FUNNY Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⠿⠿⢿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠈⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢀⣴⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣷⡈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⢻⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⢠⣿⠏⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠿⠷⠶⣤⡀⠀⠹⣿⡄⢻⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⢸⠃⠀⠀⢀⣴⡿⠟⠋⠉⠀⠀⠉⠙⠻⣶⡄⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠀⠀⠀⠀⠈⠙⣦⡀⠙⣧⠀⠹⣿⣧
⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠁⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⠀⠀⢹⣿⣧
⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀
⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠻⣿⡟⠻⠶⠶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇
⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣤⡤⠶⠋⠁⡾⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡞⠁⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣦⣄⡀⠀⢀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠙⠛⠛⠛⠋⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢷⣀⣰⣏⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠐⠛⠛⠛⢛⣛⣛⠛⠋⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⡀⣸⣇⣀⣀⣤⣤⣶⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⡈⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢈⣀⣀⡀⠀⠀⠀⠈⠷⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠁⠀⠀⡠⠤⣄⠀⠾⠾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⣠⠀⠀⠀⢀⠎⠀⠀⠀⠑⣄⠒⠺⣄⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⢊⠏⠁⠀⠠⠊⠁⠀⠀⠀⠀⠑⠈⢢⠀⢈⣧⠀⠀⠀⢀⠜⢁⡠⡙⢆⡠⢔⠂⠉⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡠⠀⡇⠀⠀⣀⣀⡀⣠⠒⠐⠀⢣⢀⠊⠀⠀⡠⠃⠴⠁⠁⣸⡤⠒⠁⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢘⠁⠀⢃⢰⠋⠀⠀⠈⠉⠁⠀⠀⠃⢺⣆⠀⡔⢡⠊⠀⣢⠴⡇⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠤⢄⣈⠉⠑⢄⡄⠄⠀⠀⠠⡶⠄⣀⠠⠃⠀⠓⠊⡔⡁⠖⠊⠁⠀⠈⢳⣈⣁⠀⠀⢀⡄⠈⠄
⠀⠀⠀⠀⠀⣀⣀⡀⡇⠀⠠⠒⠲⠤⣭⣐⡚⠷⠀⠀⠉⡉⠀⠀⠀⠈⠐⢄⣠⠊⠁⠀⠀⠀⠀⠀⠀⢀⡴⠁⢠⠊⠁⢁⠀⠠
⠀⠀⠀⠀⠘⠁⠀⠐⠛⠒⠲⢤⣤⣀⣆⣀⣸⣑⡒⢤⣔⠀⠀⠀⠀⠀⠀⣸⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⢱⠔⠋⠀⠀⠈⡆⠀⠇
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⣀⠕⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⣀⣀⣠⣴⡿⠿⢿⡃⠀⠀⠀⠀⠀⠀⡘⢈⡠⠒⠁⠈⢣⠜⠀⡰
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣹⠉⢆⠀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠛⠛⠛⠁⠀⠀⠀⠈⡆⠀⠀⠀⠀⢠⠃⠉⠀⠊⠉⢁⠆⢀⠜⠁
⠀⠀⠀⠀⠀⠈⡆⠠⡤⠭⡀⠉⢳⡳⡀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⢁⣀⡀⠀⣀⡔⢁⣀⣀⡀⣤⠎⣠⠣⢄⡠⠔⢋⡔⠁
⠀⠀⠀⠀⠀⠀⢡⠀⢇⠀⠘⠤⠜⠣⡈⠢⡀⠀⠀⠀⠑⣄⣀⣤⠚⠁⠀⠉⠙⠛⠡⠭⢀⡠⠖⠁⡰⣁⠔⠉⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠈⠆⠈⡆⢰⠚⢉⢑⣛⠂⠈⠲⢆⣛⣉⡱⠚⢀⡔⠀⠀⠀⠀⣀⠝⠓⠲⡤⠴⠚⢏⢀⡠⠚⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠙⢄⠘⠂⠀⠀⡝⠒⠤⠤⠥⠤⠒⠁⠈⠉⠉⢏⠁⠱⡤⠦⠴⠁⠀⠀⠀⢣⠀⠀⠀⠀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠅⢂⡀⠚⠢⠤⠤⣀⣀⣠⠒⠒⠢⠤⠖⠋⣄⠠⠋⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⡐⠁⠈⢢⣀⣀⡤⠒⠀⡖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠠⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⡰⠁⠀⠀⢠⡇⣇⢘⠒⢤⠆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢲⠃⠀⠀⠀⢸⡇⡏⠁⠀⡸⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠁⠀⠀⠀⠀⢸⢽⠁⠀⢠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⠀⠀⢀⠤⡀⣸⣿⡿⠀⢠⠃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⣀⣀⡤⠤⠔⠒⠊⢫⠀⢆⠀⠀⢀⠔⠁⠀⢳⡜⢿⠃⡠⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢣⣈⡦⠒⠁⠀⠀⠀⠈⠧⣏⠔⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠑⢄⠀⠀⠀⠀⠀⠐⠚⠉⠱⡀⠀⠀⠀⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⢔⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠻⢿⣟⣛⠿⢿⡿⣿⣭⣭⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⢘⡏⠒⠀⠈⡉⣉⣉⠛⠺⠿⠿⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠄⠀⠠⠤⠤⠄⠒⠒⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⡋⣶⣳⣦⣴⢤⣶⣤⣴⡒⣀⣤⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣾⣉⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣽⣴⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢄⣴⣶⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣆⣀
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡷⠄
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⣶⡀
⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣀⣤⣴⣶⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣭
⠀⠀⢰⣿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣴⣾⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⣿⡷
⠀⢀⣾⣷⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠁⠀⠀⠉⠙⢿⣆⣠⣄⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣇
⠀⣿⣾⣿⣿⣿⣿⠃⠀⠀⠀⣰⣿⡿⠋⢀⣠⣤⣶⣦⣤⣄⠀⠀⠀⣾⡏⠀⠀⢀⣄⡀⠀⠀⠈⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡀
⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⡿⠋⢀⣴⡿⠋⠉⠀⠀⠉⠻⣷⡄⠀⢻⣧⠀⠀⠘⠛⠃⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇
⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⠁⠀⣾⡟⠀⠀⠀⣠⣀⠀⠀⠸⣿⠀⠀⠙⢄⡀⠀⠀⠀⢀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠛⠛⠀⠀⢀⡏⠀⠀⠀⠀⠙⢛⠶⣾⣿⣿⣷⣶⣄⣀⣤⠶⠖⢦⠀⠀⠀⠀⠀⠀⠸⣿⣿
⢈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢒⣽⣿⣦⡀⠀⠀⠀⠀⣠⡾⣡⠀⠀⠀⠀⠀⠘⢷⣿⡟⢧⡀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠙⠻⠷⠶⣶⣟⡋⢰⣿⠀⠀⠀⠀⠀⠀⠈⢿⣄⢸⡇⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣿⣿
⠀⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡾⠋⣽⠟⢻⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠇⠀⠀⠀⠀⠀⠚⢡⡌⠁⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠛⠋⠉⠀⠀⠻⣦⡘⣿⣇⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⡤⠶⣤⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄⣀⣀⣠⣴⣿⣿⢿⠀⠀⠀⢀⣴⣶⣾⡿⠁⠀⠀⠀⠀⢰⣿⣿⠇
⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⢿⡿⠿⠿⠿⠟⠋⠁⢸⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⡀⢀⣠⣤⣤⣄⠀⠀⠀⠳⡄⠀⣀⣠⣤⣤⣼⣄⣀⣸⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠈⠙⣷⣄⠀⣀⣽⡿⠟⠋⠉⠉⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⣠⠶⠶⢶⣤⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⢀⠀⠙⣿⡄⠀⠀⣀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⣀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀
⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⠉⢠⠄⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠄⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠂⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣥⣾⣿⣿⣥⣴⣶⡤⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠈⠐⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡿⠻⢿⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠈⢠⣶⣤⣀⣠⠀⠀⡀⠀⠀⣀⠀⠹⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠫⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠳⠛⠋⠁⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠠⠖⠀⣀⠀⠀⠀⢠⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⠅⠀⠀⠀⠀⠘⢄⠀⠀⠀⡀⠀⠀⡖⠀⠀⠁⠀⠀⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠀⠀⠐⢄⠀⠀⠐⠒⠿⠛⠀⠀⡀⠀⠀⠀⡀⠀⠀⠂⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠐⠈⠑⠲⠀⠤⠤⠄⠐⠈⠀⠀⠀⢐⠀⠀⠀⠄⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⠁⢀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠄⠁⠒⠂⠂⠗⠀⠰⠁⠀⠀⠈⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⡰⠊⠀⠀⠀⠀⣰⠃⠀⠉⠀⢀⠤⠀⠀⡀⠁⠄⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢀⡒⠢⠁⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠠⠆⡴⠂⠒⠀⠈⠉⠉⠁⠀⠀⠀⠐⠀⠀⠀⠀⠂⠁
⠀⠀⠀⡈⠀⠀⠠⠀⠀⠀⠀⠄⠐⠀⣠⠦⠐⠂⠈⡠⡄⠀⠀⠀⠀⠀⠀⣀⠤⠄⣀⠠⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠌⡄⠷⢤⠤⡤⠒⠂⠹⡁⠶⠷⡖⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⢸⠰⡁⠠⣀⠔⠀⣰⠁⠀⠀⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠠⠀⠀⠀⠀⠀⠘⠤⠉⠒⠀⢤⡭⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣶⣶⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⢞⣉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⢲⠆⠀⠀⢸⣷⣄⠀⠀⠀⢸⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢⠆⠂⠀⠀⢈⣿⠻⣷⣄⡀⠘⠀⠁⢀⣆⠀⠀⠀⠀⣀⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠈⠛⠿⢿⣶⠿⠛⠿⣶⣶⡶⢿⣿⠃⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣤⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣇⠀⠸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⣠⠞⠉⢀⣀⠈⠉⡿⣧⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⢁⣠⡿⠧⠤⣄⣰⣞⢧⡀⠀⢠⠇⠀⢻⣦⡾⢫⡽⠿⠚⠛⣿⡄⠀⣇⡀
⠀⠀⣀⣠⠀⠀⠀⠈⠙⢿⡟⠁⠀⣀⡀⠀⠙⢿⡇⠙⢆⣸⠀⠀⠈⢿⣧⣘⣧⣤⠀⢀⡿⡷⠒⢳⣀
⠀⠀⠧⢀⠅⠀⠀⠀⠀⣿⣿⣴⠟⠉⠙⢷⡀⠈⣷⣅⠀⠋⠀⣴⡀⠘⣧⠉⠉⠀⣠⣾⣥⣧⣤⡾⠋⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡀⠀⠀⢨⠇⠀⣿⣿⣷⡄⠀⡏⢧⣠⣼⠿⠛⠛⠉⢾⠁⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠠⠖⠚⠛⠛⢛⠿⣿⣿⡟⠒⠒⠉⠀⣰⣿⣿⡇⠙⠛⠁⠈⠁⠀⠀⣤⢦⡤⠬⠷⠀⠀⠀⠂⡠⠇
⠀⠀⠀⠀⠀⠀⢀⡴⠋⡰⠋⠻⣷⣦⣤⣶⠾⠿⣯⠀⠀⠀⠀⣀⣤⣄⡀⠈⠈⢦⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⣧⠀⣠⠞⢁⣠⣄⡈⠳⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠔⢀⠀⠀⠀⠀⢹⣰⠃⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⣄⡆⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣴⡄⠀⠀⠀⠀⠠⠮⣷⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠥⡀⠀⠄⠀⠀⠀⠉⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢒⡒⡠⣏⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠃⠀⠀⠈⠢⡀⢀⠀⠀⠄⠀⠀⠐⠒⠢⡀⠀⠹⣄⠀⠀⠀⣀⠀⠁⢀⠀⠒⣠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⠀⠘⠀⡓⠀⠀⠀⠄⠀⠌⠀⠀⠀⠠⢤⡀⠊⠀⠀⠈⠐⢀⡙⢀⠔⠁⠀⠙⠄⠀⠀⠂⠀⠐⢄
⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⡀⠠⢀⠀⢸⠀⠀⠀⠉⠘⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⠀⢈⡉⠒⢄⠀⠙⡄
⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣁⠒⠈⣀⠀⠁⠀⠀⠀⠀⡁⠀⠀⠠⠞⠀⠀⠘⠋⠀⠀⠀⡇⠀⠀⢀⠡⣥⢀⡀⠙⠀⠈⡀⠀⠆
⠤⢵⣷⡴⠂⠀⠀⠀⠀⠀⠋⠉⠁⠀⠉⠣⠀⠀⠀⠀⠀⡇⠀⠀⠐⠍⠀⠀⠩⠄⠀⠀⣰⠀⠀⠠⡀⠁⠀⠪⠓⠀⠀⡰⠀⠌
⠀⠈⠻⣄⣀⣈⡀⠀⠀⠀⠬⠟⠀⢌⡻⠀⠀⠀⠀⠀⣠⠀⠀⠀⠙⠀⠀⠀⠀⠒⠀⠀⢾⢹⣦⠀⢨⣐⠒⣒⠎⠀⠔⣤⠊
⠀⠀⠀⠀⠉⠉⠡⠀⠀⠀⠀⡀⠀⠀⣀⣴⠁⠀⠀⠀⠈⣧⠀⠀⢀⠀⠀⠀⠀⠀⠀⣴⢟⣻⡁⠀⡸⣛⡻⠋⠀⠊⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠈⢬⠭⢚⠏⠀⠀⠀⢀⡴⣼⠆⠀⠀⠁⠂⠒⠉⠀⠚⢻⠟⠛⠣⡀⠀⠀⠀⠀⣀⣰⠋
⠀⠀⠀⡀⠀⠀⢸⡛⠾⠿⣄⡀⠀⠀⣀⢴⠉⠓⠚⠙⢲⣿⣆⡀⠀⢀⠔⡤⣀⣀⠠⠊⣀⡴⠞⠋⠐⠀⠒⣞⠁⣇⣤⣄
⠀⠀⠀⠙⠓⠶⢼⡇⠀⠀⠀⠉⢉⣭⠀⢸⡇⠀⠀⠀⠉⠃⠀⠀⠉⢷⡼⠁⢀⣀⠀⠀⠉⠙⠛⠛⣿⠇⠀⠹⡄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠳⣼⠇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠉⣿⠀⠀⠀⠀⠴⠟⠋⠀⠀⠀⠙⠛⠛⢛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠷⠶⠦⠀⠰⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠂⠀⠀⡀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆⠰⡄⣶⣶⣦⣳⣾⣾⣇⣷⣤⣿⣾⣴⣷⣼⣰⣀⣷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⢍⢿⣳⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣾⣀⡆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣼⣿⣮⣿⣿⣿⠿⠛⠛⠉⠉⠀⠀⢀⣀⣠⣤⠤⠤⣄⡀⠉⠉⠛⠻⢿⣿⣿⣿⣣⣠
⠀⠀⠀⠀⠀⠀⠐⢦⡐⢦⣾⣽⣿⣿⠟⠋⣡⣶⣾⣿⣿⣶⣶⣶⣶⣿⣿⠋⠀⠀⠀⠈⠙⣷⣄⠀⠀⠀⠈⠙⠻⣿⣿⣧⡄⢠
⠀⠀⠀⠀⠀⠐⢆⠐⣿⣷⣿⠟⠋⠀⣠⣾⠟⠋⠉⠉⠉⠛⠛⠿⠟⠛⠁⢀⡤⠴⠶⠤⣄⡈⠛⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣀
⠀⠀⠀⣀⡀⣙⣿⣿⣿⠟⠁⠀⠀⣰⠟⠁⠀⣠⠤⠖⠒⠦⢤⡀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⣀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣆⣀
⠀⠀⢄⣤⣹⣿⣿⠟⠁⠀⠀⠀⠐⠁⠀⣠⠋⠀⠀⠀⠀⠀⠀⠈⠳⣼⠁⠀⠀⢀⣀⡀⠀⠀⠀⢿⣜⣵⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣣
⠀⢀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣠⣤⡀⠀⠀⠀⣹⠀⠀⠀⠸⢿⠟⠀⠀⠀⣼⡟⠉⠉⠀⠀⠀⠀⠀⠀⠐⠨⢿⣿
⠀⣀⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣤⣿⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⡿⣇⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿
⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣩⠽⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠉⠻⣶⣶⣴⣶⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠱⠀⠆⢻
⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⣤⡴⠛⠁⠀⠀⠀⠈⠻⣦⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠘⠀⢀⠂⢸
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⡀⢀⠀⠀⠀⠀⠀⠹⣿⠀⢹⠀⠀⠀⠀⠀⢐⠀⠀⠄⠀⠰⠄⢈⢈⣸
⣾⣿⠠⠀⠠⠂⢀⠀⠀⠀⠀⡄⢠⡨⠃⣀⠀⠀⠀⠀⠀⢰⡏⠉⠺⡀⠀⠀⠀⠀⠀⢹⣇⣼⠀⠀⠀⢀⡄⠢⡨⠆⠒⠂⢒⠒⠀⠃⢸
⣿⡧⠀⠀⠀⠂⠀⠀⢁⠂⠀⠀⠐⣦⠂⠀⠀⠀⣀⠀⠀⠄⠹⣄⡀⢳⡀⠀⠀⠀⠀⢸⣿⠋⠀⠀⢀⡀⢐⠀⠃⢶⠀⢠⠨⠉⡀⠂⣼
⣿⡇⠐⠀⠀⠀⠀⠄⡀⠀⠀⡄⠠⠋⠐⠀⠁⢀⠈⠁⠀⠨⠀⡘⠉⢟⠻⣦⣀⣀⣀⣼⠟⠀⠆⠀⣀⢀⢀⡁⢂⠈⡆⠁⠌⠠⢀⣠⣿
⢻⣿⢂⠂⠀⠀⠀⠀⠄⠃⠁⡇⠂⠂⠀⠁⠠⠀⠄⠁⠐⢢⠀⠰⠀⢸⡐⢾⡏⢉⠛⢁⠂⠤⠀⠁⠉⡀⢈⢘⠐⣠⡃⠠⠈⠀⠀⣼⡿
⠸⣿⡄⡠⠀⠈⠀⡀⠀⡅⠀⠙⢶⣄⣀⣈⣀⠀⠁⣀⣐⣤⣤⠶⠶⠟⠛⠛⠛⠓⠶⢧⣤⣁⡝⠠⢐⣀⣤⠴⠚⠁⡙⠂⢀⠀⣰⣿⠁
⠀⠹⣷⡀⠂⡀⠀⠠⠈⠀⢀⠀⠀⢀⠉⠉⠉⠛⢛⡋⠉⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⢳⣊⠉⠛⠛⠋⠉⠀⠄⠀⡂⠈⡀⠈⣰⣿⠃
⠀⠀⠹⣿⡁⠀⠀⢌⠘⢂⢀⠀⠄⢀⠀⡐⢀⠐⠀⠀⠀⠁⠀⡈⠀⠀⠀⣶⢦⣤⣤⠾⠣⠀⡀⠔⠨⢡⠄⠂⠑⠀⠠⢈⣼⡿⠁
⠀⠀⠀⠘⢿⣄⠠⠂⠀⠄⠀⠀⠀⠀⢀⣂⠀⠄⡠⠁⠐⠀⠀⢂⠀⠕⠆⠙⢘⠉⠓⢷⣠⠂⠀⠀⢀⡐⠈⠀⢠⠁⣠⣿⠟
⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠐⡈⠁⠀⠠⠀⠀⠁⠀⠀⠀⠤⠤⡀⢨⠤⠈⠀⣤⠄⠂⢧⠄⢈⢈⡀⠀⠁⣋⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⣀⣀⣀⡘⠀⠀⡰⢀⠀⠁⠠⠐⠠⠂⠀⠂⠌⢩⠀⡨⠠⢸⣈⠘⠀⣀⣬⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣷⣶⣦⣤⣤⣬⣄⣠⣠⣀⣀⣤⣦⣥⣦⣾⣶⣿⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠐⢎⣀⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢦⣤⡄⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⢸⠇⢰⠇⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢏⠀⡐⡅⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⢸⠀⢸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⣿⡇⠙⢿⣷⣦⣄⣘⠀⣂⣀⣴⣷⡀⠀⠀⠀⣀⣤⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠉⠛⠿⠿⠿⠿⠛⠉⠻⣿⣿⣿⠿⢿⣿⡟⠀⠀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣀⣠⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠸⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠙⢿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣠⠖⠛⠉⠉⠉⠓⠶⣤⣿⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠇⠀⢸⣿⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣾⠁⠹⣾⡣⠀⣠⣴⣶⣤⣀⣰⣟⣹⡆⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣀⣀⣤⡾⠟⠓⠒⠶⣄⣹⣯⠝⢦⡀⠀⢀⡇⠀⠀⢻⡗⣾⠋⢰⡖⠛⠉⠉⠉⣿⣷⠀⠀⣧⣀⡀
⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠉⠻⣿⡟⠁⠀⠀⣀⠀⠀⠀⠙⢿⡯⡈⠻⣄⢸⠃⠀⠀⠀⢻⣻⣄⠸⣇⣤⡄⠀⠀⡿⣿⠖⠒⢻⡀
⠀⠀⢈⡏⠀⡣⠀⠀⠀⠀⠀⢠⣿⣷⢅⣴⠿⠛⠻⢷⡄⠀⠈⣿⣔⠀⠈⠿⠀⠀⣆⠀⠈⢷⡉⠛⠛⠉⠀⢀⣼⢃⣸⣄⣀⣼⡿⠛⠓⠒⠂
⠀⠀⠈⠁⠙⠃⠀⠀⠀⠀⢀⣼⣿⣿⣺⡇⠀⠀⠀⠈⢿⠀⠀⢸⣿⣷⡄⠀⠀⢰⣿⡆⠀⠘⣷⣤⣤⣴⡶⠟⣱⠟⠉⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⣠⡞⠀⠀⣼⣷⣿⠻⣦⣀⣸⠀⢻⡶⠾⠿⠉⢉⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⡆⠠⡄
⠀⠀⠀⠀⠐⠚⠛⠛⠛⠉⠉⣹⠿⣿⣿⣾⠉⠛⠛⠁⠀⠀⣰⣿⣿⣿⠄⠘⠛⠋⠀⠀⠀⠀⠀⠐⣤⠷⣖⠒⠒⠛⠦⠀⠀⠀⠈⢠⡤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⡰⠛⠻⣷⣧⣤⣤⣤⣴⡾⢿⣯⡁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡎⠈⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣠⠞⠁⠀⠀⠜⠋⠉⠉⠉⠀⠀⠀⠙⣷⡀⠀⠀⣠⠞⠋⠉⠉⠉⠲⣇⠀⠀⠙⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡼⠃⢀⡴⠞⠛⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠒⠈⠦⡄⠀⠀⠀⠀⠀⣿⡼⠁⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣠⣀⡎⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠃⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠴⠿⠂⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⣴⠶⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀⠀⢀⣀⣴⣆⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠈⠙⠉⠁⠀⠈⢢⠊⠈⠉⠛
⠀⠀⠀⠀⠀⠠⠆⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⠀⢜⠃⠀⢀⠍⠀⠀⠀⠀⠀⡀⠀⠀⠲⠃⢘⠘⠃
⠀⠘⡀⠀⠀⠀⠀⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠑⠀⠀⠈
⠀⠀⠈⠢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠀⢀⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⣒⠒⠠⢀⢀
⠀⠀⠀⠈⢄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠊⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠢⠀⡁⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠀⠀⠀⠘⠻⠆
⠀⠀⠀⠈⠉⠓⡆⠀⠐⠲⡄⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⢀⣀⣤⣦⠄⠀⠀⠀⠀⠀⠀⣡⣤⣉⠢⢀⣴⣤⠤
⠀⠀⠄⠀⠀⠀⠐⠀⡀⠀⠐⡀⠀⠀⠀⠀⢠⠀⠙⠛⠛⡿⠛⠛⠁⠀⡰⠀⠀⠀⠀⠀⠠⢀⣹⣷⣯⢀⢈⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡠⠁⠀⠀⠚⡅⠀⠁⠂⠀⠊⠀⠈⠐⠒⠈⠀⢀⠂⠀⠈⠋⠀⠀⠈⠉⠁⠈⠑⠀⠑⠈⢀
⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠦⢀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⠀⣀⠠⠐
⠀⠀⢋⠂⠀⠄⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⠁⠀⠈⠁
⠀⠀⠀⠓⣆⠁⠂⠀⠂⠈⠆⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠂⠁⢶⡀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡆⡠
⠀⠀⠀⠀⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠠⠶⠶⣤⣄⣀⣀⣀⣠⡤⠶⠿⠂⠀⠀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠛⠂
⠀⠰⡀⠈⠉⢉⠋⢉⠉⠀⢀⠔⠀⠀⠀⡀⠀⠀⠀⠀⣤⠈⣤⠄⠀⠀⠀⣀⠀⠀⠀⠃⠀⠈⠉⠀⠾⠀⠉⠁⠀⠐
