Pastry Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⢦⠀⠀⠀⠀⢀⠠⠉⢦⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢅⣀⡼⠁⠀⠀⠀⠈⠢⠴⠛⠀⠀⠀⠀⠐⣄⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠈⣾⠁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠇⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⡀⠀⢈⢼⡇
⠀⠀⠀⠀⠀⠀⣀⠄⢺⠀⠷⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠃⠀⢣⣾⠟⠶⠶⢄⡀
⠀⠀⠀⣀⡴⠛⠁⠀⠈⠠⣵⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠑⠀⠐⠈⠀⠀⠀⠀⠀⠈⠤⠒⠛⠁⠀⠀⠀⠀⠉⠳⣄
⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠛⠄⠄⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠒⠒⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠙
⠀⠀⢸⠃⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠀⠀⠠⠤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠶⠒⠒⠒⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢸⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠉⡀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡖⠀⠀⠀⠁⢂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠂⠀⢁⠀⠀⢻
⠀⠀⠀⣧⣼⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣠⠚
⠀⠀⠀⢹⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣤
⠀⠀⠀⢘⠣⠀⠀⠂⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣠⣿
⠀⠀⠀⠸⡇⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠐⠀⡀⠀⠀⠀⢀⠠⠤⠀⠤⢀⠀⠀⠀⠀⠀⠀⠢⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣏
⠀⠀⠀⠀⠁⣆⣀⡀⢠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠏⠉
⠀⠀⠀⠀⠀⠈⠃⠰⣄⠘⠻⠢⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠞⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠑⠢⢤⣌⣉⠉⠁⠒⠲⠦⠤⣄⣀⣀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠒⠉⠉⠋⠉⠁⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣄⣉⣀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣄⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣏⣉⣩⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢹⡇⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⠃⣾⠟⣁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⠀⠉⠻⣄⠀⠈⠉⢉⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣵⠀⠀⠴⠀⠀⠙⣦⡀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠤⠀⠘⢡⠄⠉⣁⠀⢸⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⠀⠱⣆⠀⠘⠀⣥⣠⣟⣀⣀⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠛⠛⠛⠉⠉⠉⠓⠶⠶⠛⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⣠⣶⠛⢳⡄⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣠⡴⢦⠀⠀⠀⠀⠀⠀⢠⡞⠁⠘⠷⠞⠁⢺⠀⠈⣧⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⣼⠃⠀⢸⡆⠀⠀⠀⠀⣰⢿⡇⠀⠀⠀⠀⠀⢸⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣠⠟⣿⠀⠀⠀⣿⠶⣤⣤⠞⠃⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠘⣧⣀⣴⡟⢳⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠞⠋⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠉⣧⠈⣇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠉⢿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⡇⠀⠀⠀⠿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢹⠀⠀⢸⡎⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠶⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠤⠶⠶⠖⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀
⠀⠀⢀⠚⠁⠀⠀⡄⠀⢀⠀⠰⠀⠀⠀⠁⠀⠀⠘⠖⠀⠰⠂⠀⢀⡀⠀⠀⠀⡀⠘⠀⠀⠉
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⢀⡄⠀⠀⠠⢠⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠚⠁⠀⠀⠀⠀⠀⢆⠀⠀⢀⠄⠀⠀⠀⠂⠀⠀⢀⣠⣤⡀⠀⢀
⠀⠀⠀⠀⠑⠢⢄⠀⠀⠀⠐⠀⠒⢊⣁⠀⢀⡀⡀⠀⢀⠀⢀⡀⡀⡀⠀⠀⠀⠘⠉⠉⠁⣄⠛⠦⠄
⠀⠀⠀⠸⠦⠄⠀⠁⠀⠀⠀⠀⢠⢸⣯⡇⣼⣇⣧⡞⢸⡤⢸⣀⠗⣇⠄⣤⠄⠀⠀⠀⠄⡈⠀⠀⠓
⠀⠀⠀⠀⠀⠒⠂⠉⠀⠀⠀⠀⠘⠘⡇⡷⠇⡇⠏⢣⢸⠀⢸⠙⡄⢸⠀⠿⠄⠀⠀⠀⠓⠊⠃⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠤⣀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠁⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠈⠃⠀⠈
⠀⠀⠀⢀⣀⡈⠀⠀⠀⠄⠀⠀⠀⠈⢠⠂⠀⠀⠀⠄⠐⠀⠀⡀⠉⠐⠂⠤⠄⠀⠠⠄
⠀⠀⠐⠋⠐⠛⠉⠿⢶⠖⢒⡤⠤⣀⠀⠀⠴⠉⠃⠁⠠⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⠂⠀⠠⠀⠈⠀⠀⠀⠤⠀⠤⠤⠄⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⢲⡀⠠⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⢹⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢢⠠⠀⠀⠀⠀⠀⢈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⠒⢠⠄⠀⠀⠈⠉⠀⠀⣀⠀⠀⠀⠀⠈⢀⡵⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠤⠀⢀⠐⣤⠛⠄⠀⠀⠀⠀⣄⠀⠨⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⣤⢤⠀⢀⠀⠀⠐⠌⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡂⠚⠋⡤⠉⡉⠭⡆⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠐⠶⠂⠐⡊⠈⡤⠙⠶⠾⠛⠇⣙⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⢀⢀⣀⡈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠉⠀⠀⠀⠤⠈⠀⠀⠙⣱⢰⢀⠀⠺⢧⠀⠀⠀⠀⠀⢀⡶⠋⠀⠑⠆⠌⠳⣤⣤⠗⠋⡉⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣠⡁⠈⣆⠀⠀⠀⢠⢾⠀⠀⠀⠤⠀⠈⢤⡄⠂⣀⠀⠙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢛⡀⠀⠑⠒⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠵⠃⢀⠀⠀⠀⠀⠦⠀⠀⠠⠿⠀⢬⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠢⠥⠠⡄⠀⠀⣉⠁⠖⠈⠉⠙⠛⠶⠂⠄⡠⢀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠒⠒⠠⠄⢀⣈⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⠀⠊⠁⠉⠓⠲⠀⠀⣀⠀⠀⠂⠈⠤⡀⠐⠀⠁⠑⠂⠶⢦⣀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⢡⡈⠰⠤⣄⢠⣄⠀⠀⠀⠀⠈⠓⠒⠀⠀⠐⠋⠀⠈⣀⠉⠀⠄⠉⠀⠀⠠⠈⢃⠰⠢⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠁⠁⠀⢀⠈⠀⠘⢯⡄⠀⡉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⢤⣀⣀⢤⡄⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢁⣈⣀⡀⠈⠗⠄⠀⠠⠘⠔⠂⠈⣘⠳⠈⠉⢽⡲⠖⠠⢀⣀⣀⠀⠀⠀⠈⠉⠉⠛⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠢⠤⠄⠀⠉⠦⠀⠓⠈⠄⠀⠀⠀⠁⠈⠐⠲⠀⠀⢍⠛⠛⠛⣦⣀⡀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠠⠄⢀⡀⠀⠐⠂⠈⢂⠀⠦⠀⠈⠀⡀⠀⠠⠘⠍⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠠⢤⣁⣀⡀⠀⠀⠘⠀⠤⣐⠒⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠲⠤⣬⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂
⠀⠀⠀⢀⠀⠀⢀⠂⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⡳⣄
⠀⠀⠀⡡⠀⡉⠳⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠈⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣥⣭⡆
⠀⠀⠀⣥⠀⠀⠂⡍⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⣢⠒⠉⢀⣑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡘⠉⠈⠁⢠
⠀⠀⡏⠈⠓⠒⠛⠟⠓⠂⠒⠋⠈⢻⠀⠀⠀⠀⠀⣨⣶⡇⢧⡼⠈⢼⡌⣿⠀⠀⠀⠀⠀⠀⠀⢻⠃⠴⠒⠀⠈⠀⢸⡉
⠀⠀⣥⣄⡀⣠⢀⡀⡀⣠⣀⢠⡴⠊⠀⠀⠀⠀⠐⣉⠉⠈⠁⠀⠀⣀⣁⢉⡁⠀⠀⠀⠀⠀⢈⡴⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠁⠀⠈⠉⠉⠈⠁⠈⠀⠀⠀⢀⠀⠀⠀⠀⠴⠛⠤⠄⠀⠀⠀⠩⠽⡿⠷⠀⠀⠀⠀⠄⠋⠉⠀⠀⠀⠀⠀⠀⠙⠂⠉
⠀⠀⠁⠶⠐⠦⠀⠀⠀⠀⠖⠀⢴⠊⠀⠀⠀⠠⣄⡀⣀⠀⠀⢀⠀⠀⡈⢁⣠⠄⠀⠀⠀⢠⣀⣀⡠⠄⣀⠀⠀⠀⠀⣤⠄⠞
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢩⠉⠉⠉⠉⠈⠉⠈⠈⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠣⣤⢀⠀⠀⠀⢀⡴⠇⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡃⠀⠀⢸
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠛⢣⡀
⠀⠀⠀⠀⣨⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⡆⠀⠀⠀⣴⣧⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⣀⣿⡀
⠀⠀⠀⠀⣡⣀⠄⠉⠈⠑⢂⠀⠀⠀⠀⠀⠀⠀⠚⢧⣸⣅⠀⠳⠾⢯⣏⡀⠈⠂⠀⠀⠀⠀⠀⠈⠁⠁⠐⡛⠋⠉⠀⠈⠆
⠀⠀⠀⠔⠪⠄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⠦⢤⣀⣠⣄⣤⡠⠴⢧⡀
⠀⠀⠴⢀⠉⠄⠤⠀⠀⠀⠀⠀⠈⣡⠀⠀⠀⡠⠀⠀⡇⡄⠀⠐⠀⠁⠰⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠘⠄⠀⠴
⠀⠀⢀⡀⠀⣠⠒⠀⠀⢀⠀⢀⠀⣉⠀⠀⠀⠰⠾⠶⢤⡄⢀⣀⣀⡀⣠⣤⣤⡶⠀⠀⠀⢠⣀⠀⣆⠀⠀⠀⠂⠀⠀⠸
⠀⠀⠹⠉⠁⠀⠉⠀⠈⠀⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠃⠀⠀⠀⠈⠉⠈⠉⠁⠀⠊⠑⠀⠀⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠥⢴⡆⠠⠤⠤⢀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⣀⢀⡀⣀⣀⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⢠⠈⠀⠠⠀⠀⠀⢀⠀⠀⠀⠠⠀⡤⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠉⠈⠀⢈⠀⠀⠀⠀⣽⣉⡛⠓⠛⠓⠒⠚⠛⠛⢀⢛⣫
⠀⠀⣖⠒⠂⠄⣀⣠⢀⠤⠤⠄⠐⢉⠅⠀⠀⠀⠰⣤⣤⠄⠀⠀⠀⠐⠲⡖⠣⠀⠀⠀⠀⣭⣭⡉⠛⣛⣛⣛⡛⢚⣛⣩⣭⡏
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠍⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠉⠉⠉⠀⡀⢠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢆⠀⠀⠓⠒⠀⠰⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠠⢄⡀⠀⡁⠒⠀⠖⣐⠀⢀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⠐⠠⡅⠀⡁⠓⠀⠲⢬⠀⢀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠘⢂⢴⢄⣠⠐⡏⢹⡦⡖⠠⣆⣠⢈⣅⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠒⢳⣶⠿⠻⡀⢻⠛⢄⣸⠛⣋⠚⠛⠓⠰⡟⠻⠠⡿⠿⣯⠻⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢦⣿⠊⠉⢀⠈⡋⠀⢦⣼⠀⠈⠁⠀⢈⠲⡃⠀⡂⢲⡶⢾⣅⣺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⢴⣶⡑⣔⣤⣿⡁⣀⢤⣠⣤⣄⢬⣶⣽⠶⠿⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡶⠀⣠⡄⠀⠀⠀⠈⠉⠉⠁⠉⠋⠉⠁⠀⠀⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠇⠆⢰⠂⠀⢀⡶⡀⠀⣴⢦⠀⢰⠄⠀⠀⣿⡷⠀⣤⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠐⠂⠘⠀⠀⠀⡧⠘⢀⡟⡀⢠⠀⡏⠂⠠⠟⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀⠀⠀⠀⠜⠀⠀⠀⡃⠀⠀⠀⠘⠛⠀⡇⠀⠀⢀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⢀⠀⠐⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠛⡛⢀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠒⠀⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⢟⡹⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣅⡀⠀⠀⠀⠹⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠫⣶⣿⣿⣶⡎⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣮⣀⠀⠀⠀⠀⠀⠀⠤⢧⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠶⣶⣶⣶⣿⣿⡿⢗⠸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠠⣎⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡱⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠾⢷⣶⡿⢿⣿⣿⣿⣿⣷⠜⣿⣿⣿⣿
