Cattle Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣀⣺⡟⠛⠿⠇⠉⠸⢿⣿⠿⠃⠺⣤⣤⡶⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠀⠀⢠⣶⣶⣶⣤⣤⡘⠫⡑⠀⢰⣆⠀⠁⢀⣄⠀⠘⡏⢖⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣥⠀⠀⠀⣀⣠⣀⠈⠙⢻⣿⣿⠟⠁⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠗⠉
⠀⠀⠀⠀⠀⠀⡠⠐⠀⠘⠛⠀⠀⣾⣿⣿⣿⡇⠀⠀⠈⠁⣀⣀⠀⠞⣙⡂⠀⠀⠀⠀⢀⡤⡀⠄
⠀⠀⠀⠀⠀⣠⠔⠒⡀⠀⠀⠀⢸⣿⣿⡿⠟⠁⠀⠀⠀⣾⣿⣿⡄⠀⠙⠃⠀⠀⠀⠀⠾⠃
⠀⠀⢀⣤⠊⠀⠀⠀⢱⠀⠀⠀⠘⠿⠋⠀⠀⣀⣀⢀⣰⣿⣿⣿⣧⠀⠐⠢⡤⣄⣀⡀⠠⠆
⠀⠀⠊⢉⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠁⡒⠊⠀⢀⡠⠔⠁
⠀⠀⠡⠌⠀⠀⠀⠀⢴⣿⣷⠆⢄⡀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠙⠛⠉⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠃⠇⠀⡀⢠⠀⡔⢲⠖⠀⠀⠀⠀⢿⣿⠀⢰⠄⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠐⠑⠂⠘⠐⠂⠈⠀⠀⠀⠀⠸⠿⠃⢨⠠⠀⢙⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⢠⠀⠀⠀⠀⠠⠀⠒⢄⠀⠀⠀⠀⢆⠀⢄⠀⠯⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠤⠔⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⡀⠀⠀⠠⠀⠀⠀⣀
⠀⠛⢿⠇⠀⠀⠀⠐⣿⣿⠗⠢⣄⡀⠒⠀⠠⠀⣄⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣄⡀
⠀⠀⠙⠂⠀⠀⠉⢃⢹⣇⣄⢀⠀⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠙⢻⣶
⠀⢠⣐⣠⠀⠀⣠⣾⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡄⢻⡇
⠀⠈⠛⠛⠒⠻⣿⣿⡎⢿⣿⣿⣿⠁⠀⡀⠰⣄⣤⡀⠀⡀⡐⡀⠀⡄⠀⠀⠀⣰⣿⣾⢕⠙⢷⠾⠇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠄⢹⣿⣿⣼⣿⣧⣠⣘⣿⣿⣶⣿⣿⣷⣾⣿⣾⣶⣼⣿⣿⣿⣦⣤⡄⡀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⢻⣿⣿⣟⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠈⠙⢿⣿⣿⣿⣷⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⣄⣸⣿⣝⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⠟⢉⡙⠚⢻⣿⣋⣿⢿⡟⠿⣯⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣽⣾⣿⣿⢯⠉⠀⠈⠉⠙⠛⠛⣿⠟⠉⠀⠀⠀⠈⣿⣿⣇⠀⢳⣴⣿⢣⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣴⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⠿⠂⠀⠹⣿⣄⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠃⠀⠀⠀⢹⠏⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡱⢿⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠘⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁⠀⠀⠀⠀⠀⠺⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠠⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣧⡀⠈⠟⠃
⠀⠀⠀⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣄
⠀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⡀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⠿⠍⠀⢀⡀
⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⠀⢀⣀⣻⣿⣿⣿⣿⣿⣿⣿⡏⢀⠖⠘⠛⠓⠒⠒⠀⠼
⠀⢹⡟⣿⣿⣿⠟⠻⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠠⠊
⠀⠈⠁⢻⣿⡟⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⣿⢟⣿⣿⠏⠀⠀⢨⣽⣿⣿⣿⣿⡿⠀⠀⠁
⠀⠀⠀⠀⡖⡇⠀⠀⠀⠀⠁⡠⠂⠀⠀⠀⠀⠀⠀⣰⣾⠏⠈⠻⠿⠁⠀⠀⣼⣿⣿⡟⢻⣿⠃
⠀⠀⠀⠀⢡⢧⠀⠀⠀⢀⡤⠤⢤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⡼⢻⡿⠋⢠⠞⠋
⠀⠀⠂⠀⡤⠚⠀⠀⣠⠎⠀⠀⠀⠘⣦⣀⡉⡀⠀⡴⡐⣠⣴⣰⣦⡶⣾⣿⡈⠁⠀⢨⣴⠏
⠀⢀⠄⣰⠇⠐⢠⡞⠁⠀⠀⢀⠠⠊⠀⠈⠙⠛⠈⠙⠐⠋⠀⠀⠀⠀⣿⣿⡇
⢰⠀⠠⡉⠄⠀⠀⣿⣶⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡏
⠀⡗⢀⡇⠀⠀⠀⠈⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠑⠲⠁
⠀⠀⠈⠁⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠦⣠⣠⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⢀⠂
⠀⠒⠂⠂⢶⣶⠛⠶⠶⠶⠼⠿⠏⢩⠿⠷⡹⡷⠖⠧⠤⠷⢾⠷⠿⠷⠶⠾⠿⠲⣶⡶⠶⠦⠔⠢⠰⠀⠀⠖

⠀⠀⠀⢤⣄⣴⣦⣤⣶⣶⣶
⠀⠀⠀⣴⣿⣿⡿⠿⠿⠟⠓⠒⠲⠶⠒⠒⠒⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⡶⠒⠒⠒⣶⣶⣶⣶⡖⢤⡀
⠀⢀⣴⣿⣿⡿⠃⠀⠀⠀⠀⢠⣴⣾⣿⣶⣄⠈⠉⠙⢿⣿⣿⣿⣿⣿⠏⠀⣠⣄⠀⠀⠀⠉⢻⣿⣿⡷⣵
⠰⡃⢉⠁⠈⢀⣀⣀⣀⠀⠀⠘⠿⣿⣿⣿⣇⠀⠀⠀⠈⠻⠿⠿⠿⠋⠀⢠⣿⣿⣆⠀⣠⡀⠈⣿⣿⡇⣿⡇
⠀⠉⠛⠉⠉⠉⠀⠙⢿⣿⣶⣶⣆⠈⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⢀⣿⣿⠀⠈⢹⠁⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⣼⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡽⣄⠀⠀⡧⠤⢤⣀⣀⣀⣀⡤⠤⠴⣶⣶⣶⣶⣦⣄⡀⠀⠀⠱⣌⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⠿⠋⡝⠢⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⢻⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠀⠀⠸⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢧⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢰⡇⠀⠀⠀⡇⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⠎⢀⣞⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣴⠋⠀⠀⠀⢀⣇⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⠀⠀⠀⢀⡀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠉⠒⠂⠀⠤⢤⣤⣤⣤⣄⣤⡤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣀⡀⠀⠀⡴⠶⣾⢄⡙⠐⢀⡀⠀⠙⡇⢀⣀⡀
⠀⠀⠀⠀⢀⠴⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠻⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠳⡍⠀⠀⠈⠁⠈⠙⠋⠉⠝
⠀⠀⠀⡴⢁⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⠀⠾⠆⠀⠀⠀⠗⠁
⠀⠀⠀⣧⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠇⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢣⠀⢣
⠀⠀⠀⢸⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠉⢄⠀⠀⠈⠀⣀⠀⠤⠧
⠀⠀⠀⠀⡆⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣿⣦⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⢀⢀⢤⢀⣘⠇
⠀⠀⠀⠀⢡⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢦⠀⣠⣬⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠈⠛⠉⠁
⠀⠀⠀⠀⠀⣆⢿⣿⡄⠀⠀⠀⢰⣿⡄⢀⠷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠇⠼⣿⡿⠀⠀⡀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠰
⠀⠀⠀⠀⠀⢹⢸⣿⣀⠀⠀⠀⣸⣿⡿⠁⠀⠈⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡌⠀⠀⢊⠀⠀⠀⠀⠀⡰⠁⠀⠀⡠⠃
⠀⠀⠀⠀⠀⣿⢀⣿⡿⠀⠀⢰⣿⡿⠁⠀⢀⠜⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠟⠛⠉⠉⡟⡄⠀⠀⠀⢠⠗⠂⠉⠁
⠀⠀⠀⠀⢰⣿⢸⣿⠇⠀⠀⠀⣼⢳⡆⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢰⠀⠀⠀⡞
⠀⠀⠀⠀⣿⡿⢸⣿⡄⠀⢠⣾⡏⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⠀⠀⠀⡇
⠀⠀⠀⠀⡝⠀⢸⠇⠘⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢁⠀⢀⠇
⠀⠀⠀⠰⣀⢠⡿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠈
⠀⠀⠀⠰⢸⣿⠇⠀⠀⠈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⢸⡇⢀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠲⠀⠀⠄
⠀⠀⠀⠀⠪⠅⢘⢆⠀⠀⠠⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠇⠨⠶
⠀⠀⠀⠀⠀⠢⠤⠃⠀⠀⠀⠨⡀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠶⠄
⠀⠀⠀⢴⣿⣿⣶⣤⡔⠁⠀⠀⠀⠐⣤⡴⣶⣿⣿⡆
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⠀⠀⢠⣾⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⣼⣿⣿⣿⣟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠙⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣶⣄⡹⣿⣿⣿⣿⣿⣿⣷⡀⣤⡀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣤⣤⣦⢿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⠿⢷⣾⣿⣿⣿⣿⣿⣿⣿⡇⢻⡿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣿⡿⣿⣿⢿⣿⣿⣿⣿⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣎⢿⠛⠻⡿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠁⠈⢉⠈⣿⣿⣿⡇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠀⠀⠰⡇⣾⣿⣿⣿⣧⣀⣀⣀⣀⣀⣴⣯⣤⡙⠿⣿⡇⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣴⣿⣿⣿⠃⠈⠉⠉⠛⠉⢿⣿⣿⣿⡄⠻⡄⠀⢁⠀⠀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⢿⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣧⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣅⣽⣄⣤⠀⠀⠀⠀⠀⠀⠀⢀⣏⣽⠀⠀⠀⢠⣇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠛⠛⠏⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠀⠀⠘⠛⠛⠃

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⡟⢦⡠⠴⠶⠤⢄⠴⡿
⠀⠀⠀⠀⢀⣤⢤⣬⣾⣄⠀⠀⠀⣈⣿⣶⠒⢶⡤⠤⢤⣀
⠀⠀⠀⠀⠈⠓⠼⠽⣇⡞⠀⠀⣸⢀⣳⠚⠒⠋⠀⠀⢯⣀⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠉⠉⠉⣉⠏⠉⠉⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⣇⠀⠀⢣⠈⡍⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠹⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⠸⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⣠⢋⡤⠒⠂⠒⠒⠒⠒⠒⠒⠤⣄⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⠒⠲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣀⣀⠤⠚⣱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠾⢖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⢤⠤⠖⠚⢳⠀⠀⢀⠞⠁⠀⠀⠈⠉⠙⠐⠢⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢰⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠑⠦⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠘⡄⠀⠀⠀⠘⣄⣀⣀⣀⣀⣀⣔⣁⣀⣀⣀⡤⠤⠒⠒⠉⠑⢆⠀⠀⠀⠀⠀⢸⢀⠇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠉⠒⢻⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⡾⢸⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠑⣶⠒⠒⠋⢣⠀⠀⠀⢷⠈⠷⠁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢈⡆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⡆⠀⠀⠘⡄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣸⡇⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⢿⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⡐⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡎⢸⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢇⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⢸⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⢤⣠⣿⣀⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁⠀⣠⠇⢀⡯⣀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠤⠐⠱⢅⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣈⡞⠁⠀⠸⠀⠤⠇

