Horseback riding Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡼⠛⢿⢿⡇⢀
⠀⠀⠀⠀⠀⠀⢠⣤⠀⢠⡘⠿⠷⠀⠀⣾⣿⣿
⠀⠀⠀⢀⣤⣌⠲⠟⠒⠚⠧⣶⠷⠾⣿⣿⣿⣅
⠀⠀⠀⢼⡿⢋⡉⠧⠀⠀⠀⠈⠳⣾⣿⡿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣶⣦⡤⣄
⠀⠀⠀⠘⠃⠈⢁⠀⢰⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⣀⠀⣤⠔⠶⣻⠀⠀⢀⠔⠉⣹⣀⠐⠀⠠⠊⠁⠰⠤⠤⠤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠠⠩⢘⠏⠁⢀⠏⠃⠀⢹⣦⣴⣿⠃⠀⠐⢠⣴⠃⠀⠀⠀⠀⠀⠉⢫⠙⡀⠀⠈⠻⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⢀⠀⠀⢸⡀⠀⠀⢰⡿⠿⠃⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⡇⢃⢀⡀⠢⠹⣿⣿⣿⣿⣝⡂
⠀⠀⠀⠀⠂⠄⡀⠋⠀⠀⠀⢸⣧⡀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⢡⡀⡇⠙⠌⠻⢿⣿⣿⡧
⠀⠀⠀⠔⢢⠀⠉⠂⠀⠀⠀⠀⠙⣿⠿⠿⠛⠋⠁⠀⢢⠀⠀⠀⠀⠀⠀⠀⡠⠒⢢⠀⠐⡀⠀⠰⣿⣦
⠀⠀⠀⡀⣰⣧⡀⠀⠀⠀⠀⡆⠀⣿⡆⠀⠀⠀⠀⠀⠀⣁⣀⠀⠀⢀⡠⠞⠁⠀⠀⢆⠀⠬⠛⣿⣿⠛⠁
⠀⠐⣀⣿⠿⠁⠙⢦⣀⣀⢴⣁⡀⠘⣿⣄⢀⣀⡠⠔⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠐⠒⠀⠈⠁
⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣶⣶⣶⣶⠶⠶⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣀⡹⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⣾⣿⣿⣿⣿⣿⠃⢠⡄⢤⣀⣦⡀⠀⠙⣿⣶⢄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣂⣿⣷⣀⣙⣿⣿⣦⣤⣿⣿⡆⢻⣄⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣸⣿⣿⣿⡿⠿⠿⠿⠚⠛⠉⣉⣩⣿⣿⣿⣿⡟⠋⠉⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣦⠀⠘⣿⣌⠛⠛⠛⠛⠓⢀⣠⣤⣶⣿⣿⣿⣿⡿⠋⣿⣧⠀⢀⣴⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⢸⣿⣿⣷⣶⣿⣿⣿⠿⣻⣿⣿⣿⣿⠟⠁⠀⣿⢸⡀⡛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣾⣿⣿⣿⣿⣿⠟⢡⣾⣿⣿⣿⣿⠋⠀⠀⠀⣿⠀⣯⣻⡿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣉⣛⣛⣽⠟⠁⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢻⠀⢸⣿⡇⢸⡟⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠰⣦⣤⣬⣿⠟⠋⢀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡆⠀⣿⠀⠀⠁⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣦⣴⣶⣿⣿⣿⣿⡟⠉⠀⠸⣿⡇⠀⠀⠀⠀⢸⣿⣦⣸⣇⣀⣠⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣄⠀⠀⠀⠈⣿⣿⡟⢻⡁⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠻⣦⡀⠀⠸⣿⣿⣦⡀⠀⠀⣿⣿⡇⠀⠃⠀⡀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠈⠻⣦⣀⠻⣿⣿⣿⣷⣦⣸⣿⣷⡇⣀⣸⣷⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⢸⡀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⠋⠉⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢻⣿⡇⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠈⣿⣷⣄⠀⠀⠀⣿⣆⠀⠀⠘⣿⣿⣿⡃⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠸⣿⣿⣷⣤⣤⣿⣿⣷⡀⠀⢿⣿⣿⣿⡀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⠻⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡻⣉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⣿⣿⣿⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣶⣤⡄⢠⣀⣴⣿⠟⢉⣴⣿⣿⣿⣻⣷⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣁⣉⠉⣉⣠⣾⡿⠿⣄⣠⣿⣿⣿⠋⠙⢻⣿⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⡶⠻⣿⣿⣿⣿⣶⣶⣶⢿⣿⣏⣀⠈⠻⣿⠏⢿⣿⠋⣠⡄⢀⣿⣿⡿⠿⠞⠛⠉⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⣼⣿⡇⢶⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣷⣦⡑⢼⣿⣿⣿⣀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢠⣿⣿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⠘⠉⠉⠁⢳⣈⣿⣆⣿⣿⣿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⢘⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣸⣿⣿⣿⡿⠀⡿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⣸⣿⣿⣿⠿⣿⣾⣿⣿⠏⠉⠛⠿⢿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣅⠻⠁
⠀⠀⠀⠀⠀⣠⣾⣿⠟⢁⣼⣿⣿⠟⠁⠀⠘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⢻⣯⣿⠏⠙⣿⣧⡄
⠀⠀⠀⠀⠀⠉⠉⠀⣸⣿⡟⠋⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇
⠀⣠⣤⣤⣤⣠⣬⣻⣲⣶⣤⣤⣤⣤⣄⡀⣀⢠⣤⣤⣤⣹⣷⣤⣤⣤⣶⣌⣿⡄⡀⣀⣀⡀⣄⡀⣴⣿⣧⣠⣶⣶⣶⣦⣦⣦⣦⣠⣤⡀⡀
⠀⠀⠈⠉⠀⠉⠉⠁⠀⠀⠈⠈⠁⠀⠁⠁⠈⠉⠉⠉⠛⠙⠋⠙⠛⠛⠋⠉⠉⠋⠀⠙⠛⠛⠛⠛⠋⠀⠈⠉⠁⠉⠉⠉⠁⠈⠉⠁⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡶⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣅⠀⠀⠀⠀⠀⠀⠐⠫⠟⠉⠙⣟⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠈⠁⢠⡃⠀⠀⠳⣍⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠘⢸⡆⠀⢶⣿⠀⠉⠓⠺⢷⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⢶⣤⣶⣺⣷⣤⠘⣆⣄⠀⠄⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⣤⣾⡉⠙⢋⡙⠻⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣿⣦⣀⠉⠻⢿⣿⡆⣀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⣶⣾⣿⣿⡏⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣆⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣧⠠⠒⠂⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⣤⡶⠂⠀⠙⣀⠀⢘⣁⠂⠈⠛⠀⠀⠀⠀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣆⠀⠸⠁⠀⢀⠀⠂⢹⡇
⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠈⠛⠃⠈⢋⣤⡀⢸⣶⣶⣀⣤⡼⣿⣿⡿⣿⠿⠟⠙⠿⠋⠀⠀⠐⠚⠛⠛⠳⢾⡇
⠀⠀⠀⢘⣿⡗⠀⠀⠀⠀⠀⠐⠂⢠⠄⠈⠀⠘⣿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠞⢷⡀
⠀⠀⠀⠀⢻⣿⠆⠀⠀⠀⠀⠀⠛⣤⡀⠀⢀⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡐⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣍⡙⠳⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠙⠻⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣦⡙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢛⣛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠟⢿⣿⣷⣦⣤⡴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣀⠀⠈⠓⠀⣉⠻⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⣤⢀⣤⣶⣶⣶⣿⣣⣾⣿⡧⠀⠀⢸⠃⠀⢹⣆
⠀⠀⠀⠀⠀⠀⣴⣘⠷⢎⠸⠋⠀⠀⠺⢯⣿⡿⣿⣿⣿⣿⠀⡄⠘⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠉⠉⣼⣿⡇⠀⠀⠀⠀⠀⠈⠙⢮⡝⢿⣿⣾⡇⠀⠀⡐⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠢⠙⠿⢁⣤⡴⠃⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣀⣀⠜⢸⡇⠀⠀⠀⠀⠀⠀⢰⡷⠛⠉⠀⠀⢀⣴⡇⢘⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠁⣩⠟⠁⣀⣨⣧⠤⠔⠒⠉⢀⡔⠁⠀⠀⣠⠤⠞⠀⠠⣴⠺⠿⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠈⠉⠁⠀⣿⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⢰⠟⠂⠀⠻⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠘⣧⣹⣿⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠉⢻⠀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠶⠿⠶⠆⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⢀⣾⣿⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡠⠚⠛⠛⠒⠒⠒⠂⠀⢻⡀⠀⠀⠀⢀⣠⣴⠞⠋⠀⢠⠂⠀⢸⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣴⠾⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢰⠋⠉⡄⠀⠀⢰⠏⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⢰⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢸⡀⠀⠹⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⢸⣇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⣧⠀⠀⠹⣆⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠿⠟⠀⠀⠀⢹⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣷⣦⡀⣀⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣷⡀⢀⣾⣟⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⠟⠋⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣽⣤⠎⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣵⣿⠀⠀⠀⢀⣰⣞⠉⠉⣀⣿⡑⠀⣀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠴⠞⢩⣤⠽⠛⠋⠁⠈⣳⡞⠁⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⠻⡟⠉⣿⣿⡧⠞⣠⠶⠊⠁⠀⠀⠀⠀⢸⠛⣷⡐⠶⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⣉⠢⣜⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⢳⡱⡄⢀⣀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠼⣿⣿⣿⣿⣿⣿⡋⠙⠻⠾⠿⠦⠤⠤⠤⠤⠤⢤⣤⣞⣉⣧⣀⣝⡿⢭⣁⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⠒⣶⡟⠻⠿⢶⣿⣿⣿⢳⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠛⢼⣏⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⣿⣿⣿⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣯⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⡽⠉⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣰⠁⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣾⣯⣋⣞⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⢀⡀⠀⠀⢀⣠⡾⠁⠀⣿⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⠿⠛⠷⠟⠀⠀⠀⠹⣇⠀⠀⣤⠀⠀⠀⠀⠠⣤⣀⢿⡃
