Hibiscus Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠜⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⣰⠃⠀⠀⠀⡰⠂⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⡴⠁⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢰⡁⣠⠄⣀⡀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⣿⣿⣃⠀⠈⠉⠑⠢⢄
⠀⢠⠖⠉⠉⠉⠓⠦⠼⢆⡀⠀⠀⠀⠀⠀⣴⡽⡶⡣⠛⠈⠀⠀⠀⠀⠀⠀⢱
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠷⣄⠀⢰⡨⣟⣽⣞⠄⠀⠀⠀⠀⠀⠀⠀⠈⣱⣀⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢹⣿⡜⣡⣯⣨⣴⣆⣀⣀⠀⠀⠀⠀⢀⠔⠁⠀⠉⠉⠑⠢⣀
⠈⠢⣀⡀⠀⠀⠀⠀⠀⢀⣒⣶⣾⣿⣋⣴⣿⣿⢿⣉⠁⠈⠉⠓⢶⣖⣊⣁⣄⣀⠀⡀⠀⠀⠀⠈⠉⠲⢄
⠀⠀⠀⠉⠓⠤⠤⠤⠤⡴⠁⠔⢋⡿⠋⠙⢏⠂⠑⡄⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠈⠀⠀⠒⠀⠀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢸⠦⠤⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢀⠜⠈⠙⢦⡀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠉⠛⠛⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣠⣄⠀⠲⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢦⡆
⠀⠀⠀⠘⠿⠟⠀⠀⠨⠀⠀⠁⠀⠀⠀⠀⠁⠀⠐⠚⠛⠉⠀⠀⠀⢀⠀⣀⣰⢤⡁⠀⠰⡉⠀⠀⢀⠀⠀⠀⠠⣿⣿
⠀⠘⢒⢎⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⣶⡀⠀⠤⠀⠀⠀⠀⠀⠀⡀⠀⠛⠁⠀⣰⣶⣆⡀⠀⠀⢘⡄⢨⣀⠀⢈⠇⠀⢀
⠀⠀⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⡴⠏⡝⠙⢃⣀⢀⠞⠀⠀⠀⢴⠿⠷⠀⠀⣁⠒⠛⠛⠋⠉⠀⠀⠈⠀⠀⠀⢀⠀⠈⠙
⠀⠀⢀⡀⢸⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠂⠠⣄⡠⠿⡀⣀⡦⠀⠀⠀⠀⠀⠲⠈⠉
⠀⠑⠰⡄⢠⡗⠈⠻⠿⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠄⠀⠀⠀⠃
⠀⠀⠈⠑⢺⠿⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⢠⠀⠀⢀⠁⠀⠀⠀⠀⠀⠋⠐⣶⡷⠎⠀⠀⠂⠀⠀⠀⠀⠀⢸⣿⣦
⠀⠀⠀⠀⠀⢀⢀⡀⠀⣀⡄⠉⠀⠀⠠⠄⢀⠀⠀⠀⠀⠄⠀⠀⠀⣄⣀⡘⠉⠉⠀⢠⠼⠂⠐⠂⠀⠀⠀⣄⠀⠀⠀⠄
⠀⡀⠀⠀⠀⠀⠋⠀⠀⣈⡀⠀⠀⠀⠀⠀⢀⡀⢁⡠⠄⠤⠀⠀⠀⢀⠶⠷⠄⢠⠀⠀⠀⠀⠀⠀⠈⢢⢠⣾⣷⣖⠂
⠀⠀⠀⠀⠀⠉⠀⠀⢺⢿⡗⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠤⡨⢋⠉⡦⠀⠒
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⠖⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠑⠂⢰⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⢠⣸⡄⢀⡆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⢦⡀⠀⡎⠀⠀⠑⣿⣿⣿⣷⣎⣀⠀⠀⠀⠈⠀⠀⠐⠤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢀⣤⣶⣶⣖⠖⠙⠻⠷⠤⣀⠀⠀⠀⠈⠙⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠙⠲⡿⢯⣀⠒⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⢉⡉⠋⠛⢋⣩⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢀⠊⠤⠞⠁⠀⠀⣰⣼⣿⣿⣁⠀⠀⠀⢀⣀⠀⢀⣀⣿⡙⠛⡖⠦⠶⣚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣃⣠⡼⢁⣄⡤⠚⢻⣿⠟⠛⠛⠉⢉⡀⠩⠃⠹⣯⡻⣿⣧⣷⣼⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠈⣿⠈⠀⠀⠀⢠⡇⠀⠀⠀⣿⠅⠈⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢀⠀⠀⠀⣸⠁⠀⠀⠈⡿⠤⠽⠊⠀⠉⠙⠻⠿⠿⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⡇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠐⠀⠈⠆⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⢀⡴⠚⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⠈⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣰⠞⠋⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠡⠶⠀⠀⠀⠄⠆⠐⠉⠈⠀⠐⢆⠀⠰⣝⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠠⢶⣄⣄⡀⠀⠀⠀⠀⠀⠈⣷⣽⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⣀⡀⡄⢠⠁⡀⠄⠀⠄⠀⢿⡴
⠀⠀⡀⠀⠀⠀⠁⠈⠛⣿⣾⣦⣤⠀⢀⡤⠲⢾⣻⣿⣿⠓⠀⠀⠀⠀⡀⠁⠀⠀⠀⠉⠑⢆⠀⠀⠀⠀⣶⡏⠀⠄
⠀⠀⠡⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠙⠃⠈⠉⡿⠛⠈⠻⡄⠀⠀⡐⠉⠀⠀⠀⠀⠀⠀⢀⠈⠆⠀⠀⢾⣿⠃
⠀⠀⢀⠁⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠎⠀⠀⠀⠀⠈⠛⢷⣲⠄⠀⠀⠀⠀⠀⠀⠀⣄⣸⢀⣾⣿⡏⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠈⠰⠄⠀⠀⠀⠰⠚⠀⡰⠖⠋⠀⠀⠀⠀⠀⠀⠀⠄⢣⠀⠀⠀⠀⠀⠀⢀⣰⣼⣿⡾⣹⡟⠐⠊
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡤⠀⠀⢀⣀⢠⡀⠀⠀⠀⠀⠀⠀⣀⡸⠓⠂⠀⣀⠤⠀⠘⢻⣿⣯⣾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢶⣧⡍⢤⠀⠐⠂⠘⢌⣡⡀⠀⠉⠑⣲⣆⡠⠒⠊⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⡴⠛⢻⣿⣍⢉⡒⠢⢄
⠀⠀⠀⠰⠿⠄⠀⠀⠀⣀⡦⠀⠀⠈⠀⠀⢰⠇⠿⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠀⠊⠀⠀⢸⠉⠉⠀⠀⠀⠀⠘⢦⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⣄⣈⠏⠀⠀⠀⠀⠀⠨⡃⣴⡀⠀⠀⠀⠀⠀⠀⠆⢀⠄⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠳⠀⠀⠀⠀⠈⠣⣵⣜⣟⠦⣰⣄⠀⠀⠀⡠⠋⠤⠦⠀⣠⡤⠊⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠠⡠⠀⠀⠀⠀⣰⠿⣿⠃⡱⠶⠦⠤⣈⡒⠊⠛⠿⣿⣿⣿⣷⠊⠁⠀⠀⠀⠀⠀⢹⢀⡀⠀⣦⣀⣀⠀⠠⣠⡄
⠀⠉⠀⠀⠀⠀⠀⣠⢞⣽⡋⠀⠀⠀⠀⣀⡍⣙⣿⢿⣯⣾⣿⣯⣴⣤⣠⣤⡴⠖⠛⠒⠺⣷⣾⡏⣿⡿⠛⠄⠉⡀⠁⠐⠀⠀⠄⢀⠐
⢠⡠⠄⠴⠦⠐⠛⠱⡫⡏⠀⠐⠊⠀⠀⠁⠀⠄⢠⡞⠛⡿⠛⠋⠙⠉⠁⠀⠀⠀⠀⠀⠀⠙⠏⢧⠀⠈⠀⠀⠒⢌⢣⣤
⠈⠀⠀⠀⠐⠂⣁⢐⠀⠴⠀⠀⢀⣴⡉⢀⡴⠞⠛⠀⠀⠀⠂⠐⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣀⡀⠀⠀⡀⢀⠃
⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠁⢀⡻⠷⠄⢺⠀⠀⣴⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠃⠀⠀⢸⡝⠛⠓⢆⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⠀⠀⠀⠈⢄⣨⣿⠃⠀⠀⠈⠲⣄⣀⠀⢀⣀⣠⠐⠂⢚⠀⠀⠀⠐⠛⠳⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠠⠈⠛⣿⣆⡀⠐⠈⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⢀⡀⠋⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⠀⠄⠀⠀⠀⠈⣽⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠐⠰⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⣀
⠀⠀⠀⠀⠀⠀⠹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣆
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⢲⡊⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣹⡇⢂⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢿⠀⠀⠀⢀⣠⣶⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⣰⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣿⣿⣿⣿⣿⣿⣿⡏⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣶⣦⣀⣀⣹⣿⣿⣯⢹⣾⢿⡿⣼⣿⣿⣿⢟⣽⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣯⢿⣵⣿⡟⡼⣣⣼⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⡿⠙⢸⣿⠋⣠⡿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣝⣳⢭⢁⣹⣿⣾⣿⣿⣿⣡⣤⣄⡀
⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⣶⣿⣿⣿⣟⡿⢋⣲⢾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣃⣤⠟⣹⣿⡕⣴⢸⣦⢹⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⡎⠀⠀⠉⠓⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠀⢤⣸⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠔⠋⠀⠉⠉⠈⠀⡀⡼⠁⠀⠀⢠⠀⠀⡄⠀⠲⠤⣜⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢦⣄⡀⠀⠏⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⢆⢸⡄⠀⢁⠄⠀⣠⠿⠶⠶⠖⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⣀⣙⣄⠀⠀⠘⢠⠇⠀⠋⣠⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⢀⣀⡉⢹⣧⣠⡴⠏⣀⡤⠞⠃⢀⡀⡀⠀⠀⠀⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠲⠇⠀⠀⠀⠉⠇⠀⠀⠀⢀⣠⣄⠈⣻⣿⣿⢿⣿⠖⠖⠚⠉⠉⠉⠑⣌⠢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢄⣲⡀⠀⠀⠀⡄⠀⠀⢉⠀⠞⠃⢉⢿⠿⡘⠿⠂⠐⠒⣤⠀⠀⠀⠈⠣⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⠽⣄⠀⠀⠇⠀⠀⡼⠀⠀⠀⠊⠀⣃⠙⠄⠰⣝⠀⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⣙⣦⡀⠀⢀⡜⠀⠀⠀⠀⢀⡴⠋⢀⠄⠀⠈⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠘⠁⠀⠘⢄⡀⠀⠀⠐⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣋⡁⢰⠿⠂⠐⠒⠶⢤⡀⢠⡿⡄⠀⠀⠀⠀⠀⠀⣠⠞⠒⠄⣠⠖⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⠙⠦⣀⣀⣀⡖⠀⠃⠀⠀⠸⣿⠀⡠⠖⠒⠊⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢀⠂⠀⠀⠀⠀⠀⢠⣤⠆⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⠀⠀⠆⡄⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⠤⠁⠒⠦⠤⠀⠢⠤⣄⠀⠀⠀⠀⢸⢲⡀⠀⣆⠷⠕⠂⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢸⠀⠳⣼⡇⠀⠄⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡀⢂⠀⠀⠀⢢⠀⢸⣂⡼⠋⠛⠦⠄⡀⠠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠂⠈⠛⠠⢦⣘⡄⢸⡇⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⡀⠴⠞⠛⣾⡀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠴⠚⠉⠳⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠄⠀⠀⠀⢀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠑⠀⠈⠇⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠈⠑⠂⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡠⡌⠃⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠘⢓⣾⢻⡍⠓⠀⠒⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⢀⣀⡈⠡⡌⣩⣩⡅⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠎⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⠀⠀⠀⠀⠀⠀⠀⠉⢍⡚⣥⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠸⠤⣌⣀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠂⠌⣤⣀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡉⢋⠀⠀⠀⠀⠀⠈⡆⠀⠄⠀⠀⡎⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠒⠉⠀⠀⠉⠀⠑⢀⠀⠀⠀⠀⣎⠀⠀⢠⡐⠀⠠⢀⠎⠐⠀⣀⡤⠴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡸⣧⣀⣼⠀⡀⣡⣧⡶⠒⠉⠀⠠⠤⠤⢤⡒⢤⡀⠀⣠⠒⠚⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣹⣿⣿⠇⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⢀⣿⣿⣷⣿⣭⣉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠀⠉⠉⠁⢀⡙⠻⡓⢍⠁⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠋⠀⠀⠈⠂⠑⡄⠀⠑⠂⠄⠉⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠘⠀⠀⠑⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠨⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠄⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⣀⠀⠀⡀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠂⠁


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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⣿⣿⣿⣿⢻⡻⡛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⢣⡘⠒⡄
