Cute text Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⡀⠀⠀⠀⠀⢸⣀⣼⢸⣣⢸⡽⣽⠘⡴⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠳⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⠸⡜⠈⣼⠀⡇⢠⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⡏⠐⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢼⢀⡀⢸⠀⢸⠀⣀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⠀⠸⠘⠃⠘⠀⠘⠂⠳⠊⠀⠀⢣⡐⣂⠎
⠀⠀⠀⠀⠁⠀⠄⠀⣔⠮⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀
⠀⠈⠀⠀⠀⠀⠀⡐⢬⡃⡀⠂⠀⠀⠀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠃⠀⡄⢀⣀⡀⠀⠰⡁⠀⢁⠘⠒⠏⠁⠀⠀⠀⠀⠀⠐⠯⠚⠀⡀
⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣄⡤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠁⠔⠀⠀⠀⠀⠸⠏⡟⣿⣇⣟⠂⠀⠀⠈
⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⣿⢻⣇⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣰
⠀⠀⠀⠘⠘⠋⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠘⠁⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠵⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠰⣀⠀⠀⠀⠀⠀⠀⠀⠪⢕
⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠒⠀⠀⣧⠠⡆⢹⡇⢸⡐⠒⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠊⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠈⠉⠉⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠈⠂⠀⠀⠀⠀⠑⠢⠤⠄⠄⠀⠀⠀⠀⠀⢀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣴⣉⠑⠀⢰⠁⠀⠀⢸⡇⠀⠀⠙⡆⠀⠀⠀⠀⡠⠖⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⣠⠀⢠⠈⠉⢧⠀⣿⡀⠀⢀⢾⣇⠀⢀⢾⡇⠀⠀⢠⠇⠀⠀⠀⢸⡇⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠈⢻⣆⠀⠀⢸⡆⣼⡇⠀⢸⠀⠈⠛⠂⠁⠀⠉⠉⠁⠀⠻⠦⠤⠊⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⢹⡆⠀⠈⠛⠀⢿⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⣇⠀⠀⠀⢀⠌
⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡇⣠⠊⠹⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢺⣦⠁⣿⠀⠀⢀⠿⣦⡀⡠⠂
⣇⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⣸⢡⡇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢲⡆⢀⣿⠃⠸⠇⠀⡟⠀⠀⡜⠀⠈⢿⡄
⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠥⣼⠀⢰⣇⠈⣆⡀⢠⡎⠉⠇⢸⡁⢀⣾⠀⢈⡿⠀⠀⠀⠀⣧⣀⠎⢀⠄⠀⠈⣿
⠀⠀⠁⠢⠤⣄⣀⠤⠄⠂⣽⠁⠀⣿⡀⠀⠉⢹⢻⠃⠸⣧⣀⡠⠏⠛⠁⠘⠧⠊⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠼⠉⠳⠤⠔⠃⣾⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠜
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠋⠃⠀⠀⣈⠁⠈⠁⠀⠀⠀⠀⠄⠝⢻⢯⡀⠀⠀⠀⣞⠹⢉⡆⠀⠀⠀⢀⣴⣤⢶⣶⡶⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⢰⣧⣾⣶⡇
⠀⠀⠀⠀⠐⢠⠘⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠓⠊⠙⠒⠁⠀⠀⢾⡏⠀⠙⣟⠃⠀⠀⢸⣿⡿⠒⠟⠀⠀⠀⠀⠈⠙⡓⠛⣿⠆⠀⠀⠘⠛⠛⠉⠃
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠁⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴
⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣄⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡍⣡⡐⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠦⢤⡀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠁⠉⠋⢘⠀⠀⠀⢘⡧⠰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠃⢠⣄⣉⠛⠛⠿⠆⠀⠀⠈⣯⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠈⠀⠀⠀⠈⠛⠋⠋⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠁⠀⠀⠄⠈⠉⠀⠀⠀⠉⠀⠈⠉⠉⠁⠉

⠀⠀⠀⣠⠀⠀⠀⢠⡄⠀⠀⠀⠀⠁⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣄⠀⠀⠀⢶⣤⡄
⠀⠀⠀⠫⡾⢂⠰⣶⠁⠀⠀⠀⠀⠊⠙⠒⠒⠀⠀⠀⠀⠀⠠⠀⠒⠠⠄⠀⠀⠀⠀⠐⢃⠀⠀⠀⢀⡐⠀⠀⠀⠻⠿⠃⠻⠿⠃⠀⠀⠸⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣄⣀⣀⣠⠀⠀⢀⣠⣤⣄⣀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠱⠀⠀⠀⣰⣶⣶⣶⡀
⠀⠀⠀⠘⠻⣿⡿⠟⠀⠀⠿⣿⣽⣽⣿⣧⠈⢣⣤⠀⣤⡈⠁⠀⠎⢥⡌⠳⠀⣠⡄⠰⣿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⠑⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠈⠁⠀⠈⠀⠀⠐⠃⠈⢵⠞⠀⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⣠⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠿⢿⣿⣿⣿⠛⠿⠿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⢋⣩⣾⣿⣿⠟⠛⠉⠀⠀⠀⠀⢸⣿⣿⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⢀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦
⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⣼⣿⡿⠁⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣀⡀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆
⠀⠀⣼⣿⡟⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⣰⠞⣩⣽⣿⣷⡄⠀⢸⣿⣿⠀⢀⡴⢋⣽⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⢠⣿⣿⠁⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⢸⡇⣼⣿⣟⠁⠈⣿⠀⣼⣿⡇⠀⣿⢠⣿⣿⡇⠀⢘⡟⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠸⣿⣿⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⣧⣿⣿⣿⣶⣶⡟⢠⣿⣿⠁⠀⠻⣜⣿⣿⣿⣶⣿⠇⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⢻⣿⣷⣄⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠋⣠⣿⣿⠇⠀⠀⠀⠉⠛⠿⠟⠛⠁⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⢀⣠⣾⣿⠏
⠀⠀⠀⠙⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⣀⣀⣤⣤⣴⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⢀⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⢿⣿⣷⣤⣀⣀⣀⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠀⢸⣿⡿⠿⢿⣿⣿⢿⣿⣿⠀⠀⠀⢀⣠⣴⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣼⣿⣿⠀⠀⠀⠀⣸⣿⣿⣤⣶⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣦⡀⢀⣰⣿⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢀⡀⢀⡈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠸⡝⣿⠃⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣶⠀⢸⡇⢰⠶⣶⠀⣶⡀⠀⢰⡆⢰⡟⠒⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣿⣄⣼⡇⣿⠀⣿⠀⣿⣧⢠⡿⡇⢸⣇⡀⠀⠀⠈⠳⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢸⡇⣿⠀⣿⠀⣿⢸⡿⢸⡇⢸⡏⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⢸⡇⠙⢷⠟⠸⣯⠀⠀⠸⡇⢻⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄⡀⠀⢀⣤⠀⠀⣰⠆⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠜⠁⠐⢞⡋⠺⠯⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢠⡆⣠⠀⡄⣰⡾⢂⣾⠗⣰⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣠⠇⠺⠀⣿⡰⠉⢿⡤⠸⣧⢜⡟⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⡀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⣼⠋⣿⠀⣿⡆⠀⣸⡏⢻⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⢾⡇⣿⠀⣿⠀⣿⢷⣰⢟⡇⢸⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⣿⣄⣿⢀⡿⠘⠟⢸⡇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠸⠃⠈⠛⠋⠈⠗⠀⠀⠘⠇⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⣠⣤⣤⣤⣀⣾⠷⠶⢶⡀⢠⣶⠶⠶⠞⠛⢻⣇⣴⠟⠋⠙⠛⢻⣶⡟⠛⠛⠛⣻⡷⠀⣠⣤⣤⣤⠀⣠⡾⠛⠛⠛⣷⠀⢀⣴⡟⠉⣩⣽
⠀⠀⣰⡏⠀⠀⠈⠻⠁⠀⠀⠘⣧⡟⣷⠀⠀⠰⣶⡞⣿⠻⣄⣀⠀⠛⢯⣯⠛⠒⣆⠀⠛⢷⡾⠏⢀⡀⠘⣿⣿⠀⢠⢞⡿⠿⠶⣾⠋⡇⠀⠙⢹
⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢿⠀⠀⢠⣾⣧⣿⣦⠶⠞⠃⠀⢠⣿⡗⠒⠋⠀⠀⡼⡿⠀⠈⠉⠀⢿⣿⡀⠈⠋⡁⠀⣀⣾⠀⡇⠀⠺⠿
⢠⣿⡏⠀⠀⢠⠶⣀⣰⢷⣄⣀⣀⣹⣾⣀⣀⣀⣀⣸⡇⢿⣀⣀⣀⣤⣾⠹⣇⣀⣀⣤⣾⠱⣧⣤⡾⠳⣄⣼⡇⠙⠲⠚⢷⣬⡏⣿⠀⣇⣀⣀⣀
⣼⠉⠉⠉⠉⠋⣀⠉⠁⣀⡉⠀⣀⣸⣏⣉⣉⣉⣹⠿⣧⣀⣉⣩⡼⠛⣧⣀⣀⣀⣤⠾⢿⣤⣤⡾⠳⠶⠶⠞⠛⠒⠻⢦⣴⠟⠀⠛⠶⠮⠥⠴⠟
⠙⠛⠲⠶⠶⠞⠉⠓⢺⡏⠙⠛⠉⠁⠉⠉⠉⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢀⣴⠟⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢀⣀⡀⠀⣨⣧⣀⣀⠀⢀⣀⣀⣤⣤⣤⢤⡄⢠⡴⠶⠶⠦⣤⣀⣤⠴⠶⠶⢶⡄⠀⠀⠀⠀⠀⠀⢀⣠⠶⠶⠿⣆⠀⠀⣠⡴⠖⠒⢶
⠀⠀⢠⡟⠋⠉⠻⣾⠋⠉⠉⢻⣆⡼⡏⠀⠀⢠⣤⣼⣷⣿⠀⠀⠀⣤⣾⡟⣧⣤⡀⠀⢾⣇⣴⡟⠛⠛⢻⣤⣿⠃⢀⡴⣤⣿⣀⣴⠿⠀⠐⠿⢿
⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣧⠀⠀⢈⣹⡇⣿⣈⣛⣳⠄⠀⢹⣿⣤⣤⠗⠀⠀⣿⣹⠀⠸⠇⠀⣿⣯⠀⠸⠼⠃⠉⠉⣿⠀⡇⠀⣤⣾
⢀⣿⡟⠀⠀⢀⣄⠀⢠⣄⠀⠀⠈⣧⣿⠀⠀⠘⠛⢻⡏⣏⠀⠀⠀⢀⣼⢿⠀⠀⠀⢀⡴⢫⡇⠀⣴⣄⠀⢹⡝⢦⣄⡴⣆⢰⡿⣿⢠⠁⠀⠈⠉
⣸⠻⠷⠶⠦⠞⠉⠷⠋⠘⠓⠚⠛⢻⡟⠒⠒⠒⢶⣾⡇⠙⠒⠒⣺⢿⡏⠈⠛⠛⢛⣹⣇⠈⢉⣽⣥⣈⣉⣿⢧⣤⣤⣀⣉⣿⠁⢿⣜⣓⣒⣲⡾
⠿⣤⣤⣄⣀⣴⠿⣤⣴⣿⡶⠴⠶⠛⠳⠶⠒⠚⠛⠉⠛⠛⠛⠛⠁⠀⠙⠒⠛⠛⠋⠁⠙⠛⠋⠁⠀⠉⠉⠀⠀⠀⠀⠉⠉⣿⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣤⣤⠤⠶⠶⢶⣤⡀⠀⠀⠀⠀⢠⣶⠶⠶⠶⠖⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣹⣧

⠀⠀⠀⠀⠀⠔⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⢂⡠⠒⠀⠀⠀⠀⠀⠀⢀⠐⠢⢀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠬⠭⠤⠥⠤⠤⠤⠤⠤⠤⠤⠴⠮⠤⠬⠶⠤⠵⠤⣤⡀
⠀⠀⠀⠀⠈⢇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢶⠀⢀⢾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⡀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠜
⠀⠀⠀⠀⠀⡞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡈⢀
⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡜
⠀⠀⠀⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⡧⢾⠀⠀⣠⠤⠄⠀⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠼⣆⠀⠀⠷⠚⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⡇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⡀⠀⠀⢀⠠⠤⠀⠀⠤⢀⡀⠀⡀⠀⠀⠀⠀⢄⠈⠑⠀⠠⠀⠊⠁⠀⡜⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠸⠤⠤⠄⠀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠤⠤⣤⣤⣤⣄⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⢀⣀⠆⠁⡠⠞⠉⠉⠉⠛⢿⡟⠳⢍⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡡⠤⣄⣀⣠⠞⠉⠉⠉⠋⠀⠀⠀⠀⠀⡀⠀⢳⣄⠀⠉⠶⣌⠑⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢰⠃⠀⠀⣌⡉⠁⠀⠀⠀⠐⢦⠀⠀⠀⠀⠂⠹⠀⠈⠾⣤⠤⠤⣌⢷⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠑⠀⠀⠀⢸⠂⠛⣦⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠰⠓⠉⠁⠀⢀⡀⠄⠀⠀⠘⠇⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⣈⢄⠀⠘⣧⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⡆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡴⣳⠤⢀⣀⢀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠃⡀⠙⢦⡘⣧⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⡇⠀⠋⠀⡠⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⢸⢉⠓⠪⡢⡀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠈⣷⣿⠄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠜⠁⠀⠀⠉⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢸⠸⡇⢀⠟⠄⠀⠀⠀⠀⠀⠠⢲⠀⠀⢀⡿⠈⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⡷⠀⠀⢀⡀⠀⠀⠀⠀⢠⣇⠀⢠⡆⠀⡀⠀⠈⠂⢣⠈⡆⠈⠗⣤⠀⠀⠀⠐⠁⢀⡴⠋⠀⢘⣷⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡉⢧⡀⠀⡀⠈⠂⠀⠀⠀⠘⡧⠀⠀⠉⠁⡆⠀⠀⠀⠰⢕⣿⣀⡼⠁⠀⠀⠀⠀⠰⡏⠀⠠⠀⢸⡟⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⢷⠀⠙⠉⠀⠀⠀⡀⠀⠱⡀⠀⠀⠤⠅⠀⠣⠤⠀⠀⢨⡿⠀⠀⡞⠂⠀⠀⠀⠙⢦⠀⠀⢸⢧⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠂⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⠀⢤⣀⠀⠀⢀⣀⣠⣨⠟⠁⠀⠀⠀⠀⠀⠀⠤⡄⠀⠁⢘⢿⡏⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠍⠽⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⢾⢮⢏⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡱⢤⣤⡀⠀⠀⠀⠀⠀⠀⠰⡂⠀⠀⢀⠀⠦⠀⠀⠀⠀⠀⠘⠁⠀⢀⡤⢶⠋⢠⠆⢫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠈⠹⡆⠀⠀⠤⠄⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⢠⠖⠒⠲⣄⢠⡟⠁⢸⡖⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠱⡀⠑⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⢅⡀⢁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣓⣂⠙⠲⣄⠀⠀⠀⠀⠀⣠⠴⠒⠚⠳⣇⣄⣀⡀⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠬⢓⣷⣶⡶⣊⣴⣡⡤⠴⠶⠚⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣤⠠⡄⠤⢀⡄⠀⢐⠠⡄⠄⠠⠆⣄⢠⠐⠆⠆⢠⠀⠀⠆⠐⠰⠀⢘⢣⠀⡄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄⣸⢸⠁⡏⠈⠁⠀⣦⢠⡃⡀⠘⠀⡇⢸⠀⡇⡇⢘⢁⡀⡃⠀⠘⡀⠘⠸⢀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠓⠈⠂⠁⠈⠀⠁⠁⠈⠈⠁⠃⠀⠐⠀⠘⠁⠈⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⢸⠀⠐⠐⠒⠒⠴⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡡⠀⠀⠀⡀⠀⠀⢄⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡄⠠⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⢄⠀⠀⠀⢰⡀⠀⠀⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠴⠖⠒⠶⠦⢤⡀⠀⠀⠜⢄⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⢁⠀⡠⠞⠋⠙⢢⡀⠙⠄⠀⠀⠈⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠁⢀⠀⠀⠀⠁⡀⠀⠀⠀⠈⠀⠀⠔⠁⠀⠀⠀⠀⠀⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢠⡀⠀⠀⠂⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠐⡄⠀⠀⠀⢀⠴⠂⠀⠀⠀⢦⡀⠀⠀⠘⠲⠤⠤⡂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⡴⠁⠢⠀⢄⡀⠄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡀⠂
⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠁⠀⢀⠄⠀⠀⠀⠀⠠⠂⠠⠀⠀⢸⠀⠀⠀⠐⠊⠀⠀⠐⢡⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⠒⠈⢡⠎⠀⠀⡀⠀⠰⡄⠀⠀⠀⠀⢂⠀⠀⠠⠀⠀⠀⠀⠘⡀⠄⠈⠀⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣿⠀⠀⡜⠀⠀⠀⣇⠀⠀⢠⠀⠀⢣⠀⠀⢲⠂⠀⠀⠀⠀⡐⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠧⠄⠀⠁⠐⠀⡇⠀⠀⠁⠀⠀⠀⠈⢀⠀⠀⠑⡄⠈⡇⠀⠊⠀⠰⠀⠈⠐⠃⠃⠈⡉⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡇⠀⠀⣅⠀⠀⠀⠀⠀⠱⡀⠀⡈⠀⢣⠀⠀⠀⠐⠒⠂⢒⠂⠀⠁⠓⠊⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠉⣀⡎⠘⡀⡄⠆⠞⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠀⠻⡄⠀⠀⢀⣀⠀⠀⢸⡏⠈⣷⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⢰⡏⠉⠻⣦⣸⡇⠀⢸⣷⠟⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠘⣿⡇⠀⣼⠏⠀⢀⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣠⡴⠆
⠀⠀⠀⠀⠀⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⢠⡶⠛⠳⢿⣦⡀⢸⡇⢰⡟⢀⣴⣟⣁⣤⣤⣿⣤⣄⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⠀⠀⠈⠻⣦⣿⣿⡶⠟⢋⣽⠟⠁⣿⠉⠛⠻⢯⣝⠻⢶⣄⢀⣴⠆⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⠉⢛⣻⣿⢿⣿⠟⠁⠀⠀⠈⠁⠀⠀⠛⠀⠀⠀⠀⠉⠳⡄⠙⢿⡁
⠀⠀⠀⠀⠀⠀⠀⢤⡀⣀⣼⣧⣀⡀⠀⠀⠀⣴⠛⠁⣠⡿⠃⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢲⣄⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠁⠀⠉⠻⣾⠃⠀⠻⠶⠞⣿⠃⣠⣶⡟⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠛⠀⠀⠀⣼⠟⠉⠙⣿⠋
⠀⠀⠀⠀⠀⢠⣤⣾⠁⠀⠀⠀⠀⠀⠸⣧⠀⠀⢀⣰⡏⠘⠁⣾⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡗⠀⣿⠀⠀⣄⣸⠇⠀⣀⠀⢸⣇⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢿⡀⠀⠀⣹⠃⠀⠀⣿⠀⠈⣷⣀⠀⠀⣠⣶⡄⢿⣠⣤⡀⢸⣆⣼⠃⠀⣿⠀⠀⠈⣿⠀⠀⠿⠀⢸⡏⠁
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢤⣿⠀⠀⠀⣿⠀⠀⣿⠙⣧⢰⡏⢸⡇⢸⡏⠈⣷⢸⡿⣇⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⣇⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣶⠀⠀⠀⡀⠀⠸⣇⠀⠀⣿⠀⠀⠀⣿⠀⠀⡿⠀⣿⠸⣧⡾⢿⡘⠇⠀⡿⢸⠇⢹⡆⠀⣿⠀⠀⣾⠁⢠⡆⠀⠀⣾⠉⠉
⠀⠀⠀⠀⠀⣤⢿⡄⠀⠙⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⠇⠀⣿⠀⣸⠏⠀⠈⠁⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣿⡀⠀⠀⠀⣶⠀⢰⡇⢠⡶⠛⢶⡀⣰⠆⠀⣴⠀⠀⠀⠀⢀⣿⠞⠋⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢰⡆⠀⠀⠀⠀⢿⡄⢻⡇⠀⠀⠀⣿⠀⠸⡇⢸⡇⠀⢸⡇⣿⠀⢀⣿⠀⠀⠀⠀⢸⡿⠶⣤⣤⣤⡴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⢻⡄⠀⣷⠈⠷⠶⠞⠁⢻⣄⣼⣧⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⣤⣤⣤⣤⠾⣿⠀⠀⠀⠈⠛⠺⣿⠀⠀⢀⡴⣤⠶⣭⠁⠈⠓⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⡿⠀⠀⠀⢸⡇⠀⡿⠟⢷⡄⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⢀⣀⣤⠶⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣦⣤⠾⠁⠀⠀⠀⢸⡇⣀⣤⡶⠟⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀
⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣠⠀⠀⠀⠀⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠓⠓⠺⠷⠶⠶⠶⠶⠳⠛⠛⣿⠃⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢰⡟⠀⠀⢀⣀⣀⣿⣤⣤⡤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⢤⣤⣤⣼⣧⣤⣀⣀⡀⠀⠀⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠾⠀⠀⠀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢤⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣼⡟⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣠⡄⠀⠀⢰⡿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⠃
⠀⠀⠀⠀⠀⠀⠿⢿⣿⡟⠛⠃⠀⠀⣾⠃⡼⠃⠀⠀⠀⠀⣀⣀⣠⣤⠀⠀⣤⡀⢀⣀⡀⠀⠀⣸⣿⠵⠶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢠⣿⣾⣴⣶⡄⠀⢠⡾⠋⠙⣿⣿⠀⠀⣿⡿⠛⢻⣿⠀⠀⣿⣥⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣾⡏⠀⠀⣿⡇⢀⣿⠁⠀⣰⣿⣿⠀⠀⣿⡇⠀⢰⣿⠀⢠⣿⠃⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣠⣾⠟⣿⡇⠀⠀⣿⣃⣾⣿⣄⣴⡿⢻⣿⣦⡾⣿⡇⠀⢸⣿⣴⣿⣿⠀⠀⣿⣧⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠁⠰⠿⠇⠀⠀⠿⠟⠁⠉⠛⠋⠀⠈⠛⠋⠀⠻⠃⠀⠀⠛⠁⠿⠟⠀⠀⠘⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⢰⣦⠀⠀⢀⣤⣶⣤⣀⠔⢲⣦⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⡿⠀⢠⡟⠀⠛⢻⡿⠀⣾⠇⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⢀⣿⡁⠀⢀⣾⠇⢠⣿⠀⣰⢿⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠾⣿⣷⠟⠻⣷⣶⠿⠋⠀⠘⣷⡾⠋⠈⣿⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣀⠁⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠢⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠉⠉⠁⠹⠖⠂⢤⡀⠀⠀⠀⠀⠀⠀⠠⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠑⢦⣀⡤⠞⠉⠱⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠰⡎⢀⡠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠖⠳⠎⠀⢠⠈⠑⠲⠦⢤⣤⡤⢀⠀⢤⡤⢤⡄⠀⠐⣠⡿⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠐⣇⡠⡏⠀⠀⢸⠃⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⡜⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣤⣤⡤⠾⣴⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠉⠁⠀⢀⡜⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠙⢧⡀⠀⠒⠒⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠉⢰
⡀⠀⠀⣠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡐⠰⠆
⠀⠀⢠⡼⠆⠀⠀⡀⠀⠀⠀⢀⡀⠂⠀⠠⠤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠄⢠⡇⠀⠀⠈⠉⠀⠀⢀
⠈⠁⢠⡜⡀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠲⠲⢤⣌⣉⠒⠠⣄⣀⡙⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⣀⠠⠤⠒⣊⣤⠖⠁⠙⢦⣀⠀⠀⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠤⣌⣉⠓⠚⠛⡿⠛⠛⠛⣿⠟⠛⠛⠉⢀⣀⣀⣀⠠⠤⠔⠒⠊⠉⠀⠀⠀⠀⠀⠈⠁⠘⠧⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡙⠀⠈⠙⠉⠁⠴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠒⠒⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⢀⣀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⠏⠀⢰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⠦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠲⠶⠶⠶⠺⠟⠋⠁⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⢀⡁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⢨
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠆⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣐⠀⣀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠆⠀⠀⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠡⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠰⠁⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠠⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠉⠒⠢⣄⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣀⠖⠒⠉⠉⠉⠁⠒⠢⢌⡄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠔⠁⠈⢀⡀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣽⠢⠀⠑⢄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡇⠀⠀⡤⠀⠀⠤⠄⢀⣠⣾⡇⠀⠀⠀⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠻⣿⣶⡶⠿⠛⢻⡟⠀⠀⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠉⠻⠄⠀⠔⠋⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠶⠤⠤⠤⡤⣤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⢠⠃
⡄⠀⠀⠀⠀⠀⠀⡀⢀⡀⠠⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⡎
⠱⡀⠀⠀⠢⡀⠀⠀⠀⠀⠑⠀⠀⢄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠘⢎⠀⠀⠈⠂⡤⢆⠀⠀⣀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠑⠦⡀⠄⠀⠀⡀⠀⠀⠁⠂⠤⣀⠈⠢⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠁⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠒⠦⠤⡄⠀⠀⠀⠀⠀⠀⠈⠶⠥⣄⠀⠀⠀⠢⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢄⠀⠀⠈⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡸⠁⣀⠀⠀⣀⠜⠀⠀⠈⠢⣀⠌⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⢠⠤⡀⢠⠙⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⣼⡀⠀⣬⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢩⠀⣠⠚⣣
⡇⠘⡁⠀⢷⠄⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣈⠷⠁⡰⠉
⠃⡀⠀⠀⠠⠠⣤⣄⣡⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣴⡇⠀⠛⠀⠼⠁⠀⢀
⠀⢡⠀⠀⠀⠀⠀⠈⠁⢠⠄⠼⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠈⠡⠀⢀⣀⣠⡀⣠⡀⠀⠀⠀⠀⠀⠙⠶⣀⠈⠃⠀⠀⠀⠀⠐⠂⡀
⠀⠀⠳⣀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠛⠀⠀⠋⠀⠀⠠⠟⠀⢹⠀⠀⠀⠀⠀⠀⠀⣹⠀⠘⠳⠄⠀⢀⡔⠦⢀
⠀⠀⠀⠈⠛⡦⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⣄⡀⠀⠀⠘⢦⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⢰⡄⠸⣧⠀⠀⠀⠀⠀⠀⠀⢴⣆⢀⣀⠠⡤⣤⢤⡄⣀⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⠌⠁⠀⠖⠋
⠀⠀⠀⠀⠀⠘⡇⠀⢹⡆⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠻⣄⠀⠀⠀⣰⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⢀⡤⠊⠁⠀⢀⣄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠙⠀⠀⣴⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠈⣦⠀⣀⣧⣠⠛⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⡆⠀⠀⣄⢠⡜⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⢨⡏⠀⠀⠀⠀⠀⠀⠐⠀⠈⠃⠀⠀⣀⡤⠞⣋⠀⠀⠀⢰⠀⠀⣿⡏⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡘⠁⠀⠀⠀⣤⣄⠤⡤⢤⣤⡤⠚⠛⠉⢀⣴⡿⠀⠀⠀⠘⠓⣤⣿⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⡇⠀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣀⣤⡴⠾⢿⣿⠃⠀⠀⢠⣄⢀⡼⠋⠙⢶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢠⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⢋⣀⣀⣀⣼⠃⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⢣⠀⠀⠀⠀⠙⢿⣟⠉⠀⠀⣀⡤⠏⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠷⣀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡶⠛⠉⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⡏⠉⠉⠉⠉⠉⠀⠲⠶⠒⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠶⡶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠉⠠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⢀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠉⠉⠉⢛⠉⠉⠀⠘⠒⠒⣶⠶⠤⣤⣤⣤⡤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠸⠃⠀⠀⠀⠀⠀⠘⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡆⠀⠀⠀⠀⠀⠀⢀⡦⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠉⠉⡷⠀⠀⠀⠀⣀⡤⠋⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⢿⡀⢠⡄⠒⠉⠀⠀⠀⢀⢼⡇
⠀⠐⠋⣀⠀⠁⠙⣀⠀⠀⠀⠀⢀⡼⠶⠊⠙⠂⡀⠀⠀⠀⠀⡰⠃⢠⠃
⠀⠈⠲⠄⣀⣉⣉⣉⣉⣉⠉⣰⠛⠤⢀⡀⠀⠀⢡⡄⢀⣀⠐⠷⢀⡙⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣠⣤⣤⣤⣬⣥⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⠻⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠲⣄⠀⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⡀⠀⢨⡛⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠓⢄⠀⣧⡉⣷⣾⣧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢸⠀⠘⢳⡆⠀⣤⣿⡇⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢆⢸⣸⣧⡰⡶⣏⣳⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠠⣄⣦⢀⡈⢦⣀⣨⣯⣿⣯⣿⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⣻⡄⡤⣀⣻⢿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣤⡟⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⢈⣷⣠⣿⣴⣤⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣀⠀⣤⣦⣤⣠⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⢦⡈⡷⡄⣾⡰⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋⠙⡷⣧⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢤⡴⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⣛⢦⣠⣾⣮⣭⣭⣚⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⡾⠛⣹⡟⣿⠙⡟⢟⠻⢿⣶⣦⣍⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠴⠊⠀⢀⡠⣄⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣴⣿⣏⣠⠞⢁⢣⠃⡧⠇⡈⠇⢀⣿⠻⣷⣍⠺⣾⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢯⡀⠀⠋⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⢾⡟⣿⡞⢏⡡⠞⠻⠽⠀⠈⠳⠃⠈⠋⣄⠈⠻⣳⣜⢷⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡏⣾⢡⣹⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠙⣿⠻⣧⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⢠⡏⢸⡇⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠈⠁⠀⡴⣂⠀⢹⡀⢻⡄⡇⠀⠀⠀⠀⠀⠀⡴⠉⠙⣦⠤⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⢨⠱⣾⠇⢠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⢸⡇⢸⢷⢸⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⢸⠀⣿⡀⠸⣌⡸⠀⠀⠀⢄⠀⠀⠀⢀⡆⠀⠀⠀⣠⡇⢠⣸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠙⣄⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠘⣠⡿⡏⠲⣀⠀⠀⠀⠀⠈⠓⠶⠖⠋⠀⠀⣠⠞⠁⡇⢸⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⣦⣿⠁⡇⠀⠀⠉⠒⠤⣤⣀⣀⣀⢠⡤⠲⣿⡁⠀⠀⠘⠮⣷⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⡏⠀⠀⠀⢀⠴⠊⣿⠀⢀⡠⠴⠳⣄⣷⠙⠦⣀⠀⠀⠈⡶⢻⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡇⣿⡀⠀⠈⠳⠦⣼⣿⡦⠋⠀⠀⠀⠀⢹⡏⠓⠚⠉⠀⠀⡇⢀⠱⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⡇⡇⠀⠀⠀⢀⠇⡇⢥⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⡦⠈⢆⡃⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢸⣵⠃⠇⠀⠀⢀⡌⢸⠀⠸⡄⠀⠀⠀⠀⡟⢨⢣⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡜⢀⠇⠀⠀⠹⣀⣤⣄⣼⠁⢸⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⡜⠀⠀⠀⠀⡟⠟⠻⠿⠆⢸⡀⠂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⡄⢰⢠⣏⠟⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠰⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠆⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⠶⡄⣄⠇⠈⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠖⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠚⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢧⣠⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⠈⠤⠵⠮⢤⣶⠦⢤⣀⠀⠀⠀⠀⣀⣀⣀⣀⠾⠤⣀⣁⣠⡇⠀⠀⠀⠀⠀⠀⣀⣧⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠈⠉⠉⠉⠉⠀⠈⠙⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠼⠁



⣿⣿⡿⠿⣿⡿⢿⢿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣵⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢚⠉⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡟⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣄⣀⣀⡾⠀⠟⣴⣿⣯⠤⢤⣄
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠛⠛⢻⣄⠀⢉⣡⠀⢀⡶⢸⠏⢀⡶⢀⡟⠻⣦
⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⣶⣿⠇⣼⠟⠛⠛⡇⠀⠚⠁⡄⠀⢨⣴⠿⢃⣴⣿⠁
⠀⠀⠀⠀⠀⢸⣇⢠⣾⣟⣡⡏⣸⠏⢀⣴⣿⣷⣤⣴⣾⣿⣤⣤⣴⣾⣿⣟⣡⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣻⠟⠋⠉⠉⣀⠉⣀⠛⢁⣴⠀⣸⠃⢈⡤⢀⡉⠀⣡⠄⢈⠁⢀⡟⠀⣾⣇⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣤⣴⠞⠀⣿⠀⡟⠀⠰⠃⢰⡏⢠⡿⠃⢨⠁⣼⠟⠀⡍⠀⠞⠀⠘⣉⠀⠉⣿⡄
⠀⠀⠀⠀⣿⠙⠶⠟⠋⠀⣸⡇⠀⢿⣤⣴⣦⡔⠁⣦⣤⣶⠇⢰⣤⣴⣾⣧⣴⠎⣰⣿⠟⠻⢷⣿⠇
⠀⠀⠀⠀⠹⣷⣄⣀⣠⣾⣿⣧⣀⣀⣿⡍⡿⠀⢸⣿⢉⡏⠀⣿⠃⠘⠷⠟⠃⣰⣿⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠙⠛⠛⠋⠘⣷⣤⣿⠇⣿⣄⣰⣿⣆⣀⣀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠋⠙⠛⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⡠⠖⢚⣉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡴⠀⢠⡄⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠖⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠰⠁⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆⠀⣀⣤⡀⠀⠈⢦⠈⢢⡀
⠀⠁⠀⠀⠀⢿⡉⢢⡀⠀⣠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠾⠷⠄⠀⠠⡶⠿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⢠⣇⡼⠋⣰⠃⠀⠀⠀⢧⠀⢳
⠀⠀⠰⣟⠓⢮⣳⣄⠱⣼⡇⣠⠏⠀⠀⠀⠀⠀⠀⢀⡾⣫⡴⠆⠀⠀⠀⠀⠀⠀⠀⣀⡉⠻⣆⠀⠀⠀⠀⠀⣞⢉⣉⡙⢿⣄⠀⠀⢾⡥⠶⣦⠀⠀⢸
⠀⠀⠀⠈⠓⢄⡙⠁⣠⠟⠁⢳⡀⠀⠀⠀⠀⠀⠀⣸⠇⢁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡦⠹⣧⠀⠀⠀⠀⠉⠁⠀⡝⠀⠈⢷⠀⠀⡤⠖⠋⠀⠀⢸
⠀⠀⠰⣏⣉⣈⡁⠰⠃⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠙⢦⣄⡀⠀⠀⢀⣠⡴⠛⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⠁⣤⣉⣱⡄⠀⠀⠏
⠀⠀⠀⠀⢠⠞⣡⣄⣀⣀⣄⠙⢦⡀⠀⠀⠀⠀⣠⣿⡀⢸⣇⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⣿⠀⢸⡷⣤⡀⠀⠀⠀⣰⠋⢠⡷⠒⠋⠁⠈⠉
⠀⠀⠀⠀⠘⠋⠀⠈⠉⠉⠈⠳⣄⠙⢦⡀⠀⠀⣧⣂⡀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⢀⣀⣸⠇⠀⢠⡞⢁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⢦⠀⠈⣿⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⠀⠀⣿⠁⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠳⢄⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣠⠞⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠈⢧⡈⠉⠙⠛⠛⢛⡿⠃⠀⠀⠀⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⡀⠈⠻⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠙⢦⣀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠦⣄⣀⠉⠛⠛⠛⠋⠁⠀⣀⣠⡴⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣤⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢦⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣀⣼⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢷⡀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠀⠀⢀⣠⠶⠛⠙⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠙⢦⡀⠀⣠⠏⣹⠛⠻⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⢻⡙⢦⣀⡴⠋⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⠲⠋⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡉⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠿⠛⠻⠟⠛⠿⠿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⡥⠄⠀⠀⠀⠀⠀⢤⡀⠈⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠘⣿⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠀⠀⣾⣷⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡐⠀⠀⢀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⡤⢴⠆⠀⠀⠠⠂⠀⠀⡠⠀⠁⣮⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢌⣀⣠⡔⢈⡀⠠⣤⠐⠈⢀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⢹⣧⣼⡷⠀⠀⠀⣿⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠠⠐⢻⡀⠀⠀⠀⠙⠈⠁⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣂⠁⠀⢀⠠⠀⠐⠛⠊⡇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠑⠂⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠇⠀⢉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠰⠀⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡻⣽⣷⠇⠀⠀⠀⣷⣿⣫⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⡻⠃⠀⠀⠀⠀⠘⠿⠿⠛⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣿⣿⣿⣻⣿⣛⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣠⡄⠀⢠⣄⠀⠀⢠⣄⠀⡀⠀⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⠟⢻⣿⡿⢻⣿⣿⡟⢻⣿⣿⣿⠟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⢿⠇⠀⠸⡿⠀⠀⠈⢿⠄⠀⠀⢿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣀⣿⣿⣀⣸⣿⣇⣸⣿⣿⣿⣀⣿⣿⣿⣂⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄⠀⢠⣤⣤⣤⡄⠀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣏⣿⣿⡇⠈⢹⣿⣿⠁⣾⣿⡟⢛⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⢿⣿⣷⠀⢸⣿⣿⠀⣿⣿⡇⠻⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⢱⣿⣿⣿⡇⠙⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡴⠘⣦⢀⡸⡄⣀⣠⡆⠘⢶⡄⠀⣿⢤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢋⣿⠙⡿⣇⣿⣿⡟⣹⣧⡛⢻⣿⠀⡛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡇⢰⡟⢸⡇⠀⢸⡏⠓⠂⣸⡇⢠⣿⢸⡁⣶⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣸⣿⢠⡇⢸⣿⡇⢰⣮⣽⡇⣼⡟⢰⡇⣾⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠂⠀⠈⠃⠀⠀⠘⠂⠈⠋⠘⠃⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣷⣼⣿⣿⣧⣿⣷⣼⣧⣽⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢠⣿⡇⣿⡿⢷⣄⢸⡿⢷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣿⣿⡿⠠⢸⠁⢀⡉⢻⡇⢀⡈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢀⣿⣿⡇⣿⡇⢈⣿⢾⡇⠈⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣿⡿⠁⠀⢸⠀⢸⣷⠀⡇⢸⣷⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⠀⣾⣧⣿⡇⣿⣧⣾⠋⢸⡇⢀⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠘⠋⡀⣿⠣⠘⢀⢸⢇⠘⠁⣴⡇⢸⡿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠏⠈⠿⠼⠏⠀⠿⠇⠿⠏⠻⠦⠸⠿⠟⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⣸⣷⣀⣃⣰⣿⣀⣸⣀⣸⣄⣹⣇⣊⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⠀⠀⠀⢱⣠⠔⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠠⠙⡄⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣄⠐⢀⡜⠁⠄⠀⢀⠀⠀⡇⠀⠀⠀⠘⢆⠀⠀⠀⢸⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⢿⠟⣻⠟⡝⡟⢷⣶⣤⣀⣀⠞⠁⠀⢀⠀⠀⠈⠧⠀⠀⢈⣀⡀⠈⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠋⢀⡬⠐⠋⠘⠁⠁⠀⠐⠦⠙⢷⣦⣀⠀⠈⠙⠂⠀⡠⠚⠉⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⣡⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⣯⡣⡀⠒⠀⡼⠁⣰⠃⠀⠁⠀⠀⠀⢳⠐⠚
⠀⠀⠀⠀⠀⠀⠐⠟⡴⢡⣇⠛⠀⡀⠀⠀⠀⠐⠂⠀⠈⠀⢀⠀⠛⢸⣻⡷⣵⡀⠀⠱⡀⠹⣄⣀⣀⡤⠀⢠⠏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠹⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢀⠏⠀⠇⠻⠁⠀⠀⣹⢶⠤⢍⡭⠤⠖⠁⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠑⠦⢄⣀⣀⡠⠴⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠜⠃⠀⣀⠀⢰⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠦⠤⠤⠤⠤⠔⠚⢿⢄⡀⠀⠀⣀⢀⡠⠊⠁⠀⠀⠀⡇⠀⠀⢇
⠀⢠⠊⢉⣚⠉⢹⠄⠀⢀⣀⣠⠔⠋⡽⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠑⣾⡷⠏⠀⠀⠀⠀⠀⠀⣃⣀⠀⠈
⠀⢿⢠⠋⢀⢱⠈⠓⡄⠀⠞⠿⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⠞⠁⠀⠀⠀⠀⠀⣀⣴⡉⠵⠮⣗⠒⣄
⠀⣰⠛⢻⠾⠊⡤⠞⠁⠀⠀⠀⠀⠘⠓⠋⢹⡏⠉⠉⠉⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⣅⢎⣥⡼⢴⠃
⠀⠈⠋⢉⣓⣚⣆⡴⣦⣀⡠⠤⠤⠒⠒⢃⣸⠇⠉⠉⠁⣇⡀⠉⠙⠓⠒⠒⠦⠤⢄⣀⠉⢱⣌⡹⠯⣀⡼
⠀⠀⠀⠈⠓⣮⠿⠛⠉⠁⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⡀
⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢘⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠋⠔⠋⠄⡰⠀⠀⠀⠂⠠⠀⠀⠂⠱⠘⠀⠶⠂⠋⠇⠃⡇⠱⠀⠀⠰⠂⠁⠀⠀⠴⠀⠆⠀⠸⠉⠱⠋⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠿⢿⢻⠿⡿⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠒⢶⣎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⣸⠟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠋⠉⠁⠀⠈⣿⠹⣆⡀⠀⠀⠀⣀⣀⣤⠞⠋⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⡞⠉⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠈⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⠙⢦⣤⣄⣠⣤⡴⠶⠋⠁⠀⠀⠀⢠⡄⠀⠀⠀⠀⣴⠂⠀⠀⠀⢸⣷⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡆⠀⠀⠀⠀⠀⠀⠠⣄⣀⡤⠶⠚⠛⠛⠋⠙⠛⠛⠻⠦⣤⣀⠀⣼⠋⢀⣠⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢠⣀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠉⠻⣧⡀⠀⠈⢉⡴
⠀⠀⠀⠀⠀⠀⠀⣶⡄⠸⣿⡄⠀⠙⣦⠞⠁⣀⣠⣤⣤⣴⠆⠀⠀⠀⠀⠀⠉⠻⣟⠲⠄⠀⠈⠻⣦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠙⠁⠀⣴⣧⠶⠛⣩⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠸⣇
⠀⠀⢀⣠⡤⠶⠦⣤⡀⠉⠛⠶⣼⠃⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡤⠤⠦⣤⣀
⠀⢠⡟⠁⠀⠀⣀⣀⣽⣦⣄⣀⡟⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣀⡀⠀⠀⠙⢷
⠀⣿⠀⣠⡴⠚⠉⠉⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠙⠳⢦⡀⢸
⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⢀⣀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠙⢿
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⢦⣄⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠶⣤⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⡼⢷⡄⠀⠈⠛⢯⣙⠛⠛⠛⠉⢉⣥⠞⠉⠀⠀⣼⠃⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⣴⠏⠀⠀⢻⡄⠀⠀⠀⠙⠷⣄⣀⡴⠋⠁⠀⠀⢀⡾⠉⢳⡄⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡾⠃⠀⠀⠀⠀⠻⣄⠀⠀⠀⢀⡼⢿⡄⠀⠀⠀⢀⡾⠁⠀⠀⢻⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⣿⣁⣀⣽⣦⡀⢠⡞⠁⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠁⠈⠉⠉⠀⠈⠳⠟⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⢀⣀⣀⣠⣤⣤⣤⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⣴⠞⠋⠉⠉⠀⠀⢀⣠⢴⡏⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⣷
⠻⣤⣀⣀⠀⠀⣰⠟⠁⢰⡇⠀⠀⠀⠀⠉⠛⠳⠶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⢾⣏⣠⡴⠋
⠀⠀⠉⠉⠙⠛⠻⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠙⠶⣤⣀⣀⣀⣀⣀⣀⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠈⠉⠛⠒⠲⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠠⡄⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠺⠳⢾⡆⠰⠛⡠
⠀⠀⠀⠀⠲⡀⠘⡀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⣴⣀⢀⡀⠀⠰⠈
⠀⢰⠀⠀⡀⠑⠄⠀⠄⣀⠀⠀⠀⢀⠄⢀⠔⠀⠀⠈⠑⠒⠀⡀⠉⠉⠉⠆⠀⡀
⠀⠀⠑⢄⠈⠢⣈⡄⠘⠋⠀⢰⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠙⠶⠈⠀⢠⠄⠉⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⢦⡀⠂⡀
⠀⠀⠘⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⢀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢙⡷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠘⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠉⠀⠀⠊⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢂⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⠶⠀⠉⠉⠉⠛⠻⠶⣿⡄⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢠⠀⠀⢀⡠⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢦⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⡄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠔⠋⠀⣼⣷⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢰⠀⠘⢷⠒⠂⠐⠒⠒⠊⠉⠁⠀⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢻⠀⠀⠀⢧⣤⣄⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⡷⠀⣀⡀⠀⠀⣀⡀⠐⠈⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⡀⠠⠿⢻⡟⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠓⠴⠂⣀⣀⣀⠴⠋⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠐⣂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠷⣤⣤⣀⣀⣠⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⣤⣤⣤⣠⣤⣤⠴⡾⠋⣀⠀⠷⠈⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢻⡅⠀⠀⡇⠀⠈⠁⠶⠂⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢄⣀⣀⠀⠀⠀⠀⠀⢀⣀⠴⠛⠁⠀⠘⠀⢆⣤⠁⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠈⠁⠀⠀⠀⠀⠀⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠈⢛⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠘⠃⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡀⠀⠀⠀⠀⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠛⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠸⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣄⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⣤⡞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⠶⠞⠁⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⠴⠞⠉⠀⠻⣆⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡴⢾⠁⢠⣼⣁⣀⣀⣀⣀⠀⡴⢶⡞⠉⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢇⠀⠁⠀⠀⠀⠀⠀⠀⠄⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠡⣀⠀⠀⠀⠀⠀⢠⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⢦⣤⣤⡴⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⠁⣰

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣄⠀⢀⡀⠀⠀⠀⠀⠀⠤⡄
⠀⠀⠀⡔⣓⢒⢒⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠉⠀⠀⠈⣐⠀⠀⡂⠀⠈
⠀⠀⡀⠷⠟⡐⠾⠇⠀⢠⡄⠈⠀⢀⡀⠘⠀⠀⠀⠠⠨⠀⠀⠈⢀⠀⡈⠀⠀⠀⠀⠃⠐⠀⠐⠂⠂
⠀⠀⢠⣤⠄⠀⣤⡀⠀⠈⠁⠀⠉⠉⠀⠀⠤⡀⠀⠀⠀⠐⠖⠀⠀⠀⠐⠀⠀⢀⡀⠀⠀⠀⠄⠄⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠁⢀⡀⢠⠠⠀⠠⠈⠀⠈⠈⢀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣄⡀⠀⠁
⠀⠀⠁⠀⠂⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⢠⠀⠣⡀⠀⠀⠀⠉⢳⢂⡀⠘⠛
⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠈⢰⡇
⠀⠀⢠⡤⢤⠄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠇
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠘⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢀⡀⠀⣀⠀⠉⠈⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⡀⠀⣠⠤⠀⢀⠀⡠⣶⣠⠾⡄⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⣅⡀⢀⡀⠀⠀⠀⠀⡃⠀⠀⠀⣀⠋⠀⠣⣽⣿⣧⠇⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠛⠃⠘⠓⠀⠀⠐⠀⠀⠐⠀⡌⠉⠀⢀⠀⠁⠀⠁⡤
⠀⠀⠀⠀⠀⠀⠠⠮⠄⠈⠦⠀⢀⡀⠐⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠂
⠀⢠⣤⣀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡁⠀⠀⠀⠀⠈⠀⠴⠆⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣴⣶⠠
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡟⣱⡿⠈⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣾⣟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠘⠻⠷⠶⠶⢺⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣠⡤⣄⠀⠀⢀⣴⠄⢀⣴⠆⠀⢠⣾⡟⢀⣤⠀⠀⣠⡀⢀⣾⣏⡼⠁
⠀⢀⡴⠶⠶⣤⡀⠀⠀⢀⣿⡏⣴⣿⡁⠘⡇⢀⣾⡟⠀⣼⡏⠀⣰⣿⠏⢠⣿⠏⠀⣾⡟⠀⣼⡿⠋⠀⡀
⢰⡏⠀⠀⠀⠸⡷⠀⠀⣼⡿⠀⣿⡏⠛⣾⠗⠻⣿⣀⣴⣿⠣⢶⣿⠷⠖⢾⡏⣠⣼⣿⢀⣼⡿⠀⠀⡼⠁
⠸⣇⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠈⠛⠚⠋⠀⠀⠉⠉⣼⡏⢠⣿⠋⣇⠀⠈⠛⠉⠀⠛⠋⠸⣧⣠⠞⠁
⠀⠈⠛⠶⠶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⣴⠋⠉⢉⣿⠟⠲⢾⡟⠋⣿
⢰⣇⠀⡴⣿⡄⣰⢻⣷⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠸⣧⣠⡏⠀⠀⠀⠀⣼⣄⡀
⢸⣿⣸⠃⣿⣷⠇⢸⣿⠀⢀⣤⡄⣤⡄⠀⠀⢠⢤⠀⠀⠀⠀⣨⠉⠀⣤⠀⠀⢠⣿⣿⡟
⢸⣿⡏⠀⣿⡿⠀⢸⣿⢠⣿⣣⠇⠙⡿⢤⣤⠈⢻⠦⣤⡄⠀⣿⠀⢠⣿⡆⢠⠈⣿⣿⣿⠆
⢸⣿⡁⠀⣿⡇⠀⢸⣿⢸⣿⠁⠀⡰⠁⣼⡿⢀⠏⢠⣿⠇⣸⣿⣄⡞⣿⡷⠋⠘⠻⣿⡏⣤⣀⣤⣦⣄⣀
⠈⠛⠁⠀⠀⠀⠀⠀⠋⠀⠙⠛⠋⠀⠀⣿⣧⠞⠀⢸⣿⡴⠁⢙⣋⢤⣿⡇⠀⠰⣿⠿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⣠⠖⠚⢻⣦⣀⣀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⠀⠀⠀⢰⡋⢀⣼⡿⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⡉
⠀⠸⠥⠂⣠⡿⠋⠉⣸⡷⠀⣰⡿⢡⠇⠀⠀⠀⠀⣀⣀⠀⠀⢙⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⢀⣀⣼⡟⠁⠶⣾⡋⠀⢰⣿⡵⢃⣴⡾⢛⡆⠸⣿⡀⠁⠀⢿⣄⠉⠀⢠⣴⠞⢳⠀⢀⣴⠶⣾⡏
⡼⠉⢸⣿⠙⣦⠀⠈⣿⢀⣿⠋⠀⣼⡟⠓⠋⢡⢞⣘⣿⣆⡠⣋⣻⣷⣠⣿⠟⠚⠋⣰⣿⠃⣸⡟⢀⡖
⢧⡀⠀⠓⠀⠟⠀⢠⣿⢹⡇⢀⡼⠙⠧⡤⠖⠋⠯⡥⠿⠃⠸⢭⠼⠟⠀⠻⢦⠤⠚⠙⠷⠖⠻⣧⠞
⠈⠛⢶⣤⣤⣤⣾⠟⠃⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣤⣿⣷⣾⣷⣶⣶⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⣼⣿⡏⠀⠀⠀⠉⠉⠈⠙⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆
⠀⠀⠀⠀⣿⣿⠟⠋⠛⠛⠿⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠏⠋⠉⠈⠁⠀⠈⢻⣿⣿
⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠘⣿⡇
⠀⠀⠀⠈⣜⠀⠀⠀⠁⡀⢀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠗⠎⠀⠄⠀⠁⠄⠠⠀⠀⠀⠀⠐
⠀⠀⠀⢠⣿⣦⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠤⠠⡉⠈⠀⠀⠀⠀⠀⠀⠀⢤⡀⣀
⠀⠀⠀⣸⣿⣿⣿⣿⠗⠐⢿⣿⣷⠀⠀⠀⠂⢀⠄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡛⠃⠓
⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠈⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎
⠀⠀⠀⠈⠉⠉⢱⠀⠀⠀⠀⢈⠁⠀⢠⠀⠀⠀⠀⠀⠈⠩⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠦⠲⠀⠀⠀⠀⠸⠲⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢒⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠥⡄⠈⢴⠀⠀⠉⡙⠀⠀⠀⠀⠈⡤⠏⠘⠀⠀⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠠⢺⠇⠀⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⡂⣲⠿⣿⣿⣿⣿⣶⣤⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣴⣾⣦⣤⡀⠀⠀⠀⣤⣄⠀⢻⡇⣷⢆⢠⣶⡆
⠀⠀⠀⠀⣇⣿⣸⣋⡿⣽⣻⠟⣏⠁⠀⠀⣯⠹⢇⡏⠶⣿⠫⠜⡏⠸⠎⣷⠀⠀⠀⠈⠟⢷⡾⣿⣿⣴⣟⣩⡄
⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣾⡼⠏⠂⠀⠀⢻⣇⣿⣇⣛⣳⣰⣇⣇⣺⣇⡿⠀⢠⣤⡄⠛⣻⣜⣪⣀⣹⣺⣧⣤⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠰⡿⠟⢩⡟⢻⡛⣯⠓⠈⠛⠁
⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠈⢷⣦⡀⢀⡀⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠿⠇⠈
⠀⠀⠠⣤⡼⢿⣿⡿⣦⢔⣄⠀⠀⢈⠿⢿⡟⢻⣏⢿⡉⣧⠄⠀⣠⣤⣤⣴⣿⣿⠷⣄⠀⠀⠀⣂⣀
⠀⠀⠀⢿⣮⣧⣧⣿⣾⣼⠝⠁⠀⢨⡇⢈⣥⠘⣷⠘⣟⣳⠀⠀⣏⡉⢴⠋⠩⡄⢂⡜⠀⢠⣾⣿⣿⣷⣾⣷⢲⡄
⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠶⢰⣿⣶⢿⡟⠿⠉⠀⠀⠹⢧⣼⣿⣿⠟⠋⠀⠀⡞⢱⣾⢫⡝⠱⠎⡘⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠻⣬⣩⡶⠴⣷⡾⢿⡁
⠀⠀⠀⢀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⣀⣰⣶⣶⣶⡄⠀⠀⠀⢀⡀⠂⢰⡤⡀
⠀⠀⣾⢻⣟⢟⣛⢛⢻⣦⠀⢀⡞⠟⢟⡛⢛⠻⢻⣹⡆⠀⢤⣍⣹⣶⣿⣶⣏⣶⡉⠀⢀⠴⣾⢿⡿⢿⠿⢷⠶⣦
⠀⠐⠿⣬⣴⣯⣵⣿⠿⠟⠀⠈⠳⢿⢷⣾⣷⠞⣛⣏⠀⠀⢺⣦⠷⣴⣦⣶⢿⣭⣄⠀⢿⣖⣯⣴⣇⣸⡆⣿⣀⣿
⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⠆⠀⠀⠘⠐⠛⡖⠃⠁⠁⠀⠀⠘⠿⠶⣿⡧⠾⠧⠿⠴⠋
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣾⠿⡿⢿⣷⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣼⠆
⠀⠀⠀⠀⠀⠀⢸⣱⡎⠣⡦⠁⢫⡆⠽⢿⠀⠀⠀⣠⣴⠶⠞⡿⠻⠛⠛⡉⣽⣿⡶⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠈⢧⣶⣷⣶⣿⣿⣿⣿⠏⠀⠀⠘⠿⣿⣴⣦⣶⠶⠧⠞⠛⠛⠉⠀⠀⠀⢀⣀⣀⣀⣀⣠⣀⣀
⠀⠀⠀⢰⣦⣀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⣏⣉⣋⣉⣉⣉⣩⣭⣿⡿⠃
⠀⠀⣠⣾⣿⣿⡿⣿⣦⡀⠀⠀⠀⢀⡀⣄⢂⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣀⡀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⢰⡟⢿⢟⣭⣧⣹⣽⡏⠀⠔⣠⣻⡏⣟⢻⡚⡟⠤⡔⠄⢼⣍⢫⡟⡟⡟⠋⠋⢣⢿⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⡄
⠀⢀⢻⣬⣿⣶⣿⣿⠟⠁⠀⠀⣙⡫⣧⣽⣼⣷⠿⠟⠀⠀⢰⡿⠼⠷⠶⠶⠾⠟⠛⠁⠀⠀⠺⣿⣤⣴⣤⣦⣤⣷⡇
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠈

⣿⠟⠛⠻⠟⠛⠻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⢽⡏⠉⢙
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠛⠛⠓⠛⠛
⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠂⢀
⠀⢸⣿⡉⠙⠏⢉⣿⡇
⠀⢸⣿⣷⠀⢰⣿⣿⡇⠀⠟⣧⠀⡿⠁⣏⡷⡿⠇
⠀⢸⣿⣿⣤⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠰⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⡀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠐⠁⠀⠀⠀⠀⠀⠀⣠⠍⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠠⣶⢀⡈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⡉⣉⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⣀⣀⡀⠀⠐⠁⠀⠀⠀⠀⠴
⠀⢀
⠀⠀⠈⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣭⣭⣿⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣾⣿⣽⣿⣶⣿⣷⣿

⠀⢀⣀⣀⣤⠶⢾⣿⠿⠿⣿⣶⣤⡀
⠀⢣⡀⣩⡧⣤⠎⠀⠀⠀⠀⡈⠻⣿⣦⡀⠀⠀⠀⠀⠀⢀⣠⠞⢉⡳⢤⣀⣠⣤⣤⣤⠤⢤⣀⡤⠾⡉⠙⢦⣀
⠀⡿⣹⣿⢁⡎⠀⠀⣶⣀⣀⢹⡀⠹⣷⢹⠓⢦⡄⠀⢰⠉⠀⢀⣞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣸⣀⠀⠀⢱
⠀⡇⢹⠇⡜⠙⠉⠉⠀⠁⠉⠉⠱⡀⢹⡈⡇⡴⠁⢠⠊⠀⡤⠊⢿⠁⢀⠔⠉⠓⠒⠒⠒⠚⠲⡄⠀⡟⠻⣦⠀⠈⢢
⠀⣇⢼⡴⠁⠚⠙⠀⠀⠀⠚⠙⠂⠳⣤⣷⡏⠀⠀⢹⠄⢠⠏⠀⢸⣤⡎⠀⣀⡀⠀⠀⢀⣀⠀⠸⣤⣇⡴⠛⣦⠀⢞
⣠⠊⠀⣇⡀⠘⢗⡒⠾⠖⠒⡾⠀⣤⡏⠸⡄⠀⠀⠸⡄⢸⠀⠀⢧⡀⠀⠀⣁⣁⠠⠄⢈⣈⠀⠀⠀⡸⠀⠀⣳⠀⡞
⢧⠀⡴⣏⠓⠒⠬⡓⠦⠖⡞⠚⠉⣁⢧⠀⡽⠀⠀⠀⠳⠞⠀⠀⠀⣿⡷⣄⣘⢯⣉⣉⣡⣯⠤⢿⣿⠃⠀⠀⠙⠚⠁
⠀⠹⡀⠈⡷⠀⠀⢻⠛⣻⠀⠀⠸⡅⢀⣟⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⠳⡄⠈⢱⡬⢥⠏⠀⢰⠊⢹
⢀⡴⢳⡀⡇⠀⠀⠘⡦⡇⠀⠀⠀⣇⡞⠈⢧⠀⠀⠀⠀⠀⠀⢀⡜⢇⢠⠇⠀⠀⣇⣸⠀⠀⠸⣆⡎⢣
⠛⠠⠤⠽⣇⠀⠀⣸⣁⣱⡀⠀⣠⣏⣀⣀⣨⠇⠀⠀⠀⠀⠀⠛⠲⠼⢿⡀⠀⢀⣇⣹⡀⠀⣠⣏⣠⡤⠗
⣤⣤⣤⣤⣬⣵⣾⣥⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣶⣮⣤⣤⣭⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠛⠃⠠⠦⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠃⠀⠀⡀⠀⡀⠀⠀⠁⠤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠰⠄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠈⠁⠉⠀⠁⠀⠃⠀⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠡⠀⠀⠲⡀⠀⠀⠀⠬⠀⠀⠐⠀⠈⢀⣀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠂⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⠃⣀⢀⡀⠀⡄⠀⡰⠀⠐⠀⠐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠰⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠁
⠀⠀⠀⠀⠈⠀⠀⠉⠁⡀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⢀⡀⠀⠄⠠⠀⠀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⣀⠀⠀⠀⠀⠀⠒⢀⡀⢀⠀⠊
⠀⠀⠀⠀⠀⠈⠀⠠⠞⠋⠉⠉⠛⠆⠁⠀⠄⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠂⡀⣀⠀⠀⠀⠀⢠⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⡀⠀⠀⠰⠦⠀⠰⠄⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠈⠒⠀⠨⠁⣀⠈⠀⠀⠠⠀⠀⠄⠀⠀⡀⠄⠀⢄
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠀⠀⠉⠀⠈⠡⠀⠘⢠⠰⢀⠱
⠀⠀⠀⢀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠐⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃

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


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣭⣯⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠀⠀⠀⢀⠀⡀⡀⡠⢸⠠⡂⢠⠠⡀⡄⡂⠄⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢖⠂⣆⠗⠁⠇⠀⠣⠸⠀⠚⠘⠀⠃⠃⠁⠀⠀⡏⢀⠇⠄⠐⢰⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠤⠄⠤⢄⠈⠁⠀⠈⢁⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⠎⠉⠀⠁⠈⠀⢀⣀⠀⠈⠑⠒⠖⠢⠤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠔⠉⠁⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠠⡉⡅
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡀
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠐⠢⠭⢥⡝⠀⠀⠁⠀⣀⠖⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⠄
⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠷⣮⡍⠁⠈⢣⠀⢀⣀⠆⠁⠀⠈⠙⠔⠆⠤⠤⠦⠀⠀⢀⡀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⠀⠀⢸⢸⢀⠆⠋⠁⠀⠀⠀⢹⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⢇⠀⢁⠏⡼⠀⠀⠀⠀⠀⠠⡘⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠃⢣⠀⠀⠀⠀⠀⢠⠕
⠀⠀⠀⠀⠀⠀⠈⢢⣀⠜⠀⠀⠶⠀⠀⠀⡀⡄⢂⠀⠀⠀⠰⡇⠀⠀⠀⠠⠦⠀⠀⠣⣤⢠⡀⡰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡙⣦⣀⠀⠀⠀⠀⠀⢀⣠⠞⠓⢤⣀⠀⠐⠐⠀⠀⠀⠀⢀⡠⠔⠁⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⣿⠐⠒⢲⣙⠷⡀⠈⠑⠀⠓⠋⠁⠀⠒⠒⠂⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣠⡿⠃⠀⠸⠄⢠⣆⠀⠀⠀⣀⠀⣀⠐⠤⣦⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢄⠀⣈⠀⠛⠂⢸⠀⠉⠉⠂⠴⠗⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⢀⠄⠉⠁⠰⠦⢼⡀⢀⢀⠀⡀⡀⢄⡒⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠃⠴⠻⠦⠐⠛⠒⠀⠀⢘⠁⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠠⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡃⠀⠐⠀⠀⢀⠀⡀⠐⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡁⠀⢈⢩⡀⠀⠀⡀⣄⡄⠀⢈⡁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⢀⠀⠀⠀⣀⣄⣠⣀⠀⠀⢀⣀⣀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢼⡁⠀⡇⠀⡇⠀⠙⠂⢸⠀⢸⠀⢠⡾⠋⠀⠀⠉⠛⠛⠋⠉⠉⠉⠁⠑⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⣀⠔⠆
⠀⠀⠀⡞⠁⠀⠷⢀⡇⠀⡆⠀⣾⠠⠘⠀⠉⡀⠐⠀⠀⠀⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⢀⠀⠤⠀⠐⠒⠉⠁⠀⠀⠉⡖⠒⢲⡏
⠀⠀⠈⠃⠀⠀⠀⠚⠁⠀⠁⠐⠋⠐⠋⠀⠀⠐⠈⠈⠀⠀⠁⠀⠈⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⡠⠒⠐⠐⠒⠠⡄⠀⠀⢀⣧⣤⢼⡇⡄
⠀⠀⣀⠂⠀⢐⠂⠛⠘⡒⠀⠀⢰⠈⠉⡆⢀⡄⠀⠐⠆⠀⠀⠲⡂⠀⣀⠀⠀⣠⠄⣠⡤⢠⣄⢠⣶⠀⣤⠌⢡⡀⠠⠄⡄⣰⡀⠀⡄⠉⠀⠀⡐⡈⢁⡄
⠀⢘⡜⠀⣀⢠⢤⠀⠠⡄⣀⠀⠀⠓⠐⠀⡈⠁⠀⠀⠀⠀⡀⠐⠀⠀⠋⠁⠀⠙⠂⠉⠑⠉⠉⠋⠃⠀⢋⠀⠀⠈⠀⠂⠈⠐⠀⢀⡀⠀⠄⢀⠄
⠀⠀⠇⠀⠰⡀⡁⠑⡈⡀⠇⠐⠀⠅⠈⠀⠀⠄⠀⠁⠤⠀⠀⠠⠂⠰⠤⠀⠀⡁⠀⠐⠀⠀⠈⠀⠈⠀⠁⣤⠀⠈⠳⠲⠞⠀⣠⡄⠁⠀⠸⡏⠀⢆⠀⢰
⠀⠀⠄⠀⠀⠆⣙⢚⣋⠰⠀⠀⠀⠁⠠⠀⠤⠀⠀⠀⢰⡆⠀⠿⠀⠀⢀⡠⠂⢠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠉⠀⠅⠈⠠⢈⣠⡶⠀⠀⠇⠀⠈⠉⠙
⠀⠀⠀⠠⢀⠀⠹⠨⠇⠤⡈⠂⠠⠀⠀⠁⠀⠀⣀⠁⠀⠈⠁⠁⠉⠀⠉⠀⠀⣀⣀⣈⣀⣂⣀⣁⡀⠀⠀⢄⠀⠠⠄⠁⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠂⢴⠠⠠⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⣿⡁⢀⣁⡀⠀⠀⠀⠉⠉⣉⣉⣉⣉⢉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠡⠈⠀⠀⠀⣄
⠀⠀⠀⡀⠓⠬⠂⠀⠀⠓⠒⠁⠠⠀⠈⠀⠀⠀⢰⡏⠀⠉⠁⣿⠈⠉⠻⠋⠉⢳⡄⢿⡄⢠⣭⣉⢀⣥⡿⠀⢀⣀⠀⢀⠀⠀⠈⠀⠨⠁⠈⠀⠀⢀⡄⣷
⠀⠀⠠⠀⠀⢸⠀⠊⠀⠚⠀⠀⢀⡀⠈⠀⠀⣀⠘⡳⡄⠀⠀⣿⢸⣷⠀⢠⣿⠀⡇⠀⡇⢸⣿⣿⠸⡇⠀⠐⠛⠛⠒⠛⠛⠀⠀⠀⠀⠀⠂⠀⠁⠈⣤⠄
⠀⢀⡀⠀⠂⠈⢀⠀⢀⠈⠀⠀⠐⢲⠐⢤⠤⡖⠀⠈⢪⣂⠀⣿⢸⡿⠀⠹⠟⢰⡇⣀⡇⢸⣿⡿⠀⡇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⢨⣧⠀⡀⠃⢚⠀⢐⠐⢂⡀⢀⣺⠀⣘⢀⡇⠀⠀⠀⣽⡀⢿⡤⠴⠳⣤⡴⠎⠘⡯⠤⠤⠽⣷⣴⡇⠀⠁⢈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢄
⠀⠀⢀⣀⡁⣤⡁⠀⢀⠀⡈⠁⠀⠉⠉⠁⠀⠀⠀⣀⣀⣬⣥⣄⣀⣀⣀⣋⣀⣀⣀⡀⢀⣀⢀⣀⣛⣀⣀⡀⢈⣀⣈⣀⡀⠉⠈⢀⠀⠀⠀⠀⠀⠀⠅⢀⠬
⠀⠐⠈⢡⡤⣤⡄⢻⠁⠠⠤⠀⠀⡀⠠⠆⢻⡙⣿⠏⣩⠀⣤⡀⠉⢿⣿⠈⠀⣶⡌⠹⢋⣉⠙⢠⣤⣾⡇⣿⢸⡅⠶⢾⡇⠠⡀⠀⠀⠠⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⣶⡀⠁⠀⠀⠀⢷⡘⢠⡿⢸⣿⡇⠀⢸⣿⠀⠀⠛⣡⣶⡸⢿⣶⠘⢿⣿⡇⣿⢸⡇⡶⠺⡇⠀⠄⠀⠀⠄⠸⡤⠶⣾⣿⠄
⠀⠠⠰⠹⢻⠣⠄⠈⠈⠀⠀⠈⠁⠀⠀⠀⠀⢸⡇⢸⣿⠘⠿⠃⡄⢸⣿⠀⠀⣷⡌⣿⢻⡆⠙⠠⣿⣿⠀⣇⣸⡇⣷⠀⠠⢄⡤⠀⠀⠀⠀⢆⢹⣸⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⡀⢀⠀⠀⢰⣤⣤⡄⠀⠀⣧⣸⡟⠷⠴⠞⠳⣤⣥⣾⣤⣿⣧⣽⣦⣤⡾⡦⠤⠾⠷⠭⢽⣧⣿⠈⣿⢻⣹⡇⣰⣾⠀⠚⣿⠋⠉⡀
⠀⠀⠈⢶⠃⠀⠀⠀⠄⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⡉⣁⣠⡄⣀⠀⠉⠀⠈⠉⠙⠀⠀⢸⠇⠀⡴⠖⠶⠂⠀⠀⠛⠉⠀⠸⢿⡿⠐⠟⠁⠀⡼⡏⠐⣿⣿⠃
⠀⠀⢀⡀⠀⠀⠀⠈⠉⡉⠁⢀⣀⢀⣀⠀⠀⠀⠀⠉⠁⠠⠀⠁⠀⠠⡀⠀⠀⠂⠀⢀⠀⢀⠐⠷⣀⡰⠟⢀⣠⣄⣀⡀⠀⠛⠃⠘⣿⢿⣿⡏⠃⠀⢹⡏
⠀⠀⢈⡀⣥⠀⠠⠄⠀⠀⠀⠤⣬⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁⠆⠀⢠⣂⡞⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⠏⡁⠀⠀⠸⠇
⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⡀⠁⠇⢆⠀⠀⠈⠀⢀⣾⠀⠀⡀⠄⠀⠀⠈⠠⠤⠁⠀⠀⢀⠀⡀⠀⢀⡀⠈⠤⠁⠀⠀⢀⠄⠀⠒⠑⠂⢄⠃⠁⠀⠀⢤⡀
⠀⠀⠀⠀⠁⠀⡷⠂⠀⠐⠺⠇⠀⡇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠁⠀⠐⠀⠀⠀⠀⢀⢶⡤⣒⡆⠀⠀⠰⠀⠘⡆⠀⠊⠂⠍⠀⢀⡀⣀⡹⠀⠙⠈
⠀⠀⠀⠀⠄⠀⠀⠅⠀⠨⠄⠀⠁⡄⡁⠀⠈⠀⠀⠀⠀⠀⣀⠈⠀⡁⢀⠀⢀⠁⠂⠀⠀⠂⠁⠀⠀⠀⠂⠀⡀⠀⠨⠅⠀⢶⠂⠀⠀⠀⠈⠀⠀⠀⠀⢨
⠀⠀⢸⠀⠇⠀⠠⠀⠠⠀⡀⠀⡄⠃⣡⠀⠀⣨⠃⠀⠀⠂⠈⠐⠀⠄⠂⠐⠀⠀⠃⠀⡐⠂⢄⣐⠄⠀⠀⠀⠀⠀⠈⡥⠀⠙⠁⣠⣤⠀⠀⢠⣤⡀⠀⢻
⠀⠀⠘⠀⢂⡀⣀⠘⠓⠛⢀⣀⡅⠀⠃⠀⠀⣮⠀⠀⠀⠂⠀⠀⠂⠀⠀⠉⢠⢀⠀⠀⢀⠀⠀⡇⠀⣀⢀⡁⠀⣀⠀⡉⢀⣀⡈⡉⠉⠀⠀⠈⣉⣉⣀
⠀⠀⢈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠩⠐⡂⠀⠀⠃⠀⢠⠀⠈⠀⡘⠀⣀⠀⢀⡘⠌⠀⠰⠀⠀⠀⡇⢸⣏⡸⠇⠀⡷⠀⠿⠌⠉⠁⡇⠹⣾⠁⡏⠉⠉⠘⡇
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠀⠀⠁

⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠱⡀⣀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡄⠀⠆
⠀⠀⠀⠀⠙⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠎⠀⠀⠀⠀⠀⠑⠢⣶⣧⠀⠀⠀⠀⠀⠀⣢⣿⡤⡇⠀⠀⠀⠀⠀⢀⣿⠗⠊
⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⢼⣿⡀
⠀⠀⠀⠀⠸⠃⠻⠀⠀⠀⠀⠀⠐⢢⣼⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡇⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠸⡜⡇
⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠎⠘⠄⠀⠀⠀⠀⠀⠰⠀⠡⠀⠀⠀⠀⠀⠀⠐⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⣠⣀⠔⠁⠀⠀⠘⡀⠀⠀⢀⠄
⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠳⢄⣶⣀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠈⠙⢿⣶⠄⠀⠀⠺⣿⠁⠀⠀⠀⠀⠀⠳⣿⡴⠊
⠀⠀⠀⠓⢲⣾⠆⠒⠈⠀⠀⠀⠀⢿⡏⠑⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣰⢿⡟⠀⠀⠀⠀⠀⠟⢻⠀⠀⠀⠀⠀⠀⠀⡟⢹⠀⠀⠀⠘⠃⣇⠀⠀⠀⠀⠀⢸⠋⣷
⠀⠀⠀⠀⠚⠟⠃⠀⠀⠀⠀⠀⠸⠈⠛⠐⠆⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⠀⡄⠰⠀⡄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣿⠛⡇⢸⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡔⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠻⣤⣤⠀⣿⡇⢠⣤⡴⠟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠅⣠⡝⠀⠹⠀⠘⣥⡀⠭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠈⠠⠠⠀⠀⠀⢠⠀⠈⠠⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠤⠤⠀⠈⠛⠀⠀⠀⠘⠃⠀⠠⠤⠴⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⡀⠈⠀⠀⠁⢠⣤⣀⣠⣤⠂⠁⠀⠈⠀⡀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢃⠀⠈⢂⠀⠀⠙⢻⠛⠁⠀⢀⠊⠀⢀⠃⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠦⣀⠀⠐⣤⡴⢾⠶⣤⡔⠀⢀⡠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢈⠒⠹⡄⠀⠀⡼⠑⢊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠓⠀⢰⣄⠀⠀⠀⢀⣴⠀⡐⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠸⡿⠟⠋⠛⠿⡿⠀⢀⣀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠳⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠂
⠀⠀⠀⠀⠀⠲⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣌⠢⡀⠀⠀⡾⢶⣤⡀⠀⢸⠀⠀⠀⠀⠀⡠⠔⠈⢠⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣍⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⡇⠚⢉⣁⡀⠈⣢⣞⣀⣠⢤⣁⣀⠀⠣⣀⠠⠐⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠙⠒⠢⠤⠤⢃⡜⠉⠀⠀⠉⠳⣴⠋⠀⠀⠀⠈⢻⡙⠒⢤⡀⠀⠀⢠⠃⠀⠀⠀⣀⠤⠐⠒⠈⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⢀⡴⢻⠁⠀⠀⠀⠀⠀⠘⡄⢀⣀⠀⠀⠀⢣⠀⠀⠈⠳⣄⠺⠤⠐⠂⠉⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢠⠎⠀⢸⡀⠀⠀⣖⣆⠀⠀⢳⢰⣿⡆⠀⠀⢸⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠕⢠⠇⠀⠀⠀⢣⡀⠀⢿⡿⠀⠀⣾⡀⠛⠁⠀⣀⠞⠀⠀⠀⠀⠀⡄⢣⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠲⠶⣒⡈⠉⠁⠀⠀⡸⠀⢤⠀⠀⠀⠙⠦⣤⣤⠴⠚⠀⠈⠙⠋⠉⠁⠀⠀⠀⠀⢀⠘⠀⠀⡇⠑⠢⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⡀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢸⠀⠀⠀⢀⣀⠬⠵⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⢡⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⢸⢠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠸⡀⠀⠀⠸⡀⠀⠒⠀⠤⠤⠠⠤⠀⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠖⠉⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⣀⠔⠊⠁⢀⣀⣀⠤⠤⠤⠀⠒⣦⠈⢧⠀⠀⠀⠀⠀⠁⠀⠦⠀⣀⡀⠴⠔⠊⠁⠀⠀⠀⠀⠀⢀⡴⢁⠤⠀⣀⡀⠀⠀⠀⠀⠑⠢⣀
⠀⠰⠞⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠘⢆⠀⠀⠀⠉⠉⠁⠒⠂⠤⠤⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠠⠄⠒⢌⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢁⡤⢄⣀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠗⠊⠉⠀⠀⠀⠀⡆⠀⠀⠈⠉⠓⣒⠲⠲⠶⠖⠒⣋⡉⠀⠀⠀⠀⡁⠀⠀⠉⠒⠤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡴⠋⠀⢇⠀⠀⢀⠜⠀⠙⣄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡴⠋⠀⠀⠀⠘⡀⢀⠎⠀⠀⠀⠈⢢⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡠⠊⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⠀⠀⠀⠀⠱⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢛⡻⢿⣿⠇⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣷⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠛⠀⠀⣄⣠⡄⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⠉⠐⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⡠⠊⠁


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⠶⠶⠶⠶⢶⣶⠶⠶⣶⠶⠶⠶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠕⢀⠀⠀⠄⢀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠞⠀⢀⠚⡁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⡴
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠆⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡏
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⢠⠘⠁⠀⣀⠀⠀⠀⠀⢀⡴⠋⢃⠀⢱⠀⢀⡀
⠀⠀⠀⠀⠈⠤⠂⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⡘⠀⠀⠀⡆⠸⠀⣠⠋⠀⠀⠀⠔⠋⠀⠀⢸⠀⠈⡆⢾⢋⡴⠒
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢾⠔⠁⠙⢦⠀⠀⠀⠀⠀⢰⢡⠃⠀⠀⠸⢀⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢱⣬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⡃⠀⠀⢀⡦⠃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⡍⡅
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⠃⢀⠔⢛⢳⠀⠀⠀⣾⠁⠀⡘⣃⣼⠋⠂⢸⣻⠉⣀⠰⠅⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡆⠀⠀⠀⠇⠘⠀⢀⡼⠃⠀⠘⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠣⠀⠈⠂⠀⠠⠖⠉⠀⠀⠐⠁⢠⡄⠃⠀⠀⠀⠀⣀⠤⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠶⣶⣄⠀⠀⠀⠀⠀⠀⠐⠿⠂⠀⣸⠓⠒⠒⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠇⢀⡴⠆⣠⡄⢠⡄⣴⢺⡇⠀⢠⠇⠀⠀⠀⢀⣔⡿⢄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠏⠀⢼⣏⠴⡽⡧⣾⡼⠻⠛⡃⣼⣿⠀⠀⠀⠀⢦⡜⠷⠊⠄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢤⣾⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠈⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣴⠾⠁⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠇⠀⠀⠘⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⣀⣀⡴⠤⠤⠤⣇⡀⠠⣾⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠙⠣⠔⠋⠀⠀⠀⢠⠀⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⢀⡠⢤⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⡊⠀⠀⠀⠠⠀⠘⠀⠸⣦⣤⣤⢠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣼⠀⢠⠀⣀⡄⠀⠀⢳⠖⠀⠀⠀⠀⠀⢸⣆⣀⠀⠀⠀⣈⣃⣀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡴⠉⠀⠁⠀⠁⠳⠒⠄⢠⡀⠀⡤⠀⠀⠀⣀⣉⠉⠙⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠶⣄⠀⠀⢵
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠑⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡖⠈⠀⠀⠀⠀⠉⠙⠒⠤⠤⢀⣀⡀⠀⢈⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣄⠀⠀⠀⠀⣠⠞⠁⣰⠏
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⣶⡞⠀⢀⣤⠞⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⣤⣴⣾⣯⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠉⠙⠳⣦⡀⠀⠀⠀⠀⢀⣠⣤⠶⠾⠿⠿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠘⣧⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⣨⣿⣷⠀⠀⠀⠀⣿⠀⣼⣅⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣽⣿⠟⠀⠀⠀⠀⣿⠀⠘⠧⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⢀⣀⠀⠈⢷⡀⠀⠀⠀⠤⠄⣄⣀⣀⣀⣀⠠⠤⠤⠤⠤⣰⡟⢻⣤⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⢀⣼⠋
⠀⣠⠊⠁⠀⡜⠁⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠙⠻⣦⣄⣀⡀⠀⠀⣀⣀⡄⠀⠈⠁⠀⠀⠀⢲⠂⠤⡀
⠀⠙⢤⣤⠞⠀⠀⠀⠀⠀⡀⠀⠀⠰⢦⣤⣀⣀⣀⣀⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⠂⠀⠀⠀⠀⢧⠀⣸⠆
⠀⠀⠀⠀⠀⢀⠀⡖⠀⠀⢇⠀⠀⠠⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢇⣠⠃⠀⠀⠈⠑⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠟⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠠⠞⠛⠉⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣀⣀⣉⣀⡐⠀⠐⠒⠮⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢟⣛⣩⣭⣭⣛⣓⡀⠀⠀⠀⢮⣷⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣋⠵⣾⢿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⢿⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⡼⠁⠈⠀⠀⠀⠀⠐⠒⠲⠄⠀⠀⠀⠀⠀⠀⠸⣷⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠠⠚⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠁⠀⠀⢀⠤⡀⠀⠔⡡⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡤⣄⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣧⠃⠀⠈⢀⠡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠁⠀⢰⠚⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⡇⠀⠀⠀⠀⣄⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢸⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢙⠂⠤⠞⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣏⠀⠀⠀⠀⠀⠈⣏⠉⠁⠀⣠⠔⣻⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢠⢂⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠘⢇⡉⣉⡠⣺⠏⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⡠⠚⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠉⠒⠚⠁⠀⠀⠀⠀⣠⠞⠁⠀⣀⠴⣌⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⡀⠀⠀⠀⣀⣠⡴⢾⠁⠒⠒⠉⣁⡠⠟
