Hairstyle Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⣥⣶⣾⣿⣶⣦⣌⠹⣦⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⣾⣿⠟⠛⠛⠛⠻⣿⣆⢹⡇⢹⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢣⣿⡟⠁⠀⢀⡤⠤⠄⠘⣿⣿⠃⠈⠀⢸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣫⣴⣿⠟⡄⠀⢰⡟⣠⠒⠀⠀⠹⣧⣤⣤⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⢋⣡⡜⠁⢠⣿⢱⢃⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠵⠒⠛⠉⣁⣠⣴⡿⣣⠏⠈⠀⠀⢀⡀⠀⠻⢿⠿⣿⡟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣴⣶⣾⡿⠟⠛⣉⠥⢚⡏⠀⠀⠛⠛⠛⠂⠀⠀⠈⣸⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢫⣿⣿⡿⠁⠀⢠⣾⣧⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⠃⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣧⠀⠀⢸⣿⣿⡄⢠⣤⣤⣀⠀⠀⠀⠀⢠⣿⣿⣿⠃⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠛⢿⣿⣷⣦⣄⡙⠿⣿⡜⠻⠛⠁⠀⠀⣀⣴⣿⠹⣿⣿⡀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡆⠀⠈⢿⣿⣿⣿⣷⠈⣿⣦⣤⠀⠀⠈⠁⠘⣿⣧⠙⢿⣷⡀⢻⣷⡀
⠀⠀⠀⠀⠀⣠⡶⠟⠛⣉⣁⣀⣠⣤⣿⣿⣿⣿⢟⣠⣿⣿⡟⠀⠀⠀⠀⠀⠈⢻⣷⣄⠈⢻⣆⠹⣿⣆
⠀⠀⠀⠀⢸⡏⢠⣾⠿⠟⠛⠛⠛⣛⣋⣭⣵⡾⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣰⣿⠀⣿⣿
⠀⠀⠀⠀⠘⢇⢸⣿⡀⠀⡖⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣩⠴⠾⣛⣡⡾⠟⠁
⠀⠀⠀⠀⠀⠈⠈⠻⣷⡘⡇⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠇⢸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣠⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠸⣿⣿⣿⠿⣿⣿⢿⣿⠿⣿⣿⡀⠀⠀⠀⠀⢠⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢻⣿⠁⠀⠈⠉⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⠙⠻⢿⣿⡘⢻⣿⣿⠏⠁⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠈⠉⠉⢹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠹⠃⢸⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡄⠀⠀⠀⠀⣺⡿⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⡀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠁⠀⠀⠀⠙⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⡿⠿⡿⠏⠿⢿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠻⠧⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠈⠻⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠇⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣸⣿⠀⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠈⠟⣿⣿⡟⠀⠀⠀⠀⠹⣿⣿⡟
⠀⠀⠀⠀⢰⣿⣿⡿⠉⠙⠋⠙⠛⢻⣿⣿⣇⠀⠀⠀⠀⠀⠉⢿⡿⡦⠀⠀⠀⠐⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠛⢷⠄⠀⠀⠀⠀⠀⠀⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣶⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⣀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠛⠛⠛⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢼⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠿⠋⠙⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⠀⠀⠈⢿⣿⡏⠁⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠰⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣼⣏⠃⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⣿⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⢿⠿⣿⣿⣿⣧⡀⠀⠀⠀⢀⢠⣿⣿⣿⣾⣿⣷⣆⡀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⠆
⠀⠀⠀⠀⢀⡀⠀⠙⠻⣿⠀⠀⠀⠀⢸⣿⡟⠃⠈⠀⠁⠙⣿⣿⡧⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⣿⡗⠀⠀⠀⣿⣿⣿⣿⡟⠋⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠉⠁⠀⠈⠀⢻⣿⠆⠀⠀⠀⢻⣿⣿⣿⡿⠗⢀⣀⠈⠀⠀⠀⠀⢻⡟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⣿⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⣿⣷⣤⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦
⠀⠀⠀⠀⣤⣤⣶⣴⣤⡄⠀⠀⠀⠀⠀⠀⢄⣠⣤⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣤⡆⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⠂
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣲⣾⡿⠟⠛⠛⢻⣧⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⡏⠁⠐
⠀⠀⢻⣿⣿⡟⡿⡿⠀⠹⡇⠀⠀⠀⠈⠀⣿⠠⠤⠀⠤⠄⠗⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⣿⣿⠃⠀⠀⢀⣤⣶⣾⣿⣿⡃
⠀⠀⠀⠘⠋⠛⠃⠑⠋⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢰⣤⡀⠀⠀⠀⠘⠋⣀⡀⠀⣀⢹⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⢀⠀⢿⣿⡉⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⠀⠀⣿⣿⣿⡿⠫⠛⢿⣿⡄
⠀⠀⠀⠀⠙⣤⣠⣀⡴⠂⠀⠀⠀⠀⠀⠀⢸⣿⠂⠙⠉⠀⢸⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠟⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⡀⢀⠀⠀⠀⠀⠀⣁⣰⣶⣶⣴⣦⡁⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅
⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⢀⣿⠋⠉⠉⠉⠻⣷⡀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣦⡄
⠀⠀⠀⡤⠀⠈⠉⠉⠉⠙⣿⠁⠀⠀⠀⠘⠃⠀⠙⠛⠛⢿⣿⣿⣿⣿⠆⠀⠀⢸⣇⢀⡀⠀⡠⠄⣹⡇⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠈⡿⠻⡿⢻⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠻⠁
⠀⠀⠀⠂⢀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣰⡇⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠿⠍
⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠖⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣿⣽⣯⣮⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣽⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢶⣼⣿⡿⠛⠛⠉⠉⠉⠙⠛⠛⠛⠿⠷⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢖⣭⠷⣿⣿⢿⣿⣿⡆⠀⠀⠀⢀⣤⣤⣶⣤⣄⢲⣤⣌⡙⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣋⣥⣶⠟⠁⠀⢳⡉⠸⣿⠀⠀⠀⠀⠀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠃⠀⡜⢀⠈⢳⡀⠻⠀⡆⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡍⠻⣿⣧⠙⢿⣷⣽⣿⣿⣦⡀
⠀⠀⠀⠀⣠⡾⢻⣽⠟⢋⣽⣿⣿⣿⣿⣿⡇⠀⠀⠿⢸⡄⠀⠙⠶⣄⣱⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠈⢿⣧⠀⠈⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠰⡏⣱⠏⢀⣼⡿⠛⡿⠟⠛⣱⣿⣷⠀⠀⠀⠡⣿⡴⢀⡆⠀⠉⠻⢷⣦⣀⠀⢄⠀⣄⠀⠀⢻⣿⣇⠀⠹⣧⠀⠀⠙⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⡟⠀⣾⡟⠀⠀⢀⣴⠟⢻⡟⣿⣧⠸⡀⠀⠈⠻⣯⣿⣴⣇⠀⣤⡈⠙⢷⣄⢷⡘⢧⡀⠀⢻⣿⣆⠀⠘⠆⠀⠀⠘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢾⠀⣿⣧⣲⡼⠋⠁⠀⠈⢿⣽⣿⣷⣽⣦⡀⠀⠈⠙⠻⣿⣧⡈⢿⣦⡀⠙⢿⣷⡘⣷⡀⠀⢻⣿⡀⠀⠀⠀⠠⣄⠘⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠃⢻⣿⡿⠁⠀⠀⠀⠀⠀⠙⢿⣌⠻⣿⣿⣦⣄⡀⠀⠀⠉⠛⢶⣽⣿⣧⣌⢻⣧⠸⣷⡀⠈⣿⣇⠀⣷⡀⠀⢿⡄⢹⡏⣿⣿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠛⠻⢿⣷⣶⣤⣄⡀⠈⠙⠻⣿⣎⣿⣇⣿⣧⠀⢻⣿⡀⢸⣷⠀⠸⣿⡈⣿⣹⣿⣧⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠶⠛⠛⠛⠋⠙⠻⠿⣷⣤⡀⠈⢻⣾⣿⣿⣿⠀⢸⣿⡇⢸⣿⡇⠀⣿⣇⢻⡎⣿⣿⣇⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⡛⠂⠀⠀⠀⠀⠘⠉⢡⣴⣶⣶⣶⣤⣤⣤⣤⠂⠈⠙⣿⣄⠀⢹⣿⣿⣿⡆⠀⣿⣷⢸⣿⣿⠀⣿⣿⣿⡇⣿⣿⣿⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⣿⣷⡄⠀⠀⠀⠀⠀⠛⠁⠹⠿⠟⠼⠛⠋⠀⠀⠀⠀⠈⣿⡆⠀⣿⣿⣿⡇⠀⣿⣿⣾⣿⣿⠀⣿⢿⣿⡇⣿⣿⣿⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣻⣿⣿⠁⠀⣿⠟⣿⡟⣿⣿⡇⠈⣿⠁⣿⣿⣿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⠀⣿⣿⣿⠀⢰⣿⠀⣿⠃⢹⣿⠃⠀⠛⢸⣿⣿⣿⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢠⣿⢠⣿⣿⡇⠀⣼⡏⠀⠃⠀⢸⡟⢰⡄⢀⣿⣿⣿⣿⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⡀⣾⣿⣾⣿⡿⠀⢰⣿⠁⠀⠀⠀⠈⠀⣾⠁⣼⣿⣿⣿⣿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⣼⢳⣿⢟⣿⣿⠃⢀⣿⡏⢀⠀⠀⣤⠀⣸⡟⣼⠟⣾⣿⣿⡏⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢰⡏⢸⢏⣾⣿⡟⢀⣾⡿⠀⣼⠀⢰⣿⢠⣿⣿⠋⣼⣿⣿⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢸⡏⠀⣿⡇⠀⣸⣿⣿⠁⣼⣿⠃⣸⡇⢠⣿⣿⣿⡿⢁⣾⡿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⢠⣿⣿⠇⣼⣿⡏⣰⡿⣠⣿⣿⡿⠋⣰⣿⠏⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣿⡇⢸⣿⡿⣰⣿⡟⣰⣿⣵⣿⡿⠋⢀⣼⠟⠁⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⢹⣇⢸⣿⣧⣿⣟⣼⣿⣿⡿⠋⢀⡴⠟⠁⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠰⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠉⠀⠀⢀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣶⢹⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⢀⠄⢠⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠉⣿⣿⣿⡅⠀⠀⡀⠀⠀⢀⡴⠋⣰⡿⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠂⠀⠀⠀⠀⠀⢿⡆⢸⣹⣿⡏⢁⣴⠟⣡⢀⣴⠟⢀⣾⠏⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⢠⡿⣿⣆⢯⣿⣿⣿⣯⡾⣡⡟⢁⣴⡿⢁⣼⠋⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢿⣎⣿⣻⣿⣿⡿⠁⣠⡾⠋⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⢿⣿⣿⣿⣯⣠⣾⠋⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢀⡟⠀⠙⢿⣿⣿⣿⠀⣠⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣷⣾⢠⡟⢿⣿⣾⠏⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⣿⣿⡟⢀⣾⣿⡏⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣧⣼⣿⣿⠇⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⢻⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠸⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠁⠀⠁⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢒⣈⣻⣦⣾⣿⣿⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢋⠉⣡⣥⣿⣿⣿⣿⡳⠆⠠⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣴⣆⡄⣠⡿⠿⠋⠀⠀⠉⠳⣦⡄⠐⢜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢯⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⡇⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⣤⣧⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⡟⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢰⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠰⡟⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢾⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡻⣿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣟⠛⢌⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⢷⣌⢿⣷⣾⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡛⣿⣿⣹⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣷⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢠⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⢂⠠⡈⠦⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁⠄⠀⠀⠀⠀⠠⡮⠉⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⣾⠂⠈⠢⡀⠀⠀⠀⠀⡀⠀⢀⠀⢀⡾⠂⠀⠀⢠⠤⠖⠊⠁
⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠼⣇⠈⠀⡏⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⣠
⠀⠀⠀⠀⠀⠇⠀⠠⡀⠂⢀⡤⠤⡤⢤⣤⣜⣧⣤⣰⣷⡾⠛⠧⠀⠤⠤⣤⡀⠀⠁⠀⣀⡔⠁⠈
⠀⠀⠀⠀⠀⠈⢄⡀⠀⠚⢁⠄⠀⠀⢀⡤⢔⣛⣻⠵⠿⠚⠓⢀⠀⠈⠄⠈⠍⠉⠉⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⡟⠲⠬⡴⠞⠋⠁⡀⠀⠀⠉⠃⠀⠀⡰⠀⠈⠢⣵⣄⠀⣀⢤⣀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⢣⡄⠄⠈⠀⠀⠉⠳⠄⠀⠀⣠⠤⠴⠓⠂⠀⠀⠀⠀⠁⠉⠑⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠉⠚⠢⢀⠢⣦⠏⠀⣀⠼⠁⠀⣁⣀⡀⣄⡤⠐⢠⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠠⡌⠀⡆⠀⡃⣤⢞⠡⠀⠀⠙⠉⢉⠇⡈⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠁⠀⡼⠁⡼⠀⡰⠀⠀⡠⠁⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢦⢰⡇⠀⣠⠚⢁⡴⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⣼⠀⢑⡼⠀⢂⠅⠀⠃⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡻⠧⣸⠇⠀⠉⣠⠀⠋⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⢧⡴⠋⠙⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢠⠊⠀⠀⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡠⠔⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡠⡉⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠶⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠙⠁⡄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⠄⠀⠇⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣤⣀⣒⣒⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣤⣀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢿⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣿⠿⠟⠛⠻⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠿⢻⣿⠇
⠀⠀⠀⠀⠋⠀⣤⠀⠀⠀⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⡤⠀⠀⢠⣤⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠁⠀⠠⠄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡃⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠐⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⣛⣭⣭⣟⡿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠋⠁⠀⠀⠈⠙⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠿⠿⠿⠿⠛⣿⣇
⠀⠀⠀⠘⣿⣿⠿⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⠀⠀⢀⠀⢸⡏
⠀⠀⠀⠀⢻⠏⠃⠀⠈⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡁⠈⠁⠀⠀⠈⠁⢈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⠐⠂⠈⠁
⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄⠀⠀⣠⣾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠉⠀⠙⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠁⠉⠀⠉⢷
⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢃⣀⠀⠀⢀⣘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⡀⠀⠀⢀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠉⠀⠀⠈⠁⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⠈⠢⡀⠀⡀⠀⢸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⣦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣶⣉⣁⣉⠉⠓⠤⡀⠀⠈⣟⡀⠀⠀⠬⣉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠐⠂⠬⣖⠠⢤⡬⠭⠥⠽⢷⣴⠟⡉⠓⣌⠳⢦⣕⠢⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠚⠒⡑⠫⣑⢤⡙⢶⣄⡉⠀⠒⠀⣸⠀⠘⡀⢸⣄⡀⠙⢷⣌⣢⡉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠈⠳⡀⠱⡱⡄⠹⡘⡟⠭⢉⣙⢧⠀⣣⢺⠀⢹⠐⡄⠱⡝⡕⢄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⢱⡀⠱⢱⠀⢱⠈⣳⢖⠂⠵⣿⠃⡏⣠⡾⡀⢱⠀⠹⡌⣎⢆⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡏⡇⠈⡄⠹⣄⠈⠒⠌⢲⡞⠁⠇⢹⠸⠀⠀⢧⠸⡘⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠠⣦⣤⣄⣀⡀⠀⠀⣧⠀⠀⡇⠀⡇⠀⡟⢍⠒⠒⠢⢿⡜⣠⠞⢆⠀⠀⢸⠀⡇⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⡀⠀⠀⠀⠀⠉⠙⠳⡄⢾⠀⠁⡇⠀⡇⢀⠘⠢⣍⣀⣢⣄⣷⠁⠀⢸⡶⣄⢸⢀⠃⡇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠘⠿⠿⠷⠦⠄⠀⠀⠀⠀⢹⠀⠀⡇⠀⠇⠈⡄⢂⢫⡀⠄⠉⡙⢆⢀⡼⡇⢸⡇⡘⢀⠇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠸⡀⠘⡌⠂⡿⡙⠒⠒⠾⢿⠇⠇⠞⠛⢆⠸⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠸⡀⠀⠱⡀⠈⢆⠱⣌⣑⠒⠤⣘⣦⡾⠀⡆⠀⣧⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⢆⠀⠘⢤⠈⠀⢸⣷⠌⣉⠉⠙⠳⣄⡇⡜⢸⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢝⡦⢄⠀⢀⡿⠊⢳⣄⣀⣉⣒⣈⣿⡥⠊⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠙⠂⢣⡈⠢⠭⠭⠭⢍⡉⠁⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢌⠢⣙⠒⠶⠶⠶⢤⡈⠑⠒⠋⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠢⠄⣁⠀⠬⢕⡌⢂⡤⢖⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⣀⣀⣀⣀⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠉⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡈⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣴⡿⣷⣶⣿⣍⠓⠶⠟⠻⢿⣤⡲⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⢿⣶⣶⣭⠛⠲⠞⠛⠿⣧⣔⢦⡄
⠀⠀⠀⠀⠀⠀⠉⠅⠁⠈⠻⣿⣆⠀⠀⠀⠀⠈⠷⣍⣀⣀⡀⠀⠀⠀⠀⠀⢈⠉⠘⠀⠙⢿⣷⡀⠀⠀⠀⠀⠹⢮⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠿⣷⣤⠴⠖⠚⢿⣿⡄⠉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⣀⠈⠻⢿⣦⡤⠖⠒⠻⣿⣧⠉⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⢸⣷⡀⠀⣆⠀⠀⢿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠁⠀⣿⣆⠀⢰⡀⠀⠸⡏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠻⣦⣝⣷⣤⣈⣄⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠙⢷⣬⣻⣦⣄⣡⣀⡴
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⣶⣦⠱⡄⠘⣿⢻⠈⠛⠟⣧⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣴⣶⡌⢦⠀⣿⡟⡇⠙⠻⢻⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⢻⣾⠋⢈⣤⡶⢣⠟⣠⡇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⢉⠀⠘⣷⡟⠁⣡⣴⠞⡼⢃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣧⣰⣿⣿⠁⢏⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣔⣾⣿⡏⠼⣡⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⣷⣝⢆⠹⣇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠙⢿⣮⡳⡈⢿⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠰⣿⡀⠀⢸⠏⢹⣇⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⣾⣇⠀⠈⡿⠉⣿⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠉⠙⣶⡉⣠⢾⣿⡀⢀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡈⠉⢳⣎⢁⡴⣿⣇⠀⣸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣼⠩⠎⠀⠘⢿⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣴⡏⠵⠁⠀⠻⣿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⠈⢹⡄⠀⢤⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⡇⠉⣷⠀⠠⡀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠈⠣⢀⣿⠀⠀⠑⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠹⠄⣸⡇⠀⠉⢢⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⠀⠀⠐⠋⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠚⠁⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧
⠀⢠⣾⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣰⣿⣿⣿⣿⡟⠋⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣶⣿⣟⣿⣿⣿⣿⡇
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢼⣿⣿⠏⠁⠉⠙⣿⣿⢿⣿⡆⠀⢸⣿⣿⣿⣿⡿⠡⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⣾⢷⡾⠿⣿⠿⣿⣿⣿
⠀⠀⠀⢿⣿⣿⠛⠻⠃⠉⠉⠂⠁⠁⠀⠘⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⢸⣿⣿⣿⣏⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⠋⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⢡⠟⠀⠀⠘⢻⣿⣿⣿⣆⠀⠀⠰⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⣿⣿⣿⣿⡆⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠈⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⣿⣿⣿⣦⡀⠀⠀⣰⣶⣶⣿⣿⣶⣶⡄⢸⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⠿⣿⣿⡿⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠟⠿⠿⠿⠀⠀⠀⠀⠀⣹⣿⠟⠉⠉⠛⢿⢿⣿⡇⢀⣿⣿⣿⣿⣿⢿⡿⣿⣿⢸⣿⣿