⣘⣏⠛⠋⠈⠁⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢀⣿⡀⠀⠀⠀⠀⠀⠙⢷⣽⣦
⠘⠧⣄⣠⠀⣠⣶⠊⠈⠀⢹⡄⠀⠀⠀⠀⣼⠛⠻⣿⡉⠛⢿⣿⠒⠶⠤⠤⠤⠶⠒⠛⠋⠉⠛⠓⠒⠓⢦⣄⣀⡀⠈⠉⠓⢦
⠀⠀⠙⠛⠛⠁⠁⠀⠀⠀⠀⣷⠀⠀⢀⡾⠁⠀⠀⠀⠻⡄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡈⠉⣹⢶⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⡟⠀⠀⠀⠀⠀⠀⣷⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣩⡏⠀⠙⢁⡼⠻⣄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠶⠎⠀⠀⢹⡀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡙⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣉⣙⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣉⢹⣆
⡶⠒⠲⡶⠶⡶⡶⡶⢶⡶⣶⡶⡶⣿⢿⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡭⠄⣀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠀⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠐⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠳⠂⢠⡀
⠀⠀⠀⠀⠀⠀⠗⢆⠘⠆⢣⣀⠤⣄⣀⠀⠀⠀⡆⡌⠑⠦⠀⠀⡠⠀⠀⠃⠠⡄
⠀⠀⠀⠀⠀⠀⣰⠋⠉⠑⣰⡌⠆⠀⠈⠉⠓⠦⢅⠁⠀⠠⠒⠪⠴⠒⠁⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡇⢀⡔⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣉⠀⣤⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠈⢃⡞⠈⠁⢸⠇⢀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⢄⠘⣆⠀⠘⠆⠀⡀⡀⠠⣄⠀⠀⠀⠀⠀⠀⠀⡠⢞⡭⢭⣉⡓⠲⢖⡂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠀⣸⣧⠔⠋⡁⠀⠀⠀⠀⠀⠀⠘⠦⠘⢦⠀⠀⠐⠁⠸⡔⢬⣀⠑⠒⠒⠶⢴⣋⠐⠁⠐⠒⠦⢭⣉⣩⠴⠂
⠀⠀⠀⠀⠀⡞⠀⠉⢉⠀⠀⠚⠉⠈⢧⠀⠙⠄⠀⢀⣠⠴⠂⠀⠀⠀⠈⠳⣄⠈⢦⡀⢻⡀⠈⣳⠀⠠⡀⠀⠈⠳⣄
⠀⠀⠀⠀⢸⡇⠺⢀⡝⠊⠀⠀⠀⠀⢸⡆⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠱⠀⢏⠉⠁⠀⠀⢹⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠘⠃⠀⠀⠀⠀⠀⠈⠋⠉⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡄⠀⣀⠘⢦⡀⠀⠀⠀⠇⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠁⠤⠤⠤⠄⠀⠀⠀⠀⠀⣸⢠⠇⠀⢹⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠉⠀⠐⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡾⠀⠀⠀⠁⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢠⣀⠀⢳⠀⡇⠀⠈⠉⠁⠀⠀⢀⠞⠀⡇⠀⢀⣀⡤⠴⠚⠁⠀⠀⠳⡀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⡁⠸⠀⠇⠑⠲⠤⠤⢀⡴⠟⠒⠀⠀⠉⠉⢠⣀⣀⣀⣀⣀⡤⠤⠌⠓⠒⠀⠀⢠⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡄⢰⠆⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠈⠀⢈⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡄⠀⠀⣧⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣈⠀⠠⢿⣀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣉⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⡀⠀⠘⣿⣀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⣛⣫⣥⣤⣶⡾⣡⣤⠤⠀⠁⠈⠀⢀⠀⠀⠀⠀⢀⡿⢹⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣤⠀⠘⠡⠭⠭⠵⠶⠶⠦⢤⣴⣟⣿⣶⣤⡀⢀⡴⠋⠀⠀⢀⣀⠉⡰⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠶⠄⣸⠷⠂⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠙⠻⠷⢏⠀⠀⠀⠀⠀⢠⠞⠀⠀⡴⠁⣲⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣿⠟⠛⠉⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⢠⡿⠇⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⢶⠻⠿⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⣿⣿⠁⠳⡀
⠀⠀⠀⢀⣿⡇⠀⠀⠀⣠⡆⠐⢲⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄⠣⣴⣶⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢸⣿⡟
⠀⠀⠀⡞⢿⣦⣤⣴⡾⠛⣠⡴⠋⠀⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⢦⣈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀⣻⠀⠀⠈⠙⣧
⠀⠀⣼⣇⣀⣼⢛⡥⠖⠋⠁⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠬⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠘
⠀⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⣠⠄⠀⠀⢀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠘⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣂⣠⠴⠖⠋⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠛⠋⠁⣀⣤⠶⠛⠉⠀⠉⠀⠀⠀⠀⠀⢀⣀⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣰⣾⣿⣿⣤⣤⣤⣤⣤⣤⡶⠀⠀⠀⢀⣀⠤⠤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢹⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣾⡇⠀⢐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠉⠈⠉⠛⠛⠟⠛⠙⣿⣿⡄⠀⢀⠀⠀⠀⠀⠀⡘⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠁⠢⣶⣾⣿⣿⣿⣦⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡖⠶⠀⠀⡀⠈⠋⠀⠀⠀⡤⠀⠀⠀⣠⠀⠀⢋⠁⢂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⡩⠁⠈⠀⡄⠀⠀⠀⡀⠀⢀⡀⠈⠀⠀⠋⣰⣿⣷⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢄⠀⠀⠘⢄⠀⠀⢻⣤⣤⡔⠀⢀⠌⠀⢻⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠁⠂⢠⠀⠑⣄⠀⠉⢉⠠⠐⠁⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠬⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢤⠀⠀⠀⠀⠀⢀⠈⡄⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠿⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠘⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣤⣤⣤⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠂⣀⣻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠟⠛⠛⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣨⠀⠀⠀⠀⠀⠀⠀⠄⠻⣿⣯⣟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠠⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠔⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢶⣾⣿⠉⠻⢿⣿⣶⣤⣤⣀⣠⣤⣴⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉⠁⣄⡈⠂⠀⠀⠤⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠁⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠄⠄⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠒⠀⠉⠁⠒⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠹⣿⣧⠀⠀⣀⠠⢆⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠁⠐⠛⠛⠃⠉⠀⠀⠀⠱⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⡰⠀⠀⠀⠀⠠⠂⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⡄
⠘⢿⣦⣤⣄⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡏⠀⠊⠀⠀⠀⠀⠐⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠑⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⣀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡻⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣬⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠻⣷⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠯⣍⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠛⣯⣿⣿⣯⣱⣎⡛⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⠱⣾⣤⣀⠀⠀⠀⠀⠀⢠⡾⡿⠻⡉⢠⣿⣿⣿⣿⣿⣿⣽⣶⣏⣬⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣌⠉⢉⢩⡁⠈⢰⣤⣿⣿⠁⠀⠁⠾⠁⣿⣿⠉⠦⣈⠉⠛⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⢀⣼⣿⣅⠁⢈⠀⠀⠀⠀⣠⣾⣿⣿⣷⣤⡀⠘⠀⠀⢠⡇⠀⠀⠀⠉⣙⠿⠟⠻⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠁⠀⠀⠀⠈⠙⢿⣾⣿⣟⣿⡗⠐⢾⣷⡦⠀⠘⠑⠽⠿⠿⠏⡈⠉⠛⠛⠒⢾⣗⣒⣒⠒⠌