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣊⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⣤⣦⣾⣿⣶⣾⣶⣄⢰⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣦⠃⢸⣿⡿⠿⢿⣿⣿⣿⣿⠸⢟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣷⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠻⠿⠿⣿⢠⢻⠟⠁⢀⡄⠈⠙⣿⣿⡦⢺⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡀⠀⡀⠀⠙⣿⢸⢠⡆⣿⠀⡀⢀⣾⡿⠃⠾⠿⢿⡿⠋
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡅⠀⠹⣄⢰⡘⣿⣾⣇⡏⡸⢃⡼⠿⠾⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣻⣷⣦⣞⣷⣿⣿⣯⣻⣿⣿⡥⢖⣀⣀⣌⡙⢿⣿⣷⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⠉⠱⢛⣛⠯⣿⣿⣷⣽⣿⣿⣿⣿⠛⠷⠄⠈⠀⣾⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⠀⢠⠞⠋⠀⢐⣻⣿⣿⢹⡏⣿⠿⣷⢦⣄⣀⣤⣤⣿⣿⠏
⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⡄⠀⢀⣠⡿⣻⠇⠉⠀⢷⠘⠆⠙⣷⣝⣿⣿⣿⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣜⠻⠿⣿⣿⣿⡿⢱⣿⣧⡄⠀⠘⠂⠀⠀⣿⣿⣷⠈⢱⣾⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡿⢃⣠⣶⢰⣆⢸⣿⣿⣷⣤⣤⣶⣶⣶⣿⣿⡿⣸⣷⣼⣿⣇
⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⣿⣿⡿⣡⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⠉⠉⠉⠉⠉⠀⠛⠻⢿⣿⣿⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⡀
⣿⣿⣿⣿⣫⡽⣿⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢻⣿⠆⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠉⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠶⢦⠤⠶⣶⣼⣿⣷⡌⢀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⣿⣧⣾⣿⠤⠀⠀⠀⡀⠀⠀⠀⠠⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢴⣿⠁⠈⠈⠛⠋⠟⡹⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢤⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠐⠄⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠤⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢀⣾⠃⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠉⠁⢆⣀⣄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⣄⠙⢻⣅⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢠⣶⣢⣶⡟⠉⠁⣀⠈⠣⢤⡀
⠀⠀⠀⠀⠀⡠⠒⠈⠁⢦⣄⡀⠀⠘⢄⠀⠉⢣⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⣿⣿⠿⠿⣷⡾⣿⢿⣿⣦⣀⠙⠂
⠀⠀⠀⢤⣠⣤⡄⣀⢤⠞⣹⣿⣶⢊⣶⣟⣤⣤⣿⣄⣀⠀⠀⠃⠀⢠⠚⣿⣯⠀⠻⣆⠀⠀⠀⠀⠁⠌⠻⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠙⡏⣹⣿⠟⢛⣿⠋⠉⠉⠂⠰⣇⠀⠘⢧⡀⠀⠘⢧⡀⠐⢷⣤⣔⣿⣥⣈⠃
⠀⠀⠀⠀⠀⠀⠑⢄⣈⣬⣖⣉⣀⣠⣴⣿⣷⣾⡿⠁⠀⠀⠀⠀⠀⠉⢤⡀⠈⠑⠦⣤⣾⣌⣷⣾⠿⠟⠛⠋⠉⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⠽⠿⢿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⢴⣧⠆⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⢡⣤⡄⠀⠀⡀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⣾⠏⠁⢀⡤⠟⠛⠷⠶⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠻⢦⡄⠈⢿⡀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠛⠋⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢀⡾⡿⢃⣠⣶⣋⣤⣤⣀⣀⡄⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣷⣌⣿⣿⣷⣀⠀⠀⠀⠀⢤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡄⢰⣾⣴⣾⣿⣿⣿⣛⣿⣿⣿⣿⣿⣷⣶⣦⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠟⠉⠂⠀⠀⠀⣟⣀⣀⡀⠀⠀⢀⠀⡀⠀⠀⠀⢀⣼⡿⠀⣾⣿⣿⣿⣿⣻⣯⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠺⢿⣿⡟⠙⠁⠀⠀⠀⠀⠘⣿⠛⠛⠛⠗⠀⢿⠛⠁⠀⠀⠀⠘⠛⠐⠾⠿⣿⣿⣿⣿⣿⣯⣙⣿⣿⣮⣿⣿⣿⣿⡿⠛⠋⠙
⠀⠀⡀⣀⠀⠀⡶⠀⠀⠀⠀⠀⠘⠁⠙⠆⠀⠀⠀⠀⠀⠀⠛⣿⣾⣶⡶⣾⠟⠚⠳⣆⠀⣰⢷⡞⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠟⠛⠉⠁
⠲⠶⠁⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡆⠠⡀⠀⠈⣿⠃⠈⢸⢿⣾⣶⣖⡒⢢⣀
⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡾⠁⠀⠠⣎⢸⡏⢻⣿⣟⠀⠤⢻⡄
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⠞⠀⠀⠀⣤⣼⡟⢀⡀⠿⢿⡷⣀⠀⠙⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠈⠁⠛⠉⠁⠐⠒⠋⠀⠀⠀⢠⠋⠀⠀⠀⠀⢿⣿⣤⣟⠃⠀⠈⣿⣿⡀⠀⢃
⠀⠀⠀⠀⠈⢀⣴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠸⣿⣾⠃⢠⠆⠀⠘⣿⡃⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠛⢧⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⣸⠃⠀⠀⢻⡇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⢀⣀⡀⢣⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣶⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣠⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⡰⠦⡀⠀⠀⢰⣆⣻⣷⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠙⠣⠉⠁⠀⠀⠀⠀⢈⡛⡿⢏⣷⣿⣿⣿⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣑⣶⣿⣭⡱⠞⠁⠈⠑⡶⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠒⠚⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⠙⠆⠁⠉⠀⠈⠁⠀⠀⠈⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠋⢀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⢴⡉⠁⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⢁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡜⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠰⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⢀⡞⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢻⣆⢠⡀⠇⣿⢀⠀⢀⣴⡾⠒⠛⠛⠓⠒⠚⠛⠓⠒⠲⠎⡀
⠀⠀⠀⠀⠈⠁⠼⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⢿⣿⣿⣿⣿⢀⣿⣿⣾⠟⣁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣿⣿⣿⣿⣿⢸⣿⣿⣷⣾⣿⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⢀⠀⠀⠀⠀⠀⣤⡾⠛⠋⣉⣶⣾⣿⣿⣿⣾⣿⠿⠯⠴⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⣀⠀⢀⣠⡮⠊⠀⠀⠀⠀⠈⡿⡿⣿⢿⡿⢿⡿⢦⡄⠀⠀⠈⠉⠑⣦⡀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠐⠂⠐⠠⣀⣀⠀⢀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⡇⠈⠙⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠄⢢⡈⠉⠈⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠤⠤⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⠶⠤⣃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⢀⣙⢳⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢔⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠙⡜⢤⠀⠀⠀⠀⠀⠀⠀⠀⣴⠎⢁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢦⣤⡤⠰⠦⠶⠖⠊⠀⠀⢁⡾⠳⡄⣀⡤⠦⢼⣤⣤⣋⠀⠀⠀⠀⠑⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠳⡀⠤⢀⠈⢧⠀⠀⣼⠃⢀⣨⡿⠷⠞⠛⠉⠀⠉⠙⢍⠙⠛⠁⠤⣉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⠲⢄⠘⢿⠄⣰⣧⠔⠋⠀⠈⠑⠤⢀⣀⣀⣀⣀⠀⠀⠄⠤⠤⠤⠵⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢹⠢⡀⠀⠀⠀⠀⠑⣌⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡞⠁⠐⡀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠁⡇⠀⠀⢠⠀⠀⢠⣾⣣⣴⡤⠴⠶⠾⠯⣷⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡧⠀⠀⠀⣠⣴⠟⠉⠁⠂⠤⠈⠲⠤⠄⠀⠒⠛⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠀⡇⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣧⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢠⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⡿⢿⣿⠿⢿⠿⣿⢿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣶⣼⣦⣶⣤⣾⣦⣴⣿⣼⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢤⡄⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠘⢦⣤⠟⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢄⠀⠀⠙⠀⠀⢀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⣀⣦⡀⡿⠰⠊⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠑⠀⠰⠐⠁⡇⠀⠀⠀⠀⠈⣿⣵⢿⣿⠁⢀⠀⢀
⠀⠀⠀⠐⡠⡄⠀⠀⠠⠄⠌⠉⠁⠐⢆⠀⣠⣇⣠⠄⠀⠀⠀⠀⠀⣴⣀⠄⠀⢱⠀⠀⠀⠀⠀⠈⠁⠈⠡⠀⠈⡄⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢶⣤⣄⡀⠀⠀⠀⠀⠀⢷⣿⣿⣿⡋⠀⠀⠀⠀⠀⢸⣏⣰⢀⠄⣀⠀⠀⠀⠀⠑⢶⠖⠃⠀⠀⢷⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠿⣾⣤⣄⡀⣤⣺⣫⣿⢿⣏⠁⠀⠀⠀⠀⠀⠂⠘⠛⠉⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⢀⠝⠁⠀⠉⢤⣤⣀⢀⠀⠌⠛⣤⠆⠀⠀⠀⠀⡀⠀⠈⠂⠀⠠⠰⡉⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⣠⠊⠀⠀⠀⠀⠀⠀⠹⠦⠀⠀⠀⠀⠀⠀⠀⢠⣰⢿⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⢀⣾⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡰⠄⠀⠀⠀⠀⠀⠁⠀⠃⢀⠾⠀⠀⠀⠠⠄⠀⡀⠀⠘⠀⠀⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠂⠀⠀⠘⡀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠄⠰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢀⡀⣸⣀⠔⣀⡄⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠈⠧⣼⠊⠀⠀⠃⠀⠀⠀⠈⠻⣿⣿⣿⣷⠿⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠆⡜⠀⠀⠀⠃⠀⠀⠀⠀⠇⢀⠀⠀⠀⠈⠛⠛⢻⣆⡀⠀⠀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠴⣄⠤⣤⠊⠈⠉⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢀⡀⠀⠀⠀⠂⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠸⠆⠖⠁⠀⠀⡀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢰⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⣀⠀⠀⠀⢀⠀⢀⠀⠀⠠⠄⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣌⠻⠛⣉⣥⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀⣀⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢠⣌⡙⠻⢿⣿⣿⣿⣿⡿⠿⢉⣁⣤⣶⣾⣿⣿⠿⠟⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠛⢿⡷⢤⣈⡙⠋⢤⣶⣾⣿⣿⣿⡿⠛⢁⣀⣤⡴⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣎⢻⡏⢶⣤⣉⠛⠛⣫⣥⣶⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡄⠀⠀⠙⣿⢶⣄⢋⣉⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⢸⣾⣿⣿⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣼⣛⢷⣆⠀⢸⠃⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⡿⠿⠿⢿⣿⣈⢻⣆⠘⠁⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⠀⠀⠀⠀⣾⣿⣿⣿⣦⣴⣼⣾⣿⣿⣿⣿⣿⡆⠀⠀⣧
⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⣿⣿⣿⣿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⢀⠀⠹
⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣭⡄⠀⠀⠻⠿⠁⢻⡟⠹⣿⣿⠀⠃
