Blissfulness Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠿⠛⠛⠛⠻⠁⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣴⣿⠀⠀⣠⣤⣦⣴⢟⣱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⢀⣤⣴⣟⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡟⠀⠀⣴⠀⠀⠀⢰⣿⡙⠆⠀⣿⢀⡤⣀⣄⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣤⠿⠃⢠⣤⡽⣀⠀⢠⢉⡘⡃⣄⣀⢽⣯⣼⣿⣿⣇⢀⣀⣀⣀⡾⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⢿⣿⣽⣽⣿⠁⠀⠉⠉⣶⣾⣿⢙⣿⠿⣧⣴⣶⣶⣿⣏⠉⠉⠉⢻⣧⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⡿⢸⣵⣾⣇⣀⣀⣙⣿⣿⠀⠀⠀⠀⣿⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⡇⣿⣥⣤⡟⣛⠛⠋⢹⡇⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣸⠿⠿⠿⠟⢧⣄⣀⠀⣿⣿⠀⠹⣿⣬⡿⠿⠃⠀⣼⣷⣄⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⡄⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⢸⣿⠿⠃⢸⣿⣿⠀⠈⠛⢧⣤⣴⣾⣿⡿⠋⠀⢀⣼⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⣴⣾⠉⠹⣿⣿⣿⣿⣿⠀⠀⢠⣤⣿⣿⡇⠀⠀⢸⡿⢿⣿⣿⡇⠀⠀⠸⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣷⠀⠀⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠘⡿⠿⠻⣿⣶⣾⠘⠙⠿⣿⣿⣷⣶⣶⣦⣬⡟⠃⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⠀⠀⠈⣿⣿⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⠀⡆⠀⢻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡿⠀⠀⠀⣿⣿⡆⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⣁⣸⡇⠀⠸⣿⣿⠛⣿⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀⢸⣿⣷⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢀⡟⠉⠸⣿⣿⣿⣷⣄⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣆⢸⣿⣿⠃⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡀⠀⠀⣾⡇⠀⠀⣿⠟⣻⣿⣿⣷⡀⠈⠻⣿⠟⢿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⣿⡇⢀⣴⠷⠾⣋⣽⣿⣿⣧⠀⠀⠀⠀⠈⠛⠛⠛⠛⢳⣤⣴⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣩⡴⢾⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⢹⣷⠀⢹⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⡀⠘⣿⣿⣿⣿⣿⣿⠀⠉⠻⢿⣀⣀⣀⣾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣇⣀⣈⣉⣉⣀⣶⣶⣶⡶⠶⠞⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⢳⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠿⢿⠇⠀⠀⠀⠀⠀⠀⣾⣦⠾⣇⠀⠺⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡈⠓⠦⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⡙⠻⠷⣶⣾⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣽⡿⠿⠛⠋⠉⠉⠀⠈⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠁⠀⠀⣠⣶⣶⣤⡀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⢿⡆⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⣻⠿⠿⠿⠿⣿⠟⠀⣠⡶⠞⠳⠶⣄⠈⠁⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⢸⡇⠀⠀⣴⣦⢸⡇⣰⠋⠀⠀⢀⣄⢸⡇⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠁⠀⠀⠀⠘⣧⣄⣀⣈⣥⡟⠁⠙⣦⣀⠀⠈⣋⣾⠃⠀⠀⠀⠀⣿⣇⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠘⠛⠛⠋⠉⠉⠁⠀⠀⠀⠾⠛⠋⠙⢻⣧
⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⠿⠟⠁
⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣯⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠈⠻⢿⣶⣦⣤⣤⣴⣶⣶⡾⠿⠟⠋⢻⡏⠀⠀⠀⠹⣦⣀⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠛⠛⠛⠛⠛⠛⠿⣿⣷⣦⣤⣤⣤⣤⣴⣶⠶⠾⢻⣿⣿⣿⣿⡿⠿⠟⠛⠛⠻⠿⣿⣷⣦⣄
⠀⠀⠀⠀⢠⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⡀⠀⠀⣠⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⢀⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣤⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇
⠀⠀⣸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠇
⠀⠀⠹⠿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣦⣤⡄
⠀⠀⢾⣿⣿⣿⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⢿⣷⣮⣭⣩⣍
⠀⠀⠰⣶⣶⣶⣿⣿⢟⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⣷⣮⣍⣟⠛⠛⠉
⠀⠀⠀⠀⠉⢩⣽⣶⣿⠏⠙⠻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⠈⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠛⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⢿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠛⠻⠿⣿⣶⣤⣤⣀⣀⣤⣴⣾⠿⠛⠉⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⡀⠀⠉⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣸⡇⠀⠀⠀⠀⢀⣀⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⢉⣉⠻⣦⠀⠀⣴⠛⠉⠁⠀⠀⣀⠈⢷⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣷⣶⣶⣶⣾⣛⣻⣦⣾⣃⣀⣙⣶⣶⣶⣖⣛⣹⣷⣾⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠟⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢪⢏⠰⠀⢠⡇⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠁⠀⡀⠀⠐⠈⠁⠀⠀⢀⠀⠀⠀⠁⠐⠉⠉⠀⠀⠔⠃⠀⠘⠀⠀⠀⠀⠐
⡸⣼⠁⠀⢸⠇⠀⠀⡰⠁⠀⠀⠀⠀⠀⢠⠊⠁⡠⠈⠀⣀⣀⡤⡴⠞⠃⠀⠀⠀⠀⢲⠦⡄⠊⠁⠈⠀⣠⠓⠀⠀⢰
⠁⠁⠀⢀⡜⠀⠀⢈⡀⠀⠀⠀⠀⠀⠜⢁⢺⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠴⠋⠁⠁⠈⠙⠄⠀⠀⠀⢆
⠀⣠⠴⠋⠀⡠⠊⠠⠀⠀⠀⠀⠀⠀⠀⡎⠘⢀⠀⠀⠀⠀⠀⠉⠀⡠⠀⠀⠀⠀⡤⢡⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⣤⠈⠓
⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠂⠄⣀⣀⠉⠠⠈⠀⠀⠀⠀⠂⡀⠂⠀⠀⠀⠀⢡⡀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠨⠀⠀⠀⠀⠀⠐⠊⠠⡤⠀⠄⠀⢀⠀⡀⠀⠀⠘⡀⠀⠘⠦⠀⢀⡀
⠠⠀⠁⠀⢡⡔⠀⠈⠀⠤⡀⠀⠀⠈⠁⠀⠀⠐⢠⠁⠐⠒⠒⠈⢁⡀⢀⠑⡄⠀⢠⠡⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⢰⠆⠔⠛⠢⠄⠙⡀⠀⠀⠀⠈⠀⠀⠀⠙⠀⠀⠀⠀⠀⢇⠈⢀⠈⠲⢄⡀⠰⢆⠀⠀⠈⢂⠀⠀⠀⡀⡠⠊
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠐⡀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠒⠐⠂⠑⢤⡀⠂⠀⠀⠀⠂⠀⠀⡷⠁
⠀⠀⠀⡠⠆⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠁
⠤⠂⠔⠁⠀⣀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠈⡀⠂⠀⠀⠀⡀⠀⠀⠀⠀⣐⠂⢠⠀⠁⠀⡆⠀⠀⠀⠀⠀⠀⠐⠒
⠇⠀⠀⠀⠀⢀⠡⠒⡠⠊⠀⠀⡀⠀⠡⠀⡀⠠⠀⠠⠉⠁⢀⡛⠈⡃⢀⠀⠀⠀⠀⠀⠈⠀⠄⠰⠀⢠⠃⠀⠀⠀⠀⢢⠈
⠀⠀⡑⠒⠀⠀⠂⠈⡐⠀⠀⡀⠹⠀⠂⠰⠀⢀⠄⠀⠀⠀⠀⠀⢉⠳⡄⠀⠀⠌⢀⣀⣀⣠⠔⣁⠜⡡⠤⠐⠀⠀⠀⢈
⠀⠄⠂⠀⠀⠀⠂⢈⠀⢀⠎⠀⡀⠀⠡⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠑⡌⠂⠀⠀⣀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡠⠒⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠈⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⣀⡠⠋⠀⠀⠀⠀⠀⡉⠒⠂⠀⠘⠃
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂⠈⠀⠈⠄⠀⠀⠀⠤⠀⢁⣀⠀⣔⣁⡀⠀⠁
⠈⢈⠓⢀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠈⠥⡀⠀⠀⢀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠬⠀⠀⣁⠀⠁⠒⠤⣄⡐
⠇⠀⢣⠐⠀⢀⠀⠀⡼⠀⠀⠀⠀⠉⠉⠒⢀⠙⠀⠀⡰⠈⠀⠀⠀⠀⠇⢰⠀⠅⠀⠀⢠⠁⠀⠀⠀⠀⠈⠉⠀⠈⢢⡌⠓
⠀⠀⢋⠀⢀⠀⠒⠠⡄⠀⠀⠠⠀⠀⠀⡠⠝⠀⠀⠀⠀⡈⡀⠀⠀⠀⠈⠄⠀⠀⢀⡙⢸⠀⠀⠁⠀⠀⠀⠀⠌⢀⡀⠙⠂
⢄⠂⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡙⠠⠈⠒⠀⢄⡐⠂⠀⡠⠊⠂⠀⠀⠀⠀⠀⣠⢀⠀⠃
⠂⠄⡀⠀⠈⠀⠀⢸⡆⠀⠀⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠀⢀⣀⡀⠀⠀⠈⠁⢁⠤⠤⠖⡉⣢⠄⠲⡎⡀⠘⠀⠡
⠀⠀⢀⠀⠂⠈⠀⠯⢷⡀⠀⠐⡀⠀⠀⠀⠀⡈⠀⠀⠀⢀⣊⡁⢈⡉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠉⠀⠠
⠀⠈⣉⠠⠋⠀⠁⠀⠀⠁⠀⠀⠈⠠⠀⠀⣰⠊⠀⠀⢰⠏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠈⢀⠀⠃⠢⠀⡁
⢀⠀⠀⠐⠂⠀⡸⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠄⠀⠱⠀⠈⠂⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠰⠈⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠔⠂⠘⠲⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠐⡎
⠀⠀⡐⠀⠀⠀⢀⠃⠀⠀⠀⠄⠀⢀⡠⠔⠈⠉⡉⡑⠾⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠲⠄⣀
⠐⠒⠀⠀⠀⢉⠘⠀⠀⠙⠃⠀⠉⣀⠄⠀⠀⣨⠡⠘⠚⠉⠢⢄⠀⢀⡠⢂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⡴⠊⠁⠀⠀⠀⡄⠀⠈⠃⠀⠂⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⣀⠄
⠈⠁⠠⠀⠃⠀⠐⠁⠀⢠⠕⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠌⠀⠠⠀⠀⢀⠄⠂⠂⠀⠄⡀⠀⠁⡴
⡇⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠠⠂⠀⠀⠰⠀⠀⠣⢀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡁⢸⠀⣄⠉⠉
⠱⡀⠀⠇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠄⡀⣉⣀⠀⠀⣀⡀⠀⠀⠇⠈⢧⠐⢀⠀⠀⠀⠀⠈⠂⠂
⠀⠑⠚⠄⠠⠀⡔⠀⠀⠀⠐⠒⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠀⠀⠈⠣⠀⠀⡀⠀⠗⠨⡖⠀⠀⠀⠀⢠⡀⠂
⠒⠲⠤⡀⠀⢀⠀⠑⠠⠐⠒⣒⠀⠀⠰⠈⠐⠁⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠊⠀⠀⠀⠀⡰⠀⠀⠈⠀⠀⢀⡰
⠄⠀⠀⠈⢆⡀⠀⠀⠀⠉⠊⠁⠄⠀⠠⠂⠀⠀⢀⡾⠀⠂⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⡀⠠⣀⠀⠀⠀⠀⠀⠀⢠⠊⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣖⣂⣀⠄⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⡆⡠⠤⠀⠀⠀⠀⠀⣶⡄⠀⠀⡀⠙⠀⠀⠀⠀⠀⠈⡀⠀⠀⠯⣦⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⠀⠙⢯⣡⡿⠁⠐⠂⠀⢹⣧⠀⡀⠀⠀⠀⠀⠀⠰⠆⠀⢀⠀⠐⠚⠁⣀⣤⡄⠀⠀⠀⢀⠠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⣀⠀⠀⠀⠼⠛⠉⢀⠈⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠐⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣰⡿⠋⠉⢻⣧⠀⣀⣀⣀⣤⡤⠤⠤⠤⠤⠴⢒⣶⠶⠂
⠀⠀⠀⠈⢹⡏⠉⠁⠈⠉⠙⢷⡄⢠⡆⠀⠀⠈⣛⠁⠀⣰⡟⠀⠀⠀⠾⠏⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⣀
⠀⠀⠀⠀⢸⡇⠀⣀⡀⠀⠀⢨⡟⢸⡇⠀⠀⠀⣿⠀⠀⣿⠃⠀⢠⡾⢷⡆⢸⣧⠤⠤⠶⠖⠒⠒⠒⠚⠛⠉⠉⡉⠉
⠀⠀⠀⠀⢸⡇⠀⠛⠃⠀⣠⡿⠁⢸⡇⠀⠛⠀⣿⠀⠀⣿⡀⠀⢿⣇⠀⠀⢸⡇⠀⠀⢀⠀⠀⢠⡄⠀⡆
⠀⠀⠀⠀⢸⡇⠀⠀⣠⡾⠋⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢻⣇⠀⠈⢻⣦⠀⢸⡇⠀⠀⣾⠇⠀⣸⡇⢸⡇⠀⠀⡀
⠀⠀⠀⠀⢸⡇⠀⠾⠿⢦⣄⠀⠀⢸⡇⠰⠀⠀⣿⠀⠀⠈⢿⣆⠀⣄⢻⡇⢸⣷⣶⡄⣿⠀⠀⣿⡇⢸⡇
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠙⣷⡀⢨⡇⠀⠀⠀⣿⠀⠀⠀⠈⢻⣦⠙⠋⠀⢸⡏⠈⠀⣿⠀⢸⣿⡇⢸⡇⠀⠶
⠀⠀⢀⡀⠀⣿⠀⠀⠀⠀⠀⢹⡇⠈⡇⠀⠀⠀⣿⠀⠀⠀⠂⠀⢻⣧⠀⠀⢸⡇⠀⢰⣿⠀⣾⣿⡇⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠉⠀⠀⠀⣾⠇⠀⣧⣤⡤⠤⢤⣤⠄⢠⡆⠀⠀⣿⠀⠀⢸⡇⠀⠸⣿⢀⡟⢿⡇⢸⠋⠉⠹⢿⣯
⠀⠀⠀⢀⠀⣿⠀⠀⠀⣠⣾⠏⠀⠀⣷⠀⠀⠀⣩⣵⠒⢸⣧⠀⢀⡿⠀⠀⢸⡇⠀⠀⣿⣸⡇⢸⡇⢸⠀⠀⠘⢛⣥⡄
⠀⠀⠀⠀⠀⣿⣤⣴⠾⠋⠁⠀⠀⠀⣿⣀⣀⣤⠤⠽⠛⠃⠛⠷⠟⠁⠀⠀⠘⠃⠀⠀⠹⠟⠀⢸⡇⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠰⠾⢛⡉⠀⠀⠀⠀⣀⠀⢀⠉⠁⢀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⡀⠛⠀⠀⠀⣄⠀⠀⠀⠀⡀⣀⡀⠀⠁
⠀⠀⠀⠀⢠⣨⠟⠂⠀⣠⣾⠏⡤⠀⢀⡴⣗⠄⠀⠀⢰⣿⠀⠀⠀⠀⠸⣴⠆⠀⡀⠀⢿⣆⠀⠀⠀⠉⢯⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⢀⡼⠷⠀⠀⠐⠀⣿⡏⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠉⠁⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⠿⢿⣿⡇⠀⠀⠀⠈⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣯⣿⣿⣿⣿⠛⠳⠶⣶⠂⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣿⣿⣿⣟⠛⠁⢀⣤⣌⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠝⠙⠊⡽⠟⣿⣟⠿⠳⣞⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠙⠦
⠀⠀⠀⠀⠀⠀⠀⡿⢫⡤⣠⠀⢀⢠⡄⣹⠁⠀⠀⠸⣿⣿⠇⢀⣠⣀⣑⠦⡀⠀⠀⠀⠀⠀⠀⠜⠢⣄
⠀⠀⠀⠀⠀⠀⣼⠃⣛⣿⠋⠀⠻⣜⢧⢻⡄⠀⠀⠀⢿⠀⠀⠀⢳⣄⠈⣡⠑⠀⠀⠀⠀⡆⠀⠰⡶⣎⠑⢦⡁
⠀⠀⠀⠀⣠⠾⠻⣼⣽⣿⡑⢀⡀⢹⣿⣦⡘⠀⠀⠀⠘⣧⡀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⣿⣴⡷⣆⠙⢦
⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⢿⣤⣿⣞⢿⣿⣿⣆⠀⠀⠀⠘⣟⠷⢤⣤⣀⠀⠰⣀⠀⡠⠊⢤⣿⣤⡛⠛⢛⣽⠇⠀⠃
⠀⠀⠀⠀⣘⣿⣿⣿⣿⢿⣾⣿⣿⣿⣷⣿⣿⣿⡆⠀⠀⠀⠘⢦⣠⠀⡙⢿⠳⣞⢆⠁⠀⠈⠛⠛⠧
⠀⠀⠀⠀⢨⡿⠙⣿⣿⠈⣿⣿⣿⣿⣿⣿⣋⣿⣿⣦⠀⠀⠀⠀⠙⣂⣷⢸⡷⢾⣀⠀⠀⣀⣤⣞⣏⠈⠀⠀⠀⣠
⠀⠀⠀⢀⡜⠧⣉⣿⡏⠀⣿⣿⣿⣿⣟⣿⣿⣿⡟⢛⣷⣦⣄⠀⠀⠻⢻⢘⢿⠀⠈⣿⠛⠉⠉⠁⠙⠀⢀⣴⢊⡴
⠀⠀⠀⢾⠀⢠⣾⣿⠁⠀⢸⣿⣿⣎⣿⣿⣷⣾⣷⠿⢿⠋⢙⣷⠶⠿⢿⡎⣼⣿⠋⠈⠳⠆⠀⠀⠀⢠⣿⣿⣿⠃
⠀⢈⡄⢴⣿⣿⣿⠿⠿⠀⡴⠛⠛⢿⣏⣿⣪⣶⠝⣿⣾⣵⡟⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣿⠁
⢠⣾⣦⣾⣿⣿⣿⣦⣤⣀⣴⣿⣷⣸⣿⣧⣥⢻⣾⠘⢿⣿⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠃
⠀⠉⠻⠿⣟⢿⣿⣿⣿⡿⢯⠀⠻⣿⣿⣿⣿⣿⣵⣤⣾⣿⣿⣌⠻⣦⡀⠀⠀⠀⠀⣰⣿⣿⡟⣿⣿⡿⠁
⠀⠀⠀⠀⣾⣀⣽⣿⡟⠀⠄⠀⠀⠉⢛⣛⣿⢿⣿⣿⣿⣿⣿⣿⣷⡈⠻⣦⢀⣴⣾⡿⠋⢈⣴⣿⡟⠁
⠀⠀⠀⠘⢿⣷⣶⣭⣝⣛⠛⠛⠛⠛⠉⣉⣤⣾⣻⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⠟⠉⠀⠀⢸⣿⣿⡁
⠀⠀⠀⠀⠀⢻⣿⣈⡉⢹⠉⠉⡟⣏⠙⣏⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠸⡟⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣶⣿⠟⢋⣥⣾⡿⣿⠉⠋⢻⣹⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢻⣿⣟⠛⠋⢉⣴⣶⣙⢷⠁⢙⣀⡤⠲⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⡇
⠀⠀⢀⠐⠀⠒⠾⣿⣿⣿⠶⡞⠛⠻⣿⣧⡴⠋⠁⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⡇
⠀⠀⠁⣀⣥⠭⣾⣿⣿⡭⡚⠟⢷⡄⢻⣏⣀⢀⠤⣄⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⣶⣧⣾⣿⣿⣿⣿⠏⢱⣼⣾⣷⣀⡈⠝⠀⠀⣀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠻⣿⣿⣿⣿⣿⠠⠀⠀⠉⠁⠀⠙⣻⣦⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⢀⢼⣿⣿⣀
