Spoon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⣠⠞⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⢀⣤⠞⢉⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⢀⣠⠴⠞⣋⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣠⡴⢞⣫⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⢀⣤⣶⣿⡷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣤⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⢀⣠⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣞⣫⡥⠶⠶⣦⡀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣚⣭⠶⠛⠉⠀⠀⠀⠀⢸⡇⠀⢠⡾⠁
⠀⠀⠀⠀⠀⣀⡴⣛⡵⠞⠉⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⣰⡟⠁
⠀⠀⠀⣠⢞⣭⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⢾⡟⠁
⠀⣠⢞⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣴⠞⣡⠟
⣼⢫⡟⠁⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⣁⡴⠋⣡⡾⠃
⣿⠈⠷⣤⣤⣤⣤⠶⠾⠛⠉⣀⡴⠞⠉⣠⡾⠋
⠘⢷⣤⣄⣀⣠⣤⣤⠶⠞⠛⢉⣀⣴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠛⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠏⢯⣭⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⠿⠛⢉⣇⣴⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⢀⣀⣾⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⣉⣠⣤⣤⠶⠾⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⣥⣶⠾⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣡⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠚⠉⠉⠻⣿⠉⢠⡟⠁
⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⠃
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⡿⠋
⠹⢴⣤⣤⣤⣤⣶⣶⣞⣻⠭⠭⠚⠋⠁

⠀⠀⠀⠀⠀⣠⠶⠈⠛⠛⠛⠋⠱⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⣤⡄⠀⣴⡆
⠀⠀⠀⣰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⣇⠀⣿⣷⠀⣿⣿⡀
⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⢹⣿⠀⣻⣿⡄⡏⢹⡇
⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⣿⡆⢿⢿⡇⠀⠸⣿
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡆⢸⢸⡇⠀⠈⣧⠀⠀⣿⡆
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡇⣼⢸⣧⠀⡸⣿⢀⡄⢹⡇
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣇⣿⢸⣿⠀⡇⣿⢸⡇⠘⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⡏⠘⣿⠀⡇⣿⣾⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⡇⡀⣿⡖⡇⢹⣿⠃⠀⢿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⡇⡇⢻⡇⡇⢸⣿⢰⠀⢸
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⡇⢸⣿⡇⠘⣿⢸⠀⢸
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⣷⡇⠸⣿⡆⠀⠿⢻⠀⢸
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⠾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⣰⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣼⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣰⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢰⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢀⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⣀⣠⠞⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠉⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⣋⣁⣤⣀⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣾⡭⠿⠿⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⣽⠟⢹⠃
⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⢠⡟
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⠼⠖⠋⠀⠀⠀⣠⠟
⠀⠀⣇⠠⢠⣤⠤⠤⠴⠒⠛⠉⠁⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠙⠷⣦⣄⣀⣀⣀⡀⠀⠀⢀⣀⣀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⢀⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⣀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⢀⡠⠔⣒⣚⣉⣛⠒⠒⠒⠋⠁⢀⣠⠖⠋⠁
⠀⠀⠀⢀⠄⣊⡵⠚⠉⠀⠀⠀⠀⠙⢆⠀⢀⡴⠋
⠀⢀⠔⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡟
⢀⠊⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡜
⡇⣸⣿⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⣡⠎
⢧⠘⢿⣿⣶⣤⣤⣴⡶⠟⣋⠵⠋
⣀⣑⣦⣭⣭⣭⣭⣶⣞⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⣼⢻⡆⣼⢿⠀⣿⢷⠀⠀⠀⢠⡾⡋⠉⠉⠙⢶⡀⠀⠀⠀⠀⠀⠀⢀⡟⣷⢀⡟⡇⢸⡛⡆⠀⠀⠀⣴⢟⠉⠀⠉⠻⣦
⠀⢀⡏⢸⡇⣿⢸⡀⣿⢸⡇⠀⢰⢯⡞⠁⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣸⠁⣿⢸⡇⣷⢸⡇⢿⠀⠀⡼⡱⠃⠀⠀⠀⠀⠈⢧
⠀⢸⡇⢸⠇⡟⢸⡇⣿⠀⣷⢀⡟⡿⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡿⠀⣿⢸⠁⣿⢸⡇⢸⡆⣸⢳⠃⠀⠀⠀⠀⠀⠀⠘⣇
⠀⣸⠀⢸⣰⡇⠘⣇⣿⠀⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⢸⡇⠀⠀⠀⠀⡇⠀⣇⣾⠀⢸⣸⡇⠘⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⡄⢿
⠀⢿⡀⠈⠉⠀⠀⠉⠁⠀⣿⢸⡏⣧⠀⠀⠀⠀⠀⠀⣾⢸⡇⠀⠀⠀⠘⡇⠀⠉⠁⠀⠈⠉⠀⠀⡇⣷⢸⡀⠀⠀⠀⠀⠀⢀⡇⣾
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡿⠈⣧⠈⠷⣤⣀⣠⣤⠞⠁⣼⠁⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢸⠇⢹⡄⠑⢤⣀⣀⣀⡤⠋⢠⡏
⠀⠀⠻⣦⣀⡀⠀⢀⣠⡾⠁⠀⠘⢧⣄⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⣀⣤⠏⠀⠀⠻⣄⡀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⢹⠃⠀⢹⡅⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⡏
⠀⠀⠀⠀⣸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠁⠀⠸⡇
⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣇
⠀⠀⠀⠀⣿⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⢀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹
⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⡀
⠀⠀⠀⠈⢷⣄⣀⣤⠟⠀⠀⠀⠀⠀⠸⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣴⠃⠀⠀⠀⠀⠀⢷⣄⣀⣠⡾
⠀⠀⢀⠀⢀⡉⡉⠁⠀⠀⣀⣀⣀⣀⣀⢀⣉⣉⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⡀⣀⣀⣀⠀⢀⠀⠀⢈⠉⠁⠀⠀⠀⢀
⣿⣻⣿⣻⣛⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣀⣀⣀⣠⠤⢤⣾⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣛⣿⢻⣷⣄⠀⠀⠰⡾⣿⣿⣿⣿⣿⣿⣷⠆⣸⡒⢖⠒⠛⣻⣧⠀⠀⠀⣛⣳⢤
⠀⠀⣿⠁⡒⢂⣈⣩⡅⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⢇⢒⣚⣿⣸⣼⣿⣦⣤⣄⣷⣠⠤⠤⠤⠤⢤⣼⢐⡏⠉⣉⣉⡉⢹⣿⠀⢀⣸⣿⣿⣏⡀
⠀⠀⢹⡏⠖⠓⠙⠙⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠹⢹⣟⢐⢚⣿⡏⣛⣻⣾⢹⠰⠆⠶⠶⢿⢸⠀⣧⠪⠤⡠⢹⣾⣿⢀⣿⣯⣿⣿⣿⣿⡀
⠀⠀⢸⢳⣴⡴⠖⠴⢿⣼⣿⡟⠿⠛⠛⠛⢻⣿⣿⣯⣼⣾⣿⣿⣿⣿⣯⣿⣿⡿⠾⢓⣛⣉⣙⣛⠲⢿⡇⠑⠒⠒⠋⣾⣿⢸⣿⣾⣁⣽⣿⣿⡇
⠀⠀⢸⠚⠀⠀⠀⠐⢺⡿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⡿⣞⣼⣌⣽⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣟⣀⣀⡀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣤⣴⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢓⡛⠍⣏⠭⣡⣿⣿⣿⡀⢙⡟⠙⡿⠙⠃⣸⣿⣿⣿⣿⠷⠿⢿⣿⣿⣿⡿⣿⡿⠛⠋
⠀⠀⠀⣼⣻⡿⠿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣦⣄⣀⣀⣃⣴⣿⣻⣿⣿⣛⣤⠦⣤⡉⠒⡟⠒⠂
⠀⠀⠀⢼⡩⠿⣿⣿⣿⣿⡿⣭⣽⣿⣿⣾⣿⣦⣭⡿⠷⢮⣭⠽⣯⠯⠿⠚⢛⣛⣙⠉⠉⢉⡛⠿⣿⠿⠛⠛⠉⣼⠻⠛⠉⡇⠀⠁⠀⠀⠉
⠀⠀⠀⠈⠙⠛⡛⠛⢉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⠉⠉⢁⣶⣾⣿⢿⡻⣿⣿⣷⣶⡤⣄⢀⠀⡂⠤⢄⢸⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣿⣿⣿⣯⠭⠭⢉⣿⣿⣭⡓⢦⡜⢫⣾⢿⣿⣿⣮⣿⣿⡿⣻⣿⣿⡌⢃⢸⠿⠆⡜⠘⠻⠿⠟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡆⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⡇⢻⣿⣣⣸⣿⢿⣿⣧⠞⣽⡟⣿⡇⢸⡟⡀⢰⢅⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⣭⣍⣉⣉⣉⡩⠭⠗⢚⠋⢙⠀⣿⣯⣿⣿⠵⣩⢿⣿⣿⣾⣵⠟⡠⡻⠱⢁⣏⡀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⡘⢿⣿⣿⣾⣷⣿⣿⢿⣿⣵⠊⠰⢣⠃⡸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠩⠭⠭⠞⠛⠉⠀⠀⠉⠛⠛⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠈⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠂⠀⠊⡄⢈⠕⠊⠀⠀⠁⠀⠊⢀⠀⠀⡀⠊⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⡐⠐⠡⡀⢠⠖⠁⠀⠀⠁⠂⠉⣀⠀⠀⡀⠊⠀⠄⠀⡠⠀⠀⠀⢀⠔⢀⡆
⠀⠀⠀⠀⠀⠠⢂⠀⠀⢉⠐⠊⠤⠀⠀⠤⣕⢤⣈⠐⠀⢁⡀⠀⠀⡀⠈⠀⠀⠀⠀⠈⠀⠂⠀⠠⢀⣔⣵⠃
⠀⠀⠀⠀⠀⢎⡑⠢⢄⡁⠄⡀⢠⠄⠁⠐⠉⠳⢦⣉⡓⠢⢄⡐⠊⠀⡀⠀⡠⠈⠀⠂⠀⡠⠂⡠⣫⡞⠁
⠀⠀⠀⠀⠀⠀⠑⠱⢂⢤⣁⠒⠤⢀⠠⢀⠎⠀⠀⠈⡛⢷⣦⣌⡑⠢⢄⡉⠀⠠⠀⠀⠄⢀⢊⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⢌⡐⡂⠅⡂⢊⠔⣡⡾⠋⠙⠳⢦⣬⣑⠢⠤⣡⠔⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠫⠖⡀⢐⡺⠋⠀⠀⠀⠀⠀⠈⠑⠣⠴⢒⠬⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆⠰⢀⠤⡄⣴⢠⡇⡙⢀⢤⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⢷⠁⢧⠸⠅⡇⢸⠀⡇⢺⡈⠠⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠤⠤⢤⠀⠀⣤⠠⠀⠀⠠⣐⠲⣖⠒⠒⠒⠒⢒⣶⡒⠒⣀⣢⡒⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣞⠟⣀⢀⠦⠀⠀⣀⡤⣉⣉⠻⠯⠉⡀⠀⠠⢍⡰⠤⠤⣤⡤⠰⠏⠉⢐⠢⣔⠃⣀⠠⢴⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡻⢝⡶⣝⡪⢐⢨⠛⠒⠒⠒⠁⠂⠀⠉⠛⠒⠂⠒⠒⠓⠈⠓⠐⠂⠀⠉⠁⠀⠀⠀⠤⠄⠀⢎
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣜⠻⢳⣬⣓⠫⠓⢦⣥⠤⣤⡤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠄⠒⠒⠒⠒⠒⠒⠒⠙⠉⡉⣽⡀⢀⣀⡀
⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⢪⣟⢦⣄⠉⠓⢦⣤⣄⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡤⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠒⢺⣄⣀⡀⠀⠉⠉⠒⠠⣄
⠀⢸⠀⠀⠀⣠⡋⡀⢒⢲⣾⣦⣍⡲⢭⢒⢤⣈⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣈⣆⠒⢼⣿⣦⠀⠀⠀⠈⡇
⠀⠈⠷⡢⣄⣀⠙⠢⠄⢈⠈⠛⠻⢿⣶⣮⣑⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⠀⠀⠛⠁⠀⣀⣤⡾⠁
⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⠶⣖⣒⣀⣬⣬⠭⣭⣭⣄⠀⠀⠀⠉⠉⠀⠁⠀⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠥⠤⠀⢒⣒⡒⠊⠩⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠺⠯⠭⠭⠥⠤⠤⠤⠤⠶⠞⠓⠒⠲⠖⠖⠦⠤⠀⠠⠄⠀⠀⠤⠭⠭⠭⠉⠉⠉⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠒⠒⢒⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢋⠥⠤⠔⠉⡍⠓⠋⡍⠑⠤⠤⢍⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣁⠤⢃⣀⣀⣸⠀⣇⣀⣀⡇⢸⣀⣀⣀⠣⢄⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣾⠀⡆⣠⠤⠤⢤⠀⡤⠤⠤⡄⢠⠤⠤⢤⡀⡆⢸⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠖⠁⠀⡇⣿⠀⠀⢸⠀⡇⠀⠀⡇⢸⠀⠀⢸⡇⡇⠀⠑⢦⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢘⡆⣉⣉⡁⢈⣉⣉⣉⠀⣉⣉⣉⡁⢈⣉⣉⣉⠀⣉⣉⡁⣞⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡞⠀⠀⠈⡇⣿⠀⠀⢹⠀⡇⠀⠀⡇⢸⠁⠀⢸⡇⡏⠀⠀⠘⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⡄⠴⠴⠃⠹⠴⠦⠞⠀⠷⠴⠶⠇⠸⠦⠶⠼⠁⠳⠴⠄⡜⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⡀⠉⠉⡆⣼⠉⠉⢻⠀⡏⠉⠉⡇⢸⠋⠉⢹⡄⡎⠉⠁⣸⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠉⣶⠀⡇⢿⣀⣀⣼⠀⣇⣀⣀⡇⠸⣄⣀⣸⠇⡇⢠⡎⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡘⠦⣅⡠⠴⠤⢦⠀⡤⠤⠤⡆⢠⠦⠤⠤⣀⡥⠜⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠣⣀⣀⡘⠀⡇⠀⠀⡇⠘⣀⣀⡠⢃⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣈⣓⠚⠉⠑⠒⣋⡠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀⠆⠀⡂⠀⡆⠀⡄⠀⡆⠀⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠃⠊⠙⠀⠀⠀⠁⠀⠃⠀⠃⠀⠀⠃




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠉⠐⠀⣄⠀⠀⠀⠀⠀⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⠉⠂⠤⠄⠀⠀⠄⣀⢎⠀⠀⠀⠜⢷⠟⠀⢀⠀⠀⠀⠐⠀⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⣸⣶⡄⠀⡀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠙⢆⣠⣼⣵⠀⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⡄⡀⠀⠀⠀⠙⠀⠀⠐⢄⠀⠀⠠⣄⠀⠈⠑⠾⣤⠀⠀⠀⠀⠉⢻⠋⠀⠀⢉⡐⣠⡀⢌⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠓⠢⢄⠐⠁⣐⠀⠀⠀⠈⠓⠿⣻⠟⠀⠠⠄⢀⠀⠙⠢⣄⣀⡠⠁⠀⠀⠀⠘⠻⢿⣿⠈⣧⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⣶⠀⠀⡀⠛⠋⠄⡀⠀⠀⢀⠋⠀⠀⠀⣶⣴⣿⣆⢲⡄⠱⡀⠰⡇⠀⠀⠀⠀⠀⠏⢰⠃⢰⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⡈⠁⠀⠀⠀⠁⠂⢄⡈⠑⠒⠁⢠⠂⠄⠀⠀⠈⠻⡏⠠⠃⡀⡡⢀⡈⠑⠀⡀⢀⠎⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⡈⠐⠐⠁⠠⠠⠀⠈⠁⠐⠻⡿⠂⠀⠀⠘⠢⠀⠀⠀⠀⡔⠀⠊⠐⢸⠁⠤⡀⣱⢄⠀⠁⠠⠃⢠⢛⠎
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠠⢽⡆⠀⣀⣁⠂⠤⡀⠀⠀⡠⠁⠀⠀⠀⠑⠢⣄⠁⠢⠊⢀⠂⢀⣾⡿⠁⠀⠈⢛⠟⠀⠀⠀⠀⠢⠂
⠀⠀⠀⠀⢰⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀⠉⣲⣌⠒⠒⠁⠀⠀⢀⠔⠙⠠⣾⡷⠀⠀⠀⠀⢊⡜⠃⠄⡀⣀⠊⠀⠀⡔⠀⠔⠁
⠀⠀⠀⢳⡈⠦⣈⠀⠀⠌⠀⠀⠀⠀⠈⠙⢿⣾⠃⠀⡀⠻⢠⡁⠀⠀⠀⠜⠀⠀⡠⠀⢠⠮⢤⣷⡄⠀⠀⠀⡠⠊⢀
⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⢷⡀⠀⠀⠀⡠⠁⠀⠀⠈⠉⠢⡀⠁⠒⠊⠀⢀⠔⠁⡠⠃⠀⠀⡹⠃⡠⢂⠊
⠀⠀⠀⠀⠀⠀⢛⠦⡄⠀⠀⠀⠈⠐⠀⠔⠁⠀⠀⠀⠀⠉⠛⢿⠂⢀⠄⡀⠀⢀⠼⣍⣒⣒⡋⠤⠊⣠⡁⠀⠌
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠄⢀⠀⠀⠀⠀⠀⠦⣈⡂⠤⢀⣀⠔⢁⠴⢁⠊⠀⡰⠀⠀⠐⠂⠠⠀⢠⡔⡷⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠉⠓⡒⠒⠊⠁⣠⠮⢂⠄⠀⠀⠁⠀⠬⠀⠀⠠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠁⠀⠙⢀⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢃⣴⣿⣷⣾⣿⣷⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⡿⠉⡀⠛⢠⡤⠿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⣦⣣⣤⠒⠀⠀⠀⠀⠉⠉⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣿⣋⣤⠖⠀⢀⠀⠀⠲⢶⣤⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⢀⣽⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠧⠠⠶⠾⢿⣭⣭⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡛⠓
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠻⠿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⡻⣿⣦⡝⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⡿⣯⣍⠉⠉⠀⢠
⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠌⠛⠃⠠⣰⡆
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡟
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⡇⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⢠⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⢸⣿⡇⠀⡰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡸⠋⠁⣆⠀⠈⠀⢰⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣶⣤⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡟
⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠁⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢸⡇
⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⡇⠒⣿⠇⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⣿⣿⠀⠘
⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⠀⠀⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠃⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⣿⠀⠀⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠂⠀⠀⠀⠀⠀⠀⠀⣾⠇⢠⣿⡇⠀⠀⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣾⣿⠃⠀⠀⢃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⢠⣿⡏⠀⠀⠀⣼⣿⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⣼⡿⠁⠄⠀⢠⣾⣿
⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⣿⠁⠀⠀⢀⣾⣿⡇⠀⠀⠆
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⣼⢟⣿⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠜⢁⣾⠋⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣰⡿⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⣶⡾⠋⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢀⣾⡿⠋⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠀⣤⡴⠟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠀⠀⠀⠀⠁⠀⡀⠀⠀⠛⠁
⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠒⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠁⠀⠀⠀⠀⢰⠇
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⣀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠒⠐⠲⡄
⠞⠃⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡿
⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠋⠋⢉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠭⠭⠭⠷⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣀⢠⠦⢤⣲
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⢀⣯⡀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢠⠗⢲⠀⡉⢀⡘⡆
⠀⠀⠀⠀⠀⡴⠒⠚⠻⠲⣒⠒⠉⡇⣀⠼⠖⠛⠳⢤⠀⠀⣀⡼⠁⠀⠀⡠⠒⢎⠀⠈⠁⠐⠬⡹⠁
⠀⠀⠀⠀⢎⠀⣎⣝⠑⠢⣄⠛⣯⡟⣠⠄⡶⠒⡄⢸⠒⠋⠉⠀⠀⠀⢀⡇⠀⢸⠀⠀⢀⡠⠊⢱⡀
⠀⠀⠀⠀⠘⣄⠈⠻⢏⣑⣚⣷⡇⣸⠽⠿⠔⢚⣀⠏⠀⠀⣠⠄⣒⡚⢩⠋⠈⢢⠑⠚⢉⠖⠀⠙⢎⣉⢶⡒⢦
⠀⠀⢀⡴⠋⠀⠉⠒⠒⣤⠋⣠⠷⣏⠓⡖⠒⢅⠀⠀⣰⢍⣨⠝⢛⡁⠈⠂⠀⠊⠒⠤⠼⣄⡀⢀⡜⢈⣳⠉⢉⡵⡄
⠀⢠⠊⠀⠀⠀⢀⡤⡨⠁⡴⠁⠀⠈⡆⠘⡆⠀⠑⡄⢯⣸⠀⢰⢍⣙⡆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⣋⡥⠒⠉⢀⠇
⢰⠃⠀⠀⢀⠔⢉⣼⠀⡼⠁⠀⠀⠀⢸⠀⡇⠀⠀⣸⡏⠉⠓⢯⡀⡝⣠⠮⣱⠄⠀⡀⠀⢠⣞⠷⡄⢹⢀⡤⠞⠉⡹⣆
⡏⠀⠀⠀⠈⠛⠁⠘⠒⠁⠀⠀⠀⠀⠸⠴⠃⠀⠀⣇⠈⠓⠦⣀⢹⠁⣧⡀⡼⠰⠛⠂⢳⢸⠀⣀⡇⠀⣏⣠⠔⠋⠀⣿⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠲⢄⡀⠈⡹⠀⣇⣘⠀⣠⣀⣀⣸⠈⢟⢁⡵⢄⠘⡄⣠⠴⠚⡡⠟⡄
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠲⢤⣉⢺⠁⡎⠀⠉⠚⠧⣀⣀⡨⠦⠼⠁⠀⣸⠀⡋⣡⠔⠋⠀⢠⣇⡀
⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢻⣦⣌⡀⢈⡝⡰⢯⣓⠦⣀⠀⠀⠀⠀⠀⣀⠴⢋⡩⢄⠙⢦⢀⡠⠞⣷⢄⡉⠲⡄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡜⠁⢸⠀⠉⠉⢸⣁⠀⠈⠑⠢⢽⣒⠤⠖⢋⡥⠚⠉⠀⢀⡱⠈⠉⠀⢀⡝⠀⢱⠀⠘⡄⠀⠀⠀⣠⠔⠉⢀
⠀⠀⠀⠀⠙⠢⢄⣀⣀⠀⠀⠀⢀⣀⣼⡀⠀⢇⠀⠀⢧⡀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠉⠉⠁⠀⢀⣠⠖⠋⠀⠀⠀⣠⠋⠀⡠⠊⠀⣰⡇⠀⢀⡔⠁⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢸⡑⢄⠀⠑⠠⢄⣉⠑⠒⠒⠊⠁⠈⠙⠢⢤⣀⣀⡤⠖⠉⠀⠉⠑⠒⠒⣊⠡⠖⠋⣀⡤⠊⡴⠁⣠⠊⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡉⠒⠦⢤⣀⣉⣉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⢈⣉⣉⣀⡤⠤⠒⠋⣁⠴⠋⢀⡴⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣄⣀⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣀⣠⠤⠔⠚⠉⣀⡠⠔⢉⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⡴⠊⠉⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣶⣶⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢄⠀⠀⠀⠀⠀⡄⠀⡇⢀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠈⢷⠀⠀⠀⢰⡿⣄⠐⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⠜⠀⠀⠀⠈⡧⢈⠑⢄⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣧⠀⠀⠀⠀⠀⠘⢖⠁⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠈⢸⠀⡼⠀⠀⠀⠀⠀⠑⣤⠂⢀⠙⣆⠀⠀⠀⢀⠞⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⢀⠨⣸⠀⢇⠳⡀⢤⣀⠀⠀⠈⢢⠀⢐⡘⡆⠀⢠⢁⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠍⡂⠑⠄⢳⠀⠀⠁⠺⠌⡮⠳⡄⠀⢸⠂⡁⠁⢵⠀⠘⣡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡇⠀⠘⢄⠈⠢⡀⠀⠀⢠⠇⠂⣻⢠⠏⠀⠇⠠⡍⠀⢰⢻⡀
⠀⠀⠀⠀⠀⢯⠢⣄⡀⠀⠀⢳⠅⠘⡀⠑⢄⠙⣆⣠⠋⣠⠀⠿⠉⡠⠁⠂⢠⠃⠀⡼⠐⣇
⠀⠀⠀⠀⠀⠈⠢⡀⠙⡄⠀⠀⠱⡄⠑⡀⠀⠳⡈⠃⡐⠀⡄⢀⠎⠀⡐⢠⠏⢀⣴⠇⠀⢻⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠰⣤⣅⡚⠀⠀⠀⠘⣦⠐⡀⠀⠱⡐⠀⠀⡖⠁⠀⡐⢠⣮⡴⠛⢁⡀⠀⣼⠀⠀⢀⠜⣹
⠀⠀⠀⠀⠀⠀⠀⠈⠑⡌⠓⢤⠀⠀⢸⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⠛⣀⠄⠒⡉⠀⣴⠏⠀⢐⡡⠞⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢠⡀⢳⡀⢸⠁⡀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠊⠀⢀⠎⢀⡤⠁⠀⠀⢈⠔⢫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⡄⢷⠟⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡘⠀⡜⢁⣴⠏⡴⠉⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠐⠀⢠⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠘⣵⠯⢹⢰⠃⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⠃⢦⢘⠟⡌⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠈⢦⡰⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⠀⠀⠀⣀⣀⠀⠠⠌⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠡⠐⠈⠐⠠⠀⠠⠀⠤⠂⠄⠂⠀⠠⠀⠠⠤⠆⠑⠀⠀⠁⠒⠒⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢒⣁⡤⣠⣦⣤⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠛⠛⢻⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⣤⠀⡏
⠀⠀⠀⠀⠀⠀⢠⡲⣿⣿⡆⠀⠀⠀⣠⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⣀⢰⣿⡄⠀⠀⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠟⠁⢀⣀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠈⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠀⠀⠀⡀⠒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣇⠂⠀⠀⠀⠁⡴
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⡻⣿⣿⣷⣄⡀⠶⣾⡁
⠀⠀⠀⠀⠀⢀⠖⠛⢢⡀⠙⢮⡛⠿⠿⢿⣿⣿⡻⡢⡀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠹⡄⠀⠱⡄⠀⢰⣿⣿⣿⣇⢡⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢹⡀⠀⠙⣄⠀⢹⣿⡿⣿⣿⣇⠀⠀⠀⠀⢾
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠈⠉⠈⢿⣷⠘⠿⠸⡄⠀⠀⡰⠛
⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢱⠀⡸⠁⠀⠘⢿⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣰⠁⠀⣤⠀⢺⡏⠁
⠀⠀⠀⡇⠀⠀⠀⢀⠀⢾⣣⡟⠀⠀⠀⢀⣀⣠⠀⠁⠀⠈⢁⡠⠂⠀⠙⠛⠛⠀⢀
⠀⠀⠀⢡⠀⠀⠀⡡⢖⢛⡷⠒⠘⠉⠉⠁⠀⢰⠀⠀⠀⠀⢸⣽⣇⠤
⠀⠀⠀⠘⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠖⠒⠉⢸⠐⠄⣾⣛⠛⠛⠛⣛⠛⠃⡄
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠏⠀⢀⠀⠀⢸⡄⡆⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⠲⠆⠶⢶⠒⢚⠋⠍⠅⠤⢨⡧⠷⠶⠶⠾⠶⠶⠞⠣⠶⠀⠀⠀⠀⠀⠠⠀⠼⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡆
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡺⠉⠩⢕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠀⠀⠀⠈⣆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠾⠳⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⣀⣠⡤⠶⠖⠛⠉⢁⣀⡤⠤⣄⠀⠘⢧⡀⠘⡜⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡥⠴⠚⠋⠉⢀⡠⠤⠔⠚⠉⠉⠀⠀⠀⠈⢆⠀⠀⠻⣄⠈⠒⠡⠙⠡⢐⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⠋⠁⠀⡤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠙⣆⠀⠀⠀⠀⠀⠙⡜⡄
⠀⠀⠀⠣⡀⠀⠀⠠⠀⠀⠀⠀⠌⠀⠀⣠⠏⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠘⣧⠀⠀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⢀⠎⠀⠀⡴⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡤⠚⠁⣷⠀⠀⠀⠘⣧⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠘⠀⢀⡞⠀⣠⣤⡀⠀⡇⠀⠀⠀⡠⠒⠉⠉⠀⠀⠀⣨⣧⠔⠋⠁⣀⡤⠚⠁⠀⠀⠀⣠⠾⡆⠀⠀⠀⢇⢇
⠀⠀⠀⠀⠀⠀⡀⢀⠊⢀⠄⢀⡞⠀⠀⠀⠈⢻⣤⡷⠤⣄⣀⣟⠶⠶⠶⠶⢒⣫⠕⣃⡤⠖⠋⠁⠀⠀⠀⢀⡤⠚⠁⠀⣿⠀⠀⠀⠈⠢⣕⡂⠤
⠀⠀⠀⠀⠀⠔⠠⠁⠰⠁⢀⡞⡴⠾⣯⠞⠉⠙⣿⢧⣀⣀⣀⣈⣩⠭⠭⠿⠛⠛⠉⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⠀⢀⡠⠟⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢈⠀⠱⠀⠀⠀⡞⠰⡁⢿⡏⠀⣾⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠉⠉⠳⣤⣬⣿⣡⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠑⠒⠒⠲⠦⠤⠤⠤⢤⠶⢶⣶⣖⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⡠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⣠⠃⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣸⠃
⠣⣈⠢⢄⡀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠶⠚⠋⠓⠚⠋⣡⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖⠛⣉⣠⠴⠊⠁
⠀⠀⠑⠢⠬⣙⡒⠲⠦⠤⢤⣤⣤⣤⣤⣤⣤⣬⣿⣿⠥⠤⠶⠒⠚⠋⣉⣁⡤⠴⠖⠋⠉
⣀⣀⣀⣀⣀⣀⣈⣉⣙⣒⣲⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣖⣒⣚⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⣛⢟⣙⠛⣛⢏⣿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡶⠒⠒⠒⠒⠒⢲⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⡇⠠⠴⠆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠒⠒⢒⣒⡒⠒⠒⠒⠒⠒⠚⠃⣠⠗⠒⠒⠒⠒⠒⠚⢧⡀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣠⡽⣛⡛⢦⡀⠀⠀⣞⢓⣒⣒⣒⠒⣒⣒⡒⣒⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠞⠹⡟⠁⠉⢻⠇⠀⠀⠉⠉⠉⠉⠉⣩⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡶⢶⣏⣀⠀⠀⠀⠀⠀⢯⠀⢸⠆⢸⡄⠀⠀⠒⠒⠲⡖⠒⢲⡖⠒⢶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠉⠉⠀⠈⣷⠀⠀⠀⠀⢘⣀⣤⣄⣘⠁⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡴⠀⠀⡶⢳⢄⣿⡀⠀⣀⣰⠯⠥⠤⠤⠭⢷⣀⡀⠀⠀⠀⡇⠀⣸⣇⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣅⠀⠘⠳⢦⣠⣟⡏⢠⠈⠓⠶⠯⣿⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⡞⢹⣆⡏⢹⢰⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡶⠴⣇⣹⠇⢺⠶⠶⠶⠶⢾⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠙⠚⠙⠓⠚⠈⠓⠋
⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠳⠶⠶⠶⠶⠞⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⢸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⣶⠶⠶⣶⣶⡶⠶⢶⡶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣿⠸⠭⠇⠸⠭⠭⠿⠀⠯⠟⢸⠀⠘⠚⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢛⣛⣛⣛⣛⣛⣛⣛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣈⣉⣉⣉⣉⣉⣉⣉⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⠐⢀⠠⣄⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠈⠁⠈⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⠠⠤⠂⣩⠕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀⠀⠀⠀⡠⠀⠀⠔⠈⠐⠁⢄⣼⠑⠀⡀⠘⠫⢷⠘⠠⢄⡀⠔⠒⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠒⠄⠂⠀⠁⠀⡀⠘⠗⠒⠊⠉⠑⠢⡀⠀⠀⠀⠀⢀⡴⠋⣿⣱⣤⣀⠐⠠⠊⢀⣴⢺⠇⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣀⠀⢻⠀⠀⠀⠀⠂⢁⡀⠐⣮⠉⣄⡦⠅⠛⠳⠀⣀⠐⢯⣢⡴⠋⠪⣹⠾⠃⢀⡀⠙⠾⡷⠂⠣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⡒⠋⠀⣁⠂⠀⠁⣀⡤⡖⣾⣿⣿⡄⠘⣿⡁⠀⢀⠈⠀⠀⠀⠘⣆⡉⠂⠄⠔⠁⣀⠞⢿⣿⣗⠤⡉⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⡠⡾⡉⠀⢮⠤⠐⠀⢀⣠⣄⠀⢻⣿⡿⠟⠋⠘⣿⡄⠈⠓⠈⣁⠤⠖⢡⠀⠀⢹⢯⠆⠀⠀⠐⢧⣵⠟⠈⠈⠂⠉⠀⣀⠐⢿⣨⡀
⠀⠀⢀⠔⠁⠀⡰⠘⠀⠀⢠⣶⢿⣿⡯⡿⣆⠀⢻⢇⡀⠀⠂⢉⣀⣄⠀⢿⣖⠔⠻⠉⠀⠀⡟⠀⣠⠺⣗⠢⣄⠈⠂⠤⠐⢁⡤⢞⣿⡙⢄⠙⠌⠑⢄
⠀⡰⠁⠀⠠⠊⠀⣈⢻⡄⠈⢿⠞⠋⠀⢀⡼⠃⠀⠀⣤⡔⢚⣭⣾⣿⣄⠈⢿⠁⠀⠀⢈⡄⢸⣿⣽⡷⠛⢃⣿⡭⠂⡀⠀⠉⡻⠟⠣⡛⡈⢀⠖⠀⠁⠑⡀
⠀⠀⠀⠀⢃⠀⠀⠻⠈⢿⡄⠈⠚⠒⢊⣠⣴⣾⣧⡄⠘⣿⡿⠛⠉⠸⡙⠦⠈⠓⠂⣁⣀⡀⢻⠘⠫⠄⠀⡨⠋⣠⣾⣿⢶⣄⠈⠢⡀⢨⠓⠃⠀⠀⠀⠈⠜
⡆⠀⠀⠀⠈⠰⠀⡀⠀⠈⢁⡀⠀⢾⣿⢿⣿⠷⢿⣷⡀⠙⢷⡀⠰⠂⢉⣠⣆⠀⠻⣾⣿⣯⣽⣿⢢⡀⠁⠠⣾⡻⢿⠟⢌⠛⠑⡄⠈⠈⡀⠀⠀⠀⠀⠀⠐
⡇⠄⠀⠀⠀⡰⠁⢀⠄⠒⡉⡿⡄⠈⢷⡏⠀⠀⠀⠥⠐⠀⠀⣤⢖⣲⣡⢾⣿⡆⠀⠳⢼⠀⠈⡻⠁⡠⢰⣶⡀⠙⢤⠀⠀⢁⠀⠁⢀⠜⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠀⠀⠀⡄⠠⢀⣷⡷⠞⠻⣿⡄⠈⠓⠒⢁⣀⠤⣲⣱⡀⠘⣿⠟⠋⠁⠀⠙⠀⠀⠈⣧⠊⠀⡔⢀⣼⠀⠳⡀⠀⠱⡈⠀⠉⠉⠁
⠀⠁⡀⠀⠀⠈⠢⠤⠄⡀⢀⠄⠈⢁⡄⠀⢲⣽⣮⡻⠏⠻⢷⡀⠸⢦⠀⠀⠀⠜⡡⠤⠴⠋⠢⡘⢀⠨⠀⠀⠀⡃⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐
⠀⠀⠈⠢⡀⠀⠀⠀⠀⢱⠄⢰⠀⢸⣞⠀⠀⢻⡅⠀⠀⠀⠀⠃⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡡⠊
⠀⠀⠀⠀⠈⠀⢄⠀⠀⠘⠤⠼⠤⠉⢽⡄⠀⠀⠛⢆⣀⣀⠀⢀⣀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠀⠉⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠒⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠉⠂⠀⠁⠀⠀⡄⠀⠀⠄⠀⠀⢾⢶⣶⠁⠀⠀⣀⡀⠀⠀⠀⠦⣤⣀⣀⠀⠀⠀⠈⢻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⣿⣴⣶⣾⣿⠿⠷⠖⠒⡒⠒⠛⠿⠿⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠀⠒⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⢻⡟⠛⣫⣭⢥⡴⠛⠙⣋⠃⢋⠋⠒⢠⠄⡁⠈⠉⢹⡏
⠀⠀⠀⡌⠃⢒⡀⠀⠀⠀⠀⣼⠂⠀⠀⡴⢂⡀⣼⣿⣶⠛⡫⡄⠠⠀⢾⡷⣾⣿⡧⡅⠁⠈⡘⠡⣀⣸⣧⣀
⠀⠀⡀⠀⠈⣈⣢⣀⠀⡀⣦⡀⠧⠀⠀⡅⠻⠞⣿⣟⠁⠊⠀⠀⠁⠁⠀⠀⠈⠉⠁⠉⠉⠉⠀⠀⠀⣻⣽⠿
⠀⠀⠀⠀⠀⠉⠎⠈⠏⠃⠈⠇⠀⠀⠀⠀⢠⠀⠀⣉⠀⠐⠀⠂⠀⠀⢠⠀⢈⠀⠀⠐⠄⠀⠀⠀⠀⡈⣥⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⠄⠀⠈⠀⠀⠀⢀⡍⠀⠀⠀⠉⠀⠈⠀⠀⣈⠀⠀⠈⠀⠠⠐⠀⠀⠐⠁⠀⠈
