Adjustable wrench Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣫⣯⠝⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠐⠿⠿⢂⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⣠⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⡠⢊⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢀⡴⣫⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⣠⠖⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠊⠀⠀⠀⡠⢚⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡵⠋⠀⠀⢀⡴⣫⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⠖⠛⠤⣄⡀⠀⣠⢔⡩⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⡾⠙⠚⠉⠀⠀⠀⠀⢩⢿⠕⠋
⠀⠀⠀⠀⠀⣠⠖⠯⢥⣀⠀⣠⢶⢚⠲⢄⡀⠀⠀⡹⠁
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠸⣅⡚⠏⣾⣦⢭⠖⠒⣿
⠀⠀⠀⠀⡇⠀⡠⣖⣉⣒⠦⣄⡉⠓⠦⢽⠟⠤⣰⡿
⠀⠀⠀⠀⣇⡜⡵⠁⠀⠀⡹⠋⠉⠑⠲⢤⣀⣠⡿⠃
⠀⠀⠀⠀⠘⠞⠀⠀⢀⡜⠁⠀⣀⡤⣺⠟⠓⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠛⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⣴⣿⠋⠀⠀⡼⠁⠀⠀⠀⡰⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⠻⢦⣄⣼⠁⠀⠀⠀⡼⡃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠑⠶⣦⣄⡀⠉⠻⢷⣶⣦⣾⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢀⣄⡌⢰⢉⢻⠷⣦⣄⡈⢹⣦⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠈⠈⠙⢷⣾⠏⠀⠈⠙⠻⠿⠿⠿⢃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣀⣠⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠔⠀⠀⠀⢀⠄⢂⡠⠤⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠔⠁⠀⠀⡠⢊⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡤⠊⠀⠀⢀⠔⣫⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣡⠖⠉⠀⠀⣠⢞⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⡵⠊⠁⠀⢀⡠⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣫⠖⠋⠀⠀⣠⠔⣫⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢚⡵⠚⠁⠀⢀⡤⠞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣫⠶⠋⠀⠀⣠⡶⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⠞⠁⠀⢀⣴⠟⣉⠔⠉
⠀⠀⠀⠀⢀⡴⢊⡴⠋⠀⠀⢀⡾⠟⡡⠞⠁
⠀⠀⣠⡴⣫⠔⠉⠀⢀⣠⠴⢋⡴⠊
⢠⠞⣩⣮⡁⠀⢀⣤⠎⣁⠔⠋
⣿⣾⠁⠀⢸⡆⠈⣠⠞⠁
⠹⢯⣓⠶⣋⡴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣄
⠀⠀⠀⠀⠈⠉⠛⠿⢟⣽⣿⠟⣥⢥⣛⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠸⣏⠀⣼⠇⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠶⠶⠶⠶⠤⠤⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠈⢿⣶⣤⣀⣀⣠⣿⣿⢟⣴⣦⣝⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣯⣭⣭⣭⡻⣿⣿⣿⡿⠷⣶⣄
⠀⠀⠈⠻⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠒⠶⠭⠭⠭⣭⣛⣛⣛⣛⣻⠿⠿⠿⢿⣿⣿⣿⣿⢇⣿⣿⣿⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠈⠻⠿⣿⢣⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠓⠒⠒⠲⠶⠿⠿⠿⢿⣶⣶⡾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣄
⢠⡶⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⡟⠁⠀⠀⠉⠙⠻
⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⠇⣿⣿⣿⡅
⠈⠻⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣾⣿⣏⣼⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠿⠿⠿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⠠⠐⠀⠉⠀⠀⠈⠐⢢⣀
⠀⠀⠐⠄⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⢀⣿⣿⣷⣄