⠀⠀⠀⠉⠉⠠⠉⠙⠛⠶⠷⠷⠶⢾⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⣶⣏⣹⣶⡦⢀⣼⡿⡿⠿⠿⠿⣿⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠙⠋⠉⠉⠙⠉⠋⠉⠙⢉⣉⣈⡉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣦⢚⡵⣦⣤⣴⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠤⠽⠡⣯⣭⣉⣚⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⠀⠀⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣼⣀⢀⡀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠉⠀⢸⣿⣿⣿⣷⣾⡟⢿⢷⠾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢶⣆⣈⣿⣿⣿⣯⠬⠙⠋⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⢿⣦⣾⠟⣱⣾⣆⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⣿⣿⡆⡙⢻⡟⠛⠿⠻⠝⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠃⠀⠰⡴⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⡀⢁⣼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⣿⣿⡟⠉⡙⠶⣶⣾⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⣶⣿⣿⣤⡜⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⡇⠀⠈⠹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣧⣿⣿⣿⣿⣾⣇⣤⣀⣠⡽⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠹⣿⣿⣿⣟⡋⠀⠀⠀⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⢶⣶⣿⣷⡽⢷⡖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠻⠿⠿⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣰⠀⡀⠀⠀⠀⠀⠀⣀⣤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣳⠋⠸⠃⠀⠀⠀⢀⡾⣩⣴⡄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣁⣁⣤⣤⣴⠖⠒⢦⡿⢠⣿⣯⡇⠀⢸⡇⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠉⠻⣆⠀⣰⠟⠁⣀⠙⠋⠉⠋⢀⣠⡁⢀⣴⡄⢀⣿⣿⡟⣼⠀⠘⠁⣸⣿⡟⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⣠⡶⣶⡀⠀⠘⣿⠃⠀⣸⣿⡇⢸⣿⢀⣾⡏⣷⣿⣇⡇⢸⣿⣿⢱⠋⠀⠀⢠⣿⡿⠁⠘⣭⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣼⠟⣿⣿⡇⠀⠀⣿⠀⠀⣿⣿⡇⢠⣤⢸⣿⣇⢿⣿⡿⠀⣾⣿⡇⣀⣴⢠⡶⣸⣿⠃⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⠁⠀⢹⣿⠇⠀⠀⠙⠀⠀⣿⣿⠁⣼⣿⢸⣿⡟⠘⣿⣷⠀⣿⣿⡛⣹⣧⣿⠇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠇⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⡟⠈⣿⣿⡼⣿⣿⣰⣿⡿⣧⣿⡟⣿⡴⢿⣿⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⢰⣿⣵⣾⣟⣷⣦⡀⠀⣿⠀⢸⣿⡇⢀⢿⣿⡇⢸⣿⠃⣿⡇⡿⠉⠀⠉⢁⡈⢿⡿⠏⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣠⣿⠿⠟⠛⠿⣿⣿⣷⡼⣿⡆⡼⢻⣧⡞⢠⣿⡇⢸⣿⠀⢻⣇⡇⢰⠶⠖⠻⡇⠀⠀⣠⡞
⠀⠀⠀⠀⠀⣀⣀⡀⢸⣿⠃⢴⠟⠁⠀⠀⢀⣀⠘⣿⣿⣇⠹⣷⠃⠈⡉⠀⡾⢿⡇⣏⡟⠀⠘⠿⢁⡟⠀⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠉⣩⠄⢸⣿⠀⠀⠀⢀⣴⣾⡿⠋⠀⣿⣿⣿⢠⣤⡤⢾⡇⠀⢧⠿⠁⡉⢁⡼⣦⣤⠞⠁
⠀⠀⠀⠀⠀⠚⣣⠀⢸⣿⠀⠀⣰⣿⣿⡟⠁⠀⠀⣿⣿⡿⢸⡇⠀⠀⢷⣀⠀⣀⡼⠙⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠈⣿⠀⢀⡿⣾⣿⠀⠀⠀⢰⣿⣿⠇⣼⠀⣰⢀⠀⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⡇⣿⣿⠀⠀⢠⣿⣿⡟⣰⠇⢠⡟⣼⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢿⡹⣿⣷⣶⣿⡿⠋⣴⠋⠠⠟⢱⠏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⣉⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⢀⡆
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⡇
⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠒⠒⠒⠤⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡇⠀⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠁⡄⠀⠀⠀⠀⠀⠀⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⡇⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣤⣤⠄⢀⠠⠔⠒⠒⠀⡇
⠀⡇⠀⠀⠀⠀⢀⡀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣄⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⢤⠤⠖⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠛⠛⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣀⠈⣃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢇⡀⣈⣀⡈⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⡄⢀⡼⠀⠀⠀⠀⠀⠀⠀⣤⠤⣤⣀⡀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⢠⡇
⠀⡇⢸⠃⠂⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⢀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣁⡀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠤⠀⠁⠀⠂⠠⠀⢀⣀⣀⠀⠄⢁⣀⣀⣀⣄⣂⣈⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣦⣠⣀⣌⣀⣀⣀⣠⡇
⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡏⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⣿⡯⢿⣿⡽⣿⡏⣿⣏⣿⣟⣽⢏⣿⣍⣿⣿⣋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠂⠓⠀⠀⠀⠠⢿⣿⣧⠿⣶⣯⡿⣇⣯⡟⣮⣯⣾⣞⣹⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⡇⠀⠀⠀⠀⠀⠀⠀⢈⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⣿⣽⣿⣽⣿⣾⣿⣷⡿⣾⣽⣟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡
⡇⠀⠀⠀⠀⠀⠀⠀⢈⡛⠛⠛⠓⢶⡀⠀⠀⠀⠀⠀⠀⢉⠽⠛⢿⢿⣾⣯⣿⣷⣶⢿⠟⠻⢌⠀⠀⠀⢰⣿⣶⠀⠀⠀⠀⠀⠀⠀⠤⡀⠠⠃
⡇⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠋⠩⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⡟⠙⠉⠀⠀⠀⠀⠠⠀⠀⠘⠛⠛
⡇⠀⠀⠀⠀⠀⠀⠀⠹⣶⠶⢶⣶⣶⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠈⠈⠑⣦⡤⠀⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢾⡀⠀⡀⠀⠘⠡⠔⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⠌⠩⣤⣶⡶⠟
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠢
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⡠⠌⠀⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠖⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣒⢶⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢧⣛⡼⠥
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇⠘⠋⢀⡟⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠋⠈⠉⠉⠉⠉⠉⠙⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⣀⡀⠤⠀⠐⠂⠒⠒⠒⠂⠤⢄⣀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⡤⠒⠉⠀⠀⢀⡀⠤⠤⠤⠤⠤⠀⣀⠀⠀⠈⠐⠤⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⠞⠁⠀⠀⠀⠈⠀⠀⢀⣀⡀⠀⢀⣀⣀⡀⠀⠉⠒⠤⡀⠀⠑⢄⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡠⠊⠀⡠⠂⠁⠀⠀⠐⠈⠀⢀⣀⡀⠀⢀⣀⣀⠉⠉⠒⠤⡀⠈⠑⢀⠀⠉⢦⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡔⠁⡠⠊⢀⠤⠊⢀⡠⠔⠊⠉⠁⠀⣀⣀⣀⠀⠀⠉⠑⠂⢄⡀⠑⢄⡀⠑⢄⠀⠱⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡜⠀⡔⠁⡠⠁⣀⠔⠁⢀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⠀⠀⠈⠢⡀⠑⢄⠀⠳⡀⠱⡀⠈⡆
⠀⠀⠀⠀⠀⠀⣀⠼⠤⠴⣀⡜⢀⣎⣀⡔⠁⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠢⠀⠣⠀⠱⡀⢱⠀⢰
⠀⠀⠀⠀⣀⠎⠁⠀⠀⠀⠈⠖⠋⠁⠀⠈⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⢱⣀⠷⠤⠷⡀⣦⠚⠁⠒⠒⠒⠐⠢⡀
⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⡠⠒⠠⠔⠚⠁
⠀⠀⠈⠒⠢⠤⠒⠉⠑⠤⠀⣀⣀⣀⡠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠂
⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠴⠓⠁⠀⠀⠀⠀⣀⡤⢴⠒⡖⣲⢦⣀
⠀⠀⠀⠀⠀⠀⢠⣞⡍⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣀⡀⠤⠊⠀⠀⠀⠀⠀⢠⠺⡅⠃⢰⠀⠀⠁⠈⡘⢹⢦
⠀⠀⠀⠀⠐⠀⠈⠙⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠂⠱⠀⠀⠀⠀⠀⠐⢀⠊⡼⡇
⠀⠀⠀⠀⠀⠘⠒⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡢⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⠠⢤⠄⠁⠀⠀⠀⠀⠀⠙⠦⣬⠁⢀⡠⣤⢄⡀⣤⠔⠛
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⡍⠀⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⣤⣶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⡄⠀⠰⠂⠀⠀⠂⠀⢀⣀⠀⠀⠀⠄⠲⠀⠀⠀⠀⡀⠀⣠⠆⠀⠀⠆⠀⢀⠀⠀⢀⠀⠀⠀⠰⠀⠀⡠⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⡀⠁⠀⠀⠁⠓⠀⠀⠁⡄⢀⠆⡰⢡⣷⣊⡄⠀⠔⠀⢀⠀⠀⠀⠄⠈⠀⠐⢤⣄⠀⠀⠀⠐⠈⠁⠀⢀
⠀⠀⠈⣄⡠⠁⠀⠀⠉⠀⠃⠀⡄⠀⡇⢰⠃⠈⢠⣶⡪⠥⠂⠀⠃⠀⠠⠀⠐⠀⠀⠔⠠⠠⠄⠀⠀⠉⠓⠤⡄⠀⠀⠀⠉
⠀⠈⠁⠀⠁⠀⠠⠤⠀⡀⢰⠀⠙⠸⠀⡀⢠⣶⠋⠄⠄⠒⠂⠐⢁⠀⠀⠀⠠⠆⠀⠀⠀⠠⣠⠎⢀⠀⠀⠀⠀⠺⢆⠀⠈
⠈⠀⣄⠀⠀⠀⠀⢰⠀⡇⠈⠀⡆⢸⡰⠷⠇⠀⠀⠀⠒⠒⠀⡀⠀⠀⢀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠘⠀⡤⠀⢠⠂⠘⠃
⠀⠀⠀⢄⠀⡆⠀⢀⡀⠀⢰⠀⣧⣈⣉⠓⠂⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠠⠀⢀
⠀⡀⠰⠸⠀⢇⠀⠀⡇⢻⣘⠁⠀⠀⠀⠁⠀⠉⢉⡁⠀⣀⠀⠀⠄⠀⠀⠀⠀⠟⠂⠀⠀⠐⠀⠀⠀⠈⠂⠀⠀⠀⠂⠐⣄
⠀⠓⠀⠀⠀⢸⠀⠀⠣⠤⣬⡉⢀⠁⠒⠦⠄⠀⠞⠙⢦⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⣇⠘⣤⣘⣓⠒⠂⠠⠤⣈⠛⢂⡤⢨⢥⠛⡀⣁⠐⠆⠀⠀⠀⢀⠆⢀⠀⠀⠊⠀⠀⠐⠒⠀⠀⠿⠄⠀⠀⠀⢁
⠀⠀⠀⠀⠐⠓⠒⠀⠠⢄⣈⡑⠂⠀⠀⣉⠝⣇⠈⠆⠁⣨⠀⠘⠃⠈⡡⠄⢀⠀⠀⠈⠀⣀⠄⠀⠀⠀⠛⠀⠑⡄⠀⠀⠈
⠀⡠⠂⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠈⠁⠀⢠⠀⠺⠀⠀⠀⠀⠀⠼⠃⠈⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠐
⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠘⠀⠘⠀⠀⠀⡠⠚⠀⠀⠀⠀⢀⠠⠋⢀
⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⣢⡄⠉⠀⠀⠀⠀⠄⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⢆⠀⠀⠀⠀⣰⠦⠤⠄⠀⠀⠀⠤⠀⡀⠄⡀⠀⠀⠊⠀⠀⠉⠀⠀⠀⠈⠁⣀⠜⢏
⠀⠀⠀⢀⣀⠄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⡜⠓⠀⠂⠀⢀⣀⠐⠀⠐⠃⢀⡠⠀⢰⠀⠁⠀⢀⡠⠀⠀⠰⠀⣠⠒⠀⠘
⠠⠤⠒⠊⠉⠀⠀⠈⢀⠀⠈⠀⠐⠄⠀⣴⣋⡁⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⠔⠋⠀⠂⠀⠔⠀⠀⠤⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠂⠀⠀⠰⠯⠀⠀⠀⡀⠀⡋⠀⠀⠂⠀⠀⠱⠀⠀⢠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡲⠄⠀⠰
⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢣⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠦⡀⠀⠊⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠜⠊⠀⠀⡀⠀⠀⢀⠔⣴⣾⣿⣿⡿⣿⣿⣿⣿⣷⣦
⠀⠀⠁⡀⠀⣐⠆⠂⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠡⠐⠀⠊⠀⠀⢆⠀⠀⠈⡠⠀⠁⢸⣿⣿⡿⢿⡷⣿⣿⡿⣿⢿⣿
⠀⠀⠃⠀⠀⠀⠿⠰⠙⠀⠒⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠱⠀⠀⠀⠀⠀⢸⣿⢸⡇⣻⡇⢹⠃⡆⣿⡸⣿
⠀⠀⠀⢀⠠⠊⠀⠄⠀⠀⠀⠀⠀⢠⠀⣤⢀⣀⣐⠀⠀⠀⠀⠀⠀⠈⠁⡠⢐⠊⠔⠃⠀⠘⣿⣼⣧⣻⣴⣾⣴⣇⣿⣣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠓⠶⢤⣀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠀⠀⠀⠈⠉⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣠⣶⠾⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠇⠀⢀⣀⣠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠘⣆⠀⠀⢀⣠⣤⣷⣤⣄⡀⠀⢹⣧
⠀⠀⠀⠀⠀⢰⣿⣠⡾⠟⠛⠛⠿⣶⣄⣤⣤⣼⣧⣤⣀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⢸⣤⣾⠟⠉⠁⠀⠈⠙⠻⣦⡘⣿
⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠈⠛⠉⠁⠰⠶⢭⣙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣠⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⢀⣴⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣤⡀
⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠙⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣮⣭⣋⣠⣤⣶⣧⡀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠻⠷⠶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠒⠂⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠦⠤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠑⠄⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠉⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠁⠀⠄⠀⠀⠊⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠰⢷⠀⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⡂⠀⠡⠂⠀⠄⠀⠀⠀⠀⠠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⡁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠔⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⠀⠄⠞⠂⡑⢄⠀⠀⠀⠀⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠊⠈⡀⢀⠀⠀⠀⠀⠘⢄⠁⠀⠀⠀⠈⠢⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠄⠰⡄⠀⠄⠈⠕⠀⠀⠀⠀⠀⣬⡤⠴⠓⠀⡐⠀⠀⠠⠑⠀⠀⠠⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠢⡑⢄⠂⠀⠀⢈⠢⡀⠢⡑⣌⠢⣀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣦⠀⠊⠁⢈⣣⡚⠀⠀⢂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⠁⠁⢀⠀⠋⠜⠂⠈⠑⠶⠈⢢⡄⠀⡀⠤⣖⡱⠐⠀⠀⢀⠀⠰⡣⠀⠀⠨⠓⠁⠀⢀⢘⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⢌⠢⢃⠂⢄⠈⠀⠀⠒⠲⠦⣤⣤⠖⠋⠁⠰⠂⠁⠘⠛⠛⠃⠁⠀⠀⠁⠘⠁⡤⣌⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢡⣌⠓⡀⠄⠐⣊⣤⠗⠋⡙⠦⢰⢤⠂⡿⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡆⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⠜⢋⡡⠶⡛⠁⠀⠀⣚⣅⢀⡉⡆⠰⡏⠀⠀⠀⠉⠉⠉⠉⠙⢻⠀⢸⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⠡⠂⠀⠀⠀⠢⡙⢯⠀⠈⠁⠀⠀⠀⢠⣘⣇⠀⠀⣠⣤⡀⠀⠀⠀⠌⠀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠢⣑⠄⠀⠀⠀⠰⡏⠀⠀⣹⣿⠁⠀⢙⣷⣤⣤⣤⣤⡞⢠⠍⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠊⠁⠈⠑⠒⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⢡⠀⠀⠀⠀⠠⠂⠄⠈⠀⠀⠜⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣐⣰⢁⠀⡈⠡⠔⠩⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠘⠈⠁⠒⢠⠃⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠳⣄⠀⠀⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⣓⡔⠀⠀⠀⠀⠀⠀⠒⠤⠀⠒⠁
⠀⠀⠀⠀⠀⠒⠂⠀⠁⠀⠀⠀⡅⠀⠀⠈⠠⠆⠙⠛⠁⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠋⠇⡀
⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠓⠒⠀⠑⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠈⠀⠀⢀⢷⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠪⠥⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠀⠀⠂⠀⠀⠄⠀⠀⠰⡙
⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⡆⠀⠀⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠈⠡⠤⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡀⡇⠰⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠎⡄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠙⠒⠂⠂⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⢀⢤⣤⣤⢤⣤⣀⢀⡀⠀⠀⠠⠌⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡀
⠀⠀⠀⠀⠀⠀⠸⠟⠁⠁⠀⠀⠈⠓⠇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⢀⠀⡰⠊⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸
⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠠⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢁⠜⠁⠀⠀⠁
⠀⠀⠐⡵⢋⠞⠡⠄⣀⢀⠀⣀⠀⡄⢢⡘⢮⡳⠀⠀⠀⠀⠀⠀⠀⡀⠀⠼⠠⠇⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢡⠏⢀⠉⠐⠃⢈⠀⠸⠀⢠⠀⢱⣌⡇⠀⠀⠀⠀⠀⠀⠀⠈⠘⢸⠸⠀⠀⢀⠄⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠳⢾⡀⢼⠀⢸⠀⠠⡄⠀⣧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⡇⠀⣀⠔⠁⠀⠀⠀⠀⠈⠀⢔⠢
⠀⠀⠀⠀⠀⠀⠑⠚⠐⠚⠀⠐⠃⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⡐⠀⠀⠈⠔⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠇⠀⠀⠀⣀⢀⠀⠀⠀⠀⡞⠀⠃⡀⠀⠆⢀⠖⠁⡀
⠀⠀⠀⠀⠀⠀⣠⠖⣄⠗⠚⡡⠐⠀⢘⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣷⣤⡀⣼⠃⣦⡥⣦⣥⣔⣃⡴⠿⠋⠉
⠀⠀⠀⠀⠀⣰⣫⣴⣋⣉⡀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡷⠒⠉⠓⠃⠀⠀⠀⠈⠀⢀⡑⣾⠟⠓⠚⠻⢷⢝⡇⠁
⠀⠀⠀⠒⠈⠉⠉⠉⠉⣠⣄⠀⠀⠀⣇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠰⣆⠑⠤⠔⢈⣿⡓⠃⠀⠤⢶⢤⣄⡀⢣⣠⣤⡀
⠀⠀⠀⠀⠀⠀⢸⠀⣉⣿⠙⡎⣄⣀⣡⠀⠀⣀⣀⡟⠀⢾⡁⠀⠀⠀⠀⠘⢦⠤⠴⠾⠛⢿⣦⡀⢀⢠⣟⠊⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠈⠉⢹⣯⠀⠹⡌⠧⣿⠀⢀⡩⢋⠀⠀⢸⠋⠁⠁⠀⠀⠀⠀⠀⣠⡀⠀⠀⠉⠻⠷⢿⣀⠈⠀⠀⠒⠲⠦⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠠⡀⠀⠀⠀⢉⣁⡠⢂⢄⢿⠀⣄⠀⠀⠀⠀⠀⡼⣧⠡⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⠶⠶⠶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠻⣄⠘⠦⣀⡀⠀⢀⣴⢏⡞⢸⠀⢹⡀⠛⠀⢀⡸⣿⡇⠀⠐⡀
⠀⠀⠀⢸⠟⠫⠀⠀⡿⠀⠀⢹⢷⠀⣤⣉⣡⠀⠐⡇⠀⣼⠃⠀⢳⡀⢀⠀⠀⠀⠻⣆⢰⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⢰⡇⠀⢀⠈⠁⠀⠊⠁⠀⡟⠛⠻⠀⠈⠳⠂⠋⠀⠀⠀⠑⠾⣬⣀⠬⣷⣌⡋⠁⠀⢠⡞⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢹⠷⢄⣢⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⠋⠁⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⢰⡷⠾⠷⠶⠾⠿⠛⡄⠀⣀
⠀⠀⠀⠀⢡⠖⠠⢌⠳⡈⠆⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⢫⣶⣶⠄⢠⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣆⠀⡀⠀⡀⢶⠃
⠀⠀⠀⠀⠁⣴⣶⣄⡽⠁⢸⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⢀⠥⠀⣲⠏
⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⡼⠀⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠈⣿⣟⣻⠁
⠀⠀⠀⠀⠀⠢⠀⠄⠙⢻⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⣱⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠶⡀⠀⠀⠀⠀⠀⠸⣿⡅
⠀⠀⠀⠀⢀⢦⠀⠀⠀⢸⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣬⣛⡻⢿⣿⣦⣄⠀⠀⠀⠀⣀⠴⠚⣁⡤⠶⠿⣧⠀⠀⠀⠀⠀⣀⡇⣀⣀
⠀⠀⠀⠀⠼⢦⣤⣙⠲⢿⠗⠑⠀⠀⡇⠀⠀⠀⠀⢠⣿⣀⣠⣭⣭⠿⡻⠿⢷⠄⠠⠊⠀⠈⣠⡴⣶⡮⠶⣶⣂⠀⠀⠀⠘⠯⠁⠑⠋⡁
⠀⠀⠀⠀⠀⠈⠀⠀⠚⠋⠀⠀⠀⠀⠇⠀⠸⠀⠀⠿⠷⠶⠒⠛⠛⠛⠛⠛⠓⠶⠷⠒⠛⠛⠛⠛⠛⠛⠻⠿⠿⠆⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠿⠛⠛⠛⠋⠙⠛⠛⠛⠿⢿⣿⣿⣶⣤⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠉⢠⣤⠀⠀⠀⢰⣿⠄⠀⠀⢀⣤⡀⠈⠙⠻⣿⣿⣷⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣠⣾⣿⡿⠋⢁⡀⠀⠀⠈⠋⠀⠀⢀⣀⣀⣀⠀⠀⠈⠛⠁⠀⠀⣀⠈⠙⣿⣿⣧⡀⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠻⠟⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠛⠲⢤⣀⠀⠘⠿⠃⠀⠈⠻⣿⣿⣄⠀⠈⠁
⠀⠀⠀⠀⢀⡀⠀⠀⢠⣿⣿⡟⢁⣤⡀⠀⠀⣠⠞⠉⠀⣀⣤⣶⣶⣿⣿⣶⣶⣦⣄⡀⠈⠳⣦⡀⠀⠀⣤⡄⠹⣿⣿⣆⠀⠀⣀⡀
⠀⠀⠀⠀⠈⠁⠀⢠⣿⣿⡏⠀⠀⠛⠁⢠⡞⠁⢀⣴⣾⠟⠋⠁⠀⠀⠀⠀⠈⠉⠻⢿⣦⡀⠈⠳⣄⠀⠛⠁⠀⠸⣿⣿⡄⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⣤⡄⠀⣠⠏⠀⢠⣾⡟⠁⠀⣀⣤⠶⠞⠳⠶⢦⣄⠀⠀⠙⣿⣆⠀⠹⣆⠀⣠⣤⠀⢹⣿⣿⡀⠀⢀⡀
⠀⠀⠀⠻⠀⠀⢸⣿⣿⠁⠀⠙⠁⢠⡏⠀⢠⣿⠏⠀⢀⡼⠋⠀⠀⠀⢀⡀⠀⠙⢷⡄⠀⠘⣿⣇⠀⢹⡄⠘⠋⠀⠈⣿⣿⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣀⠀⠀⣾⠀⠀⣿⡏⠀⠀⣾⠁⠀⠀⢺⣷⣿⡗⠀⠀⠀⢻⡄⠀⢸⣿⡀⠀⢷⠀⢀⣀⠀⢹⣿⣿
⠀⠀⠰⠖⠀⢀⣿⣿⡇⠘⠛⠃⢠⡇⠀⢸⣿⠁⠀⢸⡇⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⢸⡄⠘⠟⠀⢸⣿⣿⡀⠀⠲⠆
⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠁⠀⠘⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠃⠀⠈⠁⠀⠀⠀⠀⠛⠛






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠁⠀⠀⠀⠉⠙⢿⣿⣦⡀
⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢁⣴⣾⣿⣿⣿⣿⣿⣶⣄⠙⣿⣇
⢠⣿⣏⣿⢻⣧⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢺⣿⡿⠋⠉⠛⠿⠿⣿⣿⡆⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡄
⣼⣿⣹⣼⣆⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡧⣶⣶⡀⣴⣶⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⢣⣿⣿
⢿⣏⠿⠟⢻⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠈⠉⢹⣿⠉⢹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣷⣯⣟⡾⣿
⠈⣿⣆⠀⠘⠁⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣰⡾⠿⢿⣷⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠘⢿⠁⠈⠉⣼⡏
⠀⠘⢿⣦⣴⡆⣾⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠈⢁⣠⣼⡿⠁
⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡟⢀⣼⣿⡏
⠀⢀⣾⣿⣿⣿⣿⢻⡏⣿⣿⣆⠀⠀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣍⡻⠆⠀⡿⠃⣹⣿⠿⣿⣿⣿⣶⣦⣤⣄⡀⠀⠀⠀⣾⡟⣿⣿⣷⣾⣿⣿⡇
⠀⣾⣿⣿⣿⣿⣿⠘⠃⣿⣿⣿⣿⣿⡿⢁⠈⢿⣿⠁⠈⢿⡟⢿⣿⣿⣷⣤⣴⣿⣿⣿⠀⣿⣿⣿⡟⢻⣿⠿⢿⣷⣶⣶⣿⡇⠉⢿⣿⣿⣿⣿⣇
⢸⣿⣿⣿⣿⣿⣿⠀⠀⣿⠋⣿⠁⣿⡇⣾⠃⠘⣿⠀⠀⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⡇⠀⣿⡟⡿⠀⣿⡏⢠⣾⣿⠉⣹⣿⠃⠀⢸⣿⣿⣿⣿⣿
⢸⣿⢻⣿⣿⣿⣿⠀⠀⣿⡇⣿⣷⣿⡇⣿⠀⠀⠉⠀⠀⠀⠀⠀⣿⣇⠸⣿⠟⣡⣿⡇⢸⣿⡇⠀⢸⣿⢰⣿⣿⡟⢰⣿⣿⠀⣀⢸⣿⣿⣿⣿⣿⡆
⣿⣿⢸⣿⣿⣿⡇⠀⠀⣿⡇⢻⣿⣿⣿⣿⡄⢀⠀⠀⣤⠀⠀⠀⣿⣿⠀⣠⣴⠟⣹⠃⢸⣿⡇⠀⣼⣿⣿⢻⣿⡇⣾⣿⣿⠀⣿⢸⣿⣿⣿⢿⣿⡇
⣿⣿⠘⣿⣿⣿⡇⠀⢰⣿⣿⡸⣿⣿⣿⣿⣷⢸⣇⠀⣿⡇⢸⡆⣿⣿⣾⠟⠁⣠⣿⠀⢸⣿⡇⠀⣿⣿⡿⢸⣿⣿⣿⣿⣿⠀⣿⠸⣿⣿⣿⢸⣿⡇
⢿⣿⡆⢿⣿⣿⠁⠀⣸⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣾⣿⣿⠟⢁⣤⣾⣿⣿⠀⢸⣿⡇⢀⣿⣿⡇⣸⣿⢸⣿⡿⣿⡇⣿⠀⣿⣿⣿⢸⣿⡇
⠸⣿⣿⣬⣿⠏⢸⠇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡿⣋⣥⣶⠿⣿⣿⣿⣿⠀⢸⣿⡇⢸⣿⣿⡇⢿⣿⡄⠉⠁⣿⣷⣿⡆⢻⣿⡟⣸⣿⡇
⠀⠹⣿⣿⣋⣴⣟⣼⣿⣷⣿⠿⠛⠉⢁⣼⣿⣿⣿⣿⣿⡿⠿⠛⣉⣴⣾⣿⣿⣿⣿⠀⢸⣿⡇⢸⣿⣿⡇⢸⣿⣿⣦⣾⣿⣿⣿⡇⢸⣿⠃⣿⣿⡇
⠀⠀⠈⠙⠻⠿⠿⠛⠛⠛⠁⠀⠀⠀⢸⣿⣧⣉⣉⣉⣀⣤⣶⠿⢛⣿⣿⣿⣿⣿⡟⠀⣸⣿⡇⢸⣿⣿⡇⣸⣿⡟⠿⠿⣿⣿⣿⣿⡌⠋⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠛⠛⠛⠋⢉⣠⣴⣿⣿⣿⣿⣿⣿⡇⠀⢩⣍⡁⢠⣯⣿⡇⢸⣿⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣶⣶⣶⣾⣿⣿⡿⠟⢉⣾⣿⣿⣿⡇⠀⢽⣿⣧⢸⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⡉⠉⠉⠉⢁⣠⣴⣿⣿⣿⣿⣿⡇⠀⢸⣿⣷⣼⣿⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣍⠉⠉⢉⣡⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡻⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢿⡦⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⢀⣩⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡇⢹⣿⣿⠀⠀⣿⣿⣿⣿⡇⢿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⡇⢻⣿⣿⡇⢸⣿⣿⠀⠀⣿⣿⣿⣿⡇⢸⣿⢸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠔⢉⡤⠒⢶⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⡗⠒⠦⡈⠒⢄
⠀⠀⠀⠀⢀⠞⠁⣴⢋⠔⡩⣻⡆⠀⠀⠣⣀⣀⠀⠀⠀⣀⣠⠜⡀⢈⣰⣟⢌⠢⡘⢦⠀⠑⡄
⠀⠀⠀⡠⠁⣤⠚⡧⡎⡼⢨⢯⢟⡷⣦⣄⣠⠬⠷⠀⠚⠤⢄⣠⣴⢾⡻⡝⡅⢣⣹⢼⡓⣦⠈⢆
⠀⠀⡰⢁⡴⢋⡾⣱⢫⢗⡿⣼⣨⣊⡶⠋⠀⠀⠀⠀⠀⠀⠀⠙⢶⣐⣅⣷⢿⡺⡝⣎⢳⡜⢲⡈⢆
⠀⠠⢁⠞⣠⠟⡴⢣⡯⠞⠚⢧⡇⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣸⠼⠉⠓⠽⣌⢢⡙⣄⠱⡌⠄
⣐⡡⠮⠴⠷⠚⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠙⠚⠳⠽⢮⣢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠤⠈⠀⠀⠀⠀⣀⣀⣀⣀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢁⡾⠤⠒⠒⠚⠛⠛⠓⠒⠒⠤⢄⡀⠉
⠀⠀⠠⢤⡀⠀⠀⠀⠐⠢⠄⣸⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡐
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠉⠒⠤⠤⠒
⠀⠀⠀⠀⠀⢱⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠠⠐⠈⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⠒⠁
⠀⠐⠓⠲⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠙⢦⡀
⠀⠀⠀⠀⠈⠢⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢤⣀⣀⡄
⠀⠀⠀⠀⡠⠔⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠜
⠀⠀⢠⠊⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣀⠀⠄⠂⠁
⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡄
⠀⠸⠈⠁⠉⠐⠠⢀⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠔⠂⢙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡈⠀⠈⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣤⡤⠖⠋⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣀⠤⠚⠩⡀⠀⠀⢀⠞⠉⠢⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡴⠋⠁⠀⠀⠀⠀⠑⢄⡀⠏⠀⠀⠀⠈⠑⠒⠠⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠿⠛⢻⣿⣿⡟⠛⠿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠁⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⢀⣴⣿⣿⡿⠋⢸⣿⣿⡇⠙⢿⣿⣿⣦⡀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏
⣴⣦⣄⢇⣰⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣴⣿⣿⡿⠋⠀⠀⢸⣿⣿⡇⠀⠀⠙⢿⣿⣿⣦⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣆⡸⣠⣴
⠙⠻⠿⢿⡿⠛⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡋⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢙⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠿⠟
⢠⣤⣤⣀⢣⢠⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⢸⣿⣿⡇⣀⣀⣤⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡄⡜⣀⣤⣤
⠘⠻⠿⠿⠿⢿⠛⠉⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠉⠛⡿⠿⠿⠿⠟
⠀⢠⣤⣤⣄⣈⢧⢰⣿⣿⡿⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⢿⣿⣿⡆⡼⣁⣤⣤⣤⡄
⠀⠹⠿⣿⣿⣿⡷⠿⡟⠉⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠉⢻⠿⢾⣿⣿⣿⠿⠏
⠀⠀⠀⠀⣠⣤⣄⣀⡘⢦⡸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢇⡴⢃⣀⣠⣤⣄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡿⢿⡋⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⢿⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠙⠺⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢺⣷⣀⠔⠋⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠟⠛⢻⣷⠀⢀⣀⣀⠀⠀⠀⠀⣀⠀⠀⣠⣤⣄⠀⣿⣭⡿⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠲⣶⣾⣋⣠⣿⣧⣿⠇⢰⣿⠛⣿⠇⠰⣿⡀⠋⣀⣿⠿⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠉⠉⠉⠻⠷⣦⡶⠿⣷⣾⠿⣧⣤⡿⠛⠛⠋
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⢀
⠀⠀⠊⠉⠳⢄⠈⠙⠋⠉⠉⠀⠁⠀⣁⠨⠜⠋⠁⠀⠀⠀⠀⣠⠀⠤⠈⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⡀⠴⠒⠋⠁⠀⢀⠐⠊⠈⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⢃⣀⣀⣀⡴⠏
⠀⠀⠀⠈⠐⠠⠖⠋⠀⠉⠀⢀⡀⣀⠀⠀⠀⠈⠁⠀⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠚⠁
⠀⠠⢀⣀⠠⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠂⠛⠂⠃
⠀⠀⠀⠀⡠⠴⡄⠤⠠⢨⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠸⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⢅⠀⠀⡄⠀⠀⠀⡤⢀⡄⡄⡄⡀⠀⠀⠀⠀⠀⠘⠦⠀⠠⣔⣰
⠀⠀⠰⡀⠠⠆⠠⠤⠴⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠋⠁⠉⠀⠁⠉⠙⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⠀⠐⠒⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⢀⡞
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢆⠀⠀⢠⠅
⠀⠀⠀⠀⢀⠐⠒⠂⠄⠀⠀⠀⠈⡄⠀⠄⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠐⠀⠀⠀⠈⡀⠀⠀⠀⠐⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠐⠄⠀⠀⠀⠀⠔⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⢀⡴⠞⠁⢠⣀⣀⣠⠤⠖⠒⠲⠶⠶⠶⠄⠀⠉⡑
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⠉⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁

⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠦⠀⠄⠂⠀⠀⠀⠁⠀⠔⠃⠀⠀⠀⠀⠀⡤⠂⠤⡄
⠀⠀⠀⢀⣯⣤⣶⣶⣄⣄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠆⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠘⠛⠟⠁⠀⠸⡆⠀⢀⡤⢀⣀⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊⣉⠥⠐⠛⠁⠀⠈⠈⠩⠉⠀⠂⠀⢼⣆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⠁⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠀⣠⠶⠦
⠀⢀⠈⡠⠂⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⠀⠀⠀⠄⠀⠀⡀⢀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠘⠁⠔⠀⠀⠀⠀⠀⣸⠏⠀⠀⢼⣒⠲⠞⢒⣠⣈⡀⣸⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠓⠀⠀⡆⡂
⠀⠀⠀⠰⠖⠀⠒⠀⠀⠞⠁⠀⠀⠀⠀⠉⠛⠛⠛⠻⠿⠶⠞⠁⠀⠀⠚⠓⠚⠓⠀⠐⠐⠛⠓⠛⠂⠀⠀⠀⠀⠀⠄⠀⢀⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢡⠋⠔⠁⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣠⢀⡀⢀⣠⣤⣤⣶⣶⡆⢾⠁
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠄⠀⠠⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠋⡽⠋⠹⠈⠈⢣⡼⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⣀⡀⠂⠀⠀⠤⣤⣤⣤⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠦⠄⠀⠀⠀⡀⠠⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⢀⠴⠶⢾⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠀⠄⠈⠆
