Finger game Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢰⠩⠕⠒⠤⣀
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⡠⠤⠶⠛⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊⠷⠤⣄⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠂⢷⠀⠈⡆
⠀⠀⠀⢀⠂⠀⣀⠤⠒⠉⠁⠈⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠒⠤⡃⠀⠰
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡧⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡁⢤⠚⠀⠊⠉⠁⠀⠀⠀⠀⡅⠀⢀
⠀⠀⠀⠃⠀⠈⡆⠀⠀⠀⠀⠀⠀⠠⡀⠀⢙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⡤⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⣄
⠀⠀⢸⠀⠀⠀⢱⠀⠀⠀⠀⣀⣀⠀⠘⠦⠼⠠⠇⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠐⠶⠆⢰⠁⣏⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⢆
⠀⠀⠸⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠒⠋⠉⠁⠀⠀⡜⠀⠠⢄⠀⠀⠈⢣⡀
⠀⠀⡆⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡴⠁⠀⠀⠀⠙⢆⠀⠀⠱⡀
⠀⢰⠃⠀⠀⠀⠀⠀⠢⣀⠀⣠⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⣀⡠⠊⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠙⣄
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠐⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⢆
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠀⣀⡀⠠⠴⠋
⠀⠀⠠⠀⠀⢀⡤⠊
⣤⣤⣤⣵⣶⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡆⠀⠀⠀⠀⠀⠀⢀⣠⠖
⠀⠀⠀⠀⠀⢄⠀⠀⡠⢄⠀⠀⠀⠀⢀⢫⣧⠀⠀⠀⢀⣠⠞⠋⢁⠄⠀⢄⠀⠀⠀⠀⠀⡠⣄
⠀⠀⠀⠀⠰⢿⡅⠀⢱⣿⠀⠀⠀⠀⠢⢌⣾⢟⢤⠖⠋⡀⠀⠀⣜⠂⠐⠐⠀⠀⠀⠀⢀⠿⢧
⠀⠀⠀⠀⡃⢰⣷⣤⠂⣺⣧⣀⠀⠀⠀⣠⡔⠁⠁⠀⠀⢳⣈⣱⡨⠆⠔⠂⠐⠢⡀⡠⢎⣀⣘⣶⡄
⠀⠀⠀⠀⠀⠉⠉⠈⠂⠰⠿⠁⣰⢈⣈⣈⣱⠀⠀⠀⠀⠘⢀⠹⡤⠄⠬⢒⠒⠂⠁⠈⠒⠈⠛⠁⡄⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠒⢠⡴⠞⢓⣠⣾⣾⣿⢀⠀⠀⢀⠃⠀⠄⢻⣤⣠⠔⡯⠀⣤⢤⣧⡀⠀⠀⠢⠦⣿⣿⠆
⠀⠀⠀⠀⠀⠀⣠⣴⢼⢟⠀⠀⠀⠹⡁⣎⠛⠊⠁⠀⢞⠤⢀⣠⣤⡿⠀⠀⠈⠚⠓⠛⠉
⠀⠀⠀⣠⡴⠋⠁⡌⢸⡘⣆⠀⠀⢀⠋⡝⡄⡔⠊⠈⠈⢩⠉⠀⠉⠀⠀⠀⠀⠐⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⢀⢴⠋⠁⠀⠀⡛⢄⣠⣡⣿⣇⣀⡌⠀⢰⢻⣖⠒⠒⠒⠈⢀⠀⠀⠀⠀⠀⠀⡘⢺⡇⠀⠀⠀⠀⠀⠠⢆⠀⠂⢟⠒
⠸⣶⣭⣐⠠⠄⡈⠈⠀⠉⠁⠀⠣⡑⠠⢼⣾⠏⡠⣟⠀⠤⢤⣧⠄⠀⠀⠀⢀⠀⢈⣹⣄⡠⠰⡇⣀⣤⣾⣧⠄⠔
⠀⠀⠈⠉⠛⠷⣶⠝⠂⠀⠈⣰⣀⠀⠀⠀⠀⠀⠑⠤⢙⠛⠽⠯⢀⠄⠂⠠⣬⣀⢸⣿⣿⠿⠦⠭⠿⠟⠋⣉⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠘⢍⣠⣘⣿⡿⠿⡷⣭⣄⣂⠠⠀⡀⠀⠀⠀⠀⠘⠂⠤⠀⠴⢌⡟⠚⠒⠢⣀⠀⠰⠞⠛⠛⣋⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠉⠛⠛⠶⣤⣭⣐⡂⠀⠄⣀⠀⠀⠀⠑⠦⠤⠭⠽⠥⡴⠒⠒⡂⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠀⠀⣀⣼⣄⠀⠀⠀⠉⠙⠛⠛⠷⢶⣬⣕⣒⠢⣀⣀⠠⠬⠁⠙⠦⡤⠤⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣬⣝⣂⠦⢄⣀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣾⣿⣿⢿⣋⡙⠒⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⠿⣛⣛⣛⣛⣛⣛⠓⠦⣬⡉⠻⣯⣅⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⢢⠈⢿⣦⣾⡟⠋⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣤⣀⣀⣀⣀⠀⢀⠀⠀⡀⣀⣘⡆⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣼⣿⠃⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣋⡴⣯⣧⣝⠉⣩⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⣶⣓⣯⡍⠙⠀⠒⣒⣊⡉⠃⠣⣤⠿⠉⣰⢯⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠘⡅⣿⡁⠀⠀⠀⢹⣟⠉⠀⢰⣿⠀⢠⣯⡟⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣾⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣧⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⡄⠈⠓⠈⠁⠀⠀⠀⠀⢀⡿⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠹⠋⠁⠀⣠⣴⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣢⣤⣶⡿⠟⠁⠀⠇⣤⣤⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠲⣻⢿⣿⢣⠀⠀⠀⠀⡠⠞⠉⠑⣠⠟⠉⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⢀⣿⠇⠈⠻⠦⠤⠤⠖⣋⣴⠎⡐⣸⠃⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⣿⣭⠀⠀⠀⠓⠒⠚⠋⠘⠁⠀⣓⡏⠀⠀⠀⠀⢫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡈⠀⢹⣿⡇⠀⠀⠀⠠⠖⠀⠤⠄⢤⡀⣿⣇⡄⠀⠔⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠴⠛⢻⣦⡀⠀⠉⢺⣿⣿⠇⠀⠀⢠⡄⣰⡶⠶⠂⠠⣄⠻⣿⣿⡏⠀⢀⣘⣻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡡⢿⣷⠀⠀⢸⠙⣿⠀⠀⠀⠘⠾⠡⠄⠐⠀⠀⠘⣇⣹⣿⣶⠟⠋⠉⢻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢚⣽⠃⠀⠈⢰⣿⠀⠀⠀⠀⢏⣶⠐⠀⡀⠀⢀⣿⢫⣽⡿⡀⠀⠀⠠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠶⣦⣼⡟⠀⠀⠀⠀⠘⠛⠉⠉⠙⠦⢾⣿⡻⣿⣿⠻⠂⠀⠀⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡄⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡤⢿⣷⣿⣿⣿⣿⣶⡶⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠋⣀⣤⠴⡶⣾⣿⡟⠾⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣷⣾⣿⣿⣷⡟⢫⣭⣧⣄⣠⠖⠀⣈⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣻⣼⣿⣿⢶⣿⣿⣿⣿⣤⣀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⡿⣛⣿⣯⣭⣭⠿⠿⣿⣿⣿⠉⢋⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠿⠿⣿⣿⣿⣿⣿⡷⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⢦⡀⠈⠊⠹⣿⣿⣿⣷⣽⣲⢤⣤⣤⣤⣤⣤⣤⡶⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⢻⡄⠀⠀⢹⣿⣿⠁⠉⣩⣭⣶⠄⠀⢠⣶⣽⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣸⣇⣠⣶⣼⣿⣿⠀⠀⠀⠈⠁⠀⠀⠀⠰⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢋⣿⣿⣿⣧⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣽⣿⣿⣦⣀⠀⠀⠀⠩⣡⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣮⠻⣿⣿⠿⠓⠲⠀⣴⣿⡿⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⢿⣇⠘⢄⡀⠀⢀⣠⣾⠿⠀⠈⡀⢀⣀⣁⠀⠄⢠⣶⣶⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠛⡿⢯⡻⢦⣉⠛⠦⣍⣛⡻⠟⠅⠀⢠⢘⡿⠿⠾⣹⡄⣿⠀⣿⣿⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣇⠀⣿⠀⠙⠣⣹⡇⠀⠀⠀⢣⠀⠀⣠⠇⡼⢁⣤⡶⠟⡇⠘⠃⢻⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡉⢻⣿⡹⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⢨⣤⡾⣣⠞⣠⠟⣃⡳⠾⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡛⠿⡄⢻⣧⢀⡏⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⡟⢁⡈⢁⣼⡇⠀⠀⠀⠀⠀⣹⣀⣠⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠳⣤⣿⣾⠃⠀⠀⠀⠀⣧⠀⠀⠀⣿⣿⣧⡘⠁⠋⣼⣇⣠⣤⣶⣶⣿⣿⣧⡶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡷⢹⣿⣿⣴⠇⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⠇⠀⠀⠀⣼⡏⠈⠻⣿⣿⣿⣿⣟⣭⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⠶⠦⠄⠻⠿⠏⠀⠀⠀⠀⢴⡾⠛⠛⠈⣄⠀⠀⠀⠀⠼⠟⠀⠀⠀⠙⢿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣠⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣧⣽⣿⣷⣩⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠹⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢻⣽⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣁⣀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣿⣿⣿⣦⣾⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠻⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢖⡋⢙⡶⠖⠒⠚⢛⡆⠀⠀⠀⠀⠀⠀⠀⡴⠒⢾⠉⢙⠦⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣼⠀⡾⠶⠶⢿⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠚⠛⣇⠘⣆⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉⣿⡛⠓⠶⣦⠤⢤⣬⠇⠀⠀⠀⠀⠀⠀⠀⢹⠛⢉⣉⣻⣏⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠾⣄⡉⠓⢦⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣉⣁⣤⡼⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠎⢀⣴⣥⠤⠤⠶⢦⠀⠀⠀⠀⠀⣰⠒⠒⠶⠦⢾⠉⢓⠦⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡞⠀⠤⢤⣶⣶⣞⡀⠀⠀⠀⠀⠈⣛⣒⣶⡶⠾⣇⠘⣆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠁⠀⠤⣤⣤⣤⣤⠇⠀⠀⠀⠀⢺⣁⣠⣤⣤⠴⠛⢚⣏⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⣄⡀⠰⢦⣄⣉⠙⡦⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠴⠚⢉⣸⣦⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣹⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠴⠚⢙⡦⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣤⣽⣦⠈⠳⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠁⡼⠓⠶⣯⠀⠀⠀⠀⠀⠀⠀⢈⣳⣦⣤⣤⡄⠈⣇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠋⣹⡒⠛⠓⠲⡏⠀⠀⠀⠀⠀⠀⠀⢯⣤⣤⣤⣤⠄⠀⠈⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣴⣏⣉⡉⠙⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡖⠋⣁⣠⡴⠀⢀⡤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠹⣏⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣠⣾⣿⣧⠀⠈⢳⣤⣾⡟⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣾⡿⡀⠀⠉⠑⣿⣿⣿⣿⠀⠀⠀⢻⣷⣆⡀⠲⡄⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠉⠀⠹⣿⣯⣿⣷⠀⠀⠘⡛⣿⣿⣿⠀⠀⠀⣸⣿⠋⠄⢨⣽⣶⣬⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠈⣻⣿⣿⣽⡇⢠⢮⢠⣾⣿⣿⣤⣶⣿⣿⣿⣴⣲⡇⠈⣉⣩⣠⣤⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⢿⣿⣿⣿⣃⡌⠀⢸⣿⣿⢿⣷⡿⢿⣿⣿⣿⡧⢁⣬⣿⠿⡛⠻⢷⠟⠷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢸⣿⣿⡵⢋⡀⠀⢾⣿⣩⣿⠟⠃⠹⠓⣹⡿⠛⢿⣿⢟⣿⠿⠂⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡧⠀⠀⢸⣿⣯⠑⠇⡁⢀⣻⡿⢋⣿⠀⠀⠀⠂⠈⣿⡋⠈⢫⡸⣿⠀⠀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⢸⣿⠯⠀⠂⢀⠴⣿⡅⠿⠉⠁⠀⠀⠀⠀⣿⠗⠀⠀⠉⠛⠺⠺⠖⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡗⠀⠆⠹⢿⣦⠀⠀⠡⠀⣿⣷⣶⣿⣿⣗⣒⠦⢄⣿⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠙⢆⠀⠀⠀⢹⣿⣿⠋⠀⠀⠈⠙⣦⠈⡑⠲⠮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣿⣿⣷⡴⠶⠶⠞⢷⣄⣀⣸⡿⣏⠀⠀⠀⠀⢠⡟⡤⠁⠀⣠⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠿⠛⠓⠶⢤⣤⣌⢹⣿⣷⣌⠓⠒⠶⠶⠛⠁⠀⠀⡰⠋⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⣿⣿⣿⣏⠀⠀⠀⠀⠠⡙⠂⠀⠙⢿⡛⠿⣶⣦⣤⣤⣤⣄⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⠉⣰⣿⡿⠋⡝⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣁⠈⠁⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⣀⣼⣟⠋⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⣀⢄⠀⣠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠻⢟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣤⣄⣤⣀⣤⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣾⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟⣿⣿⡿⠁

⢀⣴⠾⠿⠿⠷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠾⠿⠿⠚⠛⠛⠛⠓⢿⣿⠓⠒⠶⣄
⢻⡇⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⢹⡆⠀⠀⢹⡆
⢻⠇⠀⢸⡏⠉⠉⠁⠀⠀⠀⠈⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄⠀⢸⣇⣤⣤⣸⡇
⢸⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⣿⡇⢸⣿⡇
⣾⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⢿⡇⢸⣿
⣽⡇⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡇⢸⣿
⢻⡅⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡇⠸⢻⠇
⢸⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⢿⡇⠀⢸
⢸⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡎⠓⠊⢸⡄
⣿⡃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇⡀
⢻⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡟⢻⣾⡟⠙⠳⢶⣤⣀
⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡇⢸⣿⡇⠀⠀⠀⠈⠉⠛⢦⣄
⣺⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⣿⠀⠀⠘⢧⣤⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⠘⠛⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⢹⠆⠀⠀⠀⠀⣿⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⣀⣤⣤⣬⣙⢷⣄⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⣿⠀⠀⢰⣟⠛⠛⠀⠀⠛⠓⠂⠀⠀⠀⠀⠀⢠⡟⠀⣼⠋⠀⠀⢀⣹⠿⠛⢷⣄⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⣿⠀⠀⢸⣷⣤⣤⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠸⣇⠀⣇⠀⢀⣴⠟⠁⠀⠀⠀⠙⢿⣄⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⣽⡄⠀⠀⠀⠈⣿⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠀⠞⠁⠀⢀⣤⠖⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠸⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢷⣄
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⣉⠉⠉⣄⠀⠀⠀⢠⠈⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢸⠻⡄⠀⢸⣄⣀⣤⣾⠀⠀⣠⢾⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡞⠉⠹⡄⠀⣇⠀⠀⡟⢀⡔⠓⢾⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠁⠀⠀⠁⠀⠈⠀⠀⠁⠈⠀⠀⠸⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⢤⣤⠤⠤⠤⠖⠒⠲⣄⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⡆⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠳⠀⠈⠁⠀⠎⠀⢀⣠⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢀⡞⠉⣱⠒⣦⠖⠉⠀⠀⢀⡔⠉⠉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⢺⠀⠀⡇⠸⡀⢣⠒⠒⠂⡞⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡀⠉⠉⢣⡀⡸⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢳⡀⠀⠀⠳⡇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡼⠳⡀⠀⠀⠈⡆⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣀⣀⣀⣀⡤⠼⠓⠋⠉⢳⡄⠀⢹⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⡛⠲⠚⠁⠀⣀⡤⠤⢤⡀⠀⠀⢧⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣿⣲⠖⠒⠋⠁⠀⠀⠀⠙⢦⠀⠈⢣⡀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⢤⣤⣤⠤⠴⡆⠀⠀⠀⠈⢳⡀⠀⠉⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡤⠖⠋⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠋⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠙⠒⠶⠶⣶⠖⠚⠉
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠸⡇⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⣿⠃⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠃⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠖⠀⠀⣿
⠀⠀⠀⠀⠀⣠⠀⠀⠀⢹⠀⠀⠺⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠇⠀⢀⠇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠘⢦⠀⠀⠘⠃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠘⡿⢠⣿⠿⠀⠀⠀⠀⠀⣀⡶⠀⠀⠀⢦⣀⠀⠀⠀⠀⠈⢿⣿⡰⢿⠠⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡽⠂⠀⠀⠀⠂⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠒⠀⠀⠀⠸⢯⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣧⠀⠀⢐⣤⣤⣆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣴⣤⣴⠀⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⠛⠉⠁


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

⠀⠀⠀⠀⡤⠤⡤⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣦⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⣸⠀⠀⣳⠀⠀⠀⠀⣰⢋⣴⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⢨⡷⡇⡤⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀⡾⠁
⠀⠀⠀⢹⠁⢐⡷⠀⠀⠀⠀⠘⢿⡟⣾⢂⣶⢐⣶⢰⣆⠀⠀⠀⠀⠈⠀⠈⡯⡇⠀⠁⠀⠀⠀⠀⠀⠨⠉⠉⠁⡾⣆
⠀⠀⠀⢩⡣⠊⠀⠀⠀⠀⠀⠀⠀⢬⡯⢨⣯⠨⣿⠬⣿⡄⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠙⠄
⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢙⣿⠉⠋⠉⠁⠀⠀⢀⣀⣀⣤⣋⣼⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠐⠠
⢤⡀⢀⣴⣦⣾⣷⣤⣄⠀⠀⠀⠀⠀⢀⡀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢳⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⢸⡇⣸⡇⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠿⠉⠀⠹⠇⠀⠀⠀⠈⡿⠿⣿⢸⣿⣿⡏
⠀⠘⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢼⣹⣏⣿⣻⣻⡇⠀⠀⠀⠀⣁⠀⢰⣶⠆⠀⠀⠀⠀⠀⠀⢰⡉⡎⣹⢸⣿⣿⣷
⠀⠀⠉⠾⠎⠛⠱⠿⠊⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠠⠿⠀⠾⠀⠧⠀⠠⠄⠀⠀⠀⠾⠿⠿⠿⠯⠿⠿⠿⠆
⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠞⠳⢴⠀⠀⠀⠀⠀⠀⢰⣷⠖⣲⠒⡶⢲⢲⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⣇⠘⠇⣸⠒⠀⠀⠀⠀⠀⣼⠏⠀⠁⠈⠀⡿⣼⡇⠀⠀⠀⢀⣀⣰⣺⣲⣀⣀
⠀⠀⠀⢀⣻⣟⡅⠀⠀⠀⠀⠀⠀⢀⡀⣋⢙⡋⣙⣀⡀⠀⠀⠀⢀⣿⢀⡀⠠⠀⢸⣇⣿⡇⠀⠀⠀⢈⣿⣉⢹⠉⣹⣏
⠀⠀⠀⠚⠓⠓⠓⠂⠀⠀⠀⠀⠀⠐⠂⠒⠐⠂⠒⠐⠂⠀⠀⠀⠈⠀⠀⠁⠀⠀⠉⠙⠛⠃⠀⠀⠀⠐⠂⠒⠐⠒⠂⠒
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⡎⣭⣭⡝⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⡀⡴⠋
⠀⠀⢰⣿⠀⠀⢰⡇⠀⠀⠀⠀⣀⣤⣄⢴⠟⠻⣇⠀⠀⠀⠀⠀⠀⠀⡇⠶⠶⢮⠀⣼⣿⡀⠀⠀⠀⢀⣴⣿⣿⣦⡀⢀⡴
⠀⠀⠘⣿⠀⢠⣿⡇⠀⠀⠀⠀⢿⣿⣿⣦⣄⢀⣭⣦⣄⠀⠀⠀⠀⠀⣏⣛⣛⣉⠀⠛⣿⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣮
⠀⠀⠀⠻⡄⣾⡿⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⢺⣿⣿⣿⡇⠀⠀⠀⠀⡧⠷⠿⢼⠀⠀⠁⠀⠀⠀⢀⣼⣿⠿⠻⠿⠟⠁

⠀⠀⠀⠀⠀⢀⡀⠀⣿⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠈⠉⣤⣶⣦⡉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣷⣿⣷⡆
⠀⢰⣶⣶⣶⣷⣿⣿⣿⣿⡇⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠹⣿⡿⠁
⠀⠀⢻⣿⣿⣻⣿⣻⣿⡁⢤⠈⠁⠀⠀⠀⠀⠀⠀⠐⢤⠤⣿⡧⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠿⠿⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠇⠻⠿⠇

⠀⣀⣠⣴⣦⣤⣤⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⡀⠠
⠀⠛⢛⣉⣉⣉⢩⣭⠡⣤⡄⣶⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢸⣿⢸⣿⠀⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠢⠄
⠀⠀⢸⣿⢸⣿⠀⣿⡇⣿⣇⣿⣇⡀⠀⠀⠀⠀⢸⡇⠀⠀⡀⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢰⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⠠⣾⣿⣿⡆⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⠿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠟⠁⠀⠀⣿⣻⣿⣿⣛⣿⣻⡿⢿⣛⢿⣿⡟⠿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠶⠿⠿⠿⠷⠾⠿⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣄
⠀⠀⠀⢀⡒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠛⠓⠂
⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣤⣤⣀⣀⡀
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙
⠀⠀⢰⣿⢻⡖⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⢀⣀⣀⠘⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⢀⣸⣿⣼⣧⣿⣼⣇⣴⣿⣦⣤⣀⠀⠀⠀⣀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣙⣀⡀⠀⠀⠀⠒⣁⡐⠀⠀⠀⠀⠀⠀⠼⠾⠆
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠰⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠰⠄⠀⠀⠀⠁⠀⣤⠀⠀⠀⠁
⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⡌⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⢰⠀⠃⡆⠀⢠⣤⣤⡀⠆⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠑⠂⠀⠴⣤⣄⠀⠀⢀⣴⣶⣶⣦⠀⠀⣤⡀⠒⠀⠀⠀⠀⠐⠓⠂⠀⠐⠀⠛⠛⠀⢰⡆⣿⡉⢸⣿⣿⣡⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⠙⢯⣽⣽⣿⣛⣁⣀⣉⠋⠐⢲⣶⣶⡀⢀⣀⣀⣀⠀⠀⠀⠈⠉⠙⠉⣩⠄⣾⣿⣿⡦⠀⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠊⠀⠀⠀⠒⠀⠀⠺⠿⠿⠿⠿⠿⠶⠶⠶⠛⠛⠙⠉⠉⠉⠁⠀⠀⠀⠀⠁⠒⠲⠬⢴⣿⣏⣹⣷⣠⣶⣿
⠀⠀⠀⢠⠀⢠⠀⠀⠇⠀⠉⣀⣌⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣏⣩⣉⢀⡒⠂⣰⠄⠐⠢⠀⠠⠤⠄⢀⢩⣙⡛⠿⣿⣿
⠀⠀⠀⠈⠠⣤⡰⣶⡎⠿⣷⢹⣿⡜⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢐⠒⠂⡮⠤⢴⣀⣠⡂⡀⣼⠃⠉⡸⠁⠑⡒⠚⠀⡤⠆⠀⣀⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠙⡇⠀⢱⠀⠸⣆⠈⢷⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠀⢀⠌⠀⢠⠃⠀⣰⠏⠈⠉⠋⠑⠓⡖⠐⠥⡤⢰⣀⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢿⠀⠘⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠤⢤⣆⣀⣠⠁⠀⣰⡟⠀⠀⡌⠀⠀⡌⠀⠀⢰⠁⠀⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠁⠀⠀⠀⠀⠈⠻⠿⣶⣶⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣶⠛⠠⠤⠼⣀⣀⠰⠁⠀⢀⡇⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⡖⣾⠖⠤⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠉⢉⣡⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠄⢀⣀⠤⠀⠀⠀⠀⠀⠀⢀⢡⣶⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢁⠠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⢰⠁⢰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠘⡀⠛⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣄⢠⣦⠈⠒⢄
⠀⠀⠀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⣹⢿⣥⠀⠀⠀⠑⠢⡀
⠀⠀⠘⠀⢨⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⡘⠛⠋⠷⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⣶⣿⣿⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣴⣿⣷⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠙⠛⠋⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⣯⣥⡀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⡟⠀⠻⣿⠟⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⢠⠀⠀⠀⢃⠠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠢⡀⠀⠀⠀⠀⠂⡀⣀⣠⣜⡱⠤⠢⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠙⣄⠀⢀⠔⢺⣟⠫⠊⠁⠀⠀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠁⠀⠀⠊⠁⠀⠀⣠⢖⣫⠕⠛⠉⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠓⠉⠁⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢄⡠⠔⠀⠀⠀⠒⠒⠚⠀⠀⠀⠀⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠠⣠⠏⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡚⠀⠀⠀⠀⠀⣀⡴⠞⣁⠄⢰⠁
⠀⠀⠀⠀⠀⣀⣤⣴⣾⣷⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠁⡠⠃
⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⡄⠘⡄⠀⠀⠀⠀⢀⠴⠋
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡄⠘⡄⠀⢀⡴⠃
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⡀⠏
⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰
⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁
⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠈⢻⢿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⣩⠟⠋

⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣶⣦⡀⢸⡟⣁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⡀
⠀⠀⠀⠈⠙⠻⠌⠜⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢠⡀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠛⠙⢏⡇
⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⡆⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠞⢛⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣷⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠸⡆
⠀⠀⠀⠀⠀⣿⡥⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢾⡧⣿⠴⡧⢼⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⠓⠒⢻⡀⠀⠀⠀⠤
⠀⠀⠀⠀⣸⡏⢉⡺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺⡗⣿⠒⡗⢺⡗⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⡖⠒⠒⢧⠀⠀⠀⠶
⠀⠀⠀⠠⣿⣿⣧⣤⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇
⠀⣀⣀⣀⣀⣤⣤⣴⣶⡞⢠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⢹⠋⠉
⠀⠻⣿⣿⣿⣿⣿⣿⡟⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⢠⣤⣄⣼⣿⡁⢹⣿⠏⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣽⣄⣀⢀⣀⡀
⠀⠀⠈⢻⣿⠿⠟⠋⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⢨⣭⣯⣿⣭⡅⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⢡⣏⣺⣯⠽⠛⠉⠁
⠀⢰⡟⢳⡴⠖⠻⣭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣿⣼⣿⣯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢳⣿
⠀⠈⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠓⢾⡇


⠀⠀⠀⢀⣀⣤⣄⣀
⠀⣠⡾⠋⣤⣶⣶⠍⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠺⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣯⣭⣤⣦⡔⣠⡀
⢠⡟⠀⠀⠘⢿⠏⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣀⣆⣀⣀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣵⣿⣷⡀
⢸⡇⣶⣶⣶⠎⢶⣶⣶⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣽⢹⣿⣿⡗⡀
⠀⢻⣜⠿⠋⠀⠈⠻⢟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣉⣿⠻⠟⠃⢻⣧⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣇⣺⣿⣿⡇⡇
