Black star Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢀⣰⣷⣤⡤⠀⠀⠠⣤⣤⣀⣴⣿⡇⠀⠀⠀⠀⠺⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠙⢻⣿⣿⡀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⡶⠀⠀⠹⠿⠂
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⣿⣿⣷⡄
⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠋⠉⠉⠙⢿⡇⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⢠⣾⣦
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠁⠀⠀⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣶⣶⡶
⠀⠀⠀⠀⠀⣤⣤⣤⣾⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⣿⣦⣤⣴⣾⠇⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⠻⠇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠺⠿⠿⣿⣿⣿⡿⠿⠦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢤⣾⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⣠⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣾⣆⣀⣀
⠀⠛⠻⠁⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠻⣿⣿⣿⣿⠋⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⣤⣾⣿⣿⠀⠀⠀⠀⠀⣿⠟⠻⠿⠀⠀⠈⢻⣿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠛
⠀⠀⠀⠀⠀⠀⢀⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓
⠀⠀⠀⠀⠀⠀⠛⣿⡿⠧⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⣼⣿⣦⣀⣀⣀⣀⠀⠀⠀⣀⣤⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣤⣤⣤⣤⡄
⢀⣠⣤⣶⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⡀
⠀⠙⠻⢿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠛⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣇⠀⠀⢲⣾⣷⣄
⠀⠀⠀⢸⣿⣿⠿⠿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣠⣴⠀⠀⢀⣤⡀⠀⠀⠀⢺⣿⣿⠟⠿⢿⣿⡄⠀⠚⠛⠿
⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⢀⣼⣿⣿⣷⣄⠀⠈⠛⠁⠀⠀⠀⠸⡋⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣿⣿⣷⣤⣄⡀⠀⠈⠹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⣀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⣠⣆⠀⠀⢹⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣿⠟⠁⠀⠘⠟⠁
⠀⠀⠀⠀⢘⣿⣿⠋⠀⣼⠿⠛⠻⣿⡇⠀⠀⠀⠀⠀⠀⢦⣴⣿⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡼⠿⣿⠋⠁⠀⠀⠀⠘⠋⠀⠀⠉⠁⠀⠲⣿⣿⣷⡶
⠀⠀⠀⠀⠰⣿⣗⠀⠀⠀⠐⣦⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⢿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠛⠿⠉

⠀⠀⠀⠀⣀⣀⣾⣆⣀⠀⠀⠀⠀⢦⣼⣶⡆⠀⠀⠀⣰⣼⣾⣴⡀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠰⣄⣇⠔
⠀⠀⠀⠀⠈⣻⣿⣿⠋⠀⠀⠀⠈⣻⣿⣿⡏⠁⠀⠀⢺⣿⣿⣿⠂⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⢉⠿⡿⣍⠁
⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠠⣄⠀⢀⡤⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⢶⠆⠀⠀⠀⠀⠀⠬⣾⢟⠂⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⢈⡷⣏⠀⠀⠀⠀⠀⢺⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠓

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠠⣾⠦⠀⠀⠀⠀⠠⠤⢼⠦⠤⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠈⣷⣾⠁⠀⠀⠀⠀⣴⣷⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣴⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣤⣤⣤⣶⠶⠿⠁⠀⠀⠀⠈⠿⠶⢶⣤⣤⣤⣄⡀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠛⠛⠛⢋⣉⣁⣼⣿⣿⣿⣿⣄⣉⣉⠛⠛⠛⠻⢿⣿⣿⣿
⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⠿⢿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣇⣠⣴⠾⠛⠉⠛⠷⣦⣄⡘⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠿⠛⢉⣠⣴⣦⣌⡙⠻⢿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣴
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣿⣧
⠀⠀⠀⠀⠀⠈⢿⣶⣄⠀⠀⣠⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢀⣼⠏⠈⣿
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⣀⣠⣿⣧⡶⠃⣿
⠀⠀⠀⠀⠀⠀⠹⠿⠟⠹⣿⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⠟⠀⣘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠙⢿⣦⡀⠀⠀⠀⢀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠻⣦⣀⠀⡀⢀⣀⠀⠀⠐⠆⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡶⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⡅⠤⠀⠀⡀⢠⣴⣿⣿⡟⠁⠈⠙⠿⠿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣧⣀⡀⣠⡽⠋⠰⡿⠋⠀⢀⡀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣤⣀⡈⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠁⠀⠈⠉⠙⠓⠲⢤⣄⣀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⢀⣠⠄⠀⠀⢀⣀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⠟⠓⠒⠦⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⢀⡀⢼⣿⡿⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣼⠏
⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣷⣾⠟
⠀⠀⠀⠘⠉⠉⠉⠙⣿⣿⡟⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⡿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⠀⠀⠈⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠻⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣿⣶⣿⣿⣯⣀⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠁⢹⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣤⣤⣤⣶⣾⣿⣿⣿⣟⠛⠉⠁⠀⠀⠉⠙⢛⣿⣿⣿⣶⣦⣤⣤⣤⣀⣀⣀
⠠⣤⣤⣶⠂⢲⣶⣿⣿⣯⡉⠁⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠉⠿⢿⣿⣿⣿⡟⠛⠃⠐⠒⢲⣶⣦⣤
⠀⠈⠻⣿⣶⣾⣿⣿⣿⣿⡏⣀⣄⡘⣿⣿⣿⠿⠋⠻⢿⣿⣿⣿⠃⣀⣤⣄⡀⢻⣿⣿⣿⣿⣿⡆⣀⣰⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⡿⠋
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣿⣿⣾⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠫⡁⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣈⣿⣿⣿⣿⣿⣿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⠉⢉⣽⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣁⣤⣶⣦⣄⣸⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣿⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢠⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣿⣿⣿⣿⣀⣸⣿⣿⡿⠟⠋⠁⠀⠉⠛⠿⣿⣇⣴⣦⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠟⠙⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠙⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢂⣀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣇
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⢀⣤⣾⣿⣿⣷⣤⡀⠀⠀⠀⠀⠘⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⣠⣶⣿⣿⣿⡿⢿⣿⣿⣿⣶⣄⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⣀⣴⣿⣿⣿⡿⠛⠁⠀⠀⠈⠛⢿⣿⣿⣿⣦⣀⠈⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣾⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠐⢶⡾⣿⣶⠖⠀⠀⠲⣾⣿⡶⠖⠀⠀⠲⣶⣿⣶⠆⠀⠀⠒⢶⣿⣿⡖⠂⠀⠐⢶⣾⣿⣶⠖
⠀⠀⠀⣸⠟⠻⣧⠀⠀⠀⢠⠟⠛⠷⠀⠀⠀⠀⠟⠛⠳⠀⠀⠀⠀⡸⠟⠻⡆⠀⠀⠀⢠⠿⠛⢧

⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠈⠛⣺⣿⡿⠂⠀⠀⠲⣈⠁⢀⠟⠁⠀⠲⣶⣿⣷⠖⠂⠀⠒⢶⣿⣷⠶⠂⠀⠘⠳⣾⣿⠿⠛
⠀⠀⠀⠼⠋⠙⠃⠀⠀⠀⠀⡿⠚⠺⡆⠀⠀⠀⡾⠛⠻⡄⠀⠀⠀⠼⠛⠻⡆⠀⠀⠀⠠⠟⠁⠲

⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠘⢷⣿⣿⡶⠒⠀⠀⠛⣿⣿⡿⠃⠀⠀⠲⣶⣿⣷⠶⠂⠀⠐⢶⡃⠙⡶⠂⠀⠐⢶⣾⣿⡶⠒
⠀⠀⠀⠸⠋⠙⠧⠀⠀⠀⠠⠛⠉⠳⠀⠀⠀⠀⡾⠛⠻⡄⠀⠀⠀⡼⠗⠻⢇⠀⠀⠀⢰⠟⠛⢧

⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠰⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠠⢆
⠀⠀⠀⠤⠴⣿⣿⡷⠶⠄⠀⠀⠀⠀⠀⠀⠴⡚⠘⣧⠌⠀⠀⠀⠀⠀⢰⣂⠒⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢤⣠⣦⣤⡲⠂
⠀⠀⠀⠀⠀⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠓⠘⠦⠀⠀⠀⠀⠀⠀⢈⣁⣴⢤⣈⠀⠀⠀⠀⠀⠀⠄⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡿⠻⡆⠄
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠛⠁⠀⠈⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⢀⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣷⢀⣀
⠀⠀⠀⠀⠐⠀⠀⡂⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠛⠁⠀⠉⠀⠀⠀⠀⠐⢀⠈⣤⡤⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⢷⣂⠐⠛⠃
⠀⠀⠀⠀⠈⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠨⢀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⢘⡭⠺⠗⡦
⠀⠀⠀⠀⠀⠀⠁⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠄⠀⠀⠰⠆⢀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡄
⠀⠀⠰⠄⢰⡇⣄⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠰⢊⣥⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣅⣄⣀⠀⠀⠀⠀⣤⣼⣿⣤⠄⠀⠀⣠⠞⠀⠀⠀⢀⡀⠀⠻⠀⢤⠄
⠀⠀⠀⠀⠀⢤⠐⡒⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡤⠤⠄⠀⠀⠀⠀⠈⠉⣼⡁⢸⣿⠀⠀⠀⠀⠀⢸⣿⢿⣷⠛⠛⠋⠁⠀⠀⠀⠀⠀⠠⠒⡀⠰⠁
⠀⠀⠀⣜⡤⠠⠉⠃⠸⠿⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠟⠳⢼⡀⠀⠀⠀⠀⠚⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠈⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠆⡐⠂⠀⠠⠒⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⢠⣿⣀⣀⠀⠀⡋⠀⠀⠀⠀⠀⠴⠄⠒⠀⠧⠄⡤⠀⠀⠀⠀⢠⡤⠴⠾⠿⠶⠖⠀⠀⠀⠀⠀⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣾⣿⣿⡿⠋
⠀⠀⠙⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⣛⠛⠛⣭⠄⠀⠀⠀⠀⠁⣓⢻⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠿⣿⣧
⠀⠀⠐⠋⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠁⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠂⠀⠀⡑⠀⣰⠀⠀⠀⠀⠀⠀⠀⢀⠊⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠈⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⡄⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠖⠀⠀⠀⠐⢛⣳⣼⡯⠶⠛⠁⠀⠀⠀⠄⠤⠀⠀⠀⢠
⠀⠀⠉⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢨⠠⠐⠀⢰⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠆⠀⡖⠀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⢠⡀⠀⠀⠀⡀⠀⠀⠀⣧⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⢠⠀⠐⠠⢠⠄⠀⠀⠀⠀⣰⠶⠂⠈⢡⡿⠄
⠀⠀⠠⡀⠊⡡⠊⢁⢀⠀⠀⠀⠀⠀⠀⠉⢺⣉⠀⢫⡴⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢀⠀⠀⠀⠀⠀⢀⣼⠇⡠⠢⣄⣣⡀
⠀⠀⠁⠀⠭⠀⠈⠙⠉⠠⠌⠀⠀⠀⠀⠀⣤⡴⠛⠳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⠀⠀⠁⠆⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⡆
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠈⠛⢿⣯⣭⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠈⢻⣿⣿⠀⢀⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠙⣿⣠⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢋⣿⢳⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠟⠛⠉⠁⠀⠀⢠⣾⣿⠀⠹⣿⣿⣿⣿⣷⣶⣤⣤⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⣦⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠉⠀⠀⠙⠷⣤⡀⠀⠀⠀⠙⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣴⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠈⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⠙⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠰⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠓⠀⠀⠀⠘⣿⣿⣷⣶⣾⣿⣿⠇⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⡶
⠀⠀⠀⠀⠀⢾⡷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⢿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠉⠙⠛⠛⢿⣿⣿⣿⠿⠿⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠈⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢀⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡆⠀⠀⠀⠀⢀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠉⠛⣿⣿⠿⠷⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣤⣤⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣀⠀⠀⠀⠀⠀⣠⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡏⠁⠀⠀⠀⠚⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣿⣿⣿⣿⣿⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠛⠻⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⣼⣿⡆⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⡀⠀⣸⣿⡆⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⢠⣿⣿⣿⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣿⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢹⣿⣿⣿⠏⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠀⠀⢻⣿⡿⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠋⠁⢻⣿⣿⠉⠙⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀
⠀⠀⠀⠀⢠⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