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇⠀⣠⡶⠂⠀⠀⠀⠀⢻⣿⣿⣾⣟⠀⠀⢶⣾⣿⠆⠀⠀⠀⠀⠀⢻⣦⠀⠀⢀⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠁⠁⡄⠀⠀⠀⣀⠀⠙⠻⠿⣿⣆⠀⠈⠁⡟⠀⠀⠀⠀⠀⠀⢸⡏⠀⠒⢿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣧⡀⠀⠀⠀⠉⠉⠐⠒⠺⣿⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡋⠁⠀⢀⣬⣶⣦⣾⣧⣴⡄⣤⡀⢰⢿⡏⠀⣰⠀⣰⠀⠀⠀⠀⠀⢀⣀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀⠀⡸⣿⣿⣿⠟⠻⣿⣿⣿⣷⣸⣾⣷⣏⣹⣾⣿⠀⠀⠀⣠⣶⣿⢏⡴⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⡰⢡⡟⠉⠀⠀⠀⠀⠉⠙⠻⠿⠿⣿⣏⢸⣿⣿⠀⠀⠠⢿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢀⡜⣱⣿⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⠛⢻⡄⠀⠇⠸⣿⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡇⠸⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣄⠀⡀⠀⢻⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠘⣻⣦⡀⠈⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢤⣀⣀⣀⣻⣎⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣙⣧⣡⠀⠈⠙⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣯⠇

⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣶⣶⣿⣼⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡛⠋⠁⠀⠀⠀⠀⠀⠀⣀⣶⡿⣫⣴⣿⡿⣿⣿⣤⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣅⣀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣄⠠⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡄⠀⠀⠀⠀⢲⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣤⡾⡇⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⣈⣿⣿⣼⣿⣿⣿⣿⣿⡿⣯⠉⢙⠿⣿⣿⣹⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠆⠀⠀⢺⣿⡇⣿⣿⣿⣿⣿⣿⣿⡜⡗⣩⠞⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣄⠀⣽⣿⣷⣿⣿⠻⣿⣿⣿⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣾⠿⣿⣿⣿⣿⠞⢛⢿⣯⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⢿⡛⣻⣤⣀⣼⣿⣦⣀⠉⠈⠙⠻⠷⠌⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⡿⠁⠀⠀⠈⠻⣿⣿⡝⢿⣿⣿⣿⣷⣶⣤⣤⣀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠟⠛⢻⣿⣿⣧⣄⡀⠀⠀⠀⠈⠻⣿⡀⠹⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣤⣴⣶⣿⣿⣭⡉⠙⢿⣶⡆⠀⠀⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⡾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡟⢿⣷⡀⢸⣿⣿⣤⣼⣿⡇⠀⣼⣿⡿⣿⣿⣿⢻⣿⣶⣶⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⠘⣿⣿⣧⣿⣿⣷⣼⣿⣿⣿⣿⣿⣥⣼⣥⣽⡿⠛⠁⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⣷⣼⣿⣇⣹⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⢏⠁⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢻⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠈⠛⠿⣿⣾⣷⠀⠀⠀⣀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠈⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣈⣿⣿⣿⣿⣿⣿⡟⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⣹⣿⡅⠀⢰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠟⠛⠛⠛⠿⠿⠛⠓⠈⠀⣴⣾⣿⣤⣤⣴⣶⡿⠿⠛⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢻⣿⡿⢿⣿⣿⣿⣿⡆⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠟⠋⠁
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⣠⣾⣿⣿⣌⣻⣿⣿⣿⣿⠾⠃
⠀⠀⠀⠠⠶⠟⣻⣿⣿⣿⣿⣿⢸⠏⠀⠀⠀⣹⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠃⠘⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣧⡀
⠀⠀⣤⣭⣿⣿⣿⡿⢻⡿⠃⠀⠀⠀⠀⢹⣿⣿⠟⠀⠀⠀⠈⠛⣿⣷⡄
⠀⠀⠀⠈⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⡿⠟⢻⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣊⣥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⡴⠂⢋⠏⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡀⢀⣴⠟⢀⡴⠇⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⡆⠀⠀⠀⢀⣀⣀⠹⠿⠋⢈⣁⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣠⡤⠶⣿⣫⣿⣥⠴⠓⠁⢨⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⡿⠟⠉⠀⣠⠲⠛⠛⠟⠃⠀⠀⢀⣿⠠⠄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠀⠀⢠⠞⠁⢠⣰⠆⠄⢠⣶⠞⠋⠁⠀⢀⣠⠖⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⠿⠋
⠀⠀⠀⠀⠀⠀⢀⣄⣴⣿⣿⠟⠁⠀⠀⠀⢠⡇⠔⠀⣼⠏⠀⢠⡿⠛⠿⠳⠟⠇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⠀⠀⢰⣠⣾⡏⠀⣴⣾⡟⠐⢦⡿⠁⠀⠀⠀⠀⠀⢀⢀⣀⣄⣿⠁⠀⠀⢠⡆⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⢀⣀⣾⣿⣿⣿⡗⣾⣏⠛⠃⠀⡿⣧⣶⣶⣶⣶⣿⣏⣿⣿⣿⣟⡍⠀⠀⠀⢀⣿⠛⠿⠛⠋
⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⣶⣿⡿⠋⠉⠈⣷⣼⡏⠑⠲⡄⠘⠛⠻⠿⢿⣿⡿⠿⢿⣿⣯⣿⡇⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠸⣿⠃⠐⠋⡙⢏⠀⠀⠀⢠⣿⣿⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢠⣾⣾⠋
⠀⠀⠀⠀⠹⠿⣿⠖⠋⠉⣿⣺⣆⠀⣠⣾⡿⡩⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣇⠚⢿⣿
⠀⠀⠀⠀⠀⠀⠙⣷⣶⣞⣽⣿⡶⠖⢻⣿⠃⢷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⣧⠀⠀⣿⡄⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠀⣼⠇⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣷⡍⠀⠀⢸⣷⡀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠷⠙⢿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠈⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⢼⣿⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⠂⠀⠸⢋⠅⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢠⠄⠀⠁⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣶⣶⠶⠦⣤⣤⠆⣤⣤⣤⣤⣶⡷⣿⠿⢗⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣀⣤⢀
⠀⠸⣷⣾⡿⠀⠀⣄⠀⠀⣄⡀⠀⠀⠀⢀⠀⠸⠂⠀⢸⣹⣃⣴⣄⠀⠀⢀⣤⣶⣿⣿⣾⣿⣿⣿
⠀⠀⣾⣿⣧⠀⠘⣏⠠⠿⠿⠗⣰⣿⡅⢸⣷⠶⠃⠠⡺⠀⠉⠙⠿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟
⠀⠀⠈⠁⠈⠀⡠⠈⠀⣀⠠⠘⡛⠻⣿⣿⣿⣄⡀⢀⠀⠠⢠⠀⡀⠀⠀⠹⣿⣿⣿⡿⠻⠿⠟⠛
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠋⠀⡔⠀⠀⠀⠹⣿⣿⣿⣮⠏⡇⠢⠄⠄⠀⠀⠀⢹⣿⣿⣇
⠀⠀⠀⠔⣈⡀⠙⢦⢐⡥⠚⠁⡄⢀⠀⠀⠈⢿⣿⣗⠓⡿⠊⠱⣶⣤⣀⠒⠚⠻⠿⣁
⠀⠀⠠⣤⣈⣡⠆⠈⣧⣤⡤⢾⠀⠀⠀⠀⠀⠀⠻⣿⣶⣷⡄⠙⣿⣋⠈⠙⢦⠀⠀⠀⠙⢄
⠀⠀⠀⠰⢦⣅⠎⠻⢄⡀⠉⠚⡦⢄⣀⣀⣀⣀⣀⠼⠋⠹⣷⠀⢻⣿⣆⠀⢸⡇⢐⡄⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⢷⣄⣹⣧⢀⡾⠀⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠀⠀⠀⠀⢀⠔⠀⠀⠹⣦⣽⣿⣿⣿⡀⠀⠀⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⡀⢹⡇⣷⣿⠏⠀⣰⠁⠁⠀⡸
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣤⠦⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⡇⣼⠇⠉⠉⣀⠔⠳⡄⠀⠰⠁
⠀⠀⠀⠀⠀⠀⢈⣿⡟⠻⡟⠀⠠⠀⠀⠀⠀⠀⡔⠂⠀⠀⡄⣰⣟⡠⠔⢺⠁⠀⠀⢸⢀⣠⠀⢀
⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠘⢆⠀⢀⡴⠤⠷⢤⡇⠀⠂⢸⣿⣿⣿⣶⣿⣾⣦⡀⠀⢸⣼⣿⣋⠀⠈
⠀⠀⠀⠀⠀⠈⣿⣿⣀⠀⠀⠀⠉⠉⠀⠀⠀⢀⠇⠀⣠⣿⣧⡀⠉⠉⠙⠛⠛⠁⠀⠈⠻⠛⠁⠱⠀⢄
⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡎⣠⡜⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣄⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⣀⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⡿⠆⣉⠽⢛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⣾⢁⠀⠈⠃⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⢨⡟⠀⠀⠀⠀⢶⣶⠏⠀⠀⢸⡜⠛⡄⠙⠋⠲⡍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣀⣼⣷⡦⠄⠀⢀⣸⡿⠀⠀⠀⡈⠀⡀⠹⣆⣈⠀⣠⡶⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⢇⠀⠀⠀⢘⡂⠻⣇⠀⠀⠀⠟⡃⠘⢶⣾⣏⡼⠋⣀⠳⡄
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⢀⠀⠀⠸⣿⣶⡉⠦⡀⠀⠀⠡⡀⠉⢢⡙⣷⢲⡏⢋⡁
⠀⠀⠀⠀⠀⠄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠈⠳⣤⡀⠁⢠⣤⠿⣁⡷⠈⠋
⠀⠀⠀⠀⠀⠀⠀⡴⣯⣤⡀⠀⠀⠀⠀⠀⣿⡽⢻⡇⣀⠀⠀⠀⠉⣉⠉⠉⠀⠈⣤⣀
⠀⠀⠀⠀⠀⠀⡄⠀⠹⣦⡀⠀⠀⠀⠘⣻⠞⠁⠙⣇⠐⠡⡀⠙⠋⡁⠉⢳⠀⠈⣠⠀⠁⢦
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣷⠅⠀⠠⠊⡁⠀⠀⠀⣿⠀⠀⠈⠃⠀⠉⠈⡌⠀⠀⠁⠀⡀⠀⠣
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡷⢈⣴⠀⠀⢇⣀⡀⢸⣿⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠘⠊⡀⣡⠀⠀⠀⢀⠀⠀⠅
⠀⠀⠀⠀⢠⠄⣶⠀⠠⡟⠉⢘⠁⠀⢸⡏⣿⣿⢿⢁⠀⠀⠙⠀⠀⠀⠴⢞⠂⣀⠉⠂⠀⢀⠀⠁⠤⠀⣠⠜⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣀⢷⠀⣆⠀⠀⣸⣧⣿⣿⠈⣆⠁⢀⡀⠀⠰⠁⠀⠈⠀⠈⠁⢀⢀⡎⠐⠀⠀⡠⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠤⠘⠼⠿⣿⣿⣿⣿⣧⣿⣿⡄⡘⣦⠈⣧⡀⠀⡄⠚⠳⡌⢂⣤⠀⣄⡴⠄⠴⠋⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣵⢞⣿⣿⢣⡾⠁⠈⠑⢬⣁⢀⠘⠢⢀⠘⣮⡧⣽⠃⠀⠀⢀⠴⠓⠊⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣥⠀⠆⠀⣿⣿⢉⣠⣐⡛⠲⢄⠉⠛⠦⡂⠀⠀⠈⠲⡀⠀⠀⠀⢨⡐⢤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠶⠀⠀⠀⢿⠛⠤⠀⠀⠀⠀⢀⣽⣷⣶⢶⣿⡷⠆⡀⠀⠐⠀⠀⠀⠁⠁
