡼⠁

⠄⢏⣶⠶⣄⠀⠀⢀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠻⠧⠜⣴⡟⢷⡀⠀⠀⣴⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⡹
⠀⠈⠿⠶⠏⠀⠀⠈⠻⠿⠏⠀⠀⠀⠀⠀⠀⣴⣿⣷⡹⠷⠞⠀⠀⠀⠙⣺⠟⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁
⠀⠀⡾⠋⠀⢀⢀⢠⣞⠁⣡⠀⠀⠀⠀⠀⠀⠙⠿⠟⠽⠟⠁⢀⣀⡀⣾⠉⢠⡄⠀⠀⠀⠀⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠠⡟⢛⣧⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠙⣿⠌⠛⠊⢼⡟⠻⡆
⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠛⠈⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡈⢈⢘⢣⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣦⣁⡀
⠀⠀⠀⠰⡀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣠⡀⢺⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠼⠚⠛⢊⠩⠤⠀⠀⠀⠠⠤⢸
⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣞⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠈⠀⠋
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠹⠛⠿⠟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⡴⠄⠀⠀⢠⠀⠀⠀⠀⠠⠤⢤⣀⡀⠀⠀⠀⢀⡠⠄⠸⣀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⠶⠶⠶⠒⠒⠒⠶⣿
⠀⠀⠀⠀⠀⢸⡟⢷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠮⣤⣄⡀⠀⠀⠉⡤⠆⠀⠀⠀⡀⢈⣻⡴⠃⠁⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⡐⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠑⠿⠀⠀⣀⣂⣀⠀⠐⠁⠁
⠀⠀⠀⠀⡇⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠐
⠀⠀⠀⠀⢥⡀⠀⠀⢿⣗⡀⠀⡀⠀⠀⠀⠐⣶⠞⢻⡀⠀⠀⠀⠀⠀⠀⠀⣴⣂⣽⠒⠀⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣠⠇
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠙⠾⠁⢿⠀⠀⠈⠉⠹⠶⡔⠋⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠂⢤⡼⣴⠀⠀⠀⠈⣉⢿⣿⣛⣟⠛⠃
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⢷⠃⠀⠀⠀⠀⠀⣸⠙⢱⡪⡇
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⢛⣉⣥⣤⣾⡇⠀⠀⠀⠀⠀⣠⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⢋⣡⣴⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠰⢾⡁⠀⣩⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⢉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠘⡾⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠠⢶⡋⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣾⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⢀⣿⣿⠟⢿⣿⣿⣥⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⢸⣿⠇⠀⣾⣿⣿⡏⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡶⠶⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣸⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣉⣥⣶⣿⣿⣟⠛⠻⠟⢻⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⡀⠀⠀⠹⣿⣿⣷⣶⣾⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣭⣭⣭⣽⣽⡍
⠀⠀⢀⡴⠙⢦⡀⠀⠘⢿⣿⣿⣿⣧⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠈⠓⢤⢀⡴⠛⠁⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠈⠟⠀⠀⣴⡀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠻⣤⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠟⠃⠉⠙⠂⣤⡾⠋⠉⠉⠓⠂⣴⣾⠟⠉⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⢀⣠⣿⣀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠉⠀⠈⠉⢲⣶⠟⠉⠀⠈⠛⢢⡞⠋⠁⠀⠁⣰⣴⣿⣧⣄⡀⣤⣻⢸⣾⠟⠋⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠹⢿⠿⡟⠉⠁⠉⠈⠺⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣧⡀⠀⠀⠀⣠⣼⣧⣀⠀⠀⠀⣠⣼⣄⡀⠀⠀⠀⢀⣾⣆⠀⠀⠔⠀⣠⣤⡀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⢰⡿⠏⠁⠀⠀⠙⠰⡟⠉⠀⠀⠉⠃⣴⡿⠏⠁⠈⠉⠒⣶⡾⠏⠁⠉⠙⠒⣾⡿⠋⠈⠉⠓⠀⣴⠟⠉⠉⠉⠓⠄
⠀⠀⠀⠀⠀⣸⠃⢴⡆⣸⣠⠀⠀⣀⣤⡂⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⡯⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠈⠂⠀⠁⠋⠉⠘⠻⢿⣿⣿⣷⢀⣠⣽⣀⠀⠀⠀⢀⣠⣗⣀⠀⠀⠀⣀⣼⣧⣀⠀⠀⠀⣀⣼⣇⠀⠀⠀⠀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠄⠀⠘⠉⢹⣿⡿⠉⠀⠈⠉⠀⣾⠛⠁⠀⠈⠓⢰⣾⠟⠁⠀⠉⠑⣶⡾⠟⠁⠈⠉⠂⣶⡿⠋⠁⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⢀⣤⣼⣇⣀⠀⠀⢀⣠⣶⣇⡀⠀⠀⠀⣠⣬⣃⡀⠀⠀⢀⣠⣿⣀⠀⠀⠀⢀⣠⣿⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠈⠁⣶⡿⠋⠀⠀⠉⠁⣶⡿⠋⠁⠈⠙⢁⣾⠟⠁⠀⠈⠙⢲⡶⠿⠋⠀⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⢠⣾⣿⡿⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣠⣶⣽⣄⡀⠀⠀⣠⡈⠁⠀⢀⠠⡾⠿⢻⣧⡀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠁⠀⠀⠉⢱⡟⠋⠀⢀⡐⢮⡓⠀⠀⠈⠈⠙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠛⠂⢣⡀⠀⠀⠀⠀⠀⠀⢠⡤⢤⡀⠤⠄⠤⠠⡤⠀⠄⣤⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢸⣗⣻⡄⣸⠃⢃⠀⣟⠘⣠⣍⠛⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⢿⣿⣿⠿⢿⣿⡿⠿⣿⣿⣿⣿⠟⢿⡟⠛⡟⠉⢹⣿⠏⠉⠙⢿⣿⠏⠀⢹⡿⠉⠉⠙⣿⡟⠀⠀⢹⠛⢻⡿⠛⠻⣿⡿
⠀⠀⢹⠃⠀⠀⣿⠀⠀⢹⠋⢻⡇⠀⠈⡇⠀⡇⠀⢸⡏⠀⠀⠀⠸⣿⠀⠀⠀⡇⠀⠀⠀⢹⠁⠀⠀⢸⠀⠈⡃⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠋⠀⠀⢸⠀⠸⠀⠀⠀⡇⠀⠁⠀⠈⡇⠀⠀⠀⠀⣿⠀⠀⢀⡇⠀⠀⠀⢸⠀⠀⠀⠈⠀⢸⡇⠀⠀⢸
⠀⠀⠸⠇⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠸⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⣗⠀⠀⠘⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠃⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡀⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿













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

⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⣴⢶⡦⠀⠀⠀⠀⡀⡀⣄⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⢰⣌⠉⠉⢹⡥⠄
⠀⠀⠀⢀⢴⡿⠻⣆⡄⠀⠀⠀⠐⣿⣾⠗⠀⠀⢠⣿⣷⣼⣲⣶⣴⣶⣆⠀⠀⠀⠀⠰⠀⠀⠠⠞⠛⠒⠂⠚⠓
⠀⠀⠀⠀⠆⢸⣼⠙⠆⠀⠀⠠⠀⡧⣼⠹⡀⠀⠐⠛⠛⠉⡟⠀⠈⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠻⠛⠒⠞⠋
⠀⢀⠄⠉⣠⣀⠔⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⢀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⢀⣈⣼⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠘⠀⠀⠀⠈⠀⠀⢸⠀⠤⠤⠄⠀⠀⠀⠠⢤⡿⡿⣿⡿⣧⣀
⠀⠀⠛⠿⢾⣿⣿⠮⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠊
⠀⠀⠀⠀⣤⡀⠀⠀⣾⣿⣿⡇⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⣀⠘⢿⣧⡀⠙⠛⠛⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣀⣀⡵⠃⠀⠀⠀⠈⠁
⠀⡚⠛⢛⣷⡘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠛⢦⡀
⠀⠀⠀⠀⠀⢀⣁⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡄⠀⢰⡄⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠸⣷
⠀⠀⠀⣀⣠⣏⣉⡉⣙⣀⠀⠀⠀⠀⠀⠈⠁⠀⢘⠈⠁⠀⠀⠀⠈⢸⠧⠆⡄⠇⠀⠀⠀⠀⢸⣅⡀⠀⠀⠀⣂⣿
⠀⠀⢈⡉⠙⠉⠉⢛⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⢀⣃⢀⡀⠀⠀⣸⣿⣶⡀⢐⣲⣯⣿⡇
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠁⠀⠀⠸⠃⠃⠻⠛⠼⠇⠀⠀⠿⠿⢿⣿⣿⣿⠿⠿⠇

