Vegetable oil Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡇
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣶⣶⢀⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⣀⣀⣀⣀⣨⣿⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣿⠀⠀⢢⡀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⢠⡿⠿⠿⠿⠿⠿⠿⣷⠀⠀⠀⠀⣿⠀⠸⢿⢃⢹⡇⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀⠀⠀⢸⠉⠉⠉⠉⢻
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢰⡿⠻⠿⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠂⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⢸⡇⠀⣶⠗⠳⣆⠀⣿⠀⠀⠀⠀⣿⢀⠀⢀⣀⢸⡇⠀⠀⠀⠀⢸⠀⠀⢀⣤⣶⣴⠞⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⡄⢸
⠀⠀⠀⢸⡇⠈⢷⣤⣴⠏⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⣼⣿⠿⠛⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⢠⣴⠇⢸
⠀⠀⠀⠸⣧⣤⣤⣥⣥⣤⣤⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣶⣶⣿⣿⣿⣿⣾⡿⠀⠀⠀⢸⣤⣤⣤⣤⣼
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠘⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⡿⢷⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣄
⠀⠀⠀⠀⣾⣿⣿⣿⣿⡈⢻⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⢻
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡈⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⣾⣿⣿⣀⠀⠀⠀⠀⠀⠀⢸⠀⣤⣄⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⡿⠿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠼⣿⣿⣸
⠀⠀⠀⠀⠉⣉⣉⣩⣉⣉⣉⠉⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣻⡟⢀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸⠀⠙⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠰⠤⠄⣀⣀⠀⠀⠀⠀⠀⣿⠐⠒⠒⠀⠒⠈⡇⠀⠀⠀⠀⣻⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⢀⡀⢸
⠀⠀⠀⠀⠀⣤⣤⣠⣴⣾⡿⠛⠃⠀⠀⠀⠀⣿⠀⠀⣶⣴⣿⣠⡇⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⣀⣈⣋⣈⣛⣋⣀⣀⡀⠀⠀⠀⠀⣿⠠⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⣸⣿⡶⢸⡇⠀⠀⠀⠀⠀⢸⠀⠈⠀⢸
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣤⣤⣭⣭⣽⣭⡇⠀⠀⠀⠀⣻⣇⣀⣉⣀⣸⡇⠀⠀⠀⠀⠀⢸⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠙⠛⠿⠿⣿⣷⡶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠙⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠘⠻⠿⠿⠿⢿⣶⣶⣶⣶⣶⡿⠿⠿⠟⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⢀⣰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀
⠀⠀⠀⣰⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⡀
⠀⣿⠇⠀⠀⠐⠂⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠸⣿
⣾⡏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣿⠃
⣿⡆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⣿⣿⣿⣄⠀⠸⠿⠿⠀⠐⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠈⣿⣿⣿⡷⢴⣶⣿⡇⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⣹⣿⣿⠇⢀⣿⣿⡇⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⣿⠿⠋⠀⢸⣿⣿⣷⠀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠈⠻⣷⣼⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⢀⣤⣤⣤⠴⠛⠛⠛⠓⠀⠀⠀⢠⣤⣤⣤⣤⣤⡤⠂⢠⣾⡿⠁
⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⢀⣿⡏
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⢀⣴⡟⠀⢠⣶⣶⣶⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⣶⣶⡦⠀⠀⢸⣧⡀
⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠹⢿⣄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿
⠀⠀⢿⣿⣶⣤⣄⣀⣀⣀⣀⣤⣤⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣄⡀⠀⢀⣀⣤⣾⡿⠁
⠀⠀⠀⠹⠿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠉⠛⠿⠿⣿⣿⣿⣷⣶⣶⣾⣿⣿⠿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⠿⠏
⣤⣀⣤⣄⣀⣄⣀⣀⣀⣀⣠⣤⣄⣀⣤⣤⣤⣀⣀⣽⣿⣿⣿⣿⣯⣍⣀⣀⣤⣤⣤⣠⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠉⠀⠙⠛⠛⠉⠉⠋⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⣸⡀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⠀⠀⠀⢀⣀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣖⣽⣽⣟⢧⡄⠀⠠⣳⠓⢕⣄⣈⠖⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⣿⣿⣿⣿⣻⠀⠀⢱⡇⣀⢍⡛⡕⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⢿⣿⢿⣫⠟⠀⠀⢺⢇⠣⣀⠇⡜⡆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡳⠟⢯⠗⠛⠉⠀⣰⣆⠀⠛⠷⠲⠮⠮⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡍⢹⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢠⠯⢤⣤⡽⡄⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠉⠑⡄⠃⡀⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣤⣠⣄⡄⣤⣠⣠⣤⠀⣤⢠⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠁⠁⠀⠉⠉⠁⠁⠁⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣾⣷⡀⠀⠀⢀⣠⡀
⠀⠀⠀⢀⣾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⢸⣿⣿⣷⢀⣴⣿⣿⠇
⠀⠀⠀⣾⣿⠀⣿⠆⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣶⣾⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣾⣿⣿⣿⣶⣶⣤⣀
⠀⣴⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠿⣿⣿⣹⣿⣿⣿⣿⣿⠿⠗
⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⣹⣿⣿⣿⣿⣿⢹⣿⣷⣿⣿⣿⣿⣷⣄
⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠼⠿⠛⠋⠀⣸⣿⣿⡿⠹⣿⣿⣿⡆⠀⠉⠛⠛⠃
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠃⠀⠙⢿⣿⠇
⠀⠈⠛⣙⣛⣛⣛⣛⣛⣉⣛⣛⣉⣛⣛⣋⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠙
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠹⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣦⣼⡿⠟⠁
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⣦⢰⠆⣞⡃⣰⠚⣃⢰⣛⠒⢻⠓⣰⢷⠀⣾⣳⢰⡆⠀⣾⣓⠀⣰⠚⢲⣰⡆⣶
⣀⣀⣀⣀⣀⣀⣀⣀⣸⣟⣀⣷⣤⣙⣦⣿⣸⣧⣄⣸⣀⣟⣹⣇⣿⣼⣻⣷⣦⣿⣤⣀⣘⣦⣞⣸⣇⣿⣤⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠤⠤⠤⠤⠤⣀⣀⡀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⣤⣤⣤⣤⣤⣤⣭⣤⣩⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣿⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⢉⣹⣿⣿⣿⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢸⣿⣿⣿⣿⡈⡄⠀⠀⣀⣀⣀⣀⣀⡉⠙⣻⣿⣿⣿⣿⡿⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣿⣿⣿⣿⣧⣤⠀⠀⣀⣀⣈⣉⣉⠙⣻⣿⣿⣿⣿⣿⡇⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣧⣤⠀⠀⢈⣀⣉⠉⣉⣹⣿⣿⣿⣿⣿⣿⢁⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡼⣿⣿⣿⣿⣦⡀⠀⢀⣀⡉⣉⣩⣿⣿⣿⣿⣿⣿⡏⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⣿⣿⣿⣿⡄⠀⢈⣉⣀⣽⣭⣿⣿⣿⣿⣿⣿⠁⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⡇⠀⢨⢤⣤⣤⣿⣿⣿⣿⣿⣿⡟⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣿⣿⣧⠀⢰⣦⣤⣽⣿⣿⣿⣿⣿⣿⠁⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⣿⣿⣿⣷⠀⢰⣦⣼⣿⣿⣿⣿⣿⣿⡟⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣿⣿⣿⣿⠆⢠⣼⣿⣿⣿⣿⣿⣿⣿⠇⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣗⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⡿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢹⣿⣿⣿⡏⢀⣤⣭⣬⣽⣿⣿⣿⣿⣿⠙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⡾⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡈⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣾⡿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⣿⣶⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⣠⣤⣤⣀⠀⠀⢀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢀⣾⣿⠏⠈⠹⣿⣷⡄⠈⢹⣿⣿⠉⠀⠀⢹⣿⣿⠉⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢸⣿⣿⡀⠀⠀⣿⣿⡿⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠈⠻⣿⣧⣀⣠⣿⠿⠁⠀⣸⣿⣿⡀⠀⠀⢸⣿⣿⣀⣀⣀⣴⣿⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠘⢿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⠋⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡉⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠠⠭⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⡏⣨⣿⣿⣧⣤⠤⠄⠀⠀⠤⠤⠤⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⡇⠉⣿⡟⣫⠛⠓⠐⠒⠒⠶⠶⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣿⣿⣿⣿⣿⣿⣇⠀⠚⠛⠓⠒⠛⠒⠒⠒⠖⠲⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣟⣛⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠒⠒⠂⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⠀⠀⠀⣐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡄⠀⠀⠐⠲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⡁⠀⢒⡀⠉⠙⣻⣟⠳⢒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣈⣹⣉⣀⣀⣈⣥⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⡆⠀⣀⢰⣽⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⡀⠊⠳⠶⠦⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⣀⠦⠤⣄⡀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠔⠄⠀⠀⠀⣇⢀⣀⣀⣀⣀⣀⣐⡞⠀⠀⠀⠀⠈⠳⣄⠀⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠙⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠘⣆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣻⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡀⠀⠀⢀⠀⢀⣆⢹⡀⠀⠀⠀⠀⠀⢀⠇⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠘⠀⠀⢠⠂⠀⠈⠀⠀⢀⣠⠖⠊⠁⣈⠇⠀⠀⠀⠑⠒⠋⠁⠙⠳⢦⣀⣀⡴⠋⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⡖⢀⠀⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠉⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠙⠷⢄⡀⠀⠞⠁⡡⠤⠶⠦⠼⡈⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⡹
⠀⠀⠀⠀⠀⠀⢀⡤⢀⡸⠉⠉⠙⠛⡑⢦⡀⠀⢺⣴⠟⠁⠂⠀⠀⠀⠀⡦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⣻
⠀⠀⠀⠀⠀⠔⠁⠀⢨⡗⠀⠀⠀⠀⠀⠈⠹⣆⢻⡇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠈⢀⡄⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⣿⢹⣇⠀⠀⠀⠀⠀⣀⣾⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣦⡀⠠⠶⣷⡆⣸⡷⠶⠛⠛⠋⢩⢙⠏⠑⠂⠠⢤⣤⣀⣤⣀⣀⣀⣠⡤⠀⠀⠟⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⢀⠐⠈⠐⠋⠉⠀⠀⠀⠀⢸⣾⡄⠀⢄⠀⠀⠀⠀⠀⢀⡀⣀⣁⠀⠀⠀⢠⣖⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠙⠂⠤⠷⠄⠀⣀⣤⣤⣤⣤⣬⡤⠤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⡄⡄⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⢷⠃⡆⡔⢰⣴⢰⠆⠀⡇⠀⢀⡇⡂⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠘⠘⠁⠃⠘⠙⠀⠀⠀⠃⠀⠘⠈⠀⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⣉⣉⣉⣉⣛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⣭⣍⣭⣯⡵⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠒⠲⠶⠶⠖⠒⠙⢦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡤⣄⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣋⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣀⢳⡀⠙⣆⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠿⣄⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠈⠙⠒⠒⠶⠶⠶⠶⠖⠒⠚⠋⠉⠀⠀⢿⣁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠙⠒⠶⠤⠤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠖⠒⠋⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⣭⣓⡒⠶⠤⢤⣤⣤⣀⣀⣀⣀⣀⣤⡤⠤⠴⢒⣚⡁⠺⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠛⠒⠒⠒⠲⠶⠶⠶⠖⠒⠒⠚⠉⠉⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⡴⠛⠳⡄⠀⣶⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠸⣇⠀⢠⡇⠀⣿⠀⢸⣇⣀⡀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡙⠲⠤⣄⣀⣈⣛⡋⠀⠀⢉⣀⣀⣉⣉⡤⠤⠖⠚⡁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⠑⠲⠤⣄⣉⣉⣉⣉⣉⣉⣉⣉⣁⣠⡤⠴⠒⠋⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣀⣀⣀⣀⣀⣠⣤⡤⠴⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠔⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡔⠉⠡⠀⠀⠠⣄
⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡜⠁⣠⠀⠀⠀⠆⠀⠑⡄⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠯⠀⢄⣀⠀⠀⠀⠀⠀⠀⢸⠅⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠄⠀⢄⡀⠱⣆⠀⠀⠀⠀⢸⡆⠀⢇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⣀⣀⣀⡴⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠹⡶⣠⠀⠀⢠⠞⠀⠀⠀⠀⠀⢀⠃⢀⣿⣆⠀⠀⠀⠘⣿⣄⠈⠦⣀⣀⠀⠀⠁⢰⠇⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠌⢀⠞⣿⠟⠀⠀⠀⠀⠈⠻⣦⣄⣀⡀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡅⠰⣠⠤⠤⠊⢁⡤⠊⣸⢦⠃⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣧⣤⣤⡄⠀⠚⢩⣄⣴⠟⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⠦⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠙⠷⠦⢄⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠄⢁⣀⣉⡀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣾⢦⡈⢫⠁⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⣿⢹⡇⠀⠧⠄⡀⠀⠀⢀⡆⠀⡆⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷
⠀⠀⠀⠀⠀⢹⡀⠁⠀⠀⠄⡀⠀⠀⢉⣀⣴⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡏
⠀⠀⠀⠀⠀⠀⠙⢤⣀⡀⠀⢀⢀⣉⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⡀⠀⠀⢀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⢰⣿⣦⠀⣰⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠚⠛⣿⣛⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⠤⠤⠂⠀⠲⣟⠻⣿⡿⠿⣉⠐⠒⢦⣝⢿⣿⣿⣿⢸⣿⠇⠳⡄
⠀⠀⠀⠀⠀⠀⠒⢲⠠⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⡁⠉⠀⢨⣉⠉⠉⠙⠟⠿⠏⢛⢣⣤⣠⣿
⠀⠀⠀⠀⠀⣿⠀⠸⣄⡙⠟⠛⢿⣧⣄⢠⣄⣠⣼⠇⠈⠁⠀⠈⠳⢦⣤⢽⣔⡄⠈⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠶⠾⠻⠛⢋⠲⣌⠻⠿⢞⡉⠉⠀⠀⠀⠈⣿⠶⠖⠀⢸⣿⣷⠈⡽⣹⣿⠇
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠑⠌⠛⠛⢋⣠⣤⡀⠀⠀⠀⠈⢑⣠⡄⣼⣿⣿⡆⢸⣿⡟⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠘⣤⠲⣦⠀⠀⠀⠀⠀⠘⠛⠁⠈⠉⠀⠀⠀⠉⢉⠉⡰⠃⣽⣿⠇⠸⣿⣧⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢯⣀⣤⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠻⠞⠧⡴⢛⣿⠈⠳⣌⣹⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢱⣿⠀⠀⠀⠀⠀⠁⣿⡿⠆⠀⠀⠀⠀⠀⡟⠁⣿⣾⠇⠙⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡽⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠿⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠙⠆⠐⠆⠑⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⢾⣋
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠃⣀⣤⣤⣄⣀⣀⡤⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⣧⡀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠘⠿⠿⠋⠀⠀⠀⢠⡔⠒⠉⠉⠉⠉⢉⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣹⠉⠙⠛⠛⠛⠋⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠠⠶⠶⣏⠘⠀⠀⠀⠀⠀⣀⠀⠀⠗⠚⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠈⢻⡅⣀⣙⠀⠏⣩⡟⣁⢀⡴⠋⠁⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡆⠀⣖⡚⠇⢹⣿⣇⠀⠁⣛⡟⢃⡴⢊⡴⢧⠀⢀⣠⠞⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡾⠁⠀⠀⠙⣿⣾⣿⣿⡆⠘⣻⣶⣫⡴⢋⣤⡾⠶⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣦⡄⢀⡾⠁⣿⠀⠀⠀⠀⠀⢨⣿⣿⣭⠀⣀⠀⣻⣟⠶⠋⣡⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡇⢹⡾⠁⠾⣧⣀⡀⠀⠀⠀⠈⣟⣛⣋⠀⡈⢙⡛⡋⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⠀⠀⠠⣬⣭⣿⡄⠀⠀⠈⣿⣿⠾⠿⠓⠾⢷⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠰⢤⣈⣹⠀⠀⠀⠙⠿⠶⠶⠶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣀⣀⣀⣈⠉⣳
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣰⡏⠀⢈⣥⠞⠋
⠀⠀⠀⠀⣿⠃⠀⠀⠀⢀⣴⠟⠀⠀⠈
⠀⠀⣴⢶⣯⠀⠀⠀⢶⡟⠁
⠀⠀⢰⡞⣻⣷⣀⠀⠘⠃⣶⡄
⠀⠀⠀⠉⣅⣻⡿⣿⢋⣼⣏⠁
⠀⠀⠀⠀⠙⠉⢠⣿⡆⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢂⡿⣿⣿⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⠿⢹⡿⢃⠾⣋⣿⠋⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣯⡿⠁⣿⣵⣫⣒⣁⡠⢤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⣄⣿⣿⣋⣿⡅⠊⠀⠘⠛⠉⠉⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠈⢳⣨⢹⣿⢟⡉⠌⠻⣶⡶⡶⠾⠖⢚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⡿⣿⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⣡⡿⢵⣶⣯⣓⢶⣶⣦⣤⠴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠿⣄⡘⢮⣀⠀⠀⠀⣂⣤⣦⠴⢏⣆⠀⠀⠀⠈⢉⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⠀⠀⠀⠀⣝⣶⣼⣿⣿⠛⠋⠉⠂⢰⣍⣿⠿⠾⠛⣻⣏⣴⣆⣄⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⢿⣉⠛⠛⢋⣁⠀⠿⢽⣿⣷⣆⣀
⠀⠀⠀⠀⠀⣀⣤⣴⣄⢙⣓⣧⣿⠶⣬⣁⠀⠀⡀⣀⣜⠁⠦⡔⠁⠀⢀⡄⠙⠁⠀⠀⢃⢝⣬⠂⠈⠙⠛⠁
⠀⠀⠀⢠⠚⣓⣢⠔⣫⠽⢣⣿⠏⢠⣾⣉⣽⠟⠛⠉⢿⠃⠘⠃⠃⠘⠋⠀⠀⠀⣀⢔⡼⠋⠼
⠀⠀⠀⠘⠡⠿⢱⠾⠿⠴⠛⠓⠈⠉⠉⠁⠀⠀⠀⠀⠈⠳⣦⡀⣄⣀⣀⣤⣤⠿⠟⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠒⠒⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⣿⡿⠿⠭⢟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠹⠄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣦⠄⠀⠀⠀⢰⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠼⠃⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣴⡀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠀⠀⣸⣟⣦⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⢠⣸⣿⡇⠀⠀⠀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⢠⣷⡿⠉⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠛⢳⣿⢀⣤⣾⣿⣿⣿⣿⣶⡤⠄⠚⠀⠰⠶⣾⣿⣿⣿⣿⣿⣾⡀⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢠⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⣾⣿⣖⣾⣿⣿⣿⣿⣿⣿⣿⡆⢸⡆⠀⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡜⠛⠀⢻⣿⣿⣿⣿⠿⠿⠣⢎⣼⣿⣿⣾⡜⢿⣿⣿⣿⣿⣿⡿⠁⠸⣷⣶⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠉⠉⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣉⣄⠀⣀⡀⠉⠀⠄⠀⠀⢸⣍⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣯⠏⠃⠁⠀⠠⠀⠀⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⠀⠉⠺⡿⠁⠁⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⡌⢿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣠⣤⣠⣤⣽⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣆⠈⠻⣿⡏⣌⠃⡏⢸⡃⡏⣏⣙⣩⣿⣿⠿⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠀⠈⠑⠓⠦⠶⠸⠿⣹⡤⣭⣴⠿⠃⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠈⠃⠀⠀⠀⠀⠈⠋⠉⠙⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠃⠀⠀⠠⢈⣿⠇⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⠂⠀⢠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⣴⣿⣿⣿⣿⣿⡀⠀⣹⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣆⠂⣼⣿⣿⣿⣿⣿⡯⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⡟⣡⣼⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⢿⡆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠋⣙⠻⣿⣿⣿⣿⠟⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠁⠉⠛⠋⠀⠀⠀⠀⠀⠈⡙⢂⠆
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⣈⡀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠈⠉⠉⠉⠀⠀⠀⣿⠿⠿⠋⠉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠂⢐⡴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⣐⡞⢤⡤⠶⠀⠀⠀⠀⢸⢇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⢄⡀⠀⣀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢱⣦⣄⣀⣠⡴⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠋⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠧⠀⠀⠒⠂⠀⠒⠀⠄⡀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡄⠀⢀⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⣠⣿⡿⠀⠀⠸⣿⣿⡇⠀⠀⠀⢤⢾⣧⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡅⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠿⣿⡿⠀⢀⣴⣦⡄⠀⣴⣶⡄⢠⣄⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡙⢣⣤⣄⡀⠀⠀⠀⠈⠻⠿⠟⠀⠻⡿⠇⠘⢿⡇⠀⠐⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⠿⠿⠃⠒⠈⠀⠈⠋⢠⡄⠀⠀⢠⣶⣄⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠋⣆⣰⡎⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠸⣿⠟⠀⣾⣿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⢠⣴⣤⠀⠙⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠻⠿⠟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⢀⣤⡶⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⣰⡄⠉⠁⠀⠈⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠿⠇⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣦⣶⣴⣶⣦⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶
⣿⣿⣏⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠉⠁⠀⠀⠈⠁⠒⠤⡀
⠀⠀⠀⢀⣀⡀⠀⡠⠊⣁⣀⣀⠀⠐⠒⠤⠤⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⡥⠄⡶⠉⠀⠢⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢉⠄⠀⠀⠀⠈⠑⢍⠁⠒⠠⣀
⠀⠀⠀⠀⠰⢡⠀⠀⠀⠙⡆⠀⡗⠒⠠⠴⠤⠤⠤⠤⠽⠉⠐⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠖⠠⠃⠀⣴⠂⠀⠀⠀⠀⠑⡀⠀⠈⢳⣄⣀
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠙⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣂⢀⡁⢀⡌⡇⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⢯⠉⢆
⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠁⠀⢀⠖⠒⠒⠀⠓⠀⠉⡏⢑⡄⠀⠀⠀⠀⡍⠉⠀⠀⠀⠀⠈⠙⠃⠒⠀⢤⢀⣸⠀⠀⠀⠀⣼⠀⢨
⠀⠀⠀⠀⠈⠆⠀⠀⡜⠉⠱⠉⠀⠀⠀⠀⠀⠀⡀⢼⠀⠐⣆⠀⡤⠴⠾⣏⡁⠁⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⠰⢄⠀⠀⠀⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠈⢆⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⣆⠬⠁⣰⡇⠙⠢⠴⡖⠁⠀⠀⠀⠘⠈⠀⡄⠀⠀⠀⠓⠀⠀⠀⠀⠘⠤⠀⢄⠀⠀⠀⡌⢰
⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢚⡩⠋⠉⡆⠀⠸⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠜⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠂⡄⠀⠀⠲⡒⠉⡇⠀⢀⠜⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⢄⡠⠐⠈⠉⢘⠅⠀⠀⠀⠀⠀⠀⠀⢈⠦⠻⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⠀⢤⣿⡦⣤⠴⠋⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠎⠀⡠⠶⣶⢻⠀⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠒⠢⠼⠛⠉⠱⡀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠈⡎⠉⣿⠁⠀⠀⣸⠦⡀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢰⠁⠀⠀⠀⠀⠀⡸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⣇⠀⠘⠳⠶⠚⠋⠀⠈⢢⠀⠀⠀⠑⢄⡀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⠄⠀⠀⠒⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣼⠀⠀⠀⠀⣀⣀⠀⠀⢡⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⣂⡀⢰⡀⣀⠤⠚⡅⠀⠀⡠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣟⠀⠁⠀⠀⠀⠀⣀⠬⠦⠞⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡨⠋⠉⠘⠃⠉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⠶⣐⣂⣙⢲⣖⣖⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠈⠀⠔⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠒⠀⢠⢠⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⣉⣉⡉⠈⠉⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠸⠖⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⢀⣀⢀⣀⣀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣈⢉⣉⣀⡀⠬⢥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠸⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⢆⡀⣙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠤⠴⠃⠀⠀⡗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠄⠤⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⠿⢿⣿⠋⠀⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⠶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣛⣛⡛⠻⠇⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣯⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠿⠿⣿⣶⡄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣋⣥⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⣀⣀⣠⣼⣿⡿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⢹⡇
