Slice Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠉⠉⠓⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠈⠩⠿⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡋⠀⠀⠉⠉⠙⠳⠦⣶⣀⡄⢀⠀⠋⢉⡭⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢃⡼⣻⣆⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣰⠆⡀⢀⠚⣛⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⠟⣠⠟⡴⢃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣇⡿⢀⣵⡶⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠙⠺⠧⠾⠷⠛⠁⠀⠀⣠⠶⣻⠟⣿⢳⣦⡀⠀⠀⠙⢷⣾⢰⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣥⣤⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠞⣡⢞⡵⣫⠞⢻⣀⣤⡶⢺⠏⢸⣧⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢰⣿⠞⣡⢞⣩⢿⡆⠀⠀⠀⠀⠀⠀⠘⣧⡞⣵⣏⣴⣿⠞⢻⣃⣸⣷⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠘⣷⣋⡵⢛⣵⣻⠇⠀⠀⠀⠀⠀⠀⠀⣨⢿⣟⣹⣧⣾⣾⡿⠿⠛⠉
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⣀⣀⣀⣀⠀⠀⠀⢰⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣤⣄⠀⠀⠀⣴⣿⣹⣭⣿⣿⣷⣦⣤⣿⡿⠉
⠀⠀⠀⠀⠀⢻⡀⠀⢰⢏⡏⣾⣷⠀⠀⣿⣿⣿⣿⠿⠛⠉⠙⠻⠛⠁
⠀⠀⠀⠀⠀⠈⣇⠀⢸⣿⣿⣿⣿⠀⢠⣿⡏⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⡟⠛⠉⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⣿⡀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠻⣤⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠉⠲⣄⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣮⡻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣉⣀⣀⣤⠾⠀⠀⠀⠀⠀⡀⠈⡆⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠟⢋⣼⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢀⡴⠚⣠⠤⡉⠉⠁⡀⠀⣀⠘⠶⠶⠞⠃⠀⣹⠀⠀⢀⡟⠀⠀⠀⣀⣴⡿⣿⢧⣶⣶⣿⣿⣿⣿⣏⣛⣋⣡⣾⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⣀⠔⠉⠀⠀⢷⣄⣼⡀⠒⠁⠈⠁⠀⠠⠒⣒⣈⣉⡥⠤⠖⠋⠀⠀⣠⣾⣿⣿⠸⢿⡗⣿⣟⣽⣿⣷⣾⣿⣿⣟⣿⣭⣭⡵⠿⠟⠋
⠀⠀⣠⢚⣁⠀⠄⠤⢐⣊⣉⠩⢄⣀⣠⠶⣄⠀⡏⠉⠉⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣟⣷⣤⣤⢿⣿⣿⠿⠿⣿⡟⠉⠉⠉
⠀⠀⠘⠓⠚⠛⠋⠉⠉⠀⠀⠀⠀⠈⠀⠀⢸⣀⡿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠛⠛⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠠⠎⠀⢰⣿⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣀⠀⠀⠀⠀⠈⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡰⠁⠀⣠⣄⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡜⠁⠀⠀⠻⠋⠀⠀⠀⢸⣷⡄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣠⣶⠄⠀⠀⠀⠈⠉⠀⠀⢠⣤⡀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠈⢣
⠀⠀⠀⠀⠀⢀⠞⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⡠⢧⡀
⠀⠀⠀⠀⢠⣾⣷⣄⡀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⣀⣴⣷⡀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣦⣄⣀⠈⠉⠐⠒⠒⠒⠠⠤⠤⠤⠄⠒⠒⠒⠊⠉⠀⣀⣠⣴⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠻⣅⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠈⢆⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⢋⠁⠀⢀⠧⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⡟⠁⠱⡍⢳⡀⠀⠀⠉⠉⠒⠂⠤⣄⣀⡀⠀⠀⠀⠀⢸⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠐⠀⠀⠀⣇⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣛⠉⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⠁
⠀⠀⠀⠀⠀⣰⡿⡍⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣼⣿
⠀⠀⠀⠀⠀⣿⠀⠹⣆⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⠇⢠⣿⡏
⠀⠀⠀⠀⢸⣿⠀⠀⠈⢧⡀⠈⠲⡀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⣠⠇⢀⣾⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠙⢦⡀⠈⠲⣄⣀⠼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠒⠚⠁⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠈⠙⠒⠢⣀⠀⠀⠀⣸⠛⣆⠀⣀⣀⣀⣠⠴⠋⠀⣠⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣀⡀⠉⠉⠉⠁⠀⠈⠁⠉⠉⣁⣠⠤⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠒⠚⠋⢉⣡⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣆⠀⠡⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡋⠔⠀⠘⡆⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠊⠀⢀⡄⠀⢸⡀⠈⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠕⠁⡠⠐⠈⠀⠀⠀⠀⠇⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⡡⠐⠁⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠕⠀⠀⠀⣀⠠⠄⠀⠐⠂⠉⣀⣀⡇⠀⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⣀⣀⣀⡬⠥⠤⠤⠒⠒⠒⠉⠉⠉⠉⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⢀⣀⣎⠰⡀⠀⠈⠂⠄⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⡟⠉⠀⡌⠢⡈⠢⡀⠀⠄⡀⠀⠒⠠⠀⠀⠀⠀⠀⠀⢀⠃⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢋⡤⠀⠀⠀⡇⠀⠀⠈⢂⠈⢢⡈⠢⠀⠈⠐⠠⡀⠀⠀⠈⠁⠀⠀⡘⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⠔⠁⠀⠀⢀⢀⠇⠀⠰⠀⠀⠑⡄⠙⢦⡀⠑⢄⠀⠀⠁⠀⢀⠀⠀⢠⠃⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠐⠁⡀⠀⠀⠀⡄⢸⠀⠸⠀⠀⠀⢦⠈⠢⡀⠑⢄⠀⠑⠀⡀⠀⠀⠀⢠⠃⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠔⠀⠀⠐⠀⠠⠃⠀⠀⡘⠀⠀⠀⠀⠀⠘⠁⠀⠑⢄⠀⠱⣄⠀⠀⠀⠀⡰⠃⢀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠔⠁⠀⢀⠌⠀⠠⠁⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠑⠀⠈⠳⡄⣠⠞⠀⡐⣡⠋
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠔⠁⠀⠀⠀⠂⠀⢠⠁⠀⢀⠃⢠⡇⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⠞⠁⡠⢊⠜⠁
⠀⠀⠀⣠⠞⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⣨⠖⠁
⠀⠀⠈⠣⢄⡂⢄⠈⠙⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠈⠀⢀⣀⡤⠖⠋⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠈⠑⠢⢅⡂⠠⠀⡈⠉⠉⠒⠒⠢⠤⠤⠤⠧⠤⠤⠔⠒⠒⠉⠉⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⡠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠸⠀⠉⠉⠙⠊⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠲⡄⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⠀⠀⠀⠀⠀⢠⠰⠌⡡⠃⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠅⠾⠃⠀⠀⠤⠒⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡙⠂⠀⠀⠴⠶⠶⣤⡀⠀⠀⠺⠂⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢹⠀⠀⠐⠀⠀⠀⠀⠀⠠⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠀⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⠞⠀⠀⠀⠈⢰⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠈⠁⠀⠀⠀⠀⠀⠸⠀⢀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⡀⠀⠀⠀⠐⢒⠲⡄⠀⠀⢀⡤⣶⠄⠀⠀⠀⠀⠠⠀⠀⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠆⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⢰⣘⣊⠀⠀⠀⣖⣩⠴⠋⠀⠀⠄⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⡀⠀⠀⠠⠤⣄⠀⠀⠀⠀⠀⠘⠂⠀⠀⢉⡁⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢤⡐⠎⡀⠀⠀⢀⠀⠀⠀⠀⠀⣠⢏⡴⠃⠀⠀⢀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠲⢤⠀⠀⠈⠙⠉⠀⠀⢀⣀⣀⣀⣀⠀⠀⠈⠋⠀⣀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣧⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠉⠓⠤⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡾⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣥⡀⠀⡾⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⡴⠤⠴⠞⠉⠀⠀⠁⠀⡇⠀⢀⡴⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠤⡲⡄⠀⠘⠊⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠘⢜⡣⠂⡀⠀⠀⡀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠤
⠀⠀⠀⠁⠴⠾⠃⠁

⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻⣿⣿⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠶⠶⠶⠶⠶⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡛⠛⠛⠿⠓⠦⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡾⢿⠾⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⢀⣀⣶⣶⣿⣷⣶⣶⣤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠿⠿⡃⠀⠀⠀⢀⣠⣤⣀⣉⣶⣶⣶⡶⠾⠛⠋⠉⠉⠉⠉⢻⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠁⠀⠀⠀⢀⣠⣶⣤⣼⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠻⣷⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢁⠀⠀⠀⠠⣄⠀⣀⣸⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠈⠳⠘⢻⣦
⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠛⠁⠀⠀⠀⢠⣶⣾⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⢀⣤⠞⠛⠉⠀⠀⠀⠀⢢⣤⣉⠙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⣠⣾⣿⣿⣶⣶⣀⠀⠀⠈⠉⠉⠛⢻⣟⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠘⢿⣧
⣼⣿⡍⠉⠁⠀⠀⠈⠉⠛⠻⠿⣶⠶⠿⣿⣿⣦⣄⡀⠀⠀⠠⢄⡀⠀⠀⠀⡀⠈⠑⢦⡀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⡄
⠉⠻⢿⣶⣤⡀⠀⣶⣤⣦⣤⣄⡈⠑⠂⠀⠉⠙⠻⣿⣷⣄⠑⢦⡙⠲⣄⣀⠈⠂⢄⡀⠈⠲⣄⠀⠀⠈⠙⢷⣤⡈⠢⣄⠰⣄⠀⠀⠐⠘⣿⡆
⠀⠀⠀⠉⢿⣷⡀⠸⣿⣿⣿⠿⣿⣿⣾⣶⣤⣄⠀⠀⠙⠻⢿⣦⣍⣳⣤⡙⠳⣤⣤⠉⠳⣤⡈⠓⢷⣄⠀⠀⠙⢿⡦⠈⠓⠌⠑⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠈⢿⣧⠀⢻⣿⣿⣤⣿⣿⣿⣿⣙⣿⣿⣿⣷⣶⣤⣈⡉⢉⠉⠛⢷⣬⣿⣿⣿⣦⣿⣶⣤⡈⠻⣦⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠘⣿⡄⠀⢻⣿⣿⣿⣧⣄⣼⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣅⡀⠀⠈⠙⠛⠿⠿⠿⢿⣿⣿⣿⣆⠹⣄⠀⠀⠁⠀⠳⣄⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢹⣷⠀⠈⣿⣿⣽⣿⣿⣿⢿⣿⣿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠈⠙⠻⠿⣿⣷⡘⣷⣤⠰⡘⢷⡑⢄⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠸⣿⣿⠿⢿⣷⣴⣿⠻⣧⣼⣿⣶⣿⣤⡿⠋⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⡀⠀⠈⠙⠻⠿⣷⣾⣦⣿⣌⠳⡄⠱⣄⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢻⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⠉⣻⣿⣿⣶⣿⣷⣾⡿⠛⢻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠉⠙⠻⢿⣧⡙⣆⣘⣆⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⣿⣿⣿⡃⣰⣿⣿⣀⣸⣿⣿⡟⠉⣻⣿⣿⣿⣿⣷⣦⣿⣿⣦⣠⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠁⠘⠿⢿⣷⣌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣌⠉⠙⠛⠿⢿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⠋⢙⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣤⣴⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠙⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣦⣄⣀⠈⠉⠛⠻⠿⠿⠿⢿⣿⣿⣷⣾⣿⣿⡟⠛⢻⣿⣿⣷⣴⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣶⣤⣤⣄⣀⣀⠀⠉⠉⠛⠛⠿⣿⣶⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⡁⢰⣿⣿⡉⣹⣿⣿⣀⣼⣏⣈⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢿⣶⣦⣤⣀⡀⠀⠈⠙⠿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣶⣦⣤⣀⠈⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣏⣁⣽⣿⣿⣿⠋⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢷⣶⣤⣀⡀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣧⣠⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣤⣀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣄⣀⠀⠀⠉⠛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣦⣤⣤⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠡⣄⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠚⠠⠶⣿⠿⠿⣷⠦⡀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡋⢠⡀⠨⣀⠀⠀⠠⠈⠑⡄⠀⠱⡌⢂⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⢠⣼⠏⠀⠀⠀⠀⠀⢀⣵⠆⠀⠪⡖⠘⡀⠀⢘⡀⡀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⢈⠔⠁⠐⣿⡿⢀⡐⣆⣀⠀⠀⠙⠿⠃⢠⣾⡿⠞⠀⠀⠸⢀⠇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠈⠀⠀⠀⠄⠏⠀⠀⠀⢻⣿⡐⠌⠿⠟⠁⠀⣀⡤⠶⡛⠄⠀⣀⣠⣴⡷⠃⠘⠀⠀⠀⠀⠀⠀⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣀⡡⠐⠀⠀⠒⠒⠤⡁⠀⡄⠀⣾⠿⡟⣧⣡⣤⣤⠶⠾⠋⠉⠀⠀⠈⠛⠛⠟⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠽⣿⣿⣿⡟⠀⢀⡀⠀⠀⠀⠀⠈⢆⠈⠂⠤⠐⣡⡼⣿⠛⠛⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⠠⠀⠈⠹⣧⣤⣶⣿⣿⣿⣿⣷⠄⣿⠿⠆⠀⠀⠀⢀⠸⠀⠀⣠⠎⠀⠛⠛⠀⠀⠀⠙⠁⠀⢙⣆⣀⠠⠤⠴⠋⠳⠤⣀⢂⣍⣟⡆⠀⠀⠀⠀⡇
⠀⠠⠃⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠋⠴⠊⠀⡠⢶⣶⠄⠀⠀⠄⠀⢠⡏⠀⠀⠀⠀⣎⠶⠀⠀⠀⣰⠟⠉⠀⠀⠀⢀⣴⣶⣦⣌⣿⣿⣿⡿⠀⠀⠀⢀⠃
⠀⠈⢦⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠴⠋⠀⠀⠄⡤⠴⠂⠀⠀⠀⢷⡀⢤⡤⠀⠀⣀⠠⣴⣿⢃⡤⠋⠁⠙⠒⠺⢿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠸
⠀⠀⡄⢀⣠⡴⠶⠶⣦⡀⠀⢀⣠⣤⣤⣠⣤⣤⣄⠒⠒⠂⠀⠤⠄⠀⠈⠙⢷⣤⣄⣀⣀⣀⣾⣿⣼⣆⠀⠀⠠⠀⠐⠂⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⡖
⠀⠀⠙⢏⠁⠀⠀⣀⣀⡙⣖⣉⣁⣀⣀⠀⠀⠀⢻⣄⣰⠟⠛⠛⠛⠻⣷⣀⣤⣤⣤⠉⠉⢉⣁⣘⠿⠟⠁⠄⠀⠀⠀⢀⣤⡶⠶⠒⠶⣦⡄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠉⠡⠤⠤⠄⢀⡀⠀⠀⠀⠐⢿⡀⢠⡿⠉⠉⠉⠙⠉⠙⠶⣤⡴⠋⠀⠁⠀⠀⠀⠈⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠂⠉⠁⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⢠⡤⠄⠂⢒⠂⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠘⢉⠔⠀⠀⠀⠁⠂⠠⠊⠁⠀⠀⠀⠂⢌⠁⠀⠠⣈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠤⠒⠁⠀⠀⢀⣀⣤⠤⠄⠠⣠⣄⣀⣀⣀⣄⡀⠀⠀⠀⠀⠁⠀⡡⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⣀⡀⠔⢊⣀⡠⠀⠀⣀⠉⠁⣀⠀⠉⠉⠁⠭⠀⠈⠙⠳⢂⠀⢊⢊⡆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⢻⡀⠢⠎⠀⣴⣾⣿⣿⣿⣷⣦⡉⠀⡀⡞⠙⠒⢋⠤⠀⠀⡝⠪⠦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠂⣾⣿⠛⠙⢿⣿⠛⠻⣿⡀⠥⠃⠘⢀⣴⣶⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣃⡄⢸⣿⣧⣀⣠⣿⣿⣶⣾⣿⡇⠀⡀⣴⠿⣿⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣿⣿⣿⠿⣿⣏⠉⣿⡿⡃⠀⢺⣿⣶⣿⣦⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⢿⣿⣶⣿⣿⣿⣿⠟⠀⢠⣻⣿⠉⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠉⠛⠛⠛⡫⠥⠀⠸⠀⠫⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣠⠰⠀⠀⢠⠆⢠⠀⢦⡄⢀⠉⢻⡟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣶⣶⣤⡈⠁⡀⠀⠄⠂⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡁⢀⣿⣻⠀⢤⠄⠀⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣿⣿⡟⠇⢀⠤⢈⡀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣿⡿⠁⠀⠀⢀⡾⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉⢀⠀⠠⠆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⡎⠀⢤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠉⠙⠻⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠖⠛⢋⠛⠓⢦⡀⠙⠫⡑⢦⡀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⡞⠁⠀⠀⠛⠃⠀⠀⢻⠀⠀⠘⢦⡙⢦⡀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣼⠀⣤⡀⠀⣀⡀⠰⠀⡾⠀⠀⠀⠀⠙⠦⡙⣆⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⢻⡀⠸⡄⠉⠀⠀⠙⢁⣠⠞⠁⠀⠀⣠⠴⠶⠶⢽⣎⢳⡀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣰⠋⠀⢸⡇⠀⠙⠳⠶⠶⠒⠋⢁⣠⠴⠖⠚⠳⣄⠀⠀⢀⣨⠿⠻⡄⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⡇⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠏⣠⡄⠀⠀⢰⠎⠙⣟⠉⠹⣄⠀⠹⣄⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⣠⡤⢤⣀⠙⠋⠁⠀⣀⣤⣤⣄⡀⠀⠀⢸⡀⠈⠀⣠⡀⠀⠀⠀⡿⠀⠀⠈⢳⡀⠸⡆⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⡰⠋⠀⠰⠆⠀⠹⡄⠀⠀⢧⡀⠀⠈⠙⢦⡀⠀⠙⠦⣤⣈⣀⣈⡤⠞⠁⠀⠀⠀⠀⢹⠀⠹⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢰⠁⣀⠀⢀⡀⠤⢠⠇⠀⠀⠀⠓⠶⠶⠖⠚⠋⣀⣀⣀⣠⣤⣤⠤⠤⠤⠤⠶⠦⠴⠶⠿⠤⠤⠿⣄⣀⣠⢾
⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠘⣆⠉⠀⠈⣁⡴⠋⠀⣀⣠⣤⠶⠶⠒⠛⠉⠉⢉⣁⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⡤⠞
⠀⠀⠀⠀⠀⢀⡞⣸⠃⠀⠀⠀⠈⢉⣉⣩⡵⠶⠚⠋⣉⣠⡤⠶⠖⠚⠛⠉⠉⠉⠉
⠀⠀⠀⠀⢀⡞⢰⣃⣠⡤⢴⣶⠿⠛⠋⣁⡤⠶⠚⠉⠁
⠀⠀⠀⠀⠸⣇⢀⣠⠴⠚⠉⣀⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠈⠙⢦⡤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠒⠈⠉⠉⠁⠐⠒⠒⠀⠀⠐⠢⠄⠀⠀⠤⠤⣀⡀
⠀⠀⣀⠤⠐⠒⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡷
⡰⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⣒⠚⠛⠉⠉⠉⠉⠉⠉⢉⡉⠓⠒⠒⠒⠒⠒⠒⠠⠀⠀⠀⡰⠁
⢇⠐⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⣰⠿⠛⠛⠓⠀⠀⠀⠀⠀⠚⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠈⠳⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⡠⠄⠒⠂⠀⠀⠁⠀⠀⠀⠀⠀⠐⢀⡜
⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⣀⠀⠀⠚⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣿⢛⣷⠀⠀⠀⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⡖⡇⠀⢂⠀⠈⠉⠁⠀⠘⢄⡈⠉⠁⢀⠄⠀⠀⠀⠀⢠⠃⠀⠔
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣷⠹⡀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠄⢠⠏⠀⠀⡌⠀⠀⡐⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢸⣦⡘⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠎⠀⠀⠀⡴⠀⠁⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠀⢻⣿⣷⣶⣤⣥⣼⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠴⡁
⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠙⠿⡉⠉⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠤⣄⠠⠄⠂⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡔⠁⢀⠀⢢⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠧⣄⣀⣀⣀⠤⠐⠀⠀⠀⠀⠀⣀⡀⠔
⠀⠀⠀⠀⢀⡞⠀⡠⠃⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈
⠀⠀⠀⠀⣼⠀⡜⠀⠀⠀⠀⠀⠱⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠔⠈⠁⠁⠐⠁⠂⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⣼⣷⡄
⠀⡔⠉⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠹⡄⠀⠀⠀⠀⣰⠁⢻⣿
⠀⡄⠀⢰⠋⠀⠑⠠⠀⠀⠀⠀⢸⣿⡇⠀⠙⢄⡂⠀⣰⠃⠀⢸⣿⡇
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠉⠉⠁⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣼⣷⣤⣄⠀⠀⠀⠀⣀⣤⣾⣯⣤⣤⣤⣤⣄⡀
⣀⣀⡀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣀⣀⣀⣀⡀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⢀⠉⠁⠀⠀⠀⠀⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠠⢤⠤⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠒⠒⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠉⣉⠒⠒⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠀⠀⠀⠀⠀⠀⢠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢄⠀⠀⡐⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⢉⠁⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠐⣷⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⣉⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠃⠀⠈⠉⠀⠐⠀⠀⠀⠀⠀⢠⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠘⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⡤⠆⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠒⠈⠁⠐⠊⠉
⠀⠀⠀⠀⢀⡰⠃⠀⠀⠄⠃⠀⠀⠀⢀⡀⠤⠚⠋⣁⡠⠴⠒⠉
⠀⠀⠀⢀⠞⠀⠀⠰⣇⣠⠤⠖⠂⢁⣠⡤⠶⠚⠋⠁
⠀⠀⠰⠁⠀⠀⠀⢀⡉⠤⠐⠒⠉⠁
⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠉⠉⠀⠀⠀⠀⠠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣂⠀⠤⠄⠴⠀⠐⠲⠶⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠲⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⣬⡀⣉⡄⠀⠀⠄⠀⠀⠀⠄⠀⠠⠤⢚⣓⠒⠲⠤⠤⢀⣀⣀⡀⠀⠀⠠⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⡀⠀⠉⠰⠀⠰⡀⠀⢠⠆⠀⠀⠀⠀⠀⠉⠉⢁⠈⢉⠀⠀⠠⠌⠐⠀⣧⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠠⠍⠾⠅⠀⠀⠲⠄⠔⢲⣐⠄⠀⠀⠀⡈⠕⠛⠒⠂⠀⠛⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠁⠀⠙⠳⠦⣤⣆⠀⠀⠀⢀⠀⠀⠀⠊⠳⠀⣄⠀⠎⠉⠀⠀⣀⣤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⢀⡹⠅⠀⠀⣠⠔⠉⠀⠅⠀⣤⠀⠐⠀⠁⠀⠀⠀⠀⠊⠉⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠰⠋⡀⠀⠀⠈⡠⠀⠀⡈⠀⠀⠀⠀⠀⠂⠀⠐⠂⢀⠠⠤⠚⠋
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠙⠂⣈⣠⠴⠂
⠀⠀⠀⠀⡴⠁⡀⣠⡀⠜⢃⡀⠀⠀⢀⣀⡠⠴⠒⠋⠉
⠀⠀⠠⠊⠐⠦⠉⠐⠈⢁⣤⠴⠒⠋⠁
⠀⠀⠳⡀⠀⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠉⠓⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠀⠐⠦⠐⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⣄⠀⠀⠀⠀⠀⠀⢀⡀⠂⠠⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠀⠄⠀⠈⠀⠐⠀⠀⠒⠀⠀⠀⠀⠀⠒⠀⢠⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡀⠤⠀⢠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠤⠤⠀⠐⠄⠀⠀⠀⠀⠐⠁⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠁⠿⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠋⠁⠀⠀⣀⡠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠂⠉⠀⠰⠒⠛⠁
⠀⠀⠀⠀⠀⠀⢠⠗⠀⠀⠀⡀⢀⠀⠀⠀⠀⠤⠂⠀⠀⠈⠀⡒⠤⠔⢂⣀⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠀⠀⠀⢀⣀⠠
⠀⠀⠀⠀⡐⠏⠀⠀⢀⡀⠀⣐⠀⠄⠉⢀⣀⡤⠴⠒⠋⠁
⠀⠀⢀⠔⠁⠀⢀⠀⠤⠉⢁⣀⠤⠔⠛⠉⠁
⠀⠀⢬⠀⠀⠀⠀⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠠⢪⡞⣡⣶⡏⣸⢁⣨⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⣭⠴⠒⣛⣛⣛⣂⠀⠀⠀⠠⢏⣾⣿⣿⡇⠋⣈⣤⣤⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣡⣴⠾⠟⠛⠛⠛⠛⠻⠷⣶⣄⣸⣿⣿⣿⣣⣾⣿⣿⡏⡾⠀⢀⣀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣏⠁⠀⠀⠀⠀⣴⣦⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⢷⣇⣤⣭⣭⣶⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢡⡿⠛⠀⠀⠀⠀⠼⠛⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣟⣷⠟⣡⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣸⡿⠏⠀⠀⠀⢰⣿⣷⢸⣿⣿⣧⡀⠀⣾⣿⣿⣿⣻⣿⣯⣥⣤⣀⡀⠀⢤⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠐⠛⠋⠋⢸⣿⣿⣿⣷⠀⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⣿⣦⣄⠉⠢⡹⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢠⣿⡿⠀⠀⠀⣴⣦⡄⣦⣀⠀⠀⢀⣿⣿⣿⣿⣿⣇⡿⠋⡡⠄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠙⣎⠆
⠀⠀⠀⠀⢀⡎⢠⣿⠁⠀⠉⠉⠀⠀⠀⠰⠿⠛⠁⠹⣿⣷⣶⣬⣍⣉⣙⣻⣿⣟⣄⠈⡄⢀⠀⠀⠁⠀⠀⠄⠀⠀⠘⢿⣷⡀⠘⡆
⠀⠀⠀⢀⡞⢀⣿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡿⠿⠛⠁⡃⠀⣤⡉⠲⠤⣄⣀⠀⡀⠀⠀⠀⠠⠀⠈⢿⣷⡀⠘
⠀⠀⠀⣾⡇⣸⣿⣿⠇⢠⡿⠗⠀⠀⢀⣤⡄⠀⠀⠈⣿⣿⠟⠋⠀⠂⠘⠃⡇⠻⣿⣷⣄⠀⠸⣍⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠻⡇⣿⡏⠁⠀⠀⠀⠀⠀⠀⠺⠟⠁⠀⠀⢸⣿⠃⠀⠀⠠⠀⠀⡄⢄⠀⠙⢿⣿⣄⠀⠈⡟⠗⠀⠀⡀⠀⠀⠀⠀⢹⣿⡄⢠
⠀⠀⠀⠀⣇⢹⣧⢠⣿⡷⢀⣤⣶⠀⠀⠀⢀⣀⡀⣿⣿⠀⠀⠀⠀⠀⢠⠀⣀⢇⠀⠀⢻⣿⣧⠀⢳⠃⠐⠃⠀⠀⠀⠀⠘⠀⣿⣧⠈⡇
⠀⠀⠀⠀⠘⠈⢿⣆⠁⠀⠈⠛⠉⠀⠀⠰⠿⠿⠃⢻⣿⡀⠀⠐⠊⠀⠀⠀⠁⠀⡑⢆⠀⠻⣿⣇⠀⡄⠶⠀⠁⠀⡀⠀⠀⠀⣿⣿⠀⣿⢳
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⣾⠿⠆⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠈⠀⠀⠀⠁⠈⠓⢄⡈⠻⣆⠡⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣤⣤⣤⣤⣤⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠸⠂⣀⠘⠁⢈⡲⣝⠆⢃⠰⠆⠀⠀⢀⠀⠀⣿⣿⠀⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⣍⣉⣉⣉⣀⣀⠀⠙⣿⣧⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⡂⣀⠀⠀⠀⠐⢀⣿⡏⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠀⠀⠀⠈⠻⣿⣦⣄⠀⠈⠀⠀⢀⠀⠀⠀⠛⠁⠀⠆⢉⢉⠀⠀⠀⠀⣼⣿⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⣼⡿⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣶⣦⣤⣀⣀⠀⠀⡀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣉⠙⠛⠿⠿⢿⣿⣿⣷⡾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡉⠓⠢⠤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠛⢦⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⢀⡄⠉⠁⠀⠙⠛⠛⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠾⢷⡾⠃⣤⠀⠀⠀⣀⡀⠀⠀⠈⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣀⣀⡀⠀⠀⠙⠛⠛⠛⠟⠛⣦⠀⣀⡀⠀⠀⠉⠛⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣀⠉⠉⠙⠓⠀⠀⠶⣤⡄⠀⠀⠻⠞⠙⣧⣤⡶⠻⣦⠀⠀⠈⠙⠛⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⡀⠀⠈⠉⣷⣀⡀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣄⡉⠻⠖⠀⠀⠀⢀⣀⠛⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⣠⠿⠃⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠙⢦⡀⠀⠛⣶⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀⠀⠉⠀⠀⠀⠻⣦⠐⢿⣤⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⣀⣤⠶⠂⣠⡼⠃⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠞⠛⠋⠉⠁⣠⡾⠋⠀⣀⣠⣄⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠆⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡤⠶⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⣤⠞⠋⠁⠈⠉
⠀⠀⠀⠀⠀⢠⡾⠁⠰⠄⠀⠃⠀⠀⠀⣀⣀⣠⣤⣤⡴⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣠⠟⠁
⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⣤⠶⠞⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⠟⠁⢠⡾⠃
⠀⠀⠀⠀⠀⢻⡎⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⣀⠈⠀⠀⣠⡾⠁⢀⣴⠏
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣤⡾⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠓⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠛⠛⠛⠛⠋⠁⢀⣤⠞⠁
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠃⠀⠀⣀⣀⣀⣤⣤⣤⣤⠴⠶⠶⠞⠛⠋⠉⠀⢀⣀⣀⣀⣀⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⣤⠶⠶⠶⠖⠛⠛⠋⠉⠉⠁⠀⢀⣀⣀⣠⣤⣤⡤⠶⠶⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠹⣦⣀⣀⣤⣤⣤⠤⠶⠶⠚⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠉⠙⠒⠲⢦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠛⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠙⠖⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⢀⢠⣀⠀⡀⡇⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠈⠙⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠚⠓⠻⢾⣇⣡⠐⢀⣀⡀⠀⡸⠀⠀⡀⠀⠀⠀⠀⢀⡠⠈⠉⠙⣳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⠈⠉⠓⠮⠿⣿⣇⡇⠀⠀⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⣉⣉⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢀⠔⢢⡀⠀⠉⠙⣤⡀⠟⡀⢠⢀⡏⠀⠀⠀⢀⡾⠋⠁⠀⠀⠈⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠐⡕⡄⠀⠈⠀⢹⣧⠀⠀⡞⠀⠈⠙⠷⣼⣸⡇⠐⠀⠀⡾⠀⠀⠠⠀⠐⠂⣀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠕⠀⠀⠀⠐⢐⡀⠀⡄⢸⡇⠀⠀⡇⠀⠀⠺⠆⠀⠉⠳⣇⣰⡀⡇⠀⠰⠒⠀⠐⠂⠉⠴⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢘⠃⠠⢸⠀⠀⠱⡘⢧⡀⠀⠱⡀⠀⠀⢎⡱⠀⢠⡈⠙⢷⣻⡄⠀⠀⠐⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠤⠃⠀⠯⠃⡸⠈⠀⠀⠀⢱⣢⠟⠀⠀⠱⣔⠠⣄⡀⠀⠈⠁⢀⣤⡽⠳⣄⠀⠀⠀⠈⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠠⣖⠁⠁⠐⠀⠀⠀⠀⠀⢀⠀⠀⠈⠑⠒⠞⠛⠛⠶⠒⠁⠀⠀⡬⢳⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠶⠖⠓⠊⠁⠀⠀⣀⣤⣴⠚⠛⢦⣀⠀⠀⠀⢀⡤⣄⣀⣀⣤⠴⢶⠀⠈⠀⢸⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠄⣒⣤⣄⣨⠃⠀⠀⠛⠢⣄⣌⣥⡄⠐⠟⢁⣤⠤⣋⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠠⣤⣤⡄⠀⠀⠀⠀⠁⠒⠉⠀⠉⠉⠁⣀⣤⡤⢤⣄⣀⠀⡠⠊⠀⠀⢸⣦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣀⣀⡀⠛⣄⠀⠘⡀⠀⠀⠀⠀⡠⠖⠋⢴⡶⠀⠀⠀⡈⠛⠁⠀⢀⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⠉⠙⠮⠤⠞⠀⠀⠃⠀⠀⢀⠞⠀⠀⣠⠀⠀⠰⣒⡾⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇⠒⢲⡆⠀⠀⢠⣤⣄⠀⠀⠀⢊⡀⠸⠇⠀⢐⡶⠋⠁⠀⣀⣺⡆⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠴⠒⠢⠃⠀⠐⣅⠀⠈⢷⣄⠀⠘⣇⠀⠀⠀⠈⡔⢢⣀⣠⠏⠀⢣⣄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠤⠤⠤⡀⠀⠀⠈⠆⠂⢈⣾⠀⠀⠙⣡⢊⠔⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠑⠈⢦⡀⠀⢰⣲⠝⠚⠀⢀⠞⠁⠸⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠤⡀⠈⠀⣧⠀⠈⠀⠀⠀⢀⣉⠀⠀⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢛⡁⠀⢸⡟⠀⠀⠀⠀⣰⠃⣸⣆⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡄⣄⠙⣡⣴⠟⠁⢀⢔⣀⡴⢃⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠈⢕⣪⠔⠁⠀⠔⢡⡏⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠉⠉⠀⠀⠔⠆⠀⣼⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠔⣂⠤⠊⢀⡄⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠊⠁⢀⡴⠞⣄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡴⠋⠀⠀⠘⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠚⠛⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠛⠀⣿⡁⢘⣀⣀⡤⠢⡀
⠀⠀⠀⣀⠤⠤⠄⣀⠀⠀⠀⡰⠊⠀⢀⡤⠤⢄⡀⠈⣧⠀⠀⠀⠀⠀⡖⠲⣄⠇⠀⣸⣆⢀⢧⡏⠈⠀⠸⠁⡜
⠀⠀⡼⠁⠀⠀⠀⠀⠉⠲⠎⠀⢀⡔⠁⠀⠀⠀⢻⠀⢸⠀⠀⠀⣠⡉⠣⡈⠻⡅⠀⢩⢿⣏⠀⠛⡄⠀⠀⢰
⠀⢰⡇⠀⡔⠉⠙⠓⠦⡄⠀⢠⠯⡀⠀⠀⠀⠀⡸⠀⢸⠀⠀⢮⡈⠿⡆⠀⠀⠀⠀⠀⠜⢿⠀⠀⠃⠀⠀⠈⡇
⠀⠈⡇⠀⠱⡀⠀⠀⠀⢇⠀⠊⠀⡃⠀⠀⠀⠀⠇⠀⣼⠀⠀⠀⠈⠢⣄⠀⢀⠠⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠹⡀⠀⠱⡀⠀⠀⣨⠂⠀⡰⠦⣀⠀⠀⡸⠀⢠⡇⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠙⣄⠀⠙⣤⠞⠁⢀⡞⢦⠀⠈⠑⢶⠃⠀⡞⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠈⠣⣀⠀⠀⢠⡎⠀⠀⠑⣤⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠹⠤⢖⠁⠈⠓⠒⠊⠀⠀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⣀⡤⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣀⡠⠴⠶⠊⡉⠉⠉⠩⠉⠉⠙⠓⠲⢤⣀
⠀⠀⠀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⣠⠔⠚⠉⠉⡉⠉⠉⠉⠓⠒⠦⢤⣀
⠀⠀⠀⣹⠓⠒⠒⠂⠒⠒⠂⠂⠒⠒⠒⠒⠀⠒⠒⠀⠀⠀⢧⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠸⡇⠀⠀⠀⠀⠑⠁⠀⠈⠐⠀⠀⠀⠀⡀⠀⠀⠀⠹⡄
⠀⠀⡠⠏⠀⠉⠈⠁⠁⠀⠀⠂⠀⠀⠀⠔⢎⠐⠂⠁⠀⠀⠘⢲⠀⠀⢳⡄⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⣿
⠀⠈⡷⠈⠓⠀⠀⠄⠄⠀⠀⠄⠂⠄⠀⠠⠐⠄⡀⠂⠀⡢⣤⡼⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠉⢻⡐⠒⠉⠑⠠⠔⠀⠄⢀⣀⠖⠒⠠⠴⠐⠐⠊⣠⠎⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠁
⠀⠀⠀⠀⠙⠒⠦⠤⢦⣄⣠⣤⣀⣀⣠⣀⣠⠤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠊⠉⠁

