Sacred lotus Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⣠⡤⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠋⠓⠀⠀⣿⣿⢀⣼⣿⡇⣠⡅⢀⡤⠖⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠀⠘⣿⣷⣦⡄⣿⣿⣿⣿⡿⡟⣾⣿⣇⣼⠀⢀⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠘⢿⣿⣇⣿⣿⣿⣯⣿⢸⣿⣻⣿⠛⠊⠁⣸⠃⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⠛⠒⠤⡻⣶⣭⣿⡿⣿⡿⣼⣿⣹⢿⣿⣿⢀⡀⠀⠃⠈⢡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠹⣿⣿⣿⣎⢇⠸⠁⢀⣾⣿⠇⣠⣿⣿⡿⠣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠌⠒⠤⠀⠙⢿⣿⣿⣄⡀⣠⢾⣛⣵⣿⣿⡿⠋⠠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠙⡛⠛⠛⠉⠉⠀⠀⣀⡴⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠋⠁⠀⠀⠀⠈⠙⠒⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣀⢀⣴⠟⠙⢷⣄⢀⣠⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣸⡏⠀⠈⢹⡿⠃⠀⠀⠀⠻⣿⠉⠀⠘⣿⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠷⢶⣤⣿⠁⠀⠀⠀⠀⠀⢹⣧⣴⠶⠟⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢸⡟⢷⣄⠀⠀⢀⣴⠟⣿⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢸⣧⠀⢻⣆⢠⡿⠃⢠⡿⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⢻⣆⠀⢿⣿⠃⢠⡿⠃⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣀⠀⠀⠹⣷⣸⣿⣴⡟⠁⠀⢀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠿⠛⠿⠷⠾⣿⣿⡿⠶⠿⠟⠻⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⢀⣴⠿⣿⢷⣄⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠷⠶⠶⠾⠛⠁⠀⣿⠀⠙⠻⠶⠶⠶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠁⠀⠀⠈⠉⠉⠛⠷⣶⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⠀⠀⢀⣀⣀⣤⡶⠿⠛⢿⣦⡀⠀⣀⣠⣴⡶⠶⠿⠷⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⢙⣿⣿⣏⡉⠀⠀⠀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⣄⣀⠀⢀⣴⠟⠁⠀⠉⠛⠷⢶⣦⣤⣤⣶⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠀⠀⠀⠀⠀⠉⣙⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣀⣠⣤⣴⠾⠋⠁⠈⠻⣦⡀⢀⣠⣤⣾⠾⠟⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢈⣿⢿⣯⣀⡀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠈⠉⠛⠻⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⢸⡀⠀⢸⡇⠀⠘⢀⠀⢸⡄⠀⢴⡄
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⠺⣾⡇⠀⠀⠀⠹⣾⠋⠀⠈⢷⣶⠋⠀⠀⠀⣀⣊⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠹⠦⠄⣀⠈⢢⡈⢷⣦⠶⣾⣦⠅⡀⣠⠀⠈⠁⢀⣤⣶⣾⡿⠗⠛⠛⠛⠛⠓⡊
⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠈⠑⢄⣷⣼⣿⢠⡈⠁⡀⣹⣿⢟⡃⣀⡿⠋⠉⠉⠀⠀⠀⠀⢀⠄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠢⡀⠀⠻⣇⠈⠳⣿⡿⡿⠷⣿⡟⠙⣇⣆⣀⡀⡀⠀⠀⣀⠔⣡⠞
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠺⣷⣄⠱⣤⣽⢀⣴⠽⠷⠧⣴⡞⠁⠀⣿⡿⠋⠀⡀⣠⢞⣵⡞⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠐⠒⠠⠍⣳⣾⣿⡇⢁⠀⠀⠀⠀⢐⣄⣰⡟⣀⣼⠿⣿⣿⠿⠛⠉⠀⠐⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣾⣆⠀⣷⣴⠾⠛⠛⠋⠉⠉⣡⡏⠁⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⢀⡄⡀⠒⠚⠷⢦⣄⣀⠀⠀⣈⣛⣿⣷⣿⣧⣀⣠⣤⣶⣶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⢀⠔⠁⠀⠀⠈⠉⣹⣿⡿⠟⣿⡍⠉⠉⠉⠀⠈⠈⣼⢿⣿⢿⠛⠓⠂⠠⣤⣤⠤⠤⠶⠒⠋⣁⡀⠤⠒⠁
⠀⠀⡂⠀⠀⠀⠀⠠⠶⣾⣿⣧⡀⠀⠛⢦⡀⠀⢀⣠⣜⠃⢧⠙⠁⠀⠑⠄⠀⠈⠋⠉⠀⠀⠉
⠀⠀⠈⠁⠒⠂⠤⠤⠤⠴⠛⠛⠋⠉⠒⠒⠒⠒⠉⠀⠈⠢⡀⠁⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠘⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⢁⠀⠀⢀⠀⠀⠀⠀⡀⠀⢐⠘⣆⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⢤⡀⢹⠇⢰⠀⡆⠰⡟⢀⣤⠖⠉
⠀⠀⠀⠀⢀⠀⣠⡀⠀⠀⠀⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣤⡗⠀⢀⠈⠁
⠀⠀⠀⠀⠀⠉⠛⠷⠆⠰⢾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠴⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠴⠶⠛⠳⠖⠄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⢰⠀⠊⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢂⠀⠀⠀⠀⠄⢀⠂⡰⠀⠀⠀⠀⠀⠀⢸⠋⠒⢢⠜⠁⠱⡄⠒⠉⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠐⢀⡀⠀⣤⠀⠠⠀⠀⡄⠀⢠⠐⢒⠆⠀⢖⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⢲
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢱⡀⣧⠀⢀⠀⢀⡇⣠⠃⣀⠀⠀⠀⠘⢆⠀⠀⠀⡇⠀⠀⠀⢨⠀⠀⠀⡠⠃
⠀⠀⠀⠈⠠⠀⠀⣀⣀⢀⣠⡀⠀⠴⠀⠀⠀⠀⠀⠀⠈⠢⣵⣜⣄⠀⢀⣘⣵⡧⠖⠁⠀⠀⠀⠀⠀⡀⠄⢠⣥⣀⠀⣀⣬⡄⠠
⠀⠀⠀⠀⠀⣀⠈⠉⠉⡈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠴⠔⠀⠀⠠⠋⠉⠉⠱⠀⠀⠀⠦⠄⠀⠀⠠⢾⣀⣀⠀⠌⠉⠀⠉⠁⠀⣀⣀⡵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⠀⠀⠀⠀⠀⢰⣿⡿⠛⢿⣿⣧⠀⠀⠀⠀⠀⣀⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⢸⣷⣌⠛⢁⣶⡄⠛⢋⣴⣷⠀⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⣿⣿⡟⢠⣿⣿⣿⣆⠹⣿⣿⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠇⢹⣿⢁⣿⣿⣿⣿⣿⡆⢻⣿⠠⠟⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦⣌⠛⢸⣦⣄⡋⢸⣿⣿⣿⣿⣿⣧⠘⣃⣤⣾⠸⢋⣴⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⢿⣿⣧⡈⢿⣿⣿⣿⡿⠃⣰⣿⡿⠃⣠⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡙⠿⣿⣿⣦⣙⠻⠿⠶⢌⣉⡁⠴⠾⠿⣋⣥⣾⣿⠿⠛⣡⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣷⡶⢈⣩⣩⣥⣦⢰⣿⣿⣿⣧⢠⣬⣍⣭⣉⠰⣶⣿⣿⣿⣿⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⣴⣿⣿⣿⠟⠁⢸⣿⣿⣿⡟⠈⠻⣿⣿⣿⣧⡀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠋⠁⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠉⠛⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡄⠀⣴⣷⣾⣦⡀⢠⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠋⢀⣾⠋⣿⣿⠙⣷⡀⠙⠋⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣤⡄⠀⠀⡼⣿⠢⣄⠀⢀⣾⢣⢰⣿⣿⣆⠜⣷⡀⠀⣠⡔⣿⢧⡀⠀⢀⣤⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⡙⠿⠋⠀⡼⠁⣿⣧⠋⢣⡼⡇⠐⣸⣿⣿⣧⠀⢸⢧⡴⡑⣰⣿⠈⢷⠀⠘⠿⠟⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⣿⠙⠦⠀⣸⡇⠉⡙⣌⣻⣾⣷⣿⣾⣿⣿⣿⣿⣷⣾⣮⣿⣿⣁⢟⡩⢘⣇⠀⡴⠋⣿⣿⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣼⣈⣿⢉⣿⡇⠀⣹⣿⣿⢥⣞⠋⣡⢫⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣟⢮⠙⣳⣤⣾⣿⣏⠀⢰⣿⡇⢻⣀⢷⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠁⣀⣗⣒⣧⡈⢻⣇⣾⠋⠈⣹⠋⢿⣿⣵⣿⡿⠋⣼⣿⣿⣿⣿⣦⡈⣿⣿⣮⣿⡿⠙⡏⠂⠙⣷⣈⡿⢁⣸⣓⣸⣀⡀⠛⠃
⠀⠀⠀⠰⣦⢀⣀⠀⢰⣿⠛⠋⡏⣽⣿⣟⢧⣀⠀⢀⡇⣸⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣇⢠⠁⠀⣀⡼⣻⣿⣯⠹⠉⠛⣿⡇⠀⣀⡠⢰⠆
⠀⠀⠀⠀⠸⡆⢠⡕⢾⣏⣦⣠⢠⣿⣿⣘⣷⡝⢦⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣇⡴⢋⣾⣋⣿⣿⡄⠆⢾⣹⡷⢪⡅⢠⡏
⠀⠀⠀⠀⠀⣷⠀⣤⣬⣿⣿⡷⣯⡟⣿⡷⢛⣿⡆⢿⣽⣿⣿⣧⣾⣿⣿⡟⣿⢹⡟⣿⢹⣿⣿⣿⣼⣿⣿⣧⡿⢡⣿⡛⠷⣿⢛⣝⢾⣶⣿⣧⣤⠀⣼⠁
⠀⠀⠀⠀⠀⡼⡆⠘⣿⣿⡿⠻⣮⣽⣿⢒⣿⡞⢿⣼⣟⣿⠛⢿⣿⣿⢹⣷⣿⢸⡇⣿⣶⡏⣿⣿⣿⠟⣿⣿⣧⡿⢹⣿⡒⣿⣿⣵⡞⢿⣯⣿⠇⢰⠟
⠀⠀⠀⠀⠀⢇⠹⡄⢿⣯⢤⣪⡕⣻⣿⣼⣿⣷⣯⣿⢿⣿⣷⣾⣿⣿⢸⢿⣿⢸⡇⣿⡯⣧⢹⣿⣿⣶⣿⣿⣿⣿⣾⣿⣷⣿⣟⢣⣵⡤⣽⣿⢠⡏⢸
⠀⠀⠀⠀⠀⠘⢆⠙⢿⣿⣯⢋⠜⡸⣿⣼⣿⣿⣿⣿⢸⣿⡏⢻⣿⣿⢸⠋⣿⣾⣧⣿⠙⡏⣼⣿⡿⢩⣿⡏⢸⣿⣿⣿⣿⣿⣇⠣⡙⣽⣿⡿⠋⣠⠃
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢧⠻⣯⠪⢏⣿⣿⣿⣿⣿⣿⡈⣿⡿⣾⣿⣿⣾⣷⡟⢿⣿⢻⣾⣷⣿⣿⣷⢿⣿⢃⣿⣿⣿⣿⣿⡿⡱⠗⣹⡟⣼⠧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠳⢾⣬⣽⣿⣿⣿⣿⣿⣾⣿⣦⣬⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣥⣴⣾⣷⣿⣿⣿⣿⣿⣯⣥⣵⠞⣫⡞⠁
⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠈⠓⣦⢤⣀⣈⠙⠿⢿⣿⣿⠭⠿⢷⣶⣬⣿⣿⣿⣿⣿⣿⣥⣶⡾⠿⠭⣽⣿⡿⠿⠋⢁⣀⣤⣴⠚⠁⠀⠀⢰⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣤⡋⢙⣦⡼⡿⢛⣿⠖⠛⢛⣻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⡛⠛⠲⣿⡛⠿⢧⣴⡋⣙⣦⡀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⣴⠋⢹⠀⢀⣧⡾⢁⡤⢊⣩⡴⣟⣽⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣯⣻⢦⣌⡑⠤⡈⢿⣼⡄⠀⡏⠙⣦⢝⡄
⠀⠀⠀⠀⢰⣦⠀⠀⢠⣋⣀⣺⠀⡎⢀⡞⣿⠔⢁⡘⠯⠑⢚⣉⣴⡟⡿⢿⣿⣿⣿⣿⣿⢿⢻⣧⣍⡓⠊⠭⢃⡈⠂⣿⣱⡄⢹⡀⣛⣀⣙⡆⠀⠀⢴⣦
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠉⠉⠉⠉⠉⠉⠉⠁⠳⡟⠻⠋⠛⢻⣧⢻⢸⣿⣿⣿⣿⡇⡼⣼⡟⢛⠉⠙⢛⠗⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⢳⠢⢤⣼⣿⣯⠻⣏⢿⣿⣻⠟⣱⣿⣧⡤⠔⡲⠁⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠑⠂⠨⣿⠹⣧⡺⣼⢧⠟⣸⠟⣼⠇⠴⠊⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠹⣇⢸⡿⢦⣴⣿⡏⢠⡟⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠹⣆⠻⣿⣿⠟⣠⠟⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⢿⣿⠐⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠂⡴⠂⠀⠳⣄⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠈⠁⣠⠞⠀⠀⠀⢀⠈⢦⡀⡉⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠉⠲⣴⢃⡆⠀⢀⣄⠀⠀⢎⢳⡴⠊⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⢀⠏⠀⠀⠀⣿⣾⠀⢠⡞⡜⣦⠀⢸⣾⡇⠀⠀⠈⢦⠸⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠈⢁⡞⠀⠀⠸⠀⢿⡟⣠⠎⠁⠄⠙⢦⡘⣿⠇⠘⠀⠀⠘⣆⠉⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠻⣾⢁⠀⠀⠁⡁⣈⡿⠃⠀⠀⠀⠀⠀⠻⣏⡀⡀⠀⠀⢂⢹⡾⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣿⣼⡄⡀⣠⣾⠋⠀⠀⠀⠀⠄⠀⠀⠀⠈⢻⣧⡀⡘⣬⢸⡇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡐⠘⢿⡟⠀⢻⡿⠁⠀⠐⠀⢀⣀⡅⡀⠀⠐⠀⠀⠹⣿⠃⠘⣿⠏⠀⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠁⠀⡇⣿⣾⠁⠀⠀⢷⣀⠘⠀⠀⣀⣾⢹⣆⠀⠀⠈⢀⣰⠃⠀⠀⢹⣾⡇⡇⠀⢻⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡆⠇⣷⢸⡇⠀⠀⠀⡀⠻⣄⠀⢐⣾⡇⡆⣿⣆⠄⢀⡼⠃⡀⠀⠀⠀⣿⢰⡇⡆⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢨⣍⠻⣆⣻⣿⠀⢠⠢⠀⠘⣄⠙⢿⣾⣿⡟⠐⣿⣿⣾⠟⢁⡔⠀⠠⢠⠀⢸⣿⣃⡼⢋⣭⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⠁⠉⠻⣿⠀⠠⡀⠳⠀⠈⢷⣤⣸⠋⠀⠀⠀⠻⣠⣴⠏⠀⠠⠃⣨⠀⢸⠿⠋⠁⠸⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⠀⣣⠀⠁⠐⣄⢻⠀⠀⠇⢀⠱⠂⠀⡿⠁⠀⠀⠀⠀⠀⠹⡇⠀⠲⢁⠀⠇⠀⣸⢃⡔⠀⠁⢠⡃⢀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⡀⠀⠀⠘⣿⣇⠈⢚⠀⠀⠀⢺⠇⠄⠀⠀⠂⠀⠀⠄⢿⠊⠀⠈⢰⠂⢀⣿⡟⠀⠈⠀⣼⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠋⠁⠰⠾⠷⡄⠀⠠⠘⢿⡄⠰⠂⠀⣧⣿⢀⠀⠐⢀⣁⠘⠀⢀⢸⣧⡇⢀⠶⠀⣼⠟⠀⠀⢀⣴⠿⠶⠀⠉⠛⠳⢤⡀
⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠐⠀⠀⠀⠙⠶⣄⣀⠀⠙⢆⠀⣆⠀⣿⣿⡌⠀⠀⠁⠀⠀⣼⣾⡇⢀⡞⢀⠞⠁⢀⣀⣤⠞⠁⠀⡀⠀⠀⠀⡀⠀⠉⢢⡀
⠀⠀⠀⢀⠞⠁⠀⠀⠈⠁⠀⠈⠀⠉⠈⠁⠐⣨⠿⠛⠓⠛⠓⣬⣣⠙⣿⡅⠚⢠⣦⠘⠀⣽⡟⢡⣯⡔⠛⠳⠛⠻⣯⡐⠀⠈⠈⠁⠀⠁⠀⠉⠀⠀⠀⠙⢆
⠀⠀⠀⠊⠠⠞⠛⠛⠶⣤⡀⠀⢠⣄⡀⡀⠚⠁⡄⠂⠀⢀⣠⣴⠿⠷⢮⣿⣾⣿⣯⣿⣾⣯⠶⢟⢷⣤⣁⠀⠀⠂⠀⠙⠂⠀⣀⣤⠄⠀⣠⣴⠞⠛⠓⠦⣌⠂
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣬⡟⠁⠀⠂⠀⢀⣴⡿⠋⠀⣡⡾⢛⡿⠉⠔⠛⢈⠻⣿⠻⣮⡂⠈⠻⣷⣄⠂⠀⠂⠀⠘⣯⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠏⠀⠀⠀⠀⢀⡾⣿⠁⠀⣰⡟⣇⠈⡇⠊⢰⡷⠈⠂⡇⢀⡟⣷⡁⠀⢹⣿⣆⠀⠀⠂⡀⠈⢿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠁⠀⠐⠀⠒⠀⣸⢿⠇⠀⡄⣿⡄⠽⡀⠘⣆⠀⠀⢀⡞⠀⡰⠅⣼⡇⡄⠐⢻⣿⡀⠐⠂⠈⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⢐⡀⠅⠐⠀⢐⣡⡿⠄⠀⠀⡀⢿⡝⣄⠈⠀⠈⠷⠰⠇⠀⠈⢀⡞⣽⠇⣀⠀⠀⠿⣿⣙⠀⠠⠀⠁⣀⠈⠑⢦⣄⡀
⠀⠀⠀⠀⠈⠛⠻⠷⢤⣤⣤⣤⣤⡴⠶⠾⠟⣻⠃⠀⠀⠈⢀⣈⣿⣄⡀⢄⠀⠀⠀⠀⢀⡄⣨⣼⣏⣀⠈⠀⠀⠀⢻⡛⠿⠶⠶⣤⣤⣤⣤⣤⠤⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⢈⣠⣴⠿⠟⠋⠉⠛⠶⣤⡀⢀⣠⡴⠞⠉⠉⠛⠿⢷⣤⣈⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠁


⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⢀⣤⣾⣿⣷⣄⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣄⡀⠀⢠⣿⣿⣿⣿⡿⣡⣾⣿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⠀⠀⢀⣠⣶⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⢸⣿⣿⣿⡟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⡇⣶⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠘⣿⣿⣿⣿⣿⢸⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⢇⣿⣿⣿⣿⡿⠁⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡘⢿⣿⣿⣿⣆⢿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡟⣼⣿⣿⣿⡟⢁⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡘⠿⣿⣿⣦⣝⠻⣿⣿⣦⠻⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⢏⣼⣿⡿⢟⣩⣾⣿⣿⠿⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣶⣦⣤⣶⣤⣭⣛⠷⡝⢦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡼⠡⠞⣋⣥⣴⣦⣥⣴⣶⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣕⢙⢿⣿⣿⣿⣿⣿⡿⡃⣨⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⢀⡀⠀⠀⢀⣴⣦
⠀⠀⢠⣀⡀⠀⠀⣰⣿⣿⣿⢄⣴⣿⣿⣷⣄⣾⣿⣿⣧⠀⠀⠀⣀⣄
⠀⠀⢸⣿⣿⣶⡄⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣮⢿⣿⣿⣆⣴⣿⣿⡿
⠀⣦⡈⢿⣿⣿⣇⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⢻⣿⣿⣿⠃⣴⠆
⡀⢿⣿⣦⣛⢿⣿⣞⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢫⣿⣿⢟⣵⣾⡿⢀