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

⣀⢠⠛⣄⣀⠀⠀⢀⡀⠰⠂⣀⡀⠀⠀⢀⠀⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⡀⠀⠀⠀⣀⣰⠆⣀⠀⠀⠀⢀⣀⣖
⠉⡆⣀⢰⠋⠀⠀⠀⢑⢀⠀⡌⠁⠀⠀⠈⣫⢟⣟⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⢂⡀⠄⠁⠀⠀⠀⢙⡧⢿⠈⠀⠀⠀⠈⣻⠀⡈
⠀⠉⠀⠉⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⣠⣰⢄⠀⠀⠀⠀⣤⡴⢧⣀⠀⠀⠀⢠⠀⠋⠠⡄⠀⠀⢠⡶⠊⠙⢶⡄⠀⠀⢀⣀⠿⣀⡄⠀⠀⠀⣄⠘⠃⣤⠀⠀⠀⡤⠤⠐⠤
⠀⠰⠽⠇⠀⠀⠀⠀⢰⠗⢮⡁⠀⠀⠀⠀⣠⠀⢰⠀⠀⠀⠀⢸⡠⢄⡇⠀⠀⠀⠀⡴⠀⢦⠀⠀⠀⠀⢨⡤⠰⡄⠀⠀⠀⠀⣣⠤⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣄
⠐⢖⣛⡲⠂⠀⠀⠀⢶⣿⣷⡶⠀⠀⠀⠠⡉⠀⢉⠄⠀⠀⠐⢄⠀⠀⠒⠂⠀⠀⠀⢤⠛⡦⠀⠀⠀⠀⢶⠊⠑⡶⠀⠀⠀⠲⡄⠁⠐
⠀⠘⠉⠃⠀⠀⠀⠀⠸⠛⠛⠇⠀⠀⠀⠀⠡⠒⠌⠀⠀⠀⠀⠠⠔⠀⠇⠀⠀⠀⠀⠜⠉⠣⠀⠀⠀⠀⠘⠓⠚⠇⠀⠀⠀⠀⠶⠀⠻

⠀⠀⠤⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢀⠶⡀⠀⠀⠀⠀⣤⡶⢶⣤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣤
⠘⢧⣀⡰⠃⠀⠀⠈⠃⠀⠀⠐⠁⠀⠀⠙⡄⠀⢠⠋⠀⠀⠸⣷⢀⡀⣾⠇⠀⠀⠘⢂⠀⡘⠁⠀⠀⠈⠡⢀⣴⣌⠁⠀⠀⠘⠃⠀⠙
⠀⠋⠉⠙⠀⠀⠀⠀⠘⠂⠐⠂⠀⠀⠀⠀⠋⠉⠙⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠐⠘⠋⠃⠀⠀⠀⠀⠋⠀⠙

⠀⠀⣀⠀⠀⠀⠀⠀⣀⡰⢆⣀⠀⠀⠀⢀⠠⠚⠄⡀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠠⠼⠁⠢⠄⠀⠀⢀⠀⠜⢠⢄⠀⠀⠀⢐⠋⠀⠙
⠀⠨⠛⡇⠀⠀⠀⠀⢈⡥⢬⡁⠀⠀⠀⠀⣂⣀⣰⠀⠀⠀⠀⢹⣿⢷⠀⠀⠀⠀⠙⠆⣀⠰⡏⠀⠀⠀⠙⣠⠐⡆⠀⠀⠀⠳⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠉
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢔⠚⠀⠓⡢⠀⠀⠀⢤⠞⠳⣤⠀⠀⠀⠠⣴⠿⣦⠄⠀⠀⠀⡒⠃⠘⢒⠀⠀⠀⠠⣄⠋⠤⠄⠀⠀⠠⣆⠋⠀⣰⠄⠀⠀⠠⣄⢇⠤
⠀⣧⠤⢌⠀⠀⠀⠀⠨⠗⠪⠇⠀⠀⠀⠀⠿⠛⠿⠀⠀⠀⠀⠸⠤⠤⠇⠀⠀⠀⠀⠴⠂⠧⠀⠀⠀⠀⢸⠴⠦⡅⠀⠀⠀⠀⠴⠊⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⢤⡀
⠀⡌⠀⢡⠀⠀⠀⢀⡀⣾⣷⠀⡀⠀⠀⠲⡈⠀⢈⠁⠀⠀⠀⠲⠈⢐⠖⠀⠀⠀⠐⢶⣿⡶⠂⠀⠀⠐⠂⠀⠀⠐⠂⠀⠀⠺⡍⣶⢩

⠀⠀⠀⠀⡀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⡈⠀⠀⠁⡐⠀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⣾⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣿⣷⠟⠃
⠀⠀⠀⢀⠀⠄⢈⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠋⠙⢂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠻⡆

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⢠⣤⣼⣿⣤⣄⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠠⢴⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠑⠤⣄
⠀⠀⠀⢹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠈⠁⠀⠙⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠙⠛

⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠀⠜⠂
⠀⠀⠙⢦⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠙⢿⣿⣿⡿⠋⠀⠀⠀⠣⠀⠀⠀⠀⠋⠀⠀⠀⠐⠀⠀⠀⠐
⠀⠀⠀⢠⠴⠂⠸⡀⠀⠀⠀⠀⣀⠤⠢⢸⡀⠀⠀⠀⠀⡼⠛⠻⢧⠀⠀⠀⠀⠀⡤⠄⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⢤⡶⠋⠈⠓⣢⠄⠀⠀⠄⠐⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⣷⣤⡤⠀⠀⠠⣄⠘⠁⠐⠒⠦
⠀⠀⠀⣹⢀⣀⢸⠁⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠈⠃⣀⠀⢆
⠀⠀⠀⠋⠁⠀⠙⠁⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠋⠁⠀⠙

⠀⠀⠀⠀⠐⠱⡀⠀⠀⠀⠀⠀⣀⢰⣧⢀⠀⠀⠀⠀⠀⣀⡼⢣⣀⡀⠀⠀⠀⢀⣠⠎⢠⡀⠀⠀⠀⠀⠀⢀⣼⣄
⠀⠀⠉⢢⠀⠀⢠⠎⠀⠀⠀⠙⢻⣃⢑⡻⠋⠀⠀⠀⠙⢦⠀⠀⣼⠋⠀⠀⠀⠑⡄⠀⠀⡰⠁⠀⠀⠀⠙⣿⣿⣿⡿⠃
⠀⠀⠀⠼⠖⠒⠾⠀⠀⠀⠀⠀⠼⠛⠘⠿⠀⠀⠀⠀⠀⠿⠚⠓⠾⠀⠀⠀⠀⠀⠄⠒⠂⠠⠀⠀⠀⠀⠀⠟⠋⠛⠧

⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠁⠀⠀⠀⠄⠀⠈⠀⠀⢀⡈⣻⣿⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠁⠀⠀⠀⠄⠀⠈⠁⠀⢀⡈⢻
⠉⠛⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡍⠙⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠛⠋⠉⠛⠃⠒⠀⠀⠀⠀⢀⠀⠀⠀⠁⠘⠉⡍⠙⠁⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠚
⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠁
⠀⠀⠀⠀⠀⣤⣾⣿⣷⣶⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢤⣶⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷⣶⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢤⣶⣿⣷⣶⠂
⠀⢀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣽⡿⣿⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣿⡿⣿⣧
⠀⠈⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠
⣦⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⣰⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣰⣧⠉
⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠂⠀⠲⣾
⠿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠿⠿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⣠⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣄⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⣠⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣄⣀
⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠻⣿⣿⣿⡟⠁⠀⠠
⡀⠀⠀⠀⠀⠀⠛⠋⠛⠷⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⠋⠛⠷⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠇
⡄⠀⠀⠙⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠙⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀
⣿⣤⣤⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣾⣷⣤⣤⠀⠀⠁⠀⠀⢀⡀⠀⠃⣀⣤⣾⣿⣤⣤⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣤⣤⠀⠀⠁⠀⠀⢀⡀⠀⠀⣀⣤
⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠁⠀⠀⠀⠄⠀⠈⠁⠀⢀⡈⢻⣿⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠁⠀⠀⠀⠄⠀⠈⠁⠀⢀⡈⢻
⠉⠛⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡍⠙⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠛⠋⠉⠛⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⡍⠙⠁⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠚
⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠁
⠀⠀⠀⠀⠀⣤⣾⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣷⣶⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷⣶⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢤⣶⣿⣷⣶⠂
⠀⢀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣿⡿⣿⣧
⠀⠈⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠
⣦⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⣰⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⣰⣧⠈
⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠲⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠲⣾
⠿⢿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⡿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠿⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⣀⣾⣆⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣄⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⣠⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣄⣀
⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠻⣿⣿⣿⡟⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠻⣿⣿⣿⡟⠁⠀⠠
⡀⠀⠀⠀⠀⠀⠛⠋⠛⠷⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⠋⠛⠷⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠇
⡄⠀⠀⠙⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡄⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⣀
⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣤⡄⠀⠀⠁⠀⠀⢀⡀⠀⠂⣀⣤⣾⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣤⣤⠀⠀⠁⠀⠀⢀⡀⠀⠀⣀⣤