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣿⣥⣭⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣷⣿⣿⣾⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠂⢂⣲⣶⣦⣤⡤⢤⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠠⣄⡖⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠀⠻⣿⣿⣿⣿⣧⡈⠈⢻⣿⠿⢆⠀⠀⠀⠀⠀⠀⠘⠿⣿⡄⠀⣽⣾⣯⡻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⡠⠈⠛⠉⣿⠟⠃⡠⠀⠀⠉⠠⣿⣦⠀⠀⠀⠀⠀⠀⢠⣿⢇⣀⢿⣿⣿⠥⣹⡇
⠀⠀⠀⠀⠀⠀⠀⢰⢸⡏⡰⢊⡳⢦⣤⣀⣉⣀⣤⣆⠀⢀⡄⢰⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⢿⡿⣿⡟⣫⠀⢘⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣼⠃⠸⠀⠀⠀⠀⠀⠀⠀⠹⠆⠈⠛⠒⠈⣄⣹⣭⡱⠀⠀⠀⠀⠀⢦⣅⠁⣠⢻⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠙⢿⡁⠀⠀⠀⠀⠀⢀⠙⠊⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠓⠀⠀⠀⠀⠀⠉⠀⠘⠓⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠇⠇⠛⠷
⠀⢠⣴⣶⣤⠤⠤⣄⣀⣀⣀⣀⣠⡤⠄⣤⣀⣀⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠚⠤⠛
⠀⣸⣿⣿⡿⠇⠀⢾⣿⣿⣿⣿⣿⣧⠰⣾⣿⣿⣿⡿⠿⣿⡀⠀⠀⠀⣀⣢⠄⠒⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⣿⡏⠛⠸⣃⠀⣾⠿⢿⣿⡿⠋⠁⠀⡀⠸⠿⣿⠷⠦⠽⠯⠆⠀⠀⠙⠛⡆⢀⣾⣿⣿⠇⠀⣿⣿⣾⣿⣿⣿⣿⢃⡌⢹⣿⣷
⣰⣿⡄⣠⠶⢧⡀⠉⠀⠀⣉⣤⣴⡄⠀⡏⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣞⣻⣿⣿⡿⠀⠀⣽⣿⣿⣿⣿⠿⠃⠉⢈⣿⣿
⠈⡿⣰⠓⣀⠠⠋⠙⠛⠛⠉⠀⠀⠹⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⢀⣤⡐⡙⠛⠋⠙⠋⠀⠀⢇⠀⠉⣿
⠀⡄⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⡈⠹⢯⣷⣤⣤⣤⡴⠖⠋⢌⠱⠀⣸
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠰⠃⠂⠸
⠀⠀⠀⢠⣾⣿⣿⣿⣯⢹⣿⣿⣿⣿⣶⣶⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⢸⣿⣿⡟⢟⡃⢸⣿⣿⣿⣿⣿⣿⡿⠂⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⡤⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠚⠛
⠀⠀⠀⠸⣿⣿⡉⠈⠁⠀⣿⣿⣿⡿⠛⠿⠃⢀⣿⣿⡆⠀⠀⠀⠀⠀⢠⣀⠐⢰⣤⣀
⠀⠀⠀⣄⣿⠿⠂⢠⣾⣀⠈⠀⠈⢁⡅⠀⣀⣨⣿⣿⣿⠀⠀⠀⠀⠀⠈⠃⣠⣾⢷⣾⣿⡏⢠⣿⣶⣶⣶⣶⣶⡦⢠⣀
⠀⠀⠀⠿⡏⡤⢀⠃⠊⠉⠉⠋⠉⠉⠁⠀⢛⣿⣿⢋⢹⡿⠶⠂⠀⠀⠘⠿⠉⠱⣿⡿⡧⢀⣬⣿⣿⣿⣿⡟⠋⢀⠈⢼⣿⣶⣄
⠀⠀⠀⠀⠀⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⢩⡄⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⣡⠄⠀⠉⢉⣀⠘⠛⠁⠀⢸⠠⡶⢿⣿⣿
⠀⠀⠀⠀⠓⠂⠹⠷⠀⠀⠀⠀⠀⠀⠳⠆⠀⠛⠃⠷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠳⠤⠄⠸⠿⠛⠛⠻⠿⠦⠈⠄⠠⠛⠻⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣠⣤⡄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢠⣤⣄⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⢸⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣄⡀⠀⠉⠉⠉⠀⠀⠀⠉⠻⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⣠⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⡆⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⣀⠀⢰⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⠿⠛⠃⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⢀⣴⠘⠛⠿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠘⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣶⣤⣄⣀⣀⣠⣤⣶⡿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠛⢻⣿⣿⣿⣿⡟⠛⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⣶⣾⣿⣿⣿⣿⣷⣶⠾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠘⣇⣀⡀⠀⡀⢠⣄⡤⢤⡤⠖⠦⠤⢤⡟⠠⢄⠂⠤⣀⣀⡀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠓⢄⣩⡝⠀⠈⠁⠀⠘⣌⣤⡴⠋⢦⠀⠈⠁⡀⢄⣀⠀⠀⠀⠠⠀⢤⠀⠀⠀⠀⠀⠀⠙⠂⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠐⠘⣫⣿⣇⠀⠀⡀⠀⠀⣮⣧⠛⠁⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⡀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢰⠀⠁⠀⠀⢁⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠊⠀⢀⡼⠃⠀⢠⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡐⠂⣠⠎⡾⠁⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⡀⠐⠋⠀⠀⠀⣬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡌⠡⡶⣸⠟⠀⠠⠔⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⢀⠈⣁⠀⠀⣠⡞⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠁⣱⣿⠁⠈⣀⠀⢠⡀⠀⠀⠀⢀⣀⣈⡉⡀⠀⢠⣾⠿⢳⡄⢺⠃⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠐⠋⡄⠀⠈⠉⡐⣋⠅⠀⠀⠉⠉⠤⢬⠁⠀⠈⠁⠛⠁⣘⠗⣎⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠍⣿⠇⠀⢫⡝⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢢⠣⠋⢸⠙⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡔⠀⠈⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡴⠀⠀⠀⠀⠃⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⢋⡀⠀⠀⠀⠀⠀⠀⣀⡀⢮⣔⡃⠀⠀⠀⢰⡆⢠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠧⠤⢿⡤⠤⠅⠈⠥⠉⠀⠀⠀⠀⠀⠐⠋⠉⠭⠷⠤⠄⠠⠾⠭⠆
⠊⠐
⠀⢀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⢲⣀⡗⠒⠢⣄⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠈⡡⠘⣟⣿⣚⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢼⡏⣄⣽⣷⣿⣿⣿⣿⣿⣿⣿⡶⠀⢠⡤⢤⣄⣀⣀⣀⡠⢀⣄⡀⢠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠈⢛⠉⠉⠛⠉⠈⠻⣿⣿⡟⠁⠀⣴⣿⣶⣿⣿⠟⠋⠀⠈⠙⠃⠀⣿⣿⣯⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉⠉⠉⠈⢧⠀⢾⣿⣦⣀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣷⡄⢀⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⣿⣿⣿⡧⠀⠀⠀⠀⠻⣿⣿⡿⢿⠇⠀⠁⠀⠀⠀⠀⠀⠙⢿⣿⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⢿⣆⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣇⠀⠀⠀⠙⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡆⠀⢠⣿⡮⠡⠴⠒⠀⠀⠀⠀⠡⡄⠀⠀⠀⠀⣦⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⢸⣿⠟⢆⠈⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡟⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠂⠀⠀⣤⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣴⣁⡴
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣀⡀⣀⣀⣤⣀⣀⣀⣀⣹⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⣾⣷⣾⣿⣿⣿⣿⣿⣿⡿⠻⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠹⢹⣿⡿⢻⣿⡏⠏⠛⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢸⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣦⣠⡿⠀⠈⠈⠙⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣽⣿⣿⢿⣿⠁⢀⡀⠱⡕⠪
⠀⠀⢀⣀⣀⣀⣠⣤⣤⣶⠒⢒⣒⣒⠀⠐⠒⢶⣶⣶⣶⣖⠒⠠⠤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣼⡝⡆⢹
⢀⣾⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠉⠻⣿⣿⣦⣄⠀⠀⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠈⠻⠃⠀⣴
⣼⡏⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣆⡀⠀⠀⠈⣹⣿⣿⡀⠀⠀⢀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⢹
⢻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⡟⠃⠀⠀⣾⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⡀⠀⠀⠘
⠈⢷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣸⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠑⣄⣀⣳
⠀⠘⣇⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⢿⠟⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⢿⠘⣿⣮⠛⢿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⣼⠀⢿⣿⣿⡆⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣩⠏
⠀⣴⣇⠀⢸⣿⣿⡧⠀⢸⠿⣿⣿⣿⣷⠀⠀⣴⠇⠀⠀⠋⠀⠀⠀⠀⠀⢸⡏⠀⠀⢹⣿⣿⣿⣿⣿⠿⠻⠋⢰⠏
⢠⣿⡏⠀⠀⣿⣯⠀⠀⠀⠀⠹⣿⣿⣿⣇⣴⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣸⣆⠀⣿⣿⡿⢋⠄⠀⠀⢀⠏
⠘⣿⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⢹⣿⣿⡟⢿⠀⠉⠉⠓⠚⠋⠉⠉⠉⠉⠉⠀⠀⠘⡇⠛⠋⣴⠿⣄⡀⣀⠎
⠀⣿⠀⠀⣰⣿⣷⠀⡔⠀⠀⠀⢀⣿⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇⠀⢹⠉⠁
⠀⡟⠀⠀⢻⠟⠁⢰⠇⠀⠀⠀⢸⣿⡇⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⡇⠀⢸⡆
⠀⠀⠀⠀⢸⡄⠀⡏⠀⠀⠀⠀⠈⢟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢰⢳⡀⢰⠇
⠀⠀⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⠈⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣇⡜⠀⡞
⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⢸⠃
⠀⠀⠀⠀⢠⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣧⡏
⠀⠀⠀⠀⢸⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⢧⣄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⠀⢹⡀
⠀⠀⠀⠀⠀⠸⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⡿

⠀⣀⣀⠀⢀⠋⢆⠀⢀⡀⠸⠳⡀⣸⣿⢆
⠀⣿⣮⣑⡾⠤⠞⠁⠀⢿⣷⣤⣿⣿⡏⢸⠄
⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⢉⠻⢿⣿⠀⡼⠀⢀⣀⣤⣤⣴⣶⣶⣶⠒⠒⠒⠒⠒⠠⣤⣤⣄⣀⡀
⠀⠀⢹⠟⡡⣂⠐⠖⠉⣉⢳⡀⠀⠉⡞⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣄
⠀⠀⠸⣀⣄⡽⢁⡠⠤⠬⢴⣃⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠁⠀⠙⢆
⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄⠀⠀⢀⠀⢡
⠀⠀⡇⠀⣶⡄⠀⠀⠀⠰⣿⠆⠀⢸⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠈⢱⡄⢣
⠀⠀⠱⡀⠉⠁⠀⠀⠀⠀⠀⢶⠂⡜⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠋⠀⠀⠀⠀⠀⠈⠉⠁⠉⠛⠋⠀⠀⠀⢰⢻⢸⡆
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⣠⣋⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⢆⡇
⠀⠀⠀⠀⠀⠉⠓⠒⡲⠚⠙⡇⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠰⡄⠀⠀⠀⠀⡀⠀⡜⠀⢠⣾⢿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⢀⣸⠀⠀⠀⠀⠀⢀⠁⠒⠤⢤⣶⣾⣿⣿⣿⣤⠤⠖⠋⠙⢦⡄⠀⢸⡥⠊⠀⠀⡏⠃⢸⠸⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⢠⡄⠀⠰⡀⠀⠘⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠘⢄⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⠉⠒⡇⠀⠀⠀⢷⠂⠤⠄⢀⡤⢇⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠀⠀⢱⠀⠀⠀⢸⠀⠀⠀⢸⠀⠘⢴⠛⠚⠉⢿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⣴⠀⠀⠈⣧⣄⣀⣼⠀⠀⠀⠘⣦⣴⣾⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⢃⣤⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡴⢁⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⢸⠅⠘⡻⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⣉⣧
⠀⠀⠀⠀⠀⠀⡔⠁⣴⠋⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠂⠀⠝⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢣⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠐⣠⠞⠡⠂⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⢠⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠐⠢⠜⠋
⠀⠀⠀⠀⣠⣾⡫⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⡛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⠄⠊⣀⡀
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠙⠘⠁⣟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⢿⣷⡴
⠀⠀⠀⠈⣆⡀⠸⢰⠄⢸⠂⣃⡈⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡀⣠⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠿⠀⠀⣼⢧⡀
⠀⠀⠀⠀⠀⠑⠀⠍⠀⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠁⣟⡄⠀⠀⠀⠀⠀⠀⠰⡇⠠⠈⠓⢬⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢤⠀⠒⢀⡧⠄⠀⠀⠀⠀⠀⠀⠀⠁⢢⣠⠇⠐⣾⠿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣀⢠⠀⠀⠀⠐⠄
⠀⠀⠀⠠⡄⠄⠽⠞⠛⠒⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣷⢉⣹⣿⣄⣌⢠⣤⡇⠀⠀⠀⠀⠀⣴⠁⠀⠄⠂⠀⠐⠂⠀⠠
⠀⠀⠀⠀⠁⢠⡖⣤⣀⢢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣟⠃⠀⢽⡄⠀⠈⠁⠀⠀⠀⠀⠀⠁⢴⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠆⠈⠈⢙⣏⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠔⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢤⡄⣁⡀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡧⠤⢤⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣤
⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⣂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣾⡅
⠀⠀⠈⠀⠀⠸⡇⠄⢀⠰⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣆⢰⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣴⠿⢿⣤
⠀⠀⠀⠀⠀⢠⡇⠀⠨⠄⢻⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠛⢠⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠁⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⢥⣝⣀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰⣶⣛⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⢤⡤⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠄⢀
⠀⠀⠀⠀⡠⠈⠁⠁⣀⣠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡄⠀⠀⠐⢢
⠀⠀⠀⠀⣇⣈⡤⠞⠋⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⣿⣦⣤⣦⣼⣤⣶⢴⡆
⠀⠀⠀⠀⣿⠃⠀⠐⠀⠠⣶⡏⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠤⠲⣦⣀⡟⠒⠒⠿⣶⣦⠉
⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠆⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠉⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣸⡏⢹⡛⠛⠻⡟⠶⠶⢶⠶⠶⠶⡶⠶⠶⣶⠶⠶⢲⡖⠞⠻⡟⠋⢻⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣇⣀⣇⠀⢘⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⡇⠀⢘⡇⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠈⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠇⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠟⠀⠀⠀⠀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⡀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⡟⠀⢸⡏⠀⠀⠀⢸⡀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⠸⠷⣤⣤⠶⠾⠷⠶⠶⠶⠋
⠀⠀⠀⠀⢠⡴⠶⠶⠶⣶⠶⣤⣤⣈⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣴⠶⠲⢶⣄⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢰⠃⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⠀⠈⣿⣄⠀⣠⠞⠛⢶⣄
⠀⠀⠀⠀⠙⢷⣄⣀⣸⣄⠀⠀⠀⣀⡾⠃⢀⡀⠀⢰⡟⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣄⣴⠟⠙⢷⣇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣛⣯⡶⠛⠋⠙⢷⡈⠻⣄⠀⣠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢸⡅⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠷⣤⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠳⡄⠀⢀⣼⠇⠀⠈⠻⣧⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⣿⠶⠟⠁⠀⠀⠀⠀⠈⠻⣦⣀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠈

⠀⠀⠀⠀⢠⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢢
⠀⠀⠀⠀⢿⠀⠙⢤⠖⠒⠛⠛⠓⠒⢤⠞⠁⢸
⠀⠀⣠⣶⣿⣦⡤⠊⠀⠀⠀⠀⠀⠀⠈⢢⣤⣾⣦⣄⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀
⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠉⠒⢤⡀
⣿⣿⣿⣿⡿⠃⣠⣄⠀⠀⠀⠀⠀⢀⣠⡀⠙⣿⣿⣿⣿⣷⠀⠀⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠙⣶⠶⣤⣄
⠻⠿⠿⡏⠁⠀⠿⠾⠃⠀⠀⠀⠀⠸⢷⠞⠀⠈⠻⡿⡿⠟⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣰⣿⣆⠀⠉⢳⣄
⠀⠀⠀⢳⠀⠀⢀⠔⠊⠉⠉⠉⠉⠑⢦⡀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠙⢷⣄⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠣⡀⡏⠀⢤⡀⠀⠀⣠⠄⠀⢣⠀⣰⣿⣿⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⢀⣠⠷⢾⣿⣿⠿⠂⠀⣀⣤⣴⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣗⢒⣂⣉⠉⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⢋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠋⠉⠉⠉⠀⡆⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠿⣠⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⢀⡀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⣷⣿⠆⠀⢰⠧⠤⠤⠤⠐⠒⠺⡋⡍⠉⣄⣧⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣤⣤⣿⣿⣀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠈⣮⣭⣤⣽⣀⣀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠉⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠏⢻⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣸⣿⣢⠀⢀⣄⠀⠀⢀⣴⡜⡉⣀⣤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⠿⠛⢉⣻⠘⣻⣇⣻⣾⣯⣼⣻⠷⣠⣼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⡟⠃⠈⡅⡀⢀⣼⣮⣹⠗⢈⣼⠦⢉⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡤⣐⠠⠸⣿⡟⣾⢸⠠⠋⠚⠟⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡟⠉⠵⣬⣷⣍⢿⠀⠀⢷⡏⣴⠶⣹⢻⠿⣦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠀⠀⠈⠽⣿⣾⡇⠀⢻⣿⣯⣿⣿⣿⣁⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠀⠀⠐⠋⠙⠣⣤⣾⢿⣿⣎⠛⠫⢶⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠄⠀⠀⠀⠀⣭⡀⠀⠈⠉⣹⣿⣿⣯⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⡀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠊⠀⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⢿⣽⣿⡿⢻⣿⣷⣿⡟⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠛⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⢲⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡐⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⣭⡛⠫⠭⠙⠉⠒⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣆⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠉⠛⠢⢄⠠⣴⣵⡄
⠀⠀⠀⠀⠀⢸⡷⠲⠶⢶⠒⣿⠀⠀⠀⣀⣹⣄⠀⠀⠘⡿⠿⠿⠿⠶⣶⡶⠶⣤⣧⣀⡏⠉⠁⠒⢲⠀⠈⡆⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣧⣀⣠⣸⠀⢋⡄⠀⣾⡟⠙⠻⣇⣀⣴⠗⣤⠀⠀⢀⣀⣈⣲⡀⠈⣿⣿⠀⠀⠀⢸⠀⠀⡇⣿⣿⡇
⠀⠀⠀⢠⡞⠉⠛⠾⠭⠭⠷⣿⠙⠓⠛⢻⡷⢾⠿⠿⣥⣾⣷⣤⡤⠴⠿⠿⠿⣿⣿⡿⠋⠀⠀⠀⢸⠀⠀⣟⣿⣿⡇
⠀⠀⠀⢸⠉⠓⠒⠒⠀⠐⢺⣿⣿⠛⠉⢹⡇⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⢀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢸⠀⡖⠲⠤⠤⠤⠞⣿⣻⡶⠶⣾⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣤⣿⡛⣉⣃⡨⡳⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⡉⠉⠀⢀⣲⡄⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⣼⣽⣿⣷⣿⣿⣯⠨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⠁⡇⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡟⠻⠿⠿⠿⠿⠿⠂⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⡓⣒⣒⣛⣩⡵⡀⠀⠀⢸⢿⣿⣇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⠀⠰⢤⡰⡶⠶⠀⢸⣷⢄⣀⠀⠀⠀⠀⠀⢀⣷⢤⣄⣈⣉⣉⣁⣤⢴⡟⠋⠉⠙⠛⠻⠷⢤⣄⣀⡀
⠀⠀⠀⢸⠀⠧⢄⣀⣀⡇⠀⣴⠋⠀⠈⢲⠄⠀⣿⣿⠟⠻⠿⠿⠿⠿⠓⡏⠙⠓⠒⠶⠒⠒⠊⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢓
⠀⠀⠀⠘⠦⣄⣀⣀⣀⡇⠀⣈⡳⣤⡔⣁⠀⠀⣿⡟⠀⠠⡤⠒⠚⢿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⠉⠉⠉⠉⢀⣠⡟⠧⢤⣀⣷⣷⡶⡟⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣤⡴⠊⠁⠀⢀⡤
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⠿⠿⣿⣿⣿⠇⢿⠇⡀⠀⣠⣯⣧⠤⠂⡼⣿⠢⢤⣄⣀⣀⣠⠤⠖⢻⠿⣿⣿⣿⣿⣿⠀⢀⡤⠞⠉
⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠒⠊⠁⠘⠿⠾⠉⠉⡟⠒⠚⠋⢻⡀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠉⠉⠛⠻⠖⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠼⣧⣤⠴⠠⡄⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠋⠁
⠀⠀⠀⣿⠤⠤⠤⠀⠐⠒⠒⠒⠒⠂⠉⢻⠀⠘⠶⠒⠊⠉⠁
⠀⠀⠀⠹⠴⠶⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉

⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⢀⣾⣿⡟⠻⣿⣿⡄⠀⠀⠀⠀⢀⣀⣀⣸⣉⣉⣹⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⠛⢻⣿⣶⡀
⠀⠀⠀⢸⡿⠟⠛⠚⠛⢿⡇⠀⠀⠀⢸⣿⣿⣿⡿⠛⡛⠻⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣸⣿⣇⣀⣀⠀⠀⠀⢰⣿⠿⠿⠇⠀⠸⠿⠿⣿⡄
⠀⠀⠀⠈⠀⠀⣀⣀⡀⠀⠁⠀⠀⠀⢸⣿⣿⣿⢠⣴⣿⣤⢸⣿⣿⣿⠀⠀⠀⠀⠿⠿⢿⣿⡿⠿⠿⠀⠀⠀⢸⣿⣀⣀⡀⠀⢀⣀⣀⣿⡇
⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⢛⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠈⠻⣿⣿⠿⠃⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⡿⠿⠟⠋


⠀⢰⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣤⣾⣿⣷⣆
⠀⢸⡇⢰⣦⠀⢀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⡿
⠀⢸⡇⠸⡿⠀⠸⡯⠀⠸⡧⠀⣿⠀⠀⠀⠀⠀⠀⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⣿⣿⣷⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠁
⠀⠸⠗⠚⠛⠒⠚⠛⠒⠚⠓⠚⠿⠀⠀⠀⠀⠀⠀⢾⣻⠇⠀⠀⠀⠀⠀⠀⠀⠠⣟⣿⣿⣤⣿⣿⣷⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⢠⣾⣿⣿⣷⣶⢰⣶⣿⣿⣿⣧⠀⠀⠀⠀⣴⣶⡟⢛⠒⣦⠀⠀⠀⠀⠀⠀⠎⠉⣠⡴⣭⡑
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃⠀⠀⠀⠻⠿⣿⣿⡏⠀⣿⣿⡿⠿⠋⠀⠀⠀⠀⣿⣿⣌⠻⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡼⠃
⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢅⡀⠀⠀⢀⡠
⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠠⠤⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⠟⢷⡜⠀⠀⠀⠀⠀⠀⣿⣿⠋⣴⡌⢻
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣤⣴⣶⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⢱⠀⠀⠀⠀⠀⠀⣿⣿⣧⣍⣥⣿
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠻⠿⢿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣤⣀⣀⡤⠚⠀⠀⠀⠀⠀⠀⠙⢻⡿⢿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠒⠤⢤⡀⠀⣀⣀⣰⡿⢯⡙⠃⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠞⠀⠀⠀⠁⠀⡀⠀⠈⠜⢇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠉⡆⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⢀⠃⠀⢠⡇⡟⠁⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⡴⠫⣤⣤⡀⠀⠀⠀⡎⠀⠀⣸⠁⠩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠩⠀⠀⠈⠁⠂⢀⣀⣼⡄⠀⠒⠋⠀⠀⠈⠁⡄⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠑⠀⠀⠀⠁⠀⢀⡰⣄⠀⣀⡔⣇⠀⠀⠀⠈⠀⡐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡤⠈⠁⢏⠲⢶⡶⠸⢇⠀⣀⡀⠀⠸⠋⠙⠉⠀⡞⠓⠀⠣⠔⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡁⠀⢀⣨⡷⡾⠀⠀⠀⢢⡿⠿⠶⣾⣦⣶⠖⠛⠛⠂⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠧⣤⠼⠷⣶⣿⡏⠀⠈⢤⠞
⠀⠀⠀⡀⣠⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣾⣶⣿⢶⡄⠀⠈⠓⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⢻⠀⠒⠀⠄⠤⠄⠑⠒⠊⠘⠉⡉⠹⣭⣠⡦⠴⠉⠒⠈⠓⠀⠈⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡨⠀⣠⡆⠀⠀⠂⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠖
⠀⠀⠀⡠⠄⠀⠀⠐⢾⣆⠀⠀⠀⠀⠀⠀⡘⠁⠀⠃⠁⠀⠀⠈⣀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠠⠊⠀⢄⠀⠈
⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠜⠋⠔⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣸⠶⠞⠋⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢧⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣦⣄⠀⣸⡧⠉⠙⠐⠛⠢⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠂⠀⠈⢢⠠⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣀⣀⢀⣠⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⡶⢦⡀⢳⠀⠡
⠀⢀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣭⣤⣤⣶⣶⡄⠀⠀⠈⠻⢿⣿⣿⣷⡀⠈⠉⠙⠻⢷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢿⣯⡇⠈⠇⣰
⢠⣿⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠙⢿⣿⣿⣶⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠋⠈⠈⠙⠁⠀⢸⠁
⣾⡏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣤⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⢀⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⡆
⢹⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⠛⠀⠀⠀⣾⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢀⡀⠀⠀⠀⢧
⠈⢿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠣⣀⣀⣻⡾
⠀⠈⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⡿⠋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠁
⠀⠀⢹⡆⣿⣮⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠘⣷⡆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⢸⡇⢸⣿⣷⣤⡙⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠋
⠀⠀⣸⠃⠀⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣷⡄⠀⠀⠀⣀⡄⠀⠀⣿⠃⠀⠀⠀⠀⠀⢿⣿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡼⠁
⠀⣼⣿⠀⠀⢹⣿⣿⠟⠀⢠⠟⠻⣿⣿⣿⣿⡄⠀⢸⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡧⠀⡀⠀⢻⣿⣿⣿⣿⡿⠛⠉⠉⠀⣼⠁
⠀⣿⡿⠀⠀⠘⣿⣧⡀⠀⠈⠀⠀⠹⣿⣿⣿⣧⣴⡿⢥⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡿⡄⢸⣿⣿⠟⢡⡆⠀⠀⠀⢰⠃
⠀⣿⡇⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⢻⣿⣿⡟⢻⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢻⠈⠛⠃⣴⠿⣄⡀⠀⡰⠃
⠀⣿⡇⠀⠀⣼⣿⣷⡀⢸⠀⠀⠀⠀⢸⣿⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⢰⠇⠀⢸⡍⠉
⠀⢸⠃⠀⠘⣿⡿⠉⢀⡟⠀⠀⠀⠀⣼⣿⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⡄⠀⠘⡇
⠀⠁⠀⠀⠀⢿⠀⠀⡼⠁⠀⠀⠀⠀⠹⡿⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢠⣧⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⢠⡇⠀⠀⠀⠀⠀⠀⢹⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⡎⢸⠂⢰⠇
⠀⠀⠀⠀⠀⠘⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣧⡏⠀⡿
⠀⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡁⢸⠃
⠀⠀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣧⡏
⠀⠀⠀⠀⠀⣾⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⢹⡁
⠀⠀⠀⠀⠀⠀⢹⣶⣶⣾⡄⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⣿⠀⢶⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠠⣴⣿⣾⡂⠀⠀⠁⠀⠀⠀⠀⢸⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠏⢀⣬⡄⠹⢿⡟⠁⠀⠰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢶⣄⣹⡏⠀⠈⠛⠛⢀⣤⡄⢇⣀⠀⠀⠀⠀⢴⣿⣿⣿⣦⠀⠀⠀⠀⡄⠈⠀⠀⠀⠈⠀⡿⢃⣤⡀⣀⠀⠀⠀⡴⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠚⣿⣭⣻⡷⠖⣰⢃⣼⣶⣷⡄⠀⢀⠀⢒⠂⢻⣿⣿⣿⡿⠃⠀⠀⠈⠀⢀⣄⠈⠶⠄⠈⠁⣘⠛⠙⠿⠁⠞⣿⠁⠀⢠⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠸⠈⣿⠿⠏⠁⢀⡉⢸⣿⣿⣿⡿⢀⡃⠀⣀⠀⠀⠙⠙⢿⡠⡆⠀⠐⠛⠐⣤⡈⠑⠀⢀⡢⢠⡟⢰⣇⣠⠄⠀⢤⣀⡙⢾⠀⠀⢙⡃
⠀⠀⠀⠀⣠⠟⢠⣶⣷⠀⠐⣶⡿⣧⡤⠉⠛⠉⣠⠘⢧⣀⠁⠰⠐⠆⠀⠸⠗⢀⣠⡄⠀⠀⠀⠉⠀⣀⠀⠀⠛⠠⢾⣯⣿⣾⣿⣷⡄⠀⣠⣦⡀⠀⣛⠄
⠀⠀⠀⠀⠿⠀⣿⣿⢏⡀⢿⣿⣿⣿⡄⠂⠀⢾⠃⠀⢀⠙⠀⣠⣤⡀⢀⣀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠙⠿⠲⠄⣰⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⠏⠀⠀⠃
⠀⠀⠀⠀⠀⢸⣿⠏⠸⡇⢸⣿⣿⠋⠀⢄⠀⠀⠀⣀⠸⣇⠀⢨⣽⣷⣿⣿⣷⡀⠀⡙⠁⠀⠀⠀⠄⢠⢀⠀⢀⡘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡆⠄
⠀⠀⠀⢀⡀⠘⣃⠀⣤⣆⠀⠈⡀⠀⣀⢚⡄⠧⠻⠌⠀⠉⠀⠸⣿⣿⣿⣿⣿⠇⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠘⠁⢈⠻⣿⣿⣿⣿⠿⠃⢰⠀⠈⠀⠀⠹
⠀⠀⠀⠈⣇⠈⣿⣷⣈⢻⣿⣠⣤⡀⠈⣉⣁⡀⢀⠘⠓⠚⠛⠀⠙⠻⠛⠛⠁⢰⣤⣴⡆⠀⣬⡃⠀⠀⠀⠀⣰⣿⣿⠄⠈⠛⠋⢉⡴⠖⠘⢄⠀⠄⠀⠈⣤
⠀⠀⠀⠀⠙⠁⠛⠛⠛⠷⣿⣏⡉⢀⡾⢹⡉⢻⡝⠷⠀⢀⢈⠁⢀⣠⣬⠑⠒⢈⡀⠈⣠⣄⠈⠛⠶⠀⢀⡀⠈⠙⠏⠀⣰⣷⠀⠙⢁⣤⣤⣠⣤⡄⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⣷⠀⣾⣿⣿⡿⠘⢧⣈⢁⣼⣯⠑⣀⣤⣾⣄⠘⣿⣿⠃⠀⠘⠿⢾⣿⠏⠀⠞⠀⢠⠞⣿⣄⠀⣠⣶⣿⣿⠀⠀⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⢻⠃⠀⢀⣉⣉⠀⠉⢸⡏⢸⡄⢻⡄⣈⠁⣠⣾⣿⣿⣿⣷⡆⢸⠀⠣⡈⠛⠛⠁⠀⠻⣿⣿⠟⠀⠀⠄⠙⢿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣖⣄⠀⠘⣿⣿⡟⠀⠀⠈⠳⢦⡤⠟⢠⡟⣼⣿⣿⣿⣿⣿⣿⠃⠰⡄⠀⠉⢠⣼⣿⡆⠀⠀⣠⠀⠞⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣬⠓⣄⡀⠀⠁⠘⠀⠀⠐⠀⢠⠀⠋⠀⠈⠻⣿⣿⡿⠿⠋⠀⣠⣴⣾⣆⠙⠿⠟⠁⠚⠋⢩⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢯⣽⡶⠖⠀⠀⠀⡀⣼⡼⠆⠀⠀⠀⠀⣠⣶⣾⡂⠈⢳⣿⣿⠏⠰⣾⣿⣿⠀⣾⣿⡄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⡌⢳⠀⠀⢰⣶⣶⡆⠀⢉⠛⠋⠃⠀⠀⢈⡀⠠⣄⠈⠋⠋⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⡄⠀⠀⠀⠀⠻⠏⠀⠀⠁⠈⢰⢄⠴⠀⢸⠀⠀⠀⢰⠇⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⢠⣶⣥⣤⡀⠀⠀⢌⠡⠇⠀⠀⠀⠀⠈⠳⠄⠀⢠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢿⣿⣿⣶⣤⡀⠀⠀⣴⣿⣿⣿⣷⡆⠀⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⣤⣤⡈⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⠷