⠀⠀⠀⠀⣀⡀⠀⢀⡞⠀⠀⠀⠡⡄⠀⠈⠀⠀⠀⠀⠀⠐⠋⠐⣿⣿⡿⠟⠁⠀⠀⢬⠃⠀⡄
⠀⠀⣠⡞⠛⣻⣿⣿⡇⠀⠀⠀⠈⡛⢶⢶⣤⢤⡶⠀⠀⣠⣀⣮⠔⠉⠀⠀⠀⠀⠀⠀⠙⢦⠠
⠀⠀⢿⣤⣿⣧⣉⡻⣧⠀⠀⠀⠠⠀⣜⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢣
⠀⢠⣾⣿⣿⣏⣉⣿⣿⡇⠀⠀⠂⠀⣸⡿⠻⣿⣿⣿⣿⡟⠋⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢱
⠀⠀⠈⠛⠛⠛⢶⣄⣮⣇⢀⠀⠀⠀⣼⠁⠀⠈⢻⣿⣿⠇⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸
⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡆⢀⠀⢀⡟⠀⠀⠀⢸⠗⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⣀⣃
⠀⠀⠀⠀⢐⣿⠛⢙⣧⣾⠇⠀⢠⡎⠀⠀⠀⠀⠈⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠈⡹
⠀⠀⠀⠀⣺⣿⢿⠿⠛⠏⠀⢠⡆⠀⠀⠀⠀⢠⡘⠀⠸⡀
⠀⠀⠀⠀⠻⡏⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠑⠡⡂⠱⣄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣈⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠂⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠤⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠘⣇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠟⠿⢿⠟⢻⠿⢿⠿⠻⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣾⣷⣿⣶⣿⣷⣾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⣿⣻⣞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⡽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⢄⣀⠀⠀⠀⢀⣿⣄⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠋⡁⣀⣀⡼⢿⣿⣿⠟⠛⠛⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣾⣿⣿⢿⣇⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⢧⣸⣿⣌⠀⠀⣱⣄⣀⣀⣀⡀⠴⣿⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣾⣿⣿⣿⣿⠃⠀⠝⣿⣿⣷⣾⡉⣉⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣁⣸⣿⣿⣿⣿⠏⠀⠀⠀⠹⢮⢻⣿⣷⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⠛⠋⠙⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣶⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣄⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢿⡏⢸⠿⠀⠀⠀⠀⢐⣃⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣏⣿⣿⣿⡹⣆⠈⠆⠀⠔⠈⢫⣀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⢻⣷⣽⡳⠄⣤⢰⣿⣾⠟⡋⣸⣯⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡅⠈⠹⠟⠉⠋⣠⣇⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠿⠛⣷⣄⡀⠀⠀⢠⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⡆⠀⠀⣾⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣾⣻⡀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣿⣿⠁⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠘⠟⢀⣞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣶⣶⡶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡦⣄⠀⠀⠀⠀⠀⠀⠀⡠⠄⡖⣿⢐⠺⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠛⠀⢀⠀⠀⣰⡊⠀⢸⣇⠐⠂⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡈⢿⠿⡇⠀⠀⠀⠀⠁⢀⣴⠉⠀⠀⢠⡎⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠘⠂⠈⡀⠀⡀⢸⡋⠀⠀⠀⢸⠻⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡙⠒⠲⠾⡀⣟⡄⠀⠀⠀⠈⢧⣿⣤⡴⠛⠙
⠀⠀⠀⠀⢀⠄⠠⠳⠀⠸⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡸⠀⠀⢸⡇⠀⠀⠀⠠⣄⣘⣿⠤⢀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠒⢈⠀⡆⠄⠘⣧⠀⠀⠀⠀⠀⠀⠁⠁⠌⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠰⠀⠎⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡄⢀⠀⠀⠹⠀⠀⠠⣀⡠⠆⠐⣶⠀⠀⠤⠀⠈⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡤⠈⠀⠀⠀⠍⠀⢰⣶⡄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣼⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢰⣿⣿⡀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢹⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠁⠀⠀⠀⠁⠀⠀⠉⠉⠁⠂⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⡀⠀⠐⠊⠀⠀⠀⠴⠉⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠰⠀⠀⠉⠰⠂⠀⠀⠀⠀⠀⠠⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠚⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣇⠀⠀⢀⣠⣤⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠛⣻⣷⣦⣀⣉⣡⣤⣤⣶⣾⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠺⣿⣿⠀⢠⣼⠟⠉⠀⠀⠁⠘⠻⠷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣷⣤⡈⣿⠁⠀⢈⡄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣦⣤⡷⠒⢩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀⣰⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⠛⠁⠀⠛⠋
⠀⠀⠀⠀⠀⢠⡴⠶⠛⠉⠀⢻⠹⣿⡟⡹⠋⠻⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⣿⠟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡆
⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⣿⡶⣶⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡱⠟⢽⠯⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⢀⣘⣧⣰⣤⣶⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⢾⣥⣿⣿⣷⣾⣯⡈⠉⠛⠻⠞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠜⣱⣾⣿⣿⣿⣿⠟⠛⣿⣿⣦⣤⡀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣌⠲⡦⣸⣾⡏⠀⠀⠀⠀⠀⠀⢀⡿⣽⣿⣿⣷⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠄⢀⡀⠀⠀⠀⠀⠉⠻⡿⢃⡔⢿⣿⣷⡾⠧⠀⠀⠀⠀⣸⣷⣿⣿⣿⠟⡁⠀⡄
⠀⠀⠀⠀⠀⠀⢀⡐⢊⡤⠖⣛⣛⣛⠻⢷⣦⣀⠠⡤⣎⣴⢻⣿⣸⣿⡇⠐⠒⣶⠶⠂⠈⠉⠉⠉⡉⠋⠉⠠⡤
⠀⠀⠀⠀⠀⠀⠎⢠⠏⡐⠀⠀⢀⠀⢙⠒⣌⡻⠃⢠⣿⣿⣇⢿⣧⢣⡿⡀⣦⡈⠀⠀⠀⢐⡀⠀⠈⠀⣠⠄
⠀⠀⠀⠀⠀⢐⠀⡟⠀⠀⠐⢄⡴⠂⠒⣂⠈⠀⡴⢿⣽⣿⣿⣼⣿⡆⢰⣣⣿⣿⠶⣄⠢⣀⠿⣀⡀⠔⠁
⠀⠀⠀⠀⠀⢸⣾⡇⠁⠀⠄⣾⠀⣾⣟⡧⣀⡈⡄⠘⣿⠫⠿⢧⣤⢻⣮⢾⣿⣿⣞⢧⠀⠀⠀⡿⢶⣤⣀
⠀⠀⠀⠀⠀⠸⣿⣿⡀⡀⢀⠼⢧⡈⠛⠋⡉⠀⠀⠀⣿⡆⠴⣿⣿⠈⣧⢰⢾⣭⣬⣆⠂⠀⠈⠀⠀⠈⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣷⡐⠀⠀⠌⠉⠹⠁⠀⠁⡂⢀⣿⢟⣸⣽⠾⠴⠧⢖⡛⣿⣾⣿⡆⠀⠒⠀⠀⠀⠀⢀⣤⣴⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠤⠀⠀⠀⡀⠔⣡⣾⠏⠀⢸⢀⣤⣄⠶⣘⣇⣾⣟⣻⣥⠀⠀⠀⢰⣒⣾⡀⠈⠉⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣶⣦⣴⣶⣾⡿⠋⠀⠀⠀⠈⡅⠠⠈⠻⢿⡮⣿⣯⢶⣆⣴⣾⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣝⣾⣿⣟⡿⣭⡟⠏⠙⠄⠉⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⡷⣿⡀⠀⢴⠤⠦⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⣿⣿⣶⣄⠘⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠙⢻⣿⡎⡑⠖⠈⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠁⠘⠳⡄⠡⠆⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠄⠀⠀⠀⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣦⣥⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⣿⣿⣿⡤⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⣿⠆⠀⢸⡿⠛⠉⠀⠀⠀⠀⠀⣼⠧⡄
⠉⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡏⠀⠄⠈⠟⠿⠀⢈⡛⠆⠀⠀⡀⠀⠀⣀⣿⡀⠨
⠞⠛⠉⠳⣄⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠂⢆⠐⠂⠀⠀⠀⢀⣴⣿⣧⣴⡞⠀⠀⠈⠀⠀⠾⠿⣦⡀⢠⡧⠀⠠⣼⣿⣦⡈
⠀⠀⠀⠀⠙⣿⠀⠀⢀⠸⣂⡀⠁⠀⠀⡠⠃⠀⠱⡀⠀⠀⠀⠛⢿⣿⣿⣿⠶⠂⠀⠀⢀⠀⠀⠀⠀⣽⣃⠂⠘⣿⣇⡜⣛
⣶⣾⣦⢀⡀⠹⠷⣶⡮⠴⠙⠛⡂⠀⠠⡿⢦⣴⣶⣧⡀⠠⠄⠀⠀⠉⠙⠟⠓⠀⠀⠀⠀⠂⠀⠀⣐⣯⠀⠐⣿⠿⡛⠗⠹
⣹⡝⠈⠁⠀⠠⡤⠀⠀⢠⣮⠀⠋⡀⠀⠃⠀⠉⣸⠁⠄⠀⠀⠀⣀⠀⢺⣧⣄⠀⠀⠀⠤⠀⠀⣠⣾⠟⠡⠥⢘⣾⣃⣼⣳
⢿⣿⠢⠤⠐⠀⡀⢀⠀⠈⠉⢠⠆⠀⢀⡠⠤⠜⠁⠀⠀⠀⠀⣄⠀⠀⠀⡀⠉⠉⢉⡀⠀⠀⠉⢽⣷⣽⣀⠈⠻⠟⠛⠛⠛
⠀⠉⠁⠀⠘⠁⠀⠠⢠⣀⠄⠉⠀⠀⠈⠐⠂⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠉⠀⠠⢿⣿⣷⠀⠀⠀⠉⢹⣤⠀⠀⠀⠠⡴⠆
⠘⠋⠉⠀⠀⠉⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⢤⡆⡀⠀⠀⠠⠀⠀⠀⠀⠀⠲⠒⠂⠀⠀⠉⠁⠐⠶⠦⠈⠃⠂⠀⠠⢶⣿⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠞⠀⠀⠀⠀⠀⠠⣤⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠃⠐⣦⣤⣶⡿⠟⠛⠉⠛⠛⠻⢷⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠛⠋⠙⠻⢿⣿⣿⣿⠟⢿⡃⠂⠀⠀⠀⣀⠀⣀⢰⣱⣿⡃
⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣷⣦⣀⠀⢀⣀⣀⣀⣀⣀⣰⣷⣶⣤⡄⠀⢙⠻⣿⣶⡾⠋⠢⢄⡀⠀⣠⢭⣵⠻⠡⠍⡋
⠀⠀⠀⢀⣴⣿⣿⢿⣿⣿⡿⢿⡿⠛⠉⠀⠀⠀⠀⡀⠙⠛⣻⣻⣿⣶⣿⡇⢉⠁⠀⠻⡂⢀⣼⡞⠥⡢⢇⢰⢂⢀⡇