⣆⠀⠀⠉⠁⠀⠀⣄⣀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠉⠀⠀⠀⠀⠀⠙⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢾⣶⠀⠀⢠⣤⠀⠀⠈
⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠠⣶⡆⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠿⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⣶⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⢠⡄⠀⠈⠁⠀⢠⡀⠀⠀⣀⣠⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠆⠀⠀⢶⠆⠀⠀⠀⠀⡀⠀⠐⠿⠇
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⠓⠀⠀⠀⠘⠻⠁⠀⠀⠀⣤⣦⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠚⠙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⠄⠀⠀⠛⠀⠀⠀⠿
⠀⠀⠘⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠰⣾⣞⠀⠀⠀⣤⠀⠀⢠⣤⠀⠀⠀⣀⣴⣀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⡏⠀⠀⢀⣠
⠁⠀⠀⠶⠄⠀⠈⠛⠃⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠸⠛⠇⠀⠀⣀⠀⠀⢠⡄⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿
⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⢠⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡀⠀⠀⠶
⠀⠀⠈⠀⠀⠀⠁⠀⠐⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠠⠆⠀⠘⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣤
⠀⠲⠀⠀⠰⠆⠀⠀⠈⠉⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡄⠀⠀⢀⡀⠀⠀⠀⢀⣷⣾⡀⠀⠀⢀⢀⠀⠀⠀⠈⠙⠁⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⣦⡆
⠀⠀⣶⡆⠀⠀⠁⠀⠀⠀⠁⠀⠀⠈⠀⢀⡀⠀⠀⠘⠁⠁⠀⠀⠸⢿⠂⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡤⠀⠀⠈⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣶⣆⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡄⠀⠀⠰⠆⠀⠀⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠾⠆⠀⠰⠆
⠀⠀⠀⠐⡾⠇⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣴⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠈
⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⡀⠀⠸⠛⠇⠀⠀⠈⠁⠀⢠⣤⠀⠀⠈⠁⠀⠘⠁⠀⠐⠻⠃
⠀⠠⡄⠀⠐⠗⠀⠀⠀⠀⠀⠰⠆⠀⢀⣶⡧⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⣦⡄⠀⠀⠉⠏⠁⠀⠀⠀⠀⡄⠀⠀⣀⠀⠀⣀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⠀⠀⠀⣤⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠉⠀⠀⠉
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠠⣴⣆
⠀⣀⢀⠀⠀⠀⣠⣆⡀⠀⠐⠆⠀⠀⠲⡿⠧⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠐⠙⠃
⠀⠺⠿⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢶⠄⠀⠀⠓⠀⠀⠀⠁⠀⢀⣀⠀⠀⠀⠀⢀⣶⡤⠀⠀⠀⠶⠀⠀⠀⠨⠿⡗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣠⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢠⣿⣧⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢠⣿⠿⣿⣆⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢠⣿⠏⠀⢻⣿⡄⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣶⣶⡶⠿⠿⠿⠛⢀⣿⡏⠀⠀⠀⢿⣿⡀⢿⣶⣶⣦⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠐⠶⢾⣿⡟⠛⠛⠛⣉⣉⣉⣥⣤⣤⣤⣶⣶⣶⡶⠿⠟⠀⠀⠀⠀⠈⣿⣷⣶⣤⣤⣌⣉⣉⣙⠛⠛⠛⠿⠿⠿⣶⣶⣶⣤⠄
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣈⠙⠛⠿⣿⣯⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣛⣿⣿⡿⠟⠋⢀⣀⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠉⠙⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⡿⠟⠋⣁⣠⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⡆⢰⣿⠇⠀⠀⠀⢀⡀⠀⠀⠀⢻⣿⡅⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢁⣿⡟⠀⠀⣠⣴⡿⢿⣦⣀⠀⠘⣿⣧⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⣼⣿⢁⣤⣾⠿⠋⣠⣄⡙⠿⣷⣄⣹⣿⡄⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢰⣿⣿⡿⠛⢁⡴⠟⠁⠈⠻⣦⡈⠻⣿⣿⣧⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢀⣿⠟⠉⣠⡶⠋⠀⠀⠀⠀⠀⠈⠻⣦⡀⠙⢿⡄⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠈⢁⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠁⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⡀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣹⣾⣿⣀⠀⠀⠈⠋⠀⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣀⠀⠀⠈⠋⠀⠀⠀⠀⠠⣶⠄
⠀⠈⠉⠻⠇⠉⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⣄⣴⡆⠀⠀⠀⠈⠉⠹⡇⠉⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⣄⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⠃⠀⠀⠀⠀⠀⢠⠿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⠃⠀⠀⠀⠀⠀⢠⠿⣿⠟⠃
⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠈
⠀⠀⠙⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⣇⡀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⣇⡀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⢸⣦⣴⠆⠀⠀⠀⠀⡼⠿⣏⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢸⣦⣴⠆⠀⠀⠀⠀⡼⠿⣏⠉⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠐⠛⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⡀
⠀⠀⣀⡀⠀⠀⠀⠀⠸⠿⡏⠀⠀⠀⣤⡄⠀⠀⠈⢻⣿⣿⡁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠸⠿⡏⠀⠀⠀⣤⡄⠀⠀⠈⢻⣿⣿⡁
⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣹⣿⣿⣀⠀⠀⠈⠋⠀⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣀⠀⠀⠈⠋⠀⠀⠀⠀⠠⣶⠄
⠀⠈⠉⠻⠇⠉⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⣄⣴⡆⠀⠀⠀⠈⠉⠻⡇⠉⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠠⣄⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⠃⠀⠀⠀⠀⠀⢠⠿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⠃⠀⠀⠀⠀⠀⢠⠿⣿⠟⠃
⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠈
⠀⠀⠙⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⣇⡀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⣇⡀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⢰⣦⣴⠆⠀⠀⠀⠀⡼⠿⣏⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢰⣦⣴⠆⠀⠀⠀⠀⠼⠿⣏⠉⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠘⠛⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⣀
⠀⠀⣀⡀⠀⠀⠀⠀⠸⠿⡏⠀⠀⠀⣤⡄⠀⠀⠈⢻⣿⣿⡁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠸⠿⡏⠀⠀⠀⣤⡄⠀⠀⠈⢻⣿⣿⡁
⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣰⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⣿⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣸⣿⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢠⣿⣿⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣾⣿⣿⠀⠀⠀⠈⣿⡀
⠈⠻⣿⣟⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢰⣿⣿⣿⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣿⠟
⠀⠀⠀⠙⠿⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠈⠛⢷⣤⡉⠳⣤⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣠⠖⢋⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠉⠳⣬⡳⣤⣀⠀⠀⠈⠿⠀⠀⠀⣀⠄⣠⣴⢟⡥⠋⣡⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠙⠲⢝⡓⠂⠁⣴⣆⠀⠉⠙⠛⠋⠁⢁⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠥⣀⠀⣠⣾⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠬⠑⢂⣴⣿⣿⣿⡿⣿⣿⣦⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠢⠍⣰⣿⣿⣿⠛⣡⣄⠻⢻⣿⣷⣄⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⡐⢠⣾⣿⠟⣃⣴⡿⠋⠙⢷⣦⣙⠻⣿⣦⡀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢐⣴⠟⣋⣴⡾⠛⠁⠀⠀⠀⠀⠈⠛⢷⣦⡙⠷⣄⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢚⣥⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣬⡁⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣼⣧
⠀⠀⠀⠀⠀⢀⢀⣄⣴⣿⣩⣤⣠⣠⣠⣠⣤⣤⣄⣄⣄⣤⣤⣠⣠⣠⣄⣄⣤⣠⣠⣠⣄⣝⣿⣆⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠁⠀⠀⠈⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡀
⠀⠀⠀⠀⠀⠀⣼⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢁
⠀⠘⠻⣭⣉⡉⠻⡇⠀⠉⣉⣩⠿⠋⠀⠈⠻⢍⡉⠉⠉⠃⠀⠉⠉⢉⡽⠛⠁⠀⠙⠿⣍⡉⢉⣹⣷⣈⡉⢉⣩⠝⠋
⠀⠀⠀⠈⠙⡟⢓⣥⡘⠻⡟⠁⠀⠀⠀⠀⠀⠀⠙⡷⠒⢀⠀⠒⠟⠋⠀⠀⠀⠀⠀⠀⠈⠻⠍⣿⣿⣟⠛⠋⠁
⠀⠀⠀⠀⡘⣠⣾⠿⢿⣆⢣⠀⠀⠀⠀⠀⠀⠀⢀⠃⣠⠵⠷⣄⠸⡀⠀⠀⠀⠀⠀⠀⠀⡜⣴⡿⠿⢿⣄⢁
⠀⠀⠀⢠⡟⣋⣀⣀⠀⠉⠻⣆⠀⠀⠀⠀⠀⢀⡼⣊⣁⣀⣀⣈⡓⣧⡀⠀⠀⠀⠀⠀⣰⡟⠋⣀⣀⠀⡙⢳⡄

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⣠⡠⠆⠀⠀⠀⠀⠀⣠⡀⠆⠀⠀⠀⠀⢀⣠⣆⣀⠀⠀⠀⠀⠀⣤⣤⡄
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⣈⠹⠉⠀⠀⠀⠀⠀⠈⡿⢿⡉⠀⠀⠀⠀⠀⠿⠿⠇


⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⡐⠀⠀⠀⠀⠀⣠⣄⠂⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢀⣶⡄
⠀⠀⠀⠀⠛⠀⣤⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠨⠹⠋⠄⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠉⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⣴⣦⠉⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠦⠈⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢀⣠⡀⠄⠀⠀⠀⢀⣤⡀⠃⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠦⡀
⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠈⠻⠉⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣛⣛⣛⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⠿⣇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠐⠁⠘⠁⠀⠘⠂
⠀⠁⡇⠀⡀⠀⠀⠀⠀⠤⣤⣤⣼⡶⠛⠉⠀⠀⠀⠀⠀⣴⡧⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠘
⠒⣾⣿⠋⠁⠀⠀⠀⢀⡀⢀⡼⠉⢻⡄⠐⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠐⢁⠈⠇⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⡞⠁⠈⠀⠀⠀⠀⢀⠈⠀⣿⠀⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⢀⡀⠈⢙⣿⣿⠛⠉
⠀⢀⠀⠀⠀⠰⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠹⠀⠈⠂
⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⡄⠀⠀⠀⠀⠀⠀⣆⡄⢀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡇⣈⡀⠀⠀⠀⠠⠶⠶⢶⣿⡞⠉⠀⠀⠀⠀⠀⠀⠠⡷
⠀⠀⠀⠀⠀⠈⡹⠻⠀⠀⠀⠀⠀⠀⠠⠄⢀⣽⠿⡟⠉⡀⠀⠀⠀⠠⠀⣠⠋⠈⢷⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⡄
⡏⢀⣁⠀⠀⠀⠀⠀⠀⠀⠠⡧⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀
⣟⠋⠁⠀⠀⠘⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠠⠀⠀⣩
⠹⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢋⢃⠀⠀⠀⠀⠀⠀⢀⠀⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣶⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⡄⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈
⠠⠆⠀⠀⠀⠀⢶⠀⠀⠀⠀⠰⢤⣤⣧⣤⠤⠀⠀⠀⠀⠀⠀⢀⡆⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠈⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⡴⠋⢿⠀⠤⠀⠀⠀⠀⠐⠶⣾⣷⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢸⠀⢐⣀
⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠄⠂⠀⠀⠀⠀⠀⢠⡄⠀⠀⠶⠶⢶⣿⡞⠋
⣸⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡷⠀⠀⠀⠀⠀⠠⠄⢠⠞⠈⠻⡄⠉⠀⠀⠀⠀⠀⢀
⠟⢯⠀⡀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠴⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢾
⠄⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⣰⡀⠀⠀⠀⠀⠀⢠⣤⣾⡤⠖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡀⠀⢸⠀⢀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠁⠀⠀⠀⠀⢀⠀⠴⠛⢧⠠⠀⠀⠀⠀⠀⠀⢺⠆⠀⠀⠀⣀⠀⣾⣠⡴⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿⣿⣿⣿⣿⣿⣿⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣽⠟⠋⠀⠈⠙⠿⣿⣻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠐
⠠⠀⠊⠀⠑⢒⠆⠀⠀⢲⡲⠓⠘⠒⡶⠂⠀⠀⠄⡄⠀⠃⢠⠀⠂⠀⠠⣤⣤⣿⣤⡤⠂⠀⢀⡀⠑⠀⠚⠀⠠
⠀⢠⠀⡀⠀⠁⠀⠀⠀⠀⡹⢀⣀⢫⠀⠀⠀⠀⠀⠀⠄⠠⠇⠀⠀⠀⠀⠀⣽⠿⣿⠀⠀⠀⠀⠀⠚⠀⠙
⠀⠘⠁⠀⠈⠃⠀⠀⠀⠐⠋⠁⠈⠙⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣼⡳⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠊⠁⠙⠂
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⠀⠠⡇⣀⣀⣀⠀⠀⠀⢀⡈⣀⢀⡀⠀⠀⠀⣀⣀⡠⢄⣀⡄⠀⠀⡀⠀⠈⠧⠀⣀
⠐⠒⠛⢲⡟⠛⠒⠂⠀⠈⠙⢓⡟⢯⡅⠀⠀⠀⠀⠐⢀⠐⠀⠀⠀⠀⠀⠈⡿⣿⣿⠀⠀⠀⠀⠀⠀⣀⠠⡞⠁
⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠰⠋⠁⠈⠧⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠘⠁⠀⠈⠓⠀⠀⠀⠀⠚⠁⠀⠃

⠀⠀⠀⠠⠀⠀⠠⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣤⡌⢲⣄
⠀⢀⠀⠀⠀⡀⠐⠀⠀⠒⠀⠀⡄⠀⠐⠂⠀⢀⣀⣀⣯⡤⠤⠤⠀⠀⠠⣤⡞⠙⣦⡤⠀⠀⠀⢮⡉⠀⠀⢨⡌
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡀⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⢸⠗⠛⠧⠀⠀⠀⠀⢘⢣⣴⣦⠜⡁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣁⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⢿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢤⣶⡄⠀⠀⠀⠋⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡄⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⡀
⢀⣤⠀⠀⠀⠀⠀⠈⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠐⣿⡇
⠸⠿⠁⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁
⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠏⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠀⠀⠀⣠⣄⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿
⣴⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢀⣀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠻⠇⠀⠀⠀⢸⣿⠂⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡏⠁⠀⠀⠀⠀⢶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠇⠀⠀⢰⡆⠀⠀⠀⢀⣤⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀
⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠠⣴⡦⠀⠀⠀⠠⣾⡦⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣧⣀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⢴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⢰⡦⠀⠀⠀⣸⣿⣿⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⣰⣦⡀
⣀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⣿⣿⠉
⡽⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡗⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠰⣾⣿⠦⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣴⡤⠀⠀⠀⠀⢤⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠀⠀⠀⢠⣦⡄
⠀⠀⠀⠀⠀⠹⢿⠃⠀⠀⡀⠀⠘⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠿⠏⠀⠀⠀⠀⡀
⠐⣾⡷⠀⠀⠀⠀⠀⠐⠛⠻⠀⠀⠀⠀⠰⣶⠀⠀⠀⠀⢰⡆⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣶⣷⠄
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠉⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣆⡀⠀⠀⠀⢲⣿⠄⠀⠀⠰⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀⣼⢿⡏⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠐⣾⣿⠶⠀⠀⠹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⣿⡿
⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠛⠃⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠇⠀⠀⠀⠉⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⢀⡀
⠀⠀⣤⣼⣧⣀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⢻⣿⡿⠂⠀⠀⠀⠀⢀⠀⠀⣴⣤
⠀⠀⣼⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠠⣴⣦⠀⠀⠀⢀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⢸⣿⠂⠀⠘⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⢘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢸⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢾⣿⡷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣷⣆⡀
⠀⠀⠀⠀⠀⣴⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢸⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡿⠏⠁
⠀⠀⠀⠀⠀⠚⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⣦⣾⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠂
⠀⠀⠀⠀⠀⠉⠙⣻⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠟⠍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠂⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠐⢿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣀⣸⣿⣿⣿⣿⣿⣿⣿⣯⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⡀⠀⠀⠂⠈⠀⡀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠐⢻⣳⡖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠁⠀⣸⡄⠀⠀⠀⠀⠲⠤⠤⡄⠂
⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠆⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢨⣽⣷⡟⠁⢀⣄⠀⠒⠀⠂
⠀⠀⢀⠀⠀⠀⢠⠀⢀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⢶⣻⠶⠂⠀⠀⠀⠀⠀⠀⢀⣶⠀⠈⠁⠀⠘⠉⠈⠳⠀⠘⠉
⠀⠀⠀⢀⢆⠀⠀⠀⠈⠇⠾⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠚⠉⠃⠀⠀⠀⠀⠠⣤⠤⠜⠘⠦⠤⣤
⠀⠐⢖⡋⠈⢒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠀⠈⢳⠀⠀⠠⡞⠁⠀⠐⠇⢀⣄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢸⠤⠢⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡾⠖⠉⠲⢧⠀⠀⠰⢶⣾⣿⣶⠶
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡿⠻⣧⠀⠀⠀⡀
⠀⢁⠀⠐⠁⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠶⣿⣿⣿⣧⣶⣶⣷⠆⠀⠈⠿⠏⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⠀⠀⠈⣀⣀⡀⣷⠀⠀⡀
⠀⠀⠀⢀⣀⡤⢋⣾⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈⣿⣿⣿⣿⣟⠁⠀⠀⠀⢠⠀⠀⠙⢤⡀⠀⠀⠉⠙⠁⠀⢀⠀⠀⠀⣩⡵⣗⠲⠋
⠀⠀⠙⢟⣉⣴⠋⣡⣾⣷⡟⠁⠀⠀⠀⠀⠀⠀⠃⣠⠀⢸⠿⠛⠙⠻⢿⠀⠀⠰⢶⣿⣷⠖⠀⢀⣠⠄⠀⢣⠀⠀⠈⡵⠎⠀⠀⠟⠀⠙⠦
⠀⢠⡄⠀⠝⣡⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠻⠆⠀⠈⠡⠄⠀⠈⢀⣤⠀⠀⠀⢀⡠⢄⡀⠀⠠⠄⡄
⠀⠀⠀⠀⠽⠙⠉⠙⠹⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⠀⠀⠀⢰⠆⠀⠀⠀⠀⡴⠞⠉⠷⢤⡤⠈⠷⠾⠁⣀⣄⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠾⠂⠀⠀⠀⠀⠀⠀⠈⠟⠯⠀⠐⢟⠋⠈⣛⠗⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⡉⠈⠉⠃
⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠏⠈⢧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢸⠥⠦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⣀⣤⣤⣿⣷⣤⣤⡄⠀⢀⠀⠘⢯⡁⠠⣴⣧⡄⢀⡤⠋⠀⣀⠀⠀⣀⣀⣠⣿⡆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢠⠳⡀
⠀⠈⠙⣿⣿⣿⡿⠋⠀⠄⠀⠀⡤⠀⢹⠀⠛⠙⠂⢸⠀⠠⣤⣿⣤⠄⠈⠙⢟⣙⣭⡞⠁⠀⠀⠐⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠘⢯⠁⠀⢠⠜⠁
⠀⠀⢰⠟⠋⠛⢿⡀⠀⠠⠀⠠⠀⠀⣿⠔⠊⠉⠳⢼⡄⠀⠼⠛⠧⠀⠀⠀⠟⠉⠛⠧⠈⠀⠀⠀⠙⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠂⢬⡄

⠀⠀⠤⣿⠧⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠟⠂
⢀⠀⠀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⢾⠆⠀⠀⠀⠀⠀⣼⣴⣀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠙⠛⠀⠀⠀⠄⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⠆⠀⠀⠀⠀⠀⠀⠀⣶⣷⠅⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠁⠀⠀⠀⢀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⣰⣴⣆⠀⠀⠀⠀⢀⣾⣿⠂⠀⠀⠀⠀⠼⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠻⠁⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⡀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛
⠀⢀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣇⠀⠀⠀⠀⠀⠠⣶⣔⡀⠀⠀⠀⠀⠀⢀⣀
⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⡄⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⠹⠻⠀⠀⠀⠀⠀⢐⢿⣿⠂
⣿⠓⠀⠀⠀⠀⠀⠠⠀⠀⠜⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣴⣤⠂⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠀⠀⣠⣦⣆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠟⠍⠀⠀⠀⠀⠘⢻⠛⠀⠀⢀⠀⠀⠀⠀⢰⡧
⠀⠀⠀⠀⠊⠛⠃⠀⠀⡀⠀⠀⠘⠿
⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢤⣦⡆⠀⠀⠀⠀⠀⠀⠀⣠
⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⣂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠚⠟⠏⠀⠀⠀⠀⠁⠀⠀⠊
⠀⠀⢀⡀⡀⠀⠐⠀⠀⠁⢀⢀⣤⠀⠀⠂⠀⠀⠀⠻⠋⠂⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⣄⡠