⠀⠀⢻⣿⣿⣿⣿⣿⡗⠐⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⡼⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⢳⡿⠁⣿⣿⡷⣌⠹⠧⠘⠂⠈⠉⢸⣿⣿⡆
⠀⠀⠀⠙⢿⡟⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣞⠀⠀⠀⠀⠀⠀⠄⠘⠋⠧⠻
⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⢾⣿⣿⡟
⠀⠀⠀⢀⣠⣴⣶⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⢰⡿⠋⠀⠀⢀⣀⣀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢿⣿⣿⡿⠁⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⣿⢿⣿⣿⣆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣸⣿⣿⡿⡿⠉⠉⠙⣿⣿⣿⣦
⠀⠀⢻⣿⣿⠁⠈⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⡿⡟⠏⠀⠀⠉⣿⡿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢾⣿⣿⡿⠿⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠈⣿⣯⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⢱⡏⠀⠀⢻⣿⣿⡿⠙⠋⠉⠩⠉⣿⣿⣿⠁⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⣿⠇
⠀⠀⠀⠈⠿⠄⠀⠀⠀⠀⠘⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠀⠀⠀⣼⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠂⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣟⣿⣋⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣽⣯⣭⣿⣿⣽⣿⣯⣽⣿

⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⢀⣀⡀⠀⠀⡀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⢀⣠⣤⣤⣄
⠀⠀⢀⣴⣶⣶⣯⡛⢿⠓⣿⣿⣿⣶⣿⣿⡇⠀⢸⠟⠉⠻⣿⣷⠀⠀⣼⣿⠋⠁⠈⢻⣆⠀⠀⠈⠙⢻⣿⣿⣷
⠀⠠⣿⢛⣿⣿⣿⣿⡦⠀⠈⣿⣿⠟⠁⡀⠀⠀⣿⠠⠀⠠⢽⣿⡇⢰⣿⣿⠀⠈⠀⢠⣿⣧⠀⠀⠀⠀⠈⢱⡟
⠀⠀⠀⠀⢿⢿⣛⣿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⣿⡇⢸⣿⣿⣧⡀⠀⢸⣿⣿⠀⠀⠀⣀⠀⠀⡗
⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⡿⠀⠀⢸⣿⠁⠐⣿⣿⣿⡇⠀⠸⢿⣿⠀⠀⡰⠋⠀⢰⠃
⠀⠀⣠⣶⢶⣶⣦⡀⠀⣰⣿⣿⣿⣿⣿⣶⡀⢠⣤⣤⡄⢀⣤⣷⣦⡄⠻⠿⠟⠁⠀⢀⣤⣤⣄⠈⠀⠀⠀⡎
⠀⣸⣿⠟⠀⠉⠙⣷⠀⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠾⣿⣿⣿⣿⠀⣀⠀⠀⠀⣾⣿⣿⣿⣤⣤⡀
⠀⢻⣄⠀⠀⠀⠀⣿⠀⠈⠃⠀⠹⠛⣿⠋⠀⠙⠛⠟⠀⠀⠀⠙⠋⣠⣾⣿⣷⣆⠀⠈⣿⣿⣿⣿⡿⠿⠂
⠀⠀⠉⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠈⣿⣿⣇⠀⠻⣿⡛⠋
⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⣤⣶⣶⣦⡄⠀⠀⢸⡇⠀⠀⢻⣿⣿⠀⠀⠈⠁
⠀⢀⣾⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⠆⢸⣿⠟⠋⠉⠙⠀⠀⢸⣿⣄⠀⢸⣿⣿⠁⠀⣠⣶⣿⣿⣷⣦
⠀⣾⣿⡏⡀⠀⢹⣿⣿⡀⢠⠿⠛⠛⢿⡀⢸⣧⠀⠀⠐⠂⠂⠀⣼⣿⡇⠀⢸⣿⣿⠀⠀⠙⠿⢻⣿⣿⣿⣇
⠀⢿⣿⡇⠀⠀⠀⣿⣿⠀⠸⠐⠂⠐⠒⠃⣿⣿⡀⠀⠀⠀⢀⣾⣿⣿⡇⠀⣾⣿⣿⠀⠀⠀⠀⠸⡅⢰⣿⣿⠄
⠀⠈⠻⣿⡄⠀⢼⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⢸⣿⣿⣿⠇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡇⠻⠇⠀⠘⠿⣿⠿⠀⠀⠻⢿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣻⣿⣿⣿⣷⢦⣶⣿⠿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣾⠏⣾⡟⣿⢿⣿⡏⣿⣫⡴⢋⠭⠒⡛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠇⡆⣻⣼⡇⡞⢳⣽⣿⡟⠔⠁⣈⣤⣌⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣟⢳⡘⣿⣧⣧⢨⣿⣿⣧⣠⣾⣯⣽⣿⣿⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣿⣦⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣾⣶⣾⡦⠺⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡺⣿⣿⣿⣿⣟⠛⠻⠿⠿⣿⣿⣿⣷⣦⣌⠑⢦⣄⡈⠻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣝⣀⡘⣿⣿⣿⣿⡿⠶⠦⠼⣯⣿⣿⣿⣭⡂⠀⢄⡿⠙⢶⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣯⣛⣏⣉⣹⣿⣿⣿⣿⣶⣦⣤⣀⣉⣿⣿⣿⣶⣌⣿⡏⢰⠙⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢂⣻⣿⠟⡟⣡⠞⡙⡿⡟⣿⡏⣿⣏⢿⡟⣿⣿⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣴⣿⣿⡟⣼⣽⡿⠀⡇⠱⢳⣿⢀⣿⣿⢸⣧⢹⢻⣸⡇⢿⣿⣟⠳⡹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣾⣿⣿⡏⣵⣿⣿⢇⣰⡇⣎⢸⡟⣼⣿⣿⣼⣿⢸⢸⢹⡇⠸⣿⣿⣧⡄⢹⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⣿⣿⡇⢿⣿⣿⣸⣿⣧⣿⣿⣧⣿⣿⣿⣿⣼⣾⢸⣼⣿⠀⣿⣿⣿⡇⠈⣿⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣷⣤⣿⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣜⠿⣿⠻⢿⠿⠛⠟⠿⠿⠟⠟⡿⢿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠛⠛⣿⣿⣿⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⢻⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣫⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠘⠛⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠃⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠐⢦⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣀⣤⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡍⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠑⠛⡇⠀⠀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠐⠶⣦⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠈⣿⡤⠔⠀⣈⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠠⢶⣾⣯⠙⠿⠿⠒⠢⢤⣤⣽⣿⣿⣾⣛⣿⡦⢀⣼⣿⡆⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣂⠈⢀⣩⣿⣿⣿⣿⣿⡍⠙⢿⣿⣿⣿⣇⡔⠀⢀⠠⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⡟⢻⣿⣿⣿⠏⠀⢀⣾⣿⣿⣿⣿⣿⡟⢛⠤⣀⣄⣈⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣅⣈⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠻⠿⠟⠀⠀⠘⢿⣿⣿⣿⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠪⠻⣧⠠⠀⠀⠀⠠⢆⣈⣿⣿⣿⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⠄⠀⡜⢢⠀⠀⠀⠙⠻⢩⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠄⠀⠘⠁⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⡃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠠⠾⣿⣿⣿⣿⠀⠁⠘⣷⣶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣠⣿⣿⡿⠇⠀⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⣿⣿⣿⠿⠿⣿⣿⣿⣿⠁⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠙⡄⠀⠿⣷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⡏⡂⠀⠀⠈⠻⢇⡀⠘⢀⡿⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠢⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠑⢤⣼⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡳⣄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢊⣿⣿⣿⠷⢶⣦⣀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢱⡇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣇⣾⠟⠋⠁⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⢷⣄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⢷⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⢾⡿⠿⢿⣿⣟⢿⣿⣿⣿⡟⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⢍⠙⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⣈⠀⠈⠘⣿⣿⡇⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⢉⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⡌⢈⡉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⢻⣿⣿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠚⠋⢸⣿
⠀⠀⡠⠖⢒⣛⣛⣛⠒⠲⡄⠀⠀⠀⣾⣿⡿⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡦⢐⣷⡆
⠀⠀⡓⠶⠤⠭⠭⢭⢤⠔⣻⠀⠀⠈⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⡂⠀⠐⠹⠆⠀⠀⠀⠈⠢⡑⢄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠇
⠀⠀⢏⠒⠦⠤⠤⠤⠀⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠗⠷⠚⠛⠒⣄⠀⠀⠀⠀⠀⠀⠈⠲⡕⠄⠀⠀⠀⢸⣿⣶⣿⡿
⠀⠀⠀⠁⠒⠀⠂⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠸⡇⢠⠤⠔⠒⢲⡄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠸⡜⢋⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢹⠀⠀⠀⠀⠀⠀⢻⡈⠉⠁⠀⠈⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⠄
⠀⠀⠀⠀⠀⠰⡶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣀⣰⢶⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠈⠻⣏⣀⡇
⢀⠤⠚⠆⠀⠀⠀⠀⠀⣴⣾⣿⣦⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⢹⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⢠⠑⠁⠀⠈⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠰⡒
⠀⠀⠄⠀⢃⠀⠀⠀⠀⠀⠈⠉⠛⢦⣘⣷⠀⡀⣠⣛⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠰⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣿⣿⣿⣦⠀⠀⠀⠘
⢂⠉⣀⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂⠁⠀⠀⠀⠀⠀⠀⠀⢷⣺⣿⣿⣿⡿
⠀⢣⠄⢀⠈⢸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⠛⠛
⠀⠀⠳⡤⢤⠊⡧⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠙⠒⠋⠁⠀⠀⠀⠀⢀⠀⠰⠷⣶⣶⡶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⡝⢶⡆⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠊⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠤⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡉⠢⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠑⠒⠀⠉
⠀⢰⠀⠀⠀⠀⠀⠤⢂⠔⠁⠀⠀⠀⠀⠀⠀⠀⣠⠊⡀⢀⠀⠼⠂⣈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡾⠑⠒⠓⠒⠬⣉⠹
⠀⠀⠓⠀⠀⠀⠀⡀⠙⢄⡠⠀⠀⠀⠀⠀⠀⡔⠁⢠⠀⠈⡀⢀⢠⠀⢑⡬⠂⠀⠀⠀⠀⠀⠀⠁⣀⣠⣶⣒⣓⣓⣶⣀
⠀⠀⠀⠀⢀⡴⠛⠷⡤⠊⠀⠀⠀⠀⠀⢠⠎⠠⠀⠀⠠⠄⠀⢠⡤⠒⠁⠀⠀⠀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠢⡀⠀⠒⢀⡤⠚⠁⠀⠀⠀⠀⢀⣸⡍⢆⠀⠀⠀⠘⣿⣿⣉⣉⡉⠛⠛⣿⣿⡇⠀⠀⠀⢠⣤⡴⢦
⠀⠀⠘⢄⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡒⢈⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢧⣠⠏
⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣁⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⡿⢿⣿⣿⡟⠿⣿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠞⠁⠀⠀⠙⠻⣿⣷⣦⣍⣙⡒⠾⢭⣤⣈⡙⠲⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣝⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠋⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣬⣍⣙⠓⠲⢮⣭⣳⢮⣷⣵⡝⣿⣿⣿⣿⣿⣿⣿⣿⣦⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠭⢷⣒⣶⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⠓⠂⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⠈⠀⠹⣿⣿⣿⣿⣿⢧⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠰⠿⠋⢁⠀⣀⣀⣀⡀⢀⡠⠤⠒⠉⠁⠙⣿⣿⣿⣿⣧⡐⢀⣿⣿⣿⣿⣿⣷⡁⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢰⡶⠿⠗⠀⣠⠊⠉⠀⠉⠻⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠸⡟⠘⣿⡞⣿⣾⣿⣿⣿⣿⣿⣿⣷⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣷⠬⢄⣀⢠⣀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣀⡼⡟⢺⢋⠳⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⢃⠀⡇⠀⠙⠢⢄⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣆⠀⠈⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⡇⡿⣸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢠⠉⠉⠑⡄⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣏⠄⠀⠀⠈⢆⢈⡤⠴⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡟⣦⠀⠀⠀⠀⠡⡄⠐⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡏⢿⣿⣿⣿⣿⡟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢱⠘⣷⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⢸⠻⣿⣿⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡇⠈⢿⣄⠀⠀⠀⠀⠈⠂⠀⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠈⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄

⠀⠀⠀⠀⠀⠀⠀⠰⠍⠉⠉⠋⠙⠭⡆⠀⠀⡠⠤⠤⣤⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡆⠀⠀⣰⠂⠀⠰⠂⠀⠀⠀⠀⠋⠁
⠀⠀⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢲⡐⣀⣿⠀⠀⠈⢹⠁⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠄⠁⠀⣠⢀⡀⠀⠀⠈⠀⠁⠁⠀⠀⠀⢸
⠀⢀⡴⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂⠈⠉⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠠⠆⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠰⠃⠀⠀⠐⠀⠀⠀⠠⣂⠄⠀⠀⢰⠀⠀⠃⠀⠀⠰⠘⡄⠀⠀⣗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⡠⠄⠈⠁⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠹⠁⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⡀⠀⠀⠀⠀⢀⡠⠒⠉⣠⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⡀⠀⠁⠀⠌⠂⠀⠀⠀⣀⠔⠉⢀⡴⠊⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠇⠄⠂
⠀⠀⠀⠄⠈⠀⠠⠀⠀⠀⠀⢀⠤⠊⢀⡠⠞⠁⠀⡠⠔⠋⠀⠀⠀⠀⠀⠀⣀⡠⡠⠁
⠤⠈⠀⡀⠄⠀⠀⠀⠀⡠⠖⠁⣀⠔⠋⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠐⠈⠕⠂⠀⠀⠀⠒⠀⠀⠀⣴⣾⣧
⠘⠁⠀⠀⠀⠀⣀⠔⠊⢀⡤⠚⠁⠀⠀⠂⠀⠀⢀⠔⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃⠀⠸⣿⣿⡡
⠀⠀⠀⠀⡠⠞⣡⢀⠖⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠰⠋⠁⠀⣠⠺⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢈⠀⣀⠔⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⣀⡀⡄⠀⣀⠈
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣤⣤⠤⠔⠒⠈⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⣰⣿⣿⡟⠉⠛⠛⠛⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠿⠿⠿⣿⣿⡆
⠀⠀⢺⣿⣿⠿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡇⣿⣿⡿⢹⡟⠁⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⡿⠋⠁⠞⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⢩⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣻⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⡉⠙⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠐⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠳⠀⠀⠀⠀⠀⠰⣿⠻
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⢰⣏
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⣀⣠⣤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠙⣿⡄
⠀⠀⠀⠀⣴⣾⡿⠿⠛⠛⠛⠻⠿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣤⣀⠀⠀⠀⠀⠀⣰⣿⠿
⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢀⣾⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⠋
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢚⣿⣿⣿⢿⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⠦⠀⠀⠀⣼⡟⠉⠉⠀⠉⠉⠉⠉⠉⣿⡄
⠀⠀⠀⠋⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⠃⠀⣸⣿⣿⣿⠈⠓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠛⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠘⢧⡄⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠹⠷⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢀⣼⣿⣿⣿⡇⢿⣿⣿⣿⢿⡯⢻⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠸⣿⣿⡆⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠸⣿⣿⠹⣿⣿⣿⣿⣷
⠀⠀⠀⢸⣿⣿⡏⠁⠘⢿⣿⡇⠸⠇⠀⣿⣿⡟⠀⠀⠀⠀⣿⣿⡟⣿⠉⢿⣿⠁⠀⠀⠀⣿⣿⣷⠀⠀⠐⠋⣿⣿⣿⡇⠃⠀⠀⡿⠁⠀⢹⣿⣿⣿⡏
⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠻⠁⠀⠀⢰⣿⡇⠇⠀⠀⠀⠀⢿⣿⡇⠘⠂⠘⠿⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⡿⣿⣿⡃⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠘⠋⠣⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠀⠀⠀⠀⠀⠀⠻⣿⡓⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙
⠀⠀⠀⠀⠀⠿⢧⡀⠀⠀⠀⠀⠀⢀⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⢿⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⠀⠀⠀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠁⠀⠀⠀⠀⠀⣀⡀⠈⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡤⠞⠋⠉⠁⠀⠀⠀⠈⠉⠙⢦⡀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠎⠀⣠⡴⠒⠀⠀⠀⠐⠒⢦⣄⠀⠹⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠈⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠹⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀⣼⠋⠉⡒⠲⠄⠀⠀⠀⠰⠖⡚⠉⣿⡄⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡏⠀⣿⠋⠹⣿⠂⠀⠀⠀⠀⠀⢸⡿⠉⢻⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⡀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⢻⣆⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢻⣆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣰⠃⠀⠀⡆⠐⣄⡀⠀⠀⠈⠀⠀⠀⢀⡜⠁⠀⠀⠹⣆⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢰⠃⠀⠀⢰⠃⣤⢹⠈⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡆⠀⢻⡼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠀⠀⠀⡞⠀⢿⡆⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡇⠀⠈⣇⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠈⠀⠀⠀⡇⠀⠘⣷⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⠁⠀⠀⢻⠀⢹⡆
⠀⠀⠀⠀⠀⢀⡤⠒⠀⠈⣷⡀⠀⠀⠀⠀⠹⡀⠀⠙⣷⡀⠀⠀⠀⠀⢳⠀⠀⠀⡇⠀⠀⠀⢸⠀⢸⡇⠀⠑⠦⣄
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠑⠀⠀⠈⢻⣄⠀⠀⠀⠈⢣⠀⠀⠃⠀⠀⠀⡌⠀⢸⡇⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠾⠿⠿⠟⢛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡏⠀⠀⠙⠋⠁⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡸⠁⠀⠀⠀⠀⠀⠐⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⢁⣴⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡿⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠸⣄
⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠙⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠙
⢀⣀⠀⢀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⡟
⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠋⢉⣼⠟⠋⠀⠘⣿⣷⡀⠙⠜⠿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⠁⢿⣿⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠞⠋⠁⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠈⠛⠻⠿⠿⠟⠉⠀⢸⣿⡿⣧⠀⠈⠻⢷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉








⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⡀⠀⠀⠀⡠⢠⣠⠤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠚⠁⠀⠀⠀⠒⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠋⠀⢴⣶⠆⢀⢠⣦⡆⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠤⠇⢀⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠋⠀⠀⡀⠀⠈⠐⠃⡠⠂⠀⠀⠀⡯⣁