⢸⣷⣾⣭⣭⣧⣬⣟⡯⠳⠹⣿⣿⣿⣿⣿⣿⡟⠜⢱⣛⣭⣤⣭⣭⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⡘⢿⣿⣿⣿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠻⡿⠑⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⠀⠀⠀⠀⠀⠀⢀⠶⣄
⠀⠀⠀⣀⡀⠀⠀⢠⠏⠀⠀⢀⡴⠋⠙⠢⣀⠀⠀⠙⣆⠀⠀⢀⣀⡀
⠀⠀⠀⡏⠀⠀⠀⡼⠀⠀⢠⠏⠀⠀⠀⠀⠘⢆⠀⠀⢹⠀⠀⠀⢸⡇
⠀⢰⡆⠹⡄⠀⠀⢹⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⡄⠀⣸⠀⠀⢀⡞⠀⡆
⢀⡸⣇⠀⠈⠢⠀⠈⠂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠁⠀⡠⠊⠀⣸⢇⡄
⠀⢿⡀⠀⠀⠀⠀⠐⠀⠠⢀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠉⠲⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠴⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣾⣦⠀⠀⣾⠋⠉⠀⠀⣼⠏⠀⠀⠐⠚⠀⠀⡰⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠸⣿⡟⡇⢸⡇⠀⠀⠀⣼⡟⠀⠀⠂⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⠀⠀⠀⠋⠏⠀⠸⡇⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡠⠤⠒⡿⠃
⠀⠀⠀⠀⢿⡶⢤⣄⠀⠀⠀⢻⣟⠛⢦⠀⢠⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⣀⠀⡖
⠀⠀⠀⠀⠈⠣⡸⣿⣷⣦⣀⠀⠋⠀⠀⠀⠀⢃⠀⠀⠀⠀⠦⠡⠀⠦⠀⠀⠀⠀⠀⣀⠄⠈⠀⠀⠀⡏⠜
⠀⠀⠀⠀⠀⠀⠈⠹⡟⠉⠙⣷⣦⡀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡰⠋⠀⠀⠀⠀⢜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢿⡇⣄⠀⠀⠀⢨⣷⣴⣿⣷⣾⣷⢰⣶⣄⢠⡿⠁⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠖⢦⠀⠀⢻⣿⡟⢿⡏⠻⣧⣿⣿⡘⣀⣾⠀⠀⠀⢀⣯⢀⣴⣤⣶⣶⣶⣶⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠙⢿⣿⣶⣦⣤⣤⡀⠀⠀⠀⢹⣼⣾⣦⣀⣾⣿⠀⠀⡇⠀⢹⣯⠛⢩⣼⡏⠀⣠⠴⢋⣴⣿⣿⡿⣿⣿⣻⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡇⠀⠀⠀⠈⠙⣿⣿⡿⢻⣻⣆⠀⡇⢀⡿⠃⢀⣾⣯⠀⣊⣤⣾⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠢⠤⠤⠀⠈⠻⠿⠶⠶⣾⣿⣿⣿⣷⣶⣿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣍⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡐⠁⠢⣀⠤⡄⠀⠀⠀⠀⠠⠄⡀⠄⠈⢂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡌⠡⠀⢠⠃⣼⠛⣆⠦⢀⠁⣠⣄⠈⡀⠤⣰⠋⣧⠈⡆⠀⠌⢡⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⢇⠀⠀⢸⣼⠃⠀⠹⡀⢀⡶⠁⠘⢶⡀⢀⠏⠀⠘⣧⡆⠀⠀⡸⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⢸⠀⠐⣼⠏⠚⠤⡀⢱⠏⠀⠀⠀⠀⢹⡞⢀⠴⠒⠹⣧⠀⠀⡇⠀⠀⢄
⠀⠀⠀⠀⠀⠀⣠⠤⣀⠀⠀⠀⠀⣟⠳⢄⠘⣆⢠⡇⠀⠀⠀⠈⠺⡇⠀⠀⠀⠀⢸⠗⠁⠀⠀⠀⢸⡄⢰⠅⣠⠞⣻⠀⠀⠀⠀⣀⠤⣄
⠀⠀⠀⠀⠀⠀⠰⣄⠀⠉⠒⠤⣀⠸⡀⠀⠑⢽⣼⡇⠀⠀⠀⠀⠀⠱⡄⠠⠄⢠⠏⠀⠀⠀⠀⠀⢸⣧⡯⠊⠀⢀⠇⣀⠤⠒⠉⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠲⡢⠀⠀⠈⠙⢷⡄⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⢻⣀⣄⡏⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢠⡾⠋⠁⠀⠀⢐⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣌⠂⢀⡀⠹⣄⠀⠀⠈⣿⣌⠀⠀⣀⡴⠞⢉⡉⠳⢦⣀⠀⠀⣠⣿⠁⠀⠀⣠⠏⢀⡠⠐⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢌⡒⢌⣻⣆⡀⠈⢻⣤⠊⠁⠤⠀⠈⠁⠀⠤⡈⠑⣤⡟⠃⢀⣠⣞⡡⣒⣡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣶⣤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣤⣶⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠙⠦⣀⣀⠤⠒⠊⠉⠉⠉⠙⠷⣤⣄⣠⣄⣀⣤⠾⠋⠉⠉⠉⠑⠒⠤⢄⣀⠴⠋⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡈⠙⠳⢤⣀⡀⠀⠀⢀⣠⡴⠟⠁⠈⠳⢦⣄⡀⠀⠀⠀⣀⡴⠞⠋⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠚⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠒⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣀⣀⠈⠠⡀⠀⢤⣤
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠄⠀⠀⠀⠀⠀⠀⠠⠔⢲⡶⢉⠁⠀⡑⡴⠁⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢶⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠌⠲⠶⠦⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⣀⣀⠀⢀⡞⠁⠀⣀⡤⠔⠂⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠿⠻⠛⠉⠁⢀⣌⣉⣀⡀⠀⠀⠐⠉
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠲⠀⠀⠀⠀⠀⠀⠀⢀⠏⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠔⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠢⠤⠀⠀⠀⠐⠻⣷⣤⣀⠀⢀⡀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠤⠀⠀⠊⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠃⠻⡄⠀⡀⠀⠀⠀⣴⢿
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⡘⠀⢷⠊⠀⠀⠀⠈⢇⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠙⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡷⠈⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠈⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡺⡛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠀⠈⠀⡸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⢀⡇⠀⢙⠈⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⠀⠀⠀⠀⢄⡇
⠀⠀⠀⠀⢠⠐⠁⠀⠀⠀⠀⠀⠀⡏⠐⠈⡆⠀⠀⢀⣴⣯⣦⣿⠋⠉⠍⠉⠉⡉⠙⠒⣦⡀⢀⡼⠀⠀⠀⠀⠀⣰⣸⡁⠀⠉⠀⠀⠀⠂⣀
⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⢁⠀⠜⠉⠀⣿⠈⠁⠀⠀⠠⠄⠀⠀⠴⢿⠻⣟⢾⡃⠀⠀⠀⠀⢰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠡
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢾⠀⠀⠀⢹⠈⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠘⡆⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀
⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢻⣆⡀⠀⠈⠌⠀⠘⠔⠀⠀⠂⠀⠀⠀⠀⠀⠘⠀⢂⡠⠂⠀⠀⠀⠀⠠⠤⠤⠤⢤⣀⣀⣀⡠
⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠈⠉⠋⠓⠋⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⢠⠞⠀⠀⠠⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⣀⣐⣀⣀⡠⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠢⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⠐⡀⢀⡀⡀⠀⠒⠒⠁⠉⠉⠑⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⠉⠓⢲⡶⠶⠦⠄⠾⠒⠄⠒⠿⡂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠀⢐⠒⡒⠀⠉⠂⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡶⠾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠉⠙⠛⠓⠲⠶⠶⠒⠒⠒⠚⠉⠋⠉⠀⠀⠀⠙⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠲⢆⠄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠳⢬⣤⣄⢀⠔⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⡴⢣⠀⠀⢀⡤⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠢⡑⢄⢰⠁⠀⢳⣶⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠑⢄⠀⠀⠳⠦⣀⢿⠁⠀⠙⢄⢻⠀⠀⢸⠃⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⢈⣧⠀⡄⠀⠈⢻⠀⠀⠀⠈⢾⠀⠀⡎⠀⠀⠀⠀⠸⡀⠀⠀⢀⡠⠖⡩⠊⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⠈⠑⠳⠤⣀⢸⠀⠀⠀⠀⠀⢣⠀⡇⠀⠀⠀⠀⠀⡇⢀⠴⠋⢀⠞⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⢧⡇⠀⢀⡠⠔⠚⠉⠉⢱⡤⠋⠀⡼⠁
⠀⠀⠀⠀⠀⠰⡤⢤⣤⡤⢄⣀⡀⠘⣇⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠘⣧⠔⠉⠀⠀⠀⠀⠀⡼⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠲⢄⡈⠑⠻⣆⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢠⣃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⠢⢄⡈⢢⡀⠀⠀⠀⠀⠀⢸⠀⠀⡎⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀⠈⠑⠳⢄⡀⠀⠀⠀⠀⢧⣠⠇⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠛⢒⡤⠤⣤⡴⡟⡤⠤⢤⡤⠒⠻⠤⣀⣀⣀⣀⣀⣀⣤⢴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠲⠶⢖⣒⣒⣒⣒⣉⣉⠥⠔⣪⠋⠀⡇⡇⠀⠀⠙⢗⡒⠠⠤⠄⠒⠒⠋⢉⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⡇⡇⠀⠀⠀⠀⠉⠓⠒⠂⠐⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠉⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠐⣦⢀⠀⠀⠀⡇⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⡈⢯⠀⠞⠀⣴⠁⣾⠀⣠⠞⢁⣴⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣄⡄⢷⢨⣧⣾⠾⢿⣶⣿⣶⣷⣴⡏⢀⣸⣷⠴⠟⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⠳⡆⠙⢿⣷⡈⠏⢻⣿⠋⢳⣿⣿⣷⣿⣿⠟⠀⡛⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠲⣄⡙⢿⣿⣄⠀⠈⠳⣦⠀⠁⠀⠀⢻⡟⠁⠈⠋⠀⣰⣇⠄⣠⢂⠆⠒⠲⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠉⣳⣯⣿⣷⣤⣀⡈⢦⡀⠀⠀⠈⠁⠄⠀⠀⠈⣟⣥⡞⣡⣾⣷⠄⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣛⣦⣭⡷⠖⠛⠛⠛⢟⠀⠉⠛⠓⠦⣄⡴⠊⠀⠀⠀⢠⣿⣫⠾⠿⢿⣷⣶⣋⠁
⠀⠀⠀⠀⣀⣀⡠⠬⠽⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣺⣶⣤⣀⣀⢀⣈⣹⣦⣤⣤⣶⣿⣯⣤⣤⣀⠀⠈⠙⠿⣿⣿⣿⡦⠤
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣥⣄⣀⡀⠀⠀⠀⢀⣀⣀⣾⣿⣿⢿⢿⠿⠙⠿⣿⢿⣭⣙⣛⣛⣛⣭⣤⡴⠾⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠭⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠈⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣛⣛⠒
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡈⠉⠛⠿⠷⣅⢀⠀⠀⢀⣴⣿⡿⠿⢏⣀⡀⠀⠒⠚⠛⣛⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠐⠻⠻⢛⣗⣚⣻⣿⣒⣒⣒⣒⣒⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠂⠀⠀⠒⠲⠭⠥⠭⠍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⣀⣤⠤⠤⠶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠄⡈⠓⢄⠀⠀⡀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣇⠀⠈⠢⣠⠇⠀⠀⠟⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⡤⣑⢦⣸⣷⣦⣀⣀⣦⠎⢻⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠚⠇⠘⠛⢬⣯⠈⢿⣿⠇⠘⢿⡟⠁⠀⢠⢀⣤⠌⠀⠀⠀⠀⠀⠀⢠⣀⠀⠴⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠘⠀⠀⣹⠀⠀⠘⠀⠀⢠⣾⠟⠃⠀⠀⠀⠀⠀⢀⡖⢸⢃⠀⠀⠴⠛
⠀⠀⠀⣀⣀⣀⢡⡀⠈⠀⠁⠀⠠⣧⣃⡟⠀⢀⣄⣠⡶⠏⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠏⠰⠀⠐⣯
⠀⠠⠟⡉⠉⠉⠉⠉⠓⠐⠢⠤⣤⣤⣼⠷⠶⣿⠷⠤⠤⡀⠀⠠⠴⠂⠀⠀⠀⠀⣻⣴⢣⡆⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠂⠄⢂⡤⢦⡴⠎⠁⠀⠀⠐⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢾⣷⣶⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣀⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⢨⠋⠀⠀⠀⡀⠂⠀⠀⠀⠀⠄⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣴⠃⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠚⠀⠖⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣴⠀⠀⠀⠃⠀⠀⠀⢀⠀⢢⠀⡀⠂⢀⡤⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠇⠀⠀⠀⠀⠀⠀⠀⠐⠩⡶⢿⣷⣱⣶⣴⠦⠀⠀⠚⠂⠀⠀⠀⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⡄⠂⠀⠀⠀⠘⠁⠶⠺⢧⠩⡭⣝⠀⠠⠀⠐⠖⠶⠤⢄⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠃⠃⠀⠐⢤⠀⠀⢀⣒⠐⠂⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢸⠀⠀⠀⠻⣟⠣⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠄⠀⠀⠀⠈⠙⠲⢴⣶⣆⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢁⠀⠀⠰⢂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⠉⠉⠋⠚⠛⠲⠤⠬⠦⠤⠵⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠠⡇⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡘⠃⠀⠀⠀⣰⡏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣁⣀⣀⣀⣀⣠⣆⣀⣀⣀⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠄⠱⢠⡤⢄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⣠⣄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠇⢰⡄⠃⠀⣠⠖⢢⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡶⣼⠙⢟⠇⠺⠘⣌⠋⡇⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡹⣠⠀⠈⠀⠀⠎⠀⠘⢡⢾⡄
⠀⠀⠀⠀⠀⠀⠀⣤⢹⣘⠀⠈⡄⠀⠃⠀⣰⠋⠁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⠛⠀⠈⠀⠐⠀⠀⠀⠀⣈⠝⠁
⠀⠀⠀⠀⠘⢯⡉⠛⠄⠉⠀⠀⠀⠀⢀⠀⢀⣠⢆⡀⢠⢆⡤⠶⠆⠀⢤⡄⠀⠀⠐⠢⢄⣤⡄⠀⠀⠀⠉⠉⠉⠒