⠀⠀⠀⠀⠈⠛⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠁⠀⠀⠀⠀⠀⣸⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣶⣤⡰⣿⠏⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣠⣆⠀⠀⢠⡿⣫⡞⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢪⡻⣿⣶⣶⢟⣵⡟⠀⠀⠀⠀⠀⢤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠂⠀⠀⠀⠰⢦⡀⠀⠀⠁⠀⠈⠻⣮⣷⣶⡿⠋⠁⠀⠀⠀⠀⠀⠈⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠖⢶⠿⠏⠛⠓⢦⣀⠀⠙⠣⣴⠀⠀⠀⠀⠈⣉⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣤⣤⣴
⠀⠀⠀⠀⣀⣀⣠⡤⠶⠶⠿⠿⠿⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡈⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠛⠯⢭⣙⡛⠂
⣶⣶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣀⠤⠄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣠⣤⣤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠂⠀⠀⠀⣠⣴⣾⣯⠥⠤⠄⠆⠀⠀⠀⠈⠙⠿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠀⢀⣤⣶⣿⣿⣋⣡⡤⠤⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣦⡀⠀⠀⠀⠀⠀⠶⠶⠂⠀⠒
⢤⣄⣀⡀⠀⠀⠀⠀⠊⠀⠀⠀⣀⣤⣶⣾⠟⠛⠋⠉⠉⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⣶⣾⣿⣿⣦⡀⠻⣿⣿⣿⣿⣧
⠀⡈⠛⠉⠁⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣧⠤⠶⠶⠖⠒⠒⠚⠋⣩⣍⣀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⡄⠈⣿⣿⣿⣿⡇⠀⠀⢀⣦⠤⠤⠤
⠀⠀⠀⠀⣀⣤⣾⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣾⣿⣿⣿⣷⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⡽
⢀⣤⣶⣿⣿⣿⣿⣿⣥⣤⣤⣤⠤⠤⠤⠴⠒⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⢿⣶⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⠃
⣿⣿⣿⣿⣿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠃⠘⣿⣧⣀⣈⣻⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣀⣀⣀⡀⢀⣀⣀
⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣠⣄⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛
⣷⣦⣤⣤⣶⣶⣶⡶⠶⠶⠾⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠙⠻⠿⠟⣿⣿⣭⣽⣿⣿⣿⣿⣿⡏
⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⢉⣽⣿⣿⣿⣧
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣇⣀
⢀⣀⣀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣀
⠿⠿⢿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛
⠀⠀⠘⠛⠻⠿⠿⠿⠟⠛⠉⠈⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡆⢸⡃⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠦⢉⣡⣰⣆⡔⣄⣆⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣼⣿⣾⠃
⠀⠀⠀⠀⢀⣤⡸⠇⡐⠀⠀⠂⠲⠀⠀⠀⠀⠠⣀⣸⠆⣘⢶⢿⠿⡦⡖⠞⠀⠁⠀⠀⠀⠀⠀⠀⠙⢿⡿⢊⣡⣤
⠀⠀⠀⣰⠞⢉⡔⠊⣩⢀⠀⠠⠈⠀⠀⢀⣻⠧⣄⣸⠇⣼⣷⣿⡟⠁⣉⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠘⠿⠟⠁
⠀⠀⢰⠏⠀⢼⠀⣼⠦⠦⢤⠀⠀⡆⠀⠀⣿⡖⣳⡀⢐⢛⣻⣿⣿⣿⠛⠿⠘⠄⠀⠀⠀⠀⠀⣰⣾⣅⣦⣶⣤⡀
⠀⢀⡞⢀⡿⢁⣿⢋⣩⠂⠀⠂⠄⠀⠀⠀⠸⠿⣿⣤⣁⣨⢉⣩⠇⡛⠄⠀⠀⠀⠀⡤⠀⠀⣤⣿⣿⣿⣿⣿⣿⡏⡿⢰⡄
⠀⠀⣿⣿⣽⡟⣱⣟⠉⠀⠀⠰⠷⣄⠀⠀⠀⠈⠛⢿⣷⣾⣉⣵⣤⠣⣀⣴⣤⠎⠈⠀⠀⣶⣿⣿⣿⣿⣻⡏⡝⠁⠀⠘⣱⡆
⠀⠈⣿⣯⣾⣿⣻⣄⡄⢡⡄⠁⠀⠀⠑⠀⠀⢀⠤⠀⠁⠛⠩⠿⣧⠀⣧⢉⠂⢀⣦⣼⣿⣿⣿⣿⣿⡿⢿⣿⣀⠀⠀⠈⠉⠰
⠀⠀⠸⣿⣿⣿⠛⠝⠁⠀⠀⠀⠀⠀⠀⢠⣆⣈⡠⢀⣮⠆⠀⣠⠀⠈⣿⠀⢠⠀⢻⣿⣿⣿⣿⣿⣋⣘⠐⣿⡯⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠠⣤⣀⡀⠀⢠⡀⠀⠿⣿⣿⣾⡏⡀⠀⣿⡇⠀⢸⢠⠏⣀⠈⣿⣿⣿⣽⣿⣿⣿⣿⡟⠃⢢⣔⠒⠦⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⣷⣿⣶⠢⠄⠱⡀⢱⢰⣾⣿⣿⣶⢰⡏⠀⠈⣆⠜⢻⢟⣽⡿⠉⢏⡋⡄⠀⠀⢉⣳⣦⠄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣇⣦⡘⢳⠸⣾⣿⣿⣿⣿⣸⠀⢀⡾⠁⠀⡜⠻⣯⣴⠄⣸⢣⣇⢴⡳⡼⠞⠁
⠀⠀⠀⠘⣿⣇⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢻⡍⢻⣿⣿⡇⣿⢠⡞⠀⠀⣼⢁⡤⡄⠁⠈⠉⠋⠙
⠀⠀⠀⠀⣉⣉⣳⣞⡠⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠳⣸⣿⣿⣥⣻⠟⠀⡄⠀⠇⢸⠿⠃⠀⣠⠁
⠀⠀⠀⠐⠻⠟⢁⣜⠁⠠⣀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠞⣿⣀⣃⣿⠀⣶⣾⠗⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢳⣴⡷⠒⠒⠂⣉⣀⡐⢀⣨⣿⣿⣿⣿⣿⣟⠠⠀⣀⣴⣿⢿⣿⣿⣿⣿⣥⣤⠄
⠀⠀⠀⠀⠀⠀⠦⠾⠁⠾⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠏⢰⣿⣿⣿⢿⡜⣸⠟⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢽⣿⣿⣿⣿⣿⡿⠟⣿⣦⡿⠋⢀⣴⣦⣜⠷⣿⡟⣸⣃⣴⣾⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⢀⣴⣿⣿⠧⠂⢈⣉⣛⡿⡆⢿⢹⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠹⢿⣿⣿⢰⣿⣿⣟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠋⠉⠉⠉⠛⠓⠠⢄⢀⣠⡤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣠⣤⣼⣧⣄⣀⣀⣀⣀⣠⣏⠀⢀⣀⣀⣀⣀⡉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣡⡾⢛⣿⡿⠻⠛⣻⡟⠛⠛⣿⣿⣿⣿⣟⠛⢉⣉⣍⣙⡳⢦⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⠋⢀⣿⠁⠊⠹⣿⣿⣿⠇⢡⠇⢾⡷⢠⣿⣷⡗⠈⠚⣿⣿⣧⡈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠸⣿⠀⣀⣀⣀⢞⠃⢠⠃⠀⠀⠀⢸⠀⠀⠹⣄⠈⢸⣿⣿⣇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠱⣭⣾⡿⠶⠋⣰⠇⠀⠀⠀⠀⠸⠀⠀⠀⢹⣿⠛⠛⠛⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⠀⠀⠀⠀⢀⣠⠞⠋⣀⠀⢀⣀⠠⠄⠠⠀⣀⣀⠌⠙⢦⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡶⠶⠶⠞⠋⠁⠀⠀⠻⠋⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠰⠶⣦⣤⣀⣀⣤⣤⠴⠀⣀⣀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣶⣦⣤⣀⡀⠀⠙⠛⠋⢉⣁⣤⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠙⠛⠛⣋⣩⣤⣽⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠠⠩⠍⠑⠲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠐⠒⠒⠒⠚⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠻⠶⡶⣤⡤⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠳⠶⠤⠄⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠲⠦⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡤⠖⠺⣿⡀⠀⠀⠀⢦⡈⠑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠈⠉⡏⢸⣏⠀⠀⠀⠈⠛⠳⠂⠀⠀⠙⠲⠦⣄⡈⠙⢲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠻⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⣄⠀⢣⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠀⣉⣈⣉⣉⡀⠺⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⢣⡄⢀⡀⣀⠀⠙⢿⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠙⠬⢷⠀⠈⣧⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠈⢢⡀⢸⠃⠀⠈⡆⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠤⠀⡀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⢠⡀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⠉⠀⠀⠀⠀⣸⠀⠀⠀⢠⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢧⠀⠀⢸⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⢀⡀⡇⠀⠀⢀⠃⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢨⡆⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡴⠂⠐⢦⠀⡇⠀⡴⠃⠀⠀⠀⠃⡈⠢⡀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠄⠁⠀⠀⠀⢣⡄⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢱⡇⠜⣁⠀⠀⠀⠀⠀⠘⠀⣡⠀⠀⠀⠀⢀⠐⡰⠀⠀⠸⢸⡦⠀⠀⠈⠄⠈⣧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡥⠀⠀⠀⠀⠘⢇⡼⠋⠉⠓⠚⠛⠙⠛⠛⠣⡀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠙⠆⠈⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠋⠀⠀⠀⠀⠀⠀⠈⢃⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⣆⠠⠛⢚⡲⢤⣀⣤⡤⣤⠆⠀⠀⡴⠂⠔⠁⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣉⠲⢤⡴⠶⠶⣤⣤⠖⢾⠠⣤⣶⣦⣄⣀⣤⠖⠊⠉⠀⠐⠒⢦⣤⣤⣬⣤⣀⣀⣰⠆⣀⠦⠤⠶⠦⣤⣤⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⣤⣀⣀⣀⣠⣤⣄⣀⣈⡆⢾⠀⠄⠈⠉⢸⠀⠀⠉⠳⠠⠂⢢⡀⠀⠄⠀⣏⣉⡡⠶⢀⣤⣀⣀⣠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠆⢹⡉⠉⡅⠁⡤⠀⠀⠈⠀⠐⠲⠒⠚⠳⠞⠀⠀⠀⠀⠀⠚⠉⠙⠓⠖⠰⢇⠀⠀⠀⠀⠀⣸⣋⢉⢀⡀⠐⢄⡀
⠀⠀⠀⠀⡀⠠⠀⠛⠙⠛⠷⠛⠚⠦⠶⠆⢠⡇⠀⠀⠖⠒⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣄⠈⠀⠀⠘⠀⠀⠀⠁⠀⠁⠈⠃⠀⠉⠐⠠⣄⡀
⠀⠀⠈⠉⠀⠀⠴⠂⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁⠀⠀⠠⠤⠤⣀⣠⣄⢀⣀⣀⠀⠀⠀⠁⠈⠤⣤⠄⠠⢤⣤⠤⣤⣤⡿⠦
⠀⠀⠀⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⠛⠛⠛⠛⠛⠲⣶⢤⠶⠶⠖⠒⠒⠚⠛⠋⠉⠙⠛⠷⣄
⠀⠀⠀⠀⠀⠀⣠⠊⣀⣀⣀⣀⣀⡤⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⢀⣀⠶⠖⠒⠶⠶⠾⣷⣄
⠀⠀⠀⠀⠀⣼⡷⡫⠛⠉⠩⠍⡙⠶⣖⣁⣤⠴⠁⠈⠛⠶⠶⠖⡒⠋⢀⣠⣤⣤⣀⠢⡀⠀⠘⣆
⠀⠀⠀⠀⢠⠏⠀⢀⣴⡾⠻⣿⣶⣧⡈⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣾⡛⢿⣯⣣⠉⢿⡄⠀⡀⠘⡆
⠀⠀⠀⠀⣼⠀⡀⣿⢸⣿⣶⣿⣿⢏⣷⢀⡤⡒⠶⠒⣙⢲⢄⠀⢺⡹⣿⣿⣿⣏⣠⠞⠀⢠⠃⢀⡇
⠀⠀⠀⠀⢿⠀⢣⡈⠛⠿⠿⠿⠛⠉⢠⠊⠒⠙⠒⠒⠉⠉⠀⠱⡄⠈⠛⠛⠛⠋⠁⢀⡴⠃⠀⣼⠁
⠀⠀⠀⠀⠈⢧⡀⠙⠲⠤⠤⠤⠒⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢀⡀⠂⠐⠊⠁⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠈⠻⢦⣈⣀⢀⣤⠎⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠻⢶⣶⡦⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⡠⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⡇⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠉⠑⠒⠤⠄⠠⠄⠒⠊⠁⠀⠈⢀⠜⠀⣎⡉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣤⣤⣤⡤⠶⠶⠛⡇⠀⠀⠙⠢⡄⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡀⠜⣧⠀⠀⠀⠁⠈⢦⡀⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⣽⡀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠤⠤⠄⠠⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠔⢿⠀⠀⠀⠀⠀⢠⠦⢄⢸⣼⠋⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠀⠀⠀⠀⡠⠚⣧⣄⣀⡀⠀⢸⡆⠀⣨⠇⠀⣠⡔⠊⠉⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠲⠎⠳⠀⠀⠀⠒⠈⠀⠀⠔⠀⠀⠀⠉⠉⢻⡇⠔⡟⠀⡐⡞⠀⢠⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠞⠉⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠸⣇⠸⣀⡔⠳⣯⠀⢀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠘⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢡⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢲⢿⣿⡇⠈⠈⠉⠃⠀⠐⠀⠀⠀⠊
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣿⡿⠃⢠
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠃⠀⠀⢅⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡀⠔⠀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿
⠞⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠠⠄⠤⠄⢠⠄⠒⠒⢤⠀⠀⠈⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣠⣶⣿⠋
⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⣄⠀⠔⠲⠀⠀⠀⠀⠀⠀⠈⠀⠺⠿⢿⣿⣿⣾⣿⣿⣟⣁
⣄⠀⠀⠈⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠤⡄⠀⠀⠀⣀⠀⠀⠨⣿⣿⠻⢿⢿
⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠀⠀⠀⢠⣿⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⣬⠄⠀⠀⠀⠀⠀⠀⠀⣀⣧⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠂⡀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⡶
⠀⠀⠀⠀⢋⠁⠀⠀⢀⡱⢤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠁⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠉⠙⣿⣿⣿⣠⣿⣶⣾⡷⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣿⠿⠛⠃⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠘⠄⠀⡜⢀⠀⡦
⠀⠂⠠⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢤⡾⠟⢿⡆⠠⠄⠀⢀⣀⡀⠀⠀⠇⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠈⠳⠄⠀⠀⠀⠈⠀⠀⠀⠀⠠⠤⡤⠀⡰⠚⠣⠄⠀⠀⠙⣄⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠀⢀⣀⣤⣀⣐⡀
⠠⠄⠀⠀⠀⠀⠀⠃⢄⠀⢀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠈⠙⠛⠃⠲⠤⡀⠀⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠂⠂⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⣆⠐⢀⣠⣾
⠀⠀⠀⡈⠉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢦⣠⠀⠀⠀⢸⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠈⣿⣴⣿⡿⠿⠟
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠘⣿⣷⡄⠠⠁⠀⠀⣤⣾⡷⠀⠀⠀⠀⠀⠀⠀⡿⠿⢯⡀
⣀⠀⠤⠀⠠⠀⠀⡀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠒⠤⠀⠀⠘⢿⣿⣶⢶⠀⣾⣿⢟⠀⠂⠀⠀⠀⠈⠀⡐⠀⠀⠀⠙⠢⠬⢉
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣦⣤⣝⢛⠠⢈⢻⡿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠔⠒⠊⠉⠝⠛⠛⢻⡿⡿⠁⣠⠘⣽⣿⣁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⠀⢀⠀⢰⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣋⣭⣚⣷⣮⣷⡷⠎⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢿⣿⠛⠁⠀⠈⠿⠊⠙⠳⠰⣣⣴⠆⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⢀⡰⣢⣿⣶⣶⣮⣾⣽⠇⠁⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠠⣼⣛⣛⣿⣉⣩⣭⣿⠿⠿⢛⡵⠛⠉⠀⠁⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢠⣤⣤⡼⠿⢻⡿⣏⠳⠤⣤⣀⢯⡞⠋⠀⠀⣼⠖⠡⠿⠿⠗⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠐⠰⡏⠁⠛⠓⢶⣤⣀⠀⢀⡶⠦⠐⢁⢀⣀⣀⣀⡤⠄
⠀⠀⠀⠀⣀⣤⣥⣶⣶⠚⣒⠒⠒⠛⠒⠂⢤⣷⡀⠀⠀⠈⣿⣿⠞⠉⣀⠠⠔⠛⠉⠀⠚⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⠃⠀⢀⣀⣀⣀⣀⣬⡿⠶⣶⡾⠿⠓⠓⠛⠷⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⡻⢛⡩⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣁⡤⠟⠉⠀⠀⠀⠀⡈⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠁⠀⠀⠀⠀⠀⠀⢠⡧⠶⠾⠿⠿⠛⠒⠷⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⢤⣤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠨⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⣛⣋⠁⠘⠛⠋⠡⠄⠀⠀⠀⠀⠀⠒⠶⠿⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠉⠉⠉⠙⠓⠆⠀⠠⠤⣄⠀⠀⢀⣠⡴⠶⠿⠿⠿⠿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠤⢐⡦⠿⠶⠦⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⢄⣀⣤⡴⣤⣤⡄⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡰⢋⣾⣶⣶⣶⣄⣠⡙⡿⠲⠒⠒⠁⠀⠀⠀⡙⠶⢶⡴⢚⠏⢁⣈⣉⣛⣤⡉⢷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠁⠸⡏⣾⣟⣿⣿⡟⡇⢸⡆⣸⠿⠾⠆⠀⠐⣒⠅⢸⢠⣷⡾⣿⡿⣿⣿⡝⣧⢸⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢀⠳⠿⣿⣿⣿⠔⠁⡜⠀⡵⢊⣁⠀⠀⣉⡙⢳⡀⢢⠻⣄⣿⣿⣟⣿⣷⢁⡌⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠘⢶⡶⣊⣫⠵⢛⡫⡊⠜⠣⠟⠉⠀⠘⠙⠿⠌⠱⡈⠣⠈⠉⡉⠉⠻⢗⠉⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⠤⠀⠀⠔⡩⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠠⣌⣙⠋⣁⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⠀⢠⠎⣟⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢬⣳⠲⣜⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢾⣄⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠃⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣤⣈⡉⠓⠶⣶⠶⠟⣋⣉⣤⡴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠉⠙⠛⠛⠛⠋⠉⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠁⠀⠀⠀⠀⠀⠈⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠦⣄⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⠴⠳⣈⠑⠀⠀⠀⠀⠀⠀⢈⠹⠷⣄⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⠀⠀⠈⠙⠋⠉⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠀⠀⠀⠈⠉⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠂⠒⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠉⣉⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⢠⡴⠋⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠙⢷⣆
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣀⣈⣿⣧
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⣶⣦⡖⡶⣶⠒⣶⣶⣦⡆⣶⢲⡖⣦⣶⣴⣶⢠⣆⣴⠀⢰⣴⣴⡖⣦⣆⣶⣶⠒⣦⡖⢶⡶⠀⡶⡆⣶⣰⣴
⠀⠀⠀⠀⠿⠿⠇⠇⠸⡥⠏⠿⠿⠿⠿⠼⠇⠿⠿⠿⠻⠾⠿⢿⡄⠸⠿⠏⢧⠿⠿⠿⢿⡥⠟⠇⠠⡽⠀⠧⠿⠿⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⣴⠛⢶⠀⠀⠈⠛⢦⡀⣠⡶⠋⠁⠀⢀⡶⠛⣆⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠀⠀⠀⣿⠀⠸⡇⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⢸⠇⠀⣿⠀⠀⠈⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠉⠓⠶⠴⠏⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠹⠦⠶⠛⠉⣩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⠳⠂⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠰⠞⣫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⠃⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢘⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣳⣄⡀⠀⠀⠀⠀⠀⣀⣠⡬⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠙⠛⠛⠒⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⠉⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣤⣄⣀⣀⣠⣤⣤⠴⠶⣿⣭⣅⣀⣀⣠⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠤⠤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⢸⡧⢰⣦⣶⣶⢴⣦⣴⣤⡶⣶⡂⣷⠄⣶⣶⢰⡖⣶⢲⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠸⠷⠜⠿⠛⠿⠻⠻⠟⠟⠶⠻⠄⠷⠆⠿⠟⠞⠃⠛⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠠⣤⡰⡦⣤⠰⠇⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠠⣤⠙⠘⣃⢀⡸⠦⠺⡎⠾⡀⢭⡸⢇⡤⠿⣀⠿⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣬⢃⡜⠃⣺⡂⡬⣥⠌⣛⢈⣟⠀⢹⡅⢶⡄⣼⠆⣤⡝⢺⣧⠍⣤⢰⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠵⠎⠘⢱⢆⡈⣍⢣⢺⣃⢩⡡⠿⠀⡍⠾⡡⣑⠛⢰⠖⠶⡄⣿⢢⡷⠀⣘⢣⡄⡴
⠀⠀⠀⠘⣃⠿⢠⡆⡉⣤⡛⣥⡔⢼⣃⠉⠸⡌⣱⢎⡃⢙⡋⢱⡾⡶⠋⣡⢀⣟⢓⣇⣽⠃⣀⠷⡙⢯⣑⠟⢠⡆
⠀⠀⠲⠎⢩⡥⠣⣜⢣⡖⣤⢀⡛⠁⢸⡏⢹⣿⢦⣘⠃⣮⠙⣼⢈⣛⠀⣍⢤⡍⡾⠴⠂⣤⢙⢞⡑⠶⠉⢴⢠⡖⣠⡄
⠀⠀⠈⢫⣤⠚⠋⠾⡟⠲⢬⣬⣋⡻⢂⣤⠀⠑⠶⠛⣷⣤⠞⠑⠶⠁⢈⡋⡺⢼⡇⣐⠷⣨⢯⡜⡣⢴⢠⡄⣤⠚⡆
⠀⠀⠶⠔⢦⠺⠜⠗⣘⡯⠖⣛⢩⣻⣦⠀⠿⡈⡶⠟⣽⡏⣠⠻⢆⣀⡘⠋⢇⣼⠁⢙⣰⣯⣼⢯⣤⠙⠀⢁⡨⣄⠟⣸⡋
⠀⠀⠐⢛⣥⢠⡌⣦⢷⢙⡓⢙⡠⣭⢹⣧⠸⠃⣇⢠⣿⢋⣥⢠⠃⣉⣡⣴⣿⠷⢿⣿⣉⡤⠙⢋⡠⡶⢷⠘⣃⠤⠰⠯⢡⠖
⠀⡈⢿⣄⠷⠎⡀⠁⠶⠎⡛⢈⡃⠰⡆⢻⣿⠓⠹⣾⡿⣠⢄⣿⡾⠟⣭⡅⣚⢣⣠⡦⢈⣱⠶⣸⠷⣚⡻⠯⢠⡴⡦⡶⢰⢖⣤
⠀⢙⡂⣦⠸⣆⣇⡻⠸⠇⢻⣈⣥⣴⠶⢾⣿⣷⣄⣹⣿⢈⣾⡟⣠⡝⠆⣤⢛⡨⢕⡱⠮⢉⣼⢫⠖⣩⠄⠳⣮⠀⣄⢶⣛⣅
⠰⠮⠉⠀⣩⢠⡎⣩⢙⡟⢩⡅⡶⠀⡛⢣⡀⢉⠻⣿⣿⣿⣿⢡⡶⠸⠇⣵⠋⠲⢎⣉⣤⡾⠟⠛⢛⡛⢫⡉⣮⢛⠉⠰⠦⠉
⠀⢟⡙⠇⢙⡄⣶⢉⡌⣣⡌⣀⠲⠆⠛⠬⢧⣘⣃⣈⠻⣿⣿⣇⠀⠀⣼⣿⡿⠟⢛⠋⣭⠰⡇⠸⠎⠃⣬⡁⠀⠘⠃
⠀⠘⠁⠀⠘⠁⠁⠈⠁⠉⢈⡍⠶⠃⣶⠸⢦⡆⣩⢉⡟⠿⣿⣿⣧⣾⡿⠁⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠏⠀⠀⠀⠀⠉⠘⠃⠀⠘⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣄⣠⠴⠛⣻⣶⣶⣶⣶⣶⣿⣿⡿⣿⠿⣿⣤⣀⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢁⣠⠞⡩⠤⡴⠛⠉⢀⣴⡟⠀⣿⠀⠙⢿⣿⠶⢦⣤⣶⣚⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⠋⠀⠀⠞⠁⣤⠾⡿⠉⢇⠀⠙⣷⣄⠀⠙⠳⣄⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠜⠀⠀⠀⢀⣼⠁⢠⡇⠀⠀⠀⢀⡟⠈⠑⠄⠀⠘⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⡜⠰⠁⠈⠀⠀⠐⠁⢣⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢶⢿⠛⣶⣦⠀⠀⡠⣶⣦⣤⠀⢂
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣷⢽⡜⡇⠀⠘⡌⣁⡘⣳⡟⢰⢣⡄⢸⠆
⠀⠀⠀⠀⠀⢠⡎⠀⢸⣿⣧⡁⠣⠀⠀⢧⣿⣷⠃⣴⣣⣿⡷⠿⠒⠲⡄
⠀⠀⠀⠀⠀⠈⣷⡀⢸⣿⣿⡇⠀⡱⣦⢸⣿⣿⠟⣅⣿⣿⡴⠀⢀⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣯⣶⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣉⡉⠛⠛⠛⢛⡛⢿⣿⡿⠉⠉⠉⠛⠛⠋⣡⣴⣾⣿⣶⡄
⠀⠀⠀⠀⠀⠀⢀⣨⡉⠻⣷⣤⠀⢾⡅⠀⠻⣄⠀⢀⣤⡤⠀⣜⣿⡋⢢⣻⣿⣿⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣾⠷⣦⣕⣾⣿⣤⠬⠷⠶⠤⢬⣷⣼⡏⠁⠐⠈⠛⣿⡿⠿⠟⣡⠀⠀⡆⢀⡂⠁⢻
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⠀⠀⢠⠏⠓⢠⣾⠁⠀⡌⠐⠋⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠒⠋⠐⡤⠤⠄⠀⢄⡀⠹⡅⠀⡄⠀⢠⣿⢿⣧⣞⣀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⣴⣶⣶⣶⣧⡄⠀⢠⣿⡃⠀⢿⣄⣷⠀⢸⡹⣿⣥⣬⣠⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣾⠉⣤⣿⣿⣽⡛⠀⣴⣿⠃⠀⠘⣽⡇⣰⡧⠿⢿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠸⣿⣀⣏⣿⣯⡿⣻⣴⡿⠃⠀⠀⢸⣿⣴⠋⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣈⣙⣿⣿⣿⠿⢻⡇⣄⠀⠀⠀⠀⣿⡇⠀⣼⠛⡟⢹⣷⡀
⠀⠀⠀⠀⠀⠰⣾⣽⣿⣯⠷⠛⠛⢻⡇⢼⣿⣸⣻⢹⡀⠀⠀⣿⠃⣿⣿⣶⣠⣼⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢳⡘⢿⡿⠿⠟⠀⠀⠀⣿⠀⠈⢻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢸⣆⠀⢱⡘⣇⠀⠀⠀⠀⢀⡿⠀⠀⠞⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⣆⡟⣄⠀⠉⢽⡆⢠⣪⠀⣸⣋⡴⠛⠛⣧⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⠺⢧⣽⣷⣶⣬⣿⡞⠁⢀⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣾⣿⡿⠋⠀⠉⠻⠦⣜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠁⠀⠀⠀⠀⠀⢀⠐⠀⢀⡀⠈⠁⠀⢀⢿⡒⣒⠉⠀⠀⠀⡖⡄⠠⡇
⠀⠀⠀⠀⠀⢀⠀⢀⣀⠰⢤⣶⡄⠈⠀⣦⠞⠁⠶⠶⠏⠠⣦⣀⠀⠶⠶⠋⠲⠿⠛⠻⠦⠙⠀⡀⠶⠶⢄⠠⡶⠶⠶⠶⠶⣶⢆⠰⢶⡄
⠀⠀⠀⠀⠀⠀⠓⣄⠉⠠⡀⠙⠻⡀⠀⠈⠻⡄⠀⠘⢦⠀⠀⠉⠁⠂⠀⠀⠀⠀⠁⡟⣅⠀⠀⠀⠀⠐⠊⠁⢃⠀⡀⠀⠈⠉⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠋⠣⠀⠀⠈⠀⠣⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠙⠛⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠀⡤⠄⢁⠀⠀⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢈⠀⠀⣁⡀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣘⣃⣰⣀⣀⣈⣁⣖⣀⣀⣁⣼⣇⠀⠀⣴⣶⡄⠀⠀⠀⣀⣐⠲⠤⢤⡄⠬⣦⡀⠀⠀⠘⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠿⠿⠟⠀⠠⠌⠀⠀⠀⠀⢉⠤⠇⣠⠋⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠐⠁⠀⠀⠀⠐⠁⠀⠐⠁⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠀⡀⠬
