Pearl Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣄⡀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣀⡤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⡀
⠀⠀⠀⠀⠀⣰⠋⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⢢⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢙⣶⠤⠖⠒⠛⠉⠉⠉⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠉⠙⠓⠒⠦⢤⣴⠋
⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢣⡀⠀⠀⠀⠀⠀⠀⡰⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠈⣳
⠀⠀⠀⠀⠀⠀⠸⡟⠦⣤⣀⣀⠀⠀⠀⡏⠀⠀⠀⠉⠓⠶⠤⠴⠖⠋⠀⠀⠀⠈⡇⠀⠀⢀⣀⣠⠤⢞⡟
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠉⠉⠙⠛⠓⠒⠶⠶⠶⠦⠤⠤⠤⠤⠶⠶⠶⠖⠒⠛⠛⠉⠉⠁⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⢯⠻⣿⢻⣯⢽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⣯⣣⠙⠀⠀⠘⢿⡿⡿⠋⢘⣿⣿⣿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣤⣤⣀⠀⣀⡤⠗⠚⠿⢟⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠻⣿⣿⣿⣒⡒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⣾⣿⣷⣤⣶⣿⣿⣿⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣟⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣄⣀⣀⣀⠀⣠⣤⡀⢾⡿⣻⣿⣿⣽⣻⢟⣠⣶⣦⣬⣵⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⣀⣴⠶⠟⠛⠛⠛⠷⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠉⠀⠀⠀⠀⠉⠛⠷⣦⣤⣴⠾⠋⠁⣀⣠⣤⣄⣀⡀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⣤⠶⠟⠛⠛⠶⣦⣄⡀⠀⢀⣠⣶⠟⠋⠉⠉⠉⠉⠻⣦⡀⠈⠿⠶⡶⠶⠶⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⠟⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠉⠛⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣄⣀⣀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⢠⣴⠟⠋⠉⠉⠉⠉⠁⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠉⠉⠉⠉⠙⠻⣦⡀⠀⠸⣷
⠀⠀⠀⠀⣴⠟⠀⢀⣴⠾⠛⠛⠛⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣿
⠀⠀⠀⢰⡟⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠸⣧⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠹⣷⣀
⠀⠀⠀⠀⢿⡄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢷⣤⣀⠈⠛⢷⣄
⠀⠀⠀⠀⣼⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠈⠙⣷⡀⠀⠹⣧
⠀⠀⣴⡾⢋⣴⠾⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢻
⢠⡾⠃⢠⡿⠁⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢸
⣾⠃⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣸⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣾
⢿⡀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⢧⠀⠀⣿⠀⠀⣾⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⢀⣼⠏
⠘⣷⡀⠀⠹⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣀⣼⡷⠶⠿⠶⢶⣧⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⣀⣤⡶⠛⠁
⠀⠈⠻⢶⣤⣀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡾⣋⡵⠖⢳⡄⠀⠀⠈⠻⣦⡴⠋⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⢠⡟⢰⠋⠀⣀⡼⠁⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⢀⣴⠾⠋⣁⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠈⣙⣷⣦⣤⣶⣦⣤⣼⡇⣨⡛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠶⠶⠿⢷⣤⣾⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠟⠛⠉⠀⠀⠠⣤⣄⣹⣇⢧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⣀⣤⣤⣤⣤⣤⣀⡀⢀⣼⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤
⠀⠀⢀⣴⠶⠟⣻⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠀⠀⠀⠀⠈⠉⠙⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠷⠶⣦⣄
⠀⢠⣿⠁⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡀⠹⣧
⠀⠸⣷⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⣿
⠀⠀⠻⣦⣀⠈⠛⠛⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⡶⠶⠾⠛⠉⣀⣴⠏
⠀⠀⠀⠹⣟⠛⠷⣦⡀⠀⠙⢷⣤⣀⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⣀⠀⠀⠀⢀⣠⣴⠟⠋⠉⣀⣀⣤⣤⣤⣤⡶⠶⢿⡿⠁
⠀⠀⠀⠀⠹⣧⣀⠈⣿⣆⡀⠀⠈⠉⠉⣉⣀⣀⠀⠈⠙⠻⢶⣤⣀⣀⣠⣤⡶⠟⠋⠉⠉⠉⠉⠙⠛⠛⠛⠋⠉⠀⣀⣴⢿⡿⠉⠁⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣟⠻⠟⠟⠛⠋⢿⡟⠛⢷⣤⡀⠀⠈⠉⠉⠉⠀⣀⣤⣶⣿⠟⠛⠷⠶⣦⣤⣤⣤⡶⠾⠋⢡⣾⣧⣤⣴⠶⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣀⣀⣈⣻⣆⡀⠈⠛⠷⣦⣤⣴⠶⠟⠋⢡⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠻⣦⣄⣀⠀⠀⠀⣀⣠⡾⠟⠉⠛⠶⣦⣤⣤⣤⣤⣴⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢤⣤⢔⡪⠋⠉⢲⣄
⠀⠀⠀⠀⢀⣀⣠⡷⢰⢸⠈⠉⠉⠄⠘⠈⠌⠟⠟⠟⠏⠢
⠀⠀⢀⠊⠗⠛⠉⠈⠀⠘⠀⠀⠁⠀⠁⠰⠈⡈⠈⠎⢊⡀⢆⡀
⠀⠀⢸⡴⢠⢰⠠⢀⠀⠀⡄⠀⠀⢠⠀⠀⢡⢰⠐⠈⠀⠀⠰⠼⣕⡄
⡠⡺⠟⠑⠀⠀⠀⠈⢠⠀⠀⠀⠀⠈⡀⠀⠈⠀⠀⢀⠄⠁⠀⠀⣈⠇
⢡⣵⡐⠀⠁⢁⠁⠐⡈⠠⠠⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠨⡢⡀
⣾⠏⠳⠀⢂⠌⡀⠈⠁⠀⠀⠘⡤⠈⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡈⡀
⠫⢈⠐⣥⠀⠆⠀⠀⠊⢀⠁⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠚⠁
⠀⠀⠈⠒⠍⡎⢄⣀⡒⠁⠀⠀⡡⢔⠢⠤⣁⠂⡀⠀⢀⠤⣀⠔⠁
⠀⠀⠀⠀⠀⠈⠑⠢⠥⣀⣀⡌⡔⠀⠀⠀⢈⣧⣐⣀⣀⠔⠁
⠀⠀⠀⠒⣶⣶⣾⡿⡿⣛⣿⡄⠀⣀⣠⠤⢂⣮⣿⠷⡶⠖⠒⠒⢶⣦⣶⣶⠶⠖⢲⣶⣐⣀⣀⣀⣀⣠⡀⠀⢀⡀
⢀⣔⣈⣭⡠⡑⢕⣬⣺⢷⡾⠾⣲⣬⣭⡴⠟⢛⣁⠀⠈⠀⠒⠠⠀⢈⡹⣯⣽⣲⡒⠂⠐⣒⣒⠒⢀⡀⠐⠀⠒
⠀⢏⠉⠙⣿⣿⣋⠂⠉⠉⠀⠀⡰⠟⠉⠉⢀⢤⡶⠶⢦⡀⠀⢀⣠⣿⠋⢨⢓⣾⠅⣩⠍⠍⠉⠁
⠀⠘⢛⢶⣍⡻⢶⣶⠊⠙⠿⣦⣔⣉⣠⡺⠗⠍⠀⠀⠀⠈⡟⠛⠻⠀⢀⣠⡞⠒⢒⡒
⠀⠀⠀⠀⠉⠻⣄⠐⡁⠀⡄⠀⠀⠀⠈⠀⢈⠠⠂⠀⠀⡀⣡⣞⣛⣉⣩⣥⠠⠄
⠀⠀⠀⠀⠀⠀⠘⢳⣤⣄⣠⣤⡀⠀⠀⠐⢀⣴⣶⡲⠞⠋⠩⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠛⣳⠶⠶⠯⠅⠉⠁⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠁⠀⠀⠀⠈⠁⠈⠀⠐⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⢀⣀⣄⣀⡴⠦⢄⣤⣤⡀⢀⣄⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡀⢀⡞⠋⠒⣛⠭⢀⠐⠒⠂⠀⠀⠀⠉⠉⠙⠓⠊⠓⣄⣈⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡏⠉⠀⣀⡤⠊⣀⣠⡤⠶⡔⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢠⠀⠄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⡀⠈⢧⣞⠙⢴⣾⣿⣾⠶⠶⢶⣄⣀⣈⣃⡀⠀⢓⠉⠥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠒⠈⠁⠲⣿⣻⣛⣽⡏⠀⠀⠀⠀⣹⠻⣿⣟⡛⠉⠉⠐⠓⢆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢤⡀⠀⠘⣤⣎⣷⣿⣿⣿⣞⡀⠀⠀⢀⣿⣽⣿⣿⣷⡶⠴⢢⣄⣶⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢈⠱⣄⣤⡘⠋⠉⠋⢛⢻⣿⣿⣶⡶⣿⣫⡽⠿⠒⠒⠐⠂⢀⡠⠼⣫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⣶⠀⡉⠉⢢⠄⠄⢀⣬⣍⣙⣿⡋⢁⣤⣠⡶⠂⢐⠋⣩⢰⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⣧⠀⡏⠀⠀⠀⠀⠀⢀⠀⢀⠀⠰⠂⢀⠇⣼⢀⣯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⣸⡄⢸⡄⢸⣆⣸⠀⡀⠀⣜⠀⡼⣠⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠺⠿⢦⣿⣿⣶⣧⣴⠷⠾⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠮⡭⠽⣖⠤⠠⣴⠿⠒⢻⠒⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢴⡿⠁⠀⢣⠀⠀⠉⢻⠁⠀⠀⢸⠀⠈⠓⣭⠷⠾⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠛⠛⠻⡀⠀⠀⠸⡄⠀⠀⢸⠀⠀⠀⣼⠀⠀⣰⠁⠀⢀⡞⢸⡇
⠀⠀⠀⠀⠀⠀⣰⡟⠀⢳⡀⠀⠀⢣⠀⠀⠀⢧⠀⠀⢸⠀⠀⠀⡇⠀⢠⠇⠀⢀⠎⠀⠘⣷⣤⣀
⠀⠀⠀⠀⢀⣴⣟⠀⠀⠀⢳⡀⠀⠈⢧⠀⠀⠸⡀⠀⢸⠀⠀⠀⡇⠀⡼⠀⢠⠏⠀⢠⠎⠀⠀⣙⣷⡀
⠀⠀⠀⢠⡟⠁⠈⢦⠀⠀⠀⠱⡄⠀⠈⣆⠀⠀⣇⠀⢸⠀⠀⢰⠇⢰⠃⣰⠃⢀⡴⠁⠀⡠⠚⢁⣿⠃
⠀⠀⠀⠀⢷⡄⠀⠀⠳⣄⠀⠀⠘⢆⠀⠘⣆⠀⢸⡀⢸⠀⠀⢸⢀⡏⣰⠃⡠⠊⢀⡴⠋⢀⡠⠞⣿⡀
⠀⠀⠀⠀⠈⠛⢷⣤⣀⠈⠳⢄⡀⠈⠳⡀⠘⡆⠀⡇⢸⠀⠀⡏⡼⡰⢡⠞⡠⠖⢁⡠⠖⠉⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣉⠲⢄⡙⢄⠘⣆⡵⠼⠦⢼⣱⣷⣵⡷⢊⡠⠖⠉⢀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣽⣿⣿⢛⣿⠃⠀⠀⠀⠀⠘⡿⡟⠲⡿⢶⣾⣛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠋⠉⠁⠀⠉⠉⠉⢻⢨⡄⠀⠀⠀⢀⡟⠉⠉⠉⠉⠉⠉⠛⢶⣄⡀
⠀⠀⠀⠀⣠⠞⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢭⣻⡤⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢳⡙⠦⣄
⠀⠀⠀⢸⢧⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠈⢳⡀
⠀⠀⠀⠘⣮⢽⣷⠭⡭⣷⣖⠦⠤⢤⣤⣄⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⢾⣴⣿⣦⣾⠇
⠀⠀⠀⠀⠘⢦⡀⠀⢇⠈⠻⣷⣖⣒⡲⠿⢲⠒⠛⠿⣭⣭⣭⣿⠿⠿⡿⠷⣦⣬⣵⠿⠛⡏⠀⣠⠿⠃
⠀⠀⠀⠀⠀⠀⠉⠑⠺⣄⠀⣇⠀⠀⠀⠀⣼⠀⠀⠀⠈⡏⠉⠀⠀⢸⠁⠀⠀⢸⠀⢀⡴⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠤⠴⠒⠒⠻⣄⡀⠀⡼⢀⣠⠤⠤⠾⢤⣀⣠⠯⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢀⣉⣉⡀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡡⠒⠉⠀⠀⠀⠀⠉⠒⢌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⠩⠭⠈⠩⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠍⠁⠬⠅⡂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠱⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠎⡄
⠀⠀⠀⠀⠀⢀⠔⡂⠕⠃⢀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠘⠪⢐⠢⡀
⠀⠀⠀⠀⠀⢎⠊⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⠑⡱
⠀⠀⠀⡀⢔⠧⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠴⡢⢄
⠀⠀⣌⠊⠀⠀⠀⠣⡀⠀⠀⠀⠘⡄⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⠎⠀⠀⠀⠀⡐⠀⠀⠀⠑⣡
⠀⠀⢻⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠘⢄⠀⠀⠀⢃⠀⠀⠀⠀⡘⠀⠀⠀⢀⠊⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⡟
⠀⠀⠈⢇⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⢂⠀⠀⢈⡄⠠⠄⢠⡁⠀⠀⡠⠃⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢣⠒⠁⠀⠀⠀⠀⣈⡒⡔⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠑⢆⣠⠁⠀⠀⠀⠀⠀⠐⠧⠄⠈⡄⡠⠊⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⣀⣀⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⣀⣀⣠⠔⠊
⠀⠀⠀⢀⡠⠤⠐⠒⠈⠈⣉⡀⠠⠄⠀⣀⣈⠦⣀⠀⠀⠀⠀⣀⠴⣁⢀⡐⠀⠤⢀⣉⡁⠁⠒⠂⠤⢄⡀
⠀⠀⠸⡥⠖⣀⢄⡈⠉⠀⡀⠤⠐⠂⠁⠈⡱⠂⠀⠨⠥⠬⠥⠀⠰⡎⠁⠀⠁⠒⠤⠄⠀⠉⠉⣀⢀⠒⢬⠇
⠀⠀⠀⠑⢄⠀⠉⠀⠚⠚⠴⠂⠶⢆⡀⢐⡡⠀⣀⠀⠀⡀⠀⣀⠀⢬⡂⠀⠀⠰⠆⠰⠜⠚⠂⠈⠁⡰⠊
⠀⠀⠀⠀⠀⠑⠂⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠐⠂⠒⠤⠀⣀⣀⠀⠠⠄⢀⣀⣀⠀⠤⠒⠐⠂⠐⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣄⣀⣴⡿⠛⠉⠉⠙⠻⣦⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠁⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠙⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠿⠛⠃⡀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⡿⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣧⠀⠀⢸⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢸⠀⠀⡎⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠋⠀⠻⣦⡀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⣴⠿⠀⠈⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⣴⠋⢉⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠁⠀⠀⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡹⣿⣿⣿⣿⣿⣿⣿⣿⢏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠛⠛⠋⠉⠁⠈⠛⠿⠿⠿⠿⠛⠁⠈⠉⠉⠛⠛⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢿⣿⣿⣿⡿⢷⣶⣶⣶⣶⣶⣶⡾⠿⣿⣿⣿⡿⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⠀⠀⢀⡤⠖⠒⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡤⠴⠦⢬⣉⢋⣡⠴⠒⠛⠲⣄⠙⠦⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠚⣰⠋⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⢈⠗⠒⠒⠦⣄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡞⢁⡴⠋⠉⠉⠑⢄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠘⡆⢸
⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢸⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣇⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡽⢸⡆⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢸⠀⠀⢠⠇⠀⠀⠀⠀⢀⡤⠊⠉⠓⣆⠙⢦
⠀⠀⠀⠀⠀⣰⢋⡴⠋⠈⠑⠢⣄⠀⠀⠀⠀⠘⡄⠀⢸⠀⠀⡎⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢸⡆⢸
⠀⠀⠀⠀⠀⡇⢸⡅⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠸⡀⢸⠀⢸⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⣀⠞⢀⡼
⠀⠀⠀⠀⠀⠹⣄⠙⢦⣄⡀⠀⠀⠀⠀⠙⢦⣀⡤⣗⣚⠓⠧⣄⣠⠊⠀⠀⠀⢀⣠⠖⣋⡥⠖⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠒⢦⣉⠓⢦⣀⠀⠀⢀⡟⣎⣠⠞⠀⠀⠘⣇⠀⢀⡴⢚⡭⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⠶⠛⠉⠉⣹⣷⠇⠀⠀⠀⠀⠀⣟⡉⠉⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⢀⡤⣤⡴⠋⠀⠀⠀⠀⠀⠀⠙⠒⠒⠓⠒⠢⠞⠉⠀⠀⠀⠀⠀⠀⠈⠳⣤⠤⣄
⠀⠀⠀⠀⠀⠠⡇⢾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⢳