⠀⠀⠀⠀⢠⠠⠈⠉⠉⠉⠡⠈⠉⠐⠒⡚⠉⠀⢈⠀⠀⠀⠀⠀⣿⣿⣿⠱⣻⣶⣶⣶⣞⣳⣶⣤⣭⢤⣶⣿⠎⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢻⡿⣾⠛⣷⠒⣶⡖⢳⡟⢹⡟⣹⡏⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⡄⢰⡀⢰⡍⢩⡄⢀⡆⢰⠀⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠸⣇⢻⡀⣿⠀⢿⠀⢸⡇⣸⠃⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄⢡⠘⡇⢸⡇⢸⡇⢸⠃⡼⢀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣿⠸⡇⢻⠀⢸⠀⢸⠁⡿⢰⡏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢸⡄⣇⢸⡇⢸⡇⣼⢠⡇⣸⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠘⠆⡇⢸⣀⣸⣀⣸⢠⡇⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣥⣛⣘⣃⣘⣃⣋⣬⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⠒⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠺⡑⠁⠀⢠⠗⢲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣿⠆⠙⢒⠒⡋⠀⡈⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⢳⠖⢒⣡⠞⣡⡞⣀⡴⠃⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠁⣀⣀⣀⡤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⠀⣀⣀⣠⣤⣤⠴⠶⠒⠛⣋⣩⠟⠚⠓⢳⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠭⠔⢒⣒⡉⠉⠉⣡⠤⠴⠚⠉⠱⣤⣠⠞⠀⠁⠀⢀⣀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠑⠶⠖⠋⠁⠉⠒⠊⠀⠀⣀⣀⣠⡤⠤⠖⠒⠒⢉⣉⣉⣁⣽⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣀⣀⣤⠤⠴⢒⣚⣋⣉⣥⠤⣄⣠⠴⠚⠉⠉⠁⠀⠀⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⡥⠒⠶⠖⠊⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠴⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠴⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⠤⠶⠒⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢳⣠⠤⣄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢤⡴⠒⣒⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠚⠀⣨⡽⠃⠈⠱⣄⡠⠴⠒⠋⠁⠀⠀⢠⠏⡴⠊⡡⠔⠒⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊⠁⠀⣤⣼⠀⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢠⠞⠀⠀⢉⣠⠖⠋⢉⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣠⣄⣸⠄⠀⢀⠀⠈⠀⠘⡆⠀⠀⠀⠀⠙⠛⠛⢻⠟⠁⠔⠊⢉⣀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠙⢛⠁⠀⠉⠠⠀⠈⠀⠀⠀⠂⢻⠀⠀⠀⠀⠀⢀⣴⣋⡀⠀⠐⠊⠉⠀⢀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢳⡶⠖⠋⠉⣀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢾⣤⣤⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣔⡚⠉⠀⢀⠊⠭⠥⢌⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣬⣉⣓⠒⠲⠤⠤⠤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⣤⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠙⠛⠛⠶⠶⠶⠦⣤⣤⣬⣭⣭⣭⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣓⣒⣑⣀⣉⣉⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠒⠒⠒⠦⠤⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠉⢉⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠒⠂⠠⠀⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⠉⠉⠉⠉⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠲⠶⠶⠦⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣦⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⢿⣿⣿⣿⡟⠀⠀⠀⠈⠉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠒⠛⠉⠉⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣀⠀⠀⠀⣠⡀⠀⠀⣠⡀⠀⠀⢀⡀⠀⠀⢀⣄⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣸⠏⠛⠛⠛⠉⠛⠛⠛⠁⠙⠛⠛⠁⠙⠛⠛⠉⠙⠛⠛⠋⠈⠛⠛⠋⢹⣄⣀
⠀⠀⠀⣠⠴⠋⠉⠀⣦⣀⣀⣀⣤⣀⣀⣀⣴⣄⣀⣀⣴⣄⣀⣀⣠⣄⣀⣀⣠⣦⣀⣀⣠⡆⠀⠉⠛⠦⣄
⠀⠀⢸⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⡆
⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠈⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⢤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠶⠶⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠋⠹⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⡳⣞⡵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠖⢿⣤⣉⣉⣤⣿⠲⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠉⣀⣤⣀⠀⠀⣸⢧⡈⠓⠤⣏⠀⠀⣀⣤⣀⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠐⡇⠀⠈⠉⠉⠹⣆⠉⠲⢤⡏⠉⠉⠁⠀⢸⡂⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡖⠒⠋⠀⠀⠀⠀⠀⠀⢯⣑⣂⡼⠀⠀⠀⠀⠀⠀⠙⠒⢲⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠉⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠙⢦⣄⠀⠀⠈⠧⠤⠴⠒⠒⢦⠀⠀⠀⠀⡴⠒⠒⠦⠤⠼⠁⠀⠀⣠⡴⠋⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣇⠀⠀⠈⠙⠲⠦⣤⣀⣀⠀⠀⠈⠑⠶⠖⠋⠁⠀⠀⣀⣀⣤⠴⠖⠋⠁⠀⠀⣸⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⡟⠓⠚⠙⣆⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣰⠛⠓⠚⢻⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢿⡀⠀⠀⠘⣆⢀⡴⠛⢦⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⡴⠛⢦⡀⣰⠃⠀⠀⢀⡿⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠉⠁⠀⠘⢧⣀⣠⡞⠁⠀⢳⣄⣀⡼⠃⠀⠈⠉⠁⠀⠀⣠⡾⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣆⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⣰⠟⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠤⠤⢤⣤⠤⠤⠶⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣼⢦⣀⣀⣤⣄⠀⠀⠀⠉⠉⠛⠒⠶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡤⠴⠶⠒⠛⠉⠉⠀⠀⠀⣠⣤⣀⣀⡴⣇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⠉⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠘⣧⠀⠀⣰⠞⠛⣦⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⣴⠛⠳⣆⠀⠀⡼⠃⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠈⠓⠞⠃⠀⠀⠸⣆⠀⠀⠀⢠⡟⠀⠀⢻⡄⠀⠀⠀⣸⠇⠀⠀⠘⠳⠚⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠋⠀⠀⠀⠀⠙⠶⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠴⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⡄⠀⠀⢀⣾⠻⣧⡀⠀⠀⣠⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢈⣿⠀⠀⢸⣇⣀⣽⠇⠀⠠⣿⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⢀⣉⣛⣉⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣧⠀⠀⢸⣿⠉⣿⠀⠀⠀⣿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣯⣀⣠⣼⣿⠀⣿⣤⣄⣀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⢿⣇⣸⣿⠉⠉⠹⣿⣤⣿⠉⠉⠉⣿⣄⣸⡟⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣌⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣡⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⣯⠉⠛⠛⢻⣿⠛⠻⠿⠟⢻⣿⡟⠛⠛⢉⣿⣧⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠙⠷⣦⣴⠟⠻⣷⣤⣀⣤⡾⠛⠷⣦⣴⠾⠃⠈⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⢻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⡈⠉⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠛⠉⣁⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡟⠛⠿⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠟⠛⢻⣯⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠾⠛⣷⡀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⣸⣿⣄⠀⠀⠀⢠⣾⠻⢷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠻⠷⠶⠾⠋⠈⠻⣶⣤⣤⣤⡾⠟⠈⠛⠷⠶⠾⠛⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⡀⠀⡀⠀⠀⣀⡀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⢸⣧⣼⠀⣼⣷⠀⣿⢹⡆⣿⢹⡎⢷⣴⠏⠀⠀⣿⣽⡇⣿⢸⡏⣷⠉⣿⠋⢸⣧⣼⡇⡟⢻⡆⣸⣷⡙⣧⡾⠁
⠀⠀⠸⠇⠹⠰⠟⠛⠇⠿⠋⠁⠿⠋⠁⠀⠿⠀⠀⠀⠿⠾⠇⠿⠸⠟⠿⠀⠿⠀⠸⠇⠹⠃⠷⠾⠳⠟⠛⠧⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⠤⠤⠤⡀⢠⠔⠒⠒⢤⡀⡠⠤⠠⢤⡀⠀⣀⣀⣀
⠀⠀⠀⠀⣀⡤⢄⡀⣰⣋⣀⡤⠽⠖⠓⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠓⠾⠥⢄⣈⣱⡄⣀⠤⢄⡀
⠀⠀⠀⡞⠁⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⠀⠘⡆
⠀⠀⠀⣧⠒⠋⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠓⢦⡇
⠀⠀⠀⡇⠀⠀⠀⠀⣷⠊⠉⠉⠑⣄⣠⠔⠒⠦⡀⠀⣠⠤⢤⡀⢀⡤⠖⠒⢤⣀⡔⠉⠉⠉⢲⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠑⢄⣀⣀⠴⣇⠀⠀⠀⠀⣸⠁⠀⠀⠀⢸⡏⠀⠀⠀⠈⡟⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⡷⢄⣀⣀⠔⠁
⠀⠀⠀⠀⠐⡅⠀⠀⠈⠢⠤⠤⠖⠙⢆⡀⠀⣀⡼⢧⠀⠀⠀⣠⠿⣄⠀⠀⣠⠞⠑⠤⠤⠴⠊⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⠳⡄⠀⠀⠀⠉⠉⠁⠀⠀⠉⢒⠊⠁⠀⠀⠉⠉⠀⠀⠀⢀⡴⠳⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡗⠒⠊⠁⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠳⣄⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠙⠒⠒⡇
⠀⠀⠀⠀⠀⡟⠢⢄⣀⠀⠀⠀⠀⠉⠲⠤⠤⠤⠖⠉⠀⠀⠀⠈⠑⠦⠤⠤⠴⠊⠀⠀⠀⠀⢀⣀⠤⠚⡇
⠀⠀⠀⠀⣠⡏⠒⠤⣈⡉⠓⠒⠦⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠖⠒⠋⣉⡠⠔⠊⣧⡀
⠀⠀⠀⢰⠁⡇⠀⠀⠀⠉⠉⠒⠒⠦⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠤⠖⠒⠊⠉⠁⠀⠀⠀⡇⢹
⠀⠀⠀⠈⠢⣈⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⢊⡡⠊
⠀⠀⠀⠀⠀⠈⠓⠦⣤⣈⣉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠚⢉⣉⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠷⣖⣒⣶⠤⠤⠤⠤⠤⠤⠤⠤⠤⣴⣖⣒⡶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡭⠭⢿⠉⠉⠉⢹⠯⠭⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠶⠶⠶⠿⠿⠟⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣧⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣅⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⡾⠛⠉⠭⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠶⠶⠶⠶⠶⠶⠷⠶⢤⣤⣤⣀
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣀⣀⡀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣧⡀
⠀⠀⠀⠀⠘⣧⠀⠀⠀⣠⡞⠉⠉⠻⣦⡀⢀⣴⠞⠛⠛⢶⡀⠀⠀⠐⠀⣠⡶⠛⠋⠙⠳⣦⡀⠀⠀⠠⠀⣠⣤⢤⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⢷⠶⠟⠉⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠙⠶⣤⠴⠞⠉⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠛⠉⠀⠀⠈⠻⢦⣤⡾⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣸⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⠶⠛⠛⠛⠉⠉⠉⠉⠉⡉⡉⠛⠛⠛⠓⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣀
⠀⢸⡇⠠⠄⠀⠀⠀⠀⣀⣀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⢷⡀
⠀⠘⢷⣀⠀⢀⣀⣴⠟⠉⠉⠉⠻⢦⣄⣀⣤⡴⠖⠛⠲⢶⣄⡀⠀⠀⣀⣠⣤⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠖⢀⣀⣀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⢹⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠙⠷⣤⣤⣤⣤⠶⠞⠋⠉⠀⠈⠙⠳⠶⣶⠞⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣴⠞⠉⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⢦
⣼⣿⠀⠀⠀⠙⠷⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁⠀⢸
⣿⠙⠷⣤⣀⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠳⠶⠶⠶⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠞⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⣠⣾
⠘⠷⣤⣀⠈⠙⠛⠶⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠶⢛⣩⠞
⠀⠀⠀⠙⠳⠶⣤⣄⣀⡀⠀⠈⠉⠉⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⢤⣤⠤⠦⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠋⢉⣉⣡⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠚⠛⠛⠛⠉⠉⠁

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄⢸⢚⡲⠄⡄⣄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠙⡟⠂⢠⣀⢂⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣤⣀⣀⣀⣀⣈⣀⣀⣭⡶
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠉⠉⢉⡉⠉⠉⠉⠁⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠁⠠⠤⠀⠀⠀⠤⠄⠐⣀⠀⠀⠂⠐⠀⠀⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⢀⢀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠈⠁⠀⣀⠀⠀⠄⠀⠐⢄⢖⡠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣧⣴⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⣁⣀⣀⣤⣤⠶⠞⠛⡃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣤⣤⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⡀⠄⢂⠀⠡⠂⠄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠍⠀⠀⠈⢵⡄⠈⠐⠢⢦⣶⣄⣀⣀⢀⡀⠀⠀⣀⢀⣀⠀⣤⠴⣖⡞⢀⠀⠀⠀⠀⠘⣡⠀⠀⠑
