Biosynthesis Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⣨⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠀⠀⣾⠏⠀⢠⣶⠿⠁⠀⣴⣶⣆⠀⠀⠀⠀⢴⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⠉⣽⠇⠀⠀⣿⠀⠀⢻⣇⡀⠀⠘⣿⣠⡿⠇⠀⠰⣷⣄⠙⢷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⢁⣴⣷⡿⠀⠀⠀⠹⣧⡀⠀⠙⢿⣄⡀⠈⠛⠃⠀⠀⠀⢈⣿⣗⣀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⠀⠁⠀⠀⠀⠀⠈⠻⢶⣤⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⢉⣻⣿⠀⢰⡿⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⣠⣿⠿⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣠⣾⡏⠀⠀⠈⠿⣶⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢠⡶⣿⣅⠀⠀⢸⣏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⢸⣏⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⣧⣼⠟⠁⠀⢰⡿⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠙⢿⣅⠀⠀⢀⣶⠿⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠉⢿⣦⣄⠀⠘⢷⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⣈⣽⣿⠀⠸⣷⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⣻⣶⡀⠀⠀⠀⠀⠀⢀⠀⢀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠉⢽⣿⡁⠀⠀⠀⣰⡿⠁⠀⣠⣾⠏⠉⢿⡆⠀⠀⠀⠀⣾⢿⠟⢁⣴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⣄⠙⢿⠆⠀⠀⣿⠁⠀⢸⡏⢹⣷⣴⣿⠁⠀⠀⠀⢰⣟⣀⣰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠗⠀⠀⠀⠀⢻⣆⠀⠈⠻⣿⡁⠀⣹⡇⠀⠀⠀⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⢈⣻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣥⡔⠾⣿⣶⣤⡀
⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡿⠿⣀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾
⢠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢠⡴⠛⠉⠉
⢾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⣿⣿⡿⠟⠁⠈⠉⠛⠷⢶⣤⣄⡴⠉⠉⣿⣿⣿⣏
⠘⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⣿⣿⣿⡟⠀⠀⣴⡆
⠀⠀⠈⠉⠉⠁⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠲⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢈⠟⠛⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣾⣄⣠⣾⣿⣿⣿⡶⠶⠶⠶⠶⠶⠾⣿⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣨⣿⣿⣿⡆
⠀⠀⠀⣠⣤⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⠇
⠀⢠⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡴⠶⠛⠛⠉⠁⠀⠀⠻⠿⣿⣿⠿⢝⢄
⠀⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⢄
⠀⠘⢿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠉⠛⠛⠋⠁⠈⠻⢷⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠈⢻⣷⣤⣤⣤⣄⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠟⠻⢿⣶⣤⣴⣶⣿⡇⠀⠀⠀⣰⡶⠀⣿⣇⣉⡉⣽⡿⠛⠉⠉⠙⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠘⣿⣇⣠⣿⣷⡀⠀⠻⠛⠁⣰⡿⠛⠛⢻⣿⠁⠀⠀⠀⣤⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⣀⣤⣿⣇⠀⠀⣠⣼⡿⠀⣼⡟⠋⠉⠙⠿⢷⣶⣶⠿⠛⠁⠀⠀⠸⣿⡀⠀⢰⣾⠟⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠛⢿⣿⠋⣙⣿⣦⣀⡉⢉⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣤⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢀⣄⠈⣿⡿⠟⠋⠉⠛⠻⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡏⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣶⡾⠏⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣤⣤⣴⡿⠋⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠉⠛⢿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⣠⣾⠟⠋⠉⠛⢿⣦⡀⠀⠀⢀⣶⡿⠛⠉⠙⠻⣷⣄⠀⠀⢸⣿⠁⠀⠀⠀⣀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠁⠀⠀⠀⣀⡀⢹⣿⠿⠿⣿⡏⠀⠀⠀⢀⣀⠈⣿⡿⠿⠿⣿⡀⠀⢰⣾⠿⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⢹⣿⡀⠀⢠⣶⡿⠁⣸⣿⣤⣤⣿⣇⠀⠀⣶⣿⠏⢀⣿⣧⣤⣶⣿⣷⣦⣄⣠⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣧⣤⣾⠿⠛⢿⣦⣄⣀⣤⣾⠟⠁⠀⠀⠉⠻⣷⣤⣀⣠⣴⡿⠋⠉⠁⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠈⠙⢿⣆⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣴⡄⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠿⠟⠁⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣶⣶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠛⠛⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠘⢿⣦⣶⡾⠿⢿⣶⣄⠀⠀⠀⠀⢀⣴⣶⠿⠿⣶⣦⡀⠀⣀⣠⣿⠇⠀⠀⠀⣀⡀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣼⡟⠁⠀⠀⠀⠈⢻⣷⣤⣤⣤⣿⠋⠀⠀⠀⠀⠙⣿⡿⠛⠛⣿⡆⠀⢠⣴⡿⠃⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡅⠀⠀⣀⣾⡇⠀⣿⡏⠉⢻⣏⠀⠀⢀⣰⣿⠀⣸⣷⣶⠾⠿⢿⣦⣄⣀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠛⠋⣀⣼⡿⠿⠿⠿⢿⣦⡀⠘⠛⢁⣰⣿⠃⠀⠀⠀⠀⠉⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠁

⠀⠠⣾⣦⡀⠀⠀⠀⠀⠀⣠⣾⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠈⠻⣿⣦⣄⣀⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠈⠉⠙⠻⢿⣷⡄
⠀⠀⠀⠀⢈⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣀⡀⠀⠀⠀⣿⣿
⠀⠀⢠⣶⣿⠟⠉⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⢿⣿⣶⣿⣿
⠀⣴⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿
⣸⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⣿⡀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣾⣿⠿⠟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣾⡿⠟⠋⠉⠉⠉⠉⠉⠀⠀⠀⢀⣿⡿
⢻⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⠁⠀⠀⠀⣿⡟⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣴⣿⡿⠁
⠀⠻⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⡿⠁⠀⠀⠀⠀⣿⣧⣴⣾⣿⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣀⣠⣤⣀⡀
⠀⠀⠘⢿⣿⣦⣀⢀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠉⠙⣿⣿⠟⠛⠻⣿⣦
⠀⠀⠀⠀⢈⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣶⣶⣿⣿⣤⣤⣀⣹⣿⡇
⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠙⣿⡟⠛⠛⠿⣿⣿⣄
⠀⣰⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣶⣤⡀⠀⠀⠀⠙⢿⣷⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⣿⣷⣄⡀⠀⠀⠀⠀⢠⣶⣶⣤⣿⣧⠀⢻⣿⡄⠀⠀⣿⣿⣿⣷⡀
⣸⣿⠏⠉⠉⠀⠀⣶⣶⣶⣶⣾⣿⡿⢿⣷⣦⣄⠀⠀⠉⠛⠿⠿⠿⠿⠿⢿⣿⣿⣶⣶⣿⣿⠿⣿⣶⣤⣀⠀⠀⠉⠙⢿⣿⣿⡀⢘⣿⡇⠀⠀⣿⣿⠈⣿⣷
⣿⣿⣶⣶⣶⡆⠀⠈⠉⠉⠉⠉⠉⠁⠀⠈⣻⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠉⣻⣿⣷⡦⠀⠀⢰⣿⡿⠿⢿⣿⣿⣶⣶⣿⡟⠀⢸⣿
⢻⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⣴⣿⡿⠟⠉⠀⢀⣀⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣤⣶⣿⠿⠛⠁⠀⠀⠀⣸⣿⠃⠀⢀⣿⡏⠈⢻⣿⣷⣄⢸⣿
⠈⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠁⠀⠀⢀⣶⣿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⣿⣿⠟⠉⠀⠀⠀⣠⣤⡀⢠⣿⡟⠀⠀⣸⣿⠃⠀⣾⣿⠻⣿⣿⡿
⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⡿⠃⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣥⣀⣰⣿⣏⣀⣸⣿⣧⣶⣿⣿⠁
⠀⠀⠀⠀⠙⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣶⣾⣿⣿⣿⡿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠛⣿⣿⡿⠿⢿⣿⡿⠛⠋⣿⣿
⠀⠀⢀⣴⣾⡿⠋⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⣀⣴⣿⠟⠀⠀⠀⢿⣿⣄⣰⣿⡟
⠀⣠⣾⣿⣯⣤⣤⣤⣤⣬⣿⣿⣦⡀⠀⠀⠀⠀⣿⡿⢿⣷⣶⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠈⠙⠻⠟⠋
⣰⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣷⠀⠀⠀⠠⣿⣇⠀⠈⠉⠙⠛⠛⠛⠛⠛⠿⢿⣷⣦
⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡇⠀⠀⠀⠻⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷
⢻⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣿⠃⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣿⣿
⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿
⠀⠀⠙⢿⣷⣄⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣴⣾⡿⣿⣿
⠀⠀⠀⠀⠙⣿⣿⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠛⠋⠉⠁⠀⣿⣿
⠀⠀⠀⣠⣾⡿⠟⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⢀⣠⣼⣿⠏
⠀⠠⣾⡿⠋⠀⠀⠀⠀⠈⠻⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣿⣿⠿⠿⠛⠁
⣶⣶⣾⢶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣄⠀⠀⠀⢀⣴⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠈⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢷⣶⣦⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣶⣶⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⣤⣤⣤⣤⣤⣤⣼⣿⡄⠀⠀⢀⣤⣶⠿⠿⠿⠿⠿⠛⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡉⠉⠉⠉⠉⠉⠉⣹⣿⠀⠀⢀⣿⠏⠀⠀⠀⠀⢀⣀⣀⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠛⠛⠟⢻⣿⡿⠃⠀⠀⢸⣿⣶⡾⠿⠟⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣴⡿⠋⠀⠀⠀⠀⢘⣿⣿⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣀⣀⣿⡏⠉⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠘⣿⡁⠉⠙⠛⠛⠛⠛⠻⢿⣦⡀⠀⠀⠀⠀⠀⠈⠙⣿⡟⢻⣿⠿⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠄⠀⠀⠀⠀⣶⣦⣄⠀⠀⠙⢿⣦⣤⣄⣀⣀⣀⣀⠀⢹⣷⣤⡀⠀⠀⠀⣶⣶⣾⣧⠈⣿⡆⠀⢸⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⣠⡀⠀⠿⠿⠿⠿⠏⠛⠿⣶⣤⡀⠈⠉⠉⠛⠛⠻⠿⠿⠿⠿⠛⠻⢷⣦⣄⠀⠈⣿⣿⣦⣿⣧⣀⣸⣿⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡉⠉⠁⠠⣶⣶⣶⣶⣦⣴⣾⠿⠋⠁⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣤⣶⡿⠟⠉⠀⠀⣿⠇⠈⣹⡟⠛⣿⣷⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠃⠀⠀⠀⠀⠿⠟⠉⠀⠀⣴⡾⠟⠛⠉⠉⠉⠉⠁⠀⣸⡿⠋⠁⠀⠀⣶⣄⣸⡿⠀⢠⣿⠇⢰⣿⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⢰⣿⣁⣀⣤⣤⣤⣤⣤⣶⡿⠟⠁⠀⠀⠀⠀⠈⢻⣿⢿⣶⣾⣿⣤⣾⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠻⣷⣄⠀⠀⠀⠀⢸⣿⣿⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⣾⠏⠀⠈⣿⣇⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⣶⣶⣾⣿⣷⡄⠀⠀⢨⣿⠿⠿⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣁⣀⣀⣀⣀⣀⣀⣹⣿⡀⠀⠈⣿⣆⡀⠀⠀⠀⠀⠈⠉⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⠛⠛⠛⠛⠛⠛⢹⣿⠁⠀⠀⠈⠛⠿⢷⣶⣶⣶⣶⣦⣤⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡾⠿⠿⠛⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠀⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠛⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠂⠀⠒⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⡄⣀⢤