⠀⠀⠀⠀⠀⠀⢳⣤⣙⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠶⢒⣋⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠳⣌⣳⣄⣉⣙⣋⣉⣉⠓⠦⣤⣤⠤⠖⣋⣙⠛⠒⠒⠋⣡⢴⡟⠉⢉⣩⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢯⣍⣀⣳⡌⠓⠦⣤⡤⠴⣫⡟⠉⠉⠉⠛⢉⣡⠞⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠓⠦⠤⠴⠚⠁⠈⠓⠒⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠘⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠁⢻⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⠀⢸⣿⣿⣿⠇⣸⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣇⠸⣿⣿⣿⠀⢸⣿⣿⡟⢀⣿⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣝⠻⣿⣿⣿⣿⣿⣄⠻⣿⣿⣿⡀⢻⣿⣿⠀⢸⣿⣿⠃⣸⣿⣿⡿⢃⣼⣿⣿⣿⣿⡿⢛⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣌⠙⢿⣿⣿⣿⣆⠙⣿⣿⣧⠈⣿⣿⠀⢸⣿⡏⢠⣿⣿⡟⢁⣾⣿⣿⣿⠟⢉⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣄⠙⠻⣿⣿⣧⠘⢿⣿⡄⢹⣿⠀⢸⣿⠁⣼⣿⠟⢠⣾⣿⡿⠛⢁⣴⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠻⣿⣧⡈⠻⣧⠈⣿⠀⢸⡏⢠⡿⠋⣠⣿⡿⠋⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣬⣉⠛⠻⢿⣿⣿⣦⡀⠙⢷⡀⠙⠀⠈⠀⠈⠀⠘⠁⣰⠟⠁⣠⣾⣿⣿⠿⠛⢋⣩⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⣄⡉⠙⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠉⣁⣤⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⠛⠛⠓⠂⠀⠀⠀⢀⣤⡴⠶⠶⣤⣄⠀⠀⠀⠀⠒⠛⠛⠛⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣷⣦⣄⠀⣰⠟⠁⠀⠀⠀⠀⠙⢷⡀⢀⣤⣶⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⠋⠁
⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠶⠶⠶⠒⠒⠒⠒⠒⠒⠛⠋⢿⡀⠀⠀⠀⠀⠀⠀⣸⠏⠛⠓⠒⠒⠒⠒⠒⠲⠶⠶⠦⠤⠤⣤⣄⣀
⠀⠀⠀⠀⢿⣷⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣕⣒⣒⣭⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣶⣿⣿⣿⣶⣬⣭⣭⣴⣾⣿⣿⣷⣶⣦⣤⣤⣶⣿⣿⣿⣿⣿⡿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣮⠻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠟⣵⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢿⣿⣿⣿⣇⢸⣿⣿⣿⣿⡇⣸⣿⣿⣿⡿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⣿⣿⣿⠘⣿⣿⣿⣿⠁⣿⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⡛⠿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⡀⣿⣿⣿⣿⢀⣿⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⠿⢛⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣤⡙⠻⣿⣿⣿⣿⣧⢹⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⡇⣼⣿⣿⣿⣿⠟⢉⣤⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⣿⣿⡆⣿⣿⡇⣿⣿⣿⡟⢸⣿⣿⢰⣿⣿⣿⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⣿⣿⣿⣸⣿⡇⢸⣿⣿⡇⣸⣿⣇⣿⣿⣿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣛⣛⠻⠿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣣⣾⣿⣿⣿⣿⠿⠟⣛⣛⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣶⣭⣛⢿⣿⣿⣮⣿⣿⣿⡿⢿⣟⣻⡟⢿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣶⣾⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡿⣽⣾⣿⣿⣿⣿⣷⣯⢿⣿⣿⣿⣷⣿⣿⠿⠿⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡿⣾⣿⣿⣿⣿⣿⡁⠀⢹⣷⢿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢺⣇
⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣴⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠯⣿⣿⣷⣦⣤⣤⣤⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠈⠛⠿⠿⠿⠿⠛⠁⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠰⡼⣿⣿⣿⣿⣿⡟⠛⠛⣛⣉⣭⣴⣿⣿⣿⣿⢟⣽⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣯⠻⣿⣿⣿⣿⣶⣭⣉⣛⠛⠛⢻⣿⣿⣿⣿⣿⢷⠆
⠀⠀⠀⠙⣮⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣵⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣮⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⣵⠋
⠀⠀⠀⠀⠈⠻⢿⣮⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣵⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣮⣟⣛⣿⣽⣮⣻⢿⣿⡿⢟⣵⣾⡿⢿⣿⣿⡿⢟⣷⣮⡻⢿⣿⡿⢟⣵⣯⣿⣛⣻⣵⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠙⠻⠿⠿⠿⠟⠛⠿⣿⣿⣿⣿⠿⠛⠻⠿⠿⠿⠟⠋⠉⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡉⠭⠅⣒⠄⠠⠄⢀⡀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠤⠤⡄⡪⠐⠁⠀⠀⠀⠀⠁⠂⠈⠀⠀⠀⠡⣡⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠒⠒⠨⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⡂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠁⠀⠀⠘⢄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⠔⠁⠀⠂⢕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠖⠚⠓⢄⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⢠⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⢀⡠⠒⠄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠐⡄⠀⠀⠘⡀⠀⠀⢸⠀⠀⠀⠂⠀⠀⠀⡔⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠢⣀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠘⠄⠀⠀⢁⠀⠀⢸⠀⠀⡐⠀⠀⢀⠎⠀⠀⠀⡠⠊⠀⠀⠀⠀⡀⠴⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠑⢄⠀⠀⠈⡄⠀⢀⡄⠀⢸⠀⢰⠁⠀⣠⠋⠀⢀⡴⠊⠀⠀⣀⠄⠂⠁⠀⠀⠰⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢓⡄⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠳⣄⠀⠘⡄⠈⡀⠀⠸⠀⡎⠀⣰⠋⢀⡴⠋⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠠⡙
⠀⠀⠀⠀⠀⠀⠀⠀⡜⡐⠀⠀⠀⠄⣀⠀⠀⠀⠙⢲⣄⠘⢧⡀⢸⡀⠁⠀⠀⠀⠆⢰⠃⣠⠞⢠⡴⠞⠁⠀⠀⣀⠤⠄⠀⠀⠰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⠉⠐⠶⢤⣀⠉⠳⡆⠳⡀⠗⠚⠀⠁⠚⠂⢎⡰⢃⡾⠋⣀⠤⠒⠂⠁⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⠎⠀⠀⠀⠀⠀⠀⠀⠀⠑⢏⠤⠊⠁⠀⣀⢠⡀⡤⣤⣤⠤⠤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠳⠖⣒⠤⠠⣀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠠⠔⢉⠤⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⢀⠄⠒⢲⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠛⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠢⢄⠐⠒⠒⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠻⡀⠘⠛⣤⢂⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⡖⢲⠀⢠⠏⢉⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠘⡖⠋⠀⢏⣤⣴⠆⡰⣀⠠⠀⡒⢠⣄⠀⠀⢀⣀⣀⡀⠀⠀⢀⢔⠀⢀⣄⡀⢪⠂⢙⠟⢲⠆⡀⠀⡜⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⡌⢂⠘⡄⠈⡄⠘⡂⠙⡀⠀⠀⠛⠖⣢⠉⠀⠀⠙⢣⠀⠕⢩⠀⠀⡏⠀⡏⠀⡌⠀⡜⡰⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠡⡙⡄⠘⡄⢳⠀⠡⠀⠀⠠⠀⠘⠀⠀⠀⠀⠰⠀⠀⠸⠀⠰⠀⣰⠁⡔⠀⡜⡐⢁⠜⠁
⠀⠀⠀⠉⠉⠁⠒⠒⠒⠤⠤⠤⠄⠈⠓⢮⣺⣆⠘⢌⢣⡀⠡⠀⠀⡆⠀⠇⠀⠀⠀⢰⠀⠀⡇⢀⠂⢠⢃⠌⢀⣾⣊⠴⢅⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠤⢠⣑⣄⠑⣄⠸⡀⢠⠀⠀⠀⡄⠀⣸⢡⠃⣰⡗⢁⠠⠛⠉⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠑⠚⠃⠳⠄⠧⠀⠾⠀⠴⠓⠇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠤⠤⢀⡤⠤⠴⣤⣤⣤⡤⣤⢄⢀⡀
⠀⠀⠀⠀⡈⠁⠀⠀⢀⣀⣤⠾⠶⠊⠛⠁⠉⠉⠂⠀⠉⠈⠙⢋⠛⠟⣲⣄⣀
⠀⠀⠀⠀⢻⡄⠀⠀⠻⣏⣉⠀⠀⠀⠀⢀⣀⣄⡔⠀⠀⠉⠈⢠⠀⠀⠉⠈⠙⠷⣶⢄
⠀⠀⠀⠀⠀⠙⣷⣄⠀⠘⢿⣄⠀⠀⢰⣿⣿⣿⡇⠘⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠢⠨⠶⣄
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢼⡄⠀⠀⠻⢿⣿⣷⣄⣀⣀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡌⠣⢦⡀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣮⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣦⣦⣤⣤⣤⣤⣼⠟⠛⠛⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤⠤⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣴⣶⠄⢴⣾⣶⡦⢨⣉⡁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⣾⣿⡆⢻⣿⡇⢘⡿⣿⡃⣸⣷⣿⢇⣤⣍⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣸⣿⣿⡌⠻⣧⠈⠿⠃⠀⠃⠠⠀⠩⠷⡏⣰⣹⡞⢣⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣾⡏⠹⢟⣟⠀⠙⠀⢠⣦⠀⢴⡆⠀⣄⠀⠈⠻⠋⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣿⣿⣷⣆⠀⠀⣴⡜⠗⠈⠽⠀⠿⠃⠸⠟⢘⣷⠀⡀⠀⠋⠀⣴⣄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⣿⢷⡄⡀⠉⣤⡀⠠⠗⠀⠂⢀⡀⢈⠀⡀⢀⡘⠁⣠⠟⢁⠀⣴⡿⠿⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠏⠙⠻⢓⣄⡀⠛⢀⠀⣣⠐⡂⡇⡃⢈⢁⡚⣡⠆⠁⢸⠿⠒⠉⢀⡰⣷⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠺⣿⢶⣄⠀⠉⠓⢀⣀⠡⡼⢧⣴⣱⣿⣊⢀⡦⣃⠀⠁⠀⠠⠶⠀⢉⠴⠋⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠧⠙⠓⠠⢄⡙⢷⣽⡿⠟⠛⠛⠿⣾⣼⣡⠔⠂⠀⠠⢶⣴⡏⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠲⢭⣿⡟⠀⠀⠀⠀⠀⡀⢹⣷⡿⠛⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⢡⡀⠀⢀⣼⡟⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣄⠉⠃⠈⠅⣡⣾⠿⠿⠿⠻⠷⣶⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢⣿⣷⣿⣿⣿⣿⣥⣭⡽⠿⣿⢻⣷⣿⣿⣭⣶⠷⣾⢟⣻⠛⠿⣿⡿⢛⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣾⡝⣿⣿⣿⣿⣭⣡⣴⠟⢡⣾⠋⢹⣏⠉⢿⣶⣶⣚⣿⣿⣿⡿⢰⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣍⣋⡉⣟⠿⣿⣿⣷⣿⣿⣶⣾⣿⣿⣻⢿⣿⡿⢋⣷⣤⡶⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡹⣿⣷⡆⣴⣾⡝⢩⠬⣿⣛⣋⣵⣤⡦⣾⣹⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⣿⣿⣮⣿⣿⣝⣿⣿⣿⣼⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⢋⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡌⢻⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠇⢠⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣷⠀⢻⣿⣿⣿⡇⢸⣿⣿⣿⡿⠀⣼⣿⣿⣿⣿⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠘⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⡇⠘⣿⣿⣿⡇⢸⣿⣿⣿⠇⢰⣿⣿⣿⣿⠋⣰⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠇
⠀⠀⠀⠀⢻⣿⣿⣦⡈⠻⢿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⡀⢹⣿⣿⡇⠈⣿⣿⡟⠀⣾⣿⣿⡿⠁⣴⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⡿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣀⠙⢿⣿⣿⣿⣷⡀⠻⣿⣿⣇⠈⣿⣿⡇⠀⣿⣿⠃⢸⣿⣿⡟⢀⣼⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣄⠈⠻⣿⣿⣷⡄⠙⣿⣿⡀⢸⣿⠇⠀⣿⡏⠀⣿⣿⠏⢀⣾⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠙⢿⣿⣄⠈⢿⡇⠀⢿⠀⠀⣿⠁⢸⡿⠁⢠⣿⡿⠛⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠻⣿⣿⣶⣬⣉⠛⠻⠿⣿⣿⣿⣦⡀⠙⠻⣆⠀⠙⠀⠈⠀⠀⠁⠀⠊⠀⢠⠿⠋⠀⣠⣾⣿⣿⡿⠟⠛⢉⣡⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣤⣀⡉⠙⠛⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⠋⢉⣀⣤⣶⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⣤⣤⣤⣄⣀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠉⠛⢷⣄⠀⠀⠀⣀⣠⣤⣤⣤⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⢿⣿⣷⣄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢠⣾⣿⡿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟
⢀⣠⣤⠤⠶⠶⠶⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠘⣷⡀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠶⠶⠶⠦⣤⣄
⠻⣿⣶⣄⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣮⣕⣒⣒⣪⣵⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⣠⣶⣿
⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⣠⣤⣶⣶⣾⣷⣶⣦⣍⣉⣉⣩⣤⣶⣾⣿⣶⣶⣤⣄⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠋⠉
⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣮⣿⣿⣿⣿⣥⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⠀⣶⣿⣿⠃⠀⠀⣸⣿⣿⣶⡀⠀⢰⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⢀⣾⣿⣿⠇⠀⠀⠀⠉⣿⣿⣧⢃⠀⠀⢹⣿⣿⣿⣄⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⣿⡟⡁⠀⠀⠴⣾⣿⣿⣿⠂⠀⠠⠤⠄⡛⠿⣿⣸⠀⠀⠀⢿⣿⣿⣿⣗⡘⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟⢠⣾⣿⡿⢋⠤⠂⠀⠁⠐⠂⠉⠥⠐⠊⠀⠀⠀⠀⠀⠐⠬⠤⠂⠈⠀⠒⢌⠻⣿⣿⣌⠊⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣿⡿⢋⠄⠤⠭⠭⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡈⠀⠀⠀⠀⠀⠀⠑⠬⠭⠉⠄⢄⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠒⣚⠉⠔⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢹⣿⣿⣆
⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠐⠈
⠀⠀⠀⠀⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⣶⣷⣮⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠉⠿⣿⣷⣒⡀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣅⠀⠀⠱⠄
⠀⠀⠀⠀⠐⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⡀⠀⠀⠀⠀⠀⠠⢿⣿⣿⠖⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⡀
⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣖⣀⣠⣤⠐⢿⣿⣯⣽⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣾⣿⡆