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠁⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠡⢁⡌⠀⠀⠀⠀⠀⠀⣈⡶⢀⠀⡀⠀⠀⠀⠀⠀⠰⣩⢹⡑⡒⠀⠀⠀⠀⠀⠀⢀⠀⣩⠏
⠀⠰⠀⠤⠀⠰⠌⠰⠀⠀⠀⠀⠸⠁⢀⠀⠈⠥⠀⠀⠀⠀⠀⠰⡃⢱⣢⢠⠀⠀⠀⠀⠀⠀⠉⠙⠚⠉⠅⠀⠀⠀⠀⠀⠴⣤⠚⠕
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠚⠻⠁⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠊

⠀⠀⠖⠒⢒⠒⠒⠆⠀⠀⠀⠀⠀⢀⠠⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡄
⠀⠀⠀⠂⠤⢤⠀⠀⠀⠀⠀⠀⢀⠚⢠⠀⠋⠀⠀⠀⠀⠀⠀⠀⣔⠙⢄⡙⠈⠀⠀⠀⠀⡱⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢠⠪⣩⠷⢱
⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠘⠉⣉⡉⠙⠀⠀⠀⠀⠀⢠⡐⢆⠱⠄⠁⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⡅⠀⠀⠀⠀⠀⠠⠙⢬⠀⠁
⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠚⠒⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠠⠒⠢⡈⠂⠀⠀⠀⠀⠐⣁⠄⡄⠡⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡀⠀⠀⠀⠀⠀⠞⠀⣀⢀⣀⠐⠷⠀⠀⠀⠀⠠⡮⡖⠿⠶⢄
⠀⠀⠈⢂⡂⡂⡊⠁⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⢾⢠⠤⠘⠀⠀⠀⠀⠀⠈⠀⢤⠤⡄⠂⠀⠀⠀⠀⠨⣀⠅⠀⠀⠀⡠
⠀⠀⠀⠨⠤⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡸⠜⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠀⠈⣄⠀⡠⠊
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢱⠊⠀⡀⢀⡞⠀⠀⠀⠀⠀⠀⢰⠦⠭⢴⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡱⠀⠀⠀⠀⠀⠘⠚⠛⠚⡃⠀⠀⠀⠀⠀⠐⠛⠄⠎⠈⠆
⠀⠈⠅⠈⠁⠉⠉⠆⠀⠀⠀⠀⠀⠠⠀⠀⠴⠀⠀⠀⠀⠀⠀⡀⠊⢥⡤⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠐⠀⠂⠂⠀⠂
⠀⠀⢾⡦⠰⣶⠄⠀⠀⠀⠀⠀⠀⠀⡁⠀⡁⠀⠀⠀⠀⠀⠈⠢⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⡉⠉⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⡽⠛⠋⠛⠛⠓⠶⢤⣄⣀⢀⣀⣠⣤⠶⠶⠶⢦⣄⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⡏⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⣰⣦⠀⠀⠙⢦⠀⠀⠀⠙⢷⣄⣀⠤⠤⢤⣤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡿⠀⠀⠀⢸⣾⡿⠀⠀⠀⣄⢠⡄⠀⠀⠈⠛⠛⠀⠀⠀⠈⢷⣄⢀⡤⣾⡁⢠⣤⡄⠛⠉⢀⣠⡍⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣰⡯⠶⠶⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡹⠿⠗⢈⣥⡄⢀⠾⠶⠀⠾⠿⠀⠰⠿⠉⢢⡀
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠐⠶⠞⠃⠀⣀⣠⣤⣤⣤⣴⠶⠦⢤⣄⠀⠀⠨⣧⠀⡼⠁⠰⠶⠆⢡⣗⠀⠶⡶⢀⣴⡌⠛⠓⠰⣿⠀⢳
⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡴⠋⣡⡴⠚⠛⠉⠉⠙⠛⠲⢬⣳⣄⠀⠀⢰⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢀⡟⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⢠⡟⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠇⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠞⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⢷⡀⢸⡇⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡀
⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⢀⣀⠈⠃⠘⣇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢸⡇⠀⣾⠀⠀⠚⠛⠉⠀⠀⠀⠹⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣶⠒⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠴⠁
⠀⠀⠀⠀⣧⠀⡟⠀⠀⠀⠀⠀⠀⠛⠳⠆⠘⠿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠨⡆⠘⠤⠊⠉⠓⠤⠤⢤⡀⠀⠀⠀⣠⠖⠦⣀⠀⠀⡰⠋⢸
⠀⠀⠀⠀⠸⡆⢿⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⠛⠷⠦⣤⣤⣤⣤⠤⠶⠋⠁⠀⡀⣣⠀⠀⠀⠀⠀⣠⣀⠀⢧⡀⢀⡴⠃⢀⣄⡀⠉⠉⠀⠀⡎
⠀⠀⠀⠀⠀⢹⡜⣆⠀⠀⠀⠀⠀⠈⠻⠂⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⠛⡿⣿⠀⠀⢦⠀⠘⢷⡿⠀⠀⢌⡤⠀⠀⢿⡿⠇⠀⢰⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠹⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣠⣴⠇⠀⠀⠀⠘⠷⠀⠀⢸⠇⠸⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠙⠲⠶⢤⣄⠀⠀⠀⠀⠀⠉⠀⠀⠈⠻⣆⢀⣀⡀⢀⡟⠀⠀⢹⡀⣈⣄⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠙⠾⠤⣴⠚⠺⠏⠉⠉⢧⠀⠸⠀⠀⠸⠀⠀⠀⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣝⣓⣲⠒⠚⠋⠁⠙⣦⣀⠀⢀⣠⠾⢦⣀⣀⣀⡴⠛⠒⠒⠀⠤⠤⠤⠀⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁




⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤





⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⡀⠀⣀⡀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡖⠿⠇⠀⠀⠀⢀⣾⣿⣷⣆
⣤⣤⣤⣤⣤⣤⣄⣴⣾⣿⣿⣿⣷⣆⠀⣠⡄⠀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠹⠐⠀⠀⠘⣿⠿⠟⠐⢀⠂⠐⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣇⠀⠀⠀⠀⠐⢀⣉⣿⣿⣿⣿⣧⣶⣾⡀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣍⣉⣉⣿⣭⣽⣿⣿⣿⣿⣀⣀⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⠿⣿⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠿⡿⠛⠻⠟⠛⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⠿⠿⠿⠟⠛⠋⠉⠉⠉
⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⡿⠿⠟⠛⠁

⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠦⠀⠀⠀⢀⠀⠀⠀⠐⠂⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⡄⢢⠀⠀⠀⠀⠀⠈⠀⠅
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢋⠀⢱⢸⡆⠀⠀⢀⡆
⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⠀⠀⠀⠀⠀⠘⠤⠬⠼⠥⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄
⠀⠀⠀⠠⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠈⠀⠀⢁⢠⡀⠀⠀⠀⠀⢀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠠⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣈⡀⠐⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠁⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠶⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠀⠁⠒⠒⠉⠀⠀⠀⠀⠀⠄⡄
⠑⠄⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠠⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣡⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⣡⣶⢶
⠀⠀⠀⠀⠀⠀⢰⣷⡈⢿⣿⡿⠀⠀⠀⠀⠀⢰⣷⣄⢿⣿⣻⠀⠀⠀⠀⠀⢀⣿⣄⢹⡿⣿⠃
⠀⠀⠀⠀⠀⠀⣘⣿⣟⡈⠙⠁⠀⠀⠀⠀⠀⣈⣻⣟⡈⠙⠁⠀⠀⠀⠀⠀⣀⣻⣟⣀⠉⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡄⠠⣿⣿⣧⠀⠀⠀⠀⠀⢀⣤⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⡄⢾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⡧⠹⠿⠋⠀⠀⠀⠀⠀⠸⣿⣷⠹⢿⠟⠀⠀⠀⠀⠀⠐⢷⣷⠞⠿⠿⠃
⠀⠀⠀⠀⠀⠠⠶⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠶⠾⠷⠶⠀⠀⠀⠀⠀⠀⠀⠴⠶⠿⠶⠄