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡔⢦⡼⠿⠏⠉⠛⠁⠘⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⠓⠀⠀⠀⠠⣿⣷⢼⣿⡦⢿⣿⠗⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡇⠀⠀⠀⠀⢀⢸⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⡠⢤⠤⠤⠘⡃⠧⠤⠊⠉⠂⠉⠁⠀⠐⢚⢀⡇⢲⠀⠄⠠⠜⢸
⠀⠀⠀⠘⢦⡠⠖⠉⢹⣁⠰⡉⠉⠃⠀⠀⠁⠀⠀⠀⠀⡧⠶⢆⠴⢧⠀⢈⠁⢈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢇⠀⠀⠀⠀⠀⠀⠀⢰⠆⡇⠀⠀⠀⠈⢀⠘⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⣚⣈⣭⡽⠀⠀⠀⡤⠤⠼⠀⠳⢴⣄⣀⣀⣸⢸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⠙⣿⠘⣰⠀⠀⠀⠉⠉⢹⢹⢹⣿⠙⣶⠒⣶⠒⠖⠚
⠀⠀⠀⠀⠀⠀⠀⣠⠀⣿⡄⠩⡄⢠⡄⢠⡄⢐⣆⢘⣶⠈⢿⠀⣿⠀⣿⠀⣥⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣀⣿⣇⣄⣄⣸⣇⣸⣇⣸⣯⣸⣿⣀⣠⣀⣿⣀⣿⣀⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡴⠀⠀⠐⠖⠠⠀⠀⠀⡄⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡤⠀⠀⢿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠄
⠤⠄⠀⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡤⠤⠤⣰⠰⠂⠀⠀⠀⠀⠀⠀⠀⠠⣂⡆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠉⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠠⢘⠀⠀⢴⡆⠀⠀⠀⢠⡾⠃⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠐⠓⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢠⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣀⠠⢄
⡤⠄⠂⡀⠀⠈⠓⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠌⡑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⢤⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠋⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠄⠁⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢏⠈⠐⠊⠁⢈⠂⠀⠀⠀⠈⠲⠐⠊⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⢀⡀⡀⠀⠀⠀⠅⡀⢀⠠⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠆⠐⠊⠀⢁⠐⠁⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠐⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠢⡀⠀⠀⢨⠀⠀⠀⠀⠠⠂⠰⠀⠀⡀⠀⠀⠨⠙⠀⠀⠘⠠⠰⠊⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠊⠁⠀⠀⡀⠀⠄⠀⠀⠰⡿
⠛⠳⠢⣄⠀⠀⢈⠆⠀⠀⡆⡀⠐⠈⠐⠈⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⡀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠈⠀⢙⡀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠐⡇⠀⠀⡮
⠀⠀⠀⣸⠁⠀⠁⠀⠀⠀⠀⠌⠀⠑⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠁⠆⠀⠧⡈
⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠁⠀⠈⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠰⠀⠀⠈
⠀⠀⠀⢀⠀⠀⡀⠀⠒⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⢿⣆⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠈⠀⢈⠀⠀⠀⠀⠐⠢⢀⠀⠘⢿⣷⣄⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠈⢻⣆⠀⠀⢀⠀⠀⠀⠦⠈⠁⠈⠁⢠⠀⢠⠚⠁⠀⠀⠁
⠀⠀⠘⠁⠀⠈⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠗⠀⠀⠈⠟⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⠀⢴
⠀⠀⢠⠀⠠⡄⠀⠠⠀⠀⠀⠀⠀⠈⠀⢀⡀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡀⠀⠄
⠀⢠⠚⠀⢀⡄⢀⡀⠐⠀⠀⠀⠀⠀⠀⣼⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⢀⠀⠄⠀⠀⠐
⠀⠈⠀⠀⠇⢤⣌⠁⠀⠈⠀⠀⠀⠴⢀⠏⠀⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡀⠈⠐⠡⠁
⠀⠀⠀⠀⢀⠀⠆⠀⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠴⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠃⠀⠗⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠶

⠉⠂⠀⠘⣇⢀⣌⢘⠠⠆⠀⠁⠸⠀⡀⠸⡄⠿⡾⠓⠀⢀⡴⡶⣶⡻⠃⠐⢿⠆⠀⠀⠀⠓⢀⠇⢀⠈⠉⢇⣤⠉⠙⢶⡞⠃⠠⠂⢨⡮⠨⡅⠀⠀⠉⠁⣠⣡⡀
⣌⠒⠂⠈⢡⠷⡄⢠⡄⠘⡁⠀⠄⢠⡀⠈⠀⠩⠐⠀⠁⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠊⠀⠀⠹⠤⢦⡼⠓⠄⢀⠢⠂⠛⠃⠀⠀⣠⠐⢾⠙⣏
⠤⣱⢄⡄⢄⠐⢱⣤⣁⣠⠢⠀⠐⠚⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠠⣀⡡⠀⠄⣴⠅⠠⣌⡰⠁
⠒⢯⡜⢔⠀⠁⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠆⢀⢘⠇⠀⠀⠂
⡤⢄⠙⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡄⡄⣠⠄⢠⢤⢀⡤⣄⢀⠤⡀⡠⢄⢀⠤⠀⢠⡀⢠⡀⡀⡄⣠⠄⣄⠀⣠⢠⠄⠀⠀⠀⠀⠀⠀⠈⠉⣀⠤⠔⢦⣀
⠧⠜⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠸⠱⠊⠄⠇⢧⡄⠸⠻⠸⢄⠼⠻⣤⠌⠜⠢⠰⣄⠦⠟⠳⠸⠑⠇⠇⢉⠗⠏⠖⠱⢨⡷⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣶⢾⠏
⠀⠀⢐⡠⠒⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠠⢴⠏⠀⡀⠔⠟⠁⠀⣄⠀⡦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢖⡚⠺⡄⠘⠃⠁
⠀⠘⠛⠋⣥⠎⠀⠀⠀⢸⠇⠛⠛⣧⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢔⠿⢧⠄⠀⠐⠝⣁⡁⠷⠂⢆