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠁⠀⠀⡄⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⢿⡿⠿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠂⠀⢀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⠳⡖⢋⠕⢊⣾⠟⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⢀⣿⠃⠀⠉⠉⢠⣿⠇⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢧⠀⠀⠀⣾⣿⣀⣀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⣧⣀⣼⡇⢀⣿⣿⣿⣿⣿⣿⠀⠀⠸⣄⠀⣀⣠⣤⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣟⢶⡀⠀⠀⠀⡼⠁⠀⣰⠋⠉⠁⢸⡇⢐⣿⣿⣿⣿⣿⣿⠀⠀⠀⣽⢫⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢠⠿⠀⢹⡆⠀⡰⠁⢀⡜⠁⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣇⢀⣠⠗⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣦⡿⣄⢀⣀⡼⢀⠔⠁⠀⡎⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⢷⡿⡆⣤⠀⢁⠀⡀⢰⠃⠀⠀⠀⠀⠀⣰⠃⣬⣿⡿⠟⠋⠉⠀⠀⣀⣤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡿⣔⣿⡻⠛⢡⡀⠀⠀⠀⠀⡴⢁⣾⣿⣿⡄⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⠀⠈⠁⠙⠉⠳⠤⠏⢹⣄⣀⢀⣜⡡⢟⣫⣥⣾⣤⣤⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠉⠀⢀⣺⣷⣤⣦⡀⠀⢀⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠸⣿⣏⠀⠉⣷⢀⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠓⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣙⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠁⣠⣤⡄⠈⡿⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⣌⠉⠃⠀⠁⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠛⢁⡄⠀⣿⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⣤⡤⣿⣿⣿⡿⢿⣿⢿⡿⢿⠧⣤⢤⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣝⣤⣻⣟⣧⣣⣧⣤⣧⣼⣬⣴⣮⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠈⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣼⣮⣵⣦⣤⣧⣴⣯⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⢸⣿⣿⣿⡿⠟⠉⠀⠀⠈⣿⡿⠉⠉⠉⠉⠉⠙⢿⡟⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⠇⠀⠀⢀⣀⣀⣀⣼⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⣿⠀⠀⠀⠾⠁⠀⠈⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⠀⢐⡿⠃⠠⢴⣶⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠉⠉⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠈⠘⡀⢀⣽⣿⣿⣿⣿⣿⡀⠀⠀⢸⣇⠀⠀⠈⠉⠀⠀⢀⡾⠀⠀⠀⡀⠀⠀⠹⣿⣿⣿⣿⠿⣏⡐⢄
⠀⠀⠀⠀⠠⠤⣴⣧⠀⠀⣶⣴⡄⠈⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣷⣤⣤⣤⣤⣴⣿⣷⣄⣀⣰⣷⡀⠀⣠⣿⣿⣿⡇⢸⣿⠁⠈⣷⠆
⠀⠀⠀⠀⠐⠒⣿⣿⠀⠀⠘⢻⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠯⢀⣦⣴⣄
⠀⠀⠀⠀⠈⢉⣻⡿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠟⠁⠐⢃⣄⠉⠙⠛⠿⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠋⠉⠉⣉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⠀⠘⡄⠀⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠠⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⢠⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡀⡜⠀⠐⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠉⣐⡉⠈⠀⠄⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠂⠀⠀⠀⠀⠀⠂⠀⡉⠃⠀⠐⢀⠀⠴⠁⠀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣯⣤⣬⣉⣁⣂⡐⠀⠀⠤⠿⠽⠛⠂⠴⢂⣄⣀⣀⣐⣷⣃⠟⠀⢀⣀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠉⠙⠋⠙⠉⠉⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⡏⢹⡅⢰⡊⠁⣀⣠⣄⡉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂⣒⣚⣻⣿⣽⡂⠨⡂⣼⡠⠊⠁⠀⠀⠹⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣚⣋⡭⠭⣖⠀⠆⣼⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠈⠥⠀⢒⣒⣛⡭⠅⢘⠁⡇⠀⠀⠀⠀⢀⠜⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠍⠩⠭⠵⣖⣒⠀⠐⠀⡇⢀⠠⠤⠒⠉⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⣨⡭⠭⠽⣒⠈⠥⢠⡗⢀⣠⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡀⣒⣺⠭⠭⠗⢀⠅⡼⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢂⣴⣾⣿⡟⠡⣡⠞
⠀⠀⠀⢀⣀⡠⠤⠤⣶⠒⠒⠒⢒⣈⣹⣦⣅⡀⠀⠀⠐⠄⠶⠀⢶⣾⣿⡟⣇⣡⣾⣿⣿⣿⣖⠒⠶⠶⠦⢤⣄⣀⡀
⠀⠀⣞⢉⢀⡀⠀⠠⡂⠀⠀⠀⠀⢄⠀⠉⠫⢉⣀⣀⠀⠀⠘⡛⢫⣭⣭⣍⣭⠽⠋⣀⠄⠈⡉⠉⠉⢓⡦⠀⣀⠙⡯⣷
⠀⠀⠈⠓⠿⣟⣒⠶⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣅⣉⣀⣀⣴⣶⣶⣦⣤⡤⠬⠴⠖⣚⣫⠽⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠦⠤⣤⣤⣤⣤⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣤⣤⣤⠤⠴⠶⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣪⣵⣒⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣫⣥⣦⣌⣛⣢⣬⣥⣿⣯⣿⠷⡶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣫⣴⣶⣿⣿⣿⣿⣿⣿⣶⣶⣭⡛⠟⢥⣶⣿⣟⠲⣍⠑⣲⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣋⣥⡖⢌⣿⣿⡿⣷⣾⣿⣷⣮⣭⡙⡻⢿⣿⣿⣧⣬⡉⢛⣫⠻⣿⣯⣉⡳⢊⣩⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠦⣙⣛⠷⣾⣿⣿⣿⠾⣭⡿⢻⣿⣿⣾⣿⣿⣿⠝⠋⣹⣾⣿⣿⣿⣷⢪⣯⡔⠋⣀⡴⢣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⡀⠉⠙⠛⣿⣻⣿⣿⣿⣶⣿⡟⢿⣿⣟⣭⣴⣾⣿⣿⣷⡬⢩⣽⣷⣿⣯⡧⢞⣩⣴⡇⠀⠈⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣑⠦⣌⢁⠂⠢⣎⣿⠀⠉⠓⠮⣍⣛⠁⠼⣿⣿⡙⣻⠉⢛⣻⣧⣼⣿⠿⣾⣧⡶⢛⣩⠞⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠳⣦⣍⣉⠒⠩⢅⣈⠓⠦⠤⣀⠉⠙⠳⢦⣭⣍⣴⠞⢋⡽⢿⡎⣿⣶⣾⣭⠶⢯⡁⠀⠉⠰⣤⣀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣿⣍⢟⢷⡶⢤⣍⣒⠦⣄⣀⠉⠀⠆⠀⠀⠻⠖⣉⣴⢾⣧⣿⣿⣋⣤⠴⠞⠳⠀⠀⠀⠀⠙⡁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡦⢤⣤⣤⣀⠘⢿⡆⠳⢷⡄⠹⣿⣿⣷⢮⣉⠓⠂⠀⢤⡶⢞⣫⣴⣿⣿⣿⢿⡤⠶⠖⠊⣈⣆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣺⣧⣠⢿⣦⡀⠈⠢⣉⣤⣤⠶⠺⡟⠷⠶⣶⣷⣿⡷⠾⢻⣿⣿⣤⡤⡶⠶⣛⣿⠍⠃⣰⣯⣿⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠙⢿⣿⣯⣿⣿⠿⢿⣿⣿⣦⠀⣻⣤⠤⠶⠂⢐⣋⣀⣩⣤⣴⡶⢶⣿⡏⣿⣿⣶⣾⣿⣿⣿⣿⣿⢿⡫⠃⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣮⣟⣿⣿⡑⢶⠶⠶⢛⣻⣿⣭⣿⣿⣶⣿⡿⠟⣿⣁⣽⣿⣩⣿⣿⣿⣾⡿⠛⠁⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣭⣭⠿⠶⠂⣉⣻⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠻⠛⠒⠒⠒⠒⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠦⠤⠤⠤⣤⣤⣤⣤⣤⠤⠤⠤⠴⠶⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣉⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⡿⢿⠙⠶⠖⠀⠀⠈⢛⡄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣌⣀⠠⠀⠀⠀⠀⠈⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⣄⠤⠀⠠⠀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⠆⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⢷⣶⠾⠛⣉⡤⠞⣡⣿⡿⠛⠷⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢡⣾⡟⠁⠀⠿⢤⡼⠥⢤⣴⣿⡿⠁⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⣾⣿⠁⠄⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣯⡀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠈⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠈⢷⡀⠀⠀⠀⣸⡿⠛⢿⣶⣤⣤⣤⣤⣤⣼⣿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⣷⡀⠀⣠⣿⡇⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣀⣀⣀⣀⣿
⢀⠀⠀⠀⠀⠀⠀⣾⣆⢠⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣰⠞⠿⠷⠛⠉⣿⠃⠀⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣷⣴⠞⠋⠉⠉⠉⠙⣿
⣼⡄⠀⠀⠀⠀⠀⢻⡜⠛⣧⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣻⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⡿⠹⡆⠀⠀⠀⠀⠀⢿
⣿⣧⠀⠀⠀⠀⢠⡜⡇⠀⠸⣷⡇⠀⠀⠀⡼⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⡧⠚⠁⠀⠀⠀⠀⠀⣸
⣿⣿⣆⠀⢰⡄⠸⠀⠀⠀⠀⣸⠇⠀⢀⡼⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿
⢹⡟⢿⣆⣺⢷⡜⢦⣀⢀⣠⠟⢀⡴⠋⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠈⣧⣈⣿⣯⣠⣿⡆⠈⢉⠁⠀⢸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⠛⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠘⣿⣇⠙⢿⠙⢿⣀⣿⡀⢀⠘⡴⢀⣴⢆⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡏
⠀⠀⠈⣿⡄⠀⠀⠘⣿⡿⣇⢸⣷⡙⡟⠼⠋⢁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢠⣾⣿⣿⣿⣡⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡀
⠀⣧⠀⢹⣷⡀⠀⠀⢻⡇⠹⣾⡏⢿⡆⠀⠀⣼⠿⣆⠀⠀⠀⠀⠀⢀⡾⠁⣤⣿⡿⠿⠛⢉⡝⠀⡔⣠⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢳⣾⣿⡇⠀⠀⠀⠀⡀⠈⠀⠀⠙⠳⠛⠋⠀⢹⣧⣀⣀⡀⢠⣞⣡⠶⠋⣁⣤⣶⣿⣿⣤⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⡀⠈⠋⠋⠀⠀⠀⢦⣿⣦⡀⢠⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠘⣧⠀⠀⠀⠀⠀⣷⣾⣿⡯⠻⢿⣿⣦⠀⠀⠀⢸⣿⣿⡿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠘⣧⡀⠀⠀⠀⢻⣿⣿⡁⠀⠀⠈⣿⣿⣀⣤⢿⣛⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⢷⣤⣤⣀⠹⠿⠿⠶⣖⣒⣭⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠈⢻⡉⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠙⠷⣤⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣭⣷⣶⣾⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⢤⣤⠤⠖⠒⠦⣄⠀⠀⢀⣠⡴⢚⣛⣓⠒⠒⠲⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠚⣋⣭⠭⠖⠢⡀⠠⡀⠲⣄⣦⣤⠴⠿⠚⠛⠛⠩⠭⠭⠭⠉⠙⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⢀⡠⠤⢀⡠⠈⣂⣼⡶⠞⠛⠉⠁⠀⢠⠴⠖⠒⠒⠒⠛⠋⡉⣹⣷⠀⠆⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⢤⣮⡤⠴⠶⠛⠋⠉⣀⡤⢖⡿⢿⠃⡀⡿⠚⠉⠓⠲⠾⠿⢷⡞⣏⡟⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡴⠞⠋⠁⢀⡴⢀⡤⢖⣋⣥⠞⢋⠠⣼⠀⡇⡇⠀⣀⢤⠲⡝⢄⡟⠁⣿⠃⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⡠⢒⣠⡄⡼⣰⡿⠼⢧⣤⣑⣝⣷⣗⣧⠀⢳⠃⣘⢎⢦⠳⡈⣼⠀⠈⡿⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣻⡿⢋⡴⢋⣴⣿⡿⠑⠃⣀⣀⣀⣀⣀⠉⢉⡙⠛⡏⠀⠘⠦⣌⡮⠦⠤⣤⣏⣀⡸⠃⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠐⣫⠟⠀⢀⡴⣫⢛⢿⡇⠀⢰⢿⡿⠿⣈⣉⣉⡉⢹⠀⠁⢀⡽⠭⣤⣐⣒⣒⣂⣀⡀⠀⡀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣰⠋⡀⣠⢯⠞⡰⢃⣾⠀⠀⣼⣿⠁⠀⢀⡤⠀⠀⢹⠀⠀⣸⠶⠤⣤⣄⣉⠭⠭⢯⣽⣧⠁⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⡼⢣⠎⢰⡃⢯⣤⣀⣁⡏⠀⠀⡏⣿⠀⠈⣁⡤⠖⠀⡏⡘⠀⡏⢀⡴⠚⢀⠈⠉⢹⢻⣿⡘⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡾⡱⢃⣤⣤⣍⣉⠉⢛⡛⢡⠇⠀⣧⣏⣰⣊⠁⡠⠀⢠⠇⡇⢀⡗⠉⣠⠞⠁⠀⠀⡞⠘⡇⡇⡏⣿
⠀⠀⠀⠀⠀⢀⣴⠞⣫⡟⠁⢠⠟⣿⣛⡛⠿⠛⠲⡄⢸⠀⣐⣎⣭⣍⣉⡉⠓⠒⠊⢠⠀⠘⣧⣾⣥⣖⡁⠀⢸⠇⢸⢳⢀⡇⡇
⠀⠀⠀⠀⢠⡞⣡⣶⠟⠀⣰⠏⡾⠋⠉⠉⠉⠉⢻⠇⠈⣼⢳⠶⣞⣉⣉⣉⣛⠛⣧⠈⢀⡦⢤⣄⣀⣉⠙⠓⠚⠒⠋⠸⢸⣧⡇
⠀⠀⠀⣰⠟⠐⣵⠋⡐⣰⢏⡜⢁⡤⢊⣠⠖⠁⣸⠀⠀⣏⡞⠁⠀⢀⡴⠂⠀⠉⡏⡀⢸⣤⣤⣄⡠⠭⠽⠿⠟⢙⣷⠀⢸⣼⠃
⠀⠀⢠⡟⠀⣾⠃⢰⢡⢏⠞⠴⢋⡴⠋⢀⡴⠊⡇⣰⢠⡟⡇⢀⡴⠋⢀⠄⠀⠀⣇⡇⣿⠀⠀⠈⢉⣹⠿⡛⢻⡿⣼⠀⢸⣿
⠀⠀⢸⠇⢠⡇⢠⠇⣿⡟⠀⠀⠀⢠⠖⠁⠀⢰⢇⣧⢻⣧⡇⠈⢀⡴⠃⢀⡀⠀⣿⠁⡇⢠⠴⠚⣩⠔⣋⠀⣿⡇⡟⠀⣿⡏
⠀⠀⣿⠀⢾⠃⠼⠀⠛⠶⠶⠶⠶⠶⠶⠦⠤⠞⠈⡽⡸⣿⡃⡴⠋⠀⠀⠋⠀⣸⢿⢰⡇⠀⠀⣩⠴⠋⠁⢸⠟⢀⡇⢀⣿⡇
⠀⠀⠹⣦⣼⣶⣖⣒⣛⠿⠶⠤⢭⣭⣤⣀⣖⣒⣚⣁⣓⠚⠛⠛⠿⠷⠶⠖⠛⠁⠀⠈⣇⠴⠋⠁⠀⠀⠀⢸⠀⣸⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠓⠒⠶⠶⠾⠭⢭⣭⣭⣉⣉⣉⣛⡛⠛⠛⠒⠒⠒⠚⠛⠯⢍⣉⠉⠛⠛⣒⣃⣀⡞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠓⠒⠶⠶⠶⠤⠤⣤⣤⣤⣤⣭⣭⣤⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢀⡄⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣴⠏⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢿⣆⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠈⢿⣦⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢻⣇⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⠏⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⠋⠀⠀⠤⠤⠫⠤⠀⠀⠀⢉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢂⣉⣩⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣌⣉⣁⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⡷⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⢸⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡠⠊⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠐⠉⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠡⠤⠤⣔⣂⠁
⠀⠀⠀⠀⡤⠒⠊⠉⣁⣤⣴⣶⣶⣾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣶⣶⣶⣦⣤⣈⠉⠑⠒⢤
⠀⠀⠀⠀⠑⠢⠤⣀⣉⠛⠻⠿⠿⢿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⣉⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⢖⡐⠒⠀⠤⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠄⠀⠒⢂⡲⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠒⠂⠀⠀⠀⠀⠒⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⠝⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⢞⠡⠊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡍⢰⢣⡇⠊⠘⠯⠭⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢈⠁⢠⠀⠳⣌⡑⠒⠒⠒⠒⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣆⠈⠣⣈⣒⣭⣯⣍⡉⠑⢢⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡖⢆⠱⣄⣸⣦⣤⣸⠋⠉⠉⢻⣿⡆⣮⡵⣦⣽⠶⣦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣁⠺⢯⣽⣿⣾⡇⠀⢹⣿⡗⡀⢀⣼⣿⢷⣿⣷⣿⡟⣖⡥⢚⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠉⠙⠻⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣯⢩⣿⣾⡿⢗⣫⣴⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣑⠀⠄⣰⡾⠠⣈⡉⠛⠥⣜⡻⠧⠝⣢⠭⣿⣾⣟⣻⣷⣫⠴⢃⠀⠀⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠈⢿⣗⢶⣬⣅⣂⠄⣉⠐⠀⠍⠉⠹⠅⢊⣵⣿⣿⣟⣋⡤⠲⠀⠉⠳⣄⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠦⢤⠤⡌⢻⡎⠻⢆⠻⡿⠷⢮⣁⡂⠀⠶⣞⡭⣾⣿⡿⠯⠗⠒⣉⡆⠀⢀⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣿⣶⡀⢰⡖⣖⣉⠙⠙⠛⠟⢛⣋⣭⣿⣷⣞⣿⣭⣟⣵⣤⡿⠟
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈⠛⠿⣿⣯⣽⣿⣿⡦⣭⠤⠶⣶⣾⣿⣯⣿⡿⢿⣃⣿⣟⣿⣿⣿⠟⡫⠒⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣷⣿⣿⣿⣿⡯⡽⠟⠒⣈⠽⠟⡛⠩⠅⠂⠁⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⣀⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠘⡤⠔⠀⠉⠉⠉⠉⠉⠁⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣀⢀⣀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣠⡟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢸⠀⠀⠀⠀⠠⣄⡀⠀⠀⠤⠄⠒⣩⠏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢻⠀⠀⠀⠀⠀⢀⠶⢆⡀⣀⠰⠚⠁⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠖⠓⠀⠤⠤⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⢌⡦⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠻⣦⠈⠡⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⢶⠶⠶⠶⠆⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠘⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⠔⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢋⡆⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⠏⠦⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠰⠀⠳⣄⠀⠀⠀⣀⢠⠔⠒⡝⠁⠈⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠈⠷⠐⠊⠁⠀⢀⡠⠟⠲⠦⣤⣀⡀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⠱⣤⡜⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⡠⠛⠻⠉⠉⠉⠁⠀⠀⠈⠒⢄⡀⠀⢀⠞⠀⠈⠙⠃⠤⠤⠌⠿⠿⣧⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠙⠓⠤⣀⣀⣀⣀⣀⣀⣀⡀⠀⡨⠛⢷⣄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢈⣳⣤⡚⢠⡄⠀⠀⠀⠀⠀⣤⣤⣤⡀⣀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠒⣒⣖⡚⠛⣻⣿⡛⢻⣿⣖⠒⠒⠖⠲⠚⠷⠲⣶⣶⡶⠶⣶⣶⡿⢵⣶⣤⢶⣤