⠀⠀⠉⠳⠶⠴⠴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠷⠝⠿⣿⡯⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣤⣀⣦⡀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣛⣿⠿⠿⠿⠛⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣁⣴⣾⣍⣿⡿⢿⡏⠉⢉⡁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⣷⣿⣷⡯⠁⠐⢚⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠟⣻⣿⣿⣿⣷⡾⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⡞⠋⠋⠉⠉⠉⠉⠉⠛⠷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣄⠈⠫⠻⣿⣿⣿⣷⣷⣤⣀⣀⣀⣀⣀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡘⣧⠀⢁⠸⣿⣿⡏⠛⣛⣻⣭⠉⠉⣩⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣹⣆⣴⣤⣿⣿⡄⠀⠉⠉⠁⠀⠀⠀⠼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠟⣻⣿⣿⣿⠀⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠈⠍⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣷⡿⢿⡿⠟⠋⠲⠒⣾⣿⠟⡀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡻⢿⣌⠣⣀⣀⣠⣴⡿⠛⠀⣁⣀⣤⣬⡄⢐⠐⣶⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡏⢹⡟⢯⣛⢦⣉⠛⠢⠭⡟⠃⠂⠀⡔⣽⠛⢟⡟⡇⢸⡇⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡝⢿⣿⣿⣇⠘⡇⠀⠉⠢⣧⠀⠀⠀⢱⠀⣠⡞⡰⢃⣶⢿⢛⣷⠈⡁⠹⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣆⠹⣿⡟⢰⡇⠀⠀⠀⠹⠀⠀⠀⣼⣿⣯⠞⡡⠚⣸⠚⠋⠉⠁⠀⢦⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⠙⣇⢹⣇⣼⠁⠀⠀⠀⣈⠀⠀⠀⣿⣿⡇⠴⢠⠾⣿⠀⠀⣀⣀⣤⣾⣖⣚⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣌⣿⣿⣏⣠⠀⠀⠀⠙⠀⠀⣠⣿⣿⣿⡄⠀⠐⢛⣾⠛⢿⣿⣿⣿⣿⡯⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⢿⣏⣉⠙⣿⣿⠏⠀⠀⠀⣀⣴⠿⠿⠻⡋⠉⠀⠀⢀⣼⠏⠀⠀⠻⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣶⣿⡯⠍⠀⡭⣙⠙⠀⠀⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡽⠾⢿⣿⠛⠁⠀⠀⠴⠀⠈⠁⠲⣄⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⠅⢀⣴⣿⣃⣠⣄⣀⡀⠀⠔⠀⠀⠀⠈⠛⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠁⡤⢫⣿⣿⠏⠀⠀⣉⠙⠳⢦⡀⠀⠈⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠫⠐⡴⠃⢠⣿⡏⠀⠀⠘⠛⣆⠀⠈⠻⢶⡀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠠⣀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢟⠀⠀⣸⡟⠁⠀⣿⣿⣄⢘⠂⠀⢠⠃⠀⠀⠃⠌⡿⣶⡇⠂⠐⠲⠀⢷⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⣆⠀⡼⢻⣿⣿⠁⠀⡴⢦⡞⢉⣾⠄⠀⠒⠈⠻⣶⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣗⠀⣿⠀⢸⣿⠀⣦⠀⣾⣥⣾⣿⢿⣶⣴⢀⣴⣻⠿⣾⣶⡆⠀⣻⣦⠀⢀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⢏⡀⣿⠀⠸⣿⣿⣇⠀⣇⠈⢉⡡⠾⣿⣿⣧⣸⠁⠸⠟⣿⠃⠠⠃⡆⠀⡏⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠐⣿⣄⡀⠈⠛⢿⣷⣿⣧⣾⣷⣤⣿⣿⣿⣿⣤⣤⣴⣟⣤⣖⣨⠃⣘⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⢻⣟⣫⣿⣦⡈⣠⣭⣿⣽⣿⣿⣉⢻⢿⣿⣿⣿⣿⣿⣿⡏⣈⢧⡀⠟⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠻⠋⠉⠉⠛⢻⣾⡿⣛⢻⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣧⣥⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠈⠛⠿⠿⠟⠷⠷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣻⠅⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠄⠀⠀⢘⠟⠋⣿⣧⣿⣿⡿⢽⡿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡄⠈⠀⠘⣭⡾⢶⣿⡻⠟⠋⣰⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣉⣁⣄⣠⣬⠋⠀⠀⣽⣿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣟⠋⠁⠀⠀⢀⣀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠻⠛⣋⣉⣻⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠛⠿⣿⢯⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋⠉⣽⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠛⠿⠷⣦⠀⠀⠰⣶⣿⠛⠛⠓⠆⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠤⠖⢻⠿⣿⠂⠀⠀⢞⠡⢤⣤⣄⣀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠙⢹⠟⣡⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡴⠀⠀⠈⠁⠉⠒⠁⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠰⢦⣤⠤⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢙⠓⠒⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠒⠀⢀⡘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠴⠛⠛⠁⠀⠀⠀⢳⠄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠴⠚⠋⡀⠙⢶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠐⠶⢤⣤⣀⣀⣠⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢧
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠠⠞⠋⠉⠙⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠐⢿⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⢸⣴⠏⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡟⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡏⠁⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⡇⠘⠏⢿⣷⡀⠀⠀⣀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⣿⡇⠀⠀⣠⣿⠃⠰⣿⠟⠋⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡴⠃⠙⣦⢠⡿⣦⡀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡞⠁⠀⠀⢸⣿⠁⠸⣷⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠠⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠙⣧⣠⠞⠁
⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠳⣤⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⣰⠋⠹⣆⠀⠀⠀⠀⠙⢿⣿⡆
⠀⠀⠀⠀⡏⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⢀⣠⣴⣶⣿⣿⣷⣶⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡁⣢⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠠⡄⠄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠊
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⠟⠀⢻⡆⠀⠉⠛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⣼⣿⣿⣿⡟⠁⠸⠟⠋⠵⠟⠛⠁⠀⠀⡸⠀⠀⣀⠀⠀⠙⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⡏
⢀⡀⣀⠀⠀⣼⣿⣿⣿⣿⠇⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⣤⠇⠀⠀⠀⠀⣍⢠⡼⠀⠀⢰⡇
⢇⠀⠀⠆⢀⣿⣿⣿⣿⠏⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⠀⠈⠉⠁⠀⠀⣼⠃
⠘⢦⣄⣠⣾⣿⣿⡿⠃⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⢀⠴⠀⠰⡏
⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⣴⠿⣆⠐⡄⠀⠀⠀⠀⢸⣿⣶⣶⣶⡶⠊⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣈⠉⠀⠀⠀⠀⠀⣿⠿⢿⡿⢿⡇⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠛⠓⠶⢤⣝⣷⣤⡀⠀⠀⠀⠈⠲⠤⠤⠄⠃⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡴⠓⠶⣤⣀⠀⠈⠉⠛⣷⣦⣄⣀⣀⠀⣀⣀⣠⣴⡞⢯⣀
⠀⠀⠀⠀⢀⡤⠞⠁⣰⠏⠀⠀⠀⠀⠈⢹⡷⠀⠀⠊⢸⡟⢿⣯⣭⣭⣽⠿⠁⢻⡄⠉⠳⣄⡀
⠀⠀⠀⢰⡋⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⣠⡾⠁⠀⠈⠉⠁⠀⠀⠀⠈⣿⢦⣄⠈⠉⠛⠒⠶⠦⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠳⢤⣀⡶⠋⠀⠀⠀⠀⠀⢰⡟⠙⠚⠛⠋⠁⠀⠀⠀⠐⠠⠀⠀⠀⠀⢹⡆⠈⠉⠛⠒⠒⠶⢦⣄⠀⢀⣈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠉⠣⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠉⢹⠓⠢⣄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠶⢦⣤⣄⣀⣀⣀⣀⣠⣤⣤⠶⢾⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠣⡀⠀⠀⠀⡎⠀⠀⠀⠳⡄
⠀⠀⠀⠀⢀⡾⡙⢷⡀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⣸⠟⠛⢻⣖⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠈⢢⠀⠸⠀⢀⣀⣠⠤⠻
⠀⠀⠀⣠⠟⠐⠀⣠⢻⡄⠀⠀⠰⣿⡉⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣠⣴⣞⠁⠀⣰⠟⠉⠙⠛⠲⢦⠀⠀⡏⠉⠑⠒⠤⢼⣇⡇⡰⠋⠁
⠀⠀⠀⠿⠶⠶⠛⢷⡀⠙⣆⣀⡴⠋⠙⣦⣀⣴⠟⠉⠙⠛⠛⠋⠉⠁⠈⠉⠛⠻⠋⠙⣳⠖⠀⣰⠟⠀⠀⢷⠀⣀⡤⠴⠋⢸⠉⣏⠙⠓⠒⠲⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠋⠀⣠⠞⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣴⠛⠁⠀⠀⠀⠈⢯⡀⠀⠀⢀⡇⠀⠈⠢⡀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠳⢴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣸⠁⠀⢀⣀⡼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡿⣿⣿⣿⡿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⢱⣿⣿⣿⣧⡀⠉⠉⠀⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⣿⡿⠀⠈⣿⡿⢀⣀⣀⡀⣿⣿⣿⣰⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠰⣿⠇⢸⣿⣿⣇⠛⠋⠁⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⣾⣿⣷⡸⠛⠉⢸⠁⢀⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠿⠋⢹⡇⠀⣀⡘⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠸⠟⠉⣿⠀⢀⣘⢳⣾⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⢹⡇⠀⢀⠛⣶⣿⣧⢸⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢳⣾⣿⠀⣿⣿⣿⢸⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠃⠘⠟⠿⠀⠻⠿⠗⠘⠿⠛⠃⠻⠿⠟





⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⣿⣶⣦⣤⡀
⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣗
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⢿⣿⠿⠗
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⢀⣀⠀⢠⣶⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⡿⢿⠁
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⡉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⡄⣾⣿⣧⠈⣿⣿⣠⠆⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣧⣀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⢀⣀⣤⣾⣿⠿⠋⢀⣿⣿⡏⠀⢿⣿⣯⡀⠀⠀⠀⠘⣿⣷⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣯⣴⣶⣾⣿⡿⠛⠀⠀⠀⠙⢿⣿⣷⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠁
⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⡀
⠀⠀⣿⣿⣿⣿⠏⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⢹⣿⣿⣿⠃
⠀⠀⣿⣿⡿⠃⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿
⠀⣴⣿⡿⠁⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⡆
⣾⣿⣿⣇⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⣠⣿⣿⣧
⠈⠙⣿⣿⣄⠀⠀⢠⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠆⠀⢤⣴⣾⣿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⣾⣿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠉⠉⠉⠉⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⠐⣒⣦⠀⠔⠯⠄⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠐⠂⠀⣀⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠛⠉⠀⠁⢀⡼⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⣄⠀⠀⢠⠞⢀⠋⣧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣿⣦⠻⣿⠿⠛⠁⡠⠀⠀⡟⠀⠈⠉⠒⠒⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠞⠁⠀⠀⠙⢯⡃⠀⠈⣰⣾⣦⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠠⠀⠀⠀⠀⠀⠉⠢⣤⢉⣿⡏⠛⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⢤⠄⠀⠀⠀⡰⠃⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠸⠀⡄⠀⠀⠀⠀⣿⣿⣿⠀⠀⠉⠁⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⣷⠀⡀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠄⢠⡇⣠⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠸⣷⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢀⡿⠋⠁⠈⢷⡠⢀⣤⡖⠀⢈⣷⠇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠖⠋⠀⠀⠀⠀⢸⠋⠁⠀⠀⠀⣸⠏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⣼⠛⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⡜⣽⠁⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⢠⡏⣼⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣄⠐⠃⠀⠀⠀⢀⡠⠚⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⣠⠖⠋⠀⠀⣿⣿⢋⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠀⠀⠀⠀⠀⠻⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢗⣻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢵⢟⣩⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠏⣿⣳⣿⣿⣯⣞⣯⣿⢿⡿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠜⠁⠙⠙⠉⣾⠋⡩⣻⣟⢕⠿⣻⢻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠺⠿⣷⠿⣻⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢊⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣠⡔⠁⠀⠀⠀⠀⠀⠀⣠⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣻⣿⣾⣿⣟⠕⠀⠀⠀⠀⢀⠀⡺⣫⣽⢟⢽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢛⣿⠟⠁⠀⠀⠀⠀⠁⠀⠈⢫⣴⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢇⣬⢠⡔⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧⣾⣿⣿⣻⣷⠛⠔⠀⠀⠀⠠⢛⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠺⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣴⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠆⠀⠀⡀⠳⣄⡄⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠂⠄⠀⠂⠄⠠⠐⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢘⡄⠒⠋⡁⠀⠘⠛⢦⢠⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢠⠁⠀⠞⠟⠀⠰⣾⡆⠛⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠘⠑⠁⠈⡄⠀⠀⠁⠀⠀⠀⠀⢀⠖⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠠⡀⠸⠶⠁⠀⠀⣠⠞⠊⠀⠀⠀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⡀⠀⠘⠢⠤⣤⠴⣺⠁⠀⠀⠀⡠⠊⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡈⠒⠀⠀⠠⠜⠀⠧⠤⠄⠂⢋⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢴⠀⠀⠁⠐⠊⠀⢤⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠁⠀⠁⠘