⠀⠀⠀⠀⠀⠀⢻⣧⠀⢤⣶⣄⠀⠀⠀⠀⠠⠤⢀⠐⠘⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⡏⠀⠀⢀⠀⠁⠀⠀⠀⢀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠻⣿⣧⠀⠀⠠⢶⣶⣄⠀⠀⣭⠿⠟⣋⣉⠛⠻⣿⣿⠟⠐⣢⣬⣍⣉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡈⢯⡷⡀⠀⠐⡛⣿⣯⠂⠀⠘⣿⣿⡻⠀⠀⠀⠀⣶⣿⣿⣿⣿⠏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠿⣆⠀⠀⠈⠛⠷⡀⠀⠘⣿⣏⠀⠀⠀⢠⢻⣿⣿⡽⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠢⡀⢄⠀⠀⠘⠆⠀⠉⢿⠀⠀⠀⣼⣿⣿⠏⠂⢠⣾⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠄⠀⠀⠀⠀⠈⠃⠀⢂⣾⣿⠃⢀⣴⣿⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⠈⠍⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⢀⠠⠂⠀⠀⠀⠀⡴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠰⡄⠲⠀⠀⠀⠀⡨⠆⠀⢀⡠⠀⠀⠀⠀⠀⠀⠘
⠒⠄⠠⠀⡰⠀⠀⠀⠀⢻⣤⠋⣐⡂⠲⡀⠀⠀⠀⠀⠐⠣⣀⠀⠉⠓⣀⢠⡄⠈⠁⠁⠀⠀⠀⠀⠀⢇⠀⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⢀⠂⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠂⠂⡂⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢀
⠀⠀⡀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⡀⠐
⠀⠠⢀⠖⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⢀
⠀⡤⠊⢰⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠔
⠀⠁⠀⡘⠀⠀⠀⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠁⢀⠀⠀⠀⠈⠢⢄⡀⠀⡄
⠀⠀⠀⠃⠀⠘⠃⡠⠀⠀⠀⠀⠀⠀⠀⠈⠃⠂⠀⠀⢠⡀⠀⠄⠁⠈⠀⠀⠀⠀⠀⠀⠈⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠖⠀⠀⠀⠀⠀⡀⠀⢔⡆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⡌⠀⠀⠀⠀⢀⠸⠩⢐⠨⡂
⠀⠀⠀⠀⠀⢸⠞⠄⠀⡠⠛⠄⠈⠹⢷⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⠀⠈⠄⡞⠁⠀⠀⠀⠀⠤⢊⠀⠄⠉⣂
⠀⠀⠀⠀⠀⢠⢀⠄⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⢀⠀⠄⡄⡁⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⢸⠃⠄⠀⠀⠀⠀⠀⡨⠆⠀⠀⠀⠀⠀⠀⢈⠒⠂⣄⡰⠁
⠀⠀⠀⠀⠀⢸⢄⠄⠐⢄⢀⠄⠀⢀⣠⠀⠀⠀⠀⠀⠀⠘⠣⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠈⠁⠀⠀⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗
⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢘⡈⠉⠁⠰⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈

⠀⠀⠀⢀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠈⠀⠀⣄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠸⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠀⠀⠀⣶⣶⣶⣶⣶⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⣿⠉⣿⠉⠉⠉⡏⢹⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⢸⠀⠀⣿⣀⣿⣀⣀⣠⣧⣸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟
⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⠀⠀⠄⠀⠠⠀⠀⠄⠀⠠⠀⠀⠄⠀⠀⠆⠀⠀⠄⠀⠀⠀⠆
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠷⠿⠿⠿⠿⠿⠿⠿⠀⠀⠦⠤⠤⠠⠤⠄⠤⠤⠠⠤⠄⠤⠤⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠛⣴⡄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⢀⠷⡄⠀⠀⠤⠐⠀⠀⠀⠐⠒⠀⠀⠀⠸⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⢀⣤⡀⠀⠀⠟⠃⠀⠀⠀⠊⡠⡄⠀⡄⠄⠀⠀⠀⠀⠀⡆⠀⠘⡀
⠀⠀⠠⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠐⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠆⠀⡜⡀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⢀⠀⠒⠀⡠⠗⠀⠀⠀⣣⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠀⠂⠀⠌⠀⠀⠀⡄⠀⠀⠐⣇⡀⣀⠆⠀⠘⢂⠊⠀⠀⠀⢤⠀⠀⠈⢅⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡦⠀⢠⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠠⠃⠈⠀⠀⠀⠀⠀⢰⠆⠂⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⢖⠆⠀⠀⠀⠀⠀⠀⠀⠀⣖⣰⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⡀⠀⡠⠠⠀⠀⢆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⡀
⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⡎⠀⡱⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠄⢀⠈⡄⠀⠄⠀⠀⠀⠀⠀⠀⠠⣄⠀⣀
⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠐⠀⠀⠀⣀
⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⡆
⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠁⠒⠁
⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠄⠠⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⠀⡀⡢⠀⠀⠠⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠼⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠓⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡀⠀⠀⠰⠄⠀⠀⠶⠂⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠦⠐⠄⠀⠆
⠀⠀⠀⠀⠀⠀⡠⠀⠀⢄⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠠⠊⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢁⠔⠁⠘⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢤⡀⢀⠌
⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠡⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢀⠀⠀⡒⠲⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⠐⠑⡀⠈⡈⠗⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠐⠀⠃⢐
⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⢀⠀⣈⠐⠸⠄⠈
⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠂⠃⠐⠀⠀⠀⠀⠀⠀⣰⠋⠉⣷⠀⠀⠀⠀⠀⠀⠀⠂⠄⠂
⠀⠀⠘⠁⠀⠑⠂⢀⠀⠀⣀⠀⠀⠀⠩⠀⠀⠘⠁⠀⠀⠀⠀⠀⠹⠦⠴⠟⠀⠀⠀⠄⠀⠀⠂⠁⠄⠁⠁
⠀⠐⢀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠤⠚⠀⠄⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢁⠀⢈⡈⠤⠁⠀⠀⠁⠀⠀⠸⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠋⠀⠀⠩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠈

⠀⠴⣶⣦⡀
⠀⠀⠈⠛⠿⣆⠀⢠⣾⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡀
⠀⠀⠀⠀⠀⠸⡄⢺⡟⢡⠀⣷⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠸⡇⠀⢀⣴
⠀⠀⠀⠀⠀⠀⢳⣸⡀⠈⣒⡁⣀⠀⢀⡀⠀⠀⠀⠉⢿⣿⣦⠀⠀⣴⣦⣼⣿⡄⠀⠀⠀⣀⣸⣷⣶⣷⣿⡁⠀⣇⣀⠠⠄⠚⠉
⠀⠀⠀⠀⢀⡠⠤⢿⣷⣤⣼⣿⣿⣷⣿⣧⠀⠀⠀⠰⣼⣿⡟⠀⠀⣿⣿⣿⠿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣣⣶⣾⠇⢀⡒⠄
⠀⠀⠀⢰⡁⢤⠀⠰⣾⣿⣿⣿⣿⡛⠉⠉⣷⣶⡄⠀⠈⠙⢧⠀⣿⡿⠋⢀⡀⠠⠶⢦⣭⣭⣽⣿⣼⣿⣿⣿⡇⠀⠀⡑⠤⠃
⠀⠀⠀⠀⣩⣼⣶⣾⣿⣿⣿⣿⣏⣿⡦⢀⣽⣿⣿⣦⡀⠀⣬⣿⣿⣤⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⣧⣼⣿⣧⢀
⠀⠀⠀⢠⣿⣿⣟⣿⣿⣿⣿⣿⣟⠁⠀⠀⠉⠀⠘⠻⠿⢷⣿⡁⢙⣿⣿⣥⣀⡀⠀⠉⠀⠀⠉⠛⠛⠿⣤⣤⣼⣯⣿⣿⡏
⠀⠀⠀⠚⠻⣿⣿⣿⠿⠛⢻⣿⣿⣿⣶⡤⣾⣶⣶⡶⠂⠽⢿⣿⣿⡟⠉⠙⢿⣷⣶⡿⠂⠠⠀⡽⠀⠀⠉⠙⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠁⠘⢧⠾⠿⢿⣭⠀⠀⠀⢀⣾⣿⠁⢤⡀⠀⠀⠻⣿⣿⠆⠀⣘⣥⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡷⠻⠁⠀⠀⣠⣶⣿⣿⠉⠀⢸⣿⠢⣄⠀⠀⠈⠛⣝⠻⣅
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠊⠄⡞⣀⠤⡀⠀⠀⢻⣿⢿⣿⠄⠀⢿⣿⣆⠈⠀⠀⡀⢤⠈⡆⠈⠳⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠙⠻⠿⠛⠉⠀⢰⡆⠳⣘⣦⡏⠀⠀⢸⢃⠜⠃⠀⠀⠀⠉⠻⠻⠀⠀⢇⣀⣠⢃⣀⠀⠈⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⣽⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⢷⡄⢀⠀⠀⠀⠀⢀⣠⢉⡀⠰⡄
⠀⠀⠀⢀⡀⠀⠀⣾⠀⢠⡆⢀⡖⠀⠀⠀⠃⢸⡇⠈⢺⠀⠀⠀⠈⡇⠈⠀⢸⡇
⠀⠀⠀⠀⠸⣶⡄⢿⠀⢠⣧⢫⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠤⠈⢿⠗⠀⣘⠷⡁⠀⠀⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⢀⠀⣀⣘⣼⡇⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠐⠒⠚⠱⠾⠻⠟⠁⠀⠀⠀⠀⠀⠘⠷⠘⠁⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⠀⠆⡀⠀⠐⠃⠀⠀⠰⠀⠀⠀⠀⡁⠀⠀⠈⠕⠄⠀⠀⠐⠀⠀⢀⡈⡀
⠀⠀⠀⠀⠀⢹⠀⠀⢀⣾⠁⢲⠀⠀⠀⠀⠉⠦⠀⡀⢀⠀⠀⠀⢰⠀⠀⠈⠀⠃⠀⠀⠀⠀⢰
⠀⠀⠀⠀⣿⠀⠀⠀⢸⡏⠀⠋⠀⠀⠀⠀⠀⠀⠀⣷⡌⠀⠀⠀⢸⠀⠀⠸⠸⠀⠀⠀⠀⠀⠛⠀⠀⡀
⠀⠀⠀⠀⢸⡦⣀⠔⢺⣷⡎⢠⡾⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠸⡀⠀⣬⡼⠀⠀⠀⠀⠀⠟⠀⠸
⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⣷⠀⠀⠀⢀⠀⠀⠁⣠⡀
⠀⠀⠀⠀⠁⠀⡴⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠚⠥⠐⠊⠁⠉⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡍⠠⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢀⠔⠢⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠤⡐⠊⠐⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⡠⠀⠀⠀⠐⠤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠆⠀⠸⠃⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⠢⡀⠀⠀⠀⠀⠐⠾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣑⣀⠈⠢⢀⠄⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⢠⠔⠀⠀⡀⠀⡀⠀⠼⢠⠐⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠠⠀⠀⠀⠀⡔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠑⠄⠀⠄⠀⠀⠀⠴⠀⠢⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣀⠆⠀⠈⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠤⡀⠀⠀⠀⠀⠀⠁⠀⠬⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠁⠘⠡⢀⠀⠀⠀⠠⠀⡆⠠⠀⠀⠀⢀⡠⠚⠀⠉⠒⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠖⠒⠚⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂⠀⠀⠁⠀⠀⠠⣀⠀⠀⢀⠉⠀⠀⠐⡀⠄⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠐⠂⠀⠀⢀⠁⠢⡄⠁⠀⠂⠀⠀⠀⠈⠤⠆⢈⠀⠀⠀⠐⠀⠀⠈⠳⣱⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠠⠃⠀⣀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢀⠀⠀⠀⠀⢀⠀⠘⠠⠈⠀⠀⠀⠀⡐⠀⡀⠀⡻
⠀⠀⠀⠀⠂⡀⠀⠀⠀⢈⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⢀⠠⠄⠁⠀⠁⠁⠀⠀⣿⠆
⠀⠀⠀⠀⠘⢠⡄⠀⠀⠠⠂⠊⠀⠁⢀⠀⡀⠀⠐⡀⠀⣴⠀⠀⡀⠀⠀⠀⠀⠐⠰⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠈⠂⠈⢀⠀⠄⠀⡠⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⡄⡆⠃
⠀⠀⠀⠀⠀⠀⡈⣁⠀⠀⠀⠀⠀⡱⠊⠂⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⢉⣃
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠄⠀⠀⠀⠀⢀⠁⡀⠀⠉⠀⠂⢀⡀⠀⠀⠁⠀⠐⠒⠀⠐⢁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⡀⠂⠀⠀⠀⠊⢛⣄⠘⠸⠀⣬⠛⠃⠀⠀⠀⠀⠠⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁⠀⠀⠀⢀⠔⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠐⠀⠈⠢⠀⠀⠀⢠⣀⣀⣀⠀⠀⠀⠈⠀⠀⠐⠢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂⠐⠀⡀⠀⠀⠣⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠄⠀⠀⠈⠀⠈⠄⠁⠘⠀⠀⠀⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡨⠉⠀⠔⠀⠎⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⠔⢀⠐⠁⠀⠀⠀⠀⠀⢶⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠑⠀⠀⠐⠀⠐⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠒⠡⠄⢠⠀⠀⠀⡠⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠈⠢⠔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣋⠐⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⢈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⡱⡻⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣊⡁⠀⡜⠀⡇⢱⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡓⠦⣄⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡝⢆⢸⠁⣸⣄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢸⡈⠑⠊⠑⠢⡄⠀⠀⠀⡌⠀⠀⢠⠁⠀⡟⠊⡸⠀⢉⡻
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡎⠈⠑⠢⢄⡜⢡⠀⠀⠀⡇⠀⠀⡎⠀⢰⠁⢀⠇⠀⣞⠃
⠀⠀⠀⠀⠀⠀⢸⡒⠤⡜⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⠀⠀⢸⠁⠀⡎⠀⡸⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⣇⠀⢳⠀⠀⠀⠀⠀⡇⠀⡇⠀⡎⠀⢀⡇⠀⢸⠀⢀⠇⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠘⡆⠀⠀⠀⠀⡇⠀⢇⢠⠃⠀⣸⠀⢀⠇⠀⡸⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢱⠀⠀⠀⠀⣷⠀⢸⡸⠠⠀⡇⠀⣸⠀⢀⡇⢀⠇⣀⡤⠴⢲⣒⡶⢶⢆
⠀⠀⠀⣰⡶⣖⠶⠦⢼⡄⠈⡇⠀⠀⠀⣿⠀⢸⡇⡇⢸⠀⢀⠇⠀⢸⠀⣜⠉⣀⡤⠒⠙⢦⣠⣃⣸
⠀⠀⠀⡇⢱⠀⠙⣲⡆⣧⠀⢹⡀⠀⠀⢹⠀⠈⣿⣏⣾⡒⠉⠑⢤⣇⠴⣗⠉⠁⠀⠀⠀⡴⢁⡴⠋
⠀⠀⠀⣇⣀⢧⠚⠁⠸⡘⡆⠈⡇⠀⠀⢸⠀⠀⡿⠋⢹⡉⡲⠒⠉⡇⠀⢈⣦⠀⠀⢀⡜⣀⠟
⠀⠀⠀⠑⢄⠀⠳⡀⠀⠙⣷⠀⢹⣀⡠⠿⠤⠾⢼⣠⠤⠛⠳⠤⢄⡧⠖⠁⠘⡆⢠⠎⡰⠃
⠀⠀⠀⠀⠀⠑⢤⣘⣦⠤⠚⠋⠉⠀⣀⣠⠤⠒⠋⠹⡄⠀⠀⠀⠀⢱⠀⠀⠀⣱⠿⡎
⠀⠀⠀⠀⠀⠀⣰⠋⠒⢤⡤⠖⠚⠉⠁⠀⢀⣠⠴⢚⡇⠀⠀⠀⠀⠀⣇⠀⡰⠁⠀⢣
⠀⠀⠀⠀⠀⣴⣫⠔⠊⠁⢳⠀⣀⠤⠖⠊⠁⠀⣀⢼⡤⠤⣤⣀⣀⣀⣸⣼⡡⠤⣶⠞
⠀⠀⠀⠀⠀⠙⠫⣍⠉⠉⡽⠉⢀⣠⡤⠖⠾⣉⠀⠀⢳⡀⠀⠀⢀⡴⠊⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⠒⠋⠉⠓⠢⢤⣀⡀⠉⠒⠤⣷⡠⢚⡡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠞⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⠖⠒⢞⠋⠑⣖⠲⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠒⠛⢤⠀⠀⣱⠀⣸⠇⣀⡟⠀⣸⠄⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⡀⠀⢹⡄⣸⣧⠴⠛⠛⠛⠛⠛⠶⢾⣯⣴⣿⣿⣿⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⢹⣤⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠁⢀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠈⢳⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡞⠋⠙⢦⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠞⠋⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢾⡋⠀⠈⢳⣀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠿⣄⠀⠀⣿⣀⣤⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⣋⠉⠉⡆⠀⢸⡦⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠁⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡖⠉⠉⠑⣆⠀⢸⣆⣴⠷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠓⠒⢦⡼⠃
⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠈⣷⠀⣠⡿⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢻⡍⠛⣾⢿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠦⠤⣄⣸⡇
⠀⠀⠀⠀⣰⠟⠉⠙⢶⡀⣠⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠀⠀⢸⡟⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠈⣯
⠀⠀⣀⡤⠿⢤⡀⠀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⡀⢀⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠒⠦⣼⠏
⠀⢰⡏⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⢀⣿
⢠⡞⠋⠉⠓⣦⣼⠇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣝⣛⠲⢤⡀⠀⠀⠀⢀⡴⠾⢿⠓⢶⡦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⢳⡟⠋
⣿⠀⢀⣀⣀⣿⠁⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⢿⣿⣋⢉⣹⣿⡷⠀⣿⠀⠀⠀⡞⠀⠀⠘⠁⢸⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⣿⣀⡀⢀⣾⠇
⣸⠟⠉⠀⠙⣧⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⣠⣾⣿⠿⠻⢿⢿⣷⣤⡿⠀⠀⠀⠹⣄⠀⢀⣀⣼⣿⠟⠻⠿⡿⠃⠀⠀⠀⢰⠏⠁⠀⠈⣿⠁
⠹⡆⠀⣀⣀⣿⡀⠀⠀⠀⠀⠸⡞⣧⣀⣿⣿⣿⠁⠀⢀⠼⠀⢹⣿⡀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡼⠖⠦⣄⣤⠿
⠀⢨⡟⠁⠀⠀⢹⡆⠀⠀⠀⠀⠙⠶⣍⣹⣿⣿⣆⠀⠀⠀⣠⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣀⠀⠀⣸⡆
⠀⠸⣇⠀⡴⠂⠉⠉⢳⡀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠙⡞⠋
⠀⠀⠀⠹⡄⠀⠀⣠⠞⠋⠙⣦⡀⢀⡀⠀⠀⠈⠻⠿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠛⠲⣄⠀⣰⡟
⠀⠀⠀⠀⠙⠲⣾⡁⠀⠀⢠⠞⠋⠉⠙⣦⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣴⠛⠉⠙⢦⡀⠀⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠘⠧⣀⣀⣿⠀⠀⠀⣾⠁⠀⠀⣼⠛⠋⠛⣶⡶⠛⠉⠛⣶⠞⠋⠉⢙⡾⠁⠀⠀⢹⡆⠀⠀⢸⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡤⣿⠀⠀⢸⡇⠀⠀⠀⣿⡀⠀⠀⠸⡏⠀⠀⠀⠘⣧⠀⠀⣀⣼⣇⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠓⠦⠤⠖⠛⠻⢦⣤⡶⠟⠶⠶⠾⠛⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⡀⠐⢲⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀
⠀⠀⢠⡆⢘⡧⠌⡃⠘⠆⠀⠀⠀⠴⠊⠱⣀⡈⠶⠁⠢⡄⠀⠀⠀⠀⠀⠀⠀⣎⣩⢢⠀⠀⠀⠀⠀⠀⡠⢹⠆⡙⠆
⠀⠀⢿⡤⠎⠀⠀⠱⣤⡌⠀⢀⣦⣀⡠⠂⠁⠀⠀⢢⠄⡟⠂⠀⠀⠀⠀⠔⢠⠂⠈⣌⠳⡀⠀⠀⠀⠠⡧⠂⠀⠘⣮⡀
⠀⠀⡄⢰⠀⠀⠀⠀⣇⢘⠂⠸⣁⠠⠀⠀⠀⠀⠀⠀⠄⢀⡶⠀⠀⢀⠆⢠⠂⠀⠀⠘⣆⠀⠀⠀⠀⢰⠻⠀⠀⠀⡇⡳
⠀⠀⢴⠒⢇⠀⠀⡠⠸⣆⠀⠀⢤⡇⠀⢄⡀⠀⢀⠴⠒⠃⠀⠀⠀⡞⠀⠁⠀⠀⠀⠀⠘⢇⠳⠀⠀⠨⡼⡄⠀⢠⢾
⠀⠀⠘⠄⢈⡔⢺⡁⣠⠇⠀⠀⠈⠣⠀⠰⡍⠁⠶⡤⠐⠃⠀⠀⣼⣓⠶⠒⠒⠀⠀⠒⢖⣸⡙⣧⠀⠀⢣⣼⢦⣀⡌
⠀⠀⠀⠀⠰⢥⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠑⠄⠃
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⢀⡀⢀⠀⣀
⠀⠀⠀⠀⠐⡘⢣⡠⠀⠀⠀⠀⡠⠀⡒⠖⢤⡀⠐⠀⠧⠤⡀⠀⠀⡐⠀⠲⢄⡀⠀⠁⠠⠀⠘⡀⠀⠀⢸⡇⠉⠳⣧
⠀⠀⠀⡜⠋⠌⠠⡇⠱⡀⠀⠀⢓⡀⠟⠉⠑⠂⠉⠑⠄⣀⠀⠀⠀⠈⢳⠖⠆⠈⠉⠓⣆⠀⠃⡀⠀⠀⠠⠤⠶⠚⠤
⠀⠀⢠⣤⠊⠀⠀⠘⣄⠁⠀⠀⠛⢃⠃⠀⠀⠀⠀⠀⢎⠵⠃⠀⢰⡀⠀⣂⠀⠀⠀⠀⢸⠀⠀⠸
⠀⠀⣀⢀⠀⠀⠀⠀⡏⢲⠀⠀⠀⠐⢜⠦⠀⣀⡤⠃⡁⠀⠀⠀⠠⠑⡤⠉⠁⠀⣀⡤⠦⢤⡀⠀⠀⠀⢀⡈⠂⢌⠠
⠀⠀⠉⡛⢣⣀⡀⡰⢾⠊⠀⠀⠀⠀⠈⠙⢦⣈⠓⠋⠀⠀⠀⠀⠀⢡⣀⠴⣀⠀⠀⢀⠰⣤⣤⠁⠀⠀⢤⣧⡀⡠⠤
⠀⠀⠀⠈⠁⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠁⠀⠈⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠍⠐⠒⠷⡉⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣠⡀⠉⠀⣼⠋⠑⠀⠀⠀⢈⣈⠓⠀⠀⠀⠀⡰⣆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠛⣀⣀⡀⢂⡒⠠⣀⣀⠱⡆
⠀⠀⡠⠤⠃⠈⠉⠁⠈⠁⣇⠰⡀⠀⠋⢙⣷⠂⠲⣌⡀⠐⢀⡠⠀⢸⣄⠀⠀⠀⠀⠀⠛⡀⠂⠀⠀⠀⠀⠀⠀⢘⠢
⠀⠀⣁⣤⡇⠀⠀⠀⠀⠀⠈⢢⡁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠂⡄⠄⠀⡀⢀⣄⣀⡀⣀⠀⠀⣀⢼⡀⣦
⠀⠀⢇⡈⡣⠀⠀⠀⠀⠀⣔⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣇⠀⠀⠀⠀⢀⠂⠀⠀⠙⠡⠤⠤⠤⠶⠶⠦⠤⠤⠄
⠀⠀⠀⠁⢉⡉⠓⢤⡈⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⠄⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠂⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⡾⣿⢣⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣇⣦⡀
⠀⠀⠀⢀⣠⣀⡤⣮⡾⣫⠞⢡⣾⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡏⣾⢏⣿⢠⡀
⠀⢀⣴⣿⣿⡗⣺⢫⡾⠋⣰⡿⣻⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⡤⣄⣴⣾⣿⣿⣿⣷⣿⣼⣇⣾⡿⡇⡀
⣴⣿⣿⣿⣿⣗⡿⣸⡇⣾⡟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣷⣧⢻⡆⣤
⣿⣿⣿⣿⣿⣿⡇⣿⢱⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢷⣝⠷⣝⡻⣿⣿⣿⣿⣿⣏⣾⣿⢻⣮⣻⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣧⡣⡻⣿⣿⣿⣿⣿⣿⣿⣿⣯⡝⢷⣍⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣙⣿⣿⣶

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡠⢾⠉⡹⠻⡉⢹⠦⡀⠀⠀⠀⠀⢀⡴⠋⢧⣀⣀⣰⠋⢢⡀⠀⠀⠀⠀⣠⠔⠋⢹⠙⠢⣄⠀⠀⠀⠀⠀⢀⣤⠔⠚⢹⠉⠒⠦⣄
⠀⠀⠀⣠⣎⣀⣸⣞⣁⣀⣙⣾⣀⣘⣦⠀⠀⠀⢸⠉⢳⠋⠀⠀⠈⡗⠉⣿⠀⠀⠀⣾⠣⣤⠔⠛⠢⣤⠜⢳⠀⠀⠀⠀⡼⠉⡳⠒⠋⠑⠲⡞⠙⣆
⠀⠀⠀⠈⠳⡀⠀⢧⠀⠀⢠⠇⠀⡰⠋⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⣿⠀⢸⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⠥⢴⡃⠀⠀⠀⠀⢹⠤⢼⠄
⠀⠀⠀⠀⠀⠈⢢⡘⡆⠀⡞⡠⠊⠀⠀⠀⠀⠀⢸⠀⣸⡀⠀⠀⠀⣇⠀⣿⠀⠀⠀⣿⡠⠾⢄⡀⡠⠷⢄⣸⠀⠀⠀⠈⢇⠀⣣⣀⠀⢀⣠⡏⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠙⢾⣼⠞⠁⠀⠀⠀⠀⠀⠀⠘⢯⡁⡽⠒⠒⢺⡁⡹⠋⠀⠀⠀⠈⠳⢄⡀⢹⢀⡠⠖⠁⠀⠀⠀⠀⠘⠻⢄⣀⢹⠁⣀⡬⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⣀⣀⡤⢒⡻⠍⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⡄⢰⢲⠟⡒⡞⢹⠀⡜⠰⢠⢿⣷⣒⣒⣒⡦⣄
⠀⠀⠀⠀⠀⣀⠤⠤⣖⡿⢫⢠⠃⡇⠸⢠⢁⠁⠇⢠⢁⢃⡇⡞⢠⢃⠎⡔⡡⠈⡇
⠀⠀⠀⢀⠋⠴⡎⢹⠁⡇⠈⠘⠀⡇⡄⠸⢸⢰⠀⡈⠸⠸⢰⢡⠇⡎⡞⡰⢡⢂⠹⣄
⠀⠀⠀⢸⢠⡄⡇⢸⠀⡇⠃⢰⠀⠁⡇⠰⠀⢠⠀⡇⡆⡆⡇⡌⢸⢠⠁⠇⠋⠁⠀⣪⣩⡓⢆
⠀⢀⣠⣞⡞⡄⢡⠈⡄⠃⢰⢸⠀⡇⡇⢀⠀⢸⠀⠇⠃⠠⠀⠇⠂⠀⠀⠀⠀⠄⠀⠉⠉⠸⢸⡀
⢸⢩⢊⣃⢃⢃⠘⡀⢃⢠⢸⠘⠄⡇⠃⢸⠀⢈⢀⢰⢀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⣤⠚⡇
⢸⣨⡼⡸⡘⡌⡆⢣⠘⡈⡜⡀⡆⠇⢰⠈⢀⠘⠀⠸⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢠⢰⠧⠃⣝⠲⡄
⣸⣿⢡⢣⢣⠱⠰⡘⡄⢃⠠⢃⠇⢰⠘⡀⣿⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠜⠀⠀⠀⠀⠑⢸⡀
⡿⣏⠆⢇⢆⠆⢣⢡⠱⠘⡨⠘⡸⠈⡄⠆⠥⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⢠⠸⢘⡼
⠙⠮⣌⡊⢮⡌⡄⢃⢂⢃⢡⢣⢅⢇⠙⠈⢀⠀⢀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠃⡡⠖⠉
⠀⠀⠀⠉⠓⠬⡘⣌⢄⢎⢎⢆⠎⠀⣄⠀⠈⣀⠤⠤⢤⣄⡁⠠⠂⠀⠀⠀⠀⣀⠆⢂⠔⠋
⠀⠀⠀⠀⠀⠀⠈⠓⠮⣉⠚⠎⠀⠠⠌⢁⠞⡁⠊⠁⠀⠀⠉⣦⡀⢁⠄⠀⠃⢈⠔⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣉⣒⣲⣶⡇⡼⠀⠀⠀⠀⠠⢀⠗⣧⣤⡤⠤⠖⠃
⠀⠀⠀⠀⠒⠒⣶⣶⣾⣛⡭⡝⢏⢻⣝⣇⠀⠀⡀⡄⣦⣶⠋⣰⢷⣿⡿⠿⡿⠛⠋⠒⠛⢛⣲⣤⣭⡭⠭⠭⠭⠭⠭⢭⣭⣭⡤⠤⠤⠤⠤⣤⣄⠀⠀⠀⣀⡀⡀
⠀⢀⠔⠒⢒⡉⣄⠫⣝⢦⣑⢬⣓⡬⣷⣮⡷⢬⣉⣊⣉⣠⣞⣻⣿⡅⠈⠉⠓⠕⠠⠠⢀⠀⠈⠙⢗⣿⡛⡻⢭⡭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠤⠬⠁
⠀⢷⠴⠷⠵⣽⣮⣷⣮⣕⡺⠵⢾⠭⠉⠀⠉⡑⠿⣿⡷⠶⠒⠀⠒⠒⡯⠄⠀⠀⠀⠀⠀⠈⢰⢞⡫⠿⢿⡟⣛⡯⠭⠥⠤⠤⠤⠬⠭⠍⠉⠉⠉⠉
⠀⠘⣆⡒⠰⢨⣳⡯⠥⠄⠀⠀⣀⣀⣀⠀⢤⣛⣋⡁⠀⠀⣠⠖⡫⠝⠫⠝⠻⣆⣀⣀⣀⢴⣻⡟⠀⠀⡎⣠⣟⣒⣂⣒⣒⡒⠂
⠀⠀⠚⢛⣳⣦⣈⠻⢿⣿⣶⠏⢁⢒⠾⣷⢤⡒⠉⣁⠴⣪⠵⢩⠁⠀⠀⠀⠀⠀⠹⢻⠻⢛⡇⠀⠄⢆⣦⣟⣒⣒⣒⡒⠂
⠀⠀⠀⠀⠀⠐⠞⣻⡆⠉⣴⠜⠸⢸⠀⠉⠉⠉⠉⠡⠙⢠⠰⠈⠐⡔⠀⠀⠀⠀⢞⢀⣶⣷⣒⠚⠚⠛⠁⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⡆⠃⠇⢃⠃⠀⠀⠀⠀⠀⢃⢃⠇⠆⡁⣀⣁⣀⣀⣦⣾⣞⣓⣒⣒⣒⠒⠛⠊⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣾⣴⣬⣴⣦⣆⡀⠀⠀⢈⢘⢀⣦⣟⣛⣛⣛⣛⣒⣂⣲⠦⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠛⢷⣤⣾⣾⣟⣋⣀⣐⣒⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⢒⣒⣒⣒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣎⢌⡖⣁⢤⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⣴⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⠀⢀⣦⣷⡛⠛⠁⠤⠴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⠇
⠀⠀⢻⣼⣯⣹⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣹⣿⡹⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟
⠀⢸⣿⣿⣿⣏⣻⣾⣿⡿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢈⢾⡏⠉⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠉⠁⡷⢼⣿⣷⣷⣷⣾⣷⠆⠀⠀⠀⠀⠀⡄⢂⠀⢀⢴⣋⡼⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠳⠿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠘⠥⣬⠔⠁⠈⡸⡇⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡔⠁⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠠⣤⡤⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠢⣠⣤⣤⣄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⠿⠿⣳⡄
⠀⠀⠈⢿⣿⣿⣻⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢕⣶⡿⣯⣴⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⣹⡇
⠀⠀⠀⠀⠙⣯⣿⣿⣫⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣱⣿⡿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣷⣋⡅⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⡞⠽⢛⠻⠟⢶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⢘⣷⣿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⡉⢐⠋⠶⠉⣼⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣮⣞⣧⣷⡟⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⣟⣿⣛⣿⣿⢶⣗⣸⡋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⢟⠟⣏⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⡀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⠟⠃⠈⠓⠧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡒⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉⠀⠀⠀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠓⢤⠀⠀⠀⠀⡀⢠⠀⠀⠜⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⡀⠀⠓⠚⠉⠀⠁⠁⠀⠁⠂⢀⡤⠀⠀⡔⠢⣀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⡀⠀⠠⠔⠚⠀⠀⠄⠫⠤⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⢀⠀⠁⠀⠀⠀⠀⣰⠶⠡⠀⠀⠀⠀⠀⡀⠀⠶⠦⠈⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠅⢐⡠⣌⠀⠤⡀⠀⠀⢴⠃⠀⠀⠀⠀⠀⠠⢭⠐⠂⠀⠀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠁⡌⠙⣆⣆⡤⠞⣓⠒⠢⢄⠀⠀⣀⠀⢠⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣉⢉⢉⣩⠞⠁⢰⠒⣏⠑⡢⣠⣇⡎⣡⠤⠶⣐⠒⡒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠁⡴⣴⠋⡜⣡⢋⢧⠀⠸⡯⠤⠴⣂⠑⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⢠⡿⣌⣛⡻⢢⠤⠻⠂⠂⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡈⠳⣄⢀⣠⣾⣷⣦⠀⠀⠀⡈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠿⠏⢰⣈⠉⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣬⣁⣤⡈⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⢉⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠾⠁⠙⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⣶⡶⠲⠶⠒⠲⠶⠒⣀⠦⣄⠀⠀⠀⠀⠀⠀⢀⣴⡊⣩⠟⣅⢠⡄⠀⠀⠀⠀⠀⠀⢀⣤⢶⣶⠶⠖⠒⠲⠒⢶⣶⣤⡀
⠀⠀⠀⡟⠦⢩⠀⠀⠤⠄⠀⣀⠁⢴⢻⡄⠀⠀⠀⠀⢠⠞⠁⠀⠉⠀⠉⠀⠉⡄⠀⠀⠀⠀⠀⣾⣧⡀⠀⠀⠀⠀⠀⠀⠈⢀⡿⣷
⠀⠀⢠⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⣟⡵⠎⠀⠀⠅⠀⠀⡧⠘⡄⠀⠀⠀⠀⣿⠃⠉⠲⣄⣀⠀⣀⡤⠒⠁⢹⡟
⠀⠀⢸⣆⠀⡖⠀⠀⠀⠀⠀⠀⠂⠀⣸⡇⠀⠀⠀⢸⣏⠀⠀⢤⠀⠀⢲⠁⡆⢀⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⣇⣀⡇⠀⠀⠀⠀⡇
⠀⠀⢸⣿⣿⣧⠂⠀⣀⠀⠀⢀⣸⣶⢻⡇⠀⠀⠀⢸⣿⣷⣶⡁⢦⣠⣆⣑⣿⣻⡇⠀⠀⠀⠀⣿⣄⣠⠄⡠⠋⠁⠀⢄⠠⣀⣼⡇
⠀⠀⠘⢿⣧⣿⣞⣉⣀⠈⣓⣶⣿⣿⡾⠀⠀⠀⠀⠀⠻⣿⣿⣿⣾⣿⣾⣻⣿⡿⠀⠀⠀⠀⠀⣿⣿⣥⣌⣁⡀⠀⠀⣈⣷⣼⣿⠇
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠓⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀
⠀⠀⠀⠀⠞⠁⠂⠀⡀⠀⠄⠀⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠛⠀⠀⠀⠘⠗⠒⢂
⠀⠀⠀⢀⠠⠀⠚⠁⠀⠀⠐⢆⠐⠁⠀⠀⠀⠀⠀⢀⣤⡀⢀⣆⢀⣀⠀⣀⡀⢀⠀⠀⠀⠀⠀⡼⠈⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⡇
⠀⠀⠸⣅⡀⢌⠀⠀⠀⠀⠀⠸⣆⣠⣼⠂⠀⠀⠀⣼⣏⠀⠜⠀⢨⡅⠀⠘⡀⠀⡇⠀⠀⠀⠀⣿⣆⠈⠀⠀⠀⠀⠀⠀⠀⠄⢀⡷
⠀⠀⠀⠹⣿⠉⢱⣠⣤⣄⣰⠉⣹⣾⠃⠀⠀⠀⢀⡇⠸⣰⠀⢧⡇⢰⡼⠀⣇⡔⠸⠀⠀⠀⠀⢻⣿⣁⣶⣀⣠⣠⣀⣠⣦⢶⣿⠇
⠀⠀⠀⠀⠙⠷⢿⣷⣄⣴⡯⠿⠟⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⠙⠻⠿⠿⠿⠶⠿⠿⠿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⡤⢀
⠀⠀⢀⡴⠂⠁⢄⠀⠀⠐⠀⢀⣰⡦⣄⠀⠀⠀⠀⠀⠀⡀⠄⠀⠘⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠏⢀⠈⠁⢃⡘⠁⠂⡀
⠀⠀⢸⠐⣢⠀⠈⠀⠀⠄⠀⢉⠁⣰⣿⠀⠀⠀⠀⠀⢈⠓⢅⠐⢠⡄⠀⢉⠜⠃⠀⠀⠀⠀⠀⢰⢁⣇⢀⡠⠔⠓⠂⢄⡀⢰⠇
⠀⠀⢸⠀⠁⢸⠀⠀⠀⠀⠀⢸⣿⡿⣧⡆⠀⠀⠀⡤⠂⠀⠚⠳⣼⣀⠝⢁⡐⠂⢀⠀⠀⠀⠀⣇⣴⠞⡿⠁⠀⠀⠀⠈⣿⠃⢶⣆
⠀⠀⢸⢣⣀⣾⠀⠀⠀⠀⠀⢸⣟⠁⡽⡇⠀⠀⠈⠩⣉⡽⣏⡻⣿⣿⡀⢻⠻⣿⣿⠃⠀⠀⠀⣿⣷⣤⣷⠀⠀⠀⠀⢠⣿⣠⣴⡏
⠀⠀⢸⣾⠏⢹⣷⡶⠶⢶⣶⡟⠿⣯⣄⠃⠀⠀⠀⢸⡡⢿⣟⣶⣥⣿⣞⣿⣍⢿⡟⠀⠀⠀⠀⢹⣿⡿⠙⣷⣦⣤⣴⡟⠉⣿⣮⠁