⠀⠀⢀⠀⠀⡀⠀⢀⡀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⡀⠀⠀⠈⠁⠠⠄⠈⠈⢀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⢾⣷⡶⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⢀⣯⠀⠀⠀⠀⠀⠠⣤⣭⣤⠄
⠀⠙⠄⠀⠀⠀⠈⠀⠈⠀⢠⠄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠐⣻⢿⣶⡷⠋⠀⡀⠀⠤⠀⠦
⠀⠀⠀⠀⡀⢀⠀⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⣄⣾⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠺⠀⢠⠿⠋⠻⣇⠀⠸⠛
⠀⠀⠐⠈⢀⠀⠀⠁⠀⢙⣉⣗⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡸⠓⢧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠹⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⣀⡰⠋⢆⣀⡀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠻⣍⠁⠀⠈⣩⠟⠁⠀⣠⡄⢀⠀⠀⠀⠀⠀⡀⠀⢂
⠀⠀⢉⡆⣀⠰⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡈⠀⠀⠀⣼⣀⡤⣄⢧⠀⠀⠀⣀⣀⣸⣇⣀⣀
⠀⠀⠘⠋⠉⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢠⡆⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⠛⠀⠀⠀⠉⢻⣿⣿⡟⠉
⠀⣀⠀⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⡶⢀⣀⣀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠿⠋⠙⠷⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⢠⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠘⠋⠃⠀⣀⠀⠀⠏⠀⢀⣀⣀⠀⠀⠀⠀⠠⠤⢴⣄⣿⠂⣀⡤
⠀⠀⣀⣀⣠⣴⢋⣼⡿⣤⣤⢀⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⣦⠀⠀⠈⠲⠄⠀⠀⠀⠀⠁⠀⣀⣄⡀⠀⠀⣤⠞⣯⡙⠋
⠀⠀⠈⠹⣡⣰⡟⢁⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢁⡴⠀⡼⠟⠋⠉⠛⠿⡆⠀⠀⠻⣿⣿⣷⠟⠀⢠⣤⠆⠀⢘⡄⠀⠀⠹⠾⠇⠀⠀⠏⠀⠉⠳⠄
⠀⠠⣦⠀⠸⣋⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡠⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⠻⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⡨⠛⠋⠉⠋⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣆⣀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⡅⠀⢶⣖⠃⠈⢓⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢉⠐
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣽⡠⢄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈
⠀⠀⠀⣀⣼⣿⣄⣀⢁⠀⠀⠀⠀⠘⢏⠉⠉⣁⣴⣀⡉⠉⣩⠖⠀⠀⠀⠀⠐⠀⠀⣼⣧⠀⠀⠉⠀⠀⠉⠀⢀⠀⠀⠀⠰⠖⠀⠀⠀⠂⠀⠀⢀⠶⡀
⠀⠙⠿⣿⣿⣿⣿⡿⠋⢁⠀⠘⠀⢀⠀⢳⡄⠸⠿⡯⠀⡞⠁⣀⣀⣿⣀⣀⠈⠻⣿⢟⡏⣂⠔⠀⠀⠀⠠⣴⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠰⡒⠊⠀⠙⢒⠶
⠀⠀⠀⣿⡿⠿⣿⡇⠀⠈⠀⠀⢀⠉⠀⢸⣁⡠⠴⢦⣀⣷⠀⠈⣿⣿⣟⠁⠀⠀⣰⡿⠿⣿⡀⠠⠀⠀⠀⠼⠟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⡐⡇
⠀⠀⠘⠉⠀⠀⠈⠙⠀⠀⠈⠀⠈⠀⠀⠘⠉⠀⠀⠀⠈⠙⠀⠀⠁⠀⠉⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣢⣧⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀
⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡏⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠟
⠀⠀⠀⠀⠘⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢨⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⣶⡦⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠛⡟⠃⠀⠀⠀⠀⠀⠀⠀⣀⣷⡀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣽⣿⣿⣿⣿⣿⣿⣅⣀⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣅⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⠑⠄⠀⠐⡀⠁⠁⡀⠀⢀⡄⠀⠀⠾⣿⠇⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢰⣾⣷⡤
⠀⠁⠀⠀⠀⢀⠀⠀⠌⠁⢄⠀⠈⠃⠀⠀⠘⠀⠂⠚⠀⢀⡾⢻⠀⠀⠀⠀⠀⠀⠐⠄⠀⠠⠀⠀⠀⠠⠴⠶⣿⣿⠋⠉⠀⠘⠉⠻
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠈⠖⠂⠠⠀⠂⠀⠀⠲⠒⢒⡾⠳⠺⣷⣤⣤⠄⠀⠀⠀⠐⠂⠀⠁⠀⠀⡀⠀⠀⡏⠉⢇⠀⠀⢀⠄
⠀⢠⣤⡄⠀⠄⠀⠠⠀⠓⠀⠈⡠⠚⠀⠀⠀⠀⠀⠀⡟⢅⣀⣠⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⡎⣧⣄⠀⠀⠀⠀⠀⠰⡋⠀⢁⡆
⠀⠰⠻⡟⠂⠀⠈⠂⠀⠀⡂⠐⢈⢢⠀⠀⡀⠀⠀⣼⡴⠞⠙⠳⣼⡇⠀⠠⣤⡴⠀⠀⠀⠀⠰⠛⠲⣏⠀⠀⠠⠦⠁⠀⠈⠣⠴⠶⠁
⠀⠀⢀⣀⠀⠀⠀⢀⠩⠊⠀⠁⠊⠀⠀⢸⣿⣄⣀⣥⠀⠀⠀⠀⠈⡙⠀⠀⢀⠵⠀⠀⠁⠀⠰⠄⣦⠄⠀⠀⠀⠀⣀⣬⡀⠀⠀⢀⡀
⠀⢀⡏⢸⣇⡖⡆⡄⢀⠀⠀⠀⠀⠠⣶⣿⣟⣿⣿⡁⠀⣈⣿⣒⣾⣅⡀⠈⠀⠀⠁⠀⢠⣾⠄⢀⡀⣀⣀⡀⣠⣼⣿⠿⡇⠀⠶⠂⠉
⠀⠙⠃⠏⣼⡞⡼⣧⢧⡏⠀⠀⠀⠀⠀⢸⡿⠛⠛⠛⠂⠀⠈⠟⠁⠀⠀⣸⢣⡀⠀⠀⠀⠀⠀⠀⠙⣿⠓⡸⠟⣩⣶⣮⠷⣤⣀⠘⠁
⠀⠊⠔⡀⠀⠈⠁⠃⠏⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠣⠈⠹⢚⠞⠀⢄⠰⡀⠀⠈⡦⢴⣻⣿⣿⣿⣯⢷⣾⣷⠦
⠀⠀⢠⠀⠈⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠈⢳⠁⣠⣀⢻⠀⠀⠚⠲⠏⢀⣾⣾⣿⣿⠿⣛⣭⡾⠉⠁⡀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⢾⠀⠀⠀⠀⢀⣨⣿⣿⣧⡀⢨⠟⠁⠈⠙⠃⠀⠀⠀⢠⠚⠉⠀⠉⠀⠻⣿⣿⡇⠀⣒⠅
⠀⠀⠀⠀⠐⠀⠀⣷⣤⣶⠀⠀⠀⡃⠀⠀⡹⠂⠀⠀⠉⠉⠈⣿⠀⠀⠀⢀⣄⠀⠀⠀⡀⡀⠀⠀⠀⢠⡀⠀⠀⠀⠈⢯⡅⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠾⢿⣿⠿⠦⠄⠀⠁⠉⠲⠁⠀⢀⠆⠀⠀⠀⠁⣀⡴⡀⢷⡹⡇⠀⠀⠀⠀⠀⠀⠀⡀⢔⣲⡍⠀⠀⠀⢡⠎⠀⠙⠁
⠀⠀⠀⠀⡀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠔⣰⠖⠀⠀⠙⣦⠘⠘⠁⠀⠀⠀⠀⠀⡀⠀⠈⠁⠈⡌⠀⠁⠀⡤⢿⡢⠴⢦⠆
⠀⠀⠀⠀⣠⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⡆⠲⠠⠠⠄⠀⠀⠀⣀⣀⣄⠈⠁
⠀⢦⡀⠔⢹⡀⠀⠀⠀⠀⠴⠇⠈⠂⠀⣤⡀⠀⠀⠀⣀⠀⠠⣴⣦⡀⠀⠀⠄⢈⠀⢀⣀⠀⠐⠃⠄⠀⠀⢨⣿⣿⠓
⠀⠀⠇⠀⢀⠌⠛⠀⠀⠐⠀⠀⠀⠀⠀⢀⠉⠳⠄⢀⡏⠀⠀⠺⣏⣃⠀⢀⡚⠁⠁⠈⠉⠀⣀⠐⠀⠂⠀⡀⠀⠙
⠀⠀⠀⠉⠢⡄⠀⠀⡄⢀⡀⠀⠀⠀⢀⡠⠃⠀⠀⠈⠢⣄⠀⠀⠈⢿⠀⡀⠀⠴⠀⡆⠀⠀⢌⠃⠀⠀⠀⡉⢦⡀⠀⠀⠀⠀⡀
⠀⢀⣄⢰⡄⢠⡄⠀⠃⠞⣠⡄⠀⠀⠾⠖⠒⡄⡠⠀⠂⠈⠃⠀⢀⣀⣠⣷⣀⠀⠀⠀⠘⠀⠀⠀⢀⣤⠐⡟⠉⢙⡄⠀⢀⡴⣓⢲⠆
⠀⢠⣈⣳⠉⢸⣿⣦⣀⣈⡥⠀⠀⠀⠀⠀⠀⢱⡷⠀⠀⠀⠀⠀⠀⣹⡿⡑⡉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⡇⠰⠦⠀⢄⠀⠹⠟⠉⠂
⠀⠀⠀⣤⣴⣿⣿⣿⣿⡿⠡⣴⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣰⠂⠈
⠀⢀⣀⡤⠉⢻⣿⠿⠹⣧⠐⢭⠙⠀⠀⠀⠃⠀⠀⠀⠀⡄⠀⠀⠰⡋⢸⢃⣤⠐⡄⠀⠉⠳⣠⢤⣉⠀⠀⠀⠀⠀⠀⠀⠠⣤⡴⣇
⠀⠈⠡⡾⠁⠘⠃⡄⢦⡀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢙⠮⠌⠁⠁⠁⠀⠀⠘⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠷⢾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⡗⠃⠀⣀⣠⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢀⣀⣤⡴⠀⢲⣦⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇
⠀⠙⢠⡄⠀⠈⠉⢻⣿⠿⠛⠛⠀⠀⠳⣶⣶⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⢻⣿⣷⣤⡀⠀⠀⢠⣾⣿⣿⠃
⠀⠀⢸⣿⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣶⣿⣿⣿⡏
⣀⣀⣿⣿⣇⣠⣴⡾⠀⠀⠀⠀⡄⠀⠀⠀⢸⣿⠟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣤⣤
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢲⣼⣧⣤⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⠛⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⠿⠛⠉
⠟⠋⠁⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣾⣷⡖⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁










⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠴⢿⡿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⣀⣠
⠀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣤⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠛⢻⡟⠧⠀⠀⢀⣼⣿⣿⣿⣿⣿
⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣴⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⡾⠟⠋⢹⣿⣿⠉
⠀⠆⣸⣿⣿⣿⡿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈⣿⡇
⠀⢠⣿⣿⡿⠃⠀⠀⠈⠛⢿⣿⣧⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠿⠿⢦⠀⠀⣠⣤⣶⣿⣧⣀⡀⠀⠘⠃⣄
⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠻⠧⠀⠺⠛⠉⠁⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠋⠉⠀⢠⢴⣿