⠀⠀⠀⠀⠀⠀⢸⣿⢿⣟⠻⣿⣿⣿⠿⠷⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠾⠛⠋⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣦⡛⢷⣤⣍⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣍⠻⢶⣬⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⡙⢷⣤⣈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠿⣦⣌⡙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⣝⠛⠿⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡾⠟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣧⡈⠛⠷⣶⡄⠈⠉⠛⠛⠿⠷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⠶⠶⠶⠿⠿⠿⠿⠟⠛⠛⠋⠉⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣏⠛⠷⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠷⣦⣀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣦⣄⡀⠀⠀⠀⢀⣤⣠⣀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣈⠛⠿⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣌⠛⠻⠷⠆⠀⣿⣿⣿⣿⠋⠉⢹⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⢿⣶⣶⡆⢸⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⠄⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢷⣦⣤⣀⠀⢸⣿⣿⣿⡀⠀⢀⣾⣿⣿⣿⠀⠀⢀⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠉⠙⠀⠸⣿⣿⣿⣷⣶⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠻⠿⡶⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣿⣶⣤⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠿⣿⡿⠃⠀⠀⠈⢿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⠙⠿⣿⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠷⢶⣦⠈⠉⠛⠛⠿⠷⣶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⡶⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠷⣶⡶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣬⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣴⣶⣶⣾⡿⠿⠟⠛⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⣇⠈⡇⡀⠀⠀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠲⠚⢻⣿⣿⣿⠿⠶⠶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡆⢻⡜⡄⠀⢠⠀⠄⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠚⣡⡾⠉⠉⡡⠄⢀⣈⢩⣶⣾⢣⡀⠀⠀⠀⠀⠀⠀⠀⣦⡆⢧⠈⢿⣜⠀⢐⡄⢀⠈⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠘⠹⣦⠟⣿⣿⣷⠀⠀⠀⠀⢠⣶⣼⣿⣧⠈⢇⠈⢿⡂⠀⠀⣀⣠⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠚⣡⣿⣿⣿⣿⠀⠀⡀⠀⠈⠿⢿⣿⣿⣿⣎⠢⣀⠛⠲⣶⣝⣿⣦⣿⠇
⠀⠀⠀⠀⢀⣎⡀⠠⠃⠀⠀⠀⠀⠠⠐⢁⣴⣿⣿⣿⣿⠟⠀⠀⠀⣠⣤⣤⣀⣿⣯⣿⣿⣷⣬⠑⢄⡙⠿⣿⣿⡿
⠀⠀⠀⠀⢠⠟⡄⠁⠀⠀⠀⠐⢀⣴⣀⣨⣿⡿⠛⠃⠀⠀⠀⠾⡿⣿⣟⣻⡿⠛⠙⣿⡿⢹⣿⣿⣦⣬⣑⡢⣝⡗
⠀⠀⠀⠀⠀⣆⠀⢀⣀⢤⣔⠠⢚⣽⣿⡿⠋⠀⣠⠎⠀⠀⠁⣰⠟⠉⠉⠙⢿⣤⣴⡿⢁⣾⡿⠿⠿⠛⠛⠛⠺⠃
⠀⠀⠀⠀⠀⠘⠢⢽⣞⠯⣖⣤⣿⣿⣿⣷⢴⡶⠋⣀⣀⣤⣾⠏⠀⠀⣀⣤⡾⠃⣀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠀⣸⡀⠊⠀⠉⢙⣥⣄⡠⠴⠋⣀⣴⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣍⣙⣒⣒⢒⣁⣀⣠⣤⠖⠋⠁⢓⣿⣯⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡟⣻⡟⠁⠀⠉⠀⣰⣯⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣷⣍⣀⣠⠀⣀⣭⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡯⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢼⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠗⠻⠿⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢫⣴⣶⡏⠀⠀⡹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣾⣿⣷⠀⠀⢠⡇⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢘⣿⣿⣯⠀⠀⢸⣇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⣿⣿⣗⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢈⣿⣭⣥⣤⣤⣤⣌⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠉⣩⣭⣍⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢀⣾⢿⣿⡿⣆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢡⡿⢡⡎⠹⣷⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣟⣱⣿⢾⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣺⠟⣿⡇⣼⣿⣿⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠻⠶⠟⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢯⡷⣦⠀⠶⠀⣿⠆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⢸⡇⢿⡆⣴⠀⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡜⢇⡾⠃⠿⠀⠿⠶⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⡄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠃⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⠿⠿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠻⣿⣿⣄⡀⠀⠀⠀⠀⡾⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣯⣭⣭⣭⣶⣤⣤⣶⣶⠾⠃
⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣥⣤⣶⣿⣖⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠠⡇⠑⠦⠀⣀⡀⣠⡀
⠀⠀⠀⠀⠀⠀⣴⡃⠙⢦⡄⠀⠀⠉⠙⠶⠶⠦⣄⣀⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⢷⣄⢀⠃⠀⠀⢀⡄⠈⠙⠱⣦⠼⢷⡀
⠀⠀⠀⢠⡾⢟⠁⠀⠄⢠⠤⠽⣦⡀⠀⢀⣈⠤⠄⠀⠀⠀⠀⠈⢷⣦
⠀⠀⢀⡸⠃⠀⠡⢀⠀⠀⠀⠀⠙⢿⣦⡟⠀⠀⠀⠀⠀⡰⠥⠄⠀⠙⢶⡀
⢀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⢿⣷⡀⠀⢀⠄⠁⠀⠀⠀⠀⢀⠈⢷⣄
⠈⣏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠉⣷⡴⠋⠐⠐⠰⣔⠃⢀⠦⠄⠈⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⢀⣀⠀⠀⢀⡀
⢰⣿⠂⠀⠀⠉⠁⢂⡠⠤⠀⢄⣀⡀⡀⠱⣿⣷⠀⠀⠀⠀⣠⡴⣥⣀⡀⠀⢿⠄⠀⠀⣠⠶⠶⠖⠟⠃⠀⠉⠉⠙⠋⠉⠉⠹⠓⠂⠴⠢⠄⡰⠂
⢸⣇⠀⠀⠀⠂⠞⠀⠀⠀⡠⠄⠉⠉⠉⠻⣿⣿⡀⢀⡴⠋⢀⢴⣿⢏⡁⠖⢸⠆⣤⠞⠉⠀⡁⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⣀⣀⡤⠖⠁⢠⠃
⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢈⣿⡷⠋⡾⠋⢀⣾⣵⣾⡇⣿⣯⡼⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣦⣴⠟⠋⠅⠀⠀⠀⡀
⠈⢧⣄⠀⠀⠀⠐⠂⠚⡙⣿⣆⡂⠠⠀⡂⢨⣿⣧⠞⣁⠴⠛⣱⡟⠉⣟⠻⢏⠀⣀⠀⠀⠀⠀⠀⠈⠑⡀⣀⣶⠿⠟⠛⠂⠀⠀⠀⠀⢰⡇
⠀⠈⢧⡀⠀⠀⢸⡶⢾⡿⠻⣌⠛⢓⢦⣼⡟⠉⠀⠈⠀⠀⣴⣿⡄⢠⠌⠀⢰⡆⠀⠀⢀⠀⠀⠀⠀⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠁⠠⠈⠁⠀⠈⠀⠋⡙⣲⣤⣽⣿⣿⠀⠀⠀⠀⠐⠁⠀⣴⡇⣰⣆⣸⣀⠀⠀⠀⢑⠄⣠⣾⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢘⡷
⠀⠀⠀⠀⣤⠀⡄⠀⠀⣀⣠⠿⠗⠀⠀⢻⡟⡀⠀⠀⠀⠀⣠⣾⣿⣶⣿⢿⣿⡿⣀⣴⠾⣛⣿⣿⣿⡦⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢛⠊⠑⢀⡀⠀⢹⣆⣀⡀⠠⣼⣷⣆⠀⠀⠀⣈⣩⣭⣭⡿⢷⣾⣿⣿⢋⣴⠛⠉⠉⠀⠉⠁⠘⢿⡶⣤⠀⠀⠀⠀⠀⠀⢀⡷
⠠⠄⣀⠐⢼⣄⣷⣿⣟⣛⣛⢛⡛⣻⠿⣿⣟⢛⠛⣿⣿⠋⢀⡾⠋⠈⠀⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⡛⠳⠆⠀⠀⠀⣠⡏
⠀⠀⠀⠋⠀⠹⢿⣿⠻⠿⢿⣿⣿⠁⢀⡟⠋⠙⢻⣿⣯⡖⠁⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⢀⡠⠖⠛
⠀⠀⠀⠠⠚⠀⠜⠋⠁⠲⢿⣿⣷⢀⡾⠓⠀⢀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣤⣤⣠⣴⣿⣿⣿⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣇⠀⢀⣤⣿⡿⣿⣿⣼⣄⠀⠀⠀⢀⡔⡺⢿⣿⣿⣿⣿⡿⣫⣿⣿⡿⠏⠀⠈⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⢑⣿⠟⠛⠁⠈⠑⠉⢻⣿⣦⣤⠾⠒⣀⣀⡉⠉⠛⠛⣟⢿⣿⡇⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡶⢛⠋⠁⠀⠂⣀⠀⠀⠀⢿⢉⡴⠛⠛⠛⠻⣍⢢⡀⠀⣿⡗⢸⣷⠄⠀⠀⠀⠀⣴⣿⣠⠀⠀⡐⠀⢀⣠⣶⡿⠋⠀⠀⠸
⠀⠀⠀⠀⣀⠄⠒⠂⠀⠈⠉⠒⢝⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠆⠀⠀⠀⠀⠈⠇⢹⡀⠸⣧⣾⣿⣶⣦⣤⣤⣼⣿⣾⣧⠅⠀⠁⠀⠈⠉⠀⠀⠀⠀⣰⣿
⠀⠈⡍⠁⢤⣴⣶⣶⣤⠤⠀⣀⣼⣾⣿⣿⣯⡀⠀⠀⢀⣀⣀⣤⣿⣿⣄⠀⠀⠀⠀⢄⠘⣺⡇⠀⠙⠿⣿⣿⣿⣭⣭⣿⠿⠋⠀⠀⠈⠠⡀⠀⠀⢀⣀⠔⣺⣿⠏
⠀⠀⠷⣀⠀⠀⠀⢀⣀⣤⣶⣿⠟⡇⠻⣿⣿⣿⣷⣿⣿⣿⡿⠛⠙⢿⣿⡄⠀⠀⣀⠀⣀⣿⠃⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠶⠞⠚⠉
⠀⠀⠐⡀⠈⠉⠉⠉⠻⠋⣹⣿⡾⠁⠀⠀⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠙⠻⠿⠦⠼⠿⠛⠒
⠀⠀⠀⠈⠒⣶⣤⣦⣴⡞⠉⠉
⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣘⠃
⠈⠀⠀⠘⠄⠀⠀⠀⠀⣀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠌⠀⠔
⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡀⠀⡆⠀⣂⠀⠀⠀⠀⠀⠈⠱⠄⠀⠀⠀⠗⠀⠀⠈⠓
⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡠⢃⠀⠁⠀⠻⣤⠀⠀⠀⠀⠠⠀⠀⠰⠄⠀⠰⣄⠀⠀⠀⠘
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠉⠁⠀⠀⠀⠀⠉⠳⢄⣀⡀⠀⠀⠀⠒⠂⠀⠀⠈⠽⠠⠄
⢀⡔⠢⠄⢤⣀⠀⠀⠀⠙⠁⣀⡤⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠂
⠋⠀⠀⠀⢀⣿⠆⠀⡴⠚⠉⠀⠀⢠⠏⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠄⠀⠀⠈
⢷⣤⣤⣤⠾⠋⢀⡎⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠂⠀⠀⡐⠀⠄
⠀⠀⠀⢀⣤⠖⠛⠁⠀⠀⠀⢀⡤⠒⠀⠀⠀⠀⠀⢠⠶⠛⠛⠒⠠⠂⠠⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⢰⠋⠁⠀⠀⠀⠀⠐⠀⡸⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠸⣄⡠⠄⠂⠀⠀⠀⠀⠀⠒⠀⠀⠀⢼⠁⠀⠀⠀⠀⠄⣀⡀⠔⠁⠀⠀⠀⠂⠀⠀⠌⠁⠀⠈⠀⡀⠈⠂
⠤⠄⠀⠀⠀⢈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠐⠀⠀⠀⠀⠀⠁⠀⢂⠄⠀⣢⡷⠀⠐⠏⠀⢀⣠⢄⠔⠀⠀⠀⠀⠀⠠⠔⠂⠀⠈⠀⠀⠀⠠⠄⠀⠀⢰⡇⠈⠙⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠖⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⣀⠔⠋⠈⢷⡀
⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠙⢦⡀⢀⠀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⡁
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠳⣄
⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤
⢁⡀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⠀⠀⠀⠀⠅⠀⠀⠀⠠⠂⠠⠍⠁⠀⠚⠛⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠈⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠈⠈
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠊
⠀⠈⣆⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠶⠶⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣀⠀⠀⠾⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠒⠒⢲⠒⠒⠛⠛⠉⠉⠉⠉⠉⠉⠏⠁⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢲⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⢆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠸⠒⠒⠚⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠸⠀⠀⠀⡀⠀⡶⠶⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡠⠔⠦⣄⠀⡤⠤⠤⠤⠤⡄⢰⠒⡇⠀⡼⠉⠚⡃⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡞⠀⢀⠀⠈⢃⠓⠒⡆⢰⡒⠁⢸⠀⢱⢀⡇⠀⠀⢸⣀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⡇⠀⠯⠇⠀⢸⣴⠒⠃⠀⠉⢳⠸⡆⠀⠉⠛⠉⢹⠀⡤⡀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠳⢤⣀⣀⠴⠃⠙⠒⠒⠒⠒⠉⠀⠷⠤⠴⠶⠶⠚⠀⠑⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠶⠶⠤⠤⠤⠤⠶⠶⠦⠤⠤⠤⠤⠴⠶⠒⠒⠒⠚⠋⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠲⠤⠤⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡁⠶⠂⠉⡑⡖⠒⠠⡉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡰⠋⠈⢄⢣⡀⠇⡇⢀⡠⢊⠦⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢰⣀⣀⣀⣈⣧⠙⠠⠖⣩⠖⠁⠀⢱⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡆⠐⠒⠀⢠⡄⢀⡀⢈⡉⣀⣐⣒⣚⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠦⢤⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⣰⡀⣀⣴⢾⠶⠋⣽⡌⠣⡀⠉⠉⠹⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠍⠣⡉⠔⠀⠀⠀⣿⠈⠣⡹⢄⡰⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠐⠀⠀⠄⣹⡀⡠⠜⢋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⠶⢤⣤⣠⣤⠤⠶⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⠦⣄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⠀⠀⠀⠀⠀⢀⡠⠔⠈⠉⠑⡉⠒⠢⠤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠈⣳⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠐⠁⠀⣠⠴⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡆⠀⠀⠀⠃⠀⠈⠀⠀⠘⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠐⣬⠒⠒⠒⠒⠒⠒⢦⡀⠀⠀⠀⠀⢸⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⠀⠀⠀⠈⢆⢄⡀⠀⢀⡠⠔⢸⠀⠀⢠⠀⠀⠀⠀⠘⢆⠀⠀⠀⣼⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠀⠈⠢⠤⠚⠉⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡄⠀⠀⠀⠀⠀⠀⣠⠒⠢⢄⡘⢠⣀⠈⠀⠀⠀⠀⢀⢸⠀⠀⢠⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣷⠀⠀⠀⠀⠀⡰⠁⠀⢀⠀⠈⠙⠷⠄⠀⠀⠀⠀⠊⠜⠀⠀⢸⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢱⠀⠀⠀⠀⡐⠁⠀⡠⠉⠐⠢⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⢃⠆⠀⠁⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⢀⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢇⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢻⠀⠀⠀⠀⠀⠉⠂⠄⡠⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠦⣈⠉⠙⠛⠛⠛⠛⠛⠋⢉⣁⠴⠖⠋⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠤⠤⠤⠤⠤⠤⠶⠖⠋⠁


⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣭⣭⣬⣭⣭⣉⣍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⣦⣤⣿⣿⣿⣭⣿⣿⣽⣿⣯⣭⣽

⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡄⢀⢄⢀⠀⠀⠀⠀⠀⠀⡖⠈⣀⢀⢰⡆⠀⠀⠀⠈⠁⠈⠉⠙⡇
⠀⠀⠀⠀⠀⠀⣟⣛⡟⠚⣿⡇⠀⠀⠀⠀⠀⡀⠰⠀⠌⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⡃⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢾⠃⠀⠀⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠓⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠀⠑⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠰⠆⠈⣴⠟⠀⠀⠀⠀⠀⠀⠳⠄⣀⣠⠾⠀⠀⠀⠀⠐⠦⠀⠐⠶⠃⠀⠀⠀⠀⠀⠠⠐⣠⣴⠇⠀⠀⠀⠀⠀⠸⠦⠀⣀⣀⣀⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⢀⠀⣀⡀⠀⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠰⣾⠀⠀⠨⢷⣩⡗⠀⠀⠀⠀⡋⠀⠀⠀⠁⠀⢹⠀⠀⠘⢆⠀⠀⠀⠀⣼⠃⠀⠀⢸⡛⠀⠒⠒⠒⠛⠻⠂
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠠⠋⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠀⠈⢢⠀⠀⡜⠁⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠰⠀⠀⢠⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠀⠀⠀⢃⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⣿⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣏⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⣀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠐⠄⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠘⠤⠄⠀⠐⠀⠀⠀⠀⠀⠀⠢⠀⠠⠀⠂⠀⠀⠀⠀⠛⠀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢰⡶⠊⠉⠉⣀⣨⣷⠀⠀⠀⠀⢠⣇⣤⣾⣧⣤⡄⠀⠀⠀⢠⠀⠀⠄⠀⣄⠀⠀⠀⠀⢰⠏⠉⠉⢭⣿⠀⠀⠀⠀⢠⣄⣒⣒⢒⢲⣦⡄
⠀⠀⠀⠀⠈⡇⠠⠆⠤⠖⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣁⠀⠀⠈⣿⠀⠀⠀⠀⢰⠂⣠⢿⡴⣣⢰⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠤⠀⠀⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣗⠀⠀⠀⡟⠀⠀⠀⠀⢸⠢⠔⠪⠃⡼⠀⡇
⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⡀⠁⠀⢀⡅⠀⠀⠀⠀⠀⢹⠀⠀⠀⡇⠀⠀⠀⠀⢘⡀⠈⠉⠉⠁⣐⡀
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠚⠃⠀⠀⠀⠀⠀⠀⠘⠂⠐⠚⠃⠀⠀⠀⠀⠀⠂⠀⠐⠛⠀⠀⠀⠀⠀⠀⠘⠀⠀⠚⠁⠀⠀⠀⠀⠈⠓⠂⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠠⣉⠀⠂⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠤⠤⠔⠀⠀⡤⠀⠀⡈⢰⠀⠀⠁⠛⡚⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⠐⢀⠖⡈⣀⡀⠡⠋⣠⢠⠉⠠⠢⡐⠀⠃⠴⠓⠂⠀⣰⠝⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢤⡀⣀⣀⠚⢀⡍⠐⠄⠀⣿⢻⡀⠂⢀⡄⠒⢉⣤⠐⠁⠐⢿⡨⠆⢀⡄⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡙⠿⣉⠠⠽⢀⠱⡖⠛⠂⠊⠉⠉⠀⠂⠀⠀⡄⠘⣟⠀⠸⢷⡾⢃⣠⡼⠛⠠⠆⣡
⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⣀⡘⢿⣿⡞⡌⠠⢲⠤⠊⠁⠸⣥⣶⠀⠀⢹⠀⠈⣚⠉⠃⠉⠨⣶⡣⠰⢿⠁⠦⡔⠞⠴⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠒⠀⠀⠐⠡⠀⢅⣼⠉⠹⢇⡈⠃⠁⠀⠀⠻⡅⠀⠄⣀⠀⢀⣤⠀⣈⡀⣤⠚⢙⡏⡈⠀⢠⣢⡞⣣⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡖⠻⢶⣾⣋⠃⢐⡶⠈⣙⠂⡀⢋⠠⣼⡯⢘⣯⡠⢛⣀⣉⠀⠀⠊⢤⢰⡷⣶⡟⢸⣿⣯⡄⠘⣰⢖⠉
⠀⠀⠀⠀⠀⢀⠳⡖⢤⡖⢎⠹⠿⡿⠯⠘⠉⠀⠄⠰⡄⣀⣄⠊⣀⢁⠀⠟⡅⠫⠅⣍⣷⠁⠀⣛⡆⣤⠚⢷⣾⡷⠷⠂⢀⢿⠊⠡⢄
⠀⠀⠀⠀⢀⠀⡀⠁⠠⠜⠖⠤⡁⣽⣿⡟⣃⠸⢣⢨⡤⢏⡍⠀⠈⣤⠴⢡⡡⠀⠀⠋⣤⠠⣰⣏⣁⣸⣃⣼⢋⠗⢨⣐⢶⣾⠷⡀
⠀⠀⠀⠀⠀⠀⣿⣂⠀⢢⡆⢾⠥⠉⠹⠃⠉⢸⡇⡈⠃⠀⠀⠀⠒⢢⡿⣛⠙⡢⠿⢟⣌⠀⣘⠋⣡⣹⠡⠜⣦⣼⠷⢁⣻⠉⠆⠗⠂
⠀⠀⠀⠀⠀⢙⠻⠟⠇⢾⠟⠋⠓⣓⣦⣛⣝⢓⡄⠁⠰⠀⢢⣦⣎⢾⡭⢿⣦⢱⡿⢾⣿⣃⠀⣤⠁⠉⠥⡜⡿⣿⣿⡯⣿⣶⡅⠐⢻⠢⠤⠐
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢀⡴⢤⠦⣭⣷⡜⢉⡈⠃⠈⠓⠀⠈⠀⠛⢯⢌⢳⣷⡶⠈⣳⣿⠁⠦⠟⠀⠒⡀⢸⣦⡶⣿⣿⣿⣾⢶⡁
⠀⠀⠀⠀⠀⠀⢀⡒⠖⢡⣴⡟⢋⡩⠅⡠⢔⠄⠐⢃⠀⣀⢈⠄⣈⠀⠼⢟⡝⡣⣤⡽⢿⡷⣀⣈⡝⠂⢖⠻⠜⣁⣙⣳⣝⣧⡾⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⢈⠐⠿⠡⠄⠈⣋⠠⣁⣨⣷⣾⢷⣄⣈⣏⠈⠳⠼⢾⠃⡀⠫⢟⢻⠠⣶⣿⣾⠈⣻⣇⡹⢁⣠⠙⠛⢝⠎⢙⠲
⠀⠀⠀⠀⠀⠀⠀⠈⢐⣠⡔⠁⠌⡹⢻⢿⡽⠋⣽⠿⢪⣮⣝⣉⡞⢧⠘⠀⠑⢋⣩⠽⢳⡚⢫⣞⠃⢈⣻⣷⠯⡽⣷⣺⣷⠴⠈
⠀⠀⠀⠀⠀⠀⠀⢰⣹⠙⢁⠀⠀⢄⢠⠉⡁⠞⣱⢳⠏⠹⢷⠇⠿⣰⡟⣱⡋⠉⠷⢳⠐⡒⠺⠫⠷⣦⠑⣷⢭⡃⠛⠟⠋⢐⡴
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠐⢠⠈⡜⠙⢁⠊⣷⡴⣟⣴⢿⣷⢀⡉⠹⠩⠉⣠⡨⠥⡄⠐⠁⣀⠤⡚⣆⢠⡁⢿⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠨⢓⣴⠀⠐⠄⠲⢛⣿⣿⡛⢺⢴⢆⣴⡾⢸⢟⠒⢀⡀⢊⡀⣼⣿⡞⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠳⠀⠁⠀⣄⠌⠯⣮⣸⠂⠀⢧⣟⡇⠀⡘⢂⣨⠓⠊⣰⢥⠉⠸⠃⠄⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠒⡊⠔⠁⣁⠘⡿⠿⠃⢷⣿⣭⡁⠀⠘⣏⡀⠀⢀⠈⠠⡐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃⠙⠀⠈⠛⠂⣼⡋⠑⠀⠀⠈⢠⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣜⢃⡸⢶⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠈⣇⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠰⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⢠⠄⠀⣰⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠘⠀⠀⢠⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⡆⠀⠀⢠⣿⡿⠿⡟⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⣃⣶⣿⣿⣽⢧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⡤⠤⠚⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠊⠘⢷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⣸⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⣾⣷⣿⣐⣂⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠦⣼⡄⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢠⡌⠙⠛⠻⠿⠿⠛⢩⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣿⡇⠀⠀⠀⠀⣇⣀⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠲⡾
⠀⠀⠀⠀⠀⢸⣇⣀⡀⠀⠀⠀⣁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠋⠓⠒⠒⠛⠛⣛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠤⠶⠶⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠈⠷⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠤
⠀⠀⠀⠀⠀⠀⣤⠄⢤⣤⣤⣤⣄⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⠀⠀⣀⡀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⠀⠠⠤⠤⠤⠀⠀⠐⢢
⠀⠀⠀⠀⠀⠀⡿⠀⠘⢻⣿⡿⠛⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠉⠁⢲⣤⣄⣉⡁⢀⣤⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠈⠁⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢲⡇⠀⠀⠀⠀⠀⠀⣰⣃⠀⠐⠒⠒⠒⠶⠶⠦⠤⠴⡦⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⢠⣤⣶⡆⠀⠀⠀⠀⠀⠀⣿⣷⣶⣴⣶⣶⣦⣤⣶⣶⣶⣶⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣉⣻⣷⠊⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠄⣿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣔⣁⡈⠓⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⢀⣿⣥⠭⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡄⠀⢂⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣛⣆⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠐⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠶⠾⠿⣟⠁⠒⠂⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠿⠦⣷⣶⣒⣄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢫⣭⣙⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣀⢁⣂⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠶⠶⣴⡏⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡶⠛⠿⠻⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠟⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⢣⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠆⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡌⡈⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠊⠘⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠰⢠⠅⠀⠀⠀⠐⣷⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢠⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⡄⡘⠀⠀⠀⠀⠀⠫⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠁⠀⠀⠀⠀⠀⠸⢁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠘
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢰⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢦⠦⠤⠐⠒⠀⠐⠂⠤⠤⠒⢒⡠⠃⠀⠀⡇⠈⠢⠤⠤⠤⠤⠔⠂⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠚⠚⠀⠀⠁⠉⠀⠀⠀⠈⠀⠀⠋⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⠤⠤⠤⢤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣯⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣶⣶⣭⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣁⣀⣀⣠⣟⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠉⠉⠉⣿⣿⠷⠛⠛⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⢼⣧⠞⣉⣙⠲⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⣿⣷⠊⠁⠈⢳⡿⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⣼⣿⠀⠀⠀⢸⣷⠃⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠙⣿⣦⡀⠀⣼⠟⡴⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⣶⣿⡙⠛⢛⣡⠞⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⣿⣿⠙⠻⠿⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⠀⠀⠀⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡇⠀⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⠃⠀⠀⠀⢸⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⡟⠀⠀⠀⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠤⢷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢉⡟⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠂⠉⠉⢉⡉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⢀⣠⠤⣒⣬⠿⢛⣻⡿⠁⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡅⠀⠀⢀⣤⣾⡭⠖⠋⣉⣤⣶⣿⣯⣤⣤⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣠⣾⣫⣥⣶⣾⡿⣿⣟⣉⡭⠞⠋⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⠟⠹⣿⡻⡄⠀⢸⣿⡇⠀⠀⠀⠀⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡏⢧⠀⠻⣿⣷⠶⢚⡼⠃⠀⠀⠀⠀⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⢿⣌⣳⣶⡿⠉⠉⠉⠀⠀⠀⠀⠀⠀⡏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡷⠶⠶⣶⣶⣶⣶⣶⣶⣖⣒⣖⠶⠶⠿⣽⠟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢧⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠴⠞⣃⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠛⠓⠒⠚⠛⠛⠛⠃⠒⠒⠒⠒⠚⠉
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠁
⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠉⠈⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦
⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠋⠙⠛⠓⠦⣄⡀
⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣠⡟⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣰⡏⠀⢀⡎⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⣿⡇⠀⣸⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠀⣰⡟⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣼⠏⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠤⠤⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⠤⠤⠔⠒⠒⠒⠒⠒⠒⠒⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⢹⠇
⠀⠀⠀⠀⠀⢠⡤⠤⠶⠶⠒⠒⠚⠛⠋⠉⠉⢉⣉⣉⣉⣉⣤⠤⠤⠤⠶⠶⠒⠒⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠙⣦⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⡤⠴⠶⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡾
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠞⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠙⠦⣤⣀⣀⣠⣤⣤⠤⠤⠴⠶⠖⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣤⡤⠤⠤⠤⠤⠶⠶⠶⠖⠒⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⣤⣤⣤⡤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠲⠶⡄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠇⡤⠴⠶⡄⣴⠶⣦⣶⣒⣲⡆⣞⣛⡷⢰⣯⡽⠆⣿⡭⠷⠸⠯⠷⠀⣿⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⠀⠛⠚⠋⠁⣉⣉⣁⣈⣡⣥⡄⣤⠤⣤⣠⠤⢤⡄⣠⠴⢶⢰⣟⣻⠀⢻⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⠀⣾⢛⣛⣇⡿⢫⠟⣡⠗⢺⣟⣓⣒⣛⣻⣿⡉⢻⡙⣯⢭⡀⣉⣤⡀⢸⡀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡏⠀⡿⠛⢳⠟⢰⠋⣰⠃⣰⢛⣿⢿⣤⢼⡙⠢⡷⣄⠳⡘⢧⠙⣇⠀⣇⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡇⠀⣿⣶⠏⠀⠉⠰⠃⠰⢣⠞⣀⡖⠛⢲⡝⢦⡘⢾⣦⠙⠈⠃⠘⣆⢻⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⠇⠀⢷⡏⠀⠀⠀⠀⠀⢰⢏⡞⢡⠟⠛⣋⡁⣾⢳⠀⠉⠀⠀⠀⠀⠘⡟⠀⣇⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⢸⠁⠀⠀⠀⠀⠀⠻⠚⢀⡏⠀⠘⠧⢍⡙⠛⠀⠀⠀⠀⠀⠀⠀⣷⠀⢹⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡞⣶⣒⣛⣛⣻⠉⠳⡄⠀⠀⠀⠀⠀⠀⢹⠀⢸⡀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢿⢀⣠⠇⠀⠀⠀⠀⠀⠀⢠⠯⠤⠤⠥⠤⠤⠤⠤⠤⠿⡄⠀⠀⠀⠀⠀⠘⡷⠾⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢉⡟⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢻⡀⣀⣀⣀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠤⠴⢶⡞⠀⠀⠀⠀⠀⠀⠀⣸⠶⠒⠒⠒⠛⠛⠛⠛⠛⠒⠚⠛⡆⠀⠀⠀⠀⠀⠈⢯⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠂⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡀⠀⢀⠀⠀⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⠆⢠⠸⡄⠠⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⣿⠀⠀⢸⠀⠀⠀⢱⠀⠀⡀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⠙⠉⠁⠞⠓⠲⡶⠧⢤⡾⠗⠋⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣉⣉⣉⠛⠛⠛⠒⠒⠒⠲⠶⠖⠚⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠞⣋⡡⠔⠒⠚⠿⠓⠲⢄⡀⠀⠀⠀⠀⢰⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠰⠚⠉⠁⠔⠂⠀⠀⠀⠀⡄⠈⠻⣄⠀⡆⢀⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠥⠚⠁⠀⠀⠀⠀⠴⠊⠉⠑⠒⠒⠊⠀⢀⡄⢹⡞⣠⠏⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⢀⣾⠿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡉⠛⠒⠂⠀⠀⣀⡤⠔⠈⠉⠉⠙⠒⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣦⣤⣤⣤⡴⠶⠛⠛⠛⠛⠛⠋⠁




⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠤⢶⡶⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠟⠿⠿⢿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠉⠀⠀⠀⠀⠉⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⡀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠛⠛⠛⠛⠓⠶⣤⡀
⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⣰⡟⠁⠀⣠⠒⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⡟⠀⠀⢠⣧⣠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⢹⣿⣿⡆⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⠇⠀⣼⡟⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀⣼⡟⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣾⠏⠀⠀⠀⠀⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣤⣤⣴⣶⠾⠟⠋
⣿⣿⠿⠿⡿⠿⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢰⣶⣆⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠠⣄⠀⠀⠀⢸⣻⢶⡠⡀⢹⠄⠀⠘⠇⠀⠀⠀⠀⠐⢆
⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠐⠀⠠⡟⠀⣤⠂⠈⡇⠀⠀⠘⣿⡗⠋⠡⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣵⣄⣀⡀⠀⠀⡀⣀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢨⣍⣀⣀⡀⠀⠀⠀⢈⣻⣍⣏⣐⠞⠁⠀⠀⠀⣿⣇⠶⢦⠠⠈⠳⠈⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⠖⠂⣤⠄⠀⢠⠋
⠀⠀⠀⠀⠀⠀⢸⣡⣍⠁⠿⢀⠀⠀⠈⠠⣿⠋⠁⠀⠀⠀⠀⠀⢺⣇⠳⣀⠶⠦⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣌⠁⠖⡔⠁
⠀⠀⠀⠀⠀⠀⠸⣿⢿⡷⠾⠽⠶⢶⠖⠈⣻⠀⠀⠀⠀⠀⠀⠀⣾⣄⢴⣟⡀⢠⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠈⠏
⠀⠀⠀⠀⠀⠀⠀⢿⡟⠓⠂⠀⢶⠀⢠⠋⡏⠀⠀⠀⠀⠀⠀⠀⡿⣟⣟⠋⠀⠻⠄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⢸⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠟⠳⢴⡀⡁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⠸⡏⠀⠀⠈⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣠⣄⠀⠣⡖⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣋⠠⠃⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠄⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡛⠛⠓⠓⠛⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⣀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣀⢀⠠⠐⠀⠀⠡⠄⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡄⠠⠠⠄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠛⠉⠀⠀⠈⢦⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣤⠀⠀⠠⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⠒⢀⡬⠷⣄⣻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣿⣀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⡛⠳⠖⠉⠙⣣⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠿⠛⠋⠉⠁⠿⠀⠀⠀⠀⠀⠀⣄⢦⢀⣠⠀⠀⢠⣠⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠯⢅⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠎⣤⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⣧⣄⡰⠂⠁⠈⠣⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⡀⡀⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠹⡀⠶⠎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⡀⠀⠈⢀⣤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠾⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠶⠄⠸⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠀⠐⠁⠀⠀⠀⠀⠀⠀⠙⠚⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⣼⣿⣷⣾⣷⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠉⠉⠁⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⡷⠾⠶⠾⢆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣿⡗⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢸⡟⠀⢀⣴⢦⣤⣀⡀⠀⠀⠀⠀⠰⠀⢸⣯⠀⠀⢐⣤⣽⡯⢼⣿⢿⣰⣦⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠸⡇⠀⠈⠉⠈⠁⠙⠣⠑⠀⠀⠈⠘⠀⢸⡏⠀⠀⠀⠀⠹⠉⠀⠁⡀⠘⠿⢣⠏⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⡄⣿⣦⡄⠆⢀⣹⣷⠀⠀⠀⠀⠀⠄⣆⠀⣿⣄⠀⠀⠀⠀⠀⠀⣥⣦⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠹⣿⣿⣿⣿⠻⣬⠀⠀⠀⠀⠀⠈⡕⣻⡄⢻⣿⣿⣿⡅⡟⢀⣀⣤⣶⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣝⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⣳⡀⢿⣿⣿⣿⣿⣿⣷⡿⢿⣍⡉⠁⠶
⠀⠀⠀⠀⠀⠀⠒⠲⣤⣀⠈⢻⣎⢿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠉⢷⡈⢿⣿⣿⣿⣿⣿⣧⣄⣹⣿⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠙⠯⢿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⡝⢿⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⡆⠀⠀⠀⠀⢰⣦⡀⠀⠈⣿⣷⡌⢿⣿⡟⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⣆⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠻⢷⠀⠀⠨⠿⢿⡌⣿⡇⠀⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⢋⣴⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⢻⣿⣿⣷⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⣿⣿⣿⡿⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠀⠀⠀⠛⠁⢀⣹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠁⠀⠀⠀⠀⢸⠙⠛⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⣸⠀⠀⠈⠛⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⢀⣠⡴⠚⠈⠉⢓⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⢈⣿⠤⠀⢀⡠⠂⠀⠀⠀⠘⢢⡀
⠀⠀⠀⠉⠀⠈⢁⣠⣤⠾⠛⠀⠀⠀⢀⣠⣴⣾⢿⡿⠤⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⢁⠠⠔⢋⣽⣏⡀⠀⠀⢀⣤⣶⡿⠟⢭⣱⠎⢣⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⢻⣷⣦⣼⣿⣿⣿⣷⣾⡿⢛⣁⣬⠛⠊⠻⢯⣷⣉⡙⠂⠀⠀⠀⠠⠄⠠⠖⠄⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠘⢿⣿⣿⣿⣿⡻⠛⣿⢦⣶⣋⣗⠣⠀⠀⠀⢿⡿⠿⢿⡷⣾⣷⣠⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠉⠛⠻⢦⡄⠉⠓⠿⢿⣿⣷⡆⠀⠀⠸⠀⠀⠀⢀⡼⠟⠻⠄⠤⢄⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⣿⣿⣄⠀⠀⠀⠀⣠⡼⠛⠁⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡶⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⣰⣾⡄⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⡄⠐⢰⡄⠀⠀⢀⡾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⡁⠀⠀⠀⠀⣠⠞⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠢⠊⠁⠀⠀⠀⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⢻⠀⠀⢠⠇⢠⠇⡶⠘⢀⡞⠁
⠀⠀⠀⠀⢀⣀⠂⢳⣦⡀⠀⠀⠀⠻⠀⠁⠀⠏⠀⠞⠰⠇⠀⠸⠀⠀⠀⠀⠉⠉⢲⣷⡄
⠀⠀⠀⠶⣻⣿⡇⠈⢻⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⠚⣛⣛⣛⠃
⠀⠀⠀⢀⣿⡿⠁⢀⣤⣽⣿⡆⠀⠀⡀⠀⠐⢲⣄⠀⠀⠀⠀⡀⠀⠀⠀⠋⠉⠉⠉⠉
⠀⠀⠘⠿⠛⠁⢀⠚⠻⣿⣿⠻⣧⠀⠿⣷⣿⣿⠿⠃⠀⠀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⣀⣤⣄⠐⣀⣻⣿⡇⠙⠃⠀⠀⠀⠀⠀⠀⢠⣔⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈⢹⣿⣿⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⢀
⠀⠀⠠⣤⣿⡿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣴⠶⢦⣤⣤⣤⣤⣶⣦⡀⠁
⠀⠀⠀⠙⠋⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡾⠁⣰⠿⠿⠿⠿⠿⢿⣿⣷⣶
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⢹⠞⠀⠀⢠⠏⠀⠈⠀⠀⠀⠀⠀⠤⣯⣽⣿⣧⡀
⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠀⣠⢾⡿⡳⢠⡏⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠹⣧
⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⢀⡾⣽⡟⡁⠀⣸⠀⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠄
⠀⠀⠀⠀⠀⠈⠞⠀⠀⠀⢠⣿⠞⠋⠊⠀⠀⢹⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⡴⠀⠀⠀⠸⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⣿⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⢱⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠾⡄⠉⠆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢳⢧⠄⢰⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡞⡞⡄⢌⣆⠀⠀⠡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⡑⡑⡀⣍⠂⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣹⡱⡔⣌⢦⡀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠋⣀⡠⠀⠠⣄⡀⠀⠀⠸⢧
⠀⣠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⣮⡣⣝⠶⣌⡂⠀⠀⠀⢀⣀⠂⢈⠈⠤⠀⠀⠀⠀⠀⠠⠀⠀⠘
⢀⠁⡠⣐⡪⢥⣐⣒⣒⣒⡆⠤⠄⡀⠀⠀⠀⠀⠀⠀⠐⢌⠳⣮⣕⢮⣍⣛⠒⠤⠤⠤⠤⠤⠄⠐
⠀⠀⠈⠒⠍⢯⠙⠤⠣⠬⠭⣏⡒⠀⠑⠄⠀⠀⠀⠀⠀⠀⠁⠈⢛⣻⢾⣭⣛⡓⠒⠲⠒⠒⠒⠃⡉⡠⠀⠂⡀⠀⠀⠀⢀
⢠⠆⠡⠤⠄⠌⠉⠉⠉⣉⠁⠚⢼⡑⠄⠀⠀⠀⠀⠀⠀⠀⡆⣇⢢⢹⣿⣦⣯⣉⣉⡉⠋⠉⠉⣉⡀⠄⠒⢀⡀⢀⠀⡰⠂
⠀⣦⠀⠀⠀⢀⣒⢒⠤⠤⢈⠑⠤⠉⠀⣠⠖⠂⠀⠀⠀⠀⡇⢸⢸⠀⣏⡓⠺⠭⢭⣉⣉⣉⢉⡁⠤⠄⠒⣀⠔⠁⠊