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⡀⠔⠢⠀⠠⠊
⠀⠀⠀⠀⣀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢀⠤⠄
⠀⠀⠐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⠀⠀⢀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠘⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠟⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⡈⠁⠀⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣌⠉⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢀⣆⠈⠁⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠛⠻⡀⠀⠀⠀⠐
⠀⠐⠺⡖⠀⠑⠀⠤⠐⠊⠀⠁⠐⠂⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠐⠀⠀⠁⠒⠊⠁⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠈⠦⢀⡀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠁⠈⠈⠁⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⢀⢀⠤⠊⠁
⠀⠀⠀⠀⠠⡄⠁⠀⡃⠀⠀⡃⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠘⠪⡁⠀⠃⠀⠉⠁⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠐⠀⠀⠂⠉⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⠒⠒⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⢀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠁⠈⠉⠈⠉⠉⠙


⠀⠀⠀⠀⠀⠀⣴⠶⠖⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠂⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠄⠀⠀⠀⠀⢴⣦⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠐⠀⠠⡀⠀⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠈⠁
⠀⠀⢀⡀⠀⠀⠉⠙⠀⠀⠀⠀⠐⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣠⣤⠑⣊⣤⣤⣌
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡈⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⣿⣿⡿⢃⠛⢿⡿⠟⠀⠀⠀⠤
⠀⠀⠀⠀⠑⠂⠄⠀⠀⠀⠀⠀⣀⠠⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠠⠊⠉⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠠⠈⠉⠄⠊⠁⠂⠀⠐⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠑⠀⡀⠂⠐⠀⡱⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠤⣠⠖⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⣀⠄⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠄⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⢃⡠⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠭⠤⢀⠀⠀⡀⠉⡓
⠀⠀⠀⠀⣉⠉⠙⠿⡷⠶⣶⡶⢶⢿⠛⠉⠁⠰⠀⠀⠀⠀⠀⠐⣊⠁⠠⣤⠄⠀⠇⠤⡤⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠘⠦⡀⠀⠀⡠⠂⠘⠄⡀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣠⠧⢀⡀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⢀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣀⡀⠠⠊⠓⠀⠤⠐
⠀⠀⠀⠀⠀⠀⣠⠔⠈⠉⠁⠀⠀⡇⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢶⣦⣀
⠀⠀⠀⠀⢠⡞⠐⠒⢲⠐⠀⠐⡎⠁⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠈⣁⠤⠄⠚⠒⠒⠀⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠧
⠀⠀⠀⠀⠑
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣯⣥⣬⣧⣴⣠⣽⣮⣼⣯⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠃⠀⠀⠀⠠⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠈⠀⠐⠂⢄⡀⠄⠀⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠃
⠀⠀⠀⠀⠂⠀⠀⣀⡀⠈⢀⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣄⠈⠁⣠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣘⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⡰⢄⠁⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡰⢄⠈⠀⢀⠌⠀⠀⠀⠀⠀⢀⡀⠐⡀⠀⠀⠙⠻⠀⠀⠀⠠
⠀⠈⠙⣍⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠈⡗⢤⠀⢀⠀⡀⣀⠀⢠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠘⣆⢀⠨⢀⡀⠀⡀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠺⠄⢀⡀⠀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⢀⠈⠁⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣆⣀⣀⣀⡀⠆⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠁⠀⠀⠀⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠁⠀⠀⠀⠀⠛⠻⠄
⠀⠀⠀⠀⠀⠠⠶⠄⠀⠀⠀⠀⣤⡤⠄⠀⠀⠀⢀⠀⠀⠀⠀⠔⠋⠀⠀⠉⠢⡤⠂⠀⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠐⢄⠀⠀⠀⠠⡀
⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⠆⡷⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⢾⣿⣿⣿⠄⣷⣿⣿⡇⠀⠀⢀⡀
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢀⠔⠣⢀⣀⡀⠔⠀⠀⠀⠀⠀⠚⡇⠀⠡⠈⠛⠛⢋⠔⠢⢉⡉⠠⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠓⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⠀⠤⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢀⡰⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠀⡀⠀⠀⢈⣛⠃
⠀⠀⠀⠉⡏⠙⠻⢿⡶⢦⣶⣴⣶⡟⠋⠉⢩⠆⠀⠀⠀⠀⠀⡎⠉⣀⣠⠄⠸⠅⢤⡄⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠈⠀⠀⠈⠂
⠀⠀⠀⠀⠑⢄⠀⠀⢀⠐⠀⠢⢀⡀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡰⠆⢀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠟⠀⢀⠛⠃⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠠⠊⠂⠤⠠⠔⠁
⠀⠀⠀⠀⠀⢀⢤⠂⠀⢉⠀⠀⠈⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢶⣤⣀
⠀⠀⠀⠀⢠⠛⠚⠒⡆⠉⠀⢸⠉⠉⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⢀⠸⠵⠄⠂⠋⠈⠀⠉⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠙⠲⢤⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠁⠀⠈⣡⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠉⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⢰⠇⠀⣠⡀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢃⠀⠀⡑⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⡔⣦⠠⡀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠱⠀⡃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⣋⣸⢁⣤⡌⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠰⠞⠂⢀⡌⠳⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠐⠁⠀⢸⠆⠀⠀⠀⠀⠀⢀⡜⢣⡈⠉⠟⢻⡞⡁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡦⢉⣉⢣⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠈⠳⣄⣹⣾⣣⡄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠛⠃⠀⠙⠀⠀⠀⠀⢀⢒⡼⠀⠀⠠⠴⠖⠋⠀⠀⠀⠠⡀⣠⠏⢳⡄⠀⠀⠀⢀⠏⢰⢟⡥⠲⠌⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡔⠀⠀⠢⡀⠀⠀⠀⠀⢨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⣠⠋⠀⠀⠀⠀⢸⡀⠀⢸⣼⢧⢞⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⣀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢁⡼⠁⠀⠀⠀⠀⠀⠀⠉⠙⢦⠐⣨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢉⣉⣁⡀⠈⠑⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠱⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⢤⣤⠌⠀⢀⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⢋⡾⣡⢆⡀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⡀⠀⣧⠀⠙⠒⠤⠖⠚⠉⠀⡇⢸⠀⠀⠀⠀⠀⠀⡠⢡⠞⣴⢣⡞⠡⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡈⣏⠀⠀⣀⠀⠀⢀⡴⠀⢸⣀⠴⠚⠳⡄⠠⡁⠈⠘⢡⠏⡐⠉⡂⠆
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡘⣎⠓⠋⣙⠓⠊⠁⠀⢀⠜⠁⠀⠀⠀⠷⠀⠙⣦⣀⠀⡸⢧⡞⠉⡆⢄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢻⣦⠞⠉⠉⠙⢦⡔⡁⠀⠀⠀⠀⠀⡎⢈⢦⠷⣈⠉⠀⢰⢀⡼⢁⠎
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣠⠶⢿⡀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⡇⠀⠒⢂⢮⡉⣇⠈⠉⠓⠋⠛⢳⡆
⠀⠀⠀⠀⠀⠀⠈⠳⣄⣤⡶⢫⠁⠀⠈⠓⠦⡴⠾⠋⠲⡄⠀⠀⠀⠀⠀⡇⠀⢀⠃⠀⡗⠹⡄⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡂⠀⠀⢀⠹⣆⠀⠀⠀⢸⡇⠀⠘⡆⠀⡇⠀⠙⢦⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠘⠀⡈⠳⢦⣴⠟⠀⠀⠀⢱⠀⢣⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠁⠀⠀⠰⠠⡀⠀⠀⢸⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠰⡀⠀⡟⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢧⢀⡀⠀⠀⢧⠑⢤⡴⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠦⡇⠀⠀⠀⠀⢸⡇⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠸⣦⣄⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣇⢀⣀⣀⣀⣀⢸⠀⠆⠀⠀⠀⢧⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠤⠤⠤⠤⠤⠴⠒⠃⠀⠀⠀⠀⠛⠛⠛⠛⢛⠓⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠀⠀⠀⠀⣀⡤⣞⠁
⣠⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡾⠉⠛⠓⠒⠛⠋⠉⡇⠘⡆⠀⠀⠀⠀⠀⣠⠴⠒⠒⠲⢦⡀
⡇⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⣾⢰⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⢸⡇
⢹⡀⠀⠀⠀⠹⣆⡤⠶⠂⠀⠀⣛⠈⢃⡀⠀⠀⠀⠀⡴⠓⢧⠤⠷⠀⠑⢶⠁⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠳⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⡉⠉⠀⢧⠀⠀⢸⠀⠀⢀⣀⣀⡀⠀⠈⠀⠀⠢⣀⣀⡴⠛
⠀⠀⠙⠳⢶⣤⠾⠋⠉⠛⠲⠶⠾⣇⣀⣀⣼⠀⠀⠘⠦⠤⠤⠃⠈⠉⠙⠛⠛⠛⠛⠋⠉
⣿⣿⣿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢰⡄⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⠗⠘⠓⠒⢦⡒⠒⠓⠀⠀⠀⠀⠀⣀⣤⢄⣀⠬⠷⠶⠶⠻⢄⣀⠞⠀⠀⠀⠀⠀⠒⠲⣄⣈⣇⣼⡀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⣠⠃⡋⣉⡧⢀⣤⡟⠛⠒⠂⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢠⣮⠉⣄⠀⠀⠉⢉⡽⣷⣮⢭⡉⠁
⠀⠀⠀⠀⠀⢳⠀⠙⠋⠁⢿⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠶⢤⡀⠀⡠⣄⠀⠸⡀⠀⠀⠀⠀⠘⣔⠤⠞⠰⠤⠆⠰⠬⢜⡷
⠀⠀⠀⠀⠀⠈⢣⡀⠚⠓⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠧⡘⠴⠃⠀⠵⠬⠃⢠⠇⠀⠀⠀⠀⠀⢦⡈⢩⠆⠀⠲⡂⢈⡡
⠀⠀⠀⠀⠀⣤⢾⠇⠀⠀⠀⠘⢯⡙⢢⠀⠀⠀⠀⠀⠀⠀⠈⠓⣶⠀⠰⠦⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⢉⡏⠀⠀⠀⣟⠉
⠀⠀⠀⠀⠸⠁⢸⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⡠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠳⠋⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠈⢢⡤⠀⠠⠤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠁⠒⣲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢱⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠂
⠀⠀⠀⠀⠀⡀⢀⡈⢱⣀⡠⠔⠛⠛⠛⢦⡀⠀⠀⠀⠀⠀⠠⣀⠐⣆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⢀⣠⠤⠴⠯⠤⣄⡤⠤⠄
⠀⠀⠀⠀⠠⠤⠤⣬⠞⣡⣖⠲⠐⣏⣿⠆⡇⠀⠀⠀⠀⠀⠀⣼⢷⡋⠈⣓⣲⣄⠀⠀⠀⠀⠀⢀⣞⡤⣄⢾⡅⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠳⠭⠞⣀⠴⢀⡞⠁⠀⠀⠀⠀⢰⠱⣟⡠⠇⠸⣛⣨⠻⡀⠀⠀⠀⠀⢸⡙⠓⢚⡴⣦⢰⠦⢄⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠓⣄⠀⠀⠀⠀⠘⠦⣄⠀⠠⠄⠀⠀⠀⣇⠀⠀⠀⠀⠀⡟⢲⡬⣿⠷⠋⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢦⠀⠀⢀⡎⠀⢸⠄⠀⠀⠀⠀⠀⢸⠀⢦⡀⠸⠀⠀⢸⡆⠀⠀⠀⠀⡄⢸⠀⠇⠀⠀⣰⠃⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠉⠃⠈⠀⢀⡜⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠃⠘⠂⠘⠀⢠⡇⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠹⢄⡀⠀⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡶⠖⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣀⡠⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠉⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢋⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⣉⣵⡤⠤⡧⠤⣖⠉⠉⠀⠀⠀⠀⠀⢀⡤⢴⢡⠤⡀⠀⣀⣙⢞⠓
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠛⠓⠲⣍⣁⡀⠀⠀⠀⠀⠀⠀⢀⣠⠏⣬⣸⡇⢞⢩⡆⠀⠙⣏⠉⠃⠀⠀⠀⠀⡔⣛⢷⠄⣻⢰⡁⠌⣮⡙
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠞⢩⡇⠰⠤⠴⠶⠶⠷⠶⠖⢀⡼⠀⠀⠀⠀⠀⠀⠀⢻⠀⠙⠁⠀⠉⠋⢸⡇⣠⠇
⠀⠀⠀⠀⠀⢠⡇⢀⡔⣻⢲⡀⢠⣖⢮⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡴⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⢼⠀⠀⠒⠒⠀⠀⠀⡏⠁
⠀⠄⠀⠀⢠⡟⡄⠀⠓⠒⣚⠀⠈⠛⠋⡜⢧⠀⠀⠀⠀⠀⠇⠱⣄⠀⠀⠀⠸⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠈⢲⡤⠤⣬⡭⠭⢴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠤⠤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣀⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢀⣠⣤⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣾⣿⣿⣿⣶⣶⣿⡿⠖⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡃⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⣠⣄⡀⠀⢈⠉⠃⠀⠀⠁⠀⠉⠉⠹⣿⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⣤⡀⠀⠄⠈⠐⠀⠀⠀⠀⠀⠘⠉⠉⠛⠚⠋⠀⠀⠐⢦⢠⠴⠶⠆⠀⠟⠀⠀⠄⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡆⠀⠀⠀⠘⠃⢀⠤⠀⠀⠀⠀⠛⠀⠀⠐⢃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠆⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⢠⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠐⠶⠶⠞⠋⠀⠀⡠⠂⠄⠀⢀⠀⠀⠰⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⡠⠄⠓⠢⣄⠀⣀⣀⣀⣀⡤⢊⠁⠀⠀⠀⠌⠀⠀⠀⡀⠀⠔⠊⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠈⠀⠀⡈⠀⠀⠀⠀⠀⠉⠀⢂⠐⠄⣀⣀⠤⢳⡄⠀⢠⠅⠀⠀⠠⠒⠒⣄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠁⠀⢀⡠⠂⠀⠀⠀⠀⣀⠁⠀⠶⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⢢⠃⠀⠀⠀⠀⢀⠴⡇⠀⠀⠀⡀⠤⠂⠂⠂⠰⠀⠀⠑⠤⣀⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠳⠀⠀⠀⠀⠐⢊⠙⡀⠆⠀⠀⠀⠀⠀⠀⠞⠠⠛⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠉⠆⠀⠠⠀⠀⠀⠀⠠⠄⠜⠀⢀⡴⠤⠒⠁⠈⡀⢬⠀⠂⠀⠀⠒⠈⠀⢀⡀⠦⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡔⡡⢲⣤⣄⣀⣀⠖⠒⠈⡏⠠⣬⢥⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⢠⠳⠀⠀⠀⡰⠁⢠⡆⠀⠈⠠⠶⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⡸⣄⡉⠋⠀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠈⠐⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠙⢋⣉⡛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢸⠿⠿⢟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠿⠿⠿⠿⠿⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⢀⣤⣶⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⡙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⢻⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⢠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠻⣿⡄
⠀⠀⠀⠀⠀⢠⣾⡿⠁⢀⡿⠋⠀⠀⢀⣠⣴⡶⠶⠶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠳⢦⣄⠈⢿⡆⠹⣿⣆
⠀⠀⠀⠀⢠⣿⡟⠀⠀⠸⠃⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠙⣦⠀⠳⠀⠹⣿⣆
⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⣿⣆
⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣻⠇⠀⠀⢸⠀⠀⠀⠀⠰⠄⠀⠀⠀⢠⡿⠀⠀⠀⠀⢻⣿⡆
⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢿⣿⡄
⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠙⣷⣄⡀⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠘⣿⣷
⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠙⣿⡙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠚⠛⠉⠀⡏⠀⠀⠀⠀⠀⠀⠈⢿⣄⡴⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣻⣆⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣷⣤⣀⣀⣀⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⠉⠉⠉⠉⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠤⠴⠾⠷⠾⠷⠶⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢻⣧⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣯⣤⣤⣴⣶⣿⣿⡿⠟⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡋⣶⣲⣶⣡⣦⣴⣦⣤⣄⡂⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣠⣿⢻⣿⣟⣿⣷⣿⣿⣿⣿⣷⣿⣿⡿⣿⣾⣿⣿⣿⣿⣾⣥⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣞⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣬⣿⣾⣿⣿⣿⣿⣿⢷⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡗⣤⡀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡯⣥
⠀⠀⠀⠀⣰⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⢿⣦⣿⠦⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣤⣶⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣵⣆⡀
⠀⠀⡀⣿⣛⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠿⠿⠿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟⣿⣿⣇
⠀⣠⠽⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠈⢻⣷⣴⣦⠄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣻
⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣼⣿⠟⠁⢀⣴⣶⡾⠿⢷⣶⣤⡀⠀⠀⢸⣿⠀⠀⠀⣴⣦⠀⠀⠀⠀⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡇
⠀⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢰⡿⠃⢀⣼⡿⠋⠁⠀⠀⠀⠀⠙⣿⡆⠀⠘⣿⠀⠀⠀⠙⠋⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟
⢰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠀⠀⣾⡿⠁⠀⠀⢀⣤⡀⠀⠀⠘⣿⠀⠀⠈⠣⣄⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠈⠛⠃⠀⠀⢀⡏⠀⠀⠀⠀⠈⠙⡻⠿⣿⣿⣿⣷⣶⣤⣀⣤⡶⠶⠲⢄⠀⠀⠀⠀⠀⠀⠈⣿⣿
