Sustainability Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⣤⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢾⣟⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⣿⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⣭⣅⠀⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⢀⣀⣤⡿⠀⠀⠀⠀⣾⡛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢷⣄⠸⢯⣤⠀⠀⠀⠀⠀⣸⠇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⠈⣷⠀⠀⠀⣀⣽⠇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⣷⣺⡏⠀⢠⡾⠋⢀⣠⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣬⡷⠶⠶⢦⣼⣿⣁⠀⠈⠷⡴⠾⠁⣼⣏⣤⠶⠳⣦
⠀⠀⠀⠀⠀⠀⢸⡏⣩⣭⡉⣿⠉⠁⠀⠠⣤⣀⠀⠉⠉⠛⢷⠀⢀⣠⣾⠟⠋⠁⠀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠻⠾⠃⣿⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⠿⠛⠋⠉⠀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣴⠿⠛⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠟⣃⣤⣶⣶⡿⠿⠿⠿⠿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠀⣴⣾⠟⣋⣥⣄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡀⠉⠁⣠⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣤⣉⡙⠻⢿⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣷⣌⠻⣿⣿⡷⠂⣡⣴⢶⣿⡟⢛⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣷⣿⠟⣠⣾⣿⣿⠘⢁⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⣿⡟⢠⣿⣿⠟⢁⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣇⢸⡟⢁⣤⣬⣭⣽⠟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡀⠛⠛⠛⠉⠀⠀⠀⠀⣠⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⣴⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠋⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⣦⠙⢿⣿⣿⣿⣿⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣄⠀⠙⠿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣆⠀⠈⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠤⡀⠉⠉⣉⠀⠀⠁⠀⠀⡉⠉⠩⢿⣿⣿⣿⣿⣿⣿⡟⠻⠟⠻⣿⣿⣿⣿⣿⣿
⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⣟⣛⡛⠛⠿⣷⣶⣾⣿⣿⣿⣟⣷⣶⣦⣽⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣷⣶⣴⣶⣶⣿⣿⣿⣿⣿⣷⣤⣙⡛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣃⡀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣌⣿⣿⣭⣥⣶⣦⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⡿⠃⢀⣤⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⣴⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿⠿⠁⣠⣄⡉⠛⠻⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⢰⣿⣿⠀⣾⣿⣿⣿⣇⠀⠛⠛⢿⣿⣧⡀⠙⠛⠛⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀⣿⡇⠀⠀⠀⢸⣿⣿⡀⠹⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣦⡀⠻⣿⣿⡇⠀⠀⠀⢸⣿⡀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⡇⠀⠀⠀⢸⣿⣿⣷⡀⠙⣿⣿⣿⡿⠿⠀⢸⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⡇⠀⠀⠀⢸⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⡄⠘⣿⣿⠀⢰⣶⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⡿⠁⠀⠀⠀⢸⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣧⣼⣿⣧⠀⠀⠀⠀⠈⢿⣿⣿⣅⠘⢿⡟⠀⣿⣿⣿⣿⣿⣿⣿⠁⢰⡿⠟⠋⠁⠀⠀⠀⠀⣼⣿⣧⣼⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠻⣿⣿⣧⣀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⠄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣶⣶⢠⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⢎⣻⣿⡈⢿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣾⣿⢟⣵⣾⣿⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠃⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠿⣿⣿⣿⣿⡿⠿⢃⣀⠀⠀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣶⣦⣤⣀⡀⣠⣶⣿⠟⠁⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣯⣭⣶⣭⣭⣵⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠛⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢋⣟⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣿⣿⠟⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⢛⣷⠛⣻⡚⢻⡟⢠⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢏⡛⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⣿⠀⣿⡇⢸⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿⠀⢿⠇⢸⡇⢻⣿⣿⣿⠇
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠿⠟⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠟⠋⢀⣀⡄⢿⣿⠟⣄⣀
⠀⢀⣠⣴⣿⣿⣿⣿⣿⣶⣦⣤⣄⢠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⣿⢠⣿⣿⣿
⠺⣿⣿⣿⣿⢿⣿⣿⣶⣶⣶⣶⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣿⣼⣿⣿⣿
⠀⠀⠉⠁⠀⠀⠀⠈⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢶⣶⣤⣤⣤⣤⣤⣤⣶⡶⠾⠟⠛⠉⠁
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⠿⣿⡿⠿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⢋⣽⡿⠋⠀⠀⣿⡇⠀⠀⠙⢿⣏⠛⢿⣦⣀
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢀⣾⠏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠻⣧⡀⠈⠻⣷⣄
⠀⠀⠀⠀⣠⣿⠛⠿⢶⣦⣾⣧⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣽⣷⣴⡾⠿⢿⣦
⠀⠀⠀⢰⡿⠁⠀⠀⠀⣼⡏⠉⠉⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠉⠉⢿⡇⠀⠀⠀⢻⣧
⠀⠀⢠⣿⠃⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⢻⣇
⠀⠀⣼⡏⠀⠀⠀⠀⢰⣶⡶⠶⠶⠶⠀⣠⣶⠿⢷⣦⡀⢀⣴⡶⠿⣶⣦⠀⠀⠀⠀⠘⣿
⠀⠀⣿⣧⣤⣤⣤⡀⢸⣿⣤⣤⣤⡀⠀⣿⡇⠀⠀⠉⠁⢸⣿⠀⠀⢸⣿⡇⢠⣤⣤⣤⣿⡇
⠀⠀⣿⡏⠉⠉⠉⠀⢸⣿⡉⠉⠉⠀⠀⣿⣇⠀⢀⣴⡄⢸⣿⣄⠀⣸⣿⠃⠀⠉⠉⠉⣿⠇
⠀⠀⢸⣇⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠈⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⢰⣿
⠀⠀⠈⢿⡆⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠘⢿⣄⠀⠀⣀⣸⣷⣤⣶⣶⡶⠶⠶⣿⡿⠶⠶⠶⣶⣦⣤⣿⣇⣀⠀⢀⣾⠏
⠀⠀⠀⠀⠈⢻⣿⡟⠛⠉⢻⣯⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣿⠏⠙⠛⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠻⣧⡀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣾⠏⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣽⣿⣦⣀⠀⣿⡇⢀⣠⣴⣿⣷⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠛⠛⠉⠁

⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠿⠿⠿⢿⣷⣦⣄⣀
⣾⡿⠛⠻⠿⢿⣶⣶⣤⣤⣀⡀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣶⣶⣤⣀
⠻⣿⣶⣤⣀⠀⠀⠉⠉⠛⠛⠿⢿⣷⣶⣾⣟⠉⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠈⢹⣿
⠀⠀⠉⠛⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣰⣿⠏⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣀⡀⢀⣀⣠⣤⣶⣶⡿⠿⠛⠛⠉⠙⠻⣿⣯⣀⢀⣾⡟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣿⣿⣟⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣿⣿⣟⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠋⠉⠁⠀⠈⢿⡀⠀⠉⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⢀⣸⡧⠀⠀⠀⠀⢀⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣠⠞⠛⠉⠉⠀⠀⠀⠀⢀⡿⠁⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣷⠀⠀⠀⣴⠟⠉⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⡀⠀⢰⡏⠀⠀⠀⠀⢸⡏⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⠳⣄⣿⠀⠀⠀⠀⠀⢸⡇⠘⢧⣠⡴⢦⣄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⠀⢠⣟⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠉⠙⠓⢦⡀⣰⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⠀⠀⠀⠀⠀⠠⣾⣵⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⣹⣷⣄⡀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⢀⣴⡟⣻⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠛⠇⠙⠻⢶⣤⣀⣀⣉⣀⣀⣀⣠⣤⣶⡾⠋⢰⣿⠏⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠙⢯⠉⠉⠉⠉⠉⠉⢡⡏⠀⠀⠈⠁⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⢻⣿⣿⣿⣿⢟⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠚⠛⠛⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣛⣵⣿⣿⣿⣿⡿⣢⣿⡿⣛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠿⠟⡀⣤⣤⣤⣤⢀⡀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠃⠿⠿⣿⣿⣿⣿⣧⠻⣿⢸⡿⠇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠠⠞⣣⣾⣿⣿⢇⣹⣿⣆⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠡⣿⣿⣎⣛⢿⣿⣿⣷⣶⢸⡿⠇⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣌⢈⣛⠻⣿⣿⣜⠿⢿⣿⡆⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡙⣿⣿⠿⢳⣿⣿⣿⣿⢸⡿⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⡸⣿⣷⡎⣿⣿⣿⡇⣿⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢸⡏⣾⣿⣿⣿⣿⡿⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⢷⠸⢇⣶⣿⣿⣿⣇⠛⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣿⣿⣿⣿⣿⠱⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠁⠸⠿⠿⠟⠛⠁⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣤⣀⣀⣠⡤⠴⠊⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣛⣯⣭⡟⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣱⠿⢿⣿⣿⢢⣿⣦⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠍⡏⠭⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⣏⢾⣦⣝⢻⣎⣛⢿⣇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⣤⢸⡟⡻⡟⡛⡇⣤⡤⠤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣿⡎⣿⢫⣾⣿⠟⣼⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣣⣿⠸⣧⣵⣷⣥⡇⢿⣇⣃⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠻⣦⣿⣿⣿⡶⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⡐⢶⣶⣶⡶⢆⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣶⣥⣶⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢸⣿⢇⣾⣿⣿⢫⣵⣶⣮⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⣛⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡛⣺⣿⣿⣧⣝⣛⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⡆⠉⠁⠰⠤⠀⠙⠊⡤⢉⠉⠒⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⢀⠝⠉⠀⠀⠴⠀⠃⠊⡀⡀⠠⠊⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡏⠀⠀⠀⠀⠀⢇⣀⡠⠀⠐⠊⠉⠓⠘⠐⠋⡄⠠⠀⠂⣀⠄⠒⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⢐⡫⠇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠢⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⡿⢂⠖⠢⠤⡀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⢀⠜⢂