⠀⠀⠈⠻⣶⣾⣿⣄⣀⣀⣼⢻⣶⣿⠟⠀⠀⠀⠀⠛⢶⣿⡁⣎⣷⡏⢯⣿⣿⠿⠁⠀⠀⠀⠀⠀⠻⣿⡿⣿⡅⢠⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⣨⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⡄⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠨⠟⠋⠙⣯⠀⣿⣿⣿⣿⣿⡠⡟⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣘⠃⠆⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢀⠠⠤⠰⠀⠲⠶⠋⣙⠛⠋⠉⠉⣿⣿⣿⣿⣤⡥⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡀⠀⠂⠀⢸⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⠈⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠧⣀⡀⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⠈⠁⠂⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⢀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⠂⠈⣠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣾⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣼⣿⡞⣷⡘⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⣰⡹⠧⣿⣽⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⠟⠉⠈⢟⠀⠀⢀⣼⢃⢃⣶⡟⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⡤⠀⢾⡟⢋⡌⠦⣿⣻⣭⣿⡿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣿⠈⠁⠀⠀⠀⠀⠀⠻⣟⡼⣴⣏⣷⣿⣿⡔⢛⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣼⣿⣿⣿⣼⣿⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⢧⣴⣦⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣬⣿⢺⣡⣾⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣶⣶⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢹⣿⡿⠿⠟⠛⠋⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢨⣿⣃⣀⣀⣤⣾⣿⡁⠄⠒⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢰⡿⠋⠉⠉⠉⠀⠀⣹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣿⣟⡿⣷⣄⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠈⠻⢷⣄⣀⣤⠾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⡀⠀⣹⠋⠉⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⠇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡞⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⡯⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣿⠀⠀⠀⠀⣸⢱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠸⣦⢠⣶⣽⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣴⣸⡇⠀⠀⠀⠀⢀⣤⡴⠊⠁⠀⠀⠀⠀⢻⡆⣱⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣴⡿⠟⠛⠳⣄⡀⣀⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⢘⣿⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠐⢷⣏⠀⠀⠀⠀⠀⠈⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⠠⠠⢒⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢸⡇⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⡇⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠁


⣿⣏⢹⣟⠿⣿⢟⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠑⢿⣀⣮⣤⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠛⠛⢻⠋⣷⣄⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢣⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣄⠙⣿⣦⡄
⠀⠶⣿⣼⣿⣿⣿⠟⢀⣠⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣿⣿⣿⠁
⣶⣶⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠿⠛⢯⣿⣿⣿⣿⣿⣿⣧⠀⣦⣾
⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠏
⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣬⣉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣤⣀⣀⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣽⣿⣿⣿⣶⣶⢈⠉⠉⠙⠛⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠉⣉⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣧⡸⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠿⢿⣿⣿⣿⡿⠋⢻⣿⣿⣿⣿⣷⡌
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣴⣿⣿⣿⠏⠀⠀⠈⣿⣿⣿⠈⢿⣿
⠟⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠈⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣿⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⠀⠀⢿
⠀⣾⣿⣿⠟⣿⣿⡿⢿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡆⠀⠸
⠸⡿⠻⣿⢰⣿⢰⡇⠈⢿⠀⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⣸⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⢰⣿⣿⣆⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⢻⡀
⠀⠀⠀⢀⣿⠘⣻⣿⣿⣿⣿⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢦⣾⣿⣿⣥⣄⢸⡇
⠀⠀⠀⢸⡏⢀⢼⣿⢿⣿⡿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣯⡥⢼⡇
⠀⠀⠀⣾⠇⠀⠈⠁⢸⡏⠀⠈⠃⢀⣤⣿⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⡄⠀⠰⡛⠛⢹⢿⡏⠙⠿⠀⣷
⠀⠀⢀⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⡾⢿⡿⠶⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠀⠀⢴⢾⣿⣿⡅⠀⠁⠀⠚⠈⠁⠀⠀⠀⣿
⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠂⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⣀⣀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⣸⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡴⠞⠋⠙⠳⢦⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠉⠉⠁⠘⣁⡤⠤⠤⣤⣈⠃⠈⠉⠉⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠘⠁⢠⡖⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠲⡄⠈⠃⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡴⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⢦⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠾⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠳⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠠⣤⡀⠀⠀⣠⠶⠒⠒⠶⣄⠀⠀⢀⣤⠄⠀⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢤⡤⠤⠤⣄⠀⣸⠃⣰⠞⠂⠀⠘⣇⠀⣠⠤⠤⣤⠤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠤⠴⠶⠆⢹⡀⠉⠀⠀⠀⢀⡟⠰⠶⠦⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠳⠤⠴⠶⠦⣤⣀⡤⠶⠶⣤⣀⣀⣤⠶⠶⢤⣀⣤⠴⠶⠦⠤⠞⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢦⡀⠀⠀⠠⡆⠀⠈⠁⠀⢠⠄⠀⠀⢀⡴⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠿⠶⢤⣄⣹⣦⣀⣀⣴⣏⣠⡤⠶⠿⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⢸⠁⣰⢆⠸⠕⢐



⡶⣶⢶⢷⡷⠾⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⡾⣷⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⣤⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠀⠀⣸⣿⣿⠁⠀⠀⣿⣿⣿⡀⠀⠘⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠉⠀⢀⣴⣿⣿⡇⠀⠀⠀⠻⣿⣿⣧⡀⠀⠘⣿⣿⣿⣮⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢀⣴⣾⡿⠋⡂⠀⠀⠉⡛⠿⢛⡁⠀⠈⠉⠀⠈⢙⠛⢋⠀⠀⣝⠻⣿⣿⡇⠘⣿⣦⣄
⠀⠀⠀⠀⠀⠀⣰⣿⠟⡁⡚⠛⡋⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠐⠜⡛⡛⣂⠘⢻⣿⣧⡀
⠀⠀⠀⠀⠠⠔⠛⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠩⠬⠑
⠀⠀⠀⠐⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢿⣿⣷⣤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠻⣿⣿⡦⠀⠈⢁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢐⣿⣿⣯⡀⠀⠀⢁
⠀⠀⠀⠀⠐⣶⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣀⢀⣀⣀⣾⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣾
⠀⠀⠀⠀⠀⠹⣧⠀⣀⣤⡀⠀⠀⠀⢀⣀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣰⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠙⣧⡈⢻⣷⡄⠀⠀⢴⣦⣌⠀⢠⡿⠿⠛⣛⠛⠿⣿⣿⠋⢀⣠⣘⣚⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡙⢿⡆⠀⠐⠹⢿⣟⠀⠀⢺⣿⡿⠆⠀⠀⠀⣶⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⢷⡀⠀⠀⠙⠧⡀⠀⢿⣷⠂⠀⠀⣠⣿⣿⡯⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣢⡀⠀⠙⠄⠀⠙⡅⠀⠀⣵⣿⡟⠁⣠⣾⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⣥⣿⠿⠀⠼⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢶⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠻⠿⠿⠿⠿⠿⠿⠶⠶⢶⣶⠶⠶⠶⠶⠿⠿⠿⠟⠟⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡄⠀⠀⡾⣕⢄⠀⠀⠀⣀⣤⠀⠀⠀⠀⣠⢧⡄⠀⠎⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⡁⠀⠙⢦⣼⠟⠀⠀⡐⠿⠿⠃⠀⠀⠻⣧⡴⠋⠀⣌⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠲⠶⠶⠥⣥⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠶⠒⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣧⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡠⢑⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⣤⣤⣤⣤⣬⣤⣤⣤⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡍⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠠⠓⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠰⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠷⢶⣶⣶⣶⣶⣶⣶⣶⠶⠾⠿⠛⠋⠁

⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣠⣾⣿⣿⡄
⣀⣴⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣌⣿⣿⣿
⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠞⠁
⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣠⣾⣿⣿⡄
⣀⣴⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⣿⣿⣿
⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠟⠁

⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀
⢤⡀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠈⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠂⠀⢀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣀⣀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠃⠠⢻⡧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣀
⠉⠙⠛⠈⠉⢧⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠼⠁⠀⠀⠀⠀⠀⠀⢻⣥⠤⠖⠶⠚⠋⠉⠁
⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣠⣒⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉
⠖⠒⠒⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⢀⠞⢱⣤⣀⠀⠈⠁⠀⠀⠀⠀⠀⣯⠀⠀⠀⠠⣿⣦⣄⡀
⠀⣀⣀⠠⠤⠀⠂⠈⠁⠀⠀⠀⡰⠁⠘⣿⣿⣿⡆⠀⢀⠃⠀⠀⠀⠀⠙⠀⠀⠀⢀⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣼⣿⣿⣿⣿⡄⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⠹⣿⣷⡂⠀⢸⡄⠀⠀⡀⣀⠀⠀⣿⣿⣿⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⢸⣿⣿⣇⠀⣽⡿⠀⠀⠈⡇⠀⠀⢱⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣿⣿⣿⣾⣿⠇⠀⠀⠀⡇⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⢤⣄⡀⠀⠀⠀⢀⣠⡤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣠⡴⠶⠒⠲⢦⣄⣀⣀⡤⠶⠛⠛⢦⡄⠀⠉⠓⠶⠶⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⡤⠴⠦⠴⠶⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣠⡤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠳⡄⠀⠀⠀⣧
⠀⠀⠀⠀⣼⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢿
⠀⠀⠀⣰⠇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠘⢧⡀⠀⠘⢦
⠀⢀⡴⠋⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠈⢳
⣰⠋⠀⠀⠀⢀⡾⠋⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⡇⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢸⡆
⢻⡀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣷⠀⠀⡼⠁⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⢀⡾⠀⢀
⠈⢧⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⢹⣄⣀⣀⣏⠀⣼⠃⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⣠⠟⠀⢀⡼
⠀⠈⠳⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡤⠖⠋⠉⠉⠉⠉⠙⠷⣄⣠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠈⠛⢦⣀⠀⠈⠳⢦⣄⡀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⢈⣉⣿⠶⠚⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠒⠾⠯⢤⣄⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠋⠁⠀⠀⠀⠀⠘⣧⠀⠀⢀⣀⣀⣀⣀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⡀
⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠟⠛⠉⠉⠉⠉⠉⠙⠳⢯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⣰⠟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⢿⡀⠙⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⡇
⠀⠀⠀⠀⠀⣿⠳⣦⠀⠈⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⠲⠶⠒⠋⢀⡾