⢈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢶⡺⣿⣦⡀⠀⠀⠀⠀⠀⣠⡾⢁⠀⠀⠀⠀⠀⠀⠻⣾⣿⡿⣧⡀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⠁⠙⠿⢷⣶⣶⣶⠿⠋⢠⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢸⣇⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⣿⡷⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼⡇⠀⠀⠀⠀⠀⠠⠟⣉⠙⠃⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠾⠿⠛⠋⠁⠘⣿⡀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⣀⣀⠀⠀⠀⠀⠈⠛⢶⣿⣿⣆⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⢀⣀⣀⣼⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠙⣧⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⣿⣿⣿⡿⠋⢹⠀⠀⠀⣰⣿⠛⠛⠋⠁⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡉⠉⠉⠉⠁⠀⠀⢸⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣴⡾⠿⠿⣷⣄⠀⠀⠈⠳⣄⣤⣶⡾⠿⠷⢿⣷⣦⣾⡟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣴⣾⠿⠋⠁⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣠⠞⠋⠛⠻⣶⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢤⠀⠈⣿⣇⠀⠀⣀⣴⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠔⠊⠉⠉⠒⢄⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢢⠀⠀⢀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠃⠀⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⢳⠃⣐⠢⣄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠴⠀⢈⠳⠀⠀⠀⠘⠁⠀⠀⠀⠀⠂⠀⡆⠀⠀⠀⠀⢀⠜⣄⠛⠿⢯⢟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡆⢉⡑⠀⠀⠀⠠⢄⠀⠀⠀⠀⡠⠊⠀⠀⠠⢄⣀⠀⠀⠀⠑⣆⢽⣯⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡉⠁⠀⠁⠀⠀⠀⡬⠞⠀⠐⠂⠉⠀⠀⠀⠐⢤⠎⣨⠂⠀⠀⠀⠃⠘⡵⣉⢣⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡴⠁⠀⠀⠀⠈⠢⢤⡙⠙⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢓⣒⣉⠀⠢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠊⠣⡎⠀⠀⠀⠀⠀⠀⠀⠀⢣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⡀⠤⠤⠁⣠⠇⠀⡇⠀⠀⠀⠀⠀⡐⣱⣣⢆⡌⡦⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⠐⠀⢄⡐⣦⠈⠉⠈⠉⠁⢀⠁⡇⠀⣀⡀⠀⠄⠸⡱⣣⢏⣜⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠜⠦⠴⠦⠤⠔⠁⠀⠷⠉⠀⢸⠀⢢⣀⠀⢡⣆⡬⢆⢀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠺⣄⠖⠃⠒⢄⠀⠀⠀⠀⠀⢠⠀⢐⣏⠓⠃⢨⢀⡜⡘
⠀⠀⠀⠀⠀⢡⠀⠀⠀⣠⠴⢻⡀⠀⠀⣸⠋⠀⠀⠀⠀⢸⠀⠐⡠⢏⢡⠈⠉⠊⠁⣱⠄
⠀⠀⠀⠀⠀⠈⠳⠶⠋⠅⠀⠀⠙⠒⠚⠉⠱⣄⠀⠀⠀⢸⠀⢠⠁⢸⠉⢆⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⢦⣀⣀⡟⠀⠀⣇⠸⠀⠀⠳⠼⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢠⠀⢸⠀⠀⢀⡜⠀⠈⢁⠀⠀⠀⣹⠀⣇
⠀⠀⠀⠀⠀⢂⠀⠙⠀⠀⠀⢸⠀⠸⠀⠀⠀⠇⡄⠀⠘⡎⠢⠴⠃⢀⡟
⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⠸⠂⠀⠀⠀⠀⡇⠀⠀⠀⢹⠦⢤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢇⠐⠒⠒⠂⣧⠉⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢰⠅⢤⡤⠤⠤⠼⠀⠀⠀⠀⠷⠶⠶⢶⠦⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢦⣄⣀⣀⣀⣠⣴⢺⡁⠀⠀⠀⠀⠀⠀⣀⡀
⡞⠉⠓⢤⠀⠀⠀⠀⠀⢀⡇⡏⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡠⠚⠉⠀⠈⢳
⢧⠀⠀⠀⢳⣀⡠⠄⠀⠘⠃⠇⡀⠀⠀⠀⡠⢸⣁⡧⠀⢠⡎⠀⠀⠀⠀⢀⡾
⠈⢧⡀⠀⠀⢉⣀⠀⠀⠈⡉⠉⠀⡆⠀⢸⠀⠀⣄⢀⣀⠀⠁⠀⢀⣀⡤⠞
⣀⣀⣙⣳⣶⣋⣉⣉⣛⣚⣷⣤⣤⣇⣀⣈⣒⣒⣃⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢀
⠀⠀⠀⠀⠞⠃⠀⠀⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠐⠢
⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠂
⠀⢀⣀⠀⠀⠈⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⢁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠃
⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠐⠠⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠠⡉⠀⠀⠀⡀⠩⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠙⠢⢈⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠐⠀⠐⠐⠆

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀
⠀⠀⠀⠀⢈⡀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠃
⠀⠀⠄⠀⠉⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣆⢣⣤⣦
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠙⠛⠁⠂⠉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠘⠃⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠐⠶⠶⣤⣄⣀⣀⣤⡴⠖⠛⠂⠀⠀⠀⠠⠔⠋⡉⠰⠊⠉⠒⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠡⠀⠈⠁⠍⠡⠉⠀⠀⠄⠀⠀⠀⠀⠘⠀⠈⠁⡠⠄⡁⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠁
⠀⠀⠀⢠⠔⠅⡀⠄⢠⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠨⠤⠀⠒⠂⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣻⣉⣛⣿⣹⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠒⠂⢌⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢒⠶⠦⠄⠀⠀⠀⠃⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢠⠂⠉⠒⢌⢉⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡥⢲⠋⠁⠠⠒⠀⠀⠀⠐⠈⢂⠀⢑⡄⠀⠀⢀⠔⢈⡒⢄⠀⠄⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠀⡇⠀⠀⠀⢀⡠⠂⠀⡣⠠⠁⠀⠠⠂⠌⠁⣨⡬⠊⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢅⣀⠁⠈⠀⠀⠀⠉⠀⠀⡁⠹⣄⡔⡡⠁⡀⠖⢇⣀⣀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢠⠊⢉⣐⣂⠠⠀⣡⡆⠀⠀⠜⠋⠀⠀⢁⠀⢉⠴⠐⠁⠀⠀⠀⠘⠢⠄⡠⠔⠆
⠀⠀⠀⠠⠒⠀⠼⠤⢤⣀⡁⠉⠐⠲⠠⢀⣠⠂⠀⠀⠀⠀⢱⣷⡄⠀⠀⠀⠀⠀⢰⢇⠰⠀⠀⠰⠀⢡
⠀⠀⠀⠐⠀⠀⠀⠀⠀⣈⠇⠉⠉⠉⠉⢸⣿⣄⣀⣀⣀⣴⡿⢿⡇⠀⠀⠀⠀⠀⡈⣀⠄⠂⠁⢦⠆⢀
⠀⠀⠀⠀⢰⠀⠀⢀⣸⣙⢄⠀⠀⠀⠀⠘⢿⡿⠛⠋⠛⠁⠀⠀⠀⡂⠀⠀⠀⢀⠃⠁⠀⠉⢡⠃⡰⠃
⠀⠀⠀⠀⠀⡆⢐⠒⢄⠈⣻⠢⡀⠀⠀⠀⢈⠀⠀⢀⡤⠠⠄⣤⡴⠥⠀⠔⡰⠋⡜⢑⠖⠂⡡⠊
⠀⠀⠀⠀⠀⢠⠈⠆⢀⠭⠠⠥⡈⠢⣀⠤⠄⢓⠖⢃⠀⠀⠀⠀⢨⠍⣀⣈⡠⡮⠂⢁⠄⠊
⠀⠀⠀⠀⠀⠀⢆⠈⠺⡀⠳⠈⠀⡲⠤⢉⣁⠡⠔⠉⠒⠐⠖⠘⣥⢤⠴⠁⠀⠀⢆⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠐⢀⠚⠂⠤⠄⢀⡠⠒⠂⠤⠔⠹⠤⠜⠀⠀⠀⠀⡠⠞⠀⠀⠰⠁⠑⢄⣀⢤⠂⠰⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢀⢠⠁⠀⠀⢸⣼⠨⠁⠶⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠃⠀⠀⠀⣼⡍⠀⢠⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⣀⠀⣴⣿⠇⢀⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⠠⠠⠄⠒⢏⠡⠀⠀⢀⠌⠀⢣⡹⡿⢀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⣄⣵⠊⠁⠀⠀⠈⠺⡅⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠈⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣤⣴⣶⣷⣚⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⠢⠍⠉⠒⣚⡛⠿⠿⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣆⡀⠀⠀⠀⠀⠠⠬⣝⣆⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⡉⢀⠀⡀⠀⠀⠀⠐⠙⠻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢀⡜⠁⠉⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠊⠐⠁⠙⣄⠀⠀⠀⠀⠁⡀⠐⢀⡀⠤⢀⠀⠀⠘⣦⠀⢀⠀⠀⠀⠀⠢⠔⠒⠀⠤⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡜⢠⡃⠀⠀⠀⠀⠈⢑⠔⠂⠉⠀⠁⠀⠐⢢⠀⠀⠱⠤⣀⠈⢷⠀⢀⠄⠒⠢⡀⠀⠂⠁⠐⠛⢍⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⠀⠀⠀⠀⠈⠄⠀⠀⠀⠵⢀⡎⠀⠀⠀⠐⠈⠓⢮⠀⠁⠀⠀⠀⠀⠱⡄⠰⠁⠀⠀⠀⠨⢀⣀⣄⡂⠀⠀⢩⡀
⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠤⣈⠒⠐⡂⠾⠤⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀⠀⠀⠀⡇⠁⠀⠀⡠⠤⠆⠀⠤⣄⠈⢢⠀⠀⠃
⠠⣄⣶⠀⠀⠀⡁⠀⠀⠀⠀⢀⣤⣌⠁⢠⣄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠒⣋⠀⠀⢀⡉⠀⠀⠀⢠⠁⠀⠀⠠⡐⠦⡄⣤⠀⠉⠀⠀⡇⠀⡇
⠴⢾⣿⡶⠓⠀⠇⠀⠀⠀⠀⠉⡀⡀⠀⢀⢈⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠋⠀⠀⠀⠕⠀⠀⠀⣌⡀⠀⠐⢀⠀⠀⠐⠒⡃⠀⠀⡜⠀⡜
⠀⠀⠙⢧⣀⣀⣡⠀⠀⠀⠀⠦⠭⠃⠠⣙⡟⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠘⠂⠀⠀⡏⢳⣦⠀⢈⣅⠒⢒⣲⠃⢀⠌⣄⠎
⠀⠀⠀⠀⠉⠉⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠀⠀⠀⠀⠀⢷⡀⠀⠀⡄⠀⠀⠀⠀⠠⠀⢀⡴⡟⣯⠁⠀⢘⡛⢻⠿⠁⢀⠂⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈⢏⣉⡩⢞⠏⠀⠀⠀⠀⢀⣎⣷⠀⠀⠈⠒⠂⠐⠒⠁⠠⠾⣿⠿⠏⢧⠀⠁⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⣼⠶⣵⣶⡀⠀⠀⠁⠀⠁⣠⠒⠤⠤⠒⣥⣼⣧⠀⠀⠀⠀⣠⣀⠀⠀⠀⣠⠎⠀⣠⡴⠗⠠⠀⣀⣤⠞⢹⠃⣀⡀
⠀⠀⠀⠲⣦⣄⣀⣸⡄⠀⠈⠉⠒⠶⠶⠒⠋⢹⠀⠀⠀⠀⠰⢻⠙⠛⠒⠒⣞⢠⠏⠁⠀⠉⠀⠀⠾⠥⣤⣤⣤⡦⠀⠘⣇⠘⠷⠟⠋
⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⢀⣾⢷⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣯⣤⡴⢶⡆⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠹⣦⣤⣤⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁

⠀⠀⠀⠀⠴⠿⠂⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⣴⠶⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀⠀⢀⣀⣴⣆⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠈⠙⠉⠁⠀⠈⢢⠊⠈⠉⠛
⠀⠀⠀⠀⠀⠠⠆⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⠀⢜⠃⠀⢀⠍⠀⠀⠀⠀⠀⡀⠀⠀⠲⠃⢘⠘⠃
⠀⠘⡀⠀⠀⠀⠀⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠑⠀⠀⠈
⠀⠀⠈⠢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠀⢀⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⣒⠒⠠⢀⢀
⠀⠀⠀⠈⢄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠊⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠢⠀⡁⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠀⠀⠀⠘⠻⠆
⠀⠀⠀⠈⠉⠓⡆⠀⠐⠲⡄⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⢀⣀⣤⣦⠄⠀⠀⠀⠀⠀⠀⣡⣤⣉⠢⢀⣴⣤⠤
⠀⠀⠄⠀⠀⠀⠐⠀⡀⠀⠐⡀⠀⠀⠀⠀⢠⠀⠙⠛⠛⡿⠛⠛⠁⠀⡰⠀⠀⠀⠀⠀⠠⢀⣹⣷⣯⢀⢈⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡠⠁⠀⠀⠚⡅⠀⠁⠂⠀⠊⠀⠈⠐⠒⠈⠀⢀⠂⠀⠈⠋⠀⠀⠈⠉⠁⠈⠑⠀⠑⠈⢀
⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠦⢀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⠀⣀⠠⠐
⠀⠀⢋⠂⠀⠄⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⠁⠀⠈⠁
⠀⠀⠀⠓⣆⠁⠂⠀⠂⠈⠆⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠂⠁⢶⡀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡆⡠
⠀⠀⠀⠀⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠠⠶⠶⣤⣄⣀⣀⣀⣠⡤⠶⠿⠂⠀⠀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠛⠂
⠀⠰⡀⠈⠉⢉⠋⢉⠉⠀⢀⠔⠀⠀⠀⡀⠀⠀⠀⠀⣤⠈⣤⠄⠀⠀⠀⣀⠀⠀⠀⠃⠀⠈⠉⠀⠾⠀⠉⠁⠀⠐
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⡀⠔⠢⠀⠠⠊
⠀⠀⠀⠀⣀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢀⠤⠄
⠀⠀⠐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⠀⠀⢀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠘⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢠⡶⠆⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠛⠀⠀⠀⠰⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢄⡠⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⣠⡄⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⠀⣤⠀⠀⢐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣨⠁⠁⠀⠀⢰
⠀⢀⣀⡀⠀⠀⠀⠀⢀⠔⢄⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠆⡀⠀⡠⠂⠀⠀⠀⠀⠀⣠⠀⠣⠀⠀⠈⠉⠂⠀⠀⠠⠂
⠀⠈⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎
⠀⠀⠀⠀⠅⠦⠀⢠⠀⠀⡄⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠀⠄⠀⠀⠀⢠⠐⠊
⠀⠀⠀⠀⠘⢤⠤⠀⠠⠀⠠⠄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⡀⠀⢀⠸⠀⡀
⠀⠀⠀⠀⠀⠀⠙⠂⠴⠀⠠⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠂⠀⠂⠐⠀⠃⠂⠘⠆


⠀⠀⠀⠀⠀⢀⡴⠶⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⢰⣤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠐⠀⠤⡀⠀⡀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⠀⠀⠀⡀⠈⠁
⠀⠀⣠⠄⠀⠈⠉⠁⠀⠀⠀⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⢀⡘⣏⡀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠠⢃⣤⣤⣤⡌⢆⣤⣤⣌⠂
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠈⢁⡏⠀⠀⠀⠠⠃⠀⠀⠀⠀⣤⠄⠠⠈⠿⣿⡿⠃⡜⠻⠿⠋⡠⠀⠐⠆
⠀⠀⠀⠀⢙⠂⠄⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⠤⠐⠁⠈⠐⠒⠈⠁⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠤⠔⠊⠀⠑⠒⠈⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠑⠒⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⡀⠀⠀⡀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠃⠀⠀⠀⠀⠿⠦
⠀⠀⠀⠚⡟⠻⢶⣦⣤⣀⣄⣤⣴⠶⠛⠛⡏⠁⠀⠀⠀⠀⡤⠚⠋⢁⡀⢸⡃⣀⡉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢢⡔⠀⠉⠐⢀
⠀⠀⠀⠀⠣⡀⠀⠈⠀⡩⠉⢌⠉⠀⠀⡠⠃⠀⠀⠀⠀⠀⠨⡀⠈⠉⠀⠠⡄⠈⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠴⠖
⠀⠀⠀⠀⠀⠈⠐⠀⠉⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠔⠣⠄⠀⠠⠊
⠀⠀⠀⠀⠀⠀⣠⠐⠀⡏⠀⠈⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣦⣀
⠀⠀⠀⠀⣰⠓⠚⠰⠂⠃⠀⡆⠁⢐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⢀⠫⠠⠤⠐⠓⠂⠀⠁⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠂
⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠶⠶⣶⣤⣀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣠⡿⠋⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⡟⠁⠀⢠⣾⣿⣷⠀⢰⣿⣿⡇⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢸⣿⠿⢃⣄⠘⢿⡛⠁⠀⠀⠀⡐⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣬⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⣼⠟⢠⠃
⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁⢈⡏⢿⣷⣤⣀⣀⣀⠀⢀⠀⢀⠀⢀⣀⣀⣠⡴⠟⠁⠀⠑⠐⠂⠀⠀⠀⣠⣤⣀⣴⠶⣦
⠀⠀⠀⠀⣠⡶⠛⠁⣠⣴⡋⢀⡈⠻⣿⣿⣿⣯⣀⣾⣀⣿⣀⣼⡿⠋⠁⠀⣠⣤⡄⠀⠀⠀⠀⢠⣶⡏⠉⠋⠁⢀⡿
⠀⣠⡶⠛⠉⠉⠲⣄⣿⠉⠙⠛⠛⢷⣄⢀⣼⣿⣿⣿⣿⣭⣽⣿⣿⡿⠿⠿⢧⠀⠻⣦⣤⣤⣤⣿⠀⠳⠤⣴⠶⠛
⠀⢿⣀⣤⠶⢦⣴⠟⠁⠀⠀⠀⠆⠀⢙⣿⣯⣉⣉⣙⣿⠉⣿⣭⣤⠤⠴⠶⢿⡿⣶⡀⢀⣼⠛⠁⣠⡶⠟⠋⠐⠁⠂
⠀⠀⠀⠀⠀⠀⠂⠔⠀⠀⠀⠀⢀⠐⣿⣍⣉⠉⣉⣙⡿⠀⣿⠶⠦⢤⣶⣶⡟⠁⠘⠷⠞⠹⣧⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡿⠛⠉⣋⣹⣷⢨⣿⡻⢷⣶⣤⣭⣿⢸⠀⢀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠟⣉⣵⣿⠿⢿⣿⣦⣌⣻⣧⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⣈⡿⢿⣉⣛⠳⣶⡿⠛⣉⡭⠟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⢦⡀⠈⠉⠉⣀⢀⣽⠉⢁⣸⡇⠘⣿⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡛⠉⠀⣿⣦⡶⠟⠋⠛⠷⠶⠛⠉⠻⠦⠼⢷⡀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠈⠻⢶⡄⠀⠀⠀⠀⠀⣤⠀⠀⠀⢸⣇⣤⣤⣸⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢠⡔⢻⠟⢷⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⠉⣻⡦⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢻⡿⠁⣿⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠟⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣄⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠉⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⢻⡉⠓⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣧⣀⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⣠⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⢶⣤⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣼⡿⠋⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣾⡟⠁⠀⠀⣴⣿⣿⣿⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⠁⠀⠀⠀⣿⣿⣿⠟⢀⠀⢸⣿⠿⠃⠀⠀⠀⠀⠠⠀⢸⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢿⣿⠀⠀⠀⠀⠉⠉⠀⠀⠉⠁⠀⠙⠃⠀⠀⠀⠀⡠⠃⢀⣿⡏⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠛⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣿⠏⢀⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⣀⡿⠈⢿⣿⣷⣦⣤⣤⡄⠀⢠⡄⠀⣤⠀⢰⣤⣤⣴⡶⠟⠋⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⣴⣶⣦⣴⠿⠛⣷⡄
⠀⠀⠀⠀⠀⣰⡿⠛⠁⠀⣤⣾⣉⣀⣀⠈⠻⢿⣿⣿⣿⣧⣀⣼⣄⣰⣿⣀⣼⣿⠋⠁⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⣴⣾⡏⠀⠉⠁⠀⢀⡿
⠀⢀⣤⠾⠛⠋⠙⠳⣆⢀⣿⠉⠛⠛⠛⠻⣷⣄⠀⢠⣿⣿⣿⣿⣿⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⢷⣤⣠⣤⣄⣸⡿⠀⠳⢤⣤⣤⠶⠟⠁
⠀⣾⡃⠀⣀⣤⣄⠀⣼⡟⠃⠀⠀⠀⢠⡄⠈⠻⣶⣿⠛⠛⠛⠻⢿⡟⠹⣿⣛⣉⣁⣀⣠⣤⣾⣷⣤⣄⠉⠉⢉⡿⠟⠃⢀⣤⣴⡾⢃⠠⠂⠄
⠀⠘⠛⠛⠋⠉⠉⢛⠋⢀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠿⠿⠷⠶⢶⣿⠇⠀⣿⣛⠉⠉⠉⣉⣉⣽⡿⠘⣿⣄⣰⣿⣦⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⢤⠈⠻⢷⣦⣤⣤⣤⣴⣿⠃⢸⣿⣏⣛⠛⠛⠿⣿⣏⠀⡔⠈⠙⠁⠀⠹⠷⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡋⢉⣀⣡⣼⣿⡇⢸⣿⡙⠻⢿⣷⣶⣤⡿⢇⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⠛⣉⣴⣿⡿⠿⣿⣿⣷⣤⣙⢿⣦⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⣻⣶⣟⠛⠻⢿⣦⣴⣿⠿⠛⢛⣻⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠙⠛⠿⠿⠛⠀⠉⢻⡟⠂⠈⣿⠁⠰⣾⡟⠁⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠏⢻⣆⠀⢀⣠⣴⣦⣴⡟⠀⣠⣴⣿⣄⠀⠹⣧⠀⠀⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⠀⠀⠸⣿⣿⠟⠋⠁⠀⠈⠛⠛⠉⠀⠀⠉⠛⠛⠛⣷⠀⠀⠙⢷⣄⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠈⠻⢷⣦⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠠⣿⣤⣴⣦⣤⡿⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢀⡴⢿⡿⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣅⠈⠙⠛⣷⡄⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣿⠇⣸⣧⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⠟⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⣿⠁⠀⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠻⣦⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣥⣤⡀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠋⠙⣧⠀⠙⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⢿⣄⣀⠈⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣠⣤⠶⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠛⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⢙⣿⣦⠀⠀⠀⠀⠀⢸⡇⣴⡁⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡋⣻⣿⡿⠀⠀⠀⠀⠀⣸⠇⠻⣅⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠈⠻⣶⣄⣀⡀⠀⠀⠀⣀⣠⣴⠟⠉
⠀⢰⣾⡿⠿⣿⡛⠛⠛⠷⣄⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣀⣤⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠁⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠉⠛⣷⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡶⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⣼⠃⠀⠈⠉⠙⠛⠛⢻⡶⠶⠶⠶⠶⠶⠶⠶⠿⡿⠛⠛⠉⠉⠁⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣸⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⠶⠶⢶⡶⠶⠶⠾⠷⠶⠶⣶⠶⠶⠶⠶⠶⠿⠶⢶⡶⠶⠶⠛⠛⠛⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢸⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⣿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠾⢷⣤⣤⣤⣤⣤⣤⣶⠿⠾⠛⠋⠉

⠀⠀⠀⠀⠀⣠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢋⢀⣎⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢢⣀⣀⣄⠀⢸⠀⠀⠀⠀⢀⡀⠙⡄⣸⠀⠀⢀⡤⠒
⠀⠀⠀⠀⢠⠫⠒⡄⢀⣱⠦⠤⠀⠀⠀⠀⠈⢡⠊⠁⠀⠀⠈⠑⢇⠀⠀⠀⠀⢀⡜⢓⠛⠓⠒⢲⣯⣔⡒⠂
⠀⠀⠀⠀⢇⠘⠚⠡⢧⡼⠀⠀⠀⠀⠀⠀⠀⡆⣠⠤⡄⠀⡠⡀⠘⡂⠀⠀⠀⠸⣇⠼⠐⠤⠀⠽⣽⡇⠈
⠀⠀⠀⠀⠈⣂⠈⠉⠶⣁⣀⠀⠀⠀⠀⠀⠀⠣⣓⠑⠋⠀⠚⢊⡠⠃⠀⠀⠀⠀⠢⣨⠇⠀⢫⣡⠔
⠀⠀⠀⢠⠊⡇⠀⠀⠀⠘⢆⠑⠀⠀⠀⠀⠀⠀⠀⠇⠀⠉⢀⠀⡇⠀⠀⠀⠀⠀⠀⠞⠀⠀⢸⡅
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠱⠔⠁⢀⠂⠀⠀⠀⠀⠀⠀⠰⡀⢀⡼
