Pooh bear Emojis & Symbols

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣁⠀⢠⣤⣄⣰⣂⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⢏⠻⣿⠗⠉⠉⠻⠟⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⢀⠹⣦
⠀⠀⠀⠀⠀⠈⠙⢳⣶⡔⡶⣤⠲⠶⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠔⠚⠓⠻⠆
⠀⠀⠀⠀⡄⠀⠤⣭⣿⡏⠴⠉⡄⠂⢤⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀
⠀⠀⠀⠠⣥⣤⡴⢏⠄⠠⠀⢀⣀⢀⣈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣠⣤⠀⢀⡄
⠀⠀⠀⠀⢤⣤⠄⣤⡄⠀⢀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠒⠒⠲⢬⡏⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⢠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢛⠏⠈⠿⣤⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠴⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠤⣤⣦⡹⠧⢿⡀⠂
⠀⠀⠀⠀⢀⠀⣴⠛⠲⣶⠄⠀⠀⠀⢰⣟⠀⠀⠀⠀⠀⡀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇
⠀⠀⠀⢀⣷⣾⣿⡇⠙⣷⡂⠀⠀⠀⢸⠟⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⢀⣀⣤⠀⠀⢸⣿⠀⡿⠃
⠀⠀⠀⠺⡾⢿⣯⣴⣃⡤⠁⠀⠀⠀⢸⠆⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠉⡏⠀⠀⢸⠃⠰⠁
⠀⠀⠀⠸⠟⠙⠛⠛⠛⠓⠇⠀⠀⠀⠸⠄⠟⠀⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⡏⠀⠈⠃⠰⠆
⠀⠀⣀⣀⣀⡀⠀⣀⣀⣀⡄⠀⠀⠀⠀⠺⣤⠤⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢤⣤⣿⣿⣯⣽⣿⣿⣇⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⣀⠀⠆
⠀⠀⠈⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⡿⡄⠀⠀⢀⡰⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠑⡆
⠀⠀⠀⠛⠻⡽⢿⣿⣿⣋⡇⠀⠀⠀⠀⡇⠇⠀⠀⣄⠀⠀⠀⠈⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠈⡿⠿⣿⣻⣿⡁⠀⠀⠀⠀⡇⠐⣀⠀⠁⠀⠀⠀⠐⢦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⣀
⠀⠀⠀⠀⠐⠒⠐⠚⠉⠃⠇⠀⠀⠀⢀⡿⠋⠛⠀⠀⠀⠀⠀⠀⢸⠃⠚⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣷⠇⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠤
⠀⠀⠀⠁⠀⠀⢶⣶⣶⠛⡇⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢶⠤⠄⠠⠄⠀⠀⠀⠀⠀⠀⢰⣎⡿⢷⢾⡗⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⡀
⠀⠀⠐⠀⠀⠻⡼⢏⡿⠂⡇⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⠀⠀⠤
⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⡷⠀⠀⢀⣿⣿⣯⣶⡀⠀⠀⠀⠀⠰⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖
⠀⠀⠀⣤⣤⣤⣶⣶⣶⣶⣷⡀⢠⠀⣿⣿⣿⣿⡇⢻⣶⣶⠋⣼⡿⣿⢫⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⠿⠿⣿⣾⣿⣿⣷⣿⣿⣿⣿⡟⡛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠟⠿⠤⠄
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂⠈⠉⠛⢿⣷⣦⣭⣉⡊⣩⠥⠤⡼⠮⠡⢉⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⣐⠒⠒⢲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢏⣩⣤⣄⣀⣴⠷⢚⣿⣩⣤⣭⡉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢨⣅⣹⣿⡦⠴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠴⠗⠀⡀⠉⠉⠛⠛⠉⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢙⣀⣀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠔⠋⠉⠁⠀⠉⠀⡾⠋⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢒⡋⠘⠷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢸⣿⣿⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⢄⣀⠀⠴⠂⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠂⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠈⠙⠲⢄
⠀⠀⠀⡴⠚⠛⠛⠲⠶⠤⣤⣄⣀⣠⠶⠸⡟⢦⢀⣀⡤⠶⠛⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠧⢄
⠀⠀⢠⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠘⢆⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠘⢧⣀⣀⣨⠊⠁⠀⠀⠀⠀⠀⣠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡘⣆⠀⠀⠀⠀⢀⡼⠁⢷⡀
⠀⠀⠀⠀⠀⠁⠈⠑⠶⢤⣤⣄⣀⣀⣣⠉⠉⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⢀⣈⣹⠷⡄⡤⠖⠋⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠛⠉⠁⠀⠀⠀⠘⢦⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠰⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢹⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣾⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠳⢤⣄⣀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⡍⠛⠓⠲⠆⣿⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢷⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠁⠀⠀⠀⢸⡄⠀⠀⠀⢿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣀⣀⣠⡾⠀⢠⠞⠉⠉⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠸⣆⣀⡀⣀⣀⣠⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠣⣀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢪⠱⡄⠀⠘⢶⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⠀⠀⣀⣐⣁⠀⠱⠀⠀⠀⠀⠀⠀⠀⢢⠉⠀⠁⠀⢀⡼⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠓⠉⠀⠀⠀⠉⠉⠒⠢⠤⢤⣀⡀⠀⠀⠉⠉⠒⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠠⠃⠀⠀⠀⠀⣠⡄⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠍⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⣧⣄⢬⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠆⠀⠀⠉⠀⢿⣿⡿⡍⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡞⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠢⣀⡀⢀⡠⠎⢠⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⡠⠒⠒⠦⣀⠀⠈⢩⠆⡠⠋⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠙⠊⠉⠙⠒⠒⢼⠀⠀⠀⠀⠀⠉⠒⢥⡼⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠐⠬⡳⣄⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⡄⠀⠀⠀⠀⠈⠱⡉⢒⠆⠀⠀⠀⠈⡆⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠋⠁⠀⠀⡀⢃⠀⠀⠀⠀⠀⠉⣩⡎⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠳⡄⠀⠀⠈⠺⣄⠀⠀⠀⣠⠊⠀⠁⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠈⠢⢄⡀⠀⠈⠢⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠇⠤⠤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠓⢼⣰⣄⣀⠀⠀⠀⢀⢰⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⠀⠀⠀⠉⠁⠀⠙⢄⡧⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⢀⣀⡔⣋⠓⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⠁⠈⢄⠈⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢸⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⠛⣄⠀⠀⠀⠀⠀⠘⠀⠀⠀⡞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⣀⠀⠀⠀⢀⢖⣩⠔⠊⠀⠑⢄⠀⠀⠀⠀⠀⢀⡴⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠙⠢⠦⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣧⠀⣀⣀⣼⡿⠟⠳⠞⣿⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠠⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⣀⠀⠀⣠⠔⠒⠛⠀⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢞⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠞⠀⠀⠀⣠⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢹⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣾⣇⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⠀⠈⠀⠙⠋⠉⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠛⠛⠛⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣛⣛⡒⠒⣲⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠋⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠞⠡⠄⠊⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣆⢨⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⠥⠐⠒⠋⣉⠉⠉⠀⠀⢀⡀⠀⠠⢴⠖⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠘⠆⠳⡸⣆⠀⢀⣀⣀⡤⠤⠒⠒⠉⠀⠀⢀⣠⠴⢒⣀⣀⣤⣀⡀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠹⣄⠀⠀⠀⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡴⠚⢉⣤⡶⠛⠋⠉⠉⠉⣀⠀⢀⣴⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠓⠑⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⢽⠷⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠈⠳⡄⢀⣤⣀⠀⠀⡠⠤⠤⠀⣀⣀⣀⡎⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⡀⠀⠀⠀⢈⡟⠋⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢮⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢸⡀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⣠⠪⠿⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⡧⢼⣆⣀⣤⠤⢤⣄⣀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⡴⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠉⠀⠀⠀⠀⡠⠃⡀⠀⠀⠀⠀⢰⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⢸⠞⠉⠉⠉⠳⡄⠀⡼⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠉⣒⣤⠴⠊⠁⠀⠀⠀⠀⠀⣟⡼⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠉⣀⣀⣠⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠦⣄⣀⣀⣀⡠⠴⠒⠉⠉⠉⠉⠉⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢤⣄⣀⣰⠇⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⢹⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⢧⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠁⡠⠬⠆⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⢺⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⢤⣀⣀⣀⣠⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍⡁⢐⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡶⠛⣯⣤⠴⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣼⣧⡤⠞⣫⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡜⠛⠛⠋⣉⠛⣽⣿⣶⠟⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⠲⡀⠀⠹⠈⣠⣿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⢠⡇⠀⠀⠈⠉⠉⠛⠀⠲⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⣀⣀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⣴⡶⠈⠉⣿⣿⠓⡿⠃⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⣶⣿⣿⣿⣿⡇⠘⠐⢈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⢹⡇⠀⠀⢀⠦
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⠇⢸⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢹⠀⢈⠀⢶⡀⠀⢂⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣼⡷⢲⢀⠀⢳⡄⠀⢀⠀⢘⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢈⣿⣿⣿⣿⣿⣿⣗⠁⢸⡆⠈⠻⣦⡀⠀⠼⢦⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⢿⠿⠿⡟⢻⣿⣯⣿⡾⠶⠿⠶⣄⡀⠙⢲⡆⠈⣄⣠⡄
⠀⠀⠛⠀⠉⢠⡤⣴⠀⠀⣀⣀⣸⡗⢒⣯⣿⣿⡟⠉⠀⠀⠀⠀⠊⣿⡄⢀⣿⣀⠉⠉⠀⠀⠀⠀⡀⣤⣾⠓⣴⣸⣃⣠⣄⢀⡀
⠀⠀⠈⠰⡆⠈⠁⠾⠂⠀⢹⣿⣯⠟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣼⠿⠧⠤⠀⠉⠀⠁⠀⠐⠶⠶⢿⣿⣿⣿⢿⣿⣿⡟⡚⠒⠓⠂