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠘⠋⠉⠃⠈⢉⠉⠃⢹⣏⣹⠃⠀⠀⠀⠀⠀⠰⣿⣽⣿⢺⣿⣹⡿⢺⣯⣽⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡦⠤⠴⣦⠤⠤⠤⣤⡤⣥⣤⣤⣤⠤⠤⣤⣤⣤⣬⢭⣥⣤⣭⣭⣥⣬⣭⣉⣠⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⢠⣀⣀⣠⣘⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣻⣯⢸⡇
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠐⠒⠚⢦⠔⡄⠤⠀⠀⠀⠤⠄⠤⠤⠤⠤⠤⠤⠤⢤⣤⣄⠀⠀⠈⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠰⣆⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠍⢹⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⢘⣄⠀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠭⠥⠤⠬⠤⠤⠤⠤⠤⠤⠤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠓⢤⣤⣇⠀⠱⢦⣄⠀⠠⣄⡀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⢀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠛⠓⠒⠚⠛⠛⠛⠒⠛⠓⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃

⠀⠀⠰⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠈⢻⣷⡀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣬⠀⣥⡀⠐⠄
⠀⠀⠀⠀⢻⣷⡄⠀⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡤⣿⣦⢤⣀⠀⠀⠀⢶⡤⠄⠂⢆⡀⣀⢀⡀⠰⠠⢰⣶
⠀⠀⠀⠀⠀⢻⣿⣆⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠒⠒⠀⠀⢑⡏⣦⣄⡾⡆⠀⠀⠘⣷⠞⠛⡈⠉⠉⠉⠁⠘⠲⢾⠃
⠀⠀⠀⠀⠀⢀⣗⣈⣽⠟⠳⣀⠀⠀⢠⣤⣒⣀⣲⣇⠈⢩⠭⠙⠠⠿⠧⠤⠶⢼⣿⣾⢿⡏⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠚⣓⣦⡀
⠀⠀⠀⠀⢰⡟⠉⢻⡇⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡀⠙⠀⠀⠀⢰⣿⣴⠃⢸⣿⣿⣿⣿⡏⠻⣿⡄
⠀⠀⠀⠀⠀⠿⠆⠀⢻⡆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⣿⣿⣄⡈⠻⢭⣵⠿⠁⣀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⡄⠀⠀⠀⠀⠀⠀⢈⠙⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣝⠋⠀⠀⠛⠻⠗⠉⠒⠂⠀⠒⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⠄⠀⠀⠀⠀⣠⣤⣻⡟⢙⡶⣤⣤⣤⣴⣤⣤⣤⡴⢾⡙⢿⣳⣥⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠴⠲⣭⠗⢓⡀⠱⡆⠈⢆⠀⠀⡰⠟⠛⠻⡱⠛⠳⠋⠀⢡⣿⣷⡈⠈⠱⠞⠳⣜⠛⠛⠿⡄⠀⠀⠀⠀⠈⠀⠀⠀⢀⡄
⢀⣶⠲⡀⠀⢼⠀⣛⡀⢘⠂⠀⠹⣤⠈⢆⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⣿⡾⣇⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠔⢲⣿⣂
⠀⢶⣖⣧⠀⠘⡆⣿⣿⡼⠀⠀⠀⠸⡆⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢣⢴⣿⡟⡘
⠀⠀⢻⡛⣄⠀⢹⡟⢻⠃⠀⠀⠀⠀⢡⠀⡈⠆⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣾⡷⢇⡷⠄
⠀⠀⠀⠹⣿⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠳⡐⣨⠀⠀⠀⠀⢻⡽⣛⢛⣚⣛⣛⢛⠛⣟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⡿⡑⠁
⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⣯⣤⠈⠋⠹⣟⣠⠀⠙⠋⣧⡵⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡟⠋
⠀⠀⠀⠀⠀⣠⣾⡿⡻⣳⣤⣤⠤⣤⣄⠀⠀⠻⠀⠀⠀⠀⠈⢷⣀⠀⠀⠙⢉⠀⠀⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡔
⠀⠀⠀⣠⠞⠉⠀⠀⠀⠘⠯⣿⣆⠀⠈⢻⢿⡆⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣿⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡌⠀⣠⢦
⠀⠀⢰⡇⠀⠀⠀⠀⠀⢢⠰⠟⢿⢿⣶⣾⠋⣷⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡴⠀⢎⠷⣾⠀⠀⢀⣤
⠀⠀⣾⠀⠀⠀⠀⡴⠀⠸⣣⡶⣾⡽⠹⣿⣶⣄⡇⠀⠀⠀⠀⠀⠀⠈⣿⣖⣺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠵⠁⠀⠈⣧⣬⣸⣿⠿⣿⠟
⠀⠀⢿⠀⠰⢠⡼⠁⢀⣿⡿⣿⡿⠁⣠⣬⣿⡿⣧⠀⠀⠀⠀⠀⠀⠸⣏⣁⣉⣿⠂⠀⠀⠀⠀⠀⠀⣀⣼⠷⠀⢸⣏⢩⡝⣯⠵⣚⢦⠹⠆
⠀⠀⢈⣧⣕⣶⣾⣞⣯⠛⠈⡴⠞⠀⢝⣿⢏⣤⡼⠀⠀⠀⠀⠀⠀⣠⠋⠛⠛⢳⣀⠀⠀⠀⠀⠀⠀⣽⣿⠷⠀⠈⠙⠲⠤⣶⣿⣷⣦⣤⡀
⠀⠀⠸⢿⣞⣓⣻⣞⣶⣦⣴⡇⠀⠀⣠⡀⢈⣣⠁⠀⠀⢰⣶⣶⣯⣡⡆⠀⠀⣷⣝⣷⣒⣶⠄⠀⣸⣿⠇⠀⠀⠀⠀⣠⠤⣼⡿⢟⣫⡰⡇
⠀⠀⠀⠀⠻⣿⣿⣿⣯⠝⠻⣷⣿⡞⣏⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠻⢧⡀⢀⡿⠛⠉⠉⠁⠀⣰⣿⠏⠀⠀⠀⢴⢻⡷⢿⢟⣛⣬⠞⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠉⡧⠀⠀⠈⠃⡟⢹⢷⢴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢏⠀⠀⠀⠀⠯⢅⣿⡒⠋⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠤⣀⡀⡁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢠⣤⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⢀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠉⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠚⠓⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡞⣆⣀⣄⡀⠀⠀⣀⣀⠀⠀⠀⢬⣽⣿⡿⠀⠀⠀⠀⠀⢶⢶⢶⡆⠀⡀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠾⠁⠀⠉⠀⠀⠈⠋⠉⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠛⠃⠀⠀⠀⠀⢰⣷⣿⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠉⠉⠉⠀⠀⠀⠀⣀⣀⣀⠀⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢋⠀⠀⠀⠐⠀⠀⣀⢀⣰⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠈⠀⠀⠀⠀⢠⣿⡟⠛⠛⡛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠁⠙⠋⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿
⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣶⡶⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣷⣭⣷⣶⣶⣶⣶⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠊⠁⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⣀⣀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠑⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠔⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠊⠁⠯⠽⠭⠇⠤⠀⠿⠿⠼⠵⠸⠥⠁⠸⠿⠫⠼⠯⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠁⠀⠀⠀⠀⠈⠶⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛⠂⠀⠀⠀⠢⣤⣀⣠⣴⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠙⠢⢄⣀⡀⠀⠀⢀⣀⣠⠟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠅⠠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢁⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⠒⠂⠀⣀⠄⠀⠀⣀⡄⣀⡤⠞⣹⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⠀⠈⠉⠁⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⣉⠙⠛⠛⠉⠁⠉⠁⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢅⣀⠤⣤⢤⣤⢤⡤⠼⢑⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⡄⠀⠜⣀⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠼⡇⠂⠀⠒⠒⠒⠒⠂⠀⠐⡁⠀⠠⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⠜⠉⡤⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡖⠂⠉⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠢⣀⡠⠆⠀⠀⠀⠀⠀⠀⡠⢶⠁
⠀⠀⡀⠀⠠⠀⠀⠀⠀⠇⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠀⠀⢀⣀⠀⠀⠀⠀⠑⠢⢄⣀⣀⣀⣀⣀⣤⣤⡲⠯⠖⠋
⡀⢀⡍⠀⠐⠒⠒⠂⠀⢸⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⢀⠀⣤⢯⡑⢢⣀⠀⢀⡔⠙⣏⡙⠉⢹⠏⠀⠀⠙⣄⠀⠀⡀
⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡦⢀⢀⡀⠀⠀⡀⠀⣀⠠⠤⠌⠀⠠⠀⠘⢯⣻⠄⠈⠒⠚⠳⠆⠀⠀⠉⢹⠀⠀⠀⠀⡇
⡇⠠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⠠⠀⢀⠀⢀⡀⠀⢀⠤⢄⠀⠀⢀⡤⠴⠖⠊⠷⠀⠚⠀⠘⠒⠲⠤⢄⣸⠒⠤⣀⡴⠁
⡇⠀⠈⠦⠤⢤⠤⠤⠴⠏⣄⠀⠀⢩⠀⠀⠀⠁⠀⡯⠉⠐⠅⢤⣀⠀⠀⠘⡄⠀⠈⠁⠠⠠⠠⠄⠀⠀⣀⡤⠞⠋⠀⢠⣧⡴⢲
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣟⠀⠀⠀⠐⡬⠤⣈⡤⠼⡆⠁⡀⠀⠀⠀⣺⠌⠉⠀⠀⢀⣠⠔⠉⢹⣤⠶⠥⠤⠤⠤⠤⠤
⡇⠁⠈⠁⠀⠉⠁⠉⠉⠉⠉⠁⠈⠈⠉⠁⠁⠁⠁⠉⠐⡀⠀⡌⠁⠉⠉⠁⠉⠁⠐⠠⠄⢀⣀⠳⣊⣤⠤⠚⠉⠀⠀⠀⠸⡎⡅⠉⠁⠉⠉⠈⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖
⡇⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠉⢹⠃⠀⠒⠂⠒⠁⢧
⡇⠀⠀⠀⠀⠀⠈⠉⠒⠂⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄
⠧⠤⠤⠤⠤⡌⠀⠀⠀⠀⢨⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡔⠉⠑⠲⠤⢤⡼⠀⠀⠀⠀⠀⠀⠀⢣⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢣⡀⠀⠀⠀⢀⠷⠤⣄⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠐⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⣄⠀⠀⠀⠉⠉⠐⣒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠂⠉⠁
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠐⢀⡔⢄⠠⠄⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣴⣿⠦⠅⢀⠺⣿⣟⠒⠀⣔⠻⢿⡁⢀⡄⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢥⣾⣦⣉⠂⡰⢿⡟⠂⠈⣁⠻⢿⡓⠀⣰⡿⣁⠮⣿⠇⠀⢠
⠀⠀⠀⠀⠀⠀⣴⣿⡦⣰⣄⠐⠬⣕⠀⢼⣿⡦⡈⣉⠼⣿⠓⠀⢁⣾⠏⢰⡿⠶⠌⢁⡐⢿⣇⠄
⠀⠀⠀⠀⠀⢰⡆⢀⣜⠻⢿⣙⠐⣰⣍⡒⠬⣉⠱⢿⡗⠄⠉⣰⡿⠃⣼⣬⠙⠒⠠⣿⡟⠢⡄⢠⡘⢇
⠀⠀⠀⠀⠀⠀⠡⣿⣿⣿⡦⣠⣌⠻⠇⠉⣠⣞⠛⠂⢬⣠⣾⠋⢰⣄⠙⠂⢀⣬⡷⠬⠉⢀⠶⣿⠓⢆⠠
⠀⠀⠀⠀⠀⠰⣿⣦⡉⢉⠰⣿⣿⡃⣠⣦⡙⠻⡍⣠⣶⡿⠛⠦⣍⠀⠀⣀⣲⠌⠁⠀⢤⣾⠷⢬⢉⡁⣶⠃
⠀⠀⠀⠀⠀⠀⢿⠗⣵⣿⣷⠄⢉⡕⠿⡏⠈⠀⣠⣿⠟⠁⠾⠁⠀⠙⠲⢌⡃⠀⢀⣼⣦⣍⠓⠠⣾⡿⠆⡆
⠀⠀⠀⠀⠀⠀⠡⣄⠉⠙⠛⣷⣾⠋⠁⠀⢈⡘⠛⢁⣼⠓⠀⠀⡀⠂⠓⠢⠈⢑⠮⣙⠢⢀⣴⡷⢦⠉⢠⡇
⠀⠀⠀⠀⠘⢀⠀⠈⡧⢠⣾⣷⣌⡓⠄⡰⡿⠁⣾⡦⠉⠀⠠⣴⡟⠂⠀⢀⠠⣾⣷⣦⢙⡶⢮⣝⡂⣀⡹⠁
⠀⠀⠀⠀⠀⠈⠳⠀⠀⠋⢻⣿⣮⣡⣾⠟⣄⠘⠿⣀⠀⣠⣷⣬⡁⠂⣴⣿⠓⠀⠉⣑⠻⣿⣷⢀⠛⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣻⣿⡿⢃⣴⣿⡷⠂⠀⣌⠻⠿⢤⢄⣼⣧⣌⠑⠠⠾⠟⠓⠃⢀⣿⣦⣿⡅
⠀⠀⠀⠀⠀⠀⠐⠆⠑⢾⣿⣿⡿⠀⠁⠀⠉⠳⠂⣾⠿⠛⠓⠄⠚⠉⠀⠈⠱⠂⠀⣴⣦⣀⣾⢿⣍⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣿⡟⠁⠠⣄⠀⢀⣠⡀⠀⠀⢀⣄⠀⠀⠀⢠⣶⣀⣀⣼⢿⡟⠛⣩⡿⠛⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡀⠀⠉⠉⠁⠉⠲⠶⠛⠉⠓⠶⠶⠛⣍⠉⠉⢁⣸⠟⠛⠉⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⠒⠂⠠⠶⠤⣀⣀⣠⣴⣄⣀⡤⠴⠟⠓⠚⠉⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠀⠀⠈⠉⠉

⠀⠀⠀⣀⡤⢤⣄⡀⠀⠀⠀⠀⣀⠤⢤⣄⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⢀⡤⠤⢄⡀⠀⠀⠀⠀⣀⡤⢤⣄
⠀⠀⡜⠁⠀⠀⠀⠙⠄⠀⠀⡎⠁⠀⠀⠀⠱⠀⠀⢠⠋⠀⠀⠀⠈⢣⠀⠀⡰⠉⠀⠀⠀⠈⡆⠀⠀⡞⠁⠀⠀⠀⠑⡄
⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢠⠀⠀⠸⡀⠀⠀⠀⠀⡸⠀⠀⢡⠀⠀⠀⠀⠀⡆⠀⠀⢄⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠓⠤⠤⠔⠋⠀⠀⠀⠈⠂⠤⠤⠐⠁⠀⠀⠀⠙⠢⠤⠤⠚⠁⠀⠀⠀⠑⠠⠤⠔⠊⠀⠀⠀⠈⠒⠤⠤⠔⠁

⠀⠀⠀⣠⠤⠠⠤⡀⠀⠀⠀⢀⡠⠄⠠⢄⡀⠀⠀⠀⢀⠤⠄⠤⢄⠀⠀⠀⠀⣀⠤⠀⠤⡀⠀⠀⠀⠀⡠⠄⠠⠤⡀
⠀⠀⡜⠀⠀⠀⠀⠈⠄⠀⢀⠎⠀⠀⠀⠀⠐⠀⠀⢠⠁⠀⠀⠀⠀⢡⠀⠀⡘⠁⠀⠀⠀⠈⠂⠀⠀⡎⠀⠀⠀⠀⠈⡄
⠀⠀⢇⠀⠀⠀⠀⠀⠆⠀⠀⡄⠀⠀⠀⠀⢀⠁⠀⠸⡀⠀⠀⠀⠀⡸⠀⠀⢣⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠑⠀⠀⠐⠈⠀⠀⠀⠈⠂⠠⠄⠐⠁⠀⠀⠀⠈⠂⠤⠀⠊⠀⠀⠀⠀⠑⠠⠄⠀⠊⠀⠀⠀⠀⠀⠠⠄⠐⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠄⠔⣀⡠⠤⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠁⣀⡨⢄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠠⠊⠀⢰⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠁⠀⡀⠸⠈⡁⡇⡠⠀⣠⣔⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠃⣀⢵⣄⠀⠃⢞⡈⢉⡽⠠⠔⠁⠀⠉⠉⠉⠉⠉⠁⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⣚⠳⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠈⠉⠀⠒⠤⠄⡀⠀⣀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣼⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⢊⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢑⠃⡠⠃⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⡀⠑⢌⡠⢁⣳⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠁⡀⡈⣿⣛⡠⠊⠁⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣉⠀⠐⠲⠖⠀⠉⠀⣰⢿⡵⡂⢠⠆⠀⠀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠑⣔⠀⠀⠀⠀⢀⡷⢛⡗⢞⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⢄⡀⠅⠋⠘⠤⠊⡶⢯⡶⠛⠹⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠈⠦⣙⣀⢠⠛⢄⠊⢃⠸⢷⠆⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣿⠀⠆⡡⢚⠀⣆⠤⠢⠊⡜⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠢⠀⠠⠔⠂⣡⣂⣤⣤⣾⣽⡾⠷⠔⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠒⠛⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢀⡾⠃⠀⠀⣴⣿⣁⠀⠀⠀⠀⠀⠀⠀⣀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⢸⣿⣿⠀⣀⣴⡿⠁⢀⣠⣾⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣌⣿⣿⣾⣿⣿⣷⣾⣿⣿⣿⣿⣻⣿⣿⣷⣶⣼⣿⣿⣿⣿⡏⠉⠁⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠈⠉⠉⠙⢷⡙⣢⣄⣹⣿⣿⣿⣤⣄⣀⠀⠀⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢿⣦⣸⣦⡀⠀⠀⠀⠀⣿⣿⡏⣹⢦⢀⣹⣦⣀⣀⣴⣶⣬⣿⣿⡿⠿⠿⠏⠀⠉⠛⢿⣿⣶⣤⣈⠻⣦⡀
⣷⣦⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡿⠷⠿⢻⣇⣿⣿⡟⠉⠛⠿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣷⣿⣟⣻⣿⣷
⠉⠛⢿⣶⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠂⠀⠀⠀⠹⡿⣗⣀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠉⠉
⠀⠀⠀⢹⡿⡟⣷⣦⣄⡀⠸⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠠⠀⠄⠀⠃⠙⠿⢳⠀⠀⠈⢿⣆⠀⠀⢀⢴⣵⠟⠉
⣴⣄⠀⠀⠀⢈⣽⣿⡿⠋⠛⠋⠻⠿⢿⣿⣿⣿⣄⣀⣀⣴⠟⠉⢶⣤⡀⠉⠆⠉⢓⠀⠈⣿⣆⣴⣽⡟⠁
⡿⢿⣆⣴⣦⠀⠀⠞⠁⣀⣀⠞⠁⠐⠛⣿⣿⣿⣷⣿⣿⠿⢴⣏⢙⢦⣈⣿⠶⠶⠞⠛⠿⢮⣿⣾⠋
⠁⠈⣿⡿⠹⣷⡾⢶⣿⣉⣿⡄⠀⠀⠀⣨⣿⣿⡏⠀⡽⠀⣸⠈⢿⡤⡽⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⡀
⠀⠀⠈⠁⠀⣈⣀⣿⣿⣿⣿⣿⣾⣦⣼⡿⠛⠛⠀⣶⠃⢴⡛⠷⡄⠘⠓⠶⠂
⢀⣤⣶⡿⠟⠛⢛⡿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠳⣄⠙⠺⢾⣷⣞⣷⣋⠁
⡿⠛⠁⠀⠀⠠⣞⣇⣀⠈⠉⠉⠛⠻⡟⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡿⠉⠉⢳⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣠⡾⠋⠀⠀⢀⡜⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠙⣿⠀⢀⠞⢻⣿⣆⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣷⠀⢰⡀
⠀⠀⠀⠀⢹⣿⠘⠀⠈⢻⣟⣷⣄⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢠⣿⠀⣿⡇
⠀⠀⠀⣠⣺⣟⣠⣷⡄⠀⡌⠻⢯⣷⣄⠀⠀⠈⠓⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡾⠛⠓⠛⣻⣼⣿⠇