⠀⠀⠀⠀⠀⠀⠦⢄⡀⠀⠀⢀⣠⠁⢨⣀⣀⠀⠈⡑⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠃⢀⢀⢀⣑⣲⠽⠦⠤⠤⠄⠀⠒⡘⠁
⠀⠀⠀⠀⠀⠀⠘⠀⢌⠉⠚⠲⠾⠄⣀⠙⠓⢎⡀⠑⠈⡀⠀⠄⢀⠔⡀⠄⡠⢀⢄⠠⠂⢀⠔⠀⢔⡵⠛⠈⠁⠀⠀⠀⠀⠀⢀⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠉⠒⠢⢵⡎⡜⢷⠆⡊⢔⠨⢒⠡⠢⢑⠠⠂⢔⡡⢾⠔⠁⠀⢰⠀⠀⠀⠀⠀⠀⡰⠁⠈⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢦⠀⠀⠀⠀⠀⠀⠀⠉⠲⣕⠪⢐⠅⡂⢐⠡⡂⣥⢨⡴⢫⠕⠁⠀⠀⡜⠀⠐⠄⠀⠀⢀⠊⠠⠀⢱⢸
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠒⠙⢄⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠨⣂⠕⡨⡰⢒⠨⡶⠃⡀⠀⠀⠰⠃⠀⡸⢈⠀⠔⠁⡀⠀⡆⢈⣸
⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⣀⡀⠀⠢⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠳⣔⠚⠨⡐⢅⠟⠰⠀⠈⡆⠀⠀⠣⣤⣴⡿⠋⠀⠀⡅⠀⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⠒⠤⠀⠁⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠘⣖⠈⣰⠋⠀⠘⢤⡼⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠁⠀⣇⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡐⢒⠀⠬⠉⠁⠀⢓⢄⠀⠀⠠⠄⠀⠀⢸⡷⠁⠀⠀⠀⠠⠀⢀⠤⠊⠁⠀⠐⠀⢠⠀⣀⡤⠊⠁⡐⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢔⠂⠀⢉⣀⣀⣞⣓⣦⡀⠁⠐⠀⠘⠃⠀⠀⠀⢀⠠⣔⣁⡀⠀⠀⡀⠄⣀⣰⠚⠁⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠁⠀⠀⠀⠉⠉⠐⠚⠒⠀⠶⠄⠴⠞⠛⠉⡁⠈⢉⢢⣀⠥⠚⠉⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠀⡰⡘⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠄⠀⠀⢀⡨⠵⠊⠀⠀⠀⠆⠈⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠉⠉⠉⠁⠀⠀⠀⢠⠀⠈⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠄⠤⠀⠈⣀⣀⣀⠀⠀⠀⠀⣈⡈⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀⠀⠀⡈⠅⢀⠉⢐⠀⢀⠈⠐⠈⠀⡈⠀⡈⢀⠀⡀⠀⠠⢈⠄⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠈⠀⠂⠀⠈⠀⠀⠁⠀⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠀⣾⠟⠉⠑⠂⠀⠠⣴⣿⣷⣦⣤⣤⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣽⣿⡇⠀⠀⠀⠀⠀⠐⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠟⠈⠁⠀⠀⠀⠀⠀⢰⣾⣟⣛⡿⢿⣯⣽⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣴⣯⣽⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢠⠟⠋⣽⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀
⠀⠀⠀⠀⠸⠺⣇⣈⣭⣩⡇⠀⠀⠀⠀⠀⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠹⡟⠃
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢣⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣿⣷⠀⠀⠀⠀⣠⣤⣤⣤⣤⣶⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠾⠿⠿⠿⠿⠿⠟⠛⠋⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⡢⠄⠉⡁⠀⠀⠀⢀⠉⢀⠰⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢦⠁⡠⠐⠅⠀⡀⠔⠁⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⡄⠊⠴⠔⠐⣡⢠⠀⠀⢀⠔⢈⠉⠈⡦⠊⠐⠃⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⡔⢁⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠫⣀⡟⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠓⠲⠒⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠀⠈⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⢦⡇⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⠈⢨⠱⡀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⣀⠔⠊⠉⠀⠉⢆⢀⠾⡖⠋⠀⠀⠈⠢⣸⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠸⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠐⠊⠉⠀⢀⠀⠐⢉⡀⠑⠊⢈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢐⢰
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠉⠈⠁⢊⣆⠀⠀⠈⢯⡡⢬⠉⠑⢆⠀⡠⠈
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⠀⠀⠀⠀⢀⠆⠀⠀⠇⠰⡀
⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⣄⠠⠖⠁⠀⠀⠀⠈⠱⢰
⠀⠀⠇⠀⠡⠀⠀⠀⠀⠀⠡⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠆⠇⠀⠀⠀⠀⠄
⠀⠀⠀⡄⠀⢰⠀⠀⠀⠀⠀⠅⠒⠄⠠⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⠈⢠⠃
⠀⠀⠀⠱⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠐⣌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⣨⢁⠒⡁⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠐⠄⡀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⡠⠊⠁⡣⠀⠁⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣈⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀⣀⠤⠒⠁⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠤⠀⣀⣀⡀⠀⠀⣀⣀⠠⠤⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⣹⣿⣿⣿⡿⠿⠟⢿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⣀⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⡟⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⣨⣤⣶⡄⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣦⣄⡀⠀⠀⠀⠹⢿⡦⢻⣿⣿⣿⣟⢳⡄
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣷⡀⠠⣤⡀⠀⠘⠿⠙⢿⣿⣿⣿⣿⡆⣠⣤⠀⠀⢦⣄⣻⣿⣿⣟⠣⣿⣆
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣽⣧⣴⣺⣷⣦⡀⠉⢻⣿⣿⠀⠙⠁⠀⠀⠘⠯⠛⣿⣿⡇⢠⣽⣿⣆
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣼⣿⠆⠈⠿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣼⣿⣿⣿⡄
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣷
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼
⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡿⠉⠉⠋⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣇⠀⢀⡀⠀⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣇⣀⡀⠀⠉⠁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⢀⣠⣤⣤⣤⣤⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡿⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡞⢫⡌⣿⣿⡿⠁⠈⠀⠀⠀⠈⠉⠓⢲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠈⢸⣿⣷⣾⡟⠆⢻⡿⠃⠀⠀⠐⠆⠀⠈⠙⢄⠀⠛⡙⠿⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⣿⣿⣿⣿⠿⠂⠀⠃⠀⠀⠀⠀⠀⢀⣀⡆⠀⣠⣤⣿⣶⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⣇⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠁⠐⠂⠆⠀⠀⠀⠀⠀⠀⠤⠀⣾⣿⡿⠋⠉⡟⡬⢿⡿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣾⣿⣷⣽⡀⣈⣀⡄⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣿⣿⡟⠉⠉⠀⠛⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠿⣧⣤⣶⣈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠙⣿⡁⢀⣄⣀⡀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣟⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢐⠀⠀⠀⠀⠀⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⡿⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠉⠀⠐⢸⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⢁⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⢻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠂⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠁⠀⠀⠻⠳⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⠒⠴⢦⣾⣄⠀⠠⠄⠀⢀⣤⣶⣶⣾⣶⣶⣶⣞⡁⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠿⢿⣿⣷⣶⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⢸⡇⢸⡇⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣦⠀⠸⣇⠹⡆⠸⡇⢸⠇⢸⠇⣸⠇⠀⣤⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⢷⣄⠹⣆⢿⣀⣷⣾⣀⡿⣰⠏⣠⡾⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡈⠙⢶⣽⣶⠟⠋⠉⠀⠀⠉⠙⠻⣶⣯⡴⠋⣁⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣌⣙⠳⢶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⢞⣋⣡⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣈⣉⣙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣤⣤⣬⣭⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢭⣥⣤⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣠⡴⠟⣉⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣉⠛⠶⣤⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣠⠾⢋⡾⠋⣿⢲⣤⣤⣤⣤⡖⣿⡙⢧⡙⠷⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢁⡴⠿⠷⡾⢧⠿⠶⡿⢿⠶⠿⡼⢷⠾⠿⢦⡈⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣱⣁⣀⣠⢛⣇⣀⣀⡄⢠⣀⣀⣸⡚⣄⣀⣈⣎⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣜⣀⣀⣀⡌⣎⣀⣀⣀⡅⢨⣀⣀⣀⣱⢡⣀⣀⣈⣣⡹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢣⠊⠉⠉⠉⡹⢰⠉⠉⠉⠉⡧⢾⠉⠉⠉⠉⡆⢏⠉⠉⠉⠑⡜⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡡⠋⠉⠉⠉⢉⠃⡎⠉⠉⠉⠉⡃⢘⠉⠉⠉⠉⢱⠘⡋⠉⠉⠉⠙⢌⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠛⠓⠛⠛⠛⠛⠒⠓⠚⠛⠛⠛⠓⠚⠛⠛⠛⠓⠚⠓⠛⠛⠛⠛⠛⠛⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠉⠉⢹⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠶⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠲⠤⣄⡀
