Swine Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄⠄⠀⠀⡀⠀⠀⠀⠀⠄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⠀⣠⣾⣃⢄⣀⠦⠐⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠁⠀⠨⠛⣶⣿⣿⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠅⠀⠀⠀⢰⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠖⠀⠒⠀⠀⠑⢫⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⠀⠀⠀⠀⠈⣳⣿⣿⣿⣷⠀⠀⢴⣂⡴⠂
⠀⠀⠀⠀⠀⠀⢀⣿⡟⣷⠂⠀⠀⠀⠐⣿⣿⣿⡧⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠠⠄⣰⣿⣿⣿⣿⢇⣀⣤⣀⠋
⠀⠀⠀⠀⠀⠀⣜⣿⣷⣿⣧⣾⣶⣶⣄⣽⣿⣿⣿⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠛⠉⣿⣿⠃⢈⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⡀⠀⠀⠀⠀⠈⠀⣿⣿⠟⠁⠀⠀⠀⠀⠐⢦⡄⠀⢸⣿⡟⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠘⣿⣽⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢿⣿⣷⣦⣂⠀⡐⠀⠰⣴⣿⡿⠂⠀⠀⠀⠀⣀⣀⠸⣷⣀⣿⣇⠀⠀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠁⣿⣿⣿⣿⡄⠀⠉⠙⠻⢳⡦⡀⠠⠈⣿⣿⣿⡟⢠⣴⣿⣿⣿⣿⣷⣿⣿⣿⣆⡀⣿⣾⣴⣮⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⢸⠹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢻⣤⠈⡾⡛⣿⣿⣿⣿⠁⠀⠀⠈⠉⠉⠙⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⣸⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡏⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣽⡇⠈⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⠃⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢇⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃
⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⢤⢤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⢠⡖⢦⣀⣤⡶⠛⠉⠐⠉⠉⠁⠀⠀⠈⠀⠉⠉⠛⢉⣿⣽⣦⠁⠀⠐⢲⣦⣤⣀
⠀⠀⠿⣿⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡀⠀⠀⠀⢿⣿⠛⣿⡗⠿⠂⢀⢀⡀
⠀⠀⢰⡇⢠⠀⠀⠀⠀⠀⠈⠶⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠻⠈⡇⣰⣌⠻⣶⣾⠓
⠀⠀⢸⠁⣄⠀⠀⠀⡄⠠⣦⣶⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⡀⢰⡷⠙⣿⣿⣿⣇
⠀⠀⠈⣿⠘⠃⠠⡀⠀⢠⣾⣿⣛⣛⣂⡂⠀⠀⠀⠀⣴⣶⣿⢀⠀⠀⠀⢴⠃⣸⣷⡴⣹⣿⣱⠯⣤⡾⠂
⠀⠀⠀⠘⣿⡀⠀⢴⣴⣿⠏⠈⠙⠻⠿⠽⠿⠤⠤⠬⠼⠿⢧⣴⠀⠀⠀⠸⠟⠛⠉⠛⠛⠛⠉⠉⠉
⠀⠀⠀⢀⠙⠡⢴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄
⠀⠀⠀⠈⠀⠀⠀⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡟⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢦⠀⠀⠀⡀⠀⢀⠀⠀⠀⡀⣀⢻⠀⡀⠀⢀⠡⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠿⠁⠄⠙⠠⠍⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠓⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⡀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⡄⠘⣿⢿⠿⠟⡛⠩⡿⠋⠻⠄⠈
⠀⠀⠀⢤⠟⠉⠀⡄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠈⠀⠠⠴
⠀⠀⠀⠈⠖⠓⠈⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠣
⠀⠀⠀⠀⠀⠈⠀⠀⣀⣀⠀⠀⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠶⠤⠆
⠀⠀⠀⣠⣄⣄⣀⠀⠀⠈⠂⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣷⠦⢤⠀⠀⠀⢄⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠉⠉
⠀⠀⠀⠉⠻⠿⠿⠉⠉⠛⣃⢀⡀⢀⠼⡶⠄⢀⠘⢛⡻⠿⣿⣷⣄⠀⠀⠀⠀⢀⣀⣤⣶⠀⠀⢀⡆⢤⠔
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⡆⠐⠋⡛⣿⣿⣷⣶⣬⣥⣽⣛⡁⠀⠈⠁⠉⠉⡆⢰⣿⣷⣄⡈⠓⢦⣄⡀
⠀⠀⠀⠀⠀⣀⣄⣀⣰⣙⠛⡛⣿⣿⣿⣧⢹⡓⢀⣾⣛⣿⣿⣿⣿⢿⣿⣿⣶⣿⣶⣶⣦⣇⢾⣶⡻⣿⣿⣷⣤⣬⣽⠷⠄
⠀⠀⠀⠀⠀⠲⠿⠿⠿⡿⠶⠴⡶⠝⠻⣿⣿⣇⣲⡿⣙⡿⣟⡻⠓⠻⠶⣥⠟⣭⣿⣿⡯⣽⢒⣀⣉⠛⠛⠟⠛⠓⠒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠒⠀⠀⠀⠐⡀⣀⣤⠄
⠀⠀⡀⠀⠀⠔⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠱⣤⡤
⠀⠀⠈⠓⠒⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⢆⡿⠂⠠⠄⠐
⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠹⣿⠄⠀⠀⠀⠀⢀⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠔⢤⠄⠀⠀⠀⠀⣠⣿⣶⣤⣄⣀⣤⣬⠽⠟⠁
⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢰⣿⣿⣿⣷⣤⣼⣷⣶⣦⣾⣤⣶⣺⣿⠄⠄⠀⠀⣠⣾⠟⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢀⣿⣿⠋⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⢧⡀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣇⠀⠀⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢁⡀
⠀⠀⠐⠃⠂⠒⠀⠐⠚⠋⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀⠉⠀⠉⠁⠀⠙⠒⠓⠒

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢿⣦⣤⣀⡀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⡑⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⣿⣿⣿⡿⢻⡇
⠀⠀⠀⠀⠀⠀⠈⣟⡿⣿⣿⣿⣿⣿⣄⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⣶⣵⣿⣿⣿⣿⠿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⡿⠛⢿⣿⣿⣿⣿⣏⣷⡀⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣾⣷⡝⣻⣿⣿⣿⣿⣿⡶⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢸⣷⣄⣨⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⡏⣼⣿⣿⣿⣭⣵⣤⣤⠼
⠀⠀⠀⠀⠀⠀⣾⡁⠙⠋⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⣿⣿⣿⣿⠭⠉⠈⠀⢠
⠀⠀⠀⠀⠀⠀⣯⡑⢲⠶⣶⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠓⠀⠀⡈
⠀⠀⠀⠀⠀⠀⢹⣿⠿⢛⡿⣿⣿⣿⣟⣽⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣮⣀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠙⢶⡌⠙⢻⣿⣿⠿⣿⣫⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣘⣛⣻⣿⢿⡉⠛⠦⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⢹⣿⣿⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠐⠆⣰⡯⠙⠻⠿⠶⠽⠟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢹⣿⣿⡗⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⣿⣿⠏⢐⣠⠔⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴⣿⡟⢩⣴⠉⠑⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⣴⠟⠁⢰⣶⣿⣷⣦⡄⠉⢲⡄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢁⠀⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠃⣰⣿⣿⠉⠉⠙⠻⢿⣷⡄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠱⠒⠉⢿⡿⠀⠀⠀⠀⢾⣿⠿⠦⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣴⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣷⡙⣿⣿⣶⣾⣾⣷⣶⣷⣤⣀⣀⡼⠋⠀⢀⡼⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⣿⣿⣯⣿⣿⡟⠐⠁⣠⣄⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣿⣿⣿⣿⣿⣿⣥⣠⣴⣾⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⢀⣠⡄⢀⣀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣶⣼⣷⣾⣿⡿⠿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠈
⣤⣤⣦⣤⣴⣤⣤⣤⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣅⣮⣭⣤⣯⣽⣥⣾⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡠⠒⠉⠙⠢⣄⠀⠀⠀⠀⣀⣀⣠⡤⠤⢤⣤⣀⣀⡀⠀⢀⡠⠖⠋⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡜⠁⠀⠀⠀⠀⠀⠑⢦⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠋⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷
⣸⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⣷⠖⠚⠋⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⡴⠊⡉⠲⡄⠀⢱
⡇⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢸⡀⡎⠈⢣⠸⠀⡌
⡇⠀⠀⠀⣠⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠱⣌⢲⠎⢰⢋⡴
⢧⠀⢀⡴⠁⡾⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠘⢦⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠒⠒⢋⡠⠋⠁
⠈⠶⠋⠀⠀⣇⠀⢸⣿⣿⡗⠀⢀⣠⠤⠤⢤⣀⠀⠀⣿⣿⣿⠆⠀⠀⠀⠀⠀⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠊⠉
⠀⠀⠀⠀⠀⢿⠀⠀⠉⠉⠀⡰⠋⣀⠀⠀⣀⠈⢳⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇⠈⠿⠀⠈⠿⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⠦⣀⡀⠀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠳⣄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠙⠲⢤⣼⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠦⠤⠤⠤⠤⠤⠤⣤⠤⠶⠖⠒⢻⡇⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⣸⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢸⡇⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡤⠛⢆⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⠏⢳⡀⠀⣠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠫⡿⡿⢿⢿⡿⢿⡿⢿⡟⠿⠿⣿⢿⠿⢿⣿⣿⣿⣿⣦⣶
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠛⠻⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁⠘⠀⠁⠀⠀⠈⠀⠀⠈⠉⠙⣟⣻⣿⢳⡀
⠀⠀⣄⣀⣀⣰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠉⣋⡙⣿⣿⡌⠃
⠀⠀⠈⠛⠻⠛⣿⣿⣷⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⡨⠀⣶⡶⣼⣼⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡤⠸⡿⢻⣿⠃⣰⡅⣶⣤⣾⣡⠤⣆⡃⣿⣧⢟⣷⣤⣾⣶⡐⡂⣠⣢⣡⣷⣾⢡⣥⣿⣷⣽⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠸⣧⣶⣶⣿⣀⣿⣿⣯⣻⣷⣿⣿⣦⢻⠺⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣕⣾⣿⣿⣿⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⣶⣿⣴⣶⣶⣶⣾⣿⣿⣿⣯⣹⣧⣯⣭⣭⣽⣿⣭⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣽⣿⣩⣀⣈⠙⢿⣿⠀⠠⡔
⠀⠀⠀⠀⠀⠉⠉⠋⠉⠛⠙⠛⠛⠻⠿⠟⠿⠛⠛⠛⠋⠉⠋⠋⠛⠛⠉⠛⠉⠙⠉⠛⠛⠛⠛⠿⠿⢿⣿⣾⣿⢠⡞⠻⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣄⣀⣴⣤⣾⣤⠶⣊⠔⡀⠀⢀⠀⢀⣀⣤⣤⠴⠶⣖⣛⡭⢡⡏
⠀⠀⠀⠀⠀⠀⠈⢮⣟⣓⠶⠶⣶⣭⣭⣝⡳⣮⡳⣄⣼⢟⠿⠛⠝⠡⠚⠑⠛⠿⠷⠿⣶⢞⡵⠞⣋⣭⣶⣶⣿⣿⣿⡿⡂⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣷⣦⡙⢷⣌⢻⣾⡇⠿⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⣰⢧⡟⣰⠟⣽⣿⣿⣿⣿⣿⣿⢞⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢀⢨⣟⢿⣿⣿⣿⡌⣿⣷⣿⠃⠀⠊⡀⡀⡀⡀⡀⡴⠀⠀⠀⠀⣿⣾⣼⠏⣼⣿⣿⣿⣿⣿⣿⣿⠇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠸⣾⣷⣿⣿⣿⣷⢸⣿⠃⠀⠀⣸⣴⡿⢽⠳⠁⠀⢀⡄⠀⡠⠸⣿⣯⠀⣿⣿⣿⣿⣿⣿⡭⠶⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠫⢻⣿⣿⣿⣿⢸⡏⠀⠀⠀⠙⠘⠁⠀⠀⠀⠀⡠⣢⣾⠄⠀⣈⣿⣶⣿⣿⣿⣿⣿⢭⡷⠞⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠭⣿⣿⢟⣼⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢺⢟⡵⠞⢛⢿⣿⣿⣿⣿⣿⣚⣿⣐⣒⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠾⢛⣿⠀⢱⠑⠄⠀⠀⠀⠀⠀⠀⠀⠁⡥⠀⠀⠈⣷⣿⣿⣟⢿⣽⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣏⣳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣴⣻⣧⢸⣏⣸⣿⡆⠈⠉⠉⠑⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠿⣿⡴⠂⠀⠀⠀⠈⢶⣤⡀⠈⣆⠘⠛⠋⢀⡄⢽⣿⣧⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡼⠛⠀⠀⠀⠀⠀⠀⠀⠚⣿⣶⣌⠢⠉⠁⠉⠀⢼⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠃⠀⡀⠀⠀⠀⠀⣀⠀⠠⡐⠻⢿⣷⡄⠀⠀⢤⡦⣽⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣡⢠⠞⠃⠀⠐⢶⣄⠺⣷⣎⠪⡢⡀⠈⠻⡄⠀⢪⣿⣿⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡰⢃⣠⣤⣤⣄⣀⠀⣿⣷⡌⠻⣷⡜⠄⠀⠀⠀⠀⢽⣿⣿⡏⠀⠀⠀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠛⠉⠲⠶⠆⠉⠛⢷⣮⡈⠻⣆⠈⠁⠀⠀⠀⠀⣄⣿⣿⣿⠃⠀⢀⢀⡇⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣱⣿⢆⠀⠀⠀⣼⣻⣦⠹⣧⢴⠙⠀⠀⠀⠀⣀⣷⣿⣿⣿⠃⠀⠀⢸⣸⡇⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⠿⠟⠀⠀⠀⢻⠿⠿⠃⣯⣾⢰⣆⣀⣠⣾⣿⣿⣿⠟⠁⠀⠀⣆⣿⡿⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣤⣐⣒⣂⣤⣤⡴⢞⣽⣯⣾⡿⠿⠿⠿⠛⠉⠀⠀⠀⢀⣼⣿⡿⢣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣯⣭⣭⣵⣶⠾⠟⢋⠡⣠⣄⣦⣴⠆⠀⢀⢔⣴⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣶⣶⣶⣄⣷⣷⣿⣿⠟⢡⢆⣴⣵⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⠃⠀⢸⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠄⠲⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠂⠠⠀⡀⡀
⠀⠀⠀⢤⡤⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⡝⠦⢄⢀⢤⡀
⠀⠀⠀⠛⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠇⠀⠀⠠⡎⠁
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠓⠀⢰⡇
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣼⡀⣤⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⣤⠧⡄
⠀⠀⠀⠀⠀⠀⣹⡁⠀⣠⣾⣷⣦⣦⣼⣤⣤⣤⣤⣤⣤⣾⣿⡆⠀⢠⣿⣿⣦⣤⣤⣶⡶⠶⠖⠃
⠀⠀⠀⠀⠀⠀⢿⠀⡞⢿⣿⡟⠛⠻⠛⠛⠛⠛⠋⠉⠉⢹⣿⢿⡄⡼⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠸⡇⣇⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠸⡇⢣
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠂⠈⠛⣀⣀⠐⠀⢐⠒⠒⠀⠀⢈⠛⠀⠈⠛⠂⠀⠒