⠀⠀⠀⠀⠀⣀⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠠⠀⠄
⠀⠀⠀⠀⠀⡏⠀⣡⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⠄⠤⠀⣀⣀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡤⠤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠔⠀⠢⡄⢼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⠀⠀⢸⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⣨⣸⡀⠀⠀⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠉⣭⣄⣀⢸⠖⠊⠀⣨⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣈⣁⣉⣀⣤⣠⣴⣉⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣀⣀⠀⣠⠤⠶⠤⣄
⠀⠀⠀⠀⣠⠚⠉⠉⠉⠙⠢⠤⢤⡞⠑⠞⠁⠀⢸⠁⠀⠉⡡⠤⢤⡀⠈⢳⠲⠤⣄
⠀⠀⠀⢰⠁⢀⡤⠒⠦⣀⣄⡀⠀⠓⢤⡀⣠⠒⢉⣰⠉⠉⠀⠀⣀⣱⠀⠸⣄⠀⠈⠣⢤⡀
⠀⠀⠀⢸⡀⢺⠀⠀⠀⠉⠀⠃⠀⠀⠀⢱⣇⠀⠏⠀⠀⠀⠀⠘⠁⠀⣳⠀⠈⠳⠤⡀⠀⠙⠦⠲⢄
⠀⠀⠀⠀⢳⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⣌⡶⠒⠲⠤⠒⠢⢤⡀⠀⠁⠀⠀⠀⠀⢸⡤⠔⠒⠤⡼
⠀⠀⠀⠀⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡔⠙⠚⠉⢦⡀⠙⣄⡀⠀⠀⠀⡴⠲⠔⠉⠉⠳⡘⡆
⠀⠀⠀⠈⣇⠈⠉⠉⠱⣄⠀⠀⣀⢔⣒⣦⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣹⣄⣀⠀⠀⠀⠀⠀⠀⠰⢣⡃
⠀⠀⠀⠀⠈⠑⠒⢤⣀⠴⣍⠉⢁⡜⢲⠚⡖⢻⠒⠒⠒⣿⠒⠒⢺⠓⡞⢲⣾⣦⣀⣤⣄⣀⣀⣀⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⡏⣏⢹⠉⠉⠉⣿⠉⠉⢹⠉⡏⣟⣏⣻⣛⣛⣻⣛⣛⣿⣹⣛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣲⣀⣀⣖⣆⣯⢿⢹⠉⠉⠉⣿⠉⠉⢹⢹⢋⣧⣯⢼⠤⠤⣼⠤⠤⣯⣼⡼
⠀⠀⠀⠀⠀⢀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣹⢸⢸⡇⠀⢠⡛⡄⠀⢸⢸⢸⢹⣷⢸⠀⠀⢸⠀⠀⡇⣸⡇
⠀⠀⠀⠀⠀⠘⢦⢤⣤⣤⣤⣤⣤⣤⣤⣼⣼⣸⣇⣠⡻⠋⢞⣆⣼⣸⣼⢸⣿⣸⠀⠀⣸⠀⠀⣇⣻⡇
⠀⣀⣀⣀⣀⣀⣸⢸⣽⢼⢽⣭⡯⡯⣯⡽⡿⢸⡵⣿⣧⠀⣼⣯⢿⠘⡿⣼⡏⢹⠉⠉⢹⠉⠉⡏⢹⣇⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣸⣸⣺⢺⢺⣒⡗⡗⣗⡇⡇⣼⡝⠉⢉⣿⡉⠁⢻⣣⡇⡟⡇⢸⠀⠀⢸⠀⠀⣇⢸⢻
⠀⠀⠀⡏⢉⣉⠉⣉⠉⣉⠉⣉⠉⣉⣹⢡⠿⣼⠷⠶⠾⣿⠷⠶⢾⡧⢧⢹⠃⡎⠀⠀⢸⠀⠀⢸⠘⡜⡄
⠀⠀⠀⡇⢸⣿⠀⣿⠀⣿⠀⣿⠀⣿⡏⡸⠀⡇⠀⠀⠀⣿⠀⠀⠈⡇⠸⡈⣦⣇⣀⣀⣸⣀⣀⣸⣄⣧⣷
⠀⠀⠀⡇⢸⣿⠀⣿⠀⣿⠀⣿⠀⡿⢳⠗⢒⠗⠒⠒⠒⣿⠒⠒⠒⢷⠒⢷⠻⣄⣀⣀⣸⣀⣀⣀⣇⣘⣆⣧
⠀⠀⠀⢧⣸⣿⣤⣿⣤⣿⣤⣿⣴⠧⡼⠤⣼⠤⠤⠤⠤⣿⠤⠤⠤⠼⡤⠼⡦⢵⡤⠤⢼⠤⠤⠤⢼⡤⠽⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⡾⠒⢲⠗⠒⠒⠒⠒⣿⠒⠒⠒⠒⢷⠒⠺⡖⢻⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣶⢶⠶⢤⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣯⣭⣭⣤⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠁⠉⠉⠉⠉⠀⠀⣼⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠿⠶⣦⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠖⣤⣼⡆⠀⠸⣭⣄⣀⠀⠈⠀⠀⠀⢹⣿⠟⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⡰⠃⠀⠀⠉⠁⠿⠛⠖⠀⠀⠈⠿⢡⠌⢇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠰⠀⠤⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠐⡖⠦⡄⢀⣀⣀⡘⠆⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢫⡁⠓⣤⠒⣆⠀⠀⠀⠀⠀⠀⠀⠘⣷⡛⠷⠶⣦⣴⠟⠁⠀⠀⠀⠀⠀⣰⠟⣿⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠰⠷⢾⣌⠁⢸⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⢹⠙⠒⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠀⡿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠶⠶⢤⡀⠈⢃⣸⣿⠀⢀⡅⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⡼⠁⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⣤⣀⣤⠀⢿⡄⠸⠟⠃⠄⢸⠃⠀⠀⠀⢀⣠⣴⡞⢻⣶⣦⣤⣤⣶⣾⠃⠀⠀⠀⢀⡾⠁⠀⢀⡀⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⣿⣿⣧⡈⠻⠟⠀⠀⢀⣿⠖⠛⠛⠛⠉⠁⢸⡇⠸⣿⣿⣿⡯⠉⠀⠀⠀⢀⡴⠋⠀⠀⢀⡞⠀⠀⠀⠀⠉⠓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠛⣻⡿⠃⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠈⣧⠀⠙⢷⣾⣧⡀⢀⣠⠞⠉⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣶⠗⠈⣀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠹⣿⡴⢿⡀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠡⢿⣿⠀⠀⠍⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠈⣇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠈⠑⠐⠤⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢻⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⡉⠙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⡟⡉⠻⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠅⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿
⣿⣝⠻⣿⣿⣿⣿⠃⠀⢀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⢟⡿⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣿⣿
⣿⣿⣿⡌⠀⠀⠉⠃⠂⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢣⣿⡇⣿⣧⡹⣿⣿⡟⣩⠆⠀⠀⠁⠄⢀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣼⣿⣿
⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠣⠟⠉⠀⠉⠉⠁⠙⠉⠈⠉⣀⡀⠐⣀⣀⠉⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣿
⣿⡿⠛⠁⠈⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠁⠚⠈⠁⠒⠲⢒⠞⠀⠠⠄⠀⠀⠀⠀⠀⠙⢿
⣯⣤⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⡉⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠒⠂⠀⠀⠙⠒⠀⠄⡀
⠀⠀⠀⢀⡠⠴⠛⠛⠉⠉⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀
⢀⡴⠊⠁⠀⠀⠀⠀⢀⣀⣀⣠⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⡏⠀⠀⠀⣀⠔⢲⣿⠭⠥⠔⠓⠒⠀⠀⠀⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⢳⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣰⠋⠀⠀⠀⣀⣠⡤⠶⠖⣒⣈⣉⣩⠭⠉⠒⠲⣄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢿⡀⠀⣀⡻⠮⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠏⠀⠁⠂⠆⠀⠀⠋⠈⠀⠇
⢈⠟⠋⠁⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠰⠶⠶⢋⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⣿⠀⠀⣀⠤⠶⣚⣛⣯⠥⠶⠒⠚⠃⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢱⠀⡄⠁
⠙⢦⣀⣀⡴⠋⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠴⠋⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⢀⡞⢡⡞⠀⠀⢀⡤⠶⢶⣽⡋⣩⠟⠉⠋⠛⠢⡄⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠀⠸⡀⠀⢀⡿⢱⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠁
⢸⠀⣀⣈⣩⣭⠤⠼⠤⠤⠤⠤⠧⠤⢤⣤⣀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠠⠁
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡀
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣼
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠼⠀⠀⠀⠀⣸⣄⣀⣀⣀⣴⠁
⠀⠀⠘⢦⠤⠄⠲⠶⠒⠒⣶⣒⣒⣲⡒⠲⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠤⢀⠃
⠀⠀⠀⢸⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⢀⣀⣀⣀⣀⣂⣉⣭⣽⡇⢈⠆
⠀⠀⠀⢼⠃⠀⢤⣤⣤⡤⠤⠤⠴⠶⡒⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⣀⣀⣈⣭⣤⣵⡶⢈⠆
⠀⠀⠀⣼⡃⠤⠤⠤⠤⠴⠶⠿⠿⠝⡓⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣐⣢⣭⣭⣥⢈⠆
⠀⠀⠀⢼⡃⠤⠤⠤⠤⠴⠶⠿⠿⠿⡖⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠉⠉⠉⢉⣩⣭⣥⣶⡎⣈⠂
⠀⠀⠀⠘⢧⣀⠀⠐⠒⠒⠒⠺⣋⣗⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠉⡭⢛⠜⠁
⠀⠀⠀⠀⠀⠉⢻⠛⠛⠛⠛⡿⢹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡛⣛⣷⠞
⣤⣤⣤⣤⣤⣤⣤⣽⣷⣶⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⢸⣿⠀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⣯⣼⠟⠉⠀⠈⠹⣷⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⢋⡀⠀⠀⠀⠀⢻⣟⠉⠉⠉⠛⣷⡶⠶⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣤⣿⠀⠀⠀⠀⠀⣸⡇⠀⠘⠓⠲⢾⣷⠀⠤⠦⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢆⠀⢹⣿⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢤⡈⢳⣀⣿⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢀⣴⠞⠛⢿⠛⠿⠷⠶⠶⠶⢾⣧⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣼⡇⠀⠀⠀⣸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⣤⣀⡀⢀⣀⣠⡾⣧⣀⣀⣠⡾⠛⢷⣄⣀⣴⠋⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⠉⠉⠓⢤⡈⠛⠛⠛⢧⣀⠀⠉⠉⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⢀⣾⡟⠷⣄⠀⠀⠙⢦⡀⠀⠀⠈⠙⠂⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣠⠞⣹⠃⠀⠈⠆⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢛⣿⡷⣦⣤⣤⣤⡤⠶⠖⠂⠀⣤⡤⠴⠶⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⠙⠳⢦⣤⣀⡀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠘⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠿⢷⣦⣤⣀⠀⠉⠙⠛⠶⠾⢷⣤⣤⣀⣀⣀⣀⣿⣉⠛⢿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠛⠻⠷⢶⣦⣤⣀⣀⣀⠀⠈⠉⠉⠉⢁⣀⣀⣼⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠛⠛⠉⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠧⠷⠾⠼⠶⠧⠿⠼⠼⠧⠧⠾⠼⠶⠧⠷⠾⠼⠶⠧⠷⠼⠼⠧⠷⠾⠼⠼⠧⠷⠾⠼⠶⠧⠷⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢻⡹⡏⠉⠉⠋⠙⢟⢻⠉⠉⠉⠉⠛⡟⡟⠉⠉⠉⠉⢻⠻⡏⠉⠉⠉⠉⠛⡟⡟⠉⠛⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣠⡇⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢠⠞⣽⢸⠀⠀⠀⡠⢋⡇⡇⠀⠀⢀⡔⣹⡇⡇⠀⠀⢠⢞⡵⡇⣿⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⣰⠣⠎⣸⢸⠀⠀⡼⠱⠃⡇⡇⠀⢠⠎⠜⣹⡇⡇⠀⣰⠣⢎⠐⡇⣿⠀⢠⠎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢰⠃⢂⠎⢾⢸⠀⡼⠐⣰⠃⡇⡇⢀⠏⠐⡼⢹⡇⡇⣰⠃⢃⠎⠞⡇⣿⢀⠎⠐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⠇⢀⡄⠈⣼⢸⣼⠁⢠⠀⢁⡇⣧⡞⠀⡤⠀⣹⡇⣧⠇⢀⡄⠈⡜⡇⣿⡞⠀⡤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠏⠀⠀⠀⠘⢹⣸⠃⠀⠀⠀⠊⣇⡟⠀⠀⠀⠀⢻⣇⠏⠀⠀⠀⠘⠁⡇⡿⠀⠀⠀⢸
⠀⠀⠀⡠⢤⣤⢞⡩⣍⠲⡤⣬⢏⡔⣒⢢⣀⡁⡸⠃⢂⣀⡄⠈⢀⡟⠐⠂⢀⠀⠉⢰⠏⠐⠀⡀⠀⠁⣀⡟⠐⠂⢀⠀⢹
⠀⣠⠞⠀⠀⢯⣏⢀⡀⠀⠀⠈⠛⠙⠀⠁⠉⠉⣧⡯⡾⠶⣄⣢⠎⡰⣣⠃⠋⢐⡷⢃⡜⡼⡐⡁⠘⣠⠟⡰⣣⠃⠋⠀⢻
⠀⢧⠀⠀⡔⠋⠁⢏⠙⠋⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢳⣴⣵⣳⣳⡷⠋⣠⢞⣜⣝⣝⣽⠟⢁⣞⣵⡵⣱⣳⢣⣾
⠀⠀⠭⠭⠭⠭⠉⠉⠉⣭⣭⡍⠉⢉⣉⠉⢉⡉⠉⣉⠩⠭⡉⠉⠹⠿⠏⠉⠉⠉⠩⠭⠭⠭⠉⠭⠉⠩⠭⠭⠭⠉⡩⠭⠉
⠀⠀⠠⠬⠭⠉⠉⠥⠤⠀⠰⠆⠀⠐⠒⠒⠒⠀⠀⠐⠲⠈⠉⠉⠀⠉⠉⠩⠍⠉⠉⠡⠄⠀⠀⠒⠒⠂⠘⠛⠦⠌⠵⠶
⠀⠀⠀⠀⠚⠛⠓⠀⠀⠀⠉⠁⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢹⣆⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡾⠀⠀⠀⠛⠛⠛⠋⠉⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠟⢷⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⡞⠁⠀⠀⠙⢦⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠙⠋⡀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢿⡻⣆⢻⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⢷⣌⣷⡘⢿⣷⠘⣧⡾⢻
⠀⠀⠀⠀⠀⢰⣦⡀⣿⣇⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣦⠉⠛⠁⠈⠉⠀⠛⢃⡟
⠀⠀⠀⢠⣦⣌⣿⡻⣿⢿⡿⣿⣴⢻⡆⠀⠀⠀⠀⠀⠈⠻⢦⣤⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠹⢮⡛⠃⠀⠀⠀⠙⢣⡞⠀⢀⣀⠀⣤⡀⢠⣄⠀⠈⢿⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢠⡏⠀⠀⢸⡝⣿⡇⣿⣿⢹⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢀⣤⡀⣼⢧⢀⡶⣦⢸⡇⠀⣶⠾⣷⠈⠃⠘⠋⢾⡾⢻⠆⣿⠀⠀⢠⣦⡀⣿⡆⢀⣤⡄
⠀⠀⡶⣼⡏⣷⣿⢸⣿⠃⡿⢸⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⣰⠏⠀⣿⢀⠀⢸⡌⣷⡟⣿⣸⢃⣇⣴⡦
⠀⠀⢷⡘⣿⠘⠟⠈⠛⢸⣧⡿⣦⠀⠀⠀⠹⡆⠀⠀⠀⣴⠃⠀⠀⣿⣏⠻⣾⡇⠻⠃⣿⡟⢸⡟⣹⠇
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢁⣴⡃⠀⠀⠀⢠⡇⠀⠀⠀⣿⠀⠀⠀⣿⠙⢷⡀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⢀⡇⠀⠀⠀⢠⡴⠋⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢿⡀⠈⠷⣄⣀⠀⠀⠀⢰⡏
⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⠈⣷
⠀⠀⢀⣿⠀⠀⠀⠀⢸⡇⠀⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠸⣇⠀⠀⠀⠘⣧⠀⠀⠀⢸⣇
⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢻⡆⠀⠀⠀⢻
⣿⣿⠟⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠋⠉⠉⠉⠉⠙⠛⠓⠒⠶⠶⠤⠤⠤⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣀⡠⠤⠤⠤⠶⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠙⢦⣀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣠⠶⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣗⠦⡀⠀⠀⠀⠀⠈⠉⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡜⠁⠀⠀⢀⡴⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠈⠓⠦⣤⣄⣈⣩⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⡸⠁⠀⠀⠀⢈⠤⠒⠒⠢⡀⠀⠀⠀⢀⠤⠒⠒⠢⣄⠀⠀⠀⠀⢹⡄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⡎⠀⣠⣶⠆⢸⠀⠀⠀⡇⠀⣴⡖⢀⠈⡆⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⠀⢵⣀⠙⠿⣿⠞⠀⠀⠀⢣⡀⠻⠿⢋⡰⠃⠀⠀⠀⢰⢃⡏