⠀⠀⠀⠀⠠⠀⠀⠀⠘⠄⠐⠓⠀⠂⠐⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠤⠤⠖⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠠⠤⡄⣤⣤⣤⣠⣀⣤⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠉⠐⢄⡀⠀⠂⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⡘⠀⢀⣀⡀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⣀⣀⠘
⠀⠀⠀⠀⣀⡷⠛⠋⠉⠙⢠⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⠀⡠⠊⠉⠙⠛⢷⣀
⠀⡰⠖⠛⠉⠉⠀⠀⢀⣄⡐⠋⠙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⢂⣤⡀⠀⠀⠉⠉⠛⠲⢆
⠀⠁⠀⠀⠀⠀⢠⡞⠉⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠉⣳⠄⠀⠂⠀⠀⠈
⠀⠀⢳⡄⠀⠀⠀⢻⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⢀⣠⠏⠀⠀⠀⢠⡟
⠀⠀⠀⠷⣤⣤⣤⣤⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠋⠳⣤⣤⣤⣤⠾




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠽⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣀⣀⣀⣤⡙⢛⣷⣶⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠒⠂⠋⠉⠑⢒⡒⠒⠓⣶⠀⢂⡒⠘⢽⣿⣿⣿⣆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠻⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠞⠛⢓⣛⣫⣽⣿⣿⣿⣿⣽⣭⡿⠷⣦⢤⡀
⠀⠀⠀⠀⠀⢠⠖⠀⠄⠠⢄⠽⠠⠦⠤⠼⠬⣥⠬⣿⣿⣽⣿⠭⠿⠿⢿⣿⣟⣽⣿⣿⣷⣮⣄⣙⠋⠙⢷⣄⡀
⠀⠀⠀⠀⣰⠋⠁⠠⢤⣤⣀⣆⣀⣐⣀⣄⢤⣤⠠⠤⠤⢤⣴⣶⣶⣶⣿⠿⣾⣿⡷⣿⣿⣿⣿⣿⣷⣦⣄⠙⠻⣤⡀
⠀⠀⠀⢀⠎⠀⠂⠉⢁⣈⣈⣁⣀⣉⣁⣈⣉⣙⣏⣉⣉⣉⣉⣭⡤⠤⢶⣶⣿⡿⠗⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢸⣷⣄
⠀⠀⠀⢠⠀⠀⢌⠐⠒⠂⠐⠳⠒⠒⠒⠒⠒⠲⠗⠒⠒⠒⠖⠛⢛⣋⣉⣯⣿⢷⣫⣿⣿⠛⠛⢿⣿⣻⠓⠂⠀⠐⠉⢻⡆
⠀⠀⠀⠘⢀⡠⢼⣒⣒⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⢭⣭⡭⢽⠿⠿⢿⣟⣯⡥⣶⣿⣷⣦⣛⣿⣿⣖⠲⠤⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢀⠀⠂⠹⢯⣀⡠⠤⠌⣃⠀⠀⠀⠠⠠⠟⠂⠀⠀⠒⢒⣚⣻⣿⠿⢷⣾⣿⣿⡿⣿⣿⣿⣿⣉⠄⣒⠀⠄⣀⠀⠘⡙
⠀⠀⠀⢨⠀⡄⠈⠻⡄⠀⣀⡠⠄⠀⠀⠀⠀⠀⣚⣉⣀⣉⣭⣥⣼⣗⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠈⣀⠀⠀⠀⢈⡓⢱
⠀⠀⠀⠀⣅⠋⠘⠑⢨⡥⠤⠐⠂⣐⣀⣀⠈⠭⠭⣥⣀⣖⣾⣿⣯⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡛⠛⠷⢮⣍⡒⠀⡀⠉⠹
⠀⠀⠀⠀⢨⡀⠼⠂⣀⠴⠒⠈⣉⣠⡤⠤⠶⣒⣺⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣈⡁⠂⠤⡙⠳⢬⣑⠀⠂
⠀⠀⠀⠀⠀⠉⡼⠋⣠⡴⠚⣁⣭⠴⢒⡻⠭⣵⣶⣿⣿⣿⢿⣿⣿⣿⣿⣽⣭⣿⣿⣟⣿⣿⣿⡍⠉⠉⠛⠛⠶⣤⡑⠢⣙⠻⠃
⠀⠀⠀⠀⠀⠀⠐⢾⠁⡠⠚⣁⠴⣚⡽⣶⣿⣿⠿⠛⠉⣱⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠤⢈⡒⠤⣀⠉⠛⢷⣄⡑⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢅⡼⣡⠞⣡⣮⢞⠁⢀⠀⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⠀⠈⠹⢷⣮⡛⠦⣄⡉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣼⢵⠁⠈⠔⡁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⠋⠙⣶⣤⣀⠠⢉⠛⣷⣬⡙⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡀⠀⢐⢿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣟⠋⠉⢷⠦⣄⠀⠙⠛⢿⣦⣁⠀⠈⠻⢦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣾⡄⠹⣿⢸⣿⣿⣿⣿⣻⣿⣶⠬⠉⠁⠀⠀⠀⠀⠙⢶⣄⠀⠉⠛⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠄⡀⢿⣿⡆⠟⣾⣿⣿⣿⣿⣿⡿⠗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡅⢸⣿⣿⢠⣿⣿⣿⣿⣿⣿⡗⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠊⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡃⢸⣿⣿⣼⣿⣿⣿⣿⣯⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠛⡷⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⠻⣿⣿⣿⣿⡿⣿⡧⡉⠢⡀⠀⢢⡀⠀⢠⡀⠀⠳⣄⠀⠸⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⣿⣿⣷⡙⣮⠳⡙⠄⠈⢆⠀⠹⣆⠀⢹⣄⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠏⠉⠛⢿⡜⣧⢹⡈⢆⠈⢧⠀⠸⣧⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠱⢸⣎⡇⠘⣇⢸⡇⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡠⡀⠤⢀⣐⠀⢀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣋⠑⡟⢉⣛⠧⠤⠍⠰⣼⣿⠆⡔⣻⠁⡫⢄⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠈⡰⢷⣹⢆⡊⠀⠀⠀⠘⠁⠀⠚⡴⢷⡎⢟⠲⣷⢀⡄⠲⠫⠄⢄⡀
⠀⠀⠀⠀⠀⣠⣖⢽⡆⢭⣤⡁⢉⡐⠀⠊⠈⠀⠀⡀⠀⠀⠈⠀⠀⠒⠚⠂⡦⡄⠗⠀⢈⡡⣀
⠀⠀⠀⢀⠀⣽⣟⣏⡱⣇⠏⠁⠀⠀⠀⠀⠀⠸⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠈⠍⣀
⠀⠀⠀⠎⠀⣴⡭⡩⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⢂⡰⠀⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢠
⢀⡯⠦⠱⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⢀⣀⣍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠋⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡀⢣⠄⢠
⠀⠀⠂⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠈
⠀⡀⠀⠥⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⡄⠠
⠀⢋⠁⠄⡜⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠰⠁⠀⠀⠳⠂⠀⠠⠘⢃⠀⠄⠀⠀⡄⠀⠀⠀⠠
⠀⠈⢧⣀⠀⠉⠶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⣾⠃⠀⠀⠀⠟⠠
⠀⠀⠀⠂⠀⢡⣡⢀⣠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠋⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠟⡇⠆⣸
⠀⠀⠀⠀⠄⠀⢻⠟⡚⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢜⢰⡀⠀⠀⠀⠀⠀⠠⠂⠂⠄⠳⢁⣠⡧⠄
⠀⠀⠀⠀⠈⠀⠨⣀⡀⠀⠀⠀⠀⠉⠀⠠⠄⠀⠀⠤⠷⠇⡠⠀⠀⠈⠀⢀⠈⠘⢃⡑⠀⠹⠂
⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠐⠍⡀⡀⠘⡂⠂⠁⠀⡴⠆⠀⠀⠂⠀⠐⠀⠈⡀⠹⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢈⣀⠸⠋⢣⠠⠀⡕⠀⠀⠓⠀⣩⠇⠈⠁⠌⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠲⣀⣉⢀⣤⢀⠂⠃⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣀⣠⣤⣬⣥⣤⣄⣀⠀⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡦⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢴⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠈⠉⠛⠛⠻⠟⠛⠛⠉⠁⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⡀⠀⢀⢰⡄⠀⠀⠀⠀⠉⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠘⡀⠀⠀⠀⠁⠦⠽⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠇⠀⠀⢠⣤⣀⣀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⢀⣿⢣⣦⡀⠀⠀⠀⠀⡃⠀⠀⣕⠦⣙⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⣠⣎⣿⡄
⠀⠀⠀⠀⠀⣸⡇⣿⠍⠁⠀⠀⠀⠀⠇⠀⢀⣸⠓⠈⠛⠛⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠉⢸⣧
⠀⠀⠀⠀⠀⣿⠃⠂⠀⠀⠀⠀⣀⣠⣟⡉⣾⠿⡀⠁⠤⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢈⡜⠉⣿⣿⡇⠀⠀⢀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⡄⠄⠼⢶⣿⣿⣿⣿⣫⠛⠻⠆⠀⠀⡀⡀⢸⡟
⠀⠀⠀⠀⠀⠈⣿⡌⣴⣦⡄⠀⠉⡇⣿⣿⡷⠦⠶⠠⢜⣿⣿⣿⣿⣿⣦⣴⠊⣱⣛⢾⣆⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣷⡽⣿⣷⡆⠀⡇⣸⣿⣿⢳⡲⡶⢶⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⢟⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⣿⣯⣤⡇⢿⡿⠁⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣶⣿⡿⣳⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣮⣻⠆⠈⠏⠠⢸⣿⡀⠀⣿⣿⣿⣿⣿⡿⣟⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣥⣄⣘⣻⣷⣈⣿⣟⣻⣯⣷⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠸⠀⠀⢸⠀⢀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠂⢀⡠⠅⠰⠒⠀⠐⠆⠤⣈⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠓⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠈⠁⣀⡔⠊⠑⠢⠤⣀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢆⠈⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡁⠀⠀⠏⠙⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⢱⠒⡛⠤⣀⠴⠒⠚
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠒⠒⠾⢄⡉
⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒⡀⣈⢆⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⡖⠉⠉⠀⠀⠀⠀⢫⠳⡀⢀⡜⠁⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠤⢄⡀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢰⢊⡄⣨⠟⠁⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠈⢣⠀⡀⠄⣀
⠀⠀⠀⠀⠈⠒⠲⣀⢀⡤⠤⠊⠉⣰⡏⠀⠀⡰⠋⠀⠀⣀⠴⠒⠋⠉⠙⠒⠦⣄⠀⠀⠈⢆⠀⠀⠀⢏⠀⠀⠈⠓⠒⠖⠂⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡸⠁⠀⢀⠞⠁⣀⡠⢤⠤⠤⢄⠀⠈⠳⡀⠀⠹⣇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠁⠀⢠⠃⠀⡶⠋⠀⠀⠀⠀⠀⠑⡄⠀⠱⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠌⠀⠀⡌⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⠀⠠⠀⠀⡀⣀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠚⠢⠴⠣⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠧⣀⡰⢇⣀⡠⠛⠒⠊⠁





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢳⡀⠀⠀⡇⠀⢸⠃⠀⢀⠞⠁⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠐⢄⠈⢢⠀⡀⢣⠰⠀⡇⠆⢏⠄⣠⠋⠀⣠⠖⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⡑⢄⠑⠌⠀⠂⠀⡇⠘⠌⡔⡡⡢⠞⢁⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⡀⠁⡂⠀⠀⠀⠀⣀⠀⠁⠀⠪⡈⢀⠠⢚⡡⠀⣀⡤⠴⠂
⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⣀⣀⡉⠑⠀⠀⡐⢡⠊⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢉⣀⣠⣄⣠⣤⡴⠒⠦⠤⠴⠒⠶⠄
⠀⣀⣀⣀⣀⡤⠴⠤⠤⠤⢄⡀⠀⠄⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣁⠀⣀⠴⠉⠉
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⢄⣀⣀⠨⠤⠤⠤⠤⠔⠊⠉⠀⠀⣀⠜⢁⡤⠂⠀⠐⠀⢀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠁⠐⠄⠄⠀⣀⠐⠄⠀⠀⠵⢦⣒⠂⠀⠀⠐⠒⡴⠊⢉⠁⠂⠉⠀⠶⠀⣒⠍⣁⣀
⠀⠀⠒⠐⠒⠐⠀⠐⠂⠐⠒⠀⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⣰⠚⣡⣀⣄⣖⡰⠀⠀⠂⠁⠚⠀⠘⠲⠗⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢤⣭⠴⠞⠟⠋⣁⣉⠁⣀⣈⠛⠛⠛⠋⠉⠉⠓⠒⠛⠛⠚⠓
⠀⠀⠀⠠⠶⠒⠒⠛⠒⠛⠓⢾⣍⠉⠁⠀⠩⠤⠬⢒⣐⠈⠁⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠰⠤⠤⠄

⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⣤⡤⣀⡀
⠀⠀⠀⠀⡈⠘⢄⠠⢔⡲⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡞⠓⢺⣅⠀⠏⣷⣰⠉⢲
⠘⠯⠭⣉⠁⡷⡆⣰⠋⠀⠀⠀⣰⢹⣭⡭⠷⠦⢙⣶⣶⣶⠆⠀⠀⠀⣀⣀⠠⢤⣀⠀⠘⢯⡿⣿⠇⢰⢻⡁⠠⣁⣿⣿⣆⠘⡇
⠀⠀⠀⡜⣠⠖⠢⡘⣆⠀⠀⠈⠻⣇⣛⣛⣋⠉⣈⠿⠋⠀⠀⢀⠴⠿⠤⣍⢢⡀⣿⠈⢢⡀⠉⢿⡇⠘⣗⠀⢘⢠⡅⠙⢿⣶⣿⣄
⠀⠀⠈⠚⠁⠀⠀⠙⠚⠃⠀⠀⠀⠘⠛⠒⠂⠉⠀⠀⠀⠀⠀⢮⣿⣿⣷⣮⣿⣧⣇⡠⠏⠁⠀⠈⠋⠙⣯⠀⣰⣰⣀⡴⠶⠻⠿⣿⡧
⠀⠀⠀⣀⢤⠴⠶⡶⡤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠤⢤⠠⠀⠀⠉⠙⢫⠞⠻⣟⠒⠒⡏⠀⠀⠀⠀⠈⠋⠉⠉⠁⢠⡴⠶⢤⡀
⠀⣴⠻⠹⠀⠀⡄⠀⢀⠃⠞⣳⣄⠀⠀⡠⠊⠣⡀⢣⡀⣹⠀⠇⠀⠀⠀⠘⠣⣧⠈⠹⠞⠀⠀⠀⠀⢀⡄⠀⠀⠀⡠⣿⢏⠢⠡⢹⡄
⠈⡎⢂⠁⠃⠀⢀⠀⠈⠈⡰⠡⢋⠆⡐⠙⠢⣤⠟⠉⡏⢻⢆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣸⣷⠀⠀⠀⡇⡈⠘⡄⡂⠆⣧
⠀⠘⢆⢢⢠⣠⢘⠀⠀⠐⠐⡡⠋⠀⡗⠲⠴⡟⢒⣶⡷⣯⠤⡇⠀⠀⣰⠇⡢⠀⠄⡁⠨⢳⡄⠀⠀⡯⠰⡄⠀⠀⢻⢁⠀⠀⠀⠀⢻
⠀⠀⠀⠳⣕⢷⣿⣾⠌⣠⠊⠀⠀⠀⠘⢦⠒⢛⠥⣮⢶⠛⣤⠇⠀⠀⣥⠊⣠⠎⡔⢠⠁⡅⡇⠀⣘⣋⠉⢵⠀⠀⠸⡼⡠⡀⠀⠀⡿
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠈⠙⠻⠤⠧⠜⠛⠁⠀⠀⠀⠋⣴⠃⣼⠁⣾⠀⣇⡿⠀⠫⣤⣺⣿⡷⠀⠀⢿⡵⣣⢇⢢⡇
⠀⠀⠀⠀⣠⡤⣀⢤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠒⠛⠴⠟⠒⠉⠁⠀⠀⠸⠿⠋⠁⠀⠀⠈⠻⣵⣯⠞
⠀⠀⡄⠊⠀⢳⡀⠈⢁⡆⠙⢦⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠻⣟⠛⠒⠚⠳⠲⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⣼⣀⣀⣠⡜⢋⠓⠺⢀⠠⠈⢳⣄⠀⠀⡼⣛⣫⡈⠛⣷⣄⠀⠀⠉⢢⡀⢀⠀⠃⠈⠙⠦⣄⠀⠀⠀⠀⠀⢴⣾⣿⣿⢧⣄
⠀⢱⠀⠏⣇⡼⣟⡖⠈⢹⠶⠛⠉⣿⠀⠀⡏⣴⣾⣿⣮⡟⣿⣆⠀⠀⠀⠙⠒⠒⠓⠒⠒⠒⠚⠓⠀⠀⠀⣠⡾⣿⣛⣫⣤⠛⠙⡦⡀
⠀⠘⣦⠚⠙⠑⡎⠉⠺⡇⢠⠀⣆⢺⠀⠀⢣⡻⣿⣿⣿⣿⡿⠛⠀⣀⠤⢤⠞⠛⠙⣟⠓⠦⣄⣀⠀⢠⢞⡙⠀⠈⠀⠀⠀⠐⡜⡄⢽
⠀⠀⠈⠙⠲⠶⠧⠖⠲⠶⠚⠒⠛⠛⠁⠀⠀⠙⠚⠛⠋⠉⠀⠀⢰⡡⠊⠀⢂⠀⠀⠘⣄⠳⣈⡟⠀⠸⡕⢡⢀⠁⠃⡛⡈⡁⡐⡜⣼
⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣔⣚⠉⠓⢔⠄⡄⠈⣳⠋⠀⠀⠀⠘⠧⣼⢐⡃⡃⡇⢡⣱⡴⠋
⠀⠀⠀⣴⣿⣿⣛⡷⡄⠀⠀⢀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⠈⠳⣝⣛⢛⣿⣚⣷⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠉⠁
⠀⢠⢚⢝⡉⠀⢉⣶⡿⡆⠀⡟⡩⠋⡥⠼⣧⡈⠉⢀⣴⣦⡌⢷⡀⠈⠈⠉⠀⠉⠀⠀⠀⠰⡒⡖⡲⠉⡟⠉⢹⠖⠘⠳⢦⣄
⠀⣇⢏⢮⠸⣼⣿⡿⣿⠁⢠⡋⢰⠺⢷⡄⠈⠻⣦⠈⢿⣿⣿⡎⣧⠀⠀⠀⢀⡖⠒⠦⣄⠀⠘⢶⠃⢀⠀⠀⠀⠀⢐⠈⠀⢘⢆
⠀⠈⠲⢽⣽⣿⣫⡞⠁⠀⢈⣶⡛⠳⣆⠙⠷⣄⠙⣦⢸⣿⣿⣧⣽⠀⠀⣀⡼⠅⠀⠀⠠⠛⣄⠈⠛⣇⠀⢠⠀⠀⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠘⢏⠙⠶⢌⣙⡓⢮⣿⣌⢣⣻⣿⣯⠏⠀⢸⠙⠌⠀⠀⠀⠀⠄⢹⠀⠀⠈⠛⣇⠀⠐⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣭⣭⣴⣍⣰⣇⠉⣿⡟⠀⠀⠈⠣⣀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠘⢶⣄⡀⠀⠀⠠⠀⢛⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠓⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠘⠄⠀⠃⠀⠂⠠⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢀⠔⠂⠈⠀⠀⠀⠈⠀⠢⡈⠠⠆⠀⡠⠠⢄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠠⡀⡹⠀⠀⠀⠀⠉⠀⢑
⠀⠀⠀⠀⠠⠤⣀⠁⢠⠀⢀⣄⡀⠀⠀⠀⠀⠀⠉⠈⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠈⠀⠀⠀⠀⠄⠀⠆⠀⠀⠀⠀⢣⡀⢄⠀⢀⣀⠜⠉
⠀⠀⠀⠀⠐⠤⠤⠀⠰⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠠⠤⣀⠂⠉⠁
⠀⠀⠀⠀⢀⣀⠤⠭⠤⣣⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢀⠅⠀⠀⠀⠀⡸⠑⢠⠞⠀⠀⡠⠔⠊⠉⠉⠉⠉⠒⠤⡀⠀⠈⢢
⠀⠀⠀⠘⠤⡄⠀⣀⡠⠒⢡⠋⠀⢠⠊⠀⢀⡠⠤⠒⠦⠤⡀⠀⠈⣦⠀⠀⢱⠊⠉⠢⠤⠤⠠⠄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⠃⠀⠰⠁⠀⡔⢁⣠⠤⠄⠤⣀⠈⠢⡀⠘⣇⠀⠀⡆⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠀⡌⠀⡞⠁⠀⠀⠀⠀⢣⠀⢡⠀⠸⡀⠀⢰⠀⠀⠀⢀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡨⢄⣀⣇⡰⠀⠀⠀⠀⠀⠀⠀⡀⢨⡀⢀⡀⠀⡼⠤⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠉⠉

⣄⢌⠀⠰⡘⢃⠀⠀⠋⣰⠟⣱⡿⣻⣿⡟⠀⠀⣰⣿⣿⣿⣄⠀⠘⢀⢀⡄⠐⣶⣌⣿⣿⣿⠿⠟⠋⠁⣿
⡮⣑⣇⠀⠀⠈⠀⠀⠘⠃⠀⠋⣈⣼⣿⣀⣀⣀⣿⣿⣿⡻⡿⢷⣦⠀⠳⣿⣶⣾⣝⣿⣿⡇⠀⠀⠀⠀⠻
⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣿⣿⣿⣿⡿⣿⡝⢿⡄⠈⡯⠳⠀⠀⠉⠛⠿⢿⣿⡏
⠀⠉⠢⠄⣈⢦⡀⠀⠀⠀⠠⠒⠁⠈⣦⣍⠙⠻⣷⠈⢿⡄⠀⠀⠀⠀⠤⠀⠀⣠⣄⠀⠈⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⢦⣄⡀⠀⠘⢯⣝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⢙⣧⣤⣄⣠⣼⣿⡿⢷
⠀⠀⠐⠂⠀⠀⠀⠀⠀⢠⣐⡽⠃⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠲⢿⣿⣿⡷⢞⡫⠅