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠝⠋⢋⡀⢀⡞⢰⠒⠊⠉⠁
⠀⠀⠀⠀⠀⡠⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠒⠒⠒⠉⣀⣤⡆⠀⠉⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡴⠂⠤⠤⠤⠤⠖⠚⠦⠔⠒⠋⠁⡼⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡒⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠃⠈⠙⠲⠤⣀⡉⠑⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠲⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣦⠤⣄⢀⣀⣠⠋⠑⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⡭⢷⡄⠀⢀⣀⣀⣀⣈⠑⠲⠦⢤⣤⣀⣀⡀⠀⣀⡁⠀⠀⠀⠀⠀⢸⠀⡟⠈⠀⠀⠈⠉⠉⠉
⠀⠀⠒⠄⠀⠀⠀⠀⠀⡰⢮⡠⠚⠁⠀⠀⠛⠉⠉⠉⠁⠈⠉⠁⠢⢤⣀⡀⢀⠉⠉⠉⠉⠴⡦⠀⠀⠀⢠⠋⡰⠃
⠘⢌⠢⡀⠈⠑⠢⢄⡘⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡀⠀⠀⠀⣸⠣⠤⠔⣊⡭⠛⠁
⠀⠈⠱⣈⠢⡀⠀⠀⠈⢳⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⠏⠙⠋⠉⠁
⠀⠀⠀⠈⠑⢌⠳⢄⢀⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⣀⡉⣒⡶⢤⣍⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢦⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⣿⣯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠠⡹⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣾⣿⣿⣿⣿⣿⣿⣧⣿⣭⢫⣞⣿⣿⠐⣷⠻⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠸⢸⡟⠛⠛⠛⠋⠙⠁⠉⠋⠿⢻⣾⣿⣿⣼⠘⢢⡟⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡆⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣯⣂⠛⢹⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢿⣴⣯⢟⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣿⣿⣯⣐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡇⠀⣷⣤⣤⠀⠀⠀⠰⠿⣿⣯⣭⣍⠑⠀⠘⣿⣿⡷⣭⣋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠹⠾⠦⠀⠀⠀⠀⠀⠁⠀⠈⠙⠃⠀⠀⠹⣿⣿⣦⠌⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡳⣄⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⣻⣿⣿⣮⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⣀⢀⣼⣿⣿⣿⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡖⠛⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⣿⣿⣿⡿⢹⢸⠹⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡇⠰⢸⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⣿⣿⣿⣿⡃⠀⠈⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡲⢤⣀⣀⣀⠠⠒⠉⠀⠀⢠⣿⣿⣿⣿⡇⠀⠁⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⡃⠀⠣⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣧⡰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⢦⣤⡂
⠀⠀⠀⠀⠀⡀⠀⡀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠆⠀⠶⢮⣭⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠊⠢⠙⢿⣷⡖
⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠛⢀⠀⠀⠹⣆⠀⠀⠀⠀⢠⣿⣿⡿⣿⣧⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠈⠘⡉⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠹⠀⠀⠀⢀⠃⣿⣿⠃⠘⢿⣷⠀⠀⣀⣀⢿⢿⡀
⠀⠀⠀⡀⠹⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠀⠀⢀⠂⢠⣿⣡⢖⡒⢚⠻⡈⠋⠉⠀⠀⠂⠃
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢲⠏⠀⠀⠀⠀⢝⠉⠑⠋⠀⠀⠀⠈
⠜⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⢠⡄⠀⣼⠁⠀⠀⠀⢀⣀⡀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣾⣶⣾⣶⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠿⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⠿⠿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⣤⣤⣤⣄⡈⠉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣤⣤⣤⣤⣀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣸⣷⡄⠀⠀⠀⠀⢸⣧⠀⠀⣿⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠈⠛⠟⠃⠀⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⣠⡼⠏⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢀⣠⡾⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡁⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠶⠶⠶⠊




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⠀⠀⠀⢀⡤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢦⡘⠁⠀⢧⡠⠒⠁⠀⣏⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠒⠦⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠩⠿⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠰⢤⠤⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⣀⣠⡌⠑⠚⠉⢉⠙⠲⢭⣑⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⣀⣀⣈⡉⢀⠀⠔⣛⡋⠁⠀⠀⠈⠳⣜⠉⠉⡹⠋⠀⠀⢀⠤⢄⠀⡀⠀⢙⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⡖⠊⠁⠀⠀⠈⠲⠊⠉⠀⠀⠈⠑⢤⡀⠀⢈⢦⠀⠈⠓⣀⠄⠳⣄⠀⠙⠑⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡟⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⣼⠊⡇⢠⠊⠁⠠⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠁⠀⣨⠟⠉⠉⠀⠀⠀⠰⠶⣴⠄⠀⠀⠀⢀⠘⠀⢱⠀⢉⣦⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡸⠒⣲⣾⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠈⠀⠀⠂⠀⠀⠀⠤⠀⠀⠀⡇⠀⠀⡰⢁⠞⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⡀⠀⠀⠀⠀⠀⠀⡔⠄⠀⠀⢀⡴⠃⠀⠀⣇⡼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⢀⠊⠈⢇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡠⢈⡁⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠁⠀⠀⠈⠳⣄⠀⠀⠀⠳⢖⠶⠆⠀⢀⠀⢀⠔⠁⠀⠑⠶⠊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠒⠒⡡⠔⠁⡀⠀⠙⠒⢦⠄⠀⢀⠔⠉⠀⠧⣎⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⣀⠀⠀⣀⡤⠖⠒⠒⡛⠀⠀⢊⡀⠈⠀⠀⠀⢙⣦⡀⣀⡤⣪⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⡠⠺⣅⠀⠀⠀⠉⣿⠶⠖⢉⣉⡘⠀⣦⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠈⠑⠒⠐⠚⠷⠖⠀⠀⠀⠉⠉⢻⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢚⡃⠀⠀⠀⡀⠘⡇⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡍⡁⠀⠀⠘⣇⠀⢳⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⡉⠀⠀⠀⠸⡄⠎⠧⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⢠⣇⣀⣀⣀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⡟⠂⠀⠀⠀⠀⠀⠀⠘⢟⣀⠀⢰⠉⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⢀⠸⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⡂⢸⣹⡽⡸⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠿⠶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣥⣴⣶⣶⣶⣶⣦⣤⣉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠙⠛⠛⠛⠛⠛⠟⠻⠿⣿⠂⠀⠀⠀⠀⠀⣿⣿⠉⠁⠀⠀⠀⠈⠉⠁⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⢇
⠀⠀⠀⠀⠀⠀⠀⢀⠿⢿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⡞⢙⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠊⣇⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣀⡄⠀⠀⠀⠀⠀⠠⢬⣤⡄⠀⠀⠀⠀⠀⠀⣴⡆⢰⡤⢧⣦
⠀⠀⠀⣀⣢⡷⠠⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠛⠤⢀⡠⣦⡶⡀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⣴⣿⠧⠘⠀⠐⠛
⠀⠀⠀⠐⠋⠀⠀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠌⣁⠠⡉⠁⢴⣤⣤⣤⡀⠀⣠⣤⣶⣾⠟⠋⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠑⠀⡁⠂⢁⠂⠄⢀⠀⠀⠀⠀⢀⠀⠀⠠⡊⠄⢈⠀⠊⠀⠀⠀⠐⢀⡘⠙⠛⠣⠄⠻⠋⠁⢡⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠂⠀⢀⠤⣀⠨⣀⠄⠆⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠂⠀⠀⠀⠐⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠁⠀⠃⠀⠖⢂⠢
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⢀⠠⠐⠻⣀⠇
⠀⠀⠀⠀⠀⠀⡔⣀⣡⠉⠑⠐⠀⠀⠀⠀⠐⠒⠒⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⠮⡄⢨
⠀⠀⠀⠀⠀⠀⠃⠘⠁⠑⢀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⢣⡄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠂⡡⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢀⠀⠀⡆⣔⠀⡇⠀⢳⣠⠀⠀⡀⢻⠀⠀⠀⡠⡀⡀⠀⠀⢰⣆⢠⡄⢰⠀⣶⢠⡤⢰⣦⡆⢔⡅⡼⠀⠀⢦⢴⡅⠀⠀⠀⠀⢀⠠⢀⠄⢠⠄⣶⠐⠂⢆⠀⡇
⠀⠀⢣⡶⣦⢹⠔⠸⠊⢈⠁⡄⣮⠀⠘⢇⠀⠀⢌⢒⡈⠀⠐⡏⠹⢸⠹⠆⠟⠻⠘⠁⠈⠉⠋⠙⠐⠃⠀⠀⠉⠛⠀⠀⢀⡀⢌⠎⠳⠣⣾⠘⠢⠉⡄⠃⠒⠀⠄
⠀⠀⠀⠁⣈⠀⡀⢰⠒⡾⡗⣼⠹⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀⠤⣄⡀⢀⣀⡀⢠⡄⢰⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀
⠀⠀⠀⠀⢹⣀⡜⠈⠓⠁⠀⠀⠁⣀⠀⢲⠀⠀⠀⠀⣠⠂⢰⣠⡇⣼⡄⣷⣤⠞⢸⠖⠁⣷⣃⠝⡿⣼⠇⠸⠀⠀⠀⡰⠉⠉⣧⡰⢀⡄⣀⡀⠀⠀⠀⠉⠸⠐⠂
⠀⠀⠀⠀⠀⠟⠀⠀⢠⣀⠀⢦⢠⡃⣤⠈⡇⠀⠀⠀⠧⠎⠘⠀⠋⠁⠃⠇⠉⠸⠘⠂⠀⠁⠉⠀⠃⠘⠀⠒⠀⠀⠀⠿⣤⣶⢫⡇⡼⣰⠃⢀⣟⠂⣶⠀⡄⢀⡀
⠀⢨⣗⣞⠀⢀⢠⠆⢳⣯⠓⢬⡆⠢⠻⡄⠰⠀⠀⣤⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⡗⠀⢀⡾⠀⠀⠀⠀⠀⡠⠒⡠⠀⠀⠀⠈⠃⠉⠁⠛⠂⠼⠄⡼⢻⡼⢁⡞
⠀⠀⠋⠀⠀⠀⢻⡒⠠⠁⠀⠀⠉⠀⠀⠀⠀⠀⠐⣄⠲⣣⠀⠀⠀⠈⢟⠢⣠⠃⠸⡴⠋⡇⠀⠀⠀⠀⠚⣤⡻⠂⠀⠀⠀⡆⢠⠰⠂⠀⠀⠀⠀⠀⠘⠁⡘
⠀⠀⢶⠂⢤⠀⠀⠀⠀⠀⠀⢠⢤⣶⣎⠀⠀⠀⡀⠈⠲⠉⢧⠀⠀⠀⠘⡶⠶⢶⣖⣾⣿⡅⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠐⠒⠈⠐⠰⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢠⡵⠄⢳⡀⠀⠀⠀⣠⠀⣠⠈⢅⠂⣴⢢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⣀⢀⠄⡤⠀⠀⡄⢠⠀⣄⠀⠂⠰
⠀⠀⠀⠙⠪⣧⡀⠀⠀⢸⠟⡎⣓⠀⠔⠃⠀⢈⠀⠀⠀⢀⡄⡄⠀⠀⣀⡀⠀⡀⠀⠀⢲⡸⠆⣰⠀⣖⡁⠸⠀⠀⠠⠇⠀⠉⢈⢀⡋⠈⠁⠉⠈⠀⠀⠀⠀⠂
⠀⠀⢀⢔⠀⠈⠙⠀⠀⠘⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣜⡧⢸⡸⡤⢹⠖⢀⠈⣢⢣⡠⡗⠘⠃⡇⡧⠂⠀⠀⠀⠀⠀⠒⠉⠁⠚⠂⠉⠀⡀⢀⡀⡔⡄⣷
⠀⠀⠂⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⢀⡷⣴⠂⠀⠀⢸⠁⡇⠀⠃⠃⠼⠋⠁⠘⠁⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡠⠀⣆⡇⣿⡀⡷⡜⣇⡿⠁⣿
⠀⠀⠀⣴⡸⠓⠿⢁⡠⣀⡀⠀⠀⠀⠀⢹⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠆⡆⣯⠇⠀⠀⠀⠀⠀⣰⡄⠀⠀⠰⣅⡄⢹⢹⠋⠁⠃⠀⠻⠘⠀⠴
⠀⠀⢀⢀⠀⠶⠶⠜⠉⠈⠀⠀⠀⠀⡀⠀⣀⡀⠀⢠⠀⢠⡿⢀⠞⠈⡆⠀⠀⠀⠀⠃⠃⢁⣠⡐⡆⠀⠀⠙⣯⣽⠛
⠀⠀⠘⠋⠁⠀⠀⢀⡴⠂⡀⣏⠖⣸⣧⠈⡇⢶⡁⢸⠀⠀⠀⠘⠚⡆⢻⣀⡀⠀⠐⣯⣞⡎⡏⠀⡃⠀⠀⠈⠁⠈⠁⠀⣄⠀⡤⠀⢠⠀⠄⠀⣰⡀⢤⠆⡆⢸
⠀⠀⠀⠀⢄⣠⠀⢾⣠⢿⠀⡟⢦⡉⢸⠀⠃⠴⠋⠀⡄⠀⠀⠀⠴⠇⢈⠉⠇⠀⠀⠉⠀⠀⠀⠀⠁⡔⢒⠢⡀⠀⠀⠀⠩⠁⠑⠀⠸⠂⠂⠀⠀⠁⠈⠀⠁⠐
⠀⠀⠀⠰⢦⠷⠄⠀⠀⠉⠀⠀⠀⠉⠈⠁⠀⠀⠀⢀⣠⠄⠀⠀⠈⠈⠀⢀⣠⣄⠰⠂⣂⠞⠁⠀⠀⠱⠤⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠌⣃⠑⠀⠀⠀⠀⠀⠈⠉⠀⠋⠈⠁⠀⠀⠀⠀⠀⠀⢉⠁⠀⢠⠀⡆⡆⢠⠄⢴⠖⡠⣄⣞⣲⠞⢦⡟⠀⡇
⠀⠀⢀⣶⣼⣰⢗⡖⡆⠰⡐⢄⠆⡄⣶⠀⡇⠀⠀⠀⢰⡂⡖⢲⡀⣶⢲⣠⡼⠐⢱⣆⡖⠐⠶⡅⣊⡄⢸⠀⠀⠸⣾⠁⠗⡧⠆⢸⠸⡤⠏⡏⠳⣄⣸⠀⠀⠃
⠀⠀⠘⠃⠀⠃⠈⠁⠉⠀⠁⠀⠀⠁⠉⠀⠂⠀⠀⠀⠸⠊⠉⠚⠂⠈⠈⠘⠀⠀⠀⠈⠈⠂⠁⠁⠈⠁⠐⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠄⢀⣠⠎⠉⢷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡞⠈⠀⠀⠀⢀⠈⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢧⢱⠀⠒⠂⡀⠈⠀⢀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡀⠈⠓⠂⠀⠀⠀⡀⠀⠉⠀⠙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⣀⣹⠀⠀⠀⠀⠀⡀⠤⠀⡂⠱⠌⡰
⠀⠀⠀⠀⢀⠔⠊⠒⠒⠀⢄⡀⠀⠰⠈⠈⠉⠀⠀⠀⠁⠀⠈⠈⠀⠉⠁⠠⠀⠀⠀⠀⠘⠰⠈
⠀⠀⠀⠔⠃⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⣆
⠀⠀⡎⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠈⠠⠀⠀⠀⠑⢢
⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⢀⡴⠒⠒⠒⠲⢄⡀⢠⠀⢸⠀⠀⠈⠀⠀⠀⠂⠀⡇
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢸⡧⠀⠀⣿⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡀⠀⣤⠀⠀⠀⠀⠹⠃⠀⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠙⡒⠒⠠⠤⠤⠤⠴⢤⠂
⠀⠀⠀⢱⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠈⠲⠤⠤⠤⠴⠚⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠤⠄⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠋⠐⠀⠀⠀⠀⠀⠀⢂⠀⡀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠈⠈⡐⠀⠂⠀⠀⠠⢄⠊⠐⠄⠀⠄⠡⠜⠀⠀⠀⠁⡀⠐⡂⠢⠀⠀⠰⠀⡐⠁⠁⠀⠀⢠⠁⢄⡔
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠑⠀⠀⠀⠁⠀⠂⠀⠀⠀⠠⠀⠈⠑⠆⠀⠀⠢⠀⠀⠁⠂⠀⠀⠀⠂⠤⠀⠁⠁
⠀⠀⠀⠐⢀⠀⠠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⣀
⠀⠀⠀⠠⠮⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠄⡀⠀⠀⠈⡀⢀⢂⡂⠁⠀⢠⠔⠉⠀⠐⠀⠀⠐⢀⡄⢡⠀⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠄⡀⢁⠀⠀⠀⠀⠈⠂⡀⡀⣀⠀⠀⠀⠄⠀⠋⣈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣾⣷⣤⣤⣤
⣠⡄⠈⠃⠉⠘⠁⣦⡄⠀⠀⠀⠀⠀⠀⠀⡸⠏⠀⠻⠙⠉⢧⠀⠀⠀⠀⠀⠀⠀⠸⢉⣤⡀⢀⣤⡙⠃⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠈⠻⢿⣤
⢸⣏⠁⢐⣀⡀⢈⣹⠁⠀⠀⠀⠀⠀⠀⠠⣯⣁⣤⣤⣤⣄⣽⡆⠀⠀⠀⠀⠀⠀⠇⣾⠟⠃⠈⠻⣿⠸⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀⣀⠀⠀⢸⡟
⡀⠲⠂⠀⠉⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⠛⠀⡠⠃⠀⠀⠀⠀⠀⠰⣿⣷⣀⠀⠈⠉⠀⣠⣾⠿
⢛⠀⣘⠀⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣷⣶⣶⣿⠛⠃
⠘⣴⡇⢠⠄⡤⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠭⢭⢭⠽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⣶⢰⡆⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠠⠃
⠈⠛⠆⣸⡀⣇⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⢉⣻⣛⣼⡉⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⢿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⢿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⣆⢀⣶⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠈⠁⠀⠉⠙⢿⠟⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⡀
⠀⢀⠀⠐⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣠⣤⣤⣤⣀⣈⠀⠀⠀⠀⠀⢠⠋⣸⣾⠿⠿⠿⣷⣄
⠣⠁⠀⠀⠀⠀⠀⠡⠇⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⢻⡟⠁⠠⠀⠀⠀⢻⡛⣷
⠠⠀⠀⢿⣿⠿⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠹⣏⠳⢄⠀⠀⠀⡀⠈⢛⡯
⠀⠑⠤⠀⣀⠠⡔⠁⠀⠀⠀⠀⠀⠸⢿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠉⠹⣷⣄⢿⣞
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠈⣬⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣿⣜⡞
⢠⠂⠀⠀⠀⠀⠀⡓⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⢃⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢘⠀⡄⣤⢚⠎⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣤⣾⣿⣿⣿
⠈⠉⠺⠭⠶⠭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠖⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠻⠆⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠋⠛⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠙⣿⡇⠀⠀⣼⡟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣸⡿⠀⠀⣼⡟⠀⠀⡀⠀⠀⠀⢠⣾⠂⠀⠀⢀⣶⠆⠀⠁⢀⣀⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠷⠶⣾⡿⠀⣠⡾⠛⣿⠂⢠⣿⡗⢩⣿⠀⣾⡧⠊⣿⠂⢻⣿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣿⠇⢰⡟⢁⣾⡇⢀⣾⣯⢤⣾⠏⣼⣿⢤⣼⠟⢀⣿⠃⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢿⣄⠈⠛⠁⠘⠛⣽⡏⠙⠋⠁⢰⡿⠙⠛⠉⠀⠀⠛⢋⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠃⠀⠀⠀⣴⠞⣻⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⡀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣴⡆⢀⣴⡷⠀⠀⢰⣄⠀⠀⣶⠄⠀⠀⠀⠀⠀⠐⠛⠟⠁
⠀⠀⠀⠀⠀⢠⣶⠿⣿⡟⠉⠙⢦⠀⠁⢀⣤⠉⠉⠉⠛⠛⢻⣾⢿⣶⣿⣯⣤⣀⣠⣼⠟⠀⣼⡟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠹⠅⣰⣿⣀⣀⣤⠏⢀⣠⣌⠉⢰⣛⡆⠀⠀⣼⠏⢠⡿⢁⣭⣭⡍⢉⣡⣤⣴⡟⠀⠀⢠⣴⠶⣤⠀⢀⣴⠆⢠⣶
⠀⠀⠀⠀⠀⠀⣰⡿⠉⠉⠉⢹⡄⢹⡿⠁⢀⣼⢛⡿⠀⣸⡏⠀⣾⡷⢋⣿⠋⣴⠟⠉⢠⡟⠀⠀⣴⡿⢁⣼⠇⢀⣾⠏⣠⣿⠃
⠀⠀⠀⠀⠀⢠⣿⡃⢀⣀⣤⠟⠁⣿⣧⠶⠋⢰⣿⣥⢾⣿⠀⢸⡟⠁⢼⣇⡤⢿⣤⡶⠻⣧⣴⠞⢿⡥⠊⣿⡤⢺⣿⠔⣿⠏
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣴⡟⠀⠐⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠶⠶⠶⢶⣶⣦⣤⣤⣤⣤⣤⣤⣾⣯⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣬⣿⠟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⡾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⡀⠈⡄⠀⠀⠠⠀⡠⠆⢀⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠄⠀⠀⠀⠀⠈⠊⠀⠘⠁⠐⠀⠀⠀⢈⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡖⠠⠤⠀⠠⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠢⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡀⠘⠂⣾⣿⣿⣿⣿⣿⣶⠀⠂⢂⣤⣤⣤⣀⡒⠀⠀⢁⠂⠄⡀⠀⠘⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⡠⠲⣹⣿⣿⣿⣿⣿⡿⣠⡀⣾⣿⣿⣿⣿⣿⣿⣶⢀⡟⠀⠌⠂⡀⠀⠀⠀⡠⢁
⠀⠀⠀⠀⠀⠀⠒⡂⠀⠂⠀⠠⠊⠀⠀⠙⠿⣿⣿⡟⠉⠀⠁⠁⠻⣿⣿⣿⣿⣿⣿⢋⠞⠙⠢⢄⡀⠈⠁⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠠⠈⠀⠀⠉⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠮⠭⠿⠭⠖⠁⠀⠀⠀⠀⠉⠲⢄⣀⣤⠁⠀⣀
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠁⠋
⠀⠀⠠⢆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠐⢄⠀⡀
⠀⠀⠄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⢂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⢠⠊⠀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠠⠄
⠀⠀⠠⠀⠁⠀⢀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠑⠀⢀⠃⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢀⠀⢨⠀⠀⠠⠌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢠⠀⠀⠀⢀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠂⢀⠠⠇⠀⠠⠒⡀⠀⠀⠜⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠈⠐⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢸⠀⡏⢠⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠁⣀⣀⣀⡀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠊⠀⠀⠀⠈⢢⠀⢁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢸⠀⠀⣀⡀⠀⡸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠉⠑⠤⠤⡑⠤⠤⠤⠖⠁⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠀⠀⢀⠤⠠⢀⠔⠚⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⠢⠖⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠲⢤⠞⠁⣀⠴⠒⠒⠒⠲⢀⡴⠚⠉⠀⠈⠉⠓⢄⠱⠤⠠⠤⣄⠀⠀⡀⠠⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠁⠉
⠀⠀⠀⢀⡴⠒⠒⠀⠀⢀⡤⣖⠋⠩⡍⠉⠉⠓⠲⣤⡀⢀⠔⠋⠁⠀⠀⠈⠙⠦⣄
⠀⠀⢠⠏⠀⠂⠀⠀⡰⠋⠀⠃⠘⠐⣇⠀⠀⠀⣍⠁⠛⣎⠀⠀⢀⠄⠚⢆⡀⠀⠘⣦
⠀⠀⢸⠀⠀⠀⠀⠰⠁⠀⠀⠐⠐⠉⠁⠀⠀⠀⠀⠓⠀⢸⡀⠀⠈⠢⣉⠔⠁⢀⠀⢸
⠀⠀⠸⡄⠀⠀⠀⢀⠀⠀⣀⠀⡀⠀⠸⡄⡄⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⡼
⠀⠀⠀⠙⢦⣄⡀⠸⡄⠀⡆⢂⡑⠀⠀⠣⠂⠈⠁⠀⠀⡼⠀⢤⣀⣀⣘⣑⣠⡶⠚⠁
⠀⠀⠀⠀⠀⠀⣄⠀⡙⢦⡙⠃⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡀⢰⠀⢈⡭⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠃⡴⠈⣝⠒⠒⠒⠒⠂⡀⠀⠀⠀⠀⢱⠈⢠⡎
⠀⠀⠀⠀⠀⠀⢀⡇⢰⡇⠀⠈⢦⠀⡏⢠⠞⠀⠀⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⡸⠀⢸⠇⠀⠀⢸⠀⢰⠋⠀⠀⠀⠀⠀⠀⢰⠃⢸
⠀⠀⠀⠀⡤⠖⠒⠒⠶⢄⠀⠀⢸⠀⢸⢀⣄⣀⡀⢀⡤⠤⡼⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡟⠀⢸⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠃⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢐⡈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠠⠇⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠀⣰⣷⢀⢤⠀⠀⠀⠀⠈⠀⠐⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠠⠀⢠⣿⣄⠂⠈⣦⡰⠙⢄⣾⣝⣻⠀⢸⠀⠀⠀⠐⠀⠂⢀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡝⣿⡿⡿⣄⣰⢿⡟⣤⣿⠟⠻⣿⣦⣼⣿⡿⠒⡇⠀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣘⠉⠐⣿⣦⣿⣿⣿⣿⡿⠿⣿⣿⣷⠶⢴⣿⣿⣿⣿⣤⣶⣿⣿⡿⠠⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣭⣷⣦⣯⠷⢷⠋⠙⠋⠀⠀⠀⠙⠁⠀⠈⠉⠙⠉⠀⠙⠙⣿⡟⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢻⣛⣛⣿⠁⢀⣀⡀⠀⣠⣤⣤⣀⣴⣶⣤⣰⣶⣤⣶⣆⠀⢠⣟⣛⣟⣛⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠀⢾⣟⣿⣿⢸⣿⡿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⡄⠀⠙⣿⣿⢿⣩⣂
⠀⠀⠀⠀⠀⠀⠐⢎⣉⣿⣿⣿⣄⠀⢸⣿⠿⣿⣿⣿⣧⣿⣿⣷⣶⣿⣿⣿⠙⠛⣿⣷⢀⣰⣿⣿⠉⣻⣿⡿⠟⠂
⠀⠀⠀⠀⠠⢶⣿⣿⣿⣋⠉⣽⣽⠃⠈⣿⠷⠿⠟⠙⠛⠛⠁⠉⠉⠉⠉⢁⣀⡀⠉⠀⠀⣿⣿⣿⣺⣍⠙⣄
⠀⠀⠀⠀⠀⠀⠈⠙⡻⢿⣟⡿⣿⠀⠀⡀⠀⢀⡀⠀⠀⢰⣀⠀⣰⢦⣤⡼⣹⣷⣶⣶⣾⣻⡿⣿⡿⣟⣯⡁
⠀⠀⠀⠀⠀⠀⡤⠊⠠⢤⣼⣿⡿⣿⣿⣿⣤⣼⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⢁⣿⣿⣿⣿⡉⢻⠻⠷⡄
⠀⠀⢀⠄⠴⠀⠀⠀⣠⣿⠿⠿⠋⣽⣿⣿⣿⣿⣿⣿⠞⠉⢉⣷⣿⣿⣿⣿⣿⣾⠿⣝⡟⠳⢝⢻⣷⠒⠂
⠀⠀⠣⡀⢀⠀⠀⠄⠉⠀⠀⠓⠁⠹⠴⡟⣻⠟⢻⣝⣦⣤⣯⡟⠹⠿⢋⣿⣻⡿⠀⠉⠀⠁⠀⠙⠿⡇⠅⠀⢰
⠀⠀⢸⡀⠸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠟⠡⢀⠊⢿⣿⣿⠟⠐⠃⠀⠀⢹⡟⠀⢳⠀⠀⠀⠀⠀⠀⡠⠀⠠⢈⠆
⠀⠀⠀⠉⠳⣀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣷⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠖⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢀⠲⡄⠀⠀⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠢⡜⢱⠀⠣⠤⠧⣤⠎⠙⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⣧⠈⢧⠀⠀⡴⠙⢄⣀⡎⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢫⢣⡀⠑⢌⡲⢤⣀⡼⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠳⣝⠢⢄⣉⠑⠚⢒⣚⡩⠥⢺⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣠⣀⠀⠀⠀⠀⠉⠒⠂⠬⠝⠓⠚⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⢤⣀⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠶⠠⠤⡀⠀⠀⠀⠑⠐⠷⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠳⠀⠀⣀⠄⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡼⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡠⢾⠀⡰⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖⡏⠀⢸⠀⡧⣂⠢⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣇⠀⢸⠀⠳⠽⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠒⠚⠀⠀⠘⡆⠈⢧⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠵⢖⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠲⠤⠄⠀⠀⠀⢸⠤⢄⣀⣋⣻⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⠤⠖⠚⡗⠒⢶⠒⠋⠀⠐⢲⡏⠣⣌⡉⠓⠚⠉⢉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡸⠁⠀⢸⡀⠀⠀⢀⡜⠙⢦⣀⠈⠉⠉⣉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢢⡀⠀⠀⠀⢀⠇⠸⡀⠀⠀⠀⢀⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⢄⠀⠀⡼⠀⠀⢧⠀⠀⡰⠋⠀⡇
⠀⠀⠀⠀⠀⠀⢻⡒⠤⣀⠀⠀⠸⠀⠀⠈⠳⣠⠃⠀⠀⠘⣤⠎⠀⠀⢠⠁⠀⠀⣀⠤⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠢⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠔⠋⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠉⠑⠒⠤⡀⠀⠀⠀⠀⢀⠎
⠀⠘⠳⣒⠒⠒⠒⠂⠤⠵⠀⠀⣠⠞⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠮⠔⠒⠒⠒⠒⣨⠟⠁
⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⡔⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⢘⣢⠀⠀⣸⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣔⡁
⣀⡠⠤⠒⠒⠉⠁⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠒⠒⠤⢄
⠈⠉⠑⠒⠤⢤⣀⡀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠛⢄
⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠔⠥⠤⠤⠒⠒⠒⡲⠀⠀⠈⠢⣑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢖⠒⠒⠒⠒⠤⠬⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡀⠈⠑⠲⠭⠍⣉⣀⠠⠤⠖⠊⠁⢀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⡤⠒⠉⡇⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠉⠒⢤⣀⠀⢣
⠀⠀⠀⠀⠀⠀⡼⠔⠊⠁⠀⠀⢠⠁⠀⢀⡔⠙⡄⠀⠀⢠⠋⠢⡀⠀⠀⡆⠀⠀⠈⠑⠢⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠋⠀⠀⢱⠀⠀⡎⠀⠀⠙⢆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⠁⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠱⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⣤⣼⣇⡀⣼⠈⣿⠃⠀⠀⠀⠂⡠⢰⠀⠀⠀⠀⠠⡄⠀⡀⠀⠀⠀⠀⠀⠠⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢀⡠⠔⠀⠀⠀⠒⠤⠤⠀⠀⠀⠀⠀⠀⡐⠈⠈⠁⠀⠋⠙⠀⠟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⠉⠀⠐⠀⠺⠁⠀⠘⠃⠾⠁⣀
⠀⠈⠀⠀⡰⠀⠐⠀⢄⠀⠀⠀⡀⠀⡠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣾⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠁⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠂⠀⠀⢀⠄⠀⠠⠀⠔⠢⠃⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠄⡀⠀⢸⠀⠀⠠⠞⢹⣿⠧⢤⡆⠀⠀⢀⢤⠶⠒⠲⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠠⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠈⠀⠀⠀⠀⠉⠻⠄⣜⣀⢀⡄⠛⠁⠀⠀⢀⡇⠀⠀⡏⠀⠀⢠⠞⡰⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠸⠋⠀⠀⠀⠀⠀⡜⠃⠀⠀⠿⠚⣦⠏⣰⢷⠄⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢃⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣺⠃⠀⠀⠀⠀⠀⠈⠐⠁⡜⠸⡉⠛⡼⠛⡆
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⠎⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠁⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⠀⣀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠈⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢿⡄⠻⣷⣤⣸⡟⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠙⠁⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣿⠁
⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠈⣿⣀⣀⣼⣿⠀⠈⠙⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⣴⠀⠀⠀⠀⡀⠀⢳⡾⠁
⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠘⣿⠀⢸⣿⠏⠉⢻⡇⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⡀⠈⣿⡀⣤⡀⣿⠀⢸⠀⣠⡇⠀⠀⣷
⠀⢀⣀⠀⠀⠙⢻⣄⠀⣿⣷⣤⣿⠀⠈⣿⡆⠀⠈⠿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⣿⠏⢳⣿⠀⠸⡃⠉⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡟⠈⠻⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠟⠞⠀⠘⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠁⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠶⠀⢀
⠀⢀⣰⣶⠀⠀⠀⠂⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡤⠀⡄
⠀⠀⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⡀⣀⣠⠀⠱⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠀⠀⣀⡀⠀⠀⠀⠠⡀⠤⠂⠉⠀⠀⠈⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠄⠀⠀⡄⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣰⠆⣴
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠐⠠⠦⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠒⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⠀⠀⡀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⠀⠀⠈⠀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠄⠃⠀⠀⠙⠦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠇⠀⠀⠀⠀⠠⢔