⠀⠀⠀⠀⠈⠒⠠⠤⠖⠀⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡳⠋⠁⣽⠀⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠛⠒⠋⣻⡧⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⢿⣆⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⣧⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢀⣴⡏⠍⠀⠈⢹⣷⣄⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⡄⢸⣿⣷⠀⠀⠀⣸⣿⣿⠀⠀⠀⡠⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣳⠀⠛⣿⣯⣾⣶⣿⣭⣍⡀⠀⠸⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠉⠋⠉⠁⠁⠉⠛⢿⣿⣿⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⡄⠀⠀⠀⠀⠀⠀⠐⣿⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⢀⣾⣏⣄⠄⠀⡀⠀⢀⢠⣤⣿⠷⣄⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣶⣖⣶⢊⠿⠏⠀⢢⠆⠯⠿⣿⣷⣾⡷⣿⣾⣿⡿⣿⣫⠅⠄⠀⠈⢳⣶⣶⠦⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠃⡤⣶⣶⠛⠉⠍⠁⠛⠋⠁⣳⢶⣖⢤⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠘⢈⢿⠙⠛⡦⣤⠄⡤⠤⠴⠟⠛⠈⡍⠉⡀⠀⠀⠀⠀⠀⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢀⠂⠀⠘⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠌⠀⠠⠀⢹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢪⡟⠙⠃⠀⠄⠀⠠⠄⠀⠐⠁⣉⠀⠰⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣡⠋⢰⡀⣀⠀⠀⠀⠀⠀⠀⢠⠰⣿⠀⠀⠙⢮⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠈⠛⠙⠂⠀⠀⠄⠠⠤⠖⠂⡉⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⣀⣤⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠉⠋⠋⠉⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠞⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣛⣛⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣩⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣴⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⢊⣭⣍⢺⣿⣿⣟⣋⡥⠾⢿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⡘⠿⠟⣸⣿⣿⣿⡏⢼⣿⡇⢹⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣴⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⠟⣩⢹⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠟⣡⣾⣃⣚⣛⣛⣛⣛⡛⢦⡙⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣭⣭⢉⣭⣥⣾⣷⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠷⠶⢆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⣛⣛⣛⣛⣃⣼⣿⣿⣿⣿⣿⣿⡿⠟⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣭⣭⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠦⣤⣤⣀⢀⣀⡀⡄⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣷⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⡭⢽⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⢱⣆⠀⠀⢿⣷⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣶⣿⡏⠁⠀⠀⡀⠂⠀⣤⠞⠉⢠⠏⠀⠀⠀⣸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⣬⣿⡵⠋⠠⠀⠀⣼⢶⢦⣀⢷⣿⣿⣿⣯⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⡟⢉⠆⠀⠀⠀⣼⣷⢸⣿⣾⠏⢻⡌⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⡃⠀⠀⡀⠀⣼⡿⠉⠀⣿⡆⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⣶⣿⣿⣦⡶⠋⠀⠀⠀⠁⠀⠂⢀⣾⠉⠀⠀⠀⢸⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠈⠻⢿⣿⡿⠁⠀⢀⠀⠀⠀⢀⣤⢻⣿⠀⠀⠀⠀⠈⢿⡆⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⢀⣿⠇⠀⣿⠀⠀⠀⠀⠀⢀⠇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⡷⢀⡄⡀⠀⠀⠀⢾⠀⠀⠀⢀⣀⣴⣿⠇⠀⢀⣿⡆⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢷⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⠇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢏⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢉⣼⣿⡏⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⣆⣿⣰⣶⣶⣵⣿⣿⣿⠿⠁⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠛⠛⠻⡿⣿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀⣠⣤⣠⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⢀⠂⠀⣀⠀⠀⠀⢠⣢⡘⠋⢈⠷⣣⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢃⡸
⠀⠀⠀⠀⠀⢤⣈⠂⠀⠀⠎⠁⣏⠹⢗⣋⢁⠙⠧⢔⡄⠀⠀⠠⠺⠇⢀⠀⠀⠀⠀⠈⠁⣠⣞⠱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠙⠁⠛⢣⣄⣓⢬⠄⣬⡒⠇⠀⠠⠀⠀⡀⠀⢉⠖⠀⠀⠾⢿⡟⠉⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢶⢄⣤⣼⢀⠁⠾⠧⠕⡀⡄⠀⠀⡀⣠⢴⠛⢋⠠⢂⠀⠤⣀⡄⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠡⠐⠂⢌⠉⠰⠆⠁⠀⠈⠉⢿⡁⠊⠁⠀⠀⠀⠀⠈⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠈⠑⠂⠤⡀⠀⠀⠁⠈⠼⠀⠀⠀⠈⠙⠷⠤⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠢⣄⠉⠒⠄⣐⠂⠀⣆⡀⠀⢀⠀⣀⠂⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⠀⠄⡠⠀⠀⠤⠀⠀⠀⠠⢠⠐
⠀⠀⠀⠀⠉⠀⣠⣿⡟⠓⠚⢷⣾⡚⠛⠋⠙⠲⠀⠀⠀⠠⡀⣠⡆⠀⠈⢹⣦⡇⣀⠀⠂⠠⠠
⠀⠀⠠⠊⢀⠾⠛⣿⠷⠒⠂⠀⠀⠘⠯⠶⠲⢾⠆⠀⠐⣎⠂⠀⠀⠀⠀⠈⠨⠛⡧⢶⣠⣇⣰
⠀⠀⠀⠈⠁⠜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠁⢀
⠀⠀⠀⠀⠘⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠖⠦⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢡⣶⡀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⣦⠀⠉⠀⣐⠆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣦⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⠉⠉⠉⠉⠈⠉⠉⠙⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⢾⠟⢛⠛⠻⡷⠀⠀⠀⠀⠀⣠⣴⣶⠿⠃⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠛⠛⢉⣠⣤⣀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣸⣿⠀⠀⠀⠀⠀⢰⡿⠋⠙⢻⣷⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⠘⠿⢷⡾⠟⠃⠀⠀⠀⠀⠀⢻⣷⣀⣀⣼⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⣠⣾⠿⣿⡆⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⣼⡧
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⡿⢃⣼⡟⠁⠀⠀⠛⠛⠛⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⢗⣴⡿⠋⢠⣾⣿⣤⣤⣤⣤⣤⣤⣤⣤⡀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠈⠉⠉⠉⢩⣭⣭⣭⣭⣿⠇⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⡯⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⣀⣀⣀⣀⣈⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠻⣵⣦⣤⣤⣀⣀⣀⣀⣤⣤⣶⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⠿⠿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⣠⣾⡿⠋⢀⣤⣤⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⣴⣿⠋⠀⠀⠻⠛⠉⠉⠉⠉⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣦⣤⡀⠀⠈⢿⣷⡀
⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠈⣿⣧
⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠺⠿⠿⠿⠿⠿⠿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⢻⣿⡄⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠻⠟⠀⠀⢀⣿⡟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⣿⣿⠀⠀⣀⣠⣤⣴⣶⣿⡿⠿⠛⣋⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣿⣿⣾⡿⠿⠛⠛⠉⣥⣴⣶⣿⠿⠿⠛⠁⠀⠀⠀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣹⣿⡇⠀⠀⠀⢀⣠⣴⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠀⠀⠀⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡿⠃
⠀⠀⠀⠀⠀⠘⢿⣧⣀⠀⠀⠀⢀⣀⣠⣤⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⠿⠿⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⡀⠘⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢦⠘⢦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠓⢤⡀⠀⠀⢣⡀⢻⡆⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⡀⠉⠓⢄⠈⢷⠈⣷⠀⠀⠀⣧⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢢⠈⢧⢹⣇⠀⢠⣿⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⣆⡑⢬⡳⣿⣦⠘⢇⣤⣤⣶⣦⣄⡟⢀⡤⠤⡄⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠝⣶⣭⣿⣿⣿⣧⡈⠉⠻⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⢠⣶⣶⣶⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠛⠛⠛⠛⠁⠙⠛⣿⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣷⣶⣶⣶⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣴⠿⣿⡿⠋⠙⠉⢿⣿⣿⣿⣿⣿⣴⣻⣿⣿⣿⡠⣦⣌⡀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⠟⠋⠁⠀⣰⣿⡃⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡻⣧⢾⣝⠻⢷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣼⢟⠟⠁⠀⠀⠀⣰⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣟⠛⠋⠈⠳⣮⠛⠦⣬⡉⠛⠒⠠⣄⡙⠛⠏⠩⠭⠙⢲⡀
⠀⠀⡀⣀⡴⠞⠉⠋⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢻⣿⢿⣄⠀⡀⠀⠠⠀⠀⢀⡉⠉⠀⠂⠀⠉⠉⡁⠉⠐⠀⣸⠟
⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⢀⣸⣿⠈⢿⣷⣷⠀⠀⠀⠐⠠⠙⢶⣤⣄⣀⠀⠀⢀⢑⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢄⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠤⣀⠙⢿⣿⣿⣿⠿⠋⠀⣾⡏⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠛⠛⠉⠀⠀⣠⣾⡿⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣾⣿⡟⠁⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠙⣆⠡
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠉⠉⠛⠶⣤⣀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡼⠁⠀⣈⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣸⠴⢒⣾⣷⢴⡏⠁⠀⠘⠛
⠀⠀⠀⠀⠀⠀⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣠⠋⠀⡜⠁⢀⠈⢳⣈⣦⡀
⠀⠀⠀⠀⠀⠀⠙⢄⡈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠇⠀⠀⢄⠻⠿⠃⡜⣀⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠲⠄⠉⠓⠢⠤⣄⣀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠈⠑⠒⠉⠐⠭⣁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠾⣿⣷⣍⠉⠉⠻⣿⣯⠱⣄⠀⠐⢦⣀⣀⣀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⠀⠀⠈⢿⣿⣦⠀⠀⠙⣿⣧⠈⢳⡦⠤⠭⠥⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡄⠀⠀⢻⣿⣇⠀⠀⢹⣿⠀⡼⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆⠀⠈⣿⣿⠀⠀⢸⣿⢟⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⢿⣿⣿⣷⠀⠀⣿⣿⣀⣤⠞⢁⣼⠇⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠛⠛⢩⡿⠁⣾⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠟⢠⣾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠾⠿⠟⠛⠛⠻⠿⠷⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠀⠁⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⢀⣴⠾⠷⣶⡄⠀⠀⠀⠀⢰⡿⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠻⠃⠀⣾⠏⠈⢻⡆⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠛⣷⡄⠀⠀⠀⠀⠀⠀⣿⡀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠿⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⢿⡆⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⡦⠀⠀⠀⣠⣶⠟⠉⢀⣴⡿⠃⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⣴⡾⠿⢷⣦⡀⠀⠀⠀⠀⢀⣤⡾⠛⠁⣠⣶⠟⠉⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠙⢷⣄⠀⠘⢿⣦⡀⣀⣴⠿⠋⠀⠠⡾⠛⢻⣦⠀⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠈⢻⣦⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⣤⣾⣧⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⡀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡤⣄⠀⠀⠀⡠⢤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠃⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣤⠀⣀⠈⢧⠀⠐⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⣞⠀⠀⠀⠀⠀⠱⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠍⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⡍⠠⠇⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠤⠀⠀⠐⠉⠀⠀⢀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠀⠀⢘⠂⡢⠀⠀⠀⣇⣸⠁⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠀⠔⠀⠀⠀⠀⠀⠈⠱⠀⠀⠄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⠀⠀⢠⣀⠀⠁⠀⡀⠀⠀⠀⢀⣀⠀⠀⠄⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⠀⠀⠀⠚⠋⠀⠀⠄⠁⠀⠀⠀⡀⠀⠀⠠⠀⢠⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠈⠀⠀⠎⢀⡀⢀⠀⠆⠀⣀⣀⠇⠀⠀⠄⠂⠀⠒⠐⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⢀⠔⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠀⠒⠒⠶⠒⠒⠚⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢷⣤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⢤⢀⣀⢛⡿⣿⣯⣿⣿⡃⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⡤⢚⠤⡢⠌⡙⢻⠽⠛⠛⠋⠉⠉⢗⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⡠⠀⠀⠘⢦⡹⠛⢀⢻⡤⠐⠀⠒⠒⠘⠙⡆⡛⡀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢈⠀⠀⠀⣌⣀⡃⠀⠀⠀⠣⠶⠶⣶⣶⣶⣶⣷⣣⡙⠙⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢠⠉⠱⠃⠀⠸⠀⠤⠀⣒⣂⠒⠂⢹⣷⡿⢋⡗⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⡀⠘⠀⢀⠤⠀⠰⠀⠀⠀⠬⠝⠀⠀⠘⣇⠄⠜⢋⣄⡲
⠀⠀⡀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠁⠀⢀⠄⠀⠘⠀⠐⢊⠀⡗⠀⠀⢄⡐⠆⠀⠀⢠⠯⢰⡊⢳⡧⠄
⠀⠀⡇⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡅⠂⢆⢀⣸⠀⠀⠀⠰⣄⣼⢃⡟⠭
⠀⠰⠁⠀⠀⢀⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠄⠀⠀⡃⢀⢰⣿⣿⡇⠀⠀⠄⣏⣼⡎⣵⡂
⠀⣇⠀⠆⠀⠀⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠠⠔⠋⡰⡜⠁⠀⡀⠀⡇⠀⠀⢻⡟⠷⠂⠀⡾⢃⡾⠺⠁
⠀⡧⠀⢇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠠⠤⢀⠴⢒⠈⠂⠁⠹⠯⠒⣀⠃⠀⠀⣇⣃⣶⠀⠀⣷⠾⠄⠀⣆⠃
⠀⢣⠡⢈⡂⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠗⠀⠖⠀⠂⠀⠀⠀⠀⠀⠈⠛⠿⠟⠉⠀⢛⡕⠀⠀⠀⠁
⠀⠀⡇⡰⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠃⠄⠀⢔⠂
⠀⠀⠣⠤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠁⠀⠈⠁⠐⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢰⠂⠀⠀⠠⢄⡀⠤⣀⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠁⠘⠀⠀⢄⠀⠀⠉⠒⣝⠢⣉⠢⢕⣦⡀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠺⠃⠂⠀⠀⢀⠀⠀⢄⢠⡉⠢⢄⠀⠈⠑⠢⢕⣄⠙⢷⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠤⡀⢀⠂⠷⣄⣢⡓⢝⠲⢤⣉⠒⢄⡀⠀⠈⠑⠦⡉⢧⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠃
⠀⠀⠀⠀⠀⢀⠃⡄⠀⠀⢰⠋⠑⠉⠐⠂⠥⠝⢻⠷⢾⣿⣯⡢⣈⠢⡀⠀⠀⠈⠢⣃⠀⠀⠀⠙⠢⢄⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⢸⡀⠇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⠈⠂⠀⠀⠠⡙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠴⠒⠋
⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⣇⠴⠒⠲⠶⢤⡄⠀⠀⠀⢠⡴⠶⠒⠒⢿⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠉⠀⠀⠉⢒⡄
⠀⠀⠀⠀⠀⢸⠀⢃⠀⠀⡇⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠑⣄⠀⠀⠀⠀⢷⠀⠀⠀⠳⠖⠒⠒⠒⠋
⠀⠀⠀⠀⠀⡎⡄⢨⡄⡇⢰⠙⠃⠘⠛⠀⠁⠀⠀⠀⠈⠀⠛⠓⠈⠋⠀⠙⢧⠀⢡⠀⠈⡀⢧⣀⣩⡄
⠀⠀⠀⠀⠀⢱⢸⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠀⠘⡆⠀⠇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⣾⠀⢠⡇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⡿⢀⠏⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⢻⠀⢸⢰⠁⣻
⠀⠀⠀⠀⠀⠀⡇⢸⠀⢿⢻⡄⠀⠀⠀⠠⠀⣤⣤⣤⠀⣀⠀⠀⠀⠀⡏⣼⠀⣼⠃⡰⡃
⠀⠀⠀⠀⠀⠀⡄⠸⠀⠘⡘⣷⡀⠀⠀⠀⠲⢤⣤⡤⠖⠁⠀⠀⢀⢼⠁⡇⡰⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠱⠀⢣⡀⠇⡇⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢸⠀⡱⢁⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠇⠀⢳⠀⠃⡷⠃⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⢀⠁⠆⣾⠁
⠀⠀⠀⠀⠀⠀⢸⠘⡆⠈⡟⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⣼⣿
⠀⠀⠀⠀⠀⠀⡜⠀⣧⠀⢧⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⢸⠇⢡
⠀⠀⠀⠀⠀⢰⠇⠀⡿⠀⡘⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠈⡄⠀⢣
⠀⠀⠀⠀⠀⡏⡇⢸⠃⠀⡇⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⢁⠁⠀⠁
⠀⢀⣀⠠⠄⠛⢅⡘⠀⡘⠡⡀⠷⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣿⠀⢸⢀⠀⡀⠲⠄⣀⣀
⠉⠁⠀⠀⠀⠀⠈⣡⣼⣡⡔⠱⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡄⢨⠌⡀⠀⠀⠀⠀⠀⠉⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠞⠉⠈⠉⠙⣧⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⢹⡿⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡜⠻⢦⣄⠀⠀⠀⢀⣠⠾⠋⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠛⠆⠲⠋⠀⠀⠀⡠⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠑⠀⠉⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠃⠀⠀⠈⠐⠐⣠⠈⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠇⠀⠒⠰⠤⠒⠉⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠡⠆⠠⠌⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡺⣿⠕⠁⠀⠀⠀⠀⣀⣔⣤⣂⣠⢄⡤⢒⣈⡩⠤⣔⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⣿⠿⣶⣄⠀⣀⣔⣮⣷⠿⢶⣀⡤⠝⠫⠤⠤⠜⠒⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣴⣿⢿⡿⣿⣿⣿⣿⣿⡿⣟⡿⠿⣿⣭⣶⣿⣿⣅⣀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠨⣼⣿⣿⣿⣿⡵⣫⣵⣶⣿⣿⣿⣿⣿⣿⣿⢻⣷⣶⢀
⠀⠀⠀⠀⠀⠀⢸⡟⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⠃⣼⣿⠟⢰⣷⡀
⠠⠄⠒⡨⠑⠓⢾⡇⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠐⡂⠀⠛⠃⢠⣿⣿⡿⣦
⠀⢠⠎⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣻⣿⣿⣿⣿⣿⣿⣾⣿⡶⢀⡀⠈⠙⠟⣹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠋⣁⣩⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⣀⣼⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣼⣿⠟⠛⠋⠙⠛⢻⣿⣿⣌⠛⠛⢻⣿⣿⣿⣿⣿⣿⣶⣿⡿⢛⣩⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⠀⠀⠀⠀⠀⣾⣿⠛⢿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⢻⣆⠀⠀⠀⣠⣿⠏⠀⠘⠛⠷⠄⣽⣿⡈⠻⣿⣿⣿⣿⣿⣷⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠈⢿⡄⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠈⠙⠿⢿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠼⠋
⣿⣿⠛⢿⢻⠿⡿⢻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⣰⠁⠀⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠈⠓⢴⠁⠀⠀⠋⠈⡇⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⢱⠀⠀⠀⠈⡃⣠⠶⣀⡜⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠸⠇⠀⠀⠀⠒⠧⣄⢸⠀⠀⠀⠀⠀⠀⠐⠁⢀⡴⠁⠀⡰⠁⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠴⢆⣀⣔⢦⠀⠀⠈⢦⡀⠀⠀⠀⠀⠌⢀⡴⠋⠀⠀⠀⠠⠄⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡌⡅⡀⠈⡀⠨⠈⠀⠀⠀⠈⡇⠀⠀⢀⢊⡼⠁⠐⠒⠀⣈⡡⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⠑⠣⠥⠜⠀⠀⢰⠆⢠⠙⡄⠠⠂⡾⠐⠈⠉⠉⡩⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠒⠂⠀⠀⢀⠔⡩⣠⡃⠀⠈⠀⠊⠀⣀⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣤⣤⣴⣶⣿⣿⠟⣿⣿⣯⠙⢿⣿⣿⣷⣆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣹⣿⣿⣿⠟⠁⠄⢸⣿⣿⡆⠀⠹⣿⣿⣿⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉⠉⠀⠀⠀⢸⠀⣿⣿⣿⠀⠀⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⢀⣠⣿⠀⣿⣿⣿⣄⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⠊⣀⡱⠀⠀⡠⠘⢿⡤⣟⠛⡓⢌⠑⠠⣖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⡄⠙⡄⠀⠀⠑⠲⠀⠀⣘⡠⠼⣦⠿⠭⡊⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠰⣉⣀⡠⠗⢹⡇⠀⢃⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠓⠒⠒⠊⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡤⣠⣤⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡅⡘⢡⢆⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⡧⠌⠻⢨⣻⢤⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠌⠩⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⢀⣀⠀⢀⠀⠠⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡿⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣦⠄⢐⡀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠙⢤⠛⠉⠉⠉⠀⠀⡀⠀⠘⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⣧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀⡀⠀⡠⠒⠠⡀⠀⠀⠀⡼⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡃⠀⠀⢹⣀⢀⡴⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠇⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⡏⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠁⠐⠀⠀⠀⢀⣟⣋⣭⡭⡭⠙⢦⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠛⠁⠄⠀⠀⠀⡠⠞⡭⠿⠿⠏⠴⠶⠐⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⣼⠋⠑⠊⠀⠒⡄⠀⡦⣀⠆⠙⠻⡆
⠀⠀⠀⠀⠀⠀⢠⡏⠡⠀⠀⠀⠀⠀⢸⠇⢠⠀⣀⠀⠀⠑⠤⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣧⡶⠒⠒⢤⠀⠀⢸⡏⢸⢓⡿⣰⠶⣷⣼⣷⠿⢲⡞⠀⡷⠀⡀⠲⡄
⠀⢀⡀⠀⠀⠘⠀⢾⠀⠀⠀⠀⠁⠀⠈⢧⠄⡀⠀⠈⠀⠀⠁⠀⠀⠜⠁⢰⣗⠀⠀⠀⡇⢀⠲⣄
⠀⠀⡌⠉⠁⣰⢒⠉⣓⢦⡀⠀⢀⢴⣀⣸⣞⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢀⠀⢀⢠⢣⢣⠂
⠀⠀⠀⠀⠀⢿⠁⠀⠈⠁⠀⢠⠎⠀⠀⠀⠹⢍⠁⠀⠀⠀⠀⠀⠀⢀⡞⠙⡲⠂⠘⠁⠛⠁⠒⠊⠄⠂
⠀⠀⠀⠀⠀⠀⠙⠷⢤⣀⡀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠐⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠢⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⡀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠄⢀⣀⠀⠄⠀⠢⠤⠄⠤⠄⠐⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠈⠉⠈⠉⠲⢄⠀⠐⠈
⠀⠀⠀⠀⠀⠀⡀⠀⡁⠂⠀⠑⡄
⢀⡂⠀⠀⠀⠘⠟⠀⠏⠀⠀⠀⢱
⢠⠑⡄⠢⠄⣀⠀⠀⠀⡀⠀⠀⠘
⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⡌⠑⠢⢄⣀⢀⠀⡄⠊
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠢⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠒⢄
⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠁
⣶⣶⡶⡶⠶⢶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠱⢃⡴⠖⠶⢤⣀⠀⠀⠀⠀⠀⢠⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡀⠀⠀⢌⠳⢄⡀⠀⢀⣼⣜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠏⠉⠉⣩⠍⣓⠳⢤⣵⡒⣮⠻⠟⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣆⣀⣈⡴⠲⢤⣵⢤⠤⠃⣼⡷⠖⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣴⡙⠷⣤⡗⣿⠁⠈⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⡄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣛⡷⡟⢸⠀⠀⠀⠀⠀⠀⣴⣋⠭⠖⠒⠂⠈⠁⠀⠉⠀⡨⢿⠿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠟⠀⠛⠀⠀⠀⠀⠀⠀⢸⡷⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⢦⡀⠀⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⣤⣄⣁⣀⣀⣀⣀⣀⣀⣸⣇⠀⠠⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡉⠙⠯⠍⠉⠙⠛⠛⠛⠉⠉⠩⠽⣶⣬⢹⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠑⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡓⠆⠀⠀⠀⠀⣀⠤⠤⠶⠤⣄⣀⡀⠀⠸⣧⠿⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣤⣀⣀⣠⠞⠁⢀⣠⣤⡀⠀⠙⣦⠀⠀⢰⢾⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⣴⣿⣿⣿⣿⣷⡄⠘⣿⣿⣿⣛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡿⢭⣿⣧⠀⢿⣿⣿⣿⣷⣿⠁⢠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣒⡢⠔⠛⣦⣬⠉⠛⠿⠋⠡⣪⠟⢩⠤⢌⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣗⡀⠀⠀⠙⠳⠶⠶⠖⠛⠁⠀⠠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠐⠩⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣄⣀⣀⣤⣤⣄⣀⣀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠶⣤⣌⡒⠦⣄⡀⠀⠀⠀⠀⠀⠸⣯⣀⣉⣛⠙⠛⠛⠛⠉⢙⣻⣿⠇⠐⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⠬⠙⠓⠶⣭⣓⠦⢄⡀⠀⠀⠀⠈⠉⠙⢛⣛⠛⢛⣛⣋⣉⣁⠀⠀⣀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢙⡻⢶⣮⣀⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠢⡈⠙⠽⠳⢶⣄⡀⠀⠀⠈⠑⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡈⢦⣄⣐⣐⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣄⣭⣤⡁⢂⣡⡼⣁⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣿⠛⠋⠥⠤⠤⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⣀⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣠⣤⣤⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣀⠀⢀⠀⠀⠀⠀⢠⣶⢾⣏⠁⠉⠁⢨⣿⠷⣶⡀⠀⠀⠀⠀⠀⢀⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣧⡀⠀⠀⣿⣿⣦⣽⡀⠀⠀⣾⣷⣴⣿⡇⠀⠀⢀⣤⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⡈⢿⣿⣿⣿⣷⡀⣀⣿⣿⣿⣿⢃⣤⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⡿⠿⠛⠛⠿⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⠃⠀⠀⠀⠀⠀⢬⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣾⣿⣯⠀⠀⠀⠀⠀⠀⡀⣢⣿⣿⣿⣷⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠜⠈⢉⣽⠟⠛⠻⠿⢿⣿⣠⣆⣀⡀⢠⣥⣿⡿⠿⠿⠿⢿⣟⠶⠟⢧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⢀⣴⠟⠁⠂⣠⣶⣾⣿⠟⠉⠋⠉⠹⠈⠃⢹⣾⣶⣤⡀⠀⣻⣦⠀⠈⠹⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢀⣴⠟⠉⠀⠀⢸⣿⠟⣿⣥⣤⢀⣀⡀⣤⣴⣶⣾⣿⣿⣿⣿⡆⠀⠙⢧⡀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢀⠀⠀⢼⣿⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡇⢹⣷⠀⠀⢈⠻⣦⡀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⠀⠀⠀⠀⢁⣿⣿⢸⣆⣀⣀⣈⢀⡀⠉⢉⣀⣠⣴⣾⡇⠸⣿⣧⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠈⠀⠀⠀⢀⣾⣿⠁⢸⠹⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠀⠙⣿⣦⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠈⣷⣆⣤⣄⣠⣄⢀⣤⣴⣶⣶⣾⡇⠀⣄⠘⠻⠷⣄⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢀⣴⠾⠋⡀⠀⠀⠀⠀⠸⣍⣛⠛⠛⠿⠿⠟⢛⣛⣩⣿⠁⠀⢸⢆⠀⠀⠙⢦⣤⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣾⣿⣿⣿⡿⣿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠛⠋⠀⠀⢀⣡
⠀⠀⠀⠀⠀⠀⠸⠷⠤⠤⠴⠞⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⣠⣤⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣀⠤⢄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⠞⠁⠀⠀⢣⠀⠀⢸⡆⠀⠀⠀⠀⠀⡰⠁⣀⣀⣀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⡞⠀⠀⠀⣠⣸⡆⠀⠀⠇⠀⠀⠀⠀⣠⠗⣩⣄⠀⠈⢳⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢸⠁⠀⠀⢰⣋⣿⣇⠀⠀⠀⠀⠀⠀⣰⠏⣸⠛⣿⡇⠀⢸⡆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⣰⡏⠀⢹⣾⣿⠇⠀⢸⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣶⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⡿⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠀⠀⣼⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢹⢀⣠⡤⠾⠦⢤⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠈⠓⢄⣸⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⣀⠴⠖⠒⠉⠉⠉⠉⠁⠒⠢⢼⡀⠤⠤⠤⠤⠤⠏⣀
⠀⠀⠀⠀⠀⣠⡧⠤⠤⢀⡀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠉⠑⠤⡀
⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠈⠲⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠈⢻⡶⢤⣀⡀⠀⠀⠀⠀⠤⠴⠚⠁⠀⣀⡤⠴⠖⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢳⡀⠀⢀⣀⣀⣀⣀⣀⣀⡤⠖⠋⠁⠀⠀⠀⢀⡼⣕⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡅⠀⠈⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠠⠴⠒⠋⠁⠀⢀⡞⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠀⠀⠀⠀⠀⣀⣀⡤⠴⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠠⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠒⢛⣉⣩⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠛⠉⠁

⠀⠀⠀⠀⠀⢰⢠⣀⣂⣀⡄⡀⠤⠀⠀⠀⡠⣀⣀
⠀⠀⠀⠀⠀⠘⠚⠀⠛⠃⠓⠃⠃⢀⡰⠚⠁⠁⢹⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣤⢫⠓⡄⠀⠠⡌⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⢸⣷⡏
⠀⠀⠀⠀⠀⠀⠀⣇⠑⢁⠄⠀⠀⠈⠙⡶⠀⠀⠘⢻⡂⠀⠀⠀⠙⢿⣾⠃
⠀⠀⠀⠀⠀⠀⠤⡷⣴⠝⡆⠀⠀⢀⣶⠢⡌⢠⡇⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣆⣀⣀⣤⣤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣧⣇⣀⡘⠉⠀⠘⣿⠟⢀⡎⣍⠗⠒⠀⠀⢀⢂⡿⢻⣷⣀⠀⠀⠀⠀⠀⢀⣦⣾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣭⣮⣄⠀⠀⢠⣡⠴⠃⢌⠉⠀⡆⠀⠀⣸⣧⣃⣠⠀⠻⢷⣄⠀⠀⢀⡿⠋⣁⣄⢀⡀⠀⠀⠀⠀⠀⠀⡄⠀⢿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡃⢹⣆⠀⠀⠙⢿⠀⢈⣠⡞⠀⠀⠉⠛⢛⠿⡧⠀⢠⣾⢿⡆⣠⣾⡦⠀⠹⠋⠻⡄⢠⣄⡀⠀⠀⠀⡇⠀⣼⢁⠇
⠀⠀⠀⠀⠀⠀⠠⠈⠟⢳⠊⠿⠀⣀⣠⣔⣀⣼⣡⠧⠤⠤⠀⠀⢈⢦⣄⡀⠀⢛⣸⣷⣤⢭⣇⣴⠗⠂⠀⠙⣨⡩⡉⠉⠉⠉⡧⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠑⠯⠊⠀⠀⠀⠉⠀⠀⠀⠀⠛⠂⠛⠃⠀⠀⣴⡷⠚⠿⠗

⣿⠛⣿⠛⣿⠛⣿⠛⣿⠛⣿⠛⣿⠛⣿⠛⣿⢛⣿⢛⣿⢻⣿⢻⣿⢻⣿⢻⣿⢻⣿⢻⣿⢻⣿⢻⡟⢻⡟⢻⡟⢻⡟⢻⡟⢻⡟⢻⡟⢻⡟⢻⡟
⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠰⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⣸⣷⡾⠷⠾⠧⣼⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⠟⠁⠀⠀⠀⠀⠀⠑⠸⠷⠾⢧⣼⣇⢸⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⠸⣿⡼⠟⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠈⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⢠⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⢸⣿⠞⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⣀⠿⣴⣿⣼⣿⣼⣿⣘⣿⣸⣿⣸⣿⢸⣧⢲⣶⢹⣿⢦⣤⣀⣀⣠⡤⢺⡗⢲⡶⢿⡟⢻⡇⢸⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⣀⠟⠊⠁⢁⡉⢩⣭⣍⣻⣿⣿⣿⠿⠷⢶⣯⠻⢿⠿⣼⡿⢸⣿⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⠀⣿⣠⠟⠁⠀⣀⣤⠶⠶⠶⠾⠿⣿⣿⡿⢯⡻⣓⠢⢀⠁⠂⠀⠀⠙⠺⣿⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⢀⡟⠁⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⢧⡀⠀⠳⡀⠁⠄⠀⠀⡀⠀⠈⠻⣇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⠀⣿⠀⣿⠏⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠙⣆⠣⡈⠀⠀⠀⠀⠀⠄⠀⠠⠙⣾⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⠀⣿⡠⠃⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⢣⡰⣄⠀⠀⠀⠀⠀⠂⠀⢠⢹⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⠀⡟⠁⠀⠠⢰⠃⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠾⠿⠗⠶⢬⠢⣀⠹⣎⣧⡀⠀⡀⠀⠀⠀⠸⣾⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⡔⠀⠀⠐⠀⣾⠴⠶⠿⠿⢆⠀⠀⠠⠈⠁⣀⣤⣤⣤⣀⠀⠀⠈⢷⠶⣿⣷⠀⢱⠀⠀⠀⠀⣿⣇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⠁⠀⠀⠀⣼⣿⣤⣶⢶⡶⡄⠀⠀⠀⠀⠘⠉⢀⣂⣬⠟⠀⠀⠀⠀⢳⢶⢿⣧⢸⠀⠀⠀⠀⢸⣇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⠀⠀⠀⣸⣿⣿⠛⠦⠮⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⢸⣿⠀⢸⠀⠀⡆⠙⣾⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⠦⠀⠀⢿⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠿⡀⢸⣇⠀⢻⡀⢈⠳⣼⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⠀⣿⠀⣷⢄⢘⡾⡇⠀⠀⠀⠀⠱⢤⠀⠢⠄⠠⠃⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢈⣷⡀⠈⠉⠛⠚⠦⡙⢆⠁⠸⣇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⡀⣿⠀⣿⠈⣿⡷⢻⡀⠀⠀⠀⠠⠀⢠⠈⠂⠠⠤⠀⠀⠀⡐⠄⠀⠁⠀⠀⠀⢸⡟⣿⣷⣦⣄⠉⠢⡀⠘⣧⢹⣿⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⡇⣿⠀⣿⠀⡿⠁⡌⢳⡀⠀⡴⢁⣘⡥⠂⠒⠈⣁⠉⠘⠛⠁⠀⠀⠀⠀⠀⢀⣾⢱⡇⢸⡝⢛⠙⡄⢹⠀⢙⣼⡟⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⡇⣿⠀⣿⡄⠀⠰⢀⡞⢹⣦⡀⠈⠩⡉⠁⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣠⡿⣿⠸⠀⡀⠳⣄⣀⣰⣸⢠⣿⢿⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⡁⣿⠀⣿⠇⠀⠀⠊⣰⡏⣏⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⢹⣧⡱⣌⣲⣬⣽⣷⣿⢿⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⡇⣿⠀⣿⠈⣷⡀⡀⢿⢟⢻⣷⢭⣽⣦⡀⠀⠀⠀⠀⣀⣤⠴⠛⠉⠀⠀⠀⠀⢸⡏⠙⠲⣿⢿⡟⢻⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⡇⣿⠀⣿⠀⣿⠙⣦⢬⡢⣥⣿⡶⣿⠀⣿⢹⣶⢸⣿⠙⣧⡀⠀⠀⠀⠀⠀⠀⣼⠁⢀⣼⣿⣿⣇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇
⣿⣧⣿⣤⣿⣤⣿⣤⣿⣤⣿⣤⣿⣤⣿⣤⣿⣬⣿⣼⣿⣼⣿⣷⡀⠀⠀⠀⠀⢀⣿⣶⣿⣿⣿⣿⣷⣼⣧⣼⣧⣼⣧⣼⣧⣼⣧⣼⣧⣼⣧⣼⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠛⠛⠲⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢶⣄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⣤⠶⠚⠛⠛⠛⢶⣄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠙⣷⡀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⠋⠁⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠸⠿⠋⠙⢷⡄⠀⢸⡇⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡇⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠷⠿⠶⣤⣀⠀⠀⠀⠀⠻⣦⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠙⢳⣶⣶⠚⠛⣿⣿⣶⣾⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⠤⣄⠀⠀⠀⠀⣼⣿⣿⠀⠀⣿⣿⣿⡇⠈⣿⣿⣿⠉⠙⣿⣯⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⢰⣿⣿⣿⠁⠀⣿⣿⣿⠀⢀⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣀⣠⣾⣿⠟⠀⢠⣿⣿⣿⠏⠀⣸⣿⣿⡟⠀⢸⣿⣿⠇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⢧⣀⣴⣿⣿⣿⠏⠀⢠⣿⣿⣿⠁⢠⣿⣿⡟⠀⣸⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠃⠀⣠⣿⣿⣿⠃⢀⣾⣿⡿⠁⣰⣿⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣾⣿⣿⡿⠁⢠⣾⣿⣿⣡⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⠀⠐⠂⠀⢄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠁⣤⠀⠀⡀⠔⠀⠒⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⠀⡄⠄⠐⠑⠀⡃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⠀⠀⠀⠀⡘⠀⢈⡄⠀⠀⠀⠀⠀⠸⣁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠄⠊⠀⠀⠠⠈⡀⠀⠀⠀⠀⡘⠄⠀⠀⠀⠀⠀⠂⠐⠒⠠⠂⠀⠈
⠀⠀⠀⠳⠀⠀⠀⠀⢀⠎⠈⠀⠀⠉⠘⡄⠀⠠⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠀⠎⠑⠂⠀⠀⡀⠀⠀⠀⠀⠀⣀⠄⠄⡀
⠀⠀⠀⠀⡀⠀⠀⠀⢪⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⡀⠤⣠⠊⠁⠀⠉⠦⠠⠤⡀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⢠⠊⠁⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢄⠀⡀⠀⠰⠉⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠒⠢⡀⠀⠀⠀⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰
⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢠⢲⢀⡔⢦⢠⡖⡄⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠈⢄⣀⡀⡀⡀⢀⠝
⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⡇⠀⠀⠀⠀⠘⠁⠈⠣⠞⠘⠋⠐⠆⠀⠀⠀⠘⠀⠀⢀⠀⠄⠀⠀⠠⠀⠀⠉
⠀⠀⠀⠀⠀⣀⣀⢀⡀⡸⠀⠀⠀⠀⠀⠀⢠⠛⠀⠠⡆⠰⠗⠰⢒⠀⣂⠀⣖⠀⠠⠀⠆⠀⡜⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠤⠀⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⠠⡀⠀⠀⠀⠀⠀⠔⠀⠀⠘⠀⠁
⠀⠀⠀⠀⢠⣀⡀⠀⠈⠀⠀⠀⠀⠀⠈⣄⠀⠑⠂⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠒⠘⠁⠀⠀⠀⠈⢰⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠈⠒⠀⠒⢄⣀⣀⠔⠓⠂⠂⠀⠀⠀⠀⡰⠤⠤⡀⠀⠀⠈⠂⠀⠉⠀⠉⠀⠩
⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡤⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠐⡁
⠀⠀⢀⠂⠈⠀⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠄⡀⠀⠀⢠⠋⠀⠀⠀⠀⠉⠠⠀⠀⠀⠐⠂⠁⠀⠠⠄⠄⡀⠀⠀⠀⣰⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠞⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠡⠀⠱⡀⠀⠀⠀⠀⢀⡪⠀⢀⠄⠐⠐⠀⠂⠠⡀⠀⠀⠀⠉
⠀⠀⠂⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠉⠓⠒⠢⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠑⠂⠅⠉⠀⠀⠀⣴⠀⠀⠀⠀⠈⠢⠀⠀⣀⠄⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠁⢀⠀⠀⠀⠀⡀⠈⠀⢀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⣒⠄⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢻⣛⣟⣙⣛⣟⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠄⢣⣶⢶⡄⠀⠀⣰⣿⣷⡀⠀⠀⠀⠀⠀⠻⠆⢣⣾⠻⣆⠀⠀⣰⡿⣷⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣎
⠀⠈⠻⡾⠃⠀⠀⠙⣻⠟⠀⠀⠀⠀⠀⠀⣾⣿⣧⣛⣚⠃⠀⠀⠈⣛⠛⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏
⠀⠀⠟⠉⠀⣀⣀⢾⡁⢰⠄⠀⠀⠀⠀⠀⠙⠛⠃⠛⠁⠂⣤⣄⢺⣁⢰⠆⣀⣀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠈⠺⣉⣹⠆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⠃⠉⠁⢺⣏⢹⠂
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡄⣄⣼⣗⠶⠖⠒⠒⠒⠒⠒⢦⠒⠒⠚⠓⠖
⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣤⣇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⢀⡆⠈⠁⠀⠀⠈⠉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢷⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈
⠀⠀⠀⠀⠀⢈⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⣀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⡠⢄⡀⣤⣶
⠀⠀⠀⠀⠀⢿⠶⡄⠀⢘⡃⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⣀⠉⠀⠈⠛⣀⡄⠀⠀⠀⠀⠲⣿⡵⠂⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠰⠋⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠾⡇⠀⢀⠀⠀⠠⠐⠊⠁
⠀⠀⠀⢠⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠈⣄⠀⠀⠸⣿⡂⠀⣀⠀⠀⠀⢰⣾⠚⢗⠀⠀⠀⠀⠀⠀⠀⣴⣂⣽⠒⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⣷⣰
⠀⠀⠀⠀⡅⠀⠀⠀⠘⠻⠃⢻⠀⠀⠈⠉⠿⠶⠞⠁⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠰⣤⢧⠆⠀⠀⠀⡉⢟⣿⣻⢏⠛
⠀⠀⠀⠀⠛⠀⡀⠀⠀⠀⠀⡘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠛⠞⠀⠀⠀⠀⠀⣼⠈⢑⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠰⠛⠉⠉⠈⠉⠉⠛⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠛⠛⠓⠀⠀⠀⠀⠘⣧
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣴⠛⢻⡆⠀⠀⠀⠉⠀⠀⠈⠉⠉⠉⠉⠛⠛⠳⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢻⣄⠀⠀⠀⣰⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠙⠀⠀⢠⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣠⡤⠶⠞⠛⠉⠁⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣿⣤⠶⠾⠛⠋⠉⠀⠀⠀⣀⣀⣤⡴⠶⠚⠛⠉⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⢳⡀⠀⠀⠠⠶⠞⠛⠉
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣟
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠙⣧
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠋
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⣷
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠶⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠒⠒⠂⠀⠐⠒⠠⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⠆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⢤⡀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠰⡄⠆⠀⠀⠀⠰⡆⠀⠀⢀⣀⢉⢲⣄⣄⢀⣀⣠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢰⠃
⠀⠀⠀⠀⠀⢀⠇⠨⠧⠦⠆⠦⠽⠶⠤⠤⠰⠒⢳⣳⣋⡭⠶⠷⢿⠛⠿⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡜
⠀⠀⠀⠀⢰⣅⡰⢀⢠⣀⠴⢬⣀⢀⣠⢀⡴⠖⠉⠈⣃⠀⡀⡄⠈⡆⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠱⠚⠓⠊⠉⠓⢳⢹⣔⣃⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡼
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢰⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⠛⠶⢦⣀⡋
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡴⠛⠂⠉⠒⠀⠤⡀⠈⠑⢆
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣸⡅⠤⣠⣤⡀⠀⠀⠀⠐⠢⣈⡇
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣼⣁⡀⠀⠀⠀⠀⠉⠙⠢⣀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⠑⠒⠂⢤⡀⠀⠀⠹⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠶⠴⠶⠒⠐⠋⠁⠀⠀⠀⠀⠀⠀⢸⣀⣀⣤⣤⣀⠀⠀⠀⠈⠒⢴⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠀⠀⠀⠀⠉⠒⠤⡂⠄⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠠⠄⣀⣤⣈⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠳⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠐⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⠂⠁⠠⠀⠐⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢑⠆⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠑⢦⠀⠀⡀⠀⠈⢀⠀⠰⡆⠁⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠤⠚⠃⠀⠀⠁⠀⡃⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣀⣀⠀⠀⣼⠃
⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠶⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠛⠉⠉⠛⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⠶⢦⣤⡀
⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢶⣤⡀⠀⠀⠀⠀⣠⠟⠁⠈⠀⠀⠀⠀⠁⠈⠻⣆⠀⠀⠀⠀⢀⣤⡶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⣿⠟⠉⠉⠉⠉⠻⣿⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⠾⠟⠛⠉⠁⣴⣯⣤⣤⣤⣤⣤⣤⣽⣦⠀⠉⠛⠻⠷⣶⣦⣤⣤⣄⣀⣀⣀⣀⣠⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣩⠿⠛⠉⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠉⠛⠿⣌⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣼⣷⡄⠀⠀⠀⠀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⣀⡴⠛⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠛⢦⣀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠉⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠛⠛⠛⠛⠛⠛⠟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠉⠉⠩⠙⢋⡀⡈⠉⠉⠩⠰⡒⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢄⣠⠀⣠⠖⠋⠉⠀⠀⠀⠀⠉⠙⠲⢌⠀⠣⡀⠉⢙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡤⠊⢀⠞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠱⡀⠈⡗⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣠⠃⢁⠎⠀⠀⠀⣠⣴⠒⡶⣋⠶⢆⠀⠀⠀⠀⢱⠀⢣⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠖⠂⢸⠀⠀⠀⠘⡄⠓⠀⠓⠉⢁⠎⠀⢀⠀⠂⢈⠀⢀⠕⠀⠀⠀⠀⠀⠀⢀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣔⠁⡀⢸⠀⠀⠀⡀⢸⡀⠀⠀⠀⡎⠀⠀⠀⠀⠁⡸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⡄⠈⢆⠀⠀⠠⢀⡇⠀⠀⢸⠀⠀⠀⢠⠐⢠⠃⠄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠴⠎⣀⠀⠈⢦⡀⠀⠀⠛⠀⠀⡃⡀⡄⡆⠀⡰⠃⠀⠀⡔⠋⠁⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠤⠤⢄⠀⠸⠀⠀⠀⠀⠀⠀⠀⢱⣠⡄⡉⠢⢄⣸⡀⢑⣇⣠⠤⠔⠋⠀⠂⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠑⠀⢇⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠰⣎⡀⢘⡽⢟⡆⠈⠑⢦⡜⠁⠈⠺⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⠀⠠⠔⠁⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣉⣉⣤⡴⢞⡧⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡘
⠀⠀⠀⠀⠀⠀⣠⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⢠⣀⣴⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡌⠀⡜
⠀⠀⠀⠀⠀⠰⡁⠀⢀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠠⠀⠀⠀⠀⠀⠈⠻⣙⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠘⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠊⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⣀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠰⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡔⠉⠉⠲⡀⠀⠀⠀⢻⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢥⣌⣊⠔⠰⠀⠆⡔⡠⢠⢀⠎⡞⠠⠃⢋⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠑⠂⠄⠊⠀⠀⠀⠀⢸⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠢⠤⠤⠤⠤⠤⠔⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣱⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢣⡸⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡠⢈⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡴⠆⣨⢔⠵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⣷⠆⢐⠵⣪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠕⡪⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣩⣂⠅⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣩⣿⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢘⣻⢹⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢕⡏⢸⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⡠⢀⠴⣂⢔⡢⢊⠤⣂⠔⡪⠔⡡⢐⡠⢂⠴⣂⠔⣢⢔⡠⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠥⢻⡰⣛⢕⡾⢳⣄⣿⢔⡠⢂⠄⡢⡤⠔⠔⠠⠀⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣴⢯⣉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠛⣦⡼⠟⠛⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠳⠶⢿⠁⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠳⠦⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⣴⠎⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣱⣾⡄⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢿⣯⡼⠛⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠘⣃⡀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡿⣶⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⡾⣿⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠈⢧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢉⣿⣾⠟⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠟⠷⠟⠈⢇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢀⣠⠴⠖⠛⣛⣛⣛⣋⣉⣉⣉⣉⣍⠩⠭⠭⠽⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠴⠶⠶⠶⠶⠶⢶⣟⣛⡳⢶⣤⡀
⢠⡞⢻⡷⠖⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠉⠙⡆
⢻⡄⠈⠳⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⣤⡤⠴⠶⠞⠋⠁⠀⠀⠀⢹
⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⣄⠀⠀⢀⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⢠⡇⠀⠀⠀⠀⣠⠛⢳⡀⠀⣸⠀⠀⢧⣀⣠⠟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⡄⠀⠀⠀⢰⠋⠉⢻
⢸⡇⠀⠀⠀⠀⣿⠆⠈⠳⠞⠃⠀⠀⠈⠉⠁⠀⠀⠀⢨⡇⠀⠀⠀⣠⠞⠋⠛⠳⣄⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣿⠀⠀⠀⢀⡄⢀⡼
⣾⠀⠀⠀⠀⢸⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢠⡇⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⣹⣦⣤⡴⠾⠛⢻
⡿⠀⠀⠀⠀⣿⠿⠦⠤⣤⠤⠤⠤⠶⠶⠶⠶⠶⠖⠂⣾⠀⠀⠀⠘⡷⠒⠒⠲⠖⠛⠷⢶⡄⠀⠀⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡆
⠱⣄⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢹⠀⠀⠀⠀⠀⣀⣀⣤⠴⡇
⠀⢹⠶⣮⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⠤⠤⠤⠤⢾⡀⠀⠀⠀⣸⠓⠚⠛⠛⠉⠉⠁⠀⠀⢸
⢀⡟⣁⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠈⠁⣈⡉⠉⠉⡁⠀⢠⡀⢀⣀⡀⢀⡀⠛⣷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⣿⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡆⠀⡟⠉⢹⠀⠘⡛⠳⣼⣇⢸⡦⠀⠀⠙⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠁
⠀⠈⢳⣾⣥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠛⠀⠙⠶⠞⠀⠀⠁⠀⠈⠋⠈⢉⣉⣀⡀⣥⣤⣤⣤⣤⠤⠄⠶⠶⠒⠉⠉⠀⠀⡇
⠀⠀⡿⠂⠀⠈⠉⠉⠉⠛⠋⠙⠛⠛⠒⠋⠘⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠰⣟⡡⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠈⠙⣿⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⠄⠒⠛⠋⠉⠹⡆
⠀⠀⠀⠸⣧⠀⠈⠉⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠈⠉⠉⠉⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠸⣧⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠃
⠀⠀⠀⠀⠀⠈⢹⡷⢦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠶⠶⠶⠖⠊⠉⠉⠸⠁
⠀⠀⠀⠀⠀⠀⠘⣶⡠⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣋⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠚⠛⠛⠙⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⢂⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡟⣩⣉⣐⣀⡜⣁⠀⣠⣀⡜⣠⠆⣠⠆⣤⣤⣼⣷⠷⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢠⣴⡶⢤⣤⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⣽⠤⠖⠛⠉⠉⠉⠀⠀⠛⠻⢶⣄⠀⠀⠀⠀⣀⡠⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣠⠊⠁⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡠⠊⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢤⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠆⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠺⠿⠃⠀⠀⠀⠀⠐⠶⠄⠀⠀⠀⣠⡄⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀⠀⠀⠀⢿⠷⠤⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠀⠀⠀⠀⠀⠀⠚⠉⡇⠀⠀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡤⢤⣤⣀⣀⣀⣠⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣒⣢⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⡠⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⣄⠀⠹⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⣀⡠⠤⠤⠴⠖⠒⠒⠚⠁⠀⠉⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢷⠘⡌⢷⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠟⠛⠉⠀⠀⣀⠐⠐⠒⠂⠀⠐⠀⠠⠈⠙⠁⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠀⠀⠀⠈⣈⣧⡤⠤⠶⠒⠚⠉⠁⠀⠀⠀⣠⠴⠚⣉⣤⣶⠶⠶⠶⠂⠀⠀⢀⡤⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⣀⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣰⡄⢳⡟⠻⠼⡁⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣯⡀⠀⠻⣦⠀⠀⠈⢒⠦⣀⠀⠀⣸⠉⠛⠒⠦⣄⣴⡄
⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠀⠀⠙⠿⠭⡷⠿⡡⠒⠉⠉⠁⠀⠈⢱⣏⠉⠀⠀⠀⡤⠀⠀⡿
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣀⠠⠠⡿⠞⠀⠀⠀⣠⠀⠀⠀⢀⣍⣷⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⣴⣿⣿⣫⣷⢦⣤⣒⣨⣤⡴⠞⢳⣀⣠⢴⣾⢟⣀⠀⠀⠈⣿⠷⢄⠂⠀⠠⠄⠳⣄
⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠟⠁⣀⠔⠉⠉⣔⣬⣿⣆⠉⠃⠀⠀⣻⡆⠀⠱⡄⠀⠀⠀⢎⢣
⠀⠀⠀⠀⠀⠀⠈⠉⠹⣄⣀⠴⠾⡣⠒⠶⢀⣜⣹⣿⡝⢎⠢⡀⠀⢸⡟⣦⡀⠘⢦⠀⠀⠘⣾⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⡐⠉⠻⣿⡈⢆⠑⠌⠀⠸⣷⡈⠳⡄⠈⠳⡀⠀⢸⠈⣇
⠀⠀⠀⢀⣤⡄⠀⠀⣠⣴⣿⣿⣷⣄⡜⢰⣇⠀⢸⣟⡘⠪⠀⠀⠀⠀⣻⣧⣀⣼⠦⣄⣕⣴⠻⡖⢃⣤⡀
⠀⠀⠀⢻⣿⣿⣶⣶⣿⣿⣿⣿⣿⣋⣴⣶⣿⣿⣶⣦⣡⡔⣠⠄⣤⣴⣯⣬⣛⣷⣄⠀⠙⢿⠖⢛⠏⣼⡥⠚
⠀⠀⠀⠀⠙⠻⣿⣿⣿⠿⠟⠉⠉⠉⠀⠀⠋⠀⠀⠘⠋⠠⠋⠈⠈⠁⠉⠙⠛⠙⡿⢷⣦⣴⣴⡿⠊⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠀⠶⠀⠠⠄⠠⣤⠀⣠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠴⠀⠠⡄⠀⣤⠀⢠⡄⠀⣈⠀⠀⠁⠀⠘⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠶⠀⠰⠆⠀⣤⠀⣠⡄⢀⣀⠀⣈⠁⠀⠛⠀⠘⠃⠀⠖⠀⠰⠄⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠠⡄⠀⣤⠀⢠⣄⣀⣈⣁⣈⡋⠀⠛⠃⠘⠟⠀⠶⠆⢰⡦⠀⣤⠀⢀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠰⠆⠀⣤⠀⣠⡄⢀⣤⠖⠉⠀⠀⠀⠀⠀⠉⠛⢿⡀⢾⡦⢠⣦⠀⣤⡄⢀⣀⠀⢈⠁⠀⠉⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⣤⠀⢀⡄⠀⣈⠀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⠖⠁⠀⠀⠀⠀⠘⣏⠀⠛⠁⠘⠇⠀⠶⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠤⠀⢠⡀⢀⣀⠀⢈⡁⠀⣻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⡶⠿⠀⢶⠆⢠⡄⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⡩⠊⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠂⠀⠀⠄⣠⡀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠉⠀⠘
⠀⠀⠀⠀⠀⠈⠁⠀⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇⠀⠖⠀⠠
⠀⠀⠀⠀⠀⠛⠀⠰⠆⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠄⢠⡄⠀⣀
⠀⠀⠀⠀⠰⠦⠀⣤⠄⢠⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣤⠀⢀⡀⠀⡀
⠀⠀⠀⠀⢠⡄⠀⣀⠀⣈⡉⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⢀⡁⠀⠈⠀⠀⠁
⠀⠀⠀⠀⣀⠀⠀⠁⠀⠙⠁⠘⠟⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢉⣉⠀⢈⠁⠀⠛⠀⠘⠂
⠀⠀⠀⠀⠉⠀⠘⠃⣴⠟⠋⠙⠣⢰⣶⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠛⠀⠛⠃⠐⠗⠀⠰
⠀⠀⠀⠀⠀⠀⠺⢸⣏⠀⠀⠀⠀⣤⣤⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠇⠐⠷⠀⢰⠄⠀⡀
⠀⠀⠀⠀⠀⠀⣦⠀⢻⣦⣤⣤⠖⣉⡁⢈⡛⠻⣷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⠆⢰⡆⠀⣤
⠀⠀⠀⠀⠀⣾⠁⢀⣄⠀⢀⡁⠀⠙⠁⠘⠛⠐⠿⠛⢿⡿⢿⣿⡿⣿⣿⢩⣭⡁⣙⡻⣿⣶⣤⣤⣤⣤⣴⣶⣿⡟⢠⣦⠀⣠⡀⢀⡀
⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠘⠃⠘⠛⠀⠾⠇⢰⣶⠀⣴⡄⣠⣭⢀⣭⡁⢈⣛⠀⠛⠃⠸⠿⠛⢿⠟⢻⣿⠁⣤⠀⢠⡄⠀⣈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠚⠀⠰⠆⠀⣶⠀⣠⡄⢀⣭⠀⣈⡉⠈⡛⠁⠻⠟⠘⠿⠃⢾⡷⢠⣶⠀⣤⡄⢀⣌⠀⢈⠁⠀⠉⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣄⠀⣈⠁⢈⡋⠀⠛⠃⠘⠿⠀⠿⠇⢰⡶⠀⣴⡄⢠⣄⠀⣉⠁⠈⠉⠀⠛⠁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠘⠋⠐⠿⠂⠲⠖⠠⣶⠀⣤⡄⢀⣌⠀⢈⡁⠀⠉⠀⠘⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠰⡶⠀⣤⡄⢠⣄⠀⣈⠀⠀⠉⠀⠙⠁⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⢠⡶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢂⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣤⣤⣤⠋⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣹⡷⠴⣠⣄⠱⣿⣶⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣚⠋⠶⣦⣝⣿⣷⠘⣿⠇⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠞⠉⠐⢿⣦⣈⣿⣷⣻⣧⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠏⡀⠀⠐⠄⠙⡿⣮⣿⠛⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠦⡀⣊⣢⠟⡫⠃⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢈⠭⠁⠜⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠤⠄⠠⡇⠀⣤⠀⠤⠤⠤⠤⠤⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣂⣉⣀⣲⡤⢶⠤⠃⢀⠰⣶⠦⠴⠄⠀⣀⣀⡀⠀⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠴⢏⣙⣇⣸⡠⡧⠼⣦⠀⠈⠐⢦⣤⠤⠤⠤⢤⣄⠀⠙⠢⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣶⢮⣉⣉⠭⠄⣀⠀⠠⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢑⣤⠃⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣽⣂⠈⣉⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⠀⡄⠐⣁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣝⡻⣟⠀⣴⡂⠀⠀⠀⢠⣶⡄⢰⡯⢦⡀⢂⡀⣇⢈⣀⡥⡞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢈⢀⡇⠁⠈⠋⢮⡇⠀⠀⠂⢨⠟⡻⢿⠺⠾⠟⠛⠋⠙⠁⠃⠃⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠜⠻⠀⠀⠀⠀⢀⠀⠀⢀⠓⢸⡃⢌⢂⢃⠀⡀⠠⠠⠀⠀⡘⢰⠀⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠃⠀⠀⠀⠀⣠⣆⠀⠤⠅⣼⡷⠶⠶⢄⠀⠀⠁⠆⡀⠀⠃⡈⠀⠁⢈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⣠⡾⠃⠈⠳⠶⠞⣦⣀⠀⡀⢋⣆⠀⠀⠠⠀⡘⢀⠃⠃⠠⢸⢠⠑⠄
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠂⠀⠀⣔⠝⢁⡀⠠⠠⠤⠤⣴⣿⣤⡟⢀⠄⠘⣧⡀⠀⠈⠁⠸⢰⡖⠓⠮⡈⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠉⠠⢄⠀⣠⣶⣯⢁⣿⠃⠀⠀⣀⠘⢟⡄⠀⠀⠃⣼⠀⠀⠀⠡⡆⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠆⠀⠨⡥⣀⡠⢶⣦⣙⡿⣿⠀⢀⡄⠀⠀⡜⡌⠀⠀⢀⠻⠀⣄⠀⠀⠀⠠⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣁⠀⠔⢸⠷⣶⣝⣿⢷⠻⡃⠈⣠⠂⡘⡘⠀⠀⢨⡘⢀⠶⣈⡁⠾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠴⠐⠀⠀⠀⠀⠰⠘⢆⠶⠻⠷⠼⢋⢾⡈⠤⠁⠐⠁⣲⠌⠀⠀⠀⠀⠃⡈⡀⢁⠁⠆⠀⢠⡸⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠱⠈⠖⢎⢦⡀⠋⠀⠀⠀⠖⢠⡳⠁⠀⠠⢀⠂⠈⠰⢡⠁⠄⡘⠰⠀⠂⡉
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠚⠭⠴⠶⠖⣂⣀⣀⣰⠏⠀⠀⢀⠂⠌⡀⢀⢃⢃⠆⡠⢁⢃⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠐⡐⡀⢀⠎⠎⡰⢁⠎⣀⠎
⠀⠀⠀⠀⠀⠀⠐⠢⠀⠂⠀⠊⠑⣠⣉⠂⠑⢊⠔⡠⠂⠂⠐⠀⠁⡠⢁⠌⠔⠜⠀⠀⠎⠈⠀⣤⠞⣣⠀⡠⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢂⠠⠀⠄⢉⡰⠛⡰⠦⣤⢀⣀⣀⢀⢀⡀⣀⡀⢀⡤⠀⠄⣐⢞⠕⢁⠈⡡⢊⠐⢁⠔⡡⢂⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠡⠒⢁⠔⢉⠔⢊⠤⠂⠠⠀⠀⠀⡁⠀⡠⠂⠔⠠⠂⡠⢁⠄⡡⠊⡄⠁⠔⢁⠘⠁⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠊⠐⠀⠐⠀⠊⠀⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣜⣁⠴⣛⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢉⠙⢋⣉⣿⣭⣖⠒
⠀⠀⠀⠀⠀⠀⢀⢆⠀⡁⠀⠀⠠⢾⣿⣽⡏⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠇⠀⠀⠀⠀⠀⠀⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠀⢀⣀⣀⣀⣀⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣛⣠⣬⣿⡏⠃⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⡇⠀⠈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡇⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣆⡀⠐⢆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣯⠂⣄⠘⢦⡀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠿⠟⢟⣿⣽⠶⠾⠶⣄⠉⠲⡄⢡⣀⠄⠀⠀⠀⠀⡀
⠀⠈⠀⠁⠲⢢⡀⠠⣤⣼⣯⠶⠿⠿⠁⠀⠀⠀⢉⣇⠀⠿⠄⠀⠀⢀⣀⣤⣼⣡⡶⣵⣤⣢⡀
⠀⠀⠀⠃⠄⣈⡄⠰⣿⠏⠀⠀⠀⠀⠀⠀⢀⠄⠉⠉⠁⠀⠀⠀⠀⠈⢩⠽⠟⢻⠙⠻⠇⠂
⠀⠀⠀⠀⠀⠄⠒⠚⣻⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠄⠀⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠶⠛⠛⠉⠉⠉⠉⠙⠿⢿⣦⣛⠓⣦⣄⡀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⠚⠛⢿⣆⠄⣨⠽⢦⡀
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠐⠀⠁⠀⣀⣀⣀⣠⡤⠖⡡⣘⣿⡏⠀⠀⠒⠨⢦⡀⠀⠀⠀⠀⠀⠀⠀⡼
⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣠⠊⠀⠀⢀⠀⠒⠈⠉⠀⠤⠄⠭⠅⠐⠚⢵⣍⣾⣟⡛⠛⠉⠀⠈⠻⣄⠀⠀⠀⠀⣠⠛
⠠⠠⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⡜⠁⠀⠀⠂⢀⠠⠄⠒⠒⣀⣠⣴⣿⣷⡿⠿⠚⠿⢿⣿⣿⣿⢋⠑⠂⠄⠙⣆⣀⠠⠎
⠀⠁⠁⠌⠍⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡞⠁⠀⠀⠀⣀⠄⠒⠒⢉⣛⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣄⠀⠀⠀⠘⢏⠌⠀⠀⠀⠈
⠀⠀⠀⠐⡐⠀⠀⠉⠛⠂⠤⡄⣀⣀⢀⠀⠀⠀⠀⢠⠋⢠⡟⠀⠀⢀⡀⠂⢁⣠⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡂⠀⠀⠀⢘⡔
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠠⠀⠄⣤⠤⢤⠀⢠⡏⠀⠂⠀⠀⢀⣔⠔⣪⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠈⣵
⠀⠌⡄⢡⠡⢠⠀⠄⠀⠠⠡⢡⠉⡼⠀⠀⠀⣷⡾⠀⠀⠀⠴⢀⡾⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡧⠀⠰⠸⣇
⠐⡐⡐⢂⢂⢂⠂⠐⠀⠀⢂⢂⠒⡘⡙⠂⢚⣿⠇⠀⠀⡸⢂⣾⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠑⡀⠂⣧⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠚⠒⣀⠓⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⣿⣿⣧⢰⣿⢸⠆
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⡈⠀⢁⠀⠀⣼⠻⠦⠔⠹⣄⣿⣿⠠⠛⠛⠛⠛⠷⠶⠀⠀⠀⠀⠀⠀⠰⠛⢋⣉⣀⣀⠀⠈⠀⠀⠀⠀⠀⢿⣿⣿⣇⢿⣾⡄
⠀⢂⠂⡐⡐⡐⡀⢂⠀⠐⡐⡐⣀⢂⢂⠀⠛⣇⠀⠀⠀⣿⣿⣿⠀⢠⣶⣿⡿⠶⢭⡀⠀⠀⠀⠀⠀⠀⣰⡿⠻⠛⠛⠿⢶⠄⠀⠀⠀⠀⠃⠙⣿⡏⠐⣿⣄
⠀⠂⠂⠰⠐⠐⠀⠀⠀⠐⠐⠐⠀⠂⠀⠀⠲⢿⠀⡄⠀⠃⣿⣿⡆⠀⠈⠑⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⣿⡁
⠀⠀⠀⠡⠁⠀⠁⠀⠀⠀⠠⠁⠉⠈⠀⠀⠠⣼⠀⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⠇⢹⡇
⠀⡀⡀⢂⢀⠀⠀⠀⠀⠀⢀⢂⠀⡀⠀⠀⠀⣾⠀⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠿⠿⠾⣸⣃⡀
⠐⠐⠀⠆⠆⠀⠂⠀⠀⠀⠀⠆⠂⠰⠐⢀⣤⣿⣼⠇⡄⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⡀⠀⠀⠀⢹⣿⣿⣿
⠡⠡⠉⠌⠌⠌⠄⠀⠁⠀⠈⣬⣼⣿⣿⣿⣿⣿⣿⡀⠃⠀⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⢰⠀⠀⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠀⠉⢻⣿⣿⣿⣶⡀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠙⡀⠀⠀⢸⠀⢃⣿⡏
⠀⠀⠀⠰⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠘⣿⣿⣿⣧⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⠀⢠⠀⠀⠀⠇⠀⠀⠈⠀⢸⣿⡇⢀
⠀⠌⠄⠡⠡⠡⠁⠈⢼⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢹⢿⣟⣿⣷⡀⠀⠀⠀⠈⠙⠷⠾⠛⠛⠁⠀⠀⠀⠀⠀⠀⢄⠂⠀⠀⠀⠸⠀⠀⡀⢰⣸⣿⠇⣾
⠀⣈⡀⢡⢁⢁⠁⠀⣼⣿⡇⠀⠀⢠⡀⢱⡄⠀⠀⢿⣿⣿⡇⠈⠀⠈⢻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣤⣿⣿⣿⣼⡟
⠀⣸⡀⠀⠂⠀⠀⠀⣿⣿⡇⠀⠀⠀⢷⡄⢻⣆⠀⠘⣿⣿⣿⡠⠀⠀⠈⡽⣿⣿⣿⣷⡄⠀⣀⠀⠀⠀⣀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠓⠃⢸⣿⣿⣿⣿⡇
⠀⠽⠁⠄⠌⠄⠀⢠⣿⣿⡇⠀⠀⠀⠈⣿⣆⢿⣆⠀⢹⣿⣿⣧⢂⠀⠀⠀⠙⣯⣿⣿⣿⣦⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢺⢿⣿⠏⡀⠀⠀⣿⣿⣿⣿⣷
⠀⣳⢃⡘⡘⡈⣀⢠⣿⣿⡇⠀⢠⡀⠀⠘⣿⣾⣿⣆⠘⣿⣿⣿⡞⣄⠀⠀⠀⠹⡺⣻⣿⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⣴⣿⣀⡀⢰⠐⢿⡼⠃⠀⠀⠘⢻⣿⣿⣿
⠀⢒⠂⠐⠐⠐⠀⢸⣿⣿⡇⠀⢸⣿⣦⡀⠹⣿⣿⣿⡆⣿⣿⣿⣿⣿⣆⢆⠀⠀⢻⣣⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣧⣇⣼⠀⢸⡇⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠾⠄⠀⠀⠠⠀⢸⣿⣿⣿⢀⠸⣿⣿⣿⣄⢻⣿⣿⣿⣿⣿⢹⣿⣿⣿⣾⣄⢣⠈⣿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⡔⠘⣷⡀⠀⠀⡀⠠⠀⣿⣿
⠀⡘⡀⢀⢀⢀⠀⢸⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡜⣧⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⢇⣿⣷⡄⢠⣧⠀⡆⢸⣿
⠀⣰⡐⢂⢂⢂⠀⠸⣿⣿⣿⢸⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⠀⢿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣼⣿⣴⣇⣸⣿
⠀⢸⠁⠄⠆⠄⠀⠰⣿⣿⣿⢸⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⢸⡇⢈⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣔⣒⣒⣀⣀⢠⣤⣄⣒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠾⣟⣋⣉⠉⠉⠁⠀⠀⠈⣀⠈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠨⣗⡲⠦⢭⣍⡉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣊⢻⣿⣿⣶⡖⠒⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠶⠋⠀⣤⡀⠉⢿⣿⣍⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠀⠰⠶⠶⣾⡋⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⡉⠁⠀⡄⠀⠀⠝⠃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠤⢤⣀⣀⠀⢀⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⢀⡀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣏⡛⠻⠿⠿⠿⠯⠷⠢⢒⣣⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⠽⠛⠓⠒⠶⠖⠚⠛⠉⠁⠀⠀⠀⡀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⡜⢆⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⢧⢹⣾⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡿⠿⠿⠃


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

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⣎⠀⢉⣓⠐⠲⠤⣀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⣤⠔⠒⣋⠉⠉⢱
⠀⠀⠀⠘⠄⠀⠀⠓⠢⡀⠀⠉⠒⠤⣀⠀⠈⢦⠀⢳⣠⣀⣄⡞⠀⡴⠁⠀⣠⠔⠊⠁⣠⡞⠚⠃⠄⢠⠃
⠀⠀⠀⠀⠈⠀⣉⠄⠀⠌⠳⣔⠱⣄⠀⠑⠦⡄⠑⣤⡟⠉⣻⣤⠞⣀⠴⠋⠀⠀⡤⢊⠥⠈⠉⠉⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠐⠈⢉⠲⡒⠠⣄⠀⢐⣮⠷⠤⢿⣧⠊⢀⠆⠴⢒⢋⡁⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠠⢠⡈⠒⠤⣤⡞⣴⠟⠛⠳⣜⢦⡤⠂⠀⣀⠠⠄⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⣬⠽⣿⣷⣟⠀⠀⠀⢹⢸⡿⢧⣤⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣶⣦⠻⣶⣤⣴⠟⣼⣴⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⣴⡎⣥⣶⣶⣶⣤⡝⣦⣄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⢀⣾⡔⢷⣤⣭⣭⣭⣥⣴⣯⣿⣆⠀⠓⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⣇⢣⣭⣉⣉⣉⣉⣵⡏⣿⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠈⣟⠈⢨⣭⣉⣫⣭⡟⠁⣻⠁⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠙⠻⠟⠋⢀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⢶⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣁⠈⠙⠷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠷⣶⣤⣈⣉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢶⣦⣄⡉⠙⠳⠦⡤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⠀⢀⡞⢉⡼⠛⣫⣷⠆⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣀⡟⢁⡞⢁⡴⠋⣺⣎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣾⡄⣼⡁⣼⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡴⢆⢀⣀⠀⠀⠀⠀⠀⠀⠉⡛⠿⣿⣷⡿⡿⢃⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠢⣼⡈⣻⡇⣸⠃⣸⠤⠄⣀⡴⠖⣋⣩⣥⡷⢤⡉⠧⠆⡼⠀⣉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠚⠢⣼⣿⣿⣿⣿⣿⡇⢠⠞⣡⣶⣟⣭⠵⠶⣒⣚⣗⣛⣒⡇⠀⠀⠀⠀⠀⣄⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣁⠒⣿⣿⣿⣾⣧⣿⢧⡏⣼⣿⣿⣽⢶⣛⣋⣭⡭⣯⠭⢽⠃⠀⠀⠀⢈⡲⢤⡙⠌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⡬⣝⠛⡿⢿⢿⣻⢸⡇⡜⢿⣿⣿⣻⣭⡷⠶⠖⡟⠲⢺⣷⣶⣤⣄⣲⣽⣶⡝⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⣞⣾⠉⢻⣧⡼⣾⡟⣼⣷⣜⠦⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠿⢛⣩⣾⣿⣿⣆
⠀⠀⠀⠀⢠⠖⠦⣄⣇⠀⠘⣇⠀⣸⡏⠀⠸⣼⣿⣿⣿⡷⣤⣉⠀⠀⠀⠉⢉⣉⣉⣩⣭⣥⣴⣶⣾⣿⣿⣿⣿⡿⢿⡆⠀⠀⢀⡀⠀⡀
⠀⠀⠀⣀⣈⣣⣀⠀⢽⣾⣶⣿⣾⣿⣾⣤⢶⣿⣟⠷⣬⡛⠲⢭⣙⠛⠶⠶⠶⠶⠶⠶⠶⠶⢛⣛⣯⣿⣿⣿⣿⡿⣻⣿⠐⢦⡏⠱⡾⢹⣤⢤⡀
⠀⠀⠸⣅⠀⠈⢽⣿⣿⣿⡿⣛⣛⣻⣿⣯⢸⣿⣝⠷⣄⠉⠓⠂⠀⠈⠀⠀⠀⠀⠐⠒⠛⢛⣋⣩⣥⡾⣿⣿⣿⡿⣫⣿⠰⣴⣿⣶⣿⣟⣅⡼⠶⣄
⠀⠀⡴⠚⠛⠓⠺⣿⣿⣯⣾⣿⣿⣿⣿⣿⡞⣿⣟⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣩⣥⣶⡾⣿⣿⣿⣿⣫⡿⢬⣿⣿⣽⣯⣿⣿⠦⠶⣅
⠀⠀⢙⡶⠖⠶⠚⢿⣿⣿⣿⣿⣿⣿⣿⣉⠳⢻⣿⣿⢶⣍⡑⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣉⣥⣤⠶⢾⣿⣿⣿⣿⣿⣃⡤⠾⣿⣿⣿⣿⣿⠣⣴⠚
⠀⠀⠘⠲⣦⠶⠒⠚⢛⡿⠋⢹⡏⠙⡄⠈⣳⣿⣿⣿⣷⣦⣍⣙⠒⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⢶⣿⣿⣿⣿⢿⣿⣿⣯⣤⡞⠁⡾⢻⡟⢱⡦⠼⠃
⠀⠀⠀⠀⠿⠶⠴⣖⣉⠀⣠⣿⣇⣠⣿⣶⣿⣿⣿⣿⣿⣿⣦⣭⣙⡓⠒⠶⠤⠤⠤⢤⡶⠶⠶⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣷⣾⣧⣸⣓⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣯⣝⣛⠳⠶⠶⠶⠶⠶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠯⠭⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠚⠛⠛⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⡤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⢀⣰⠀⣠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠏⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢲⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⢺⠇⠀⠀⠀⠀⠈⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡛⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢌⡒⢄⠀⠀⢡⣀⠠⠈⠁
⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡱⡆
⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⡴⠁⠈⠢⣄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢙⣧
⠀⠀⠀⠀⡎⠀⠀⢀⢴⡟⠀⠀⠀⠀⠀⠙⠒⠤⣀⡈⠑⣀⠀⡴⠊⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠏⢢
⠀⠀⠀⠀⠳⠤⠒⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢆⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢀⠊⠀⠈⣀⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠢⢀⡀⠀⠀⠘⠀⡠⠤⠞⠃⠠⠘⠅⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⢛⢳⠄⣀⠃⡷⠀⠀⠀⠀⡐⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡰⠁⠀⠀⠀⠀⠈⠣⡉⠢⣡⣤⣤⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠢⣄⡀⠀⠀⠀⡎⠀⠀⠀⠉⠣⡀⠀⠀⠀⠀⠀⠀⠈⢢⣟⢀⠈⣏⣁⡒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡏⠁⠒⠒⠳⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⡼⠓⠂⠀⢿⡙⢷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢳⠄⠀⠀⠟⢤⠀⠀⠀⠀⠀⠀⡏⠄⠀⠀⢽⣷⣊⡘
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠋⢳⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠳⣎⡠⣀⣽⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⠠⠊⠀⠀⠀⠀⠀⠈⠓⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⡠⠏⠅⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⠿⠿⠟⠛⠛⠿⠿⠿⠿⢶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⣤⡶⠿⠟⠛⠛⠿⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣠⡾⠛⢿⣆⠀⠀⠀⢀⣀⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⢀⣿⠁⠀⢸⡿⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠿⢿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⣸⡏⠀⠀⢿⣧⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠀⢠⡿⠁⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠸⠿⣶⣶⣦⣤⣤⣤⣶⣶⣶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡀⠀⢠⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⣰⣞⣋⣙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠁⡄⠀⠀⠀⠀⣠⡤⠶⠴⠢⢤⣤⠤⠤⠬⢧⣤⡉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠶⠶⠖⠒⠒⠛⠻⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠢⣹⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠖⠒⠒⠒⠀⠀⠀⠘⠒⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡍⠳⣿⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠁⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣐⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡤⠤⠀⠹⣇
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡄⠀⡤⠀⢠⠲⡀⠀⠁⠈⠁⠘⠒⠄⠀⠀⢿⡀
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠃⡅⡌⠉⢠⠋⠀⢱⠸⠙⢦⡃⢰⠖⠑⡞⢀⡱⠞⡔⠢⣀⠔⡆⠀⠀⠀⠸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠐⠃⠀⠈⠈⠙⢸⡗⢠⣄⠑⢪⡄⠀⡇⠡⢄⠀⠘⢆⢠⠊⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⡀⠔⡆⢠⢰⠈⠂⠘⠃⠀⡀⠑⡄⠀⠀⠇⠏⠁⡀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠳⠤⠡⢠⠀⠢⠤⠌⠘⠒⠀⠀⠘⠢⠃⠣⠤⠤⠇⠀⢧⠃⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣤⣤⣤⣤⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠣⣄⣤⣤⣠⠞⠀⠀⢀⣾⠏
⠀⠀⠀⠒⠂⠐⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢠⣶⣿⣿⣿⣿⣶⡄⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠂⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠑⠂⢀⡀⠀⠀⠈⢿⣦⡼⠟⠛⠙⠋⠛⠻⢧⣴⡿⠁⠀⠀⢀⡀⠔⠊⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠐⢠⣄⣀⣯⠀⠀⠀⠀⠀⠀⠀⠀⣽⣀⣠⠄⠂⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣽⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣯⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢠⣾⡿⠝⠛⠛⠛⢛⣭⣭⡛⠛⠛⠛⠫⢿⣷⡄⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⣾⠉⠀⠀⠉⠙⠛⠻⠏⠹⠟⠛⠋⠉⠀⠀⠉⣷⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⣸⡿⠀⠀⢆⣀⣀⡀⢀⣀⣄⡀⢀⣀⣀⠰⠀⠀⢿⣇⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢿⠇⠀⠀⡀⠈⠉⠉⠉⠁⠈⠉⠉⠉⠁⢀⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⡆⠀⠀⠹⣶⣶⣤⣤⣴⣶⣦⣤⣴⣶⠏⠀⠀⢰⣷⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠻⠇⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⣠⣶⡿⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣠⣤⣴⣤⣄⡀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⢠⣾⠟⢩⣿⠟⠻⢿⣦⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢻⣿⡀⢀⣼⣿⡆⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⣽⡿⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠙⠻⠿⣿⣿⠁⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⣿⣇⡀⣠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠈⠛⠿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢀⣶⡿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠸⣿⣄⠀⠈⠛⠿⣷⣤⡀⠀⢀⣤⣤⣄⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠙⠻⢿⣦⣄⠀⠈⠙⠿⣷⣬⣉⠛⠛⠛⠛⠁⠀⠀⣴⡿⠛⠉⢉⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠉⢻⣿⣦⣄⡀⠈⠙⠿⣷⣦⣀⠀⠀⢠⣾⠟⠁⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⣿⡟⠉⠻⠿⠀⠀⠀⠀⠙⠻⣷⣶⡿⠋⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⣀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢀⣠⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣾⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠷⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠛⠛⠛⠳⢦⣄⠀⠀⠀⠀⠈⢿⣇
⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⣿⡆
⢀⣿⠇⠀⠀⠀⠀⠀⠐⢤⣄⣀⣀⣀⣀⣠⣤⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣹⣿⣭⣭⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣖⠄⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠟⠛⠻⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠛⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣄⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠾⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣶⣶⣶⣶⣶⣶⣶⣶⠿⠿⠛⠛⠉⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠢⢀⠀⡁⠀⡀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣻⣿⢷⡤⣀⠀⠀⠀⠀⠀⠐⢄⡀⢠⣹⣥⣔⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⡶⣦⢳⣱⣿⠿⠿⢯⡀⠀⠀⠀⠀⠀⠁⠀⠀⠏⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⣿⣮⡷⠉⠁⠐⢆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⡃⣿⢿⣿⡿⣃⡈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠛⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢀⡜⠀⡄⠐⢇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣄⢠⣤⡄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣠⣄⠀⣭⡈⠀⣰⡈⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠚⠛⠃
⠀⠀⠀⢀⣀⠀⢈⣀⠁⢉⡀⠉⣁⡉⢉⣩⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠚⠉⠁
⠀⠀⢠⡋⠉⠁⠁⢉⡀⠉⣹⠚⠉⢓⠋⢉⡋⠁⠀⠀⠀⣠⣼⠾⣏⠙⣧⠈⣧⢈⣠⠤⠔⠚⠉⠉
⠀⠀⠈⠇⠙⠈⡃⠉⠛⠐⠊⠑⠘⠛⠃⢘⠋⠀⠀⠀⠀⡏⢹⡆⢹⣆⢽⣶⣾⡿⠃
⠀⠀⠀⠘⠃⡈⠛⠆⠛⠛⠀⠞⠛⢆⠘⠀⠶⠀⠀⠀⠀⠸⣿⣿⣷⣿⣾⣿⠛⠁
⠀⠀⠀⠈⠳⠶⡄⠜⠶⠤⠋⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⠨⡝⠃⠀⣚⠠⠌⢹⡻⠦⣥⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⡀⠈⢘⠷⢤⣀⣈⣵⡒⠜⢃⡴⠋⣛⣻⣿⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡉⠀⠀⠈⠐⠯⢁⠵⠔⣩⡿⠙⠈⠉⠒⢊
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡟⢶⣴⠀⢳⢉⣶⢻⡇⢠⡴⠖⠚⠩
⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀⣀⠀⠀⠐⢀⣺⣖⢂⣸⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⣦⡙⠛⠟⠀⢸⡏⠀⠀⣠⢤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢉⠛⠳⠛⠛⢻⡯⡹⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡤⡼⠧⠤⠞⠛⠉⡇
⠀⠀⠀⠀⠀⠤⠀⠐⣷⠀⠁⠀⠒⢄⢚⡄⣿⡝⠯⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣤⣄⠠⢀⡀⠀⠀⠀⠀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠠⠝⠻⣦⡵⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡛⠊⠿⢶⣥⠴⡧⠤⠆⠂⠈⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠓⠀⠀⡠⠀⠳⡟⠃⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠅⠀⠀⠈⣀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣦⡇⢀⢓⣶⣾⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⡤⠀⡶⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⢀⣾⣿⠃⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⣾⣿⠃⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⣼⣿⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣾⡿⠋⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠿⠿⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣾⣿⣿⣶⣦⣭⣛⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⣾⣿⠿⠛⠉⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⣿⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⣿⠄⢀⣀⣤⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⣼⣿⠃⢀⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠛⠻⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⣰⣿⠏⠀⠈⠛⠉⠀⠀⠀⢴⣾⣿⣿⣿⣷⣦⣤⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣷⣄⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡏⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣷⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣀⣿⣿⣀⡀⡀⢀⣀⣀⣀⣠⣤⣴⣶⣾⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣤⣴⣶⣿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡖⡟⠸⠃⠯⢾⣣⠻⠜⢸⡠⢏⡰⣛⠵⠠⣇⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠄⣠⢄⡀⢠⠀⠀⢀⣦⢼⣅⡀⢀⠀⣄⣀⠀⢸⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⠀⢀⣀⣠⣄⣾⡁⠉
⠞⠣⠟⠧⠟⠚⠁⠀⠧⠾⠁⠓⠻⠤⠟⠘⠶⠺⠉⠒⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣿⠉⠀⠀⠀⠀⠀⢀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⢀⠠⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠱⠆⣠⣞⠅⠀⠴⠤⠒⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣶⠖⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢾⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠯⣼⡂⢀⣀⣀⣠⣤⣤⣤⣤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢄⣼⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠑⠄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⣷
⠀⠀⠀⠀⠀⠀⡐⠦⢤⠀⠀⣤⠐⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠊⠀⣿⢹⡀
⠀⠀⠀⠀⠀⠀⠹⢤⡏⠀⠀⠘⠤⠗⠊⡇⠀⠀⠀⠀⠀⠀⠀⣟⣆⣀⡿⢻⡑⢄
⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⢸⡇⠀⠑⠤⣀⡀⠀⠀⢀⣠⠴
⠀⠀⠀⠀⠀⠀⠀⣾⣋⠉⠙⠲⠤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⢸⣿⠛⠛⠙⣷⢨

⠀⠀⡔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢃⠀⢠⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⢀⣠⠖⠂⢉⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠦⠄⠀⣴
⠀⠀⠈⡄⠀⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⡀⡎⠀⠀⠠⢴⠋⠀⣀⠴⠟⠀⠀⠀⢀⡀⠱⠶⠄⠀⣒⡲⠔⠒⠀⠀⠀⠈⠁
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠴⠀⡀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⡇⠀⠶⢅⡀⠀⣱⠛⠁⠀⢰⠃⠀⠈⠠⠀⠈⠀⢀⠂⠁⠀⠈⠀⠀⢀⠂
⠀⠀⠀⠀⢱⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠄⠐⠀⠐⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠀⠀⠀⠀⠀⠈⠀⠀⠡
⠀⠀⠀⠀⢀⠷⠊⠉⠭⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠄⠀⢠⡶⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢦⠂⢀⠤⠒⠒⠚⢆⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠸⠎⢀⠄⠐⠀⠉⠙⡄⠀⠀⠀⢀⠀⠀⠘⠀⡄⠀⠀⢠⠀⠀⢸⠀⠀⠆⠀⢀⡇⠀⡤⠀⠀⠀⡓⠀⢼⣷⡆⠀⠀⠀⠀⠀⠄⠋
⠀⠀⠀⠀⠀⠻⠁⡠⠒⠊⠉⠁⣇⠀⠀⠀⢸⠀⠀⡇⠀⣇⠀⠀⢸⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠂
⠀⠀⠀⠀⠀⠀⠙⢤⢀⠀⡠⠀⠁⠀⠀⠀⠆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢀⡀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠠⢄⡀⠐⠋⠁
⠀⠀⢀⠀⣀⠙⠀⠀⡇⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠤⡀⠀⠀⠀⢀⠀⠀⠀⢀⠀⡀
⠀⠀⢈⢺⡇⠀⠀⠀⠄⠂⠀⠀⡀⠀⠠⣌⠀⢉⢢⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣠⠜⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⢋
⠀⠁⠀⠜⠀⠀⠀⠀⠀⠀⠀⣄⣉⣉⠉⠉⠉⣩⡝⢛⢛⠉⠋⢱⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡐⠐⠉⠀⠈⠀⠘⠀⢄⠉⠀⢌⠀⠈⠁⠀⠀⣁