⠀⠀⠀⠀⠀⠀⢀⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⣤⢨⣯⠘⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠄⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⡿⢰⠟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠿⠰⠄⡀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣿⣷⠏⠀⡛⢢⡄⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⢀⣎⠷⣀⡡⠴⠆⠉⣾⣿⡧
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣤⢴⡆⣤⢺⣿⠶⠂⠀⠤⠍⠉⠃⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣃⢠⡶⠀⠀⠓⢹⡟⠛⠛⠁⢀⣢⢀⡝⠣⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢠⡀⠀⠀⢸⣿⠏⡅⠀⣉⣗⡠⠈⣥⡀⠒⢲⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⣴⡏⠸⠁⠀⠀⢠⣼⠿⠒⠂⠒⢈⣿⠿⠶
⠀⠀⠀⠠⠀⠀⠀⠀⠀⢈⣭⢿⡇⠓⠀⢠⠀⠀⠀⣈⢻⡏⠤⠈⠈⠛⢿⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠙⠁⢁⣀⠀⣼⡃⣶⣖⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⣴⠾⠇⠠⣤⣴⣾⣄⠁⠸⠀⠀⠀⠈⠣⠟⠀⠈⠀⠀⠀⠠⢎⠙⡇⢀⡀⠀⠀⠀⠈⣊⠀⠘⢲⠜⠃⡼⠛⢷⣿⣤⣦⡀
⠀⠀⠠⣀⣀⣀⠀⣰⠞⠀⠴⢟⠀⠀⠀⢿⣿⣿⣦⠀⠀⢀⠆⣀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠈⣤⡇⢾⣾⣧⣺⡿⠰⠏⣳⣀⠁⠀⡾⠁⢰⣶⣶⣽⣿⣴
⠀⠀⠀⠬⠛⢿⡠⠀⠀⢠⠾⣚⣻⡷⢀⣻⣿⠇⠐⠀⠀⡏⠀⠙⢦⡀⠄⠀⠀⠀⠀⠷⠀⢘⣿⣷⣾⣿⣿⣿⣷⣄⠐⠟⠙⠃⡝⠁⣠⡤⠀⣻⣿⣿⡿
⠀⠀⠀⠀⠀⠈⠓⢠⣶⠏⢈⠇⠀⣹⠿⣿⠛⠆⠐⢦⢸⡇⠀⠀⠸⣧⠀⣤⡄⠀⠈⢁⠀⠉⣁⣿⣿⣿⣏⣹⣿⣿⣷⡀⠀⣼⢳⡦⠛⠃⠀⢀⡧⠀⠋
⠄⡓⢀⡄⠀⠀⢠⣿⡃⠀⠞⠀⠈⠁⠲⠛⠀⠘⣀⣤⣾⣇⠀⢠⣴⣦⠔⠿⢣⣷⠀⠈⢁⣼⣿⣿⣿⣿⡇⠃⣿⢿⠍⣧⣼⣯⡟⠁⠀⡛⠐⢠⣶⣾
⠀⠀⢤⣶⢀⡀⠂⢉⣿⠔⠲⣀⡀⠴⢿⠿⢿⣾⣿⣽⣿⠏⠐⠀⠉⢸⣦⣰⢸⣿⠀⠙⠛⢷⣏⢛⣿⠟⢳⣿⡇⠁⢀⣽⢛⣿⣟⣦⣿⣷⣾⣿⣋⣹⣯
⠀⠀⠘⢑⢌⠛⠙⢿⣿⣂⣼⣟⠀⣠⣿⠀⠀⠈⢻⡛⢿⠃⠀⠀⠀⠙⣋⡤⠾⠻⣿⡆⠀⡌⠉⠀⠁⠀⠨⠟⠀⢠⢋⣼⣟⣻⣽⣿⣿⣿⣿⣿⣋⣿⡛
⠀⠀⠀⠀⠘⠀⠀⣿⢧⠀⢻⡿⠠⣿⡟⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⢰⠃⢠⠞⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣠⠟⠋⣛⡿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⠀⣴⣶⠿⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡠⣴⠛⣥⡟⠁⠀⠀⠀⠈⠁⣟⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢹⠏⠛⠋⢫⡤⠒⠀⢈⠂⢀⢀⡀⢀⣀⠀⠸⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣦⣶⣆⢘⣿⣀⣰⡅⢀⣿⠿⠿⠏⠁⠀⠐⠮⢩
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠹⣿⣿⡿⣿⠿⠿⣷⢿⡋⠀⢶⣶⣧⣥⣤⡶⡙⢢
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⢀⠀⠟⡏⢰⢸⣄⣤⡷⢚⣿⣿⡜⠿⣿⣿⣿⡟⢀
⠀⠀⠀⠈⠉⡙⠂⣧⠀⠸⠞⠀⠀⠀⢸⡀⣿⡸⣦⣾⡅⠁⢸⠐⣿⣿⢿⠷
⠀⠀⠀⠀⠀⠀⠀⢹⣆⣰⣇⡀⠀⠀⠀⢁⡘⢷⡛⣿⣧⢰⢿⣷⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠉⠉⡄⠀⠀⠀⠀⠀⢀⣀⣴⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡠⠄⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⢀⣿⣇⡀⠈⡁⠀⠀⠀⠀⠠⣽⣿⠿⣿⣻⣦⣴⠾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⣀⢀⣹⣤⡴⠤⠄⠀⠀⠀⠀⠀⣴⠻⢖⡻⣫⣟⣁⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣰⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⠠⠘⠛⠻⠻⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢀⠹⡏⠉⠳⡀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠡⡀⠀⠈⢦⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠙⠀⠀⠠⢀⠀⠈⠀⣀⠀⢣⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠
⠀⠀⠀⠤⠐⠀⠐⢈⠈⠇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠙⠢⣧⣠⠁⣀⠴⠦⠤⠄⣀⠀⠀⣶⢴⠏
⠀⠀⠀⢀⠄⠈⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡞⠁⢠⠀⠀⠀⠀⠢⠾⣷⣄⣀⣀⣀⣐⢛
⠀⠀⠈⠀⠀⣶⢋⡄⠀⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠂⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣷⣾⠮⠋
⠀⠀⠀⠀⠀⠠⠀⠩⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢷⠐
⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠑⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀

⠀⠀⠀⠔⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠢
⠀⠀⠀⠀⠀⠀⠀⡖⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣣⣜⡄⠀⠀⢠⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⢀⡤⣄⠀⠀⠀⢠⢠⡄⠀⠀⠀⡠⢀
⠀⠀⠀⠀⠀⠔⠙⣇⣸⠋⠢⠀⣾⣉⣵⠄⠀⠀⣄⣢⡀⠀⠀⠀⡇⠀⢸⠀⠀⠀⣘⢅⡽⡀⠀⠠⣮⣉⣷⠀⠀⠀⣏⣹
⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⡠⢲⠉⠱⢤⠀⢀⢧⡼⣀⠀⠀⠀⡇⠀⢸⠀⠀⡔⢻⡉⣹⠗⣄⡠⠚⠉⡖⢄⡰⠻⣸⣁⠟⠆
⠀⠀⠀⠀⠀⠀⠀⡏⢹⠀⠀⠁⢘⢉⢹⠀⠰⠉⡾⢧⠊⠱⠀⠀⡇⠀⢸⠀⠀⠀⠀⠉⢹⠀⠈⠁⡏⣉⢱⠈⠀⠀⣿⣭
⠀⠀⠀⠀⠀⠀⠀⡇⢘⠀⠀⠀⢰⠜⡞⠀⠀⠀⡷⢳⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡖⠊⠀⠀⠀⢹⠻⡆⠀⠀⡔⠃⠘⢢
⠀⠀⠀⠀⠀⠐⡍⢉⡉⠹⠀⠸⠉⣉⠉⠅⠀⡎⢉⡉⠩⠂⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠺⠉⣉⠉⡇⠀⠏⢉⡉⠹
⠀⠀⠀⠀⠀⠀⠃⠈⠁⠈⠀⠈⠀⠉⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠐⠁⠘⠀⠀⠈⠀⠉⠀⠁⠀⠁⠈⠁⠈
⠀⠀⠀⠄⣀⣀⣀⡀⠀⡄⡔⣤⢤⣤⡄⢠⠠⢠⠀⢀⣀⣀⣀⡀⠃⠀⠘⢄⣀⣀⣀⣀⡀⠀⡆⡴⣤⣤⢠⠠⡄⠀⣀⣀⣀⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣴⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠈⠁⠀⠀⡆⠀⢀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡭⢓⢤⣄⣅⣸⣄⢔⣘⣧⣿⣷⣶⡖⢀⡈⠈⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠉⣟⣻⢿⣏⣾⣻⠿⣻⢷⣿⠏⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠌⢧⠀⣾⠦⣸⢾⡜⣶⢳⡩⣵⣲⣻⡿⠔⠒⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣜⠂⢻⡄⠀⠀⠀⠀⠀⠀⠘⠳⣾⡓⣿⡌⣧⡡⠦⡛⡓⣎⡻⣧⡔⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡬⠦⠤⠚⠉⢑⣲⢄⡀⠀⠀⠈⠀⠲⣯⡬⢻⣦⡾⠺⣤⡥⢆⣽⣅⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠠⠈⢟⠀⠀⡶⣦⠔⠙⢿⣷⣬⠿⡆⣀⠀⠀⠜⠛⢶⢴⣼⡟⢛⣶⣒⡩⡖⢿⡐⠀⠘⠁
⠀⠀⠀⠀⠀⠀⡘⡤⠀⠀⠀⢮⢤⣤⡤⠻⣷⠀⠀⠈⠀⢮⠀⠀⣀⡼⠁⠙⠉⠉⠀⠀⠙⠎
⠀⠀⠀⠀⠀⠃⠗⠋⡄⠀⠀⠊⠉⡍⠀⠀⠀⠀⠀⠀⡀⠈⠴⡏⣷⠊⠀⠀⠑⠄⠠⠐⠲
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣘⡿⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠑⢄⠦⣕⣤⡀⢀⣠⡴⠖⠚⠛⠛⠛⠚⠃⢒⢦⣮⡁⡄⠀⢢⡞⠉⠀⠀⠀⠀⢤⠐⡄
⠀⠀⣤⡄⣴⣤⣾⡓⣻⣿⣿⣿⣷⣶⣦⡀⠀⠀⠈⠀⡨⠥⠧⣬⣿⢹⡤⢸⡁⠀⠀⠴⡾⢁⠁⠈⠃
⠀⠀⠁⣄⣋⡀⠒⠺⣿⠿⣿⣿⣯⠚⠉⠁⠀⡈⠀⠀⡤⠀⠄⠀⢈⡃⣧⡀⢃⠀⠀⣄⢀⠘⢠⠀⠠⠂
⠀⠀⠀⠛⢌⠁⠀⠀⡏⠀⠁⠙⠂⠁⣨⠄⠀⠂⠰⠀⠀⢀⠤⠐⢀⠰⣮⣷⡚⠧⡀⠄⠀⠘⠻⡄
⠀⠀⠀⠀⠂⠀⠀⠐⣃⠄⠀⠀⠰⠄⠀⠀⠀⠀⠃⠀⠀⠈⢁⠈⠉⠔⠀⡉⠿⠶⠬⠂⢢⣄⡲⣇⡁⣄
⠀⠀⠀⠈⠒⠈⠀⠢⠐⠢⡀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠛⢸⡤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠤⠀⠀⣸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢠⡆⣤⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡛⢀⠔⠀⠀⠀⠀⢤⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢄⠀⠐⠁⠀⠀⠘⠁⡀⠀⠒⠲⢄⢀⠠⠀⠀⡥
⠀⠀⠀⠀⠀⠀⠣⣀⠂⠠⠆⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠡⠈⣿⣵⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠳⢄⠤⣤⣀⣁⠐⠤⠀⠐⢞⣻⠎⡁⠀⢭⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠠⠅⠀⣼⣿⡿⠀⠒⢄⠀⠀⠉⡆⠈⠀⠀⠉⠸
⠀⠀⠀⠀⢀⠄⠀⠀⠼⠀⠀⠀⠐⢇⠀⠋⠹⠁⠀⠀⠀⠑⠀⠁
⠀⠀⠀⠀⠂⠀⠀⢀⡜⠒⢀⣤⡂⠀⠀⠀⢰⡀
⠀⠀⠀⠁⠀⠀⠁⢁⣤⣴⠊⢨⠀⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠁⡾⠆⢀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠲⠀⠈⠀⠰⠀⠀⠀⠀⢰⠄⡃⠰
⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠈⠂⠤⣤⣷⣠⠀⠀⠀⢐⠂⡀⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⢠⠰⠆⠀⠀⢀⢿⣾⡯⠓⠒⢀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡐⠀⡀⢈⠠⠁⠀⡏⡐⠒⠠⢀⣰⠿⡐⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠈⠆⢘⠀⠳⡀⠀⣰⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢢⠀⠀⠀⠴⠐⠀⢠⠃⠀⡬⣿⣹⠶⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠈⠀⠁⠢⣤⡷⠛⣮⣀⠤⠚⡁⢀⡄⠀⠀⠻⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠰⠄⠱⠤⢴⣀⡀⠠⢽⣷⣤⡿⣇⠀⠀⠀⢨⠃⢶⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⡄⠒⠁⣘⢹⡀⢀⠀⠀⡘⠙⠀⠘⢆⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⣀⠠⢶⠻⠠⠂⣡⠀⡛⠰⠀⠈⢃⡀⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠀⠀⠸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠖⠚⠋⠉⠉⠉⠉⠉⠙⠒⠲⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠋⢂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠃⠀⠀⠢⡀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⡎⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⠀⠁⠂⠀⠀⠀⠑⢤⣀⠀⠀⠀⠱⡄⠀⠀⢠⠁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢆⠀⠘⢀⠄⠀⣀⣀⡀⢱⠄⠀⠀⠀⠀⠀⠀⠎⢀⣀⣉⠀⠲⠘⢦⠀⡨⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠸⠃⠦⢨⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠇⠀⣧⠃⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢆⡀⢣⡀⠀⠑⠼⠿⣧⠾⠃⠀⠀⠀⣤⠀⠀⠀⠙⢧⣼⠿⠇⠂⠀⢀⡍⠀⠘⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠷⡈⠀⠂⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠘⠀⣀⠞⠁⠀⠠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⣬⠷⠦⡄⣀⠀⠈⠒⠀⠤⠀⠀⠀⠀⠀⠀⣀⠀⠴⠞⢅⡀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡴⠋⠀⠀⠀⠀⠈⠈⠳⣀⠀⠀⠀⠀⠀⠀⠚⢀⡝⠀⠀⠀⠀⠉⢧⡀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠤⠔⠋⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢀⡴⣋⣀⡠⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣀⡳⣄⡀
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⡇
⣤⠤⢤⣤⣤⣤⣤⠤⠤⢼⠁⠀⠀⠀⠀⠀⠀⠈⢦⠤⠤⠄⠀⠠⠤⠤⠄⠀⠀⠀⠀⠠⠤⠴⠀⠀⠀⠀⠀⠀⢹⣤⣠⣤⣤⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠒⠂⠀⠀⠀⠀⠀⠐⠀⠚⢃⠀⠀⠀⠀⠀⠀⠇⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠘⡟⠃⠀⠀⠀⠀⠈⢦⠀⠀⠀⠄⠀⠠⢜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣠⠀⠀⠐⢆⠁
⠀⠀⠀⠀⠀⠙⣟⡁⠀⠀⠀⠀⠀⠀⠳⣤⣁⡔⠉⠰⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⠐⠀⠀⢁⠾⡙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠀⡄⢰⡙⡄⠓
⠀⠀⠀⠀⠀⠙⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⡡⠶⠇⡀⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠈⡗⠆
⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠃
⠀⠀⠀⠀⠀⠈⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢈⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢈⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠒⠒⠒⠂⠚⠤⢄
⠀⠀⠀⠀⠀⢠⣧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣈⣄⠀⠓⠢⠤⠄⣀⣀⣀⡀⠕
⠀⠀⠀⠀⠀⠠⣧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠰⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠋⠛⠉⠛⠉⠁⠀⠤⠀⠀⠒⠚⠉⠛⠛⠯⠭⠭⠉⠙⠛⠋⠥⠀⠂⠤⠶⠒⠋⠻⡖⢀⠳⠲⠶⠶⠶⠶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⡠⠀⠀⠀⠐⠂⠐⠄⠀⠀⠀⠀⠄⠤⠂⡀⠀⠀⠰⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⣀⡀⠔⠁⠀⠀⠀⡀⠉⠐⠠⠂⠀⠐⠌⠡⠄⠑⠀⠀⠀⡔⢢⠄