⢀⣼⣿⣿⣷⠦⠀⠀⠀⠀⠀⢈⡷⠒⠛⠀⢠⡼⠧⣤⠀⠀⠠⠾⣿⣿⡄⠀⠀⠀⠀⠀⠠⣤⡿⣶⠂⠀⠀⠾⣿⣿
⠀⠀⠀⠹⡇⠀⢀⣀⢀⢴⠀⠀⠀⠀⠀⠀⠀⢹⠴⠷⠀⠀⠀⠀⠘⠃⠀⠀⣰⡄⠀⠀⠀⠀⡿⠻⠆⠀⠀⠀⠻⠉⠃
⠀⠀⠀⠀⠀⠀⠀⡳⠀⠈⣳⡦⠀⠀⢠⡄⠀⠀⠀⠀⠀⢠⡆⠀⠀⠠⣤⠴⠋⠈⢘⡽⠂⠀⠀⠀⠀⠀⠀⠀⡦⠲⡀
⠀⠀⣧⣤⡴⠀⠚⠛⠙⣼⠁⠀⠐⢶⣿⣿⠟⠁⠀⠈⢻⣿⣿⡛⠀⠀⠀⢹⢀⡤⠬⠷⠀⠀⣄⣀⣼⠃⠀⠰⠗⢤⠟
⠰⢿⣏⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠏⠙⠇⠀⠀⠀⠋⠁⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣨⣿⣿⠟⠂⠀⠀⢀
⠀⠸⡟⠉⠃⢠⣤⣴⣆⡀⢀⣄⣀⣴⡀⠀⠀⢤⣷⣄⡤⠀⠀⢀⣠⣄⡀⠀⢀⣄⣴⣀⡀⠈⠉⠀⠙⠀⠀⠀⠰⣾⡶
⠀⢀⠀⠀⠀⠀⡿⠷⡏⠀⠀⡇⠉⠘⢅⡀⠀⠀⣽⠿⡄⠀⠀⠈⡷⢿⡀⠀⠀⢹⡿⣏⠁⠀⠀⠀⠀⢠⡆⠀⠀⠋⠙
⣤⣼⣧⣤⣀⡀⠀⠀⠀⠀⣞⠤⡄⣴⠛⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠶⣶⢿⣷⠖
⠉⣿⢾⣷⠋⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⣀⢀⡄⠀⠀⢀⣸⣷⣾⡀⠀⠀⠀⢀⣀⣦⣀⠀⠀⠀⠴⠟⠛⠿⠀⠀⢠⡄
⠀⠛⠁⠈⠁⠀⢀⣿⣾⡁⠀⠀⠀⠀⠠⠮⣀⠷⠀⠀⠀⠈⠏⠉⠁⢀⠀⠀⢈⣿⣾⠏⠀⠀⢀⠀⠀⠀⠀⠀⢹⢿⡗
⠀⣄⠀⣀⠀⠀⠉⢻⠋⠉⠀⠀⡀⠀⠀⠀⠁⢀⡀⢀⡀⠀⠀⣦⣤⣻⡄⠀⠈⠀⠈⠁⠀⣠⠞⠙⡟⠀⠀⢀
⠠⠾⣿⣿⡄⠀⠀⠀⠀⠀⠠⣤⡿⣶⠆⠀⠐⠾⣿⣿⠁⠀⢀⣼⣿⣿⣷⠦⠀⠀⠀⠀⠀⠈⡷⠒⠛⠀⢠⡼⠧⢤
⠀⠀⠈⠃⠀⠀⣰⣄⠀⠀⠀⠀⡿⠻⠆⠀⠀⠀⠻⠉⠃⠀⠀⠀⠀⠹⡇⠀⢀⡀⢀⢴⠀⠀⠀⠀⠀⠀⠀⢽⠴⠷
⡆⠀⠀⠠⣤⠶⠛⠈⢛⡽⠂⠀⠀⠀⠀⠀⠀⠀⡦⠲⡂⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠈⣳⡦⠀⠀⢠⡄
⣿⡛⠀⠀⠀⢹⢀⡤⠬⠷⠀⠀⣄⣀⣼⠃⠀⠰⠗⢤⠟⠃⠀⠀⣧⣠⡴⠀⠚⠛⠙⣼⠁⠀⠐⢶⣿⣿⠟⠁⠀⠈⢻
⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣨⣿⣿⠟⠂⠀⠀⢀⠀⠀⠰⢿⣏⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠙⠇⠀⠀⠀⠋
⠀⢀⣠⣄⡀⠀⢀⣀⣴⣀⡀⠈⠉⠀⠙⠀⠀⠀⠰⣾⣶⠂⠀⠸⡟⠉⠃⢠⣤⣴⣆⡀⢀⣄⣀⣴⡀⠀⠀⢤⣷⣄⡤
⠀⠈⡿⢿⡀⠀⠀⢹⡿⣏⠁⠀⠀⠀⠀⢠⡆⠀⠀⠋⠙⠀⠀⢀⠀⠀⠀⠀⡿⠷⡏⠀⠀⡇⠉⠘⢄⡀⠀⠀⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠶⣶⣿⣷⠖⠀⠀⠀⢠⣤⣼⣧⣤⣀⡀⠀⠀⠀⠀⣎⠤⡄⣴⠛⠉
⣷⣾⡀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠴⠟⠛⠿⠀⠀⢠⡄⠀⠉⣿⢾⣷⠋⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⣀⢀⡄⠀⠀⢀
⠏⠉⠁⢀⠀⠀⢈⣿⣾⠋⠀⠀⢀⠀⠀⠀⠀⠀⢹⢿⠗⠀⠀⠛⠁⠈⠁⠀⢀⣿⣾⡁⠀⠀⠀⠀⠠⠦⡀⠷
⠀⣤⣤⣻⡄⠀⠈⠀⠈⠁⠀⣠⠎⠑⡏⠀⠀⢀⠀⠀⠀⠀⠀⣄⢀⣀⠀⠀⠉⢹⠋⠉⠀⠀⡀⠀⠀⠀⠁⢀⡀⢀⡀

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

⠀⠀⠰⠆⠀⠀⢀⠠⠄⠀⠀⢀⠀⠀⠀⠀⠠⡀⢃⡤⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⡄⠐⠀⢀⠄
⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠄⡀⠂⢁⠀⠀⢀⢄⢠⠜⠂⠀⠀⠀⠀⠁⠸⠀⠀⠠⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈
⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠐⢂⠈⠅⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂
⠀⠈⠐⠓⠀⠄⢀⠑⢠⣠⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠀⠀⠀⠀⣀⠜⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠦⡟⢱⠦⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠠⠐⠀⠀⠄⢐⢑⠠
⠀⠀⢀⡤⠠⡀⠀⠀⠀⠀⠇⠀⠐⠒⠁⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⢨⠄⡠⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⢄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⡸⡽⢖⠀⠀⠀⢠⠻⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢢⠴⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠉⠙⠀⠉⠀⠀⠐⠃
⠀⠀⢀⠀⠀⢀⣀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⢀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⡀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠢⠀⠀⠠⠀⠀⠉⠁⠀⢨⠍⠠⠀⠀⠀⠀⢠⠊⠀⠀⢠⡀⠑⡒⠀⠀⠀⠀⠀⠀⠐⣁⣈⠇
⠀⠀⠀⠐⠀⠀⡄⠀⠐⠒⢠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠀⠃
⠀⠰⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡴⢀⡀⠀⠀⠀⢀⠂⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠰⠄⢀⠄⠁⠀⠀⢀⠾⢄⠀⠀⠀⢨⠐⠀⠀⢁⠂⠀⠀⠀⡀⠀⠀⢠⠀⠀⠠⣷⡄⠀⠀⠀⠐⠀⢈⠑⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠑⢮⠞⠁⠀⠀⠐⠨⢔⡨⠐⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠰⠊⠀⠈
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⢀⠀⡀
⠀⠀⠀⢣⡀⠀⠼⠀⠀⢄⠀⠀⢇⡄⠀⠀⠀⠀⠀⠀⠀⢀⠓⢄⢤⠄⠀⠀⠀⠀⠀⠉⠀⠀⡀⢈⡑⢞⠃⠂⠅⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠡⠐⣈⣐⢢⠀⠀⠀⠀⠀⠲⢭⡀⢀⢺⡀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠠⠩⠅⠄⠍⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢊⠀⢈⠇⠄⠉⠁⠀⠀⠀⠀⠗⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠈⠂
⠀⠀⠀⠄⠁⠄⠀⠀⠐⠂⠀⠒⠩⠁⠈⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⡿⠻⠁⠀⠀⠀⠀⠀⠆⠑

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇
⡀⠀⠀⠀⠐⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⡧⠀⠀⢠⣴⡀⠀⠀⠀⠸⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢠
⠃⠀⠀⣀⡀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⣠⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠛⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠁⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⢴⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠶⠆⠀⠀⣼⣶
⡀⠀⠀⠺⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⣠⡀⠀⠀⡺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣴⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⡀
⣴⠄⠀⠀⣾⣷⠀⠀⠀⠀⠀⠈⠋⠀⠀⠘⠻⠁⠀⠀⢠⣦⠀⠀⠐⣾⡖⠀⠀⠀⠀⠀⠙⠁⠀⠀⠚⠻⠁
⠈⠀⠀⠀⠀⠀⠀⠀⣠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣰⣤
⠐⠷⠀⠀⠀⠀⠀⠀⠘⠙⠂⠀⣼⡦⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠛⠙⠀⠠⣶⡄
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠁⠁⠀⢀⣄⠀⠀⠀⣀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠁⠁⠀⣠⡀
⡇⠀⠀⠀⠀⠀⠀⠀⡶⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠽
⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⢾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣦⠄⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣤⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠚⠙⠃⠀⢠⡀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠀⠀⣠⡀⠀⠀⣠⣄
⠀⠀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠛⠄⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠟⠳
⠇⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠺⠂⠀⠀⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢀⠀⠀⠀⣰⣤⠀⠀⠀⠀⠀⠠⡦⠀⠀⢸⢿⠖⠀⠀⠀⣀⠀⠀⢀⣴⡤⠀⠀⠀⠀⠀⢠⡦⠀⠀⡽⣿⠂
⠛⠁⠀⠀⠋⠙⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠋⠃⠀⠀⢀⡀
⣀⣤⣀⣀⣀⣀⣀⣀⣺⣿⣁⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣤⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣄⠀⠀⠀⠀⢠⣤
⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢠⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⡀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠘⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠀⣤⣦⣀
⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣽⣿⡟⠋⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣷⣄⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣧⣀⠀⠀⠀⠀⢠⣠
⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣶⣦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢰⣶⣦⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠛⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠐⠿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣼⣁⣧⣀⣀⣄
⠀⠀⠀⠀⠀⠐⢶⣖⣮⠟⠃⠀⠛⠛⣻⣿⠖⠀⠀⠀⠀⠀⠀⠶⣚⡿⣛⠵⣫⣵⠟⣫⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢰⠇⠀⠸⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠉⢳⢑⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣵⡿⣋⠴⣫⢖⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣯⣀⣠⠞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣐⣶⣤⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⢞⣵⣎⡴⣫⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡴⠛⠳⣄⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠈⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠔⠋⠁⠀⠙⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⠙⠷