⠀⠀⠀⠀⠀⠀⠀⢠⢊⢀⠘⠀⠀⢀⢀⠉⠐⠀⠐⠊⠀⠀⠀⠀⠀⢘⣰⣦
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢡⠠⠄⠐⠒⠈⠊⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠆⠀⠠⣔⣃⠒⠻⢀⣀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢡⠀⠀⠀⠀⠄⠀⠀⣠⠃⠈⣂⣼⠞⠁⡺⣶⡔⡄⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⠔⠂⠁⠠⠔⢛⣃⣊⠔⠀⣿⡀⠙⢦⡀⠇
⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠑⠤⠒⠉⠀⠀⡠⠂⠀⠀⢸⣻⠁⣥⡄⠋⠇⣤⡍⠈⢀⣀
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠚⠢⡀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠈⢻⠀⠋⠀⠀⠀⠉⠁⠀⣿⠜
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⠑⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠀⠀⠀⠂⠀⢀⠐⠙⣧
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⡵⠘⠛⠆⣠⡏⠀⠷⢀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⣀⠈⠁⢴⡆⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠸⠇⠀⠀⠋⠀⣠⡄⠀⠐⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⣀⣤⣖⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣌⣿⣯⣟⣹⣬⣿⣷⣿⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣿⣿⠿⠛⠻⠻⠿⠿⠿⠿⣿⣿⣿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡧⢶⣶⣦⣀⣀⣠⣶⣶⣖⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣈⣻⣿⣿⡏⣒⡀⣿⣿⣿⣿⣿⣿⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡹⠟⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⠦⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⡇⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⣅⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣍⣁⠲⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣆⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣦⣀⠀⣰⣟⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣳⣶⣾⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⡄⠀⠀⠀⢠⡾⣻⠏⣿⢻⣇
⠀⠀⠀⠀⢀⣸⢃⣿⠀⣿⠦⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⢏⠹⡇⡹⡆⠋⠀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠋⠸⠟⠀⣴⣿⣿⠛⢿⣿⣦⡀⠀⠀⠀⠀⡄⡆⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⡟⠀⠈⢻⣿⣿⣦⡀⠀⢀⡡⠐⠊⠁⠀⠀⢀⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣷⠀⠀⣀⣹⣿⣿⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣯⠀⠀⢹⠀⠀⠀⢸⣿⣿⣿⠀⣠⣄⠀⠀⠀⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⡄⠀⠀⣀⠀⠀⢸⣿⣿⠿⢐⣇⣈⡄⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠾⢿⣿⣿⠦⣀⠀⢀⣠⠞⣿⡿⠀⠘⠉⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠛⠉⠁⠀⠀⠀⠃⠀⡀⠠⣥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⣿⠀⠠⠄⠀⠄⠄⠤⠂⠈⠀⠀⠀⠑⣄⢚⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣛
⠀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡀⠀⠔
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣇⡀
⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠋⠘
⣿⣶⠀⡀⢀⠀⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠀⣠⠞⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡂⠀⠀⠀⠀⡀⠀⣀⠂⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⣤⡄⠂⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⡗⠀⠀⠈⠀⠀⠀⣄⡀⠀⢀⠒⠉⠛⣇⠀⠀⠀⠀⠄⠀⠀⠀⠃
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣝⡇⠀⠘⠀⠀⠀⢸⠃⠀⠀⡀⡀
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠀⠀⠀⠈⣠⠀⠀⠀⣌⠃⠀⠀⠀⠀⠀⠐⡇⠀⠀⠤
⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠐⢸⠀⠘⠋⠃⠀⠘⠉⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⢀⠀⠀⠀⠀⣸⠋⠉⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠌⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠙⠉⠙⠋⢁⡄
⠀⠀⠀⣤⡄⠆⠀⠀⠀⠐⠀⠀⢿⠃⠆⠀⠀⣽⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠄⠆⠐⠐⠀⠀⡔⠃⠀⠀⠀⡀⠇
⠀⠀⢠⡌⠁⠛⢣⣦⠀⠀⡄⢀⡿⡄⠀⠀⠀⣽⡆⠀⠀⠀⠀⠠⠽⠧⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶⠀⠀⠀⡇⠃
⠀⠀⠘⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠠⠠⠀⠶⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠓⠃

⣿⣿⢛⠻⣛⡛⣻⣟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⢀⡜⠁⠀⠀⣠⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠙⠉⠀⠀⠀⡴⠁⠀⠀⠀⠁⢀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⣵⣶⡶⠂⠤⣄⣠⡼⠁⣠⠞⢁⠀⠀⡈⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣿⡟⠀⠀⡀⠀⢉⣴⡖⠁⠊⠉⣀⠀⢉⢀⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠀⣠⣾⢃⣠⡾⢹⡇⠀⠈⠉⠉⠀⠈⠛⢿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⣷⠿⢻⣿⣿⠋⠀⠈⢀⣀⠀⠀⠀⣠⠖⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣿⡙⣅⡀⠸⠘⣿⢠⡎⠀⠻⠿⠗⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡌⢳⡘⢿⣷⣄⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣦⠃⢸⢿⣿⣵⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⣴⣡⣾⠟⠁⢸⡟⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢸⣿⠀⢿⡀⠀⣸⡿⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠐⣿⡄⢀⣽⣟⠧⣄⢵⣏⠁⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⠋⠀⠈⢣⢹⣧⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢰⠀⠀⣼⠉⢀⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠆⠁⠀⢼⣏⠀⠾⡆⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠉⠳⠀⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠐⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠘⠂⠇⠀⠀⠈⠈⡃⠀⠀⠀⠃⠀⠀⠀⢀⠄⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⠀⠄⠂⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣤
⠀⠀⠴⠒⠒⠒⠒⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⢱⡆⠀⠀⠀⠀⠀⠄
⠀⠀⡇⢀⠖⠉⠁⠉⠢⡀⢰⠉⠉⡆⡊⠀⠙⠄⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠞⠃⠀⢀⠀⠀⠀⢀
⠀⠀⡇⡌⠀⠀⠀⠀⠀⠱⠈⡲⣒⠁⢙⡶⡊⠀⠀⠀⠀⠀⠀⠀⣀⠀⣃⠀⠀⠠⢀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠛⠄
⠀⠀⡇⠡⡀⠀⠀⠀⠀⡔⢸⠀⠀⡇⣇⠀⢈⠀⠀⠀⠀⠀⠀⠀⡅⠀⠬⠀⠀⢀⣀⣀⡀⠀⠠⠀⠰⠀⠀⠀⠀⠁⠤⠀⠄
⠀⠀⣇⠀⠑⠢⡤⠄⠊⠀⠀⠉⠉⠀⠈⠉⠁⢸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⠀⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⠌⡆⠀⠀⠀⡇⠘⠀⠀⠀⠀⠅⡀⠀⠀⠀⠀⡈⠂⠀⠰⠰⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠁⠀⠀⠁⠀⠀⢮⡰⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡾⢩⠏⢿⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢤⢀⠠⢄⡀
⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⡅⡆⠀⠹⢍⡘⢹⠀⢀⠔⠛⠋⠲⡄⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡁⠀⠀⢻⡀⢀⢈⡬⢷⡾⠀⢸⠀⠀⠀⠀⡸⠀⠀⠀⠀⡇⠀⢠⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠢⡉⠓⠛⠛⠉⠀⠀⠀⠓⠤⠤⠖⠁⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⢢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠠⢄⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠒⠂⠒⠀⠘⠀⠀⠀⠀⠸⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠄⠀⠀⠀⠀⡀⠀⠀⠡⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠘⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠴⠒⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠤⠄⠀⠀⠀⠀⢀⣤⡤⠤⠀⠀⢢⣤⣄⡀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣶⣯⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡏⠬⡙⡻⠮⠿⣇⠀⠀⠀⠀⠀⢠⣾⣿⡿⠿⣷⣾⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣤⣾⡟⢹⣿⡿⣇⠀⠀⠛⠋⠀⠈⠀⠀⠀⠀⠀⠂⠸⠿⠯⠴⠟⣹⠀⣿⡟⣿⣿⡄
⠀⠀⠀⠀⡴⠋⣠⠉⠀⢸⣿⡇⠘⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⣿⠇⣿⣿⣷⡀
⠀⠀⠀⠘⠀⡼⠋⠀⠀⡞⣿⣧⠐⣄⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠈⠸⣱⢸⡟⠀⣿⣿⣟⣧
⠀⠀⠀⠀⣸⠋⠀⠀⢸⡇⢻⣿⠀⠁⣦⡀⠀⠀⠀⢤⣤⡀⠤⡀⠀⠀⠀⢀⠀⢃⣿⣼⠃⢀⣿⠁⢿⢸⡄
⠀⠀⠀⠀⢟⠀⠀⠀⣸⡇⠸⣿⠇⠀⠻⣿⣦⡀⠀⠀⠘⠉⠀⠀⠀⣀⢴⡏⣜⣿⣿⠏⡀⠈⠟⠀⢸⣄⡇
⠀⠀⠀⠶⠈⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⣿⣿⡏⠑⢤⡀⢀⣀⠴⠊⠁⣾⢁⢿⣿⡏⢀⠃⡜⠀⡀⢸⡟
⠀⠀⠀⡀⢀⡄⠀⠀⣿⣿⠀⣾⠀⠀⢀⣿⣿⠇⠀⠀⠉⠉⠀⠀⠀⠀⣿⣸⣿⣿⡄⠸⣰⠁⣰⢁⣿⠁
⠀⠀⠀⢀⡈⢀⠀⡁⣷⣿⠀⡟⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡗⢠⡟⢰⢟⣾⡿
⠀⡠⠚⠉⠈⣿⣆⢳⣿⡇⢰⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣿⣿⣇⣿⢡⢯⣾⣿⠃
⠘⠁⠀⠀⠐⠈⢿⣾⣿⠃⡘⠀⢡⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢻⣿⡇⣼⣾⣿⠋⠙⢆
⠀⠀⠀⠈⠀⠀⢸⣿⠇⢠⡗⢣⡿⠋⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⡁⠀⠀⣼⢉⣿⣿⣿⡇⢀⠨⣇
⠀⠀⠀⠀⠀⠀⢸⠃⢠⣿⠶⠋⠀⠀⠀⠈⠑⠒⠠⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⣸⣾⣿⣿⠏⢰⡁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⢸⠃⠀⣿
⠀⠀⠀⠀⠀⠀⣠⣿⣾⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣽⡏⣿⣿⣿⡧⠊⠀⠀⣿

⠀⠀⠀⠀⢀⣰⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⡿⠻⠟⠙⠻⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⢯⣳⡄
⠀⠀⢰⣿⡿⠿⠿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⠀⡠⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠾⢟⠁⠠⠄⠀⠉⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠆⠀⠀⠀⠀⠀⠀⠂⠀⠐⠒⠀⠈⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣏⡉⢙⣢⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⣰⣾⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⢀⣤⣤⣬⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⢾⣿⣿⣿⣿⣿⡿⣿⣿⣷⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⠟⠛⢩⣟⣿⣿⣿⣦
⠀⠀⠛⠟⠉⠉⠉⠁⠘⠻⣿⡟⠀⠀⠀⠀⠈⠉⠁⠈⠉⢀⣿⣿⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠹⢾⣿⣿⣿⡷
⠀⠀⠀⠐⠠⠀⠠⠀⠀⠀⠟⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠈⣿⠛⠓⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⡝⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⣠⣇⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⣞⠛⠶⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⣩⣾⠟⣹⠿⢿⠷⠂
⠀⠀⠀⠀⠀⠐⠅⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⢠⣤⣐⠻⣿⣿⡇⣿⣧⠀⠙⠻⣿⣿⣷⣶⡄⢀
⠀⠀⠀⠀⠀⢰⣿⠟⢋⣩⣽⠧⠄⠙⢿⣿⣆⠙⢡⣿⣿⠀⢸⣇⢸⣿⣟⢿⣿⠘⣿⣦
⠀⠀⠀⠀⢠⡟⠁⢠⣾⢏⣴⣶⣶⣦⡈⣿⡿⢠⣾⣿⡟⣠⣿⡏⣸⣿⣿⡎⡿⢀⡿⢃⣾⠀⣶⣦⡀
⠀⠀⠀⠀⠸⠀⠀⣾⢃⣾⣿⠿⠿⣿⡇⠿⢡⡿⢛⣿⣴⡿⠋⣰⣿⣿⠿⠃⢀⣠⣴⣿⡿⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⡼⢋⣤⣶⣶⠦⡀⠀⠟⠁⠘⣛⣭⡄⠀⣠⣤⣴⣶⣾⣿⣿⣿⡿⠁⡼⠿⠟⠁
⠀⠀⠀⠀⠀⠀⡸⠀⣰⣿⣿⠿⣯⠃⠀⠀⠀⠀⠀⠉⠉⠉⠁⡀⢨⣭⣭⣍⣩⣭⣥⣴⣶⣾⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣌⡛⢿⣿⣿⣿⢿⣷⡄⠐⢬⣍⡙
⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣝⣿⣷⠎⠙⠂⠀⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣾⣼⣿⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⠦⠀⠀⠀⠀⠙⢿⣿⣷⣌⡻⣷⡆⢼⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣸⢸⡦⣤⡀⠀⠀⠀⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⠛⠛⠻⢾⣿⠸⣿⣿
⠀⠀⠀⠀⠀⣤⢸⣿⣿⣷⣿⢸⣷⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡾⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣄⠹⠀⣿⣿⡆
⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⢸⣿⣷⠶⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⡇⢹⣿⣿⣿⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠂⣿⠀⣿⣿⣷
⠀⠀⠀⠀⠀⢹⣿⠘⣿⣿⣿⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⣿⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⢰⡏⣸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡟⢰⡀⠸⣿⣿⣆⢲⣟⡁⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⡇⣿⡇⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠸⠃⠀⢸⣿⠀⣼⠃⡄⣿⣿⣿⣿⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⢸⣷⠘⠇⠹⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡿⢰⡇⢸⡟⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡇⢸⣿⣧⡀⠀⠈⠻⣯⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠐⢁⣾⡇⢸⡇⢻⣿⣿⣶⠄⢰⣶⣶⣷⠈⢿⣿⣿⣿⣿⣿⣇⠀⠻⢿⣿⣦⡀⠀⠈⠃⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣼⣿⡇⠈⠇⣾⣿⣿⡟⢀⣾⣿⣿⣿⡇⠸⣿⣿⡟⣿⣿⡿⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⣼⣿⣿⡇⠀⠀⣿⢸⡿⢁⣾⣿⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢠⡇⢠⠇⠞⣡⣾⣿⣿⣿⣿⣿⡏⠀⣿⡿⠀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣼⡇⡜⠀⣴⣿⣿⣿⡟⣿⣿⡟⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢰⣿⡇⠀⢀⣿⣿⣿⠏⣰⣿⠏⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣾⣿⠀⠀⣼⣿⡿⠃⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣿⣿⡏⣰⣿⠟⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⢻⡿⢠⡿⠃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⡴⣾⣿⣟⢦⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣹⣿⣦⠀⠀⠀⠀⠀⠀⠀⣠⣾⣽⣿⣿⡗⡆
⠀⠀⠀⠀⠀⣸⠱⠏⠀⠀⢰⣾⠄⠀⠀⠀⠀⠀⢸⣿⡏⠁⠀⠀⢻⣧⠀⠀⠀⠀⠀⠘⢧⠸⠋⠙⢻⢣⣇
⠀⠀⠀⠀⠀⣿⣄⠂⠀⠀⢀⣿⡆⠀⠀⠀⠀⣤⣾⣧⢷⡄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄
⠀⠀⠀⠀⠰⣿⣩⡦⣘⣣⢾⣿⡷⠀⠀⠀⠀⠘⢿⣿⣶⡃⠶⢢⣿⠏⠀⠀⠀⠀⠀⠀⠀⣄⠖⡠⢸⠏⢸⡇
⠀⠀⠀⢀⡴⣯⢱⡆⢀⣅⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⣯⣀⣾⡇
⠀⠀⠀⠘⢧⣬⡟⠀⢸⡟⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⡇
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠈⢸⠛⠁
⠀⠀⠀⠀⠀⢀⣤⠶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢷⣺⣯⣶⣄
⠀⠀⠀⠀⢠⣿⠛⣾⠿⠟⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢻⣧⢱⣿
⠀⠀⠀⢠⣾⢿⠗⠝⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⡄⡀⡀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⡿⡿⠏
⠀⠀⠀⠘⠿⢿⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⢍⡁⠀⠉
⠀⠀⠀⠀⠀⠊⠀⠀⠂⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢢⡄
⠀⠀⠀⠀⠀⣠⠞⠋⠙⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠿⠟⠉⢻⣿
⠀⠀⠀⠀⣠⣿⠀⣠⠔⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇
⠀⠀⠀⠀⣿⣽⢧⡷⡄⠀⢸⡆⠀⠀⠀⠀⠀⠀⢠⠻⠃⠠⠟⠻⣝⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⢠⣾⣿⣇
⠀⠀⠀⠈⣿⠱⢾⣦⠑⣣⣿⣄⠀⠀⠀⠀⠀⢠⣿⣠⠂⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠞⠟⣿⡆
⠀⠀⠀⠘⣟⢣⡞⠋⠀⣿⣤⠟⠀⠀⠀⠀⠀⣸⣌⠻⡀⢤⠄⡰⡿⠿⣆⠀⠀⠀⠀⠀⠀⠀⣾⣴⣶⣾⠋⠉⠁
⠀⠀⠀⢰⣿⡿⠋⠀⠀⠘⢻⣷⠀⠀⠀⠀⢸⡏⢁⣤⡯⠐⠊⢷⣉⢻⡿⠀⠀⠀⠀⠀⠀⠀⢿⠋⣋⢸⠄
⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠁⠻⠟⠁⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⡀⢀⠀⡔⠀⠢⠀⠀⡀⣀⠀⠀⣀⠀⠀⠀⢰⠄⢰⠂⢀⠆⠀⢲⠀⣀⠀⠀⠔⠒⠒⡄⠀⣀⠀⠀⡠⠄⠤⡀
⠘⠁⠃⠀⠀⠁⠀⠀⠀⠄⠘⠀⠀⠑⠂⣤⡈⢿⣵⣮⠣⡈⣄⠾⠲⣤⣘⡠⢃⣀⠀⠀⠀⠀⠘⠨⠁⠀⠈⠀⠀⠀⠸⠀⠀⠀⠉
⠀⠤⢄⠀⠆⠉⠁⠀⠀⠀⢀⠀⠰⠃⠀⢻⣝⣶⣇⣉⢦⢋⣤⣶⣶⣄⣈⡶⣋⠏⣄⠀⠴⠤⠀⠔⠀⠀⠈⢢⠠⠄⠀⠂⠈⠁⠂
⠀⠤⠄⠀⠀⢂⠀⠘⠁⠀⠀⠀⠠⡔⢂⢦⣽⣿⣿⣄⣶⠸⣿⣟⠛⠛⣇⡶⠧⠾⣥⣄⣀⠀⠀⡀⢐⠈⠉⠀⠀⠀⠀⠉⡀⠀⠁
⠀⠀⣠⠴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠙⠣⠿⢿⠛⠛⣏⣉⠭⣿⣶⣾⠟⠃⣸⠒⢾⣿⣿⣿⣷⠄⠀⠀⠱⣠⣶⣶⣾⣿⣳⣶⣤⡀
⢠⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣛⣀⡤⠞⣹⠉⡸⣧⢴⣇⣴⡦⠻⣎⢙⠉⠙⠈⠛⢯⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡽
⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠁⠐⠃⠚⠅⡾⢳⡈⠁⠈⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣶⣄⠀⠀⠀⠀⢠⠞⠀⠀⠙⣄⠀⠀⠀⠀⢠⣴⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠈⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣰⠋⠀⠀⠀⠀⠈⢦⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⠸⡻⠟⠋⠹⡄⡴⠁⠀⠀⠀⠀⠀⠀⠈⢧⢀⠟⠉⠛⠛⡏⠉⠛⠛⠛⠛⠛⠋⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣀⣳⡀⠀⡇⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠄⡀⠀⠲⣭⣯
⠠⣶⣦⢠⣤⣄⢀⣄⡀⠙⠿⠋⢀⡀⣧⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⢾⠁⠀⠀⠀⡏
⠀⢹⠇⠂⠻⠃⠘⠿⠃⠒⠚⠒⢻⠟⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⣇⣀⣀⣠⣤⣤⠴⢻⠲⠤⠒⠊⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⢾⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠉⠉⠉⠉⠉⠉⠉⠀⠐⠀⠐⠒
⢠⣀⣀⣄⡄⣀⢠⣀⣀⣀⣤⣤⠤⠖⣺⡆⠀⢨⡴⣖⣋⠉⠉⠉⠉⠉⠉⣓⣲⢤⢰⠀⠀⣼⠆⣄⡀⡀⣀⣀⣀⠸⠴⡇⠀⠤⠤
⣼⣿⣿⠿⠿⠟⠛⣋⡉⠀⠢⠃⠫⣯⢽⢳⠀⡿⢸⣏⡛⠻⠿⠿⠿⠿⠛⣋⣿⡜⣿⠀⢠⣿⠈⣐⡪⣳⠐⢚⡀⢀⠐⠀⢀⠊⢰
⢀⢢⢤⠤⣷⡉⠉⢤⠐⣾⢫⡶⡂⢠⢸⡘⣷⠇⢸⣿⣿⡆⠀⠀⠀⢠⣾⣿⣿⡇⢻⡄⡼⢸⢰⢢⠢⠄⠡⠠⣤⠳⣞⣀⡸⠱⣅
⠐⢽⡉⢡⣈⡟⣉⣉⣇⣼⠐⠀⠅⣀⠘⣷⡇⠀⠘⠿⢿⣧⣶⣤⣦⣼⣿⣿⡿⠁⠀⢻⡇⣾⢀⠝⢁⡂⣸⡀⠨⠤⠏⠋⣠⣀⣤
⠰⣄⡈⠣⡜⡷⣨⠃⡦⢤⠼⠲⠠⠁⠄⣟⠧⣴⣶⣾⡿⠿⠿⠿⠿⠿⠿⣿⣷⣶⡦⠞⢡⡇⡜⠋⢯⢔⡹⠈⠞⠆⢒⠫⣥⡽⠥
⠀⡁⢈⠀⢿⢻⡁⡈⢤⡾⣤⢺⡜⡼⠀⡜⢦⡀⠉⢪⡻⠭⠭⠭⠭⠭⠭⢋⡞⠁⠀⣠⠏⠄⢧⠆⣸⣁⡄⠁⡘⠧⣾⠤⢃⠰⢰
⠀⡧⢸⠎⠉⢸⡈⢣⡘⠿⠛⡯⡠⠃⡂⠹⣄⠳⢄⡀⠳⣄⣀⣀⣀⣀⣠⠞⠀⡠⢚⡁⠐⣞⡎⢉⠓⢴⠘⣒⢡⣥⡌⣢⢌⠄⢛
⠀⠎⡆⢼⠫⣳⠙⡼⣗⠓⢊⡅⡀⠼⣡⠀⡏⠳⣄⠉⠓⠦⣍⠉⣉⠭⠖⠒⠚⠱⡱⠀⠆⢻⠘⢤⡾⠀⡣⣠⠸⣍⡆⠣⡜⢢⠐
⠈⡄⡱⠼⣥⡥⡜⢫⣘⢾⠄⣹⠁⡄⠀⡴⡁⠸⡈⣉⠙⢲⢬⡛⢁⡴⡞⠛⡩⢠⠁⣶⠀⣟⢉⡌⠩⢹⢴⠈⢏⢸⠰⣃⡨⢶⢸
⠀⠻⠆⠲⠑⠃⠣⠇⠋⠖⠈⠻⠄⠫⠁⠠⠅⠸⠰⠇⠎⠀⠰⠟⠻⠴⠁⠘⠓⠚⠷⠠⠆⠨⠉⠃⠰⠚⠖⠖⠉⠾⠰⠡⠰⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⣦⣄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⡦⠀⢀⣠⡾⠛⠛⠒⠒⠒⠚⡛⣦⣄⠲⢄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠒⠿⢶⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣿⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⢠⠚⠁⡄⠸⣇⠀⡀⠀⠀⠀⠀⠀⡠⠀⠐⠋⠀⠘⠁⠚⠿⢿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡄
⠀⠀⠀⠀⠀⠈⠄⡄⠰⠀⢛⣼⠀⠀⠀⠤⠂⠉⠀⢀⡀⢀⣀⣐⣄⣠⠀⠀⠈⠉⠻⠷⠀⠀⠀⢀⣀⣀⣀⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠾⣦⡳⡀⡟⠀⠀⠀⠀⢀⢴⠀⡀⠙⠿⢿⣿⣿⣽⣝⣢⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠙⠿
⠀⠀⠀⠀⠀⠀⢀⠠⠟⠿⣿⣿⠀⣴⠋⠀⡂⠀⠈⠉⠲⣶⣤⡝⠋⠃⠀⠹⠗⠒⠢⡀⠀⣀⣤⡶⢦⣤⣞
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠹⣇⢸⠇⣴⡹⠁⠄⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣇⣀⣉⡿⠛⠐⣼⣿⠛⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣠⠎⠉⠉⢿⠀⠀⠀⠉⣤⣷⠀⠈
⠀⠀⠀⠀⠀⠰⡀⢆⠀⠀⢀⠀⡋⢸⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣀⡴⠞⠡⠄⠀⠀⠠⠀⠀⠀⠀⣠⢏
⠀⠀⠀⠀⠀⠀⠙⢦⣥⣄⣈⢳⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠞⠁⢸⠂
⠀⠀⠀⠀⠀⠰⠁⠈⠀⠈⠉⢿⡏⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢿⡆⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⠶⠐⠆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣿⡟⠀⢑⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⠀⡀⣿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡦⣤⣰⡿⠀⠀⠀⡀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⡀⢁⠬⠁⠌⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⣁⢰⣧⡞⠂⢤⠀⠈⠀⠀⠀⠀⠐⠖⠆⢸⡷⠋⣠⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢯⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢲⣄⡈⠳⣏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷⠀⠀⢰⡇⠀⠀⠀⠀⠀⣾⢉⢻⣶⠿⠀⣀⣷