⠀⠀⠀⠙⠀⠀⠽⣴⠟⣠⣛⡿⣦⠈⠻⣷⣄⣀⣶⣾⣿⣿⡦⣀⠀⠀⠀⣠⣾⢤⣸⣿⣿⣟⡁⣉⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣿⣿⠀⢠⣬⣿⣿⣿⣿⣿⣟⡀⠀⠉⠙⠋⠉⢹⠿⠧⣀⣿⠛⡿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣤⣀⡤⠤⢤⡀⠀⠀⠀⠙⠆⣰⠿⠃⠀⠀⠀⢀⣶⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢱⠀⠀⢀⡀⠀⠀⢠⡞⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⠀⠀⢸⣧⠀⢰⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢧⡉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⡴⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⠃⠀⠀⠀⠚⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠈⠲⠤⠞⠋⠛⠿⠿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠈⢧⣄⣀⣠⡞⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⢀⣤⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⡂⠀⠀⢸⣧⣤⣤⣤⣄⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣿⣿⣄⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⢸⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡿⣿⣿⣿⣷⡀⠀⠀⠛⠻⠛⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣇⣽⣿⣿⣿⡇⠀⣀⣀⣀⢀⣀⣀⠀⠨⣿⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⡿⠁⠀⢨⡟⣱⣿⡇⠀⢿⣿⣿⣿⣿⣿⠁⠈⣿⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣷⠀⠀⠀⠁⠙⢿⡇⠀⠀⠛⠻⠿⠛⠁⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣾⡇⠀⢀⠀⠀⠤⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⡇⠀⢈⠀⢁⠀⠆⠀⣠⣴⣿⣤⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⢠⣄⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠙⠻⠟⠛⠁⠀⠀⠀⠙⠛⠟⠋⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⡿⣱⣿⣿⣿⣯⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⢣⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⢿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣤⠀⣀⣷⠀⢠⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⢻⣿⣿⣿⣿⡿⠿⢶⣿⣿⣤⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⣿⣿⣿⣿⡇⠠⠼⢠⡀⡇⠰⠆⢘⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣇⣀⣿⣷⣾⣧⠀⠀⢸⣿⣿⣿⡇⢰⣾⣈⣁⡇⠀⣄⢘⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⡟⠛⡟⠛⠛⢻⡿⢿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⡇⠀⣇⠀⠛⢻⡆⠘⠀⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣵⣿⣿⣿⣿⣿⣇⠀⣿⠒⠃⠸⡇⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠙⢿⣿⣿⠿⠿⣟⣛⢩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣷⣾⣷⣿⣿
⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣵⡞⠀⠀⡶⠶⢿⣿⣿⣿⣶⣝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⠿⠛⢉⠀⠛⠻⠿⠟⠢⣄⠁⠀⢸⣿⡿⣿⣿⣿⣿⣶⣌⡉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢁⠀⠸⢿⣿⡿⣿⡏⣿⣻⣿⣧⣶⣦⣄⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢳⡀⢸⠀⠀⠀⣿⡇⣾⠃⣿⡏⠉⠀⠙⢻⠹⣧⡀⠀⠀⢰⡹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⣷⣼⡇⠀⠈⠋⠁⠁⠀⠈⠁⠀⠀⠀⠀⠀⢿⣿⣦⣶⠈⣧⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢻⣿⣇⡠⠁⠀⠀⠠⠤⠈⠁⠀⣄⠀⢰⡀⠸⣿⣿⣿⠀⣿⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠘⣿⣏⠀⠀⠀⠀⠒⠀⠀⢰⣾⣿⣷⣜⠃⠀⢿⣿⣿⢀⠇⡀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣶⣦⡀⢀⣴⣿⣿⣿⣿⣿⣦⠀⠸⣿⡿⢀⣼⡇⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣷⡀⠻⠇⣸⣿⣷⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠉⠙⠻⣿⣿⡿⠋⠀⡟⠀⠻⡿⢋⡔⠀⠘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⣿⣿⣿⠀⠀⣾⠀⣉⠁⢀⣼⠃⠀⢀⠀⠙⢀⡀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠈⠁⢀⣿⡿⠿⠀⣸⣿⡇⠹⣷⣾⠃⠀⠀⣾⣦⠀⠈⠻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣉⣥⣶⣿⣶⣿⣿⣷⡄⢈⣁⠀⠀⣸⣿⣿⢸⣆⠀⠘⠿⢿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣧⣼⣿⣿⣿⣾⣿⣇⣄
⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠋⣿⡇⠀⠀⠀⠀⠀⠀⢰⠞⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⣿⣿⡿⣹⣿⣦⡀
⠀⠀⠀⠞⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⢋⣽⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⣿⣿⣿⣧⣿⣿⣿⣿
⡶⠋⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠘⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢹⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣄⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢃
⠀⠀⠐⠀⠤⠀⠒⠈⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛
⣿⠀⡆⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠠⠀⠀⡄⡤⠠⠄⢤⠤⠤⠠⠤⠄⠠
⣿⠀⡇⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢰⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠏⡏⢰⣀⣀⣀⣺⡗⠀⡆
⣿⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡇⠀⠀⠀⠠⢸⡿⠀⠀⠀⢶⠀⠀⢳⢀⠛⣛⠛⣿⡇
⣿⠀⣧⠀⠀⢸⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⡿⠃⠐⣿⣷⣧⠀⠰⠰⢾⣷⠀⠀⠀⢹⢰⡤⣾⡇⣞⠿⠻⣿⡇
⣿⠀⣿⠀⠀⢸⡅⠀⠀⠸⡇⠀⠀⠀⠀⠀⠸⠋⡁⣉⢹⠟⠙⠁⢤⡀⠺⣿⢀⢀⠀⠼⠾⠈⠿⠿⠀⠀⠘⠿⢧
⣿⠁⡉⣀⠈⠿⠑⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⠟⠛⠟⠛⠟⠛⠛⠿⠛⠛⢻⠈⠈⠿⠿⠿⠿⠿⠿⠟⠟⡿⡛⠻
⣿⠀⠃⠀⠠⣄⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⢸⣦⠀⠀⣠⣤⡄⠀⢠⠀⣤⣤⠀⠀⠀⠀⢄⣠⠄⠀⠀⠀⠆⡇⡀
⣿⢤⡅⣈⠀⠈⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡿⠄⠠⣿⣯⣇⠀⢺⠄⢸⡷⠀⠀⠀⠀⠞⢷⠀⠀⠀⠘⢁⣻⡀
⣿⢄⡀⠈⣶⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⢘⡇⠀⠀⣹⣿⢹⠀⠀⠀⢘⠃⠀⠀⠀⢤⣠⣀⡠⠀⡇⠀⢴⣿⡷⠀⠇
⣿⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠃⠀⠀⠚⠛⠛⠀⠀⠀⠘⠃⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⠃
⣿⠀⠀⠀⢠⠀⣄⣀⠀⠀⠀⢸⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⠀⠀⣧⣢⣠⣁⠀⠀⣠⢼⣄⠀⠀⠉⡟⠉⠉⠉⠻⠈⠉⠉⢹⠉⠉⠉⠹⠋⠉⠉⠙⡏⠉⠉⡉⡏⠉⠉⠉⠿⠉
⣿⠀⠀⠀⡇⠙⣅⢸⣕⢦⡷⣏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠻⣄⡀⢀⣀⠀⠀⠀⣾⣿⡇
⣿⠀⠀⠀⢸⠺⠏⡀⠤⠌⠓⣿⠀⠀⠀⡐⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⢸⠃⠀⢻⡛⠉⠘⠃⠁⠀⠉⠉⣁⡀⡂
⣿⢀⣀⣀⣙⣀⣙⢀⣀⣘⡋⣈⣀⣀⠠⣧⢀⠀⠀⠀⠸⠀⠀⠀⡀⢀⢸⠀⠀⢸⡇⠠⣾⠀⠀⠒⠲⣶⣿⡇⣷⠆
⣿⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⣶⠔⡄⠀⠘⠀⠀⢸⡇⡤⢷⠀⠀⠀⠀⢉⣿⡇⡇
⣿⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⣶⣤⠀⠠⣤⣤⣶⢀⡀⣸⡗⠊⢀⢨⡇⠀⠀⣾⣿⡅⣀⣀⠀⠀⠀⢀⣨⣷⣆⡆
⣿⣬⣤⣥⣥⣤⣤⣬⣬⣭⣥⣥⣤⣤⣭⣭⣥⣤⣤⣥⣤⣤⣤⣭⣥⣤⣤⣤⣄⣠⣤⣄⣬⣭⣤⣤⣤⣤⣤⣬⣭⣤⣬
⣿⠀⠰
⣿
⣿⣤⣤⣤⣤⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠈⢷⡄⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⠎⠐⠀⠀⠀⠀⠀⠀⠙⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣟⠈⠻⠟⠒⣶⣢⠀⠀⠀⠀⠀⠀⣠⡾⠑⠚⠋⠀⠀⠉⠉⠙⢢
⠀⠀⠀⢀⡞⠀⢀⣠⠀⠀⠠⢄⡀⠀⣿⣷⠴⢆⠀⢀⡀⢨⡀⠀⠀⠀⠀⠀⠀⢀⣴⣯⠇⠈⢡⣤⣄⣴⣿⣿⣼⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠂
⠀⠀⠀⡜⠁⣤⡩⠀⠀⠀⠀⠀⠱⡀⢹⣿⠀⠀⠀⠈⢻⡌⠃⠀⠀⠀⠀⠀⢠⣾⣵⣤⣶⣶⣾⣿⢿⡷⠈⢛⣿⠀⠀⠀⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢶⣯⠔
⠀⠀⢰⡇⢸⠏⠁⠀⠀⠀⠀⠀⠀⢱⠘⣧⡄⠀⠀⠀⣬⢻⡆⠀⠀⠀⣀⣴⣿⣿⡿⣿⢟⠛⢾⣿⣾⣾⣿⠿⠟⠀⠀⢸⣯⣝⣛⣃⣀⡀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⢸⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⠀⠀⠀⡠⡿⣸⠀⠀⠀⠈⡟⣾⠉⠙⠹⠯⠘⠀⠾⢉⡿⠋⠀⠀⠀⠀⠀⠈⠻⠯⣯⣉⣟⣛⣻⠿⢶⡾⣿⡽⠁
⠀⠀⠘⡆⠀⠓⠄⠂⠀⠀⢀⣠⡴⠃⣸⣿⣗⣔⣣⢤⢴⡏⠀⠀⠀⢐⣷⣿⣆⣦⣀⣠⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠚⠛⠉
⠀⠀⠀⠈⠢⣀⠙⠛⠛⠒⠚⠉⣀⣴⣿⡿⠿⠛⢻⣻⠟⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠚⠛⠛⠛⠷⠶⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣤⣤⣤⣤⣀⣈⡐⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢤⠤⠤⠤⠤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣛⠛⠉⠉⠀⠀⣀⣠⣭⣿⣶⣷⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣭⣤⣶⡾⠶⢲⠷⢶⡶⠒⠲⠶⠦⢭⣿⣆⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣟⣛⣻⣿⣿⡿⢿⡋⣸⠓⢲⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡾⢫⡁⠀⢀⠄⢉⠀⢠⠆⠐⠆⣡⡴⢋⣹⢿⡆⠀⠀⠀⠈⡇⣿⡧⠭⠯⠩⠉⠉⠁⠀⠀⣼⡃⣧⠴⡫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣷⣦⣴⣓⣀⡀⣉⣀⣀⣀⣀⣤⡥⢘⣋⠴⢻⠀⠀⠀⠀⠀⠹⣜⠿⣀⠀⢰⣶⠀⠀⠀⡰⢿⡼⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢿⣿⣿⠛⠛⠛⠛⠛⠛⠛⡻⠉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠘⢻⣍⡳⠶⠶⣶⣒⣻⣷⠞⠁
⠀⠀⠀⠀⠀⠰⣶⡆⠤⣄⡀⠀⠀⠀⣿⣿⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠛
⠀⠀⠀⠀⣴⣶⠋⠉⠓⠲⡿⣄⠀⠀⠘⢿⡷⣽⣾⣿⣷⣦⣤⣤⣤⣠⣴⠃⢠⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣶⣶⣤⣄⡀
⠀⠀⢀⡾⠟⠁⠀⠀⢀⣼⣥⣹⣛⣢⠀⠀⠙⠲⠬⣻⣿⣿⣿⣿⣿⣿⣷⠾⠟⠋⠀⠀⠀⢀⠴⠂⠀⢀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⡀⠙⠒⠋⢹⡆
⠀⠀⣿⠏⠓⢦⡀⣠⣞⣯⣿⡿⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⣀⠀⡀⠁⡀⠑⢮⠻⣀⠀⠀⠀⠀⣽⢿⡟⠋⠁⠈⠀⠀⠉⡄
⠀⠀⣿⡇⠀⠀⠁⣿⣿⣿⢁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠻⡷⠈⢀⣷⡙⣌⣷⠟⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⢀⠜⠃
⠀⠀⣿⣇⣤⣀⠀⢸⣿⣷⣧⣤⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢿⡆⠀⢰⠈⣷⣿⡟⠀⠀⠀⠀⠐⣻⣶⠀⠀⠀⠀⢀⡾⠃
⠀⠀⣿⣿⣿⣋⠛⢿⣿⡟⠉⠉⠉⣿⠀⠀⠀⢀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⢀⣲⠀⡀⠈⡇⢀⡟⢁⣀⣯⣠⣿⣿⠁⠀⠀⠀⠀⠀⠈⠛⠛⠳⢆⠶⠗
⠀⠀⣿⣿⠟⠝⠀⢸⣿⡇⠠⠀⠀⣿⠀⠀⢰⣯⣤⣖⣂⣉⣽⣿⣿⡆⠀⠀⢈⠁⠠⠽⢿⣧⠼⠤⠿⠉⠁⠈⠛⠉⢀⣀⣀⣀⡀
⠀⠀⣿⠋⣄⠆⠀⢸⣿⠇⠀⠈⠀⣿⠀⠀⠈⡄⡆⠀⠉⠉⢉⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠂⡚⢩⣶⣰⣯⡝⠛⠓⠲⢤⡀⠀⡐
⠀⠀⣿⠀⢀⣆⣠⢸⣿⣦⠀⠀⠀⣿⠀⠀⠀⡇⡟⠀⠀⠁⢸⣿⢸⠀⠀⠀⠀⠀⠀⢀⠔⠋⠈⣁⣤⠼⠛⣉⣉⠙⠓⠈⠉⠁⢀⣠⠤⢀⠀⠈⢶⣮⠓⢤
⠀⠀⣿⣤⣈⣿⣿⣸⣿⢿⣴⣶⠶⢿⡄⠀⠀⢻⣷⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠐⠁⠜⣠⡞⠁⠠⣾⢿⢋⢉⡿⠆⠀⠀⠀⣿⣟⠀⣸⡇⠀⢸⣿⣣⣸⣇⡀
⠀⠀⣿⡯⡿⢿⠻⣿⡟⢾⠉⠀⢀⢸⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠰⡀⠀⡗⠦⠀⠀⣙⣛⠛⠋⠡⣀⣀⣀⠀⠈⠉⠛⠋⠀⣠⡾⢛⣿⣿⡯⠁
⠀⠀⣿⡟⠿⠎⠀⣿⣇⠘⠀⢀⠛⢘⠀⠀⠀⠸⡇⠀⠀⠀⢸⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⢿⣿⡟⠻⢷⣀⠈⠩⠉⣉⣀⣠⣤⣾⡿⠟⣚⡭⠟⠉
⠀⠀⠉⠻⢷⣤⣀⢿⡿⢶⣾⡷⠚⠁⠀⠀⠀⠀⢧⣴⣶⣴⣊⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣉⣉⣉⣉⣉⣉⣭⣥⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠈⠉⠙⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⢄⣀⠀⠀⠐⢴⡟⠆⠀⠰⣾⠧⠀⢰⢦⠀⡀⢂⠁⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠘⠤⠄⠞⠻⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⢀⠊⡇
⠀⠀⢀⡀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠚⠉⠐⠒⠲⠤⣀⠀⠀⢀⠄⣠⠄
⠀⠀⢸⡅⢸⡁⠀⠀⠀⢸⠀⠒⢒⠢⡀⠀⠀⠀⡠⠺⠷⠶⠀⠀⠀⠀⠀⠀⠐⠛⠺⡗⢦⡀⠐⠁⢀⡀
⢾⠀⢺⠀⢮⢠⠆⠀⠀⠈⠦⠼⠷⠤⡐⠀⢀⠞⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠑⡄⠀⠹⠛⠂
⢻⠀⣻⠄⡿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣷⠶⠸⠀⣰⠀⠀⠀⠸⠿⣆⣸⠀⠀⠀⠸⠀⠠⣤⣄
⣹⠀⢻⠀⠗⣧⠀⠀⠀⠀⠂⢤⣀⠤⠀⢸⠀⠀⠀⠀⡀⠀⢎⡀⢤⠄⣤⡀⠀⠀⠉⠒⠀⠀⠀⡇⠀⠛⠁
⢹⠂⡠⠲⡄⢁⣀⠀⠀⠑⢄⣤⡕⠀⠀⢸⠀⠀⡠⠚⠀⢀⡀⠀⠀⠀⣀⣙⠦⠤⢤⠀⠀⠀⠀⡇⠀⢠⢄
⠈⠁⢈⠟⠓⠚⢤⡠⢦⠀⠀⠀⠀⠀⠀⠈⡆⠀⠁⠈⠣⠤⣀⣀⣀⣀⣀⠤⠜⠃⠄⠀⠀⠀⢠⠃⠀⠲⠄
⠀⢰⡃⠀⢰⡀⠀⢣⠀⠀⠒⠤⣀⣀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠩⢂
⠀⠈⣧⠀⠈⣧⠀⠈⡆⠀⠐⢄⣤⡶⡀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠰⠽⠇
⠀⠀⠸⡆⠀⠺⡏⠀⠸⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⣀⣀⣀⡀⠀⠔⠊⠁⠀⠀⠀⣱⠒⠒⠄
⠀⠀⠀⢻⡀⠀⢻⡆⠀⢣⠀⠀⠀⠀⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠑⠂
⠀⠀⠀⠈⢷⠀⠀⢷⠂⠈⢆⠀⠀⡠⠉⠀⡣⠀⡐⡀⡀⠀⢀⠀⠠⠂⠀⠀⢠⡀⠰⣄⣀⣛⡃⢹⠀⠈
⠀⠀⠀⠀⠘⣇⠀⠘⣧⠀⠘⡄⠂⠀⠀⠉⠀⠀⡧⠁⢣⠀⡷⠷⣧⠀⠸⡿⠂⠃⠀⠀⠀⠀⠙⠈⣄
⠀⠀⠀⠀⠀⢹⡄⠀⢹⣄⠀⢱⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠈⠄⡀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠐⠄⠀⠑
⠀⠀⠀⠀⠀⠀⢷⠀⠸⠿⢇⣀⠇
⣀⣀⣀⣀⣀⣀⣘⣧⣴⣚⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠄⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣄⡀⣤⣿⣷⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⢻⠄
⡀⠀⠠⢠⣤⣤⣤⡄⠀⣠⡤⠀⠉⠉⠀⢻⠻⢛⣛⡿⢸⡧⢏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡴⣿⣷⣴⡄⢠⣄⣠⣤⠀⠀⠀⣃⠘
⠁⠉⠀⠀⠀⡀⠌⠁⠀⠀⠐⠂⠀⠄⠀⣽⠶⠸⣯⡇⠘⣗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢹⠘⠉⢡⡾⣿⡉⣴⢾⣿⣧⡄⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⣠⢦⢤⠄⠈⠃⠠⣤⡖⠀⠀⠀⢀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠂⢠⡏⠀⠘⣇⡰⠿⠥⠜⠀⣀⢴⠊⠧
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢳⡾⠁⠀⠂⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣼⠃⠚⠃⠀⠀⠙⣿⠇⠀⠀⣼⡿⠯⠀⠠
⠀⠀⠀⠀⠀⠁⣛⢓⡒⢀⡠⠀⠀⠀⢠⡀⢑⣾⣶⠶⣄⠒⢆⡀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢁⡶⠿⢦
⠀⠀⠀⠀⠀⣤⣿⣯⣁⣰⠃⠀⠀⡀⠀⠸⣿⣯⣙⣷⢤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠲⡾⣿⣢⣾⢇⣲⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠛⠛⠻⠟⠁⠉⠙⠋⠁⡀⠀⠀⠀⠀⠀⣤⠤⢡⠀⠴⠀⠐⠈⠁⠀⠀⠀⠈⠳⣾⣻⠏⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠁⠴⠀⠀⠀⠀⠘⠛⠃⠀⢀⣀⡀⠀⠀⠀⢀⣀⣈⣶⠹⠟⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠄⠐⠀⠛⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉
⠀⠀⠉⠀⠀⠀⠚⢁⢀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣿⣶⣦⡀⠀⣀⣴⠄⠀⠀⣀⣴⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠤⠄⠀⠀⠀⠀⠀⠀⠐⠲⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣼⣿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⠆⠀⠀⠀⠀⠄⠀⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⣴⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠎⢠⡆⠀⠂
⠀⠀⠀⠀⠀⢀⣠⣴⣾⡽⠟⢹⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆⠀⠀⠀⠤⠀⠀⠀⠑⠀⠄⡀⠀⠀⠀⠠⠂⠉
⠀⠀⠀⠀⣾⠿⠟⡟⠃⣧⣸⠴⠇⠀⢖⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⢹⣀⣾⠴⠛⠉⠀⠀⠀⠀⠀⡠⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⠒⠠⠀⠀⠊⠀⠀⠠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡐⠙⣂⡀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠁⡡⠮⠁⠵⠢⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠋⣣⡐⠛⣀⡐⠙⣀⡐⠉⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠂⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⢦⠁⡡⢌⠁⠁⠀⠀⠀⠀⠀⠔⠊⠉⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡀⠀⠀⡡⠄⠒⢀⠀⠦
⠀⠀⠀⠑⠀⣠⠄⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠠⠃⠀⠀⡄⠁⠐⠨⠤⢄⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠢⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠄⡀⠀⠀⠀⠣⢴⡁⠀⠠⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡸⠐⠁⠀⠀⠀⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠄⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠘⡀⠀⠀⠀⠀⢀⠀⠀⠙⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒

⠀⠀⠀⠀⠀⠀⢀⠤⠔⠢⢤⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⣤⢤⠀⡠⢠⣄⢀⣄⢀⣀⠀⢠⣤⡀⣠⠄⡤
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠀⠁⠉⠉⠉⠉⠈⠁⠁⠈⠉⠀⠉⠉⠁
⠀⠀⢀⡴⠊⠁⠀⠀⢀⡤⣄⠀⠀⠀⠀⡼
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠙⠒⠒⠊⢳
⠀⠀⠈⠓⠒⢷⠒⠂⠸⠤⠖⠉⠛⣄⢀⡮⣀⡀
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⡨⠋⠀⠀⠉⠓⢤⡀
⠀⠀⠀⢀⠎⠈⠙⠒⠒⠒⠒⠋⠁⢀⠀⠀⠀⠀⠀⠀⠘⢉⡆
⠀⠀⠀⡜⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠑⠄⠀⠐⠠⠀⣀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⢳⠤⣀⣈⡠⢄⣀⠈⣀⣤⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠈⡄⢀⠀⠀⠀⠀⠀⢧⠀⠤⠀⠀⠈⠉⠁⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢐⠀⠀⠀⠀⡀⠠⠤⣌⠢⡀
⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠉⠉⠉⢨⠀⡠⡖⠁⠀⠀⠀⠀⠀⠈⡖⢄
⠀⠀⠀⡇⢠⠀⠀⡆⠀⠀⡇⠀⠀⢀⡀⢀⡠⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⡌⠉⠭⠭⠭⠭⠍⠋⠥⠎
⠀⠀⢴⠃⠠⠀⠀⠀⠀⢀⣇⣀⣀⠀⠈⣉⣠⣴⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⡀⠀⠀⠉⠳⣄⣠⣄⡀⢸⠉⠙⢏⠙⠛⢡⡟⢦⡀⠀⣀⠄⢢⢧⠄⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⣤⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢘⡀
⡇⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠘⡏⠉⠀⠰⠚⠂⠀⠀⢴⠋⠂⠄⡀⠀⠀⠐⠂⠤⠔⠒⣁⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠶⣼⣄⣀⠤⢞⡥⠒⡂⠉⠁⠙⠁⠀⠊⠓⠲⠦⣅⠀⠀⠁⠀⠀⠀⠈⠀⠈⠗⠀⣤⠀⠀⣸⡀⠀⠀⠀⠀⠀⢸⠗
⠇⠀⠀⠀⠀⠀⠈⠂⡤⠏⠡⡀⠈⠑⠨⠑⣒⠀⠀⠀⠀⠒⠒⠂⢁⠅⠀⠀⢠⣀⣀⣀⣠⠀⠰⡀⠀⠇⠀⡀⠩⣷⣦⣤⣤⣤⣶⡧
⡆⠀⠀⠀⠀⠀⠀⡔⢸⠁⠀⠘⠢⠄⡀⠀⠀⠰⢁⠀⠀⠀⢀⡠⠂
⠁⠀⠀⠀⠀⠀⠀⣗⠃⣀⠀⠀⠀⠀⠈⠐⠒⠚⡳⣶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡬⠤⠭⢭⡭⠄⡾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠙⢄⠀⢀⡾⠄⡀⢥
⠁⠀⠀⠀⠀⢀⠞⠁⠉⢦⠤⠉⣽⠂⠠⠐⠚⡦⡀
⠁⠀⠀⠀⠀⠘⡀⠀⠀⠘⢄⣀⠼⡄⠀⠉⠈⠀⠈⠆
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡳⠄⣀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠚⠁
⣶⡶⢶⢶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⢶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄
⠀⠀⢾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⡀
⠀⠀⢼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⠛⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢀⡴⢋⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⠞⣡⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣀⡴⢋⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡤⢞⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⢖⡫⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⣫⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⢞⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡴⢋⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡴⢫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡠⢋⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠏⢰⢡⠋
⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⠉⠁⢀⣇⡏
⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠸⣸
⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⡇
⡼⠁⠀⠀⠀⠀⠀⠀⢀⡠⠚⣡⠟
⡇⠀⠀⠀⢀⣀⠤⠚⠉⣠⠔⠋
⠙⠷⣀⣉⣉⣠⡤⠖⠋⠁
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿

⠛⠛⠛⠲⠶⠦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠄⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣀⠀⠀⢁⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠠⢰⡤⠀⠀⣤⣤⠀⠀⠀⠰⠶⠿⠿⠃⠀⠀⠀⠀⠀⠺⠟⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⣤⢠⣀⣀⣤⣄⠀⠀⡄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⣍⣉⡘⠿⢿⣿⣿⣶⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢇⡇⠀⠙⣿⡏⠀⠁
⣿⣯⢹⣟⠿⣿⠟⢟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠭⠩⠉⠓⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢀⠤⠲⢲⠲⢤⡀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡴⡷⠑⠺⡇⠀⠤⠝⢦⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣗⠋⠤⠀⠀⠀⠀⠀⢸⠦⢤⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠉⠉⠉⠉⠉⠉⠉⠒⠢⢄⡀⠀⠀⡇⠀⠀⠳⣀⠊⠄⣀⠑⡀⣄⡾⠛⠉⡼
⠀⠀⠀⠀⢀⡤⠚⠁⠀⣠⣤⣖⠊⠉⢉⣿⠛⡟⢶⠦⢄⡀⠈⢑⢄⣽⣄⠀⠀⠉⠓⠧⠥⠾⠚⠉⠀⠀⡰⠁
⠀⠀⠀⡤⠋⠀⣠⡴⠛⡿⢷⣤⣿⣙⠀⠻⣵⡀⠘⠣⣀⠉⠲⢄⠘⠙⢿⣶⣄⡀⠀⢀⡀⡄⠀⢀⡠⠞
⠀⢀⠎⠀⣀⡾⢿⡧⣤⣧⣄⡄⢈⠙⠲⣄⠘⣶⢀⡀⠨⢳⠀⠈⠣⡀⠀⠹⡆⠈⠙⠒⠒⠒⠈⠁
⠀⠎⠀⢠⡇⣧⣮⡠⠼⣁⡼⢯⡟⠢⣀⡈⡙⠻⢿⣧⠆⠈⠷⣄⠀⠱⡄⠀⠹⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⡘⠀⠀⣿⣿⠀⣰⣁⣠⠿⠤⢼⣦⣄⠈⠓⠾⢿⣦⣈⢳⡄⢀⠘⣆⠀⢱⠀⠀⣇⠀⠀⡠⠔⠊⠉⠀⠀⣀⠤⣌⠉⢒⣤⡀
⡇⠀⢸⣏⠈⣯⠜⠁⠀⠀⠀⠀⠀⠈⠉⠑⣄⣀⠘⠻⣽⣧⡀⠀⠘⣷⣾⣇⠀⢸⡶⠣⠊⣀⠴⣲⠿⠋⠁⢀⡿⣤⠋⢡⠈⠢⡀
⡇⠀⢸⡟⣿⠋⠀⠀⢀⡠⠴⠒⠢⣄⠀⠀⢹⡳⠀⠀⠀⠉⠳⣐⡄⠘⣷⣺⠇⢸⠀⣠⣾⠵⠊⠁⠀⠀⠀⠞⢠⠃⠀⠈⡆⠀⠱
⢇⠀⠸⡍⢿⠀⠀⠀⡎⠀⠀⠀⠀⢸⡴⠒⠛⠋⠉⠙⢦⡀⠀⢹⢆⠀⢸⠇⠀⡈⢰⡟⠁⠀⠀⠀⠀⠀⡜⢠⠃⠀⠀⠀⣷
⠘⡄⠀⢣⡊⢇⠀⠀⠑⢤⣀⣡⣤⠟⣠⠚⠉⠓⠲⡀⠀⠳⡄⡈⠶⣴⠞⠀⢠⠁⣼⣿⡀⠀⠀⠀⠀⡰⢁⠋⠀⠀⠀⠀⢸⡇
⠀⠱⡀⠀⢻⡍⠵⡄⠀⠀⠠⡇⠀⢰⡏⠀⠀⠀⠁⣹⠀⠀⢿⣀⣴⠏⠀⢠⡇⠀⢸⡹⣧⠀⠀⠀⢰⢅⠎⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠘⢆⢀⠙⢄⡺⢤⣀⣠⣧⠀⠀⠳⢤⣠⣤⠴⠃⠀⠀⠀⢻⠁⠀⡰⠋⠹⡀⠀⠻⣯⢳⠀⢠⣏⡏⠀⠀⠀⠀⠀⢀⣴⠇⢀
⠀⠀⠀⠀⠙⢿⡀⠉⠢⢌⡀⠈⠓⢤⣄⡀⠀⠀⠀⠀⠀⣀⡠⠜⡠⠊⠀⠀⠀⠑⡄⠀⠙⣿⣄⣿⡾⠀⣀⡠⠤⣴⠾⠛⠕⣡⠊
⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⡀⠉⠙⠛⠒⠛⠛⠉⠉⢉⣉⠤⠒⠁⠀⠀⠀⠀⠀⠀⠈⠓⢄⠈⠋⠙⠿⠟⠛⠛⠉⠁⢀⡠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⠒⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⣰⠋⠉⠉⠉⣗⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣧⣄⠀⢀⣀⡈⠲⣀⣤⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢘⡷⡆⠀⢠⣄⠁⠀⠋⠀⣹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⢸⠀⣄⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⢰⡬⢤⡤⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⣆⠓⠊⠀⠀⣠⠔⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⠒⠉⠀⠀⠹⣷⣄⣀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⢧⡀⠀⠀⢀⡏⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠓⠢⠞⠀⠀⠀⠀⠀⠘⢆
⣠⠶⠿⣽⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠁⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣧⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠦⣤⣀⣤⠖⣫⡥⢭⣑⣶⠚⠛⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣤⠖⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠔⠋⠀⠀⠀⢯⠙⢷⡄⠀⢧⡀⠀⠀⠀⠀⠀⠀⣸⠀⣞⢇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠻⣦⡀⠱⣄⠀⠀⠀⠀⠀⡇⠀⠘⢾⣷⢄⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠈⠻⡓⠾⢦⣄⣀⣀⠀⣷⣄⠀⠀⠻⣮⠳⡄⠀⢀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠳⣄⠈⠓⠒⢶⡙⠲⣝⢷⠈⠓⠦⣄⣹⡷⡈⠢⣼⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⢄⡀⠀⠹⢤⣈⣻⡆⠀⢀⣀⣩⢃⣷⣄⣈⣳⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠛⠛⠛⢻⠿⠆⠀⠀⠉⡿⠯⢭⣉⣽⣟⣋⣉⣉⣉⣉⣉⣉⣉⣩⠭⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠘⠒⢾⠀⠀⠈⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⠤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠙⠲⢤⣄⡀⠀⠀⠉⠳⣶⣦⣤⣤⣤⡤⢤⣤⣤⡶⢶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠒⠤⢄⣉⠉⠉⠁⠀⠀⢀⣤⣤⣭⣭⣥⣤⡴⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣤⡤⠶⠴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣀⣼⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⠉⠓⠲⢤⣉⡙⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡇⣰⡄⣄⢠⡀⣼⡇⢸⡇⢢⣰⢠⢠⣠⠋⡿⡶⣤⣬⣙⡶⡦⣶⣀⣠⠂⣼⣦⣾⣾⢦⠀⠀⡀⠀⠀⢉⠧⡎⡦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠁⠈⠀⠁⢹⠉⢹⡏⠉⠈⠈⠈⠈⠀⠁⠁⠋⠉⠉⠛⠧⢬⣉⠉⠛⠻⠇⢿⢹⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣓⣦⣄⣸⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣷⣴⣿⣦⣼⣿⣿⣾⣿⣿⣴⣶⠿⠿⢿⣷⣄⡀⠀⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⢉⣿⣿⣦⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠿⠿⠿⣿⣿⣿⣦⣠⣼⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⠈⠙⠻⠿⠿⣛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⢡⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠀⠀⡔⠀⠀⠘⣄⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢂⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿⡏⠀⢀⠎⠀⠀⠀⠀⠈⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠣⡀⢱⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⢦⡀⠀⠀⠀⠒⣂⣠⣤⣵⣄⢳⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀⡾⠋⡛⢷⢦⣔⠲⠄⠀⢥⢿⣖⣤⣖⣛⣋⣩⣀⣹⣿⣧⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⢨⣍⣛⣟⡛⠛⠋⠁⣠⣀⠀⠀⠈⠉⠉⣩⣭⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⢾⣿⡏⠉⠁⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣟⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠿⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢦⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⠀⠀⠀⠉⠿⠿⠿⠛⠿⣿⣿⣿⣿⡄⠀⠀⢀⣴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣪⣾⠅⣪⠢⣄⠀⠀⢀⣠⠤⢖⣊⡩⠀⣴⠾⢏⢀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣩⡆⢈⠻⠶⣋⡴⠞⣃⢉⣵⣶⠂⢻⡟⢠⣰⠘⠧⠴⢛⣀⢣
⠀⠀⠀⠀⠀⠀⡠⠚⡥⠘⢿⣤⡼⠣⠊⡁⣾⠿⠃⠈⢿⣄⡴⠀⠛⣋⣡⡤⡄⣿⠗⠀⢂⢣
⠀⠀⠀⠀⡠⢞⠱⣿⡋⢢⡆⢉⠠⠇⢂⠹⡘⠷⠒⠋⡀⢠⣶⡋⠀⠹⣿⠁⣀⠘⠷⠖⣋⡈⢧
⠀⠀⣰⢪⣾⠗⢄⣈⠛⢋⣴⡌⢽⣦⢢⠁⠐⡀⣿⠓⠀⡈⢷⣠⡧⠇⠙⣉⣡⠲⡈⣿⠛⢀⡎⢣⡀
⠀⠰⢈⠪⡻⣧⡼⢋⣴⠈⠻⣦⡼⢻⣧⡡⠀⠐⡜⠶⠚⢋⡀⢠⣶⣄⠂⢻⣏⣐⡴⠈⢛⣩⡥⠄⠳⡀
⠀⠀⢧⡁⠙⢦⡐⢿⣧⣀⡾⢈⡁⢾⣛⣷⡑⡀⠘⠀⣿⠏⠀⡌⣷⣤⠶⠀⠉⣥⣖⠂⡈⣿⠉⣮⡆⢱
⠀⠀⠈⠻⣦⠀⠈⠢⡙⠋⣴⠗⢢⣤⡝⠋⣷⡀⠀⠀⡘⠿⢚⡫⡀⣴⡾⢏⠀⢻⣄⣶⠷⠈⣋⣭⣤⣾
⠀⠀⠀⠀⠈⠳⣤⠀⠈⠢⡙⠷⣾⠏⣴⡗⢈⢳⡀⠀⠠⡸⣿⠉⣄⡘⣧⡼⠟⢀⣉⡤⢶⣟⣯⣽⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠳⢔⠀⠈⠳⢄⠻⣯⣄⣹⠇⣷⠡⠁⢳⡘⢛⣋⣡⡤⢖⣛⣭⣷⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⡀⠙⠪⡙⣡⣾⣿⠇⠁⡠⣽⣿⣯⡵⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⢸⣽⠟⠁⠀⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⠀⠈⠡⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄
⠀⠈⠁⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⣴⠥⠀⠰
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠠⢄⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠂

⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣆⠄⢀⠀⠀⠀⢰⠀⣰⠀⠀⠀⢰
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠏⠾⠈⠳⠁⠼⠸⠇⠘⠠⠿⠑⠼⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⣀⡀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠱⡀⠈⠁⣀⣼⢀⡀⠜⠀⠀⠀⠀⠀⠀⠇⢀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠀⠀⠀⠀⠀⠀⠈⠉⡋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣀⠄⠐⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠠
⢀⡀⠀⢰⢁⡈⢀⡶⢾⣹⡾⡿⠂⠀⠀⠄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢐⣒⠀⠂
⠈⠻⠀⠈⠁⠠⢭⣙⣤⣄⣘⣭⡼⠶⠞⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠪⢙⠒⠀⠤⠤⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠉⠂⠒⠒⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢻⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣀⡉⢻⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠃⣸⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⡙⠋⠙⠉⣿⠉⣿⠋⠙⠋⠋⠛⠉⢉⡋⠉⠛⠉⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⣉⢘⠀⠀⣿⠀⣿⠀⡇⠀⠀⠀⡄⢈⡃⠀⢠⠈⢰⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⣿⠘⢀⠀⠛⠀⠛⡀⠃⡇⢀⠀⡇⠘⠃⡀⢀⠐⢠⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠂⡀⠀⠠⠁


⠀⠀⢀⣴⡖⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⢤⡤⣢⠀⣀⡀
⠀⠀⡈⡯⣿⢾⠇⠀⠀⢀⣀⡀⠀⠘⣥⡤⣄⢀⣀⠀⣀⠀⠀⠀⢀⠀⠀⠐⣤⠀⠀⠀⠀⡰⢂⣡⣮⣴⣃⡴⢋⡕⢀
⠀⠀⠉⠑⠛⠋⠁⠀⠰⡀⠁⠀⠄⠀⠙⠲⠶⠮⣌⣛⣉⠙⡓⠲⠶⠤⢦⠀⠸⠁⢀⡀⣏⣰⠏⢨⣟⡽⠋⢰⢋⡼⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣬⠅⡡⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠒⠚⠃⠀⠀⠀⠑⣩⣀⢀⡸⠛⠓⠀⠼⠏⠔⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠁⣁⣀⣀⣈⡀⠤⠚
⠀⠀⠀⠀⠀⢀⣀⠔⠋⠉⠉⢤⠀⠀⠀⠀⠀⠀⠀⠀⠠⡻⠖⠀⠉⠀⠄⣀
⠀⠀⣠⢤⡞⠉⠃⠀⠀⠀⠀⠊⠉⠉⢢⡀⠀⠀⠀⠀⡦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠐⠒⠤⠄
⠀⠀⠁⢄⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠓⠀⠀⠀⡷⠶⠤⢤⣁⣉⡀⠉⠀⠃⠃⠈⠉⠀⠀⠀⠀⣤⣀⣀⣀⣀⣠
⠀⠀⠀⠀⠈⠉⠀⠤⢀⠠⠇⠄⠐⠓⠒⠉⠉⠀⠀⠀⢧⣀⣀⣀⡈⠀⠈⠉⠉⠛⠉⠛⠃⠀⠀⠀⠀⠉⠍⣉⣉⠩⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠒⠒⠒⠃
⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠲⠖⠒⠢⣄
⠀⠀⡴⣾⣻⣻⢹⡗⣟⣺⣭⡶⡖⢠⣀⠀⠀⠀⢀⠊⠐⠂⠀⠒⡀⢠⣌⡀⠀⠀⠀⠀⢀⡘⣫⡟⣡⡟⢃⡾⢃⣰⢳
⠀⠀⠂⠀⠈⠙⠛⠽⠗⣾⣻⣏⠯⠝⠩⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠶⠈⡖⠋⠴⠏⣰⠻⠠⠞⠁⡸
⠀⠀⢁⡐⠀⠤⢀⡀⠀⠀⠨⠁⠀⠀⠔⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⢀⣘⢋⣐⠋⣁⡚⢁⡚⢁⡘⠁⢀⠞
⠀⠀⠀⠀⠀⠒⠤⠀⣈⠀⠲⠂⠡⠀⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⠀⠨⠁⠈⠀⠀⠉⠀⠈⠀⠘⠫⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠠⢐⠠⠄⡐⢠⣀⠀⠀⠀⡏⠉⢳⠁⣀⣀⠔⠉⠉⠀⣀⡠⠤⠤⡞⢁⠀⠑⢄⠀⠠⠤⣀⠀⠀⢠⡞⢢⠀⠀⢠⡞⠳⠦⣤⠒⠒⠦⣄⡀
⠀⠀⢀⠢⢄⠙⢆⠰⡇⠀⣩⠆⠀⠀⠙⠒⠋⠸⡁⠈⣱⠀⠀⣾⡁⠀⠀⠀⠈⠊⠁⠛⠈⣀⡀⠤⠺⣄⠀⢸⡄⣸⠀⢀⡞⠀⠀⠀⠈⠙⠲⠤⣤⣉⠉⠛⠛⢶
⠀⠀⠀⠇⠤⣑⣾⡷⡿⠊⢁⡤⠔⠒⠒⠦⣄⡀⠉⠈⠁⠀⠀⣿⣍⣀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠈⢒⡿⠂⠀⡟⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢀⡞⡀
⠀⠀⠀⢰⠊⢉⠙⠉⡠⠊⠁⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⡿⢁⠀⠉⠉⠒⠒⠒⠒⠒⠒⠉⠉⠀⣿⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⡽⠀⠀⡞⣰⠁
⠀⠀⠀⠈⠒⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠛⠧⣉⡉⠒⠒⠒⠂⠀⠐⠒⠒⠂⢉⡷⠀⠀⢰⡋⠀⠀⠀⠀⡀⠀⠀⠀⡼⢡⠎⠀⠀⢸⢇⠇
⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⣴⠟⠛⠓⠲⣄⠀⠀⢸⡆⠀⣀⣤⣤⠉⠉⠉⠉⠉⠁⢉⠉⠉⠁⠀⠀⠀⠈⢿⡲⠤⣄⡀⠀⠁⠀⣼⢡⠇⠀⠀⠀⣼⢸