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⣀⡀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⠂⠑⠂⠈⢀⠙⢉⠀⠁
⠀⠀⠀⠀⠀⢇⢂⠳⠰⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠄⠨⢅⠢⡀⠀⠀⠀⡠⢒⡎⡑⢄⡠⠂⠙
⠀⠀⠀⠀⠀⠀⢂⠂⠀⠁⠀⠀⠀⡀⡀⢠⠀⠀⢀⢀⢃⢊⢂⠅⠀⢕⡱⣊⠔⠂⠥⣊⠽⡆⠁⠈⢀⠂⢰⠖⠂⢐
⠀⠀⠀⠀⠀⡠⢂⡣⢠⠂⡀⠐⠀⠁⠀⠀⠀⠀⢀⣀⠉⠓⢇⠀⠀⠀⠈⠂⠅⠀⠨⡰⠒⠉⠉⠁⠓⠴⡕⣈⠔⠁
⠀⠀⠀⢠⢊⢔⢍⠔⠡⠊⠀⣴⡄⠀⢠⣀⣀⡆⠘⠛⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠐⠀⠐⠃⢠⢤⡀⠀⠈⠄
⠀⠀⠀⡃⠀⠀⠆⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⡇⠂⠀⠀⠀⠀⠁⠙
⠀⠀⠀⠐⡌⠎⣪⠃⠀⠀⠀⠀⠀⣀⡀⢤⡄⠐⠂⠀⠋⠁⠈⡀⠀⡃⠈⡀⠀⢀⡃⠀⠀⢀⠀⠀⠀⠀⢠⢂⣠⠂⠌⠠⠤⠤⡀
⠀⠀⠀⠀⠈⠑⠨⠀⡀⠠⡀⠈⠄⠀⣀⠠⠥⠀⠐⠀⠈⠀⠀⠀⠀⠀⠄⠁⢀⠂⠙⠐⠀⡄⠠⠀⡀⠔⠁⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠉⢀⠀⠔⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡁⠒⠠⠉⠰⠄⠒⠉⠀⠀⠀⠠⠃⠂⠄⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠦⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠀⠀⠀⠀⠈⡀⡠⠀⠤⠆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢄⠀⡤⠀⠀⡄⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠠⠤⠂⠀⠀⣀⠀⢲⠮⣐⠃⠀⠀⠀⠐⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⡀⠀⠀⠰⠶⢠⡤⣄⠀⣈⠀⢈⠘⠁⢀⠐⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠄⠤⣀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡈⠉⠀⠀⢂⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⡀⢠⠈⢆⠀⡀⠀⠀⠀⠀⡀⠀⠠⠀⠀⢄⠄⠀⠰⠠⠀⠅⢠⢊⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠆⠀⠀⢀⡏⠄
⠀⠀⠰⡉⢉⠑⢀⡣⠘⠉⠉⢁⠒⢄⠈⢚⢀⠄⠀⠀⠀⠐⢀⠀⠈⡥⡀⢠⠀⠀⡐⠅⠀⠂⠀⠈⡄⡆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠂⢬⠏⠀⢀⡠⠄⠙⠁⠐⠱⡅⠀⠁⠀⠀⠀⠈⠐⠈⠀⠈⠀⢸⡆⠀⠁⢂⠀⠀⠀⢀⠂⠃⠀⠀⡄
⠀⠀⠀⠀⠀⢈⠀⠶⠈⠁⠁⠀⠀⠀⠀⣇⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⢢⣁⣀⠠⠀⠀⠅⠀⠀⠅⠀⠀⠀⢠⠁⢀⠄⣊⠐
⠀⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠀⠀⠀⡧⠔⡀⠖⣒⡊⢷⡍⡠⠤⠄⡢⡆⢄⢠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠄⢰⠀⠶⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠠⢠⠁⡈⠔⠁⠀⠀⠑⢌⡚⠄⠬⢚⡴⠢⡠⠁⠀⠀⠀⠀⠂⠀⠀⠊⠀⠢⠋⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⣹⠗⠛⠉⠁⠐⠈⠉⠛⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠈⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠈⣽⣿⣿⣦⣤⡤⠤⡦⠦⣴⢦⣴⠶⠶⠚⣛⣿⣿⣷⣾⡯⣭⡙⠲⡄⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣿⠟⠛⣿⣿⣫⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠋⠁⠀⠠⢶⣾⣥⡈⠀⠠⣄⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣇⠀⢰⣼⣿⡿⠻⢆⠀⠐⠒⢄⡀⠀⠀⠀⠀⠀⡞⠁⣤⠈⣥⠙⣦⠄⢸⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⡴⠋⢴⣩⣭⢤⣶⣶⣿⢠⣤⡀⠀⣴⣦⠀⠁⠀⢁⣀⡀⠀⠛⠀⠉⠸⠏⣀⠈⠆⠈⠀⠀⠤⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠐⢷⣤⣾⣷⣶⣿⣿⣿⠛⠻⢿⠃⠀⠉⠀⠤⠀⠀⠈⠛⢏⣦⣀⡀⠒⠀⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⢛⡛⠛⠉⠁⠀⠀⠀⠀⢀⣄⣤⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣤⣴⠟⠛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⡀⢀⣶⡾⢛⣫⣴⠖⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣝⣶⣀⠀⢀⡀⠀⢀⣂⠐⠂⣀⣉⣩⣤⠾⢿⡿⠿⠿⠛⠛⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⠀⠀⠀⠉⠉⠛⠿⠿⠿⣿⡿⠟⠛⠁⠀⠀⠀⠸⣶⣤⡴
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⣀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⣦⣤⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠹⣤⣤⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠘⠦⠀⠀⠉⠀⠰⢦⢀⠴⠤⢀⠀⠀⠀⣸⣉⡛⠛⠒⠀⠀⠈⠲⣀⠀⡀⠀⠀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⢈⠹⡙⠿⡿⢷⣄⠀⠀⢀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⡀⠀⣀⣤⣶⣭⣉⡈⠑⢠⣤⡀⠀⠀⠀⠀⠀⠀⠈⠳⠬⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠨⡇⠀⠿⠿⡿⣿⣿⣷⣤⣤⣿⣷⠀⠀⠀⠘⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⣴⠀⠀⠀⠀⢰⣾⠿⠿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⡄⠘⠛
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠒
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠼⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣀⠲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⡄⠀⣎⠀⠀⠀⠀⠀⠀⠑⠦⣀⢠⠆⠀⠀⠀⣼⣿⣷⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠂⠀⠈⢦⣯⠖⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⠀⠈⠉⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠁⠉⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢠⠀⠀⠀⢀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⠎⠀⠀⠀⠀⠻⠿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠦⠠⠄⠀⠀⢹⠄⡄
⠀⠀⠀⠀⠈⠓⠶⢄⡀⢆⡔⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⡴⠀⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠰⠈⠀⠙⠀⠉
⠀⠀⠀⠀⠀⠢⠤⣤⡀⠀⡤⠊⠀⠀⠀⠀⠄⢤⣘⣤⡈⡐⣶⠆⡘⠀⣸⣧⠀⠀⠰
⠀⠀⠀⠀⠀⠂⠀⠀⠁⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡶⠡⠊⡇⢰⡿⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⢀⠄⠴⠏⠀⠀⠀⠀⠀⠀⢀⠈⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⣠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⣀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠙⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣦⣠⣾⣿⣿⣿⣿⣦⣴⣾⣿⣶⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣴⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡻⣿⣿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠄⠆⢿⣷⣤⣤⣀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣀⠀⠀⠈⣛⡛⠛⠿⠿⠿⠿⠿⠿⠿⣿⡏⡇⠤⠐⠛⠇⠸⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⠿⠿⠧⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⣠⣶⣶⣦⡀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⢿⣿⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⣿⡿⢿⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠁⠀⠀⠀⠀⠀⣿⡀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡤⠙⠻⣿⣄⠀⠀⠠
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⢻⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⢀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣼⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⣿⢃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⢹⣿⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⠐⠘⠛⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣦⠠⢿⣿⣯⣶⣤⡀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣸⣿⠀⠀⠀⣴⣿⣿⣿⣿⣷⣶⣮⣝⣤⠾⠛⠻⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢸⣿⣿⠘⠇⢶
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢨⣿⡟⣿⣿⣿⣿⣿⡟⠁⣠⣶⣶⣄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣿⣿⠀⠀⢸⣷⡀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⠟⠁⠿⠟⠿⠛⠏⢀⣾⣿⣿⣿⣿⣦⠈⣉⠁⠀⠂⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠟⠀⠁⠀⠻⢏⠀⠐
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀⣾⣿⣿⣿⣿⣿⣿⣆⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉
⠀⢺⣿⣿⣿⡇⠀⠀⠀⣀⣸⣿⣷⣿⠁⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣾⣿⣿
⠀⠙⠛⠛⣿⣇⠀⠀⢀⣿⣿⣿⣿⠃⢀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⢸⣧⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠻⠿
⠀⠀⠀⠀⠿⠟⠀⠀⠘⠿⠿⠿⠟⠀⠸⠟⠀⠿⠿⠿⠟⠿⠿⠿⠟⠀⠗⠀⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠶⠛⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠰⣾⢿⠃⢠⡈⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠠⠤⢄
⠀⠀⠀⠀⠀⠂⠀⠀⠇⠀⢧⠀⠀⠠⠈⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⠖⠒⠢⠄⣤⡁⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠓⠐⣆⠀⠀⢀⡀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠶⠀⠀⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠃⠀⡀
⠀⠐⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡴⠀⠐⠂⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⢄⠊⠄⠚⡑⠀⠀⢤⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢸⡄⢠⡀⢀⣐⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⡒⠑⠤⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣶⣿⣶⣖⣰⣿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣜⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣎⢣⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠺⢛⣿⣯⡝⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡓⠤⣀⣀⣀⣀⣀⠀⣀⡠
⠀⠀⢀⡀⠄⣨⣴⣾⠓⠻⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⢀⠄⠈⠁
⠀⠀⠀⢈⣾⣿⣿⣿⣦⣥⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⣿⣶⣮⣤⣁⡾⠁
⠀⠘⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣠⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠘⣿⠏⠁⣿⠟⠁
⠀⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠁⠀⠀⠉⠀⠞⠁
⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡟⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣏⢸⣿⡟⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠸⣿⣷⢿⣿⡿⠿⢸⠃⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢸⡆⢸⡏⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣮⢀⣹⡤⠐⠒⢸⠇⠈
⠀⠀⠀⠀⠀⣠⣠⡶⠛⠉⡏⠀⠀⠀⢘
⠀⠀⠀⠀⠊⠋⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠴⠶⣿⣿⣿⣷⣶⣶⡦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢉⠔⠀⠀⠀⠀⠈⠉⠛⠿⣿⡻⣮⡹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠞⣁⣤⣶⣀⡀⣠⡄⡀⠀⠀⠢⡁⠙⣿⡝⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠟⣿⣯⣋⠑⠄⠘⠛⠷⣶⣆⠀⠹⡄⠼⢃⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀⠙⠀⠾⣣⢝⣛⣿⣷⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⣀⡾⣴⣾⣷⡄⠈⠿⣀⡆⠀⢿⠀⠠⠂⠁⠉⠁⣠⡿⠁⠈⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡇⡄⢀⣩⠷⠡⠀⠈⠐⠤⡀⠀⣀⡈⠓⠀⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠢⢩⣿⠏⡀⢀⣠⣶⣦⡀⣄⠈⠛⠯⠃⠀⢀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⡄⠀⠤⠃⠉⠙⠻⠋⠈⠈⠉⠒⠀⠀⠀⠑⠤⣀