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠹⡄
⠀⠀⠀⠀⠀⢀⣀⣤⠤⠞⢡⣷⠙⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣌⠀⣿⡷⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⢳⢧⠳⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠈⠳⣄⠚⢷⣿⣿⣿⠿⣢⠖⠁⠀⠀⠀⠀⠀⠀⠈⠫⡉⠛⢛⣷⣿⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠑⢦⡐⠾⡍⢈⡽⢃⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣼⠟⠙⢿⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡟⠁⣿⣄⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⠟⠛⠧⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠖⠒⠦⣄⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⠠⠔⠻⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡴⠋⠉⠓⠦⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⡼⣆
⠀⠀⠀⠀⠀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠲⡘⠀⠁⠀⠀⠀⠈⠁⠁⢂⠒⠀⠀⠀⠀⠀⠀⠶⣞⠛⠉⠁⠈⡄⠈⠩⠋⣿⠗
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆⢂⠌⡀⠀⠠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣐⡀⠁⡉⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠑⠂⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠋⠉⠉⠓⠶⠷

⠀⢤⣄⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠤⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⡄⠀⠠⠀⠀⠀⡀
⠀⠉⠋⠀⠀⢀⣄⠀⠀⠀⢠⣴⡀⠀⠈⠛⠁⠀⠀⣤⠀⠀⠀⠀⣴⡄⠀⠀⠙⠉⠀⠀⣠⡀⠀⠀⠀⣤⣦
⠀⣤⠀⠀⡀⠈⠁⠀⠤⠀⠈⠉⠀⠀⢠⡄⠀⢀⠀⠉⠀⠠⠀⠈⠈⠀⠀⠀⡄⠀⠀⡀⠈⠁⠀⠄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⣤⣆⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠒
⠀⠠⣷⠇⠀⠀⠉⠁⠀⠀⠀⠀⠂⠀⠠⢾⠮⠀⠀⠈⠉⠀⠠⠀⠀⠐⠀⠀⠼⡿⠀⠀⠀⠉⠁⠀⠄
⠀⠀⠀⠀⠠⣦⠀⠀⡀⠀⠠⣶⡄⠀⠀⠀⠀⠀⣴⠄⠀⣀⠀⠀⣴⡦⠀⠀⠀⠀⠀⢠⡄⠀⢀⠀⠀⢴⣦
⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈
⠀⣲⡦⠀⠀⠃⠀⠀⠠⠀⠀⠀⠀⠀⢰⣾⠄⠀⠛⠀⠀⠠⠄⠀⠀⠁⠀⢀⣶⡆⠀⠘⠀⠀⠀⠆⠀⠀⠈
⠀⠀⠁⠀⠀⠰⠦⠀⠀⠀⠸⣿⠂⠀⠀⠈⠀⠀⠀⠶⠀⠀⠀⠠⢿⠆⠀⠀⠈⠀⠀⠀⠴⠆⠀⠀⠀⠿⡷
⠀⠲⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠰⠆⠀⠠⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠖⠀⠀⠄⠀⠀⠀⠃⠀⢀
⠀⠀⣀⡀⠀⠀⣲⡷⠀⠀⠈⠀⠀⠀⠀⢀⣀⠀⠀⢰⣾⠄⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠐⣾⡆⠀⠀⠈
⠀⠘⠟⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠓⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠘⠟⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣀⠀⠀⠐⠷⠀⠀⠄⠀⠐⡿⠇⠀⢀⠀⠀⠀⠾⠂⠀⠤⠀⠀⠿⠏⠀⠀⡄⠀⠀⠸⠇⠀⠠⠄⠀⢺⠿
⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠺⠗⠀⠀⠀⡀⠀⠘⠀⢀⣀⠀⠀⠘⠿⠂⠀⠀⠀⠀⠘⠃⠀⣀⡀⠀⠀⠿⠓⠀⠀⠀⠀⠀⠃⠀⣀⡄
⠀⣀⠀⠀⠀⠘⠋⠀⣀⠀⠘⠛⠁⠀⢀⠀⠀⠀⠀⠛⠀⢀⠀⠐⠻⠃⠀⠀⡀⠀⠀⠀⠙⠃⠀⡀⠀⠛⠏
⠀⠉⠀⠀⠁⠀⠀⡀⠀⠀⢠⠄⠀⠀⠈⠁⠀⠈⠀⠀⣀⠀⠀⠀⡄⠀⠀⠀⠉⠀⠀⠁⠀⢀⠀⠀⠀⢠
⠀⢀⣦⡄⠀⠀⠽⠟⠀⠀⠀⠀⠄⠀⠀⣠⣤⠀⠀⠸⠿⠁⠀⠀⠀⠠⠀⠀⣰⣤⠀⠀⠀⠿⠏
⠀⠀⠋⠁⢀⣀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠘⠉⠀⣀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠈⠉⠁⢀⡀⠀⠀⠀⠀⣀⣄
⠀⠖⠀⠀⠈⠉⠀⠀⠂⠀⠈⠛⠃⠀⠰⠀⠀⠀⠉⠀⠀⠒⠀⠀⠛⠃⠀⠀⠆⠀⠀⠈⠁⠀⠐⠂⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡰⢀⡄⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠨⡀⠁⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠁⠀⠅⣐⡀
⠀⠀⠀⠀⠀⠀⠈⠃⢀⠀⡠⠋⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠘⢎⢧⡀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠒⠀⠀⠀⢀⠀⠀⠈⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡱⡄⠀⠀⠀⠀⠀⠁⠄⠠⠈⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⣆⠀⠀⠀⠀⠀⡄⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠍⠀⠌⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡀⠀⠀⠂⢀⠉⠉⠁⠉⠩⠤⠄⠄⠀⠀⠀⠀⠀⠠⢀⠀⠐⠄⠈⠉⠉⣉⣀⡒⠂⠀⠀⠀⠠⢀⠀⡀⠀⠂⠤
⠀⠀⠀⠀⠀⠀⠈⠁⢀⠂⠀⠁⠀⠀⠑⠌⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢂⠀⠀⠄⢀⠠⠀⠀⠀⠀⠀⡠⢋⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠘⠪⡢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢊⠀⠂⠠⢀⠠⠂⠡⠂⢁⠔⡩⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠘⠪⡲⣄⠀⠀⠀⠀⠀⢀⠠⠂⠡⢀⠡⠂⡁⠀⠀⡠⣞⠔⠋⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠦⢀⡀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠠⠀⠠⠀⠡⠂⠡⠀⠠⠀⠐⠊⠚⠁⠀⠀⠀⠲⡀⠀⡈⠂⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠁⠀⠡⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡠⠠⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠑⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠀⠡⠀⢁⡀⢄⡀⠀⠐⠡⢀⠄⠀⠰⠀⠀⠀⠀⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀⠤⢚⡩⠆⠒⢍⠢⢀⠀⠀⠀⠈⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡠⢐⡩⠔⠊⠁⠀⠀⠀⠀⠑⠪⡓⢤⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣨⠕⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢝⡲⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⢆⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⡒⡚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⡈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠈⠀⠀⠀⢠⠀⣠⠀⠀⠁
⠀⠈⠁⠀⢠⠄⠀⠂⠀⠀⠀⠀⠈⢱⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠠⠄⠀⠀⠀⠀⠹⠡
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢐⠠⠠⡀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⠀⠛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⣠⡴⠖⠛⠋⠀⠀⠀⠀⠀⢠⡄⠁⡀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠈⡿⡟
⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠘⠀⠀⠀⠀⠐⠿⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣄⠀⠀⢀⡀⠀⠀⠠⢴⡷⠄⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠠⣦
⠀⠈⠀⣀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⠈⠋⢀⢄⠈⠁⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠈⠀⢀⣴⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⠉⠎⢁⡀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠠⣶⠄⠂⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠄⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⣠⣾⡏⠀⠈⡁⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⣀⡐⣾⡖⠀⠀⠀⠀⠙⠟⠁⢀⡄⠈⠙⠁
⠀⠀⠀⣠⣾⣿⣿⣦⡄⠰⠚⠀⠀⠀⠀⢠⠚⠉⠉⠁⠀⠀⠀⠀⠠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣦⡄
⠀⠀⠾⠿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠙⡟⠁

⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠃⠀⠀⠡⠀⠀⠀⠄⠀⠀⠀⠄⠄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⠉⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠉⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠔⠂
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠨⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⢰⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡦⣤⣔⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡼⢫⣌⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠕⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠲⢶⣤⣤⣄⣀⠀⠀⠀⠀⢠⠃⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠉⠛⠿⣿⣿⣿⣶⣶⡂⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⠈⠙⠻⢿⣿⣷⡀⢀⣿⡿⠟⠁⠈⠀⠐⠒⠀⠤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠈⠛⠷⡸⢋⣀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣶⣾⡿⠋⣦⠙⠻⢿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠋⠀⢰⣿⣧⠀⠀⠈⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⡀⢼⣿⣿⣧⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣰⣿⠟⠁⣀⠤⠂⠁⠀⠀⠻⣿⣿⣆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⣀⠄⣪⡞⠁⠀⠀⡴⢋⠥⠐⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⡆
⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⢻⣿⠊⣠⣾⠟⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆
⠀⠀⠈⠉⠩⢉⠛⠛⠻⠷⢌⣇⠴⠟⠫⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤
⠀⠀⠀⠀⠀⠀⠈⢱⣶⡶⢋⣎⠳⣶⣶⣤⣬⣐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣠⡿⠋⡀⢼⣿⡀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣰⠋⠔⠈⠀⠀⠻⣧⢀
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠾⠀⠀⠀⡄⠀⠀⠐⣶⣧⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⢼⡶⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠼⣿
⠀⠀⠀⠰⠆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⣶⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠼⣿⠅⠀⠀⠤⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⣤⣆⡀
⠀⠀⠤⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠃⠀⠀⠈⠀⠀⢠⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠋⠋
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⢠
⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠐⠂⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠯⠀⠀⠀⠀⢶⡆⠀⠀⠀⢠⡄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⣤⣄⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⢰⣾⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⡀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣾⠄⠀⠀⠀⠀⠀⠖
⠀⢠⠄⠀⠀⠀⠀⡀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠀⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀
⠸⠷⠀⠀⠀⠃⠀⠀⠀⠠⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⡄
⢀⡀⠀⠐⠂⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⣲⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠁
⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡀⡀
⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣾⡄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠠⠿⡟⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠒⠀⠀⠀⠀⢼⡶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠻⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉
⢀⡀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣠⡀⠀⠀⠀⠤
⠀⠁⠀⠀⠀⠀⠀⠀⠽⢿⠂⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⢺⠷⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠀⠀⠀⣤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠀⢠⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⣰⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙
⠀⠈⠹⠻⠀⠀⠀⠀⠄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠆⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠂⠀⠀⠀⠀⡷⠆⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠚⠿⠓⠀⠀⠀⠐⣾⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠿⡗⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⣰⡤⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠠⣼⡤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠁⠀⠀⠀⢴⡄
⠈⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠰⡦⠀⠀⠀⠀⣠⣦⠄⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