⠀⠀⠀⠀⠀⠑⡤⠀⠄⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠐⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠩⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠐⢠⠀⢀⡳⠼⢴⡁⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣋⡀⡀⣀
⠀⠀⠀⠀⠥⢍⡶⣫⣄⠄⢖⡶⢹⠀⠀⠀⠀⠀⣹⣖⠓⢓⣤⡀⠀⠀⠀⠀⣴⡩⡩⣟⠉⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⡇⠑⠑⠣⠴⢠⡋⠀⠀⠀⠀⡇⠯⠜⠀⠟⠼⢣⠀⠀⠀⠀⣏⠓⢣⣲⢰⠖⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⡖⠑⡄⠀⠀⠀⠙⢢⢀⠁⢀⠀⠘⡆⠀⠀⠀⠏⠹⢺⠛⠁⢀⠅⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢰⠁⠀⠑⠤⠐⠁⢀⠃⠀⠀⠀⠀⢸⡈⠁⠈⠀⢀⠇⠀⠀⠀⠠⠸⠀⠆⢀⡇⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠈⢦⣀⢀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠑⢦⠄⠒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢄⡀⢴⠊
⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⢀⡆⣀⠄⠤⠀⠀⠀⠀⠀⢀⠔⠒⠒⠂⢤⠤
⠀⠀⠀⠀⠀⠀⡰⠧⠾⠤⣖⣂⠀⠀⠀⠀⠈⠉⣹⢖⡫⡏⠝⢫⠉⠲⡖⠂⠀⠀⠀⢩⢾⢯⢹⡆⠊⢀⡓
⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠈⢣⠁⠀⠀⠀⠐⠉⡇⠠⠥⠒⠒⠓⠒⣀⠇⠀⠀⠀⠀⠀⠸⠈⠉⠀⠁⠉⢻⣠⠇
⠀⠀⠀⠀⣼⠀⢎⣿⡱⠀⣮⡾⣆⠀⠀⠀⠀⡰⢇⠀⠀⠀⢰⡏⠉⠀⠀⠀⠀⠀⠀⢠⠚⠀⠈⠉⠀⠀⢸
⠀⠀⠀⠘⠘⢦⣀⣀⣒⣒⣀⡴⠉⠃⠀⠀⠀⠁⠈⢢⡀⢀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⢀⠀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⡆⣱⣜⣿⣷⣼⣾⣿⣧⣷⣾⣿⣷⣿⣾⣼⣬⣇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⣽⣽⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣾⣿⣧⣦⡴
⠀⠀⠀⠀⠀⠀⡀⢀⡀⡺⣶⣿⣿⡿⠟⣛⣭⣥⣄⣀⣀⣀⣴⣶⠞⠋⠙⠒⢦⣄⠀⠈⠉⠛⠿⣿⣿⣾⠄
⠀⠀⠀⠀⠀⡀⠈⣷⣭⣿⡿⠛⠁⣠⣾⠿⠛⠻⠿⢿⣿⣿⠿⠋⠀⣀⣀⣀⡀⠹⠷⠀⠀⠀⠀⠈⠙⢿⣿⣶⡇
⠀⠀⠀⠀⠒⢾⣶⣿⠟⠉⠀⢀⡾⠋⠀⢀⡠⠤⠤⣄⡀⠀⠀⡴⠋⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⣈⣙⣿⣿⡟⠁⠀⠀⠀⠎⠀⢠⠞⠁⠀⠀⠀⠀⠉⠢⣸⠁⠀⠀⣀⡀⠀⠀⠘⣧⣾⡥⠀⠀⠀⠀⠀⠀⠻⣿⣯
⠀⣀⣬⣿⣿⠋⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⣤⣄⠀⠀⠀⣹⠀⠀⠀⠿⠿⠀⠀⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⢴⣿⣿⠃⠀⠀⠀⠀⠀⢀⣰⣼⠀⠀⠀⠀⠛⠛⠀⠀⢀⡿⣦⣀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿
⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠰⠚⠛⢧⡀⠀⠀⠀⠀⠀⣠⡞⠀⠈⠙⢿⡟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀⠡⢐⢸
⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠻⣦⠒⢦⠀⠀⠀⠀⢀⠀⠀⠀⠁⡀⠀⠄⢸
⣼⣿⡐⠀⠀⠀⠀⠀⠀⠀⠐⡀⡄⠀⠀⠀⠀⠀⠀⡴⠲⢴⠀⠀⠀⠀⠀⢹⡆⣸⠀⠀⠀⠀⠀⢀⣀⠀⠀⠌⠄⠠⢻
⣿⣇⠀⠀⠀⠈⠀⠂⠅⠈⠀⢍⠀⠉⠀⠀⠀⠀⢀⠱⣄⠀⢧⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠉⠀⠏⢤⠀⢄⠐⠂⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠈⠀⢀⠀⠜⠀⠀⠀⢀⠉⠀⠀⠀⡘⠛⡞⢷⣄⡀⢀⣰⡿⠀⠄⠀⡀⡀⡀⢀⠈⡄⠠⠀⠌⣀⣾
⢿⣟⠀⠂⠀⠀⠀⠄⠊⢸⡐⠀⠀⢀⠠⠀⠀⠀⠂⠀⠀⠀⢹⡐⢻⡉⠙⢉⠈⠄⡀⠀⢁⠀⡑⠐⡠⡁⠀⠀⠀⢸⣿
⠘⣿⡀⠀⠀⠁⠄⢀⠀⠀⠙⠦⣤⣤⣄⣀⣀⣤⣤⠶⠶⠛⠛⠛⠉⠛⠛⠷⢦⣤⣄⣀⣠⡤⠖⠋⠁⡈⠀⡀⢠⣿⠃
⠀⠹⣷⡠⠀⠀⢐⢀⡀⠀⠀⠀⠀⠂⠀⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠉⠉⢄⠀⠀⢀⠁⠀⠄⣠⣿⠃
⠀⠀⠙⣷⡀⠀⡁⠀⠀⠀⠐⠀⠂⡂⠀⠂⠀⠄⠀⠀⠀⠀⢀⠘⣟⡿⢟⣋⠁⡀⠀⠀⠀⠂⠀⠀⠄⢁⣴⡿⠁
⠀⠀⠀⠈⠻⢦⡀⠀⠁⠀⠀⠂⠀⠒⠀⠐⠀⠀⠀⢀⢀⠀⠁⠁⠄⢂⡀⠉⣎⠀⠂⠄⠀⠰⠤⢈⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⢈⠀⠠⠄⠀⠀⠀⠐⠀⠀⠀⠃⠈⠀⡐⡊⠁⣂⢸⠣⠠⠀⢀⣢⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣶⣷⣤⣤⣤⣌⣀⣀⣠⣀⣀⣠⣈⣤⣾⣵⣶⡿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢀
⠀⠀⠀⠀⠾⠃⠀⠀⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠛⠉⢀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠐⠢
⠀⠀⠀⠀⠀⢀⡀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡒⠂
⠀⢀⡀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠀⠁⠠⠀⠀⠀⠀⠀⠄⠐⠀⠀⠉⠃
⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⠀⠠⡀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠠⡉⡀⣀⠐⣀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠙⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠐⠐⠒⠈⠂

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠃
⠀⠠⠄⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣆⢢⣦⣦
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠢⠀⠀⠄⠀⠀⠀⠐⡂⠀⠀⠙⠛⠡⠂⠙⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⢀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠐⠶⠶⣤⣄⣀⣀⣠⡴⠶⢻⠂⠀⠀⠀⢠⠔⠚⡉⠰⠊⠙⠒⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠠⠀⠈⢁⠍⠡⠉⠀⠀⠌⠀⠀⠀⠀⠘⠀⠈⠁⡠⠄⠉⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⡒⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠂⠐
⠀⠀⠀⢀⠔⠅⡀⠆⠠⠀⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣀
⠀⠀⠀⠈⠤⠀⠓⠒⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠾⠃⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⢧⠀⡠⠒⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⢈⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣫⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣏⠚⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣛⣽⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡛⠛⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡏⠀⠀⠛⠛⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⡿⠀⠀⢸⣿⣷⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡾⠁⠀⠀⣼⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣽⠃⠀⠀⠀⠚⠻⠿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⢠⣿⣷⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠚⠻⠿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣶⣦⣤⣤⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⠶⠶⠦⠬⠄⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⢀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⠉⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢀⠀⠀⠄⠈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣿⣷⣶⣿⡳⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⣤⣷⣤⣬⠛⠿⠀⠀⣿⣽⣿⣷⣶⣄⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡾⣿⣿⠻⣿⡟⢠⡀⠀⢠⡟⢛⣿⠟⠿⣟⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣯⣿⣀⣈⣿⣿⣿⣿⣿⠿⠛⠃⠀⠘⢙⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣹⣶⣼⣿⣿⣇⣠⡴⣤⠀⠀⠺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠿⢻⠏⣿⣿⡝⣿⣿⣿⣟⣻⢶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⡞⠀⠹⣿⣾⣿⣿⡙⣹⣿⣶⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠇⠀⢀⣿⣿⢜⣿⣼⣏⣹⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠇⣠⣾⣿⣿⣿⡟⣿⡛⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⣿⣿⣿⣹⠿⣿⣿⣿⡿⢿⣿⣿⣶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⡿⢻⣿⣿⣿⣆⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣇⣛⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠏⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⢿⣿⣿⣿⣿⣿⡄⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⡘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣯⡧⠘⣧⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⡿⣿⣴⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣧⢻⡏⡀⢻⣀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⠀⠀⡾⣿⣿⣿⣿⣿⣌⠇⣥⠊⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠁⣹⣿⣿⣿⣿⡇⠰⢸⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠘⣿⣷⡀⠸⡇⣿⣿⣿⣿⡇⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣷⣿⣿⠀⢄⣠⣿⣿⣿⣿⣇⠀⡇⠀⢰⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣨⣿⣿⣿⣿⣿⣿⣆⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣹⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠛⣿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⡟⢺⣿⣿⣿⣿⣯⣭⠛⠿⠛⢿⣯⣹⠛⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣛⣛⣋⣁⣀⣛⣛⣈⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡠⠖⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⢀⡄⠀⢀⣾⠁
⠀⡐⠋⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠃⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢷⠀⣠⢤⡀⠀⠢⡈⢢
⠀⠀⣀⣀⠸⡌⠳⡀⡴⠋⣹⠂⠀⠀⠀⠀⠀⣠⠞⠛⠛⠓⠀⠐⠚⠛⠲⣤⡀⠀⠀⠀⠀⢀⡤⠤⣄⡇⠺⠞⣡⠞⠀⠀⠀⢳
⠀⠀⠙⢤⡙⠾⠂⣱⠧⢼⠁⠀⠀⠀⠀⠀⣼⠓⢾⠁⠀⠀⠀⠀⠀⠀⠲⣤⠻⣆⠀⠀⠀⠸⠔⠒⡌⠙⢦⠀⠙⣋⣹⠇⠀⢸
⠀⠀⣤⠒⠘⠃⠸⠁⠀⢸⡆⠀⠀⠀⠀⠀⡟⠀⡏⠳⣄⡀⠀⠀⠀⢀⡴⢿⠀⢻⡄⠀⠀⠀⠀⠐⣇⠀⠈⠃⣈⡓⢄⠀⠀⡜
⠀⠀⠀⢉⠝⣡⣄⣀⣠⡘⢦⡀⠀⠀⠀⣨⣇⠀⣷⠀⠈⠉⠛⠛⠛⠉⠀⢸⡄⢘⡧⣄⠀⠀⠀⣠⠋⣰⠶⠚⠁⠉⠉
⠀⠀⠀⠈⠉⠀⠈⠉⠀⠑⢄⠙⢆⠀⠀⢧⣤⠀⢹⣷⣤⣀⠀⠀⠀⢀⣀⣼⡇⠀⣀⡼⠀⢠⠞⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠑⢄⠈⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⢀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠱⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⠎⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇⠀⠀⠘⣏⠙⠛⠻⠿⢿⡿⠃⠀⠀⣿⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠰⡄⠈⠷⣤⣤⡴⠋⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠈⠲⣄⣀⣀⣀⡴⠃⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠲⠤⣤⣉⣉⣁⣠⡤⠴⠒⠋⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠐⢁⡔⠋⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⣤⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣰⠛⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⢆⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣤⢶⠃⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠳⣄⠀⠈⣹⢷⡦⣤⣤⣤⣀⣤⣤⣤⣤⡴⢶⠻⡃⢀⡤⠞⠉⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⠳⠴⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣘⠋⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣠⡴⠛⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⡟⣻⠇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⣿⡿⡿⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡛⠫⠿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⡿⠀⠀⠘⠀⠄⠒⢨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⠑⢢⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢿⣦⣠⢄⠀⠀⠀⠴⠶⠾⠿⠟⠛⠿⠖⠀⠀⠋⢉⣿⣿⣿⣿⡙⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡟⢿⣿⣆⠀⠀⠀⢰⣴⣶⣾⣶⣶⠂⠀⠀⠀⠀⠸⣿⣿⣿⣟⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠚⠛⠯⠀⠀⠀⠈⣿⣤⠿⠛⠛⡁⠀⠀⠀⠀⠀⠈⣿⢹⣽⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣝⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⣇⠀⢀⠐⢦⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢀⣬⡛⣷⣿⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣄⢂⣰⣬⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢐⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣆⣀⣉⠩⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠸⣿⠿⠛⠻⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡷⡉⠁⠀⡀⠀⠀⣀⣶⡿⠋⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣰⠏⣴⢏⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢲⡶⠛⠉⣼⠃⣇⢙⢲⣶⣦⡐⠺⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠘⣿⣼⣷⣿⠟⠻⣿⣿⣷⣤⣀
⠀⠀⠀⠀⡀⢠⣶⡿⠃⠀⠀⠀⠀⠀⢹⡄⢹⡌⢾⡉⠋⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⣿⡿⠀⠀⠉⣽⣿⣿⣿⣿
⠀⠀⡠⠊⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣿⡘⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⠀⠀⠀⠉⠁⠛⠻⠿
⠀⢀⣄⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⣿⣷⡿
⠀⣤⡛⠷⣤⣀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢏⡇⢷
⠀⢻⠁⠀⠀⠉⠉⠛⠒⠆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⢀⡄⣧⠘⡄⠀⢠⣦⣄
⠀⠈⠇⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠰⣿⡆⠀⠲⠶⣦⣄⣀⠀⠀⠠⠈⠰⠠⠀⠀⠀⣀⣀⡀⠀⠠⢴⡎⠁⠀⠈⣷⣄⠂⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠁⠀⠙⢦⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⠶⣄⢀⣄⣳⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⠶⣤⠞⣶⡋⠀⣈⣉⠀⠙⣆⠀⠀⠀⠘⢒⠖⢀⣠⠔⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠶⠦⠤⢥⡎⣤⢹⣼⢱⡎⡶⠒⠻⢳⠀⡠⣚⠥⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠧⣄⠀⠀⠀⣄⠳⢤⠞⠸⠦⠜⡡⠀⣸⠛⠞⠋⢧⡖
⠀⠀⠀⠤⡼⠀⠀⠀⠘⢆⠀⠀⠈⠑⠒⠶⠖⠒⠉⠀⡴⠃⠀⣀⠴⠃⠉⠁
⠀⠀⠀⠉⠁⠙⠳⢦⣀⠈⢑⣦⣄⣀⡀⢀⣀⣠⢴⣾⣃⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣿⠙⠺⢭⣽⣹⠶⠋⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡏⡇⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠉⠁⠀⠀⢘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡟⢳⠒⡖⢶⠲⡛⢏⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡇⡜⢠⠃⠈⢆⠱⡈⢆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢸⠀⡇⢸⠀⣶⡈⢧⠱⣈⣦⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢺⠶⠶⠼⠋⠳⠚⠋⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⣄⣨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⠯⡉⢉⣙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⠤⠤⠶⠶⠤⢤⣅⡀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣸⢄⣀⣀⣀⣀⣀⡤⢶⡇⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢻⣤⡀⠉⠉⠉⢀⣠⡾⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⣼⠧⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠣⢤⡀⠀⠀⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠛⠲⠦⢤⣤⣤⢤⡶⠿⢥⡀⠀⠀⠉⠳⣄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⢀⡠⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⢀⣀⣴⠏⠀⠀⠀⠀⣀⣠⠔⠋⠀⠀⠀⢹⠆⠀⠀⠀⠘⢦⠀⠀⠀⠀⠈⢳⡀
⣤⣀⠖⢡⠀⠀⣦⡀⣐⡆⠈⠉⣙⣛⣉⣉⣁⣯⣤⠤⠶⢖⠋⠉⠀⠀⠀⠀⢀⡴⠋⠀⢀⡠⠀⠀⠈⢧⠀⠀⠀⠀⡸⢻⡄
⣇⣈⣉⣙⡓⠒⠃⠉⠉⠓⠒⠤⣧⠀⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⠡⠔⠊⠁⠀⠀⠀⠀⠘⡇⠀⠈⠁⠀⠀⢷
⠀⠀⠈⠉⠉⠉⠉⠉⠓⠒⢆⠠⣌⣛⢧⣀⡴⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢿⠈⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢿⠀⠙⠲⢌⡳⠤⣤⢶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⢸⡄⡇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⡏⠒⢧⡼⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⢸⡇⣿⠀⠐⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠾⠄⠀⠀⠀⢷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⢸⠃⡟⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡿⢀⠇⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠈⢳⣄⠀⠀⠠⣄⣀⣀⣀⣀⣤⡤⠴⠚⠉⠀⠀⢀⣼⣁⣼⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣠⠋⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠈⠛⠶⠶⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⠉⡽⠛⠒⠒⠒⠚⠋⢻⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⢀⡤⢴⡒⠒⠾⠼⣤⠖⠛⠳⣿⠀⠀⡀⠀⠀⢀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⡼⠞⠋
⠀⠀⠀⠀⠀⢠⡏⢀⡦⢷⡀⠀⣰⠁⢠⠤⡀⢸⡉⠛⠓⠶⠶⠾⠖⠚⠛⠲⠶⠤⣤⣤⣤⠖⠒⠲⣄
⠀⠀⠀⠀⠀⠘⣇⠀⠋⠉⡝⠓⡇⠀⢧⡴⠃⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⡔⢲⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⠁⠀⢳⡀⠈⠀⢠⠟⠀⠀⠉⠉⠉⠉⠉⠛⠛⠒⢲⡖⠒⣇⠀⠳⠋⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠼⠦⣄⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣠⡶⠗⠀⠀⠠⣤⣄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠰⠋⣀⡀⠀⠀⣀⡀⠙⠆⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⡞⢱⣿⣦⡎⢹⣿⡆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢋⠓⠀⠀⠀⣧⣈⣛⠟⠣⣄⡡⠇⠀⢀⣀⣼⣷⠶⠾⠟⠛⠿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠲⠄⠀⠀⠀⠀⠉⠀⠀⠀⠠⠶⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠋⠀⠀⢲⡖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⡀⠈⠛⠷⢶⣤⣤⣤⣤⣤⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢧⡀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠳⣄⡀⠀⠈⠛⠶⠴⠞⠁⠀⠀⠀⠀⢀⣠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⢁⣿⠀⠈⠙⠳⠶⣷⣶⣶⣃⣠⣤⣤⡶⠾⠛⠉⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣠⡶⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠳⣄
⠀⠀⢠⠦⣄⠀⠀⣀⣀⣠⠞⠋⣠⠞⠉⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣦⡈⠳⣄
⢀⡤⠤⠵⠦⠙⠋⠉⠀⠁⢰⡟⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⣦⡈⠳⣄⠀⠀⠀⠀⢀⢄
⣜⠂⠒⠂⠂⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠻⣦⡈⠻⠶⠶⠔⠡⠟⣊⠇
⠈⣟⣉⣉⡥⠔⠒⠉⠉⡆⠸⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣀⡴⠃⣀⠀⠀⠀⠐⢛⣑⣹
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠹⣤⣨⠗⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⣤⡤⠞⠉⠓⢤⡈⠙⠻⢭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠙⠷⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠹⣄⠀⠀⠀⠀⠀⠀⢸⡍⢿⠙⠛⠛⠛⠛⢻⡟⣿⠋⠉⠁⠀⠀⠀⢀⣤⠞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠻⡷⢶⣤⣤⣤⣤⣼⡇⢸⡀⠀⠀⠀⠀⢸⡇⣿⣀⣀⣀⣀⣀⣴⠟⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢷⡀⠀⠀⢰⠟⠀⠉⠉⠉⠉⠉⠉⠁⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠶⠶⣦⣤⣤⣤⡾⠃⠀⠀⠘⠷⣤⣤⠤⠶⠶⠶⠶⠾⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠴⠛⠂⢠⢶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠐⠂⠀⠠⠄⢀⣀⢀⣇⣈⠠⠬⠬⣀⣖⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢩⠀⠀⠀⠅⢆⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠠⠀⠀⡞⠀⠀⠒⠀⠀⠀⡀⠀⠀⠒⠀⠢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠙⡑⠀⡆⠤⠀⠀⡀⠀⠀⠀⡋⡀⠄⠀⢃⠐⡑⠁⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠅⠤⠈⠀⠧⠄⠠⠀⠀⠀⠀⠀⡋⢐⠢⢤⠊⠈⠰⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠒⢀⠀⢀⡎⠀⠀⠀⠀⠀⠀⡋⠰⡍⡂⠀⠀⠈⠑⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⠀⠃⠀⠀⠀⠀⢀⡐⠁⠘⠈⡏⡂⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⠈⠁⠀⢠⠂⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠊⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢄⣀⡜⢀⣊⣀⠤⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠓⠚⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢄⠀⠀⠀⠩⠄⠀⠀⢀⠍⠀⠀⠀⠀⠀⠀⠴⠿
⠀⠀⠀⠀⠀⠀⠀⠘⢍⠀⣠⠵⢄⡀⠀⠀⠀⠰⠇⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⢣⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠐⠚⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡳⢄⠀⢱⠠⣀⣠⣁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠈⠢⡨⢳⡌⠀⠈⠛⠉⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣈⣊⣀⣀⠀⢸⣤⣤⣤⣤⣤⠬⠷⡶⠶⢦⠀⢒⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠁⠈⠉⠀⠀⠀⠁⠀⠐⠚⠉⠁⠀⠈⠙⠉⠈⠑⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⢀⣿⠏⢀⣤⡴⠛⠛⠛⠛⠛⠛⠿⠷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠶⠶⠾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠘⢣⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣦⢀⣼⣶⠟⢹⣿⢷⠿⣆⠘⣷⡄⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢰⣿⣾⣿⡿⠁⠉⠀⠘⠃⠀⠀⢻⣾⢷⣾⠇⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⠟⢠⣿⠇⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⠀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⡟⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡟⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣿⢇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠛⠁⣇⠀⢺⠇
⠀⠀⠀⠀⠀⠸⡏⢸⡇⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⡟⢰⡇
⠀⠀⠀⠀⠀⠀⢻⡎⢻⡄⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⢷⡄⠻⠆⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠈⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⣀⡀⢤⡤⠛⠃⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠙⠛⢳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣴⠦⣀⣀⣀⠀⢀⣀⣀⣠⡶⠞⠛⣿⡇⠀⠀⠀⠀⠈⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠋⠹⣷⣄⠈⠉⠉⠛⠋⠉⠉⠁⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣀⣀⣤⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⢀⣴⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣴⣿⣿⡿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠶⣄⣀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠋⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠶⣬⣭⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣻⣧⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⣿⣿⣶⠶⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣾⡿⠿⠟⠙⣿⡠⢄⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣴⣆⠀⣿⠁⠈⠉⠛⠛⠛⠿⠿⣷⠶⠶⢾⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⢡⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⡾⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢸⣇⣤⡾⠛⠛⠳⣦⣄⡀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢀⣠⠶⠖⠉⠙⠛⠛⠷⢦⣼⠟⠁⠀⠀⠀⠀⠀⠈⢳⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⣄⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⣠⣤⣤⣤⣤⡴⠛⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣦⣴⣾⡻⠾⠋⠈⠛⠛⠛⠶⠶⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠛⡟⠛⠛⠟⠛⠛⠛⣧⠈⠛⠛⢿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣏⣹⣿⣉⣉⣉⣉⣉⣩⣉⣉⣽⣿⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠐⣶⡄⠀⠀⠸⡿⣿⡿⠀⠀⠀⠟⠻⡏⠀⢸⣿⣿⡆⠀⠀⡀⠀⠀⠸⣿⣿⡟⠀⢀⣿⣿⡿⠀⠀⠐⣻⠷⢄
⠀⠸⠿⣿⣿⠃⠀⠀⠀⠀⠀⣄⡀⠀⠀⡀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠁⡎⠀⠀⠁⢈⠀⠀⠀⠛⠉⠁⠀⠀⠀⠘
⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⡀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⢢⣴⠄
⠀⠀⠀⠀⠛⣿⣿⣿⠀⠀⠁⢻⣿⣿⡀⣾⣷⣿⡆⠀⠀⣷⡶⠀⠀⣤⢤⠀⠀⠀⠀⠀⠀⠀⣷⣶⣼⠁⠀⠀⠸⡿
⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⢸⣿⣿⡗⣿⣿⣿⡃⠀⢸⣿⠿⠀⠘⢹⠀⠀⠀⠀⠀⠀⠃⣠⣿⣿⡏⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠄⢛⣿⡄⠀⠀⠀⠀⠛⣿⠀⠻⣿⣿⡿⠀⠀⣉⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⣙⡇
⠀⠀⠀⠀⠀⠀⢻⡇⢸⠀⠀⠀⠀⣿⡆⠀⠹⣿⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢳⠉⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠠⠀⠀⠀⠀⣌
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡞⠀⠀⠀⠐⢀⣄⠀⠁
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠛⠲⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠤⠤⢤⠤⠠⣤⡤⣤⠄
⣤⣤⣤⣴⣴⣶⣶⣴⣦⣶⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠐⢾⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢛⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠘⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⢠⣀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠯⠁⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢘⠉⢹⠇⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄⣀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡆⠁⠸⠘⠛⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠀⠀⠈⠂⠾⠀⢀⠀⠀⠀⠀⠀⠸⢙⣿⡿⣦⡄⠈⠀⠠⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡗⠁⠈⠂⣰⣦⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣦⡴⣶⣾⣿⣿⠀⠀⠀⠀⢠⡜⢻⣧⣜⣿⣧⠶⣶⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣠⡟⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣹⣿⣿⣟⣿⢻⡿⠛⢠⣄⠀⠀⠀⣿⠇⣼⣿⣿⣿⡿⣧⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⢻⠀⠀⢰⣏⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠩⢹⡏⠀⠀⡼⠁⠀⠀⢻⣦⠀⠀⣿⠀⣿⣿⡿⠏⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⠀⠀⢸⠋⡈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⡾⠀⠀⡰⠁⠀⢀⣴⠛⠁⠀⢰⡟⠀⣿⣿⣿⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⣾⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⠜⠀⠤⣴⣤⣤⡴⢛⠁⠀⠀⠀⢘⠃⠀⣿⣿⣿⣀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⠉⠉⣿⠉⠁⠀⠀⠀⠀⠀⣈⠉⠀⣰⣿⣿⣿⣿⣷⠀⠀⢸⠇⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠇⠀⢦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⡹⠃⠀⣿⣿⣿⣿⣿⣽⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⣴⠾⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⠧⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠰⢤⡀⠀⠀⠀⠀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠠⡏⠀⠋⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡹⠛⢻⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠛⣸⡇⠀⢸⣀⡁⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠈⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⠤⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠋⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠁⠀⠀⢀⠀⠀⠀⠄⢀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⠃⠀⢠⡄⠀⠀⠐⠂⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡘⢿⣦⡀⠠⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠐⠈⠟⠋⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣤⣀⣤⠤⠖⠉
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠰
⠀⠀⠀⢠⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠊⢐⠀⠀⠀⠀⠀⡀⡀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠥⠤⢼⠀⠂⠀⢀⠴⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠰
⠀⠀⢀⡠⠀⡤⠀⠀⠀⠀⠠⠀⠂⡩⠀⠀⠀⠀⠀⠝⠢⠤⣀⣀⣄⠀⠑⠀⠴⠇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠋⠁⢦⣄⠀⣀⡴⠠⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⠉⠉⠁⡀⠀⠀⠀⠈⡀⠈⠢⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡜⢃⠀⠀⠀⠀⠃⠀⢠⠂⠀⢀⢀⠀⢀⠀⢀⠀⠀⠠⢀⠈⠌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠠⠀⠀⠄⠘⡀⠀⠒⠂⢰⠀⠁⠀⠀⠈⢂⠀⢀⠀⡰⠒⠠⠂⡄⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⡀⢀⣀⠀⠀⢧⣀⣀⣀⠨⢤⠀⠀⠀⠀⠀⠀⠈⠒⠳⢀⠤⠐⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⡄⠀⠦⢀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⡳⠤⠈⠒⠛⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢎⣰⣀⣸⠂⠈⠉⠓⠒⠲⠖⠒⠲⢍⡀⠀⡀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠓⠋

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠈⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⣾⣋⠇⠀⢰⠏⡵⠀⠀⢠⣶⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣄⡀⠀⢀⣠⣴⠏⣴⡿⠀⢠⢿⣇⠀⠀⡸⣿⣀⣠⠖⣿⡏⠀⡴⢻⡇⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⡋⠀⠻⠞⠹⣷⣠⠎⠀⢻⣶⠋⢀⡼⢿⠁⠀⠙⠷⠞⠁⣾⣇⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⣿⡇⠀⠀⠀⠀⠈⠁⠀⡴⠁⣻⠄⠈⠳⠛⠀⠀⢀⣤⠤⢶⣿⠉
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⣰⠋⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠴⠞⠁⢰⠀⠈⡏⠠⣠⢆⠋⠁⠀⡷⠴⡇⡇⢠⣶⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠰⣇⠐⡓⠀⠀⡇⠀⡇⠉⢁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠉⠁⠀⠁⠀⠁⠀⠉⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⢠⣶⣶⣶⡄⠀⣶⡄⠀⣶⡆⢰⡶⢤⣤⠴⡶⠀⣛⡃⠀⣰⢶⣶⡶
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⢸⣿⣿⣿⡇⠀⣿⣿⡄⣿⡇⠀⠀⢸⣿⠀⠀⠀⣿⡧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⡄⠘⣿⣿⣿⠂⠀⣿⠈⢿⣿⡇⠀⠀⢸⣿⠀⠀⠀⣿⡗⠀⢹⣿⠟⠃
⠀⠀⠀⠀⠀⠘⠿⠃⠀⠻⠃⠀⠛⠿⠟⠀⠀⠻⠀⠈⠛⠃⠀⠀⠘⠟⠀⠀⠀⠻⠃⠀⠸⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢒⢒⠢⡀⠀⢀⢀⠀⠀⠀⡀⡀⠀⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢛⣙⡩⠋⠉⠙⠙⠉⠙⠉⠛⠋⠉⠹⠿⠋



⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣿⣿⣻⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⠀⠀⠀⠀⢸⣷⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠞⣛⣃⣀
⠀⠀⠀⠀⠛⢻⣿⣿⠋⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠶⢿⣿⡿⠋
⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⢀⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⢀⣤⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣿⣿⣶⣶⣦⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣷⣦
⠀⠀⣸⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡼⢿⡿⡏⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠈⠻⣷⣄
⠀⠀⣿⠃⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡼⣿⠀⠀⠀⠀⠀⠀⢀⣼⠟⠘⢿⣿⣿⣿⠏⢻⡇⠀⠀⣿⠟⣿⣿⣿⣿⠁⠀⠀⣸⣿
⠀⠀⣿⡀⠈⠿⢿⣿⣻⡇⠀⠀⠀⢀⡆⠀⢜⠀⣿⠀⠀⠀⠀⠀⠠⠿⠿⠛⠻⣿⣿⣿⠏⠀⢸⣷⠀⣸⡟⠀⡿⢯⣭⣅⣀⣤⠞⠋⠁
⠀⠀⠘⣷⠀⢰⣿⣿⣿⣧⠀⠀⠀⠎⠀⠀⠀⢀⡿⠀⠀⠠⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣠⡾⠟⠁⢰⡿⠁⠀⠁⠀⠈⠛⠋
⠀⠀⠀⣿⡄⠈⣻⣿⣿⣿⡀⠀⠀⠆⠂⠀⠀⠈⡇⢀⠀⠀⠈⠑⢶⣤⢀⣾⣿⣿⣿⣿⣿⠀⠀⢠⡟⠁
⠀⠀⠀⠙⠓⠰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠶⠁⠠⣀⠀⠀⠉⢸⣿⣿⣿⣿⣿⠃⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠄⠀⣧⠀⠀⠀⠀⠀⠈⠳⡄⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠠⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⣸⣷⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⠃⠀⠀⠀⠘⣠⣾⠿⢷⠢⠴⠖⠉⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⢻⡟⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣿⢻⣿⠀⠀⠀⠀⠀⣸⡏⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⣸⠃⣼⠇⠀⠀⠀⠀⢠⡟⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢸⡇
⠀⠀⠀⣼⡏⣰⣿⠀⠀⠀⠀⠀⣼⡇⣸⡟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣇
⠀⢀⣼⡟⠀⢊⡿⠀⠀⠀⠀⢀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿
⠀⠈⠛⠀⠀⠘⠷⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠀⠀⠀⠘⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠠⡢⠀⠠⠀⢠⡊⠑⡄⠠⡀⠀⠀⢀⡐⠢⡄⠀⠀⠀⡤⠤⠄⠀⠤⠀⢀⠀⠓⢒⠀⠒⠀⠀⠠⠀⢀⠾⠶⣭⡾⠉⣯⠓⢢⣄
⠀⠀⠀⠠⠊⡱⠊⠁⣀⣠⡑⢢⡔⢠⠀⠰⢈⠐⠁⠀⠀⠀⢗⢭⡉⠀⠛⠀⢅⣤⢀⡄⡁⠀⠈⡁⠀⠀⠿⢶⠦⡂⢩⢀⠁⡠⠋⠂⠂
⠀⠀⠀⡊⢙⠁⠀⠏⢼⡧⣿⠀⢡⠴⡀⠀⠀⠀⠠⠈⢢⠀⢸⢺⠣⠁⠆⠀⡙⠇⠹⠆⠅⠀⠀⠇⠀⣸⢶⠦⠀⠈⣤⠮⡼⠐⣂⡷⠁
⠀⠀⠀⡌⠉⡀⠀⢌⠉⠙⠡⠀⡬⢤⠃⠀⢄⡀⠈⠃⠁⠀⠀⣌⣂⣠⠀⠀⡅⠀⠈⢀⠀⠀⢀⠀⠀⠰⢰⣀⣀⡠⢧⠀⠈⠟⠉
⠀⠀⠀⠈⢊⠑⠦⣀⣈⣁⡠⠚⡤⠈⠀⢤⡘⠮⠂⠀⠀⠀⡀⡀⠀⠠⡢⠀⠀⠀⡄⢄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⠃⠀⠨⠀⠀⣼⠃
⠀⠀⠀⠀⣤⣍⡃⠤⠧⠀⠕⡂⠁⡄⠀⠀⠀⠀⠀⢀⡀⠢⡔⠊⠀⠀⠀⣀⠀⠀⠁⠂⠀⠐⢀⠴⠃⠘⢤⠀⡂⠀⠀⠆⠀⠀⠀⠨⠜
⠀⠀⠀⣠⣬⡝⠓⠀⠒⢠⡖⣀⠔⢁⠄⢄⠀⠀⠀⠈⠷⠀⣍⠄⠀⠀⠀⠈⠁⠀⠀⠀⢀⠼⢁⡴⠆⠲⢦⠰⠦⡀⠀⢄⢀⡐
⠀⠀⠐⠛⠊⢦⠠⡄⠘⠁⠀⠀⠀⡬⠰⠠⢧⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡠⠑⠢⠀⠩⢠⠄⠊⠀⠀⢀⣀⠓⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠈⢀⠇⠀⠀⠀⠘⠸⣰⢋⠆⢂⠀⠀⠀⣤⢤⣀⡄⠀⠠⢠⢤⡔⣌⠂⡀⢠⠑⠤⠬⠧⠴⠁⡇⠀⠀⠀⠃⠈⠒⠀⡘⠋
⠀⠀⠀⣀⠄⠀⠠⠊⠀⠐⠅⠀⠠⢀⣭⠄⢦⣬⠀⠀⠀⠷⠘⠧⠁⠀⠀⠀⠘⠃⠉⠀⠃⠀⠀⠀⠑⢊⠀⡀⡐⠈⠉⠐⡀⡀⠈⠂⠂⠃
⠀⠀⠈⠀⠂⠀⠀⢀⠠⠠⡀⠀⠀⠉⠻⠀⢸⠁⠀⢀⡊⠀⠄⡠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠋⠀⠀⠈⠄
⠀⠀⠀⠀⢀⡔⠪⢙⠀⠅⠨⠢⠀⠀⡆⠀⠰⠀⠀⠈⠉⠀⠀⠀⢀⠴⠘⠃⣛⠰⣀⠀⠀⠈⠀⠀⡡⣀⠀⠀⠈⠔⠐⢌⠀⠀⢀⠠⠁
⠀⠀⠀⠀⣥⠮⢙⣭⣒⡰⢅⣂⡥⠀⠀⠉⠀⠀⠔⠆⠀⠀⠀⠀⠬⠀⢩⣿⢸⣷⢰⠳⣆⠀⢠⠁⠀⠀⠀⢵⢰⡟⠀⡀⢱⠅⠀⠀⠀⢡
⠀⠀⠀⢄⠈⢻⠏⢁⠿⠷⠦⠣⠂⠀⠠⡄⠤⣊⣀⢰⠤⢠⠄⠀⢘⡀⠌⠩⠈⠅⠰⠔⠃⠀⠀⠀⢀⠀⠠⠘⠢⡁⠀⡀⠘⠠⠀⢀⠀⠈
⠀⠀⠀⠁⢀⠂⠀⠆⠀⠀⢀⢀⡀⠄⠀⠈⠂⠡⠿⡾⠗⠁⠀⠀⠠⠃⠃⠈⠀⠁⠣⠀⠀⣄⠀⠀⠊⠀⠀⠀⠀⠁⠉⠐⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠨⡀⡰⠀⠀⠀⠀⠂⠅⠁⠀⢠⡁⠄⠰⠄⣘⡀⠀⠀⠀⠇⠒⠒⠒⠒⠂⠀⠜⠒⠆⠀⠀⠄⠀⠠⡆⠀⠀⠀⠦⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣴⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡤⠴⠶⠂
⠀⠀⠀⠸⣿⢿⣻⣯⡿⠀⠀⠀⠀⠀⠀⠀⢰⢣⣎⣴⠶⠶⢶⣦⡀
⠀⠀⠀⠀⠐⠿⣿⠟⠁⠀⠀⠀⠀⣤⡀⠀⢸⣾⡿⡡⢊⣉⠓⢌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⢻⡆⠀⣀⣀⣀⣤⣬⣿⣷⣦⣿⣿⣧⣑⠐⢊⢦⠑⣌⢷⣄
⠀⠀⠀⠀⣀⣤⡾⠿⠛⠋⠉⠉⠉⠉⡽⠋⠉⢉⣙⢿⠙⠛⠿⣷⣥⡈⠢⡙⢷⣄
⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠙⠏⣸⠃⠀⠀⠀⠙⢿⣷⠘⣜⣿
⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠶⣾⡁⠀⠀⠀⠀⠀⠈⢿⣧⢸⡿⣄⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠸⣿⣮⣷⣀
⠀⠹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⢿⡝⠂⠀⢀⡴⠿⣿⣿⡿⠇
⠀⠀⠈⠙⠻⠶⠶⣦⣤⣤⣤⣤⣴⡶⠶⠀⠀⠀⢀⣴⠋⠀⣧⠀⠀⠀⠀⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣤⡤⠶⠛⠁⠀⣠⣿⠀⠀⠘⢷⣶⠾⠋⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧⣀⣠⣴⠾⢻⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡟⣠⣴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠿⣏⣁⣠⠟⢀⡄⠀⠀⢸⡟⠀⠀⠀⠺⠿⣿⣿⣿⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠁⠠⠴⠛⠀⠀⠀⣼⠇⠀⠀⠀⢀⣴⠟⠛⠛⠁⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣙⣒⣒⠶⠶⢦⡀⣠⠤⠤⠤⠤⠶⢶⣿⢀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠉⠉⠉⠉⠙⠛⠛⠓⠒⠒⠒⢺⡟⠋⠉
⠀⣠⠞⢲⡀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⡟⠀⢸⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣠⣧⢠⠏⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠧⠴⠛⠛⠶⢶⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠘⠻⠶⢤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠷⠶⢶⡶⠶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣙⢲⡶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣾⣋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠿⢿⣿⡟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠋⠁⠀⡀⠈⠉⠉⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡀⠀⡠⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠠⠀⠐⠆⠥⠆⠀⠈⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠧⠜⠀⢀⣔⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠠⠊⠀⠀⠀⠁⢄⠀⠀⠀⠣⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠘⠋⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠘⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢂⠀⢀⠀⠀⠱⡀⠀⢀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠙⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⠁⠀⠀⠀⠐⣄⣄⠀⠀⠀⠀⠀⠀⠀⣸⠔⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠐⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠀⠸⠀⠀⠀⠀⠀⢠⠉⠓⠄⢀⣀⠀⠤⠊⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠱⣶⡿⠇⡀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠌⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠱⠒⠉
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡄⠻⢷⠂⠠⠄⣀⣀⣀⣀⣀⣀⡀⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⢠⠁⠀⠀⠀⠀⡠⠚⢁⠃⠀⠀⠀⠀⡇⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⡠⠚⠀⠀⠀⠀⢺⠀⠀⢸⠀⠀⠀⠀⠀⠘⠻⠟⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡠⠊⠀⢀⡤⠒⡖⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⡶⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢇⣀⣴⢉⠃⠀⢇⠀⡸⠁⠐⢿⡦⠀⣀⣀⣀⣀⠀⠀⢀⣤⡀⠱⡀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢾⠆
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠈⠛⠛⠉⠀⠀⠀⠛⠋⠀⠈⠲⣶⣶⠶⠒⠒⠒⠂⠒⢶⣶⣾⡟⢡⠀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠘⠃⠀⠀⣴⣿⣿⣷⠀⠀⠀⠀⠀⠆⠀⣴⣶⣷⣦⠀⠀⢈⣅⡀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢣⢾⡷⠀⠙⠛⠋⠡⠆⠀⠰⣿⣿⠆⠀⠙⢛⠛⠋⢀⡀⢿⡿⠗⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠱⡤⣄⢠⠀⣠⣴⢄⠀⢠⣾⣷⡀⣨⢥⢄⠉⡡⢄⡠⠚⠉⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠉⠙⠋⠀⠙⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠫⠕⠊⠀⠀⠉⠈⠈⢄⠀⠀⠀⡠⠀⠉⠉⠀⠀⠑⠫⠝⢲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠤⠚⠒⠂⠉⠉⠙⠃⠈⠀⠀⠀⠁⠘⠉⠉⠉⠐⠒⠓⠤⠚⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣴⡷⡲⣳⣶⣶⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣼⣾⣿⣿⣻⡿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣠⣶⣶⣦⣼⣿⣯⣤⣤⣄⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣿⣿⣽⣿⣿⣿⣿⣿⡿⢿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣩⣿⣿⣿⣿⣿⣿⣧⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣿⠀⠀⢷⠀⠈⢿⠟⠟⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⣯⠀⠀⢸⡆⠀⢸⠰⢸⢻⣾⣧