⠀⠀⠀⣠⡴⢞⣉⣩⠋⠉⢉⣳⠦⣀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠰⠊⠉⠙⠆⠈⠛⠊⣉⣁⡀⠀⠀⠀⡞⡼
⠀⣠⠞⢁⣀⡠⠔⠉⡱⠶⣉⠀⣀⠈⢳⡀⢠⠞⠉⠉⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⡆⠀⠀⠀⣼⡿⠖⠒⢦⡀
⣰⠟⠉⠁⠀⠀⢠⠞⠁⠀⠜⠻⡀⠈⠙⢳⡸⣆⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠡⠀⠀⠀⢀⡇
⡏⠀⠀⠀⠀⡰⠁⠀⠀⡈⠀⠀⠘⡄⠀⠀⡇⠈⠉⠉⠙⠲⠞⠳⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠴⠚⠁⠀⣀⠴⢧⡀⢀⡴⠒⠋
⣇⠀⠀⠀⡐⠀⠀⠀⠀⡇⠀⠀⠀⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠶⣒⡠⠴⠚⠁⠀⠀⠉⠉
⠸⡄⠀⡸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⢸⠉⠉⠁
⠀⠙⢦⡃⠀⠀⠀⠀⢀⡃⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡤⡴⠃⠀⠳⡤⡤⠒⢤⡀
⠀⠀⠀⠙⠲⢤⣄⣀⣜⣀⡤⣴⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡤⢄⠃⢫⣀⢀⠜⠀⡇⡐⡆⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡈⠳⡀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠋⡜⠀⡞⠀⠀⠀⠀⠀⠀⠰⣆⠈⠢⣄⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠂⢺⣉⣉⢽⡀⣀⠤⠀⠔⢃⡜⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢘⡤⣚⠥⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⢉⢙⣇⠀⢁⠀⣀⡠⠞⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢨⠈⠳⣄⢀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣰⡀⠤⠗⡸⠁⠀⠀⠀⠀⠀⠀⠈⡦⠤⠤⠤⠤⠤⠀⠀⡼⠦⣀⣈⠵⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡤⣄⠀⠠⢇⣀⣀⣀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢴⠀⠀⠀⠀⢹⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⢜⠀⠀⠀⠀⢀⠷⠚⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠦⡤⠼⠀⠀⠀⠀⠈⡷⠶⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⠩⠄⣀⣀⡤⢔⠃⠀⠀⠀⣠⠷⠖⠓⠒⠲⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠶⠶⠶⠖⠚⠁⠀⠀⠀⠀⠻⣤⣀⣀⣀⣤⡤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡿⢀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠠⠋⢠⡄⠡⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢃⠀⠰⣦⠙⣾⡿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⡆⠀⠘⠛⣿⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠛⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠐⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠛⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⢀⡙⠲⠦⠀⠀⣀⣀⠄⠈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠙⠙⠛⠂⠀⠀⠻⢥⣤⡄⠀⣿⠟⠁
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠙⠛⠓⢒⠒⠀⠀⣠⠋
⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⡀⠈⠙⠀⢀⣠⣶⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⡴⠖⠒⠲⠦⣀⠀⠀⠀⠀⠀⠁⠀⠙⠲⠶⣶⠿⢻⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣴⠋⠀⠀⠀⠀⠀⠈⠛⠹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⠀⠀⠤⣀
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⡄⢰⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⢀⡀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠑⠠⠤⣀⣀⡀⠀⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠛⠿⣻⡋⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⢸⡏⠀⠐⠀⢀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡴⠀⡀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠧⢻⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠀⠻⠂⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠛⠁⢁⣀⣀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⢤⣀⣠⣤⢶⡾⣿⣿⠦⠶⠛⠋⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣋⣏⣹⣹⣿⣭⣽⣻⣋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣭⣭⣿⣿⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⡉⠉⢻⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣥⣤⣀⣤⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⡿⠋⠁⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣉⠉⠙⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⠟⠁⠀⢀⠴⢶⣶⣶⣄⠀⠀⣠⣴⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣴⣶⠾⣤⡾⢿⠟⢿⠛⣧⠐⢿⠇⠾⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢛⣙⠛⢿⡟⠀⠀⠀⠘⣇⠀⠀⠀⢸⡏⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣞⡼⠁⠀⠁⠀⠀⠀⠀⠈⠙⠒⠚⠉⢠⣀⣤⣀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡜⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡦⣶⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠛⠷⣦⣤⣀⡀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠃⣀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⣷⠀⢸⠓⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠙⠹⠏⠀⡼⢀⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣷⣶⣮⠊⣠⠊⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠈⠛⠲⢤⣀⡀⠀⠀⠀⠀⣯⠀⠚⠉⠻⢟⢿⣿⡾⠟⢳
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢀⣢⠀⣮⣄⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠸⡆⠀⠀⠀⠈⠀⠀⠀⢀⡿
⠀⠀⠀⠀⣠⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠻⣄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⢸⡿⢻⣿⣿⣇⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⢷⡀⠀⠀⠀⠀⢹⡀
⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣼⣧⣤⡴⠶⠞⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⣿⠋⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢺⡐⠭⣧⠇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣸⣥⣤⠖⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠒⡂
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣷⢶⣄⠀⠀⡀⠀⢖⡲⠀⡊⠁⡆⠈⠉⠁⠀⣼⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⡝⠛⣏⣹⠄⠀⣠⡄⠉⠈⠁⠀⠀⠀⠀⠀⡟⠻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⢡⡀⠀⢽⠆⠀⢀⢠⠀⠀⠀⡀⡔⠃⠀⠁
⠀⠀⠀⠀⠀⡀⠖⣀⣀⠀⢠⠖⠒⢄⠀⢿⡀⠀⠀⠀⠀⠄⠂⠀⠠⢇⣹⠃⠀⠄⠒⢌⠂⠀⢀⣼⠃
⠀⠀⠀⠀⣼⣿⠉⠉⠁⠀⠹⣀⣀⠜⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠸⡀⠀⡠⢀⢠⣾⡿
⠀⠀⢀⣴⠟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠉⠀⠀⢨⡿⣿⡀
⠀⠰⠟⠁⠠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉

⡴⠋⠙⠲⡀
⢳⢆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠖⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛
⠈⢦⡀⠀⡀⠘⢦⡀⠀⠀⠀⠀⢀⣀⣤⡤⣤⡀⠀⡴⠛⡭⠭⠍⠳⣄⢠⠏⠘⠛⠋⠁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣰
⠀⠀⢻⣀⠀⠀⠀⠱⣄⠀⠀⡴⠫⠕⠒⠂⠀⠉⢺⠃⠀⠁⠀⠀⢀⠘⡟⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠳⣄⠠⠒⠀⠘⢦⡀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⢴⡇⠀⠀⠀⠀⠀⣷⠀⢸⡀⠀⠀⠀⠀⣼⣥⣤⡄⠀⠀⢠⠏
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⢠⢸⡀⠀⢄⠀⠀⠀⣾⡇⠀⠒⠲⠄⠀⢹⡇⠈⡇⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠹⡄⠄⠀⠀⡀⠹⣇⠀⠒⠃⠀⢸⣾⡇⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⣼⠃⠀⣷⠀⢠⠞⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠹⣦⡴⠊⠀⠀⢹⡄⠀⠀⠀⠈⢷⡇⠀⠀⠀⠀⠀⢻⠀⠀⠀⡀⠀⠀⣿⠀⠙⢻⣀⡞⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⡄⠀⠀⢀⠈⢿⠀⢀⡤⠒⠀⢸⡆⠀⠀⠀⠀⢠⣿⠀⠀⢼⡿⠓⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⠀⠀⢻⣄⠀⠁⠀⠘⣧⠀⠀⠀⠒⠘⣇⠂⠀⠀⠁⣸⣿⠋⠒⠛⠛⠲⠄⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠋⠁⠀⠀⠤⢿⣆⣆⠀⠀⢸⣧⡄⠀⠀⠀⣿⡀⠀⠀⣸⣿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡴⠀⠀⠀⢉⡿⣿⣦⣶⣿⣿⣿⣄⣤⡾⢿⣿⠿⠿⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠀⠀⠀⠀⠈⠙⠛⠋⠙⠉⠩⠔⠒⠊⠥⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡰⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡤⠔⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⡙⠒⠀⢀⣀⣀⠀⠀⠀⠰⢤⣀⣀⣀⣀⣀⣴⡞⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠉⠉⠉⠁⠀⠀⠀⠀⣧⠀⠀⠉⠉⠉⠀⠈⠃⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⣇⠀⣇⠀⠀⠀⠀⢀⣀⣠⡴⠎
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣳⣶⣶⣤⣤⣾⣿⣶⣛⣒⣛⣛⣋⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠴⠋⢳⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠴⣞⠙⠲⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡾⠀⡾⠲⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⢻⡀⢹⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠛⣷⠾⠓⠲⠶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠖⠚⠳⢾⠛⠃⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣸⡉⠙⠓⠒⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠖⠚⠛⠉⣷⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠋⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠛⣱⠀⣸⠋⣉⣁⣀⣤⠇⠀⠀⠀⠀⠸⣧⣀⣈⣉⠉⣷⠀⢮⠙⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡤⣇⣠⡏⠛⠛⠓⠶⠦⡄⠀⠀⠀⠀⢀⡴⠶⠚⠛⠛⢙⣆⣸⣧⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠯⣅⡉⠛⢿⠒⠲⠶⠃⠀⠀⠀⠀⠈⠳⠖⠒⣾⠛⠉⣈⡼⢧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠳⢤⣀⠉⢳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⠋⣁⡤⠞⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠴⠃⣠⡾⠥⠤⠶⠖⢦⠀⠀⠀⠀⠀⠀⡴⠲⠶⠦⠤⢽⣦⠈⠳⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡇⠀⠤⣴⣶⣶⣞⡀⠀⠀⠀⠀⢀⣙⣶⣶⣦⠤⠄⠘⣆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠀⠀⢤⣤⣤⣤⣤⠟⠀⠀⠀⠀⠸⣥⣤⣤⣤⡤⠀⠀⠉⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⣀⠀⠰⣤⣀⡉⠓⣦⠀⠀⠀⠀⠀⠀⢰⠚⠉⣁⣤⠴⠀⢀⡤⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡈⣻⠉⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠉⢿⢁⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠈⠉⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠠⠀⢀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⡀⢀⠂⠀⠀⠀⠀⠀⣤⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠑⠁⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⢸⠀⠀⢦⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⢿⡿⠿⠿⠓⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠑⠦⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠠⠐⠒⠠⣀⠀⣄⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠐⠻⠇⢰⣦⢀⡀⠀⠂⠄⠀⠀⠀⠀⠄⠒⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨⢀⠃⢨⡀
⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⠉⠁⠄⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠠⠀⠀⠀⡈⠉⠉⣶⡆⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠁⠀⡀⠀⠴⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠁⠚⠛⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⠛⡀⠀⠉⠑⢦⡀⠈⢀
⠀⠄⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠁⠀⠀⠀⢈⣤⣀⡠⠊⠘⢆⠀⠄
⠀⢀⡈⠀⢀⠂⠀⡁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣷⣄⠀⠀⠰⣿⣿⣿⡇⠀⠀⠘⡆
⠀⠀⠀⠂⠈⠀⠈⠀⠀⠀⠀⢀⡀⠈⠛⢲⡤⠄⠀⠀⣀⣀⡤⠴⠒⠉⠀⠀⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠿⠿⠁⠀⠀⠀⠈⠛⠉⠁⠢⢀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢸⠀⢸⣇⠀⠀⠠⠀⠁⠀⠀⢀⣀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢀⠀⠀⡘⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠀⠘⡆⠈⠿⣦⣤⣤⡶⠶⠾⠟⠛⠋⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⣽⣿⣿⠦⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠈⠆⠀⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠍⣩⠤⠤⠒⠉
⠀⠀⠀⠀⢀⠔⠀⠀⠆⠀⠀⠀⠘⠁⠀⠀⠉⠑⠒⠒⠒⠀⠀⢈⠉⠉⠀⢠⡀⢀⡀⠀⢊⠁⣀⡠⠐⠒⠋⢑⡆
⠀⠀⠀⢠⠎⠀⠀⠀⡀⠀⠀⠠⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⠈⠐⠄⢀⠴⠋
⠀⠀⢠⠋⠂⠄⠤⠆⠁⠰⠀⠀⠀⠀⠈⠑⠢⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡠⠀⠀⢀⡠⠚⠁
⠀⢠⠃⠀⣀⠔⠁⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠈⢀⠀⠐⠁