⣠⠎⠀⠊⢀⠄⠠⠀⠙⠋⡠⠲⠒⠉⡦⡄⠈⣄⡠⠉⣀⠀⠀⢠⠖⡬⠀⠀⠀⠀⣇⡀⢤⠧⢀⣀⡄⠀⠰⢎⠙⠄⠜⢸⡶⠀⣄⡤⠂⡂⣯⡆⠀⠁⠴⡂⢿⠆⡕
⣷⣦⣤⣤⣷⣶⣾⣧⣤⣼⣧⣤⣴⣾⣶⣤⣤⣤⣷⣮⣤⣼⣦⣬⣿⣧⣤⣤⣤⣾⣷⣴⣦⣴⣿⣧⣤⣴⣷⣴⣧⣤⣴⣾⣧⣼⣧⣤⣴⣷⣿⣤⣤⣤⣬⣴⣶⣾⣦
⣿⣿⣇⣀⣈⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⠠⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡓⠃⡠⠀⠀⠈⠑⢄⢈⡀⠀⠀⠀⢄
⠀⠀⢀⡀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⢄
⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠢⠄⠀⠀⠀⠀⠲⡀⠀⠆⠀⠀⠀⠀⢁⡀⠀⠀⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢂⣀⠀⠀⠀⠐⠀⡀⠠⠶⠶⠶⢦⠄⠂⠀⠀⠀⠀⠠⠀⠀⠸⣁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠈⠀⠀⠿⠿⠇⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠉
⠀⠀⣠⠂⠀⠀⡀⠠⠀⠀⠀⠀⢠⡀⠰⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠠⡦⠀⠀⠀⠀⠈⠀⠀⢰⢀⠀⠀⠀⠀⠀⠑⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⢀⣄⠀⠀⠁⠠⡀⠉⢂⠘⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠠⡀⠄⠀⢀⠄⠀⠈⠁⠘⡆⠀⢶⣤⣄⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⢀⡀⠀⢇⣀⡸⠀⠄⠀⡇⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⡤⠦⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠟⠁⠀⠐⠘⡆
⠀⠀⠀⠀⢠⠀⠱⠴⠃⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⡀⠀⠘⣇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠃⠀⠈⠒⠆⠔⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠹⠤⣠⠖⠀⠀⠀⠀⠀⠀⠶⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡀⠀⠀⡠⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠄⠀⠀⡀⠀⠀⠈⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⣠⠊⡠⠒⠂⣉⡁⠀⠀⠀⠉⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠑⠊⠀⠀⠀⠈⠉⠙⠒⠲⠤⡄
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⡶⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠛⣠⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡔⠁⠇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣰⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣂⠀⠀⠃⠀⠀⠙⠛⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠨⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢁⣄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠁⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡼⠀⠀⠀⠈⠀⠐⠂⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⠧⣛⡫⡰⠀⣠⠁⡃⠸⠃⠀⠀⠀⠠⠜⢢⡑⠊⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⢣⣛⡫⡸⠀⣠⠁⠇⠺⠃⠀⠀⠀⠠⠜⢢⡑
⠀⡁⡉⢶⠀⠀⠀⠀⠀⢀⣧⡠⠤⠞⠁⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠈⡉⡈⢶⠀⠀⠀⠀⠀⢀⣧⡤⠤⠞⠁⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⢨⣶⣎⠀⡯⠄⠀⠀⣠⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⡡⡠⡍⢦⠀⠀⣉⡏⢨⣶⣎⠀⠧⠄⠀⠀⣠⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠞⡡⡀⡍⢦⠀⠀⣉
⢤⣉⡡⢜⠑⠂⠀⠀⡏⠀⠀⡔⢉⡠⠤⣉⠆⠀⠀⠘⣌⢜⢋⠆⢃⠀⠀⠁⡱⢤⣉⡡⢜⠁⠂⠀⠀⡏⠀⠀⡔⢉⠠⠤⣉⡆⠀⠀⠘⡄⢜⢛⠆⣸⠀⠀⠁
⠃⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠁⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠚⠁
⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⡀⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡄
⢂⠀⠀⢢⡏⢙⡦⠄⠀⠀⠠⢜⣶⣕⣢⠀⢉⣧⠀⠀⠀⢜⢀⣹⡆⠀⠀⠳⡌⢢⠀⠀⢢⡏⢹⡦⠄⠀⠀⠠⠜⣶⣗⣢⠀⢉⣧⠄⠀⠀⢜⢀⣙⡆⠀⠀⠳
⠤⠀⠀⠀⠹⠙⠈⠃⢀⠀⠀⠀⠊⠝⡦⣶⡿⠻⣦⠀⠀⠈⠑⠉⠀⠀⠀⠀⠘⠦⠂⠀⠀⠹⠙⠈⠃⠀⠀⠀⠀⠊⠕⡶⣶⡿⠻⣦⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠠⡀⢨⠀⠀⠀⠀⠀⠁⠁⠈⠀⢹⢆⠀⠀⠀⠀⡄⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⢛⢆⠀⠀⠀⢀⡤⠂⢢
⢀⠂⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢠⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟⠀⠀⢀⠒⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢀⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟
⡎⡸⠀⠀⠁⠀⣰⢱⣶⡆⢸⡖⠊⠀⠀⢧⠰⡀⠀⠀⠀⠀⡌⠀⢠⠎⠀⠀⠀⡌⡼⠀⠀⠁⠀⣰⢱⣷⡆⢸⠖⠊⠀⠀⢧⠐⡀⠀⠀⠀⠀⡜⠀⢰⠎
⠷⠃⠀⠀⢀⡡⠘⡦⣄⣨⡶⢍⡁⠀⠀⠸⣄⡇⠀⢀⣀⣼⡀⣤⠂⠀⠀⠀⠀⠧⠃⠀⠀⢀⡡⠘⡦⣄⣠⡶⢍⡁⠀⠀⠸⣀⡇⠀⢀⣠⣼⡀⣠⠂
⠀⡀⠀⠈⠁⠀⠜⠀⠂⢃⠘⠀⠈⠂⠀⠀⠉⠀⠶⠡⢊⢊⠍⡅⠀⠀⠰⡀⡐⠀⣀⠀⠈⠁⠀⠞⠀⠆⢡⠘⠀⠈⠂⠀⠀⠉⠀⡶⢡⢊⢊⠍⠁⠀⠀⠰⡀
⡛⡥⠆⠀⠀⡠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⣡⢃⠃⡰⠀⠈⢱⢊⣅⠭⡛⡥⠆⠀⠀⠠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⠡⢋⠁⡰⠁⠈⢱⢊⢍
⢃⢙⠉⠀⠀⠢⠾⠁⠀⠀⡔⡽⣷⡖⠸⠀⢀⠇⠔⣡⡎⠐⠃⠀⠁⢹⡘⢝⡣⢃⢻⠉⠀⠀⠢⠶⠃⠀⠀⡔⡑⣷⡶⢱⠀⠀⠆⠔⣡⡎⠐⠃⠀⠁⢹⡘⢟
⠠⠎⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣪⠎⠀⠚⢠⠃⠈⠀⠀⠀⠀⠈⠀⠜⠲⡄⠠⠮⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣊⠎⠀⠚⢠⠂⠈⠀⠀⠀⠀⠈⠁⠜⠢
⠠⣂⡢⠙⡄⠂⠀⠀⠀⣴⠟⠊⠉⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤⡆⠠⣂⡢⠙⡄⠀⠀⠀⠀⣴⠟⠋⠋⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤
⠘⠿⠑⢠⢏⡁⠀⠀⡾⠁⠀⢀⠤⠄⠀⠤⡀⠀⠀⢠⠁⢪⣦⡃⡙⠄⠀⠖⢆⠘⠿⠗⢠⠍⣁⠀⠀⡾⠁⠀⢀⠤⠀⠀⠤⡀⠀⠀⢠⠁⢪⣦⠃⡹⠀⠀⠖
⡝⠒⢊⠱⠀⠀⠀⠀⠃⠀⠀⠣⠘⠈⠉⠓⠃⠀⠀⠀⠣⢑⣐⣡⠜⠀⠀⠀⠊⡙⠒⢂⠱⠀⠀⠀⠀⠃⠀⠀⠣⠚⠊⠉⠓⠁⠀⠀⠀⠣⢑⣐⣁⠞
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠠
⡀⠀⠀⡙⡼⣴⣁⠀⠀⠀⠀⢲⡋⢍⡉⠓⠮⡔⠀⠀⠀⢠⠒⢢⡀⠀⠀⢆⠢⡀⠀⠀⡙⡼⣤⡁⠀⠀⠀⠀⢲⣋⣍⡉⠓⠪⡔⠀⠀⠀⢠⠒⢦⡀⠀⠀⣇
⠘⡀⠀⠘⢧⢴⠣⡅⠀⠀⠈⠐⡻⢗⢛⣄⣴⣿⡁⠀⠀⠱⢄⠾⠃⠀⠀⠈⢣⠘⡀⠀⠘⢧⢼⠣⡅⠀⠀⠈⠐⡻⢗⢛⣤⣴⣿⡁⠀⠀⠱⢴⠶⠃⠀⠀⠈
⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⡏⠟⠫⠈⠿⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⠏⠟⠫⠈⡿⡀⠀⠀⠀⠀⢀⡀⡀
⠀⡀⠀⠀⠀⠀⡈⢆⢸⠀⡠⠀⢀⠄⠀⠀⠀⠀⠐⢕⣄⠀⠀⡰⠋⠀⣴⠀⠀⠀⣀⠀⠀⠀⠀⡈⢆⢘⠀⡀⠀⢀⠄⠀⠀⠀⠀⠘⢕⣄⠀⠀⡰⠋⠀⣴
⠰⢠⠃⠀⠄⠀⢉⢞⣍⡙⢣⡊⡥⠀⠸⡌⢂⠀⠀⠀⠀⠀⠰⠁⠀⣠⠃⠀⠀⠰⢠⠃⠠⠄⡀⢙⢞⣍⡑⢣⣂⡥⠀⠘⡍⢂⠀⠀⠀⠀⠀⢰⠁⢀⡰⠃
⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣘⠧⠄⠀⠀⢸⠀⡆⠀⠀⠀⢠⠃⠀⡘⠁⠀⠀⠀⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣨⠧⠄⠀⠀⢹⠀⡆⠀⠀⠀⢠⠃⠀⡸⠁
⠉⠀⠀⠠⠔⠊⣠⠋⡓⠞⢫⠑⠢⡄⠀⠈⠧⠃⣀⠔⡪⡻⠮⠟⠀⠀⢀⠀⢀⠉⠀⠀⠠⠔⠊⣠⠋⡓⡞⢣⠑⠢⡀⠀⠈⠶⠃⣀⠔⡺⡻⠮⠟⠀⠀⢀
⣤⠆⡀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢋⠌⡘⡔⢁⠅⠠⢄⡠⠆⠢⣤⠆⡀⠀⠀⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⢉⠌⡴⠕⢁⠆⠠⢄⡨⠆
⡆⢯⠥⠀⠀⡊⣹⠆⠀⠀⢀⢴⣖⢒⢢⠀⠀⡔⢁⠞⡰⢀⡎⠀⠄⢼⢰⣷⡌⡆⣯⠥⠀⠀⡉⣙⠆⠀⠀⢀⢴⣖⣒⢆⠀⠀⡔⢁⠎⡰⢀⡎⠀⠄⢼⢰⣷

⠀⠀⠀⡀⢠⠀⡀⠀⠀⠀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠁⠀⠀⠀⠀⠀⢂⠀⠨⣀⠀⠀⠀⠁⠂⠀⠀⠀⠈⠀⠁⠀⠀⠰⠊⠁⠉⢡⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢠⠀⠌⠀⠂
⠀⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠂⠀⠀⠐⠈⠀⠀⠘⣀⠀⠀⠔⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠂⢀⡀⠁
⠀⠀⠘⠀⡄⠐⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠒⠀⠐⢄⠀⠂⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⡀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠄⠁⠈⠂⠀⡃
⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠈⠈⠀⠀⠉⠀⢀⢀⠤⠞⠀⠀⠀⠠⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⣀⣀⣤⣤⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠘⠀⠄⠀⠀⠀⣠⣾⠟⠛⠫⠛⡛⡛⢉⣙⡻⢯⡀⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠔⠐⠢⠀⠈⠀⢠⣿⠘⢸⡄⡄⣌⣳⣜⣈⣯⣩⣼⠿⡿⡏⠉⣿
⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠁⠒⠂⢀⠁⠀⠸⡿⠶⢾⠛⠻⡏⣭⣭⡩⡇⠒⢓⡐⢠⡀⢰⣽⠄
⠀⡠⠂⠀⠢⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⣌⠌⠂⢦⣀⣝⣉⣷⣹⣌⢉⣣⣠⣥⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⠀⠄⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠙⠉⠋⠛⠛⠛⠉⠁⠀⠀⢀
⠀⠀⠁⠀⠁⢀⠀⠀⠀⠀⠀⢍⢈⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⠱⠃⠚⠁⠀⠀⠀⠄
⠀⡊⠀⠀⠌⠀⠀⠀⢀⠀⠂⢀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠐⠠⠛⠁⢀⡀⡀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠂⠀⠀⠀⠀⠈⠀⠀⠐⠰⠖⢲⢸⡣⢈⠄⠂
⠀⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠘⠁⠁
⠀⢀⠂⢐⠈⠀⢃⠂⠀⠐⢈⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠐⠁⠀⢀⠃⠀⠀⠀⠊⠐⠆⠀⠀⠀⠀⠀⠀⠄
⠀⠠⠢⠀⠀⠀⠀⢄⠀⣀⢂⠐⠀⡜⡠⠐⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠄⠐
⠀⠈⠀⠡⠠⠐⠀⠊⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⢋⣉⣉⣤⣤⣤⣤⣉⣉⡙⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⣁⣤⣶⠿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠻⠿⣶⣤⣈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠉⠻⢷⣦⡈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⡟⢁⣴⡿⠋⠀⣿⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠹⣧⠀⠀⠀⠀⠙⢿⣦⡈⢻⣧⡀
⠀⠀⠀⠀⢀⣾⠏⢠⣾⠏⠀⠀⢀⣿⣿⣷⠶⠓⣠⣤⣤⣄⠀⠀⠹⣦⣼⠋⠀⢀⣤⣤⣤⡀⠙⣿⡄⠹⣷⡀
⠀⠀⠀⠀⣾⡏⢠⣿⠃⠀⠀⢀⡿⣹⡏⠀⠀⠀⢻⣆⣀⣹⢷⣴⠾⠋⠙⠷⣦⡾⣃⣀⣼⠇⠀⠘⣿⡄⢹⣷
⠀⠀⠀⣸⡿⢀⣿⠇⠀⠀⠀⣼⢷⡟⠀⠀⠀⠀⠀⠉⠋⠙⣷⠀⢈⣀⠲⠂⠀⣾⠋⠉⠁⠀⠀⠀⠸⣿⡀⢿⣇
⠀⠀⠀⣿⡇⢸⡿⠀⠀⠀⢰⣏⣾⠃⠀⠀⠀⠀⠀⣀⣤⣤⡿⠀⣏⣍⣳⠀⠀⣿⣤⣤⡀⠀⠀⠀⠀⢿⡇⢸⣿
⠀⠀⢀⣿⠀⣿⡇⠀⠀⠀⣾⢛⡟⠀⠀⠀⠀⠀⣼⠏⠀⣱⡟⠻⢾⡍⣥⡶⠛⢷⣍⠈⢹⡆⠀⠀⠀⢸⣿⠀⣿⡀
⠀⠀⠈⣿⠀⣿⡇⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⣸⠇⢻⣄⠀⠀⠙⠛⠛⠁⠀⠀⠀⢸⡿⠀⣿
⠀⠀⠀⣿⡇⢸⣷⠀⠀⠀⢻⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿
⠀⠀⠀⢹⣷⠈⣿⡆⠀⠀⢸⡟⢿⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣾⡏
⠀⠀⠀⠀⢿⣇⠘⣿⡄⠀⠀⣿⣼⡇⠀⠀⠀⠐⣶⣼⡷⢦⣤⣤⠶⠾⠛⠛⠛⢷⣴⡟⠀⠀⠀⢠⣿⠃⣸⡿
⠀⠀⠀⠀⠈⢿⣆⠘⢿⣆⠀⢸⡇⣿⠀⠀⢘⣻⡏⢀⠰⠖⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠃⠀⣰⡿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣧⡈⠻⣷⣌⠛⠛⠀⠀⠉⣹⣷⣬⣀⡐⠀⠀⣀⣀⣠⣴⠾⠋⠀⠀⣠⣾⠟⢁⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠻⢷⣦⣀⠀⠀⠉⠰⠟⢹⠟⠛⠛⠉⠉⠁⠀⠀⣀⣴⡾⠟⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡉⠛⠿⣶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⣶⠿⠛⢉⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣌⣉⣉⠛⠛⠛⠛⣉⣉⣡⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⠟⠿⠿⢿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠉⠛⢿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣍⡻⣿⡿⢸⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⡿⢛⣛⣿⠿⠿⣿⣿⣿⣿⣶⣄⣀⠀⠀⢨⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣶⣿⣿⡏⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⣫⣥⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢸⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠀⠈⢿