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠲⢿⡇⡀⠘⡟⠀⠀⠀⠀⠀⢹⣧⣾⠁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⡒⣾⣿⣀⣶⡇⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠻⠿⠋⡕⠀⠀⠀⠀⢀⠐⠉⡒⠖⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⢲⣆⠁⠑⣄⠀⠀⣾⡠⢠⣇⠨⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠋⠆⠀⢻⡆⠀⣿⢃⣾⠃⢸⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠰⡸⡄⠈⠟⠀⢹⣾⡏⢠⡏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣀⢷⡁⠀⢸⠀⠈⣽⡁⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⠏⠿⡀⢸⠀⠀⠙⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣙⣛⣛⣹⣯⣩⣉⣿⣋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣽⣭⣽⣿⣯⣭⣭⣭⣭⣿⣭⣭⣯⣭⣽

⠀⠀⠀⠀⢀⡀⠀⠐⠦⣄⣀⠀⠀⠀⣀⠀⢀
⠀⢀⠀⡠⠚⠒⣶⡄⠀⠀⠠⣘⣊⡩⠀⠐⠀⣈⠢⡀⠀⠀⠀⠀⠠⠤⡀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢨⠎⠀⠀⢠⠈⠸⢗⠐⠛⠉⠉⠉⠩⠈⠀⢙⢧⣈⢦⣀⠀⠀⢀⠤⢼⠧⠀⠠⠦⠔⠀⠤⠐⠒⠦⣄⡀⠀⠀⢀⠅
⠀⡆⢀⣉⠀⠈⠲⢄⡄⠢⢀⢀⠀⠀⠀⠳⡄⠑⢦⣍⡛⠫⣉⣀⣉⣠⡮⠴⠂⢀⠉⣛⣉⡛⣒⡾⠶⠤⠤⠬⢍⣀⢤⣀
⠀⠀⠀⠉⠀⠀⠀⢸⠇⡐⠀⢿⠑⠶⠶⢶⣬⣆⡀⠘⠿⣶⡴⠉⠁⠀⠠⡤⠬⡿⠿⠵⢄⠀⠢⠉⠓⠦⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⡏⠠⠁⣤⢈⢗⢋⡀⢆⠻⠿⣿⣗⠢⢌⠹⠓⢶⢛⠟⠲⠶⠾⣄⠒⠢⣕⣄⠀⣑⢀⠀⠀⠈⢉⣤⣀⢀⣀⠀⠀⠀⠀⠀⠔⠐
⠀⠀⠀⠀⠀⠀⠘⡄⡆⠀⢾⠆⠱⣄⠑⠊⡶⠶⣌⠻⠷⣬⡕⣂⠀⠀⠀⠀⠀⠠⠄⠙⠆⡈⠙⠙⠻⣟⣿⣷⣀⡀⢀⡀⠀⠈⠑⠲⢤⣀⡀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠙⠐⠿⣮⣧⡀⠈⠙⠉⠀⠀⠈⢦⠻⢯⡛⠷⠍⠀⠀⠀⡰⠉⠀⠉⠒⠾⡶⢦⣤⠾⣫⣭⣍⠉⠙⠙⠲⠶⠤⠄⠀⠀⠉⠁
⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠟⠛⠿⢟⠛⠛⠁⣀⢈⠢⡈⠛⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⣄⠤⠀⠐⠀⠛⠻⢄⠀⡄⡀⠀⠀⠀⠐
⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠚⢂⣀⡀⠙⠉⠁⠀⠀⠀⣈⠢⡀⠙⠳⣖⠦⣦⡤⠄⣀⣐⡸⠷⣌⠑⠲⣶⡐⠢⢄⢀⣤⡇⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠓⠲⢯⡉⠠⡍⡉⢩⣭⣭⡀⠀⠁⢳⡀⠀⢀⠉⠁⠺⢵⣤⣌⣉⣉⡊⠱⣦⡀⠉⠒⠂⠐⠲⣇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⢦⠘⠻⠀⠀⠉⠃⡄⣿⣾⣗⢤⣤⠄⠀⠊⠙⠉⠉⠉⠣⠈⠙⢢⠀⠉⠀⠒⢄⣀⣘⣦⣎⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠄⠀⠀⡘⠀⠈⢣⡀⠀⠀⠙⠤⢾⣿⣷⣤⣁⠀⠀⠀⠠⠒⠀⠀⠇⠀⠈⡗⠀⠡⠌⠶⠤⠤⠤⠄⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠈⠀⠀⠈⠉⢻⠐⠢⠄⠃⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠉⠉⠉⠃⠁⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⢻⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡔⣠⡾⣫⡖⣩⡶⠋⠀⠀⠀⠀⢸⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣾⠏⣴⡿⢰⣿⢊⠔⠂⠀⠀⠀⠀⠀⠀⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣧⠀⣿⡏⢰⣿⠁⣿⡇⡎⠀⠀⠀⠀⠀⠀⠀⠠⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡅⠀⠀⢸⡆⠘⠇⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⢀⣀⡤⠀⠀⢪⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣠⡾⠃⠀⢰⣿⡇⢸⣿⣿⣇⠀⠀⣴⠾⠋⠁⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⠗⠊⣡⣶⠞⢹⣧⣸⡏⣿⣿⣆⠀⠀⣀⣀⣤⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠉⠁⠁⢀⡄⣿⡿⠁⢹⣿⣿⣆⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡤⠂⠀⣀⣀⣤⣴⠟⢠⢿⡇⠀⠀⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣰⣶⣿⡿⠛⠉⠀⢀⣴⢸⡇⠀⠀⢸⣿⡿⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣿⣿⣿⣷⣶⣶⣿⠿⠃⡼⠁⢠⠀⢰⣿⠇⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠉⠉⠀⣀⣀⣄⣀⣀⣀⣀⠅⣠⣾⠏⠀⠀⣠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢠⠂⢀⣴⡿⠛⠉⠉⠉⠉⠐⠖⢚⣩⡿⠀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣾⡿⠅⠀⠀⠀⢀⣠⣤⣶⡿⠟⠀⠀⢹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⣴⣴⣾⡿⠟⠋⠁⣰⠈⣧⠀⢨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⣿⣿⡿⠉⢀⣀⣴⣾⠟⣼⣿⡆⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣠⣶⡿⠿⠛⣡⣾⣿⡿⣱⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⢀⡆⣴⣿⣿⣟⣿⡿⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣾⢸⣿⣿⣿⡿⠋⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⢫⡄⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠻⡇⢾⣧⣫⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⢲⠁⠐⠋⠀⣀⡀⠉⢷⠉⡴⢟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⢀⣎⣀⢠⠔⠀⠀⠀⠀⡀⠀⠀⢁⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠓⠉⠎⡉⠣⠀⡀⣤⠔⠒⠉⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠘⠛⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠚⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠰⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣭⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠿⠿⠿⠿⠿⢭⣽⣓⠂⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⣾⣛⣛⣛⣛⣛⡿⢶⣦⣍⡛⠶⣄⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⣙⣛⡛⠻⠿⣿⣿⣶⣝⠻⢷⣌⠻⣄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠉⠛⠿⣿⣷⣦⣍⠻⣿⣷⡤⡝⠳⡌⢧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⢉⠻⢿⣷⣼⣿⣿⡹⣆⢢⡀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠸⣷⣄⠙⣿⣿⣿⡇⢿⣆⢳⡰⡰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣦⠸⣿⣿⡇⢸⣿⡄⣷⣷⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡿⡄⣿⣿⠇⣿⣿⡇⣿⣿⡇⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⡟⣸⣿⣿⢣⣿⡿⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣼⣿⣿⢫⣿⡿⢁⣾⢏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⣵⡿⠋⣠⠟⢡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢫⣾⢟⡔⢈⣵⢢⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢡⣿⣏⣾⠃⣾⡇⡟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⢿⡘⣿⣦⣿⡇⠁⠀⣩⣰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠘⣯⣁⠹⣿⣿⣷⡀⢒⡬⠥⢞⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢦⠻⣷⡙⢿⣷⣌⡛⢿⣿⣶⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⠈⣷⣮⡓⠀⢌⡛⢿⣦⠹⣯⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢜⣼⡿⣿⣦⡠⣺⢷⠙⡧⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠙⢛⣭⣾⣿⡿⠃⠐⢚⣼⡇⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠀⠀⠀⠀⠀⠰⡟⠋⠉⠁⠀⠀⠀⠴⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠞⣄⣡⠤⡠⣴⢀⣄⡤⡰⢓⣄⡤⠀⢀⣤⡤⣠⣤⢄⣤⡞⠁⠀⣠⢋⣤⡤⡠⡆⣰⣫⣠⢌⣤⣆⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠙⠊⠁⠙⠈⠉⠃⠛⠈⠽⠃⠀⠈⠈⠃⠉⠙⠈⠉⠃⠀⢠⡻⠉⠉⠋⠙⠉⠉⠉⠙⠈⠋⠉⠉⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢀⡠⠞⠛⠋⠉⠉⠀⠉⠛⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠙⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣤⣀⣀⠹⣿⣿⣿⣇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⡴⢶⣖⡀⣀⣰⣿⣿⡿⣟⣿⣿⣿⡇⠈⠉⠛⢻⣿⡿⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣤⣾⣿⣿⣿⣟⠉⠈⣿⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⣾⠁⠈⠸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠻⢿⡿⠟⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣠⣾⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣥⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠋⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠻⠀⠀⠀⠀⠀⠛⠃⠀⠘⣿⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠚⣭⣶⣿⣷⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⣴⣾⣿⣷⡀⠈⣿⣿⣿⡇⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⣛⢉⣩⣭⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⢛⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣰⣿⣤⠀⢀⣠⣿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⠛⢛⣉⣉⣭⣬⣽⣿⣦⣀⣀⣀⣴⣿⣿⡿⣣⣾⣿⡿⢋⣿⣟⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣟⣵⣿⣿⡟⢠⣿⣿⣿⡏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣬⡙⢿⣿⣿⣿⣿⠿⠛⢛⣉⣉⣉⣩⣭⣥⣤⣶⣿⣿⣿⣿⣿⠟⢁⣿⣿⣿⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣦⡙⢿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢛⣉⣥⣴⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⢀⣶⣦⣬⡙⠿⣿⣿⣿⣿⣦⡹⣿⠿⠛⠻⠛⠛⠛⢛⣋⣥⣶⣿⣿⣿⣿⣿⣿⣷⣤⣬⣉⠁⣁⣴⣿⣿⣿⡆
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣌⠻⢿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⣛⣉⠽⣟⣫⣴⣾⣿⠋⣾⣿⣿⡇⣴⣄
⠀⠀⢀⣴⣦⣄⣈⡙⠻⢿⣿⣿⣿⣦⡙⢿⣿⣟⠻⠛⠻⠿⠿⠿⢛⣫⣴⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⢸⣿⣿⡟⢠⣿⣿
⠀⢠⣾⣿⣿⣿⣿⣿⣶⣤⡙⠿⣿⡿⢻⣾⣷⡾⢿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠟⣛⣯⣥⣤⣴⣷⣿⣟⣋⣠⣴⣿⣿⣿⢁⣿⣿⡿
⢀⣙⣙⠛⠛⠛⢿⣿⣿⣿⢿⣷⣾⡆⣷⣿⣿⣴⣷⣿⠛⣿⣿⣿⣎⢻⣿⣿⣦⠀⠉⠉⠉⠉⠛⠛⠻⣿⣿⣿⣿⠟⢡⣾⣿⣿⠇
⣿⣿⡿⠿⠛⢛⣛⠟⣽⢃⣿⣿⣿⡇⢹⣿⣿⣷⣹⣿⡇⢹⣿⣿⣿⣆⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣙⡻⢧⣴⣿⣿⡿⠋
⠋⣡⣴⣾⣿⣿⢋⣾⡇⢸⣿⣿⣿⡇⢸⣿⡟⢿⣿⣿⣿⡈⢿⣿⣿⣿⣇⢹⣿⣿⡇⠀⠀⠀⠀⠠⡄⠘⠛⠁
⣿⣿⣿⣿⠟⣵⣿⣿⡇⢸⣿⣿⣿⠇⣾⣿⣇⠸⣿⣿⣿⣷⠈⣿⣿⠿⠟⠀⠉
⣿⣿⠟⢡⣾⣿⣿⡿⢀⣿⣿⡿⢣⣾⣿⣿⣿⠀⠿⠿⠟⠛⠁
⠟⢁⣴⣿⣿⡿⠏⣴⣿⣿⣿⠇⠘⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣀⣀⣤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⣇⢸⣻⣿⡇⠙⢶⡀⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠈⣏⠟⠓⠲⣾⣿⣷⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⡀⢐⡶⢿⡗⢠⡄⠀⠙⢻⡟⣉⣉⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣨⣃⡈⠙⠊⢱⠀⢠⡄⢀⡬⡟⢿⡟⠷⠀⠀⢠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠬⢭⣀⠀⠀⢢⠀⠀⣈⣿⡟⡮⢁⣄⠐⣜⣳⣿⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣿⢽⣛⡟⠡⠴⠷⣾⣿⣿⣎⠝⠋⠀⢀⡜⠿⢽⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣾⣧⣞⠉⠀⢤⢞⠀⠀⠈⢉⣀⡤⡄⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠈⠋⠤⠴⠿⠿⢟⢵⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣽⣿⣷⣦⠀⢀⡀⠀⣀⠜⠫⠄⠂⢈⣷⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⡯⢾⡟⠉⠀⠀⡐⢈⢂⣾⣿⣮⡽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠙⢳⣸⠃⣍⣷⣤⣤⠾⠛⠁⠈⣻⠟⠉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⠟⠛⠋⠉⠀⠀⠀⠀⠼⠣⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠀⠰⠄⠀⠀⠀⠀⠈⠻⣿⠿⠀⠐⠾⣻⢓⣧⠀⠀⠀⢠⠤⢀⠀⠀⠀⠀⣀⠒⢀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢤⡀⠰⠦⠐⠓⠸⠃⠶⢰⠦⠒⠘⠛⢶⣶⣿⡄⡀⡍⡉⡁⠰⠃⠀⠀⠀⣴⣦⡤⠀⠀⠙⣉⣿⣿⠏⠁
⠠⢊⣠⠀⠀⠀⠤⠀⠆⠐⠂⠛⡀⠛⢠⣮⣤⠆⠀⠀⠀⠈⢹⠇⠆⠻⠃⠓⠀⠀⠀⠀⠀⣿⡟⠁⠀⠠⠾⠟⠛⠁
⠀⠈⠀⠀⠰⢠⡄⠰⢂⠐⠃⣈⠁⠶⠂⣈⠙⠀⠀⠀⠀⠀⣾⠀⠀⣀⣀⠀⣵⣦⡤⣴⢶⣿⠈⠠⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⡄⠗⠈⢁⣄⠋⡀⠒⠀⠉⣀⠉⠁⢠⡤⠚⠽⣏⣻⠟⣡⣼⣿⣿⣿⡇⣓⠿⡻⠆⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠋⡀⠛⣀⠁⠘⠋⣠⣏⣭⣽⢛⣛⠭⠥⢲⣿⠿⣿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠛⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠠⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⢻⠿⠋⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⠂⠀⡠⠶⠖⠀⠖⠀⠆⠀⠆⠀⠛⠒⠠⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⣀⣈⠁⠀⢠⠂⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⣀⠀⢐⠀⠀⠁⠀⠀⠄⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢀⡯⠖⠀⠀⢹⠁
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢸⠉⠃⠀⠀⠀⠀⠀⠀⠀⠓⠀⢒⠒⠐⠂⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠓⠋⠉
⠀⠀⠀⠀⠠⡀⢰⠀⠀⡆⡆⠘⠀⠀⡇⠀⠀⡏⠀⠀⡔⢸⣽⢲⡄⢁⣈⠀⠀⢀⡀⠐⠃⠀⢀⠉⠀⠀⠘⡁⠀⠒⠒⢀⡀
⠀⠀⠀⠀⠀⠁⠈⢀⠟⠛⢻⡁⠀⢠⡇⠄⢠⠃⠀⠸⣚⣚⣗⣰⡇⢀⠀⠀⠀⠈⠀⠀⠀⣰⠛⢿⡄⣴⠀⠀⠀⠀⣄⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⢸⡇⠀⠈⠁⠀⠀⠙⢋⠏⠃⠄⢀⠁⠀⡀⢠⠀⠀⠀⠘⠳⠾⠃⢸⠀⠀⠀⢰⡟⠊⠃⠀⢠
⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⣿⠀⠘⠓⠀⠀⢸⢠⡖⠀⠸⠀⢰⠀⢸⠀⢀⣇⢀⠀⠀⢰⠛⠉⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠈
⠀⠀⠊⠀⠀⠀⠀⠈⠆⠀⢰⠏⣀⠯⠀⠀⠀⠈⢸⡇⠀⠀⠀⢸⠀⠈⠀⠐⠶⢺⡀⢀⡀⠧⠔⠰⠶⠆⠀⠀⠐⠀⡇⠀⣷
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢒⡋⣀⢹⠀⠀⡄⠀⠀⠠⠁⠆⡏⠀⢸⠀⠀⢠⡆⠀⠀⠀⠈⢱⢸⠀⠀⢆⠉⠀⠀⠀⢰⡇⠀⠁
⠀⠀⠛⠒⠋⠁⠀⠀⠀⠸⡝⠹⢸⡀⠀⠳⠀⠀⡄⠀⠀⠁⠴⠞⠀⠤⢹⠀⠘⠌⠀⠀⠈⢘⠀⠀⢸
⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠑⠃⠀⢡⣤⣤⡄⢰⠁⠀⠀⠀⢠⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠇⠀⠀⠀⣀
⠐⠒⠒⠒⠒⠒⠒⠀⠒⠒⠓⠒⢢⣤⣤⣤⡄⢸⠀⠀⠀⠀⠘⡇⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⡄⠀⢀⡃⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠘⠀⠀⠂⠀⠀⠏⠀⠀⠀⠀⠀⠋⠀⠀⠄⠀⠃⠀⠀⠳⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⠀⢠⠞⢉⢤⡈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⢠⡏⠹⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⢀⠉⠀⠀⠀⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⣠⡄⢰⣅⢀⡀⠀⢀⠙⠀⠀⠀⣠⠀⠀⠀⠀⠂⢹⠃⢀⡾⠁⠀⠛⠍⠀⠀⣀⣷
⠀⠀⠀⠠⢀⡸⠀⡠⠆⡠⠼⠿⠨⠦⣤⣄⡙⠲⣼⡄⠀⠂⣤⣤⣿⠶⠯⠴⠿⣿⠶⢤⣤⣤⣭⠟
⠀⠀⠀⠀⠙⠀⠀⠇⣀⠃⢀⣨⣤⡶⠶⣿⣿⣷⡘⣿⣆⣼⡿⠛⠉⠐⠀⠈⡀⢈⣳⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡸⠋⠀⠁⡀⣀⡀⠈⢿⣿⣾⣿⢏⣴⠶⠛⠛⠓⢒⡀⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠻⠆⡮⠚⢿⡰⣶⠀⠙⣿⣿⡟⢀⣠⠘⡄⠁⢈⣉⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠋⡀⠉⠁⠂⠀⢘⣿⠇⠐⠂⠁⠀⠀⠉⠘⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡿⣹⡆⠀⠉⠀⠈⠀⢨⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⠄⣸⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠟⡁⠀⣼⠞⣧⡤⢸⣦⠀⣳⡶⠶⠀⣬⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠁⡸⡝⠀⣈⣵⡄⠈⢬⠃⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠘⣤⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡐⠐⢶⠄⠦⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⠈⠡⡗⢤⢳⠄⣤⣱⠉⢨⠕⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⢹⣲⠇⠊⠀⠀⣼⣷⣦⣚⣙⡁⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⡖⣸⣤⡾⠎⠀⠀⠀⠙⢯⣟⡟⣷⣿⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠝⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠀⠨⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢺⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠈⠉⠁⣶⠆⠀⠀⣶⡆⠁⢸⣼⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠠⢀⠄⠛⠳⣤⠴⡋⠗⢀⣼⡿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠗⡄⠇⠀⠀⠘⠀⠀⠁⠀⠘⢿⣷⣜⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠁⡄⢸⠀⠀⠀⠀⠀⢰⠀⡄⣎⣿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣏⠀⢄⠀⣸⠀⠀⠀⠀⠀⠸⡁⠀⠏⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠎⢈⠁⠀⠄⠀⠀⢀⠀⠉⠀⢲⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⠛⠃⠀⠂⠀⠀⠐⠀⠄⠀⠀⠘⣯⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠣⢀⣀⣀⣀⠀⠠⠤⠔⠓⠒⠒⠐⠒⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣾⡥⣄⠀⠀⢄⠀⢀⣠⠀⠀⠉⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠁⠀⠀⢦⠀⠀⠱⠂⠀⢀⣀⣀⣨⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠱⠶⠖⠁⠀⠙⠛⠁⠀⢀⣀⠁⠊⡠⠂⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢿⣸⡇⠈⠀⠀⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠉⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⣼⡇⠀⠀⠐⠒⠉⡄⠀⠸⣠⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠸⠿⠇⠀⠀⠀⠀⠀⠸⠆⠀⠛⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠁⠀⠀⠀⠡⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠛⠃⠀⠀⠀⠈⠀⠀⣀⡜⠁⣀⠆⠀⠀⠀⠀⠀⠘⣄⡀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⠆⠘⠀⠀⠀⠀⠀⢄⡀⠀⠌⠀⣶⡄⠀⠀⠀⠀⠀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣿⠏⢣⠀⠈⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠊⠋⠀⠀⠃⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠙⣾⣿⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢄⠀⠀⠀⠀⠀⠀⠀⢁⡽⠀⠾⣹⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢮⣃⠀⠀⣴⢀⡀⠡⢆⠜⠃⠀⢩⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⡦⢿⣒⣠⢏⡀⠺⠔⠋⠀⠀⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡇⠙⢟⡋⡿⠃⠁⡀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢈⣀⢠⠀⠀⡀⠀⠀⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢻⠃⠀⠀⠇⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠐⢼⣴⠀⠀⠀⠰⠀⠀⡠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⠀⢸⡆⡼⢣⠀⠀⠀⠇⠀⢰⣷⡛⠋⢁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡄⠀⠀⠄⠀⢺⡇⠀⠇⠀⠠⢠⡦⠈⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣻⠃⠀⠀⠀⠀⣟⡐⠀⠀⠀⠀⠈⢇⠀⠠⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡄⠀⠀⠀⠘⣃⠀⠀⠀⠀⠀⠈⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡄⠀⠘⣿⠀⠀⢀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⡄⠙⠏⡀⢀⠈⠀⡴⠀⠰⡅⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠞⢰⡟⡇⠈⡿⠀⠀⠈⠃⣅⡠⣀⣶⣶⣾⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⡟⠀⠀⡀⡻⠆⡀⠀⠘⠆⠳⠚⠋⠉⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢿⣷⠂⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠈⠆⠚⠳⢾⡷⠛⠋⠁⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢠⡆⠀⣸⡗⠀⢀⠀⠀⠀⠦⡘
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⢇⠀⠻⠀⠀⠀⠇⣠⡖⣡⠃⠀⢀⡇⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠇⡀⠀⠄⠀⠶⠟⡄⠧⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠀⣅⠀⠱⡘⢶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡏⠀⠀⠱⡄⣸⡶⠀⠙⠃⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢍⠲⡄⠙⠟⠁⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠂⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠁⠐⠉⠝⠻⠛⠛⠛⠈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡱⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⡀⠠⡀⢀⠐⢄⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⢡⠁⡜⢰⠀⠀⠁⠀⡌⠘⠀⡰⠻⡀⠳⣌⠀⠈⢢⠀⠈⠇⢀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠀⠃⣸⡀⠀⣴⣧⣦⠞⠁⠀⠱⡔⡌⠁⠀⠀⠀⠀⠀⠈⡞⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⣿⠿⠚⠛⠉⠁⠀⠀⠀⠀⠘⢮⡢⡀⠀⠀⠀⠀⠀⢷⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⣆⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⣾⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡂⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⡄⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡜⠀⡀⠀⢀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣷⠐⢤⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣄⣾⣿⣴⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠻⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠉⠉⠁