⠀⠘⠒⠉⠁⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣡⠞⠋⠛⢦⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡟⣰⠋⠀⠀⠀⠈⢷⣘⣧⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⡤⠶⠶⠶⣾⢠⣏⣙⣳⡶⠶⢛⣉⣭⣤⡶⠶⠶⠦⣍⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⢰⡇⣼⠿⢋⣡⠶⢾⣉⠻⢿⣄⣧⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣆⠀⣠⣾⠇⣿⠞⠋⠀⠀⠀⠈⠛⢦⣌⠻⢦⡀⢀⡾⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⢿⣡⣾⠀⡏⠀⢀⡴⠖⢦⡀⠀⠘⡏⢻⣦⣹⠟⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣦⡙⢿⠀⣇⠀⠘⢧⣀⣼⠃⠀⢠⣇⣼⠟⣡⣾⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⠏⠀⠙⢿⡆⣿⢦⣀⠀⠀⠀⢀⣤⠾⢋⣥⠞⠁⠈⢷⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠸⡇⢻⣦⣍⡛⠶⣾⣋⣥⣾⠋⡟⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠳⠶⠶⠶⢿⠘⣟⣩⡽⠷⠦⣬⣙⡛⠺⠷⠶⠶⠶⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠛⠛⣇⢹⡅⠀⠀⠀⠀⡽⢩⡟⠛⠓⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡙⢦⣀⣠⠞⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣬⡤⠞⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⣿⣼⢒⡯⠁⣯⡷⢼⢫⡌⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠀⠉⠁⠁⠉⠈⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡗⣭⢛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣰⡏⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⢰⣟⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣷⣾⣷⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠛⠀⠀⠀⢀⣀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣶⣶⠞⠀⠀⠀⢤⣤⡴⠀⠀⣤⡄⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠹⣆⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡟⠀⢀⣤⡀⠘⣿⠁⢠⡄⢸⡇⣠⣼⠇⣄⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⢸⣿⣷⣾⣿⠀⣿⣿⣿⡇⠙⢻⡇⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⠀⣿⡿⢿⡇⣶⣾⠻⡆⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⠸⣿⡏⠈⣿⠀⠙⠃⣸⡇⠉⠸⠆⠐⠃
⠀⠀⣠⣴⣶⣶⣿⡇⠀⠀⠀⣤⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠸⣿⡿⠃⠀⠠⣿⣿⡀⠀⠀⠀⠈⠛⠃⠀⠀⠉⠁
⠀⠾⠿⠛⠛⠉⠉⣿⣷⣶⣾⣿⡇⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛



⠀⡁⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡂⠁⠀⡀⡖⠤⠀⠀⡀⢢⣮⠇⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⡴⠉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡉⠠⣴⡏⠀⠀⢈⠉⣃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣅⠄⣴⣗⣦⢈⠅⣠⣄⠀⡤⣼⡿⠃⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠤⠨⠁⠘⢴⣿⠟⠀⢀⠹⠀⠀⡇⠀⢀⠔⠛⠁⠀⠹⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠒⣶⠀⠀⠀⠀⠰⢓⠒⠀⠀⡜⠀⠀⣿⡄⢠⣾⣿⣆⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⡔⠴⠖⠤⠀⢀⡀⢀⣀⡠⠔⠊⠀⠀⠀⢫⠀⠀⠛⠛⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠈⠱⠞⠈⠁⠀⠀⠀⠀⠀⠀⠙⠻⠄⠠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠤⠊⠀⢀⣾⢥⡀⠀⠀⠠⠀⠀⠀⠄⢀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡂⠀⠀⠓⠞⠃⡀⠂⠀⠀⠀⠀⠀⠹⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⠐⠀⠀⢠⠁⠀⠀⠐⠀⠀⠀⠀⠁⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⢂⣠⠾⠣⢀⣠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⢈⠝⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠂⠀⠀⠀⠀⠠⠘⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢖⡔⠒⠒⠫⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠤⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠠⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⡆⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣷⠀⠀⠀⢳⣶⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡀⠤⠹⣿⣷⣿⣿⣿⣤⣤⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⠀⠀⠀⠻⠛⠛⠿⠿⠿⠿⠿⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⡀⠀⠀⠙⡇⠀⠀⠐⣦⣀⠈⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣼⣷⡀⠀⠀⢱⢠⡶⡶⣿⣿⣿⣶⣦⣤⣄⣤⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠛⣿⡇⣬⣙⡿⠀⠀⢀⣿⡿⢿⣿⣿⣿⣏⠁⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⡧⠅⣹⣧⣇⠀⣿⣿⣿⣿⡿⠟⢹⠿⢷⡐⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡿⠿⢿⡿⣿⣿⣍⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠐⠀⠀⡿⠿⠻⣬⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢁⠀⠀⢸⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠁⢀⣴⡟⢿⡈⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣉⠀⢸⣿⣦⡀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠁⠀⠻⣿⣿⣶⠶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠈⠉⠁⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣤⣤⣤⣶⣶⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⣚⣯⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⠶⢀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⢈⣻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⠿⠿⠿⠛⠛⠉⠉⣰⠾⠿⠿⠛⠋⠉

⣿⣿⣿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠎⠁⠈⢙⣿⣿⣿⣿⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣾⣿⣵⣾⠟⠀⠀⠉⣹⣿⣿⣿⠄⠉⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⣋⣠⣧⠄⠊⠛⠉⠻⢿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣴⣦⣄⢀⡸⡿⢠⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠁⠐⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⢁⣠⣄⡀⠀⠚⢉⡤⠤⠄⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠴⠶⠆⠀⠀⠀⠾⠟⠂⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⣠⣶⣧⡀⠀⠀⠀⢀⣀⡀⠀⠀⢠⣍⡒⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⡴⠚⠁⠀⠀⠀⠈⣧⢿⡿⣆⡀⠀⠈⠉⠁⢀⣴⣿⣿⠿⠋⠀⠙⢤⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣾⣿⣿⣿⣿⡿⠁⠈⠀⠀⠀⠀⠀⠸⠀⢳⡹⣿⣶⣤⠄⠐⣸⣿⢹⣿⠀⡀⠀⠀⠈⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⡄⠠⡀⢡⠀⢂⠀⠀⠙⢮⣑⠀⠀⣊⡼⡡⢸⠃⢸⣇⡆⠀⠀⠀⠹⣿⣿⣆⣀⣀⣤⣖⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⠋⠁⠀⠀⢱⣀⠱⣼⠀⠘⠀⠀⠀⠹⠈⠉⠉⠁⠀⠀⠀⠀⢸⣿⠀⠀⢀⡀⠀⠹⠿⣿⣿⣿⣋⣭⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡿⠄⠀⠉⠻⣷⡀⣿⣿⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡎⣴⠟⣡⠖⡁⠀⢀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠛⠛⠶⣌⡐⢽⣷⢸⣿⡇⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣄⢻⢸⠗⠉⣠⡽⠟⠻⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠛⠻⢬⣷⣾⣿⣷⣿⣷⡀⢰⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⣸⠿⠛⣻⣿⢿⣤⣾⢋⡠⠂⠀⠀⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠃⠀⠐⠢⠈⢻⣿⣤⠤⣤⣤⠤⣤⣴⣿⣿⣯⠟⢀⠀⠈⠙⢅⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⣀⡀⠀⠀⠀⠰⠂⠀⠒⠒⠢⢀⢻⣧⡞⢳⡿⣿⠓⣴⡆⣸⢿⣷⡔⠁⠀⠔⠀⠀⠐⣶⣶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣤⠀⠀⢉⡁⢀⣼⣿⣧⣴⣿⣧⣼⣷⣴⣴⣿⣿⣿⣿⣁⡤⠂⣀⠀⣀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣶⣿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣀⣤⣄⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡉⠁⣀⣸⣿⣿⣭⣭⣭⣿⣯⣭⣭⣿⣿⣿⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⡿⠛⠉⠁⠀⠀⠙⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠻⠟⠿⠛⠀⠀⠀⠀⠀⠉⠛⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⣰⣿⣿⠀⣾⣿⣷⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣰⣿⣿⡏⢸⣿⣿⣿⡆⢹⣿⣿⡀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠐⠿⠿⠿⠀⠿⠿⠿⠿⠷⠈⠿⠿⠷⠀⠀⠀⠀⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣴⠟⣿⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠶⠟⠁⠀⣿⡇⠀⠙⢷⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⡀⠰⢶⣾⣿⣿⣷⣶⣶⣤⣀⡀⠀⠀⠀⠈⠇⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣠⣶⣿⣿⣿⣷⣦⣌⡙⠻⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⣰⣿⡿⢋⣡⣌⠹⣿⣿⣿⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣷⠄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⣾⣿⣿⡄⠻⠿⢿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⠋⣰⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠸⣿⣿⣿⣿⣷⡄⢹⣿⣿⣤⡙⠛⠿⠿⠟⢃⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣌⡙⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠧⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⡀⠀⣺⠀⠀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠐⠺⣷⣄⣿⡋⠁⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢼⣧⡐⠖⠀⠈⠉⠙⠣⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⢽⣿⣿⣷⣤⣄⡀⠀⠀⠈⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢹⣆⠚⠻⣷⣌⣿⣿⣿⡅⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠄⠹⣦⡀⠀⣹⣿⣿⣿⣿⡷⠤⠀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠘⠻⣾⣿⣿⣿⣿⡿⠷⣬⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣦⣾⣿⡟⢿⣿⡿⠀⠀⠈⠛⣻⣣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢾⡙⣿⢿⣿⣷⣿⠁⠀⠀⠀⠀⣬⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣎⠁⠛⠋⠁⠀⠀⢀⣠⣾⣿⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⡄⢀⡀⢰⣶⣶⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⢻⡆⠹⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢠⡈⠻⠂⢸⢿⣿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⠗⠀⠀⠀⠀⠀⢀⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⣀⣠⡤⣶⣾⣽⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠿⢦⣶⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⣿⠿⡿⠛⠙⠋⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⡿⠟⠋⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠘⠲⠶⣤⡀⠙⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢨⣽⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⣌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⡖⠀⠀⠀⠀⡀⠀⢰⠄⢠⡇⡠⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠄⠀⣙⠀⠁⠈⠀⠀⠀⢀⣀⠘⠢⠼⡀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠏⠀⡤⠊⠁⠀⠀⠉⠻⠆⠀⠀⠀⠐⠋⠁⠀⠀⠀⠙⠒⠀⠀⠀⠘⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠴⣄⠰⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠄⡸⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣈⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢰⠆⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣄⡀⠀⠀⠙⠲⠖⠚⠁⠀⠀⣀⡤⠚⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠟⠶⢶⡶⢶⣶⡶⠟⠉⠉⢡⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⡘⠙⠒⠒⠒⠀⠀⠀⠈⡇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠶⠶⠒⠶⠛⢦⣄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠉⠻⠾⠶⠦⢤⣄⡴⠙⠳⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢀⡌⡠⠒⠒⠒⠒⠒⢦⠀⠀⢸⠋⠉⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠨⡀⠀⠀⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡏⠀⢳⣤⣀⣀⣀⣀⣠⠂⠀⠀⠓⠒⠒⠛⠋⠉⠙⠻⣆⠀⠀⠀⢀⣠⡤⠶⠚⠁⢹⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⢏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⢹⣄⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⢀⡎⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡸⠶⠶⠶⠶⠚⢉⢙⠦
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠙⡶⠒⠚⠛⠛⢻⡃⠀⠀⠙⣿⣛⣋⣉⣀⣀⣀⣠⠷⠤⠤⠤⠤⠤⢦⣤⠤⠢⣤⣀⣙⣎⠡⠃
⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠖⠁⠀⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠘⣄⡰⠙⣄⣤⢀⡿⠀⣠⠴⡇
⠀⠀⠀⡀⠀⠀⢠⡄⣽⠑⠾⠀⠈⠃⠀⠙⠈⠃⠰⠞⠁⠐⠇⢀⣠
⠀⠀⠀⠙⢟⠃⠶⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⢩⠃
⠀⠀⠠⣤⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⣠⠶
⠀⣀⣀⠨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠏⣀⣀