⠀⠀⠀⠀⠀⠐⣄⠁⠀⠀⠀⠰⠀⠈⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⣃⡒⣂⣄⣀
⠀⠀⠀⢀⣰⡞⠋⠃⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣷⣿⢿⣠
⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⡋
⠀⠀⠀⠐⣿⣿⠋⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⣌⠉⣿⣿⣿⡿⣿⡿
⠀⠀⠀⠀⠀⠁⠀⠸⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠈⣲⣶⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠋⡄⢲⡆⣴⣦⣻⣷⣶⣤⣴⣶⣴⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠘⠀⠠⠐⠛⠃⠈⠙⠛⠛⠛⠛⠋⠉⠈⠙⠉⠉⠉

⠀⠀⠀⣠⠄⠠⠠⢀⢠⠠⡄⠀⡄⢀⢀⠀⣰
⠀⠀⠀⠭⠄⠣⠜⠘⠊⠐⠂⠀⠃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡔⠀⠀⠀⠀⠀⠀⢠⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⡀⡀⢀⠀⠤⢤⠀⡀⠀⠀⠀⠀⠀⠇⠀⠀⢰⠇⠀⠀⠆⠀⠀⠀⠀⠂⠐⠀⠀⡀⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⡄⠈⠀⠀⠀⠀⠛⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠂⠀⠘⠁⠲⠁⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⡄⠀⠀⣠⠈⠁⠀⣀⠀⢀⡠⠀⠀⠀⠀⠂⠔⠂⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⠊⣨⠍⣁⡇
⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡤⠂⠋⠉⣯⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠚⠋⠉⠉⢉⢽⠀⠀⠀⢸⣥⠄⠀⠰⡏⢹⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⢸⠸⠀⠀⢀⡼⠃⠀⡀⠀⣵⠁⣶
⠀⠀⠀⠀⠀⠀⠀⠆⠌⠈⠁⠉⠱⠃⠀⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠹⠀⠁⠋⠀⠀⢀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠠⠀⠡⠀⠀⠀⠀⣐⠊⠁⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡰⠞⠁⠀⠀⠀⠀⠁⠢⢤⡀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠪⢧⠀⠀⠀⠤⠄⠌⠉⠁⠀⠢⡀⠀⣸⢃⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⣀⠀⠀⠀⠀⠀⠀⢹⣮⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠈⡀⢀⠀⠄⠀⢾⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠻⣷⣮⣤⣄⠀⣀⠴⠶⣛⣿⣿⡟⠂⠀⠀⠀⠀⠒⠀⠀⠀⠈⠛⢤⠁⠀⠀⠀⢴⡎
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠠⠈⠈⠩⠋⠂⠈⠙⢹⠟⠃⠙⢧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠙⠻⣖⠤⠀⠀⠀⠀⠀⠀⠀⢀⣸⡆⣾⣿⡟⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⠈⠀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠠⠨⠄⠀⠀⠀⠀⠀⠀⣰⣼⣿⣾⢙⡿⠁⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⡄⠀⠀⢠⣀⣄⠀⠀⠀⠀⠀⠀⢀⣀⠚⠂⠄⠠⠤⠀⠐⢛⣿⣿⣵⣿⡧⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢿⡧⠍⢄⠀⠀⠀⠓⢨⣄⡀⠀⠉⢒⣶⣄⠔⠒⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⡠⠻⢹⣿⣿⣉⡉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⡼⠘⡏⠀⠀⠀⠀⢈⡈⠂⠀⠀⠀⠀⠈⠀⠀⠘⠇⠈⠀⠀⠀⠀⠈⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⣼⠃⠀⠀⠀⠀⡀⢸⠰⣇⠀⠀⠀⠀⠈⠀⠸⠀⡠⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠁⠀⠀⠠⢀⠈⢢⣧⣹⣗⢄⣧⡀⠀⢀⡠⠚⠠⠖⠀⢠⡴⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣐⠤⠀⠀⠈⢉⡽⢟⣟⣁⠖⠒⠒⠤⣌⣐⣙⣛⣿⡿⣿⣿⡞⠁⠀⠀⠀⠀⢀⡘⠆⡀⠀⣷⣤⣠⠀⠀⣤⡄⡰⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⡴⣩⣿⠁⠀⠀⠀⢀⡤⠤⠽⠿⣟⣵⣿⣿⣶⣦⣤⣤⣶⠒⠋⠉⠙⣿⣾⡇⢻⣿⠛⠂⠀⢀⠁⠀⠀⠐⠂⢄
⠀⠀⠀⠀⣸⡶⠂⠒⠂⠈⠁⢈⠛⠁⠀⠊⠁⠀⠀⡀⠐⢀⣼⠉⠹⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠊⣿⡄⠀⠀⠀⠉⠠⠱⠢⡀
⠀⠀⠀⠀⠈⠁⠑⡀⠐⢁⠄⠄⠀⢂⠀⠀⣠⡏⠀⣴⠛⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣤⣤⠀⠀⢄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠓⠈⣧⠀⣠⣇⠀⠀⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠁⠀⠀⢸⡇⠉⠉⡣⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀⣀⣾⡿⠀⠀⠀⠘⠲⠴⠄⠀⠤⠤⠒⠁⠈⠆⠀⢀⠘⢉⡙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠂⠈⢹⣿⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣿⡤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣨⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢚⣋⣈⠣⢍⠫⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣯⣝⣛⣾⠿⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣛⠿⠿⣷⣽⡳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢀⢶⡇⡀⣙⡆⠲⠄⢹⣟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⠈⠉⠀⠂⢰⠄⢈⠁⠅⠀⠙⢯⡤⠽⢦⡄⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⠈⢅⣿⡄⠘⣄⠇⠢⠀⠀⢧⢀⡼⢠⠃⠾⡇⢠⢖⣂⢸⡠⠔⠂⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⡁⠻⣄⠌⠂⢐⢸⣆⣴⠞⣀⠀⠀⠀⢱⣿⣿⣷⣿⣷⣾⣭⣿⣞⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⢤⣽⠿⠷⠞⠋⡐⡤⢴⡋⢅⣀⣀⡀⠤⠖⡉⠉⠸⡿⡟⠋⠳⠔⡓⠍⠫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡜⠓⠀⢐⡁⠀⠀⠁⠀⢿⣿⣣⠀⠀⠖⠂⠀⠀⠀⠀⠈⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢵⡆⠐⢂⣤⣿⠆⠈⠠⣼⢿⣷⠶⠶⡂⠀⠀⠀⢠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢣⡈⠉⠁⠀⠀⠔⢃⠁⠘⠓⢚⣛⣁⢀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠴⠿⣿⡃⠀⠁⡀⠛⠁⠀⣠⣭⣤⣾⣴⡾⢹⡧⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡙⢹⣦⣤⡤⣤⢶⣿⠿⣮⢹⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⣴⡚⠿⠡⠬⠬⠷⣿⣧⣴⣯⡆⢠⡆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠙⢦⡀⣀⣶⠀⣿⠹⡇⣘⡓⠾⠋⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⣶⣶⣶⡦⢤⡤⠤⠄⢀⡀⠀⠀⠀⠉⢿⣾⠀⢘⠀⢻⣽⣿⡻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⡛⠶⠦⢤⣀⡁⠠⠀⠀⠀⠻⣇⠘⡀⠈⣿⡁⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠲⢤⣀⣀⠉⠒⠶⣷⣼⠀⠹⡇⠋⠀⢻⣻⠟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⠉⠛⢷⣿⡔⢀⣸⣇⣶⣀⣄⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠹⣿⣞⢿⣿⢻⡟⠉⣉⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⣀⣈⣭⣾⣿⡜⠇⢹⡏⠉⠉⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠹⣿⣟⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⡇⢿⡂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⣤⡀⡄⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠄⠈⣦⡄⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢠⣿⣷⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢻⣿⣧⡀⠀⠙⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⡜⠀⠀⢀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡀⠐⠉⠀⠀⢠⡏⠀⣿⠀⢘⣧⡈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠒⢄⠀⠀⠀⠀⡌⠀⠃⢀⠴⡁⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⠄⠑⣄⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⡄⠀⠀⠀⠀⢠⢠⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠁⠀⠀⢴⣷⣾⡧⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠉⡿⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠈⣀⠀⠀⢰⠃⠀⠀⠂⢤⣄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣷⣤⣄⡴⠂⠀⠀⢀⣴⠾⡿⣧⣾⠋⠀⢀⡆⠀⠀⠀⠐⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣤⣿⠟⠀⠀⠀⠀⣦⡡⠀⠀⠹⠋⣠⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣤⣤⣄⠦⠀⠀⢸⣟⣿⣯⠀⠀⡀⠀⠀⠀⣽⣿⠿⠟⠀⣼⣧⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⠆⢈⡟⠈⢷⣤⣧⠀⠀⣼⡁⠀⠀⠀⡘⠛⠉⢸⠀⠀⠀⠀⠀⢀⣌⣴⣿⣄⡀⠂⠀⠀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣡⠀⣴⠇⠀⠀⢀⡾⠁⠀⠀⡾⠀⠀⠀⠀⢀⣾⣿⣿⠛⠙⢷⣄⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠰⠟⠀⠀⠀⡾⠁⠀⠀⢠⡇⠀⠀⢀⣿⣿⡽⢿⡟⠀⠀⠀⣿⡆⠀⡀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢸⡇⠀⠀⠾⢿⠏⠀⠃⠁⢀⡄⠀⠙⡅⠀⠀⠀⠀⠁⠚⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠂⠀⠀⠀⠀⣶⣄⠀⠀⠉⠀⣠⠀⠀⡘⠃⠀⠀⠀⠀⢠⠀⣸⠿⠋⠀⠀⠀⠀⠀⠀⢁⣾⡇⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⠂⠀⠁⠀⢸⡼⢯⡴⠿⢋⣤⡀⠀⠀⠀⢰⡆⠀⠠⠀⠀⠀⠀⠀⠀⠚⡰⣾⣿⠏⠀⠀⢸⣟⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⡀⠀⠁⠀⠀⠀⠀⢷⡌⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠊⠁⢠⣾⢶⡞⠿⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⢻⣷⠀⠀⠀⣼⣷⠀⣠⡀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠛⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠶⣿⠀⠀⢰⡏⠻⠀⢿⡇⣤⣠⣷⣤⣴⠎⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣤⡀⣦⠀⠀⢸⣦⠌⣿⠟⠛⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢦⠈⠻⣿⠀⠀⢸⡇⣼⠃⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⣦⡀⢸⡿⠁⢀⣤⣏⠀⠀⠀⠀⠀⠠⣄⠀⠰⠖⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠘⡟⢷⣈⠇⠀⣾⣿⣿⠆⠀⠀⣀⠀⠀⠀⢠⣿⣶⣦⡄⠀⢀⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣧⢸⠀⣿⠀⠁⡆⠀⣿⣿⠋⣄⡀⢀⢉⣀⠀⠀⠈⠛⠛⠋⠀⠀⢸⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣿⡟⠀⣿⣀⠀⠃⠀⠘⡇⠀⢻⣥⡟⢿⡏⡟⠀⠀⣀⣠⡖⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢂⡀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠄⢸⡇⠀⠀⠀⠀⡇⢀⡆⢀⣀⠸⠇⣠⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⢰⣤⣾⣿⣿⣿⠁⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⣷⠀⣸⡇⣼⣦⣾⣿⣿⠟⣁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⡀⠀⠀⢿⢀⡿⣿⡿⠿⠛⢉⡀⢰⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠊⠉⠁⠀⠀⠀⡀⢸⣾⡇⣿⣦⡴⣿⣿⣿⣾⣏⣿⣴⢾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡀⠀⠀⠀⠀⠀⠀⠱⠈⣻⠇⣿⡷⠀⠈⢻⣿⣿⣿⣿⣷⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋⠀⠈⠙⠷⣦⣀⠀⠀⠀⠀⣷⡟⠀⣿⣷⡞⣼⣿⣿⣿⡟⣿⡶⣾⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⢼⣿⡜⣿⠟⠀⠉⠉⠉⢻⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⢸⣿⣾⣿⠀⠀⠀⠀⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⢸⣿⠈⢻⣀⣀⣀⠶⠶⠶⠤⠀⠠⣤⠤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⣴⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠿⠻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⢏⠤⠄⠀⠀⠀⠀⠂⠀⠠⠤⡹⢐⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⡈⢁⡀⠀⠀⠀⠀⢀⡈⢁⠀⢸⣿⣿⣿⠿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣰⣿⢿⡿⣿⠷⣿⣿⢿⡀⠈⠛⠿⢛⠴⠀⠀⣦⡚⠿⠛⠁⢀⡿⣧⢅⠀⣤⢿⡿⣿⣆
⠀⠀⠀⠀⠀⢠⣿⣟⠿⠿⠋⠀⠛⠛⠿⢷⣄⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⣠⣞⡻⡿⣟⡻⠿⢟⡻⢿⣿⡆
⠀⠀⠀⠀⠀⣾⣿⣛⡻⢟⣃⠀⢾⣛⡻⢿⣛⣷⠀⠀⠀⠆⠰⠀⠀⠀⣾⠿⣛⣻⠿⣛⣛⠿⣛⣛⠿⣿⣷
⠀⠀⠀⠀⢸⡉⠙⣿⡟⠻⣯⡛⢟⣭⡛⢟⣫⣛⢧⡀⠀⠒⠒⠀⢀⣼⣛⠟⣫⣙⠟⣫⣝⣿⠟⢻⣿⠋⢉⡇
⠀⠀⢠⡟⠻⣧⠀⢻⣧⠀⢿⣛⣛⣭⣙⣛⣭⣙⡿⠷⣄⡀⢀⣠⠾⢿⣝⣛⣭⣝⣛⣩⣝⡿⠀⣼⡟⠀⣼⠟⢳⡄