⠀⠀⠀⣠⣤⣠⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢻⡿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⣿⣿⡇⠀⢰⡇
⠀⠀⠀⢸⣷⣶⣶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠅⠀⠀⠀⣿⣿⣷⠀⠸⠇⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⣤⣾⠀⠀⣶⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⡏
⠀⠀⠀⠀⣿⣿⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⡞⠂⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡷⣿⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⡇
⠀⠀⠀⠀⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⣴⣧⠀⣿⡇⠀⠀⠀⠀⣿⣇⡀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣷⣿⢰⣾⣷⡆⠀⠀⢀⣘⣿⣧⣇⡀
⠀⠀⠀⠀⢿⣿⣿⠃⡇⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡇⡇⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⢠⡇⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡇⡇⢸⣿⢈⡇⠀⠀⠘⣿⠂⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠘⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠈⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣠
⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⣀⣤⣄⣀
⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢹⣶⣾⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⡾⠋⠀⠀⠙⢷⡄⠀⠀⠀⠀⣀⣙⣛⣛⣛⣛⣛⣋⣠⠀⠀⠀⠈⠻⠟⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣾⠁⠀⠀⠀⠀⠘⣷
⠀⠀⠀⣿⣿⢶⣶⣶⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠉⠉⠉⠉⠋
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢹⡄⠀⠀⠀⢀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠻⠲⠒⠓⠓⠚
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠙⢶⣤⣾⡷⠏⠀⠀⢀⣤⣤⣤⡄
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⢚⣛⣾⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⣈⡇⠀⠀⠀⠀⠀⣾⠉⠙⠻⣿⣿⠟⠋⠉⣷
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠘⡆⠀⠀⠀⢠⣾⣿⣿⣧⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠦⣄⣰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣀⣴⡾⠃
⠀⠀⠀⠿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠙⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣰⢣⠃⠀⠀⢀⣸⣿⣿⣿⠟
⠀⠀⠀⠀⠀⡇⡇⠀⡌⠀⠀⣛⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠃⢰⠀⠀⠀⠸⣿⣿⡗⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⣽⡄
⠄⠀⠀⠀⠀⢻⡀⢰⠀⠀⠀⠀⣻⣿⣿⣄⠀⠀⠀⣿⣦⡀⡀⡀⣾⡟⠀⠀⣠⣼⣿⣿⣧
⣧⠀⠀⠀⠀⠀⢳⡀⢆⠀⢀⣶⣿⣿⣿⣿⣤⣤⣤⣻⣿⡿⣷⣿⣿⣅⣶⣿⣿⡟⣿⣿⢯⢃⡀
⣿⣧⡀⠀⠀⠀⠀⠙⢌⢲⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⡿⡌⠛⢸⣿⡿⠉⠙⠜⢋⣵⣿⣿⣷
⣿⣿⣷⣶⣦⣄⣀⢀⣼⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣾⣤⣼⠿⢤⣤⡴⣚⠛⢛⣛⡿⠟
⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠛⠀⠀⠈⣿⣿⣯⣿⠿⣿⣿⠁⠀⠀⠉⢅
⠀⠀⠀⠀⠅⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⡀⠀⣠⣿⣿⣟⢃⣶⣤⣭⣔⢦⣄⠀⠀⠱⡀
⠀⠀⢠⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⢫⣿⣿⣿⢿⣿⣷⡄⠀⠐⡀
⠀⠀⢼⢷⣿⣿⣿⣿⣿⣿⡿⠙⠛⠉⠙⣿⣿⣿⣿⣿⣟⣿⣿⣿⣦⣾⣿⣿⢹⣿⣿⣿⠛⠀⠀⠱⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⠛⠉⠻⢧⣅⣈⣿⣿⣤⣿⣿⠃⠀⢀⣴⣶⣿⠇
⠀⢠⠷⣿⣿⣻⣿⣿⠟⡃⠀⠀⠀⠀⠀⡿⠛⠃⣥⣿⣧⡄⠀⠀⡀⢰⣼⣿⣿⣿⣹⣾⣟⠞⣻⡿⡏
⠀⠀⢠⠟⢿⣿⣿⣧⣦⢉⠁⢀⠆⢸⣾⣃⠀⠀⠉⠿⠏⠁⠀⣼⠇⣸⣿⣿⣿⣿⣶⠁⠈⠉⠁⠀⡁
⠀⢰⣧⣦⣶⣿⣿⣻⠇⠘⠐⣿⠀⠀⢻⣿⢷⢦⡀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠋⣠⡖⠀⠀⠀⠀⠀⠃
⠀⢰⣿⣿⣿⣿⣿⡁⠀⣆⢤⠉⠀⠠⣾⣿⣅⣁⢡⠀⠀⢀⣤⣆⢀⣙⠋⠉⠀⠁⠀⠀⠀⠀⠀⠰
⠀⠈⠇⣿⣹⣿⣿⣿⣦⡘⣤⡀⠀⣼⣊⣿⣝⠈⠳⠀⠀⣿⡻⣿⠇⠀⠀⠀⠠⣀⢠⣀⠀⠀⢠⠁
⠀⠀⠀⢻⣷⣿⣿⣿⣿⣿⢛⣿⠛⠿⣿⣿⣿⣆⠀⠀⠐⣿⡿⠯⠀⠢⠀⠀⠀⢽⣿⣿⣷⣶⣧⣤⣀⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠆⢤⡤⢘⠻⣷⣄⡀⠀⠀⠙⣷⢂⠀⠈⠢⡀⠀⠀⢋⠟⠿⢿⣿⣿⣿⣦
⠀⠀⠀⠀⢰⢿⢿⠿⣿⣫⣿⣿⣿⣿⣆⣿⣿⣾⣿⣿⣦⣈⢿⣿⣿⣆⡀⠀⠀⡡⠖⡁⠀⠀⠈⠈⠙⢿⣿
⠀⠀⠀⠀⢸⣆⡴⣷⡿⣿⣿⣿⣟⢿⣿⣿⡿⣿⡝⡿⣿⣿⣿⣿⣿⣿⣶⡶⠉⠀⠈⢊⠲⡀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠟⢰⢻⢹⢻⢉⣎⡾⢿⣿⣿⠻⢿⡿⡸⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢃⠙⣆
⠀⢤⠄⠀⠀⠀⠘⡆⡸⣼⠞⠋⠀⢠⢏⡿⠀⠀⠙⣧⡼⠏⠉⠀⠈⠹⣿⣿⡇⠀⠀⠀⠘⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢼⠃⠀⠀⠀⢸⠞⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⢰⠀⢠⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣿⣿⣯⡅⠀⠀⠂⠀⡌⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠈⠉⠉⠉⠉⠉⠉⠁⠒⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠰⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠆⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⢠⠀⠀⠀⠀⣆⠀⠀⠀⠸⡄⠀⠀⠈
⠀⣀⠤⢤⠀⠀⠀⢸⠀⠀⠀⠀⠀⡶⠀⠀⠀⠈⡇⠀⠀⠀⢘⠀⠀⠀⠀⢹⠀⠀⠀⠀⡧⡀⠀⢠⡤⠠⢤
⡎⠁⣀⠈⢣⡀⠀⢠⠆⡀⠀⠀⣠⢧⠀⠀⠀⡸⢣⠀⠀⢀⠞⠣⡀⠀⢀⡜⠣⠀⢀⡴⠀⠉⠀⠋⢀⡀
⢇⠀⣷⡀⠈⡁⠒⠂⠀⠉⠚⠂⠁⠀⠐⠒⠋⠀⠀⠑⠒⠋⠀⠀⠉⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡷
⠈⠢⣈⣁⣀⢇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⣰⠄⣉⣠⠔
⠀⠀⠀⠀⢩⠈⢆⠀⠀⠀⠑⠶⠔⠖⠂⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠘⠶⠶⠚⠀⠀⡠⠁⠀⠀⠀⡇
⠀⠀⠀⠀⡘⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠇
⠀⠀⠀⠜⠁⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣁⡻⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠐⡶⣤⠤⠄⠀⠀⠀⠀⠠⠤⠤⢰⠖⢏⠀⠱⡄⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⠂⠀⣼⠀⠀⠲⢄⠀⠀⠀⠀⠀⢀⡴⠋⠀⢨⢆⠀⠙⡄⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠃⠀⠜⠀⠑⠂⠒⡂⠁⠒⢒⡒⠈⠁⠀⡌⠉⠁⠈⢃⠀⠘⡄⠀⠀⠀⠀⠀⡄
⠀⠀⢠⡄⠀⠀⠀⠀⢠⠃⠀⡘⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠒⠈⠀⠀⠀⠀⠀⠡⠀⠘⡄⠀⠀⠀⠐
⠀⠀⠈⠁⠀⠀⠀⡠⠃⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠙⡄⠀⠀⠃
⠀⠀⠀⠘⠀⠀⡰⠁⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⢆⠀⠘⡄
⠀⠀⢠⠎⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡀⠀⢰
⠀⠀⢀⠀⠀⡎⠑⠂⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠒⠈⠃⠀⠈
⠀⠀⠈⣡⠀⡆⠀⢀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠀⠀⡠⠀⠸
⠀⠀⢀⡁⠀⠈⠉⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠉
⠀⠀⢨⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠳⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠳⣀⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠒⠂⠀⢲⠂⠐⠂⠒⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡄⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠇⠀⠸⡀⠀⡸
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⠈⢉⣁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣄⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣻⡕⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢻⣿⣿⣿⠟⣉⣿⣿⠿⢛⠅⠱⢟⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣾⣿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠜⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣿⣿⣿⠀⣨⠀⠀⠀⠀⠀⢸⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠃⠀⡏⠀⠀⢾⠖⣾⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⡶⠶⢟⣸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢀⡀⢣⣠⠞⠁⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⡎⠈⠑⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣤⣶⠾⠿⢿⣿⣛⠓⠲⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣛⡛⠛⠶⠦⣄⡉⢳⡄⢀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣿⢻⣿⡛⠿⢭⣉⠒⢦⡈⢳⡄⢿⡌⡇⢻⡽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⡟⣆⠙⢿⣕⡲⢬⡻⣆⣷⣹⣷⣿⣿⣿⣾⣷⣏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣳⣜⢮⣙⢦⣜⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⡋⠁⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠉⠙⠛⠛⠋⠭⠒⠁⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠰⣿⣿⣿⣶⣤⣠⡾⣦⣤⣴⣾⣿⣿⡷⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠻⠿⠿⢿⡿⠟⣤⡜⠿⣿⠿⠿⠿⠃⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⠀⣀⠀⠀⠀⣸⣿⣿⡀⠀⠀⢀⡀⠀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣧⠀⠀⠉⠁⠉⠁⠀⢰⡿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢿⡒⠒⠒⠲⠲⠒⠒⣺⢳⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠘⢯⣭⣤⡀⣠⣬⡽⠟⣸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⣿⣹⣿⣿⣿⣿⣻⣟⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣽⣿⣿⣿⣿⣿⣿⣼⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣭⠉⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡡⠞⠉⣽⢿⡝⠗⢦⡀⠠⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠈⠀⣠⠊⣿⠸⣿⡈⣎⢳⡄⢎⠲⣄⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣠⣤⡴⠖⣋⣤⠞⢹⡆⠙⠓⢾⡄⠻⣎⠆⠈⠳⢦⣬⣛⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠿⠋⣡⣴⠿⠋⠁⠀⠀⢻⡄⠀⠀⢿⡀⠹⣧⡀⠀⠀⣀⡤⠔⠈⠳⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⣠⣾⣿⣇⣀⠀⠀⠀⠀⣀⣻⡄⠀⠀⠳⣄⣪⣝⣛⡫⠅⠀⢀⢀⣴⡟⠉⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣣⠆⣰⣿⣿⣿⣦⣬⡁⠀⠀⠘⣩⣴⣿⣖⢦⣄⣈⣉⣉⣭⣶⣥⣤⣶⡿⣿⡻⢄⣰
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣿⣿⣿⡿⠉⠉⠁⡆⠀⠈⠁⠘⠛⠉⢷⣿⣿⣿⣿⣿⣆⡱⡙⢿⡹⡿⣿⣦⣬⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣿⣿⢋⣷⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣧⢿⡿⢻⡿⢧⠘⣿⢹⡶⢿⡿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢁⣼⣿⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠇⣩⡿⠁⡾⠁⢸⠀⣿⡇⢿⡜⣷⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣆⠻⣿⣛⠿⠂⠀⠀⠀⡠⢊⡼⠋⢀⠜⢁⡄⣿⢸⣿⣷⢸⡇⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠋⢸⡟⢿⣿⣿⣆⠀⠁⠀⠀⢀⣴⣾⠟⠋⣠⡴⢋⡴⠋⣰⡏⢸⣿⣿⡼⢡⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⣿⠓⣎⢻⣿⣿⣷⣶⣶⣾⣿⠟⢁⣤⠞⣡⠖⣩⡤⠔⠋⣷⡈⣿⣿⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠸⡇⠘⢷⣟⣿⣿⣿⠇⣿⢋⣴⢟⡵⠋⢀⡼⢑⣲⣯⠞⠛⢷⡽⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⡝⢹⡄⠹⡄⠘⠃⢿⣿⠋⣼⠃⣾⢏⡞⢠⡞⠁⣠⢟⣿⠃⠀⢀⡼⠓⣿⢻⢮⡳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡾⣰⠁⣼⣿⡄⠹⡆⠸⠟⢁⣾⣿⣾⡇⣿⢠⡟⠀⢰⡏⠀⣿⠀⠀⡋⠀⠀⠹⡌⢧⠙⢮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠃⢸⡟⣿⡇⠀⢻⣀⣴⣿⠇⣿⣿⣷⠈⣾⡇⠀⣿⠁⢸⡇⠀⠀⠁⠀⠀⠀⢳⡈⢳⣄⠙⢦⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇⢸⣇⣴⡾⠋⡱⡛⢸⣿⣿⣿⣇⣿⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢷⡀⠹⡷⣤⡙⢦⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⣷⠞⠋⠁⢀⠜⡰⢡⣿⣿⡇⢹⣿⣿⡁⠀⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠈⢢⡙⠲⣽⣄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣴⣋⣤⡤⠴⢊⣡⠞⣱⣿⢟⣿⢧⣾⣿⣿⡅⠀⡇⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣝⢦⡀⠙⢶⣄⡙⠀⡇
⠀⠀⠀⠀⠀⢀⡴⠚⣉⣤⣶⣶⣾⣿⣵⣿⣿⠏⣾⡿⢸⢹⣿⢿⠇⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣝⠷⣦⣬⡽⢿⠁
⠀⠀⠀⠀⠀⣾⣴⡾⣟⣛⣩⣽⣭⣭⡽⠟⣁⣾⣿⢃⢏⣾⠏⣿⠀⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢻⡿⡏⢳⡀⣿⢀⠌
⠀⠀⠀⢀⡼⢻⠏⣼⣿⡿⣩⣢⢰⣿⠛⣿⣿⠟⣁⣤⣿⡟⢰⣿⠀⢰⡇⣼⠇⠀⠀⠀⠀⠀⠀⣰⢇⣠⣴⠟⠁⠟⣼⢟⡵⠊
⠀⠀⠀⠸⣇⠘⢆⠹⣿⣇⣯⢿⡆⠉⢱⣿⣛⣛⣫⣵⠎⢠⢿⠇⠀⣼⡞⢻⢤⣀⣀⣤⠴⠒⠋⠉⠱⠟⠁⣀⢼⣼⠵⠋
⠀⠀⠀⠀⠈⠙⠶⣍⡻⠿⣾⣦⣙⠒⢮⣉⢹⣽⠟⠁⡴⣣⠋⠀⣼⡿⣇⣹⣷⣤⣤⠴⠶⢶⣶⣶⣶⣚⣩⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡦⢌⣉⠙⠋⠉⠉⠀⠐⣫⠾⢁⣠⣾⠏⣾⠛⠁⢀⣀⠀⢀⡀⠼⢿⢃⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠓⢾⡟⠷⢶⣶⣶⣯⡥⠖⢿⠁⡹⣄⡛⠂⢀⣥⠤⠒⠒⠛⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠞⠊⠉⠀⠀⠈⠁⠲⠶⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢔⣠⣾⣿⣿⣿⣿⣿⣧⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣁⣥⠖⠛⠛⠛⠿⣿⣿⣿⣿⣿⣷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡗⣒⣂⡀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⣹⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⣀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⡀⠀⠀⠸⣿⣿⣿⣿⣆⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⢰⣯⣥⣾⠃⠀⢀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡿⣿⣿⣿⣿⣧⡀⠀⠈⠈⠉⠀⢠⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠹⣿⣿⣿⣿⣿⣷⡶⠆⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣹⡄⣈⣛⣛⣛⣛⠻⢫⡄⠀⠼⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠟⠉⠙⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⣿⣧⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡽⣿⣿⣿⣿⣿⣆⠈⣻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣾⠟⠛⠟⠚⠛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠊⠁⠀⠀⠀⠀⠺⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⠛⠁⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠻⣧⡀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠘⢿⣄⠀⠀⠀⠀⠀⡉⢠⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠈⢻⣦⠀⠀⠀⡰⠁⣾⠃⠀⣿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠛⢀⡠⠀⠈⢿⡄⠀⢻⣧⠀⢰⠇⣸⡏⠀⢸⣿⠀⠀⠀⢂⠄⠉
⠀⠀⠀⠀⠻⣿⣛⠛⠻⠷⢶⣤⣄⡒⠉⠲⣄⠘⣿⡀⡄⢻⣆⠈⢰⡿⢀⠆⣼⡇⠀⣠⠔⠁⠀⣀⣤⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠈⠉⠻⢷⣤⡈⠳⣼⣧⠰⠈⣿⣧⣿⢁⡞⣠⡿⢀⠜⣁⣤⡶⠟⠋⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠠⣀⠉⠻⣦⡙⣿⡆⠃⢸⣿⡇⠎⢠⣿⣷⡷⠟⢋⠁⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡙⢦⡈⠻⣿⣷⣿⣿⣿⣿⣶⣿⠟⢋⡠⠖⣁⣴⠿⠋⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⢲⣿⣿⠏⣁⠉⠻⣿⣿⡎⣁⣤⣾⠿⠥⠖⠚⠉⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠒⢂⣴⣿⣿⣿⡏⢀⣭⠖⢀⣿⣿⣿⠿⠿⠿⠶⠶⠶⠶⢶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠁⠀⢀⣤⣾⠟⠋⡩⣿⣿⣷⣤⣥⣤⣾⣿⡿⠉⠈⠛⠒⠀⠀⠂⠀⠀⠀⠀⣉⣉⣛⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣶⠿⠋⠔⣪⣵⠞⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠶⠶⠶⠶⠶⠿⠿⠿⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣤⡶⠛⠉⢀⣴⣿⢃⠏⣸⣿⣿⢰⠀⢿⣿⣌⠲⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠞⠋⠁⠀⠀⡠⠊⣼⡏⡎⢰⡟⢸⣿⡀⠆⠸⣿⢻⣆⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⢀⠜⠁⢰⡿⡘⢠⡿⠀⡟⢻⣧⠘⡀⢿⡄⢿⡄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠑⠀⠀⣾⠃⢡⡿⠁⢠⠇⠈⣿⣆⠀⢸⡇⠸⣷⠀⠀⠳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⡿⢠⡿⠁⠀⡞⠀⠀⠘⣿⡄⢸⡇⠀⣿⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⣾⠁⠀⠰⠃⠀⠀⠀⠹⣿⣸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠃⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣼⡇⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢷⢀⣿⣡⠞⠫⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⢸⣿⡿⠋⠆⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⣸⣿⠁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣿⣧⡾⠋
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠉
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀
⠀⢈
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⣀⣀⣀⡀⠀⣀⣠⣔⢂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣻⣿⣿⣿⣿⣿⣿⢿⣿⡤⢐⡀⣀⠀⠀⠀⠄⠈⢷⡀⠈⢮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⣼⣿⢸⣿⠶⠟⠛⠋⠀⠀⠀⠀⠀⠀⠙⢷⣾⣧⣠⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣚⣿⡿⣻⣿⣧⡈⢷⣿⣷⣔⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣽⣸⡿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣿⠿⠉⠛⢿⣿⣾⢿⠉⠋⠛⠿⠿⠤⠀⠀⠀⠀⠀⠑⢹⣿⣿⣿⣿⣿⡿⠛⠛⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢛⣹⣿⣿⣧⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⣠⣾⣷⡿⢟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢄⠀⠀⠀⠀⠀⠀⠀⠈⣉⣽⠿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡀⣀⣀⠀⠀⠈⠀⣈⡴⣞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢿⡏⠛⠑⣲⠚⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢈⡘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄
⠀⠀⠁⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⣿⣼⡇⢸⣿⣧⠙⣿⠃⢸⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⢹⡇⢸⣯⣿⠀⣿⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠛⠘⠃⠙⠁⠛⠁⠋⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⣤⡴⠆⣶⢸⡆⢿⣟⠀⣿⢹⡇⢹⣿⡏⢸⡏⣿⢸⣷⣾⢰⡶⠆⠀⢀⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣇⠠⠈⣿⠀⢹⣿⡇⢸⡏⠀⣿⢿⡇⠀⣿⠁⢸⣇⣿⢸⣿⣿⣸⠋⠀⠀⠛⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠨⡇⠀⠙⠶⠀⠻⠃⠘⠛⠃⠛⠈⠋⠀⠙⠀⠈⠙⠋⠘⠋⠃⠛⠃⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠦⠒⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠀⣖⠀⠀⠀⠀⣀⠀⠀⡀⢐⠀⠥⠒⠉⠀⠀⢀⡀⢠⠜⢲⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣰⣆⣐⡄⠀⠀⠀⠀⠰⣖⣂⡀⠀⠀⠀⣴⣤⣄⠀⠀⠀⢀⣤⣦⡀⠀⠀⢀⣾⣷⡄
⠀⠀⠀⠀⠀⢸⣟⣹⡇⠀⠀⠀⠀⣀⣿⣻⠁⠀⠀⢠⣿⣭⣿⡀⠀⠀⣼⣿⣿⣷⠀⠀⠸⠿⢿⣯
⠀⠀⠀⠀⠀⢼⠜⢋⣿⡆⠀⡠⠦⠉⠈⠉⢣⠀⠀⠈⣿⣿⣿⡃⠀⣠⣿⣿⠜⣿⣧⡀⠀⣠⣿⣿⣏⢐⡀
⠀⠀⠀⠀⢰⠢⣆⣺⡓⡃⠀⣹⠃⠀⠀⠀⠘⠂⠀⣦⣿⣿⣿⣿⣠⣿⣿⣿⢀⣿⣿⡇⢠⢿⣿⣿⣿⡆⠀⡀
⠀⠀⠀⠀⢸⣷⣿⣶⣷⣧⠐⠞⠇⡀⠀⠀⣺⠇⠀⢻⣿⣿⣿⣿⡟⣿⣿⣏⢸⣿⣿⣷⠗⡟⡏⢻⣿⣿⡄
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⣻⣇⡠⠀⡘⠉⡦⢠⠸⣿⣿⣿⢿⣇⠸⢿⣇⢀⣿⢿⡏⡔⣀⣥⣸⣈⣏⣇
⠀⠀⠀⠀⠇⢹⣿⢻⣿⠉⠀⠈⠙⣿⠸⣷⠉⠀⢸⠀⣿⣿⣿⣿⠘⡀⢸⣿⣾⡇⠸⠶⠥⣿⣿⣿⡯⠜⠛
