Sunflower seed Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠠⣄
⠀⠀⠀⠀⠀⠀⣸⡯⠿⠿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠘⢷⣦⡀
⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣗⡪⣝⡻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⢧⠻⡝⣿⣿⣿⣿⠿⣾⣿⣷⣬⡛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⣿⣦
⠀⠀⠀⠀⠈⢣⡙⢾⣿⣿⣿⣷⣮⣙⣿⡿⣿⣷⣽⣿⣯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⢹⣧
⠀⠀⠀⠀⠀⠀⠈⠲⣍⠻⢽⡛⠿⣮⣝⡿⣶⣍⡛⢿⣿⣿⣮⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣷⠀⠀⠀⠀⠀⠀⠸⡇⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢍⣓⠦⣍⡛⢿⣿⣿⣶⣽⣿⣿⣧⡳⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣇⠀⠀⠀⠀⠀⠀⣷⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠭⣝⣺⢿⣿⣿⣿⣿⣿⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠻⠀⠀⠀⠀⠀⠀⢻⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠭⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⢀⡀⠀⢸⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠻⣶⡾⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣩⠔⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠞⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡸⢡⠏⠀⠀⠀⠀⠀⠀⠀⢡⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣯⠍⠉⠩⢭⣭⣽⣛⡻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⠀⠀⠀⠀⠀⣠⡴⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠮⠙⠆
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⡄⣴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡄
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⡼⠁⠀⠀⠀⠈⠳⠌⢀⠐⠲⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣠⡿
⠀⠀⠀⠀⠀⠀⠘⡇⢻⠀⠀⠀⠀⠀⢀⡴⣣⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣬⣉⣛⡛⠻⠿⠿⠿⠛⣛⣋⣥⡾⠛
⠀⠀⠀⠀⠀⠀⠀⢧⢸⡀⠀⠀⣠⢖⡭⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠓⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠂⢰⡀⠀⣠⣾⣿⣿⣶⠀⠀⠀⠀⢠⣾⡿⣿⠁⠀⠀⡠⠀⡀⠀⠀⠀⢀⠀⠀⢀⣸⣦⣶⣿⣿⣿⡆
⠀⠀⠀⡀⠀⠀⠘⠀⢰⣿⣿⠟⠡⠁⠀⠀⠀⣰⣿⡿⣱⠇⠀⠀⠀⣅⣶⣷⠀⠀⠀⠀⠀⠈⠁⠉⣉⣽⠿⠟⠋⠁
⠀⠀⠀⠆⠀⠁⠀⠀⠘⠋⠀⠁⠀⠀⠀⠀⠰⣿⡟⡡⠋⠀⠀⠀⠀⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣶⣆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣦⠀⠀⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢘⢯⣽⣿⣷⣦⠀⠀⠀⠀⠀⠀⠠⣡⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⠻⢿⡿⠏⠀⠀⠀⠙⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠈⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣠⣴⡆⠀⠀⠈⠉⠀⠀⢀⣀⣠⣴⣶⣦⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠟⠋⠁⠀⠀⠀⢀⣞⡇⠀⠀⠀⠀⢠⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡾⣼⠁⠀⠀⠀⡴⠋⣸⡿⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠱⡌⠛⢶⣄⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠀⠘⣡⠞⠋⠀⠁
⠀⠀⠀⣀⣄⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡙⣾⣦⢻⡆⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠙⠁
⠀⠀⣾⣿⣿⣿⣿⣿⠏⠀⠀⠚⣿⣿⡆⠀⠀⠀⠀⠘⠮⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠆⣿⡆⠀⠀⠀⠀⡀⢄⣰⣦⣄
⠀⠀⠈⠛⠟⠉⠀⠀⠀⠀⠀⢃⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣿⣷⠀⠀⠀⠐⠈⠉⠅⠂⠟
⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡤⣴⣷⣆⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢜⣡⠴⠞⢋⠝⠀⠀⣴⣦⠀⠙⠿⠟
⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠀⠈⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣤
⠀⠀⠀⠀⠀⠘⢿⡿⠇⠀⣤⣶⣾⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⣴⣾⣿⡛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙⣛⣻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠈⠛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢁⠆⠀⠀⠰⡈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⡎⠀⠀⠀⠀⢳⡀⠘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⢀⡞⠀⠀⠀⠀⠀⠀⢷⡀⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟
⠀⠀⠀⠀⠈⠻⢿⣿⣶⣄⡀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⢀⣠⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣦⣤⣤⣤⣤⣤⣤⣴⡾⠏
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⠈⣉⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⠁⠈⣏⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠏⣰⠃⠀⠀⠘⣆⠹⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⠂⢠⡏⠀⠀⠀⠀⢹⡄⠐⡕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⠃⢀⡞⠀⠀⠀⠀⠀⠀⢳⡀⠘⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠘⣇⠀⠘⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠃⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠩⡄⠀⠐⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠆⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠠⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡈⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠈⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⢰⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠀⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡄⠀⠀⠀⠀⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⠀⠀⠀⠀⢠⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠱⡀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⢀⠆⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣐⢄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡠⣃⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠓⠦⣤⣈⡃⠀⠀⠀⠀⠀⠀⢘⣁⡤⠴⠚⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢀⣀⣀⡀⠤⠃

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

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢈⠙⢶⣬⣉⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣲⠽⣋⡴⣹⡆
⠀⠀⠀⠀⠀⠈⢎⢦⡙⢿⣿⣦⣄⡙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣵⠟⣡⣾⠟⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠳⣝⢷⣍⡻⢿⣿⣶⣝⣷⠀⠀⠀⠀⠀⠀⡰⣱⠟⣡⣾⡿⠃⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠽⣻⣷⣭⣙⠿⠃⠀⠀⠀⠀⠀⠀⢣⢏⣾⡿⠋⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠙⠫⠶⠟⠛⠁⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣾⢰⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⣩⢶⠈⡆
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣦⡀⠀⠀⣿⡆⢻⣦⠑⢕⢄⠀⠀⠀⠀⠀⢀⣔⡕⠉⠀⢸⡆⡇
⠀⠀⠀⠀⣠⡾⢛⣥⣾⣿⣿⡿⢛⣡⡇⠀⠀⢸⣷⠈⢿⣧⡈⢯⢣⠀⠀⠀⢠⢮⠎⠀⠀⠀⣸⢹
⠀⠀⠀⣞⣡⣾⠿⠟⣛⣩⣥⣶⡿⠟⠁⠀⠀⠀⢿⣧⠘⣿⣷⠈⡇⡇⠀⠀⣞⡏⠀⠀⠀⣠⢃⠏
⠀⠀⠀⠓⠤⠶⠾⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠺⣷⣌⢿⣧⣧⠇⠀⠀⢣⣓⠢⣤⠴⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠄⠀⠤⠀⢀⡀⠀⡀⢠⠴⡟⣿⣿⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⢀⣤⣶⣶⣶⡶⣻⣿⢆⣪⡄⠀⡜⡽⣯⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣠⣶⠿⡛⣉⣭⣞⣽⣿⣿⣿⠉⠃⠌⠐⢱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠳⠟⠛⠳⢾⣿⣿⢏⢾⡟⢸⣿⡿⡟⠀⢀⡔⠾⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢊⡠⠔⣢⡳⢾⡿⢿⡏⠁⠊⠀⣿⣿⠸⡆⣔⠡⠔⢚⡋⠙⠛⠓⠶⣿⣄⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⠄⢀⢔⣡⡶⠚⣁⢈⢄⡚⣽⠅⠀⡎⢠⣯⡏⡄⡇⢸⣺⠩⠔⠀⠀⠉⠉⢙⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣆⡀⠀⣰⣾⣿⣿⡻⠿⣒⠋⠩⢈⠾⠀⠈⣇⣾⢹⣧⣟⡇⣼⣦⣔⣂⣀⡤⢔⣶⠿⣛⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠍⠀⠈⠞⠻⠿⠿⠿⡿⢛⡉⣁⣥⡤⣶⣧⡹⣿⣿⣼⣿⡟⣰⣿⢥⡉⠉⣄⡬⠥⠔⠚⠥⠬⣷⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀⠀⠑⢄⠀⠀⣽⣫⣾⣿⠿⡋⠭⣔⣚⣻⣥⠄⡾⠻⠫⠕⠉⠛⠢⣄⠉⠳⣤⣤⣭⣽⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢉⠒⠶⢤⣍⣾⢏⡩⠍⠍⣛⣛⣛⠛⣋⣩⣤⡚⠉⠓⠦⠢⢝⣶⣶⣦⣝⣦⣙⠁⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⣒⣒⣈⡁⠀⠀⠀⢸⣿⡛⠭⠁⠑⠛⢾⣄⡀⠀⠀⠐⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠤⠒⠀⠭⠤⣽⣿⠆⠀⠀⠸⣧⡈⠈⠀⠀⠈⠒⠍⠻⣷⡔⢄
⠀⠀⠀⠀⠀⠒⠸⠿⣿⣯⣕⣀⣠⡤⣒⠠⠜⠛⡡⠄⠀⠀⠀⠉⠂⠑⠄⣢⣒⣤⣠⣬⣿⣿⣦⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠉⠉⠉⠉⠁⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠋⠉⠉⠉⠂⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠚⠉⠉⠀⠀⢸⠹⣄⠢⣄⠀⠀⠀⠀⠀⠀⠉⠻⣍⠉⠉⣉⠒⠒⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⡉⢁⣀⣤⠤⠶⠒⠋⠁⢀⡨⢧⣄⡉⠂⣁⣀⣀⢀⡀⠀⠀⠀⡈⠳⣄⠀⠀⠉⠉⠓⠒⠮⢽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠾⠟⠋⠉⠁⠀⠀⠀⢀⡀⠊⣁⣤⠶⠟⡛⢍⣁⣤⠤⠶⠛⠒⠲⣄⣈⣦⠼⣦⣤⣄⣒⠢⠤⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡉⠀⠀⡀⢀⡤⢖⣫⠽⠛⠓⠲⣟⠉⠀⠀⠐⠊⠉⠀⠀⢀⣀⣠⠤⣾⢟⡡⠖⠋⠁⠀⠀⠈⢹⡀⣒⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢭⣭⢟⡥⠒⠉⠀⠀⠀⠀⠀⢸⡆⠀⠀⡀⠤⠴⢒⠛⠭⣡⡶⢊⠕⠋⠀⠀⠀⠀⣀⢔⣠⢾⡷⠾⣏⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠫⠐⠁⠀⠀⠀⣀⣤⠶⠴⠾⣟⠳⣄⣀⣀⡀⠤⠤⢾⡷⠋⠀⠁⠀⠀⠀⡀⢔⡪⠖⢋⡴⠋⠈⠁⠂⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣐⣨⣴⠃⠀⠀⠀⠪⡑⢌⠳⡀⠀⠀⢀⡮⢀⣀⣀⣀⣀⡀⣈⣊⣥⠴⢾⣛⣒⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢾⣁⡀⠀⠀⠀⠀⠈⠀⣾⠘⣆⠀⡀⠀⠀⠈⢢⠡⡘⢄⠀⠀⠙⠫⡀⠀⠀⠀⠉⠉⠉⠛⣓⠶⠤⣤⣉⣉⣉⣀⣀⣀⣀⣰⠾⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠙⢧⣈⠓⢮⡢⢀⠀⠀⠑⠌⠈⢢⠀⠀⠀⠈⠲⣔⠄⡠⢀⠀⠀⠀⠈⠁⠒⠿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣌⡓⠧⣄⠀⠀⠀⠀⠳⡀⠀⠀⠀⠈⠳⣌⠢⢕⠢⢄⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣥⣀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠈⠳⢤⡁⠢⣍⡂⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⢀⠀⣀⠀⡀⢀⡀⠀⢀⠀⠀⢀⠀⡀⡀⢀⠀⡀⢀⠀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠲⠀⠇⠠⠀⠈⠑⠄⠠⠒⠀⠠⠀⠀⠃⠀⠇⠸⠎⠦⠀⠸⠀⠀⠸⠒⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠦⠀⢶⠀⠰⠄⢰⠄⡰⠄⢰⡆⠰⢄⢠⡔⠂⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣉⡳⠄⣼⣉⣠⠄⣸⣉⣃⡆⢸⣇⣀⠜⢠⣍⣉⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠁⠈⠀⠁⠁⠀⠀⠀⠈⠁⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⡶⠟⠛⠀⠀⠀⠀⠀⠀⢀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠲⣠⠖⠉⣱⢏⣠⡶⣢⠴⠖⢋⣩⠙⢿⠧⡜⠉⢠⣇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢸⡇⣸⣼⣁⠀⠀⡟⢉⡭⢌⡥⣤⣤⠋⠀⢀⡸⣆⣃⢀⣚⡡⠃⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⡠⣩⠀⣘⠇⣛⡸⠿⠤⣼⢳⠏⢀⡾⠛⣩⢟⣀⣀⡸⠃⣟⣡⡿⠋⢰⠟⡽⣔⢷⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⡟⡁⣼⠉⠁⡁⠉⠙⠲⣤⢜⡴⠃⣠⠼⠛⣉⣤⢶⡴⡻⠻⠟⣠⠀⡠⠞⠁⠛⢦⡀⠀⣬⡳
⠀⠀⠀⠀⠀⠀⠀⡽⠛⣩⣥⠀⣿⡀⡄⠱⡄⢠⣄⢈⣾⡇⢤⣀⣀⣉⣀⣛⣹⡕⠁⠀⣠⠃⣣⠴⢚⣽⡀⠀⠹⡗⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠙⣢⠔⣫⡴⢛⣫⡭⠾⢟⡶⠽⣾⣿⡂⢤⣵⣈⡙⣿⣟⠻⢄⢲⣴⡧⣾⠇⢰⡿⢋⡄⣴⣆⡗⡈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⡞⣡⣚⣉⠀⣉⠀⣐⠒⠛⠲⠤⣾⡇⠙⠲⣤⣍⣉⡻⢿⣗⡠⣿⡿⠛⡛⠀⡼⢁⡾⠀⡏⡏⢷⣷⠸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣚⣷⡤⠻⣷⢴⣦⣄⡀⢹⣶⡿⠋⣀⣨⠍⡯⠿⣍⣕⣶⣾⣀⡾⣇⠘⣧⢸⠃⣇⡎⢻⡀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡤⢒⣌⠓⢭⠭⣡⣿⠟⢠⠾⠟⣩⢞⠁⠀⠀⠉⠛⣿⡧⠴⠮⠓⠈⠰⢾⡙⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠠⣿⢏⡞⠁⢰⢩⡟⢀⣠⠴⣋⠁⠈⠳⣘⠷⣬⠓⠘⢳⣶⣦⣤⣤⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡵⢿⠀⡿⠃⡾⢑⣸⢱⡀⠿⠁⣠⣆⠘⠛⣖⢋⣤⣤⠈⠉⠙⠢⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠞⡟⠉⠠⣤⣽⣶⣿⣥⠻⢧⠴⠻⠬⣿⣛⡯⠵⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣉⣭⠭⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣱⠏⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⡟⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢘⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡝⢦⠀⠀⠀⢀⠂⢠⣾⠇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣠⣺⣷⡰⠆⠉⠳⢵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⡌⡳⡄⠀⡀⠀⣿⣿⠀⠀⠘⠀⠀⡧⠀⠀⣼⣦⣾⣿⡿⠋⠀⠀⢠⣾⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠱⣖⠘⢤⡃⢸⣿⡟⠀⠀⠀⠀⠀⠆⠀⢀⣸⣿⡿⠋⠀⠀⠀⣴⣿⡿⡻⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠌⣷⠀⠀⠹⣧⠈⣇⠈⣿⡇⠀⢠⠆⠀⠀⠀⠀⢞⣿⡟⠁⠀⠀⢀⣾⡿⢻⠟⠁
⠀⠀⠀⠀⠀⠀⠈⡄⡀⣼⣧⠀⠀⠹⣿⡌⣇⣿⠁⣀⣼⠂⠀⠀⠀⠀⣾⠏⠀⠀⣤⠄⡽⣫⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣿⡇⠀⠀⠹⣧⠸⡿⠤⠟⠁⠀⠀⠀⠀⣼⠃⠀⠠⠞⠁⡠⠚⠁⠀⢀⡠⠤⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡄⠀⠀⢻⠀⠃⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠐⠋⠀⡠⠔⣊⣥⠴⠖⠃⠀⠀⠀⠀⠀⢀
⠀⠀⢠⢻⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠻⣿⣷⡄⠀⠀⠀⠈⠀⡀⠀⠀⠀⠂⠀⠀⠀⠠⣾⣯⠀⠀⠀⢀⣄⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠁
⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠲⢤⡭⣭⣅⣤⡢⡤⡀⠀⠈⡟⣿⡇⠀⣾⢟⢉⣤⣤⣶⣤⣤⣤⢤⣶⠶⠶⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠻⡛⢿⡔⣄⠀⠙⠻⣽⣿⣾⡄⠁⠀⢸⠇⣿⠀⠀⠈⠉⠙⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⢿⣷⢄⡀⠀⢮⡿⠁⠀⠀⣼⠐⢿⣤⣤⠴⣶⣶⠶⢖⡒⠀⢐⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠏⠰⢝⡆⠉⠄⠀⠀⣴⠇⠀⣾⠦⠈⠹⠃⠀⠀⢀⣡⠀⢀⡤⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⡇⠀⠀⠀⠀⡞⠀⠠⠀⠀⠀⣀⠀⢀⣤⣴⢾⠂⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢠⣾⠃⠀⣤⣤⢶⠄⠗⠃⣈⠥⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⢀⠏⠀⣸⢉⣀⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣃⠀⠘⠞⠰⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⡠⠚⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢨⣑⠞⡀⠀⠀⠲⠀⠀⠀⣤⠀⣩⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⡈⠀⠈⠢⣀⠀⠀⠀⠃⠀⢠⠟⠉⠀⠀⠀⣤⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⣀⠘⣄⣇⠀⠀⠀⢩⢢⡀⢀⣆⣴⣿⢀⡀⣀⡠⠊⠀⠀⠀⢨⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠢⣀⠀⣜⣿⣴⣿⣟⣿⣿⣧⣶⡒⡤⠤⠄⠠⠒⢁⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⣀⠀⠀⠀⢈⣷⣯⣭⣿⡿⠛⠛⡛⠿⣿⣿⣧⣴⠀⠂⠉⠁⠀⢑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡤⠚⠉⠁⠉⠲⢿⣟⣿⣿⡏⣁⣴⣿⣶⣴⢙⣿⣿⣆⠑⢂⣤⣤⠚⡹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠆⠠⠔⠒⠒⢺⣿⣿⣿⣏⠽⣿⣿⣿⠏⢢⣿⡾⣇⡘⠁⠁⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣓⠦⠀⢀⡼⣿⣿⣿⣻⣿⣵⣴⣬⣴⣿⣿⣿⡿⠋⠉⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠴⠥⣬⠋⠀⢀⠄⠒⠹⣻⣿⣿⣿⣿⣿⣽⣿⣿⣿⡷⠶⠤⠤⡀⢀⠤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠤⠤⣤⣴⠁⠀⠀⢠⠟⠻⣏⡿⠉⢻⣙⠯⡟⠋⠉⠉⠉⠒⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣇⢀⡀⢴⠇⠀⠀⢸⠀⠑⣄⠈⠂⠈⠦⡀⢀⣀⢀⡔⠉
⠀⠀⠀⠀⠀⠀⠀⡀⣀⡘⡮⠆⠀⠀⠀⠀⠀⠼⢸⠋⠁⠀⠹⡄⠀⢀⠆⠀⠀⠙⠀⡈⠀⠀⠈⠉⡉⠈⠁
⠀⠀⠀⠀⠀⢀⡤⠛⠉⠁⠃⡎⠀⠀⢀⠀⠀⡇⡇⠀⠘⠈⠀⢰⠄⠉⠀⠀⠀⠁⠐⠁⠀⠆⡘⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⢀⢴⠎⠀⠐⠀⠀⡨⠁⠀⠀⠈⢷⣀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠈⡀⠖⠂⠀⠀⠀⠀⠁⠀⠠⢾⣿⣷⡾⠇
⠀⠀⠀⡼⠂⠀⢀⡀⠤⠒⠁⠀⠀⠀⠀⠀⢻⠀⠁⠀⢀⡤⠴⡤⠤⠰⠾⣈⡛⠳⠂⠡⠀⠀⠀⣠⣶⢤⡀⠀⠀⣠⣶⠄⠒⢶⡄
⠀⠀⠈⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡇⠀⡎⠀⠀⠀⢃⠀⠀⠀⡍⠓⢔⠂⠢⠕⠀⠻⢿⣿⣿⣄⠀⠈⠉⠛⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣹⢄⣀⡀⠀⠁⠀⠀⠐⠀⠀⠘⠣⠀⢡⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠃⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠈⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠐⠂⠈⠉⠐⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⣿⠃⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣀⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡋⠉⠙⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢿⣷⣄⠀⠀⠀⣼⡛⠉⠛⠛⠛⠳⠶⠄⠙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠈⢿⡙⣧⡀⠀⢻⡟⠛⠳⠶⠶⠶⣶⣤⣤⣤⣤⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠘⣷⡈⢷⡀⠈⠻⢶⣤⣄⣀⣤⣤⣴⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠘⣧⠈⣷⡀⠀⠀⠀⣩⣍⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡇⢸⡇⠀⢹⡆⠸⣧⠀⠀⢾⡛⢿⣝⡛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣿⠀⣿⠀⠀⣿⠀⣿⠀⠀⠘⣧⠀⠈⠻⣦⡀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣦⣻⣄⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⢀⣠⡶⢻⣷⡄⠀⠈⠻⣦⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡏⠉⢿⡙⢳⣄⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠀⣾⣿⠇⠀⣀⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠘⣷⠀⠘⣷⠀⠹⣧⠀⠀⠀⣠⡾⣻⠟⠁⠀⠀⣼⠃⣿⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠹⣇⠀⠸⣇⠀⢿⡄⠀⣾⢫⡾⠋⠀⠀⠀⣼⠏⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢻⣆⠀⢿⠀⢸⡇⢸⣷⡟⣡⡶⠀⠀⣼⠏⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⢻⣆⠀⠀⣸⡇⠈⢿⣷⡏⠀⢀⣼⠏⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡻⣆⠀⣿⠀⠀⠀⠙⠷⣶⣾⣧⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡷⠟





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

⠀⠀⠀⠀⠀⠀⠀⠜⠁⠈⠻⠟⠁⠀⢀⣄⡀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠙⣋⠀⠀⠀⠀⠀⠀⠘⠿
⣀⠀⠀⠀⠀⠁⢀⣀⣀⡀⠀⠀⠀⠀⠙⠻⣿⣷⣦⠀⠀⠀⠀⠀⠀⠐⠲⣀⣴⣿⣿⡷
⠿⡧⠀⠀⠀⠐⣿⣿⣿⣿⣷⠄⠀⠀⢀⣤⠀⠉⠉⠀⠀⠀⠀⠀⠀⠠⠘⠛⣻⠿⠋⠀⠀⠀⠀⢀⡠⣚⣫
⢈⡀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⢰⣿⣿⠀⠀⠰⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠹⠀⠀⠀⠀⣠⣶⣶⡦⠀⠀⠀⣿⣿⣿⠀⠀⠀⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣄⡀
⠔⠀⠀⠀⠀⢀⣿⣿⡋⠀⠀⠀⠸⣿⡇⠋⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡄⠀⠀⠙⠿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠈⠛⠿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠁
⣠⣴⣾⡿⠀⠀⢀⣠⣄⣀⡀⠀⠀⠀⠀⢌⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⣿⢯⡟⠀⠀⠀⢸⣽⣿⣿⡿⠂⠀⠀⠀⣼⣿⠏⠀⠀⢀⣠⣤⡄⠀⠀⠀⣷⠀⠀⠀⢀⡞⣻⡟⠁⠀⠀⣀
⠕⠋⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⠀⠀⠉⠁⠀⠠⣶⣿⠿⠋⠀⠀⢀⢸⣿⠄⠀⠀⡜⣰⠏⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣴⣿⠃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣷⣾⡟⠀⠀⠀⠐⠋⠀⠀⠀⢀⣀
⠀⠀⠀⣠⣴⣦⡀⠀⠀⣿⣾⣿⡿⠀⠀⠀⠀⢪⣕⠲⢤⣄⠀⠀⠀⠈⠁⠀⠀⢰⣄⠀⠀⠀⣤⠾⡋⠙⠇
⠀⠀⡾⣿⣿⠟⠁⠀⠀⠙⠟⠛⠀⠀⠀⠀⠀⠀⠉⡻⣷⣼⡇⠀⠀⠀⠀⠀⠀⡞⣿⣆⠀⠠
⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⣀⡀
⣠⣤⣤⡀⠀⠀⠀⠀⣀⣤⣴⣦⡀⠀⢹⣿⣿⡆⠀⠀⠀⠀⢀⠼⣿⣦⠀⠀⣶⣄⠉⠉⠁⣀⣴⣿⡿
⣴⠿⠿⠃⠀⠀⠀⣾⣿⣿⡿⠛⠀⠀⠀⠻⣿⣷⠀⠀⠀⢰⡡⠞⠁⠊⠀⠸⣿⣿⣆⠀⠐⠟⠋⠁⠀⠠⢚
⠀⠀⠀⠀⠀⢀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣀⣤⣤⡀⠙⠉
⠀⠀⢀⣴⣿⣿⣿⡄⠀⢀⣀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠠⣾⣿⣿⡿⠁
⠀⢠⣿⣿⠟⠋⠙⠀⠀⣾⣿⣧⠀⠀⢰⡿⠿⠿⢛⡿⠃⠀⢀⣤⡄⠀⠀⠀⢀⡀⠀⠀⠈⠛⠋⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠔⠲⡄⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠠⡌⢿⣿⡆⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠛⠥⢍⠑⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠚⠛⡿⡇⠠⡀⠀⠀⠀⠀⠀⠀⠉⠳⣶⡶⠦⠤⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⢀⣀⣀⠤⠀⠀⢧⠘⠲⢍⡲⠄⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠐⠂⠤⠤⢌⣉⣛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣉⣤⣤⡤⠶⠖⠛⠉⠁⠀⠀⡠⠴⠊⢻⣶⣤⡤⠴⠖⠒⠒⣦⣀⣀⠀⠀⣄⠹⣦⠀⠀⢀⡀⠀⠈⠉⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠋⠉⠀⠀⢀⣀⣀⣀⣠⠔⣀⣠⡶⠞⠋⢍⣴⡴⠶⠖⠚⠋⠉⠉⠉⣷⣤⡼⢓⣻⠿⠷⠶⠬⣍⣓⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⢄⡤⠞⣫⠵⠚⠉⠉⠙⠻⡅⠀⠀⠈⠉⠀⠀⠀⣀⣀⣤⠴⢖⣿⢟⡥⠞⠉⠀⠀⠀⠀⠀⢸⡄⢤⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠾⣫⠔⠋⠀⠀⠀⠀⠀⠀⢀⣻⠀⠀⠀⠤⠖⠚⠋⠩⠥⣲⡾⢋⠔⠋⠀⠀⠀⠀⢀⠤⣂⡴⣿⣟⣛⠧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠅⠊⠀⠀⠀⠀⣀⣤⠾⠗⠺⢯⡙⠳⣤⣤⡤⠤⠤⠶⢿⡿⠋⠀⠁⠀⠀⠀⢀⢄⣪⠵⢚⣡⠶⠋⠀⠈⠁⠊⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣂⣥⣶⠃⠀⠀⠀⠐⢌⠳⡌⢦⡀⠀⠀⢠⡿⢂⡠⢀⣀⣀⣀⣈⣒⣩⡤⠶⢯⣍⣒⣂⠤⠀⠀⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠉⠀⣾⠘⢧⡠⡀⠀⠀⠀⠑⣌⠢⡑⡄⠀⠀⠙⠻⣀⠀⠀⠀⠈⠉⠉⠙⣛⠳⠶⢤⣤⣌⣉⣉⣀⣀⣀⣀⣠⣶⠟
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⢷⣄⠙⢮⣢⢄⠀⠀⠈⠂⠑⠈⢆⠀⠀⠀⠈⠳⣄⠢⡀⢀⠀⠀⠀⠀⠉⠀⠲⢭⣿⣦⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣈⠛⠯⣆⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠈⠳⣌⠂⢌⠢⢄⡀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣍⣀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⠻⣦⡁⠢⢌⡒⠤⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⣤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣭⣷⠶⠶⠚⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢐⠀⡆⠀⠂⢰⠦⣐⠂⢰⢀⠂⢰⠀⠀⡔⠀⢢⠰⣀⣆⡐⠀⣶⠄⠂⢲⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠈⠂⢁⠘⠀⠈⠁⠘⡀⠀⠘⠀⠂⠈⠒⠉⠀⠉⠈⠁⠀⠓⠀⠁⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣥⣍⡃⠈⣯⣭⠉⠀⢹⣥⡌⠁⠈⡏⠈⠙⡆⠺⣥⣍⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠴⠃⠐⠇⠀⠞⠁⠾⠂⠴⠎⠐⠗⠐⠚⠁⠓⠢⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠄⠀⣀⡀⡀⣀⠀⡀⡠⠀⠀⠀⠀⣀⠀⠀⡀⡠⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠃⠀⠊⠀⠀⠈⠀⠐⠀⠓⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠁⠘⠁

⠀⠀⠀⠀⠀⢀⣠⣿⣷⣦⣤⣤⠦⡽⠦⢤⣞⢱
⠀⠀⣀⣠⣶⢏⡵⠋⣁⡾⡿⠿⢶⣧⡾⠿⢿⣗⡦⣀⠀⠀⠀⠀⠀⠠⠂⠂⠲⣏⣥⣷⣤⣄⡀
⠰⣿⣛⣛⣻⣿⠳⠾⢋⣷⣤⣸⣿⣿⢁⣠⡾⠛⠓⠛⠁⠀⠀⠀⠀⢢⠀⣒⡤⠟⢣⡀⠈⢝⡺⣄
⠀⠈⠉⠙⠿⣿⣿⠿⢳⡟⠋⣈⣉⡽⠿⣋⠄⠀⠚⣩⣿⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠛⢴⣤⣽⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣩⠤⠴⡆⠉⠛⠉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⠀⠀⠀⠀⠀⡀⠀⠸⣻⣧
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⣬⣗⣋⡿⠀⠀⠀⠀⠚⠤⠤⠐⠚⠃
⠀⠀⠀⠀⠄⡤⠀⠀⠈⠃⢀⠀⠀⡐⠀⠀⠀⠀⠉⠉⢀⡀⠀⠰⡆⠀⢀⢤⡀⠀⠀⠀⡠⠖⠒⢠
⠀⠀⠀⠀⠀⠐⠀⠀⡀⣀⣈⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣆⣠⡾⠁⢠⡀⠀⠈⠀⡄⠀⣴⣠⠔⢁⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠓⠒⠲⠋⠀⠉⠁⠀⠝⣀⣨⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐
⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⡈⠹⡄⠀⠀⠀⣠⢸⡄⠀⡠⠀⠀⠀⢀⠀⢡
⠃⠸⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⠀⣘⡄⣧⠀⠀⢰⣷⣸⡇⠐⠀⠀⢠⠀⠊⢸⢘⠀⢠
⠀⠆⠀⠀⠀⠉⠉⠉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠙⠛⠁⠈⠢⠄⠀⠀⠙⠛⠛⠀⠀⠁⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⡤⢄
⠀⠀⠀⠀⠀⣁⣉⣿⣋⠛⢛⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠁⠚⠯⠤⠽⠷⣤⣽⠞⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠀⡄⢀⠁⠀⣀⠀⠀⠐⠀⠀⠀⠠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠈⠀⢰⠈⠀⢀⠁⠀⠀⠞⠁⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⣄⣸⡶⠼⠿⠦⣶⡼⠀⠀⠀⠀⢀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⣶⣿⣿⣿⣷⣿⣶⡉⠁⠀⠀⠀⠠⠈⠒⠀⠀⢨⡟⠁⠀⠀⠀⠀⠀⠹⣶⢈⠀⠠⠄⠀⠀⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠄⠀⠀⠤⠖⠒⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠀⢀⠐⠂
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢄⢀⠀⣀⣠⠺⣇⠀⠀⠀⠀⠀⠀⠀⡘⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣉⣷⣤⣀⣀⣀⣠⡾⠛⠈⡀⠀⠐⠂⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠤⠐⠁⡨⠘⠉⠉⠹⡆⠈⠀⠀⠐⣄⣀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠐⠀⠀⠀⠀⠈⠀⠐⣄⠀⠙⠈
⠀⠀⠀⠀⠀⠈⠠⠀⣀⣀⡑⠊⠁⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⠈⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣤⣠⣤⢄⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁
⠀⠀⠀⢠⡶⠶⢿⣷⣫⢶⡿⢛⣾⡶⠿⣿⣧⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠉⠙⢿⣿⠧⣾⠿⠚⢿⣥⠞⠉⣉⣉⠀⠀⠀⡌⣧⠀⠀⢀⡒⣧⠀⠀⠀⡀⢀⠄⣼⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣩⠥⡐⠒⠲⠶⠟⠀⠀⠰⢾⡿⠀⠀⠹⠿⠿⠀⡄⢀⠃⠸⣼⡿⠀⠀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠄

⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⠀⠀⠒⠀⠀⢀⣴⣾⣿⣿⣿⠗⠀⠀⠀⠀⠊⠀⢀⠀⢀⣬⣤⣀⣀
⠀⠀⠀⠀⢸⣷⣄⠀⠀⠁⠀⠀⠀⣠⣄⠙⠛⠉⠫⠁⠀⠀⠀⠀⠀⢀⣀⠔⠃⣠⡸⢿⣿⣿⣿⣿⣷
⠀⠀⢀⠀⠸⣿⣿⠀⠀⠀⠀⠀⢴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐⢀⣈⡀⠀⢰⣿⣷⣰⡎
⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠠⠀⠀⠀⢀⣴⣿⣿⠟⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠈⠛⢛⣁⣀⠀⠀⠀⠀⢀⠉
⠀⣀⣤⣤⠀⠠⠔⣿⣿⣿⢠⣿⣿⣦⣄⠀⠀⠀⠀⣀⠄⠀⠀⢰⣿⣷⡀⠀⣴⣾⣿⡿⠃⠀⢀⣴⣿⡟
⣾⣿⣿⠟⠀⢠⣄⢿⣿⠇⣀⠙⠻⣿⣿⣷⡄⠀⠀⢀⠀⢀⣤⣀⡙⢿⣿⠀⠹⠿⠋⠁⠀⠀⢾⣿⠟⠁⢀
⠉⠀⠀⠀⢠⣿⣿⠈⠁⠘⠃⠀⠀⠀⣈⠉⠉⠀⢠⣿⣷⠸⣿⣿⣿⣷⣮⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠂⠀⠀⣼⣿⣧⠀⠀⢸⣿⣿⡆⠀⠉⣩⡝⢛⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠒⠓⠀⠘⠛⠃⠀⠀⣠⣤⠀⠀⣿⣿⣿⢀⣤⠘⠿⠿⠃⢠⣾⣿⢡⣿⣷⡆⢀⠀⠀⠀⠀⠉⠸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣤⡀⠘⠛⠛⢸⣿⣇⠀⠀⣴⣜⠛⠁⣿⣿⠟⠰⣿⣿⣆⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⢹⣿⣷⠀⢀⠀⠸⣿⠿⠀⢰⣿⣿⡄⠀⠛⠁⠀⠀⠈⠻⢿⡆⢀⡀⠀⠀⠀⢀
⠀⢀⣴⣦⠀⠀⠀⠀⢀⣦⢸⣿⣿⠀⡁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣤⣦⣤⣤⣤⣀⠀⠀⣾⣿
⢠⣿⣿⢏⣀⠀⠀⠀⢸⣿⣇⠉⠁⠀⠠⠀⢠⠀⣠⣤⣆⠉⢉⡀⠀⠈⠛⠿⢿⣿⣿⡇⠘⢿⡟
⣘⠉⠀⣾⣿⡆⠀⠀⠸⣿⠟⠀⠀⠀⠀⠁⠊⠀⢹⣿⣿⡄⣼⣿⣿⠀⠀⠀⠀⣠⣄
⠀⠀⢀⣿⣿⣷⣠⡀⢰⣿⣶⣤⣀⠀⠀⠀⠐⠀⠀⠹⣿⠃⢻⣿⡟⠀⠀⠀⣸⣿⣿⣰⣶⣦⠀⠂
⡀⠀⠐⠻⠿⠏⣿⣿⡈⠛⠿⠿⢿⣿⠖⠀⠀⠀⠀⢠⣀⣀⠘⠋⠀⠀⠀⠀⣿⣿⡿⢻⣿⣿⠀⣼⣦
⠀⠀⣀⠀⠀⠸⣿⣿⡇⣾⣿⣧⠀⠀⠀⠀⠀⠠⠔⣿⣿⣿⠀⣿⣿⣶⣄⠀⠉⠛⠁⠸⣿⠏⠀⣿⣿⡆
⠀⠄⠀⠀⠀⠀⠉⠋⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠉⠻⢿⣿⣷⣄⠀⠀⠀⠉⠀⠀⠻⠛⠁
⠀⣀⠀⣀⠀⠀⠀⠀⠀⠹⠏⣀⠀⢀⠀⠀⠀⠀⣀⣨⣥⡀⡀⢀⡀⠀⢀⡉⢏⡀⢀⡀⡀⡀
⣏⣈⣯⣿⣿⣯⣿⣽⣽⣿⣍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢠⠖⠻⠶⠶⠶⠤⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢸⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⢘⣇⣀⣸⣇⣸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿⠀⠀⢻⣄⣀⠀⠀⠀⠀⠀⣀⡿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⡟⠉⢉⣩⣍⡉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠙⠛⠛⢛⣋⣉⣀⡀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸⡄⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠟⠛⠛⢉⣉⡉⠙⠛⠿⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢳⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢁⣤⡶⠟⠋⠉⠉⠉⠉⠛⠶⣤⡈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⠀⠀⠀⢣⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⠀⠀⠀⢀⣉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢠⡟⠁⠀⠀⣠⡴⠿⠛⠛⠻⠷⣦⡀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⣇⣴⠞⠛⠉⠉⠉⠛⢿⣦⡀⠀⠀⠀⢸⡿⠀⢠⣿⠁⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣤⣼⡿⠁⠀⣠⠶⠦⣄⠀⠀⠙⣿⡶⠶⠶⣾⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⣾⠁⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⣿⡇⠀⢸⣇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠹⣦⣀⣀⡼⠁⠀⠀⣼⠇⠀⠀⠻⠷⠦⠼⢿⡄⠀⠀⠘⢷⣄⣀⠀⠀⢀⣠⣴⠟⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⣠⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠚⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣥⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⣀⣤⣖⣰⣤⢤⠤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠛⠲⣄⠀⣷⢸⡇⢰⣶⣶⣿⣶⣶⣆⣀
⠀⠀⠀⠛⠛⠛⠛⠿⠴⠿⢿⣿⣿⣿⣶⣦⣄⠀⠀⠀⢠⣤⡀⢰⣾⣿⣷⣶⣤⠀⠀⠀⠀⢀⣾⢸⣏⣷⢘⠀⢸⣾⡗⣼⣿⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣷⡀⠀⡂⢀⣴⡶⣶⣤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣜⣓⢄⠀⣿⣿⢛⣉⣉⣠⣹⡁⣿⣿⣋⣲⣹⣧⣥⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣂⢃⠈⢿⣿⣿⣯⣿⡉⠀⠀⠀⠉⠙⠛⠛⠻⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢟⠹⣿⣿⣍⢦⣼⣿⣿⣿⠿⢟⠛⠶⠦⣄⣄⣀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢈⠀⣿⣿⣷⢸⣿⣿⣿⣿⣶⣾⣿⣷⣶⣤⣄⡁⠘⠻⠟⠂⢀⣃⡄⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⠀⣽⣿⣟⣼⣿⣿⣿⣿⣿⡿⣃⡿⣿⣿⣿⣿⣷⡄⠀⢸⣿⢽⣿⣿⠿⣷⣌⡆
⠀⠀⠠⠄⠀⣀⠀⠀⠀⠀⢿⣿⣿⣧⣠⣿⣿⣿⣻⣿⠀⠿⠿⠿⢇⣿⣿⣿⡒⠬⣿⣻⣷⡀⣹⣿⣻⣿⢇⠑⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠒⠦⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⠘⣿⣛⡃⣛⣉⡴⢿⣦⣤⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⣿⣿⡏⡀⣿⣿⣧⣿⠻⡿⠿⠛⠁⠀⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⠇⠀⣿⢛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢼⣿⣷⠾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣭⡭⠥⠤⠤⠤⠤⠬⠤⣤⣤⣤⡦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢰⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠤⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴⠞⠂⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢀⣀⣀⠀⠠⠄⠀⠀⠼⠇⣀⣸⡇⡄⢠⠀⢸⠀⢀⡄⠄⠄⢀⡟⠂⢀⠀⠈⣢⠀⠀⢀⣯⡀⠀⡸⡿
⠀⠀⠠⢘⡩⣐⣀⢁⡤⣄⢀⣉⣀⠂⠌⡑⠍⡈⠢⡉⠀⠺⠐⢠⠉⠀⡇⠀⠀⢠⡏⠁⠀⠀⠀⠉⠀⠀⠁⠈⠁⠐⢠⡀
⠀⠀⠈⢁⠴⠋⠁⠜⠠⠀⠄⠡⠈⢑⠤⣌⠐⠈⠢⠈⢟⠋⠀⠀⠐⠒⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⢹⣹⠁
⠀⠀⡞⠃⠐⣊⣤⣶⠶⠶⢶⣦⣄⠑⠂⡉⢢⡀⠂⠑⣞⠒⢒⣒⡒⠒⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿
⢠⢎⠈⢊⣾⠟⡁⢐⠆⠠⣒⣌⡙⣷⡄⠑⠀⠙⡏⢱⠷⠶⢾⠅⠀⠀⡷⡶⠰⢾⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⣼⣿⡀
⠘⠢⡅⣼⡏⡈⡚⠡⠒⡖⢀⠹⠵⠘⣿⡀⢈⡐⣯⠫⠭⠭⠥⠝⣯⡍⠉⢠⡤⠬⢽⠁⠀⡠⠤⠀⠀⠤⢄⡘⠳⡄⠙⠃
⢟⠂⠀⢻⡇⠇⣇⠰⡊⠓⡢⠠⢑⠀⣿⠇⠠⡈⡋⠀⠀⠀⠀⠀⠹⡋⠋⠋⠀⠀⢸⡯⠉⠀⡠⠤⠤⣄⡀⠈⢻⡅⠀⡀⢔
⠀⣀⠀⠨⣷⡌⠲⡳⠄⠀⣴⠯⢂⣼⠟⢀⠐⢌⡇⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠸⠁⢠⠎⢄⠄⠀⡀⡹⡄⠀⠷⠈⠂
⠀⠳⡄⠐⠈⠻⢷⣤⣤⣤⣤⣶⠟⠋⠀⠎⢢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⡄⡐⠀⠀⢀⢃⡇⠀⡀
⠀⠀⠈⢦⣉⠑⠀⠠⢉⠉⡀⠠⠀⠊⣁⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠙⠦⢥⡤⠵⠋⠀⡐
⠀⠀⠀⠀⠀⠑⠣⠶⠅⣴⣤⠇⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⣀⣀⣀⠄⠊
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⣤⣤⣤⣨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⠒⠒⠀⠀⠰⠆⠀⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠰⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣎⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢊⠀⠀⠈⡄⢀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠘⢄⠀⠄⠀⠠⠄⠀⡀⠀⠀⠀⠀⢀⡄⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠃⠀⠀⠈⠁⠀⠀⢨⠗⢄⠘⠁⢠⡄⠀⡆⠀⠀⠰⢣⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⠈⠤⠀⠀⠀⠂⠀⢀⠴⠳⠀⠀⠀⢱⢀⡄⠀⢈⠈⢱⡌⡆⠀⠖⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⡀
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠⠀⠀⠀⠋⠴⠀⢀⡄⠀⢨⠀⠀⠀⠉⠀⠁⠀⠀⠀⢰⠁⡇⠂⠀⠀⠠⠀⢰⠆⠴⠀⠀⠀⠃⠀⠐
⠀⠀⠀⠀⠀⡌⠀⠃⠀⠀⠀⠀⢠⠇⡀⠀⠀⠈⠁⠀⢸⠅⠀⠀⠀⠀⠀⠀⡀⠀⠘⠰⠿⣇⠀⠉⠈⠀⢨⣀⠀⠀⠛⠆⠁⠀⡁
⠀⠀⠀⠀⢠⠃⣆⠀⠀⠀⠀⢀⡇⣀⠀⠀⠘⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡏⢠⠄⢨⠀⣸⠀⠀⣀⠀⠠
⠀⠀⠀⠀⠈⣢⣀⠀⠁⠀⠀⡾⠠⠀⠀⠀⠋⠁⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠗⠂⠀⠂⠀⠁⠀⠀⠘⠀⡀
⢀⠀⠀⠢⣴⠉⠉⠛⠻⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⡜⠢⠀⠀⠀⠀⠀⠀⠴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⠒⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠑⠒⠤⢄⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠈⠁⠒⠀⠤⠤⠤⠄⠀⠀⠀⠀⢱⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠈⠁⠀⠛⠁⠴⠂⡀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠰⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠐⠂⠁
⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣈⣀⣀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⣴⣿⣶⣦⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠘⡛⠃⣐⣿⣿⣿⡟⠶⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠗⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣄⠀⠀⢿⣿⣿⣿⣿⣇⢰⡀⠀⢀⣤⠼⠧⠦⣿⣷⣴⣶⡦⠐
⠀⠀⠀⠀⢀⠄⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⠀⠀⢘⣿⣿⣿⣿⣗⣼⣅⠀⠙⣿⣷⣀⣀⡹⣿⣿⣥⣤⣼⡌⣀
⠀⠀⢠⣖⠁⣴⢆⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠙⣿⣿⣿⣿⣿⣿⣫⣴⣿⣿⣿⣿⣿⣋⣀⡀⣹⣿⠋⡏⢹⣿⣿⣻⡉⡍⢉⡭⣤⠬⠂
⠀⢠⣾⣟⣓⣈⣤⣴⠄⠛⠋⠋⠉⠁⠒⠒⠂⠙⠓⠿⠿⠿⠿⠓⠿⠿⠟⠻⠿⠟⠛⠿⠿⠿⠿⠛⠛⠀⠂⡛⠛⠛⠿⠅⠰⠈⠉⠉⠈⠁⠈⠀⠀⠀⠠
⠀⠀⠀⠈⠉⠁⠄⠈⡉⠈⡀⠀⠀⠀⣀⠐⢀⠀⠐⢚⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠐
⠀⠀⠠⣌⡃⢿⡌⣉⡂⢱⣝⠲⡏⣙⢳⣴⠈⠍⣴⡍⠊⣇⠥⡂⠀⢀⠶⠞⠦⢼⠀⡆⠠⢈⡤⠸⢵⢂⣶⢁⡔⠂⢲⡐⠆⠐⠈⠄⠰⡤⢆
⠀⠀⢀⣿⢙⡆⢸⢫⠁⠔⢿⠇⠘⡸⢻⠛⣤⠗⣾⢈⡝⣺⢶⣧⢡⠙⠤⢠⣐⣦⣾⡅⣶⠻⣍⡆⠞⣀⣽⡆⠶⡏⠋⡍⡉⠁⣀⡛⠃⣷⡤⠖⠣
⠀⠀⢈⣿⢸⣇⣷⡫⠜⢻⣴⡏⠰⣉⢾⣀⣻⡀⢾⠀⠼⢋⢸⡇⡛⠷⢬⡘⢼⡡⡤⢀⣅⠔⢻⡳⢦⡥⠺⢛⠿⠁⠦⣯⡌⠷⡋⠁⠀⣾⣁⣀⠁
⠀⠀⠀⣿⢸⣏⢸⡇⣿⠛⢸⣇⢘⣟⢾⡑⢽⡆⣿⠳⣿⣯⢱⣎⢵⠻⠎⢣⠿⣵⣄⢸⡇⢠⣬⠁⠀⣿⡶⣻⢧⡀⣶⡰⢶⠶⡀⢆⡿⣡⠈⠒
⠀⠀⠉⣿⠘⠷⢸⡦⠯⣀⢸⡇⣀⣉⣻⡓⢺⠇⢹⡘⣿⠣⢸⡅⢒⡼⢦⡡⠾⢼⡇⢸⡏⣈⣭⠗⠀⣿⠒⡯⢿⡁⣽⡵⢿⣷⡅⣬⡝⣡⢌⡉
⠀⠁⠈⠉⠛⠒⠺⠧⠤⠤⢼⣅⣈⣁⣽⡉⠉⠁⢻⠃⠒⠒⢾⠔⠠⠜⢵⣧⠀⠼⣆⢡⡦⠩⡍⠁⠙⣿⠃⠑⢻⡓⣿⡴⣿⣶⠄⢼⡅⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠶⠶⠼⠧⢤⣀⣘⡇⠀⠀⠀⢰⡎⠁⠈⠂⠐⣿⠂⠰⢼⠳⣿⠤⠟⣀⣀⣾⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠷⠤⣤⣄⣀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢘⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠓⠛⠒⠤⠤⠀⣭

⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠋⡄
⠀⠀⠀⠀⠀⠀⢠⡿⠀⢀⣀⣀⣀⣽⣄⡀
⠀⠀⠀⠀⠀⢀⡼⠿⠟⠛⠛⠉⠉⠉⠙⠛⣻⣥⡶⠦⠀⠀⠀⢀⣀⣀⣤⣤⣤
⠀⠀⠀⣠⡶⠋⠀⣀⣀⣀⡠⣤⣴⡖⢺⣿⣿⣧⢤⠀⠶⠚⠛⠉⠉⠁⠀⠀⢸
⠀⠀⠘⠛⠛⠉⢩⠏⠘⠛⠀⠈⡟⣷⠞⠁⢸⠀⣎⡄⠀⠀⠀⢀⣠⡄⠀⠀⢸
⠀⠀⠀⠀⠀⢠⣯⠤⢦⣀⡀⢰⣿⡿⢤⣤⢾⡄⢻⡄⣀⠴⠚⠋⢹⠃⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⣾⡿⢳⣄⠀⠈⡇⠀⠙⢦⣀⣀⣀⡟⠀⠀⢠⠃⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢲⣴⡟⠁⠈⣿⠣⡴⠞⠀⠀⠀⠀⠉⣹⣿⣿⣶⣾⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠸⣇⠀⠲⣦⡀⠀⠀⡰⠋⢑⠞⠉⠁⠀⠀⠀⠀⠙⢿⣧⡔⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢻⣦⡼⠁⠀⡏⠀⠀⠀⠀⠀⠀⢀⣤⣾⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠘⣿⡁⠀⠀⣇⠀⠀⠀⠀⣠⣾⣿⠷⣫⠑⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢹⢇⣿⠶⣿⣿⣶⣴⣾⣿⡫⠕⡡⣐⡵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢸⢸⣡⡶⡟⢝⢝⡿⢿⣭⢖⠔⣊⠤⢚⣽⣷⡀
⠀⣠⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡟⢸⡻⡌⣌⢇⠡⣻⣶⣿⣷⡫⣷⢯⣣⢿⡻⣧
⠀⠙⡟⠳⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⣿⠝⣎⢂⣦⣷⡿⠟⠉⠘⢿⣕⢿⣷⠱⣒⣽⣇
⠀⠀⢧⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⢿⠧⡇⣿⣮⣶⠿⠛⠉⠀⠀⠀⠀⠈⢻⣯⢾⣿⡻⣝⣿⡄
⠀⠀⠈⠉⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡹⡀⡟⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⢻⣾⣷⡽⣧
⠀⠀⣦⡀⠈⣇⠀⠀⣀⣼⠀⠀⠀⠀⠀⢻⣗⡝⣽⣿⢷⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣛⡭⢔⣿⡆
⠀⠀⠘⢏⢳⢸⡄⢀⡍⢙⡖⠀⠀⠀⠀⠀⠹⣮⣪⢿⢸⠟⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⡛⠽⠧⠀⣀
⠀⠀⠀⣼⠈⣦⣧⢾⠀⣯⠀⠀⠀⠀⠀⠀⠀⣬⠇⣸⢸⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⣠⣴⣶⣿⠿⡃
⠀⢳⡲⡈⣇⣹⣻⡼⡰⠃⠀⠀⠀⠀⠀⠀⠀⠙⠦⡇⡎⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠋⠉⠀⣿⣿
⠀⢠⣷⣉⢫⣹⡟⡗⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠾⣄⠧⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠳⣆⠀⢀⣠⢄⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠘⢤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣽⠞⠛⠉⠉⣩⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣀⣤⣿⣃
⠀⠀⠀⠀⠀⠀⢛⣷⠀⡀⢠⠀⢀⠀⠀⣀⣐⣊⣼⣟⡀⢀⣀⣀⡀⠀⣼⠁⣠⡞⣠⠟⠀⠀⠀⠀⢀⣠⠿⠂⠶⠖⠠⢶⡟
⣀⣀⣀⣴⠛⠦⡼⠿⠜⢳⠿⣤⣯⠀⣸⣿⣿⣿⣿⣿⣿⣟⣁⠈⠉⣉⣉⡴⠛⠫⠿⢾⣥⣀⣰⣛⣉⣁⣀⣀⣠⣄⣠⣼⣥⣾⣥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠃⠀⠚⠛⠓⠀⠀⣶⣦⣄⠀⢼⠇⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣋⠁⠀⠀⠀⠀⠀⠘⠢⣀⡙⠛⠛⠓⢨⣄⠋⠉⢴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢷⣄⠾⠏⢠⣀⠀⠀⠀⠀⠀⠀⢠⣬⣛⠓⠒⠀⣙⡀⠀⠀⠠⣌⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⢲⣯⣀⢠⣴⣶⠤⣶⣬⡉⢉⣅⢠⣾⠿⣃⡄⣠⣄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⢠⡄⠲⣶⡍⠉⠈⢻⠀⠀⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠰⠞⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣧⣤⣤⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢍⠙⡶⠊⣀⡤⠬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣶⣿⣷⡟⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⠉⠘⢶⣟⣺⣿⢦⣴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⢉⣿⠞⣹⠮⠿⠟⠂⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⣠⢽⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⣷⠞⢉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠖⠻⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠌⣿⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠺⠻⠿⣯⣟⢻⣿⣾⣿⣤⣊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠘⠛⠽⣿⢿⣽⣗⣖⣠⢄⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣄⣀⣀⣀⣀⣀⣰⣧⣤⣿⣥⣤⣭⣭⣋⣉⣀⣀⣰⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣝⣛⣩⣛⣻⣟⣽⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣎⣁⣙⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠤⣤⣤⣤⢤⣤⣤⣤⠤⣼⣠⢄⠀⢠⢔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⢸⠠⠀⠀⠀⢃⢃⢀⢸⠀⣇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠀⠀⢸⠸⠤⠤⠤⠼⠸⡌⣁⣠⠗⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢷⣻⣿⠦⣾⢞⠭⡉⠉⢹⢠⠀⠀⢸⠀⠀⡇⠭⠍⠉⠓⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣵⠙⠃⠁⠈⠁⠚⢩⢮⣢⡸⢸⠀⠀⠈⠁⡨⣲⣭⣿⣽⣁⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠄⠀⠔⠉⠉⠉⢢⠀⠒⢧⡏⠉⠉⠉⢛⢮⡾⡏⠃⣁⣈⠘⠩⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠂⠸⡀⠀⠀⠀⢠⠀⢈⢻⣿⣉⣉⣹⣾⣾⣛⠀⡎⠀⠀⠙⡄⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣁⡀⠙⠢⠤⠔⠃⠠⣌⠏⠿⠤⠤⠽⢰⡻⡧⠀⠣⣀⣀⠴⢁⣲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣆⣠⡀⣆⣸⠖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠫⣖⣠⢠⣄⠦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠃⠀⠀⠀⣀⣀⣀⣠⠟⠉⠉⢀⠙⡄⠀⣀⣠⡤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⢀⣴⢊⣵⡒⣶⣾⡀⠀⠀⢸⢸⠷⠋⠁⠀⠀⠀⣠⡤⣾⡷⣄
⠀⠀⠀⠀⠀⣠⡴⣒⣚⣛⣉⡉⢉⣉⣉⠉⠭⠭⠭⠭⠹⣶⢥⡷⢷⢰⣸⢃⣀⣀⠀⠀⢀⡼⠑⠃⠈⢻⡈
⠀⠀⠀⣀⣼⠉⠀⢴⠆⠀⠀⢸⠀⠀⣶⠀⠀⠀⠀⣋⡱⢸⠿⠭⠭⢽⡟⣽⡙⠘⢉⠝⠓⡢⠀⣀⡀⠀⢻
⠀⢠⣮⠔⡏⣾⠭⢱⣸⠩⢱⠘⣴⠟⢯⠉⢲⡤⠒⢲⢾⡿⠤⣤⠤⠼⣾⣇⠙⡄⠈⠉⠁⠀⢰⡟⢧⠀⠘
⠀⠈⢯⣤⡇⡏⠰⢸⣽⣒⢸⠀⠏⢆⡸⢀⣮⣬⡟⢋⣿⣆⠀⣉⣈⢹⣽⡇⠉⢁⠔⠂⢱⠀⡞⠀⣸
⠀⠀⣀⣀⣧⣿⢩⢴⢹⠶⠬⠀⠀⣿⠿⠿⠋⠛⠧⡬⡿⠰⠹⢷⣼⠸⢹⣌⣢⠈⠉⠉⠀⠀⡇⠀⢹
⢠⠞⠁⡜⢻⢸⣒⢸⢸⣏⠀⠀⡇⢸⣠⠖⠒⡲⠾⣟⣻⠍⣩⠭⣭⣤⢼⡄⠀⢀⠔⠒⢲⠀⢷⠀⡞⠀⢰
⣾⠀⢸⢠⣻⣎⣑⣊⠈⠛⠒⣁⡇⢸⠁⠀⡐⢀⣄⢸⣐⣟⠝⡄⠀⠈⡿⣄⣱⠈⠈⠉⣀⠀⠘⢟⠀⠀⣾
⡷⠀⢸⢸⠣⢷⣄⣀⣦⠀⣀⣀⣀⡏⠀⠀⡇⡆⣸⢸⣿⠿⠚⠛⠋⠉⠁⣟⠦⡀⠯⠉⠤⠃⠀⠀⠀⢰⠋
⢻⣶⡼⡄⠒⣹⠁⠈⠉⠉⠉⠁⠀⣇⣀⠀⡇⢃⠸⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣅⣀⣰⣖⣩⣝⡠⠶⠋
⠀⠙⠺⠿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠻⣇⣦⡧⠈⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⣀⣀⠀⡀
⠀⠀⢠⣤⣤⣤⣦⣤⡤⢶⠆⠀⠀⢩⣥⣭⢄⣈⠀⠀⠀⠀⠀⠺⠀⢉⡉⠹⣦⠀⠀⠉⠙⠻⣿⣿⣶⡀
⠀⣠⣿⣿⣿⣿⣿⣿⣄⡞⢡⡀⠀⠈⠙⢿⣾⣿⣦⣄⠀⠀⠀⠀⠀⠈⠁⠸⠤⠂⠀⠀⢳⣌⠉⠉⠙⢿⡄
⠀⣿⣿⣿⣿⡿⣿⠿⡟⠃⣀⣠⠠⠀⠀⠀⠈⠟⠋⠀⠀⠀⢀⣤⣶⣿⣷⣄⣼⣧⡿⠂⠉⢁⠀⠀⠀⠘⠁
⠀⢿⣿⢿⣿⣻⢻⠿⣿⠿⣿⡧⠌⠷⠤⠀⠄⠤⠂⠀⠤⠀⠀⢙⣿⣿⣾⣿⣿⣿⣧⣶⣾⣿⣿⣿⣿⣿⡇
⠀⣾⣿⣧⣮⣭⢠⣰⣿⣦⣴⢃⣀⣉⠋⢽⣶⡄⠈⠁⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⣹⢿⣿⠇
⠀⠻⣿⣿⣿⣿⡶⣿⣿⣿⡇⢸⣿⣿⣶⣾⣷⠄⡀⣝⣿⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐
⠀⠐⣿⡿⠾⠿⣷⣿⣿⣿⣧⣠⣭⣭⣡⣬⣽⣷⣩⣿⣟⡀⣿⣶⣶⣶⣤⡼⠛⢻⣧⣸⣿⣿⣿⣿⠏
⠀⠀⢤⠀⡀⢀⠀⣿⡏⡽⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⡛⠳⡤⠜⠛⠿⣿⣿⣿⣿⠃
⠀⠀⠀⠚⢿⣿⣅⣸⣇⠉⢿⡿⢿⣿⣿⣿⣿⡏⣦⠻⠿⠿⠟⠿⠙⠿⢯⣙⡶⠶⠟⡓⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠺⠷⠦⣘⣻⠿⣿⠿⠿⠗⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡾⠟⠁⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⡀⠀⣸⠇⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⣸⡏
⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣶⡿⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⣀⣼⠟
⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠶⠖⠶⠶⢦⣤⣄⡙⠃⣴⠋⠀⠀⠀⠀⣀⣠⣴⡾⠛⠁
⢿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⣴⣶⡶⠟⠛⠉⠁
⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⣦⣄⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⣶⣶⠶⠶⠾⠛⠛⠉⠀⠀⠀⠀⠙⠿⣦⡀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠛⣉⠛⢿⡇⠀⢸⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠙⠻⠿⣦⣤⡟⠉⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣶⣤⣄⣀⣀⣀⣀⣀⣀⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢘⣿⣟⣿⠋⠉⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⣿⣿⠟⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⠀⠀⠈⠻⠾⣿⣷⣶⣶⠶⠶⠶⠶⠶⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢩⣷⣤⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠈⠙⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⣿⠋⣿⡏⣿⡏⠉⠁⠀⠀⠀⠈⠉⠙⠻⢶⣄⡀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢸⡏⠀⢻⣧⠘⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢿⡇⠀⠀⠹⢷⣄⡉⠛⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠘⣿⡀⠀⠀⠀⠙⠛⠿⣶⣶⠿⠃⠀⠀⠀⠀⠀⠀⢸⡇⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠈⠻⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠈⠉⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠷⠶⢶⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠀⠀⠁⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⣀⠀⠈⣢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⢞⣥⠞⠉⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣿⠁⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢻⡄⠀⠀⢀⡟⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠙⠶⠶⠛⠀⡏⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢳⡀⠀⠀⠀⠀⠃⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠀⢣⠀⠀⡀⢠⣦⠀⠀⡖⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣼⡇⡠⢷⢂⡍⠉⠓⠛⢾⠤⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⡼⠉⣿⠀⠀⠁⠀⠀⠀⠀⠸⢦⠀⠀⠈⢣
⠀⠀⠀⠀⠀⢀⣾⠃⠀⢲⡆⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⠈⢷⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠙⠢⣄⣸⢀⣀⡀⠀⠀⠀⠀⢸⠀⠀⢳⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⡴⠛⠉⠈⣍⡳⡄⠀⠀⢸⠀⠀⠈⢷⡀⠀⣠⢾⣀⣠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣾⣀⣠⡤⢜⡶⠳⠀⠀⠀⢸⠀⠀⠀⠈⢷⡞⠻⡄⠀⢠⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⠛⡶⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡸⢻⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡇⢸⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⡇⢸⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡾⠀⢸⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢀⡇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⣇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⠀⠀⡿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⢱⡇⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡎⠀⢸⣇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠃⠀⠀⣽⠋⠉⠉⠁⠈⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢠⡄⠀⢀⠀⠀⠀⠻⠖⠚⠛⠛⠒⠒⠋⠀⢀⡴⢇⣤⢤⡤⢴⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⡠⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡛⠋⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠞⠶⠟⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⠂⡀⠀⢀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡿⠘⡇⠘⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢰⣿⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣤⣾⡏⢀⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣸⣿⣿⣿⣿⣿⣧⠋⠀⠘⢶⡄⣟⣘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢽⣿⣿⣿⣿⣿⣿⡀⠀⠀⠁⠞⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀⢀⡀
⠀⠀⠀⠀⣀⠀⠀⠈⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠄⠂⠀⠂⠀⠀⠔⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠛⠻⠟⢿⠂
⠀⠀⠀⠀⠀⠀⢀⠤⠐⠁⠀⠀⠀⠀⠀⡀⠀⠈⣀⣠⣤⠤⡤⠀⠐⠀⠲⠛⢻⣿⣿⣿⣾⣿⠷⠶⠶⢦⡀⠠⠶⢖⠉⣀⡟⠁
⠀⠀⠀⠁⠢⢄⡋⠀⠀⠀⠀⠀⠀⠀⢉⡽⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣶⣦⡀⢰⡆⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⡟⢻⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣇⠘⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢹⣿⣿⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠘⣿⣿⣧⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⣿⣿⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠘⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⡇⠀⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⠇⠀⣹⠿⢿⣙⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⣦⣶⣶⣶⣶⣶⣶⣦⣶⠾⠿⠿⠛⠁⠀⣠⣤⣶⣿⣿⣾⡿⠃⣠⠾⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢋⣴⣿⣿⣿⢿⠟⠛⠁⢉⣁⡀⣀⣀⣀⣀⣤⣤⠝⠛⠟⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠐⠋⠈⠉⠁⠁⣠⠄⣠⣾⣿⢿⡿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠘⠡⠞⠱⠋⠁⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⢀⣀⣀⣀⣀⠉⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠀⢠⡾⠛⣿⡏⣿⣽⡿⣷⣦⣄⡀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠉⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⣾⣿⠀⢸⡇⠀⠻⠀⣿⠟⡄⠉⣸⠿⠿⢷⣤⣀⠉⠓⢦⡀⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⠀⢰⣿⣿⡀⠸⣧⠀⠸⠀⣿⠀⠁⠀⠁⠀⠀⣴⡿⣻⢷⣤⡀⢩⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⢸⡿⠈⢷⡀⠹⣧⡀⠀⠘⠀⠀⠀⠀⠀⢞⡔⠁⠁⣴⠿⣿⡿⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⢸⣏⠀⠈⢷⡀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡵⣾⡿⠁⣰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⢿⡶⢤⡀
⠀⠀⠀⠀⠀⠈⣿⡀⠀⣨⣷⣄⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⣾⠃⠀⣿⡇⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣼⡇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠸⣷⣀⠟⠁⠙⢷⣄⠀⠈⠓⢦⡀⠀⠀⢸⣿⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣸⡟⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠉⠳⢦⡀⠀⠉⠓⠶⣬⣿⡷⣄⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⣀⣴⠞⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠉⠳⢤⣀⡀⠀⢹⣷⠀⠙⠳⢤⣀⠀⠉⠙⠓⠶⠶⠶⠶⢶⣶⠶⠶⠖⠀⠀⠈⢀⣠⠴⠚⠉⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣷⡀⢄⠀⠈⠙⠓⠲⠦⠤⣤⣄⣀⣠⣤⣤⡤⠤⠶⠒⠋⠉⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢃⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣤⣴⣿⣷⣜⣆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣶⣤⣄⣀⣀⣀⣀⣤⣴⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉

⠀⠀⠀⠀⡤⠤⡤⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣦⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⣸⠀⠀⣳⠀⠀⠀⠀⣰⢋⣴⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⢨⡷⡇⡤⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀⡾⠁
⠀⠀⠀⢹⠁⢐⡷⠀⠀⠀⠀⠘⢿⡟⣾⢂⣶⢐⣶⢰⣆⠀⠀⠀⠀⠈⠀⠈⡯⡇⠀⠁⠀⠀⠀⠀⠀⠨⠉⠉⠁⡾⣆
⠀⠀⠀⢩⡣⠊⠀⠀⠀⠀⠀⠀⠀⢬⡯⢨⣯⠨⣿⠬⣿⡄⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠙⠄
⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢙⣿⠉⠋⠉⠁⠀⠀⢀⣀⣀⣤⣋⣼⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠐⠠
⢤⡀⢀⣴⣦⣾⣷⣤⣄⠀⠀⠀⠀⠀⢀⡀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢳⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⢸⡇⣸⡇⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠿⠉⠀⠹⠇⠀⠀⠀⠈⡿⠿⣿⢸⣿⣿⡏
⠀⠘⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢼⣹⣏⣿⣻⣻⡇⠀⠀⠀⠀⣁⠀⢰⣶⠆⠀⠀⠀⠀⠀⠀⢰⡉⡎⣹⢸⣿⣿⣷
⠀⠀⠉⠾⠎⠛⠱⠿⠊⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠠⠿⠀⠾⠀⠧⠀⠠⠄⠀⠀⠀⠾⠿⠿⠿⠯⠿⠿⠿⠆
⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠞⠳⢴⠀⠀⠀⠀⠀⠀⢰⣷⠖⣲⠒⡶⢲⢲⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⣇⠘⠇⣸⠒⠀⠀⠀⠀⠀⣼⠏⠀⠁⠈⠀⡿⣼⡇⠀⠀⠀⢀⣀⣰⣺⣲⣀⣀
⠀⠀⠀⢀⣻⣟⡅⠀⠀⠀⠀⠀⠀⢀⡀⣋⢙⡋⣙⣀⡀⠀⠀⠀⢀⣿⢀⡀⠠⠀⢸⣇⣿⡇⠀⠀⠀⢈⣿⣉⢹⠉⣹⣏
⠀⠀⠀⠚⠓⠓⠓⠂⠀⠀⠀⠀⠀⠐⠂⠒⠐⠂⠒⠐⠂⠀⠀⠀⠈⠀⠀⠁⠀⠀⠉⠙⠛⠃⠀⠀⠀⠐⠂⠒⠐⠒⠂⠒
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⡎⣭⣭⡝⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⡀⡴⠋
⠀⠀⢰⣿⠀⠀⢰⡇⠀⠀⠀⠀⣀⣤⣄⢴⠟⠻⣇⠀⠀⠀⠀⠀⠀⠀⡇⠶⠶⢮⠀⣼⣿⡀⠀⠀⠀⢀⣴⣿⣿⣦⡀⢀⡴
⠀⠀⠘⣿⠀⢠⣿⡇⠀⠀⠀⠀⢿⣿⣿⣦⣄⢀⣭⣦⣄⠀⠀⠀⠀⠀⣏⣛⣛⣉⠀⠛⣿⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣮
⠀⠀⠀⠻⡄⣾⡿⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⢺⣿⣿⣿⡇⠀⠀⠀⠀⡧⠷⠿⢼⠀⠀⠁⠀⠀⠀⢀⣼⣿⠿⠻⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡾⡧⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡷⣥⡀
⠀⠙⠋⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣽⣯⡧⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠠⡷⠷⢚⠆⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣟⠐⠀⠀⠀⣀⠀⠀⠀⣴⣖⣉⡁
⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡷⡿⠉⠀⠠⠤⠴⠦⠄⠀⠗⡆⣖⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠤⠰⠀⠀⠀⢛⣻⣿⠒⠒⠒⠒⠶⠒⠂⠈⢷⡥⢶⠛
⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡤⠄⠀⠀⢀⠀⠀⠀⡼⠓⢘⡆⠀⠀⠀⣶⣾⠄⠼⢾⡗⢀⣸⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠨⠇⠀⠀⠈⢉⠀⠀⠰⠛⠃⡠⠷⠀⠀⠀⣟⠻⠀⡈⢿⡅⠸⠁⣇
⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠘⢶⡀⠀⠀⢀⡤⢾⠭⣧⢀⠀⣂⣀⡀⡰⠛⢠⣤⣼⣉⢛⣿⢻⠄⠀⢀⡇⠀⣧⠁⡞⣇⠐⡟⣿⠒
⠀⠀⠀⡇⠀⣼⣠⣸⣧⣷⣶⣶⣿⢶⠶⠿⠿⢷⣛⣛⣛⡙⠯⠭⢿⣷⢰⣾⠿⠻⣿⡿⣿⡟⣷⣾⣿⣴⣦⣻⣶⣯⣿⣅⣿⣿⣷⡆
⠀⠀⣠⣧⣸⡭⣟⣹⣿⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠛⠓⠦⠬⢭⣍⣀⣚⠛⠾⠿⢿⣷⣿⣿⣿⣿⠍⣿⣿⣿⣷⡽⠿⣷⠃
⠀⢠⠤⣗⣨⠶⣫⠽⠋⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⢠⡀⠀⠀⠀⠀⠉⠉⠙⠓⠒⢶⣤⣤⣥⣉⡛⠺⠿⠿⣿⣿⣷⣶⣾
⠀⠀⢘⣩⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢯⣷⣦⣤⣄⡉⠁
⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶

⠀⠀⠀⠀⠀⢀⡀⠀⣿⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠈⠉⣤⣶⣦⡉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣷⣿⣷⡆
⠀⢰⣶⣶⣶⣷⣿⣿⣿⣿⡇⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠹⣿⡿⠁
⠀⠀⢻⣿⣿⣻⣿⣻⣿⡁⢤⠈⠁⠀⠀⠀⠀⠀⠀⠐⢤⠤⣿⡧⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠿⠿⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠇⠻⠿⠇

⠀⣀⣠⣴⣦⣤⣤⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⡀⠠
⠀⠛⢛⣉⣉⣉⢩⣭⠡⣤⡄⣶⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢸⣿⢸⣿⠀⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠢⠄
⠀⠀⢸⣿⢸⣿⠀⣿⡇⣿⣇⣿⣇⡀⠀⠀⠀⠀⢸⡇⠀⠀⡀⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢰⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⠠⣾⣿⣿⡆⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⠿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠟⠁⠀⠀⣿⣻⣿⣿⣛⣿⣻⡿⢿⣛⢿⣿⡟⠿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠶⠿⠿⠿⠷⠾⠿⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣄
⠀⠀⠀⢀⡒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠛⠓⠂
⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣤⣤⣀⣀⡀
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙
⠀⠀⢰⣿⢻⡖⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⢀⣀⣀⠘⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⢀⣸⣿⣼⣧⣿⣼⣇⣴⣿⣦⣤⣀⠀⠀⠀⣀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣙⣀⡀⠀⠀⠀⠒⣁⡐⠀⠀⠀⠀⠀⠀⠼⠾⠆
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠰⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣼⣟⣀⣀⡀⠄
⠀⠀⠀⢀⣴⣾⣿⣿⡿⠶⠶⢦⡀⠀⢰
⠀⠀⠀⠈⠛⠿⠟⢿⡏⠹⠁⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⣈⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡠⠔⢺⡙⢧⣴⡇⢙⡦⡀⠰⢊⡩⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣦⣤⣄⢰⣀
⠀⠀⠀⢠⡎⠀⠀⠈⠙⠲⣿⠟⡉⡀⠙⢲⡎⠀⠀⠈⠀⠀⠀⡀⠤⠀⠀⢀⠜⢡⠤⠈⢻⣿⣿⣿⣿⣄⠀⠀⠀⢄⣀
⠀⠀⠀⢸⣇⠀⠱⣦⣠⣶⠹⢄⣛⡤⠀⠺⠷⢤⡀⠀⣀⡀⠀⠀⠀⠀⠀⡀⢠⣤⠀⣤⠀⣬⠉⣭⣽⣛⠃
⠀⠀⠀⠘⣿⣄⡤⢿⣧⣿⣷⡿⣵⡛⠁⣀⣔⡿⣿⣿⣿⠀⠀⠀⠀⡀⠀⢀⣈⣉⣀⣉⣀⣿⣶⣿⣿⣿⣿⣦⣀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⢻⣿⣾⠟⠓⢦⡀⠀⠈⠁⠈⠉⠹⠛⢛⡏⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠘⢿⣿⣷⣦⣀⡉⠓⠶⠚⠓⢛⣷⣰⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣤⣴⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣾⠿⠾⣫⠀⠀⢠⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢰⣿⣿⡋⠀⠀⢠⡾⠀⢀⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣾⡇⠀⣸
⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠟⠀⠀⠁

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣠⢞⡥⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⡖⢋⣩⡼⠷⡄⠀⠀⠀⠀⠀⠀⢠⢞⡭⠂⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⡞⢡⠘⣿⡆
⠀⠀⠀⠀⣏⢸⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣼⠛⣉⣥⠴⠾⡇⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⡇
⠀⠀⠀⠀⠹⣌⠆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢼⣋⠉⣤⠶⡟⠁⠀⠀⠀⠀⠀⠀⣧⢣⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡧⢸⠀⣿⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣤⣿⣤⣧⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⣯⣼⣤⣿⡇
⠀⠀⠀⠀⠀⠈⣳⣶⣶⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠐⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿

⠀⠀⠀⠀⠀⣀⢀⣤⢠⣄⢀⡀⠀⠀⠀⠀⠀⠀⢠⠖⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⣤⣶⣤⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⣰⣞⠛⣶⡀
⠀⠀⠀⢀⣘⠋⢾⡏⠉⡽⠎⢛⣀⠀⠀⠀⠀⠀⠙⠦⣀⣬⣬⡃⣤⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⡿⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡙⠿⠾⠏⡁
⠀⠀⠀⠾⠿⠸⡿⠀⠀⢛⡿⠸⠿⠆⠀⠀⠀⠀⠀⢠⣿⣿⡸⢞⣵⢟⣀⠀⠀⠀⠀⠀⣧⣿⣿⡇⠀⠘⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡸⠁
⠀⠀⠀⢶⣶⠰⣿⡶⢠⣾⡷⢰⣶⠆⠀⠀⠀⠀⠀⠘⣿⣿⣧⣌⠡⠿⡋⠀⠀⠀⠀⠀⠹⣿⣿⣷⡗⣰⣿⣿⠇⠀⠀⠀⠀⠀⣠⠀⣾⣮⣩⣶⡆⢠⡀
⠀⠀⠀⠈⢩⣄⢶⣷⢻⣶⢆⣬⠉⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢻⡂⢯⡀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⠀⠿⠿⠿⠿⠇⢸⣿
⠀⠀⠀⠀⠀⠈⠀⠛⠘⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠑⠻⢦⡀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⣀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡀
⠀⠀⠀⣿⣿⣷⣿⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⢸⠟⢉⣉⠛⣿⠀⢠⢀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠻⣿⣿⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠳⣄
⠀⢀⡄⣿⣿⣿⣿⢰⣀⣠⣶⢾⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⣴⣴⠀⠀⠀⠀⠀⣿⣿⡈⠀⢁⣿⣿⠀⠀⠀⠀⠀⡞⠀⢠⡀⢙⣶⣄⠀⠀⠸⡆
⠀⠘⠇⣿⣿⣿⣿⢸⣿⠶⠶⢸⣿⠀⠀⠀⠀⠀⠀⣿⣶⣷⣾⣷⣿⠀⢿⢿⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⣿⠀⠀⢀⡇
⠀⠀⠀⣿⣿⣿⣿⠸⣿⠛⢻⢸⣿⠀⠀⠀⠀⠀⠀⠙⠿⣿⢿⠿⠟⠀⢸⢸⠄⠀⠀⠀⠀⣿⣿⣈⣠⣀⣿⣿⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠉⡇⢀⡼⠁
⠀⠀⠀⠛⠋⠩⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣄⣀⣠⣎⡞⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣤⠼⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄⠀⠀⠀⠀⢼⠄
⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⢫⣻⠇⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⢀⠰⠚⠋⠁⠸⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠀⠀⠀⣾⣭⣶⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣤⡤⢸⠩⣭⣭⡭⢻⠠⣤⡀
⠀⠀⠀⠉⠛⠗⣶⣶⣤⣀⡀⡶⠒⢦⠀⠀⠀⠀⠀⠀⢨⡿⢿⡅⠀⣴⡟⠉⢻⣆⠀⠀⠀⣶⡆⠀⢬⡥⠀⢠⣥⠀⠀⠀⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡆
⠀⠀⢠⣶⣶⣴⣬⣿⣿⣿⣿⣿⣾⣿⣷⣦⣄⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⣾⣧⠀⢸⣷⠀⠀⠀⠿⠟⣵⡎⠿⠿⠿⠿⠏⣶⠹⠿⠃
⠀⠀⠘⠿⣟⢙⡿⠿⠿⠿⠿⠿⢿⡟⢙⡿⠿⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⡟⠀⠀⠀⣿⡇⠀⣿⣿⠀⢸⣿⠀⠀⠀⢸⣿⣮⣴⣿⣿⣿⣿⣷⣭⣾⣿
⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠉⠀⠀⠉⠀⠉⠀⠀⠀⠃⠀⠀⠀⠙⠁⠀⠙⠋⠀⠈⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠁⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⠆⣀⣤⣤⣿⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⢛⣵⠟⠉⠀⠈⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣾⣿⠇⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⢿⡆⠀⠀⠀⠀⢰⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⡀⢀⣠⡞⠀⣿⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣇⠀⠙⡛⠛⠉⠀⠀⠋⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠹⡆⠀⠐⠀⠀⠀⢠⠀⠀⡆⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢸⣇⠀⠁⢠⡶⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣸⡆⠀⢳⣰⡀⠲⠲⢾⣭⣤⣄⡸⠁⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣰⢿⣧⡰⠋⠷⠤⠞⠀⠀⠀⠀⠈⣟⠛⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⢰⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⢶⣤⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠻⢦⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠙⠓⣾⣧⠶⠶⢦⣀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢻⡄⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⢠⠞⠉⠀⠀⠰⢦⣌⢵⠀⠀⠀⠀⣷⠀⠀⠀⠀⢿⡄⠀⣠⡴⠻⣤⣤⠶⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣰⣇⡀⢀⣤⢤⣙⣷⠸⠦⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⢿⡴⠋⢻⡄⠀⠀⣴⣾⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⢦⣬⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣠⣤⡀⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣰⢏⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⡿⠸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢸⡄⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣸⠀⠀⣿⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢰⠃⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⣸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⣶⢸⡇⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡏⠀⠀⣾⠃⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⣮⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢸⠃⠀⢰⡟⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢿⠀⠀⠘⢿⣶⠤⠤⠤⠖⠈⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⢀⡀⠀⠀⠀⣾⠃⠀⣀⣀⣀⡀⠀⠀⢀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣒⣦⠀⠀⣸⠇⠀⠀⠀⠙⠛⠛⠉⠉⠉⠉⠛⠛⠉⠀⠀⡀⣴⠞⣤⣴⢦⣶⠖⢾⡤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠔⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠛
⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠿⢿⢿⣿⡿⠿⢿⡿⠿⣿⠿
⣿⣶⣷⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢠⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡤⠆⠒⢄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠠⠤⠀⠀⠤⠿⣀⠀⣿⠀⠀⠀⠀⠠⠀⢀⠄⠤⠀⡀⣿⠢⢀⠀⠀⢡⡀⠀⠀⣸⡇⠀⠈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠄⣊⠁⠐⠀⢁⣀⡀⠈⣀⠂⠤⢙⠪⢁⠘⢌⠉⠒⠺⠀⠤⠀⠀⣿⠀⠀⠀⡞⠉⠀⠀⠀⠉⠉⠀⠉⠀⠃⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠊⡩⡟⡏⢁⡁⠌⢠⠈⡩⠛⠢⣀⡑⢄⠑⢄⠑⡖⠚⠓⠚⠒⠒⡿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣻
⠀⠀⠀⠀⠀⠀⠀⣴⢋⠀⠄⣁⣤⣤⣶⣦⣤⣀⡘⠀⠀⠛⠄⠑⠄⢢⡼⠤⠤⠤⠤⠤⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⢀⣔⠉⠄⣠⣾⠛⡩⠄⣐⡠⠌⡙⢿⣦⠈⠄⠈⣷⡞⢶⣯⣤⣼⣃⠁⠀⢁⣶⣴⣦⡇⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢀⣿⣿
⠀⠀⠀⠀⠀⠸⢄⢢⢰⡿⢁⣚⠗⡩⢄⢌⠁⡭⠄⢻⡇⠀⠆⠌⡇⡞⠀⠀⠈⢲⣶⣀⣃⣙⣙⣉⣓⡄⠀⠀⣀⣀⠀⣀⣀⠀⠰⢄⠙⠿⠆⠐⢢
⠀⠀⠀⠀⠀⣴⠄⡁⢸⡇⢸⠰⠠⡤⠾⣄⡁⠰⡱⢸⣿⠀⡈⠐⡇⠀⠀⠀⠀⠐⠻⠷⠶⠶⠍⠀⠉⣗⡶⠊⠀⣀⣀⣀⠀⠐⠲⣾⠀⠀⠀⡠⡼
⠀⠀⠀⠀⠀⠙⠂⠼⠸⣷⡀⠅⡦⡀⠀⢊⡠⣅⠃⣼⡇⠀⢍⢢⡅⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠰⠎⠀⣠⢞⠍⠀⠩⡑⣆⠀⠹⡀⢀⠅⠊
⠀⠀⠀⠀⠀⠀⢷⡒⢂⡙⢿⣦⣁⠛⠋⠃⣊⣠⣾⠏⠀⠔⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⡀⠀⢈⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠑⣄⠤⠠⡉⠛⠟⠛⠻⠛⠉⢀⢤⠀⣢⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠱⣄⠀⠀⠁⣢⠞⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠡⣠⢀⡱⠂⡐⢀⠃⣠⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠙⠛⠋⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⣂⣂⣀⣀⣐⠒⠒⠒⢒⠒⠒⠂⣀⣐⠐⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠤⣄⣀⣐⣂⣒⣂⣀⣐⣒⣒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⣤⠤⢶⠶⣶⣶⠾⠿⠒⠀⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠀⠀⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⢛⣂⣶⣾⣽⢋⠙⣿⣻⣿⣹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣻⠫⢛⢛⢛⣛⣛⠛⣉⠛⠋⣩⣿⣿⣯⣙⡛⠛⡙⠉⡛⢛⡛⠛⢋⣙⠻⣛⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣒⣛⣯⣯⠯⠿⣿⣞⡿⠯⠀⠀⠭⣿⣿⠿⣤⡉⠳⢾⣶⣌⡳⣮⣝⠳⢾⣍⡓⠶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣷⠶⢟⣛⣿⣿⡾⣞⣿⣷⠃⣶⠀⠑⣠⣿⣿⣿⡶⡇⢿⣷⣮⠛⢿⣶⣭⣙⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣥⡶⣿⠿⣫⣿⣿⣿⣿⣿⡋⣸⢣⠊⢹⡟⢯⢻⣿⣷⡏⣯⣿⣿⣿⣄⠛⢿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣋⣵⣾⣿⣿⣿⣿⢿⡏⠙⢠⣿⡏⢠⡿⠋⠀⢻⣏⡉⠤⢝⣿⣷⡹⣿⣷⢷⣞⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠟⢹⡿⡏⠦⡸⣟⣼⣿⡇⣾⡇⢀⣧⠰⣿⣟⣇⡚⣿⣿⣧⠩⢻⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⣠⡎⡛⣑⡁⣞⣿⣿⣿⣿⠀⣿⢳⣾⣿⡀⣿⣿⣷⡍⣽⣿⣿⣧⠀⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⡿⠧⢭⣬⣷⣿⣿⣿⡿⢻⣤⣿⣿⣿⣿⣿⣿⣿⣿⢧⣳⣿⣿⣿⡆⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠭⢛⡦⡬⣾⣷⣿⣿⠟⠁⢷⣿⣿⣿⣿⣿⡟⣿⣿⣿⣻⣦⣽⢿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠐⠙⠛⠝⠻⠋⠀⠀⠀⠉⠀⠀⠁⠁⠁⠀⠙⠿⠟⠛⠘⠛⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⡤⠤⠴⠶⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⢀⠀⠠⠤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠏⢢⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⠀⠤⣉⠒⠒⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠑⣮⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡒⠤⣍⣉⠀⠀⠼⡆
⠀⠀⠀⢀⣀⣀⣀⠀⠀⡀⠀⢀⠀⢸⠀⢠⠀⠀⢂⠀⠀⣡⡇⠀⡀⠀⢈⠓⠂⠤⠀⠀⢚⡇
⠀⢀⡾⠿⠿⣯⣿⣷⣀⣷⣤⣾⣀⢸⠀⢸⠀⠀⠉⠾⠀⠋⠀⠙⢄⠀⠀⠉⠁⠀⠀⠀⠉⡇
⠀⡟⠀⢁⡀⠘⣮⣙⣿⣿⣿⣿⠉⣸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⣤⠤⠤⠃
⢸⠃⠀⠎⠀⠀⢹⡙⢿⣿⣿⣿⣿⡇⣀⣀⣀⣠⠤⠴⣰⡖⠶⢿⣟⣛⣛⣿⣿⣿⣯⣤⣤⣶⣾⣷⣤⠀⣀
⢿⠀⢸⣠⠴⣆⢸⠿⣶⣿⣿⣿⣿⣿⣴⢊⠩⣙⢿⣞⢿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⣼⣿⣿⣷⣄⠑⡄
⢾⠀⠸⠘⠉⠛⢸⣷⣌⣻⣿⣿⣿⣿⡇⠃⢔⡝⢷⣿⣏⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣸⡟⢸⠉⠹⣿⡀⠐
⠸⡇⡀⢇⠢⡈⣸⠻⣿⡿⠿⠿⠿⠿⣇⠀⠠⣷⠈⣿⣿⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠁⣾⢲⢻⣿⡇
⠀⢻⡀⢀⠀⢠⣿⣷⣬⠇⠀⠀⠀⠀⢻⡀⢴⡟⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⡄⠉⠈⣺⣿
⠀⠀⠻⣶⣶⣿⣌⡻⠛⠀⠀⠀⠀⠀⠈⠳⡀⠁⢠⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⣿⠏⠀⠈
⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠩⠞⠋⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠒⠂

⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⡴⠋⠉⠉⣹⣦⠀⠀⠀⠀⠀⠐⣠⠔⠣⢄⠂⠀⠀⠀⠀⠀⠀⣼⡁⠀⢈⣳⠀⠀⠀⠀⠀⢰⠋⠀⢰⣿⣿⣿⣿⣷⡄
⠀⠀⠸⡇⠀⣠⣾⣿⣿⠆⠀⠀⠀⠀⠄⡇⠀⠀⢸⠆⠄⠀⠀⠀⢠⠎⠡⣀⠉⣄⠜⠹⡄⠀⠀⠀⢿⠀⠀⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠳⢾⣿⣿⡿⠟⠀⠀⠀⠀⠀⠠⠊⠒⡔⠋⠄⠀⠀⠀⠀⠘⢇⡀⠘⣁⡃⢀⣰⠃⠀⠀⠀⠈⠳⢤⣈⠿⠿⣿⠿⠟
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⡞⠉⡍⠙⡄⠀⠀⠀⠀⠀⢠⠊⠉⠉⠳⡀⠀⠀⠀⠀⠀⢸⠑⢄⠀⠰⠀⢀⣴⣿⠀⠀⢀⡀⠀⠀⢀⡤⢄⣀⣠⠞⢀⡀
⠀⠀⠈⢇⠈⠋⢀⡏⠀⠀⠀⠀⠀⠸⣄⠉⠉⣰⠃⠀⠀⠀⠀⠀⢸⠀⠀⡱⠰⠰⣿⣿⣿⠀⠀⠈⠉⡩⠛⠉⠳⠞⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠉⠉⠉⠑⢄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠳⣄⠀⠀⠀⠀⢸⡠⠊⠀⠰⠀⠈⠻⣿⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠘⠃

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⣀⣠⣤⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⡔⠁⠀⠀⠈⠳⡀⠀⠀⠀⠒⢺⠒⠒⠒⢒⢾⠁⠀⠀⠀⠀⠀⢰⡞⠉⠀⣶⣭⠻⣶⠀⠀⠀⠀⠀⢀⡞⠀⢣
⠀⠀⠐⡁⠀⠐⠆⠀⠐⠷⠀⠀⠀⠀⢸⠀⢀⠔⠁⢸⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⣿⡇⣿⡁⠀⠀⠀⠀⡜⠀⠀⠀⢇
⠀⠀⠀⠑⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣔⣁⣀⣀⣸⣀⡀⠀⠀⠀⠀⠸⣷⣄⡀⠿⣛⣼⠷⠀⠀⠀⠀⠀⣇⠀⢀⡰⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠋⠛⠈⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠁

⠀⠀⣴⠒⠒⠒⠒⠒⠒⠒⢲⠀⠀⠀⠛⠀⢀⣀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣧⣤⡄
⠀⠀⣿⠀⠀⠺⠂⢀⣤⠀⢸⠀⠀⠀⠀⠄⠘⣄⣱⣄⠀⠀⠀⠀⠀⠀⢀⡤⠙⣯⣍⠉⠓⢦⡀⠀⠀⠀⢠⣼⡏⠀⠈⢻⣧⡄
⠀⠀⣟⣠⣾⣷⣴⣿⣿⣷⣼⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠻⢄⡀⠿⣿⢷⣀⡠⠟⠀⠀⠀⠈⣹⣷⣤⣤⣾⣏
⠀⠀⠙⠉⠙⠉⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠀⠀⠀⠀⠀⠀⠉⠛⠒⠂⠙⠀⠀⠀⠀⠀⠀⠈⠀⠻⠇⠈⠁