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠂⠀⠱⠀⣀⣋⠀⢠⢙⠃⢠⠀⢼⠉⠷⢶⠀⡀⠠⢐⠃⠀⠊⠙⠂⢠⠀⠐⠤⠌⠀⢀⠀⣀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡷⠧⠉⠒⠄⠁⣄⡀⠂⠈⠀⠠⠀⠀⠂⠀⠙⠀⠁⠀⠈⠀⠀⠀⠁⠀⡀⠀⠀⠂⡙⠃⠢⠐⢉⡂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣇⡀⠀⠀⢀⠐⠒⠄⠈⠁⢀⠐⡀⢠⠀⠀⠀⠐⠀⠐⠀⠀⠀⢤⠦⠀⡄⠀⠀⠀⢐⣤⣶⣶⣿⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⠛⠻⣶⣦⣤⣤⣄⡂⠀⠀⠀⠀⡉⠀⠑⠂⠀⠀⠀⢈⠀⠀⠀⣀⣠⣤⣦⣴⣶⣿⡿⠛⠋⠁⡐
⡇⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠑⠀⢬⡀⠀⠍⠉⠛⠻⠿⢿⠿⠿⢶⣶⣶⣶⣶⣶⣿⣿⡿⠿⡿⠟⠛⠛⠉⠉⢁⠀⢈⠀⠄⠊⠀⠐⢄
⡇⠀⠀⠀⠀⠀⠀⠈⢻⡀⣀⠀⠀⠀⠀⠉⠒⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⣈⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠤⠾
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⣤⡤⣆⠀⢀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠒⠃⠀⠀⠒⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⢠⡖⠟
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢧⡤⢤⣀⣠⡀⠀⣀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⢀⣀⢀⡦⣄⡞⠲⠾⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠒⠈⠉⠉⢛⠋⠉⠷⢞⢹⡶⠎⠳⢶⠉⢲⠋⡙⠛⢋⠛⠁⠉⠠⠤⠤⠤⠤⠀⣀
⡇⠀⣀⠠⠀⠀⠒⠈⠉⠉⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⣀⠄⠂⠘⢀⠀⢀⡘⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⢠⢀
⡇⠁⠀⠀⡤⠀⠀⠀⠀⠤⠀⠀⠀⠤⡦⠀⠀⠀⠀⢠⠄⠰⡀⠀⠀⠩⠄⡆⠠⠣⠈⡃⠀⠐⠀⡠⠀⠀⣀⠐⡄⠀⠶⣀⠀⣀⢀⠀⢀⡀⢀⠀⠀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡂⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠂⠀⠤⠬⢀⠤⠄⠀⠀⠐⠁⠀⠀⢀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠐⣨⠂⠀⠘⣈⠂⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠶⠀⠘⠠⠒⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠑
⠏⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠙⢄⣠⠴⠚⢉⡀⠙⠒⢦⣀⡠⠞⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⣄⡞⢁⣤⣶⣄⠀⠙⣦⣾⣿⣿⣷⣆⡜⠁⣠⣤⡀⠈⠳⣀⣠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢁⡰⠃⠈⣵⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣦⠞⠉⢀⡴⠈⠳⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢋⡱⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠉⢀⠔⠋⢠⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠒⢋⡔⣈⢦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠏⡀⢠⠎⢸⠄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⠤⠖⡉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠙⠲⢤⣁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠈⡞⠁⠤⠚⢡⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠁⠀⡇⢲⠀⠈⣷⠛⡇
⠀⠀⠀⠀⠀⠀⠀⡿⡀⣇⠀⣀⡤⠊⠀⢀⠜⠋⡰⠉⠻⢿⡿⠿⣿⡿⠛⢿⣿⢿⡿⣿⠟⠋⠰⢈⠙⢧⠀⠊⢀⡜⠀⠀⡼⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠘⢾⡦⣄⣀⢀⣰⠃⢀⡴⠃⡟⠀⠀⢻⠞⠁⢠⠏⠀⠙⢦⡾⠁⢀⡰⠃⢸⠀⠀⣇⣀⠀⣀⡠⠞⣡⠋⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⢬⣁⠹⣄⠀⢀⠔⠁⠀⢀⣾⠐⠚⠁⠠⠃⠀⠀⣧⡀⠈⠀⠰⠃⠀⣠⠏⠉⠉⢁⡠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠠⣄⡀⠀⠀⠈⠑⠺⠷⣶⣶⠖⠒⠋⠘⠦⣀⣀⣀⣀⡤⠞⠀⠉⠒⠲⠶⠖⠚⢁⣠⠤⠒⠉⠀⢀⡠⠄⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣄⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠶⠶⠶⠶⠶⠖⠒⠒⠚⠋⠉⠁⢀⡴⠒⠒⢀⣞⢀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠈⠙⠒⠒⠒⣞⠉⠉⠓⠦⡀⢀⣀⣠⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠖⠒⠂⠀⣮⣀⣀⡠⠞⠀⠉⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠈⠙⠲⠤⠤⠖⠻⣄⡀⠀⠉⢓⣠⠖⠉⠉⠉⠃⣀⠜⠡⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠓⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠉⢹⠁⠀⠀⠀⡏⠉⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠣⣄⣠⠜⠁⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡠⢄⠀⠀⡠⠤⠀⢀⡀⢀⡀⠀⠀⢀⠀⣠⠲⡄⡠⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣠⠇⢸⠀⢰⠃⠀⠒⠋⡇⡏⠘⠀⠀⡏⠉⠁⠀⠧⠇⢸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠸⢤⠼⠀⠀⠀⢠⠃⢹⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠘⣤⠎⠀⠳⠴⠃⠀⠀⠀⠀⠀⠀⡏⠉⠓⠦⣀
⠀⠀⠀⠀⠀⢀⣞⠁⢰⠉⡳⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⢞⠉⡦⠈⡳⡀
⠀⠀⠀⠀⠀⠸⡌⠂⠀⠀⠀⠀⠀⠀⠀⠉⠩⡙⠓⠒⠒⠒⠒⠒⠒⠒⢋⠍⠉⠀⠀⠀⠀⠀⠈⡠⠚⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⡀⢢⠀⠀⠀⡀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢠⠇⡜⠁⢸⠀⠀⠀⠈⠋⠀⢱⠀⠀⠀⠀⢰⠙⢦⡀⠀⠀⢀⠀⠀⠀⣼⠵⠤⣄⠀⣴⡸⡀
⠀⠀⠀⠀⠀⠈⢲⠃⠀⠸⡄⢀⠆⠀⠀⠀⣼⠀⠀⢀⡀⢸⠀⠀⡇⠀⠰⠛⣆⠀⢀⡇⠀⠀⠘⠚⢹⠃⢣
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠑⠊⠀⠀⠀⠀⢹⠀⠀⣼⠐⠁⠀⠀⢧⣠⠇⠀⣿⠀⠈⡇⠀⠀⠀⠀⠸⣆⡼
⠀⠀⠀⡠⠤⡴⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠁⠀⠀⠀⠀⢈⡗⢦⠤⣄
⢀⣠⠞⠧⠴⠃⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠘⠦⠼⠳⣄
⡏⢯⠀⠀⠀⠀⠀⠀⣙⣒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣒⣋⠀⠀⠀⠀⠀⠀⡽
⠘⢆⡓⢤⣀⠀⠀⠐⢅⡨⠂⠀⠈⠉⠉⠓⠒⢒⣶⠶⠶⠶⠶⠶⠶⣶⡒⠒⠚⠋⠉⠁⠀⠐⢅⡨⠂⠀⠀⣀⡤⢚⡱
⠀⠀⠙⠲⢬⣙⠓⠶⠤⣤⣀⣀⡀⠀⠀⠀⠀⢧⣠⠇⠀⠀⠀⠀⠸⣤⡼⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠒⣋⡥⠖⠋
⠀⠀⠀⠀⠀⠈⠉⠒⠶⠤⢤⣉⣉⡉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⢉⣉⣉⡤⠤⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⢀⣀⢛⡦⢄⠀⣀⣀⣀⡳⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⠚⠛⢇⣀⣭⠙⠤⡶⠆⠸⢉⣵⡐⠲⠗⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢣⠖⣂⠄⠀⢁⡀⠀⡀⢀⠀⡀⣤⠄⡤⠤⣢⡎⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠤⢬⡕⣴⣆⡿⠁⢈⢰⠴⡇⣉⣣⣇⣰⠀⡷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠶⡒⣄⡀⣫⠈⢉⢁⢸⣆⣀⣏⣉⣉⣀⣤⣭⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣁⠒⠤⠤⣌⣉⣈⣂⠉⡙⠉⠉⠈⠉⣉⣉⣠⣥⠴⠞⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣄⣉⡸⣂⠤⣠⡄⢤⣈⡩⣉⣉⣉⢉⣉⣠⢁⠄⢰⡆⠚⢠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⡌⢒⠛⠛⠲⠨⢤⣼⣤⣙⣁⣼⣀⣹⣌⣧⣭⣭⣲⠟⢟⢛⣹
⠀⠀⠀⠀⠀⠀⣀⣠⣸⠧⣄⠉⠃⠙⠓⠖⠶⢲⡤⡬⣀⣩⣭⣥⣤⣤⣽⡴⠶⠶⢛⢋⣩⣀
⠀⠠⡀⠒⠐⢅⠀⠀⠙⠲⢄⣁⠘⠙⠼⠶⠤⢤⣤⣨⣄⣄⡤⣤⣤⣤⣔⣦⢴⠶⠟⣋⣹⠏⠉⢓⠅⣀⠂⠄
⠀⠀⠀⠁⠐⠀⠠⠄⠀⠀⠀⠀⠉⠀⠂⠠⠄⠤⠤⠤⠤⠤⠀⠠⠤⠤⠤⠶⠒⠒⠉⠁⠀⠀⠀⠁⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⡀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢱⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢠⡞⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⠇⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⣫⣍⡀⠀⠀⠀⠀⠀⠀⣴⠞⣛⣥⡀⠀⠀⠀⠀⠀⠀⣀⣩⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⠑⠚⢿⠀⠀⠀⠀⠀⠀⣯⠉⠉⠙⡏⠀⠀⠀⠀⠀⠀⣻⠳⠾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠒⠶⢾⠀⠀⠀⠀⠀⠀⡏⠉⠓⠲⡇⠀⠀⠀⠀⠀⠀⣿⠲⠦⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣄⣀⣸⠀⠀⠀⠀⠀⠀⡿⠢⣄⣀⣯⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⢻⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⡿⠀⠀⠀⠀⠀⠀⣿⠀⠉⠒⢿
⠀⠀⠀⠀⠀⢀⡴⠢⣤⣀⠀⠀⠀⣀⣀⣀⣿⣦⣄⣀⣸⣄⣤⣤⣤⣄⠀⡿⢢⣤⣤⠷⠤⣤⣀⠀⠀⣀⣿⣄⡀⠀⣸⠀⣀⣀⣤⣀⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠉⢳⣴⠛⠉⠉⠉⠉⠑⣦⡝⠋⠁⠀⠀⠀⠈⢻⣧⡞⠉⠀⠀⠀⠀⠉⢧⡞⠉⠀⠈⠙⢿⣿⡞⠉⠁⠀⠈⠙⣦⠞⠉⠉⠉⣷
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⣷⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠷⣄⣀⣀⣀⣾⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠀⠉⠛⠲⠤⠴⠚⠋⠉⠓⠤⠤⢄⣤⠤⠞⠋⠙⢦⣀⣀⣀⣀⡤⠞⠻⢤⣀⣀⣠⠞⠉⠓⠦⠤⠴⠋⠀⠈⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⣄⡀⠀⡇⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡼⠋⠀⠀⠉⠛⢧⣤⠞⠁⠀⠀⠀⠀⠈⠻⣄⣠⠶⠛⠋⠉⠉⠉⠛⢶⡄⢀⡴⠚⠋⠁⠀⠈⠉⠻⣆⣠⠶⠊⠙⠋⠑⠶⣄⣠⠶⠚⠛⠛⠛⠛⢶⣜⡶⠞⠋⠙⠶
⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠟
⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣼
⠀⠀⣟⠉⠉⠓⠚⠋⠙⠶⢤⣤⣤⣤⣤⡤⠖⠲⢦⣤⡀⠀⠀⠀⣀⣤⡴⠖⢶⣀⠀⠀⠀⠀⠀⣀⡤⠾⣄⡀⠀⠀⠀⣠⠞⠳⣤⣄⣀⣠⣴⠏⠀⠙⠒⠒⠚⠉⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠑⠒⠶⠖⠊⠉⠀⠀⠈⠉⠓⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡞⠛⠛⠳⢦⡀⠀⢀⣀⠤⠤⠦⠤⣤⡀⠀⢀⣀⠴⠶⠶⠖⠶⠦⣄⠀⠀⣀⡴⠆⠛⠛⠓⠶⢦⡀⠀⣠⡤⠤⠤⢄⡀⠀⠀⢀⡤⠶⠶⠶⠦⣄⠀⢀⡤⠦⠤⣮
⣯⠀⠀⠀⠀⠀⠙⣶⠋⠁⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠀⠀⠀⠀⠈⢣⡼⠋⠀⠀⠀⠀⠀⠀⠀⢹⡾⠁⠀⠀⠀⠀⠙⣦⡼⠋⠀⠀⠀⠀⠀⠘⣷⠋⠀⠀⠀⠈
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠
⠀⠈⠛⠲⠶⠤⠤⠶⢦⣄⡀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⢀⡜⠛⠶⣤⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠉⠛⠓⠶⠶⠶⠞⠛⠁⠀⠈⠳⠆⣀⣠⣠⡴⠞⠋⠈⠛⠶⠦⠤⠶⠛⠁⠀⠙⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣤⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⣶⡜⠫⣽⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣆⢀⣥⣿⣠⣤⣤⣾⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⡿⠓⣤⡤⠜⠋⠁⣯⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠲⠀⠀⠀⠀⠈⠀⢠⣤⣿⣿⣿⣿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⣄⡀⠀⠀⠀⢀⣠⣤⡾⠟⠛⠉⠉⠁⣤⡀⢠⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠀⠈⣩⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠤⠄⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⢶⡒⡟⢿⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠄⣀⠀⣀⠀⠀⠀⠈⡉⠉⢩⡹⣦⣄⠂⡑⣰⣩⣿⡜⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡯⠑⠻⢭⠞⡓⣶⢲⢠⠞⢻⣿⠉⠻⣿⣧⠉⠛⣿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⢀⠀⠀⠉⠁⣸⠁⠀⠀⢉⡇⠀⢸⣿⠀⣼⣇⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡀⠀⡆⠀⣿⣸⣵⠀⢸⣷⠀⣼⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣸⡇⢠⣏⡀⣿⣿⣿⠀⣿⣿⠁⣿⡿⢸⡟⣿⣿⢀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⣿⢼⣿⡇⣿⣾⣿⣠⣿⣯⢸⣿⣿⣾⣿⣿⣿⡺⢛⣓⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣘⣿⣟⣘⣻⣿⢻⣿⣿⣸⣿⣷⣿⣿⣿⣿⣻⣿⣉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠻⠿⠾⠿⠿⠿⠿⠷⠛⠚⠒⠂⠄



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⢠⠐⢀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⠢⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⠒⠠⠤⠤⣤⣄⣀⣀⣀⣀⣠⣤⠄⠠⠤⠒⠒⠋⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢤⣶⡿⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡋⠀⢹⣄⣼⢿⡄⣦⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⣴⡻⣺⢶⣿⡿⣦⢀⢄⡤⠀⠀⠀⠀⢀⡜⣅⣿⣧⣸⡿⣿⡿⠉⠛⢻⣼⣿⣉⠆
⠀⠀⠀⠀⠀⠀⢀⡠⣞⣿⣿⢗⣿⡿⣺⣷⣿⡿⡮⣫⠵⠋⠀⠀⠀⣀⣠⠞⣼⠛⣿⡿⠇⠀⠠⠤⣀⠀⠀⠁⢹⠟
⠀⠀⠀⠀⢀⡴⣿⣾⡿⣿⢟⠝⣮⣾⣿⣿⢟⡫⠞⠁⠀⠀⢀⡠⣿⡌⣁⣠⣿⢺⠉⠁⠀⢠⣀⢀⡈⠀⠀⢠⡌
⠀⠀⣠⣶⣿⣿⢟⡵⡮⣾⢵⣟⣿⡿⢛⠵⠋⠀⠀⠀⢀⡴⢻⣄⡶⠶⠛⢻⣙⡷⠀⠀⠀⠀⠉⠋⠀⢰⣤⠞⠁
⠐⣿⡾⣫⣿⢕⢝⣦⣾⣿⣵⣟⣪⠞⠁⠀⠀⠀⠀⠀⣼⣶⣬⡉⢀⣳⣾⣿⣿⠅⠀⠀⠀⢀⣀⣀⠀⠖⡈⠀⠀⠀⠀⢀⣴⣿⣆
⠀⠀⢨⣎⣷⠵⣿⣯⣾⢟⡵⠋⠀⠀⠀⣠⣄⡀⠀⠀⠘⢻⣿⣿⠛⢯⣿⡾⠋⠀⠘⣄⠀⠈⠳⠽⣃⠜⠁⠀⠀⣠⣾⣿⣿⣯⣾⠁
⠀⠀⠘⠞⠁⠀⠀⠉⠙⠁⠀⠀⣠⠤⠼⣃⡀⠙⣆⢀⣀⣤⢽⣟⠟⠛⠋⠀⠀⠀⠀⠈⢳⣤⣤⣼⡧⠀⠀⠀⠈⠙⢻⣿⠟⢋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠎⠀⠉⢛⡿⢇⠀⠀⢺⡜⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⣟⣀⠤⠲⢄⠀⠀⠀⣡⣶⣻⣅⠀⠀⢰⠀⠀⢀⠞⡡⢊⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢰⠋⢀⣘⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠞⢳⢣⠈⣇⠀⠀⠀⠀⢸⡇⠀⢺⣿⠿⠋⠀⠀⠀⡆⣄⡴⠁⠞⠱⢃⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⠈⠳⣆⠸⡇⠀⠸⡄⡇⠀⠀⠀⠀⠀⠀⢸⣯⠀⣻⠀⠀⠀⣴⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠈⠢⠀⠀⠀⢋⠌
⠀⠀⠀⠀⠀⠀⣠⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⡇⠀⠀⠃⠇⠀⠀⠀⠀⠀⠀⣼⢡⠀⣿⢄⡀⠀⢣⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣠⢯⣳⣄⡀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⡇⠀⠀⢻⡘⢠⠀⣀⣀⣀⣀⠟⡣⢀⡇⠀⠀⢀⡴⢹⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣠⠞⠁
⠀⠀⢀⡴⠋⠁⠀⠙⠻⠿⣦⡴⣦⠶⡇⠀⠘⠦⣄⠈⡇⠀⠀⠀⠉⠉⠑⠀⠒⠒⠐⠊⠁⢸⠀⢀⡞⠉⠀⠘⡆⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⣰⠃
⠀⣰⠋⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⡇⠀⠀⠀⢈⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡄⠀⠀⠀⢧⡄⠀⠀⠀⣠⠞⠁⠀⠀⡴⠃
⣰⠃⠀⠀⠀⠀⠉⠙⠳⢤⣀⠀⠀⠀⢧⠀⠀⠀⡞⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡒⣠⠇⠀⣀⠤⠶⠀⠀⣠⠞⠁⠀⠀⠀⡼⠁
⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣼⣀⠀⠀⠙⣢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠞⠙⣏⠉⠀⠀⠀⡷⠊⠁⠀⠀⠀⢀⡞⠁
⠀⠈⠙⠲⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠿⠄⡀⠀⠀⠀⠀⠀⢀⠄⢀⣑⣆⣠⠇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⣶⡖⢲⣤⠤⡀⠀⠀⠀⠀⠀⣬⠱⣄⠀⠀⣠⣧⣄⡎⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠉⠛⠛⠿⣄⠀⠀⠀⠀⡙⠗⠀⠮⣧⠙⣐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣿⣷⣶⣾⣦⢲⡜⠄⢡⣌⢠⣤⡿⢿⣿⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢸⢿⠀⡍⠉⠉⠓⠻⠾⠬⠿⠉⠾⣷⣮⡁⠀⠀⠹⡄⠀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⣼⠘⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠓⠎⢈⣬⣿⣿⡹⠿⣺⣿⣷⡳⣯⠵⣆⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠛⠀⠀⢸⣽⡄⠀⠀⠀⠀⠀⠀⢴⠇⣼⣜⡐⠀⣝⠁⡻⣟⡐⣳⣇⣻⡟⢉⠠⠤⢛⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⡛⡦⢹⡜⣏⠙⢷⠲⡖⠺⢶⡖⣿⠒⠶⡲⣖⠛⣯⢋⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣇⢳⡀⣿⡘⡄⠈⣷⢱⡀⠀⢻⡜⣆⠀⢳⡘⣆⠘⢇⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣆⢻⡉⢳⡙⡄⠈⣧⠱⡄⠀⢻⣜⣆⠀⠱⣌⢦⠈⣾⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣝⡒⠧⠤⢽⣜⣧⣈⣳⣝⣆⣀⠙⣎⣧⠠⠜⢒⣡⣼⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⡿⠟⠛⠁
⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠱⢴⠢⣄⠀⠀⣀⡠⠤⠐⢲⢒⠩⠒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⢀⣰⠋⠀⠈⢲⠉⠀⠀⠀⢠⠃⠀⢂⡡⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡠⢬⡇⠀⠀⠀⠀⢇⠀⠀⠀⠙⠒⡻⠃⠐⢊⣁⣹
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠘⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠾⠥⢤⣌⣀⡠⠄⠣⡄
⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠈⠓⠶⠦⢦⣤⡤⠞⠀⠀⠀⠀⠀⢠⡔⠊⠁⠐⠂⠉⣳
⠀⠀⠀⠀⠀⠀⠀⡷⠮⢭⣄⣐⣒⡠⠤⠤⠤⠤⠤⠄⠀⠀⠀⣀⣀⣀⣉⣉⣛⣶⣤⣤⠜
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⣀⣉⠉⠉⠙⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡏
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠦⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⠄⠠⠤⠤⠞





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⢀⡤⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⠀⠀⡌⠀⢰⠀⢠⠎⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠱⡈⠉⢲⠆⠂⠛⠀⠏⣠⣪⡟⣉⣱⡂⢢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠄⢀⡴⠃⠚⡀⠸⡉⣦⡀⢱⣄⠇⠀⠀⠀⠀⠈⢣⠀⣀⠤⠊⠀⢹⠄⡸⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠼⢼⣗⡑⣸⢇⣰⠂⢛⡀⣽⡿⡿⣿⡧⣄⡀⠀⠀⡘⡋⠤⢂⣱⠒⠃⠀⢸⠒⢞⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠘⠛⠀⠱⣸⣨⡀⠐⣇⣨⣿⣣⢏⣋⣍⢖⣟⣶⢺⠃⡴⢚⠝⠉⠢⠠⡏⠈⠢⠰⡔⢳⠤⣀
⠀⠀⠀⠀⢀⡤⠒⡉⢱⠀⠀⠀⠀⠀⠎⠘⠃⣸⢟⢿⢻⢿⣿⣷⣷⣷⣺⡾⠚⠉⠁⠈⠉⠉⠲⢖⡀⢸⠈⠉⣄⠊⢹⠀⡌⠳⡄
⠀⠀⠀⣰⠋⠀⠀⠀⠀⠓⠤⣀⣀⣴⣆⠀⢀⣿⣿⣭⣖⠎⣵⣿⣾⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣱⣈⣀⠖⠊⠀⠀⠀⠘⡄
⠀⠀⠀⡇⠀⢠⠀⠐⠒⠀⠀⠀⠀⠀⠈⠙⠚⢿⣿⣾⣯⣿⣗⡾⠁⡟⢄⣀⡀⠤⢤⣀⠀⠀⠀⠀⠀⠻⡄⠀⠀⢠⠐⣠⠀⠛⠀⡅
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠙⠻⠟⠛⠉⠀⠀⠙⠒⠒⠒⠒⠒⠪⣕⠤⣀⠀⠀⠀⣻⠀⠀⢀⡉⠉⠀⠀⣠⡇
⠀⠀⠀⡏⠳⢄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠶⠀⠈⠑⠮⣕⣲⣶⠟⠀⠀⠈⠀⠀⢀⠎⠀⠇
⠀⠀⠀⡇⠀⠀⠣⡀⠀⠀⡀⠀⠠⠈⢛⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣤⣢⡄⠀⠀⠀⣠⠀⠠⠄⠀⠒⢀⣀⠤⠤⠔⠊⣠⢾
⠀⠀⠀⠳⣀⠀⠀⠈⠁⠀⠈⠢⠤⠤⢬⡈⡁⠒⠀⡀⣀⠀⠀⠐⠒⠒⠠⠀⠐⠂⠀⠀⠀⠀⣀⣀⣀⣠⣶⢯⡄⢠⢾⠓⠒⠋⡸⡆
⠀⠀⠀⢀⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠐⠤⠤⠀⠀⠤⠐⠉⠁⠀⠀⠉⠀⠀⣰⠏⢁⠄⣿⢸⡄⠀⢀⠔⠁⣇⡀
⠀⠀⡠⢾⠘⢬⣹⠀⢀⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⢒⢶⣄⣀⣠⣀⠀⢠⡇⠀⠀⠀⢎⢠⣧⠐⠀⠀⠀⡇⠉⠢⡀
⢀⠞⠁⡞⠀⠀⢸⠀⣾⢃⡢⢀⠉⢻⣷⣄⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠈⠉⠁⠉⢻⡇⠘⡇⠀⢀⠀⢼⢎⠀⠀⠀⣀⡴⠁⠀⠀⠙
⡎⠀⠀⢘⡦⡀⠈⠑⠁⠀⠀⠉⠐⠂⠨⢻⡆⠀⠀⠀⡧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡏⠀⠀⠀⢸⢸⢠⠚⠉⠁⣇
⡇⠀⠀⢸⡇⠹⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢰⠁⠀⠀⣀⣼⡸⠎⠀⠀⠀⣿
⠹⡀⠀⠀⠉⠦⡀⠙⢷⣦⣤⣀⠀⠀⢀⣀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⡟⠸⣀⠤⠚⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⢠
⠀⠙⢄⠀⠀⠀⠨⠒⠄⡈⠉⠛⠻⠞⠉⠙⢻⠀⠀⡟⠷⠶⠶⣦⣄⣀⡤⠶⠶⠞⠉⠀⠀⠉⢇⣠⠃⠀⠀⠀⠀⢀⡠⡊⠁⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠉⠒⠤⢀⡀⠀⢸⠀⢸⠃⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠪⠑⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠈⢸⠀⠸⡄⠤⠀⠤⠤⠤⠀⠀⣤⡤⠀⠤⣤⠀⠲⠂⠉⠉⠀⠀⠀⠀⣀⡠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⢤⣄⡌⠀⠀⣇⠀⠀⠀⠉⠈⠁⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⡟⠛⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠸⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠙⠲⢤⣄⣀⣀⣠⠤⠴⠒⠒⠒⠋⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣠⠷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠓⠒⠒⠲⠶⠤⠤⠤⠤⠤⠤⠴⠚⠉⠀⠀⠉⠉⠉⠁⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢦⡀⣠⠚⢦⡜⠳⣤⠞⢦⡴⠳⣤⠞⢦⡔⠳⣤⠚⢦⡴⠳⣤⠞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠙⡅⠀⠈⡄⠀⢰⠀⢸⠀⠀⡇⠀⠸⠀⢀⠃⠀⡘⠀⢠⠁⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠰⡀⠀⢰⠀⠘⡀⢸⠀⠀⠁⠀⡇⠀⡜⠀⢠⠃⠀⡎⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢱⠀⠀⠇⠀⠇⠀⠀⠀⡀⢠⠁⢠⠃⠀⡌⠀⢰⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢃⠀⠸⡀⢸⠀⠀⠀⡇⡘⠀⡘⠀⢠⠁⠀⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣆⣀⢃⠈⡄⠀⠀⡇⡇⢠⠃⢀⣎⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠓⠶⠶⠷⠖⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣧⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣅⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⡾⠛⠉⠭⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠶⠶⠶⠶⠶⠶⠷⠶⢤⣤⣤⣀
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣀⣀⡀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣧⡀
⠀⠀⠀⠀⠘⣧⠀⠀⠀⣠⡞⠉⠉⠻⣦⡀⢀⣴⠞⠛⠛⢶⡀⠀⠀⠐⠀⣠⡶⠛⠋⠙⠳⣦⡀⠀⠀⠠⠀⣠⣤⢤⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⢷⠶⠟⠉⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠙⠶⣤⠴⠞⠉⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠛⠉⠀⠀⠈⠻⢦⣤⡾⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣸⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⠶⠛⠛⠛⠉⠉⠉⠉⠉⡉⡉⠛⠛⠛⠓⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣀
⠀⢸⡇⠠⠄⠀⠀⠀⠀⣀⣀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⢷⡀
⠀⠘⢷⣀⠀⢀⣀⣴⠟⠉⠉⠉⠻⢦⣄⣀⣤⡴⠖⠛⠲⢶⣄⡀⠀⠀⣀⣠⣤⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠖⢀⣀⣀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⢹⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠙⠷⣤⣤⣤⣤⠶⠞⠋⠉⠀⠈⠙⠳⠶⣶⠞⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣴⠞⠉⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⢦
⣼⣿⠀⠀⠀⠙⠷⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁⠀⢸
⣿⠙⠷⣤⣀⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠳⠶⠶⠶⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠞⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⣠⣾
⠘⠷⣤⣀⠈⠙⠛⠶⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠶⢛⣩⠞
⠀⠀⠀⠙⠳⠶⣤⣄⣀⡀⠀⠈⠉⠉⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⢤⣤⠤⠦⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠋⢉⣉⣡⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠚⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠒⠄⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢄⠠⠊⠀⠠⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠁⠠⠐⣂⠠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣉⡀⢀⢈⠉⣀⡠⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈⠁⠃⠉⠀⠀⢀⢠⢄⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠠⡐⢀⠁⢀⠥⠼⡁⢄⠑⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⡗⡌⢄⡤⢾⢉⠉⠉⠑⡓⠀⠀⠘⡦⢀⣲⠃⠀⠀⠀⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠄⠀⠀⠈⣉⣁⣈⣂⣀⣀⣒⡀⠀⠀⠀⠉⠠⠀⠀⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠠⠤⡀⠀⠀⠀⠠⡀⢀⠀⠐⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠒⠤⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠤⠐⠈⠁⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠐⠒⠂⠀⠤⠤⠀⠀⠀⠤⠤⠀⠒⠒⠒⠂⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⣀⡀⡀⠀⠀⠀⠀⢀⡀⠁⠲⢾⡷⠀⠀⠀⠀⠀⠀⠀⣀⣁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠂⠀⠹⡛⠛⠳⣿⣿⣾⣟⠁⢀⡄⠘⢛⢀⣸⣿⣿⣷⡶⠄⠉⣨⣶⡅⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠲⠘⠀⣾⣿⣿⣶⣦⣤⣦⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣭⣥⣶⣶⣷⡿⠃⣘⠦⢀
⠀⠀⠀⠀⠀⠀⢀⡒⠉⠁⡤⠼⠆⠉⣿⠏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠖⠀⠘⣣⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣷⣶⣾⣿⠏⠀⢶⡎⠙⢿⣿⣿⣿⣿⣿⣿⡿⠃⢠⠉⣿⣿⣿⣿⣿⣿⣿⣿⠏⠠⠶⠌⠛⣿⣦⣀⣒⣩⣡⣥⡞⣷
⠀⠀⠀⠀⠀⠀⠄⢩⡟⠿⢿⣿⣿⠟⠀⢀⣉⠲⡄⠘⢿⣿⣿⣿⣿⡿⠀⠈⠙⠁⠀⠨⣿⣿⣿⣿⣿⠿⠘⠀⠐⠢⠶⠘⢻⣿⣿⣿⠿⡋⠁⠻
⠀⠀⠀⠀⠀⠀⠈⣤⠒⢂⡤⠬⡛⢓⡒⠎⠤⠶⣥⣶⣿⣿⣿⣿⣿⠋⠁⠀⠀⠂⢉⡄⢨⣿⣿⣿⣿⣧⣤⣖⣠⠤⠞⡴⠊⠉⢡⠆⡀⣰⡔
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣶⣎⣉⣤⠀⠀⢀⣀⡠⠄⠀⠈⢉⠁⠀⠀⠁⠀⠀⣉⡑⠋⢉⡤⠀⠈⢉⣁⠀⠈⢁⡤⢀⡠⠊⣰⣫⣬⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡏⢹⣏⠻⢿⣿⣿⣿⣿⣯⣶⣦⣐⣛⣩⣡⡄⠚⣁⠄⢒⣁⣠⠤⠚⠁⣀⡤⠞⣋⣀⣐⣚⣡⣤⣭⣴⣿⣿⣿⣿⣿⢁⡄
⠀⠀⠀⠀⠀⠀⢸⡇⢸⣟⣿⡿⢀⡟⢻⣍⣛⣛⡛⡛⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⡏⢸⣇
⠀⠀⠀⠀⠀⢀⢢⣷⣸⠿⡿⢣⣾⣅⢹⣿⣿⣛⣻⣿⡿⠟⢸⠏⢻⣾⣿⣿⣿⣿⣿⣿⣿⠃⣼⡍⢿⡿⣿⣿⣿⣿⡏⢠⣶⣼⣿⣿⣷⣿⡿⢄
⡄⠀⠀⠀⢀⣆⣘⣿⣿⣾⣿⢿⣷⣿⣥⡿⣿⣟⣻⡿⠟⣠⣿⣷⡌⢿⣿⣿⣿⣿⣿⡿⢃⣾⣿⣿⣞⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⠻⠃⣼⡇
⢇⠀⠀⠀⠀⠹⣥⠂⣹⡟⠹⢿⣿⣿⣭⣿⣿⣽⣿⣧⣿⣿⢿⣿⣿⣦⣹⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣷⣽⣿⣿⣵⣿⣿⡿⣿⠟⠛⢉⣄⣦⡟
⠘⢧⡀⠀⠀⠑⢌⠻⣥⡄⣒⡦⠤⠈⢛⣉⡻⠟⠛⠛⡛⠿⠿⠿⡷⠾⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⡿⠿⠿⠛⠛⢋⠉⠃⡰⢁⡴⣴⣯⡾⢋⠄⠀⠀⠀⣠
⠀⠀⠉⠳⢤⣀⠀⠀⠀⠙⢳⠶⠾⣿⣭⣤⡴⠖⣉⣁⣤⡤⠖⣀⡤⠂⠀⣤⠤⠊⣉⣠⡤⠔⢈⣁⡤⠒⢀⡠⠔⢨⠤⣾⣶⠧⠚⠋⠃⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣀⡀⠈⠀⠀⠉⠙⠛⠛⠷⠾⠿⣯⣥⠶⢶⣿⣵⣶⣮⣭⡥⠶⠾⣿⣿⠶⠿⢿⠶⠟⠿⠛⠃⠈⠀⣀⣠⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠶⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣠⣤⣤⠤⠶⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠰⠄⠈⠀⠀⠀⠀⠒⠂⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢢⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⢀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠤⠤⠀⠀⠀⠀⠂⠺
⠀⠀⠀⠀⠀⠀⠀⣈⠡⠀⠀⠐⠀⠀⢠⡀⢀⣈⠀⠠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⡖⠐⠀⠀⠀⠀⠀⡀⠀⣀⠜⠓⠂⡉⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⢤⠀⠂⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠂⠐⠚⠉⠀⠑⠒⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⡀⣠⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠱⡤⠖⠀⢁⡀⠠⠴⠂⠀⡀⠀⠀⠀⠀⠀⠈⠀⠠⠈⠀⠀⠀⠂⠀⠀⠄⠀⡀⢂⠀⣴⣡⠤⠁⢈⠉
⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⠀⠀⠀⠂⠛⠁⠀⠀⠠⠛⠠⠈⡗⠲⣶⠛⠶⠒⠒⣩⣤⡀⠤⣽⡂⢴⣶⢬⡶⠿⠿⠟⠛⠷⠎⣠⠄⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠄⡀⠀⡆⠀⠀⣤⠀⢸⠀⠐⠀⠀⠀⠤⠄⢙⡖⢃⡀⠀⠀⠀⢀⢀⠀⣠⠌⢹⡉⣤⢶⡴⠶⠶⠟⠛⠀⡀⠠⡄⠀⠲⠈⠠
⡀⠀⠀⠀⠀⠊⠀⣆⠀⠚⠣⠜⠁⠀⠀⢷⠐⠂⠂⠀⠄⢀⣄⣀⠈⣥⠀⠀⠀⢀⣀⡤⠀⣠⣄⣴⡈⢦⡴⠶⠾⠿⠂⣈⣙⡦⠔⢢⡴⠀⠀⢸
⡇⠀⠀⠀⠀⠰⣀⠉⠂⠄⠀⠀⠀⠀⠈⠀⣧⢒⣆⣀⡤⠮⢤⠄⡠⠈⠢⠄⣀⡀⢀⠀⣴⠤⢤⡤⣴⠮⣳⠿⠟⢃⣔⣉⣠⠤⡶⠀⠀⠀⢀⡞
⠘⣆⠀⠀⠀⠀⠐⢖⣂⠀⠀⠀⣉⠀⠔⠀⠼⠃⠽⠋⠀⠤⠤⣄⣀⡠⠘⠻⠶⠾⢦⠥⣤⣤⠤⣶⠶⣶⠿⠶⠞⠛⠛⠋⠉⠈⠀⢀⢈⣠⠞
⠀⠈⠓⢤⡀⠀⠀⠀⠈⠐⠮⠥⣤⣒⠒⠀⠠⠤⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣁⠀⠀⠀⡀⠀⡀⢀⣠⡀⠤⠟⠉⠀⠀⠀⠀⡀⠔⠉
⠀⠀⠀⠀⠉⠑⠢⢤⣀⡀⠀⠀⠀⠀⠈⠉⠒⠒⠲⠭⠤⣤⢄⣊⣠⣄⣀⣀⣀⡀⣚⣉⣤⣤⣄⣉⣤⠤⠤⣤⠴⠂⠴⠋⠁⠀⠀⠀⣀⣠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠤⠤⣄⡀⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠴⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠹⡄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⣆⡟⠀⠀⠀⠀⢀⠎⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⢠⡟⣻⠀⠀⠀⠀⠀⡏⡤⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⣧⠇⠀⠀⠀⠀⠀⠀⠀⢸⣋⣽⠀⠀⠀⠀⠀⢹⣷⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⡆⠀⠀⠀⠀⠀⠀⠀⢸⡭⢾⠀⠀⠀⠀⠀⡿⢽⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢿⡀⣀⣴⣯⣛⣦⠤⣾⢒⣻⣄⣴⡖⣄⣰⢯⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⠴⣯⣟⣻⡇⠙⠿⠟⠃⢴⣍⣛⣛⣹⠆⠈⢛⠻⣶⣷⣾⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⠇⠀⢸⣝⣛⣳⡀⠀⠀⠀⠀⣀⠉⠉⠀⠀⣠⢾⣶⣽⡇⠉⠛⠛⠉⢳⣾⠟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠉⠁⠀⠀⣼⣯⣉⣩⢿⡇⠀⠀⠈⠛⠀⠀⠀⢞⠻⣦⣝⣛⣿⡄⠀⠀⠀⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠛⠀⢀⣠⣄⠑⠠⠴⠖⠋⠀⠀⢀⣤⡤⣄⠀⠀⠈⠙⠲⠶⠶⠞⠁⣀⣀⠀⠀⣭⡍⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢿⡷⣿⠃⠀⠀⢀⣀⠀⠀⣏⣬⣿⡿⡇⠀⠀⠀⠀⠀⠀⢀⠼⢷⠿⣷⡆⠈⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣴⣾⣷⣶⣬⠑⠒⠁⠀⢀⡘⠛⠀⠀⠱⠭⠭⠖⠁⠀⠀⢰⡶⠀⠀⠈⠳⠶⠿⠋⠀⢠⣶⣾⡏⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⣾⠷⣿⣿⣿⣿⣿⠇⠀⠀⣠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣴⣆⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡯⢼⣷⣷⡚⢻⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⡇⠀⠀⣦⡀⢀⠀⠀⠀⣴⣦⠀⢠⣿⡀⠀⣸⣿⣿⣶⣿⣿⣿⡗⢦⣀⡀
⠀⠀⠀⠀⠀⠀⢘⣶⣏⣰⣃⣹⣿⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⣧⠀⢰⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣳⣿⣳⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⡼⢻⢏⣳
⠀⠀⠀⠀⠀⢸⣿⡟⠿⣿⡏⠀⠀⠀⢹⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣦⣼⡟⢻⠟⢿⣿⣿⣿⡉⠉⢹⠁⠀⠀⣈⣿⣾⣿⣾⡾⢻⡇
⠀⠀⠀⠀⠀⠈⢧⢷⡀⠀⠙⢤⡔⠛⢾⠛⢳⣾⣿⣿⣿⣿⠛⢻⣿⡀⠀⢈⣿⣿⡏⠉⣱⣦⣔⠉⣿⠋⠉⠙⣷⠾⢦⣀⣈⣿⣏⠀⠙⠧⣣⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠳⡙⢦⣔⡓⠉⠛⠿⣷⡄⠻⣿⣿⣿⠿⣶⣿⣿⣿⣶⣾⣿⣿⣅⡔⢨⠛⢦⣨⣿⠷⠤⠴⢋⣴⡇⠀⠁⠀⠁⣀⠤⢚⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣌⡙⠳⠦⣤⣀⡀⠀⢀⣀⣀⡀⠈⠛⠛⠋⠈⠉⠉⣩⠻⠷⣿⣶⡾⠟⠁⠀⠀⠀⢈⣉⣠⡤⠶⠚⣉⣥⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣈⡙⠛⢯⣁⣀⣹⣦⣤⢠⣤⣤⣤⣤⣭⣤⣤⣤⣤⡤⠶⠶⠶⠛⠛⣋⣉⣤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠺⠧⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠶⠶⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⠀⠀⠀⠀⢰⡦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⣶⠀⢀⣦⠀⠀⡆⠀⠿
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣭⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⣄⠀⢀⡇⠀⣿
⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣦⡄
⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣽⣿⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀⣄⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣤⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢯⣿⣿⣿⣿⣻⣿⣻⣿⡟⣿⣯⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣾⣿⣿⣿⣷⣿⣻⣿⡇
⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⣾⣦⣤⣤⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠛⠛⠋⠁
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣶⣶⣤
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠛⠋

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⡀⠀⠀⢠⣓⡄⠀⠀⢀⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠇⠀⠀⣿⣩⡇⠀⠀⢿⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣭⡇⠀⠀⣟⢩⡇⠀⠀⣟⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣵⡇⠀⠀⣟⢥⡇⠀⠀⣟⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⡇⠀⠀⣯⣵⡇⠀⠀⣿⣥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣴⡇⠀⠀⣯⣴⡇⠀⠀⣯⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠆⠒⠛⠛⠓⠀⠉⠉⠉⠉⠉⠁⠉⠛⠓⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡖⠉⢢⢀⡴⡄⡎⢸⠀⢸⠁⢸⠀⡇⢡⠀⡎⠀⢱⢠⠒⠀⢴⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢴⠁⠀⢸⠈⡇⠓⠂⢸⠀⠸⠀⢼⠀⢃⠼⠀⡇⠀⣆⢈⠀⠓⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠒⠁⠀⠀⢨⠀⣸⠃⠈⠒⠂⡇⠀⢸⠀⠈⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠤⠤⠆⠒⠒⠒⠚⠛⠉⠀⠉⠉⠈⠁⠒⠚⠒⠂⠤⠤⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠒⢤⠀⢀⣀⢀⡊⢦⠀⡰⠋⢱⡀⡎⠱⠀⢠⠊⠑⡄⢀⢤⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⠇⠀⢰⠀⢂⠸⣠⠆⠘⠀⢃⠀⢘⠃⢣⢀⠀⢣⠀⠀⡇⢸⠐⠤⣼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⣄⡸⠀⠀⠀⡇⠀⠸⠀⠹⣀⡸⢸⠀⠈⡄⠀⠣⠞⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠼⡄⠀⠀⠀⠀⠀⠀⠀⠳⠤⠚⠀⠀⠀⠀⣈⠀⠀⡇⠀⠀⠀⠀⢠⠧⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⢠⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⡜⠒⡄⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠈⠲⠤⠍⣐⣒⠒⠐⠲⠆⠀⠀⠤⠤⠤⠄⠀⠀⠐⠶⠒⠒⣒⣒⡩⠤⠖⠁⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠬⠭⠍⣉⣉⣁⣀⣀⣀⣀⣈⣉⣉⠉⠭⠥⠤⠤⠐⠒⠂⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠚⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⣒⠤⢤⣀⣀⣀⣀⣀⣀⣀⣤⠤⣖⡋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠈⢣⣀⡤⠤⣄⠀⣠⠴⢤⣀⡼⠁⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠘⢄⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣠⠏⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠉⠓⠲⠦⠤⠤⠤⠤⠤⠴⠖⠒⠉⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠒⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠋⠉⢳⡀⠀⢈⣉⣉⠉⠉⠉⢉⣉⡁⠀⠀⡴⠉⠙⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡇⠀⠀⠀⠓⠒⠋⠀⠈⠢⣤⠴⠋⠀⠉⠒⠚⠁⠀⠀⢸⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⡀⠀⠀⠈⠉⠒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠋⠁⠀⠀⢀⡠⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⠲⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠚⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠚⠉⠙⢦⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣰⠋⠉⠑⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠦⣀⡤⠞⠉⠙⢦⡀⠀⢀⡴⠋⠉⠓⢤⣀⡴⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⢤⣀⣀⣀⣀⣀⣠⠤⠤⠴⠖⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣙⣋⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⢿⣿⡿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣫⣶⣦⡙⢷⡾⢋⣾⣷⣝⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣼⣿⣿⣾⣿⣧⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣛⣟⡻⣿⣿⣩⣿⡿⣛⠿⣿⣏⣹⣿⠟⣛⡛⢿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⢛⣿⣿⣜⡻⢟⣫⣾⡛⣿⣮⣛⣛⣵⣿⣟⢻⣷⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⡁⢑⣻⣿⣿⣿⣟⡈⢀⣻⣿⣿⣿⣓⠁⢙⣿⣿⣿⣿⣃⠉⣚⣿⣿⣿⣿⣓⠁⣙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣶⣿⠿⣋⠻⣿⣶⣶⣿⠟⡙⢿⣷⣦⣿⡿⠟⡙⢿⣷⣾⣾⡿⢋⡻⢿⣷⣦⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣭⣭⣭⣴⣾⣿⣷⣦⣭⣭⣵⣾⣿⣶⣬⣭⣭⣴⣿⣿⣦⣭⣭⣥⣶⣿⣿⣶⣬⣭⣭⣥⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣟⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⡿⣻⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡇
⠀⠀⠀⠀⠀⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⡀⠀⠀⠀⠀⠀⡠⠊⢢⠀⠀⠀⠀⠀⠀⢀⡔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⣱⠀⠀⠀⠀⠸⡀⠀⢠⠁⠀⠀⠀⠀⠀⡁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣢⡐⠁⠀⠀⠀⠀⣠⣬⠯⣅⠀⠀⠀⠀⠀⢀⡙⢂⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡐⠚⢷⠀⠀⠀⠀⡷⠤⢈⣉⠀⠀⠀⠀⠀⢸⣉⠁⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠀⠀⠀⠀⡇⠀⠀⠈⡄⠀⠀⠀⠀⢸⠀⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⢸⠀⠀⠀⠀⡟⠲⠤⣠⡇⠀⠀⠀⠀⢸⠦⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣹⠠⠤⠤⠤⠷⠤⠤⠴⠧⠤⠤⠤⠤⠼⠄⣀⣉⣇⣀
⠀⠀⠀⣀⡠⠤⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠠⠄⣀
⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠀⠀⡜⡇⠀⠀⠀⠀⠀⠀⢀⠤⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠢⣀⣀⣠⡀⠀⠀⠀⠀⢀⡴⠢⡀
⠣⣀⣠⠔⠁⠑⢄⡀⠀⢀⣠⠔⠁⠀⠀⠀⠈⠢⢤⠀⣀⢠⠤⠔⠊⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠒⠉⠀⠀⠈⠑⢲⠒
⠀⠀⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣧⠔⠊⠉⠉⠉⠑⠢⠤⣀⣀⣀⣀⣀⠤⠔⠊⠉⠉⠉⠉⠉⠉⠒⠤⢀⣀⠠⠤⠔⠊⠁⠀⠉⠒⠤⣀⣀⠠⠴
⠀⠀⡇⠀⢀⣀⡀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠐⠒⠒⠢⢄⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⣀⡀⠀⠀⣀⢴
⠀⠀⡟⠉⠁⠀⠀⠀⠀⠉⠒⠒⠂⠀⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⢀⠴⠠⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠒⠓⢄
⠀⠠⣀⢀⡎⠁⠈⢱⠒⠉⢒⠔⠒⠒⡤⠒⠒⡤⠒⠒⢢⠔⠒⢲⠔⠒⢢⠄⠒⠤⡔⠒⠲⡔⠈⠑⢺⠁⠀⢈⡆⠤⠊
⠀⠀⠀⠀⠙⠒⠒⠙⠢⠤⠜⠦⢀⠠⠧⢄⡠⠷⠄⡀⠜⠦⢀⠸⠦⣀⠸⢄⣀⡠⠧⣀⡠⠞⠤⠤⠊⠑⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢦⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⡄⠀⠀⠀⠀⢠⠃⢆⢣⠀⠀⠀⢀⠇⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡆⢱⠀⠀⠀⠀⢯⢸⢸⢸⠀⠀⠀⢸⢠⠱⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣄⣄⡜⠀⠀⠀⠀⠈⣻⣿⢿⡄⠀⠀⠘⣼⣾⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⣯⢲⡀⠀⠀⠀⡞⠛⢩⣼⠃⠀⠀⡴⠻⠛⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣴⢸⡇⠀⠀⢸⣴⣿⡗⣿⠀⠀⠀⣷⣰⣧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢚⣿⡇⣀⡀⢈⣿⠦⣌⣏⠀⣀⠀⢸⣿⠽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⠶⣤⣶⣾⣿⣻⡏⠭⠛⣿⣿⣭⣿⡯⣑⠢⣿⣿⣭⣿⣿⠿⣋⣿⣷⣶⣶⡴⢶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣤⢾⣿⣷⣿⣛⣛⠋⠉⠉⠉⣸⡧⢐⣫⣧⠀⠀⢰⡗⠠⢍⣿⠀⠀⠀⣿⣈⠤⣿⠉⠙⠛⠛⠛⣷⣶⣽⣟⣛⣳⣆
⠀⠀⠀⠀⠀⢾⣷⢻⣽⣶⣿⣭⣭⣿⣶⡞⠲⣮⣩⣭⣭⣥⣤⡶⢮⣭⣛⣋⣭⣴⡶⢦⣭⡿⡿⢭⣴⡞⣛⣛⠺⣿⣷⣴⡟⣿⢻⡿
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣯⣚⣿⡸⣿⣿⣿⣿⣾⣽⣶⢶⣾⣿⣿⣶⣮⣻⢯⣯⣭⣿⣶⣿⣯⣿⣷⣭⣿⡿⣿⠿⢿⣿⣿⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡯⣽⣽⠿⣿⣿⣿⣮⣿⣯⣿⣾⣿⣯⣽⣿⣽⣿⣿⣟⣟⣫⣾⣯⣿⣷⣿⣷⣷⣿⡿⣿⣻⣿⣟⡾⢻
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡷⡏⣵⠟⣿⣿⣿⣞⣭⡭⢿⣟⣯⣿⣿⣟⣯⣭⢯⣟⣿⣯⣷⣿⣿⣷⡿⠞⢾⣿⢿⣿⢫⡷⣿⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⣸⠇⠀⢹⡟⣿⠉⣿⡝⣹⠟⠉⣿⣯⡿⠁⠹⣟⣿⣿⠿⣿⡿⢡⡟⠀⠀⠀⢻⣏⢃⡾⠀⣿⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡋⠀⠀⠘⣷⣻⡿⠃⣴⠏⠀⠀⠉⠉⠁⠀⠀⢿⣭⣿⣠⣿⠇⣼⠃⠀⠀⠀⠀⠙⠛⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣘⣻⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⠟⢁⣴⡟⠀⣀⣀⣀⣠⣤⣴⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣭⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⣫⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠩⠻⣯⡛⠿⠗⢒⣺⣾⠶⢾⣖⠾⣿⣿⠿⢟⣫⡶⠞⠛⠻⢮⣟⣟⣩⡴⠞⠉⠉⣇⡀
⠀⠀⠀⠀⠀⣀⣀⣠⠶⣻⣄⣀⡀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠉⠓⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠈⠉⠁⣀⣀⣠⡶⠿⣟⣷⣄⣀⡀
⢀⣠⠴⠞⠋⠉⠉⢿⡟⣽⢿⣯⣟⢛⣶⡶⢦⣤⣤⣄⣤⣤⣀⣤⣤⣤⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣶⣶⣿⣻⣭⣽⣿⣿⣿⡿⠋⠉⠉⠛⠶⢤⣀
⣾⣧⣄⡀⠀⠀⠀⠈⠻⠾⢿⣽⣿⡿⡷⣿⣿⣷⣷⣿⢿⣿⣫⣴⣶⣮⣿⣿⣛⣿⣭⣴⣦⣽⣷⡾⠿⣶⣾⢿⣻⣿⣵⠟⠋⠀⠀⠀⠀⠀⠀⣀⣽
⠈⠛⠿⣿⣷⣶⣦⣤⣄⣀⣀⣀⠈⠛⠿⠿⠻⠷⡿⠿⣿⣯⣿⢾⣿⣿⠿⣯⣭⣽⡽⠿⣿⡿⠟⠛⠛⠛⠛⠛⠉⠀⢀⣀⣀⣀⣤⣤⣶⣶⡿⠟⠋
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠿⠿⠟⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠒⠉⠁⠀⠐⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡏⠀⡏⠀⠀⠀⠀⠀⢀⡆⠓⠓⣒⠀⠱⡄
⠀⠀⠀⠀⠀⣀⠤⠔⠒⠋⠉⠉⠁⠀⠀⠀⠀⠈⠍⠅⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣂⣈⠁⣀⣰⠃⢰⠂⠈⢠⣴⡶⢶⠾⣧⣴⠿⣿⠀⠀⣷
⠀⠠⣄⠒⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⢈⠂⠀⠀⡊⠀⠀⠀⡠⠔⢀⡠⣴⠠⣞⣿⣽⢛⢩⡟⠀⡞⠀⢀⡿⡇⠘⠞⣠⠿⠒⠛⠉⠀⣰⣿
⠀⠀⠘⠠⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠜⠁⠀⢀⠎⠀⢠⡏⢀⡏⠄⣼⣍⣳⡟⢨⠇⢀⠃⠀⠈⡳⣶⣬⣭⣅⣀⣀⣤⠴⠞⠡⠃
⠀⠀⠀⠀⠀⠘⠓⠠⠐⠂⠠⠤⢀⠀⠄⠠⠖⠐⠂⠀⠀⠀⠀⡞⠀⢐⣏⡓⢾⣯⢿⣤⣿⠇⠘⠁⢀⠜⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⣵⠭⡽⢀⣄⣠⠜⠉⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠖⠒⠲⣤⣄⡀⠀⠀⠀⠀⠀⢠⠃⠀⣼⠿⠖⠋⠉⠀⣀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⢀⠀⣸⠁⠀⠈⠲⡄⠀⡀⠄⡞⠀⠐⠁⣀⡤⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⡤⠖⠉⠈⢗⡋⠀⠀⡀⠘
⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⡂⣇⠀⠀⠂⠀⠀⠐⠄⢤⡇⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⣤⢴⠁⠀⠀⠈⠷⠀⠀⠀⠈⠄⠐
⢰⠃⣀⣀⡀⠀⠀⠀⠀⠰⠐⣠⠟⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠼⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⢈⡀⠦⠐
⢸⠉⠀⠀⠉⢳⣄⣀⡤⠔⠋⠀⢠⠃⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⢴⠁⠀⠀⠀⠘⠂⠀⠀⠀⠐⠀⠠⠰⠀⠀⠉
⢰⠀⣀⡀⠀⠿⠣⠤⠤⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠲⡴⡇⠀⠀⠈⠚⠀⠀⠀⠀⡀⠀⠀⠖⠊⠉
⠈⠳⣅⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⡠⠒⠲⣞⡀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⢦⣄⣀⡤⠤⠤⢀⡀
⠀⠀⠈⠉⠒⠒⠂⠈⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⣿⣞⠟⠁⠀⣄⣾⠕⠋⠀⠀⠀⣰⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢸⡟⠁⠀⠀⢸⡟⠁⠀⠀⠀⢀⡼⣋⡤⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠐⠒⠠⠤⠤⢀⡀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠾⠋⠁
⠀⠁⠀⠀⣠⠔⠊⠁⠶⠶⠦⣤⣭⡑⢦⠀⢀⡔⠉⢀⡤⠴⠚⡓⢚⡷⠤⡤⣄⠈⠳⡄⠈⢧⣁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴
⠀⣀⡴⠋⠀⠐⠒⠶⠶⣤⣄⠀⣉⡵⠞⠀⠎⠀⠀⠻⠰⢶⠶⠽⠆⠀⣴⡴⣋⠝⠀⠘⠀⠐⠨⠉⠒⠦⠤⠤⣤⣤⣤⣤⡤⠤⠤⠖⠒⠋⠉⢠⡇
⣰⡯⠠⡭⣛⡛⠳⢶⡄⢀⡽⠚⠁⠀⠀⠀⡀⠀⠠⠀⢀⠛⠂⠶⠦⠶⢒⠫⠐⡈⠂⡀⠀⠀⢷⠄⣈⡀⠀⠂⠀⠀⠄⠀⠰⠀⠀⠂⠀⠘⢡⡞
⢇⡾⠿⠿⣶⣮⠱⣠⠞⠉⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠘⠀⠄⠡⠀⠂⠂⠁⣠⠖⠁⠀⠀⠈⠳⢦⣄⣁⠐⠐⠂⠂⠒⠒⠐⠐⢀⣁⡵⠞
⠀⠉⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⣤⣤⣤⠴⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠼⠷⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢦⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠉⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣿⣽⣷⣶⣧⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢩⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠋⢿⣿⡇⠀⠀⠈⢿⣉⠋⠁⠀⠻⠋⢛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⠶⠃⠀⠀⠀⠀⠁⠀⠀⠀⣤⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿⠇⠀⠀⠀⠀⠰⣿⠆⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣼⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣼⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢉⣼⣿⣿⡿⠿⠿⠿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠟⠛⠿⠿⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⣿⢿⣿⠋⠉⣉⡙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⠶⠋⠀⠀⠈⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣧⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣾⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢰⡏⣠⣾⡟⠛⠿⣿⡿⠃⠀⠛⠛⠻⣿⣿⣿⡏⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠿⠟⠛⠛⠿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠈⢻⡿⠟⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣻⠃⠀⣶⠆⠀⠀⠘⢌⡉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠘⠦⠟⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⣿
⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⢠⡴⠚⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⢏⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⣰⠋⢀⣤⣾⠿⠛⠉⠉⠙⠿⣿⣿⠟⠛⠻⠿⠃⠀⠀⠀⠀⠀⠑⠢⠤⠤⠖⠋⠁⠀⠈⠻⣏⠛⢿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣍⠉⢻⡿⠿⣿⣿⡿⢿⣷
⠻⠷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣆⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣀⣠⠎⠉⠉⠀⠀⠀⠀⠈⠙⠋⠀⠀⠿⠋⠀⡾⠙
⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠇⢀⣤⡀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠘⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠶⠶⠶⠶⠶⢤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠴⠶⠾⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⢀⠞⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣧⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡤⠔⠢⢄⠀⠀⢀⠴⠒⠢⡼⠥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠁⠀⠀⠈⡄⠀⡎⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠀⠚⠣⡀⠀⠀⠀⣀⠜⠒⠢⠧⡀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡩⣤⡤⠴⠶⠶⠬⠥⢶⣒⣫⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡮⠓⠉⠁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡏⠀⠀⠀⣎⣀⠜⠀⠀⠀⠀⡠⢢⠀⠀⠀⣀⠤⣄⠀⡟⠀⠀⢀⡴⠅
⠀⠀⠀⠀⠀⢧⠀⣀⠔⠉⠒⢄⠀⠀⣀⣀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠊⠀⠀⠀⠙⠒⠁⢠⣃⣠⣖⣋⡀⠠⡄
⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠑⠤⠤⠤⠞⢱⠀⠀⠀⢎⣑⡄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠒⡺⢻⠙⡝⠢⣀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⢏⣑⠄⠈⠀⡤⠊⠀⡘⠀⠘⣆⡀⠙
⠀⠀⠀⢰⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠒⠒⠛⠀⠀⠀⠃⠠⠀⠀⠛⠒⡆
⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⡶⠒⢶⡶⣶⣶⣶⢶⣶⢶⡶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠂⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠤⠿⣤⣐⣠⠾⠦⠤⠤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⠉⢉⠉⠉⠉⠛⠛⢛⠛⠋⠉⡍⠩⠉⡇⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢧⣸⠆⠀⢄⡴⣄⠈⡀⠠⠀⢂⡶⣄⠠⠀⡇⢀⡜⠝⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⣏⣌⣠⢿⡀⠄⡞⠔⠈⣧⠀⠄⢠⠎⡌⠌⣧⢀⡟⣯⡨⢈⡼⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠒⠶⠭⠥⣬⣭⣽⣻⣾⣶⣛⣒⣒⣛⣷⣶⣶⣯⣭⡥⠤⠽⠿⠒⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⢖⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄⠀⠀⠀⠀⣀⣤⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣇⣙⠶⣃⡟⣄⠀⡴⣺⠷⣤⡀⠀⣄⢸⡸⣭⠼⡾⢠⣦⠀⢯⣶⢾⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢺⡇⢂⢊⡏⠉⢉⡜⠩⢳⡷⣭⣻⡽⢡⡞⡙⢦⠙⠛⠋⣡⠟⢌⢿⠓⠶⡞⢅⠡⢹⠓⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⠤⣝⣒⡛⠓⠶⠾⣌⣒⣡⣧⣤⣤⣄⣼⣌⣌⣸⣇⣤⣤⣧⣀⣠⠾⠶⠶⠛⢒⣒⣫⡤⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣶⠛⡎⢉⡭⣟⠛⣻⣷⡒⠲⣶⣶⠶⢶⣮⡿⠶⢶⣶⠶⠖⣶⣶⠚⢛⡿⢯⠉⢹⠋⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇⢸⠀⢸⠀⡏⠀⡇⢰⡇⢸⡇⢸⠀⣿⠀⣯⠈⡇⠀⡇⢸⡇⠘⡇⢸⡆⢸⠀⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇⢸⠀⢸⠀⡇⠀⡇⢸⡇⢸⡇⢸⠀⢿⠀⣿⠀⡇⠀⣇⠀⡇⠀⡇⠸⡇⢸⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣻⠴⠃⢸⡀⣸⠀⣷⠀⡇⠈⡇⢸⡇⢸⡀⢸⠀⢿⠀⣷⠀⣿⠀⡇⠀⣧⣀⡇⠘⠦⣞⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠿⠷⠤⠽⢾⣥⣤⣷⣾⣁⣈⣷⣞⣀⣘⣶⣏⣤⣬⡯⠥⠤⠶⠿⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡱⣞⠄⠀⠀⢠⠄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠐⠈⠀⠑⠢⠤⠤⠼⢄⣀⡠⠦⠄⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠲⣰⣶⢀⠄⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢸⠁⠀⠀⠇⢀⠤⠄⢠⠦⡀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢴⡦⠀⣀⢀⣀⠀⡀⠄⠀⠰⡌⠈⠛⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠘⠋⠒⢣⡀⠀⠳⠃⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡐⠓⠂⣠⢤⡥⠀⠀⠀⠈⠉⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠍⠅⢊⡉⠤⢴⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠊⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⠀⠐⠀⠀⢀⢠⠄⠂⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠁⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈⠁⣈⠉⢧⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠉⢀⠂⠈⠠⠍⠁⠀⢾⠀⠀⠀⠀⢀⠔⠚⠏⡒⢄⣀⡴⠶⢢⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠀⣡⠀⠀⢠⡏⠀⠀⠄⠈⢤⠁⣀⠈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢎⠇⠀⠉⠃⠠⢀⠤⠀⣀⣀⠀⠁⠂⠈⠀⠀⠀⠀⠀⣀⠀⠃⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⠐⠢⠄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠠⢤⡀⠀⠀⠁⠈⠚
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⡀⠂⠤⠤⣀⠀⠀⠈⠓⠀⠀⠊⠀⠡⠌⡀⠈⠀⠀⠂⠁⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠠⡀⠙⠂⢠⠈⠂⢤⠀⢤⣄⠀⠀⠀⠀⠑⠒⠸⠧⢄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠤⠀⠀⠲⠀⠂⠁⠀⠀⠁⠀⠢⠁⢀⡒⠒⢦⣀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠁⠀⠄⠂⠀⠀⠄⠀⢘⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠂⠠⠀⢈⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠉⠱⠈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣌⠀⠀⣦⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡁⠁⢀⡌⠈⡄⠀⠠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡡⠀⠘⠀⠀⠰⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⡘⢤⠗⣁⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣠⡄⠄⠀⢻⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⢶⠡⡰⠄⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠠⡼⠀⠀⠀⠀⠉⠁⢈⠀⣀⡠⠄⣛⠡⠉⢄
⠀⠀⠀⠀⠀⠀⠰⡑⠀⠁⠒⠈⠐⠊⠑⠨⠦⠤⠤⠤⠤⢤⠤⠄⠤⠥⢀⠀⠀⢀⡂⠈⠐⠓⠀⠀⠉⠉⠀⠀⠀⢊⡄
⠀⠀⠀⠀⠀⠀⢡⣁⣀⣠⣤⣤⢄⣀⠀⠀⠀⢀⡀⠀⠀⢈⡀⡈⠀⠀⠀⣀⣠⣀⠀⠀⠀⣀⣀⠀⣠⠶⣄⣵⠻⣄⠇
⠀⠀⠀⠀⠀⠀⢸⠀⡘⠈⠑⠀⠁⠻⣕⠀⠀⠏⣇⣰⡶⡫⢋⠝⠱⢛⠋⠔⡡⡪⡿⣀⡰⠿⠫⠫⠓⠒⠒⠁⠁⡇
⠀⠀⠀⠀⠀⠀⢸⠥⠾⡫⢑⠾⠄⠠⢨⡖⢈⡀⣁⢈⠀⡀⢀⠀⣀⡀⢠⡀⣀⠀⣀⣤⣀⠄⠠⠠⠶⠔⣒⣙⣩⡇
⠀⠀⠀⠀⠀⠀⢸⡀⡀⠁⠈⠉⠻⠉⠒⠓⡖⠢⠭⠕⣒⠢⠽⠥⠖⡒⠭⠽⠔⣒⠦⠤⠔⠊⠯⠙⠒⠉⢸⢂⡀⡁
⠀⠀⠀⠀⠀⠔⠙⢮⣬⣐⡕⡡⡠⡠⠠⡠⢀⢀⢄⠄⡡⣀⢀⢀⢀⠁⡀⡀⡀⣁⡠⡄⡠⣠⣶⠶⠚⠒⠷⠛⠃⠙⡢⡀
⠀⠀⠀⠀⠠⣤⠦⣤⢀⣀⡈⠉⠛⠲⠾⠴⠕⠛⡿⢞⠚⠓⠷⢵⡟⠛⠛⠛⠩⠉⠙⠛⠙⠛⠀⢀⣀⠀⢠⣶⣶⣄⢻⡟
⠀⠀⠀⠀⢀⠋⠪⠹⠿⢝⣷⡄⢨⣶⠀⣦⣤⣤⠀⢀⣀⠀⠀⣀⣄⠀⠐⢂⡀⠀⠀⢲⢛⣙⣶⣿⣿⡧⠾⠉⠛⠛⣿⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⢼⣧⣠⣿⢽⡶⠟⠝⠻⠿⠛⠿⠿⠦⠿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢉⡹
⠀⠀⠀⠀⢸⡂⠽⢐⡒⠠⠷⠔⠒⢄⠠⡄⠀⠀⢁⡀⠀⡀⠀⣐⠀⠀⠀⠀⡀⠀⠀⣀⠀⣀⣀⣴⡠⠂⢼⠗⢈⣒⡟
⠀⠀⠀⣀⣨⠉⠉⠉⠸⠉⠒⠚⣍⠳⠿⠥⢥⠬⣬⣩⡤⢔⠻⣟⣉⣡⢭⣚⣃⣨⡤⣿⣉⣠⠤⡴⠴⠋⡍⠙⠉⠑⢠
⠀⠀⡀⠀⢸⡗⠧⢠⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠉⠀⠓⠀⠀⠀⠓⠀⠀⠀⢈⡁⠀⠄⠀⠀⢀⣠⡴⠂⢀
⠀⠀⠔⢂⠡⠜⢒⡤⢀⡈⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⣀⢀⠄⡠⣠⡢⣢⢂⠔⠔⠖⠐⠐⠉⠀⠀⢀⣠⡔⢊⠕⠁⡠⠖⢁⡠
⠐⣂⠨⠔⠂⣈⠤⠂⢂⠠⠉⠒⢀⡰⠶⠠⠤⠤⠀⠀⣁⠀⣀⠈⢀⡀⠁⢤⡤⠤⣠⠴⠂⡰⠛⡩⠔⡡⠔⣁⠔⠉⡠⠔⢁⠔⣈
⠉⠠⠄⠂⣉⠠⠔⠈⣀⡠⠔⠊⢁⡀⠄⠒⢉⡠⢔⡢⠕⢊⡡⠐⢉⡠⠒⢁⡠⠊⣀⠔⢁⡤⢊⠤⠊⡠⠊⣁⠔⢉⡠⠊⠡⠊⠑
⠀⠐⠊⠁⣀⠠⠐⠈⢁⠠⠐⠈⠀⡀⠔⢊⡡⠒⠁⡠⠒⠉⡠⠔⠁⡠⠒⢁⡠⠊⣠⠔⢁⠔⢁⠔⠉⡤⠊⠀⠀⠉
⠀⠀⠀⠈⠀⠀⠐⠊⠁⣀⠄⠒⠉⡠⠒⠁⡠⠔⠈⡠⠔⠊⢀⠔⠋⢀⠔⠁⠠⠊⠁⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣇⠀⠀⠀⠀⠀⠀⠀⢠⡷⣄⠀⠀⠀⠀⠀⠀⠀⣸⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⡆⠀⠀⠀⠀⠀⢀⡞⠀⠘⣆⠀⠀⠀⠀⠀⢰⠃⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⠰⠃⠀⠀⠀⠀⠀⠈⠷⢽⠴⠃⠀⠀⠀⠀⠀⠘⢆⡧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⡄⠀⠀⠀⠀⠀⠀⣰⠛⢦⠀⠀⠀⠀⠀⠀⢠⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡄⣿⠀⠀⠀⠀⠀⠀⡇⣠⣾⠀⠀⠀⠀⠀⠀⣿⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⢻⠀⠀⠀⠀⠀⢰⡇⣠⡟⠀⠀⠀⠀⠀⠀⡟⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⢺⡀⠀⠀⠀⠀⢸⡇⢁⡿⠀⠀⠀⠀⠀⢀⡇⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣿⣵⣾⣶⣶⣶⣶⣶⣾⣷⣿⣿⣶⣶⣤⣤⣤⣼⣧⣭⣿⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⣿⡱⡀⠀⢠⡿⠉⠀⠙⢿⣦⡐⠤⣤⡤⠔⣀⣴⠟⠋⠉⠙⠻⣦⣀⠀⢤⣀⣀⣠⠔⢀⣴⠟⠋⠉⠻⣦⡀⢀⡆⣿⠃
⠀⠀⠀⠀⠀⠀⠘⢷⣬⣶⠟⠁⠀⠀⠀⠀⠉⠛⠷⠶⠶⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣶⡶⠾⠛⠁⠀⠀⠀⠀⠈⠻⠶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣧⣤⣄⣀⣀⣀⣤⣴⠶⠟⠛⠛⠛⠛⠷⠶⣦⣄⣀⣀⣠⣤⡶⠶⠿⠿⠶⢶⣤⣄⠀⠀⢀⣀⣠⣤⣤⣿⡀
⠀⠀⠀⠀⠀⢰⣿⠁⣀⠀⠀⠉⠉⣉⣉⡉⠀⢀⡀⠀⠀⣀⡀⠀⠀⢀⣉⣉⣉⠉⠀⣀⠀⠀⣀⡀⠀⠀⠙⠛⠛⠛⠉⠉⠀⣀⠉⣿
⠀⠀⠀⠀⠀⠀⠹⢷⣬⣭⣵⠶⠟⠋⠉⠛⠷⢶⣭⣭⣭⣥⡶⠶⠟⠛⠉⠉⠙⠻⠶⣮⣭⣭⣭⡶⠾⠛⠛⠛⠿⠶⣦⣭⣭⣵⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠶⠶⠶⠶⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠶⠶⠶⠶⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢶⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠐⠁⠸⡀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠊⠁⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠙⠠⡀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒⠒⠒⠓⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠖⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⠤⠒⠒⠂⠤⣄⠀⠀⠀⠀⠀⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠒⠊⠉⠒⢤⡀⠀⠀⠀⠀⢁⠔⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢀⡼⣄
⠀⠀⠀⠀⠀⠀⠀⠰⠟⠲⢄⠀⡠⠖⠲⠀⠀⣀⠝⠒⢦⡔⢊⠕⠒⠢⡀⢀⠤⠒⠲⣄⢀⡸⠓⠲⡖⢈⡥⠒⠪⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠙⠀⣀⠀⠀⠀⠁⠀⠀⠀⠙⠁⠀⠀⠀⠙⠁⠀⠀⠀⠈⠃⠀⠀⠀⠘⠋⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡅⠀⠀⢠⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢤⠀⠀⠀⡇⠈⠂⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡌⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⡀⠠⠠⠭⠭⠍⠁⠀⠀⠀⠀⠀⠀⠀⠉⠭⠭⠭⠥⠤⠀⢀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠠⠬⠍⠁⢀⣀⣀⣐⣂⣐⣀⣀⣀⣀⣀⣀⣀⡀⠉⠭⠤⠤⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠄⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠐⠂⠀⢀⣀⠄⠀⠀⠀⠀⠀⡊⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠠⠁⠁⠀⠀⠀⠄⢉⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈⡁⣈⠉⠳⡀⣀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠉⢀⡐⠀⠁⢬⢁⠁⠸⡄⠀⠀⠀⠀⡤⠒⠋⢑⢦⣀⣰⠶⠖⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠂⠤⠀⣰⡀⠀⢀⡼⠀⠀⠄⠀⠠⡌⢀⠀⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠃⠀⠉⠁⠠⢀⠠⠄⣄⣀⠀⠈⠐⠂⠁⠀⠀⠀⠈⢀⡀⠈⠀⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠐⠢⠤⠀⢀⠀⠀⠘⢀⠀⠀⠀⠠⠤⣀⠀⠀⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⡄⠐⠠⠠⣄⠀⠀⡈⠑⠂⠀⠐⠁⠀⠌⣀⠂⠁⠀⠀⠁⠐⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⡄⠈⠃⠰⠌⠑⢠⡀⠤⣄⡀⠀⠀⠀⠘⠒⠢⠧⠤⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠢⠄⠀⠰⠀⠂⠁⠀⠀⠉⠀⠰⠉⠈⡐⠒⠲⣄⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡈⠈⠀⠐⠀⠀⢀⠀⠀⡋⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠠⠄⠀⣑⡂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣦⣄⠀⠻⡧⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠂⠁⠈⠁⠀⠀⠀⣀⣈⣬⡉⡛⠿⣷⣄⠀⠀⢸⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠉⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⣉⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠾⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠀⡇
⠀⠀⠀⠀⢀⠤⠐⠈⠁⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣷⣸⠇
⠀⠀⠀⠀⠦⠤⠴⠦⠤⠤⠤⠤⠤⠤⣤⣠⠀⠤⢀⢠⣠⠠⣄⣀⣤⣤⣤⣀⢠⣤⣤⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⢈⢻⣿⡟
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⢀⡤⠄⠀⠀⠀⠀⠉⠉⣉⠉⠉⣉⠉⠉⠛⢻⠁
⠀⠀⠀⠀⠙⠊⠁⣤⠀⡔⠠⣠⠎⠐⡀⠀⢰⠀⠂⠚⠁⠘⢆⠼⠉⠂⠀⠀⡰⠓⠆⠼⠁⠙⠤⠞⠁⠀⢡⠀⠀⡼⠣⠼⠁⠒⠞⠁⢇⠀⡰⢚
⠀⠀⠀⠀⡦⠀⠀⠰⠾⠀⠀⠀⢀⣀⣈⠐⢁⡀⣀⣀⣀⢀⡀⠀⠀⢸⡀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠁⠀⠀⠀⠀⠀⠀⠈⢉⣡⣿
⠀⠀⠀⠀⡃⠀⣀⣀⣀⣀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⣿⣿
⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠿⠷⠾⠿⠿⠿⠿⡿⡷⣦⣔⣶⣶⣤⣿⣽⢯⣽⣿⣥⣶⣲⠶⠶⠦⣤⣄⡒⣆⡀⠀⣀⣀⢀⡀⠀⠀⠚⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠛⠛⠙⠀⠀⠀⢘⢻⡇
⠀⠀⠀⠀⠀⠁⠐⠒⠒⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠠⢴⣤⣠⣀⣀⣀⣀⣀⣤⣤⣄⣄⣀⣠⣀⣀⣠⣄⣠⣀⣀⣀⣀⡀⣀⣀⠈⣲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠚⠉⠉⠠⠄⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠡⠀⠀⠀⠂⠀⠀⠀⠐⠂⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠁⠠⠄⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⡀⠀⢠⠄⠀⢀⡀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣌⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⠀⠉⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⢹⠀⡾⣆⡌⠙⠲⠤⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⡄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣘⡦⠃⠉⡀⠀⣿⣧⢦⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⠛⠷⣶⣆⢸⡁⠉⢸⠀⠰⢳⠀⡨⡙⢒⠦⢤⣈⣁⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠘⠛⠛⠿⢾⣄⣧⣘⠞⠁⠓⠉⣇⡔⢦⠀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⣀⠀⠀⠈⢉⠛⠻⠷⣦⣤⣈⡀⢸⣠⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⡀⠀⠀⠀⠈⠉⠛⠿⢷⣦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⢄⣀⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣧⣤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⠷⣽⣭⡻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠋⡖⠻⠛⢳⡟⠛⠋⣿⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣢⣧⣘⠉⣸⣇⡉⣀⣿⢃⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡽⢶⣻⣭⣽⡟⢻⣮⢭⣏⣟⠳⣷⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠿⣿⡽⣿⣷⣾⣿⣫⣵⣾⣽⠿⣿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣆⣿⣠⠷⡀⣿⢠⠧⣿⠀⡰⠆⣿⣠⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣍⣿⡇⠁⢻⣿⡗⠀⢿⣶⢋⣁⣿⣯⣴⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣎⡛⣏⡿⠵⢭⣟⡿⠯⣟⣻⠿⠼⣥⡟⡭⠼⢿⣆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣿⢇⡀⠈⠏⢉⠙⠩⠻⠓⡷⡹⠊⡍⠡⠊⠰⠀⢢⢼⣿⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠰⠆⣶⢀⡁⢰⠀⢒⠓⡇⢰⣒⢠⡆⢹⡅⣿⠘⠀⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣻⡇⠀⣿⡄⠁⢼⡄⠈⡤⣿⠤⠁⢸⣷⠄⠀⣿⠂⢸⡿⢛⡿⡶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡝⠶⢃⡼⣷⢶⣿⣤⡠⣼⣇⣀⣰⣿⣦⠀⣨⣿⣄⣴⡿⡿⢿⣛⡦⠉⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣿⣯⣘⣧⠇⢨⣯⡽⠋⢹⣭⣟⠉⠹⣭⣇⣈⣳⣯⣴⠿⣿⠿⠟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠈⠋⠈⠻⠟⠳⡿⠘⠿⡿⠟⢿⠝⠿⣿⠋⠙⠿⠛⢿⣁⠀⠈⠀⢦⣠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⠀⣦⢠⡏⠁⠀⣃⡀⡎⠂⠀⣈⡀⠀⠙⠣⢤⡤⠀⠀⠈⠐⡟⠀⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⣁⡀⣾⠨⠡⠀⠄⢸⡞⠡⠀⠄⢸⡇⠄⢀⠀⢸⠇⠀⣀⢂⠀⢧⣡⣤⡏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⢿⡿⠋⠳⣶⣿⣦⠘⠱⣵⣿⣷⠊⠀⣾⣷⣆⠌⠈⠺⡿⣿⡎⣀⡹⠏⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠿⠸⠧⠤⠤⠼⠤⠧⠤⠤⠼⠬⠷⠤⠤⠖⠓⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡀⠀⠸⣿⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠄⠐⠒⠉⠉⠉⠉⠙⠋⡛⠻⢿⣷⣄⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠉⠉⠈⠈⠻⣷⣠⠀⠘⠓⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠘⠒⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⣤⣤⣤⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠉⢱⡄
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠁⠀⠀⢀⠀⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⣿⣷⡀⢸⡇
⠀⠀⠀⠀⡔⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠊⠛⠂⠛⠚⠛⠚⠚⠛⠛⠛⠚⠐⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠠⠶⠶⠶⠶⠶⢶⣦⢤⣭⣿⠃
⠀⠀⠀⠀⢠⣀⠄⠀⠀⠀⣀⠀⢀⠄⡀⠀⠀⡰⢢⠀⣠⠖⢀⠀⣠⢤⠀⠀⠀⢀⣀⠀⢀⡞⢢⡀⢠⡞⠉⢢⠀⠀⢀⣄⠀⣴⠂⡀⣴⢂⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠸⢀⡞⠀⠐⠋⠀⠰⡀⣠⠇⠀⠈⠁⠀⠈⠒⠁⠀⢇⠀⢀⡎⠀⠑⠊⠁⠀⠙⠉⠀⠀⠀⢂⠀⡼⠉⠙⠁⠀⠉⠁⠈⠦⠰⢋⡍
⠀⠀⠀⠀⢙⠉⠀⡈⠙⠐⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠸⠦⠾⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣾⣇
⠀⠀⠀⠀⢠⢠⣤⣤⣤⣤⣤⣤⣀⣀⣀⣤⣤⣄⣀⣀⡀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣀⡀⣐⡂⠀⠀⠀⠀⠀⠰⠶⠗⠛⣉⡉⠉⢠⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠙⠉⠙⠛⠛⠛⠛⠛⠛⠓⠛⠻⠿⠿⠿⠯⠿⠿⢿⢶⣿⣿⣽⣿⣏⣙⣛⣉⣙⣇⣈⣀⣉⣉⣉⣋⠉⢙⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢻⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠖⠶⠶⠶⠤⠤⠴⠤⠦⠴⠶⠦⠶⠤⠤⠦⠤⠤⠶⠤⢦⣤⣤⣄⣠⣠⣤⣄⢀⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⣀⠀⢀⡄⠀⢃⠀⠀⢀⠀⠈⢈⠉⠈⠉⠈⠀⠀⠀⠁⠀⠙⠆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠆⠀⠀⠀⠀⣄⠉⠁⠀⠙⠀⠀⠸⠦⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠀⣤⠟⠀⠀⠀⠓⠀⠀⠀⠰⠦⡴⠤⠴⠶⠟⠂⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠆⠀⠀⠀⠀⠄⠊⠁⠰⠦⠀⢠⡄⠀⠀⠎⢰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢀⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⡄⠀⢠⡏⠆⠀⠀⠀⡐⡔⠀⠀⢀⡠⠔⠉⡠⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣀⠚⠃⠀⠀⠁⠀⠀⢀⠄⠈⢀⣴⣛⡁⠘⠀⠢⠰⠃⠚⠐⢒⣁⠠⠐⠈⠀⠀⠀⠈⡅⠐⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠊⠀⢀⡴⣋⡀⠍⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⠀⠊⠉⡠⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠉⠉⠀⠀⢁⡀⣀⠠⠐⠈⠀⠑⠢⣄⡀⠈⠣⠀⠠⠚⠂⠒⠢⢤⠀⠀⠀⠀⡀⠄⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠐⠀⠒⠐⠒⠒⠂⠈⠁⣀⣀⡤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠒⠂⠤⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠤⠤⠒⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⡞⡁⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⡸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠘⠗⠉⠉⢢⠀⠀⡔⠉⠉⠙⠓⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣼⠀⠀⠀⠀⠀⢠⣁⠀⡄⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⠒⣁⣀⣈⣙⡢⠄⢀⣤⡔⠁
⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡒⠾⠛⠉⠉⠉⠉⠉⠉⠁⠒⠙⠙⠛⠓⠒⢤⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡵⠉⠀⠀⡔⠈⡱⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⡇⠀⠀⢀⡜
⠀⠀⠀⠀⢸⡀⠀⡠⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠨⠤⠃⠀⠀⠘⠤⠃⢠⠁⣠⠴⠋⢀⣀
⠀⠀⠀⠀⠀⡏⠈⠀⠀⠀⠈⠁⠈⠉⠉⠢⣀⣀⠠⠛⡄⠀⠀⣖⠢⡀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠄⡰⢺⠻⡳⢌⡀
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠉⠀⠀⠀⠀⠰⡉⡦⠀⠀⡠⠊⠀⡎⠂⠱⣀⠈⠂
⠀⠀⠀⢖⠐⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠘⠂⠀⠈⠁⠁⠀⠘⠁⡲
⠀⠀⠀⠈⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠐⠀⠀⢀⢠⠄⠂⠀⠀⠀⠐⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣉⠐⡠⠉⠣⣀⣠⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠈⠠⠐⠈⠀⡤⡀⡀⢾⠀⠀⠀⠀⢠⠔⠋⠭⡑⢄⣀⠶⠒⠲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠂⠤⢀⢧⡀⠀⣠⠏⠀⠀⠀⠈⠠⠀⣤⠈⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠎⡃⢀⠉⠁⠀⢀⠂⠤⢤⡀⠀⠈⠉⠉⠀⠀⠀⠀⠩⠀⠀⠁⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠁⠂⠂⠀⢀⠀⠀⠉⢀⠀⠀⢀⠠⢤⡀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠡⠄⠁⠢⠴⣄⠀⠀⣈⠉⠀⠀⠈⠀⠠⠄⣀⢀⠀⠀⠂⠁⠑⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠠⠄⠉⠁⠰⠄⠑⠦⠐⢠⣤⠄⠀⠀⠀⠉⠛⠚⠳⠤⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠢⠄⠀⠑⠀⠂⠀⠀⠀⠀⠀⠒⠁⠠⠐⠛⠢⢄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠁⠀⠂⠃⠀⠀⡄⢀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠀⠀⠤⢍⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠀⣉⡽⠀⠙⢆⣀⠤⠖⠚⠉⠁⠀⡜⡡⠚⣩⠤⠚⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠉⠀⣤⠿⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⡴⠁⠀⢈⡠⠖⢉⣉⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣎⣰⢦⣼⠀⠀⡀⠀⠀⠈⣇⠀⠀⠀⠀⠉⠉⢉⠟⠀⠒⢉⣀⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⢶⣥⣤⣀⡈⠁⢀⣠⠬⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠙⠶⣥⣀⣀⡀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣈⠽⠛⢉⠠⠤⠤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠦⠤⣄⣀⣀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⢤⣄⡀⠀⠉⠐⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠲⠶⠦⣤⣭⣍⣉⣒⣒⣒⣒⠒⠒⠒⠂⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠭⠿⠶⣶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⣀⣀⣀⡀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⠂⠀⠀⠤⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠀⠉⠃⠀⠀⠈⠁⠀⠘⠦⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄⠀⠀⠀⢠⠀⢀⠀⠀⣴⠂⠀⠀⠀⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠆⠀⠁⡌⠌⠀⡆⡟⠀⠀⠃⣰⠃⡔⢰⡆⢠⡟⡰⢠⠆
⠀⠀⠀⠀⢈⠢⡳⡄⠀⠀⠀⠃⢰⡀⠀⠀⢰⠀⠃⠀⠀⡀⠁⠘⠀⠈⠁⠈⠃⢔⠕⠀⠀⠀⣠⢄⡤⠂
⠀⠀⠀⠀⠀⠑⢌⡪⠀⣼⠀⠀⢠⡇⠀⠀⢀⠀⠀⠀⣬⠇⠀⠀⡄⠀⠀⢸⠇⠈⠀⠀⡀⠊⢉⠡⠤⠄
⠀⠀⠠⠤⢔⡀⠄⠈⠀⣾⠀⠀⠘⢻⠀⠀⢻⡄⠀⠀⠻⡆⠀⠀⣹⠀⠀⡾⡆⠀⠀⣸⠇⠀⡀⠈⠍⠉
⠀⠀⠀⠠⠤⡤⠬⠀⢸⠋⡇⠀⢀⢸⠀⠀⠼⣇⠀⠐⢸⡇⠀⠀⠿⡆⠀⡇⡇⠀⢰⢻⠂⢀⣤⠍⡉⠉⠉⠒
⠀⠀⠀⣈⠤⠔⠂⠁⠀⡇⣇⠀⣸⢸⣀⡀⡇⣿⠤⠴⢸⡧⠤⢠⡀⣇⣀⡇⡇⠀⡄⣸⠀⠀⠀⠉⠒⠦⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠇⢻⠉⠿⠾⠆⠀⡄⢿⠀⢶⣼⡷⠀⠀⡇⡇⢀⣇⢯⠐⠇⡧⢄
⠀⠀⠀⠀⠀⠀⢠⠋⠠⣷⣾⠆⠀⠀⠀⢀⣇⣸⡀⠀⠀⠀⠀⣠⢇⣧⡈⠉⠉⡴⣴⣅⠀⢧
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠁⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠉⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢏⡴⢲⠀⣀⣀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣄⣠⣄⢀⣠⠤⣀⠀⢀⡖⠦⡼⢢⡷
⠀⠀⠀⠀⠀⠀⣴⡁⠀⠉⠁⠀⠑⠴⠚⠉⠀⠙⠢⠤⠞⠀⠁⠈⠉⠀⠀⡀⠑⠚⠃⠀⠀⣸⡷
⠀⠀⠀⣀⠤⠤⢻⠿⣖⠤⠄⣀⡖⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠙⡾⣤⣶⡶⠛⠹⣇⠈⠉⠉⠐⠢⢄
⠀⢠⣊⣀⠀⠀⢟⣄⠀⠉⠑⠋⠓⠒⠳⠽⣶⣖⣤⡤⡤⣤⣐⣖⡨⣧⠦⠂⠙⠀⠀⠀⠀⣠⣣⠇⠀⠀⢀⣀⡸
⡔⠉⠉⠁⢀⠀⠀⠙⠲⣶⡤⣀⣀⠀⠀⠀⠈⠉⠈⠋⠉⠛⠉⠉⠁⠀⠀⢀⣀⣠⣔⡶⠿⠋⠁⠀⠀⠀⠈⢉⡇
⠈⠙⠓⢞⠉⠀⠀⠀⠀⠀⠈⠉⠓⠙⠲⠶⢶⠶⢶⣶⢶⣶⠶⢶⠶⠻⠿⠛⠒⠉⠁⠀⠀⠀⠀⠀⢛⡷⠚⠉
⠀⠀⠀⠈⠙⠒⠲⣞⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⣠⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠦⠤⣤⣤⡤⢴⡖⠀⠀⣀⣠⣶⣀⣀⣀⣠⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⡀⠀⠀⠀⢠⡶⣄⠀⠀⠀⠀⣠⢶⡀⠀⠀⠀⢀⡴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⣷⠀⠀⠀⡟⠀⢸⡇⠀⠀⢸⡇⠀⢻⠀⠀⠀⣾⠁⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⠏⠀⠀⠀⠻⣤⡼⠁⠀⠀⠈⢧⣠⠟⠀⠀⠀⠹⣦⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠾⠷⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠾⠷⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⣤⣄⣀⣠⡴⠶⠶⣤⣀⣀⣠⠴⠦⣄⣀⣀⣤⠶⠶⢦⣄⣀⣠⣤⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⣄⣀⣀⣀⣠⠤⢤⣄⡉⠉⣁⣤⣤⣀⠉⢉⣠⡤⠤⣤⣀⣀⣀⣠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠋⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠁⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠻⣿⣯⣭⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣠⡾⢿⡏⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣼⡇⠀⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⠿⠟⠛⠋⠉⠉⠉⢉⣀⣰⡾⠻⢷⣄⣤⡾⠛⠻⣦⣀⠉⠉⠉⠉⠛⠛⠻⠿⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⢰⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⣴⠾⠛⠛⠛⣿⡀⠀⣸⡟⣿⡀⠀⠀⣿⠟⠛⠻⠷⣦⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡄
⠀⠀⠀⠀⠀⣼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣦⣤⣬⣿⣿⣋⣀⣈⣻⣷⣿⣯⣤⣴⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⢿⣿⡇
⠀⠀⠀⠀⠀⣾⣿⡇⠀⠉⠛⠻⠿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠿⠿⠟⠛⠉⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⠀⠀⠀⣸⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⣤⣴⣾⣿⡿⠃⠙⢿⣿⣶⣤⣤⣴⣾⣿⠟⠻⣿⣷⣤⣴⣾⣿⠟⠙⢿⣿⣷⣦⣤⣴⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⢸⣿⡇
⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⡀
⠀⠀⣼⣿⠟⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡿⠛⢿⣿⣦
⠀⠸⣿⣿⡀⠀⠈⠙⠻⢿⣿⣷⣶⣦⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⡿⠟⠋⠀⠀⢀⣿⣿⠁
⠀⠀⠙⢿⣿⣶⣤⣀⡀⠀⠈⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉⠀⠀⢀⣀⣤⣶⣿⡿⠃
⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣶⣶⣦⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣾⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡏⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠻⣆⠀⣠⠞⠉⡟⠀⠀⣠⢞⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠚⠛⠻⢿⣇⠀⣸⣇⡤⢚⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⠏⠉⠀⠙⠁⠴⠆⠙⠿⣿⣩⣾⣫⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⠒⠛⠛⠉⠉⠉⠉⠉⠁⠀⣠⡟⠙⠁⠘⠃⣠⡄⠀⠀⠺⠀⠉⣿⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠖⢀⠀⠀⠀⢠⡄⠀⠐⠇⠀⢹⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡥⠤⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⢶⡿⠃⢠⡄⠀⠉⡁⠀⠀⢈⡀⠀⠀⡦⢀⡾⠳⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠙⣧⣀⣤⡞⡋⠉⠀⠀⠀⠀⠈⢷⡆⠀⣤⠀⣀⣉⠀⠀⢈⡁⠀⢰⣤⠾⣧⣀⣀⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣿⣯⣍⣉⠉⠉⠓⠒⠶⠶⠤⣤⣍⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠉⠉⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⡇⠀⠈⠉⠛⠲⠶⠦⢤⣄⣀⡀⠈⠉⠙⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠦⠤⢤⣈⡉⠙⠓⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠤⣤⣄⣈⣙⣓⠲⠦⠤⠤⡤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢠⡏⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠓⠶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢳⣄⠀⠀⠀⠉⠛⠶⢦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⠻⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠓⠒⠒⠶⠶⠶⠦⢤⣤⣤⣀⣀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠻⢦⣀⣀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠛⠲⢦⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⢦⡄⠀⠀⠀⠀⠀⠈⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣤⣤⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣼⠁⠈⣇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣠⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⡿⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠛⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠛⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠒⠒⠒⠒⠒⠛⠛⠒⠒⠒⠒⠶⠦⠤⠤⢤⣤⣤⡤⠴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣟⣛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⢀⣼⣿⡿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⣿⡇⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣿⣤⣤⣼⣷⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⣀⣀⣠⣤⡿⠛⠛⢿⣦⣴⡟⠉⠙⢻⣦⣄⣀⣀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠉⠉⢹⣇⡀⢀⣼⡏⢿⣆⠀⠀⣸⡿⠉⠉⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣤⣤⣽⣿⣿⣋⣀⣈⣻⣿⣿⣿⣥⣤⣶⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠉⠛⠻⠿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⡿⠿⠟⠋⠁⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⡀⠀⠀⠀⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣶⣶⣶⣶⣿⣿⠟⠁⠙⢿⣿⣿⣶⣶⣶⣶⣿⣿⠟⠛⣿⣿⣶⣶⣶⣿⣿⠏⠈⠻⣿⣿⣶⣶⣶⣶⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⢸⣿⣿
⠀⠀⠀⠀⣠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀
⠀⠀⣠⣾⣿⡿⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡿⢿⣿⣷⡄
⠀⠀⣿⣿⡃⠀⠀⠙⠿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⠿⠋⠀⠀⢹⣿⣿
⠀⠀⠻⣿⣷⣤⣀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⣀⣤⣾⣿⠏
⠀⠀⠀⠈⠻⢿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣆⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣿⣿⣿⢏⣛⣛⣭⣾⡿⠟⢂⣰⠇⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⣿⠟⠛⢛⣡⣾⣿⣿⣿⡟⣴⣿⣿⣭⣾⣿⡁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡟⠻⢛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣷⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⣋⣴⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⠉⠛⠛⠛⢿⣯⣍⣙⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⠻⣶⣶⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠘⠿⠿⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⠶⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠳⠶⠶⢦⣤⣤⣀⣀⣀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠋