Milk Tea Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠶⠴⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⣿⠀⠀⣿⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣠⠞⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⡼⠋⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣀⣀⣁⣀⣀⣀⣀⣀⣿⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠸⣇⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⢠⡄⠉⠛⠉⠀⠀⠀⣠⣤⣄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣴⠶⠶⣄⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⣧⣀⣠⡟⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠉⠉⢀⠀⠀⠘⠁⠀⣹⡀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡜⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠚⠛⠒⠒⠒⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⡟⠉⠉⠉⠉⠉⠉⠉⢙⠏⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢀⡠⠴⠒⠒⠒⢺⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⡴⠋⠀⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠒⠦⠤⣀⣀⣀⣠⡧⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⡾⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⡄⠀⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡁⣹⠀⢎⢈⡷⠀⠀⠀⠀⢀⠴⢤⠀⠓⠔⠃⢰⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⢀⡠⣄⠉⠀⢰⠉⢱⠀⠘⠦⠜⡠⢄⡀⠀⡜⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠘⢄⡼⠃⢀⣀⡉⢁⡞⠓⡄⠈⢧⡠⠃⢠⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠸⣀⡼⠀⠑⠚⠁⠀⠀⠀⢀⡎⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢌⣉⠓⠒⠒⠒⠒⠒⠒⢚⣉⣡⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⢠⣤⡂
⠀⠀⠀⠀⠀⠶⠂⠀⠙⠒⠓⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⣲⣾⣟⣹⣯⣩⣿⣿⠆
⠀⠀⠀⠀⢤⡀⠐⠒⠒⠚⠓⠀⠓⠢⠀⠀⠀⠀⠁⠐⠼⠿⠤⠿⠟⠛⠛⠉⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢠⠒⠤⠄⣀⡷⠉⠉⠀⠀⣀⡴⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⢸⣶⣶⣤⣄⣀⣉⣉⣉⣀⣀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠹⠉⡿⠻⢿⠿⣿⣿⡆
⠀⠀⢸⣿⣽⣿⣿⣿⢿⡿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⠀⠀⠀⣤⣴⣶⡀⠀⠀⠀⠀⠀⢈⠁⠀⠀⢁⡄⠉⠀⡈⠹⠁
⠀⠀⢸⢿⣿⣿⣽⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣁⣀⡤⠶⠊⣿⡏⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⠁
⠀⠀⢸⢸⣟⣝⣻⣻⣻⣿⢻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡉⠀⠒⠆⢁⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢸⢸⣿⣿⣿⣿⣟⣻⣿⢧⠁⠀⠀⣀⣤⣄⠒⠀⠀⠀⢻⣿⣿⣶⣦⣶⣿⣿⣯⡇⠀⠀⠀⠀⠀⢰⣆⡀⢴⢆⡄⠐⠟
⠀⠀⠀⢜⣿⣿⣿⣿⣿⣻⣿⡌⠀⠀⠀⢿⣱⣿⠇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠘⠋⠘⠟⠛⠃⠻⠃
⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⢠⣦
⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⡀
⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠫
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠙⠋⠙⢿⠿⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢈⣇⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣦⣄⣀⣀⣀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⣶⢀⣠⠄⣀⢠⡄⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⡀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡋⠾⣯⡇⢀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣖⢾⣿⣟⢻⣏⣙⡛⣿⡷⠀⠀⠀⠀⠀⠀⠡⣸⣗⣸⣿⣋⣁⡘⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠄⠰⠦⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⠆⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⡠⠔⠀⠈⢓⠀⠋⠠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠈⠉⠀⠀⠌⠀⠀⠀⠀⠈⠀⠀⠀⠀⠱⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡰⠥⣄⣀⣀⠀⠀⠀⠀⠖⢀⡐⠀⠁⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠉⠀⠀⠀⠁⠈⠉⠩⠍⠡⠈⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠷⠷⠟⠋⠀⠀⣤⣤⣄⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⣤⣤⠄⠀⢠⣤⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠒⠋⠅⣿⡇⠀⢸⣿⣿⣭⣿⣿⣻⣿⣿⣿⣿⣿⠃⣀⠠⠄
⠀⠀⠀⠀⣴⠦⣶⢶⡄⠄⠈⣿⣷⣶⣾⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⢰⡾⠗⠀⠛⠃
⠀⠀⠀⠀⠀⠈⠉⠿⠘⠀⠈⠘⢩⠿⣽⣻⣾⠷⣿⡿⠿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠀⠀⠀⠠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣓⣹⠛⣿⣦⣷⣷⣤⡗⣶⠿⠛⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠙⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠠⠀⠠⢀⠀⠀⢠⠀⠀⠀⠤⠄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠈⠧⠠⠸⠉⠺⡀⠘⠄⠈⠀⠀⠀⠠⠀⡂⠀⠆⠦

⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠒⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⠤⠄
⠀⠀⠀⠀⢀⢀⠀⠀⢡⡀⠀⠀⠀⢀⠈⠃⠲⡄⠠⡄⠀⠀⠀⠀⠀⠛⠁⠀⢀⡇⠀⠀⠀⠀⠀⣀⠤⠔⠒⠲⡉
⠀⠀⢅⠠⠬⠤⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⠀⠨⣤⣤⣤⣴⣶⣾⣿⡇⠀⠀⠀⠠⠎⠁⠀⠀⢀⡀⣈⡄
⠀⠀⠀⣤⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢿⡿⡿⣿⠋⣿⡏⠁⠀⠀⠀⠘⣶⣶⣶⣶⣴⣤⣴⠃
⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠈⠆⠀⠰⡷⠀⠀⣿⢿⡟⣿⢻⣿⠏
⠀⠀⠀⠀⢿⡋⣿⢹⡇⠀⠀⠀⣀⠒⣀⢀⡰⠀⠀⠺⠖⠀⠀⠒⡀⠌⡘⡌⠑⠄⠀⠀⠀⠀⣿⣹⣜⣽⣳⡟
⠀⠀⠀⠀⠸⠿⠾⠛⠂⠀⠀⠀⢠⢒⡰⢆⠓⠀⠀⠀⠀⠀⠀⠐⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁
⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠐⠀⠀⠀⣢⠀⠀⠀⠀⠀⢀⠀⡀
⠀⢀⡂⠬⠸⠛⠂⠀⠛⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⠈⠈⠀⠉⠢⡀
⠀⠀⢂⡀⣀⣤⣶⣶⣾⠀⠀⠀⠓⠒⠒⠶⠶⠤⠤⠬⠵⠀⠀⠁⢠⣦⣤⣤⣤⠀⠀⠀⣖⠒⠂⠂⠒⢀⡒⡆⠀⣤⡄
⠀⠀⠈⣿⡿⣿⢻⡟⣿⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⣾⠿⣿⡻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁
⠀⠀⠀⠘⣷⢣⣳⣎⣿⡄⠀⠀⠀⠐⠂⠤⠘⢠⡄⠀⠀⠀⠀⠀⢿⣹⠓⣗⣾⠀⠀⠀⠀⢀⠀⢠⡄⠠
⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⠀⠀⢀⠋⡄⢣⡘⢠⢀⠂⠀⠀⠀⠀⠙⠉⠉⠉⠁⠀⠀⠀⠀⢠⡔⢢⣜⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠃⠈⠃

⠀⠀⠀⠀⠀⠀⠐⢀⠐⡆⣠⠆⠀⢲⡀⡶⠀⠀⠐⣶⠀⢀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠁⠀⢶⠀⠹⣇⠀⠀⣀⡼⣇⠸⣤⠞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣄⡀⢻⠉⣉⠙⢿⡀⢹⠴⠚⠣⣄⠘⣄⣣⠀⠀⢹⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢺⡞⠉⠀⠀⠙⣾⠀⡀⠀⣄⠀⢸⣃⣤⠖⠋⠉⠈⠀⠀⢀⡴⠛⢫⣋⠍⠏⣏⡛⠗⣤⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢐⡧⠚⠁⠀⠘⣦⡏⠁⠈⡆⠀⠀⠀⠀⡴⣋⣤⣤⠀⠙⣷⠶⠶⠶⠾⠾⢷⠆⡇
⠀⠀⠀⠀⠀⠀⢰⠤⠴⠖⠷⠶⠿⠷⠾⠧⢤⠤⣿⣤⣾⣀⣴⣈⣓⣾⠓⣶⠾⣇⢹⠠⢸⠀⠀⣿⣿⢻⢹⡆⠀⢸⡶⡇
⠀⠀⠀⠀⠀⠀⠘⠚⠓⠛⠛⠛⠛⠓⠒⠒⠦⠤⣤⡀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠻⠚⠶⠼⢦⣄⣾⣈⢙⠉⠁⠀⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣄⣀⣄⣀⣀⣄⣀⣀⣀⡀⡀⠀⠀⠀⠈⠉⠋⠓⠒⢼⣍⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠠⠄⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠒⠲⠦⠤⣀⣀⣈⡇
⠀⠀⠀⠀⠀⠀⢸⢀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠤⠤⠤⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⡃
⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡠⢠⠴⣿⢻⡆⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⡀⢀⣀⢀⠉⠉⠉⠙⠒⠒⠶⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡋⢳⣯⠭⡇⠀⠀⠀⠀⠀⠀⠀⠹⣟⠿⠿⠉⠩⠉⠍⠉⠙⢛⣺⡶⠦⣤⡀⠀⡅
⠀⠀⠀⠀⠀⠀⠐⠀⢀⣤⠶⣄⠀⢹⡉⡾⠴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡒⠂⠀⠂⠀⠂⠾⣍⣽⠁⠂⡌⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⡞⢩⠷⣤⣳⢷⡊⠀⢀⣤⠞⢻⢉⣯⣿⠃⠀⠠⠀⠀⣽⢷⣮⡀⡂⠐⠀⢾⡆⢄⣅⣠⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠲⢷⠋⣰⢻⠻⣾⢇⡴⡇⢸⣤⠞⠛⡶⠃⠀⠀⠀⠀⠀⣳⠾⠃⢹⣭⣅⣁⣹⡗⠻⣤⡿⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠲⠼⡞⠁⡞⠀⣏⣾⣠⠷⢯⣬⠽⠋⠀⠀⠀⢀⠀⠀⠀⣇⣤⡀⠀⣿⡏⠁⢽⡏⣁⣽⡉⡒⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠦⣧⢞⡁⠘⢿⠛⠛⠉⠉⠀⠀⠀⠀⡀⣹⡛⠻⡆⢸⠿⣼⠇⠀⣿⡧⠰⢾⡇⠦⢿⠀⣤⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠶⢾⡿⠛⢷⣮⣧⣶⣤⡦⠀⠀⠸⠀⠙⡹⢿⡴⠃⢸⠀⢿⠀⠀⡟⡇⠘⣸⡗⢐⢸⠒⠂⡇
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠧⠤⠤⠤⠵⠿⠩⠤⠦⠤⠾⠤⠴⠥⠤⠧⠠⠼⠦⠼⠤⠤⠧⠯⠩⠽⠍⠍⠽⠭⠭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢠⠙⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣷⣼⡄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⣶⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣿⣿⣿⣿⣽⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠐⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢃⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣍⣉⠉⠉⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣟⡂⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣦⠄⠀⠀⠈⠩⠽⠿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣛⣛⣀⠀⠈⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢇⣀⠀⠀⠀⢤⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢀⣔⣉⣉⣀⣀⣀⠤⠚⠉⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⢀⣤⡴⠚⠉⠁⠀⠈⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣦⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠲⢤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢨⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣾⠁⠀⠀⠀⠀⠈⢳⣰⠟⣿⠲⡀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠳⡴⠶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⢀⣼⣿⠉⠳⡄⠀⠀⠀⢀⡴⠋⣸⡏⢳⡀⠀⠀⣠⠖⠶⠞⠃⠀⢿⡑⠉⠢⣄⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠙⣦⣠⣴⠟⠀⣾⢧⣙⡢⠙⠲⢮⣁⣀⣀⠀⠀⠀⠈⢿⠂⣀⣈⡷⢾⣧⡾⠁⠀⠀⠀⠀⢺⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⢀⡴⣾⠉⠀⠀⠀⠀⠻⣄⠀⠉⠂⠀⠀⠀⠉⠉⠑⠄⠀⠀⠈⠋⠉⠁⠀⢾⡈⠛⠶⢤⣤⣤⠞⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁⠀⣿⡄⠀⠀⠀⠀⢠⡘⣯⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⢸⡀⠀⠀⣸⠃⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⢸⣿⡇⠀⠀⠀⠀⠈⢿⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⡀⢻⡄⣿⡇⠀⢠⢿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣾⣿⣿⡀⠀⠀⠀⡄⠘⣧⠈⠓⠦⢄⠀⣀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣿⠀⢹⣿⣿⣠⣯⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣷⠀⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣿⣿⣧⠀⠀⢸⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣏⢢⡄⣸⣿⡄⠙⢆⠀⠀⠀⢸⣿⡇⠀⠀⢀⣿⣿⣿⠀⠀⣾⣿⣧⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠁⠀⠀⣾⣿⣿⠀⠀⢾⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡉⢻⠋⢲⠾⣿⣿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⡄⠀⠃⠀⠀⡀⠀⠀⠀⠐⠐⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠙⢆⠀⠀⠀⠀⠀⡴⠋⡂⠔⠸⠀⠀⠤⠼⢦⠀⠿⠃⠀⠀⠀⠀⠈⣀⡶⠒⢡⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣤⠀⠀⠀⠀⠀⠀⠤⠀⠒⠀⠀⠰⠀⠀⠈⠃⠀⢐⠀⡸⠏⠀⠀⠀⠀⠀⠀⢠⡤⠀⣶⣶⠐⠿⠂⠀⠀⢯⡈⢇⠀⣠⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⡀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⢰⡇⠀⠀⠀⠀⠀⠀⠀⠰⠂⣤⠈⠀⣦⠀⠀⠀⠀⠙⠵⡎⡘⡳⠈
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡄⠀⢨⠀⠀⢀⡀⠀⠀⢃⠀⠁⠀⠓⠀⡠⠀⠀⠀⠁⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠖⠈⠀⠀⠀⠀⢠⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠃⢀⠀⠀⠇⠸⠃⠀⠀⠀⠑⠤⢀⢀⣀⣀⠤⠂⠀⠀⠀⠀⠀⡈⡠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠰⠄⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣰⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠆⠀⠘⢰
⠀⠀⠀⠀⠠⠀⠀⠠⠐⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⡀⠀⠀⠀⢀⠃⠁⣟⡀⠈⠀⠀⠀⠀⢀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠
⠀⠀⠀⠀⠄⠠⠀⠀⡀⡄⠀⠀⠀⠀⢆⠄⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠉⠄⠀⠀⠈⠁⢸⣏⡀⠀⠀⠀⣀⠀⡀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠤⠀⢐⢤⠼⠔⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⢀⠀⠀⢀⡀⢰⠀⠀⠀⠀⣶⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⠄⠠⢄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠐⠈⠈⠀⠀⠈⢁⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⠀⠀⠀⢇⢒⠆⠀⢱⠀⠀⡈
⠀⠀⠀⠁⠀⠀⠀⠀⡄⢠⡀⠃⠀⠀⠀⠀⠀⣇⠀⠀⠄⠀⠳⠀⠄⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢳⡄⠀⡠⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡀⠀⠈⠫⡀⢀⣠⡰⡶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠄⠁⠀⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠰⢁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⠄⠘⢋⣉⠘⠑⠢⡀⠀⠀⠀⠀⠀⠤⠈⠀⡀⠄⠋⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠘⠛⡠⠀⢀⠜⠀⠀⠀⠀⣀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠔⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠦⠴⠖⠚⠁⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠰⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠐
⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠞⠁⣈⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠚⠀⠄⠰⠀⠀⠄⡡⠆⠀⠀⠀⠀⠀⠀⣤⠀⠈⠒⠀⠀⠑⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠚⠐⠂⢀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠉⠑⠲⢼⡀⠀⠀⣆⠲⠀⡠⠠⢄⠀⠀⠀⠰⠞⠀⠀⢰⣤⣼⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠘⠄⡃⠀⠚⠃⣀⠨⠵⠤⣀⠉⠀⡟⠀⢶⡸⠀⠀⠀⠀⠀⠀⠘⣿⣭⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠀⠀⠑⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣀⠀⢇⠀⠲⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⢀⠀⠱⣄⠊⠀⠘⢀⡤⠀⠀⠀⠀⠀⠀⡸⢁⣀⠀⠀⠱⢸⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠢⣌⣁⣄⢸⣇⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠰⢈⡁⠀⠀⠀⣿⡰⠊⢁⠑⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠈⠙⠷⢶⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠐⢣⠃⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠟⠛⠛⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣶⢶⠿⢿⠟⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷⠀⡆⣾⢸⢁⡜⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢸⡀⡇⠙⢸⢸⠇⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⡇⢳⢀⡇⡼⢠⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣥⢸⠆⡇⡇⢸⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢹⠘⡆⢱⢀⡆⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡆⣷⢸⠈⠃⡇⢻⡇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⡇⢹⠀⡆⢰⢡⠸⣿⣛⣿⣭⣭⣭⣭⣭⣭⣿⣿⣭⣭⣭⣽⣿⣛⣛⣻⡷⠶⢶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣠⣴⠾⠇⢸⣧⢰⢰⡆⡿⢸⢸⠀⣿⠤⠶⠶⠶⠶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠻⠶⢾⣭⣙⡛⠷⣦⣄⡀
⠀⠀⢀⣴⠾⢛⣥⠶⢛⣋⠈⣿⢸⠂⡇⢸⡀⡄⢀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⠿⠟⠻⣶⣬⡙⠷⣤⡀
⢀⣴⠟⣡⠾⣫⣴⠞⠉⠀⠀⣿⡇⣄⢱⢸⡇⡇⢺⢸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠀⢐⣶⣿⣛⡉⠁⣤⣴⠶⢞⣛⣯⣿⠿⣶⡌⢿
⣼⠇⣼⢋⡾⠋⠀⢀⣠⣤⡾⢿⣇⡿⢸⠀⡇⢀⠀⣬⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣭⣤⣶⣾⡿⠟⢛⣉⣥⡴⠟⣓⣴⣿⣭⣁⡀⠀⠈⣿⠈
⢿⣇⠹⣄⠁⢠⣶⣿⣿⣿⣇⠈⠛⠿⢾⣶⣿⠾⠿⠛⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡿⠟⢀⣼⠃⣸
⠈⠻⣦⡙⠷⣤⡙⠛⠿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣶⡞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢉⣤⡶⠛⣡⣾⠏
⠀⠀⠘⣿⠷⣬⣙⠳⠶⣤⣌⣉⠛⠻⠿⠿⢿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⣉⣠⣤⠶⠟⣋⣥⡶⠟⣿⡇
⠀⠀⠀⣿⡀⠀⠉⠛⠷⢶⣭⣭⣛⣻⠶⠶⢶⣤⣤⣤⣤⣤⣉⣉⣉⣉⣉⣉⣁⣀⣀⣤⣤⣤⣤⣤⠶⠶⠶⢛⣛⣩⣥⣴⠾⠛⠋⠁⣀⠀⣿⠃
⠀⠀⠀⣿⡇⣿⣷⣦⣤⣄⣀⡉⠉⠙⠛⠛⠷⠶⠶⣶⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣶⠶⠶⠶⠛⠛⠋⠉⢉⣀⣠⣤⣴⣾⣿⣿⠀⣿
⠀⠀⠀⢹⡇⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣯⠉⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡿
⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇
⠀⠀⠀⠘⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣛⠿⣿⣿⣿⠇⣿⠃
⠀⠀⠀⠀⢻⡄⣿⢛⣩⣴⣶⣤⣝⣿⣿⠟⢉⣤⣿⣿⣿⣿⣿⠿⢿⣿⣿⡻⢿⣿⠟⣫⣴⠶⢶⣿⣿⠿⣥⡟⠁⣸⣿⣿⣷⡈⢿⣿⠀⣿
⠀⠀⠀⠀⢸⡇⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠿⣿⣿⣿⣿⠟⣵⣿⣿⣿⣿⣿⣿⣎⢿⣿⣦⡀⠀⢸⣿⣷⡙⣆⣠⣿⣿⣿⣿⣧⠘⣿⠀⣿
⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣶⠟⣽⡶⠿⢿⣿⣶⣌⠻⣿⣼⡟⠉⠉⣿⣿⣿⣿⣿⣯⣿⣿⣷⣀⣾⣿⣿⡇⢹⣿⣿⣿⣿⣿⡿⢀⣿⢰⡇
⠀⠀⠀⠀⠘⣷⢸⣿⣿⣿⠏⣴⣿⠛⢶⣾⣿⣿⣿⣿⣯⣿⣇⣀⣀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⡿⢁⣼⡟⢸⡇
⠀⠀⠀⠀⠀⣿⠘⣿⣬⣿⢠⣿⣿⡀⢸⣿⣿⣿⣿⣿⠉⠋⢩⠉⢛⣻⣟⣿⡿⠛⣙⠻⣿⣿⣿⣿⠿⣡⣿⠿⠿⣿⣿⣯⣶⣿⣿⡇⣸⡇
⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⡟⣴⣿⣿⣟⣻⠻⠿⡛⠻⣾⣻⣿⡿⠿⣾⣶⣿⠛⠛⢻⣿⣦⣉⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⣿⡀⣿⠁⣹⣿⣷⣝⠻⠿⢿⠿⢟⣭⢾⣿⣿⣷⣿⣽⡻⣿⣷⡿⠿⠛⢿⣿⣿⣮⡻⣿⣦⠀⢀⣿⣿⣿⣿⣿⣿⣿⠃⣿⠁
⠀⠀⠀⠀⠀⢻⡇⢿⣶⣿⣿⣿⢟⣽⣿⣾⣿⡟⣱⣿⠟⠁⣠⣿⣿⣿⣎⢿⣦⠀⣴⣾⣿⣿⣿⣧⢸⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⢡⡿⠳⣬⣿⣿⢡⣿⣿⣷⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠟⣼⣿⣿⢰⣿
⠀⠀⠀⠀⠀⢸⣇⢸⣿⠿⡇⣾⡇⢠⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⡿⢃⣿⣏⣉⠙⠿⣿⣧⣾⠟⠋⡟⢸⡇
⠀⠀⠀⠀⠀⠈⣿⢸⣿⣶⣧⠹⣷⣼⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⠟⣡⣿⣯⣙⡛⠛⣛⣩⣴⣿⣿⣿⣏⠛⣦⠙⣯⣠⣴⣾⡇⣸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣷⣝⠻⣿⣿⣿⣿⣿⡷⢶⣌⣩⣥⡶⠟⣛⣛⡻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⠃
⠀⠀⠀⠀⠀⠀⢻⡇⣿⣿⠛⣿⣿⣿⣶⣾⣿⣫⣵⡿⢿⣿⣿⣿⣵⣿⣿⣿⡿⣫⣵⣶⣶⣶⣮⣝⢿⣿⣿⣿⣿⣇⣿⣿⣿⣿⠁⣿
⠀⠀⠀⠀⠀⠀⢸⡇⢻⣿⣆⠈⢻⣿⣿⣿⢱⣿⠃⣠⣼⣿⣿⣿⣿⠈⣿⣯⡿⠃⢠⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣾⡇⠀⣿⣿⢠⡿
⠀⠀⠀⠀⠀⠀⢸⣇⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⡇⣿⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣇⣼⣿⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡈⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⡜⣿⣿⣿⣿⣿⣿⣿⣋⡽⢺⣿⣿⣿⣿⣿⠟⣼⠇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣟⠛⠿⣿⣴⣾⣿⣮⡛⠿⠿⠿⠟⢋⣠⡿⠿⢿⣌⠻⢿⣿⣿⣿⡿⢋⣵⣦⣌⣉⣉⣉⣡⣾⣿⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣬⣙⡛⢿⣿⣿⣿⣶⣶⣾⣿⣿⣷⣶⣾⣿⣿⣶⣶⣶⣶⣾⣿⡿⠿⢿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣷⣦⣭⣉⣉⣉⣉⡉⠛⠋⠛⢉⣉⣉⣉⣁⣤⣤⣤⣶⡿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⢠⣾⣷⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⠖
⠀⠀⠀⠀⢀⣥⠼⢻⡿⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣤⢀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡄⠀⠀⠀⠐⢻⣿⠟⠉⠉
⠀⠀⠀⠘⠆⠟⢠⣾⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡀⠀⠀⠄⠀⠀⠀⢹⡫⢿⣿⡇⢀⣴⠏⠀⠀⠁
⠀⠀⠀⠰⡐⡦⠀⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠀⠀⠀⢃⣾⣿⣷⣼⣿⣄⣠⣄⣀⠠
⠀⠀⠀⠀⢋⣀⣤⣤⠀⡀⠀⠀⠀⠀⠀⢀⠀⠶⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠛⡿⢏⡉⠉⠉⠉⠚⠛⠀⢠
⠀⠀⠀⠀⠆⠈⢳⠉⠶⠃⠀⠀⠀⠄⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⢤⡀⠀⠀⠀⠀⠃⣤⣹⣤⣠⡄⠰⠆⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⢲⡀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠋⣰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣶⡀⠀⠀⠀⠀⢀⡞⠁⠀⠸⠀⠂⠀⣀⡀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠁⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠉⣿⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠘⠃⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡄⠀⢠⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⣦⠀⣰⣶
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⢸⡇⠀⠀⢀⣠⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠆⠈⢡⡶⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠀⠸⣿⣿⣷⡄⡀⠃⠀⠀⠘⢿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠹⢿⣦⡀⠀⠀⠀⠀⣠⡴⠃⠀⠀⣸⡶⠃⠙⠇
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢻⣿⣿⢹⣿⣿⡇⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣿⠄⠀⠀⠀⠉⠐⢦⡄⡀⢈⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠉⢠⣼⡿⢹⠀⠐⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠂⠁⢀⠈⢁⡀⢉⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⢿⡇⠀⠀⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢿⣵⠿⠂⠤⠿⠟⠉⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣷⠀⠀⣶⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢀⠀⠈⠠⠖⠈⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⢷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠰⢾⡷⠀⡈⠁⠛
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠄⠘⠀⠀⠀⡄⠀⣾⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠄⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠎⢹⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⡇⠀⢹⠀⢀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠲⠶⠛⣉⠁⢀⡀
⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠘⠀⠼⠄⣸⠆⠈⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣸⠀⠀⠘⠄⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡚⢛⣿⣿⠟
⠀⠀⠀⠀⢠⡯⠙⠁⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢀⠀⠈⠉⠿⠉⣠⡤
⠀⠀⠀⠀⠼⠖⠂⠀⠀⠀⠀⢠⣠⡄⢸⠀⢸⠀⠀⠀⣷⠈⢳⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⣲⠆⠘⠀⠀⢀⡀⠀⣩⣴
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⢾⠀⣿⣧⣸⠀⡆⠀⠀⠀⢩⠀⠈⠀⠀⠀⠀⡟⠀⠀⠀⢘⡇⠀⠀⠀⠀⣶⣶⣤⣄⠀⠀⠀⠀⠀⠈⣿⠿⠆⠀⠀⠀⠀⠙⣾⠟⡁
⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⢠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡿⣿⣷⢂⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢹⣿⣿⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢣⡘⠁⠀⠀⠀⠀⠀⢸⠟⠻⣿⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠇⠀⠀⠀⡀⠸⠇⡀⠀⠀⠀⠀⠀⠀⠛⠖⡉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠠⠄⠷⣤⠀⡀⠀⠰⠀⠀⠀⢸⠀⠀⠁⠀⡄⠀⠀⠀⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣀⣀⢠⣶⣏⠉⠃⠀⠀⠀⠀⠀⢨⡇⢰⠀⠈⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢾⠿⡏⢰⣷⣷⣔⣀⠀⠀⠀⠀⠀⢺⡇⠘⠀⠀⠀⠀⠀⠀⢀⡛⢗⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠛⠾⠟⢻⣿⣯⣀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⣀⠈⢱⣎⣹⣇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⡟⠉⡄⠉⣶⣦⡀⡿⠁⠜⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⣹⡆⠰⢃⠀⠠⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠘⠂⠀⠀⠀⠀⠃⠀⠁⠸⢿⣈⣄⣷⠞⠛⠀⠀⠀⠘⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⠷⠒⠞⠳⠶⣦⡀
⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣄⣀⣏⢈⣀⠀⠚⠀⠀⠀⠀⣿⠀⠀⠀⣀⢠⣴⣾⣷⠒⢠⣄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠉⠉⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙⣏⠛⠃⣴⠆⠀⠀⠀⡟⠀⠀⠀⢫⣶⣯⣽⡏⠐⢀⡽⠻⡇⣸⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠃⠀⠀⠀⠀⠀⠄⠀⢀⠀⠄⠀⣀⠄⠀⠀⠀⠀⠀⠘⢶⡸⠇⠀⠀⠀⠀⠃⠀⠀⠀⢣⣾⡿⡏⢙⠀⠹⠀⠀⠀⢉⠀⠀⠀⠀⠀⠠⠿⡿⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠃⣴⠃⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠿⣹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⠀⡰
⠀⠀⠀⠀⠀⠀⠉⠀⠐⢦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠜⠓⠠⠰⠇⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⡀⣀⣀⡀⢀⣀⣀⣀⡀⣀⠀⢀⡀⠀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀⣀⠀⢀⣀⢀⣀⢀⣀⣀⣀⣀⡀⢀⣀⠀⣀
⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣜⣋⣻⣧⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢼⢸⡆⠀⠀⣷⠀⠀⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⡇⠀⠀⠀⡄⢴⣯⣿⡄⠀⠀⠀⠀⠀⠀⢀⡀⢰⡇⠀⠀⠀⠀⠀⢸⣇⣿⣀⣾⣮⣇⣄⠖⣿⠀⣴⣠⣗⣷⢴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⣸⣷⠸⡀⢀⣇⣿⣿⣿⣷⠂⠀⠀⠠⣄⣀⣸⡧⢸⣧⣰⣆⠀⢀⣈⣿⣿⣿⠟⠻⣿⣿⣿⠤⠿⣞⣻⣷⣹⣿⢉⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢰⣿⣿⣿⣿⡈⡒⠘⣿⣿⣟⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⢻⠃⠀⠀⠹⢿⢛⣘⣧⣾⠛⣽⣟⠡⣛⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣆⣷⣿⣿⣿⣿⡿⢳⡏⠀⢻⣿⣿⠁⢅⢠⡀⠀⠀⡙⠈⢿⣿⣿⡿⠋⠃⠰⠴⠦⣴⡏⠀⠀⠀⠀⠼⣟⣡⡿⣟⠛⣿⠋⣸⣿⣗⣠⣿
⠀⠀⠀⠀⣠⣴⣿⣿⣻⣿⣿⣿⣻⣿⢋⣽⠀⠀⠘⣿⠟⣀⠈⣟⣰⣤⣴⡁⠈⠙⣿⣿⠀⠀⠀⠀⠗⠀⢈⡧⠀⠘⠐⠦⠀⣸⣿⠀⢸⣷⣾⠿⣗⡼⠳⣄⡀
⠀⠀⠀⣸⣿⣿⣿⣷⣿⣿⣿⣿⠽⢿⣼⠋⠀⠀⠀⣿⠍⠀⠀⢿⣌⣿⠇⠀⠀⢀⠻⣿⣿⣤⣤⣶⣄⡾⠁⠀⠀⠀⢀⠀⠀⢈⡿⣦⣿⢽⣿⠂⣹⣿⣤⡧⠁
⠀⠀⢠⣿⣿⠿⠟⠛⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⠐⠏⠀⠑⠒⢘⠛⠟⠀⠈⢁⡠⠄⠈⠀⠀⠀⠙⠘⠳⠀⠀⠰⠛⠻⠟⠟⢿⣤⣾⠸⠯⠐⠂⠉⢧⠀⠈⠆
⠀⠀⠈⠉⠀⠀⢺⠇⠀⠀⠐⠚⢻⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠁⠋⠛⠿⠶⠆⠊⢉⣉⡲⠏⣹⣦⡨⠷⢶⣄⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠤⠤⣄⠀⠐⠶⣦⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠛⠓⠒⠚⠛⠛⠻⠓⠒⠺⠿⠀⠀⣀⣄⣀⣀⣀⠛⣫⣉⣱⡖⠂⠉⣳⣀⣀⣸⡧⠄
⠀⢠⠀⠰⠖⠀⢀⣠⣤⣄⠄⠀⠀⢠⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠙⠛⠛⠿⣷⣶⣾⣤⣼⣿⣠⡀⠰⣿⣆⢀⡄⣤⢷⣀⡄⡀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣄⣩⣿⣾⣧⣽⣧⣿⣷⣞⣻⢻⡄⣿⡆⠀⠄⠀⡀⠀⠀⠀⢰⣧⣦⡀⢂⢰⣄⠀⠀⠀⠘⣆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⢿⡿⢿⣿⣟⣉⣉⣹⣿⣿⣿⡇⠀⢠⡄⣧⣶⣄⣦⢸⡿⣿⡇⠘⡞⣿⠀⠀⠀⡄⢻⢄⠀⢠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠏⠛⠛⠛⠾⣓⠀⠠⠅⡽⢳⣿⣿⣼⣿⣿⣷⢀⣦⣿⠄⠀⠀⢸⢸⣿⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣉⣉⣁⣈⡁⠀⠀⢰⣉⣉⣩⡍⣻⣿⣿⣭⣄⣀⣦⠚⠀⢺⣿⢿⡟⠋⠁⢓⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠑⠈⠙⠋⠉⠍⠭⢙⣿⣦⡤⢤⣶⣾⣟⡿⣯⣭⡭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢶⠲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⡇⢿⢹⣿⠾⡵⠆⢀⣴⣶⣀⣶⣿⣿⣿⣿⣦⠀⠀⠉⠙⠋⠉⠛⠛⠛⠛⠓⠒⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠖⠮⠅⢀⠸⢾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠌⠛⢻⠛⠛⠟⠋⢩⢥⠌⠟⠗⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⠚⠻⣶⣌⣁⡋⢠⠭⠬⣿⣶⡆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⠇⡉⠲⠒⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣼⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡢⢻⠇
⠀⠀⢰⡇⠠⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⣀⠞⠁⣾
⠀⢀⣿⠀⠀⢧⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢆⡰⠛⠉⠀⣿
⠀⡼⡿⠀⠀⠈⡇⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⡄⣀⠀⠀⠀⠀⠀⢠⠏⠀⡀⡼⢁⠀⠀⢸⢿⡀
⠀⡇⡇⠀⠀⠀⢳⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⣧⠀⡟⢤⡉⠲⢄⠀⠀⡇⠀⠀⢹⠛⠁⠀⠀⡾⢸
⠀⡇⣷⠀⠀⠀⠀⢃⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⡲⡇⠀⠀⠀⠀⢠⠁⠀⢼⣧⣳⠈⢧⣀⠈⠳⡀⡇⠀⠱⡏⠀⠀⢀⡜⠁⠁
⠀⢹⢻⡀⠀⠀⠠⣸⠀⠀⢸⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⣠⠎⢰⠃⠀⠀⠀⠀⢸⠀⠀⢀⢣⣻⣆⠀⡙⡄⠀⢹⣇⠀⢠⠗⠀⣠⠞
⠀⠀⠞⣇⠀⠀⠀⠈⣧⠀⢸⠀⠀⠀⢀⡔⠋⠀⠀⢀⡴⠊⠀⢀⡟⠀⠀⠀⠀⠀⠸⡀⠀⠀⠙⡏⡏⠳⣄⠙⢦⡈⡟⡄⣸⣠⠞⠁
⠀⠀⠀⠘⣆⠀⠀⠀⣽⠀⡆⠀⠀⣰⠋⠀⠀⣠⠖⠉⠁⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢣⡀⠀⠑⢿⡿⠀⠈⠑⠦⣧⣇⣷⡟⠁
⠀⠀⠀⠀⠈⠳⡀⠀⢸⠀⠇⠀⢰⠃⠀⣴⠞⠃⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⣀⠤⠴⠒⠓⢄⠀⠢⣿⡇⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠢⣈⣷⠀⠀⡟⢠⠞⠁⠀⠀⠀⢀⡴⠟⠁⠀⠀⣀⠔⢊⣁⠀⣄⣀⠀⢦⣙⠢⢌⡻⣄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⢠⣄⣧⠏⢀⣀⡤⠶⠚⠁⠀⠀⠀⠐⠛⠳⠯⣍⡉⠉⠁⠀⢉⣉⣩⠭⠤⠽⣿⣷⣄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡿⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠉⠁⠀⠀⠀⠀⠀⠉⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⣠⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠌⡀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠝⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠆
⢢⡀⠀⠀⠀⠀⠁⠒⠀⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡊⠅⠀⠀⠀⠀⢀⠴
⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠔⠀⠀⠘⠓⠢
⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠂⠈⠲⡀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠑⡀
⠀⠀⢀⠄⠀⠢⢄⠀⠀⠀⠀⠠⡧⠶⠒⠒⠻⠀⠀⠀⠀⠀⠀⠋⠙⠛⠛⠿
⠀⠀⣁⣀⣀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⢂⠃⠀⠀⠀⡠⠔⠒⠺⢀⢲
⠀⠀⠀⡀⠢⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠁⠛⠀⢸
⠀⠀⠀⠡⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢃⢀⠂⢈
⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠔⠁⠐
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣨⠔⠂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠔
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠁⡆⠀⠀⠀⠀⠀⠈⠛⠛⠻⠷⡷⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⢠⠀⠀⠀⠀⠰⠒⠒⠊⠁⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠃⢉
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⡀⠀⠀⠀⠀⠀⢀⡘⣐⠂⠀⠀⠀⠀⠀⠀⠂⠀⣀⣠⡼⡦⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠉
⠀⢰⠀⠀⠀⠀⠀⠀⠈⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠠⠈⡀
⠒⡗⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒
⠚⠉⢠⠁⠀⠀⠀⠀⠀⠀⠀⠄
⡠⠀⡈⠀⠀⠀⡈⠁⠀⠀⠜⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⢂⠊⠀⠀⠀⠀⠀⠀⠀⡒⢆⡂
⠀⠐⠀⠀⠀⠀⠏⠑⠒⠂⠰⠃⠀⠀⠀⠀⠀⠰⠷⠦⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣁⣠⣼⣶
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠀⠀⠀⠀⠀⠀⠀⢙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠉⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⠀⠀⠀⠤⠀⣶⣾⣿⣿⣿⣤⡖
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⢷⣄⠀⠐⢇⢹⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠙⢿⡄⠀⡐⢛⡻⣿⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠟⢤⡀⠀⠀⠀⠈⠃⠀⠈⠀⠁⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⢦⠀⠀⠀⠠⠐⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠤⠀⠄⠠⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⠀⠀⠀⣠⣤⣦⣴⣤⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠁
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡴⢀
⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠐⠳⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠙⠷⠃⠈⠿⠟⠷⣤⡄
⠀⠀⠀⠀⢸⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄⠀⣸⡟⠛⢢⡤
⠀⠀⠀⠀⠀⠠⠙⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣷⣠⠀⡀⠀⠀⠀⠀⠀⠌⣡⠈⠛⠀⢀⠄⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡌⠻⡇⢠⠀⠆⠀⠀⠀⢀⡄⢀⢸⡟⠃⠐⠛⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠹⡆⠀⠀⠀⠀⠀⢾⣠⣿⠦⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⣀⠶⣿⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠛⣿⡏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠹⣏⢛⣛⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣘⣠⡄⠀⠀⣤⠀⡀⠀⠀⠀⠀⠐⠋⢈⡯⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣂⠀⣄⡀⠀⠀⠀⠂⠀⠀⢸⣆⢠⡿⠀⠇⠀⠀⠀⠂⢀⠀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⡾⣟⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⢠⣿⡼⠃⠀⠀⠀⠀⠀⠀⣼⣟⣧⣶⣶⣠⢶⠟⠠⠒
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢬⣿⢰⣿⣿⣿⣿⣿⣾⣷⣇⡆⠉⠀⠀⠀⠁⠀⠀⠀⣀⠂⠀⠀⠛⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠹⠦⠀⢸⡞⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠀⠀⠀⠀⣀⠀⠘⢧⣄⣁⡀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⢽⣿⣿⣿⡋⢨⣿⣯⡀⠀⠀⠀⠀⠀⡀⠐⠃⠈⢻⣿⡅⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⠈⠁⠉⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠋⠹⣿⡀⠀⠀⠐⢂⠀⢠⣽⠟⣻⣷⣿⢦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠠⣼⡟⣾⣿⣿⣿⣷⣌⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠱⠀⠀⠀⠀⠀⠼⡿⠛⠿⣿⣿⣿⣿⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚⠛⡻⣦⣤⣤⣄⠀⠀⠠⣤⣤⡤⠡⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠌⣀⠀⠋⠀⠛⠁⠀⠀⠐⢶⡿⢛⣿⢉⣼⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠴⣿⣿⡣⠙⢧⣄⠐⠈⢻⣿⣷⣤⡀⠀⠀⠀⢀⣤⠞⠛⠛⣰⠛⠃⡀⣀⡠⠞⠀⠄⠤⣀⣀⢈⣙⠂⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡳⠛⡀⠘⠃⠀⠀⢘⠇⠘⢿⣶⡙⢠⡀⠈⠀⠇⠄⠀⠚⠀⠀⢐⠛⢧⡄⠀⠀⠀⡉⠉⠈⠛⠲⣦⠈⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠟⠗⠀⠁⠀⠀⠀⠀⠸⠀⠀⠜⣿⡷⣀⠁⠀⢀⣠⡴⠶⣶⣬⣄⠀⠀⠀⠀⠀⠄⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⡉⠂⠀⠀⠉⠀⠈⠉⡉⠿⠆⠀⠶⠶⣶⣗⡀⠛⠶⡾⠹⠒⣶⠂⠡⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠸⠛⣷⡄⠀⠀⠀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠻⠙⠿⡟⠙⡿⠻⣟⠿⢛⣻⠟⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣶⣷⣾⣷⣶⣿⣶⣾⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣆
⠀⢶⣄⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⡟⣻
⠀⢼⣿⣷⡄⠀⢻⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣿⢛⡇⠀⠀⠀⠀⢀⣠
⠀⣷⣿⣿⡹⡄⠈⢻⣛⢳⡔⠄⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣾⣻⣟⣹⠇⠀⢀⣤⣶⣿⠇
⠀⢻⡄⠽⣿⣹⣦⡀⠙⠢⣽⣆⣰⠋⠀⠀⠀⠀⡠⢶⣖⣾⡜⠁⠀⠀⠀⠀⠀⢸⣿⣿⣋⡟⠀⣴⣿⣾⣿⠏
⠀⠈⢷⠶⢿⣿⣭⢷⡄⠀⠈⢿⠃⠀⢀⣴⣾⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡾⢁⣷⣿⣯⠝⠁
⠀⠀⠈⢆⠰⠿⣿⣼⢟⣆⠀⠈⢀⣴⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠂⠠⠚⠛⠁⠀⣀⣀⣴⡶⢠⣄
⠀⠀⠀⠰⣶⡖⠛⣿⣿⢙⣆⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡆⠀⠀⠀⠀⡗⠁⠀⠀⠀⢠⣾⡿⣿⢘⣷⣻⣿
⠀⠀⠀⠀⠈⠙⠻⣭⢿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⣽⠿⡿⠀⠀⠀⠀⠀⡇⠀⠀⣠⣶⣿⢹⣇⣹⣿⣿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⡇⠀⠀⠀⠀⣀⣴⡆⣸⣿⣟⣉⣹⠃⠀⠀⠀⠀⠀⠁⠀⢸⡿⣿⣿⣿⣿⣿⣷⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣼⣿⣦⣿⠿⠧⣀⡴⠃⠀⠀⠀⠀⠀⢰⠀⢠⣿⣷⣿⡿⢯⣭⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡼⢋⣠⡿⠛⠒⣶⠟⠁⠀⠀⠀⠀⠀⠀⢸⠀⣼⣿⠿⣉⣑⡶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⣣⣼⠛⢉⡵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⡤⠋⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣯⠉⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠋⣱⣾⣿⣷⣿⡟⠛⠈⡻⠋⠁⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠛⠋⠀⣿⡀⠀⢀⠀⠀⠠⣿⣇⠀⠀⣾⣇⠀⠀⠀⠀⠃⠀⠀⠀⠀⣧
⣶⣶⣿⡿⠀⠀⠀⠀⢀⡄⠁⠀⣰⣿⠆⠀⠀⣼⣿⡇⠀⣼⡇⠀⣨⣿⣧⡀⢠⣿⣧⡀⠀⢸⡄⠀⠀⠀⠀⣰⣿
⣿⣿⡿⠁⣀⠀⠀⠀⠈⠁⠀⠀⣿⣿⠇⠀⢘⣻⣿⠷⠄⣿⡷⠀⣸⣿⣷⠀⡠⣿⣿⢀⣴⣿⣷⠀⠀⠀⣴⣿⣿
⣿⣿⡇⣼⣿⠀⠀⠀⠀⠀⠀⠠⢿⡿⣦⠀⣈⣿⣿⣁⠰⣿⡟⠒⢻⣿⡏⣾⣿⣿⡷⣶⣿⣿⠷⠀⠀⠀⠻⢿⣿
⣿⣿⣧⣿⡏⠀⠀⠀⠀⠀⢰⣗⢿⣷⣤⠀⢻⣿⣿⣟⣰⣿⣿⢐⣯⣿⣧⣾⣿⣿⡟⠂⢾⣿⣷⠀⠀⠀⠀⠀⣿
⠻⢿⣿⣿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣤⠀⢾⣿⣿⢛⣇⣿⣏⣸⣿⣿⡯⣏⠹⣿⢷⣆⣹⣿⣟⠀⠀⠀⠀⠀⡟
⠀⣼⣿⡏⠀⠠⠀⠀⠀⢼⣿⣿⣿⣿⣼⡹⡒⣿⣿⠘⣿⣿⣿⡟⣿⣻⡆⣰⣶⣿⣰⣏⣽⣿⣏⠁⠀⠀⠀⠀⡇
⢰⣿⣿⠁⢀⠆⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⡆⢿⣿⣿⡿⣿⣠⡮⠸⣾⣿⣽⣿⡏⣍⣽⣿⣟⠃⠀⠀⠀⠀⠃
⣾⣿⡟⠀⡼⠀⠀⠀⠀⢸⣿⡏⣼⣿⣿⣿⣿⣤⡟⣿⣾⣿⣿⣿⣷⣶⡏⡗⢸⣿⣨⣽⣿⣿⡌⠁
⣿⣿⡇⢰⠇⠀⠀⠀⠐⠻⣿⡿⡿⠛⠟⣿⢷⢿⠉⢿⣿⣿⡏⢹⣿⣿⣷⠇⢨⣿⣿⣿⣿⡇
⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢸⣿⠈⠀⢿⣾⠿⡏⣵⡜⣿⣿⣿⣶⡇⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⣿⡄⠀⠘⣿⣾⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣼
⣿⣿⡏⠀⠀⠀⠀⠀⢰⢠⠏⠀⠀⠀⣿⣿⡇⠀⠀⠸⣿⣀⣼⣿⣿⣿⣿⣿⡿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣿
⣿⣿⡇⠀⠀⠀⠀⠀⢛⠿⠻⠿⠶⠶⠿⠿⠳⣤⠀⣀⣿⣿⣿⣿⣛⣋⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⣰⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠐⠿⣿⣷⣲⣶⣶⣶⣷⣶⣠⣶⣶⢶⣶⣼⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠟⠛⡛⠿⠯⠾⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⣿
⣿⣿⣷⣤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⠤⠤⠀⣾⣧⣤⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⢦⠀⠰⢄⣀⡀⠀⠀⠂⠸⡆⠀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢸⠇⠀⢿⡑⡈⠁⢒⢨⣿⠃⠀⠘⠫⣼⣭⣭⡻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣶⡾⠇⠀⠀⠁⠙⢻⠋⠋⠀⠀⠀⢠⣶⣯⣿⣿⡄
⠀⠀⠀⠀⠀⢺⠤⢄⡀⠈⠈⠀⠂⠀⠀⠀⠀⢰⡆⠀⢰⣧⡀⠀⠉⠙⡏⠛⠁⠀⡤⠓⠀⠀⠀⠀⣤⣀⣤⣀
⠀⠀⠀⠀⠀⠐⠀⣜⡳⣶⣤⢀⠀⠀⠀⠀⠀⠀⡇⢀⣺⣾⣧⡄⠀⠠⠀⠀⢤⠒⠻⣀⣀⣻⠿⢟⠟⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢥⠈⠙⠿⣧⠀⣄⠀⠀⠆⢳⠀⠈⠇⣷⣆⠀⣈⠰⡖⠻⢇⣴⠌⣋⡵⣂⠱⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠐⡮⣷⣝⠿⠁⠀⢻⣦⡄⠈⠿⣗⣠⡟⠉⣡⣾⣿⣿⠯⠅⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠔⠀⠛⠀⠿⢿⣦⢻⡧⠀⢚⣿⣿⣴⠿⠿⡙⣭⣿⡶⣯⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⡀⠀⠠⢂⣀⣶⣮⣝⣿⡂⢨⡿⢟⣾⣭⡎⠄⠩⠜⠙⠀⠙⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣈⣍⠉⣲⣿⣿⡏⠃⠀⣿⣿⣿⣿⣿⠾⠶⠶⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠙⠛⠓⠛⠛⠋⠙⠛⠃⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⣀⠘⠒⡀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠹⣄⠀⠈⠂⠀⠀⠀⠀⢠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⠀⠀⠨⣆⠴⠁⠀⠀⠀⠀⠸⡇
⠀⣠⡠⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠈⠻⣆⠀⠀⠀⠀⠀⢄⣡⠄
⠀⠀⠀⠮⠿⢦⣀⠀⠀⣀⠠⠝⠓⠦⣀⠀⠀⠀⠀⣀⣹⣆⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠘⣡⢘⡅⠀⠀⠀⠀⠀⠨⠟⠚⠛⠋⠉⠉⣩⠽⠒⠢⠄⣩⡆⠈⠳⣄
⠀⠀⠀⠀⠶⢦⡁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠖⠛⠛⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⣨⠐⠻⠶⣦⣄⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡄⠀⠀⢀⠀⠈⠉⠛⠶⠷⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⢬⠁⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠉⠉⠀⠀⠀⠀⠀⠀⠲⢀⠎⠀⠂⣀⠐⠂
⠀⡀⠀⢸⡄⠀⠀⠀⠀⠐⣄⠀⠀⠀⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠐⠲⠉
⠀⠘⢶⣄⢻⡄⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡷⢸⡿⠿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠻⣿⣷⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⣾⣿⣿⣵⠀⣇⣴⣿⣿⣧⠀⠀⠀⠀⠀⠸⣯⠸⠇⣀⣴⣿⠁
⠀⠀⠀⠀⢀⣀⣠⣴⣿⡿⠛⠛⢋⠝⠀⠀⠀⠀⠀⠘⠛⠁⢷⡼⢁⠜⢻⡿⠋⠀⠀⠀⠀⠀⠀⠘⢆⢸⣿⡟⢃⡀
⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣶⣿⢪⣷⠟⢁⡀⠀⠀⠀⠀⠀⠉⠛⠉⠙⠛⠛⠛⠛⠛⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⣿⣿⡿⣾⠁⠾⣿⡿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⡜⢿⣿⣿⠙⣷⡴⠻⣍⡙⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⢟⠻⠛⠀⠀⠀⢠⣿⠀⢀⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠙⢦⣰⣆⠀⢸⣇⠠⣶⣿⣿⣿⡗⠉
⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣼⡟⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡟⠟⠀⠒⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠉⠊⠓
⠀⠀⠀⠀⠀⠸⣶⣄⠸⢆⠀⠀⠀⠈⠉⠋⠀⠀⠀⢹⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⢙⣻⣧⣼⣤⣶⣶⣦⣤⣄⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠿⠿⠖⠚⠛⠂
⠀⠀⠀⣴⣾⣿⣿⡟⠉⠙⠻⠀⠈⠉⠉⠀⠀⠀⠀⢀⣀⣻⣿⣀⣀⣀⣀⣠⢔⣒⠼⠟⠋⠁
⠀⠀⠰⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠴⠖⠚⠛⢉⣉⣉⣉⣹⣿⣿⣯⣉⣉⣉⠉⠙⠛⠛⢷⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠙⠿⢿⠷⣶⣤⣙⡛⠿⣶⣶⢶⣦⣤⣤⣄⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣷⣶⣷⣶⣾⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⢠⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣓⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠙⣇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⣞⣁⡠⠤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⡼⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢀⡴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡽⡌⢳⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄⣇⠀⠈⣧⠖⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⠞⡥⠖⠛⠁⠀⠉⠛⠻⢿⡒⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⡇⠘⡆⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠢⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣇⠀⣀⠿⠀⠀⠀⢠⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠃⢸⣴⡷⠒⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⣼⡟⠀⠀⠀⠀⠀⢀⠠⠞⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡋⠀⠀⢀⡠⠔⠚⠥⠾⠲⠶⣶⠿⣤⣴⣿⣾⣶⣤⣤⠴⡂⠖⣤⣄⡀⠀⠀⠀⠀⠀⠀⠘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠡⠐⠪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣄⡉⠿⣿⣿⣷⣶⣷⣾⠿⣻⡿⡱⣆⠤⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡈⢣⡀⠙⢿⡛⠿⣶⣶⣷⣿⣶⡺⠟⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠒⠀⢳⡀⠀⠉⢿⡿⣿⣧⣀⣠⣤⣦⡀
⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣱⣆⠀⠈⣧⠀⠙⢿⣯⣼⣯⣽⣆
⠀⢀⡠⠶⠋⠀⣀⣤⣴⣲⣾⣯⢿⣯⣯⣽⣿⣿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄⣈⣧⣄⣈⠻⣏⠻⣿⣽⣦
⠈⠉⠀⠤⣶⣾⣯⣿⣿⣟⣿⣿⣿⣏⣿⠛⢻⣭⣤⠄⠶⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠻⠾⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠋⢀⠴⠀⣀⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣟⣛⣿⣿⣿⣟⠓⢦⣾⣿⡡⠂⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣻⣿⣿⣿⣷⣄⢻⣯⣉⠳⣾⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣷⣔⡘⢿⣿⠍⠓⢦⡄

⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢠⠘⠃⠀⠀⠀⠀⠀⠀⡘⠆⠀⠀⠀⢀⣠⣼⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⠒⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠱⡀⠀⠀⠃⠀⠀⠀⠀⠤⣙⡠⠀⠀⠀⠰⠵⢞⣯⠉⠃⠀⠀⠀⠀⠀⡇⠀⠀⠘⠃⣣⠀⠛⠁⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠰⠆
⠀⠀⠀⢓⡀⠀⢰⠃⠀⠀⠀⠶⠆⣮⡄⠀⠀⠐⣄⠀⢹⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠉⢠⣐⡾⠶⠀⠀⠀⢠⣿⣿⡿⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⢀⣁⡋⠀⠀⠀⠸⡆⠘⠀⢠⠆⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⢄⠀⠾⠇⢸⠀⢿⠟⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⢰⠈⢅⣀⠀⠀⠀⢻⣄⢠⠃⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢠⠄⡀⠀⠀⠀⠙⣆⠀⢘⡶⠀⢀⡞
⠀⠀⠀⠀⠠⣼⠎⠀⠀⠀⠪⡛⡚⠀⢙⠦⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠈⣇⢸⠃⠀⠘
⠀⠀⠘⢃⠔⡻⠁⠀⠀⠀⠀⠁⠍⠡⠂⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣴⣾⣿⠒⠲⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠈⠸⠅⠀⠀⠀⠀⠀⠀⠀⢻⠘⠋⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠘⠃⠀⠀⠀⠀⠀⢸⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡶⡀⠀⠸⣷⣿⠀⠀⠀⠀⠀⠲⠞⠂
⠀⠀⠀⣠⣤⣄⡀⠀⠀⠈⢲⣇⡂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⣾⣶⡄⠀⠀⠀⠀⠸⣛⣿⠏⠀⠀⣿⡏⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠼⠿⣿⣿⡇⠀⠀⠐⠀⠉⠵⠀⠀⠀⠠⣴⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠄⠛⡉⣶⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⢡
⠀⠃⠀⠀⠸⠻⠤⠀⠀⠀⣠⠁⠀⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠉⡀⠉⠀⠀⠈⠀⠀⠀⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠘⢀
⠀⠂⢠⡶⣶⡶⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠑⠤⠤⠀⠀⠀⢶⣧⠄⠀⠀⠀⠀⠀⠀⠤
⠀⡀⠘⣾⠿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠅
⠀⠄
⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠙⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠻⣿⠛⠛⣿⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⣠⠞⠁⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢀⡾⠋⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⢀⡾⠁⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⢀⡄⠈⠙⠛⠉⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠈⠳⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⢹⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠻⢦⣤⠾⠃⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢰⡏⠁⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠷⣤⡴⠟⠀⠀⠀⣰⠞⠛⢷⡄⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣿⣀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢁⣿⣿⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢈⡷⠞⣋⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣡⣿⡾⠓⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢍⠿⣭⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠛⠻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢌⡋⠿⢿⠿⢿⣿⣸⡟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡿⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣅⠀⠈⠙⣂⠉⠿⣿⡌⢿⣄⠀⠀⠀⠀⠀⠀⢠⡾⢻⣿⣟⣿⣿⡿⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠙⠀⠀⠀⠀⠀⠉⠻⣯⣿⡄⠀⠀⠀⠠⠀⠛⣿⡟⠋⢻⣿⣿⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠰⣀⣀⡈⣀⣛⣿⣿⡀⠀⠀⣦⢀⢤⣿⣷⣤⣴⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣭⣍⣉⡉⠙⣛⣿⣧⠀⠀⣸⣿⣾⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢤⣤⣼⣿⠀⢰⠋⠁⢀⣦⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⣿⡝⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⢁⠟⣧⣤⣼⣿⢿⣿⡟⢀⣿⣉⣽⣿⣯⣴⣿⣿⣿⡿⢿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡉⠛⠻⢿⣾⣄⠘⢦⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⡠⣠⣠⣾⣿⣿⣿⣿⣽⢿⡾⠻⠿⣿⡋⠙⠻⣯⣑⠿⣷⣬⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠕⠒⣤⣤⣉⣛⣷⣜⡄⠁⣤⣀⡂⠀⠀⠠⣠⠤⠀⣿⣮⣠⣿⣻⣷⣿⢿⠻⠿⣭⣋⡈⠳⠀⠀⠙⣦⣄⠨⣛⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣀⣐⣒⣊⣉⠉⠙⢷⣄⣸⠙⢻⡆⢠⠀⢴⡂⠁⢸⣿⣿⣿⣟⣻⠷⢶⣄⠘⠺⠻⣿⣦⠂⠑⠀⣬⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣭⣭⡭⠛⠛⠛⠛⠻⢿⣿⡄⠚⣿⣀⣰⡏⠀⣴⣿⣿⡿⣦⣌⠉⢻⣄⠙⢷⣤⣐⣬⣹⡿⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢺⣦⣤⣤⣤⣀⣀⣀⣬⢻⣶⡜⢸⡟⠻⡃⢹⡿⠛⠉⠉⠛⠛⠋⠛⠋⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣍⡙⠶⢌⢉⣍⠉⠛⠛⠿⣧⣾⣷⠀⢁⠏⠀⠀⠀⠀⢀⣀⣤⣤⢶⡾⢛⣾⠟⣿⠟⢛⣿⣿⣿⠿⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡁⢤⣤⣤⡀⠀⠹⣿⠋⡆⣾⢋⡁⠓⣴⣾⡿⢙⣿⠃⣾⣠⡾⣳⣾⣿⣿⡟⠻⠿⢞⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡿⠻⠟⣷⣿⣿⣿⡷⠋⠁⢀⠈⠹⣿⣼⣯⣾⣿⣿⣿⠿⠿⢯⣭⣿⣿⣾⠟
⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣿⣿⣿⣿⡀⠀⠘⣄⡤⠀⣿⣿⣿⣿⣿⣷⣷⡔⠛⠻⠲⢾⡟⠃
⠀⢿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢻⣇⠀⠀⠀⠐⢌⣿⣿⣏⣛⡿⣿⣿⣿⣥⣆⡙⠋
⠀⠸⣿⠟⠿⣿⣿⣝⠳⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⣿⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣯⣯⡿⠋
⠀⠀⢹⣿⡿⠿⣿⣛⠿⢾⣿⣿⣷⣝⢓⣦⣄⠀⠀⠀⠀⠀⠀⠀⡟⢰⣿⣿⣿⣯⣻⣿⣯⣭⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠈⢿⣿⣿⣷⣾⣷⣿⣵⡿⠟⢛⠷⣵⣙⢿⣦⣄⠀⠀⠀⢠⡇⣾⣿⣟⠫⠟⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠹⣯⣭⠇⢂⡩⠕⢒⣠⣽⡿⠿⠿⠿⣿⣿⣦⠀⠀⢸⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠻⣾⣭⣵⣶⠿⢟⣧⡵⢾⡿⢟⣻⣿⣿⣇⠀⡟⢸⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣥⡾⢷⣟⣿⣿⣿⣿⣿⢰⢇⡿⠀⠀⣀⣠⣤⣶⣿⣟⣽⣿⡿⠿⢿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿⠿⢿⣿⡟⣸⣇⣴⢞⣿⣟⣵⣿⣿⣿⣻⣿⣿⣶⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⣿⢃⣿⣿⣿⣿⣿⠿⣷⣅⠁⠽⣻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡏⣸⣿⣿⡟⢿⡿⣷⣮⣝⣿⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣰⠿⠿⠿⠿⠶⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⣀⣾⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⡆⢰⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⣿⣠⡀⠀⢀⡀
⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣧⣽⡵⣿⣨⣥⠸⡷⣠⡀
⠀⠀⠀⠀⠸⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⡛⠩⠁⠊⠀⠀⠀⠸⡛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣯⣧⣿⣧⣤⣶⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠒⠒⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠂⠀⠉⠉⠉⠉⠉⠉⠙⠛⠇
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⣤⡀⠀⠀⠉⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠴⠶⢄⡀⠉⣠⣶⡀⠀⠿⢇⠀⠀⠀⠀⠀⠀⠈⣁⣄⠀⠀⠀⣀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣤⡄⠈⠛⠛⣀⣙⠋⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠻⠿⠁⠐⣿⣿⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⣴⣦⠸⢿⡿⠃⢀⣉⡁⠠⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⠿⠇⡀⢰⣶⡆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡆⠉⢁⡃⣴⡆⣴⠈⠉⡁⠔⠀⠀⠀⠀⠀⠐⠈⠛⢋⡀⠀⠘⡃⠈⠉⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠘⠓⠒⠂⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠡⠀⢾⣿⠆⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣤⠀⠀⢠⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠙⠀⠀⠀⠃⠀⠀⡆⠀⠀⠀⠀⠴⠆⢀⡈⠁⡀
⠀⠀⠀⠐⠃⢠⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣀⠀⠙⠋⠀⠁
⠀⠀⠀⠀⣰⠘⠃⠀⠀⢀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡀⠀⠀⠀⠟⠁⠀⡄
⠀⠀⠀⠀⠪⠈⠀⠀⠀⠈⠀⠀⠀⠘⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⢠⢀⡄
⠀⠀⠀⠈⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⣈⠂
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠹⠀⠀⠀⠀⠙⡄⠀⠆⡔⡡⠐⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢨⠆⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⡆⣾⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣦⣮⠤⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠘⡿⠀⠠⠀⠀⡐⠀⠀⠀⢀⡨⠖⣯⣱⠘⠆⠀⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠘⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠆⢰⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠐⡄
⠀⠀⠈⠀⠀⠠⠀⠀⢀⠠⠁⢠⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠀⠀⠀⠀⠱⣦
⠀⠀⠀⠑⠆⠀⠀⠀⢀⠤⠘⢶⡷⠃⠀⠀⠀⣾⡻⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠠⡄⠀⠀⠀⡔⠁⠀⠀⠀⠀⠘
⠀⡂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠉⠑⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠁⠀⠀⠀⠁
⠀⡀
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⠀⠀⠀⠏
⠀⡀⣀⣰⠀⢀⡀⡀⣄⠀⢀⣰⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⢠⣷⣿⣿⣾⣾⣿⣷⣿⣷⣿⣿⣿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠀⠠⠄⠀⠀⠀⠀⠀⢬⡧
⠸⠟⠟⠿⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢺⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠩⢍⡧⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠀⠳⠪⣽⣷⣂
⢀⣰⣷⣠⣼⣥⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⢠⣿⣀⠛⢭⣽⣯⠶
⠀⣿⣿⣿⣿⣿⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡧⠀⠰⢬⣿⠔⠂⠰⣬⣷⠞
⠀⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⣷⣄⠨⠽⣿⠭⠄⡼⣿⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⢶⣿⣿⠀⠀⣿⣷⠲⠶⠶⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣛⣫⣭⣶⣶⣿⠿⠿⣿⣿⠀⠀⣿⡿⠿⠿⠿⣿⣷⣾⣭⣟⣳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⣶⣿⠿⠛⠋⠉⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇⠀⠀⣠⠶⠛⣩⡽⢟⣿⣷⣭⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⣾⡿⠋⠁⠀⠀⠀⣀⣴⢶⣴⣶⣿⣿⠀⠀⣿⣷⠤⣤⣤⣶⣟⣉⣚⠉⠀⠀⠙⣷⡌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⢸⣿⡁⠀⣀⣤⠶⠛⠋⠁⣈⠀⢰⣿⣿⣀⣀⣿⣷⠘⠋⠀⠀⠉⠉⠟⠿⢶⡄⠀⣿⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡻⣷⣄⢉⣤⢶⣠⠴⢛⡁⠀⠀⣭⣍⠉⠉⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣮⣝⠻⢷⣯⣥⣖⠋⠁⠀⠀⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⣀⣀⣤⡶⢟⣫⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢈⡙⠳⠦⣭⣝⣛⡛⠿⠶⣶⡶⠶⠶⣶⣶⠾⠛⣛⣛⣭⡭⠷⠚⢉⣥⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠙⠷⢶⣤⣌⣉⡙⠛⠁⣛⢃⡀⠀⠛⢃⣈⣋⠉⠉⣀⣠⣤⠾⠋⠁⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠈⠉⠙⠛⠻⠟⠛⠋⠹⠟⠛⠿⠉⠹⠛⠛⠋⠁⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⣀⠀⠀⢠⣤⣤⡀⠀⣴⣦⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⣴⣿⣿⣷⡄⢻⣿⣿⡟⠀⣹⣏⠀⠘⠿⠿⠃⣴⣶⣶⣄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢿⣿⣿⡿⠃⣀⣈⡁⠀⢾⣿⣿⡇⢠⣶⣦⡈⣿⣿⣿⡿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣈⣉⠀⣼⣿⣿⣿⡆⢀⣉⡉⠀⣸⣿⡿⠃⢈⣉⠉⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠐⢿⡿⠃⠙⢿⣿⡿⠣⣿⣿⣿⠸⣿⠇⠀⢰⣿⣿⣷⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣴⣿⣶⡄⣴⣿⣶⡄⠙⠛⠋⢰⣾⣿⣦⠀⠛⠛⠋⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠸⣿⣿⣿⠇⠹⠿⠟⣵⣿⣷⡄⠈⠻⠟⠃⣴⣿⣷⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢈⣭⣁⠀⢀⣤⣀⠿⣿⣿⢇⣾⣿⣿⡆⢙⡛⠋⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣿⣿⣿⢰⣿⣿⣿⡇⢀⣤⣄⠻⠿⠟⠁⣿⣿⠆⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣮⣍⡁⠀⠙⠛⠛⠁⢿⣿⡿⠀⢾⣿⠀⠈⣁⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⢂⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⠿⠿⠿⠿⠿⠿⠿⠿⢿⣟⣻⣟⠃⠀⠀⠀⠀⠀⠤⡘⠉⠉⠙⠛⠛⠛⠛⣛⠛⠛⠻⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢶⣦⣤⣬⣭⣭⣤⣤⠴⠶⠖⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠀⣤⡀⠀⣠⡄⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⣿⠉⡿⠻⡋⡹⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⢿⢇⣭⡘⠟⢈⣅⠿⠗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢤⡜⠉⠷⠲⠏⠙⡤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠷⣈⡿⠋⣛⠘⣛⡸⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡼⠃⢰⡟⠚⣷⠚⠣⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⡻⠟⠸⣿⠃⠻⣟⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠛⠦⠾⠧⠠⠿⠦⠘⢁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠓⠲⠶⠶⠶⠶⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠸⠟⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠈⣻⠿⠚⠟⠘⠿⡃⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠆⣾⣿⡀⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉






⣿⠿⠿⠿⠿⢿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⣛⣻⣿⣿⣿⣿⣛⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣴⢟⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡞⠁⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⣸⢾⣿⣯
⠀⠀⠀⠀⠀⠀⣰⢿⣿⣿⣆⣸⣿⣿⣿⣷⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢠⡏⣺⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⣾⡀
⠀⠀⠀⠀⠀⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣸⣿⡧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴
⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣷
⠀⠀⠀⠀⠀⣿⡻⢿⣿⣿⣿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢻⡿⠿⢟⣿⣿⣷⣤⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⠿⣿⣦⣴⣦⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣷⣶⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠯⠀⠀⠈⠉⠁⠉⠁⠀⠀⠁⠀⠉⠉⠉⠻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠋⡁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠠⢾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢻⠇⠀⠀⢀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⣇⣸⣤⣶⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⠃⠀⡼⠁⢸⠀⠸⡄⢩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣀⣀⠤⠶⠚⠉⣡⠎⢰⡄⠀⠀⠀⠀⠀⠀⠑⠂⢤
⠀⠀⡠⠀⠀⡟⠁⠀⠈⠀⠀⣡⠘⠌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠩⠍⠁⠀⠀⠀⠀⠀⠐⠁⢀⠏⠃⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠁⢀⠜⠀⠀⠀⠀⠀⣀⡛⡆⢂⠀⠻⣄⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⡰⡆⠀⠀⠀⠀⠤⠖⠉⠁
⠀⣠⡠⠃⠀⠀⠀⠀⠠⢚⡟⡇⠸⡀⠀⠀⠈⢣⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢜⡿⢃⠏⠀⢐⡇
⠴⠮⠐⠃⠀⠀⠀⠀⢰⡞⠀⠁⠘⠳⡄⠀⠀⠀⠙⢢⡀⠠⡀⠀⠀⢀⡴⢖⡭⠄⠀⠈⣠⡌⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠜⣴⠂⠀⢸⡇⢹⡄⠀⠀⠀⠀⠘⠢⢵⣄⡐⠉⠁⠀⠀⠀⣠⠞⢱⠂⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⡴⠃⠈
⠀⠀⠀⠀⠀⠀⠀⢺⡣⠃⠀⠀⠸⠃⠀⢻⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠐⠋⢠⡏⠀⠀⠀⢸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⡰⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⢘⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣆⠀⠀⢻⡢⡀
⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠳⢈⠁⠂
⠀⠀⠀⠀⡾⡡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠒⣄
⠀⠀⠀⡴⠱⠇⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⢿⣿⣿⣿⢿⡿⢿⣿⢿⣿⣿⡄⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⠱⢦
⠀⢀⢸⠇⡀⠀⢠⡾⠋⢀⣀⣤⣤⣄⣀⠀⠾⡿⡾⠾⢿⣿⣿⠿⠷⡿⢿⢷⠿⠿⢾⡿⡃⠀⠀⠀⠀⠀⠈⠙⠲⠦⣄⡀
⠀⢸⡿⠊⢀⡴⠥⠖⠚⠋⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠲⠶⠶⠦⠽⠖⠤⢤
⢠⡮⠔⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢒⣲⣶
⣁⠴⣈⣁⣀⣤⣤⠤⠤⠤⠤⠄⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠑⠂⠀⠀⠀⠀⠀⠀⠀⣀⢄⣒⠩⠴⠞⠉⠔⠁
⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠉⠙⠂⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠢⡀⠀⠀⠚⠋⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡠⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠰⢦⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠉⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⠴⠊
⠀⠀⠀⠀⠘⡙⠦⠀⠀⠀⠀⠘⡇⠀⢀⠊⠀⠀⠀⠀⢀⠀⠤⠤⠄⠤⣤⣤⠍⣣⣄⡀⠠⢀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡴⠙⠁
⠀⠀⠀⠀⠀⠁⠈⣆⠀⠀⠀⠀⡇⢀⡿⠀⠀⢀⡠⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣈⡑⣲⣌⢉⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢇⡘⠁⠀⠔⢋⠜⠍⠀⠀⠀⢀⡠⠔⣒⣁⣤⠖⢚⡿⠃⠀⠀⠀⠉⠓⢾⡤⡀
⠀⠀⠀⠀⠀⠠⠀⠀⢹⡀⠀⠀⢘⠁⡰⢀⠴⠋⠀⠀⠀⠀⠈⠉⠙⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⢀⢈⡖⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠂⠸⠐⠗⠣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠛⠋⠉⠉⠀⠀⠀⠉⠒⠄

⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⢳⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻
⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⣻⣿⣿⠟⠿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢠⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣶⣦⣾⣿⣿⣿⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⠃⣹⠇⠀⠀⠀⣤⣴⣶⣶⣾⣿⠋⢻⣿⣿⡛⠁⠀⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠃⠰⣿⣷⠀⠀⠀⠀⠈⠉⠙⠋⠹⣷⣴⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠛⠙⠏⣻⣤⣄⣀⣀⡀
⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠙⢿⣿⣿⣧⣄⣬⣤⣆⣤⣤⣴⣿⣿⡿⠟⠋⠉⠁
⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡟⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣻⡿⣧⣤⠀⠀⠀⠀⠀⠀⠀⡿⢹⣿⡿⠛⣿⣿⠿⠿⣿⣿⣿⣧⠀⢀⣴⣶⣄⣢⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣽⣿⣿⠀⠀⠀⠀⠀⢀⣰⡄
⡟⠁⠉⠛⠀⠀⠀⠀⠀⠀⠐⣿⢿⣿⣲⣀⡀⡻⡆⣀⡼⣿⡿⢿⣿⣏⣨⣿⣩⣿⢋⣿⣿⡿⣻⣉⠀⣌⣩⠿⣜⣿⢟⠀⠀⠀⠀⠀⢨⣿⡀
⡁⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⢉⣻⣿⣿⢿⢫⣿⢷⣾⣵⢿⣩⠁⠙⠿⣿⣖⣾⣿⣿⡿⡛⢿⣷⣿⠿⣿⣧⣽⡆⠀⠀⠀⠀⠀⠈⢻⣿⡄
⡶⠂⠠⣷⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣟⣽⡿⣍⡋⠀⠈⢹⣯⣟⣷⣦⣽⣾⣿⣟⡋⣤⣴⣿⡗⣋⣁⣼⣏⣍⣽⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠓⠀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⠭⢩⢩⡗⣈⣻⣿⣷⣶⡿⣿⣿⣿⠿⠯⣽⣿⣾⣿⣻⣍⣥⣹⣿⠭⣿⡵⠤⣷⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⣠⣬⣨⣶⣠⣿⠾⢿⡿⠟⢛⣋⣉⠱⣿⣿⣿⣿⣿⡶⠁⠈⠛⠿⠿⣶⣾⣷⣦⣷⣾⣁⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠹
⢀⣿⣿⡗⣠⣾⡀⠀⠀⠀⠉⣿⣿⣯⣉⣁⣽⣿⠁⠀⢻⡿⠀⣀⣈⣭⣿⣿⣿⣿⣿⣶⡀⣤⣀⣹⣻⡷⣿⠿⣿⣿⣿⣿⠃
⣸⣿⣿⢱⣿⣿⠇⠀⠀⠀⠀⠈⠙⠻⣯⡻⣾⣶⣿⢶⡆⢘⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠨⠭⢁⣈⣠⣨⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢠⡀
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⢠⣶⣶⣶⣶⡿⣿⣽⡋⠋⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢿⠟⢀⡀⠀⢸⡟⢻⡆⣿⣿⣿⣿⡿⢿⣿⣾⡶⢾⡿⢓⢻⣿⢡⣿⣿⠟⠀⣀⡙⠛⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡆
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠀⢸⣿⠐⠙⣿⣯⣼⣿⡀⡌⢿⢻⠀⣿⣷⣿⣿⣥⣻⢿⣿⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⠸⣿⢠⣶⣿⣿⣿⣿⣿⣧⣸⠀⢂⣿⣿⣿⣿⡟⠁⢸⣿⣀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⣍⠛⠟⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡿⢿⠋⠀⢸⣿⠛⣿⠿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠃⢀⣀⡀⠀⠀⠀⠀⠀⠇⠀⠸⣿⣿⠂⠀⣿⣿⣿⡇⠹⣿⣿⣄⣿⣿⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿
⣿⣿⣿⣿⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢁⡄⠀⢸⣿⣿⡇⠀⢻⣿⣿⡟⣧⣤⣤⡴⠂⠀⢸⠟⢀⣤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⡇⠀⣿⡏⠋⠀⣿⠿⣿⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⠈⠙⠛⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⢯⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠓⠘⠀⣦⡀
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠰⠏⢩⣿⡿⣭⠁⠀⢀⣴⣦⡤⣀⠀⠀⠀⣿⣿⣦⣤⣶⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢰⡷⢶⢀⠙⠁⠀⠄⣤⡄⠀⠀⠙⠞⠉⠁⠀⢰⣯⢞⣻⠿⠞⠁⠀⣀⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣦⣸⣿⠦
⠈⠀⠀⠶⠀⠀⡀⠀⠀⠄⣴⣦⣦⠀⠀⠀⠀⠈⢁⣼⣷⠀⠀⠀⠀⠙⣏⠙⠛⠛⠛⠋⠙⢢⣶⡔⠁⢀⡔⠆⠀⠀⠀⠘⠛⠓⠂
⠀⠀⠀⠀⠀⢸⡿⠀⠲⠖⠀⠈⠛⠀⠀⠀⠀⢠⣟⡵⢫⣦⣵⠂⠀⠐⠁⠀⣤⠀⢶⡀⠰⢟⡟⠻⢄⢾⡷⠤⡀
⠀⠀⠀⠀⠀⠠⢆⡆⠀⠀⣠⣶⡆⠀⠿⠿⠆⣼⠅⠀⢸⡿⡟⠀⠀⠀⢀⢤⣽⣶⠀⡿⠠⠈⣟⠀⣿⣎⠀⠀⣻⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣤⣾⣿⣟⣡⠀⠑⠃⠒⡋⡅⡠⢋⢁⠛⣤⠀⠘⡄⡙⠂⣹⠯⠀⠀⠈⠀⣤⣄
⠀⠀⠀⠀⠋⠿⠀⠀⠀⢸⣦⡀⠀⠈⠻⣿⣿⣿⡿⠋⠀⢀⠤⣨⡖⢫⢣⣡⠀⢇⡅⢣⣴⠇⢿⡾⠛⢷⠀⠀⠺⣄⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠉⠁⢰⣦⣤⠈⢯⣟⡛⠀⠀⠈⠚⠋⠪⣵⣦⣬⡁⠀⠡⠵⢰⠀⠀⠰⣦⠟⠀⠀⢠⡄⡦⠀⠉⡉⠀⠘
⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⣲⣂⣔⡏⠛⢁⠂⣹⣿⠀⢀⡄⢠⡆⢺⣿⣿⣻⡟⣆⡀⠀⣀⠀⠀⠀⣎⢝⡉⢢⣤⠈⡡⢾⠛⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢸⠢⡤⠜⠪⡿⠏⠁⠀⣈⣄⣻⣿⠵⠛⣇⢸⡇⣸⠉⢉⠟⠉⢹⠙⠯⣾⣷⡶⠀⠉⠀⠉⣹⠲⠤⢥⡤⣀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠘⢧⡝⣈⢄⠐⠀⢁⣴⣿⣿⡜⣱⢦⡄⢸⡸⡇⡇⡴⢁⡤⢞⣵⣿⣿⣍⠛⠉⠀⠀⠀⠀⢸⠂⠀⠈⢽⣭⣷⠄⣸
⠀⠀⠀⠀⠀⠀⠀⡈⣧⣬⠀⢀⠿⢿⢉⣿⣿⣿⣻⠀⣌⢢⢟⡉⡉⠳⡫⠴⢾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⡀⠀⣰⣾⡿⣷⡰⠁
⠀⠀⠀⠀⡈⠂⠀⠀⠀⠊⠀⠸⡆⢸⠎⡼⠁⠐⢙⡀⠀⠉⠈⣶⠈⠂⠟⠿⡍⡫⢯⠉⠀⠀⣰⣶⣤⡀⠀⠀⠁⠀⠉⠺⣿⠛⠝⠟
⠀⠐⢄⠀⠑⠀⠀⠀⠀⠀⠀⠀⣏⢨⡴⡇⠀⣰⠟⣿⣇⠀⠀⠋⠀⠀⠀⠁⠊⣵⢋⣀⡀⢰⡿⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⠃⠁⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢙⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀
⠀⠀⠀⠀⢽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠉⠒⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡀⢄⠀⠔⠀⠀⠀⠀⠀⠀⢀⣼⣿⡣
⠀⠀⠀⢱⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠘⠂⡁⠀⢁⠄⠀⠀⠀⢤⣿⣿⣟⣅⠡⠂
⠀⠀⠠⣕⣲⣿⣿⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠈⠀⠀⠀⠀⠀⠩⡷⠀⠀⠀⠀⠠⠬⣀⠾⠀⠀⠀⠀⢀⣹⣯⣿⣿⣩⣶⠥⠄
⠀⠀⠨⣓⣿⣿⣷⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣈⠡⠔⠀⠀⠀⠲⣿⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠀⢉⣹⣿⡿⣯⣤⠵⠖⢒⣀⡀
⠀⠀⠀⠤⣿⣿⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠅⠀⠂⠀⠀⠀⠀⠁⠂⠀⠈⣙⣓⠦⣽⣿⣡⠴⠖⢛⣉⣁⡀
⠀⠀⠈⠽⣿⡲⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠨⢇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⣶⡶⡼⣻⣯⣭⠥⠖
⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢤⣈⣹⣿⣫⡶⠶⠖⢚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡧⠄⠀⠀⠀⠀⠀⠀⢠⡃⠀⠘⠻⢷⡴⠀⠀⠀⠀⢀⣉⣉⣁⠾⣛⣋⣉⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⣉⣉⣀
⠀⠄⠀⠀⠁⠀⢰⡄⠀⠀⠀⣇⠀⠀⠀⠀⠀⣰⣇⢀⠀⠀⠀⠀⡌⠀⠀⠀⢀⠀⠀⠁⠀⠰⣄⠀⠀⠀⢠⡆⠀⢠⣴⣤⠀⠀⠁⠈
⠀⠀⠀⠀⠀⡐⣾⣯⠀⠀⠀⣿⠄⠀⠀⠀⠀⢨⢉⡁⠀⠀⠀⠀⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠘⢻⡍⠀⠀⠀⠀⣤
⠀⠃⠀⠀⠀⢸⣿⣷⠀⠀⠀⡿⠀⠀⠀⠀⠀⠠⠀⢀⠲⠃⠀⠀⣿⠀⠀⠀⠘⣿⠀⠀⠀⠀⢸⠇⠀⠀⠈⠀⠀⠀⠀⢻⠀⠀⠀⠀⣿
⠀⡊⢸⠀⠀⠈⢸⡇⠀⠀⠀⡇⠀⠀⣾⡀⠀⠀⠀⠀⠁⠀⠀⠰⠿⢤⠄⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣪⠀⠀⠀⠀⠟
⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡞⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠃⣤⣤⡄⠋⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢟⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠃⠀⢠⣶⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⣾⠷⠶⢤⣶⠒⠢⢰⣤⡖⢉⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠴⡖⠲⠶⠦⠤⢤⣤⣤⣤
⠀⠀⠀⠀⢀⠀⢀⣀⡼⠫⠀⠀⠀⠀⠙⣇⠀⠘⠃⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠘⢿⣿⣿⡟
⠀⠀⠒⠻⠿⣟⠛⠿⣄⡄⢀⠀⠀⠀⠀⠙⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⠳⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢤⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠈⠀⠹⣿⣿⣠⣷⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣈⣿⡧⠀⠳⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⣈⣿⣿⣁⠀⠙⡆⠀⠀⠀⠀⠰⡍⠀⠀⣀⣠⣤⣤⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠏⢀⠇⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⣸⠁⠈⢉⣿⣿⣥⠄⠀⢹⡀⠀⠀⠀⠀⢣⠀⠀⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀⣄⣴⣠⣦⣾⣷⡛⠷⢦⣄⠀⠀⠀⣿⠀⢈⣉⣻⣿⡥⠖⠀⠈⡇⠀⠀⠀⠀⠀⠁⠀⠉⡉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⣿⠿⢛⣫⠟⠉⠉⠉⠉⠀⠀⠈⠁⠀⠀⢸⠀⠙⠻⢿⣿⣦⠆⠀⢸⡇⠀⠀⠀⠀⠀⢀⠄⠐⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⠓⢿⣿⣧⠴⠂⡸⠀⢀⣄⠀⠀⣠⡿⠤⠤⢾⣿⣿⣆⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠚⢻⣿⡶⠂⡴⠁⠀⠀⠉⠻⣿⡏⠀⠀⠀⢤⣿⣿⣿⡟⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡧⠊⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣤⣿⣿⣿⡿⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣮⣵⣌⡥⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡿⠀⣾⣿⣿⣍⣧⡄⠀⢠⣄⠧⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⠦⢀⣠⡶⢿⣜⣴⢗⠛⠋⠙⠋⠉⠟⠒⣦⡽⣶⣾⣤⣼⡝⢲⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡶⣳⢎⣰⣟⣩⣿⠛⣴⣿⣏⣉⣹⡿⠚⣩⡑⠖⠶⠍⠛⢿⡽⠿⢣⡀⢘⣠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⣷⣿⣿⣿⣿⡾⣿⣿⣿⢛⡟⣿⣛⠻⣿⡀⣴⡤⡎⢱⡄⠑⠉⢠⣆⡇⣨⠷
⠀⠀⠀⠀⠀⠀⣀⡖⣄⡊⢠⣥⣴⣿⢿⣿⣿⡾⣿⡟⠓⢿⠶⠿⠶⠿⡷⠿⢷⢹⣷⡞⠀⠀⠈⠉⣷⡁⠒⢒⡆
⠀⠀⠀⠀⠀⠘⠷⣾⣿⣧⣼⣿⣿⣄⣿⡟⡃⢴⣾⠖⢻⣿⠿⠷⠆⠀⣰⠆⠀⠀⢭⣳⣀⡠⣶⣴⡶⠟⢣⡟
⠀⠀⠀⠀⠀⠀⠀⣹⣹⣿⣿⡿⢷⣤⣽⣷⣿⡿⣿⣿⣷⣷⣆⣸⣆⣾⣿⣦⣴⣏⣤⡾⣻⣿⣯⣭⢈⣿⣦⠸⠆
⠀⠀⠀⠀⢀⣠⣾⣿⣏⣿⣿⣶⣆⣹⡟⣿⣯⣗⣋⣿⣟⣝⠿⢿⣿⡿⣿⠆⡼⣿⢿⣿⣻⣿⣿⠋⠀⢳⡄
⠀⠀⠀⠀⠉⠉⠽⢿⣿⣼⣿⣿⣿⣽⣿⣿⣿⣻⣷⣺⣿⣏⣳⢾⣿⢋⣿⡤⠫⣷⣤⠤⠀⠀⠉⢦⣤⣅⡁⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣋⠀⢀⣝⢿⣿⠿⠫⠋⠉⠻⣿⣿⣄⠛⡾⠻⣿⢶⣶⣈⢘⡛⠁⠀⠠⡤⢀⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠛⡿⠿⠟⠾⠃⠀⠀⢸⣿⡘⡖⢳⠀⢀⠙⠑⠿⠿⠇⠀⣠⣀⣠⣤⡂⣀⡄
⠀⠀⠐⠖⢀⣶⣞⢢⢄⡠⢀⣴⠶⣄⠙⡃⢀⡀⠐⠂⠀⣼⣿⠃⢠⢸⡄⠛⠃⠠⠂⠚⠛⠨⠉⠩⠉⠉⠉⠉⠁⠂
⠀⠀⠙⢃⢸⣿⡷⢿⢦⡇⢺⡿⣿⣼⢫⢱⣿⣬⣱⠺⣲⡿⣿⠀⣾⠴⣇⠰⡄⣰⣖⣓⠢⠀⣤⠦⡀⢀
⠀⠀⠀⠐⠡⠀⠒⠊⠃⠈⠠⠒⠃⠨⠏⠀⣨⣽⣷⣶⣿⣴⠋⣴⣿⣤⡹⠶⣴⢬⣍⣋⡛⡺⣛⡗⢺⢴⣯⣆⢠⣀⣀
⠀⠀⠀⠀⠀⠐⠒⣒⠛⣛⠻⠖⢺⠿⢻⡟⢛⡉⠀⠋⠉⠀⠀⡀⠀⠀⠉⠛⠲⠶⠚⠲⠯⠙⠋⠉⠑⠒⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⠂⠲⠴⠀⠠⡬⠛⠛⠂⠂⠂⠤⠤⠌⠒⠐⠂⠀⠀⠈⠐⠀⠀⠀⠁

⡄⠀⠀⢠⠀⠀⠀⠀⠀⠘⠢⢌⣉⡙⠒⠣⣄⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⢘⣷⡂⠀⢻⠀⣇⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡇⠀⡇⠀⠀⠠⡒⡉
⠀⠀⢀⠎⠀⠀⠀⠀⠀⣤⣀⡀⠠⢈⠑⠀⠀⠀⢀⠘⠀⠀⠃⠄⠀⣠⣑⣒⡮⣧⠠⠀⠀⠏⣸⠀⠸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠸⣄⠀⠀⠄⣂⡱⠭⠖
⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠁⠀⢄⠀⠀⠈⢀⠀⢉⠉⠿⣷⣐⠀⠐⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠑⠂⠠⠔⠒⣂⢀
⠉⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠈⠈⠰⢀⠄⠀⠀⠀⠀⠀⠀⠡⠈⠀⡀⠀⠀⠤⡀⠣⠴⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⠐⣆⠐⠈⠉⠈
⠄⠀⠀⠄⣀⠤⠴⠶⠌⠀⡢⢂⡤⢖⣠⠴⠤⠀⠑⠀⠠⠀⠀⠨⡐⠀⠀⠀⠀⠄⠄⠔⠉⣤⠶⠖⠛⠐⢤⡤⢊⠔⣝⡲⢤⣄⡀⠀⠀⠀⠐⠀⢀⠀⠈⢦⠀⢀
⠁⠀⢀⡀⠀⠀⠀⠀⠀⢀⡰⠋⡴⠫⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢸⠀⠸⠀⢀⠴⠶⡋⠡⣴⡁⡢⣄⣙⠛⠲⣍⠳⠄⠀⠀⠀⠈⢣⡀⠀⠀⠀⠑
⠁⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠜⡠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⢀⠈⠀⠀⠀⠁⠀⠈⠘⠉⠈⡁⠀⡈⠆⠆⠀⠂⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠀⠀⠰⠀⠀⠠⠀⢁⡘⢦⠢⡠⡀⢦⣄⡤⠴⠶⡷⢶⡳⣶⣴⠖⠂⡀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠀⠀⠈⠀⠠⠂⠀⣀⠤⠶⣤⡀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠈⢿⠀⠂⠙⢦⠤⠠⠤⠀⡊⠠⢫⡾⠃⡀⠐⠄⡀⠀⠀⠀⡀⠀⠀⠀⠠⢀
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠀⠀⠔⠀⡠⠋⠀⠀⣀⡈⠙⠧⠊⡑⢀⠈⠀⠀⠀⠀⠂⠲⣆⠀⠀⠀⠀⠀⠀⠀⠠⠐⠹⠉⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⡌⢰⢃⠀⠀⠀⠀⠙⠲⢄⠀⢀⢘⡤⠠⠀⠀⠀⠀⠀⢀⡉⠳⠲⠄⠀⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠤⠀⠀⠀⠀⢀⡀⠀⡀⠠⠤⠤⡊⠀⠈⣸⢡⠐⠄⠀⠀⠀⠀⠔⠡⢂⢚⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠀⠀⠑⡀⠀⡀⠀⠀⠀⠀⣤⠔⠊⠑
⣀⣒⠒⠢⣄⡈⠂⠁⠀⠀⠀⣿⠀⠀⠀⡧⠈⠸⣆⠀⠀⠀⣟⣠⡇⢸⣸⡅⠀⠈⠉⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⢠⠔⠁⠊⠀⣀
⡁⠅⠀⠀⠀⠑⣄⠀⠎⠀⠁⣈⢧⠀⠀⠈⠀⠀⠌⠙⢦⡄⠈⠸⠳⠈⢳⢳⡒⠂⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⠂⠈⠀⠂⠤⠀⠀⠀⠐⠊⡀
⠀⠀⢀⣸⠀⢠⡏⡀⠀⢄⠈⠁⠀⠣⡀⠀⠀⠀⠀⢀⣒⣛⡷⡀⠄⠀⢸⢀⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠄⠀⠊⠀⠀⠀⢠⠀⠐⡀⡀⢰⠏
⠀⢌⢢⠇⠀⠞⠀⢁⠔⠀⠀⠀⠀⠀⠈⠀⠄⠠⢒⣀⠦⢤⠮⢯⣅⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢠⠆⢀⡎⣐⠋⠂⠀⢀⣀⠈⣆⢣⠀⢠⡞
⠫⠔⠇⣂⠊⡁⠑⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠜⠁⠀⠀⠀⠀⠋⠉⢀⠔⠈⠀⠀⠀⠀⠆⠀⠠⠁⠀⠀⠂⠀⢠⠏⠀⡚⢀⠁⠠⠀⠀⠀⠍⠈⢿⡌⣦⠟⢁⣰
⡥⠬⡂⡈⠺⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠄⠀⢀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃⠀⠠⠞
⠖⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⢠⠀⢀⣚⡀⠀⡃⠰⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠤⠤⢖
⠉⠀⠀⡀⠀⠀⣆⠀⠀⠀⠀⠐⠀⠀⣠⡤⢤⢀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠋⠉⠙⠳⣥⣾⡀⠀⠀⠀⡄⠀⠀⠈⠁⠀⠰⠚⠉
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⣠⣾⠗⠋⠱⣸⡇⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠐⡇⣾⡠⠐⢉⣛⢶⣤⢫⡟⣦⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣶⣯⢟⣭⣾⠧⣴⣿⣗⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⡞⠠⢫⢷⣎⠂⠀⠛⢿⣻⡝⡞⡅⠀⠁⠀⠰⠄⠀⡀
⠠⠄⠀⠀⠀⠀⠀⠀⠀⣻⠿⣽⣿⠿⠋⢰⡿⡜⢞⡷⠂⠀⠠⠀⠀⠀⠀⠀⠀⢈⠀⠐⠀⡀⠀⢹⡀⠃⠸⣎⡘⠦⣄⡀⠸⠿⣧⢳⣷⡀⠀⠄⡀
⠀⠀⠀⠀⠁⠐⠠⢄⡀⣿⠁⣿⠉⠀⠀⣾⠀⢃⡘⠇⡁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠈⢱⣄⠀⠈⠈⠂⠈⠻⣦⡀⠙⠀⡽⢻⡀⣀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠀⢀⠱⣏⠀⠫⣀⢚⣿⣃⡼⠡⠑⡌⠈⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠁⡀⠒⢀⣂⠐⣛⣷⡾⢿⣦⡈⢀⠂⠀⠀⠀⠁⠀⠀⢁⣀⣀
⣲⠀⠄⡀⠀⠀⠄⠀⠁⠈⢓⠶⠤⠽⠷⢁⠐⢀⠾⣍⠀⠄⠀⠀⢀⡠⠖⠐⠚⢶⣄⠄⠈⠀⠀⠀⠈⠀⠀⠈⠀⠈⠀⠁⠠⠈⠀⠉⠁⠀⠀⠀⠀⠀⢀⡜⣩⠄⠂
⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠋⠉⠙⠉⠛⠉⠀⠋⠱⢀⡜⢡⢟⠀⠀⠄⢤⡁⠙⢷⡐⢂⠀⠰⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣪⠞⢀⡀
⢣⢳⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠞⠀⡔⠋⠀⢁⡶⣀⠀⠀⠀⠙⠢⠀⠕⡡⢀⠂⠀⠀⠀⠀⠀⠀⠌⠀⢀⠀⠀⠀⠀⠀⠀⠒⡩⠚⡁⣴⣏⠀⢐
⠀⠃⠋⠱⠀⠀⠀⠓⠆⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠰⡇⠀⠀⢞⠐⠈⡆⠀⠀⢠⡄⢡⡎⠀⡟⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠈⠀⢠⠴⡑⢌⠠⡁⡈⠉⠀⣼
⠘⠘⠀⠀⡇⠀⠀⢀⠀⡈⠢⣀⠀⠀⠁⠀⠀⠀⢱⠀⠡⠀⠀⠈⠂⠈⠳⣄⠀⢨⡅⣧⠁⡆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢠⡎⠀⡇⠘⠀⠀⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡞⠁⠀⠀⠀⠀⠀⢀⣤⣤⣤⣠⠏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣴⠃⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡞
⠀⠀⠀⠀⠀⢠⣿⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀⣰⣯⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣾⣽⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣯⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠠⣬⣭⣉⣛⣛⣛⣉⣭⠀⠀⠀⢠⣭⣍⣉⣛⣛⣋⣉⣅⠀⠀⠀⠀⢨⣭⣉⣙⣛⣛⣉⣩⡄⠀⠀⠀⣭⣍⣉⣛⣛⣛⣉⣥
⠀⠀⠀⠀⡀⠸⠀⢩⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠈⣉⠉⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠉⣉⠁⡀⠀⠀⠀⠀⢠⠈⢩⠉⢉⡉⢀
⠀⠀⠀⠘⠳⠄⠀⠀⠠⠄⠀⠀⡣⠞⠃⠀⠀⣸⣀⣤⠀⢠⣄⣸⠀⠀⠀⠀⣀⣀⡆⠀⠀⠀⠀⠀⣇⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⠴⠐⡀⠆⣀⡇⠀⠀⠀⠀⢹⡉⠤⢐⠠⢌⣹⠀⠀⠀⠈⠋⠁⣇⠠⠄⡂⠤⣀⡇⠉⠋⠀⠀⢸⡀⠤⢐⠠⢄⣸
⠀⠀⠀⠀⠀⠀⠳⠾⠬⠧⠷⠞⠀⠀⠀⠀⠀⢈⠳⠧⠼⠴⠶⢋⠀⠀⠀⠀⠀⠀⡙⠶⠦⠯⠼⠞⡁⠀⠀⠀⠀⢈⠳⠾⠼⠧⠷⢋
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠀⠤⠒⠒⠒⠒⠤⠄
⠀⠈⠻⣖⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠀⠀⢀⠜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⣄⢸⡇⠀⠀⠀⠀⠀⠀⣀⠄⠂⠁
⠀⠀⠀⠈⠄⠠⡈⠑⠦⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢀⠄⠠⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢀⠆⢀⠔⠋
⠀⠀⠀⠀⠈⡄⠀⠢⣄⠈⢢⠀⠀⠀⣆⢠⠌⠀⠀⠀⡀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣘⠔⠁
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠑⢄⠑⡀⠀⠘⣿⠀⠀⢀⠊⠀⠠⠁⠀⠂⠀⠀⢤⣄⣐⠒⠂⠠⠄⡀⠀⠀⠘⣇⣰⠏
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⠳⡘⠄⠀⣿⡆⢀⠂⠀⡐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠢⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⡙⢌⡄⢿⡇⠘⠀⡜⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠡⢸⣿
⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣾⡇⠀⡘⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣼⡇⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠈⠑⠀⠠⠀⠀⠠⢀⠀⠀⠀⠈⣿⡇⢠⠇⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠈⢆⠀⠑⠄⡀⠑⠄⠀⠀⣿⡇⡾⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠣⢄⠀⠈⢦⠈⢆⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣡⠣⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣕⠌⠄⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠗

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣦⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⢹⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠠⠈⠀⡔⠀⠠⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠈⠉⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉⠁⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⣀⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠘⢤⠤⡀⢺⣱⢤⠶⡋⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠋⠀⠀⢰⠰⣄⠼⢀⡱⣏⢸⢧⡰⠉⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡀⠀⣀⣔⡃⢰⡳⣶⣈⣂⠙⠊⠀⠀⠂⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠚⠼⠁⢘⢛⡤⠔⠀⠉⠁⠀⡀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠐⡑⠒⠉⠀⠀⠀⠀⠖⠉⠀⣩⣤⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⡀⠀⠀⠀⣠⣶⣄⠈⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡏⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⢿⡿⠟⠁⠀⠀⠀⠙⠋⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠌⠑⣤⣀⣀⣀⣀⠀⠀⠀⢀⡈

⣴⣦⣀⡟⠀⢸⣿⣧⡀⠀⠀⣠⣶⣷⡀⠘⣿⣷⣶⣤⡀⠙⣿⣿⣶⣤⣄⠀⢻⣿⡄⢰⡿⠛⠻⠿⠏⠀⠿⠿⠿⣦
⡟⠉⠉⠳⠶⠟⠉⢹⣟⣿⣿⣿⠁⠉⣿⠏⠁⠀⠀⠙⣿⣿⠟⠉⠙⣿⡟⠀⠀⠙⣷⣾⡄⠀⠀⠀⢀⣤⣄⡀⢀⣏⣸
⠿⣦⣶⣶⡆⢠⡎⠙⣟⣿⣬⣿⠀⣴⡏⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢸⣧⠀⠀⢀⣿⡿⠛⠒⠲⢾⣿⠀⢈⣛⠉⠉⠙
⣠⣿⠟⣨⣤⣴⣿⠀⣿⠉⣠⠟⠀⢿⣿⣦⣀⠀⠀⠀⣿⣿⣦⣄⣀⣀⡛⠿⠿⢛⣡⣀⠀⠀⠀⠀⢻⣿⡿⠛⠛⠶⣾
⢿⣧⣴⡟⠉⣿⠏⠀⠈⣿⠏⠀⠀⠀⠉⢻⣿⣷⠀⣠⡀⠈⠉⠉⠙⢿⣿⡿⠂⣿⠟⠛⢧⠀⠀⠀⢠⡟⠀⠀⢠⣄⠙
⠀⠹⣿⡇⣸⣿⣄⣀⣠⣿⡀⠀⠀⠀⢀⣴⡿⠁⠀⣿⣿⣄⡀⠀⢀⣾⡏⠀⠀⢸⣷⣤⠈⣷⣦⡶⠟⠁⢀⣴⣿⣿⣿
⣀⣴⣿⠇⠈⠉⠉⠉⠉⠙⣧⠀⠀⢰⣿⣿⣧⣀⣠⠟⠉⣹⣿⠟⢋⣿⣷⣤⣴⣿⣁⣿⣷⠋⠀⡾⣿⠇⠘⠋⠀⠈⣿
⠛⠉⠁⢠⡾⠷⣄⠀⠀⠀⣿⠳⣤⣀⠈⠉⣻⡟⣡⣶⣾⠟⠛⠒⣿⡅⣸⡟⠁⠀⠀⠙⣧⡀⣠⣧⡼⣷⣴⣶⣄⢸⣿
⡀⠀⣠⣿⡇⢀⣽⣶⣤⣾⠿⠟⠳⠿⢿⣟⣉⣿⡿⠟⠁⠀⠀⠀⢸⣧⣿⡅⠀⠀⠀⠀⠘⢿⣿⣏⣀⣠⣌⡉⠛⣾⣿
⠿⠛⢿⣿⠋⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣠⣿⣿⡝⣿⡿⠛⠛⢿⡄⠀⠈⠉⠉⠛⣿⡉⢻⣻⡿
⠀⠀⠈⣿⣦⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣾⡿⠋⠉⠉⠙⢿⣷⠠⣤⣾⡇⠀⠀⠀⠀⠀⣼⣧⣾⣿
⠀⠀⠀⣿⣀⣻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠈⠻⣿⣄⠀⠀⠀⣠⣿⠃⠈⠙⢷⣀⠀⠀⢀⣴⣿⠁⠀⢻⣿
⣀⣤⣤⣀⠉⣻⣿⣦⣄⣀⣀⣀⣠⠴⣿⣿⡇⠀⠀⠀⠀⢠⠛⠉⢀⣴⣾⡿⣇⠀⠀⠀⣸⣿⣋⣻⠿⠿⣿⢧⣴⠋
⠻⣿⡟⠉⠙⣿⠉⣿⡏⠉⠉⣫⣥⣴⣾⣿⣿⣤⣀⠀⠀⣿⣦⣤⠞⠛⠛⢦⣀⠙⣶⣿⡟⠙⢿⡁⠀⣠⣿⡾⠋
⣾⡿⠃⠀⣼⣿⡇⠈⠑⢲⣾⡿⣿⠋⠀⠀⠀⠙⢻⣿⣦⡍⠋⠁⠀⠀⠀⠀⠹⣿⣮⠻⠿⠿⣿⣿⡄⠻⣿⠀⠀⣶⣶
⠋⠤⠄⠀⠘⠛⠓⠀⠀⠀⠛⠀⠘⠀⠀⠒⠒⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠐⠛⠛⠂⠀⠀⠀⠛⠁⠀⠙⠂⠀⠘⠂
⠀⠢⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠐⠘⡇⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⡀⣸⣿⡜⠰⣆⠀⠀⠀⠀⠄⠀⠀⠀⢠⣯⠙⣩⡃⢶⣴⡄⣿
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣤⢤⢰⡶⠔⢤⡝⠛⠉⠀⣆⠈⠀⠀⠀⢀⢠⡄⠀⠂⣿⠷⠿⢈⢥⢸⡿⠵⣏
⠀⠀⠀⠀⠀⠐⠛⢦⡀⡀⠿⠛⠀⢨⣧⠈⣦⣐⡇⠀⡘⠋⠀⠀⠀⠠⡾⢘⠁⠀⢠⣾⠓⠲⠆⣿⠿⠆⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠎⣣⡁⠐⢀⡀⠆⠉⠐⠀⡌⡗⠀⠃⠀⠀⡀⡄⠀⠀⠀⢀⣀⠀⠉⢨⡄⣸⣗⣶⠦⠀⣿
⡀⠀⠀⣀⠀⣠⠀⣹⠋⠁⢻⣿⣏⠁⠀⠀⠀⠁⠃⠀⠀⠀⠄⢁⣗⣰⣄⣠⣤⣼⡄⠘⠋⣠⢁⣙⣿⣿⠆⣿
⠁⠀⠝⢻⡇⠁⢠⣟⣶⡆⣸⣿⠉⠁⢸⠀⢳⡀⠀⠀⠀⢰⠀⢸⣿⣽⣿⣿⣏⠈⡗⣶⣰⠃⣘⠛⣿⣿⡿⣿
⢀⡀⠀⠀⢁⣴⠏⡜⠀⡿⢿⠛⠀⠢⣽⠀⠀⢷⢀⣄⠀⠐⡀⢉⣽⣿⣿⣹⣿⣷⡀⢠⣷⡔⠟⠀⢻⡉⠃⣿
⠃⢐⣃⠀⡸⢿⣀⡁⠀⣈⣭⣄⣠⣶⣿⠀⢰⢶⠚⢳⣿⢀⣁⣾⣿⣿⣿⢉⡿⡏⣧⣿⣟⠁⠘⠀⣸⣾⡆⣿
⠀⠈⠏⠲⠤⣾⠅⣼⠎⢩⡏⠙⢿⡿⡇⠀⠀⢸⠷⢣⣿⣄⠉⡿⠎⠟⠁⣿⠃⢠⣿⣽⣯⣿⣿⣿⣯⣭⣧⣿
⠀⠀⠀⠀⢰⣿⡈⣿⠀⣿⠁⠀⠀⣆⡇⠀⠀⢠⠞⡱⠘⠋⠀⠀⠀⠀⠀⠁⠀⢡⠟⢻⡿⣿⣿⣿⣷⣿⡇⣿
⠀⠀⠈⠉⠉⠁⠉⠈⠉⠉⠁⠀⠀⠉⠉⠂⠒⠊⠒⠙⠒⠒⠒⠓⠐⠒⠂⠐⠐⠋⠐⠃⠖⠚⠟⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣹⣿⡁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⣛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠾⠋⠀⢠⣄⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣇⠀⠀⠀⠀⢠⣤⣬
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠄⠀⣾⣿⣶⣧⣤⠀⠀⢰⣆⠀⠀⠀⠀⢌⣧⣄⣤⠤⢶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣶⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠾⠿⠿⠿⠿⠿⠿⠶⢶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⢁⠀⠠⠠⠐⠐⠐⠀⠀⠀⠀⠄⠀⡉⠙⠻⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⡠⠔⠈⠀⣤⡰⠒⣄⡎⢹⠄⣤⠀⠀⠀⠀⠀⠁⠢⢀⠈⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢀⠀⠁⠀⠀⠀⢠⠇⣇⣰⠛⠦⠞⠀⠉⠁⠀⠀⠀⢀⣾⡇⠀⠈⠀⡀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠄⠀⠀⠀⠀⡀⠀⠈⠀⢠⡄⠀⠀⠀⣤⣠⠀⣠⠶⡶⢸⠟⠀⠀⠀⠀⠀⠠⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⠈⠀⠀⣼⡇⢸⠇⡤⣴⠌⡟⢡⡇⣸⠃⣯⡟⢰⡏⣼⣃⠿⠤⠃⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣿⣿
⠀⠀⠀⠀⠀⢀⣿⠃⢀⠂⠀⠀⢰⡏⣷⡟⣾⢁⡟⣸⣇⠼⠵⠻⠞⠀⠑⢉⣉⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠸⠀⠙⠃⠙⠋⣉⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⣹⡏⠀⣠⡄⢘⣿⡇
⠀⠀⠀⠀⠠⠿⠀⠐⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣟⣉⠉⠈⢣⡄⠀⣾⣿⡄⠘⣿⡇⠀⣿⣿⠋⢻⣷⡀
⢠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠟⠉⣉⠉⢻⣿⣿⠀⢠⠀⢻⣿⣿⡀⢰⡄⠙⠀⢻⣿⠇⠀⠛⢻⣄⣈⣁⣠⣾⣿⣿⡄
⠀⠻⣿⣿⣿⡿⠛⠛⠻⣿⣉⡁⢠⣤⠀⢸⣿⠀⢸⡟⠒⠚⢻⡟⠀⣠⡤⠀⠻⠟⠃⢈⣙⣦⣠⣼⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠹⣿⡟⠀⣼⣿⡄⠈⣿⡇⠀⣠⡀⠉⢿⡄⠈⠛⠃⠀⣿⠁⢠⣤⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⣭
⠀⠀⠀⢹⣿⡀⠸⠿⠇⢀⣿⠋⣀⣈⣵⣤⣤⣿⣷⣶⣿⣿⣿⡆⣶⣬⡛⢿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⠁⢰⡿
⠀⠀⠀⣼⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠁⣾⣿⣿⣦⡀⠀⠀⢀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠂⢀⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⣿⢟⣩⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⠂⢀⣾⠏
⠀⠀⠀⠉⠉⠉⠀⠐⣶⡄⠀⠄⠀⠀⠀⠀⠀⠀⠤⣶⣶⣿⣿⣿⣿⣿⣶⣌⡻⣿⡿⣿⣿⣿⠀⠀⠀⠀⠠⠂⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠐⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣻⡿⠿⠿⠿⣿⡔⣿⣿⣿⠇⠀⠀⠀⠂⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠁⠢⠄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣅⡛⠛⠁⠀⠐⠈⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⡈⠐⠠⠠⢀⢀⢉⠉⠉⠉⠉⠀⠄⠙⠒⠁⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣶⠾⠟⠋⠁
⣶⣶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡠⠤⣄
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠈⡙⣆⠀⠀⠀⠀⠀⠄⠀⠀⢰⡋⢹⡆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠚⠋⠉⠁⠀⠀⢀⣈⡹⡆⠀⠀⠠⣃⢀⡏
⠀⠀⢰⢃⠀⠃⠀⠀⠠⠄⠁⢸⡄⠀⣀⣀⠀⠀⢀⣤⡀⠉⠉⠀⠀⣠⡴⢒⡺⢭⢗⡶⣦⡀⠀⠀⢯⢩⡍⢀⣐⠉⡉⢉⡀⢢⡇⠀⠀⠀⠸⡉⠁
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠒⠀⡼⠀⠀⣿⣹⡀⠀⠱⣤⠞⠀⠀⠀⣿⣽⣯⣦⣇⣷⣾⣝⣳⣿⡆⠀⠈⢦⡱⣀⡕⡢⡙⢝⣠⠟⠀⠀⠀⠀⠀⢳⡀⠀⠛⡇
⠀⠀⠀⠙⢦⣀⡀⢀⣀⡤⠞⠁⠀⠀⣸⠛⣇⣀⣀⠀⠀⠀⠀⠀⡇⠀⠉⠋⠹⠏⠉⠩⠅⠱⡇⠀⠀⠀⠉⠛⠲⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⢧⠀⠠
⠀⠀⠀⠀⠀⠀⠉⠉⢁⣤⡄⠀⡤⠊⢹⡿⣇⠀⠀⠙⢦⠀⠀⠀⡏⠀⠀⠀⠂⢀⠉⠠⡜⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠑⠶⠋⢱⠀⠀⢸⡀
⠀⠀⢀⣀⡀⠀⠀⠀⢊⡷⠂⡞⠀⠀⠈⠃⠋⠀⠀⠀⠀⠇⠀⠀⢇⠀⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠦⡄⠀⣠⢶⠀⠀⠧⣀⣀⣀⠞⠀⠀⣸
⠀⠀⠈⠉⢿⡀⣠⡀⠈⠀⠀⣇⡀⠂⠀⠀⠐⠀⣀⡠⠴⡇⠀⠀⢸⢀⠛⠀⡀⠐⠂⠀⠀⢸⠀⠀⡀⠘⠲⠾⣀⠗⠛⠀⠀⠀⠀⠈⠁⠀⣀⡴⠃⢀⠤⡀
⠀⠀⠀⣰⠊⠉⠑⠷⢄⠀⠀⡇⠈⠉⠉⢉⠉⠉⢁⡀⢸⠁⠀⠀⢸⠀⠀⠈⠉⠀⠀⠀⠀⡌⠀⡴⣷⠀⠀⠀⠛⠀⠀⠀⠀⣠⠤⠤⠴⠛⢱⡄⠀⠘⠶⠃
⠀⠀⣞⠁⠩⠭⠤⠤⠸⡆⠀⠇⠰⠄⠀⠈⠀⠀⡀⠀⣸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢛⣏⠓⡴⠲⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢹⡀
⠀⠀⢼⠷⠟⠙⠛⠒⢲⡇⠀⢸⠀⠀⠀⠁⢠⡄⠀⠀⡏⠀⠀⠀⠈⠓⠦⠤⠤⠤⠤⠴⠚⠁⠀⣏⢈⡗⠙⣚⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣈⡇⠀⢀
⠀⠀⠸⡦⡀⠒⣤⠀⣻⠀⠀⢸⠀⠐⠀⢀⡀⠀⠂⠀⡇⠀⢀⡀⠀⠀⡠⠖⠦⡄⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⠇⠀⠀⠀⠀⠸⠤⠴⠶⠒⠋⠀⠀⠀⡏⢀⡄
⠀⠀⠀⢳⠈⠑⢤⡉⡯⠀⠀⠀⡆⣠⡄⢀⢀⣀⣀⣠⠇⠰⣁⠝⠀⠰⡁⢶⠇⢘⡦⠀⢀⣀⠤⠤⠤⠤⡾⢽⣀⡀⠀⠀⠀⡀⢠⡖⣦⠀⣟⡆⠀⢠⣗⡉
⠀⠀⠀⠈⢆⡁⢶⣍⡇⠀⠀⠀⣿⢣⡱⣶⣽⣾⣟⣿⠀⠀⠀⠀⠀⠀⠙⠒⠒⠃⠀⠀⢿⠤⣀⣀⣀⣀⣙⣃⣠⣽⠂⠀⢎⢉⡏⠙⠁⠀⣿⡇⠀⠉⠁
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⠦⢥⣬⣩⡥⠤⠋⠀⠀⠀⣠⣄⠀⢰⠛⡄⢀⣄⠀⢸⡀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⣀⣉⣀⣀⣀⣠⣿⣧⡤⢠⡄
⠀⠀⠀⣠⠤⡤⢾⣉⠿⣹⡦⢤⣀⠀⠀⠀⠀⠀⣠⡀⢀⡀⠀⡷⣻⠀⠘⢶⣷⣇⡼⠀⠘⡆⠀⢀⠄⠀⢰⡀⠀⡏⠀⠸⡧⠄⠒⠒⠒⠒⠒⠒⠒⢿⠁
⠀⠠⣿⢘⡶⢳⣏⣉⠶⢤⡜⢚⣸⣇⡀⠀⠀⠀⠙⠀⠘⠏⠀⣟⡅⠀⠀⠀⣟⠉⠀⠀⠀⡇⠂⢀⠀⠄⠀⠁⠀⡇⠀⠀⢣⢀⢀⠀⠀⠀⠂⠀⠀⡟
⠀⠀⢿⢟⢿⠯⣤⢭⣵⡶⠿⠿⠛⣇⠈⢳⠀⢮⠂⢀⣤⣤⠤⠯⠷⠤⡄⠀⠈⠀⠀⠀⠀⢱⠀⢠⠀⠀⠀⠀⢰⠃⠀⠀⠸⡄⠁⠀⡀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠈⠀⠀⢀⠀⠀⠀⠀⣘⠇⡧⢘⡇⠀⠀⢸⠒⠒⠚⠉⢉⢙⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢷⠀⠈⠀⠀⠀⠀⢠⠇
⠀⠀⠈⣆⠀⢃⡀⠀⠤⠀⡀⠀⢻⡰⠃⢸⠀⠀⡴⠋⠙⠒⠚⠋⠋⠉⠈⢻⠙⠓⢢⡀⠀⠀⢉⠛⠒⠒⠛⠋⠁⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢇⠀⠀⢀⠀⠀⠀⠀⠀⣿⢀⡠⠃⠀⢸⠁⠀⢴⠀⠀⠀⠠⠆⠀⠀⡟⢆⠰⡇⢀⡞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⣾
⠀⠀⠀⢸⠀⠐⠀⠀⠀⠀⠂⠀⡏⠁⠀⠀⠀⢸⠀⠈⠀⠀⠀⡶⠀⠈⠀⠀⣧⢸⠀⣷⢸⣀⣾⡤⣤⠀⢀⠴⠒⠈⠐⠢⣄⠀⢻⡀⠁⠀⠂⢃⡇⠀⠀⡀
⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⠀⢀⠤⡀⠀⠀⣀⠀⠀⠀⣿⢸⠀⡏⠀⠻⠓⠚⠁⡰⠁⠀⠀⠀⠀⠈⠊⢧⠀⠈⠉⠉⠉⠁⠀⣠⣀⡟
⠀⠀⠀⠀⠉⠛⠛⠶⠶⠴⠒⠋⠀⠀⠀⠀⠀⢸⣀⡄⠉⠀⡀⠀⠉⢀⡄⠀⣿⠃⣠⠃⠀⠀⠀⠀⠀⡇⢀⠚⠀⠀⠈⢀⠀⢸⠀⣏⠉⠉⣿⡄⠀⢈⡏
⠀⠀⠀⠀⠀⡄⠀⠀⢀⡖⢦⡀⠀⠀⡄⠀⠀⠸⠀⠀⡶⠈⠁⡀⠀⠀⠀⠄⣿⠔⠁⠀⡤⠀⠀⠀⠀⢧⠁⠀⠐⠒⠃⠀⢀⡞⢰⡇⣀⡀⣏⣧⠀⠁
⠀⠀⠀⠀⠀⣇⠀⠀⠈⢧⢸⠆⢀⡜⠀⠀⠀⠀⣇⢀⢀⡀⠀⣀⠀⡀⣀⠀⡏⠀⠀⠀⢆⠀⣞⡆⠀⠈⠳⢤⣀⣀⣠⠴⠋⠀⠘⡇⠉⠀⢸⣸
⠀⠀⠀⠀⠀⠈⠢⣄⣀⡤⠋⠉⠉⠀⠀⠀⠀⠀⠈⠳⠤⣬⣌⣀⣉⣤⠶⠚⠀⠀⠀⠀⠀⠉⠻⢤⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣴⣾⣿⣿⣿⡿⠟⠻⠛⠛⠛⠛⢿⡿⡿⣿⣿⣿⣿⣿⣶⣴⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢾⣛⣋⠉⠉⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠨⠙⠙⢻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢹⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡄⣠⣐⣚⣷⣷⡦⢀⣀⡀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⣤⣴⣦⣦⣽⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣶⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠛⠉⠉⢹⣏⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄⠀⠀⣀⣴⣿⣿⣀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣷⣾⣴⣦⣤⣤⣤⣤⣤⣶⣾⣿⡛⠭⠥⢤⠤⣴⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣽⣽⡏⣿⡿⢿⣿⣽⣿⣿⡷⠁⠀⠀⠀⠄⠘⠟⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣧⠌⣷⢻⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣦⣧⠀⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡷⣧⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣯⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡷⢜⠂⠀⠀⠀⣀⣴⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⣿⣀⣀⣤⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣻⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹

⠀⢀⣠⣤⡄
⠀⠹⠿⠿⠛⠀⠀⠀⡀⠀⠀⣤⡄⣀⢠⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠋⠆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣴⢿⣿⣿⠻⣇⠀⠀⠀⠀⢂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠘⢀⣴⣤⣿⠯⣼⣿⡂⠀⠀⠀⠘⠀⠀⠀⠀⠈⢣⡴⢤⡀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠟⠉⠸⠃⠤⣊⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠴⠆⠈⠀⠀⠆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⢒⣾⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠐⠂⡸⡇⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠖⠂⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⠈⠛⠿⠗⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⠀⡲⢄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢋
⠀⠀⠀⠐⠀⠀⠀⠀⠁⠛⢠⣳⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⠉⠛⠰⠆
⠀⠀⠀⠈⢑⡀⠀⠀⠀⠷⡄⢄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠞⠋⠀⠀⣀⠀⠀⠀⠒⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠐⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡈⠛⠠⣄⠀⠀⠀⠢⡍⠀⠙⠀⠀⠀⠒⠁⠀⠀⠀⢀⡀⠀⠀⠀⠘⣤
⠀⠀⠀⠘⠛⠆⠐⠂⠀⠀⠀⠀⠀⠀⡀⠉⠠⠀⠀⠀⠀⠛⠃⠠⠄⠀⠀⠀⠐⠈⠁⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⠟⢠⡄
⠀⠀⠉⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⠷⠂⠀⠀⠀⠀⠘⠷⠘⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠦⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠁⠀⠀⢀⢤⢀⣜⠋⠀⣄⠼⠷⠆⣀⠀⠀⠄⠀⠀⡠⠀⠀⠛⢪⣤
⠀⠀⠀⠀⠀⠀⡀⠤⢸⠇⣀⠀⠀⠀⠀⠀⢀⣤⡶⡶⠖⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠀⠘⣭⠾⠆⠀⠀⠠⢈⡛⡇⠀⠀⠘⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣄⣀⠀⢘⢀⣿⣄⠀⠀⠀⣤⢟⠰⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡶⢤⣁⣀⣛⣒⡀⣤⣇⠈⠂
⠀⠀⠀⣬⡋⠁⠀⠀⣾⠀⠬⢹⣿⣆⠀⢻⠏⠀⠀⠀⠀⠀⠁⣸⢱⡆⠀⠀⠠⣄⠄⠀⠀⢸⠀⠀⠀⠀⡀⣤⠲⣿⡟⠀⠀⠀⠀⢀⣤⡄⠀⠀⠰⠶
⠀⠀⠀⠸⣋⠂⡀⠈⢻⣦⣼⡿⡿⠀⠀⠀⠀⠀⣀⡴⠖⠐⠀⡟⠺⠿⣦⣠⠀⠀⠀⠀⠀⢮⡀⠀⠀⠀⠉⠉⠐⣿⡄⠀⠀⡴⠀⢀⣀⡀
⠀⠀⠀⠀⡛⠀⠐⠰⠾⠿⠿⣿⠫⠀⠀⢀⠀⠐⢿⡄⠀⠀⢠⣇⣀⣡⣽⣿⠇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⣟⢰⠀⠈⠉⠉⠉⠁⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠈⠋⠀⠀⠸⣦⠀⠀⣀⣽⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⠀⠀⢀⡀⠀⣀⠀⣾⢸⠀⠀⢴⡠⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⡤⢹⠀⠀⠈⠉⠉⠉⣿⡈⢁⡄⠀⠀⠀⠸⠾⠇⢨⡦⠀⣩⣴⡇⡇⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡤⢸⡇⢀⣄⠀⠀⠱⡜⢾⠃⠀⠀⠀⠀⠀⣻⡷⠀⠁⠀⠀⠀⠀⠶⢟⣀⡤⣴⡾⣾⣧⠃⠀⣠⠤⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠸⣠⣀⣤⠤⡿⢀⣾⠀⠀⢨⠀⠀⠰⣈⣿⡀⠀⠀⠀⢀⡀⣽⡇⠀⠀⣀⠀⠀⠀⠀⠻⣍⡐⠇⣠⠿⠌⠀⠀⡟⠢⢤⣄⣠⣼⣀⠤⣰
⠀⠀⠀⠀⠀⢙⢿⡤⢼⢾⣿⡿⠀⠀⢸⠀⠀⠀⣬⣩⡄⠀⠀⠀⣿⢛⣼⠇⠀⠀⠟⠀⠀⢀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠢⣄⠀⢀⡀⣃⡀⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠉⠒⠈⠀⠈⠀⠀⠀⡏⠀⠀⠀⠀⢹⣷⡞⠓⣙⣯⣼⣄⣀⠀⢀⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠹⡷⡇
⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠺⢛⣋⠾⢙⠛⠋⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⢘⣗⠇
⠀⠀⠀⠀⠀⠀⢠⡖⠒⠋⠉⠛⠃⢸⠗⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢠⡄⠀⣀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⠿⣷⠒⠀⢐⠃⢛⣿⣿⠀⠀⠀⠀⠸⠶⠀⠀⠀⣠⣤⢄⣠⣤⡀⣠⣤⣄⡀⠀⠰⠷⢠⡀⠀⠀⠀⠀⡟⠟⠠⠵⠀⠨⣴⢺⣹
⠀⠀⠀⠀⠀⠀⠊⠙⠛⠲⠦⠤⠒⠶⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣓⣿⡾⣷⢿⣿⣷⣾⣿⡗⠀⠀⠀⠛⠃⠀⠀⠀⠀⢸⢻⣧⣤⣴⠾⢷⣿⡏
⠀⠀⠀⠀⠀⠀⠂⠀⣀⠠⣄⣤⡶⠦⠀⠼⣿⢁⠒⠀⠀⠣⠀⠀⠘⣮⣵⠧⠉⠿⠯⠉⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡯⢼⣿⣶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⢸⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⡠⠞⠁⠄⠀⢀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢁⣤⡄⠀⠀⠸⠇⣤⣀⡀⡀⢀⠀⠀⢲⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠁⠀⠀⢀⠀⣶⣀⣉⣻⣇⣾⣾⣟⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⡇⠘⠠⢔⣤⠀⠀⠀⠸⠐⠀⠀⠀⠀⠀⠀⢸⡤⡅⠀⠀⣠⣤⡶⢞⣽⣻⣿⣼⣟⣿⣾⣷⣍⠩⠕⠶⣦⡄