⠀⠀⠀⠀⠀⢀⣀⣠⡾⠟⠛⠛⠛⠳⢶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢘⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠙⣿⣦
⠀⠀⠀⠀⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⣴⣶⡄⣶⣶⣶⣶⠶⠖
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣼⠋⠉⠉⢹⠋⠉⠉⢹⡏⠉⠉⠙⡏⠉⠉⠉⣧⠀⡇⠀⠀⢀⣶⣮⣭⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠰⠿⣧⡀⠀⠀⠀⢰⠿⠒⠒⠲⣿⠖⠒⠒⢾⡷⠒⠒⠲⣿⠖⠒⠒⠿⣆⠘⠀⢀⣾⡟⢹⣿⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⢈⣷⣦⣀⢠⡟⠀⠀⠀⣰⣇⠀⠀⠀⣸⣇⠀⠀⠀⣸⣇⠀⠀⠀⢹⡄⠀⡾⠋⠀⢸⣿⠀⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⡾⠛⠛⠛⠛⣿⠟⠛⠛⠛⢻⡟⠛⠛⠛⠻⣿⠛⠛⠛⠛⢷⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠈⣧⠀⠀⠀⢸⣿⠒⠒⠒⠒⠒⣿⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠶⠶⠶⠿⠿⠶⠶⠶⠶⠿⠿⠶⠶⠶⠶⠿⠿⠶⠶⠶⠶⠿⠆⠀⠀⢸⣿⠀⠀⠀⢐⣿⣿⣿⡿⣿⠉⢹⡻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⢸⣿⠀⠀⠀⢰⣿⣿⡟⣴⣏⡀⠛⣿⡎⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠸⣿⣿⣧⠻⣿⡇⠘⣿⢇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠰⣿⣿⣿⣷⣬⣽⣼⣵⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⡤⠠⡄
⠀⠦⠤⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢻⡟⠻⢵⣶⣮⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⢉⣥⣴⡾⢟⣴⣿⣏⣀⣴⣶⣿⣯⣿⣿⣿⠟⠁⣴⡀⠘⠋⠉⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⠹⠋⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣏⡻⠋⠚⠋⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⢀⣤⡤⡄⢀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠚⠛⠉⢿⡿⢿⢶⡦⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢰⠀⢰⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠳⠶⣤⣤⣠
⠀⠀⠀⠀⠀⠀⢸⣦⣬⣁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣯⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣰⣿⣃⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣰⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠋⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣯⢡⡴⣶⣤⠞⠛⠋⠉⠛⢳⡄⠀⠀⢀⣤⡴⠟⠛⠛⠷⣤⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠸⠧⠴⢬⣩⣽⡛⣦⡀⠀⠀⠈⢷⠀⠀⠘⠷⠶⠶⣦⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⡟⠀⢀⡤⠟⠀⢀⣤⣤⣤⠶⠟⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠳⠤⠟⠀⠀⠀⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢰⡇⠀⠀⢀⣠⣤⣤⣀⣀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⡛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⣼⠛⢶⡀⢸⠁⣠⣤⣈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⠁⠀⠉⠛⣯⠉⢿⣄⠀⠀⣴⠲⣄⠀⠀⠀⣧
⠀⣿⠀⠸⣧⣿⣀⣉⡙⠛⠃⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠸⠿⠶⣦⣻⣤⣤⡿⠀⠈⣿⠀⢀⣿
⠀⣿⠀⣰⠟⠀⠀⠈⠙⠦⣤⡀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⠇⠀⠻⡴⠋⡿
⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠈⠛⠛⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢠⡇
⠀⢸⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣶⠛⠀⠀⣠⠖⠒⢺⠇
⠀⠀⢻⡙⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⢿⣤⡄⢼⡋⠀⢠⡿
⠀⠀⠈⢷⡀⠀⠙⢳⡄⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣼⣿⡇⣸⡃⣠⡿⠁
⠀⠀⠀⠀⠳⣄⠀⠀⣿⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡟⢹⠟⠁⢉⡽⠋
⠀⠀⠀⠀⠀⠈⠳⣄⠹⣆⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡴⠟⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣳⣾⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⣭⣭⣭⡅⢀⣭⣭⣭⣭⣭⡅⢨⣭⣭⣭⣭⣭⡀⢨⣭⣭⣭⣭⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⠀⣤⣤⣤⣤⣤⣤⡀⢀⣤⣤⣤⣤⣤⣤⠀⢨⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁⠘⠛⠛⠛⠛⠛⠛⠁⠈⠛⠛⠛⠛⠛⠛⠃⠈⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⣿⣿⣿⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣠⡖⡆⡇⡰⡆⡶⠀⢰⢲⣄⣶⣴⣶⣤⣶⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠁⠉⠁⠁⠀⠘⠉⠀⠉⠀⠀⠁⠉⠀⠁

⠀⡀⠀⠀⡀
⠀⠁⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢠⡕⢄⢡⡀⣴⣶⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠠⣾⣿⣿⣂⣘⠇⠠⣤⡄⠀⢀⠀⠀⠀⠀⠺⠛⡃⣿⣿⡋⢸
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠒⠀⠀⠂⠀⠘⠛⠛⠛⠓⠒⠛⢉⠉⠉⠁⠀⠀⠀⠀⠒⠲⠿⣽⣧⣶
⠀⠀⠐⣀⣠⣄⣶⣴⣶⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⡉⣙⢈⠂⣲⠜⠣⠈⠀⠌⣀⠄⢀⠋⠙
⠀⠀⠀⠈⠇⢸⡀⣧⠈⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠉⠁⠑⠒⠂⠄⠦⡀⠞
⠀⠀⠀⠀⠀⠈⠿⠘⠂⠀⠀⠘⢦⣤⣤⣀⡀⠀⠀⠀⠀⠉⠱⢶⣤⡴⠃⢀⡀⠀⠄⠀⠀⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠲⠗⠀⠈
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣀⣠⣤⣤⣤⣤⡤⣤⣬⣍⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠐⡿⠛⡟⠉⠏⢀⡀⠬⠷⣌⡉⣫⣹⢿⣿⣷⡒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡄⠀⠀⠀⠀⠀⠀⠁⠛⢿⣧⠀⠀⠀⠈⣿⣿⠛⣿⣿⣿⡝⣷⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⣀⣤⣴⠃⣨⡿⠀⠀⠀⣸⡿⣻⣿⣿⠟⠙⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡿⠋⠀⠀⠀⠀⠀⢿⡿⠁⢹⣤⣿⣇⣠⣴⣾⣯⣾⠁⣉⡸⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣷⠏⠀⠀⠀⠀⣴⡀⠀⠈⠁⠀⠈⢸⣿⡿⠉⠙⠛⠋⠚⢓⢿⣧⣤⢀⣾⠆⠀⠀⠀⠀⠀⣠⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠋⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⢰⠖⢙⣿⡗⠺⠇⠠⣤⣤⡎⣠⠹⠟⠈⠁⠀⡠⠃⢠⢆⡀⠈⢧⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⢠⡞⠀⢀⠀⠀⠀⠀⠀⠀⣡⣶⣷⡶⠞⠛⠋⠃⢀⠀⠀⠸⣿⣿⣿⡅⠀⠂⠀⠀⠄⠀⠘⠟⠋⠀⠀⠁⠀⠀⡀⡀
⠀⠀⠀⠀⠀⣤⠀⢀⣾⣇⠀⠀⣀⡀⠀⠀⣠⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠶⠀⠀⢘⣿⡟⠛⢀⣴⣿⣾⣕⣆⣰⣤⣴⡆⠀⠀⢦⡾⣧
⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⠁⢰⣿⣟⣹⡆⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⣿⣷⡤⠐⠛⠋⠉⣿⣿⡟⠛⠛⠡⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣄⠺⠋⣿⣭⣛⠿⢿⣿⣗⣀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣾⣿⠟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢢⡀⠀⣾
⠀⠀⠀⠀⠀⠘⠀⠛⠻⣿⣿⣷⡄⢹⡟⢿⣤⣄⣻⣶⣾⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠞⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠘⣿⣧⣘⠳⠛⠻⠿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⢀⣟⠀⢆
⠀⠀⠀⠀⠀⠀⢙⠀⠀⠐⠦⢈⢻⣷⠇⠀⢀⣀⢈⡙⠿⣿⡁⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣼⠃⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠈⣦⣢⡀⠀⠘⣿⠃⡤⠒⠃⠈⠀⠁⠀⠈⢹⡄⠀⠀⠀⠈⠁⠈⣿⡧⠀⠀⠀⣀⣠⣤⣀⡄⣶⣷⡟⠉⠣⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢈⠡⡈⠢⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⠲⢤⣔⣦⣦⠀⠀⠀⠻⠷⢿⣿⣿⣿⣿⠇⠋⣬⠀⠀⠀⠀⣛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠐⠿⣦⡀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠛⣧⣤⣄⠀⠀⠀⠀⠈⣽⢿⣿⣿⢸⣥⠀⠀⢸⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠢⠀⠀⠈⢳⡄⢹⡿⢶⡄⠀⠀⠀⠀⠀⣴⣾⣿⠋⠁⠀⠴⠂⠀⠈⠠⡜⣿⠏⠀⠙⠂⣠⢿⠁⡘⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡂⠀⠠⣌⣇⢾⠀⠈⢱⠿⠂⣀⣄⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⢀⡼⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⢈⣿⣼⠀⠀⠀⢁⣠⣿⣿⡟⠀⠀⠀⠀⢀⡠⠴⠒⠚⠋⠉⣻⣿⣡⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠳⢌⣿⣦⠀⢰⣾⣿⣿⣷⣦⣴⣊⣅⣀⣠⣄⣘⡁⢀⣦⣴⡿⠛⠙⠋⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠻⢾⣿⣿⣿⠿⠟⠛⠋⠉⠋⠉⠉⡉⠛⠙⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⡴⠶⣤⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣰⠟⠁⠀⠀⠀⠈⢷⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠻⣆⠀⠀⠀⠀⢀⣼⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⠶⠶⠾⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡍⠉⠉⠉⠛⠛⡟⠛⠻⠿⠿⠿⠷⣶⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⠉⠀⠀⠀⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠉⠉⠹⡍⠙⠛⠛⠛⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠉⠉⠉⠛⠛⢻⡖⠒⠒⠒⠢⠤⠾⣦⠤⠤⢤⣀⣀⣵⣄⣀⣀⣀⠀⢹⣧
⣴⣶⢦⣤⣤⣤⣤⣀⣀⣀⣀⡀⠈⣿⣿⣧⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⢻⠀⠈⠉⠉⠉⢻⣧
⠹⣿⣆⠀⠀⠈⡄⠈⠉⠉⠹⡉⠛⠛⣿⣿⣟⠙⠓⠒⠒⠚⢿⠖⠒⠶⠤⠤⠤⢷⣤⠤⠤⢄⣀⣠⣧⣀⣀⣀⣀⡀⣿⣆
⠀⢻⣿⡄⠉⠉⠙⡃⠀⠒⠒⠳⠒⠂⠺⣿⣿⣆⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠉⠉⢿⡆
⠀⠀⢻⣿⡄⠀⠀⠶⡄⠀⠤⠤⢧⡄⠀⢹⣿⣿⡖⠒⠒⠒⠢⠾⣶⠤⠤⠤⠤⠤⠬⣷⣤⢄⣀⣀⣀⣸⣦⣀⣀⣀⣀⣘⣿⡄
⠀⠀⠈⢿⣷⡀⡀⢀⣰⣀⡀⠀⠀⣂⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠙⡅⠀⠀⠉⠉⠙⣿⡀
⠀⠀⠀⠈⣿⣧⠀⠀⠀⢣⠀⠀⠀⠉⠏⠉⠉⢿⣿⣷⡒⠒⠒⠶⠶⢿⣦⠤⠤⠤⠤⠤⢼⣦⡤⠤⠤⢤⣄⣽⣄⣀⣀⣀⣀⣹⣷⡀
⠀⠀⠀⠀⠘⣿⣏⠉⠉⠈⢛⠀⠀⠀⠚⡖⠐⠘⣿⣿⣧⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠹⣿⣦⣤⣤⣬⣦⣤⣤⣤⣴⣤⣤⣼⣿⣿⣧⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣽⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⢤⣤⣿⢤⣬⣭⣭⠉⠉⠉⠉⠁⠉⠁⠉⠉⠉⢿⡉⠈⠉⠈⡏⠈⠁⠉⠁⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠗⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠿⣿⣛⣿⣛⣳⣶⣶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠶⠶⠖⠚⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠂⠈⠉⠀⠠⢤⠔⡉⠉⠐⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠼⠃⠀⠐⠁⠀⠀⡆⣄⣶⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠴⠀⠀⢀⠔⡌⣡⠦⠂⠉⠈⠋⠀⠀⠀⠀⠀⠀⢩⡄⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢀⡄⢠⣯⣔⣐⠽⠚⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢸⡌⢂
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢚⣞⠄⠾⠁⠊⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⠉⠀⠀⠀⠀⠀⠀⠀⠠⡡⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⢀⡞⢁⡀⠀⠀⠀⠀⢀⣤⣠⠀⢀⢄⠦⠠⠆⠀⠀⠁⠀⠀⠀⠀⠡⠀⠀⠀⠀⠐⠱⡀
⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⢊⡯⠚⠉⢷⣗⢆⣀⣰⣈⣉⣑⠆⠈⢂⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⢣
⠀⠀⠀⠀⠀⠐⠀⠁⠀⡸⠭⠄⠐⡄⠀⠋⢸⠏⢯⣴⣤⠄⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡋⠈⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠼⠀⠀⠀⠀⠑⢄⣠⠤⡀⠀⡀⡸⠀⠀⠀⠀⣀⢀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠐⠉⠣⣄⢈⠀⡅
⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣶⣄⠀⠀⠀⠂⣉⣋⠗⢉⠉⠈⠻⠴⡄⠀⢀⠀⠀⠀⠘⡊⢁
⠀⠀⠀⠀⠀⠠⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢷⣀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠙⢏⠈⠀⠀⠀⠀⠘⠚⡆
⠀⠀⠀⠀⠀⠰⠈⢧⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠹⣧⡀⢀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠀⠉⢳⠁
⠀⠀⠀⠀⠀⠀⢃⠈⢿⣢⡀⣀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⢋⡉⡄⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⠷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠁⠀⠀⠈⡠⠄⠂⠀⠒⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡸⣀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⣈⠆⠀⠀⠔⠁⠀⠀⠁⢀⠠⠒⠁⠠⠒⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠢⡀⠈⢿⣶⣂⠀⠀⠀⣄⠛⠀⢠⡁⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⡄⠈⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡀⠀⣿⣹⠀⠀⠀⠈⠀⢦⠈⢢⠀⠀⠤⡀⠀⠀⠀⠀⠀⠠⢊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣌⡳⣎⣤⠀⠀⠀⠀⡴⠊⠀⣧⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⣶⣼⣃⣈⣀⣈⣀⠤⠤⠖⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡁⣠⣄⡾⡠⢤⢠⡀⠀⠊⣿⢸⢦⢤⢠⣤⡄⡠⢸⢧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠋⠃⠋⠓⠓⠛⠈⠃⠀⠀⠋⠀⠘⠚⠚⠁⠋⠓⠘⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠆⠳⠶⠶⠶⠀⠶⠶⠆⠶⠶⠷⠾⠂

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣯⣩⣩⣍⣍⣿⣁⣁⣉⣉⣽⣅⣈⣀⣀⣀⣀⣿⣁⣁⣈⣁⣹⣍⣉⣉⣌⣹⣧
⠀⠀⠀⠀⠀⢠⣟⣀⣀⣀⣀⣰⣏⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣈⣷⣀⣀⣀⣀⣘⣧
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠘⣧
⠀⠀⠀⢠⠏⠉⠉⠉⠉⠉⣹⠏⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⢿⡉⠉⠉⠉⠉⠙⣧
⠀⠀⢠⣿⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⡼⣧⣤⣤⣤⣤⣤⣤⣴⣷⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣼⣇
⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⣀⣀⣀⡀⠀⠀⠾⣿⡇⠰⠀⠀⢀⣀⣀⣀⠀⠀⣤⣤⣤⣤⣤⣶⣶⣶⡆
⠀⢀⣮⣽⣯⣽⣤⣼⣯⣽⣭⣧⠐⠛⢻⠛⠓⠀⠀⠀⣿⡇⠀⠀⠀⠚⠛⠟⠛⠃⣴⣯⣿⣽⣯⣤⣿⣬⣯⣽⡄
⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣆⣉⣻⣇⣈⣀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⣾⣿⢺⣿⡶⣿⣇⠀⠀⠀⠀⠀⣠⡟⣻⢧⡶⣤⣀
⠀⠀⠀⢀⣶⣶⣶⢦⢿⣿⢿⢿⡷⢶⣶⣶⣆⠀⠀⠀⠀⢾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⣿⣸⣿⣏⣿⣿⡀⠀⠀⠀⠰⡾⣴⢋⡟⡰⠏⠀⠃
⠀⠀⠀⣼⣿⡿⡿⢈⣿⣿⣽⣿⣧⠹⣿⣿⣿⡆⠀⠀⠀⠘⢷⣄⣀⣤⠞⠁⠀⠀⠀⠀⠀⣼⣿⣿⣼⣿⣧⣿⣿⡤⠀⠀⠀⢰⡟⠳⣿⣼⠛⢰⡆
⠀⠀⠀⠀⠐⠛⠀⠈⠉⢩⣮⠉⠙⠀⠐⠓⠀⠀⠀⠀⠀⡆⠀⠀⠁⠀⠀⣶⠀⠀⠀⠀⠀⠠⠄⠄⠖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣿⣿⡀⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡧⠀⠀⠁⠀⠀⠀⠀⠀⠑⠖⠢⠆⠰⣿⣿⡇⡷⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢀⣤⣤⣀⣤⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠘⢻⣿⠻⣿⡟⢿⣿⠃⠀⠀⠀⠀⠀⢰⠒⡒⠒⡖⠐⡖⠒⠀⠄⠀⠀⠀⠀⠀⣴⠞⠋⠙⠻⣧⠀⠀⠀⠀⠀⣺⣿⢻⣿⠏⣿⡿⢿
⠀⠀⠀⠀⠸⣿⣿⢿⣿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠉⡏⠈⡏⠉⡏⠉⡆⡃⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⡗⠀⠀⠀⢀⣿⡟⣿⣿⢻⡿⠿⠎
⠀⠀⠀⠀⢰⣾⣿⣶⣿⣷⢞⣵⣶⠦⡄⠀⠀⠀⡏⠉⡏⠉⡏⠉⡏⠉⡇⢉⠀⠀⠀⠀⠈⢳⣄⡀⢀⣠⡾⠁⠀⠀⠀⢸⣿⢻⣿⡿⢎⣶⠋⣷⡄
⠀⠀⠀⠀⠈⠉⠉⠈⠉⠁⢸⣉⣧⣤⡟⠀⠀⠀⠋⠙⠙⠉⠋⠋⠛⠙⠁⠈⠀⠀⠀⠀⠀⠈⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠊⠿⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣢⣼⣧⣖⢀⠀⠀⠀⠀⠀⠀⡸⣽⣿⣿⢩⣿⣿⡍⡅⠀⠀⠀⠀⠀⢰⣶⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡞⠀⠀⠀⡰⠀⠀⠀⠀⠀⠠⢼⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⡏⢿⢿⡟⠸⡟⣿⠃⡄⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⢀⣊⣀⣀⣀⣀⣀⡼⠀⠀⠀⢀⠃⠀⢠⠀⠀⠀⠀⠊⠻⣿⣿⠟⠑⠀⠀⠀⠀⠀⢠⢹⣿⣻⣟⣺⣿⣿⣇⡇⠀⠀⠀⠀⠸⠿⢿⣿⠋
⠀⠀⠀⠈⠭⠭⠭⠭⠭⠭⠤⠭⠭⠭⠭⠬⠍⠁⠀⠀⠀⠀⠀⠁⠨⣅⣈⣀⣀⠀⠀⠀⠀⢸⢼⠟⡟⠧⡽⠿⢟⣡⠅⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠤⠦⠦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓
⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⣟⠀⠀⠈⡇
⠀⠀⠀⠀⠘⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣤⣤⣬⢡⣤⣤⣍⡆⠀⠀⠀⠀⣄⢰⣘⣇⡆⣠⠄⠀⠀⠀⠀⣠⣶⣦⣴⣶⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠃⣾⡿⢳⣿⢟⠎⠀⠀⠀⠒⣿⣿⣿⢸⣿⣿⡗⡇⠀⠀⠀⠐⢰⣿⡟⣿⣿⣧⠂⠀⠀⠀⠀⢶⣿⡷⣾⣿⣶⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣺⡿⢋⣾⡟⢱⣿⢫⠏⠀⠀⠀⠀⡧⣶⣶⣶⢰⣶⣶⡦⡇⠀⠀⠈⢉⢽⣿⣶⣴⣿⡿⡍⠁⠀⠀⠀⣾⣿⡇⣿⣿⡖⣿⣿⡆
⠀⠀⠀⠀⠀⢠⣽⣿⣧⣿⣿⣱⣿⣯⠏⠀⠀⠀⠀⠀⡎⠿⠿⠿⠸⠿⠿⠏⡇⠀⠀⠀⠀⠞⢩⢻⡟⠏⠻⠀⠀⠀⠀⠘⠛⣻⣓⣛⣟⣓⣻⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠛⠛⣛⠟⠁⣿⣿⡿⠿⠃⠀⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⡇⠀⠻⠟⠁⠺⠇⠀⠀⠀⠀⠀⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠀⢸⣿⣿⣿⣦⡀
⠀⠀⠀⡴⣿⣿⠋⠁⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠀⡜⠸⣿⣧⣀⡀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠈⠟⠿⣿⣿⡄
⠀⡸⠁⠀⠈⢹⣿⠁⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣤⡈⠉⢷⡀
⢀⠇⠀⠀⠀⠀⢹⡀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢣⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿
⠸⡀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿
⠀⢇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇
⠀⠘⡆⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟
⠀⠀⠘⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠈⢦⡀⠀⠀⢸⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠑⢄⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠔⡳⠀⠀⠱⠀⠀⠀⠀⠡⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⢣⠀⠀⠀⡘⠀⣀⣀⡠⠀⠀⢀⠂⠀⠠⠈⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠤⠄⡈⠀⠀⠀⠸⠆⠀⡁⠈⠑⠂⠠⠧⣠⡛⢢⣾⠛⠛⠋⠻⠛⢻⣻⣯⡎⠀⠀⠙⣼⣟⡛⠛⠛⠛⠛⠟⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠈⠗⠂⢦⠘⠂⠀⠀⠀⠀⢀⡿⣶⢻⠁⠉⠈⠻⠶⣶⣶⠿⠟⠿⠛⠃⠀⠀⠀⠛⠻⠻⠿⣶⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⣀⠃⡰⠐⠄⠀⠀⠀⠀⢸⡷⢁⠄⠀⠀⠂⠀⠰⢈⠟⠛⠒⠶⢴⡃⠀⠀⢸⢦⠴⢶⡓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣄⠀⢀⠀⠀⠀⠀⠀⠄⠠⡀⠠⠀⠀⡀⠀⣸⠗⠀⠀⠁⠀⠀⠁⠀⠀⡇⠀⢀⡠⠜⣣⠀⢀⡂⠀⠀⠀⠉⠑⢦
⠀⠀⠀⠀⢀⣀⣀⣤⡀⢀⠀⣤⣌⠋⠊⡿⠣⡄⠀⠉⠀⠘⠀⠀⠉⠑⡄⠈⠹⡿⢤⠀⠀⠄⠀⠀⢀⢢⠛⠀⠀⢈⠇⠘⢿⣇⣿⠟⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⣠⣦⣭⣭⣽⣷⣞⣷⡟⢻⠟⠈⠀⠀⣄⠀⠡⠀⠇⠀⢆⠀⠐⠌⠀⠀⠈⠑⠐⢟⢠⡚⡈⠈⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣭⣍⣙⠻⠏⠀⠈⠿⠃⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⣔⢂⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢻⡿⠛⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠡⠘⡄⢀⠳⣦⠀⢀⢀⣀⣀⣠⣤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠄⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠳⡀⣥⠀⢉⠄⠀⠆⠁⢄⠉⡇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠁⠀⠀⡀⠀⠓⠀⠀⢀⠈⠧⠘⡌⠻⡊⠄⠑⠆⠀⠸⠁⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⠲⠒⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠑⠀⠂⢀⠀⠂⢤⠀⡅⠠⠡⠀⣠⡔⠂⠀⠚⢃⠀⣾⡷⡄⠁⠀⠀⠀⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠠⠀⠀⠀⠀⠂⠓⠀⠀⠀⢀⣀⠤⠀⠂⠉⠉⠀⢀⠸⡁⡇⢰⢦⡄⠰⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢳⠀⠀⡀⠉⠐⠀⠤⡀⠀⠀⠀⠶⠆⡀⠄⠠⠀⠀⠂⠠⠀⠀⠀⠈⢇⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⡇⠠⠀⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠐⠐⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⢀⣠⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠄⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⡛⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠀⠄⠋⠲⠅⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠎⠰⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣟⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣼⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⣼⣧⣴⡄⠀⠀⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⣿⣿⣿⣿⣷⠀⠘⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠉⠀⠘⢿⣿⣷⣦⣤⣌⠻⠿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡇⠀⠀⠀⠉⢻⣧⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣶⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⠋⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠁⠀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠐⡶⠣⠌⣁⠒⠠⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠄⠀⣠⢃⢀⠀⡜⡀⠀⡠⠁⠀⠉⡱⠒⠠⠤⡈⠁⠒⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠉⠐⠧⠹⢒⣢⢮⢄⡑⠰⢠⢀⠀⠜⠀⠀⢀⠎⠀⠈⠁⠖⠠⠨⣀⣂⣥⡒⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠂⠀⡠⠊⠀⢀⠌⠀⠈⡰⠊⠕⠂⠆⢮⣈⠲⠠⠂⠆⠀⠀⠎⠀⠀⠀⠠⠃⠉⠑⠲⠄⠤⣀⠈⠁⠒⠀⠄⡀
⠀⠀⠀⢀⠄⠒⠉⠧⣀⢀⠔⠡⡀⡠⢣⠀⢀⠞⠀⠀⢠⠂⠈⠁⠢⠍⣓⠢⢤⣁⠎⠸⠄⡀⠠⢁⠀⠀⠠⠁⠀⠀⣰⡅⠀⠀⠀⠀⠀⣩⡦
⠀⠀⠀⠈⠂⠢⢄⡀⠀⠉⠛⠒⠸⢅⡁⡠⢂⢁⠀⡔⡁⠀⠀⡔⠁⠀⠀⢉⠐⠠⢍⡐⠢⢤⣁⠈⠆⡠⠁⢄⠀⣠⢉⡿⠒⠀⢀⡤⠞⢉⠃
⠀⠀⠀⠀⢀⠀⢀⠈⠀⠂⠄⠐⠄⠀⠈⠉⠒⠤⣌⠔⠄⢀⢎⢀⠀⠀⠠⠃⠀⠀⠀⠁⠋⠐⠢⠍⠑⠣⢤⣈⣰⠏⠀⠀⣠⠞⠋⠁⠀⠈
⠀⠀⠀⠀⠀⢂⠀⢦⠄⢀⠀⠀⠈⠐⠨⢐⠀⠀⠀⠉⠑⠢⢌⡀⠃⠔⠁⠂⠀⠀⡐⠁⠀⠀⠀⣼⡡⣀⠀⠀⠀⣠⡴⠛⠍⠀⣀⠂⢠
⠀⠀⠀⠀⠀⠈⡀⠈⠄⠈⠗⠂⠴⣀⠀⠀⠈⠑⠢⠅⡂⠄⡀⠈⠙⠲⠤⣄⣀⠌⢢⢃⠄⢀⠎⠙⠃⠀⢀⡴⠛⠇⠐⢀⢠⠃⣍⠀⠆
⠀⠀⠀⠀⠀⠀⠐⡀⠈⠄⢈⡀⠀⠁⠈⠳⠤⣰⠀⠀⠀⠑⠠⢅⡂⠤⢀⠀⠈⠓⠦⢤⡠⠋⠁⢀⣤⣮⠋⠁⠈⢀⠖⠁⡀⢠⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠀⢤⡀⠰⠀⠈⠁⠂⢦⡀⠀⡀⠀⠑⠂⠬⡒⠠⢄⡀⠀⣠⡴⠽⠋⠀⠄⣠⠀⠁⠆⣠⠊⢰⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠰⠄⡄⠀⠄⠈⡖⠤⡅⠀⠀⠀⠑⡧⢀⡀⠄⠀⠀⠉⠑⠪⠵⠛⢁⠀⠌⡬⠂⠁⠀⡪⠀⠁⢀⣄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠁⠘⠙⢴⡀⠁⠀⠈⠉⠰⢄⠄⠀⠀⠀⠓⠠⢀⡀⠀⠀⠰⢀⢈⠄⠈⠐⢠⡧⢊⡁⢠⠆⠘⢨⠡⠄⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠁⠀⠀⠙⠂⢤⡀⠈⠀⠈⠓⠤⣂⠀⠀⠀⠁⠀⠀⢠⠀⠌⠊⠰⡀⢛⠀⢸⢄⡧⠀⢁⠂⠀⠀⠄⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠉⠂⢥⡀⠀⠀⢀⠀⢔⡠⠚⢀⢎⠔⡋⠈⠀⢃⡜⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢁⠀⠀⠀⠀⠀⠀⢈⠀⡠⠠⠁⣦⠃⠈⠀⢀⠴⠋⠀⡐⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡜⣀⠀⠁⠢⣀⠉⠂⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠘⠐⢀⡁⠊⠀⠂⢀⡜⠉⠈⠀⠀⣀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢁⡂⠀⣆⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡘⠠⢁⠁⠀⢀⡔⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠓⠃⠀⠈⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠂⠀⡴⠊⢀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⡇⠀⢀⠎⠁⠀⠀⠀⠠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢶⢢⣤⠀⠀⠀⠁⠢⡀⠀⠁⡴⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠉⠉⠙⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡆⠀⠀⠀⡠⠀⠀⠀⢀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢠⡤⣀⠀⠀⠰⣄⠀⣠⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⣇⠀⠀⠀⠈⠑⠂⠀⠙⣷⡿⢿⣿⡿⢀⣠⠠⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠐⠀⠀⣀⠀⠘⣿⣷⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⠂⠀⠉⠐⠾⣿⣿⣿⡟⠁⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠈⡀⠀⢀⡤⢶⣶⣾⣿⣷⣉⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠈⢳⠆⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣰⣟⢠⣟⣻⣿⣿⣇⠙⠛⣆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢦⠀⣸⠟⠉⣾⣟⠺⢿⣿⡟⠀⠀⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠲⠆⣐⠦⠀⠀⠀⠄⠃⠀⠀⢹⣧⣴⣿⣿⠇⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⡌⢻⣿⡿⠋⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠰⢇⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠑⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⢀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠒⠀⡀⠀⠀⠀⠀⠀⢀⠈⡈⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢻⠀⠀⠀⠑⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⣠⡄⠈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⡇⠀⠀⠘⠧⠀⠀⠄⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⢰⠁⠀⠀⠀⡀⠳⣄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⢀⣄⠀⠀⡆⣾⠈⡌⠀⠀⡰⠃⠀⠈⠱⣄⠀⠈⠢⣆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣿⡄⠀⢸⡇⣠⠃⠀⠐⠁⠀⠀⠀⠀⠈⢷⡈⢄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠘⣷⠀⣼⠀⡏⠀⣴⡷⠃⠀⠀⠀⠀⠀⠈⣷⠼⣷⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠈⠄⢀⠸⣧⡏⢠⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢇⠹⣆⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⢠⠄⠘⣧⡉⢀⢸⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⡇⠈⠨⣿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⡀⡏⢢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⡿⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⠄⢹⣏⣋⡟⡿⢛⣉⣛⣏⣽⢛⣙⠋⣿⠋⠛⢉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣻⣿⣟⣻⣟⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⢀⠏⠀⠀⢃⠀⠀⡞⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢀⠊⠀⠀⠀⠱⡞⠀⠀⠀⠈⡄⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⡄⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⡏⠀⠀⠸⠀⠀⠀⠀⢀⡤⠖⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⣲⠟⣻⣀⣤⣄⠀⢀⠔⠉⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⣴⢛⣭⠵⠛⠉⠉⢀⣽⠔⠁⠀⢀⡞⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠈⠳⡀⠀⠀⢸⡀⡠⠒⢠⣾⣿⣿⣿⣯⣥⣤⣶⠶⠞⡟⠁⢀⠀⣠⢋⣤⠞⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠹⡄⠀⠀⠉⣿⡆⢸⣿⣿⣧⣿⣿⣃⢼⣿⢇⡀⠀⠰⠃⣼⡵⠋⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⣆⠠⠚⣿⢏⠈⠙⣻⠟⠻⢿⣿⢛⣥⣻⣷⠀⢁⡾⠋⠀⢀⡞⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⣀⡀⠈⠻⢦⡀⠀⢀⣀⣬⣧⡔⣛⣱⣶⠶⠚⢷⣿⣽⡿⣼⣴⠟⠀⠀⣀⡾⠞⠉⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠻⢦⣀⡿⣿⣷⣞⠻⢿⣿⣻⠷⢾⢻⣿⡾⣿⢁⢀⣤⠾⠉⠀⣠⣴⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣛⣶⡶⠶⠶⠶⠶⣶⣿⣦⠼⣭⣿⡓⣮⣾⠛⢻⢟⡆⠹⣾⢇⣼⠟⠃⣀⣴⡾⠟⠋⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠀⠀⠀⠒⠊⠉⢁⣀⣽⣍⢿⣫⣥⣦⡟⡡⢶⡃⡩⠼⡿⢨⣾⣿⣴⠿⠿⡟⠁⢄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠛⣫⣿⣿⣆⣶⣻⣶⣦⣽⢛⣿⣡⣋⣵⣿⠿⠋⠀⠀⡼⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠛⠋⠉⠉⠀⠀⣠⡴⠛⠛⠻⣿⣧⣬⣥⣿⣭⣤⡞⠋⠉⠀⣸⠋⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠴⠚⠋⠹⣤⡴⠶⡈⠀⠀⠀⠀⢀⣠⡞⠀⠀⣠⣾⣥⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠒⠋⠀⠘⣷⣾⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣏⢁⣤⣤⣤⣤⣠⡶⠛⠛⠛⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⢀⣾⠏⠀⠙⠦⡿⠱⣯⣤⣄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢰⣿⣋⣁⣀⣀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠈⠛⠛⠛⠛⢷⡶⠿⢶⣆⠹⣦⣀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⠉⠛⠛⠛⠻⣷⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢠⡟⠀⠀⢀⣠⡾⠋⠀⠀⣀⣀⣀⣀⣤⣶⡿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠸⣧⡀⢀⡿⠁⠀⠀⠀⢸⣿⡛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⣼⣧⣀⠀⠀⠀⣴⡿⠛⠛⠛⠷⢶⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣦⣄⣻⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⢀⣿⠉⢻⣷⠀⢸⣿⠀⣠⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⡟⠀⠀⠀⠀⠉⠻⣷⡀⠉⣿⣆⠀⠀⠀⢰⡟⠛⣷⡀⠀⠀⠀⠀⣿⡀
⠀⢸⡿⠀⠀⣿⣄⢸⡿⠀⠙⠛⠻⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠉⠁⠀⠀⠀⠀⠀⣾⣿⣤⣤⣈⢻⣇⡀⠀⢸⡷⠀⠈⠙⣷⠀⠀⠀⢹⡇
⠀⢸⡇⠀⠀⠘⣿⡘⠳⠞⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⢿⣿⣛⣿⣯⣥⡀⠀⠐⣿⠀⣠⣴⣾⠇
⠀⢸⡇⠀⢀⣾⠟⠀⠀⠀⠀⠀⠘⠻⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣽⠃⠀⠀⠹⠷⠟⠀⣿
⠀⠸⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠛⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠀⠀⠀⠀⣀⣀⣀⣸⡏
⠀⠀⢹⣇⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⢠⡾⠋⠉⠉⣽⡇
⠀⠀⠀⢿⡌⠻⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣄⠀⣴⡟⠁⠀⠀⣰⡿
⠀⠀⠀⠈⢿⡀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⢙⣷⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠉⢿⡆⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⠀⣼⣇⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⢸⣿⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡿⠋⣿⡷⠋⠀⠉⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⣿⡀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⡀⠀⣠⣾⠃⠀⠈⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡘⢿⣦⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠋⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣍⠻⣮⡛⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⡶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⣶⠶⢶⡶⠶⠶⠶⢶⡶⠶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠤⢀⠀⠤⠤⠄⠂
⠀⠀⡀⠀⡀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠤⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡄⠴⠒⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⣿⢧⢯⡾⡜⡀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⡜⠀⠀⠀⠔⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⣼⣿⣟⣼⡿⡴⣵⢯⢃⢁⡕⠂⠀⠀⠂⠀⠠⠤⡀⠀⣀⡀⢀⠀⠀⠀⠀⠀⣴⢿⣷
⠀⠤⠀⠠⠀⠤⠀⠐⠀⠀⠈⢀⣠⣾⣿⣿⣿⢿⣾⢟⣗⡿⡧⢣⣧⣞⡰⠥⠀⠀⠀⠀⠀⠠⠁⠀⠄⠠⢁⣼⣁⢀⢀⣴⣋⡈⠫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡿⢷⣾⢿⣵⣳⡿⢩⢌⣡⢞⡬⡭⠉⣯⠒⠤⢤⠠⠀⢀⠀⠀⠁⣸⣿⡎⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣝⠞⣳⠝⠡⠜⡡⢮⠜⡠⡪⠢⠏⣀⠂⠀⣠⡞⠁⠀⣼⠇⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⢥⣘⠱⣳⡂⠆⡜⠁⡴⢁⢨⣴⣿⣯⠉⠙⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢼⡀⠏⢐⣽⠟⠁⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠋⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣎⡛⣻⢿⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣽⣿⡟⠛⠛⠋⣹⣿⡜⣿⣝⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣒⣫⣿⣿⣿⣿⣦⣰⣿⣯⣭⠀⠀⠙⠛⠁⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠀⠀⠀⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⡿⠋⠀⠈⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣷⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣷⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠁⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢶⣤⣤⣿⣧⠤⠴⠆

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀
⠀⠀⠀⠀⠀⠈⡀⠠⠄⠤⠒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢠⡄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⣠⣮⣀⠀⣠⡶⠋⠀⠀⣠⠆⠀⠀⢠⠄⠈⢄⢀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⣽⠏⠘⠶⢦⡀⢾⣋⡀⠀⡴⠁⠀⣨⡦⠀⣴⢄⠡⠀⠀⠠⠀⠀⠈⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⢶⠔⢿⣁⠀⢀⣤⠞⠈⠈⢉⡏⠀⠵⠖⠺⢋⡰⠊⠀⠈⢧⠐⡀⠄⠀⠀⠈⠀⠄⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣐⠄⠀⣠⠦⠈⠁⠉⣭⡉⢷⣤⡀⠴⠋⠀⠀⣤⠀⡠⠊⠀⣀⢦⠄⠀⠣⡈⢣⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣈⠙⠊⠡⣄⣀⡰⠞⠁⠀⢀⡼⠖⠈⢙⠒⠛⡡⠞⠀⠀⠀⠹⣸⠀⠀⠀⠙⢄⠱⡀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⢆⡀⢀⠀⠓⠲⠆⡋⠀⠀⣠⡾⢃⠞⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠣⡘⢆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠑⠂⢥⢀⣄⡈⠙⢊⡕⡰⠋⠀⠀⠠⢀⠀⠀⠂⠐⢲⠄⠀⢸⣹⠀⢙⢜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠉⣬⠨⠀⠀⠐⡀⣀⣸⡆⠀⢴⣨⣼⠅⠀⠐⣼⠀⠈⣠⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠑⠲⣄⠀⢀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⡅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣽⠀⢐⡛⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠴⢂⢀⡀⠀⣯⠇⠀⡀⢈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⠘⠳⢶⡸⠀⠂⠀⠀⠀⢠⠒⠒⡏⣱⠀⠀⠄⣠⣄⣫⡵⠆⠀⠇⠁⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⢄⡀⠀⠀⠀⡄⢀⡂⠰⠀⠀⢸⠠⠮⠥⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡀⡸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⢁⠀⠀⠀⠀⠀⢸⠀⠀⣀⣇⣀⣀⣀⣤⠤⠤⠖⠒⠚⠓⠋⠁⠠⠤⠶⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣀⠂⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⡔⠁⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠑⠀⠉⠉⠉⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠤⠄⠒⠒⠠⢄⡀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠑⠢⠄⣀⣀⠠⠔⠊⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⠘⢄⠀⠀⠀⢀⠔⠁⠈⠉⠁⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡰⢁⣾⣿⡿⢁⣿⣿⡟⢘⣿⣿⣇⢹⣿⣿⣇⠻⣿⣿⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣼⣿⡿⢃⣿⣿⣿⢈⣿⣿⣟⠘⣿⣿⣏⠹⣿⣿⣆⠳⡄
⠀⢠⠊⣰⣿⣿⡟⢁⣾⣿⣿⠇⢸⣿⣿⣷⠀⣿⣿⣿⡆⠹⣿⣿⣦⡘⢆⠀⠀⠀⠀⠀⢀⠞⣠⣾⣿⡿⠁⣾⣿⣿⡇⢰⣿⣿⣿⠀⢿⣿⣿⣆⠙⣿⣿⣷⡈⢢
⣴⣡⣾⣿⣿⣿⣤⣾⣿⣿⣿⣤⣼⣿⣿⣿⣤⣼⣿⣿⣿⣤⣽⣿⣿⣿⣦⣱⠄⠀⠀⣴⣥⣾⣿⣿⣿⣥⣼⣿⣿⣿⣤⣼⣿⣿⣿⣤⣼⣿⣿⣿⣦⣼⣿⣿⣿⣦⣱
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣧⣠⡤⠤⣠⣤⣤⡠⠤⣤⣤⣤⡤⠤⣤⣤⣤⡤⠤⣧⣤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣬⣤⣤⣤⣤⣤⣤⣤⣤⠎⢠⣼⣿⣿⡿⠁⣼⣿⣿⣿⡇⢠⣿⣿⣿⣯⠀⣿⣿⣿⣿⡄⠹⣿⣿⣿⣤⠈⢢⣤⣤⣤⣤⣤⣬⣤
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠟⢁⣰⣿⣿⣿⡿⠁⣰⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣷⡀⠘⣿⣿⣿⣷⣀⠙⢏⠙⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢠⣾⣿⣿⣿⡿⠁⢰⣿⣿⣿⣿⡏⠀⢼⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣦⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣄⣤⣤⣤⣄⣄⣀⣤⣤⣤⣤⣀⣤⣤⣤⣤⣅⣠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠀⠐⠒⠒⠒⠂⠐⠒⠐⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠋⡡⠔⠋⠁⠈⣹⠀⠀⠀⠀⠒⠒⠀⢠⡞⠁⠈⠁⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢟⠆⢀⠔⠋⠑⠀⣀⠤⠊⠀⠀⠀⠀⣀⡀⠀⠀⠀⠧⢄⠢⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⡤⠚⠰⡧⠒⠒⢫⠄⢢⠀⠀⠀⢠⠖⠉⠈⠉⠹⣦⠞⠉⠚⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢠⠤⠜⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠰⣃⠀⣞⠧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠅⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⣘⡛⣋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠱⢼⠇⢀⡀⢀⣤⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢰⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢀⠴⠊⠉⠁⠀⠑⢆⠀⢠⢮⠒⠚⠀⠀⠀⠘⠢⡀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⣜⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠍⠥⠴⠒⠠⡄⠀⠀⠨⠗⠊⠈⠣⠤⠊⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⡀
⠀⠀⢠⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠘⠒⠄⡀⡴⠶⠤⢀⣀⡀⢇⠀⠀⠀⠀⢰⠦⡄⠀⣄⠤⣄⠀⠀⠀⠰⠘⡇
⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡆⢇⠀⠀⠀⠀⠳⠴⠊⢓⠀⠈⠙⣄⠀⡼⠀⡇
⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢳⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠆⠰⡄
⠀⠀⢠⠀⠷⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡑⢆⠀⢀⣠⠞⠁⠀⠀⠀⠀⠑⢂⡇⡆
⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⢄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡛⠥⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠇⠀⠈⢀⠀⠀⠀⠀⠀⠰⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠃⠊⠀⠀⠀⠀⠀⢠⠃⡘
⠀⠀⠀⠸⡄⠀⠀⡧⠀⠀⠀⠀⠀⠐⠦⡙⠒⠂⠀⠒⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠹⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠎
⠀⠀⠀⠀⠀⠱⡌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠘⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠤⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⡘⠁⡌⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⣎⡤⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠋⠉⠀⠀⠀⣀⠠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠉⠁⠀⠀⠀⠀⠼⣏⣿⠿⠖⣲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠀⠀⠀⢠⣤⡘⡛⢁⠀⠰⠜⠛⠁⢶⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣤⣶⣤⣀⣤⣤⡐⠿⠿⠃⣡⠠⠾⢷⣄⠀⠀⠘⣿⣿⣿⣿⣿⡇⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⠖⠀⣀⣿⣇⠀⠀⣻⣿⣿⣿⣿⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣵⣾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢁⣤⣈⠛⠁⠀⠀⢿⣿⠋⠉⠁⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡼⠐⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣨⣿⣷⣶⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠈⢙⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣿⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⣁⡉⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠋⠉⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣀⡀⠀⠀⠸⣿⠁⠀⢀⣀⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠰⣃⠾⠋⡴⡦⠀⠲⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⣤⡄⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠯⣸⣲⠁⡀⠀⠀⠠⠄⠐⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⢀⠀⠀⠀⠀⢀⠁⡰⡬⠀⡬⠃⣘⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠄⠀⠈⠁⠀⠰⢀⠒⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠤⠋⠁⠢⡂⠀⠀⠀⠀⠐⠚⠣⠚⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⡈⢁⠀⠃
⠀⠀⠀⠀⠀⠀⢰⠆⠀⠠⠔⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣎⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠠⠄⠠⣀⠈
⠀⠀⠀⠀⠀⠀⡞⠁⠉⠀⠉⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢣⣱⣧⡈⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠆⠀⠄⡀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢧⣞⠖⠀⠀⠀⠀⠀⠠⣬⢤⡄⣞⡄⠀⠑⠀⠀⠀⠜⣈⡒⠁⡀⠀⠀⠀⠀⡀⡑⠀⠀⠀⠀⠔⠀⠢⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠠⣀⠀⠀⠶⠃⠀⠀⠀⠀⠀⠀⠙⠾⡇⣻⢵⠔⠂⠀⠐⠄⡂⠓⣀⠁⠀⠀⠀⠀⠂⠀⠄⠐⠂⡈⠀⠀⠂⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡡⠈
⠀⠀⠀⠀⠀⠀⡀⠈⣦⡀⠀⠀⠀⠀⠀⠄⠈⠆⢸⠀⠀⠀⠄⠀⢃⠔⠀⢀⣃⠀⠰⡀⢿⡀⢠⠈⠑⠿⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⣠
⠀⠀⠀⠀⠀⠀⠉⠃⠙⠃⢐⡀⠀⠤⣢⠀⠄⠙⠄⠈⢄⠁⠀⠨⠄⣄⠐⠈⠁⠀⣀⠍⣄⡁⣠⠓⠄⠀⢀⡄⠒⠃⠆⠰⠒⠋⠿⠂⠂⠆⢁⠋⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣤⣶⠟⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣄⡀⠀⠀⠀⠇⣴⠛⢋⣀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡝⠻⣷⣄⠀⠈⠥⠾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣷⣦⡙⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢀⡀

⠀⠀⢠⠤⢠⡄⣤⢠⠤⠠⣤⠄⣤⡀⣤⢠⡄⡄⢠⣤⠀⡤⡄⢠⠀⢠⠤⠀⢠⠤⣄⣤⠤⢤⢀⡄⣤⠄⣤⠀⣠⠤⡄⡤⣤⢠⡄⣤⢀⡤⠄⣤⢠⡤⣤⠄
⠀⠀⠨⡽⠘⢧⠟⠨⠽⠀⠿⠸⠛⠧⠿⠸⠙⠇⠾⠻⠄⠯⠗⠿⠤⠸⠯⠀⠸⠤⠟⠿⠭⠈⠿⠁⠿⠅⠿⠄⠷⡤⠇⠟⠉⠸⠻⠹⠗⠯⠅⠏⠻⠇⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢬⠂⡔⢂⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡇⣠⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉
⠀⠀⠀⠀⢀⢶⡀⠀⡴⣺⣫⣟⣗⢦⠀⠀⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡰⠰⠰⠔⢆⠀⠀⢠⡄
⠀⠀⠀⠀⡜⣸⠀⢸⠥⣯⢬⡧⢼⠤⡇⠀⣇⣳⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣚⡃⣛⢘⣓⢛⡃⠀⠘⣷
⠀⠀⠀⠀⡇⢧⠣⡈⢦⣷⠲⡗⡾⡴⢃⡜⡹⢹⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠘⣃⢩⢨⣏⡛⠃⢀⣾⣿
⠀⠀⠀⠀⠙⣄⠳⠙⢆⠉⠛⠛⠉⣰⠋⠜⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠈⠀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠈⢧⠀⡜⠀⠀⠀⠀⢣⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠸⠴⠃⠀⠀⠀⠀⠘⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⡰⠔⡒⣮⡍⠙⣯⡼⣮⣶⡦⠆⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠛⠋⠁⠈⠁⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡡⠖⠲⠶⢶⣄⠀⠀⣀⡀⣠⠤⡬⢤
⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠅⠀⠁⠀⠈⠀⠍⠍⣬⠉⡑⢶⠔⠊⠐⠑⣄
⠀⠀⠀⠀⠀⣠⣾⣸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠀⠐⠀⠀⠀⠀⠀⡀⠘⠂⠙⠒⣈⣁⡋⣟⠉⢁⣄
⠀⠀⠀⢀⠐⢿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠏⠀⣀⠀⠀⠐⠀⠓⠄⠀⠉⢂⠀⠋⠁⠉⠃⠀⠀⠀⠈
⠀⠀⠀⣤⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⡲⣄⠈⢀⠀⠂⠀⠀⠉⠀⠀⠠⠀⡄⡁⠀⠀⠀⠂⠀⠰⢶⡝
⠀⠀⠖⠠⠆⣛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢠⣞⠜⠋⠠⠀⠐⠐⢋⠈⠀⢘⠃⠠⠀⠀⠀⠀⡂⠀⡁⠁⡀⠠⠀⠰⡾⣳⢒
⠀⢠⣔⠛⠀⠀⡰⣍⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡷⡞⠀⠀⣈⠓⣒⣠⠀⠄⢁⠀⢁⣀⡀⠀⠀⠀⠀⠁⠐⠂⠀⡀⢀⠀⠀⠈⡋⠩
⢠⠞⢉⣉⣁⣨⠞⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡣⠤⢄⡊⡳⠓⠁⡄⢩⣁⢀⡱⠙⣁⠇⢼⠠⠞⠠⢀⠀⠀⠃⠀⠐⡀⠁
⢠⢤⡭⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⡵⠋⠀⣈⢳⡼⠲⣄⡀⠠⢤⠠⠀⠀⣄⢎⡁⠰⠇⠈⡑⠁⠴⠀⠒⠀⢄
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡶⡿⠞⠻⠛⡛⠻⣦⣤⣍⣳⢀⣄⠒⢁⠸⣟⠧⢼⡆⠰⠃⠀⠀⢠⡄⠘⡫⡃⠈
⠀⣳⢀⡀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠌⠀⠠⠀⢀⠃⠸⣝⣆⠀⢰⡆⠘⢀⠀⠙⢷⡀⣀⡦⢠⠼⢻⠇⣦⢆
⠻⠯⣯⣼⠤⢶⡆⠂⣤⡀⠀⠀⠀⠀⠀⣼⢹⡄⣀⣠⣃⣄⡄⠁⠀⠰⠀⠀⢆⡐⠊⣯⡳⡼⢷⣚⠉⠀⠀⠀⠉⢢⣿⠃⠀⠻⣸⡇
⠀⢠⣯⡚⢺⠃⡏⡛⣻⢦⣤⡀⠀⠀⠀⠻⡈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣫⠼⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⠻⣿⡀
⠀⠀⠙⣟⠢⠠⡅⡏⣛⣚⠴⢽⡄⠀⠀⠀⠙⠲⣴⡤⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⣠
⠀⠀⢀⡷⠊⣀⢌⢣⠱⣻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣍⠁⣻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠠⠂
⠀⠀⠘⢧⢁⣹⢠⢈⡧⢜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠠⢄⡠⠀⠖⣶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠘⣇⠙⠿⠾⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠂⠼⠔⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠘⡀⢀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⠍⠀⢠⡽⢁⡤⠄
⠀⠀⠀⠀⠀⠀⠻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣶⠟⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠤⣤⣴⣶⣶⡤⣤⣀⣀⣁⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣿⢾⡒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠐⠒⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢱⢀⠤⠒⠒⠀⢄⠀⠀⠀⠀⠀⠔⢆⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⡌⢀⢀⡃⡠⠊⠀⠀⠇
⠀⠀⠀⠄⠂⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⢩⡟⠒⠠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢱⠀⡼⠀⠀⠀⠀⠀⡈
⠀⠘⠀⠀⠀⠀⠀⠀⠠⠤⠖⠒⣽⣟⡾⢖⡁⠀⠀⠀⢀⡠⠂⠀⠀⠀⠈⣴⡁⠀⠀⠖⣮⡗⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡃⢸⢄⡃⠀⠃⢀⡀⠴⠓⠒⠂⠁⠐⠄⠀⡀⠉⢥⣁⠲⠉⡑⡟⠂⠀⠀⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠀⢙⠇⠀⡁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⡆⡀⠉⢣⡤⢉⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠠⡀⠀⣀⠠⠇⠀⠀⠘⠀⠀⠈⠳⢄⣀⣀⢀⠀⠀⠀⣀⣰⠡⠀⠀⠻⡀⠀⢫⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠉⠉⠉⡩⡒⠅⠈⠀⠀⠀⠈⡗⣻⠀⠀⠀⠀⠀⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠓⠦⣀⢀⡀⠤⠄⠒⠁⠀⣠⡫⠊⠀⠀⠀⠀⠀⠀⠀⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⢂⠀⢀⡀⠄⠈⠁⢠⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠎⠀⡀⠎⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠉
⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⢛⣿⡿⠛⠁⠀⢸⣿⠀⠀⠉⠻⣿⣿⡻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⣴⣿⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠻⣷⣄⠈⠛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⢙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣿⠟⠛⠻⠿⣷⣾⣿⣧⣤⣄⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣠⣤⣿⣿⣶⡿⠿⠛⠻⣿⣆
⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢠⣿⠏⠉⠛⠛⠛⠛⠻⠿⢿⣿⠿⠿⠛⠛⠛⠛⠋⠉⢻⣿⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⣤⣤⣤⣤⣄⡀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⢀⣿⡇⠀⠀⠀⢰⣿⠋⠉⠉⠛⠁⠀⣿⣟⠉⠉⢻⣿⡄⠀⣿⡟⠋⠙⠿⠷⠀⠀⢀⣀⣀⣀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⢸⣿⣷⣶⣦⠀⠘⢿⣿⣶⣦⣤⡀⠀⣿⡿⠀⠀⢸⣿⡇⢸⣿⡇⠀⣤⣤⣤⠀⢸⣿⣛⠛⠛⠁⢠⣶⣶⣿⡇
⠀⠀⠀⠸⣿⡏⠉⠁⠀⢀⡀⠀⠈⠉⣿⡧⠀⣿⣇⠀⠀⣸⣿⠇⠸⣿⣇⠀⠉⣽⣿⠀⠈⠛⠛⠿⣿⡆⠀⠉⠉⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠚⠿⣿⣿⡿⠟⠁⠀⢿⢿⣿⡿⠿⠋⠀⠀⠙⠿⣿⣿⠿⠃⠀⠸⠿⣷⣾⠿⠃⠀⠀⢸⣿⠃
⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀⣀⣀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⣀⣠⣴⣿⣷⣶⣿⠿⠿⠿⠿⠿⢿⣿⠟⠻⠻⠿⠿⠿⣿⣶⣿⣿⣤⣄⡀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠛⠉⠙⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⡿⠉⠙⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠘⢿⣧⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣾⡟⠀⢀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣈⠻⣷⣄⠀⠀⠀⢸⣿⠀⠀⠀⢀⣴⣿⢏⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣶⣤⣼⣿⣤⣤⣶⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⠿⠿⠿⠿⣿⣿⣶⣤⣄⡀
⣴⣿⡿⠿⢿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣤⣦⣤⣀
⢿⣿⣤⣀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣶⣶⣤⣤⣀⣰⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠛⠻⢿⣿
⠈⠙⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠺⠇⣼⣿
⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⣾⣿⠏⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⡿⠿⠛⠛⠛⠿⣿⣿⡏⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣶⣶⣾⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣷⣶⣿⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣯⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠂⢀⡴⠊⠁⠀⠀⠈⠐⢀⠀⠰⡀
⠀⠀⠀⠤⠐⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠
⠀⠀⠀⠈⠂⢄⠀⠢⠀⠀⠀⠀⠀⠀⡠⠎⠀⢀⡤⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡎
⠀⠀⠀⠀⠀⠘⠋⠀⡀⠀⠓⣤⠊⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠂⠀⠀⠐⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣁⠀⠆⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠼
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢁⡀⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠚⠒⠂⢰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⢀⣀⣀⣀⡀⠀⠀⠀⠁
⢰⠂⠐⠈⠁⠈⠀⠈⣀⢀⡀⣰⣤⣴⣾⠀⢠⠀⠄⠀⡄⠀⠄⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢢⡄⠀⠀⠀⡀
⠉⡆⠈⡀⢁⠀⣁⣀⣀⢀⣁⣈⡋⠉⠙⣦⡤⠤⠤⠤⢰⣤⡤⠤⠦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠊⠀⠀⠀⠀⠇
⠀⢉⠉⡉⠉⠥⠿⠛⠣⠀⠀⠀⠄⠀⠀⣴⠀⠂⠀⠂⠈⡉⠈⡀⢉⠀⣱⠄⠤⠤⠤⠤⠤⠤⠄⢷⠤⠤⠼⠀⠀⠀⠀⠨⣀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⢸⠀⠠⠀⠄⠠⠄⠐⠒⠒⠀⢸⣭⣭⣿⠀⢈⠀⢁⠀⠁⠀⠁⢀⣀⣐⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠘⣆⣠⢤⠤⠤⠦⠤⠦⠰⠲⠒⠀⠀⠀⠃⠀⠉⠉⣉⠉⠉⠩⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠈⠀⠀⡁⠀⢀⡁⠀⠀⢰⣾⠀⠀⠀⠁⠀⠀⡀
⠀⠤⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠧⠀⠀⠈⠁⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣨⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠙⠹⢋⠋⠙⠩⠋⠙⠉⠙⠉⠝⠁⠍⠩⠉⠀⢁⠌⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡠⠀⠈⡀⠁⠈⠀⠀⠠⠂⡠⠀⠌⢀⠈⡀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢱⡀⠀⠀⠀⠀⣠⠔⢙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢦⠀⠀⠈⠃⠀⠀⣠⠞⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠈⠉⠒⠂⢌⡣⡀⠀⡁⠀⣰⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⢀⣀⣙⣮⡱⠆⢰⠇⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠⢄⠀⠈⠇⣼⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠁⠀⠀⠀⠑⠒⠺⣇⣠⠔⠋⠀⣠
⠀⠀⠀⠀⠀⠀⢐⠲⢄⡀⠀⠀⠞⠁⠁⡰⠋⠀⠙⢆⠀⠀⣘⠀⠀⡰⠊⢡
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠉⠲⣄⢦⡀⠀⢇⠁⠀⠀⢸⠆⢰⡟⠀⡼⠁⢀⠆⠀⠀⠀⣀⡀⠀⠎⣳
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⢆⡉⠀⠀⠙⠒⠒⠁⠀⢸⠡⡔⠇⣠⠎⠀⠀⢸⠋⠁⢨⠛⣯⣉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⢸⡈⠢⡀⢀⡤⠒⠒⠲⣇⠀⣿⠚⠁⠀⠀⠀⠘⣄⠴⢁⠜⡠⢷