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⡖⠀⣼⠇⠀⠀⠆⣸⣾⣿⣿⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣼⣿⣿⠇⣸⡟⢀⡆⠀⢿⣿⠿⠿⣿⢿⣦⡀
⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⡴⡏⣿⣿⣴⣿⣿⣿⣷⡙⣜⡇⠀⠀⠈⠨⣯⣻⡗⠲⣶⠤⣄⡀
⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠈⠸⢰⣿⣿⣿⣿⣿⣿⣽⣧⢹⣶⢰⣷⣶⣾⣿⣮⣿⣄⠀⠉⠐⠻⢦⣀
⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠴⢾⡿⣿⡟⣿⣿⣿⣿⣿⣦⢻⣼⣿⣿⣿⣿⣿⣿⡟⢧⠀⠠⠀⠀⠉⠳⢤⣀
⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠗⣿⣇⣿⣿⣧⣏⣿⣿⣦⣳⣿⣿⣿⣿⠿⣿⣿⣾⡧
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⡉⠉⠀⢻⣿⡯⠉⠉⠉⠉⠙⢿⣿⣧⠀⠀⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡶⠀⠀⠀⣀⣠⣤⠶⠶⠚⠛⠛⠛⠛⢛⣓⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⣠⢞⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⣠⡤⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣛⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢶⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣋⠁⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⡴⣫⡴⠒⠛⠛⠓⠶⣄⠈⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣳⡶⠆⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠠⣌⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠰⣞⠉⠀⠀⠀⢠⠞⠉⠁⠀⠀⢸⡀⠀⣠⣤⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⣦⠀⢠⡴⠶⢦⡀⠀⠨⡅⠉
⠀⠀⠀⠀⠀⡞⣩⣷⠀⠀⠀⠀⠀⢶⡞⠂⠀⠀⠀⠟⠀⠀⣠⡶⠚⠛⠛⠲⣥⣽⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣀⣀⠈⠳⡜⠦⣤⠞⠉⠙⢳⣠⣤⡀
⠀⠀⠀⠀⠀⠟⢹⠃⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⣹⡆⠀⠀⠀⠀⢀⡴⠃⠀⠰⠊⠁⠀⣽⠛⠓⢿⣠⠏⠉⠉⠡⠋⠀⢀⡽⠀⡶
⠀⠀⠀⠀⠀⠀⣿⠀⣠⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⣷⡀⠀⠀⠀⠐⢻⡷⠶⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⣸⠗⠲⣌⠉⠀⠀⢀⡤⠞⠋⠉⠀⠘⠡
⠀⠀⠀⠀⠀⠀⠸⣶⢻⡀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠳⢦⣤⣤⠴⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⢁⡀⠀⣸⡇⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⣤⡤⠴⠶⠒⠲⠦⠾⡄⠀⣠⣴⠂⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢎⡁⠀⣰⢻⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⣠⡶⠒⢲⡦⡄⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢾⠉⠉⠳⣄⠉⠻⣥⠞⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠁⠉⠉⠉⣀⣴⠛⠦⣄⡀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠚⠛⠉⠁⠀⠀⣈⣷⡄⠀⠈⠓⠀⠈⢳⡄⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣶⢶⡶⠖⠛⠉⠀⠀⠀⠈⠙⠳⠦⣄⣀⣀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠛⠉⢰⠟⣆⠀⠀⠀⠀⣸⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠱⣏⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⡽⠿⠶⠶⠤⢤⣄⣼⠓⠛⠳⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⣀⣾⡋⢳⡄⣠⣿⣿⣦⣄⡀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠸⡅⠈⠳⠜⠟⠁⢈⡹⠋⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⡾⠓⠒⠀⢀⣠⠞⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠾⠃
⠀⠀⠀⠀⢀⡼⠛⠓⠒⠚⠋⠁⠀⠀⠀⠀⣨⠟⣩⡟⠛⠛⠋⠉⣩⠞⠋
⠀⠀⠀⣀⣞⠁⠀⠀⠀⠀⠀⣀⠀⢀⣠⠞⣡⠞⠁⠀⠀⢀⡴⠛⠁
⣰⠚⠉⣩⣿⠳⣦⣄⣀⠀⠀⠈⠉⣹⠛⠛⠛⢒⣂⣤⢾⠯⣤⡀
⣿⣀⣀⣏⣈⣛⣉⣀⣭⡽⠷⢶⡾⣷⣶⣚⣛⡙⠿⠖⣹⣃⣠⡿
⠻⠤⠤⠬⠥⠤⠴⠶⠖⠒⠛⠉⠉⠓⠲⠭⢭⣍⣉⣉⣩⣭⠽⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡀⣶⣄⣴⣦⣄⣦⡀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣾⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣭⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣾⣿⣿⠏⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⡤⠖⠛⠋⠙⠳⣦⣄⠀⠀⢻⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠇⢠⣶⣿⠟⠋⠉⠉⠉⠙⠋⠁⠀⢀⣀⣀⡀⠀⠈⣿⣷⠀⠈⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡏⢰⣿⡿⠋⢀⣠⡶⠞⠛⠶⣄⣠⠞⠉⠁⠈⠙⢷⡀⠘⠛⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠈⠋⠀⣰⡟⠁⠀⣠⣄⠀⠘⣯⠀⠀⢴⣦⠀⠈⣷⠀⠀⠀⠀⠀⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠙⠋⠀⠀⣿⣄⠀⠀⠁⠀⠀⣿⠀⠀⠀⠀⠀⢻⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣠⡾⠋⠙⣷⣦⣤⣤⡾⠋⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠉⠛⠷⣿⣿⢿⠁⠀⠀⠈⢿⡿⣿⣒⠒⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡩⠟⠁⣸⠀⠀⠀⠀⠘⣿⡤⣌⠁⠀⠀⠀⠀⠠⠌⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢹⡆⠀⠀⠀⠀⣿⡇⢸⡆⠀⠀⠀⠐⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⣷⣄⣀⣀⣴⡿⢷⠾⠇⠀⠀⠀⠀⢀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠐⠐⠀⠀⠤⠀⠀⠄⠈⠙⣟⢻⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣧⠀⠀⠀⠂⠐⠀⢀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⢄⠀⠀⠀⠀⠀⠀⢀⠀⢻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⢷⡀⠀⠀⠂⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠤⣤⣤⣤⣤⣄⣀⣀⣈⣃⣸⣧⣶⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉


⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣾⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣁⠀⡙⣻⡷⢒⡶⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠈⠉⠀⠁⠁⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠻⣷⣤⣀⣤⣄⣀⣤⣤⣶⣤⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣿⣦⣉⣻⣿⣿⣿⣿⣿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⢻⡇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⠇⠸⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠦⣀⠲⣮⣿⣿⠀⠀⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣄⠀⠀⠀⠀⣠⣴⠷⢬⣙⣿⣿⣿⣦⠠⣇⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢷⣄⠀⣴⣿⣧⡀⠀⠙⠋⡟⠿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣻⣷⣦⣤⣈⡑⠪⢽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⣿⢻⡟⢻⡟⢻⣿⣿⣿⣷⣦⣝⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣸⣇⣾⠁⠘⠇⣠⠂⠘⢉⣿⣭⡻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢠⡟⣽⠇⠠⠇⠀⠉⠀⢂⠸⠀⠉⢳⣌⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡟⢰⠏⠀⣠⣤⣴⣶⣦⣤⣇⡀⠈⡈⠙⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⢀⠞⢁⡟⠀⣴⡿⣿⣿⣿⡿⢿⣿⣿⣦⢡⠀⢹⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⣠⠌⠀⣤⠀⣼⣿⡅⢸⣿⣿⠀⠀⣿⣿⣿⣯⢳⡘⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢃⡴⠊⠀⠀⠐⠁⠀⣿⣿⣧⠀⢻⣿⡀⢠⣿⣿⣿⣿⡇⢱⣼⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⡞⠁⠀⠀⠀⠇⠀⢠⣿⣿⣿⡆⠈⢿⡇⢸⣿⡘⣿⣿⣿⡌⠘⣿⣿⣿⡙⣿⡙⠻⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠘⡃⠀⠀⠀⡼⠀⠀⣼⣿⣿⣿⣿⠀⢸⡇⣸⡿⣿⢀⢿⣿⣷⠀⠐⢻⣿⣷⣜⣿⣄⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡗⠀⢀⡼⠃⠀⣼⣿⣿⣿⣿⡿⠷⢾⣷⣿⡇⣧⠸⢸⡟⣿⡄⠀⠈⣿⣿⢿⠿⣿⣆⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠇⠀⠎⠀⢠⡞⣱⣿⣿⣿⣿⠇⠀⣸⣷⣿⡇⣿⠀⠚⣇⢿⣷⡑⠀⣿⡇⠈⢇⡈⢿⣷⡀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠨⠀⠀⢼⣧⣿⣿⣿⣿⣿⠀⠀⣹⣷⣿⡇⢿⡰⠀⣿⢸⡏⣿⣄⠹⣷⡀⠀⠹⡌⢿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡿⠘⢾⡇⠀⣿⣺⡇⡀⢹⣦⣿⣯⡁⠠⡘⡇⢹⣿⠏⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠆⠀⠀⢸⣠⡿⢳⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⠃⡀⢸⡇⢀⣿⠸⣇⠱⡀⢿⠀⠙⢿⣦⡘⠈⢻⣿⡇⠀⢻⣇
⠀⠀⠀⠀⠀⢠⣼⡀⠀⠀⠀⠀⠀⠀⢘⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⡿⠀⠠⢸⡇⢸⣿⠀⢻⡄⠁⠈⡄⠀⠀⠛⣷⡀⠈⢿⣷⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⢀⣴⠾⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣧⠀⢀⡿⠀⢸⡏⢠⠈⣿⠀⠀⢡⠀⠀⠀⢸⣷⡄⢸⣿⢃⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⣶⣿⣅⣰⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⣦⣸⡏⢀⠚⡇⠀⢸⡇⠨⡄⣿⡆⠀⠈⣄⣀⡀⠀⣻⠇⢀⣷⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣶⣿⣿⢸⣿⣿⠃⣿⠙⣧⡌⠀⠀⠀⢠⣷⣤⣴⣿⣿⣄⠀⢿⡿⠿⠟⠉⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠹⢿⣿⣿⠿⣏⢸⣧⠀⢻⣷⣤⣤⣤⣼⡿⠟⠛⠿⠿⣿⢶⠾⠃⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢻⡿⠁⢀⣨⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣈⣤⣉⣧⣤⣌⣠⣽⣌⣠⣿⣋⣶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠋⠉⠉⠉⠉⠉⠛⠛⠒⠲⠶⠤⠤⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⣠⠤⠶⠒⠒⠒⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀⠳⢤⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⡴⠋⠓⠒⠋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣯⠲⣄⡀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠀⡜⠀⠀⠀⠰⠛⣉⡉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠁⠀⠉⢳⡒⣶⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⡔⠉⢀⣀⠑⡄⠀⠀⡰⠈⢀⣀⠉⢢⠀⠀⠀⠀⣧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡆⠀⠀⠀⠀⣇⠀⢿⣧⣥⠇⠀⠀⢇⠀⣿⣧⡆⢸⠀⠀⠀⠀⡿⡸
⠀⠀⠀⢀⣠⠔⠒⡒⠒⠲⢤⣀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠉⠓⠖⠛⠉⡠⠴⠢⣌⠓⠤⠥⠒⠃⠀⠀⠀⢰⢣⠇
⠀⢠⠞⠉⠉⣉⠟⠣⣤⡒⠉⠉⠑⢄⠀⢠⠖⠒⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠻⡉⠀⠀⢀⣿⡯⠤⢄⡀
⢰⠗⠚⠉⠉⠀⡠⠊⠀⡹⢲⡉⠐⠺⣇⢻⡀⠈⠈⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠘⡡⠀⠀⠀⡇
⡏⠀⠀⠀⢀⠜⠁⠀⢀⠀⠀⠹⡄⠀⢸⡄⠉⠋⠙⠢⠔⠣⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠚⠁⠀⣠⠶⣄⠀⣠⠖⠚⠁
⣇⠀⠀⢀⠎⠀⠀⠀⠸⠀⠀⠀⢱⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⣀⡀⠀⠀⠀⠀⢴⣒⡤⠔⠊⠁⠀⠈⠉⠁
⠸⡄⠀⡎⠀⠀⠀⠀⡄⠀⠀⠀⠈⣅⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⡏⠉⠁
⠀⠙⢶⡀⠀⠀⠀⠀⡇⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢢⢶⠊⠀⠙⡶⠶⠒⠢⡀
⠀⠀⠀⠉⠓⠲⠤⠼⠤⠔⡾⠋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠒⣬⠈⠦⠄⠔⠁⠅⡌⢆⠘⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡑⣤⡀⠤⡄⠀⠀⠀⠀⡜⢡⠃⢠⠃⠀⠀⠀⠀⠀⠈⢣⠀⣑⠆⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⠵⣤⠂⠳⠀⠒⠉⢉⠤⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠸⢪⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡐⢘⢢⠀⡆⠐⠊⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠧⢂⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⢰⠉⠉⠀⠉⠉⠉⠉⢡⠈⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡀⠀⣿⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠬⡇⠀⠀⠉⠹⡉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠠⡇⠀⠀⠀⠀⡵⠚⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠼⠦⠤⠇⠀⠀⠀⠀⠓⠒⠻⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠃⠤⠤⠠⢄⡞⠀⠀⠀⢠⠛⠚⠓⠒⠚⢳⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠛⠉⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⣠⣴⣶⣶⣶⣄⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣶⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⠿⠿⠛⠟⣯⣿⣽⠻⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠀⠀⠀⠀⠀⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣼⣿⠿⠏
⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡴⠦⠟⠛⠛⠉⠀⠀⠀⠀⢠⣿⣷⣿⡿⠁
⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⢻⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡵⠟⠀⠀⠀⠀⠀⣀⡤⠀⣌⡜⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠈⡆⠈⣄⣀⣀⣤⣴⣶⡿⠋⠀⠀⡟⠀⠹⣿⠿⡄
⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣄⣀⠀⠀⠘⢆⢀⠍⠁⠀⣿⠏⠀⠀⠀⡼⠁⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣦⣌⠉⠂⠤⠀⡿⠀⠀⠀⡜⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⣀⠴⢊⠟
⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣶⣤⣀⣟⠀⠀⠞⠀⠀⠀⡠⠐⠈⠀⠀⢙⣦⠊⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⡜⣿⣿⣿⣿⣿⣿⠿⢻⢿⠀⠀⠀⠀⡠⠊⠀⠀⢀⣤⣾⡿⠁⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⡀⠀⢸⢸⣿⣿⣿⠟⠁⠀⠈⡄⠀⠠⠐⠈⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡌⣿⣿⡏⠀⠀⠀⢀⣄⠀⠀⢀⣠⣤⣤⣄⣿⣿⣿⡿⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⡇⠀⠀⠀⣈⣁⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣇⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⡇⡼⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⢷⠀⠀⢀⣠⡮⠼⠟⠒⠚⠛⠛⠛⠓⠒⠶⠶⣭⣙⡇⠀⠀⢀⠎⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣚⡶⠚⠉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠉⠛⠦⣤⢞⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠀⠀⠸⠀⠘⠀⢠⠔⠒⢦⡀⠀⠀⠁⠀⠁⠀⢀⣠⡄⠈⠳⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣔⡹⠋⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡼⠀⠀⠀⠀⠀⠀⠐⠋⢀⡝⠠⠞⠀⣠⣟⡠⠤⢤
⠀⡴⠋⣆⠀⠀⢠⠋⠀⢰⣋⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠘⣦⡠⠊
⠀⠻⠤⢬⣷⣴⠃⠀⠀⠀⠉⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠀⠀⠀⠀⠀⠀⠀⣀⢤⡘⣇⠀⠀⢀⡠⠤⣄
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⡸⠀⠀⠀⠀⠀⠐⢊⡁⢀⡗⠸⡤⢔⣪⣤⣄⡽
⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢺⣿⡆⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⣻⡉⡀
⠀⠀⠀⢸⣽⠀⠐⡶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠊⠁⠀⠸⡿⠇⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣍⣉⡟
⡠⠴⠤⠤⡅⠀⠀⠘⣄⠀⠉⢻⣿⡗⡲⠖⠀⠀⠀⠈⠉⠓⠒⡒⠒⣋⡡⠖⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⠀⠀⢈⡇⠤⡄
⠳⠤⠔⠂⣻⠀⠀⢀⡈⠳⠤⠴⠞⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣀⣤⠄⠀⠀⠉⠀⠀⠀⠈⠳⣤⠇
⠀⠀⠀⢮⣸⡄⠀⠀⠉⠓⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠉⣇⠀⡴⠂⠀⠀⠀⠀⠀⠀⡤⠚⣦⠀⣀⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣸⠄⠀⢀⠀⢤⣄⡀⠀⠈⢳⡀
⠀⠀⠀⠀⢀⠻⣆⠓⠶⠀⠀⢀⠔⢦⠀⢸⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠁⠀⡀⢈⢇⡞⠀⢹⡄⠀⠀⢷
⠀⠀⠀⠀⠘⢤⡽⣆⠀⠀⠀⠈⢧⡨⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡸⠆⠀⠀⠀⠀⠀⠀⠀⠉⢁⡞⠳⡄⠀⠻⢤⣀⠸⡇
⠀⠀⠀⠀⠀⢰⡀⠿⢧⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⣠⠞⣇⠴⠃⠀⠀⠀⡝⠀⠉⠓⣄
⠀⠀⠀⠀⠀⠘⣇⣠⠜⡹⢦⡀⠀⠀⠀⣸⠀⢿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠦⠞⠀⠀⣠⣞⢱⣄⠸⡄⠀⠀⠀⠀⡇⡠⣄⢰⡘⡆
⠀⠀⠀⠀⠠⣎⠀⢀⡎⠀⠀⢹⠳⢤⣀⠘⠛⠉⠀⠀⠀⠀⢷⣄⠇⠀⠀⠀⠀⠀⣀⡤⡔⠋⠁⠘⣇⢈⠇⢧⠀⠀⠀⠘⣷⠁⠘⣦⠛⡇
⠀⠀⠀⠀⠀⢉⠛⢫⠀⠀⠀⢸⡄⠀⢨⠟⡟⠲⠶⡶⢦⠤⡤⠴⠶⡖⡒⠚⠛⡏⣍⠃⠙⢦⡀⠀⠈⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⣼⠀⣇⣀⠀⠀⠈⡇⢰⠁⢸⠀⠀⡼⠐⠁⠀⠄⡆⠀⠉⠀⠀⠀⣧⣈⡱⠀⠀⠙⠲⣄⣀⠀⠈⠳⡆
⠀⠀⠀⠀⠀⡆⡀⠹⡎⠣⠀⠀⢻⠈⠉⠉⢀⡜⠁⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⠀⠀⠘⡇
⠀⠀⠀⢀⠘⣇⣙⢾⣙⡶⠀⠀⠘⡧⠀⠠⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣿
⠀⠀⠀⠈⠁⠀⠉⠉⠉⠀⠀⠀⠀⠛⣷⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣩⠵⠚⠲⠒⠦⠟⢠⠽⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠁⠈⠠⠤⠀⠤⠂⠤⣄⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⣾⢋⠴⢶⣄⡤⠚⠲⠤⠴⠋⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠥⠒⠒⠦⣤⠴⠒⠢⣆⣀⣠⣸⢷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠳⡏
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠶⣤⡀⠀⣀⣤⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠈⠙⢾⣏⠀⠀⠀⠙⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣀⣀⣀⣙⣷⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠛⠉⠉⠉⠉⠛⠛⠶⣤⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⢀⡴⠖⠀⠀⠴⣦⡀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⢠⠖⠛⠲⣄⡴⠖⠮⡝⠀⠀⠀⠀⠈⢻⣆
⠀⣠⣄⡀⠀⡔⢉⡇⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢸⣄⠙⣣⣿⡀⠸⢇⡿⠀⢀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣶⠒⣦
⠀⠳⢤⣉⠓⡇⠺⠢⣤⡤⠤⠤⠤⣼⡇⠀⠀⠀⠀⢀⣉⣉⣡⡟⠉⠛⠋⠁⢀⣾⡄⠀⠀⠀⠸⣷⠀⢀⡀⠀⠀⠀⢀⣘⡆⣸
⣞⣉⡩⣯⠀⠣⠀⠀⡤⠤⠶⠒⠒⢺⡇⠀⠀⠀⢸⡏⠉⠉⠉⠀⢤⡀⠀⣠⡞⢸⡇⠀⠀⠀⠀⣿⠭⠭⣭⣍⣙⠛⠋⠉⢰⠷⠤⠤⣄
⠀⢰⣊⡭⠖⠒⠒⠊⠁⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠙⠛⠶⠶⠶⠟⣠⡴⠋⠀⡴⡇⠀⠀⠀⢸⡟⠀⠀⠀⠀⠉⣷⠀⠀⣸⠀⢹⣦⣤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⣦⡴⠞⠁⡇⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠈⠳⠦⢤⡀⡟⢦⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡼⠃⣴⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⡄⣠⠀⢀⠀⢀⠀⠀⣰⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠀⡟⠳⠾⡇⢸⡟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣧⠀⠀⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠒⠛⠂⢹⡄⢸⡇⠈⠉⠛⠛⠳⠶⢤⣄⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣺⣿⣥⣤⣤⣶⣶⣶⣶⣖⣋⣀⣈⣛⣛⣲⣶⣶⣶⣶⣶⣾⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣸⣇⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⢻⣶⣄⣰⣿⣿⣆⣠⣾⡇⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⢰⡟⠀⠀⠀⢀⣴⠟⠙⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⣼⠃⠀⠀⠀⣼⡟⠀⢀⠁⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⣛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⢰⠏⠀⠀⠀⢰⣿⠃⠀⡜⠀⠀⠀⠀⠀⠀⣰⣾⢳⠀⢠⣿⠏⡕⠀⣴⡄⠀⠀⢀⣄
⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢠⠞⠀⠀⠀⠀⠀⠀⠀⣿⣧⠋⠀⢸⣿⡞⠀⣸⣿⠀⢀⡴⠋⣿⣆⣀
⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⢠⣴⣶⣤⣶⠀⠀⠹⣿⡴⠞⠉⢻⣷⡟⠉⠻⠶⢛⣡⠶⣿⡏
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡇⠀⢰⣿⡟⠉⣿⣿⠀⠀⣰⢿⣿⡀⣠⠟⣿⣧⠀⢀⡴⠛⠁⢸⣿⠁
⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⣿⡇⠀⣿⣿⢀⣴⣿⣿⠀⣸⠇⢘⣿⣇⡏⠀⣸⣿⢠⠟⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠻⣿⣦⣤⣤⣤⣶⡿⠟⠁⠀⠀⢿⣧⢀⡿⢿⠟⠁⢻⣿⣠⣿⡀⣸⡿⠙⣧⣠⣿⢻⡏⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⣈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠉⠁⠈⠛⠋⠁⠀⠈⠉⠀⢸⡇⠀⢀⣼⡿⠁⠀⣾⣿⣷⡄⢀⣀