⣶⣶⠶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠒⠉⠀⠀⠀⠈⠙⠃⣴⡏⠀⠈⠰⠆⠒⠂⠤⢠⣤⣤⣤⠄⠐⠀⠀⠀⠀⢲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⡆⢰⡀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⣶⣾⣿⣿⣷⣦⣀⣀⣀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⣶⣾⡷⠀⢰⡟⠉⠁⠟⠃⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠛⠙⠿⣃⡀⠈⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠟⠋⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠬⡑⠀⡀⠀⠐⢿⣿⠇⠄⠀⠠⠟⠃⠀⠀⠀⠀⣾⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠂⠀⠬⠐⡀⠀⠀⢀⡬⠀⠀⠀⠀⠀⢀⣤⡦⠀⠀⠙⠛⠋⠀⢀⠘⠋⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠾⠿⠗⠛⠉⠐⣶⠀⠀⠀⠀⠸⡿⠋⠀⠀⠀⡀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⣾⡿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⣦⣴⣆⣠⡄⠀⣶⠄⠀⢷⣶⡿⠿⣿⣿⡿⡆⠀⠀⠈⠉⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⠿⠛⢻⡀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⡀⠀⠶⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⢠⠇⠀⠀⠀⣀⠀⡘⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁






⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣕⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠙⠢⢄⡀⠀⠀⠀⣀⣀⣤⣀⡀⠀⠀⢿⣿⣿⡄⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⢀⣡⠶⠛⠛⠋⠉⠉⠉⠛⠲⠬⣿⣯⠘⡄⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢸⠀⠀⠛⢶⣤⣤⣤⣤⣴⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢀⠀⠀⢠⠀⢉⠒⠊⠿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡜⠀⠀⠇⠀⠐⠒⠀⠀⠝⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⠮⣒⠀⠀⠀⠀⠀⠀⠀⠀⠢⢍⣀⠈⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣯⣷⣶⡦⣄⠀⠀⠀⠀⠘⢄⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂
⠀⣠⠴⠶⣶⠶⡤⡤⣴⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⡿⠃⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⡀
⢰⠁⣄⠀⠈⠳⡝⢦⡌⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠩⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄
⢈⣸⡎⢢⠖⢁⡀⠱⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠈⣆⠃⠀⠀⠈⣷⢠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠥
⠀⠈⠂⢤⣄⡀⢉⠟⣾⣀⣠⣤⣴⡶⠶⠶⠶⠷⠶⠴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠰⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⠆⠬⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢶⡦⣤⣴⣤⣤⣤⣤⣤⣴⣤⣴⠾⠟⠉⠀⠀⠀⠉⠛⠷⠮

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢰⢯⡠⡀⠀⠀⢠⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣬⣀⡀⢡⠀⢠⠆⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⣿⠀⡆⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣿⣿⡟⠰⠀⣾⣿⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣾⣿⠉⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⣿⣿⣿⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡼⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⣧⣄⡀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠈⠉⠉⠀⠉⠀⢠⡞⣰⡇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠹⠦⠀⠀⠀⠀⠀⠀⢀⣾⣇⠈⢁⣴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠛⠛⢋⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⢠⣦⣀⣀⣠⡴⠋⢀⡞
⠀⠀⠀⠀⠀⠀⢀⣴⠿⣇⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠉⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⣰⡟⢋⣶⣿⡄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⣴⠟⣀⣼⣿⣿⣷⡄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡏⠁
⠀⠀⠀⣼⠋⣠⣿⣿⣿⣿⣿⣿⣦⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣦
⠀⠀⠘⠿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣽⠿⠋⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠓⠶⢤⣴⡶⠴⣿⣿⣻⣯⣶⣦⠀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠰⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠠⣴⣿⣿⠛⠛⠻⢿⡿⢸⣿⣿⣿⣿⢿⡏
⠀⠀⠀⠀⠀⠙⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠻⠿⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠱⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⠙⠛⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠋⠳⠑⠑⠝⢿⠿⢿⢷⡀⠀⠀⠀⣰⠃⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠈⠁⠁⠀⠀⢀⠏⠀⡜⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣙⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠳⣤⡈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⣠⠾⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠈⢳⣄⠀⣹⡇⣀⣤⡴⠶⠛⠛⠛⠛⠶⢶⣤⣀⠰⣏⠀⢠⡾⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠹⢾⣿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣿⡷⠟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⣴⣟⣥⠶⠖⠲⢦⡄⠀⠀⠀⠀⢀⡴⠖⠒⠶⣮⣹⣦⡀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⣀⣴⣿⡿⠋⢻⣿⣷⡄⠀⣿⠀⠀⠀⠀⢿⡀⢠⣾⣿⡿⠙⢿⣿⣦⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣰⠏⣀⣤⣤⣬⣥⣥⠾⢃⣠⣤⣤⣄⣘⠷⣬⣤⣥⣤⣤⣀⠹⣦⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣼⠋⠀⠀⠀⡀⢠⡾⠋⠁⠀⠀⠈⠙⢳⣄⠀⠀⠀⠀⠙⣷⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⡀⠀⠐⠛⢷⣿⠀⣾⡷⠀⠀⢾⣷⠀⣿⡾⠛⠂⠀⠀⣼⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠛⣷⠀⠀⠀⢻⣷⣮⣥⣀⣀⣤⣭⣾⡟⠀⠀⠀⣶⠛⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡀⠀⠀⠀⠹⢦⣍⣉⣉⣉⣵⠟⠀⠀⠀⠀⣿⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣮⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣤⣤⣤⣤⣤⣤⣶⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠘⢛⢃⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠒⢒⠓⠓⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠈⢉⢁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠂⠀⠐⠚⠘⠘⣤⡀⠀⠀⠄⢀⣀⠀⠀⠀⠀⢰⠶⢀⣠⡴⠄⠁⠀⠀⣍⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⡤⠆⠲⡄⠀⣌⡓⠀⠤⠔⠒⠒⠉⠉⠉⠀⠈⠉⠉⢉⠙⢒⠤⢤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⡀⠀⢀⠀⣀⣀⣷⠀⠁⠀⠀⠀⠀⠀⢀⡀⠄⠤⠶⢶⡟⠛⠁⢀⣠⣧⡬⢄⣀⠈⠁⠒⠆⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠨⠁⢀⡾⠀⠀⠀⠀⢀⠀⣈⣒⡤⢓⣂⠄⢐⡀⠄⢈⡀⠠⠥⠀⠠⢉⡉⠥⠄⠌⠐⣀⡠⠽⠧
⠀⠀⠀⠀⠀⡍⠀⠀⠐⠊⣳⢸⠀⠈⡀⠈⠀⠀⢈⢉⠉⢰⠒⣶⣌⣘⠳⡖⡭⠐⠚⠭⠤⣍⡉⠚⢯⠥⢞⡩⠤⣀⠈⠠⣄⣲⣤⠶⠍⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡀⠀⠀⢀⣈⣁⣸⣄⣌⠂⠤⠤⠤⠤⠤⠆⠹⠒⠀⠀⢆⠻⡇⢈⠁⠀⠈⠁⠀⠈⠑⠒⠠⠔⠠⠀⠐⠀⠈⠁⠤⣐⠤⣐⡢⢀⣀⣵⠠⠔
⠀⠀⠀⠀⠈⠁⠒⠒⢺⠙⠉⠐⠒⢜⠂⠀⠀⠀⠀⢀⠁⢾⣣⠄⠀⠰⣒⡟⢛⠾⠛⠴⠖⠢⠾⢷⣶⣦⣴⣄⡀⠇⠴⠖⢒⣉⡁⠥⠔⠒⠋⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠥⠬⠼⠦⠤⣀⣀⣀⣠⡴⠋⠉⠉⠋⠉⣕⠖⠅⠿⠁⠀⠀⢀⠀⠀⠈⠈⠉⠓⠑⠠⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠉⠀⠀⠈⡍⠁⡟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠐⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⢔⡲⠈⠐⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣂⣥⣾⡷⠛⠁⠀⠀⠀⠀⣠⣭⡒⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠙⠲⢿⡛⠻⢥⡀⠀⠀⠀⢀⣤⣮⡥⢋⡴⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢐⣠⣭⣿⣶⣤⣀⠀⠀⠀⠈⠙⠲⢽⣦⣴⣾⠿⣛⣥⣺⢵⣚⣭⣶⡆
⠀⠀⠀⠀⠀⠀⣀⣠⢤⢲⣻⠿⠟⠋⠉⠘⢦⡉⠛⢦⣄⡀⠀⠀⠀⠈⣉⢲⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠈⠐⠠⢉⡛⠋⠁⠀⠀⠀⠀⢀⣠⣤⣿⣷⡶⣞⣻⣷⡆⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢄⡀⠀⠀⣊⠕⡢⢄⡠⢶⣯⡥⢞⣛⣭⣶⣿⣿⣿⣽⡇⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⢷⣶⣍⡂⠀⠉⠓⢶⣾⣿⣿⣿⣿⣿⡿⢿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠑⢤⡀⠨⡛⢿⣷⣤⣀⢸⣿⡿⢿⣻⣭⣷⣿⡿⣟⣯⣷⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠈⢹⣾⣭⣶⣿⣿⠿⣛⣭⣷⣿⡿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠢⣀⠈⡳⢦⣸⡿⢟⣛⣭⢶⣻⣿⣿⣿⡿⣟⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⡂⠙⠿⣟⣭⣾⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⢸⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⡴⠈⠙⡆
⠀⠀⠀⠀⣷⡑⢤⠀⠀⠀⡸⣷⡄⡀⠰
⠀⠀⠀⠀⣿⡁⠀⠙⠉⠉⠁⠸⣿⡇⠀⣦⡀⣀⣀⣀⣀⢀⠀⠀⠠⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄
⠀⠀⠀⢠⡽⠀⠀⢀⣠⣀⠀⠀⠹⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⣀⠔⠀⠀⠀⠘⠛⠟⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣾⢯⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠻⣶⣵⡶⡶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠈⠙⠓⠶⠦⣀⠀⠀⠀⠀⢀⣀⡤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢄⡀⠀⠄⣠⣅⣄⡀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠈⢱⣄⠁⠀⠀⠀⠀⡈⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣾⣷⣾⣿⣧⡙⠀⠀⠀⠀⣼⣇⣰⣧⣴⣿⣧⣴⠆⢀⣠⣶⣾⣿⡆⠀⠀⠀⠈⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⡿⡯⠁⠀⠀⠀⠜⠉⠉⠉⠉⠉⠙⠛⢿⡿⠛⠉⠀⠘⡿⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢰⠁⡆⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣼⡇⠰⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⣴⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠁⢰⣷⣴⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⣺⣿⣀⠾⠃
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠙⢿⡆
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⣼⢷⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⡿⡇⠀⠀⠀⣀⣠⠞⠀⠀⠀⠘⠁⠀⠉⠉⠉⠻⢶⣟⣋⠻⠥⣤⡀⠀⠀⢀⣀⣀⣤⣴⣖⣀⣀⡀
⠀⢰⡟⠷⣤⣸⡇⢷⠶⠚⠉⠩⢴⣶⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠉⠉⠉⠉⠉⠉⠁⠀⠈⠀⠀⠈⠙⢧⡀
⠀⢨⡇⠀⣿⢇⢇⢌⠣⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⣤⠴⠒⠒⠒⢤⣄
⠀⠈⣷⠆⠘⠈⠛⠊⠛⠠⣤⣴⡆⠀⢦⠀⠀⠀⠀⠀⠤⣤⣀⠀⢸⠳⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣋⡠⠤⠴⠦⠤⠤⠬⠆
⠀⠀⠙⠒⠒⠒⠶⠶⣤⣷⡈⠉⠀⠀⠈⣧⠀⠀⠀⠀⢀⣈⣿⡟⡾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⡄⠀⠀⠀⠀⠀⢺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⡀⣀⣿⣆⠀⠀⠚⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢧⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠉⠓⠶⢄⠀⠀⢠⣠⡀⠀⠀⠀⢠⣰⣷⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠁⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠙⠛⠤⠀⠀⢸⠙⠀⠀⠀⠀⠀⠀⠀⢈⣵⣤⣀⡀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢰⣃⣀⣀⣀⡀⠀⣀⣀⡴⠋⠳⡄⠈⢹⡷⢦⣄⡀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠠⣮⡉⠉⠻⣍⣉⡉⠉⠁⠀⠀⢀⡿⠀⢀⡷⠀⠈⠙⠳⣤⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣠⠞⠉⠀⠀⠉⠙⠳⢦⣀⣙⣲⣄⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠹⣦⠈⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠺⠛⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣥⡴⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠂


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠉⠑⠒⠒⠤⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡚⠛⠉⠉⠉⠉⠒⠤⣔⣲⠶⣤⡀⠀⠀⠀⠀⠀⢀⣤⠞⣉⣉⣽⡶⠆
⠀⠀⠀⠀⠙⠛⠿⣯⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣽⣗⡢⢄⣀⠀⠠⢀⡀⠈⠉⠓⡓⠤⢤⣀⣴⣾⣯⣷⣿⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⣿⠒⠦⣌⡙⠓⠦⣄⣀⠀⠀⠀⠀⠀⠈⢙⣛⣛⣈⣉⣲⣤⣤⠝⠒⠋⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⢸⡷⠦⣄⡉⠙⠲⢤⣉⡛⢒⣛⣛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⡀⣻⡿⠿⠿⠿⠿⠯⠅⠀⠐⠒
⠀⠀⠀⠀⠀⠈⣗⠀⠀⠀⠀⠀⠀⠀⠉⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠠⣟⡒⠤⣀⠀⠀⠀⠀⣹⣟⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⢍⡓⠦⢍⣀⠒⠠⠄⠙⣩⠵⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠈⠁⠀⠉⠓⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣍⣙⠒⠒⠖⠋⣱⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠐⠒⠛⢣⣄⡀⠀⠈⠐⠛⠷⠆⠀⠀⠀⣀⣠⣤⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⢟⠂⠤⣀⠀⠀⠀⠀⠀⠈⠙⢋⣉⣐⢤⡶⠒⠋⠀⣻⣿⣿⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢤⣤⣤⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠉⠒⠲⠶⣾⣿⣿⣿⣿⣿⣽⡇⢀⣀⣤⣿⣿⣯⣴⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⣉⡒⠾⣿⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⠤⣀⠀⠈⢿⣿⣿⣿⠿⠟⢛⣳⣯⠛⠉⢁⣼⣿⣯⡽
⠀⠀⠀⠀⠀⢈⡀⠠⢤⣴⣿⠢⠬⣭⣿⣿⣿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠿⢤⣀⡈⠀⠒⠛⠉⢀⣴⣾⣿⣿⡿⠒⠚⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠬⢭⣛⣿⣊⣁⡒⠺⣿⡿⣿⡀⠤⢤⣴⣿⡆⠀⠀⠀⠀⢸⡏⠑⠒⠤⢍⣀⡐⠀⠀⢼⣻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⢀⣑⠒⠶⣿⡟⠢⢬⣽⣿⣿⣿⠌⣙⣻⣿⣛⣧⠄⠀⠀⠀⠈⠣⠄⣀⠀⠀⠀⠉⠉⣒⣭⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠬⢉⣛⣿⣛⡁⠒⠲⢿⣯⣿⡓⠲⢾⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠒⠶⠚⠁
⠀⠀⠀⠀⠀⠐⠓⠶⢾⣿⣧⠬⢐⣒⣶⣿⣿⡅⠙⠛⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠲⢾⣿⣿⠿