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⡙⣿⣿⣿⠿⠿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣻⣿⣿⣦⣀⣠⣿⣿⣿⡿⢃⢿⣯⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣧⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣯⠀⠀⢀⣿⣿⠟⠉⡉⠙⠻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠿⢿⣿⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠂⠀⣿⣿⣷⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⢀⣹⣿⣿⣷⣶⡀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣷⣤⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⢦⣶⠛⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⠀⠀⠀⠙⠘⡀⠀⠀⠀⠁⠉⣦⠂⠆⣔⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠂⠂⠀⠀⠀⠀⢎⣱⣿⠷⣶⠉⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⢻⣄⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠄⠈⢋⣿⠢⠁⢄⠈⢸⣏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢠⣧⠘⠺⠅⠀⠀⠔⡀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡛⠃⠀⠐⠚⠻⠏⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⡟⠀⠀⠠⠀⡗
⠀⠀⠀⣀⠀⠐⠈⠀⠀⢀⣔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢄⡂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⡀
⠀⠀⢸⣿⠀⠀⠀⠀⣤⡼⠟⠒⠒⠀⠰⠂⠀⠀⠀⠀⢰⡀⠚⠀⠀⠀⠀⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⡇
⠀⠀⢸⣿⡄⠀⠀⢤⡏⠁⡀⠀⠀⠀⠀⠘⠗⠁⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⠀⡆⠀⠀⢂⣀⠃⢉⡽⡀
⠀⠀⢸⣿⡇⠀⠀⠈⠛⠚⣁⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣆⠀⠀⣤⣦⣞⡜⠁
⠀⠀⢸⣿⣷⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠿⠟⠻⢿⡿⠇⠀⠀⣽⠝⣸⣃⠄⠀⡀
⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⠄⠒⠢⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⢬⠀⣴⠞⠶⣿⡿⣿⣶⠋⠀⣿⣿⠆⣸⠃
⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⠀⠀⢰⡟⡰⠁⣄⡠⠄⠀⠀⠀⠀⠀⠀⢁⡂⠀⠈⠙⠻⠆⠠⣈⠋⣈⢫⣤⣤⣿⣿⣿⣇⣆
⠀⠀⠈⢿⣿⣿⣿⣄⣆⠀⢀⣤⣶⠀⠀⣿⣷⡇⠀⡀⣰⡷⠀⠀⠀⠀⣤⣦⣄⢀⠀⢀⡄⠀⠀⠀⢻⡿⠿⠿⣿⡿⠿⠿⢛⡠⠝⠁
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣧⣡⠍⠀⢸⣿⡇⣠⡘⢛⣻⣿⡀⡀⡄⠍⠁⠉⠻⠀⣣⡜⡂⠀⠀⠀⣾⡇⠀⠠⣶⡄⠒⠒⠁⠐⠀⣀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣛⢙⣇⣼⢻⡟⣀⣸⣿⠛⠉⠀⠀⠙⣯⠀⠀⠀⡀⠸⢿⣿⣷⣶⠄⡀⣿⣧⣾⣦⡛⠂⠀⠀⢠⡶⠋⢁
⠀⠀⠀⠀⠀⠉⣶⣿⣿⡏⠋⠻⢿⣷⣾⠃⠀⠈⣷⠀⠀⠀⠀⢰⣧⣤⣀⣤⡇⠀⣤⣷⠚⡛⠊⢳⣿⡿⠟⢻⣿⡆⠀⠀⡎⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⢀⢸⣿⣿⠈⣷⣤⠏⠀⠀⠀⠀⠈⢻⠿⢫⠥⠁⠀⠛⠉⠀⢛⣛⣤⣶⣷⠆⠀⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠀⠈⠘⠛⢿⡈⠿⠿⠦⣀⣤⣤⣤⡤⠜⠀⠀⠀⠀⠤⠴⠶⠿⠿⠛⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀⣠⡀⣀⠀⣀⡀⣠⢀⠀⡀⢀⣀⢠⠠⣀⢀⠀⣀⠀⢄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠁⠈⠀⠀⠁⠈⠈⠀⠀⠀⠁⠀⠈⠁⠁⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡆⢀⠀⡀⠀⡄⠘⣆⣘⣄⣸⣤⣧⣴⣥⣎⠎⡠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⢰⠸⡀⢠⠀⣇⢈⣆⣡⣤⣧⡼⠶⠷⣚⠛⠻⠉⡉⢩⠄⠀⠀⠀⠈⢝⢿⣴⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢱⠀⢇⣀⣱⣬⣦⡴⠶⢷⡛⠛⠋⠉⠉⠑⡀⢀⠦⢠⠄⠀⠀⠶⠀⠁⡄⠀⠀⠀⠀⣘⠃⠁⢹⣷⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⣼⠞⠛⠩⠉⣅⠀⠀⣈⣙⡤⣄⡀⢀⢀⠁⠀⠁⠀⠀⠄⠀⠙⠀⢠⠄⠀⠤⠀⠀⢠⡀⠀⠠⠆⠀⣷⣒⠂⠈⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣹⡞⡑⠙⠆⠀⠀⠀⠀⠀⠐⠢⣌⠁⠮⠋⡣⠑⠀⠘⡃⠀⠀⠁⠀⠀⠀⠀⠋⢀⡀⠀⣀⡀⠀⠖⠐⣼⡓⠤⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠤⡤⣿⠀⠸⠃⠛⠀⠀⠀⠀⠀⢸⣀⣼⣧⠶⠠⠃⡜⠀⢀⠀⠠⠠⠀⠀⠀⠀⠖⠀⠆⠀⠲⠈⠠⣐⣥⢾⡓⠬⠁⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠐⠒⣿⡀⡠⡄⠉⢀⡄⠶⠀⠀⠀⠓⠀⠉⠤⠍⠙⠁⠤⠈⢐⡀⠫⠄⣀⣀⣀⣤⡤⣶⠶⡖⢛⠻⡙⠄⠣⠉⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⡨⢷⣜⠀⢃⠀⠀⠶⡀⠀⠀⠘⠀⣀⣒⣠⣤⣤⡴⠶⡖⠺⡟⢻⠉⠋⠃⠘⠀⠉⠀⠁⠈⣠⣴⡶⠶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢊⡝⢻⠶⡶⡷⢶⠶⡞⢻⠛⢏⠹⡉⢣⠸⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠘⠀⠃⠘⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢶⡶⠾⠋⠀⠀⠀⠀⠀⠂⠀⠂⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⢠⡄⢤⣤⢤⣤⡄⣤⣤⢠⣄⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣇⣾⣿⣿⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣬⠀⠀⠤
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⣿⣿⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⣿⡇⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⣿⠀⠀⠀⠀⠀⡄⠀⠠
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣗⣿⡿⠀⠀⠀⠀⠀⠀⢰⡆⠈⣿⠀⢻⠇⠘⡟⠀⠀⠀⠀⠀⢸⣿⣶⣶⣿⣠⣾⣿⣷⣄⣿⣿⡧
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠉⠀⠈⠀⠀⠉⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡡
⠀⠀⠀⠀⠀⠀⢠⡿⣟⠽⠋⢹⣿⣿⣿⠟⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⡂
⠀⠀⠀⠀⠀⢀⡿⢊⠁⠀⢀⣿⣿⣿⠃⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⢀⡤⠒⠒⣀⠒⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠐⠻⠃