⠀⠈⠳⠀⠀⠒⠒⠬⠉⠀⠀⠀⠁⠀⡠⠃⠈⠀⠀⡄⡐⢠⠃⠆⠸⢠⡷⠦⠍⣒⠒⠢⠤⠠⠤⠀⠄⢐⣂⡤⠖⠁
⠀⠀⠀⠀⠀⠐⠒⢲⣦⣤⣀⡀⠀⠀⠀⠀⠀⠡⠈⠐⠁⠀⠀⠠⠃⢆⡇⠀⠈⠉⠛⠛⠿⠶⠾⠓⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠄⣀⠤⣀⡴⣢⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢋⢞⠵⣫⣔⡎⢗⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢯⠞⠓⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠶⠧⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡿⠀⠈⠳⣄⣠⣤⣤⠤⠶⠶⠶⠦⢤⣤⣴⣋⠀⠀⢹⣼⡆
⠀⠀⠀⠀⣠⠶⠚⣛⣿⡟⣁⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢤⣹⠿⢿⠓⠦⣄
⠀⠀⣠⣞⣡⠤⣶⣿⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡟⢿⣒⠺⢷⡄
⠀⢠⡟⣿⠒⠛⠁⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⢉⡿⢻⡀
⠀⢸⡇⠘⢷⣄⢀⡏⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠟⠁⢸⡇
⠀⠘⣇⠀⠀⢉⡿⠀⠀⠀⠀⠀⢀⡏⠙⠦⣄⣀⣙⣷⣤⣀⡀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠈⢷⣄⡀⣼⠁
⠀⠀⢿⡀⣴⠞⠁⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⣠⡬⠁⠀⠠⣭⡉⠉⠉⠁⠉⠳⢦⣀⣀⠀⢀⣠⡼⢁⡟
⠀⠀⠘⣇⢹⣷⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠁⣴⠀⠀⢠⣦⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⡍⢧⣼⠃
⠀⠀⠀⢻⣯⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⡏
⠀⠀⠀⢸⡏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⣤⣀⣤⠟⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣤⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠳⣤⣀
⠘⢯⣄⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⣠⡿
⠀⠀⠉⠳⢤⣀⣀⣈⣳⣄⡀⠀⠀⠀⠀⢀⡴⠲⠤⢿⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣃⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⢠⡞⠃⠀⠀⠀⠀⠀⠛⣦⠀⠀⣀⣠⡴⠚⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⢿⣿⣶⣶⣶⣶⣶⣿⢻⣟⣻⣯⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡞⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⢹⡆⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⠃⢸⠀⢀⣀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠿⣤⠾⠛⠋⠹⣆⣀⣀⣀⣼⠋⠓⠶⣤⣽⠇⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠈⣩⣭⣿⡁⠀⠀⠀⠈⢷⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⢸⡀⠀⠀⠀⠀⠀⢠⣤⣤⠏⠀⠀⠀⠀⢸⠀⠀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⠾⠷⣤⣄⡀⠀⠀⢤⣤⡽⠂⠀⢀⣀⣤⡿⠶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⠙⠛⣶⣴⣯⣤⠶⠛⠋⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠴⠿⠭⠤⠭⠶⠆⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠶⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠶⠞⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⢹⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣴⣶⣤⣤⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡋⣿⣿⣿⣿⣿⣿⣿⠇⣿⡁⣿⣿⣿⣿⣿⣿⣿⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢦⣤⣀⣀⣀⣠⣤⢞⣿⣟⢦⣄⣀⣀⣀⣀⣤⢴⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⣴⣠⢄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠲⢒⣼⢿⣖⣾⣹⣷⢧⢼⠃⡘⣆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠶⢶⣳⣯⣿⡛⡷⣤⣍⣯⣉⣷⣞⣷⡾⠼⣅⠺⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢑⣧⡼⢯⡷⣿⡟⢯⣠⣤⣯⣿⣯⣉⣿⣱⣿⣿⣇⣔⣆⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⣷⡾⠿⣿⣉⣶⣿⣿⣯⣿⣿⣿⣿⣭⡿⣿⣿⢿⣹⡷⡞⠋⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⢾⡷⣾⣿⣿⣾⣿⣧⣽⣿⣭⣿⣿⣿⣶⣽⠶⠟⡳⠁⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣗⣶⢶⣿⣿⢿⣿⣿⣿⣿⣿⣹⡿⡿⣟⣷⡿⣡⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣻⣟⢙⣿⢷⣾⣿⣿⣿⣺⡟⣭⠿⡩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠿⡿⣿⣿⣿⣼⣿⣟⣿⣿⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡻⣿⣿⣥⣿⣿⣿⣯⣶⡎⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣻⣯⡿⠿⠇⢚⣽⣿⣧⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠃⠠⠀⠀⢘⣻⠝⠶⠗⠀⠀⠀⠀⡀⡠⠬⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⢊⡏⢄⡲⢢⢿⣤⠊⠣⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢘⣃⠿⠉⢟⣮⡘⢇⠼⣀⡀⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠿⢿⡿⣾⣻⣶⡿⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠀⠉⠈⠛⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣼⣿⣿⠏⠉⠀⢉⣉⢀⣀⣶⣶⣦⣄⠀⢠⣿⣿⡟⠉⠉⠉⠙⠛⠛⣿
⢠⡿⠏⠋⠀⠀⠀⠈⢙⠋⢋⣀⣡⣬⣿⣷⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⡇
⣸⠃⠀⣀⣤⣤⣿⣦⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣿⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠋⣧⠀⠀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⣴⣿⠞⠋⠉⠳⣄
⠀⢻⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠚⠉⠛⠁⠀⠀⢠⠞⠁⠀⡠⠊⣹⠈⠓⢄
⠀⠀⠹⣿⣿⡏⢠⠖⠶⣦⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠎⠀⣘⡡⠄⠐⠢⣝⢦⣤⣄⣀
⠀⠀⠀⠹⣿⣇⠈⠀⠠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢠⠁⢠⠞⠁⢀⡤⠒⠊⢁⣴⠈⠳⣄⠉⠲⢄
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠸⠀⠉⠀⠰⠋⠀⡠⠖⠋⣠⠃⠀⠈⠓⢄⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢆⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢶⡄
⠀⠀⠀⠀⠀⠀⢀⣠⠾⣥⣄⡀⠀⠈⠉⠛⠷⢦⣤⣄⣀⡀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⡉⢢⡀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠉⠛⢶⣄⡀⠀⠀⢀⣼⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣤⡀⠀⠀⣸⠋⠀⠀⠀⠀⡰⠁⠀⢳⡀
⠀⠀⠀⢀⣾⡷⠞⠋⠉⠓⠂⠀⠀⠀⠈⢙⣶⣤⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠙⣿⣿⣿⣶⣄⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⢳⡀
⠀⠀⠀⣾⠋⢀⡠⠀⠀⠀⠀⢀⡠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠉⠈⠿⠃⠀⢹⣿⣿⣿⣿⣿⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⢷
⠀⠀⢰⣷⠞⠋⠀⣠⡴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢻⣟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠀⠀⠀⠀⢸
⠀⢀⡾⠋⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣿⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠘⢿⣦⠀⠀⠀⠀⢸
⢀⡾⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣤⣤⣽⣿⣶⣤⣶⠟
⣾⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠷⠶⠶⠿⠟⠛⠋⠉⠉⠉⠉
⢹⣧⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠙⣧⣿⣿⣿⣷⣤⣀⣀⠀⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⣿⠿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⡿⠀⠀⠀⠙⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃

⠀⢰⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⠀⣄⣤⡄⣀⣀⣀⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣓⣿⡿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠶⣶⣶⣶⣦⣦⣤⣤
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡏⣿⣿⣿⣿⠀⠀⠀⠀⠰⡶⠶⠶⣶⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣻⣿⣿⠀⠀⠀⠀⢸⠁⠀⠀⢣⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠂⣸⣿⡿⣿⣿⣿⣿⣿⣿⣠⡄⣀⣠⣷⢀⠀⡀⣸⣦⣠⠀⠀⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣃⣻⠈⢹⣻⣿⣿⣿⣿⡋⠋⠙⠛⠙⠟⢿⣏⣿⣧⣄⣰⣿⣯⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣏⣁⠀⠀⠀⠀⠈⠙⠺⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣙⢿⣧⡇⢀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⢿⠛⡿⣿⣄⠀⠀⢀⣉⣸⣿⣿⢸⡀⠀⠀⠀⠀⡰⣿⣿⣿⣿⠟⠀⠀⢸⣿⢉⣉⣉
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢻⠇⠀⠀⠀⠠⣶⣿⣿⣽⣿⡀⣰⣿⣼⣿⢺⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⢿⠽⠀⠀⣀⣿⣿⣿⣿⣿⣿⠟⠉⢸⡇⡯⢸⠄⠀⠀⠀⠀⢸⣿⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣫⠘⣿⠀⠀⣼⡇⣿⠄⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣰⣿⣶⣀⠟⠋⠀⣀⡀⠀⢐⣰⣢⣮⣿⠠⠀⠀⠀⢸⣾⣿⡿⣟⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣿⣶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣮⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠏⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠉⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠄⠀⠀⠀⠀⠀⠀⠀⢠⣭⣍⣩⣶⡟⠋⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣤⣤⣀⣀⡀⠈⠙⠛⠀⠤⠄⠠⠄⠀⠀⠀⢘⣿⣷⡇⢸⣧⡠
⠀⠀⠀⠀⠀⠀⣠⢼⣂⣤⠍⣉⡉⠙⠛⠛⠿⠶⠶⠤⣄⣀⡀⠀⣤⣾⡿⡿⣇⣷⠾⡃
⠀⠀⠀⠀⢠⠞⠁⣄⣽⣟⣻⠿⣶⣯⣤⣖⣠⡄⢀⣀⢀⠉⢢⣾⣿⠁⠀⠰⡍⠀⢀⠇
⠀⠀⠀⢠⠟⠔⢶⣾⣯⣿⣛⣿⢿⣾⣯⣽⣟⣻⡟⡷⢊⣴⠋⣿⡇⠀⠀⠀⣀⣴⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⢸⣄⡀⠺⠿⣶⣾⣭⣟⣛⡳⠾⢯⣿⣻⠋⣴⡟⠁⠀⡿⠃⣀⣴⣿⣿⣿⣿⣿⣿⠿⠟⠒⠂
⠀⠀⠀⠘⣷⣤⣀⣀⠀⠀⠉⠉⠛⠛⠿⠃⠀⠀⢸⣿⠀⠀⣈⣵⣿⣿⣿⣿⣿⣿⠟⠛⠻
⠀⠀⠀⠈⠉⠉⠛⠻⠿⢿⣶⣶⣤⣭⣗⣶⣖⡞⠹⣷⣶⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⡿⠿⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⣒⣯⣽⣵⣒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣷⣾⣿⣿⣿⣿⣿⣿⠿⠗⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠀⠈⠉⠉⠻⡶⣶⣦⣤⣤⣤⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠑⡎⠩⣿⣿⣿⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠰⠖⠂⠀⠀⠀⢞⣁⣘⣿⣿⣿⣷⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠃⠀⠀⠈⠋⠀⠀⠀⢸⣽⡿⣛⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠁⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠈⣠⣶⣅⠀⠀⠀⠀⣠⠏⠀⠠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠀⠀⠂⠐⠂⡆⠀⠀⠀⠀⠀⡴⠚⠀⠐⠊⠁⠣⡰⠙⠃⡸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⣬⠃⠀⣀⠀⠀⠃⠀⠀⣀⠴⠞⠁⠀⢀⠐⠢⠀⢠⠇⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⢀⣹⣄⣈⣀⣵⠒⠔⠉⠀⠀⠀⠀⠀⠎⠀⢠⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠄⠀⠀⠀⠀⢙⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡉⢻⡏⣾⣿⡇⠊⠀⢠⠎⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⠊⠀⣀⣤⠴⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠉⣻⣿⣼⣿⣿⠁⠀⠀⢸⡄⠀⠀⠀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠁⢠⠎⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠈⠀⠉⠉⠁⠀⠀⠀⠀⢧⠀⠀⢸⠁⠙⠀⠀⠀⠀⠠⢄⡀⠀⠀⠈⢢⠀⠈⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⡴⠁⠀⠀⠀⠀⣰⠏⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⢣⡀⠀⠀⢀⠀⢧⠀⠀⢺⡁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣇⣠⣖⣁⣤⡜⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⢀⣧⡴⠖⠒⠒⠒⠢⠤⢀⡀⠀⢸
⠠⣄⣀⡀⠀⠀⠀⢀⣸⣦⣤⣤⡔⠒⠙⠛⠉⠉⠁⢸⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸
⠀⠀⠀⠉⠙⣢⠞⠁⠀⠀⠀⠀⠉⠙⠓⠦⡀⢀⣀⣋⣀⣀⣘⠀⠀⠀⣀⡤⠤⠂⠀⠀⠑⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠀⠀⠀⠳⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⣀⠞
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠳⢦⣤⣀⠀⡠⠤⠀⢸⣅⡧⠠⣤⣾⢿⣛⠛⠋⢉⡉⣉⢉⡟⠛⠛⠋⠉⠁
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠉⠛⠦⡀⣀⣠⠼⠒⠋⠁⠀⢀⣿⢠⣆⣼⣷⠿⣾⠃⢀⠂
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⡠⠖⠋⠉⠀⢀⣀⠤⠶⡞⣹⠏⣾⣿⠻⠏⠀⠁⠀⢸
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣠⠋⠀⢀⡤⠖⠋⠉⠀⢲⡄⣷⠏⠀⠀⠁⠀⠀⠀⠀⠀⣼

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⡔⣀
⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⡂⠡⡇⢀
⠀⠀⠀⠀⠀⠛⠂⠀⠦⠀⠀⢀⠀⠀⠠⣄⠳⠿⣆⣣⣠⣤⡄⡀⠚⠳⠈⢱⡦⣀
⠀⠀⠀⠀⠀⠀⠋⠀⢀⢐⡟⣨⡀⠖⠲⠆⠖⠲⡄⠠⢭⠈⠄⠶⠊⡠⣥⠚⣽⣆⣳
⠀⠀⠀⠀⠀⠀⠀⠂⠊⡟⡬⡷⢑⣛⡻⠚⠛⢿⣆⡶⠶⢦⡒⢋⣻⣠⣴⢛⣴⢿⣿⣷⡄⠠⠌⠤⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⢿⣟⣓⢀⣹⣠⣷⠉⢐⣀⡉⢥⡟⡻⣿⣿⣼⣿⣳⣾⣿⠧⠖⡶⢒⣦⠶⣶⣦⡄
⠀⠀⠀⠀⠀⣠⣤⠶⠖⠒⠒⠲⢭⣭⣭⣿⣿⢠⣯⣬⣷⣶⣶⣇⢹⣿⣿⣿⣿⣿⣿⣿⣾⣯⣰⣭⣴⡿⠟
⠀⠀⠀⠰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣈⡩⠽⠟⠛⠛⠥⢄
⠀⠀⠀⢱⣬⣲⢤⣤⣀⣀⣤⣴⣤⣴⣾⢟⣿⣿⣿⣿⣾⣿⡿⠿⠿⣦⣄⠀⠀⠀⢀⣠⣷⠆
⠀⠀⠀⠈⢛⣻⣿⣿⣿⣿⣻⠿⢖⡻⠟⠛⠙⠛⢻⠟⠉⠀⠀⠀⠀⠀⠉⠻⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠉⠙⠺⠷⠈⠐⠈⠉⠀⠀⠀⠀⠀⢸⣤⣤⣀⠀⠀⠀⠀⠀⢀⡹⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣠⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⡀