⠀⠀⠀⠀⣀⣀⡛⠻⠶⠄⠀⢠⣾⠓⠀⠀⣠⢾⡆⠀⢠⣾⠋⠂⠀⣴⡟⠠⠀⣸⡇⠀⢸⡇⠀⠀⠙⠛⠛⠉⠀⠀⠀⠈⢿⣿⣷⣿⣿
⠀⠀⠀⠻⠿⠿⠿⠿⠖⠀⠀⠘⣿⡄⠀⢀⡃⢸⣷⠀⠈⢿⣆⠀⠀⢻⣧⠀⠀⣿⠃⠀⢸⡇⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠈⠟⠛⠛⠋
⠀⠀⣀⣠⣤⣤⡄⠀⠀⠀⠀⡀⠈⢿⡄⢸⠁⠈⣿⠀⠀⠈⢻⡆⠀⠀⠹⣧⠀⢻⣄⡀⢿⡇⠀⠘⠻⣿⠟⠃⠀⢠⣤⣤⣀
⠘⣿⣿⣿⠿⣿⣿⣶⣶⣄⠀⠣⣠⠾⠃⠀⠀⠀⣿⠀⠡⢄⡼⠃⠀⢄⡤⠟⠀⠀⠠⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆
⠀⢹⣿⣿⣦⣀⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⡤⠀⠀⠀⠈⣿⣿⣿⣶⣾⣿⣦
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣶⡆⣤⣴⠀⡴⣾⠃⠀⠀⢠⣶⡆⠀⠀⠀⣟⢤⠀⡤⣸⠃⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠙⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠚⠀⠁⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⢄⠀⠀⣴⣦⢀⣴⣶⡄⢀⣴⣿⣷⠀⠀⠀⢀⣴⣦⡀⠀⠀⢀⣶⡄⣠⣶⣦⠀⠀⣀⣠⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠈⠀⠀⣿⣿⠏⠈⣿⣿⡾⠁⢸⣿⠀⠀⢀⡞⠙⣿⡇⠀⠀⢸⣿⡟⠁⢹⣿⡇⠈⠉⢸⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⢸⣿⡟⠀⠀⣿⣿⠁⠀⢸⣿⠀⠀⣸⠁⠀⣿⣷⠀⠀⣿⣿⠁⠀⣸⣿⠁⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⢸⣿⠇⠀⠀⣿⡟⠀⠀⢸⣿⠀⠀⡟⠉⠀⢹⣿⠀⠀⣿⡇⠀⣰⡿⠃⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢹⣿⠀⠈⣿⠀⠀⠀⣿⠇⠀⠀⢸⡟⠀⢠⠇⠀⠀⢸⣿⠀⠀⣿⡟⢻⣏⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠾⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠈⠀⠀⠀⠸⣿⠀⠀⠈⠁⠀⠻⣷⣄⠀⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⣠⣤⢄⠀⣠⡶⡦⠀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⢀⣀⣀⣀⡙⠛⠷⠆⠀⠀⢠⣾⠟⢻⣿⠃⠀⣿⡷⠃⣘⣿⡖⢁⣠⣿⡁⢀⡴⠋⣿⣤⡤⠀⠐⠛⢋⣉⣤⣤⣤⣀
⠀⠀⠀⠀⠛⠿⠿⠿⠛⠛⠂⠀⠀⠀⣿⣇⡴⢿⣿⢀⡼⢹⣿⡞⠉⣹⣿⡏⠀⠙⢛⡩⠖⢻⣿⠃⠀⠀⣀⣀⡉⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠟⠋⠀⠀⠈⠉⠀⠈⠙⠉⣰⠋⢹⣿⣼⠃⢸⣿⢀⡴⠋⠀⠀⣾⡟⠀⠀⠀⠈⠙⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣼⠟⢿⣤⡾⢏⡏⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⢧⣤⣴⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣂⣈⣁⠀⠀⠀⠀⢸⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡠⠂⠉⠉⠁⠀⢀⠠⢀⡀⠰⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣀⠀⠀⠀⠀⠃⠀⠀⠈⢆⠐⠺⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠡⠀⠨⡆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠣⣐⠁⠀⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⢘⠀⠀⠀⠀⠀⠀⠀⡇⠉⢀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣑⡂⠤⢀⣱⡆⠀⠀⠀⠝⠁⠂⠊⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⢢⠄⢀⠤⢃⠀⢃
⠀⠀⠀⠀⠀⠐⠀⠀⢆⢀⣅⠈⠉⠙⠒⠠⠅⢀⠀⠔⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠰⢇⣠⠃⠀⠈⠄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠁⠚⠒⠚⠒⠒⣿⣇⠀⠀⠀⠀⣠⣾⣿⡗⠀⠀⠀⠀⠀⠀⡄⠈⣀⠄⠒⢤⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡒⢣⠀⠀⠀⠀⠀⠘⣿⣿⡿⠷⠾⠟⠉⠀⠀⠁⠠⠀⠀⠀⠀⢀⠇⠋⠠⠖⠂⡸⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⠲⡥⡀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⣀⣀⠎⡰⢄⣀⡀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡠⠳⡈⠢⡀⠀⠀⠀⢦⣀⢀⠀⠀⠀⠀⠘⠣⠍⠀⢈⠄⠋⡰⡁⠔⠁⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡙⠂⠈⠲⠈⠋⠉⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠀⠚⠎⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠸⠦⠚⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⡄⢆⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⢀⣧⡧⠼⠉⠚⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠇⠀⠀⠀⠘⠛⠇⠀⢠⢃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣼⣷⠀⠀⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⡀⠀⢴⠈⡄⠀⠀⠀⡠⠀⢸⣘⣿⡏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠋⠀⠀⠀⠀⠀⢂⠘⡄⠠⠊⠀⠀⠀⠋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠋⠡⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢂⡀⠀⠀⠀⠀⣀⠔⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⠻⢿⣟⣻⢿⣿⠿⠭⢭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⡅⠀⠀⠈⠉⠉⠭⠟⠛⠛⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠐⠒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠆⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡰⠁⢀⠃
⠀⠀⠀⢀⣀⣀⣠⠋⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠒⠤⡀⡇
⠀⠀⠻⣍⠀⠀⢹⢦⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠱⠃
⠀⠀⠀⠀⠉⠀⠉⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠤⠀⠀⠒⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠈⠐⠠⠤⠀⠀⠤⠄⠒⠈⠁⠀⠀⠀⠀⠀⢤⣶⣶⣄⠀⠀⠀⠀⡼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠘⢿⣿⣿⠆⠀⢀⡜⠁⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⠊⠀⡠⠊⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⡂⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀⢮⣀⣀⣤⠴⠋⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠀⠀⠀⠀⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠛⠷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⠀⠦⠀⠱⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠈⠀⠀⠀⢰⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⡠⠀⠀⠀⠀⠀⠈⠐⠠⣀⡀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣷⡀⠀⠀⠀⠀⠀⠠⢄⣉⣙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⡀⢻⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⢻⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣟⢿⣿⣿⣿⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠛⠛⠉⢸⣿⣷⣝⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢳⡄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇

⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠒⠋⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢰⠇⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⢳⣸⣰⢃⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢷⣿⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣞⡷⣾⣽⢷⡾⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⣼⢷⠷⡿⢾⡧⢿⠋⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⣶⣋⣟⢺⡗⢺⡗⠺⣟⠁⣿⡀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢲⣧⣼⣏⢩⡟⢻⡷⠶⣿⠛⢉⣇⠀⢀⡼⠋⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⡄⠀⠀⠀⣼⠓⣾⢧⣼⣌⣽⣟⣋⣿⡛⢩⣟⣋⣽⣴⠏⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⣄⠀⢀⣞⢛⡿⠶⣿⠻⣼⣍⣉⣿⡉⢉⣿⡉⣠⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⢷⣸⣍⣹⠷⠶⣿⠀⠹⣎⣉⣿⡉⢉⣿⡉⢉⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⣈⣿⠓⠶⣿⠀⠀⢻⣉⣸⣙⠉⣻⡉⢉⣸⢃⡟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⣄⢻⡄⢀⡷⣤⣿⡓⢚⣿⠀⠀⢸⣏⣽⡏⠉⢹⣏⣉⣹⣿⣿⢫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⢿⣷⢠⡷⠶⣯⣉⣹⠇⠀⠀⠀⣧⣼⣏⡓⢛⣿⣉⣠⣿⠇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣴⡗⠶⢧⣩⡟⠀⠀⠀⢸⣧⣼⣧⣉⣉⣿⣉⣠⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢻⣝⠒⣿⣿⠁⠀⠀⠀⢸⡧⠾⣧⣉⣩⣿⣌⣽⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣿⠙⣿⡏⠀⠀⠀⠀⣾⠶⠶⣿⣌⣠⣾⣼⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠘⣯⢹⡇⠀⠀⠀⠀⣿⠶⠾⣤⣀⣠⡽⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣿⠳⠶⣾⡶⠃⠀⠀⠀⠀⢠⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸⡟⣿⠏⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠘⣇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠘⢧⡀⠀⠀⠈⡧⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣤⣙⣷⣤⣼⡷⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣤⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⢀⣤⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠞⠀⠀⣠⡶⠶⣦⠀⠀⣾⣏⡽⠀⢠⣿⣁⡟⠀⣼⡿⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠹⢿⣶⣄⠀⢸⡿⠀⣼⣿⠀⠀⡿⣿⡄⣀⠼⢿⣿⣤⠴⣿⡇⢀⡴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⠈⠓⠋⢸⡏⢀⡜⢀⠼⣿⠁⢠⠞⢹⣿⠀⠙⠟⠋⢠⣿⠃⠀⡦
⠀⠀⠀⠀⠀⠀⠀⢯⣀⣠⠟⢀⣀⠀⠀⠉⠉⠀⠸⠴⠟⠀⠘⠷⠟⠋⠀⡤⠒⢛⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⣤⣤⡤⠤⠴⠶⠚⠛⢛⡷⠀⠀⠀⠷⠶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣴⢶⡄⠀⣶⠀⢠⣤⡀⠀⣴⠀⣠⣶⣦⠀⣴⡶⠆⠀⠀⣤⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠁⠀⣿⡇⢸⣿⣷⡀⣿⢠⣿⠃⠉⠀⣿⠀⠀⠀⠀⡇⠛⣫⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⣿⡇⢸⡇⢿⣧⡟⠸⣿⠀⠀⡀⣿⠛⠃⠀⠀⠳⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠶⠾⠋⠀⠿⠁⠸⠇⠈⠻⠃⠀⠹⠷⠞⠁⠻⠷⠆⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣤⢶⠀⢀⣤⣄⠀⠀⢠⣶⡄⣠⡀⠀⢀⡀⠀⢀⣶⠄⠀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠙⠺⢀⣾⢃⡿⠀⠀⢀⡍⠀⣧⣻⢀⣈⡙⠛⢻⣿⠛⢻⣿⡏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢞⡁⠀⣠⣿⡏⠀⠀⡟⢩⣿⡇⠀⢸⣿⠀⢸⣿⣣⠏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⣏⠁⣿⡇⢀⡼⠁⣾⡟⠀⢀⣾⣿⠀⢸⣿⡏⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⣠⡏⠀⠈⠛⠛⠁⠀⢿⣇⣠⠟⠈⠻⠷⠋⠙⠁⢺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞


⣏⣈⣯⣭⣯⣭⣿⣽⣽⣽⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⠀⠀⠀⠠⢤⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡇⠀⠀⠇⠸⠀⠀⢘⢸⠇⠀⠀⢰⠁⡹⠀⠀⡌⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⣇⠀⠀⠈⣀⣧⠤⠼⠾⠦⠤⠤⣬⣴⣁⠀⡐⡼⠀⠀⢀⠔⢙⠇⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠤⣄⠀⠀⠙⣾⠆⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠧⣄⡠⢊⠔⠁⠀⠀⡠⠂⠉⢹⠘
⠀⠀⠀⠀⠀⡇⠈⠳⣄⠀⠈⠢⣌⠳⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⠀⠀⠈⠙⢦⡀⢀⠠⠊⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠘⠦⣀⠈⠣⣀⠀⡸⠃⠀⠀⠀⠀⠀⢀⠤⠖⠂⠀⠀⠀⢀⠤⠶⠦⢤⡈⠑⠀⠀⠀⠀⠙⢧⣠⠞⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢬⠏⠀⠀⠀⠀⠀⠀⠀⠁⢀⡤⠤⣄⠀⡴⠁⢀⣀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠈⢧⡠⣐⢈⡡⠃
⠀⠀⠀⠀⠀⠀⠀⡄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⡎⡇⡇⠀⢿⡿⠃⠀⠀⡼⠀⠀⠀⠀⠀⠀⠈⣯⠉⠀⠀⠀⢀⠠⠤⠐⢦
⠀⠀⣀⠤⣀⠀⠀⠘⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣀⡠⠃⠙⢦⣀⡀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠭⠤⠤⠤⠔⠊
⠇⢸⣀⠀⠀⠑⠦⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠤⠄⠀⠀⠐⠪⠭⠭⠓⠂⠀⠀⢀⣀⣀⡤⠂⠀⠀⣇
⠀⠀⠈⠉⠉⠉⠙⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡤⠤⡤⡴⢒⠖⢞⠉⡏⠹⣤⠃⠀⠀⠀⣯⣍⣉⡉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠙⣽⠙⡏⡟⠙⡏⡝⢹⠁⡏⢹⢀⠏⢣⣸⠀⢹⣼⠀⠘⣶⠁⠀⠁⠀⠀⠀⢠⡇⠀⠀⠈
⠀⠀⠀⠀⠀⢠⠊⠉⠽⡄⠀⠀⠀⠈⠀⠹⠁⠀⢳⠃⠀⠿⠀⠀⠟⠀⠈⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢭⣒⠤⠄⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠁⠁⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠈⠙⠲⣄⡀⠀⠀⣱
⠀⠀⠀⢀⡠⠤⠄⠒⢈⡠⠟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⣍⡙⠒⢤⠀⠀⠈⠉⠉
⠀⠀⣔⠀⠀⠀⡠⠚⠁⠀⡠⠄⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠉⠓⠚⠁
⠀⠙⠜⠲⠴⠊⠀⠀⠀⠀⠧⠤⠊⠀⢙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠓⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡡⠋⠀⠙⢓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠳⡀⠀⠀⠳⣍⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⡼⠁⠀⡔⠁⡎⠀⠀⡌⢹⠋⠛⣒⠒⡖⠒⢺⠹⡅⠀⠀⢸⡄⢹⠀⠀⠀⠈⠲⣄⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠊⠀⠀⠀⠳⠊⠀⠀⠠⠁⡇⠀⠀⢻⡠⠃⠀⠘⡆⢣⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢀⠇⠀⠀⠀⠀⠀⠀⠀⣇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡸⢀⠆
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠉⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠛⠛⢲⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡀⠀⠀⠀⠀⣰⠖⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⠄⠀⠀⣼⠃⠀⠀⠀⠀⠈⠙⠶⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⢣⠃⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠎⠀⢀⡼⠁⢀⣀⣀⣀⡀⠀⠀⠀⠈⠓⢮⣿⣿⠢⣄⡀⢂⠀⠀⠆⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠿⠶⠞⠋⣴⠞⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⠚⠛⠶⣏⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠀⠈⣁⢴⣾⣟⡿⠷⣄⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⠘⢧⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⣿⣿⣿⣧⣴⡇⡡⠀⡔⠁⣿⣿⣾⣁⣹⢦⠀⠀⠀⠈⠁⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢦⡘⠿⠿⠿⢋⠔⠁⠀⠱⡄⠻⣿⣿⣿⠟⢸⡄⠀⠀⢹⡶⠞⠁
⠀⣀⠀⢠⠤⠀⠀⠀⠀⠀⢷⡀⠀⠀⠈⠙⠛⠒⠉⢡⡤⠀⠀⠀⠈⠳⣤⣤⣤⠖⠋⠀⠀⠀⣸⠇
⠀⢣⡑⣬⠄⢃⡴⠒⡆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠃⠈⣿⠁⢴⠉⢰⡎⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⢰⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠐⠥⠴⢄⠈⡀⢼⡁⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠈⠳⠤⠴⠋⠀⠀⠀⠀⢀⣀⣴⠞⠋
⠀⠀⠀⠀⠈⣹⠋⠈⠲⣄⡀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣦⢤⣤⡴⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⡐⡹⢀
⠀⠀⠀⠀⠀⠧⣤⡇⠀⠀⠉⠓⠲⠤⢤⣀⣀⡀⣠⠞⢳⡜⠋⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⣎⠁⢣⠔
⠀⠀⠀⠀⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠃⠹⣆⡴⠁⠉⠓⠦⣄⣀⣀⣀⣠⡤⣤⠒⢦⢇⠀⢸⠀⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠤⢴⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⠈⠁⠀⠀⠈⠀⢘⡏⠙⠒⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠓⠲⠦⠤⠤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⠐⠂⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠤⣤⣤⣤⣤⣽⣀⣀⣀⠀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⣷⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣷⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⠦⢤⣤⣤⡼⠆⠘⡷⠦⠤⣤⠤⠶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠊⠉⠁⠀⠀⠀⠀⣀⣀⡗⠀⢾⣀⠀⠀⠀⠀⢀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠐⠒⠲⠿⠿⠻⠏⠉⠙⠃⠀⠘⠫⢝⣛⣛⣛⡩⠽⠃

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣧
⠀⠀⠈⠉⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⣠⣀⣼⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⠀⠉⢁⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣷⣶⡆
⠀⣿⠛⣿⣿⣿⣿⡇⠀⠀⠀⢀⡾⠋⠀⠀⠀⡰⣇⠀⣴⠛⠋⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⣿⠛⣿
⠀⣿⠀⠹⣿⣿⣿⡇⠀⠀⠀⢹⣇⠀⠀⠐⠄⣠⢿⡾⠁⠀⠀⠀⠀⣿⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿⣿⡿⠀⢹⡆
⠀⠹⣆⠀⣾⣿⣿⣿⠀⠀⠀⠀⠹⡄⠀⠀⠀⣿⢀⡀⠀⠀⠀⠀⠀⣿⡆⢸⣿⣿⣿⣦⠀⠀⠀⠀⠘⢷⡔⠛⠛⢈⠁⣾⠁
⠀⠀⣿⡀⢙⣿⣿⣿⡄⠀⠀⠀⠀⠙⡿⠀⠀⠙⠀⠁⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠁⠐⠀⠀⠁⠁
⠀⠀⠙⠃⢺⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⡁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢏⡀⠀⠂⠠⡀⠠
⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⡆⠐⠈
⠀⠀⠀⠀⠀⣺⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡌
⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⢰⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⡾⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⢀⣾⠃⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⢀⣾⠏⠐⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠁⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣶⣶⡶⠶⢦⣅⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠚⠛⠚⠋⣢⣤⣬⣉⣉⠉⠉⠒⠻⢼⣃⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠉⢀⣯⣽⠟⠛⠛⠿⢿⣿⣿⣒⣀⣄⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣷⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⡿⣿⣰⡟⢁⠞⠉⠉⣹⠟⢿⢷⣶⣦⡄
⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⡟⣿⡿⠀⠀⠀⠠⠊⠀⠀⠀⠈⢿⣿⣿⡦⠀⢰
⠀⠀⠀⠀⠀⣿⣿⣥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⢟⡠⠔⣊⣉⣉⠉⠉⠉⠁⠐⠒⠦⢤⡀⠿⣩⡍⣷⣤⠀⣀⢀⡄⢤⣤⣔⠶⢞⣡⣾⡀⠀⠺
⠀⠀⠀⠀⠀⢿⣿⣿⡈⢻⣿⣿⣦⣤⣄⣀⣤⣤⣤⣤⣂⠴⠋⣴⡻⢍⠉⡉⢝⡟⣶⣄⠀⠀⠀⠀⠈⠑⢿⣧⠸⣿⡇⢽⣿⣿⡌⢿⣿⡆⡟⠀⠹⠃⡁
⠀⠀⠀⠀⠀⣤⡙⠻⣷⡀⢻⣿⡿⠉⢹⣿⣿⣏⢙⡿⠃⠀⣾⣵⣬⣤⠶⠾⠻⠒⠛⠚⠓⠀⠀⠀⠀⠀⠀⠹⡠⠟⠋⠀⠈⢙⠿⣤⡿⠟
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⡉⠃⠀⠀⠟⠿⢿⠎⠀⠀⠴⠛⠉⠁⢀⣀⣤⣤⣤⡤⣤⣤⣤⣤⣀⣀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⠞⠁⠐⠀⠐⠈⠄⣌⢴⡊⠠⣤⣤⣶⣟⣽⣿⣿⡿⢼⡵⠿⢿⡹⠿⠿⣿⣿⡿⠆⡀⠈⠓⠀⠀⠛⠿⠶⠂⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠜⢀⣄⠀⠀⠀⠀⠾⠁⣸⣷⡿⠛⠉⠁⠈⠉⠀⠀⠀⠀⠈⠀⠉⠀⠀⣬⠿⢿⣿⣯⣽⡃⠀⠀⠈⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠁⠰⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢰⣃⡃⠈⠿⣿⣇⢈⡆⠠⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⠐⠀⠤⠂⠀⡠⢻⣿⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣤⠼⠁⣠⣶⣾⣿⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠒⠊⠀⠼⣿⣟⠲⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣴⣾⣿⣿⣿⡿⢻⣧⡄⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣴⣭⣶⢾⣿⠿⣿⣶⡄⠘⣿⣿⣿⣿⣶⣶⣶⣿⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢸⣟⠑⢺⣿⣷⣶⣦⣀⣀⢀
⠀⠀⠀⠀⠀⣠⣛⡿⠋⠑⠂⠀⠀⠨⢐⣿⣿⠿⢣⣿⠿⢿⣿⣿⣿⣿⣿⣦⡀⠀⢙⣿⣿⣿⠿⠛⠁⠀⠀⢸⡄⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣴⡵⠋⠀⣀⠀⢠⠠⠶⠲⢦⣽⣿⣾⡦⣞⠆⠀⠈⠙⠛⠛⠛⢻⠛⠋⠙⠟⠉⠀⠀⠀⠀⠀⠀⢸⣧⠟⠛⠛⠿⣿⣛⣯⣽⡷⣏⢙⡿⣆
⠀⠀⠀⢠⠊⠀⢠⣾⣷⠞⠓⠒⠀⠀⠁⠀⠀⠀⠙⠟⢷⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⢕⠀⠀⠀⠀⠀⠀⠀⡜⠹⠀⠀⠀⠀⠈⠉⠉⠙⠻⣿⡎⡟⣿⡆
⠀⠀⠀⢰⢃⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠘⠧⠤⠀⠴⠚⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣧⣿⡇