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄
⠀⠀⠀⠀⣠⣤⣬⣧⣄⣖⣄⠀⠀⠀⠀⠀⠲⢉⣃⠀⠀⠀⠀⠀⠀⠀⠙⠇⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⡤⠲⡒⠠
⠀⠀⢄⠀⠘⢿⣭⠛⢻⣿⣸⣂⠀⠀⠀⠀⠤⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣿⡿⠛⠈⠀⠀⠀⠂
⠀⠀⠀⠑⠲⢬⣿⡿⠿⣯⡾⢻⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⠚⢿⣏⠻⡆⢀⣀⣀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⣿⢫⡾⣫⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡙⣿⡿⣟⡴⠚⡺⠋⠙⠓⠫⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⢿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣶⣤⡘⢡⠈⢱⠏⢢⣼⣧⣤⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⣶⣛⠀⣟⣽⣿⡷⣤⣤⣼⡻⣟⡛⠉⢭⣻⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠰⡇⢹⠛⣷⣄⠀⠀⢠⣿⣿⡪⢿⣿⡋⠀⣿⣿⣿⣿⢛⣟⠛⠦⢜⣿⣿⠿⢶⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠏⠩⣿⣷⣧⣼⡿⢿⡟⠠⢶⣿⣏⢄⣡⣿⣿⣿⠆⠛⡛⠛⢫⣾⣿⢻⣷⡞⣿⠖⠚⢏⣿⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣾⣿⣶⣿⣿⣧⠀⠹⣿⢇⠽⣷⣶⣌⣠⢞⣿⣿⡎⢛⣛⡛⢵⣿⣿⣿⣿⣞⢿⣿⡅⣿⢇⣬⣥⣚⠃⡴⡟⢁⣶⡄⡏
⠀⠀⠀⠀⠀⠘⢯⣿⣋⡍⢛⣿⣽⣶⣯⢸⡐⠿⢿⣇⣉⠟⣏⠉⠐⣿⣿⣿⣆⠻⠿⠳⠟⣩⣴⣯⣭⡑⣿⣿⣿⣿⡇⢹⢃⣼⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣌⠙⣿⠇⠁⣒⡊⣃⣤⣴⣿⣷⠘⠿⠭⠽⠋⣶⣾⣷⡌⣿⠿⣿⣿⡧⠻⠭⣿⠟⣋⣀⡉⠛⡥⣒⣰⣦⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢯⣈⣽⣧⣴⣿⣿⣿⡎⢛⣛⡘⢉⠐⣿⣶⣦⡰⣿⣏⣿⢋⣨⣙⡛⢉⢀⣿⣷⣦⢰⣿⣿⣿⡄⠷⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢿⡿⠃⠣⠄⠛⠇⣧⡿⣿⡆⢴⣻⣿⠿⠃⢤⣤⡐⡤⣿⠿⣿⠈⢬⣌⣝⡿⢈⡛⠿⢛⣴⣤⣭⡉⣴⣾⣶⣄⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣿⣿⣧⢰⢦⠑⣈⠋⣛⠃⡠⢤⣄⠰⣾⣿⣟⠷⠙⡰⡁⢠⢾⣷⣦⡀⢸⣿⣿⣷⢸⢟⣻⣿⡇⢿⣿⣿⡟⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⠻⡿⢀⣭⠘⠬⠗⠐⠃⡀⠨⠽⠀⢈⡉⠁⢘⡆⢀⣥⣜⠀⠌⣿⢃⡀⠈⢘⣡⣬⡉⠙⣭⣤⠈⣭⣿⣶⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣦⣄⠀⠀⠐⠚⢡⢴⡄⠀⠠⠝⠀⠀⡄⠈⠀⣲⣄⠀⢀⣨⡿⠀⣶⣶⠘⠃⠾⣻⣽⣿⡗⣀⣊⠁⣼⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢶⣦⣞⣼⠆⠈⢛⠃⠀⢀⣄⠀⠘⡃⠀⠀⠻⠿⠀⣠⣥⣄⠀⠠⠰⢶⡆⠀⠤⣭⠉⡄⣸⣿⡇⣨⣷⣞⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⣿⣿⠶⣤⠀⠋⣉⠇⣀⣛⠁⠀⠈⠻⡇⠀⢰⣶⢸⠙⠛⢿⡇⠀⠀⠈⠁⠀⢰⣤⠀⣩⣍⠋⠌⠙⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣿⡿⢿⣷⡤⡀⣿⢃⣀⣀⠛⣃⠀⢨⣅⡀⢉⣠⣏⣁⠂⢟⣿⠆⠂⣠⣟⢰⣈⣻⠯⠓⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣿⣿⣿⣿⣟⣻⣶⡏⢛⣿⣾⡁⠀⢸⣿⡷⣭⠵⠿⠛⠙⠈⠉⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠛⠛⠟⠛⠛⠛⠋⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠴⢦⣎⡀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣶⢟⡛⢴⣦⡹⣿⡅⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡿⠟⣠⣌⠻⣷⣿⣧⣸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠄⠙⣿⣿⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⢄⣀⣡⡽⡻⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠚⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠉⣍⣠⣈⠁⠈⣅⣀⣉⠉⠈⠉⠁⠐⠒⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢡⣞⣛⣉⣋⣽⢨⣧⠀⠁⢨⣥⣤⣤⣄⣍⡉⠘⠦⡀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠐⠁⢰⠾⣭⣉⠁⢠⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⡀⡤⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣀⡬⠁⣀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢆⢀⠀⠄⢈⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠝⢣⢜⢿⠀⠀⡀⢸⣷⣬⣻⣱⣤⣴⠼⠄⡖⡏⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠢⢀⢴⠋⠀⠀⠀⠉⠀⠀⠄⢸⠐⠌⠈⠈⠀⠀⠀⠠⠠⢀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⣈⠀⣾⣦⣤⢌⠀⠁⠀⠀⠂⠃⡈⠘⠈⠳⡀
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢀⣴⠞⠉⠑⠤⠚⣆⣀⡀⠘⣆⠀⠀⠄⡐⢀⠃⠂⠄⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠋⡀⠀⠄⠀⠠⣼⣷⣬⠁⠄⠈⢦⡀⠀⠁⡘⢰⠊⠑⠄⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣐⡿⣷⣼⡏⠀⠀⠔⠈⡷⠄⠀⠁⣎⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠄⠈⡑⣦⣭⠻⣾⣏⡧⠀⠊⡀⠀⠜⠀⢰⢠⠈⡈⠢⢀⡀⠈⢸
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢡⠲⡌⡤⢧⡹⠟⣝⠒⡀⢀⠊⢀⠊⠀⠀⠄⠆⠘⠘⠙⢠⠀⢀⠸
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠣⠡⠢⡠⡀⠊⠀⠀⠠⠀⡰⠃⠀⠀⠐⠐⠠⢣⠡⢁⠂⠀⠊⠃
⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠐⠫⠶⠶⠖⣠⣤⣠⠞⠀⠀⠀⠀⠠⠠⢡⢡⠂⠌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠡⢃⢃⠎⠈⣠⠊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠒⠦⣠⡅⣂⠐⠀⠀⠁⠀⠐⠐⠀⠈⠀⠀⢁⣠⠴⠛⠕⡡⠈⠔⡠⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡥⢊⠁⢋⠐⠃⠀⠀⠒⠐⢀⠛⠀⡁⢀⠄⠀⡠⢊⠄⡡⠊⠔⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁⠂⠐⠀⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⡶⠶⠆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠋⠉⠻⠛⠀⠀⠀⠀⠀⠙⢻⡦⠀⠀⠀⢀⣤⣿⠙⠋⠙⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠟⢀⣠⡶⢾⣛⣛⣛⠶⣦⡀⠘⠷⠶⣦⠀⣸⡷⠀⣴⠟⠻⣦⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⣠⡞⠁⣰⠟⠉⠉⠙⣷⡈⠹⣦⡀⠀⣸⡇⢻⡦⠀⢿⣤⣠⡿⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠇⢠⡟⠀⠐⣿⡀⠀⠀⠀⣸⡇⠀⠸⣧⠈⠿⢦⡌⠻⣶⣀⡈⢁⣀⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠘⢷⡄⢀⣴⠏⠀⠀⠀⣿⠀⠀⢸⡇⠀⠈⠋⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡇⠈⣷⡀⣠⡶⠟⣃⣀⡛⠷⣦⡀⣰⡏⠠⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠈⠷⠟⠀⠀⢹⡏⠀⠀⠸⠷⠋⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⣷⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⢰⡟⠛⢋⣤⣤⡶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⡶⣶⠀⠀⢰⡶⣦⣤⠾⢃⣴⠿⢁⣬⣴⣦⣭⡀⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⣸⡧⢰⡟⠁⠀⢤⣌⢻⣆⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⢻⡄⠀⠀⣠⡿⢀⡿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣈⠻⣦⣀⣉⣤⠾⣁⣸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣤⣤⣍⣩⣤⣤⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠋⠁⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠁⠠⠀⠀⠀⡄⠠⠀⠆⠀⠀⠄⠠⠀⠀⠲⠀⡄⢀⠀⠀⠀⠒⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠀⠁⠈⠐⠀⠀⠀⠃⠀⠃⠀⠀⠀⠀⠸⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠈⠐⠄⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⢰⠀⢠⣿⣿⣿⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⣀⣀⣀⣘⣦⣠⣿⣿⣿⣦⣾⣥⣤⡤⠤⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠉⠙⠛⣻⣿⣿⣿⣟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠠⠔⣪⠞⠻⠯⠿⠛⠻⠧⢶⡛⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠴⠁⣴⠛⡶⠦⢶⣶⣾⡌⢻⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⡿⠿⢾⢿⣿⡟⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢰⡏⠹⢼⡄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠘⢿⠶⠾⢿⣿⣿⠀⠸⡷⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀
⠀⠀⠀⠀⠀⠀⠈⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⣿⢿⣿⣿⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣴⠂⡠
⠀⠀⠀⠀⠀⠀⠀⢨⡏⠳⢦⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠙⣿⣿⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⣀⡤⠴⠖⠒⠛⠛⠉⠉⠉⠛⠓⠒⠦⢤⣀⡠⠖⠲⣄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⣢⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⣌⣉⣢⠀⠀⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠲⠤⠤⠤⠴⠒⠋⠉⠁
⠀⠀⠀⣠⣖⣒⣈⠉⠉⠒⠒⠘⢆⠀⢀⣤⠶⢛⠉⠁⠉⠛⠝⢋⠝⠋⠉⠉⠻⠶⣤⣀⠀⠀⣴⡤
⠀⠀⠀⠀⠀⣀⠤⠙⠃⠀⠀⠀⠀⠳⣭⡤⠞⣫⡇⡀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠘⠋⠉⠓⠁
⠀⠀⠀⠀⠴⠕⠒⠒⠀⠒⠒⠒⠒⠒⠂⠀⠙⢿⡄⣙⠂⠀⠀⠀⠰⡎⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈

⣶⣶⠶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣦⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⢀⠀⣀⡄⣀⠻⢄
⠀⠀⠀⣴⠏⣴⠟⣡⣶⣷⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣠⣶⣷⣦⣀⠀⢀⣤⣶⣷⣤⣀
⠀⠀⠀⠈⢼⠏⣴⣿⣿⣿⣡⣤⡟⣀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇
⠀⠂⠶⠛⠂⠨⢻⠿⠿⣿⣿⣿⣿⣣⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢛⡟⠻⠿⠃⠀⣀⣤⣶⣮⣟⡿⡿⣟⣭⣶⣮⣟⡿⡿⣛⣭⣶⣦⣄⡀⠀⢀⣤⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣀⠀⠀⣠⣴⣾⣽⣻⢿⠿⣻⣵⣾⣽⡻⢿⠿⣻⣵⣾⣽⡻⢿⢿⣻⣽⣶⣽⡻⢿⡿⠛⠉
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠛⠿⣿⢟⣫⣷⣯⣟⢿⣿⢟⣫⣷⣯⣟⣿⣿⢟⣫⣷⣯⣙⣛⣛⣻⣿⣷⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⢾⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡿⣟⣽⣾⣝⡻⣿⡿⣟⣽⣾⣝⡻⣿⡿⣟⣽⣾⣝⡻⣿⡿⠟⠉⠈⠙⠻⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠟⠋⠁⠙⠻⢿⣿⠿⠋⠁⠉⠻⢿⣿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣆⢻⣿⣿⣿⣿⡟⣰⣶⣶⣶⡀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡦⢙⣛⣛⡋⢼⣿⣿⣿⣿⣿⠄⣀⣀⣀⠠⣿⣿⣿⣿⣿⡧⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣡⣿⣿⣿⣿⣌⢿⣿⣿⣿⢏⣼⣿⣿⣿⣧⡹⣿⣿⣿⡿⠡⢿⣿⣿⣟⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⢻⣿⣿⣿⣿⡟⣠⣶⣶⣦⡘⣿⣿⣿⣿⣿⢃⣴⣶⣶⠄⠲⣛⣿⣷⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⢛⣛⣛⠛⢴⣿⣿⣿⣿⣷⠜⣛⣛⠛⠃⡞⠛⢟⣷⣾⣄⡟⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣡⣿⣿⣿⣿⡌⢿⣿⣿⣿⠏⣼⣿⣿⣷⣆⠹⣟⣿⣿⣿⣿⣿⠿⢿⣛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⡿⣻⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⠞⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣫⠔⣋⢉⣤⣶⣷⡌⠓⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠁⠀⢧⠻⠿⠛⢁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠾⠟⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣧⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡾⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢡⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢸⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⢸⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠛⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣼⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣡⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰⠃⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠰⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡠⠚⠉⠙⠢⡀⠀⠀⠀⠀⠀⢿⡏⢝⡿⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠇⠀⠀⠀⠀⠀⣴⡻⢽⣿⣆
⠀⠀⣗⣇⢾⢆⣗⡇⠀⠀⠀⠀⠀⠸⢷⡶⠇⠀⠀⠀⠀⠀⠀⣀⣤⣀⣤⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠙⢿⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⠀⠀⠀⠀⠀⢩⣁⣁⣡⠅⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛


⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⡛⠀⠀⠀⠀⠀⠀⣴⣟⠛⣿⣆
⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⢠⣤⠤⣤⡤⡄⠀⠀⠀⠀⠀⠀⠈⠟⡁⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿
⠀⠀⢰⣾⣿⣿⣿⠀⠀⠀⠀⠀⠘⣻⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛


⠀⠀⣠⣶⣶⣶⡄⠀⠀⠀⠀⠀⢀⠖⣫⣍⠓⣄⠀⠀⠀⠀⠀⡴⠲⠿⠖⡆⠀⠀⠀⠀⠀⣴⠋⢹⣿⣆
⠀⠀⣿⣿⣽⣿⣿⣀⠀⠀⠀⠀⣾⠀⠹⠟⠀⢸⠀⠀⠀⠀⠀⡏⡍⠈⠀⡇⠀⠀⠀⠀⠀⢻⣦⣤⣾⣿
⠀⠀⠈⠻⠿⠇⠉⠉⠀⠀⠀⠀⠈⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢷⣂⣀⣀⡇⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛


⠀⠀⡰⡪⣈⢵⢢⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⡇⠀⠀⠀⠀⠀⣷⣷⠶⣤⡆⠀⠀⠀⠀⠀⣴⣿⢻⣿⣆
⠀⠀⡸⡨⣲⣅⡁⠀⠀⠀⠀⠀⣀⣶⣀⡍⠃⠀⠀⠀⠀⠀⠀⡟⠙⠚⠿⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠑⠩⠤⠻⡇⠀⠀⠀⠀⠀⠸⠟⢿⠗⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣿⣿⣿⣿⡦⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠻⣿⣿⡿⣡⣿⣿⣿⣧⡀⠀⠀⠀⢠⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⣰⣶⣶⣦⡹⣿⣿⣿⡿⣱⣶⣶⣶⡙⣿⣿⣿⡿⢡⣶⣶⣶⣀⣀
⠀⠀⠀⠀⠀⠀⣭⣭⣭⡸⣿⣿⣿⣿⡗⣭⣭⣭⡐⣿⣿⣿⣿⡗⣨⣭⣭⠁⣶⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠙⣛⣛⡋⣼⣿⣿⣿⣿⡜⣛⣛⠛⢰⣟⢿⣿⣽⣼⢻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠘⢿⣿⣿⢏⣾⣿⣿⣿⡜⢿⣿⣿⢏⣼⣿⣿⣿⣌⠿⣻⣿⣿⣿⡿⢛⡯⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⣶⣿⠿⣿⡿⠛⣑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⠟⠵⠉⡆⣴⣿⡿⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⢡⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⢾⣿⣷⣦⣄⠀⠀⠀⠀⠀⣀⣤⣶⣷⣶⣤⡀⠀⠀⠀⠀⠀⣠⡤⠾⠿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣏⠁⠈⠫⢻⡿⠀⠉⠛⢶⣶⠶⠟⠉⠙⢿⡿⠿⣿⣿⠷⣦⣤⠖⠋⡁⠀⠀⠀⢶⣮⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠷⠀⠀⢀⣨⡅⢤⣀⠀⢸⡟⠀⠀⠀⢀⣠⢄⡀⠀⠈⠁⢸⡇⠼⠋⡉⠐⠤⣌⠙⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⠂⠉⠀⠀⠀⠈⠃⣼⡇⢀⡴⠚⠉⠈⠀⠙⠐⢠⠀⢸⡇⣀⣔⡤⠰⠀⠀⢩⡌⠀⠻⣸⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⡀⠀⣿⡀⠀⠀⠄⠀⠀⣁⣿⣇⠠⣇⠀⠀⠠⠨⠈⠁⢸⠀⣸⣇⢽⣂⠃⠋⠤⡖⡀⡇⣰⣠⣷⣼⣧
⠀⠀⢀⣠⡤⠶⠛⠿⠿⢿⠻⣶⣥⡘⠤⣀⣤⣶⠿⣿⣿⣭⡓⢦⣝⡤⡘⠰⢈⣠⣴⣾⣿⣿⢷⣯⣟⡿⢶⡧⠓⢃⡻⢿⣿⣿⣿⣤⣀
⠀⣴⣿⣿⣶⡀⠀⠀⠀⠀⠠⣈⠉⢻⣿⣿⣿⠇⠀⠈⠉⣥⣈⠀⠈⠙⢶⣾⢿⣻⠽⠛⠙⠛⠷⠎⠙⠻⣶⣤⣤⡶⠞⠋⠁⠀⠈⢯⣝⣻⣶⣤⡀
⢠⣿⣿⣿⣻⡇⡤⠊⠁⠀⠀⠈⠕⣾⣿⣿⠋⣤⠔⠃⠀⠒⠶⢶⣤⡀⣸⡇⢉⣤⡤⠛⢻⣲⣤⣀⠀⠈⣿⣿⡇⢠⠖⠓⠠⣄⡀⠻⣿⣿⣿⣿⢻
⣸⣿⣿⣯⠉⠠⠇⠀⠀⠀⠀⠠⠀⣿⡟⠈⠀⠇⠀⠀⡀⠐⠐⣤⣘⠃⣿⡇⡇⠀⠀⢀⢀⢈⣙⠙⣷⠀⡟⣿⡇⠠⢀⠂⠀⠀⠉⠓⡊⠙⣫⢻⡸
⣿⣿⣿⡇⠀⣘⡀⠀⠀⠀⠀⠠⣰⣿⡇⠀⠀⠆⠀⠀⡂⡦⠧⠉⢘⠇⣿⡇⠇⡀⠠⠲⠙⠮⡾⢶⣿⢸⠃⢹⣷⢸⠵⠖⠂⡐⡤⡀⡇⢀⣩⣼⣧
⠈⠙⢿⣷⣖⡈⠓⢤⣀⣤⠖⠋⡭⠉⠛⢷⣼⡲⢤⣄⡂⡯⢖⣫⣵⠾⠛⠻⣦⣗⢤⣀⢐⠗⠚⠛⠛⣉⣤⠿⠿⢮⣟⣦⣶⣇⣧⡧⠅⢾⣿⣿⣿
⠀⠀⠘⠾⣿⣿⣶⡟⠉⠠⠞⠊⠀⠀⠀⠀⠈⠛⢶⣬⣵⠾⠿⢋⣤⠤⠐⠀⡀⠙⠿⣾⣥⣤⣤⡶⠟⠉⠀⠀⠀⠀⠈⠙⢷⣧⣅⣀⣠⣷⣿⠟⠉
⠀⠀⠀⠀⠈⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢱⡞⠛⠑⠨⠸⠘⠑⡗⣬⣷⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⢿⣟⠋
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢀⠀⢠⢸⠀⣆⣸⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⣷⡄⠑⠫⠴⢸⡅⡷⣻⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡘⢿⣷⣦⡀⣨⠸⣀⡧⢝⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣄⠈⠃⣿⡍⠓⢁⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣷⣶⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠉⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⣶⣶⡶⠶⠶⠶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣷⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⣠⠆⢀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠠⠀⢠⡔⠈⠁⠀⠀⠁⠐⠆⠀⠐⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢀⠀⢀⠷⠓⠀⠀⠀⢀⢆⡀⢀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⡀⠀⠀⠀⢀⠏⡡⠀⣀⠀⠀⠀⠀⢈⠘⠰⠑⠃⠀⠁⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢤⡀⢀⡔⢃⠀⠢⠄⠴⢋⣀⡀⢠⠤⢦⠤⣤⣂⣽⣀⣂⠐⠀⠁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠫⣕⡋⠓⠀⢈⡥⣀⣈⡰⠂⠈⠀⣁⡀⠀⢀⡂⢀⣔⠀⠸⡼⢠⡿⠪⠄
⠀⠀⠀⠉⠀⡄⢀⠀⠀⠈⠲⡠⠾⠐⢊⡕⠀⠠⠐⢉⠀⠈⢚⡁⠈⠁⠼⠀⠀⠀⠀⠀⠀⠠
⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠘⠛⠢⠖⠐⣺⡥⣀⡔⠁⠀⠐⠀⠀⠀⠠⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠄⠀⠀⢰⡂⠀⠀⠀⣠⠋⠂⠀⠀⡄⣸⣖⡇⡀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠛⢎⠀⠈⠁⠉⠈⠀⠀⠀⠊⠐⠉⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠁
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠁⠐⠈⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⣤⢾⠅⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠰⣞⠁⠔⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⢀⡤⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢀⣿⣴⠠⠈⠄⠀⠐⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡦⠃⡈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⣄⡀⠀⠀⠠⢀⠀⠀⠀⢠⣤⡄⠘⠃⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⠿⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠆⠀⢰⠸⡆⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠓⠁⠈⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣥⣄⣀⣀⣠⣤⣤⣿⣏⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠧⠀⠉⠉⠉⠉⠀⠓⢾⡈⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠒⠂⠀⠚⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⢀⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⢸⠤⠤⠤⠤⠤⠄⠀⠀⣀⣀⢀⣀⠀⠀⣀⠀⣰⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣰⠶⡶⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⠂⢊⢀⡀⠀⠢
⠀⠀⠀⠀⠀⠀⢯⡘⠟⠠⠃⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢣⡽⠳⠂⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⠉⠪⡰⠀⢠⢀
⠀⠀⠀⠀⠀⠐⠐⠁⠪⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢀⡀⢀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢓⡈⠍⠒⢄⠀⠀⣼⠁⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠂⠀⠤⠀⠀⠀⠀⠀⠀⠿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠒⠃⠀⠀⠀⢠⠏⠀⢺⡿⡄
⠀⠀⠀⠐⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠶⠿⡄
⠀⠀⠀⠀⠀⠀⠠⠌⠁⠀⠒⠂⠂⡀⡀⠀⣰⠆⠀⠀⠀⠀⠀⣄⡀⠀⠈⠀⠀⠈⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⡟⠛⠀⠀⠀⣲⢶⢿⣦
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢾⠀⠀⠀⠀⠀⠀⡟⠛⠛⠀⠀⠀⠂⠘⠻⠛⠀⠀⠀⠀⠀⢀⢋⡴⠀⠀⠀⠀⠘⣶⠦⡿⡆
⠀⠀⠀⠀⠀⠁⠰⠄⠀⠀⠀⠀⣀⠀⡀⠀⢰⠂⠀⠀⠀⠀⠰⣧⠄⢀⡀⠀⠀⣀⣀⣤⡶⠆⠀⠀⠀⠠⠀⠘⠃⠀⠀⠀⠀⠀⢿⠆⣿⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢶⣤⠤⠤⠤⠀⠀⣠⣤⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠒⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢻⣿⣇⣠⠀⠀⠀⢠⠤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⣾⠀⠀⠀⠀⠀⠀⢷⡆⠀⠀⠀⠀⢀⠀⣴⡿⠀⠀⠀⠀⠀⣘⠿⢫⠡⠴⠶⠆⢠⣠⣽⣿⣷
⠀⠀⠀⠀⠀⢀⠀⠢⠀⢠⢀⣀⠀⠤⠶⠦⠈⠆⠀⠀⠀⠀⠀⠸⣮⡀⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⢰⡋⠁⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠀⠙⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡒⢖⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣀⠠⣤⠔⣇⣦⣀⢌⡑⠂
⠀⠀⠀⠀⠀⢀⠶⡋⢁⡀⡀⠑⢎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡐⢋⡤⠔⠒⠉⠡⢠⠆⡀⠉⠑⠦⡐⣄
⠀⠀⠀⠀⠰⠂⡂⣾⡿⠋⠑⠀⠈⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⢠⠗⢾⣷⡆⡆⠀⠀⠈⠑⠁
⠀⠀⠀⠀⠸⣀⠀⠔⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣄⡀⠀⠀⡠⠭⠔⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠉⠐⠀⠄⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠖⠒⠲⠒⠒⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠎⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⡀⠀⢀⠐⡠⠒⠂⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠄⢩⠀⠉⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⡄
⠀⠀⠀⢀⡠⠚⠷⠻⠧⡀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠴⠀⠀⠀⠀⠀⠄⠰⠆⠰⢄⠀⠘⠉⠉⠀⠀⢀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⣀⡀
⠀⠀⡇⠀⠈⢡⠤⡤⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⣀⣀⣀⠀⣠⠄⠀⠌⠀⠀⠀⠀⠂⣀⣀⣄⠀⠀⠀⠀⠀⠈⠀⠀⠈⣉⠁⡀⢀
⠀⠀⡝⠀⠀⢠⠔⠆⢀⡀⠘⠔⠀⠀⠙⢆⠀⠈⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠁⠠⠀⠀⠂⠀⠀⠀⠠⠈⠩⠁⠄
⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⢀⠀⠑⢀⠰⠁⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠠⢀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠈⠀⠀⠀⠀⠈⠱⠀⠠⠀⠔⠁

