Sashimi Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⣄⠀⡀⠀⡷⠅⠄⠀⠀⠀⠀⠀⠀⢀⣠⣖⠄⢀⢀⡀⡀⠌
⠀⠀⠠⠘⣉⠀⠑⠀⢐⢦⡀⡄⠀⠐⠒⠚⠋⡉⠉⡀⠀⠠⠀⠠⠄⡪⠣⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠠⡀⢎⡃⠘⠅⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠄
⠀⠀⠀⠄⠹⠕⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣷⣿⣿⣮⣿⣿⣿⡷⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣻⡟⡿⢹⢀⡻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡀⠀⠈⠄⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠉⠐⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⣠⠘⠀⠊⣂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠐⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⡠⠐⠂⠀⠒⠢⣄⠀⠀⢀⠤⣒⢖⢒⠠⣄⠀⠀⢀⠤⣲⣖⡒⢤⠀⠀⠀⡠⠄⠤⢤⣄⣀⣀⣀⡀
⠀⢀⠎⡠⠴⣤⣄⡀⠀⠈⡇⠀⡧⣈⡒⡂⢒⢁⠜⡆⠀⣧⣌⣙⣛⣡⣴⡇⠀⢸⠀⠀⢠⣾⣿⠟⡀⠀⠈⢣
⠀⢜⡸⠀⡮⢤⠋⡟⠒⢲⠁⠀⠁⠀⠀⠄⠁⡀⠡⡇⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⠈⠁⢻⣿⣿⠀⠀⠀⠉⠸
⠀⠀⠉⠀⢈⢐⢉⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠄⣱⠃⠀⠻⢿⣿⣿⣿⠿⠁⠀⠀⠦⣠⣸⣿⣿⣄⣀⣠⠕⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠠⠤⢄⡀⠀⠀⠀⢀⡀⠀⣤⠄⣀
⠀⠐⠉⠀⢀⣾⠏⠈⠙⠒⡄⢀⡴⢩⢥⡞⢿⠲⣤⠀⠀⡴⠋⠉⠙⠻⢷⣄⠤⡟⠀⣐⠋⢰⢖⣾⣋⠆⢀⣵
⠸⣀⣀⡀⢸⣿⠤⠤⢀⣠⠇⠀⠑⠬⢊⣓⡊⠎⠀⡇⢪⣄⡀⠀⣀⠔⢾⣿⣈⠏⠀⢹⣿⣶⣶⣶⣾⣾⣿⡿
⠀⠀⠱⠤⠸⡿⠄⠀⠔⠁⠀⠘⠄⠀⠀⠀⠀⠀⣠⠁⠘⢆⣀⠀⠀⢀⠠⠋⠁⠀⠀⠈⠛⠿⠿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠐⠊⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⣀⢠⠤⠤⠒⠲⠦⠄⣠⣤⣄⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⣀⠤⠰⠒⠢⢄⡀
⠀⠀⣎⣰⢥⣕⣾⡆⠀⡰⠚⠁⠂⠀⠀⠉⠁⠈⢉⠽⠿⠿⠃⡎⠠⣤⣄⣀⢀⣱⠀⠀⡜⠕⡀⡤⡀⠠⠀⢱
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠑⡤⣄⣠⣀⠠⠄⠚⠋⢩⠇⠀⠀⠘⡋⣎⡧⢨⠎⠙⢸⠀⢸⡟⡎⣤⢍⣦⢀⡆⣤⠁
⠀⠀⠻⠿⣿⡿⠿⠃⠀⠀⠑⢔⣀⣀⡤⠤⠴⠒⠉⠀⠀⠀⠀⠱⢌⣑⣉⣠⠮⠊⠀⠀⠑⠿⣦⣭⣅⡾⠖⠁

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢳⠀⠀⠀⢀⡄⠀⠀⠀⠤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢸⠀⠀⠀⠘⠄⠀⠽⠐⠀⡈⢂⠤⠘⠀⡀⠀⠄⢠⠀⡐⠉⠠⡄⠁⠈⠐⢤⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠈⡆⠀⠀⠀⡂⠀⡅⡈⠐⡀⠃⡠⠨⠝⢃⠀⠀⠀⢀⠁⢀⢀⢳⠀⢀⢄⠀⠐⠄⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠐⢆⠁⠇⠁⠀⠆⠀⠀⣆⠀⠀⠀⠘⠀⠀⠀⠀⣜⠀⠀⠡⠡⠤⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠃⠐⠇⡼⣂⠄⠀⠀⣣⠄⢒⢡⡸⢦⡐⠷⠠⠂⠥⠆⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠒⠃⠀⠀⠀⠄⡡⢜⠜⣅⠂⢁⣎⡔⢦⡀⠈⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠂⠆⢠⢄⠀⠀⠀⢡⢎⢊⠤⢂⡩⢔⠜⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠓⠛⠒⠛⠀⠀⠀⠈⠰⡁⠠⢁⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⣇⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉





⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⢴⣇⠀⠀⠘⠠⡄⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂
⠀⠀⠀⢀⡀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠈⠁⠀⠀⠀⠀⠁⠐⠈⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠛⣿⣆⠀⠀⠀⠉⠀⠂⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠛⠃⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠈⠀⣀⣀⠀⠀⠈⢧⡀⠀⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣴⢲⢲⣢⠀⠀⠀⠀⢀⡴⣄⡖⠆⠀⠀⠀⠘⠛⠛⠁⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢈⠀⠋⠉⠀⠀⠀⠀⠀⢀⣄⠀⠀⡟⠜⠓⢻⠀⠀⠀⠀⣾⠧⡤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣤⡶
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠒⣀⡘⠂⠀⠀⠀⠀⠀⠀⢤⣴⣶⣾⣿⡆⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠛⠛⠻⣧⡀⡀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠉⠛⠗⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠠⢤⣤⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢹⡗⠀⠀⠀⠀⠀⠠⣶⡦⠄⠂⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠤⢐⡀⠀⠐⠠⠀⠀⠀⠀⠀⠐⠢⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠲⣦⣭⣥⣶⣄⣐⠶⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣾⣋⠹⠿⠉⣙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣀⡀⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣷⡄⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣷⣦⣄⣀⠉⠛⠛⠛⠉⠻⠿⠛⠋⣿⣏⣁⣴⣴⣿⡿⢻⣿⠉⣡⡄⣀⣤⡆
⠀⠀⠀⠀⠀⣄⠠⠀⠀⠀⠀⠈⠁⠈⠉⠛⠻⠿⣷⣶⣦⣤⣀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠠⠴⣻⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠉⠙⠒⠦⣤⣀⡠⢤⣀⡀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣷⣶⣤⣄⣈⢀⣠⣴⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢭⣓⠲⠤⣀⡀⠀⣀⠀⠀⠀⠉⣿⠿⢿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠼⣿⣿⡻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⢤⣀⡀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣠⠖⠉⠉⠀⠈⠉⠒⢄⢠⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠉⠑
⠉⠁⠀⠁⠁⡰⠀⠀⠀⠀⠀⠐⢎⢱⡠⠴⠄⢀⠀⠀⠀⣌⡰⠁⠀⠶⢀⠀⠐⠒⠀⠀⠣⡡⠀⢀⠃⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⢁⠀⠈⠁⢀⡀
⢀⡀⠠⠤⠐⠁⠀⠀⠀⠀⠵⠀⠣⠠⣃⢐⠃⢪⠁⠀⠀⠉⢁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⠊⠀⢀⠄⠀⠠⡈⠉⢢⡀⠀⠀⠀⠠⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡦⢧⣤⣥⣤⣷⣶⣿⠀⠀⠀⠀⠈⠀⠒⠐⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⣀⠀⠐⢄⠀⢀⠀⠀⠀⢀⠇
⠤⠤⠤⠤⢀⠀⠀⠀⠀⢸⣿⢱⣲⣻⣿⢫⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠄⠀⣀⠀⠀⠀⠀⢹⣶⠤⣀⣀⣤⣤⣤⡾⠉⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣀⡀⠄⡀⠈⢢⠀⠀⢸⣿⡬⢉⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡴⢁⠠⠔⠤⠀⡀⠂⠀⠀⠀⠀⠀⢸⡯⢀⣼⣿⣿⣟⣿⡿⢹⠀⠀⠀⠀⠀⡠⠈
⠀⠀⣤⠕⢎⠂⠀⡆⠀⠈⠙⠓⠤⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⡸⠉⠐⠀⠀⠀⠒⠉⢧⠰⢰⡄⠀⠀⢸⣷⠈⣵⣏⣹⣿⣿⠧⡸⠀⠀⠀⠀⠈⡰⠂⣁
⢉⠠⡄⠀⠀⢣⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢂⠀⠀⡦⠂⠆⠀⠀⠀⠙⠦⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠁⠀⢀
⢄⡁⢸⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠘⠀⠴⠀⠈⠀⠀⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠄⠀⢿
⠓⠐⠁⠀⠀⠰⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠃⣄⠈⠐⠈⠀⡀⠔⠋⠀⠀⠀⠀⠂⠁⠀⢈⡖⠀⠄⠀⠀⠀⢀⠄⢂⡀⢤⠘⣄⠈
⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⡌⠀⠀⠀⠠⠁⢀⠁⠀⠀⠀⠀⢀⠂⠈⠀⠘⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⡀⠀⠈⠑⣤⠤⣀⣀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡀⡇⠀⠗⠂⠤⠤⠐⠂⠉⡆
⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠠⠤⠈⠈⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⣀⡀⠀⠀⡀⠀⠀⡄⠀⠀⠘⢀⣀⠚⠀⠀⡃
⢄⡀⠀⠆⠈⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠤⠐⠒⠁⠀⠀⠀⢀⠐⠃⠘⠃⠀⠈⠋⠀⠀⠀⠁⠀⠀⠠⠄⠤⠀⠇⣀⣀⣀⣀⠤⠊⠀⠀⠀⠀⡔⠈⣁
⠀⠠⠑⢦⠠⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠉⠀⠂⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠃⠅
⠰⣆⠀⠈⢦⠌⡇⠀⠀⠀⢀⡠⠤⠀⠰⠀⠔⠠⡀⠀⠀⠀⡔⠊⢀⢀⠀⠀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠄⣟⠀⠀⠋⢠⠀⠀⠀⢌⠁⠠⡚⢉⣵⣺⣤⠞⠙⡆⠀⠀⠃⠀⠈⠀⠠⠀⠈⢐⠁⠀⠀⢀⠀⠀⠀⢀⠠⠂⠱⢁⠀⠤⠈⠈⠉⢢⠀⠀⠈⡀⠀⠇⠐
⠐⠃⠀⡠⠖⠁⠀⠀⠀⢸⣷⢤⣈⣉⠛⢉⣁⣠⣼⠁⠀⠀⠈⠐⠄⣀⠁⢀⡠⠌⠜⠀⠔⠁⠀⠀⡔⢁⠀⠀⠀⢐⣀⠄⠀⠐⠀⠀⠀⠀⠀⠐⢄⠈⠒
⠒⠚⠁⠀⠀⠀⠀⠀⠀⢸⣟⢣⣽⣿⣿⣿⡟⢿⣸⠀⠀⠀⠈⠀⠐⠒⠒⠒⠒⠂⠈⠀⠀⠀⠀⢸⠄⠁⣀⠀⠤⡀⠈⡏⠀⠀⠀⢠⠀⠀⠀⠀⠀⠉⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⢰⣟⢛⣿⣶⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⢀⢘⠀⡆⡂⠀⢀⠌
⠀⡏⠀⠂⠠⢀⠀⡀⠀⠘⢿⡃⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⡠⠤⠂⠒⠂⠀⠒⠒⠤⢀⠀⢰⢂⠀⠃⠤⠀⠊⠀⡇⠀⡤⠊