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⣉⣩⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢁⣤⠖⠋⠉⠀⠀⢸⠆⠀⠀⢀⣀⢠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠉⡤⠚⠁⠀⠀⠀⠀⠀⡰⠋⢀⡴⠚⡥⠞⠋⠉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢏⣠⠋⠀⠀⠀⠀⠀⢀⡤⠊⠀⢀⠎⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⣾⠁⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⣸⠢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⢨⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣼⡆⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⢉⣀⠤⠷⣜⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣦⣄⡀⠀⠀⠀⠀⣰⠏⣉⣍⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⢀⡴⠚⠉⣀⣤⣶⣾⣷⣷⣦⠤⠔⠒⠀⠈⠉⠉⠉⠉⠉⠉⠛⢷⣤⡀⠀⢿⡀⢿⡿⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠈⠑⠶⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⢶⡴⠟⠋⢀⣴⣍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠙⢶⡞⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣄⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠄⠒⠒⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠠⢤⡄⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⣤⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡏⠀⠀⠀⠀⠀⠀⢀⣤⣶⢿⣿⠿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⢸⡿⠃⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣰⣿⠋⠀⣸⣿⣤⣿⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠻⣿⡿⠿⢻⣿⠛⣿⡟⠛⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⢠⡾⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⡏⣰⡄⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣇⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⢸⠇⣿⡧⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣿⡿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⣾⠀⢿⣷⢼⣿⢹⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⢸⡆⠸⠛⣼⡏⣼⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠈⠻⣦⡀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⠀⣀⡤⠒⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡗⠲⠤⣤⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣴⠶⠾⣯⠁⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣁⣠⡾⣧⡀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠉⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⢿⣄⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣣⣾⡿⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠙⣿⣿⣿⣇⠀⢠⡀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⢀⣴⣾⠟⠀⣿⣿⣾⠷⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⠸⣿⣿⣷⠀⡞⢣⡀⣠⣶⠶⠂⠄⠈⠿⣶⣦⣼⣿⣟⡊⢠⣿⣿⠁⠐⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣉⠀⠻⣿⣿⡀⣰⣿⠛⢋⠡⣀⠁⠀⠀⠓⠀⠉⠃⠙⣿⡇⣸⣿⡯⠀⢠⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⠀⠀⣹⣿⣷⡟⠀⣸⣏⠐⠟⠃⠀⠄⠀⠀⠀⠀⠀⠙⢰⣿⣿⣆⠀⠀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠂⣠⣼⣿⣿⢁⣾⠯⠽⠒⢿⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⣲⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⢠⣆⣤⠀⠽⠶⣶⠀⠸⣼⡇⡼⠇⠀⠀⠠⢎⡀⢀⣷⡦⢈⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢍⡝⢿⣿⠄⣿⣿⣯⡀⠀⠻⠃⢠⠀⡀⠀⠀⠿⣟⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡘⢀⣼⡇⠀⠛⣁⠀⠈⢣⡄⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⣄⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠇⣺⣿⠀⢰⢯⠗⢀⠴⠉⠁⣀⣤⠀⠀⠀⠀⠀⢠⣥⠀⢙⡀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⢫⣿⡏⠀⣸⠁⢰⡿⠀⣰⠟⢋⣉⡀⠀⠈⠲⠀⠈⠈⠀⢘⣥⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠤⢟⣿⡇⠀⣸⠁⣾⠃⠀⡿⣶⠛⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿⠶⢾⡇⠀⠛⠀⠟⠀⢀⡴⢁⣴⡿⠃⠀⠀⢿⣿⣦⠀⠀⡠⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣾⡇⠥⣼⣆⠸⣆⢁⠀⣿⠁⠈⠉⣀⣀⠀⢀⣀⠀⠼⠀⠀⠛⠂⣈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⢳⣛⣡⣭⣷⣌⠺⠁⢸⡄⠀⠸⠿⠋⠀⠘⠛⠛⡁⣀⢖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⡭⠄⣐⣋⡹⢻⣶⣦⡑⢀⣀⣀⣀⣠⣤⠄⢊⣤⠃⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠩⣟⣃⣀⣉⣷⣶⣿⣟⢻⣷⣄⣩⠍⠉⣀⠲⢈⢷⣲⡆⠀⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣛⣻⣶⣷⣤⣾⣽⣟⣽⣯⡟⠀⠠⣜⣷⣋⣛⣴⣷⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⢉⣩⣭⠉⠭⠟⡋⣽⣧⣾⣳⡆⢘⠦⢛⣦⣉⣻⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⠭⣿⣶⡆⣰⣊⠃⢻⡟⣿⠀⢈⠷⣄⣼⠚⡡⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠈⠸⢿⣷⣿⣷⣄⠘⠻⠻⣿⣾⢿⣛⠮⠁⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠐⠀⢡⡮⢿⣿⡇⠀⠀⢀⣿⣯⣆⠁⠀⢠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡷⢻⠀⣱⣿⡇⣇⠀⠀⠈⣽⣿⣟⠁⠀⢸⣏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠈⣇⣨⣟⡿⣿⠀⠀⠀⣿⣧⣽⡇⠀⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣖⣈⢈⡄⠀⠀⣿⣿⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢹⣿⡯⠈⠃⠀⠀⡏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⠓⠘⠛⠃

⠀⠀⠑⢶⣷⣾⣔⠒⢄⠀⠀⣀⠠⠦⠄⠄⠀⠀⢀⠄⢂⣮⣷⠏
⠀⠀⠀⠀⠉⣩⣽⣷⠀⠑⠈⠀⠀⠀⠀⠀⠈⠑⢁⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠐⣂⠶⠀⠠⢲⡞
⠀⠀⠀⠀⠀⠈⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡿⠁⡠⠀⠀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠑⠀⠈⣹⡇⢴⡆⠀⠀⠀⠀⠀⠀⣴⡆⣼⡙⢁⡰⠀⠀⠀⠀⠀⠀⠇⠀⠲⠆⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠠⠀⠀⠀⠀⠃⢰⡀⠀⠀⠀⠀⠀⠀⢠⠩⣕⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⠆⠴⠓⡄⠀⠀⢰⠱⡀⠀⠀⠀⠀⢀⡤⠉⠻⠥⣀⣀⣀⡀⠜⠁⠀⠀⠀⣆⠀⠀⢀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠑⠮⣶⣤⡵⠋⠀⢀⠌⠀⠁⢚⣿⣶⠛⢯⣗⠀⠀⠀⠀⠈⢧⢈⡀⠀⡀⠀⠐⡏⠀⠀⣼⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⢦⣀⡀⠈⢵⣪⡤⠔⠋⠀⢸⡀⠀⣝⠋⢉⣤⠀⠉⣿⣿⣶⡤⠀⢆⢹⠋⠁⠀⡼⠉⠉⢻⢻⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡉⠁⠀⠉⠉⡀⠀⠀⠀⣿⠇⠀⠉⠣⢾⡏⣾⣇⣼⣿⣿⠇⠀⠸⠈⠀⡁⢸⠁⠀⢠⣂⡾⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠙⣶⣤⣴⡞⠁⠀⢀⡜⠋⠀⠀⠀⠀⠈⣿⡿⠉⢹⣟⡧⠀⠀⠷⠚⠀⠷⠞⠈⠀⠉⠉⠷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠉⠉⠛⠋⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠛⠸⠃