⠀⠀⠀⡆⠀⠀⠹⣆⠑⠀⠀⠀⢸⡇⠀⠀⠀⢀⢸⡆⠀⣸⠀⡼⠁⠍⣙⡇⠀⠀⣀⣀⡀⠀⠉⠛⠒⢦⠀⠀⠀⠀⠉⠛⠺⢯⣓⢦⡴⢃⣾⣑⣒⠒⣚⣁⠟
⠀⠀⢠⠗⠳⢦⡀⠈⠳⣤⠀⠀⠈⢷⣐⠦⠤⣊⡼⠁⢠⡏⠀⣇⣀⣠⠞⠁⠀⢸⡡⠀⠈⢧⠀⠀⣠⡼⣷⠶⠶⠶⠶⠶⢤⡄⠈⠓⠒⠋⠀⠈⠉⣉⣉⠁
⠀⠀⣿⠀⠀⠈⠙⢦⡀⠈⠳⡄⠀⠀⠉⠛⠛⠉⠀⣠⠏⠀⠀⢈⣉⣀⣀⣀⡀⠀⠑⠶⠴⢏⠀⠘⡛⠒⠿⡶⠶⠒⠒⠚⠉⡅⠀⠀⠀⠀⠀⢠⠞⠁⠈⠹⡄
⠀⠀⢻⣧⠀⠀⠀⠀⠙⠢⣄⡈⠢⣄⣀⣀⣠⡴⠞⢡⡴⠚⠋⠉⠉⠭⠍⠉⠉⠓⣆⠀⠀⠀⠀⠀⡇⠀⠀⢻⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡞⠀⠀⠀⢠⠸
⠀⠀⠀⣿⣆⠀⢀⡴⠶⢦⣀⠉⠲⣄⠀⠀⠀⢀⡴⠹⡆⠀⡀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠲⣄⠀⠀⣧⡔⠖⠚⣿⠒⠒⢒⣶⡇⠀⠀⠀⢠⣾⣇⣀⣀⢀⣈⣀⣷
⠀⠀⠀⢸⢻⡄⠘⣇⠀⠰⡝⡆⠀⢸⡆⠀⠀⡞⢀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠈⡷⠀⢸⡉⠉⠉⠙⣏⠉⠉⢀⡇⠀⠀⠀⠀⢧⠈⡍⠉⠉⠉⠀⡴
⠀⠀⠀⢸⡄⢳⡀⠈⠳⠤⠴⠃⠀⣸⠃⠀⢰⠛⢮⡂⠀⢳⣀⣈⣩⣭⣄⣀⡼⢧⣀⠈⣡⠞⠙⡆⠘⡇⠀⠀⠀⢹⡆⠀⢸⠃⢀⣀⡀⠀⠈⠛⠿⢶⣴⠴⠛⠁
⠀⠀⠀⠀⠳⣄⡙⠶⣤⣀⣀⣤⣾⠏⠀⠀⢺⡘⣀⡷⠶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⣀⡇⠀⠹⣄⣀⣀⣀⣉⣠⠞⠀⢿⠁⢱⡀⠀⣀⣤⠎⠀⢦⣄⡀
⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠛⠋⣁⣀⣀⡀⠀⢉⣉⡀⠀⠀⠀⠀⢿⠶⣦⣀⡇⠀⠀⠀⠀⠈⠁⠀⣠⣶⣬⣉⠉⠉⠀⠀⠀⠀⠈⠓⠛⢥⣀⡓⠶⠤⠤⠴⠟⠃
⠀⠀⠀⢠⡤⠤⣤⡔⠒⠋⣉⣉⣉⣀⠈⠙⢦⡋⠀⣸⠂⠀⠀⠀⣨⠷⠽⣿⣇⣀⣤⣤⣄⡀⠀⠰⣯⡛⢿⣮⣭⣛⣛⣛⣛⣛⠓⠶⢤⣀⠈⠉⠛⠲⣄
⠀⠀⠀⠀⢏⡀⢘⣭⣒⢤⡀⠀⠀⢀⣀⠀⠀⠻⡀⠈⡧⠀⢀⡞⢡⠂⠀⠀⠉⠁⠀⠀⢨⠹⡄⠀⠹⢿⣷⡶⣭⣭⣭⣝⣛⣛⡻⠿⣶⣍⠳⣄⠀⠀⠈⢳⡄
⠀⠀⠀⠀⣾⣧⣀⠀⢻⣿⢺⢷⣦⣄⡀⠀⠀⠀⠑⣌⢧⠀⢸⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⣤⣌⣉⡉⠙⠛⠛⠛⠛⠿⢿⣶⣌⡷⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠳⣅⠢⣝⠌⠻⠷⠊⡞⠙⠿⣷⣤⣀⠀⠘⢾⠀⠈⣧⠀⠀⠀⢀⡖⠰⡄⠀⠀⢀⡏⠀⠀⣗⣢⣬⣭⣭⣭⣉⣉⡓⠒⠤⣈⠙⠃⠀⠀⣰⠒⠚⠓⣦
⠀⠀⠀⠛⢦⡈⠙⠲⣝⡲⣄⡀⠑⠶⢄⠈⠙⠪⣝⣓⡾⢁⠄⠘⣆⢀⠀⠀⠀⠀⠀⢀⠀⣸⠁⠀⠰⣷⣭⠭⠭⠭⠥⠭⣉⣉⠙⠲⣤⠇⠀⠀⢰⢧⡠⢤⢤⣿
⠀⠀⠀⠡⣧⣷⠀⣀⣀⣉⠲⣝⠲⣄⡈⠢⠔⢢⣄⠀⠀⠀⠀⠀⠈⠳⣽⣢⣤⣤⣬⣥⠞⠁⠀⠀⢀⣀⣉⣉⣛⡛⠛⠛⠲⢦⣉⠒⢼⠀⠀⢠⣟⣰⣁⠰⡾⣿
⠀⠀⠀⢀⣼⣿⢿⣖⣉⠼⠁⠀⠙⠦⣙⠒⡶⠊⠀⢀⡤⠖⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠁⠀⠉⠉⠓⠦⣄⠀⠉⠓⠚⠀⠀⠀⠈⠉⠙⠛⠳⠛
⠀⠀⠴⠯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠞⠉⠀⠀⠀⠀⠈⠙⠲⠤⣀⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡆⠀⠀⢀⣠⡤⠶⡶⠦⣤⣀
⠀⠀⢀⣠⣶⣒⣊⣤⣤⣤⣴⣶⣖⣒⡦⠀⠀⣿⣙⠚⠛⠚⠒⢿⣛⡳⠶⠦⢤⣭⣳⡄⠘⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⢊⠜⠁⢠⠞⢉⣸⠍⠉⠀⠀⠀⠉⢳⡀
⠀⠀⢯⢰⣇⠸⡉⠉⠉⠉⠉⠉⠉⠁⡇⠀⠀⣠⠽⠂⠀⣤⣄⠀⠈⠀⠀⠀⠀⠀⡽⠂⠀⠙⢮⡛⢦⠀⠀⠀⠀⠀⠀⢸⡀⠀⡟⠀⢻⡄⣰⠞⠛⣷⡄⠀⠀⣇
⠀⠀⠈⠳⣿⡄⠡⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢿⡄⠀⠈⠓⠋⠀⢀⡴⠶⣄⠀⠀⢹⡆⠀⠀⠀⢹⠘⡇⠀⠀⠀⠀⠀⠈⣇⠀⣧⢰⠋⠀⢻⣄⣠⣧⠇⠀⠀⡿
⠀⠀⠀⠰⣎⣻⣄⣀⣀⣀⣀⣀⣼⣓⠆⠀⠀⢻⠁⠀⠀⠀⠀⠀⢀⠙⠛⠃⠀⠀⢸⠂⠀⠀⠀⠸⡆⣿⠀⠀⠀⠀⠀⠀⢹⠀⢻⣜⠦⡤⢤⣈⣩⢤⣰⢋⡿⠁
⠀⠀⠀⠀⠀⠉⠻⠯⠭⠭⠽⠛⠉⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠙⠛⠛⠛⠒⠛⠀⠀⠀⠀⠀⠙⠾⣦⣤⣤⣤⠤⠤⠞⠀⠀⠉⠳⠦⣤⣌⣡⣤⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⠤⠀⠄⠀⣀⠀⠀⠀⠀⣀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣟⣁⣀⣤⣤⣤⣤⣠⣀⣀⣀⣀⠈⠀⠒⠿⡞⢷⠺⡶⢷⡼⡴⠄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⠦⣄⡀⣽⣏⣹⣍⣻⣛⣟⣆
⠰⡒⠀⠠⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⡿⠟⠹⡃⠈⣻⣿⣿⣷⡷⠤⢧⡬⣭⢆
⠡⠁⠀⠄⡀⠀⠻⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷⡫⠋⠁⣿⣷⣿⣖⢳⡚⠶⠧⡀
⠀⠢⠀⡐⢀⠀⡀⠙⢧⣈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠟⣹⣾⢟⠕⠀⠚⠻⣿⣿⣿⣿⣿⡘⢓⠓⡄
⠀⠀⠑⠀⠤⣤⣤⠬⠿⠏⠑⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣛⠉⠀⠀⢶⡀⠀⠼⠿⣫⣾⣍⣹⣉⣉⣉⣄
⠀⠀⠀⠀⠀⠀⠙⠷⢤⡀⠀⠀⠀⠀⠐⠂⣠⣤⣤⣾⠿⠿⠟⢛⠯⠟⡫⠙⠁⠐⣹⣯⠽⡆⢷⡤⠵⡤⠭⡤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣶⢶⣶⠾⡿⠉⠉⠀⠀⡀⠤⠤⠒⠈⠀⠀⠀⠀⠀⠀⠚⠻⠿⠛⠛⠛⠛⠒⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⣀⣴⠁⠀⣿⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡣⠀⠈⠛⠿⠶⠃⠀⣼⡏⠓⠶⡏⠀⢙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢹⣿⣿⠷⣶⡆⠀⠀⠈⠛⠓⠶⡾⠃⢀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠻⢿⣧⣀⡎⠀⣠⡿⠷⢶⣦⡄⠀⠀⠈⠛⠳⠿⠦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣴⣶⣦⣄⡀⠉⠀⠀⢿⣇⣀⢀⡽⠃⢠⡿⣧⣤⣀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣴⣿⠋⠙⢻⡇⠀⣶⣶⣄⡀⠉⠛⠁⠀⣿⣃⠁⠈⣿⠁⠀⣶⣮⣷
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠉⠛⠦⣴⠏⠀⣾⡟⠙⠉⠛⣿⠀⠀⣀⠀⠙⠓⠾⠇⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⡷⣦⣄⠀⠀⠀⠀⠻⠧⣄⠀⣼⠃⠀⣼⠿⠻⣷⣦⡀⠀⠀⠘⠻⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣿⠃⠀⣠⣤⣄⡀⠀⠉⠁⠀⢸⡟⠀⠀⠉⡿⠁⢀⣾⣶⣦⣤⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣸⣿⠏⢹⠿⡷⠀⠀⣀⠀⠙⠛⠶⠾⠃⠀⢸⣿⣉⣈⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣿⣟⣀⠀⢰⠃⠀⣸⡿⢿⣶⣤⡀⠀⠀⢀⣿⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⣷⠀⠀⢰⣿⢁⣠⣤⡶⢿⣧⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣠⣾⣷⠏⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⡀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⣸⠶⠿⠋⡡⠜⠶⠆⠀⠱⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢠⠞⢉⣀⣤⡸⢷⠀⠛⠀⠀⠘⠑⠢⢀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⣨⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠘⠄
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⢀⣼⢫⠁⠄⠀⠰⢀⠀⡔⠋⠁⠀⠐⠄⠈⢣⠀⠀⠀⠀⠰
⠀⠀⡜⠀⠀⠀⠀⠀⢀⠀⠀⣀⣻⣾⠁⠀⠀⣾⣡⡔⠀⠀⡀⠑⠀⠀⠐⠀⠀⠀⠀⡼⠀⠌⠀⠀⠀⠀⠀⡄
⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⣶⣿⠇⠀⠀⢰⡿⠁⠃⠀⠀⠀⠀⠂⠀⠀⠠⠀⠠⠜⠁⠀⠈⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⣷⠀⠀⠀⣻⡇⢌⡇⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⢀⣀⡟⣄⢀⣵⠏⢹⣷⠇⢶⡖⠢⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⡇
⠀⠀⢱⠀⠀⠀⠀⠀⠀⠓⠴⠋⡡⠀⠈⠀⢲⠀⠉⠉⠉⠠⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⢰⡇
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠸⣀⠀⠀⢦⢀⠜⢁⠀⢄⡀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠢⢤⡀⠀⠀⠀⠀⡾
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠸⢀⢄⠀⡐⠋⠛⠠⡡⠰⠸⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⠀⠘⠀⡁⠁⠀⠀⠀⡃⠁⡐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⣤⣤⣄⣀⣀⣀⣀⣤⠄⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⣻⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠀⠊⠑⠀⢙⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⣀⠄⡀⠀⠀⠀⠀⠀⠘⣰⣤⠔⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠋⠐⠲⠟⡩⢆⠈⠀⠀⠀⠀⠀⠀⢇⣀⠀⢠⡴⠂⠸⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣢⣬⣤⡀⠀⡄⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⡇⠀⠙⣄⠀⠀⢨⡛⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⢣⡀⠀⠁⠀⠀⠀⠀⠀⡴⠀⠀⠀⠈⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠱⣤⠁⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠳⣄⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣀⣤⣤⣄⣀⠀⣀⣀⡄⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⣴⣻⠃
⠀⠀⠀⠀⢀⣠⣴⣶⣆⠈⣿⡟⢳⡄⠈⢹⣿⠿⠟⠋⢉⣭⣅⣀⡀⠀⠀⢰⢻⣆⡀⠀⠀⠀⡠⠀⠁⠀⠀⠀⢀⣴⡾⢡⡏
⠀⠀⠀⠀⠈⢛⠻⣿⣿⣶⣿⣭⣬⠍⢠⡀⢲⣿⠻⠇⠈⠳⣮⣛⣄⡈⠀⣿⠘⠿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠁⣼
⠀⠀⠀⠀⠀⠈⢦⡹⣿⣿⣿⣿⣿⠦⣈⠁⣼⠿⠀⠀⠀⠀⠈⣿⣾⢁⣀⡏⠀⠀⣿⣿⣦⣄⠀⢀⣤⣶⣿⡿⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠿⠛⠛⠛⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⠇⠀⠀⠈⠙⢿⣿⣿⣿⡿⠛⠉⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣜⡻⢿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⣤⣤⣤⣤⣤⣀⣀⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⡾⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣠⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣶⣿⣿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠈⠋⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣀⢉⣙⠻⠿⣿⣿⣿⣿⡛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣭⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⠛⠿⠿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢶⡄⠀⠀⠙⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⢁⣴⣾⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠛⠁⠀⠀⠀⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠛⠋⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣶⠆⠀⣤⡀⠀⠐⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡶⠀⠀⠈⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠋
⠀⠀⣰⣦⠀⠀⠀⠀⠈⠙⢿⡄⠀⣀⠀⠀⠀⠀⠀⠛⣧⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠋
⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠉⠙⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢸
⠀⠉⠛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣀⣤⣤⠶⠶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠏⠡⢀⡼⠋⠀⢠⡖⠋⠉⣩⡟⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡿⢰⠁⣿⣧⣤⣤⣤⣹⣦⣀⣿⣃⠀⠐⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠳⣜⣦⣀⠉⣡⣤⣼⣟⠿⠿⢿⡹⢻⣦⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣦⠄⠈⠛⡦⠶⠟⠛⠛⢟⢻⣦⠀⠈⣦⢹⡆⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⠞⠁⠀⠀⠀⠀⠀⢻⣿⠆⠀⣽⣿⠁⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡔⠋⢉⣽⠃⢸⡀⠀⣚⢂⠦⠀⢠⣾⡟⠀⣠⣿⠉⡀⠡⠄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣰⡿⠡⢹⣾⣧⡈⠉⠉⠀⠀⢸⡟⠀⢰⣿⡿⣷⡙⠶⣾⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⢼⠛⣿⡿⠀⠀⠀⠀⠜⢣⡆⢸⡟⢀⢉⢻⣶⣤⣄⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣿⠷⣄⠀⠀⢶⠆⢈⣧⣀⠑⠀⠠⣤⣝⢿⣍⡙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠒⠒⠲⠶⠶⠾⠛⢹⡆⠈⠂⠀⢀⣤⣿⣿⣿⣿⣷⣦⠠⡙⢷⡈⠙⢦⠘⠆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠲⣤⡀⢿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠄⣸⡇⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠇⢀⠀⠙⠛⠉⠁⠀⢸⣿⡯⠀⣰⡟⢠⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠁⠠⠟⠀⠻⣿⡏⠑
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⣄⡑⢀⠠⠀⢉⠛⠳⣎⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣯⡙⠀⠸⡇⠀⠛⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣄⡀⠀⠀⠀⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣦⣀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⡀⢷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠉⠓⠤⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⣤⠤⠖⠒⠒⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⡾⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣿⡁⠀⢸⠟⠛⠉⠀⠀⠀⠀⠀⠐⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠠
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣀⡀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠈⠉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠐⡀⠀⢰⣿⣿⡿⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠢⠄⠠⢀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠀⠀⠀⡀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠁⠀⠀⠈⠀⠀⠐⣯⠁⠀⠀⠈⠱⡕⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⡰⠀⠀⠀⠀⠠⠐⠛⠒⠒⠒⠒⠚⠓⠠⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⣃⠀⠀⣀⡀⣒⠨⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢰⡀⢀⠀⠠⠄⠀⠐⠊⡃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠹⠃⠇⠂⠀⡤⠒⠤⠄⠀⠀⠞⠃
⠀⠀⠀⠰⠀⠀⢠⣶⣶⣦⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠑⠂⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠘⠿⠿⠟⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⢠⡊⣢⠀⠀⠀⠖⢀⢀⣈⢩⠅⠀⠈
⠀⠀⠀⠀⠈⢒⠒⠂⠀⠀⠁⢀⠀⠀⠀⠤⠄⡂⠤⢔⠀⠩⠉⠡⠐⠐⠀⠀⠀⢀⠨⠤⠤⠤⠄⠚
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠂⠁⠀⠀⠀⢉⠉⢔⠀⡁⡀⠄⣀⠄⢄⠐⡄⠀⠀⢀⠀⠀⡀⠀⠀⠀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⡀⠀⠀⠀⠀⠖⢀⠐⡀⠀⠅⠠⠑⠣⠩⠄⡁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠁⠂⠠⢀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⠴⠒⠉⠁
⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⠀⠀⠀⠀⠀⠀⡠⠀⢀⡒⢒⠒⢛⡂⠀⠤⡀
⠀⠀⠀⠸⠛⠻⠷⠾⠿⠿⠿⠟⠛⠛⠛⡣⠀⠀⠀⠀⠀⠸⠲⠉⢲⣖⣸⣒⣑⣪⠹⠴⠚
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠤⠤⠄⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⠀⢀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀
⠀⠀⠀⠀⢸⠀⢸⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢸⠀⣿⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⠀⣿⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣄⣿⣆⣿⣤⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⢄
⠀⠀⠑⠦⣀
⣀⠀⠀⠀⠈⠉⠒⠀⢀
⣿⣷⣦⣄⣀⣤⡀⠀⠀⢱⣄
⠉⠛⠛⠛⢿⣯⠔⠀⠀⠀⠙⠛⢦⡀
⠀⠀⠀⠀⠀⢷⣾⠀⠀⢠⠀⠢⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢻⣿⢁⡀⠀⣱⠀⠙⣦⢄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡄⢠⡏⠀⣶⡏⠀⣿⠈⣇
⠀⠀⠀⠀⠀⢸⣿⡿⢀⣿⡁⢠⣿⣇⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⣧⣾⣿⣿⡀⠙⣷⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣍⠓⢆⣻⡀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣹⡇⠈⡇⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠸⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠚⠛⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠅⠀⠀⠀⠙⠲⢌⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠙⢴⡠⠀⢰⠁⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠠⠀⣀⣀⠛⠁⠀⠀⠦⠀⠸⡀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣆⠀⢰⣶⣄⣀⢤⣤⣤⣦⣴⣥⣀⣀⣀⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣷⣾⣿⣿⣮⡻⠛⠻⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠓⠒⠛⠛⠛⣛⣿⣿⣿⣿⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠦⠤⣤⠤⠤⠤⠴⠾⠿⠛⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣠⣖⣲⡄
⠀⠀⠀⠀⠀⠀⢀⡴⣫⣽⣿⣿⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣧⣰⣃⡀⠀⡴⠶⠶⢦⠀⠀⢹⣿⢡⡏⠀⠃
⠀⠀⠀⠀⠀⠀⣾⠼⠿⠿⠿⠿⠿⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠒⠒⢾⢀⣏⣉⣉⣹⡀⠀⡼⣿⡆⢣⠀⠀⠀⠐⠂
⠀⠀⠀⠁⠀⠀⠳⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣽⣿⣿⣟⣸⣉⣉⣉⣙⣇⣀⣯⣿⣇⣼⣇⣀⣀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣩⠇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⢻⢃⡼⠉⠁⠀⠀⠀⣀⣤⣤⣶⣦⣤⣄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠸⣏⠀⠀⠀⠸⠭⠿⣿⣿⣷⣶⣿⣿⣿⡿⠭⠗⢸⠙⡇⠀⢀⣠⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠘
⠀⣀⠀⠀⢀⡀⣼⣿⣿⣿⣀⣸⡆⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠁⠀⠀⢸⣤⡇⠀⢈⣹⣿⣿⣿⣿⣿⣿⣿⢉⠁⠀⠀⣀
⠯⠭⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠯⠭
⠀⠀⠀⢸⡇⡈⠁⠀⠀⠀⢀⣬⡆⢹⠀⠀⠀⠀⡇⠀⢰⣉⡧⠀⢼⣹⠦⣏⣱⠀⢸⡇⢴⠋⣳⢠⡏⢹⡄⣾⠉⣧⢸⡇
⠀⠀⠀⢸⡇⠃⠀⠀⠀⠀⢸⡏⠀⢸⠀⡠⡀⠀⡇⢠⠤⠭⠤⠤⠤⠤⠤⠬⠤⡄⢸⣦⠬⠽⠥⠤⠭⠭⠤⠬⠭⠥⣼⡇
⠈⠁⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢸⢼⢳⣟⡆⡇⢸⣾⣿⣿⣿⣿⣿⣿⣿⣷⡇⢸⡇⢰⠒⣒⣒⣒⣒⣒⣒⡒⣦⢸⡇
⢀⠀⠀⢸⡇⡀⠀⠀⠀⠀⢸⡇⠀⢸⠘⣞⣿⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⣀
⠉⠀⠀⢸⡇⡇⠀⠀⠀⠀⢸⡇⠀⢸⢰⢃⣿⡄⡇⢸⣛⣛⣛⣛⣛⣛⣛⣛⣛⡇⢸⡇⢸⠹⢿⣿⣿⣯⣿⣿⠟⣿⠀⡇
⠀⠀⠀⢸⡇⢇⠀⠀⠀⠀⠘⢷⡤⢸⡾⣼⣿⣿⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡀⠙⣦⡠⠄⠒⠒⠒⠒⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢰⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠋⠀⠀⡴⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠁⣀⠰⡟⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢠⣼⠀⠀⠀⠀⠀⠙⠋⣀⠀⠉⠉⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠋⠉⠲⠄⠒⠉⠀⠀⠀⠀⡄⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⣀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡰⠋⠁⠐⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠤⡱⢄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠹⣦⡈⠋⠴⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⣤⣤⣤⠤⠤⠐⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠘⢷⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣀⠠⠄⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠸⢡⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣾⠢⠄⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠂⠘⢆⠀⠀⠀⠀⠀⢀⡀⡤⢸⠇⠀⠂⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠓⣤⠠⠔⠒⠈⠁⠀⣸⢤⣄⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠦⡀⠀⡴⠁⠀⠀⢀⡠⠔⠋⠀⠀⠈⠉⠛⠲⠦⠴⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢟⡤⠤⠤⠤⠴⠀⠉⠳⢄⠀⠀⠀⠀⢀⡜⠛⠦⢤⡄⠉⠀⠀⢦⣤⣄
⠀⠀⠀⠀⠀⢀⡴⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡄⣠⠊⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠛⢷⣄⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠉⠑⠒⠒⠒⠀⠐⠒⠒⠢⣤⠔⠁⠈⠻⣦⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠵⠾⠅⠴⠂⠀⠀⠀⠐⠀⠒⢾⣶⣦⣠⡄
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢐⠋⢉⣉⣉⡙⢛⣛⣛⡛⢛⣛⣋⡉⠉⠉⠉⠀⠉⠛⠛⣛⣛⣛⠛⣛⣛⣛⠁⣀⣦⣀⢰⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠿⠉⠉⠁⠘⢋⣉⡟⠸⣏⡉⠟⠀⠀⠀⠀⠀⠀⠸⣿⣩⣿⠺⣿⣭⣿⠺⣿⣭⣿⢿⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⠦⠤⠴⠦⠤⠬⣭⠤⢤⣤⢤⣤⠤⡤⢤⣤⣤⣤⣤⣬⣭⣥⣤⣬⣭⣥⣤⣈⣉⣅⣸⡇
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡧⠀⠀⣴⣀⣀⣂⣆⣀⣀⣀⣠⣀⣀⣒⣲⣒⣒⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣿⠍⢹⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡅⠀⠀⠀⠀⡤⠤⠄⣠⡀⣀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⠁
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠂⢰⠒⠒⠒⠒⡖⠲⠒⠒⠒⠒⠋⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠧⢤⡤⢤⣤⣤⡤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠙⠲⠤⢧⡀⠘⠒⡤⢄⡀⠠⢄⡀⢀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠒⠛⠛⠋⠛⠓⠛⠛⠃⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⡀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠈⠡⡈⠆⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠠⠓⠉⠁⠀⠀⠀⠠⡄⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠐⢄⠀⠀⠁⠀⠀⠐⣦⡀⠀⠠⠼⠃⠀⠀⣠⠞⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠋⠀⠀⠀⠀⢢⡀⠈⠁⠀⠀⠀⠀⠀⠈⢧⣦⡀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠈⠉⢳⡎⠀⠐⠒⠂⠚⠉⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⡔⠁⢀⠄⠀⡼⠠⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⡐
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⣾⠁⢀⠎⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠁⡰⠀⠀⡄⠀⡌⠀⠈⠘⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠣⠀⡸⠠⠚⠀⠠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣀⣀⣄⣠⣶⠾⠟⠁⠀⠀⠀⠃⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢁⣠⡔⠁⠀⠀⠀⢀⠀⠀⠀⠉⠛⣿⣿⣿⡿⠿⢻⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠀⡤⠤⠞⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋
⠀⠀⠀⠀⠒⠢⣀⣀⣄⠀⠒⠁⠈⢠⡀⠀⠀⠀⠀⠀⠀⢀⠈⠐⠒⠂⠀⠀⢀⠀⣀⡀⢈⡇⡀⠀⠁⢀⣠⣴⠄⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠐⠾⠁⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠼⠷⡼⠷⠋⠀⠀⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡤⠔⠊
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠶⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⣿⣷⡷⠀⠀⣴⢰⠰⡆⢖⠀⠀⠀⠀⠀⠘⠏⣡⣿⣿⣣⡷⠠⠄⡀⠀⠀⠀⠗⣙⣭⠆
⠀⠀⠀⠀⠐⠘⠠⠄⠉⣩⠿⠉⠀⠀⠀⠸⡜⣃⢻⢸⡤⠀⠀⠀⠀⣷⣾⣿⡟⡴⣏⣱⣛⠰⢇⠄⠀⠀⢻⠙⢥⠺⠃
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡠⠀⠀⠀⠀⣷⢹⡨⠧⢻⡄⠀⠀⠀⠛⢿⣟⣿⡷⢧⣿⡥⣯⡾⠀⠀⠀⠀⠑⠎⣴⠷
⠀⠀⠀⠀⣠⠶⠟⢿⠸⡌⢣⠱⡀⡀⠀⠠⠟⠒⠛⠛⠉⠁⠀⠀⠀⠀⠛⠛⠢⣰⣿⡬⠟⠋⠀⠀⠀⢀⣠⢠⣄⣀
⠀⠀⠀⠻⣮⡻⢷⡄⢳⣩⣄⢦⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣁⡾⢠⡍⣠
⠀⠀⠀⠑⠈⠻⣾⣳⡀⢷⣜⣮⡵⠾⠃⠀⠀⡆⡆⡴⣀⡀⣖⣖⣾⢂⡀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠰⢠⣍⢱⠟⢢⣧
⠀⠀⠀⠀⠀⠀⠢⠟⠁⠚⠉⠀⠀⠀⠀⠀⠀⠓⠓⠛⠛⠿⣷⣗⠧⠺⠕⠟⠀⠀⠀⢠⠠⢤⡇⠀⠀⠉⠠⠟⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢄⣯⣾⣿⣷⣶⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣔⢿⣡⣼⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⢤⣠⣴⢶⡏⢹⣧⣷⣶⢂⠀⠀⠀⠀⠀⠀⢀⣀⢀⡄⠀⠀⠈⠉⠹⢿⡿⢿⣿⡾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠹⠛⠺⠻⢟⣻⣿⣿⡿⠁⠀⠀⠀⠀⡴⠇⢳⠐⣗⢛⠆⠀⠀⠀⠀⠀⡀⢀⣀⢀
⠀⠀⠀⠀⠀⠠⣤⣜⣟⠱⢶⣄⣠⣶⣿⣛⣢⢈⡁⠀⠀⠀⢹⣏⣝⣃⣙⣭⣏⠀⠀⠰⠆⢖⢶⢒⣥⡺⣁⠆
⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣯⣶⣶⡿⢿⡿⠟⠋⠁⠀⠀⠀⠀⠹⠩⣷⠙⡣⠍⠀⠀⢚⣁⢩⣍⢿⣄⣙⡏⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠲⠼⠢⠾⠀⠉⠘⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣴⣿⣿⣿⣿⣿⣿⡿⢋⠁⠀⠀⠨⠻⢯⣵⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠄⠈⠈⠳⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠘⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣵⣿⣿⣿⣿⣿⣿⣥⣀⠀⠀⠀⢀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣱⣿⣿⣿⡿⠋⠉⠛⠛⠿⢿⣷⣦⣄⣀⣤⣾⣿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠃⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣤⣀⣀⡀⠀⠁⠉⠉⠿⣿⣿⣿⣋⡀⢿⣿⣿⣿⣿⡟
⠀⢀⠀⠀⠀⠀⢠⣠⣿⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⣦⣀⣀⡂⢭⣿⣷⣿⣄⡽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⣽⣷⡤⢶⠤⠖⠐⠒⠚⣟⠁⢸⣿⣿⣿⣿⣿⣿⣿⡿⢟⠉⢀⣨⣾⣿⢿⠛⠉⢙⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠛⠛⣇⣈⣀⣤⣤⣤⣤⡇⠀⢸⣿⣿⣿⣿⣿⣍⣩⣁⣤⣾⡿⢿⢿⣿⣿⣶⣿⣸⠿⠟⠛⣿⣿⣿⣿
⠤⠔⠒⠀⠀⠀⢠⠤⠐⠒⢀⢹⡍⠉⡉⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⣛⣣⣤⣾⣿⣿⠿⣟⡏⠸⠞⢻⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣦⣀⣀⣸⡟⣿⣀⠶⢀⠛⢻⣿⣗⠃⢸⣿⣿⣿⠛⠿⠤⠷⢿⠿⣿⣿⣿⢿⠓⠛⢹⡃⠀⡔⢿⢸⣿⣿⣿⡇
⠀⠀⣀⡀⠀⠀⠀⠉⠀⢀⡸⣿⢹⡈⠙⠀⡀⢸⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⢠⡶⡴⣿⣯⡙⠌⠰⣾⢹⠀⢰⠷⢣⣿⣿⣿⣿⠁
⡀⠀⠉⠁⠀⠀⠀⠈⠛⠉⢻⣿⣿⣇⠀⠀⠀⠀⡿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠈⠛⢴⣿⣿⢿⡇⠚⣿⠩⠀⠒⠀⢀⣿⣿⣿⡿
⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⡀⠀⠀⠀⡆⣹⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢉⣰⠂⠁⣼⣁⡶⠀⠀⣤⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⢹⣾⣿⡟⠀⠀⠀⠀⢁⢹⠀⠀⣿⣿⣿⣄⡀⠀⠀⠁⠰⣿⢿⠀⠀⠉⠙⠇⢀⣾⣿⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⠀⢈⢹⠀⠀⣿⣿⣿⡟⣟⠛⠛⣿⠆⣿⢸⠀⠀⣤⣸⡀⢸⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡅⠀⠀⠀⠀⠈⠙⡇⠀⣿⣿⣿⡃⣿⠻⡟⣿⠠⣿⣾⠆⠀⠯⣿⠀⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢻⣿⣿⠀⠀⠐⠂⠘⠁⡇⠀⣿⣿⣿⣷⡟⠀⣁⠿⢀⢿⡿⠄⣸⣂⣿⢀⣿⣿⣿⡿⢻⣿⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡧⣶⠂⣠⣤⣲⣞⣧⠀⣿⣿⣿⣿⠞⠐⡟⡷⢦⠼⣫⠀⡼⡉⡿⢸⣥⣿⣿⣿⣾⡟
⠀⠀⠂⠈⢠⠄⠀⠀⠀⢸⠀⢸⣿⣿⣿⣁⣉⣯⣈⣤⣿⡄⢿⣿⣿⣿⣤⣤⣾⣝⠿⣦⠙⢆⡿⣵⠦⠔⠚⢻⣿⠟⣿⣗
⠆⠀⣆⣤⣀⠀⠀⠀⠀⠀⠅⠘⢿⣿⠙⠋⠻⣿⣏⠉⠉⠁⠺⡿⠿⠿⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⡶⣷⣿⡇⣤⡟⠉
⠐⠛⣿⣿⠿⠷⠾⠗⡃⠀⢣⠀⢾⣿⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣿⣿⣿⣿⣿⠗
⢀⣀⣤⠀⢀⣀⡀⠀⠀⠀⢨⡆⠘⣿⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠈⠉⡶⢮⣵⣿⣿⣿⣿⠁
⠈⠟⠃⠀⠈⠉⠁⠀⠀⠀⠀⢷⠀⣿⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠀⠂⠀⡀⠐⢻⣿⣿⣿⡇⢠
⡞⣫⡄⠀⠐⠈⢁⠀⠀⠀⠀⠸⡄⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⣀⠀⠒⠄⠈⠑⣾⣿⣿⣿⢴⡇
⣿⣿⣷⣶⣌⣉⠉⣀⣀⣀⠀⠀⠧⢘⣇⣀⣀⡄⠀⠠⠀⠀⠘⢁⡀⢀⠀⠀⠲⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⣿⢯⡟⠀⠀⠀⠀⠐⠖⠂⣠⣀
⣷⣿⣿⣿⣿⣿⣿⣦⣘⣠⡞⠀⠐⠀⣿⣿⣿⡇⠀⠀⠄⠀⠀⠋⠃⠈⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠿
⠟⠉⠉⠈⢻⣟⠛⠣⠀⠘⠇⠀⢀⣝⡩⠏⠓⠤⢀⣠⠀⠀⠀⠀⠀⢿⣶⠰⠆⠀⠀⠀⠀⣰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠠⠶
⠀⠀⠀⠀⣼⣿⠀⠀⢴⠅⠁⠀⠀⠈⠇⠸⠀⠸⠀⢈⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠛⠀⢀
⠀⠀⠀⠙⠿⣷⣶⣆⠀⠀⠀⠀⡀⢼⣄⠻⣦⠄⠄⠐⠆⠀⠀⠀⠀⢸⣧⠄⠀⠰⢶⠀⠰⣾⣿⡀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠐⡄⠸⠆
⠀⠀⠀⠀⠀⢻⣿⡿⠂⠀⠢⣼⣆⠘⢿⣷⡶⠂⡀⠀⡄⠀⠀⠀⢀⠄⠬⠀⠀⠐⠈⠀⠰⣿⣿⣧⣀⠀⠀⠀⢀⢸⣯⣆⣀⠀⢿⠍
⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠈⠀⢠⣿⣿⣷⣦⢺⡾⣧⠀⠀⣀⡀⠀⠀⢀⣷⣇⠀⠀⢸⡛⢧⠘⠻⠆⢖⡱⡁⢸⣯⡗⠀⠀⢀
⠀⠀⠀⠀⠀⠖⢤⣿⣧⠀⠚⠦⡄⢲⡌⠹⢿⡟⠁⠈⠛⣛⣻⣿⣿⣶⣖⡁⠙⣿⡇⢀⡘⢿⡌⠃⠀⠀⠀⠀⠴⠉⣿⡏⡀⡶⠁⠀⡀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠜⠁⣠⢚⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⣠⠒⢀⠀⠀⢀⠀⢀⡀⠀⠀⢰⣄⡤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢲⡜⠁⠀⡵⠀⠙⢁⡴⠉⡴⢡⠏⣴⡁⠚⠠⠃⡜⣡⠃⡄⣈⢠⠋⠀⠀⠀⠓⠚⠷⣄⣀⣠⣿⣶⣄
⠀⠀⠀⠀⠀⣀⢈⣦⡀⠘⠁⠀⠀⡀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠋
⠀⠀⠀⣸⡿⠿⣿⣿⣿⣷⢺⠆⡄⡁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⣾⣶⣶⣖⣲⣲⣶⣶⣆
⠀⠀⠀⣿⣷⣾⣿⣿⡿⡿⠉⠁⣀⠀⠀⠀⠀⠐⠲⣦⣭⡀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣶⣿⣿⣿⡶⠤⡐⡄
⠀⠀⣰⣿⣿⡟⣿⡟⡀⠀⠀⢰⣗⠀⠀⠀⠀⠀⣈⣿⣿⣿⠈⠠⠀⠀⠀⣤⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⣿⣿⣿⠋⠀⠀⢔⡇
⠀⠀⠿⣿⣼⣿⡟⣴⠃⠀⠀⠀⠉⠳⠤⠀⢠⣬⠽⠿⠟⠁⠀⣠⡀⠀⢈⡻⠃⠤⡠⣄⣀⣰⠆⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⡤⡴⠒⠈
⠀⠀⠀⠙⠛⠿⠼⣥⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣠⣤⣶⠾⢛⠄⠀⢯⣉⣊⡧⣵⠏⠀⠀⠀⠀⣀⠀⠀⠀⢀⣾⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠻⠣⠶⠛⠛⡟⡽⠛⠒⠲⠖⢿⣿⣿⣼⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣧⣹⣿⡆⠀⠀⣭⣿⣿⣿⣿⣿⣿⣿⣶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣍⣛⠻⠿⠿⠦⠶⠿⠿⠿⠿⠿⠿⣛⣋⣭⠎
⠀⠀⠀⠀⠀⣀⣤⠄⠄⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡄⠀⠀⠀⠉⠻⣯⣙⣛⣛⣶⣶⣶⣶⣾⣿⣿⡿⠋⠁
⠀⠀⠀⢠⣾⣿⣿⣷⡀⠀⠀⠉⠙⣿⠐⣦⡀⠀⠀⠀⠀⡀⠀⠀⠠⠂⢁⣫⠜⠳⠂⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⢠⡟⠉⠉⠋⠻⣿⣦⣀⡀⢀⣿⣾⣧⣿⣦⣀⠀⠀⢉⣑⠞⠦⠚⠀⢠⣄⡀⠒⢀⣀⡰⡆⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⡾⢧⣀⠀⠀⠈⠸⣿⣿⣷⣾⣿⠿⠿⣿⣧⣠⡷⠀⠈⠛⠀⠂⠀⠀⠀⠀⠈⠑⠛⠐⣾⠀⠀⠀⢀⣴⣾⣿⠿⠿⠿⠿⣿⣶⣄
⠀⠀⣯⣷⣿⣿⣿⣦⣤⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢯⣿⣾⣿⣿⣶⣄⠙⢿⣧
⠀⠀⢵⣟⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣽⣿⣿⣿⣿⣿⢷⠄⠀⠼⣿⣿⣿⣿⣿⡯⠝⠈⠻⣿⡇⠈⣿⣆
⠀⠀⠈⠛⠛⠀⢀⣀⡀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⠶⠀⠶⢻⣿⡿⢿⣿⣧⣤⣤⣼⣿⠏⢠⣿⣿⡀
⠀⠀⠀⢀⣠⠼⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣄⠀⠀⠀⠀⠘⡟⠠⠀⠀⠀⠀⠀⠀⠈⠹⠀⠀⠘⠹⣿⣿⣯⣍⡉⠉⠉⠉⠁⣀⣿⣿⡿⠁
⠀⠀⢀⡘⠛⠛⠛⠛⠻⣧⣽⠿⠿⣿⣿⣽⠟⠿⢃⡄⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⣿⣿⣿⣷⣶⣾⣿⣿⠟⡩⠃
⠀⠀⢨⣿⣓⣶⣦⣤⣤⣀⣠⣄⣘⣛⣏⣡⣶⢼⣿⡟⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠉⠉⠛⠛⠉⠙⠁⠈
⠀⠀⢠⣿⣿⣿⡿⢾⡾⣭⣭⣯⣭⣭⣭⣿⣾⣖⣿⣯⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢺⣟⣛⣿⣟⣿⣿⣻⣿⣶⠶⡾⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣤⡤⢠⣰⣷⠆⠀⢤⣶⡦
⠀⠀⣾⣿⣿⣿⣿⣛⣛⣻⡏⠹⠿⡿⣛⣿⣿⣿⣿⡿⢷⡷⠀⠀⢇⠀⠀⠀⠀⠀⠀⠌⠀⢰⣙⣿⠟⠻⠐⣿⠯⢶⡾⡿⠧⠀⢶⣶⠸⣷
⠀⠀⠙⠛⠉⠉⠉⠙⠛⠛⠟⣻⢻⣿⣿⡿⣿⠟⢿⡷⠀⠀⠀⠀⢸⣤⠀⠀⠀⠀⠀⡆⠀⠈⠻⠷⠤⠤⠶⢯⣶⡁⠀⠀⢘⣿⣅⣩⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠢⠐⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⢠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠂⠰⠀⠀⣠⠿⢀⡠⠴⣄⠀⠀⠐⠋⠀⠢⠀⠀⠀⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂⠀⠨⠀⠁⠀⠄⠀⢈⡉⠀⢀⠠⠀⠀⠀⡀⠀⠉⢄⠀⠀⠑⡄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠁⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠠⢄⠀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⢠⠇⠉⠀⠒⠲⠦⠤⠄⠀⠨⠸⡄⠀⠀⠀⠀⠀⠐⢆⠂⠀⠑⠀⠀⠀⠀⡀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⠌⠀⠀⢀⠆⠀⠀⠀⠁⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢦⡀⠀⠙⠆⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢍⠈⠶⣤⣈⠀⠀⠀⢀⣀⣀⣀⢠⡬⠿⢎⢄⠀⠀⠀⠀⠀⠙⠂⠀⠀⠁⢄⠀⠀⠑⠄⠀⠈⠂⡳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⢄⣀⢀⠀⠀⠀⠈⠁⠉⠉⠀⠀⢀⡀⠀⠈⠁⠀⠃⡀⠀⠀⠐⢄⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠛⠀⢤⠀⠀⠀⠀⠀⠈⠉⠐⠖⠤⢤⣀⣀⠀⠀⠀⠀⠨⠁⠀⠀⢀⣠⡼⢮⡢⠀⠀⡃⠀⠀⠀⠀⠀⠀⣀⢀⡀⠤⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠉⠀⠶⠄⠂⠤⠤⠤⠌⠉⠙⠒⠲⠦⠴⠶⠚⠛⠀⠂⠉⠁⠐⢆⣠⣤⠤⠴⠆⠒⠈⠁