⠈⠙⠒⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠒⠊⠉
⠀⣠⣔⣋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠦⠄
⠀⠀⠀⠀⣼⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣘⣆
⠀⠀⠀⠈⠁⠀⣯⠴⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⡄⠁⠀⠀⠀⠀⠀⡴⠈⠀⣠⠛⢩⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣇⠞⠻⢀⡜⢧⡞⣆⡞⠳⣄⣯⠙⠶⣄⡘⢆⠀⠀⠀⢀⣼⡗⠀⠀⢿⠀⠛⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠟⠀⠀⠀⠈⠀⠀⠀⠙⠀⠀⠀⠙⠺⣦⠀⠀⣼⠏⠀⠈⠁⠀⠀⠠⡀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⢸⡇⢀⡖⠂⠀⠀⠐⣒⣚⡇⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠚⠁⠀⠀⠀⣾⢡⡀⠀⠀⠀⠀⠀⠀⠈⣡⠀⢡⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣾⣇⠀⣠⠀⠀⣀⠀⠀⣿⡀⠈⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠹⣤⣤⠋⠀⣴⢟⣧⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠖⠟⠛⠛⣡⣠⠆⣀⣀⣴⡿⠋⠘⣿⣷⣄⠀⠙⣿⡳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⣾⠛⠄⠀⠀⠈⠃⠉⠀⠉⠛⣯⠠⠶⣄⠈⠉⠻⠷⣦⡈⠹⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⢦⡀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⣤⣹⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡶⡄⢀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠃⠀⡈⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⣀⡀⠀⠀⣦⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣠⡤⠀⢀⣴⣿⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠀⠀⢿⠇⠀⠀⠀⠉⣿⠨⠲⠕⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠀⠘⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡗⠀⠀⠀⢧⠀⠀⠀⠀⣿⡄⠀⡢⠀⡀⢅⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠈⢣⠀⠀⠀⠸⡇⠂⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⡏⠀⢦⡄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠫⠄⠀⠀⠀⠇⢠⠈⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⠆⡀⢀⠀⠀⠀⢠⡄⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠣⣈⣀⣴⠆⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠉⠑⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⢀⣿⣿⡄⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⢠⡆⠠⣄
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢧⠀⠀⠀⠀⠀⠀⣀⡴⠂⠰⣴⠏⠀⠀⣄⠈⢳⡄⠀⠀⠀⠀⠀⢀⡴⠚⠉⢁⣴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠠⡈⢧⠀⢀⡴⠊⠁⢿⠀⠀⠀⢹⡄⠀⠀⢹⡄⠀⠙⣦⡀⠀⢀⡴⠋⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠈⢧⠸⡇⠀⠀⠸⡆⠀⠀⠘⣇⠀⠀⠈⣷⠋⠀⠈⠳⢠⠞⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⢧⢿⡀⠀⠀⣿⡀⠀⠀⣿⣆⡠⠤⣿⠔⠀⠀⣰⠏⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⢧⠀⠀⣸⣧⡔⠲⣼⠘⣧⠀⢻⠀⣠⠞⠁⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⢿⡅⠈⣿⢧⠀⠻⠀⠈⣁⡵⠞⠁⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠙⠆⠘⢀⡄⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⣈⠃⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⣠⣤⠤⠙⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⡠⠋⠀⠀⢀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⠄⠀⠈⢠⣀⡄⠀⠀⠀⢀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣀⢤⣤⠄⠛⠛⠡⠯⠉⣦⣤⣴⡇⠀⠀⠀⣀⣀⣀⣤⣤⣤⠴⠶⢦⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣟⠃⢀⣤⠀⠀⠀⠀⢩⠇⠀⠀⠻⣶⢶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣀⣤⠄⠀⠀⣦⣀⠀⢀⠆⠸⠀⠀⠉⠀⠀⠀⣀⣤⣤⡴⠟⠛⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡤⠊⠰⣝⣒⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢸⡇⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⣇⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡁⠀⠀⠀⠀⢨⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠀⠀⠀⡿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣯⠈⠙⢶⣄⢀⡴⠋⠀⠈⠛⢦⣤⣀⣀⣀⠀⠀⢀⡠⠂⠼⢴⢇⠎⣼⣇⠇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠀⠀⣠⠞⠙⠉⠀⠀⠀⠀⠀⠀⠀⢉⣿⢯⡶⠚⡡⠀⠀⠀⢈⠛⠋⠀⠉⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⠛⠀⠀⣡⠞⡀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠀⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣦⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⢀⡼⠉⠉⢻⣷⡀
⠀⠀⠀⠀⠀⢀⠔⣫⣴⣾⢻⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠐⣰⡟⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣿⠧⣤⡾⠳⢦⠠⠄⠻⣧⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠒⠒⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢦⡈⠹⣦⠀⣳⢀⠀⠙⡙⣷⡄
⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⡀⠀⣀⣀⣠⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠹⣆⠘⡿⠻⢿⣤⡀⠃⠈⣿
⠀⠘⠒⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢰⡟⠀⠀⠀⠀⠀⠀⢠⡴⠁⠀⠀⠀⠀⠀⠀⢀⣿⣤⠗⠀⠀⠈⠻⣤⣠⡿
⠀⠀⠀⠐⣧⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠣⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⣀⣠⡴⠞⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡊⢱⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⣀⣀⣀⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣎⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣞⠋⠙
⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀
⣞⠁⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⡾
⠹⡄⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡒⠒⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⣸⠃
⠀⠹⣄⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣛⠛⠳⢾⠁⠈⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⢀⡟
⠀⠀⠘⢦⢀⣠⠀⠂⠙⣦⠀⠀⠀⠀⣠⣤⣄⣰⠇⠀⠁⠀⠈⢾⡇⠀⠀⠀⠀⢰⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⢿⡁⠀⠀⠀⠈⢷⡄⢠⠞⡵⠒⠀⠈⣧⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⡇⠀⠈⢷⡀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠳⡄⠀⠰⠀⠀⠙⢿⡄⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠹⣆⠀⠈⠀⠀⣷⠀⠀⠈⢧⠀⠀⠀⢀⡿⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠹⣇⠃⠀⠀⠀⠈⢳⡀⠀⠀⠀⠠⢿⡄⠀⠀⢀⣀⢹⡄⠀⠔⠀⠸⣄⠰⠄⠈⢷⡀⢀⡞⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠊⢳⡄⠀⠀⠀⠈⣿⡄⠀⠉⠀⠀⢿⣀⠄⠀⠐⣽⡦⠀⠔⠛⠛⠻⢦⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣠⠀⠀⠀⢹⡄⠀⠊⠁⠘⣿⡀⠀⠐⠂⢸⣿⣆⠀⠀⣸⠗⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠙⢆⠀⡀⠀⠻⣷⡇⠀⠀⢈⣿⡿⠿⠟⢫⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣠⠄⠀⠀⠈⢷⣇⠀⠀⣹⣿⣶⢶⠟⠉⢉⡀⠀⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠠⠞⠁⠈⠙⠓⠻⣛⣭⠄⠀⡀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡂⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢄⠳⡀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢷⣍⠂⠉⠐⠀⢀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠑⠀⠒⠛⡉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣕⣦⡤⣤⠀⠀⠀⠀⣠⡶⠂⡀⠀⠀⢀⣀⣠⠌⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠨⠍⡀⠐⠒⣩⠵⠞⠛⠛⠛⠒⠒⠀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠀⠀⢠⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⢸⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢷⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠈⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣶⣶⣶⠶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠿⠛⠛⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠛⠛⠿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢿⣷⣤⣴⣿⠿⠛⠿⢶⡄⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⠛⢿⣷⣦⣤⣾⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠠⣿⣿⡿⠻⠻⢶⣶⣶⢾⣇⠀⣀⣀⣤⣀⣀⠀⣸⣷⣶⣶⡾⠛⠟⢿⣿⡷⠄⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⣦⣾⣿⡟⣠⠶⣲⣾⠛⣛⠛⠛⠿⣿⣧⣠⣿⡿⠿⠿⠛⡛⢟⣗⣲⢦⣀⢻⣿⣶⣴⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣿⣿⣿⣿⠟⠁⢸⣿⣿⡇⠀⠑⣄⡒⢚⣿⡇⣠⡒⣒⠠⠊⠀⢸⣶⣾⠀⠈⢻⣿⣿⣿⣿⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢳⣿⣿⣿⣾⣿⣿⡝⢫⣿⣿⣿⠸⣝⣻⣿⡇⢨⣛⡯⣵⣟⣿⡏⠖⠆⣽⣯⣷⣿⣿⣿⡜⠀⢿⣇
⠀⠀⠀⠀⠀⠀⢠⣿⡥⠤⢾⣿⣿⣿⡙⠛⢹⣶⣷⠏⣋⣿⢼⣛⢿⢿⣿⡄⡠⣰⡯⣧⣛⣲⣬⣤⠚⠓⢫⣿⣿⣿⡷⠤⢼⣿⡀
⠀⠀⠀⠀⠀⠀⣾⣿⠟⠛⢻⣿⣿⡟⠻⣦⣘⢿⣿⣿⠟⢁⣾⣿⢧⢺⡏⡘⡞⢿⣧⡈⠻⣿⣯⣽⣀⣴⡿⢿⣿⣿⡟⠛⠻⣿⣷
⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⡎⣿⡿⠀⠀⢈⣩⠿⢿⣡⣴⢟⣿⣵⢯⣿⣿⣷⡻⣾⣿⡻⣦⣨⡿⠿⣏⡁⠀⠈⣿⣿⠃⠀⠀⠘⣿⡆
⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠸⣿⡇⢀⣴⣿⠿⣷⣴⣿⢿⣛⣲⣾⡿⠃⠀⠙⢿⣓⣲⣿⡿⣿⣦⣾⠿⣿⣦⡀⢸⣿⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⣸⣿⡀⢠⣴⣶⡾⣿⣷⣿⠟⠁⣠⣿⣿⠇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠸⣿⣷⣄⠈⠻⣷⣾⣿⢷⣶⣦⡀⣀⣿⣇
⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠛⢿⣧⡙⣦⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣴⢋⣼⡟⠛⠿⣿⣿⣿⣿⣿
⠀⠀⠀⣸⠋⠀⠀⡇⡇⠀⢀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣄⡀⠀⢸⢰⠀⠀⠹⡇
⠀⠀⠀⡿⠀⠀⠀⢧⣷⣶⣿⣿⣿⢏⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡻⣿⣿⣿⣶⣿⡌⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⢠⣾⣿⣿⣿⢟⣵⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣮⡻⣿⣿⣿⣷⡀⠀⠀⢸⡆
⠀⠀⠈⢷⣶⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⡞
⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣿⡛⠦⣭⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠀⠀⠀⠀⠀⠐⢈⠹⣦⣽⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣤⣤⣤⣀⠀⠀⢠⣼⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣶⣾⠟⣰⣿⡿⠻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣟⣫⡝⠉⠉⣷⣘⠋⢠⡽⢁⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⣸⠘⠃⠀⠀⠙⠃⠀⢸⣧⣸⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣆⠐⠀⠂⠀⠀⠀⢸⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠋⢀⣠⡾⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣶⡿⠛⠉⠀⢈⠟⠓⡲⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣰⡏⠘⠦⠤⠀⣊⠔⠁⡼⠁⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠈⣉⢁⠀⠀⣼⡇⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠶⣦⡀⠐⢰⣾⡏⠀⠀⡌⣠⡤⠄⢈⠻⣿⡶⠀⣀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣷⠀⠸⢹⡇⠀⠀⢺⠁⠂⠀⠀⢻⣽⣷⠋⠉⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⢤⣄⣼⡇⠀⠀⠰⠧⠐⠢⣀⣿⣾⣿⣦⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡄⠀⠀⠶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠟⠋⠁⠀⠀⠀⠀⠉⠛⠏⠈⠉⠉⠙⠛⠿⢿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⠿
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣦⣤⣤⣄⣼⣷⣦⣄⡀⠀⠀⢠⣶⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⢿⣿⡿⠟⠋⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⠉⠉⠛⠛⠿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠉⠙⢿⠿⠟⠃⠀⠀⠀⠀⠐⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠰⠆⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⡖⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⣀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠐⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⣰⣧⠀⠙⣶⣶⠠⠼⠀⠺⡉⠀⠀⢀⣀⡀⠤⠔⠁
⠀⠀⠀⠀⠀⠂⢀⠠⠐⠒⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠢⠄⣀⡎⠑⢄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠠⠄⢒⠦⠀⡰⠂⠀⠈⢿⡟⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈⠃⠨⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⡠⠄⠤⠄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠁⠀⠈⠁⠀⠀⣀⠠⠤⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠀⠐⠂⠉⠲⠀⡁⠑⠀⠂⢀⡠⠔⠒⠒⡲⠦⢄
⠀⠀⠀⠀⠀⠀⢀⡠⠄⠚⢳⠀⠀⠀⠀⠎⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠈⠀⠀⠀⠑⢄