⠀⠀⡇⠘⣦⠈⡇⠀⠀⣿⠀⢀⡄⡇⠀⣶⠛⣿⠀⠀⢸⠀⠛⢣⣿⠣⡆⢸⠀⠀⡶⣾⡏⢻⡇⣼⠃⣸⡏⠀⠠⡗⠀⠀⠀⣿⡾⠈⢿
⠀⠠⣇⠀⢘⢧⢻⠛⠛⣟⢛⡛⠛⣟⠛⣛⣛⡿⢛⢛⢻⠟⠛⠛⡇⢸⠀⠸⠀⠀⡇⢸⠀⣼⢱⢏⠀⣿⡗⠒⠺⡿⠒⠒⢲⡗⠒⠒⣾
⠀⠀⣿⣀⣾⢾⢿⡇⠀⣿⠙⠃⠀⠁⠀⢀⠀⠀⠀⠀⠈⠓⢆⠀⡇⢸⡀⠀⢰⡄⠇⢸⠀⣿⡿⢸⠀⣏⣇⣰⠷⡇⠀⠀⠀⡇⠸⡿⢹
⠀⠀⣿⠻⠃⢸⣈⣃⣀⣿⣠⠃⢀⣈⡓⠀⠀⠀⠀⠀⡄⢀⢈⣆⡇⢸⣅⣤⠟⢿⡇⢘⠀⣿⠁⢸⡆⡇⡏⣛⣀⣇⣴⣶⣾⣷⣶⣦⣼
⠀⠀⣿⠀⢀⢸⢤⠀⠀⣿⢸⠽⠛⣓⠛⠀⠀⠀⠀⠀⠀⠉⢸⠁⡆⢸⠉⢟⣀⡾⠃⢸⠀⠁⣠⣼⡷⠆⣧⡀⠀⣿⡏⠛⠿⠛⠙⣿⣿
⠀⠀⣿⣿⣿⣿⡄⢁⡀⣿⠀⢄⠠⠇⠐⢚⣳⠦⠄⠀⢀⣀⣼⣦⡇⠈⠀⠈⠻⠃⠀⢘⠀⡀⠛⠛⠂⠀⡇⠘⠀⠻⣧⡀⠀⣀⠈⣿⢿
⠀⠀⣿⣿⣿⡿⢀⢂⢉⣿⡄⠆⠀⠀⠀⠈⠉⠁⠀⠀⠛⢲⣛⣻⣿⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣶⣤⡀⠧⠀⠠⠀⠈⡆⠠⠀⠀⣉⢸
⠀⠀⣿⢗⡓⣦⠒⡼⢘⣿⡾⠂⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⣿⡿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠄⠈⢫⠀⣀⠔⢹⣿
⠀⠀⣿⠀⠀⠉⠛⠷⣾⡟⠁⠀⢀⠀⠀⠀⠀⣀⣀⠀⣰⡋⠄⣼⣿⠿⡟⣵⣿⣿⣿⣿⢾⣯⣽⣭⡻⣿⣿⡄⢠⠄⠸⢾⣩⣄⠀⣾⣿
⡀⣀⣟⣀⣤⣤⣶⣿⣿⡀⠀⢢⠘⣷⣄⠀⠀⠀⠁⡼⡅⠀⢸⣿⣿⣾⣿⣿⡟⠛⠋⠁⠀⠙⢿⣿⣿⣿⣿⣇⡀⡴⣆⠟⣸⡇⢸⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠑⠾⣿⣿⡿⠟⣯⡐⢃⠀⢸⣿⡟⡿⠋⠁⠀⠠⠤⣄⡀⠀⠀⠈⠉⣿⣿⠇⠀⠉⡹⢲⠟⢷⣾⣿⣿
⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣥⣄⠀⣿⣿⣦⢨⣈⠿⣷⡅⠀⠀⠀⠦⢥⡀⢁⠀⣠⠴⢶⡟⢁⠀⠀⡼⢡⡇⠀⠈⢻⣿⣿
⣎⠂⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡴⠋⢹⣿⠙⠧⣿⣿⣿⠿⠟⢳⠏⡆⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⢳⡇⠈⠀⡼⠁⠸⡇⠀⠀⠀⠹⣿
⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣾⡿⠖⠒⣩⣽⣟⣦⡀⠀⠛⡄⠻⣄⠀⠀⠠⣤⣴⠃⡄⢸⠀⢿⡄⡼⠁⠀⠀⠙⠐⣄⠀⠀⠘
⣎⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡜⠉⠀⠀⠉⠀⢀⣀⣉⡛⠀⠀⠘⠱⢹⣶⣤⣀⣀⠏⠀⠀⠀⠀⠘⡟⡅⠀⠀⠀⢠⣴⣿⣷⣄⡀
⡙⠳⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡎⠀⣠⠊⠀⠀⠀⠐⠀⢈⣿⠿⣶⣄⡀⠈⠘⠙⠹⡟⠀⠀⠀⠀⠁⠀⠙⡘⡄⠀⠀⢠⣿⣿⣿⣿⣿
⣿⡷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⡔⠁⠀⠀⠀⠀⢀⡀⢸⣯⣿⢬⣿⣿⣿⡗⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⢑⡞⠀⣠⣿⣿⣿⣿⣿⣿
⣿⣦⣸⣿⠿⠿⣿⣟⣿⣿⡟⠀⣼⠀⠀⠀⢀⡴⠊⣷⡞⣻⣿⣿⣾⡿⣾⣿⣷⣾⣷⢶⢺⣵⡦⣄⣠⣴⣾⠁⣠⠄⢿⣿⣿⣿⣿⣿⣿
⣵⣿⣷⣶⣴⣿⣿⣿⣿⣿⡇⠀⢻⣤⡖⠉⠁⠀⢰⣿⣿⣏⣿⣽⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⠉⠉⢆⠀⠀⠈⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⡴⡆⠰⣊⡥⠎⠀⠀⠀⠀⠀⠀⢀⣴⡟⠛⠃⣀⠈⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣤⡄
⠀⠀⠀⠀⠀⡀⣇⠣⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢀⣤⠾⠉⠻⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣟⣻⡿⢾⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣵⣁⣼⠀⠀⠀⠀⠀⠀⠀⣭⣤⣤⣥⣤⣤⣤⣤⣤⡍⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣷⣽⣛⣿⣥
⠀⠀⠀⢀⣼⣿⣉⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⣤⣤⣤⣤⡀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣟⣯⣿⠉
⠀⠀⢀⣺⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠙⠛⠛⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣄⣈⣙⣿⡇
⠀⠀⠈⠉⠙⠷⠿⢿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠾⢯⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣒⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢀⡴⠛⠻⠋⢓⣦⡀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠠⠀⠠⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⣋⣭⣴⣾⣿⣿⠄
⠀⠀⠀⣾⠛⠀⣶⢀⣨⣭⡇⠀⠀⠀⠀⠀⠀⠘⠳⠤⣄⡀⠀⠀⠀⢀⡴⣚⠁⠀⠀⠀⠀⠀⣴⣭⣶⣾⠿⠟⠋⠁⠈⠹⡏
⠀⠀⠀⠻⣾⠂⣴⡏⢥⣄⡄⠀⠀⠀⠀⠀⠀⠀⠰⠿⣶⣍⡲⠤⢞⣭⣾⣿⡄⠀⠀⠀⠀⢺⣿⣿⠁⠀⠀⠀⠀⠀⣀⣴⠇
⠀⠀⠀⠀⠙⠳⠾⠇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣻⠿⣛⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠻⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠰⢿⣶⣤⣉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢲⣄⣿⢰⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡈⠛⠁⠀⠀⠀⠀⠀⠀⠰⡖⢾⠸⡇⣿⢸⡿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣷⣶⣶⡄
⠀⠀⠀⣿⣿⣿⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣬⣶⣷⣷⣾⣧⣬⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣀⠀⠀⡟
⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣾⣿⣦⣶⡇
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢿⣿⠟⢻⡇
⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⣠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣙⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡠⢂⢭⣬⣭⡐⡢⡀
⠀⣀⠝⢄⠱⠤⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠌⡂⠀⠀⢀⡀⣀⠀⠀⠻⠟⠂⠀⠀⠈⠀⠁⠁⠀⠠⡈⢊⢪⠢⡀⠀⠀⢀
⠀⠒⠉⢎⢒⡢⡑⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⣷⣶⣦⡑⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⣑⠨⠲⢙⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠀⢀⣀⠐⠀⠀⠀⠀⠀⠀⠀⣸⠋⠤⠄⠉⠓⠄⠀⠀⠀⠀⠀⠐⡤⠀⠀⠀⠀⣀⠀⠀⠩⠭⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠱⡤⡀⠀⠀⠀⢠⡎⠋⠀⠀⠀⠀⠐⣤⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⢈⠀⡄⠀⠀⢀⠜⠀⡟⠁⠀⠀⠐⢯⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢴⡇⢈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠁⠉⠁⠀⡐⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠑⢌⠑⠒⢉⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⠀⠒⠉⠀⠀⠀⠀⡀⠘⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⡢⡑⢄⠀⠀⠀⠀⠀⠲⠤⣜⠛⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣎⢢⠀⠀⠀⠈⠒⠋⠀⠡⠀⢀⡥⠶⡀⠀⠤⠀⡠⡀⠀⠀⠀⠀⠀⣀⠎⠔⠥⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠉⠀⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡰⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⡀⠰⡀⠀⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠐⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⢠⢠⠀⢃⠀⠱⢄⠀⠈⠢⠄⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠤⠀⠊⠁⠀⠀⠀⠀⠀⠐⠒⠒⠊⠁⠀⠀⠀⢠⣄
⠸⡀⢢⡀⠑⠀⠀⠉⣐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢟⠘
⠀⠑⠄⠀⢐⣒⣀⣀⣤⣍⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡎⠉⢁⠠⡀⠀⠀⠀⠀⢀⣤⡩⠿⣭⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁⠈⠁⠈⠁⠀⡂⠀⠀⢀⠎⠊⠁⠉⠀⠀⠀⠈⠢⠑⣜⠀⠀⠀⢀⠈⠝⣏⠀⠀⠁⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⢱⠀⠂⠀⠀⠈⡌⠀⢀⠀⠀⠀⠀⢠⠀⠃⢸⡄⠀⢀⢼⠈⠓⠈⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠜⡄⠣⡀⣀⠴⠃⢀⠂⠀⠀⠠⡠⣰⠈⠦⡀⢀⡠⠊⢀⢃⣼⠁⠀⠀⠙⢄⠘⢄⣀⡠⠖⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⠀⠔⠁⠀⠀⠀⠀⠈⠉⠑⠤⠀⠀⠤⠐⠉⠚⠁⠀⠀⠀⠀⠈⠓⠤⠤⠤⠐⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠐⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠒⠋⠉⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⣫⠱⢄⡐⣖⣉⣤⣤⡀⠜⢦⠤⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡀⢐⠓⠀⡄⢰⣿⣿⣿⣿⣿⡇⢂⠄⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡀⠔⠁⠀⠀⡠⠀⢾⣿⣿⣯⣿⣿⡿⠃⠠⠄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠋⣀⠀⢰⠌⠀⠀⠀⣦⠈⠉⠉⠉⡁⠠⠠⠂⢀⡀⢠⣌⠙⢦⡀
⠀⠀⠀⠀⠀⣴⢃⠀⠀⠀⢺⣿⡿⣸⣄⡀⠀⠀⠀⢀⢀⣴⣶⣦⣄⠀⠀⠞⢊⣨⢉⣴⣶⣿⣷⣦
⠀⠀⠀⠀⢰⡁⢻⡔⢱⣿⡷⢿⣿⣿⣿⣿⡷⢀⣀⣀⠘⢿⡿⣿⣿⣿⡿⠟⠻⠟⠈⠻⣿⡿⣿⠿⣀
⠀⠀⠀⠀⠈⢿⣄⠉⣶⠀⢀⣄⠈⠉⠉⠉⠀⠷⡿⠿⢠⡤⠞⠁⠀⠀⠀⡤⢀⠀⠀⢀⣈⡠⠖⣤⣬⢣
⠀⠀⠀⠀⠀⠀⠉⠙⠻⡀⢸⠿⠷⠤⢤⣻⠀⠀⣠⠓⠶⠤⠖⠠⣄⡀⠀⠀⠀⠐⠀⠁⠀⠀⠶⢭⣥⡬⠱⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠳⠔⠉⠉⠙⠋⠉⠙⠛⠓⠤⢄⣈⣱⣊⡐⠀⠀⠀⠀⢠⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠛⣤⡰⠓⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠦⠀⣤⠀⢰⡶⠶⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡸⠼⡆⢸⠓⠀⠾⠲⠀⠀⠀⠀⠀⠀⠀⡀⣿⡏⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⠔⠃⠀⠛⠘⠂⠀⠙⠛⠀⠀⣠⠄⣴⠟⠛⠃⠈⠓⠒⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀⣤⢰⣶⣆⠀⠘⡆⢿⡄⢰⢶⡇⠀⢀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⠇⠀⠀⢀⣠⡄⠀⠈⡏⣷⠀⢯⠙⢿⣆⣻⡘⣷⣤⣠⣷⡀⠰⣄⣀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠙⠿⣠⣶⣶⠸⣧⠹⣄⠀⡇⠸⣇⠘⡆⠀⠙⠿⠇⠀⠉⠉⠉⣁⣀⡈⠉⠉
⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⢀⣴⠋⢹⡟⢠⣸⣧⠘⢷⡇⠀⢹⡆⠛⠀⢀⡠⠖⠂⠒⠒⡞⡁⠀⠹
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠘⠙⣆⢾⡀⢸⠁⠸⠷⠀⠁⠀⢀⣀⢀⡠⠏⠀⣠⣄⠀⠀⠈⠁⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢻⡌⢷⣼⣂⣀⠀⠀⠀⠀⠨⣀⠂⢠⣋⠀⠡⢌⣀⡤⠆⠀⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⢠⠈⡷⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⢆⣯⠅⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠋⠀⠀⣤⠀⠠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣿⣾⣦⠀⠓⣄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢊⠁⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢻⣄⣤⠛⢁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠬⡥⠾⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠉⠿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢛⣟⠒⢦⠀⠀⠀⠀⣠⠆⠀⢂⡔⠥⣤⣤⠴⠊⢈⠁⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠘⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡯⠭⠭⡤⢛⡄⠀⠀⠀⢀⡿⢉⣶⢧⡀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⡄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡛⠛⠒⢻⣶⣿⣤⡤⣀⠘⢅⡾⣣⡀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⡀⠠⣿⣿⡟⠊⢉⠘⢮⡉⠀⠉⠛⠷⠶⠦⣦⠀⣸⡆⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠁⢚⣟⡇⣼⡿⠟⠋⠀⣿⠂⢁⣀⣀⡄⠀⠠⣄⢈⡿⠏⠉⠱⣤⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠐⠚⢥⣐⣓⠛⡓⠒⢒⣒⣟⣉⡉⠌⡁⠀⠀⠀⠀⢫⠁⢀⠂⠄⣤⠃⠀⠀⢀⠀⠀⡄⢠⣶⢶⠖⠀⠀⠀⠀⡄⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡆⠀⡤⠘⡋⠩⠉⡍⢉⠉⠙⣇⣞⢰⡂⠀⣤⣄⣽⡶⠌⠃⠲⢦⣀⣽⣿⣭⣴⡾⣷⠾⠿⣤⣄⠀⠀⠀⢒⣲⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠯⣄⡀⠠⠀⠌⠀⠈⠀⠛⣈⠋⡛⣀⣸⣝⠐⠃⠗⠘⢋⠉⠉⠀⠀⠀⠀⠘⠁⠤⢤⣁⡀⣀⣠⣿⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠢⠶⠓⣦⣄⡴⠶⣄⣤⣤⡉⠻⣿⣷⠶⠒⠛⠓⠀⣠⣄⣤⣬⣱⠾⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠲⠀⠀⠀⠀⠀⠁⠈⢈⣋⡙⠋⠉⠙⠒⠚⠉⠉⠋⠀⠉⠀⢀⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣤⢰⠀⣀⣠⠀⠀⠀⠀⠀⣯⣽⠂⠀⣀⡀⢀⡀⠀⢹⡄⠴⣄⣾⡜⡁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣱⢁⣿⢿⣣⣙⠁⠾⠑⠀⢠⣤⠃⢸⠶⢦⡄⡆⣸⡏⠁⣼⣁⢽⡏⡏⠇⠫⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠈⠀⠙⢅⡄⢀⣉⡛⣁⣉⠈⣩⢥⡀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠚⠛⠛⢻⠋⠉⠉⠛⠛⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢉⣀⣀⣠⣤⠴⠖⠚⠻⡏⠙⠛⠲⠦⣤⣀⣀⡀⠉⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⣁⠤⠖⠛⠉⠉⠁⢀⣠⣤⣄⣀⣠⣧⢀⠀⠀⠀⠀⠈⠉⠉⠛⠳⢦⣀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⡤⠊⠁⠀⠀⠀⡤⠶⢒⡯⠶⠦⣤⡈⠀⢺⠀⠑⠶⠚⠙⠶⣒⡶⠦⢤⣀⠈⠳⢤⡀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⡀⢠⠒⠒⠚⠁⢠⣯⠞⠋⠙⠲⣝⢦⠀⠀⠀⠀⠀⠀⡞⡱⠊⠉⠓⣌⠻⣄⣀⣉⠳⢤⡈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⣴⠏⠀⡠⠋⠀⠀⣀⡼⢧⠀⠀⠀⠀⠘⡏⠠⢀⡀⠀⠈⢿⡆⠀⠀⠀⠀⠐⣇⢣⡀⠀⠀⡸⠀⣿⠀⢸⡇⠀⠙⢦⡀⠙⢷⣄
⠀⠀⠀⠀⢀⡾⠁⢀⡞⠁⠀⠀⢀⣽⣀⡀⠑⢄⠀⠀⠀⠘⢦⡀⠈⠉⢲⡞⢠⠀⠀⠀⠀⠀⠙⠶⣬⣉⣩⡤⠞⡗⢦⡀⠉⠑⢲⡄⢹⡖⠂⠙⣧⡀
⠀⠀⠀⢀⡾⠁⢠⠏⠀⠀⣠⠞⠉⠀⠈⢻⡳⡌⢢⡀⢀⣄⠀⠉⠛⠛⢋⠀⢘⠀⡴⢦⡀⠀⣀⣀⠀⠀⠀⠀⡰⠃⡼⠀⠀⠀⠀⠧⣄⠙⣆⠀⠈⢿⡄
⠀⠀⢀⡾⠁⢠⠏⠀⠀⢀⡏⠀⠀⠀⠀⠀⣧⢹⠀⠱⡞⢄⡙⠒⠒⠚⢉⡇⠸⠀⢹⡀⢱⡞⠁⠈⠹⣶⡒⢋⡠⠞⠀⢀⡠⠂⠀⠀⠀⠙⣌⢳⣄⠀⢻⡄
⠀⠀⣼⠁⢀⡏⠀⠀⢰⠋⢧⠀⠀⠀⠀⢀⠏⣼⠶⢄⠈⢢⡈⠙⠒⠋⠁⠀⠀⠀⡼⠁⡾⠳⣄⣀⣠⠏⠈⠁⠀⣀⠔⠋⠀⢀⡴⠚⠛⠓⢾⣄⠙⣆⠈⣷
⠀⢰⡇⠀⣼⠀⠀⠀⢸⠀⠈⠳⣄⣐⣂⣡⠞⠉⠓⣄⠳⠀⠙⢄⠀⠀⠀⠀⢸⠛⠥⠞⠀⣀⠤⠒⠲⢤⡀⡠⠊⣁⡤⣤⣤⡏⠀⠀⠀⠀⠈⡏⣷⠘⡇⠸
⠀⣾⠀⢰⠇⠀⢀⡤⠞⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⠄⡧⢴⣦⢧⡀⠀⠀⢸⠀⠀⠀⡜⠁⠈⢉⣽⠾⢷⣠⠞⠁⡎⠁⠘⣇⠀⡀⠀⢀⡴⢃⡟⠀⢻
⢠⡿⣤⣞⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⡜⢋⡼⡇⠀⠀⠀⢹⡄⠀⢸⠀⠀⢸⡀⢤⣾⠟⠁⠀⡀⣿⠀⣏⠁⠀⠀⠈⠳⠦⠭⠵⠖⠛⢦⡀⢸
⣼⠁⠀⠉⠅⠁⠐⠒⠠⢤⣀⣀⠀⠀⠈⠑⠬⠄⠐⠋⠀⠘⠤⣀⡠⠞⠈⠄⢸⠀⢀⣠⢶⠛⢄⡀⢀⠴⢡⡟⠳⠬⠃⠀⣠⠴⠒⠒⠒⠢⢄⡀⠀⡇⢸
⣿⠀⢠⠀⡜⠀⢀⡴⠋⣉⣉⣉⠛⠮⡉⠈⠀⠐⠂⠀⠀⠀⠀⠀⠤⠤⢄⣀⣽⠶⠋⠀⣀⣙⣲⠶⠶⠒⠋⠀⠀⠀⠀⠀⠙⠦⠖⠛⠛⠲⣄⠉⢲⡁⠸⡇
⣿⠀⢸⠀⢧⠀⠀⠓⠚⠉⠀⠈⠙⠲⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡠⠊⢹⠀⠀⢄⠀⠀⠀⠀⠉⠉⠉⠉⠁⠐⠒⠒⠲⠤⠤⢤⣤⣀⣈⡓⢿⡀⠀⡇
⢻⡄⠈⡆⢸⡇⠀⢀⡤⢖⣒⡒⠲⣤⡀⠀⠀⠀⠀⣰⠇⡷⠀⢀⢔⠁⠀⠀⠀⠀⡴⢚⣛⢢⡀⠀⠀⠀⠀⡔⢉⡷⢀⡴⢾⠛⠻⣖⢦⡀⠈⣩⠟⠁⢰⠇
⠘⣧⠀⢳⡘⢧⠀⡏⠜⠁⠀⠀⠁⠀⢻⣾⣉⠛⢋⣡⠜⡡⠂⠀⢏⠓⠤⣄⠀⠘⡀⠅⢈⠆⡍⠢⡀⠀⢸⠀⣾⠀⢸⠀⠈⡄⠀⠈⣧⢳⠀⢧⠀⢀⡞
⠀⠹⣆⠈⢧⠀⠑⢿⡀⠀⠀⠀⠀⠀⢀⡇⠀⠉⡁⠀⠈⡠⠔⠒⠚⠻⢶⡞⠀⠀⠈⣢⡤⠴⠥⣄⠈⠢⡈⢇⠹⡄⠈⢧⡀⠀⠀⢀⡞⣸⢣⠏⢀⡾⠀⢰
⠀⠀⠻⣆⠈⢧⡀⠈⠳⣄⡀⠀⢀⣠⠞⠁⠀⠂⠀⠀⡞⠀⠀⠀⠀⠀⠀⢻⡆⢠⠎⣡⡖⠉⠑⢦⠙⣆⠈⠪⡒⠉⠀⠀⠉⠓⠾⠿⠚⣱⠃⠀⣼⠁⢠⡿
⠀⠀⠀⠹⣦⠀⠱⣄⠀⢀⡟⠉⠉⠁⠀⢁⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣾⡇⠄⢨⠀⠀⠀⠀⣀⠧⠿⠶⠤⣌⠲⢀⠀⠀⠀⠀⣠⠖⠃⠀⢰⠇⢠⡿⠁
⠀⠀⠀⠀⠘⢷⣄⠈⠳⣄⢧⣀⣀⡀⠀⡌⢼⠁⠀⠀⠈⢦⣀⠂⠤⣔⡿⠋⡅⠈⠊⠁⠀⠀⡾⠡⠒⠉⠉⠐⠪⣷⡀⠰⠄⠀⢀⡇⠀⠀⣠⠋⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠸⠳⢌⡀⠙⢦⣱⡘⢄⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠇⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⢸⣇⣀⡞⠛⠁⠀⢀⠜⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⠀⠙⠦⣀⠈⠙⢤⡘⠦⠔⢓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⢀⣠⠟⠀⠀⠀⠀⣠⠞⠁⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠈⠓⢦⣀⠉⠹⢯⣁⣠⡤⠶⢤⣀⠀⠀⠀⣠⠖⠛⠓⠦⢤⠴⠋⠉⠉⠀⠀⣀⡤⠖⠋⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠈⠙⠒⠦⢤⣀⣀⡀⠀⠈⠑⠛⠋⠁⠀⣀⣀⣀⣀⣠⠤⠤⠒⠚⠉⠁⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠈⠉⠉⠉⠛⢻⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠋⠉⠁
⣿⣿⣿⢿⣿⠿⢿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣷⣾⣶⣶⣦⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠶⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⡶⠶⢿⡟⠛⠛⠉⢻⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⢿⠛⠋⠉⠹⣇⠀⠀⠈⣧⣀⣠⣤⣼⡷⠾⠿⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠟⠛⢿⡁⠀⠀⠘⡇⠀⣀⣠⣿⡶⠶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⢀⣤⣴⡶⢿⡟⠋⠁⠹⡆⠀⠀⢘⣧⣠⣤⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠸⣿⠀⠀⠈⢧⠀⣀⣠⣿⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⠶⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠹⣧⣤⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠌⠁⠈⠻⠀⠀⠀⣀⣠⣤⠴⠖⠛⢿⣆
⠀⣸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠛⠋⠉⠁⠀⠀⠀⠀⠈⢿⡆
⢰⡟⢹⣧⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⣾⡇⠀⣿⡆⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⣿⠀⠀⠸⣷⠀⠀⢻⣧⠀⠀⠀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⣿⡀⠀⠀⢿⡆⠀⠀⢻⣶⠚⠋⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⢻⡇⠀⠀⠘⣷⠀⠀⠈⢿⡄⠀⣠⡾⢁⡾⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⢸⣧⠀⠀⠀⢻⡆⠀⠀⠘⣷⡀⠉⢠⡟⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⣿⡀⠀⠀⠘⣷⠀⠀⠀⢹⣧⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⣠⣶⠆⠀⢿⡆
⠀⢸⣧⠀⠀⠀⢻⡇⠀⠀⠀⢿⡆⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢿⣤⡷⠀⢿⣤⣀⠀⠘⣿⡀
⠀⠀⣿⡆⠀⠀⠘⣿⡀⠀⠀⠈⣿⡀⠀⠀⣾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠈⣿⣷⣄⠀⠉⠹⣷⠀⢹⣧
⠀⠀⠸⣷⠀⠀⠀⢹⣇⠀⠀⠀⠸⣷⠀⠀⠻⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⣦⡀⠀⣿⡀⠀⠀⠀⠘⣿⠙⠃⠀⠘⠋⠀⠀⢿⡆
⠀⠀⠀⢻⡇⠀⠀⠈⣿⡄⠀⠀⠀⢻⣇⠀⠀⠀⠉⠻⢶⣄⡀⠀⡀⣀⣄⡀⠀⢰⡟⠀⠀⣿⣧⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠘⣿⡀⠀⠀⠸⣷⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠙⢿⡌⣿⡟⠙⢷⡄⠘⢷⣤⣴⡿⠙⠃⠀⠀⠀⠀⠀⢀⣠⡤⠶⠂⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⢹⣇⠀⠀⠀⢻⡇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠘⣷⠸⣷⡀⠈⢿⡄⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⣿⡀⠀⠀⠀⢹⣇⠀⠀⢀⣀⣀⣸⡟⠀⠉⠁⠀⠀⠀⣀⣠⣤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⢰⡆⠀⣰⠀⣀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠸⣧⠀⠀⠀⠀⢿⡀⠀⠈⠙⠛⠋⠀⠀⢀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⣿⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢻⣆⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⢿⡄⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠘⣷⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠹⣧⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢻⣇⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⢿⡆⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⣿⡀⠀⠀⢿⡆⠀⠀⣀⣠⣤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠸⣧⠀⠀⠸⣿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢻⣇⠀⠀⣿⡄⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⢿⡟⠋⠉⣷⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠈⣿⡄⠀⢻⡇⠀⠈⠳⣄⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠻⣏⠉⠀⠀⠈⣷⣠⣴⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢸⣷⠀⢸⡇⠀⠘⠳⢮⡻⠆⠀⠀⠀⢀⣠⣤⣴⣶⠟⠛⠉⠙⣧⠀⠀⢀⣹⣦⣴⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⢿⡇⣾⡇⠀⠀⠀⢀⣀⣤⣴⠶⢿⡟⠋⠉⠀⠸⣇⠀⠀⣀⣼⣶⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣁⣤⣶⡾⠛⢻⡅⠀⠀⠀⢻⡄⠀⣀⣤⣿⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠉⠁⠘⣧⠀⢀⣻⣤⣤⣴⡾⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⣶⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠏⣂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⠯⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣯⠋⠻⢿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣁⣔⢀⠓⠈⣤⣀⡀
⠀⠀⠀⠀⠀⣤⣿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣬⣰⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢐⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣹⣿⣿⣿⣅⠀⠁⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠤⠼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣀⠦⡈⡀⣿⡗⢰⣼⡀⢰⣦⣶⣶⡀⢉⣡⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⢳⣿⣿⣿⠿⡇⠐⢻⢟⡛⠁⠹⣿⣁⡀
⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣿⡇⠐⠃⠘⣻⣿⣿⣿⣿⡟⢡⣽⠁⢀⡘⠀⠀⢀⢧⠀⠚⠂⠀⠰⡎⠃⢀⣤⣀⣀⣠⡄
⠀⡀⢀⢀⣸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣳⠁⡐⠛⠀⠀⠀⢾⣿⣿⣿⣿⡏⢀⣸⣿⣄⡉⠄⢸⡆⡈⢰⡀⢿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠀⠈⢳⡀⠀⠀⠹⣿⣿⣿⠁⢸⣿⣿⣿⣿⣶⣿⣿⣵⣿⠀⠈⡄⢀⣀⣵⣞⣸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢈⣀⠀⠀⠘⢷⣤⠀⠐⠿⢿⠋⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠇⠸⢻⣿⡖⡘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣇⠀⠀⠰⣏⢀⣤⣀⡘⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣄⡆⢹⣿⡟⠀⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⠂⠀⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢭⠃⠀⠀⠀⠀⢱⣐⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀⠀⠀⠀⠽⠿⠿⠿⠛⠋⠉⠠⠞⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡞
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣲⠆⠀⠀⢀⡀⠀⠀⠀⠀⠙⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠉
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⡄⠴⠞⠀⠀⠀⡰⠏⠀⠀⠀⠀⣦⠐⢯⣤⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣥⣄⠀⠀⠀⠀⠛⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⡍⠙⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣿⠟⠟⢋⠉⠉⠀⠀⠀⠻⣄⠀⠉⠉⠉⠉⣏⣙⣇⠀⠂⠀⠀⠀⠀⠀⠀⢺⣯⢻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣀⠠⠄⠀⠉⠻⣀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠀⠀⠈⠛⠛⠓⠢⠄⢀⡴⠟⠋⠉


⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⢰⣖⣴⢄⡀⠀⠈⠓⠶⠚⠁⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⣙⣻⣷⣎⡼⠆⠀⢀⡄⢠⣄⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠃
⠀⠀⠀⠀⢩⣭⠿⣿⡴⢎⠾⣌⣷⣾⡿⢭⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠷⣿⡿⣯⣙⠓⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⠰⡷⡄
⠀⠀⠀⣀⢶⣘⣷⢰⡀⠀⠀⠘⠳⠆⠉⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠒⠒⠀⠛⠛⠃
⠀⠀⠈⠫⡟⣻⡿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠁⠉⠀⠀⠀⢺⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡮⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠬⡗⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⣾⡿⠾⠼⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣴⣦⡀⠀⠀⠐⢆⡀⠁⣀⡐⣹⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⢯⡓⣿⡄⠀⠀⠀⠀⠈⠊⢥⣿⡏⡉⠀⠙⣿⣧⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⢾⣿⣷⣠⣏⢠⣀⡀⡀⠀⢀⣿⠿⣿⣷⠋⠙⢷⣿⣿⣿⡟⢿⡄⠀⠀⠀⠀⠀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡖⠘⠛⠋⢸⡟⢤⣹⠀⠻⠈⠀⠘⠛⢿⠀⠀⣿⡏⠋⠱⢿⡄⣿⡄⠀⠀⠀⠀⠀⢆⠸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠓⠀⠀⡀⢰⠖⠻⠿⠚⠏⢈⡈⣿⡤⠀⠀⡀⠀⠸⠁⠀⠀⢀⣭⣤⣬⣽⣿
⠀⢀⣀⣴⡶⢚⣁⠀⠄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠂⠒⠤⠠⡠⠐⠁⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉
⢀⡩⠤⣞⠟⡉⠀⠄⠀⢢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠠⢦⡀⠻⠁⢀⡀⢠⠔⠀⠀⠀⠀⠴⠀⠀⠀⠈⠀⠀⣠⣼⣿⢤⣤⣤⣴
⠨⡁⠀⡷⠰⡅⠀⡨⠄⣠⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⠄⡘⠢⡿⠃⠀⠀⠀⠀⠀⣀⡐⡀⢀⠀⠆⠀⠀⢸⡇
⠀⢳⣰⢵⡀⠨⠁⠺⣿⠄⠀⠀⠀⠀⠈⠃⠀⠤⡆⢠⠀⡾⠠⠴⠄⠑⢤⠎⠀⠀⠀⠀⡀⡴⢚⡾⢿⠗⠶⡌⠀⠀⠀⡾
⢀⣹⡋⠛⠓⠂⣀⣴⢻⣇⡀⠀⠀⣤⠈⠛⠠⠏⠻⠈⠋⠀⠣⠀⡴⠂⢸⡀⠀⠀⠀⠹⠇⣠⠟⠁⠁⠀⠀⣨⣵⠙⣺⡓⠦⢴⡷⣴⡦
⠠⣟⡷⢈⠓⠖⠛⠛⠷⠼⠃⠀⠉⠁⢠⣎⠐⠀⠸⣼⡄⠀⠀⠀⠀⠀⠀⠧⠤⠶⠤⠤⠬⠴⠾⠆⠀⠠⠞⢿⣿⠂⠙⠓⠒⠈⠁