⠀⠀⠀⠀⢀⣤⣤⡄⠠⠤⠄⠀⠀⠜⢶⣄⠀⠀⢠⠛⠄⠈⠁⢿⠀⠀⠀⠀⠀⠀⠈⠲⠧⠴⠱⠋
⠀⠀⠀⠀⠀⠑⠲⠤⣄⣀⣀⣀⣀⣠⡤⠞⠓⢄⠸⠀⣏⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠻⣴⠃⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢎⢱⠊⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡠⢿⠙⡍⢏⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣶⠀⠀⠀⠀⠀⢀⣤⡔⢢
⠀⠀⠀⠀⠀⢰⡁⠀⢣⠘⣈⠿⢤⠄⠦⢄⠀⠀⠀⠀⠀⠈⢧⠀⠉⠀⠀⠀⠀⢀⣽⠦⠷⣮⣀⡀
⠀⠀⠀⠀⠀⠀⠙⣲⠜⢛⡩⢀⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣇⠰⠀⠀⠀⠀⢈⠀⠸⢀⠃⠸⢫⠳⠖⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠎⠀⠀⡎⡀⠄⠀⢓⠀⢴⠁⠀⠀⠀⠀⠀⠀⢩⡄⡄⠀⠀⠀⡜⠣⣤⣬⣀⣴⣃⡀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢢⣀⠀⠱⣄⠀⣠⠆⠀⢘⠀⡴⠤⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⢧⡀⠀⠀⡞⢁⠀⠈⠆⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⣠⡄⠤⠊⠀⠈⢆⠀⠈⠑⢢⡀⢸⡇⠀⠀⠀⢠⡇⠀⠀⠳⣀⣤⠴⠃⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠚⠉⣆⠀⠀⠀⠀⠀⠑⠦⢀⣀⠙⢼⡇⠀⢀⠔⢻⠣⣀⡀⣤⡀⠀⠀⢀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠀⠀⠀⠈⠑⠻⡇⣰⠃⠀⢸⠀⠀⠀⡆⠙⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⡰⢻⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⡌⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠟⠲⢄⠀⠀⠀⠀⡇⠀⡜⠀⡦⠀⠀⠀⠀⠀⠀⣿⠀⢀⠞⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠙⢦⡀⠀⡇⡜⠀⢀⠃⠀⠀⠀⠀⠀⠀⣯⠔⠁⢠⡀⠀⠀⡇⠀⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠱⡄⢸⠆⠀⡼⠀⠀⣖⢤⡀⠀⠀⠁⠀⠀⠈⠱⡀⢀⠃⠀⣠⠞⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⢡⡜⠀⡜⠀⠀⠀⠘⢆⡈⢳⣐⡇⠀⠀⢃⠀⢣⢸⠀⡰⠁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣿⠎⠀⠀⠀⠀⠀⠀⠉⠒⢼⡇⠀⠀⠘⣄⠀⣟⠰⠁⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢢⣿⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢻⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡉⠉⠛⠛⣻⠷⠀⠀⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⡇⣀⡴⠛⠁⠀⠀⠀⣀⠶⡄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢼⠾⠋⠀⠀⠀⠀⠀⡜⢁⢰⠇⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⡀⠀⠀⣠⠄⠓⠛⠁⠀⠀⢀⣄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⣯⠙⠲⡌⢳⣄⡼⠛⠛⠋⠀⣀⠀⡴⠋⢸⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢦⣑⡿⠀⠻⣅⠀⠀⠀⠀⣿⠸⣥⡥⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⣽⣆⠀⠀⣠⡿⠤⠤⠄⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣠⠴⠒⣓⣦⡀⣿⡴⠛⠉⠀⠀⠀⣀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠙⠛⠲⠶⠞⠁⣿⠀⠀⠀⠀⣠⠞⣿⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠛⠀⠀⣠⠞⠁⠀⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⠀⢠⣾⣥⣤⣤⣤⣬⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⣴⣿⣿⣦⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠘⠿⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣤⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣤⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣛⠻⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣠⣾⣿⡿⢛⡛⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⡛⣣⣿⣿⣿⣇⢸⣿⡟⢩⣍⢻⣿⡇⢰⣿⣿⣿⣧⣙⣋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⠀⠹⣿⣿⣿⣿⡿⠿⣿⢸⣿⣿⣎⢡⣾⣿⡇⣼⡿⢿⣿⣿⣿⣿⠏⠀⣀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣏⠸⠷⣸⠘⣿⣿⡏⢸⣿⣿⠇⣏⠺⠗⣹⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣿⣷⡸⣿⣇⢻⣿⡇⢸⣿⡿⣸⣿⡇⣾⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣧⠹⡿⠆⠻⠃⠘⠟⠱⢿⡟⣸⣿⢟⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣦⡙⣡⡰⣿⣿⣯⣸⣿⣿⠆⣀⢋⣴⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⡇⢿⣿⣾⣿⣿⣿⣿⣿⣾⠟⣸⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣮⣍⣙⣛⣛⣋⣩⣵⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⣴⢶⡶⠶⢶⣟⣿⣿⣿⣿⣗⣲⣐⠐⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢿⡽⠯⠾⠧⢷⡂⢀⣀⣩⣯⣣⢿⣿⠟⠉⠛⢿⡿⢛⢤⣌⠑⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠃⠉⠘⠿⢋⣶⠦⡀⠙⣿⠷⣻⡄⠀⠐⡩⡢⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠁⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⡘⣿⢵⣚⠁⠠⣉⢞⡡⡷⠀⠑⠌⠉⠀⢶⣀
⠀⠀⠀⠀⠀⢀⢴⠋⡤⢾⣲⠀⠀⠀⠀⢒⣈⠡⠄⠀⠀⠀⠀⠀⣜⢕⠙⡡⡢⣲⠉⠙⢷⢷⣟⡟⣫⡽⡆⠀⠠⠤⡶⡚⠛⢢⡀
⠀⠀⠀⠀⠠⡡⢪⢔⡫⢐⠬⡆⠀⠀⠩⠄⠒⠀⠈⠁⠀⠀⠀⠀⠈⠲⢜⣨⣪⡇⠀⠀⠘⠋⢹⣯⣻⡯⢕⣢⡼⠛⠜⡀⠫⡱⠑⢄
⠀⠀⠀⡐⠘⡁⢜⢕⡪⠔⡓⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣏⠇⠀⠀⠀⠀⠀⠈⠳⡥⢞⠫⡐⠄⠀⡁⠄⢀⠠⠀⠈⢢
⠀⠀⡜⠠⡐⠨⡑⢌⠛⢶⡌⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢤⠤⢤⠤⣏⠐⡉⠤⢒⠡⠐⢈⡠⠔⠀⢰⢆⢡
⠀⡰⠀⠐⠨⠑⡢⠑⡪⢒⣈⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠒⡎⠐⠺⠀⠒⢉⡠⠔⢊⠡⠄⠀⠀⠐⠾⣤⢆
⢀⠁⠀⠉⠒⠂⠤⣁⠊⠲⢷⠀⠀⠀⠀⠐⣩⠔⢀⠠⠐⠀⠀⠀⠐⡂⠅⠀⠀⡀⡎⡉⠍⣒⠌⢒⡡⠔⢊⠥⠒⢈⡠⠄⡂⠁⠠⠀⠀⡇
⠈⠀⠀⠀⠈⠀⠀⠀⠀⠁⠸⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠒⠀⠁⠀⠚⡂⠄⢂⠡⠐⣉⠡⠐⢈⡠⠔⡊⠥⠒⠁⡀⠄⠨⢀⡅⠁⡖
⡆⠀⠀⣀⡀⠩⠄⠐⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⡠⠔⢀⠤⠐⢈⠠⠐⡊⠅⠒⢉⡠⠄⣂⠥⠐⢀⠨⠁⣛⠼⠦
⡇⠀⠠⠄⠒⣀⡈⠅⠂⠀⠀⠀⢦⣆⠀⠀⠀⠀⠀⠠⢠⠤⡂⠒⠄⠣⠀⠄⢂⡨⠄⣂⠩⠔⢂⡁⠤⠒⣈⠥⢒⡉⠄⠂⠀⢐⡀⠅⡀⠀⡀
⡇⠀⠀⢒⡉⠤⠐⣊⠤⡐⠀⡀⠈⢯⠱⡀⠀⠀⢰⠣⢐⠨⣒⠅⡑⡔⠐⢊⠅⠐⢁⠤⠐⢊⡡⠄⢒⡩⠔⢊⡁⠤⠒⢁⢀⠥⠂⠜
⠀⠀⠈⠀⠒⡀⠍⢂⠡⢒⡩⢐⡠⠀⠀⢀⡀⠀⠈⢆⡡⠚⣳⠜⢂⠔⣍⣦⠨⠄⠀⠀⠈⣠⠖⠈⠡⠐⢈⡁⠄⢂⠨⠄⠀⡀⠀⠀⠀⠬⢄
⠨⠀⠀⠀⠠⠔⢈⠤⢂⡡⠒⡡⠐⡠⠀⠀⠈⠒⠄⠤⢀⡀⠢⠻⠕⣉⢔⠹⢊⠕⢋⠔⣊⠔⡩⠀⠀⣈⠥⢒⡉⠤⠂⠀⠀⡂⢸⠀⠰⠛⠉
⠀⢂⠀⠀⠒⣈⠄⠂⣁⠔⢉⠤⢊⠤⢂⠴⢂⡴⠀⠀⠀⠈⠣⡐⣉⡂⣁⠔⠓⠒⠡⠜⠠⡙⠪⢐⠅⡀⠀⠡⠒⠊⠀⠀⠄⢂⠄⠑⣀⠤⢠
⠀⠈⡄⠀⠈⣀⠔⠊⡠⠒⡡⠔⢁⠔⢁⠔⠋⡠⠀⠀⡀⠀⠀⠀⠉⠑⠀⠀⠀⣀⠤⠀⠀⠈⠀⠢⡈⠐⠀⠀⠉⠀⠀⡀⠭⣐⠡⢀⠀⢠⠁
⠀⠀⠰⡀⠀⠠⠒⢁⠤⠊⡠⠞⢁⠔⢁⠴⠊⣀⠔⠁⠀⣈⠔⡀⢀⠜⠀⠔⡪⢒⠉⠀⠀⠀⠀⠀⠐⠆⢄⠀⣀⠀⠀⣒⠩⢐⠪⡐⢠⠃
⠀⠀⠀⠱⡀⠀⠀⣁⠔⠈⡠⠊⡡⠔⢁⠠⠊⡠⠂⠀⠀⠔⡩⠀⢜⠀⠀⠀⡪⠐⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢇⠠⢐⡈⢐⠜⡠⠃
⠀⠀⠀⠀⠘⢆⠀⠀⠐⢊⠄⠊⡠⠒⣁⠔⡊⠔⢁⠔⠀⠀⢒⡡⠂⡱⡀⠀⠀⠭⠐⠀⠀⠀⢐⠪⠀⠀⠀⠐⠁⢐⡪⠕⡪⢐⠔⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢉⠔⢊⠠⢊⠤⢊⠡⢊⠀⠀⠁⠔⡨⢒⠈⠒⢄⠀⠑⠀⠀⢆⡢⠁⠀⢀⣀⠎⠀⠤⠂⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠁⠊⠡⠒⡡⠒⣁⢔⡡⢂⢀⠀⠑⠠⡀⠨⠀⠄⠀⠀⠀⠀⠀⡜⠁⣀⠠⠄⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠈⠐⠊⠒⠡⠊⢔⠕⡠⢀⠀⠀⠈⠀⠀⠀⠀⢀⡰⠊⠀⠐⢂⠥⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⡤⠊⠁⣀⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣶⣿⣿⣿⣷⣾⡿⠿⠗⢠⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣗⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠛⣫⡟⠋⠁⠀⠀⠀⠀⣻⠿⠛⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢹⡟⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠑⠄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⢫⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠈⢢
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡯⢿⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢂
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⣿⣿⠀⠀⣙⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢸⡿⣼⠃⣿⣇⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣟⡀⠙⠦
⠀⠀⠀⠀⢸⠁⠏⠀⢋⠋⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⢠⣦⣀⠀⠀⠀⡆
⠀⠀⠀⠀⢸⠀⠀⠀⢺⢀⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣦⠀⠀⠇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⢆⠛⠻⠀⠲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⣀⠘⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠰
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⣴⣿⣧⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢁⠃
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢻⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠄⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠸⠶⠆⠐⠠⠐⣀⣠⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢨⠂⠀⠀⠂⡆⢠⢻⣗⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣰⢡⠀⠀⢀⡎⠀⠀⠀⡘⢀⡆⠀⠹⣔⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠐⠤⠦⣄⠀⠀⠀⢠⡁⠁⢂⢐⢚⠠⠠⠤⠴⢀⡎⠀⠀⠀⠹⡧⠜
⠀⠀⢀⠀⢤⢼⡤⠣⢴⡤⠺⠇⠀⠀⠀⡜⠐⠀⠈⣰⠁⠀⠀⢠⠂⡼⢄⠠⠄⠠⢠⢹⡌⠡⢀
⠀⠀⠀⠁⠤⣭⠇⠀⠈⠀⠠⣐⣲⣤⡴⣅⣀⡀⣠⡁⠀⠀⢀⠆⡼⡇⠀⠀⠀⠂⢠⣴⣶⡴⣠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣤⣇⡈⠉⠉⠐⠘⠣⠭⠵⡲⡎⡰⡇⠀⠀⠀⠀⠀⠈⢸⡠⣀⣨⠯⠤⠄
⠀⠀⠀⠈⠁⠈⠉⠉⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⢀⣀⣄⣤⠶⠚⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⠀⣶⣶⣶⡄⢰⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⢸⣿⣿⣿⣧⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠁⠸⠿⠿⠿⠿⠿⠇⠀⠿⠿⠿⠿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⢸⣿⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠻⣿⣿
⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢸⣿⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣛⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠘⢃⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⣄⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⣾⣿⠿⠛⠛⠛⢿⣿⣿⣿⣿⣷⣦⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⢠⣾⣿⣿⠁⣠⣶⣿⣦⠀⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⣿⣿⣿⣿⣄⠈⠛⠛⠿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣷⡀⢹⣿⣿⣷⣄⡈⠛⠿⠿⠿⠿⠟⠁⣴⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⡈⠛⠿⣿⣿⣿⠟⠀⣼⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