⠀⠀⠀⠀⢠⣾⣿⡿⠿⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢠⣿⣿⣿⠧⠠⠠⢾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠋⠙⢿⣿⡏
⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠁⠈⠈⠋
⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⢤⣴⠶⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⢀⣶⠏⡀⠀⡈⢧⣱⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣇⠇⢘⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣵⠙⣠⣿⣿⡀
⠀⠀⠀⠀⠀⡴⣾⡆⠁⠀⠁⣼⣿⣣⠀⠀⠀⠀⠀⠸⣿⣿⣿⡃⠀⠀⢸⣿⣿⢷⠂⠀⠀⠀⠀⠀⠒⠛⠁⠀⠀⠘⠛
⠀⠀⠀⠀⢸⠱⠶⠟⠀⠀⠘⠽⣯⠙⠁⠀⠀⠀⠀⠈⠙⢻⣿⣧⡀⢀⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣾⣿⣦⣄⣀⣀⣀⣤⣾⣿⡅⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣶⣦⣄⣀⣀⣀⣀⣤⣶⡀
⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⣴⣆⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣌⠀⡤⢼⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣓⣿⣿⣷⣾⣿⣿⣿
⣦⣀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣢⣽⣿⣽⣿⣿⣿⣿⣿
⣿⣿⡆⠀⠀⠀⠀⠀⢰⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣘⣻⣿⢿⣿⣿⣿⣿⣿
⣿⡿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣿⣿⣧⣾⣿⣿⣿⣿⣿
⣿⣿⡀⢀⣀⠀⢻⣿⣿⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣉⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣯⣻⣿⣍⠻⠀⠸⣿⣿⣧⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣝⣷⡄⠨⣿⣿⡟⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⠶⠟⡿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣼⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⣿⣿⣟⣿⢿⣿⡗⡈⣠⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣾⣿⡧⣀⡌⣙⢯⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣿⢻⣿⣿⣿⣿⣿⣿⣿⡌⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣼⣏⣹⣿⡟⣿⣷⣆⣼⣥⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣭⣦⣤⡄⠀⠀⠀⠀⢀⡀⠐⢻⣿⠀⣽⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⢶⣶⠄⠀⠀⠀⠰⣇⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠇⢸⣏⢘⡃⠀⢰⠀⠀⢀⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⣿⡇⢻⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⡶⢾⣟⠛⠁⠀⠈⡀⠀⠸⣼⣿⠿⣿⣿⣿⠙⢿⣷⡟⠻⣿
⣿⣷⣾⣶⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⡁⢨⣿⡏⠀⠂⠀⠛⠀⣰⣻⣿⣀⣼⣿⣿⣦⣿⣿⣿⣴⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⢿⡟⢰⣿⣿⣷⣤⡀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⠀⠁⢀⣿⠛⠋⠿⠃⠀⠀⠀⢸⣿⣿⣹⣿⣿⣹⣹⣿⣏⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣤⣤⣼⣿⣆⠀⣰⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣤⣤⣬⣍⢹⣿⢿⣿⠇⠀⠀⢀⠘⠻⠟⠻⠿⠿⢿⢿⡿⣿⣿⣿
⣿⢻⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⢿⡿⠙⠛⠛⠛⠐⠿⡿⢿⡶⠀⠀⢀⡹⢿⣿⣴⣿⣿⣿⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣻⣿⣿⣿⣶⣼⣇⠀⠀⠀⠀⠀⣶⣶⣿⡇⠀⢀⣿⣧⠈⠟⡿⢻⣿⡿⣦⣼⣿⣿⣿
⣿⣿⣿⣋⣯⣿⣿⣿⡿⣾⣶⣿⣿⣿⣆⠀⠀⠀⠀⠿⢻⣿⠃⠀⠀⣿⣯⣦⠀⢷⣾⠦⠤⣤⣬⣿⣿⣿
⣿⣿⣿⣿⣻⣯⣿⠿⢷⣾⣿⣿⣿⣿⣿⠆⠀⠶⠀⠐⢸⡏⠀⠀⠀⢸⡽⣷⣸⣍⣡⣴⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣾⢿⠁⠀⠀⣼⣿⣿⣿⣿⣏⢧⡆⠀⠀⠀⠈⠁⠀⠀⠀⢸⣷⠿⠶⣾⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠉⠀⢀⣴⣿⣿⣿⣿⣿⣇⣷⡟⠁⠆⠀⢀⠀⠀⠀⣤⣤⣼⣿⣶⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣋⢀⠀⣀⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣻⡁⠀⣭⡄⣤⣼⣀⢻⣿⣿⣯⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣤⣿⣇⣿⣟⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠻⠿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠁⠉⠉⠉⠉⠉⠉⠉⠙⠉⠋⠋⠉⠛⠛⠋

⠀⠀⠀⠀⣀⠤⠒⠂⠉⠉⠉⠉⠉⠁⠒⠢⢄⡀
⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠄⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⢼⡇⠙⠋⣿⢂⡥⡐⡄
⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⠖⣫⣽⠶⠖⠒⠈⣑⣳⣤⡇
⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢀⣼⠋⣡⣴⣿⢧⠀⠀⠐⢮⣽⣿⣿⣿⡀
⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠛⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠐⡄⢰⠒⠒⠂⢙⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠋⠀⠀⢙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣄⠀⠀⢈⣙⠀⠀⠀⠊⠁⢀⠀⠀⠀⢶⣖⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠃⠙⠀⠀⠀⠈⠙⠃⠀⠀⠈⠛⠉⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢨⠤⠤⠤⣀⠀⠀⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠶⠞⠁⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆⠀⠀⠈⠀⠀⣴⣄⣠⣶⠟⠁⠀⠘⠆
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠦⣥⠀⠀⠀⠀⢀⡿⠉⠉⠀⠀⠀⠀⢀⠀⠁⡀
⠀⠀⠀⠀⠀⠆⠂⠀⢀⣤⠀⠀⠀⠈⠁⣆⣀⡐⢏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣄⣀
⠀⠀⠀⠀⢠⠀⠀⠀⢸⡇⠀⠀⣠⣶⣿⣿⣿⢡⣿⣧⠁⠀⢀⣠⣴⣶⣦⠀⠀⢸⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣧⡀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠠⠀⠐⢆⡀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣰⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⢰⢍⡀⠠⠐⠨⢤⠁⠀⠁⠈⠙⠒⠦⣴⠾⠋⠁⠀⡇⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⡄⢰⠁⠉⠀⠀⠀⠈⡀⠀⡎
⠀⠈⡀⠀⠞⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠃⠀⡥⠀⣖⣛⣿⣿⣻⢼
⠀⠀⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢂⠀⡏⠀⠸⠾⠗⠗⠿⠈
⠀⠀⢰⠀⠀⡄⠀⢐⠣⠀⠄⡀⠀⠀⠀⠀⠀⠀⡀⠄⠃⢸⣄⣠⣄⣀⣀⣠⣶⡉⡀⢩⣄⣈⡇⠀⠆⠀⠀⠀⠀⠀⠈⠀⣗⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠁⠀⠒⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠷⠒⠒⠒⠛⠀⠐⠶⠶⠒⠶⠠⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⣀⢀⣀⡀
⠀⠀⠀⢀⠶⠂⠈⠉⠀⠂⡹⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠠⠄⠀⠀⠀⠀⠠⠀⠀⠀⡤⠄⠀⠠⠄⠤
⠀⠀⢀⠂⠀⠀⠀⠀⠒⡀⢡⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠤⠠⠄⠀⠐⠀⠰⠶⠖⠀⠀⡀⠀⠀⠁
⠀⢀⢎⡀⠀⠀⠀⠠⣰⠉⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⢏⠉⠉⠀⠀⠀⠀⠀⣼⠁⠀⠸⣄⣤⣂⣀⣀⠲⡆⢂⣀⣒⣀⣴⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢐
⠀⠈⠉⠉⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠳⠲⠶⠃⠀⠀⠾⠭⠤⠤⠶⠒⠲⠃⠀⠛⠻⠏⠉⠉⠁
⠀⠀⣠⠄⠂⠀⠀⠀⠀⠀⡡⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⡷⠧⣐⢠⠄⣀⠄⠄⠒⣻⠀⠀⠀⠀⠀⢀⣴⡿⢿⡿⠿⣿⠿⣿⢿⣿⠿⢿⣶⡄⠀⠀⠀⠀⡖⠒⠒⠒⠒⠲⢆⠀⠀⠒⠒⠒⠒⠢⠄⠄
⠀⢀⠷⢄⡀⠉⡉⢀⠠⠔⠁⢉⡄⠀⠀⠀⠀⣾⣿⠀⠀⡇⣶⠋⢰⢸⠀⣼⡀⢿⣿⣿⡄⠀⠀⠘⡗⠀⠀⠀⠀⠀⣉⠀⠰⠀⠀⠀⠀⠀⠀⠁
⢠⡼⢍⡐⠈⠳⢋⠁⢀⠤⠊⠅⢹⠀⠀⠀⠀⣿⣿⣄⣠⣆⣁⣧⣈⣼⣀⣜⣇⣨⣿⣿⡇⠀⠀⢈⠗⠀⠀⠀⠀⠀⣉⡁⠀⡄⠀⠀⠀⠀⠀⠈⡄
⠀⡇⠀⠀⠉⠀⠒⠓⠁⠀⢀⠔⠉⠀⠀⠀⠀⢿⣿⣿⣿⠉⠉⠉⠉⠉⣽⢹⣿⣿⣿⡿⠀⠀⠀⢈⠏⠀⠀⠀⠀⠀⣈⠁⠀⠁⢀⣀⠀⠀⠀⣀⢦
⠀⠈⠑⠠⠀⡀⠀⢃⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣶⣶⣶⣶⣶⣴⣾⡿⠿⠛⠁⠀⠀⠀⠀⠫⠀⠀⠀⠀⠠⠏⠀⠀⠘⠓⠒⠒⠋⠉⠩⠍
⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠒⠒⢄⠀⡀⠠⠀⠀⠐⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀
⠀⢸⠀⠀⡆⠖⠓⠀⠂⠏⠀⡅⢀⡆⠠⡖⠀⡏⢠⠀⡄⠀⠀⠊⠉⠉⠉⠉⣉⠐⡀⠀⠀⠀⢠⠌⠁⠀⠀⠀⠈⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⡆
⠀⠈⢠⡄⠁⠁⠠⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢮
⠀⠸⢘⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠫⠄
⠀⢸⠰⠀⠆⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⢀⢀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⢨⠅⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂
⠀⠘⡀⢐⡃⣂⣈⠀⠀⣃⠀⡁⠈⡄⠀⣄⢀⡇⢰⠀⡄⠀⠀⠀⠻⠭⠭⠭⠍⡟⢹⠿⠀⠀⠐⣅⣀⡀⠠⠤⠤⢤⠇⠀⢀⣠⣄⣀⣀⣀⣀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠀⠤⠤⠄⠀⢂⣒⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠉⠩⠤⠶⠒⢂⣀⠩⠀⠴⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠤⠖⠂⠈⢀⣤⠤⠄⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⣀⣉⡁⠠⠄⠐⢀⣀⠀⠀⠄⠀⠒⠒⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠔⠒⠂⡀⣉⠀⠀⠤⠀⠒⢃⠀⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣉⣉⡡⠀⠐⠂⠐⠛⡉⠉⠀⠀⡀⢀⡔⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⠤⠴⠒⢒⠂⣀⡄⠀⠘⣉⡡⠄⠀⠐⠒⠀⢀⣀⠀⠀⠀⠀⡸⣄⣀⣁⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣤⠀⢻⣇⠀⠸⢉⢙⣆⣠⣤⣴⡟⠹⠈⢿⠿⢻⣿⣿⣶⣶⣿⣶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣄⣼⣯⣲⠾⣷⣿⣿⣿⡇⢙⣆⠹⠃⣴⣶⡟⣹⡗⢰⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣿⡛⢿⡿⣿⣿⣿⣿⣷⣝⢿⣶⣾⣿⣻⣴⠟⣡⣾⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠈⣿⣿⣿⣋⣩⣽⣿⣷⣮⣭⣭⣤⣴⣾⣿⣿⣿⣿⠿⣿⣛⣿⣩⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣟⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⡿⢿⡟⢻⣏⣹⠯⣭⠓⣶⢋⣿⠏⣽⠃⠾⢹⡏⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣎⢿⣿⣿⠧⣿⡁⠾⢁⣟⠐⣯⣸⠿⣬⡛⣼⣍⠾⠦⢜⣓⣺⡟⣥⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣌⡻⣷⣄⡈⣋⠐⠥⢾⡶⢛⣛⣩⣭⣴⣶⣾⣿⣿⣿⣽⣾⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣝⢿⣶⣶⣿⣷⣮⣭⣿⠷⠾⠿⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠉⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣤⡾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⡇⠀⠀⢠⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠖⠘⠛⠛⠋⠀⠀⠀⠀⣀⠀⠀⢸⠃⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠳⠶⠶⢦⣤⣀⡀
⠀⠀⠀⠀⢀⣀⣤⣶⠾⠿⠋⠉⠁⠀⠀⣀⣤⡔⠓⠂⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠷⠶⣤⣄⡀⠀⠠⣤⣄⠀⠀⠈⠉⠻⢷⣄
⠀⠀⢀⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⢠⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣆⣀⣀⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣯
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⠶⠾⠛⠀⠀⠀⠀⠀⢀⣠⣴⡿⢇
⠀⠀⠻⢿⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⣤⣤⣤⣶⣾⡿⠿⠛⠁⠀⠘
⠀⠈⠶⠦⠞⣻⣟⠛⠻⠷⠶⠶⢶⢶⣶⣴⣦⠤⣤⢶⡶⠤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠶⠶⠖⠛⠋⠉⠉⠉⠁⠀⢠⠛⠉
⠀⠀⠀⠀⡆⠉⠉⠛⠛⠲⠶⠶⠆⣠⣴⣦⣤⣤⣤⡤⠤⠠⠄⣀⠴⠦⠤⠄⠀⠀⠀⠀⠀⣀⡴⠦⢀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⣀⣀⣠⡴⣶⠚⠋
⠀⠀⠀⠸⡧⠠⢤⣀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⡶⠾⠛⠛⠉⠉⠁⠀⣾
⠀⠀⠀⠀⠃⠀⠀⠈⠉⠉⠛⠺⠷⠶⠶⠶⠶⣶⣶⣤⣤⣴⣦⣤⣤⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠾⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠒⠚⠒⠂⠀⠋⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡄⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣧⢀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣼⠇
⠀⠀⠀⠀⠀⠀⣿⣆⡀⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠁⠀⠀⠀⠀⢀⡰⠶⠛⠛⠛⠛⠲⠦⣀⡀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⣿⡏⠛⠢⠤⠄⠀⣰⡁⠀⠀⠂⠀⠀⠀⠀⠠⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠒⢦⣤⣾⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⠶⠶⠒⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠁⠀⠀⠀⠀⠉⠻⢈⠙⠉⠛⣻⠟⠛⠉⠉⠙⠛⠛⠛⠛⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠻⠇⡀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢠⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠂⣀⠀⠀⠀⠀⠡⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠠⠀⠀⠀⣠⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠻⠀⠀⠀⣻⠄⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠤⠤⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠈⠢⠀⠀⠈⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢀⣀⡄⠺⠶⠀⠈⠉⢣⣤⣀⣀⣀⣤⠶⠶⠀⠀⠀⠀⡄⢨⠀⠈⠉⠉⠛⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠤⠉⠁⠀⠀⢀⣴⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣀⡀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠋⢀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⠶⣤⣤⣀⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠿⠋
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣶⣦⣤⣄⣀⣤⣀⣀⣀⣀⣀⣀⠤⡴⠾⠛⠛⠉
⠀⠀⠀⠀⠀⠙⠻⢦⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣄⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣷⣾⢛⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡛⣾⣏⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡏⣿⣿⠸⣧⣔⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣼⠄⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠇⠨⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠿⠙⠋⢿⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢝⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⣶⡾⣿⣇⣀⣀⣹⣿⣷⣶⣶⡤⢄⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⢏⣾⣋⣁⣉⣻⣦⣍⣉⣉⣡⣴⣚⣁⣉⣙⣦⢱⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣶⣦⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⣂⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣴⠖⠒⣶⡖⠒⣶⡖⠒⣶⡖⠒⣶⡶⠒⢶⡶⠒⢶⡶⠒⢶⡶⠒⢶⡶⠒⢶⣶⠒⢲⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡿⠿⢾⡿⠿⢾⡿⠿⢾⡿⠿⢾⡿⠿⢾⡿⠿⢾⡿⠿⢶⡿⠿⣷⠿⠿⣷⠿⠿⣷⣿⣿⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⣿⠶⠾⣿⡶⠿⣿⡶⠿⣷⡶⠿⣷⡶⠿⢷⡶⠿⢷⡶⠿⢷⡶⠿⢷⡶⠿⢷⣶⠿⢿⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣿⣿⣷⣶⣿⣷⣶⣿⣷⣶⣿⣷⣶⣿⣷⣶⣿⣷⣶⣿⣷⣶⣿⣿⣶⣿⣿⣶⣾⣿⣶⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣧⣀⣠⣿⣤⣼⣿⣤⣴⣿⣤⣴⣿⣤⣤⣿⣤⣤⣿⣦⣤⣿⣧⣤⣿⣧⣤⣿⣧⣤⣿⣧⣤⣿⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⠛⠉⠉⠉⠉⠉⠛⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠛⣿⠛⡖⠲⡞⠻⢛⣛⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⠿⠶⠷⣶⠷⠾⠿⠛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⠶⠶⠶⠶⠶⠶⠖⠛⠉⠻⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠉⠉⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠛⠳⢦⡀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢷⡀⠀⢻⣆⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⣷⡀⢀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠻⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠛⠉⢻⣾⠃⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠸⣧⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠛⠳⠶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠶⠞⠛⠉⠀⠀⠀⠈⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠺⠶⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠆⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠛⠳⠶⣤⣍⣉⣙⠛⠛⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⢋⣉⣉⣥⡴⠶⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠒⠒⠒⠒⠖⠶⠶⠒⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⡀⠀⠀⣤⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⢘⣿⠀⠀⣿⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⣸⡟⠀⠀⣿⠀⠀⢸⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠈⠳⢦⣀⡀⠀⠀⠈⠙⠿⠿⠋⠀⠀⠀⠙⠁⠀⠈⠙⠛⠉⢁⣀⣀⣤⠴⠞⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠳⢦⣄⡈⠉⠛⠓⠶⠶⠶⠤⠤⠤⠤⠤⠤⠴⠦⠶⠶⠚⠛⠋⠉⠁⢀⣠⡴⠖⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠈⠉⠓⠶⠦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠖⠛⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⣤⣤⣤⣤⣤⡴⠶⠶⠶⠖⠛⠛⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠟⠿⣿⠛⠻⠿⠿⢿⠻⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣾⣶⣿⣶⣿⣷⣾⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠠⠼⠥⠽⠯⠤⠄⠠⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠰⠶⠖⢶⡀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⣿⣿⡇⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠀⠉⠁⠀⠙⠙⠉⠉⢉⡁⡴⠂⡻⣻⠏⠀⣠⠤⠊
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠀⠀⠀⠀⠂⢀⢾⠷⡮⣽⣳⢶⢷⡟⣥⣞⡁⢀⡀⠀⠀⣀
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠤⠟⠉⠁⠁⠉⠈⠉⠀⠀⠀⠀⠟⠀⢛⠒⢒⣚⣃⣘⣂⠉⠀⠈⣆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢰⡀⠴⠤⠀⣄⠀⠀⠀⠀⠀⠀⣥⡧⢹⣿⣿⡿⣿⣿⣽⣿⢸
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣿⣧⣄⠀⠀⠘⡝⡄⠀⠀⠘⢧⡀⠀⠀⢐⠀⣩⣦⠘⢹⠿⠿⠟⡃⢸⢿
⠀⠀⠀⠀⠈⣧⠄⠆⠐⡂⣀⢩⣭⡛⣟⣿⣿⢿⡟⠿⢿⡾⣷⢦⡀⠘⠜⢆⠀⠀⠈⢷⡀⠀⢸⠀⠀⡀⠀⠀⠤⠄⠀⠦⠴⠞
⠀⠀⠀⠀⠀⠣⢂⠋⠀⠀⠘⠘⠇⠧⠙⠛⢉⡈⠁⠒⠀⠈⠁⠀⠙⠦⡈⢪⣖⣢⣖⣎⣽⠀⡈⠙⠃⣙⠛⡂⢰⣶⡶⠶⣶⠷⠿⠾⠾⠿⠶
⠀⠀⠀⠀⠀⠀⠡⠢⠑⠀⠀⠈⠁⠀⢆⢀⠀⠀⠀⢆⣀⣀⣠⣤⣴⠶⠟⠀⠙⠻⠿⠧⢟⣉⡀⠀⣊⡉⣉⣉⣉⣉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠡⡁⢀⡀⣀⣀⣤⣤⣴⠶⠖⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠈⠠⠀⡀⠈⠀⠁⡐⠤⠀⠉⠂⠀⠻⠅⢢⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣁⠙⢥⡴⠂⡀⠀⠀⢀⣀⡤⢀⠀⠁⠂⠀⠀⣠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⢸⠀⠀⠠⠘⠑⠉⣤⢥⠤⢊⣥⣾⣿⣯⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣬⠠⠀⠰⠀⠸⠿⠟⢛⡹⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠴⠤⠿⠟⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠀⠄⠀⠗⠂⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡈⠀⠄⠀⠐⠂⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠄⠀⠒⠀⠈⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠠⠌⠉⠁⠒⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠱⠆⠚⠉⠁⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣁⠀⠠⡀⠀⠔⠀⠀⠀⠔⠁⣀⡼⠁⠀⠀⠀⠀⡀⢀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣖⠀⠀⠀⠀⡀⠀⠀⣁⣠⠜⠉⠀⠀⠀⢀⠔⠺⠀⠛⠀⠉⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠲⠖⠒⠊⠉⠀⠀⠀⠀⠀⣰⠛⠀⠀⡔⢁⡀⠀⠴⢊⡤⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠘⢀⠄⠀⠈⢰⣯⠴⠁⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠑⠘⠅⠀⠀⠈⢀⠀⡀⠊⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⡜⢠⡀⠀⠀⠀⠀⠀⠀⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠒⢠⠐⠀⠰⠖⠂
⠀⠀⠀⠀⠀⢤⡀⢀⡀⢠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠄⠤⠍⠉
⠀⠀⠀⠀⠘⠈⣧⣸⣇⡘⢰⢲⡄⣿⢰⡖⣦⢰⡄⡦⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠃⠛⠁⠻⠘⠃⠛⠘⠃⠏⠘⠓⠛⠘⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡄⣀⠰⣏⣁⠈⡁⠐⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣶⡄⠈⢺⣗⡤⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠁⣀⣸
⠀⠀⠀⠀⠀⡜⠻⠿⢤⣈⣉⠻⠿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠐⡀⠚⠉⢉⣹⡿⠃⠨⠂⣸⣼⡦⠀⠀⠀⢀⠀⠚⠀⠈⣡⡤⠞⣋⡥⠰⠢
⠀⠀⠀⠀⠀⢳⣦⣴⠚⠛⠛⠲⢦⣄⣙⠿⡁⠀⠀⠀⢀⣼⡟⠀⡄⠂⠈⠉⠑⠋⠉⠙⡉⢹⡿⡆⠀⠀⡴⠀⢀⣴⡋⠤⣤⣴⡃⠀⠀⣰⣷
⠀⠀⠀⠀⠀⠈⠇⠻⠀⡀⢤⣦⣄⠀⠙⢛⡁⠀⠀⠀⠸⣜⠧⢄⣤⡀⠀⢀⣴⣇⠠⠷⠻⣃⡼⠃⠀⠀⢁⡐⠁⢀⣠⣤⡞⠁⢀⣨⠋⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠦⢬⣿⠝⠛⠁⠀⠀⠀⠀⠀⠈⠿⣄⠠⡌⣉⣤⣤⣤⣶⣶⣿⠟⠁⠀⠀⠀⠈⠠⠶⠟⠻⠁⢠⣦⣼⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠷⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠘⣒⣆⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠄⠈⠀⣀⣔⣺⣷⣤⡀⠀⠀⠀⠀⣠⠄⣠⢮⣉⠓⢠⣤⠢⠄⡀⠀⠀⠀⠀⣄⢹⣖⢠⣼⣀⡅
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣴⡶⠿⢉⡍⠠⡟⣿⣷⠀⠀⠀⡜⢿⣶⣧⡀⢻⣿⡅⠻⠤⡀⢺⡢⡀⠀⠀⠐⢄⠈⠀⠀⡅⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣈⢶⠶⠛⠁⠀⠀⠂⠀⡀⢐⣿⣿⣿⠀⠀⠘⢦⣯⡄⠉⡛⠈⠙⠊⡀⠀⠁⠀⣿⡎⠀⠀⠀⠀⠈⠐⠔⠃⠀⠠⠆⢹⣦
⠀⠀⠀⠀⠀⠀⢿⠛⠀⠀⠀⠀⠀⠀⡐⣑⣿⣿⣷⡏⠀⠀⠀⢤⣉⡓⠸⢷⣄⣄⢀⡀⢀⣀⡽⢛⡲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠈⢦⡀⡀⠀⢀⡐⣤⡝⣾⣷⣾⡿⠁⠀⠀⠀⠀⠹⣿⣷⡖⢲⡨⠩⣭⠭⠤⠔⡿⠁⠀⠀⠀⠀⠀⠀⠸⡆⢐⣄⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢼⣿⠵⠶⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡔⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠘⣿⢿⢋⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠁⠀⢀⣼⠿⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢸⠃⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⡠⢎⡠⠊⢀⣼⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⣠⡿⠟⠋⠉⠻⣦⣴⡄
⠀⠀⠀⠀⣤⣶⣶⣶⣤⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⠀⠀⠀⣒⠁⠁⠱⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⠀⠀⠀⠀⠀⢀⡄⣻⣿⣿
⠀⠀⠀⢰⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠏⢡⠀⠀⠳⠀⣠⢠⣄⡀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⣼⡇⣟⣿⣿⡇
⠀⠀⠀⠈⣷⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣷⣝⣷⣿⣾⡓⠠⡤⠐⠪⠁⠀⠒⠶⢶⠆⢹⠁⠀⠀⠀⠀⢠⡟⣹⣻⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⠃⠀⠀⠀⠈⠓⠢⢬⡆⣜⢀⠀⠀⠀⢠⣋⣰⣳⣿⣿⣿⡇
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣭⣭⠬⠇⠀⠢⢤⡀⠀⠀⠀⠀⢀⢪⠳⡀⠀⣠⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠲⢤⡀⠀⠘⠀⠃⠀⣰⣿⣿⣿⣿⣿⣿⠛⡿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠜⢰⣿⢿⠟⠁⠈⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣀⣀⣀⡀⣸⡆⠀⡊⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣠⣶⣻⣿⣿⣿⣿⣿⣧⡼⢥⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠺⠄⠀⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠛⠛⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⡙⠋⠁⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⢩⡀⣀⣀⣠⣤⣶⣾⣿⢣⡆⡀⢀⣇⠄⣽⣿
⠀⠀⠀⠀⠀⠀⣼⠀⠀⣴⠀⣀⣸⡄⠀⠂⣤⠀⣀⠢⣔⠺⣿⣿⣿⠿⡿⣿⡿⠟⠁⣼⣇⠀⢸⣷⢈⡉⠉⠁
⠀⠀⠀⠀⠀⠀⣿⡀⣶⠿⠊⢀⠝⠓⠴⠀⠍⠉⣠⣐⡩⠌⠋⠉⣀⠀⢠⠀⠒⠒⠤⠄⣠⠉⠛⠛⢄⡀
⠀⠀⠀⠀⠀⠀⠟⢁⠄⠀⠀⠉⠀⡆⡀⠀⠤⠀⠉⠀⡀⠀⠂⠁⢀⡄⣿⡀⠀⠂⠀⠄⠋⠑⡄⠀⠈
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⡛⠉⠠⡄⠀⣀⢠⣧⢤⡦⠀⠼⠗⠛⠓⠈⠁⠀⠁⠀⠀⠇
⠀⠈⠀⠁⠠⢀⠀⠀⢀⡀⠙⠛⠛⠋⠀⠀⠀⠀⠈⠈⠛⠀⠐⠡⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠙⠻⠷⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢲⠛⢶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢟⠟⢡⠂⡰⢹⢻⠟⣦⡀⠀⣠⢞⠏⠍⠀⠀⠀⠈⠀⠁⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⢀⣾⠏⡌⡎⢀⠏⢰⠃⡎⣼⢀⢇⢻⣶⠣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠉⢉⡟⡏⡼⢸⢀⠞⠀⠀⡸⡐⡏⠸⡌⢠⢻⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠰⡄⣼⢡⡇⠇⣜⠂⠀⡆⢀⡟⢰⠃⣴⠁⡈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢨⡇⠘⢰⢠⢿⠀⡸⠃⡘⢀⠏⡸⢃⣴⢃⡿⡀⠂⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⠁⠀⡆⠌⡞⢠⢡⡶⠁⡞⠀⢀⠏⡈⣼⡇⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠒⠚⠋⣿⡸⠀⣤⠰⢡⠇⡞⠀⠸⢃⡴⢁⡜⣼⠓⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢸⡇
⠀⣀⣠⠤⠖⠚⠋⠉⠀⠀⠀⠀⠤⢀⡀⣿⡇⠀⠇⠀⡏⢰⠇⠠⢟⡽⡠⢊⡼⠃⠠⠀⠹⣆⠠⡐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠙⠳⢦⣀⠀⠀⠀⠀⠈⠦⠀⢀⡀⠙⣿⠇⡄⠀⡼⣡⠞⠀⡠⠂⣶⣡⢾⡀⠀⠀⠈⠦⢌⢧⡈⢦⡠⠀⠀⠀⠀⠆⠀⠀⠀⠁⣾
⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⠀⠐⠉⠀⠀⣿⠀⠇⠘⡰⠁⡠⠚⢁⣴⠿⠓⠒⠛⠶⣤⠤⠤⠤⠷⠽⣦⣙⠢⡀⠀⠀⠀⠀⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⢹⣄⠀⡰⢁⠜⢁⣤⠞⠁⠀⠀⣤⠔⠊⠁⠀⠀⠀⠐⠚⠃⠈⠳⢤⡀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣶⡵⢾⣞⣋⣀⣀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣀⣠⡤⠴⠒⠋⠉⠛⠲⠶⠤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠙⠛⠛⠛⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⠀⠀⠛⠛⠉⠀⠀⠀⠘⠒⠒⠒⠢⠤⠤⠤⠤⠬⠶⠖⠋⠉⠙⠛⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡔⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⠀⠀⠀⠀⠀⠀⠀⠓⠋⠀⢎⠉⢹⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢀⡤⠒⠚⠲⡀⢴⠒⡆⢸⠀⠸⡄⠤⢤⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠸⡀⠰⠷⠀⡇⢸⠀⢡⠀⡆⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠑⠤⠤⠞⠁⠀⠉⠁⠀⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠘⠒⠒⠤⠤⢄⣀⣀⣀⣀⡀⠀⠀⣀⣀⣠⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠶⠦⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠛⠁


⠀⡉⡉