⠀⠀⠀⠀⠀⠀⢻⣼⣿⠀⠀⠀⠀⢻⡇⣿⠀⠀⠈⠐⠧⣿⣿⠸⠀⠁⠀⣿⣿⠃⠀⠀⠀⠘⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⠀⠀⠀⠈⠇⡟⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⠿⠀⠀⠀⠀⠀⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⣷⣇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠈⢿⠇⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⢻⠟⠀⠀⠀⠀⠀⢻⠘⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢀⣥⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢨⣠⠀⠀⠀⠀⠀⠘⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣀⣐⣒⡂⠀⢦⡀⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠛⠃⠚⠻⣯⣙⠛⢷⠦⣽⣸⣿⡷⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠗⠛⠉⠙⢢⡈⢿⡷⠄⢃⢹⣿⣟⣇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⣷⣸⣿⠀⠸⢸⣿⣿⡿⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡦⠀⠀⠠⠒⠠⣿⣿⣿⠧⢀⣿⣿⡿⢁⣴⣿⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠐⠀⠀⠈⠳⠉⠛⠿⣐⢿⣽⠻⣿⣿⣫⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⣷⣅⠿⣿⣿⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⢿⡀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢠⣿⣿⣷⣌⠻⣧⡙⠛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣸⣮⢯⡁⠀⠀⠀⠀⠀⠘⠿⣧⣌⠻⢿⣿⣿⡆⠹⢟⡶⡈⢲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⡃⣧⡀⢀⣀⡤⠀⠀⠀⢘⣿⠇⢸⡿⠛⢀⣶⢸⣇⠘⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠟⠟⠛⠉⠁⠀⠀⠀⠀⠀⢠⠞⣩⡤⢿⠁⡴⠛⢃⣾⠏⠀⣰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣣⠘⢦⡑⣿⡟⠁⢠⣾⣿⣿⣿⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣿⣷⠀⢻⢜⣿⣦⣙⠻⣿⣝⠳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣿⣛⣠⣿⣿⣿⣿⣿⠂⣹⣿⡷⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⣀⣀⣤⡤⠖⠂⠒⠀⠀⠀⠀⣿⣿⣥⣿⢿⣿⣯⣿⠟⢁⡴⢫⡿⠁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⡶⠈⢻⣿⣾⣿⣿⡿⢿⣄⡘⠷⡿⣿⣦⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣤⣤⣤⡴⠶⡾⠛⠋⠉⠀⠀⡸⣿⣧⠘⢿⡄⣠⣽⠿⠀⣽⡟⡫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⢀⣔⣁⣄⡀⠀⣾⡏⠀⣤⡿⠀⣠⡿⠻⠁⠈⠉⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠉⠁⠀⠀⠙⢷⡀⠻⡀⠞⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⢤⣤⣦⣤⣤⣤⣤⣤⣤⡴⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣼⠇⣿⢻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣰⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡿⠻⠿⣿⣿⡿⢿⠟⣱⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢀⣿⢣⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣠⣿⣯⣿⣟⣋⠙⣿⠁⠚⠁⠈⣿⡿⢉⣉⣉⡽⢉⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠙⠿⣍⣀⣀⣿⣿⡇⠙⠀⠀⠀⠀⠀⣰⠭⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠸⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠼⠿⠋⣿⣿⣿⣿⣿⣿⣿⡸⡀
⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⢹⡇⠁
⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢸⡇⠈
⠀⠀⠀⠀⠀⠀⣸⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡞
⠀⠀⠀⠀⠀⢠⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠰⢾⣿⣿⣿⣿⠿⠋⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⠤⠤⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠇⢹⣿⡟⠿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⢠⡟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠿⠛⠛⠋⠙⣿⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⣥⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠘⠷⣬⠝⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠛⠛⠛⠉⠀⠀⠙⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⢿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣠⣴⣿⣿⣿⣿⣿⣿⡯⣿⣷⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⣴⣀⣾⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣦⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⢟⣩⣵⣶⣿⣿⡿⢶⣿⡻⠿⠿⢯⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣛⠽⠛⠉⠉⠀⠸⣏⠻⣧⣦⣄⢰⣿⣔⣮⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢹⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠙⠿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣿⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣸⣿⣥⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⣼⢻⣿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⣠⣬⣭⡙⠃⠀⠀⠀⠋⢩⣭⠤⣄⠀⠀⢸⡿⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣼⣿⣿⡄⠈⠓⠚⠃⠈⠀⠀⠀⠀⠀⠀⠛⠀⠉⠀⢠⣿⢃⣼⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣣⣾⡇⠈⢷⢻⡀
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡄⢸⣇⣷
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢻⡇⣿⡀⣷⢹⣧
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⡟⣷⣿⡇⣿⣷⠸⣧⠃⠂
⠀⠀⠀⠀⠀⢠⡀⢿⣿⡇⢿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣀⣿⣿⡴⡟⢷⣀
⠀⠀⠀⠀⠀⠈⡇⢸⣿⣇⠈⢸⣿⡟⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢟⡜⣿⣿⢸⡇⣿⣾⣿⡄
⠀⠀⠀⠀⠀⢀⣇⣜⣿⠹⣦⡈⢻⣷⢡⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣼⣷⡹⣿⣿⣷⣿⢸⣏⢿⡀
⠀⠀⠀⠀⢀⣾⡟⣻⢸⣧⢽⣷⡜⢱⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣿⣷⣽⣿⣿⡏⡌⣳⠈⣇
⠀⠀⠀⢀⣨⢿⣵⣿⣷⣿⣿⣿⣿⣦⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣿⣿⣿⣿⣿⣷⡇⣧⢇⣿
⠀⠀⢰⠋⣇⣸⡿⣹⣿⣿⣿⣿⣿⣿⢇⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⡏⣿⢻⣿⣿⣿⣿⣽⣎⣿⡀
⠀⢠⠃⡰⠋⢉⣼⣿⣏⣾⣵⣿⣿⡿⣛⣵⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⣧⣷⡙⣇⢻⣿⣿⣿⣿⣿⢿⣇
⠀⠇⠈⠀⢠⣾⣿⣿⣸⣿⣿⣿⣿⣾⡿⢣⠊⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣿⣌⢻⣿⣿⣎⢻⠟⣿⣿⣿⡄⢻⡀
⠀⠀⠀⠠⢻⡟⡅⠘⣿⡟⣱⣿⣿⣿⣧⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣮⣝⠻⢿⣿⡆⡇⣿⣹⣿⠇⠀⠱
⠀⠀⠀⠀⣸⡀⠀⠀⢻⣾⢿⣿⣿⣿⣿⢳⣵⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⡼⣷⡻⣿⣿⢶⣝⣿⣷⣽⣿⣿⡏⠄
⠀⠀⠀⠰⠛⣷⡀⢠⡿⣿⣼⣿⣿⣿⣿⡇⢿⡿⣆⠀⠀⠀⠀⠀⢿⣿⠇⢸⣧⣿⣿⣎⣿⣮⣻⣿⡏⣿⣿⣿⢰⠈⠄
⠀⠀⠀⠀⠀⠈⢳⣼⠃⣿⣿⠉⣿⣿⣿⣿⠀⢳⠹⡄⠀⠀⠀⠀⢸⡿⠀⢸⠟⣿⣿⢿⡾⣿⣷⡿⣵⡜⣿⡇⠈⠇⠐
⠀⠀⠀⠀⠀⣠⠞⠘⢇⣽⡏⣰⣿⣿⣿⣿⠀⠀⠀⠃⠀⠀⠀⠀⠸⢀⢀⡟⢠⣿⡟⢸⡇⢸⣿⣧⡟⣿⣬⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠃⠀⠀⣼⣿⣟⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⣿⠃⣿⢃⡏⣿⣿⢃⣹⡏⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢈⣿⠟⣹⣿⠟⠁⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢧⡟⣼⠀⡏⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠋⢀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢺⣿⣿⣀⡇⠈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢻⡟⠘⠆⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⢸⣿⡆⠀⠀⠈⣹⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⡄⠀⢸⡇⠀⡀⠀⢿⣿⠂⠀⣴⣶⣶⣶⣦⣴⣶⣶⣶⡄
⠀⠀⠀⣼⣿⣧⡀⠀⣾⣿⣿⣆⠀⠘⣿⣿⣿⣿⡇⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⣶⠀⠀⡇⠀⢸⡇⢰⡇⠀⢸⡟⠀⠀⡿⠉⠙⡟⠉⠙⡟⠉⠙⡇
⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⢘⣿⡀⠀⠀⠀⠀⠀⢾⣿⠀⠀⣿⡇⠀⣿⠀⠀⡇⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠻⠦⠶⠿⠦⠾⠷⠦⠾⠃
⠀⠀⠘⣿⣿⣿⠃⠀⣿⣿⣿⣿⠀⠀⢿⣿⣿⡿⠀⠀⢸⣿⡇⠀⢸⣿⡆⠀⢺⣿⠀⠀⣿⡇⠀⣿⠀⢠⣷⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠐⠀⠐⠒⠒⠒⠒
⠀⠀⠀⢻⣿⡿⠀⠀⢿⣿⣿⡟⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⠇⠀⢸⣿⠇⠀⢸⣿⠀⠀⣿⠇⠀⣿⠀⠐⣿⠀⢸⡇⠸⡇⠀⠀⡇⠀⠀⠚⠂⠚⠛⠛⠛⠒⠒⠒⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣾⣯⡀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⢀⣿⣿⡟⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣿⡟⡇⠀⠀⢠⣤⡹⢿⠃⠀⢰⣿⣦⣤⣤⣴⣾⣷⣶⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡄⠀⠀⠀⠀⣬⣬⡉⠀⠀⠀⣿⣿⣿⣿⠿⢿⣿⣿⣿⡇
⠀⠀⢠⣿⣿⡇⠀⠀⠼⠿⠇⠀⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣷⠀⠘⢠⣶⣿⣿⣷⣤⠀⠀⣿⣿⣿⣿⣶⣾⣿⣿⣿⡏
⠀⠀⢸⣿⣿⡗⠀⢁⠰⠶⠀⡇⠈⠀⠀⠈⠻⢿⡿⣿⣿⣿⣿⣿⠀⠀⣼⣇⠀⠀⣼⣷⠀⠈⡏⠀⢠⣿⡈⠄⠀⢸⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀⡀
⠀⠀⠐⠿⠿⠇⠀⠸⠦⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁⠀⠸⠿⠿⠃⠘⠿⠿⠃⠀⠁⠀⠻⠿⠗⠀⠀⠘⠿⠿⠿⠿⠟⠀⠀⢿⠿⠿⠿⠷⡿⠿⠿⢿⡇
⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣄⣄⣄⣤⣠⣀⣠⡀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⢹⣟⢸⠠⠀⠆⠀⠀⠀⣿⣿⣧⣤⣼⣿⢿⡃⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣴⡿⢻⡟⡝⠙⢻⣷⡀⠀⠀⠀⠀⣼⣿⣄⠀⠀⠀⠀⠿⠶⠶⠶⠶⠷⠶⠶⠾⠇
⠀⠀⢸⡇⢸⢐⠀⡇⠀⠀⢸⡏⠈⡉⠀⠉⠁⢹⡇⠀⠀⠀⣿⣿⣄⠀⠀⠀⢸⣿⢠⡿⡱⠀⢀⡿⢻⡷⠀⠀⠀⢀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣄⡀
⠀⠀⢸⡇⢸⢈⠀⡇⠀⠀⠘⡅⠀⠁⠀⠀⠀⢨⡇⠀⠀⡆⢡⣠⡌⢰⠀⠀⠘⣿⣿⡱⠁⢀⣾⣣⣿⡏⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣞⣩⣶⠟⠋⡲
⠀⠀⢸⡇⢸⠘⠀⠇⠀⠀⠀⡟⠈⠉⣿⣿⣿⣿⠁⠀⠀⣇⠈⠉⠀⣾⠀⠀⢀⠈⢻⣿⣶⣾⣿⣿⠋⣀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡿⠛⠁⢀⣤⡇
⠀⠀⠈⠃⠘⠈⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠒⠛⠋⠀⠀⠈⠛⠛⠓⠒⠒⠚⠛⠛⠋⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠀⣀⠴⠚⠳⠦⣴⡋⣸⠁
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢷⣦⣄⠀⣀⡴⠛⠁
⠀⠀⢈⣩⠿⠛⠻⢯⣉⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⢠⡟⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⢿⢏⣤⡄⠀⠀⠀⢸⣿⣿⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣷⣶⡆
⠀⢾⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣰⠋⢋⣼⣿⣧⡀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠘⣧⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣿⣿⣦⣤⣄⣀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠔⠁⠀⠘⣿⣿⣿⠆⠀⠀⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠙⠲⠦⠶⠚⠋⠀⠀⠀⠀⠻⠿⠛⠤⠬⠿⠀⠀⠀⠀⠘⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠿⠿⠿⠃⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⡍⣿⠛⠿⠿⠿⠻⠟⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢚⣩⡵⠖⠒⠒⠀⠀⠛⠿⠿⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⣴⠟⠁⠀⢀⣠⡴⠦⠀⠘⢤⡀⢤⣄⡉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡴⠋⢀⣴⠟⠁⠀⣠⠞⠋⠁⠀⢀⡄⠀⠀⠉⠓⢾⣽⣷⣤⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢡⠞⠀⢠⡾⠋⠀⠀⠀⣁⡤⠂⠀⣠⡾⢁⡄⠀⣄⠀⠀⠈⠙⠿⣟⢦⡈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣰⠋⠀⣰⠟⣀⣤⡴⠞⠛⢉⣠⣴⣾⠟⣡⠎⠄⠀⠘⢧⡀⠀⠲⣄⠈⠻⣧⡈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠠⠁⠀⠾⠵⠚⣉⣠⣤⣶⣾⣿⣿⢟⣭⣞⠕⠁⠀⠀⠀⠈⠻⣷⣤⡈⠳⣦⡈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠁⠀⣀⣤⣶⡿⠿⣛⣻⡿⠟⣩⡴⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⠞⠋⣩⣴⡶⠟⠋⣡⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⢿⡄
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢁⣴⡿⠛⠉⣠⠴⠋⠀⠀⠚⠛⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⣿⡀
⠀⠀⠀⠀⠀⠀⢸⠃⢀⡴⠟⢁⣠⡶⠋⠁⠀⠀⠀⠀⢄⣲⣶⡦⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠸⢠⠞⣁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⢦⣄⣸⡇⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠗⢢⠀⣹⣿⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣠⠟⢻⣆⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡿⢿⣷⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⣰⠏⢠⡆⠻⣆⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⢸⣿⠀⡀⠀⠀⢻⡆
⠀⠀⠀⠀⢠⠇⠀⠀⣷⠀⠙⢦⡙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢀⣾⠋⣿⢸⡇⠀⠱⡀⠀⠆⢻⡀
⠀⠀⠀⠀⡘⠀⠀⠀⢿⠣⡀⠈⠳⣜⣿⡄⠀⠀⠀⠀⢶⣄⣀⣄⡀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣿⣿⢡⡄⠀⣿⡄⠀⠘⣧
⠀⠀⠀⠀⠁⠀⠀⠀⠈⢧⡈⠀⢀⠙⢿⣷⠀⠀⠀⠀⠀⠻⣯⣿⣿⣿⠆⠀⠀⢀⣴⣿⠆⠀⠀⣿⠇⢸⠇⠀⣿⣷⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⡄⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣴⣿⣿⢻⡄⠀⠀⡟⠀⣿⠀⢀⡿⢸⠄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣧⢹⣿⢸⡇⠀⠀⠃⢸⡇⠀⢸⡇⠈⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡿⠀⠀⠀⠀⠀⠈⠉⠛⠛⠙⢿⣿⣿⢨⡟⢸⡇⠀⠀⠀⢸⣧⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠘⢣⡿⠀⠀⡀⠀⠀⢿⠀⢸⣿⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢀⣾⠃⢀⡞⠀⠀⠀⠘⣇⠈⣿⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣸⡏⢠⡿⠀⠀⠀⠀⠀⢹⡆⢻⡇⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⡇⣼⠇⠀⠀⠀⠀⠀⠀⣧⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡇⢻⠀⠀⢠⡄⠀⠀⠀⡿⢸⠇⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⡆⠀⠀⣷⠀⠀⢰⡇⡎⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢃⠀⠀⣿⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣃⠀⠀⠀⠀⠀⠙⠋⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠘⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠙⠀⢀⠈⠁⠀⠺⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢛⢫⡀
⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⢀⡀⠀⠀⠀⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠉⠁⠛⠑⢯
⣶⣼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⡀⣿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢠⡶⠖⠒⠀⠀⠀⠸⠆⢀⡀⠤⠀⠒⠐⠒⠂⠠⢸⠁
⣎⣿⡇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢷⠇⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣍⣩⡆⠀⠀⠀⠀⠀⠴⡀⠣⡀⢠⡄⠀⠀⠀⢴⡄⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠠⣀⣤⡀⠀⠀⠀⠸
⠉⠀⠀⠀⢀⠀⢀⡀⠈⠅⠀⠀⢀⠀⢠⠼⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠋⠁⠀⠀⠀⢀⡀⢐
⠀⠀⠐⠇⢀⡠⠀⠀⠀⠀⢀⡀⠛⠛⠛⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣸⢒⣶⠶⠆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⡀⡠⠀⠠⢰⡀⣴⠶⠶⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠪⠟⠷⢆⣤⠦⣀⣤⠂⠀⢦
⠀⢀⣤⠀⠀⠀⠓⠀⢤⠀⣌⡁⠀⠀⢊⣡⡍⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣴⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠓⣄⠀⠀⡀
⠀⠈⠙⣄⢀⠀⠈⠁⠀⠀⡏⠉⠀⠀⠨⠉⠹⠶⣤⣿⣤⣴⠆⠠⠲⢲⠚⠧⠤⠤⢀⣀⠀⣿⢀⢀⡄⣀⡀⠢⣠⡏
⠀⠀⠀⠍⣧⢀⠀⡈⠁⣁⣁⠀⠀⠀⠀⠀⠁⠀⠈⡈⠁⠀⠊⠀⠀⠈⠀⠀⠀⠀⠀⢈⡧⠒⠻⠙⣷⠉⠻⣏⠑⠂
⠀⠀⢠⠆⠁⠘⠉⠉⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠚⠁⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠡⡀⠀⢈⠁⡈⠐⡾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⡟⢿⡄⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⢾⠋⠩
⠀⠀⠀⠈⠉⠀⠀⢉⠖⠤⠀⢃⠀⠀⠀⠀⠠⡀⠀⠀⠀⢠⠋⠀⠀⠹⡄⠀⠀⢀⠶⠦⠐⡀
⠀⠀⠀⠀⠀⠙⠀⠀⢟⣿⠶⣾⡄⠀⠰⡖⠋⢹⠀⢀⣴⠁⣠⡄⢀⡀⢰⡀⢠⠿⠀⠂⡐⠉⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢠⠒⠒⠉⣿⣾⡟⢼⡧⠤⠧⠀⠺⣤⠟⠁⠚⠛⣣⠾⠿⠈⠛⠋⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣴⣤⠈
⡀⣀⣠⠀⠀⣤⡄⠀⠀⠙⠛⠻⠦⠄⠰⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠈⠛⠷⠚⠀⠀⠀⠀⠀⠸⠋⠠⠤⠀⠂
⠅⠈⠀⠂⠀⠼⠤⠊⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠖⠖⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡠⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⠂
⠀⣶⠄⠁⠀⣀⣥⠰⠃⠀⠈⢡⠀⠌⠀⠀⠀⠀⢀⣀⢀⢀⣠⣴⠶⢶⡀⢀⡀⠀⠀⠀⠀⠀⠰⠀⠶⠂⠀⠀⠀⠀⡀⠀⠀⠓
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣚⣭⣥⣶⣶⣤⣌⡙⠻⢿⣦⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠃⣠⣾⠟⢋⣉⣀⣀⡀⠉⢉⡓⠀⠙⢿⣽⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⡇⣰⡟⢡⣾⣿⣿⣿⣿⣿⣷⣄⠹⣦⡀⢀⢻⡇⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⣿⡇⣿⠁⣿⡿⠛⠉⠙⠻⣿⣿⣿⡆⢹⣿⣾⡆⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣜⠿⣿⣧⡘⠆⠛⠀⠀⠀⠀⠀⢹⣿⣿⡿⢸⣿⣿⡗⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⠷⠬⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⣼⣿⣿⠃⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⠂⢀⣀⣀⠀⠀⠀⠀⠀⢰⣿⣿⠏⣼⣿⠟⢁⡼⠟⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠀⠉⠙⠛⢷⣤⡀⢠⣿⣿⠋⣼⡟⠁⠀⡩⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⠃⠘⣿⠛⠒⠢⠀⠈⠀⢸⣿⠇⢸⡏⠐⢠⡾⠁⠀⢾⡷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠁⠀⢾⣷⣤⣤⠄⠀⠀⢸⣿⢰⡘⣇⢸⣿⣇⠠⣀⣙⣛⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢻⡌⢿⣬⡂⠹⣿⣧⣈⠉⠉⣉⣀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡛⢿⣶⣌⡻⣟⠿⠶⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⣭⣛⢿⣾⣷⡀⢤⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣾⣶⠄⠀⠀⣸⣿⣷⡜⣿⡇⢸⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣀⠀⠀⠈⠛⠛⠛⠋⠀⢷⡾⣟⣿⠟⠡⠟⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣴⣶⠿⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠋⣴⠏⣠⠆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢣⣾⠃⣴⠁⡠⠃⠀⠀⠀⠀⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣡⣿⢃⣾⢃⣞⢅⠀⠀⠀⠀⠀⠀⠀⠉⣛⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡷⡿⢡⢏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢉⠙⢿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢟⡝⡰⢣⡿⣡⡃⠀⠤⠀⠀⡆⡀⠀⠀⠺⠃⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢟⠜⣱⢏⣼⡿⣡⠀⠀⠦⣽⢣⡇⠀⠀⠀⣀⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⡾⣣⠎⡜⡕⡵⣱⢗⡆⠈⠓⢤⠀⠀⠀⠹⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⡴⠁⠈⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠎⠀⠀⠀⣤⣄⣀⣀⠉⠙⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⠿⠿⠿⢿⣿⣷⣦⣤⣶⡾⣷⣿⣿⡿⠟⠛⠉⡀⢸⣿⡏⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣈⣉⠁⢀⣀⣀⣠⣶⣶⣿⣿⠼⣿⠀⢠⣾⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠻⣿⣿⣿⠿⠿⠿⠿⠿⠀⠈⣿⠿⠿⠛⠋⠉⠉⠀⠉⠀⢾⣟⣡⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⠾⢻⣿⡄⠁⠀⣀⣀⣀⣤⣤⣄⠀⠀⠀⣀⣠⣤⣤⣶⣶⣦⠀⠀⠀⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⢏⢆⡈⠻⠿⠿⠿⢿⡿⠄⠀⠀⢻⣿⡿⠿⠟⠛⠋⠀⢀⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⠁⢠⣤⣶⣦⣄⣠⡀⠀⠀⠀⠀⣀⣀⣤⣴⣆⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠻⠿⡿⠇⠀⠀⠸⣿⣿⣿⠿⠛⠛⠠⢤⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡴⢣⣊⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠐⠶⢤⠀⠉⠁⣀⣠⣤⣾⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢴⡿⣡⣶⠀⠐⠀⠾⠻⠿⠿⢿⡟⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠋⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣻⡿⣿⣿⣿⣿⣡⣴⣿⣭⣭⡟⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠿⠛⠉⠙⠿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⡹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⢶⠀⠀⠰⠾⠛⠁⠀⠀⠀⠈⣿⣿⣿⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⡇⢰⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⣿⣿⣯⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢈⣿⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣝⢻⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣿⣻⣿⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⠟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⣿⣿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢻⣿⣧⡉⠻⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠋⠀⠀⠀⠀⠀⠀⣀⡶⣶⠄⠀⠆⠀⠀⠀⠀⠈⡎⣹⣿⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢽⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⣿⣆⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⢸⡀⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣠⣀⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⣢⣭⡭⣭⣭⣫⢭⢭⣭⣅⡓⢄⡀
⠀⠀⠀⢀⣤⣶⣶⣿⣶⣦⣀⠀⠀⠀⠀⣀⡴⣿⣷⣿⣿⡙⠋⢟⣱⡮⡽⠟⡕⣿⣾⣾⣿⢦⣄⡀⠀⠀⠀⢀⣤⣶⣾⣶⣶⣤⣀
⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣙⣫⣷⣿⣿⠟⠛⣿⣷⢀⡄⠚⡛⠠⢀⣷⣿⠋⠛⣿⣷⣾⣭⣋⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⠏⢘⠽⣦⣫⣽⣿⣿⣟⣩⣿⢶⠂⠀⡻⠿⣶⣦⣾⣾⠿⣟⠀⠐⣶⣿⣭⣿⣿⣿⣯⣭⣅⡟⠓⣈⣻⣿⣿⣿⣿⣿
⠙⣿⣿⣿⣿⣿⣷⣼⣷⣛⣽⣻⣴⠿⢯⡁⠀⠙⠏⢿⡀⠁⡀⠘⢻⡿⠡⢐⠉⢀⡿⠝⠉⠀⢈⡽⠿⢶⣟⣯⡟⣿⣯⣷⣿⣿⣿⣿⣿
⠀⠀⠛⢿⣿⣿⣿⣿⣯⣵⣮⣾⣷⣖⣢⡈⢂⠀⠈⡇⠹⣟⡛⢷⡃⢨⡞⡋⢟⡋⣬⠀⠀⠐⢁⣔⣲⣾⣷⣽⣧⣭⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⡿⣿⠻⣿⣿⣿⡄⡇⠀⣷⠀⢀⣟⣼⣁⣈⣧⣯⡜⠀⣾⠀⢸⢠⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠀⣿⡿⢿⡿⣧⡀⠟⡠⡾⠁⠀⠀⠀⠀⠉⢳⢄⠁⢀⣾⢻⡿⢿⣿⠀⠀⠀⠙⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⠸⣷⡘⣇⠠⢀⠤⣒⠋⠙⠛⠑⣒⢌⡀⠀⡾⢡⡾⣇⡟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣇⠀⢣⣸⢳⢹⡶⣭⠀⠉⠀⣆⣡⠄⠉⠑⣝⢦⡇⡾⣷⡼⠀⢸⢄
⠀⠀⠀⠀⠀⠀⠀⡀⢠⣾⠏⣩⠗⣻⡄⠈⣿⣼⣼⢱⡀⢰⡖⠈⠀⠀⠉⠰⡄⢀⡟⣷⡇⣿⠁⢀⣟⢹⣉⡝⣷⡦⢄
⠀⠀⠀⠀⠀⠀⣸⡴⠟⠛⠋⢿⢸⠁⠻⣄⣿⣿⢻⠁⣈⠃⠱⠤⠄⠤⠤⠌⢸⡁⣁⡇⣿⣿⣠⠞⠀⣇⡿⠙⠛⠳⢦⣡
⠀⠀⠀⢀⠋⠀⡟⢀⠀⠀⠀⢸⡾⡄⠀⠈⣿⢹⣼⣫⠥⠖⠓⠋⠉⠉⠙⠛⠺⠮⣟⣣⣿⣿⠁⠀⢠⣿⠇⠀⠀⠀⡈⢷⡀⠑⡆
⠀⠀⠀⠁⠀⠘⢷⡀⣸⡆⢀⡼⠃⢽⠂⠒⣾⣿⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠙⣿⣿⠒⢐⡏⠼⠦⣀⠠⠾⣀⡾⠃⠈⠉⡄
⠀⠀⠀⣆⠀⠀⢨⠈⠀⠀⢈⣧⡟⠷⠃⣼⣹⠇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⣿⣧⠘⠾⢻⡼⣇⠀⠀⠀⢕⠀⠀⣀⠁
⠀⠀⠀⡏⠑⠓⡻⠂⠶⣀⠉⠀⢨⠎⠉⢹⡿⠀⣸⣿⣿⣿⣷⡙⣿⣿⢫⣿⣿⣿⣾⣧⠀⢻⠋⠉⢻⡁⠀⠉⢩⠖⠂⢞⠓⠪⢹⠂
⠀⠀⠀⢹⣤⢰⡀⠀⢀⠘⡶⠖⠻⢇⠠⣼⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠀⢸⡇⠄⡸⠗⠲⢶⠁⡀⠀⢀⣅⣠⡄
⠀⠀⠀⡇⠀⢀⡵⢤⡏⠩⠰⠐⠀⣄⡷⣽⢻⡀⠀⠙⡻⢿⡿⠿⠿⠿⠿⠿⡿⢟⠋⠀⢀⡞⣿⢿⡤⠀⠀⠈⡉⠰⡤⣮⡁⠀⢸
⠀⠀⠀⢳⠀⢸⠀⢈⣷⠀⠀⡀⠀⠐⠛⢸⡷⠿⠿⣿⣿⣦⣄⡀⠀⠀⠀⣀⣤⣿⣿⠿⠿⢾⠃⠿⠀⣀⣈⠁⢀⣿⡀⠀⡇⠀⡚
⠀⠀⠀⡴⠓⠛⠻⢹⠀⠱⡶⠀⠀⡓⠐⣸⠃⠀⣴⠳⢼⣾⡍⠉⠉⠉⠉⢉⣷⠋⠲⡆⠀⠘⡆⠀⢎⠀⠠⢷⠀⢀⡟⡟⠓⠛⢳
⠀⠀⠀⣧⡀⣰⠞⢸⡗⠀⠀⠠⢎⠄⡰⠙⣄⢀⡿⠀⠚⢇⠙⠶⣤⣤⠔⠋⡸⠃⠁⢦⣀⣰⠹⣄⠨⠓⠠⠈⠠⣶⠗⠚⡄⠀⣸
⠀⠀⠞⠉⠉⡻⣄⣠⣝⣚⣓⡠⠄⠈⣇⣀⡟⠈⠀⠀⠀⠀⠉⢲⡇⢸⡗⠉⠀⠀⠀⠀⠉⢻⣄⣸⢁⠬⡀⣐⣛⢫⣄⡴⡟⠉⠁⢁
⠀⠀⡇⠀⠀⣐⠀⠀⠈⡸⠛⠙⠷⣋⡽⢅⣸⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⣧⣠⢿⣈⠻⠛⠙⣇⠀⠀⠁⣃⠀⠀⢈
⠀⠀⠈⠀⠈⠿⡦⡀⢾⠁⢀⠀⣸⡝⠈⠀⣀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⠀⡀⠩⣇⠀⠀⠘⡷⠀⣴⣿⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠑⠀⣛⣒⠪⠊⠈⠁⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠁⠀⠀⠃⠙⠗⡒⠃⠀⠈

⠀⠀⠀⢀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⣯⢺⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠘⣎⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠙⡆⠀⠀⠀⠐⠋⢹⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣮⣿⢫⣿⣿⣦⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⣷⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠙⢮⡙⢿⣿⣿⣷⣄⠀⠀⠀⢀⣧⣤⣤⣤⣤⣤⣧⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠻⣿⣿⣿⣦⡀⠀⢰⣿⡀⢀⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡜⠁⢺⣿⣿⡄⠘⣛⣣⣬⣭⣭⣭⣭⣄⣀⠀⢸⣿⣿⠀⠀⠀⠀⣠⡾⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⢀⣀⣤⣶⣦⡀⠀⠀⠀⠻⣄⠈⢛⣩⣶⣿⠿⠛⠋⠉⠉⠉⠉⠛⠻⢿⣷⣌⡻⠀⠀⠀⣰⡟⢀⡄⠈⢙⣿⣿⣿⡿⠃⠀⣠⣶⣦⣄⡀
⢾⣧⡤⢿⣿⣿⡟⡆⠀⠀⠀⠈⣱⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⣰⡟⢠⣾⠁⢠⣾⣿⣿⡿⠀⠀⠀⡇⠀⠈⠙⢿⣦
⢺⣿⣷⠀⣿⣿⣷⢹⡄⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣟⣠⣿⠃⢠⣿⣿⣿⡿⠁⠀⠀⡜⣰⡀⠀⠀⠀⢹⠂
⠈⢿⣿⣧⢻⣿⣿⣧⢻⡀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⠟⢤⣿⣿⣿⡿⠁⠀⢀⣼⣿⡟⢡⠆⣠⠎⠁
⠀⠘⣿⣿⣇⢻⣿⣿⣯⢷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢀⣾⣿⣿⡿⠁⠀⣠⣾⡿⠋⣰⣿⡿⠁
⠀⠀⠸⣿⣿⡆⠿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⣿⣿⠙⠺⣿⣿⡿⢁⣤⡾⠋⠎⢀⡼⣿⡿⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠹⣿⣿⣷⠹⣿⣿⣿⣷⠀⠀⠀⣠⣴⣾⡿⢿⣛⡿⠭⠭⠭⠭⠭⠽⣟⣿⢿⣿⣧⣄⠀⣼⡿⢡⣾⣿⣦⣀⠀⠞⢱⣿⠁⠀⢠⠂⢿⣿⠇
⠀⠀⠀⠀⢻⣿⣿⣆⢻⣿⣿⣿⣧⣴⣿⣿⡯⠗⠋⠁⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠉⠺⢻⣿⣿⣿⢡⣿⣿⠛⣿⣿⣷⣤⣼⣿⠀⣰⠟⣡⣿⡿
⠀⠀⠀⠀⠀⢿⣿⠈⣦⡹⣿⣿⣿⣿⡿⠋⢀⡠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⡀⢹⣿⣿⣿⣿⠧⢄⣿⣿⣿⣿⣿⠃⣴⠃⣴⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣦⠛⠛⣾⣿⣿⠏⢀⠔⠉⠀⠀⢀⣄⣀⢸⣧⣀⡤⢖⣀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣧⢀⣼⣿⣿⣿⣿⠃⠚⢅⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⣸⣿⣿⡀⠁⠀⠀⠀⠀⣀⡤⠟⠋⢻⣥⠶⣈⣭⠉⢀⠀⠀⢀⣼⣿⣿⣿⣿⣸⣿⣿⣿⣿⠇⠀⠀⠀⣰⣹
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⣻⣿⣧⡳⣄⠀⠀⠐⠿⢥⣭⣶⣒⣻⡧⠞⣋⡤⠖⠁⣀⣴⣿⣿⣿⣿⣿⣏⣝⣻⣿⡿⣵⡆⠀⠀⡴⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠙⣿⣿⣷⣬⡑⣢⣄⣀⣀⠀⠀⠉⠉⣉⣉⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⡿⠛⣽⣽⡇⢀⣼⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠉⠀⠀⠀⠑⢦⡙⠻⢟⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣬⡛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⣉⣠⣽⣿⠟⠀⠀⠀⠀⠀⠀⢰⢸⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣯⣿⣿⣿⣿⣿⣥⣴⣶⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡜⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⣠⣾⣾⣿⡟⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⢶⣤⣤⣤⣿⣾⣿⡿⢋⣤⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⠾⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠛⠉⠙⠛⠿⠟⢻⠅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠁⡀⠀⠂⠀⠀⠐⠃⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⢠⠢⢈⣶⣤⣤⣤⣦⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠚⠀⠀⢀⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀

⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⠀⠈⣹⠿⡏⠀⠀⡠⠤⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⣿⡆
⠀⠀⢩⣯⠽⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠃
⠀⠀⢀⣠⣤⣤⣶⠀⠀⠀⠀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣄⠀⠀⠀⠀⠀⡼⠛⠈⠁⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠘⠋⠉⣁⣀⠀⠀⠀⠰⣿⣿⣿⠿⠆⠀⠀⠀⠀⢠⣤⠀⠀⠀⠈⢦⡄⣀⣠⠞⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣷⡿⠀⠀⠀⠀⣠⣴⣿⣿⣿⣦⣄⡀
⠀⠀⠰⠿⠟⠛⠋⠀⠀⠀⠀⣉⣁⣀⣤⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⣼⡽⣃⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣤⣴⣶⠾⠀⠀⠀⠈⠛⠉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⣼⠏⠀⢻⣆⣰⣿⠟⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⢸⠛⡟⡿⢻⢻⢻⢻⣿
⠀⠀⠈⠉⣀⣀⣤⠀⠀⠀⠠⠟⠛⠛⢉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣅⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⣿⠿⢟⠿⡿⡇⠀⢸⠂⡇⡇⠸⢸⢸⢸⡿
⠀⠀⢶⣾⣷⣿⣾⠆⠀⠀⢠⣴⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠻⢷⣄⡴⠋⠘⣆⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⡏⡇⠀⠈⠀⠀⠁⠀⢸⠈⢸⡇
⠀⠀⠈⠛⢿⡿⠋⠀⠀⠀⠀⠙⢻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢠⠆⠉⠁⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⠀⠀⠀⠘⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢆⠀⢀⣄⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣼⠏⠀⡰⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⡁⠀⡱⡁⠀⡀⠀⣿⢒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠊⠰⡖⡁⢀
⠀⠀⠀⠀⠀⠀⠀⢠⢯⣼⠏⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠈⢻⠁⢘⠏⠀⠀⣿⠬⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠂⢴⠀⣽⠁
⠀⠀⠀⠀⠀⠀⣀⠍⣾⠏⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠸⡆⢸⠀⠀⠀⣿⣚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠰⡇⠀⠀⠀⠀⣇⢺
⠠⣠⡖⠀⢲⣄⣈⣻⣃⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣿⡇⠀⠀⠀⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠇⠀⠀⠀⠀⢸⡟
⠀⠀⠑⠒⠊⠀⣰⠃⠈⢻⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⣸⠃⠀⢀⠏⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⡇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡰⠃⢀⠤⢾⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⢤⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠁⠀⠠⣀⡠⠁⠀⠀⠀⠀⠈⠐⢾⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢦⣀⡼⠁⠀⠀⠸⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠸⣿⠀⠀⠘⠃⠀⠀⠀⠆⠀⠀⠀⠀⢀⡴⠞⠁
⠀⠀⢀⣄⣀⣀⣀⣀⠀⠀⠀⢠⠉⠉⡲⠦⠤⠤⢸⣷⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡖⣀⣀⣀⡤⠞⠧
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠙⢷⣍⠙⠓⠶⠤⠀⠀⠀⠀⠀⠤⠴⠖⠚⢋⣵⠟⠁⠀⠀⠀⠑⠄
⠀⢀⣾⣾⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣿⡄
⠀⠸⣿⢿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢸⣿⠖⠖⡇
⠀⠀⣿⣾⣿⣿⣿⣾⡇⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢩⣙⠀⠀⢸⣿⣋⣉⡇
⠀⠀⢸⣟⣿⣿⣷⣿⠀⠀⢸⢠⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢻⣿⠤⠤⠀⠀⢸⣿⡥⠤⡇
⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⢸⢸⢀⢠⢸⢸⠀⠀⢰⢰⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⡇⡇⡀⠀⠀⠀⠀⢺⣿⠒⢚⠀⠀⢸⣿⡓⠒⡇
⠀⠀⠀⣧⣿⣿⣿⡇⠀⠀⢸⣸⢸⣸⣸⢸⣸⠀⢸⣸⣠⣀⣀⣸⡀⠀⢀⣄⣀⣇⣇⣆⡀⠀⣇⣄⣇⡇⣇⣇⡀⠀⠀⠀⢹⣿⢩⣩⠀⠀⢸⣿⣭⣍⡅
⠀⠀⠀⣿⣽⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⠰⠶⠀⠀⢸⣿⠶⠶⠆

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⣿⣀⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣦⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠋⠀⠛⠉⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢠⣶⣾⣿⣿⣶⣦⡀⠀⠀⠀⠀⠂⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣆⢀⢀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣉⣿⣿⣿⣿⣷⣀⣷⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣮⣿⣦⣴⣦⣤⣤⣤⣍⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠿⠿⠟⢿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⠶⠓⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠻⡄⠚⠲⢶⣤⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠹⡇⢹⡏⠉⠉⠘⠆⠈⣿⠛⠛⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⣤⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢢⠼⠕⢻⣿⣿⠷⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠉⠓⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⢒⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠄⣀⣤⣴⡶⠿⠅⢀
⠀⠀⠀⠀⠀⠀⢠⠶⠶⣾⡷⠷⠾⣯⣿⣿⠻⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠶⠚⣿⡍
⠀⠀⠀⠀⠀⠀⠸⣦⠒⠈⣇⠀⠀⠙⠒⣋⣀⡩⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠐⠃⢀⡖⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢷⣿⣄⠀⠀⢀⣭⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡼⣅⢠⠖⣶⢰⣦⡏⢸⡗⡶⢰⣟⠝⠾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢻⡿⣿⣥⣾⣇⠀⠀⠀⠀⠀⠀⠀⢸⣏⢰⠃⣿⠰⡯⠀⢸⠅⠿⠝⠁⠻⠄⠀⠀⠛
⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠘⣿⣷⣿⣧⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢾⡧⠁⠀⠀⠀⣴⠒⠂⢠⡎⠄⠀⣀⠀⢀
⠀⠀⣠⠀⢀⣴⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣤⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠠⣿⢥⠄⣾⠁⣇⣿⢠⠇
⠀⠀⢸⣤⣾⣿⣿⠦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢠⠖⣹⢿⡏⠿⠈⠻⠛⢸⡟⠁
⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠂⢰⣻⣿⣿⣿⣿⣿⣿⡏⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠳⠶⠋⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⠁⠀⠈⠈⠁

⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⣀⣀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⣄⢸⡭⢟⣯⣼⣽⣦⣿⣾⣣⡆⠀⠀⠀⡇⠀⠀⠀⠀⠠⡷⠈⢻⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⡀⠀⣀⣀
⠀⡇⠠⢹⡋⢨⣏⣃⣾⣁⣽⢯⢻⡞⣯⠀⠀⠀⡇⠀⠀⠀⠀⢈⣠⣴⣤⡀⡀⠀⠀⠀⠀⠀⡇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡀
⠀⡇⠀⠈⠙⣯⠹⣿⣿⡽⣿⡯⣿⠇⠁⠀⠀⠀⡇⠀⠀⠀⠰⣿⠉⠉⠉⢿⡇⠀⠀⠀⠀⠀⡇⠀⢼⣿⣿⣭⣤⣤⣤⣿⣿⣷
⠀⡇⠀⠀⠀⡿⣧⣿⢽⣿⣿⣷⣿⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡀⣀⣀⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠛⢿⣿⣿⣿⣿⣿⡿⠃
⠀⡇⠀⠀⠀⣽⣿⣿⣻⣿⣽⣶⣻⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⣯⣴⣿⢿⣯⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡄⠀⠀⠀⠀⠀⠀⣠⣶⡴⢦⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⣠⣴⣧⣾⡃⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⣀⣀⣠⣄
⠀⡇⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠉⠉⠉⠉⠉
⠀⡇⠀⠀⠀⠀⠈⢿⣿⣟⣟⣷⣮⣄⠀⠀⠀⠀⡇⠀⢠⣿⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠶⠆⠒⠒⠒⠒⠒
⠀⡇⠀⢀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⣲⠀⠀⠀⡇⠀⠸⣿⡇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⡄
⠀⡇⠀⢂⠀⠀⠀⠀⢸⣿⠿⠿⠛⠋⠁⠀⠀⠀⡇⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡿⣿⣿⣿⣿⣛⣻⣿⡇
⠀⡇⠀⠀⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢷⣀⣀⣰⣶⣶⣿⣷⣄⠀⠀⠀⡇⠀⣠⣿⣿⣿⣿⣾⣿⣿⣿⣷
⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠛⠛⠛⠛⠛⠋⠈⠁⠀⠀⠀⡇⠀⢿⣿⠿⠿⠿⠿⠿⠿⠛⠛
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠳⡈⢲⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢸⢂⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⢀⣀⣀⣤⣴⣾⣿⢇⡆⠈⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣴⣾⣿⣿⡿⠿⠿⠛⣋⣵⡟⠀⠀⠘⠏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠋⠁⠀⢀⣠⣴⣾⡿⠋⠖⠚⠉⠁⢼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢀⣤⣾⣿⣿⡿⠋⠀⠀⠐⠶⠿⠆⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣴⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⣿⣿⣿⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢸⣿⣿⣿⣿⡇⣸⣇⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣿⣿⣿⣿⡁⢿⣟⢆⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣇⠘⣿⣮⠁⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆⠈⠻⣷⣦⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⠈⠙⠻⢿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡀⡈⠛⠿⣿⣿⣷⣦⣄⠀⢀⠉⠛⢿⣶⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⡇⣿⡀⠀⠀⠈⠙⠻⢿⣿⣦⡙⢦⡀⡈⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⢹⣿⣦⣀⠀⠀⠠⢤⣬⣻⣿⣦⠑⢹⣆⠈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠻⣷⣯⣙⡂⠀⠀⠈⠙⣿⣿⡇⢈⣿⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠻⣿⣿⣷⣤⡀⠀⢸⡟⠁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⠰⣆⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣛⣛⡻⠶⣤⣀⣀⣠⣴⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡞⣽⠿⣿⣿⣷⡄⠉⠉⠉⠉⠙⠲⠶⣦⡝⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠉⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠘⢿⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⣀⣀⣤⣤⣶⣶⣶⣯⠉⠛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠀⠀⢩⣝⠛⠉⠉⡀⠀⠀⠙⣿⣿⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⢸⡟⣧⡀⠀⢷⣄⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠹⣿⣦⣈⢿⣷⣄⡀⢡⣀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⣀⡀⢳⡀⠈⢻⣿⡻⣯⠛⠿⣯⡻⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⢿⣿⠿⠀⢹⣆⢀⣿⠇⡹⠀⠀⣈⠇⣿⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠐⠀⠀⢀⣀⠐⠈⣿⣾⠋⠀⣠⣴⣿⠏⣰⠟⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢰⣾⣿⣿⠃⢰⠃⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⠻⣿⣿⣝⢿⡄⠘⣾⡟⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡿⠀⠈⠻⣿⣷⣜⣦⠙⠧⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡰⠀⠀⠀⢠⣾⠀⣿⣷⠀⠀⠀⣿⠇⠨⣿⣇⠀⠎⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠈⠙⠳⣤⡔⠋⢀⣴⣿⣷⠀⠀⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⣠⡾⢟⡴⠋⠁⣿⣿⣦⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡧⢿⡄⣾⠀⠀⠀⠙⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣇⠀⠉⣿⠀⠀⢰⡀⠁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠻⣆⠀⢹⣷⠀⠀⠑⢠⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⣠⠾⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣤⣄⣀⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⢠⣿⠛⢦⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠀⠈⣿⡀⢸⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢀⣴⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⠹⣧⠀⠀⠀⢿⡇⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣿⡄⠀⠀⢸⣷⠀⢹⠀⠀⠀⢀⣿⣿⡇⠀⠉⢹⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣹⣷⠀⢠⣾⣿⡖⠘⣿⡇⠀⢸⣿⣿⡇⠀⠀⡞⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⣹⠿⢇⠈⣿⣿⣷⠆⢿⣿⠀⢸⣿⣿⠃⠀⢰⠇⠀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠸⡀⣿⣿⣿⡂⠸⣿⡇⢸⣿⡿⠲⠤⡜⠀⡼⢁⣼⣿⠏⠙⠻⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣷⣾⣿⣿⡇⠀⢸⣇⣿⣿⡇⠀⣾⠃⡼⢡⣾⣿⡟⠀⠀⠀⢈⡿⠛⠋⠉
⠀⠀⠀⠀⠀⣠⣴⣾⠿⠿⠟⠋⠉⠉⠉⠙⠻⣿⣿⣷⡀⠸⣿⣿⣿⡯⢉⣿⡼⣡⣿⣿⣿⣄⡀⠀⢠⠎
⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⣿⣿⣿⠙⢺⡿⣵⣿⣿⣿⣯⣀⣼⣷⠋⠀⠀⢀⠀⠀⢐
⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⠁⠀⣼⣿⣿⣿⣿⣟⣵⣿⣿⣷⡶⣶⡆⢸⣷⣴⡟
⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⢹⣿⡀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⡇⣿⡇⢸⠛⠛⡇
⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢰⣿⣿⣿⣷⡼⢤⣤⠧⣄⠠
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣽⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⠀⣸⣿⠀⢸
⢻⣿⣿⣦⣀⡀⠀⠀⢀⣀⣤⣶⢿⣿⣿⡿⠛⠉⠉⢙⣿⣿⣾⣿⣿⣿⣿⣿⣀⢐⣗⣀⣽⠀⢸⣿⣿⣿⣿⠁⣿⣿⠃⢹
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠋⠉⠻⣦⣤⠞⠋⠀⢈⣹⢿⣿⣿⣿⣿⣮⣽⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⣿⣿⡇⢹
⠀⠀⠉⠛⠛⣻⣿⡿⠋⠉⠉⠻⣦⣴⠞⠋⠉⢙⣷⣶⡞⠉⠀⢀⣉⣿⣿⣿⠫⣭⣿⣯⣿⠀⢸⣿⣿⣿⣿⠀⣿⣿⡇⢸
⠀⠀⠀⠀⢸⣿⣿⣷⣤⣤⠶⠋⠉⠙⣷⣶⠞⠋⠁⢀⣙⣷⣾⣿⣿⣿⡿⢿⠀⢿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⣿⣿⡇⢸
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣤⠖⠋⠁⠉⣻⣶⣾⣿⣿⣿⣿⠿⠛⠉⠀⢸⡇⢸⣿⣿⣿⠀⠘⠻⠿⠿⠟⠓⠛⠛⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣛⡻⣿⣭⣯⠻⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏⠁⠀⠀⠀⠈⠉⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣗⣿⠁⠀⠀⠀⠀⢀⡀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣿⣿⣿⢿⣟⣒⣂⠀⠀⣫⣭⣥⣄⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⢻⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⣿⡿⣹⣿⣿⠟⠀⠀⠙⠿⠿⠋⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⣰⣿⣟⣿⣧⡀⠀⠲⠶⠂⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⣾⣵⣟⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣤⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢳⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣶⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣾⢿⢻⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠸⡿⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠐⠃⠀⠀⠈⠉⠉⠉⠉⠋⠉⠙⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⠿⢶⢤⣦⣤⣄⣄⣀⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣴⣿⣿⠟⠉⠐⠒⣒⠦⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠃⠀⠀⠀⠐⢦⣉⠓⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠐⠲⢤⡀⠀⣠⠴⠒⠀⠘⣇⢀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠾⣶⠤⠀⠀⠠⢴⡾⠆⡇⣿⢸⡆⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣿⢸⣿⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⢀⠀⢴⣶⠄⠀⢠⡟⣸⣟⣿⣿⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡌⣦⣄⣀⡄⣠⡟⣰⣿⣿⣿⡟⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢹⣷⢸⣿⠏⣴⠏⣼⣿⣿⣿⣿⠁⣼⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢸⣿⢸⢯⡾⢃⣾⣿⣿⣿⣿⠃⢀⡟⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣠⣿⠃⣰⡟⣡⣿⣿⣿⣿⣿⠃⠀⣸⠇⢸⣷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣤⡤⠴⢛⣵⡾⠟⢁⣼⠋⣰⣿⣿⣿⣿⣿⡏⢀⢠⡟⠀⢸⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⢠⣾⠃⢠⣿⣿⣿⣿⣿⣿⠀⡇⣼⠁⣇⠈⣿⡆⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⢰⣿⠇⠀⣾⣿⣿⣿⣿⣿⡇⢸⡇⣿⠀⣿⡄⠹⣷⡈⢧⡀⠀⠀⠀⠀⠀⠀⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡴⠃⠀⠀⢠⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣷⣷⠀⢻⣷⡄⠙⣷⣄⠙⠶⣤⣄⣠⡤⠞⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡀⠈⢿⣿⣦⣌⡙⠿⢶⣦⣤⣤⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⡄⠀⢸⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⡀⠻⣿⣷⡀⠀⠛⢿⣿⣿⣿⣷⣤⣴⣶⣶⠾⠿⠶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢻⣿⣧⡀⠈⢿⣿⣝⠿⣿⣿⣿⣄⠈⠻⢿⣦⣀⠀⠀⠉⠉⠉⠉⢁⣀⣠⣤⣤⣀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣙⢿⣷⣄⠀⠻⣿⣦⣌⠉⠛⠻⠷⠦⡄⠀⠉⠁⠀⣀⣤⣶⣾⠿⠛⠉⠉⠉⠛⠻⣦⡀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣦⡈⠛⢿⣿⣶⣤⣤⣤⣤⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠈⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠴⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣋⣥⢶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⠟⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢉⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⣠⡀⠀⢀⣽⣿⣿⡿⠿⠿⠛⠻⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢿⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡿⢛⣿⣿⣿⣿⣿⣿⠿⢿⢿⡿⢿⠟⡟⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣿⣿⠏⠀⢹⡇⠃⠈⠀⠁⠀⠘⠀⠸⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⣿⡏⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠹⣧⠙⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣸⣿⢃⢠⠀⣿⠀⡀⢠⢠⠀⡀⠀⣀⡄⡸⣷⡀⣔⣼⣧⡈⢿⣿⣿⣿⣿⣿⣆⠀⠀⡠⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⡀⢀⠀⠀⣿⣿⣾⣾⣶⣿⣴⣿⣼⣼⣆⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⢿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣼⡄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣦⡈⠻⣿⣿⣿⠻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⠁⠈⠻⣮⣺⣿⣆⠀⠈⠻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠛⠟⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⡀⠀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣴⡾⠇⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄⠀⢽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣶⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢻⣿⣿⣿⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⢨⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠉⠒⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⠂⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠏

⣀⣀⣀⣀⠀⠀⣀⣤⣶⣶⣶⣶⣦⡀
⠀⠉⠙⠻⣿⣾⣿⣿⣗⣼⣿⣯⣭⡝⢷⡄
⠀⠀⢀⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⣦⡀
⠀⣰⣿⣟⣿⣿⣦⣴⣿⣿⣿⣿⣿⣽⠻⣽⣾⣻⣆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣾⣷⢮⡻⣿⣿⣿⠶⣄⡀
⠀⢹⣿⣿⣿⣿⣿⡿⣿⣿⣿⡽⣿⣿⣿⣻⡷⠙⠉⠓⢿⣬⣻⣄
⠀⠈⣿⣿⣿⣿⣿⣿⡹⣟⣿⣿⣿⡿⠃⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⢿⣿⣿⣿⣿⣷⡝⢮⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⡌⢻⣷⡀
⠀⠀⠸⣿⣽⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⣽⣿⣿⣡
⠀⠀⠀⢿⢻⣿⢿⣽⢿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠘⣯⣿⡎⢿⣯⢻⣿⡀⠀⢀⣤⠶⠒⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠘⣿⣿⢸⣿⠘⣿⣿⣄⠀⢀⣤⣴⣾⣷⣿⣿⠉⠛⠛⠋⠉⣿⣷⡀⠀⠀⢁
⠀⠀⠀⠀⠀⠹⢿⣧⣻⣆⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⢀⣔⠂⢸⣿⣿⣿⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣯⠙⣾⣻⣿⣿⠿⠟⠉⠀⠀⠁⠀⢀⣼⣿⠘⣿⣿⣦⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣈⠧⠻⣟⡷⣄⠀⠀⠀⠀⠀⣢⡿⣽⡇⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣻⣻⣟⠴⠗⠋⠃⠛⠃⠀⠀⠀⢀⡿⢃⣿⣷⢸⣿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡿⠋⠀⠀⠀⠀⡄⡀⠀⠀⠀⠈⠁⢾⣿⡿⢯⣿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠶⣃⣄⣴⠄⠀⠈⠿⣿⣸⠟⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠡⠟⠐⠲⠶⣤⠄⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⣿⣷⠀⠀⠈⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢸⡏⠀⠀⠈⠓⠠⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇⠀⠀⢠⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠸⡎⠀⠀⠀⠀⠁⠰⠄
⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⡀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⣀⠀⠀⠀⠀⠀⠀⢹⡗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣶⣾⣷⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡇
⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⣿⡇⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠲⠂⠀⠀⠰⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⡇
⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠻⣿⣿⣿⣿⣿⣟⠇⣟⠀⠀⠀⠀⠀⠀⠀⠈⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣄⠙⢦⠀⣤⣶⣦⡄⠀⢀⠂⢸⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣦⡀⠳⡈⠙⠉⠀⠔⠁⢀⡿⠉⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⠀⠀⣧⠀⢹⡟⠋⣠⠖⠊⠁⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢸⠇⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣼⠀⠀⠀⡇⠀⠀⢸⡆⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢀⢾⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠊⡼⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⡴⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣿⠀⠀⢀⣠⠎⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠒⠒⠒⠒⠒⠂⠒⠆⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡠⠄⠀⢀⠠⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⡔⠒⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡚⠀⣀⣀⢘⢲⡀⠐⠀⠀⠀⢰⠒⢢⠤⠄⠀⠀⠠⠄⠀⠀⠀⠀⢃⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢸⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡔⠃⠊⠙⠂⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠘⢀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠂⠘⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⡆⠀⠀⠀⠀⢀
⠀⠀⠀⠖⠲⠖⠒⠒⠒⠂⠒⠂⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡇⠀⡠⠒⠂⠐⠒⢤⠀⠀⡴⠂⠑⢢⠀⠖⠉⠙⢆⢸⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠇
⠀⠀⠀⡇⡘⠀⠀⠀⠀⠀⠀⢱⡀⢣⡀⢀⡼⠀⢦⣀⣀⠎⢸⠀⠀⠀⠀⠂⠀⠀⢸⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⡃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⣠⠤⢤⠄
⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⣠⠆⠠⢄⠀⡴⠒⠢⡄⢸⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠧⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⡇⠱⡀⠀⠀⠀⠀⠀⣰⠁⣇⠀⠀⣸⠀⣄⠀⢀⡄⢸⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠰⠄⠀⠀⠠⠄⠄⠤⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡇⠀⠈⠢⠤⠀⠤⠞⠁⠀⠈⠉⠈⠁⠀⠈⠉⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⡀⠀⢀⣄
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠳⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠉⠒⢄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠢⢀⣀⣀⣀⣀⡀⠠⠊⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣅⠼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠴⠊⢠⠘⠅⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠤⠀⡀⠤⢀
⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠄⡀⠀⠀⠀⠈⠀⠄⠀⠀⠤⠂⠀⠘⡆⠀⢀⡔⠚⠒⠒⠢⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⠀⠀⠀⢨⣀⠠⠀⠠⠐⠨⠀⠐⡇⠀⡎⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⢀⡠⠀⠀⠀⠀⠑⢤⡐⣀⢶⠡⡈⠎⠀⠀⠡⡀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠔⠉⠑⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠈⠛⠂⠑⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⢐⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡦⠀⠀⠠⠄⠀⢠⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠢⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠊⠀⠁⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⡭⣃⣀⣠⠶⠶⣾⣿⣿⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡭⣀⣀⡰⠶⠶⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⠿⠶⣦⣤⣀⠀⠈⠛⢿⣦⣍⠳⡝⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣿⣯⣤⣄⣀⠀⠀⠉⠻⢶⣌⠻⣮⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⡛⠿⣦⣳⣄⠻⣿⣦⠙⢸⡆⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⠉⠛⣿⡷⣦⡙⣦⡈⢻⣷⡈⠊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣤⡄⠀⠀⠀⢴⣟⣀⣈⠻⣿⣇⢻⣿⡆⢸⡇⠀⠀⠀⠀⠀⠀⢸⣀⣄⣀⠀⠀⢰⣟⣁⣤⣙⢿⣷⡀⣿⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠷⠀⠀⠀⠀⠀⣿⡿⠟⡛⣿⣿⣼⣿⡇⢸⠇⠀⠀⠀⠀⠀⠀⡜⠸⠖⠀⠀⠀⠀⣏⣭⡶⠟⢿⣿⣇⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠘⠋⠠⠟⣹⠟⣿⣿⣿⡇⡟⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢠⣾⡟⠁⠴⢋⡿⢻⣿⣿⡿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⣇⠀⢿⣿⣿⡾⠁⠀⠀⠀⠀⠀⠈⢳⠬⣤⣶⣾⣿⣆⢻⣧⡀⠐⢻⠁⢸⣿⣿⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠦⣤⠽⠟⠁⠀⠀⠀⠀⠀⠀⠀⣹⣶⣶⣮⣽⣿⣿⣾⣿⣿⠁⠘⠧⣤⡽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⠀⣀⣀⣀⡤⠴⠋⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢹⠇⣿⡿⠿⢋⣼⠃⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣼⣏⣀⣀⣤⣤⣤⣴⡶⠟⠁⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⠶⠶⠶⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠶⠶⠶⠦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣵⣂⣤⣤⡒⠻⠿⣿⣿⣿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣵⣠⣤⣴⠚⠻⢿⣿⣿⡿⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠛⠳⠶⣦⣤⡀⠀⡙⠻⣷⣮⠙⣎⢷⡀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠛⠲⠶⣦⣄⡀⠀⠙⢿⣷⣌⠻⡝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⣿⣿⣷⣹⣦⡘⣿⣷⡈⠸⡇⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⣿⣿⣦⣻⣦⠹⣿⣧⠈⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⠤⠤⠀⠀⠰⣿⣿⣿⣿⣿⣷⢸⣿⣇⠀⡟⠀⠀⠀⠀⠀⠀⡧⣤⠤⠄⠀⠀⢾⣿⣿⣿⣿⣿⣧⢹⣿⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠛⠂⠀⠀⠀⠀⣿⡿⢟⣛⣿⣿⣇⣿⣿⢸⡇⠀⠀⠀⠀⠀⡠⠁⠛⠀⠀⠀⠀⢸⣿⡿⢛⡛⣿⣿⣼⣿⡇⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐⠛⣰⣿⣿⣿⣿⡇⡾⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⡾⠃⠔⢛⣼⣿⣿⣿⣿⢇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⠘⠛⢿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢟⠉⠉⠁⠀⠀⠀⠀⣠⠀⠀⠙⠻⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣠⣤⠤⠖⠋⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣠⡤⠴⠚⠃⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⣀⠉⠉⠓⠉⠀⣀⠀⠘⠛⠊⠀⠉⠀⠀⠀⢀⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⡶⢃⡄⠀⠀⠀⠀⠈⠛⢏⠂⠈⠉⠀⠀⠑⠒⠀⠀⠀⠀⠀⣀⣨⣤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠉⠀⠀⠀⡞⠁⠀⢀⡀⠀⠀⠶⠤⣄⢀⣀⣀⣐⣂⣠⣤⣶⣶⢚⡉⠉⠁⠀⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡆⢾⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣩⠖⠋⠉⠉⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠈⢂⡀⠔⠡⢄⠀⠀⠀⠑⢌⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠅⠀⠀⠀⠀⠀⢠
⠀⠈⠀⠀⠨⠀⠀⠀⣀⣤⣤⡤⢶⡷⡉⠢⠀⠀⠀⠀⠀⠂⠄⠀⠣⢄⠀⠈⠉⢑⡀⢈⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⣐⡊
⠀⠀⠰⠂⠰⠀⢠⠎⠁⠻⠋⠀⠀⠈⠀⠀⠑⢄⠈⠓⠰⣤⣀⠀⠀⠀⠀⠈⠓⢿⡃⠌⡁⡶⡤⠤⠓⠶⠶⠖⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠠⠄⠀⠀⠠⠜⠲⠤⠵⠶⠤⠶⠿⣿⢿⣿⣶⣤⣤⡶⣿⡦⣈⠀⠀⠀⠀⠄
⠀⢰⠀⠀⠀⠈⠀⠔⢃⠐⠀⠀⠀⠀⠀⠀⠢⣰⣤⣄⠉⢑⠷⠚⠛⠛⢉⠏⠑⠲⣿⠁⡼⠉
⠀⠈⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡈⢃⣤⠀⣀⠀⢀⠏⠀⠀⠸⠋⡀⠑⠀⠀⣀⡦
⠀⠀⠐⠄⠀⠄⠤⠀⡀⠀⠂⠀⠀⠀⠆⢠⠀⠀⠀⠉⠀⠈⠙⠓⠈⠁⠀⠀⠀⠰⠤⠬⢻⢿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠒⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⢸⡇⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣥⡜⠀⠀⡴⠞⠛⠻⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⣸⡇⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠠⠾⠟⠛⣸⠀⠀⣿⡗⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⢀⣴⡷⠿⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠻⠀⠀⠈⠉⠉⠀⠀⠐⠑⠛⠀⠀⠀⠀⠀⠀⠐⠋⢹⠀⠀⠀⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⣼⡇⠘⢹⣿
⠀⠀⠀⠀⠀⠀⢀⣿⢸⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⡇⡅⢸⣿⠄
⠀⠀⠀⠀⠀⠀⡸⡏⢸⣧⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠈⠀⠀⣿⡇⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠱⠇⢀⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⢰⠀⠀⢠⣿⠃⠀⢸⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⢸⣾⣇⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⠈⠀⠀⢸⡸⠆⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠁⠀⢰⢸⢸⢻⣿⣆⠀⠃⠀⠀⠀⠀⠀⠐⠀⠘⠋⠀⠀⠄⠀⠀⢠⠀⠈⡇⠛⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⢸⢸⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠈⠀⢰⠁⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⢸⣿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⢸⠀⣠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣾⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⣸⠀⡏⢸⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠟⠀⡇⢸
⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⢠⠀⠀⢻⢸⣆
⠀⠀⠀⠀⠀⠀⢁⠀⠀⣸⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣸⠀⢄⡿⢸⠌⡆
⠀⠀⠀⠀⠀⠀⡘⡆⠀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⣰⠀⠀⠀⡇⠀⢸⡇⠎⢦⣙⣶⣦⣤⣤⣀⡀
⣀⣠⣤⣤⣤⣤⣴⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢙⠇⠀⢰⠁⠆⠀⣿⣷⣮⣭⣭⣿⣿⣿⣿⣿⣷⣤⣀⡀
⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⢸⠀⠀⢸⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⠀⠀⠀⠀⠘⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⣴⣿⢠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⢸⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣤⣄⣀⣠⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⢀⣀⣀⣀⣾⣿⣿⣿⣼⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⡿⣿⡿⣿⡟⣿⣽⣿⡟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⣿⣿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⠀⠀⡟⠀⠀⢿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⢠⠎⢀⡞⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠋⠀⠌⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠦⢤⣤⣄⣀⣀⣠⣤⠤⠚⣁⠄⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣀⣀⣀⣠⣤⡤⠖⢋⡀⠀⢀⡿
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢀⣀⡤⠞⠋⠀⠀⣼⠃
⠀⠀⢸⡀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⢤⣄⠀⢰⠆⠘⠁
⠀⠀⠸⣧⠀⠀⠀⠀⠀⢀⣴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡆⠈
⠀⠀⠀⣹⣄⣀⠀⠀⠀⠋⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⡼
⠀⠀⠀⢛⣹⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢸⡇
⠀⣀⠜⠁⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢠⢋⡴⠒⠚⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⢨⡏⡰⢷⣀⣈⣿⣶⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠎⠀⡴⢋⠲⡆⠉⢿⡟⠋⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠈⢸⡁⠈⠃⠜⠃⠈⢿⡄⠀⠀⣀⡤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠈⠃⠈⠲⠦⢤⣄⡈⠛⠟⠛⠉⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠠⣀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⣸⡷⢦⡀⠀⠀⠀⠀⠀⠀⡄⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀
⠀⠀⠀⠀⢰⡿⠀⠀⠈⢳⡀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⠀⠀⠀⢠⠁⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠟⠛⠛⠛⠛⠉⠉⠉⢉⣾⣿⣿⣿⣿⡿⠻⣦
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡟⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⠁⠀⠹⣷⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠃⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⣿⠀⠀⠀⡼⠁⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⣿⠀⠀⢰⠃⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⡟⠀⠀⡞⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⡇⠀⡼⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