⠀⠀⠀⠀⠀⢀⣦⡄⠀⡀⢠⠀⠀⢀⣴⣼⣧⠐⠚⠛⠋⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣶⣿⡥⠀⠀⠀⡟⣷⣷⣻⣶⣻⣿⣽⣿⣯⣿⡷⣿⣿⣶⠎
⠀⠀⠀⠀⠀⠸⣿⣯⣧⡸⣟⣦⠀⣞⣿⠹⡿⠀⠀⠀⠀⢰⡤⠀⠀⢀⣘⠞⠀⣀⢀⠠⣿⠰⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⢉⢝⠁
⠀⠀⠀⠀⠀⠀⠀⡻⠄⠛⠋⠹⡾⠧⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⡿⠶⠋⠀⠀⠀⠀⠀⠈⠲⢦⣀⠀⠀⢀⣀⣠⣴⡾⠟⠁⠀⢶⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢦⣄⣀⣠⣄⠚⠁⡀⣊⠀⠀⡆⣀⠠⠀⠀⢠⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⣄⣐⡀⢀⠰⣤⢀⣦⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⡹⣷⣞⠛⢋⣡⣼⣯⠴⣠⣀⣴⣷⣾⠥⣤⡴⣶⣶⣋⠀⠀⠀⠀⠀⠸⡀⠉⢙⠿⢿⣼⡥⠟⡟⠀⠀⢀⡀⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢌⠣⠈⠻⣟⠺⡿⢿⣿⡿⠃⠙⢿⣟⠛⠲⠦⠑⢄⠈⠀⠉⠀⠀⠀⠀⠀⠈⠙⠋⠀⠩⣭⣥⣤⡘⠛⢉⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠈⠐⠀⠀⠈⠻⡎⠀⠀⠹⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠶⣤⣇⠈⠙⢢⠀⠠
⠀⠀⠀⠀⠀⠀⠛⠄⠠⠀⠐⠀⠠⠄⡄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⠀⠀⠘⣗⠒⠒⠴⠚⠉⡩⠖⡎⢹⠻⣄⣀⢀⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠘⣧⣀⠁⢀⡜⠁⣸⠇⢠⣿⠅⠀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠈⢻⢀⣿⣆⣴⣿⣝⣿⣷⣶⡽⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⡾⠋⢠⠗⡄⠀⠀⠀⠀⠂⠂⠒⠆⠁⠒⠀⠀⣀⡉⠀⠀⠀⠀⠀⠀⢻⣿⠟⠉⠀⠀⠈⠱⠆⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠈⡉⠹⣧⣀⣈⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⢧⣀⡄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠇⢀⠀⠁⢄
⠀⠀⠀⠀⠀⠉⣀⢀⠴⠒⠬⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠂⠀⠀⣀⣙⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠈⠑⠉⠁⠀⠠⠀⠀⣴⣇⡀⠀⠀⠀⣠⡆⠀⡷⠀⠀⣸⣿⢛⠈⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⢐⠀⠀⠹⣦⣀⠉⠄
⠀⠀⠀⠀⠀⠚⠃⠈⣬⡀⠀⠀⠁⠀⣹⠇⡀⠀⠀⠀⢻⡑⢾⣥⠄⠀⣉⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠓⠾⡆
⠀⠀⠀⠀⠐⠻⠛⡹⠿⢿⡀⠀⠏⠛⠁⠀⠀⠀⠀⠀⠙⣍⡀⠀⠀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠠⠂⡴⠉⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠆⢲⡶⠶⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠋⣿⡀⠀⠀⠀⡀⠀⠀⡔⡄⢠⡀⣠⠤⠂⠔⠂⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠈⠀⠠⠤⠀⠀⢠⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠙⠃⠀⠀⠈⢇⠀⣴⠏⡇⢸⡾⠋⠐⠀⠄⠀⠀⠀⠀⠨⠆⢠⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⣤⠀⠀⠀⠁⠀⠀⠀⢰⠄⠀⡆⣻⠏⢸⡇⣸⣅⠈⢀⠀⠀⠀⠀⠀⠀⠂⠀⠲⠓⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠔⠋⠙⠀⡁⠀⠀⠀⠀⠀⠀⣬⡄⠀⠀⡿⢀⣾⡧⢿⢁⣀⣤⣀⠶⠋⠁⠀⠢⠈⠀⢢⡀
⠀⠀⠀⢰⡆⢄⣀⠀⠀⠀⠀⠀⠀⢀⡆⡄⢠⠄⠀⠐⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⡇⢺⣿⡷⠛⠁⢁⡠⠜⠀⠀⠀⠐⢀⡄⡀⢀⢠⣴⡲
⠀⠀⠀⢐⠀⠢⠀⠉⠐⣄⠀⠀⣄⣸⡧⢠⡞⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⣿⡄⠁⢹⣿⢋⣠⠴⠚⠋⠀⠀⠀⠀⠐⡶⠟⠛⡠⠛⣈⠉⠶⠂
⠀⠀⠀⠀⢦⠀⠁⡆⣀⢸⡆⢸⣢⡈⣿⣿⠃⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠘⣇⣠⣼⣿⠛⢁⠀⠀⣂⡐⠞⠀⠀⠀⣀⡞⠀⠁⠞⢁⠀⡀
⠀⠀⠀⠀⠈⠻⢶⣿⣿⣿⣿⡀⢻⡷⣿⣿⣤⣦⣤⣤⣄⡀⠀⠀⠈⢧⡁⠄⠈⢿⣏⣷⣿⡷⢞⡿⠀⠀⠀⠀⠀⠐⠈⡉⠈⡸⠀⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙⣻⣿⣿⣿⣿⣿⡟⠙⠛⠯⡉⠖⠀⠀⠳⣿⡄⠀⡸⠛⠛⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠏⣁⢌⣉
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣉⢘⣉⢸⣻⡿⢋⣝⠶⠄⠊⠀⠀⠀⠀⠀⠘⢿⣦⡃⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⠐⠁⠒⠂
⠀⠀⠀⢀⣾⡿⠛⠛⠉⠉⢙⠛⠋⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⠀⢠⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⢀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⡟⢹⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠎⠀⠀⠀⡇⢸⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⠒⠒⠒⠈⠀⠁⠒⠒⠂⠛⡆⠀⠀⢀⠞⠒⠀⠀⠀⠃⠘⠀⠀⠐⠚⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡖⠒⠒⠀⠀⠀⠀⠐⠒⠒⡊⠁⠀⠀⠈⠰⠒⠒⠂⠀⠀⠀⠀⠒⠒⢲⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡁⠀⠉⠀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⢰⡦⣀⣴⣦⠀⠺⠂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠺⠣⡾⢱⡔⠿⠇⡄⠀⠀⠀⠀⠀⠀⢰⠐⠟⢴⠮⡧⠺⠿⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠂⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠐⠀⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡖⠖⣦⠀⣤⠐⠒⢲⡄⢠⡖⠒⡒⣦⠀⡔⡒⠒⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠛⠊⠀⠉⠛⠚⠚⠁⠈⠑⠋⠓⠉⠀⠙⠃⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⡿⠀⠐⢾⣿⣿⣦⡀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡀⠰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⢲⣼⣿⠿⠀⠀⠀⢀⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢠⣇⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣸⡼⠛⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠀⢸⣿⣦⡙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⣸⣷⠀⣼
⣿⡀⠀⣼⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⠀⠀⣴⣿⠿⣿⣿⣷⣦⡀⠀⠀⠀⠈⠻⠿⠛⣿⣿⠟⠟⢛⣿⣿⣁⣼
⣿⡆⢐⣿⡆⢸⡆⠀⠀⣘⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣴⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢀⣿⣿⡂⠀⠰⣿⣿⠷⣿
⣿⣗⣸⣿⣇⣼⡧⠀⠀⢽⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⣨⣿⣿⣧⠀⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠐⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠐⠂⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠈⡇⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⢠⠃⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⡇⢀⡟⠀⢠⠞⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣇⡞⠀⡴⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⢤⡄⣀⡈⡿⢀⡞⠁⠀⡀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠷⠀⠒⠒⠒⠂⠲⠦⣄⣀⡉⣷⠏⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⠀⠀⠀⠉⠙⣿⠀⠀⠀⠀⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⢸⠃⠀⠀⠀⢰⡁⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣸⡄⠀⠀⠀⠈⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣧⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⣠⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⣿⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠚⠀⣩⡤⠒⡩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢠⡆⠀⠇⠀⠀⠀⠀⠀⠀⣀⠔⠉⢀⣠⠔⠋⠁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⣇⢸⠀⠀⠀⠀⠀⠠⠞⠁⢀⡴⠋⠁⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⡤⡀⢀⣀⠀⠀⠀⠀⠀⠈⢷⡄⢹⣼⠀⠀⠀⠀⡰⠀⢀⡴⠋⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠶⢤⡀⠀⠀⠀⠛⢺⡿⠀⠀⠀⡰⠀⣴⠋⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠢⢄⡀⠂⠒⠂⠀⣤⠄⢀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠰⣳⡀⠀⠀⠃⣸⠁⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠐⠒⠴⢤⡀⠀⠐⠈⠳⣄⠀⢡⢣⠀⠀⣠⠏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠈⠓⠢⢄⣀⠘⢦⡀⢏⣦⠀⣿⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⢤⣤⣀⣤⣤⣈⣉⣘⣦⡙⢾⣜⠃⢉⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⡆⠻⡄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢱⡄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⡆⡄⠰⠠⠐⡆⢠⠀⠀⠀⢮⢠⠠⠴⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠁⠉⠀⠁⠀⠁⠈⠀⠀⠀⠈⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠻⠙⠿⡟⠛⡿⠻⣟⠿⢛⣻⠿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣶⣿⣾⣷⣶⣿⣶⣾⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⡡⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⡄⠀⢀⣴⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡧⡄⠀⠞⠁⠁⣀⢀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠺⡁⠀⢁⡞⠖⡇
⠀⠀⠀⠀⠀⠀⠀⡀⣇⠱⠀⠀⠤⠿⠚⢉⠉⠉⠁⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣈⣙⣆⠀⠙⣼⡷⠊⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⣁⡈⠀⡄⠀⠀⠀⢠⣞⣆⣄⣤⣀⡀⠀⠀⠀⠀⡀⢚⣉⣩⣉⡛⢀⠀⠀⢻⢃⣰⡟⠆
⠀⠀⠐⢖⠠⢄⡀⠀⠀⢁⣴⠴⠖⣉⡥⠂⠀⠀⠀⠀⠀⠘⠁⠤⠀⠠⠁⠂⠀⠀⠀⠀⠀⠒⠶⠈⢱⣾⠦⢀⣗⣻⣽⠿⠃⠀⣀⡀
⠀⠀⠀⠀⠙⠾⠅⠀⠀⠉⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣚⠛⠁⠉⠋⡱⣼⡈⡄⠀⠤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡚⢡⠉⢉⡉⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠥⡄⠘⣒⠷⢁⣄⠀⠀⠀⠀⠀⠀⡰⢒⣯⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢖⠩⠃⠀⣩⡼⠠⢀⠎⡰⠀⠀⠀⠀⠀⠀⢀⡾⠃⣔⠾⠁⠀⠀⠀⠀⢰⢤⠀⠀⢀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠸⣇⠡⠀⡤⣩⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⠹⠀⠀⠓⡿⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⣲⣽⣦⣤⠀⢀⠐⢿⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠻⡁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⢀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⢆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠒⠨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠀⠔⠀⠀⠀⠀⠀⠉⠋⠉⠒⠋⠁⠀⠠


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⡶⠆⠘⢛⠿⢿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⠀⠈⢻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⣀⣸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠽⣿⠿⠛⠃⢹⣟⠿⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠠⠄⠒⠒⠀⢘⠛⠛⠛⢿⣿⡯⠛⠹⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣀⣀⣀⣀⡀⢀⣀⣀⣿⣦⣀⣠⣤⣀⣤⡀⢀⣀⣀⣀⢀⣿⣇⣠⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠛⡛⠋⠉⠉⠉⠉⠉⠁⠈⠉⠉⢿⣿⡟⠉⠉⠉⠉⠁⠈⠉⣩⣯⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⣿⠶⠤⠤⠤⠀⠀⠀⠀⠀⢀⣸⣋⣤⣤⣴⣦⣶⡄⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣯⠥⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣯⣭⣭⣭⣿⡿⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣮⣭⠀⠀⠀⠀⠀⠀⠐⣿⠟⠀⣛⠀⠀⠀⠀⢀⢈⣛⣡⣿⣿⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠿⠀⣬⡭⠅⠀⢠⡀⠙⠉⠉⠉⠉⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣴⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣁⡀
⠀⠀⠀⠈⣿⣿⡗⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠈⠀⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢻⠟⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠠⠃⡀⠀⡎⡀⣀⠀⠀⠀⢰⠁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡰⠁⠁⠈⠉⠈⠈⠀⠀⠀⠇⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡈⢻⣿⡏
⠀⠀⠀⠀⢸⣧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣈⠋⣼⣿⡃
⠀⠀⠀⢀⣼⣿⣧⣿⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣶⡄⣾⣽⣿⡇
⠀⠀⠀⠈⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠠⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡒⠀⠴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⢴⣦⣤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠆⣠⣚⣟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢠⣤⣤⣿⣿⣷
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣤⢰⡾⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⢀⡄⢞⣤⣿⣿⣤⠀⠄⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⣄⢰⣬⣾⣿⣿⣿⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣾⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣬⣔⣾⣿⣇
⠀⠀⠀⠈⡁⣠⠀⠉⠛⠿⠿⠿⠿⣧⠐⠂⠀⠀⠀⠀⠀⠀⢉⣿⣿⠛⠛⣻⣯⣧⡼⠄⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⣿⣿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡿⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣃⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⠿⠃⢀⣄⡸⠆⠀⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠝⠟⣣⠀⢐⣿⣾⣿⣵⣐⣿⣷⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣶⡆⠀⢰⠟⠿⠏⢲⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢠⠛⣿⠀⠋⠈⣴⣤⣾⣿⣦⣾⣿⣵⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢀⠸⠁⠀⡀⣾⣿⣿⠟⢙⡻⣿⣿⠝⠿⢛⠛⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⡴⠉⠀⠿⢋⢛⣿⣿⠋⣰⣿⣦⣝⣿⣶⣾⣿⡖⠀⠰⠖⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠚⠿⣿⠿⢛⠀⠠⢿⣬⣻⣿⣡⣿⣿⣿⡿⣿⣿⣿⢋⡠⠤⠀⠀⠁⠀⠘⠛⠀⢀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠈⡻⣶⣄⡠⣄⡄⠀⣠⠔⠃⢁⡀⣹⣿⣶⣿⣇⠀⢉⡋⠙⠛⠛⠛⠚⠳⠍⠀⠀⠄⠀⠀⠀⠀⠀⠐⠊
⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⢀⡔⣿⣿⣼⣿⡼⠿⠝⠉⠀⠀⢹⣿⣿⣿⣿⣿⢛⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⡀⠀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⢀⣀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⣿⣿⣷⣴⣶⣷⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠊⠀⠉⠈⠀⠈⠻⣿⣿⣿⣿⣟⣻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⡔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⢶⣒⠻⣯⡙⠻⣯⡉⠙⢯⡙⢿⠲⡖⢦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣚⠛⠻⠶⣬⣙⠳⠮⣝⡲⢍⡓⠤⣙⠲⣄⠑⢌⠣⡙⠸⠸⠸⢩⢟⡷⢦⣄⡀
⠀⠀⠀⠀⠀⣠⡶⠛⠲⢟⠉⠉⢓⡛⠒⠬⢝⡓⠦⢍⣓⠮⣕⡊⠑⠢⠑⠀⠀⣀⠤⠤⢄⡁⠊⠐⠩⠔⢛⣲⣄
⠀⠀⠀⡴⣛⣟⠋⢀⡤⠮⡃⠀⠺⠀⠐⠃⠀⢹⣷⢶⣮⣍⡒⠨⠁⠀⢀⣠⣴⠁⠀⠀⠀⠙⡄⠀⡴⢯⡭⠵⠒⣛⣦
⠀⢠⣾⣯⣥⣶⣿⣿⣤⡀⡬⠒⣤⡤⠶⣤⠔⠋⠀⢻⣿⠃⠙⠢⢤⣖⡛⠀⣿⣠⠴⠦⣄⣠⣿⡟⠁⣼⡿⢶⣛⣯⠽⠳⡄
⢠⣿⣿⣿⣿⣇⣨⡍⣙⠳⢾⡉⣀⣤⡚⠁⠀⠀⠀⣣⣿⡇⠀⡾⠛⠦⡉⠛⠤⣤⣶⢶⡿⢿⠍⠁⠀⢹⣇⠀⠙⣾⣵⣴⣿
⣾⣿⣿⣿⣿⣞⢿⣿⢿⡿⣶⣌⠛⠿⣿⣷⣤⠀⣼⠟⠁⣠⣾⣵⣤⣰⢃⣀⣠⣬⣽⣯⣄⠁⠀⣀⣤⣿⣷⣴⣿⣿⣻⣿⣿
⣿⣿⣹⣿⢻⣻⣞⣿⣿⣿⣿⣿⣿⠦⢤⣙⠻⢾⣷⣶⣾⣿⣯⣭⡿⣿⣿⣿⣿⣿⣿⠿⠟⣛⣲⣿⣿⢻⣯⢿⣿⣿⣿⣷⣿
⢿⣟⣿⣿⡻⣭⡟⣿⢾⣿⢿⣿⣿⣷⣆⡉⠳⣦⣮⣉⡟⢿⡿⢿⠟⠋⣩⣭⣴⣒⡺⣿⢟⣿⣿⣛⣯⣿⣿⣽⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣼⣿⣿⣿⣿⣦⡌⠙⠫⣽⣿⡀⠙⠶⢦⣤⣉⡭⣩⣭⣽⣯⣷⣿⣛⣯⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⣟⡿⣿⣿⣿⣿⣿⣿⣷⣿⣽⢿⣿⣾⣿⣿⣵⣮⣿⣯⣳⣦⠀⠀⠉⠻⣿⣿⣿⣾⣿⣿⣿⡭⣽⣛⡳⢿⣿⣿⡿⠃
⠀⠀⠀⠻⣿⣷⣿⣻⣿⣿⣿⣿⣿⣻⢿⣶⠭⣒⢭⣻⣿⠿⠛⠉⠀⠀⠀⠀⠐⢸⣿⢿⣿⣿⣷⠾⣿⣛⣻⣯⣭⣭⠟
⠀⠀⠀⠀⠀⠙⠿⣿⣫⢯⣯⣽⣿⡿⣯⣺⣽⠾⠛⠉⠀⠀⠠⠀⠀⠀⠀⠀⢀⣼⣿⣻⠿⢟⣻⡭⢭⣖⣲⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣽⣷⣿⣻⣿⡀⠀⣀⠀⠀⠰⡀⠀⠀⠂⣠⢞⡯⣟⣭⢖⣻⣽⣒⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢭⣤⣾⣏⣈⣀⣀⣼⣿⡿⠾⠿⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⣉⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⢀
⠀⠛⠟⠀⠀⠈⠉⢀⣶⣦⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢉⣙⣾⠛⢦
⠀⠀⠀⠀⡀⠀⠀⠈⠛⠋⢀⡀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⣤⣀⠀⠀⠀⠘⠉⣻⣿⠰⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⣤⣌⣉⣹⣷⣦⣤⣏⣹⣿⢡⢰⡇
⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠁⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠶⣠⣞⣛⢿⠟⣩⣿⣿⣿⣿⠟⣿⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠶⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⢀⡀⠀⠀⠴⠟⠉⠁⢰⣾⠗⣫⣷⠟⣿⣡⣴⣿⠇⠁⡿⠁
⠀⠀⠀⢀⣾⣷⡄⠀⠀⠀⠠⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢳⣶⢦⣀⡏⠷⠀⡀⠀⢀⣠⠖⢂⣴⣾⠟⠇⠘⣿⡿⠿⢃⣴⠞⠁
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠐⠂⠀⠀⠀⠀⣮⣿⡀⠝⠡⠀⢤⠀⠐⠋⠀⠰⡯⠞⠁⠊⠀⠀⠛⠿⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢠⡐⠑⡄⠐⡀⠀⠁⠀⠀⠆⠠⠀⠀⠁⠘⠀⢀⣂⠀⣠⠾⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠂⠀⠀⠀⢄⠀⣄⢀⣿⣼⣷⣿⡇⠈⠙⠀⠇⠈⠀⠀⠀⠀⠲⣦⠀⠉⠉⠀⢀⣠⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⠂⠆⠀⡿⢿⣿⠟⡠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠾⣂⠀⠀⣠⡾⠟⣽⠟⡟⢷⣦⡀⠀⠀⣰⢦⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⢀⠀⠈⠶⠁⠘⠿⠀⢠⠀⡷⡀⠀⠀⠀⠀⠠⠎⣡⠄⠉⠷⢶⣄⢀⣾⡟⠰⣿⠀⠙⣣⢀⣴⡾⢋⣌⢇⣼⣥⡤⡀
⠀⠀⣀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⠘⠀⠈⠃⡴⡆⠁⢸⢆⡀⠳⠦⣉⡜⣿⣦⣴⣃⣀⡄⠀⡀⢿⠈⣿⠤⠴⢛⣧⢠⢿⡟⣉⣿⣜⡿⣈⣷⡆⣺⣧⣀
⠀⠀⠁⠀⠑⠈⠀⠀⢠⠀⠀⠀⠀⠀⠰⡁⠀⠓⠀⠠⠋⠄⠊⡀⣃⣼⡁⢀⣼⡟⢋⣥⠌⢿⣶⠋⠦⠖⢀⣿⡄⠀⢸⡏⢤⣄⡀⡻⣿⡶⣥⡙⠦⠀⣹⡅⢏⠁
⠀⠀⠀⠀⠀⠰⠄⣄⢀⠋⠀⠠⠀⠘⠀⢁⠀⣠⠄⡀⠈⠤⠀⠀⠁⠆⢁⣿⣿⠀⠟⢤⣤⡰⢮⡴⡦⢠⣾⡿⠀⠢⡈⠳⠟⣹⣿⣷⡌⣴⣻⣙⣧⣀⣤⡴⠎
⠀⠀⠀⠂⠀⠀⣠⠁⣬⣿⡞⠁⠀⠀⠀⠀⠐⠋⠐⠃⢻⡄⠀⠀⣤⠟⣻⣿⣇⠀⠘⠂⠃⣬⡎⠹⠾⠿⠋⠀⠀⣠⣾⣶⣾⠟⠀⠀⠉⠁⢸⣦⢙⣙⡋⠃
⠀⠀⠀⠀⠀⠀⠀⠤⠰⠟⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⡘⣧⠀⠀⢀⡁⠙⣿⣿⠀⡴⣦⠐⣧⠔⠃⠌⢱⡟⠻⠟⡿⠛⡉⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠁⢀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⡀⣤⢦⣄⠀⠀⠀⠀⢀⠀⠐⢁⡀⠀⢸⡶⠓⣦⣿⣤⣿⡿⠀⠰⡞⢠⡉⡀⠀⠄⣼⠇⠆⠈⣷⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⢀⠀⠠⠀⢣⡀⠀⠈⠀⣄⠀⣠⣿⣧⣤⣾⡇⠀⢾⣇⠤⣿⡿⣿⣿⣿⣤⢴⣿⠰⢱⣏⣁⣴⠏⢀⠃⣀⠁⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⢀⣼⣿⣿⠟
⠀⠀⠀⠊⢀⡤⠊⠀⠀⠀⢁⡶⠂⠀⠈⠻⣷⠴⢿⣧⠴⠚⣿⡶⠿⣧⠀⢠⠃⢀⡼⣏⠀⢀⣬⣩⡀⠶⠉⣹⠿⠃⢋⠠⢘⣯⠹⠎⠛⢛⠶⠶⣾⠿⠿⠛⠁
⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠙⣷⠛⠻⣷⡞⠙⣷⠶⣿⡇⣸⡀⣼⢀⠉⠃⠀⠈⠿⣁⣴⠛⠛⢠⠢⡌⠀⣸⠃⠀⢬
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢍⠁⢦⠀⠀⠀⠀⣿⠋⠛⣿⡶⢿⡿⢛⣿⠃⠉⠈⢳⣼⠀⠀⠀⡈⢀⠈⠁⠀⠀⠀⡤⡌⠀⢸⡆⡅⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠹⢦⡀⢸⡀⢻⡶⠋⠀⠀⠀⠀⣿⡛⠺⣿⡗⢿⣧⣼⣏⢠⣅⡀⠀⠀⣱⠄⢺⣄⣨⠟⠀⠀⡐⠴⠀⠀⠀⣼⡇⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢼⡗⠀⠀⠔⠲⠉⢉⢿⡏⠻⣧⡀⢻⡿⣧⡌⢤⡙⢀⢢⡙⠶⠛⢡⡀⠀⠀⠀⠈⠆⡄⠁⢀⣿⡟⢀⠁⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠀⢀⠤⢷⡁⠀⢨⢀⡈⢑⠄⣱⡟⠳⡄⣇⠼⣣⡝⠃⠚⠁⠀⠀⠀⠀⠀⠆⠤⢀⣼⡿⠁⠀⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢐⠇⠀⠀⠀⠀⠀⠀⠃⣸⣏⠁⠈⠁⠰⣤⣼⠁⣈⠃⠀⠖⠉⠁⣀⠀⠀⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡘⠓⠀⠀⠀⢀⠈⠀⠘⠻⡿⠓⠀⠄⠀⠀⠁⠀⠉⠀⠀⠀⠘⠃⠉⠤⠀⠀⠁⠀⠀⠈⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⢀⠀⢀⣉⠉⠐⣭⡀⢀⠁⠀⢰⠄⠀⠰⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⠤⠼⠗⠂⠀⠀⠀⠢⡞⠋⢰⡟⡹⠟⠉⠀⠀⠓⣀⠀⠀⢈⡄⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⣽⣉⡿⣿⣿⡄⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢽⡖⠒⠳⡄⠁⠀⠀⠰⢀⣀⠀⠀⠀⣧⠥⣼⠿⣴⠂⠀⠀⠈⠀⠈⠀⠀⠀⠀⣀⠀⠀⠘⠀⠀⠈⠃⠀⢠⣼⣿⢨⣷⠿⠇⠀⢀⣼⣿⡿⠃
⠀⠀⠀⠀⠠⠀⠈⠃⠀⠀⠈⢢⠀⠀⢠⠘⢃⠀⠀⣠⠀⡀⢶⠂⠀⣤⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠚⠀⠀⠀⠀⠀⠸⣿⣼⣿⣤⡄⣄⣴⣿⣿⡃
⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⢣⡔⠂⠀⠀⠉⠾⣽⣔⡷⠛⠓⣡⣟⣦⠤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⢀⡼⡏⠁⠙⠛⠙⠁
⠀⠀⠀⠀⠀⠀⠉⠣⠀⠀⠀⠀⠀⠱⣄⠀⠀⢈⡁⠈⠋⠿⠾⠾⠷⠋⠀⠀⠀⠈⣁⠀⠀⠀⠀⠠⠶⠀⠀⠀⠰⠆⠀⢀⣴⠛⣬⡇⠈⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⣆⠀⠀⠑⠀⣾⢀⡀⢀⠀⠀⠤⠒⠊⠉⠉⠁⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠝⠛⢋⢸⣧
⠀⠀⠀⠀⠀⣠⠶⢦⣄⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠻⠦⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⢰⣾⢱⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠳⣄⠀⢾⣷⠃⠀⢀⡀⠖⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠹⣆⡞⢁⡤⠖⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⣽⠗⡋⢠⠤⠟⠉
⠀⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠝⢿⣼⡆⢀⠗⠀⠀⠀⠀⠀⠀⠀⣴⠂
⠀⠀⠀⠀⠀⠀⠘⢢⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣸⡗⠀⠀⠀⢰⡄⠀⠀⠀⠀⠐⠺⣿⣯⡎⠀⠀⠀⡀⡀⣀⡔⡋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⣀⠀⠀⠀⠀⠀⠰⣿⠃⠀⠀⠀⠈⠛⠀⢀⠐⡀⠀⠀⣼⡿⣀⠐⠀⠴⣴⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣺⠏⠀⠀⠀⠀⠒⣼⣤⠀⢍⡙⠶⠀⢿⢃⣀⡂⢈⣤⣓⠒
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠀⠀⠀⠀⠀⡑⢦⣽⠶⣼⣆⠀⢠⣧⡞⠛⠉⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⢈⠐⠼⣎⠸⣟⡀⠛⠁⠀⠀⠀⠀⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠱⡍⠓⠤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⢻⢔⣟⠁⠀⠀⠀⢠⢠⠦⠗⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡿⠃⠀⠀⢄⡇⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠐⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠷⠶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠾⢿⣿⣿⣿⣀⣀⠀⠀⢀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⣤⠶⠛⠋⠉⠁⢸⡏⠉⠉⠙⠛⣿⣟⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠻⢦⣤⣀⣀⠀⣸⠇⠀⠀⠀⠀⣿⠟⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢀⣿⣁⣤⣤⡴⠶⠶⠶⠞⠛⠛⠉⠛⠛⠛⠛⠛⠋⢹⡟⠛⠛⠻⠲⣿⠷⠶⠶⠶⢶⣤⣤⣤⣀⣀⠀⠀⠀⠀⢻⣆
⠀⢀⣴⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⣦⣤⣿⡀
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦
⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢻⣇⡀⠀⠀⢀⣤⣤⡶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⠒⠶⠶⠿⠶⠶⠶⠶⠶⠶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠉⠛⢶⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⢶⣄⣀⢀⣠⣼
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠟⠉
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣤⡄⠀⠀⣠⣴⣤⣄⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⡆⠉⠛⠛⢁⣤⣴⣤⡀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⢹⡇⢀⣶⣿⣿⣶⡀⠈⠻⠿⠟⠋⠀⠀⠛⠿⠿⠛⢀⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠘⣿⣿⣿⣿⠃⠀⠀⢠⣤⣤⣄⠀⠀⠀⢠⣾⣿⣿⣦⠀⠈⠛⠿⠟⠃⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⢉⣁⣀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⡿⠁⠀⣀⣤⣄⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢰⣿⣿⣿⣷⠀⠙⠿⠿⠛⠁⣀⣠⣀⠈⠉⠉⠀⠀⢰⣿⣿⣿⣿⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⠘⠿⣿⣿⠟⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⢀⡜⠡⣞⢋⣱⠋⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⡸⣌⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢸⣆⢂⣀⠄⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠘⢛⠁
⠀⠀⠀⠀⠀⢠⠀⠀⠒⠀⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠌⠣⠃⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢤⢐⣋⢇⠸⢩⠄⠀⠀⠀⠀⠀⠀⠙⣮⣿⣧⣼⣿⣷⠋
⠀⠀⠀⠀⠀⢸⠀⠉⢤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢄⢌⡂⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⡼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠈⠉⡿
⠀⠀⠀⠀⠀⠘⡦⢦⠤⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠒⢠⠌⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠎⠡⢼⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⡤⢤⠆⡇
⠀⠀⠀⠀⠀⠀⡧⡌⡬⠧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⠣⠬⠄⡃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠭⠬⢥⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠡⠭⣤⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠰⡶⠶⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣇⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣜⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⡇⠀⠀⠀⠀⠀⠀⢲⠚⣭⡑⢂⢱⠒⢈⡍⢲⠆⠀⠀⠀⠀⠀⣿⣭⡽⠫⣍⣽⠁⠀⠀⠀⠀⠀⠀⠈⣯⣭⠝⠫⣭⣿
⠀⠀⠀⠀⠀⢀⡀⢀⣯⣉⣽⣀⡀⠀⠀⠀⠀⠀⡀⢧⠀⠉⡁⡈⡇⠄⢀⡏⢀⠀⠀⠀⠀⠀⣇⢸⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠆⠲⠆⡼
⠀⠀⠀⠀⠀⠉⠉⠩⣉⣉⣩⣍⠉⠉⠀⠀⠀⠻⠤⠈⣇⠌⡥⢌⣹⠒⡜⠠⠼⠃⠀⠀⠀⠀⢸⠀⠠⠄⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠍⠭⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣻⠃⠀⠀⠀⠀⠀⠀⠘⣶⡬⠷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⢉⡌⣍⡟⠀⠀⠀⠀⠀⠀⠀⠀⢗⣦⢢⣂⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠒⠛⠁

⠀⠀⠀⠀⠀⠀⣀⠀⣴⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣀⣂⣲⡆⠀⠀⠀⠀⠀⠀⠀⣰⠒⡖⢲⠒⣖⠲⣄
⠀⠀⠀⠀⠀⠘⠾⠇⠈⠛⠁⢺⡟⠀⠀⠀⠀⠀⠀⡰⠊⠳⣄⣉⡴⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⡗⠐⠉⢹⠀⠀⠀⠀⠀⠀⠀⠘⢿⡾⢿⠾⠷⠿⢷⠿
⠀⠀⠀⠀⠀⠀⢰⢶⠓⣶⠚⡖⡄⠀⠀⠀⠀⠀⠸⣕⣠⠞⠁⠀⠙⢦⣐⣼⠀⠀⠀⠀⣠⠤⠤⠧⢤⢥⠼⠦⠤⢤⠀⠀⠀⠀⠀⢈⡃⢀⠾⢧⠀⢸
⠀⠀⠀⠀⠀⣠⠞⢲⢪⡍⠱⡖⣳⡄⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠄⣄⠹⡄⠀⠀⠀⠀⢸⠟⠫⠩⡏⢸⠯⠍⠛⡟⠀⠀⠀⠀⠀⡏⠉⠻⠿⠿⠏⠉⡇
⠀⠀⠀⠀⠀⠹⢶⡸⢦⣀⠴⢧⡠⠏⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠥⠤⠚⠁⠀⠀⠀⠀⢸⣀⣀⣀⡇⢸⣀⣀⣀⡇⠀⠀⠀⠀⠀⣷⣒⣒⣒⣒⣒⣲⡇

⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⣏⣩⣍⣉⢉⠃⠀⠀⢸⣭⣭⣍⣉⡝⠀⠀⠀⣏⣉⠉⡉⣉⠃⠀⠀⢸⣉⡉⠉⠉⡏⠀⠀⠀⣯⣭⣍⣉⣉⡇⠀⠀⠘⣍⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⣿⣇⠀⠀⣿⠀⠀⠀⢸⣿⠄⠀⠀⡇⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢽⣿⣿⣷⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢹⣧⣶⣤⣿⠀⠀⠀⢸⣿⣶⣦⣴⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣯⣄⣤⣠⡾
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢿⣾⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠤⠄⠄⠀⠀⠀⠀⠀⠄⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠀⠀⠀⠀⠀⠒⠀⠀⠓⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣼⣯⣽⣦⣿⣾⣾⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣿⣷⣾⣿⣷⣶⣶⣶⣿⣷⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⢠⣄
⠀⠀⠀⠀⡀⠀⠀⠀⢠⠃⠀⠻⠃⠀⠀⠀⠀⠸⠇⠉⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠁⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠛⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠠⠲⣤⣮⢁⢠⠖⠛⠛⣠⣄⠀⠐⢀⣀⡰⠀⠀⠉⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠃⡟⣰⡀⠀⠀⠀⠠⣴⠞⣻⠛⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠠⠀⢘⠚⠻⠁⢀⣀⡂⠨⢹⠀⡀⠈⠁
⠀⠀⠀⢀⡴⠖⠂⢠⡇⠾⠷⣄⡄⠀⣿⣧⠊⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠲⠲⠎⠥⢒⣲⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢿⣄⠀⠀⣼⣃⢨⣬⣿⡷⠀⠘⠁⠀⠀⣀⣀⣀⢀⣇⣿⣄⠀⠀⠳⠃⠀⠀⡸⢀⠀⠀⠠⢶⠏⣽⣿⠀⠀⠀⠀⠑⠞⠂⠀⠀⠘⠋
⠀⠀⠀⠈⡦⠐⡀⣨⣿⣿⣿⡿⠁⠀⠀⠀⢀⣾⠉⠁⠀⢸⠁⠩⣩⣷⣇⠀⠀⠀⠀⡛⠂⠀⠀⠀⠀⣀⢼⡗⠀⠀⠮⠥⠴⠖⠂⠀⠀⠀⢠
⠀⠀⠀⠐⡇⠀⠀⠈⠉⠉⢹⣼⠀⠐⠽⠂⠀⢻⠁⠠⠀⠻⣶⣾⣿⣿⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢉⡄⡆⠀⢀⢀⠀⠀⠀⠀⡤⠂⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠠⡈⣟⠀⠈⠛⠛⠿⣿⡋⠅⡀⠀⠀⠀⢸⣤⡄⢺⡀⠰⢇⣸⢻⠁⠀⠈⠋⠀⠀⠀⢰⠂
⠀⠀⠀⠀⢠⠀⠀⠀⢀⣤⡴⡇⠀⠀⠀⠀⢌⠧⣿⠀⠀⠀⠀⠀⢘⣿⡀⠣⠀⠀⠀⠈⣤⡦⢉⢁⣠⣟⣿⡾⠀⠀⣀⡠⠤⠤⠄⡌⣀
⠀⠀⠀⠀⠏⣂⢀⣀⣴⡏⢸⡇⠈⢙⠂⠀⢨⠱⣿⠀⠀⠀⠀⠀⢚⣿⠀⠀⢐⠀⠀⠀⠡⢾⡛⢥⠍⣸⠿⠃⠀⡸⠤⣀⣀⢀⣰⣀⣀⣴
⠀⠀⠀⠀⠘⠻⣯⣥⣾⣿⣿⠇⠀⢸⠀⠀⠀⢉⣻⠀⠀⠀⢐⡿⣻⣿⠀⠀⡾⠠⠀⠀⠀⠀⠛⠷⠞⠃⠀⠀⠀⠇⣀⠀⠉⡉⠋⠀⣾⣿
⠀⠀⠀⠀⠀⠉⠓⠂⠉⠀⠀⠀⠀⡼⠀⠀⠀⠈⣿⣶⡶⠊⣻⣧⣿⣁⠀⢼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠋⠀⠀⠀⠀⠀⢹⡿
⠀⠀⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠝⣟⠳⠯⡛⠛⠋⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⡇⠀⠀⠀⠀⠀⠀⢈⣁
⠀⠀⠀⠀⠀⠀⣴⠒⠊⠉⠙⠃⢰⡗⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⠀⡤⠀⣠⡀⣸⣽
⠀⠀⠀⠀⠀⠀⣙⣿⡿⠉⠀⠉⠩⣿⣿⠀⠀⠀⠀⠻⠇⠀⠀⣠⢤⡄⣤⣤⣄⡠⢤⡄⠀⠀⠺⢇⢤⠀⠀⠀⠀⢘⢛⡁⠾⠂⠰⡶⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠚⠛⢿⣧⡀⠀⠀⢀⠀⠀⠀⣭⣿⣿⣿⣾⣿⣟⣿⣿⡇⠀⠀⠈⠋⠀⠀⠀⠀⠈⢙⣧⣶⣾⠟⣻⣿⠇
⠀⠀⠀⠀⠀⠈⠀⠠⠐⠤⠤⠾⠛⠀⠺⠟⠀⠁⠀⠀⠁⠀⠀⢻⡾⠟⠀⠹⠛⠀⠛⣿⡀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠈⠛⣢⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈⣿⡇⠀⠠⠞⠁⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇⠀⠀⠰⠖⠀⠀⠀⣋⠲⠶⣦⡂⢠⣤⣤⢽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⢀⠀⣀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⢠⢿⠇⠀⠀⠀⠀⣀⡤⣦⣼⠗⣦⣶⣓⣿⠿⠷⢊
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢈⢸⡧⢀⣤⠜⠋⠀⠀⠀⢁⠀⠀⠀⠀⠀⣠⣼⠏⠀⠀⢠⣾⣿⣯⣟⣷⣯⡿⣷⡿⢿⣿⣷⣬⣐⠭⠛
⠀⠀⠀⠀⠀⢼⣿⣤⠘⣶⢇⠀⢰⣿⣿⣿⠀⠀⠀⠀⡀⡀⠀⠸⠠⣴⡆⠀⢀⠙⣿⢣⠀⠀⠈⠙⠻⠿⠾⢶⣟⡿⠿⠿⠿⠷⠿⡿⠛
⠀⠀⠀⠀⠀⢈⠻⢏⢱⡾⠻⣤⡞⠛⠈⡁⠀⠀⠀⠀⠙⠁⠀⠈⠳⣦⣼⣿⣶⣮⡿⠈⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⣀⣤⡶⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠛⠋⠁⠀⠀⠀⠉⠁

⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠋⠁⠀⠀⠑⠂⠄⠀⠐⠖⠠⠀⠀⠀⠀⣠⡤⠀⠀⣠⣶⣶⡤⠖⠋⠀⠀⠠
⣆⣠⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠁⠀⠀⠘⣛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⠤
⣿⣿⣿⣷⣶⣷⣶⢀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⣠⡶⠚⠃⠀⠀⠀⠀⠀⢀⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣾⣴⣾⣦⡆⣶⢀⠀⣿⡀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⠟⢿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⢸⡇⣦⣿⣿⣷
⠟⠛⠛⠋⠋⠋⠉⠈⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⣾⡀⠀⢀⡄⢀⢠⣀⡀⣶⢀⣆⣿⣿⣤⣦⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⢰⣿⣧⣆⣼⣧⣿⣾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠟⠻⣿⡿⠿⢿⡿⣿⢿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠙⠉⠀⠁⠙⠙⠋⠛⠻⠻⠛
⣿⡿⣿⣿⣿⣿⣧⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⣯⠀⢻⣿⣿⣿⣿⡆⣼⣿⠀⠀⣀⠀⠀⠀⣼⡂⠀⠀⠀⠀⠀⣾⣧
⠃⠀⢺⣿⣿⣿⣿⣿⣿⣿⣗⢠⣿⡀⠀⢠⣿⣧⠀⢠⡄⠀⢰⣿⣿⠆⠀⠀⣄⠀⠀⠀⢠⡄
⠆⠀⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣾⣿⣯⣄⣼⣧⠀⣺⣿⣿⣶⡄⢸⣿⠀⠀⠀⣾⣷
⠀⠀⠈⢻⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣼⣿⣿⡿⢻⣿⣿⣬⣿⣿⣿⣿⣥⣿⠿⠇⠀⢸⣿⣿⠂
⠀⠀⠀⢀⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢰⣦⣿⣿⣿⣶⠄⠀⢠⣇
⠀⠀⠐⠶⠿⣿⣿⡃⠀⢐⣿⣿⣿⡏⢹⣿⣟⠀⠐⣺⣿⣿⣿⣿⣿⣿⣿⡃⠀⢒⣿⣿⣿⣿⣿⣆⠀⣾⣿⠄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠉⣛⡻⠯⠀⠀⠀⢸⣿⣿⠀⠨⣿⠥⠀⠀⠈⣿⣿⡿⢻⣿⣿⡯⠀⠀⠀⢹⣿⣿⣿⣿⣿⣼⣿⣿⣦⠀⣦⠀⢀⣿⡇
⠀⠀⠀⠀⣀⡤⠂⠀⠀⠈⠭⢿⠇⠀⠀⠘⠀⠀⠀⠉⠽⣿⠁⠸⣿⡿⠃⠀⠀⠈⠭⢿⣿⡿⠉⣿⣿⡿⢿⣿⣲⣿⡂⣸⣿⣷⠄⡄⠀⢀
⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠿⠛⠀⠀⠀⠀⠀⠤⣿⠃⠀⢹⣿⠇⠘⣿⢻⣿⣿⡿⢹⣿⣿⣿⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢉⠉⠀⠀⠈⠋⠀⠀⠃⢘⣿⣿⠃⠈⣿⣿⣿⣷⣿⣿