⠀⠀⠹⣿⣶⣶⣶⣤⣤⠁⠀⢀⣸⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠙⢿⣿⣿⣿⡿⠀⢀⢡⣶⠊⠩⣽⡛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠙⠻⣿⡇⠀⠀⣸⡯⠀⢰⣿⠁⠀⠉⠛⠿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠐⣪⣭⣤⣛⣛⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠛⠛⠛⠛⠻⠿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⢀⣶⡿⠛⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣀⡀⢾⣟⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣄⣀⣀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡾⠽⠿⠉⠙⠓⠲⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡕⠀⠀⠀⠀⣠⣤⣴⡶⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⢏⣿⣿⠀⠀⢀⣀⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⠤⢤⡘⡼⣽⡻⠓⠉⠁⡰⡳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠞⣷⣒⣛⣇⢳⢿⠃⠀⢠⢞⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣴⡟⠀⢹⡵⣒⣺⡄⡞⣦⣾⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠃⢀⣠⠴⠛⠓⠋⠁⠀⢻⣟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⢀⣴⢿⡺⠿⠛⠋⠉⠉⠙⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠟⠁⢀⣴⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡫⠞⠁⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡫⠊⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⢀⣴⣟⡯⠊⠀⢀⣴⢿⡿⠋
⠀⠀⠀⠀⣰⣯⣜⣎⠀⠀⣰⣿⡷⠋
⠀⠀⠀⠀⣿⡸⡄⢻⢣⡾⡫⠊
⠀⠀⠀⠀⠙⠷⣿⣿⠿⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⢈⣉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢻⡀⠀⠀⠀⢀⣤⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢹⡄⠀⠀⠸⣆⠀⢀⣠⡴⠖⠛⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⢷⡀⠀⠀⠈⢿⠉⠁⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣤⠶⣚⣋⠉⢷⠀⠀⠈⠄⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⣧⠈⢿⣻⡆⢸⡇⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠹⣦⣬⠵⠶⣟⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣆⣀⣀⣤⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣫⡴⠒⠶⡄⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣡⠞⠉⠀⠀⢀⡿⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡵⠞⠁⠀⠀⢀⡴⢋⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣫⡴⠋⠀⠀⠀⣀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣡⠞⠁⠀⠀⠀⣠⠾⣫⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡵⠛⠁⠀⠀⠀⣠⠞⣡⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣫⡶⠋⠀⠀⠀⠀⣠⠞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣡⠞⠁⠀⠀⠀⢀⣴⠞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⣇⠀⠀⠀⢀⡴⢛⣵⠟⠁
⠀⠀⠀⠀⣠⠞⢋⣀⡀⠀⠀⠙⠶⠤⠶⢋⡴⠋⠁
⠀⠀⠀⣼⢃⡞⠉⠉⠙⢧⠀⠀⠀⢀⡴⠋
⠀⠀⠀⣿⠸⣇⠀⠀⠀⣼⠁⣀⡴⠋
⠀⠀⠀⠘⢦⣈⠓⠒⠛⣡⡾⠋
⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁

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

⠀⡀⠀⠀⠀⠉⠀⠀⠲⣄
⠘⠀⠀⠀⠤⢀⠀⠀⠀⡁⠁⡀
⡄⠀⢀⡀⠀⢀⠀⠀⠀⠁⠀⠀⢄
⠐⢄⠀⠀⠀⠈⠀⠀⠰⡀⢤⢀⡀⠀⡀
⠀⠀⠑⠄⠀⠀⠀⠀⢸⠇⣾⠀⠀⠐⠠⠐⠀⢀
⠀⠀⠀⠀⠈⠀⠀⠢⠜⠀⠃⠃⠀⠀⠀⠀⠈⠐⠨⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠒⠀⠠⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠅⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⡀⠀⡀⠀⠀⠀⠀⠀⠁⠂⠀⢐⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠂⠄⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠅⠐⠠⠠⠐⠠
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶

⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⣠⣶⣿⣿⣿⣿⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠶⢤⡀
⠀⠀⠉⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣻
⠀⠀⠀⢀⣀⣠⣼⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢦⣤⠴⠋
⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⣀⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠚⠛⠉⠉⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡟⠁⠀⠈⢢
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣧⡀⠀⢀⠞
⠀⠀⠀⠰⠶⠾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⢻⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⣿⣧⠀⣾⣷⣶⡆⠀⠀⠀⠀⠀⣠⣿⣿⣷⣄⠁⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆⣼⣿⣿⣿⣾⣿⣿⡿⠃⣠⣶⡀⣀⡴⠋⠀⠈⣿⣿⣿⣶⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠛⠛⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣴⡿⠿⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣾⠟⠁⣀⡀⠤⠖⠀⠀⠀⠀⠈⠹⣿⣿⣅⣀⣤⠀⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠃⠀⣠⡤⠀⠀⠀⠀⠀⠀⣠⠆⠀⠈⢿⣿⣿⣿⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠇⠀⣼⡿⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⣿⣿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⢰⣿⡇⠀⠀⠀⣠⠞⠁⠀⠀⣠⣾⠇⠀⢸⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣟⠀⢸⣿⠀⢀⣠⠞⠁⠀⠀⣠⣾⠟⠁⠀⠀⢸⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠀⠸⣿⡷⠋⠁⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⡴⠋⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡽⠋⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣴⡿⠋⠙⠳⠤⠀⠀⠀⠀⠀⣠⣾⣿⣷⣶⡀
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡾⠋⠀⠀⢀⣴⡿⠻⣿⣶⣤⣀⣀⣀⣀⣠⣴⣾⣿⠟⢿⣿⡿⠛
⠀⠀⠀⠀⣴⡿⠿⠿⢿⣿⣿⣇⠀⣀⣴⡟⠉⠀⢸⣿⣿⣿⠿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠉
⠀⠀⠀⢸⠏⣤⠖⠂⠀⠈⢻⣿⣿⣿⠏⠀⠀⠀⠈⠻⠿⠋⠀⣿⣿⣿⡇⠘⠿⠛⠛
⠀⠀⠀⠠⡾⠁⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠛⠋


⣶⢶⢾⢷⢿⠿⢾⠿⠿⣿⣷⣶⣿⣿⣿⣶⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣷⣾⡿⢶⣿⣶⠶⢶⡿

⠀⣠⣶⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠞⠛⠛⠉⠻⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠉⢻
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣸
⠀⢠⣤⣶⣾⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠁
⠀⠀⠀⠉⠉

⠀⣀⣴⣶⣾⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠘⠛⠋⠉⠻⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡟⠁⠀⠈⢳
⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠
⠀⢀⣤⣤⣶⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠚⠁
⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠈⠃⠭⣍⡉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⣉⡭⠅⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣰⠛⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡀⠙⡄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢻⡓⢦⣀⠀⢀⡔⠁⠀⢠⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢃⠀⠈⠢⣀⠀⣀⡤⠞⡻
⠀⠀⠀⠙⢄⠈⠙⠉⠀⣀⠔⠁⢠⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠈⠳⢄⡀⠉⠋⠉⣠⠞
⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠚⠲⣄⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢠⡶⠓⠂⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⣏⠉⠻⣦⡀⠀⠀⠀⠀⠀⣠⠞⠉⢉⡅⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠻⣦⡀⠀⣠⠞⠁⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠈⠻⣾⡁⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠈⠻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢙⣿⣦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⡿⠋⠙⢿⣦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣰⡿⠋⠀⠀⠀⠀⠙⢿⣦⡀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⣷⣄
⠀⠀⠀⠀⢀⣀⣤⣤⣠⡄⢶⡿⠃⠑⠚⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠒⠈⢻⡷⢤⣄⣤⣤⣀⡀
⠀⠀⢀⡴⣫⣶⠾⠷⣶⣭⡳⣄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢀⡔⣫⣶⠾⠷⢶⣭⡳⡄
⠀⠀⡞⣼⠏⠀⠀⠀⠀⠙⣷⡸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣼⠏⠀⠀⠀⠀⠘⣷⣹⡄
⠀⠀⡇⣿⡀⠀⠀⠀⠀⠀⣿⢇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⠀⠀⠀⠀⠀⢀⣿⢿⡇
⠀⠀⠹⣜⢿⣤⣀⣀⣠⣼⢏⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡜⢷⣤⣀⣀⣠⡾⢏⡞
⠀⠀⠀⠈⠳⠬⢭⣭⠭⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣭⣭⠭⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢩⡇⠀⠀⠀⣼⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣇⠀⠀⠀⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠉⠉⠛⠋⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢰⠏⠀⣠⣤⣤⣀⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢸⡀⢸⠇⠀⠀⠈⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢷⣼⠀⠀⠀⢠⣇⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠉


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

⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠉
⠀⠀⠀⢠⣤⣀⡀⢀⣼⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠞⣛⠻⢿⣷⣶⣄
⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠔⢶⣤⣤⣴⣿⣿⣿⣿⢳⣦⡀
⠀⠀⠙⠟⣛⣻⣿⣛⠵⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠹⣻⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⢟⡿⣿⣿⣿⡷⢲⠶⠶⣒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢿⣿⡁⠀⠈⠀⠉⠱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡱⣄⠀⠀⢀⢔⣼

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

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⢮⡙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡵⠛⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⢦⡙⠷⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⠞⢉⡴⠋⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⢳⡄⠙⢮⡻⣦⣄⢲⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣠⣴⢏⡼⠋⢠⡞⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢤⣤⡶⠿⠀⠀⠹⣎⢿⡛⢿⠙⠳⣄⣀⣀⣠⠞⠋⡿⢛⡟⣱⠏⠀⠀⠿⢶⣤⡤⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢤⣬⡿⠶⠀⢀⡤⢞⡥⠟⠀⠀⠀⢨⡏⢹⡅⠀⠀⠀⠻⢬⡳⢤⡀⠀⠶⢿⣥⡤⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⡿⢁⡴⣫⠞⠋⠀⠀⠀⠀⠀⡟⠀⠀⢷⠀⠀⠀⠀⠀⠙⠶⣝⢦⡈⢿⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⣸⡷⣫⠞⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠈⠳⣝⢾⣇⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⡀⠀⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⠀⣀⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣟⣡⣥⣤⡤⠀⠀⠴⠶⠒⠶⣤⡀⠀⢸⡆⢰⡇⠀⢀⣤⠶⠒⠶⠤⠀⠠⢤⣤⣭⣌⣻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢩⢞⡴⠋⠀⠀⠀⢀⡤⠤⢤⡀⠁⠀⠈⡇⢸⠀⠀⠈⢀⡤⠤⢄⡀⠀⠀⠀⠙⢦⣷⡍⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠟⠀⠀⠀⠀⠀⢞⢀⣴⣶⡝⠀⢀⡴⠃⠘⣦⡀⠀⢫⣶⣦⡀⡃⠀⠀⠀⠀⠀⠻⡝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⠏⠀⠀⢀⡴⠛⣦⡘⠢⠿⠋⠀⣠⠞⠁⠀⠀⠈⠳⣄⠀⠙⠿⠔⢃⣴⠛⢦⡀⠀⠀⠹⡞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣰⠋⠀⠀⠈⠙⠲⠶⢂⡴⠃⠀⠀⠀⠀⠀⠀⠘⢦⡐⠶⠖⠋⠁⠀⠀⠙⣆⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠖⣶⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠸⣆⠐⣖⠲⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣟⣠⣤⣤⡀⠀⠀⢀⣸⠁⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠈⣇⡀⠀⠀⢀⣤⣤⣄⣻⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠀⠀⠀⢷⡀⠀⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⢻⣿⠀⢀⡾⠀⠀⠀⠉⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠳⣤⣿⡇⠀⠀⠀⠀⠙⢻⡟⠋⠀⠀⠀⠀⢸⣿⣤⠞⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀⠀⣀⣠⠴⠞⠳⠦⣄⣀⠀⣀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⡴⢾⡇⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠦⠤⠤⠴⠶⠿⠛⠉⠀⠀⠀⠀⠀⠀⢸⡷⢦⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠒⠚⠓⠒⠲⠶⣄⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢻⡄⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢠⡟⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠁⢸⣿⣿⠀⠻⢿⣿⠇⠸⣿⣿⠟⠀⣿⣿⡇⠈⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡄⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⢠⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢿⣿⣆⠘⢿⣿⣷⡄⠀⠀⢠⣾⣿⡿⠃⣴⣿⡿⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠛⢷⡈⠻⣿⣿⣆⠀⢿⣿⠟⢁⡾⠛⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⣿⣿⣷⡈⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡈⢿⣿⣿⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣤⡾⢁⣴⣿⣷⠄⠹⣿⣿⣦⡈⢷⣦⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣾⣿⠏⢠⣾⣿⡿⠃⠀⠀⠘⢿⣿⣷⡄⠹⣿⣷⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠃⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⠘⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⡀⢸⣿⣿⠀⣴⣾⣿⡆⢰⣿⣷⣦⠀⣿⣿⡇⢀⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣿⡉⠙⠀⠀⣠⠆⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣶⣿⡇⠈⠁⠀⣠⣾⠏⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⢿⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⢀⣴⠟⣡⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠟⠹⠆⠀⠀⣠⣾⣿⡿⠃⠀⠀⠀⢰⣿⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠀⣠⣾⣿⣿⠟⠀⠀⢀⣴⣿⣦⡙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⠟⠁⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⠟⠁⠀⢀⣴⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⢀⣴⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠁⠀⢀⣴⣿⣿⡿⠋⠀⠀⣠⣾⣿⣭⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡾⠛⠛⠁⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⢾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡿⣏⠀⠀⠀⣀⢀⣴⠟⠉⠋⠀⠀⢀⡀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠩⡾⣫⡾⠋⠀⢠⣿⠛⣿⡇⠀⠀⠀⠀⠀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠛⠿⠟⠁⠀⠀⠀⠀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡄⠀⠀⠀⠀⠀⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡿⠛⠂⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣴⣿⡿⠋⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡤⠀⠀⠀⠘⣿⣿⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⢿⣿⣇⠀⣾⣿⡏⠀⢀⣀⣤⣤⣴⣶⣶⣶⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠙⢿⣷⣦⣀⠀⠈⢿⣿⣶⣿⣿⣤⣾⣿⡿⠿⠛⠛⠛⠉⠛⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠙⢛⣿⣿⣿⣿⣿⣿⡛⠿⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣤⣀⣀⣤⣤⣶⣾⣿⡿⢿⣿⣿⠻⣿⣷⡀⠀⠈⠛⢿⣿⣦⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠿⠿⠿⠿⠟⠛⠋⠁⠀⣼⣿⡏⠀⢹⣿⣧⠀⠀⠀⠀⢙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⣿⣿⡄⠀⠀⠀⠛⠛⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣴⣿⡿⠋⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⠀⠀⠀⠀⢠⣤⣿⣿⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠓⠀⠀⠀⠀⠀⠙⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠐⠛⠁⢸⡇⠈⠛⠂⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣉⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⢉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠈⠻⣧⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣴⠟⠁⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄
⠀⠀⠀⠀⠀⢠⣾⣿⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣿⣷⡄
⠀⠀⠀⠀⠀⠈⠻⣿⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⣴⠟⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠻⣷⣄⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥⣤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⣬⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠠⣦⣄⢸⡇⣠⣴⠄⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠙⢷⣄⠀⠀⠀⠀⣴⠟⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢷⡆⠀⣶⠿⠷⠀⠀⠾⢷⣦⠀⣶⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢰⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠀⠀⠀⠀⠀⠸⣧⠀⢹⡇⠀⠀⠀⠀⣾⠃⢠⡿⠀⠀⠀⠀⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠛⠛⠛⠛⠛⠶⢦⣿⡀⠈⢿⡀⠀⢀⣼⠃⠀⣼⠿⠛⠛⠛⠛⠋⠀⢙⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣿⠛⠳⠶⢦⣤⡀⠘⣷⡀⠘⣷⣠⡿⠁⢀⣾⣃⣤⡴⠶⠟⠛⣿⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠙⠷⣼⣷⡀⠈⢿⣄⣰⣿⠟⠋⠁⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢀⣀⣼⣿⢿⣄⠀⠹⣿⣥⣀⡀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⣤⣴⠶⠶⠟⠛⠉⣼⠏⠀⣹⣷⣄⠈⠻⣏⠛⠻⠶⠶⣤⣤⣿⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⣀⣀⣀⣀⣤⣤⡶⣾⡏⠀⣸⠏⠀⠻⣦⠀⠙⣷⣤⣤⣀⣀⣀⣀⠀⢈⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⠉⠉⠉⠀⠀⠀⣿⠀⢰⡟⠀⠀⠀⠘⣧⠀⢹⣇⠀⠉⠉⠉⣿⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡇⠀⣾⠃⠀⠀⠀⠀⢹⡇⠀⣿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⣿⣀⣀⠀⠀⣀⣨⣿⠀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⠁⠀⣩⡿⠋⠀⠀⠙⢿⣅⠀⢈⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠾⠋⠀⠀⠀⠀⠀⠀⠙⢷⠟⠁





⠀⠀⡀⠀⣀⣀⡀⡀⡀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⡀
⣿⣏⢩⣟⡛⣛⣛⡛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡀⣀⠀⢀⢀⠀⣠⣤⡠⢀⠀⡀⣾⣶⣤⣀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⣾⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣸⣿⣷⣶⣤⣀⣀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡋⢸⡇⠀⠀⠀⢹⣿⣮⣷⡄⠀⠀⠀⣴⡃⢸⡇⠀⠀⠀⣿⣿⣮⣷⡄⠀⠀⠀⣠⢟⣦⠀⠀⠀⠀⢻⡌⠻⣿⣽⣦⡀
⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⣧⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⡇⢸⣧⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢠⡟⢸⣿⣧⠀⠀⠀⣀⣷⠀⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠸⣿⡇⠈⠻⠶⠶⠞⢻⣿⣿⣿⣿⠀⠀⢸⣿⡇⠈⠻⠶⠶⠖⢫⣿⣿⣿⡿⠀⠀⢸⡇⠘⣿⣿⣧⠶⡛⠉⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠘⣷⠞⠋⢉⣚⠭⣤⡀⠀⠀⢠⣿⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠄⠀⠀⠀⠐⣿⡟⠁⠀⠀⠀⠀⠀⠙⣷⠄⠀⠀⠀⠐⣿⡟⠁⠀⠀⠀⠀⠻⣆⢸⣝⣧⡶⣿⣧⠀⢠⣿⣣⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣀⣀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⣀⡀⢰⣿⠀⠀⠀⠀⠀⠀⠈⢿⣆⠻⠷⠛⠉⠀⠀⡾⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠀⢸⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣾⠀⢸⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢰⡿⣦⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⢸⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣽⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣻⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⢸⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣹⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⢸⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⢀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠈⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠨⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⣀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⠁⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⣸⠃⣀⣤⣄⡙⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠤⣒⡢⢄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⣴⠶⠶⣾⣿⣿⣿⠀⠀⠀⠀⠀⣸⢣⡞⠉⠀⠈⢻⡎⢷⠀⠀⠀⠀⠀⠀⠀⢸⡇⢱⠏⠉⠙⣦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢸⡇⠀⠀⢹⣿⣿⡟⠀⠀⠀⠀⠀⢻⡸⣧⠀⠀⠀⢨⡇⡾⠀⠀⠀⠀⠀⠀⠀⠀⢷⡘⢦⣀⣠⠟⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣿⠀⠀⠘⣯⠟⠀⠲⠲⠒⠂⠀⠚⠷⣾⣿⡶⣾⣿⠾⠃⠀⠀⠀⠂⠀⠀⠒⠂⠈⠓⠦⢤⠴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢷⣦⣙⠀⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠰⠺⢿⣷⡌⡞⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⡰⠋⢤⠀⣴⡾⠛⢳⣿⢹⡁⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡄⢹⠀⠀⠀⠀⠘⢸⣇⢧⠻⢶⣿⣃⢷⢧⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠁⡒⠁⣴⠐⠐⠦⡆⠈⢿⣮⡻⣄⢻⡟⣡⠟⣠⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣩⠁⠀⢠⡎⠋⢰⡿⢃⠰⣄⣬⡦⣵⡽⣷⢸⢎⣾⣵⡾⣯⡆⣷
⠀⠀⠀⠀⠀⢀⠂⠀⠀⣀⣿⡘⢊⣴⡇⠀⢧⢰⢹⣿⣣⡉⣎⢿⣟⣾⡇⡿⣱⢿⣿⡿⣿⡟⢠⣿⠇
⠀⠀⠀⠀⠐⣌⣇⢣⡑⠇⠻⣷⢸⣿⠁⣾⣦⣻⣧⡟⣹⣷⣿⢞⣫⣾⡿⣽⢛⣭⣴⠾⣛⣵⣿⢏⡠⠃
⠀⠀⠀⠀⠀⠘⠻⣷⣝⡲⢤⣙⠷⡻⣮⣿⣛⣯⡿⠃⠘⠿⣞⡻⢫⣿⢱⣱⣿⡿⢛⣻⣭⣽⠶⠋⠁
⠀⠀⠀⠀⠀⢠⡶⡒⢾⣽⣿⣿⣿⣿⣿⣿⠟⠩⡀⢡⣐⣦⣽⣿⣷⣬⡛⠿⢯⣾⠿⢋⣴⣷⠿⣶⡀
⠀⠀⠀⠀⠀⠘⣷⣌⣛⣻⣽⣿⠿⣟⡋⢠⣄⣸⣿⣾⣿⣟⣽⣷⣽⣿⢿⣿⣶⣶⣞⡿⣿⣿⠉⣸⠇
⠀⠀⠀⠀⠀⢀⠀⠉⠉⠛⢿⣷⣦⣿⣿⣾⣛⣻⣿⣿⣿⣿⣿⣹⣿⢟⣼⣿⣗⣋⣹⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠐⠦⢄⣀⡀⠈⠛⠛⠚⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣉⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⢦⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉

⠀⠀⠀⢀⡴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⣤⡀
⠀⠀⣰⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⢦⡀
⠀⣼⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢷⡀
⢰⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⡄
⡾⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠹⣆
⡇⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣷⠹⣦
⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⢸⡟⠓⠘⢷⡀
⠈⢷⣄⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⡿⣷⠀⣿⠋⠿⠛⠿⠁
⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⢸⡇⣌⠁⣽⢠⡌⣿⠀⣇
⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⢸⣷⣿⣾⣷⣾⣧⣿⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⢸⣿⢛⣟⢻⣟⢻⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠉⠉⠉⠉⠉⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀⣀⡀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢠⡿⠁⠀⠉⠆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⣇⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⡆⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡄⠀⠀⠀⠀⠆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢳⡀⠀⠀⠀⠀⠂⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢧⠀⠀⠀⠀⠈⠄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢇⠀⠀⠀⠀⠈⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⣆⠀⠀⠀⠀⠘⠄⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠘⡄⠀⠀⠀⠀⠘⡄⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⡀⠀⠀⠀⠀⠘⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢱⡀⠀⠀⠀⠀⠸⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢳⠀⠀⠀⠀⠀⠹⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⢧⠀⠀⠀⠀⠀⠹⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⣆⠀⠀⠀⠀⠀⠻⡌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⡆⠀⠀⠀⠀⠀⢻⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⡄⠀⠀⠀⠀⠀⢳⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡄⠀⠀⠀⠀⠀⣷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠻⣆⡀⢀⣀⡼⠃⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⠙⢉⣥⠶⠶⠶⢤⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢠⡟⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⡇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⣀⡼⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣽⣛⣋⣭⠶⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣤⣄⠀⢠⣤⣽⣷⡄⠀⠀⠀⠀⢠⣾⣯⣤⡄⠀⣠⣤⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠈⠀⠈⣿⠀⢸⡏⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⠁⠁⠁⢠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⣿⡁⠀⠀⠀⢿⡄⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⣿⠀⠀⠀⢐⣿⠙⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡋⠁⠀⠀⠙⠛⠛⠛⠷⠿⠇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠸⠿⠿⠛⠛⠛⠋⠀⠀⠈⢙⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⣶⡶⠶⢶⣦⣤⣤⣄⠙⢿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠋⣠⣤⣤⣴⡶⠶⢶⣷⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⡆⠀⠀⠀⠀⠈⠻⣷⣄⠙⢿⣦⡀⢀⣴⡿⠋⣠⣾⠟⠁⠀⠀⠀⠀⠰⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⠿⠿⠋⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⢸⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣠⣶⣶⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠅⠀⠀⠀⠀⢀⣴⡿⠋⣠⣾⠟⠁⠈⠻⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀⠰⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⢿⠷⠶⠾⠿⠛⠛⠋⣠⣾⠟⠁⠀⠀⠀⠀⠈⠻⣷⣄⠙⠛⠛⠻⠷⠶⠾⡿⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣅⡀⠀⠀⣠⣤⣤⣤⣶⣶⡆⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢰⣶⢶⣤⣤⣤⣄⠀⠀⢀⣨⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⣿⠅⠀⠀⠀⣾⠃⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠘⣿⠀⠀⠀⢈⣿⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⢀⠀⢀⣿⠀⢸⣇⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣸⡇⠀⣿⡀⢀⠀⠈⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠛⠋⠀⠘⠛⣻⡿⠃⠀⠀⠀⠀⠘⢿⣟⠛⠋⠀⠙⠛⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⡀⡈⡠⡀⡠⡈⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡀⣠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢦⡀⣠⢾⢦⡀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⣿⡀⠁⠁⢸⡇⠁⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢸⠀⠀⠀⢸⠀⠀⢠⡀
⠂⢨⠀⠀⢤⠁⠀⡀⢠⠄⠀⠨⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠚⠲⢮⢷⡄⣰⢯⠶⠚⢺⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠺⡗⠒⠒⠌⢳⡀⣠⢋⠖⠒⢒⡿
⠀⣨⠀⠀⢀⢀⡀⡀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⢀⢀⡻⣆⢀⠀⠀⢨⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⢀⢀⡹⣆⠀⠀⠀⢨⡀
⢆⠨⠀⠀⡉⠄⠀⠐⠈⠁⠀⠨⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠶⠶⣫⡟⠁⠙⢯⡛⠶⢾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⠒⠒⢫⠞⠀⠘⢧⠑⠒⠒⡿
⠀⠈⠀⡀⡀⣀⡀⡀⡀⡀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣄⣿⣀⡀⣀⣸⣇⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⢸⢀⡀⣀⢸⣁⡀⠈
⠀⠀⠀⠐⠤⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠈⠻⠋