⠀⠀⠀⠀⠀⠈⠳⠾⣧⣀⣀⣀⣈⣉⣉⣛⠛⠳⢦⣀⣀⣀⣠⡤⠶⠶⠶⠦⣤⣤⣤⠶⠋⠀⠀⣀⡴⠖⠛⠛⠛⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠉⠉⠉⠉⢻⡙⢦⣄⠈⠉⠉⣀⣤⠶⢒⡶⠲⢤⣤⣀⣠⣤⠴⢚⣿⣅⣀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠴⠶⠻⣄⠈⠙⠛⠉⠁⢀⡴⠿⣄⣀⣀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠖⠛⠉⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣸⡄⠀⢑⣆⡶⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⢸⠁⠀⠈⣩⣄⠀⠀⠀⠀⣠⢄⣿⠿⠂⠀⠀⣲⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⢼⠀⠀⠐⣏⣸⡇⠀⠀⡼⠋⢸⣿⣀⡆⠀⠀⠈⢷⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⢸⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⢸⣿⣿⣧⡀⠀⠀⢸⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠂⠀⢸⣿⡏⠈⡇⠀⡄⢎⠚⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡿⠛⠋⠀⠉⢹⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠗⠀⠐⠠⠚⢦⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⣸⡇⠀⠀⢀⣀⡾⠃⠀⠐⠄⣶⣤⣄⣀⣀⠀⢸⣿⡶⠁⠀⠀⠀⢾⠀⠀⠃⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⢸⠇⠀⢠⣭⡍⣄⠀⠀⠀⠒⠀⠉⠉⢧⠀⡆⢸⣿⣣⡇⠀⠀⠀⠸⢷⣷⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⡀⠀⢼⡇⠀⠀⢹⣷⣹⣦⡀⠀⠀⠀⠀⠀⠘⠀⡗⠀⣿⣿⠃⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣿⠀⢸⡇⠀⠀⣮⢿⡿⣟⡣⠀⠀⠀⠀⠀⠐⢂⣇⠀⣿⣿⡆⠀⠀⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⢸⡇⠀⠀⠙⠾⠿⣿⣶⣶⣶⣶⠶⠻⠟⠛⠋⠀⢻⣿⡆⣠⣄⠀⠀⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⡇⣀⣟⢻⣲⣤⢦⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠛⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢹⡷⣼⡇⠀⠀⠀⠀⠀⠘⡷⣿⠯⠚⣁⡴⣾⢿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢟⡐⢫⣏⠠⠴⠟⣡⡶⠀⠀⣷⣴⣿⡅⠀⠀⠀⢀⣤⡶⢛⣥⣶⢯⢟⣽⣷⣿⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣶⣭⣿⡷⠶⠾⠋⠀⠈⢿⣦⠀⠰⣟⣿⣟⣿⣛⢿⣿⣿⢫⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠈⠿⣷⡄⠀⠀⠀⠀⠹⣧⠀⢨⣯⣿⣿⡟⠻⠾⢻⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣾⠆⢿⡇⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠸⣿⡄⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠙⠳⣄⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠟⠛⠦⠛⠀⠀⠀⠀⠀⠘⠿⣦⡀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡟⠋⠑⢶⣤⣀⡺⠷⣛⣿⣿⡇⠀⠀⠀⠀⠈⠻⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠾⠿⠿⠿⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣈⠛⠛⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⣰⣿⠀⣀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠰⠀⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣂⠤⣄⢉⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠂⠠⠤⠠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠉⣻
⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀
⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡃
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⢸⡂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠁⠀⠠⠀⠀⠀⠀⠀⣠⣴⡾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⣀⡀⠀⠑⠄⠀⠐⢄⠀⠁⠀⢀⠀⠀⢸⠀⠀⠀⠀⠠⠃⠘⠀⠀⠀⠀⠀⠊⢀⡴⣀⣤⠶⣛⣥⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⡀⠀⢢⠀⠓⠀⠑⡀⢃⠀⢀⡆⠁⠀⠀⢀⠀⠀⢠⠆⣠⠃⠀⢀⣽⣿⣥⢶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣄⢡⡀⠈⠠⠘⢦⡀⠈⠅⠀⠀⠀⠋⠀⡐⢃⡼⠁⢀⣴⡿⠏⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣱⣤⣤⣉⣤⣴⣴⣶⣶⣶⣶⣤⣔⢠⣞⡁⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣤⣤⣤⣤⣤⣤⡴⡞⣽⠯⠉⣹⣿⡿⠛⠋⠙⠋⠉⠙⠻⣿⢯⣽⣌⣷⣟⣢⣤⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⡀⠄⠐⠂⠤⠠⠴⠚⠻⠋⡁⢖⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠟⢛⠿⠯⠙⠋⢍⠉⠉⠛⠛⠶⢤⡀
⠀⠀⠀⠀⠀⢀⣠⠶⠋⠔⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣯⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠹⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏
⠀⠀⠀⠀⠀⠀⢿⠘⡆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⠃
⠀⠀⠀⠀⠀⠀⠈⠆⠀⠈⠈⠱⣄⢀⣀⡀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⣼⡟⠀⠀⢀⣀⡀⠀⠀⣠⡔⠛⠛⠛⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠉⠉⠁⠉⠲⠶⠤⠴⠟⠻⣆⠐⠀⢀⣠⣤⣄⠀⣀⣠⠶⠖⠛⠲⢾⣯⣀⣠⠜⠉⠉⠉⠛⠉⠁⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⣽⡀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠈⠃⠚⠛⠁⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⢀⡶⠀⠀⠀⢀⠞⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠘⢷⡄⠀⠀⠙⣄⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⣠⠂⠀⠀⠀⣤⠏⠀⠀⢀⡴⠿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠠⠈⠳⠶⠤⠄⠘⣧⡀⠀⠀⢀⡈⠀⠀⠀⣠⡞⠁⠀⢀⡴⠟⢡⠴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠒⠛⠁⠀⠈⠉
⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⢿⠿⣿⠿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⣿⡿⠿⠿⠿⠿⠿⢿

⠀⠀⠀⠀⠰⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠁⣮⠊⠀⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⡀
⠀⠀⠀⠀⠀⠚⠛⣤⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⡄⠑⠂⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠇⠰
⠀⠀⠀⠀⠐⢲⠂⠸⠿⠷⠇⠀⠁⠀⠀⠀⠀⠀⠀⠊⠀⠰⡀⠀⠄⢀⠀⢤⠀⠀⠀⠀⠀⠀⡀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢈⠒⠀⠀⠀⠀⡀⣐⠀⠀⠀⠀⠀⠈⡐⠰⠀⠀⠀⠰⠱⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨
⠀⠀⠀⠀⠠⢾⡌⠄⠀⢀⡀⣘⠋⠅⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠀⠀⠀⠀⠀⠀⠀⠂⢜⠀⢀⣀⡁
⠀⠀⠀⣠⢀⡉⠡⠿⢐⠃⠬⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠙⠇⢤⡤⠹⠒⠶⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⢾⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠠⠰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⠀⠀⠀⠀⠁⣀⠀⠀⢀
⠀⠀⠀⠘⠐⠀⠀⢵⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠀⠀⠀⠠⣄⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠀⠀⢘⠂⠀⠀⠀⠀⠀⠀⠀⢠⡴
⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠁⠀⠀⠀⠀⠉⢀⣰⠀⡌⢉⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⠔⣰⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⡶⠂⠀⠈⢻⠷⠄⠀⠀⠀⢰⡒⠺⠉⠀⠚⢉⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⢀⣄⠀⠀⣤⣠⡄⠀⠀⠀⠀⢨⡀⣄⠀⠀⣰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⡟⠉⢀⠀⠙⢿⣇⠀⠀⠀⠀⠀⠀⠉⠳⠰⠀⢀⠃⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣧⣄⠀⠀⠙⠀⠀⠀⠀⠀⠈⠧⢀⣄⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋


⣿⠿⠿⠿⡿⣟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣛⣻⣿⣿⣻⣿⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⡀⢠⣤⣀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢈⠑⠀⠀⠐⠘⠀⠀⢀⠁
⠀⠀⢠⣥⠶⢤⣀⣤⡑⢦⠴⣈⣠⡀⡀⠶⠱⣄⢀⢄⠀⠘⢄⢀⠀⣠⠞⠢⠤⠜⠙⠲⢺⠇⠀⠀⠀⠀⠀⠀⡀⠠⢀⣀⠀⠀⠄⣀⠀⠄⢀
⠀⠀⣷⡁⠀⠉⠝⠺⠯⢠⡤⡽⠟⠁⠀⢶⠀⣛⠈⠘⢦⡤⠊⢠⠁⢀⡐⠤⠀⠠⣥⣤⣼⡄⠀⠀⠀⠀⣠⣾⣤⠄⠴⠁⣤⣠⣤⠀⢦⠄⣀⡷⢄
⠀⠀⠻⣄⡠⣤⣶⣷⣤⣈⣠⣤⡏⣿⣶⢤⣤⡽⠁⠀⠀⣿⣶⣾⣯⠶⣲⡛⠋⠉⡙⣉⡀⠀⠉⢣⡀⢾⠁⠘⠁⠀⠀⠚⠛⠛⠛⠂⠀⠀⠈⠁⠀⡷
⠀⠀⠀⠙⢇⠀⠈⠺⠛⠛⠛⠛⠗⠀⠀⢈⠏⠀⠀⠀⠀⠘⡛⠉⣏⣬⣉⣁⣙⣏⣁⣉⣡⣬⠁⠘⠓⠀⠡⣀⣠⡀⠀⠀⠀⣄⠀⠀⠀⢀⡄⢀⠞⠁
⠀⠀⠀⠀⠈⠢⡀⠀⣄⠀⠀⢠⣦⣀⡴⠁⠀⠀⠀⠀⠀⠀⠈⢶⡎⢻⠛⠋⠛⠘⠙⠋⢹⢱⣀⠊⠀⠀⠀⠈⠻⣷⣶⣶⣦⣿⣤⣿⣶⣾⡷⠁
⠀⠀⠀⠀⠀⠀⠑⣾⡾⣷⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠈⣆⠀⠀⠀⠀⢠⠇⡾⠁⠀⠀⠀⠀⠀⠀⠙⢄⠙⡿⠈⢿⠏⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⡿⡿⠃⠀⢀⣠⣄⣀⡠⠄⣀⠀⠀⠀⠀⠁⣸⠀⣠⣧⠐⣻⡔⠁⠀⣀⠄⠄⠠⠄⢀⡀⠀⠠⣤⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⡠⢰⠯⠛⢼⠋⠀⠀⠀⠀⠻⣶⣤⡀⠀⠘⢧⢹⡿⢰⠏⡠⠒⢻⣅⠺⢧⣤⣀⡌⠻⣶⣄⠈⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡍⠀⠰⠀⠓⢤⡤⣤⣤⣤⣾⣿⠟⣆⠀⠈⢣⣷⠃⡔⠁⠀⠈⡹⠓⠀⠃⠁⢀⠀⠈⠿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣴⡤⢠⡄⠀⠈⠅⠁⠐⠒⢂⠛⠉⢣⠀⠀⠁⢰⣷⣦⠈⠃⠀⠀⠀⠀⠀⠀⠁⢨⠇⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠱⠚⠦⣄⣄⣀⢠⡄⠈⠀⢺⡀⡇⠀⠀⠸⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣿⣄⠀⡈⠀⠈⠒⠊⠙⡿⠤⠚⠁⠀⠀⠀⣤⣜⣇⠠⡄⠀⠀⠀⠀⢀⣤⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⢧⣿⣶⡿⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠘⢏⠀⠀⠀⣰⣶⣲⠎⠈⠋⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡛⡃⢀⣠⡴⠄⠊
⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⡠⠄⠤⣠⣠⡀⠀⠀⢀⡀⡶⠛⣉⡙⠉⠉⢈⣷⠄⠀⠿⠉⠂⢄⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⣠⣮⠄⠀⢠⣽⡆⠀⣛⢁⣬⣙⣆⠴⣿⣷⣤⠤⣌⠠⠾⠷⢈⣡⣴⡟⠓⠤⡤⠴⡧⠆⢰⠖⠉⠉⠉⠓⢖⣠⣠⣤⣽⣿⣶⠦⣄⡀
⠀⠀⠀⠀⣯⣿⠄⠽⣿⠛⠓⠺⣟⣯⡤⠈⣼⠀⠈⠫⡃⠀⠀⢀⢀⣀⣾⡿⠛⣇⡀⢀⣄⠔⠀⠀⠈⣏⠙⠲⣄⢄⣀⠀⠀⠈⠙⠻⠰⠛⠻⠷⡄
⠀⠀⠀⠀⣿⠇⠀⠀⠁⠀⠀⠀⠈⢿⣥⠸⣿⠀⠀⠀⠈⠀⢄⣿⡿⡟⠙⠀⢰⡏⠠⠟⠁⠀⠀⠀⠀⠸⡄⠀⠈⠈⠉⠁⠈⠀⠀⣤⢠⣀⠀⢴⠟⣆
⠀⠀⠀⠀⣿⠀⢹⡀⠀⠀⠀⠀⠀⢰⣅⣀⢿⠀⠀⠀⠀⠀⠈⠙⢿⣄⣀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢰⡀⠀⠀⠀⠀⠀⠁⠀⠀⣸⠟⠁
⠀⠀⠀⠀⡟⠀⠰⠀⠀⠀⠀⠀⠀⢨⠈⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣷⣤⣤⡴⣡⣄⣄⡤⠊
⠀⠀⠀⠀⣿⣆⠀⠘⣦⠀⠀⠀⣴⣇⠀⣷⠘⠀⠀⠀⠀⠀⠴⠟⢙⣃⣈⣟⠉⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⣵⣿⡿⠋
⠀⠀⠀⠀⡿⢿⢡⠛⢻⠃⠙⠻⠋⠉⡿⢉⣻⠀⠀⠀⠀⠰⣶⣶⡚⠉⠉⠙⣳⢶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⣿⢏⣾⠟⠋
⠀⠀⠀⠀⠈⠻⣤⡴⠛⠀⢠⣴⣿⢶⣧⠜⠁⠀⠀⠀⠀⠀⠈⠁⠑⣄⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠐⠆
⠀⡜⠄⠀⠀⣼⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠙⠒⠲⣿⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢢⢸⡄⠀⠀⠀⠀⠀⠀⠀⡀⠌
⠀⠀⠀⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⠀⡀⣉⣀⠀⠀⠈⠀⡐⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⡨⠑⢸⣾⡟⠉⢙⣶⣒⠂⢀⠀⠀⠀⠀⠀⠀⣅⡸⢰⠐⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⣍⡤⠍⠙⢻⣶⠾⢛⠉⠭⡹⠁⠀⠀⠀⠀⠀⠘⢤⠌⠀⡰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣠⣠⡀⠀⣀⣠⠞⠁
⠀⠀⠀⡄⠀⠰⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⠀⡀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠘⠷⠿⠦⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠁
⠀⠀⠈⠁⠑⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠐⠊⠴⠋⠀⠀⠀⠀⠀⠀⠀⠘⠒⠈⠉⠓⠒⠒⠒⠄⠒⠚⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣶

⢄⠀⠸⠏⠀⠀⠀⠀⠁⠁⠀⠈⠣⣀⣀⠠⠃⠀⡁⠀⠀⠀⠠⠀⠀⡀⠀⣄⠀⠁⢀⠄⠈⠀⠀⠁⡀⠀⠀⢡⠀⠀⠔⠀⠡
⠀⠃⠀⠀⡠⠂⠐⠠⠀⢏⠩⠢⡀⠈⠁⡄⠂⢀⠀⢄⡀⠈⢀⡀⠀⠀⠀⣀⢀⠈⠁⠀⡠⠤⡀⠑⠤⡀⠠⠂
⡐⠀⠀⠐⠀⠀⠀⠀⢁⠈⢄⠀⠀⢀⠐⡀⠀⢀⠃⠀⠀⠀⠈⠁⡠⠊⠀⠀⠀⠘⠀⢰⢀⢂⠈⡀⠀⠀⣀⡀⠀⠂⠀⢀
⣁⣀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠢⢂⣸⠀⠀⠉⢀⠀⠐⢆⠀⠀⡌⠠⠀⠀⠀⠀⠠⠀⠈⠢⠎⠊⠀⢠⠁⡀⠈⢂⠀⠑⠤⠐
⠄⠂⢂⠈⠄⠀⠀⢠⠄⢀⠤⠀⠤⡁⠀⠀⠀⠌⠀⠀⠀⠱⠀⢃⠀⠀⠀⡀⠒⢁⠄⠀⠀⢄⠀⠀⠚⠀⠀⠀⠀⠑⡄
⠠⠅⠘⠀⠀⠁⡈⠁⠀⡂⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢈⣤⠀⢀⠁⠐⠀⠂⠀⠂⠰⡀⠈⠀⠀⡀⠀⠚⠂
⠢⠀⠀⠆⠁⠠⠉⠂⠀⠐⠢⢀⣀⠀⠈⣄⠈⠀⠀⢀⠄⠀⣀⠀⠐⠁⠄⠄⢸⠀⠀⠀⠀⠀⠀⠀⠈⡉⠄⠠⢀⠀⠀⠠⠂
⠜⠀⢠⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠉⠀⠘⠋⠀⠀⠀⡗⠉⢣⠀⢠⠀⠰⡀⠀⠀⠀⠠⠀⠀⠉⠀⠀⠠⠀⠈⠂⠈⠄
⢠⣄⠀⠑⠄⠀⠀⠀⠠⠄⠀⡄⠘⠢⠀⠀⠠⠈⠉⡀⠐⢀⠀⠺⠾⠵⠊⠀⠀⠈⠉⠉⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀
⠂⠀⠈⠢⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠰⠊⠍⠒⡀⠀⠀⠑⠤⠀⢁⣀⠔⠁
⡀⠂⠈⠀⠀⠀⠆⡉⠁⠀⠂⠀⢂⠂⠇⠠⠄⠀⠐⠀⠀⢀⠀⡐⠁⡀⠑⡀⠀⠘⡀⢀⠱⠁⠀⠀⠀⣀⡀⣀⠀⢀⠶⡀
⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠙⠀⠀⠀⠁⠂⠐⠀⠉⠀⠀⠀⠀⠀⠑⠀⠀⠈⢀⠀⠀⠀⢀⠀⠘⡠⠀⠈⠃⢡⢀
⣀⠀⠙⠇⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠠⠊⠌⢠⠀⠀⠀⠾⠀⡀⠀⠀⠘⠀⠇⢀⠀⠁⠀⠐⠀⠀⢡⠀⠀⠐⢤⠈⠝⠃⣄
⠀⠑⠀⡀⠀⠐⠀⠀⠤⠔⠃⡰⢆⠀⠘⢄⣂⠔⠀⠀⣀⣀⢀⠀⠀⠉⠀⠉⠀⠀⠀⢀⠀⠀⠀⡠⠂⠀⠀⢀⠀⠠⡀⠀⢡
⠀⠄⣒⣩⠀⠀⣀⣀⡀⠀⠘⠐⠐⠃⠀⠀⠀⠀⡠⠊⠀⠐⡌⠀⠰⡻⠀⣐⡄⠉⠀⠄⠀⠀⠉⠀⢴⡒⠀⠀⠀⠂⠈⢠⡀
⠄⢀⠀⠀⢰⠙⠀⠄⡁⠀⢸⠀⡠⠋⠇⡇⠀⡞⢂⡀⠐⠈⠀⢀⠄⠛⠐⠚⠵⠀⠀⡠⠐⠒⠢⡀⠀⠀⠐⠠⢀⣀⠠⠊⠁
⠀⠀⠐⢄⠈⠓⠥⠔⠁⡀⠀⠒⠶⠥⠂⠀⠀⠁⠀⢀⡀⠀⠀⠦⡀⡂⠔⠊⠁⠀⠊⠀⠀⠀⠀⠰⠀⢀⣀⡀⠀⠀⠀⡠⠂
⠀⠀⠀⡼⠀⠀⢠⠀⠁⠀⠀⠢⡄⠀⢠⠆⠈⠉⠀⠄⠈⠆⠀⢀⠀⠀⠀⠀⠐⠃⠀⠀⠌⠀⠒⠁⠀⠭⠄⠊⠂⠀⡈
⢀⠀⠂⠀⠀⠀⠀⠀⡄⠁⠠⠀⢁⠀⠰⡀⠉⠀⠀⠀⠈⠀⢐⠀⠀⠀⠁⢀⠀⠀⠀⣀⠀⡀⠀⠀⠈⠃⠤⠅⠒⠀⠁
⠁⠀⡤⡄⠀⠀⠃⠀⠀⠀⠐⢀⠜⠀⠀⠈⠀⢄⠀⢀⠁⠀⢀⠀⠀⠀⠐⠀⠀⠀⠣⠌⠀⠀⠀⠈⣠⡄⠀⡤⢀⠀⠀⠀⠈
⢀⠊⠀⠀⠀⡀⠀⠑⠂⠀⠐⠃⢀⠄⠚⠣⡀⠀⠙⠃⠀⠀⠀⠣⡀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠁⠉⠀⠀⠠⠠⠒⠁⡤⣲⡄
⠈⡀⠀⠈⠠⠁⠀⡄⠀⢄⠀⠀⠆⠀⠀⠀⠑⠀⠀⠀⡀⠠⢀⠀⠈⠓⠀⠂⢀⠔⠉⠀⠈⠇⠀⠀⠓⠀⠀⠱⡀⢠⣠⢀⠂
⠀⠀⡀⢀⠀⠀⠸⡀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠢⠀⠀⠰⠁⠀⠀⠀⠀⡤⠀⡈⠀⡀⠢⠀⠁⠓⠉⠉⢀

⠀⠀⠀⢸⣘⡯⠯⣭⡟⠋⠁⠀⠀⠀⠈⠑⢻⣭⠽⢽⡋⡇⠀⠀⠀⠀⠀⠀⢸⢘⡯⠯⣽⡟⠊⠁⠀⠀⠀⠈⠑⢻⣯⠿⢽⡃⡇
⣀⣀⡀⠈⠽⣧⣽⠦⠉⠀⡀⣠⣿⡀⢀⠀⠉⠴⣯⢼⠿⠁⢀⣀⣀⣀⣀⡀⠈⠿⡧⣽⠦⠉⠀⣀⣠⣟⡄⢀⠀⠉⠴⣯⣼⠯⠁⢀⣀
⡶⡼⠾⡧⡅⠉⠈⠀⣀⣦⡹⡞⣽⢹⢏⣴⣀⠀⠁⠉⢨⣼⠿⢦⢶⡷⡴⠿⣧⡅⠉⠈⠀⣀⣦⡽⡏⣯⢻⢏⣴⣀⠀⠁⠉⢨⢼⠿⢧
⠟⣧⠳⡟⠂⠀⠀⠀⢮⣧⣥⢮⣿⡽⣬⣽⡵⢀⠀⠀⠐⢻⠿⣴⣸⣅⣦⠳⡟⠂⠀⠀⠀⠮⣧⣥⢧⣿⡵⣬⣼⡵⠀⠀⠀⠐⢻⠞⣼
⡿⠉⠃⠀⠤⣼⠮⣿⡅⠉⠓⠒⠚⠒⠚⠉⠨⣼⠷⣧⠄⠀⠘⠑⢟⡻⠈⠃⠀⠠⣼⠾⣧⠅⠉⠓⠒⠛⠒⠚⠉⢨⣼⠵⣧⠤⠀⠘⠋
⠁⠀⠀⣈⣳⠮⡥⣟⢹⠀⠀⠀⠀⠀⠀⠀⡇⣻⢌⠵⣾⣅⠀⠀⠈⠁⠀⠀⣨⣷⠯⡡⣟⢸⠀⠀⠀⠀⠀⠀⠀⡏⣻⢌⠵⣞⣅
⠀⠀⠛⠾⢗⣛⣛⡿⢺⠀⠀⠀⠀⠀⠀⠀⡇⢿⣻⣛⣻⠷⠛⠀⠀⠀⠀⠛⠼⣟⣛⣛⡿⢸⠀⠀⠀⠀⠀⠀⠀⡟⢿⣛⣛⣺⠗⠛
⣆⠀⠀⠐⢉⣵⣂⣿⡞⠀⠀⠀⠀⠀⠀⠀⢳⣿⣰⣮⡙⠃⠀⠀⡰⢆⠀⠀⠘⢋⣵⣆⣿⡞⠀⠀⠀⠀⠀⠀⠀⢳⣿⣰⣾⡙⠃
⡟⣶⢃⡄⠀⠘⠑⠃⣂⣦⣭⣩⣭⣍⣽⣶⣐⠘⠋⠃⠀⢠⣘⣯⢿⡿⣵⢃⡄⠀⠘⠙⠃⣂⣶⣯⣩⣭⣍⣭⣶⣐⠙⠊⠃⠀⢠⡘⣶
⣟⣅⣋⣟⡅⠀⠀⠀⠵⣧⣆⡕⣿⢺⡰⣾⠯⠀⠀⠀⢨⣿⣛⣸⣺⣗⣅⣛⣿⡅⠀⠀⠀⠵⣷⢆⡇⣿⢪⡰⣼⠯⠀⠀⠀⢨⣻⣙⣸
⠭⠬⠟⠃⣂⣶⣴⣀⠀⠁⠞⢿⢾⡞⠷⠈⠀⣀⣦⣶⣐⠘⠻⠥⠭⠯⠬⠟⠃⣂⣶⣴⣀⠀⠁⠞⢱⠷⡿⠳⠈⠀⣀⣦⣶⣐⠘⠻⠥
⠀⠀⠀⢰⠻⣇⢛⣧⢖⠀⠀⠀⠛⠀⠀⠀⡲⣼⡛⣸⠟⡆⠀⠀⠀⠀⠀⠀⢰⠻⣇⢛⣥⢖⠀⠀⠀⠛⠀⠀⠀⣢⣬⡓⣸⠟⡆
⠀⠀⠀⢸⢼⡷⡷⢞⣿⡱⠆⠀⠀⠀⠰⢎⣿⡳⢿⢾⡧⡇⠀⠀⠀⠀⠀⠀⢸⢸⡷⡷⢾⣿⡷⠆⠀⠀⠀⠰⢎⣿⡰⢾⢾⡗⡇
⠀⠀⠀⠸⣴⡏⢬⡟⠮⠀⠀⠀⣤⠀⠀⠀⠵⢻⣥⢹⣦⠇⠀⠀⠀⠀⠀⠀⠸⣴⡏⣬⡟⠯⠀⠀⠀⣤⠀⠀⠀⠴⢻⡥⢹⣦⠇
⣒⢒⣦⡄⠍⠿⠻⠉⠀⡀⢦⣾⣾⢧⡶⢀⠀⠉⠟⠿⠩⢠⣴⡒⣒⣒⢒⣦⡄⠍⠿⠻⠉⠀⡀⢢⡼⡶⣷⡴⢀⠀⠉⠟⠿⠩⢠⣰⡒
⣯⡏⣍⣯⡃⠀⠀⠀⣲⡟⠎⡣⣿⢼⠱⢿⣖⠀⠀⠀⢘⣿⣭⢙⢽⡯⡋⣭⣿⡃⠀⠀⠀⡲⡿⠎⡇⣿⢜⠹⢻⣖⠀⠀⠀⢘⣽⣩⢙
⣷⠿⡌⠃⠀⢠⡠⣄⠍⠟⣛⣙⣛⣋⣻⠻⠩⢠⢄⡄⠀⠘⢩⢿⣾⣷⡻⡍⠃⠀⢠⡠⡄⠍⠿⣛⣙⣛⣋⣻⠿⠭⣠⢄⡄⠀⠘⢡⢿
⠏⠀⠀⢠⣌⡻⠍⣿⢧⠀⠀⠀⠀⠀⠀⠀⡞⣿⠹⢟⣡⡄⠀⠀⠹⠏⠀⠀⢠⣌⡻⠏⣿⢧⠀⠀⠀⠀⠀⠀⠀⡼⣿⠹⢿⣡⡄
⠀⠀⣤⢶⣯⣭⣯⣷⣼⠀⠀⠀⠀⠀⠀⠀⡇⣾⣽⣭⣵⡖⣤⠀⠀⠀⠀⣤⢶⣯⣭⣯⣷⢸⠀⠀⠀⠀⠀⠀⠀⣧⣾⣭⣭⣵⡶⣤
⡀⠀⠀⢉⡽⢞⡑⣯⣸⠀⠀⠀⠀⠀⠀⠀⡇⣽⢊⣲⢿⡋⠀⠀⢀⡀⠀⠀⢉⡿⣖⡑⣯⢸⠀⠀⠀⠀⠀⠀⠀⣇⣽⢊⡳⢿⡋
⣵⣀⡄⠀⠒⢻⢶⡿⡃⣀⡤⠤⣤⠤⢤⣀⢐⢻⡶⡟⠂⠀⠠⡠⣮⣵⢀⡄⠀⠐⢻⢶⡟⡃⣀⡤⠤⡤⠤⢤⣀⢐⢻⡲⡟⠒⠀⢠⣀
⣧⡟⡴⣧⠄⠀⠀⠀⢞⡟⡛⢞⣿⣳⢛⣻⡳⠀⠀⠀⠠⣼⢶⠻⣹⣎⠟⣶⣧⠄⠀⠀⠀⢞⣟⡛⡞⣿⡳⢛⢻⡳⠀⠀⠀⠠⣼⢦⢻
⠷⠳⡶⡟⡃⣀⢀⠀⠉⠟⣱⢧⣻⣸⣞⠻⠉⠀⡀⣀⢘⢺⣶⠞⢾⡷⠳⣶⡟⡃⣀⢀⠀⠉⠟⣳⣏⣿⡽⣎⠻⠉⠀⡀⣀⢘⢺⣶⠞
⠉⠉⠁⢀⣶⡗⣻⠖⣀⠀⠁⠘⣽⠁⠉⠀⣀⠲⣟⢺⣶⡀⠈⠉⠉⠉⠉⠁⢀⣲⡗⣻⠖⣀⠀⠉⠘⣯⠋⠈⠀⣀⠲⣟⢻⣶⡀⠈⠉
⠀⠀⠀⢸⣨⣗⣖⡛⣧⢄⡀⠀⠀⠀⢀⣠⣼⣛⣲⣺⡅⡇⠀⠀⠀⠀⠀⠀⢸⢨⣗⣔⣻⣯⢄⡀⠀⠀⠀⢀⡠⣾⣟⣶⣺⡅⡇

⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠠⠀⠀⡄⠀⠁
⠀⠐⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⢀⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠐⠀⠀⠀⠀⡄⠀⠄⠈⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠠⠄⠚⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠐⠀⠀⠀⡀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠰⠀⠀⠀⠀⠔⠁⠀⢀⠀⠀⠀⢀⡄⠠⠌
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠃
⢀⡠⠄⢒⠋⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠐⠀⠀⠀⢠⠉⠀⠀⠠⡀⠀⠀⠘
⠉⠂⢀⠂⠀⠀⠈⠂⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠠⠀⠁⠀⠀⠠⠀⠀⢀⡇⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠀⠀⠉⠒⠐⠂⠚⠀⠀⠀⣐⠁⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠡⡀⠀⠀⠀⠐⢀⠂⠀⠀⠀⠀⠀⠒⠀⠈
⠀⢡⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡼⠂⠀⠀⠀⠀⠀⠁⠀⠤⠄
⠀⢀⡄⠤⠀⠠⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄
⠰⠁⠘⠁⠀⠐⠀⠁⠀⠀⠃⠀⠔⠀⡄⠀⠀⠀⠀⠀⠈⠄⢀⠆⠀⠄⠀⠀⠠⠀⠀⢀⠀⠀⠃⠀⠀⡀⠁⠀⠀⢀
⡂⠡⠀⠀⠀⢀⠆⢈⠀⠤⠀⡀⠠⠀⠀⠠⠀⠀⡐⠆⠀⠀⠀⠀⢀⠀⠀⡀⢀⠀⠀⠀⠀⢀⡄⠀⠀⠃⢠⠀⠔
⠐⢂⠃⠐⠰⡀⡠⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⢀⠞⢀⠀⠀⡀⠐⠀⠀⠀⠀⢂⠀⠀⠀⠐
⠀⠀⠀⠈⡀⠈⠀⠀⠀⢀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠁⠀⠈⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠊
⠀⠀⠀⠈⠈⢀⠀⠀⠀⠁⠀⠀⠆⡠⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⠅⠀⠀⠆⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠐⠀⡇⠀⠀⡖⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠊⡐⢀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⠙⢤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡢⠌⠀⠀⠘⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⣊⡀⠀⠎
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠴⠾⠿⠏⠀⠀⠀⠀⣐⡤
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⡅⠶⣶⣶⡖⠶⠠⠿⠫⠉⠩⠉⠝⠛⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢬⠈⠉⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠘⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢂⡀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢺⣇⡀⢠⣹⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣿⡆⣥⢤⠤⠔⢐⣒⣒⠀⠀⠀⠈⠁⠉⠉⠀⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣆⠳⠒⠀⠀⡀⡀⢀⠠⢀⣄⢆⡀⠄⠸⠿⣛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡛⡿⢷⣌⢻⣮⣝⠳⡍⢧⠔⣻⡬⡿⢬⠢⡄⢈⡩⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠌⠻⠃⠙⣷⡙⢮⣷⡝⣯⠼⠷⠶⢜⣃⣓⣈⡉⠭⠬⠤⢶⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠘⢆⠉⣿⣶⡥⡖⠒⠒⠉⠛⡿⠶⡘⠁⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠪⠛⢢⡀⡀⢀⣿⡟⠁⠉⠀⡀⠤⠴⡟⠳⠃⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠑⣌⢀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠶⡇
⠀⠀⠀⠀⠀⢀⡀⣤⠠⣄⡠⢀⡀⠀⠢⡀⠈⣻⡼⠀⡶⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠴⠙⠃
⠀⠀⠀⢀⣀⡶⢽⣎⡹⢭⣛⠰⡸⣍⠀⠈⠲⣷⠇⡠⠤⠄
⠀⠀⠀⠐⠉⠀⠉⠈⠉⠉⠈⣁⢠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣶⣤⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠂⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠈⠙⢿⣧⡀⠀⠀⠹⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⢀⡾⠁⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⣀⣴⠾⠟⠛⠻⠷⣦⣄⠀⠀⠀⠘⢷⡀⠀⠀⣸⠁⠀⢀⣴⠟⠋⠁⠀⠀⠀⠈⠉⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠘⣇⠀⠁⠇⠀⢠⠞⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⡀⠀⠸⡀⠀⠀⠀⠊⠀⢀⣴⡾⠿⠿⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠷⠶⣤⡀⠀⠘⠄⠀⠃⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠐⠂⠀⠀⠉⠲⠄⠀⠀⠀⣼⣾⣀⠞⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⣰⣶⡀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠴⠚⠉⠙⠛⢿⣦⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠃⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⣿⠟⠉⠀⠀⠉⠀⠀⠀⠸⠧⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠸⠁⢠⣤⠀⠀⢰⡿⠁⠀⠀⠀⢠⣶⠶⠆⠀⠀⠀⠀⠈⠁⠈⠙⣷⡀⠀⠀⠀⠀⢹⡆⠀⢠⣿⣿⡄⠀⠀⠆
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⠁⠀⠀⠀⢠⡟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠼⡿⠆⠀⠀⠸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣿⠛⢿⣯⡉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⢛⣿⠟⣿⡟⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⣿⡇⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣿⣿⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⣿⡇⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢹⣿⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⣀⣤⣴⡶⠂
⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠙⠻⣦⡀⣠⡶⠛⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣤⣤⣿⣷⠀⢠⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⢷⣶⣶⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣈⣻⣏⣀⣀⣀⣀⣠⣤⣤⣤⠴⣿⠿⠛⠉⣱⣿⠟⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠈⢻⡍⠉⠉⠉⠉⠉⠉⠉⢻⡟⠋⠉⠉⠉⠉⠁⠀⠀⣰⠃⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡟⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⢳⡀⠀⠀⠀⣾⠀⠀⠀⠀⣰⠟⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠀⢳⡀⠀⠀⣿⠀⠀⢀⣼⠏⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⢳⡀⠀⡿⠀⢠⣾⠃⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠱⡀⡇⣠⡿⢃⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣆⢹⣿⣟⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⢀
⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣤⣤⣾⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⡀⠀⠄⠀⠀⠀⠀⠀⠀⠨⢀⣴⣿⣿⣿⣿⠛⣿⣿⣦⠀⢨⡶⣾⣷⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠄⣡⣾⣿⣦⡀
⣿⣿⣿⣷⡀⠐⢀⣴⣶⣦⣤⣶⣿⣿⣿⠟⠻⢿⠀⠈⠻⣿⣿⣿⡇⢈⣿⣦⣀⠀⠢⠀⡀⠀⠀⠀⠀⢀⣀⣾⣿⣷⡄⠈⠀⠴⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⣄⠈⠉⠻⣿⣿⡿⢿⣿⣿⣄⠀⣠⣴⣿⣶⣝⠻⣿⣿⣿⣿⢯⠙⢿⣷⣌⠀⠀⢄⣠⣤⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣆⠀⠀⡙⢿⣿⣦⣉⣻⢿⣾⣿⣿⣿⠟⣿⢿⣷⣈⣻⣿⣾⣤⣾⣿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀
⠈⠻⣿⣿⣿⣿⣿⣷⣾⣿⣆⠛⠛⢿⣿⣦⣝⣿⣋⣤⣾⣿⣷⣬⡋⠉⠉⢻⢿⡿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣠⣦⣤⣾⣿
⣿⣶⣍⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣤⣉⡋⠛⠻⣿⣿⣿⣿⣿⠟⠁⠀⢠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣦⣩⡿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡙⣿⠟⢁⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣮⣿⢀⡟⡯⢸⠻⢸⠃⡏⠿⠻⠁⠀⠛⠙⠻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣄⡒⠁⠄⠂⢁⠀⠠⠀⠀⠀⠀⠁⠸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣤⣴⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠴⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⣐⣂⣉⣭⣭⣤⣤⣤⣶⣴⣶⣶⣶⣶⣶⣶⣶⡆⠐⠒⢦⣿⣶⣤⣀⢀⣀⣀⣀⣀
⠀⠀⢠⢖⣿⣶⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠃⠀⢸⡷⠿⠛⡏⠉⠓⠢⢤⣤⠬⠉⠒⢤⣀
⠀⠀⣌⠘⡇⠈⠉⠉⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢘⢺⡇⠀⠀⠙⢄⣀⠀⠀⠈⠉⠒⠦⣄⣈⡙⠒⠤⡀
⠀⠀⣿⣿⠇⠀⠀⢀⡏⣿⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆⡇⢰⣄⣀⡀⠈⠙⠓⢶⠠⣄⡀⠀⠉⠙⠻⠿⣿⡆
⠀⠀⠉⠉⠀⠀⠀⢸⣵⢸⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠸⠈⣿⣿⠀⠀⠀⠀⣇⠀⠈⠙⡖⠢⢤⣀⠀⠉⠐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⡿⡟⢸⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⡿⣿⠀⠀⠀⠀⢹⠀⠀⠀⢣⠀⠀⢳⠈⠹⡖⢦⣼
⠀⠀⠀⠀⠀⠀⢀⡇⡇⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡄⣿⠠⣄⣀⣀⡘⠀⠀⠀⢸⡀⠀⢸⠀⠀⡇⠀⠛⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠉⠙⠧⠤⠤⠤⠀⠐⠒⠒⠂⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⢸⠀⢸⡇⣿⠀⠀⠀⠀⠀⠉⠉⠉⠒⠁⠀⠀⠀⠀⢁⣀⣾⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⠤⠐⠒⠂⠚⠉⠉⠁⠀⠀⢁⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠀⠀⣧⢸⢀⠀⠀⠀⠀⠐⠀⠀⠈⢑⣚⣓⣁⣠⣭⣭⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣾⣶⣶⣶⣶⣶⣒⣲⣾⣓⣈⠉⣩⣿⣏⣩⣭⣭⣭⣽⣿⣿⣿⣿⡆⠀⡟⢸⠀⠵⠶⠖⠒⠒⠒⠒⠛⠉⠉⠉⠉⠉⠉⢙⣿⣿
⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠁⠀⠀⢸⡇⠀⣀⣀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⣾⣸⣇⣽
⠀⠀⠀⠀⠀⠀⣤⣌⣥⣄⡀⠀⠨⣭⣤⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⠂⠀⢀⣤⣤⣤⣤⣤⡤⢤⠀⠀⢸⣧⣾⣿⣿⣇⠀⠀⠀⢀⡀⠤⠄⠒⢰⣿⡇⢀⠴
⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣡⡀⠀⠚⡷⠆⠀⠀⣀⠀⠀⢠⣼⠷⠂⠠⢠⣿⣿⣿⣿⣿⣿⡇⢸⠀⢰⠘⣿⣿⣿⣿⣿⠀⠉⠁⠀⠀⠀⣀⣠⣼⣿⠁
⠀⠀⠀⠀⠀⠀⣟⣿⣿⡿⣟⠁⠀⢤⣭⣭⣤⣤⣭⣤⣤⣭⣭⣥⣤⠂⠨⠭⠭⠭⠭⠭⠭⠭⠥⠀⠸⠁⣿⣿⣿⣿⣿⠀⢀⣀⣀⣼⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠬⠷⠶⠶⡶⠒⠒⠒⠒⠒⠒⠖⠂⠀⠈⠉⢛⣟⠉⠩⠁⠀⠀⠈⠁⠀⢀⣿⣿⣿⡿⠁⠀⠭⣻⣿⣿⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠳⣶⣶⣶⣦⡤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⢀⣠⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⢿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⣿⣿⣿⣿⣉⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠙⡏⠀⠀⠀⠀⠀⠀⣿⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢧⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢷⠀⠀⠀⠀⡿⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠙⢦⡀⠀⠀⠀⠈⢧⠀⠀⠀⢸⡀⠀⠀⢀⡇⠀⠀⠀⡞⠀⠀⠀⠀⢀⡞⠁⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠳⣄⠀⠀⠀⠈⢧⠀⠀⠈⡇⠀⠀⢸⠃⠀⠀⡼⠁⠀⠀⢀⡴⠋⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⠳⣄⠀⠀⠈⢧⢀⡤⠷⠶⠦⠾⣄⠀⡼⠁⠀⢀⡴⠋⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠓⢦⡀⠀⠀⠈⢣⡀⢀⡜⠉⠀⠀⠀⠀⠀⠈⠹⣇⠀⣠⠏⠀⠀⠀⣀⡴⠚⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠉⠲⣄⠀⠀⠙⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠁⠀⢀⡤⠚⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀⠙⢦⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡤⠞⢉⣀⡤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠲⢬⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⣉⡤⠞⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠉⢻⣦⣄⣀⣀⣀⣀⣤⣾⠟⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠳⢬⣭⣭⠴⠋⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠁⠂⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠤⠀⠐⠀⠠⠀⠀⢰⣶⣶⣵⣶⣶⡀
⠀⠀⠀⠡⠀⠀⠀⠀⠠⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⡁⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⢿⠀⠀⠠⠀⠀⠀⠀⠀⠴⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠂⠀⠐⠀⡀⠀⢠⣴⣿⣿⣿⣷⣤⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⣠⣷⣧⡀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⢀⡠⣤⣤⣀
⠀⠀⠠⠂⠀⠀⠀⠐⠄⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⣰⣿⣿⣷⣷⡀⠀⠺⠂⣀⠀⣀⠐⠕⠀⠘⢽⡿⣿⡿⣿⠕
⠀⠀⠀⠀⠂⠌⠐⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⢴⠀⠀⠀⠀⠀⢰⡄⠐⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⣀
⠀⠀⡐⠀⠀⠀⠀⠠⡀⠀⢠⣴⣶⣶⣶⣶⣶⡄⠀⠀⠂⠁⠈⠑⠀⠀⠀⣠⣾⣿⣿⣄⠀⠀⠀⠤⠀⠂⠑⢐⠀⠀⢀⣤⣶⣶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠤⠀⠀⠀⠀⠠⠀⢀⣿⣿⣿⣿⣿⡂⠀⠈⡁⠀⠀⠀⠀⠀⠀⠻⢷⣿⣿⣿⣿⡿
⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠸⣿⣿⣿⣿⣿⣿⠏⠀⠂⠀⠀⠀⠐⠀⠁⠘⠛⠿⠿⠿⠛⠃⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠤⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠰⠂⠀⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢠⠄⠀⠀⠙⣻⡿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠦⢤⣀
⠀⠀⠀⢐⣶⣿⣤⣤⡤⣄⠀⠀⠀⢼⠀⢀⠀⠀⠘⡆
⠀⠀⠀⠛⣿⠋⠀⠀⢱⠈⢳⠀⠀⠈⠲⣎⠀⢸⢂⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⡷⣀⢀⡗⠊⠀⠈⡇⠀⠀⠀⣹⡄⣴⣾⣡⣠⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠳⣌⠁⠀⠀⠀⠀⠙⠀⠀⠠⠅⡜⠊⣉⣀⣔⡽⠁⡀⠀⢀⡀⠀⠑⠄
⠀⠀⠀⠀⠀⣀⠉⠒⠢⠄⠀⠠⠀⢀⡤⠄⡔⠊⠀⠉⢳⣠⠎⠀⡎⠁⠀⠀⠀⢸⢀⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠉⠉⠀⠀⠀⠀⠀⠀⠜⠑⡆⠀⢇⠀⠀⠀⣀⡞⠁⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⣀⠤⠤⢤⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣀⠉⠛⠉⠁⡅⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⣠⠎⠀⠀⠐⠦⠉⠀⠤⠶⠤⣤⣖⡻⠯⣄⡋⠰⠀⡈⠠⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⡅⠀⠂⡀⢀⡴⢧⠀⠀⠀⠠⠚⠁⢺⠀⠀⠀⠀⡼⢯⣷⣀⠉⠒⠤⣁⠂⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠐⣿⡷⢲⡀⠀⠀⠀⠈⠀⢀⡠⠞⠁⠐⠈⠂⠀⠀⠓⠂⠤⠤⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠁⠒⠒⠚⣻⠁⠀⠈⠑⣄⠔⠀⠀⠐⠀⢀⠄⣀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⣀⣠⣂⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠋⠁⠀⠈⠢⢀⣀⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠰⢄⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠲⠂⠀⠀⠀⠀⠀⣠⠏⡐⠶⠃⠀⠀⠀⢀⡐⠂⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⢀⣞⠉⠳⠞⠀⠀⠀⠀⠀⠀⠀⠡⡌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⡂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢦⡵⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⠸⠃⠀⠀⠀⠀⠀⠀⠀⣾⠤⣌⠆⠀⠀⠀⢰⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢥⠊⠀⠀⢔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣤⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢢⣀⡀⠀⠀⠀⢤⡐⠀⠁⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⡀⠀⠈⠢⡤⠀⢄⠀⠀⠀⠀⠀⠀⠠⣎⢂⢈⡰⠂⠁⠀⠀⠀⠀⢈⡤⠂⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡐⠉⢆⠀⠀⢄⡀⣠⠀⠀⠀⠀⡖⢢⠀⣩⠜⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡐⠀⠀⠀⠑⡄⠀⠀⠀⠑⢤⡈⢆⢙⡸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠒⠣⣰⣁⠁⠑⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⠁⠀⠀⡠⠊⠈⠢⡀⠀⠀⡠⣅⡜⠉⠀⠀⠀⢀⠊⠈⠲⠀⠀⠀⠀⢀⣠⢉⠀⠐⠗⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⠀⠀⢀⠔⠁⠀⠀⢀⠜⠓⢄⠑⠉⠈⢢⠀⠀⠀⠀⠢⠄⠘⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠃⡜⠀⠀⡰⠃⠀⠀⡠⠖⠁⠀⠀⠀⣁⠦⢀⡀⠡
⠀⠀⠀⠀⠀⠀⡌⠌⠀⡠⠊⠀⢀⠤⠊⠀⠀⢀⠠⠒⠉⠀⣀⠠⠘⠋
⠀⠀⠀⠀⠀⡐⠌⢀⠔⠁⡠⠐⠁⢀⡠⠐⠈⣀⠠⠐⠊⠉
⠀⠀⠀⠀⢰⠏⡠⢃⠴⠊⡀⠄⢂⠡⠔⠒⠉
⠀⠀⠀⢠⣏⣨⢔⣡⠔⠍⠒⠉
⠀⠀⢠⡿⠟⠛⠉


⣿⢿⠿⡿⡿⠛⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡟⣦⠀⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠄⢹⣿⢽⣷⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠆⠁⠄⠀⠀⠠⠄⠀⠀⢀⠄
⠀⠀⢸⣴⢀⠀⣄⠀⠀⠀⢠⠀⠀⢸⣿⣯⣯⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠽⢹⠀⠀⠀⠀⠀⡄⠀⠀⣽⣾⣼⣙⣙⣷⠀⠀⠀⠀⡗⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀⣀⢠
⠀⠀⠀⢀⠐⠁⠀⠀⠀⢀⠁⠀⠀⢿⣽⣯⣿⣿⣵⣄⠀⠀⠀⠡⠨⢷⡈⠀⠀⠀⠀⠀⠀⢀⡠⠬⠐⠂⡇
⠀⠀⠈⢀⠀⠠⠀⠀⠀⡌⠀⠀⠀⣿⣾⣷⣥⣿⣾⡟⠀⠀⠦⠄⠉⡁⠦⠀⣀⠀⠀⠀⠀⢦⢰⣛⡹⢃⠦
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠳⠀⠀⠀⠈⡛⢉⠃⡛⠁⠀⠀⠀⠈⠃⠁⠀⠀⠀⠁⠀⠀⠀⠈⢣⣗⡝⡖⠕⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⡀⠀⠀⠀⠂⠀⢈⠁⡲⢱⣠⠀⠀⠀⠀⠴⠂⣂⢀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠘⢀⠓⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡰⣀⢀⠀⠈⡰⠑⢂
⠀⠀⠀⠀⠪⠀⠀⠀⣀⡀⠀⠀⠀⠉⠉⠓⠐⠀⠅⠽⣠⣦⠃⠐⠶⣤⣀⣠⡤⠀⠀⠐⡈⠀⠄⡌⡡⠵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠤⢄⡀⡠⡆⣀⠷⡶⢥⡙⢉⡮⢶⠮⣀⢰⣄⢀⡠⠤⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠻⡑⡞⠙⠠⢹⣜⢤⡲⣝⣫⢖⡤⣣⡏⠄⠋⢣⢊⠟⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠲⠺⠃⢓⣚⣰⢡⡃⡋⠌⢦⢺⡾⢷⡇⡰⠡⢉⢘⡌⣆⣒⡚⠙⠷⠶⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⡛⣬⣠⠒⢾⣗⣹⣷⣏⡄⣨⢻⠛⠛⡟⣅⢠⣹⣾⣟⣺⡷⠒⣄⣥⢛⢸⣇
⠀⠀⠀⠀⠀⠀⠱⡟⣭⡓⢯⢀⢠⠚⡴⠏⠷⡽⣟⢉⠷⣾⠍⣿⡻⢟⣿⠩⣷⠾⡉⣻⢯⠾⠹⣦⠓⡄⡀⡽⢚⣭⢻⠊
⠀⠀⠀⠀⠀⠀⠀⠱⣱⠬⢘⣸⢾⢷⣝⡧⢮⢗⢿⡙⣓⢿⡿⢿⣗⣺⡿⢿⡯⣚⣋⡿⠲⡥⢮⣫⡾⡷⣇⡃⠥⣎⠎
⠀⠀⠀⠀⠀⠀⠠⠾⠓⡀⠡⠲⢿⣾⡟⢙⣟⠳⣾⠟⡧⣲⣯⠋⠿⠿⠙⣭⣖⢼⠻⣷⠞⣻⡋⢻⣷⡿⠖⠬⢀⠚⠵⠄
⠀⠀⠀⠀⠀⠀⢄⡜⣓⢶⡋⠌⠋⠽⣹⣧⣽⣜⢩⣫⡅⣭⣾⣾⣿⣿⣷⣷⣭⢨⣝⡍⣣⣏⣼⣏⠯⠙⠣⢙⡶⣚⢣⡤
⠀⠀⠀⠀⠀⡠⢜⣏⢠⡳⣈⣓⣦⣞⣧⣥⣿⣏⡧⠛⣺⣿⣟⣽⡷⢾⣯⣿⣿⣟⡻⢼⣹⣿⣬⣼⣱⣴⣚⣥⢞⡄⣹⡣⢄
⠀⠀⠀⠀⢾⠰⡇⢈⡷⣹⢾⣋⣿⠀⣿⢎⣹⣹⣿⡇⣿⣿⣹⣏⢾⡿⢹⣟⣿⣿⢸⣯⣏⣏⡱⣿⠀⣿⣙⡷⣏⢾⡁⢼⠆⡷
⠀⠀⠀⠀⠀⠑⢪⣏⠘⡵⢛⡩⠟⢍⡟⡛⣿⣏⡗⣤⢽⣿⣯⣻⡷⢶⣟⣽⣿⡯⣤⣺⣹⣿⢛⢻⡭⠻⢍⡙⢮⠃⣹⡔⠊
⠀⠀⠀⠀⠀⠀⠊⢣⡭⠾⡅⢂⣄⣲⣹⡟⣛⢫⣘⣝⡃⣚⢿⢿⣿⣿⡿⡿⣛⢘⣫⣃⡝⣟⢻⣏⣖⣠⡐⣨⠷⢭⡜⠓
⠀⠀⠀⠀⠀⠀⠐⢶⡤⠁⡒⠴⣾⢿⣧⣨⣯⡴⣿⣦⡗⠽⣛⣄⣶⢶⣠⣻⠯⢺⣴⣿⢦⣽⣅⣼⡿⣷⠦⢒⠈⢤⡲⠂
⠀⠀⠀⠀⠀⠀⠀⡰⡹⢒⢨⢹⢾⡾⣫⡗⠞⡦⣾⣡⡍⢾⣷⣾⡯⢽⣷⣾⣗⢭⣍⣷⠴⡣⢺⣝⢷⡷⡏⡅⡒⢏⢆
⠀⠀⠀⠀⠀⠀⡰⣧⣛⠥⣞⠘⠘⢤⠱⢦⡶⣳⣯⣈⡶⢿⣂⣿⣵⣮⣿⣐⡿⢾⣁⣽⣞⢴⡴⠞⡤⠃⠃⣳⠬⣛⣼⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣥⢛⠙⠤⢾⡯⣽⡿⣏⠃⢑⣼⣤⣤⣧⡊⠘⣹⢿⣯⢽⡷⠤⠋⡛⣬⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠼⢶⣄⡭⠭⠹⡘⡅⣍⢂⠞⢼⢷⡾⡧⠱⡐⣈⢨⢃⠏⠭⢥⣠⡦⠶⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣴⡡⢧⣠⠐⣸⢫⠊⠵⣫⣝⠮⠃⡝⣇⠒⣄⡼⢌⣦⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠒⠊⠁⠙⠇⠉⡲⠷⡚⣡⣈⢓⠾⢖⠉⠸⠋⠈⠐⠲⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡥⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠄⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠃⠀⠀⠀⠀⣿⠀⠀⢘⠧⣀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠆⠀⠀⠀⠀⠀⠙⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⣿⡇⠀⠢⣠⣯⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣛⣋⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⣠⠔⣄⣼⠟⢩⠉⠀⠀⠈⣳⡄⢀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⠀⠀⠀⠀⣿⡀⠀⠀⠀⣿⠁⢹⡇⠀⠀⠀⢀⡾⠗⠊⣿⣿⠀⣺⡀⠀⠀⠀⠙⢿⡌⣷⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠸⠶⠿⠃⠀⠀⠀⢸⠁⠀⢠⣿⣿⣶⣿⡇⠀⠀⠀⠀⠈⣷⢘⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡶⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⣿⣿⣿⣻⣧⣄⠀⠀⠀⠀⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠸⣿⣿⡿⠉⡍⡏⠀⠀⠀⠼⠑⡟⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣽⡿⠃⠀⠻⠲⢿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⡄⠩⢁⠤⠈⣥⣄⠛⠀⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢱⣿⠋⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣘⠛⠊⠁⠴⠠⠐⠂⠀⠙⢓⠀⠉⢉
⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⢸⡏⠀⠀⠀⠀⠀⢀⣀⡿⠧⠀⠀⠀⢀⢨⣤⣤⣄⣀⡀⠀⠀⠀⠀⣻⣿⣿⠉⠁⠀⠀⠀⠀⢰⡇⠀⠀⠘⠃⢰⡄
⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⢙⡛⢃⠀⠀⠀⠀⠀⢠⡄⠙⠛⠛⢋⣉⠉⢡⡀⠀⣸⣿⢟⢆⠀⠀⠀⠀⠀⠘⣿⣤⣄⣠⣸⣾⡧
⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢼⣾⣇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⡇⠀⢻⣿⣸⣼⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡿⠟⠁
⠀⠀⢠⣿⣿⣷⠀⢐⡂⠀⠀⢹⣿⠀⠀⠀⠀⣿⣿⡄⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇⠀⢸⣿⢻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿
⠀⠀⢸⣿⣿⣿⣷⡘⣿⡃⠀⢸⣧⠀⠀⠀⢸⣌⣿⡿⣾⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡇⠀⢸⣿⢿⢶⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿
⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⢸⣯⠀⠀⠀⠸⣅⣙⣷⣬⣟⣓⣉⣉⣀⣀⣀⣀⣀⣤⣤⣵⣾⡿⠀⠈⣿⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣇⠀⠐⣿⠀⠀⠀⠀⠈⠛⠿⠟⢻⣿⣿⣿⣿⣿⡿⠟⠋⠙⠋⠉⠈⠀⠀⠀⣿⡧⡿⠃⣺⣧⡆⠀⠀⠀⠀⡀⣿
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣾⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⡿⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡷⢧⠀⣿⣿⡿⠒⠀⣤⣆⣵⣿⡀
⠀⠀⠀⠀⢸⡙⣿⣿⣿⣿⣿⣿⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⡁⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠶⡀⡽⢡⣾⠟⠋⣃⣨⣿⣯
⠀⠀⠀⠀⠈⠛⣁⣈⣻⠿⠿⢿⣿⡝⠿⠆⢠⣄⠀⠀⠀⠀⠀⠀⠸⠏⠛⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣹⡿⠓⢊⣠⢠⣿⣹⡞⢋⡿⢖⣦
⠀⠀⠀⠀⠀⠀⠳⢿⡟⠂⠙⢮⣴⡉⢤⣵⡦⠏⢀⣴⡆⠀⠀⢈⣷⣤⣾⣿⡄⠀⠀⠀⠀⠀⢀⣠⢶⡖⠚⢉⣤⣖⣯⣴⠟⣡⣟⣿⣯⡿⢿⣟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣿⣿⣿⣷⣾⣥⠔⢊⣋⣽⣄⣀⣒⣼⠟⠉⠀⠘⣿⣀⢀⠀⠀⠰⣮⣽⣫⡶⣾⡯⠼⣯⣶⣿⢿⣟⠰⣋⣽⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⣿⣍⡉⠉⠁⠀⠀⠀⠀⠈⢿⣿⢐⠂⠙⢧⣟⣿⣶⣯⣇⣮⡿⢟⣫⣷⢬⡿⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⢿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⢠⣷⣶⢿⣅⢿⡇⠋⠛⠛⣋⣥⠶⠏⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣇⢩⣿⡄⣽⣿⡆⠀⠀⠀⠀⠀⠀⠉⢻⣷⣄⡀⠀⠀⠀⠀⠀⢸⣿⡇⠂⠁⠛⠓⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠟⠁⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠻⠛⣆⡸⠇⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣦⡀⠀⢿⣿⠆
⠀⠀⠀⠀⠀⠀⢀⣴⣦⡶⠞⢋⣭⣅⠀⠀⠁⣠⣤⣠⣴⣤⣶⣷⡆⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠻⢗⣂⣀⠈⠙⢣⣬⣭⡤⢔⣚⣩⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠛⠛⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⣾⠁⠀⠀⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠤⠻⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣿⠐⠀⠳⠄⢰⠀⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠻⡔⢁⣀⠀⠀⠧⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠼⡦⠉⢉⣥⡶⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠂⠈⠀⠀⠀⢀⠞⢑⣤⢞⢡⠹⠚⢢
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢈⡀⠀⠀⠈⠡⠀⢸
⠀⠀⠀⠀⠀⢀⠔⠈⠀⢡⠀⠀⠀⠀⠀⢀⢀⠌⠀⠀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠈⠀⠀⠀⠀⠠⢠⠸⣄
⠀⠀⠀⠀⢠⡅⠚⡄⠀⡤⢤⠀⠀⠀⢀⠁⠈⠰⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠇
⠀⠀⠀⠀⠸⡄⠀⢰⠀⣣⣮⠀⠀⠀⢰⠄⠀⡇⠀⠁⠀⠐⠀⡀⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⡄⣺
⠀⠀⠀⠀⠀⠈⠑⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠇⠀⠄⠀⠘⢄⡔⠀⠀⠀⠀⠀⣠⡀⠀⠀⡐⠀⠀⠀⠀⠀⣁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢀⠀⠀⠀⠘⣄⠀⠀⠀⠰⡋⢀⡀⠘⠀⠁⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠈⠀⠀⠀⠀⡎⠀⠀⠀⠀⠱⣌⣀⠀⠀⠣⣸⡤⠋
⠀⠀⠀⠀⠀⠀⠀⡴⠛⠦⡀⠀⠀⠀⠀⠈⠒⠲⢄⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠁
⠀⠀⠀⠀⢀⡠⠞⠄⠀⠀⠈⠻⢦⠀⠀⠀⠀⠀⠀⠑⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⢁⢀⢈⢢
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡀⢢⡇⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠎⠀⠡⠀⠀⠀⢸
⠀⠀⠀⠀⡅⠀⠀⠀⡀⡀⠀⠀⢁⢀⡇⠀⠀⢀⠈⠀⠀⡀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢴
⠀⠀⠀⠀⢀⢀⡠⢊⠀⠉⠑⠢⢼⣜⡄⠀⠀⠃⠀⠠⠈⢐⣀⠈⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠂⠃
⠀⠀⠀⠀⠸⣈⠔⠁⠀⠀⠀⡰⢪⠎⠀⠀⠀⢘⡀⠀⠀⠊⠀⠁⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⡸
⠀⠀⠀⠀⠀⠈⠲⠤⠄⠤⠋⠚⠁⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⡄⠀⡸⠁⠀⠀⠀⠀⠘⢦⣈⣀⣀⣩⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡄⠀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢀⣀⢹⣿⣿⡇⣾⣿⠆⠀⠀⠀⠀⢀⣶⣿⣶⣶⡄
⠀⠀⠀⠀⣰⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠠⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⠄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠙⠛⠿⠟⠛⠛⠛⠋
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡍⠛⠛⠻⠯⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣿⢿⡇⣼⣿⠆⠀⠀⠀⠀⠀⣴⡆⣀⣤⡄
⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣼⣿⡿⣿⣿⣥⡀⡀
⠀⠀⠀⣾⣿⣽⣷⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣿⣿⣷⠀⠀⠀⠐⠩⣿⣿⣦⣾⣿⣾⠁⠀⠀⠀⠀⠉⠙⠛⠛⠉⠈⠋⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣗⢽⣿⡀⠀⠀⢀⣾⣿⣿⣽⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⠛⠛⠟⠛⠋
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⣼⣿⣼⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣄⢠⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣡⣄⣀⣈⣿⠃⠀⠀⠀⠀⢀⣀⣀⠠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⠄⠉⠉⠻⠅⠀⠀⠀⠀⠀⠿⣿⠆⣀⣼⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⡀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠸⢷⣄
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢞⠛⢶⠹⡊⡴⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⣶⢏⢹⣿⡐⠢⣜⠐⠀⣣⠔⢒⣿⡏⡹⣖⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⠁
⠀⠀⠀⠀⠘⣿⣏⣾⣺⠁⠙⢽⠻⡟⠑⡼⠂⣰⢿⡟⣧⠙⢿⣦⡑⠂⠘⢊⣴⡾⠋⣾⢛⡿⣆⠐⢤⠊⢹⠿⡯⠋⠉⣗⣷⣻⣿⠃
⠀⠀⠀⠀⠀⠙⣿⣡⣿⣭⣒⡬⢄⡁⠠⣕⣻⠃⢾⠧⠟⣤⣦⡍⠛⢦⡴⠛⢩⣴⣤⠷⢾⣷⠘⢟⡫⠄⢈⡠⣥⣖⣽⣿⣬⣿⠋
⠀⠀⠀⠀⠀⠀⠘⣿⣉⡽⣿⡿⣷⣌⠄⠩⢙⡲⠛⠉⢰⣿⣿⡏⠀⠘⠋⠀⢹⣿⣿⡆⠹⠛⠖⢏⠌⠐⣡⣾⢿⣿⢧⣘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣞⢟⡄⢙⣿⡌⢠⡆⢀⡀⠰⠄⢸⣿⡇⣤⣠⣆⣤⢸⣿⡃⠰⠄⢀⡀⢰⠄⢁⣿⡋⢠⡻⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⢰⣷⡇⠀⠁⡿⡏⢠⢒⡟⢢⢹⣾⠳⢞⣷⡏⡔⢳⡒⡆⢹⣿⠈⠀⢸⢿⡄⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣗⡇⠀⠀⡇⢠⠌⠉⢸⡟⣸⠛⠃⠘⠛⣇⢿⡇⠉⠡⡄⠺⠀⠀⢸⣸⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⢿⣳⣶⣾⣧⣿⡀⠀⠀⢀⣿⣼⣷⣦⣞⡿⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⣷⣽⣆⣸⢿⢧⡀⢀⡼⡿⣅⢰⣯⣾⠷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