⠀⠀⠀⠨⡎⠐⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡸⣄⠀⠀⠀⡠⠄⠀⡀⣀⣁⠒⠀⠀⠀⠀⣤⣽⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃
⠀⠀⠀⠀⢳⣸⣏⠁⢀⣀⣀⣀⣤⣀⣀⡀⢀⣠⣿⡉⠻⣿⣟⢆⠀⠀⠐⠿⠛⠛⠋⠙⠋⠀⠀⠀⣰⠳⣿⣿⡏⢹⣷⣦⣀⣀⣤⡤⣤⣄⡀⠀⣿⢋
⠀⠀⠀⠀⠀⣿⠛⢿⢽⣿⣧⡀⠻⣿⣿⠟⠛⢿⣿⣿⣄⣸⣿⡀⠛⣄⠀⠀⠀⠐⠂⠀⠀⠀⢀⡴⠁⠀⠈⠛⠿⢴⠿⠿⠻⣿⣿⣇⠘⣿⣿⣾⠁⡟
⠀⠀⠀⠀⠀⢁⠘⠂⠙⢿⣿⣷⣄⣽⠇⠀⠀⠨⠉⠋⠉⠁⢸⠁⠀⠀⠓⠢⠤⣀⣀⣠⠴⠞⠋⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠙⠛⠋⠉⠁⢶
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⠉⢁⠔⠀⠠⢤⡤⠆⠀⣲⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢠⠃⠀⠀⠀⠀⠈⠅⠐⢀⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡆⠀⠀⠒⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⣀⣀⣀⣠⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⡾⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣌⢲⣿⣿⢃⣾⢋⣦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢶⡘⡗⡏⢋⣿⣤⣯⣯⣌⣙⣿⣷⠾⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢦⣄⣇⢹⡾⣏⡴⠊⠁⠀⠀⠙⠿⣯⡴⠖⢀⡀⠀⠀⠀⠀⠀⣧⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⣾⠃⠀⠀⢠⠶⣤⢈⢿⣿⡾⠋⠙⠀⠀⠀⠠⠞⠃⠘⢿⣿⠶⣆⠀⠀⠀⠀⠀⢹⣴⣏⣴⠞⠃
⠀⠀⠀⠀⠲⢦⣄⠀⢻⣼⣧⡀⠀⠀⠛⣓⠺⣏⣾⠏⢰⣧⡌⠂⠀⠀⢠⠞⡉⠓⠘⣿⡉⠁⠀⠀⠀⠙⢲⣿⠛⣿⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣨⣽⣾⡇⣸⣧⠀⠀⠉⠉⢨⣾⡏⠀⠻⢿⠇⠀⠀⠀⢨⡸⠿⡠⠀⣿⡇⠀⠀⠀⠀⠀⢘⡿⠟⠁
⠀⠀⠀⠀⠀⠉⠙⠁⢸⡟⠛⢻⡿⣄⠀⠀⢿⣿⠀⠀⠢⠤⠞⠀⠛⠁⠀⠉⠊⠁⠀⣩⣿⡆⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠙⣌⢳⡄⠘⣧⢣⠀⠀⠀⢠⣶⡿⢿⣷⣦⠀⠀⣠⣿⡿⠀⢀⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣽⠷⣘⢦⠳⣄⡀⢾⣽⣵⣶⣾⠏⢀⣴⡿⠋⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⡄⠘⢦⣷⢦⣻⣶⠤⣍⡀⢀⣴⠟⠋⣠⠾⢿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠈⠁⠈⢻⡏⠛⠚⡿⠙⢷⣴⡾⠃⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⣀⠀⠀⠙⢦⣼⠁⠀⠀⠉⠁⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠈⠛⠀⠀⠀⠀⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⠤⣤⣤⣤⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡤⠀⠀⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠈⣱⣷⡦⠤⢴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣀⢀⣼⠏⢸⣿⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠿⠿⠋⠀⠸⡿⣷⣶⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡟⠳⢤⣤⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⢰⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠖⠊⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣧⠶⠞⠋⠉⣿⣟
⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠻⣦⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠄

⠀⠀⠀⠀⠀⠀⢀⡀⠒⠀⠐⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⡀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠉⠓⠂⠠⠀⡀
⠀⠀⠀⠀⠀⣀⠉⠀⠀⠐⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢈⠂⠒⠒⠒⠒⢀⠈⡆
⠀⠀⠀⠀⠀⠙⠇⠈⠇⠀⠠⠠⠒⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡰⠄⡔⢀⡀⠀⠀⡀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡌⠘⠀⠀⠀⡤⠀⢀⠃
⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠃⠰⠁⠦⠈⠈⠁⠚⢠⠴⠀⠇⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⣀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣠⡞⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠁⡄⠀⡀⠌⣀⠀⠉⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠄⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠊⠿⠁⠀⡠⠁⠀⠢⡀⠀⠀⠀⠀⠀⠈⠚⠉⠢⢌⣐⠒⠂⣠⠆⢀⡃⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⡄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠒⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⠤⠐⠒⠂⢄
⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠀⠀⠀⠈⠳⢤⠀⠀⠀⠀⠀⠀⠀⣀⡰⢤⠴⠒⠛⠉⠉⠉⠒⠲⢤⣀⠀⠀⠀⠀⠀⢖⠶⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠲⡀
⠀⠀⠀⠀⠀⢰⢁⡀⠀⡀⢀⡀⣠⣤⡄⠈⡇⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⢀⢀⡀⢀⣀⠀⢀⣀⠀⠩⡇⠀⠀⠀⠘⠥⣀⠀⠀⠤⠴⠒⢹⢶⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠧⠀⠀⠈⣉⣉⠀⠸⠀⡒⢣⠀⠀⠀⠀⠀⢸⠁⠀⠀⡜⢁⠤⠍⠉⠀⢉⣥⣀⠙⡖⠃⠀⠀⠀⠀⠀⡇⠀⢠⣦⠀⣤⡄⠈⣶⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠘⣯⡅⠀⠰⠖⠀⠀⠀⠁⠘⠀⠀⠀⠀⢠⠞⡲⡆⠀⡇⠀⢀⣤⠀⠀⢀⣠⠀⢠⠇⠀⠀⠀⠀⠀⠀⡇⠀⢺⣯⠀⣿⡁⠀⠸⠔⣚⢢
⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⢀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠸⣄⡁⠈⠛⠃⠀⠘⠋⠀⠠⡈⠛⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⢀⣈⠉⠀⠉⢁⡀⠀⠀⠈⡰
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠵⠂⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠈⠙⢄⠀⠀⠀⠀⠠⣄⣐⣋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠘⠣⢏⣞⣺⡹⠟⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⣄⣀⣀⣠⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠠⢄⡀
⠀⠀⠀⠀⠀⡠⠖⠈⠉⠉⠁⠀⠒⠒⠒⠂⣙⡠⠊⠁⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⠀⠈⠁⠂⡀⠀⠀⠀⠀⠀⢀⡤⠖⢻⠏⠉⠛⠲⢤⡀
⠀⠀⠀⢠⡏⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠅⠀⠀⠀⡇⠀⠀⡘⠋⠉⠉⠒⠀⠀⡀⢰⠀⠀⠀⠀⢠⡏⠀⢀⡏⠀⠀⢀⣀⣀⣹⣆⣀
⠀⠀⠀⠀⢉⠀⠐⠁⠀⠀⠉⠉⠉⠒⠒⠒⠂⢹⣄⡴⠃⠀⠀⣠⠤⣀⡎⢀⣀⣀⠀⠀⠠⠤⢸⠎⠀⠀⠀⠀⣿⠀⣀⣸⣴⠞⢫⣍⠉⣵⡚⢻⣿⣿⣷⡄
⠀⠀⠀⢀⠘⠄⡀⠀⠀⠀⢽⣷⡄⢀⠂⠹⢿⣦⡇⠀⠀⠀⠀⠇⠀⠉⠀⠀⠐⠋⠀⠐⡄⠁⢸⠀⠀⠀⢠⠖⣛⠻⣩⣤⠟⠀⢈⣿⠂⣻⡷⠘⣟⠛⠉
⠀⠀⠀⢠⡈⢇⡀⠀⠀⠀⣰⡿⠃⡈⠢⢰⣿⠟⡅⠀⠀⠀⠀⠈⠐⡇⠀⡀⠀⠀⠄⠀⡳⠀⠘⠀⠀⠀⠸⣄⠀⣀⠀⠀⠀⠀⠈⠋⠀⡙⠃⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⡉⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠠⠤⠤⠀⠀⡘⠀⠀⠀⠀⠈⠙⢧⡄⠀⠂⢀⠀⠠⠤⠄⠀⠄⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠁⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⢀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⠷⣤⣤⣦⣤⣶⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉

⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⢸⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⡶⢆⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠉⢟⣩⣶⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⢸⣸⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣄⡀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠐⣿⣷⣸⣿⣿⣷⣿⢟⣩⣭⡾⠿⢿⣿⣿⣿⣾⣼⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡷⢻⢷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣾⣿⡿⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⣶⣶⠀⠈⠉⠁⠀⠉⠉⠀⠉⠉⠉⠛⠛⣿⣿⡷⣮⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⣹⣾⣿⣿⣿⣿⣿⣁⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣴⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣯⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠉⠉⠛⠃⠀⠀⠀⠟⠋⠉⠁⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣻⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⢻⡇⠀⠚⠶⠶⠖⠁⠀⠀⠀⠀⠀⠈⠓⠿⠿⠟⢿⣿⣿⣿⣿⡏⣷⢹⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⠀⣠⢼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠶⠠⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⣯⡙⠛⡆⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⣶⣾⡆⠀⡀⢀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠁⣨⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣧⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢤⡄⠀⠀⠈⣿⣿⣿⣿⣿⠿⠿⠿⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⣀⣀⣸⣿⡇
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢢⣴⠇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢠⢰⠶⣿⠘⣷⡎⠸⣧⡾⣫⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⡈⣮⡤⢛⡿⠛⠛⠓⢾⣿⢋⣠⠀⠀⠀⠀⠀⠀⣠⠀⢰⠆
⠀⠀⠀⠀⠀⠀⢰⡀⠀⣴⠀⠀⠀⣤⣈⠑⣷⣯⡿⠓⠀⠀⠀⢠⠴⠙⢿⣶⣬⣄⠀⠀⠀⠀⢸⣇⡟⣠⠴⠂
⠀⠀⠀⠰⢦⣀⠈⢷⣼⣇⠀⠀⠸⠒⠹⢎⣾⠋⣴⣄⠀⠀⠀⣠⠞⠓⠈⣿⡏⠁⠀⠀⠐⠢⣼⠟⣿⣡⣀⡀
⠀⠀⠀⠀⢀⣈⣽⣾⣇⣽⡆⠀⠈⠉⢰⣾⠃⠘⠿⠟⠀⠀⠀⢃⠺⢇⠀⣸⣇⠀⠀⠀⠀⢀⡿⠟⠁⠀⠈⠁
⠀⠀⠀⠀⠈⠉⠁⢸⠟⠋⢿⠳⡀⠀⢸⣿⠀⠈⠠⠐⠀⣉⣁⠀⠉⠁⠀⢸⣿⠆⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠱⡙⢦⡈⢧⢣⡀⠀⢠⣾⡟⠻⣿⡆⠀⣠⣿⠟⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠛⢮⡣⡙⢦⣜⠳⠾⠿⠛⣀⡴⠏⢁⣤⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠻⠏⢿⡿⢭⣶⣦⢾⡋⣡⡾⠉⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠻⣄⣰⠃⠀⠙⠟⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣃⠀⠀⠈⠿⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠖⠶⠶⠶⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠻⣖⣀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⢀⣼⢻⣏⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣦⡾⠃⢸⣿⣄⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠉⢹⣯⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢦⣀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡴⠖⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡴⠶⠚⠉⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⢦⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⡿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣷⡶⠆⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠈⠁⠚⠛⠛⠓
⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀
⠀⠀⠀⠀⠀⠴⣆⠀⠀⠀⠁⣠⣶⡀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⢀⣶⣄⢀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣶⣤⣾⣿⠋⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣿⡟⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢐⡅⠀⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⡦⠁⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣤⣭⣍⣬⣥
⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠠⣇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⣿⣿⠛⠻⣿
⠀⠀⠀⠀⠀⠀⢸⣷⣤⠐⠀⢶⣿⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠂⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣾⡿⠀⠳⠄⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⡀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⣩⡇⠀⠀⢀⡍⠈⠛⢷⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⢿⣦⣽⣿⣟
⠀⣠⠰⠿⠛⠓⡿⠿⠷⣶⡿⠃⠘⠛⠛⠀⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣾⣏⠀⣿⢩⣿⢋⣿⣦⣄⣀⡀
⠰⣿⠂⠀⠀⠀⣿⢘⠻⡍⠁⠀⠀⠀⠀⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⡟⠁⣼⠁⣼⣟⣻⣿⣿⣿⣿⡡
⠐⣿⠑⠢⣤⡀⣿⣻⣾⠁⠀⠀⢀⣤⡾⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡷⣿⣿⠁⠀⠁⢰⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠀⠀⠘⢿⣿⣿⡯⠀⢀⣴⠟⣿⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣗⣹⡿⠀⣶⠤⣾⣿⣿⣟⣿⣛⣿⣿⣿
⢸⣿⠀⠀⠀⢠⣿⣿⡗⣠⣾⡟⠀⠧⠸⢺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⠃⢐⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⢈⣿⠀⠀⠀⣼⣿⣏⣻⣿⡿⠃⠀⠀⢀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⢨⡅⢸⣿⣿⣿⣿⣿⣏⣿⣿⡟⢡
⠀⠇⠀⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⡀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⡟⣿⣿⠃⠀⢈⡇⠸⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿
⠀⠒⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡳⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⠁⠀⢸⡇⠀⣿⣿⣿⣿⡿⠂⠘⣿⣿⡆
⠀⠀⠀⣾⣿⣿⣟⣿⣿⠀⠈⠁⠀⠀⠙⣵⢪⣿⡷⣿⠀⠀⠀⠀⠀⠀⠈⡏⠀⣿⣟⡀⠀⠀⠘⣇⠀⢸⣿⣿⣿⡋⣷⠀⣿⣿⡷
⢄⣀⣸⣿⣿⣿⣿⢻⣿⣶⣂⣿⣀⣀⣀⣤⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣦⠀⣿⣿⡇
⣸⣿⣯⢿⣿⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠿⠄⢤⣿⡿⣟⣯⡙⠿⣿⣿⡾⠃⠀⢻⣿⣁
⣏⢩⣭⣟⣹⣿⢿⣽⣿⡿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣴⣶⣶⣶⣯⣿⣿⣏⣩⣅⠀⠀⢸⣿⠉
⠻⣖⣉⠉⣉⠋⣹⢾⣿⣿⣷⣿⡿⠋⠉⠛⢷⣾⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⣤⣤⣦⣤⣏⢙⣩⡄⠁⠀⠀⠀⢸⣿⠂
⠀⠙⠻⣇⡁⠀⢻⣾⣿⣿⣿⠋⠀⠀⠀⠠⡎⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣉⣉⠛⢛⣿⣿⣛⣟⡛⠀⠀⠀⠋⠁
⠀⠀⠀⠈⠹⡟⠙⠛⡏⢹⠃⠀⠀⠀⠀⢀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠛⢛⡋⠙⣷⣼⣿⢿⣿⡿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⢸⡄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡛⡻⠧⣀⣉⣏⣱⣬⣿⣄⣸⡃⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣛⣶⣾⢶⣿⣿⣿⣿⣿⣾⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠛⣡⣴⣿⣿⣿⣿⣿⣟⡻⠆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣶⢼⣿⣿⣿⣯⣽⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣤⣤⣽⣿⣿⣟⣻⣟⣿⣿⡃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠛⠉⢿⣿⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠐⡓⢰⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣶⣶⣷⠀⠀⠀⠀⠀⠀⠀⣀⢀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠟⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⢸⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⣇⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠈⠻⠿⠏⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⢠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠁⠀⠀⠠⣄⣀⠀⠀⠀⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢠⡄⠀⠀⣀⠀⠀⠙⢦⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠠⠀⠐⠈⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⢀⠀⣿⢠⣶⡐⠀⠀⠀⠀⠀⠀⠹⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡁⠀⠀⠈⠉⠀⠈⠀⠀⢠⠄⠀⠀⠀⠀⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠙⠒⠒⠋⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⢰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠈⠂⠂⢀⡠⠴⠋
⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡋⡋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠑⠂⠀⠢
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠐⠄⡀⠀⠀⠂⠄⡔⠀⠀⠁⠀⠀⠀⠀⠀⠠⠉⠀⢠⠠⡠⠐⠃⠀⠀⠀⠀⠀⠀⠀⠠⠢
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠁⠂⠐⠉⡁⠀⠰⠈⠂⢧⡀⠀⠀⠀⠀⢀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠤⠔⠁⠀⠀⢠⠀⠀⠀⠙⢔⠂⠐⠊⠁⠀⠀⠀⠠⠀⠀⠀⠀⠃⢠⠤⠀⠂⠁
⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠂⢎⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡆⠀⡀
⠀⠈⠢⡀⠀⠀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠀⡆⡆⠘⡄⢂⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠄⠀⠀⡏⠂⠐⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠙⢆⣑⣄⠀⠀⠀⠈⠧⣄⣱⣀⣀⡀⠉⢹⠓⠃
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠝⠋⠑⢄⡀⠀⠀⠀⢀⡔⠁⠈⠳⠀⡄
⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⡤⠎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⡋⢹⠀⠀⠀⢀⠀⢇
⠀⠀⠀⠸⡄⠀⠀⢀⡧⠠⢤⠀⠀⠀⠀⢸⠸⠀⠠⠀⠀⠐⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡎
⠀⠀⠀⠀⠉⢀⠤⢊⠀⢀⠆⠀⠀⠀⠀⢸⠀⠀⢈⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⡇
⠀⠀⠀⠪⡀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢐⠙⡾⠀⠀⠀⠳⢀⠃⠀⠀⠀⢤
⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠜⡀⠀⠀⢑⠘⡀⠂⠀⠀⢀⡀⠐⠤⣀⣀⣠⣀⣀⠤⠐⠈⠀⠀⠀⠀⠉⠂⠥⣀⡀⢀⣀⣀⠴⠂
⠀⠀⠀⠀⠀⠰⠀⠀⠀⣤⠃⠀⠈⠁⠉⠀⢧⣀⣀⣀⡤⠃
⣶⣶⡶⠶⠶⢶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠋⣉⣷⣖⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠘⠟⠀⢬⣾⡋⠁⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠔⣰⠇⣰⠒⠛⠀⠀⠽⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡖⠀⠀⠀⠈⠉⠠⡄⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠎⡻⠁⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⠻⣾⣳⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢰⣷⣖⠃⠀⠰⡿⣏⣊⠀⠀⠌⢻⡧⠨⢻⣷⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣴⠎⢻⣧⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢽⣿⢰⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠶⠓⡦⠀⠀⠀⠀⠀⠀⠀⠉⣺⡙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢢⢰⡇⠀⠀⠉⠀⠀⠀⠀⢠⡖⣦⢔⣿⡟⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⣼⣇⣤⠀⠀⠀⡀⠀⠀⠀⡠⠎⡸⠀⠀⠈⢑⡄⠀⠄⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣽⣿⡆⠀⠰⠟⢛⠂⠉⢀⡔⠁⠀⠤⠚⠉⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⢛⣻⡟⠁⠀⠀⠠⠇⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠏⡻⠁⠀⠀⠀⠼⠀⠀⠀⠀⠀⢀⡆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣶⢏⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⡾⠟⠀⠀⠐⠛⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣿⣿⡘⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⣀⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⢸⠃⠀⠀⠠⡀⠰⡀⠀⠀⢓⣶⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⣄⠀⠀⠀⠁⠀⠀⠀⠂⢈⣙⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣠⡜⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠟⢠⠀⠀⠀⠉⠙⢯⣀⢦⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠄⡀⢁⣄⠲⣽⣷⠦⣿⢳⣔⠏
⠀⠀⠀⠀⠉⠉⠙⠛⠋⠙⠋⠉⠉⠋⠐⠀⠀⣀⣇⠀⠀⠀⠀⠀⡙⣦⠙⢷⠀⠹⡷⢻⠆⠐⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡀⠀⠀⠀⠀⠁⣈⣠⣬⣇⣀⠀⠀⣧⢦⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣷⡿⣟⣿⣿⣄⠰⣻⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠹⣯⠙⢿⣿⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⠀⢰⠂⢰⠀⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⠇⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠀⠀⠀⠀⠀⠀⢰