⠀⠀⣠⣾⣿⣿⠇⠽⠛⠉⢠⠏⡄⠀⠀⠀⠀⠀⡰⠃⢠⣾⡟⡹⠿⣿⡟⠀⡘⠀⠀⠀⠀⠼⠟⠉⠈⣿⡿⠻⣿⠉⣁
⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⣠⠄⠀⠰⡈⠙⠿⠓⠀⠹⣷⡀⢹⣄⠀⠘⠈⠁⣢⣶⡖⢹⣇⠀⠛⠦⠋
⠀⠀⣨⡿⠟⠁⠀⣀⠤⠤⠋⠆⠃⠀⠠⢚⣥⢶⣶⣦⣍⣂⠀⠀⠀⢀⣘⣿⣾⡿⠶⢤⣠⣾⡏⠿⣲⣾⠋
⠀⠀⠀⠀⠀⠀⠀⡇⢀⣠⣤⣤⠤⠖⠒⠋⠀⠀⠀⠀⠉⠉⠉⠉⠋⠉⠉⠉⠀⠀⠀⠀⠘⠿⠂⠊⠉
⠀⠀⠀⠀⠀⠀⣰⣤⠋⠀⣿⡇
⠀⠀⠀⣠⡤⠴⢧⢇⣀⣰⣿⠇
⠀⠀⠰⠿⠇⠒⠁⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡄⠀⠀⣀⣤⠿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣿⣿⡿⠃⢠⣾⣿⣿⣾⣿⣿⣏⡀⠀⣀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢈⢻⣿
⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛
⠀⠀⠀⠀⠘⠛⠉⠁⢸⣿⡿⢿⣿⣿⠻⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡛⠛⠻⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⣹⡟⢰⣿⣿⡟⠁⠈⢿⡇⠀⠀⢈⡟⠀⠀⠀⠈⣻⠿⣦
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢿⣇⢸⡇⢻⡄⠀⠀⠈⣷⠀⠰⠞⠁⠀⠀⣤⠼⠋⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠙⢾⣧⡄⠻⣄⡀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠁⠀⠈⠉⠻⡿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠹⡇⠀⠀⠀⠀⠀⠀⢱⠹⣿⣿⣿⢴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⠀⠀⠺⠇⠀⠀⠀⣿⣿⣿⣿⣿⡛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠘⠙⡿⣿⣿⣯⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠖⣈⣴⣿⣿⣾⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡉⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠿⠦⣀⣬⠋⢀⣄⠀⣀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢃⣴⣶⠾⠿⢷⣿⡏⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡏⣠⣴⡶⣮⠙⠃⠀⠒⠰⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣦⣀⡉⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠶⠦⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠂⠒⠀⠆⠀⠀⠒⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⢀⡀⣈⢀⡁⢈⡉⣙⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⡁⣨⢀⡇⢨⡀⣩⢸
⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠠⠠⠦⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⡀
⠀⠀⠀⢀⣤⣤⣶⠿⠛⠛⠘⠛⠻⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠘⡛⡛⠛⠛⠻⢿⣿⣦⣄
⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⣷⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⢠⠀⠀⠴⠀⠀⢹⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠹⣿⣧
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠛⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⢀⣶⣶⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣿⣿
⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⠏⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣶⣾⣿⡿⠟⠋⠀⠀⠀⠂⠄⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣶⣶⣶⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡉⠆⠀⠀⠀⠀⠀⣤⢾⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡏⣻⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣀⣀⣸⣿⣿⣿⣿⣿⣿⡀⠀⠀⡀⠼⠻⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⢴⣾⣿⣿⣧⣽⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⡎⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⣀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠾⠟⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⣀⣰⣿⣿⣿⣾⣏⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⠄⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⢿⢿⣿⣿⠟⣛⣿⣏⣿⣿⡿⢿⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣹⣿⠿⠟⣿⡇
⠀⠀⠀⢀⣴⣿⣿⡟⠁⢹⡟⢿⣿⡿⣸⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠤⠿⠿⣿⣶⣶⣿⡇
⠀⠀⠀⣸⣿⣿⡟⠀⠀⠘⣿⣶⣶⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣧
⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠹⣧⡀
⠀⠀⠀⠸⣿⣿⣿⣿⣄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣯⣵⡄⠀⠀⠀⠀⠙⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠙⠛⠹⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⢠⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣍⡛⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠙⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣦⡀⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣿⣦⡀⠀⠀⠜⠁⠀⠈⢦
⠀⠀⠀⠀⡄⢰⢄⣖⠠⠶⠿⢿⣿⣿⣾⣿⣿⣇⠀⠀⡆⠀⠀⠀⢸⡆
⠀⠀⣾⣤⢌⣤⡘⠁⠀⠀⠉⠛⠶⣭⡻⣿⣿⣿⣠⡇⠁⠀⢀⢀⣾⣇
⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⢿⠿⠁⠀⢀⡌⠈⠙⢿⡀
⠀⠀⠀⠀⣿⡇⠀⠀⢀⠸⡄⠀⠀⠀⠀⠀⠈⢀⣀⣴⡿⠛⠀⠀⠀⡌⢙⣆
⠀⠀⠀⢀⡟⣧⣤⡤⠊⠀⡇⠀⠀⢀⣀⠠⠀⡸⠋⠁⠐⠂⢀⠖⠚⢃⣠⣿
⠀⠀⠀⢸⣅⣤⠋⠠⠤⠴⣿⠒⠉⠉⠀⣠⠎⠀⠀⠀⠔⠚⣩⣀⠀⢻⠈⠉⠀⠀⠀⠀⠒⠒⠦⣄
⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⢸⡆⠀⠀⠀⣇⢷⣿⡆⠀⠀⡰⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠹⢦⣿⡇⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⡇⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢠⣾⣿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠚⠛⠛⣿⣀⣀⣀⣀⣀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣀⡴⠞⠀⢠⠀⠀⣾⣿⠃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⣠⠀⠀⡠⠊⠉⠉⠉⠉⠉⠀⠀⠀⢳⡄⠀⠀⢠⡴⠟⠋⠀⠀⢠⠇⠀⠀⠁⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣵⠟⢻⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡏⠀⠘⣆⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠀⠀⢸⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣿⡀⠀⠘⣆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⢿⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣧⠀⠀⠘⣷⡈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠋⠁⠀⠀⠀⣹⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣤⡀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⠀⢰⣿⡯⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣇⣴⣾⣿⣿⣿⣤⣀⣀⠀⠀⢀⣶⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⡁⠀⠀⠉⠻⣿⣿⣇⢰⡇⣿⣿⣿⣿⣿⢿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠉⣉⢻⣦⠀⠀⠀⠈⣿⣷⡿⢳⢿⣿⣿⣿⣁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡝⠃⠀⠀⠀⠸⣿⣵⣿⣻⡻⣿⡿⠃⠀⠀⣀⣀⣤⣤⣾⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠗⢾⣇⠀⠤⣀⠀⣈⣿⣶⣭⡛⢿⠃⠒⠅⠀⠛⠿⢿⣿⣿⣿⣿⣯⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠼⠪⠯⣄⠀⢀⣼⣿⣿⡿⣩⣿⣶⠅⢀⡠⠀⠘⠂⠐⢂⠈⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⡀⢀⣼⣿⣿⣿⡿⠁⠘⣿⣿⠶⣭⣤⣶⣶⣶⣿⣦⠓⢆⡀⢿⣿⣧⡀
⠀⠀⠀⠀⠀⣀⣼⣿⡷⠄⠀⠀⠀⢸⣿⣟⣛⡻⠿⠱⣖⣦⣾⣿⣷⣹⣿⣿⣿⣿⣿⣿⠶⠚⠛⠁⠀⠙⢻⡀
⠀⠀⠀⠀⣾⡟⠁⠀⠃⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀⠀⢀⣴⡻⠿⣿⡿⠽⠏⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢹⡷⠄⠀⠀⠄⢀⣀⠀⢺⣸⡈⠙⡟⣼⣺⡅⠻⣿⣿⣿⠂⠈⠻⠆⠐⣠⣶⣦⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠓⠻⠇⢇⠀⢑⣾⣭⣴⣾⡿⠛⠁⠀⠀⠀⠄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⣾⣱⢿⣿⣿⣿⣻⠎⠀⠈⠁⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣴⣄⠀⠈⠙⠻⠿⣿⡇⠀⠀⠁⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⣄⠀⢀⢐⣈⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣔⠨⣝⣻⣿⣿⣿⣿⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡖⠙⢀⠦⠙⣿⣿⣿⣿⣿⣟⠂⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠁⠀⠀⠀⠈⠈⠁⢼⡟⢹⣿⣿⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠘⠙⠀⠀⢹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣏
⠀⣀⡀⢀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⣀⣉⡍⠀⠀⠀⠀⡀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠋⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢛⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠈⠈⠛⠿⠲⡆⠀⠀⢀⣀⡀⠀⠀⢀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⣀⠼⠃⡀⣶⣿⠃⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣼⠇⢀⡞⠁⠀⣾⣇⡅⢻⣧⡀⠀⠀⣠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⡟⠛⠓⢻⡄⠈⣿⡿⠦⢈⡼⠁⢀⣿⣿⣠⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠟⠉⢀⠾⣾⣿⡄⢸⡇⠸⠿⠿⠋⠉⢦⣾⣿⢿⣿⣿⣿⢟
⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⣠⣾⣾⣿⡟⠁⠸⠇⠀⣿⣷⣴⡆⢸⠟⠁⠸⡿⠙⢡⣿⣀
⠀⠀⠀⠀⢀⣶⢟⣁⣤⣶⣿⣿⣿⣿⣿⣧⠈⠐⠚⢉⣿⣿⡿⠇⠀⠀⠀⠀⠈⠲⡌⠙⡿⠃
⠀⠀⠀⠰⢮⣻⣾⠬⢿⣿⠋⠁⠀⠀⠀⠹⡇⠀⢀⣾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⣵⠞⠁
⠀⠀⠀⠀⠀⠻⣽⣶⣾⣿⡄⠀⠀⠀⠀⣸⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣴⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣳⠄⠈⠀⢀⠏⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⣸⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠁⠚⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢀⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣤⣤
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⠀⠈⠙⠛⢻⠓
⠀⠀⢰⣿⢿⣿⣿⡟⠻⠿⢿⣿⣿⣿⡇⠘⠋⠀⠀⠀⡚⠉⢳⡁
⠀⠀⠸⠋⡾⠋⣿⠁⠀⠀⠀⢸⠃⠙⢷⡀⠀⠀⠀⢰⡇⠀⠇⠇
⠀⠀⠀⣸⠁⠀⠈⢧⡀⠀⣰⠋⠀⠀⠀⢳⡀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠁⠀⢀⠘⠛⠉⠙⠻⣤⡄⠐⠭⠭⠖⠒⠒⠲⠯⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠒⠒⠲⢶⣤⣼⢷⡬⢦⡀⠀⠈⢙⢦⡀⢀⡄⢀⣠⡤⠖⠈⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⠟⠁⠀⠀⠀⢀⠈⣿⠋⠈⠀⠀⠃⠀⣸⣿⠇⠈⢺⣷⣿⡿⢿⠟⠓⣾⣿⡟⠋
⠀⠀⠀⠀⠀⠀⢠⣿⣿⢻⡄⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠈⢹⠀⣿⠁⠠⡀⡌⡿⠛⢄⣤⠈⣨⠟⠏⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠈⣿⠀⠀⠀⣠⠿⠿⣿⣷⣤⣀⢀⡆⠘⡏⣿⡀⠙⢁⡇⠀⠘⢿⠟⠁
⠀⠀⠀⠀⠀⢀⣿⣿⡇⢠⠇⢀⢠⣴⡿⠀⠀⠀⠈⠉⠙⠛⠷⢿⣿⣿⠷⣀
⠀⠀⠀⠀⢀⣼⡿⠋⠰⡟⡴⠃⠸⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠈⢣⣰⡄
⠀⠀⠀⠀⠉⠁⠀⠀⢀⡜⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⢀⠔⠔⠁⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⣤⡅⠀⠀⠀⠀⠀⠀⠀⠓⣷⡀⠀⠀⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣄
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠛⠿⢿⣿⣿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⠀⢀⣤⣶⣶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠆⠀⠀⠈⠋⠀⠀⢤⠀⠀⢀⡀⠀⠉⠑⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡉⠈⠀⠄⠀⠀⢀⠀⠀⠀⠁⠀⠁⣼⣿⣦⣄⠀⠀⠸⠿⠿⠿⢿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⡀⠘⢷⠶⠁⡀⠂⠀⣹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠘⠀⠀⠲⢀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⢂⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢢⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⣀⣠⣤⣤⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠉⠉⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⣀⣨⡿⣿⣦⣀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠙⣿⡇⠈⠉⠛⠿⠿⠿⠿⠿⠟⠃⡀⠢⠀⠀⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣤⣀⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⣧⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠊⠁⠀⠀⠀⠀⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠘⠛⠃⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃
⢄⡀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣆
⠈⢻⣶⣶⣴⣶⣿⣿⣿⣿⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠙⠻⠿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠉⠉⠁⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⣀⣐⡐⣖⠒⢄⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠋⠑⠀⠌⠔⡠⢌⡐⠠⢄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⢧⡂⠄⢀⡀⠀⠀⠀⠈⠉⠛⣲⣾⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠌⢠⠉⠓⠶⠤⣭⢤⣴⠶⠾⢿⣋⣡⠗⠈⢀⠁
⠀⠀⠀⠀⠀⠀⢠⣌⣄⡊⠔⠁⠀⠀⠀⡂⢠⠀⠀⠀⠀⠀⠀⠘⣗⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢤⡀⠀⠒⠒⠤⡒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡡⠀⠤⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⢁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⡖⠒⠂⢪⠀⠆⠀⠀⢠⣄⣀⣀⣀⣀⣀⡀⠤⠄⢒⣈⡥⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⣀⠀⠀⠁⠁⠐⠒⠻⣿⠶⠖⣚⣩⣽⣶⢺⣏⢿⣈⣧⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣠⡤⠐⠂⠉⠉⠉⠀⠀⠒⠿⣟⣋⠭⠔⣚⣇⢻⣓⣋⡭⣵⠲⡞⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡏⡏⠉⣀⡲⠦⠀⠀⠀⠸⠖⠚⣩⠞⣹⡞⢿⡌⣷⣹⣇⠿⢜⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⣟⣉⠥⠔⡾⠀⠀⠀⢠⣠⠞⣡⠞⠁⢹⡛⡯⠭⠑⠒⠉⠁
⠀⠀⢀⡤⠒⠋⠉⠉⠉⠙⠲⢤⡠⢊⡴⡇⡇⠀⢀⠌⡁⠀⠀⠀⠘⣡⠞⠁⠀⣀⠴⢧⢻⠉⠉⠉⠒⠦⣀
⠀⡴⠁⣠⠖⢫⠉⣏⠉⡵⡲⢊⡴⢏⠀⡇⡇⢠⡂⢠⣀⠠⠤⠀⠚⡅⠀⢀⠞⠁⡠⣞⡌⣯⠏⢉⠖⢄⠈⠳⡀
⡼⠀⡰⢥⡀⠈⡆⢇⡼⢋⡴⢋⣆⠈⣧⣇⣧⠨⡷⢾⢛⣷⢦⠤⠴⠃⢀⡏⢀⣎⣀⠈⢿⡸⣧⠏⠀⣀⡵⡀⠹
⡇⠀⡧⠤⠬⠵⣞⠛⡴⠟⠛⠋⠉⠉⠁⠀⠀⠀⢇⠮⢊⠗⠃⠀⠀⠀⢸⠀⢸⣀⣈⡭⢶⡟⢳⣎⠭⠤⠤⡇
⢇⠀⢇⢀⡤⠚⡽⡟⣝⠫⢍⡉⡶⠓⡶⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠸⡄⠸⣀⡤⠚⣱⢻⢻⠈⠓⠦⣀⠇⢀
⠘⢆⠈⠣⡀⡰⠁⢳⠘⢆⣀⠝⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠙⢄⡰⠁⢸⠀⢧⠀⣠⠎⢀⠞
⠀⠈⠳⢄⡈⠙⠒⠚⠒⠋⢁⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠉⠒⠚⠒⠚⠉⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⣶⣄
⠀⠀⣦⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠉⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⢁⣤⣾⢆⣀
⠀⠀⢿⣿⣷⣿⡿⠀⠀⠀⣦⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⣿⢉⠟⣀⣾⣄⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣶⣿⣿⣿⣿⣗⠁
⠀⠀⠀⣹⣿⣿⡆⠀⠀⢸⣏⠢⣠⣶⣾⣿⣆⠠⣴⣾⠂⠠⣽⣦⣤⣤⠄⠂⣠⢟⢋⡛⠻⢿⣿⣷⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣥⣶⠄
⠀⠀⠀⢿⣿⠏⢿⠀⠀⠈⢻⡤⠉⠋⠉⠛⢁⣾⣿⣿⣧⣤⣽⣟⠋⠁⠀⠘⠓⠈⠀⠀⠱⠀⠉⠙⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠁⠀⠀⠀⢀⠄⠊⠄⠀⣀⡐⠄⠉⣉⠉⠻⣿⣿⣿⣿⣆⣀⡁⢀⠃⠀⠠⠆⣦⢑⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠰⠛⠀⠀⡰⠇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣴⡱⢸⠍⠴⣀⡁⡰⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⠤⠚⠳⣦⡁⠀⢀⡤⣀⣾⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣛⡳⡘⣧⣀⠭⣁⣀⡀⠀⠀⢀⠀⢸⣿⣿⣿⡟
⠀⠀⠀⠀⠚⠁⣴⡄⠀⠈⢳⣀⣩⠞⠁⡂⠀⡶⠈⢆⠀⠀⠀⠀⠹⣿⣿⣧⠉⠉⡿⢉⠒⠙⣿⣿⣾⣭⣀⠈⠉⠉⠛⠓⠤⣄
⠀⠀⠀⢀⣁⣀⠉⢀⣰⠄⠀⢻⢤⣀⣠⢥⣾⠀⠀⠀⠑⠀⠀⠀⠀⠘⢿⣿⣷⣶⣷⡄⠈⠛⣿⣟⠃⠀⠉⠳⣆⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠉⣡⢍⠛⢁⠴⢶⡊⠁⠈⠓⠤⣹⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⣿⠟⢿⣿⡄⠀⢿⣿⣿⣄⠀⠀⢸⡇⠠⢀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠈⠛⠣⠊⠀⠀⠙⠶⣄⡀⣀⡀⣿⠐⠒⠼⡦⠤⠤⠤⠴⠒⠋⠁⠀⠈⣿⣧⠀⠈⢿⣿⣿⠀⠀⢸⡇⠀⠠⢃⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡹⣷⣤⣀⣽⣯⡀⣠⡟⠀⠀⠀⠏⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸⣧⡈⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⡰⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠣⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢸⡎⠛⢿⣿⡿⣏⣿⣿⣦⠀⠀⢀⡇⡰⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢣⠀⢸⣿⢇⣼⣿⣿⠃⠀⢀⡾⠀⠁⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣤⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠸⠀⢸⣿⠀⠉⠉⠉⢀⣠⠿⢦⡀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠀⠀⠀⠀⠑⠀⣀⣄⠀⠀⠀⢀⠸⢀⣿⠇⠀⢀⣠⣴⠏⠁⠀⠀⢻⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠈⢻⡀⠀⢄⠓⠀⠀⠀⢀⠀⠀⢰⠃⠀⠀⠀⢀⡞⢠⣾⣿⠶⠚⣉⠁⣇⠀⠀⠀⠀⠀⡇⣠⣴⣇⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠳⣄⠈⠀⢀⣰⠦⠼⠷⣄⣽⠀⢀⠜⠀⢈⣿⣿⣿⣿⣿⣶⣿⣷⣾⣧⡀⠀⠀⠀⣧⢿⣿⣏⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠈⠑⠲⠊⠁⠀⠀⠀⠀⢹⠀⠁⡀⢠⣾⣿⡉⠉⠙⠛⠛⠿⠿⣿⣿⠇⠀⠀⠀⢿⣿⡿⠋⠙⣦⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣀⣈⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢀⣴⡞⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠋⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣦⡀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠐⠢⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⢎⣡⠵
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠐⠀⠀⠐⠒⣘⣀⠀⠠⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠬⠤⠤⠤⠥⠬⠬⠱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⠉⠉⠉⠉⠉⢩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⣲⢷⠀⠀⢀⡀⠀⠰⠖⠚⠉⠁⡼⣆⣀⣀⣀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⠶⢶⣤⣄⢀⡔⠁⠈⡗⠛⠋⠸⣀⠀⠀⠀⣠⢊⣠⣽⡶⠶⢶⣾⣄