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⡿⠀⠀⠀⠀⠀⠀⣼⣴⣿⣿⣿⣿⣷⣼⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣥⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠀⠀⢰⡿⣛⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠁
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠸⣇⡁⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⡷
⠀⠀⠀⠀⠻⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠈⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣤⢠⣀⡄⣀⣠⢀⡀⡄⡀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠰⠇⠎⠼⠰⠡⠆⠮⠠⠠⠠⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣴⣶⣿⣶⣦
⠀⠀⠀⣰⣋⡘⣘⣁⢋⡋⣘⢁⢀⢀⠈⠀⠐⠁⠀⠀⢀⡔⠄⠠⠁⠀⠀⠀⠉⠀⠠⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⢰⠆⡴⠰⠤⠆⡶⠴⠠⠀⠄⠤⠠⣀⠁⠀⠀⠀⠈⠁⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠲⡎⠱⢠⡔⢤⡔
⣧⠍⠈⠀⠔⢲⣆⡀
⠛⠳⢄⡂⣰⠟
⠀⠀⠞⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⣀⢀⣀⣤⠀⡀⠀⢀⡀⠀⣀⢀⣄⣄⢀⡀⠀⢀⢀⣄⣠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡿⣄⣿⢸⣧⠤⢸⡇⠀⢸⡇⠀⣿⢸⡧⠄⢸⡿⣆⣸⠀⣠⡟⠁⢠⡛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠃⠈⠟⠘⠇⠀⠘⠷⠦⠈⠳⠾⠃⠸⠷⠦⠸⠃⠈⠛⠐⠿⠶⠀⠟⠁⠙⠇
⠀⠀⠀⡀
⣰⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣢⡀
⠎⢳⣿⢲⡆⣠⠎⠀⠀⠀⠀⠀⠀⠙⠋
⠠⠈⢀⡁⢠⣿⡄⢀⡤
⠠⠄⠈⣀⠉⠉⣘⣡⠄

⡆⠠⡄⠀⠀⠴⣯⡅
⠀⠠⡄⠀⠑⢆⢀⡋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢲⠀⣄⠀⣴⣠⡿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠠⢅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⣤⣄⣹⡰⢿⡉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢁⡄⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠙⠃⠸⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⣠⣜⠓⠂⠀⠀⠀⠀⠐⠶⢤⣴⢧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠿⢹⡈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠗
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣷⣶⠾⣶⣶⠜⠀⠀⠀⠀⠀⠀⠠⣄⠈⢛⠀⢸⠃⢰⡆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠛⠋⠁⠈⣦⡄
⠐⠾⠇⠀⠀⠀⠀⠀⠙⣹⣧⣤⣿⡛⠳⠆⠀⠀⠀⠀⣤⠀⣘⡶⠾⠛⠛⣟⠿⠃⢴⡎⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠉⡿⠟⢋⠀⠀⠀⠀⠠⣄⣩⠾⠇⠘⢗⠀⠀⠉⠀⠀⠰⠞⠛⣶⡞⠉⠀⣀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠂⠀⠈⠀⠀⣀⡀⠀⢨⡟⠘⠳⡄⠈⢀⠀⡿⠁⢀⠴⠃⠶⠟⢷⠖⠛⠁
⠀⠀⢀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢙⣋⠀⢈⡁⠈⠳⠈⠀⠰⠂⢀⣄⠰⠶⠿⢶⡗⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⣨⣄⣠⣃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡋⠀⡈⣁⢀⡀⠀⠷⠀⡀⠀⠀⡀⠀⠠⣴⡇⠄⠀⠀⠀⠀⠀⠀⠀⣀⢰⡭⢱⡄⠀⠀⠀⠈⠷⠘
⢻⣌⠁⠈⠀⠿⠄⡶⢀⢀⡤⠚⠁⠀⠀⠀⢠⣤⠄⢿⡴⠟⠉⠀⠀⣠⠀⠀⢁⠐⠶⡉⠳⣶⡾⠷⠄⣠⠄⠀⠀⠀⠀⠀⠈⠳⠴⠛
⡀⠙⠀⢀⡔⢀⠘⣧⠈⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣀⣰⡆⠀⠉⠀⣤⠀⣧⠄⠀⣦⡸⠷⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠲⠀⠈⠀⠀⠀⠀⢤⠿⡞⠁⠀⠀⠀⠀⠀⠀⠚⠋⠀⣘⡿⢅⣠⣜⣇⠀⢀⣼⣀⠴⢾⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠛
⢀⠤⠀⠀⠀⠉⠛⠰⠖⢀⡷⠄⠀⢤⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠉⢻⠛⡛⠙⠇⠀⠀⠻⠖⠀⠀⠀⠀⣿⢀⠤⢤⡄⢻⡁⠀⠀⠀⠀⠀⠘⢋⡰⠖
⠋⠠⠄⠸⡏⠐⣤⠔⠶⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠁⠀⠀⠷⠀⠀⠐⢷⣆⡀⠀⠀⠀⠈⡷⢠
⡄⠦⠀⣤⠤⠦⡁⢠⠤⡀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⢀⠁⠀⠀⠀⠀⠀⣠⠀⠠⢈⣡⡞⠃⠀⠈⠁
⠱⠶⢆⡻⠀⠄⠉⠲⠀⠈⠣⡤⠀⠀⢠⣄⠀⣱⣄⡄⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠳
⠇⠀⠘⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣁⢈⡁⠶⠈⠷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⠀⠈⠴
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠓⠻⡧⠌⣠⠀⠴⠒⢴⣧⣀⠀⠀⠠⠼⠃⠀⠀⠀⠀⠘⣭⠀⠀⠴⠀⠀⠀⠰⠆⠀⠀⠈⠀⠄⡴⠀⠀⠀⠋⠓
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣶⡀⠰⠂⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⣦⠔⠁⡴⢤⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠉⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠿⢧⠄⠐⡦⠀⣀⠀⢠⠿⠾
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠠⡬⠁⠐⠈⠁⢡⡄⠀⠀⠀⠀⠀⠀⡀⠀⢠
⣰⢦⡗⢀⣸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣧⠸
⠉⠉⠁⠁⠩⠶⠒⢄⣰⠃⠀⠀⠀⠀⠀⣎⣷⠀⠀⠀⠀⠐⢢⡄⠀⣀⢨⡄⠈⠀⠉⠀⠙⣿⠶⣆⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠁⠘⠆
⠀⠀⢌⠁⠀⠀⠈⠙⣃⣢⠀⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠋⢠⡀⠁⠀⠐⡂⠀⠀⠁⠀⠉⣱⣖⠁⠀⠀⠀⠀⠀⠀⣀⡱⠀⠀⠈⠉⣻⡉⢁⡄
⠀⠀⠀⢀⠈⠋⠀⠀⡡⠙⡶⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠛⢀⠀⠀⣠⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡯⣤
⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣦⣤⣶⣤⣴⣶⣶⣶⣶⣾⣶⣤⣶⣶⣶⣶⣶⣶⣶⣴⣾⣷⣶⣷⣶⣿⣶⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣦⣶⣿⣦⣶
⣿⣿⣿⠻⠍⠛⠟⠉⠙⠛⢻⡟⠏⣹⡿⢻⠝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠋⠀⠀⠀⠀⣤⣖⣲⣴⣲⣰⣒⣦⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠶⠊⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⡟⡏⠙⢹⣩⢹⣿⢹⡇⠀⠀⠀⠀⠂⣾⣿⣿⡆⠀⠀⠀⠀⠈⢧⡚⠟⠂⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠠
⠀⠀⠀⢀⣎⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⡇⠻⠟⠸⠿⠘⠿⢸⡇⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⢷⣄⠀⠀⠀⠀⠀⠀⠃⠀⢨⡇⠀⢀
⠀⠀⠀⠸⠏⠻⠇⠿⠸⠇⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠀⠀⠀⠨⠇



⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄
⠀⠀⠀⠀⢀⣸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠉⢸⣿⣿⡎⢒⠂⠀⠀⠀⠀⠀⠂⠘⣿⣿⣿⠂⠐⠀⠀⠀⠀⢠⣾⢻⢯⣽⢿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠳⡀
⠀⠀⠀⠀⢰⡾⠿⠿⡁⠂⠃⠀⠀⠀⠀⠀⠀⠄⠻⠿⠟⠀⠀⠀⠀⠀⠀⠈⢿⣯⣾⣹⣾⠷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣷⢳
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉



⠀⠀⠀⢀⡴⠚⠉⢉⡓⢤⡀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠛⠢⣄⠀⠀⠀⠀⠀⣠⢖⠛⠉⠛⠢⣄⠀⠀⠀⠀⠀⠀⣆⠶⢆⡤⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⡀
⠀⠀⠀⡏⣀⣄⠀⠿⠟⠀⢳⠀⠀⠀⠀⣸⢁⣾⣿⣯⣠⠄⠘⡆⠀⠀⠀⢸⠁⠸⡅⢄⢠⠴⠚⡆⠀⠀⠀⠀⠀⠈⣓⡺⣅⠀⠀⠀⠀⠀⠀⠀⢿⠟⠛⢻⡿
⠀⠀⠈⡇⠻⠟⢀⣤⣶⡄⢸⠀⠀⠀⠀⢻⠀⣻⠿⣿⣿⡄⢀⡇⠀⠀⠀⢹⠀⠀⢸⠴⠋⠀⠀⡇⠀⠀⠀⠀⠘⣆⠣⠇⠘⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡾⠁
⠀⠀⠀⠙⢦⣀⠈⠻⣛⡵⠃⠀⠀⠀⠀⠈⠣⣄⠀⠟⢉⣠⠞⠀⠀⠀⠀⠈⠳⣄⡘⠦⢀⣠⠞⠁⠀⠀⠀⠀⠀⡼⠍⠙⣆⠀⠀⠀⠀⠀⠀⠈⢘⣻⣯⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⡤⠠⡄
⠀⢄⣀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⠖⠻⣗⣶⣾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢿⠁⠰⣆⡀⠈⡉⠀⢹⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠉⠉⠀⠀⢳⡬⠛⠉⠠⠘⣧⣧⡀⠀⠀⠀⠀⣠⡄⠀⠀⢠⢦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠻⡖⢤⡀⢀⣄⡈⠀⢀⠉⣏⠁⠀⠀⠰⣒⡋⡷⠖⠓⠚⣇⣩⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡛⣅⠀⣸⠎⠀⣸⡤⠚⠛⣂⣰⣧⡀⣤⡀⣴⠉⠉⠁⠀⠀⠀⠈⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠟⢦⣤⢀⠄⠛⠀⢀⣴⣧⠎⠀⠀⡱⠙⣯⠀⢀⡤⠜⡇⠀⡼⡂⠀⢬⠶⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠟⠣⢵⡖⠚⠋⠉⠛⠀⠀⠚⠊⡿⠁⣠⣄⡈⠙⠁⠀⠓⠚⠃⢸⡟⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠸⣅⠌⣱⡼⠀⡰⣩⠵⠆⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡤⢼⣢⠉⡼⡳⠦⣄⠀⢠⡄⠀⠀⠀⠘⠷⣍⣄⠄⢙⠁⣠⣰⠻⢥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠸⡏⠀⢊⡁⠙⠀⣀⠀⡑⣷⠎⠧⣀⡀⠀⠀⣴⡫⡸⡋⠉⠉⠉⠸⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠋⠁⣀⡜⢹⠀⢰⠙⢦⡄⠈⡺⣯⠉⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡏⠀⠀⠉⠑⠋⠀⠀⠉⠁⡄⠠⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢈⡽⠀⠾⣁⢒⠄⠀⡔⢒⡦⠀⠀⣤⠿⡲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⣤⢠⡈⠚⠀⠀⠷⠁⠀⠃⠀⣿⠳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠚⣦⣄⠀⣊⣵⢶⡶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢣⡇⠉⠉⠉⡝⡤⠽⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⢀⠀⠠⠀⠂⡄⢀⠀⢀⠔⠒⠒⠤⢀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⣠⠠⣄⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠀⠒⠂⡀
⠀⠈⠀⠀⠀⠈⠤⠄⠘⠂⠄⠤⣀⠀⠀⠈⡀⣀⣀⠀⡸⠀⠀⣌⠀⠀⠀⢃⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⢀⠇⠱⠄
⠠⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠁⠀⠀⠀⠀⠁⠦⠠⠄⡃⠀⠀⠀⣀⠀⠀⢠⠂⠀⠀⠀⠐⢶
⢀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠁⠄⠠⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠤⢀⠀⠀⠈⠁⠉⠁⠂⠀⠐⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠈⠀⢈⠄⡀⡐⠀⡀⠀⢠⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠨⠠⠀⠀⠀⠄⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⢀⠀⡀⠁⠀⠀⠈⠢⡀⠈⠓⢦⠀⠀⠀⡀
⠀⠁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠀⠀⠀⠀⠠⠀⢀⡴⠀⠇⠀⠰⠀⠁⠀⠀⠀⠂⠈
⠈⠤⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀⠤⠐⠁⢠⠞⠀⠀⠈⢀⡗⠀⠀⠀⠀⠀⢀⢠
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⠀⠀⠒⠈⠉⡁⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⡶⣶⠶⠶⣾⣿⡟⠛⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⡀⡀⠁⠠⠀⠀⣾⢹⢡⠀⠈⠰⠎⠦⢰⡶⠎⣻⣮⣼⠟⢿⡆
⠀⠀⢠⠀⠀⠀⠀⡀⠀⠘⣀⠸⠀⠠⠀⢸⣿⣀⣼⠦⣶⠗⢾⡒⢺⠛⣻⡏⠍⡈⠆⣼⡇⠀⠀⠈⠈⠀⠂⠐⠀⠀⠄
⠀⡀⠤⢄⠀⠀⠀⠀⠀⠄⢀⡀⠐⠂⠀⠈⢯⠀⡹⠀⡌⠘⠿⢿⡜⣇⠰⠶⠀⡓⢀⣿⡏⠀⠀⠀⠀⠀⠠⠀⠄⠀⡀
⢐⠀⠀⠀⢱⠀⢀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠓⠧⠶⠿⠾⠷⠾⠿⠿⠶⠶⠿⠿⠟⠋⠀⡀⠀⢢⠀⠀⠐
⠈⠢⠄⠤⠃⠀⠀⠀⡀⠁⡐⠒⡄⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡐⣰⠈⠾⠄
⠀⠀⡄⢠⠊⠉⠁⠢⠀⠤⠈⠂⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢄⠀⠀⠀⠄⢠⠂
⠈⠒⠁⢂⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠔⠁⠑⠀⠀⠀⠘⠠⠜⠀⠀⡠⣤⣠⡔⢶⢰⡖⠢
⠀⠂⡀⠀⠑⠒⠂⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠝⠛⠀⠁
⠀⠠⠠⠔⢀⠀⠀⠆⡡⡀⡂⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢠⠢
⢄⠁⠊⠁⠈⠀⠈⠀⠀⠈⡢⠅⠀⢀⡤⠒⠉⢑⡄⠀⠀⡀⠒⢠⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⢈⠀⠀⠀⠀⠄⠀⠀⡀
⢂⡀⣀⠀⠀⠀⠀⠀⢀⠈⠐⠀⡰⢃⠤⠒⠂⠈⡀⠠⠂⠀⣀⠜⠀⠀⠈⠀⠀⠀⠀⠂⢠⠀⠔⠀⠀⠀⠈⠀⠄⠀⠂
⠀⠂⠂⡁⡉⠂⠊⠀⠁⠀⠁⠀⠈⠁⠀⠀⠀⠈⠒⠒⠂⠈⠀⠀⠀⠀⠁⠂⠀⠀⠀⠐⠀⠐⠀⠀⠀⠂
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