⠉⠀⢀⡀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⠢⡀⠀⡨⡢⠜⠢⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠐
⠀⠀⠀⠀⠉⠉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠀⠀⠄⠀⣀
⠀⠀⠀⠀⣄⣠⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠤⠤⠄⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠔⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠉⠁⠀⡶⠂⠒⠒⠀⠀⠠⠙
⠀⠀⢄⢀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⠂⠀⠠⠤⠤⠤⠧⠀⢀⣀⣀⣀⣀⡄
⠀⠀⠀⠈⡂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣶⠄⠀⠀⠀⠀⠀⠀⡈⠀⠉⠉⠉⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠠⠼⢤
⠆⠀⠀⠂⢁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠀⠀⠐⠀⣄⣀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⢄⠡⡀⠀⠀⠘⢄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠒⠒⠂⢰⣦⠆
⠀⠀⠀⠀⠃⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⢕⠁⠀⠑⠈⢢⠀⠀⠀⠑⡀
⠀⢁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡠⡀⠀⠈⢢⡑⢄⠀⠀⠈⠢⡀
⠀⠈⡄⠀⠀⠄⢢⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠢⡴⠞⠙⢌⠢⡀⠀⠀⠑⢄⣀⠀⠀⠀⠀⠀⢀⣠⠀⡀
⠀⠰⣧⢀⡀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠕⢄⠀⠀⠓⡈⢆⠀⠀⠀⢹⠃⠀⠀⠀⠀⠸⠁⠀⠈⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡠⡀⣀⢜⠦⠵⠤⠂⠁⠀⠀⠀⠀⢀⠁⠀⠀⡐⡰⠇⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡐⠠⠁⠀⠠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠈⠧⢄⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡐⢠⠁⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⡐⠠⠋⠓⠶⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⡠⠠⠁⠀⢀⠠⠁⠀⠀⠀⠀⠀⣀⡠⢄
⠀⣨⠂⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⡀⠀⣐⢡⠅⡀⠠⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⢅⠠
⢉⠣⢀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠋⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠂⠡⠁⠀⠀⠀⠀⠀⠀⠳⠢⢀⠀⠀⠈
⠀⠈⠂⢑⠠⢄⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀
⠠⢀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⠀⢀⠔⠁⠀⠙⢄
⠀⠀⠑⣤⡀⠂⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣀⡇⠀⠈⠐⠀⠀⠀⠀⠀⢠⡓⢄⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⡡⠋⠢⡑⢄⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠀⡀⠀⠈⠢⡑⢄⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡀
⡄⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡀⣠⡞⠢⡑⢄⠀⠀⠀⠙⢦⣤⡀⠀⠀⠀⠀⠀⠀⠈⠌⠁⠀⠀⠉
⠀⠀⠀⠈⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡀⠀⠈⠢⡉⠢⡀⠀⠀⡨⠃⠀⠀⠀⠀⠠⠴⠙⡂⠀⠠⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⣄⠄⠀⠀⢠⠃⠀⠀⠐⡀
⠀⠀⠀⠄⠠⢀⠀⠄⠀⠀⠀⠀⠀⣤⣤⣄⢾⠀⠀⠀⢈⣯⡭⠭⣅⠀⠀⠀⠀⡐⣠⠤⠤⣄
⠀⠀⠀⠐⢤⠀⠀⢨⢂⣠⠀⢀⡞⠀⠀⠈⢣⢳⣤⣤⢿⠏⠀⠀⠈⣦⣒⣒⣚⢴⠁⠀⠀⠘⣆⣀⣀⣀
⠀⠀⠀⠀⠠⠄⠄⣿⣿⠿⣁⠀⠱⣄⣀⣠⣿⠋⠈⠈⠻⣷⣄⣀⡴⡿⠉⠁⠉⢯⢧⣤⣤⢼⡟⠁⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠛⠎⠻⡿⠃⣠⠛⠛⠳⡽⣄⠀⠀⣴⡷⠛⠛⠳⣷⡀⠀⢀⣾⠟⠉⠉⢻⣧⣀⣀⣠⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⣸⡼⠿⠿⣽⡅⠀⠀⢀⣿⠽⠿⠿⡹⡄⠀⠀⢠⣧⠟⠛⢣⡀⠀⠀⠀⢀⠜⡠⠔⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠚⢿⠀⠀⠀⢈⣟⣶⣶⣾⣏⠀⠀⠀⢹⣽⠶⠶⣿⡇⠀⠀⠀⡱⠀⢰⢶⣬⣥⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣤⡀⠈⠣⠤⠤⢾⠏⠀⠀⠈⢿⢦⣤⣴⢿⠃⠀⠀⠘⡿⣦⣤⡜⠁⢤⣶⣏⣿⣯⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣿⣿⣼⠋⠁⢠⠏⠉⠉⢣⣳⣀⣀⣰⡿⠋⠉⠉⢯⢧⣀⣀⣼⡟⠁⠀⠙⢆⠈⠋⠁⠊⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠄⠹⡙⠿⠁⠀⠹⡄⠀⠀⣰⡷⠛⠛⠳⣷⡀⠀⢀⣼⡗⠛⠛⢮⢧⡀⠀⢠⣾⠞⠛⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠜⠀⠀⠀⠀⠀⡹⠿⠿⡽⡅⠀⠀⢀⣿⡽⠯⠯⣿⡀⠀⠀⢀⣧⠟⠿⢯⣯⡀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢘⣜⣶⣶⣞⣞⠀⠀⠀⢹⣗⣖⣶⡻⡇⠀⠀⠀⣹⣳⣶⣾⡁⠰⢿⣷⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣤⣤⢾⠏⠀⠀⠘⣿⠦⠤⠤⣿⠃⠀⠀⠙⡝⣦⣤⡼⡿⠁⠀⠀⢱⡀⢼⣶⣿⣧⠘⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣰⠋⠀⠀⠀⠘⢆⣀⣀⣴⡟⠉⠉⠙⢟⣄⣀⣀⡞⠀⠈⠉⢰⠠⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡠⠂⠐⢈⢧⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⡀⠀⠀⠀⡇⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠊
⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡛⣙⢟⣉⡛⣻⣛⣹⡟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡙⣿⣿⣿⡟⣱⣿⣿⣿⣆⠀⠀⠀⠀⢀⣼⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢇⣴⣤⣴⣄⢿⣿⣿⣿⡿⢣⣶⣶⣦⡸⣿⣿⣿⣿⡟⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⢙⣛⣛⡃⣾⣿⣿⣿⣿⡎⣛⣛⣛⠱⣿⣿⣿⣿⣷⢘⣛⣛⡋⢠⣽⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡌⠿⠿⠿⠏⣼⣿⣿⣿⣧⡹⠿⠿⠿⢣⣾⣿⢿⣑⡎⡶⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⢣⣶⣶⣶⣆⢻⣿⣿⣿⡟⣱⣶⣶⣦⡄⣶⢶⣿⣿⣿⣷⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢿⣿⣿⣿⣿⠇⠉⠉⠉⠰⣿⣿⣿⣿⣿⣤⣽⣿⣿⣿⣿⠖⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠻⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢿⡥⢚⢋⣥⣶⣦⠙⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠈⠀⢸⠘⠟⠋⣁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⠋⡡