⠀⠀⠀⢀⡤⠚⠁⢀⡠⠤⢎⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⣄⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⢀⣴⠃⠀⠀⠀⢰⠀⠠⠀⢢⡸⣿⡛⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣔⠁⠀⠤⠄⠐⠈⠀⠈⢄⡔⠁⠙⠛⠋⠄⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢀⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⣀⡠⠔⠋⢸⡄⢀⣀⠴⢿⠃⠀⠱⡄⠀⠀⠀⠀⠀⢀⡀⠀⠠⡤⠘⠦⡀⢠⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢝⠄⠀⠃⠡⡀⡠⠂⠉⠄⠀⣤⠞⠁⠀⠀⠈⠉⠐⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡐⠄⢈⠄⠂⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⡠⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⣄⠈⣿⡆⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠉⣦⣿⡇⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⡇⠣⣀⡀⠻⣿⣷⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠀⣴⠏⠀⠈⣷⣀⠀⠀⠀⠘⣿⡄⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠤⢠⣴⠋⠀⠀⣼⠏⠀⠀⠀⣿⣬⠄⠀⠀⠀⢿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠒⣌⣴⣿⣆⠀⠀⠀⠸⣧⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⢸⠆⠀⠀⠀⣿⢀⣤⡀⢹⣿⡇⠀⠀⠀⠀⠀⢿⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡎⠣⡀⠸⡀⠀⠄⠀⣿⡇⠀⢀⡀⣿⡷⠂⠀⠀⠀⠀⠘⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣇⠘⠉⢀⣿⠀⠈⠘⠒⣶⣴⣾⣴⣿⡁⠻⠀⠀⠀⢀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡔⠙⢦⣤⣴⣸⣧⣀⣤⣄⣿⡫⠵⢂⠀⠛⠒⠀⠀⠀⠀⢸⠆⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠙⠛⠙⠻⢿⣿⣿⡁⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣹⠂⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⡤⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀⠀⠀⠀⢰⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠠⠺⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡔⠀⠀⠀⠀⣁⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⡀⠀⡀⠁⠈⠛⠷⢀⡠⠀⠀⢀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡌⣻⢿⠿⠷⣤⣤⣤⣶⣯⣥⣀⣈⣀⣀⣀⣠⣼⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣧⣶⠄⠀⠀⠈⠉⠉⠉⠉⠉⠉⢉⣉⣁⣀⣠⡿⠿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠉⠉⠉⠙⠲⠀⠒⠰⠶⠦⠤⡤⠤⠤⠤⠉⠀⠠⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣦⠀⣀⣀⣀⣀⣀⣄⣀⣀⣀⠀⠀⠠⣤⣀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⠛⠛⠋⠋⠠⠤⠤⠤⠤⠤⠤⠶⠒⠒⠒⠁

⣀⣀⣀⢀⡀⣀⣀⣀⣀⣀⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠂⠀⠀⠀⠀⠹⠿⠿⡿⠛⠛⠻⢿⣿⣿⣭⣿⣿⡷⠀⠀⠀⠠⢀⣀⣀⣉⠉⠉⠁⠀⠀⠀⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢄⣀⣀⣀⣀⠀⢀⣤⠆
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠗⠋
⠀⠀⠀⠀⠀⠀⡠⠄⠂⠀⣀⠀⢈⠁⠢⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠎⠀⡏⢁⠀⠁⡇⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⣆⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠐⢄
⡀⠀⠀⠀⠀⢄⠀⠑⠊⠀⠉⣀⡀⠀⠂⠀⠀⠀⠀⠀⠔⠚⠛⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠌⠁⢈⡇⢘⠛⠃⠇⠀⠀⠀⠀⠀⢀⠀⣴⠲⣄
⣭⠥⠀⠂⠀⠈⠉⠀⠈⠁⠀⠀⠀⠙⠀⠀⠀⠀⡐⠀⠀⠀⠁⠀⠀⢀⠀⡠⢄⣼⠏⠀⠀⠐⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢨⠀⠛⠶⠋⠀⠀⠁⠀⠛⠨
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⢀⠞⣠⣾⠟⠀⠀⠀⢀⢁⠀⠀⠐⠒⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⣤⢤
⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠋⣉⠉⠳⡄⠀⠀⠀⠉⠁⠀⠀⠀⢠⠈⠀⠛⢁⠈⠀⠀⠀⠊⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡄⠀⠀⠀⠀⠀⠀⣸
⠃⠀⠀⠛⠉⠀⠀⣶⣾⣿⡆⢀⣍⠁⠂⠘⣆⠀⠀⠰⣶⣦⡀⠀⡀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣤⣤⣶⣶⡆⠀⠀⡤⠀⠈⠀⠁⠀⠆⠀⠀⠀⠀⠙
⠀⠀⠀⢀⡶⣠⡄⠈⠉⠁⠀⡀⠀⠘⠀⠀⢹⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠉⠙⠇⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣶⣶⠆⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⡄⠀⣀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢀⡟⠀⠀⠈⢴⡶⠆⠀⠀⠀⠀⠀⡀⠅⠈⠀⠉⠥⠀⣣⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠐⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢰⣿⣧⣀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠀⢸⡇⠀⠀⠈⢠⡄⠰⠀⠀⠀⠀⠏⠀⢂⡀⢀⡀⡖⠉⠁
⣀⡀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠑⡀⠀⠀⠀⠀⢨⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠈⠚⠉⠑⡀⣁⡸
⣀⡨⣧⠂⠀⠀⠀⠠⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⢀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡴⠖⠋⠉
⠁⠀⣇⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠍⠀⢤⡄⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⢼⠲⠖⠒⠂
⠀⢠⠏⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠢⢈⢁
⡴⠋⠀⠀⠀⠀⠀⣼⣿⡿⣟⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⢀
⠈⠄⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠿⠿⢿⣶⣶⣶⣦
⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣭⣷⣾⣿⡇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⣴⠆⠀⠀⠀⠀⠀⠈⢀⡴⠦⡄⠐⢸⣿⡇⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠋⠀⠀⠀⠀⢸⣿⣿⣭⣻⣿⣿⡼⣿⠟⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⡘⢃⡜⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⣿⡺⣿⣶⣿⣟⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣿⡿⠀⠀⠀⠠⠤⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠰⣪⠟⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⢂⣌⢢⠀⢸⣿⠇⠀⠀⠀⠀⠀⠠
⠀⠾⠀⠃⠀⠀⠘⠃⠒⠁⢰⡇⠀⠀⠀⠘⡄⢤⠤⠤⠬⠂⠰⠆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠉⠚⠀⣿⣿⠀⠀⠀⠀⢠⠀⠀⣄
⢀⡤⠤⠤⠤⠀⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠈⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠰⠟⠁⠀⠀⠀⠀⠀⣀⣀⣀
⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠙⣷⡀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⣤⣤⣤⣤⣴⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡆⣷⣦⢲⣤⣤⣾⡧⢨⣿⡟⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⡟
⠠⠈⠄⠀⠀⠀⠁⠉⢀⣴⡿⢟⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠘⣿⡄⠁⠱⣬⣵⡟⠉⢉⣿⠃⠐⠛⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠨
⠁⠀⠀⡀⠀⠀⠀⠀⣼⣿⣿⣯⣷⣿⣿⣿⣿⠿⣽⣿⣷⡄⠀⠀⠀⢠⠛⠿⣦⣠⣿⣇⣠⣴⠟⢁⠀⠈⠉⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⠘⠃⠀⠃

⣴⠟⠛⠳⣦
⣿⠀⠀⠀⠘⣧
⠸⣆⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣤⣤⣤⣄
⠀⠹⣦⠴⠚⠀⠈⠻⣄⠀⢀⣤⣤⣀⣴⠟⠉⠉⠙⢷⡟⠁⠀⠀⠉⠻⣆
⠀⠀⠹⣆⠀⠀⣀⠀⠹⣶⠋⠁⠀⠉⣯⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢹⡆
⠀⠀⠀⠙⢧⡰⠛⠁⠀⡏⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠸⣇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠘⣧⠀⠀⠀⢷⠀⠀⠀⠀⠸⡆⠀⢀⠀⠀⣧⠀⠄⠀⠈⣏⡀⠹⣆⠀⠀⠀⢀⡴⢾⡋⠁⠀⠀⠀⠈⠙⢷
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠘⡆⠀⠠⠄⠀⢻⠈⠁⣂⠀⠸⡄⠀⠀⠀⡟⠒⠀⠹⣆⢀⡴⠋⠀⠀⠙⠀⠀⠀⠀⣀⣀⣼
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠤⠼⣆⠀⠥⠀⠈⢧⡀⠀⠀⢀⣷⣄⣀⡤⠛⠒⠂⠠⠛⠋⠓⠀⠀⠀⠀⠀⣀⡴⠟⠋⠉
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠼⠧⣄⣀⣵⠿⠿⣷⡶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠐⠉⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢂
⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠂⠀⠀⠀⡀⠤⠐⠂⠁⡠⠌⡃⠛⠢⢀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠈⢢⠂⣔⣈⣀⡉⠀⠢
⠀⠀⠐⠄⡁⠐⢂⡄⠣⠊⠀⠀⠀⠒⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠢⢀⠐⠄⠀⠀⠀⠀⠠⠊⠛
⠀⠀⠀⠀⠀⠀⠀⠘⡏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠔⢀⠼⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠊⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠤⠆⠀⠀⠒⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠙⡖⠀⠈⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⠑⠒⡦⠀⠔⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠐⠀⠈⠉⠉⠉⠉⠉⠁⠀⢸⠀⠰⠄⢀⠀⠀⣀⠀⠠⠇⠀⠐⠂⠀⠐⠠⠄
⠀⠀⠀⠀⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢰⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠀⠁⠐⠂⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠦⠄⠀⠐⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠄⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡀⢀⡀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠊⠀⠐⠒⠒⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⠰⠶⠄⡀⠀⠒⠀⣀⠠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢩⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠐⠃⠀⠐⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⡌⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠲⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠓⠀⢀⣀⡐⠂⠀⠝⢁⡀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠘⡄⠐⢈⡠⠤⢤⡀⠀⠰⠁⣠⣾⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⢢⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠰⠄⠤⠊⠀⢀⠊⠀⢰⣿⡽⠀⠱⡖⠉⠉⠉⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⣺⠀⠀⠀⡆⠀⠀⡧⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠂⡰⠲⠀⠀⢀⡶⠀⠁⠀⠀⠀⠈⠁⢀⡤⠊⠀⠀⡇⢀⢤⠤⠤⠦⢄⠀⠀⠀⢀⠴⠊⢀⠐⡊⣉⠳⢄⡀⣈⠶⠋⠁⢎⢃
⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠑⢐⡄⠀⠀⠀⠘⠳⠶⣆⠀⠤⠴⠊⠀⠀⢀⣴⠂⣡⡀⢀⢠⠀⢨⠆⠄⢀⠡⠖⡐⢁⡆⣿⣽⢰⡦⣤⡆⠀⠀⠀⡌⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠀⢙⣀⣁⠄⠀⠀⠀⠀⠰⠠⠥⠬⠤⢴⡎⢀⡁⠦⡜⠠⠁⣁⣧⢹⢹⣒⡇⡅⠇⠀⣠⠎⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠙⢆⡰⠖⢨⠋⠀⠁⠀⠀⠀⠀⣀⠐⠂⠐⠈⠁⠒⠀⠀⠈⠓⢄⡀⠣⣐⠿⠸⠛⠃⢋⣡⠄⢊⡡⠊
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠊⠀⠀⡰⠉⠀⠀⡶⠤⠤⡤⠀⠶⠂⠉⠁⠈⠉⠒⡄⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣉⣉⣉⣉⡡⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠷⣀⡠⠔⠊⠀⠀⠀⠀⠁⠤⠠⠤⠷⠔⠊⠀⠀⠶⠄⡀⠀⠀⠀⠘⠁⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠀⠀⠀⠈⠑⠄⠛⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠐⠀⠁⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠐⠶⠂⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠤⠀⠀⠀⠀⠀⠀⢰⣀⣫⠵⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠁⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠖⠉⠀⠀⠀⠀⠀⢠⠤⡄⠊⠀⢀⢠⠴⣍⠉⠂⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡤⠄⡀⠀⠀⠀⠀⢀⠃⠀⠈⢤⠔⠋⢦⠀⠀⡅⠀⠈⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡄⠈⠑⣦⣀⣠⠀⠀⢀⡔⠁⠀⠀⢀⣤⠄⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢹⡍⠀⢢⣠⠊⠣⠠⠒⠉⠀⠸⠀⠳⣤⡀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠠⠀⠈⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠘⠃⡀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡢⢄⠠⠛⠀⠉⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠒⠙⠊⠀⠀⠀⠀⠀⠄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡣⣄⠀⠀⠀⠄⠀⡀⠠⠄
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣟⣳⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡿⠋⠉⠉⠛⠿⠿⠛⠁⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡟⢠⠶⠒⠒⢶⡄⠈⢠⡶⠚⠓⠂⢸⣗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢦⡽⣇⠀⠲⠏⠛⠛⠃⠀⠸⠋⠋⠙⠀⢨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⣿⣹⡆⠀⠀⠀⠀⡀⠀⠀⢄⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣷⠀⠀⡀⠈⠴⢄⠤⠚⠀⠠⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠆⠘⣶⢶⡒⠒⠐⢒⠶⠋⢠⡇
⠀⠀⠀⠀⠀⣠⠤⠘⢃⠉⣽⣆⡠⣀⠀⠀⠀⠀⠀⢽⣆⠀⠉⠓⠈⠁⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⢀⡟⠀⠀⠀⢠⣿⡏⣀⣼⠀⠀⠀⣠⣾⠸⣿⣦⣄⠀⠀⠀⠀⠀⣠⡾⢹⠛⡆
⠀⠀⠀⠀⢸⡇⠀⢀⣤⣼⣿⠟⢩⠃⢺⣿⣿⣿⡏⠧⠻⣿⣿⣷⣤⣤⣤⣴⠏⡠⠃⠀⠙⢦⣀
⠀⠀⠀⠀⣾⡏⠀⠙⡷⠚⠉⢀⡜⠀⠀⠙⠿⣿⣧⡀⠑⠈⠻⣛⠛⠛⠋⠁⠀⠀⠀⢀⠀⠀⠉⠛⠶⢤⣀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠈⠻⢆⠀⠀⣠⣷⣴⣿⡀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠈⠙⠶⣦⡀
⠀⠀⢀⡼⣷⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⣧⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⢀⡞⠀⠟⠢⠄⠀⢸⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡄⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠸⠁⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠋⡿⠃