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

⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⡂⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣷
⠀⠀⠀⢤⣖⠒⠈⠁⠀⠓⠐⣲⠶⠀⠀⠀⠀⠀⢠⠶⠆⢋⡹⠆⣴⣦⡤⠄⠀⠀⠀⠀⠖⠒⢲⡟⠒⠻⣷⣶⡶⠂
⠀⠀⠀⠀⠈⢡⠆⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠠⢔⠍⠪⠞⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⢄⣀⡴⢿⡏
⠀⠀⠀⠀⠀⣾⡴⠋⠀⠄⢹⡀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠊⠉⠺⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣴⠞⠉⠳⢬⣷
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠰⡀
⠀⠀⠠⠶⠶⠖⢶⠷⠆⠺⡖⠀⠀⠀⠀⠀⠀⠰⣶⣶⣿⣿⣿⣿⣿⣶⣶⠖⠀⠀⠀⠀⢫⡉⠉⠀⠀⠀⠈⠉⡩⠂
⠀⠀⠀⠀⠐⢲⡯⠀⠀⢀⣽⠊⠁⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢀⡞⠀⠰⠲⢅⡀⢇⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠙⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠚⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡜⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢇
⠀⠀⠀⣠⡤⠠⠀⠀⠀⠐⠒⠒⣠⠄⠀⠀⠀⢤⣤⠠⠶⠚⠀⠹⠶⠶⣦⠤⠀⠀⠀⠠⢤⣶⠶⢟⣷⣿⣿⣷⡶⠖
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⠁⣤⣻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⡏⠀⠀⠰⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠤⢤⡘⣆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⠋⠺⣿⠇
⠀⠀⠀⠀⠐⠃⠁⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠠⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⢾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣄⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠄
⠀⠀⠀⠀⠀⠀⠘⢻⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣀⣷⣀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


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

⠉⠀⠀⠀⠀⠀⢾⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣹⠿⣧⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢸⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠞⠁⠀⠙⠆
⠀⠀⢠⠐⠄⠄⠀⠀⠀⠀⠀⠀⣀⡀⣸⣇⣤⠖⠂⠀⠀⠀⠀⠀⣀⣼⣀⠐⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣀⣀⣾⣤⡴⠂⠀⠀⠀⠀⠈⠉⠉⣹⠿⣿⡀⢀⣀⠀⠀⠀⠀⠀⠜⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠛
⠀⡽⠻⣇⠀⡀⠁⠀⠀⠀⠖⠀⠴⠋⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠀⣀⠀⠀⠀⠀⠀⠀⠆⠀⢰⠀⢀
⠈⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠉⣻⢿⡁⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣿⢀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠀⠀⠀⠀⠀⡠⠀⠀⣩⡿⣿⠛⠉
⠀⢀⠀⠀⠀⠀⠰⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠸⡆⠈⠑
⠀⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠘
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⡇⠀⠤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡇⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⣸⣧⣤⠶⠂⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠸⠁
⠃⠀⠀⠀⠀⠀⢤⣤⣷⠞⠀⠐⠀⠀⠀⠀⠀⠀⠐⠶⣦⣼⣧⡤⠖⠀⠀⠀⠀⠈⠉⠉⢉⡿⢿⡅⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠞⠉⠆⠀⠁⠀⠀⠀⠀⠐⠂⠀⣠⠞⠛⣧⠀⢤⡀⠀⠀⠀⠐⠂⠠⠏⠀⠀⠻⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠰⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡄
⡿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⠞⠋⠀⠀⠀⠰⠆⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻
⢿⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⡏⠁⡀⠀⠀⠀⠀⠀⠈⠁⠀⠴⠛
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠔⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠟⠀⠀⠀⠀⠈⢻⠈⠀⠀⠀⠀⠙⠶⣶⣿⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⡾⠋⢻⡄⠠⢄⠀⠀⠀⠀⢀⠲⠶⣾⡷⠛⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢸⡇⠀⢋⡀
⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠻⡄⠐⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠠⠤⠤⢤⣼⣷⠟⠉
⢰⡇⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⠉⠀⠀⢀⡀⢀⡴⠋⠻⣆⠀⠒⠀⠀⠀⠀⠀⠀⠐
⣾⣿⠋⠁⠠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⡀⠈⠀⠀⠀⣠⡄⠀⠀⠀⠘
⠁⠙⠆⠘⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙
⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡇⠑⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠂⣀⣼⣀⠀⠀⠀⠀⠀⠀⠰⠶⣼⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢦⠀⠀⣼⠀⠠⠄
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⢀⠀⡴⠋⠻⡄⠰⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⣀⣀⣀⣿⣠⡴⠖

⠀⠀⠀⠀⠀⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠰⡐⠈⠀⠈⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢤⣾⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣾⣿⣶⡶⠂
⠀⠀⠀⠈⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣧
⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁

⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠳⡀
⠀⠀⠐⢿⣿⣿⣷⡶⠂⠀⠀⠀⠐⠈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠔⠻⠛⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⡹⠆
⠀⠀⠀⠀⣿⠿⢿⣇⠀⠀⠀⠀⠀⢈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠶⠖⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢠⠟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⢀⣼⡡⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⢦⡀⠀⠈⡉⠉⠀⠀⠀⠁⠀⠀⠀⠀⡴⠋⠀⠀⠀⠻⣿⣿⣷⣿⠋⠀⠀⠀⠘⠇⠀⠀⠀⠀⠋⠀⠀⠀⠀⠂⠀⠀⠀⠐
⠀⠀⠀⢀⣤⠖⠀⣷⠀⠀⠀⠀⠀⣀⡠⠤⢄⡇⠀⠀⠀⠀⠀⡿⠟⠻⣷⠀⠀⠀⠀⠀⢠⡤⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⢀⣀⣰⠏⠣⣀⣀⠀⠀⠀⡀⠀⠄⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣧⣀⣀⠀⠀⢀⣀⣠⠾⠙⢦⣤⣀
⠀⠀⠈⠳⡄⠀⠀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣿⣶⡶⠉⠀⠀⠀⠙⢦⠀⠀⢠⡖⠁
⠀⠀⠀⢸⠵⠚⠲⣷⠀⠀⠀⠀⠀⠆⠀⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠻⠇⠀⠀⠀⠀⠀⠤⠔⠂⠠⡇

⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⠀⠐⠁⠱⠀⣀⠀⠀⠀⣀⣤⡸⡿⣠⣤⡀⠀⠀⠀⣤⠤⠞⠹⠤⣤⠀⠀⠀⢀⠤⠔⠁⠲⠀⡀⠀⠀⠀⢀⣀⣼⣷⣤⣀⡀
⠀⠀⠀⠑⠄⠀⠀⡞⠁⠀⠀⠀⠈⢛⣭⢠⣝⠋⠀⠀⠀⠀⠈⣷⠀⠀⢰⠁⠀⠀⠀⠀⠱⠀⠀⠀⡞⠀⠀⠀⠀⠀⢹⣿⣿⣿⠋
⠀⠀⠀⠸⠖⠉⠑⠷⠀⠀⠀⠀⠀⠘⠋⠈⠛⠇⠀⠀⠀⠀⠀⠟⠋⠙⠺⠀⠀⠀⠀⠀⠠⠐⠉⠒⠄⠀⠀⠀⠀⠀⠘⠋⠉⠛⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣤⣤⣤⣾⣯⠞⠁⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠈⠁⠀⠀⠀⠈⠛⠛⠷⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠿⠶⠿⠁⠀⠀⠀⠀⠀⠀⣰⣿⢋⣀⣤⣶⠾⠟⠻⣷⣄⡀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠉⠻⣦⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⡟⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣼⠁⠀⠀⠀⢻⣆
⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣼⠃⠀⠀⠀⠀⠀⢻⣧⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣆
⢻⣿⣿⣍⡉⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⠉⠉⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠿⡾⠟
⠀⠙⢷⣌⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⢰⣿⣩⣿
⠀⠀⠀⠙⢷⣄⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⢰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠙⢿⣦⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣇⠙⢿⣦⡀⠀⣀⣠⣴⠾⣿⠆
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠉⠻⠿⠛⠉⠀⢰⡟
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⣠⡶⠛⠙⠻⢦⣄⡀⠀⠀⠀⠈⣿⡀⠀⠀⣶⠶⣆⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠟⠛⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⣤⠶⣛⣥⣶⠾⠿⠿⢶⣮⣽⣶⣤⡀⠀⠘⣧⠀⠀⠻⠿⠛⠀⠀⠀⠀⣶⣾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀
⠀⠀⠀⢀⣾⠃⢀⣤⣾⣿⣷⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢷⣦⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⣾⣷⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣝⣷⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣽⣿
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣠⡿⠋⠁⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣿⠆⠀⠀⠀⠀⠀⠀⠀⣿⣋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄
⠀⠀⠈⠀⠀⠀⠀⠀⢺⠆⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⢩⣿⡷⠖⠀⠀⠁⣿⡷⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙
⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⣤⣼⣦⡄⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡇⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀
⠀⠄⡂⠀⠠⠀⠀⠤⣾⣧⠤⠀⠀⠄⣴⣷⠠⠀⠀⠀⠀⠀⠀⢰⣳⠄⠀⠀⠀⠀⣾⡦⠀⠀⠀⠠⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠛⠀⠀⠐⣾⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠛⠀⠀⠐⣾⣿⠂
⠀⠐⠀⠀⠀⠀⠀⠘⠉⠙⠂⠀⠀⠐⠉⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠂⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⣾⠻⣶⣄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⣶⣿⣷⡶⠀⠀⢴⣾⣷⣦⠀⠀⠀⠀⢸⣧⠀⠀⢨⣿⠆⠉⢻⣿⣿⠛⠀⠈⠃⠁⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠽⠿⠿⠇⠀⠀⠸⠿⠻⠇⠀⠀⠀⠀⠈⠻⣴⣷⡼⠟⠀⠀⠜⠉⢙⠂⠀⠐⠜⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⣸⣶⣾⡀⠀⠀⢀⣦⣴⡀⠀⠀⠀⠀⠀⠒⢶⡼⣤⠄⠀⠀⢦⠚⠣⡤⠀⡁⣤⣼⣧⣤
⠀⠀⠀⢀⠀⠀⠈⢹⡿⢿⠉⠀⠀⠈⡿⠻⠁⠀⠀⠀⠀⠀⠠⠋⠘⠆⠀⠀⠀⠸⠂⠺⠄⠀⠁⢠⠟⠿⡅