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽

⠀⠀⠒⣆⡖⢒⡠⠒⣒⠢⣀⠒⠢⡐⠒⡔⠒⣒⡶⡒⠶⢒⠆
⠀⠀⡀⡔⡄⢘⢃⡘⠔⢀⢜⡀⡲⡉⢘⣇⠀⠶⡄⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢮⡁⠰⣉⠇⠸⠩⠉⠆⢸⣩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠦⡀⣠⠴⠲⢤⡀⠀⠀⠀⡏⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⣇⠀⠀⢀⡇⠀⠀⠀⠙⠦⠤⠞⠁
⠀⠀⠀⠀⢀⡤⠒⢤⡀⣀⠴⠲⢤⡀⣠⠔⠲⢽⣒⡯⠗⠪⣝⢒⡭⠒⠦⣄
⠀⠀⠀⠀⢸⠀⠀⠀⡇⣏⠀⠀⠀⡇⡇⠀⠀⢸⣿⡇⠀⠀⣸⢸⡀⠀⠀⣸⠀⠀⠀⠀⠀⢀⡤⠖⠢⣄
⠀⠀⣠⠴⠺⢝⡒⡪⠕⠮⣗⢒⡯⠖⠮⣓⢚⠽⠒⠯⡓⣺⠵⠲⢭⡒⠊⠁⠀⠀⠀⠀⠀⢸⡀⠀⠀⣸
⠀⠀⡇⠀⠀⢸⣿⡇⠀⠀⢸⢸⡀⠀⠀⣸⢸⠀⠀⠀⡇⣇⠀⠀⢀⡇⠀⠀⠀⠀⠀⣠⠴⠒⢯⡓⣪⠕⠲⢤⡀
⠀⠀⠉⠓⢖⡭⠒⢯⡓⣚⠽⠲⢽⡲⠚⠁⠈⠙⠒⡫⠗⠪⣕⢒⡭⠖⠦⣄⠀⠀⠀⣿⠀⠀⢀⡇⣇⠀⠀⢐⡇
⠀⠀⠀⠀⢸⠀⠀⠀⡇⣗⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⢸⢸⡀⠀⠀⣸⠀⠀⠀⠈⠙⠒⠋⠀⠈⠑⠚⠉
⠀⠀⠀⠀⠈⠙⠒⠋⡡⣌⠑⠒⠋⠀⠀⠀⢀⡤⠒⠯⡓⣺⠽⠲⢽⡒⣪⠕⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠈⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⣇⠀⠀⢀⡇⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠤⠴⠃⠀⠀⠀⠀⠀⠈⠙⠒⡫⠗⠪⣕⢒⡯⠖⠮⣗⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⢸⡀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠁⠀⠉⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⡿⢿⣻⣛⣓⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠻⠿⢿⣿⡿⠿⠿⢟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠠⠶⢤⡀⠀⢀⣀⣀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠀⠓⠂⢻⠀⠤⠤⠀⢁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⠀⢀⠰⠆⠠⠀⠀⠀⡌⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠒⡂⠤⠈⡠⢊⠵⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠻⣷⡄⠀⠉⠀⢰⣡⢋⠊⣄⠙⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣿⣿⣿⣿⢻⠀⢩⡛⠓⠒⢂⡿⢿⠾⢻⠟⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⡿⠟⠻⠿⠛⠋⢉⡆⢸⡏⢸⡀⠀⠑⣄⡠⠼⣷⡀⢠⠂⠀⣰⢿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠀⢧⠀⠀⠀⠀⠀⡼⠀⠈⠁⠀⡇⢀⡴⣿⣿⡄⢻⣿⡀⠀⠀⠈⢆⠀⠈⠉⠙⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⣦⠀⢸⡀⠀⠀⠀⠸⠁⠀⠀⠀⠀⢳⠈⣴⣿⣷⡀⢸⣿⣷⠀⠤⢂⡌⠱⡀⠀⠀⡔⠀⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠧⡐⠦⣄⠀⡇⠀⣌⠉⠉⠉⠛⠃⠀⠀⢸⣴⣿⣿⣿⣇⣿⣿⣟⡃⢀⣾⠀⠀⠑⣄⠘⢀⣴⡇
⠀⠀⠀⠀⠀⠀⣴⠛⠧⣀⡀⠀⠈⢳⣷⡀⢿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣷⠀⠀⠘⡆⠀⠀⠈⢲⡟⣹⣇
⠀⠀⠀⠀⠀⢰⡟⢆⠀⠀⠻⢯⡛⣯⣽⠇⠈⢻⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⠘⢿⣿⣷⠀⠀⠑⠀⠄⠀⠀⢻⡁⠈
⠀⠀⠀⠀⢀⣿⠇⠈⠑⠢⠤⠤⣙⣰⣿⠀⠀⣸⡿⡄⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠘⢿⣿⣧⣀⠀⠀⠀⠀⠀⠀⡳⢬⡳⡀
⠀⠀⠀⡠⣫⠵⣚⣛⡛⠛⠟⠞⣿⣿⣿⠀⠀⣿⠁⠹⡄⠀⠀⠀⠀⠘⣿⣿⠁⠀⠀⠀⠈⢿⣿⣿⢧⡀⠀⠀⠀⠀⢱⠈⠇⣷
⠀⠀⢸⣿⡿⠏⠁⠘⠙⠳⣄⣴⣿⣷⡛⡀⢰⡏⠀⠀⠱⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢈⣿⣘⣧⡙⠂⠀⠀⠀⠀⢇⢀⡏⣠
⠀⠀⢸⠉⡜⠀⢀⡤⠆⠀⠈⡙⢿⡿⠛⢥⢾⢧⡀⠀⠀⠹⡀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⣾⣿⣟⠉⢿⣤⡀⠀⠀⠀⠈⠚⣴⠃
⠿⠿⠿⣦⣀⣴⠋⠀⡠⠔⣫⣾⡏⠐⠦⡀⠓⢟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⢾⣯⣛⣷⣄⢀⣠⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠙⠿⠷⣶⣦⣼⣄⣏⣻⡅⡙⠶⢁⠐⠠⠜⣿⠿⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣈⡹⠿⠆⠉⠳⣝⣃⡀⠈⠗⠒⠙⠇⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⠀⡀⣀⡤⣤⣀⠠⠴⠶⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠶⠖⠁⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⢀⢀⣀⠤⠴⠞⠓⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⢀⣠⣄⡀⠀⠀⣀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⠀⠀⢰⠋⠀⠀⠈⢱⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⣸⠀⠀⠀⢀⣸⡀⠀⠀⢀⠘⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠁⡞⠉⠀⠈⠁⡖⠁⠀⠀⣴⣾⣷⡤⢠⢾⢸⠟⠁⠉
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢐⡄⠀⠀⠀⢀⡇⠀⠀⠀⠉⡏⠋
⠀⠀⠀⠀⣴⠞⠉⠉⠐⢤⠞⠉⠉⠒⢠⠶⠋⠉⠒⢠⡴⠞⠙⠒⢠⣴⠟⠉⠒⠀⡤⠞⠉⠒⠄
⠀⠀⠀⠀⡇⠰⡇⣧⣄⣀⣤⣄⡀⠀⢾⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠁⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠿⠿⣯⡴⠒⠢⠄⣀⡴⠒⠂⠄⣀⣴⠞⠲⠄⣀⣴⠞⠢⠄⢀⣤⠖⠂⠄
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢘⠏⠀⠀⠀⠀⠋⠀⠀⠀⠀⡟⠀⠀⠀⠀⡟⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⠼⠧⣀⠀⣠⡴⠧⣄⠀⢀⣤⠥⣀⠀⣀⡤⠧⢄⠀⠀⣠⠼⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⢸⠉⠀⠀⠀⢸⠋⠀⠀⣠⣼⡏⠀⠀⠀⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣠⣾⣀⠀⠀⣀⠈⠀⠀⠠⠿⢿⣅⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠁⠀⠀⠀⡞⠁⠀⣄⢺⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢻⢽⡂⡯⠌⢸⠥⠁⠾⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠑⠀⠈⠁⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⣼⢀⡀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠉⠻⡄⠀⠀⠘⠇⣠⠋⠉⠉⠙⣄⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢴⠁⠀⠀⠀⠀⢘⡤⠤⠤⢴⠃⠀⠀⠀⠀⠘⡦⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⢧⠀⠀⠀⢀⠞⠀⠀⠀⠀⢣⡀⠀⠀⢀⡜⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⡟⡟⢷⡀⠀⠀⠀⠀⡸⠋⠉⠉⠹⡄⠀⠀⠀⠀⢠⠟⠛⢻⠛⣆⠀⠀⠀⠀⢠⠏⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠸⠇⠀⠁⡇⢱⣤⣤⣤⣼⠁⠀⠀⠀⠀⢘⡤⠤⣤⣴⠱⠆⠀⠘⠀⠈⣦⣤⣤⣤⡋⠀⠀⠀⠀⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢠⠋⠋⠈⠁⠈⢧⠀⠀⠀⢀⠎⠀⠀⠒⣿⠳⡀⠀⠀⢀⡜⣿⡀⠇⠀⠱⡀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠉⠉⠱⡰⠇⠀⠀⠀⡼⠉⠉⠉⠙⡄⠀⠀⠀⠀⣠⢻⠛⠋⡟⢆⠉⠁⠀⠀⢠⠻⠛⠿⠟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⢹⠤⠤⠤⢼⠁⠀⠀⠀⠀⢘⣦⣤⠤⢴⠁⣸⡄⠘⠛⠈⡦⠤⠤⢴⡃⠀⠀⢠⡀⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⣠⠋⠀⠀⠀⠈⢧⠀⠀⠀⢠⠎⠈⢸⠀⠀⢳⡈⠁⠀⢀⡞⠀⠀⠀⠀⠱⡄⠀⠈⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⠙⠛⠳⡀⠀⠀⠀⠀⣼⠛⠟⠙⡿⡄⠀⠀⠀⠀⣰⠋⠉⠉⠙⢆⠀⠀⠀⠀⢠⠋⠉⠉⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠁⢹⠤⠤⠤⢼⠉⠱⠇⠘⠋⢘⠦⠤⠤⢴⡁⠀⠀⠀⠀⠈⣦⣤⡤⠴⡃⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⣠⠋⠀⠀⠀⠈⢣⡀⠀⠀⢠⠎⠀⠀⠀⠀⢳⡀⠀⠀⢀⡞⠇⣀⠀⠀⠱⡄⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠉⠉⠱⡄⠀⠀⠀⠀⡴⠉⠉⠉⠙⡄⠀⠀⠀⠀⡰⠋⠉⠉⠙⢆⠀⠉⠀⠀⢠⢟⢻⢛⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⢹⣤⣤⣤⢼⠁⠀⠀⠀⠀⢘⡦⠤⢤⢴⡁⠀⠀⠀⠀⢈⡦⠤⠤⠴⡃⠸⠂⠈⢰⡇⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⣠⠿⢸⠀⠰⠈⢣⡀⠀⠀⢠⠎⣷⠀⢰⡀⠳⡀⠀⠀⢀⠞⠀⠀⠀⠀⠹⣄⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠱⡄⠘⠁⠀⠀⡼⠉⠉⠉⠙⣄⠀⠀⠸⠃⡰⠋⠙⡛⡟⢆⠀⠀⠀⠀⣠⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠤⠤⢾⠀⠀⠀⠀⠀⢈⠦⠤⠤⢶⡁⠀⠀⠗⠀⢈⡶⠠⠤⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣠⠏⠀⠀⠀⠀⠱⣀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⣆⠀⠀⠀⠀⡰⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠖⠁


⡿⠿⠿⠿⠿⢻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠂⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⢸⠀⠀⠀⠀⠀⢰⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⠀⡁⢸⠀⠀⠀⠀⠀⢸⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠀⡄⢸⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡄⢸⠀⠀⠀⣀⣀⣸⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠇⢸⠀⠀⠀⠉⠲⣄⠀⠀⢀⡤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠐⢤
⠀⠀⢀⣀⣀⡤⣤⡀⠑⠐⠂⠁⡠⠎⠉⠐⠐⣄⠤⠇⢀⠀⡅⢣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠨⠀⣀⠬⠃⢀⡄⠠⡀⢀
⢠⠤⠋⠀⠀⠀⠀⠑⢤⠀⠀⢠⠀⠀⠀⢀⠎⠀⠀⠀⠂⠀⠃⠠⢀⠈⢦⣠⠖⠀⠚⠉⠓⣄⠀⠀⠀⢰⠉⠀⠀⠀⠈
⡔⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠈⠆⠀⠀⡞⠀⢠⠁⠀⠀⠀⠀⠀⠀⠁⠈⣇⠀⠀⠀⠀⠀⠀⢱⠀⠀⢏⡀
⢳⠀⠀⠀⠀⠀⠀⢀⠇⢀⣀⠀⠀⠉⠉⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠃⠔⠤⠠⠒
⠀⠓⠐⠂⠄⠂⠀⢠⠂⠈⠀⠉⠀⠠⠀⢱⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣀⣀⠠⠄⢊⠤⠐⠲⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⡨⠳⣀⠀⠑⠀⠀⠐⠊⢀⡴⠃⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⡗⠀⠈⠑⠢⡤⠤⠤⣖⠋⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⢄⣀⣀⠤⠒⠁⠀⠀⠀⠀⠣⠀⠠⠜⠀⢠⠔⠠⠄⡀⠀⠀⠀⠡⡀⢀⠀⠀⠀⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣰⠊⠑⠋⠉⠳⣀⠀⠀⠀⡘⠁⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠓⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⡃⠀⠐⢅⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈⠂⠒⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⣀⡀⠤⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⣠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡰⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⣰⣿⣿⣿⣥⣄⣦⣀⠀⠀⢀⢠⣠⣤⣾⠀⠀⠀⠀⠸⢯⢿⡑⠀⠀⠀⠀⠀⠛⠺⠃⠀⠉⠀⠀⠀⠀⠀⠀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠈
⢀⡤⠊⠉⠁⠀⠀⣸⡟⠋⠛⢻⣿⣿⣿⡏⢯⠀⠀⠀⠀⠀⠀⠀⠀⠛⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠂⢀⠤⠊
⠳⣄⡀⠀⠀⠀⢠⣿⠀⠀⠀⣠⣿⡟⣼⣻⡌⢧⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠳⣄⠀⠲⣤⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠀⠠⠁
⠀⠀⢹⠓⠚⠃⠛⠓⠂⠈⠉⠙⢻⣧⢿⣯⡷⠀⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠡⡀⠈⢦⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀
⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠶⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⢄⡀⡿⠁⠀⠀⠀⠀⡀⠔⠀⡀⠀⠀⠀⠀⡀⠀⠰⠆⠃
⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠹⠀⢠⠃⠀⠀⠀⠀⣤⡦⠂⠀⠀⠀⠀⠉⠚⠒⠘⠋⠀⠀⠀⠀⠠⢊⡴⡇⢻⣿⠶⠲⠖⠒⢶⠒⠙⢿⠁
⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠃⡞⠙⠀⢀⠀⠀⠸⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠙⢄⡀⠀⢄⡀⠀⣀⢀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⠰⠖⠒⠛⠉⠉⠉⠀⠉⠓⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠩⠟⠃⠛⠒⠛⠯⠁⠀⠀⠀⠀⠐⠿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡷⠦⠠⠤⠤⠄⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠤⠎⠵⠩⠖⣢⢀⣶⡖⠶⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⢠⡐⣠⣀⠀⠀⠂⢀⣇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠨⡣⡟⢿⣴⣧⣄⠻⣿⢸⣿⣢⣟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠦⠀⠄⠀⠀⠀⠀⠀⠀⠈⠺
⠠⣀⠄⠢⠁⠂⠀⠃⢐⣚⠛⠛⠋⠛⠙⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠘⠓⣥⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣟⣀⡀⠀⡀⠀⠀⢀⠀⠀⣠⣾⠄
⠀⠀⠀⠀⠄⠀⠤⠄⠀⠀⠀⠤⠀⠄⠠⠀⠀⢀⣀⡔⠀⠉⠀⠀⠀⠈⠠⢯⠀⠙⠃⠐⠀⠔⠀⠀⠀⠀⠀⠀⠀⠑⠋⠙⠛⠛⠿⠿⠻⠟⠛⠺⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡜⠁⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣇⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠅⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤
⠀⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⠙⢿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠆⠀⢠⣿⣿⣿⣿⡈⠉⢁⣴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿
⠀⠀⣰⣿⣿⣿⣿⣿⣷⣶⡷⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⡋⠉⢼⡀⠀⠀⠀⠼⠿⡿⠛⠹⣿⣿⣿⣿⣿⡿⠯⣿⣿⣿⠿⢿⠛⣿⣿⠋⠉⠉⠀⠻⠿⠿⣿
⢸⣆⡄⣠⠈⡙⣿⣄⡀⠳⣄⠀⣀⡀⠀⠀⠀⠀⢠⣿⡿⠁⠘⠃⠀⠉⠉⠁⠀⠀⢺⣿⠃
⠙⠻⣿⣿⣿⣿⣿⣿⣿⣆⣨⣷⣿⣿⣶⣤⣤⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⠃⣠⣤⣤⣴⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠈⠀⠉⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢀⠆⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢘⠤⠤⠤⡎⠀⠀⠀⠀⢱⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⢠⠎⠀⠀⠀⠹⡀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠉⢆⠀⠀⠀⣰⠉⠀⠀⠑⡀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢧⠀⠀⠀⠀⡼⠑⠒⠚⢇⠀⠀⠀⠀⠄⠒⠒⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠐⠀⢾⠁⠀⠀⠀⢈⡶⠆⠄⠎⠀⠀⠀⠀⢈⡶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢓⡄⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡜⠁⠀⠀⠀⠣⣀⣀⣀⡎⠀⠀⠀⠀⢀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢤⠊⠠⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢀⠏⠀⠀⠀⠳⡀⠀⠀⣠⠃⠀⠀⠀⢂⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⡵⡀⡄⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠱⡀⠀⠀⠀⠠⠋⠉⠉⠣⠀⠀⠀⠀⡰⠀⠋⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡰⡹⠿⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⡱⠤⠴⢔⠁⠀⠀⠀⢀⠆⠐⠲⠀⠀⠀⠀⠀⣼⠇⠼⠄⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⢢⣀⣀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠋⡆⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⣀⠎⠛⠉⠹⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠚⢯⣂⠀⢀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣳⣾⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣰⡁⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⢆⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⠻⡵⡄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠪⠷⠾⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠁⠈⣴⠟⠛⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⡉⠠⠀⠀⣸⣧⣤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠵⠾⣝⢅⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠈⠑⠀⠀⣐⣒⡍⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠙⢎⣦⣴⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⣷⡀⠀⠀⢀⢀⠞⠋⠉⠉⢦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢁⠈⠹⢷
⠀⠀⠀⠀⠴⠒⠲⡵⡂⠀⢀⣟⢁⠞⠛⠳⠾⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡅
⠀⠀⠀⠃⠀⠀⠀⠀⠉⠀⠀⠈⠃⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠈⠈
⠀⠀⠀⠀⣐⠂⠂⠃⢀⠀⠀⠂⠀⠀⠒⠂⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃

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

⠀⠀⡔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢃⠀⢠⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⢀⣠⠖⠂⢉⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠦⠄⠀⣴
⠀⠀⠈⡄⠀⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⡀⡎⠀⠀⠠⢴⠋⠀⣀⠴⠟⠀⠀⠀⢀⡀⠱⠶⠄⠀⣒⡲⠔⠒⠀⠀⠀⠈⠁
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠴⠀⡀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⡇⠀⠶⢅⡀⠀⣱⠛⠁⠀⢰⠃⠀⠈⠠⠀⠈⠀⢀⠂⠁⠀⠈⠀⠀⢀⠂
⠀⠀⠀⠀⢱⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠄⠐⠀⠐⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠀⠀⠀⠀⠀⠈⠀⠀⠡
⠀⠀⠀⠀⢀⠷⠊⠉⠭⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠄⠀⢠⡶⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢦⠂⢀⠤⠒⠒⠚⢆⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠸⠎⢀⠄⠐⠀⠉⠙⡄⠀⠀⠀⢀⠀⠀⠘⠀⡄⠀⠀⢠⠀⠀⢸⠀⠀⠆⠀⢀⡇⠀⡤⠀⠀⠀⡓⠀⢼⣷⡆⠀⠀⠀⠀⠀⠄⠋
⠀⠀⠀⠀⠀⠻⠁⡠⠒⠊⠉⠁⣇⠀⠀⠀⢸⠀⠀⡇⠀⣇⠀⠀⢸⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠂
⠀⠀⠀⠀⠀⠀⠙⢤⢀⠀⡠⠀⠁⠀⠀⠀⠆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢀⡀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠠⢄⡀⠐⠋⠁
⠀⠀⢀⠀⣀⠙⠀⠀⡇⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠤⡀⠀⠀⠀⢀⠀⠀⠀⢀⠀⡀
⠀⠀⢈⢺⡇⠀⠀⠀⠄⠂⠀⠀⡀⠀⠠⣌⠀⢉⢢⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣠⠜⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⢋
⠀⠁⠀⠜⠀⠀⠀⠀⠀⠀⠀⣄⣉⣉⠉⠉⠉⣩⡝⢛⢛⠉⠋⢱⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡐⠐⠉⠀⠈⠀⠘⠀⢄⠉⠀⢌⠀⠈⠁⠀⠀⣁
⠀⠀⠀⢀⠀⠀⠐⠒⠀⠀⠀⠜⠀⠀⠀⠠⠜⠉⠉⠀⠉⢷⠓⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢁⠈⠠⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘⠆⠀⠀⡀
⠀⣁⠰⠀⣅⠀⠀⡁⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠙⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⡁⠂⠠⠌⠙⠁⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⢤⠀⢄⠀⠀⡀⢠⠄⠁⠀⠀⠲⠀⢠⠀⠀⠀⠀⢦⣈⠀⠀⠀⠀⠀⠀⠀⡨
⠀⠂⠀⠀⠐⠔⠀⠈⠈⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠑⠈⠒⠘⠂⠀⠀⠠⠀⠠⠈⠀⠈⠀⠀⠀⠀⠀⠛⠥⣴⣀⣀⣀⡩⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⢿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⡀⠀⠀⣸⣿⡟⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⠿⣷⣠⡾⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡀⣴⡿⠁⠀⠙⠟⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠹⣿⣿⣿⣿⣿⣿⠏⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⣠⡶⡄⡴⢦⣠⠶⣄⡤⢠⢠⠴⠄⢶⠆⡄⢤⢠⢠⠀⣴⠠⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠉⠂⠓⠚⠘⠓⠃⠙⠚⠈⠓⠂⠘⠀⠃⠈⠃⠘⠀⠛⠀⠘





⣿⣿⠿⢿⡿⠿⠿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⡴⠞⠳⢦⣀⣠⠴⠛⠲⣤⣀⣤⠖⠛⢦⣄⣠⡴⠞⠳⢦⣀⣠⠶⠛⠶⣤⣀⡤⠞⠛⢦⣄⣠⡴⠚⠳⢤⣀⣠⠶⠛⠶⣤⡀
⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⡇
⠀⢀⣠⣧⣀⠀⠀⣀⣼⣇⡀⠀⠀⣠⣿⣀⠀⠀⢀⣸⣧⡀⠀⠀⣀⣼⣄⡀⠀⢀⣠⣿⣀⠀⠀⢀⣸⣧⡀⠀⠀⣀⣿⣄⡀⠀⢀⣠⣧⣀
⣾⠋⠁⠀⠉⢳⡞⠉⠀⠈⠙⣷⠛⠁⠀⠈⠛⡞⠋⠁⠀⠉⢳⡞⠉⠀⠈⠙⣷⠋⠁⠀⠉⠻⡞⠋⠀⠀⠙⢳⡟⠉⠀⠈⠙⣶⠋⠁⠀⠉⢻
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠙⠳⢦⣤⠶⠛⠛⠶⣤⡤⠞⠋⠳⢦⣤⡴⠚⠙⠳⣤⣤⠶⠛⠛⠶⣤⡴⠞⠛⠳⢦⣤⡴⠛⠙⠲⣤⣤⠶⠋⠛⠦⣤⡴⠞⠛⠳⢦⣤⠶⠛
⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⣀⡴⢧⣄⡀⢀⣠⡼⢦⣀⠀⢀⣤⠿⣄⡀⠀⣀⡼⢧⣄⠀⢀⣠⡾⣦⣀⠀⢀⣤⠿⣄⡀⠀⣀⡼⢧⣄⠀⢀⣠⠿⣤⣀⠀⣀⣤⠷⣄⡀
⣿⠉⠀⠀⠈⢹⡏⠁⠀⠀⠉⣿⠋⠀⠀⠀⠙⡟⠉⠀⠀⠈⢹⡏⠁⠀⠀⠉⣿⠋⠀⠀⠈⠙⡟⠁⠀⠀⠈⢻⡏⠁⠀⠀⠉⣿⠉⠀⠀⠈⢹
⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠉⠛⢦⡴⠞⠋⠙⠳⢦⡴⠛⠉⠙⠶⣤⠖⠋⠉⠛⢦⡴⠞⠉⠙⠳⣦⡶⠛⠉⠙⠶⣤⠞⠋⠉⠓⢦⡴⠞⠉⠙⠳⣤⠶⠛⠉⠛⠶⣤⠞⠋
⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⡇
⢀⣠⡴⠷⣤⣀⣀⣤⠾⠧⣄⡀⣠⡴⠿⢦⣄⢀⣠⠾⠷⣤⣀⣀⣤⠾⢦⣄⡀⣠⡴⠿⢦⣀⢀⣠⠾⠷⣤⡀⣀⣤⠿⢦⣄⣀⣠⡴⠷⣤⣀
⣿⠁⠀⠀⠀⢹⡏⠀⠀⠀⠈⣿⠁⠀⠀⠀⠈⡏⠁⠀⠀⠀⢹⡏⠀⠀⠀⠈⣿⠁⠀⠀⠀⠉⡏⠀⠀⠀⠀⢹⡏⠀⠀⠀⠈⣿⠁⠀⠀⠀⢹
⣿⡀⠀⠀⠀⣸⣇⠀⠀⠀⢀⣿⡀⠀⠀⠀⣀⣇⡀⠀⠀⠀⣸⣇⠀⠀⠀⢀⣿⡀⠀⠀⠀⣠⣇⡀⠀⠀⠀⣸⣇⠀⠀⠀⢀⣿⡀⠀⠀⠀⣸
⠈⠙⠳⡶⠛⠁⠈⠛⢶⡞⠋⠁⠉⠳⣶⠚⠉⠈⠙⢳⡶⠛⠁⠉⠛⢶⠞⠋⠁⠙⠳⣶⠛⠉⠈⠙⢲⡶⠋⠁⠉⠛⣶⠞⠋⠀⠙⠳⡶⠛⠉
⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠛⢦⣄⣠⡴⠟⠳⢤⣀⣤⠶⠛⠶⣄⣀⡴⠞⠳⢦⣄⣠⡴⠛⠳⣤⣀⣤⠶⠛⠶⣄⣀⡴⠞⠳⢦⣀⣠⠴⠛⠶⣤⣀⣤⠞⠃