⠀⠀⠀⢧⡀⢻⣧⠀⢹⣇⠀⢻⣫⣥⣽⠿⠟⠉⠇⠀⢻⠉⠉⡏⠀⠸⠉⠻⠧⣍⣛⣥⡟⠀⣸⠏⠀⣼⡟⢀⡼⠁
⠀⠀⡖⠲⣿⡀⠹⣆⠀⢻⡆⠘⡏⠁⠀⠀⢀⡈⠀⠀⠀⠀⠀⠁⠀⠀⢁⡀⠀⠀⠈⢹⠃⢰⡟⠀⣰⠏⢀⣿⠖⢲
⠀⠀⠹⣄⠙⢷⡄⠙⣆⠈⠛⠀⠹⡄⠀⢰⠋⢹⡆⠀⠀⠀⠀⠀⠀⢰⡏⠙⡆⠀⢠⠏⠀⠛⠁⣰⠋⢠⡾⠋⣠⠏
⠀⠀⠀⠘⢧⡈⢻⡄⠀⠀⠀⠀⠀⢷⢀⡏⠀⡾⠀⠀⠀⢀⡀⠀⠀⠀⢷⠀⢹⡀⡾⠀⠀⠀⠀⠀⢠⡟⢁⡼⠃
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡠⠀⠈⠉⠀⡼⠁⠀⠀⠀⢸⡇⠀⠀⠀⠈⣧⠀⠙⠁⠀⠄⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠇⠀⠀⠀⣰⣃⣠⠤⠤⠶⠛⠛⠶⠦⠤⣄⡘⣆⠀⠀⠀⠘⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⢀⣴⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣦⡀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠋⠉⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠀⠉⠙⠦⠤⠞⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⢀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠀⡄⠉⠀⠀⠀⠉⠠⠀⠄⢹⣿⣿⠀⠀⠀⢸⣿⣿⡇⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⣶⠒⠒⣶⣶⠒⢲⣶⡖⠒
⠘⠐⠁⣀⠀⠀⠀⣀⠀⠒⠀⣸⣿⣿⠀⠀⠀⢸⣿⣿⡇⢸⠩⢽⣿⣿⣸⣿⣿⠻⣹⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡏⠁⠈⢹⠉⠀⠈⢹⠉
⠀⣠⠄⠉⢠⣤⡄⠉⢠⡤⠀⢹⣿⣿⠀⠀⠀⢸⣿⣿⣧⡾⠿⡿⡿⠋⠉⠻⣿⡟⣿⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⠀⠀⠀⢸
⠐⠯⠂⣀⠘⠛⠂⠀⠨⠿⠃⣸⣿⣿⠀⠀⠀⢸⣿⣿⡿⣧⣴⣤⣷⣀⢀⣠⣿⣧⣼⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⠄⢀⠀⢼⠀⢀
⠉⢭⠉⠉⠈⠉⠉⠉⠉⠉⠉⢹⣿⣿⠀⠀⠀⢸⣿⣿⡇⢸⢙⢹⣿⡟⡛⣿⣿⡏⣿⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⠄⠑⠀⢼
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⢸⣿⣿⡇⠸⠿⠿⠿⠷⠵⠿⠿⠿⠿⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⣧⣬⣤⣼⣤⣼⣤⣼⣤⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣴⡆
⠠⢸⣿⣿⣿⠀⣿⣿⣿⡇⠄⢹⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⢰⣿⣿⣷⣿
⠢⢸⣿⣿⣿⠀⣿⣿⣿⡇⠂⢸⣿⣿⠀⠀⠀⢸⣿⣿⣿⡿⢛⡇⠄⠐⠒⠚⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠘⠛⡛⠛⠛
⠒⢸⣿⣿⣿⠀⣿⣿⣿⡇⠃⢸⣿⣿⠀⠀⠀⢸⣿⣿⣿⠁⠾⠗⠲⢖⡶⢶⡄⠻⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⣰⣿⣿⣿⠀⠀⡿⣿⣿
⣘⣸⣿⣿⣿⠀⣿⣿⣿⣇⣃⣸⣿⣿⠀⠀⠀⢸⣿⣿⣿⣄⠹⢿⣿⣿⠟⢠⣿⣤⣴⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⢛⣿⣿⠿⠀⠀⠥⣿⣿
⣛⣛⣛⣛⣛⣀⣛⣛⣛⣛⣛⣿⣿⣿⠀⠀⠀⢸⣿⣿⣟⣛⣓⣀⣀⣀⣒⣛⣛⣛⣛⣛⣿⣿⡇⠀⠀⠀⣿⣿⣿⡀⠈⠉⠉⠀⠀⠀⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⡀⠀⢔⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠦⣰⣿⣿⣿⣽⡻⣿⢷⣦⡳⣄⢤⡀⢠⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣠⡿⠋⣀⣌⡉⣋⣟⣩⡙⢿⡶⣄⠙⠌⠹⣷⡄⢿⣿⣿⣷⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⢹⣷⡿⣾⡋⢥⡻⢿⣿⣿⣷⣷⡟⢣⡀⠑⠘⣿⡀⠈⢻⣿⠃⠀⢀⣦⣾⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣼⣿⣿⡙⣿⣿⣿⣿⣮⣭⣿⢯⣙⠻⣦⢱⡄⢀⢸⣿⠀⠀⢻⣿⣆⣾⣿⣿⣿⣿⡿⠿⠿⠻⠟⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⢈⡑⠛⢿⣶⡼⢿⣿⣿⣿⣯⡃⢿⡀⢻⣦⢿⣮⣷⣿⡀⠀⢸⣿⣧⣿⣿⣿⣷⣧⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⣾⣷⣶⣿⢏⣤⣴⣽⣿⣿⣿⣿⡦⣻⡆⢿⡎⣿⣿⣿⡇⠀⣸⣿⣿⠏⠙⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⣛⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⢋⠁⣿⣿⣾⣇⡟⢁⣿⣿⣄⣽⣿⡏⠀⠀⠀⠈⠙⠿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⢸⣸⡇⠚⠛⠛⢿⣿⣿⣟⣿⣿⣿⣿⠋⢸⡇⢸⣿⣿⡟⣾⣟⣼⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣷⢘⢀⣤⣾⣯⣛⣿⣿⣿⣿⣿⢀⣾⠇⣼⠏⠊⠀⢫⡤⣿⣿⣿⣿⡜⠀⠀⠀⡀
⣷⣶⣦⣄⡀⠀⠈⢻⣿⣤⣺⠉⠭⣀⣉⣉⣩⣿⣿⣇⣼⣿⣾⣟⣼⡶⣎⡾⢡⣿⣿⣿⡿⠁⠀⣤⣾⡇
⢻⣿⣿⣿⣿⣷⣦⣄⠙⠻⠿⢷⣤⣀⣉⣽⣿⣿⣿⠛⢩⠐⢋⣭⣿⣿⠛⣀⣾⣿⣿⠋⢠⣶⣾⣿⣿⡇⢀⣀⠀⣀⣀⣀⣀⣤⣤
⠘⢿⣿⣿⣿⣿⣿⣿⣦⠀⢠⣄⢈⣛⣙⢛⡙⣉⣤⣖⣠⣾⣿⡿⢿⢟⣾⣯⠁⣸⡏⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠈⠿⣿⣿⣿⣿⣿⣿⣧⣺⣿⣶⣍⠻⢿⣿⡋⠛⠛⡟⠋⠋⠀⢸⣿⣿⡟⣰⡿⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠉⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠛⠻⠿⢦⠠⡄⠀⠀⢶⣦⠙⣿⡾⠏⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⢀⣠⣬⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⡀⠁⢿⡄⠀⢸⣿⣿⠟⢁⣴⣶⣦⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉
⠀⠀⠀⣴⣿⣿⣿⣿⣿⠉⠹⣏⠁⠀⣰⣾⣿⣿⡇⠀⢸⡇⣠⣿⣿⣥⣤⣤⣹⣿⣿⣠⡼⣿⣯⣭⣭⣉⣁⠁
⠀⠀⠀⢿⣿⣿⣿⣿⠁⣤⡄⠈⠳⣀⣿⣿⣿⣿⠁⠀⣾⣾⣿⡿⠿⠛⠛⠷⠀⠀⠙⣷⣦⡈⠙⠿⣿⣿⣿⣷⣦
⠀⠀⠀⠘⣿⣿⣿⠃⠀⢾⣿⣧⡄⣧⢿⡿⠋⠁⡀⣸⡿⠋⠁⠀⢀⣀⡀⣀⠄⠀⠀⢿⣿⣿⣦⡀⠈⠻⣿⣿⣿⡆
⠀⢀⠀⠀⠈⠻⣿⠀⠀⠈⢿⣿⣿⣿⣿⣶⡀⠀⣿⣿⣅⠀⣠⣾⣿⣿⣿⠏⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⡧
⠀⠹⣿⣦⣆⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡷⣸⡿⣿⣿⠠⣿⠿⠛⠉⠁⠀⠀⠀⣼⣿⣿⣿⡿⠃⠀⠀⠀⠈⠻⡇
⠀⠀⠹⣿⣿⣷⡀⠀⠀⢸⡿⠿⠛⠋⠻⠟⣠⣿⣵⠞⣿⣾⣷⠖⠲⠶⣤⡀⢀⣠⣾⣿⣮⣥⡀⠀⠐⢀
⠀⠀⠀⠘⢿⣿⣷⢰⣿⠈⠀⠀⠀⠈⢷⣿⣿⡟⠉⣴⠟⠁⢹⣿⣧⡀⢈⡿⠋⣹⣿⣿⣯⡛⠿⢿⣦⣈⠇
⠀⠀⠀⢀⣀⣈⣙⣿⣿⠀⣀⠀⢰⣧⠈⣿⣿⠁⣼⠋⠀⠀⠘⣿⣿⢧⣾⠀⠀⣿⣿⠋⠀⢈⣵⣾⣿⣿⡇⢴⣶⣶⣤⡀
⠀⠀⢸⣿⡿⠉⡀⠈⠉⠓⢿⡇⣸⣿⠀⣽⣏⣼⣯⣤⣤⣀⠀⢸⣷⣾⣟⠀⢠⣿⠞⡴⣚⣯⣛⢻⡿⣿⣷⡀⠻⢿⣿⣷⡄
⠀⠀⠻⡟⠁⣸⣷⣄⠙⠻⢶⣿⣿⠟⢀⣿⡿⠋⠀⠀⢀⣼⣷⣾⣿⣧⣬⢰⡟⠃⢾⠁⣼⣿⣿⡿⣷⣸⢿⡇⠀⠀⠈⠿⣷
⠀⠀⠸⠇⠀⣿⣿⣿⡀⠀⠀⢻⣿⣠⣿⣿⠀⠀⠀⢴⣿⣿⣿⣿⡿⣿⣿⢈⣧⣶⠘⣿⣿⣿⣟⣵⣿⣿⡇⡸⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⣸⣿⣿⣿⠇⠀⠀⠐⣿⣿⡗⠛⠉⢹⣿⣭⣿⣿⢿⣆⣿⡍⠛⣿⣫⠿⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠙⠇⠀⣠⣾⣿⣿⣿⡿⣶⣶⣄⠀⠛⠁⠀⠀⣰⣿⣿⣿⣛⣿⡈⢿⣿⣿⡀⣸⢡⣶⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⣼⣿⡟⠀⠀⠀⠉⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣦⣭⣥⣤⡀⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⣰⣿⡟⠷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠏⢹⣿⣿⣿⣿⣆⠙⢿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠄⣿⠋⠀⠀⣐⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠉⠁⠀⠀⢸⣿⣿⡇⠙⢿⣆⠀⠙⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠉⠉⠀⠘⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣦⣄⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠏⠀⣀⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⠀⠀⠈⠙⠛⠛⠉⠀⣰⠟⠉⠁⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣀⣀⣀⣀⣤⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡍⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉⠉⢉⣵⣄
⠀⠀⠀⠀⠀⠀⠀⢰⡟⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣧⢹⣇
⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠸⣇⠰⣟⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢻⡆⣠⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠙⢷⣽⣧⣈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⢁⣴⣿⡴⠋⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠈⠙⠛⠃⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠐⠛⠋⠉⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⣦⡿⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣭⣭⣭⣭⣭⢻⡆⠀⠀⠀⠀⠀⣾⢫⣍⢷⡀⢠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣘⣡⣿⣿⣿⣿⣿⣌⣃⠀⠀⠀⠀⢰⣿⠸⠟⣸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣮⣭⣵⡆⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣮⢙⢟⠋⣵⣿⣿⣿⣶⣤⠀⠐⢻⡟⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣸⣿⡇⣿⡿⠿⠿⣿⣿⡇⠀⢸⡇⠀⠀⠀⢠⣴⣶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⢸⣿⣿⢻⣿⣿⡇⣿⣿⣿⢸⣿⣿⡟⣿⣿⡇⠀⢸⡇⠀⠀⠀⣸⣿⣿⢫⣍⢻⣿⣧
⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢱⣿⣿⣿⡜⣿⣿⡇⣿⣿⡇⠀⢸⡇⠀⠀⠀⣿⣿⣿⣘⣛⢿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣷⡙⡿⢋⣾⣿⣿⡇⣿⣿⡇⠀⠘⠷⠶⠄⢀⣿⣿⣿⡙⢛⣼⣿⣿⡄
⠀⠀⠀⠀⢸⣿⣿⠸⣿⣿⣿⣿⣶⣿⣿⣿⣿⠇⣿⣿⠇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣸⢏⡀⠙⠲⠤⡄⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⢀⡤⠶⠓⠁
⠀⠀⡀⠀⠀⠈⣰⡄⠀⠀⣍⠀⠿⠘⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠄⠀⠀⠀⣈⠅⠀⢢⣢⡄
⠀⠀⢈⡃⠀⠀⠛⠁⠰⠘⠋⠀⠒⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢸⡄⠀⠀⠻⠇⠀⠀⠙⢏
⠀⠀⠀⠉⠀⡀⠀⠁⠀⠀⠀⢀⢠⡀⠘⠇⠀⠀⠀⠀⣠⣤⣴⣄⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⢠⠄⠀⠆
⠀⠀⠀⠀⠀⠈⠁⠒⠏⠠⠄⠀⠈⠋⠀⢀⡀⠀⠀⠘⠁⠀⠀⠙⠇⠠⡆⠂⠀⠀⠀⠀⠠⠀⠠⠀⠀⠐⢚⡀
⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⡐⢠⣀⣀⣀⣀⠀⢀⣀⠀⠀⣤⣄
⠀⠀⠰⠖⠀⠐⡆⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤⠀⠀⠀⠿⢿⣿⣿⣧⢀⣿⣼⠖
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣸⠹⠉⡛⠽⣋⠇
⠀⠀⠀⠀⠀⠈⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉
⠀⠀⠀⠰⠐⡂⠐⠂⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠘⠛⠁
⠀⠀⠀⠀⠀⠘⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠀⠁⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⠀⠐⠂⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡠⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣀⠀⠀⠿⡂⠀⠀⠀⠀⠀⠘⠄⠐⠀⠠⠀⣨⣷⣦⣀⠀⠀⠀⠀⢧⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⣈⣀⡎⠁⢠⡤⠴⠂⠀⠀⠀⠠⠀⠀⠠⠀⠨⠀⠀⠙⠻⠛⠂⠁⡀⠀⠀⠶⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠈⠁⠁⢰⠂⢦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠰⡤⣄⢵⠀⠀⠀⠂⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⡆⠐⠀⠀⢀⣀⡄⠀⠊⡀⠀⠀⠀⣠⣤⣠⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠀⠶⠂⠈⡀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠠⠀⠀⣤⣶⡆⠀⠀⢁⠀⢹⣷⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠛⠛⠃⠐⠀⠊⢁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡀⠀⠀⠟⠿⣿⠀⠀⡀⢀⠘⠿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢴⡂⠀⠀⠸⠄⠠⠤⣀⣀⡀⠀⠀⠀⠀⣴⠂⠐⠋⠁⠀⡀⡀⠀⠀⠀⠀⠰⠈⠁⠓
⠀⠀⠀⠀⠀⠀⣀⣠⡤⠦⠀⣩⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⡏⠀⠈⠀⠌⠀⠠⢠⣄⡠⠤⠅⠀⠈⢹⠳⠦⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠀⠀⠀⠈⠒⠒⠒⢒⡂⠀⠃⠀⠀⠀⠃⠀⢺⠀⢀⠀⠀⠀⠀⠀⠘⠌⡶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢀⣠⠄⠀⡇⠀⠈⠀⠀⠀⠀⠀⠁⠀⠈⠓⠦⡀⠀⠀⠀⠐⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠄⠤⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠤⠠⠀⠀⣀⠦
⠀⠀⠀⠀⠺⠣⠦⠁⠀⠀⠀⠀⠰⠀⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠅⠀⠀⠀⠀⠈⠴⠌⠗
⠀⠀⠀⠀⠀⢤⠀⣄⠠⠀⣀⡻⠰⠆⠁⠄⣀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⣀⠠⠈⠰⠆⢟⣀⠀⠄⣠⠀⡤
⠀⠀⠀⠀⢀⠀⠀⠉⠀⠈⠋⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⠁⠀⠙
⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⣇⢸⠀⠀⠀⠸⡇⡇⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⡇⠀⠀⠀⢸⢸⡇⠀⠀⢤⣼⣿⣤
⠀⠀⠀⢴⣿⣾⣦⠀⠀⣶⣷⣷⡆⠀⢰⣾⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢠⣾⣾⣷⠄⠀⢽⣿⣿⣿
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⠉⠉⠉⠁⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