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠾⠶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠊⠙⠛⠛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⡖⠀⡠⠀⠐⠙⠛⠻⣶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠳⢷⣤⡇⠀⠀⠀⠀⠰⠋⠉⠉⢛⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠃⠀⠀⠀⠈⡛⢾⣧⡀⠀⠀⠀⠀⠈⠉⣀⣉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡐⠀⠂⠁⠈⠠⠈⡆⠈⠻⢦⣀⣶⡆⢠⠏⡁⡈⡧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢡⡀⠁⠄⠀⠌⣠⠃⠀⠀⠀⠉⠻⣧⡘⠦⠗⠛⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠉⠀⠉⠓⠲⠖⠚⠁⠀⠀⠀⠀⢀⡀⠭⠻⢶⡶⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠁⡏⢉⣩⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠎⢢⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠉⡉⢀⠀⣎⣩⣦⡀⠀⡗⠙⠦⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣠⣄⠀⢸⠛⠉⠃⢁⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠢⠼

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣟⣛⡛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣄⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠸⣟⣛⣻⡿⠀⠒⢠⣿⣷⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠐⢉⡿⢇⣉⠋⠀⠀⡉⢸⣿⣿⢨⡅⠀⠈⠉⠉⠉⠛⠛⠿⢷⣦⣦⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⣿⡿⢮⣿⣿⣿⠂⠀⢸⣿⣿⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳
⠀⠀⠀⠀⠿⠿⠷⠿⠿⠿⠿⠀⠀⠘⠿⠟⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠀⢀⣀⡀⣀⣄⡀⣀⢀⡀⠀⠀⠀⠀⣠⣴⣾⣿⣟⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⡟
⠀⠀⠀⠀⠀⠀⣼⣿⡟⣼⡇⢀⣿⣿⢰⡿⠛⢳⣿⡿⠁⠀⠀⠀⢸⣿⣛⢋⣵⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢠⣿⣽⢇⣿⣄⣼⣿⣿⢾⣷⡶⣾⢻⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣤⠤⠥⢤⡤⡤⣤⣤⠀⠀⠀⢸⠟⠉⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⢙⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⠀⡟⠀⡌⠀⢱⢰⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⣤⢠⣤⣤⢤⣤⣤⣤⣤⣭⣭⠉⠉⠉⠉⠉⠉⠀⠀⠀⢰⣶⣶⣤⣤⣶⣿⣿⣿⣿⣧⣍⠹⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣶⣶⡀
⠀⠀⠀⠀⣿⠀⣿⢻⡽⣷⢾⡿⣿⢿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠀⡿⣿⣾⣿⣿⣷⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣉⣀⣀⣉⣉⣉⣉⣉⣉⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠺⠦⠴⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⢁⡄⡤⠔⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠊⠁⠒⠚⠀⠀⠀⠀⠀⣀⠤⡔⠁⠀⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠒⠢⡀⠉⠀⠀⠀⠀⢀⠔⠂⢰⠒⠉⠀⠀⠣⡀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠌⠀⢘⠀⠀⠀⠀⢀⣇⣀⠁⠀⠉⠡⣀⡀⠀⠈⠉⠉⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠄⠀⠀⡀⠠⠒⠪⡀⠀⠀⡐⠁⠀⠀⠉⢆⠀⠀⠀⠘⠢⢄⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠉⠁⡠⠊⠀⠰⠢⠀⢡⠀⠀⢡⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠉⠀⠂⠒⢉⠑⡄
⠀⠀⠀⠀⠀⡠⠚⠁⠀⠜⠀⠀⣠⠎⠀⣼⠁⣈⠻⡁⠘⠀⠀⠆⠉⠒⢤⢀⡀⠀⠀⠈⠒⠤⢀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⣠⣊⡀⠀⠀⠀⡠⠒⠁⠀⢠⠤⡘⣆⠙⠆⠱⠀⢡⠀⠄⠀⠀⡆⠀⠀⢉⠖⠂⠤⣄⣀⠈⠳⠀⠀⠀⠀⠄
⠀⠀⠘⢡⠠⠌⢂⠠⠊⢀⡀⢤⠀⠀⠙⠃⠈⠓⠶⠊⠀⢂⢳⠀⠀⠀⠀⠀⠢⡜⣄⡀⢀⡇⠀⠀⢩⠃⠒⠒⡞
⠀⠀⠐⣌⢢⠔⠁⠀⠀⠚⠉⢡⠒⠒⠢⢄⠀⠀⠀⠲⡒⡀⠈⡀⠀⠸⠀⠀⠀⠇⠀⠈⡌⠑⠈⢀⠇⠀⠀⡐
⠀⠀⠀⠀⢹⠀⠀⢠⢤⡀⠀⠹⢦⡘⠓⠀⢑⢠⡀⠀⠐⠓⠀⣇⠀⠆⠀⠀⡘⠀⠀⢠⠁⠀⠀⡎⠀⠀⡰
⠀⠀⠀⠀⠃⠀⢠⠉⠒⢬⠇⠀⠀⠉⠛⠛⠋⠸⢌⡤⠀⢤⡀⠸⡀⠀⠀⢀⠃⠀⠀⠄⠀⠀⡜⠀⠀⡰⠁
⠀⠀⠀⠀⠢⠔⠁⠀⠀⠸⣀⠠⠲⢵⠀⠈⠀⠀⠘⣇⠰⢦⠘⠄⠹⠤⠄⣜⠀⠀⡘⠀⠀⡰⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢍⡢⡀⠈⠳⢤⣤⢜⡀⢣⠀⠀⠈⠉⠑⠂⠤⠧⣀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢍⡐⢄⠀⠈⠮⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢕⢄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠚

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢖⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⢀⣠⣤⣉⡛⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠉⠹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠷⠦⠤⠾⠋⢹⡆⠀⠀⢀⣠⠶⢻⡟⠀⠈⠉⢉⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠲⠦⣄⣹⡎⠙⠶⣤⣀⣤⣤⣴⠶⣾⠁⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠉⠁⠀⣾⠁⠀⠀⣠⡟⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⣀⣀⣠⣿⠾⠛⠀⠀⠀⠀⠀⢸⠻⡇⠀⠀⠀⢸⡇⠀⠀⣰⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⠉⠛⠛⠋⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⢀⡿⠀⣷⠀⠀⠀⣾⣀⣤⠾⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⣸⠷⠶⢿⡶⠚⢻⡏⠉⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡇⢻⣄⠀⠀⠀⣠⡏⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⡇⠀⠙⣶⡀⠀⠟⠀⠀⠀⢨⣧⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢹⣇⣠⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⣀⣀⣤⣤⣿⠀⠀⠀⠀⠈⢷⣤⣀⣀⣀⣀⣠⣤⣤⠤⠶⠋⠀⠀⢸⡇⠀⠀⠉⠉⠉⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⡟⠛⠋⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠄⣸⠏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠉⠐⢿⣤⡀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⠀⣿⡀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠙⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠙⠿⠆⠀⠰⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠙⠛⣛⣛⠛⠛⠉⠙⠛⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠸⣖⠀⢀⣀⣀⣀⣠⣠⣤⣄⣀⣀⠀⠀⢀⡿⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠀⠈⣷⠀⠘⣏⠉⠁⠀⠴⡄⠀⢠⠖⠑⠄⠉⠙⡏⠁⣼⠭⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢀⡠⠖⠛⣄⠀⢻⠀⣀⠤⢄⡀⠀⠈⠣⠞⡁⠀⣸⠁⢠⡟⢦⣀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⣠⢞⡡⠀⢀⠔⡫⠐⢄⠀⠘⣆⠈⣷⠁⠀⠀⢸⠀⡖⠢⢀⣉⣠⠇⣰⠏⠀⠀⠈⠓⢄⠀⠱⠝⢦⣄
⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠁⠀⠣⠤⠝⠘⠀⡸⣆⠸⡗⠤⠔⠋⢀⡈⠀⡧⢀⠏⣰⡷⠒⠲⡄⠰⠇⠀⠙⢄⠀⠀⠈⠳⣄
⠀⠀⠀⣼⠁⠀⠀⣠⠏⠰⠲⠀⠀⠀⢤⠢⠀⣡⠘⡆⢻⡄⠀⢀⣈⠁⠀⢑⡞⣰⠿⡀⠀⠀⡸⠀⠀⢠⠖⠢⠱⡄⠀⠀⠽⣆
⠀⠀⠀⠻⣴⣀⣴⠃⠀⠀⣠⠚⠈⠒⡌⠉⣀⠈⠀⠹⡄⢷⠀⡅⢂⠇⢀⡞⢠⠏⠀⠉⠐⠊⢠⠐⡄⠘⠴⠔⠁⠘⣄⡀⣠⡟
⢀⡴⠖⠶⣄⠀⠈⠛⠦⣄⣳⡀⠀⢀⠆⠀⠉⡠⢄⠀⢳⠈⣧⠀⠁⢀⠞⢠⠏⡠⠀⡀⠚⠇⢀⡩⠤⡈⠉⣀⡤⠖⠋⠉⢉⣀⣀
⣾⠃⠀⠀⡟⠉⠙⠲⠤⣄⣉⠛⠿⢥⣀⡀⠀⢄⣡⠃⠈⡇⠈⠳⠴⠋⢀⡟⠀⠣⠈⠂⠀⠀⣂⣩⠤⠟⢋⣁⣤⡤⠴⢶⠋⠓⠈
⣿⠀⠀⢰⢁⠄⣤⠀⠆⠸⣉⡙⢲⢤⣈⠙⠓⠶⣤⣀⣀⡟⢀⡠⠤⣄⡘⢧⣠⡤⠤⠖⠚⣉⣡⠴⢶⠟⠛⠳⡄⠀⠀⠸⡆
⣿⠀⠀⢸⠹⡄⠴⠀⢠⠒⡌⠉⠁⠀⠈⠙⠲⢤⡀⠀⠁⠀⠁⠀⠀⠀⠙⣦⠀⣠⠴⠚⣋⢉⠀⠀⠸⡀⠀⠀⡸⢀⣤⠀⡇
⣻⢰⠀⢾⠀⠀⠀⠀⣈⢉⡀⠘⠃⢰⠁⢑⠀⠀⢙⡆⢰⠀⠀⡀⡈⠡⠀⢸⠺⣄⠀⠐⢀⣄⠇⢠⡄⠈⡀⠈⠀⠀⠁⠀⡇⠀⡇
⣿⠀⠀⢸⠀⠋⠀⡞⠀⠀⠙⡄⠀⠀⢁⣩⡤⠖⠋⠀⠈⢧⡀⠀⠁⠀⣠⣏⡀⠈⠓⠦⣀⠀⠀⢀⣀⡘⠤⠃⢠⠖⠒⡄⡇
⡇⠀⠀⢸⡄⠀⠀⠑⢤⣠⣴⡥⠖⠛⣉⡥⠴⠒⠚⠋⢳⡄⠈⠉⠈⠉⣼⠉⠉⠛⠲⢦⣌⣙⠲⠧⣈⡈⡆⠐⠌⠳⠄⢡⠇
⢻⡀⢀⢀⡧⠶⠖⠚⠋⣉⣤⠖⠚⠩⠀⠀⠠⡂⢢⠀⣼⠁⣠⠖⢲⡀⢸⡄⠰⢉⠙⠄⠀⠉⢙⣶⣦⣍⡓⠲⢤⣀⣀⣾⠀⠀⣠
⠀⠙⠛⢋⣀⣀⠤⠒⠉⣡⡈⠒⣚⠁⢠⡠⠘⠀⠊⣰⠃⡰⠁⠀⠀⢹⡄⢣⠀⠉⠈⡠⡀⢰⠁⠀⠀⢳⠉⠳⢦⣄⣈⣹⠦⡤⠞
⠀⠀⣰⠋⠉⠹⡄⠀⠴⠦⡄⠈⠤⠃⣀⢀⣀⠀⣰⠏⡸⠁⠰⠡⢈⠄⢳⡈⣧⠤⣀⠉⡀⠈⠢⠄⠴⠋⠀⠀⢠⠞⠉⠏⢷
⠀⠀⠸⣶⠀⠀⠘⢆⠦⠤⠏⠀⠀⡌⠀⠀⠈⣦⠏⣰⢅⠀⢀⡉⠁⠀⠈⢧⠘⣆⢛⠄⠢⠚⠀⠀⠀⠾⠂⡰⠋⠀⠀⢠⡟
⠀⠀⠀⠙⢦⡀⠀⠈⠳⣄⠀⢰⡂⠘⠦⠤⢴⡟⣰⠃⢶⠀⣈⠁⢠⠔⠒⢺⣇⠘⡎⠐⡆⣴⠉⢲⠀⣠⠞⠁⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠙⠳⣔⢦⠈⠑⢦⡀⠀⠀⢠⠏⢠⠏⣉⠁⠨⠤⠁⢇⠀⠀⢀⠿⡄⠘⣆⠀⠘⠒⣪⠞⠁⠀⢊⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠉⠳⣴⠏⠀⡞⠀⢈⡤⠠⡀⠀⠀⡑⠒⠉⠀⢷⠀⠘⢦⠴⠋⠁⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢐⡾⠀⣸⣇⣀⠘⠄⡤⠃⠀⠈⠓⠀⢀⣀⣸⣆⠀⢻⣄⣀⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢼⠁⠀⠀⠉⠉⠉⠙⠉⠉⠉⠉⠉⠁⠀⠼⣧⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢴⣤⣀⣀⣤⣤⡬⠭⣤⣤⣤⣤⡤⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠦⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠄⡀⠀⠀⠈⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⣾⣏⠀⠈⡄⠀⠀⠀⠀⠀⣾⠿⣄⠀⣰⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⢱⣿⠇⠀⠢⠒⠘⠀⠙⠿⠇⠿⠟⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⣀⡤⠴⠒⠒⣚⣉⠉⠉⠉⠉⠉⠉⠙⠒⠒⠶⠤⣄⣀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢯⠉⠀⠀⠀⢠⠋⠁⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⣄⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⣠⠚⠉⠙⢦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡼⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢠⠇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠒⠉⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⡴⠒⠒⢦⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢯⠹⡄⠸⡇⠀⠀⢸⠇⠀⠀⣰⣧⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣧⠀⠈⠓⠚⠁⠀⠀⢀⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⡀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠀⢧⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠶⠶⠶⠶⠶⡶⠶⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠶⠦⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠴⠟⠋⢁⠀⠀⣀⣤⢤⡤⠤⠴⠂⠀⠀⠐⠶⠤⠴⠶⠶⠿⢶⣤⣀⡀⠀⠀⡀⠈⠉⠉⠉⠙⠛⠶⣤⣄⣀⣀
⠀⠀⠀⣠⡴⠟⠋⠉⠀⠀⣰⠀⠀⠴⠿⠟⡛⠉⢀⣤⣤⣄⠀⠀⠀⠂⢄⣠⢤⣤⡐⢀⡤⠀⠀⠉⠉⢛⣛⠁⠀⠈⠳⠦⠤⠤⠀⢤⡀⠉⠉⠙⠳⢦⡀
⠀⠀⡔⠋⠀⠀⢠⣤⡴⠞⠃⠀⠄⣂⠀⠄⢠⠀⢬⣥⣬⣿⠃⣠⣤⡀⠀⠀⠀⠈⠁⠉⠀⢸⠀⠀⠘⠀⢀⣒⣣⣴⣤⡐⠶⠖⠀⠈⠻⢦⣤⣄⠀⠀⠉⢢
⠀⢀⣀⡀⠀⠤⠞⠁⠐⠒⠂⢌⣒⣀⢀⡛⠈⣇⠀⠈⠙⠛⢣⣘⣛⢁⣀⣀⠀⠀⠀⢀⠀⢸⠀⠈⠀⠀⠀⠛⠿⢿⣿⡯⠒⠿⠀⠀⠀⠀⠉⠙⠳⠄⢀⣀⡀
⠀⠀⠀⠙⣧⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⡀⠀⠈⣩⣿⠅⠀⢉⣉⡉⠉⠀⠁⠀⢀⠐⠉⠀⠀⢀⣀⣀⣀⣠⠾⣬⠴⠂⠀⠀⠀⠀⢰⡏⠀⠈
⡀⠀⠀⠺⣇⠀⠰⣷⣄⣀⠀⢚⣶⠀⠀⠈⠂⠀⠀⠰⢤⣭⡴⠞⣿⣿⣿⡿⠛⠿⠛⠀⠀⢱⡄⠀⠙⠒⣚⠛⠉⠀⣀⠀⠠⠚⣉⠑⠂⠐⠀⠀⠀⣸⠗
⡇⠀⠀⠀⢸⠆⠀⠠⣬⣹⣿⣿⡿⠋⠙⠛⠋⠀⠀⡤⠶⠶⠤⣄⡈⠻⠿⡿⠿⠶⠥⠴⠆⠜⠁⣉⡛⢿⣿⣦⣰⣦⡈⢳⠀⣾⣿⣤⣴⣶⣷⠄⠀⡏
⢇⠀⠀⠠⠾⠦⣤⡀⠉⠛⠛⠋⢠⣀⣉⣠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠂⠀⠄⠠⢀⣀⡤⠒⠈⠛⠻⠿⠟⠛⠋⠀⡈⠀⠙⢿⣿⣦⡦⠀⣀⣤⣿⡄
⠘⣷⠀⠀⠀⠀⠀⠉⠳⠀⠀⠀⠀⠈⠀⠀⢀⠀⢀⣤⢀⣸⣷⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⡒⣀⡦⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⣠
⠀⠙⣆⠀⠀⠀⠀⠀⠠⠐⠒⠒⠒⠦⣄⡀⠘⢧⡙⠿⢿⣿⣿⡶⠞⠃⠀⠀⣀⠚⠁⠀⠀⣀⣀⣀⣀⡴⠊⠉⠁⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠈⠷⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣥⣤⣄⣀⠀⢀⣀⠀⠀⠈⠓⠒⠚⢋⣁⣀⣀⣀⣠⣤⠶⠖⠒⠒⠒⠶⠤⣀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠈⠻⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠛⠂⢀⡴⠚⠉⠉⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠴⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠴⠶⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣀⣥⣤⣄⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠀⠀⣀⠀⠀⠑⢄⠉⢠⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡞⠁⠀⠀⠀⣠⣖⠀⣸⣀⠀⠀⠄⡀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⡇⠐⢷⡶⠀⢀⣡⡼⠋⠉⢀⣠⠕⠡⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣄⠁⠀⠀⠀⠀⡀⢀⠀⡾⠾⣮⣤⣤⠶⠚⠉⠀⠀⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠠⡀⢀⣨⣿⣿⣏⢀⣤⡀⠀⠀⠈⠀⠁⢀⠐⢺⡏⠉⠠⠄⠢⢄⠀⠀⢀⡤⡖⠶⠲⢤⡀⠀⠀⠀⠃
⠀⠐⠀⠀⠀⠙⠿⣿⣿⠟⠫⠈⠁⢤⡄⠀⠀⠀⢰⡏⠀⠀⢠⡀⠀⠀⣠⠞⠂⠀⠀⣠⣤⣙⣾⣿⡷
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠤⠒⠀⠀⠘⢧⡠⠄⠀⠀⠠⣾⢣⠂⠀⠁⠚⠻⢿⣿⣿⠟⠃
⠀⠰⡴⠚⠋⠉⠳⣄⠴⠚⠓⠚⠛⢦⠀⣤⠤⠤⢤⡀⢙⣓⠲⠶⠚⠻⣿⡆⠀⠀⠀⠀⣀⣠⢤⣀⡀⠀⠀⠇
⠀⠀⠈⠀⠀⠀⠁⠀⠈⠁⠀⠀⠐⠈⠉⠀⠀⠀⠀⠉⠉⠙⣇⢠⠞⠙⠁⠒⠓⠤⠤⠚⠉⠀⠀⠈⢷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠤⠤⣄⡀⠀⢰⡃⠡⠀⠀⠀⠀⠐⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⠋⠐⠑⠁⠈⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠒⢀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠐⠚⡄⠀⠈⢀⠆⠀⠀⠀⠅⠂⠀⠦⡀⠀⠀⠠⠐⠀⠀⡀⠴⠳⣱⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠞⣁⠀⠈⠁⠀⣠⠆⠀⠀⠀⡀⠐⣒⠖⢲⢫⠀⠀⠀⢀⡱⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠈⠃⠉⡀⠙⠐⠒⠒⠉⠀⠀⠀⠀⢸⢸⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠤⠤⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⢃⡀
⠀⠀⠀⠀⠀⠰⠂⠐⠎⠁⠀⠀⢸⣀⣠⢀⠅⠀⠀⠀⠀⠀⠉⠛⡛⠐⠒⠔⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠡⡀⠀⢀⠜⠀⠀⠀⡄⠀⠀⣄⡀⠀⠀⠀⠀⢀⣀⡇⢸⡀⠀⠀⠀⢂⠖⠉⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠘⠁⢠⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⡀⢠⡦⠂⠀⠊
⠀⠀⠀⠀⠨⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⡀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠇⠀⠰⠗⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣀⡰⠄⠀⣀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣲⠚⠙⠛⢋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠙⠛⠁⠿⠛⣆⣰⣧⣿⡖⠀⢰⣶⣤
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠂⡴⡗⠺⣽⡵⠙⠋⠀⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣤⡀⠀⢤⣤⣀⣀⣠⣴⣾⡷⡶⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡧⠀⣼⣿⣿⠙⣿⣿⣿⣿⡄⠀⢻⣿⣿⠇
⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣤⣿⣿⣿⣿⣿⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣡⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⢀⠀⣀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠐⠀⠤⠤⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⣶⣰⣦⠀⠀⠀⠀⠀⠀⢐⠀⠄⢂⠈⢀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⣠⠐
⠀⠀⢀⣠⣤⣴⣶⡆⠀⠸⠀⠈⠹⠀⠀⣠⠀⠐⣥⣤⣤⡄⣤⡄⠀⡂⠀⣀⠄⠁⠀⠀⠣⠀⠀⠠⠰⠀⠀⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠐⡐⠈
⠀⢸⡿⢟⡿⣱⣼⡇⠀⠠⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠁⠀⠀⠀⠄⠀⠀⣠⣴⠀⡄⣐⡥⠤⠄⣀⣤⠀⠆⠐⢀⣀⠐⠓⠒
⠀⢸⡷⠶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢿⣻⠀⠃⠀⠁⠈⡛⠛⠁⠠⠀⠀⢿⢸⠠⠈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠸⠂⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣹⡴⠛⠁⠀⠀⠀⠀⠙⠃⠄⠈⠀⠀⠈⠈⠉⠀⠀⠁⢰
⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣞⣁⣀⣺⣆⠀⡅⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡿⠋⢀⡄⠀⠀⠀⢄⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠈⠀⢼
⠀⠸⢯⣿⣿⣽⠻⠇⠀⠀⣾⠙⡋⣩⡇⣜⡷⠀⠀⠀⠠⡰⠖⠊⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠺
⠀⠈⠂⠤⠠⠄⠐⠁⠀⢀⠈⠒⠻⠟⠛⠛⠁⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⣄⠐⠑⠄⠀⠐⠐⠁⠀⠀⠐⠀⠀⠀⢐⡹⢄⠀⠀⢘⠀⠀⠀⠀⠀⢰
⠀⠀⢀⡀⠀⠀⠒⠨⠊⠀⠁⠂⠀⠀⠀⠐⠈⠀⠈⠐⠀⠀⠀⠐⠊⠀⠀⠀⠈⠁⠐⠓⠈⠀⠀⠐⠊⠁⠂⠢⠀⠀⡐⢃⡄⠀⠐⠀⠀⡀⠀⠀⠄
⠀⠀⠈⠉⠀⠀⠄⠲⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠠⠄⠀⠀⡀⠀⠀⠈⠄⠂⠀⢞⣘⠀⢈⠒⡆
⠀⠀⠃⠂⠀⠀⡀⣀⡤⠖⠉⠀⠀⠀⢸⡿⠛⠛⡃⠀⠀⠀⠀⠀⠀⣷⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀⠰⠾⠃⠁⠀⠀⢀⡀⠠⠤⠄⠠⠄⠀⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠃⠀⠀⠀⢸⣧⣀⠘⠓⠒⠰⠆⠂⠲⠂⠙⠀⠈⣹⠃⠀⠀⠀⠀⠀⠀⠀⡰⢂⣀⠀⢰⡀⠀⢀⠀⠀⠀⢀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣏⠉⣀⣄⣀⣀⣀⣀⣀⣈⣙⣀⣀⣘⠃⠀⠀⠀⠀⠀⠀⠀⠑⣆⡠⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⣜⢁⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠆⠀⢀⡁⠀⠐⠉⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⣾⡶⡎⠁⢸⠀⠀⠨⠀⠒⠀⠀⢒⣀⣠⣴⣶⣖⡒⠂⠒⠆⠠⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⠀⠀⠀⠀⠤⠤
⠀⠀⠄⢀⠀⠀⢾⡏⠀⠐⠁⠀⠀⢜⠀⣠⠶⠿⠟⢋⡙⢫⣼⠰⢜⡆⠀⡁⠀⠀⠀⠀⢰⠰⣴⠀⡄⢀⠅⢸⡇⣇⡿⠀⣼⡟⠁
⠀⠀⡀⠀⠀⠉⠉⡀⢀⣀⠀⢀⠀⠀⠀⢧⣛⣣⣦⣦⣵⣷⣶⠿⠋⠀⠀⡇⠤⠠⠤⠠⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠄⡈⠀⠉⠀⠀⠀⠀⠀⠀⣼⠂⠐⠀⠈⠉⠛⠛⠋⠉⠁⠰⣯⣩⡿⠀⡆⡠⠀⠀⠐⠀⣀⡀⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⠐⢠⠤⡄
⠀⢈⣈⣁⣀⣀⣈⣉⣉⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⣰⠺⡄⠅⢔⠐⠊⡀⡆⠀⠀⠀⢀⠀⠀⠀⠈⠄⠣⠀⠰⠂⠃
⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⣄⠔⢨⡅⠖⡄⠀⡆⠔⠀⠑⡆⢦⠀⠣⡀⠁⠀⠀⠀⠈⠁⡐⢀⠠⠀⠈⠀⠈⠁⠂⠀⣠⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⢨⠀⠀⠀⠉⠀⠀⠁⠁⠀⠁⠁⠂⠐⠉⠉⠀⠀⠈⠢⠄⠀⠀⠔⠊⠀⠀⠀⠁⠒⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⡈⠐⠁⡀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢰⣀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⠀⣀⣤⣤⣀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⢿⠿⡿⣷⡄⠀⠀⠀⠀⠀⠀⢄⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠸⣿⣥⣭⣿⢈
⠀⠀⠀⠀⠓⠲⡀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣿⣶⣷⣿⣇⡀⠀⠀⠀⠈⠀⢠⣤⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠
⠀⢰⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠂⠀⠀⠀⠠⠀⡀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠠⠀⠐⠄⠀⠀⠀⠀⠴
⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠃⠀⠀⠂⠀⠄⠀⠐⠁⠀⠈⠉⠀⠒⠈⠀⠀⠀⠀⠈⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠁⠀⣀⣠⡴⠖⠒⠛⠛⠛⠿⣓⠒⠒⠲⠤⢄⡀⠀⠈⠙⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⢀⣠⣶⡿⢋⣥⠴⠤⣄⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠈⠙⠲⣄⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⣠⠶⠛⠛⣿⣶⣾⣄⢛⣠⣤⠁⠀⢀⣴⣿⣄⡴⡞⢫⠻⣍⠐⠀⣤⣙⢢⣀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⣠⠞⠁⣀⢰⣾⡿⡿⢿⡁⠸⡧⢀⠀⠀⣸⣿⣿⣿⣘⠂⠃⡴⠉⠀⣠⣾⣿⠁⠙⢦⡀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⣠⡟⠁⠀⣼⠁⣴⡟⠏⠍⡛⠄⣿⣤⣭⡓⠒⠁⠀⠀⠹⣿⣿⠟⢿⣎⠁⣤⠀⠈⠻⠟⣻⠷⠤⣄⠙⢆⠀⠈⢳
⠀⠀⠀⠀⢰⡿⠁⠀⡴⡏⠈⡇⠤⢘⠀⠗⠀⠘⠿⠿⣿⣶⣀⠀⠀⠉⠉⠁⠀⠀⠈⠉⣠⣴⣶⡗⣼⡑⠫⡍⠠⡕⠈⠆
⠀⠀⠀⢠⣿⠃⠀⣸⠁⣗⢀⣙⣦⣌⡠⠀⠀⠀⠀⠀⠀⢻⣿⣷⣾⡴⢶⡦⣄⠀⠐⠺⢿⠿⠟⠁⠹⣥⡇⢼⢃⠀⠀⠈
⠀⠀⠀⣼⡏⠀⢰⣇⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠃⠨⣏⡉⣇⠰⢋⡅⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒⠁
⠀⠀⠀⣿⠇⠀⣼⠏⠀⢉⡿⠛⢿⠋⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⢤⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣦⣄
⠀⠀⠀⣿⠀⠀⣿⠀⣰⣋⠓⣀⠾⠁⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠉⠓⠈⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⢈⡿⢿⣿⡷
⠀⠀⠀⣿⠀⠀⢿⡄⢸⡐⢆⠉⠶⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠉⠉⠀⢰⡯⠘⠀⡅⠼⠆
⠀⠀⠀⣿⡆⠀⢸⠻⣄⠙⠳⠤⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣱⢃⠴
⠀⠀⠀⢻⣇⠀⠸⡇⠘⢦⡀⠸⣿⣷⣦⡦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠙⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠃
⠀⠀⠀⠘⣿⡀⠀⢹⡀⠀⢣⠀⠛⢋⡟⢿⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠶⢄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠸⣧⠀⠀⢳⡀⣾⠀⠀⢺⠛⠶⣘⠈⣁⣴⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡟⣓⢰⠀⣰⠁
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠳⣷⠀⠀⠘⢿⣃⣥⡀⠉⠙⠿⠿⣿⡿⠟⡧⣄⡀⠀⠀⠀⠀⣰⣿⣿⣆⢻⣁⢩⠄⢶⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠘⢷⣄⡀⠀⠀⠁⣄⠀⠀⠀⠀⢰⠦⠄⠀⢆⠑⠀⠀⠀⠀⣿⣿⣿⣿⠀⠈⠑⠊⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⠀⠙⠻⣟⠓⠶⣿⣿⣷⣄⡀⠸⣖⠆⣉⠈⠶⠀⠀⠀⠠⣼⡿⠿⠁⠀⣀⡤⠔⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠈⠛⠶⣌⡛⣟⡛⠁⠀⠈⠓⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⡀⠀⠉⠙⠛⠶⠤⠤⣶⣤⣤⣤⡤⠤⠤⠤⠴⠞⠉⠀⢀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣤⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠓⠚⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡴⣀⣤⣤⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠑⣀⡁⠶⡉⣣⡜⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⣟⡄⡸⣾⠀⠀⠀⠐⠠⠀⡐⠂⡂⢢⡀⠀⠀⢀⠰⣄⠩⢤⠘⢣⣄⠹⣆⡙⣥⠚⡾⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠚⠛⠘⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡈⢤⡈⢤⡀⠻⡤⠑⢢⡈⢵⠆⠓⠀⠈⠈⠀⠸⢡
⠀⠀⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠱⠦⠉⠠⠚⠓⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠖⠃
⠀⠀⠀⠀⠛⠃⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⢠⡤⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⣀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣠⡤⠧⠀⢀⡤⠀⠀⠀⠀⠀⠀⡤⢀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⡀⠛⠀⣠⡶⠀⠀⠀⠠⠇⠉⠉⠉⠉⠛⠉⠉⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⢀⡤⠖⠀⠀⣀⣠⢠⣤⣤⠶⠶⠴⠁⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⣀⡀⠰⠁⠀⡀
⠀⠀⠀⠀⠀⢈⠛⠃⠀⠀⠀⠀⢲⣶⣾⡦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠘⠲⠆⠒⠊⠀⠀⠀⠀⠈⠉⠠⠈⠀⠁⠉⡗⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠓⠁⣀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠄⢤⠀⠀⠧⠎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠹⠁⠠⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠈⡦⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠰⠀⠘⠀⠀⠃⠀⠅⠀⠐⠀⠀⠀⠀⡶⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣐⢁⠺⠁
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠁⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠈⠀⠐⠀⠀⠀⢄⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⠤⠊
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠠⢤⠄⠈⠀⠀⠀⠈⡀
⠀⡀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⢆⠴⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠉⠁⠉⠀⠀⠀⠂⠀⠠⠤⠄⠤⠔⠈
⠀⠀⠀⢀⡀⡧⠀⠴⠆⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⢂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠙⠓⡼⠆⠀⣀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠐⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠐⠒⢤⡄⠀⠈⠁⠀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠈
⠀⠀⠀⢀⡀⠀⠀⠟⠀⠀⠴⠀⢁⢄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣚⠁
⠀⠀⠀⠀⠁⠀⠷⠀⢰⡀⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠐⠆⠀⠀⠌⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠒⠹⠀⠀⠀⠀⠀⡶⢠⡀⢒⠝⣇
⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠠⠈⠃⠀⠀⠀⣀⠀⠀⠀⠈⠇⡈⠕⠉⠀⠉⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⢁⠀⠃⠠⠄⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⠤⠤⠤⠤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠠⢄⣀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢀⡴⠋⠀⢀⣤⠤⠶⠤⠭⠭⠍⣉⡓⠒⠦⢤⡀⠀⠉⠢⢄⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣰⡟⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡈⠑⢦⡀⠀⠙⢆⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠁⠀⡘⡌⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⢄⠀⠀⢣⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡜⠀⢰⠽⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠆⠀⠈⠆⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡇⠀⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠸⡀⠀⢰⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⢿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡇⠀⣈⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠀⠰⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢡⠀⠸⢣⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡄⠀⢻⣆⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⡀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⡄⠀⠻⡧⡀⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⡔⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡙⠦⡀⠙⠮⣦⣀⠈⠙⠒⠤⠤⣀⣀⣀⣀⣀⣀⡤⠤⠂⠉⠀⢀⡤⠊⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠈⢦⣄⠀⠙⠻⢶⡆⠠⢄⣀⡀⠀⣀⠀⢀⣀⣠⢄⠶⠚⠉⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⡀⠉⠒⡤⣄⣀⠉⠉⠉⠀⠀⠉⠁⠉⠉⠀⠀⠀⣀⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⢌⣀⠀⢉⢳⠒⠒⠀⢰⢶⠆⠐⢒⡖⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠀⠒⠐⠓⠓⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⣲⣿⣿⠇⠈⠈⠙⠀⠀⠂⠀⠀⠐⠁
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⣿⡟⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠾⡿⠁⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢀⠄⠒⠀⠂⡀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣿
⡋⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠒⠉⠉⠐⠄⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⣀⣀⣄⣄⢀⣤⣾⣿⡋
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠒⢦⠀⠊⠙⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢿⣿⣿⣿⣯⣤
⠦⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⡠⠄⠀⠀⣻⡿⠜⢻⠻
⠀⠀⠀⠀⠈⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠠⣼⣦⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠱⡦⠀⡀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠑⠀⠀⠀⠐⠈⠻⠆⠀⠀⠀⠀⠤⢤⣾⣿⣷⠀⣿⣀⣠⣀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠤⠾⠿⣿⣾⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⢀⠃⠀⣀
⠀⡄⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡅⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠉
⠀⠀⠼⢆⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⡂⡬⠞⡉⠀⠉⢧⡀⠀⠀⠀⠐⠂⠀⠄⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠎⠀⠀⠀⠀⠀⠀⠳⢀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠷⠶⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠢⠄⠤⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⣤⠀⠀⢀⣴
⠀⠀⠀⡃⠒⠂⠴⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢆⣠⠀⠀⠀⢰⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢻⣤⣿⣶⣿⠿⠁
⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⣿⣧⡀⢠⠋⠀⠀⣠⣶⡥⠀⠀⠀⠀⠀⠀⣸⡿⣿⡁
⡀⠀⠤⠀⠄⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠒⠤⡀⠀⠸⣿⣿⣤⡆⢀⣾⣿⠋⠠⠀⠀⠀⠀⠐⢀⠂⠀⠀⠙⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⣀⣈⣠⣤⣤⣙⠛⠠⡘⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⠒⠒⠉⠭⠛⠛⢛⡿⡿⢉⣤⠚⣽⣯⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣈⠉⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠉⠀⠀⠉⠳⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣛⡀⠠⠀⠀⠀⠀⠀⠀⢣⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⣛⡡⠀⠀⣒⣀⠀⠀⠀⠀⠐⡇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣿⣿⣿⣟⣻⡿⠯⢅⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠉⠁⠀⢿⣿⣿⣿⣿⣿⣷⡾⢫⣤⣤⠤⡤⣄⣀⣀⡰⠂⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠋⠉⠀⠀⠀⢀⣶⣾⣿⡿⣯⣿⣿⣏⣙⣒⠠⠅⠰⠦⠀⠈⠉⠱⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠄⠀⠀⠀⠚⠁⠱⠜⢿⣿⣿⣽⣿⣛⡛⠻⠥⣤⣝⠶⠤⠀⠀⠀⠀⠀⠘⣧⠈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⠀⠀⠀⠸⡟⢠⣶⣾⣷⣾⣿⣿⣿⣷⡿⣛⣉⠠⢦⣤⡄⠠⠄⠈⠀⠀⠀⠀⢹⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣾⣿⣿⣿⣿⣿⡿⢀⣤⣶⣶⣄⣻⣿⣿⣿⣿⣿⣾⣿⣹⣿⣯⣅⠰⠶⣦⠭⠀⣄⠀⠐⠀⠀⠀⣸⠇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢉⡄⣠⣾⣿⠟⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣷⣿⣯⣹⠝⠻⣷⣤⣖⠂⠀⠀⠀⡀⠀⢠⠏⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⢁⡤⠓⠟⠋⣠⡴⣿⠎⣸⣷⣿⣿⣿⢿⣿⢟⠿⣿⣧⣷⣾⡙⢯⠙⡷⠘⣎⡛⠣⠀⠉⠈⠉⠑⠀⣀⣀⡤⠚⠁⠀⠀⡿
⠀⠀⠀⠀⠀⣠⠴⡟⠁⠒⠀⠁⡄⠀⠀⠾⠋⡀⢉⡿⣽⡿⢋⣽⣧⡤⠛⠛⢸⣿⣿⡟⢿⡙⢷⠁⠙⡀⠑⠈⠂⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⢀⣼⠇
⠀⠀⠀⣴⠋⠀⠀⢧⠀⠀⠀⠀⠁⡈⠀⣀⠆⢠⠄⣼⣿⠀⡟⣳⢹⡧⣦⠘⠿⢻⣿⡗⠈⣷⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣾⡏
⠀⠀⠀⣏⢦⠀⠀⠈⢳⡀⠀⠀⠀⠀⠊⠀⠀⢀⡞⡄⢩⠀⣿⠉⠄⠁⠿⠣⠀⢁⡻⣷⠀⣿⠑⢀⠀⠀⠁⠀⢀⠀⠐⠀⠀⠀⣠⠊⠀⠀⣠⣾⡟
⠀⠀⠀⢹⡞⢻⣆⠀⠀⠈⠷⣤⡀⠀⠀⠀⢀⡞⠀⢃⠀⠀⠋⠈⡄⠺⠀⠀⠀⠀⠅⠈⢠⠈⠂⠀⠀⠀⠀⡁⠀⠃⢈⣤⠔⠊⠀⠀⡠⠞⣡⠏
⠀⠀⠀⠀⠹⣦⡙⢷⣄⡀⠀⠈⠛⠷⠖⠚⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢤⣄⣀⣀⣤⡵⠶⠛⠉⠀⠀⣠⠔⢈⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠳⣦⢉⠙⢶⣤⣀⠀⠀⠀⠀⠙⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡀⠈⠙⠓⠦⣄⣀⠀⠀⠈⠉⠻⠾⠷⠤⠤⠶⠶⠶⠿⠛⠙⠁⠀⠀⠀⣀⡤⠄⠀⠋⢀⣴⣷⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠄⠀⠉⠙⠒⠲⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠤⠶⠒⠋⠉⠀⠀⢀⣠⡴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣗⣀⣤⣶⡴⠖⠀⠀⡬⠉⠉⡉⠀⠈⢠⣄⣤⣴⣦⣴⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⠿⠶⠾⠶⠶⠶⠞⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠘⠿⠟⠀⠀⣀⡀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⠏⠶⣭⡛⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⡿⢣⢞⡓⣮⡻⣎⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⣵⣿⠷⢾⢽⣷⡹⠆⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢋⣾⣶⠷⣥⣾⣿⠩⠶⣋⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⢿⣿⠁⣭⠵⢖⣚⣈⡻⡯⢸⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⣬⣥⠀⠀⠀⠀⠀⣾⣿⠗⠒⣛⣛⠛⣛⣛⣒⢛⡻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢟⣤⣶⣶⣶⣶⣤⡀⠀⠀⠻⣿⣮⡓⢝⡻⣄⣽⣉⣹⢮⡇⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣾⣿⣶⣝⠮⣙⢿⠟⡼⣱⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢿⣿⣿⣿⣷⣮⣓⣎⣵⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⡙⣿⣿⣿⠇⠀⠀⠀⠉⠉⠁⠻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣬⣙⣃⣥⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⢠⣍⡁⠉⠐⠂⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⢈⣀⣤⣦⠀⡖⢪⢉⣌⡛⢳⠚⠲⢦⡀⢑⡆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣤⣾⣤⣾⠿⢓⣚⣓⢃⣿⣥⣬⣿⣄⣐⡄⡟⠟⠀⢠⣶⠍⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠄⣐⣤⢻⠐⣾⠀⠉⢢⠋⢻⡿⢸⠋⠁⢸⣿⢻⣿⠞⠀⠀⢰⡏⠙⠗⣆⠈⢂
⠀⠀⠀⠀⠀⠀⡼⠁⣰⠿⣿⣿⣻⠿⢦⡁⢀⢿⣯⠩⡝⢶⣶⣟⡼⠟⠋⠀⣰⡈⡿⠁⠉⢸⣏⣃⠀⡄
⠀⠀⠀⠀⠀⡸⠁⣸⣿⣯⠟⢺⣱⡤⡞⡿⠿⢿⢿⣛⡷⣈⣼⡋⠂⠀⠀⠀⠈⣿⡇⠈⠈⣸⢿⣿⠄⢻
⠀⠀⠀⠀⠀⠇⢰⣿⣏⣿⠀⢀⣿⣿⡟⠀⣰⠻⣿⣌⣼⣉⠉⠀⡀⢴⣧⣤⣦⡿⠥⣴⠾⠋⢭⡿⣇⣠⡆
⠀⠀⠀⠀⢸⠀⣽⣿⣰⡟⠀⢊⣿⣿⣆⣱⣀⣀⣸⢟⠉⠀⠀⠘⠿⠛⠋⠀⠈⠉⠐⠚⠉⠀⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠈⢈⣩⣯⣕⡭⣁⣼⣬⡭⢽⢿⣿⣴⣶⡂⢆⡴⢲⣦⢶⣶⢐⣶⠖⡒⠲⢶⢿⡛⠗
⠀⠀⠀⠀⠘⠀⢸⣧⣿⢿⡕⠩⠗⡋⡶⢛⣿⣿⣿⣽⠃⣬⡿⢿⠉⠛⠿⢳⣿⠤⣀⣸⣿⣶⠂
⠀⠀⠀⠀⠀⠄⠀⣿⡇⠀⢿⡤⠨⢷⣟⣻⡿⢿⣴⣿⡽⢏⣿⠛⣿⢇⡀⠀⠛⢻⠟⠈⢱⠟
⠀⠀⠀⠀⠀⠘⡀⠈⣿⣾⣿⣿⣷⢾⣯⠟⢱⢯⣏⣼⣧⠄⠁⠄⠚⢳⢆⠖⣾⠀⠋⣰⡏⠀⠎
⠀⠀⠀⠀⠀⠀⠐⠀⠉⢻⡿⢟⣾⢿⣇⢻⣀⠀⡙⣿⣛⣾⣃⣤⡂⢚⡎⠶⡙⣥⡞⠁⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⡀⢻⣿⣿⣟⠘⠉⢁⣴⣍⣿⣀⣥⠀⠉⠩⣤⣶⡿⠿⡍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠛⠺⢿⣿⣷⣿⣸⣉⣿⣤⣴⡶⠛⢉⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠰⠄⠀⡩⠵⢸⣁⣈⠀⠄⠖⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢰⡏⠙⢦⣄⣀⣀⣀⣠⡼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡿⠙⢧⡀⠈⠉⠉⠉⣵⠞⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢠⣿⠁⠀⢸⡇⠀⠀⠀⢰⡏⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢀⣿⣃⣀⣴⠟⠀⠀⠀⠀⠈⢿⣄⣀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢀⣾⠷⣿⣥⣶⠶⣄⠀⠀⠀⡠⢶⣿⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⡾⢯⣸⣿⣿⣤⣤⣿⠀⠀⠀⣇⣿⣿⣧⣤⣤⡟⢻⡄⠀⠀⠀⢀⣠⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⣼⠃⠘⢿⣿⣿⣿⡿⠃⠀⠀⠀⠙⢿⣿⣿⣿⡿⠁⠀⢿⡀⠀⣴⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠃⠀⠀⠀⠉⠛⠋⠀⠀⠰⠚⠆⠀⠀⠉⠛⠉⠀⢀⣤⣬⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣠⡾⠛⠉⠉⠉⠛⢷⣄⠀⠀⣄⡷⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢰⡏⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠶⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣀⣤⡶⠟⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⠀⠉⠛⠻⠶⢦⣤⣤⣄⣼⣏⣀⣀⣀⣀⣀⣀⣤⣤⠿⠟⠛⠉⠀⠀⢀⡼⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⠛⠛⠛⠛⠛⠶⣤⡀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣠⡤⠶⠾⠋⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣄⣀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠶⠶⠶⠶⢦⣤⣄⣠⣤⠾⠋⠀⠀⢀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣏⠉⠉⠉⠉⠙⠻⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⠀⠀⠀⠀⠀⠈⠙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠠⠠⠀⠐⢄⡀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠑
⠀⠀⠰⠀⠀⠀⠀⠈⠀⠆⠂⠀⡂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠰⢀⢀⢀⡀⠀⡔⠓⣀⠰⠃⠀⠀⠈⠀⢀⡈⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠒⠒⠒⠈
⠀⠀⠀⠀⢀⠄⠀⠂⠤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⢱⠠⢍⠉⡠⡀⢠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⢁⠀⡉⠀⠀⠑⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠐⠒⠑⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠤⠠⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠄⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠓⠒⠶⠼⠧⠀⠐
⠀⠀⠀⠀⠀⣀⠀⠀⠡⡀⠀⠀⠀⠠⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⡆⠀⠀⠀⠘⠄⠁⠁
⠀⠀⠀⠨⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⡌⢐⠨⡟
⠀⠀⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⠀⠀⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢀⡀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠂⠑⠀⠀⠂⠀⠀⠀⠀⠉⠀⠒⠃⠠⠀⠌⠠⠨⠁⠌⠄⠸⠸⠀⠀⠀⠀⠨⠝⣂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢌⡠⢄⣆⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠈⠀⢠⡀⠀⢈⠰⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⠔⠠⠔⠀⠀⠀⠀⡂⠈⠐⢠⡄
⠀⠀⠀⠀⠀⡐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠁⢀⠀⠘⣁⣛⠀⠀⡁⠀⠀⠀⠑⢔⡢⠊⠀⠀⢠⡒⠀⠠⢄⡐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠄⠀⠀⠀⠀⠐⡔⠀⡇⢢⡔⢸⡇⢢⡂⠐⠀⠀⠀⠈⡀⠀⡄⢀⡀⠀⡃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠄⠀⠈⠁⡀
⠀⢀⡀⣀⠀⠂⠀⠀⠀⢲⡂⠂⠒⠒⠲⠀⠐⠐⠀⠃⠂⠐⠘⠂⠂⠂⠀⠤⠀⢸⠀⡇⢠⡤⠈⡀⠀⠁⠀⣲⡆⠀⠀⠀⠀⠀⠀⠸⠁⢀⡄⠘⠛
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠧⠿⠯⡿⢿⡷⠀⠶⡆⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠀⡇⠘⡏⠘⠂
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠈⠈⠉⠉⠉⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣀⠀⠀⠴⠒⢦⡀⠀⠉⠉⠉⠉⠉⠋⠉⠙⠉⠁⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠃⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣄⠛⣠⠇⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠁⠈⠀⠀⠁⠈⠀⠀⠈⠴⠄⠠⠄⠡⠦⠀⠤⠀⠀⠀⠉⠀⠀⠀⢀⠀⠠⡀⠀⠀⠀⠘⠀⠀⠀⣻⡍
⠀⠰⠠⠠⠆⠆⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⢴⣴⣴⠄⠀⠀⠀⠀⠴⠂⠠⠀⠲⠠⠄⠠⠀⠀⠄⠠⠀⠀⠠⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠗⠀⠁⠀⠀⠹⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⠏⢉⠀⡈⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠂⠀⠀⡍
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢇⠳⣀⢦⡤⡎⠑⠒⠲⢤⡀
⠀⠀⠀⠀⠀⣠⢋⡀⠀⠀⠈⠦⢎⣹⠒⠁⠀⠀⠀⣀⣨⣦⣤⣀
⠀⠀⠀⠀⠀⡇⠀⠈⠂⠀⠀⠀⣸⠙⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⢸⠀⣷⠀⠀⣿⣿⣿⠿⣋⣌⠻⡏⢹⣧⣀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⢸⠀⢸⠀⢠⢋⠋⡾⣪⠞⡩⡇⠀⠈⢁⠛⣍⠉⠓⠒⢦
⠀⠀⠀⠀⢰⡧⠖⠒⢤⡇⠀⠀⢸⠀⢸⠀⢸⢸⠀⠀⠀⢜⡾⠃⣠⠃⡸⠀⠟⠤⣷⣯⣿⠗⢄
⠀⠀⠀⠀⠸⠤⠒⠒⠢⣵⢀⣀⣸⠀⢸⣤⡼⡍⠀⡴⠒⠉⠈⡏⣉⣦⠁⣤⡄⠀⠀⠈⠋⠀⠀⠳⡀
⠀⠀⠀⠀⠀⣴⠀⠀⢸⠈⠀⠐⠺⣄⢸⠃⣷⡇⠀⡇⠀⠀⠀⠘⠏⢻⢶⠏⠀⠀⠀⠀⢀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡟⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⣿⠀⠀⡇⠀⡀⠀⠀⠀⡜⠉⡆⠀⠠⠄⠀⠈⡄⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡇⡇⠀⡇⠀⠀⠀⢠⠀⠀⠀⣿⠀⠀⢳⠀⣱⡀⠀⢰⠇⠀⣧⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢱
⠀⠀⢀⣀⣰⡇⡃⢀⡁⠀⠀⠀⡄⠀⠀⠀⡏⠀⠀⢸⢠⠇⠙⡄⡼⠀⢀⣿⡄⠀⠀⠀⠀⠀⣴⠒⣛⡓⠺⡆
⠀⠀⠀⣈⣭⠋⢀⠈⡟⠛⠓⠒⠓⠒⠲⠶⣇⠀⠀⢸⢻⣀⣀⣸⢃⡤⠾⢌⣁⣀⣠⠤⠴⠒⠋⠉⠉⠉⢣⢹
⠀⠀⠰⠿⠓⠊⢩⡔⠁⠀⠀⠀⠀⠀⠀⠀⠘⣄⣠⣯⠏⢠⠞⠁⢼⣿⡆⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⡤⠾⠯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠓⠒⠒⠋⠙⠂⠛

⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣠⠖⠋⠉⠁⠉⠉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠀⠀⠉⠙⠶⣄
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠋⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡋⠀⠀⠀⠀⠀⠀⠀⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠈⠙⠒⠦⠤⢤⣤⡤⠴⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⣀⡠⠤⠔⠁⠀⠀⠀⠀⣀⣀⣀⠀⣠⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠉⠙⣦⠀⠀⠀⠀⠀⠀⢀⣀⠛⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠉⢷⡈⠉⠙⢄⣀⡀⠀⣀⣀⣠⠤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠉⠀⡴⠋⠉⠙⣆⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⣼⠃⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣒⡚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⢀⣿⡀⠀⠀⠀⠀⢀⣠⣬⣙⣛⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⠙⣷⣤⡀⠀⠀⠀⠀⠀⣸⠃⠙⠲⠶⠛⠉⣷⣀⣀⣤⠖⢫⡏⠀⠀⢉⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠙⠲⢾⣄⠙⠓⠒⠒⠛⠛⣿⣠⡄⠀⠀⠀⠀⣿⡏⠁⠀⠀⣾⠀⠀⣠⠏⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠓⠶⠶⠖⠒⠛⣿⠁⠀⠀⠀⠀⢰⡇⣷⠀⠀⢰⠇⣀⡴⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⣾⠶⢾⡶⠶⣾⠋⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡏⢷⡀⠀⠀⣼⠃⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢸⡇⠀⠙⠆⠀⠃⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣠⡤⠟⠀⠙⡟⠙⠛⠛⠛⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡶⠛⠋⠉⢹⠁⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⢹⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣼⠋⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣻⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⠀⠀⠀⠀⢿⣤⡀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⠸⢷⡄⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠉

⠀⠀⡀⠀⠄
⣀⠀⡀⡄⠀⣠⡄⠀⢀⠀⠀⠀⠀⢀
⠁⠈⠁⠀⠋⠁⠈⠀⠻⠄⠔⠠
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢉⡀⠠
⠀⢳⠶⢈⡆⢠⠈⠁⠀⠀⠀⠀⠐⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈
⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠂⠈⠀⠀⠁
⠉⡥⠠⢀⠄⢀⡀⡀⠀⢈⠑⠄⠈⠀⠠⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈
⠶⡶⢆⠘⠀⠟⠀⠋⠀⠀⠀⢀⣀⠀⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠐⠋⠈⠀⡠⠄⠀⠀⠀⠐⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄
⠁⠈
⠀⠀⠈⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠠⠀⠀⣠⣤⣄⡀⢠⠔⠆⠀⣀⣀⠰⣇⠆⢰⠀⣦⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢰⣛⣯⣍⢹⣿⠷⠤⠞⠿⠷⠥⠤⠇⠀⠘⠶⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠈⠀⠀⠀⣰⠛⠂⢀⣄⣜⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠎⠛⠛⠛⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⠀⠀⠀⢀⡀⡀⠀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣈⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⣧⣉⣭⣿⣟⣿⣉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣉⠉⣉⡉⣙⣻⠀⠀⡁⠀⠀⠀⠀⣁⠀⠀⠀⢰⣶⣶⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠈⠀⢰⠶⠓⠀⢰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡖⣴⠾⣾⠏⣽⠐⣮⡀⣞⠚⠛⣧⣟⣶⡄⠀⠎⠉⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣇⣴⣖⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠚⣿⣇⣼⣄⠁⠈⠅⢈⡀⣁⠀⢄⡀⢀⣤⣤⣤⣤⣤⣤⣴⣧⣿⠷⣶⠀⠀⠀⣤⣀⣼⣯⣈⣉⣿⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣿⣿⡘⣿⣿⣿⣿⣿⣾⣿⣿⣤⣼⣿⣿⣿⣽⣽⣿⣿⣷⣤⣤⣄⣀⣠⣾⣥⣤⣿⣿⣭⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠀⠂⠀⠀⠀⠀⠀⡄⠀⢂⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠛⠀⢈⠉⠁⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⡇⠀⣀⣠⠀⠑⠀⠂⠀⠰⠂⠀⡀⣉⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠉⠉⠁⠈⠀⠉⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠠⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠠⠤⠀⠀⢠⣄⣀⣀⣀⠀⠀⠀⣀⡀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠀⠀⠀⠀⢀⡀⠠⠄⠀⠒⠒⠒⢒⡒⠦⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⣀⣠⠤⠀⢉⣤⣤⣶⠎⣛⣛⣉⠛⢁⣤⠐⣦⣤⣄⠐⢶⣦⣄⣀⣀⠀⡀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠛⡌⠀⠁⢈⣽⣃⣬⡁⣀⠀⠂⣙⡁⢹⡀⠉⠓⢶⣶⣠⡑⢄⠀⠀⠀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⣦⠏⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠻⠿⠿⠋⠀⠀⣀⠀⠀⠈⠁⠀⠀⠂⠁⠀⠀⠁⠘⢦⡀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⣠⡴⠋⡴⠊⢡⠀⠀⠀⠀⠀⢀⣀⣀⡸⠃⠀⠀⠀⠀⠀⠀⣾⡿⠓⠀⠠⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡰⠁⠀⢀⡬⠟⠐⠚⡀⠤⣀⠳⣄⡀⣀⠔⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⣯⡄⣄⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⡜⠀⠀⣠⠏⢠⠰⠞⡛⠛⠀⠉⠃⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⡋⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⡘⠀⠀⠠⠋⠈⠞⡠⠔⣂⠥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠢⡄⠄⠀⠉⠐⠂⠀⠐⢃⠁⠀⠀⠀⠡
⠀⠀⠰⠁⠀⢠⢁⡟⡒⠚⠡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⣄⢈⡀⢀⠀⠀⠀⣃
⠀⠀⡄⠀⠀⠆⣸⢁⡁⡇⣃⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⣦⢀⠀⠀⠀⠄⠀⠙⠒⠀⠀⠀⠀⠀⠀⠣⣀⢀⠀⣀⡴⠋⢀⣤⣤⣶⠀⣡⠀⠸⣧⠀⠆⠀⠀⠨
⠀⢀⠁⠀⠘⠀⡟⠸⠀⠛⠉⠀⠀⠀⠀⠀⠄⣠⡤⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠈⠈⠁⠀⠀⠀⠸⠿⠟⡁⢀⡘⠄⠐⢹⡆⠸⠀⠀⠀⡀
⠀⢸⠀⠀⡄⠀⡇⣨⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣤⣰⡐⠿⠃⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠐⠂⠒⠀⠀⠀⢀⠀⠀⠀⠀⣰⢤⣼⠏⠈⣠⠃⠈⢿⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠁⠀⡷⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠴⣧⣬⣤⢰⠋⠁⠀⢰⢸⠀⠁
⠀⠀⠀⠀⡀⠀⣷⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢘⠀⠄⠀⠀⢸⢸⠆⠀⠀⠀⡀
⠀⢰⠀⠀⠇⠀⢸⠻⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⢀⣸⠅⠀⠈⠉⠀⠀⡌⡐⠀⠀⠀⣈⢸⠀⡆⠀⠀⡇
⠀⠸⠀⠀⠐⠀⠈⢿⡀⢰⣿⣶⣷⡖⠚⠁⠈⠀⠒⢤⡀⠀⠀⠀⠀⢀⠠⠀⣀⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡝⠾⢀⠀⠀⠀⠃
⠀⠀⡀⠀⠀⢡⠀⠘⡇⠀⠈⢙⠋⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠘⠁⠀⠀⠀⠀⢱⠤⠔⠀⠀⢠⣶⣶⣶⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡘⢰⠈⡆⠀⠀⠠
⠀⠀⠅⠀⠀⠀⢂⠀⠱⣀⢖⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠤⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠻⠿⠟⠁⠠⠀⠀⠀⠀⣼⡷⠂⠁⣀⡃⣠⢃⡟⡸
⠀⠀⠐⡀⠀⠀⠀⠀⠀⡋⠈⠈⢧⡀⠀⠀⢀⠴⠒⠒⠂⠀⠀⠀⠀⠀⠤⣀⠀⣰⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⠀⠀⠀⢿⡆⡀⢀⣼⡿⢀⠞⠙⠁⠀⠀⢠⠁
⠀⠀⠀⢡⠀⠀⠀⠀⢂⠰⡘⢄⠀⠉⠶⠒⠁⠀⢠⣶⣾⡿⠀⠀⠀⠈⠀⡀⠀⠀⠀⡀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢱⠀⠈⠉⠛⠴⠿⣋⣱⠏⡀⠁⠀⠀⢀⠆
⠀⠀⠀⠀⠣⠀⠀⠀⠀⠡⡈⠢⢁⣢⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠘⡄⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⣤⡿⢃⠔⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠐⢄⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠐⠚⠃⠀⠀⢀⢔⡱⢋⠔⠁⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡀⠀⠙⢀⠀⠉⠈⠀⠀⠀⠀⠈⠂⠀⢀⠄⠀⠀⠄⡀⠀⠀⠀⠀⠐⠋⠀⠀⣀⠤⣊⠵⢋⠔⠁⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢄⠀⠙⢶⣤⣀⠒⠈⠉⠉⠀⠰⡔⠞⠉⠡⢦⡠⣄⠀⠀⢀⡀⠤⢒⣪⠴⠚⠡⠀⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠁⠢⢀⠉⠛⠯⣔⣒⡂⠤⠤⠤⠤⠴⠖⠂⠀⣸⣋⣡⠤⠖⠚⠩⠔⠂⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⣀⠀⠀⠈⠐⠀⠄⠀⠉⠉⠉⠉⠋⠋⠉⠉⠉⠉⠠⠀⠒⠈⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⠒⠒⠒⠒⠒⠀⠉⠉⠁
⣶⣾⣷⣶⣶⡾⢷⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣿⣿⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⡿⣶⢾⠿⠷⢶⣶⣶⠶⠶⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢚⣉⠉⢷⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢖⣫⡭⠶⠛⠉⢹⡆⢸⡇⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠷⠛⠉⠁⠀⠀⠀⠀⢀⡇⢸⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣋⣙⣛⣛⠓⠶⠒⠛⠛⠛⠛⠒⠲⠖⠛⢁⡿⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⣾⣿⣿⣿⣿⣿⠻⠿⠮⣭⣍⣛⠛⠛⠓⠶⠶⠦⢤⣤⣤⡾⠁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⢚⣋⣥⠶⠛⣩⣿⣿⢻⡟⣯⠳⡄⠀⠀⠈⠉⠙⠛⠓⠲⡄⠀⠀⣠⠟⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⢛⣩⣥⠶⠞⠋⠁⠀⠀⣴⢣⡟⡿⠀⣷⠸⣆⠙⣦⠀⠀⠀⠀⠀⢀⡼⠃⢀⡼⠃⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⣴⠞⠛⢿⡉⠀⢰⡞⠋⠁⠀⠀⠀⠀⠀⢀⡾⠁⣾⢹⠇⠀⢸⡄⢹⡄⠈⢳⡄⠀⠀⣴⠟⢀⡴⠋⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠈⠳⣄⠀⠙⠳⣌⡛⠦⣄⡀⠀⠀⠀⣰⠏⠀⢰⠇⡿⠀⠀⠈⣷⠀⢻⡄⠀⠙⠳⠛⣁⡴⠋⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠙⠶⣌⡉⠛⠲⠞⠁⠀⢀⡟⢰⡇⠀⢀⣀⣽⠀⠀⠹⣆⣀⡴⠞⠉⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠈⠙⠳⠦⣤⣤⣀⣼⣁⣈⣛⣛⣉⣉⣠⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠤⣤⣤⣤⣤⠤⠶⠖⠛⠋⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡴⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⣹⠆⠣⢤⠜⣠⠤⠤⣠⠖⡒⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠈⠁⠀⠀⢀⡼⠁⠀⠀⢀⠾⢍⠓⢄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣳⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⡰⠋⠮⢆⠑⡌⢧⠘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⠒⢦⡀⠀⠀⢀⠜⠂⠀⢀⡜⠓⠰⠷⠐⣠⠼⢺⠄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⢤⣄⣵⠀⠀⠸⣄⡀⢠⡮⠔⣒⡻⢦⡀⡟⠉⠁⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡼⠼⠖⠺⠦⣀⠀⢸⠁⢀⣭⠭⠤⠤⠤⠽⣥⢄⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⡰⠋⠀⠀⠀⠀⠀⠈⠳⡘⢦⣈⠳⣕⢤⡛⠒⠷⢸⢸⠀⢰⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠥⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡏⠀⠀⠙⢮⡲⣤⣃⠎⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡀⠀⡖⣆⠀⠀⡞⠀⠑⢤⣀⣠⡀⠈⠛⠁⡸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠉⠛⠋⠁⣠⠞⠁⠀⠀⠀⠀⠀⠓⠤⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣙⣒⣚⣉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠀⠂⡐⠀⠆⠀⠰⠀⠐⠀⠂⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣸⣤⡾⠻⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⢀⣴⣏⡾⠁⠀⡀⠀⠀⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢦⣤⠶⠛⠉⠘⠷⣤⣤⡤⠖⠋⣡⣏⣀⡀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣤⡀⠙⢦⣄⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⢾⡏⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠙⢷⣄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠛⠻⣾⣧⣀⣀⣀⣠⣶⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠙⣧⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⣿⠀⠀⠀⠙⣦⡉⠉⢩⡿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣿⡀⠀⠀⠀⣼⣇⣰⡟⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠋⣿⣏⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣾⣧⣤⠤⠤⠴⠶⢶⣶⡶⠶⠶⢼⡇
⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣧⡾⠉⢿⣆⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⣠⡿⠁⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⡟⠀⠀⠀⠻⣆⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣾⣿⠟⠀⠀⠀⣠⡶⠛⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢹⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠛⠁⠀⣠⡴⠛⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣠⣄⣠⡾⠋⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣩⠟⢿⣄⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣀⣴⢟⣡⡾⠟⠁⠀⠀⠹⣷⡄⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠘⣧⠀⠀⢀⣠⣾⣯⡶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠙⣷⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠈⠻⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣶⡄⠉⠀⠀⠀⠀⠀⣠⣤⣬⣿⡀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠓



⠀⠀⣀⡀⠀⠀⢀⠀⠀⡀
⣿⡟⣉⣻⠿⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣤⣤⣤⣤⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠁⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠴⠚⢛⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⣶⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣠⣿⠿⠿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣠⣾⠟⠁⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣶⣴⣿⡟⠁⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠐⣤⣄⣀⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⣿⣿⣿⠶⠶⠶⠀⠀⠀⠀⠠⣾⣿⣧⣄⡠⠐⣠⣤⣼⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣤⣤⠀⠀⠀⠀⠀⠀⣠⣬⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠸⣿⡆⠀⠀⠀⠀⠀⠻⣷⣾⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡄⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⡟⣯⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⡀⠈⠂⡀⠀⠘⠁⠀⠀⢀⣠⣾⣿⡟⣿⣿⣿⣏⠇⠘⢲⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⣴⠾⣿⣿⣿⣿⣏⣷⢹⣿⣿⣶⣄⠐⣙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⢻⣿⣿⣏⣯⣔⣧⣿⣿⣿⣿⣷⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠿⢿⣿⣿⣯⣟⢫⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠙⣿⣿⣿⠻⡷⣻⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣴⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣹⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⠉⠁⠀⠀⠤⠤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢧⣴⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠈⠈⡀⠀⠒⠩⠐⢀⣀⡀⣾⣽⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠈⠀⢀⠀⠀⠀⡀⠀⠀⣿⡛⢿⣿⠀⣤⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢾⣧⡌⠳⣤⡀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠠⠀⠠⠀⠀⢀⡴⢻⣿⠂⢻⡀⢸⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⡄⣿⡈⠳⣤⣉⠓⠒⠶⠤⢤⣤⣤⣤⣤⡤⠤⠴⠶⠖⢋⡩⠖⣼⣏⠄⣼⠄⢫⣀⣀⣠⡤⠶⠚⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠁⣌⠻⣿⣶⣄⣈⡙⠓⠶⠦⠤⣤⣤⠤⠦⠤⠴⠖⠚⣋⣉⣴⡾⠟⣫⠞⠁⠀⠘⣿⣿⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠹⢦⣭⣙⡛⠿⠷⡶⢶⣶⣶⣶⣶⣶⣶⡶⠾⠛⣛⣻⣥⠶⠛⠟⢀⡀⠀⠀⢸⣿⣆⠀⠀⠀⠀⢹⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠶⠶⢾⣿⣶⣷⣶⣿⣿⣛⠋⠉⠀⠀⠀⠀⠈⢿⠀⠀⠾⠿⣿⣆⠀⠀⠀⠀⢿⣿⣿⣱⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠙⠛⠋⠉⠉⠙⠛⠳⠾⢿⣦⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣦⣄⡀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠆⠈⠁⠁⠀⠈⠁⠂⠐⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠁⠀⠀⠔⠠⠀⠀⠈⠃⠸⠃⠀⠀⢠⡄⠀⠀⢀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠡⠏⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⠜⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠂⠀⠒⠠⡀⠀⠀⠀⠀⠀⠀⢠⣀⠤⠤⠤⠤⢤⣠⠀⠀⠀⠀⠂⠇⣀⣖⣀⡂⡈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⢠⠐⡟⠓⠂⠀⠚⠒⠲⠄⠕⢀⠀⢰⠄⠀⠅⠁⡬⠃⠄⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠔⠉⠀⠂⠉⠀⠀⠀⠀⢢⠀⠀⠀⠀⠸⡇⠐⠂⠀⠀⠃⠀⠐⢚⠀⠀⠘⠀⠀⠈⠙⠊⣤⢦⠀⠀⠀⠀⠀⣄⢀⠠⣡⣃⠀⠀⠀⢀⣀⣰⡄
⠀⠀⠀⠀⢲⣤⠐⠀⠘⠀⠀⠘⢀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⢀⢀⡠⢫⠈⠁⠀⠀⢀⣀⣹⠛⢚⣻⣍⣓⠒⠒⠋⢁⡟
⠀⠀⠀⢀⠞⢻⠄⢀⠀⣀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡁⠑⠀⠀⠀⠀⠀⠠⠇⠀⢨⣟⡧⣍⡀⠚⢓⣊⣮⡛⠛⠓⠛⠉⢲⡾⠿⣿⢟⣿⠉
⠀⠀⠀⠀⠁⠀⢀⠎⠀⠉⣄⢐⡡⢄⠀⣀⡀⢠⠤⣄⢘⡖⠃⠅⡁⠀⠀⠀⠐⠓⠚⡣⠸⣇⡠⠊⠙⠂⡜⠑⠃⠿⠻⠈⢁⣹⠏⠉⠀⠚⣸⠇
⠀⠀⢀⡀⠠⠄⠠⠐⢴⣥⣿⡼⠣⠸⠇⠀⡀⠚⠠⠂⣏⡡⠀⡲⢥⠒⠀⠀⠀⠀⠒⠒⠚⠋⠀⠀⠀⠀⠄⠀⡼⠶⠯⣁⡾⡇⠀⠀⡠⠈⢹
⠀⠀⠀⠀⠐⠊⠉⠛⣌⢉⣀⢈⣷⡧⠀⠒⢣⣀⣀⣤⣉⠙⠺⠯⣀⠀⠉⠒⠬⠀⠐⠦⠀⠀⠀⠀⠀⢈⠀⢠⠀⠀⠀⢈⠏⠁⡀⠈⠄⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠙⠛⢄⠀⠉⠉⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠖⠁⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣚⣛⣉⣝⡓⠲⣤⢠⣞⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡶⠿⠿⠿⢿⣶⡆⢀⡸⣷⣄
⠀⠀⠀⠀⠀⢀⡴⣫⠾⢿⡁⠀⠀⣶⡏⡽⣡⢏⣬⡳⣌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣋⣄⢾⣿⣿⡋⢱⠆⢀⣾⢛⢮⡙⣷⡀
⠀⠀⠀⠀⢀⡞⡴⢫⣶⡄⢳⡀⣶⣄⡼⣱⣧⡌⠛⠁⠹⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣵⢫⠙⣦⢻⠋⢹⠏⢠⡿⠻⣬⣾⣧⡻⣷
⠀⠀⠀⠀⢸⢡⡇⠀⠉⠁⠀⠹⣄⡞⠰⠧⠿⠧⠬⠤⠴⠷⠿⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⣷⣾⣿⣧⠹⠋⠰⠿⠷⠶⠿⠿⠿⠃⠿
⠀⠀⠀⠀⢸⠹⡏⠍⠉⣽⣍⢩⠿⣏⠉⠉⢉⠉⠙⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⢰⣶⣶⡖⡒⡶⢢⡰⣶⣶⣶⣶⣶⡄⣶
⠀⠀⠀⠀⠘⣆⢧⡀⣤⡌⣡⠏⣶⡿⣆⠀⠻⠇⡼⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡜⢿⠛⢳⡾⣱⡏⢁⡜⣿⣧⣠⡏⣼⡟
⠀⠀⠀⠀⠀⠘⢦⡳⣍⣰⠣⣖⡆⠀⠈⢧⣠⠞⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡳⠞⣱⠫⢝⣿⣿⣌⠿⣫⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠾⣟⣲⡛⠶⠴⣚⣫⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢴⣭⣭⣍⣛⣭⣵⡄⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⢀⠦⠄⠀⠀⠀⣤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠈⡞⡀⠀⠐⠤⡴⡃⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⠀⠠⡀⠐⠁⠀⢤⠀⠠⠀⣰⣁⠄⠐⠒⠁⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠟⢂⠨⠀⢀⠄⠼⣧⠀⡰⠁⠐⠀⣀⣁⡤⠐⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠈⠀⠐⠀⠈⢲⠈⣈⡔⠷⠚⠚⡉⢁⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠸⢇⣀⡠⠀⠐⠉⢀⣚⡓⠀⠀⠠⠜⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠐⠈⢁⠀⠢⠃⠀⠀⠄⢀⠠⠜⠀⠀⠐⢀⠴⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠄⢠⠃⠀⠤⠘⠀⠂⠀⠀⡈⡀⠂⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⠀⠠⠀⠒⢊⠀⠃⠀⠄⠂⠒⠁⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠀⠄⠀⢠⡀⠀⠹⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠛⠁⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠁⠉⠉⠑⠂⠀⠒⠀⠒⠂⠄⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠉⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣠⡄⠀⠀⠀⣤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡰⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⡄⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣁⠤⣀
⠀⠀⠀⢀⡤⠤⣠⡾⠛⠉⠉⠉⡇⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠜⠁⠀⠀⢹⠈⣆
⠀⠀⢀⠸⡀⠰⠏⠀⡀⠀⠀⠀⢸⠀⠘⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡠⠴⢄⠈⠓⢶⡯⠚⡰
⠀⢰⡡⠴⠈⠁⠀⠉⡱⠀⠀⠀⢸⠀⡀⠹⠟⠛⠿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣀⣦⠀⢁⠰⠊⢗⣊⡠
⡴⠉⠀⣠⡴⠒⠒⢄⠈⣱⠀⠀⠈⡇⠁⠀⠀⠂⠐⠀⠀⠀⠀⠠⠈⠀⠀⢀⠴⠛⠿⠶⠿⠛⠉⠀⠀⠜⠢⠤⠚⠁
⠑⠒⠯⠽⠀⠀⠀⠀⠉⠁⠀⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠠⣀⠀⠀⠀⡀⠐
⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⠇⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠈
⠀⠘⠻⠿⠿⠿⠿⠛⢻⣏⠁⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⣼⠀⠀⠀⠀⣰⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣾⠿⠛⠣⣄⡠⠊⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣴⣾⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠉⠉⠉⠉⠛⠲⠦⣄⡀⠀⠀⣸⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠆⠀⠀⠀⠀⠀⠀⠀⡴⠛⢷⠀⠀⢠⡇⠀⢠⡏⠀⠀⣀⡙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣤⣤⡀⠀⠀⠀⠀⠻⣤⠞⠀⠀⡾⠀⠀⣼⠀⠀⡏⠉⣷⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⡄⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⠇⠀⠀⠙⠚⠃⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡄⠀⠀⢀⠀⢀⡟⠀⠀⡟⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠶⠋⠀⣼⠁⠀⣸⠃⠀⠐⠲⡄⠀⠀⠳⠶⠞⠁⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡏⠀⠀⠀⣠⠟⠀⠀⠀⠀⢀⣤⣤⠀⠀⣧
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣾⣀⣀⠀⠈⠁⠀⠀⠀⠀⠀⢺⡀⣸⠇⠀⢹
⠀⠀⠀⠀⢰⡇⠀⠀⠀⣀⡀⠀⠀⠀⢠⠞⠋⠀⠀⠀⢀⣀⡀⠀⢸⣇⣀⠀⠀⠈⠉⠙⠓⠶⠦⣤⣀⣀⠀⠀⠉⠁⠀⠀⢸⡆
⠀⠀⠀⠀⢸⡇⠀⠀⣟⠉⢹⠀⠀⠀⠘⢧⡀⠀⠀⢰⡏⠉⡧⠀⠀⠈⠉⠙⠓⠲⠦⣤⣀⣀⠀⠀⠈⠉⠙⠓⠶⠦⣤⣀⣸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⣤⣀⣀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢳⣀⣀⡴⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠹⣤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣴⠛⢳⡄⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢙⡇⠀⠀⠀⠀⠹⠦⠞⠁⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣄⣀⣀⣀⣀⣀⣀⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠖⣂⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⣲⡦⠤⠤⠀⠀⠀⢈⡞⣵⣿⡇⠜⠐⢋⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢚⣭⡴⠶⠛⠛⠷⠶⣤⣄⢸⣿⣿⣇⣴⣿⣿⢸⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⠁⠀⠀⠀⣴⣆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣤⣬⣭⣶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠾⠋⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⣻⢃⠞
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⢠⣶⡆⠀⠀⢀⣤⡀⣿⣶⡄⠀⢠⣾⣿⣿⣿⡿⠞⠁⠊
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠚⠉⠀⠀⠠⠾⠿⠃⣿⣿⣿⡆⢸⣿⣿⣷⡿⠿⠿⠿⣷⣦⡈⠻⣕⢄
⠀⠀⠀⠀⠀⠀⣼⠇⢠⣿⠇⠀⠀⣤⣤⢰⣄⠀⠀⣰⣿⣿⣿⣿⣸⠟⠉⠀⠀⠀⠀⠀⠀⠙⢿⣦⠈⢫⡂
⠀⠀⠀⢀⠆⣸⠏⠀⠈⠁⠀⠀⠰⠛⠋⠈⢿⣿⣶⣮⣭⣬⡿⡿⠥⢀⠄⠀⠀⠈⠀⠀⠀⠀⠈⢿⣧⠀⢣
⠀⠀⠀⡞⢰⣿⣄⠀⣠⡄⠀⠀⠀⠀⠀⠀⢴⣿⣿⠟⠛⢩⡈⠀⣰⣆⠉⠐⡤⠄⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠈⡇⣾⠟⠋⠀⠋⠀⠀⢰⡿⠃⠀⠀⣾⡟⠁⠀⠀⠀⠀⠁⠹⣿⣷⡀⠈⢦⡤⠀⠀⠀⠀⠀⠘⣿⡆⢀
⠀⠀⠀⢃⢻⡆⣰⣶⠀⣤⣄⠀⠀⢀⣀⢸⣿⠂⠀⠀⠀⢀⠁⡑⡀⠈⢿⣿⡄⠰⠂⠰⠀⠀⠀⠀⠂⢹⣷⠘⡆
⠀⠀⠀⠈⠈⢿⡌⠀⠈⠋⠁⣀⠐⠛⠛⠸⣿⡄⠀⠀⠀⠀⠀⠁⢈⢢⠈⠻⣿⡀⡄⠦⠀⠀⠀⠀⠀⢸⣿⠀⡗⡆
⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⠸⠛⠃⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⣀⠀⢁⠢⣌⢳⡐⡀⠀⠀⠀⠀⠀⢸⣿⠀⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠾⠛⠛⠛⢻⣧⡀⠀⠀⠀⠀⠁⠀⠀⠀⠚⠑⢍⠠⠈⠀⠀⠀⠀⢸⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣙⣛⠍⠁⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⡌⠓⠃⠀⠀⢀⣾⠇⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣤⣤⣀⣀⣀⣀⣀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣉⠉⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⣉⣉⣉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠛⠛⠒⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣷⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠘⢼⣿⣰⣆⣀⡤⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡠⠤⡌⠉⠉⠉⠛⢧⣇⡆⡄⡀⣀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠈⠒⠊⠀⠀⠀⠀⠀⣐⡌⠙⠛⠛⠷⠦⣮⣖⡤⠀⠀⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣀⡤⠴⣶⡶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢡⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⢫⠗⠉⠀⠀⠋⠉⠳⠊⠳⡄⠀⠀⠀⠀⠀⠀⣿⡇⡆⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢸⠃⠀⣀⣀⡀⠀⠀⣠⣤⣄⡀⣽⠀⠀⠀⣠⠴⡄⠹⣇⠇⡆⡀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠘⣷⣞⣭⣤⣿⠀⠀⣧⢧⣾⠽⠃⠀⠀⠀⠓⠊⠁⠀⠈⠳⣅⠷⡆⡄⡀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠑⢦⡀⠀⠀⠈⠀⣸⠃⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠧⣤⣑⡳⠀⣀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡈⢣⣀⢳⠀⠀⠀⠀⢧⡰⠤⠤⢀⡿⠀⠀⠀⠀⠀⣀⡠⠤⠤⠶⠶⢤⣤⣀⡀⠀⠈⠙⢶⢃⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢉⠝⠁⠀⡇⠀⠀⠀⠀⠙⠛⠋⠉⠀⠀⠀⢀⠔⢉⠔⠢⡀⠀⠀⠔⠀⢀⠈⡙⢷⣄⠀⠘⢯⡇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠁⢏⡦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠈⠓⠊⠁⠀⠀⠈⠀⠉⠈⠀⠀⠹⣇⠀⠀⣧⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⣔⣦⠀⠀⠀⢰⠇⠀⠀⢀⡀⠀⠀⠀⠀⢠⠞⠁⠀⡀⠀⠀⢹⡄⣼⡷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⣀⣈⡇⠀⢀⡴⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣾⠀⠀⠀⠒⠃⠀⠀⠀⠀⠈⠳⠔⠋⠀⠀⠀⢸⡇⣿⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣼⣃⣀⣉⣠⣤⣞⠉⠀⣰⠚⠽⢶⣶⣦⡀⠀⠀⠀⠀⢻⡀⠀⡠⠂⠀⠀⠀⠒⡆⠀⠀⠀⡠⠄⠀⠀⣼⢸⣷⡫⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢠⠞⠁⣿⣱⡄⣹⠀⠀⠀⢀⣫⠟⠀⠀⠀⠀⠘⣷⣋⡠⠊⠀⠀⠈⠉⠀⠀⠀⠀⠓⠒⢠⣾⠃⣸⢻⣧⠀⠀⢸
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⣄⠀⠙⠛⠟⠃⠀⢀⣞⣉⡀⠀⠀⠀⢠⢲⠀⠘⢿⣴⣁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠛⠁⠀⣿⡼⠿⢷⢶⣾
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⣧⠄⠀⠀⠀⠀⠀⠸⠿⡽⢿⡆⠀⠀⠀⠁⠀⠀⠀⠉⠛⠛⠿⠷⠶⠾⠛⠛⠉⠁⢀⣀⣀⣼⢏⠆⠂⠇⣯⢻
⠀⠀⠀⣰⠃⠀⢀⣀⣀⠀⠀⠘⢮⣂⠀⠀⠀⠀⣀⡤⢂⡼⠁⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣶⢶⡶⢿⠟⡻⠋⠍⠉⠀⠀⠀⠀⠊⢀
⠀⠀⢠⠏⠀⠀⢎⡀⠔⠁⠀⠀⠀⠉⠛⠲⠶⠤⠶⣞⣋⣤⣤⣶⣶⣾⡿⣿⢿⠟⡻⠋⡽⠁⠋⠀⢁⣈⣀⣀⣤⣤⣤⠴⠶⠶⠶⠖⠒⠒⠛
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⢾⠟⡿⠻⠫⠋⠈⢈⣁⣁⣠⣤⡤⠶⠶⠖⠛⠛⠋⠉⠉⠉⠁
⢠⡏⠀⠀⢀⣀⣠⣤⢴⠖⠾⠛⠋⢙⣁⣊⣤⣥⡴⠶⠶⠚⠛⠛⠉⠉⠉
⣿⣔⣒⣉⣁⣀⣤⣤⠴⠶⠖⠛⠛⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⢛⣵⣟⣿⠘⢢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣱⣤⣤⣴⣾⣿⣿⣿⣿⣿⣻⣼⠻⣤⣸⡿
⣿⣿⣿⣿⡿⠿⠿⠿⠿⠀⣹⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷
⣿⣿⣿⡿⠀⠀⠒⠀⠀⠀⢽⣿⢿⣿⠿⠿⠿⡿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⣿⣿⡇⠀⠀⠀⠀⠀⠈⣀⣈⠃⠀⠀⠀⠘⣀⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠌⠂⠀⠀⠀⢸
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠃⠁⡄⠀⠀⢸
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠈⢠⠀⠀⢸
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⡀⠀⠠⠀⠀⢸
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸
⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣬⣧⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣾⣶⣶⣶⣶⣶⣖⣲⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣶⣒⣶⣶⣶⣶⣶⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣟⡿⣿⣿⠿⠿⠛⠛⠻⠟⠛⠛⠛⠛⠻⠿⠻⢿⢟⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠊⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠏⠁⠈⡄⠉⢳⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⠀⠀⠀⠀⠀⢰⡇⠀⠀⢐⡀⠀⠀⣤⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡏⠀⠀⢀⣠⣀⡈⢷⡄⠀⠐⠀⠀⣰⠃⣀⣀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡃⢉⣿⠀⠙⠷⠶⠶⠚⣡⣏⡹⠈⠛⣦⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢸⣙⣓⣿⠀⠀⠀⠀⠀⠐⣯⠢⡅⣢⠜⣸⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⢺⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢷⡤⡤⠴⠋⠀⠠⠇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣇⡀⢸⣒⣔⣶⣘⣆⡠⡤⠀⠀⠀⠀⣰⣶⣶⣼⡆⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣒⣻⣿⣿⣻⣶⣒⣦⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠉⠉⠉⠹⠿⣛⢛⡛⠛⢛⣛⡛⣛⣛⣛⣛⣛⠛⠛⢻⠋⠋⠋⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄⡇⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣉⣉⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⡉⠉⠉⢁⣀⣀⣀⣈⣉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠇
⠀⠀⠀⠀⠐⣶⡀⠀⣹⣦⠀⣴⠁⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡅
⠀⠀⠀⠀⠀⢻⣿⡷⣾⠗⣿⡿⡄⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠸⣿⣷⢸⢹⣿⠃⣇⣀⣀⣀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠀⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣮⣼⣿⠀⠠⠀⠀⡆⢰⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡀⡆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢻⣠⣤⣦⣤⣥⡼⠿⠻⠛⠻⢳⣶⣶⣶⣶⣶⣶⠶⠿⠾⠿⠿⢦⣷⣶⣦⣬⡄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢻⣯⣤⣤⣤⣤⣤⠜⠛⠛⠛⠛⠻⠛⢤⣤⣤⣤⣤⣤⡿⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢟⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⢀⣀⣀⣀⣀⣀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀
⠀⠸⠄⠤⠀⠠⠄⠼⠀⠀⠘⠈⠠⢄⡀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⡇⠀⠀⠀⠠⠐⡈⠄⡐⠣⡀⠀⣔⠂⠉⠉⠉⠉⠉⠉⠁⠐⡄⠧⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⣀⣤⣤⣴⠀⠀⠀⠀⠀⢻⣄⡀⢘⠀⠠⢌⣁⣀⣄⢈⣡⡀⠀⠆⠀⠀⡤⠉⠀⠀⠸⣁⠀⠐⡄⢨⠉⠁⠐⠒⠒⠒⠂⠉⠉⠁⡇⠀⠀⠄⠤⢠⠘
⠀⢰⡾⣿⢿⠏⣯⣽⠀⠀⢠⢀⠈⠀⠀⠉⠙⠀⠁⠈⠉⠉⠉⠈⠉⠀⡀⡇⠀⠛⠀⠀⠀⢄⠀⠀⠀⢀⡄⠀⠀⡠⣊⣀⣀⠁⣢⠀⢰⠀⠇⠀⠀⠴⠮⠅
⠀⢸⣧⣏⡾⠾⠛⠛⠀⠀⠈⠈⢉⣉⣁⣀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠠⠀⠀⠀⠀⣠⣾⡟⣧⠀⠀⡏⠇⠰⠮⠿⠟⠀⡄⠀⣰⡏⣇⣐⣒⡂
⠀⠘⢋⡁⠀⠠⠀⠀⠀⠀⢎⡁⠀⠀⠀⠀⠀⢈⡃⠀⡏⠉⡍⠨⡅⠨⠀⠀⠀⠀⠀⠀⠀⢰⠾⡿⣤⠟⠋⠀⡃⠃⠀⢿⣿⣀⠀⢁⠁⠀⡇⠿⠏⠁⠠⠄
⠀⠀⠀⠍⠁⠀⠄⠀⠀⠀⠀⠀⣤⠬⡉⣩⡅⠀⠁⢠⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣻⠟⠁⠀⠀⠀⢠⠈⠨⠀⠀⠥⠌⡘⠀⠀⡇⢀⠀⠐⠤
⠀⢰⡦⣤⣤⣤⣤⣴⠀⠀⢀⣴⣷⣷⣿⡿⣻⣦⠁⢸⠀⠄⠀⣀⣠⢰⣆⠀⠀⡄⠀⠀⠀⠘⠁⠠⠚⠆⠀⠀⠀⠑⠠⠀⠀⠠⠐⠁⠀⠀⡇⠄⠀⠀⠀⠀⡁
⠀⠘⡛⠛⠚⠓⠒⡹⠀⠀⠘⢿⣸⣖⣾⣷⣯⡟⠃⠘⠀⠀⠱⠋⠁⠀⢸⠀⠀⡇⠀⣀⠀⠀⠀⠃⣠⠀⡀⠀⢀⠀⠀⠀⢀⣠⡀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠈⠉⠉⠁⢀⣀⡀⠠⡀⠉⠉⠉⠉⠁⢀⠆⠀⡄⡃⠀⠀⠀⠀⡸⠀⠀⠷⠁⣀⠑⣀⢀⠩⠐⠈⠀⢀⢠⡀⠀⠀⢸⠖⡓⠄⠀⢰⠅⠀⠀⠀⠀⠀⢽
⠀⠀⢠⣄⡀⠄⠚⠁⡚⠀⠀⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠄⠂⠉⠀⠀⠀⠘⠀⠀⢤⡭⢞⠀⢈⡉⣀⠤⣀⠀⠀⠊
⠀⠀⡄⠀⢀⠤⠔⡊⢓⢠⢤⡄⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠣⠀⠁⠐⠀⢀⣠⡄⡂⠀⠀⠒⠉⠀⠸⠥⣇⠀⣨⢹⠆
⠀⠀⠏⠐⠐⠄⠄⠠⣴⠶⠃⡀⠀⠀⠀⢸⣿⠋⠉⢻⠀⠀⠀⠀⠀⠀⠀⣿⠋⢿⣿⡇⠀⠀⠀⠄⠉⠀⠀⠸⠛⠓⠁⠇⠀⠀⠀⠀⠠⠠⠄⠀⠈⠄⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠈⡇⠀⠀⠀⢸⣿⣄⠈⠛⠒⠒⠖⠂⠐⠒⠂⠙⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡖⢣⢠⠄⠸⡤⠀⣀⣀⡀⠀⢀⣀⣀⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢸⣏⠈⢀⣤⣀⡀⣄⣀⣀⣀⣈⣹⣀⣀⣈⠃⠀⠀⠀⡇⠀⠀⠀⠀⣐⣇⡠⠀⠀⠆⠀⠀⠀⠈⠉⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⣠⡛⢀⠄⡄⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢤⣈⠀⣀⢁⡠⠖⠉⠀⠀⠈⠲⣀⠀⠀⠃⠀⠃⡠⠊
⠀⠀⠀⠀⠀⠀⢰⣿⣥⡟⠁⡇⠀⠀⢰⠀⠒⠀⠀⠒⠀⣀⣀⣀⣐⡒⠂⠀⠐⡄⢀⢀⣀⣀⣀⣀⣀⣀⣉⣁⣀⢀⣀⢀⢀⠀⠀⡀⢁⣀⣁⢀⣁⢀⣀⣀⢤
⠀⠀⣀⠀⠀⠀⢨⣿⢏⡠⠔⠃⠀⠀⡸⠀⢀⣬⣴⡾⡿⠛⠿⣫⡏⢥⢱⡄⠀⡇⠀⠀⠀⠀⠀⡄⣄⣔⢰⠠⢠⠀⢰⡆⣆⢲⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠁⠒⠒⠋⠁⠀⠀⠀⠀⠀⠨⠀⣾⢰⢷⢠⣠⣛⣰⣭⣽⡶⠞⠁⠀⡇⣀⢀⣀⡀⢀⠃⠈⠃⠘⠀⠛⠀⠘⠃⠉⠋⢠⣿⡏⠀⠀⠈⠀⠀⠀⣀⣀
⠀⣐⠩⠅⠱⠎⠀⠉⠀⠉⠉⠉⣰⠀⡨⠀⠘⠳⠿⠿⠿⠿⠛⠋⣽⣶⢖⣦⠀⡇⠀⠀⣀⠠⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⡀
⠀⠠⠼⠤⠤⠤⠤⠤⠼⠥⠬⠼⠏⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠘⠛⠛⠃⠂⠃⡈⢥⣤⡃⠾⢚⡭⣤⢦⢱⡀⠀⠀⠀⠀⢤⠀⠀⠀⡏⣹⠑⠄⣹⣸⡆
⠀⢰⠒⠒⠒⡒⠒⠒⣒⠒⠒⠒⢶⠀⠀⢀⢀⠤⠤⣀⡀⠀⢀⡀⢀⠤⢄⡀⡀⠈⡇⠚⠭⠹⢩⠭⠢⠭⠘⢸⠁⠀⢀⠠⠔⡠⠤⢀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠀⠀⢿⢩⡘⠃⠬⣸⠀⢸⣨⣅⠀⢀⠇⠽⠀⠈⠢⣀⠀⠀⠀⠀⣀⠔⠁⡖⠊⠄⣀⠀⠀⠀⠨⠀⡐⠛⠁⠈⠈⠛⢂
⠀⠀⠀⠀⠀⠒⡆⣲⠖⠀⠀⠀⢸⠀⠀⣤⣀⡀⠁⡀⠀⠀⠀⠀⠈⠉⠁⠀⣤⡄⠀⢀⡈⠡⠭⠭⠍⢁⠀⠀⠁⠀⠀⠉⠀⠀⡀⠀⠀⡇⠈⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠤⠀⠁⠤⠐⠀⠀⠸⠀⠀⠃⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠂⠀⢸⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠃⣠⢶⠶⣶⣄⢰
⠀⠀⠀⠀⡀⠀⠠⡀⠠⢀⠀⠀⠀⠀⠀⠇⠀⢀⣾⣿⠻⢛⡿⢻⢻⣿⡆⠀⠀⠄⠀⢸⠀⠒⡄⡈⠁⠸⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⡆⠻⢷⣶⡶⠿⢸
⠀⢠⠀⠀⠉⠉⢦⣈⠴⠊⠀⠀⢰⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠧⠄⠀⡅⠀⢸⠀⠀⣴⣶⠂⢰⠀⠀⠀⠠⠀⠸⠀⠀⠀⢘⠀⡇⠀⠀⠀⠀⠀⠸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠄⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠰⡇⠀⢸⠀⠠⠄⢤⠀⢸⠀⠀⣀⠐⠀⠐⠀⢀⠠⠘⠀⢣⠀⠀⠀⠀⠀⡜
⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠃⠀⠈⠐⠂⠠⠀⠒⠈⠀⠀⠈⠉⠀⠛⠈⠁⠀⠀⠀⠀⠉⠀⠒⠀⠈

⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠂
⣀⡀⠀⠈⠀⣀⡰⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠
⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡀
⠀⠠⢀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⠤⠖⠀⢤⠀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⢀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪
⠄⠄⠂⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢿⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⡐⠀⠀⠀⠀⠀⢄⢰⢠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢄⡋⠠
⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠰⠂⢀⣀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⣷⠈⠻⠀⠀⠀⠤⠀⣁⠤⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠴⠀⠀⠱⠀⠀⠹⠆⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠁⠀⠀⠊
⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠈⠁⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠚⠛⠛⢻⠋⠉⠉⠛⠛⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⢉⣀⣀⣤⣤⠴⠖⠚⠻⡉⠙⠛⠲⠦⣤⣀⣀⡀⠉⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⣁⡤⠖⠋⠉⠉⠁⢀⣠⡤⣄⣀⣠⣧⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢦⣀⠉⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⡴⠚⠁⠀⠀⠀⡤⠶⢒⡭⠶⠦⣤⡈⠁⢻⠀⠑⠶⠚⠙⠲⣒⡶⠦⠤⣀⠈⠳⢦⡀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⠄⡰⠖⠒⠚⠀⢰⣯⠞⠉⠙⠲⣝⢆⠀⠀⠀⠀⠀⠀⡞⡱⠊⠉⠓⣌⠱⣄⣀⣉⠳⢤⡈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⣴⠋⠀⡰⠋⠀⠀⢠⠼⢧⡀⠀⠀⠀⠘⡟⢠⢀⡀⠀⠈⢿⠄⠀⠀⠀⠀⠘⣇⢣⡀⠀⠀⡼⠀⣿⠀⠸⡇⠀⠙⢦⡀⠙⢷⣄
⠀⠀⠀⠀⢀⡾⠁⢀⡞⠁⠀⠀⣀⣥⣀⡀⠑⣄⠀⠀⠀⠙⢦⡀⠈⠉⢲⡞⢨⠀⠀⠀⠀⠀⠙⠶⣬⣉⣭⡤⠞⡟⢦⡀⠉⠙⢲⡄⢹⡖⠀⠙⢧⡀
⠀⠀⠀⢠⡞⠁⢠⠏⠀⠀⣠⠞⠉⠀⠈⠻⡳⡌⢢⡀⢀⣄⡀⠉⠙⠛⢉⠀⢸⠀⡴⢦⡀⢀⣀⣀⠀⠀⠀⠀⡰⠃⡼⠀⠀⠀⠀⠧⣄⡙⣆⠀⠈⢻⡄
⠀⠀⢀⡾⠀⢠⠏⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⢹⠀⠑⣝⢤⡙⠓⠒⠚⢉⡇⠈⠀⢹⡀⢹⡎⠀⠈⠙⣦⡒⢉⡠⠞⠀⢀⡠⠂⠀⠀⠀⠙⣎⠳⡄⠀⢻⡄
⠀⠀⣼⠁⢀⡏⠀⠀⢰⠋⢧⠀⠀⠀⠀⢀⠇⣼⠲⢤⡈⢢⡈⠉⠛⠉⠁⠀⠀⠀⡼⠁⡜⠱⢄⣀⣠⠏⠈⠁⠀⣀⠔⠉⠀⢀⡴⠚⠛⠓⢿⣄⠙⣆⠈⢿⡀
⠀⢰⡇⠀⡼⠀⠀⠀⢸⡄⠈⠳⣄⣀⣀⣡⠞⠉⠑⢆⢱⡀⠙⢄⠀⠀⠀⠀⢘⠛⠤⠊⠀⣀⠴⠒⠲⢤⣀⠠⠊⣀⠤⣤⣤⡏⠀⠀⠀⠀⠈⡏⣷⠘⣇⠸⣇
⠀⣾⠀⢰⠇⠀⣀⡤⠚⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠂⡧⠖⡶⢷⡀⠀⠀⢸⠀⠀⠀⡜⠁⠈⢈⣽⠾⢷⣠⠞⠁⡊⠀⠘⣇⠠⡀⠀⣀⡴⢣⡟⠀⢿⠀⣿
⢠⡿⢤⣞⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⢀⡜⢋⡼⡃⠀⠀⠀⢹⡄⠀⢸⠀⠀⢸⡠⣴⡾⠛⠁⠀⡆⣿⠀⢏⠁⠀⠀⠈⠓⠶⠶⠶⠞⠛⢦⡀⢸⠀⢹
⣾⠁⠀⠀⢏⠁⠒⠒⠢⢤⣤⣀⣀⣀⠈⠓⠀⠡⠒⠉⠀⠘⠦⢀⠤⠊⠈⠄⢼⠀⢀⡠⢾⠛⠄⣀⣀⠔⢡⡏⠳⠤⠃⠀⣠⠴⠒⠒⠒⠲⢤⡀⠀⡧⢸⡀⢸
⣿⠀⢀⠀⡜⠀⢀⡴⠋⣉⣉⣉⡙⠢⡌⠉⠉⠁⠐⠂⠀⠀⠀⠀⠠⠤⢤⣤⣽⠖⠋⠀⣀⣙⣒⣶⡶⠚⠉⠀⠀⠀⠀⠀⠙⠦⠖⠚⠛⠲⣄⠈⢲⡇⠸⡇⢸
⣿⠀⢸⠀⢧⠀⠀⠑⠋⠁⠀⠀⠉⠲⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠤⠊⢹⠀⠀⢄⠀⠀⠀⠀⠀⠉⠉⠉⢉⠉⠒⠒⠒⠶⠤⠤⢤⣀⣈⡓⢫⡀⠀⡇⢸
⢻⡄⠘⡇⢸⠇⠀⢀⡴⢒⡛⣓⠲⢤⡀⠀⡀⠀⠀⣰⠃⡷⠀⣀⢔⠁⠀⠀⠈⠀⡴⡚⣛⢢⣄⠀⠀⠀⠀⡔⢉⡗⢀⡴⢿⠛⠛⣖⢦⡀⠀⣬⠟⠁⢰⠇⢸
⠘⣧⠀⢻⠘⢧⠀⡏⡜⠁⠀⠀⠁⠀⢹⣮⣉⣉⣉⣡⠞⡡⠊⠀⢧⠑⠦⣄⠀⠈⡌⢄⣈⠆⡏⠳⡄⠀⢸⠀⣾⠀⢸⡀⠈⡄⠀⠈⣧⢳⠀⣇⠀⢀⡞⠀⣾
⠀⠹⣆⠀⢧⠀⠑⢿⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡀⠔⠀⡠⠒⠚⠛⠛⢶⡞⠀⠀⠈⣢⠤⠶⠡⢄⡈⠢⡈⢇⠹⣄⠈⢣⡀⠡⠀⢀⡟⣸⣠⠏⢀⡞⠀⢰⡟
⠀⠀⠹⣆⠈⢳⡀⠈⠳⣄⣀⠀⣀⣠⠞⢀⠔⠈⠀⠀⡌⠀⠀⠀⠀⠀⠀⢻⡆⢠⢊⡤⠞⠉⠙⢦⡙⣆⠈⠻⣗⠉⠀⠀⠈⠓⠻⠷⠚⡵⠁⠀⣼⠁⢠⡿⠁
⠀⠀⠀⠙⣧⡀⠙⣄⠀⢀⡏⠉⠉⠀⠐⢁⣄⡀⠀⠀⢇⠀⠀⠀⠀⠀⢀⢿⡇⢂⢸⡀⠀⠀⠀⣠⠷⠞⠲⠶⣌⡓⢄⠀⠀⠀⠀⡤⠖⠁⠀⢰⠇⢠⡿⠁
⠀⠀⠀⠀⠈⢷⣄⠈⠳⣄⠣⣄⣀⣀⠀⡎⠸⠁⠀⠀⠈⠢⣈⡂⠀⣒⡽⠋⡇⠈⠋⠀⠀⠀⡞⠡⠂⠉⠉⠑⠢⢷⡀⠑⢄⠀⢀⠇⠀⠀⣰⠋⣰⠟
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠘⠓⢤⡀⠈⠦⣱⡘⠤⣄⠀⠀⠀⠀⠉⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⡧⣠⠞⠙⠄⠀⣠⠞⢁⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠙⠢⣄⠀⠙⢦⣘⠶⠖⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⣀⣴⠏⠀⠀⠀⢀⡤⠞⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠈⠑⠦⣄⡈⠙⢯⣅⣤⠴⠶⠦⣀⠀⠈⢀⣠⠞⠉⠓⠶⠤⠴⠋⠉⠉⠀⢀⣠⠴⠞⠉⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⠉⠓⠶⠤⣄⣀⣀⡀⠈⠉⠛⠉⠀⣀⣀⣀⣀⣤⠤⠤⠶⠒⠋⠉⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣄⣀⠀⠀⠈⠉⠉⠉⠹⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠶⠞⠛⠋⠉

⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡾⡆⠀⡄⢀⠀⠀⠴⠒⠋⠉⠉⠉⠀⠒⠒⠀⠤⠀⠀⠀⣐⣒⣒⣚⣿⡷⠀⠠
⠀⠀⠀⢸⠠⡏⠀⡆⡎⡇⢹⠃⣰⣇⢾⡰⡀⢀⠂⠀⠀⠀⠀⢀⡬⢒⠃⡔⠀⠀⠈⣉⣩⡭⢭⣗⢮⠁⡀
⠀⠀⠀⠈⠁⠳⠜⠛⠀⡡⠈⠉⠈⠋⠀⠀⠀⠀⠀⠀⡰⠃⠄⠀⠀⠸⠪⣖⡳⠆⠻⡉⠉⠉⠁
⠀⠀⠀⢀⡴⣢⠅⠀⠘⠻⣷⡄⡠⠀⠀⠀⠐⠒⠀⢒⡣⠎⠀⠀⠀⠀⠀⠀⢊⡀⠰⠒⡲⢒⣊⠉⠁
⠀⠀⠀⠉⠊⢔⡩⠄⠐⡂⠀⠰⠁⠀⠀⠀⢀⣠⢴⢾⠳⢴⣈⡀⠉⠁⠀⠀⡀⠀⠀⠀⠛⣉⠶⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠖⡍⠀⠀⠀⠤⠔⠊⠉⠀⠄⠁⠘⠀⠈⠉⠀⠉⢙⠀⢈⠀⢀⣤⠄⡈⠀⠀⠀⠰⠁⠇
⠀⠀⠀⠀⣴⡂⠀⠐⢀⠀⡀⠔⠀⠀⠀⢰⠀⠀⠀⠀⠁⠘⠀⡀⠀⠀⠀⠀⠀⠈⠀⠔⠠⢀
⠀⠀⠀⠈⠉⡠⠃⡴⢋⠎⠃⠀⠰⠃⠀⢸⠀⠰⠀⠀⠀⡠⠂⢁⠖⣼⡂⠢⣠⣠⡄⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠁⠜⠁⠃⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠉⠉⠛⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣠⣲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⢧⠆⠄⢠⠃⢠⠆⠼⢠⠄⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⢄⢠⣿⣧⠉⠙⠗⠀⠀⠀⠀⠀⠀⣀⠀⣠⡐⢰⠇⠟⠎⡠⠃⡴⠃⠀⢀⡎⠀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡿⡴⠀⠁⠀⠸⠀⠀⠈⢠⠞⠁⠀⠀⡜⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠙⠻⠿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⡜⠀⠈⠂⠀⠀⠀⠛⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠑⠢⡄⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣠⠃⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣀⡀⣀⡀⠀⠀⡠⠒⠂⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⠎⡄⠩⣑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡠⠋⠀⠀⠀⠈⢠⠔⠢⠤⣈⠀⠀⢀⣀⣀⠼⠀⠀⠀⠀⠀⠀⠸⢠⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠢⠘⢰⠁⠀⠀⠀⠀⠀⠰⠀⠀⡠⠂⡠⠊⠀⠀⢠⠀⠀⠑⠆⠀⠀⠀⡆⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⣠⠔⠒⠒⠚⢦⠀⠀⠀⠀⠀⠀⢀⣼⢀⡜⠀⠀⠀⠀⡇⣠⠀⠀⠸⠇⠀⠘⣱⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠖⡠⠚⠁⢀⣀⣠⠎⠀⠀⠀⠀⠀⢀⡇⠀⠀⠠⢀⠜⠁⠀⠈⠀⠀⠀⣀⠀⣶⠁⠀⠀⣸⠋⠀⠀⢣
⠀⠀⠀⠀⢀⠖⢁⠔⠉⠀⠀⡜⡩⠋⠀⢄⣀⣠⠤⠤⠐⠁⢀⡓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⢠⡏⠀⠀⠀⣿⢈⡀⢨⠀⠘
⠀⠀⠀⠀⡆⠀⣼⣦⡤⠚⡁⠐⠁⠀⠀⠀⠀⠀⣀⣠⣗⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠧⠄⠀⡾⠁⡀⣠⢲⡿⠈⠄⠀⠂
⠈⠀⡄⠀⠐⠀⠻⠽⠐⠠⠄⠀⠀⢁⣈⣩⣽⣛⡋⠍⠁⠀⠀⣓⣂⠀⠀⠀⠒⠈⠈⠉⢡⠀⠀⠀⠀⠀⣰⠃⡼⢋⡵⠏
⠀⠀⠄⠀⣀⣀⡀⠀⠀⣀⡀⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⢂⡀⠀⣠⠔⠰⠤⢼⡤⠤⠲⢖⣪⣥⣾⣿⣋⣀⣀⣀⣀
⠀⠀⠀⢀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⠫⠊⠀⠀⣀⣠⡀⡼⠀⠀⠀⢐⠀⠀⠘⠋⠉⠉⠉⠙⠛⠿⣟⡲⢤⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡥⠤⠴⠛⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⣀⠠⢄⡽⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⣠⠤⠒⠂⢼⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠑⠦⠤⣤⡯⠤⠖⠁⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢤⣤⣤⣀⣀⣤⣤⡴⠶⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠤⠤⣀⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⡀⠀⢠⠀⠀⠁⠀⢀⠀⠀⠉⠲⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣄⣀⠀⠀⠀⠤⠀⠀⠉⠀⠘⠀⠀⠈⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠬⠤⠤⠤⣤⣄⣠⣤⣤⣀⣠⣤⣤⣤⣀⣀⡤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⠳⢶⣤⣭⣿⣍⣀⣀⣀⣠⣴⢦⣤⣤⡶⠂⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⢦⣀⡀⠉⠉⠉⠉⠉⠉⠁⣉⣠⣴⠖⠋⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⣿⡀⠀⠉⠉⠛⠓⠚⠛⠛⠛⠉⠁⢀⣠⠄⠀⠀⠀⠈⠻⠷⣦⣤⣤⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⢠⡏⠀⠀⠀⠀⠈⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⠶⠞⠋⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣠⠤⠒⠛⠋⠉⠉⠉⠉⠛⠛⠻⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢋⣁⣀⣀⣀⠠⢤⣤⣄⣀⣀⡀⠀⠀⠀⣸⣿
⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⣀⣈⣙⠛⠛⠛⠉⠻⢶⣄⡈⠉⠉⠁⠀⠀⢠⣿⣿
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⢶⣶⣤⣈⠉⠛⠿⣷⣦⣄⠀⠀⠉⠻⠷⠄⠀⠀⢀⣾⣿⠇
⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀⠀⠀⠀⣴⠟⠁⠘⠳⢦⣄⡉⠛⠿⢷⣦⣄⡉⠛⠿⣶⣄⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒⠀⠈⡙⠷⣤⣀⠈⠙⠻⢷⣦⠈⠙⠋⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠙⠛⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣀⣀⣀⣠⣤⣤⣤⣴⣶⣾⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠈⠉⠉⠁⠒⢒⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢒⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡜⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠜⢇⡀⠀⠀⠀⣦⠰⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⢀⣀⣀⠠⠤⢄⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠀⠀⠀⠀⠈⠑⣯⠤⡃⠀⠀⠀⠀⠀⠀⠨⠛⠲⠖⣚⡱⠢⣀⡠⠂⡂⢸⢘
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠾⠍⣱⢊⠯⢭⡁⠢⡏⠀⠹⣖⡠⠄⢀⡀⠤⢞⢢⠀⠀⠀⠀⠀⠀⡤⠐⠙⠚⢿⡖⢄⡀
⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⢋⠼⢮⡉⠂⠀⠀⢱⠀⠀⢡⠈⠓⢦⢄⠀⠀⢇⣢⣀⣀⠀⠤⠊⠀⠀⠀⠀⡰⠁⠀⠈⠑⡄
⠀⠀⠀⠀⠀⢰⠁⢸⠀⠀⢸⢀⡝⢻⡄⠀⠀⢸⠀⠀⠈⡆⠀⠈⠶⢄⢘⡀⠀⠀⠱⡀⠀⠀⠀⠀⣠⠞⢀⡤⠶⠚⠋⡁
⠀⠀⠀⠀⠀⠠⣀⣾⠀⠀⡔⠋⠀⠈⠙⡄⠀⠀⡆⠀⡀⡇⠀⠀⡀⠀⠉⡇⠀⠀⠀⠑⠤⠤⠔⠊⠀⠀⠉⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠱⠀⣧⠃⠀⠀⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⡆⠀⠀⠀⠀⠈⡀⠀⠀⢣⡟⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢷⡀⠀⡸⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠷⡠⠃⠀⠀⠀⠀⠀⠀⠉⠗⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠴⠂⠀⠀⠀⠀⡰⠁
⠀⠀⠀⢠⡄⣀⠼⣦⣀⢴⠗⠁⠒⠒⠠⠤⠤⢼⣤⡀⠤⠇⣀⠀⣀⡀⠤⠐⠒⠂⠉⠁⠀⠀⠀⠀⣀⠠⠞
⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠑⠀⠒⠂⠀⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⠂⠀⠀⠐⡀⠐⠂⠘⠀⠒⠒⠒⠦⠤⠤⠧⢈⣁⡀
⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⠀⢀⠄⣡⠖⠋⠁⠀⠀⠀⢀⣡⠐⠀⠃⡆⢂⠀⠀⠀⠀⠐⠒⠂⠐⠛⠉⠑⢤⢀⣃⠐⠂
⠀⠀⠀⠀⠘⠀⠀⡿⠀⠈⠄⠉⠈⣁⢩⣈⠁⠂⠀⠀⠀⠱⠤⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡥⠄⠀⠉⡑⢆⠈⠑
⠀⠀⠀⠀⡆⠀⠰⠃⡄⠀⠠⠀⠀⠈⠒⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⡠⠀⠀⠀⠀⢀⡀⠀⡌⠁⠃⠠⢷⠂⠀⠂
⠀⠀⠀⠀⢟⠀⠀⢱⡄⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠄⡝⣦⣳⠗⠖⠀⠈⠄⢀⣀⡀⠀⠀⠐⠀⠐⠀⠞⠋⠀⡰⡇⠀⠘⡆
⠀⠀⠀⠀⠈⢦⡀⠈⠁⢡⣶⡀⠒⠀⡀⢠⣄⣶⠠⣔⣶⣿⡄⠃⠁⠀⢀⠀⠠⠞⡀⠈⠁⠀⠈⠀⢀⠁⠀⠀⠀⠀⠈⠏⠁⠀⣘
⠀⠀⠀⠀⠀⠈⢳⣄⡈⠀⢰⡷⠶⣶⡿⣮⠿⠚⠁⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⡀⠁⠀⣈⠄⠀⣀⡤⠔⠀⢀⠠⠬⠂⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠀⠀⠀⠀⠀⠉⣥⠤⠃⠀⠂⠀⠈⠠⠠⠄⠀⠀⠀⠠⡈⠁⢉⢉⠀⠀⣠⡆⠁⠀⠀⠀⢢⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠇⣴⠀⠀⠀⠀⠀⠀⠈⠐⠉⠉⠀⠃⢰⡖⠒⠒⠒⢻⠍⠀⠀⠀⠀⠁⠁⢀⡀⡴⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠤⠄⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡄⠤⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠐⠒⠒⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⡀⡀⡀⢀⠀⣀⠀⠀⡀⡀⡀⠀⢀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠐⠀⠂⠃⠀⠃⠘⠀⠀⠀⠂⠀⠀⠀⠀⠃⠂⠂⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠖⠇⠀⠱⠈⠀⠠⠡⠀⠈⠰⠒⠀⠀⠀⠇⠰⠸⠸⠀⠀⠀⠀⠀⣾⠿⠟⠛⠉⠀⠀⠀⢀⡀⠀⢀⠘⣷⣶⣶⣶⣶⣶⡶⣦⣠⡶⠀⠀⠀⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣤⣤⣤⣴⣶⡆⢠⣴⣿⣶⣤⣬⣅⣶⣾⣷⣤⣀⡚⢽⣿⣶⣦⡴⣶⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠀⡀⡆⠂⡂⠀⢂⢀⠐⢰⢠⠀⠐⠠⠀⡐⢀⠂⠀⡄⠀⠀⠀⢸⡿⠋⠁⠀⠉⠉⠉⠀⢁⣉⢻⣿⣿⣬⣼⣿⣿⣿⡿⢻⣿⣿⣿⣿⠎⣩⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⣿⣿⣿⣿⣿⢿⢴⣿⣦⢳⣽⣟⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠤⠠⠀⢀⠀⡄⠄⡄⡀⡀⢠⡀⡀⠰⠀⡄⠀⠠⠀⠀⠀⠀⠀⣠⡄⠀⠀⠰⢾⣿⣿⣿⣷⣴⣿⣦⣽⣽⣾⣵⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣿⡿⣿⣟
⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠁⠀⠁⠉⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠻⠿⠢⠖⠖⢸⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⣿⣿⣽⣟⢿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢶⣏⣿⣿⣿⣿⣿⣿⣟⣛⣣⣬⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡦⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⣎⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡁⣠⣄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠚⠶⠗⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⣀⣐⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⡿⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠯⠄⡾⢀⠝⠋⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡴⠤⠄⣠⢂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣶⡾⠿⠦⠤⣤⣌⣉⠙⠒⠦⣌⣣⠀⠀⠀⠙⢦⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠙⢦⡀⠀⠀⠀⢳⡄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢚⠋⠉⠉⠉⠉⠙⠒⠮⣖⡠⡀⠀⠈⠳⣄⠀⠙⣦⡀⠀⠀⢳⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣋⡤⠴⠞⠓⠛⠛⠛⠒⠶⠦⣤⣀⠉⠳⢄⠀⠀⠙⣦⠀⠘⣷⡀⠀⠈⡇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠉⠳⢦⡀⠑⣄⠀⠘⣇⠀⢸⡇⠀⠀⡗⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠀⠀⢀⡤⠶⠛⠛⠛⠒⠒⠲⠦⣤⡀⠀⠀⠈⠻⡵⣸⡆⠀⢹⠀⠈⡇⠀⠀⡇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡴⠚⠁⠀⣀⣤⡤⠶⠶⠶⠶⠶⣶⣌⠳⢦⡀⠀⢹⣵⣿⠀⢸⠄⣶⠃⠀⣸⠃⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡱⡄⠀⣧⠈⠀⣈⠃⡏⠀⣰⠏⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡕⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡜⡄⣧⢀⡀⢋⠎⣠⣾⡯⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⡞⠁⠀⠀⠀⠀⠀⢀⡴⣲⠦⠀⠀⢀⠀⠀⣀⠀⠀⠘⢱⠇⠟⣴⠶⠚⣹⣽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠛⠋⠉⠉⠉⠁⠀⠉⠐⠠⠟⠒⠒⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⣂⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



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

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡤⠤⠤⢤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠈⠲⣄
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠈⠓⠦⡤⠤⠴⠾⠇⠒⠒⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣻⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢰⡏⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⢰⡏⠀⠀⣻⣿⣧⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡄⠸⠄⠀⠀⠀⢸⣷⣦⣶⠋⢻⡿⠀⠀⠀⠀⠀⢸⣿⣶⣶⠉⢹⡿⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠙⠿⠿⠶⠟⠁⠀⠘⠄⠠⠀⠀⠙⠻⠿⠷⠛⢁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢡⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⠀⠀⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠻⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠀⠀⠂⠀⠀⠀⠀⢀⡶⠀⠀⠀⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠄⠀⠂⠀⠀⠀⢠⠞⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢠⠀⠀⠀⠀⡷⠋⠀⠀⠀⠈⣝⣩⡟⠧⣤⣭⡼⠿⠿⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡰⠒⠀⠀⠀⠀⠀⠀⣟⣱⣞⣻⣦⠙⣼⡛⣷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⣿⡃⣛⠈⣛⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣚⡻⠋⣿⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⢨⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡿⢊⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠉⢹⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⣲⠍⠀⠀⠈⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⣉⠉⠙⡦⠒⠒⢫⡀⠀⠀⠑⢀⠀⠘⠂⢀⠀⠉⠉⠉⠀⠀⠀⠀⢸⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠒⠊⠉⠀⠀⠴⠋⠁⠀⡸⠀⡀⠀⡆⠑⣄⠀⡀⠀⠈⠢⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⣖⠉⠀⠀⠀⠀⠠⠀⠁⠀⠀⡠⠀⢰⠁⠐⠀⠀⠈⠀⠈⢢⡐⠌⠢⡀⠀⠑⠠⡀⠀⠀⠀⠀⠀⡸⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠎⠹⡄⠀⠘⢆⠀⠀⠐⠀⠀⠄⠀⠀⠊⠀⢠⠃⢀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⡈⠢⠀⠀⠀⠀⠰⠄⠀⡰⠁⠀⡜
⠀⠀⠀⢀⡔⡁⠀⠀⠙⡄⠄⠈⠳⡀⠀⠀⠀⠀⠐⠁⠀⠀⠎⠀⠂⠀⠀⠀⠀⠀⠡⠀⠀⠈⢢⡈⠢⡀⠀⠀⠀⠀⠀⡔⠁⠀⡰⠁
⠀⠀⢀⠎⠈⠀⠀⠐⠀⠈⢎⠂⠀⠈⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⣄⠈⠂⠀⠀⡠⠊⠀⢄⡔
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠳⡔⢄⠀⠉⠢⣀⠀⠀⡸⠁⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⡀⠈⢢⣀⡤⠊⠀⠀⡠⠊
⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠈⠢⣁⠀⡀⠈⠑⠴⣅⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁⠀⢐⡡⠊
⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⢀⠈⠓⢬⡀⠀⡀⠀⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠖⠒⠊⠁⠀⠀⢀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠀⠀⠤⠤⠤⠄⠈⠛⠛⠛⠒⠂⠈⠉⠉⠁

⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤
⠀⠀⠊⣴⡔⡄⢁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣟⣷⡉⠀⠀⠀⢀⡆
⠀⡀⢰⡿⣷⣠⣾⣇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢠⡄⠐⠋⣀⢤⡄⣘⠋⠀⠀⠀⡀⠸⠁
⠀⠁⡉⠁⠉⠉⠸⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠅⢨⣿⠇⠈⢀⠀⢈⡋⣡⠨⠕⢃⣼⡅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⣼⠿⠀⠀⠈⠩⠆⠈⠀⠀⡎⣰⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⠐⠀⠀⠀⠀⠈⠙⠁⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢶⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⣤⣤⣴⡶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢹⡿⠓⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⢑⣀⡅⠴⠐⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠐⣿⣶⠿⠀⣤⠀⠀⠀⠝⠇⢸⣿⣿⡿⣡⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠁⠀⠀⢹⠇⠀⡘⠀⡇⢸⡟⢋⡐⠿⠿⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⡂⠀⠀⠀⠀⠀⣷⠀⠂⠱⡋⠀⠀⡄⢠⡇⠀⢡⠀⢹⣆⠐⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠼⠦⠹⠷⢅⠆⡀⠀⠀⡠⠁⠀⠀⠀⢰⠀⠀⣰⡟⢷⢀⡀⠀⠀⠂⢁⣌⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⡛⠀⡄⢀⠀⢸⡁⠀⠀⢀⡠⢶⣄⣠⣤⣶⣾⣿⣿⢂⢘⡿⣦⡀⢰⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢭⣠⡍⠼⠟⠁⠀⠠⠉⠀⠀⢻⣿⣿⣿⣿⠿⣿⣿⡇⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡄⢀⡀⠀⠀⠀⠸⡿⢿⡿⠁⠐⢋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⡤⠐⠛⠛⠷⠀⠀⠀⢀⣀⠞⠁⣴⣿⣟⣓⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣶⣾⣿⣷⡄⢹⣦⠐⠐⠂⠀⠀⠀⡀⠊⠁⠀⣠⣬⣵⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣈⢈⣷⣤⡔⣧⠀⣴⠁⡄⠀⢸⣿⣿⣿⡜⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⣼⡃⢠⠞⠑⢦⣞⢡⣚⣣⠀⠈⠘⠋⠁⠀⠙⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢷⡁⢁⠞⠓⠒⢾⣿⣭⠟⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠯⠥⠞⠁⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⢀⡶⠀⢠⠖⢠⠀⠀⢀⣀⣼⣟⣫⣀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⡋⠀⠀⠈⠁⠀⠘⠋⡀⢿⠉⣥⠲⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡤⠄⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠀⣿⡟⣥⠶⣬⠹⣿⠀⢲⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣍⡻⠇⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠈⠷⣴⣶⣦⠾⠃⠀⠈⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣙⠻⢿⣿⣷⣦⣀⠀⠀⠀⢀⣀⣠⣤⠶⣀⣤⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⠉⠛⢿⣿⣿⣶⣿⣿⣿⠟⣡⣾⢿⣿⣿⣿⣿⣿⡿⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠙⠛⠉⠁⢀⣾⠟⠀⢸⣿⣿⣿⣿⣿⡇⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⡆⠀⠀⠛⠟⠁⠀⢸⣿⣿⣿⣿⣿⣧⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡏⠁⠉⠉⠉⠉⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣷⡀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⠿⠁⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⢿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠦⣤⣤⣤⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢠⡖⠲⢄⠉⠉⠑⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠈⢳⡄⠒⠠⠤⠜⠀⠀⠀⢀⣸⣟⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠋⠁⠀⣀⡀⠲⣄⠀⣎⠀⠈⣛⠇⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣄⡀⠀⣀⠀⠯⣁⣀⡤⠃⠈⠓⠚⠃⠀⠀⠂⠀⠙⠳⣀⣤⢖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⢛⡏⠀⡉⣹⠀⢀⢄⣤⡖⠀⢀⡔⠊⠍⠙⢲⠀⣀⠤⠜⠠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⢬⢶⡶⠒⠁⠀⠈⠉⠛⠃⠀⠀⠹⠦⠶⣾⡾⢞⡡⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠊⣀⡗⢀⡔⠒⠓⣢⠀⠀⠀⠀⠀⠀⢀⠜⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠁⠀⠈⢇⣨⣤⡼⠁
⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⡆⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠘⠃⠂⠖⠚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⣠⣴⣊⣭⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢸⠒⡖⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉⠀⠈⢻⡓⣄⠀⠀⠀⣾⢸⠁⣀⡴⠛⠁⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⢀⡇⣧⠀⠀⠀⠀⢱⠘⡆⠀⠀⡇⣸⠞⣏⢧⠀⠀⠀⠀⠀⠀⢠⠏⡽⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢯⡀⠀⠀⠀⠈⣇⢸⡀⠀⠀⠀⠸⣇⡇⠀⢸⠃⡇⠀⠘⣎⢧⠀⠀⠀⠀⣠⢃⡼⠁⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠙⢦⠳⣄⠀⠀⠀⠘⢦⣷⣄⠀⢀⣸⠏⠀⠀⠚⠺⠇⠀⠀⢸⣌⣇⠀⠀⡴⢣⠞⠉⢲⠖⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠳⡌⢦⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⢤⡏⠀⠀⠈⠀⠀⠀⠀⣠⠔⢋⡽⢆
⠀⠀⠀⠀⠀⡴⠋⠙⠀⠀⠀⠀⠀⠀⠘⢦⣱⠆⠀⠀⠀⣀⣠⠴⠒⠚⠋⠉⠉⠉⠉⠙⠓⠲⠤⣄⡀⠀⠀⠈⠓⢤⡴⠂⢀⡴⢊⡥⠚⠉⠀⠀⣣
⠀⠀⠀⠀⢸⣧⣀⣤⠴⠚⣋⡓⣆⠀⠀⠈⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⢘⠢⡄⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠲⣩⠖⠋⠀⠀⠀⠀⣰⢻
⠀⠀⠀⠀⠀⠓⠦⠤⠖⠋⠉⠉⣿⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⢄⡀⢀⣀⠴⢋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠃⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡠⢄⠘⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠉⠛⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⠀⠀⠈⠀⣣⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠐⠁⠀⠄⢠⠀⠨⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⣀⠀⠢⢤⠄⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢌⡃⠐⢒⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠀⠀⠀⢠⡄⠀⠀⠀⡦⠀⠀⠀⡄⠀⠀⢀⡤⠀⠀⠀⢠⠦⡄⠀⠀⠀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠬⠂⠀⠀⠘⠄⠃⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠖⡖⠒⢶⣦⡀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⢨⣇⡇⢠⡭⡄⠀⡴⠀⢠⢤⡄⠀⡴⠂⢠⢤⡄⠀⢀⠤⢤⣄⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡧⠴⠛⠋⠀⢘⡃⡇⠀⠀⣰⢣⠎⠀⠀⠁⣠⢫⠞⠀⠀⠁⢀⣸⡆⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠇⡇⠀⣰⢣⠏⠀⣀⠀⣰⢣⠏⠀⣠⢀⡾⣁⣈⡇⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠚⠛⠓⠀⠀⠀⠀⠘⠛⠃⠀⠛⠛⠒⠚⠋⠀⠛⠛⠒⠒⠋⠀⠙⠛⠉⠙⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠡⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠄⠀⠇⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢁⣀⡀⣀⠠⠤⠤⠄⠒⠒⠈⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢂⠠⠒⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣉⠀⠀⠸⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡁⠀⠁⠀⠀⠆⠀⠀⠀⠀⠄⠑⢄⠁⠄⠀⠀⠀⠀⠀⠀⠎⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⡀⠀⡀⠳⡄⠀⠠⠀⠀⢀⠜⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⡠⠊⠀⣠⠃
⠀⠀⠀⠀⢀⠔⠉⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠖⠁⢀⠔⠁
⠀⠀⣀⠔⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠄⠀⠀⠀⠀⣀⠤⠊⠀⣀⠔⠁
⠀⠀⠙⠢⢄⡀⠈⠁⠒⠠⠄⣀⣀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡀⠤⠒⠉⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠈⠑⠂⠤⢀⡀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠁⠀⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠒⠒⠒⠂⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