⠀⠀⠀⠀⠀⠀⠄⠐⠂⠉⠉⠉⠛⠢⣍⡀⡂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⣠⡄⢻
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠁⡘
⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠁⠒⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠀⠔⠒⠀⠒⠒⠒⠒⠀⠀⠀⠤⠀⠤⣄⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠙⠂⠀⠀⠤⠤⠀⢀⠔⢁⣀⠈⢳⡶⠶⢶⠄⠀⠐⢤⣤⣤⣤⣀⡄⠀⠀⠀⠀⠁⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡴⠀⠀⠁⠀⠀⣴⡧⠄⠀⠀⠀⢣⠀⠘⠪⣙⠋⢀⠔⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⡘⠁⠀⠀⠛⢉⡙⠛⠛⠓⠒⠶⠦⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢀⠁⠀⠀⠀⠠⠤⠼⠆⠼⣀⡘⠊⠀⠀⣀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⡄⠀⠈
⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⠛⠓⠒⠶⠦⠤⣤⣤⣄⡀⠀⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡇
⠀⠀⠀⠀⠀⠠⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⡆⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠄⠒⠉⠀⠀⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠉⠉⠀⠐⠒⠒⠒⠀⠀⠤⠤⠀⠀⡇⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠣⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡇
⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⣇⡀
⣡⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⡀⠀⢀⣀⢀
⠀⠀⠀⠀⣀⠔⠛⣷⣄⠠⠒⢿⣦⡄⠀⠀⠀⠀⢈⣿⣽⣽⣿⣟⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤
⠀⠀⠀⣰⣧⣤⣴⣿⣿⣷⣶⣴⣿⣇⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠰⠛⠛⠋⠉⠀⠀⠀⠀⣀⣤
⠀⢀⣰⣿⢿⣿⣿⡟⠻⣿⣿⣿⡿⢿⣷⣦⠀⠀⢿⣇⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁
⠀⢸⣧⣤⣼⣿⣿⣧⣴⣿⣿⣿⣤⣴⣿⣿⠀⠀⠈⢻⣦⡀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁
⠀⠈⠻⣿⡿⠟⠛⢿⣿⣿⠟⢿⣿⡟⠋⠁⠀⠀⠀⠀⠙⠻⠿⠿⠛⠃⠀⡀⢀⡴⢶⣢⠟⠋⠀⢀⣀⣠⣀⣀⡀
⠀⠀⠀⢸⣷⣤⣤⣾⣿⢿⣧⣶⣿⡇⠀⠀⠀⠀⢸⣦⣄⠀⠀⠀⠀⠀⢸⣧⣾⠉⠁⠀⠀⠀⣼⣿⢻⡍⢭⠙⣿⡆
⠀⠀⠀⠈⠀⠹⠿⠋⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣰⢿⠇⣸⠃⢸⡆⢿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⠀⢿⠀⠸⡇⢸⣼⣇
⠀⠀⣠⠶⠒⣦⠔⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣄⠀⠀⣿⡍⠀⠀⠀⠀⢿⣿⡀⣾⠀⢠⡧⢸⣿⡏
⠀⠀⠙⠿⣿⠏⠀⠀⠀⠀⣀⣤⡶⠂⠀⠀⠀⠀⠸⠿⠿⠿⠟⠟⠻⠗⠀⠛⠁⠀⠀⠀⠀⠘⣿⣗⢿⠀⢸⡇⡾⡽⠁
⠀⠀⠀⡇⢛⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠿⣾⡆⢸⣰⠿⠁
⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⣷⣿⣶⠟
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⡀⢀⡀⠠⡀⠀⡀
⣠⣴⣶⣀⠀⠀⠐⣢⣤⡀⠀⢶⣶⣿⣿⠆⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠰⣄⠙⣆⡻⣦⣿⣠⣼⣤⣮⠔⠃
⠸⣿⡿⠶⠤⠄⠲⢻⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⢣⢞⡷⠿⣿⣿⣿⣿⣷⡞⠳⢆
⠀⠈⠻⣶⣤⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⡤⣀⡴⢿⣿⣿⣿⣛⡍
⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⢖⠿⣿⣿⣶⣿⣿⣿⣿⣿⣯⠼⠆
⠀⠀⠀⠀⠀⣀⢀⠀⣸⣿⣿⡥⠀⠀⠀⠀⠀⠙⣿⣧⣿⣯⣼⣿⡟⠁⠀⠀⠀⠀⠉⣰⠉⣿⢿⣿⣿⣿⣿⡟⢾⡝⠲
⠀⠀⠀⠀⢴⣿⣿⣦⠐⠻⢟⢡⣠⡄⠀⠀⠀⠀⢻⣿⢻⠻⡿⡿⡇⠀⠀⠀⠀⠀⠐⢋⠊⠻⠞⣧⣸⢻⡌⠻⡄
⠀⠀⠀⡀⠜⠻⠿⠓⠀⠀⣾⣿⣿⠟⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣁⣈⣀⠀⠀⣷
⢀⠴⠮⣶⣶⣤⣃⡿⠦⠀⠈⠉⠀⠀⠀⠀⠀⠀⣼⣨⢰⠀⡆⡇⡇⠀⠀⠀⠀⠀⣴⠿⣿⠟⣻⠿⡿⣿⠃⢄⡁
⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣻⣾⣿⣿⣟⣁⣀⣀⣀⣀⣈⣉⣈⣁⣈⣁⣈⣁⣈⣀⣈⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡔⠦⣠⠲⡄⣦⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠳⠖⠙⠶⠉⠇⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢠⣄⠀⠀⠈⠻⣦⠀⠀⢀⣾⠛⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢸⣿⠀⢀⣴⠶⢿⡷⠾⠛⠁⠀⠀⠀⠈⠛⠷⠶⠶⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢀⣼⠏⢰⣟⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣻⣆⣀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠛⠁⠀⠀⣿⠀⠀⠀⠀⣠⡶⠟⠛⠛⠛⠻⢷⣤⡀⠀⠀⠀⢙⣿⠍⠉⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡀⠀⣀⣼⠏⠀⠀⢀⣾⣋⣤⡶⠟⢷⣦⡀⠀⠈⢿⡄⢀⣴⠟⠁⠀⢀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠏⠁⠀⠀⠀⣼⠟⠋⠁⠀⠀⠀⠈⠻⣦⣄⢈⣿⠟⠁⠀⢀⣴⣿⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⢿⣄⣠⣴⠾⠿⣦⡀⠀⠈⠛⠟⠁⠀⢀⣴⠟⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠘⣿⡉⠀⠀⠀⠈⠻⣦⣄⠀⠀⢀⣴⠟⢁⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⠻⣦⣄⣀⣀⣀⣨⣿⢷⣴⠟⠁⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣀⣹⣷⠶⠟⠛⠛⠛⠛⠛⠛⣷⡀⠀⢀⣠⣴⠾⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡏⠉⠀⠀⠀⠀⠰⠶⠶⠶⠶⠟⠛⠛⠛⠉⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣿⡷⠶⣶⣦⣤⣤⣤⣀⣀⣀⣀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠉⠛⠲⢄⣠⣶⠛⠛⠓⠦⢄⣤⣶⡿⠛⠓⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠈⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⡸⠛⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠉⠓⠦⣠⣴⠟⠋⠉⠲⠦⣠⡴⠚⠋⠙⠂⢀⣸⣶⣊⠀⠀⣀⣶⢰⣴⡾⠟⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⡿⠓⠃⠛⠙⢼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣯⠉⠁⠀⠠⠀⠀⠈
⠀⠀⠀⠀⠀⢠⣤⣾⠟⠙⠓⠰⢄⣤⡾⠛⠛⠓⠦⢀⣠⣶⠿⠛⠳⠦⡄⣠⣤⡾⠛⠲⠤⢀⣠⣶⡿⠙⠲⠤⠀⣀⣴⠾⠛⠲⢤⡀
⠀⠀⠀⠀⠀⢸⡏⢁⣠⢠⡄⠀⠀⠉⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠰⡟⠉⠀⠀⠀⠀⢰⡿⠉⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⠇⠈⠟⡸⢽⠆⣤⣶⣾⣦⣤⡀⠀⠸⠇⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣥⡶⠟⠓⠦⠄⢀⣠⡶⠟⠓⠦⡄⣀⣠⡶⠟⠳⠦⣄⣀⣠⣶⠟⠳⠦⡀⢀⣤⡶⠿⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠁⠀⠀⠁⠐⣿⠛⠁⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠓⠲⣤⣀⣀⣴⡾⠛⠶⢤⡀⢀⣠⣶⠳⠦⣤⡀⣀⣤⠶⠳⠦⣄⡀⢀⣠⣶⠿⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⡿⠋⠀⠀⡀⣀⣼⣿⡁⠀⠀⠀⠀⢸⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⠇⠘⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠟⠶⠤⡀⣀⣠⡶⠄⠀⠀⣠⡰⠛⠋⡹⢷⣄⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⣿⠋⠀⠀⢰⣍⢺⡅⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠉⠀⣶⠀⠀⠀⠀⠀⠀⠀⢰⡖⣲⠄⢒⡂⡐⠀⣖⢀⠒⢰⣆⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢨⣯⣹⠆⣨⡏⣁⡄⣭⠈⡡⣦⣉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡀
⠀⠀⠀⠀⠀⠀⠈⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⢻⡄
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡈⢷⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⣼⡇⠀⠀⢸⡆⣇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣷⢻⡄⠀⠀⠀⠀⢸⠇⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⡼⢸⠇⠀⠀⠘⣷⡹⣦⡀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠘⢧⣙⠶⠄⠀⣠⠏⠀⠀⠀⠀⠈⠻⣤⣀⡀⠀⣞⡵⠋⠀⠀⠀⠀⠈⠻⢮⣭⣭⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⢸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣆
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠘⣄
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢰⠇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠘⣆
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡿⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢠⡇⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⣏⣇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⢲⢻⠀⠀⠀⠸⡇⣧⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠹⣞⢧⣀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠈⠳⣦⣀⣀⢐⣣⠟⠀⠀⠀⠀⠻⣌⠳⠤⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠈⠳⠯⣿⣿⠥⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⣀⠤⢄⡀⠀⢀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠈⡆⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣄⡀⣠⢞⣐⣤⣀⣀⠜⠰⣄⠀⢀⡴⣃⢦⡀⢀⠴⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⡉⠛⠉⠀⠙⠯⠀⠀⠀⠀⠉⠉⠊⠁⠙⢮⢰⠋⠀⠈⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⣠⠀⣄⠀⠀⢀⡄⢀⠀⠀⢀⡴⠠⡀⠀⠀⡰⠹⣀⠀⢀⡠⠡⣄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⠓⠁⠐⠙⠚⠉⠀⠘⠛⠂⠁⠈⠙⠪⢒⠉⠀⠉⠛⠏⡽⠂⠐⠊⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⠀⠀⠀⠀⢀⡆⠀⠀⠀⢰⠇⠀⠀⠀⢀⡆⡀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠺⢷⠤⠖⠁⠺⣶⠤⠔⠋⠀⠐⠢⠔⠟⠓⢿⠒⠒⠙⠛⠻⣶⠤⡾⠷⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠔⠥⣢⣄⣠⣀⠤⡲⠤⡀⢀⡨⢝⡢⣄⢔⡯⠼⢗⠦⠴⠃⠑⠦⣀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠀⠀⠀⢱⠘⠁⠀⠀⠈⡖⠉⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⢄⢲⣀⠀⠀⠴⣀⢀⠀⢀⣴⣘⢠⡀⢀⡠⠏⠠⣄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠋⠁⠈⠋⠉⠐⠉⠉⠁⢉⠋⠉⠈⠙⠂⠉⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⣄⠀⠀⢀⣼⡀⠀⠀⠀⡼⢢⡀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠔⠋⠀⠀⠑⠒⠁⠀⠓⠦⠴⠊⠀⠀⠉⠒⠉