⠀⠀⠀⠀⠀⠀⠙⠓⠀⣴⡀⠠⠀⢀⡐⠀⠘⣏⠻⡅⢣⡂⠁⠀⠀⠀⠃⠈⡴⠋⢆⣠⠎⠈⠷⣀⠈⠛⢛⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢟⣀⣠⠴⠘⡟⠂⠐⢧⠀⠀⠀⠃⠀⠀⡄⠀⠀⡶⠀⢀⣾⠋⠀⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢰⣮⣳⣼⣦⣀⡁⠀⠀⠀⡄⣀⣴⣿⣡⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠙⠮⣀⣀⣀⣀⣴⣶⣬⣄⣄⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢸⠧⣀⡾⠓⣌⠉⠁⠀⣿⠀⢀⡾⢱⢦⢀⡴⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠓⠓⠙⠃⠈⡃⠀⢸⡆⠺⡂⢸⠀⣼⠁⠘⠀⠛⠁⠀⠞⠫⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⠓⠀⠠⠀⠀⠀⠙⠀⣼⠷⠃⠇⠀⢶⠃⠀⢆⣧⡄⠈⠀⠀⡔⠈⠁⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠠⡈⠓⠀⠀⠀⠀⠀⠁⠀⠀⡠⠊⠀⠀⡾⡆⠀⢨⡉⠳⠈⠀⠘⠀⠐⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠢⣄⣘⠄⠀⣴⣶⠞⠋⠻⢦⡀⢸⡇⠹⣄⠀⠉⢒⣶⡄⠔⠀⠐⠒⠶⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⡽⠋⢁⣠⠾⠃⠘⢧⡀⠀⠀⠉⢻⠦⣤⣙⣦⣠⣞⣀⠷⣄⣹⣗⣒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠀⠀⠀⠀⠀⠙⢦⡀⠀⢸⠀⠀⠀⢨⠿⢤⡀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣼⡆⠀⠀⡟⠀⠀⠙⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠓⠦⣧⣄⣀⣀⡀⣀⣈⣉⠠⠶⠶⠮⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢱⡄⠈⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠙⠒⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡾⡿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⡀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⣠⣾⢟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣽⠀⠂⠀⠀⢠⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠇⠀⡀⠀⣴⡿⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠎⢀⠀⡀⣠⡎⠀⠀⠀⠀⠀⠀⣠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⣾⣧⠀⠀⠀⠀⠀⠀⣤⣠⠿⠐⠸⠿⢦⣆⡀⡄⠀⠀⠀⠀⣠⠦⠂⢀⣬⡞⣿⠏⠀⠀⠀⠀⠀⢀⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⢿⠛⢷⣤⡀⠰⣘⣶⠋⠀⠀⠉⠀⠀⠠⠈⢳⡄⡀⠀⣠⣼⠏⠀⢀⣾⢯⣾⠇⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠐⠝⢿⡖⣼⣇⠁⠄⠈⡀⠀⠀⠁⢠⣼⣽⡥⠞⠋⠀⠀⢀⣾⣷⡿⠃⠀⠀⠀⠀⢀⡾⠋
⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣇⠄⢀⡠⠤⢽⣽⣯⣷⣦⢤⣤⣤⣠⣴⣾⡷⠁⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⣀⡴⠋
⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠩⣢⡆⠀⠄⠀⢿⢿⡿⡟⠛⠙⠷⠻⣷⣿⡄⡀⠀⠀⠀⣠⡾⠟⠁⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠉⢶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⣧⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⢁⠀⠤⠤⠒⠋⠁⠀⠀⠤
⠀⠀⠀⠈⠢⣀⡙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠙⠲⢽⣻⣶⣤⣤⣄⣀⣀⣀⣀⣠⣤⠷⠦⢀⢀⠀⠀⠀⠀⠀⡤⠚⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢶⣶⣶⣶⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠁⠈⢉⣿⠀⠀⠀⠉⠫⣅⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠖⠊
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⠶⣾⠿⣿⠟⡫⠽⠯⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⣠⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⣶⣴⠏⠉⠈⢿⡄⢀⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⠀⠻⢻⠃⠀⠀⠀⢨⡷⠿⠋⢹⣿⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠀⠀⠈⢁⡀⢸⣷⠈⠀⠀⠀⢨⣿⠁⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢃⠀⢰⣿⡆⠈⢡⣯⣿⠀⠀⠀⠀⢸⠟⠀⠀⠀⠾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡄⡁⠀⠀⠀⠀⢸⣦⣠⣿⠻⣿⣆⢸⣇⣽⣇⣤⠀⠀⠀⠀⢀⠐⢀⣠⣄⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣦⣤⣄⡀⠀⠀⠘⠿⠁⠀⠻⡿⣿⠁⠀⠈⢿⡞⢁⡀⢀⡴⠞⠛⠛⠛⠷⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠛⠳⢄⠀⠀⢀⣄⣀⡘⠿⣷⣤⣴⣯⣾⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⡀⠀⠀⣿⢿⣿⠿⣶⣶⣿⣟⠛⠉⠙⠁⢀⣴⡄⠀⠠⠾⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠩⡀⠀⣄⡈⣉⠻⠿⣷⡖⠒⢈⣽⢋⣀⡤⠤⣤⣤⣤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣀⠀⠀⠀⠁⠀⠾⠋⠁⠀⠀⠀⠉⢿⣟⣉⠉⠀⠀⡀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⠄⠀⢀⣠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠙⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡿⢿⣶⣶⣶⡾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠶⠀⠛⠉⠑⠀⠘⠷⠒⠰⡄⣤⠀⣸⣿⠁⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⣿⣿
⠀⠀⠀⠀⠀⢀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⣾⣿⡿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡏⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⢋⣈⠿⠃
⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡇⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⣼⡟⠋⠁
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢠⠤⣴⠒⠃⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠱⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣿⣇⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⣠⣼⣇⠀⠀⠀⠀⢰⣿⣋⣠⣬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠈⠀⠀⠈⠀⠀⠀⠀⠀⢿⡟⡋⠀⠁⠀⠀⠀⣿⠏⠁⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣇⣀⠂⠀⠀⠀⡤⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣻⠿⣛⣛⣋⣛⢻⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣻⣟⣛⣿⣿⣟⣛⣛⣛⣻⣟⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠎⠀⠀⠘⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣰⠀⠀⠀⢀⢹⡆⢀⡌⠀⠀⠀⠀⡳⠀⠀⣠⠞⠁⠀⢸⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢀⠀⠘⢿⡇⠀⢣⡎⠀⢀⣴⠃⠀⣾⡁⠀⢀⣠⡜⠀⢀⣔⠋⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⡀⢸⡇⢀⡘⣀⡀⢸⡿⢀⢴⡟⠀⢰⡿⠁⠀⢰⣿⡟⠀⣀⣄⡄⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⢰⣼⡄⣄⠀⣿⠀⣼⣷⣾⣿⡯⢿⣿⣷⣿⣷⣿⣈⣧⢰⣾⡇⠀⣀⣸⣿⣧⡾⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣈⠙⢿⣶⣤⡏⠺⣟⣿⣿⡀⠘⣷⠟⣿⣿⣿⠖⢦⣢⡶⣾⣿⣹⣿⢿⣯⣿⡷⠃⠈⣿⠏⠁⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠠⢀⣈⢻⣇⠀⠈⠛⠿⣷⡀⢸⠀⠘⣿⠟⠀⠀⠹⣶⣯⣿⡿⠿⢿⣿⡟⠁⠀⢀⡍⠀⠀⠀⢀⡄⠁⠀⢠⠋
⠀⠀⠀⠀⢀⡀⠀⠐⠐⠻⢦⣄⡀⠚⢽⣿⣿⣆⠀⠀⠀⠙⠷⡸⡆⠀⠈⠀⠀⠀⠀⠻⣿⠏⠀⠀⠈⠟⠀⠀⢀⣿⣃⡤⠀⢀⡞⣰⢗⡴⠿⠿⠶⠶⣄
⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠈⠛⠶⣤⣝⠻⣿⣷⣄⡀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠰⣾⣿⢋⣴⣴⠏⣰⣥⣋⣀⡀
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⣀⠀⡀⠀⣠⠿⢿⣾⣿⣿⣿⣶⢶⣤⣀⣙⣦⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣿⣷⣿⠟⣡⣾⣿⣿⣿⠗⠀⠀⣀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣭⣛⡻⠶⠚⠛⠛⠋⠛⢿⠁⠀⠈⠉⠙⠛⠳⢤⣀⠀⣼⡴⠃⠀⠀⠀⠀⠀⢀⣿⠟⣡⠾⠿⠿⣿⣿⣶⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣨⣧⡀⠀⠀⠀⠀⠀⠀⠉⠛⢯⣄⠀⠀⠀⠀⢀⣴⣿⡵⡛⢁⠊⠄⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢾⣿⡲⢶⣤⣄⣄⣀⣀⣠⣴⣿⣿⣶⣶⣿⣿⣿⣿⣷⣶⣭⣵⣶⣆⣀⢀⣀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠰⢋⠀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⣿⡗⣿⣿⢻⣿⠏⠸⣿⣿⣿⣿⡿⣿⣿⣛⣛⢛⠛⡛⠋⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠤⠤⠶⠶⠟⠛⠉⠁⠀⠀⣿⡏⠀⠏⠀⠉⠀⠘⠁⢘⣿⣿⠇⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢨⢯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡣⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⡲⠖⡴⠞⠁






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

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⡞⠻⣟⢛⡻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢟⡛⣻⠟⢳⡀
⠀⠀⠀⠀⣼⠁⠀⠈⢷⣽⣿⣿⣏⡻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣹⣿⣿⣿⡾⠁⠀⠀⣧
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠹⣧⢹⣿⣿⡷⣝⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣻⢾⣿⣿⡏⣵⠏⠀⠀⠀⠀⢸⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⡘⢷⡻⣿⣿⣶⣟⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡷⣿⣾⣿⣿⢟⡾⢃⠎⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠐⡈⢷⣸⣿⣿⢿⣿⣷⣯⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⣟⡿⣿⣿⣇⡾⠁⠂⠄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢣⠘⣿⢿⣟⣾⣿⣿⣿⣿⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣿⣿⣿⣷⣻⡿⣾⠃⡌⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠄⢃⢹⣆⣿⣿⣿⣿⣿⡧⡽⠚⢻⢖⣐⢖⣨⣆⣰⣁⡲⣊⠲⡟⠓⢭⢾⣿⣿⣿⣯⣿⣴⡏⡘⢠⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⡘⡈⡌⣿⢷⣿⠟⢹⠃⣶⣇⣾⡿⣼⣟⣾⠟⣰⣌⠻⣷⣻⣷⢿⣷⣸⣶⠘⡏⠻⣿⣾⣿⢡⢁⠃⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠰⠱⢹⣿⢊⣽⢺⣿⢸⣿⣻⣿⣱⡿⠿⢗⣴⣿⣿⢷⡙⠷⣿⣞⣿⣿⣿⡇⣿⡇⣯⡑⣿⡜⡆⠆⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢡⣣⢏⣵⢸⣿⢸⡟⢾⣓⣛⣭⠿⠶⠀⣿⣿⠟⠻⣿⣷⠀⠖⠯⣭⣛⣚⡷⢻⡇⣿⡇⣮⡹⡜⡜⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢺⡏⣼⣿⡟⣫⠴⣺⣿⣿⠛⢶⣫⣭⣗⢾⡇⣸⣇⢸⡷⣺⣭⣝⣶⢛⣿⣿⣟⠦⣽⢻⣿⣵⢹⡇⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⢱⣽⢏⡿⣱⣿⣿⣿⣿⡿⠿⠟⠿⣿⣷⣷⢸⡇⣾⣾⣿⠿⠛⠿⢿⣿⡿⣿⣿⣬⢷⡹⣯⡎⡟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢉⣻⣿⣾⣿⠧⠖⠚⠉⠉⠈⠀⠀⠀⠀⠙⢿⡞⢳⡿⠋⠀⠀⠀⠀⠀⠉⠋⠓⠶⠼⢿⣷⣿⣟⡙⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣠⣟⠡⠠⠒⠐⠀⠀⣀⣠⣤⣤⣀⣀⣀⣀⣬⣽⣿⣿⣯⣥⣀⣀⣀⣀⣤⣤⣄⣀⠀⠀⠀⠐⠀⢈⣻⣄⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣀⣤⣾⣿⣿⣿⣿⡟⣫⢿⣿⣫⣾⣿⢿⡿⣿⣷⣝⢿⡻⣽⢻⣿⣿⣿⣿⣶⣤⣀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⣿⣿⣿⣿⡿⣫⢟⣽⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣯⡳⣝⢿⣿⣿⣿⣿⢻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⡿⣱⢫⣾⠟⠋⠙⠛⠋⢹⣯⣽⡏⠛⠛⠋⠙⠻⣷⡹⣎⢿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣾⣿⣯⡿⣿⢱⢏⡞⠁⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠈⢳⡹⡄⣿⣿⣽⣿⣷⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣿⣷⣿⣿⡷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣹⣟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢾⣿⣿⣾⣿⣿⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣮⠻⣿⣯⢹⡟⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⢻⡏⣽⣿⠟⣽⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢿⣿⣷⣌⢡⠾⣀⡀⠀⠀⠀⢀⣀⠴⡋⢀⡾⢷⡀⢙⠦⣀⡀⠀⠀⠀⢀⣀⠷⡌⣡⣾⣿⡿⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣥⣉⣽⡿⣤⣃⠹⠉⠽⠉⠍⢀⣠⢴⡿⣣⣘⢿⡦⣄⡀⠉⠉⠭⠉⠏⣈⣤⠿⣯⣉⣬⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⠉⠉⠛⠒⠛⠛⢉⣵⠛⣵⡟⢻⣦⠛⣦⡉⠛⠛⠒⠛⠋⠉⠁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⠤⠶⣺⣭⣞⣣⣦⢡⡌⣴⣜⣷⣭⣗⠶⠤⠤⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣾⣯⣵⣻⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⠳⣦⡀⠀⠀⣼⡇⠀⣀⡀⠀⠀⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣿⡄⠁⠹⣷⠀⣼⠟⢷⣴⣿⡶⠀⢠⣾⣿⡧⡞
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣸⡟⣿⣧⢰⠀⣿⢶⡏⣀⠀⡹⣯⢿⣦⣾⣿⢿⣷⣿⡠⡆
⠀⠀⠀⠀⠀⢠⡀⠀⡟⣿⠕⣿⠘⢿⣧⡏⢈⡿⣁⢹⣷⢸⡄⢻⣿⡿⣻⣿⡿⠀⣧⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠸⠁⢠⣧⡟⢡⡇⠐⠀⢻⣳⣼⡧⢩⢿⣿⠋⢷⣼⡟⠀⣿⣟⣿⠀⠘⣦⠛⣽⡇
⠀⠀⠀⠀⢀⡇⠀⢸⣿⢂⣿⠀⠀⠀⠀⣧⠟⠀⠨⠀⢹⡆⠘⣿⢃⠀⢹⣿⢿⡇⠀⡿⢰⡟⠀⠀⣀⣠
⠀⠀⠀⠀⢸⡇⣼⢸⣏⢸⡇⠀⢰⠀⣰⠃⠀⢠⠃⠀⠈⡧⡄⣿⡟⠀⢸⣿⢿⡇⢠⣷⡿⠟⠛⠛⣹⡇
⠀⠀⠀⢀⠠⢿⣼⣿⣿⢺⣿⡐⣸⢰⣿⠀⢠⡇⢰⠃⢠⣇⢡⡿⢹⠁⣾⣟⡿⣠⣾⣥⣖⣉⣀⡴⠋
⠀⠀⠀⠐⢆⠠⢙⣿⣿⣯⣻⣿⣿⣿⣿⡀⢸⣧⣿⣱⣿⡷⢟⡴⣣⣾⣿⣏⣴⠿⠯⠭⠭⣉⣛⠷⣤⡀
⠀⠀⠀⢀⡴⠛⠉⠉⠉⣙⣻⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠯⠽⢯⣙⡓⢶⣤⡈⠉⠉⣙⣛⠒
⠀⠀⠰⣯⣤⠀⠂⣽⣽⠿⠛⡩⣽⣿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⣿⣯⡩⠲⣌⠐⠈⠛⣄⠘⣿⡏⠙⠛⠉
⠀⠀⠀⠈⠛⠿⢻⡿⠁⠀⢊⡾⠋⣰⢯⣿⡟⣼⠋⠊⠀⢳⡈⢿⣿⣿⣿⡄⠈⣷⣄⠀⠈⠳⡈⣷
⠀⠀⠀⠀⠀⠀⡾⠀⠀⢡⠞⣠⣾⡇⣿⣿⠀⣟⠀⠀⠀⣼⠃⣼⣿⣿⡿⣷⠀⠘⣿⢷⣄⡀⠘⠺⡆
⠀⠀⠀⠀⠀⣸⠃⣀⡴⣫⢜⣽⢿⡇⢹⣹⣆⠹⠀⢠⠞⠁⣰⡟⣿⣿⡇⣿⠀⢠⡟⠦⣝⣙⠋⠉⠉
⠀⠀⠀⢠⡾⠷⠿⠷⣮⡵⠟⠁⢸⣇⢸⣧⠹⡆⠀⡟⣰⠟⠹⡇⢹⣿⣿⣯⣰⠟⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡇⢰⠃⠀⣿⣿⡇⠀⠙⠆⠙⠻⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣼⡀⣴⢛⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⢸⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸
⠀⠀⠀⢀⣤⠳⠔⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡀
⠀⠀⠀⠀⠁⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⠀⠀⢀⣀⡀⢠⣀⡄⠀⠀⣴⣶⡶⠦⠀⠀⡀⢰⣦⠀⢰⣦⠀⣶⣤⣴⣶⣤⠀⡀
⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢾⡇⠀⣷⠈⠹⣿⠀⠀⢸⣉⡇⢠⣍⡇⠀⢀⡀⠠⢤⣤⣾⡿⡃⢹⠟⠀⢹⠟⠀⢿⠃⠈⢿⠃⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠬⠤⠤⠤⠡⠶⠥⠀⠠⠬⠭⠁⠬⠍⠡⠤⠀⠙⠒⠚⠛⠛⠛⠁⠰⠤⠦⠤⠤⠶⠦⠦⠴⠤⠦⠤⠉⠉
⠀⠀⠀⡶⠶⠶⠶⠶⠶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⢀⣠⢤⣄⠀⠐⡦⠤⠤⠀⠀⠄⢸⡆
⠀⠀⠀⣟⣛⣛⣛⣛⣛⣻⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⢸⣷⣼⣿⡀⠀⣿⣯⣭⣭⣿⣯⡼⡇
⠀⠀⠀⣿⠿⢿⠿⣯⢧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢀⣯⣭⣭⣭⣤⣤⣜⡃
⠀⠀⠀⠟⠒⢲⣛⣒⣒⣚⣀⠀⢀⣀⡀⣀⠀⣀⠀⠀⣷⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣴⠆⠀⣀⣀⣀⣀⣀⣀⣀⣀⠘⣿⣿⣿⣿⣿⠿⠿⡇