⠀⠀⠀⢀⠀⠀⠐⠒⠀⠀⠀⠜⠀⠀⠀⠠⠜⠉⠉⠀⠉⢷⠓⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢁⠈⠠⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘⠆⠀⠀⡀
⠀⣁⠰⠀⣅⠀⠀⡁⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠙⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⡁⠂⠠⠌⠙⠁⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⢤⠀⢄⠀⠀⡀⢠⠄⠁⠀⠀⠲⠀⢠⠀⠀⠀⠀⢦⣈⠀⠀⠀⠀⠀⠀⠀⡨
⠀⠂⠀⠀⠐⠔⠀⠈⠈⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠑⠈⠒⠘⠂⠀⠀⠠⠀⠠⠈⠀⠈⠀⠀⠀⠀⠀⠛⠥⣴⣀⣀⣀⡩⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⣠⡤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⢠⣛⣦⣴⣶⣶⣦⣔⣿⡄⠀⢀⣤⠞⠋
⠀⠀⣠⠔⠒⠪⣉⣉⡉⣑⣒⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠹⣝⣦⠈⠿⣿⡿⠿⣿⣿⣿⠿⠁⣴⣫⠏⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⣒⡊⣉⣉⣉⠕⠒⠢⣄
⠀⠸⣇⠀⠀⠀⠀⢀⣔⣀⣩⡭⠤⠻⢤⡸⣍⠒⠢⠤⣄⣀⠀⠈⠻⢷⣾⠃⠀⠀⠀⣼⣿⣷⡾⠟⠁⠀⣀⣠⡤⠔⠒⣩⢇⡤⠟⠤⣭⣍⣁⣲⡄⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠉⢍⡉⠉⠀⠘⠢⠄⣀⣀⠨⡕⠒⠒⠉⠒⠢⠤⢦⣿⣿⣷⣿⡗⠀⠀⠀⣐⣒⣾⣇⣿⣾⣿⣿⠧⠦⠔⠒⠋⠒⠒⢺⡅⣀⣀⡠⠔⠂⠀⠉⢉⡩⠉
⠀⠀⠀⠀⠀⠉⠒⣒⠚⠉⠀⣀⡠⠔⠊⣳⠒⠒⠒⠒⣒⣒⣿⣿⣿⣿⣿⡄⠀⠀⢐⣺⣿⡯⣿⣿⣿⣿⣓⣒⠒⠒⠒⠒⣞⠙⠢⢄⣀⠀⠉⠑⣒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠭⢥⠤⠒⠘⢓⡒⠒⠋⡩⠝⠩⠴⣚⡿⠿⢿⣿⣗⣒⣒⣾⣿⣽⠿⢿⣓⠦⠍⠫⢍⡙⠒⢒⡚⠃⠒⠤⠬⠭⠍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⢍⠤⢔⣋⠤⢒⣚⣭⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⡶⣶⣶⣭⣓⠒⠤⢙⡢⠤⡉⠗⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋⠉⣩⡾⣻⣿⣿⡋⠉⢹⣿⣟⢿⣟⠳⣭⠉⠙⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠒⠛⠛⠋⠁⠀⠀⣾⣵⡿⣿⠿⢿⣿⣿⣿⣿⣿⣷⢻⢿⣮⣷⠀⠀⠈⠙⠛⠛⠒⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠋⢰⡇⠀⠀⠀⠀⠨⢿⣿⣿⡜⡆⠙⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣺⡟⠀⢸⣷⣶⣤⣤⣤⣬⣭⣿⣿⡇⡇⠀⢻⣗⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⢸⣎⠉⠙⠛⠛⠛⢿⣿⣿⠇⡇⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠘⣟⠻⠿⣷⣶⣾⣿⣿⣿⢳⠃⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⢻⣶⣤⣤⣄⣠⣿⣿⣏⡞⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣭⣭⣽⣿⣯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣿⠿⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠛⢦⡀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⣴⠟⠋⠙⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠻⣟⠙⠛⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠿⠿⠷⣶⣤⣀⣸⠃⠀⠀⢀⠀⠈⡇⠀⡴⠛⠉⠉⠛⢦
⠀⠀⠀⠀⠀⠀⣴⡟⠉⢀⡤⠶⠶⠦⣤⡀⠉⠻⢿⡀⢰⣦⣼⣷⠀⡇⡼⢀⠀⢠⡄⠀⠈⡇
⠀⠀⠀⠀⠀⣸⡏⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢄⣛⣛⣣⠞⠁⢧⢸⣷⣿⡿⠀⣰⠇
⠀⠀⠀⠀⠀⣿⡇⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢳⡄⠀⠀⠈⠳⠭⣉⣤⣴⣿⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣦⣀⠛⠶⠤⠤⠀⣀⣴⠟⠁⠀⠀⠀⢀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠈⠙⠛⠿⢿⣷⣶⣶⣿⣏⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣤⣤⣤⣴⣿⣦⣄⡀⠀⠀⠀⠀⠀⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠉⠁⠀⢨⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⡞⠁⠀⢀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠃⠀⠀⢸⡇⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⣦⡀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⢻⡇⠀⠀⠈⢿⣶⣶⠶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢶⣾⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠀⠀⣀⡾⠁⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠿⠛⢷⣦⣤⣀⣡⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠞⠛⠛⠛⠛⠛⠛⠳⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢿⡄⠀⠀⠀⢀⣾⢻⡆⠀⠀⠋⠉⠁⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⢸⡇⠀⠀⠀⣼⠃⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠘⣷⠀⠀⣸⠏⠀⢸⣏⣀⣤⣤⡶⠶⠞⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠹⣇⣼⠋⠀⠀⠙⠉⠉⠁⠀⠀⣀⣤⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠶⠶⠶⠶⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠛⠛⠋⠉⠉⠛⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢚⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣇⢣⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣔⢟⢯⣎⡿⠾⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⢀⡾⣝⢮⣮⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⣜⣓⠦⢝⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⣯⠬⠭⠭⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠸⣍⡭⠭⠭⠛⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠈⢙⣶⡯⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠓⠶⢤⡀
⠀⠀⠀⠀⠀⣴⠭⣒⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢰⣛⡭⢖⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣾⢒⡪⠵⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⢹⠥⢒⡩⠽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠈⢯⠥⣒⠭⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠲⠦⣄⣀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠈⠫⡖⣋⠥⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⢋⣤⠶⠶⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣎⡥⣚⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠮⣼⣛⡶⣦⣤⣀⣀⣀⣀⣠⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣤⡤⠤⠊⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⡟⠁⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣤⡤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠬⠙⠲⡀
⠀⠀⠀⠀⠀⡀⠤⠐⠒⠒⠒⠀⠄⡁⠀⠀⠈⠠⡀
⠀⠀⠀⠀⢤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⣍⣀⣀⣀⠐⢤⠐⠀⠁⠀⠙⣶⣴⢷⣶⣦⣤⣤⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⡷⣶⣖⣦⣀⣈⡱⣴⣄⣤⣿⣿⢿⣿⣏⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⣧⣶⣿⣿⣿⣿⣟⢟⠛⢿⣼⣿⣿⣤⣿⠏⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠘⣿⣿⣄⠘⣿⣿⣿⣿⢻⣿⣦⣻⣿⣿⠛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⠻⣿⣿⣟⣿⡟⢙⣿⠇⠉⠹⡧⠃⢳⡈⠛⠷⠖
⠀⠀⠀⠀⠀⠀⠀⣰⠈⢿⣿⣧⣶⣬⣷⣿⠋⠀⣸⠿⠀⠀⠀⠀⠀⠀⠻⣆⢀⣄⠀⠀⠀⠀⠂⠁⢀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣈⡝⣫⣿⡟⠁⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠊⠀⠀⠘⠋⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣿⡿⢻⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢺⣶⠌⢡⠀⠀⠀⢀⡤⠐⠀⠁⠀⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠰⣧⣗⡡⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠊⠀⠀⠀⠀⣻⣿⡑⢂⡁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⢽⣯⡍⠀⠀⠀⡀⢀⣼⣿⣟⠛⠛⠓⠦⠀⠀⡀⠀⠀⠀⣀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢉⣀⣄⣀⣠⣶⣿⣿⢧⡈⠉⠀⠀⠂⠀⠀⠀⠈⠑⠂⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠔⣻⢿⣾⡟⣿⡏⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠉⡞⠏⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠠⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣎⣷⠀⠀⠀⠀⠘⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠙⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠛⠋⢉⣉⣉⣩⣥⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠈⠉⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⢀⡴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡽⠃⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⠳⠶⢤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠶⠚⠛⠉⠁⢀⣀⣠⣴⠾⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠷⢶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⡶⠶⠾⠛⠛⠉⠁⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠿⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣴⠶⠾⠛⠋⠉⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠙⠓⢦⣄⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢠⠞⠉⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠀⠀⠀⢹⡀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⡴⠛⠛⠳⡄⠀⠀⠀⠀⠘⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⣀⣤⣤⣀⠀⣼⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⣿⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠠⣴⡏⠀⢀⣿⣿⡿⠓⠦⣾⡃⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⣤⣼⣿⣿⠀⠀⣴⣿⣿⣆⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⣫⠟⠻⣧⣀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠠⡇⠀⠀⢀⡿⠙⣿⠋⠉⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡇⠙⠶⠶⠋⠀⣴⠛⠛⠲⢤⠀⠀⠀⠀⢀⣼⠃⠀⣼⠇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⣿⠀⠀⢨⡿⠶⣤⣀⣠⠞⠁⠀⠀⠀⢸⡇⣀⣤⠾⠋⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⣿⠀⢠⡟⠀⠀⠀⠈⣿⠀⠀⣀⣤⡴⠾⠛⠉⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⣿⠀⢹⠀⠀⠀⣀⣤⡿⠶⠛⠉⠁⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣀⠀⠀⠀⠀⠀⠂⠴⠞⠁⠀⠀⡇⠀⠀⢿⣤⣼⠶⠞⠛⠉⠀⢀⣠⣤⡶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣄⣀⡀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⣿⣿⣶⣶⣶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢤⣀⣠⣄⣀⣄⡀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣶⠙⠛⠿⠿⠿⠛⣯⡄⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣁⣀⣀⣄⣀⣄⣀⡹⠇⠀⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠖⠒⢲⣤⡎⢩⡬⠿⠰⢼⣼⣭⣽⡆⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠙⡧⠟⠀⠃⠨⣤⠉⡤⠹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣼⡇⠀⡶⠂⠀⠠⡎⠿⣁⡆⠄⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⢨⡷⣞⣷⢧⠘⢃⡋⠀⠀⠠⢀⠜⠁⣸⣿⡟⠓⣤⡾⠉⠒⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠈⣿⡜⡿⢆⠈⢹⣿⣿⣿⣟⠀⢠⠟⠉⠀⣜⡧⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⢀⠀⠀⠰⣷⡾⣤⠁⠈⠋⠃⠀⡠⣛⣶⣿⠿⠋⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠃⠀⢀⠃⠘⠓⣛⣂⣤⣴⣴⡞⠛⠉⠀⢸⠀⡀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠤⠀⠘⠀⠀⠀⠀⡌⢀⣴⣿⣿⣿⢿⣿⣿⣿⣿⣦⡄⠀⡇⠸⠀⠈⠃⠀⠐⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠊⠀⠀⠀⠀⠀⠀⠀⡘⣠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⡄⢠⠀⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣾⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⠀⠀⠀⠁⠐⢸⣿⢿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣴⣶⣾⣿⣿⢿⣿⣄⠀⠀⠈⠣⡀⠀⠈⠃⠀⠹⡀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠟⠁⢸⡋⠙⠛⠙⠛⠟⠛⠿⠻⠿⠿⢿⢻⣟⠀⠙⢿⡄⠀⠀⠀⠑⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠤⠀⠀⣰⣿⠀⠀⢈⠉⠁⠈⠉⠉⠁⠀⠚⠒⠒⠊⠉⠉⡏⠀⢠⣿⠓⢄⠘⠆⠀⠀⠀⠀⠃⠀⠀⢃
⠀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⠀⠠⠊⠀⢻⣧⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠃⠀⢸⡟⠀⠀⠉⠒⠤⢀⣁⣀⣀⠀⢀⣨
⠀⠀⠀⠀⠀⠹⠇⠤⠤⠄⠒⠉⠀⠀⠀⠀⠈⣿⠂⠘⣿⣿⣿⣿⣷⣷⣶⣶⣿⣿⣿⣿⡿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠙⠓⠓⠿⠿⠿⠿⠿⠿⠛⠋⢹⠃⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣤⣤⣤⣴⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠁⠀⢹⣤⣤⣀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣶⠶⠟⠉⢉⢩⣿⠀⠀⠀⣸⠏⠀⠉⠛⢿⠏⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠁⠀⠀⠀⣰⠋⠀⠘⠂⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠁⠀⠀⠀⠀⠀⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠉⠻⣷⠀⢸⡏⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠸⣆⠸⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⢀⣼⠃⠀⠀⣀⢰⡆⠀⠀⠀⠀⢛⣷⣿⣷⣄⣀⣶⡴⠶⠖⣚⣛⡛⢳⣆⡀
⠀⠀⠀⠀⢾⡿⠒⠁⠀⠬⡛⢧⡀⠀⠀⠀⠀⠈⠛⢿⣿⣯⣿⣿⠿⠛⠛⠋⠉⣹⡿⠻⣆
⠀⠀⠀⠀⣸⡷⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡆⠀⢠⡏⠀⠀⣿
⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⣀⠈⠙⠿⣶⣶⣶⣤⣄⣀⣀⣠⣨⣯⠟⠈⣻⣿⣤⣴⠃
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡿⢿⣛⣛⠟⠋⠋⠛⠃⠉⠀⠀⢸⣠⠒⢶⣄
⠀⠀⠀⢸⣿⣇⡀⠀⢀⣴⠦⠈⠉⠉⠛⠲⣤⣨⢽⣿⣩⣥⣠⡼⠋⢹⣦⠀⠀⠀⠀⢸⡿⡏⢀⣿
⠀⠀⠀⠀⠻⣿⣿⣀⣼⠏⠀⠀⠀⠀⠀⠀⠈⠙⠧⣿⣗⣻⣿⡅⠀⠀⢹⡄⠀⠀⡀⢺⡟⠟⠈⣿
⠀⠀⠀⠀⠀⠘⣿⣮⣻⣦⣤⣀⣀⠀⠀⠀⠀⡀⠀⠀⠉⠉⠿⠀⡖⠀⣼⡇⡀⣀⣀⣺⡾⠂⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣾⣦⣭⣀⣦⠀⠰⠀⠼⡁⢰⣟⣛⣿⣯⣿⣿⣶⡦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠻⠿⣿⣷⣶⣾⣿⠟⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