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

⠀⠀⠀⠀⠀⢘⣳⣷⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣶⣶⡆⢀⠀⠀⠖
⠀⠀⠀⠀⢰⣿⠎⢹⡇⠀⠀⠀⠀⠀⠠⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢿⣯⡠⣿⡍⠉⢹⣿⣿⣷⣤⣾⣿⡀
⠀⠀⠀⠀⣾⣿⣷⣼⠀⠀⠀⠐⠽⠇⠀⠀⠉⠉⠹⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⡟⠀⠀⠀⠘⣿⡇⠛⠿⠿⠾⢿⣾⠟⠉⠋⠉⠃
⠀⠀⠀⢠⣿⣛⣟⠵⡶⠃⢀⡀⠀⠈⠀⠀⠀⠀⠀⢹⣿⣿⣿⠉⠉⢹⣿⣿⣿⣿⠃⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⢸⠃
⠀⠐⠘⠋⠈⠉⠁⠀⠀⠀⠰⢇⠀⠀⠀⠀⠀⠀⢀⣸⡟⢙⡿⠀⠀⣸⡟⠀⢙⣿⠆⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⠄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠛⠄⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡤⠃⠀⠀⠀⠀⠀⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠞⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⢞⡜⠃⠀⠀⠀⠀⠀⣄⠀⠑⠄⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⡩
⠀⠀⠀⠀⣀⣤⣴⡿⣿⣷⢉⡆⠀⠀⠀⠀⠀⠀⣿⠀⠤⠈⢶⡄⠀⢰⣿⣿⠶⠂⠀⠀⠀⠀⣤⠏⠐⢤⣾⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⣾⣿⢿⢻⡞⢛⣷⡌⣥⠀⠀⠀⣴⣦⣀⡏⠀⠀⠦⠈⠀⠀⢸⣿⣩⡴⠖⠀⠀⠀⠀⠳⠶⠶⠟⣫⠷⠉⠉⠁⠀⠉⠚
⠀⠀⠀⢻⡇⠀⠸⡇⢀⢹⠃⠀⠀⠀⢠⣅⣿⣿⣇⠀⠀⠀⠀⠀⠠⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦
⠀⠀⢀⣄⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡝⡛⢫⡭⠿⠀⠀⠀⠀⣠⣶⣾⣶⣶⣶⣶⣦⣶⡗⠀⠀⠀⠀⠀⣤⡀⣠⣾⣿⣿⠏
⠀⠀⠸⠇⠿⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠿⠿⠿⣿⣿⠋⠀⠀⠀⠀⠁⠀⠈⣰⣿⣿⣿⣿⡟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠘⠹⡋⠁⠀⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠱⠄⠀⠀⠀⠚⠀⠰⠄⠀⠀⠀⢀⣿⣿⣻⣿⣿⣿⣿⠇
⠀⠀⠐⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣟⣿⣿⣿⠏
⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠰⠟⠛⠉⢷⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣶⣆⠀⠀⠀⠀⠀⠋⠈⢿⡿⠟⠒⢶⠛⡿⠶⣦⣀⡐⠿⠻⠿⠟⠟⠁
⠀⠀⢿⣿⣿⣿⡟⢿⣿⣿⣿⣸⣿⣿⣿⣿⠿⢿⠿⢷⣄⠀⠀⠀⢠⣴⣿⣦⣀⡀⣠⣧⣀⠀⣾⠁⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢸⣿⣿⡿⠇⠠⠿⠿⠿⣿⢿⡟⠉⠉⠑⠘⠦⠼⠟⠀⠀⠀⢠⡟⠁⠉⠉⠉⠉⠀⠁⠹⡏⠀⠿⠀⠀⢠⣤⣾⣟⣿⣿⣿⣷⡀
⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⢃⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢰⢷⠀⠀⠀⠀⠀⠁⣿⠿⠿⠿⠿⢿⡋
⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣧⣀⠀⠿⠋
⠀⠀⠀⠀⠀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⡄⠀⠀⠀⢠⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣟⢻⣄
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠖⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠻⠇⠀⠀⣀⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡷⠀⢠⣬⣿⣿⣿⣿⣿⣿⣿⠁⡴⠁⠉⠉⠁⠙⠐⠚⠁
⠀⠀⠀⢸⡏⣿⣿⡿⠉⠛⢤⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣿⣿⣿⠟⠃⠜
⠀⠀⠀⠀⠀⠹⢻⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠋⣿⣿⠁⠀⠀⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠄⡆⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠐⠟⠃⠀⠈⠁⠀⠀⣸⣿⣿⠏⣸⡿
⠀⠀⠀⠀⠀⠀⡃⠇⠀⠀⢠⠊⠉⠉⠢⡄⠀⠀⠀⠀⡀⠀⣀⢀⣀⣂⣤⣅⠿⠀⠀⣃⡄
⠀⠀⠀⠀⠀⣰⠅⠀⣠⠞⠁⠀⠀⠀⠔⠛⠛⠿⠆⠚⠨⠬⠋⠉⠉⠉⣿⣿⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠋⠀⠀⢹⣧⣤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠷⢀⡆⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠲⠆
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠒⢠⣤⣄⢀⣀⡀⣀⠀⢀⠀⡀⢀⠀⣄⠀⠀⣀⡀
⠀⠀⠀⠙⠓⠀⠺⠟⠙⠛⠛⠒⠛⠋⠱⠛⠫⠽⠖⠙⠒⠛⠚⠛⠛⠛⠛⠛⠛⠲⠾⠓⠒⠚⠓⠐⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠁⢒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⡜⢩⣦⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠰⢧⣤⣿⣇⠀⡎⢀⠜⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⠀⠀⠀⢠⠃⠈⢿⣿⣿⠀⠳⠧⠤⠊⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡎⠀⡠⠤⣉⠀⠀⠀⠀⢀⣴⠋⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡸⠀⢘⢀⠔⠉⡇⠀⠀⣼⣿⣿⣷⠯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣰⠃⠀⠈⠓⠒⠊⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠈⠑⠒⠁⠀⣸⠀⠈⠑⠒⠉⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠉⠁⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠒⠒⠒⠒⠒⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣶⣤⣤⣤⣶⣾⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡞⢶⣣⠀⠀⠀⠀⠀⠠⣖⠤⠒⠒⠒⠒⠒⠒⢖⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⢿⡀⠠⠌⠳⣄⠀⠀⠀⠀⠈⠃⠘⠀⣬⣥⠈⠃⠸⢤⡤⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠈⢷⡀⠀⠀⢈⣷⡄⠀⠀⠀⢧⡀⠀⠜⠅⠀⠀⣀⡀⢠⡄⠉⠀⠰⠟⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣿⣿⡉⠳⣄⠙⣦⣤⣿⣷⡇⠀⠀⠀⠀⠉⢲⡖⠒⣈⠁⠙⠁⣈⠀⠘⠛⠀⣤⠘⠓⠀⣷⡀
⠀⠀⠀⠀⢀⣠⠖⠹⡏⠁⢿⡀⠹⣇⠈⠳⣄⠈⠳⣇⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸⡁⢀⠉⢠⣤⠀⠛⡀⠸⠇⢀⡀⠀⣶⠄⢴⢌⣑⡒⢠⣶⣶⠄
⠀⠀⠀⣰⡟⠹⣆⠀⢻⡀⠘⣧⠀⠙⣦⠀⠙⢦⡀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⢳⠀⠞⠉⠉⠉⠉⠑⠺⡏⢸⠉⡄⣇⠀⠈⠉⠉⠉
⠀⠀⢰⠅⣿⣄⡙⢦⡀⢳⡀⠈⣧⣀⠈⠷⣤⣤⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠀⢸⣴⠇⠀⠀⠀⠀⠀⠀⢹⣾⠀⣷⡇
⠀⠀⠀⠀⣇⢹⢹⡈⡟⠉⠉⠀⠀⠉⢻⡀⡏⢸⢦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⣀⢀⣀⣀⣀⣀⣠⣌⣡⣀⠈⣡⠴⢤⡀
⠀⠀⠀⠀⡟⣿⢸⣛⡇⠀⠀⠀⠀⠀⢨⣛⡇⠸⣦⡇⠀⠀⠀⠀⠀⣠⢤⣄⣶⢲⣮⠶⠭⠿⠾⠗⠚⠒⠛⠚⠓⠚⠓⠉⠉⠁⠈⠀⠉⠙⠓⠒⠒⠲⠦
⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠉⠁⠀⣠⠔⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣙⣎⣱⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠓⢦⡉⠒⠒⠒⠒⠲⠦⠤⢤⣄⡀⠀⣀⠀⠀⣠⣤⠤⠤⠤⠤⠤⣤⡀⢠⣄⠀⣤⠴⠶⠶⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣀⠀⢀⣀⣀⣀⣀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡏⢧⡼⠀⠀⠀⠀⠀⠀⠀⠀⢧⠏⠸⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠳⠍⣤⠀⠄⡀⢠⠉⡿⠃⢸⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣞⠝⠶⠒⠒⠢⢤⣠⢤⡀
⠀⠀⠀⣠⠴⠒⠛⠋⠉⢹⡇⠀⠘⡄⠀⠘⢿⠃⠀⠀⡇⠀⢸⠀⠀⢀⡠⠟⠛⢧⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣣⣏⡀
⠀⣠⢾⠁⠀⠀⠀⠀⠀⠀⢳⡀⠀⠑⠤⣈⣁⣁⡤⠞⠀⢠⠟⠀⣴⣋⣀⠀⠁⠘⡿⡆⠀⢀⡖⣋⠉⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠉⠉⠉⠓⠲⢄⠀⢀
⣰⡇⣪⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣀⣀⡤⠖⠁⠀⠀⠀⠀⠙⣧⠶⠆⢻⣳⡄⢸⡄⠋⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡼
⠉⠁⣵⠀⡴⡄⢀⣤⣤⣤⣤⣤⣤⣄⠀⡬⡍⢹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣾⡿⣆⠀⠳⣄⣀⠈⠁⢀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢸⢰⠁⡇⣿⠀⠀⠀⠀⠀⠀⢹⠀⠇⢇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⢟⣻⡀⠀⠀⠈⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠸⠞⠀⠣⠇⠀⠀⠀⠀⠀⠀⠘⠾⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⢸⣭⣇⠀⠀⠀⠀⡇⠀⢀⡀⠀⠀⡤⠦⠤⠤⣤⠀⠀⣀⠀⠀⡇
⠀⠀⠀⢀⣠⣤⣄⢀⣀⣀⣀⣀⠀⢀⡠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣄⡷⢼⡆⠀⠀⠀⣇⠀⣸⢻⠀⢀⠇⠀⠀⠀⢸⡀⣸⢿⠀⢀⠇
⠀⠀⢰⠋⠀⢀⡼⠉⠀⠀⠀⠈⢹⣏⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠈⠁⢻⡒⣇⠀⠀⠀⠉⠉⠁⠈⠓⠋⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉
⠀⠀⡿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡀⠀⢹⣿⡿⠋⣭⣭⡉⠉⠉⠉⠋⢿⣿⡗⠲⣦⡀
⠀⠀⠹⣄⠀⢿⠙⠂⠀⠀⠉⠛⠀⠼⢤⡀⠀⣀⡼⠛⠓⠶⢤⡀⠀⠀⠀⠀⠀⠸⣿⠷⠀⠀⣤⡀⠀⠻⠟⠃⠀⣶⡆⠀⠀⢀⣶⣦⠀⢻⡀
⠀⠀⠀⣈⠉⠙⣆⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢿⠀⠀⠘⠿⠟⠀⠰⣾⡦⠀⠈⠀⢰⣶⡄⠉⠁⢀⠾⡇
⠀⠀⠸⣍⠳⠶⠋⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⢀⡶⡄⣾⠿⠤⠤⠬⠤⠶⠶⠖⠒⠻⡆⣴⡆⡜⠀⣧
⠀⠀⠀⠈⠑⠲⠤⠴⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠧⠀⠀⠀⣼⢸⠇⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡇⡇⡇⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡄⠀⠀⣀⣀⣀⣠⣀⣀⡀⠀⢀⡀⠀⢸⠀⠀⠀⠀⣿⢸⠀⢻⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢳⠀⠀⡏⠀⠀⠀⠀⠀⢳⠀⢸⡇⠀⢸⠀⠀⠀⠀⢹⢸⠀⠸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣷⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⢸⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⣸⠀⠀⠀⠀⢸⣾⠀⠀⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠗⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠈⠓⠚⠁⠀⠀⠀⠀⠀⠘⠒⠋⠘⠒⠃⠀⠀⠀⠀⠀⠁⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠀⠘⠁⠀⠀⠀⠐⠀⠂⠒⠀⠃⠐⠀⠒⠐⠐⠂⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⣄⠠⠄⠒⠂⠀⠀⠒⠠⢄⡀⠀⠀⢀⠆
⠀⠀⢀⠠⠀⡀⠤⠄⣂⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡑⢤⠁⠃
⠠⠊⡠⠂⠁⠀⠀⡐⡡⠀⠀⠀⠀⠀⠔⠂⠀⠤⡀⠀⠀⠀⠀⠀⠙⣐⠠⢀
⠣⣐⠂⠀⠀⢒⡾⠊⠀⠀⠀⠀⠀⠀⠀⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠈⠢⡄
⠀⠀⠈⠉⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠑⡈⢦⠠⠄⠠⠄⢀⣀⡀
⠀⠀⠀⠀⠀⡤⠐⠂⠉⠉⠀⠀⠀⠈⠉⠉⠀⠒⠂⠠⠄⠀⡀⠀⠀⠀⡷⠤⠈⠁⠁⠂⠀⠀⠀⡠⠊⠀⠀⠀⠀⠁⠒⠤⣀
⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣀⠁⠈⠑⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⡆⠀⠀⠀⠀⡔⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⠄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠄⠠⢀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠈⠢⡀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⡠⠚⠂⠈⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠓⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠤⠀⢀⡀⠀⠀⠀⠠⠀⠂⠉⢄⠀⠀⢀⠀⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠠⠁⠐⠄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡠⠂⠀⠀⠈⠂⢀⠵⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠔⠁⠀⠀⠀⠀⠸⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠺⡄⠀⠀⠀⠀⠐⢀⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠰⡀⡠⠄⠌⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⡉⠓⠒⠒⠀⠐⠂⠀⠀⠀⠒⠒⠒⠂⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠄⢀⣐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡄⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠠⠉⠁⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⡘⠒⠀⠀⠐⠂⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠠⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠰⠅⢀⣀⣀⣀⠀⠀⠄⠊

⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠰⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠦⠀⠀⢀⠀⠀⠀⠀⠀⠀⢾⠄⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⠀⠰⠉⠀⠆⠁⣸⠆⠀⠀⠀⠰⢶⣶⣶⣦⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠁⢀⠀⣴
⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡄⠀⠈⢫⢿⣿
⠀⠀⠀⠀⠀⣶⣾⣿⣶⡆⠀⢀⠀⠀⠀⠀⢙⣿⣿⣿⠋⠀⢀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⢸⡀⠀⠀⠀⠀⢸⣾⠃⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⢀⡞⠀⠀⠀⠀⠻⠿⠛⠿⠋⠀⡼⠀⠀⠀⠀⠸⠛⠁⠀⠀⢀⣾⠃⠀⠀⠀⠀⡾⠙⢷⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠁⠀⠀⠀⠀⠀⣀⣀⣀⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠉⠛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣄⣦⠀⠀⠀⠀⠀⠀⢀⣀⣤⣠⣄⣀⠀⠀⠀⠀⠀⠀⢠⠴⠶⠦⡀⠀⠠⠀⣠⠏⠀⠀⣀⣤⣤⣤⡀⢹⣿⣿
⠀⠀⠀⠀⠀⢠⡞⢻⣏⠀⠀⢰⠀⠀⠀⢸⣿⣇⠆⣽⣿⠀⢰⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⢠⣧⢴⠀⢀⣶⣾⣿⣬⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠟⠃⠀⢀⡞⠀⠀⠀⠀⠉⠉⠉⠉⠉⣠⡿⠀⠀⠀⠀⠐⠤⠤⠤⠂⢀⣾⡟⣿⣆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠤⠴⠞⠋⠀⠀⠀⠀⠐⠀⢀⣠⣤⡶⢿⡉⢸⣿⣿⣷⣦⣤⣤⣤⣶⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠚⣴⣾⣿⣿⠟⠉⢀⣀⣀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠀⣰⣾⢿⣷⡆⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⠀⠀⠀⠠⡇⠀⠀⣶⣶⣶⡄⠀⠈⣿⣿⡏⠀⠀⢸⣿⡿⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠺⣷⣴⣿⠋⠀⢰⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⢰⡇⠀⡄⠀⠀⢹⡟⣿⠀⠀⢀⣿⣿⡇⠀⠀⣶⣿⣷⡄⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢆⡘⡔⠀⠀⠈⠀⠉⠀⣠⣾⣿⣿⣷⢄⠀⠿⠿⠿⠃⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠋⠀⠏⠁⣤⠾⣷⢶⠶⡶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠴⠒⣀⣠⣶⣶⣶⣶⣤⣶⣶⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣄⠀⠀⢰⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢻⣿⣿⣷⠀⠀⠀⠀⠀⣰⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣿⣟⡁⠀⢠⣤⡀⠀⢿⣿⣿⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣼⣿⣿⣿⣿⣿⡆⠀⢹⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⠋⠘⢿⡿⠁⠀⢸⣿⣷⡄⠀⠻⣿⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠁⢿⣿⣿⣿⢿⣯⡻⢿⣿⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣠⣴⣿⣿⣿⣿⡄⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠛⠿⣿⡇⠙⠇⠀⠀⠀⠈⠻⢿⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⢰⡁
⠀⠀⠀⠀⠀⣀⣤⣄⣰⣿⣦⣾⣿⣿⣿⣿⣿⣿⣟⠉⠁⠀⠰⡄⠀⢰⣦⣁⠃⠀⠀⠀⢀⣀⣀⣀⡀⠀⣤⣾⣿⣿⣿⣿⣿⣿⠟⠛⢫⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣄⠀⠀⠉⠀⢠⣾⠏⠐⠉⠛⠛⠻⠿⠿⣿⣿⣷⣦⣍⣉⡻⢿⡿⠟⠁⠀⠀⠀⠁⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠛⠁⠀⠈⠁⠀⠀⠙⠋⠀⠀⠀⠀⣾⡏⠀⢢⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⣄⣀⣀⠀⠰⠇⠀⠀⠀⣽⠆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡿⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡀⠀⠀⠱⡀⠀⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠐⠃⠀⠀⠀⠀⠀⠀⣠⡀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣎⡀⠺⠀⠀⣠⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠄⠄⠠⠀⠠⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⣠⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢆
⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣿⡿⣄
⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⣀⣰⣿⢴⣦⣶⡿⢿⣿⠃⣏⠁⠘⢢⣀
⣿⣿⡿⠋⠀⣠⢤⣠⠄⡚⢻⡷⠾⠛⣩⣿⠱⠟⣼⠰⠸⠆⡀⠀⠉⠻⡒⠀⢄⡀⠀⡀
⠟⠋⠀⠀⣰⣿⣧⠚⢁⠴⠀⡠⢴⣿⣣⢀⣠⣾⢿⡆⠀⡀⠸⢆⠀⠹⠀⣀⠀⠉⡓⣧⡆
⠀⠀⠀⢸⣿⣿⡿⣻⠶⣛⣡⣼⡿⢣⢇⡞⡋⢡⠎⠹⡆⠀⠲⠎⠀⡄⣸⠀⣵⣇⣤⣧⣷⡀
⠀⠀⢠⣿⠟⠁⠀⣀⠛⣋⡙⠋⠀⣠⠎⢠⠉⢠⣆⠀⢀⠠⢠⡄⣀⣡⣬⣶⣿⣿⣿⣿⣿⣧
⠀⠀⠙⠳⠚⠛⠛⠛⠛⠛⢿⡄⡄⠁⠁⣾⣇⣸⣻⣤⣸⣤⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⡅⣃⣣⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣧
⠀⠀⠀⠀⢰⡄⠀⣧⣎⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⢡⣀⣿⣿⣿⣿⣿⣿⣿⠿⠋⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠘⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣸⣾⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⣿⣿⣿⡷
⠀⠀⠀⠘⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⠟⠀⢀⣤⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⢀⡶⠋⠸⢷⣶⣶⣶⣶⣆⠀⠚⢛⠈⣷⡇⡠⠦⠀⠀⠀⠂⣠⡄⡀⠀⠀⠀⠐⠂⣀⣰⣶⣶⣶⣖⢂⣄⠘⢿⣿⣶⣤
⠀⠀⠸⡿⠀⠀⠞⢡⣿⣿⣿⠛⠁⢺⣿⠀⠹⠇⠁⠀⠀⠀⠀⢰⣛⠀⠲⡂⠀⠀⠀⣾⢿⣿⣿⣿⣿⣿⡌⣿⠃⠈⠀⢿⣿⡃
⠀⠀⠀⡇⢘⣧⡄⠀⠸⢿⣿⡀⠘⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣀⡇⠀⠀⠀⣽⣦⣹⣿⣿⣿⣋⠁⠙⠀⠀⠀⢠⠋⡇
⠀⠀⠀⡆⠘⢿⣿⡆⠀⠘⢻⣯⡄⠀⠘⢻⠉⠀⠀⠀⠀⠀⠀⠠⠐⠋⠁⠉⢆⠀⠀⠉⠁⠉⣇⠈⠉⠈⠀⢀⠀⠆⢠⡟⠀⡀
⠀⠀⠀⡇⠐⢠⣹⠿⠀⠀⠠⢿⣧⣦⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⢾⠃⠀⠉⠉⠉⠀⠀⠀⠘⢀⠋⠀⠀⠉⠆
⠀⠀⠀⠃⠀⠈⠏⠀⠀⠀⠀⠈⠋⡿⠋
⠀⠀⠀⠠⠤⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⢀⣀⠀⠀⠀⠰⠄⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠴⠠⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⡀⠀⠤⠤⢄
⠀⠀⠀⠀⠀⡴⣢⡖⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠔⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠒⠀⠀⠠⢄⠀⠀⠀⠀⠀⠉⠂⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠄⠀⢀⡄⢀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠈⠢⡀⢄⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠠⡀⢸⣇
⠀⠀⠀⠀⠁⠀⠀⠀⡼⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣾⠟⠉⠒⠒⠒⠒⠋⠱⢄⢱⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⡧⢀⡀⠤⢽⣄⠐⢦⣄⣀⣤⣴⠇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⣀⣶⢶⣶⣖⣼⢿⣟⠫⠵⠾⠁⠀⠀⠀⠀⠀⠀⠀⣠⡀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣄⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⣠⣤⣤⣤⣤⣤⢤⣤⣤⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢲⡻⡿⠹⠂⢲⣤⡄⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣦
⠀⠀⣿⣿⢻⣿⡟⣁⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀⣷⡀⠀⠀⠀⠀⠀⢁⡃⢀⠀⣼⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣀⢸⣿⢻⣿⢷
⠀⠀⣿⠏⠈⠛⠁⠟⣡⣼⣿⣿⣿⡿⣿⡿⠀⠀⢸⣷⡀⠀⠀⠀⠀⠊⠁⠳⣼⣿⣿⣿⣯⣿⣿⠿⣿⣿⡿⣦⡝⠃⠙⠁⢻⡞
⠀⠀⣿⣄⢀⠤⠤⠈⠋⠀⠈⠋⠉⢀⠉⠀⠀⠀⢄⣹⣿⣆⠀⣀⠀⠀⠀⠀⠈⠻⣹⣿⣿⣿⣀⡀⠈⠉⠀⠈⣀⠀⠠⡀⢸⡇
⠀⢠⣿⢧⣇⣀⠀⠀⠀⠤⠄⠀⢲⢿⢿⣶⣄⣀⠔⠿⡿⠃⠘⠃⠀⠀⠀⠀⠀⠀⠈⠑⢰⠟⠁⠀⠁⠀⠀⠉⠀⠐⠀⢾⡀⡓
⠀⠈⠛⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠿⠏⠀⠀⠀⠹⡀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠃
⠀⠀⢀⡀⠀⣤⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣠⡀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠀⠀⠀⢠⣦⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀
⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⢰⠆⠐⠒⠢⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠈⠙⢃⣄⠀⠀⠀⠄⠀⠀⡐⠀⢹⡀⠀⠀⠀⠀⠀⠀⡀⠄⣈⣤⡊
⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⢤⡀⢰⠋⣓⠄⠀⢀⣾⡇⠀⠀⢂⡀⠈⠃⢀⡩⠀⠀⠀⠠⣦⠀⠀⢡⡏⠉⣟⢳⠲⡄⠂
⠀⠀⠀⠀⠀⠒⠁⠀⠤⣝⡲⢭⡨⣝⡊⠓⠀⠈⠉⠀⠀⠀⠀⠘⠚⠁⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠹⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⡒⠦⠝⠲⠍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⢀⠀⡄⠀⠀⠀⠀⠀⠀⡧⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡁⠀⠀⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠋⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠞⠳⠃⠀⠙⠁⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠘⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠉⠉⢈⠀⠀⠀⢀⠰⠔⠳⠄⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡇⠘⠋⢸⠀⠀⠀⠀⢁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⢀⡀⣠⠂⠀⠀⠈⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠃⠒⣁⠆⢀⡃⠐⢠⠀⠀⠀⠀⢸⠇⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡙⠁⠤⢠⠄⣀⡰⢀⡠⠀⠀⠀⠀⢀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡸⠁⠀⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠘⠈⠓⣐⡃⠀⣃⡀⠀⢨⡆⠀⢤⠄⠀⠀⠀⢸⡆⠀⢶⣶⢆⡀⡀⠀⢀⠀⠀⠀⠀⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⠀⠁⠾⢃⡈⠀⠉⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠾⠂⠈⠃⠀⠀⠀⠀⡀⠈⠁⣄
⠀⠀⠀⠀⠀⠀⣠⠠⢄⣀⣤⠖⠒⢄⡠⠞⠀⠀⠂⠀⠀⠀⠀⠀⣀⢣⡄⠀⠠⠄⠖⠀⠀⠀⠀⠄⠀⠀⠈⠈⣀⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠜⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠲⠒⠶⠏⠋⠝⠉⠋⠙⠉⠀⠠⣭⣥⣭⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠂⢂⡈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠙⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡀⠀⠀⠉⠉⠛⢶⣄⡀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢻⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢳⡀⠀⠀⠀⠀⠀⠉⠳⢌⠀⣠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠹⠃
⡼⠁⠀⠈⢆⠀⠀⣀⡀⠀⠀⠀⢶⠘⠻⣆⠀⠀⢀⡤⠂⠀⠀⠙⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠂⠀⠀⠀⠁
⢷⡀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠈⢄⣤⣀⣄⣦⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒
⠈⢷⡀⢦⠀⣈⣆⠀⠀⠀⠀⠀⢰⣲⡀⠀⠀⢠⣤⣄⠀⠀⢄⡀⠀⠀⢘⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣠⣤⡶⠏⠀⠀⠀⠀⠀⣄
⠀⠈⣷⣾⣇⠹⣿⣧⠀⠀⠀⢀⣿⢿⠆⠔⠛⠃⠊⠚⠻⣶⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠛⢉⣡⣴⠀⠀⠀⣀⡤⠞⠃
⠀⠀⠘⣿⣿⣆⠹⣿⣆⠀⠒⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠉⠉⠫⠶⡀⠀⠀⠀⠀⠀⢷⣠⣶⣾⣿⣿⣿⠶⠚⠋⠁
⠀⠀⠀⠘⣿⣿⣦⡟⡿⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⠛⠃⠀⠸⣍⠀⠀⠀⠠⣙⣦⣄⠀⠀⠀⢀⣀⡀⢠⠤⠖⠁⠀⠀⣠⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠳⢦⣄⣠⣜⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⡇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⡀⠀⠀⠀⠀⢀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠙⠻⣿⣶⣌⠙⠿⣿⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢣⠀⠈⠻⢿⣷⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠹⢦⣄⣠⣀⡤⡤⢒⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠙⠾⣿⣷⣴⠿⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⡆⢸⠯⡀⠀⣙⡤⠀⠀⠀⠀⠠⣄⣀⣤⣀⣀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣇⣿⣿⣤⢸⣞⠆⠆⣹⡇⠀⠀⠀⠀⠀⠹⣟⡻⢾⣿⣷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⢀⣴⣌⣿⣟⣛⣩⠟⣾⡤⠖⠒⠓⠯⣌⠀⢀⠀⣼⣣⣿⣽⣿⣿⠄⠀⢐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣧⣿⣼⡿⢿⣿⡻⣶⣶⡗⠚⠂⡆⢀⠲⢶⣿⣿⣿⢿⣽⣿⣇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⠀⣠⠤⣶⣿⣿⣿⣆⣀⣽⠛⠉⠉⢯⠹⠁⠓⡲⠖⠏⢴⠞⢃⡼⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡶⠟⠲⢭⡿⠋⣹⣿⣿⠂⠀⢠⣶⣾⣶⣦⣤⣄⣨⡤⠤⠴⣿⡀⣱⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡞⣿⣔⢙⣀⣨⣼⠛⠋⣹⣷⠖⠉⠁⠈⠹⣏⠻⣿⡇⠀⠀⠀⣀⡼⣿⣿⠟⠂⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⣃⢹⣍⣿⣭⣤⠟⠢⢀⣿⡅⠀⢸⡇⠀⠀⢹⣆⣯⣤⡴⠶⢾⡁⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⣯⢘⣿⡇⠤⠄⠀⣀⠞⢿⡧⠹⣿⡇⠀⠀⢸⠟⠉⠀⠀⠀⠀⠙⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠃⠀⠀⠀⢀⣾⢇⠘⣏⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⡿⣸⠄⠙⣤⣤⠀⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢁⡾⠀⢷⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⠤⠀⢀⣄⡀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠛⠓⠘⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣡⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣶⣤⣾⣿⣻⣿⣶⡀⣶⣶⢲⠈⡝⢿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣼⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⣀⠀⣠⣶⣍⠿⣿⢿⣿⣿⣿⣿⣿⣿⠇⠉⠡⠠⣒⣠⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⢿⣿⣿⣿⠿⠇⢰⣱⠇⢻⣿⡿⣿⣿⣿⠻⢯⣽⣣⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⣽⣿⣿⣿⣇⢀⣾⢿⡿⣿⣆⢀⣾⣿⣄⢺⢸⡇⣻⣿⣿⢗⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣡⠛⠋⠉⠁⠙⠋⠛⢿⣾⣿⣼⣿⣿⡟⣾⣿⣿⣿⣿⣏⢻⣿⣟⣵⠛⠉
⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣽⡿⣣⡀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣾⣿⣦⢿⣿⣿⣿⣿⣿⡿⠨⣫⡦
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⢾⣿⣿⡿⢏⣻⣿⣟⣿⣿⣿⣿⣿⣿⢇⣼⢟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢛⠉⠋⠙⣿⣻⣿⣇⠀⠀⠀⢸⣿⡏⣿⡔⠂⣿⡇⠋⢨⣻⠝⠻⠁⠂⢄⣪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠐⣿⣿⣿⣿⣆⠀⠠⣿⣿⡇⢿⡇⠀⣿⡇⢾⣿⣿⣷⣷⣾⣾⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⣧⣿⣿⣿⣿⣿⡆⢰⣿⣿⠁⠌⠀⠀⠨⢁⠀⣭⡙⠈⠁⠩⣭⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⣿⡟⣿⣿⣿⣿⣇⠘⣿⣿⢒⠿⠗⠒⠛⠞⠃⠿⠿⠛⠲⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⢿⣿⣿⠏⠀⠘⠻⠷⠆⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠰⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⡟⠉⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⡀⠀⢸⠀⢜⡿⣿⣿⣿⣫⡾⠇⠀⠀⠀⠀⠘⠏⠀⠀⠀⢀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣰⣦⣶⣼⣷⡄⢀⠁⠠⠟⠛⠉⠉⢹⣵⣦⡀⠀⢠⣸⣵⣶⠖⠄⠀⠌⡠⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠀⠈⠀⠀⠀⠀⠀⠑⠃⠛⠑⠓⠀⠑⠈⠉⠛⠖⠀⠛⠙⠁

⠀⠀⠀⠀⠐⡦⣀⡀⢀⣀⣠⠆
⠀⠀⠀⣠⢤⣵⣧⠀⠀⡈⡿⡖⢦⠤⢤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠉⢻⢜⠀⢠⠡⡏⠉⠁⠀⠑⠠⢄⠀⠈⠉⠉⠉⠉⠁⠀⠀⢀⡀⠤⠊⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⣞⠀⠀⣇⠇⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡐⡩⠄⠀⠤⠤⠤⠤⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣟⠀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠠⠔⠊⡌⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡆⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠦⣀⡀⠤⠄⠀⢀⠔⠂⠐⠀⠤⢄⡀⠣⠀⠀⠀⠀⠀⢀⠴⠂⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠇⠀⠈⠀⠀⠀⠀⠀⠀⢱⠀⢃⠀⠀⣀⠔⠁⠀⠀⠀⢀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⠀⠀⠘⡄⠀⠀⠀⠀⡠⠁⠀⠈⢁⡉⠀⢀⠀⠀⠀⠀⠈⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠀⠆⠀⠀⡈⠉⠉⠁⠈⠁⠀⠉⠙⣄⠀⠀⠀⢂⠀⠀⠀⡆⡃⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣶⠀⠉⢂⠀⠀⠇⠑⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠃⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡎⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡈⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠻⣉⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣊⣰⠎⠀⢎⠡⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⣀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠠⡄⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢧
⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⠟⠛⠁⠀⠐⠀⣄
⠀⠀⠀⠀⠐⠈⠀⠀⠉⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⣴⡦⠀⢪⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⡆⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠺⢿⣷⠀⠀⠈⠪⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⠋⢻⣿⡟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⢀⢀⠀⣀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢄⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⢉⠀⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠀⠀⠠⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠠⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠁⠐⣤⡀⠀⠐⡆⠀⢰⣧⠠⠤⠄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⢰⣶⣶⠚⠀⠀⠁⠀⠸⣿⣆⢀⠂⠠⠈⢃⡀⠀⠀⠀⠀⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡀⢰⣿⣿⣀⠀⡠⠋⠀⡀⠀⣿⣿⠀⡀⠰⡇⠈⣅⠀⠀⠀⢦⣄⣤⣿⡿⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⣄⢘⣿⣿⣿⣿⡟⢹⠃⢀⡶⠀⠀⣿⣿⡄⠀⠊⣿⠀⠸⠀⠀⠀⣼⣿⣿⣯⠀⢠⣿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢰⣿⣿⣿⣿⣿⡿⠅⣸⠀⡆⢶⠀⠀⣿⣿⡌⠀⠀⣿⠀⢠⠠⡆⠸⣿⣿⣿⣷⣠⣿⡟⢐⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡏⠈⠉⢟⠋⢻⣿⣿⣷⡾⠁⠘⡇⢸⡆⢸⣿⣟⡟⠃⠈⣷⠀⠼⢠⡇⠀⣿⣿⣿⣿⣿⣿⠃⣾⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠓⠀⠀⠀⣠⠄⠸⠷⣌⡇⠀⠀⣁⣸⡄⣼⣿⣿⡇⠃⠀⢿⡀⠘⢺⠁⠀⡿⠟⠻⣿⣿⣿⣷⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣄⡴⠶⠞⠁⠲⢲⣀⠈⠳⣤⡀⠰⣾⡇⢹⣿⣯⣇⠀⠀⡿⠀⠀⠃⠀⡘⠁⠀⣹⣿⣁⣉⢛⣻⢿⣾⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣦⣀⠑⠀⣯⣇⣼⣿⣿⣿⣥⣀⡇⠀⠀⡇⠠⠁⢀⡴⠋⠁⠀⠙⠟⠛⠛⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⢳⣀⡗⢿⣿⡟⢯⡟⢿⣽⣷⡀⠀⡇⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡾⠧⣀⠀⠀⡠⣠⡄⠀⣸⣿⣇⣬⠅⠻⢿⣥⣿⢟⣯⢟⡀⣷⡏⠀⢠⠀⠀⠀⠰⠃⠀⠀⢀⠀⠀⠛⣷⣄
⠀⠀⠀⠀⠀⢰⠂⠀⠸⣁⠀⠋⠀⠀⠀⠐⠆⠀⠀⠀⢀⣾⣿⡏⠠⠀⣹⣲⣿⣿⡒⡳⣾⣿⣾⡇⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠁⢄⡠⢾⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⢺⣿⣿⠃⡠⢾⡟⠉⠉⣉⠛⠿⢄⠙⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡙⣧
⠀⠀⠀⠀⡀⠀⠀⠀⠔⠻⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⠊⠀⠌⣷⡇⡟⠶⣶⡣⠄⠡⠈⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⢿⣿
⠀⠀⠖⠀⠡⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⣀⠙⢶⣤⠐⢬⣅⡀⠀⠀⣸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣟⡫⣧
⠀⢐⠃⠀⠀⠀⠁⠀⠀⠆⠀⠀⠐⠀⠀⠀⡆⠀⠀⣾⣿⣵⣿⡤⣿⣯⠀⠠⣿⠀⠀⣸⣿⣼⢶⣽⣿⡗⢄⠀⠀⠐⠀⣀⠀⠀⠀⡇⠀⠈⠈⢰⠹⡇
⠀⠒⠰⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠁⠀⣸⠗⢿⡧⠘⢰⠏⠀⠀⠀⣿⠀⠒⢈⣿⡿⠀⠈⠛⠀⠀⠀⢀⡀⢀⣼⠂⠀⠘⠣⠀⠀⠀⣾⠁⠻⡄
⠀⠂⠀⡄⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⠴⠃⣠⠴⢡⣴⡿⠏⡤⠊⠀⠄⢠⠀⣿⠀⠀⠀⣄⡙⢄⣸⣧⣤⡗⢐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡟⠆⠀⡿
⠀⡉⠀⠀⠀⠀⡆⠀⠀⣠⠖⠁⠀⠀⠀⠀⣴⠞⠋⠁⠐⠊⡁⠀⠀⠀⡿⠀⢛⠀⠀⢠⣿⡿⣾⣿⣿⣌⡛⠿⣄⢰⡀⠀⠀⠠⣶⠀⠀⢸⡿⢃⠀⣹⠇
⠀⠀⠀⠇⠀⠀⢹⡀⠀⠀⠀⠀⢀⣤⣾⠛⣉⣀⡁⣀⣰⣯⡊⣠⠴⢶⠎⡉⡛⠁⠑⠾⣗⠙⠃⣈⣷⡙⠣⠁⠋⠻⣷⣄⠀⠀⠀⢨⣘⠿⣯⣧⣽⣿
⠀⠀⠀⠈⢄⠀⣸⠃⠀⣠⣶⣿⡿⡟⡽⡟⡏⢹⢿⡿⣿⣍⠻⠇⣠⣤⡇⠀⠦⠀⢤⣀⣿⡷⠊⠁⢨⣿⣶⠈⢱⢴⢮⣍⣷⣄⠀⠀⠈⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠘⡗⠁⢀⣴⢿⣿⡟⠁⠀⠠⡏⠇⠀⠀⠐⡘⡮⡁⢤⡩⣤⣼⠀⠁⠀⣌⣀⣿⡥⢒⣥⣾⠏⡞⢠⠀⠀⠀⡜⠁⠋⠻⣷⣾⣿⢟⣽⣿⠁
⠀⠀⠀⠀⠀⠹⣦⣾⣳⣿⣿⠁⠀⠆⠄⠈⠊⢄⠀⢶⣲⣑⣿⣆⠳⡉⠙⠀⡅⢐⢋⣿⡟⣰⣿⡿⠋⣠⠁⠎⡃⡄⡀⣅⠀⠀⡧⢹⣭⣽⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠄⠀⡴⣤⠀⠠⠘⣦⣀⣽⣿⣿⣿⣇⢥⠀⠀⢇⠨⣸⡿⣼⣟⣛⣥⣾⣯⠈⡰⡹⠃⢇⢅⠀⢀⡟⢸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣍⣿⣿⡆⡄⢷⡘⢗⡀⠄⢀⠈⢻⣟⣿⣿⣿⣠⡄⠀⡀⢠⣿⣿⣿⣿⡿⠿⠟⢁⣸⡟⠁⢠⡾⡀⠀⣾⣧⣘⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⡌⠿⣟⢿⣿⣷⣦⣆⣠⢬⣙⠿⢿⣿⡇⢀⣲⠺⣿⣿⣿⣿⣿⠷⠛⣫⡏⣠⣠⠞⠁⡁⣰⣿⢳⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣟⡳⢮⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣴⣶⣿⡿⣿⣿⣿⣷⡾⠷⠾⠟⡉⣠⢠⣷⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣬⣍⣛⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢁⠀⣠⢂⣔⣴⣧⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣝⡛⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⣿⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠛⠉⠀⠀⠈⠛⠷⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣶⣶⣟⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠖⢒⣶⣶⣦⣤⣤⣤⣤⣴⡶⠒⠚⠛⠛⢻⣿⣿⠛⠋⣿⣿⣿⣿⣿⣏⠉
⠀⠀⠀⠀⠀⠀⠀⡾⠁⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠈⠛⠋⠀⠀⢻⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⣤⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⢻⣿⣿⣀⠀⠀⣰⣶⣶⣤⣾⠟⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⣿⣿⣿⣿⡉⠁⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⡀⣠⣿⣿⣁⠀⢈⣹⠶⣤⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠸⣿⡇⢹⣿⠁⠙⠾⣾⡅⠀⠀⠀⠉⠉⠉⠁⣸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠟⠀⢸⣿⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⢻⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠹⢿⣄⡀⠀⠀⠀⠀⣾⡇⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⡿⠟⠋⠡⠚⢻⢱⣍⠭⡙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠉⠝⣁⢀⠄⠀⠚⢡⠸⣧⢀⡄⣤⡀⢢⡀⢈⠐⡢⣄⡀
⣿⣶⣦⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⠁⡸⢡⠃⠀⢀⡞⣾⣾⣿⢲⣿⣮⡻⣦⡓⠀⠀⠈⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣄
⠀⠈⠉⠉⢋⣴⣿⣿⣿⣿⣿⣶⣴⣾⡷⣪⣾⢠⣟⣼⣿⣿⣷⣿⣿⣿⣿⣼⣿⣦⡤⣆⠀⢸⣶⣤⡀⠀⠀⣤⣬⣤⣶⣿⣿⠿⠿⠟⠋⠉⠁
⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣇⣿⣦⣿⣿⣿⣿⣿⣶⡌⠉⠉⠁
⢟⣿⠟⣻⣊⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣯⣾⣶⢟⣭⣭⡌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⡿⠟⠋
⣿⣿⣯⣾⣿⠿⣣⣿⠋⢰⣋⣿⣿⣿⣿⣿⣿⣿⣏⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⡟⠙⠁
⣿⣿⣿⣿⣿⣢⣿⣁⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿
⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣻⣾⠟⢿⣽⣭⣭⣭⣛⣿⣷⣿⣿⡿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡵⠿⠤⡉⠉⠛⠛⠛⣠⣿⣧⢻⣿⡇⢷⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⢿⣶⡄⠴⣿⣿⣿⣿⡇⣿⡜⣮⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣘⢻⣷⣦⣴⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⣀⣠⣤⣶⣵⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⠗⡶⡆⣴⣶⢿⡿⣿⡿⠈⠉⠻⣿⣿⣿⡿⠋⢀⢹⣿⠈⠹⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠻⠄⠅⠐⠐⡰⠒⠲⠶⢠⣄⣉⣙⣀⠉⠀⠉⠀⠀⠶⢴⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠐⠀⠐⠒⠚⠛⠓⠒⠀⠛⠛⠛⠋⠋⠛⠛⠃⠀⠈⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠇⠀⠀⠘⠀⣀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣶⣤⣤⣤⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢗⡐⣂⢁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣿⣿⣿⣿⡿⣿⣏⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⡴⡰⣶⣄⣄⡀⠀⠀⠀⠀⠀⢺⣾⣾⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠛⠁⠈⠉
⠀⠀⠀⠀⠀⠀⢀⢶⡽⡿⡗⠓⠺⢏⢿⣿⢇⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾
⠀⠀⠀⠀⠀⢀⣸⣿⠻⠀⠇⠀⢸⠀⠩⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⡀
⣿⡄⠀⠀⠀⢸⠭⠭⡆⠤⢈⠀⢸⠀⠀⡒⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢄⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⣀⣀⢠
⣼⡆⠀⠀⠀⢩⡭⠭⡇⠀⠸⣶⣾⠀⠀⠳⢶⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣡⣀⡀⠀⢀
⣿⣷⠀⠀⠀⠐⣻⢭⣧⠀⠀⠈⠁⠀⠀⡸⣬⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⢶⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⡄⢾
⢿⡇⠀⠀⠀⠀⠠⡿⡷⣵⣶⣶⡖⣦⣥⣿⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠟⠀⠀⠈
⠊⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢀⣀⣀⣀⠀⣠⣤⣀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢿⣿⣿⡟⠈⢿⣿⣿⠃
⠀⠀⢀⣀⡀⡀⠀⢀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢒⣦⡀⢼⠾⠗⣰⡨⠃
⠀⠀⠘⡉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠛⠉⠁⠈⢻⣱⣦⣄⡀
⠀⠀⠀⠀⠀⠄⣠⣄⠀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠾⡏⣯⣿⠂
⠀⠀⠀⠀⠀⢰⠉⠇⡃⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣻⣇⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠤⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣒⣒⠂
⠀⠀⠀⢀⠀⢠⠀⠄⡀⠀⠠⠘⡇⠀⠀⠀⠀⠀⢀⡀⡀⠴⠒⠲⠲⠒⠤⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠙⠋
⠀⠀⠀⠀⢂⢀⠃⠈⢁⡠⠁⠀⠀⠀⠀⠀⠀⠀⣏⠾⠃⠀⠀⠉⡍⠀⠀⠈⣷⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠐⠀⣴⣶⡄⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠿⠿⠟⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣾⣿⣿⣾⣿⡇
⠀⠀⠀⢀⣤⡀⢀⣀⣀⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠻⠿⠿⠟⣿⣿⣷⣶⡦
⠀⠀⠀⠀⠁⠈⣿⣿⣽⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠀⢸⠀⠀⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢻⠟⠐⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⣀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⠀⠸⠐⠀⢻⣿⣿⡿⠃
⠀⠀⠀⢀⡛⠃⣶⣶⡾⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠑⠂⠀⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠸⣾⠂⢸⣿⣿⣿⡶

⠀⠀⠀⠀⠀⢀⣄⣀⣀⣤⣀⣀⣀⠀⠀⣄
⠀⠀⠀⢠⡄⠨⠤⣼⣏⠙⠛⢁⣿⣿⣿⣼⠤⢄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠤⢤⣤⣶⣶⢶⣶⣤⣤⣤⣄⡀
⠀⠀⠀⠿⣖⢷⣶⣽⣿⣧⣠⣾⣿⣿⣷⣶⢛⣿⣟⠋⠀⢿⣿⣿⣿⣿⠋⠰⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⠐⠀⠹⠿⠃⠈⠻⠏⣿⣿⡟⢿⣦
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢹⣿⣿⣿⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⣀⣈⡛⠁⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⡉⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⡟⠀⠸⠿⠋⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠘⣿⣶⣿⣿⠃⣀⢸⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⣁⣿⣿⣿⣿⣿⣿⡷⠀⠈⠻⠷⠀⠀⠀⢿⣿⣿⡷⠀⠴⠿⣿⣿⣿⠛⢻⣿⣿⡄⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣯⡝⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣷⣿⣦⣼⣿⣿⣿⣿⣯⠀⠀⣠⣤⣤⡀⠂⠀⠈⠻⠿⠃⠀⠀⣀⣼⣿⣿⣶⣦⡈⠉⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡧⡾⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠹⣿⠿⣿⣟⠀⠘⣿⡿⣿⣇⣴⣦⡀⠀⠀⠀⠀⠐⢿⡿⠿⠿⠿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠛⠻⠿⠟⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⢰⠀⠀⠀⠛⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣆⣴⣶⣦⠀⠀⠀⣶⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠢⣌⢢⢠⣶⣿⣿⢇⡄⠀⠄⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⡾⣿⣿⠏⠀⣷⣄⠀⠙⠁⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢻⡟⠿⠏⢻⣾⣭⠆⠘⠛⠛⠒⠒⠶⠶⠦⢤⡤⠴⠛⠉⠀⠹⡏⠂⢀⡸⣿⣇⠀⠀⠀⠸⡇⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢧⣾⣷⣨⡿⠆⠀⠀⠀⣾⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠙⢟⠃⠈⠠⠀⣼⠁⠀⡌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠙⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠇⠀⡆⠀⠀⢃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡃⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⣰⠀⢸⠀⠀⠀⠘⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡇⢠⠈⢃⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢒⣠⠂⠀⣰⠁⠀⠃⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⢠⢱⣿⣅⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠙⠋⠀⣼⣿⡄⠺⠆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉






⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠀⠀⠑⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡸⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⠀⢶⠁⣖⣒⣄⣀⠀⡠⠒⢩⠃⢀⡴⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⢧⡀⠤⣚⠉⠩⡱⢶⣿⣶⡴⣬⠾⣯⣹⢦⠑⡀⢫⠀⣠⠾⠖⢛⠀⠀⠀⣰⠃⣠⠖⠒⠒⠒⠲⠶⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠙⠲⠤⢍⣰⠧⣸⢏⡜⢐⠻⣦⣶⡼⢸⠋⢱⠟⠉⣵⣠⠴⠦⠤⢴⣎⡡⠊⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⢠⡎⠼⠳⣌⣹⣤⡜⠢⣜⣩⠔⢃⣴⢯⡤⢴⣃⠆⢀⣠⠴⠊⠁⠀⠤⣀⣖⠀⠛⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠼⡖⠛⢙⣿⠘⢠⠓⠤⢄⡨⢻⢫⠹⠦⠠⠤⡽⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢄⣀⣀⠀⢀⡨⢻⣅⠘⠴⠁⠀⠀⠀⠀⠸⣈⢠⠀⢀⠶⠁⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⣤⡤⠴⠚⠁
⠀⠀⠀⣠⠤⠤⠶⠚⠉⠁⠀⠀⡀⠀⠀⡈⠀⠀⠈⠘⢣⠦⡀⠀⠀⠀⠀⠀⠀⠁⢠⠃⢀⠤⠀⠀⠀⢰⠏
⠀⠀⠸⣇⠀⠀⠀⠠⠆⠲⠄⠊⠃⠒⠖⠁⠀⠀⠀⠤⢀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡎⢠⣿⣿⣿⡥⠀⢸⡄
⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣆⠐⣲⣿⣷⡄⢧⠀⠀⠀⠀⠀⢠⠃⠀⠛⠛⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⣤⠤⠖⠋⠁⠀⠈⢻⡉⠛⠋⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡼⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⢸⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠹⡀⣰⢃⣀⣀⣀⡀⠠⠤⠜⠦⡀⠙⢢⠀⠀⡸⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢹⡷⣁⠀⠀⠀⠀⠀⢀⣼⠀⢸⠀⠀⡇⢠⠇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣟⢱⠘⠷⠆⠀⠀⠀⠙⠁⠀⢸⠀⢀⡗⠁⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢹⠈⡇⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⣸⠁⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⢧⡘⠒⠚⠋⣉⣉⣉⣭⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠻⠯⠤⠤⠤⠤⠭⠭⠭⠽⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣤⣭⣙⣒⣒⣒⣒⣒⣒⣒⣒⣚⣩⣬⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠁⡏⢹⠉⡏⢹⠉⡏⢹⠉⡇⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⠾⣦⣧⣼⣤⣧⣼⣤⣧⣼⣤⠷⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⠿⠿⠿⠿⠿⠿⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠶⠶⢶⡶⠶⠶⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠻⠶⠶⠶⠂⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠀⠀⠀⠀⢀⡴⡖⢶⡄
⠀⠀⠀⠀⠀⢀⡴⠶⣤⣤⣄⡀⠀⠀⣿⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⣿⡀⠀⠀⣴⠟⢮⣁⣼⡇
⠀⠀⠀⠀⠀⢸⣄⣀⣸⠐⠚⣻⠀⠀⣿⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⠆⠘⣧⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠿⠋⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣉⣸⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁

⠀⠀⠰⡙⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⢋⠆
⠀⠀⠀⠱⣀⣽⣿⣿⡏⠉⠉⢹⣯⢀⠎
⢾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⠷
⠀⠈⠛⠿⣿⣿⠟⣾⡄⢠⣷⠀⠀⢸⣿⡿⠥⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢀⣏⡥⠤⠿⠤⠤⠯⠤⣤⣸⣿⣷⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⡴⢋⣤⡄⠀⠀⠀⠀⠀⠀⢠⣤⡉⢿⣧⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠐⡇⠈⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠁⢸⣿⣿⣶⣶⣤⡀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠉⠉⢻⣿⣿⣿⣿⣿⣿⣷⠦⣀⣀⠀⠀⢀⣀⣤⠿⠛
⠀⠀⠳⡄⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⢹⣿⣿⡿⠃⠀⠀⠀⠀⠻⢿⣿⣿⠟⠋⡿⠉⠒⠚⠛⠛⠛⠋⠁
⠀⠀⠀⠈⠓⠭⣟⣳⣶⣶⣾⣛⣭⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣦⣴⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠉⠙⠋⠁⠀⢀⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⡟⠋⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⢻⠀⠀⠀⡜⠉⠉⠉⠉⠛⠛⠛⠛⠉⠙⣯⣡⣄⡤⣔⡇⢸⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇⠸⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠹⡈⠀⢸⠙⡄⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣾⠀⠀⣷⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣾⠀⢻⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⡆⠀⣀⠀⢰⣱⣗⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢲⡀⠀⠀⠀⠀⣀⡀⠀⣠⠤⢏⠉⠲⢼⡄⢰⡷⠋⠁⣹⣤⣟⠒⠃⠀⠀⢠⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢧⣸⠑⢦⡞⠁⠈⣾⠁⠀⢎⠉⠓⢪⡗⢻⡴⠒⠻⢥⡎⣨⠤⢄⠀⣠⠏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠙⣄⠈⣆⣀⡴⣛⡦⠤⣾⠟⠋⣩⡟⢻⡉⠻⣲⠖⣻⠷⠶⡞⠚⠁⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣠⠟⢾⠁⠀⢹⠀⠀⠙⡖⠊⢰⠁⢀⡗⠒⠉⢺⠀⣧⠄⠜⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⣧⢤⡜⠓⠤⠚⠳⢤⣚⠁⠀⠈⠓⣋⡤⢤⡀⠈⠒⠉⣇⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢒⣛⣶⡾⠀⠀⠀⢀⠞⠉⠈⠙⢦⢀⠞⠁⠀⠀⠘⡆⠀⠀⠘⡶⠯⢭⣉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡴⢊⣩⠄⣰⠃⠀⠀⠀⢸⡀⠀⢰⣷⡌⡿⣰⣶⡄⠀⢠⠇⠀⠀⠀⢻⢦⡰⢬⣙⣦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⢉⣉⡤⠞⣿⠀⠀⠀⠀⠀⢧⣀⣈⣻⣃⣇⣻⣟⣀⣀⡞⠀⠀⠀⠀⢸⡄⠙⠦⣄⣀⣀⣀⣸⠆
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⡇⢀⣠⠴⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠲⢤⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠸⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠦⠤⠤⠤⠤⠤⠤⠶⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣖⣿⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣯⣿⣿⣿⣿⡿⣾⡟⣿⡏⢾⡿⣿⣿⣿⡏⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣉⠙⣹⠁⣿⢿⣫⢯⡟⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡜⣿⢸⣿⡼⣿⡏⣿⠀⣿⠀⡟⡾⠀⡾⢀⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⢿⡄⢿⡇⢻⡇⢿⠀⣿⢠⡇⡇⢸⠇⣰
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢿⡿⣏⢷⡈⢧⠘⣧⠘⡇⢸⡆⣿⢰⣵⠀⣾⡴⠃⡆
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢧⡙⢌⠫⣷⠘⣇⢹⣆⢿⣸⣇⣿⣼⣾⣵⣿⡷⢸
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⢦⠑⠈⢳⡈⢧⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡅
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠷⠦⣀⠀⠁⣽⣾⣿⣿⣿⣿⣿⠿⢻⠿⢿⡿⣿⣿⣦⣀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⢬⡀⠀⠀⠑⣶⣿⣿⣿⡿⢏⡁⠉⡄⠀⡂⢀⡀⠈⢋⠝⣿⣷⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⡀⠀⠀⠀⢀⣿⣿⣿⣿⢧⣄⣑⣢⣼⣿⣿⣿⣿⣷⣯⠈⠉⢽⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠈⠭⠀⠀⣬⣽⣿⣿⣷⠦⠭⢽⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠐⠫⣿⣇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣭⣥⠤⠤⠀⠸⣿⠿⠿⠟⠚⠻⠻⣿⡿⠿⠿⣿⠿⣿⣿⣿⢧⣴⣾⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣶⠒⠂⠀⠀⢿⢂⣷⣷⣵⢄⣴⢋⣿⣿⣍⣽⣾⣿⣿⣿⠯⢷⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⡊⠁⠀⠐⠀⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⠓⠫⣛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣾⡅⢤⣀⡄⣊⡾⢻⣿⣿⣿⢿⢿⣿⣿⡏⠙⢄⠀⠸⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⣫⣾⠘⠁⢠⠃⠃⡀⠀⠈⡅⠈⠁⡀⢀⡻⣮⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠆⡀⡾⢀⢀⡇⠀⡄⣸⡴⣤⣼⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣽⣿⣿⣿⣿⣿⡧⣷⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⣠⣄⠀⣿⡀⠀⠀⠀⡠⢺⠆⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⡀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠙⠋⢀⡘⠇⡴⠒⢲⠀⣿⣀⠤⢄⡀⠀⡠⠤⠤⡀⠰⡹⡄⡘⣷⡀⢠⣤⠀⢾⡷⢀⢃⢀⠅
⠀⠀⠀⠀⠀⠀⠈⠰⣔⠶⡁⠈⢲⠃⢀⡠⠾⠟⠀⠠⠀⢱⣼⠀⠀⠀⠘⠆⠼⢃⠀⣿⡇⣀⡄⠀⠀⠀⣸⣸⠏⠀⠄
⠀⠀⠀⠀⠘⠇⠀⠐⢸⠛⠛⠢⣬⣧⡎⠀⠀⡜⠂⠀⠀⣼⣿⣄⠀⠀⠚⡄⠀⠈⣇⣿⢏⡼⣥⠋⠉⣴⣵⠏⠤⠂
⠀⠀⠀⠀⠀⢀⠤⠊⠉⡕⠂⠉⡝⠁⡣⠀⢀⡅⠀⠠⠊⢸⣿⠈⠂⠀⠀⣄⠀⠐⠁⠙⣟⠀⠀⠀⠀⠋⠉⢱⠀⢠⣄
⠀⠀⠀⠀⠀⠈⠙⠻⢿⢷⡖⠈⠁⠀⠀⠀⠘⡀⠀⡀⠀⣿⣿⠇⠀⡀⢀⠄⠀⠀⠁⠐⠈⠑⣤⣄⠀⠀⠐⠣⡀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠠⣊⣴⢿⠀⠀⠘⣤⣀⠀⢐⠁⠈⠁⠀⢸⣿⠀⠀⠀⠀⠱⠀⢀⠤⡈⠀⠀⡸⠋⠀⠠⣀⣠⣃⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠛⠉⠁⡜⠳⢄⣘⠀⢨⡀⠀⠐⠂⠀⠀⢾⣿⠆⠀⠄⢢⠀⠀⡇⠀⢘⡀⠔⠙⡄⢦⣀⣨⣭⠟⢩⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠄⡀⠘⠀⠐⠄⠀⢸⠀⠀⠀⣸⣿⡄⡀⠀⡼⠀⠀⠆⠀⠈⠀⡤⠐⡧⠚⠫⡒⠲⡀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⢻⣿⠋⠀⠀⠘⢄⠀⠀⠀⠁⠈⠀⠀⣅⡰⢦⠍⣉⣀⡀⣠⠄⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡆⠀⠀⢀⠀⢀⠎⠀⠒⠄⡴⣿⣿⡷⠤⠐⠂⠈⣆⠀⣀⡃⠀⠘⠑⠋⢷⣾⡿⠟⣻⣿⣋⣀⣀⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⠀⠉⠉⣄⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⣀⡋⠉⠀⠝⠈⣤⣅⠤⠈⠁⠉⢫⡉⠉⠐⠶⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢀⠔⠉⠈⠑⢆⠀⠐⢻⣿⠓⠀⢠⠊⠀⠈⠱⢄⣀⡤⠻⠛⠢⢄⣸⠷⣦⣘⣄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⠀⠁⠀⠀⠈⡄⠀⢸⣏⠀⠀⠆⠀⠀⠀⠀⢠⣉⠀⠀⣇⢀⣠⡦⣙⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⣄⠀⠀⢀⡜⠘⣄⠀⠀⣠⠤⠄⠒⠁⠀⠉⠍⢩⡅⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⠧⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡾⠁⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡞⠁
⠀⢀⣤⠶⠶⠶⠶⠶⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟
⢠⡟⠉⠢⡀⠈⠠⡀⠀⠈⠙⠶⣄⣿⠛⠒⠒⠒⠓⠛⠛⠋⠉⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⣿⢧⠀⠀⠈⠳⣄⠈⢦⡀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⠘⣆⠀⠀⠀⠈⠳⣄⠙⢦⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠸⣆⠈⢢⡀⠀⠄⣀⠈⠳⢄⠙⢦⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠁⠀⢀⡾⠁
⠀⠘⢦⡀⠙⢦⡀⠀⠀⠀⠀⠑⢄⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠙⢦⣀⠈⠓⠶⢤⣤⣀⣤⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣤⠶⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠉⢉⣽⠟⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣠⠾⠋⠁⠠⠄⠀⢀⡤⠞⠉⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⠀⢀⣀⣠⠴⠛⠁⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⡠⠚⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⠦⠤⢤⣄⣀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⣠⠖⠁⠀⣠⠖⠉⠀⠐⠀⠀⣠⠎
⠀⠀⠀⠀⣠⣴⡛⠛⠲⢤⣀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⢴⣟⡁⢀⣠⠞⠁⠀⣀⣀⡤⠖⠋⢁⡼
⠀⠀⠀⣰⠏⠈⠙⠲⢦⣀⡈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠈⠉⠉⠉⠉⠉⢉⣀⣠⡤⠶⠋
⠀⠀⠀⣿⣄⠀⠀⠀⠀⠈⠙⠲⢤⣀⠈⠙⠲⢤⣀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⢹⣏⠑⠦⣄⡀⠀⠂⠀⠀⠈⠙⠲⢤⣀⠈⠙⠲⢦⣤⢿⡆
⠀⠀⠀⠀⠻⣆⠀⠀⠉⠓⠒⠤⠤⣀⣀⣀⣀⣬⠽⠶⠒⠉⠀⢀⡿
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⣀⠀⠀⣀⣀⣀⣤⡴⠞⠋
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠
⠀⢸⣿⡿⣛⢿⣿⡄⠀⠀⣰⣿⡉⣽⣦⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠐⠆⡄⢂⠰⠖
⠀⠘⣿⡇⠀⢸⣿⠃⠀⠀⣏⠉⣁⣉⣹⡆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠈⠷⠤⠾⠄⠀⠀⠀⢿⣿⢿⣿⢿⠇⠀⠀⠀⠀⠀⠀⢸⡻⣢⣶⣿⡇⠀⠀⠀⠀⠀⢶⣶⣶⣦
⠀⠀⠀⠐⠒⠚⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠘⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⢻⠛⠁
⠀⠀⠀⢠⣤⡄⠀⠰⠔⠁⠀⠈⠴⠇⠿⠸⠗⠗⠸⠾⠇⠿⠸⠸⠂⠷⠿⠇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠰⠠⠐⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢦⣄⣀⣴⠆
⠀⠀⠸⠀⠶⠐⠇⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⣤⡾⠼⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡽⣿
⠀⠀⠠⠤⢀⣠⡄⠀⠘⣧⠀⠀⢸⡟⠀⠀⠶⡞⠀⠂⠈⣷⠦⠀⠀⠀⠸⢷⣄⠀⠀⠀⠀⢿⡇⠀⣿
⠀⠀⢠⣤⣤⣾⡆⠀⠀⠉⠀⠀⠘⠀⠀⠀⠿⣣⣄⣀⣤⡟⠏⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠘⣇⣀⠋
⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⣻⠛⠋⠀⠀⣤⣤⠀⣛⣟⠀⢠⣤⠄⠀⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠋⠁⠀⣠⣴⣦⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠺⣿⣿⣿⣿⣦⣤⣤⣶⣿⣿⡇⠀⠀⠀⠉⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠻⢿⠿⠻⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿⠿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⠀⠀⠰⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⢀⣶⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠛⠙⠛⠛⠶⣤⣀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠛⠛⠛⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢠⡶⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣆⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢠⡟⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⠀⠹⣆⣀⣀⣀⣀⣀⠀⣿⢸⡇⠀⢀⣀⡼⠁⠀⠀⠀⠹⣆⡀⢀⣠⣤⣄⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⠉⠉⠉⠉⠙⣷⣿⢸⡇⣼⠟⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠉⠛⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠸⠿⢸⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣴⠂
⣿
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠀⣤⣤⣄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣧
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⣸⣿⡿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⢳⠦⠊⠙⠿⣿⢿⡀
⢸⠀⠀⠀⠀⠀⢾⣿⣶⣶⣶⣦⣤⣄⠀⠀⠀⠘⢿⣿⣤⣾⣷⣶⣶⣿⣶⣦⡈⢃⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣴⡄
⢸⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠠⠈⢻⣿⣿⣿⣿⠋⡽⠋
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣇⡾⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⡤⢿⣟⡻⠏⠊
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣶⡟⠉⠙⣿⠏⠸⣿⣿⡯⢀⣹⣿⣿⣿⠗⠂
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠉⠃⢹⠀⠐⣿⠁⠀⠀⠀⢿⡿⠟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁⠀⢀⠀⣴⣿⣷⡀⠆⠀⠀⠀⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢿⡌⠀⠈⢿⠀⠀⠀⡚⠃
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⢀⣀⣀⣀⣄⣀⠐⢠⡆⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣷⠹⠋⠋
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡜
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⠿⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣀⣿⣿⣿⣿⣧⣶
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠻⠾⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠓⠿⠿⠿⠿⠿⠟⠟

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⣤⣤⣤⠤⠤⢤⠀⠀⠀⠀⠀⣄⣀⣀⣀⡀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣍⢰⠃⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀⠤⠤⣄⠀⠀⠀⠀⠀⠀⡇⠀⢾⣉⣤⣀⣉⡷⠀⢸⠀⠀⠀⠀⢰⠃⠉⠉⠁⠀⠀⠉⠉⠈⢧
⠀⠀⠀⠀⣠⠤⠤⡀⢠⠇⢸⠀⠀⠀⠀⠀⢀⣀⣿⣀⡴⣠⣶⣠⣼⣤⡀⠀⠀⠀⠀⡇⠠⠒⠛⠛⠛⠉⠀⢤⢸⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠀⠀⠀⠀⡼
⠀⠀⠀⠋⡁⠀⢀⡙⠚⠁⢸⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠛⢈⡠⠋⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠐⢸⠀⠀⠀⠀⠀⢸⡗⠒⠒⠚⠒⠒⠒⢾⠁
⠀⠀⠀⢀⡉⠉⠉⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣄⣀⣸⠀⠀⠀⠀⠀⠀⣧⠀⢠⠏⠳⡄⠀⠼
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄
⠀⠀⢘⣙⣉⣋⣉⣋⣙⣋⡛⢳⠀⠀⠀⠀⣠⠤⠤⡄⠀⠀⠀⢠⡴⠲⣆⠀⠀⠀⠀⠀⠘⣶⢴⣦⣶⣴⣶⠟⠀⠀⠀⠀⠀⠀⢤⢸⡀⠀⠀⠀⢸⡡⡄
⠀⠀⢸⡏⡿⡏⡿⠿⢿⢹⢻⢸⠀⠀⠀⣼⢹⠀⠀⣷⠤⠤⠤⣼⠁⠀⡏⣷⡄⠀⠀⠀⠀⣷⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠉⣇
⠀⠀⢸⡯⡏⡇⡏⢹⢹⢸⢸⢸⠀⠀⠀⢹⣼⡄⠀⡟⠉⠉⠉⢹⡂⠀⣧⡏⠀⠀⠀⠀⠀⣿⠽⣏⢱⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡶⡀⠀⢸
⠀⠀⢸⣙⣓⣓⣓⣚⣒⣚⣚⣸⠀⠀⠀⠀⠈⠓⠚⠃⠀⠀⠀⠘⠓⠒⠋⠀⠀⠀⠀⠀⠀⢸⠖⠉⠉⠠⢼⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⣧⠀⢸
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⠀⠘⠀⠉

⠀⠀⠀⢀⡔⠲⣖⣒⠒⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣤⣤⣤⣀⣀
⠀⠀⢀⡞⣄⢘⠀⠉⠀⢀⠀⣳⠀⠀⠀⠀⠀⠀⣠⠴⠚⢋⣉⣥⠽⠷⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠶⠶⠶⠶⠶⣶⡞
⠀⠀⠀⢳⠮⠯⣥⠤⠭⡥⢾⣁⡀⠀⠀⠀⠀⠘⣧⠶⠯⣭⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣳⡟⢻⢿⣁⣄⡀⠀⠀⠀⠀⠀⣼⣡⣄⣀⣀⣀⠀⠀⢸⡆
⠀⠀⠀⢸⠀⡇⠀⡇⠀⡇⢸⠓⢸⠄⠀⠀⠀⠀⣉⣲⣦⡤⣤⣍⣙⡇⠀⠀⠀⠀⠀⣿⢹⡏⣿⣘⡿⣾⣿⡍⣿⡆⠀⠀⠀⠀⡇⢠⣤⡀⣀⡀⣀⣀⢸⡇
⠀⠀⠀⢸⠀⡇⠀⡇⠀⡇⢸⢀⢸⠀⠀⠀⠀⠀⠻⣤⡤⠶⠶⢾⣯⣅⠀⠀⠀⠀⠀⠻⠷⠶⠋⠈⠁⠘⠷⠶⠟⠁⠀⠀⠀⠀⣧⠈⠀⠉⠉⠁⠉⠉⢸⡇
⠀⠀⣴⠉⣷⣇⣀⣇⣀⣣⡿⠒⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣤⣭⣍⣉⣉⣉⡽
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣏⣹⠆⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⣀⣀⣀⣀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⢷⠿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢨⢷⡀⠀⠀⠀⠀⠀⠀⠸⣟⡻⢡⢎⣕⣶⣖⡊⡳⡄⢸⢿⠀⠀⠀⠀⡤⠒⠋⣚⣗⡛⢛⠦⡀⠀⠀⠀⠀⠀⠀⡾⢯⠼⡇⢰⠯⡏⢷
⠀⠀⠀⠀⠀⠤⠿⣤⡿⠀⠀⠀⠀⠀⠀⠀⢸⣧⡇⣾⠙⣿⠍⣻⣿⣿⣾⢸⠀⠀⠀⢸⡁⠀⠀⠀⠉⠀⠈⠁⡇⠀⠀⠀⠀⠀⠀⡇⣟⡇⡇⢸⢸⣿⢸
⠀⠀⠀⠀⠀⠀⣞⠸⠦⠤⡄⠀⠀⠀⠀⠀⢸⣿⠳⡙⢙⢶⡋⡡⣪⠏⢹⣿⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣇⣿⣷⡇⢸⣼⣿⡼
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠉⠓⠚⠛⠋⠁⠀⠸⠿⠀⠀⠀⠀⠀⠙⠦⡤⠶⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠈⠻⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⡀⠀⢀⣀⣠⣤⣤⣄⣀⡀⠀⢀⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣇⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣸⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣉⣉⡉⢹⡞⠛⠻⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢳⡏⢉⣉⣉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠉⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠁⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⡇⢀⠔⠒⡄⠀⢿⣿⣿⡏⠀⢠⠒⠢⡀⢹⠒⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠘⢷⡶⠏⠀⣾⣿⣿⣇⠀⠹⢶⡾⠃⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣠⠴⠿⠿⠿⠿⠦⣄⠀⠀⠀⡼⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣤⣀⣳⣀⣚⣀⣀⣓⣀⣟⣀⡤⢾⢱⡋⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡷⠾⠿⠛⠁⠀⠀⣸⣿⡷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢀⣤⣾⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⡄⠀⢻⣿⣿⢿⡇⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⡇⠀⠀⠀⠀⣾⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⠃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣷⡀⠀⠀⢀⣿⠀⠀⠀⠀⣿⡀⠀⠀⢀⣾⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠟⠋⠀⠀⠀⠀⠙⠿⠿⠿⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⢛⣛⣛⣛⣛⡛⠛⢛⣛⣛⣛⣛⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣏⠀⢠⣿⣿⣿⠠⡏⠀⢠⣿⣿⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠈⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡔⠚⢛⣒⣳⣦⢀⡖⠛⢛⣚⣲⣦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠳⠦⠼⠿⠿⠛⠀⠳⠤⠾⠿⠿⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⣠⠤⠤⠤⢤⣄⠀⣠⠤⠤⠤⢤⣄⢸
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣼⣤⣡⣀⣀⣛⣛⣛⠘⢇⣀⣸⣿⣿⡿⢸
⠀⠀⠀⠀⠀⢰⣿⡿⠿⢿⣿⣿⡿⠿⢿⣿⣿⡿⠿⢿⣿⣿⣿⠿⢿⣿⣇⣀⣀⣀⣀⣀⠀⢸
⠀⠀⠀⠀⠀⢸⣿⣠⠞⢁⣿⣿⣠⠔⠉⣿⣿⣁⠔⠋⣿⣿⣇⠴⠋⣿⣿⣿⣿⣭⣭⣽⣷⢸
⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣶⣾⣿⢸⣿⣿⡟⠛⠛⠁⢸
⠀⠀⠀⠀⠀⢸⣿⠟⢉⡿⣿⣿⠟⢉⡿⣿⣿⠟⢉⡻⣿⣿⡟⠋⣹⡟⠘⠛⣛⣷⣶⣖⣦⣸⣀⡀
⠀⠀⠀⠀⠀⢸⣿⣖⣉⣠⣿⣿⣶⣋⣠⣿⣿⣶⣋⣀⣿⣿⣷⣊⣠⡇⠀⡞⠉⠀⠀⢸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠈⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⣷⣀⣀⣀⣈⣭⣭⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣄⡀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢃⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢃⣾⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣾⣿⣿⣿⣼⣿⣿⣿⢃⣴⣶⣶⣶⣶⣶⣾⡟
⠀⠀⠀⠀⣴⣎⠳⡄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢃⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⡴⢋⣶⡆
⠀⠀⠀⠀⠸⣿⣧⠹⡄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡼⢡⣿⡿
⠀⠀⠀⠀⠀⢹⡇⣶⣦⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣠⣶⡆⣿⠁
⠀⠀⠀⠀⠀⠀⢿⣌⢻⣿⣦⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢀⣠⣾⣿⢋⣼⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣧⡙⢿⣿⣿⣷⣶⣤⣀⠀⠀⠈⠙⠿⠟⠋⠀⠀⢀⣠⣴⣶⣿⣿⣿⠟⣡⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣎⠻⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⡿⢋⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣬⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠁⠀⠀⠙⠉⠉⠉⠉⠁


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

⠀⠀⠀⠀⠀⢶⡀⠀⢀⠀⠀⢠⡆
⠀⠀⠀⠀⣀⣘⣼⡉⠀⠀⠙⣯⡤⣤⡀⣀⡀
⠀⠀⠀⠈⠣⠯⣏⡇⠀⢠⢉⡗⠓⠊⠀⠸⣉⡉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠉⠉⡩⠋⠉⠁⠢⣄
⠀⠀⠀⠀⠀⠀⢡⠇⠀⠘⡄⡇⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⢀⠄⢒⣒⡈⠉⠀⠀⠀⠀⠀⠀⠟⡄
⠀⠀⠀⠀⠀⠀⢸⡦⠀⢄⡟⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⡠⢪⠊⠁⠀⠀⠉⠉⠉⠉⠐⡄⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠘⠦⣤⢦⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠀⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡑⠤⠐⠊⠱⠀⠀⠎⠁⠀⠈⠉⠉⠒⢄⠘⡄⠀⠀⠀⠀⢀⠔⠁⠀⠀⢠⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢀⠃⠀⠘⡀⠀⠀⠀⠀⠀⠀⡸⠀⢰⡀⣀⡠⠔⠁⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠸⡀⠀⠀⠡⡀⠀⠀⠀⢀⠜⠀⠀⣀⡀⠤⠤⠠⡀⠀⠀⠀⠀⡆⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠒⢣⠀⠀⢠⠉⠉⠁⠀⠉⠉⠉⠉⠙⢦⡀⠀⠀⠘⡄⠀⠀⠀⡇⡁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢱⠂⠈⠉⡆⠀⠀⡇⠑⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡏⠆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠋⡇⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣷⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡘⢠⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢑⣶⠟⢤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⢄⠔⠁⡜⠢⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠉⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⣿⣷⣿⣿⡿⠿⠿⣿⣿⣿⣿⡆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⡿⠿⠇⣿⠀⠿⠿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣇⠛⠛⣿⠟⠛⢂⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣇⠛⢀⣿⣿⣿⣿⡇⠀⠀⣿⣧⡴⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢃⣠⣶⠟⠉⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⣀⣠⣤⣤⣄⣀⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠈⠉⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⣄⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⢀⣀⣀⣮⣤⠤⠀⣀⣀⢤
⠀⠀⠀⠀⠀⢛⣿⣿⣿⡟⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⠀⢠⠈⣁⠆
⠀⠀⠀⠀⣾⣏⣍⣿⡏⠀⠀⢀⣀⠀⠈⠑⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠸⠿⠿⠟⠋⠀⠀⠀⠉⠘⠁⠀⡀⠘⢿⡿⠿⢿⣿⣿⠀⠀⠀⠀⠻⠿⠟⠂⢄⠀⠀⣠⠪⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠀⠀⣴⣶⣄⠀⠀⠀⠣
⠀⠀⠀⠘⠀⠀⢠⠀⠉⡁⠐⠂⠠⢀⡈⠀⠀⣾⣿⣷⡀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⣠⠜⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠛⠿⠿⠿⠀⠀⣀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢒⣨⣽⡆⠀⠀⠀⠈⠻⣿⣿⡿⠀⠀⣼⣷⠀⠀⠀⠀⠀⢸⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⢿⣿⠃⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠋⠀⠀⠀⡈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠰⠒⡄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠇⠀⡀⢀⠁⠀⠀⠀⠀⠀⠋⠐⠂⢻⠀⢸⢱⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠀⠀⠰⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡌⠈⢦⡎