⢢⣀⣀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠕⠋⠉⠀⠈⠉⠲⣀⡀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢉⠉⠁
⠁⠀⠀⠀⡠⠀⠀⠀⢀⠀⡢⠸⡔⠛⣀⡄⠀⠀⣦⠎⠀⠘⠣⡀⠈⠁⠀⠘⠖⣀⠔⠁⠀⡀⠀⠤⠤⠤⢀⡀⠀⠀⠁⠀⠉⠀⠄
⠄⠐⠊⠉⠀⠀⠀⠀⣒⣁⡘⠐⠄⢨⣀⣢⡄⠀⠀⠠⠀⢀⠀⣀⣀⣀⣀⠤⠐⠁⠀⠀⠎⠀⠐⠂⠀⠒⠀⠘⡆⠀⠀⠁⠒⠀⠠
⢀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠁⠒⠃⠀⣀⡴⡇
⠀⠀⢀⠈⠐⢄⠀⠀⣿⣆⠛⣿⣿⣼⣿⣟⠀⠀⠀⠀⢀⡤⢘⣠⣀⠈⠡⠘⠂⠀⠀⠀⣿⡃⣹⣿⣿⣿⣿⣖⠁⠀⠀⠀⠀⠀⠂
⠉⢉⡕⢬⠂⠈⠆⠀⠙⠻⠤⠿⠿⠿⠟⠋⠀⠀⠀⠀⡞⠀⠁⠀⠀⠈⠳⡄⢀⡄⠀⠀⣿⡄⣩⣟⣻⣿⣿⢠⠀⠀⠀⠀⢎⠖⣂
⢓⠠⡀⠀⠱⡠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠄⠀⢱⠈⠇⠀⠀⠈⠣⠽⣿⣿⠿⠟⠃⠀⠀⠀⠀⠈⠀⢀
⣪⢍⠅⠀⠀⠠⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠒⢀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠⠀⠸
⣉⡀⣀⡠⠔⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠐⠤⠈⠀⠠⠐⠁⠀⠀⠠⠂⠠⠀⠠⠊⡀⠀⢀⠀⠐⠂⠡⠖⡆⠱⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠬⠐⠒⠢⢤⡀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⣐⡀⠀⠀⣀⠤⡂⠐
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⠀⡀⠐⠋⠉⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠁⠀⠅⢠⠀⠠⠄⠀⡇
⣀⠂⡡⠐⠂⠀⠀⠀⠠⠄⠀⣀⣀⠀⠠⠤⠊⠀⠀⠀⠀⠔⠸⠆⠀⠓⠃⠈⠀⠂⠀⠢⢀⣠⡀⣃⠀⠈⠁⣀⠴⠁⠀⠀⢀⠄⣂
⠈⠄⠲⡄⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡜⠁⠒⠀⠀⢂⠀⢀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢰⠟⠠
⠒⢄⠀⢱⠌⠅⠀⠀⢀⠠⠄⠀⡐⢡⠂⣆⠀⠀⠀⠓⠁⡀⠀⠀⡄⢑⠠⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠂⠈⠀⠈⡠⠀⠀⠀⣅⠀⢎⣩⣿⣿⠞⠁⡗⠀⠀⡀⠀⠀⠐⠀⠀⠨⠀⠀⡀⠀⠀⢀⠄⠂⠘⠠⠀⠂⠀⠀⠑⠀⠀⠠⠀⠐⡀
⢁⡠⠔⠊⠀⠀⠀⠀⣿⡗⢲⣤⣥⣤⣴⡿⠇⠀⠀⠁⢈⣂⣀⣐⣒⣁⡄⠂⠀⠀⠠⠫⠀⠀⠀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠛⣿⣿⣿⣫⡷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠐⠔⠈⢢⠀⡁⠀⠀⠰
⠀⠐⠀⠀⠀⠀⠀⠀⢿⡇⢰⣿⣶⣿⣿⡷⠀⠀⠀⠀⠀⣀⠀⠤⠄⠤⠤⢄⡀⠀⠠⡄⠰⢀⠐⠝⠀⣇⢀⡐⠁⠀⡀⠄
⣀⣀⣀⣀⣀⣀⣍⣀⣀⣉⣚⣛⣛⣛⣋⣁⣀⣀⣀⣐⣈⣄⣐⣒⣒⣂⣀⣀⣈⣢⣈⣱⣲⣤⣤⣤⣖⣅⣋⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣃⣀⣀⣀⡀⠀⠀⠀⡐⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢤⣶⣶⣶⣶⢶⣭⣉⣉⡛⠻⠿⠷⣶⣤⡴⣸⣿⣤⣄
⠀⠀⠀⠀⡀⠴⠶⠿⠷⠶⢤⣤⣴⣶⣤⣈⣉⠛⠛⠻⣿⣗⣤⠀⣱⣿⣦⠈⣌⣧
⠀⠀⣴⣾⡷⠶⣶⣶⣶⣶⣦⡀⠉⠉⠉⠉⣿⣿⠂⠀⢿⣿⣿⣶⣿⣿⣿⣐⡿⠟
⠀⠀⠙⠿⠿⠿⠿⠿⢿⣿⣧⣽⣿⣷⠀⠀⣿⣿⣧⣤⡾⢿⢿⣿⠟⠛⠋⠙⡃
⠀⠀⠀⠦⣤⣤⣤⣤⣄⣀⡉⠉⢻⣿⣤⠖⠛⠉⠀⠀⠀⢨⣿⠏⠀⠀⠐⠁⡅
⠀⠀⠀⢰⠂⠀⠉⠙⠛⠛⠛⠂⠉⠀⠄⠀⠀⠀⠀⠀⢀⣿⡟⡀⠀⣌⢁⠞
⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠉⠂⠤⠤⢄⣀⠀⣀⠀⠤⠤⠒⠂⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡿⢆⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠣⡀⠀⠀⠀⠘⣌⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠙⢄⠀⠀⠀⠹⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⢢⠀⠀⠀⢣⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠱⡀⠀⠀⢇⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡝⣄⠀⠈⢆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⣹⠟⠁⠀⢀⡤⠖⠋⠛⠛⠒⡄⠀⠀⠀⠈⢮⢢⠀⠈⡆⢇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⢰⠋⠀⠀⠀⡴⠋⠀⠀⠀⣶⣠⡶⠁⠀⠀⠀⠀⠀⠱⡵⡀⠘⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡜⠀⠀⠀⡼⠁⠈⠀⠈⢡⡞⢡⢎⡠⠤⠔⠒⠲⣄⠀⠈⢾⣆⠹⡰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⡀⠀⠀⢠⡯⢞⡝⠋⠀⠀⠀⠀⠀⢸⡆⠀⠀⠹⣦⠱⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠞⠀⠀⠀⠣⣄⣠⣰⠏⢠⠞⠀⢸⠀⡄⠀⢀⣴⠟⠀⠀⠀⠀⠘⢧⢣⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⠀⠨⣀⣴⡪⠟⢋⣀⣀⡀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠶⠛⣩⠔⠒⠋⠉⠁⠁⠉⠋⠲⢤⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠲⠶⠶⡄⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠁⠀⠐⠀⠀⡠⠞⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⠔⠋⠁⠀⠉⠒⢄⢳⡀⠀⠀⠀⡟⠀⢀⣀⣄⠀⠀⣀⣠⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡎⠀⠀⠀⠀⠀⠀⠈⡆⢷⠀⠀⠀⠉⠉⠉⠉⣉⣛⣉⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⡤⠖⠛⢋⠉⠉⠉⢛⠑⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⢦⡀⠀⠀⠀⡠⠎⣰⠏⠀⠀⠀⠀⠣⣤⣀⠀⠐⢀⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢬⣁⣈⣩⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣾⢤⣔⣀⣠⠔⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠁⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠡⠤⣀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⢀⡔⠈⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⣀⣈⣄⡀⠀⢀⣀⠀⠤⠤⠀⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠼⠧⣤⣤⠞⠙⠉⠀⠀⠀⠙⠢⣤⢀⣠⣤⠴⠆⢀⠠⠀⠄⠤⠅⢒⡠⡄⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢴⠊⠀⠀⠀⠀⠀⣸⠃⡄⠀⠀⠀⠀⠀⠀⡴⠋⠘⠁⠀⠀⠀⠀⠘⠢⡄⠀⠀⠀⠤⠠⡤⠙⠛⠶⣴⣤⣤
⠀⠀⠀⠀⠀⢈⢀⡠⠒⠉⠉⡏⠜⠀⠀⠀⠀⠀⠀⡆⡸⠁⠀⠀⠀⠀⢀⠞⠴⠁⠀⠀⠀⠀⠀⠀⠀⢀⣨⡶⠚⠛⠈⢉⡩⠭⠑⢂⣠⡾⠋
⠀⠀⠀⠀⠀⡸⠏⠀⠀⠀⠈⡇⢡⠀⠀⠀⠀⠀⢸⢀⠃⠀⠀⠀⠀⢠⣇⠞⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠊⠀⠀⠄⠀⠩⡠⠐⡠⠚⠅
⠀⠀⠀⠀⡠⣧⡄⠀⠀⠀⠰⡇⠻⠀⠀⠀⠀⠀⡆⢲⠀⠀⠀⠀⠀⢎⡎⠀⠀⠀⠀⠀⠀⢀⡴⣃⠿⠀⠀⠀⠀⠀⠀⠀⢰⠊⡠⠂
⠀⣀⠔⠈⠀⢸⢠⠀⠀⠀⠀⣇⢸⡀⠀⠀⠀⠀⡇⡏⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠠⠊⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋
⠎⠀⠀⢀⠤⠊⢧⢆⠀⠀⠀⠾⡄⠇⠀⠀⠀⠈⡇⡇⠀⠀⠀⠀⡧⣰⠀⠀⠀⠀⠀⣰⠁⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠐⡄⠊⠁⠀⣀⠜⢿⣆⠀⠀⠀⢱⡀⡄⠀⠀⠀⢃⢓⠀⠀⠀⠀⡇⡿⠀⠀⠀⠀⠰⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠐⡤⠔⠊⠀⠀⣈⣏⢃⠀⠀⠀⠹⣝⠆⠀⠀⠈⢶⡀⠀⠀⠀⢳⡇⠀⠀⠀⠀⠃⢸⠃⠀⠀⠠⠀⠀⠀⠀⢀⠌
⠀⠀⠐⡀⠄⠊⠁⠀⠀⠳⢷⣦⣀⣀⡸⠪⠶⠄⡒⠭⠟⠂⠐⠒⠚⠓⣄⠀⠀⢸⡇⣘⠀⠀⠀⠀⠀⠑⢀⠔⠁
⠀⠀⠀⠰⠄⠒⠈⠀⠀⢀⡀⠤⠉⠁⠒⠈⠀⠀⠀⢀⣀⠠⠤⠐⠊⠉⠀⠈⢉⠩⢧⣿⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠡⠄⠒⠈⠁⠀⠀⠀⠠⠄⠐⠒⠂⠉⠀⠀⠀⠀⢀⣀⠠⠔⠒⠉⠀⠀⠀⠉⠒⠶⠀⠒⠁
⠀⠀⠀⠀⠀⠱⠂⠀⠁⠀⣀⣀⣀⢀⣠⠤⠤⠄⠒⠒⠊⠉⠁
⣶⣶⣶⣶⣶⢶⣿⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⢸⣷⣦⣼⠛⢷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⣶⣾⣿⢹⣿⡇⣿⠁⠙⣇⠀⠈⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢻⣿⠿⣿⣿⡏⢸⡟⣿⣿⣤⣴⣾⣾⡟⣿⣿⣿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⢺⠏⢀⢹⣿⣵⣿⣷⣿⣿⡽⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⡶⣿⣿⣿⡎⠻⣿⣿⣿⣧⣸⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠸⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣋⣿⣷⣴⣾⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⢿⣿⡟⠛⠉⠙⣯⣄⠀⠻⣿⣷⡀
⠀⠀⠀⠙⢿⣿⣟⠀⠀⢹⣿⣿⣿⣿⣟⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⢠⠹⣿⣦⡰⠂⠘⣿⣧⡀⢹⣿⣿⣦⡀
⠀⠀⠀⠀⠈⢿⣿⣧⣀⣠⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣯⣷⣌⠛⢿⣿⣷⣧⡣⠈⠿⢷⣦⠀⠘⣿⣵⣦⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡓⠈⠹⠟⢿⣿⣷⣵⣠⡻⣿⣿⣧⠀⠀⣼⣿⡄⠀⣿⣼⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢲⠀⠈⠹⣿⣿⣿⣇⠀⠋⢹⡇⢠⡿⣿⡇⢼⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠹⢻⣿⠀⢾⣿⠇⢸⣷⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⡄⢶⢸⡟⠰⣼⣿⣴⣾⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡊⢁⣤⣾⣥⣾⣿⣿⣿⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⣿⡿⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠐⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣀⠒⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠉⠉⠉⣉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣠⠆⠀⠀⠀⠀⢀⣠⠔⠀⠀⠀⡀
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⢠⠐⢂⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣿⠛⠀⠀⠀⠊⠉⠈⢁⡐⠖
⠀⠀⢠⣿⣛⣿⠟⠋⠉⠁⠀⠹⡇⠀⠀⠀⠀⡀⠁⠀⠀⠈⠀⠀⠈⠀⠈⠸⡄⠠⠇⠂⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠁⠠⠀⠉⠀⠠⠂⠐⡍
⠀⠀⢸⣿⣿⡟⠈⠀⠀⢲⣶⠔⣿⠀⠀⠀⠈⠀⢠⢶⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⢀⣀⠀⠀⠁⢘⡄⢐⠃⠀⠋
⠀⠀⢸⣿⣿⣇⠀⠀⠠⣈⠋⢤⡟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠚⠁⠀⠀⠀⠙⠈⠉⠉⠉
⠀⠀⠀⠙⠻⠿⣦⢤⣧⠶⠗⠛⠁⡀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠄
⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⢰⡏⠀⠀⠤⠆⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⡴⠒⢀⣈⡁⡀
⠀⠀⠀⢰⣻⠾⡹⣭⢦⠀⠀⠓⠽⢀⣤⣀⡄⠀⠀⠠⠀⠀⠀⠀⣦⡀⠰⢿⣧⢿⠄⢀⡀⠀⠀⠀⠀⠀⠀⣠⠴⠦⢤⠀⡀⠈⠀⠀⠀⠀⠡⠴⠄⠈
⠀⠀⣲⠶⣈⣒⣓⣈⢡⡆⠀⠀⠀⠀⠀⠀⠁⠸⠀⠂⢀⠀⠀⠀⡁⠀⠑⣦⠶⠒⠈⠻⠀⠀⠀⠀⠀⢀⡜⢁⠀⠀⢠⠸⣅⠀⠀⠀⠀⠀⠀⠰⠳⢄⠁
⠀⠀⢸⠀⠀⠀⠈⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⢈⡄⠀⠀⣧⠀⠀⠅⠀⠀⠀⠀⢠⠀⣇⡄⠀⣈⠅⠇⠀⠀⠈⠅⠋⠀⠀⠀⠀⠀⠀⠐⠸⠄⠰
⠀⠀⣾⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⢼⠩⡅⠀⠀⠙⢀⠀⡄⠀⠀⠀⣤⡀⠀⠈⡙⠐⠋⠀⠠⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠐⢜⠓⡤⠃
⠀⠀⠈⠳⢤⣀⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⣤⣄
⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⠂⠀⠈⠉⠁⠀⣠⡆⠀⠀⠀⡠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⠂⠁⠐⠀⠈⠂⠀⠀⠀⣴⠛⣇⡚⣱⣼
⠀⠀⠀⠀⠀⠒⠂⢤⡀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠀⢸⠁⠀⠀⠀⡤⠴⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠙⠋⠀⠀⠍⣿⠀⢸⣡⣿⡵⠞⠁⠠
⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⣾⠀⠀⠀⡏⠀⠀⡀⠀⠀⠀⠀⢘⠂⠘⠉⠀⢀
⠀⠀⠀⠠⣀⣀⡀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠐⡀⢀⡅⠀⠀⠐⠁⠀⠀⠀⡏⣠⠜⠀⠐⠉⠀⢠⠀⡄⠠⠸⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢀⠀⠸⠀⢀⠠⠄⠀⠀⠠⠀⢀⠀⠀⠉⠈⠀⣀⠖⠁⠀⠀⠀⠀⠙⢇⣠⠂⠀⠀⢆⣸⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠁

⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⢀⢠⠄⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⢀⡉⢉⡁⠀⡄⢀⠀⠀⠀⠀⡠⢎⣭⣷⠟⡛⠃⠀⢠⣾⡶⠒⣚⣛⢳⡄⠀⠀⠀⣰⠟⢿⣯⠿⢆
⠀⠀⢸⣟⣿⣿⢠⣿⣿⠀⠀⢠⣞⣥⣾⡟⠁⠈⠀⠀⠀⠀⠀⠁⠘⡿⠟⠀⠀⠀⢀⣾⢃⠀⣔⣿⣷⣙⣧
⠀⠀⠆⠉⠙⠛⠼⠟⠁⠀⠀⠫⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠤⠀⠀⠘⠣⠄⠉⠈⠈⠿⠟⠁

⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⢠⠤⣔⣂⠀⠀⠀⠀⠀⠀⠀⢰⣀⣇⢃⣄⠀⠀⠀⠀⢀⠄⠀⠀⣤⣄⡀
⠀⠀⠰⠀⠉⠁⣤⢠⣶⡄⠀⠀⡞⢆⡙⠛⠀⠄⠆⠀⠀⠀⠘⢉⡀⠈⠙⣰⠆⠀⠀⠸⠈⠀⠀⠀⢿⣿⡇
⠀⠀⢂⠈⠉⠀⠀⠈⠐⠃⠀⠀⠀⠈⠻⠖⠷⠛⣻⠀⠀⠀⠀⣿⣽⣧⠈⣧⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠐⠂⠤⠖⠀⠒⠀⠀⠀⠀⠀⠙⠛⠶⠶⠒⠁⠀⠀⠀⠄⠙⠛⡛⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⣄⠀⠀⠀⠀⠀⠀⢠⢠⣾⠄⡀
⠀⢀⢀⠉⠉⡹⣯⣤⡞⠚⠋⠀⠀⠀⢄⡴⣾⡇⠀⠀⠀⠀⠀⠀⠙⢢⣴⡞⡁⠀⠀⠀⣴⣐⣩⣮⣵⣾⡇
⠀⠈⠁⠈⠈⠑⠛⠉⠀⠀⠀⠀⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠂⢺⣤⡏⠀⠈⠀⠀⡇⢸⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠔⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⣒⣀
⠀⠀⠀⢀⠀⠀⢀⢘⣎⠀⠀⠀⢸⠁⠀⠀⢰⣶⣶⠀⠀⠀⡠⠃⢀⡴⠖⠛⠉⠀⠀⢸⠀⠀⠀⠒⠀⠀⡀
⠀⠀⠀⠈⠀⣿⣿⠀⡿⠃⠀⠀⢸⡀⠀⠀⣸⣿⣿⠀⠀⣀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀⠁⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠛⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠄⠒⠊⠉⣿⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⢀⣀⣠⡅⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢻⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣡⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠟⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣻⣿⣿⣿⣷⣾⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠉⠁⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠿⠿⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣀⣹⣁⣼⢿⣿⡿⠛⢩⢿⠟⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠻⠿⣅⣛⣋⡹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢦⣤⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣃⣠⣤⣀⢀⠀⡀⣖⣿⣭⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣷⣶⣮⡝⣧⢾⣱⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠛⣿⡮⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣽⣟⣴⣿⢷⡿⠿⠋⡏⠈⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⣏⠉⠉⢁⣤⣶⣤⡀⡇⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛⣿⣿⡄⠀⢿⣷⣷⣿⡟⡃⠀⣸⠿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⣤⠁⢸⣍⣻⣦⣌⠙⠋⠁⢀⣧⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⣤⠾⣻⣇⠘⡿⢷⣴⠖⠿⡏⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣋⠠⡿⢺⣾⣁⠀⠀⠀⢠⡇⢀⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠸⠟⣩⣧⣥⣬⣤⡔⠀⢀⡊⣃⡤⠋⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⡿⢿⣿⡷⠀⣸⣿⣿⣟⣦⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣟⣿⡟⠻⠿⢯⡿⠿⠶⠄⠿⠝⠿⠷⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠘⣇⠀⠀⠀⠀⠀⠀⣸⠇⠹⣦
⠀⠀⠀⠀⠀⠀⣸⠋⢻⣄⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠹⣄⠀⠀⠀⠀⣰⠏⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⢷⣄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠹⣆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣄⢸⠃⠀⠀⣴⡀⠀⠀⠀⢹⡾⠃⠀⠀⢠⣦⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⡇⠘⢦⣀⠀⠈⠀⣀⣠⠔⠃⠈⣆⠀⠀⠀⠀⠈⢷⡀
⣤⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠙⠓⠛⠋⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⣧
⠈⢿⡛⠶⢦⣄⡈⣇⠀⠀⠀⢀⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣴⠒⠒⡶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⢳⡀⠀⠈⠙⠻⠆⠀⠀⠀⡏⠳⢄⣸⠁⠀⠀⠀⠀⢰⠃⠀⡼⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⢀⡀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⠲⣄⡀⣸⠀⡟⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⠉⣙⣻⣧⣀⡀⠀⠀⠀⠰⠿⠞⣷⠀⠀⠀⠀⢰⠇
⠀⠀⢰⡇⠀⠀⠀⠸⠓⠦⣤⣸⠀⠀⠀⠀⣠⠖⠛⠶⢤⣄⣠⠟⠉⠙⠳⣄⠀⠀⠀⠀⡏⠀⠀⠀⢠⡏
⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠁⢀⣤⣄⠀⣠⠶⠖⠶⣄⠀⠈⢧⠀⠀⠀⡇⠀⠀⠰⢿⣤⠴⠶⠛
⠀⠀⠈⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠁⠀⡏⠠⠎⢻⠁⠀⡶⠀⠈⡇⠀⠘⡆⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⡆⠀⠙⠦⠤⠾⣧⡀⠀⢀⣰⠇⠀⠀⣷⠀⠈⣩⠗⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠁⠢⣀⠀⠹⣄⠀⠀⠀⣀⡈⠉⠛⠉⣀⡄⠀⠀⣽⠖⠋⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠙⠒⠾⠷⢦⡀⠈⠉⣟⠛⡟⠉⠀⠀⠀⡇⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡖⣇⠀⠀⠀⣼⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠲⠶⠶⠖⢻⡄⠈⣧⢹⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⠿⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠠⠤⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠲⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣶⠓⠟⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢦⣤⣤⣤⣤⡤⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢰⣿⠁⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠟⠁⣴⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠋⠀⠀⠀⠀⠀⠛⡛⠛⠃⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣈⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠿⠇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡴⢾⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣇⡏⠘⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡀⢸⠛⣦⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠷⣿⡴⠏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣀⠀⠀⠐⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦
⠀⣤⠖⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡞
⠘⢧⠾⠻⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷
⠀⠀⠀⠀⠀⠹⣆⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢧
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠉⠓⠒⠒⠒⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠤⠀⢀⡴⠃⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡷⣄⣀⣀⣠⣤⠶⠭⣀⡠⠒⠀⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢋⣉⢳⠀⠀⡸⠓⠒⣲⡞⢑⡒⠐⢆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⣤⠀⠈⡇⠰⠄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠋⠈⠉⠀⠀⡇⠀⠀⠉⣇⡈⠀⢀⠞⠀⡀⠸⡇⠠
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠱⡀⠀⠀⣠⠗⡤⡀⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡏⠀⠀⠀⠀⠀⠘⢲⣴⣚⣉⣉⣉⠥⠔⠊⡇⢠⡇⠄
⠀⠀⠀⠄⠀⠀⠀⠻⡄⠐⢷⠬⢥⣉⣁⣀⣀⡀⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡇⠀⠀⠀⢀⠄⠀⠸⣀⢈⠀⠀⢀⣀⠠⢾⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⣄⣀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⢹⠉⠉⢉⠀⠀⠐⠉⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡼⠳⢤⣀⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⡟⠉⠉⠉⢻⠈⠉⢻⠀⠀⢀⡤⠒⠒⠺⣅⠀⣀⣈⣉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠐⠀⠀⠸⠋⠀⢀⠈⠱⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⢸⢀⠀⠘⢄⡀⠀⣀⣧⠀⠀⠀⠀⢠⠃⢠⠏⠀⠑⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠣⣀⠀⠀⠀⡠⠎⠈⠀⠀⠀⠈⣹⡁⠀⠑⠦⠤⠒⣁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠉⠉⢉⣀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢿⡿⠿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢠⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠸⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠚⠁

⠋⠀⠬⠘⠀⠀⠀⠀⠀⠁⠀⠀⢰⠂⡀⠀⠀⠀⠊⠀⠀⠀⠉⠀⠀⠁⠀⠁⠈⠈⠀⢈⠉⠀⠀⢮⣭⡷⠂⠀⠀⠈
⠏⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠨⡀⠆⠀⠀⠀⠀⠤⢀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁
⠀⠀⣀⡔⢒⠙⠛⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣀⠂⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⣠⠂⡸⠂⠀⠰
⠁⠀⠈⢁⡉⠀⢬⠀⡀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠘⠁⠀⠀⠁⠀⠀⠸⠁⠐⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⣑⢶⣄⡀⠀⠀⠀⠀⠘⠁⠀⣀⡀⠀⠀⠀⠀⠘⡅
⠃⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠂⠀⠀⠀⠀⠀⢀⠠⠝⠛⠖⠀⣀⠀⠀⠃⢀⠀⢰⠒⢰⡄⠀⠲
⠁⠠⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠁⠀⠀⠀⠉⣈⠁⠠⡌⠁⠀⠀⠀⠂⠙⠀⠀⠁⠩⠤⠀⠀⠁
⠀⢀⡀⠀⠀⠀⡆⠀⠉⠠⠄⠈⠇⠀⣠⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠀⠠⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰
⠰⠈⠀⠀⠀⠀⣁⠀⠀⠀⠀⢱⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠋⠙⢠⠁⢐⣀⡄⠀⠀⡀
⠀⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢠⠴⣶⣧⠀⠀⠨⠁⠀⠀⠀⠂⠀⠀⠑⠘⠾⡌⠁⠙⠀⠀⠀⠋⠠⡐⠆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠖⠐⠀⠀⠠⠀⠀⠈⠙⠉⠁⠀⠀⠀⢠⠄⠀⠐⠀⠤⠄⠲⠄⠀⠀⠀⠀⢠⠆⠀⠀⠀⠡
⠲⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣛⡂⡀⠀⠀⠀⣀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠈⡀⠀⠈
⠄⠀⠠⠤⠒⠂⠀⡀⠘⠠⠐⠂⡀⠈⠁⠀⠻⢡⡗⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡅⠀⠀⠈⠀⠀⠀⢃⠀⡅⠀⠀⠀⠀⠶
⣄⠀⠳⠀⠀⠀⠙⠉⠁⠀⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡁⠀⠀⠢⠀⠀⠀⠀⠖⠆⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⠳⠀⠀⠀⢠⠁⡸⡃⠀⠀⠀⠀⠀⢠⡄⠘⠁⠀⠀⠐⠀⠀⠀⢀⣀
⠷⠃⠀⠀⣀⣤⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢲⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢲⡀⠀⠀⠀⠀⡠⡐⢰
⠀⠀⠀⠯⠽⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠑⢀⠀⠀⢀⠀⠀⠀⠀⠆⠀⣀⠀⠀⠀⠀⠈⢄⠸⠀⠀⢱⠈⠁
⠀⣶⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⠩⠡⢤⠄⡀⠀⠀⠲⠊⠁⠀⠀⠀⠉⠁⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠁
⢠⠋⠠⠂⠀⠀⠸⠸⢰⠋⠁⠀⠄⠀⠀⠰⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⢠⡄⡀⠀⡄
⡮⢄⠢⠀⣤⡴⢒⢉⣢⠖⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠎⠸⠇⠀⠈⠠⠀⡀⠐⠚⢀⣠⠀⠀⠀⠠⡌⠀⠀⠀⠁⠈⠐⠆
⠁⠁⠀⠀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠂⠛⠠⠁⠀⠈⢃⣘⠆⠀⠦⠄⠀⠀⠀⠁⠀⠀⠄
⢀⠀⠀⠀⠀⢰⠂⣢⡀⠀⠆⠀⠀⠀⠀⠀⡀⠀⡒⡒⡄⢂⠀⠀⠀⠀⠀⠀⠴⡿⠞⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⣀⠁⠀⢀⠀⠀⢈⢉⡅⠁⠀⠁⠀⡇⠀⠀⠟⢋⠄⢁⠪⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⣠⠐⠂⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢱⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢉⠀⠀⠜⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣨⠤⠉⠐⠊
⠀⠀⠀⠀⠀⢇⠂⠔⠊⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⣀⠀⠀⠀⠀⠀⠀⠀⠎⢦⣀
⠀⠀⠀⢀⡀⠊⠀⠀⠐⠣⣀⠀⠀⣀⠏⠂⠐⡦⠀⠀⠤⢊⠀⠠⣫⠀⠀⠀⠀⠀⠰⢥⢀⣐⣱⠄
⠀⠀⠀⠀⠀⠀⠱⡄⠌⠀⠉⠀⠀⠉⢢⡀⡼⠅⠀⠀⠀⠸⠎⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠉⢁⡀⠀⠀⠀⠀⠀⠉⠀⡀⠤⠄⠠⠄⡀⠀⠀⠀⢰⠲⢄⢀⣤⠆⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡰⠘⠀⠰⡄⠀⢀⠔⠁⠐⠀⠀⠀⠀⠈⢦⠀⠀⠀⠄⠀⠁⠮⢀⠀⠀⡀⠜⠀⠱⢤
⠀⠀⣀⠀⠀⠀⠈⠓⢦⠀⠀⡞⠀⠀⠆⠀⠀⢀⡠⠖⠲⠤⡀⠀⢳⠰⠧⠠⠀⡠⠄⠒⠃⠈⠑⡆⢠⡈⣘
⢀⠼⠁⠓⡖⠀⠀⠀⠸⠴⠉⠓⠀⠀⠀⠀⢀⡞⠀⣀⣀⣀⣸⠀⠀⡀⠀⠀⠢⠁⠀⠀⠀⠀⠀⠖⠈⠀⠈
⠉⢰⠐⠒⠚⢀⠔⠒⠂⠐⠒⠒⠃⠈⠁⠀⠘⠉⠉⠉⠉⠉⠉⠄⠀⠉⠓⠒⠒⠀⠀⠄⠤⠀⠀⠀⡖⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⠀⠀⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠤⠀⡀⠀⠀⠀⠀⠤⢄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀⠒⠐⢂⡉⠉⢄⠉⠐⡆⠤⣀
⠀⠀⠀⠀⠄⣄⣠⣀⣀⣀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢅⡀⠀⣤⠀⠘⣖⠀⣸⣆⡀⣸⠄⢻⠲⡀
⠀⠀⠀⢁⠚⢸⡃⡩⡆⠀⡗⠁⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⢰⠎⠉⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⡀⠈⠳⡂⠸⠒⠈⠉⠐⠀⠈⠁⠈⠑⢇⣰⠅
⠀⠀⠀⣖⣂⡯⠀⢴⡁⣨⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⢲⡀⢂⡸⠀⢘⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠅⠀⠠⠄⠀⠀⠀⠀⠐⠂⢈⠈⠋
⠀⠀⠀⢠⡠⠕⢞⡷⣿⡿⢾⡀⢨⠀⠀⠀⠀⠀⡆⢃⠡⠴⠀⠘⠾⠇⠀⠉⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠐⠂⠀⠀⠐⠀⠀⠄⠆
⠀⠀⢠⠈⠲⠆⠘⠉⠻⠛⠉⠠⢀⠠⠀⠀⠀⣜⠩⠀⠾⣀⣀⡀⠀⠀⠀⠎⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡁⢀⠀⠀⠀⠉⣿⠀⠀⡌⠱⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠇⠈⢰⡯⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂⠘⠉⢁⢈⠁⢈⢐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢄⣹⢤⠛⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠜⠁⡌⡄⠘⠈⠢⠈⢸⣄⢀⡸⠀⠀⣸⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⡅⠀⠀⡴⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢦⠀⢇⠀⡨⠤⠄⠉⠀⠀⡘⠉⠙⢀⠙⠷⠺⢍⡔⠠⢤⡀
⠀⠀⠀⠠⡎⠀⠰⠃⠀⡠⠁⠀⡴⠁⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠘⠉⠉⢃⠐⠀⠀⠡⠂⠀⠴⠂⠈⠀⠐⠀⠀⠀⠙⢦⣀⡴⠆
⠀⠀⣿⠀⠉⡒⠚⠁⠒⠓⠄⣠⠃⠀⡞⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣾⡀⢠⠄⡘⢤⣶⢀⡄⢹⢀⠜⢁⡼⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠙⡀⠘⠀⡹⠂⢠⠚⠃⠘⡧⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠁⠐⢤⢱⠈⠰⡤⠠⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⣘⠁⠀⠀⢸⡇⠀⠐⠉⠂⠖⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣌⠁⠀⠀⠀⠀⠀⠀⠐⢄⣀⡀⠀⡇⠀⠀⠀⢸⠤⠬⠿⠻⠃⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠗⠛⠛⠛⠂⠹⢻⠀⠀⠀⢸⠙⠈⠳⠚⢃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢺⠤⢮⠹⢟⣂⣀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⠀⣄⠀⠨⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⣴⠩⠗⣈⡑⢦⠈⢂⡬⡀⡎⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⠂⠈⠱⡀⠀⠀⠀⠀⠀⠅⠈⠚⠤⠝⠘⠏⠹⠀⠎⠐⠑
⠀⠀⢀⢀⠀⣁⣉⠉⠙⣏⣩⡟⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣄⡄⠀⡀⢠⡄⠀⣴⢀⢠⡄⡀⢀⡖⠲⢰⡆⠢
⠀⠀⢸⠀⠀⠉⢠⣷⣋⠉⠁⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡹⣿⠞⣋⡉⢶⠄⢉⣴⠒⣁⣤⠉⠀⠄⣊⢨⠟
⠀⠀⠀⠀⠀⠰⢸⡥⠐⠙⠿⠍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠄⠘⠆⠀⠀⡜⠀⠀⢰⠈⠘⡆⢵⢀⢰⠃⠛
⠀⢀⠀⠀⠠⠀⠉⠀⠈⠀⠀⠀⠀⠰⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠱⠀⡴⠀⠀⠀⠃⠀⣠⠃⠀⠐⡀⠀⢟⠃⢸⠂
⠀⠀⠂⠄⠀⠀⠀⠄⠀⠀⠀⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠰⠁⡴⠁⠀⡔⠁⣠⠀⠁⣀⠊⣼⡅⡠⠴⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⢈⢀⡃⠀⠀⠀⠀⠸⢤⡀⠀⠐⡄⢿⠂⠀⠀⠞⠭⠇⠀⠀⢐⢠
⠀⠀⠀⠀⠀⠐⠞⣮⢫⢧⡀⠀⠀⠀⢂⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠢⢀⡀⠀⠠⣄⠠⠤
⠀⠀⠀⠀⠀⠀⢠⡹⣇⣩⣆⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡄⠠⣤⠀⠀⠀⠁⠲⠦⠤⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠶⠇⢠⠀⠀⡀⠀⠀⠀⠀⠉⠰⠬⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠸⠒⠒⠚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠀⠀⠀⠀⠆⠐⢢⡀⠀⡀⠈⢲⠑⢲⣀⡐⠁
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⡀⣠⠔⠀⠀⢠⠞⠁⠀⠀⠀⣀⠔⠚⠓⢲⣷⡀⡉⠫⢿⣤⡧⠉⣹
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⢠⠟⠘⠁⠀⠀⠆⠀⠀⣰⣦⣆⣿⣿⣿⣠⣴⣿⣤⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠴⣴⣻⠖⠁⠀⠀⢟⣃⠈⠀⠀⠀⠀⢶⣶⣿⠿⠛⠋⠉⠙⠛⠛⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠠⢀⣈⣥⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠚⠻⣦⣀⡀⠀⠀⢀⣄⣹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢱⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢉⠀⠀⠜⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣨⠴⠋⠐⠊
⠀⠀⠀⠀⠀⢇⠀⠔⠈⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⣀⠀⠀⠀⠀⠀⠀⢀⠎⢦⣀
⠀⠀⠀⢀⡀⠊⠀⠀⠐⠧⣀⠀⠀⣀⠏⠂⠰⡦⠀⠀⠤⢊⠀⠠⣫⠀⠀⠀⠀⠀⠰⢥⢀⣀⣱⠄
⠀⠀⠀⠀⠀⠀⠙⡄⠌⠀⠉⠀⠀⠉⢲⡀⡼⠅⠀⠀⠀⠸⠊⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠉⠀⡀⠤⠤⠠⠄⡀⠀⠀⠀⢰⠒⢄⢀⣤⠆⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠰⠘⠀⠰⡄⠀⢀⠔⠁⠐⠀⠀⠀⠀⠉⢦⠀⠀⢀⠄⠀⠁⠮⢀⠀⠀⡀⠜⠀⠱⢤
⠀⠀⣀⠀⠀⠀⠈⠓⢦⠀⢀⡎⠀⠀⠆⠀⠀⢀⡤⠖⠒⠤⡀⠀⢳⠰⠧⠠⠀⡤⠄⠒⠃⠈⠑⡆⢠⣌⣈
⠀⠘⠁⠓⣖⠀⠀⠀⠸⠴⠉⠛⠀⠀⠀⠀⢀⡞⢀⣀⣀⣀⣸⠀⠀⡀⠀⠀⠢⠁⠀⠀⠀⠀⠀⠒⠉⠀⠈
⠉⢰⠔⠒⠚⢀⠔⠒⠀⠒⠒⠒⠃⠈⠁⠀⠘⠉⠉⠉⠉⠉⠉⠄⠀⠁⠓⠒⠒⠂⠀⠠⠤⠀⠀⠀⠖⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢨⠀⡀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⢈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠋⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⢿⠿⢿⣶⣶⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡇⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢤⣬⣭⠤⠶⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⢠⣤⣀⣤⡄⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣄⣀⣉⣠⣄⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⡇⠀⠀⠀⠀⣈⣉⣩⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠟⠀⠀⠀⠀⠈⠉⣉⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠘⠉⠉⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡀⠀⠀⠀⠀⠀⠒⠛⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣼⠃⠀⠀⠀⠀⣘⣋⣉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⢀⣀⣩⣭⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⡏⠀⠀⠀⠀⢈⣉⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⡟⠀⠀⠀⠀⠀⢬⠍⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⣠⠏⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⠁⠰⠋⠀⠀⠀⠛⠓⠚⢒⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⣀⣘⣛⣛⣓⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠤⣤⣉⡉⣩⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠶⢦⣤⣤⣠⣤⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢀⣀⣀⠙⠛⠶⠦⣴⣾⡿⠋
⠀⠀⠀⠀⣀⣠⣶⠿⠋⢀⡀⠴⢤⣀⣉⣉⣙⣛⣿⣿⠟⠁
⣀⣤⣾⡿⠟⠋⠁⠠⣤⣀⠙⢻⣶⣤⣽⣿⠿⠛⠋⠁
⠛⠻⠿⣶⣶⣴⣿⣿⣿⣿⡿⠿⠛⠛⠉
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠁⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⢦⣀
⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣤⣶⣶⣾⠯⠟⠓⠒⠒⠒⣂⡈⢳
⠀⢸⢇⠀⠀⠀⠀⢀⡠⠔⣒⠭⠕⢒⣉⠽⣿⣿⣿⣿⣍⣉⠩⠭⠭⠤⠤⠌⡷⣄
⠀⠈⢎⢣⡀⠀⠀⣿⡈⠩⠴⠒⣉⣩⠤⠒⢊⣻⣿⣿⣿⡶⠒⠒⢒⡒⣒⠊⢹⠈⠣⡀
⠀⠀⠈⢣⡱⡄⠀⢰⠈⠓⠢⠬⠥⠒⠒⢩⡍⢸⣿⣿⠿⣇⠀⢈⠥⠭⣍⢁⣼⣄⡀⠈⠢⡀
⠀⠀⠀⠀⠱⡜⢆⠸⡀⠐⠒⠒⠀⠀⠀⢀⣠⡚⢻⠀⠀⠀⣟⣇⠀⠀⢈⡇⠀⠀⢸⠉⠙⢿⢦
⠀⠀⠀⠀⠀⠘⢎⢣⣧⡀⠀⠀⠤⠆⢰⠁⢠⠝⠚⠢⣤⡞⠉⠈⣷⠊⠉⠳⣶⠖⠋⠳⣄⡸⠉⡗⢄
⠀⠀⠀⠀⠀⠀⠈⢢⠱⡉⠓⠒⠒⠚⣿⣦⣧⣀⠀⠀⣸⢳⡤⠤⠻⣀⠀⣠⢧⣀⣀⣴⣿⣤⣶⡇⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡙⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⢛⡿⣟⠓⠒⠒⠤⢤⣈⢦⣤⣤⡤⢒⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠳⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢡⠖⢉⡥⣀⠉⠲⠼⠃⢸⠀⠀⠀⠀⠀⠈⣗⣉⠶⣍⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡑⣄⠉⠛⠻⠿⣻⠟⢋⢄⠀⠀⢸⢀⠋⠀⠀⠉⠑⢒⣒⣁⠀⠀⠀⣀⣀⣀⢟⠛⠛⠋⢟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⢆⠀⡴⠋⠀⠀⠸⣌⠲⠤⠞⣸⠀⢀⡠⠔⠊⠉⢀⠀⠀⠀⠀⠀⢀⠀⠘⡄⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢣⣧⠀⠀⠀⠀⠈⠉⣛⡩⠕⠚⠉⠀⠰⠒⠒⠉⠁⠀⠀⠀⢠⠋⠀⢰⠁⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠹⡗⠤⠤⠔⢒⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣠⠔⠁⠀⠀⠀⢀⣠⠤⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⢾⡄⠀⠈⠙⠓⠀⠀⠀⠀⣀⣀⣤⠤⠤⠖⠒⠉⠉⠀⠀⠀⣀⡤⠖⠊⠁⣀⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢫⡳⠤⠴⠖⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⢀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⢆⠀⠀⠀⣀⡠⠔⠚⠉⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢳⠒⠉⠁⣀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠤⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲
⠀⠀⠀⠀⠀⠀⢰⣦⣻⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢧⣀⣀⣻⡶⠆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠫⡀⠀⢀⣁⠠
⠀⠀⠀⠀⢰⣻⣻⣿⣿⣯⣻⣿⣿⣟⡀⠀⠀⠀⠀⢠⣬⣤⣄⠐⢌⠻⢇⡀⠀⣄⠀⠀⠀⠀⢠⠬⠤⢌⠙⢦⡳⠄⣀⠂⠠
⠀⠀⠀⢀⣿⣿⣿⣷⡻⣿⣟⣿⣿⠿⣧⠀⠀⠀⠀⠿⠑⠾⣽⣷⡀⠁⢤⣤⣶⡟⢢⠀⠀⠀⠠⣀⣀⡀⠱⣄⠑⠤⠀⢐⣁⠑⡄
⠀⠀⠀⣼⣿⣿⣿⣮⡙⣾⣿⣿⣿⣟⣫⡄⠀⠀⠐⢁⣀⡀⠙⢿⣿⣦⣄⣀⣉⣤⡏⠀⠀⠐⢁⣀⡀⠉⠳⣌⠓⠄⢀⣉⡠⠞⡄
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⡿⠁⠀⠀⠀⠿⠛⠛⢷⣤⣙⠻⡛⠛⠛⣋⡄⠀⠀⠀⢠⠀⡀⢀⠀⠈⠣⢄⠀⢀⢀⡴⠃
⠀⠀⠀⠀⠸⠉⠉⠀⠀⠉⡩⠌⠉⠀⠀⠀⠀⠀⠀⠀⣿⢺⢶⠏⡿⣿⠩⡆⡭⠼⠀⠀⠀⠀⠀⠹⠀⠀⠉⠀⢁⠄⠃
⠀⠀⠀⠀⠀⠁⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣽⣹⡗⣿⣸⣃⣃⠃⠀⠀⠀⠀⠀⠀⡄⠀⢀⠰⠈
⠀⠀⠀⠀⠀⠘⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡷⣺⢗⡇⡾⢰⠒⠀⠀⠀⠀⠀⠀⠀⠐⠠⠐⠃
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⡯⣸⣯⣏⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣑⡓⡾⠲⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⡏⣛⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠧⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⢫⣵⢤⣤⣤⣤⣤⠀⣠⣬⡙⠿⢀⠙⠿⣷⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠀⠀⣀⠐⠟⠁⠀⢠⠊⠁⠀⠀⠡⣀⣀⣸⡿⠀⢠⣤⠈⠉⠀⠀⠀⠈⠨⢀⢁
⠀⡝⢟⣿⢵⣿⣿⣿⣿⣷⡶⠀⠀⢰⣄⠘⠃⠍⠑⡀⠈⠇⠀⠀⠀⠀⢤⠀⠁⢀⠇⠀⡩⠤⠄⠄⠀⢀⠠⠀⠸⢦⠀⠈⣉⠉⠀⢠⣶⠿
⢦⣀⣀⠈⠙⠇⢻⣷⠈⣿⣿⡦⠀⠀⢑⡙⠄⠸⡀⠀⠀⠀⠀⢀⠀⠀⡈⠃⢠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡐⢒⠉⠀⣀
⠻⠿⠟⠁⠀⣀⠀⠈⠀⠙⢋⠀⠶⠀⠈⢴⣤⠄⣀⣈⠀⠐⣤⡀⠀⡼⢇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢠⠘⢇⣴⡀
⢀⡆⠰⡄⠺⠿⢣⠀⠀⠀⠘⠁⠀⠀⢴⡄⠙⣀⣴⠋⠀⠀⠹⣤⣶⣤⣮⠤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠑⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣡⠆⠚⠛⣦⢾⣿⣿⡛⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⢯⠿⣦⣀⡠⠤⠄⠀⠀⠀⠀⠀⠀⣠⣾
⣶⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠞⠫⠰⠀⠚⠋⠈⣿⡿⠁⠲⠷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣽⡿⢷⣿⢋⣠⡤⡠⠀⢤⡶⠄⣀⣴⣿⢋
⡧⣷⣞⡷⠀⠀⠀⠀⠀⠠⠀⣸⣿⡆⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠂⠀⠁⠀⠀⡀⡈⠙⠋⠁⠈⠛⠀⠀⠘⠉⠀⠈⠉⠉⠀⢸
⠛⠚⠋⢀⣀⣠⣤⠶⠆⠁⠀⢈⢉⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣶⣾⡇⠀⣤⡀
⠚⠛⠛⠛⠉⠁⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠉⠀⢠⣽⠗
⠀⠰⠂⣀⡴⠟⠉⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠃⠀⠀⠀⠉⠢⠀⠀⠀⠈⠁
⠀⠒⠛⠉⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠈⢻⠓⢄⡛⠁⠐⠒
⠰⠵⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⢀⡐⣷⠄⠒⠲⠈⡆⠀⠉⢀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣦⠉⠀⠀⠀⠀⠀⠀⠔⠂⢀⣈⣿⣿⣤⣿⣿⢷⣟⢷⢛⠁⠀⢠⠃⡀
⠀⠀⠒⠰⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠚⠀⡀⠀⣄⠀⣠⣽⣿⢋⣽⡿⢾⠏⠋⠁⠘⣠⢀⠠⠂⠀⠀⠁⠀⠰⠆⠐
⠀⠂⠀⠀⠘⠒⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⠀⠀⡈⠆⠙⠻⠟⡘⠋⠁⠀⠀⠐⢾⣶⡷
⠒⠀⠀⠀⠀⠀⠰⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠠⠖⠂⠀⠀⠷⠀⡰⣧⠀⠀⢀⡀⠀⠀⠉⠀⠀⠠
⠀⠀⣉⣀⡀⢀⣤⡄⠈⠁⠀⠀⠀⠲⠶⠤⠰⢂⠀⠀⠠⡤⠀⠀⠠⣤⠆⠀⠀⠀⣤⣀⠀⠀⠀⠐⢶⠶⢤⣇⣤⣔⣨⠟⠀⢆⡀⢧
⣿⣿⢿⣿⣷⣿⣽⣶⡖⠀⠧⡀⠇⢀⡈⠑⠚⠁⠀⠚⠀⠀⠐⠈⠢⡀⠀⠀⠀⠢⠛⠛⠀⡯⢸⡆⢀⠔⠚⣿⣿⣿⣁⣤⣄⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡠
⠚⠙⠽⣟⢿⣷⡌⣿⣿⡗⠀⠀⠀⠈⠘⠐⣶⣄⣠⠞⠀⠀⡄⠈⢢⢑⡄⠀⢠⡄⠐⠂⠀⢤⡍⠐⠛⠓⠈⣿⣟⠏⢿⡌⠁⠐⡦⠀⠀⠀⠐⠦⢤⣤⡴⠶⠚⣁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠆⠙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⢀⡠⠚⣩⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢋⣡⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠓⢀⢐⡉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠵⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣴⠁⣀⠔⠈
⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠠⠴⠞⠋⠀⠀⠀⠀⠀⠀⢀⣒⣼⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠇⠿⠇⠟⠁⠀⠀⠀⠀⠀⠀⢠⡠⠀⣐⡤⠤⡂⠀⠀⠀⠀⠀⢀⠀⣀⡀⡀⣀
⠀⠀⠘⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢌⣐⠀⠀⠀⠁⣈⠀⠀⠀⠀⠰⠈⠀⠁⠀⠁⠀⠁⠐⠦⢀
⠀⠀⠀⠀⠢⡀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠚⣻⠧⡀⠀⠀⣈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⢣⡌⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣯⠏⠁⡀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠁⠨⣯⣆⠹⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⡆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠹⣧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠙⢿⣾⣆⢄⢀⠀⠠⠖⠂⠈⠀⠀⠀⠀⠰⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⡠⠈⠛⠣⣂⣀
⠀⠀⠀⠀⠀⠄⠐⠁⠁⠐⠆⡀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⢿⣷⡀⠀⠀⠀⠀⢠⠀⠠⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠤⣀⠀⠈⠉⡁⡀⣀⣹⠀⠀⠀⠰⠇⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠩⠈⡅⠱⠀⠀⠀⠀⠀⠀⠰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠀⠀⠀⠠⠠⠧⠚
⠀⠀⠀⠀⠀⣰⠤⠀⠀⠀⠀⠀⠀⢰⣰⡶⠄⠁
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡈⠒⠄⢶⣦
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡁⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠒⠾⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⡠⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠉⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠑⢄⣀⠀⢀⠀⠀⢠⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡆⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⡄
⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠘⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢹⡄⢷⡀⠀⠀⣀⡀⠀⠀⠀⠻⠀⠀⡴⠳
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠓⠤⠜⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠈⢧⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⢧⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠇⠛⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⡇⡀⠀⠈⢟⠉⠀⠀⠀⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⢀⢀⣉⣐⣀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⣠⣤⣤⣬⣤⡤⠤⠤⠤⠤⠀⠁⠳⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠉⠒⠒⠦⠤⡄⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠐⠒⠒⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣾⠀⠀⠈⢰⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⠃⠀⠀⠤⠤⠐⠊⠀⠀⠀⠀⠀⡰⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠐⢤⣀⡀⠈⢳⣇⠀⣀⡠⠋⠀⠀⡀⢤⡀⠀⣿
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣷⠀⠀⣄⠀⠀⠀⠀⠀⠀⠉⠀⠉⠘⠉⠁⠀⡀⠈⠉⠁⠀⢻⠀⣿
⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠱⣄⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠤⠤⢬⣍⣁⠂⠀⠀⠀⠀⠀⢟⠀⣀⣀⡤⣔⣒⣪⠭⠓⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡤⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠗⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠰⠲⠶⠛⠋⠉⠉⠉⠉⠀⠙⡆⠀⠀⢸
⠀⠀⠀⠀⠀⣧⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⣿⠀⢰⠇⠀⠀⠄⣠⣴⣶⣶⣦⡄⢀⠶⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠐⠦⡄⠁⠀⠀⠀⠀⠀⣠⣤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⣾⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣦⣕⣄⠀⠀⠀⡇⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⢹⠀⠀⠀⠘⢈⢻⣟⢿⣋⣿⣿⣿⣿⠀⠀⠀⠇⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢸⡇
⠀⠀⠀⠀⠀⢺⠀⠘⣇⠀⠙⠲⡄⠐⠹⠧⣈⣽⣯⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⣡⡇⠀⢸⡇
⠀⠀⠀⠀⠀⡏⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠈⠭⠔⠁⢀⡤⠀⠀⠐⠀⠤⠀⠀⢀⡒⣂⣀⣀⣉⣭⠥⠤⠴⠒⠛⠉⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠀⢀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⣀⣀⣀⣤⡤⠤⠤⠤⠤⠤⠬⠶⢤⡤⠤⠤⠤⡤⠤⠤⠤⠴⠖⠒⠋⠛
⠀⠀⠀⠀⠉⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⡠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⡤⠄⠀⢀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡠⠊⢉⢠⡄⣀⠔⠁⠀⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⡶⠿⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢠⣤⢴⡾⣿⠶⠚⠛⠶⣶⣤⣄⣀⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⡴⢋⠔⠁⠀⣰⠤⠿⠛⠛⠛⠛⠛⠓⠒⠛⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⠟⠡⠃⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠠⣊⠔⠁
⠀⠀⠈

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

⠼⣆⣄⣿⣿⣿⡏⣿⣽⣿⣿⣿⣷⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿
⢀⣿⣹⣿⣿⣿⣿⣿⣿⣿⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣸⠃⢹⣿⣿⣿⣿⣿⣿⣏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿
⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⢋⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠟⠛⣛⡛⠻⢿⣿⣿⣿⣿⣿⣯
⠏⣿⣿⣿⣿⣿⣿⣿⣾⣇⣠⣤⣶⣾⣷⣦⣤⡀⣀⣀⣀⣀⣀⠔⢋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿
⠀⣿⣿⣿⣿⣿⣿⣿⠿⣋⣩⣭⣤⣬⡉⠛⣿⣿⣏⢀⣀⡹⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠀⣹⣿⠉⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿
⣸⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⡀⡹⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿
⢾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⠃⣿⣿⡿⠷⢿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿
⠼⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⠄⣼⣿⣿⣴⣤⣾⣿⣿⣷⣭⣝⣻⣿⢋⣩⡴⠿⣿⣿⣿⣿⣿
⠠⣶⣿⣄⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠟⣃⣼⣿⣿⣿⣿⣿⣿⠟⣿⣿⠏⠈⢈⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠁⡟⢱⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⡶⣾⠿⠛⢷⡿⠇⠈⠉⢉⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠰⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⢀⣠⣬⣽⣶⣦⣤⡀⠀⢸⡇⠀⠀⠀⣺⣿⣿⣿⣿⣿
⠀⠀⠎⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⣰⣿⣿⠿⠿⠛⣛⣿⣿⣷⣸⡇⠀⠀⠀⡼⣿⣿⣿⣿⡿
⠀⠀⠀⠈⢿⣿⡹⢟⠛⣿⣿⣿⣿⣧⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⣰⣿⠿⣿⡟
⠀⠀⠀⠀⢠⠿⢀⡤⠈⠉⡿⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⠛⠁⢸⡇⢀⡀⣨⣾⡏⠉⠀⠸⡗
⠀⡀⠀⠱⣤⡀⣴⠀⠀⠀⣥⣟⠈⠻⣿⣶⣤⣄⠀⠀⠀⣴⠛⠛⠉⠀⠀⠀⢸⡇⣩⣾⣿⣽⠁⠀⠀⠀⠐
⠔⠀⠀⢆⣼⣿⣿⠀⠀⢰⣿⣿⣷⣶⡾⠿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⡀⣀⣼⣷⣿⠋⠟⠁
⠀⠀⠀⣼⣿⣿⠏⣀⡀⣼⡿⡿⢻⣿⡇⠀⠈⣿⣿⣿⣯⣄⣀⣀⣠⣴⣾⣿⢿⡏⠁⠀⠀⣾⡀
⠀⠀⠀⣿⠛⠈⣾⣿⣿⡏⠀⣧⣼⡿⣷⠀⠀⠘⠟⠉⠛⣿⣿⣯⣥⠠⠞⠁⢸⡇⠀⠀⢀⣿⣷⣀⡀
⠀⠀⠀⠀⠤⠺⣿⣿⠏⠀⠀⣿⢿⣤⢽⡀⣾⣾⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣿⣿⣿⡟⢂
⠀⠀⠀⠀⠠⠂⡜⣡⣶⡄⠉⣿⠪⢤⣼⡿⣿⡷⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⢰⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⡿⡡⠋⣿⠀⠈⠛⢀⡙⠁⠀⠀⢰⣤⡄⠀⠀⠀⢀⣿⢻⡇⠠⠀⠸⣿⠿⣷⣞⠳⠄
⢉⡉⠛⠉⢙⡒⠟⢋⣀⣠⣴⣿⣴⣶⣾⣿⡿⢿⣷⣛⢋⡉⠀⠀⠀⠀⣈⡁⢸⣇⣴⣶⠞⠋⣀⠿⡛⣿⣤
⣦⣷⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧⣿⣿⣿⣷⣄⠀⠀⠀⣹⣿⣿⢾⣿⣟⣿⣶⡀⢇⢸⣿⡏⢻
⢿⣿⣿⣾⣿⣿⡿⣿⡟⣉⢻⣿⢹⣿⡛⠹⣛⣯⣽⣿⣿⡿⠀⠀⢆⣹⣿⡿⢿⣿⣧⣧⣘⡿⣦⠺⣿⣿⣿
⡸⠙⢘⣿⣟⣿⡿⣟⣷⡿⢸⡿⣸⣿⡿⠰⣶⣿⣿⣏⡁⠀⠀⠀⣾⣿⡷⢶⣿⣿⣿⡋⠘⢿⡿⠛⠛⠛⠛
⠁⠀⣿⣧⡬⣿⣿⣾⠉⠛⠺⣏⢹⣧⢴⣿⣿⣿⣯⣅⣿⣾⣆⠰⠽⣿⣿⡔⠿⡿⢿⡿⣾⣷⡶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣠⠀⡀
⠀⠀⠀⠀⠀⢀⡠⣴⣿⣷⣶⣄⢀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⢷⣶⣧⣼⡀⢠⠆
⠀⠀⠀⠀⠔⠃⠀⠀⢸⠋⢹⡿⣿⣷⣄⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿⢸⡏⢹⡟⢻⣦⡾⠂
⠀⠀⠀⠀⠤⠒⠒⠤⢤⣀⠸⣇⣿⣿⣿⣷⡀⠀⢸⡀⠀⠀⠀⠀⠀⠐⠁⠰⠃⡼⢃⣠⠇⣺⡷⡿⠚⠯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣿⣿⣿⣿⣿⣷⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠿⣄⣁⣦⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠟⠃
⠀⠀⠀⠀⠀⢀⣤⠤⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⣴⣾⣷⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⢤⣀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠀⢰⣿⢯⣾⢻⣷⣤⣄⣀
⠀⠀⠀⠀⠈⢓⡦⣴⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸⣷⣿⣖⣿⣿⣿⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡗⣤⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡠⠔⠢⡄⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠁⠱⡀⠀⠀⠉⠀⠀⢀⡜⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⣀⠀⠀⠱⡦⠦⣀⠀⣠⠎⠠⣇⡀⢀⠠⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⢀⡠⠔⠈⠀⠀⢀⡀⡖⢼⠄⠁⠀⠀⢣⠀⠈⠻⣄⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢐⠈⠀⢀⡀⠀⠀⢐⠐⠬⠈⠁⠀⠀⠀⣀⠤⠃⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢃⠀⠘⠑⡢⠀⠈⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢆⠀⠈⠁⢀⡠⠔⠈⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⢦⠄⠺⠁⠀⠀⠀⠀⠀⢀⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠤⢄⣀⣀⠆⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠧⠤⠒⠒⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠒⠒⠐⠒⠂⠈⠀⠀⠉⠁⠐⠒⠒⠂⠁

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢈⣙⠻⢦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣶⣟⣉⣈⣭⣿⣿⣿⣿⣯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠟⠉⢭⣽⣿⣿⣿⣿⣿⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠐⣺⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣯⠁⠀⠀⢤⣼⣿⣿⣿⣿⡭⠪⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⢒⠺⢿⣿⣿⡋⠐⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⡀⣸⣿⣿⠿⡉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠈⣙⣿⡿⠓⠚⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣀⣂⣈⡉⠉⠁⠀⠀⢴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣴⣿⡿⠇⣠⠄⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⢀⣤⡾⠃⠀⣠⣴⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣀⣤⣶⡿⠟⣡⣶⣿⣿⠏⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⢀⣾⡿⠛⢉⣐⣿⣿⣿⠿⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠚⠉⠀⠀⢀⣤⠞⠋⠀⣀⣼⣿⣿⣿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠖⠒⠋⠉⠀⠀⠀⢀⣠⣤⡤⠈⠉⠀⠠⢀⣨⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣤⣾⡿⠋⠉⣀⣠⣤⣶⣶⣾⣿⣿⣿⣟⢛⣋⣀⣤⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠰⣿⣏⠠⠚⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

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

⠀⠀⠀⠀⠀⢀⣰⡦⢀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢀⣀⡠⠄⠀⢐⡀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠂⠋⠈⠀⢸⢑⠀⠀⠄⠐⠂⢀⠄⠀⠄⠀⠘⠁⠀⠴⠀⠠⠄⠀⠩⠀⠀⡄⠈⠙⠆⠀⡀⠀⡶⣄⠉⠈⠀⠈⠁⠠⡐⠬⠐⠄
⠀⠀⠀⠀⡀⠀⢀⣂⠀⠠⠄⠀⠀⠠⠰⠆⠀⢐⠢⠐⡀⠀⠐⠀⠢⠒⠘⠄⠀⠀⡼⠙⢦⠀⠀⡌⠀⠄⠀⠻⠡⠼⣠⠂⠀⣀⠀⠐⠀⠀⠓
⠀⠀⠀⠀⠘⣲⠚⢎⠼⠀⡀⢀⠀⠁⡀⠀⠉⠁⡀⠀⠅⠀⠰⡄⢀⠀⢠⠀⡀⠈⡄⠀⠈⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠃
⠀⠀⠀⢀⡄⢱⡱⢈⡇⠀⡀⠀⠑⠄⠈⠀⠀⠀⡀⠔⠀⠠⠀⢀⠀⠀⠈⠀⡅⠀⠈⢄⠄⠀⠀⠁⠁⠀⠊⠀⠀⠐⠐⠠⠁⠀⠀⠂⠇⠀⡀
⠀⠀⠀⠀⠂⠈⡷⡈⠀⠀⢸⢖⠒⠀⠀⡤⠀⠀⠀⠄⢐⠒⠀⠠⠀⠀⠀⠀⠀⠠⠀⢂⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠃
⠀⠀⠀⠀⠐⠀⠶⡏⢀⣀⠀⠈⢀⠠⠩⠉⠀⠴⠆⡀⠈⠈⠁⠠⠂⠀⠞⠟⠀⠈⡐⡀⠎⠀⠈⠑⠀⠈⠀⢃⠀⠲⡀⠀⡌⠂⢀⠀⠸⠆
⠀⠀⠀⠐⠘⠀⠘⠀⠈⣁⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠈⠁⢁⠀⠀⠀⠀⢀⠀⠐⠀⠀⡷⠏⡉⡉⠉⠆⠀⠙⠠⠄⠀⢨⠀⠀⢡⠀⠸⠂
⠀⠀⠀⢀⠁⡰⠈⠄⠀⠀⠠⢂⠀⠲⠀⠰⠐⡄⢢⠘⠐⠀⠀⠀⡄⠀⢀⠀⠠⠀⢀⠀⠐⣖⡀⠀⠀⠀⠐⡚⠀⠄⠀⢀⡀⢀⣀⡀⠡⠀⠆
⠀⠀⠀⢠⠀⠐⠒⠄⠀⠀⠘⠁⣀⣤⢄⠀⠀⡀⡀⠀⠁⠺⠀⠀⠀⠨⠈⠁⠁⢰⡺⠀⠀⠈⠀⠀⠀⠉⠀⠁⠀⢰⠤⠈⠀⢴⣿⣦⢀⠀⠄
⠀⠀⠀⠀⡤⠀⠀⠤⠀⠠⠀⢸⡁⠀⠀⠃⠐⠓⠓⠂⠀⠀⠛⠀⠀⠬⠾⠤⠀⠈⣀⡀⠀⠀⠈⢀⠄⠐⠀⠘⠀⠰⠈⠀⠠⠀⠉⠀⠄⢠⡀
⠀⠀⠀⢀⠑⠄⠀⠀⠀⠐⠁⠀⠁⠄⠔⠀⡶⠇⠀⢾⣼⡭⠄⠐⠀⣀⡄⠀⡀⠐⠷⠏⠀⠀⠠⠀⠀⠀⠠⠀⠀⣠⣀⠀⠀⢀⢴⠦⠀⠩⠁
⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⢰⡆⠀⡀⠔⠂⠐⠢⣄⠀⠘⠷⠀⡰⠋⠀⠀⠀⠌⠀⠀⠀⠀⠀⢄⡀⣄⠀⠀⠀⣈⣤⠊⠀⠀⠄⠉⠀⢀⡦
⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⣄⠀⡀⠁⠀⠠⠀⡀⠈⠑⠀⠀⢰⢀⠀⢃⢈⠀⠆⠐⠀⠄⠀⢒⡀⠉⠈⡀⠀⠀⡈⠉⢁⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⢀⠀⣆⠀⠀⠈⠂⠉⠀⠀⠀⠀⠀⢄⡂⠀⡀⠀⢠⠇⠀⠀⠐⠀⠀⠀⠀⠖⢄⠀⠵⠀⠀⢀⠢⠀⠀⢀⡎⠃
⠀⠀⠀⠈⠀⠌⠀⠃⠀⠀⢨⠀⠐⣄⠢⠄⠀⠀⡠⠀⠀⠈⠁⠀⠈⠀⠘⠀⠁⣀⠀⠘⢄⠰⡀⠀⠠⠀⢲⠀⢠⡄⠀⡀⠁⠃⠄⠈⠁
⠀⠀⠀⠘⠃⠀⠀⠋⠀⡄⠀⡠⠄⠀⠉⠀⠀⠀⢀⠴⡆⠐⡖⡞⠃⠂⡄⢠⠀⠀⡀⠀⡀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠡⡑⠒⠂⠁⠀⠐⠈⠂
⠀⠀⠀⢀⠒⠀⠒⠈⠁⠀⠀⢤⡠⠓⠒⠂⠐⡀⠸⡤⠀⢀⡁⠀⡉⠉⠁⠊⠠⠀⡁⠀⢢⡆⠠⢴⡀⠀⠀⡔⣰⠆⠀⠀⠁⠀⡔⠀⠁⢀⡀
⠀⠀⠀⠠⠀⠀⢀⠅⠤⡒⠄⠀⠀⣀⡀⠀⠀⡋⠢⠀⠀⠘⠀⠠⡍⢐⠀⠀⠈⠐⠁⠀⠌⠁⠀⠱⠜⢆⠀⠠⠀⠄⠀⢀⡄⠀⠡⠤⡀⠈
⠀⠀⠀⠰⠈⠈⠁⠀⠀⠡⠔⠂⠀⠉⠀⠠⢶⠈⠛⣀⣔⣢⡤⠀⠀⠈⡄⠀⠃⠀⠠⠄⠠⠄⠀⢀⠀⠊⠀⠀⣖⠆⣀⢤⠀⠀⠀⠠⠁⠘
⠀⠀⠀⠀⢨⢯⣿⣟⣏⣿⣡⣷⣶⣲⡆⠰⠊⠀⠚⠀⠀⡁⠀⠀⠀⠀⠓⠀⠀⠸⠊⠊⠢⠁⠐⣀⠃⠀⣀⠀⠈⠀⢼⢨⠐⠄⢀⠰⣷⣌⠁
⠀⠀⠀⢀⣀⡖⢻⣶⣷⠶⣾⣭⣿⣽⣣⠀⠀⠀⢘⠀⠀⠈⠀⠐⠃⠀⠉⠀⠀⠘⠀⠀⠀⠀⠒⢠⠁⠀⠂⠀⠀⢚⠮⡇⠌⠀⢀⠢⠡⠫⠓
⠀⠀⠀⠸⠤⠇⠸⡥⠯⠬⠽⠾⠷⠾⡕⠀⠙⠃⠈⠀⠀⠀⠀⠘⠀⠱⠨⠆⠀⠰⠠⠤⠤⠁⣀⣊⠀⠀⠀⠘⠆⠀⠉⠈⠀⠘⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣠⡟⢡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡋⠉⠛⠛⠋⠉⠉⠳⣄⠀⠀⣴⠏⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣉⣤⠶
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠛⠛⠋⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⢁⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⣡⡴⠟⠉
⠀⠀⠀⢀⣠⣤⢶⣿⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠀⠀⣰⠟⣰⡟⠉⠙⠛⢶⡄⠀⠀⠀⠀⠀⢀⣠⡶⠛⣉⣤⠾⠋⠁
⠀⢀⡴⠛⣁⣤⠾⣗⠶⠀⠀⣤⠶⠄⠀⠀⠀⠀⠿⠀⠀⢀⡾⢋⣼⠋⠀⠀⠀⠀⠀⡿⠳⣦⣀⣴⠞⢋⣡⡴⠛⠉
⣰⡏⣠⡾⢯⡜⠓⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣡⡿⠁⠀⠀⠀⣀⠀⢘⣻⡶⠟⣉⣴⠞⠋⠁
⣿⠀⣿⣹⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⠏⠀⠀⠀⠀⣀⣼⠷⢋⣥⡶⢻⡏⢸⡇
⢻⣦⡟⠷⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣠⡴⠞⣩⡴⠞⠋⠁⠀⢸⡇⢸⡇
⠈⣿⣿⣗⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣥⠶⠛⠉⠀⠀⠀⠀⠀⢈⣹⣿⠁
⠀⠘⣿⡙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⣿⠃
⠀⠀⠘⢷⡝⠶⠍⠛⠻⠶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣶⠶⠟⠛⠉⠀⣼⠏
⠀⠀⠀⠈⠻⣾⠛⠦⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠙⠷⣝⡛⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣭⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢦⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢼⣿⡧⠄⠀⠐⠊⠃
⠀⠀⠀⠠⣒⣁⠰⠃⢀⡠⠄⠀⠀⠀⠀⠀⠀⠄⠀⠸⣿⣇⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠆⠀⢤⡀
⠀⠀⠀⠀⠋⠈⠉⠁⠲⢄⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⡎⣿⣿⡀⠈⠀⠀⢪⠉⣲⡄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠻⣿⣧⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⡀⡀⠀⠈⠲⡏⠀⠀⠙⢿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄⠀⠀⠠⠈⡀⠀⠀⠀⠐⠂⠈
⠠⢴⠀⢰⠒⠰⠢⣀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⣾⣿⣿⣿⣷⣶⣶⣿⠃
⡲⠚⠛⠉⠐⠒⣄⠉⠒⠀⠀⠀⠈⠉⠉⠉⠁⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠠⠄⠀⠖⠠⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢠⠈⠀⡰⠁⠈⠙⠀⡀
⠀⠀⠀⠀⠀⠀⡾⢭⠹⢸⡁⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋⠉⠁⠐⠓⠠⢆⠀⠠⢐⡀
⠀⠀⠀⠀⠀⣾⢿⣕⣐⣨⣿⣿⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⣀⢤⣀⠤⠤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢳⣀⠠
⡿⠊⠀⠀⠀⠙⠷⣦⠴⠶⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⡴⡎⣀⣄⣄⣵⣬⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⢿⣷⣤⠤⠀⠀⠀⠀⠀⢀⡽⠛⠉⠉⠉⠙⠛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛
⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢾⡀⢠⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⡀⠂⣀⣀⣤⡾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠒⠂⠉⠁⠙⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢀⡀⢀⠄
⠀⠀⠄⠤⠤⠤⠤⢤⣀⣀⠀⠀⠰⠀⠀⠀⠀⠀⠺⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⠊⡁⠁⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⢀⡇⢠⡎⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠤⠶⠄⠀⠀⠀⠺⠃⠊⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣀⠀⠀⠀⢠⣦⢀⠀⡤⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣉⣉⣀⢀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⢭⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⢀⡀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠐⣯⠙⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⢢⣬⠗⠀⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⣤⣄⣁⡀⣸⣿⣿⣿⡿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⣿⣿⣿⣿⣷⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⢤⣴⣤⢦⣄⡀⠀⠀⢀⣠⡿⢧⠈⡷⣠⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⣿⡟⣾⣇⣿⢦⣍⣵⠀⢠⣿⢻⣏⠦⣈⠀⣾⣀⣉⣀⡀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠌⠑⠢⡀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⢰⠙⠋⠉⠉⠀⠀⠻⣿⣿⡀⠘⣿⣦⡉⠛⠶⢾⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⣷⣄⣑⠂⠄⠀⠀⠃⣠⡇⠀⠀⢸⡿⢿⢻⢛⣿⢿⢿⠅
⠀⠀⠀⠀⠒⠀⠀⠀⣀⠄⢱⠀⢸⣼⠃⠀⡰⠛⠛⠻⠿⣿⣿⡿⠤⠤⠄⠀⠀⠊⠂⠀⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⠀⠀⣾⡗⣚⡂⢼⣿⣼⣇
⠀⠀⠀⠀⢘⠀⠀⡈⢰⠁⡮⠀⢸⣿⠇⠀⡁⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣧⣼⣥⣤⣽⣿⣾
⠀⠀⠀⠀⠘⢀⣀⠀⡈⠈⢀⠠⠾⠋⠀⠀⠁⠠⠄⣀⠀⡈⣿⣿⣧⣀⣤⠀⠄⠊⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣽⡿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠚⣡⠠⡿⢥⣿⣿⣟⡀⠀⡲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠋⠉⠀⠂⠀⠀⠉⢿⣿⡇⠀⠀⢸⠀⠈⠀⢀⠠⣾⣿⣿⠄⠀⠎⠩⢀⡀⠙⡤
⠀⠀⠀⠀⠀⢰⠤⠴⠖⣿⣿⣿⠒⠒⠒⠒⠒⠒⠋⠛⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠘⣿⡇⠀⠀⠘⢶⠞⠁⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠘⡇⠑⢄⠂
⠀⠀⠀⠀⠀⢸⡀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⢄⠀⠀⢔⢀⠌⣼⡟⠀⠀⠀⠀⠸⡀⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⡰⠁⠘⢼⡖
⠀⠀⠀⠀⠀⠈⠓⠠⠀⠈⣿⣿⣧⣀⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠓⠀⠦⠀⠹⠿⠿⠆⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⡄⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠷⣴⢴⡡⠀⠒⠊
⠀⠀⠀⠀⠀⠀⡰⠃⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠻⡒⠀⠀⣀⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠙⣄⠀⠀⠈⠉⠁
⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠈⢦
⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠹⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠟
⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⡆⠀⠀⠀⠀⠇⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢱⠀⠀⠀⢸⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⡄⠀⠀⡎⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢣⠀⢰⠁⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⡀⡎⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣷⠟⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠄⠀⠀⠀⠀⠀⢀⢠⣴⣶⣶⣶⢶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣒⣒⢒⠒⣒⣒⣒⣒⣒⣲⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠠⠤⠴⠒⠒⣚⢒⢒⣐⣐⡇⠀⠠⠤⠤⠤⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠉⠉⠀⠐⠒⠒⠒⠒⠒⠂⠠⠬⠭⠭⠭⠭⠍⠉⣹⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠒⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣉⣛⣟⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣶⡄⠀⠀⠀⠙⠻⠿⣿⣿⣿⣶⡀⠀⠀⠙⠻⠿⢿⣿⣶⡀⠀⠀⠀⠀⢠⣾⣆⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠾⣿⡿⠄⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⠀⠀⣠⣤⠄⠀⠀⠀⠀⢀⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⣤⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠈⠙⣿⡿⢥⣄⣀⡄⠀⠀⠀⠈⢻⣿⠯⢤⡀⠀⠀⠀⠀⠈⢹⣿⠿⠿⣿⣿⡆⠀⠀⠀⠈⠙⣿⡿⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣀
⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣐⣖⡸⢶⡶⡇⠀⠀⠀⠀⠀⠀⣀⡈⠹⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠿⡿⣷⣯⣵⡆⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉


⣿⣿⢟⠿⠛⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢰⡾⠻⠛⢛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠄⣿⠀⠀⠀⠀⠀⢀⣤⡶⠶⣾⣇
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢿⡇⠀⢀⣠⡾⣿⠁⠀⠐⠋⠹⡇
⢀⣤⠶⢿⣆⠀⠀⢹⡇⠀⠀⢸⣧⣴⣟⠁⠀⢹⣆⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤
⢻⣅⠀⠀⢻⣆⠀⠘⣷⠁⠀⢾⡇⠀⠉⡈⠒⠀⠉⠛⠛⢛⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⢀
⠀⠻⣆⠀⠀⢹⣦⠀⢿⡄⢂⣸⣷⡀⠀⠈⠁⠀⡉⠉⡩⠉⢻⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠹⣧⠀⠘⢹⣧⢸⣷⠟⠉⠈⠻⢷⣤⣉⣑⣂⣁⣠⣴⠟⢷⣄⠀⠀⠀⠀⣠⡞⠁⠴⠄⠀⣠⡶⠋⠁
⠀⠀⠀⠘⣷⡄⠀⢹⡿⠁⠀⠔⠒⡄⠀⠈⡉⢍⠉⠉⠁⠀⠀⠀⠹⣦⠀⠀⣴⠏⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠈⢷⣄⡟⠀⠁⠈⠀⠀⠃⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡾⠃⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠈⢛⣿⣷⠶⣤⡀⠀⠀⢄⢀⡀⠀⠀⠂⠀⠂⠀⠈⠰⢆⣨⣿⣧⣤⣞⣿⠏
⠀⠀⠀⠀⠀⡟⠁⠙⠂⠈⣷⠶⠶⠶⢦⣄⠀⣀⣤⡴⠶⠶⠶⢶⡿⠁⠀⠸⠏⠙⣧
⠀⠀⠀⢀⣼⢿⣄⣀⣀⣴⠟⠀⠀⠀⣠⡼⠟⠉⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣠⣿⣄
⠀⠀⢰⡟⠁⠀⢈⠉⠉⠀⠠⠎⣰⡾⠋⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠻⠶⠶⠾⠋⠀⠈⢷⡄
⠀⣠⣿⠀⠀⠀⠁⠀⠱⠀⠀⣴⠏⠠⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠈⠀⣿⢶⡄
⢸⡟⢿⡐⠀⠐⠁⠀⠀⠀⢰⡏⠀⡄⠀⠀⠘⠀⠀⠀⡄⠉⠑⠀⠀⠀⠈⠀⠀⠀⠀⡁⣰⠟⢠⡗
⢸⡇⠈⠳⣄⡀⠀⠀⠈⠀⣾⠁⠒⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⢀⠀⡠⠀⠀⢀⣈⣴⠟⠋⢠⡾⠁
⠀⣻⣦⡀⠈⠛⠷⢦⣤⣄⣿⣀⣀⣀⣀⣀⣈⣀⣀⣀⣬⣠⣤⣤⡴⠶⠶⠛⠛⠉⢀⣠⡶⣿⠁
⠀⣿⠀⠙⡳⠶⣤⣤⣀⣈⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢁⣀⣀⣀⣤⣤⠶⡶⠟⠋⠁⠀⡿
⠀⣿⡄⠈⠀⠀⡠⠈⠉⠉⠉⢛⠛⠛⠛⠛⠛⡻⠛⠛⠛⠉⠙⠋⠉⠀⡠⠂⠀⠀⠀⡠⢰⡇
⠀⣿⠀⠀⡠⠊⠀⠀⠀⢀⠄⠁⠀⠀⠀⠠⠊⠀⠀⢀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠊⠀⠀⠀⢀⠐⠁⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⡠⠊⠀⠀⠀⠠⠂⠀⠀⠀⢺⡇
⠀⢸⡇⠀⠀⢀⠄⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⡠⠊⠀⠀⠀⣠⠊⠀⠀⢀⠔⠀⣸⡇
⠀⠈⣷⠀⠐⠁⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⡠⠊⠀⠀⠀⢠⠞⠁⠀⠀⠔⠁⠀⠀⣿
⠀⠀⠻⣇⡀⠀⢀⠔⠀⠀⠀⣀⠔⠀⠀⠀⡠⠈⠀⠀⠀⢀⠔⠁⠀⠀⡠⠂⠀⠀⢀⡾⠃
⠀⠀⠀⠈⠙⠷⣦⣄⡀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠁⠀⠀⠀⠊⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⢶⣶⣤⣤⣀⣠⣤⣀⣀⣤⣤⣶⡶⠶⠟⠋⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠛⠟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡔⠀⣼⣃⠀⢀⠈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠛⢅⣺⣤⣴⡿⢿⣿⠭⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⣄⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡏⠀⢠⣤⣤⣄⠀⠑⢆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠋⠉⠙⠳⣤⡴⠄⣇⠀⠈⣿⣿⣿⣷⣆⠀⠑⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢰⡈⠛⢿⣷⠀⠀⠙⠙⠛⢿⣿⣷⣄⠀⠉⠠⣀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⢘⣇⠸⠁⠀⠀⠀⠀⠀⠀⢻⣿⠿⣳⣤⡀⠈⠙⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡘⠎⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠈⠈⠻⣿⣷⣤⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⣀⣀⠀⠀⠀⠀⢀⣾⣿⣷⣦⣄⡀⠉⠑⠻⣷⠀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣴⣾⣿⣿⣿⣶⠾⣿⣽⣿⣿⣿⣿⣟⣿⣿⣷⣤⣿⠂⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠛⠿⠿⢿⣿⣦⡀⠀⠀⠸⠙⣿⣿⣿⣾⣽⡿⠏⠀⣴⣿⣇⠀⠀⢀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠄⠀⢀⡀⠉⠙⠷⣦⣴⣄⣫⣿⣿⣿⣿⠀⠀⠞⠁⠉⠉⠉⠀⠁⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠉⠙⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠶⠶⠖⠛⠛⠋⠉⠉⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣏⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠙⢷⡀⠀⢸⡇⠀⠀⠀⢀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡈⢻⡄⠈⣇⠀⢼⣁⡟⢹⡗⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⢻⠀⣿⠀⠀⠉⠀⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠶⠿⠶⠶⠶⠶⠶⠶⠾⢧⣄⡀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠞⠋⠙⠛⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢋⡤⠒⠂⢀⠀⠀⢙⡆⠀⠀⠀⠀⢀⣠⠔⠚⢉⠀⠀⠀⡉⠉⢑⠀⠀⠀⠀⢀⣤⣴⣶⣮⣍⣉⠉⠒⢤
⠀⠀⠀⠀⠀⢀⠎⣀⠈⠁⠀⢀⢀⣨⠇⠔⡊⢠⠀⠀⣠⡖⢩⠀⠀⠀⠀⡨⠖⠈⠀⠀⠁⠀⠀⡠⠂⠉⠉⠉⢛⠤⣀⣀⣱⡆⠈⢱
⠀⠀⠀⠀⣠⣧⡊⢀⡰⠆⠒⡉⡠⠀⣀⠬⠐⠁⠀⢰⡡⠄⠒⠒⡠⠔⠉⠀⠀⢀⣁⠔⠀⠀⢸⡁⠀⠀⢀⠔⣡⠤⠺⣿⣿⣿⠔⠉
⠀⠀⠀⡜⠘⣡⠞⠲⠤⣌⠭⠉⠒⠉⠀⠀⠀⠀⠀⠸⣉⠒⠒⠩⠄⠀⢐⡮⠔⠁⠀⠀⠀⠀⠘⢆⠉⠀⡉⠉⠀⢀⡘⠿⠛⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠛⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠤⣞⣩⠊⣙⣯⠵⡤⢄⠀⠀⠀⠀⠀⢀⡴⢉⡯⢥⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠠⠤⢤⣴⣀⡀
⠀⠀⠀⠀⠀⡴⢳⡴⣏⡠⢏⣀⡽⢤⠚⠚⡄⠀⠀⠀⠠⣾⠀⠊⣀⣠⢥⡴⡗⠲⠦⡀⠀⠀⠀⢀⣤⡄⡀⢠⣙⣃⠨⡀⠽⣃⢠
⠀⠀⠀⠀⠀⠑⣾⣀⣸⣀⣀⣽⣄⣠⠶⡞⠀⠀⠀⠀⢠⠛⡚⠿⢸⢉⣳⡾⠢⢤⡈⠀⠀⠀⠀⢀⠝⣶⣾⣵⣮⣷⣬⣥⢲⣮⠞⠳
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠄⠀⠇⠀⠀⠀⠈⣈⠂⡘⠦⠊⣎⣠⠓⢀⡾⠁⢠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⡄⠸
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⣀⠀⠀⠀⠀⠀⠈⠁⢧⡐⠀⠓⠛⠉⣁⡤⠒⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⢠⠈⠊⠀⠀⢀⢐⠀⣐⡂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⠷⢀⠀⡀⠀⠙⠃⡈⠄⠘⠁⠀⠀⢄⡐⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡅⣀⠀⠀⠠⠀⠠⠥⠀⠷⡤⠀⠀⡁⠀⠘⡂⠀⠠⠀⢄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣟⢁⡋⢤⠤⡐⡺⠠⠀⠐⠃⢠⠀⡘⠒⠀⠤⠀⢀⣌⣁⠂⣐⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⡤⠘⣆⣼⣿⣸⢇⣋⣄⡄⡅⠐⠂⠈⠐⡀⢲⡬⡀⡀⠑⠂⠀⠈⠉⢋⡐⠛⠤⡈
⠀⠀⠀⠀⠀⠀⠲⠤⣄⠸⠃⢤⠈⠙⡮⣹⠁⠁⠹⡈⢡⡂⠉⠛⣃⠤⣄⠨⣠⣉⢀⣘⠀⣁⣀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⡘⠒⠈⠍⠀⢀⡄⠠⠜⠋⠑⣈⢊⠁⠉⠐⢍⠥⠀⠹⠍⠁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⠀⠘⠠⠈⣉⠈⠠⢼⣤⠄⣕⠂⠐⠀⠂⠀⢀⠋⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡈⠀⠆⠂⡀⣠⠿⡦⠁⠈⠽⠒⠀⢙⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠿⠂⠀⠈⢀⠄⢂⡐⣄⠛⠳⢶⣷⡒⠊⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢶⡙⡶⠖⠙⠎⢀⠀⢀⠀⠀⠛⣍⣤⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⠐⠉⠉⠀⠀⠀⠠⠀⠉⠁⠒⠀⠒⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡿⠁⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⢀⡆⢀⡞
⠀⠀⠀⠀⠀⠀⢸⢥⠞
⠀⠀⠀⠀⠀⢀⢁⠎
⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠐⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠴⠦⢤⣀⡞⠀⠈⢳⡀⡴⠚⠒⢦
⠀⠀⠀⢠⠎⠉⢢⡞⠁⠙⡦⠒⠲⣄⠀⠀⠀⠀⠀⢠⡟⠉⠉⢻⡆⠀⠀⠀⢰⡇⠀⠀⠀⠉⠁⠀⠀⠀⠻⠁⠀⠀⠀⢣
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠓⡄⠀⠀⠘⢷⣤⣤⠟⠁⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢉⡤⠦⠄⠀⡄⠀⢠⠀⣠⣤⣤⠀⢰⣦⠀⠀⣴⠲⢤⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⠀⠀⠀⣇⣀⣸⠀⣿⠀⠀⠀⣸⠘⣇⠀⣿⠀⣸⠇⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣇⠀⠀⠀⠀⡏⠉⢹⠀⣿⠓⠀⠀⣿⣤⣿⠀⢸⠛⠁⠀⠀⠀⠀⢀⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠦⣤⡄⠀⠇⠀⠸⠀⣿⣠⣤⠀⡇⠀⠸⠇⠸⠀⠀⠀⣀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣴⣴⣶⣤⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⣀⣴⠾⠋⠉⢰⠶⠄⢠⡀⠀⡤⠀⡶⢤⡀⢰⠶⠦⠀⣄⠀⢠⡄⢠⠶⠀⢰⡆⢠⠀⠀⡤⢠⡶⠆⠀⠀⣿
⠀⠀⠀⠠⣾⡋⠀⠀⠀⠀⢸⣀⡀⠀⢳⡾⠁⠀⣇⣀⡷⢸⣤⠄⠀⣿⡄⢸⡇⠸⣄⠀⢸⡇⢸⡀⢰⠇⢸⣇⡀⠀⠀⣿
⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⢾⠉⠁⠀⡼⢳⡄⠀⣏⠉⠀⢹⠀⠀⠀⣧⠹⣼⡇⠀⠘⡇⢸⡇⠈⣇⣾⠀⢸⡏⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠿⠤⠦⠸⠃⠀⠛⠀⠋⠀⠀⠘⠒⠒⠀⠛⠀⠘⠃⠐⠚⠁⠘⠇⠀⠘⠇⠀⠸⠧⠤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇

⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⠁⠀⠀⠀⢢⡀⠀⠀⠀⠀⡀⠂⠐⢀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠉⢠⡈⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠐
⠀⠀⠀⠀⢰⢄⠀⢀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠑⢤⠀⠈⠃⠐⠄⠀⠀⠀⠀⠀⠑⠠⠐⠐
⠀⠀⠀⠀⣀⠀⠀⠘⣃⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⢢⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣷⡾⠛⠀⠀⠀⠈
⠀⠀⢰⢔⣽⠄⢀⣼⡿⣶⡄⠀⠹⠛⠿⣷⣦⠀⠀⠀⠀⠁⠀⠀⠀⠐⠈⠋⠁⠀⠀⠀⠀⠱⠒⠀⠀⠀⠈⢿⡽⠷⠛⠉⠀⠀⠀⠀⠀⠀⢶⣢⠀⠀⠉
⠀⠀⠀⠉⠁⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠀⠘⠀⠢⠄⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⡠⠖⠀⠀⠀⠀⣿⣿⣻⣿⡆⠀⠀⢀⣰⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⡄⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠈⠃⠀⠀⠼⠂
⠀⠀⠀⡀⠻⣄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠬⣤⢁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁
⠤⢄⠀⠀⠀⠐⠀⠀⠀⣠⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠰⠀⠀⠀⠀⡀⡤⢦⡄
⣰⠀⠌⠁⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⣆⠰⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀
⠀⠖⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠉⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠊⠂⠀⠠⠀⢀⡀⠑⠕⠢⢀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⣲⣿⣾⢁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⡴⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠋⠚⠁⣿⣀⣠⠟⢚⡷⠶⢀⡤⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠐⠋⠤⣀⠐⠀⠀⠀⠀⣀⠠⠖⠨
⠀⠀⡄⠀⠀⠀⢀⡀⢀⠀⠀⠀⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠁⠠⠎⠀⣰⠟⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⡁⠀⠂⠀⠀⠀⠀⠐⠆
⠔⠈⠀⠀⠀⠀⢸⣥⡛⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠈⠀⠀⢀
⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣤⣤⣤⣤⡄⠞⠃⠘⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⢀⣾⣄⣀⠀⠀⠀⠀⠸⠷⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾
⣿⣿⣯⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡀⡖⠀⠀⢀⣾⣿⣿
⣿⣿⣿⣿⡿⠁⠀⣀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⣉⣡⠔⠂⠀⠀⠹⣿⣿
⠛⢉⡉⠉⠀⠀⠀⠜⢀⠂⠀⡄⠀⠤⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⡠⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠉⠀⠐⠇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠲⡄⠐⠀⠀⠄⠀⠀⠀⣠⠁⠀⠀⠠⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⢠⠀⢒⠀⠀⠀⠀⠐⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈
⠀⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠠⠀⠀⠇⠀⠌⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤
⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠞⢀⠈⡁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠂⠸⠀⠀⠀⠄⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⡶⣆⣀⠐⠃⠀⢀⢰⣯⡴⢇⡴⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠈⠁⠓⠆⢹⠄⠀⣴⣟⣸⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠠⣤⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣾⣿⣶⣿⣿⣷⣾⣿⣦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⠿⣛⣩⣭⣴⠶⠶⢶⣤⣭⣙⡻⢿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⢋⣵⠾⣋⣭⣶⣶⣾⣿⣶⣶⣦⣍⡛⢷⣌⡻⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣴⢟⣵⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣷⣝⢷⣌⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢋⡾⢣⣿⡏⣿⡏⣿⡏⣯⢋⡏⣿⡏⡏⠤⢹⡙⣹⣧⡹⣇⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⣼⣣⣿⣿⣧⣭⣷⣬⣵⣧⣦⣷⣬⣴⣧⣿⣼⣧⣿⣿⣧⢹⡆⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣭⣥⣴⣶⣶⣶⣬⣭⣭⣙⣛⠻⠿⣿⣿⣿⣿⣿⠙⣃⣙⢉⣿⡌⣧⢹⣿⡆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⢿⣿⢛⣛⢻⣿⡿⢟⠿⣿⣿⣷⣦⣭⣙⡻⠿⣧⣭⣥⣾⣿⠇⡿⢸⣯⠸⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠸⢇⣿⢈⣋⢰⡏⣼⣿⣷⢸⡏⣶⣬⢻⣿⣿⣿⣶⣦⣭⣭⣉⣚⣃⣛⣛⣁⣂⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆⣿⣿⣿⣸⣿⣿⣼⣿⣾⣿⣮⣝⣥⣾⡇⠿⠟⣸⡇⣿⣿⠀⣿⢟⣛⡻⣿⠿⠿⣿⣿⣿⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⣿⡿⠿⠟⣛⣛⠛⣛⣛⡻⠿⠿⣿⣿⣿⣿⣿⣧⡙⠟⣡⣇⢿⣿⣿⣿⣿⢰⣿⣿⣿⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣉⡲⠾⣿⡄⠿⠿⣷⣝⠿⣬⡛⠿⣶⣮⣍⣛⠶⢭⣙⡛⠿⣿⣶⣭⣴⣿⣿⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠁⠀⠀⠀⠀⢻⡿⠿⣦⣍⣛⠲⠶⠮⠽⠿⠷⢆⣉⣙⡛⠶⠮⠭⣭⣭⣭⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⢻⣿⡿⠻⣿⡿⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠉⢿⢰⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣟⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⢳⢾⣿⡟⠰⠀⠀⠀⡴⠃⠀⠀⠙⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⣠⢰⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠡⠟⠸⡛⣛⣯⡿⠁
⠀⠀⠀⠀⢀⣸⣿⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⡿⠸⠀⠀⠀⠀⠀⠀⠀⣬⣿⣷⢿⠰⣾⡳⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⣘⣛⢣⣬⣤⣂⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⡹⠟⣼⠁⢹⣆⠙⣯⠘⡿⠇⠀⠀⠀⠀⠀⠀⠈⠈⠙⠽⢿⣿⣿⣿⣿⡿⠿⠋⣀⣀⠔⠁
⠀⠀⠀⠀⠘⢿⡇⡄⠀⠀⢨⣭⣶⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠹⠀⠀⣿⠂⡸⣄⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⣠⣴⣶⣾⣭⡏
⠀⠀⠀⠀⠀⢸⠃⠁⠀⠀⠠⣿⣿⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠘⢀⢙⡝⡃⠀⡈⢹⠀⠀⠠⠤⢴⡗⠀⠀⠀⠀⢠⣾⣿⣿⡟⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠈⠙⠻⠅⢈⡉⠉⠌⠋⠓⠊⠣⡜⠀⠀⠀⠀⠾⠇⠀⠀⠀⣠⣿⣿⠿⢿⣿⣬⣿⠆
⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣾⡄⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢸⢹⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠰⠾⠒⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉
⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⣶⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣤⢸⠁⠀⠀⠀⢠⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⣀⠀⢿⣿⠷⠶⠶⠀⠀⠀⠐⠺⣷⣿⣿⣄
⠀⠀⠀⠀⢀⣿⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢠⡿⢟⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡧⢼⣿⣢⣾⡁⠈⣿⡃⠀⠀⠀⠀⠀⠠⢶⣯⣿⠁⠀⠉⠁
⠀⠀⠀⠀⠸⠁⣿⠀⠀⢀⣤⣿⣧⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⢹⡇⣶⣯⡘⠛⠟⠛⠻⠏⠁⠀⠀⠀⠾⣴⣿⠃⠀⢰⣦
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠿⠏⣼⡿⠀⠀⠀⠸⠛⣻⡄⠀⠀⠀⠀⠠⠿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⢁⣾⣿⣷⡀
⠀⠀⠀⠠⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢠⣤⣤⣠⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠈⠉⠀⠉⠀⣤⠀⠀⠀⠀⠀⢸⣿⣯⠏
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⢀⠃⠀⢠⠄⠀⠀⠀⣶⡟⠀⠀⠀⠸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣾
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢾⣦⣠⣸⣀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠐⢀⠀⢀⣀⣸⣦⡙⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣧⣬⣿⣧⣼⣿⣵⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠶⠦⢄⡓⠚⠻⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢰⣶⣯⣀⣀⣀⣀⠗⠻⠿⣿⠷⣤⡀⠀⠀⢲⣦⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⡼
⠀⠀⠀⠀⠀⠉⠁⠀⠐⣲⢇⡦⣶⡙⡀⡉⠙⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠊⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣄⣀⣀⣸⠀⠴⠁
⠀⠀⠀⠀⠀⠀⢀⠀⡰⠋⠸⠀⢿⠓⠈⢄⣈⠄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁
⠀⠀⠀⠀⠀⡠⣿⠟⠁⠀⢠⣀⣼⠀⠀⠐⠉⠘⠀⠀⠀⠙⠛⠁⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⢀⣀⠀⣾⣻⡆⢠⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠷⠂⠀⠀⠀⠀⠀⠠⢄⣀⣄⠀⠀⢠⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠈⢹⣯⡿⠷⠏⠀⠀⠰⣿⠆⠀⠀⠀⠀⠁⠀⠀⠀⠈⠳⠶⠶⣄⢀⣀⡽⠉⠁⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣂⡀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡄
⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⣿⣿⠏⠠⣾⣿⣿⣿⣿⣿⣇⣠⣤⣤⡀
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢺⣿⣿⣿⣿⡿⠿⣛⣉⠀⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠙⠿⠿⠏⣿⣿⡿
⠀⠸⠿⠛⠉⠡⠶⠊⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠋⢸⣿⣿⣿⣿⣿⡷⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⣀⡤⠀⠐⠒⠀⠀⡀⠙⠟⠿⠋⠉⠀⠠⣀⡀⣤⣀⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⢀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠇⠜⠣⠸⠸⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠖⠂⠀⠀⠀⠀⢠⡄⠀⡆⠀⣄⠀⢤⢠⠀⣄⠀⢦⡀⢰⠄⢤⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠃⠂⠃⠂⠈⠙⠂⠃⠂⠂⠃⠘⠃⠒⠈
⠀⠀⠀⣴⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠴⠿⠿⠛⠛⠯⠭⠤⢬⣅
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣿⣷⣦⡄
⠀⠀⣰⣾⣿⣿⣿⣎⣙⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣤⣠⡄
⠀⠀⠈⠛⣿⣿⣿⣿⣿⣷⣦⣍⠻⠟⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠙⠛⠛⠻⣿⣿⣿⣿⠇⠀⠀⠘⣷⣤⡀⠀⠀⠀⠀⠀⣠⡶⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣤⣴⣮⣽⣧⣾⡷⣾⣦⣤⣿⣧⡄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡞⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢠⠄⠠⠔⠈⠉⠛⠿⠿⠿⠿⠟⠋⢁⣀⣀⣠⣄⡀⠀⡄⢠
⠀⠀⠀⠀⠈⠁⠁⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠉⠛⠒⠓⠛⠛⠒⠒⠂
⡶⣶⢶⢶⠶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⢶⣶⣶⡶⣶⠶⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡀⣤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠺⡖⡷⠀⣀⠀⣦⢀⠻⣌⣧⣧⣾⡼⣋⢴⠦⣦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣽⣦⣿⠇⣠⣝⣷⣧⠟⠁⠀⠈⢻⠀⠈⢻⣸⣠⣇⡼⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠚⠋⠉⠳⣄⠀⠀⠹⣄⠀⠀⠀⣼⠀⠀⠀⣹⠟⡛⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡘⢧⡀⣰⠇⣀⣤⠞⠁⢨⣟⡷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢳⣸⢇⡀⠀⢠⡀⣆⠀⡀⠀⠀⠉⠛⢻⠟⠿⠷⠶⠶⠖⠚⠻⣟⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⣻⣼⠇⡄⠀⢳⣿⡼⠁⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠭⣽⣶⠃⠰⡄⣿⢀⡄⠀⡇⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣷⣀⢳⡌⠳⡄⢹⡿⠋⠘⢦⣧⡞⢸⠇⠀⠀⠀⠀⢀⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⣈⡽⠛⠲⠿⢯⠀⠀⢷⣨⡏⡤⣼⠀⢦⡀⡖⢀⡀⢷⣼⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢁⠀⠀⠀⠀⠈⠳⡄⠀⣿⠋⠁⡏⢠⡄⣹⠛⠀⣧⣸⠋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣷⣌⢧⠀⠲⣄⠐⣦⣹⣾⠃⠀⢰⡇⠀⢹⡿⠚⢁⡼⠛⠉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢋⡭⢟⣛⣛⣿⠋⡿⠁⠈⢷⡀⢸⠀⢀⣸⣥⣞⣉⣞⣃⣼⡥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡽⡟⢹⡌⠁⠀⠀⠀⢳⣿⠖⠋⠁⠀⠀⠙⣯⠉⠙⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠁⠀⠀⠀⠀⠈⠃






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠔⡄⠀⠀⢀⡤⠀⠀⠀⠀⢀⣀⠤⠄⠒⠀⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⠌⠀⠐⠦⠂⠀⠘⠄⠊⢁⡠⠦⠐⡊⠉⠀⠀⠀⠀⠁⣢⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠠⠠⣀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⢊⡉⠀⠀⠀⠀⢁⣀⠂⢀⠀⠆⠸⠄⡀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢀⠔⠀⠀⠘⠀⠉⠐⠆⠑⠤⡀⣄⠈⡆⠀⢡
⠀⠀⠀⠀⠀⠀⢠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠇⠈⠀⠰⡄⠉⠁⠸⠂⠀⠀⠄⠀⢁⡀⠃⠀⠀⠆
⠀⠀⠀⢀⠀⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠐⠒⠂⠹⠀⠸⠀⡁⣄⣰⠀⠀⠑⠒⠊⢀⣀⣄⠤⠞
⠀⠀⠀⠀⠠⡀⠐⢒⣢⣤⡀⠀⠀⠀⠀⠀⣔⢸⣄⠚⠀⠀⠀⠀⣀⣀⡀⡔⠁⠀⠀⢀⣀⡤⠔⠒⠋⠏⣁⡀
⠀⠀⢀⡀⠤⠃⠀⠘⠋⢀⣿⣤⠤⣤⣤⣄⡁⠀⠈⠳⣄⠀⠀⠀⠀⡀⠈⠤⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⢈⠝
⠀⠈⠁⢄⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠈⠉⠳⢦⡀⠈⠳⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣁
⠀⠀⠀⢀⠑⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡖⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠶
⠀⠠⣔⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠳⣜⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁
⠀⢠⠖⠛⠛⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠻⠓⠁⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⢿⡘⠶⠀⠀⠀⠀⠬⠿⠇⠀⠀⢀⣸⠆⠀⢀⣠⣴⣤⣄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠊
⠀⠈⣿⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣴⣿⣿⣿⣿⣿⡆⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⢸⡇⠀⠀⠀⠀⠀⣤⣶⣶⣶⣞⠛⢹⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠉
⠀⠸⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠻⣆⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠉⠁
⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⣸
⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠦⢤⣤⠤⢶⠶⢞⡻⠫⠀⠀⢀⠤⡀⠀⠀⡜⠢⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠁⠀⠀⠱⠤⠃⠀⠈⠢⡐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⣉⣦⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣀⣤⠶⠛⠉⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⣠⡴⠞⠋⠉⠀⠀⢀⣀⣤⠶⡞⠋⢉⣹⠆
⠀⠀⠀⠀⠀⠀⢰⡶⢤⣤⣤⣄⠀⠀⣀⣤⠶⠛⣁⡤⠶⠛⠉⠀⠀⢀⣀⣤⠶⠚⠋⣁⣸⡤⠷⠛⠋⠁
⠀⠀⠀⢠⡾⢋⢻⢥⣂⣰⡄⢸⣷⣛⣩⡴⠖⠋⠉⠀⣀⣠⡤⠶⠛⠋⣁⣤⡴⠞⠋⠉
⠀⠀⣰⠏⣤⡍⢊⠀⣉⡙⠙⡄⢸⡏⠁⢀⣠⡤⠶⠛⢉⣡⣤⠶⠚⠋⠉
⠀⠈⢻⡆⢔⣩⠖⢢⡄⠰⣌⣡⡼⠷⠚⢋⣡⣤⠶⠚⠋⠁
⠀⠀⠈⣷⠰⢍⣡⡼⠶⠛⣉⣡⡴⠶⠛⠉⠁
⠀⠀⠀⠈⢻⣏⣥⣶⠾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⣀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠉⣐⠒⠊⠉⠉⠍⠭⠅⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡆⠀⠸⠝⠿⠶⠿⣷⡆⠀⣾⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⢤⣤⣤⣞⣉⣤⣦⠤⢤⣄⡀⠀⠀⠁⣀⣼⢏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠥⠂⠀⠀⠀⠀⠢⠶⣦⣄⣀⣈⣉⣁⣀⣈⠅⢀⣨⣞⠕⠋
⠀⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⣤⢖⣀⡀⣀⡀⠀⠀⠀⣈⠩⠟⣉⠥⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⡞⠘⠁⠀⠀⠙⠿⠖⠋⠭⣻⡆⠠⠊⣡⠖⡩⠄
⠀⠀⠀⠀⠀⠀⠉⠒⠒⠪⠭⢑⣒⠤⢄⡈⠁⠠⠁⡼⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠤⢄⡼⢰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠶⣦⣬⣤⣴⣶⣂⠀⠶⠶⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣭⣭⣥⣶⠟⢛⣫⡍⠛⠛⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣿⣿⣿⣿⣿⣧⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⣤⣀⠉⠙⠛⠛⠛⠉⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣠⣶⣶⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣶⣤⣄⣀⠈⠉⠉⠉⠉⠁⠘⠿⠿⠛⠉⢹⣿⡇⣀⣴⣷⣾⣿⡿⠛⢹⣿⠀⢀⣴⠀⣀⣤⣴⡆
⠀⠀⠀⠀⠀⠀⢀⡀⢤⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠛⠿⢿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠋⢀⣀⡼⠿⣶⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠘⠻⢤⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠠⠂⠀⠀⢀⣠⣴⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⣍⡓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣶⣦⣤⣴⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢬⣉⠓⠶⢤⣄⡀⠀⣀⡀⠀⠀⠀⠀⢸⡿⠛⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⠄⣽⣯⣟⡻⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⢀⠀⣰⣦⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣿⣷⡄⡀⣴⣆⢀⣀⣿⣿⣿⡇⣿⣿⣿⢣⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⡛⣿⣿⣷⣿⣿⣿⠘⣿⣿⡟⣿⣷⣿⡿⣡⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡜⢿⣿⣿⢻⣿⣿⠹⣿⣷⢸⣿⡟⣱⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⣌⢿⣿⢸⣿⡿⠀⢹⣿⡌⢏⣼⣿⠿⠿⢻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⢿⣿⣎⠟⣼⣿⠇⢀⣿⡿⢣⣶⣶⣶⣾⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣷⣶⣭⡄⣿⣿⢀⣾⠟⣵⣿⠿⠿⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣿⢸⣿⡿⢫⣾⠏⢀⣀⣤⣾⣿⣶⣶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡈⠟⠴⠿⣷⣿⣿⡿⢟⣩⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣡⣶⣿⣷⡆⣶⣤⣘⡻⢿⣿⣿⣭⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⢻⣿⣿⢸⣿⣿⣿⣷⣮⣙⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠋⠁⠀⠀⠀⠀⠸⠿⣿⣾⣿⣿⡏⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠙⠁⠀⠙⠃⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⢚⣂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠞⣛⣩⣥⠴⠶⠚⠛⠉⠉⣀⣠⣤⣤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢛⣋⣩⣤⠶⠞⠛⣉⣁⣤⣤⣤⣶⡿⢿⣛⣻⣭⡽⠶⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡾⣡⢞⣫⣍⢹⡶⣤⣠⡤⠶⢞⣋⣩⣥⠶⠞⠛⣉⣉⣤⣴⡶⠿⢿⣛⣛⣭⡽⠷⠞⠛⠉⠉⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⡀⠀⣀⣄⣼⠿⢿⣷⣿⣼⣿⣿⣾⢿⣯⣷⠖⠛⣉⣉⣤⣤⣶⠾⣟⣛⣭⡽⠶⠚⠛⠉⠉⠁⠀⠀⣀⣀⣤⣤⠶⠶⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠈⢠⣞⣭⣾⣿⣿⣷⣿⣿⡿⣯⡻⣏⢷⡹⡏⢿⣟⣿⣿⠿⠟⠛⠛⠉⠁⢀⣀⣀⣤⡤⠶⠶⠚⠛⠋⠉⠁
⠀⠀⠀⢰⣿⣿⡿⠿⢛⣋⣩⣿⣿⣿⣎⣷⢻⠈⣿⣷⢸⣏⣁⣀⣠⣤⠴⠶⠟⠛⠋⡉⠁
⠀⠀⠀⣼⣿⣵⣶⣿⣿⣿⡿⠷⣿⣿⡟⣿⢸⣼⣯⣇⣼⣿⠉⠁
⠀⠀⢰⣿⣿⣿⣛⣩⣥⣴⣶⣾⣿⡿⣹⢇⣾⣽⣿⣿⡟⢯⣷⡄
⠀⠀⢾⣼⠃⠉⠉⠘⣿⣷⣿⣿⣿⣹⢻⣿⡿⣿⣿⡟⣧⠘⠿⠃
⠀⠀⠈⠁⠀⠀⠀⠀⣿⣿⢹⣿⡧⡏⣾⢸⣿⣿⣿⣿⣾⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣟⡿⣧⣿⣧⢿⣿⡿⣿⡏⣿⢉⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣼⣷⣿⣿⣹⣧⡻⣷⣿⢷⡹⣿⠿⢻⡇⡿
⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣿⣿⣯⣷⣜⣿⣿⣳⣼⢷⡌⢿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⢻⣿⣿⣿⣿⣿⣞⣿⣿⢿⣧⣿⠀⠙⢿⡝⣦
⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠘⣷⣿⣿⡙⢧⣽⣿⣿⣿⣷⡟⠀⠀⠀⠷⠟
⠀⠀⠀⠀⢀⠀⢿⢻⡄⠀⠀⣿⣿⡇⣿⡷⢾⢿⡟⠉⢿⣷⡀
⠀⠀⠀⠀⠈⠣⠈⢷⣿⡄⠀⣿⣿⣇⣿⡷⢏⡼⠃⠀⠈⢻⣝⣦
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢿⡙⣿⡿⢳⠏⠀⠀⠀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣫⣾⣟⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⣳⢿⣿⣿⣿⣷⣶⣟⣳⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣽⣾⣿⠛⠁⠀⢻⣿⣄⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⠀⠀⠀⠀⠹⣟⢦⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀⠉⠛⠁

⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⡿⠻⡿⠛⠿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢾⣿⣧⡶⠟⢋⣁⣠⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡶⢶⣄⠘⢿⣛⣥⣤⣾⣻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣯⡿⢟⣽⣷⡄⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⣠⡄⠀⢀⣀⣤⠖⣊⡤⢚⣩⡶⢟⣫⣵⣾⣿⢿⣿⠟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢪⣤⡾⢋⢔⣷⡿
⠀⠀⠀⠀⣀⡘⣷⠚⣛⢉⡥⢞⣵⠶⠋⣡⣶⣿⣿⢿⣯⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣊⣾⣿⢿⡿⣯⡾⠋
⠀⠀⠀⠀⢿⠉⢿⣽⠻⡧⠞⠋⣁⣴⣿⡿⢿⣽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣾⡿⢏⡴⢫⣾⠟
⠀⠀⠀⠀⢀⣄⣀⠻⡆⣻⣶⣿⣿⠟⣯⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠐⠀⠀⠀⠀⠀⠀⠀⢀⠔⣱⣾⡿⢛⣷⢟⣵⠟⠁
⠀⠀⠀⠀⠀⠉⠛⠃⠁⠀⠛⠻⠿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠁⠀⠀⠀⠀⣀⠠⣄⣾⠟⠋⣸⡿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠘⠏⢿⠿⢿⣶⣾⡿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⢹⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠸⡇
⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠰⡆⠀⠌⣩⡼⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠠⠤⠌⠳⡀⣿⢀⣴⠟⠋⠀⢒⣶⡶⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠈⠱⣶⣶⣶⣽⡉⢻⡿⠷⠾⠿⠟⠋⠀⠀⠀⠀⠀⠀⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣤⣾⡿⢿⣯⢿⢯⣀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣿⡟⠛
⠀⠀⠀⠘⠃⠈⠀⠀⠀⠤⠶⠟⠛⠉⠐⢁⡏⢿⡀⠙⠙⠛⠷⠞⠓⠀⠒⠀⠀⠀⠀⠀⠘⠾⢿⠿⠿⢿⠿⠟⠟⢿⣿⣿⣿⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠃⠘⢧⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠀⠚⠒⠈⠻⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠓⣼

⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠿⢿⣿⠋⣽⠍⢻⣿⣿⣭⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⡿⠀⣿⣧⠸⡟⠙⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠿⣿⡙⠄⠸⣿⡀⡇⣠⡿⠋⢘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⣟⡿⡀⠛⠑⢨⡿⣄⣴⠟⠉⢋⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢿⡧⣜⣦⣤⣼⡇⣽⣷⣀⣴⠞⢉⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣼⢸⣿⢾⢷⣿⢻⣿⣏⣴⡿⠋⣼⡿⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⣿⢹⣿⡿⣨⠟⣿⡾⣿⡇⣾⡟⣿⣿⣠⣾⠛⣰⡿⣿⣦⡀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢯⣼⣿⣿⣿⣿⢺⡇⣷⣿⠀⣿⢇⣿⣿⣿⢅⣼⠟⢡⣿⡿⣿⡄⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢞⣵⢋⣬⣭⣵⡿⣿⢸⡇⣿⢹⠀⣿⢸⣿⢹⣿⣾⣿⣤⣿⠏⣰⣿⣿⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡷⣫⡾⠛⣉⣩⣥⣦⢸⡏⣧⢹⣸⡄⣿⣿⣇⣿⡿⢻⣿⢸⣯⣰⣿⣿⣿⣇⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⡾⠋⠚⠛⠛⠉⠉⢻⡟⡇⣿⡸⣿⣿⣿⣿⣹⣿⢡⣿⣿⢸⣿⣹⣾⣿⡏⣼⠃⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡹⢻⣿⣿⣿⣿⣿⡿⢿⠇⣼⢠⡇⢸⣇⣽⣿⣿⢇⣿⡿⣼⣿⡏⣿⣿⡏⣿⣿⣿⣿⣶⣾⣼⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢋⣁⣠⣤⣤⠶⣶⢸⡇⣸⣇⣼⡿⢿⣿⢏⣼⣿⢣⣿⣿⢳⣿⣿⡇⣿⣷⣷⠹⣯⢷⣻⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠿⠟⠛⣫⣁⡶⣿⡼⠧⠛⠉⡷⣾⡿⢫⣾⡿⢃⣾⣿⣿⢸⣿⣿⡇⣿⣿⢿⣧⣿⡞⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣀⣠⣭⡿⠟⠋⠁⠀⠀⠀⠀⢳⣌⣴⣿⠟⣡⣾⣿⣿⠇⣸⣿⣿⡇⣿⣿⡜⠃⣿⣷⢹⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡉⣁⣴⣿⣿⡿⢃⣼⣿⣿⣿⡇⢸⣿⣷⠈⣿⣿⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠿⠟⠉⢠⣾⣿⡿⢃⣿⣷⢸⣿⣿⡆⣿⣿⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⢠⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⢀⣴⣿⣿⠏⣠⣾⣿⣿⠈⣿⣿⡇⢸⣿⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⣴⣶⣶⣼⣥⣤⣧⣄⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣷⣶⣿⠟⠋⣡⣾⣿⣿⡿⠃⣸⣿⣿⡇⣼⣿⢻⣿
⠀⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠘⢿⡋⢠⣾⣿⠟⠋⢁⣠⣴⣿⣿⡿⠀⣿⣿⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢻⣧⡀⠹⡿⠟⢁⣴⣿⣿⣿⣿⣿⠟⠁⣼⣿⡏⢸⣿
⠀⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠙⢿⣦⣀⣰⣾⣿⡿⠟⠋⠉⠁⢀⣼⣿⠏⣠⣿⣿
⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠉⣿⡿⠋⠁⠀⠀⣠⣴⣾⣿⠟⢁⣴⣿⢿⣿
⠀⣿⣇⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣙⣷⣄⣀⣀⣀⣀⣠⣾⣿⣛⣋⣁⣠⣿⣛⣁⣸⣿
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⢀⣀⣤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀
⠀⠀⢉⡐⠢⢵⢇⣨⣿⣿⣶⣄⠀⠀⠀⠀⠀⣼⣿⣯⣽⣙⣺⣯⡿⢯⠾⡿⣶⠀⠀⢀⡴⡚⠉⠉⠄⢋⠽⠓⠢⣄
⠀⠀⠈⠋⠉⢱⣿⣿⣿⠛⠁⢈⠶⡄⠀⠀⢀⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣽⠀⠀⠈⣷⢆⡙⣖⣢⣄⠠⠂⠉⠉⣙⣦⡀
⠀⠀⠀⠱⡂⢸⣿⣿⡏⠳⢦⣈⣥⣻⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠳⠐⠀⠌⠁⠒⠿⣆⠀⠉⡀⠀⡇
⠀⠀⠀⠀⠈⠛⠛⠻⢇⣀⣀⣉⣍⡼⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠂⠠⢤⠁⠂⠘⠶⣔⣤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠚⠊⠉
⠀⠀⠀⠀⣠⡤⠴⠶⠶⠦⠤⣀⡀⠀⠀⠀⠀⠀⢠⠖⣯⠭⣝⣒⡶⣦⣄⡀⠀⠀⠀⠀⠀⢀⣤⠶⣦⣤⣤⣤⣠⣄⡀
⠀⠀⢠⡿⠷⠤⠴⠂⣀⡀⠠⠜⠛⠳⣄⠀⠀⠀⢀⡴⠁⣠⣾⣿⣿⣿⡿⣛⠢⡀⠀⠀⠀⣚⠤⢤⣿⣾⣿⣿⣿⣤⢿⣶⣦⡄
⠀⠀⠸⠴⠖⠚⠛⢒⠦⢍⡓⠦⣠⠤⠤⢷⣦⠀⠸⡦⠀⣿⣿⣿⣿⠟⠲⢭⣙⣌⣷⣄⠀⣟⠓⢶⣿⣶⣿⣿⣯⣏⣭⣽⣣⡿
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠬⠳⣟⣄⢀⣬⡿⠀⠀⠑⠢⣿⣿⣿⣿⢀⠀⡀⢹⣍⣻⡝⡇⠹⢶⣸⣿⣿⣿⡟⠶⠦⠯⠥⠖⡗
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠄⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠐⠒⠈⠻⣼⠞⠃⠀⠀⠉⠙⠛⠻⠧⡼⠦⠶⠖⠋⠁

⠀⠀⠀⠀⣀⣠⡤⠶⢤⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠖⠲⠶⠤⣄⣀⠀⠀⠀⠀⢀⣤⡾⣎⡻⣭⡿⣿⣦
⠀⠀⣴⢯⣅⣀⣴⣾⣿⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⡞⠃⠀⣤⣴⡯⠽⢃⣶⠀⢈⠳⡀⠀⠀⣶⠘⠓⢞⣹⣞⣯⡽⠖⢣
⠀⠀⠸⠋⡓⣿⣿⣿⣿⣿⡉⠀⠀⠀⠙⠢⡀⠀⠀⠀⣧⣄⠄⠀⠈⠟⠀⠻⠁⣀⣠⠴⣇⠀⠀⡏⢻⣮⣤⣬⣤⣤⣵⣶⣿
⠀⠀⠀⠢⢰⣿⣿⣿⣿⢙⠮⡳⣄⠀⠀⠀⠈⢢⡀⠀⣿⣿⣿⣶⣶⣶⣷⣾⣿⣿⣷⣶⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠙⠿⠿⡇⢀⡂⠈⠺⣷⣄⡤⠖⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠘⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠉⠁⣀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠀⠀⠀⠀⢠⠇⠀⠠⠀⠀⠀⢠⠎⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠸⠐⠈⠀⠀⠁
⠀⠀⠀⠀⡠⠂⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⡉⠐⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠂
⠄⠐⠀⠘⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠤⠀⠅⠈⠀⢀⠀⠀⠀⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡭⢤⢀⡀⣠⢄⣀⠜
⠀⠀⡄⠀⠀⠀⠀⠀⡰⠁⠀⡠⠂⠁⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⢀⠆⡰⢃⡞⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠈⣁⠜⢡⠎⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠄⢋⠏⠀⠀⠀⢙⠴⢁⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠩⠞⠉⠁⠀⠀⠀⠀⠀⢴⣋⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣡⠃
⠀⠀⡠⠀⢂⠠⠀⠁⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀
⠀⠌⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠟⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠁⠈⠉⠉⠀⠐⠂
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠔⠀⣀⢡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠈⠀⠀⠀⠀⠀⢀⢜⠆
⠀⠀⠀⠀⠈⠌⠅⠀⠅⠴⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡪⠕⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠉⡴⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠤⠶⠚⠿⠭⠉⠉⠁⠀⠁⣀⣩⣽⣷
⠀⠀⠀⠀⢀⠌⠡⠤⡎⠁⠀⠀⠃⠀⠀⠀⢀⡴⠀⢀⡴⠃⡆⠀⠀⠀⠀⠀⠈⠓⠀⠋⠁⠀⡚⠉⡀⠬⣱⠖⠛⠋⠉⠁
⠀⠀⠀⠘⣠⠔⠁⠐⢀⠄⠦⠀⠤⠀⠀⠀⠈⢁⡴⠋⣠⠞⠀⠀⠀⠀⠀⠀⠂⠀⡂⠃⡖⢀⠊⠈⠀⠀⡖⠀⠀⠀⠀⠀⢠
⠀⠀⡠⠰⢁⠀⠀⠚⠁⣠⠖⠀⠠⠀⡤⠀⠴⠋⣠⠞⠁⠀⠀⠀⠀⡀⠀⡋⠀⠈⠔⠩⠀⠈⠜⠀⠀⠠⠀⠀⠀⠀⣀⠔⠁
⠰⠈⠀⢁⠠⠋⢀⡐⠫⣁⠁⠀⠠⠈⣠⠖⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢃⠂⠀⢂⢠⠀⣀⠀⠀⢠⠀⠚⢠⢀⡠⠊⠁
⠇⠄⢀⢠⣀⡴⠋⠀⢀⠀⠋⢀⡰⠎⡡⠚⠠⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠹⠁⠠⠘⠁⡀⠔⠃⡀⠠⡙⠉
⠀⠀⠀⠈⠁⠐⠤⢀⡀⣀⡴⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔⠁⠠⠈⠠⠀⠀⡀⠐⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠁⠀⢰⠀⢀

⠀⠀⠀⠀⠀⢀⢔⡶⠞⠳⢄
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠑⠌⠳⣄
⠀⠀⠀⠀⠀⠀⠈⢃⠀⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⢦⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢅⣀⣁⣤⡼⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠿⠶⠶⠩
⠀⠀⠀⠀⠀⣠⠎⠳⡄⠘⣧⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠅⢢⡀⢈⠢⡘⣧⠀⠀⠢⡀⠀⠘⢦⡀⠀⠀⠀⠀⣰⠃⠀⠠⠀⠀⠀⠀⢳⡀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠘⢆⠁⠀⠱⣌⢾⣷⡄⠀⠈⠓⢦⡈⠻⣦⡀⠀⡼⡉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⢒⠚⠓⠊⠀⠀⠤⡀⠀⢀⠔⠈⠳⣄⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠘⢧⡙⢿⣆⠀⠀⠀⠙⠷⣌⡻⢦⡀⠑⠄⠀⠠⡀⠀⢀⠀⠀⠇⠀⠀⠀⢀⠔⠁⢀⠀⠘⢦⠀⠀⠐⠂⠀⠳⡄⠀⡼⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⠀⠀⠙⢦⡻⣧⡀⠀⠀⠀⠀⠙⢮⣷⣤⠀⠀⠀⠑⠀⠈⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢁⣰⠃⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡾⠉⠉⠙⠳⣤⣀⠀⠙⢌⠻⣤⡀⠀⠀⠀⠀⠈⠻⢷⣄⡐⠆⠀⢀⡀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢷⠤⡤⣠⠞⠉⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢄⡀⠀⠉⠳⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠢⡉⠻⣦⢤⣨⣤⠟⢻⡄⠀⠀⠀⠀⠀⠀⠠⠊⠀⠐⠘⠂⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⢻⡀⠀⠀⠙⣆⠀⠀⠻⣆⠀⠀⠀⠈⡳⢦⡀⠀⠀⠀⠈⠀⠈⠳⢦⡀⠀⠘⢷⡀⠀⠀⠀⠀⠀⣠⣤⠴⠶⠶⠦⣦⣄
⠀⠀⠀⠀⡜⠀⢄⣳⡄⠀⠀⠉⠳⣄⠀⢻⣧⡀⠀⠀⠙⠦⣝⢦⡀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠈⠛⠖⢲⡶⠓⠛⠉⠀⠐⠒⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠐⡇⠀⠀⠱⣿⣄⡀⠀⠀⠘⣧⡾⠦⠿⣦⡀⠀⠀⠈⠳⢽⣷⣄⠐⢦⠀⠀⠀⠀⠈⠳⢦⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢻⠀⠀⠀⠈⢳⡉⠓⠒⠚⡇⠙⢦⡀⠀⠉⠓⠲⢤⡀⠀⠉⠻⢿⣦⣑⠀⠀⠀⠀⠀⠀⠙⢦⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡶⠶⡶⠚⠉
⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠙⠲⢄⠠⡇⠀⠀⠻⣦⡀⠀⠀⠀⠳⣤⡀⠀⠀⠹⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠑
⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⢷⠀⠀⠀⠀⠙⠪⣽⣦⡀⠀⠀⠀⠀⠀⠙⢦⡑⠢⠀⠀⠀⠀⠀⣠⡿⠀⠁
⠀⠀⠀⠀⠀⣀⣠⣤⣭⡿⠶⠖⠋⡎⣷⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠉⠳⣄⠀⠀⠀⠀⠀⠙⠳⢶⣤⠤⠶⠛⠁
⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠈⣇⠈⢧⣀⠀⠀⠀⠀⠀⠀⠙⢦⣾⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⡀⠀⠀⠀⠈⢦
⠀⠀⡏⠀⠀⠀⠀⣀⣠⡤⠴⠚⠉⠙⢷⣄⠈⠙⠳⢶⣤⣠⣤⣴⠾⢿⣆⣰⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠘⡆
⢀⣠⣤⡴⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⡆⠈⠳⣤⣀⠀⠀⢀⣀⡼⢧⣤⡼⠋⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣴⡏
⠛⠛⠉⠠⡀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢀⡤⠤⠤⠭⠭⠭⠭⠴⠖⠋⠁⣠⠾⠋⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠉⠓⠒⠒⠛⠋⠁⢀⣰⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠁⠀⠀⠀⠙⢦⣀⣠⣤⡀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠟⠛⠛⠷⠶⠶⢶⣶⣶⣿⠭⠥⠤⠤⠤⠤⠶⠶⠖⠛⢉⣠⣞⣀⣀⣰⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⣤⣄⣠⣤⣤⣴⡋⠁⠀⢀⣠⣤⣤⣤⣄⠀⢀⣀⣤⠶⠋⠁⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠳⠶⠤⠤⠶⠶⠶⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⣠⣘⣧⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄⠠⣄⠈⠛⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠉⣀⣀⡀⠀⠘⠃⠘⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠳⢆⠀⠀⠀⣿⣿⣩⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣄⣈⣀⣀⠀⠀⠀⣀⣾⣿⣿⠛⠂⠀⠐⣰⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣤⣤⣾⣿⣿⣿⣿⡿⡿⠟⠛⢉⣵⣖⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⢤⣀⠀⠙⣿⣿⡟⠋⠁⠁⠀⠙⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠤⣶⠁⠈⠳⣄⡀⠐⠊⢹⠂⠘⠻⠀⠶⣶⠖⠘⠒⠲⠌⠻⢿⣿⣿⣿⣿⣿⣽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣿⡄⠀⠀⠈⠳⣤⣔⢃⠀⠀⢾⠀⠀⠘⠷⣤⣀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⣠⡀⠀⠀⠀⠹⠁⠀⠀⠀⣸⣇⠀⠀⠀⠈⠛⠙⠁⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⢦⣤⣴⣀⣀⣀⣾⣿⣧⣀⢀⠀⠀⠀⠀⠤⠀⠈⠉⢀⡀⠉⢛⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠄⣀⠐⠲⠶⠶⠤⣀⣀⣈⣉⡉⠉⠉⠙⠉⠙⠋⠁⢀⣈⡉⠠⠠⠲⠆⠒⠂⠀⣉⡀⠀⣈⡐⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠕⠺⢭⣒⠤⣀⡀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠂⣀⠀⠉⠁⠀⣀⡒⠆⣀⣀⣤⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠑⠢⢍⡓⢦⣄⡀⠀⠀⠀⠀⠀⢼⣷⣾⣿⣧⡄⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠀⠈⠀⠀⠀⠀⠉⠓⠮⣝⡳⢦⣀⠀⠀⣴⣿⣿⡿⠋⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠈⠙⠲⢭⣛⠶⣬⣻⠿⣿⣷⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣽⣻⢦⣝⡢⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠮⣝⡳⢯⣛⠻⠿⠿⠿⠛⠛⠽⠷⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠒⠀⠉⠀⠀⠀⠉⠓⠬⣛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