⠀⠀⠀⠀⠀⠀⣴⣶⣾⡿⠻⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠿⢿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⢿⡏⠉⠛⢷⣦⡀⠈⠻⣦⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣴⠟⠁⢀⣴⡾⠛⠉⢹⡿
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠙⣿⣤⣴⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣦⣤⣿⠋⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⡀⠀⣠⣶⠿⠿⠿⠿⣶⣄⠀⠀⣀⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⡇⣼⡟⠁⣤⠀⠀⣤⠈⢻⣧⠸⣿⣿⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠿⠀⠀⠿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠘⠻⣶⣦⣤⣤⣴⣶⠟⠃⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠶⣶⣶⣶⣶⣶⣶⠶⠶⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⢤⡄⢄⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠠⠄⠁⠠⣄⠀⠀⠃⠀⠄⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠑⢦⣠⢤⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢠⢤⣠⠖⠁⠀⢀⡀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠈⢃⡀⠁⠂⠐⠶⣀⣈⠂⠀⠠⣄⢀⠀⠀⠀⠀⠀⠀⢀⠀⢈⣀⡐⠖⠀⠂⠁⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠠⠛⠋⠀⠀⡀⠐⢌⣻⠀⠀⠀⠀⠰⠟⠁⣀⠀⠈⠛⠣⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⡃⠀⠀⠀⠀⠈⠳⣔⠦⠀⠀⣈⡀⠔⡥⠊⠀⠀⠀⠀⠀⢡⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢀⣀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⣀⠐⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢈⣿⣦⣄⠀⠀⡀⠀⢀⢀⠀⡀⠀⠀⣠⣾⣿⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⠀⣿⠿⢄⣴⠧⣀⣼⣀⡉⢷⣤⣼⣿⡇⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⠀⢰⠟⠉⠀⠀⠀⠈⠀⠈⠙⢷⠀⠠⠀⠤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢄⡀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣀⠔⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠄⠀⠛⠢⢄⡀⠙⢦⠠⡀⢸⠆⠀⡀⠀⠀⠀⠀⠀⠀⢻⣟⠡⢀⡞⢁⣀⠤⠶⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠉⠙⠚⢳⠃⠒⠁⠀⠀⠀⠀⠀⠀⠉⠒⢿⡓⠚⠉⠉⠀⠀⠀⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢀⠐⢦⠔⠃⠀⠀⠠⠀⠀⠀⠈⠑⠂⢀⡙⠒⠓⢴⠔⢀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢎⢀⠀⠀⢠⡖⡆⠀⠀⠀⠀⠒⢢⡁⠀⠀⢈⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣉⣡⣤⣤⣤⣤⣤⣤⣈⣁⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠈⠉⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⢻⣦⣤⡶⠶⠶⠶⠶⠶⠶⢶⣤⣤⣀⠀⣠⡶⠷⢶⣄
⠀⠀⠀⠀⠀⢠⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣏⠀⠀⣀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⣾⣿⠟⠉⢙⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡔⠙⢦⡀⠈⠛⢷⣆
⠀⠀⠀⠀⢀⣿⣿⣄⡀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡻⣴⡟⣷⡀⠀⢠⣿
⠀⠀⠀⠀⠀⣿⡻⣿⣟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠦⣄⣀⡀⠀⠀⠀⠀⡏⣠⡦⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠉⢉⡹⣧⡈⠻⣦⣾⠃
⠀⠀⠀⠀⠀⠘⢷⣄⡙⠛⠛⠛⠛⠛⠻⠶⠶⠶⠶⠶⠶⠾⣿⠃⠀⠀⠀⠈⠉⠙⠛⠓⠚⠁⢤⣄⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠉⠛⢶⣤⣿⠘⢷⣄
⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣿⡇⢀⡼⠁⠀⢠⠖⢳⡄⢠⡶⢤⡀⠙⢧⡀⠀⠙⢷⡄
⠀⠀⠀⠀⢠⡿⠉⠡⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢠⠏⠀⠀⢰⠏⠀⢸⡇⠈⣇⠀⠹⡄⠀⠳⡄⠀⠈⢻⡆
⠀⠀⠀⢀⣿⠁⠀⠠⠀⠀⠀⠀⠀⣀⠑⠄⣀⣀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢿⠀⠀⣼⠁⠀⠘⠦⣴⠇⠀⠀⣿⠀⠀⠈⣿
⠀⠀⠀⢸⡇⠀⠔⠀⠀⠠⠀⠈⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣸⡏
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠈⠂⠀⠐⠈⠀⠈⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠈⠳⠦⣄⣀⡀⠀⠀⠀⠀⢀⣀⡴⠚⠁⠀⠀⣰⡟
⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠳⣄⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠉
⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣦⣤⣤⣀⣠⣤⣤⣴⠶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⣀⣴⠟⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢸⠙⠲⢤⣀⣀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣼⡥⠖⠋⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⣦⡀⠘⣿⠙⠛⠛⠛⠛⣿⠀⠀⠀⢰⣿⣇⠀⢀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⠀⠸⣿⠛⠛⠛⠁⠀⠀⠀⠀⢻⡧⠀⠀⣾⠋⣿⣉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⣿⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⢴⡶⢫⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣭⡍⢩⡍⡉⠉⡿⠉⡍⢩⣷⣿⣿⣿⠿⡟⢸⣿⠟⣥⣯⣭⣭⣿⣿⣿⣿⣿⣿⣶⠸⣧⠻⠴⠛⠚⢻⢀⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣣⠾⠛⠓⠈⠁⢀⠈⠉⠁⠈⠉⣉⠝⣡⡖⢁⡇⡟⣵⠋⠀⢋⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠛⠓⠀⢸⢸⢿⡵⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠜⠁⠀⠀⢀⣤⠠⢄⠀⠀⠀⠀⡜⣠⣾⣿⢃⡼⢱⡿⣿⠀⠀⢸⠀⠀⠀⠀⣄⣠⣤⣠⢤⠀⠈⠀⠀⠀⠀⡜⡜⣼⣏⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⢎⡴⠁⠠⠄⠀⠀⠸⣌⣉⠴⠀⠀⠀⢸⣵⣿⣟⣡⢃⡆⣼⣼⣿⡄⠀⡼⠀⠀⠀⣸⢻⣿⠿⢯⠏⠀⠀⠀⠀⠀⡰⢱⠡⣽⣾⣏⡝
⠀⠀⠀⠀⠀⠀⡠⢣⠎⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠘⡻⣿⡿⢁⢾⡇⣿⣾⡿⠁⡴⠁⠀⠀⣆⠀⢀⠄⣀⡀⣤⣤⣤⣴⡖⣰⢣⢣⡜⣽⣿⡿⠁
⠀⠀⠀⠀⠀⡔⣱⣿⣶⣶⣶⡖⠰⡆⣴⣠⣞⣪⠉⡥⣤⣤⣤⣿⡟⢠⢋⣾⡇⣿⣧⣶⡧⢤⣤⢤⣤⢀⣤⣤⠄⠤⢤⡥⣭⠵⠒⠺⢃⣯⢻⣰⣿⡿⠁
⠀⠀⠀⠀⢾⢤⠴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⣤⣤⣭⣉⣉⣉⣹⣡⣏⣤⣼⣄⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣭⣭⡴⠶⠒⣒⣛⡿⣱⣷⣿⡿⠁
⠀⠀⠀⠀⢘⡿⣿⡿⢗⣒⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡷⠤⢤⣬⣿⣿⣋⠈⠀⡐⠒⠲⠶⠶⠶⢴⣶⣿⣽⣿⠃
⠀⠀⠀⠀⠸⣯⣭⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢷⣽⢿⣯⠿⠿⠿⠿⠿⠿⠦⠶⠶⠿⢿⣾⣿⣿⣿⣿⣿⢿⣻⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⡶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠢⣍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢆⠈⠳⣄⠀⠀⠀⢀⣎⡔⠂⠀⢀⡴⠚⡩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡄⢸⡄⠀⡹⠖⠒⠛⠉⠉⠛⠒⠶⣏⠠⠎⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣝⠋⠀⠀⠀⠀⣠⠴⠦⠄⠀⠀⠀⠀⠶⠶⢄⠀⠙⣦⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⡤⢄⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠀⠀⠀⠀⠀⢰⣯⣶⠒⣿⠀⠀⠀⠀⢸⣾⡃⣷⡀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠱⠃⠀⠀⠀⠀⠀⢼⣿⣿⣿⡿⠀⠀⠀⠀⡘⣿⣿⡿⠇⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⡀⠀⠀⠀⠀⠖⠀⠀⠈⠙⠟⣡⣢⠴⠒⠒⠻⢮⡁⠀⠀⠀⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⡥⠤⡀⠀⢠⠒⣝⢦⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣇⣀⠇⠀⠙⠴⠅⢸⠃⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣈⡡⠴⠛⡲⠦⠖⠁⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⡀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⡏⠀⡠⠖⠋⠉⠉⠙⠲⣌⣦⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣹⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⡀⡄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣞⠁⣀
⠀⠀⠀⢰⣀⢔⠂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣈⡛⢦⡀⠀⠀⠀⠀⠠⡇⠀⣠⠋⠈⡉⠘⣷
⠀⠀⠀⠀⠙⠪⠽⠭⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢤⡼⢹⡆⠙⢦⠀⠀⠀⠀⡇⠀⣇⣀⠐⣁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⢤⣤⣀⠘⠀⣸⢉⡾⠤⠴⠚⣇⠈⢉⡀⣹⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠲⠷⠊⠀⠀⠀⠀⠈⠛⠛⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⣲⠶⠤⢤⡀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠛⠉⠉⠀⠀⠰⡅⢃⠴⣣⡼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠲⠭⠙⠛⠫⠷⢦⣄⠀⠀⣠⣾⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⡿⠥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡐⠌⠊⠁⠀⠣⡠⠀⠐⢉⠝⣓⡶⢤⢠⠐⣸⣿⣿⠿⠏⣆⣴⣾⡆
⠀⠀⠀⠀⠀⣠⠐⢊⣥⠞⠁⠛⠀⠀⠀⠀⠀⠈⠉⠉⢉⢥⡪⣾⣿⡀⣳⣯⣿⢍⣡⣾⣿⣿⢏⡇
⠀⠀⠀⠀⠀⣾⢛⠒⠤⣼⣒⠤⣁⠀⡀⠤⣤⠄⢤⣲⣵⣿⣿⣿⡿⢐⣿⡛⠈⠀⡉⣿⡾⣻⢏⡀
⠀⠀⠀⠀⠀⡷⠈⠹⠷⣒⠭⠹⣶⣯⣠⣚⣭⣶⣽⣾⣿⣿⣿⡿⢟⣋⣀⡀⢠⢴⡃⣿⣿⠿⣤⠉⠹⡖⠤⢄⡀
⠀⠀⠀⠀⠀⠑⠢⠤⣐⡢⠭⣝⡂⠝⡓⠮⣿⣯⣷⣿⠿⠋⢉⣁⡠⢴⢻⣻⢮⠷⢻⡿⠖⠚⠹⣧⢤⡐⢋⣵⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣗⡲⢬⣙⡒⢧⣿⣿⡋⠭⠃⠀⠀⠀⡔⣵⣿⣿⠲⣱⡋⠀⢀⠔⠀⠀⠁⢚⠻⠿⡿⢿⡀
⠀⠀⠀⠀⠀⠀⣤⠒⠩⠍⠁⣂⡐⠀⢍⡛⠑⠁⠀⣀⢀⣀⡠⣪⣾⣿⣿⣿⣼⠁⠀⠒⠁⠀⠀⠀⠤⠀⠀⠀⠃⠰⣨⠉⣲⡄
⠀⠀⠀⠀⠀⠠⣗⠂⠈⠩⠥⠐⣂⡈⠓⠲⠤⢔⣉⣐⣊⢔⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣀⢕⡤⢖⡫⢔⣷
⠀⠀⠀⠀⠀⠀⢿⣊⡠⠬⠍⠁⠐⠒⢒⣀⣤⣬⢐⣶⣂⣭⣾⣿⣿⣧⣤⡠⠤⣤⠄⣀⠀⢀⡀⠠⣐⡮⢝⣪⣵⣾⣿⣾⢿⡃
⠀⠀⠀⠀⠀⠀⠉⣶⢖⠶⡮⢭⠥⡤⡥⣤⢶⢖⡶⡶⣲⢻⣿⡫⡃⠀⠙⠻⣖⠬⣙⣠⣭⣶⣦⣟⣾⣿⣿⡿⣟⣊⣥⣒⣿
⠀⠀⠀⠀⠀⠀⠈⡯⠁⠑⠊⠂⢄⣈⡘⠐⠑⠠⠊⠄⠔⠔⡠⣻⣮⡀⠀⠀⠉⠯⢃⣬⣭⣍⣬⣿⣻⢿⣷⣾⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠈⢻⢦⡉⠭⠽⢓⣾⡿⣿⣿⣿⢿⠶⠄⡀⠀⠰⣷⡶⣶⡷⠶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⢯⢍⠑⢾⣻⣷⣿⣿⠟⠋⠁⠀⠀⠀⠑⠒⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢀⠃⠐⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠢⠰⢀⠄⡠⡀⢀⠀⠀⢐⠅⡨⢀⠀⡠⠀⠔⠁⠀⢀⠔⠡⠊⠀⢀⢀⠑⡡⠂⢀⠔⡁⡠⢀⢔⢕⡔⡰⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠡⠪⠀⠅⠨⠀⠕⡨⢂⠔⠀⡨⠀⠀⡠⠪⢀⢀⠔⡡⠂⠂⠐⠁⠊⠌⠐⠁⠃⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠁⢀⡄⢈⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢁⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢠⡀⠀⢀⡄⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠁⠀⠋⠉⠀⠀⠠⠂⠁⢂⢀⣀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣐⠁⠀⠀⠀⠄⠂⠀⠈⠁⠀⠀⠀⡯⠚⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣀⠁⠀⠈⠁⠀⠐⠃⠀⠸⣄⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⡁⠀⠉⠀⠠⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⡈⠳⣄⡀⠀⠀⡀⡀⢲⣄⡴⠀⠘⠁⠀⢰⠁
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⢰⣭⣇⡀⢠⠧⢷⠀⢻⠉⠡⠥⢠⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⠳⠄⠀⠀⢄⠈⠇⠈⣧⣤⡶⠁⢠⡶⢀⠀⠠⡇⠀⣀⣀⠄
⠀⠀⠈⠀⠐⠣⠀⠀⠄⢰⠆⠰⠄⠠⠶⣄⣀⠀⠀⠁⠀⢀⡰⠌⠀⣀⣁⡂⠀⠀⠀⠈⠀⠒⠒⠃
⠀⠀⠀⠀⠄⠀⣀⣠⡄⠀⠠⡚⠀⠐⠋⠹⠤⠉⠀⠀⠬⠃⢀⡀⠤⠜⠛⢠⣤⣀⡠⠉⠀⠆⢀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠁⠐⠛⠧⡀⠀⠀⠤⠜⠳⠛⠋⠀⠄⠒⠒⠟⠁⢁⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠤⠖⠃⠀⠀⠀⠘⠂⠀⠤⠤⠶⠁⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⡶⢶⣶⣶⣶⡶⢶⣶⠖⠖⠒⠒⠦⠤⣀⡀
⠀⠀⠀⡠⢤⣄⣰⡿⠛⠉⠉⠉⠁⡀⠄⣬⠑⣊⣁⠄⢠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠸⣿⣇⣿⠟⠁⢀⠤⠂⠔⣋⠅⣀⣀⡴⡊⣁⢀⠤⠐⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢿⣿⠾⡛⠛⢋⣹⠝⠁
⠀⠀⢀⣿⣿⣿⠀⠐⠡⠶⢴⣾⡣⣾⠞⠁⡨⠖⢁⠠⣊⣵⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣿⣾⣁⣴⣿⣟⡻⠗⠂
⠀⣰⡿⢻⣿⣧⠀⠀⢠⠔⣉⠔⠊⠁⠁⠀⠀⠀⣰⠴⢿⣻⡵⠂⠀⠀⠀⠀⠀⠀⠀⠲⡾⣚⠫⢿⣿⣿⣿⣿⡄
⣾⡼⠃⠸⣿⣡⠆⣀⡤⣾⣿⣨⠀⡀⢀⠀⣂⣽⣣⢖⣭⣯⣷⡵⠀⠀⠀⠀⠀⠀⠀⣿⠖⠉⠀⣿⠇⠙⠃⡿⢷⡀
⠟⠀⠀⠀⣿⣿⣿⣻⠟⠉⣩⣽⣏⣫⣴⣾⣵⣷⣖⢛⡹⣨⢿⣿⣗⠀⠀⠀⠀⠀⠸⣿⣧⠄⠀⣝⣶⣾⣟⣤⣬⡼⢢⣤⣤
⠀⠀⠀⠀⠘⣿⣿⣿⣆⣬⣰⣴⣾⣿⣿⣿⣿⣿⣿⣭⣿⣷⣿⠿⡋⠦⡄⠀⠀⠀⢻⣿⣶⣦⣤⣿⣿⣿⣿⣟⣛⣻⢷⣶⣿
⠀⠀⠀⠀⠀⠘⢿⣿⣟⣿⡿⢿⣿⣧⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣏⠀⠀⣀⡼⣿⣿⣿⡿⠿⠛⠛⠛⠛⠋⠋⠋⠉⠁
⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠀⠀⣻⣿⡿⠇⠀⠀⠉⠉⠉⠉⠀⢸⡏⠀⠹⡆⠀⢹⠁
⠀⠀⠀⠀⠀⢹⣿⣯⠀⠀⠀⠀⢹⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⡘⢁⠆⠀⠹⡄⢿
⠀⠀⠀⠀⠀⠀⢿⣾⣆⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢻⣾⠀⠀⠀⢻⣬⣆
⣀⣀⣀⣀⣀⣀⣈⣻⣿⣆⣀⣀⣀⣈⣙⣻⣃⣀⣀⣀⣀⣀⣀⣀⣓⣳⣀⣀⣈⣙⣺⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣫⣛⣩⣛⣟⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠤⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠠⢲⢶⡄⣀⣠⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠒⠒⠲⠤⣀
⠀⠀⠀⠀⠳⣘⠒⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣑⣄⣀⠠⠤⢺⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⡔⠠⠀⠀⠀⠀⡐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⣹⠇⢀⣀⡠⠞
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢠⠐⠈⠀⡜⠖⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠸⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠢⠁⠠⠤⠀⢀⠀⠀⠃⢀⠀⠣⢣⠈⡄⢀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⢠⣤⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠐⠠⠀⢠⡁⠀⠀⠴⢤⣀⡀⠀⠀⠐⠀⠐⠀⠈⠂⠂⢃⠐⢁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠉⢁⠄⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠈⢀⡞⢳⠀⠈⢃⡏⠀⠉⠉⠐⠒⠤⠤⠥⣤⣤⣬⣬⡤⣼⡄⠀⠀⠸⢀⠧⠴⢄⣀⠀⠈⠂⠀⠢⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡨⢀⠞⠀⠈⡇⠈⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣄⠀⠀⠘⡄⠀⠀⠀⠉⠉⠑⠚⠳⠦⣄⣘⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢁⡏⠀⠀⠀⠘⣆⠠⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣀⡎⠱⣄⢀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⡇⠀⠀⠀⠀⠘⣄⠃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠰⡄⠀⠈⣆⠡⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠗⠀⠀⠀⠀⠀⠘⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠛⠀⠀⠈⠳⣤⣨⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠿⠛⠋⠉⠀⠀⠈⣿⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⣴⠶⠿⠿⠿⢿⣤⡀⠀⠀⡀⠀⠀⠀⠀⣉⣉⣠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⢿⡿⢋⠀⠰⠄⠀⠀⠒⣈⣉⣤⣤⣴⣶⠶⠿⠟⠛⠋⢿⣇
⠀⠀⠀⠀⠀⠀⣈⣤⣴⣶⠿⠛⠋⠁⠀⢀⣉⣉⣥⣤⣶⡶⠾⠛⠛⠿⢿⣭⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠘⠉⣡⣤⣤⣶⡶⠿⠿⠛⠛⠉⣹⡟⡁⠀⢐⣦⣀⠀⠀⠈⢻⣆⠀⠀⡀⢀⣀⡀⡀⣿⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⣩⣥⣤⣤⣤⣤⣤⣬⣭⣬⣤⣤⣭⣭⣬⣥⣤⣤⣥⣭⣤⣤⣥⣭⣭⣥⣥⣭⣭⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⣿⣟⠉⠉⠉⠉⠉⠉⠉⠉⣩⡿⠛⠉⠉⡉⠉⠙⠻⣯⡉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡿⠀⠀⢀⡀⠀⠀⠀⣼⠋⠀⠀⣠⠾⡗⣦⠀⠀⠈⢿⡄⠀⠀⠀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⣿⡟⠀⢠⣶⣦⠀⠀⢸⡏⠀⠀⠀⠻⣶⣇⡉⠀⠀⠀⠘⣷⠀⠀⢠⣶⣄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⣿⣷⠀⠈⠛⠋⠀⠀⢸⣧⠀⠀⠀⣤⡌⡟⢻⡆⠀⠀⢠⡿⠀⠀⠈⠛⠋⠄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠙⠲⡷⠛⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣠⣀⣀⣀⣀⣀⣀⣀⣹⣷⣦⣄⣀⣁⣀⣤⣾⣟⣡⣄⣀⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣖⢢⣄⣀⣤⣐⣐⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠈⡹⠉⠁⠀⠀⠀⠈⠉⣓⡢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡠⠄⣀⡤⣠⢇⠰⡄⠠⡄⠀⠀⠀⠀⠙⢮⡣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠈⠛⣉⠥⠚⠁⠘⢄⠘⢦⣳⡄⠀⠀⠀⠀⠀⢷⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⣀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠑⠢⠹⡟⠀⠀⠀⠀⠀⢨⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡟⠀⢈⡉⠀⠀⠀⠀⠀⠀⠀⠀⢤⡱⡀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⡇⢸⣫⣥⣌⠢⠀⠀⠀⢀⠤⠤⣀⡀⠈⡆⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⡀⠈⠘⠃⠸⣿⣿⣿⡠⠁⠀⢀⣷⣿⣷⡈⡿⠀⡇⠀⡆⢰⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⢀⢰⢐⡄⡀⢠⠀⠈⠉⠉⠀⠅⠀⠈⠻⣿⣿⡧⠃⠀⠳⡸⢠⠏⠀⠀⣆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠉⣉⢻⡁⡑⠀⠱⠄⠀⠀⠀⠠⠤⠓⠀⠀⠀⠀⠀⠀⠿⠉⢁⠅⢀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠊⠙⠛⠛⠓⠈⢁⠒⢀⣀⠀⠀⠀⠀⣀⠠⠐⠉⠀⠀⢁⣀⠞⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠠⠄⠀⢀⡀⠀⠀⠀⢲⢛⡃⠈⠉⠛⠳⠄⠀⠀⢢⡀⣰⠋⢁⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢠⢈⡓⣮⠁⠀⠀⠀⠀⣼⠓⡏⠀⠀⠄⠈⠡⣄⠀⠟⠃⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠵⠟⠀⣀⠤⢀⠌⣿⢹⡇⠀⠋⠀⠀⠀⡏⢠⣠⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⢰⠂⡉⠀⠈⠁⠛⠹⠃⠰⢦⣤⣀⣀⣷⠱⠇⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠵⠴⠎⢰⣤⣀⠀⠀⠀⠀⠉⠛⡃⠠⡆⢸⣗⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠹⠃⠲⠐⠂⠐⢲⠒⠂⠚⠓⡓⢭⣥⡾⣿⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠐⠄⠀⠀⠀⠀⠀⠈⠀⠀⢠⠤⠼⢾⣇⠢⡰⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⢿⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡐⠂⠠⠤⠀⠀⢀⣀⣀⡀⠀⠀⠤⠄⠐⣂⠩⠄⠊
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠲⠖⠀⠒⠀⠀⠒⠹⠏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⡤⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠉⠁⠀⠀⠀⠩⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠲⡀⠀⣀⠀⠀⠀⢰⡋⠦⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠟⠀⠀⢀⡭⠀⠀⢀⣾⡟⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠖⠛⠉⠀⠀⠀⠀⠠⠶⠞⠉

⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡠⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠠⠤⠤⣤⣄⣀⣀⡀
⠀⠀⠀⢰⡸⠭⠇⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀
⠀⠀⠀⠀⠉⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣀⠠⠤⢺
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠇⠠⡤⠔⠃
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⡄⠠⠦⠠⢦⠁⣤⢟⢧⣷⢠⠴⠀⣤⢤⠤⠤⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⡀⠁⠞⠁⠐⡒⠄⠙⠸⠜⡧⠓⠯⠥⡈⠠⠭⠄⠀⠀⠠⠬⠐⠴⠤⠉⠂⠀⠾⠂⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⡸⣆⠀⠠⢸⠋⠒⠢⠤⠄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠢⢠⣀⡀⠀⠊⠀⠀⠃⡀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠂⡴⠁⠸⡄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢸⠙⠀⠀⠀⢃⠀⠀⠉⠐⠒⠂⠶⠬⣀⢒⡞
⠀⠀⠀⠀⠀⠀⠀⡆⠈⣼⠀⠀⠀⠱⡄⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡎⠳⡄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢧⠀⢧⠀⠀⠀⠀⠱⡈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠐⣆⠀⠘⣄⠚⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠓⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴
⠀⠀⠀⠀⠀⠀⢸⣷⣶⡿⠋⠉⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣤⣾⣿⣿⡿
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠈⢻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⣿⡿⢫⣿⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣄⣀⡀⣀⣀⣠⣼⣿⣿⡎⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⣿⣿⡟⠀⢸⡏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣷⡘⣮⡑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢶⣦⣾⣿⣿⣷⣐⠸⡇
⠀⠀⠀⠀⠀⠀⠻⣄⣉⣅⣩⣍⣭⣩⣭⣽⣿⣿⣧⣿⣿⡷⢹⡆⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣭⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡗⢺⡦⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣍⢻⣿⣇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠵⠿⠁⣴⠟⣉⡉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣞⡻⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡭⠟⠉⣩⠛⣩⣵⣾⣿⢁⣴⣿⣾⣿⣿⣦⡐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⠃⠘⠉⣩⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠗⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠇⢀⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡽⢣⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⢀⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⣰⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⡎⠈⣿⣿⣿⠇⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⣀⡀⠸⣿⡆⣿⣸⣿⣿⠿⠟⢿⠿⠿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢸⡇⢀⡿⠹⡿⠀⠀⠀⠀⠐⠈⠈⠀⠀⠠⢐⣴⣿⣷⣤⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣷⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡰⠀⠀⣻⡃⣾⢃⢰⣿⠀⠀⢠⣴⣶⣀⠰⠛⠶⣿⣾⣋⠁⢙⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣰⠁⠀⣰⣿⣷⡇⢸⠀⠻⣷⣶⣦⣤⣥⣀⣤⣤⣶⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⣿⣿⣿⣿⣤⠀⣤⣙⣻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢠⡇⠘⣻⣿⣿⣿⣷⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣾⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣤⣀⣈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠻⢧⠺⠟⣿⡿⠿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉

⢸⣷⢤⣀⣀
⠀⠻⡶⢄⠉⠉⠉⠙⠒⠦⣄⡀
⠀⠀⢹⠀⠑⢄⠀⠀⠀⠀⣀⣉⣦⣄⣀⣀⣀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⣄⣀⣀⣀⣀⣤
⠀⠀⢸⠀⠀⠈⣦⠔⠊⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⣦⠖⠉⠀⠀⠀⠀⠀⠀⠀⢀⡨⢥⡷⠋
⠀⠀⠘⣆⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠁⡔⠁
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⡼
⠀⢀⡏⠀⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⠜⠁
⢀⠜⠋⠉⠉⠉⠑⢦⡀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠧⠤⠤⢤⣀⣀
⡏⢠⢦⠀⢀⣤⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠳⡈⠉⠀⠈⠒⠁⢀⠎⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⣴⠿⢿⣆⢀
⠀⠈⢳⡒⠀⠒⠊⠁⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢿⣦⣼⣿⠿
⠀⠀⠀⠙⣶⢤⣀⣀⣀⣀⠤⢚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠿⠋
⠀⠀⠀⠀⠈⠻⡄⠀⠀⡇⢀⡎⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠘⢦⣤⠬⣋⡴⢯⣤⡤⠤⡔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡑⢤⣤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⡄⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⠬⢆⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⡄⠀⠀⠀⠀⢀⠏⠁⣠⠧⣀⣈⣆⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡶⠠⢼⡀⠀⠀⠀⡞⠰⣞⣡⠞⠀⢀⣿⣀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣊⣀⣀⡼⢧⠤⠠⡼⠀⠀⠈⠓⠛⣽⣋⡡⠂⠈⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣯⠴⠃⢀⣰⠃⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣶⣦⣄⠀⠄⠀⠀⠀⣤⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠀⠀⠀⠀⣀⢻⣿⣿⣿⣿⠇⢀⡀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣼⣿⣿⣿⠋⣀⣼⡶⢦⡄⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⣤⣼⣿⣿⠟⠁⠀⣼⡏⠟⡁⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠁⠀⠀⠀⢻⢛⠁⠀⠀⠀⠀⡀⠀⢿⣿⣿⡆⠈⠀⠠⠀⠐⣲⣿⣽⡟⢻⢶⣿
⠀⠀⠀⠀⠀⠀⠼⠀⡄⠀⢀⠀⡤⠀⣀⠰⢸⢻⣶⠀⠀⠀⠀⣈⡴⣿⣿⣿⣧⠀⠆⢁⣂⣤⣙⣿⣿⡡⣿⣿⣿⡆
⠀⠀⠀⠀⢀⣴⣥⠀⢀⠈⠘⢐⠋⠘⠿⠀⣰⢷⣸⣷⣶⣦⠀⠀⡛⢻⣿⢿⣿⣶⣾⣭⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠐⠉⠀⢿⣧⢸⡈⣄⣸⡀⠀⠀⠀⠉⢸⣌⣹⣿⣎⡀⠘⡁⠸⢿⢟⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣌⣿⢛⣽⣧⡀⠰⡄⢀⣘⣿⣿⣿⣿⡋⡘⠁⣳⣭⣮⣽⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢳⣽⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⣇⡤⢘⣼⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⣿⠾⣿⣿⣿⠇⠉⠙⠛⠛⠛⠻⠻⢿⣿⡿⣿⣷⡃⢸⡏
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⢻⣦⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣾⡹⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣭⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⣇⢻⡄
⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣹⣿⡿
⠀⠀⠀⠀⠀⠐⠈⠿⠷⠀⠀⠿⠟⠿⠓⠑⠀⠀⠀⠀⠰⠂⠂⠀⠀⠄⠀⠯⠻⠿⠛⠓⠟⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠒⢉⡁⢰⣶⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠒⠋⣉⡠⠤⠖⠒⠋⠉⠈⢇⠀⠿⠇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠒⠚⣉⣁⠤⠤⠶⢊⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠘⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠒⠂⣉⣉⡤⠤⠔⢂⠟⠋⠁⢀⣤⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣧
⠀⠀⠀⠀⠀⡔⠒⢈⠉⢠⡤⠤⠒⠊⠉⠁⠀⠀⠀⡔⠁⠀⠀⣴⣾⣿⡿⣷⡆⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀
⠀⠀⠀⠀⠀⢱⠀⠘⣢⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⣿⡁⢹⣷⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇
⠀⠀⠀⠀⠀⠘⡆⢀⠥⠔⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⠻⣿⣾⣿⣦⣤⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹
⠀⠀⠀⠀⠀⠀⢡⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⠙⢻⣷⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠀⠏⡇
⠀⠀⠀⠀⠀⠀⠈⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢠⣿⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠰⡇⠀⢧⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠐⠿⣷⣶⣿⣿⡿⠋⠀⠀⣠⠋⠀⠀⠀⠀⣀⣠⠤⠄⠓⠀⣉⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠈⠛⠁⢀⣠⣞⠥⠤⠒⠒⢉⣁⠤⠤⠖⠒⠈⠉⠀⣳⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⡲⠶⠶⠒⠊⣉⣁⠤⠔⠒⢺⠋⠁⠀⠀⠀⠀⠀⢀⠞⢁⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢴⠀⠙⡆⠀⣀⣀⠤⠄⠒⠚⢉⣁⠠⠤⠶⣶⣿⣿⠟⠁⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⢸⡄⠈⡳⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠠⠇⠀⢉⣉⡁⠤⠔⠒⠋⠉⠓⢤⣀⠀⠀⠀⠈⠉⢀⣀⣴⣋⡠⠤⠤⠒⠒⠂⢋⣉⣉⡡⠤⠤⠰⡖⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠧⢲⠊⠙⡍⠀⠀⠀⠀⠀⣀⣀⣀⠠⠬⠽⠛⠒⠊⢉⣉⣁⡠⠤⠤⢲⠖⠂⠉⠉⠉⠀⠀⠀⠀⣀⣀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⡷⠀⠻⠒⠒⠊⣉⣁⣤⠤⠤⢤⠒⠒⠊⠉⠻⠟⠉⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠦⠤⠖⠲⠶⠬⠭⠥⠤⠤⠤⠤⠤⠤⠭⠶⠦⠤⠤⠤⠤⠶⠮⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠨⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣀⣤⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠖⠒⠚⠯⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⣀⣤⣴⣀⣠⣤⣄⣤⣤⣤⣴⣶⣶⣦⣠⣰⣄⡤⣼⣗⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⢠⣶⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣛⣿⣿⣿⣿⡟⢃⡒⠙⠪⣇
⠀⠀⠀⠀⠀⠀⢲⣄⣀⡾⢁⣤⣠⣶⣯⢻⡋⠰⣿⣿⣿⣿⣿⡿⣟⣉⠈⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠳⣦
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣖⢿⣿⣿⣿⣋⣠⣶⣧⣹⣿⣿⡿⠿⡷⢿⣿⡶⣿⣯⡟⢛⣿⣿⣿⡟⠛⠻⣿⣿⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⢻⣿⣿⣿⣇⢹⣿⣿⣿⣿⣧⣤⣶⣤⣿⣿⣿⣾⣿⡿⠋⢻⣿⣷⣤⣼⣟⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⣷⡈⢃⣿⣿⣿⡈⣿⡿⠛⠛⠻⠿⠿⠿⣿⡿⠿⠿⠛⢳⣶⣶⡏⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡀⠻⣿⣷⠾⠋⠉⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠻⠿⠚⠉⣀⣀⣠⣤⡖⠀⣿⣀⣀⣠⣤⡀⠀⠀⢴⣶⣶⡦⢶⣽⣿⡴⠟⠿⠆⠸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠎⠠⠞⠛⠛⠋⠉⠁⠁⠀⠀⠀⠀⠉⠁⠊⠉⠁⠀⠀⠀⠠⠭⠏⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⡀⠄⠒⠂⠁⠈⠀⠀⠀⠘⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠔⠉⠀⠀⢀⠤⠖⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⢀⠤⡋⢑⠢⢄⠀⠀⠀⠀⠀⠡⡀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠃⣎⣰⢸⠛⠋⠀⠀⠀⠀⠀⠀⠃⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠙⠈⠁⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⠀⣑⠢⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⠴⣍⡇⡃⠀⠀⠀⠀⢀⠇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⣉⢀⡉⠜⠁⠀⠀⠀⢀⠼⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠄
⠀⠀⠀⢨⢤⣀⣀⣀⡀⠧⠤⠄⠀⠀⡈⢻⣶⠶⢦⠀⠀⠀⠠⣀⣀⣀⣀⣤⠤⠶⠛⡀⣀⣜⠘⠀⠐⠀⠩⡁⠀⠰
⠀⠀⠀⢐⠢⠤⠤⠤⡧⣀⣀⡀⠤⠤⡆⠒⠂⠀⠈⢠⡀⠀⣀⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣉⡠⠤⠔⠒⠒⠊
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠠⠄⠤⠤⠤⠧⠄⠀⠀⠠⡌⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠦⠴⠔⠒⠉⠓⠒⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠘⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠋⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠤⠨⣄⣠⣤⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠐⠛⠉⠉⠈⠉⠉⠀⠈⠲⡄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⠇⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣴⢮⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⡀⠀⠐⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢉⣀⡀⢢⠀⠈⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⡼⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⢀⣀
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡀⠀⠀⠈⢦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⢰⠋⠙⠋⣩⠑
⠀⠀⠀⠀⠀⠁⠀⠛⠛⡇⠀⣀⣀⣠⡤⢹⠶⣶⠀⠀⢀⡦⢤⡤⠤⣶⣿⠁⠀⣏⠀⠀⠀⢘⣠⡤⠤⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⡉⠀⠚⠴⠧⣀⣀⠼⠤⠀⠉⠉⠉⠛⠄⠚⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠳⠀⠀⣠⣤⣤⠖