⠀⠀⠀⠀⡀⡀⠀⢀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠠⡀⠈⠃⠀⠀⠁⠀⠀⠀⠀⡀⡆⠐⠈⠒⣄⣄⠀⠀⠀⠀⣰⣦⠀⣤⣿⠏⠻⣆
⠀⠀⠀⢀⡌⠓⠚⠈⢄⡸⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⢠⢀⡂⠀⢀⠀⠰⠄⢀⠔⠀⠀⠀⠀⠠⠀⠀⠀⠀⢞⠀⠁⠀⠀⠀⠙⣿⣆⢸⣧⢀⡿⢻⣤⣏⣿⡄⢠⡿
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠿⠁⠎⠁⠘⠒⠇⠀⠀⠈⡀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠏⠀⠀⣀⣀⠀⠀⠘⢿⡿⠙⣿⠇⠘⠂⠘⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠠⠤⠀⠀⠰⠄⠄⠤⠤⠀⠀⠠⠀⠠⠀⠄⠄⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆⠐

⠀⠀⣠⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣤⠞⠀⠀⠀⢀⡀
⠀⠸⠛⢉⠀⠀⠀⠘⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓
⠀⠌⠀⠀⠀⢂⡀⠀⠀⠀⢀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡦⠤⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠈⡄⠀⠀⠌⠀⠀⠀⠀⢠⢠⡄
⢸⠀⠀⣤⠀⠀⡇⣠⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢶⡤⢷⠶⠾⠿⠏⠉⠀⡇⠀⠀⡀⠀⠀⢐⣆⠀⢸⡆⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠠
⠘⡄⠀⠛⠀⠀⡇⠉⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠢⢀⡀⢀⡀⠜⠀⠀⠀⢣⠀⠀⠈⠃⠶⠈⠀⠀⡰⠁⠀⠀⠠⠀⠀⢠⡦⠠⠀⠀⠀⠀⠃
⠀⠈⠢⢀⠠⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠦⠄⠀⠀⠀⠀⠀⠀⠈⠙⠂⠈⠙⠒⠂⠀⠀⠀⢀⡤⠶⠀⠀⠀⠒⠢⡀
⠀⠀⠀⢀⣴⠿⡀⢀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⡀⠀⠀⠈⠄⠀⠀⠀⢀
⢀⡤⠞⠋⠁⠀⠈⠆⠀⠈⠙⠲⡄⠀⠀⠋⠙⠛⠳⣦⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢴
⠀⢲⠀⠐⠛⠀⠀⡇⠙⠃⠀⠀⡇⠀⠀⠀⠀⠀⢠⡈⠟⠸⠀⢸⡇⠀⠀⠀⠀⠀⡄⠀⠀⠘⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠻
⠀⠘⡀⠀⠀⠀⢀⠇⠀⠀⠀⡔⠀⠀⠀⠈⠉⠩⠥⠷⠄⠀⠢⡈⠁⢀⠔⠀⠀⠀⠀⠄⡀⣠⠖⣄⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠐⠂
⠀⠀⠈⠒⠀⠔⠁⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠤⣄⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠋⠀⠀⠀⠈⠛⠳⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠘⠛⠇⠀⠀⠀⠀⠀⠀⢀⣤⠀⠐⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⡀⠀⢠⠂⢀⣀⣀⠄⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠋⠀⣐⠂⡀⠀⠉⠓⠦
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡁⠀⠀⠀⠀⡆⠸⣯⣟⠓⠀⠐⢯⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠃
⠀⠀⡀⠀⠀⠀⢣⠀⠀⠀⠈⠇⠀⠀⠀⠀⠇⠚⢿⠿⠃⡸⡀⠞⠷⠟⠀⠀⠀⠀⠃⠀⠉⠁⠀⠇⠉⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠃⡀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠊⠀⠈⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠴⠶⢄⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⠘⠛⠧⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠉⠓
⠀⠸⠛⠉⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄
⡀⠀⠀⣀⣀⠀⠀⠀⢈⣁⡀⠀⠀⡀⠀⠀⡇⠀⢠⠀⠀⠘⡄⢀⠄⠀⠀⠀⠀⢰⠀⠀⠀⢸⡇⠃⠀⠀⠀⠟⡆⠀⠀⠈⠀⠀⠀⠀⠖⠆
⠡⠀⠀⠈⠁⠀⠐⠀⠀⠈⠁⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⢀⠁⠀⠀⠀⡐⠀⠀⠘⡄⠀⠀⠀⠀⡀⠀⠀⠀⢀⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⢀⠔⠁⠂⠀⠐⠁⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠦⢤⣀⠀⠀⢠⠖⠲⢤⡀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⠓⠶⠋⠀⠀⠸⣿⡴⠚⠁⠀⣠⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣼⡆⠀⢠⣀⠀⢠⣷⣄⡁⣠⡖⢀⣾⣿⠟⠁⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠦⣄⠀⡇⠀⠀⢀⣷⠀⠸⣿⡛⠿⡟⠈⠛⣿⢠⣿⡿⠁⢀⡴⠋⠁⠀⠀⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⣼⣷⠃⠀⠀⣸⣿⣤⣤⣭⡽⠛⠓⠲⣄⠙⢾⣿⠁⣰⠋⠀⠀⢀⣠⣾⡇⠀⠀⣿⡄
⠀⠀⠀⠀⢀⡴⠃⠀⠀⡀⠀⠀⢰⣿⠏⠀⠀⣴⣿⠟⠚⠉⣽⡇⣠⠀⠀⠸⠟⠛⠛⣶⠁⠀⠀⢠⣾⡿⢻⠇⠀⠐⣻⣷⡄⠀⠀⣀⡀
⠀⠀⠀⠀⡞⠀⠀⢀⣾⠀⠀⢠⡿⠃⠀⣠⡾⠿⠿⠀⠀⢘⣿⢿⡿⠀⠀⢀⡄⠀⣸⠃⠀⠀⢠⣿⣟⡁⠘⢦⣤⣾⣿⠟⠀⢀⡜⠁⣿⣦
⠀⠀⠀⢸⠁⠀⢀⣾⡏⠀⠀⠈⠁⠀⠈⣀⠀⠀⠀⠀⠀⠘⠿⢋⡄⠀⢀⣾⡇⠀⠋⠀⠀⠀⠀⠀⣉⣉⠉⠙⢿⡍⠁⣀⠴⠋⠀⣰⣿⠇
⠀⠀⠀⢸⡀⠀⣼⣿⡇⠀⠀⢀⣤⣶⣿⠋⠀⠀⣠⣷⣦⣴⣶⣿⣦⣤⣿⣿⣹⣤⡄⠀⠀⢰⣦⣀⠘⠻⠀⠀⠸⠛⠋⠁⠀⣠⣾⡿⠋
⠀⠀⠀⠀⢧⣼⣿⠇⡇⠀⠀⠈⣿⣏⡏⠀⠀⠀⢉⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢈⣿⣿⣻⠆⠀⢀⣴⣶⣶⣶⣾⡿⠟
⠀⠀⠀⠀⠀⠙⠏⠀⢷⠀⠀⠀⠸⣿⣇⣀⣠⣶⠏⠀⠀⣀⣀⣤⣴⡶⢶⣿⣿⣿⡿⡄⠀⠀⣿⠿⠃⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢹⣏⠛⠻⣯⣴⣶⣿⡿⠛⣩⣴⣾⡿⠟⠋⠉⠀⠙⢦⣀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢶⣶⣾⡿⠂⠀⠈⠋⠉⠻⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢶⣾⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠖⡀⠀⠐⠂⠤⡀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠑⠄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠉⠁⠀⠀⠈⠁⠀⠓⠠⢤⠂⠀⠈⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⡐
⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⡠⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠑⢄⠔
⢀⠔⠈⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⡰⠟⠛⠛⠛⠀⠀⠀⠀⠙⠛⠛⠻⢦⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠃⠂⠉⠁⠢⡀⠀⠀⠌⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⡀⠀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⢡⠀⠁⠂⠀⠀⠊⢀
⠀⠀⠀⠀⠀⠱⡀⠈⠀⠀⠀⣤⣾⣿⢫⠃⣰⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⡏⡏⢉⣷⣦⡀⠀⠀⠃⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢻⣏⠇⢠⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡿⡜⠀⣾⣿⠉⠀⠀⠀⢠⠀⢀⠠⠐⠁
⠀⠀⠀⠀⢀⠠⠄⡇⠀⠀⠀⠀⠈⠻⣄⣾⣿⣿⣿⡿⠋⠀⠀⠈⠿⣿⣿⣹⠁⣼⡿⠃⠀⠀⠀⠀⠸⠉
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⢂
⠀⡔⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠰⣶⣦⡐⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⣠⣶⡞⠀⠀⠀⠀⢀⠂⠀⠡
⠈⢀⠂⠈⠁⠐⠢⠀⢱⡀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⡶⠶⠶⠶⢶⣶⣾⣿⠿⠋⠀⠀⠀⠀⢀⠎⠀⠀⠀⠑⠂⠄⠐
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠉⠛⠡⠤⠀⠀⠠⠤⠘⠋⠁⠀⠀⠀⠀⠀⢠⠮⢀⡀⠀⠀⢀⠠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⠤⠀⠀⠂⠁⠉⠐⠂⠀⠠⠤⠤⠄⠠⠀⠐⢅
⠀⠀⠀⠀⠀⠀⠀⠈⡄⢠⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠑⢄⠀⠀⠀⠢⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠘⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣬⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣄⢰⣂⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠚⠋⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠁⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⣶⣦⣌⠁⢏⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⡀⠀⢻⡏⠟⠻⣷⣦⣀⠢⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣄⠐⠻⣿⣿⣿⣷⣄⡀⢁⡶
⠀⠀⠀⠀⠀⠀⠀⢐⣿⠉⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠦⢤⣭⣿⣿⣿⣿⣿⡉⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⠀⠀⢩⡏⠀⠸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢰⢿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⢷⣶⡎⠀⠀⠀⢏
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢻⣷⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣼⣿⣾⣿⡁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢨⣉⣽⣿⣯⣿⣿⣔⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⡿⠊⠀⠀⣮⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠐⢼⣿⣿⡿⠟⠋⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⢷⣿⣴⡗⠿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣾⢋⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡆⠉⠀⠘⠇⠀⠀⠈⢷⣹⡇⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠺⣄⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⢠⣤⡄⠀⠀⠀⠀⠈⣿⡧⠀⠐⠀⠛⠀⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⣾⠘⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⠐⠁⠀⠀⠈⠃⡟⠂⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⣀⢀⣄⠀⡀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢃⡛⠈⠁⣀⡀⠀⠀⠀⠇⠳⣞⣇
⠀⠀⠀⠀⠀⠀⣧⡧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⣿⣿⣿⣿⡇⠀⠀⣇⠉
⠀⠀⠀⠀⠀⢀⡟⡇⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⣿⡿
⠀⠀⠀⠀⠀⢸⡇⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠁⢳⣷⣤⣄⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣼⣽⠿⢿⣟⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠜⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⢀⠔⠉⠀⠀⠀⠉⠢⠤⠊⠉⠒⠨⠕⠢⡀
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠘⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⡆⡇
⠀⠀⠀⠀⠀⠀⠸⡸⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊⠁⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⠑⠒⡄⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡒⠤⠤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠜⠀⠀⣆⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠉⠀⠈⠑⠂⠤⠐⠂⠁⠀⠀⠀⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⠀⠲⠀⠀⢰⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⠈⠡⠀⡄⣤⠀⠀⠀⠋⢸⠤⠈⠀⠤⠸⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⡁⣿⣜⠆⣹⠃⠸⠀⠀⠀⠀⣻⠐⠐⡀⠆⠀⠠⠐⠀⠀⠀⠀⠰⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠒⠂⠔⠲⠖⠷⠐⠚⠲⠶⠶⠶⡶⠦⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢄⣀⢀⣀⣀⣄⣠⣴⡄⡀⢀⡇⢛⡀⠡⢈⡧⡑⢀⡇⠀⠠⠀⠀⠘⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⣬⣿⢿⣿⢿⣿⢿⠋⢁⠃⣠⡄⢸⣷⣧⣤⣤⣴⣤⣤⣤⠀⠰⠔⣀⠠⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⠛⠀⢉⠉⡑⢙⠀⠘⠀⠚⠉⡘⢛⠛⡛⢛⡛⡛⣻⣿⣀⣒⣒⢈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠎⠁⠀⠀⠨⠳⠝⠮⢻⠢⠉⠺⠀⣥⢈⡄⠇⠀⠅⡇⣿⣿⣤⣤⣤⡀⢔⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⠆⣰⣺⢣⠼⠴⢶⣏⠚⠒⣾⣿⣻⣿⣿⣟⠁⠲⣆⣨⣭⡅⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⡍⠁⠉⠉⡄⢁⢈⢸⡧⢐⣓⣿⣿⣿⣿⣿⣿⠀⠀⠤⠴⠅⠂⢸⣷⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠾⠶⢿⠖⠲⢶⣷⡭⠹⠸⡗⢀⠀⡿⠿⠭⠻⢿⠷⠄⠫⠙⠉⣥⡥⢸⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢈⠐⣻⣍⣀⣢⣗⢰⠀⠒⢐⡞⠁⠁⠀⠀⠇⡴⠀⠂⠐⠀⠀⠀⠀⢹⣿⣅⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠈⠿⠻⡿⠛⡛⠀⠒⠠⢤⠄⢔⢠⡄⠠⠀⣥⠀⠰⠴⠴⣄⠀⠄⢼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠀⠀⠨⠇⠁⠀⠽⠀⡇⢋⡀⠀⠀⡀⠀⠁⠀⠀⠐⢠⡄⠤⢐⣿⠏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢲⠔⠂⣷⣿⣾⡶⠿⡷⠾⡶⣿⠿⢿⢧⠰⡤⠡⠤⣄⠀⠀⠤⠄⠀⠀⠸⠿⠃⣈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⠀⣿⣿⣿⡇⡃⠆⠣⠧⠸⠀⠘⢠⡱⡇⢺⢸⠀⠀⣀⣐⣒⣀⡀⠀⡗⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠁⢡⣤⣧⣴⣤⣤⣷⣤⣥⣧⣼⣬⡄⠀⡉⠁⢬⣥⣀⡀⢁⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠖⠸⠀⠀⠀⠉⠠⠀⠈⠀⠸⠀⠀⠀⠈⠉⡟⠉⠏⡛⠻⠛⢿⡟⠛⠛⠃⠀⠈⡄⠘⠛⠃⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠕⠌⠘⠈⠃⠀⠘⠃⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⡀⢀⡀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠓⡀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠈⠑⠂⠁⠀⠈⠂⠀⢀
⠀⠀⠀⣄⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠐⠈⠂⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠦⠀⠀⠈⣐⠁
⠀⠀⠀⣏⠀⠟⠀⢠⢨⡁⠀⠀⠀⠈⠒⠁⠀⠀⠈⡈⠀⠀⠘⡐⢂⠀⠀⠐⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢎
⠀⠀⠀⠀⠓⠀⠀⠀⠓⠉⠢⡀⠀⠀⠈⠀⠀⠀⠠⠦⠄⢀⣨⠠⠴⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⡆⠀⠀⠀⠀⠸⠆⣄⠀⠀⡀⠀⢀⠀⠀⠤⠀⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣶⡄⢀⣒⣼⡓
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠰⠿⠀⢈⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣠⡁⠄⠀⠀⠀⠀⢅⠁⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⣄⠉⠡⠋⠘⠌
⠀⠀⠀⠀⠉⠂⠂⠚⠀⠀⠀⠀⠊⠀⠰⠈⡄⠀⠀⠀⠀⠉⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠈⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠠⢀⠁⠀⠀⠀⠀⠀⡅⠀⠠⣶⠆⠀⠢⠤⠀⠀⠀⠀⡐⠁⠀⠀⠐⠂⠠⠀⢀⠁⠀⢀⡀⠀⠀⠐⠄⠐⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⢀⠂⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠂⠀⠀⠠⠚⡔⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠊⠁⠀⠀⡀⠀⠀⠀⠀⠇⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⢆⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡐⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠐⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠢⡈⠢⡡⠀⠀⠀⠠⣹⠓⠂⠀⠃⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠱⠄⠀⠀⠀⠀⡅⠁⠁⠐⠀⠀⠀⠀⠀⢀⠀⢠⠀⠠⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢖⣈⠶⢌⠀⠀⠀⠈⠂
⠀⠀⠀⣂⡠⠐⠀⠃⢀⠚⠀⠀⠀⠀⠀⢈⠂⠒⠁⠀⠀⠀⢈⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⣀
⠀⠀⠈⠚⠢⢀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠄⠤