Stick Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣀⣀⣀⣀⠀⢀⣀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠉⢉⣹⠟⠛⠛⠋⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠴⠋⠀⠀⠀⣠⠞⢹⣿⠀⠀⠀⢀⣤⠶⠖⠚⠛⠒⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡏⠀⠀⢀⡤⠞⠁⠀⢸⣿⠀⠀⠀⣿⣅⣀⠀⠀⠀⠀⠀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠞⠋⠀⠀⠀⣠⢿⣿⠀⠀⠀⣿⠈⠉⠙⠛⢛⡿⠟⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡴⠁⠀⠀⠀⣠⠞⠁⢸⡿⠀⠀⠀⣿⢀⣠⠶⠛⠉⠀⠀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢀⡴⠊⠁⠀⠀⣸⡇⠀⠀⠀⣿⠋⠀⠀⠀⣀⡴⠞⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡴⠋⠀⠀⠀⠀⡴⢻⡇⠀⠀⠀⡗⠀⣠⠔⠋⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⢀⡴⠊⠀⢸⡇⠀⠀⠀⣧⠞⠁⠀⠀⠀⢀⡠⠞⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⠖⠋⠀⠀⠀⣸⡇⠀⠀⠀⡏⠀⠀⢀⡤⠞⠉⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠋⠀⠀⠀⠀⢀⡴⢻⡇⠀⠀⠀⡇⣠⠞⠁⠀⠀⠀⢀⡰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣀⠴⠋⠀⢸⡇⠀⠀⠀⣿⠁⠀⠀⠀⣀⠴⠋⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡠⠞⠁⠀⠀⠀⣼⡇⠀⠀⠀⡇⠀⢀⡴⠊⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠊⠀⠀⠀⠀⣠⠞⣹⡇⠀⠀⢰⣇⡔⠉⠀⠀⠀⠀⣠⠜⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⡴⠊⠁⠀⢿⡇⠀⠀⢸⡏⠀⠀⢀⣠⠖⠉⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠖⠉⠀⠀⠀⢀⣿⡇⠀⠀⢸⡇⢠⠔⠉⠀⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⠁⠀⠀⠀⢀⡴⠋⣼⡇⠀⠀⢸⡷⠃⠀⠀⠀⣀⠤⠊⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡤⠞⠁⠀⠀⣿⡇⠀⠀⢸⡇⠀⣀⠴⠊⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠔⠋⠀⠀⠀⠀⡠⣿⡇⠀⠀⢸⣧⠞⠁⠀⠀⠀⠀⣠⠞⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢀⡠⠚⠁⣿⡇⠀⠀⢸⡇⠀⠀⠀⣠⠴⠊⠁⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⡤⠚⠉⠀⠀⠀⣿⡇⠀⠀⢸⠂⣠⠔⠋⠁⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠁⠀⠀⠀⠀⣠⠔⣿⡇⠀⠀⢸⡶⠁⠀⠀⠀⠀⢀⡤⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⣠⠔⠋⠁⠀⣿⠀⠀⠀⢸⡄⠀⠀⣀⠤⠚⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡴⠋⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⢁⡤⠞⠁⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣄⣀⣀⣀⣀⣠⣤⡿⠁⠀⠀⢸⠏⠀⠀⠀⠀⣀⠴⠚⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢼⠀⠀⢀⡴⠊⠁⠀⠀⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣰⠋⠀⠀⠀⢀⣜⣱⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣟⣛⣋⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⡀⠉⠻⢿⣧⠉⠛⠿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠻⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇
⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇
⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⣴⣿⡿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣦
⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⢿⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿
⠀⠀⠙⠻⠿⠿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⣀⣀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⠿⠿⢿⣿⣿⠿⠿⣿⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣾⣿⣦⣀⠀⠀⠀⣀⣠⣿⣿⣶⣶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠉⠉⠉⠀⠀⠈⠻⠿⣿⣿⣿⠿⠟⠉⠀⠀⠉⠉⠉⠉⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⢈⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣻⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⢿⣿⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⣰⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣷⡀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣄⣀⣀⡀

⠀⣠⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⣿⠀⠀⠐⠋⠉⠉⠉⠙⠛⠛⠛⠛⠒⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠶⠖⠚⠛⣉⣽⠇
⠀⢹⣆⣘⡒⠂⠠⠀⠀⠈⠉⠒⠒⠒⠒⠦⠀⠈⠉⠓⠂⠀⠀⠀⠀⡀⢀⡀⠠⠤⣤⢄⣀⠀⠙⠻⠶⠶⠤⠤⠤⡤⠤⠤⠶⠶⠶⠶⣆
⠀⠀⠈⠉⠉⠉⠛⠛⠛⠒⠲⠶⠦⣤⣄⣀⠀⠀⠀⠀⢠⡦⠤⣤⣤⣤⣤⣭⣉⣓⣓⣒⣛⣁⣀⣀⣙⠛⠒⠀⠐⠀⠀⠀⢶⣶⣶⡚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⣤⣀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠲⠶⢦⣤⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⣀⣧⠀⠀⠀⢳⡇⠀⠀⠀⠀⢻⣧⣄⠀⠈⢿⡧⠤⠀⠀⠀⠀⣸⠀⠀⠀⢠⣿⡄⠀⠀⠀⣤⣯⡄⠀⠀⢠⣿⢆⠀⠀⠀⣠⣧⠗⠀⠀⠀⣬⣥⡀
⠀⠀⠀⢠⠟⠀⠀⠀⣾⣭⠁⠀⠠⠖⣹⠇⠈⠀⠀⢸⡇⠀⠀⠀⠀⣨⠿⠀⠀⠀⠘⣿⡟⠀⠀⠀⢹⢻⠁⠀⠀⢈⣿⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⢿⢧
⠀⠀⠀⠈⠂⠀⠀⠀⠚⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠈⠘⠀⠀⠀⠈⠀⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠘⠈
⠀⠀⠀⣀⠀⠀⠀⣄⢠⡄⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠄⢀⡄⠀⠀⡀⢠⡀⣀⠀⠀⣠⣀⢄⠀⠀⢠⡀
⠀⠀⢀⣬⣷⡤⠀⠈⢻⡿⠁⠀⠀⢩⣿⠯⠤⠀⠀⣻⣠⠄⠀⠀⠀⣾⠴⠂⠀⠐⠒⣶⡖⠒⠀⠀⢸⣿⡇⠀⠀⠈⣷⡞⠁⠀⠀⠑⣷⠎⠀⠀⢠⢻⣯⠃
⠀⠘⢫⠏⠀⠳⠀⢠⠋⠙⠤⠄⠀⡼⠙⡆⠀⠀⠀⠻⠚⠃⠀⠀⠈⢻⠆⠀⠀⠀⢀⡏⢇⠀⠀⠀⢸⢻⠁⠀⠀⠀⡏⢻⠀⠀⠀⠀⠋⡇⠀⠀⠀⡞⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁
⠀⠀⢰⠠⠄⠀⠀⠀⣠⣄⠖⠀⢀⡀⢶⣀⡀⠀⠀⢀⣶⠀⠀⠀⢰⡀⡄⠀⠀⠀⠀⣶⣠⠀⠀⠀⠀⣦⠀⠀⠀⢀⣠⡆⢀⠀⠀⠀⡶⠀⠀⠀⠀⣦⡄
⠀⠀⠀⣿⣿⠀⠀⠀⣱⢿⠷⠀⠀⠉⢹⣿⠈⠀⠀⣿⣿⡑⠀⠀⠈⢹⡟⠃⠀⠀⠌⣿⠃⠀⠀⠀⢯⣿⡿⠀⠈⠉⣿⡋⠁⠀⠀⠸⣿⡇⠀⠀⠀⢹⣿
⠀⠀⠀⡗⡇⠀⠀⢠⠇⠈⠆⠀⠀⠀⠹⠇⠀⠀⠀⠈⠇⠃⠀⠀⠀⢸⢻⠀⠀⠀⠰⠿⠄⠀⠀⠀⠸⠸⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠟⠀⠀⠀⠀⢸⡏

⠀⠀⢽⡦⠞⠀⠀⠀⣬⡷⠂⠀⢀⡀⡆⠀⠀⠀⠀⠰⣿⡄⠀⠀⣀⣻⡴⠄⠀⠐⠦⣼⡴⠋⠀⢀⣿⣄⡀⠀⠀⢀⢴⣿⡄⠀⠠⢤⣯⠤⠄⠀⠀⠦⣼⡇
⠀⠀⢸⡟⠙⠄⠀⠐⠙⡗⢆⠀⠈⡽⢷⣾⣍⠀⠀⡴⢻⠈⠀⠀⠀⡴⢷⠀⠀⠀⢀⡿⢧⠀⠀⠘⣿⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⣿⠀⠀⠀⠰⠛⢿
⠀⠀⠸⠀⠀⠀⠀⠀⠐⠃⠈⠀⠀⠙⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠈⠓⠀⠘⠉⠀⠀⠳⠀⠀⠛⠀⠀⠀⠀⠈⠐⠃⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⢀⠀⠀⠀⣀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⣀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⣀⢠
⠀⢀⣀⣣⣞⠀⠀⠀⡸⣿⡁⠀⠀⢀⣾⣦⡀⠀⠠⠴⣿⠖⠂⠀⠑⢮⡥⠤⠀⠀⢘⣶⣃⡀⠀⠀⢡⡿⡀⠀⠀⠐⢹⠧⠖⠀⢠⢾⣟⠁⠀⠀⠒⠒⣿⠋
⠀⠀⠀⣠⢻⡇⠀⠀⢠⢾⠁⠀⠀⢠⠟⢳⠀⠀⠀⢠⠛⢦⠀⠀⢀⡼⠳⡄⠀⠀⡟⢧⠀⠀⠀⠀⢹⢦⠀⠀⠀⢀⡟⢻⠀⠀⠈⠈⡏⢳⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠘⠀⠑⠀⠀⠈⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠁⠘⠀⠀⠀⠀⠁⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠛⠃
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡈⢳⣚⠇⠀⡀
⠀⠀⡀⠀⠀⡀⠖⠀⠀⠀⠖⠰⠀⠀⠀⠀⠀⠐⠆⠀⠀⠠⠀⠁⠀⠀⠠⠜⡒⠒⠀⠀⠀⠀⠀⠀⠀⡀⠦⡀⢀⠃
⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠂⠀⠀⠀⠀⠀⠈⣤⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⠀⠀⠛⠀⠂⠀⠀⠀⠀⠈⠀⠉⠀⠀⠁⠈⠀⠀⠀⠀⠈⠀⠁⠀⠀⠉⠈⠀⠀⠀⠁⠉⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⢀⠠⠀⠠⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠁⠈⠁⠈⠃⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠈⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⢄⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠤⡀⠀⠀⠄⠀⠀⠊
⠀⠀⠄⠜⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠱⠰⠀⠀⠁⠊⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⢠
⠀⢀⠐⠂⠀⠀⠐⠁⠀⠀⠒⠈⠀⠀⠀⡀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠄⠀⠀⠀⠖⠐⠀⠀⠂⠲⠀⠀⠀⠀⠀⠀⠰⠓⠶⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠐⠈⠁⠀⣶
⠀⠀⠂⢠⡄⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠠⠄⠐⠀⢀⠀⠈⠀⢚⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠢⠀⣈⠁⠈⠁
⠀⠀⠀⠀⠉⠂⠠⠐⠤⠀⠀⠁⠀⠀⠀⠀⠂⠀⠂⠨⠜⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⢂⠀⡁⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡄⢀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠁⠒⠒⠀⠀⠀⠀⠀⠀⠒⠁⠐⠅⠀⠀⠀⠀⠐⠀⠀⠍
⠀⠀⠀⣠⠤⣄⡀⠀⠀⣀⡤⢤⡀⠀⠀⠀⢀⠀⣀⠀⠀⡀⢀⠀⠀⠀⠀⢠⡀⡀⣀⠀⠀⠀⠀⠀⠀⣠⠠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠶⠶⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢶⠞⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⢰⣣⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡴⠀⠀⠀⠀⠀⠈⠉⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⠁⢰⣶⣄⠀⠰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⠻⠟⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⣀⣠⠄⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠳⣤⣀⣀⣀⣠⣤⣤⠤⠴⠖⠚⠋⠉⣀⠴⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣶⡈⠃⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣤⣤⠤⠴⠖⠋⠁⠀⡠⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠹⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⢻⡀⠙⣦
⠀⠀⠀⠀⠒⠲⠶⠤⠤⠤⢤⣤⣀⣠⠟⠳⢦⣤⣄⣀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣹⠄⢭⣽⣷⣞⣹⣶⡦⢤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠀⠙⠲⢶⠚⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠚⠻⣿⠏⠛⠓⠒⠒⠶⢶⣠⠴⢚⣉⣀⣀⣀
⠀⠀⠀⠶⣎⣉⠉⠀⠤⣄⠀⠀⠈⠑⠠⠤⠀⠀⠀⠐⠤⢄⣀⠀⠀⠀⣠⠤⠤⠤⣴⣉⣁⣀⣠⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠒⠒⠶⠦⠤
⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣍⣈⠁⠀⠀⠤⠄⠀⡉⠁⠒⠠⠀⠀⠉⢘⢧⣄⣀⣠⠤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⣄⣈⠙⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⡄⠡⢀⣀⠜⢀⠎⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠐⠄⠀⠀⠘⢄⠈⠒⠤⠤⠔⠊⣠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢣⠀⢆⡀⣀⠆⢠⠑⢄⠀⢱⠀⠀⠀⠀⢸⠀⠀⠀⠀⡔⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠑⠤⠀⠠⠔⠁⡠⠃⠀⢸⠀⠐⠂⠀⠘⢀⠔⢡⠀⢆⡀⡀⠎⢠⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡎⠀⠀⠀⢸⠀⡆⠀⠀⢨⠀⠣⡀⠑⠤⠀⠠⠔⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠄⢄⠀⡇⠀⠀⠀⠘⠤⠃⠀⠤⠆⠀⠀⠈⡆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠄⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠀⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠀⠠⠤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠛⣷⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⢀⣹⣷⣄⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣿⠟⠁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠛⠛⠛⠋⠁⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣤⡀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠉⠛⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⣿⣿⡿⠟⠉⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉
⠀⠀⠀⣀⣤⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁
⣴⣾⣿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷⣶⣤⡀
⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡿⠇
⠈⠻⣿⣿⠃

⠀⠀⠀⠐⣧⡀⣤⣤⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⢀⣴⣄⢀⣴⠆
⠀⠀⠀⠀⠈⢷⣝⣋⡀⠀⠀⠀⠀⠀⢀⣬⣭⣄⠀⠀⠀⠀⠀⢀⣠⣭⣤⡀⠀⠀⠀⠀⠀⢀⣭⣥⡾⠃
⠀⠀⠀⠀⠀⢸⣿⣿⡿⣦⠀⠀⠀⣴⢿⣿⣿⣿⢷⡄⠀⠀⢰⣟⣿⣿⣿⣻⡦⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠘⠁⣼⣿⣿⣿⡄⠛⠀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠛⢁⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢹⡏⢻⡏⠀⠀⠀⠀⠀⠉⣿⢹⡏⠀⠀⠀⠀⠀⠈⣿⠉⣿⠁⠀⠀⠀⠀⠈⢹⡏⣿⠋
⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠘⠃⠘⠁⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠘⠃⠙


⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⡀⣰⣶⡀⣰⡗
⠀⠀⠀⠐⠶⠶⠶⣶⣶⣶⠶⠶⠶⠂⠀⠀⠀⠀⠻⣦⠠⣾⡆⢠⡿⠁⠀⠀⠀⠀⠀⠈⢷⣬⣭⣼⠏
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣶⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣿⣿⣿⣧⣤⣤⣤⠀⠀⠀⠀⣠⡟⠉⠉⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⠈⠿



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡶⢶⣄⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠿⠀⠀⠈⢳⣟⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⡴⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡻⣇⠀⠀⠀⠀⠀⠀⢰⣟⣿⣧⡴⠾⠛⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⣏⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢷⣿⡀⠀⠀⠀⠀⠀⠀⠉⠁⠹⣦⡀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣰⠿⠧⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡟⢦⡀⠀⠀⠀⠀⠀⠀⣀⣈⠙⠛⠛⢋⣀⡀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⣧⠀⠙⢷⣄⠀⠀⣠⡼⢻⡏⠛⠛⠛⠋⠉⣿⣦⡀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣶⠶⠟⠀⠀⠀⠉⠛⠛⠉⠀⣾⠀⠀⠀⠀⠀⠀⢻⡈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠉⠉⠉⠉⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡾⠿⣶⠄⠀⠠⣦⣴⡿⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣛⡀⠻⢦⣤⠀⢠⣿⣁⡈⠳⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠉⠉⠛⠛⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣛⣫⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⢀⣶⢀⡄⠀⠀⠀⣶⠀⠀⠀⠰⣶⣾⠆⠀⠸⣶⡆⠀⠀⠀⢧⣦⡞⠀⠀⠀⢐⣆⠀⠀⠀⠐⣆⢀⡴⠀⠀⠀⠰⣦⠇
⠀⠀⠀⠈⢹⣿⠋⠀⠀⠐⢿⣿⡿⠂⠀⠀⣿⣿⠀⠀⠀⣿⣿⡦⠀⠀⢸⣿⡅⠀⠀⠔⢻⣿⠳⠄⠀⠀⢸⣿⠁⠀⠀⢰⣿⣿
⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⡟⣿⠀⠀⠀⣿⣿⠀⠀⠀⢸⢻⡇⠀⠀⠀⢸⢹⠀⠀⠀⠀⣼⣿⣆⠀⠀⠀⣿⣻
⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠁⠉⠀⠀⠀⠉⠉⠀⠀⠀⠈⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠉⠈

⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢳⣿⠏⠀⠀⠀⠀⠀⣨⣧⡀⠀⠀⠀⠀⠤⠤⣽⡥⠤⠄⠀⠀⠤⢤⣽⡤⠤⠄⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⢀⣼⣧⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣠⣼⣿⣿⣿⣤⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⣾⣿⣷⠄⠀⠀⠀⠙⣿⣿⠋
⠀⠀⠀⠠⠏⠀⠳⠀⠀⠐⠿⠀⠀⠀⠀⠻⠇⠀⠀⠀⠞⠀⠘⠆⠀⠀⠀⠀⠸⠇⠇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠼⠁⠈⠧


⠀⠀⠀⠰⣄⣤⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⢠⡄⡴⠀⠀⢤⢠⡄⠀⠀⠀⣤⣤⣤⠀⠀⠀⣤⣠⠀⠀⠀⣤⡤
⠀⠀⠀⠀⢸⣷⣦⠀⠀⣠⣾⣿⣦⡀⠀⢠⣾⣿⣦⠀⠀⣠⣾⣿⠁⠀⠀⠈⣷⣷⣄⠀⠀⢹⣿⡁⠀⢀⣴⣾⡁⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢺⢿⠏⠀⠀⠁⢻⢿⠇⠁⠀⠀⢿⢿⠃⠀⠀⠁⣿⢿⠃⠀⠀⠀⣿⡿⠈⠀⠀⢺⢿⠇⠀⠀⢻⢿⠇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠸⠸⠀⠀⠀⠀⠸⠸⠀⠀⠀⠀⠿⠸⠀⠀⠀⠀⠿⠇⠀⠀⠀⠸⠸⠀⠀⠀⠸⠸⠀⠀⠀⠞⠹⠊⠣


⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⣄⢠⡄⡴⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢠⣄⡴
⠀⠀⠈⠉⢹⣿⡏⠉⠀⠀⠀⠀⠳⣝⣷⠋⠀⠀⠀⠀⠈⣷⣾⠀⠀⠀⠀⠱⣾⣿⠖⠁⠀⠀⠀⠀⣀⣿⡀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⢻⢻⠇⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⠀⢸⠿⢿⡀⠀⠀⠀⠀⢻⢻⠃⠀⠀⠀⢀⣘⣿⣿⣟⣀⡀⠀⠀⠀⡿⡿
⠀⠀⠀⠀⠸⠸⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠰⠋⠀⠀⠑⠀⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠰⣯⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⢧⡀⠀⠀⠀⠀⠀⣴⡿⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⢦⡀⠀⠀⠀⠙⠿⠿⢿⣷⠶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⣦⠀⠀⠀⠀⠀⠸⣿⣤⣾⢇⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠄⠀⠀⠀⠀⠈⠉⢡⣿⡋⣠⣶⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠙⠿⠟⣱⣿⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣼⡿⣡⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⠸⣿⣅⠀⣠⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⢾⣿⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠰⣷⣽⣷⠀⢹⣿⢷⢆⣄⠀⠀⠀⠀⠀⠀⠈⢹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⢿⠃⢀⣾⢏⣴⡶⣶⠄⣀⠀⠀⠀⠹⣏⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠸⣿⣤⠀⣼⣿⣴⡶⠄⠀⠈⠳⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠿⠛⣿⡀⠀⠀⠀⠀⠈⠳⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⢻⣿⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⢤⣄⣠⣾⣿⢨⢳⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣍⠤⣙⢿⣿⠼⢸⣿⠟⡥⣲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣬⣃⠽⡖⠞⡡⣈⣴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣀⠀⠀⠀⠀⢶⡉⠕⠶⠒⠒⠉⠛⠴⠂⣺⠩⠭⢟⣛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⣤⣀⠈⠙⠲⠄⣣⡄⠹⣿⣷⠶⡻⠭⢀⣶⢠⡈⡙⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡷⠾⢷⣦⣠⠎⠄⣿⣦⠬⢥⣬⢴⡦⣾⡇⠈⣷⡁⠈⡧⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣮⡑⣌⣿⠜⡼⣋⣴⢒⣠⡴⡋⣸⣿⡅⢠⣟⡛⠢⡗⣦⣄⣩⣛⠒⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⡉⠉⠩⣭⡙⡦⠝⣘⠙⣡⡾⠿⠿⢿⣣⣌⠙⠻⠿⢿⣯⣗⠨⠀⠉⠛⠿⣿⣷⣦⣭⣻⠷⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⣀⡤⣤⣤⠤⠄⠻⣷⡶⠖⠒⢂⣈⢀⠰⢿⣿⣯⠭⣷⣮⣿⠶⠄⣄⠀⠈⠙⠻⣖⠤⣀⠀⠀⠉⠛⠿⣿⣡⣾⣷⣎⢇⡀
⠀⠀⠀⠒⠒⠒⠒⠂⢠⠞⣡⣤⣈⠁⠀⠀⣠⡋⠔⢋⣵⢟⡔⢸⣇⠶⣝⢿⣿⠿⢃⣀⣴⣮⣕⡝⠢⣄⠀⠀⠉⠲⢝⡲⢄⡀⢈⡙⠿⡿⢽⣿⣸⠥⠤⠄
⠀⠐⠚⠛⠛⠛⠂⠀⢼⢸⡟⣽⣿⡆⣿⣿⣥⣶⣾⣿⣿⢸⢀⣿⣿⣦⡘⠮⣷⣿⡿⠿⢿⣿⣿⣿⣦⣄⠑⠢⠀⣉⣁⣉⢲⣭⣗⠏⣡⣶⣶⣮⢻⠒⠒⠒⠂
⠀⠈⠉⠉⠉⠉⢁⣀⣘⣦⣧⣙⣋⣐⣻⣯⣽⣿⣿⣿⣿⡁⣾⣿⣉⡛⠛⠒⠼⠟⠛⣛⣛⣛⣻⣿⣽⣿⣟⢠⣾⡿⣿⣿⢢⣿⣾⡀⣿⡿⢻⠟⣸⠛⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠉⠩⠭⣭⣭⣭⡭⠥⠤⠀⠀⠀⠀⠀⠤⢽⡯⣤⣤⣤⣤⣤⣤⣀⣉⣭⣭⣭⣭⣭⣭⣽⣷⣬⣿⣥⣿⣟⣛⣻⣿⣷⣶⣶⣛⣛⣉⣉⣉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣭⣭⣉⣉⣉⣉⣉⣉⣉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠉⢻⣶⠞⠃
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⣸⠏⠙⠷⠶⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣷⠶⠶⣾⡍
⠀⣀⣀⣸⠟⠉⠻⣦⣄⣀⣠⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⣿⡇
⠀⠈⠉⠁⠀⢠⡾⣿⠇⠀⠈⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⣶⣦⣄⠀⣠⣴⣦⠀⠀⠀⠀⠀⣠⡾⠋⣿⡇⠀⢠⡿⢁⡀
⠀⠀⠀⠀⣴⠏⢰⡿⠀⠀⠀⢹⣷⠈⠻⣦⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⣠⡴⠟⠁⠀⢠⡿⢀⣴⠟⠁⣿⡇
⠀⠀⠀⣼⠃⠀⠞⣃⡴⠋⢀⣈⡛⠆⠀⠘⢿⣆⠀⠀⠀⠀⠙⣿⣿⣿⣯⡤⠶⠛⠉⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⢸⣷
⠀⠀⢸⣿⣀⣤⠞⠋⠀⠀⠀⠉⠛⠶⣦⣄⣘⡿⠀⠀⠀⠀⠀⠈⠛⠁⠀⣀⣀⣠⣤⠴⠖⠛⠉⣴⡆⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠉⠁⣴⡆⠀⠀⠀⠀⠀⠀⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣤⣤⢤⣶⠾⠋
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠸⠿⠶⠶⢶⣦⠦⠤⠶⠶⣶⡶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠘⠿⣦⡀⠀⠀⠀⠘⠛⠛⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠚⠛⠀⠀⣀⣠⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠉⠉⠐⠒⠢⠄
⠀⠀⠀⠀⠀⠀⣀⢀⡀⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠐⠀⠀⠠⢀⠀⠀⡀⠈⠀⡠⠤⠤⠒⠒⠢⢄⠀⠈⠤⡀
⠀⠀⠀⡠⠂⢁⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠈
⠀⠀⠈⢀⠔⠈⠉⢢⠀⠀⠀⠀⠀⠀⠀⢣⠀⡐⢁⠀⣀⣀⣠⣀⣀⡀⢆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠰
⠀⠠⠔⠁⠀⠀⠀⠀⠣⠠⠤⢀⡀⠀⠀⢸⢐⠀⡈⠉⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡠
⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠄⠀⠈⠑⢤⡜⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢰⢓⠅
⠀⠀⠈⢄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠠⠀⠘⡀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢪⠦⣀⠀⠀⠄⢐⠈⠀⣀⠔⠁
⠘⠣⢄⣀⡑⠄⣈⡐⠒⠒⣁⡠⠔⠁⡠⠶⠆⠢⠠⠼⠤⡀⠀⠁⠘⢢⣤⣀⣀⣀⡠⠊⠀⠈⠙⢒⠶⠒⠶⣋⠁
⠀⠀⠀⠠⢠⠜⠁⠉⠉⠘⠉⢦⡈⡉⠀⢀⡦⠤⠤⡄⠀⠋⠉⠉⠋⠟⠐⢤⠤⠄⠒⡣⠤⠎⠀⠁⠐⠄⠀⠈⢆⡑⠒⠢⢤
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⡒⠁⠀⠘⠃⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⢀⡠⠬⢁⡀⠂⠠⣤⠤⠤⠄⠤⠆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢇⡀⠀⠀⠄⠠⠤⠤⠤⢼⣀⡀
⠀⢀⣳⡀⠀⠀⠉⠈⠈⢂⡔⠐⠒⠂⠀⠀⠀⠚⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⢀⡢⠀⠀⠀⢰⣀⣀⣀⣀⣦⠤⠔⠊⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡖⠒⠊⠉⠈⠳⣄⡴⠀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡀⠀⠀⠀⠀⠈⠁⠀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠈⢉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠛⠫⡉⢢⡉⠢⡈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣮⡄⢄⠀⡄⠲⡈⠣⠑⢲⠤⡄⠀⣼⠖⠀⠀⠀⡠⢺⠋⢍⠒⠀⠀⠁⠀⠁⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣸⢸⡀⠣⠘⠀⠁⠀⠄⠈⣏⣥⠾⠃⠀⠀⠀⠀⡔⡏⢀⡀⠀⠀⠀⠀⡀⠀⠀⢸⡱
⠀⠀⠀⠀⠀⠀⠀⢠⠿⡀⠀⠂⠀⠀⠀⢀⡄⠀⡏⢀⣀⠀⠀⠀⠀⠀⠈⢇⠀⠁⡀⠀⠀⢀⡁⠀⠀⡬
⠀⠀⠀⠀⠘⣷⣀⣈⡽⠳⡀⠀⠒⠒⠒⠉⢀⡴⠡⡋⠈⠃⢀⠐⠠⡆⠀⠈⠢⡀⠙⠂⠐⠊⠀⢀⠔⠁⢠⡤⢤
⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠈⢓⢶⡴⠦⣚⣉⣠⠔⠉⠁⠀⠈⠓⠚⠳⢄⣠⢤⡌⠓⡴⢤⣤⠖⠥⣤⠴⠚⢦⡼
⠀⠀⠀⠀⠸⣉⡹⠒⠒⠾⡉⠉⠀⠀⠀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢤⠀⠀⠀⠀⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣀⣀⣀⠠⢧
⠀⠀⠀⠀⠀⠀⠀⢜⡁⠀⠀⠀⠀⠀⠀⢀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣠⡀⠀⢀⡱⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⠒⠒⠒⠲⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⠒⠃⠑⠘⡀⣠⣻⡄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠦⠠⠃
⠀⠀⠀⠀⠀⠀⠰⢏⣈⡹⠃⠀⠰⣛⣃⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠁





⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠛⠛⠛⠛⠛⠳⠶⣤⣄⡀
⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠻⣆
⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠋⠀⠀⠀⢹⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⣀⣤⡇
⣿⠀⠀⠀⣀⣀⣤⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⢹⡇
⣿⠗⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠋⠁⠀⠀⠀⣸⠃
⢹⡄⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⢻⣄⣤⡴⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠶⠶⠶⠖⠛⣿⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠸⣧
⠀⠀⠀⠀⠀⠀⣼⠛⠛⠶⣤⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠘⣧⠀⢹⡆
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠲⣌⠻⣆⢀⡴⠞⠋⢉⡽⠛⠉⠛⣶⣄⠀⠸⣆⠀⢿⡀
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣈⠧⠹⠋⠀⠀⢠⡟⠁⠀⠀⣰⠏⠈⠳⣄⢻⡄⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠙⠃⠀⠀⠀⢠⡟⠀⠀⠀⣰⠏⠀⠀⠀⢹⣎⣿⡀⢘⣷⣶⡞⠛⠛⣿⠛⠶⣦⣀⠀⢀⣴⠟⣉⡁⠀⢿⡀
⠀⠀⠀⠀⡾⠁⠀⠐⠒⠛⠃⠀⠀⠀⠀⣼⠁⠀⠀⢠⡏⠀⠀⠀⠀⠐⠛⣽⣷⠟⠁⣿⠀⠀⠀⣿⠀⠀⠀⠙⢷⡟⣱⠞⠁⠀⠀⣼⠃
⠀⠀⠀⣸⠇⣴⣟⣋⡍⠀⣠⣦⠀⠀⢀⡏⠀⠀⠀⣼⡶⠞⠛⠛⠶⢦⣶⣾⠃⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣵⠖⠀⠀⢰⡏
⠀⠀⠀⠿⠤⢤⡭⠴⠶⠛⠉⢻⣄⠀⢸⡇⠀⠀⢀⡿⣇⠀⠀⠙⠛⠶⠌⠛⠀⠀⠀⣿⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠠⣤⣄⡀⠈⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⣧⠀⠀⢸⡇⠙⢦⡀⠀⠀⠒⠒⠂⠀⠀⠀⢻⡄⠀⠀⠘⣧⠀⠀⠀⠀⢀⡀⠂⠤⣤⣄⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⣼⡷⠶⠞⣿⠀⠀⣠⡶⠂⠀⠀⠀⠘⣷⠀⠀⠀⢹⣆⠀⠀⠀⣸⠻⣦⣘⠲⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢈⣡⠖⠀⣰⣆⡀⠀⠘⣧⡀⠀⠀⢻⣄⢀⡼⠃⠀⠀⠉⠙⠛⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣏⡵⢋⡼⠋⠛⠛⠶⣤⣬⣷⣤⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣭⠶⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⣈⣀⣀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠂⠠⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⢀⡠⠉⠀⠄⠀⠁⡀⣸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠠⠄⠨⠀⠀⠀⠘⡶⠶⠤⠞⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠈⡑⠒⠐⠂⠁⠉⠒⠆
⠀⠀⠀⠀⢐⠰⠖⠂⠀⠀⠀⢤⠆⠂⠂⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠲⣄⡀⢂⠀⠀⠴⠊⠐⠀⡀⠀⠂⠀⠀⠀⠂⡁⠐⠇⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⢄⠀⢶⡀⠀⠀⠀⢈⡽⢣⠀⠀⠂⠠⠀⠈⠃⢄⠀⠀⠔⠊⠀⠀⠀⠂⠀⠀⠐⠁⠀⣀⠄⠀⠀⠀⠒
⠀⠀⠀⠀⠘⡎⠀⠁⠀⠀⠦⠞⢁⠇⠰⡀⠠⠀⠀⠠⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠰⠁⡀⠀⠐⠀⠀⠀⠓
⠀⠀⠀⢀⡠⠁⠀⠦⡘⢦⡐⡐⠂⢤⡀⡸⢁⢠⠀⠀⠀⠠⠀⠀⠀⠤⠀⠀⠀⠄⠀⠀⠠⠄⠀⠀⠰⠀⠀⠀⠰
⠀⢀⠀⠠⠂⢰⢦⣄⠹⡬⣯⣄⣠⡿⢱⢡⣿⢡⢒⣤⠀⠀⠀⢠⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠠⠄⠀⠀⠠⠀⠀⠀⢠
⠀⠠⠀⠀⠀⠀⠀⠘⣏⣐⠪⢭⣿⢿⢷⣾⣧⣇⣾⠇⠠⢀⠀⡀⠀⣀⠠⢤⠤⡄⠀⠀⠀⠄⠀⠀⢤⡀⠀⠀⠠⠀⠁
⠀⠀⡤⠀⠀⢀⠴⠚⠩⣛⠻⣿⣿⣯⣾⡟⡿⣿⡿⠷⣶⡖⣀⡉⠤⢀⠄⣨⠖⠂⠀⡀⠀⢀⠐⠁⠀⠈⠂⢀⠀⠀⠠
⡀⠊⠀⠀⠀⠁⠀⢠⠿⣶⣼⣟⣺⣽⣿⣻⣿⣿⣬⣍⡒⣭⣤⣄⡀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠃⠰⠀⠀⠀⠁⠀⠀⢂⢠⡿⢹⢻⣿⢷⣧⣿⣓⠨⠍⣻⠉⠀⠐⠁⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⠃⣾⢃⢇⣾⠏⠙⣻⠂⠈⡇⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠚⠋⠀⠁⠀⠢⠀⠁⠀⢀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡠
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣹⣦⡀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣶⣿⣿⣿⡿⡄
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⠿⣿⠾⢶⡿⢿⢿⡿⢿⡿⠷
⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⢻⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⠟⠛
⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢹⣿⣀⣀⣀⣀⣀⣈⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⡇⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⣿⡟⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


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

⠀⠀⠀⠀⠀⣠⡄⣶⢦⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣦⣀⢄⡄
⠀⠀⠀⠀⢈⡟⠓⠙⠛⢷⣷⠁⠀⡰⠋⡹⠟⠟⠛⠳⢽⠯⡁⢱⠀⢀⡤⠞⣫⢶⣤⡘⠙⣶⢶⣶⢿⢿⣿⢿⣧⣤⣀
⠀⠀⠀⢀⡎⠀⠀⠈⠁⠀⢸⡀⠀⡇⣼⠁⡆⠀⠀⠀⡀⣇⢇⠇⠘⡏⢠⠐⠡⠀⠉⢻⢺⣿⡗⢁⠀⠀⠋⡀⢿⣿⣿
⠀⠀⠀⠙⢇⠘⢄⣀⡤⠂⡼⠋⢠⡷⠉⢆⠈⠒⠒⠊⣠⢿⠘⡄⠀⢣⡘⢤⠤⠂⢀⡼⠂⠛⣇⠘⠤⣀⠴⠁⡎⠹⡍
⠀⠀⠀⠀⢀⣱⠦⠤⢴⠊⠀⠉⠉⠀⠀⣀⣵⠒⠒⢎⠁⠀⠣⠝⢀⣠⡼⠒⢲⣒⡋⠀⢰⠷⠈⣲⠤⠤⢔⠊
⠀⠀⣀⢴⠉⡜⢦⡔⢺⢱⡄⠀⠰⣶⠊⢡⠟⢼⡀⢿⠣⡠⡦⠐⣇⡴⠁⠀⢸⣀⡟⠊⣁⣀⠼⡧⢖⠦⡜⢄⡀
⠘⠛⠀⢘⡟⠀⠀⠀⠈⡏⠈⢢⡄⠀⢠⠋⠠⠀⠀⠸⡀⠹⠖⠠⡎⠀⠀⠀⠸⠀⠁⠀⠟⣠⠊⠀⠀⠀⢰⡀⠸⠓
⠀⠀⠀⠀⣱⠲⠄⠤⢤⠃⠀⠈⠀⠀⠀⡽⠒⡶⡄⢴⠓⠀⠀⠀⡜⠉⠀⠀⢸⠁⠀⠀⠀⠙⠿⢖⠶⣲⡿⠵
⠀⠀⠀⣠⠃⠀⠔⡄⠘⡄⠀⠀⠀⠀⢠⠃⡸⠀⢧⠘⡄⠀⠀⠘⢦⠴⠓⠤⡜⠂⠀⠀⠀⠀⡤⣇⠀⠀⣣⢄
⠀⣀⠼⠤⣀⡞⠀⣟⣀⣸⡀⠀⠠⣊⣉⡻⠁⠀⠸⡟⠓⣄⣠⣒⣳⠀⠀⠀⣱⠒⣢⠀⢤⣚⣙⠇⠀⠀⠙⣉⣲⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡟⣩⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣼⠏⡠⢼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠁⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⢃⡈⣁⠐⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣻⠟⠉⡹⠛⢻⣯⣊⡔⣡⡼⠃⠀⠀⠀⢀⡠⠖⠋⠉⠉⠉⠙⢀⡀⠀⠀⢀⡸⠃⠀⠀⠀⢀⡤⡖⠛⠩⠙⠋⠽⢰⡀⡄⢨⣁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⡴⠃⣠⠞⠀⢀⠜⡏⠉⠉⠉⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠀⠀⠀⠀⣰⠛⠂⠆⣉⠰⠀⡁⠐⢨⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢰⡟⠀⡼⠁⡴⠃⠀⡴⠋⣠⡇⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣰⠧⣈⠐⠀⠄⢐⠀⠄⡃⢴⠇
⠀⠀⠀⠀⠀⠀⣿⠀⡼⠁⡼⠁⢀⠞⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⡟⡂⠤⢈⡁⠆⢨⠐⠂⣤⠎
⠀⠀⡔⣋⡽⣻⢛⣶⣃⣸⠁⢠⣏⣠⠟⠁⠀⠀⠀⢀⡔⠋⠉⠉⠙⢂⣀⡀⠀⠀⣀⣠⠞⠁⠀⠀⠀⢀⣴⠋⠛⢩⠙⣅⣂⣠⠀⣁⣰⣬⠟⠁
⠀⠈⠯⣥⠞⠁⡼⢸⡏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠦⣤⠀⠀⠀⠀⡏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠧⣤⠁⠰⠀⢆⡏⠉⠉⠉⠁
⠀⠀⠀⠘⠤⡼⢁⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡄⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢭⡄⡃⡻
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⢶⡀⠆⠠⢀
⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠘⠳⢦⠀⠀⠀⠀⠀⠀⢸⠇⠀⡀⠂⢼⡇⠀⠀⠀⠀⠀⡀⠀⠀⢀⡩⠄⠚⠻⠇⠀⠄⣀⠀⠀⠈⠂⠁⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠤⠀⢏⠀⠀⠀⠀⣹⣟⡀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣾⢡⣶⠋⠀⠀⠀⣀⣀⠐⢾⡏⠁⠀⠀⠀⠀⣸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠰⠋⠀⠀⠃⠀⠀⠀⠀⠐⠰⣤⠖⠀⠀⠀⠀⠀⠀⡄⢸⠹⣯⠀⠀⠮⠴⠊⠀⠀⠀⠀⠀⠀⢀⡜⠦⡈⠺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣤⠶⣉⠀⡩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡙⠦⡈⠲⢌⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡤⠠⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢦⡈⢳⣤⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢁⠀⠀⠠⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠠⣿⣦⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⣠⠄⣿⠃⢸⡟⠀⣿⠀⡄⡄⠀⠁⡀
⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⢭⣿⠀⣿⡀⢸⣷⠀⣿⣀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠃⠻⠇⠈⠿⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⡴⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⣠⠁⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⢀⡀⣀⡠⠀⡀⠀⠀⠀⠀⠀⢀⡤⠚⠿⢿⣷⣶⣶⣐
⠀⠀⠀⠀⠀⠀⠀⡴⠊⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣌⠀⡴⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢀⡛⣿⣿⠉
⠀⠀⠀⠀⠀⠀⣨⣤⣴⠏⠀⠀⠀⠀⠀⠀⠁⠐⠈⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠿⢇⡀⠀⠀⠀⠀⢀⡀⠀⢀⡴⠋⠄⠸⠟
⠀⠀⠀⠀⠀⠰⢋⣀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⣈⡁⢩⡌⢈⠛⡄⠀⠀⠀⠀⠁⠀⠉⣤⡄⠸
⠀⠀⠀⠀⠀⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠐⡍⢁⣌⠀⢙⡁⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠌⡅⢨⡦⠁⠒

⣿⡟⣛⡿⠿⠿⠿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡆⠐⠠⠀⠀⣀⠀⠄⢀⡀
⠀⠀⠈⠰⠐⠀⠀⠀⠀⠀⢈⣀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠀⠀⠰⠁⠀⠈⠀⠁⡀⠃
⠀⠀⠀⠁⠀⠀⠀⠠⠜⢀⠀⠀⡀⢀⠀⠠⠀⠀⠀⠀⢀⠴⠒⠍⠚⠁⠀⠀⠀⢤⠐⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠉
⢀⡄⠀⠀⠀⠀⢀⡄⠀⣄⡀⢀⠘⠀⠀⠀⠐⠁⠀⠀⢀⡀⠀⡀⠶⠀⠀⢠⠀⢀⠀⠘⠃⠀⠴⠀⠀⠀⠱
⠈⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠤⠂⠀⠀⠒⠠⡀⠰⠀⠀⠀⠈⠐⡀⠀⠀⠀⢀⠂⠐⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⡁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠒⢀⡈⠒⠀⠀⠚⠀⠁⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠈⢀⣀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠠⢉⠀⠀⢰⠋⠉⠓⠀⠀⠰⠤⢀⠀⠀⠀⠀⠀⡤⠠⠀⠀⠀⠀⠀⢦⠷⠸⠓⠃⠀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢡⡔⠃⠀⠀⠀⠊⢀⠀⠀⠀⠠⠾⡰⢄⠗⠀⠀⠄⠀⠸⡰⠀⠢⠀⠐⠂
⠀⠀⠀⠚⢀⠀⠁⠀⠐⠂⠇⠉⠀⠀⠀⠋⠛⢂⣉
⠀⠀⠀⠀⠈⠄⠀⠀⠀⢐⢐⡁⠀⠀⠀⠚⠘⠈⠒⠀⠁⠀⠀⠐⠀⠁⠃⠀⠀⠀⠀⠈⠑⠂⠁⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠉⠻⣷⣤⠶⠂
⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠈⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠻⣷⣀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⣀⣀⣴⠟⠁
⠀⠀⠀⠀⣾⡿⣿⣄⠀⠀⠀⠀⢀⡼⠃⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠉⢹⣿
⠀⠲⠶⠼⠋⠀⠀⣹⣿⡖⠒⢺⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣠⡾⢻⣿⠀⠀⠀⣿⣏⠻⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣄⣴⣿⣿⡆⠀⠀⠀⠀⣠⡶⠋⠁⣾⡏⠀⢠⣾⢃⣴
⠀⠀⠀⠀⣴⠟⠀⣿⠇⠀⣀⠀⠸⣿⡀⠈⢻⣦⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⢀⣠⡴⠟⠉⠀⠀⠠⠟⣁⣴⠟⠁⠘⣿⡆
⠀⠀⠀⣼⡏⠀⠸⢋⣴⠞⠁⢠⣤⣙⠃⠀⠀⠹⣿⡄⠀⠀⠀⠀⠘⢿⣿⣿⡿⠶⠞⠋⠁⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⢿⣇
⠀⠀⠰⣿⣀⣠⠶⠋⠁⠀⠀⠀⠈⠙⠻⠶⣤⣄⣽⠇⠀⠀⠀⠀⠀⠀⠙⢁⣀⣀⣀⣤⣤⠴⠶⠛⠉⠁⣶⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠈⠁⢠⣶⠀⠀⠀⠀⠀⠀⠀⢹⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣤⣤⣤⣴⠿⠃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣬⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⢹⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠛⢷⣤⡀⠀⠀⠀⠈⠙⠛⠛⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠛⠋⠁⠀⢀⣠⠼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣾⣿⣧⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠠⣿⣿⣿⡆⠀⠀⢀⣤⣌⠛⢦⣬⣿⣿⣥⡤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⢀⣠⠦
⠀⠀⠲⣄⣙⣿⣿⠏⠀⠀⠺⣿⡿⠃⠀⢨⣿⣿⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠑⠲⢦⣭⣿⣿⡶⠋
⠀⠀⠀⠀⠉⢻⣿⣿⠆⢀⣾⣿⣿⣄⠀⣸⣿⣿⡇⠀⠀⠀⠀⣹⣿⣯⣤⠦⠀⠀⠀⢨⣿⣿⣄
⠀⠀⠀⠀⠀⣿⣿⣿⠀⣾⣿⣿⡏⠻⠆⣹⡿⣿⡇⠀⠀⠀⣰⡿⣿⣷⡀⠀⠀⠀⢀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢰⣿⠉⣿⠰⣿⠉⣿⡇⠀⠀⣿⣇⣾⡇⠀⠀⠀⠩⣾⠿⠿⢿⡆⠀⠀⠀⠈⡿⢸⡇
⠀⠀⠀⠐⣿⣿⢀⣿⠀⠀⠀⣽⡁⠀⠀⠿⠇⣿⡷⠀⠀⠀⠀⠙⠀⠀⠘⠁⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⣼⡇⠀⣿⠀⠀⠀⢸⠁⠀⠀⢠⡄⢸⡦⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⡉⠘⡇
⠀⠀⠀⠀⠈⣿⣠⣿⠀⣯⣤⣿⡇⢀⠀⢿⡇⣹⡇⠀⠀⠀⢠⡡⡶⣶⠞⠁⠀⠀⠀⣀⣷⣸⣄⡀
⠀⠀⠀⠀⢀⢹⣿⣷⠄⠘⠿⣿⡷⠛⠀⢨⣻⣿⠇⠀⠀⠀⠀⢛⣿⡆⠠⠄⠀⠀⠀⠘⣿⣿⠋
⠀⠀⠀⠀⣡⣾⣿⡆⠀⠀⠰⠿⡷⠀⣀⣈⣿⣿⣀⣀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠈⢭⣿⣿⠓⠢⢀
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠐⠊⠀⠰⢾⠿⡂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⡖⠀⣴⣶⠀⠲⡄⠀⠀⠀⠀⢰⣿⡷
⠀⣈⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠀⠀⠀⠀⠀⣀⡻⠟⠁⠀⠀⠀⢀⣸⣿⣇⡀⠀⠀⠘⠧⣤⣽⣏⣤⠴⠃⠀⠀⠀⣰⣶⠉
⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠾⣿⣿⢦⠀⠀⢶⣻⣿⡇⠀⠀⠀⠀⢰⠏⣿⣿⣿⠹⡆⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⡿⣿⣿⣿⢸⠀⠀⠿⠃⠀⢸⢀⣿⣿⠈⡇⠀⠈⢻⣿⡿⣦⠀⠀⠀⢸⡀⣿⣿⣿⢀⡇⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣦
⠉⣿⣿⣿⠈⠀⣾⣿⣷⠀⠈⣼⣿⣿⣇⠁⠀⠀⠈⢻⣿⡟⠀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⢹⡇⠀⠀⠀⠀⠀⠀⢻⡇
⠀⣿⣿⣿⠀⠀⢹⣿⡇⠀⠀⠛⣿⣿⠛⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⢸⡏⢸⣷⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣾⡇⠘⣿⠀⠀⠀⠀⠀⠀⠿⠃⢀⣀⡀
⠀⠉⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⢀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣰⣷⣀⡀⠀⠀⠀⣠⣤⣤
⠀⠀⣀⠀⣠⡟⠋⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⣿⡟⠛⠿⠿⣷⣶⣿⣿⣿⣷⣤⡀
⠀⠀⢿⢰⣿⡟⠒⠖⣶⣶⢘⣏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⢻⣧⠀⣿⠇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢸⠸⣿⣧⣬⣭⡉⢹⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣜⠿⠃⠀⠀⠀⠀⠀⠀⠀⣹⣷⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⣸⠖⠚⢿⢉⣿⠃⢸⡇⠀⠀⠀⠀⠀⠀⢠⣾⢷⣤⣤⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⢻⡷
⠀⠀⠿⠉⠉⠻⠺⠏⠀⠘⠇⠀⠀⠀⠰⠶⠶⠿⠷⠶⠿⠿⠻⠯⠤⠿⠀⠀⠀⠀⠀⢀⣤⠴⠿⡿⠷⣄⠀⠀⠀⠀⣼⣿⡿⠛⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠰⣿⡿⠀⠘⡇⠀⠀⢠⣿⣿⠇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇
⠀⠀⢀⣤⡀⠀⣠⣄⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉
⠀⠀⠹⡿⢋⣻⠿⡿⢉⣳⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⣤⣤⡀
⠀⣴⣿⣿⣏⣿⣿⣿⡏⠁⠀⡇⠀⠀⠀⠀⠀⠐⠛⠋⠉⣻⣿⣶⣄⠀⠀⠀⢀⣀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⢰⡇⣿⣿⣿⡇⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠈⠳⣦⣴⠋⣿⣿⠧⡤⠞⠀⠀⠀⠀⣼⣤⣤⣤⣤⣤⣾⣿⣧⢤⣤⣤⣤⣼⡇
⠘⠇⣿⣿⡿⠃⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡟⠀⠀⠀⠈⠁⢠⣿⣏⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⠞⣿⣿⡿⠾⠃⠀⠀⠘⠃
⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⢀⣴⡿⠋⢰⣿⠁⠀⠀⠀⠀⠀⠛⣿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣧⣤⡄
⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠛⠋⠀⢀⣿⠃⠀⠀⠀⠀⠀⢀⣾⠏⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠉⠉⢉⣿⠃
⣤⣄⣿⣽⣧⣬⣭⣍⣡⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣼⣯⣤⣤⣤⣤⣤⣤⣽⣥⣤⣤⣼⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣦⣤⣼⣯⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣶⣤⣤⣀⠀⠘⢿⣶⣄
⠀⠀⠀⠀⠀⢀⣤⣶⡾⠿⠛⠛⢛⣛⡛⢻⣿⣶⣶⣤⣍⣉⠛⠿⣷⣦⣌⠻⣷⡄⢰⣿⠂
⠀⠀⠀⣠⣾⠟⢋⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⢀⣀⣠⡄
⠀⠀⣴⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠘⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⢀⣼⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⣧⡀
⢀⣾⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣦⠹⣿
⣸⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⣿⠟⢛⣭⣥⣴⣶⡿⠟⣿⣷⣿⡿⠟⠋⠀⠈⢻⣿⣿⣿⣿⡇⢻
⣿⡇⣾⣿⣿⣿⣿⣿⠏⣿⡿⠁⠀⠈⠉⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢸
⣿⡇⣿⣿⣿⣿⣿⠃⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢸
⢿⣇⣿⣿⡿⠻⠏⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼
⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⢀⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿
⠈⢿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠟
⠀⠀⠉⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⣠⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠘⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠛⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣾⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⢻⣧
⠀⠀⠀⠀⠀⠀⣰⡿⠁⢀⣾⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠻⣷⡀⠈⢿⣧
⠀⠀⠀⠀⠀⢰⣿⠁⠀⣼⡟⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣧⠀⠈⣿⣆
⠀⠀⠀⠀⠀⣿⡇⠀⣸⡿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⣧⠀⠸⣿⡀
⠀⠀⠀⠀⣸⡿⠀⢠⣿⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠘⣿⡆⠀⢻⣇
⠀⠀⠀⢀⣿⠃⠀⣼⡟⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢹⣷⠀⠘⣿⡆
⠀⠀⠀⣸⡿⠀⢠⣿⠃⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⣿⡄⠀⢻⣧
⠀⠀⠀⣿⡇⠀⣸⡟⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⢹⣧⠀⢸⣿
⠀⠀⠀⢿⣧⣠⣿⠇⠀⠀⠰⣿⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠘⣿⣤⣼⣿
⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⢹⣿⠉⠉⠉⠉⢻⣿⠋⠛⣿⡟⠉⠉⠉⠉⣿⡏⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣼⣿⠀⠀⢹⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣀⡀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢀⣀⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠿⠿⠿⢷⣶⣿⠃⠀⠀⢈⣿⣶⡿⠿⠿⠿⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⣤⣤⣤⣴⣶⣾⠿⠛⠁⠀⠀⠀⠛⠿⣶⣶⣤⣤⣤⣤⣽⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢯⢣⠈⢻⣄⠀⣀⡠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⡀⠀⠡⡑⣄⠹⡏⠀⠀⠀⠀⠀⠀⡴⣚⣛⠻⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠁⠀⠈⠁⠀⠀⠈⠪⡴⠁⠀⠀⠀⠀⠀⠈⠘⢐⠐⠁⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣧⡀⠋⠀⠀⡄⠀⠀⠘⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠥⢐⢫⠷⠶⠮⡙⢆
⠀⠀⠀⠀⠀⠀⣀⣀⠸⣧⠈⢔⠄⠀⡀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠠⡀⡀⡼⠄
⠀⠀⠀⠀⠰⠍⠀⠀⠀⠈⢷⡀⠢⠂⣋⠔⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⣄⣀⡀⠀⠒⣬⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⢀⠟⠓⠉⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠘⠛⠖⠀⠄⠠⠄⢀⢀⣀⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠐⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⢀⠡⡐⣂⠀⠶⢦⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢁⠀⠀⠀⠀⠀⡀⠄⠂
⠀⠀⠀⠀⠰⠚⠂⠃⠀⠀⠀⡀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠂⠀⠀⠠⠖⠥⣀
⠀⠀⠀⠀⠀⣀⠀⠼⠖⠒⠈⢁⠀⠀⢸⡆⠀⠀⠀⠑⢄⠀⠀⠀⡠⠊⠀⠀⠀⠠⠁⠀⠀⠀⠉⠒⢤
⠀⠀⠀⠀⠀⠁⠀⢀⣠⠠⠤⠐⣆⠀⠩⣦⠀⠀⠀⠀⠀⠁⠲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠈⠧⠀⠠⠔⠁⠒⠁⢀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠄⠐⠀⠈⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠄⠄⠂⠈⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠⣅⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣀⡠⢁⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡔⢋⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⣀⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠐⠀⢢⠊⠑⡄⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠈⠃⣄
⠀⠀⠀⠀⡄⠒⠁⠀⠀⠀⠀⠀⠧⢤⢤⡙⠢⢄⠀⠀⠀⡠⠊⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡰⠃⢀⠏⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠇
⠀⠀⡸⠉⢹⡀⠒⠂⠀⠀⠂⠐⠂⠇⠀⠈⠁⡀⠀⠀⠙⠤⡤⠄⠀⠄⠒⠂⠊⠉⡦⡀⠀⠀⡆
⠀⢘⠂⠀⠘⠄⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⢀⠋⠑⢄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠈⣦⡜⢄
⠀⠈⠀⠽⠛⡀⠀⠀⠠⠀⠀⠀⠀⠒⢒⠶⠂⠀⠀⠈⡂⠐⢄⠀⠤⠄⠀⠀⠀⠀⠑⣉⠘⡄⠀⠱⡀
⠀⠀⠀⠀⠀⠈⢒⣤⣀⣀⣀⣤⡄⠚⠡⢠⠶⠀⡠⡘⠀⠀⢀⠡⣶⣤⢤⡤⢠⡶⢥⡒⢄⠘⠦⠴⠁
⠀⠀⠀⠀⠀⢠⠃⠀⡿⠀⡠⠒⢌⠫⡁⠐⢶⠋⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠸⡀⠀⢱⢸⠦⢠⡄
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⡆⠀⠀⠄⠈⢂⠀⢂⠀⠀⠀⠀⠠⣰⡇⠀⠀⠀⠀⠙⠎⠉⡈⢆⣤⠁
⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⠢⢀⣀⠠⠞⠀⠀⠂⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠠⠃⢀⠁⠀⠈
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⣀⠐⠁⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⣄⣀⠄⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠈⢁⡖⠒⠒⡔⢲⠛⡫⢴⡁⠂⠀⠀⠀⠀⠀⠀⠐⡴⠒⢄⢀⠝⠣⠤⡀
⠀⠀⠀⠀⠀⢀⣤⠪⣀⠀⣰⣁⠎⡰⠄⠀⠈⢆⠀⠔⠀⣀⣀⣀⢎⠀⠀⡘⢣⡔⠁⠀⠈⢱
⠀⠀⠀⢠⠊⠩⣀⡩⠂⠈⠁⠈⠧⠤⠊⠀⠀⡸⠀⠀⠐⠁⠀⠀⠁⠁⢸⠁⠈⠁⠐⠀⠀⡸⠀⢄⡀
⠀⠀⠀⠸⡀⠀⠀⠀⠀⡰⠀⠀⠈⠦⠄⠤⠐⠁⠀⠀⠰⢄⠀⠀⠀⠀⡌⠀⠀⠢⢀⡠⠞⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠈⠈⠁⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠂⠀⠠
⠀⠀⠀⠰⠀⠀⠀⠃⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠀⠇⡂⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠀⢤⡈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠂⠄⠐
⠀⠀⠀⠀⠀⠰⠘⠈⠁⢀⡵⠀⠀⠀⠀⠀⠀⢀⣤⠀⠃⠀⢀⠄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠀⢘⡠⠀⠀⠀⠀⠾⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢃⠐⠉⢠⡀⠀⠁⠀⠀⠀⣤⠀⠀⠀⠀⠀⠠⠠⠀⠁⠀⠀⠀⠢⠄⢀
⡠⢴⡆⢠⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠘⠀⠸⠀⠀⠀⠀⠀⠐⠈⠉
⠁⠈⢁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠂⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠊⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⢀⣃⠀⠁⠀⠀⠀⠸⡋⠉⠀⠀⠀⠀⠀⠀⠉⠆⠁⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠁⠀⢉⠀⠀⠀⠀⡀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠑⠓⠀⠀⠀⠀⠂⠔⠀⠀⠂⠀⠂⡐⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠤⠸⣀⣀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠈⠒⢪⡀⠀⠀⠀⠀⠀⠀⠘⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⣤⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠎⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣶⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣻⡗⠀⢀
⠀⠀⠀⠀⠀⠀⢐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠹⠃
⠀⠀⣀⢠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡄
⢀⣾⣿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⣿⠇
⣼⣿⣯⣤⣍⣛⣩⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣬⣭⣥⣤⡀⠀⢀⣀
⠉⠙⠛⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣶⣿⡿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇
⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇
⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇
⠀⠀⠀⢿⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⢿⡿⠇

⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢾⣹⠇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢖⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⣾⣷⣠⣾⣿⣷⣄⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄
⠀⠀⣰⣿⡟⢻⣿⣿⣿⡏⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⡄
⠀⠀⢿⣿⣷⣤⣭⣭⣥⣤⣾⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣬⣿⣿⣄
⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠿⠿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣿⠇⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠂⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⢢⣀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡠⠂⠁⢀⠔⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠀⠤⠀⠈⠀⠀⡰⡄⠀⠀⠀⢀⠊⠀⣀⠖⣠⡄⠐⠈⠤⢂⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡄⠁⠀⠁⡹⠏⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠉⠀⠀⠘⢿⠁⠀⠢⠔⠈⠀⠀⠀⠀⠠⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⢠⣄⠀⠀⠀⢰⣦⠀⡀⠀⠀⠘⠀⡠⠋⠀⢀⠀⠀⢀⣅⠀⠀⠀⢾⡄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠛⠀⠀⠐⡌⠁⠀⠁⠀⠀⠀⠀⡇⠀⡆⠄⠀⠀⠀⠛⠁⠀⠂⡌⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⢀⣠⠄⠁⢀⠀⠀⠀⠀⠀⢡⢣⠀⣸⡄⠀⠀⠀⠀⠀⠄⠄⠀⢀⢜⠎⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⡀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠡⢳⣇⡈⠀⢄⡀⠀⢀⣀⡠⠔⠃⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⢂⢸⣟⠦⠤⠵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠆⠈⠀⢀⠉⠀⣠⡄⡄⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢌⠢⡑⠜⠘⠚⠒⠂⠀⠀⠶⠂⠠⠀⠲⠄⠀⠀⠀⠒⠒⢑⠁⠀⡀⠀⠀⠀⠀⠀⠀⠉⠈⠢⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠢⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡒⠒⠲⠒⠲⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠉⠀⠀⢺⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠀⠺⠂⣠⡉⠰⠦⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡁⠐⠗⢀⡉⠀⡦⠀⠘⠃⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠤⠜⢁⠤⠄⠸⠟⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡐⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⠀⡆⠀⠀⠀⠀⠸⠀⠀⢀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠁⠀⠀⠀⠀⠀⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣅⡈⠉⠡⠃⠀⠀⠀⠀⠀⠏⠉⠁⢈⡤⠆⠀⠀⠀⠀⠀⠀⢌⡁⠀⠀⠀⠀⠀⠀⠀⢈⣁⣀⠥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠚⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠔⠒⠚⠉⠁⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠒⠉⠁⠀⠀⠀⣀⣀⢤⣴⣶⡄⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠒⠊⠉⠀⠀⠀⣀⣀⣤⣴⡴⠶⣿⡏⠻⣷⣦⡻⠿⠛⠒⠀⠀⠀⠀⢈⣲⡀
⠀⠀⠀⠀⠀⠀⢴⡉⠀⠀⠀⠀⠠⣤⣶⣦⡙⣷⣝⣿⡄⠻⡷⠀⠈⠛⠀⠈⠀⠀⢀⣀⡠⠤⠒⠒⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠗⢄⠀⠀⠀⠀⠙⢿⡿⠿⠋⠉⠉⠁⠀⠀⢀⣀⡠⠤⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠘⡄⠑⣄⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⢸⠀⠱⡀⠈⣱⣤⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⢴⣿⣋⣿⣿⣏⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⡀⠋⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡄⣶⠾⣿⠋⠉⣿⠁⠿⠟⠈⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⠀⠀⠀⢰⣿⣿⣇⣿⣧⡟⠀⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠃
⠀⠀⠀⠀⠀⠀⠈⢆⡇⠀⠀⠀⡇⠀⠀⠀⠸⠿⠟⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⡇⠀⠀⠀⠀⢀⣀⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣧⠤⠔⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀⡀⠀⡜⠉⠶⠄⢖⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡰⠐⡄⡀⠀⣔⠓⠊⠀⠄⢤⠁⠋⠳⡐⣰⡆⡀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⢦⠀⡴⢶⡛⡉⠛⠛⡙⢟⢶⣸⠌⠋⡕
⠀⢱⠦⠑⠚⠫⠤⡳⣀⠀⠑⠊⡠⠤⡲⢿⠉⡀⠤⠜⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠠⠦⣬⠡⠀⢣⢡⠀⡇⠀⢸⢸⣧⡀⠀⢳
⡰⠋⠀⢀⣀⣠⡞⠉⠓⢀⢀⠀⠳⠴⠃⣼⠓⢦⠀⡞⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡀⢠⢤⣸⢶⡁⡸⣸⢀⣷⣆⣼⡼⠙⢥⠋⠁
⠣⢄⡴⠛⠳⡀⠉⢳⡒⡜⣀⠜⡠⢊⡼⠁⠓⠤⠴⠃⠀⠀⢀⣤⠔⠒⢆⡁⣋⡵⠒⠒⠤⣄⠀⠈⢩⣇⡷⠈⠁⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠉⠉⠁⠈⠓⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⣈⣀⠒⠋⠋⠙⠓⢌⢑⣾⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⡋⠉⠉⢩⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠀⠀⠀⡇⠀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠆⠱⢒⡠⡀
⠀⠀⠀⠀⠀⡠⠤⠊⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠑⠄⢬⣀⣀⣀⣇⣀⣀⡸⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠄⠀⠀⠰⣁⡨⠊⢢
⠀⠀⠀⠀⢀⡇⠘⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠤⠃⠸⣀⡵⠀⠀⠰⡈⡂
⠀⠀⠀⠀⠀⡗⢄⠈⠳⢄⡀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠢⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢀⡀⠀⠤⡀⣆⣉⠇⠈⠁
⠀⠀⠀⠀⠀⠳⡀⠑⠢⠄⣈⠉⠐⠒⢉⣡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⣠⠤⠉⠑⠒⠤⠤⣀⠀⠀⠘⢦⡇⠐⠒⠁⢀⣀⡾⢅⡀
⠀⠀⠀⠀⠀⠀⠈⡦⢄⡀⠀⠈⢉⡩⠟⠀⠀⠀⠀⠀⠀⠀⣀⡠⠐⠈⠀⠀⠀⠤⡀⠀⠈⠁⠀⠀⠀⢀⠠⠒⠉⡄⠀⠀⠀⠈⠁⠈⠲⣋⠃⡜⡖⠚
⠀⠀⠀⠀⠀⠀⢠⠃⢀⠏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣰⣉⣈⡋⠻⣀⠀⠀⠀⠀⠀⠀⠈⠙⢂⡠⠊⠁⠀⠀⡠⠃⠀⠀⠀⠀⠀⠈⠉⠀⠉⢃⠘⡆
⠀⠀⠀⠀⠀⢀⠞⢀⠇⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠉⠀⠀⠀⠀⢉⠝⡫⠦⣀⣀⣀⡠⢦⡐⠁⠸⡇⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠘⡄
⠀⠀⠀⠀⢀⡞⢀⠎⠀⠀⠀⠀⠀⠀⠀⠮⣁⠢⢀⠀⠀⠀⡀⣐⠑⠀⠀⠀⠀⠠⠘⠱⠄⠘⡀⡠⠗⠁⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠈⢦⣸
⠀⠀⠀⠀⡞⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢇⡈⠑⢢⠉⠉⠹⠊⠁⠈⢱⠊⠉⠙⠆⠀⠀⢆⣸⠇⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠊⠙⢦⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠼⠆⠂⢼⠄⠒⠒⢾⠤⠒⠢⢤⠠⠒⠁⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡠⠴⢤⣄⠠⢀⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢌⣠⣠⠋⣠⢤⠅⣺⠁⠐⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⣇⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢇⠀⢈⡦⠔⢋⢂⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⢖⠛⣍⠉⠙⣇⣀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠫⣔⠛⠲⣅⠂⠀⣸⠼⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⢊⠙⢄⠀⠀⠀⠱⡘⡄⢠⠿⢧⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠋⠉⠈⢂⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠛⢭⡀⢄⠀⠀⠐⠄⠇⠀⣀⣠⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠳⡀
⠀⠀⠀⢀⠁⠈⢏⠒⠤⠧⠄⠈⠳⠀⠙⡌⣆⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠙⢆
⠀⠀⠀⠈⡗⠒⠈⠱⠒⡦⠺⢅⣀⠤⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠜⠃
⠀⠀⠀⠸⣄⠀⣾⠗⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⠁⠈⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣾⢏⣿⡿⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢁⡼⠀⢠⣄⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠿⣶⡆⠉⠀⢰⠶⠶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣈⠉⢻⣾⣿⡏⣋⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡃⡶⠶⠞⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⣾⢩⣭⣥⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣟⢠⡟⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣭⣭⡅⠸⡏⣭⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡾⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢩⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡸⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠻⡍⠉⢻⣧⠀⠀⠀⠀⢀⣀⡤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠳⡙⢆⠀⠹⣷⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⡤⣄⠀⠀⠙⣌⠳⣄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡽⠯⢍⠙⢎⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠓⠁⠀⠀⠉⠁⠀⠀⠀⠈⠳⢌⡵⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⡏⢜⢍⡡⡡⢈⠀⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡏⠀⠾⠇⠀⠀⣀⡀⠀⠀⠀⠮⠆⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⣓⣒⡡⡾⣺⣭⣭⣍⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⢞⢦⠀⠀⠀⠀⠓⠃⠀⢀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⢸⠑⠕⠢⠑⠹⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⢻⣆⠈⢣⡳⡀⠀⣀⠀⠀⠀⡸⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⠘⣜⢪⣖⡰⢠⢀⠟⡇
⠀⠀⠀⠀⠀⠀⢰⡉⠀⠀⠀⠀⠀⠹⣧⡀⠑⢌⠢⣟⣡⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠓⠤⢭⣥⡴⠟⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠀⠀⠀⠀⠈⣻⢦⡤⠟⠋⠀⠀⠀⢀⡠⠤⠀⠀⠀⢀⠴⠊⠁⠤⢦⣤⣍⠢⡀⠀⡇⠉⠉⠙⠒⠒⠉⠉⠁⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢂⠘⡀⠈⠉⠒⠒⠒⠒⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⡤⠴⢒⣒⣲⣶⣤⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡱⠁⡔⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠂
⠀⠀⠀⠀⠀⠀⢀⣴⡂⢭⠕⠒⠈⠉⢋⠀⠀⠀⠉⣷⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢀⡜⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠇⠀⠀⠀⣈⣤⠤⠄⠂⠺⡇⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡰⠋⠉⠓⠲⢤⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠸⣀⣠⠤⠾⠖⠊⠉⠁⠰⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠓⢤⠁
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢃⠀⣀⣀⡠⣧⠒⠒⠈⣫⡆⠀⠀⠀⠀⠀⠀⠈⠳⣤⡴⠋⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡤⠖⠚⠛⡏⡡⠢⡄⣸⠆⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠
⠀⠀⠀⠀⠀⠀⠀⡠⠛⠒⠴⠒⠛⠁⠀⠈⣀⢀⡠⠤⠤⣤⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⡎
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⡤⠐⠊⠁⠈⠁⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠇⠀⠀⠀⠀⢀⡀⠀⢠⡄⠆⠢⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠴⠚⠈⠂⠉⠈⠀⠀⠀⠀⠀⢋⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⢀⠊⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠈⠓⠢⢄⡠⠃⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⡆⠀⠀⣀⡤⠖⠋⣇⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀⢁⠴⠊⠁⠉⠁⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠔⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢇⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠓⠋⠉⠀⠈⠙⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡜⢦⣀⣐⣠⣤⡼⣃⡤⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡸⠁⠀⠀⠀⠀⠀⠀⠉⢳⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠃⠀⢿⠇⠀⠀⠰⡿⠀⠈⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠵⠛⣶⢤⢄⢀⡤⡔⠾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡷⠋⢠⢀⠋⠑⢶⡴⠒⢣⢸⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⠗⢄⡼⣘⠀⠀⠈⠀⠆⠻⣼⡦⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢀⢾⣧⠇⠀⠀⠀⠀⠂⠚⢿⣇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣾⢄⡿⠀⠀⠀⠀⠀⠀⠀⢸⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡨⢠⣧⣀⠀⠀⠀⠀⠀⣀⣤⡞⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⠈⠉⠉⣉⡋⠉⠉⠊⠀⠩⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢰⠿⣇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⠀⡿⣚⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠉⢑⣤⣷⠋⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠐⠒⠒⠒⠂⠸⠿⣍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠄⠀⣠⠦⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣔⠤⢊⣉⠤⠚⠁⠀⠑⢦⣘⣳⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡍⠒⠉⠉⠂⠀⠀⠀⠐⣋⡉⠙⠀⠍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠖⣰⠀⠈⣴⣶⣷⠀⠀⠀⢸⣷⣦⡉⠀⢰⡶⠂⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢐⡇⠀⠀⠻⠿⠏⢀⠀⠀⠘⠿⠿⠃⠀⠀⣷⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⡤⠈⣁⠀⠀⠀⠀⣤⡠⠤⠤⢠⡆⠀⠀⠀⢀⡍⠠⠴⠥⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⡄⠀⠀⠀⠙⢾⡓⣛⠮⠁⠀⠀⠀⡌⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⡤⠄⠤⢤⠐⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⡖⠒⠒⠒⠒⠂⠈⠉⠁⠢⠔⠈⠉⠁⠐⠒⠒⠒⠒⢲⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠀⠀⠈⠉⠀⠀⠀⠀⠚⠛⠚⠛⢻⠒⠂⠀⠀⠈⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠠⠄⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡰⢀⠀⠀⠀⠀⠀⠀⠀⠠⣛⡓⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡯⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠻⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠟⣸⠃
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠀⠀⠠⠤⠤⠴⣈⢃⣊⡸⠤⠤⠄⠀⠀⠐⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀
⡖⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓
⡇
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠤⢤⡤⣤⠤⢤⡤⣤⢠⣤⣀⣀⣠⡤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠤⠤⠤⠤⠤⢤⣄⣀⣀⡤⢠⡤⣤⠤⢠⡤⣤⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠊⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢰⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠠⠤⢤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢢⡤⠤⠄⢲⠊⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡿⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠷⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣦⠾⣇⠀⠀⠀⠀⠀⢸⠀⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⣶⡌⣌⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢇⢱⣶⡈⠳⣄⠀⠀⠀⢸⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠓⠀⠀⢀⠞⠉⠐⢤⠟⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠹⡄⠂⠉⠳⠀⠀⠘⠉⢱⠀⠸⠀⠂
⠀⠀⠀⠀⢀⠦⢦⠀⠰⠀⠄⠀⠀⠸⠃⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⢀⠇⠀⠠⠄⠼⠀⠰⠦⢆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠁⠀⠀⠀⠀⠀⠀⡆⠀⢘
⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠤⠤⠤⠤⣴⣶⣶⡶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣧⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢉⣩⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⡶⢶⡄⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⣾⠀⠙⠇⠀⣧⡴⣳⠄⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣤⣤⣤⣤⣿⠟⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣠⡟⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠛⣉⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡇⣠⠀⠀⠀⠀⠀⢰⡞⠋⠉⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢿⣿⣟⣴⡞⠃⢀⡀⠸⣿⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⢟⣿⣿⣷⣞⢻⡿⣼⡟⣇⠀⠀⠀⠀⢹⡄⠀⠀⣀⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠶⣤⡾⠛⠋⠉⢻⣿⣿⡟⠁⠈⠁⣿⠀⠀⠀⢀⣀⣷⠶⠛⠉⠙⣏⠻⢿⣿⣿⣶⣤⣤⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⡴⠿⠤⠤⠤⠶⢶⡟⠛⠛⠶⡶⣶⠿⠶⢶⡿⢻⡏⣿⠀⠀⠀⠀⢹⡆⠀⠁⠘⠏⢻⡿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢧⡻⣄⣠⠞⣁⡞⢡⡟⠀⠀⠀⣴⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⠳⢼⣟⣛⣩⡴⠋⠀⠀⠀⣰⠃⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠛⢧⡀⠀⠀⠀⠀⠀⠀⠙⢯⣿⠀⠀⠀⣀⣰⡷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡟⠲⠶⠶⠦⠴⠶⢶⣿⡷⠛⣿⠉⢹⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠘⢦⣄⣙⠛⠛⠉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣆⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡇⠀⠀⠀⣻⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠲⢦⣴⡶⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠙⢳⣀⣄⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢠⠁⠈⠉⢉⠉⠊⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠐⠀⢀⡄⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣦⣀⡞⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠛⠻⠿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠂⠀⠀⠀⠀⠽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⢨⠆⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠑⠄⠀⠐⠙⣿⣷⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠢⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠠⠀⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢀⡀⣀⠀⠀⠀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠢⡀⠀⠻⣻⣷⡄⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠈⠢⣀⢽⣿⣿⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡦⡀⠀⠀⠈⢺⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⢀⠀⠀⠀⠹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣾⣦⡐⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣩⠟⣿⡟⣟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠐⠁⡀⠸⠃⡯⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣠⠊⣹⠊⠀⠀⣀⡳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⠴⠁⠙⠒⠒⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡜⠦⠼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢱⣄⣀⣀⣀⣀⡀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⣒⣒⠒⡒⢒⣒⠒⣒⣂⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣕⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠈⠉⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢏⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢉⢂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠈⡎⡀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠾⢶⣦⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡠⠭⡀⢣⠀⠀⠀⠀⢠⠞⠁⡀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⢀⠀⠀⠀⣠⠐⢀⠁⠀⢤⣽⣒⠶⣶⡄⠀⡦⠀⠀⢘⢸⠁⠀⢃⢸⠀⠀⠀⠀⠃⠀⠀⠠⠀⠀⠄⠀⠀⠀⠈⠇
⠀⠀⢠⡁⠀⢾⡟⠐⠊⠁⠀⠀⠀⢀⠀⠀⠘⢄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣄⠀⠀⠀⡄⢂⠀⠀⠀⡀⠀⠀⠀⢀⡀⡐⠠
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢇⠀⠀⠑⢌⠑⠒⠉⠀⠀⠀⠀⠈⡡⠃
⠀⠀⠀⠀⠀⠛⢆⠀⠀⠀⡀⠀⠀⠰⢀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣀⠀⠀⠀⠁⣢⠄⣀⣀⡤⠔⠊⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠈⠐⠊⠀⡋⢄⠁⠠⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠙⣦⣤⠴⢊⠛⠜⠁⢠⡃⠑⢆⠀⡀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨⠘⠧⠛⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⢸⡁⠀⠀⣀⣁⡠⠞⠐
⠀⠀⠀⠀⠀⠀⢀⠞⠁⡧⡸⠀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡉⠁⢸⠁⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠘⠢⠀⡷⠃⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢣⡰⠀⡀⡄⠀⠀⠀⠘⠤⠛⢤⡼⠀⠀⠀⠀⠀⠠⢀⡏⢀⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢬⡀⡀⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠪⡨⢛⢾⠇⠸⠃⡇⠀⠰⠒⠼⠀⣠⢤⡧⠀⢀⠀⠀⠀⠀⠀⢑⢀⡀⠎⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⠁⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠹⠤⢅⠼⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠵⠄⠈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⡟⠉⠉⠉⠉⠛⠛⠒⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⡤⣶⠆⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⢀⡤⠖⠋⠁⠾⠥⠤⠤⠔⠚⠉⢡⣞⣁⣠⠤⠖⢫⡇⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⠋⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢿
⠀⠀⢀⣤⡀⣠⡀⠀⠀⠀⠀⠀⢻⠀⠀⢸⠃⠀⠈⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⣤⡀⠀⢷⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡀⣠⣄
⠀⣤⣼⡏⣿⠉⣇⣤⡄⠀⠀⠀⠈⡷⢦⣼⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠿⡇⠀⠀⠀⠀⣸⠇⣤⣤⡏⢻⡏⣿⣴
⣴⡽⣮⠓⠘⠀⡟⢸⡇⠀⠀⠀⢸⡇⢢⣟⠀⠀⠀⠀⢸⣷⣿⠀⠀⣠⠃⠀⠀⠀⠀⣾⣽⡆⠀⠀⠀⠀⠹⣀⡴⠢⣠⡟⠀⣿⠘⡇⠈⠐⢫⡾
⠈⠛⢶⡀⠀⠜⠁⣸⠇⠀⠀⠀⠀⣧⠀⡟⠀⠀⠀⠀⠀⠉⠁⠀⢞⠉⠁⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠛⡴⢫⡏⠀⠀⢾⡀⠹⠆⠀⣠⠞
⠀⠀⠈⠳⣦⠀⠀⢻⡄⠀⠀⠀⠀⠘⢦⣭⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣼⠃⠀⢠⡴⠋
⠀⠀⠀⠀⠹⡆⠀⠀⢻⡄⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠈⡟⠒⠂⠤⠤⠤⠤⢤⡶⠀⠀⠀⠀⠀⠀⠀⢀⣧⡼⠃⠀⠀⡼⠃⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣠⡞⠁⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠙⢦⣀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠈⠓⠶⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⣠⠞⠃⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢀⣽⣷⣶⣤⣄⣈⣳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣡⣴⣶⣿⣇⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠲⠤⣀⣀⣀⣀⡀⠤⣴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⢧⡀⠀⠀⠀⠀⢀⡰⠋⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠉⠓⠴⠶⠒⠋⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠫⠭⣉⡉⠛⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠛⢉⣉⠭⠝⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠉⠓⢦⣙⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣋⡴⠚⠉⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠈⠳⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠞⠁⠀⠀⠀⣀⣤⠞⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣓⣶⣤⣴⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣦⣤⣶⣒⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠶⠶⡒⠛⠛⠛⢦⣠⠞⠁⠀⠘⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠛⢏⡉⠉⠀⠀⠈⠒⣄⠀⠈⢢⠀⠀⠈⣧⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⣲⠶⠤⣄⣀⠀⣼⠉⠀⠀⠉⠢⡀⠀⠙⢄⠀⠀⠀⠀⠈⢆⠀⠀⢣⠀⠀⢸⡅⠀⠀⠀⠀⢻⡀
⠀⠀⢰⡏⠀⠀⠀⠈⠙⣿⠀⠀⠀⠀⠀⠘⡄⠀⠈⡆⠀⠀⠀⠀⠈⡆⠀⠈⡄⠀⠈⡗⠶⠦⠤⠴⠶⠛
⠀⠀⠀⣹⠂⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢰⠀⠀⢰⠀⠀⠀⠀⠀⢥⣀⣀⣧⡴⠾⠁
⠀⠀⠀⢧⡀⠀⠀⠀⠀⣠⢷⡀⠀⠀⠀⠀⢀⣆⣠⣼⡤⠴⠶⠚⠒
⠀⠀⠀⠀⠉⣳⢀⣤⠞⠁⠈⠛⠒⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠁⢀⠀⠀⠀⠀⠀⠀⡀⢀⢀⢀⡀⢀
⠀⠀⠀⠫⠀⠓⠈⠹⠀⠁⠇⠈⠃⠈⠈⠸⠁⠋⠀⠡⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠛⢦⡀⣾⠁⠀⡴⠋⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣉⣉⣻⣷⣦⣷⣿⣶⠟⢓⣺⡶⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠥⡤⠶⠿⢿⠿⠿⢿⣿⣿⣷⣾⣻⢶⣄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢁⡄⠀⠀⡠⠞⢁⡤⠞⠁⠔⠊⠉⠛⢿⣦⣙⠿⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⢓⠩⠒⡥⠊⠀⣊⠴⠚⠁⠀⠐⢀⠔⠋⠀⠀⢉⣿⡿⢯⡑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣽⣋⠁⠀⠁⠀⢀⢔⣶⣍⣀⡀⠂⠀⠀⠒⠁⡀⠀⢀⡴⠋⢺⣿⠈⢿⢸
⠀⠀⠀⠀⠀⠀⠀⢰⡿⢩⣴⡶⠶⠮⠳⣄⣠⠞⠁⣾⠁⠀⡈⠙⢳⣄⠀⠀⠀⠄⣰⠋⠀⠀⠀⣿⡄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⢿⣤⠂⠀⠀⢸⡇⢀⠠⣈⠛⠛⢠⠖⠀⢻⡆⠐⡠⡾⠋⠀⠀⠀⠀⢻⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢮⡻⢶⣤⣴⣞⡵⣣⠞⠑⠁⠀⡼⢧⣀⣼⣧⠊⠀⠀⠀⠀⠀⠀⣠⢾⡇
⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⢷⣭⢄⣉⠟⠩⠞⠛⠛⠻⣦⣂⡔⢁⣞⣵⠋⠀⠀⠀⠀⡠⢂⣼⣵⠟
⠀⠀⠀⠀⠀⠀⢸⡇⢀⡶⣧⡹⠋⣁⠀⣴⠟⠛⢻⢦⡈⢿⡄⣸⡁⠈⢳⡄⠂⠀⠊⡠⠋
⠀⠀⠀⠀⠀⠀⠸⣇⠸⡇⠘⠃⢺⡅⣠⣿⣠⠀⠀⣸⠇⣼⢏⣴⡓⠒⠀⣧⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠙⠦⣀⣼⡟⠁⠙⠿⣶⣬⣤⡾⠏⢸⠀⢻⣀⢴⣏⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣟⡥⠞⠁

⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⣀⠀⠀⠀⣴⣦⠀⠀⠀⠐⣦⠀⠀⣴⣦⠀⠀⣴⠆⠀⠀⠀⢠⣦⡄
⠀⠀⠀⢠⣼⣿⣄⠀⠀⠀⠀⠀⣠⣽⣧⣄⠀⠀⠈⠻⠶⢦⣽⣯⣄⠀⠀⠀⠘⠳⢶⣽⣯⡴⠞⠋⠀⠀⠀⢀⣬⣿⣤
⠀⠀⢰⡟⣿⣿⡟⣧⠀⠀⠀⣼⢻⣿⣿⠛⠶⣤⠀⠀⠀⠀⣿⣿⡟⣧⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠠⠶⠶⠏⣿⣿⡟⣷
⠀⠀⠘⠃⣿⣿⡇⠛⠀⠀⠀⠛⢸⡿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠛⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⣿⢿⣇⠛
⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⡗⢸⡇⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⢸⣷⠀⠀⠀⠀⠀⠀⣿⣸⣿
⠀⠀⠀⠀⠿⠿⠇⠀⠀⠀⠀⠀⠸⡟⠸⠇⠀⠀⠀⠀⠀⠸⠇⠿⠇⠀⠀⠀⠀⠀⠸⠇⠸⠿⠀⠀⠀⠀⠀⠀⠿⠿⠃

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡄⢀⠀⣤⡀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢺⡿⠀⠀⠀⠀⠸⣯⣐⣿⣗⣨⡿⠂⠀⢻⣤⣀⢻⡿⠀⠀⠀⠀⠀⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠸⣿⠃
⠀⢀⣴⠞⣿⣿⡟⢦⡄⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠙⣿⣿⡟⢦⡄⠀⠀⢠⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣿⡀
⠀⠀⠙⠷⣿⣿⡷⠟⠁⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠟⠁⠀⠀⠙⢿⣿⣿⠛⠀⠀⠰⠞⠋⣿⣿⡏⠙⠳
⠀⠀⠀⢠⣿⢸⣇⠀⠀⠀⠀⠀⣼⡇⢿⡆⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣸⡏⣿⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⣸⡇⠈⣿⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢰⡿⢹⣇⠀⠀⠀⠀⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠘⣿⣄
⠀⠀⠀⠙⠁⠀⠉⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠈⠋⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⣤⣦⡀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⢠⣼⣯⣄⠀⠀⠀⠀⣀⣬⣿⣥⣄⠀⠀⠀⠀⠀⢠⣬⣿⣤⠀⠀⠀⠀⠀⣠⣽⣯⡄⠀⠀⠀⠀⢀⣬⣿⣤⡀
⠀⠀⠰⣿⣿⣿⣿⡧⠘⠛⠛⠋⢹⣿⣿⠉⠛⠛⠃⠀⠀⠸⣿⣿⡿⠀⠀⠀⣠⣴⢿⣿⣿⠃⠀⠀⢀⣴⠟⣿⣿⡏⠻⣄
⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠉⠀⢸⣿⣿⠀⠀⠀⠈⠁⠀⣿⢿⣇⠀⠈
⠀⠀⠀⠀⣿⠸⣷⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠿⠀⢿⠀⠀⠀⠀⠀⠸⠿⡿⠀⠀⠀⠀⠀⠀⠸⠟⠘⢿⠀⠀⠀⠀⠀⠸⡿⠟⠀⠀⠀⠀⠀⠠⡿⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠻⣿⣿⣶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠈⠛⠛⠛⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠛⠋⠉⠁⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠛⠉⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣏⠉⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠈⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⣠⣴⣿⣿⠟⠁
⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣷⣿⣿⡿⠛⠁
⠀⢿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠉⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠉⠉⠙⠛⠛⠉⠉⠁
⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⢻⣿⣷⣤⣤⣤⣀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣿⣷⣄⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠘⠌⠁⠀⠀⠀⠀⠈⠃⠐⠂⠁⠀⠀⠤⠄⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⠦⡀⠀⠀⠀⠀⣆⡙⢄⠐⠀⡀
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠈⠡⠚⣁⠀⠀⠀⠀⠄⣢⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⣶⠢⢹⡆⡴⢋⡩⠉⠻⣆⠴⢋⣽⡄⠠
⠀⠀⠀⠀⡅⠀⠈⡀⠀⠠⠀⠀⢠⣿⡄⢀⡀⠀⢻⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢧⡸⢟⣀⡼⢻⡇⣾⡿⠀⠀⣿⣤⣉⠈⠀⠀⠂
⠀⠀⠀⠀⠠⠀⠑⠚⣢⠅⠀⠀⠨⠟⠁⠀⠉⡷⠀⠀⢀⠀⠀⠀⢐⡀⠀⠀⠀⠐⠀⠀⠀⠙⠙⠃⠀⠀⠳⢬⣀⣀⠴⠟⠀⢹⠆⣀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢅⠈⠥⡀⠀⠀⠀⠀⠦⢠⡦⠀⠀⠀⠌⠀⠀⠀⠘⣭⡀⠀⠀⠐⠠⠒⠃⠤⠀⠀⠘⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠘⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣜⡤⢢⠴⠀⠀⠀⠀⠈⠂⠀⠀⡀⠀⠀⠀⠤⡀⣀⣀⡀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⢯⣤⣬⠦⠄⠠⠠⠀⠰⠀⠀⠀⠘⠭⠅⠀⠀⠀⢠⣀⡀⠀⢀⣤⢠⣅⠀⠡⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢰⢀⠋⡍⢸⠈⣿⡄⠀⠠⠆⣼⢃⠕⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠘⣷⡋⠀⠤⠀⠀⠛⢧⢊⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠀⠴⠀⠀⠋⢀⢨⡇⡀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠢⠤⠤⠤⠤⠤⠤⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡭⠥⠤⠤⠤⡯⢤⠌⠰⠇⠐⠆
⠀⠀⠀⠀⠀⠀⢀⠈⢀⢄⡰⢀⣀⣻⣤⣤⡀⠀⠀⠶⢒⣲⣤⠴⢶⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⢥⡐⠅⠀⠁⠀⠉⠛⠛⠛⠁⠀⠀⠀⣀⣀⣀⠐⠨⠋⠉⠉⠙⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠩⠴⡮⢄⢀⡀⣂
⠀⠀⠀⢀⡄⢉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠈⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠓⠐⠒⠀⠀⠀⠒⠀⠂⠀⡁⠈⠑⠈⡋⣂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢸
⠀⠀⠀⢸
⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠠
⠀⢀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠰⣿⣷⡀
⠀⠀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⢻⣿⣿⣀⣀⣠⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⢀⣤⣿⣿⣿⡏⠉⠉⠀⠀⠀⠈⠙⢿⣄
⠀⢀⣴⠟⠁⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⢀⡿⠹⣦
⢰⡟⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠹⣧
⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠹⣧
⢹⣇⠉⠛⠶⢦⣤⣤⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⣀⣀⣀⣤⣴⣾⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠈⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⡀⠀⠀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⡀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶
⣿⣿⣿⡟⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠙⠛⠂⠂⠄⡀
⠀⠀⢀⠀⠂⠁⠀⠀⠀⠀⠁⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠔⠕⠀⠠⠊⠀⠀⠀⠀⠀⣴⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⢀⣀⣀⣠⡤⠀⢀⠀⠀⠀⣀
⠈⠈⠀⠀⠀⠀⠀⠀⢀⠀⡴⠀⢓⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠘⠂⠁⠃⠄⠀⠈⠀⠡⡀
⡆⠀⠀⠀⠀⠀⡠⢀⠡⠚⠀⠀⠀⠁⡀⢦⠆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⢃⠀⣀⠀⠠⠁⠂⠀⠀⠀⠀⢠⠀⠀⠀⢹⢉⠀⣀⢀⠀⠀⢴⡃⠀⠀⡤⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠂
⠀⢀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⣀⠓⢄⠇⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡘⠑
⠀⢽⢣⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⢀⢴⣡⠖⠁⢀⠂⠀⠀⠀⠀⠁⢀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠔
⠀⠀⠀⡗⠤⡀⠀⠀⠀⠀⠀⠄⡒⡟⢃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⡖⠂⣀⠲⣆
⠀⠀⠀⠃⠀⠁⠀⠀⢠⢧⣀⠘⠂⠇⠀⠓⠁⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠈⠂⠛⠊⠀⠁⠢⡀
⠀⠀⠀⠁⠀⡀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⢁⡀⡆⠀⠀⠀⠀⠀⠀⠧⡠⠀⠂
⠀⠀⠀⠀⠀⢀⡀⠀⠠⢆⣀⣀⠀⠄⠀⠀⠘⠠⢤⠀⠀⠐⠢⠀⢈⡁⡗⠐⠲⡀⠠⢰⣇⣣⡤⠒⠠⢤⣀⡀
⠀⠀⠀⠀⠀⠉⠻⢦⠤⠠⠄⠀⡁⠀⠀⠤⠤⢖⣀⣓⣀⠀⠀⠀⢀⣁⡒⣒⡒⣒⣚⣋⣭⣭⣥⣤⣤⢤⣶⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠖⠶⠶⠶⠒⠒⠀⠉⠙⢌⠉⠉⠉⠀⠨⡁⠉⠉⠹⣔⠈⠉⠉⠀⢤⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢖⡀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⣤⠀⠀⢠⣀⣐⡄⠀⠀⡤⠄⠸⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⠆⠶⡄⠀⢀⠠⠄⠀⡖⠀⡙⠀⠀⠉⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢄⠄⡆⠀⠀⡁⠨⠁⠀⠀⠀⠀⠀⠀⠂⣀⠠⠀⠈⠒⠐⠇⠐⠀⡐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠪⡂⠄⠀⠀⠈⠢⢴⠄⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠒⠤⠤⠤⠖⠁⠀⠀⠀⢀⣀⣀⣀⣠⡄⠀⠁⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄
⠀⠀⠀⠀⠀⠀⢤⢤⡠⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠙⠦⠶⠲⠤⣄⡀⠀⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠃⢠⠀⢀⡠⢀⡠⢲⠄⡽⠃⠀⢀⣀⣠⣤⣦
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠀⠀⠀⠈⠀⠁⢀⡥⠞⢁⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠳⢤⡀⠀⠀⠀⠀⠀⠀⠘⣏⠉⠀⡴⠋⠀⠈⢳⡀
⠀⠀⠀⠀⠠⢴⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠉⠳⠤⣄⣀⣠⣤⣤⣸⡆⣸⢁⠎⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠢⣄⠀⢀⡴⠋⠉⢧⠀⠀⠀⠉⠛⠈⡴⠀⠀⠈⠳⠦⣄
⠀⠀⠀⠀⠸⠶⠦⠤⠈⡇⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⣹⠋⣷⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠐⠒⢂⣀⣀⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠀⠀⠀⢀⡤⠟⠂⢀⡇⠀⠸⡄⠀⠀⠘⢦⠀⠀⠀⠀⠀⣠⣀⠀⠀⠐⣃⣠⠷
⠀⠀⠀⠀⠀⢠⡴⠶⠚⠋⠉⠉⠀⠉⢑⣾⣩⠴⠿⠶⠿⡇⠀⠀⠹⣄⠀⠀⠈⠳⣄⠀⠀⠀⣸⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠐⠒⠁⢂⡀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠳⣄⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠙⠦⣄⡀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⢀⡄⠀⠀⠀⠈⢹⡄⠀⠊⡐⠀⣸⠖⠶⠤⠴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠸⣇⠀⡜⡠⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⣆⠉⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⡛⢦⡀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣿⠀⢠⡏⠙⠀⡧⠀⣼⠋⢠⡞⠧⠙⡆
⠀⠀⠀⠀⠀⠀⣏⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡽⣯⠻⡄⠹⣦⡀⠙⠒⢛⣁⣀⣿⡀⠈⠳⠦⠾⢣⡴⠖⠶⢦⡀
⠀⠀⢸⢉⢧⣀⣿⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⢧⣬⡴⠃⢀⣨⠿⠛⠋⠉⠉⠉⠉⠙⠓⠶⣄⡀⡏⠀⣴⠶⣆⣿
⠀⠀⠈⠋⡼⠩⠀⠈⡇⠀⠀⣠⠖⢋⣉⠙⢦⠀⠀⠀⠀⠀⠀⠘⢧⣄⡀⢀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⠀⠹⢦⣥⠟⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠙⠦⢤⡞⠁⢀⠞⠁⠀⢾⡿⠃⡜⠀⠀⠀⠀⠀⣀⣀⡀⠉⠉⢉⡟⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢷⡀⠀⢀⣀⡀⠀⠀⠀⠃
⠀⢀⣀⠤⠤⠤⣄⣷⣠⠏⠀⠀⠀⠀⠀⠚⠓⢢⠀⠀⢠⡞⣩⠎⢹⡆⠀⣼⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⢷⣴⠋⣉⣉⢳⡄
⡔⣩⣤⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠐⠿⠟⣠⠇⠀⢸⡄⠘⠓⠛⠀⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠃⢼⠃⣷
⢇⡻⠟⣃⡄⠀⠀⠀⠈⣿⠑⠒⠒⠒⠒⠒⠊⠁⠀⠀⠈⠳⢤⣤⡤⠶⠋⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⢸⠇⠈⠳⠤⠞⠃⠀⠄
⠀⠁⠉⡏⢰⣿⣷⢀⡞⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠲⠶⢤⣤⣄⣀⣀⣠⣤⠴⠶⠛⠋⠀⣠⠏
⠀⠀⠀⠘⠶⠭⠴⠋⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⢰⡟⠓⠶⣤⡀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠲⠤⣤⣤⣤⣤⡤⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠙⠇⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢰⠃⠀⠀⠀⠀⠀⠀⢠⠎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⢠⠇⠀⠀⠀⠀⠀⢀⣴⠋⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣤⣤⡤⠴⠖⠋⠁⠀⠀⠀⠀⡞⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠶⠖⠒⠛⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⠛⠋⠀⠰⣿⣷⠀⢀⣶⣄⠀⢀⣀⠀⠀⢠⣦⣄⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠁⠀⠘⠛⠁⠀⠻⠟⠁⠀⠙⠛⠁⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠓⠒⠲⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⡶⠶⠶⠶⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠛⠛⠛⠲⢦⣿⠀⠀⠀⢀⡴⠚⠋⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣀⣀⡀⠀⠀⢀⣽⠀⠀⠀⢸⣁⠀⣀⣀⡤⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠠⠀⠠⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⢄⡀⣀⠔⡠⠂⠀⠀⠀⠀⢀⠀⠀⠀⠿⣿⠇⠀⠄⠀⠨⠉⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢂⡲⣀⠛⠢⣀⠀⠀⠀⡰⠉⠁⠀⠀⠀⠀⠢⡐⠄⣀⠠⢂⠔⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠀⢠⠀⠀⠀⠀⡄⢀⠧⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠀⠈⠑⢄⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠩⠓⢡⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠐⠀⠒⠀⠆⠑⢄⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠃⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠂⠀⠀⢸⢠⠄⠭⡭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠛⠀⠀⠀⢸⠊⠀⠀⠈⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⡀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠱⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠉⠙⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⢈⣀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠀⠀⠀⠸⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡲⠀⠀⠀⢖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠈⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⠛⠛⠛⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠿⡟⠛⠻⢶⣄⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⣀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠻⠤⠞⢁⡤⣄⠀⠙⢷⡟⠋⠁⠀⢀⣠⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣠⣤⡀⠀⠀⢾⣠⡞⠀⢰⠞⣷⣴⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆⠀⢧⣀⡿⠀⠀⠀⠀⠀⠀⠈⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠞⢁⠀⠀⠀⣴⠦⡄⠀⢴⠋⣳⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡋⣹⠄⠀⠙⠦⠿⠀⠈⠉⠉⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⠀⠉⠁⠀⠀⠀⠀⣀⣄⠀⠀⣼⢩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣏⣹⠂⠀⡞⢻⡆⠀⣾⣁⡼⠃⠀⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠀⢻⣅⠀⠀⠙⠋⢁⡀⠀⠁⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⣀⡴⠋⠙⢶⣄⣀⣰⣏⣹⣧⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈⢹⡏⠉⢹⡇
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠸⣧⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉⠛⢶⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⢀⣠⣤⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡶⠟⠉⠈⠻⣦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢆⠀⠀⠀⠀⣀⣤⢶⠒⠒⠒⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⢦⠀⡰⠋⠀⠣⠴⠃⠀⠀⠀⠀⢀⡽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠚⠁⠀⠀⣟⣁⠀⠀⠀⠀⠀⢰⠉⢱⡄⠘⢦⣈⠟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⢰⡏⢈⡇⠀⠀⣀⡀⠀⠙⠋⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣁⣀⣀⣀⣸⠙⠋⠀⠀⣞⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⣠⠴⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠘⡆⢀⣀⠀⠈⠓⠋⠀⠀⢰⠊⠳⡄⢠⠊⢳⡟⠋⠉⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⡝⠛⢻⠒⠦⡀⠀⠀⠀⣰⢹⡇⠀⠀⠀⠹⣇⣨⠇⠀⠀⠀⠀⠀⠘⠦⠴⠃⠘⠦⣾⠃⠀⠀⠀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⣰⡋⠀⠀⠀⣀⡀⠉⠒⠋⠀⠀⠈⢢⣀⡼⠁⠘⢇⣀⣤⠀⠀⠈⠣⡀⠀⠀⠀⣠⠖⢤⠀⠀⠀⢀⡴⢧⡀⠀⠀⠀⡤⠖
⠀⠀⠀⠀⠀⢀⡼⣇⡼⠀⠀⣎⢀⡹⠀⠀⠀⠀⠀⢠⠤⣿⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠈⠓⠦⢤⣹⣤⣼⣠⠤⠒⠉⠀⠀⠉⠢⣄⠘⡇
⢀⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣀⡀⠹⣀⣼⡆⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠘⢏⠓⠦⢤⡇⢀⡀⠀⠀⡠⠒⢢⡀⠀⠰⡇⠀⣹⠀⠀⢠⠗⠒⠶⠦⠤⠖⠃
⠀⠈⡇⠀⠀⢳⡏⢹⡀⠀⠳⢤⠼⠁⠀⠀⠉⠋⠁⠀⠀⡼
⣔⠊⠁⠀⠀⠈⢟⠚⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢦⢀⡜⠁⠀⠀⠀⠀⠀⣀⠤⠒⠚⠉⠉⠓⢒⣦⣄
⠈⠉⢦⠀⠀⣠⠞⠳⣄⣸⠉⡧⠀⠀⠀⠀⠳⣤⠾⢋⡀⠀⠀⠀⠀⡠⢾⠉⡧⠀⠀⣀⡀⠀⠣⣀⣹⠙⢦⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣏⡴⠊⠁⠀⠀⠀⠉⠛⠳⠤⠤⠔⠒⠋⠁⠀⠘⡝⢦⡀⠀⡼⠁⠈⠉⠀⠀⢸⡁⣨⠆⠀⠀⠀⠀⠀⢳⡀⠀⢀⡴⢫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠉⢺⢁⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣧⠖⠁⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠋⠁⠀⠀⢸⡏⢸⠀⠀⣴⠉⠙⡄⠀⠀⡠⠦⢄⠀⡇⠀⣿⠀⠀⠀⠈⠙⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠸⡝⠋⠀⠀⠘⠲⠚⠁⠀⠀⢧⣀⡼⠀⠉⠋⡇⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣠⠤⠖⠊⠳⡀⣠⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠑⠲⠤⣄⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⠃⠀⠀⠀⠀⡎⠉⣷⢀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠒⠒⠒⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⣩⠋⣉⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⣠⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⠀⠘⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠃⢠⣦⣄⠀⢰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡈⠻⠟⠀⠀⠛⠋⠀⠀⠀⠀⢀⣀⡤⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠙⠦⣤⡤⠤⠤⠤⠶⠒⠚⠋⠉⣀⡤⠚⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⣷⠈⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠶⠒⠚⠉⠁⠀⡠⠊⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⢧⠙⢦
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠈⣇⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⢱⠋⠀⠉⢻⡟⠲⢦⣤⠤⢖⣋⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠘⠦⣤⡤⠞⠁⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⣶⣶⠶⠤⠤⠤⣤⣅⢀⣠⠼⠃
⠀⠀⠠⣤⡒⠂⠉⢁⡀⠀⠀⠒⠂⢠⣁⡀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⣀⡒⠉⢀⣀⣤⠤⠖⠊⠉⠀⠈⠉⠉⠛⠓⠒⠒⠲⠦⠤⠤⠤⣤
⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠤⠄⠀⡁⠀⠂⠀⠉⠀⠂⢿⣄⣀⣀⡤⠝⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⢤⣈⡙⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣙⢶⡄⠀⠀⣠⠤⢤⣄
⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢸⡇⠀⣾⠉⢁⡷⠀⡾⠁⢰⠛⠎⢻
⠀⠀⢀⣀⠀⢸⡐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢩⡞⠮⢳⡄⠳⣄⣈⣙⣉⣤⣤⣷⣀⡈⠓⠒⢋⡶⠛⠛⠲⡄
⠀⠀⢸⡼⣣⠼⠧⡄⠀⠀⠀⢀⣀⠤⣀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠳⠶⠋⢀⡤⠞⠉⠉⠀⠀⠀⠀⠉⠙⠳⢦⣼⠀⢰⠛⠧⣿
⠀⠀⠀⠀⣇⠂⢀⡜⠀⢀⠴⠋⣠⣦⡈⡇⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⠓⠖⠋⠀⠀⠀⢈⡁
⠀⠀⠀⠀⠈⠉⢻⠀⣠⠋⠀⠀⠙⠋⣴⣃⡀⠀⠀⣠⡴⠲⢤⡀⠀⣼⠁⠀⠀⠀⠀⢶⠀⠀⠀⠀⢴⠄⠀⠀⠀⠈⣧⢀⡤⠤⠤⣄
⣠⠔⠒⠉⠉⠉⠚⢷⠁⠀⠀⠀⠀⢠⣤⡄⢳⠀⢠⡏⠸⣍⡼⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢠⡖⢲⠸⡆
⡇⣿⣿⠀⠀⠀⠀⠈⢧⠤⢤⣄⣀⣈⣩⠴⠋⠀⠀⢷⣀⣀⣀⣠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⠸⣦⣉⣴⠇
⠈⠃⠒⡟⣴⣶⡄⢠⠟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢻⡄⠀⠠⣤⣀⣀⡀⠀⠀⢀⣀⣠⡤⠶⠋⠀⡼⠁⠀⠀⠉
⠀⠀⠀⠳⡜⣋⠴⠃⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡶⠲⠦⣄⡈⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⠦⢤⣀⣀⣀⣀⡠⠤⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠙⠏⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠏⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⠤⢤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⡜⠀⠀⠀⠀⠀⠀⣠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠊⠁⠀⡸⠁⠀⠀⠀⠀⢀⡴⠋⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠶⠶⠶⠶⠖⠛⠉⠁⠀⠀⠀⢠⠃⠀⠀⣀⡤⠞⠋⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⡀⠀⠀⠀⠀⣀⣀⡼⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠸⠿⠃⠀⣴⣶⡄⠀⣠⣄⠀⠀⠀⠀⠀⣠⣄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⠉⠀⠀⠻⠋⠀⠾⠿⠀⠀⠻⠟⠁⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠒⠒⠶⠶⡶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠖⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⣤⣀⢸⡇⠀⠀⠀⣀⡤⠶⠖⠒⠾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⢹⡇⠀⠀⢰⠏⠀⠀⠀⣀⣤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠟⡉⠉⠙⢶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⢀⣠⠤⠤⢤⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠺⠁⠄⠀⠀⢉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⢀⡁⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⢀⣡⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⣀⣀⣀⣀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⠤⠤⠄⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠠⠆⠂⢸⡇⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢨⠑⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠉⡡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠢⠀⠂⠠⠀⠀⢀⡄
⠀⠀⠀⠀⠀⡁⠀⠀⡴⠖⠑⢦⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢀⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡁⠀⠤⠒⠁
⠀⠀⠀⠀⠀⢃⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠁⠂⠈⣠⡤⣉⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠁⠂⠀⠀⠐⢀⠀⠀⢿⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢈⠂⡠⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠠⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠰⠤⠠⠄⠠⠤⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⣤⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⡆⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠉⠆⠙⠁⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡟⠒⠂⢄⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⡇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠐⠂⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡧⠤⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠈⠉⠉⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠠⠁⠐⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⢄⡀⢀⣤⣴⠟⡀⠊⣹⣿⣧⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡐⠂⡀⠀⠀⢉⡉⠀⠀⠀⣠⡟⣟⢯⠄⢛⣋⢩⠿⠇⠀⠀⣀⡽⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⣿⣿⣇⣠⡠⠌⠑⠂⠀⠀⢀⣠⣽⠾⢿⡽⣋⣀⡤⠤⠖⡚⠉⠁
⠀⠀⠀⠀⢀⢀⣀⠘⢿⣛⣿⡏⣉⡁⣠⣤⣦⣴⣾⣿⣿⣿⡥⢄⣲⡾⣧⣉⡥⠴⠚⠉
⠀⠀⠀⠀⠀⢺⣿⡾⣿⣿⣿⣿⣿⣿⡟⣩⡭⠿⠿⠛⠿⠛⡉⣄⣠⡾⠛⠉⡠⣀⣤⢴⠂
⠀⠀⠀⠀⠀⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣤⣤⠶⣿⣽⡿⠷⢤⡹⠞⠿⢃⣼⣏⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⠿⠛⠋⠁⠀⠀⢿⣿⣻⣿⣷⣥⣼⣥⡌⠝⡻⣿⣶⣮⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢾⣿⣿⣿⣿⣩⢗⣿⣦⣈⡞⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡷⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠐⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠐⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠐⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠔⡈⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠐⢤⡄⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⣠⠼⢃⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠠⠀⠈⠀⠀⠀⠀⠀⠀⣠⠖⠉⢤⠴⠂⠒⠊⠀⠀⠀⠀⢀⠔⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠪⡀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⣌⠢⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⡠⠊⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⢢⡀⠠⠐⠀⠀⠀⠀⠀⢀⠐⠀⠈⠒⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠠⢄⠱⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⠱⡄⠠⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠑⢄⡀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