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠂⠤⡀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⢳⠤⠓⠒⢘⠃
⠀⠀⢀⣀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢎
⢀⣀⢅⣒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⡀⠀⢀⡀
⠈⠁⠈⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢆⠿⠂⠈⠈⠙⣼
⠀⠀⠀⠀⡷⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠸
⠀⠀⠀⢠⠁⠘⢄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠼⢁⡰⠖⠋⠉
⠀⠀⠠⠃⠀⠀⠈⢢⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⣀⣀⡠⠔⠊⠁
⠀⠀⡇⠀⠀⣀⡠⠄⠓⡄⠀⠀⢀⠧⠤⠀⣀⣀⣀⠀⡇⠀⠀⢀⠾⠓⠉⠉⠙⡀
⠀⠀⢆⢀⣏⠀⠀⠀⠀⢰⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠆⠀⢀⠎⠀⠑⠢⢄⡀⠐⣄
⠀⠀⠀⠉⠛⠁⠀⠀⠀⠈⠑⠢⣀⢈⣦⡀⠀⠀⣴⡉⢀⠴⠃⠀⠀⠀⠀⠀⠈⠂⢬⣧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣔⠷⣧⠻⢶⡜⠲⣴⠦⣤⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠠⠴⠒⠀⠀⠉⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣾⠏⣹⡟⢹⡿⠉⣿⠒⠚⠉⠙⠳⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⡐⠀⠀⣀⡆⠀⠀⠀⠆⠠⢇⡄⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠠⡿⢀⡾⢁⣾⠃⠀⢀⣴⣤⠀⠀⢿⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡆⠀⠀⠀⠀⠀⢀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣃⣸⣃⣾⣁⣾⡁⠠⠤⢈⠉⠛⠁⠀⢨⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠠⡄⠀⠀⠀⠈⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢫⣟⣿⣋⣿⢋⡴⠒⠲⢦⡘⠄⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⣿⣿⡟⢿⣧⣴⣦⢳⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠈⠌⢃⢘⣠⢏⠙⡂⠀⢀⠀⠀⠀⢠⣿⣿⣽⣿⣿⡿⠀⢿⣷⣄⠀⠸⣻⠏⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⢸⠉⠈⠀⠀⢄⣀⠀⠀⠐⠀⠶⣿⡿⠾⣿⡟⠀⠀⡀⠛⢫⡉⠉⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⡀⠀⢃⠠⣆⠀⠀⠘⠉⠉⠀⠈⠦⠆⠈⠁⠀⣠⡉⣩⡈⠀⠀⠈⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⢸⠀⠇⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢂⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⢠⠀⠀⠀⢠⠓⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠄⠈⠀⠀⠀⠀⠀⠳⠀⠀⠀⠈⡀⠁⠀⠀⠆⠒⠦⢠⠐⠰⠰⠒⠒⡆⠖⠒⠲⠰⠒⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠐⡆⠀⡀⠀⠀⠀⠀⠈⠢⢀⠀⠡⠀⣆⠀⠂⠀⠀⠂⡆⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⠁⢘⡁⠀⣀⣀⠤⠀⠈⠀⠲⠂⠃⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠁⠁⠀⠀⠈⢀⠀⠀⢈⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢈⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠀⠀⠈⡀⠀⠈⠀⠀⠀⡄⣀⢀⠀⢅⠀⣀⠨⠀⢀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠠⠐⠀⠀⠰⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠰⠀⠀⠀⠰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡂⡂⢐⠂⢑⢂⠐⡊⠐⠀⠐⠒⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢈⠀⠀⠀⠘⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⡬⠀⠀⠐⢠⡀⠀⠀⡀⢅⠀⠀⠨⢀⠀⠀⢰⠀⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠀⠀⠀⠀⠂⠂⠀⠐⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢿⡿⣿⣿⣶⣶⣦⣤⣤⡄⢠⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣘⣿⣯⣲⣦⠀⠀⠀⠀⢀⠄⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠈⣧⠀⠀⢠⣿⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⢿⣿⣿⣆⣿⡇⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣽⣿⣿⣿⣿⣿⠷⠚⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⣩⣿⣿⣿⣾⣶⡶⢲⣾⡑⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⣤⣾⣿⣿⣿⣿⠟⣸⠃⠈⠻⡿⣄⠁⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⡀⠋⢠⡄⣤⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋⠀⢀⣴⣾⣿⣿⣶⣄⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣽⣯⠀⠀⣿⣿⡟⡇⣿⠿⠛⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡗⡀⠀⢿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡇⠀⠀⠛⢹⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠀⢠⣤⣿⢸⡟⣿⣿⡄⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢈⣹⣻⣿⣿⣷⡶⠶⢦⣤⣄⣀⣀⡀⠀⠀⠀⢀⠠⠀⠀⠀⢀⣿⣿⣼⣧⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣷⣤⣮⣿⣿⣿⣿⣿⣿⣷⣂⣀⡤⠖⣾⣿⣏⢻⣿⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⢷
⠀⠀⠀⠀⢶⣾⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣽⣿⠿⢛⣁⣀⣀⣿⣿⣷⡬⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠛⠛⣿⣯⣍⣉⣉⣉⡙⠛⠛⠻⠿⡯⠔⠚⠋⠉⠉⣙⡻⣿⣿⣧⢀⡀⢰⣁⠀⠀⠀⡆⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠐⠿⠿⠿⣿⣿⣿⣻⣻⣶⣶⣦⣤⣄⣀⡀⠐⠉⠁⣀⣿⣿⣿⣧⡬⠙⠿⠿⡿⠀⣂⣠⡤⠞⠋⠁
⠀⠀⠀⠀⢸⣶⣦⣤⣀⣀⡀⠊⠉⠉⠛⠛⠻⠿⣿⣯⡤⠴⣚⣉⣽⡿⠿⣿⣿⣿⣿⣿⣻⣟⠁⡿⠟
⠀⠀⠀⠀⠙⠿⠷⠾⣯⣿⣿⣿⣶⣶⣦⣤⣀⣤⠼⠗⠊⢉⣉⡠⠼⠁⠀⠀⣌⠁⠀⠀⢠⡿⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣧⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⡼⢽⡧⠀⠼⣏⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣻⡗⢀⡚⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠷⢦⣯⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣦⡤⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣒⣒⣢⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠄⠀⠀⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣴⣿⢁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⣿⣿⣤⣧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣐⢻⣿⣿⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣄⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣉⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⣤⣤⣤⣼⣿⣷⣶⡄⠉⠁⢀⠀⠀⠀⠀⠀⠀⢀⡸⢿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣦⠀⠶⠈⣇⠀⠀⠀⠀⠀⠀⠄⠀⠘⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣻⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⢧⠀⡄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⣻⣿⣿⠀⠀⠀⡄⠶⠶⠂⠀⠀⠛⠁⢸⢇⡇⢸⣿⢿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣠⢏⡼⠁⢸⡿⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠀⠀⠀⠀⠀⠀⠲⠾⣿⣿⣿⣿⠃⠀⣼⡃⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠷⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣠⣾⠗⢠⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠉⢷⣤⡀⠉⠀⣤⣬⣭⣿⡿⠟⣁⠴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣿⣿⣦⡀⠈⢻⣿⣦⣄⡀⢁⡐⡦⠖⢈⣤⠞⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠈⠁⢹⠍⠙⠻⠷⠤⣤⠤⠤⡤⡽⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠙⣷⣶⣦⡀⣦⣀⢀⡀⠀⠀⠀⠀⠀⢼⣿⢘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣴⣦⡀⠀⠀⠀⠀⣠⠸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⡗⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢟⣵⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡌⣿⢾⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⢎⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣯⣭⣶⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⢸⣿⣿⡟⣿⣿⣷⠀⠀⢸⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⣼⣿⣿⢠⣿⣿⣿⠀⠀⢸⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠿⠟⠿⠛⠛⠛⠛⠿⠅⠛⠿⠀⠒⠈⠛⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡵⠋⠀⠀⠀⠈⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⡺⠛⠛⠓⠶⣤⠀⠀⢸⡟⠲⠦⠤⠤⠴⢶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⠀⠀⠀⠀⣀⣼⡇⠀⣿⣝⠷⠶⠤⠤⠶⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣧⣉⡙⠛⠛⢋⣹⡿⠃⠀⢻⣍⡙⠛⠛⠛⠋⣿⡟⠀⠀⠀⣀⣤⠴⠚⣋⣥⣙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣥⣍⣉⣛⣫⣽⣿⠀⠀⠀⠀⠈⠙⠛⢛⣛⣫⣥⣤⠶⠚⠋⠉⠀⠀⠉⠁⠀⠉⠓⠌⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣀⣀⣤⠾⠛⢀⣀⣀⣤⡤⠶⠒⠛⠻⣿⣿⣿⣷⣄⠐⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣟⠋⠉⠉⠀⠀⠀⠀⠀⠀⣷⠈⠻⣿⣿⣿⣷⣄⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠟⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠈⠻⣿⣿⣿⣿⣦⡛⠀⠀⠀⢀⣠⡴⢚⣩⡴⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡛⢦⡀⠈⠳⣄⡀⢄⡀⠀⠀⠀⠉⠻⠷⣦⣬⠙⢿⣿⣿⣿⣦⡴⢞⣫⡵⣞⣫⠵⢶⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡛⢦⡙⢦⣄⠈⠛⢦⡙⠶⣤⣤⠤⠤⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⠿⢛⣋⡭⠶⣚⣻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⢦⡙⢦⡙⠷⣄⠀⠙⠶⠶⠶⣒⣛⣯⠽⣷⣿⡿⢿⣿⣿⣿⠶⣛⣭⠵⠖⠋⢩⡴⣞⠛⠛⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⢦⣙⢦⣈⠳⠶⠖⢛⣋⣭⠵⠖⣛⣭⠴⢖⣻⣿⣿⠟⠋⠁⠀⠀⠀⠀⣿⣜⣃⠀⠀⠀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⢦⣝⠷⠶⢚⣋⣥⠴⢞⣫⡭⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⢻⣤⣉⠙⠛⢋⣉⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠷⣚⣫⡥⠖⠛⠉⠁⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⣿⠦⣤⣍⣉⣩⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⠒⠁⠀⠀⠈⠙⣆⠀⠙⠶⣤⣤⣤⣤⡤⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠳⠦⢤⣤⠤⠶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢤⣤⡤⠶⠛⠁

⠀⠀⠀⠀⢠⠴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⢦⡀
⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⡇⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠒⢊⠉⢇
⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⢀⣀⡠⠤⠔⣒⣈⡭⠥⠐⠒⠉⢇⠈⠆⠘⡀
⠀⠀⠀⠀⡇⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⣗⣂⣩⠥⠴⠒⠺⠭⢄⡀⠀⠀⠀⠀⠀⠀⠉⠉⢇⢣
⠀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⡧⠋⠀⣠⣾⣦⣤⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠸⡘⡇
⠀⠀⠀⠀⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⡇⠀⢸⣿⠹⣿⠉⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢇⢣
⠀⠀⠀⠀⡇⠸⠿⠿⠿⠇⠀⠿⠿⠿⠿⠀⠸⠿⠿⠿⠇⠀⠿⠿⠿⠿⠀⡇⠀⠈⠻⠿⣿⣶⣤⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢘⡘⣆⡀
⠀⠀⠀⠀⡇⢠⣶⣶⣶⡆⠀⣴⣶⣶⣶⠀⢰⣶⣶⣶⡆⠀⣶⣶⣶⣦⠀⡇⠀⠀⠀⠀⠸⣷⠈⣿⡆⠀⠀⡇⠀⠀⠀⠀⠀⡞⢩⠀⢳⡇
⠀⠀⠀⠀⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⢠⣇⣀⠀⠰⣶⣤⣿⣿⣿⢁⣀⡜⠀⠀⠀⣀⣠⠤⠇⢀⣃⣨⡇
⠀⠀⠀⠀⡇⠈⣉⣉⣉⡁⠀⢉⣉⣉⣉⠀⢈⣉⣉⣉⡁⢀⠽⢋⣡⠤⠤⠤⠤⣉⠒⢔⢋⡠⠤⠤⠤⢤⡉⠲⣍⠥⠤⠒⠂⠉⣁⠼⠸⡇
⠀⠀⠀⠀⡇⠘⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⣧⠋⡴⠋⠀⣠⢴⣦⡀⠈⠱⡄⢳⠀⣠⢶⣤⠀⠈⠣⡈⢢⠀⠀⠀⢸⠁⢆⠀⡇
⠀⠀⠀⠀⡇⠘⠿⠿⠿⠇⠀⠻⠿⠿⠟⠀⠘⠿⠿⠿⠇⠸⠀⠀⠀⢷⣸⡀⠀⠀⠀⠸⠀⠟⢧⣸⠀⠀⠀⠀⢱⠈⡖⢒⢒⣋⡠⠬⡤⡆
⠀⠀⠀⠀⡇⢰⣶⣶⣶⡆⠀⣶⣶⣶⣶⠀⢰⣶⣶⣾⡆⢠⠀⠀⠀⠀⢸⡛⢦⠀⠀⢠⠀⡄⠀⢹⠙⣦⠀⠀⢸⠀⡏⠉⠀⠀⣀⢠⠅⡇
⠀⠀⠀⠀⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⣷⡈⢦⠀⠘⠲⢼⡶⠟⠀⢀⠎⢠⠛⠦⣼⠴⠋⠀⣠⠃⣰⠀⠀⠀⣸⠁⢆⠀⡇
⠀⠀⠀⠀⠣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣄⠑⠦⢤⣤⣤⠤⠖⢁⣴⠓⠦⢤⣤⡤⠤⠚⣁⠼⠭⠭⠭⠭⠥⠤⠥⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠖⠶⠒⠊⠁⠀⠉⠒⠲⠶⠶⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⣡⣶⠿⢷⣦⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠰⣿⡇⢀⣼⠋⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⣿⣿⡄⠀⠀⠀⢸⠇⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⢩⣤⡄⠀⠀⡜⠀⠺⣄⣀⡽⠀⢀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣀⣈⣉⣤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠘⢤⣤⠽⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⡆⠀⢀⣴⡾⠟⠛⠛⠛⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⢢⠀⠀⢀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠰⠶⠀⠀⠀⠈⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⠂⠉⠑⠦⣄⡀⠀⠀⠀⠀⠀⠃⡐⠀⠀⠠⠀⠒⠀⣀⣠⣀⡀⠀⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠈⠃⠈⠿⠷⠤⢄⣀⠀⠐⠙⠂⠀⠀⠀⢀⠔⣛⣻⠙⢃⡀⠱⠀⢡
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠤⠄⣀⠈⠑⠆⠀⡄⠀⠀⠀⠀⢶⡿⡃⠂⠀⠀⠁⠀⠌
⠀⠀⠀⠀⠀⠐⢁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠐⢀⠔⣲⡄⠉⠂⢤⡀⠀⠙⠲⣔⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⣠⠖⡧⠴⠂
⠀⠀⠈⠉⠁⠀⠀⠀⣀⡀⠀⣀⠀⠀⠈⡇⡴⠋⠀⠀⠀⢀⠔⢳⡮⠵⢡⣦⣤⣿⣂⠓⠤⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈
⠀⠁⠀⠀⠀⠄⠤⠤⠤⠤⠄⡜⠀⠀⠀⡟⠀⠀⠀⠀⡰⠋⡀⠀⠣⠀⣤⣵⣦⡞⢉⡠⠔⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢀⠎⢠⣑⣒⡣⠔⡘⠷⠞⠛⠀⠀⢀⠰⠂⠀⠀⠀⠀⠀⢠⣶⣾⣶⣿⡇⢹⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣯⠌⠀⣀⠠⠀⠀⠉⠀⢀⠠⠀⠈⢄⠠⠄⡀⠀⠀⠉⠁⠛⠿⠛⠋⠁⠀⠀⠻⣿⣿⡆
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠴⠡⠌⠐⠈⠀⠀⠀⡀⠰⠊⡤⠀⠀⠘⠦⠤⠂⠹⠀⠤⠄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠄⠀⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣿⠿⢿⣿⠟⣣⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⣵⣶⣶⣶⠞⣢⣴⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣡⣾⣿⠿⣋⣵⣾⣿⠟⣋⡛⠿⠿⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣋⣼⡿⢋⣵⣾⣿⠟⣋⣴⣿⣿⣿⣿⣿⣷⡌⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢛⣥⣾⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢟⣡⣾⣿⣿⣿⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢟⣩⣶⣿⡿⢛⣥⣿⣿⠃⣠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢠⣾⠟⣫⣴⣿⡿⢟⣡⣶⣿⣿⣿⣿⣄⠙⠛⢉⣉⠙⢿⣿⣿⣿⣿⣿⠿⣋⣴⣿⡿⠟⠉
⠀⠀⠀⢀⣴⡿⢱⣿⣿⣿⣿⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⠿⣋⣵⣾⣿⠟⠉
⠀⠀⠀⣾⣿⣿⡘⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣉⡀⢺⣿⣿⣾⣿⠟⠋
⠀⠀⠀⠻⣿⣿⣿⣌⢿⣿⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣿⠿⠋
⠀⠀⠀⠀⠈⠙⢿⣿⣦⡹⣿⣷⡜⢿⣿⣿⣿⣿⣿⡿⢟⣩⣶⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡜⢿⣿⣮⣥⣤⣭⡛⣩⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠻⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣿⣿⡟⣦⠀⠀⠀⠀⢠⣀⣸⣿⣿⡏⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⣿⣿⣧⡿⠿⠓⠒⠀⠀⠙⢷⣿⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⡧⣶⣂⠆⠀⠀⠀⠀⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠚⠉⠉⠉⠉⠉⠙⠉⠹⣿⣿⣿⡟⠋⠀⠻⠿⠇⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠳
⠀⠀⠀⠀⠀⢀⣴⢠⡎⠁⠀⢠⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢰⡛⠠⣾⠠⡷
⠀⠀⠀⠀⠀⢸⢿⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣾⡄⠙⣦⣄⠀⠀⠀⠀⠀⢿⣿⠷⠶⠖⠂
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠘⣿⡄⠹⢿⣷⣶⣶⣦⣶⣮⠙⠋⠁
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢿⣧⡀⠀⠀⠀⡀⢸⡁⠀⠀⠀⣺⣿⣿⣷⣜⠛⢹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣸⣿⣇⠀⠀⠈⣧⢸⡁⠀⠀⢘⣿⣿⣿⣿⡟⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⣿⣿⣷⣶⣄⣿⡼⣄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣻⠁
⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⣀⣿⣿⣿⣿⡟⠛⠿⢷⣷⡀⠀⣿⠿⠿⠟⢻⣿⡟⢘⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣼⢻⣿⣿⡟⠀⠀⠀⢸⣿⠇⠀⣿⠀⠀⠀⢸⡟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣿⠀⢻⣿⣧⠀⠀⠀⢸⣿⣷⠀⣿⠀⠀⠀⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⣿⡀⠸⠻⣿⡄⠀⠀⠀⢻⣿⡀⡇⠀⠀⠀⢸⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⣇⠘⢶⣿⡿⠆⠠⠄⢾⠉⢙⣧⣤⣤⣤⣼⣀⣤⣵⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠶⣿⡿⠟⠉⠁⠀⠉⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⢀⡀⠀⠀⠀⢀⠀⠀⡀⠀⣀⠤⠊⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⣀⡀⠀⠀⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠐⠊⠁⣠⢖⠋⠉⠉⠉⠙⠲⣄⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼⠡⠂⠀⠀⠀⠀⠀⠀⠈⢧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡸⠀⠀⠀⣇⢊⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡅⠀⠀⢀⣴⡹⣄⠂⠀⠀⠀⠀⠀⠀⠀⡜⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⣫⣾⢕⢝⠦⣄⡀⠀⢀⣀⡤⠊⢀⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣚⢕⡵⡫⣪⣊⣬⣏⠍⡇⠀⡤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣤⣀⠀⠀⠀⠈⢳⡩⣪⣾⣿⣿⣿⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⢢⡀⠈⠙⢶⠊⣭⣂⣉⣻⣶⣷⣷⣟⣁⣒⡒⢍⠐⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢸⠀⢱⠀⠀⠈⠃⠘⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠃⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⢀⡤⢤
⠀⠀⠀⠀⠀⢀⡔⠁⠀⠘⠦⠀⢇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢀⣀⡙⠆
⠀⠀⠀⠀⢠⠏⢤⡀⠀⠀⠀⠀⢸⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⣏⠠⡙⢧
⠀⠀⠀⢠⠏⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⣈⡹⠃⡼
⠀⠀⢀⡞⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠴⠚⠁
⠀⢀⡞⠁⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠈⠳⠦⠤⢤⣤⣀⡀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣤⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣰⠋⠙⠛⠉⠉⢧⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡴⠞⠁⠀⠀⠀⢀⠠⠀⠂⠈⠻⠶⠶⠏

⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠤⠤⠀⠀⠀⠠⠀⠀⣀⡤
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⠋⢢⣀⢀
⠀⠀⠑⠦⠬⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⣶⠆⣀⡀⠻⠁
⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠈⠃⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠐⢺⢬⡜
⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⠀⠀⢠⣴⣞⣠⣄⠀⢠⣄⣀⡂⢀⡀⢀⣀⣤⣍⠀⠀⠀⠀⠀⣽⣿⠿⠻⠿⠶⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣯⠌⠀⠀⠠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠈⠻⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢧
⠀⠀⠀⣀⠀⢀⠀⠀⠹⣾⢤⣀⣈⢻⣿⣆⣀⣀⣀⣀⠀⠀⠀⠀⣀⠀⢀⠀⢈⣷⡀⢠⣄⣀⡀
⠀⠀⠈⠉⠈⠉⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠐⠈⠉⠀⠰⠀⢀⠂⠀⢶⡔⠡⠐⡄⠀⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠁⣀⠐⣄⠈⠲⣦⠀⠀⠆⠀⠀⠀⢀⠈⠀⡐⠀⠈⠂⠀⠀⠄⢮⣱
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠘⠂⠀⠈⠁⢀⣀⠀⠀⠄⠡⠀⠀⠀⠁⠀⠐⠀⠀⢀⠈⠱⡃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⣀⠑⢐⣀⣀⠠⠀⢠⠁⠁⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠱⡄⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⣀⣁⣤⣼⡶⠂⠀⠀⠀⠈⢐⡄⠀⠀⠐⠀⢀⠄
⠀⠀⠀⠀⠀⡀⡀⠀⠈⠀⠀⠀⠀⠄⠀⠈⠉⠘⠿⠋⠊⣀⠀⠘⠀⣄⠀⠁⠀⠀⡀⠀⠀⠀⢠⠐⠀⠤⠀⠀⠀⠀⢐⠀⠀⢀
⠀⠀⠀⠀⢐⠀⠀⠀⡄⠀⠀⠀⠀⠒⠃⠉⠀⠀⠀⠁⠐⠡⠀⠀⠀⠀⠂⠀⠈⠘⡤⢔⡊⠁⠘⠠⠀⠀⠀⠂⠀⠀⠈⠠⡀⠘
⠠⠀⠌⠴⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠁⢈⣦⠞⠡⠀⠉⢦⡀⠀⠈⠁⠀⠀⠠⠑⠂
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⢈⣠⠄⠀⠀⠀⢠⠈⣂⠀⠀⠀⠀⠀⠀⠀⣴⡟⠣⠀⠀⠀⠀⢀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠒⠂⣤⣀⣀⣀⠀⠀⠀⠠⠀⠀⠐⠂⠀⠂⠀⠀⠁⠀⢀⣴⣾⡏⠁⠀⠀⠀⠀⠀⠉⠉⠙⢦⠀⠀⢀⠀⡄⠀⠤⢀⠠
⠀⠀⠀⠀⠈⠙⠛⣿⣿⡆⠀⠀⠀⠀⠐⠠⠄⠂⠀⠐⠒⠠⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣰⣶⠶⣶⣶⣦⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠁⠉⠛⠓

⠀⠀⢀⣤⣤⠠⣀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠠⣠⡤
⠀⠀⠈⠛⣻⣷⡄⠳⠈⠀⠀⠀⠀⠀⠊⢀⣾⠟⠀⠀⠀⠀⠀⠐⡠⠤⠀⢤⠆
⠀⠀⠀⠀⠈⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠇⢸⠃⠀⠀⠀⠀⠘⣷⠺⠀⠀⠁⠀⠀⠀⠠⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠗⡀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠠⢤⣤⠴⠀⢀⡜⠀⠐⣶⣴⠒⣿⠀⡀⠀⠈⠫⢀⡀⢀⠀⢰⡇⠀⣰⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡝⠢⣄⠀⢰⣥⠖⠋⠀⣠⠀⢼⡉⣱⡄⡈⢿⣿⣶⠀⢢⢹⢉⠀⡜⠉⠉⢟⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠁⠐⣄⡀⢀⡠⠀⠀⢠⡟⠀⠀⠈⢻⣾⡧⢾⣿⡏⠀⣈⡀⢀⣨⠅⠀⠶⣞⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠛⠿⠇⠀⠰⠁⠀⠀⠀⠀⠰⠿⠀⠜⠹⠁⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠹⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⡟⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⢉⣻⣿⣿⣷⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣼⣿⣿⣿⡟⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⣙⡻⣿⣿⣿⢰⡎⣦⠶⠟⢹⡇⢸⣿⣟⠶⢖⣷⡇⣿⣿⣿⡽⠗⠊⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣼⢯⣬⣿⣯⢈⣿⣿⣤⠤⡎⠀⠈⢹⡟⣾⢟⣿⡱⣿⣿⣽⡽⢇⣶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⣶⣶⣝⣿⣯⠚⡛⠁⠀⠀⠀⠀⠸⠀⠈⠁⠈⢉⠙⢿⣿⡻⠿⠿⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢈⢸⣿⣤⠆⣴⠺⠀⠀⣀⣠⣤⢀⣀⡀⡞⣢⡀⣨⣿⡥⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⠻⢿⡇⠼⣿⡷⢂⡳⠷⠋⠙⠈⣿⠁⢻⢟⠷⢺⡿⠳⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣾⠁⡘⠍⠠⠖⠉⠀⣤⣠⣄⠈⠲⣄⠈⣥⣀⢻⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇⢠⡅⠸⠃⠀⠆⢀⡴⠋⠀⠉⠉⢷⣤⠹⡆⢨⡋⠸⣧⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⢠⣖⡁⠀⠀⢊⡴⠖⠛⠛⠓⠦⡀⠄⢸⡼⢡⠀⣿⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⠈⠙⠁⠀⠠⠸⢶⣿⠇⠀⣿⡷⠾⢤⠀⠁⢿⠂⣿⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⣿⡆⠁⣤⠀⣶⡘⠆⠀⠀⠀⠈⠀⠘⣾⠆⢀⠎⠠⣿⡂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠁⣷⣿⣿⣇⣀⣵⣶⣶⠾⠷⣶⣶⣾⡟⣻⡙⣿⣿⡉⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠠⠾⠿⣛⣿⣟⣌⡉⠻⠶⠶⠏⢘⣰⣎⣛⣻⣿⢥⣉⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣬⣿⡳⣟⠰⠺⠿⣿⣿⣿⣄⣠⣶⣿⣿⣯⣋⣱⠄⣸⣿⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⣿⣟⠓⠂⢶⣿⡿⣿⣿⣿⣿⣿⣿⣮⡋⣩⣿⡿⣃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠊⢻⣿⣷⣷⣾⣿⡃⢺⡇⣹⣝⣏⣲⣶⢿⣿⢖⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠷⢼⣿⠻⠿⣿⣷⣎⣿⣿⣿⣿⣿⣿⡟⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⡿⣷⣶⣬⡿⢿⣿⣫⣿⣧⣿⡷⠄⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⠛⣿⢿⡇⠈⣿⣿⡿⠟⢿⡯⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠏⣽⡇⢰⣿⣻⣃⠀⢀⢃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⠀⣀⣿⡇⠰⢶⡿⠯⠀⠈⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⢻⣿⠀⣸⣿⠗⣶⡄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠿⠿⠷⠿⠿⠛⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠋⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡁⠀⠀⠀⠀⠀⠀⢀⣴⣴⣶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⢦⣤⠀⢰⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⣿⣷⣜⣧⣾⣵⠀⢠⡀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣤⣶⣾⣿⣿⢿⠟⠛⠷⣤⣿⣶⣦⣦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢉⣾⢻⢏⡇⠞⠈⡠⡀⠀⠆⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠸⣿⠛⠘⠀⣴⠀⠀⡀⣤⣾⣤⣤⣤⣤⡔
⠀⠀⠀⠀⠀⢀⣤⣲⣖⣂⡖⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠈⠀⠀⢿⡷⠖⠋⠉⠅
⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⢠⣶⡀⢀⡀⢰⣿⣀⣤⣤⣤⡾⠁
⠀⠀⢸⣿⡿⢿⣿⣿⣿⡇⡇⠈⣄⣀⡀⠀⠀⠀⠀⣠⣼⠏⠀⠀⢀⣴⣿⣿⢿⠿⠟⡩⣥⠀⠀⠀⠀⠘⡄
⠀⠀⢘⠛⠀⠈⠈⢠⢸⡇⡇⠀⢻⣀⣀⡀⢠⣴⣿⣿⠋⠀⠀⠀⠸⣿⣅⣿⢰⣄⡀⣠⣿⣤⣤⣤⣴⣶⡇
⠀⠀⣼⣀⣧⣧⣼⣾⣿⣇⢳⠀⠸⣿⣛⣿⣭⣽⣿⠇⠀⠀⠀⠀⠀⠙⢿⣿⣼⣟⠙⠉⠉⠉⠉⠉⠉⠉⢱
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠸⡀⠀⢻⣿⠿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡇⢧⠀⠘⡇⠀⠀⢸⡃⠀⠀⠀⠀⠀⢠⣶⡄⣿⠀⣿⢘⣿⡄⠀⠀⠀⠀⢤
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡸⣄⠀⠙⠀⠀⢺⣵⣄⠀⠀⠀⠀⠈⠻⣿⣿⣦⣿⣾⠿⠁⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣷⣻⠀⠀⠀⠀⣄⣿⣿⣿⣶⡄⠀⠀⠀⠀⠻⠉⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠆
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣦⣤⣤⣤⣄⡀⣀⣀⠀⢀⣀⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁


⣾⣷⠿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠉⠉⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡇⠀⠀⢚⠝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡇⠀⠀⠸⣊⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣤⣀⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡀⠈⢻⡷⢤⣤⠶⠚⠛⠉⠉⠉⠁⠀⠀⠀⠈⣉⣉⣛⠳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⠽⠀⠀⠀⢹⡄⠙⢦⡀⠀⠀⣀⣤⠶⠖⣛⣛⣩⣭⣭⡭⠿⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠵⠚⠁⠀⠀⠀⢻⡀⠀⠉⠀⠘⠿⠒⠛⣛⣩⣭⣍⡀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠞⠁⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠐⢁⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠘⣿⢷⡀⠀⠀⠀⠀⠀⡸⣰⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡼⢻⡄⠀⠀⠀⠀⠠⠏⣸⢻⣶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⠃⠀⠀⠀⠀⠀⣴⢣⠏⣿⣀⡽⣷⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠏⣴⢻⡿⠶⠋⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⡞⢡⣾⡇⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⡴⢁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣯⣉⡛⢳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢋⣤⢞⡽
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⣤⡈⠙⠻⣴⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⣵⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣹⡇⢰⣷⠘⣷⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡴⠛⣡⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠛⠀⢹⣿⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⡴⠊⣡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠶⡤⣤⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡴⣣⢹⠷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⢢⡄⠀⠀⠀⠀⢀⣤⠖⢋⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠷⠞⠁⠀⠈⠹⡆⠀⠀⠀⠀⠀⠘⣩⠞⣡⣿⣀⣤⠤⠶⠛⡏⠀⣺⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣻⡵⣋⡿⠁⠀⠀⠀⠀⠀⠛⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⡀⠀⠈⢉⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⠂⠀⠀⠀⠤⠤⠤⠤⠄⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠟⠛⠋⢩⠃
⠀⠀⠀⠀⠀⠶⣻⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⡶⠧⣀
⠀⠀⠀⠀⠘⡵⠀⠘⣷⠀⠀⠀⠀⠀⡀⢶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢁⣀⡈⢥⣶
⠀⠀⠀⠀⠀⠘⠀⠀⠘⣄⠀⠀⠀⠀⢀⣾⣿⣿⣦⣀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠠⣞⡢⠄⣄⡀⠀⢀⠭⠽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣳⣦⡔⠀⣾⣯⣿⠻⠷⣿⣾⣞⣒⣠⣤⣭⣿⡂⠀⠰⣿⣿⠶⠞⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⠹⡄⠰⠃⠀⠉⠻⠒⠶⠤⠬⠟⠛⠋⠉⣿⡷⣄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣠⣀⢨⣌⢄⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⣠⣎⣤⣸⣄⣤⣠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠊⠙⠙⠛⠋⠈⠛⠻⠟⠻⠻⠀⠀⠉⠭⠉⠀⠒⠉⠋⠉⠙⠛⠛⠃⠚⠑⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠋⠛⠿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠁⢀⣀⡀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠘⠛⠛⠻⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣦⣤⣤⡀⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠋⠉⠙⠛⠁⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣦⣤⠀⢀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⣠⣦⣤⣤⣴⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⢻⣿⣦⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣿⡟⠛⠿⠛⠁⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠁⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠀⠀⠀⠀⠀⠸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠀⠀⣠⣴⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠹⣿⣧⣀
⠀⠀⢀⡀⠀⠀⢸⣿⡇⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣷⣦
⣠⣾⡿⢿⣿⣆⢸⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⣿
⣿⣿⡀⣀⣿⣿⣿⣿⡇⠀⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢠⣿
⠈⠻⠿⠿⣿⣿⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣼⣿
⠀⠀⠀⠀⢿⡿⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⢰⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠀⠀⠀⠀⠀⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣶⣶⣶⣾⣿⡟⠙⠛⠛⠛⠛⠛⠛⠛⠙⣿⣿⣶⣶⣶⣶⣾⣿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⢿⣿⣿⣿⣿⣿⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢊⣭⣴⡶⠶⠾⠛⠛⠒⠂⠀⠉⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠖⣚⠲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡽⢣⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠐⣪⠍⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠂⠀⠀⣤⡄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢠⠖⠉⠉⠙⠲⡄⠀⠀⠈⠁⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣇⠰⡖⢰⡢⠀⢹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠘⢦⣀⣀⣀⣠⡯⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⣤⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⣀⠀⠀⠀⠀⢠⡄⠠⠤⠒⣒⣉⣤⡶⡻⠁⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠻⣿⠀⠀⠀⠀⢸⠟⠛⠋⣏⣉⣩⠽⢳⣣⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠦⢴⣧⣄⣀⣀⣠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠄⠀⠤⠤⠤⠤⠤⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⡖⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣠⣤⣤⣿⣿⣀⡴⠋⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣇⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠉⠉⠁⣿⣿⣭⠄⠚⣷⣿⡍⠱⣶⣄⠀⠀⠀⠀⣰⣿⣤⠄⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⢙⣽⣿⣼⣿⣿⣧⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣧⣴⣿⡀
⠀⠀⠀⠀⠀⠻⣶⣤⣤⠴⠶⠶⠿⠿⠿⠿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⠷⠀⠈⠙⠿⣿⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣀⡀⢺⣿⡅⣷⣰⠹⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⣀⠈⠛⠛⠺⢿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠟⠛⠿⣷⣼⣿⣠⣫⠅⠀⠀⠀⠛⠉⠛⠿⢿⡛⠛⠿⠟⠛⠛⠒⠾⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⢶⠶⣶⣶⠶⢶⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡿⣛⣪⡿⣟⡋⢛⢋⡉⢉⠉⡛⠛⠛⠿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⡿⢿⡿⣶⣿⠁⠀⢈⡙⢋⣳⣶⣶⣤⣩⣵⠤⠀⠘⠙⠻⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠀⣿⡇⠀⠀⠀⠈⠀⣿⣿⠁⠀⠠⣌⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⢀⣼⣯⣿⣷⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁⠂⣠⣮⡿⠐⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⠿⠟⠛⡉⠙⠏⣿⡇⠀⣀⡠⠀⣶⣞⡿⣿⣿⣿⠿⡶⣿⠆
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⡅⢲⣀⣿⠇⣋⠀⣱⡀⠀⠀⠀⠀⢾⣿⣿⣭⣭⡷⢄⡨⣇⡠⣄⣿⣿⣿⠁⢠⡄⠀⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠠⢾⣿⣧⣤⣴⠟⣿⠁⠂⠙⠩⠳⣼⠇⠀⠀⠀⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡀⢀⣽⣷⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⢸⢛⣴⠳⠾⠀⢀⢠⣴⣿⡾⠋⢸⠆⢠⣷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣶⡛⢻⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡏⣸⣿⠇⢸⣿⣿⣿⣿⣿⠇⡍⠁⠀⣿⠉⠉⠉⠉⠉⠉⠙⠻⠟⠛⠋⠉⠀⢻⣿⣷⣿⠲⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢼⣭⢽⣿⣦⣼⡿⠟⠉⠁⠀⠀⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠻⢷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠠⣠⣻⡿⠟⠋⠉⡀⠀⣀⡀⠀⠰⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠚⠿⢿⣿⣿⣿⢇⣀⣚⣿⣾⣷⣶⣦⣷⣄⣄⣤⣤⣶⣶⣿⡄⢉⣛⣏⣴⣶⣤⣰⣆⣼⣧⡙⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠈⠁⠈⠁⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠻⠁⠀⠾⠿⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⣭⣭⠿⠀⠀⠀⢠⠈⠡⠤⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠠⢜⠀⠀⠶⠖⣿⠍⠡⠤⠤⢵⠀⢚⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣉⣿⣉⠘⣛⣛⣽⡇⠀⢒⣚⡿⠀⠥⠵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢤⣷⠀⢈⣁⣀⢽⡇⠈⣉⣭⣿⡀⢒⣲⡧⠀⠀⡀
⠀⠀⠀⠀⢀⠀⡀⡤⢄⡐⢒⡲⠒⠚⠓⠒⠛⠂⠀⠂⠤⢾⡃⠀⠶⣺⣯⠄⣉⡥⣿⢉⣽⡇
⠀⠀⠀⠀⠘⠙⠓⠻⢶⠀⠈⠀⠀⠀⠀⣀⣠⠴⠖⠒⠈⢉⠉⠈⢻⣽⡻⡤⠤⣶⣷⢴⣿⣧⡆⢀⣤⣤
⠀⠀⠀⠀⢀⡀⠀⢈⢹⠀⠀⠀⠀⠀⠀⡿⠿⠷⢤⣬⣦⡶⣰⣭⣿⣶⣒⣖⣒⣲⣾⣽⠿⠿⣯⣽⣿⣿⠷⠂
⠀⠀⠀⠀⠈⠙⠊⠛⠻⢦⣀⠀⠀⠀⠀⣏⠂⠀⠀⠀⠀⡏⠁⠉⠈⠉⠩⣏⠉⠉⠾⣁⣐⣐⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠤⠹⠷⢶⣦⣄⣀⣇⣠⣤⣶⣾⠽⠏⠂⠐⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠠⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⢨⡭⠶⠒⠛⠛⠋⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣭⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠍⢱⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠈⠁⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡉⠉⣠⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠋⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠈⠉⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡸⠓⠒⠛⡋
⠀⠀⠀⠀⠈⠀⠐⠒⢻⡀⢀⣀⣀⣀⡍⡶⣤⠀⠀⠀⣄⣐⡤⠥⣶⡞⠁⢠⡇⠁⠀⠀⠃⣀⢤⣤⣤⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⣉⠁⠘⠦⠿⣀⣀⠸⠄⠀⠁⠈⡙⠃⠤⠊⠁⠀⠘⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠛⠉⠀⠀⠀⠀⠀⠸⠀⠀⣤⣤⣴⠇

⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡒⠠⢄⡀⠀⠠⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠑⢤⠑⡄⠀⠀⠀⠀⠉⠑⠢⢄⣀⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠘⡆⠀⠀⠀⠀⠃⠈⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠠⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢀⣀⠀⠀⠀⠰⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡼⠁⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢀⣠⠖⢹⡄⠀⠀⢸⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠹⣄⠀⠀⠀⠀⠀⠀⠀⠻⣤⢤⡤⠖⠚⠉⠀⠀⠀⢧⠀⠀⠘⡆⠀⠸⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠰⣛⣦⣼⠟⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠙⢦⡉⠓⢢⠆⠀⠀⠀⠸⡆⠀⠀⡟⢆⡶⢿
⠀⠀⠀⠀⠀⠈⠓⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠁⠓⣄⣀⡀⠀⠀⠉⠓⠾⢧⡤⠀⠀⠀⢻⡀⡄⣿⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣀⡀⠽⠗⠀⠀⠀⠀⠻⠀⠓




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⢀⡤⠴⠶⠦⠤⢤⣖⠢⣤⣀⡀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠉⣡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣾⣶⣾⣾⣷⡀⠀⠀⠀⠀⠀⣠⠴⠶⡿⠷⠦⣄⡀
⠀⠀⠐⠦⠀⠀⠀⠈⢳⣀⣈⣉⢀⠞⠀⠀⠀⣀⠴⠚⠁⠀⠈⠉⠉⠉⠉⠀⠙⠢⣄⠀⠀⠀⠈⢦⣀⣀⣀⣀⡜⠁⠀⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⣀⠼⢿⠿⢿⠿⣄⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⠿⢿⡿⠿⠿⢷⡀
⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢀⡤⠶⠧⢤⠀⠀⠀⠀⠀⠀⠈⢷⠁⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⡴⠁⠀⠀⠀⣠⠤⣄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣠⠦⡄⠀⠀⠀⠈⢢⡀
⠀⠀⢸⠁⠀⠀⠀⠀⢧⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⢆⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⣅⣀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢙⠆⠀⣇⢀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⡏
⠀⠀⠘⡄⠀⠀⠀⠀⠈⠛⠉⠀⠀⠘⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠉⠛⠁⠀⠀⠀⢀⡜⠁
⠀⠀⠩⢞⡦⢄⣀⣀⣀⣀⣀⣀⣀⣠⣼⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⡯⣀⡀⠀⠀⠀⠀⢀⣠⡔⣋⣀⣀
⠀⠀⠀⠀⠀⠞⠁⠼⠋⡽⢋⠜⢋⠔⢁⠔⢁⠞⣩⢟⡿⢛⡿⠋⣹⠟⣹⠋⡹⢋⡽⠁⠎⠰⠋⠞⠙⢫⠟⡽⠁⠞⠙⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠈⠀⠀⠁⠀⠁⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠒⠂⠒⠒⠒⠠⢤⣀⠀⠀⠀⢀⣀⡠⠤⠤⢐⠒⣒⣒⣒⣒⣒⣒⣒⡒⡒⠠⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⢀⣀⠤⠤⠴⠖⠶⠤⠤⣄⡀⠀⠙⠲⢏⡩⠔⠒⠋⠉⠉⠁⠀⠀⠀⣀⡀⠀⠀⠀⠉⠉⠉⠓⠒⠬⣍⡓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠑⢆⠀⠀⠀⠀⢀⣤⣶⠒⠛⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠉⢦
⠀⠀⠀⠀⠀⢀⡔⠁⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠳⡄⠀⠀⠀⠉⠛⠛⠲⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⠀⡌⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠹⡄⠀⠀⠦⠤⢤⣤⡤⠴⠿⠛⠀⠀⠀⠀⠀⠀⣀⡤⠊⢀⡤⢺⡇
⠀⠀⠀⠀⣼⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠛⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢱⡤⣄⣀⣀⣀⣉⣁⣀⣀⣀⣤⠤⠤⠖⣒⣉⡥⠶⠚⣡⡴⢫⡇
⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⢉⣉⣀⡤⠴⠒⢋⣡⢴⢿⣇
⠀⠀⠀⢰⡇⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡟⠛⠛⠛⠛⠓⠚⠛⠛⠛⠛⠉⣉⣉⠠⠤⢒⡺⠽⠚⣡⢞⢽⡄
⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡯⠭⠭⢭⣭⣭⣭⣭⠭⠭⠭⠥⠔⠒⠂⣉⣡⡤⠖⢋⡥⣫⢺
⠀⠀⠀⠀⢳⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⠇⠀⠸⠒⠲⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠒⠋⢉⣉⣠⣴⠾⠛⢉⣴⠋
⠀⠀⠀⠀⠈⢆⠀⠙⡄⠀⠀⠀⠀⠀⠀⠿⣷⣶⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠋⣉⣁⠤⢴⡞⠁⢈⡇
⠀⠀⠀⠀⠀⠈⢦⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣠⣟⣛⣛⣒⣒⣒⣒⣒⣀⣠⣤⡶⠶⠶⠞⠛⢉⣁⣤⡶⠟⢀⡠⢚⠇
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⢀⣼⠥⠤⠤⣄⣉⣁⣀⣀⣁⣀⣤⣤⣤⣤⡶⠶⠟⢛⣉⡡⠤⠒⢉⡴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀⠀⠉⠓⠒⠤⠤⠤⠤⠤⠐⠒⠋⠁⢀⣠⠶⠥⣈⣉⠙⠓⠒⠒⠒⠀⠭⠭⠭⠔⠒⠒⠒⠒⠛⢉⣉⣠⣤⡶⠞⣉⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢤⣄⣀⣀⣀⣀⣤⠤⠔⠺⢭⣈⡑⠒⠒⠤⠭⢭⣍⣒⣒⣒⣒⣒⣒⣒⣲⣶⠬⠭⠽⠛⠋⣉⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠢⠤⠤⠤⠤⠤⠀⠠⠤⠤⠤⠤⠤⠒⠒⠋⠉⠁