⢀⡞⢦⡤⠞⠉⠀⢒⣻⡷⠖⠀⠁⠀⢀⡀⠀⢑⡄⠈⢐⣤⣷⣤⣀⡠⠴⠞⠓⢻⣿⣟⣳⣷⣜⣏⠁
⠉⡵⠋⠀⠀⠀⠄⠈⠈⠃⢀⣀⣠⣞⡀⠀⠀⠈⠂⠉⠀⠀⡠⠊⠁⠀⠀⠀⡰⠉⠀⠀⠀⠈⣟⠁⠀⠀⠀⡠
⠎⠀⣀⡀⠀⠀⢀⡦⠞⠋⠁⠀⠀⠀⢽⡇⠠⡲⡶⠙⠷⠴⣄⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡟⠁⠐⠶⠁
⠿⠈⠀⠀⠉⠲⣅⠀⠀⠀⠀⠀⢀⣰⣾⡯⠀⠜⠀⠀⠀⠀⠈⢿⠀⠀⠀⠈⠃⢄⣠⣄⣤⠞⠀⠀⠀⠀⠙⡭⠛
⢆⠀⠀⠀⠀⠀⠈⢳⡤⠐⠀⠈⠈⠈⠙⠄⠠⠴⠀⠀⠀⠀⠀⢸⠂⠀⠀⠈⠂⠑⢷⡔⣩⠟⢳⡤⡀⠀⠀⡄
⡌⠣⣄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠀⠀⠀⢀⣤⣹⣄⡀⠀⠈⠀⢤⢼⡇⠁⠀⣸⠃⠀⠑⣤⠔⠒
⢹⣠⠞⠋⠀⠈⠤⠴⠦⠤⣤⣤⣶⠯⠝⠒⠶⣆⠀⠀⡔⠁⠀⠀⠀⠘⡦⢬⣥⠿⠯⠀⠀⠴⠧⡀
⡟⠈⢦⡀⠀⠀⢀⡤⠒⠉⠁⠀⣀⠀⠀⠀⣰⠧⣤⣸⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀
⡶⣤⣄⠑⢤⠀⢯⣀⠀⠀⠀⢠⠀⠉⠉⠘⠳⣄⠀⠈⠣⠄⢠⣤⣴⡟⠀⠀⠀⠀⠠⠤⠴⡶⠞⠋⠀⠈⢷⡴⠒
⠜⢉⡼⠇⠰⡄⠀⠈⠓⠶⠶⢆⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠾⣍⣻⣄⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⣿
⢰⠟⠀⠀⠀⠈⠳⣤⡀⡀⠀⠈⠢⣀⡀⠀⣠⠀⠀⠀⠀⠀⠟⠀⠀⠀⠈⠙⢶⡓⠦⣤⠾⠿⠛⣻⣦⡾⠃
⢏⠀⠀⠀⠀⠂⠐⣏⠀⠀⠀⠀⠀⠠⢭⣍⡄⠀⠀⠀⣠⡶⠁⠀⠀⠀⠀⠀⠀⣷⠖⠁⠀⠀⢀⡞
⠈⢣⡀⠒⠀⠀⠀⠈⢦⡀⠀⠀⠀⢰⠀⠈⠡⣤⣤⣴⠋⡀⠀⠀⠀⠀⠀⠶⠋⠁⠀⠀⢀⡴⠋⢠⠓⠶⡶⢆⡀
⣄⠀⠈⠓⢦⣄⣢⣙⣦⣽⢦⣄⠀⠀⣄⠀⠀⠀⠀⢸⡄⠀⢀⠀⠉⠆⠀⢀⣦⠄⠠⠶⠋⢀⠠⠜⠀⠀⠀⠀⠈
⣹⠊⠉⢉⡽⠛⠉⠁⠀⠀⠈⠈⠹⠓⠶⢢⡀⠀⢀⡟⠙⠢⣌⠁⠀⠀⢀⡈⢿⠀⠀⠀⠀⠀⠀⢲⡀
⠁⡉⠳⠶⠶⢤⡀⠀⠀⠀⠀⠐⠁⠀⠀⠸⠈⠀⣿⡇⠀⠀⠈⠙⠲⢭⣶⣽⣾⠶⠈⠒⡀⢀⣢⣼⣟⠲⣤⡤⠖
⠤⠁⠀⠀⠀⠀⠙⢦⡀⣠⡴⡇⠀⠀⠀⠉⠉⠑⣷⠟⢲⠠⠤⠒⠁⢀⣴⠟⠁⠀⠀⢀⣂⣾⠿⠙⢛⠻⠿⣃⣀
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠀⠀⠀⡀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠔⠉⠉⠀⠀⠀⠀⢱⠔⢾⣏
⠀⣀⣠⠶⠀⠠⡟⠀⠀⠀⠀⠀⡀⠘⣆⡀⠀⠀⠈⠙⠶⣤⠶⣶⣻⡀⠀⣀⡴⠂⠀⠀⠀⠀⢀⣠⡶⠋⢄⣀⣿
⠉⠉⠀⠀⠀⠀⢧⡀⠀⠀⢀⠔⠡⡟⠋⠙⠲⠦⠴⠦⠤⠿⠀⠀⠀⠙⡏⠀⠉⠉⠻⠛⠛⠛⡟⠢⣄⣐⣒⡿⠻
⠒⢶⠀⠀⠀⢀⣠⣽⡉⠉⠀⠀⢀⡱⠤⠀⢀⠀⠀⠈⠀⢁⠀⠀⠀⠀⠱⣄⠠⠦⠀⠀⠀⠈⣿⡀⢀⣀⡠⠤⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡌⠀⠀⠀⠀⠀⠀⠀⠄⠀⡦
⠀⠀⠀⠀⠀⠀⠀⢀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠌⠀⠜
⠀⠀⠀⠀⠀⠀⠐⡁⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢀⠃⠀⠀⠀⠀⠀⠀⠌⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⢀⠖⠀⡰⠆
⢀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠘⢄⠃⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⠔⢁⠄⠊
⠢⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠈⠂⡄⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⡠⣃⠔⠁
⠀⠀⠑⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠬⠊
⠀⠀⠀⠀⠈⠂⢈⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠙⠲⢤⡀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠱⣄⠀⠀⠀⠀⣠⠔⠁⠀⣀⣤⣴⣦⡀⠀⠀⠀⠴⠿⢿⣿⣦⡀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⠜⠁⠀⢀⣾⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠼⠁⣠⠀⠒⠒⠤⡀⠀⡠⠐⠂⠐⠠⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠖⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢀⣀⡈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡃⠀⠀⡴⣦⠀⠀⢸⠀⠀⣴⣶⠀⠀⠘⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡜⠉⠉⠉⢢⡤⠎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⠉⠀⠀⡘⠀⠀⠈⠉⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇⠀⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠾⠛⠁⠀⠈⢄⠀⠀⠀⠀⠠⠉⢄⠀⠀⠀⠀⠐⠁⠀⠲⠶⠄⠀⠀⢸⠀⠀⠀⠘⡅⠀⠑⠤⠐⢇⢀⡰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡃⠀⠀⠀⠁⠂⠀⠈⠀⠀⠀⠁⠒⠂⠈⠀⠀⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠉⠣⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⣤⠆⠀⠀⠀⡏⠀⠀⠀⠀⡰⢁⠞⠢⠤⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢹⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡟⠀⠀⠀⣼⣁⣀⣀⠴⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⣧⡀⠀⢿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⡿⠁⠀⢀⣼⣿⣄⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⠟⠳⣄⠈⢻⡿⠋⠉⠉⠉⠛⠉⠁⠈⠉⠙⢿⣿⣿⡿⠁⠀⡠⠊⠀⠈⠉⠉
⠀⠀⠀⡀⠠⠀⣀⡜⠁⡴⠋⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⢠⠎
⠀⠰⠉⣀⡀⠀⠈⠁⠎⢀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⢀⠗⠉⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠎⠀⠀⠀⣠⡖⠀⡄⠀⠰⡀⠀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠘⠦⠤⠾⠇⠆⠀⠱⣄⠀⣈⠀⠀⠀⠀⠀⢸⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠀⣀⡀⠀⠬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣀⠀⠤⠄⠀⠒⠂⠀⠈⠉⣀⣀⠠⠤⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠤⠤⠀⠒⠒⠀⠉⠉⣀⣀⡀⠤⠤⠤⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠆⠒⠒⠂⠉⠉⠀⠀⠀⠀⠀⡴⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠶⢄⡀⠀⠀⠀⠀⠀⠀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣶⣶⣾⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠋⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⣾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠈⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿
⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⣠⣾⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠂⠐⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠠⠒⠉⠉⠁⢀⠀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡇⢰⡟⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⡠⠖⠚⠛⠉⠛⠒⢤⣀⡀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣀⢀⡇⣿⣷⣿⣯⣿⣿⣉⣉⣉⣭⣙⣛⣳⢦⡀
⠐⡇⠀⠀⠐⠒⠒⠒⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣹⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⡙⣆
⠀⡟⢤⣄⣀⣀⠤⢶⣾⠟⠉⠀⠀⠀⠀⠀⢠⢾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾
⠀⢧⣀⣀⣀⣠⠶⠛⠁⠀⠀⠀⠀⠀⢀⠔⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⠞⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡕⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡴⠃⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠞⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠰⠄⠀⠀⠀⠁⠀⣤⠀⠀⠀⠁
⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⡌⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⢰⠀⠃⡆⠀⢠⣤⣤⡀⠆⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠑⠂⠀⠴⣤⣄⠀⠀⢀⣴⣶⣶⣦⠀⠀⣤⡀⠒⠀⠀⠀⠀⠐⠓⠂⠀⠐⠀⠛⠛⠀⢰⡆⣿⡉⢸⣿⣿⣡⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⠙⢯⣽⣽⣿⣛⣁⣀⣉⠋⠐⢲⣶⣶⡀⢀⣀⣀⣀⠀⠀⠀⠈⠉⠙⠉⣩⠄⣾⣿⣿⡦⠀⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠊⠀⠀⠀⠒⠀⠀⠺⠿⠿⠿⠿⠿⠶⠶⠶⠛⠛⠙⠉⠉⠉⠁⠀⠀⠀⠀⠁⠒⠲⠬⢴⣿⣏⣹⣷⣠⣶⣿
⠀⠀⠀⢠⠀⢠⠀⠀⠇⠀⠉⣀⣌⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣏⣩⣉⢀⡒⠂⣰⠄⠐⠢⠀⠠⠤⠄⢀⢩⣙⡛⠿⣿⣿
⠀⠀⠀⠈⠠⣤⡰⣶⡎⠿⣷⢹⣿⡜⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢐⠒⠂⡮⠤⢴⣀⣠⡂⡀⣼⠃⠉⡸⠁⠑⡒⠚⠀⡤⠆⠀⣀⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠙⡇⠀⢱⠀⠸⣆⠈⢷⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠀⢀⠌⠀⢠⠃⠀⣰⠏⠈⠉⠋⠑⠓⡖⠐⠥⡤⢰⣀⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢿⠀⠘⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠤⢤⣆⣀⣠⠁⠀⣰⡟⠀⠀⡌⠀⠀⡌⠀⠀⢰⠁⠀⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠁⠀⠀⠀⠀⠈⠻⠿⣶⣶⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣶⠛⠠⠤⠼⣀⣀⠰⠁⠀⢀⡇⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⡖⣾⠖⠤⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠰⣄⠀⣀⣸⣄⣀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⣀⣸⣇⣀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⣨⠟⠁⠀⠀⠉⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁⠀⣿⣿⣿⡅
⠀⠀⠀⠀⠠⠤⠤⡏⠀⠀⠀⠀⠀⠀⣷⠤⠤⠀⠀⠀⠀⠀⠠⠤⠤⣟⠀⠀⠀⣿⣿⣿⣷⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠰⠞⠈⠛⢲⠚⠋⠉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠛⢺⡛⠋⠉⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⣸⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡿⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣹⠞⣉⣭⣍⡛⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣢⠶⠛⠛⠓⢦⡜⠁
⠀⠀⠀⠀⢀⣤⣤⡏⣼⣿⣿⣿⣿⠈⣇⣤⣄⠀⠀⠀⠀⠀⢀⣀⣰⠇⠀⢠⣦⠀⠀⢹⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢧⡙⢿⣿⣿⠟⣰⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡆⠀⠾⠛⠇⠀⣸⠋⠉⠁
⠀⠀⠀⠀⠀⠀⣠⠞⠙⠶⢤⠴⠚⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠦⣤⣠⣤⠞⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣷⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⣴⣶⣿⣧⣿⣿⠁⠉⠙⠋⠻⠓⠶⣦⣼⣦
⠀⠀⠀⠀⠀⡇⠀⠠⠤⠤⢤⣤⣹⣵⠿⢿⣿⣿⣿⣿⣤⣤⣤⣰⣥⣴⣶⠾⢶⣷
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢘⣿⢿⠇⢰⡇⠀⡀⣿⣹⣿⠻⢏⢉⡁⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣀⡘⠻⠀⠀⣸⡇⠀⢱⡟⡿⣿⡤⠠⠄⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠈⠉⠿⠯⠓⠚⠛⠻⠷⠐⠀⣤⠀⣀⣀⣀⣘⣿⣧⣤⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⡿⣉⣤⣤⣄⡀⠀⠀⠀⡀⠀⠀⠣⠾⠿⠿⠷⠞⣁⣀⡀⠀⠈⠁⠀⠄
⠀⠀⠀⠀⢀⠀⣠⠶⠛⠉⠋⣿⣾⣿⣿⣿⣿⣿⣷⣦⣄⡈⠩⠭⠀⠀⠀⠀⠀⣠⣿⣿⡁
⠀⠀⠀⠀⣸⣆⣠⣤⣤⣀⣶⣾⣿⣧⡾⠛⢛⣩⣿⣿⣿⣿⣿⣷⣖⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠿⢦
⠀⠀⣀⣶⣭⢭⣿⣿⣟⣿⠿⠛⢻⣿⣶⣿⠛⠉⠀⢋⣴⣿⣿⣿⣿⣿⣿⣿⣛⣭⣿⣿⣿⣿⣿⠏⡠⠊⢙⠇
⠀⣾⢿⣷⣿⣿⣿⣿⡿⢁⡾⢛⡛⢻⣿⣿⣷⣤⠖⠋⠀⡉⠐⠮⣝⣻⣿⣿⣿⣿⣿⡿⠿⠯⣿⣿⠟⠀⣠⢳⣦
⠀⣷⣿⣿⣿⣻⣿⣿⠃⡞⣰⢏⣾⣟⣽⣿⣿⣧⣠⠤⠊⡁⢠⡀⠈⢻⣿⣿⡯⣿⣿⣶⣄⢸⣿⣿⣶⣿⡵⠛⣅
⠀⡏⣿⣿⣿⢿⣻⣿⢠⡇⣿⣸⣿⣸⣿⣿⡟⣿⣿⡶⠋⠀⢀⠌⠲⣤⣙⣿⣿⣹⣿⣿⡿⠛⠻⣿⣿⣿⡇⢠⠌
⠀⠸⡹⣿⣿⢿⣻⣿⢸⡇⣿⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣼⠀⠹⣿⣿⣿⢺⣽⣿⣿⢚⣿⣿⣿⣿⣿⢀⡓
⠀⠘⢯⣵⣟⣻⣿⣿⡜⡇⢻⡜⢻⣿⣶⣿⣿⣿⣿⣿⡤⠚⠉⠨⢶⣤⣈⣧⣿⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠇
⠀⠀⠀⠉⠉⠉⠉⠈⢧⢻⡈⢷⡀⢻⣟⠿⣿⣿⣿⡛⠓⡊⠁⣠⠆⠈⢯⣛⣿⣾⣿⣯⠻⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⣷⡀⠳⣄⣈⢁⡞⣿⣿⣿⣾⣵⡿⠿⣶⠄⠘⠉⠻⣿⣿⣿⣷⡿⣿⣿⠉⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣤⣴⡿⣱⣿⣯⠉⣉⣥⣤⣬⣩⠆⠀⠀⠀⠘⠿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣥⣤⣾⣿⣿⣿⠿⢛⣫⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⡿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡠⠶⠒⠛⠉⠉⠉⠉⠛⠒⠶⢤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠋
⠀⠀⠀⠀⣰⠋⡠⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠟⠀⢴⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠆
⠀⠀⠀⣰⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡄⠀⠔⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣠⠉⢠⡀⠀⠀⠠⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⢂⡀⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⢠⡀⡀⠀⠀⡰⡛⠁⠀⠀⠀⠀⠀⠀⢘⡄⣀⣡
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢆⠀⢁⠜⡝⠁⠀⠀⠀⠀⠀⢀⠤⠚⠛⠛⠋⠀⠀⠀⠀⡀⠀⠀⠱
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣿⢠⠃⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠑⠚⠋⠀⠀⠀⠐⠀⠀⠂⠁⠀⠀⠀⡀⠠⠀⠀⠒⠂⠀⠀⠀⡔
⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⡇⡞⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢀⣤⣴⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⣜⠣⢄⡀⣼⣸⠁⠀⠁⣀⡖⠋⠁⠀⠀⠀⡴⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠤⠂⠈⠁⠀⠁
⠀⠀⠀⠀⠀⣍⠳⠄⢀⠀⠈⠉⠉⠉⢑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⡡⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸
⠀⠀⠀⠀⠈⠆⠉⠒⠢⠄⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⠀⡄⢪⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠑⠢⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢢⣄⣀⣀⣀⠀⢀⠔⠒⠀⠀⠀⠀⠀⢐⣉⣶⠆⠀⣀⢬⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⣠⠴⠛⠉⢀⡤⣚⡭⠟⠀⠀⠀⣰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⡠⢚⡥⠋⠁⠀⠀⠀⠀⠐⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢢⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠛⣓⡶⠀⠀⠈⠑⣣⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠐⢁⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣸⠞⠁⠀⠀⢀⠔⠋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡰⠂⠀⠰⠤⠀⠀⠠⠂⠀⠀⠀⣠⠛⡀
⠀⠀⠀⠀⠚⠢⠀⠈⠁⠀⢀⡴⠊⠁⠀⠀⡠⠚⢁⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⣤⡄⠀⠀⢯⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⠲⠶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡴⠋⠀⠀⠀⣀⠬⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⡠⠔⠊⠁⢰⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⣀⠀⠀⡀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⢀⠞⠁⡠⠔⠉⠀⢀⡴⠒⠁⠀⠀⠀⠀⠀⠀⢰⠀⠈⠂⠐⠋⢹⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⣰⣫⠖⠉⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⣀⣀⠀⢨⠀⠀⠠⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢀⡾⠋⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠉⡄⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢲⡀⠀⠂⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠤⠤⠴⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⠀⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣤⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣰⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⠛⠛⠿⣿⣷⣤⣴⣶⣶⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀
⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣦⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣤⣴⣶⣿⡿⠛⠛⠛⠛⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠋⠻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠈⠙⠿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉

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

⠋⠂⠀⠀⠀⠀⠀⡵⠃⠀⠀⠀⠺⠉⠉⠉⠀⢠⣄⠀⠀⣠⠏⠀⠘⣏⢂⠀⠀⠚⠊⠁⡔⠀⠀⢰⠏⠀⠀⠈⠓⠦⠕⠀⢩⡁⠀⠀⢯⡄⠀⠉⠋
⠀⣀⠀⠘⣇⠀⠀⠀⢀⣄⣠⠾⠀⠀⢰⣀⢠⡈⢇⠀⠀⠁⠀⠀⠀⠈⠳⠇⠀⠀⠀⠀⠹⣤⠀⠸⠄⠀⠀⠀⠰⡄⠀⠐⣸⠃⠀⠀⣄⠠⣆⡀
⣨⠟⠀⠐⡼⠀⣤⠀⠀⠉⠀⠀⢀⡀⠀⠈⠉⠁⠀⠀⠀⢤⣄⣤⣄⠀⠀⠀⡴⠒⠗⠀⠀⠀⠀⠀⢀⣠⠴⠀⠀⣷⠀⠙⠃⠠⣠⠞⠁⠀⠀⠙⠛
⠀⠀⣀⡀⠀⠀⠈⠳⠶⠀⢀⣀⡼⠃⠀⠀⠀⠛⠶⠶⠒⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠋⡳⣄⠀⠛⠂⢀⡤⣀⠉⠀⣀⠀⠀⢠⡔⠚⠃⢀⡶
⠀⠀⠑⠭⡷⠀⠀⢠⣤⣄⡀⠁⠀⠀⠈⠳⠤⠤⠀⠀⠠⠖⠒⠶⠀⠀⠘⢧⡂⠀⠀⣀⠀⠈⠁⢀⣤⡀⠀⠙⠲⠖⠀⠉⠳⡄⠈⠀⠀⠚⠋⠀⣀
⡳⣄⠀⠀⠀⢠⡀⠀⠁⠒⠋⠀⢠⣄⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⣀⡀⠀⠙⠂⠀⠉⢳⣄⢰⡋⠈⠀⣠⡀⠀⣀⠀⠀⠈⠃⠀⢤⣀⣀⣠⠄⠈
⠈⠉⠀⢀⡀⠘⢦⣀⠀⢰⠀⠀⠀⠈⢳⡀⠚⠒⠚⠉⠀⠀⡽⠀⠈⠋⠍⠳⠀⠸⡲⢤⡀⠉⠀⠀⣴⠆⠈⠉⠉⠉⢠⡀⠀⠀⣀⣠⡀⠀⣄
⠶⠀⠀⢼⠁⠀⠀⠉⢀⣸⢀⡀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠚⠃⢠⢄⠀⠀⠀⣀⣀⠀⠉⣅⠀⠀⢰⡇⠀⠀⠀⢀⡀⠀⢣⠀⠘⠓⠂⠁⢸⡋⢀⣠
⡀⠀⠀⠘⠆⠀⢠⠄⠈⠁⠀⠉⠓⠲⠃⠀⠀⠀⠊⠃⠀⠀⠀⠈⠳⢬⡄⠈⠃⠉⠝⠀⠈⣇⠀⠀⠀⠘⠓⠚⠉⠀⠀⠙⠀⠀⢀⡤⠦⠘⠃⠈⠁
⠍⠀⠀⠀⠰⠵⠋⠀⠀⣰⠆⠀⢀⣀⠀⣠⠖⠋⢀⡀⠀⠚⠛⢒⠄⠀⠀⢹⠀⣠⣄⡀⠀⠋⠀⠶⠚⠻⠆⠀⠐⠒⢤⡀⠀⠰⠍⠀⠀⠀⠀⠀⢀
⠀⠘⢳⡀⠀⠀⢀⠀⢸⠁⠀⢠⢊⡏⠀⠁⢀⠀⠈⠙⣢⠀⠀⢀⡀⠀⠀⠛⠀⠀⠐⠹⠆⠀⠀⠀⠀⠀⠴⢶⣄⠤⠀⠃⢀⢐⡆⠰⢦⣤⣤⠤⠸
⡤⣄⡀⠃⠀⢠⠏⠃⠀⠀⠀⠈⠋⠀⠘⠋⠋⠛⠀⠀⠀⠀⠀⣎⠁⠠⣆⣠⣤⠄⢀⡄⣀⡴⠀⠘⢝⢢⡄⠀⢀⠤⣠⠄⠗⠋⢀⡀⠀⠀⣀
⠈⠈⠉⠠⣄⠈⠁⠀⢀⡴⠚⠃⠀⠀⠀⡶⠀⠀⠸⣆⢀⠀⠀⠿⠀⢀⡀⠀⠀⠀⠀⠉⠁⣠⡄⠀⠀⠈⠀⠀⠛⠋⣁⠀⠀⠀⢠⠇⣠⣠⠞
⠀⢶⠀⠀⢈⢳⡀⠀⠛⢀⡀⠀⠀⠴⠊⠀⠀⣰⠀⢀⣉⠁⣤⠀⢠⡏⠁⠀⠉⢢⡀⠀⠎⠀⠀⠰⠥⠤⠟⠀⢀⡀⠉⢳⣄⠸⠟⢀⡈⠀⠀⡟
⣄⠏⠀⠀⠀⠉⠁⠀⢠⠏⠃⢠⣄⠀⠀⠶⠞⠁⢠⣋⠝⠀⣇⠀⠸⠇⠀⣤⠀⠈⠁⠀⠀⠀⣠⠄⠀⠀⠀⠀⡸⠁⠀⠀⣉⠀⠀⠈⢉⢦⠀⢧
⠀⢀⠀⣤⡶⠵⠃⠀⠘⠂⠀⠀⢈⣧⠀⠀⠤⠤⣬⡀⠀⠀⠉⠀⠀⠀⠀⢻⡀⠰⢦⡀⠉⠉⢁⣄⡦⠝⠀⠛⢁⡀⠀⣀⡟⠀⠀⠀⣀⠉⠁⠀⣤
⡰⢋⠃⠀⠀⠀⠀⠀⣀⠤⠀⢀⡠⢤⠄⠀⠀⠉⠀⠉⢀⡀⠀⢰⠀⢠⢄⠀⠀⠀⠐⠹⠆⠀⠀⠀⢠⠀⠀⢠⠏⠁⠈⠋⠀⠄⡸⠃⠹⡕⠀⢠⢸
⠧⠁⠀⢴⡤⠟⠃⠴⠑⠁⠀⠛⠐⢁⡀⠀⡦⡀⠮⠖⠚⠁⠀⣸⠀⠈⢧⡀⠀⠈⠙⣆⠀⠙⠛⢉⣉⠀⠀⠸⠀⠀⣠⡀⠘⠚⠁⣀⣤⠈⠋⠈⠋
⠀⠀⠀⢠⣀⡀⠀⢀⡀⠀⠀⠀⠀⢸⠁⠀⠙⠯⡄⠀⣦⠀⣀⠁⠀⠀⠈⠁⠀⣶⠈⠺⠀⢀⣠⡄⠉⠙⡆⠀⢄⡴⠋⣀⠀⠀⠴⠅⠀⢠⡄⠄⡀
⣀⣤⠄⠀⠀⠙⣦⠀⠉⠒⠚⠀⠀⠈⠃⠀⠀⠀⠀⡴⠃⠀⠙⠝⣶⠀⠀⠀⣠⠏⠀⠀⠴⠉⠀⢀⣀⠀⠀⠀⠀⠀⠰⡝⢰⡟⡄⠀⠀⠀⠈⠓⠶
⠁⠀⠀⢀⡀⠀⡤⠀⠀⠀⠀⡷⠀⠀⣀⠀⢿⠀⠀⠀⢠⠔⠦⠀⠀⠀⣀⠀⢀⣄⠀⠀⡀⠀⣴⡵⠋⠘⠛⠙⡳⠀⠛⠁⠀⠷⠁⢲⡄⢺⡢⡀
⠀⢠⡞⠙⠃⠀⠙⢦⡄⠀⠴⠃⡠⣠⠏⠀⠘⡄⠀⠀⠟⠈⠀⠀⣤⠴⠁⠀⢠⡌⠉⠉⠁⢀⡀⠀⢀⢴⠄⠀⠀⢀⡤⠲⠂⠀⠀⢠⡇⠀⠳⣴
⣀⠀⠀⠰⢤⠀⠀⢀⡀⣀⡀⠀⠛⠁⠀⠀⢀⡀⠀⣀⣠⠾⠃⠀⠀⠀⠀⠐⣸⠃⢀⠀⠀⢠⡇⠼⠁⠈⠀⣰⠆⠘⠀⠀⠘⢦⡀⠀⢠⡤⠶⡶
⠪⢳⠀⠀⠁⢷⠀⠈⢙⠛⠋⠀⢀⡴⠒⠂⢸⠁⠀⠉⠀⠀⠀⠛⠓⠲⡄⠈⠁⠀⠉⢳⣄⠉⠀⠀⠠⡄⠀⣧⠁⠀⠀⡆⠀⠐⠽⠀⣠⠀⠀⣀
⡄⠀⢴⠒⠲⡦⠀⠀⠈⡇⠀⠀⠋⠀⠀⠀⠈⠧⠀⠉⠓⠴⠆⠀⠀⠀⣠⠚⠦⣤⡄⠀⢀⡀⠀⣠⠞⠀⠀⠀⠀⡤⠎⠀⠀⠀⢠⡴⠋⠀⡼⠁
⢜⡆⠀⠀⣀⣀⡀⠀⠀⠿⠀⣠⢴⠂⢠⣤⠀⣠⡀⢀⣠⢤⠄⠀⢄⠴⠋⢀⡔⠂⠀⠀⠀⡙⣆⠉⠐⠦⣄⣤⠀⢀⡤⡖⠖⠀⠀⠀⠀⠘⠃
⢀⡤⠶⠀⠉⠀⠉⠃⣤⠀⠘⠁⠁⠀⢀⣈⠉⠉⠀⠈⠀⠁⣦⠀⠀⠀⠀⠸⠂⠀⡠⣰⠆⠈⠛⠀⣀⠀⠀⡄⠀⡈⠁⠀⡀⣠⠟⠀⣶⠐⣶⡢⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣻⣿⣿⣿⣿⣋⡁⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢞⠘⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠿⣿⡿⠿⠿⠟⠛⠉⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣽⡷⣾⣟⣻⣻⣿⣿⡽⣿⢶⣄⠀⣀⠔⠋⠀⠀⠐⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⡿⣶⠗⢿⣿⡏⠡⠎⢳⡀⠈⢦⠹⣿⡀⢀⣀⠀⠚⠁⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣻⠅⠀⢿⣀⣼⣿⣿⠰⡖⡈⢿⡑⡈⣧⢻⣿⠉⢻⣷⠀⢘⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠤⢸⣹⣇⣾⣿⣿⣷⣆⣘⣿⣷⣷⠿⢺⠻⣦⣿⠿⡚⡟⣧⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⣿⣖⣸⣆⣿⣿⡿⢿⣿⣏⣿⣭⣿⣴⡾⣿⣿⣿⠛⡄⣃⢡⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢷⣻⣏⣿⣧⣼⣿⣷⣾⣿⣿⢿⡟⣾⣿⣿⢿⡛⣿⡇⢡⠸⠈⡜⡗⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢺⠻⣿⡧⣈⠛⣿⢹⣿⣿⣿⣶⣿⣿⣿⠛⠀⣇⢻⣷⠈⡆⠆⢡⢻⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⡇⠉⢿⣿⣷⣿⡿⢿⣿⣾⡟⠉⠁⢸⣆⣀⣸⣨⣿⣿⣿⣼⡬⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⠀⠸⡄⠉⠀⣷⣀⣽⣷⣳⣶⣿⡿⠿⣻⢿⣿⣮⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣏⣦⣤⣷⣾⠿⢿⡟⠛⣿⣏⣽⣿⣶⣾⣿⠟⠁⢸⣿⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣽⣿⣷⣿⣷⠾⢿⠛⣉⣉⣥⡇⠀⠀⠀⠀⠀⢸⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣆⠀⠉⠉⠀⠀⠈⣻⣿⣿⣿⣷⣦⣤⣀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣦⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣟⠛⠟⠀⠈⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠘⠛⠻⢯⣽⣷⡾⠁⠀⠀⠀⢀⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⣿⡇⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣀⠀⢀⡀⠀⣀⣀⣴⣿⣿⣿⠇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⡿⠀⠈⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢩⣟⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⣟⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡂⠄
⠀⠀⠀⠀⠀⠀⡰⠋⠀⢰⣿⠟⡤⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⣾⡟⣠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠞
⠀⠀⠀⠀⠀⡼⡁⠀⣀⢵⣿⡴⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠠⣿⣰⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠏
⠀⠀⠀⠀⡼⡑⠁⠀⠴⣿⣿⠃⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣾⣷⠇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⣸⢡⠁⡄⢔⣿⣿⢷⠌⢠⠇⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⠀⣺⣿⡟⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡟
⠀⠀⢠⡇⣄⡾⢐⣭⣿⣏⡏⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢰⠃⣨⣿⣟⡙⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣿⣿⣿⡑
⠀⠀⢸⢀⢪⣟⣿⣿⣟⡞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣛⣸⣿⣽⡱⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⡳
⠀⠀⢸⢸⣾⣵⣛⡽⣾⢡⠎⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⢰⣥⣿⣿⢣⢁⠔⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣾⣿⣿⣿⢣⠁
⠀⠀⢸⣜⣽⣿⣿⣽⠖⠁⢀⣠⠦⣤⢾⣿⣏⢷⡄⠀⠀⣎⣿⣿⣿⣩⠗⠀⠀⣠⠴⣤⣾⣿⣏⢳⡄⠀⠀⠘⣿⣿⣿⣿⡶⠂
⠀⠀⠀⠙⠛⠛⠋⠁⠀⢀⡏⠀⠀⠘⣿⢻⣿⠈⣷⠀⠀⠈⠙⠛⠋⠁⠀⠀⡎⠀⠀⠈⣷⢻⣿⡀⢷⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢰⠘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠀⠀⢸⡷⣟⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠸⣷⢿⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢰⡀⡂⢸⣷⢻⣷⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡀⠀⠀⣿⣹⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢧⣃⠈⣿⣟⠉⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢧⢀⠀⢹⣿⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣻⣹⠀⣿⢛⡄⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣞⣸⠀⢸⣿⡟⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣠⠀⣿⣿⡟⢀
⠀⠀⠀⠀⠀⣀⡤⢤⣀⠀⠀⠹⣷⣻⠂⣿⢿⢡⡿⠀⠀⠀⠀⣠⠤⣄⡀⠀⠀⠘⣿⢃⠂⢸⣿⢃⡿⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠘⣿⣿⡗⣿⣿⡇⡀
⠀⠀⠀⠀⣞⢡⢷⠲⣮⣦⠀⠀⠹⣧⡜⣷⣿⢿⠃⠀⠀⢠⡞⡁⢆⠢⠽⡄⠀⠀⠙⢧⡜⣹⣿⣾⠃⠀⠀⠀⠴⠱⢿⣿⣷⡄⠀⠀⠘⢿⣿⣿⣿⣿⠁
⠀⠀⠀⢸⣩⠗⣨⡟⡟⡟⡆⠀⠀⠈⠛⠾⠿⠃⠀⠀⠀⣼⣨⠂⠹⠚⢰⢹⠀⠀⠀⠀⠙⠻⠟⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠀⠀⠀⠙⠻⠿⠁
⠀⠀⠀⡟⣼⡫⠜⠁⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢜⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿
⠀⠀⠀⣧⢾⡠⢂⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⢋⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⢸
⠀⠀⠀⡷⣞⡴⡆⡀⠐⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣃⡶⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⣧⣯⠿⢷⡷⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠻⢶⠔⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡆⡠
⠀⠀⠈⣏⠁⢿⣿⣴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠺⢿⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠁
⠀⠀⠀⠘⠷⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⢀⣠⣤⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⠻⠁⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⢀⣀⡈⠁⠉⠀⠀⠀⠀⠀⠂⠄⠀⣰⡖⠛⠣⣸⣿⠟⢀⡴⢦⠀⠤⠄⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡞⣿⡏⢻⠇⠁⠀⣶⣶⣶⣤⣤⣀⣀⡀⠀⠀⢈⣤⣿⣵⣶⣿⣧⠀⠐⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⢶⣆⢶⣮⠀⢀⣿⣿⡛⢻⣿⣿⠿⣍⡳⢤⣼⣯⣏⣽⣭⠽⢿⡄⣀⣶⡎⠀⠒⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠤⢀⣸⣛⣨⣏⢠⣭⠁⢸⣿⣿⣄⣸⣀⠠⠰⣿⣾⣿⡏⢁⣻⣿⣶⣷⡰⠛⣉⡄⠀⠀⠘⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠈⣿⠄⣿⠆⣿⠂⣸⣿⣿⣂⣻⣫⣶⡴⢿⣿⡜⣤⣼⡽⢿⣆⢉⡴⠟⠛⠁⡴⠀⠳⡄⢹⣿⣿⠀⢀⡀
⠀⠀⠀⣴⡦⣶⣗⢾⡀⢘⠀⠘⠁⠀⠀⠀⠀⠀⠰⡇⢠⡅⠀⠀⠉⠈⠉⠈⠉⠛⠭⠉⠃⠉⠀⠒⣀⠙⠋⣠⣴⡆⢰⡇⠀⠀⢧⠀⣿⣿⡄⠿⠽⠶⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣷⠀⠇⠀⠀⠀⡀⣄⠂⢴⣲⣶⣶⣝⢳⡄⠀⠙⢷⡾⠋⢁⡄⠘⡇⠀⠀⡟⢀⡿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣿⣇⣄⠀⠀⠀⠀⠘⢀⣿⠿⠛⠋⢹⣙⣫⣽⣿⠿⠿⣿⣏⢿⠂⢲⣤⣀⣴⠟⢁⠀⢳⣀⣰⠃⣸⠁⢀⣀⣀⣀⡠⠤⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢺⣿⡇⠀⢸⣷⣾⠢⢤⣤⠴⠞⠛⢣⡤⣲⣿⡏⠀⣦⢹⣿⣾⣧⣤⣤⣉⣉⣴⠟⣤⠈⠻⠤⠞⠃⠀⣠⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣩⣿⣿⡶⣿⣿⣿⣶⣶⣶⣶⣿⣿⡗⣚⡽⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣻⣉⣾⢏⣷⣄⣀⣀⣠⣴⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠥⢾⣿⢿⣿⣿⣿⡿⠟⠉⠉⠉⠙⠛⠱⣺⠿⣿⣭⣼⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠾⠯⠟⠋⠋⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢕⣯⠷⣫⣖⢋⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠰⠃⠚⣶⢶⣶⣒⣒⣂⣒⡶⡶⠶⠶⠶⠶⠶⠾⠼⠤⠤⣤⣤⣦⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⢴⡶⠦⢀⣀⣀⣀⣈⡉⢉⠉⠉⠉⠙⡒⢒⡒⣶⠖⢶⠀⠀⢹⣇⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣭⣹⣭⣭⣭⣶⣦⡄⠐⡀⠀⠀⠀⢨⠏⠉⠉⢻⣿⣿⣿⡷⣶⣶⣮⠻⡀⢶⣿⡇⣿⡿⠻⢿
⠀⠀⠀⠀⠀⣀⣴⣶⣶⣷⣴⣦⣰⢟⢿⣿⣿⣿⣿⠋⢰⠀⠀⠀⠀⠸⣧⢤⣀⣸⠿⠿⢿⢇⣞⣸⣿⠀⠀⠸⣧⣷⣿⡷⣦⣾⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣍⡸⣨⣿⡿⣿⣶⣶⡀⠀⠀⠀⠀⢸⢘⣉⡙⠃⣾⡃⣏⠉⠉⣿⠀⠀⠠⣿⣿⡏⡏⣿⣿⡇
⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⣾⣿⣿⡿⣷⠏⣸⡧⣿⣿⣿⣇⣤⣤⣤⣀⡈⠈⠛⢻⣿⠼⠆⣄⣤⣠⣿⠀⠀⢀⣿⣿⡷⡇⣿⣿⡇
⠀⠀⠀⣹⣿⢽⣿⠏⠊⢉⠘⢿⣿⣿⣮⡸⣻⣷⣶⡶⣶⠦⣀⣑⣓⡃⠉⠿⣄⠈⠀⠀⠀⠀⠃⠽⣿⠀⠀⠀⣿⣿⣇⡇⣿⣿⡇⢀
⠀⠀⠰⣿⣿⢸⣿⠀⠀⠀⣀⢰⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣟⢙⡿⣿⣿⣿⣦⣔⣀⡀⠀⠀⠠⣿⡀⠀⢀⣿⣛⡋⣁⡀⡤⡦⣿⣿⣦⡀
⠀⠀⢀⣿⣿⠈⠻⡀⡀⠤⠋⣸⣿⣿⣿⣿⣿⣿⠟⠛⠓⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠛⣇⣰⣿⣿⣿⣶⣶⠙⡏⠁⠀⠀⡇⣿⣿⣿⣷
⠀⠀⠘⠻⣿⣇⠀⠕⠈⡈⢀⣿⣿⣿⣿⣿⣿⠤⠤⠾⠑⠉⠙⠛⠛⠿⠛⠛⠉⠁⢀⣤⣶⣿⣿⣦⡙⢿⡿⣿⣿⢀⡇⠀⠀⢀⣠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣷⣄⣀⣰⣿⣿⣿⣿⣿⣿⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢤⣾⡿⢫⠟⠛⢻⣿⣴⢿⡿⠽⣿⣵⡖⢿⠏⠀⠉⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠤⠒⠀⠤⠄⠀⠤⠄⣐⣢⣾⣿⠁⠏⠀⠄⠀⣿⣿⣼⡷⢦⣿⣿⣿⣦⣀⣤⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠃⠺⡀⠀⣿⣿⣿⡇⠀⠀⠀⠉⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠤⢄⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⠒⡀⠉⢙⣆⣠⠤⣄⠀⠀⠀⡀⡤⢄⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢠⠶⠚⠐⠃⢰⠋⡞⠁⢠⠸⡄⠀⢀⣠⠔⠃⠀⠀⠁⠄⡀⠀⡡⠀⡠⢂⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡴⠋⠁⠀⠀⠑
⠀⠀⠀⠀⡜⢀⣪⠉⢠⠟⡜⠁⠈⠃⢀⠁⠀⠀⢀⠀⠀⠀⠠⣤⠀⠀⠀⠀⢸⣅⠁⠀⠀⢀⠀⠀⢀⣴⠟⠀⠀⠀⢸⡁⠀⣀⠀⣀⠀⠀⠠⡄
⠀⠀⠀⢠⠇⠺⠀⢦⠀⣞⠀⢢⠀⠀⣾⠀⠀⡔⡩⠀⠀⠀⠐⠁⠁⠀⠀⢰⠁⠀⠀⢄⠂⠀⠀⢀⡾⠁⢀⠤⡀⠀⠀⠑⠚⠁⠀⠈⢋⠀⠀⠁
⠀⠀⠀⠘⡄⠀⡠⢪⠎⠀⢠⠀⣸⡤⠏⠀⠀⠳⣅⠀⠀⠀⢸⣀⠀⠀⣠⠛⠃⠀⠀⣸⢤⡤⠴⠋⡀⠀⡶⠀⠈⠲⠤⠤⠂⠀⢢⠀⠈⠳⠖
⠀⠀⠀⠀⠀⢤⣁⠈⢀⡎⠁⡸⠁⠀⠀⠰⢩⠆⠀⠉⠓⠒⠚⠋⠀⠀⣇⠀⠀⢀⠔⠁⠀⠀⠠⡏⢦⠀⠘⣄⠀⠀⠀⠀⠀⠰⠋⠀⣀⢄⢀⠂
⠀⠀⠀⡄⢀⠀⠉⠒⠒⠒⠉⠁⡠⠀⠠⢄⠀⠀⠀⠀⣠⡴⠛⢿⡄⠀⠈⠁⠈⢁⠴⠒⠉⠀⠀⠈⠁⠀⠀⠈⠁⠂⠀⠀⠐⠁⠀⠊⠁⠃⠰⠂
⠀⠀⠀⠉⠉⠀⣀⡀⠀⠀⠀⢸⠀⠀⠀⠐⠛⠀⢀⣼⠋⠀⠀⣸⠇⠀⠀⠀⠀⠘⠒⠂⠁⠀⠀⠀⠀⠠⣶⠙⠉⠀⠀⠀⣀⡠⠄
⠀⠀⠀⢠⠔⢿⠁⠂⠰⡆⠀⠘⠎⠀⠀⣠⠞⠀⣼⠃⠀⠀⠀⠉⠀⠀⣠⢔⣶⠀⠀⠀⠀⡼⠁⢀⣀⠀⠀⠀⠀⠀⣰⢏⠁⢀⠀⠄⠈⠀⠱⡄
⠀⠀⢠⢿⡇⠈⠀⠀⠀⢳⠀⠀⠀⠉⠉⠀⠀⠀⠻⠤⠄⠐⠲⣆⢀⣰⠵⢛⠵⣲⢄⣠⣼⠃⡴⠋⣿⠀⠀⢀⠔⠉⠀⠘⣦⠀⠄⠐⠀⠀⠀⢹
⠀⠀⠘⡈⢧⡀⠀⢡⣀⢌⡄⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠣⢠⡿⠞⠋⣿⠡⠏⢸⠁⠘⠁⠀⣰⠣⠐⠋⡀⢀⡸⣆⠀⠀⠀⢊⡴⠃
⠀⠀⠀⠈⠚⠟⢛⣋⠡⠚⠁⠀⠈⠀⠚⠁⠄⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠂⠐⠀⠈⠀⠀⠀⠑⢆⠀⠀⠈⠒⠢⠬⠴⠖⠻⢍⡤⠤⠚⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠁⠀⠲⠀⠀⠘⠦⣤⣤⠶⠋⠁⢀⢤⠀⣠⡀⡄⢠⢤⡄⠀⠙⠓⠁⠀⠾⡀⠀⠀⢀⠀⢀⠔⡄⠀⣀⣀⠀⠓⠁
⠀⠀⢀⠔⠙⠪⠉⠑⣮⠀⠀⡀⠶⡄⡄⠀⢀⠀⠀⢀⠀⠀⠀⠟⠞⠠⠏⠿⠁⠿⠚⢁⣤⡀⠀⠀⠀⠀⠀⠀⠠⢡⠁⠧⠞⠁⠀⣏⠢⠑⢤
⠀⠀⢼⠤⠀⠁⢦⡀⢸⠢⠤⠀⠰⠞⠁⠰⠇⠇⢀⣿⢁⡤⠶⣆⠀⣀⠀⣀⠀⠀⠀⣾⠏⠀⠀⡰⠊⣿⠆⠀⠀⠁⢰⣒⡨⠀⠀⢧⠀⠁⣀⠱⡀
⠀⠀⠘⢷⡀⠄⢀⡨⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⠊⠀⣼⡇⣼⡏⢰⡟⠀⠀⣾⠟⠒⠂⠀⢣⡈⠋⠀⠀⠀⠀⣀⡀⠀⣀⠀⠘⠦⣄⢠⡰⠃
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡎⠠⠚⠄⢸⠀⠀⠀⣼⠃⠀⢰⡿⠀⢿⠔⠙⠧⠐⠀⢏⠀⠀⠀⢆⣀⡿⠀⠀⠀⣴⠎⠉⠐⠂⠀⠌⡳⠢
⠀⠀⠀⣠⣲⣵⡶⠀⢱⡄⠉⠠⠀⠀⠜⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⣁⣀⡀⡀⠀⢏⡛⡩⠅⠠⢤⠤⠊⠀⡠⠂
⠀⢀⡾⢋⠞⠁⠀⠀⡰⠃⡠⠐⠀⠀⠀⠂⢀⠀⠠⠒⠒⠂⠀⠀⠀⠀⠀⡰⠚⠁⠐⠀⠀⠀⠀⠳⠔⠂⢀⠀⠀⠉⠈⠉⠉⠀⣀⠀⠀⠀⠉
⠀⠈⠛⠁⠀⠤⠖⠋⠀⠀⠃⠠⢤⣤⣀⣤⣤⡇⠀⠀⠁⠁⢠⠞⠉⠣⡀⠙⠋⠁⠀⠄⠀⡐⠀⢀⠀⠰⡷⠀⠀⢀⣤⡖⠨⠯⠈⠉⠿⣷⠢⡀
⠀⠀⠀⠀⡠⠀⢀⡔⠒⢠⣄⡀⠀⠀⠈⠉⠉⠀⢠⣂⡂⢠⡏⠀⠀⠀⢱⠀⠀⠀⠸⡆⠈⠀⠀⢠⠆⠀⠀⠀⣰⢋⠏⠆⠰⢀⣀⠶⢒⠿⢻⣇
⠀⠀⢴⣿⡄⠀⠉⠀⠀⠤⢴⠟⠀⠀⠀⠀⡀⠤⢀⣤⠤⣿⢀⠤⠒⠶⠺⣤⣀⠀⠀⠑⠂⠀⠂⠀⠀⠀⠀⢰⠙⣇⢖⠀⠀⢔⡅⢈⡈⠖⣮⣿
⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⣠⠞⠉⠀⠀⢸⣇⠀⠀⠀⠀⡄⠉⣏⢢⡀⠀⢠⢴⡏⠁⢠⠀⠸⢦⣶⡤⣀⠤⠣⢀⣠⢀⣞⣽⡟
⠀⠀⠀⠀⠀⠑⠀⣇⠑⠄⠀⠀⣠⠁⠒⠉⠀⠀⠀⠀⠀⣼⣻⢦⣀⡈⢀⡀⠀⠘⣆⢇⠀⠀⠘⠀⠀⠀⠁⠀⠘⣥⣞⠡⠄⠘⠩⢑⣮⡿⠟
⠀⠀⠀⠀⠢⣀⠀⠈⠂⠀⠀⠀⠓⠒⠒⠂⠦⠴⠶⠷⠚⠁⠈⠙⠪⠭⢭⣭⣑⣊⣩⠜⠀⠑⠚⠂⠄⠂⠀⠀⠀⠈⠘⠋⠣⠍⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣦⣤⣤⠴⠾⠦⠀⢀⡀⠠⡄⠀⠠
⠀⢀⡀⠂⠂⠀⠂⠀⠀⠀⠀⣤⣾⣷⡀⠀⠀⠀⣀⠴⠻⠴⠇⠀⠀⠀⠀⠀⠀⠀⠰⠄⡷⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠉⠁⠀⠀⠚⠁⠀⠀⠘⠺⠁⠀⠀⠉⠀⠀⡛⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠲⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠒⠀⠁⢀⡛⠿⠃⠈⢡⡄⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠘⠟⠀⠀⠀⠀⠀⠀⠄⠀⡤⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⢢⡈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠈⢀⠀⢀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠸⠂⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠃⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⠀⠀⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣶⣦⡀⢸⡟⣁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⡀
⠀⠀⠀⠈⠙⠻⠌⠜⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢠⡀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠛⠙⢏⡇
⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⡆⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠞⢛⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣷⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠸⡆
⠀⠀⠀⠀⠀⣿⡥⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢾⡧⣿⠴⡧⢼⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⠓⠒⢻⡀⠀⠀⠀⠤
⠀⠀⠀⠀⣸⡏⢉⡺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺⡗⣿⠒⡗⢺⡗⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⡖⠒⠒⢧⠀⠀⠀⠶
⠀⠀⠀⠠⣿⣿⣧⣤⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇
⠀⣀⣀⣀⣀⣤⣤⣴⣶⡞⢠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⢹⠋⠉
⠀⠻⣿⣿⣿⣿⣿⣿⡟⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⢠⣤⣄⣼⣿⡁⢹⣿⠏⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣽⣄⣀⢀⣀⡀
⠀⠀⠈⢻⣿⠿⠟⠋⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⢨⣭⣯⣿⣭⡅⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⢡⣏⣺⣯⠽⠛⠉⠁
⠀⢰⡟⢳⡴⠖⠻⣭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣿⣼⣿⣯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢳⣿
⠀⠈⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠓⢾⡇