⠀⠀⠀⠀⠀⣠⡾⠋⠁⢡⠀⠀⠀⡹⠿⣆⠀⠀⠸⡆⣦⠂⠀⠀⣠⠞⣱⠟⠉⠈⣇⠀⡸⠁⠙⢷⣄
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠈⣆⣠⣎⡀⠠⢽⡦⠤⢴⢷⡿⣄⣀⡔⠁⢸⡏⠀⠀⠀⢸⣤⠃⠀⠀⠀⢻⡆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣗⣒⡒⠒⣺⣿⠒⣻⣧⢈⡝⠁⠀⠀⢿⡇⠀⠀⠀⠺⣿⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⢸⣉⣽⣧⠄⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠈⠷⣤⣀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⡀⠀⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⣿⣿⣟⣉⣠⡀⠀⢀⡀⣀⡤⣄⠀⠀⢀⣴⣿⠟⠛⢶
⠀⠀⠀⠀⠀⢦⣤⣾⣿⡿⣛⣻⣿⣿⣿⣿⣏⠀⢛⡼⢋⠳⣾⡿⣿⣿⣿⠁⠀⠁⠾
⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⣿⡛⢙⢿⣿⣿⣷⣌⣱⠇⢰⣿⣇⡋⢙⣹⣧⡤⠟
⠀⠀⠀⠀⠀⠈⢻⡟⢤⣾⠈⣯⢙⠃⠃⢻⣿⣿⢼⣟⣠⡾⢻⠻⢷⣛⣛⣋⣴⣆
⠀⠀⠀⠀⠀⠀⢙⠈⢃⡤⠀⠂⣸⠄⠈⠈⣿⣿⣿⠿⢿⡅⣄⡽⠿⣛⣻⠛⢙⣷⠂
⠀⠀⠀⠀⠀⠀⠀⣷⠿⢾⣯⣟⠀⡄⠀⡄⢸⣿⡧⣾⣼⣿⣿⢋⣀⣼⣇⣪⣾⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⣿⣿⠢⣄⣀⣀⣀⣻⣿⣾⡿⣿⣽⣿⡟⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠠⣫⠴⠟⠚⠛⢃⣤⣀⣄⣠⣀⣌⣉⡉⢙⣿⡟⢪⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠧⠖⠀⢠⡀⠉⠉⡉⠝⢛⡿⣷⢹⢿⡃⣽⣆⣤⣴⡾⠃⠀⣠⣤⣀⣤⣤⣀
⠀⠀⠀⠀⣠⠤⣼⣿⣷⣞⣶⣬⣀⣠⣤⡶⢿⣿⡖⣿⠸⠳⠪⣦⣾⣍⠛⢧⢰⣷⣿⣿⣿⣟⣿⣿⣿⣖⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠠⢾⢟⡟⣽⣿⣿⣶⡿⡶⢟⣿⣉⠷⣸⡿⡆⡗⢇⣠⣽⡿⣧⡀⠙⢟⢿⡿⢿⡟⣿⣿⣿⣿⣧⣤⣴⣿⠗
⠀⠀⠀⠀⠀⣆⡘⣠⣿⣯⣌⢯⣉⠋⠛⣉⠁⣰⢿⠗⣻⡷⣌⣿⡍⢠⡀⣷⡦⡀⠑⢝⡂⡈⢿⣿⣿⣿⠿⠿⣿⠿⣏
⠀⠀⠀⠀⢠⢋⣤⣸⣿⡇⡷⡀⠀⠀⠈⢁⣾⣽⢊⡆⡙⣷⢈⣿⣷⡄⠁⠙⣧⣄⠱⠄⠀⠠⣼⡿⠻⠿⠾⠟⠛⠃
⠀⠀⠀⡠⣨⣷⣿⣿⣿⣿⠟⡁⢢⣤⡚⣻⣿⣡⣾⢿⠟⢹⡟⣇⣘⣷⠀⠀⢹⣇⣤⠶⠐⠛⠚⠁
⠀⣠⠞⢰⡿⠞⠉⠀⣠⠋⣼⣟⡿⢿⣿⣿⣿⣿⣷⣯⠤⣾⣻⣌⠻⣿⣷⡄⢸⣿⣿⡄
⠀⢹⣻⡏⠀⠀⣰⣿⣧⠿⠋⠁⠀⠀⠈⠉⠙⠛⣷⣶⣿⡟⣿⠛⢲⡈⣿⣷⣈⣿⡎⠉
⠀⢸⣿⠀⠀⢀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⢿⣿⠀⣸⠏⠚⣿⣯⣿⣷⣀⡀
⠀⠨⢹⣷⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢇⡟⣄⢻⣿⣿⣽⣿⣿⣿⠁
⠀⠘⢈⢹⣟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡷⣞⢠⠏⠀⠀⠉⠛⠉⠉⠉
⠀⠀⠈⠛⣸⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡚⡿⠋⢀⡟⠈
⠀⢀⣶⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠧⢀⣊⡾
⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣸⠿⢿⠃⢀⣾⡟⢣⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢠⣿⡍⢲⢈⣄⡃⠀⠈⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣊⣉⣉⣉⡉⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠐⠂⠒⠢⠉⠉⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⠴⢢⡤⠲⢤⠖⠑⠢⠒⠊⠑⢤⡤⠤⣕⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡵⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠙⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⣶⣀⠤⠌⠛⠓⢊⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⣉⠭⠍⡉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡘⠁⠀⠀⠘⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⡇⠀⠀⠀⠀⢱⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳⠒⠒⠒⠒⢻⠀⠸⠶⠶⠖⠒⠲⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠨⡆⠀⠀⠀⠈⠑⠲⠧⠤⣤⣤⣞⣹⣟⣉⣉⣉⡭⠿⠟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⢙⣲⣤⣤⣄⣀⣀⣀⣀⣀⠀⣠⢿⣟⢉⣉⡤⠴⠖⣿⡽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢞⣉⣉⡤⠴⠒⢋⣙⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⠛⡟⠓⠒⠒⠤⣤⣄⠀⠀⠀⠀⠀⢏⣠⠤⠖⠛⣩⠟⢻⡤⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣯⣠⡤⠶⠚⠉⣩⡃⠀⠀⠀⠀⠩⠀⠀⣠⠞⢁⣴⠚⢧⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⠀⣿⣠⡤⠶⠚⢋⣿⠀⠀⠀⠀⠀⡇⣠⠞⠁⣠⠞⠁⠀⠈⣇⠸⡄
⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠙⠓⠲⢤⣀⠀⣠⠞⢀⣿⠀⣿⠀⠀⠀⣠⠋⡆⠀⠀⠀⠀⠀⡟⠁⣠⠞⠁⠀⠀⠀⣠⡼⡄⢿⠛⠉⠙⠛⠒⠶⣤⡀
⠀⠀⢀⡴⠋⠀⢀⣠⠤⠶⢶⠶⠦⢤⣀⠀⣨⠟⢁⡴⠋⢸⠀⣿⠀⠀⡴⠁⢰⠁⠀⠀⠀⠀⢀⣧⠞⠁⠀⠀⢀⡴⠋⠁⠀⣳⠘⣧⢶⠶⠤⣄⣀⠀⠉⠳⣄
⠀⣰⠋⠀⢠⠖⠉⠘⣆⠀⢸⠀⢀⡞⣩⠟⢁⡴⠋⢧⡀⢸⠀⣿⠀⣾⣤⣀⣾⢦⡐⠒⠒⠊⠉⠈⡇⠀⠀⢠⠏⠀⢀⡴⠻⣍⣧⢹⣼⠀⠀⡼⠉⠳⣄⠀⠈⢧⡀
⢰⠃⠀⣰⢯⣀⠀⠀⢹⡄⢸⢀⣾⠞⢁⡴⠋⣳⠀⠀⢧⢸⠀⣿⣀⣹⣿⠤⣿⢻⣾⣷⣶⣤⣤⣴⠇⠀⢠⠏⠀⢠⣏⠀⠀⠘⢿⡄⢿⢀⡞⠁⠀⠀⢈⣷⠀⠀⢷
⡟⠀⢀⡇⠀⠉⠓⠦⣄⣳⡼⣟⢁⣴⣿⣶⡯⠽⠷⠒⠛⠋⠉⠉⠁⢸⡃⢠⢇⡞⣿⣡⠎⠀⠀⠀⠀⠀⣾⠀⠀⡏⠈⠙⠓⠦⣄⣻⡼⣿⣠⠴⠖⠋⠉⠈⣇⠀⠸
⡇⠀⢸⡟⠛⠛⠛⠒⣛⣧⣀⣼⣏⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⣋⡴⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀⠸⡧⠴⠶⠒⢒⣺⢿⣀⣸⢷⣖⠒⠒⠒⠒⣿
⢻⠀⠀⢧⠀⢀⡴⠞⢁⡞⣿⢳⡉⠳⢤⣉⠉⢹⠏⠉⢻⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢧⢀⡤⠖⠋⣠⠏⣿⢹⡀⠈⠙⠲⢤⣠⠇⠀⢸
⠘⣧⠀⠈⢿⡉⠀⠀⡾⠁⢸⠀⠻⡄⠀⠈⣳⠏⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢯⡀⠀⣰⠃⠀⡇⠀⢷⠀⠀⠀⣠⠟⠀⢠⡟
⠀⠈⢧⡀⠀⠙⠦⣼⡁⠀⢸⡆⢀⣹⡤⠞⠁⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠙⢶⣇⡀⢀⡇⠀⠈⣧⣠⠞⠁⠀⣠⠏
⠀⠀⠀⠙⠲⣄⡀⠀⠉⠉⠉⠉⠉⠁⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠉⠙⠛⠛⠉⠉⠀⣀⡤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣶⣾⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣷⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⡿⠿⠏⣰⣤⡀⠀⠀⠀⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣽⣄⣠⣶⣿⣿⣿⣿⣦⠛⠑⡊⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠻⠿⣿⡿⢿⠛⠀⣳⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠋⠉⠙⠀⠄⢀⣀⠈⠉⢺⡏⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣐⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡧⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⠿⠿⠿⠿⠿⠹⠿⠿⠿⠶⣶⡿⣷⠆⢀⡆⡄⡀⠀⢄⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣋⠔⠒⠈⠉⠁⠈⠉⠐⢄⠀⠀⠉⠁⠁⠀⡠⠀⠀⠀⠀⢸⢀⣠⠖⠓⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⢀⠔⠁⠀⠠⣄⢀⣶⡿⠁⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢠⣦⣌⣈⡟⠉⠉⠉⠉⠉⠉⠉⠉⢉⠇⣑⠀⠋⠣⣀⢀⣐⡦⢾⣿⣿⠁⠀⣰⡾⠛⠛⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣶⠒⢶⣶⣶⣶⣶⣶⣶⣶⣿⣴⣤⣀⣀⣀⢀⣠⡄⠴⠛⠁⠉⠀⣾⣿⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠙⠻⢿⣿⡿⠿⠿⠿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⡀⠀⣀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⣭⠟⠿⠋⣹⣾⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠒⠺⠷⢈⡴⠋⣠⢀⣿⣏⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠈⠉⠁⠀⠀⡘⠻⣿⣶⣶⠻⠛⣁⡤⠋⡐⠀⠃⣼⠏⠀⠉⠉⠹⠾
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⢻⠁⢀⠄⠀⠀⢀⠾⠀⢨⣿⣿⠋⣴⡞⠉⠀⡰⠁⢦⣘⡟
⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⠀⢹⠀⠘⢆⡀⠀⡈⢣⡀⠀⠈⠉⠓⠈⡇⠀⢀⠀⠀⠸⣿
⠀⠀⣀⣾⡿⠟⠛⠟⠙⠁⠀⠈⠳⣼⣆⢁⠐⢼⠀⢻⣷⢤⣤⣄⣀⣡⡇⠈⢀⠀⠐⠻
⢀⠜⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣌⠀⢸⡇⠀⠀⠉⠉⠉⠛⠲⣾⣿⣶⠶⠦⠤⣄⠂
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠀⠀⠀⠶⣆⠀⠀⠉⢛⣷⡄⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⢍⡛⠶⠶⢦⣄⠈⠉⠉⠋⠋⠉⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠠⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⡀⠀⠀⠈⢍⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠒⢕⡂⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠪⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠰⠀⢀⠀⠀⣠⠒⠂⠄⠐
⡆⠀⠀⢰⠊⠁⠀⠀⠀⢆⠀⠀⠀⢀⠠⠂⠀⠀⢠⠁⠀⠀⢀⠀⠀⠀⠤⠤⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀
⠉⠒⠂⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⡇⢄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⢁⣀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠐⡀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⡀⠀⠀⠀⠐⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⠂⠄⡀⠀⠘⣄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠢⢄⣑⣲
⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢱⠀⠀⠀⠀⠑⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢃⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠃⠀⠀⠀⠀⠀⠈⢢⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠆⡸⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⢁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊
⣶⣶⣶⢶⣶⣶⣶⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣿⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣹⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⢀⠀⠀⠀⠀⣴⣄⣀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠛⢁⠀⣠⢾⣿⣿⠟⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⢿⣧⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠯⣼⣿⣎⡀⢠⣷⣄⣀⠤⠤⠴⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢰⣿⣿⣿⣿⠏⠀⠊⣽⣿⣿⣯⣀⣁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣾⣿⣿⣿⡏⠀⠀⠀⠈⢷⣹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣼⣏⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢿⢹⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⡀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡟⣿⡏⠀⠀⠀⠀⠄⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣿⣿⣷⢳⡄⠢⠀⠠⠄⠛⡀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⣿⣯⣗⡦⣤⣄⣾⣼⠿⡛⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣻⣿⣯⡀⠈⠟⠉⠙⢠⣇⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⢻⣷⡄⠀⠀⢀⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣷⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⣯⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠾⣿⡇⢀⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣾⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡏
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣺⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⡹⣾⣿⣿⣿⣿⣧⡀⠙⢮⡻⣦⡀⠀⠀⣄⢠⣤⣤⣴⣿⡇⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⡅⣧⣼⢿⡟⠷⠀⠀⣙⣮⠷⡤⠂⠀⠀⠙⢉⠟⠛⣮⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣴⡗⠒⠉⡁⠀⠀⢳⣄⣄⡀⣠⣔⠩⠶⢿⣿⡿⣆⢀⣀⣀⣠⡄⠀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⠄⠀⢸⠀⠘⣧⠀⠀⠛⠛⠙⣻⣾⠟⠀⠀⢀⣿⣾⣿⣸⣿⡿⠋⠁⠀⠀⠀⠈⣕⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⣆⣼⠏⠀⡠⠀⠀⠀⣿⢃⠀⢠⣴⣿⣿⡿⣫⠟⠁⠀⣀⠀⠀⠀⠀⠀⢻⣯⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣠⡞⠁⠀⠀⢀⠀⣬⣶⣿⣿⣿⣿⠾⠋⠀⢀⡄⢹⡆⠀⠀⠀⢀⣿⣿⠂⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣉⠀⠀⠀⠀⣾⣧⠘⠻⣷⠉⠉⣠⣴⣶⣾⣿⣧⣈⠃⠀⠀⠀⣽⣿⡏⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣥⠀⠀⠀⣿⣿⣶⠲⢿⡇⠀⢸⡿⠿⠛⠉⢻⣿⣆⠀⠀⢠⣿⣿⢁⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡿⠛⠿⠀⣾⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⣿⣿⠇⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣸⠃⢴⣇⡠⣽⠿⠀⠀⠀⠀⠀⠀⠘⢿⣿⡷⠀⠹⣿⠀⠈⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠈⢿⣇⠀⠘⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣇⠀⠈⡌⣿⡄⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡴⠃⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠒⠋⠀⠉⠀⠁⠀⠀⠀⠀⠁⠈⠐⠉⠈⠉⠉⠀⢈⣿⠁⠄⠠⠄⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡟⠿⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣀⠀⠘⠃⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣇⠂⠀⠀⢀⣤⡾⠷⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠟⣷⠈⢀⣶⣶⡄⠀⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣌⣿⣿⣿⠆⠀⠀⠈⠙⠳⠶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⢷⠶⡴⠶⠶⠶⠾⠿⠃⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢀⠀⣌⠖⠒⢶⣒⣀⣀⣁⣤⣤⣤⡔⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡷⠋⠈⢻⣿⣿⣿⠏⠉⠉⠉⠁⢀⣀⣿⠖⠒⠂⠀⠐⠀⠀⠈⠿⣯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⣾⠋⠀⠁⣀⣤⠶⠞⠛⠫⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣸⠇⠀⢀⡾⠋⠠⠀⠀⢀⣀⣠⣄⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡟⠀⠀⢸⡇⠀⢀⠀⠘⣏⣹⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⠁⠀⠀⠸⣇⠀⠈⠄⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢻⡄⣀⣡⠀⣈⣿⣄⠀⠀⠀⠀⡠⠄⠀⠉⠉⠁⠀⠄⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡉⠉⠉⠀⠐⠄⡀⠸⣧⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠉⢀⡀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟
⠀⠀⠀⠀⠀⠀⣸⣿⠃⢀⣾⡿⢉⣶⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⢻⣿⡀⠘⣿⣷⣾⡿⠃⢨⣶⡶⠾⠶⠶⠶⠶⠶⠶⠶⠾⠛⠛⠛⠛⠛⠛⣿⣿⡀⠘⢿⣿⣿⡿⠋⠀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⠉⠉⢀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠁⢀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⡦
⠀⠀⠀⢠⡀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⡆
⠀⠀⠘⢿⡟⡥⢿⣶⣤⡈⠉⠙⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣲⣾⣰⠃
⠀⠀⠀⢿⡇⣐⠈⣿⣿⡿⣷⡄⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿
⠀⠀⠀⠀⠃⠁⠲⣿⣿⣧⡏⢿⡆⠀⠀⠀⠈⠙⢧⣤⡀⠐⣶⣾⣿⣿⣿⡷⣠⣤⡀
⠀⠀⠀⠀⠀⠠⣠⡟⠈⢻⣿⣈⠇⠀⢀⣤⠀⠈⠛⠛⠁⢠⣾⣽⠹⢟⣿⠾⢃⣶⡇⡀⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠛⠾⠃⠀⠸⣿⣿⡀⠠⣿⠟⠀⠀⠀⠀⠀⣾⠟⠁⠠⢉⣴⣿⣿⣿⣇⣩⢆⠀⢈⠙⠋⢷⣶⠶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡇⠀⠀⠀⠀⠀⡼⠋⢀⣤⣵⣿⣿⣿⣿⡿⣿⡏⢶⡄⠀⢭⣒⡾⣿⠇⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⡞⣶⡇⠀⣿⣿⣿⣿⣿⣿⢟⣁⣿⣷⣦⠉⡆⠀⠉⢳⣿⠆⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡄⠀⠀⣘⣻⡧⠄⣿⣾⡏⢸⣿⣿⣿⣿⣿⣿⣿⢃⢻⡀⣀⣖⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⣹⣿⠇⢀⣿⣿⣧⠈⢿⣿⠿⠟⠛⠛⢻⣿⣦⠉⣴⣼⣯⠀⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣾⣍⣉⢠⡍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠹⣿⡄⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣿⡄⠀⠸⣿⣆⠘⢿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠆⠀⠉⡼⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡏⠀⡀⠀⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠚⠛⠋⠀⠵⠤⠽⠶⠶⠶⠖⠶⠂⠀⠀⠐⠓⠒⠀⠠⠦⠐⠾⠛⠉⣋⡄⢴⣶⣶⣶⠦⠤

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⡻⣟⡛⣻⡛⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⠃⠀⠀⠀⠀⠀⠀⢀⡞⣩⣾⣿⣿⣟⣿⣏⠩⣟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⠀⠀⠀⠀⠀⣤⠿⣿⠻⣿⣿⡟⠉⣿⠈⢳⣝⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⢻⣷⡀⠀⠀⢠⣿⣾⣿⢿⣿⣿⣿⡄⢿⣴⣦⣽⣷⠉⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣻⡿⣿⣿⡇⠀⠀⠀⠉⣉⣶⡿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢿⣷⣶⣿⣟⣿⣿⣷⣿⣿⣿⣷⣤⡤⠔⠊⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡀⠀⣨⣽⣿⠛⠻⠟⠛⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠁⠘⢿⣿⣿⣶⣤⣞⠛⠀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣼⣷⣽⣷⣶⣤⣌⠙⢿⣿⣯⣴⣤⠖⠈⠉⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠀⠀⣄⣀⣿⣯⣭⣍⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠰⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠿⠃⠀⠀⠰⣿⣿⡀⡈⠁⠉⠈⠙⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⣡⣴⣦⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠁⣤⡄⢠⡄⢴⣶⣀⡀⢿⣿⣧⡀⠀⠀⠀⠀⠛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢀⣴⡎⠀⠀⠠⣤⣶⣿⣿⣧
⠀⠀⠀⠀⠀⣠⣶⣶⣿⠟⠩⠀⠀⢈⣤⣤⠀⣤⣶⡌⠣⠄⣿⣅⣀⣀⣰⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⠟⠁⢠⣤⣼⣋⣉⠀⣿⡟
⠀⠀⠀⠀⣴⣿⣿⡿⠇⠀⠀⠀⠀⠈⠛⠛⢀⡘⢻⣷⣶⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠟⠋⠀⠀⠐⠛⠛⠛⠛⠛⠿⢿⣿⣇
⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠶⠘⣧⣤⡉⠙⠃⠸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⡿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠉⠳⣶⣿⣿⣿⣴⣷⣂⣼⣿⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠀⠘⣿⣄
⠀⠀⠀⠀⠿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆
⠀⠀⠀⠀⠀⢸⣿⠙⢮⠳⡀⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇
⠀⠀⠀⠀⠀⠀⢸⠧⢣⢐⡜⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠘⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣮⣉⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣀⠙⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⣄⡀⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