⠂⠀⠀⠀⢐⣤⠀⢀⢨⣦⣿⡆⠀⣠⣶⣬⡄⣀⣀⠀⣀⠠⠔⠒⡫⠉⠁⠀⠀⠀⠀⠈⣉⠭⣭⡶⠋⢴⣿
⣴⠋⠀⡄⢹⣿⣦⣇⢿⣿⠟⠀⠀⠒⠂⢀⡬⢔⣈⠝⠀⢀⠀⠎⠀⠀⠀⡀⠀⠀⠸⣿⣿⡿⠋⠀⠀⣰⠟
⠇⣀⣴⣃⢀⡉⠙⠛⠈⠁⠀⠀⠀⠀⠐⠻⠶⠿⠟⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠦⡄⠀⠀⣼⡇⣿
⣾⣿⣿⡿⡼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⢠⢀⢠⣀⡄⠀⢧⡀⠀⣿⠀⠀⠘⠛⠛
⠟⠸⠁⠃⠀⣿⣿⠀⠞⠙⠙⢣⣶⣶⣤⣀⠀⠀⠀⠀⠀⢿⢏⡿⣿⢸⡘⣿⠷⣦⢲⣽⣷⣾⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠍⠁⠀⠤⠤⠞⠫⠪⠫⣾⠇⠀⠀⠀⠀⡀⣤⣾⣷⢿⠜⠗⠀⠀⠘⢷⣗⣽⠇⠀⠀⠀⠈⠻
⠀⢀⠀⠀⠀⢀⡀⠀⠀⠤⣤⣾⠛⠉⣟⢿⡗⣄⡀⣠⡹⡌⣇⣿⣾⣦⠀⠀⠀⠀⠀⠀⣈⣠⠤⠀⠐⠂
⠀⢸⡇⡀⠀⠀⠀⠀⠀⠐⣛⣛⣡⣴⣷⣿⣛⠌⠻⢿⣷⠸⠸⢹⡿⠏⠀⠀⠀⢀⣤⣾⣿⠋⠙
⠀⠀⡇⠈⢢⠀⠐⠶⣬⣴⣒⡶⣶⣖⢰⡀⠉⠳⡄⠈⠁⠀⠀⠈⠃⠀⠀⠀⠸⡿⢏⡝⠁⣀⡍⣀⣠
⠀⠀⢡⠀⠈⠂⠀⠈⢺⣿⣿⠝⠛⠉⠈⠳⠦⠀⠀⠀⠀⠠⠀⠀⠀⡔⠁⠀⣘⢤⠩⠂⡴⢶⣞⣉⡀
⠄⠀⠞⡀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣦⠀⠀⠀⠀⠀⠘⣀⠴⠊⠀⠀⠠⢀⣀⣠⡿⠋⣠⢀⣼
⠄⣶⠀⢷⢹⡿⠀⣀⣴⣿⣦⡀⠀⠀⢠⡿⠭⢉⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⠛⠻⢿⣵⣾⠷⠟⠁
⢸⡟⡄⠀⠻⢁⣾⡟⢸⣿⣿⣧⣀⣠⣤⣿⣿⣿⡦⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⠿⣦⡀
⠎⣿⠡⠄⠠⡿⠘⠁⠼⠿⢻⡿⢿⢿⢿⣿⠛⠻⠿⢿⡕⣠⠞⠀⠀⠀⠀⠀⠀⠻⣦⡈⠿⡿⣷⣶⣶
⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡄⢻⣾⡇⢀⡄⠀⠀⢀⣀⠀⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠄⠙⠃⠼⠛⠀⣼⡟⠉⣷⠀⢤⣼⣿⠧⠄⠀⠀⠀⠀⠀⠠⣏⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠻⡆⠀⣠⣾⠟⠳⣶⣶⢴⣿⡇⠀⠀⠀⢰⣿⡟⠀⠀⠀⣴⣾⠟⢳⡄⠉⡟⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣠⠞⠁⢰⣿⡟⠀⢰⣿⡟⠈⣿⣷⠀⠀⠀⣿⣿⠁⠀⠀⣸⣿⣏⣤⠞⠀⣸⠃⢸⣿⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⡾⣿⠁⢀⣾⣿⠁⣸⠻⣿⣇⣀⣼⣿⡇⠀⠀⢠⣿⣿⠁⠀⠀⢠⠏⠀⣿⡿⠀⡼⠁⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⣀⡞⠁⠉⠛⠉⠸⣏⡰⠃⡴⢻⣿⠁⢸⣿⠀⠀⢠⠟⠘⣿⡀⢀⣠⠟⠀⠀⢻⣇⡼⠁⠠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠋⠀⠀⠻⠦⠶⠋⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠐⣶⡖⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢰⣿⣷⢶⣦⢸⣿⠀⣴⡞⢶⡄⣤⣶⠶⡆⣠⣴⠶⣶⢀⣶⠀⢐⣿⣧⣤⡀⠀⢀⣤⣿⣿⠁⣤⣶⠶⡖
⠀⠀⠀⠀⠀⠀⢸⣿⣃⣼⡿⢸⣿⢸⣿⣤⠾⠹⣿⣤⣀⠀⢿⣧⣄⡀⠸⣿⠀⢸⣿⠇⢸⣷⢠⣿⠋⣼⣿⠘⣿⣥⣀
⠀⠀⠀⠀⠀⠀⢠⣿⠿⠉⠀⠸⡿⠀⠻⡷⠖⠀⠀⢭⣿⠇⠀⢬⣽⠗⠠⡿⠷⠸⠿⠶⣼⣿⠸⢧⠾⢹⣿⠀⠀⢭⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⡄⣄⠀⣄⠀⣀⠀⣀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠵⢛⣼⢇⣨⡷⣈⡷⢈⣿⢎⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣐⡄
⠀⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠋⠄⠀⠀⠀⠐⠒⠀⠀⠱⠀⢀⠀⠸⣹⣿⢳⡆⠀⣾⣹⣿⡿⢿⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⣤⣦⣤⣦
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣀⣶⠀⠀⠀⢀⣀⣸⣀⣀⠀⠘⠤⠄⢻⠀⠀⠀⠀⠿⠯⠥⠥⠼⠃⠀⠀⢻⡯⣝⠛⠀⠀⠀⠷⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⢠⡶⢶⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠉⣿⣿⣿⣶⡆⠀⠠⣿⢟⣷⡿⠃⠀⠠⠒⠶⠶⠖⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠿⠦⠤⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠙⠟⠁
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣿⡿⠀⠀⠀⠰⠶⣾⣶⣶⠀⠀⠰⠶⣾⣂⣀⠀⠀⠀⡀⢸⣦⠀⠀⠀⢀⣶⣿⡏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⢺⡿⢷⡦⠀⠀⠀⠰⠴⠿⠿⠿⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⢙⣍⣙⠃⠀⠀⠠⠤⠤⠤⠿⠧⠀⣰⣷⣾⣧⣤⡀⠀⢾⣦⡎⠱⠿⠆
⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠋
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⡥⠙⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⢰⣦⣀⣠⣞⠀⠀⢠⣀⣂⡄⠀⠀⠀⠀⣠⢀⣀⣀⠀⠀⠀⣬⠀⢀⡃⠀⠀⠀⠀⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠋⠛⠛⠋⠀⠀⠀⠀⠙⠈⠁

⠀⠀⠀⢠⠞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠀⠀⠀⠀⢀⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢀⣶⣠⡄⠀⠀⠀⡶⢶⠶⢤⡀
⠀⠀⠤⠀⠀⠙⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠘⠛⠛⠉⠛⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠛⠟⠀⠀⠀⢀⣷⣾⡶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣦⠀⠀⠀⠀⠀⠸⣶⣤⢁⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣀⠘⡈⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⣀⣙⣛⠳⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣀⣴⠟⠉⣉⠙⠻⠷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠉⠀⢀⣴⠾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠶⣶⣶⣶⣶⣶⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠐⠷⠶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠶⠛⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⣼⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⣤⣴⣦⣤⡄⠀⠀⢐⠒⠒⠂⣀⡀⠀⠀⠀⢀⣰⣾⣾⡆⠀⠀⠀⠠⢤⠤⠀⠀⠀⠀⠀⣠⣾⣧⣠⠂
⠀⠘⠿⠿⠿⠿⠇⠀⠀⠘⠀⠀⠣⠀⠀⠀⠀⠻⡿⠛⠻⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⠀⠄⣦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾
⠀⠀⢸⣿⣤⣄⠀⠀⠀⠀⠸⠿⠿⠿⠄⠀⠀⠀⠀⠚⠁⠟⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢰⣾⣶⣾⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣾⣿⣄⠀⠀⠀⠀⠠⢨⡂⠀⠀⠀⠀⢸⡇⣶⣿⣿⠀⠀⠀⠀⠀⣠⡺⠟⠁
⠀⠀⢹⣿⣾⡿⠀⠀⠀⠀⢠⢏⠷⡄⠀⠀⠀⠈⣇⣻⣿⡟⠀⠀⠀⣠⣦⠟⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣀⣤⣶⡦
⠀⠀⣾⣿⣿⣿⡄⠀⠀⠈⠉⠉⠉⠈⠁⠀⠀⠀⠀⡇⢥⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢶
⠀⠀⠀⠀⠀⡀⠛⣍⠈⠁⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⠀⢢⡀⠘⣿⠁⠀⠔⠁
⠀⠀⠀⠀⡀⠀⠀⠸⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠻⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⣿⠁⠁⠀⠊
⠀⠀⠀⠀⠙⠀⠂⠠⢸⡂⠠⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⣿⡤
⠀⠀⠀⠀⠀⠂⣀⠀⠌⣇⢀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡄
⠀⠀⠀⠀⠀⠀⠁⢀⠀⢿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠚⠲⠒⠓⠚⠀⠛⠒⠓⠒⠒⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠐⠠⡀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡄⠀⠀⣸⠅⠀⠀⠀⢤⠠⠀⠙⠀⠀⠁⠉⠃⠀⡀
⠀⠀⠂⠀⠀⠀⢲⡆⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡼⠃⠀⠀⠉⠀⠀⠀⠳⢤⡄⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠠⠤⠤⢴⣾⡿⠃⠈⠉⠂⠀⠁⠀⠀⠀⢠⡼⠄⠀⠀⠀⠀⠀⠈⡓⠀⠈⠈⣙⡦⣄⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⡀⠐⠉⠹⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⢐⣂⠀⠀⠀⡶⡄⠀⠀⠀⠀⠠⠾⠆⠀⠀⠀⠀⠠⣶⠀⢶⠄⠀⠀⠀⣀⣴⣯⣬⣷⣄⡀⠀⠀⠀⠀⠀⡶⠀⠀⢴⡄
⠀⠀⠘⠁⠈⠃⠀⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⠛⣧⠀⠀⠀⢸⡇⢀⣿⠀⠀⠀⡏⠀⠈⡏⠀⠈⡇⠀⠀⠀⠂⠀⠀⠆⠀⠀⣿
⠀⠀⡶⠘⠃⢶⢰⡆⠛⠀⣶⠀⠀⠀⠀⠀⠀⢀⣤⣿⠄⠀⢻⠁⢸⡏⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟
⠀⠀⠓⠒⠒⠚⠘⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠀⠘⠀⠈⠃⠀⠀⠀⠇⠄⠀⠇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢀⡀⠀⡀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⠁⠒⢹⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⡀⠀⠀⢀⣀⠀⣀
⠀⠀⢀⣿⣷⣼⣧⣿⣿⡄⠀⠀⢀⣾⣦⠀⠙⠃⠀⠀⠈⠓⢒⡋⠄⠘⠛⠀⠀⠀⣀⠀⠰⣌⣿⡾⢿⣿⠀⠀⠘⠚⢠⣿⣄
⠀⠀⠈⠁⠘⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢘⡇⠐⠀⠀⠀⠀⠈⣿⠀⠀⠨⢾⣿⠀⠙⠀⠀⠄⠀⢿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⣿⣦⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠰⠿⠶⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⢀⣇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⣀⣬⣤⣶⣿⣿⣿⣿⣷⣶⣬⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠏⢠⡇⠘⠇⠀⠘
⠀⠀⠀⠀⣼⣻⣽⣾⣿⣯⣿⣿⣿⣿⣿⣿⣻⣿⣽⣿⡀⠀⠀⠀⠀⢀⣤⣤⣅⣀⡃⠀⠠⠄⢸⡇⠀⠄⠀⠀⣀⣠⣤⣤⡀
⠀⠀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠿⠟⠓⠀⠀⠀⠈⠙⠛⠻⠿⣿⣷⣷⣶⣼⣧⣴⣶⣾⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠉⠛⠋⠙⠛⠉⠀⠀⠉⠁⠈⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠛⠋⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⠖⠋⠉⠉⠓⢦
⠀⠀⠀⡼⠁⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢠⣤
⠀⠀⠀⢳⡀⠀⡇⠀⠀⠀⣰⠃⠀⠀⠀⡟⠺⡆
⠀⠀⠀⠀⠉⢑⣇⣀⡤⠞⣅⡀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠉⡏⠁⠀⠐⠀⠹⡆⠀⢸⡇⢸⠃⠀⠀⣠⡄⢀⡶⣄⠀⢠⠦⡀⠀⠀⠈⡁⠀⣀⡀⣀⡀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠸⣧⠏⠀⠀⢀⡇⡇⠈⢧⣿⠀⠈⠣⣧⡀⠀⠀⡇⠼⠃⣿⢋⡇⢀⡞⠁⣇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡼⠁⠀⡰⣯⠀⠀⠀⠸⡿⠁⢀⣴⡛⢦⠀⢠⣏⡙⡆⢠⡇⠀⢠⡏⢸⠃⢸⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠒⠶⠒⠋⠠⠴⠊⠁⠘⠢⠄⠠⠞⠳⠭⠉⢯⣩⡿⡵⠛⢯⣹⠿⠁⠙⠤⠸⠁⠘⠦⢞⠓⠖⢺⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣞⣺⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⡿⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢀⡇⠀⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢸⠁⠀⠀⣾⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⢀⡏⠀⠀⢰⠇⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⡜⠀⠀⢀⡞⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⡰⠁⠀⠀⡼⠁⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠐⠀⠀⢀⡜⠁⠀⢀⡞⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠠⡘⠆⢠⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢠⠎⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣤⡙⠆⠰⢫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡐⠁⢀⣾⣿⡏
⠀⠀⠀⠀⠀⢀⡈⠳⢄⠠⠏⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⣸⢃⣴⠾⠿⢷⣶⣄⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠟⠀⠒⠂⠀⠈⠻⣷⣄⠠⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠈⢿⣦⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠹⣷⡈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢀⡶⢶⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠈⠻⣌⣿⠀⠀⠀⠀⠀⠀⠀⢐⣿⠏⢀⡾⠁⠸⠁⠠⠞⠉⣩⡿⠛⠳⢶⣶⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⡞⠀⠀⠀⠀⠀⠐⠋⢁⣠⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠏⠤⠔⠊⠀⠀⠀⠀⣀⡠⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣄⣀⣀⠀⠀⠀⣀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢚⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠟⠉⠉⠀⠀⠀⢁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠁⠐⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢀⢀⠠⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠐⠀⠀⠑⠈⢀⠀⠠⠀⠀⡤⢘⠢⠀⠀⠰
⠀⡘⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢟⠃⠃⡀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠙⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠂⠀⠀⠀⠀⠀⠀⠑⠀⠄⠀⠀⠄
⠀⠴⠦⣖⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠚⠿⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠈⠣⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⡀⠀⠈⠀⠈⠀⠂⠁
⠀⡆⢐⠀⠈⠀⠤⠀⠐⠀⠋⠀⡄⠂⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠂⡀⠀⢠⡀⠀⡄⠐⢀⠀⠀⠀⡐⠌⢿⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⠀⠀⠀⠈⠏⢂⡈⠀⠀⡠⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠠⡀⠀⠀⡀
⠀⢀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⢀⠄⠁⠐⠄⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠊⠁
⠀⠀⡈⠉⠀⠀⠀⠀⠑⣄⠀⠀⠰⠀⡋⠀⠀⠀⡀⠐⠐⠁⠀⣐⠾⠛⠁⠀⢀⡀⠄⠀⢦⠢⣄⠀⣠⢀⠈⠈⠀⡄⠈⠓
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠑⠚⠓⠒⠂⠛⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⠀⠀⠈
⡈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⢠⡡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣧⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣆⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢮⣛⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣌⠳⣻⡵⡃⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐
⠀⠦⡆⠘⢄⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠈⠯⢳⡵⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢰⡄⠙⠠⠂⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢰⠀⠀⠁⠘⢃⠉⣀⡀⠛⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⣨⠃⠀⢲⣁⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⡴⠂⠈⠈⣌⠁⢋⣠⠆⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⢐⠀⠱⠀⠈⢑⠀⠈⠉⠀⠀⠠⠖⡄⠀⠞⠀⠀⠀⠀⠈⣄⠩⠖⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠾
⠠⠀⡀⠀⠀⣨⠆⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⡟⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⣀⡴⠞⡻⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿⣇⠀⠀⠀⢠⡾⢋⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢻⣄⠀⠀⠀⠀⠀⣿⢸⡇⣿⡀⠀⠀⣾⠀⡾⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⢹⣄⠻⣄⠉⠛⢶⣤⡀⢸⡇⢸⡇⠸⣇⠀⠀⢻⡄⣷⠈⣷⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠲⣤⡀⠀⠈⠻⢦⣈⠙⠲⣄⠈⢿⣾⠁⢸⡇⠀⢿⡄⢀⣼⠃⣿⠀⢹⡆⠀⠀⣀⡴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡑⢤⡙⠳⢤⣀⠀⠙⣦⠀⢻⣆⣸⣿⣤⣼⣧⣤⣼⣿⡟⠉⣠⠟⢀⣾⣃⣤⠞⢩⡖⣿⠋
⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠉⠓⢶⣿⡶⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠻⢿⣤⣾⠟⠋⣠⡴⢋⡼⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣶
⠾⠛⠳⢦⡈⣷⣄⠀⠀⠀⠀⢀⣀⣹⣆⠀⠻⣦⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡾⠋⢠⡞⠁⠀⢀⣴⠞⢛⣉⣉⣉⠙⠛⣩⡿
⠀⠀⠀⠈⢷⡹⣍⡛⠿⠿⠛⠋⠉⠙⠻⢷⣴⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⣿⣀⣀⣴⠟⣡⠞⢩⡴⠶⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠻⣦⣉⡛⠚⠛⠛⠛⠲⣦⣼⠏⠀⣠⠶⠚⠋⠻⠿⢷⣴⣿⠀⠀⣾⣆⣤⣶⣟⣿⠓⠶⣦⣄⠹⣏⠉⠉⣁⡴⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⣦⣼⠇⠀⣀⠁⢠⣶⣿⣿⣿⣿⣿⣿⠂⠀⢻⣿⣿⣿⣿⢿⣿⣦⠈⠙⣆⢻⡟⠛⠉⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠛⣿⠀⠀⠻⠷⠿⢿⣷⣯⣻⡼⠟⢿⠀⠀⢸⡏⠿⣿⣧⣽⣽⠿⠳⠞⠃⠈⣿⠻⠿⢧⣤⣀⣀
⢀⣀⣠⣤⣶⣒⣚⣛⣉⣀⣀⣀⣀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⢸⣷⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣈⣉⣙⣛⣿⣶⣦⣤⣤
⠈⠙⠛⠛⠻⠿⠧⣤⣤⣀⣀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣏⠀⠀⠀⣿⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⣀⣀⣤⡤⠴⠶⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠿⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⠟⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡶⠚⠛⠛⣷⡀⠀⠀⠀⠀⠀⣠⣀⣀⣠⣴⣤⣤⢶⣤⣄⣤⣄⠀⠀⠀⠀⠀⢠⣿⣄⠀⠻⢤⣤⣤⣤⣄⣀
⠀⠀⠀⣀⣀⣀⣠⣼⠇⣰⠏⣠⡤⠴⣾⠟⠳⣄⠀⠀⠀⠀⠟⠛⠛⢻⣿⠿⠷⠛⢻⡟⠛⠛⠀⠀⠀⠀⣠⣿⡀⠉⠳⠶⠤⠶⠶⠶⢬⣙⠳⣄
⠀⣴⢟⡭⠥⠤⡤⠴⠞⢁⡾⠃⠀⣰⠏⠀⢀⣿⢦⣄⠀⠀⠀⠀⠀⠀⠙⠷⣶⠶⠟⠁⠀⠀⠀⠀⣠⣾⡃⠈⢿⣦⣤⣠⣤⠴⠶⠾⠶⣌⢣⣹⡆
⢸⣷⡶⠟⠛⠓⠶⠶⠟⠋⠀⠀⣰⠏⠀⣴⠟⠁⣀⡽⠷⣤⣀⡀⣂⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣅⠈⠙⢦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢦⣽⣟⣳⣶
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠞⢁⣴⢾⡟⠀⢠⡟⠉⣙⣿⡿⠿⣶⡶⠶⢾⠟⢻⡇⢀⡟⠉⠻⣦⣀⠙⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣼⣥⠞⠋⠀⠘⣷⠀⣾⠀⣸⠏⠈⣿⠀⢹⠀⠀⣿⡄⠈⢧⠈⢷⣄⠀⠀⠙⠳⢦⣉⢮⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⢸⡇⢸⡆⣿⠀⠀⢹⡆⢸⠀⢰⡟⢳⣄⠈⠳⢤⡉⢷⡄⠀⠀⠀⠈⠛⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⡼⢀⡿⠀⠀⠘⣧⢸⠀⣾⠁⠀⠉⠛⠷⣦⠹⡄⢿⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡜⢁⡾⠃⠀⠀⠀⢻⣼⢰⡇⠀⠀⠀⠀⠀⢸⡆⠇⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣯⡾⠋⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣰⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣗⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠉⠛⠻⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠙⢿⣿⣿⣿⣿⣆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣿⣿⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⡇⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⣿⣿⡟⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠛⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⢉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠐⠒⠒⠢⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⢀⡀⠤⠐⠒⠒⠒⠒⠒⠂⠒⠒⠂⠤⢄⣀⠈⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠊⠀⠀⠀⠀⢀⡠⠤⠒⠂⠈⠉⠉⠉⠉⠉⠀⠀⠐⠒⠠⠄⡀⠀⠀⠈⠓⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⠔⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠈⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠠⠃⠀⠀⢀⠎⠀⠀⠀⢀⠔⠊⠀⠀⠀⢀⡀⠤⠄⠀⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠑⠢⣀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡰⠁⠀⠀⡐⠁⠀⠀⠀⠘⠁⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⢄⡀⠀⠀⠀⠀⣱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠁⠀⠀⡔⠀⠀⠀⠐⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡤⠖⠁
⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠇⠀⠀⠀⠀⠀⣤⣀⣄⣀⡀⠀⠀⡔⠁
⠀⠀⡴⠋⠀⠀⠀⠀⠈⠙⠢⣀⠔⠂⠁⠀⠀⠀⠀⠀⠈⢓⣬⠀⠄⣀⡀
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡗⠀⠀⠀⠈⠳⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠡⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⢤⠁
⠀⠀⠈⡾⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠢⢀⡀⠀⢀⣂⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⣀⡠⠤⠚⠀⠙⠢⢤⣀⡀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣿⣿⡇⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠀⠹⣿⡇⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⡞⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢿⣿⣷⣄⠀⢻⡇⠀⣸⣿⠟
⠀⠀⠀⠀⠀⠀⢸⡿⠀⡟⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⠋⠁⠙⡆⠀⠀⠀⠀⠀⠀⠈⠉⠳⠈⠃⠐⠋⠁
⠀⠀⠀⠀⠀⠀⢸⡇⢸⠇⠀⢰⡿⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⡇⢰⣿⡛⢰⣿⣧⢾⣟⡛⠻⣿⡿⢇⣿⣛⢳⣿⣿⠀⠀⢀⢀⣶
⠀⠀⠀⠀⠀⠀⢸⣷⢸⠀⢠⣿⡥⠤⣄⠀⠀⢰⡏⠀⠀⢀⡞⠀⠸⢿⡥⠿⠟⠟⢠⣼⠟⡀⢿⠃⠘⢿⣭⠸⡟⠿⠀⠻⣆⢸⠏⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠰⠛⠁⠀⠀⠘⣷⠀⢸⡇⢀⠴⣫⢦⠀⣠⡖⣦⠀⢠⡖⣦⠀⢈⠃⠀⣀⠀⢀⡴⣦⠀⠀⣠⡤⣄⠀⠒⠛⢁⡴⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⣿⡇⢸⡏⠁⢰⣿⠼⠀⣻⡾⠟⡠⢻⡿⠟⡠⣾⠁⢰⣿⢀⡏⢀⡿⠀⢰⡟⢀⡜⠹⣧⠤⠺⣧⠿⣡⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⠇⢸⡇⠀⡼⣷⠀⡰⠉⣻⣎⠀⠀⢻⣎⠀⢿⣀⡜⣿⢸⠁⢸⡇⢀⣿⣇⡞⣠⠞⣿⠀⠀⢹⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣰⠟⠀⠀⢿⡼⠁⠈⠉⠀⣴⠁⢻⡆⣴⠃⢻⣆⠀⠉⠀⠈⠋⠀⠘⢧⠞⠀⢩⠞⠁⢠⡿⠀⢠⠏⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣸⡇⢀⡟⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣰⠟⣧⣀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣰⡟⠀⠈⢷⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠞⠋⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠤⠀⢀⣄⠸⠀⠀⠀⣤⣶⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠻⣿⠗⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢰⡖⢰⣶⢄
⠀⠀⡼⠁⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡽⠟⠛⠘⡅⢆⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤
⢀⡌⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠐⡀⠀⠀⠀⠀⠐⠆⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠦⣄⠀⠄
⣿⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠄
⠋⠀⠘⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⢀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢄⠀⠠⠀⡀⠀⠑⠩⣢⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀
⠈⠀⠀⣦⡈⡢⠄⡀⠀⠀⠀⠀⠀⢉⣉⣙⡛⠙⠋⠀⠀⠀⠀⠐⠠⢀⠀⡠⡀⠰⡃⠀⠠⠎⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠂⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢶⢶⣦⣃⡀⠀⣤⣀⣉⣩⣭⣍⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠲⣆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹
⠀⠀⠀⡃⠸⣿⢿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠁⠘⣄⠀⠄⠀⢀⡀⠀⠀⠀⢀⠀⠂⠁⠠⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⢀⠀⠀⠘⠛⢿⣏⣛⠙⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢈⡁⠀⢀⡀⠈⠧⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⢤⢀⠀⠀⠀⠀⠀⠈⠙⠳⠀⠀⠀⠀⠐⠀⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁
⠺⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠰⠂
⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⣦⡀⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠘⣣⠈⠓⠘⡦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⠀⠀⠀⠀⠢⠀⠐⢄⠐⠀⠀⠀⠘⠋⠁⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠄⠘⡀⣄⢀⢃⠀⠀⠀⠀⠁⡞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢠⠼⠏⡐⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠈⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⡈⠀⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠰⣟⣿⣿⣿⡿⠟⡻⠶⠖⠲⢆⣀⣀⠀⠀⠀⢃⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠃
⠀⠀⠀⠀⠀⠇⠀⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣄⠀⠀⠀⠀⠀⠃⢠
⠀⠀⠂⢄⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉
⠀⠀⠀⠀⠀⠙⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⢀⠔⣩⠖⠈⠉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢠⣶⠠⠀⠀⠀⠀⠀⠁⠠⢁⠎⠀⢀⠔⡀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⢋⠞⡴⠁⢀
⠉⠀⠀⠀⠀⣘⠿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠐⠀⢠⠃⡠⢀
⠀⠁⠀⠀⠀⠉⠲⠠⠄⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠂⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⢁⠂
⠀⠀⠀⠀⠀⢀⡄⣧⠀⠀⠁⠄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⢸⠇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣚⣛⣛⣛⣛⣳⠶⣤⣀
⠀⠀⠀⠀⠀⢀⣴⢞⣭⢞⣫⡭⠷⠶⠶⠾⣭⣟⡷⣭⡳⣤
⠀⠀⠀⠀⣠⢟⣵⢫⡶⣫⡵⠞⠛⠉⠉⠛⠳⢮⣟⢮⡻⣮⢳⡄
⠀⠀⠀⣰⣏⡾⣱⢏⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡹⣞⢷⢻⡄
⠀⠀⢀⣟⣼⢱⢇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣹⡞⣧⣿
⠀⠀⠘⠋⠀⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋⠉⠀⠙⠃⡀
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣦⣄
⠀⠂⠄⠠⠤⠀⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠀⠤⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⣠⡄⡄⠠⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠿⣗⢮⣟⢮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⡄⠈⢳⡝⣮⢳⡝⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠐⡲⠂⠒⠐⠂⠒⠐⠀⠲⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠛⠛⠁⠀⠀⢿⣸⡏⣿⡹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⣇⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣛⣘⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠈⠀⠀⠀⠀⠁⠀⠑⢤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⣄⣀⣤⣀⣠⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⢠⡄⢀⠊⠀⠐⠦⡀⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣈⠉⠙⠓⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠤⠀⠀⠛⡀⢠⠇⠀⠀⠂⠂⠼⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠁⠀⠈⠉⠙⠓⠲⠶⢤⣄⣀⡉⠉⠛⠒⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠤⠤
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡠⠁⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠱⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢸⡤⣤⢀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⡈⠛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋⠔⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠈⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠐⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠠⠀⡀⠀⠀⠓⠐⠁⠀⠀⠀⠀⠀⠒⡌⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣴⠟⢻⣧⢀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠙⠷⠾⣿⡾⠃⢠⡞⢻⡗⣴⠟⠷⣰⠟⣿⠇⣺⠟⢃⡾⢠⡞⢻⡆⣸⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠟⠁⠀⠘⠛⠛⠓⠙⠓⠒⠛⠛⠛⠒⠛⠓⠘⠓⠚⠛⠛⠑⠋⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡂⠀⠀⣀⠊⠀⠈⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠁⠀⠁⠀⠀⠇⠓⠠⠄⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠦⠀⠀⠰⠀⠀⠀⠒⠀⢤⡄
⠀⠀⠀⠀⠀⣀⣉⡂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠟⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠈⠇
⠀⠀⠀⠘⠿⠟⠛⠃⠐⠿⡷⠆⠀⠀⠁⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⣴⣶⣄⡀⠀⠀⢀⣠⣶⣦⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢀
⠀⠀⠈⠛⠿⠋⠀⠀⠈⠿⠟⠁⠠⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⣿⠟⠃⣠⣈
⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⢠⡶⠀⡰⠠⡀⠀⠀⠠⠼⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⡀⢸⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠐⠚⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠃⠀⠠⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⣀⣁⣀⣈⣠⣏⠠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⣠⠖⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⢀⣀⣤⣄⣀⠈⠀⠤⠀⡀⠾⠅⣀⣀⣉⣴⣒⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡒⠀⢀⣠⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠋⠉⠙⠉⠉⠁⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠒⠛⠓⠂⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢀⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣿⣿⠟⠿⠛⠿⡿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⠁⠀⠀⣿⣿⠀⠀⠈⠙⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⣿⣿⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀⠀⠀⢀⣴⣿⣿⠟⠁⠀⣿⣿⠀⠈⠻⣿⣿⣦⡀⠀⠀⢀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣀⣴⣿⣿⠟⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠲⣶⣷⣆⣀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⡀⠀⠀⣿⣿⠀⠀⢀⣠⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⡄⠀⠀⢠⡆⠀⠀⢷⣀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⠳⢄⣀⣀⣀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢧⠀⠀⠀⠓⠒⢠⡄⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⢠⣦⣤⣭⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠒⢶⣾⡿⣼⣿⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢀⣤⣽⣿⣿⠋⠀⠠⡇⠀⠘⠲⣄⡀⠉⠓⣆⠀⡀⣠⣿⡇⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠠⡌⣿⣿⣿⣿⠀⢤⠀⠑⣄⠀⠀⢸⡇⠀⢠⣿⣿⢡⣿⣿⡧⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢹⣮⣿⣿⣿⠀⢠⡆⠀⢸⡇⠀⢿⣷⡆⣿⣿⣿⣤⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⠇⠀⣾⣇⠀⠈⢷⡄⠘⣿⣇⠻⣿⣿⣽⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢼⣿⣿⡿⠋⢠⡀⣼⣿⠂⠀⢠⡇⠀⢸⡿⢠⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣶⣼⡿⠿⠟⠋⡴⢀⡜⠠⣿⣏⠀⢀⣾⠁⢠⡿⠁⣠⣾⣿⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⡟⠋⠀⢠⠄⡗⠰⡃⠀⢸⠀⣿⠹⠀⢸⣧⡀⢸⣇⢠⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠋⠀⠀⣇⢸⣆⣻⣢⠟⡤⠿⠶⠿⠧⣤⣾⡿⢃⣤⣿⠸⣧⣤⣤
⠀⠀⠀⠀⠀⢀⠊⠀⠀⢠⢸⣧⠿⠊⠉⠉⠀⠀⠀⠀⠀⠒⠒⠒⠈⠽⢿⣿⣿⠶⠿⠛⠛⠁
⠀⠀⠀⠀⠀⣧⣤⣴⣶⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠉

⣿⣧⡄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠈⠀⠐⠀⣀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠐⠝
⣤⣤⣤⣴⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠈⠉⠐⠂⠀⠌⠳⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⣀⣄
⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⢤⣄⡀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠚⠀⠠⣌⠹⣷⣧⡞⠁⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣄⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⡘⢋⣴⣬⣦⢹⡆⣹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⢻⣿⣦⠄⠂⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠛⣿⢏⡾⠃⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣄⢢⡀⣹⣦⣀⣠⣿⣿⣾⣛⣁⣠⡴⠏
⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠉⠛⠿⠛⠛⠉
⠀⢇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠄
⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⣾⡧⢀⡀
⠀⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠈⠀⠀⠀⠀⠸⠏⠀⢸⡿⢦⣄
⠀⠘⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣧⠀⠀⠀⢰⡀⠀⠈⡄⢈⣄⡽⠶
⠀⠀⠘⢟⣀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢀⣀⣿⡗⠠⠖⠛⠋
⠀⠈⠉⠉⢿⣧⣤⣴⠞⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⠿⠃
⠀⠀⠀⠀⠈⠙⠛⣿⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡴⠀⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠁⠀⠁⢀⡀
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⣦⠤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠦⠴⠾⢿⣷⣦⡤⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡎⠀⣠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣍⡉⠝⠉⠁
⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⣿⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡿⠌⠑⠄⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠖⠉⣭⠿⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣎⣀⣼⡠⠃⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣛⠯⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢆⠀⠀⠄⠐⢄⠹⡂⢠⠈⢖⣠⠂⢠⠀⡀⣀⡀⠤⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠦⣸⡄⢄⠻⣇⡜⢣⣸⢁⢂⣾⠟⠋⠁⣀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⡀⠰⠈⢻⣬⣶⣿⠞⠳⣿⣿⡏⠀⠰⢀⣼⡉⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⠛⠻⣦⣴⣯⠝⠉⠀⠀⠀⠀⠉⢋⣷⡶⣋⠥⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣑⠶⠔⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⠶⠿⠒⠉⠉⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠐⠉⠀⠔⠚⢅⣻⣿⠀⠙⠒⠂⠀⠀⠑⠚⠋⢈⣿⢌⡵⠒⢀⣤⠄⠂⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣠⠔⢲⡿⢋⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣒⠻⢍⠑⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠖⠁⢂⣡⡞⠟⢭⣷⣤⣀⣀⣀⣠⣴⣯⠟⠉⠻⣦⡅⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢋⠘⠂⣡⣿⣿⡟⠷⢻⡟⢯⠻⣅⡘⠀⠘⣷⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄⠉⣀⣠⣴⢾⠏⠌⣸⡏⢶⠋⣿⣄⠣⠹⡏⢦⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠉⠁⠀⠀⠐⠀⡔⠁⢧⠀⠀⠸⣄⠑⠄⢩⠀⠌⠢⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⡶⢯⠀⠀⠀⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⠙⠃⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢾⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠙⠶⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠃⢀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⢀⠄⢀⡴⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣠⠋⠀⠈⠀⣠⠄⢁⡤⠛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡋⠁⠀⠀⠀⢈⣠⠖⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠴⢠⡴⠊⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡄⠀⠀⠀⡀⠠⠐⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⢤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣀⣠⣄⣀⣀⡀⠈⠙⣦⠡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⡀⠀⢂⣠⣠⣤⣐⣲⣤⣤⣤⣤⣀⣀⣘⣷⣿⢉⣀⠀⠈⠩⠙⣳⣶⠋⠄⢂⣠⣤⠒⣠⣐⡠⠠⠀⠄⣒⣄⣂⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢐⠪⣢⠶⠶⠶⠿⠛⣫⣩⠟⠛⣲⣶⡿⠟⠉⠉⠭⠿⠿⠍⠩⠭⠭⠿⠿⠿⠿⣿⡿⠟⠓⣲⡮⠽⠟⢛⣛⣛⣛⠛⠫⢉⢳⡄
⠀⠀⠀⠀⠀⠀⢈⠰⣿⡀⡀⢀⡠⠞⠁⠀⠀⢸⡏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡏⠀⠀⢎⠀⠀⠀⡀⠈⡆⣯⠀⡗⠀⡄
⠀⠀⠀⠀⠀⠀⠠⠁⣿⠀⡴⠁⠀⠀⠀⠇⠀⠘⢣⠀⠀⠀⢈⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀⢀⠀⠙⢆⡒⠋⠀⢷⡇⢰⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠰⡅⢻⠜⠁⠀⠀⠀⠀⠛⠛⠛⡟⠀⠀⠀⢀⠈⠁⠁⡰⠖⠀⢀⠀⠀⠀⠀⠀⠟⠉⠉⢺⡇⠀⠀⠀⠀⠀⠙⢄⣀⡜⣇⠀⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠠⢺⠀⡀⠂⠁⠂⠘⡀⠀⡠⠇⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠘⢄⠀⡠⠛⠑⠀⠀⠀⠀⠠⡐⠦⠀⠇⢻⠀⣿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠂⣿⠀⠁⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠐⡝⠀⠀⠀⢸⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢠⡀⣿⠀⠀⠁⣤⠆⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠒⠚⠈⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣿⠀⠀⠈⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⣿⠠⠁
⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠄⠠⠤⠄⡀⢨⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢨⡀⠙⠊⠀⠂⠄⡀⡇⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠁⠀⠀⠂⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠅⣁⣀⠌⠙⢺⠃⠃⡆⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣄⠀⠀⠀⠠⡀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠇⠀⠀⠓⠠⠀⠈⠁⠒⢿⠆⢀⠀⡇⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣯⠀⠣⡀⠀⣠⠶⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠠⠀⠀⠀⡀⠀⠀⡀⠀⢡⠀⠀⠀⠀⢀⢸⠀⡇⠈⡇⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡀⣿⢀⣰⠈⢦⡀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⡄⢣⡘⠆⠄⠈⡇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⠶⠶⠶⣶⡿⠶⠶⣤⢤⣼⠷⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⠀⡠⠂⢐⡦⠀⣠⣿⡶⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠻⠁⠦⠄⠐⠒⠂⠉⠀⠘⠆⠠⠁⠀⠈⠉⠉⠉⠩⠉⠙⠛⠛⠛⠛⠙⠉⠝⠓⠲⠶⠟⠛⠓⠿⠤⣤⣤⣤⡼⠋⠂⠈⠗⠀⡇
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠀⠀⠠⠬⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⣠⠤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢤⣀⠀⠀⠈⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡠⠞⠋⠀⠀⠀⣀⣤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠒⠶⢤⣄⡀⠀⠈⠙⠶⣄⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⠴⠋⠀⠀⢀⡤⠖⠋⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠈⠛⢦⡀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢁⡴⠃⠀⠀⣠⠞⠉⠀⢀⣤⠶⠚⠋⠉⠉⠀⠀⠀⠀⠉⠉⠙⠓⠶⣤⣀⠀⠀⠙⠷⣄⠀⠀⠙⢷⣄⠀⠀⠻⣆
⠀⠀⠀⠀⠀⢠⠞⢀⠀⣰⠋⠀⠀⣠⠞⠁⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠈⢷⣄⠀⠀⠙⣦⡀⠀⠙⣧
⠀⠀⠀⠀⢠⡏⠀⢀⡼⠁⠀⢀⡼⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠙⢦⡀⠀⠈⢻⡄⠀⠘⣧
⠀⠀⠀⠀⡞⠀⢀⡞⠁⠀⢠⠞⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡄⠀⠀⠻⣆⠀⠘⣧
⠀⠀⠀⣸⠁⢀⡾⠀⠀⣰⠋⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠹⣆⠀⠀⢹⡆⠀⠹⡆
⠀⠀⢀⡏⠀⣼⠁⠀⡴⠃⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠘⣦⠀⠀⢻⡄⠀⢿⡀
⠀⠀⢸⠃⣰⣇⣀⣼⠁⢠⠏⢀⣤⠖⠒⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣷⡀⠘⣧⢀⡬⠷⠒⠺⢧⣄
⠀⠀⣸⠋⠉⠀⠀⠉⠓⢯⡴⠏⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⠉⠳⢤⡼⠋⠀⠀⠚⠉⠀⠙⣆
⢠⡴⠟⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠙⠲⠶⠞⢻⡄⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠞⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⢰
⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣰⢦⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣀⣀⣀⣴⣤⣀⡀⣀⣀⡴⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣿⣿⣿⣷⣶⣶
⣿⣿⣇⣤⣍⣤⣮⣬⣧⣥⣾⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠘⠃⠊⠁⠀⠀⠈⠀⠐⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣔⠀⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠓⠢⢤⡀⠀⠀⢠⡐⢧⡀⢠⠐⠀⢠⢦⠀⠀⡀⠀⢀⣤⣀⣀⣀⣘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠀⠒⠶⣂⣀⡉⣶⡉⢨⡓⠄⠢⣤⣙⠚⠛⡉⠛⡦⡟⢋⡙⢻⠻⠛⢩⠍⠙⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢀⠘⠿⠷⠶⠄⠹⣧⣌⣻⣦⡍⠁⢒⣻⡃⠈⢱⡆⣀⠐⠀⢀⠁⢈⠂⠀⠉⣠⠾⣍⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣁⣘⡋⠀⠀⠠⢤⣀⠀⠕⠂⠛⠻⠯⠂⠰⠿⠈⢐⠒⠞⠁⠀⠈⠁⠂⢀⠀⢠⣾⠙⢦⠈⠻⣦⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣛⠉⠉⠛⢡⣤⣀⣀⣰⣍⠓⠠⠀⠀⠀⠀⢀⠉⠀⠉⡁⠀⠀⠈⠠⠔⠀⡁⠀⢿⣍⠁⠀⠀⠀⠀⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣦⣤⣤⡌⣙⠀⠀⣤⣄⠀⠀⠀⠀⢤⡾⠿⠏⠋⠉⠀⠀⠀⣠⠾⠾⢦⣽⣷⣄⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⡶⠞⠉⡙⠋⠉⢐⣠⠤⠈⠁⠦⠀⠉⠁⠀⠀⡸⠿⢷⣦⣄⡀⠀⣀⠀⠀⢡⣶⣶⣦⣽⡿⢿⣿⣦⣄⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣽⣿⡶⠛⣻⠛⠑⡾⠟⠓⢶⡀⠀⠀⠹⣿⣆⡙⢷⡈⠿⢶⣍⡻⣿⣿⣄⠀⠀⣿⣿⣿⣿⣿⣿⣦⣽⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣽⣟⢉⡩⠛⠲⠿⠷⠀⠴⣄⠙⠒⠠⠀⠙⢷⣄⠀⠀⢚⣲⣿⣗⡛⠻⣿⣷⣴⣿⣿⣿⣿⣿⣿⡿⢻⠕⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠱⠿⠷⠦⠶⡆⠘⠒⢂⠀⠀⠰⠂⠀⠀⠀⠀⠈⠀⠸⠿⢷⣮⣽⣦⡸⠏⢻⣿⣿⣿⠿⣿⠽⠊⠁⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⠶⠛⠓⠲⢶⣶⣦⣦⣤⣵⣷⠎⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠛⠿⣽⣷⣤⣹⣷⣾⣷⠄⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⢀⢀⣠⣶⣶⣶⡦⢤⣤⣌⡛⠏⣛⢛⠛⢿⡏⠘⡁⠀⣠⡀⠁⠀⠐⡦⠀⠀⠀⠀⠁⠙⠢⠄⠀⣾⣯⡉⣛⣿⣿⣧⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣈⣉⣉⣭⣿⣿⣿⣿⡽⠻⢷⡤⣤⡁⠑⠢⣈⢿⡁⠈⠉⠑⠒⠒⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠻⣿⡿⠇
⠀⠀⠀⠀⠀⠁⢉⣿⣿⠿⢿⣿⣿⡏⠻⠀⡙⡞⣾⡻⣶⡓⠈⣰⠏⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⡀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠠⠖⣶⣿⡿⢿⢓⠝⠋⠴⠁⠀⠀⠀⠀⠈⣋⠡⠽⣿⣦⠟⠂⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⡁
⠀⠀⢰⣿⣿⠋⠋⠐⠛⠠⠈⠀⠒⠀⠀⠀⠀⠀⠘⠃⠀⠁⢻⡆⠆⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠃
⠀⠀⠸⠟⡋⢠⠊⠀⠊⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠐⠤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠆⠈⠀⠀⠈⢿⣦⡐
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠞⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⢭⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⡁⠙⠗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⡷⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⢦⣤⣤⡾⠷⣀⣈⣿⠂⠔⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠟⣔⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣤⡄⠀⠀⠀⠀⠀⠈⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢸⡿⣾⢿⡝⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠈⠉⡴⠤⣤⠚⠀⠊⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⣍⣉⢺⡍⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠾⠁⠀⢹⡤⠀⠀⠈⠂⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⢉⢙⣷⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⣏⣩⣩⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣙⠗
⣀⣀⣀⢀⣀⡀⡀⣀⠀⣀⣀⢀⢀⣀⢀⣀⡀⢀⣀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⠀⠀⢀⠀⣀⣀⡀⡀⢀⠀⣀⡀⢀⡀⠀⣀⡀⠀⠀⡀
⣿⠉⠉⣿⢛⠛⢛⢛⡛⢻⡛⣻⡛⠛⢻⠟⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣻⣿⣿⣛⣛⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⠀⠀⢀⡠⠴⡚⠍⠉⠉⠙⠉⠉⠉⠩⠓⠦⢄⡀⠀⠀⠘⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⣿⠆⢀⣞⡍⢊⠀⠐⠀⠀⣀⢤⡀⠠⠀⠁⠂⠀⠑⢩⣳⡀⠰⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⣶⠝⡩⠂⠀⠀⠀⠀⢸⣿⣾⠇⠀⠀⠀⠀⠀⠀⠐⢍⠻⣶⣿⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣧⠸⣯⠈⠀⠀⠀⠀⠀⠀⢹⣾⠛⠋⠙⢠⣄⠀⠀⠀⠀⠀⠁⣽⠇⣼⡿⢠
⠀⠀⠀⠀⠀⠀⠀⢤⢻⣾⣿⣦⣘⣧⡀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣠⣤⣈⠀⠀⠀⠀⢀⣼⢃⣴⣿⣿⡟⡤
⠀⠀⠀⠀⠀⠀⠀⡰⣿⣾⣿⣿⣿⣿⣿⣦⣄⢀⡠⣴⣿⣿⣿⡿⠿⠚⠋⠈⠶⣄⣴⣿⣿⣿⣿⣿⣿⣾⢂
⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣇⣽⡾⠿⠶⢶⠀⣀⣴⣾⡀⠈⠻⣿⣿⣿⣿⣿⣿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣩⣍⡉⠛⢋⠈⣿⣷⣄⣀⣸⣿⣿⡿⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠿⣟⣻⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⢶⡟⠀⠜⢳⣿⣯⡭⢬⣿⣟⣻⠿⣇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠟⠋⣿⣿⣿⣿⠺⣿⣿⣿⣿⠉⠁⠄⠀⣹⣿⣿⣶⣤⣼⠿⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣿⣿⡻⣿⣆⢹⣿⣿⣿⡀⡀⠀⢰⣿⣿⠿⠅⠤⢱⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣿⣷⣌⠙⠄⢿⣿⣛⡛⣿⡛⣻⣿⣿⣧⡄⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣮⣸⣿⣿⣿⠿⢶⣿⡿⠋⣰⣿⣿⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡟⣠⣾⠁⢸⣾⣿⣿⣿⣧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡌⠿⣻⣏⣉⣟⠿⢥⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠉⢀⣀⡀⠤⠤⠤⠤⠤⢀⣀⡀⠉⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⣀⠤⠒⠉⠁⣀⣀⣤⠠⠤⠤⣄⣀⣀⠈⠉⠲⢤⡀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠚⠁⣀⠤⠒⠉⠁⣀⣀⠠⡤⠄⣀⣀⠈⠉⠒⠤⣀⠈⠓⢄⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡠⠊⠀⡠⠊⠁⣠⠔⠊⠉⠀⣀⣀⣀⣀⣀⠀⠉⠑⠢⣀⠈⠑⢄⠀⠑⣄⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡜⠁⣠⠎⠀⡠⠊⠀⡠⠔⠊⠉⢀⣀⣀⣀⠀⠉⠑⠢⣄⠈⠑⢄⠀⠱⡄⠈⢦⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⣜⡀⣰⠃⢀⠞⠀⡠⠊⠀⡠⠖⠋⠁⢀⣀⡀⠈⠙⠲⣄⠀⠑⣄⠈⠣⡀⠘⣄⠀⣧⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠚⠉⠉⠉⠉⠓⢮⡀⡼⠁⢠⠎⠀⡠⠚⠉⠁⠀⠈⠉⠲⢄⠀⠳⡀⠈⢆⠀⡱⠖⠋⠉⠉⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⣁⢀⠇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠱⡀⣈⡞⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢀⡤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠈⠣⣄⣀⡤⠤⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡴⢤⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠓⠲⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠚⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⢦⡴⠶⣤⡴⠲⠲⠶⠶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠉⠹⣿⠇⠀⠀⠀⣿⠇⠀⠀⠀⠀⢹⠍⠁⠈⠁⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢲⣿⡏⠁⠀⠀⠀⣿⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠿⠟⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⣿⠁⠀⠀⠀⠀⢸⡆⢀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣧⣄⡀
⠀⠀⠀⠀⠀⣠⠴⣾⡇⠀⠀⠘⡌⠀⠀⠀⠀⠀⢸⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠇⠂⠀⠀⠀⣸⠿⠿⠉⢷⡀
⠀⠀⠀⠀⢰⡇⠀⠹⣧⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠈⡧⠀⠀⠀⣸⡀⠈⠀⠀⡼⠃⠀⠀⠀⠀⡟
⠀⠀⠀⢀⣯⠀⠀⠀⢱⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⣧⠄⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⡿⠁⠀⠐⣾⠓⠀⠀⠀⠀⣼⡿⢦
⠀⠀⢠⣟⠉⢦⠀⠀⠀⢣⠀⠀⠀⠘⡂⠀⠀⠀⠀⢸⡄⠀⠀⠀⡅⠀⠀⠀⢸⠀⠀⠀⣰⠀⠀⠀⢰⠉⠀⠀⠀⠀⠼⠋⠀⢈⡇
⠀⠀⢸⡇⠀⠈⢲⣄⠀⠠⢦⠀⠀⠀⠱⡀⠀⠀⠀⠈⣡⠀⠀⠀⣧⠀⠀⠀⣾⠀⠀⢀⠏⠀⠀⢠⠇⠀⠀⠀⢀⡜⠀⠀⢀⣼⣷⡄
⠀⠀⢨⢧⡀⠄⠲⡿⣆⠀⠉⢧⠀⠀⠀⢷⣖⠀⠀⠀⡏⡆⠀⠀⡿⠀⠀⢀⢿⠀⠀⡜⠂⠀⢀⣞⠀⠀⠀⢀⡜⠀⠀⢠⠎⠀⢀⡇
⠀⠀⠸⡆⠘⢄⠄⠈⠻⡆⠀⠀⢳⡆⠀⠘⣿⠀⠀⠀⢇⠃⠀⠀⠁⠀⠀⢸⠂⠀⣠⡇⠀⠀⡟⠄⠀⠂⢀⡞⠀⠀⡴⠃⠀⡠⠎⡇
⠀⠀⠀⣿⠳⣾⢷⡀⠀⠙⢶⣄⠀⢿⠀⠀⢹⠀⠀⠀⠸⡀⠀⠀⡀⠀⠀⣿⠀⠀⡿⠁⠀⣼⠇⠀⠀⡠⡣⠄⢀⠞⠀⣰⣯⠕⣾⠁
⠀⠀⠀⠘⣷⣈⣷⡙⢦⠀⠀⢿⣆⠀⢣⡀⠀⢧⠀⠀⠀⡇⠀⠀⠁⠀⠀⡏⠀⣸⠁⠀⣰⠏⠀⢠⡞⠁⢀⡴⢅⡠⣪⣞⣵⢴⠋
⠀⠀⠀⠀⠙⢮⡻⣝⢮⡳⣤⠀⠹⣆⠀⠹⡄⠈⡆⠀⠀⢣⣠⢀⢠⡤⢴⣁⢀⡧⠀⢰⠹⠀⢀⡏⠀⣠⢞⡱⣫⣺⠖⣫⡷⠋
⠀⠀⠀⠀⠀⠀⢹⣚⢷⣝⣮⡣⣄⠘⢷⡄⢹⣤⢿⠁⠁⠸⡅⠸⣂⠀⡾⠀⡼⠛⢲⣿⣀⣠⠋⢠⢞⡕⣫⢞⣩⢶⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡿⠿⣮⣢⣌⠿⣦⠙⡄⢣⠀⠀⡇⠰⠁⢠⠇⢠⡇⢀⡾⠉⡵⢷⣶⣗⣡⣎⣪⠭⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡶⣭⣻⢷⣬⠳⡘⣌⢇⠀⢿⢸⡇⢸⢀⣾⢀⣾⢀⣼⣵⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⠷⢽⠿⢿⣦⡹⣞⢞⣆⢹⠸⣇⡏⢈⡟⣾⣫⣾⣿⣿⣿⠇⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢲⣮⡟⣁⡀⠀⡿⣿⣯⣿⡌⡄⣹⡟⣾⡼⣱⣿⡟⠉⢡⣴⡏⢁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⠤⠽⠋⠉⠙⠳⠦⢌⣿⣿⣇⣿⣴⣿⣾⡟⢡⣷⠖⢚⣿⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠷⠖⠶⠾⠗⠒⠒⠋⠉⠻⠿⠿⠟⠓⠛⠛⠛⠒⠿⠿⠶⠚

⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠀⢹⡄⠀⠀⠀⢀⡀⡂⠀⠀⠀⣠⡄⠊⠀⠀⠀⡀⠈⢿⣇⠀⠃⢀⣀⠀⠛⠻⣐⠿⢤⠔⠒⠤⠄⣿⡾⠟⠀⢊⣿⣿⣿⠏⠈⣯⡐⢀⠀⠀⠀⠈⠒⠤⣤
⠁⠀⠀⠙⡄⠀⠀⣤⡀⠡⠶⢶⣼⣯⠕⠀⠀⢂⠀⠀⡀⣸⡿⠀⠘⠀⢩⣄⠀⠀⠎⣤⢤⡴⠶⠟⠘⠈⠀⠀⢀⣌⢶⡟⡻⣄⠀⠋⠐⢦⣣⣄⡀⠀⠀⢀⣀
⡀⠀⢀⠀⠙⠂⠒⢿⡈⠳⢤⡈⠛⠻⠀⡀⠠⡤⠀⠀⠀⡿⠃⠐⠀⠀⢾⠋⡥⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠋⠑⠫⡀⠀⠀⠈⠉⠻⠻⠆⠉⠉
⡇⠀⠸⣆⠀⠀⡀⢈⣷⡀⠀⠙⠣⢀⠈⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣇⢀⠀⠘⡆⠀⣇⠀⢿⠛⠢⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠟⡌⠀⠀⠋⠂⠄⠀⢠⡀⠀⠈⠓⢆⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠠
⠀⡀⠀⠀⠠⠀⠀⠀⠀⠈⠒⠄⡀⠀⠉⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⣘⠀⠀⠀⢀⠀⢂⡐
⠟⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⡄⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣿⣦⣤⣀⠉⢷
⠀⠀⠀⠀⠃⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠈⣉⣙⠛⠶⢬
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⢠⡤
⢆⠀⠀⠀⣶⣠⣥⡀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣬⡀
⡛⣷⠀⠀⣮⣽⣷⠞⠁⡀⠀⣠⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠤⠄⠀⠀⠀⢀
⡻⣾⡇⢸⣿⣯⣿⠀⣸⠗⠊⠖⠉⠉⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠘⠓⠲
⣿⠿⣿⣼⡇⣸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢹⢶⣽⠙⣷⣿⣥⣄⣤⡴⣆⠀⢰⠴⣦⠠⢄⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠠⡀⢀⣦⠀⠀⠀⠠⠀⣴⣟⠉
⠀⣿⣽⣷⡌⠻⠟⠛⠉⠁⠀⠀⡀⢅⣨⣤⡀⠀⠀⠀⠀⢀⠃⠀⠀⠂⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⣃⠀⠀⠀⠀⢀⠀⠈⠻
⠂⢿⡏⠙⠟⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠀⡜⠀⡠⠀⣼⠏⠀⠀⢀⡤⠤⠎⠀⠀⠀⠀⠀⠁⠀⢀⡅⠀⠀⠀⠀⠀⠀⢰⡖⠒⠁⠊⢄⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡄⢠⠀⠀⠘⣃⠶⣤⠃⡀⠐⢰⣤⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡀⠑⠘⣷⢂⡮⠀⢸⠀⡜⠒⢾⠁⠁⠈⢣⡾⠇⠘⡀⢠⠴⣄⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⡼⢧⡄⢄⠰⡉⢋⢣⢰⠈⡄⡇⠀⠘⠀⠀⠀⠀⠀⠀⠈⠔⡘⢳⠎
⠀⠀⠀⠀⠀⠀⠠⣴⣝⠀⡀⠺⢚⠓⡈⢣⠐⡀⠀⠀⠀⠅⠃⡀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠔⡡⠂⡠⠂⣭⡹⠋⠄
⠀⠀⠀⠀⠀⠲⠑⣾⣙⣛⠢⣀⠠⡑⢌⠢⡁⠸⡘⠀⡀⡀⠆⠅⠂⠀⠄⠀⠀⠀⠀⠀⠊⢀⠐⣈⠔⡀⠀⢁⠄⠂⢀⠄
⠀⠀⠀⢀⣀⡈⣓⠬⣍⠢⢥⡀⠑⠬⡀⡑⢁⠤⠙⠁⠀⠀⣤⡀⠀⠀⠀⠈⠀⢠⡀⢈⠔⠡⢊⠁⠀⠄⠊⠁⠐⠙⠓⢻
⠀⠀⢀⡨⣭⣹⡭⠉⡒⠀⢀⡈⢁⡤⠈⠙⠖⠀⠀⠀⡠⠊⠀⢙⣄⣀⣤⣤⣴⡶⢶⣥⠀⣀⠀⠀⠀⠀⠄⠂⠠⠄⠃⠘
⠀⢀⡒⠀⠌⠥⠐⠂⠀⠉⠀⠀⣁⠚⣷⣏⠠⠄⢀⠖⣡⣤⣤⣤⡀⠷⣤⣌⣉⠛⣦⡙⢿⣦⣌⣁⠳⠀⠀⠐⠀⠤⠁⠀⠐⠀⡀
⠀⠀⣹⡋⣉⣀⣒⡒⠀⠀⠄⠀⣀⢼⣿⡧⡀⣺⠟⣿⣇⠀⡈⢻⣷⣀⡈⠙⣏⠓⠈⣥⣄⠙⢾⣿⣷⣌⠃⠀⠒⠀⠉⠀⢸⢋⣇⡀
⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢠⣽⣧⠞⣹⣷⣿⣧⣴⣿⣟⣓⠃⣴⣿⣯⣉⠉⢿⣷⡀⠈⡿⠷⠀⠙⢿⣝⣦⣄⡀⠀⠀⠀⠀⢁⣀⣐
⠀⡈⢉⠁⢈⠁⠠⠠⠄⢤⢌⣼⠋⠘⣰⣿⡋⣡⣼⠿⠿⣿⢦⠉⣷⠾⢿⣶⣆⠀⢩⣦⢷⣄⡀⠀⠠⣈⡩⢤⣥⠖⠀⠀⠀⢠⣄⡀
⠀⢘⣶⣦⠀⠀⠀⢀⣉⣻⣿⣷⡏⠼⣓⣸⢿⡁⢼⡄⢾⡽⣯⣷⢏⡀⠀⢀⡉⠻⢆⡀⢌⡿⠻⠀⣤⠘⢷⣈⣡⣦⢀⠀⠀⢢⠨⢏⡀
⠀⠸⠝⢋⡀⠀⠭⠀⠀⠳⣶⣶⣶⠦⡌⠙⣾⢷⣜⡂⠈⣟⠉⠛⣄⠙⣆⠈⢳⡆⠀⢱⢳⣵⣄⡀⠣⣿⡾⠉⠁⠀⡈⠀⠀⠈⠁
⠀⠈⠁⠤⠀⡂⠠⣀⠀⢐⠁⢈⡿⠿⡿⣜⣿⡟⢿⣧⠀⣿⢣⠀⠘⠓⠤⠳⣼⣷⣷⡖⢸⡁⢨⠛⡻⢳⣶⠀⣦⣶⠀⠀⠀⡤⢔⠠⠄
⠀⠀⠘⢛⣹⡆⠄⢀⠨⣀⠅⢼⡖⣉⠁⣸⣿⣷⣼⣿⣷⣀⣆⢡⣄⣀⣀⣀⣮⣰⣿⣙⣦⣽⣤⣄⣣⣤⡄⠀⣫⡀⠀⠢⢄⠙⠏⠁
⠀⠀⠀⠈⠈⣁⠤⡥⢢⡔⠙⣈⣧⡄⣸⣿⣠⣀⣈⡟⣋⣿⢟⣷⠛⣧⣤⣄⣀⣁⣀⠬⠉⠻⢿⣿⣤⣭⣬⣻⡿⠿⢆⢀⠀⠌⠂⠁
⢠⡾⠁⠀⢙⠥⠰⠶⠄⢩⣾⡟⠣⡙⡿⠋⠙⠿⣶⣿⣿⣿⡟⡁⢸⣀⣴⣾⣽⠟⢋⡹⠗⠂⣤⣉⠛⠿⢿⣿⣿⣦⣌⢺⣧⡀⢦⣄
⠈⣉⡀⠸⣷⣶⣿⣄⣾⣿⠣⠦⢀⠙⠀⠀⠀⠀⣿⢷⣿⣿⣿⡇⢸⠃⡾⠟⢡⡞⢩⠀⠀⠀⠈⣿⣿⣿⣷⣖⣼⣿⣿⣦⣘⢷⣾⣷
⢰⠶⣿⣷⣿⣿⣿⣷⣿⡿⢿⠄⠈⠁⠀⢄⡀⠂⢻⣈⣹⣿⣿⡇⠘⠘⢸⠃⣾⡇⢸⡆⡷⠀⠀⠘⠛⣿⣿⣯⣿⣻⢿⡿⢄⣬⣿⠋
⣌⣳⣾⣻⣿⡿⠻⠿⣿⣷⣯⠂⠀⣦⠀⠈⠁⠈⢛⡟⣹⣿⣿⡇⠴⠀⡇⢸⣿⠃⢸⡇⡽⠀⠀⠀⢀⠉⢻⡿⣿⣇⢸⣿⣤⣌⣳⣤
⢾⣿⣿⣇⣤⣤⠄⠀⣿⣿⣿⣟⢛⣿⠃⢀⣈⣿⣺⣿⣿⣟⣿⠆⣾⣀⠁⣸⠓⢶⠨⡇⠻⡀⠀⠀⠀⠱⣦⢣⣸⣿⣾⣍⡏⠙⠻⣶⣀
⠀⣿⡿⣿⠃⠀⠀⠀⠀⢯⣵⢾⡏⣿⡆⢫⡭⣷⢿⣏⣿⣿⣏⣼⠟⣁⡚⠛⠐⢆⢰⣿⡄⢁⡗⠀⠀⠀⠈⠃⣻⣿⡏⢻⡧⢘⣽⣿⣿
⠀⣿⣟⢟⡛⣷⣤⡤⠀⣤⣍⣿⣿⡿⠿⠟⠛⢿⠿⢿⠿⢿⠿⠿⠾⣷⣾⣷⣶⣌⡻⠿⠿⠦⠱⠜⣦⣀⣀⣀⣻⣯⣰⣿⣁⣿⣿⣿⣿
⠀⠹⣿⣶⣾⠅⢛⡓⠐⠋⠉⠉⠋⠁⠀⢰⣠⡤⡤⢂⣀⣅⠑⠀⣒⢀⠀⢝⢹⣿⠿⠿⡟⠿⠻⠶⢦⣬⡭⢭⣽⠛⠙⣿⣿⠶⣏⡻⠋
⠀⠀⠈⠙⠻⠷⣉⣀⡠⢶⣶⡍⠿⠷⠟⣿⠏⠀⢀⢈⠱⣯⣤⡄⠉⠈⢃⣤⠈⠀⠠⠀⠂⡀⠀⠆⠠⠀⠀⠀⠘⠛⠷⠞⣹⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠘⣽⡿⢀⡤⡤⢤⠤⠀⠀⢀⢦⢻⡧⣤⡤⣾⡧⣰⣶⣤⣟⢛⡒⢶⡶⠄⠀⠒⢺⣖⣀⣤⡶⠶⣒⠀⣚⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⣷⣿⣥⡛⣿⣿⠶⢞⣷⢋⣿⣃⣤⣽⣿⣽⣿⣉⣉⣼⣗⣴⠀⡙⢀⠀⣙⡷⢿⣿⣷⡷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣯⡧⣿⠧⠾⢛⣰⡷⣿⢯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣭⣏⣩⣠⣾⢿⣿⠻⡷⠚⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣬⣭⣭⣤⣤⣤⣿⣿⣿⣿⣿⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣄⣰⣆⣠⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣆⡠⠀⠀⠀⠀⠀⡄⣐⣰⣂⡀
⠀⠀⠀⣤⣿⣿⣿⣿⣤⠀⠀⠀⠠⣿⣿⣿⡧⠀⠀⠀⠀⠬⣿⣿⣿⡎⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⣽⣿⣿⣿⡧⠀⠀⠀⠐⣾⣿⣿⣿⡒
⠀⠀⠀⢠⠿⢿⡿⢯⠀⠀⠀⠀⠀⠹⠿⠟⠃⠀⠀⠀⠀⠈⠽⠿⠿⠓⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠐⢚⠿⡿⢟⠓⠀⠀⠀⠈⠝⢿⠿⠛⠌
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⣄⣂⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠀⡄⣂⡐⢀⠄
⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⢾⣿⣿⣿⣿⡇⠀⠀⢀⢹⣿⣿⣿⡧⠄⠀⠀⠀⠠⣿⣿⡯⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⢒⢾⣿⣿⢀⡒
⠀⠀⠀⠻⣿⣿⣿⣿⠏⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠚⡻⢿⠿⡓⠂⠀⠀⠀⠀⠋⠛⠑⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⠀⠀⠁⠆⡉⢁⠲⡌⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⢤⣰⣦⡆⡀⠀⠀⠀⡀⢦⣴⣤⠆⡀⠀⠀⠀⡀⢆⣶⣠⢄⠀⠀⠀⢀⡄⣴⣇⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣅⡂⠄
⠀⠀⠀⣽⣿⣿⣿⣿⡥⠀⠀⠠⣽⣿⣿⣿⣿⠥⠀⠀⢠⢽⣿⣿⣿⡯⡄⠀⠀⣀⣻⠁⠀⠙⡟⠆⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠅⣾⣿⣿⣿⡎⠄
⠀⠀⠀⠚⣻⢿⣿⡟⠂⠀⠀⠀⠊⣻⢿⢿⡛⠂⠀⠀⠀⠊⡻⠿⢿⡓⠂⠀⠀⠈⣙⣷⢤⡞⠻⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠂⠝⠿⠿⠟⡔
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁
⠀⠀⠀⠠⡰⠘⠰⢢⠀⠀⠀⠀⢀⣠⣤⣆⡀⠀⠀⠀⠀⣠⣢⣖⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣷⣶⣄⠀⠀⠀⢀⠰⣀⣆⡐⢀
⠀⠀⠠⠅⢰⣿⣷⡄⠩⠀⠀⠀⢺⡏⠀⠈⣿⡂⠀⠀⢸⣹⠁⠀⠈⣳⡅⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠌⣿⣿⣿⣿⡅
⠀⠀⠀⢫⢌⠙⢋⠠⠑⠀⠀⠀⠙⠷⡦⣶⠟⠀⠀⠀⠘⢭⡷⢤⡴⡿⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠀⠀⠀⠐⢙⠿⠿⢟⠐
⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣵⣭⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣾⣽⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣴⡖⠛⠛⠛⠛⢶⣶⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⣶⡞⠉⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⢻⣶⠶⢦⣄
⠀⠀⠀⠀⢀⣠⣴⠁⠀⠀⠈⢿⡄⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸⡇⠀⠀⠉⠳⣦
⠀⠀⠀⣰⠋⠀⠹⣆⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡷⢦⣄
⠀⠀⣰⠛⣆⠀⠀⢹⣆⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠏⠀⠀⠈⠻⣄
⠀⠀⣿⠀⠸⣆⠀⠀⢿⡄⠀⠀⠀⠸⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⡿⠀⠀⠀⣿⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢿⠀⠀⢻⡄⠀⠘⣷⠀⠀⠀⠀⢻⡆⠀⠀⠀⣿⠀⠀⠀⢰⡇⠀⠀⢰⡏⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⢀⣴⣿⢷⡀
⠀⠀⠸⡆⠀⠀⢿⡀⠀⢻⡆⠀⠀⠀⢸⣇⠀⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⣿⠁⠀⢀⣼⠃⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠙⣆
⠀⠀⠀⢳⡀⠀⠈⣧⠀⠸⣇⠀⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⣸⠃⠀⠀⣼⠃⠀⢀⣾⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⢧⠀⠀⠸⡆⠀⣿⠀⠀⠀⢀⡇⠀⠀⣼⠁⠀⢰⠏⠀⠀⣼⠃⠀⢀⡾⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣠⣾⣇
⠀⠀⠀⠀⠘⣧⠀⠀⢻⡀⢿⠀⠀⠀⢸⠇⠀⢠⡇⠀⢠⠏⠀⠀⣼⠃⠀⢠⡿⠁⠀⠀⣠⠟⠁⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠘⣦
⠀⠀⠀⠀⠀⠸⣆⠀⠈⡇⢸⠀⠀⠀⣾⠀⠀⡾⠀⢠⠏⠀⢀⡼⠃⠀⢠⡿⠁⠀⢠⡾⠁⠀⠀⠀⢀⣠⣶⠟⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠹⡆⠀⢿⢸⠀⠀⢀⡏⠀⢰⠇⢀⡞⠀⢀⡼⠁⠀⣰⡟⠁⠀⣰⠏⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⣾⠀⠀⢸⠃⠀⡟⢀⡞⠀⢠⡞⠁⠀⣰⡟⠀⢀⡼⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⣀⣤⡴⠾⠛⠋⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣷⠘⣿⠀⠀⡿⠀⣸⢁⡞⠀⣠⠏⠀⠀⣼⠏⠀⢠⠟⠀⠀⢀⣴⠟⠁⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⣀⣠⡏
⠀⠀⠀⠀⠀⣠⠞⠋⠈⣇⣿⠀⢰⡇⢠⠇⡼⠀⡴⠃⠀⢀⣼⠃⢀⣴⠋⠀⢀⣴⠟⠁⠀⣠⠶⠋⠁⠀⠀⣀⣤⡴⠶⠞⠛⠛⣿⠁
⠀⠀⠀⠀⠀⠻⡀⠀⠀⢸⣽⠀⢸⠇⡞⡼⢁⡾⠁⠀⣠⡾⠁⣠⡞⠁⠀⣠⠟⠁⢀⡴⠋⠁⢀⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⣿⡇⢸⣼⣱⢣⡞⠀⢀⣴⠋⢀⣼⠋⠀⣠⠞⠁⣠⠖⠉⣀⡴⠞⠋⠁⠀⣀⣀⣤⣤⣶⡶⠶⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣷⢸⣿⣧⡟⠀⣠⠞⢁⣴⠟⠁⣠⠞⢁⡤⠚⣡⠴⢛⣁⡤⠴⠖⠛⠋⠉⠉⠁⠀⠀⠀⢀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣿⡿⢀⡜⣁⡴⠛⢁⡤⠞⣡⣴⣫⢔⡫⠔⣚⣉⣀⣀⣤⣤⣤⣤⡤⠶⠶⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⠿⠚⣉⡤⠖⣫⣴⣞⣻⡽⠾⣿⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⢿⣵⠶⠟⠛⠋⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠤⣼⠟