⠀⠀⠀⢰⡏⠙⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠛⠀⠀⡏⠁⠠⠄⠤⠤⠤⠤⠤⠠⠄⠄⠄⠉⠄⠀⠻⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⢸⡇
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠄⠃⠀⡇⠀⠀⠂⠐⠒⠒⠶⠀⠔⠀⠀⠂⠀⡇⠂⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⠀⢀⣤⣾⣿⡿⢿⣿⣿⣿⣶⣄⠀⠀⠀⡟⠃⣄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⣠⣴⣾⣻⣿⣿⣿⣿⣶⣄⠀⠀⢸⡇
⠀⠀⠀⠀⡷⣰⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣟⣷⡀⠀⡇⠀⣿⠖⢾⡇⠀⠁⠉⠉⠛⠀⠀⠀⠀⠀⢀⣾⣿⣾⣿⣿⣽⣿⣿⣯⣿⣾⣷⡄⢸⡇
⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⠀⡇⠀⡠⢠⡄⠀⠀⠀⠀⢤⠀⠄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⡂⢸⣿⣇⣀⣀⣾⣾⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⡇
⠀⠀⠀⠀⡿⣿⢿⡥⣞⣿⣵⣿⣿⣿⣿⣿⣿⣿⡟⠀⡇⠀⠳⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⢸⠀⠀⢿⣤⣿⣟⣿⣿⣿⣿⣿⡝⢟⣝⢿⣿⢹⡇
⠀⠀⠀⠀⣿⠘⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⡇⠀⠠⠄⠠⠠⠄⡀⠀⠠⠄⠠⠀⢸⠀⠀⠈⠻⣿⣿⣿⣿⣿⣯⣿⣾⣿⣶⡾⠃⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠉⠻⢿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⡇⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠈⠳⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢸⡇
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒⠒⠒⠓⠒⠓⠒⠒⠒⠶⢆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⡼⡇
⠀⠀⠀⠘⠚⠒⠒⠒⠂⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠘⠓⠀⠀⠐⠒⠒⠒⠂⠀⠀⠂⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⠂⢠⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠈⠁⠀⢀⠠⠀⠀⠴⠆⠈⠐⠀⢀⠘⠀⠀⠀⠖
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠠⠧⠀⠁⠀⠀⣐⡄⠀⢠⠄⢈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⡌⡀⠀⠀⢀⠀⠀⣂⡀
⠀⠀⠀⠀⠑⠀⠆⠀⠠⠀⡄⠚⠀⠀⠧⡀⠄⠁⠀⢀⠀⠂⠀⠀⠀⢀⡀⢀⠀⠌⠀⠀⠬⡆⠠⠀⢐⠀⠃⠀⠄⠆
⠀⠀⠀⠀⢉⠀⠬⠀⠐⠒⠒⢢⠀⠄⠉⠂⠀⣠⡁⠀⠤⠐⠈⢐⠀⠠⢄⡀⠁⣀⣆⠠⠀⠀⠀⠉⠙⠁⠁⠀⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠃⠀⢀⠤⢰⡀⠈⠀⠄⠀⢀⠬⠯⠠⠀⢢⠀⠈⠁⡋⠈⠁⣂⣀⠀⠀⠘⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠅⠂⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠈⠀⠀⠄⠠⠤⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⡕⠀⠀⡀⠀⢀⠀⠀⢀⠀⠀⠀⠉⡀⠀⠈⢲⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⠋⠉⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢀⣀⣀⣤⡤⠴⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠲⢤
⣶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠁⠀⠀⠀⠘⡇
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠆⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⢿
⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠂⠀⠉⠀⠀⠀⣠⠀⠀⠀⢻⠀⠀⠀⠀⠀⢀⡾⠿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠐⠂⠀⠀⠁⠀⠀⠀⢀⡀⠠⠄⠒⠚⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⢠⣤⠏⠀⠀⠀⠀⠀⠀⡠⠀⢠⡞
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣀⢀⠄⠀⠄⠐⠂⠀⠉⠀⠀⠀⢀⢠⠠⠀⠀⠉⠁⠀⠀⠀⢳⠀⣀⡿⡿⠀⠀⠀⠀⠀⢀⣼⠇⠔⣹⠃
⠀⠀⢷⠀⠀⠀⠀⠀⠀⠐⠒⠂⠈⠁⠀⠀⠀⠀⢀⠀⠀⠤⠄⠒⠀⠁⠀⠀⠀⢀⣀⠠⠔⠒⠀⠀⠀⠘⣶⣿⠁⠀⠀⠀⠀⠀⣠⠿⠃⣠⠞⠁
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠀⠀⠀⡀⠀⠠⠄⠐⠐⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢠⠀⠀⡐⠀⠈⠁⠀⢙⡟
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠒⠂⠉⠁⠀⠀⠀⠀⢀⡀⠤⠐⠒⠈⠁⠀⢀⣀⠀⣷⡀⡇⠿⣿⠀⡰⠁⠀⠀⢀⣠⢿⠇
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠠⠤⠐⠒⠈⠁⠀⠀⠀⠀⢀⡀⠤⠔⠒⠀⠈⠀⠀⡇⠹⣇⠀⡇⢠⠁⠀⢀⠔⡽⢣⠏
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠐⠒⠀⠉⠁⠀⠀⢀⡀⠀⠤⠀⠄⠀⠒⠈⠉⠀⠀⢀⣀⠠⠤⠖⠚⠉⡇⠀⠀⠀⢡⠃⠀⠀⠁⢀⣰⣯⣴
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠀⠉⠀⠀⠀⣀⣀⣴⢀⡇⢀⠀⠀⠎⠀⠀⠀⠀⠉⢁⡼⠁
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠒⠀⠈⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠂⠀⠀⠀⠀⡿⣿⠇⢸⠀⠈⠀⡴⢁⠀⠀⢠⠞
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠤⠀⠒⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠂⠉⡇⠉⢸⡞⢀⠀⣞⣴⠋⠀⣰⢋⡴
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠄⠀⠐⠒⠈⠉⠀⠀⠀⠀⣀⡀⠤⠄⢹⡀⠀⠃⠄⠼⠋⠁⠀⠀⢟⡿⠁
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠐⠂⠘⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠈⠳⡄⠸⠀⠀⠀⢀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠠⠤⠀⠐⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⣠⣿⢃⡖⠒⠋⠉⣧
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⠀⠀⠠⠤⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠉⠈⢸⣧⡜⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⡾⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠇⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠤⠤⠶⠖⠒⠒⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠶⠒⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣤⠤⠴⠖⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⣀⡀⠀⣠⠤⠒⠚⠛⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠠⠤⢄⡀⢸⡇⠀⠀⢨⠟⠀⢀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠤⠤⢶⡶
⠀⠀⠀⠀⣀⣀⣀⣀⡈⠉⠛⠳⠦⣄⠈⢻⠇⠀⠀⢺⠴⠚⠻⡄⡀⠀⠀⠀⠘⡠⠂⠀⠀⠀⠀⡘
⠐⠶⣿⡉⠀⠀⠀⠀⠉⠓⢦⣧⠀⠈⠑⢼⡆⢀⠖⠁⠀⠀⠀⢳⠹⠲⢄⠀⠀⠀⢀⠄⠀⠀⠀⡧⠀⠒⠒⠺⣿
⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⢹⠀⠀⠄⠚⠿⡆⠀⠀⠀⠀⠀⣸⠇⠀⠀⠳⠀⠠⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿
⠀⠀⠀⠈⣧⠙⢆⠀⠀⠀⠀⡾⠀⠸⠒⢒⠲⢭⡒⢤⡀⠀⣰⠃⠀⡠⠖⠒⠲⢦⡄⠀⠀⠀⠀⢁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡆⠈⠓⠤⣄⣀⡇⠀⠀⠀⢀⡄⠀⢳⠀⢹⣰⠁⡠⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡆⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠻⣄⡠⠴⠒⠀⣇⠀⠀⠀⢸⠁⠀⢸⠀⠀⡟⡜⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⠃⠀⢀⣠⣎⡀
⠀⠀⠀⠀⠀⡰⡫⠂⠀⠀⠀⠘⢦⣀⠀⢸⡀⠀⠸⡄⠀⠸⠀⠀⠀⠀⠀⠆⠀⠀⢄⣀⢀⡴⠧⠖⠚⠉⠀⠀⠈⢣⡀
⠀⠀⠀⠀⢰⠕⢔⢔⠁⡀⠀⠀⠀⠈⠛⠂⠳⡄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡇⣠⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⣷
⠀⠀⠀⠀⣿⣼⣿⣟⣭⡴⠶⠒⠓⠒⠒⠒⠦⠈⠉⠀⠀⠈⠠⠠⠠⠤⠴⠾⠋⠉⢳⣤⠤⡤⠤⠤⠤⠤⣤⣤⣝⣲⣿
⠀⠀⠀⠀⣿⠿⠛⠛⠒⠒⠒⠦⠤⠤⠤⠖⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠉⠒⠒⠒⠊⠉⠁⠀⠈⠙⢻
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡐⠀⢀⠀⠀⡀⠀⠀⠀⡈⠀⡐⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣙⢦⣻⣄⡀⣔⣴⣫⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣿⣿⡿⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣿⣿⣽⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣠⣤⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⣀⠔⠂⣡⣴⣶⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠞⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⡻⢾⣿⡟⢿⣿⡧⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣯⣷⡀⢻⡃⠐⢽⣽⣿⣽⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢠⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠸⣿⣿⣿⣿⣿⠇⣸⢣⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⣿⣿⣿⣟⣡⣴⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢐⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡆⠙⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣬⡙⠿⣿⣿⣿⣿⣿⣼⣷⣯⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣭⡉⠛⠻⣿⣿⣿⣶⣌⢿⣿⣿⣷⣦⣌⣉⡛⠛⠶⠭⠽⠽⠯⢛⣻⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⢿⣿⣛⠛⠀⠅⠀⠤⣙⣿⣿⣿⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣵⣷⣶⣤⣤⡄⠀⠀⠀⠨⡙⢿⣿⣿⡂⠹⠿⢿⣿⣿⣿⣿⡿⠿⢿⣻⠟⢻⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⣰⠂⣰⠀⠀⢄⢈⣿⣿⣧⠴⡀⠀⠀⠉⠉⠓⠒⠒⢉⣁⡄⠸⣿⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣭⣉⣉⡝⣰⠃⢠⠏⠀⠀⠀⠀⢹⣿⣿⣯⡇⢸⣶⣍⣧⣝⣻⣴⣿⣿⣽⣭⡀⣰⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢮⣍⣀⣀⡀⠉⠉⠁⢀⡟⠀⠻⢀⠀⢠⠈⣿⣿⣿⡿⢸⣿⣿⠘⠛⠉⠈⢸⣿⡇⢉⡁⠏⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉⠉⠙⠃⠀⡞⡏⠀⢸⣳⣿⣿⠟⢸⣿⣿⣿⡆⠀⢀⣀⡀⣿⣃⣘⣇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣾⣿⣿⠋⠀⣸⢟⡿⠛⠓⠚⠛⠋⠀⠈⠹⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠐⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣔⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠻⠿⠃⠀⠰⢤⠀⠀⠰⠿⠿⠋⠀⠠⠴
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠸⠟⠋⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠄⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠀⠈⠛⠻⠃
⠀⠀⠀⠀⢀⣴⣶⠆⠀⠀⠀⠈⠍⠁⠀⠀⠀⠀⠰⠿⠛⠃⠀⠀⠀⠀⠁⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠰⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢠⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣁⠀⠀⠀⠀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⡄⠀⠀⠈⠳⢼⣦⡄⠁⠐⠓⠾⣦⡖⡿⢴⣂⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠉⠉⠀⡀⠀⠀⢻⠋⠀⠀⠉⠀⠀⢸⠇⣴⡷⠂⠀⠔⣀⣠⠴⠤⠒⠀⢀⠀⠀⠔⣠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠿⠿⣶⠄⠀⠀⠛⠾⣷⣾⠛⠚⠙⢟⠈⢠⢄⣡⣄⢤⡤⠄⠀⢀⠤⠀⢤⣦⡤⢦
⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣄⢳⣄⡴⠒⠀⣀⣉⡙⠛⠃⢀⣡⣾⣵⣿⣿⠟⢉⣃⣀⣤⡠⠔⢚⡋⣀⣄⡤
⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠘⣿⣀⣤⠆⠀⠀⠀⠘⣿⣿⣿⣿⣿⠋⢠⣴⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⠎⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢀⠀⠀⠀⠀⢹⡅⠀⠀⠀⠀⢀⠙⠿⣿⠻⡝⠖⠊⠁⠈⠙⣿⡿⢿⡿⣿⣿⡟⢿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠁⠢⣶⣿⣷⠈⠿⢦⣄⣀⡧⣀⣀⣤⡴⠞⠁⠀⠐⠱⠀⠉⠑⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠠⠀⠀⠃⣠⣴⣿⠿⣦⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠝⢿⠛⣿⣿⣿⡆⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠐⠒⠋⠒⠛⠉⠁⠈⢈⣧⡀⠀⠀⠀⠸⣿⣿⣤⡀⠀⠌⢲⣽⣱⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠉⠛⠻⠟⣶⣤⡑⠡⣯⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡷⠀⠀⠀⠸⢶⣤⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⣿⠀⠀⠀⠀⠀⢘⡇⣿⣿⣧⣵⣼⣿⣿⣿⣿⢿⡗⠲⠗⠚⠛⠙⠛⠉⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⣾⠁⣀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⣴⣄⠀⠀⠉⠀⠸⠃⠀⠀⠀⠁⠀⠉⠉⠙⠻⠿⠿⠋⠉⠋⠀⠀⠁⠠⡀⠀⠀⠀⠐⡀⠈⠀⠲⣀⠐⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣤⢿⣶⣆⡈⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣷⣤⣤⣿⣶⣾⣧⣤⣾⣷⣶⣿⣿⠟⠛⠛⠛⠿⠿⠛⠻⢿⣦⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠰⠆⠀⠀⠈⠙⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠈⠀⠀⠀⠈⠙⣿⣆⠀⠀⠠⠰⣄⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢆⢠⣄⠠⠷⣴⠿⠹⢿⣋⢁⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣆⢀⣤⣽⣺⣶⣾⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣷⣱⡞⣷⣤⡀⠈⣿⣿⣿⣿⣿⣿⡿⣿⣶⣶⢦⣤⣿⣇⣤⣄⣠⣤⣀⣠⣄⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉⠉⠀⠉⠳⠲⠶⠆⠐⠒⠶⠶⠶⠒⠒⠾⠿⠛⠻⠶⠮⠉⠓⠷⠶⠶⠶⠶⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣤⡀⢀⣀⣀⣀⣀⣤⣤⣤⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠛⠜⠏⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⡿⣿⣿⡿⢟⡋⠤⠂
⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⢹⡄
⠀⠀⠀⢸⣿⣿⣿⠄⠀⠀⠀⠀⠀⢛⣛⣛⣛⡛⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⡀
⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠇⡀⠀⠀⠀⠀⠄⠀⠰⣏⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⢈⣷⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠠⢶⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠀⠀⢐⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠆⢿⣦⣤⡾⠄⠀⠀⠀⠀⣠⠂⠠⠀⠐⠁⠀⣀⣴⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣶⣌⡙⠿⣷⣷⣤⣄⣀⣀⣀⣀⡤⠤⠖⠛⠉⠉⠛⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣰⠿⣿⣿⣷⣦⣭⡛⠿⠅⠀⠀⢀⡄⠀⢀⣠⡀⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣠⡴⠋⢨⣿⣿⣿⣿⣿⠟⠀⠂⠀⡚⠿⣿⣷⣿⣿⣿⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⣰⣿⣿⣿⣿⣿⠋⠀⣸⠀⠀⢹⣿⣾⣿⣿⣿⠟⡃⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣶⣶⣿⣿⡿⣻⣿⣿⠁⠀⠄⠀⠀⠀⠈⣿⣿⡿⠟⠋⠀⡇⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠉⠉⠁⠚⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⣀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠒⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠘⢷⡶⠶⠖⠂
⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡷⠀⠀⠠⠀⠀⠀⠈⣧⠀⠀⡴
⠀⠘⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠖⠊⠀⠀⠀⠀⠀⠈⠀⡴⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢦⠰⠇
⠀⢀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣴⢆⢚⡝⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠘⠀⠀⠀⠀⠀⠀⢈⢠⢄⡆⣠⠤⠎⠐⠀⠉⠈⡀⠀⢠⠏⠀⠘⠀⠀⠀⠀⠀⠄⠀⠀⠠⣿⡿⠁⢸⣷⣀⠀⠀⠀⠀⢀⣶⣿⣧⡀
⠀⠀⢳⡀⠀⠀⠀⢀⡈⠉⠀⠀⢀⣀⠀⠀⣀⣀⣴⣷⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣵⣿⠇⠀⠘⢿⣿⣶⣦⣴⣶⣿⣿⠿⠟⠁
⠀⢀⣤⣿⣄⣤⣔⣮⣍⣀⣠⣤⣴⣿⡿⠿⠟⠛⠋⠉⢹⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡏
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⣄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣶⣠⠄⣠⣦⣨⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⡀⠀⠡⠀⠀⠁⠀⠈⠀⠀⠆⠀⠰⠀⢀⠆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⡀⠀⢀⢖⣭⣇⡴⣉⢑⣄⣸⠢⡀⠄⠀⠀⠁⠀⠀⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠢⢀⠀⠑⠀⣰⢶⡀⠀⡰⡳⠋⡾⡩⢴⠹⣅⢰⠮⡣⣽⡄⡠⠛⣇⠀⠀⢀⠔⠁⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠑⠠⡀⠀⠑⠀⢠⢹⡆⢳⣠⢇⠇⠀⣵⡵⠋⠙⣍⢳⠄⢼⣮⣿⡁⢀⢿⠀⠀⠀⠀⠠⠊⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠁⠒⠤⠀⠀⣄⡀⠀⢸⠀⡇⠀⢻⣜⠒⣸⠋⠀⠀⠀⠈⢻⡀⢠⡞⡷⡆⣼⣾⡠⠔⠊⢧⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠇⠈⢩⡲⡇⠸⠀⢾⡿⢀⡇⠀⠀⢠⠀⡀⠀⢳⡠⣧⡿⣶⡿⠵⡶⡔⠀⢸⠀⢀⠠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⢸⡈⠛⠦⠧⣘⢳⢺⡇⠀⠐⢣⢰⣁⣲⡈⣧⠟⠋⠉⢀⢀⣏⡁⠀⡟⠀⠀⣀⠠⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣤⡀⢳⠀⠀⠀⠀⠉⠲⢽⡈⠐⣯⡜⡰⢹⡞⠁⠀⠀⡀⠀⡟⡠⣷⣾⣁⣀⡀
⠀⠀⠀⠀⠉⠰⣟⡉⠀⠀⠀⠈⠉⠱⠳⡀⠀⠐⢴⡄⠀⠙⢾⣼⣟⠥⣎⡀⠠⡸⢶⣏⣽⡟⠍⠀⠉⠀⠀⢈⣩⠵⠆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢶⡒⠶⠤⣄⡀⠀⠝⡦⢄⣚⢗⡩⠔⠚⠓⠉⠐⠀⠉⢩⡉⣳⢺⠔⠉⠀⠀⢀⡠⣪⠟⠁
⠀⠀⠀⠀⠀⠒⠀⠂⠀⠈⠓⠶⠦⢬⣍⣹⣿⠿⠟⠻⠷⣄⠀⠀⢀⡀⠦⠜⢋⣼⣿⣯⡭⠴⣖⣾⡧⠞⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠠⠀⠐⠀⠁⠀⠀⠀⣀⣠⠖⣧⡀⣀⠀⠘⠛⣻⡶⣶⢶⣶⣹⠺⡗⣚⠭⢽⢯⣉⣁⡀⠀⠀⠀⠈⠀⠒⠂⠤
⠀⠀⠀⠀⠀⠀⡀⠀⢤⣴⠒⠚⠉⠉⠀⠀⣪⢶⡬⣕⠮⢽⣋⠘⠉⠇⠻⠗⣶⣶⣾⣓⣫⡉⠀⠁⠉⠑⣢⡀⠁⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠧⠭⠟⠛⠉⠀⠀⠀⠀⠻⣭⣶⣦⣴⠿⠋⠀⠉⠙⠚⠭⠿⠿⠭⠽⠋⠁⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠂⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀⠀⠀⣧⣼⠉⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⢀⠊⠀⠐⠀⠀⠀⠈⠀⠀⣿⢾⠀⠀⠀⠀⠀⠀⠁⡀⠈⠢⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡔⠀⢠⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⢂⠀⠡⠀⠈⢆⠀⠀⢄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠃⠀⡘⠀⠀⠄⢿⢸⠀⠀⠀⠈⡀⠀⠃⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⢸⢸⠀⠸⠀⠀⠠⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠳⡀⣠⡜⢳⡾⣇⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢳⠏⢤⣋⠼⠛⠑⢟⣧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⢶⣲⣾⢙⡏⢷⢳⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡃⠀⠀⠸⠁⠀⢁⠐⠈⢁⡼⢛⣆
⠀⠀⠀⠀⠀⠀⠀⡖⢾⡹⣯⠀⠡⡍⠀⢃⠘⠳⠁⣿⡤⠞⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣳⡳⠀⢠⠀⠀⡜⠀⠀⠆⢠⡏⣼⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠄⣧⡀⠀⠀⠄⠀⠀⠀⠀⡠⠉⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠉⠉⠠⠀⠀⠀⠁⠀⠀⢀⠀⣀⡴⠋
⠀⠀⠀⠀⠻⣍⡉⠛⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⠀⠤⣤⡼⢿⣛⡷⠆⣤⠀⠀⠀⠈⠐⠤⢤⣤⡄⠀⠀⠀⠀⠉⠀⠈⠉⢛⡶
⠀⠀⠀⠀⠀⠈⠙⠄⣀⡀⠀⠀⢁⠀⠀⠀⡀⠀⠚⢻⠒⢾⡁⠆⡔⠛⠀⠀⠈⠁⠀⠁⢣⣠⠞⢀⠀⢠⠞⠀⢧⡀⠀⠹⡖⠒⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠰⢦⠬⠞⠋⠀⢀⣽⣿⠶⣦⡤⣿⡆⠈⠇⠈⢷⠀⠀⠲⠀⠀⠀⠀⡠⠃⠀⢸⣶⠋⠀⠀⠀⠙⠒⠶⠿⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠚⠋⠁⠸⡆⠀⢀⡘⢯⡠⢀⡀⠀⣀⠀⠀⠂⠀⠀⠀⠁⠀⣤⡾⢁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⣿⢦⣽⡾⡵⠤⣥⠀⠀⠀⠀⠀⠀⠴⠿⠿⡷⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠈⠳⠤⣐⣀⣀⣤⣀⠴⣶⠤⣀⣀⣀⣠⠥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣧⣀⢀⣟⠢⣌⠉⠉⠀⠀⣿⠀⠀⢠⡟⢰⢄⠀⢀⡤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⣾⡕⠟⠪⠇⠉⢻⡇⠑⢹⡆⠀⣤⠀⢸⠀⢀⡾⠀⢸⠌⢷⠛⣠⢏⣧⠖⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⠀⠀⠀⠘⠀⠀⠸⡇⠀⣵⠇⣰⢹⠀⠸⣇⣼⠁⢀⡈⡆⠈⠀⠿⠈⠁⠀⡉⡿⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⣆⠀⠀⠓⢄⣆⠀⣀⡇⠀⠟⠋⠁⡜⠀⠀⢻⡇⠀⠈⠣⢘⡔⠀⣀⠀⢠⠎⠀⠀⠖⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠑⠺⠄⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠊⠀⠀⢀⡿⢧⠀⠀⠁⡀⠈⠂⠀⠀⠙⠀⠀⠁⠐⠁⠼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⢀⠄⠀⢠⣶⡖⠒⠉⠙⢦⣄⠀⢸⡇⠈⢧⡀⠀⠀⠐⢲⡦⠀⠀⠀⠀⠒⠀⠴⢂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣐⣒⠶⠊⠀⠀⡠⠎⠀⠳⣄⠀⠀⠀⠉⠛⢾⣧⣀⡈⢳⣄⢀⣴⠃⠈⣄⠀⠰⡒⠂⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠯⠤⠶⠒⠋⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⢺⠀⠉⠉⠉⢛⣿⡋⠉⠁⠀⠁⠒⠚⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⢸⡄⠀⠀⠀⣾⠁⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣧⣀⠀⢸⡇⠀⠀⠀⠀⠙⠳⢤⣄⠀⠀⠀⠀⠀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠉⠛⢺⣤⣤⣄⣀⣀⣀⣀⣀⣀⣨⡽⠶⠒⠛⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢷⡀⠀⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠈⠉⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠆⠀⠂⠀⠀⠂⠀⠐⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠃

⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣿⠇⡔⠀⠀⠀⠀⣷⡀⠀⠀⠀⠠⠀⠐⠒⠒⠒⣒⡀
⠀⠀⠀⡆⠀⠀⠀⠀⠀⢘⠇⢀⣠⠀⠀⠀⠀⠀⢠⠇⠀⠀⣼⡏⡼⠁⠀⠀⣠⡾⠋⣷⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠁
⠀⠀⢰⠇⠀⠀⠀⠀⠀⣆⡴⠛⢹⡇⢠⠀⠀⠀⠘⠀⠀⣼⣿⣸⠃⠀⢀⡴⠋⠀⢰⡧⠀⠀⢀⠠⠔⠋⠁
⠀⠀⣾⡀⠀⠀⠀⢠⣠⡞⠀⠀⠈⣷⡧⠀⠀⠀⠀⠀⢠⣿⣳⡟⠀⣠⡞⠁⠀⠀⣼⢃⡴⠊⠁⠀⠀⠀⣀⣤⡾⠃
⡄⠀⢿⠑⢄⡀⠀⠀⣿⠃⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣾⣿⣿⢃⡰⠋⠀⠀⢀⣼⠟⠉⠀⠀⠀⡤⠖⠉⠁
⠱⡀⠸⣷⣆⠙⢦⣀⢻⡀⠀⠀⠀⠀⠘⢧⣀⠀⡆⣼⣿⣿⣷⡿⢁⢀⡴⣣⠞⠁⠀⠄⠰⠊⠁⠀⣀⣤⣴
⡆⠐⡀⢣⠈⠻⠦⠙⢷⣿⡀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⡟⣴⣿⡾⢋⣡⠴⠚⠛⠛⠻⢶⣾⣿⣿⠟⠁⠀⠀⠀⡄
⠳⡀⠈⠀⢣⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⢀⢰⡀⢻⣿⣿⣿⣿⠿⡿⠋⠀⠀⠀⠀⠀⠀⠐⠉⠛⠛⠓⠒⠒⠀⢠
⢶⡁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠙⠿⣦⡀⢀⠸⣿⣧⡈⣿⣿⣿⢃⡾⠁
⠀⠻⣆⠀⠀⠀⠙⠆⠀⠀⠀⠀⠤⠈⠻⣄⠳⣿⣿⣷⣿⣿⠇⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠈⠓⠲⢤⣀⠢⠙⢦⣄⡀⠀⠌⡢⣌⢣⡘⣿⣿⣿⢏⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠳⣀⠈⠻⣍⠛⠶⣬⣽⣿⣿⣿⣿⣿⣿⣆⣀⣀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠬⠙⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⡑⠒⠒⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀
⠉⠉⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⢸⣿⡝⣿⣿⡅
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠿⠋⠟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⢰⣟⢿⠘⣿⣿⡀
⠀⠀⠀⠀⣴⣿⣿⡿⠿⠟⣿⣿⠃⠠⠀⠀⢰⢿⣿⣿⠟⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⢃⠘⣿⣧
⠀⠀⠀⡼⠛⠉⠁⢀⣴⣾⣿⠏⠀⠀⠀⢠⢏⣿⣿⣿⡆⠘⡼⣿⣿⣿⣷⡝⠝⠻⠿⠭⣷⣿⣿⣿⡆⠀⠀⠘⣿⣆
⠀⠀⠜⠀⠀⠀⣰⣿⣿⣿⠇⠀⠀⠀⢠⠏⣼⣿⢫⣿⣿⠀⢱⢹⡿⣿⣿⣿⢦⠀⠢⡀⠀⠈⠉⠙⠓⠀⠀⠀⢹⡏
⠀⠨⠀⣠⡖⢉⣾⣿⢻⡏⠀⠀⠀⢰⠏⣴⣫⠃⣸⣿⣿⡇⠀⡀⠈⠼⣿⣿⣌⠳⡀⠈⢄⠀⠀⠀⠀⠀⠀⠀⡀⣃
⠀⢀⠀⣼⡇⢨⡿⠁⢸⡇⠀⠀⣠⠃⡰⢣⠃⢠⡿⢻⣿⣿⠀⢑⡄⢣⢹⣿⡏⠀⢻⡄⠀⠱⣄⠀⠀⠀⠀⠀⠀⠘
⠀⢸⣿⡟⣿⢸⡇⠀⠈⣇⢠⡾⢃⡜⡰⠃⢀⡞⢀⢏⡽⣿⣄⣐⣷⢸⠈⢿⣇⠀⠀⢳⡀⠀⠘⢧⡀
⠀⢸⠏⣼⡇⠘⣧⠀⠀⣿⠋⣠⠂⡔⠀⠀⡞⢀⣾⢎⠓⢿⠏⠉⠙⢿⣅⣼⠹⣆⠀⠀⠳⡄⠀⠈⢧⢀⡀
⠀⢨⡼⠃⢱⣮⣿⡀⢠⣿⡗⣡⠊⠀⠀⡌⠀⣼⠈⠀⠀⠀⠀⠀⠀⢧⠟⠉⠈⠉⠙⠢⠀⠘⢆⠀⠈⣆⠉⠢
⠀⠈⠁⠀⣸⣽⠟⣥⣿⣿⡿⠁⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠈⢣⠀⠘⡄
⠀⠀⢀⡼⠋⠀⢠⣿⠟⢸⡇⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢹⡀
⠀⠀⠈⠀⠀⠀⢸⢋⡤⠞⡇⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢇
⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⡇⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡑⠀⠀⠀⠀⠀⢀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡯⠈⠀⢀⣀⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠶⠶⠶⢶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⣉⢸⠒⠇⣗⠸⣁⢸⢯⠀⣇⢸⠌⣣⠨⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠧⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣇⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡞⠋⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠧⠤⠤⠀⠀⠠⠤⠤⠄⠀⠠⠤⠤⠄⣾⣿⣿⣿⡛⠛⢻⣿⣿⡿⠃⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⢻⡿⠁⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣆⣠⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠛⠋⠉

⣿⠿⠿⠿⠿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣠⣶⣢⢤⡔⣒⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⣤⣦⣬⢭⣅⢥⣩⣿⣾⣾⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⣟⣟⣽⣿⣿⣿⣿⣯⣼⣿⣿⣿⣻⣿⣯⡽⣖
⠀⠀⠀⠀⠀⠀⠀⢀⡔⣱⣽⡿⢻⢿⡿⢻⣾⡟⣿⡟⣿⢿⣿⣿⣿⢿⣾⣟⢌⣝⣤⣤⣄⡀⢀⣀
⠀⠀⠀⠀⠀⠀⣴⢋⣴⣽⣯⣤⣟⣟⣿⣟⡿⢬⣷⣿⢏⠸⣾⠏⢻⣿⣿⣿⣿⢕⣢⣬⣭⣟⣻⢏⠓⣀
⠀⠀⠀⠀⠀⢀⣋⣾⣿⣿⣿⣿⡿⣽⠳⡈⠹⣄⢙⡿⣮⣼⢿⣿⣿⣏⣉⣍⣹⣟⠱⢚⢞⡩⣻⣽⠀⠈⠁
⠀⠀⠀⠀⠀⣬⢟⣿⣿⣿⣿⣿⢷⠳⢒⡦⡵⠾⢾⣇⠘⢿⣦⢞⢾⣿⣿⣿⣷⢍⣆⠤⠄⢋⡹⣞⡧⠄
⠀⠀⠀⠐⣺⣧⣿⣿⣿⣿⣿⣾⡎⢒⠋⢰⠈⡄⠀⠻⣷⣆⣻⣧⠘⡑⡿⡳⢞⣷⣟⣦⠢⣀⢚⣞⡇⠁
⠀⠀⠀⠠⠃⣿⢿⣿⣿⣿⣿⣯⣿⠀⠀⡆⣼⣟⠦⠀⠀⠙⢿⣿⡆⠊⢻⢃⣠⠽⢿⢿⣶⠈⠀⠉⠉
⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢯⠃⠰⡁⠀⠀⢈⣿⣿⣄⣾⣾⡁⠀⢸⢫⡿⡙⣦
⠀⠀⠀⠀⡼⢰⠎⣿⣿⣿⣿⣿⡯⠁⠀⠀⠈⠀⠀⠀⠀⣀⣾⣿⣿⠏⠀⠥⠈⡳⣌⠘⣷⡷⡈⠁
⠀⠀⠀⠀⠁⠀⠀⠙⠘⢿⣿⡫⠋⣆⠀⠀⠀⠁⠀⢠⣾⣿⣿⠟⠁⠀⠀⠁⠀⢠⠃⡭⢇⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⡀⣠⣿⣻⣿⣿⠀⠀⣄⡀⠀⠀⠃⠘⠀⢠⡌
⠀⠀⠀⢀⢀⠀⠀⣀⡀⡀⣑⠀⡄⠄⠐⢐⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⡶⢤⣀⣀⡡⠀⢀⠀⣠
⠀⠀⠰⠿⢿⣿⣿⣷⣤⣭⣭⣵⣶⣶⣿⣿⣭⣽⡟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣷⣦⣬⡿⢿⣿⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠐⠄⠀⠀⠈⠁⠒⠿⢶⣾⣴⣿⣷⡴⣿⠷⠶⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢉⡽⡯⣿⣿⡅⠀⠁⠀⠀⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠄⠀⠀⠀⠀⠀⠀⠰⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠙⠲⣄⡀⠀⠀⠀⠀⢀⡔⠁⣏⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣀⣀⣉⠳⣄⠀⡴⠋⠀⠀⢹⠀⣧⠢⡀⠀⠀⠀⠀⠀⣀⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠒⠤⣄⠀⣼⠃⠀⠀⢹⡄⠈⠙⡟⠶⣇⡀⠀⠀⢈⡿⠁⠀⢳⠀⢀⡤⠖⠋⢁⣾⠃
⠀⠀⠀⠀⠀⢰⣖⠢⠽⡆⠀⠀⠙⣿⠀⠀⠀⢸⡇⠀⠀⣷⠀⠀⠙⢦⣀⡾⠁⠀⠀⠘⣷⠋⠀⠀⢠⢯⡿⡇
⠀⠀⠀⠀⠀⠀⢻⣳⡀⢻⣠⡆⠙⠛⠳⢦⣄⡀⢿⡀⣠⠿⠤⠤⢤⣀⢻⠃⠀⠀⠀⠀⡇⠀⠀⣠⢃⡞⠀⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⢷⡙⣄⢹⡇⠀⠀⠀⠀⠈⠙⡶⠋⠀⠀⠀⠀⠀⠈⠹⣄⠀⠀⠀⢸⠇⠀⣴⢃⡾⠁⢀⣇⡤⣿
⠀⠀⠀⢠⠔⠚⠛⠛⠻⣮⣻⡇⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⡟⢀⡞⣡⣿⡥⠖⠛⠉⢠⠇
⠀⠀⠀⠈⢳⡶⣤⣀⠀⠈⠙⢻⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣼⣵⣿⠞⠋⠁⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠙⢆⡉⠛⢦⣀⣀⣿⠦⠤⣤⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡤⠾⣻⠟⠁⠀⠀⠀⠀⠀⣰⣏⣤⡴
⠀⠀⠀⠀⠀⢔⡒⠛⠒⠋⠉⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⣀⣀⣤⠞⠁⢀⣀⣼⠥⠠⢤⣀⣀⡀⣠⡾⠃⣠⠴⠁
⠀⠀⠀⢀⡴⠋⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠽⠛⠙⠷⠶⢾⡋⠉⠁⠀⠀⠀⠀⢀⣨⠽⠛⠈⠉⣁
⠀⠀⣠⠊⠀⠀⠀⠀⠀⠉⠓⢦⣤⣄⣠⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⢀⣿⠓⠲⢶⣶⣒⣋⡭⠖⠈⢙⡻⠟⠁
⠀⠰⣥⡴⠒⠊⠉⠉⠉⠉⠉⠉⢀⣠⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣿⣠⡴⠋⠈⠙⠓⠒⠒⠛⠉
⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠒⠋⠉⡼⠁⠹⣆⠀⠀⠀⠀⢀⣠⠖⣋⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋⠉⠙⠂⠠⠚⠩⠒⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⡀⠀⠀⣆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⢾⡇⠰⣀⠀⢀⡝⢀⡴⠋⠀⢸⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢿⠀⣦⠈⣇⢀⣃⡀⣾⢁⣼⠃⠠⡞⠁⢰⣾⠀⣀⣀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣄⣸⣧⣼⠸⣆⣾⣿⣿⣛⡿⣿⣿⣿⢼⣷⣿⣇⠤⣼⡿⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠿⡇⠙⠻⣿⣄⠙⠉⢿⡿⠉⠻⣿⣿⣿⣿⣿⡿⠁⠀⡏⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠛⢦⣈⠙⢿⣿⣄⠀⠀⠛⢖⡄⠈⠁⠀⠀⢻⡿⠁⠀⠹⠁⠀⣼⣁⠀⣠⠎⣔⠔⠓⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈⠛⣶⣽⣿⣷⣤⣀⡈⠳⣄⠀⠀⠀⠈⠃⡠⠀⠀⠀⢸⣟⣡⡾⢫⣾⣦⣤⠀⢀⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠳⣦⣔⣲⣦⠼⠿⠻⠟⣿⠋⠙⠛⠻⠦⣀⡀⣠⡔⠁⠀⠀⠀⢸⡿⣫⡴⢿⣿⣯⣥⣶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣐⣚⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠼⣦⡀⠀⠀⠀⠀⠙⠳⣄⡀⢀⣀⣴⣿⡞⣉⡀⠀⠀⠙⠻⢿⣷⣶⣶⣦⣀⣀
⠀⠀⠀⠀⠀⠛⠛⢒⣠⣤⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠚⠛⣻⣿⣷⣶⣶⣶⣿⡟⣿⣿⣿⣿⠿⠿⢿⣿⡿⠶⠆⢀⣠⣾⣿⠿⠛⠋⠁⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⣶⣶⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⡏⠛⠉⠉⠀⠏⠻⠇⣿⣿⣷⣶⣶⣶⣿⣿⣿⣍⣉
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠠⠬⠭⠭⠿⠟⠛⠛⠛⣛⣿⣿⣿⣿⡡⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⠿⡟⠓⣒⣒⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠶⠶⠀⠉⠙⢛⣳⣤⣤⡤⢀⣠⣾⡿⠟⠛⠓⠯⠤⠌⠀⠉⠉⠉⠠⠔⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢀⡀⠈⠛⠛⣛⣿⣿⣿⣿⣯⣭⣽⣯⣭⢭⣥⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣂⣀⡀⠐⠋⠭⠥⠼⠯⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⣀⣀⣤⣤⣴⣶⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⡿⢿⣿⣦⣀⣀⡠⠐⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢘⠀⠀⠀⠀⠀⠂⢹⣿⣿⠋⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢷⣾⣆⠀⠀⠀⠀⠀⠘⠟⣧⣤⣤⣀⣀⡀⠀⠀⠼⠛⠁⠈⠀⠉⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⠀⢸⣿⠛⠋⠁⠀⠀⠀⠀⠀⢠⡖⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⣠⣾⣀⣤⣴⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠖⠶⠶⠤⢄⣀⣀⣀⣀⣠⣄⠙⣶⣿⣿⣷⣤⣤⣀⣤⣤⣶⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⣤⣄⠁⠀⠀⠀⠀⣀⣀⣠⡬⠀⠈⠉⠙⠿⠿⠗⠘⠋⣡⠈⠩⣤⣾⣿⣿⡿⠓
⠀⠀⠀⠀⠀⢠⡆⣺⣠⣟⣼⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠈⠙⠛⢿⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠉⠉⢻⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣇⣤⣤⣴⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢀⣠⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⢻⣯
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠔⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⠀⠀⠀⠀⣠⣦⣄⠀⠀⠀⣠⡿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠈⠁⢀⣴⣿⣿⣿⣿⣷⣄⠀⠉⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠷⢦⡀⠀⣸⣿⠃⠀⠀⠀⣴⣿⣿⠟⠁⠀⠙⣿⣿⣷⡄⠀⠀⠀⢻⣿⠀⠀⢀⠴⠶⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⣿⡿⠃⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠈⣿⡆⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⢿⣇⠀⠀⠀⠀⣿⡇⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⢠⣿⠃⠀⠀⠀⢀⣿⠏⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡈⠻⣧⡀⠀⠀⠸⣧⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣼⡏⠀⠀⠀⣠⡾⠋⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠈⠻⠿⣿⣦⣈⠻⢦⣄⠀⠙⣧⡀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢀⣼⠏⠀⢀⡴⠞⣉⣤⣾⣿⠿⠋⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣦⣤⣤⣤⣤⣄⣈⣁⡀⠈⠳⡄⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢡⠞⠁⢀⣈⣁⣠⣤⣤⣤⣤⣴⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡌⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠹⡄⠀⠀⠀⠀⠀⠀⢠⠟⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢩⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⣦⡙⠂⠀⠀⠀⠀⠀⢉⡴⠿⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⣠⣿⡿⠃⢀
⠀⠀⠀⠀⠀⢰⣶⣟⠁⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠟⠀⠀⠀⢙⣷⡄
⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⡀⠀⠉⠛⠿⠶⣦⣤⣤⠄⠀⠀⠀⣀⣠⠴⠂⠀⡀⢠⠀⠙⠶⣤⣀⠀⠀⠀⠀⣀⣤⣤⡶⠿⠛⠉⠀⠀⣀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠀⠀⠀⣶⣶⣶⡶⠾⠛⠉⠀⠀⣠⣾⠃⢸⣷⣄⠀⠈⠙⠻⠷⣶⣶⣶⡶⠀⠀⠀⠚⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣤⣤⣴⣾⠟⠁⠀⠀⠙⢿⣷⣶⣶⣶⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠊⠀⠀⠙⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⠳⡴⠁⢀⡤⢤⡀⠈⢆⡠⠊⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠦⣄⠇⠀⠀⠀⠈⡶⠋⠀⠀⠙⢦⠎⠀⠀⠀⠈⡤⠤⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣀⣀⠀⠀⠡⠀⠀⠀⠀⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠲⢤⣀⠐⠀⡠⠊⠁⠈⠑⢄⠀⠃⠀⣀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⢠⠔⠒⠉⠀⠀⠀⠀⣀⣈⣙⡎⠀⠀⠀⠀⠀⠀⢡⠖⠋⠁⠀⠀⠇⠀⠁⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠄⠒⠚⠉⠉⠉⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⢠⠀⢀⠄⠀⠀⠀⠀⠠⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠒⠐⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡀⠀⠀⠀⢀⣳⡤⢤⠀⠀⠀⢀⡴⠚⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠉⠳⢄⠀⠀⠀⢰⡿⠋⠙⢶⣴⣶⡟⠁⠀⠀⣧⢀⠴⠃⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠙⢦⣠⣮⠞⠛⣷⣟⠁⣈⣻⣷⠛⢦⡿⠻⣷⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣰⢶⣴⡟⠁⢀⡞⣉⠉⠛⠉⣈⠙⢦⠘⣧⣴⣿⡄⠀⠀⠀⢰⠇
⠀⠀⠀⠀⣖⠒⠒⠒⠠⠀⠄⣀⣸⠀⠀⠀⠀⢢⡇⠈⣿⠀⣠⡿⠛⠹⣧⡴⠛⠉⢳⣠⠟⠀⢻⡏⣿⠀⠀⠀⡸
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠉⠙⠳⢶⣤⣿⠀⠀⠘⣿⠋⠀⠀⣴⠋⠀⠀⠀⠀⠛⠀⠀⠀⣿⢻⡀⠀⢰⠇⡠⠔⢸⣿⠠⠄⠒⠂⠀⠉⠁⠀⣢
⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠘⣷⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣁⣴⠿⠋⠀⢠⠂⣿⠁⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠑⢝⠦⡀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⣠⠋⣼⠇⠀⠀⠀⠀⠀⡀⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡲⢄⠀⠀⠀⣼⣿⣧⣤⡀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠿⠛⠙⣿⠀⢀⡜⢁⣼⠏⠀⠀⠀⢀⣤⠾⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢍⡢⢌⣻⡇⠀⠉⠛⠶⣤⣸⡆⠀⠀⠀⠀⠀⢠⣴⠟⠁⠀⠀⠀⣿⡷⠋⣠⡞⠁⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣊⣽⣆⠀⠀⠀⠀⠉⠛⠷⣧⣄⢰⣴⠟⠁⠀⠀⠀⠀⣰⣫⣴⣿⡿⢷⣖⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠊⠉⠁⠐⠒⠛⣷⣤⣀⠀⠀⠀⢀⣀⣻⣿⣁⣀⣀⢀⣀⣤⣶⡟⠛⠁⠉⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡿⢿⢿⠿⠟⠻⠻⢿⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⢅⣒⠀⠤⠤⠤⠤⠤⠤⢝⣿⣆⠀⠀⠀⠀⠀⠀⣀⠖⣹⠧⠀⣀⣀⣀⣀⣀⠀⠤⢄⡲⠽⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠹⢷⣄⡀⡠⠖⢋⡠⠊⠀⠉⠀⠐⠒⠒⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⠄⠔⠉





⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⢀⡾⠙⢆⣠⣠⡾⢻⡄⠀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣴⡞⠀⠑⣾⣧⣴⣾⡿⣿⡀⢀⡽⠊⢿⣶⡞⠉⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⣧⣿⣿⡀⠀⣘⣿⢻⡿⠇⠈⣿⣿⣴⣀⣸⣿⣷⣶⣾⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⢻⣿⣷⣠⡿⠁⠸⡁⠀⠀⠈⢿⣿⠟⠋⠉⠉⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⣀⣼⣧⡀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⣧⣿⣿⣿⡏⠀⠀⣄⣰⡾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⣿⣧⡄⡀⣀⣀⣻⣷⣄⡸⣿⣿⣿⣿⣿⣆⣠⣾⣿⠟⠁⠈⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠜⠛⣿⢿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠉⢉⣏⣀⣴⠃⢠⡟⢹⣿⡏⣿⣿⢻⣿⣻⡿⠽⠟⠿⠻⢦⣤⣤⣤⣿⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠒⠒⠒⠒⠊⠉⠁⠳⠴⠛⠙⠛⠈⠙⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿
⠀⠀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⣿⣿⣿⣿⡿⡏⠀⢀⣀⡀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⣿⡄⠈⣿⣯⠀⠀⣷⢰⣿⣿⣿⡄⠀⠘⠛⠛⡅⠀⠀⠀⠀⠀⠀⡀⢀⣾⠏
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠈⣠⣷⠀⢹⣿⣧⠀⢸⠈⣿⣿⣿⣇⠀⠀⠀⢸⠃⠀⠀⠀⠀⢀⠮⣵⣿⡟
⠀⠈⠑⢤⣴⣾⣿⣄⠀⠀⠀⠈⢶⡄⡀⠀⢹⣿⣧⠈⣿⣿⣧⢸⡇⢿⣿⣿⣿⠀⡀⣀⣸⠀⠀⠀⠀⣰⣿⣶⣿⡟
⠀⠀⠀⠀⠹⣿⣿⣿⣦⡀⠀⠀⠘⣿⣔⡄⠘⣽⣿⡆⠸⣽⣿⡇⣧⢸⣿⣿⣿⡄⡇⠀⢼⠀⠀⠀⣼⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⣀⡀⠘⣿⡝⡄⢹⣿⣿⡄⢻⣿⣷⣿⡈⣿⣿⣿⣇⡇⠀⣼⠀⢀⣾⣿⣿⣿⡟
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡄⢿⣿⣷⠘⣿⣿⣿⡇⢻⢻⣿⣿⡇⠀⣿⣴⠺⠿⢿⣿⡟
⠀⠀⣰⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣌⣿⠛⣇⢹⣿⣿⣷⢸⣼⣿⣿⠃⢾⣿⣿⣶⣦⣄⡉⠻⢦⣄
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡆⠸⡄⣿⣿⣿⡄⣇⣿⣿⠀⢸⣿⣿⣿⡿⢿⣿⣷⣦⣉⠳⣄
⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠻⣏⣿⣿⣿⣿⣿⣿⣿⣷⡀⢳⠸⣿⣿⣇⢹⢹⣿⠀⢸⡿⣿⣍⠀⠀⠉⠻⢿⣿⣷⣮⣧
⣿⣿⣿⣿⣿⡿⠟⠋⠀⣀⣴⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣇⢻⣿⣿⣼⣾⣿⣤⣿⣵⣿⣿⣿⣦⣄⠀⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣄⣠⣴⣾⠿⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢧⣼⣾⡿⠟⠛⠉⠉⢉⣛⡻⢿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣯⣅⡴⣾⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣡⣿⣿⣿⣮⡶⠶⠛⠛⠉⠉⠛⠶⣍⢿⣿⢧⡈⠉⠛⠛⠛⠋
⠈⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⡀⠀⠀⠈⢧⢳⡈⣷
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⠛⠋⠉⠉⠉⣿⣿⣿⠁⠀⠐⠀⠀⠀⠀⠙⠁⠀⠀⠀⠌⢾⡇⢹⡄
⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⠿⠋⠠⡀⢤⡉⡻⠲⠀⣿⣿⣿⠀⠘⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⡇
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠃⠀⠀⠀⠈⠓⠛⠷⣒⠒⣿⣿⣿⣧⡀⠐⠀⠈⠀⠀⠀⠀⠈⠀⢀⣼⣿⣱⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠀⠛⠒⢺⣿⠐⠦⣄⠀⠋⣸⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⣀⣠⣴⣿⣿⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣄⣀⡈⠉⣁⣀⣠⣴⣾⡿⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠗⠛⠉⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣄⣀⡀⢸⣧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣾⢷⣀⠈⠁⠙⠂⢿⣷⢸⣿⠀⣠⠾⢻⡿⠛⣽⣶⡶⣦⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠟⠿⢧⡈⠠⡀⠀⠀⠀⠠⡈⣿⣿⣿⡟⠁⠠⠋⢀⣼⠋⠁⣰⠟⠑⠶⡤
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠑⠀⠹⡄⠀⣄⠀⣿⣿⠋⠋⠀⠀⢠⡶⠋⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠁⢜⣦⣻⣷⣻⡇⠀⣄⠀⢠⠋⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠈⠻⡿⣿⣿⡆⣾⣿⣶⡥⠀⠀⠀⠀⠀⠀⡟⠀⠀⣀⣠⠴⠚⣋⠭⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣵⣄⠀⣠⠥⣼⡿⣯⣿⣿⡟⠀⠀⠀⠀⢀⠀⣰⢷⡻⠟⣩⠔⠈⠉⠀⠀⣀⣸⣿⣇
⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣶⡒⠾⣿⣶⣣⣷⣸⣹⣿⣿⣿⡧⠀⠀⢀⣐⣡⡶⠷⠋⣤⠞⠁⠀⠀⢀⠴⡾⠛⠉⢻⣹
⠀⠀⣰⠎⠈⠉⠀⠉⠉⠉⠉⠀⠀⠉⠀⠉⢿⣿⣼⡻⡿⣿⣧⣾⣾⡿⠛⠉⠀⡠⠊⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠟
⠀⣼⣷⡔⠊⠉⠀⠈⠁⠀⠀⢒⣢⣴⣔⣲⣤⣜⣿⣿⣧⣿⣿⢯⣾⣟⡃⠋⠺⣶⣾⢟⣀⠀⢀⡠⣡⠇
⢠⣿⣉⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣵⣶⠶⠐⠠⣍⣻⣛⣛⡥⠞⠃
⣏⡼⠋⠛⠡⣴⣤⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⢛⡿⣿⣿⡿⢿⣷⣶⣄⠀⠀⠈⠙⠋
⠋⠀⠀⠀⠀⠈⠉⣻⣷⠾⣟⣛⣿⣿⣿⣿⣿⣿⠁⠈⠀⠃⠈⠁⠀⠈⠙⠫⣷⣄⠀⠀⠙⣶
⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⡉⠀⠉⠀⠰⢋⠟⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡦⠀⠀⠘⡆
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠀⠀⠀⠀⠄⠁⠴⠻⠟⠉⠲⠦⣠⣄⠀⠀⠀⠀⠀⠀⠁⠢⠀⡀⠇
⠀⠀⠀⠀⠀⢱⣄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⣠⠁⢹
⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⡄⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⢀⠐⣼⣎⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠂⠀⠷⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠦⠿⠛⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡒⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡇⠀⢹⠀⢀⣠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠙⠣⡀⣸⠞⠁⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⣰⠯⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠁⠺⣄⠀⠀⢄⢸⠀⡰⠀⢀⣴⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠬⠷⠦⢬⡟⠙⣧⣊⣁⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠒⢊⡟⣾⠳⣄⠀⠀⠀⠀⠀⢀⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⠀⠀⠀⠀⣀⡞⠀⠈⠀⠈⡏⠓⠒⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠂⠠⠄⢀⠀⠈⠉⠉⣩⠟⠁⡇⠀⠀⠀⠀⣸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠁⠢⡀⢰⠃⠀⠀⡸⡀⠀⠀⢠⢷⠒⢤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠰⡏⠀⢀⠊⡔⠙⠦⠴⠃⢺⠀⠀⡷⠊⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠼⢿⡀⠀⠸⠀⠀⢁⡤⠒⠚⢢⡿⢵⡠⠴⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣂⠈⠉⠉⠁⠐⠀⢷⡄⢰⠀⠀⠉⠢⠤⢤⡜⠹⢻⣅⠂⠈⢳⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠻⣾⡀⠀⠀⠀⠀⣼⡅⠀⣸⠉⠉⣛⣉⣴⣿⠟⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠤⠤⠜⠋⠳⣄⠀⠀⢰⣇⠳⠚⠁⡴⠊⠀⠀⠀⠈⠻⣛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢸⢸⣧⢠⣾⡿⠋⠀⠀⠀⠀⠀⣟⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢿⠘⢿⣣⣤⡤⠀⠀⠀⠀⣀⠌⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠞⢛⠏⠐⠒⠀⡩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⣿⡃⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⠓⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢣⠀⠀⢠⣷⣌⣀⠠⠄⠀⠀⠀⢠⠰⣤⣤⡿⡿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⠀⠀⢠⣼⣧⣿⢳⣆⠀⠀⠀⠈⢰⣮⣿⣿⣇⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠉⠘⡂⠀⣶⠼⠿⠿⠀⠀⠀⠿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠆⠀⠀⣀⠀⠸⠯⣽⠇⠀⠀⣶⣷⣄⣀⡀⠀⠀⠀⠠⡄⠀⠆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣟⣻⣧⣒⡃⠀⣿⡆⠀⢠⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⡄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⡿⠿⠿⠀⠀⠀⠀⠿⠇⣾⠌⠻⠟⡙⣛⣿⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⢀⣄⡋⠋⣭⣠⣤⣼⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⠀⠀⣸⣿⣇⣀⠀⣸⣿⣿⠘⠉⣡⣴⣿⣽⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⡤⢾⠿⠿⠟⣋⣛⡋⠛⠋⠀⠀⣿⣿⣷⠙⢯⠈⠉⠹⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡵⡿⢀⢐⠂⠉⠸⠇⠀⠀⠂⡀⢟⠛⠛⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣴⣠⣤⣦⠀⠀⢠⣿⣿⡇⠄⠀⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠃⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣄⡀⢀⣴⣿⣿⣦⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠋⠹⣿⣆⣴⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⢿⡍⠛⢿⣿⡇⣤⡀⣿⣿⣿⣿⣿⣧⣠⣤⣤⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠘⣇⣤⡈⢿⣿⣿⣿⠏⠐⠣⣹⣿⣿⢷⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⡀⣿⣿⡄⣿⣿⣧⡈⣾⣿⣿⣠⠀⠀⢼⡿⠃⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡀⠀⠹⢿⣿⡿⠿⣿⣷⣿⡿⠿⢿⣿⣦⡮⢄⣤⣿⣿⣾⣷⣶⣾⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣷⣦⣄⡀⠈⢻⠁⠀⠙⣿⣿⣄⠃⣸⣿⣯⣶⡾⠿⢛⣉⣻⡫⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡉⠻⢦⡈⣴⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣉⣩⣤⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⣷⡶⠼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣡⣴⣿⠿⠛⢛⣋⣉⣉⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⠀⠙⣿⣿⣿⣿⠟⠉⠛⠿⣿⣵⣾⣿⣾⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣶⣄⠀⢉⡏⠁⠀⠀⣀⠐⢸⠟⠿⢿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣶⣴⣶⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⢶⣶⣦⣤⠤⣦⣤⣤⣀⣀⠀⢸⣿⠏⠹⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡛⢇⡀⠙⠣⢙⠂⠈⢆⢹⠗⠈⢻⢿⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⡆
⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠙⠂⠀⠀⠑⠄⠀⢼⠀⠀⠀⢸⣿⣿⠿⠛⣦⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣽⣿⣿⡇
⠀⠀⠀⠀⠀⡾⠋⠓⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠇⣿⣿⠀⠠⠟⣷⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⣿⡿
⠀⠀⠀⠀⠸⣿⠋⡀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⢠⡄⠀⣿⡿⠈⠁⠀⢹⣇⠀⠀⠀⠀⠀⠀⢹⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⢿⡟⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣡⣾⡾⠿⠓⢺⣿⡇⠀⠒⠒⠛⣋⢀⣀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠛⣶⣶⡶⠛⠛⠛⠉⠉⣀⠙⠛⢛⡛⣷⠄⢀⣸⣿⣇⣤⠐⠀⣌⢹⡙⠉⣨⣶⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣇⣰⡀⢀⣟⣁⣀⠀⢸⣧⠘⡀⠀⠀⠉⣉⣿⣧⡠⠘⠂⠙⣼⣿⣛⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠲⠚⠛⠚⠓⠚⠉⣿⣿⣟⡿⠟⢻⣖⢶⣿⠟⠭⠽⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣳⣾⣋⡠⢹⡟⠑⡄⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠻⢦⣦⣶⠴⠋

⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡿⠿⠿⠛⠛⠛⠻⢷⣦⣤⣀
⠀⢰⣿⠟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄
⠀⢸⣿⠀⠈⠻⢿⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀
⠀⢸⣿⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⡶⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿
⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⢸⣿⠃⠀⠀⠀⠀⣤⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠋⠁
⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢹⣿⣧⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠿⣦⣄⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣶⣶⣶⡿⠿⠿⠛⢻⣿⠇⠀⣴⣷⣶⣶⣦⣤⣤⣤⣤⣶⡾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣛⠛⠛⠛⠿⢿⣿⣶⣿⡿⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠁⣶⣆⣀⠀⠀⠀⣻⡇⠀⠀⢸⣿⣅
⠀⠀⠀⠀⣠⣾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣆⣼⡟⠀⠀⢰⡿⠻⢿⣷⣄
⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠙⢿⣆⡀⣰⡿⠁⠀⠀⠙⢿⣷⣄
⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠛⠛⠛⢿⣦⠀⠀⠹⣿⣏⡀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⣰⣿⠃⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⡀⠀⠀⠀⣿⡇⠀⢰⣶⡄⠈⣿⡇⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠈⢻⣿⡄
⣿⡿⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠙⣿⡆⠀⠀⢿⣇⡀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠹⣿⣄
⣿⡇⠀⠀⠀⠀⣾⡟⠀⠀⣾⣿⠀⠀⣿⣷⠀⠀⠈⠻⢿⣶⣶⣿⠟⠃⢠⣆⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠸⣿⣆
⣿⣧⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢷⡄⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠘⢿⣄
⢹⣿⠀⠀⠀⠀⠀⠙⠻⣷⣶⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠋⠀⠀⠈⠁⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠘⢿⣄
⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠷⣶⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣸⡏⠀⠉⢻⣿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣇⣀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⡀⠀⢻⣿⣿⡁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠋⢹⣧⡀⠀⠙⠻⢿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⣠⣿⠿⢿⣦⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢀⣿⡏⠀⠀⠙⠛⠻⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⣷⣦⡀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠁
⣶⣶⣤⣴⣶⣦⣤⣶⣶⣶⣶⣶⣦⣶⣶⣶⣤⣾⣿⣿⣿⣷⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣤⣤⣤⣤⣴⣶⣶⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣴⣦⣤⣤⣶⣶⣶⣦⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠄⠤⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠄⠁⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⣸⠀⢀⣀⡀⡀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡀⠀⠀⠠⠉⠀⠀⠀⢹⡇⢀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⣀⡀⠀⠀⠀⠀⠡⡀⠐⣄⠐⡀⠀⠀⠀⠀⣾⣧⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⣈⣀⡑⢦⡀⠀⠀⠈⠓⠬⣓⣿⣦⣀⣀⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠈⠀⠀⠀⠀⡀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⢯⠂⡀⢀⠀⠀⢈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⠠⠀⠀⠀⠀⠙⣦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣼⠊⠀⠀⠀⠉⠲⡄⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠀⣰⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⣩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⣗⣄⣀⠤⠞⠁⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⣀⡿⢦⣤⣤⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢠⡄⠀⠀⠀⠀⠀⠀⣧⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⡙⣦⠀⠀⠀⠀⠀⡆⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠉⣵⠀⠀⠀⢀⡇⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⣿⠰⡸⣤⠀⠀⠸⡠⠁⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⢀⡠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠳⡠⡇⠘⢦⠀⣸⠇⠀⠀⡰⠁⢹⠠⠚⠛⢋⡈⠥⠞⢫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠣⡀⠀⣇⢱⡆⠀⠁⠟⢀⠤⠐⠁⠀⠀⠀⠀⠀⠀⡔⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠠⡉⢪⠲⡈⢿⠁⡆⢠⠞⢁⡄⢊⡀⠀⠀⡈⠙⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠀⢱⡀⠓⠹⣾⡌⢀⡄⣴⢋⠼⠶⠈⠳⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠳⠀⠀⣿⠀⢸⡿⠛⠁⠀⠀⠀⠀⠀⣄⢀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠢⣀⢆⠙⠀⢸⠁⠀⠀⣀⣀⠄⠲⠎⠈⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡐⡜⣿⢠⢸⡎⠀⢀⠜⠀⠁⠀⠀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠣⡈⢿⣼⠘⠃⢠⠂⠀⠀⠀⢤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡤⠀⠉⠂⠀⠀⢤⠀⠈⠺⠙⡞⡧⠊⡀⠀⣀⣀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢋⣠⢀⡠⠤⠤⠤⣤⣰⣤⣙⠢⡀⠃⢠⣇⠀⢡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣨⠡⠔⠉⣅⡠⠖⠒⠶⠤⣌⣉⣳⣷⡈⣸⣿⠆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠰⢒⠒⠒⠒⠒⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡗⠀⠀⠀⠀⣿⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣠
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⢾⣿
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠙⢆⣀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⣹
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣾⠀⠀⠀⠀⠘⣧⣄⠤⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣿⣷⠶⠶⠾⠿⣿⡷⠆⠀⠀⠜⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠺⠟⠷⠀⠈⠄⠽⠅⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⡀⠤
⠀⠀⢸⠀⠀⠈⠈⠉⢹⡁⠁⠀⠁⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⣹⣭⣽⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢿⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢸⡇
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠿⢹⡇⠀⠐
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡇
⠀⠀⠨⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⣠⠖⠂⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠃⣶⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⢫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⢮⠀⠰⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡽⡇⠀⠀⠀⠀⠒⠀⠓⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠟⡋⣡⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣦⣤⡴⠂⠀⠀⢠⠷⢽⣷⠤⣄⠐⢛⣃⢽⡁⠀⠀⠀⠀⠀⠓⠀⢠⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡶⡖⠀⠀⠀⠈⠀⠌⠡⠀⠀⠀⠀⠁⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠦⠤⠤⠼⠦⠤⠀⠴⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡓⠘⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢀⠀⠀⠉⠓⠪⣹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠞⠳⡀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢀⡴⠋⡙⢦⡔⠁⠀⠀⠈⢢⡴⢋⠙⢦⡀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⡷⠋⡘⢰⢧⡞⠀⠀⠀⠀⠀⠀⢳⡼⡆⢃⠙⢾⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡜⠁⠀⠙⣴⡷⠃⠈⠳⣄⠀⢠⡄⠀⣠⠞⠁⠘⢾⣦⠋⠀⠈⢣⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠙⣾⢰⠀⠀⡴⠻⡇⠠⠀⠀⠈⢳⡞⢳⡞⠁⠀⠀⠄⢸⠏⢦⠀⠀⡆⣷⠋⢧
⠀⠀⠀⠀⠀⠀⠀⢰⢁⠀⠘⢾⢀⡜⠁⠀⢳⣸⠀⠀⡤⠋⠀⠀⠙⢤⠀⠀⣇⡜⠀⠈⢣⡀⡿⠃⠀⡌⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣈⠀⠀⠈⡿⠀⠆⠀⠀⢹⣠⠞⠀⠀⠀⠀⠀⠀⠳⣄⡏⠀⠀⠠⠀⢿⠁⠀⠀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⢿⢹⠀⠀⠀⡇⠀⡇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⠀⢸⠀⠀⠀⡏⡿
⢀⣠⣴⣒⣛⣋⣙⡻⣿⣧⠀⡔⣇⠀⢣⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡼⠀⣸⢢⠀⣼⣿⢟⣉⣙⣛⣒⣦⣄
⠈⠙⢦⡀⠀⠀⠀⠉⠉⠻⣷⣹⣿⣆⡘⣆⠀⠸⡄⠀⠀⠀⢰⡆⠀⠀⠀⢠⠇⠀⣰⢃⣰⣿⣏⣼⠟⠉⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠓⠒⠶⣶⠖⠋⠉⣉⠿⠛⠻⢾⣧⣤⣻⡶⠒⠚⠚⠓⠗⢒⣶⣟⣿⡿⠿⠟⠛⠿⣯⠭⣛⠳⣶⠶⠖⠚⠉
⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⠞⠁⠀⠀⠀⠀⢠⡏⠈⠁⠀⠌⢬⠌⠨⠈⠀⠀⢠⣄⠀⢀⠤⣂⣌⠻⣄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢸⢇⠔⠁⠀⠀⠀⢀⣠⠔⠁⢳⡀⠀⠀⠀⢺⡆⠀⠀⠀⢀⡞⠘⠳⣄⡈⠈⠐⠑⠘⠳⠸⡇
⠀⠀⠀⠀⠀⠀⠚⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠲⢤⡀⢸⡇⢀⡤⠖⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠈⢆⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⢠⡧⢦⣄⣀⡴⠒⢱⡀⣠⠖⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠒⢄⣼⠖⣶⣏⣉⣳⡖⢦⠷⣧⠀⠀⠀⡗
⠀⠀⠀⡀⢀⣀⠀⠀⢸⠀⠀⠀⣸⢻⡟⠁⣾⢥⡈⣡⠤⡑⡼⢲⣿⡄⠀⠀⡇
⠀⠀⠀⢣⡀⠀⠀⠀⠘⠲⢤⣴⡇⠀⢳⠟⠁⣸⠋⠀⠀⠻⠁⠀⢻⡧⠀⣸⢀⠄⣶⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠻⡄⡀⠀⠀⠀⠀⢸⡇⠀⠀⢷⡴⠁⠀⠀⠀⠀⠀⠀⣸⣯⡴⠋⠀⡔⡼⠁⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠈⠪⡢⠀⠀⠀⣸⣧⣀⠀⠘⡅⠀⠀⠀⠀⠀⢠⣴⠟⢿⠀⢀⠎⣴⠃⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠱⠠⢿⡀⠉⠓⠦⣥⣀⠀⠀⢀⡴⠋⠀⠀⢸⠗⣡⣞⣁⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠐⢻⣄⡀⠀⠀⠉⠳⣾⠋⠀⠀⢀⣠⡷⠟⠛⠉⠓⠠⣀
⠀⠀⠀⠀⠀⢔⠈⠀⠀⠀⠀⠀⠀⠈⠙⣻⠿⠿⠟⠻⠻⠿⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠈⠣⢆⡄⠀⢀⣀⠀⢀⡰⣿⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠳⣄⣀⠄⢂⠔⠉⠀⠐⠁⠀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⠋⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠙⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣶⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣶⣄⡀⠀⠀⠀⠀⢀⣠⣾⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄
⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠋⠉⠉⠀⠈⠉⠉⠛⠛⠋⠉⠁⠀⠉⠙⠛⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢠⣿⣿⡀
⠀⢀⣿⣿⠛⣷⣀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣠⡞⠙⣿⣷⡀
⠀⣼⣿⡇⠀⠀⠙⠻⠷⠟⠛⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠋⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⢀⣴⠟⠉⢉⣠⣴⣮⣽⣿⣦⡀⠀⠀⣀⣴⣿⣭⣷⣤⣄⠈⠉⠻⣦⡀⠀⠀⠀⠀⠀⢠⣿⣟
⠀⢰⣿⡟⠁⠀⠀⢽⡒⣶⣿⡏⠀⠐⠋⠿⠿⠿⠧⠀⢸⣿⠩⠟⣿⠁⢨⣿⡿⠿⠏⠑⠄⠀⣿⣿⡶⣒⡶⠀⠀⠈⢻⣿⡆
⠀⠸⣿⣧⣤⣄⣀⣺⣽⣿⡇⠹⣄⠀⠀⠀⠤⠦⠀⢀⣼⠃⠀⠀⠹⣆⠀⠀⠴⠴⠄⠀⠀⡰⠃⣿⣿⣉⣀⣠⣤⣤⣼⣿⠇
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣧⠀⠈⠳⠄⡀⠀⣠⠴⠞⠁⠀⠀⠀⠀⠙⠳⢤⣄⠀⣠⡴⠊⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⣇⣀⠀⠀⠀⠀⣀⡼⢦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⢿⣧⠀⠀⢠⣤⠶⠋⠀⠀⠉⠛⠶⠶⠛⠉⠀⠀⠙⠶⣤⣄⠀⠀⣾⡿⠻⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣾⣿⡀⠀⠀⠀⠀⡆⠀⠤⢤⣤⣶⣤⣤⡤⠤⠀⢰⠀⠀⠀⠀⢰⣿⣷⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⠛⢿⣷⣤⣀
⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣾⡿⠟⠋⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⠻⢿⣷⣦⣤⣀⣀⣀⡀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣴⣿⣿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣾⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣦⣄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠐⠳⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⢠⠦⣀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢠⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣈⠀⠀⠀⢄⠀⠀⠀⠉⡠⠞⢧⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠁⡈⡄⠀⠀⡠⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣤⠄⠤⠠⠀⠀⡇⠀⠀⢀⡀⡷⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠒⠀⠀⢀⣣⠀⡁⠀⠀⡹⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⠔⢚⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠑⢦⣤⣤⣤⢖⠃⠒⠋⠀⡀⠚⠢⠠⠄⡀⠀⠀⣀⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡭⠤⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠁⡤⠀⠀⠀⠀⠉⠉⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄
⠀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣶⣟⣉⣹⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣁⣀⠀⢠⣄⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⠿⠋⠉⣩⠿⢿⡿⠃⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠿⠟⠁
⠀⠀⠀⣿⣿⣿⣷⣶⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⣿⣿⠿⠂
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣤⠀⠀⠀⠀⠀⠀⢰⣿⣿⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⡀⢀⣿⣿⡿⠿⠻⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢀⣀⣤⣤⣾⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡿⠁⠁⠀⠀⠙⠛⢷⣮⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣦⠀⠀⠀⠀⠀⠱⡐⢤⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⣷⣥⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠐⠒⣦⣠⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠀⠀⠀⠀⠀⠀⢉⢉⣽⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠂⢀⠄⠀⠀⡀⠀⠈⢹⠁⠀⠀⣰⢩⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠂⠀⢀⠀⠀⠄⡆⠀⠀⠀⠄⣭⢠⡶⠋⠃⠠⡯⢼⡭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠂⣼⢞⣶⣷⠖⠀⢄⠊⠀⠰⠀⣠⣤⣀⡃⠀⠀⠲⢳⠚⡤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠊⠉⡙⠹⠙⢄⠙⠀⠀⠀⢀⠄⠀⠾⢿⠟⠀⠀⠀⠘⠉⠉⠀⠀⠀⣀⠀⡐⠇
⠀⠀⠀⠀⠀⠀⠰⠀⡂⠀⠠⠒⢀⠀⠁⠀⠀⠀⠈⠋⠀⡄⠐⠁⠀⠀⠀⡀⠀⣾⡀⠀⠀⠀⠀⠀⣈⠴⠖⠉
⠀⠀⠀⠀⠀⠀⠂⠈⠀⠄⠘⠄⣸⣀⣀⡀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⠶⠛⠂⠀⠰⡷⢀⡤⠟⠇⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠏⠀⡀⠤⠉⢴⣶
⠀⠀⠀⠀⠀⢀⡤⣦⠃⣾⡄⢀⠔⠀⣄⠃⡀⠀⠀⠀⢠⣾⣿⣿⣿⡀⠀⠀⡀⠐⠀⡬⠉⠀⠀⠈⠁⠀⠠⠄
⠀⠀⠀⠀⣼⣿⣧⣟⣳⢿⣼⠛⠁⢈⠣⠄⠀⠈⠀⠀⢹⣿⣿⣿⣿⡅⠀⠀⠀⢀⠠⠽⠀⣤⠖⠘⠢⣄⠀⠀⠤
⠀⠀⠀⠈⠻⣿⣮⢯⣿⣷⠿⠂⡀⠀⢀⠠⠀⠀⠀⠀⠠⠉⠟⠋⠃⠀⠀⠀⠀⠁⠀⠀⢘⡅⠀⠆⠀⡐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠈⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠘⠷⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣿⠋⡀⢦⠀⢁⡀⠀⠀⠀⠸⠀⠀⣒⠄⣼⠬⢀⡴⠂⣠⡤⠿⠀⢰⡀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣸⢿⠀⠀⢘⡥⢆⠂⣀⠮⡛⠧⡅⠀⠈⠂⠀⢠⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣭⢚⡰⣿⣗⣙⢶⢮⠙⠂⠀⠀⡀⠀⠀⠰⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠁⠀⠀⠀⠀⠘⢈⡡⢪⡼⠛⠛⠁⠀⠀⠠⡈⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠓⠄⠠⠀⠀⠀⠒⢶⠄⠀⢀⠀⠀⠀⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⠀⢤⡀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡞⢳⡀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⠞⢧⡀⢀⡴⠋⠀⠀⠙⢦⡀⢀⡼⠳⣄⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢇⡴⠋⠅⢠⡆⢹⠏⠀⠀⠀⠀⠀⠀⠹⡏⢰⡄⢨⠙⢦⡘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⠏⢸⡟⠀⣸⢀⡞⢷⡟⠀⠀⠀⢀⡆⠀⠀⠀⢻⡾⢳⡀⣇⠀⢻⡇⠹⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⡞⡑⠀⠀⠹⣦⣷⠞⠀⠀⠳⣄⠠⠀⢸⡇⠀⠀⣤⠞⠀⠀⠳⣾⣴⠏⠀⠀⠈⢳⡀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢳⡾⢠⠃⠀⠀⣰⠋⡏⠀⡀⠀⠀⠈⠻⣄⡼⢧⣠⠟⠁⠀⠀⢀⠀⢹⠙⣆⠀⠀⠘⡄⢷⡞⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⢳⣸⠀⢀⡼⠁⠀⢷⠀⡇⠀⠀⠀⣠⠟⠁⠀⠻⣄⠀⠀⠀⢸⠀⡾⠀⠈⢧⡀⠀⣧⡞⠁⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠀⠀⠀⢻⣀⡞⠁⠀⠀⠈⢷⡇⠀⢀⡞⠁⠀⠀⠀⠀⠈⢳⡀⠀⢸⡾⠁⠀⠀⠈⢳⣀⡟⠀⠀⠀⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⣿⠁⠀⡆⠀⠀⠀⢳⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡞⠀⠀⠀⠸⠀⠈⣿⠀⠀⠀⠀⡇⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢐⠀⠀⣿⠀⠀⠀⢀⡇⣿
⠀⠀⣀⡤⠴⠶⠒⠒⠒⢾⣧⢧⠀⢄⡠⣿⠀⠘⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠃⠀⣿⢀⠠⠀⡼⣮⡷⠒⠒⠲⠶⠦⢤⣀
⠰⠿⣝⠒⠚⠚⠛⠛⠓⠲⠻⢿⣷⡀⢦⣻⡆⠀⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡞⠀⣠⣟⣼⢀⣾⡿⠟⠖⠚⠛⠛⠛⠓⠓⣯⠿
⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⣈⣹⣿⣮⣿⣿⣦⡀⢳⡁⡁⠹⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠇⠄⢀⡞⢀⣴⣿⣿⡵⣿⣏⣁⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⣻⠛⠉⠀⠀⣠⠜⠋⠉⠙⠷⠿⣮⣤⣽⣷⣤⣀⣄⣸⣇⣠⣀⣤⣾⣯⣴⣥⢿⠿⠋⠉⠙⠳⣄⠀⠠⠉⠛⣟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣠⠊⠁⠀⠠⠀⠠⠀⢀⣼⠃⠀⠀⠀⠉⠉⢙⡟⠉⠉⠀⠀⠀⠈⣧⠀⠀⠐⠀⠀⠀⠈⠑⣄⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠞⠁⠀⠀⠀⠀⠀⢀⣠⠞⠹⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠏⠳⣄⡀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡴⠥⠤⠤⠤⠤⠤⠴⠖⠋⠀⠀⠀⠙⢦⣀⠀⠀⠀⢸⡇⠀⠀⠀⣀⡴⠋⠀⠀⠀⠙⠲⠦⠤⠤⠤⠤⠤⠬⢦⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠸⡇⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠑⣄⠀⠀⠀⠀⣠⠴⠒⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠏⠱⡀⠈⢃⠀⡠⠊⠀⠀⠀⢃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡉⠙⠢⣀⡞⠀⡏⠀⠀⠡⠀⠀⡔⠁⠀⠀⠀⠀⠈⡇⡇⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠙⢆⠀⢸⡇⣸⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠳⣜⠀⡇⠀⠀⠀⣠⠊⠈⠙⠢⡄⠀⠁⠀⡽⢸⠁⠀⢀⣔⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⢧⡀⠀⠙⡄⢧⠀⠀⢠⠃⠀⠀⠀⠀⠘⡆⠀⠀⢱⡌⠀⣠⡾⠋⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠙⢦⡀⠘⡜⡄⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⠀⣞⡠⠞⠉⠀⢀⠖⠉
⠀⠀⠀⠀⠀⠀⠐⠉⣉⡭⠭⢽⣶⣬⡂⠄⢠⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠹⡀⠀⠀⠀⠀⡀⠔⠉⠀⠀⡠⠴⠍⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠁⠀⢒⣈⡩⠥⠤⠤⣤⠀⠀⢀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠚⠉⢉⠕⠂⠁⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠑⢦⡑⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⣀⣀⣀⢴⠎⠀⠀⠀⠢⠤⡀⠤⠄⠒⣉⣀⣀⣀⣀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⡀⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠁
⠀⠀⠀⠤⣤⠊⠀⠀⠀⠻⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⢁⠀⠀⠀⠀⠰⠄⢀
⠀⠀⢐⣺⣷⡀⠀⡀⠀⠀⠀⢸⡀⠀⠇⠀⠀⠀⠀⢸⠀⢠⡇⠀⡆⠀⠀⠈⠁⠀⠀⠦⠁⢄⠀⡀
⠀⠀⢘⡿⠟⠓⠀⠈⢳⣄⠀⢸⠀⠀⠈⡀⠀⠀⠀⢠⠀⣸⠁⣠⠁⠀⠀⠀⠀⠀⠀⢀⠀⢻⣴⣇
⠀⠀⢺⠀⠠⠀⠀⣄⣀⠹⣧⣈⠀⠀⠀⠀⠀⠀⠀⠈⢀⡟⠀⠁⠀⢀⠎⠀⠀⠀⠀⠀⠀⣺⣿⣿⣥⡀
⠐⠀⠻⡆⠀⡀⠀⠀⠈⠓⢬⣿⣇⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠂⠀⠀⣠⠖⠁⠀⠀⠉⠙⢛⠛⠉⠁⠀⠴
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠠⠁⠀⠀⣼⣧⡤⠤⠤⠒⠒⠀⠈⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⡀⠀⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠔⠀⡠⠂⠀⠀⠀⠀⠀⠈⢂⠀⠀⠘⠀⠀⣸⠀⠀⠠⠦⠤⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⣿⡗⠉
⠀⠀⠀⠀⢀⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⣿⢻⡾⢯⣢⣴⣆⠄⠐⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⠻⢿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠃⠈⠳⣬⡍⠳⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡤⠔⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠁⢄⡀⠀⠀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