⠀⠀⠀⢀⣀⣤⣄⣀
⠀⣠⡾⠋⣤⣶⣶⠍⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠺⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣯⣭⣤⣦⡔⣠⡀
⢠⡟⠀⠀⠘⢿⠏⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣀⣆⣀⣀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣵⣿⣷⡀
⢸⡇⣶⣶⣶⠎⢶⣶⣶⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣽⢹⣿⣿⡗⡀
⠀⢻⣜⠿⠋⠀⠈⠻⢟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣉⣿⠻⠟⠃⢻⣧⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣇⣺⣿⣿⡇⡇
⠀⠀⠉⠳⠶⠴⠴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠷⠝⠿⣿⡯⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠂

⠀⠀⠀⠀⠬⠀⠀⠀⣀⡀
⠀⠀⢠⣄⣾⣦⡀⣠⠤⡹⠻⣆
⠀⢀⣠⣼⣿⢿⠄⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠖⠓⠘⠛⣿⢰⡄⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣧⣿⣞⣋⠉⠈⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⠾⢻⡙⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⣿⡃⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸
⠁⠀⠸⢳⣿⢳⡦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⢙⢹⣧⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⠒⢰⣾⣖
⠀⣀⣴⣶⣿⠻⠇⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⠯⠅⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢈⣽⡟⠙⠢
⠛⠁⢘⠹⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠰⢸⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠘⠀⠉⠨⣿⣿⣤⡀
⠀⠀⡝⢂⣿⠄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⢴⣾⣟⠇⠀⠙⠆⠀⠀⡠⠖⡀⣠⣤⠀⠀⠀⠀⢀⣤⢤⣾⡶⠀⠈
⠀⠀⡄⠘⣿⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⢹⡏⠃⠀⠀⠀⠀⠀⠀⣀⡀⣹⡿⠲⢄⡀⠀⠁⠀⢘⣽⡿⠖⡤
⠀⠰⠈⢤⣿⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡇⠃⠀⠀⠀⠀⠀⠘⠉⠉⢿⣿⣤⡀⠀⠀⠀⠀⢀⢸⡇⠂
⠀⠐⠀⢸⣿⡂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⡇⠤⠀⠀⠀⠀⠀⠀⡠⠀⢺⡏⠀⠈⠀⠀⠀⠀⡀⢼⡇
⠀⠁⠈⣺⢿⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⡇⢈⡀⠀⠀⠀⠀⠀⠀⠀⢾⡟⡉⠂⠀⠀⠀⠀⠁⣸⡇⠰
⢸⣳⣄⢼⣾⡧⣀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⣭⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⢊⡇⠀⠀⠀⠀⠀⠠⠁⣼⡇⢀⡄
⣻⣀⣈⣻⣻⣃⣉⣹⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣏⣈⣿⣗⣉⣵⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣸⣉⣻⣟⣉⣇
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡄⢠⠀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣟⣿⢧⢤⡤⢀⡓⣼⠀⡇⠀⣀⠀⠈⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⢀⣤⣦⣄
⠀⠀⠀⢠⣤⣿⣷⣏⠉⠉⠁⠈⢡⠘⡀⠇⠸⠿⢧⣤⣯⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠶⠦⠴⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠓
⠀⠀⠀⠈⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣟⢛⣛⣠⢻⡤⣾⣀⣠⣤⠀⢠⡀⠀⠀⢸⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠤⣄⡨⢻⣦⣀⡻⣿⣿⣿⣩⣀⠀⠀⠈⠉⠛⠿⠷⣨⡄⠀⠸⣿
⠀⠠⣀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡶⡀⠲⢧⡁⢘⣧⣁⡨⣿⣿⣋⣰⣶⣤⣀⠀⠄⠀⠀⠀⠀⠀⠀⠛⢀⡀
⠀⠀⠈⠁⠙⠣⠴⢤⣤⣀⡀⣾⠟⠀⠀⢛⢧⠈⣼⣿⣧⣿⡇⣯⣉⠻⣿⣿⣿⣷⣶⣤⣀⡴⠒⠋⠉⣠⡅
⠀⠀⠀⠀⠀⠐⢠⣶⣿⣿⡆⣿⢸⡆⠀⣼⣕⠤⣿⣿⣯⣿⣷⣿⢿⣆⠬⠿⡿⣿⣏⠛⢿⣿⣿⣿⠉⣿⡇
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠹⡟⢀⠀⣿⣾⣷⣿⣷⡴⡔⣖⢧⣘⢿⣇⡀⡏⣿⣿⡆⠈⣿⣿⣯⠀⣿⣷⡶
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣆⠻⠎⣸⣿⣿⣿⣿⣿⣷⣾⣮⣷⠙⡓⠆⠉⢃⡸⢿⡇⡀⣽⣿⣿⠠⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⣷⣶⣹⣁⣼⣟⣿⣠⣭⣼⣿⣿⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⢻⣿⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠋⠉⠛⠉⠉⠀⠉⠻⣿⣿⣿⣿⣿⠀⠓⠘⣿⣿⣿⠉⠉⠀⠈⠻⠿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⣠⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠾⠿⠿⠛

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣸⣯⣍⣭⣭⣩⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡄⠨⡃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠈⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢐⣀⡠⠂⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠤⠤⠄⣠⢀⣂⠀⠄⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀⠄⠀⠀⠀⠀⢀
⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠿⠀⠀⠀⢄⠀⠈⡜⠀⠀⠀⠀⠀⢂⠀⠀⠀⡨⠀⠀⡀⡜⠁⠀⣠⠎
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡄⠄⠀⠀⠀⠐⠂⠀⠀⠞⠁⠀⢀⣼⠇⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠹⣿⠂⠀⠂⢤⡀⠀⠀⠓⠦⡴⠿⠟⠋⠀⠀⠀⠂
⠀⠀⠀⠀⠢⣀⡀⠀⠰⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣀⣤⣤⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⣤⣤⣶⡶⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⠉⠁⠀⡊⠐⡀⢸⠀⢱⡀
⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⢄⠀⠔⠉⠀⠀⠣⠤⠇⠘⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠠⠤⢄⡀⠀⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠠⠀⠊⠀⠀⠀⠀⠀⠉⠁⠀⠀⠢⠀⠹⡕⣿⢙⢶⣄
⠀⠀⠀⠀⠀⠐⡀⠀⠙⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠐⠀⠅⠰⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠈⠻⣦⣥⣮⠇
⠀⠀⠀⠀⠀⠀⠈⠢⠤⠜⠂⠀⠀⠀⠀⠀⠀⢀⣠⠾⠆⠁⠀⠠⠊⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠐⠀⠀⠀⠀⠁⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠢⠤⠔⠊⠉⡀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠠⠔⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠐⠀⠀⡴⠉⠀⠀⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠐⠄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠣⠠⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⢃⠌⠀⠀⠀⠀⠑⢤⡀⢀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢰⠀⠈⠂⠤⠤⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠑⠠⠤⠤⠤⠃⠀⠀⠀⠀⠈⠑⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢉⠃⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⠈⡍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢀⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡘⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣇⢻⠀⠀⠀⠀⠀⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⣀⣀⣀⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⢩⢸⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⠀⡇⠀⣀⣀⣀⣇⣸⣇⣀⣀⣀⣀⣀⣀⣸⠘⡀⠀⠀⠀⢠⡧⡇⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣹⡤⠼⠒⠒⠒⠓⠢⠤⢄⣸⡇⠀⠀⠀⠀⠀⠀⠘⡀⡧⢄⣀⣀⣸⠀⡆⠀⠀⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⡤⢤⠤⠔⠙⠦⠤⡤⢄⠈⠙⠦⡀⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⠉⠉⠉⠒⠒⠣⠭⠦⣄⣀⡀
⠀⠀⠀⠀⠀⢀⠞⢁⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⢤⠈⢢⡀⠀⠀⠀⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⢠⠃⠀⡴⠁⠀⢀⡠⠒⣉⠭⠭⢍⣑⠢⣄⠀⠀⠘⣄⠀⠹⡛⠛⠛⠛⣿⠀⢰⣶⣶⣶⣶⣶⠀⠀⠀⠀⢾⣿⣿⣿⡆
⠀⠀⠀⢀⠇⠐⡍⠀⠀⢠⢊⡔⠋⢀⡠⠤⣀⠈⠑⢄⠳⡀⠀⠈⡹⠀⢱⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⠀⠀⡠⠤⠾⠛⠿⠿⣇
⠀⠀⠀⢸⠀⢀⠇⠀⠀⡇⡜⠀⡰⢩⠒⠑⠢⡙⡄⠈⡇⢱⠀⠀⢹⡀⠈⡟⠻⠛⣿⠤⠼⠿⠿⠾⠿⢿⡖⠋⠀⣀⢤⠤⠤⣀⠈⠓⢦
⠀⠀⠀⠈⠉⠣⡀⠀⠀⡄⡇⠀⢇⢣⠀⠀⢀⠇⡆⠀⡄⢸⠀⠀⢠⡟⠈⠁⢲⣶⣿⠶⠶⠶⠶⠶⠶⡊⠀⡰⡫⢚⣭⣭⣭⡲⡕⡄⠈⢳
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢣⠹⡄⠈⠢⠭⠉⠥⠚⠀⡰⢃⠎⠀⠀⢾⣭⣭⣭⣭⡉⣿⣀⣀⣀⣀⣀⡰⠀⢠⢱⢱⡿⠁⠀⠙⣿⢸⢸⠀⠸⡄
⠀⠀⠀⠀⠀⠈⠒⣄⠀⠀⠱⢌⠓⠤⢄⣀⡠⠴⢊⡤⠋⠀⠀⡴⠾⠭⠭⠭⠭⠤⠿⠀⠀⠀⠀⠀⢘⡄⠀⣎⣌⢾⣦⣤⣔⠝⡼⡜⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠨⣂⣀⠀⠀⠉⠐⠒⠒⠒⠊⠁⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠈⠪⣗⡨⠭⣕⡪⠞⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣆⣠⣀⡀⠀⣀⣀⣄⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣄⣀⡈⠁⢁⣀⡠⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠚⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣶⣿⡯⠍⠀⡭⣙⠙⠀⠀⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡽⠾⢿⣿⠛⠁⠀⠀⠴⠀⠈⠁⠲⣄⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⠅⢀⣴⣿⣃⣠⣄⣀⡀⠀⠔⠀⠀⠀⠈⠛⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠁⡤⢫⣿⣿⠏⠀⠀⣉⠙⠳⢦⡀⠀⠈⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠫⠐⡴⠃⢠⣿⡏⠀⠀⠘⠛⣆⠀⠈⠻⢶⡀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠠⣀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢟⠀⠀⣸⡟⠁⠀⣿⣿⣄⢘⠂⠀⢠⠃⠀⠀⠃⠌⡿⣶⡇⠂⠐⠲⠀⢷⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⣆⠀⡼⢻⣿⣿⠁⠀⡴⢦⡞⢉⣾⠄⠀⠒⠈⠻⣶⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣗⠀⣿⠀⢸⣿⠀⣦⠀⣾⣥⣾⣿⢿⣶⣴⢀⣴⣻⠿⣾⣶⡆⠀⣻⣦⠀⢀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⢏⡀⣿⠀⠸⣿⣿⣇⠀⣇⠈⢉⡡⠾⣿⣿⣧⣸⠁⠸⠟⣿⠃⠠⠃⡆⠀⡏⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠐⣿⣄⡀⠈⠛⢿⣷⣿⣧⣾⣷⣤⣿⣿⣿⣿⣤⣤⣴⣟⣤⣖⣨⠃⣘⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⢻⣟⣫⣿⣦⡈⣠⣭⣿⣽⣿⣿⣉⢻⢿⣿⣿⣿⣿⣿⣿⡏⣈⢧⡀⠟⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠻⠋⠉⠉⠛⢻⣾⡿⣛⢻⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣧⣥⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠈⠛⠿⠿⠟⠷⠷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣻⠅⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠄⠀⠀⢘⠟⠋⣿⣧⣿⣿⡿⢽⡿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡄⠈⠀⠘⣭⡾⢶⣿⡻⠟⠋⣰⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣉⣁⣄⣠⣬⠋⠀⠀⣽⣿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣟⠋⠁⠀⠀⢀⣀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉




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

⠀⠀⠀⠀⠀⢠⡤⢄⡀
⠀⠀⠀⠀⡰⣿⠀⠀⠹⣆
⠀⠀⠀⡸⢠⢹⠀⠀⠀⠹⡳⣄
⠀⠀⢰⠁⢸⢸⠀⠀⠀⠀⠱⡹⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠖⠒⠒⠒⠒⠀⠉⠉⠉⠁⠒⠒⠒⠦⢄⡀
⠀⠀⡎⠀⠈⠈⡄⠀⠀⠀⠀⠱⡱⡈⠢⡀⠀⢀⡠⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⣈⡉⠭⠍⠛⠛⠛⢳
⠀⢀⠃⠀⡇⠀⡇⠀⠀⠀⠀⠀⢣⠱⡀⠘⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⡠⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⣠⠎
⠀⢸⠀⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⡗⢄⠀⠀⠔⠊⠁⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡿⠃
⠀⡈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠘⡌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⣪⢵⠏
⠀⡇⠀⠀⠰⠀⠀⡆⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠘⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⡧⢒⠥⠊⡴⠁
⠀⡇⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢱⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⣤⠇⢀⣗⠁⢀⠞
⠀⢁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢇⠀⢱⠀⠀⣀⠤⠖⣫⠔⠁⠀⣸⠈⠳⡅
⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⡗⠉⠀⢀⠞⠁⠀⠀⠀⠋⠀⠀⠹⡄
⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡀⠀⡇⠀⢁⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡀⠀⢱
⠀⠀⠸⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢠⠀⡄⡇⠀⠇⠀⣨⠤⡞⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸
⠀⠀⠀⠱⡀⠀⠀⠀⢳⠈⢣⢢⠀⠰⡀⠀⠸⠀⡇⠀⡸⠀⢠⠃⣠⡇⠀⠀⠀⠀⠀⠀⢠⠿⠁⠀⢸
⠀⠀⠀⠀⠱⡄⠀⠀⢄⠳⡀⠣⣣⡀⢣⠘⡄⢀⠃⣰⣡⠔⠉⠁⢸⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠢⣀⠈⠳⣝⢤⡙⢕⣦⣧⡿⠛⠉⠁⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠛⠛⠓⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢰⠃⠀⠀⠀⡀⣰⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡘⡆⠀⠀⢀⠇⡇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⡃⠀⠀⢀⠜⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣛⣉⣥⣴⣶⣶⣦⢹⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠿⠛⠛⠀⠙⠻⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡄⠀⠀⠀⠀⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣄⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢹⣿⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣌⣿⣿⣿⣿⣷⡀⠀⢹⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠿⠿⢶⣤⣄
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⠟⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣄⡙⠿⢿⣿⣿⣿⣿⣿⠿⢋⣡⣾⣿⣿⠟⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣶⣤⣬⣭⣥⣴⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢗⣻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢵⢟⣩⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠏⣿⣳⣿⣿⣯⣞⣯⣿⢿⡿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠜⠁⠙⠙⠉⣾⠋⡩⣻⣟⢕⠿⣻⢻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠺⠿⣷⠿⣻⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢊⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣠⡔⠁⠀⠀⠀⠀⠀⠀⣠⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣻⣿⣾⣿⣟⠕⠀⠀⠀⠀⢀⠀⡺⣫⣽⢟⢽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢛⣿⠟⠁⠀⠀⠀⠀⠁⠀⠈⢫⣴⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢇⣬⢠⡔⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧⣾⣿⣿⣻⣷⠛⠔⠀⠀⠀⠠⢛⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠺⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣴⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠁⠀⠈⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠐⢀⠄⠂⠈⠁⠈⠉⠀⠢⢄⠀⠈⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢠⠀⣆⣔⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠎⠁⠀⢈⠆⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠄⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠴⠠⠀⠀⠀⠊⠄⠀⠀⠀⠐⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠂⠀⢸⠀⠠⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣽⠟⢻⣏⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢁⢠⢴⠊⠐⢀⣨⠉⠕⡢⢦⢬⡉⠁⠀⢁⠅⢤⣀⠀⢂⢤⣄
⠀⠀⠀⠀⠀⢀⠌⢠⠔⠚⣉⡀⠀⢠⡖⠗⢒⣦⣐⣂⣁⢄⣩⡆⣤⢷⠖⠢⡆⣐⣀⢌⠑⢿⣆
⠀⠀⠀⠀⠀⡈⠀⣎⠀⠞⣁⡅⢀⠏⠘⢠⠋⠀⠀⠀⠀⠀⠀⠀⡉⠉⢹⡇⢡⠀⢈⠽⠂⢈⠈
⠀⠀⠀⠀⠀⠠⡀⠈⠓⠤⠤⣉⣀⢤⣀⡆⡄⠉⠙⠀⠀⠀⠐⢡⡴⠾⢼⡧⣤⣭⢥⣤⣴⣶⣷
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠠⠀⠼⠯⣈⡻⠓⠲⣒⠲⠶⠴⠲⢾⠷⠶⠊⡀⠤⠄⠰⠼⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠐⠉⠠⠾⠅⠠⠀⠀⠢⠸⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠄⠂⠐⢀⠀⢠⠀⠀⡐⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⠈⠀⠌⡂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠀⢁⣀⡔⢐⠨⡀⠐⠒⠑⠀⢸⠀⣀⡄⠄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠉⠚⠛⠉⠄⠂⠔⠨⢘⠳⡦⠄⡠⠐⠜⠡⢐⠠⠀⠁⠈⠪⠐⠅

⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⣟⠙⣹⠃⣺⠋⠉⣻⠀⠉⣻⠁⣽⠋⠋⢻⠛⠉⣟⠉⣿⠋⢹⣿⣿⠀⣾⠋⣙⡟⠉⠙⡏⠙⢙⣿
⣿⣿⣧⣬⣴⣧⣴⣿⣦⣾⣀⣈⣷⣴⣤⣿⣤⣿⣴⣧⣾⣤⣴⣯⣤⣾⣥⣼⣿⣧⣤⣷⣤⣼⣧⣤⣾⣧⣶⣴⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣄⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⣠⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⣀⣤⣴⣶⣶⣦⣤⣀⠀⠀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⣿⣿⣿⣿⣿⠉⠙⠛⢿⣿⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣀⣠⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠉⠛⠻⠿⠿⠟⠛⠉⠀⠀⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠋⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠙⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣀⣀⠀⣠⠤⠶⠤⣄
⠀⠀⠀⠀⣠⠚⠉⠉⠉⠙⠢⠤⢤⡞⠑⠞⠁⠀⢸⠁⠀⠉⡡⠤⢤⡀⠈⢳⠲⠤⣄
⠀⠀⠀⢰⠁⢀⡤⠒⠦⣀⣄⡀⠀⠓⢤⡀⣠⠒⢉⣰⠉⠉⠀⠀⣀⣱⠀⠸⣄⠀⠈⠣⢤⡀
⠀⠀⠀⢸⡀⢺⠀⠀⠀⠉⠀⠃⠀⠀⠀⢱⣇⠀⠏⠀⠀⠀⠀⠘⠁⠀⣳⠀⠈⠳⠤⡀⠀⠙⠦⠲⢄
⠀⠀⠀⠀⢳⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⣌⡶⠒⠲⠤⠒⠢⢤⡀⠀⠁⠀⠀⠀⠀⢸⡤⠔⠒⠤⡼
⠀⠀⠀⠀⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡔⠙⠚⠉⢦⡀⠙⣄⡀⠀⠀⠀⡴⠲⠔⠉⠉⠳⡘⡆
⠀⠀⠀⠈⣇⠈⠉⠉⠱⣄⠀⠀⣀⢔⣒⣦⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣹⣄⣀⠀⠀⠀⠀⠀⠀⠰⢣⡃
⠀⠀⠀⠀⠈⠑⠒⢤⣀⠴⣍⠉⢁⡜⢲⠚⡖⢻⠒⠒⠒⣿⠒⠒⢺⠓⡞⢲⣾⣦⣀⣤⣄⣀⣀⣀⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⡏⣏⢹⠉⠉⠉⣿⠉⠉⢹⠉⡏⣟⣏⣻⣛⣛⣻⣛⣛⣿⣹⣛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣲⣀⣀⣖⣆⣯⢿⢹⠉⠉⠉⣿⠉⠉⢹⢹⢋⣧⣯⢼⠤⠤⣼⠤⠤⣯⣼⡼
⠀⠀⠀⠀⠀⢀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣹⢸⢸⡇⠀⢠⡛⡄⠀⢸⢸⢸⢹⣷⢸⠀⠀⢸⠀⠀⡇⣸⡇
⠀⠀⠀⠀⠀⠘⢦⢤⣤⣤⣤⣤⣤⣤⣤⣼⣼⣸⣇⣠⡻⠋⢞⣆⣼⣸⣼⢸⣿⣸⠀⠀⣸⠀⠀⣇⣻⡇
⠀⣀⣀⣀⣀⣀⣸⢸⣽⢼⢽⣭⡯⡯⣯⡽⡿⢸⡵⣿⣧⠀⣼⣯⢿⠘⡿⣼⡏⢹⠉⠉⢹⠉⠉⡏⢹⣇⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣸⣸⣺⢺⢺⣒⡗⡗⣗⡇⡇⣼⡝⠉⢉⣿⡉⠁⢻⣣⡇⡟⡇⢸⠀⠀⢸⠀⠀⣇⢸⢻
⠀⠀⠀⡏⢉⣉⠉⣉⠉⣉⠉⣉⠉⣉⣹⢡⠿⣼⠷⠶⠾⣿⠷⠶⢾⡧⢧⢹⠃⡎⠀⠀⢸⠀⠀⢸⠘⡜⡄
⠀⠀⠀⡇⢸⣿⠀⣿⠀⣿⠀⣿⠀⣿⡏⡸⠀⡇⠀⠀⠀⣿⠀⠀⠈⡇⠸⡈⣦⣇⣀⣀⣸⣀⣀⣸⣄⣧⣷
⠀⠀⠀⡇⢸⣿⠀⣿⠀⣿⠀⣿⠀⡿⢳⠗⢒⠗⠒⠒⠒⣿⠒⠒⠒⢷⠒⢷⠻⣄⣀⣀⣸⣀⣀⣀⣇⣘⣆⣧
⠀⠀⠀⢧⣸⣿⣤⣿⣤⣿⣤⣿⣴⠧⡼⠤⣼⠤⠤⠤⠤⣿⠤⠤⠤⠼⡤⠼⡦⢵⡤⠤⢼⠤⠤⠤⢼⡤⠽⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⡾⠒⢲⠗⠒⠒⠒⠒⣿⠒⠒⠒⠒⢷⠒⠺⡖⢻⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡤⠤⢤⣼⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣉⣭⠿⠿⠿⠷⠶⠶⠖⢿⣿⢿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠛⣿⠀⠀⠀⢠⣶⠀⠀⠀⠀⢸⣿⠀⣿⣿⡏⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣸⡇⠀⠀⠀⢸⣿⣧⣤⡀⠀⢸⣿⡴⠛⠛⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢁⡄⢠⣤⣾⣿⣿⣿⡇⣀⢸⣿⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣬⣥⣼⣭⣭⣭⣭⣽⡇⣿⢸⣿⣿⠀⢠⣶⣶⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣼⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⢸⡟⠿⠛⢸⣿⣿⣶⣾⠟⣹⣿⣿⡿⢷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣯⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⡇⣾⣿⣿⣿⣿⣿⠋⣰⣿⣿⡿⢡⣾⣿⣭⡙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⠭⠭⠭⠭⠭⠽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⢸⣧⣿⣿⣿⣿⣿⠃⣰⣿⣿⡿⢡⣿⣯⣭⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣿⣽⣿⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣿⣿⠇⣰⣿⣿⣿⠃⣿⣿⣶⣿⣿⣿⣿⣿⡀
⠀⠀⠀⢀⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⡿⣿⣯⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⣿⣿⣼⣿⣿⣿⣿⠟⢷⡈⢿⣿
⠀⠀⣴⣿⣿⣭⣿⣿⣿⣿⣿⣿⣶⡶⠶⠶⠶⣶⣿⣿⡿⣿⣟⣩⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⢸⣇⢸⣿
⠀⢀⣿⣿⡿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⠿⢟⣿⣿⣿⣿⣿⠿⣦⠙⣿⣿⣿⣿⣏⣿⣿⣿⣿⣟⣭⣾⣿⣿⣿⣿⢣⡟⢸⣿⠃
⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣷⣾⣿⣿⣿⣿⣿⣧⡀⢹⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠏⣼⠇⣸⡟
⠀⠈⣿⣿⣯⣿⣿⣇⠘⣿⣿⣿⣿⠋⢉⣿⡿⠿⢿⣿⣾⠿⣛⣿⣿⣿⣿⣿⣿⠇⣸⡇⢸⣿⡏⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⣿⣿⣿⢏⣰⣿⠇
⠀⠀⠻⣿⣿⣯⣿⣿⣧⣌⡉⠉⣁⣤⣾⡿⠀⠀⠀⣌⢳⣿⣿⣿⣿⣿⣿⣿⠟⢀⣿⠁⣾⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⠿⣿⣿⣿⣿⠃
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢻⣿⢟⣩⣿⣿⣿⣿⣿⣤⡾⠃⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⠻⢿⣷⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠉⠉⠛⠻⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⢟⣿⣿⣿⣿⣿⣴⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢿⠟⣻⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣼⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⡴⠇⠀⠚⠖
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡶⣄⡞
⠀⠀⠀⠘⠛⢈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⡿⠀⠁
⠀⠀⠀⠀⠀⠀⢧⣶⣶⡆⠀⠀⠀⣠⣬⣗⣀⠀⠀⠀⠂⠀⠤⠄⠀⠀⠀⣀⠤⠒⠉⣿⣿⠏⢹⢳⡀
⠀⠀⠀⠀⠙⠒⠒⠛⠛⠃⢀⡠⠀⣸⣄⣉⣈⣷⣟⣒⣆⢀⠄⢂⣴⢖⠋⠁⠒⢴⢺⡿⠁⢀⡗⠂⣷⠤⠴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠈⢫⣿⣀⠤⢼⡇⣿⠋⠸⡯⠿⠽⢾⣿⣿⡖⠒⠚⢁⣄⣀⣿⠃⣠⠚⠁⢸⣿⠀⢠⣼⣿⣦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣹⣾⣿⣧⣶⣤⣧⣤⣴⣁⣇⡈⣇⠀⠀⠀⠀⢸⢃⣴⡏⡀⠀⢃⣿⡄⢠⡏⠉⢹⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠂⣼⢏⣿⢻⢹⣿⠛⢿⠻⠿⡿⡿⡿⣿⣿⣷⣶⣾⣾⣼⣿⣇⣜⣺⣗⣽⣾⣗⣤⣼⡷⢲⣶⡀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⠈⢷⡞⠈⠋⣿⣀⣌⣧⣖⣞⣎⣆⣆⠇⡇⡇⡏⢹⢸⠉⠏⡟⢻⢻⣿⣿⣿⣿⣿⣟⣽⣿⣏⣀⣀⡀
⠀⠀⠀⠀⠉⠛⠿⠟⠿⣿⣿⡟⠒⠒⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣻⡳⠹⡽⣞⣦⣇⣧⢸⣸⡏⠁⠀⢺⠓⠻⡖⠊⠽⠷⠭⠄⠉
⠀⠀⠀⠀⠀⠀⠉⢁⣐⣶⣶⣤⣤⣤⡤⠤⠤⠤⠄⠀⠈⠉⠉⠛⠛⠛⠿⠿⣾⣬⣜⣌⣎⢋⢷⡈⠀⠘⠀⠀⠱⠄
⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⣶⣶⣶⣦⠷⠶⠶⠦⠤⣤⣤⣤⣤⣤⣉⣉⣛⣛⣻⣦⠇⢀⣀⣀⣠
⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⣙⣂⣂⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠠⠀⠒⠒⠂⠠⢄⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠚⠢⢄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠠⠄
⠀⠀⠀⠀⠀⡄⠀⠠⡁⠚⠀⠆⠀⠀⠀⠀⠀⠀⠀⡜⠀⠁⠀⠀⣄⣠⢠⣤⡄⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠘⠦⡀⠈⠂⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⡜⠀⠀⠀⠀⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢⠀⡠⠈⢂⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠱⡄⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢨⠒⠆⠤⢤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠈⠀⠀⠈⠢⡀⠀⠀⣜⢉⢉⢉⣘⣻⣻⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠠⢂⠄⠈⠂⢤⣌⣉⣉⣩⣩⣽⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡂⢀⠘⠳⢛⢗⠿⡯⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠔⠁⡡⠊⠔⡡⡪⢐⠔⠀⡉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⡊⢔⠁⠠⢊⠔⠁⡠⢄⠀⠔⠄⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠔⡡⢂⢄⠁⣠⠞⡇⠀⠈⠒⠢⢄⠐⢀⣤⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠊⠄⠨⢊⠔⡁⠞⠡⠀⡇⠀⠀⠀⢀⠜⡡⠎⠅⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⢊⠔⡡⡪⠢⢪⢌⢄⢧⠀⡠⠊⠔⡼⠉⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠔⡡⡢⢊⢔⠔⠅⠕⠡⣸⠏⠀⠈⢊⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢊⢌⠔⡽⠣⠢⢊⠈⠘⠡⠀⢡⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⡡⠠⢲⢘⡁⡁⡁⠀⠑⣀⠀⠥⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⡀⢉⣬⠇⠄⡀⠀⡄⣭⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠎⠔⠁⠹⣇⠌⠔⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠈⠊⢂⢻⠎⡐⠀⢂⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡡⡁⠘⡆⠈⠀⠣⠀⢰⡤⡀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠈⠈⠄⠀⣴⠀⠀⠠⠡⠘⡇⠀⢀⣀⣀⣀⣀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢅⣀⣤⠤⠤⠤⠊⠙⠆⠀⠡⡠⡁⢙⠒⠒⠂⢀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣠⠟⠒⠲⠶⠂⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣀⣤⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠿⠿⠿⠿⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⣤⣤⡄⠀⣿⣿⠀⣤⣤⡄⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠀⠿⠟⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⠾⠿⠟⠋⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠴⠶⠖⠒⠒⠒⠛⠛⠋⠉⠉⠉⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⠶⠤⠤⢤⣤⣀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠴⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠀⢠⡀⠀⠀⠀⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠉⢹⡠⠞⢿⣦⡀⢠⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣾⣷⡟⣠⣤⣸⠀⠀⡸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠺⡤⠟⣻⠀⢿⣷⠇⠀⠀⡇⡇⣀⣠⡤⠤⠶⠶⠶⠦⠤⣧⣅
⠀⠀⠀⢀⡤⠤⠤⠤⠤⠶⠶⠶⠦⠾⠤⠤⣤⣇⣀⣀⣀⣀⣀⣤⣤⣤⣼⣀⡀⠀⠀⠸⠶⠾⠅⠀⢀⡴⠒⠋⠁⠀⠀⠀⠀⠀⣀⣀⣀⡀⠈⠓⢦⡀
⠀⠀⠀⡏⠰⠊⠀⠈⠉⠉⠉⠉⠉⠉⠑⠒⢦⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⢄⣀⡐⠳⢤⣄⣀⣀⣀⣀⡤⡦⠋⠉⠀⠀⠙⢻⣦⡀⠙⣄
⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⢛⢻⠋⠑⠊⣈⠭⠁⡪⠀⢀⣀⣄⣀⠀⠀⢳⠙⣆⠘
⠀⠀⣀⣷⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠂⢠⡊⡠⠔⠎⠀⣠⠋⣀⡀⠈⢦⠀⠈⡇⢹⠞
⠀⡜⠁⠀⠘⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⡘⡦⠰⠖⠲⠒⠀⠀⠀⠀⢤⡀⠀⠀⢀⠇⠱⠜⠀⠉⡠⠼⡀⢠⠇⡞⠑⢎⢆⠘⡆⠀⢻⢸
⠀⢣⡀⠀⠀⡇⡄⠀⠀⠀⠀⠀⠹⡶⡄⢧⠀⡄⢀⡼⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡜⠣⡀⠀⡠⠊⡠⡞⠁⣼⢸⠀⠀⠈⡼⠀⣧⠀⢸⢸⡆
⠀⠀⢙⣲⣞⢛⢁⠀⠀⠀⠀⠀⢠⣿⡄⢠⢙⠟⠿⢚⣁⠠⠤⠤⢤⡀⠀⠀⢀⢀⠀⡇⠀⠀⡞⢆⠘⣄⠑⠋⢠⡇⠀⡇⠈⠀⠀⠀⠡⡆⣿⠀⢸⢸⠁
⣠⠞⠁⠀⣸⠈⠈⢦⣀⠀⢀⣠⠞⢀⣧⢸⢸⠀⣾⣁⠀⠀⣠⠤⠤⡈⢢⠀⠀⠀⡀⡇⠀⢀⠆⠀⠓⠁⣠⠎⣠⠃⠀⡇⢸⠀⠀⠀⣴⠀⣿⠀⡿⢸
⢓⢶⢶⢾⠚⡇⡄⠀⠈⠉⢯⣄⣠⠞⣸⡘⡜⡰⢣⢫⣿⠛⢡⠤⣄⠈⢆⠣⠈⠒⠒⡏⠀⠈⣦⡑⢄⠐⠥⠊⠀⡆⠀⣇⠸⡄⠀⢠⡟⠀⡟⠀⡇⡼
⠈⠈⠀⠈⠀⣷⢡⠀⠀⠀⠀⠑⠲⠖⠃⢃⡇⠃⠂⠀⡇⢠⠃⠀⠈⡆⠈⡶⠀⠀⠀⡇⠀⠀⡇⠉⠲⠀⠀⠀⠀⠓⠄⢹⡀⠙⠒⠋⠀⣼⠃⢸⢁⡇
⠘⡄⠀⠸⡀⢸⣌⣉⣉⣉⣉⣉⣉⣛⣛⣸⣹⠀⠀⠀⡇⢸⡀⠀⢀⡇⠀⡟⠉⠉⠉⢇⠀⢰⡉⠢⡀⠀⢀⠔⢁⠴⠀⠀⠳⢤⣠⡤⠞⠁⠀⡞⣸
⠀⠙⣄⠀⠱⣄⠀⠀⠀⢀⣼⠃⠀⠀⠉⠉⠈⡇⠀⠀⢱⠀⠳⣤⠜⠀⢠⠇⠀⠀⠀⠈⠉⠉⠙⡦⡘⢦⠘⠖⠁⢠⠧⡀⠀⠀⠀⠀⠀⠀⡸⢱⠇
⠀⠀⠈⠛⠦⣤⣽⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠣⡀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠊⠀⠀⠔⣡⠞⠱⣄⠀⠀⠀⣀⠜⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⠿⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⣐⠠⢔⠁⠀⡨⠊⠉⠉⢉⡡⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣵⣿⣶⣶⣶⣭⣥⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦
⠀⠀⢺⣿⣿⣟⣠⣶⢿⢷⣦⣄⠀⠀⠀⠐⢚⣹⣿⢿⣿⡿⣿⣧⣭⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡠⠄⢾⡗
⠀⠀⢸⣿⣿⣿⣿⣿⣻⣿⣿⣿⣧⠀⠀⠐⠉⢉⡀⠘⢹⡎⠛⡂⠀⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⢇⣾⣿⣿⣶⣄
⠀⠀⢸⣿⣿⣿⣿⠉⠉⠉⢹⣿⣿⠀⠀⠀⠀⠈⠳⠀⣘⣏⠀⠙⠀⠀⠀⠀⠀⠀⢸⡿⠿⢿⡷⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠲⠆⠁⠀⠁⠀⠐⠇⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠹⣿⣿⣿⣿⠟
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠤⠄⠈⢃⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠿⢉⡋⣻⣤⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⡗⢦⡤⠞⢹
⠀⠀⢸⠀⣾⣻⣟⣻⡆⢶⠤⠀⠀⠀⠀⠀⠀⠀⡽⣧⣌⣡⣿⡛⠉⠛⠃⠀⠀⠀⠀⠀⠀⢀⡁⠀⢀⣴⡆
⠀⠀⠘⠀⠹⣿⣿⡯⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢷⡸⣿⠅⠢⢤
⠀⠀⢨⡀⢰⣿⣿⣷⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣌⣛⢃⣁⣴⠆
⠀⠀⠀⡇⢸⣿⢹⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⢎⢱⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣉⡉⢽⣿⠟⠁
⠀⠀⢴⣷⣼⡿⢸⣿⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⣸⡥⢤⣿⠬⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠙⢦⣤⡶⠒⡆
⠀⠀⠘⠛⢹⡇⠈⣏⠙⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⡱⣎⠀⠱⡑⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠈⢢⡇⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⡒⣶⣶⣶⣶⣶⡀
⠀⠀⠀⠀⢀⣭⣄⣤⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠚⢻⠙⠸⠻⠻⠻⢻⠳
⠀⠐⣦⣤⣽⣿⣟⣿⣿⣤⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⢀⣿⣟⣿⣿⢿⠀⠀⠀⠀⠀⣀⡘⢱⠀⠉⠸⠈⠈⢱
⢜⣱⣿⣿⣿⣿⣿⣿⣿⣿⣧⣱⠄⠀⠀⠀⠉⠓⢤⣴⣿⣿⣿⣿⣿⣾⣿⡂⠀⠀⠀⠉⠀⢸⣀⡤⣿⣧⣄⣼
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠉⢻⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣭⣗⣶⢶⡖⣶⣪⡅
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠋⢳⣿⣿⣷⠀⠀⠀⠀⠀⠀⢾⣵⣿⣽⣿⣯⣿⠇
⠀⠀⠘⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠉⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⠀⠀⠳⠿⣾⣽⡮⡷⠾⠃

⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⡉⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠒⠂⠀⠀⠙⠒⠀⠄⡀
⠀⠀⠀⢀⡠⠴⠛⠛⠉⠉⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀
⢀⡴⠊⠁⠀⠀⠀⠀⢀⣀⣀⣠⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⡏⠀⠀⠀⣀⠔⢲⣿⠭⠥⠔⠓⠒⠀⠀⠀⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⢳⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣰⠋⠀⠀⠀⣀⣠⡤⠶⠖⣒⣈⣉⣩⠭⠉⠒⠲⣄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢿⡀⠀⣀⡻⠮⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠏⠀⠁⠂⠆⠀⠀⠋⠈⠀⠇
⢈⠟⠋⠁⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠰⠶⠶⢋⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⣿⠀⠀⣀⠤⠶⣚⣛⣯⠥⠶⠒⠚⠃⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢱⠀⡄⠁
⠙⢦⣀⣀⡴⠋⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠴⠋⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⢀⡞⢡⡞⠀⠀⢀⡤⠶⢶⣽⡋⣩⠟⠉⠋⠛⠢⡄⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠀⠸⡀⠀⢀⡿⢱⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠁
⢸⠀⣀⣈⣩⣭⠤⠼⠤⠤⠤⠤⠧⠤⢤⣤⣀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠠⠁
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡀
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣼
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠼⠀⠀⠀⠀⣸⣄⣀⣀⣀⣴⠁
⠀⠀⠘⢦⠤⠄⠲⠶⠒⠒⣶⣒⣒⣲⡒⠲⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠤⢀⠃
⠀⠀⠀⢸⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⢀⣀⣀⣀⣀⣂⣉⣭⣽⡇⢈⠆
⠀⠀⠀⢼⠃⠀⢤⣤⣤⡤⠤⠤⠴⠶⡒⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⣀⣀⣈⣭⣤⣵⡶⢈⠆
⠀⠀⠀⣼⡃⠤⠤⠤⠤⠴⠶⠿⠿⠝⡓⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣐⣢⣭⣭⣥⢈⠆
⠀⠀⠀⢼⡃⠤⠤⠤⠤⠴⠶⠿⠿⠿⡖⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠉⠉⠉⢉⣩⣭⣥⣶⡎⣈⠂
⠀⠀⠀⠘⢧⣀⠀⠐⠒⠒⠒⠺⣋⣗⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠉⡭⢛⠜⠁
⠀⠀⠀⠀⠀⠉⢻⠛⠛⠛⠛⡿⢹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡛⣛⣷⠞
⣤⣤⣤⣤⣤⣤⣤⣽⣷⣶⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠿⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠠⠆⠈⠁⠐⠀⠀⠐⠖⢄⡀⠀⢻⣷⣿⣿⣿⣿⣿⣿⣦⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣿⣶⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⡄⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠈⠡⠀⠀⠀⠈⠙⠿⢿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡻⠻⢿⣿⣿⠀⠀⢀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠤⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣴⠀⠀⣀⣀⣉⣰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠂⠀⣀⣀⡀⡤⠤⠒⠚⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣛⣿⣿⣿⣇⠀⠠⢶⠒⠋⣁⠀⠀⠀⠀⠀⡀⢷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠁⠈⠛⢋⡩⡟⠿⠿⠛⠋⡉⠁⡞⠂⠀⠀⠀⠐⣿⣴⠆⠀⢀⡼⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢷⢀⣄⢁⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠀⠹
⠀⠀⠀⠠⣤⠴⠆⠀⠀⠉⠈⠿⠈⣿⣿⡝⣧⠦⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⢁⠈⣀⢃⡠⢀⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡠⠀⠛⠼⠇⣀⠠⣯⡀⠀⠀⠀⠀⢀⡤⢀⡀⣀⠄⠁
⠀⠀⠀⠀⢀⣄⡠⢀⣼⣧⠄⣸⡇⠀⠈⠀⠀⠀⠹⡄⢙⣥⣉⡷⠿⠀⣾⣞⣨⠃⢌⠻⠇
⠀⠀⠀⢀⣾⠏⠀⣾⡿⠃⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠛⠀⠁⠈
⠀⠀⠀⣿⠏⠀⢰⣿⡇⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⢸⣿⣾⡄⣿⣿⡇⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⣄⠀⣿⣿⣿⡇⣿⣿⣇⠀⢿⣇⠀⠀⠀⠀⠀⢸⣆⠘⠓⢤⣄
⢻⣷⣹⣿⣿⣧⣿⣿⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠙⣷⣶⣿⣿